LMFDB - Embedded newform 3201.2.a.u.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3201,2,Mod(1,3201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3201, 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("3201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3201 = 3 \cdot 11 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3201.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:	$25.5601136870$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - x^{18} - 26 x^{17} + 25 x^{16} + 277 x^{15} - 250 x^{14} - 1567 x^{13} + 1277 x^{12} + 5114 x^{11} + \cdots - 4 $ x^19 - x^18 - 26x^17 + 25x^16 + 277x^15 - 250x^14 - 1567x^13 + 1277x^12 + 5114x^11 - 3528x^10 - 9816x^9 + 5112x^8 + 10779x^7 - 3351x^6 - 6155x^5 + 578x^4 + 1433x^3 + 6x^2 - 112*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.49492$ of defining polynomial
Character	$\chi$	$=$	3201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49492 q^{2} -1.00000 q^{3} +0.234798 q^{4} -0.273931 q^{5} -1.49492 q^{6} +1.19939 q^{7} -2.63884 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.49492 q^{2} -1.00000 q^{3} +0.234798 q^{4} -0.273931 q^{5} -1.49492 q^{6} +1.19939 q^{7} -2.63884 q^{8} +1.00000 q^{9} -0.409506 q^{10} -1.00000 q^{11} -0.234798 q^{12} -3.07017 q^{13} +1.79300 q^{14} +0.273931 q^{15} -4.41447 q^{16} +4.91067 q^{17} +1.49492 q^{18} +7.38849 q^{19} -0.0643184 q^{20} -1.19939 q^{21} -1.49492 q^{22} -1.40664 q^{23} +2.63884 q^{24} -4.92496 q^{25} -4.58968 q^{26} -1.00000 q^{27} +0.281615 q^{28} -1.68517 q^{29} +0.409506 q^{30} -2.76517 q^{31} -1.32160 q^{32} +1.00000 q^{33} +7.34108 q^{34} -0.328550 q^{35} +0.234798 q^{36} +2.20677 q^{37} +11.0452 q^{38} +3.07017 q^{39} +0.722860 q^{40} -3.92821 q^{41} -1.79300 q^{42} -1.27330 q^{43} -0.234798 q^{44} -0.273931 q^{45} -2.10282 q^{46} -3.95907 q^{47} +4.41447 q^{48} -5.56146 q^{49} -7.36244 q^{50} -4.91067 q^{51} -0.720870 q^{52} -4.97686 q^{53} -1.49492 q^{54} +0.273931 q^{55} -3.16501 q^{56} -7.38849 q^{57} -2.51920 q^{58} -8.77757 q^{59} +0.0643184 q^{60} -15.2421 q^{61} -4.13373 q^{62} +1.19939 q^{63} +6.85323 q^{64} +0.841015 q^{65} +1.49492 q^{66} -15.4294 q^{67} +1.15302 q^{68} +1.40664 q^{69} -0.491158 q^{70} -0.0658854 q^{71} -2.63884 q^{72} +12.0373 q^{73} +3.29895 q^{74} +4.92496 q^{75} +1.73480 q^{76} -1.19939 q^{77} +4.58968 q^{78} +4.01725 q^{79} +1.20926 q^{80} +1.00000 q^{81} -5.87237 q^{82} +13.4680 q^{83} -0.281615 q^{84} -1.34518 q^{85} -1.90349 q^{86} +1.68517 q^{87} +2.63884 q^{88} -4.60416 q^{89} -0.409506 q^{90} -3.68234 q^{91} -0.330275 q^{92} +2.76517 q^{93} -5.91851 q^{94} -2.02393 q^{95} +1.32160 q^{96} -1.00000 q^{97} -8.31396 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + q^{2} - 19 q^{3} + 15 q^{4} + 8 q^{5} - q^{6} - 7 q^{7} + 19 q^{9}+O(q^{10}) $ 19 * q + q^2 - 19 * q^3 + 15 * q^4 + 8 * q^5 - q^6 - 7 * q^7 + 19 * q^9	\( 19 q + q^{2} - 19 q^{3} + 15 q^{4} + 8 q^{5} - q^{6} - 7 q^{7} + 19 q^{9} - 15 q^{10} - 19 q^{11} - 15 q^{12} - 8 q^{13} - 8 q^{15} + 7 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 4 q^{20} + 7 q^{21} - q^{22} + q^{23} + 11 q^{25} - 5 q^{26} - 19 q^{27} - 23 q^{28} + 2 q^{29} + 15 q^{30} - 46 q^{31} - 19 q^{32} + 19 q^{33} - 16 q^{34} - 4 q^{35} + 15 q^{36} - 21 q^{37} - 2 q^{38} + 8 q^{39} - 39 q^{40} - 29 q^{41} - 11 q^{43} - 15 q^{44} + 8 q^{45} - 33 q^{46} - 6 q^{47} - 7 q^{48} - 2 q^{49} - 14 q^{50} + 2 q^{51} - 18 q^{52} + 39 q^{53} - q^{54} - 8 q^{55} - 11 q^{56} + 13 q^{57} - 13 q^{58} + 3 q^{59} - 4 q^{60} - 36 q^{61} + 11 q^{62} - 7 q^{63} - 24 q^{64} - 33 q^{65} + q^{66} - 23 q^{67} - 16 q^{68} - q^{69} - 20 q^{70} - 18 q^{71} - 19 q^{73} - 9 q^{74} - 11 q^{75} - 26 q^{76} + 7 q^{77} + 5 q^{78} - 66 q^{79} - 40 q^{80} + 19 q^{81} - 62 q^{82} - 28 q^{83} + 23 q^{84} - 31 q^{85} - 35 q^{86} - 2 q^{87} - 15 q^{90} - 34 q^{91} + 57 q^{92} + 46 q^{93} - 32 q^{94} - 40 q^{95} + 19 q^{96} - 19 q^{97} - 29 q^{98} - 19 q^{99}+O(q^{100}) \) 19 * q + q^2 - 19 * q^3 + 15 * q^4 + 8 * q^5 - q^6 - 7 * q^7 + 19 * q^9 - 15 * q^10 - 19 * q^11 - 15 * q^12 - 8 * q^13 - 8 * q^15 + 7 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 4 * q^20 + 7 * q^21 - q^22 + q^23 + 11 * q^25 - 5 * q^26 - 19 * q^27 - 23 * q^28 + 2 * q^29 + 15 * q^30 - 46 * q^31 - 19 * q^32 + 19 * q^33 - 16 * q^34 - 4 * q^35 + 15 * q^36 - 21 * q^37 - 2 * q^38 + 8 * q^39 - 39 * q^40 - 29 * q^41 - 11 * q^43 - 15 * q^44 + 8 * q^45 - 33 * q^46 - 6 * q^47 - 7 * q^48 - 2 * q^49 - 14 * q^50 + 2 * q^51 - 18 * q^52 + 39 * q^53 - q^54 - 8 * q^55 - 11 * q^56 + 13 * q^57 - 13 * q^58 + 3 * q^59 - 4 * q^60 - 36 * q^61 + 11 * q^62 - 7 * q^63 - 24 * q^64 - 33 * q^65 + q^66 - 23 * q^67 - 16 * q^68 - q^69 - 20 * q^70 - 18 * q^71 - 19 * q^73 - 9 * q^74 - 11 * q^75 - 26 * q^76 + 7 * q^77 + 5 * q^78 - 66 * q^79 - 40 * q^80 + 19 * q^81 - 62 * q^82 - 28 * q^83 + 23 * q^84 - 31 * q^85 - 35 * q^86 - 2 * q^87 - 15 * q^90 - 34 * q^91 + 57 * q^92 + 46 * q^93 - 32 * q^94 - 40 * q^95 + 19 * q^96 - 19 * q^97 - 29 * q^98 - 19 * 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 $

$2$	1.49492	1.05707	0.528535	−	0.848911i	$-0.322741\pi$
$2$	1.49492	1.05707	0.528535	+	0.848911i	$0.322741\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.234798	0.117399
$5$	−0.273931	−0.122506	−0.0612528	−	0.998122i	$-0.519510\pi$
$5$	−0.273931	−0.122506	−0.0612528	+	0.998122i	$0.519510\pi$
$6$	−1.49492	−0.610300
$7$	1.19939	0.453328	0.226664	−	0.973973i	$-0.427218\pi$
$7$	1.19939	0.453328	0.226664	+	0.973973i	$0.427218\pi$
$8$	−2.63884	−0.932972
$9$	1.00000	0.333333
$10$	−0.409506	−0.129497
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.234798	−0.0677803
$13$	−3.07017	−0.851513	−0.425757	−	0.904838i	$-0.639992\pi$
$13$	−3.07017	−0.851513	−0.425757	+	0.904838i	$0.639992\pi$
$14$	1.79300	0.479199
$15$	0.273931	0.0707286
$16$	−4.41447	−1.10362
$17$	4.91067	1.19101	0.595506	−	0.803351i	$-0.296951\pi$
$17$	4.91067	1.19101	0.595506	+	0.803351i	$0.296951\pi$
$18$	1.49492	0.352357
$19$	7.38849	1.69504	0.847518	−	0.530767i	$-0.178096\pi$
$19$	7.38849	1.69504	0.847518	+	0.530767i	$0.178096\pi$
$20$	−0.0643184	−0.0143820
$21$	−1.19939	−0.261729
$22$	−1.49492	−0.318719
$23$	−1.40664	−0.293304	−0.146652	−	0.989188i	$-0.546850\pi$
$23$	−1.40664	−0.293304	−0.146652	+	0.989188i	$0.546850\pi$
$24$	2.63884	0.538652
$25$	−4.92496	−0.984992
$26$	−4.58968	−0.900110
$27$	−1.00000	−0.192450
$28$	0.281615	0.0532202
$29$	−1.68517	−0.312928	−0.156464	−	0.987684i	$-0.550010\pi$
$29$	−1.68517	−0.312928	−0.156464	+	0.987684i	$0.550010\pi$
$30$	0.409506	0.0747652
$31$	−2.76517	−0.496640	−0.248320	−	0.968678i	$-0.579878\pi$
$31$	−2.76517	−0.496640	−0.248320	+	0.968678i	$0.579878\pi$
$32$	−1.32160	−0.233629
$33$	1.00000	0.174078
$34$	7.34108	1.25898
$35$	−0.328550	−0.0555351
$36$	0.234798	0.0391330
$37$	2.20677	0.362790	0.181395	−	0.983410i	$-0.441939\pi$
$37$	2.20677	0.362790	0.181395	+	0.983410i	$0.441939\pi$
$38$	11.0452	1.79177
$39$	3.07017	0.491621
$40$	0.722860	0.114294
$41$	−3.92821	−0.613483	−0.306741	−	0.951793i	$-0.599239\pi$
$41$	−3.92821	−0.613483	−0.306741	+	0.951793i	$0.599239\pi$
$42$	−1.79300	−0.276666
$43$	−1.27330	−0.194176	−0.0970882	−	0.995276i	$-0.530953\pi$
$43$	−1.27330	−0.194176	−0.0970882	+	0.995276i	$0.530953\pi$
$44$	−0.234798	−0.0353971
$45$	−0.273931	−0.0408352
$46$	−2.10282	−0.310043
$47$	−3.95907	−0.577490	−0.288745	−	0.957406i	$-0.593238\pi$
$47$	−3.95907	−0.577490	−0.288745	+	0.957406i	$0.593238\pi$
$48$	4.41447	0.637173
$49$	−5.56146	−0.794494
$50$	−7.36244	−1.04121
$51$	−4.91067	−0.687631
$52$	−0.720870	−0.0999667
$53$	−4.97686	−0.683624	−0.341812	−	0.939768i	$-0.611041\pi$
$53$	−4.97686	−0.683624	−0.341812	+	0.939768i	$0.611041\pi$
$54$	−1.49492	−0.203433
$55$	0.273931	0.0369368
$56$	−3.16501	−0.422942
$57$	−7.38849	−0.978629
$58$	−2.51920	−0.330787
$59$	−8.77757	−1.14274	−0.571371	−	0.820692i	$-0.693588\pi$
$59$	−8.77757	−1.14274	−0.571371	+	0.820692i	$0.693588\pi$
$60$	0.0643184	0.00830346
$61$	−15.2421	−1.95155	−0.975775	−	0.218775i	$-0.929794\pi$
$61$	−15.2421	−1.95155	−0.975775	+	0.218775i	$0.929794\pi$
$62$	−4.13373	−0.524984
$63$	1.19939	0.151109
$64$	6.85323	0.856654
$65$	0.841015	0.104315
$66$	1.49492	0.184012
$67$	−15.4294	−1.88500	−0.942500	−	0.334207i	$-0.891532\pi$
$67$	−15.4294	−1.88500	−0.942500	+	0.334207i	$0.891532\pi$
$68$	1.15302	0.139824
$69$	1.40664	0.169339
$70$	−0.491158	−0.0587046
$71$	−0.0658854	−0.00781916	−0.00390958	−	0.999992i	$-0.501244\pi$
$71$	−0.0658854	−0.00781916	−0.00390958	+	0.999992i	$0.501244\pi$
$72$	−2.63884	−0.310991
$73$	12.0373	1.40886	0.704431	−	0.709772i	$-0.251202\pi$
$73$	12.0373	1.40886	0.704431	+	0.709772i	$0.251202\pi$
$74$	3.29895	0.383495
$75$	4.92496	0.568686
$76$	1.73480	0.198995
$77$	−1.19939	−0.136683
$78$	4.58968	0.519679
$79$	4.01725	0.451976	0.225988	−	0.974130i	$-0.427439\pi$
$79$	4.01725	0.451976	0.225988	+	0.974130i	$0.427439\pi$
$80$	1.20926	0.135199
$81$	1.00000	0.111111
$82$	−5.87237	−0.648495
$83$	13.4680	1.47830	0.739151	−	0.673540i	$-0.235227\pi$
$83$	13.4680	1.47830	0.739151	+	0.673540i	$0.235227\pi$
$84$	−0.281615	−0.0307267
$85$	−1.34518	−0.145906
$86$	−1.90349	−0.205258
$87$	1.68517	0.180669
$88$	2.63884	0.281302
$89$	−4.60416	−0.488040	−0.244020	−	0.969770i	$-0.578466\pi$
$89$	−4.60416	−0.488040	−0.244020	+	0.969770i	$0.578466\pi$
$90$	−0.409506	−0.0431657
$91$	−3.68234	−0.386014
$92$	−0.330275	−0.0344336
$93$	2.76517	0.286735
$94$	−5.91851	−0.610448
$95$	−2.02393	−0.207651
$96$	1.32160	0.134886
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−8.31396	−0.839837
$99$	−1.00000	−0.100504
$100$	−1.15637	−0.115637
$101$	3.69778	0.367943	0.183971	−	0.982932i	$-0.441105\pi$
$101$	3.69778	0.367943	0.183971	+	0.982932i	$0.441105\pi$
$102$	−7.34108	−0.726875
$103$	−16.3846	−1.61443	−0.807213	−	0.590260i	$-0.799025\pi$
$103$	−16.3846	−1.61443	−0.807213	+	0.590260i	$0.799025\pi$
$104$	8.10171	0.794438
$105$	0.328550	0.0320632
$106$	−7.44002	−0.722639
$107$	−2.93552	−0.283788	−0.141894	−	0.989882i	$-0.545319\pi$
$107$	−2.93552	−0.283788	−0.141894	+	0.989882i	$0.545319\pi$
$108$	−0.234798	−0.0225934
$109$	−4.55730	−0.436510	−0.218255	−	0.975892i	$-0.570036\pi$
$109$	−4.55730	−0.436510	−0.218255	+	0.975892i	$0.570036\pi$
$110$	0.409506	0.0390448
$111$	−2.20677	−0.209457
$112$	−5.29468	−0.500300
$113$	−13.8923	−1.30688	−0.653439	−	0.756979i	$-0.726674\pi$
$113$	−13.8923	−1.30688	−0.653439	+	0.756979i	$0.726674\pi$
$114$	−11.0452	−1.03448
$115$	0.385321	0.0359314
$116$	−0.395675	−0.0367375
$117$	−3.07017	−0.283838
$118$	−13.1218	−1.20796
$119$	5.88982	0.539919
$120$	−0.722860	−0.0659878
$121$	1.00000	0.0909091
$122$	−22.7858	−2.06293
$123$	3.92821	0.354194
$124$	−0.649257	−0.0583050
$125$	2.71875	0.243173
$126$	1.79300	0.159733
$127$	−20.9999	−1.86344	−0.931720	−	0.363178i	$-0.881692\pi$
$127$	−20.9999	−1.86344	−0.931720	+	0.363178i	$0.881692\pi$
$128$	12.8883	1.13917
$129$	1.27330	0.112108
$130$	1.25725	0.110268
$131$	0.497412	0.0434591	0.0217295	−	0.999764i	$-0.493083\pi$
$131$	0.497412	0.0434591	0.0217295	+	0.999764i	$0.493083\pi$
$132$	0.234798	0.0204365
$133$	8.86169	0.768406
$134$	−23.0658	−1.99258
$135$	0.273931	0.0235762
$136$	−12.9585	−1.11118
$137$	−18.7975	−1.60598	−0.802988	−	0.595996i	$-0.796757\pi$
$137$	−18.7975	−1.60598	−0.802988	+	0.595996i	$0.796757\pi$
$138$	2.10282	0.179004
$139$	6.12986	0.519928	0.259964	−	0.965618i	$-0.416289\pi$
$139$	6.12986	0.519928	0.259964	+	0.965618i	$0.416289\pi$
$140$	−0.0771429	−0.00651977
$141$	3.95907	0.333414
$142$	−0.0984937	−0.00826541
$143$	3.07017	0.256741
$144$	−4.41447	−0.367872
$145$	0.461620	0.0383355
$146$	17.9949	1.48927
$147$	5.56146	0.458701
$148$	0.518144	0.0425912
$149$	13.3376	1.09266	0.546328	−	0.837572i	$-0.316025\pi$
$149$	13.3376	1.09266	0.546328	+	0.837572i	$0.316025\pi$
$150$	7.36244	0.601141
$151$	3.37008	0.274253	0.137127	−	0.990554i	$-0.456213\pi$
$151$	3.37008	0.274253	0.137127	+	0.990554i	$0.456213\pi$
$152$	−19.4971	−1.58142
$153$	4.91067	0.397004
$154$	−1.79300	−0.144484
$155$	0.757466	0.0608412
$156$	0.720870	0.0577158
$157$	−4.27818	−0.341436	−0.170718	−	0.985320i	$-0.554609\pi$
$157$	−4.27818	−0.341436	−0.170718	+	0.985320i	$0.554609\pi$
$158$	6.00548	0.477770
$159$	4.97686	0.394690
$160$	0.362028	0.0286208
$161$	−1.68711	−0.132963
$162$	1.49492	0.117452
$163$	12.1813	0.954114	0.477057	−	0.878872i	$-0.341703\pi$
$163$	12.1813	0.954114	0.477057	+	0.878872i	$0.341703\pi$
$164$	−0.922334	−0.0720222
$165$	−0.273931	−0.0213255
$166$	20.1336	1.56267
$167$	9.28615	0.718584	0.359292	−	0.933225i	$-0.383018\pi$
$167$	9.28615	0.718584	0.359292	+	0.933225i	$0.383018\pi$
$168$	3.16501	0.244186
$169$	−3.57403	−0.274925
$170$	−2.01095	−0.154233
$171$	7.38849	0.565012
$172$	−0.298968	−0.0227961
$173$	10.5223	0.799996	0.399998	−	0.916516i	$-0.369011\pi$
$173$	10.5223	0.799996	0.399998	+	0.916516i	$0.369011\pi$
$174$	2.51920	0.190980
$175$	−5.90696	−0.446524
$176$	4.41447	0.332753
$177$	8.77757	0.659763
$178$	−6.88287	−0.515893
$179$	−7.67947	−0.573991	−0.286995	−	0.957932i	$-0.592656\pi$
$179$	−7.67947	−0.573991	−0.286995	+	0.957932i	$0.592656\pi$
$180$	−0.0643184	−0.00479401
$181$	−9.88363	−0.734644	−0.367322	−	0.930094i	$-0.619725\pi$
$181$	−9.88363	−0.734644	−0.367322	+	0.930094i	$0.619725\pi$
$182$	−5.50482	−0.408045
$183$	15.2421	1.12673
$184$	3.71189	0.273644
$185$	−0.604501	−0.0444438
$186$	4.13373	0.303099
$187$	−4.91067	−0.359104
$188$	−0.929581	−0.0677967
$189$	−1.19939	−0.0872429
$190$	−3.02563	−0.219502
$191$	16.1609	1.16936	0.584680	−	0.811264i	$-0.301220\pi$
$191$	16.1609	1.16936	0.584680	+	0.811264i	$0.301220\pi$
$192$	−6.85323	−0.494589
$193$	−5.11580	−0.368243	−0.184122	−	0.982903i	$-0.558944\pi$
$193$	−5.11580	−0.368243	−0.184122	+	0.982903i	$0.558944\pi$
$194$	−1.49492	−0.107329
$195$	−0.841015	−0.0602263
$196$	−1.30582	−0.0932728
$197$	5.87260	0.418406	0.209203	−	0.977872i	$-0.432913\pi$
$197$	5.87260	0.418406	0.209203	+	0.977872i	$0.432913\pi$
$198$	−1.49492	−0.106240
$199$	−2.03750	−0.144434	−0.0722172	−	0.997389i	$-0.523007\pi$
$199$	−2.03750	−0.144434	−0.0722172	+	0.997389i	$0.523007\pi$
$200$	12.9962	0.918970
$201$	15.4294	1.08831
$202$	5.52790	0.388942
$203$	−2.02118	−0.141859
$204$	−1.15302	−0.0807272
$205$	1.07606	0.0751550
$206$	−24.4938	−1.70656
$207$	−1.40664	−0.0977680
$208$	13.5532	0.939744
$209$	−7.38849	−0.511072
$210$	0.491158	0.0338931
$211$	−0.614125	−0.0422781	−0.0211391	−	0.999777i	$-0.506729\pi$
$211$	−0.614125	−0.0422781	−0.0211391	+	0.999777i	$0.506729\pi$
$212$	−1.16856	−0.0802567
$213$	0.0658854	0.00451439
$214$	−4.38839	−0.299984
$215$	0.348796	0.0237877
$216$	2.63884	0.179551
$217$	−3.31653	−0.225141
$218$	−6.81281	−0.461422
$219$	−12.0373	−0.813407
$220$	0.0643184	0.00433634
$221$	−15.0766	−1.01416
$222$	−3.29895	−0.221411
$223$	−26.0549	−1.74476	−0.872381	−	0.488826i	$-0.837425\pi$
$223$	−26.0549	−1.74476	−0.872381	+	0.488826i	$0.837425\pi$
$224$	−1.58512	−0.105910
$225$	−4.92496	−0.328331
$226$	−20.7679	−1.38146
$227$	−8.44730	−0.560667	−0.280333	−	0.959903i	$-0.590445\pi$
$227$	−8.44730	−0.560667	−0.280333	+	0.959903i	$0.590445\pi$
$228$	−1.73480	−0.114890
$229$	19.3947	1.28164	0.640818	−	0.767693i	$-0.278595\pi$
$229$	19.3947	1.28164	0.640818	+	0.767693i	$0.278595\pi$
$230$	0.576026	0.0379820
$231$	1.19939	0.0789142
$232$	4.44690	0.291953
$233$	16.3383	1.07036	0.535178	−	0.844740i	$-0.320245\pi$
$233$	16.3383	1.07036	0.535178	+	0.844740i	$0.320245\pi$
$234$	−4.58968	−0.300037
$235$	1.08451	0.0707457
$236$	−2.06096	−0.134157
$237$	−4.01725	−0.260948
$238$	8.80483	0.570733
$239$	−13.3237	−0.861839	−0.430920	−	0.902390i	$-0.641811\pi$
$239$	−13.3237	−0.861839	−0.430920	+	0.902390i	$0.641811\pi$
$240$	−1.20926	−0.0780573
$241$	10.3879	0.669142	0.334571	−	0.942370i	$-0.391409\pi$
$241$	10.3879	0.669142	0.334571	+	0.942370i	$0.391409\pi$
$242$	1.49492	0.0960974
$243$	−1.00000	−0.0641500
$244$	−3.57881	−0.229110
$245$	1.52345	0.0973299
$246$	5.87237	0.374409
$247$	−22.6839	−1.44334
$248$	7.29686	0.463351
$249$	−13.4680	−0.853498
$250$	4.06433	0.257051
$251$	10.7475	0.678374	0.339187	−	0.940719i	$-0.389848\pi$
$251$	10.7475	0.678374	0.339187	+	0.940719i	$0.389848\pi$
$252$	0.281615	0.0177401
$253$	1.40664	0.0884345
$254$	−31.3933	−1.96979
$255$	1.34518	0.0842387
$256$	5.56052	0.347533
$257$	10.4664	0.652879	0.326440	−	0.945218i	$-0.394151\pi$
$257$	10.4664	0.652879	0.326440	+	0.945218i	$0.394151\pi$
$258$	1.90349	0.118506
$259$	2.64678	0.164463
$260$	0.197469	0.0122465
$261$	−1.68517	−0.104309
$262$	0.743593	0.0459393
$263$	−6.95689	−0.428980	−0.214490	−	0.976726i	$-0.568809\pi$
$263$	−6.95689	−0.428980	−0.214490	+	0.976726i	$0.568809\pi$
$264$	−2.63884	−0.162410
$265$	1.36331	0.0837477
$266$	13.2476	0.812260
$267$	4.60416	0.281770
$268$	−3.62279	−0.221297
$269$	−14.3048	−0.872177	−0.436089	−	0.899904i	$-0.643637\pi$
$269$	−14.3048	−0.872177	−0.436089	+	0.899904i	$0.643637\pi$
$270$	0.409506	0.0249217
$271$	14.2549	0.865923	0.432961	−	0.901412i	$-0.357469\pi$
$271$	14.2549	0.865923	0.432961	+	0.901412i	$0.357469\pi$
$272$	−21.6780	−1.31442
$273$	3.68234	0.222866
$274$	−28.1008	−1.69763
$275$	4.92496	0.296986
$276$	0.330275	0.0198802
$277$	−0.0953424	−0.00572857	−0.00286429	−	0.999996i	$-0.500912\pi$
$277$	−0.0953424	−0.00572857	−0.00286429	+	0.999996i	$0.500912\pi$
$278$	9.16368	0.549601
$279$	−2.76517	−0.165547
$280$	0.866993	0.0518127
$281$	−27.1696	−1.62081	−0.810403	−	0.585873i	$-0.800752\pi$
$281$	−27.1696	−1.62081	−0.810403	+	0.585873i	$0.800752\pi$
$282$	5.91851	0.352442
$283$	8.67393	0.515612	0.257806	−	0.966197i	$-0.417001\pi$
$283$	8.67393	0.515612	0.257806	+	0.966197i	$0.417001\pi$
$284$	−0.0154698	−0.000917961 0
$285$	2.02393	0.119887
$286$	4.58968	0.271393
$287$	−4.71146	−0.278109
$288$	−1.32160	−0.0778763
$289$	7.11469	0.418511
$290$	0.690087	0.0405233
$291$	1.00000	0.0586210
$292$	2.82634	0.165399
$293$	−17.5542	−1.02553	−0.512765	−	0.858529i	$-0.671379\pi$
$293$	−17.5542	−1.02553	−0.512765	+	0.858529i	$0.671379\pi$
$294$	8.31396	0.484880
$295$	2.40445	0.139992
$296$	−5.82331	−0.338473
$297$	1.00000	0.0580259
$298$	19.9386	1.15501
$299$	4.31862	0.249752
$300$	1.15637	0.0667631
$301$	−1.52719	−0.0880255
$302$	5.03801	0.289905
$303$	−3.69778	−0.212432
$304$	−32.6162	−1.87067
$305$	4.17528	0.239076
$306$	7.34108	0.419662
$307$	6.48037	0.369854	0.184927	−	0.982752i	$-0.440795\pi$
$307$	6.48037	0.369854	0.184927	+	0.982752i	$0.440795\pi$
$308$	−0.281615	−0.0160465
$309$	16.3846	0.932089
$310$	1.13235	0.0643134
$311$	−20.5241	−1.16381	−0.581907	−	0.813255i	$-0.697693\pi$
$311$	−20.5241	−1.16381	−0.581907	+	0.813255i	$0.697693\pi$
$312$	−8.10171	−0.458669
$313$	16.6216	0.939506	0.469753	−	0.882798i	$-0.344343\pi$
$313$	16.6216	0.939506	0.469753	+	0.882798i	$0.344343\pi$
$314$	−6.39556	−0.360922
$315$	−0.328550	−0.0185117
$316$	0.943241	0.0530615
$317$	6.48334	0.364140	0.182070	−	0.983286i	$-0.441720\pi$
$317$	6.48334	0.364140	0.182070	+	0.983286i	$0.441720\pi$
$318$	7.44002	0.417216
$319$	1.68517	0.0943515
$320$	−1.87731	−0.104945
$321$	2.93552	0.163845
$322$	−2.52210	−0.140551
$323$	36.2824	2.01881
$324$	0.234798	0.0130443
$325$	15.1205	0.838734
$326$	18.2101	1.00857
$327$	4.55730	0.252019
$328$	10.3659	0.572362
$329$	−4.74848	−0.261792
$330$	−0.409506	−0.0225425
$331$	−33.2059	−1.82516	−0.912579	−	0.408899i	$-0.865913\pi$
$331$	−33.2059	−1.82516	−0.912579	+	0.408899i	$0.865913\pi$
$332$	3.16225	0.173551
$333$	2.20677	0.120930
$334$	13.8821	0.759594
$335$	4.22658	0.230923
$336$	5.29468	0.288848
$337$	−2.65301	−0.144519	−0.0722594	−	0.997386i	$-0.523021\pi$
$337$	−2.65301	−0.144519	−0.0722594	+	0.997386i	$0.523021\pi$
$338$	−5.34290	−0.290616
$339$	13.8923	0.754526
$340$	−0.315846	−0.0171292
$341$	2.76517	0.149743
$342$	11.0452	0.597258
$343$	−15.0661	−0.813494
$344$	3.36004	0.181161
$345$	−0.385321	−0.0207450
$346$	15.7300	0.845653
$347$	23.8640	1.28109	0.640543	−	0.767922i	$-0.278709\pi$
$347$	23.8640	1.28109	0.640543	+	0.767922i	$0.278709\pi$
$348$	0.395675	0.0212104
$349$	9.91530	0.530754	0.265377	−	0.964145i	$-0.414504\pi$
$349$	9.91530	0.530754	0.265377	+	0.964145i	$0.414504\pi$
$350$	−8.83046	−0.472008
$351$	3.07017	0.163874
$352$	1.32160	0.0704418
$353$	15.4377	0.821666	0.410833	−	0.911711i	$-0.365238\pi$
$353$	15.4377	0.821666	0.410833	+	0.911711i	$0.365238\pi$
$354$	13.1218	0.697416
$355$	0.0180480	0.000957891 0
$356$	−1.08105	−0.0572954
$357$	−5.88982	−0.311722
$358$	−11.4802	−0.606749
$359$	−28.4323	−1.50060	−0.750298	−	0.661099i	$-0.770090\pi$
$359$	−28.4323	−1.50060	−0.750298	+	0.661099i	$0.770090\pi$
$360$	0.722860	0.0380981
$361$	35.5898	1.87314
$362$	−14.7753	−0.776571
$363$	−1.00000	−0.0524864
$364$	−0.864606	−0.0453177
$365$	−3.29739	−0.172593
$366$	22.7858	1.19103
$367$	4.88968	0.255239	0.127619	−	0.991823i	$-0.459266\pi$
$367$	4.88968	0.255239	0.127619	+	0.991823i	$0.459266\pi$
$368$	6.20955	0.323695
$369$	−3.92821	−0.204494
$370$	−0.903683	−0.0469802
$371$	−5.96920	−0.309906
$372$	0.649257	0.0336624
$373$	11.3321	0.586755	0.293377	−	0.955997i	$-0.405221\pi$
$373$	11.3321	0.586755	0.293377	+	0.955997i	$0.405221\pi$
$374$	−7.34108	−0.379598
$375$	−2.71875	−0.140396
$376$	10.4474	0.538782
$377$	5.17377	0.266463
$378$	−1.79300	−0.0922220
$379$	−11.0459	−0.567392	−0.283696	−	0.958914i	$-0.591561\pi$
$379$	−11.0459	−0.567392	−0.283696	+	0.958914i	$0.591561\pi$
$380$	−0.475215	−0.0243780
$381$	20.9999	1.07586
$382$	24.1593	1.23610
$383$	31.3488	1.60185	0.800924	−	0.598766i	$-0.204342\pi$
$383$	31.3488	1.60185	0.800924	+	0.598766i	$0.204342\pi$
$384$	−12.8883	−0.657702
$385$	0.328550	0.0167445
$386$	−7.64773	−0.389259
$387$	−1.27330	−0.0647254
$388$	−0.234798	−0.0119201
$389$	26.5290	1.34507	0.672536	−	0.740064i	$-0.265205\pi$
$389$	26.5290	1.34507	0.672536	+	0.740064i	$0.265205\pi$
$390$	−1.25725	−0.0636635
$391$	−6.90753	−0.349329
$392$	14.6758	0.741241
$393$	−0.497412	−0.0250911
$394$	8.77910	0.442285
$395$	−1.10045	−0.0553695
$396$	−0.234798	−0.0117990
$397$	−5.60323	−0.281218	−0.140609	−	0.990065i	$-0.544906\pi$
$397$	−5.60323	−0.281218	−0.140609	+	0.990065i	$0.544906\pi$
$398$	−3.04591	−0.152677
$399$	−8.86169	−0.443640
$400$	21.7411	1.08705
$401$	−6.03477	−0.301362	−0.150681	−	0.988582i	$-0.548147\pi$
$401$	−6.03477	−0.301362	−0.150681	+	0.988582i	$0.548147\pi$
$402$	23.0658	1.15042
$403$	8.48957	0.422895
$404$	0.868230	0.0431961
$405$	−0.273931	−0.0136117
$406$	−3.02151	−0.149955
$407$	−2.20677	−0.109385
$408$	12.9585	0.641541
$409$	−8.55198	−0.422868	−0.211434	−	0.977392i	$-0.567813\pi$
$409$	−8.55198	−0.422868	−0.211434	+	0.977392i	$0.567813\pi$
$410$	1.60862	0.0794442
$411$	18.7975	0.927210
$412$	−3.84708	−0.189532
$413$	−10.5278	−0.518037
$414$	−2.10282	−0.103348
$415$	−3.68929	−0.181100
$416$	4.05756	0.198938
$417$	−6.12986	−0.300181
$418$	−11.0452	−0.540240
$419$	−18.5268	−0.905092	−0.452546	−	0.891741i	$-0.649484\pi$
$419$	−18.5268	−0.905092	−0.452546	+	0.891741i	$0.649484\pi$
$420$	0.0771429	0.00376419
$421$	3.35541	0.163533	0.0817664	−	0.996652i	$-0.473944\pi$
$421$	3.35541	0.163533	0.0817664	+	0.996652i	$0.473944\pi$
$422$	−0.918070	−0.0446910
$423$	−3.95907	−0.192497
$424$	13.1331	0.637802
$425$	−24.1849	−1.17314
$426$	0.0984937	0.00477204
$427$	−18.2813	−0.884692
$428$	−0.689255	−0.0333164
$429$	−3.07017	−0.148229
$430$	0.521423	0.0251453
$431$	18.7664	0.903945	0.451972	−	0.892032i	$-0.350721\pi$
$431$	18.7664	0.903945	0.451972	+	0.892032i	$0.350721\pi$
$432$	4.41447	0.212391
$433$	25.2448	1.21319	0.606593	−	0.795013i	$-0.292536\pi$
$433$	25.2448	1.21319	0.606593	+	0.795013i	$0.292536\pi$
$434$	−4.95796	−0.237990
$435$	−0.461620	−0.0221330
$436$	−1.07004	−0.0512458
$437$	−10.3929	−0.497161
$438$	−17.9949	−0.859829
$439$	−6.16022	−0.294011	−0.147006	−	0.989136i	$-0.546964\pi$
$439$	−6.16022	−0.294011	−0.147006	+	0.989136i	$0.546964\pi$
$440$	−0.722860	−0.0344610
$441$	−5.56146	−0.264831
$442$	−22.5384	−1.07204
$443$	9.30160	0.441932	0.220966	−	0.975281i	$-0.429079\pi$
$443$	9.30160	0.441932	0.220966	+	0.975281i	$0.429079\pi$
$444$	−0.518144	−0.0245900
$445$	1.26122	0.0597876
$446$	−38.9500	−1.84434
$447$	−13.3376	−0.630845
$448$	8.21971	0.388345
$449$	13.6796	0.645579	0.322790	−	0.946471i	$-0.395379\pi$
$449$	13.6796	0.645579	0.322790	+	0.946471i	$0.395379\pi$
$450$	−7.36244	−0.347069
$451$	3.92821	0.184972
$452$	−3.26188	−0.153426
$453$	−3.37008	−0.158340
$454$	−12.6281	−0.592665
$455$	1.00871	0.0472889
$456$	19.4971	0.913033
$457$	12.2705	0.573988	0.286994	−	0.957932i	$-0.407344\pi$
$457$	12.2705	0.573988	0.286994	+	0.957932i	$0.407344\pi$
$458$	28.9936	1.35478
$459$	−4.91067	−0.229210
$460$	0.0904726	0.00421831
$461$	12.6923	0.591141	0.295571	−	0.955321i	$-0.404490\pi$
$461$	12.6923	0.591141	0.295571	+	0.955321i	$0.404490\pi$
$462$	1.79300	0.0834179
$463$	−23.2040	−1.07838	−0.539190	−	0.842184i	$-0.681269\pi$
$463$	−23.2040	−1.07838	−0.539190	+	0.842184i	$0.681269\pi$
$464$	7.43913	0.345353
$465$	−0.757466	−0.0351267
$466$	24.4245	1.13144
$467$	4.39321	0.203294	0.101647	−	0.994821i	$-0.467589\pi$
$467$	4.39321	0.203294	0.101647	+	0.994821i	$0.467589\pi$
$468$	−0.720870	−0.0333222
$469$	−18.5059	−0.854522
$470$	1.62126	0.0747832
$471$	4.27818	0.197128
$472$	23.1626	1.06615
$473$	1.27330	0.0585464
$474$	−6.00548	−0.275841
$475$	−36.3880	−1.66960
$476$	1.38292	0.0633859
$477$	−4.97686	−0.227875
$478$	−19.9179	−0.911025
$479$	15.9003	0.726504	0.363252	−	0.931691i	$-0.381666\pi$
$479$	15.9003	0.726504	0.363252	+	0.931691i	$0.381666\pi$
$480$	−0.362028	−0.0165242
$481$	−6.77515	−0.308920
$482$	15.5291	0.707331
$483$	1.68711	0.0767661
$484$	0.234798	0.0106726
$485$	0.273931	0.0124386
$486$	−1.49492	−0.0678111
$487$	−30.4283	−1.37884	−0.689418	−	0.724363i	$-0.742134\pi$
$487$	−30.4283	−1.37884	−0.689418	+	0.724363i	$0.742134\pi$
$488$	40.2215	1.82074
$489$	−12.1813	−0.550858
$490$	2.27745	0.102885
$491$	22.8815	1.03263	0.516314	−	0.856399i	$-0.327304\pi$
$491$	22.8815	1.03263	0.516314	+	0.856399i	$0.327304\pi$
$492$	0.922334	0.0415820
$493$	−8.27532	−0.372702
$494$	−33.9108	−1.52572
$495$	0.273931	0.0123123
$496$	12.2068	0.548100
$497$	−0.0790225	−0.00354464
$498$	−20.1336	−0.902208
$499$	32.6991	1.46381	0.731907	−	0.681404i	$-0.238630\pi$
$499$	32.6991	1.46381	0.731907	+	0.681404i	$0.238630\pi$
$500$	0.638357	0.0285482
$501$	−9.28615	−0.414875
$502$	16.0667	0.717090
$503$	29.2978	1.30632	0.653162	−	0.757218i	$-0.273442\pi$
$503$	29.2978	1.30632	0.653162	+	0.757218i	$0.273442\pi$
$504$	−3.16501	−0.140981
$505$	−1.01294	−0.0450750
$506$	2.10282	0.0934815
$507$	3.57403	0.158728
$508$	−4.93073	−0.218766
$509$	−15.3527	−0.680495	−0.340247	−	0.940336i	$-0.610511\pi$
$509$	−15.3527	−0.680495	−0.340247	+	0.940336i	$0.610511\pi$
$510$	2.01095	0.0890462
$511$	14.4375	0.638676
$512$	−17.4640	−0.771806
$513$	−7.38849	−0.326210
$514$	15.6465	0.690140
$515$	4.48825	0.197776
$516$	0.298968	0.0131613
$517$	3.95907	0.174120
$518$	3.95673	0.173849
$519$	−10.5223	−0.461878
$520$	−2.21931	−0.0973230
$521$	7.62929	0.334245	0.167123	−	0.985936i	$-0.446552\pi$
$521$	7.62929	0.334245	0.167123	+	0.985936i	$0.446552\pi$
$522$	−2.51920	−0.110262
$523$	−10.1847	−0.445344	−0.222672	−	0.974893i	$-0.571478\pi$
$523$	−10.1847	−0.445344	−0.222672	+	0.974893i	$0.571478\pi$
$524$	0.116791	0.00510205
$525$	5.90696	0.257801
$526$	−10.4000	−0.453463
$527$	−13.5789	−0.591504
$528$	−4.41447	−0.192115
$529$	−21.0214	−0.913973
$530$	2.03805	0.0885273
$531$	−8.77757	−0.380914
$532$	2.08071	0.0902101
$533$	12.0603	0.522389
$534$	6.88287	0.297851
$535$	0.804130	0.0347656
$536$	40.7157	1.75865
$537$	7.67947	0.331394
$538$	−21.3845	−0.921953
$539$	5.56146	0.239549
$540$	0.0643184	0.00276782
$541$	0.410529	0.0176500	0.00882501	−	0.999961i	$-0.497191\pi$
$541$	0.410529	0.0176500	0.00882501	+	0.999961i	$0.497191\pi$
$542$	21.3100	0.915342
$543$	9.88363	0.424147
$544$	−6.48997	−0.278255
$545$	1.24838	0.0534749
$546$	5.50482	0.235585
$547$	29.3129	1.25333	0.626665	−	0.779289i	$-0.284419\pi$
$547$	29.3129	1.25333	0.626665	+	0.779289i	$0.284419\pi$
$548$	−4.41360	−0.188540
$549$	−15.2421	−0.650517
$550$	7.36244	0.313936
$551$	−12.4509	−0.530425
$552$	−3.71189	−0.157989
$553$	4.81826	0.204893
$554$	−0.142530	−0.00605550
$555$	0.604501	0.0256596
$556$	1.43928	0.0610390
$557$	31.7078	1.34350	0.671751	−	0.740777i	$-0.265543\pi$
$557$	31.7078	1.34350	0.671751	+	0.740777i	$0.265543\pi$
$558$	−4.13373	−0.174995
$559$	3.90925	0.165344
$560$	1.45037	0.0612895
$561$	4.91067	0.207329
$562$	−40.6166	−1.71331
$563$	−33.9729	−1.43179	−0.715893	−	0.698210i	$-0.753980\pi$
$563$	−33.9729	−1.43179	−0.715893	+	0.698210i	$0.753980\pi$
$564$	0.929581	0.0391424
$565$	3.80553	0.160100
$566$	12.9669	0.545038
$567$	1.19939	0.0503697
$568$	0.173861	0.00729506
$569$	39.3789	1.65085	0.825424	−	0.564513i	$-0.190936\pi$
$569$	39.3789	1.65085	0.825424	+	0.564513i	$0.190936\pi$
$570$	3.02563	0.126730
$571$	13.4085	0.561128	0.280564	−	0.959835i	$-0.409479\pi$
$571$	13.4085	0.561128	0.280564	+	0.959835i	$0.409479\pi$
$572$	0.720870	0.0301411
$573$	−16.1609	−0.675131
$574$	−7.04327	−0.293981
$575$	6.92763	0.288902
$576$	6.85323	0.285551
$577$	20.3953	0.849067	0.424534	−	0.905412i	$-0.360438\pi$
$577$	20.3953	0.849067	0.424534	+	0.905412i	$0.360438\pi$
$578$	10.6359	0.442396
$579$	5.11580	0.212605
$580$	0.108387	0.00450054
$581$	16.1534	0.670155
$582$	1.49492	0.0619666
$583$	4.97686	0.206120
$584$	−31.7646	−1.31443
$585$	0.841015	0.0347717
$586$	−26.2423	−1.08406
$587$	21.1102	0.871310	0.435655	−	0.900114i	$-0.356517\pi$
$587$	21.1102	0.871310	0.435655	+	0.900114i	$0.356517\pi$
$588$	1.30582	0.0538511
$589$	−20.4305	−0.841822
$590$	3.59447	0.147982
$591$	−5.87260	−0.241567
$592$	−9.74169	−0.400381
$593$	23.7170	0.973940	0.486970	−	0.873419i	$-0.338102\pi$
$593$	23.7170	0.973940	0.486970	+	0.873419i	$0.338102\pi$
$594$	1.49492	0.0613375
$595$	−1.61340	−0.0661431
$596$	3.13163	0.128277
$597$	2.03750	0.0833893
$598$	6.45601	0.264006
$599$	22.5154	0.919954	0.459977	−	0.887931i	$-0.347858\pi$
$599$	22.5154	0.919954	0.459977	+	0.887931i	$0.347858\pi$
$600$	−12.9962	−0.530568
$601$	−43.8970	−1.79060	−0.895298	−	0.445468i	$-0.853037\pi$
$601$	−43.8970	−1.79060	−0.895298	+	0.445468i	$0.853037\pi$
$602$	−2.28303	−0.0930492
$603$	−15.4294	−0.628333
$604$	0.791288	0.0321970
$605$	−0.273931	−0.0111369
$606$	−5.52790	−0.224555
$607$	−22.6694	−0.920121	−0.460060	−	0.887888i	$-0.652172\pi$
$607$	−22.6694	−0.920121	−0.460060	+	0.887888i	$0.652172\pi$
$608$	−9.76466	−0.396009
$609$	2.02118	0.0819024
$610$	6.24173	0.252720
$611$	12.1550	0.491740
$612$	1.15302	0.0466079
$613$	32.8420	1.32647	0.663237	−	0.748409i	$-0.269182\pi$
$613$	32.8420	1.32647	0.663237	+	0.748409i	$0.269182\pi$
$614$	9.68766	0.390962
$615$	−1.07606	−0.0433908
$616$	3.16501	0.127522
$617$	15.8510	0.638139	0.319070	−	0.947731i	$-0.396630\pi$
$617$	15.8510	0.638139	0.319070	+	0.947731i	$0.396630\pi$
$618$	24.4938	0.985284
$619$	−21.9442	−0.882013	−0.441007	−	0.897504i	$-0.645378\pi$
$619$	−21.9442	−0.882013	−0.441007	+	0.897504i	$0.645378\pi$
$620$	0.177851	0.00714269
$621$	1.40664	0.0564464
$622$	−30.6820	−1.23023
$623$	−5.52219	−0.221242
$624$	−13.5532	−0.542561
$625$	23.8801	0.955202
$626$	24.8480	0.993124
$627$	7.38849	0.295068
$628$	−1.00451	−0.0400842
$629$	10.8367	0.432087
$630$	−0.491158	−0.0195682
$631$	−31.9429	−1.27163	−0.635813	−	0.771843i	$-0.719335\pi$
$631$	−31.9429	−1.27163	−0.635813	+	0.771843i	$0.719335\pi$
$632$	−10.6009	−0.421681
$633$	0.614125	0.0244093
$634$	9.69210	0.384922
$635$	5.75252	0.228282
$636$	1.16856	0.0463362
$637$	17.0746	0.676522
$638$	2.51920	0.0997362
$639$	−0.0658854	−0.00260639
$640$	−3.53049	−0.139555
$641$	−20.5560	−0.811915	−0.405957	−	0.913892i	$-0.633062\pi$
$641$	−20.5560	−0.811915	−0.405957	+	0.913892i	$0.633062\pi$
$642$	4.38839	0.173196
$643$	−35.1175	−1.38490	−0.692450	−	0.721466i	$-0.743469\pi$
$643$	−35.1175	−1.38490	−0.692450	+	0.721466i	$0.743469\pi$
$644$	−0.396130	−0.0156097
$645$	−0.348796	−0.0137338
$646$	54.2395	2.13402
$647$	−13.8856	−0.545897	−0.272949	−	0.962029i	$-0.587999\pi$
$647$	−13.8856	−0.545897	−0.272949	+	0.962029i	$0.587999\pi$
$648$	−2.63884	−0.103664
$649$	8.77757	0.344550
$650$	22.6040	0.886601
$651$	3.31653	0.129985
$652$	2.86015	0.112012
$653$	17.4896	0.684419	0.342210	−	0.939624i	$-0.388825\pi$
$653$	17.4896	0.684419	0.342210	+	0.939624i	$0.388825\pi$
$654$	6.81281	0.266402
$655$	−0.136256	−0.00532397
$656$	17.3409	0.677049
$657$	12.0373	0.469621
$658$	−7.09861	−0.276733
$659$	24.4239	0.951419	0.475709	−	0.879603i	$-0.342191\pi$
$659$	24.4239	0.951419	0.475709	+	0.879603i	$0.342191\pi$
$660$	−0.0643184	−0.00250359
$661$	18.0481	0.701989	0.350994	−	0.936378i	$-0.385844\pi$
$661$	18.0481	0.701989	0.350994	+	0.936378i	$0.385844\pi$
$662$	−49.6402	−1.92932
$663$	15.0766	0.585527
$664$	−35.5399	−1.37921
$665$	−2.42749	−0.0941340
$666$	3.29895	0.127832
$667$	2.37042	0.0917832
$668$	2.18037	0.0843610
$669$	26.0549	1.00734
$670$	6.31842	0.244102
$671$	15.2421	0.588415
$672$	1.58512	0.0611474
$673$	−7.12476	−0.274639	−0.137320	−	0.990527i	$-0.543849\pi$
$673$	−7.12476	−0.274639	−0.137320	+	0.990527i	$0.543849\pi$
$674$	−3.96605	−0.152767
$675$	4.92496	0.189562
$676$	−0.839174	−0.0322759
$677$	8.12278	0.312184	0.156092	−	0.987743i	$-0.450110\pi$
$677$	8.12278	0.312184	0.156092	+	0.987743i	$0.450110\pi$
$678$	20.7679	0.797588
$679$	−1.19939	−0.0460284
$680$	3.54973	0.136126
$681$	8.44730	0.323701
$682$	4.13373	0.158289
$683$	−35.4956	−1.35820	−0.679100	−	0.734046i	$-0.737630\pi$
$683$	−35.4956	−1.35820	−0.679100	+	0.734046i	$0.737630\pi$
$684$	1.73480	0.0663318
$685$	5.14920	0.196741
$686$	−22.5227	−0.859921
$687$	−19.3947	−0.739953
$688$	5.62094	0.214296
$689$	15.2798	0.582115
$690$	−0.576026	−0.0219289
$691$	−1.37051	−0.0521368	−0.0260684	−	0.999660i	$-0.508299\pi$
$691$	−1.37051	−0.0521368	−0.0260684	+	0.999660i	$0.508299\pi$
$692$	2.47062	0.0939187
$693$	−1.19939	−0.0455611
$694$	35.6748	1.35420
$695$	−1.67916	−0.0636941
$696$	−4.44690	−0.168559
$697$	−19.2901	−0.730665
$698$	14.8226	0.561045
$699$	−16.3383	−0.617970
$700$	−1.38694	−0.0524215
$701$	−4.24497	−0.160330	−0.0801652	−	0.996782i	$-0.525545\pi$
$701$	−4.24497	−0.160330	−0.0801652	+	0.996782i	$0.525545\pi$
$702$	4.58968	0.173226
$703$	16.3047	0.614942
$704$	−6.85323	−0.258291
$705$	−1.08451	−0.0408451
$706$	23.0782	0.868559
$707$	4.43509	0.166799
$708$	2.06096	0.0774555
$709$	−20.3922	−0.765843	−0.382922	−	0.923781i	$-0.625082\pi$
$709$	−20.3922	−0.765843	−0.382922	+	0.923781i	$0.625082\pi$
$710$	0.0269805	0.00101256
$711$	4.01725	0.150659
$712$	12.1497	0.455327
$713$	3.88960	0.145667
$714$	−8.80483	−0.329513
$715$	−0.841015	−0.0314522
$716$	−1.80312	−0.0673859
$717$	13.3237	0.497583
$718$	−42.5041	−1.58624
$719$	−41.6219	−1.55224	−0.776118	−	0.630588i	$-0.782814\pi$
$719$	−41.6219	−1.55224	−0.776118	+	0.630588i	$0.782814\pi$
$720$	1.20926	0.0450664
$721$	−19.6516	−0.731864
$722$	53.2040	1.98005
$723$	−10.3879	−0.386330
$724$	−2.32066	−0.0862465
$725$	8.29940	0.308232
$726$	−1.49492	−0.0554818
$727$	−22.5856	−0.837652	−0.418826	−	0.908066i	$-0.637558\pi$
$727$	−22.5856	−0.837652	−0.418826	+	0.908066i	$0.637558\pi$
$728$	9.71713	0.360141
$729$	1.00000	0.0370370
$730$	−4.92935	−0.182443
$731$	−6.25275	−0.231266
$732$	3.57881	0.132277
$733$	−41.5955	−1.53636	−0.768182	−	0.640231i	$-0.778838\pi$
$733$	−41.5955	−1.53636	−0.768182	+	0.640231i	$0.778838\pi$
$734$	7.30969	0.269806
$735$	−1.52345	−0.0561935
$736$	1.85902	0.0685243
$737$	15.4294	0.568349
$738$	−5.87237	−0.216165
$739$	48.7651	1.79385	0.896926	−	0.442181i	$-0.145795\pi$
$739$	48.7651	1.79385	0.896926	+	0.442181i	$0.145795\pi$
$740$	−0.141936	−0.00521765
$741$	22.6839	0.833316
$742$	−8.92351	−0.327592
$743$	2.87870	0.105609	0.0528047	−	0.998605i	$-0.483184\pi$
$743$	2.87870	0.105609	0.0528047	+	0.998605i	$0.483184\pi$
$744$	−7.29686	−0.267516
$745$	−3.65357	−0.133856
$746$	16.9407	0.620241
$747$	13.4680	0.492767
$748$	−1.15302	−0.0421584
$749$	−3.52084	−0.128649
$750$	−4.06433	−0.148408
$751$	−39.2694	−1.43296	−0.716481	−	0.697607i	$-0.754248\pi$
$751$	−39.2694	−1.43296	−0.716481	+	0.697607i	$0.754248\pi$
$752$	17.4772	0.637327
$753$	−10.7475	−0.391660
$754$	7.73439	0.281670
$755$	−0.923168	−0.0335975
$756$	−0.281615	−0.0102422
$757$	−9.34004	−0.339470	−0.169735	−	0.985490i	$-0.554291\pi$
$757$	−9.34004	−0.339470	−0.169735	+	0.985490i	$0.554291\pi$
$758$	−16.5128	−0.599773
$759$	−1.40664	−0.0510577
$760$	5.34084	0.193733
$761$	26.1584	0.948242	0.474121	−	0.880460i	$-0.342766\pi$
$761$	26.1584	0.948242	0.474121	+	0.880460i	$0.342766\pi$
$762$	31.3933	1.13726
$763$	−5.46599	−0.197882
$764$	3.79454	0.137282
$765$	−1.34518	−0.0486352
$766$	46.8640	1.69327
$767$	26.9487	0.973061
$768$	−5.56052	−0.200648
$769$	−9.29449	−0.335168	−0.167584	−	0.985858i	$-0.553597\pi$
$769$	−9.29449	−0.335168	−0.167584	+	0.985858i	$0.553597\pi$
$770$	0.491158	0.0177001
$771$	−10.4664	−0.376940
$772$	−1.20118	−0.0432314
$773$	11.5219	0.414412	0.207206	−	0.978297i	$-0.433563\pi$
$773$	11.5219	0.414412	0.207206	+	0.978297i	$0.433563\pi$
$774$	−1.90349	−0.0684194
$775$	13.6184	0.489187
$776$	2.63884	0.0947289
$777$	−2.64678	−0.0949526
$778$	39.6588	1.42184
$779$	−29.0235	−1.03987
$780$	−0.197469	−0.00707051
$781$	0.0658854	0.00235757
$782$	−10.3262	−0.369265
$783$	1.68517	0.0602231
$784$	24.5509	0.876817
$785$	1.17193	0.0418278
$786$	−0.743593	−0.0265231
$787$	−23.7476	−0.846509	−0.423254	−	0.906011i	$-0.639112\pi$
$787$	−23.7476	−0.846509	−0.423254	+	0.906011i	$0.639112\pi$
$788$	1.37888	0.0491204
$789$	6.95689	0.247672
$790$	−1.64509	−0.0585295
$791$	−16.6623	−0.592444
$792$	2.63884	0.0937672
$793$	46.7959	1.66177
$794$	−8.37640	−0.297267
$795$	−1.36331	−0.0483518
$796$	−0.478400	−0.0169564
$797$	−32.8350	−1.16307	−0.581537	−	0.813520i	$-0.697548\pi$
$797$	−32.8350	−1.16307	−0.581537	+	0.813520i	$0.697548\pi$
$798$	−13.2476	−0.468959
$799$	−19.4417	−0.687798
$800$	6.50885	0.230123
$801$	−4.60416	−0.162680
$802$	−9.02152	−0.318561
$803$	−12.0373	−0.424788
$804$	3.62279	0.127766
$805$	0.462151	0.0162887
$806$	12.6913	0.447031
$807$	14.3048	0.503552
$808$	−9.75786	−0.343280
$809$	18.7349	0.658685	0.329343	−	0.944211i	$-0.393173\pi$
$809$	18.7349	0.658685	0.329343	+	0.944211i	$0.393173\pi$
$810$	−0.409506	−0.0143886
$811$	−48.2340	−1.69372	−0.846862	−	0.531813i	$-0.821511\pi$
$811$	−48.2340	−1.69372	−0.846862	+	0.531813i	$0.821511\pi$
$812$	−0.474569	−0.0166541
$813$	−14.2549	−0.499941
$814$	−3.29895	−0.115628
$815$	−3.33684	−0.116884
$816$	21.6780	0.758881
$817$	−9.40776	−0.329136
$818$	−12.7846	−0.447002
$819$	−3.68234	−0.128671
$820$	0.252656	0.00882312
$821$	−26.7438	−0.933365	−0.466683	−	0.884425i	$-0.654551\pi$
$821$	−26.7438	−0.933365	−0.466683	+	0.884425i	$0.654551\pi$
$822$	28.1008	0.980127
$823$	0.0161113	0.000561605 0	0.000280802	−	1.00000i	$-0.499911\pi$
$823$	0.0161113	0.000561605 0	0.000280802		1.00000i	$0.499911\pi$
$824$	43.2365	1.50621
$825$	−4.92496	−0.171465
$826$	−15.7382	−0.547602
$827$	11.8512	0.412107	0.206053	−	0.978541i	$-0.433938\pi$
$827$	11.8512	0.412107	0.206053	+	0.978541i	$0.433938\pi$
$828$	−0.330275	−0.0114779
$829$	−16.1547	−0.561076	−0.280538	−	0.959843i	$-0.590513\pi$
$829$	−16.1547	−0.561076	−0.280538	+	0.959843i	$0.590513\pi$
$830$	−5.51521	−0.191436
$831$	0.0953424	0.00330739
$832$	−21.0406	−0.729452
$833$	−27.3105	−0.946252
$834$	−9.16368	−0.317312
$835$	−2.54376	−0.0880305
$836$	−1.73480	−0.0599994
$837$	2.76517	0.0955784
$838$	−27.6961	−0.956747
$839$	9.73219	0.335993	0.167996	−	0.985788i	$-0.446270\pi$
$839$	9.73219	0.335993	0.167996	+	0.985788i	$0.446270\pi$
$840$	−0.866993	−0.0299141
$841$	−26.1602	−0.902076
$842$	5.01609	0.172866
$843$	27.1696	0.935772
$844$	−0.144195	−0.00496341
$845$	0.979036	0.0336799
$846$	−5.91851	−0.203483
$847$	1.19939	0.0412116
$848$	21.9702	0.754459
$849$	−8.67393	−0.297689
$850$	−36.1545	−1.24009
$851$	−3.10412	−0.106408
$852$	0.0154698	0.000529985 0
$853$	−41.8051	−1.43138	−0.715689	−	0.698419i	$-0.753887\pi$
$853$	−41.8051	−1.43138	−0.715689	+	0.698419i	$0.753887\pi$
$854$	−27.3291	−0.935182
$855$	−2.02393	−0.0692171
$856$	7.74639	0.264766
$857$	−11.4152	−0.389934	−0.194967	−	0.980810i	$-0.562460\pi$
$857$	−11.4152	−0.389934	−0.194967	+	0.980810i	$0.562460\pi$
$858$	−4.58968	−0.156689
$859$	−24.2353	−0.826899	−0.413449	−	0.910527i	$-0.635676\pi$
$859$	−24.2353	−0.826899	−0.413449	+	0.910527i	$0.635676\pi$
$860$	0.0818965	0.00279265
$861$	4.71146	0.160566
$862$	28.0543	0.955533
$863$	−42.9759	−1.46292	−0.731458	−	0.681886i	$-0.761160\pi$
$863$	−42.9759	−1.46292	−0.731458	+	0.681886i	$0.761160\pi$
$864$	1.32160	0.0449619
$865$	−2.88238	−0.0980040
$866$	37.7390	1.28242
$867$	−7.11469	−0.241627
$868$	−0.778714	−0.0264313
$869$	−4.01725	−0.136276
$870$	−0.690087	−0.0233961
$871$	47.3709	1.60510
$872$	12.0260	0.407251
$873$	−1.00000	−0.0338449
$874$	−15.5366	−0.525534
$875$	3.26085	0.110237
$876$	−2.82634	−0.0954931
$877$	36.6375	1.23716	0.618580	−	0.785722i	$-0.287708\pi$
$877$	36.6375	1.23716	0.618580	+	0.785722i	$0.287708\pi$
$878$	−9.20907	−0.310791
$879$	17.5542	0.592090
$880$	−1.20926	−0.0407641
$881$	3.18761	0.107393	0.0536966	−	0.998557i	$-0.482900\pi$
$881$	3.18761	0.107393	0.0536966	+	0.998557i	$0.482900\pi$
$882$	−8.31396	−0.279946
$883$	−38.8424	−1.30715	−0.653576	−	0.756861i	$-0.726732\pi$
$883$	−38.8424	−1.30715	−0.653576	+	0.756861i	$0.726732\pi$
$884$	−3.53996	−0.119062
$885$	−2.40445	−0.0808246
$886$	13.9052	0.467154
$887$	−14.5665	−0.489094	−0.244547	−	0.969637i	$-0.578639\pi$
$887$	−14.5665	−0.489094	−0.244547	+	0.969637i	$0.578639\pi$
$888$	5.82331	0.195417
$889$	−25.1871	−0.844749
$890$	1.88543	0.0631997
$891$	−1.00000	−0.0335013
$892$	−6.11763	−0.204833
$893$	−29.2515	−0.978866
$894$	−19.9386	−0.666848
$895$	2.10364	0.0703170
$896$	15.4581	0.516419
$897$	−4.31862	−0.144195
$898$	20.4499	0.682423
$899$	4.65979	0.155413
$900$	−1.15637	−0.0385457
$901$	−24.4397	−0.814205
$902$	5.87237	0.195528
$903$	1.52719	0.0508215
$904$	36.6596	1.21928
$905$	2.70743	0.0899980
$906$	−5.03801	−0.167377
$907$	8.56527	0.284405	0.142203	−	0.989838i	$-0.454582\pi$
$907$	8.56527	0.284405	0.142203	+	0.989838i	$0.454582\pi$
$908$	−1.98341	−0.0658217
$909$	3.69778	0.122648
$910$	1.50794	0.0499877
$911$	−21.4569	−0.710900	−0.355450	−	0.934695i	$-0.615672\pi$
$911$	−21.4569	−0.710900	−0.355450	+	0.934695i	$0.615672\pi$
$912$	32.6162	1.08003
$913$	−13.4680	−0.445725
$914$	18.3434	0.606746
$915$	−4.17528	−0.138030
$916$	4.55383	0.150463
$917$	0.596592	0.0197012
$918$	−7.34108	−0.242292
$919$	15.3847	0.507495	0.253747	−	0.967271i	$-0.418337\pi$
$919$	15.3847	0.507495	0.253747	+	0.967271i	$0.418337\pi$
$920$	−1.01680	−0.0335230
$921$	−6.48037	−0.213536
$922$	18.9741	0.624878
$923$	0.202280	0.00665812
$924$	0.281615	0.00926444
$925$	−10.8682	−0.357345
$926$	−34.6882	−1.13992
$927$	−16.3846	−0.538142
$928$	2.22713	0.0731091
$929$	20.2763	0.665243	0.332621	−	0.943060i	$-0.392067\pi$
$929$	20.2763	0.665243	0.332621	+	0.943060i	$0.392067\pi$
$930$	−1.13235	−0.0371314
$931$	−41.0908	−1.34670
$932$	3.83619	0.125659
$933$	20.5241	0.671928
$934$	6.56752	0.214896
$935$	1.34518	0.0439922
$936$	8.10171	0.264813
$937$	34.4726	1.12617	0.563086	−	0.826398i	$-0.309614\pi$
$937$	34.4726	1.12617	0.563086	+	0.826398i	$0.309614\pi$
$938$	−27.6649	−0.903291
$939$	−16.6216	−0.542424
$940$	0.254641	0.00830547
$941$	−55.7503	−1.81741	−0.908704	−	0.417442i	$-0.862927\pi$
$941$	−55.7503	−1.81741	−0.908704	+	0.417442i	$0.862927\pi$
$942$	6.39556	0.208378
$943$	5.52556	0.179937
$944$	38.7483	1.26115
$945$	0.328550	0.0106877
$946$	1.90349	0.0618877
$947$	27.6529	0.898597	0.449299	−	0.893382i	$-0.351674\pi$
$947$	27.6529	0.898597	0.449299	+	0.893382i	$0.351674\pi$
$948$	−0.943241	−0.0306351
$949$	−36.9567	−1.19966
$950$	−54.3973	−1.76488
$951$	−6.48334	−0.210237
$952$	−15.5423	−0.503729
$953$	58.4361	1.89293	0.946466	−	0.322803i	$-0.104625\pi$
$953$	58.4361	1.89293	0.946466	+	0.322803i	$0.104625\pi$
$954$	−7.44002	−0.240880
$955$	−4.42696	−0.143253
$956$	−3.12838	−0.101179
$957$	−1.68517	−0.0544738
$958$	23.7698	0.767966
$959$	−22.5455	−0.728033
$960$	1.87731	0.0605900
$961$	−23.3538	−0.753349
$962$	−10.1283	−0.326551
$963$	−2.93552	−0.0945960
$964$	2.43905	0.0785566
$965$	1.40138	0.0451119
$966$	2.52210	0.0811472
$967$	−14.3000	−0.459858	−0.229929	−	0.973207i	$-0.573849\pi$
$967$	−14.3000	−0.459858	−0.229929	+	0.973207i	$0.573849\pi$
$968$	−2.63884	−0.0848156
$969$	−36.2824	−1.16556
$970$	0.409506	0.0131484
$971$	46.9293	1.50603	0.753017	−	0.658001i	$-0.228598\pi$
$971$	46.9293	1.50603	0.753017	+	0.658001i	$0.228598\pi$
$972$	−0.234798	−0.00753115
$973$	7.35211	0.235698
$974$	−45.4880	−1.45753
$975$	−15.1205	−0.484243
$976$	67.2857	2.15376
$977$	21.6274	0.691922	0.345961	−	0.938249i	$-0.387553\pi$
$977$	21.6274	0.691922	0.345961	+	0.938249i	$0.387553\pi$
$978$	−18.2101	−0.582296
$979$	4.60416	0.147150
$980$	0.357704	0.0114264
$981$	−4.55730	−0.145503
$982$	34.2061	1.09156
$983$	−40.4628	−1.29056	−0.645282	−	0.763945i	$-0.723260\pi$
$983$	−40.4628	−1.29056	−0.645282	+	0.763945i	$0.723260\pi$
$984$	−10.3659	−0.330453
$985$	−1.60869	−0.0512570
$986$	−12.3710	−0.393972
$987$	4.74848	0.151146
$988$	−5.32614	−0.169447
$989$	1.79107	0.0569527
$990$	0.409506	0.0130149
$991$	32.2043	1.02300	0.511502	−	0.859282i	$-0.329089\pi$
$991$	32.2043	1.02300	0.511502	+	0.859282i	$0.329089\pi$
$992$	3.65447	0.116029
$993$	33.2059	1.05376
$994$	−0.118133	−0.00374694
$995$	0.558133	0.0176940
$996$	−3.16225	−0.100200
$997$	−5.64425	−0.178755	−0.0893776	−	0.995998i	$-0.528488\pi$
$997$	−5.64425	−0.178755	−0.0893776	+	0.995998i	$0.528488\pi$
$998$	48.8827	1.54736
$999$	−2.20677	−0.0698190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3201.2.a.u.1.14	✓	19
3.2	odd	2		9603.2.a.ba.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3201.2.a.u.1.14	✓	19	1.1	even	1	trivial
9603.2.a.ba.1.6		19	3.2	odd	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:	\( N \)	\(=\)	\( 3201 = 3 \cdot 11 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3201.a (trivial)

\(f(q)\)	\(=\)	\(q+1.49492 q^{2} -1.00000 q^{3} +0.234798 q^{4} -0.273931 q^{5} -1.49492 q^{6} +1.19939 q^{7} -2.63884 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.49492 q^{2} -1.00000 q^{3} +0.234798 q^{4} -0.273931 q^{5} -1.49492 q^{6} +1.19939 q^{7} -2.63884 q^{8} +1.00000 q^{9} -0.409506 q^{10} -1.00000 q^{11} -0.234798 q^{12} -3.07017 q^{13} +1.79300 q^{14} +0.273931 q^{15} -4.41447 q^{16} +4.91067 q^{17} +1.49492 q^{18} +7.38849 q^{19} -0.0643184 q^{20} -1.19939 q^{21} -1.49492 q^{22} -1.40664 q^{23} +2.63884 q^{24} -4.92496 q^{25} -4.58968 q^{26} -1.00000 q^{27} +0.281615 q^{28} -1.68517 q^{29} +0.409506 q^{30} -2.76517 q^{31} -1.32160 q^{32} +1.00000 q^{33} +7.34108 q^{34} -0.328550 q^{35} +0.234798 q^{36} +2.20677 q^{37} +11.0452 q^{38} +3.07017 q^{39} +0.722860 q^{40} -3.92821 q^{41} -1.79300 q^{42} -1.27330 q^{43} -0.234798 q^{44} -0.273931 q^{45} -2.10282 q^{46} -3.95907 q^{47} +4.41447 q^{48} -5.56146 q^{49} -7.36244 q^{50} -4.91067 q^{51} -0.720870 q^{52} -4.97686 q^{53} -1.49492 q^{54} +0.273931 q^{55} -3.16501 q^{56} -7.38849 q^{57} -2.51920 q^{58} -8.77757 q^{59} +0.0643184 q^{60} -15.2421 q^{61} -4.13373 q^{62} +1.19939 q^{63} +6.85323 q^{64} +0.841015 q^{65} +1.49492 q^{66} -15.4294 q^{67} +1.15302 q^{68} +1.40664 q^{69} -0.491158 q^{70} -0.0658854 q^{71} -2.63884 q^{72} +12.0373 q^{73} +3.29895 q^{74} +4.92496 q^{75} +1.73480 q^{76} -1.19939 q^{77} +4.58968 q^{78} +4.01725 q^{79} +1.20926 q^{80} +1.00000 q^{81} -5.87237 q^{82} +13.4680 q^{83} -0.281615 q^{84} -1.34518 q^{85} -1.90349 q^{86} +1.68517 q^{87} +2.63884 q^{88} -4.60416 q^{89} -0.409506 q^{90} -3.68234 q^{91} -0.330275 q^{92} +2.76517 q^{93} -5.91851 q^{94} -2.02393 q^{95} +1.32160 q^{96} -1.00000 q^{97} -8.31396 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + q^{2} - 19 q^{3} + 15 q^{4} + 8 q^{5} - q^{6} - 7 q^{7} + 19 q^{9}+O(q^{10}) \) 19 * q + q^2 - 19 * q^3 + 15 * q^4 + 8 * q^5 - q^6 - 7 * q^7 + 19 * q^9	\( 19 q + q^{2} - 19 q^{3} + 15 q^{4} + 8 q^{5} - q^{6} - 7 q^{7} + 19 q^{9} - 15 q^{10} - 19 q^{11} - 15 q^{12} - 8 q^{13} - 8 q^{15} + 7 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 4 q^{20} + 7 q^{21} - q^{22} + q^{23} + 11 q^{25} - 5 q^{26} - 19 q^{27} - 23 q^{28} + 2 q^{29} + 15 q^{30} - 46 q^{31} - 19 q^{32} + 19 q^{33} - 16 q^{34} - 4 q^{35} + 15 q^{36} - 21 q^{37} - 2 q^{38} + 8 q^{39} - 39 q^{40} - 29 q^{41} - 11 q^{43} - 15 q^{44} + 8 q^{45} - 33 q^{46} - 6 q^{47} - 7 q^{48} - 2 q^{49} - 14 q^{50} + 2 q^{51} - 18 q^{52} + 39 q^{53} - q^{54} - 8 q^{55} - 11 q^{56} + 13 q^{57} - 13 q^{58} + 3 q^{59} - 4 q^{60} - 36 q^{61} + 11 q^{62} - 7 q^{63} - 24 q^{64} - 33 q^{65} + q^{66} - 23 q^{67} - 16 q^{68} - q^{69} - 20 q^{70} - 18 q^{71} - 19 q^{73} - 9 q^{74} - 11 q^{75} - 26 q^{76} + 7 q^{77} + 5 q^{78} - 66 q^{79} - 40 q^{80} + 19 q^{81} - 62 q^{82} - 28 q^{83} + 23 q^{84} - 31 q^{85} - 35 q^{86} - 2 q^{87} - 15 q^{90} - 34 q^{91} + 57 q^{92} + 46 q^{93} - 32 q^{94} - 40 q^{95} + 19 q^{96} - 19 q^{97} - 29 q^{98} - 19 q^{99}+O(q^{100}) \) 19 * q + q^2 - 19 * q^3 + 15 * q^4 + 8 * q^5 - q^6 - 7 * q^7 + 19 * q^9 - 15 * q^10 - 19 * q^11 - 15 * q^12 - 8 * q^13 - 8 * q^15 + 7 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 4 * q^20 + 7 * q^21 - q^22 + q^23 + 11 * q^25 - 5 * q^26 - 19 * q^27 - 23 * q^28 + 2 * q^29 + 15 * q^30 - 46 * q^31 - 19 * q^32 + 19 * q^33 - 16 * q^34 - 4 * q^35 + 15 * q^36 - 21 * q^37 - 2 * q^38 + 8 * q^39 - 39 * q^40 - 29 * q^41 - 11 * q^43 - 15 * q^44 + 8 * q^45 - 33 * q^46 - 6 * q^47 - 7 * q^48 - 2 * q^49 - 14 * q^50 + 2 * q^51 - 18 * q^52 + 39 * q^53 - q^54 - 8 * q^55 - 11 * q^56 + 13 * q^57 - 13 * q^58 + 3 * q^59 - 4 * q^60 - 36 * q^61 + 11 * q^62 - 7 * q^63 - 24 * q^64 - 33 * q^65 + q^66 - 23 * q^67 - 16 * q^68 - q^69 - 20 * q^70 - 18 * q^71 - 19 * q^73 - 9 * q^74 - 11 * q^75 - 26 * q^76 + 7 * q^77 + 5 * q^78 - 66 * q^79 - 40 * q^80 + 19 * q^81 - 62 * q^82 - 28 * q^83 + 23 * q^84 - 31 * q^85 - 35 * q^86 - 2 * q^87 - 15 * q^90 - 34 * q^91 + 57 * q^92 + 46 * q^93 - 32 * q^94 - 40 * q^95 + 19 * q^96 - 19 * q^97 - 29 * q^98 - 19 * q^99

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