LMFDB - Embedded newform 6009.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71219 q^{2} -1.00000 q^{3} +5.35600 q^{4} +0.0136473 q^{5} +2.71219 q^{6} -2.53463 q^{7} -9.10211 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.71219 q^{2} -1.00000 q^{3} +5.35600 q^{4} +0.0136473 q^{5} +2.71219 q^{6} -2.53463 q^{7} -9.10211 q^{8} +1.00000 q^{9} -0.0370143 q^{10} +2.91066 q^{11} -5.35600 q^{12} -4.80165 q^{13} +6.87440 q^{14} -0.0136473 q^{15} +13.9747 q^{16} -0.272903 q^{17} -2.71219 q^{18} +0.639514 q^{19} +0.0730951 q^{20} +2.53463 q^{21} -7.89428 q^{22} -8.17747 q^{23} +9.10211 q^{24} -4.99981 q^{25} +13.0230 q^{26} -1.00000 q^{27} -13.5755 q^{28} -1.81125 q^{29} +0.0370143 q^{30} +2.80220 q^{31} -19.6979 q^{32} -2.91066 q^{33} +0.740166 q^{34} -0.0345910 q^{35} +5.35600 q^{36} +2.31299 q^{37} -1.73449 q^{38} +4.80165 q^{39} -0.124220 q^{40} -5.63968 q^{41} -6.87440 q^{42} +8.70192 q^{43} +15.5895 q^{44} +0.0136473 q^{45} +22.1789 q^{46} -9.05885 q^{47} -13.9747 q^{48} -0.575661 q^{49} +13.5605 q^{50} +0.272903 q^{51} -25.7176 q^{52} +6.57917 q^{53} +2.71219 q^{54} +0.0397228 q^{55} +23.0705 q^{56} -0.639514 q^{57} +4.91246 q^{58} -10.2144 q^{59} -0.0730951 q^{60} +0.863702 q^{61} -7.60011 q^{62} -2.53463 q^{63} +25.4750 q^{64} -0.0655298 q^{65} +7.89428 q^{66} +2.90374 q^{67} -1.46167 q^{68} +8.17747 q^{69} +0.0938174 q^{70} -6.08675 q^{71} -9.10211 q^{72} -11.9556 q^{73} -6.27328 q^{74} +4.99981 q^{75} +3.42523 q^{76} -7.37744 q^{77} -13.0230 q^{78} +7.43924 q^{79} +0.190718 q^{80} +1.00000 q^{81} +15.2959 q^{82} -11.6630 q^{83} +13.5755 q^{84} -0.00372440 q^{85} -23.6013 q^{86} +1.81125 q^{87} -26.4932 q^{88} -13.7917 q^{89} -0.0370143 q^{90} +12.1704 q^{91} -43.7985 q^{92} -2.80220 q^{93} +24.5693 q^{94} +0.00872767 q^{95} +19.6979 q^{96} +15.3644 q^{97} +1.56130 q^{98} +2.91066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * 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 $

$2$	−2.71219	−1.91781	−0.958905	−	0.283726i	$-0.908429\pi$
$2$	−2.71219	−1.91781	−0.958905	+	0.283726i	$0.908429\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.35600	2.67800
$5$	0.0136473	0.00610328	0.00305164	−	0.999995i	$-0.499029\pi$
$5$	0.0136473	0.00610328	0.00305164	+	0.999995i	$0.499029\pi$
$6$	2.71219	1.10725
$7$	−2.53463	−0.957999	−0.479000	−	0.877815i	$-0.659000\pi$
$7$	−2.53463	−0.957999	−0.479000	+	0.877815i	$0.659000\pi$
$8$	−9.10211	−3.21808
$9$	1.00000	0.333333
$10$	−0.0370143	−0.0117049
$11$	2.91066	0.877597	0.438799	−	0.898585i	$-0.355404\pi$
$11$	2.91066	0.877597	0.438799	+	0.898585i	$0.355404\pi$
$12$	−5.35600	−1.54614
$13$	−4.80165	−1.33174	−0.665869	−	0.746069i	$-0.731939\pi$
$13$	−4.80165	−1.33174	−0.665869	+	0.746069i	$0.731939\pi$
$14$	6.87440	1.83726
$15$	−0.0136473	−0.00352373
$16$	13.9747	3.49367
$17$	−0.272903	−0.0661887	−0.0330943	−	0.999452i	$-0.510536\pi$
$17$	−0.272903	−0.0661887	−0.0330943	+	0.999452i	$0.510536\pi$
$18$	−2.71219	−0.639270
$19$	0.639514	0.146715	0.0733573	−	0.997306i	$-0.476629\pi$
$19$	0.639514	0.146715	0.0733573	+	0.997306i	$0.476629\pi$
$20$	0.0730951	0.0163446
$21$	2.53463	0.553101
$22$	−7.89428	−1.68307
$23$	−8.17747	−1.70512	−0.852560	−	0.522630i	$-0.824951\pi$
$23$	−8.17747	−1.70512	−0.852560	+	0.522630i	$0.824951\pi$
$24$	9.10211	1.85796
$25$	−4.99981	−0.999963
$26$	13.0230	2.55402
$27$	−1.00000	−0.192450
$28$	−13.5755	−2.56552
$29$	−1.81125	−0.336340	−0.168170	−	0.985758i	$-0.553786\pi$
$29$	−1.81125	−0.336340	−0.168170	+	0.985758i	$0.553786\pi$
$30$	0.0370143	0.00675785
$31$	2.80220	0.503290	0.251645	−	0.967820i	$-0.419028\pi$
$31$	2.80220	0.503290	0.251645	+	0.967820i	$0.419028\pi$
$32$	−19.6979	−3.48212
$33$	−2.91066	−0.506681
$34$	0.740166	0.126937
$35$	−0.0345910	−0.00584694
$36$	5.35600	0.892666
$37$	2.31299	0.380253	0.190127	−	0.981760i	$-0.439110\pi$
$37$	2.31299	0.380253	0.190127	+	0.981760i	$0.439110\pi$
$38$	−1.73449	−0.281371
$39$	4.80165	0.768879
$40$	−0.124220	−0.0196409
$41$	−5.63968	−0.880770	−0.440385	−	0.897809i	$-0.645158\pi$
$41$	−5.63968	−0.880770	−0.440385	+	0.897809i	$0.645158\pi$
$42$	−6.87440	−1.06074
$43$	8.70192	1.32703	0.663515	−	0.748163i	$-0.269064\pi$
$43$	8.70192	1.32703	0.663515	+	0.748163i	$0.269064\pi$
$44$	15.5895	2.35020
$45$	0.0136473	0.00203443
$46$	22.1789	3.27010
$47$	−9.05885	−1.32137	−0.660684	−	0.750664i	$-0.729734\pi$
$47$	−9.05885	−1.32137	−0.660684	+	0.750664i	$0.729734\pi$
$48$	−13.9747	−2.01707
$49$	−0.575661	−0.0822373
$50$	13.5605	1.91774
$51$	0.272903	0.0382141
$52$	−25.7176	−3.56639
$53$	6.57917	0.903719	0.451859	−	0.892089i	$-0.350761\pi$
$53$	6.57917	0.903719	0.451859	+	0.892089i	$0.350761\pi$
$54$	2.71219	0.369083
$55$	0.0397228	0.00535622
$56$	23.0705	3.08292
$57$	−0.639514	−0.0847057
$58$	4.91246	0.645037
$59$	−10.2144	−1.32980	−0.664899	−	0.746933i	$-0.731525\pi$
$59$	−10.2144	−1.32980	−0.664899	+	0.746933i	$0.731525\pi$
$60$	−0.0730951	−0.00943654
$61$	0.863702	0.110586	0.0552928	−	0.998470i	$-0.482391\pi$
$61$	0.863702	0.110586	0.0552928	+	0.998470i	$0.482391\pi$
$62$	−7.60011	−0.965215
$63$	−2.53463	−0.319333
$64$	25.4750	3.18438
$65$	−0.0655298	−0.00812797
$66$	7.89428	0.971719
$67$	2.90374	0.354749	0.177374	−	0.984143i	$-0.443240\pi$
$67$	2.90374	0.354749	0.177374	+	0.984143i	$0.443240\pi$
$68$	−1.46167	−0.177253
$69$	8.17747	0.984451
$70$	0.0938174	0.0112133
$71$	−6.08675	−0.722364	−0.361182	−	0.932495i	$-0.617627\pi$
$71$	−6.08675	−0.722364	−0.361182	+	0.932495i	$0.617627\pi$
$72$	−9.10211	−1.07269
$73$	−11.9556	−1.39930	−0.699648	−	0.714487i	$-0.746660\pi$
$73$	−11.9556	−1.39930	−0.699648	+	0.714487i	$0.746660\pi$
$74$	−6.27328	−0.729254
$75$	4.99981	0.577329
$76$	3.42523	0.392901
$77$	−7.37744	−0.840738
$78$	−13.0230	−1.47456
$79$	7.43924	0.836979	0.418490	−	0.908222i	$-0.362560\pi$
$79$	7.43924	0.836979	0.418490	+	0.908222i	$0.362560\pi$
$80$	0.190718	0.0213229
$81$	1.00000	0.111111
$82$	15.2959	1.68915
$83$	−11.6630	−1.28018	−0.640090	−	0.768300i	$-0.721103\pi$
$83$	−11.6630	−1.28018	−0.640090	+	0.768300i	$0.721103\pi$
$84$	13.5755	1.48120
$85$	−0.00372440	−0.000403968 0
$86$	−23.6013	−2.54499
$87$	1.81125	0.194186
$88$	−26.4932	−2.82418
$89$	−13.7917	−1.46191	−0.730957	−	0.682423i	$-0.760926\pi$
$89$	−13.7917	−1.46191	−0.730957	+	0.682423i	$0.760926\pi$
$90$	−0.0370143	−0.00390165
$91$	12.1704	1.27580
$92$	−43.7985	−4.56631
$93$	−2.80220	−0.290575
$94$	24.5693	2.53413
$95$	0.00872767	0.000895440 0
$96$	19.6979	2.01040
$97$	15.3644	1.56002	0.780009	−	0.625769i	$-0.215215\pi$
$97$	15.3644	1.56002	0.780009	+	0.625769i	$0.215215\pi$
$98$	1.56130	0.157716
$99$	2.91066	0.292532
$100$	−26.7790	−2.67790
$101$	3.88445	0.386517	0.193259	−	0.981148i	$-0.438094\pi$
$101$	3.88445	0.386517	0.193259	+	0.981148i	$0.438094\pi$
$102$	−0.740166	−0.0732873
$103$	−9.47246	−0.933349	−0.466675	−	0.884429i	$-0.654548\pi$
$103$	−9.47246	−0.933349	−0.466675	+	0.884429i	$0.654548\pi$
$104$	43.7051	4.28564
$105$	0.0345910	0.00337573
$106$	−17.8440	−1.73316
$107$	5.55990	0.537496	0.268748	−	0.963210i	$-0.413390\pi$
$107$	5.55990	0.537496	0.268748	+	0.963210i	$0.413390\pi$
$108$	−5.35600	−0.515381
$109$	12.4099	1.18865	0.594327	−	0.804224i	$-0.297419\pi$
$109$	12.4099	1.18865	0.594327	+	0.804224i	$0.297419\pi$
$110$	−0.107736	−0.0102722
$111$	−2.31299	−0.219539
$112$	−35.4207	−3.34694
$113$	4.95264	0.465905	0.232953	−	0.972488i	$-0.425161\pi$
$113$	4.95264	0.465905	0.232953	+	0.972488i	$0.425161\pi$
$114$	1.73449	0.162449
$115$	−0.111601	−0.0104068
$116$	−9.70104	−0.900719
$117$	−4.80165	−0.443913
$118$	27.7033	2.55030
$119$	0.691708	0.0634087
$120$	0.124220	0.0113397
$121$	−2.52805	−0.229823
$122$	−2.34253	−0.212082
$123$	5.63968	0.508513
$124$	15.0086	1.34781
$125$	−0.136471	−0.0122063
$126$	6.87440	0.612420
$127$	4.44765	0.394665	0.197333	−	0.980337i	$-0.436772\pi$
$127$	4.44765	0.394665	0.197333	+	0.980337i	$0.436772\pi$
$128$	−29.6975	−2.62491
$129$	−8.70192	−0.766162
$130$	0.177729	0.0155879
$131$	−3.12608	−0.273127	−0.136563	−	0.990631i	$-0.543606\pi$
$131$	−3.12608	−0.273127	−0.136563	+	0.990631i	$0.543606\pi$
$132$	−15.5895	−1.35689
$133$	−1.62093	−0.140552
$134$	−7.87551	−0.680341
$135$	−0.0136473	−0.00117458
$136$	2.48399	0.213001
$137$	−7.38632	−0.631056	−0.315528	−	0.948916i	$-0.602182\pi$
$137$	−7.38632	−0.631056	−0.315528	+	0.948916i	$0.602182\pi$
$138$	−22.1789	−1.88799
$139$	3.86139	0.327518	0.163759	−	0.986500i	$-0.447638\pi$
$139$	3.86139	0.327518	0.163759	+	0.986500i	$0.447638\pi$
$140$	−0.185269	−0.0156581
$141$	9.05885	0.762893
$142$	16.5084	1.38536
$143$	−13.9760	−1.16873
$144$	13.9747	1.16456
$145$	−0.0247187	−0.00205278
$146$	32.4259	2.68359
$147$	0.575661	0.0474797
$148$	12.3884	1.01832
$149$	13.3827	1.09635	0.548177	−	0.836362i	$-0.315322\pi$
$149$	13.3827	1.09635	0.548177	+	0.836362i	$0.315322\pi$
$150$	−13.5605	−1.10721
$151$	3.54425	0.288427	0.144213	−	0.989547i	$-0.453935\pi$
$151$	3.54425	0.288427	0.144213	+	0.989547i	$0.453935\pi$
$152$	−5.82093	−0.472139
$153$	−0.272903	−0.0220629
$154$	20.0091	1.61238
$155$	0.0382426	0.00307172
$156$	25.7176	2.05906
$157$	22.9191	1.82914	0.914570	−	0.404428i	$-0.132529\pi$
$157$	22.9191	1.82914	0.914570	+	0.404428i	$0.132529\pi$
$158$	−20.1767	−1.60517
$159$	−6.57917	−0.521762
$160$	−0.268824	−0.0212524
$161$	20.7268	1.63350
$162$	−2.71219	−0.213090
$163$	−8.63657	−0.676468	−0.338234	−	0.941062i	$-0.609830\pi$
$163$	−8.63657	−0.676468	−0.338234	+	0.941062i	$0.609830\pi$
$164$	−30.2061	−2.35870
$165$	−0.0397228	−0.00309242
$166$	31.6323	2.45514
$167$	−16.1409	−1.24902	−0.624509	−	0.781018i	$-0.714701\pi$
$167$	−16.1409	−1.24902	−0.624509	+	0.781018i	$0.714701\pi$
$168$	−23.0705	−1.77992
$169$	10.0558	0.773526
$170$	0.0101013	0.000774734 0
$171$	0.639514	0.0489049
$172$	46.6075	3.55379
$173$	−2.81525	−0.214040	−0.107020	−	0.994257i	$-0.534131\pi$
$173$	−2.81525	−0.214040	−0.107020	+	0.994257i	$0.534131\pi$
$174$	−4.91246	−0.372412
$175$	12.6727	0.957964
$176$	40.6756	3.06604
$177$	10.2144	0.767759
$178$	37.4057	2.80367
$179$	12.4958	0.933984	0.466992	−	0.884262i	$-0.345338\pi$
$179$	12.4958	0.933984	0.466992	+	0.884262i	$0.345338\pi$
$180$	0.0730951	0.00544819
$181$	−23.9904	−1.78320	−0.891598	−	0.452828i	$-0.850415\pi$
$181$	−23.9904	−1.78320	−0.891598	+	0.452828i	$0.850415\pi$
$182$	−33.0085	−2.44675
$183$	−0.863702	−0.0638467
$184$	74.4322	5.48721
$185$	0.0315662	0.00232079
$186$	7.60011	0.557267
$187$	−0.794328	−0.0580870
$188$	−48.5191	−3.53862
$189$	2.53463	0.184367
$190$	−0.0236711	−0.00171728
$191$	9.49345	0.686922	0.343461	−	0.939167i	$-0.388401\pi$
$191$	9.49345	0.686922	0.343461	+	0.939167i	$0.388401\pi$
$192$	−25.4750	−1.83850
$193$	7.61539	0.548167	0.274084	−	0.961706i	$-0.411625\pi$
$193$	7.61539	0.548167	0.274084	+	0.961706i	$0.411625\pi$
$194$	−41.6712	−2.99182
$195$	0.0655298	0.00469269
$196$	−3.08324	−0.220231
$197$	17.2647	1.23006	0.615030	−	0.788504i	$-0.289144\pi$
$197$	17.2647	1.23006	0.615030	+	0.788504i	$0.289144\pi$
$198$	−7.89428	−0.561022
$199$	−6.94789	−0.492523	−0.246262	−	0.969203i	$-0.579202\pi$
$199$	−6.94789	−0.492523	−0.246262	+	0.969203i	$0.579202\pi$
$200$	45.5089	3.21796
$201$	−2.90374	−0.204814
$202$	−10.5354	−0.741267
$203$	4.59084	0.322214
$204$	1.46167	0.102337
$205$	−0.0769667	−0.00537558
$206$	25.6911	1.78999
$207$	−8.17747	−0.568373
$208$	−67.1016	−4.65266
$209$	1.86141	0.128756
$210$	−0.0938174	−0.00647401
$211$	−6.93367	−0.477333	−0.238667	−	0.971102i	$-0.576710\pi$
$211$	−6.93367	−0.477333	−0.238667	+	0.971102i	$0.576710\pi$
$212$	35.2380	2.42016
$213$	6.08675	0.417057
$214$	−15.0795	−1.03082
$215$	0.118758	0.00809924
$216$	9.10211	0.619320
$217$	−7.10254	−0.482152
$218$	−33.6581	−2.27961
$219$	11.9556	0.807884
$220$	0.212755	0.0143440
$221$	1.31038	0.0881460
$222$	6.27328	0.421035
$223$	−23.7367	−1.58953	−0.794764	−	0.606918i	$-0.792405\pi$
$223$	−23.7367	−1.58953	−0.794764	+	0.606918i	$0.792405\pi$
$224$	49.9268	3.33587
$225$	−4.99981	−0.333321
$226$	−13.4325	−0.893518
$227$	6.47633	0.429849	0.214925	−	0.976631i	$-0.431049\pi$
$227$	6.47633	0.429849	0.214925	+	0.976631i	$0.431049\pi$
$228$	−3.42523	−0.226842
$229$	18.1850	1.20170	0.600851	−	0.799361i	$-0.294829\pi$
$229$	18.1850	1.20170	0.600851	+	0.799361i	$0.294829\pi$
$230$	0.302683	0.0199583
$231$	7.37744	0.485400
$232$	16.4862	1.08237
$233$	−8.61991	−0.564709	−0.282355	−	0.959310i	$-0.591115\pi$
$233$	−8.61991	−0.564709	−0.282355	+	0.959310i	$0.591115\pi$
$234$	13.0230	0.851340
$235$	−0.123629	−0.00806468
$236$	−54.7081	−3.56119
$237$	−7.43924	−0.483230
$238$	−1.87605	−0.121606
$239$	−3.36164	−0.217446	−0.108723	−	0.994072i	$-0.534676\pi$
$239$	−3.36164	−0.217446	−0.108723	+	0.994072i	$0.534676\pi$
$240$	−0.190718	−0.0123108
$241$	−24.1482	−1.55552	−0.777762	−	0.628559i	$-0.783645\pi$
$241$	−24.1482	−1.55552	−0.777762	+	0.628559i	$0.783645\pi$
$242$	6.85656	0.440756
$243$	−1.00000	−0.0641500
$244$	4.62598	0.296148
$245$	−0.00785625	−0.000501917 0
$246$	−15.2959	−0.975231
$247$	−3.07072	−0.195385
$248$	−25.5059	−1.61963
$249$	11.6630	0.739112
$250$	0.370136	0.0234094
$251$	−29.1940	−1.84271	−0.921356	−	0.388720i	$-0.872917\pi$
$251$	−29.1940	−1.84271	−0.921356	+	0.388720i	$0.872917\pi$
$252$	−13.5755	−0.855173
$253$	−23.8018	−1.49641
$254$	−12.0629	−0.756893
$255$	0.00372440	0.000233231 0
$256$	29.5953	1.84971
$257$	−0.700085	−0.0436701	−0.0218350	−	0.999762i	$-0.506951\pi$
$257$	−0.700085	−0.0436701	−0.0218350	+	0.999762i	$0.506951\pi$
$258$	23.6013	1.46935
$259$	−5.86257	−0.364282
$260$	−0.350977	−0.0217667
$261$	−1.81125	−0.112113
$262$	8.47853	0.523805
$263$	12.2718	0.756712	0.378356	−	0.925660i	$-0.376490\pi$
$263$	12.2718	0.756712	0.378356	+	0.925660i	$0.376490\pi$
$264$	26.4932	1.63054
$265$	0.0897883	0.00551565
$266$	4.39628	0.269553
$267$	13.7917	0.844037
$268$	15.5524	0.950016
$269$	−20.9886	−1.27970	−0.639849	−	0.768500i	$-0.721003\pi$
$269$	−20.9886	−1.27970	−0.639849	+	0.768500i	$0.721003\pi$
$270$	0.0370143	0.00225262
$271$	30.5880	1.85809	0.929045	−	0.369967i	$-0.120631\pi$
$271$	30.5880	1.85809	0.929045	+	0.369967i	$0.120631\pi$
$272$	−3.81374	−0.231242
$273$	−12.1704	−0.736586
$274$	20.0331	1.21025
$275$	−14.5528	−0.877565
$276$	43.7985	2.63636
$277$	−0.354747	−0.0213147	−0.0106573	−	0.999943i	$-0.503392\pi$
$277$	−0.354747	−0.0213147	−0.0106573	+	0.999943i	$0.503392\pi$
$278$	−10.4728	−0.628118
$279$	2.80220	0.167763
$280$	0.314851	0.0188159
$281$	−14.4237	−0.860447	−0.430224	−	0.902722i	$-0.641565\pi$
$281$	−14.4237	−0.860447	−0.430224	+	0.902722i	$0.641565\pi$
$282$	−24.5693	−1.46308
$283$	8.11742	0.482530	0.241265	−	0.970459i	$-0.422438\pi$
$283$	8.11742	0.482530	0.241265	+	0.970459i	$0.422438\pi$
$284$	−32.6006	−1.93449
$285$	−0.00872767	−0.000516983 0
$286$	37.9056	2.24140
$287$	14.2945	0.843777
$288$	−19.6979	−1.16071
$289$	−16.9255	−0.995619
$290$	0.0670420	0.00393684
$291$	−15.3644	−0.900676
$292$	−64.0341	−3.74731
$293$	3.95271	0.230920	0.115460	−	0.993312i	$-0.463166\pi$
$293$	3.95271	0.230920	0.115460	+	0.993312i	$0.463166\pi$
$294$	−1.56130	−0.0910571
$295$	−0.139399	−0.00811613
$296$	−21.0531	−1.22369
$297$	−2.91066	−0.168894
$298$	−36.2965	−2.10260
$299$	39.2653	2.27077
$300$	26.7790	1.54609
$301$	−22.0561	−1.27129
$302$	−9.61269	−0.553148
$303$	−3.88445	−0.223156
$304$	8.93701	0.512573
$305$	0.0117872	0.000674935 0
$306$	0.740166	0.0423125
$307$	17.6968	1.01001	0.505004	−	0.863117i	$-0.331491\pi$
$307$	17.6968	1.01001	0.505004	+	0.863117i	$0.331491\pi$
$308$	−39.5136	−2.25149
$309$	9.47246	0.538869
$310$	−0.103721	−0.00589098
$311$	−18.6461	−1.05733	−0.528663	−	0.848832i	$-0.677306\pi$
$311$	−18.6461	−1.05733	−0.528663	+	0.848832i	$0.677306\pi$
$312$	−43.7051	−2.47432
$313$	−5.34429	−0.302077	−0.151038	−	0.988528i	$-0.548262\pi$
$313$	−5.34429	−0.302077	−0.151038	+	0.988528i	$0.548262\pi$
$314$	−62.1609	−3.50794
$315$	−0.0345910	−0.00194898
$316$	39.8445	2.24143
$317$	−7.93872	−0.445883	−0.222941	−	0.974832i	$-0.571566\pi$
$317$	−7.93872	−0.445883	−0.222941	+	0.974832i	$0.571566\pi$
$318$	17.8440	1.00064
$319$	−5.27193	−0.295172
$320$	0.347667	0.0194352
$321$	−5.55990	−0.310324
$322$	−56.2152	−3.13275
$323$	−0.174525	−0.00971085
$324$	5.35600	0.297555
$325$	24.0074	1.33169
$326$	23.4241	1.29734
$327$	−12.4099	−0.686269
$328$	51.3330	2.83439
$329$	22.9608	1.26587
$330$	0.107736	0.00593067
$331$	26.6923	1.46714	0.733570	−	0.679614i	$-0.237853\pi$
$331$	26.6923	1.46714	0.733570	+	0.679614i	$0.237853\pi$
$332$	−62.4669	−3.42832
$333$	2.31299	0.126751
$334$	43.7772	2.39538
$335$	0.0396284	0.00216513
$336$	35.4207	1.93236
$337$	−26.0685	−1.42004	−0.710020	−	0.704182i	$-0.751314\pi$
$337$	−26.0685	−1.42004	−0.710020	+	0.704182i	$0.751314\pi$
$338$	−27.2734	−1.48348
$339$	−4.95264	−0.268991
$340$	−0.0199479	−0.00108183
$341$	8.15626	0.441686
$342$	−1.73449	−0.0937902
$343$	19.2015	1.03678
$344$	−79.2059	−4.27049
$345$	0.111601	0.00600838
$346$	7.63550	0.410487
$347$	3.27222	0.175662	0.0878311	−	0.996135i	$-0.472006\pi$
$347$	3.27222	0.175662	0.0878311	+	0.996135i	$0.472006\pi$
$348$	9.70104	0.520030
$349$	−26.3592	−1.41098	−0.705488	−	0.708722i	$-0.749272\pi$
$349$	−26.3592	−1.41098	−0.705488	+	0.708722i	$0.749272\pi$
$350$	−34.3707	−1.83719
$351$	4.80165	0.256293
$352$	−57.3338	−3.05590
$353$	−14.1477	−0.753005	−0.376502	−	0.926416i	$-0.622873\pi$
$353$	−14.1477	−0.753005	−0.376502	+	0.926416i	$0.622873\pi$
$354$	−27.7033	−1.47242
$355$	−0.0830680	−0.00440879
$356$	−73.8681	−3.91500
$357$	−0.691708	−0.0366090
$358$	−33.8912	−1.79120
$359$	4.76758	0.251623	0.125812	−	0.992054i	$-0.459847\pi$
$359$	4.76758	0.251623	0.125812	+	0.992054i	$0.459847\pi$
$360$	−0.124220	−0.00654695
$361$	−18.5910	−0.978475
$362$	65.0667	3.41983
$363$	2.52805	0.132688
$364$	65.1846	3.41660
$365$	−0.163162	−0.00854030
$366$	2.34253	0.122446
$367$	−10.3679	−0.541198	−0.270599	−	0.962692i	$-0.587222\pi$
$367$	−10.3679	−0.541198	−0.270599	+	0.962692i	$0.587222\pi$
$368$	−114.278	−5.95713
$369$	−5.63968	−0.293590
$370$	−0.0856136	−0.00445084
$371$	−16.6758	−0.865762
$372$	−15.0086	−0.778159
$373$	2.55146	0.132110	0.0660549	−	0.997816i	$-0.478959\pi$
$373$	2.55146	0.132110	0.0660549	+	0.997816i	$0.478959\pi$
$374$	2.15437	0.111400
$375$	0.136471	0.00704733
$376$	82.4546	4.25227
$377$	8.69698	0.447917
$378$	−6.87440	−0.353581
$379$	17.7113	0.909766	0.454883	−	0.890551i	$-0.349681\pi$
$379$	17.7113	0.909766	0.454883	+	0.890551i	$0.349681\pi$
$380$	0.0467454	0.00239799
$381$	−4.44765	−0.227860
$382$	−25.7481	−1.31739
$383$	15.2385	0.778650	0.389325	−	0.921101i	$-0.372708\pi$
$383$	15.2385	0.778650	0.389325	+	0.921101i	$0.372708\pi$
$384$	29.6975	1.51549
$385$	−0.100683	−0.00513126
$386$	−20.6544	−1.05128
$387$	8.70192	0.442344
$388$	82.2916	4.17772
$389$	18.5539	0.940720	0.470360	−	0.882475i	$-0.344124\pi$
$389$	18.5539	0.940720	0.470360	+	0.882475i	$0.344124\pi$
$390$	−0.177729	−0.00899968
$391$	2.23165	0.112860
$392$	5.23973	0.264646
$393$	3.12608	0.157690
$394$	−46.8252	−2.35902
$395$	0.101526	0.00510832
$396$	15.5895	0.783401
$397$	13.7344	0.689310	0.344655	−	0.938730i	$-0.387996\pi$
$397$	13.7344	0.689310	0.344655	+	0.938730i	$0.387996\pi$
$398$	18.8440	0.944566
$399$	1.62093	0.0811480
$400$	−69.8709	−3.49354
$401$	19.2409	0.960843	0.480422	−	0.877038i	$-0.340484\pi$
$401$	19.2409	0.960843	0.480422	+	0.877038i	$0.340484\pi$
$402$	7.87551	0.392795
$403$	−13.4552	−0.670251
$404$	20.8051	1.03509
$405$	0.0136473	0.000678142 0
$406$	−12.4513	−0.617945
$407$	6.73233	0.333709
$408$	−2.48399	−0.122976
$409$	−6.48713	−0.320768	−0.160384	−	0.987055i	$-0.551273\pi$
$409$	−6.48713	−0.320768	−0.160384	+	0.987055i	$0.551273\pi$
$410$	0.208748	0.0103094
$411$	7.38632	0.364341
$412$	−50.7344	−2.49951
$413$	25.8896	1.27395
$414$	22.1789	1.09003
$415$	−0.159169	−0.00781330
$416$	94.5822	4.63728
$417$	−3.86139	−0.189093
$418$	−5.04850	−0.246930
$419$	−12.5390	−0.612573	−0.306286	−	0.951939i	$-0.599086\pi$
$419$	−12.5390	−0.612573	−0.306286	+	0.951939i	$0.599086\pi$
$420$	0.185269	0.00904020
$421$	28.7377	1.40059	0.700294	−	0.713855i	$-0.253052\pi$
$421$	28.7377	1.40059	0.700294	+	0.713855i	$0.253052\pi$
$422$	18.8054	0.915435
$423$	−9.05885	−0.440456
$424$	−59.8844	−2.90824
$425$	1.36446	0.0661862
$426$	−16.5084	−0.799837
$427$	−2.18916	−0.105941
$428$	29.7788	1.43941
$429$	13.9760	0.674767
$430$	−0.322095	−0.0155328
$431$	17.5097	0.843412	0.421706	−	0.906733i	$-0.361432\pi$
$431$	17.5097	0.843412	0.421706	+	0.906733i	$0.361432\pi$
$432$	−13.9747	−0.672358
$433$	−2.98006	−0.143212	−0.0716062	−	0.997433i	$-0.522812\pi$
$433$	−2.98006	−0.143212	−0.0716062	+	0.997433i	$0.522812\pi$
$434$	19.2635	0.924676
$435$	0.0247187	0.00118517
$436$	66.4674	3.18321
$437$	−5.22960	−0.250166
$438$	−32.4259	−1.54937
$439$	10.3115	0.492140	0.246070	−	0.969252i	$-0.420861\pi$
$439$	10.3115	0.492140	0.246070	+	0.969252i	$0.420861\pi$
$440$	−0.361561	−0.0172368
$441$	−0.575661	−0.0274124
$442$	−3.55402	−0.169047
$443$	22.8538	1.08582	0.542909	−	0.839792i	$-0.317323\pi$
$443$	22.8538	1.08582	0.542909	+	0.839792i	$0.317323\pi$
$444$	−12.3884	−0.587926
$445$	−0.188220	−0.00892247
$446$	64.3786	3.04841
$447$	−13.3827	−0.632980
$448$	−64.5697	−3.05063
$449$	−33.0462	−1.55955	−0.779773	−	0.626063i	$-0.784665\pi$
$449$	−33.0462	−1.55955	−0.779773	+	0.626063i	$0.784665\pi$
$450$	13.5605	0.639246
$451$	−16.4152	−0.772961
$452$	26.5263	1.24769
$453$	−3.54425	−0.166523
$454$	−17.5651	−0.824369
$455$	0.166094	0.00778659
$456$	5.82093	0.272590
$457$	13.7780	0.644507	0.322253	−	0.946653i	$-0.395560\pi$
$457$	13.7780	0.644507	0.322253	+	0.946653i	$0.395560\pi$
$458$	−49.3214	−2.30464
$459$	0.272903	0.0127380
$460$	−0.597733	−0.0278694
$461$	33.1480	1.54386	0.771928	−	0.635710i	$-0.219293\pi$
$461$	33.1480	1.54386	0.771928	+	0.635710i	$0.219293\pi$
$462$	−20.0091	−0.930906
$463$	−8.51632	−0.395787	−0.197893	−	0.980224i	$-0.563410\pi$
$463$	−8.51632	−0.395787	−0.197893	+	0.980224i	$0.563410\pi$
$464$	−25.3117	−1.17506
$465$	−0.0382426	−0.00177346
$466$	23.3789	1.08301
$467$	19.5897	0.906504	0.453252	−	0.891382i	$-0.350264\pi$
$467$	19.5897	0.906504	0.453252	+	0.891382i	$0.350264\pi$
$468$	−25.7176	−1.18880
$469$	−7.35991	−0.339849
$470$	0.335306	0.0154665
$471$	−22.9191	−1.05605
$472$	92.9723	4.27940
$473$	25.3284	1.16460
$474$	20.1767	0.926744
$475$	−3.19745	−0.146709
$476$	3.70478	0.169808
$477$	6.57917	0.301240
$478$	9.11742	0.417021
$479$	11.7284	0.535882	0.267941	−	0.963435i	$-0.413657\pi$
$479$	11.7284	0.535882	0.267941	+	0.963435i	$0.413657\pi$
$480$	0.268824	0.0122701
$481$	−11.1062	−0.506398
$482$	65.4947	2.98320
$483$	−20.7268	−0.943104
$484$	−13.5402	−0.615465
$485$	0.209683	0.00952122
$486$	2.71219	0.123028
$487$	−5.45728	−0.247293	−0.123647	−	0.992326i	$-0.539459\pi$
$487$	−5.45728	−0.247293	−0.123647	+	0.992326i	$0.539459\pi$
$488$	−7.86151	−0.355874
$489$	8.63657	0.390559
$490$	0.0213077	0.000962582 0
$491$	−14.7649	−0.666328	−0.333164	−	0.942869i	$-0.608116\pi$
$491$	−14.7649	−0.666328	−0.333164	+	0.942869i	$0.608116\pi$
$492$	30.2061	1.36180
$493$	0.494295	0.0222619
$494$	8.32839	0.374712
$495$	0.0397228	0.00178541
$496$	39.1599	1.75833
$497$	15.4276	0.692025
$498$	−31.6323	−1.41748
$499$	−38.9638	−1.74426	−0.872130	−	0.489275i	$-0.837261\pi$
$499$	−38.9638	−1.74426	−0.872130	+	0.489275i	$0.837261\pi$
$500$	−0.730938	−0.0326885
$501$	16.1409	0.721121
$502$	79.1799	3.53397
$503$	−24.7795	−1.10486	−0.552432	−	0.833558i	$-0.686300\pi$
$503$	−24.7795	−1.10486	−0.552432	+	0.833558i	$0.686300\pi$
$504$	23.0705	1.02764
$505$	0.0530124	0.00235902
$506$	64.5552	2.86983
$507$	−10.0558	−0.446596
$508$	23.8216	1.05691
$509$	−14.6920	−0.651209	−0.325605	−	0.945506i	$-0.605568\pi$
$509$	−14.6920	−0.651209	−0.325605	+	0.945506i	$0.605568\pi$
$510$	−0.0101013	−0.000447293 0
$511$	30.3030	1.34053
$512$	−20.8732	−0.922475
$513$	−0.639514	−0.0282352
$514$	1.89877	0.0837510
$515$	−0.129274	−0.00569649
$516$	−46.6075	−2.05178
$517$	−26.3672	−1.15963
$518$	15.9004	0.698625
$519$	2.81525	0.123576
$520$	0.596459	0.0261565
$521$	41.7569	1.82940	0.914702	−	0.404130i	$-0.132426\pi$
$521$	41.7569	1.82940	0.914702	+	0.404130i	$0.132426\pi$
$522$	4.91246	0.215012
$523$	26.4093	1.15480	0.577398	−	0.816463i	$-0.304068\pi$
$523$	26.4093	1.15480	0.577398	+	0.816463i	$0.304068\pi$
$524$	−16.7433	−0.731433
$525$	−12.6727	−0.553081
$526$	−33.2835	−1.45123
$527$	−0.764729	−0.0333121
$528$	−40.6756	−1.77018
$529$	43.8709	1.90743
$530$	−0.243523	−0.0105780
$531$	−10.2144	−0.443266
$532$	−8.68169	−0.376399
$533$	27.0798	1.17295
$534$	−37.4057	−1.61870
$535$	0.0758780	0.00328049
$536$	−26.4302	−1.14161
$537$	−12.4958	−0.539236
$538$	56.9252	2.45422
$539$	−1.67555	−0.0721712
$540$	−0.0730951	−0.00314551
$541$	−25.9345	−1.11501	−0.557506	−	0.830173i	$-0.688242\pi$
$541$	−25.9345	−1.11501	−0.557506	+	0.830173i	$0.688242\pi$
$542$	−82.9606	−3.56346
$543$	23.9904	1.02953
$544$	5.37561	0.230477
$545$	0.169362	0.00725468
$546$	33.0085	1.41263
$547$	28.7413	1.22889	0.614444	−	0.788960i	$-0.289380\pi$
$547$	28.7413	1.22889	0.614444	+	0.788960i	$0.289380\pi$
$548$	−39.5611	−1.68997
$549$	0.863702	0.0368619
$550$	39.4699	1.68300
$551$	−1.15832	−0.0493460
$552$	−74.4322	−3.16804
$553$	−18.8557	−0.801826
$554$	0.962143	0.0408775
$555$	−0.0315662	−0.00133991
$556$	20.6816	0.877094
$557$	−26.0693	−1.10459	−0.552296	−	0.833648i	$-0.686248\pi$
$557$	−26.0693	−1.10459	−0.552296	+	0.833648i	$0.686248\pi$
$558$	−7.60011	−0.321738
$559$	−41.7836	−1.76726
$560$	−0.483398	−0.0204273
$561$	0.794328	0.0335366
$562$	39.1199	1.65017
$563$	35.2785	1.48681	0.743406	−	0.668840i	$-0.233209\pi$
$563$	35.2785	1.48681	0.743406	+	0.668840i	$0.233209\pi$
$564$	48.5191	2.04302
$565$	0.0675904	0.00284355
$566$	−22.0160	−0.925402
$567$	−2.53463	−0.106444
$568$	55.4023	2.32463
$569$	33.1708	1.39059	0.695296	−	0.718724i	$-0.255273\pi$
$569$	33.1708	1.39059	0.695296	+	0.718724i	$0.255273\pi$
$570$	0.0236711	0.000991475 0
$571$	8.73921	0.365725	0.182862	−	0.983139i	$-0.441464\pi$
$571$	8.73921	0.365725	0.182862	+	0.983139i	$0.441464\pi$
$572$	−74.8553	−3.12986
$573$	−9.49345	−0.396594
$574$	−38.7694	−1.61820
$575$	40.8858	1.70506
$576$	25.4750	1.06146
$577$	−38.0852	−1.58551	−0.792753	−	0.609543i	$-0.791353\pi$
$577$	−38.0852	−1.58551	−0.792753	+	0.609543i	$0.791353\pi$
$578$	45.9053	1.90941
$579$	−7.61539	−0.316485
$580$	−0.132393	−0.00549734
$581$	29.5613	1.22641
$582$	41.6712	1.72733
$583$	19.1497	0.793101
$584$	108.821	4.50305
$585$	−0.0655298	−0.00270932
$586$	−10.7205	−0.442861
$587$	7.54723	0.311508	0.155754	−	0.987796i	$-0.450219\pi$
$587$	7.54723	0.311508	0.155754	+	0.987796i	$0.450219\pi$
$588$	3.08324	0.127151
$589$	1.79205	0.0738400
$590$	0.378077	0.0155652
$591$	−17.2647	−0.710175
$592$	32.3233	1.32848
$593$	−15.8574	−0.651187	−0.325593	−	0.945510i	$-0.605564\pi$
$593$	−15.8574	−0.651187	−0.325593	+	0.945510i	$0.605564\pi$
$594$	7.89428	0.323906
$595$	0.00943997	0.000387001 0
$596$	71.6777	2.93603
$597$	6.94789	0.284358
$598$	−106.495	−4.35491
$599$	14.9951	0.612684	0.306342	−	0.951922i	$-0.400895\pi$
$599$	14.9951	0.612684	0.306342	+	0.951922i	$0.400895\pi$
$600$	−45.5089	−1.85789
$601$	39.0747	1.59389	0.796946	−	0.604051i	$-0.206448\pi$
$601$	39.0747	1.59389	0.796946	+	0.604051i	$0.206448\pi$
$602$	59.8205	2.43810
$603$	2.90374	0.118250
$604$	18.9830	0.772406
$605$	−0.0345012	−0.00140267
$606$	10.5354	0.427971
$607$	2.11502	0.0858458	0.0429229	−	0.999078i	$-0.486333\pi$
$607$	2.11502	0.0858458	0.0429229	+	0.999078i	$0.486333\pi$
$608$	−12.5971	−0.510878
$609$	−4.59084	−0.186030
$610$	−0.0319693	−0.00129440
$611$	43.4974	1.75972
$612$	−1.46167	−0.0590844
$613$	−22.3675	−0.903414	−0.451707	−	0.892166i	$-0.649185\pi$
$613$	−22.3675	−0.903414	−0.451707	+	0.892166i	$0.649185\pi$
$614$	−47.9970	−1.93700
$615$	0.0769667	0.00310360
$616$	67.1503	2.70556
$617$	−0.221969	−0.00893612	−0.00446806	−	0.999990i	$-0.501422\pi$
$617$	−0.221969	−0.00893612	−0.00446806	+	0.999990i	$0.501422\pi$
$618$	−25.6911	−1.03345
$619$	13.0613	0.524977	0.262489	−	0.964935i	$-0.415457\pi$
$619$	13.0613	0.524977	0.262489	+	0.964935i	$0.415457\pi$
$620$	0.204827	0.00822606
$621$	8.17747	0.328150
$622$	50.5719	2.02775
$623$	34.9568	1.40051
$624$	67.1016	2.68621
$625$	24.9972	0.999888
$626$	14.4947	0.579326
$627$	−1.86141	−0.0743375
$628$	122.754	4.89843
$629$	−0.631222	−0.0251685
$630$	0.0938174	0.00373777
$631$	−34.8024	−1.38546	−0.692730	−	0.721197i	$-0.743592\pi$
$631$	−34.8024	−1.38546	−0.692730	+	0.721197i	$0.743592\pi$
$632$	−67.7127	−2.69347
$633$	6.93367	0.275588
$634$	21.5313	0.855119
$635$	0.0606987	0.00240875
$636$	−35.2380	−1.39728
$637$	2.76412	0.109519
$638$	14.2985	0.566083
$639$	−6.08675	−0.240788
$640$	−0.405292	−0.0160206
$641$	35.2300	1.39150	0.695751	−	0.718283i	$-0.255072\pi$
$641$	35.2300	1.39150	0.695751	+	0.718283i	$0.255072\pi$
$642$	15.0795	0.595142
$643$	22.2872	0.878922	0.439461	−	0.898262i	$-0.355169\pi$
$643$	22.2872	0.878922	0.439461	+	0.898262i	$0.355169\pi$
$644$	111.013	4.37452
$645$	−0.118758	−0.00467610
$646$	0.473346	0.0186236
$647$	−15.5243	−0.610322	−0.305161	−	0.952301i	$-0.598710\pi$
$647$	−15.5243	−0.610322	−0.305161	+	0.952301i	$0.598710\pi$
$648$	−9.10211	−0.357565
$649$	−29.7306	−1.16703
$650$	−65.1126	−2.55393
$651$	7.10254	0.278370
$652$	−46.2574	−1.81158
$653$	10.3456	0.404855	0.202428	−	0.979297i	$-0.435117\pi$
$653$	10.3456	0.404855	0.202428	+	0.979297i	$0.435117\pi$
$654$	33.6581	1.31613
$655$	−0.0426627	−0.00166697
$656$	−78.8128	−3.07712
$657$	−11.9556	−0.466432
$658$	−62.2742	−2.42770
$659$	38.2275	1.48913	0.744565	−	0.667549i	$-0.232657\pi$
$659$	38.2275	1.48913	0.744565	+	0.667549i	$0.232657\pi$
$660$	−0.212755	−0.00828149
$661$	−36.4663	−1.41837	−0.709187	−	0.705020i	$-0.750938\pi$
$661$	−36.4663	−1.41837	−0.709187	+	0.705020i	$0.750938\pi$
$662$	−72.3946	−2.81370
$663$	−1.31038	−0.0508911
$664$	106.158	4.11972
$665$	−0.0221214	−0.000857831 0
$666$	−6.27328	−0.243085
$667$	14.8114	0.573501
$668$	−86.4504	−3.34487
$669$	23.7367	0.917715
$670$	−0.107480	−0.00415231
$671$	2.51394	0.0970497
$672$	−49.9268	−1.92597
$673$	−10.5336	−0.406039	−0.203020	−	0.979175i	$-0.565076\pi$
$673$	−10.5336	−0.406039	−0.203020	+	0.979175i	$0.565076\pi$
$674$	70.7027	2.72337
$675$	4.99981	0.192443
$676$	53.8590	2.07150
$677$	1.74026	0.0668836	0.0334418	−	0.999441i	$-0.489353\pi$
$677$	1.74026	0.0668836	0.0334418	+	0.999441i	$0.489353\pi$
$678$	13.4325	0.515873
$679$	−38.9430	−1.49450
$680$	0.0338999	0.00130000
$681$	−6.47633	−0.248173
$682$	−22.1214	−0.847071
$683$	7.01526	0.268432	0.134216	−	0.990952i	$-0.457148\pi$
$683$	7.01526	0.268432	0.134216	+	0.990952i	$0.457148\pi$
$684$	3.42523	0.130967
$685$	−0.100804	−0.00385151
$686$	−52.0781	−1.98835
$687$	−18.1850	−0.693803
$688$	121.607	4.63621
$689$	−31.5909	−1.20352
$690$	−0.302683	−0.0115229
$691$	25.1924	0.958365	0.479182	−	0.877715i	$-0.340933\pi$
$691$	25.1924	0.958365	0.479182	+	0.877715i	$0.340933\pi$
$692$	−15.0785	−0.573197
$693$	−7.37744	−0.280246
$694$	−8.87491	−0.336887
$695$	0.0526977	0.00199894
$696$	−16.4862	−0.624907
$697$	1.53909	0.0582970
$698$	71.4912	2.70598
$699$	8.61991	0.326035
$700$	67.8748	2.56542
$701$	−25.6058	−0.967118	−0.483559	−	0.875312i	$-0.660656\pi$
$701$	−25.6058	−0.967118	−0.483559	+	0.875312i	$0.660656\pi$
$702$	−13.0230	−0.491522
$703$	1.47919	0.0557887
$704$	74.1492	2.79460
$705$	0.123629	0.00465615
$706$	38.3712	1.44412
$707$	−9.84564	−0.370283
$708$	54.7081	2.05606
$709$	26.5401	0.996736	0.498368	−	0.866966i	$-0.333933\pi$
$709$	26.5401	0.996736	0.498368	+	0.866966i	$0.333933\pi$
$710$	0.225297	0.00845523
$711$	7.43924	0.278993
$712$	125.533	4.70456
$713$	−22.9149	−0.858170
$714$	1.87605	0.0702092
$715$	−0.190735	−0.00713309
$716$	66.9277	2.50121
$717$	3.36164	0.125543
$718$	−12.9306	−0.482566
$719$	21.3361	0.795701	0.397851	−	0.917450i	$-0.369756\pi$
$719$	21.3361	0.795701	0.397851	+	0.917450i	$0.369756\pi$
$720$	0.190718	0.00710762
$721$	24.0092	0.894148
$722$	50.4225	1.87653
$723$	24.1482	0.898082
$724$	−128.493	−4.77540
$725$	9.05591	0.336328
$726$	−6.85656	−0.254471
$727$	42.6743	1.58270	0.791351	−	0.611362i	$-0.209378\pi$
$727$	42.6743	1.58270	0.791351	+	0.611362i	$0.209378\pi$
$728$	−110.776	−4.10564
$729$	1.00000	0.0370370
$730$	0.442527	0.0163787
$731$	−2.37478	−0.0878345
$732$	−4.62598	−0.170981
$733$	14.8291	0.547727	0.273863	−	0.961769i	$-0.411698\pi$
$733$	14.8291	0.547727	0.273863	+	0.961769i	$0.411698\pi$
$734$	28.1197	1.03792
$735$	0.00785625	0.000289782 0
$736$	161.079	5.93744
$737$	8.45181	0.311326
$738$	15.2959	0.563050
$739$	37.5387	1.38088	0.690442	−	0.723388i	$-0.257416\pi$
$739$	37.5387	1.38088	0.690442	+	0.723388i	$0.257416\pi$
$740$	0.169068	0.00621508
$741$	3.07072	0.112806
$742$	45.2279	1.66037
$743$	30.8328	1.13115	0.565573	−	0.824698i	$-0.308655\pi$
$743$	30.8328	1.13115	0.565573	+	0.824698i	$0.308655\pi$
$744$	25.5059	0.935093
$745$	0.182638	0.00669136
$746$	−6.92006	−0.253361
$747$	−11.6630	−0.426727
$748$	−4.25442	−0.155557
$749$	−14.0923	−0.514921
$750$	−0.370136	−0.0135154
$751$	−4.09580	−0.149458	−0.0747288	−	0.997204i	$-0.523809\pi$
$751$	−4.09580	−0.149458	−0.0747288	+	0.997204i	$0.523809\pi$
$752$	−126.595	−4.61643
$753$	29.1940	1.06389
$754$	−23.5879	−0.859021
$755$	0.0483696	0.00176035
$756$	13.5755	0.493735
$757$	40.9236	1.48739	0.743697	−	0.668517i	$-0.233070\pi$
$757$	40.9236	1.48739	0.743697	+	0.668517i	$0.233070\pi$
$758$	−48.0364	−1.74476
$759$	23.8018	0.863952
$760$	−0.0794402	−0.00288160
$761$	−49.7917	−1.80495	−0.902474	−	0.430745i	$-0.858251\pi$
$761$	−49.7917	−1.80495	−0.902474	+	0.430745i	$0.858251\pi$
$762$	12.0629	0.436993
$763$	−31.4545	−1.13873
$764$	50.8469	1.83957
$765$	−0.00372440	−0.000134656 0
$766$	−41.3297	−1.49330
$767$	49.0458	1.77094
$768$	−29.5953	−1.06793
$769$	14.9810	0.540229	0.270115	−	0.962828i	$-0.412938\pi$
$769$	14.9810	0.540229	0.270115	+	0.962828i	$0.412938\pi$
$770$	0.273071	0.00984078
$771$	0.700085	0.0252129
$772$	40.7880	1.46799
$773$	5.65090	0.203249	0.101624	−	0.994823i	$-0.467596\pi$
$773$	5.65090	0.203249	0.101624	+	0.994823i	$0.467596\pi$
$774$	−23.6013	−0.848331
$775$	−14.0105	−0.503272
$776$	−139.848	−5.02026
$777$	5.86257	0.210319
$778$	−50.3217	−1.80412
$779$	−3.60665	−0.129222
$780$	0.350977	0.0125670
$781$	−17.7165	−0.633945
$782$	−6.05268	−0.216443
$783$	1.81125	0.0647288
$784$	−8.04469	−0.287310
$785$	0.312784	0.0111638
$786$	−8.47853	−0.302419
$787$	19.6540	0.700588	0.350294	−	0.936640i	$-0.386082\pi$
$787$	19.6540	0.700588	0.350294	+	0.936640i	$0.386082\pi$
$788$	92.4697	3.29410
$789$	−12.2718	−0.436888
$790$	−0.275358	−0.00979679
$791$	−12.5531	−0.446337
$792$	−26.4932	−0.941394
$793$	−4.14719	−0.147271
$794$	−37.2503	−1.32197
$795$	−0.0897883	−0.00318446
$796$	−37.2129	−1.31898
$797$	16.1717	0.572831	0.286415	−	0.958106i	$-0.407536\pi$
$797$	16.1717	0.572831	0.286415	+	0.958106i	$0.407536\pi$
$798$	−4.39628	−0.155626
$799$	2.47219	0.0874597
$800$	98.4857	3.48199
$801$	−13.7917	−0.487305
$802$	−52.1850	−1.84272
$803$	−34.7987	−1.22802
$804$	−15.5524	−0.548492
$805$	0.282866	0.00996973
$806$	36.4931	1.28541
$807$	20.9886	0.738834
$808$	−35.3567	−1.24384
$809$	27.4567	0.965325	0.482662	−	0.875807i	$-0.339670\pi$
$809$	27.4567	0.965325	0.482662	+	0.875807i	$0.339670\pi$
$810$	−0.0370143	−0.00130055
$811$	−1.91968	−0.0674092	−0.0337046	−	0.999432i	$-0.510731\pi$
$811$	−1.91968	−0.0674092	−0.0337046	+	0.999432i	$0.510731\pi$
$812$	24.5885	0.862888
$813$	−30.5880	−1.07277
$814$	−18.2594	−0.639991
$815$	−0.117866	−0.00412868
$816$	3.81374	0.133507
$817$	5.56500	0.194695
$818$	17.5943	0.615172
$819$	12.1704	0.425268
$820$	−0.412233	−0.0143958
$821$	13.2147	0.461195	0.230597	−	0.973049i	$-0.425932\pi$
$821$	13.2147	0.461195	0.230597	+	0.973049i	$0.425932\pi$
$822$	−20.0331	−0.698736
$823$	46.3716	1.61641	0.808207	−	0.588899i	$-0.200438\pi$
$823$	46.3716	1.61641	0.808207	+	0.588899i	$0.200438\pi$
$824$	86.2194	3.00359
$825$	14.5528	0.506662
$826$	−70.2177	−2.44319
$827$	−31.1778	−1.08416	−0.542079	−	0.840328i	$-0.682362\pi$
$827$	−31.1778	−1.08416	−0.542079	+	0.840328i	$0.682362\pi$
$828$	−43.7985	−1.52210
$829$	7.18364	0.249498	0.124749	−	0.992188i	$-0.460187\pi$
$829$	7.18364	0.249498	0.124749	+	0.992188i	$0.460187\pi$
$830$	0.431697	0.0149844
$831$	0.354747	0.0123060
$832$	−122.322	−4.24076
$833$	0.157100	0.00544318
$834$	10.4728	0.362644
$835$	−0.220280	−0.00762310
$836$	9.96970	0.344809
$837$	−2.80220	−0.0968583
$838$	34.0083	1.17480
$839$	36.2326	1.25089	0.625443	−	0.780269i	$-0.284918\pi$
$839$	36.2326	1.25089	0.625443	+	0.780269i	$0.284918\pi$
$840$	−0.314851	−0.0108634
$841$	−25.7194	−0.886875
$842$	−77.9421	−2.68606
$843$	14.4237	0.496779
$844$	−37.1367	−1.27830
$845$	0.137236	0.00472105
$846$	24.5693	0.844712
$847$	6.40766	0.220170
$848$	91.9419	3.15730
$849$	−8.11742	−0.278589
$850$	−3.70069	−0.126933
$851$	−18.9144	−0.648377
$852$	32.6006	1.11688
$853$	43.2990	1.48253	0.741265	−	0.671213i	$-0.234226\pi$
$853$	43.2990	1.48253	0.741265	+	0.671213i	$0.234226\pi$
$854$	5.93743	0.203175
$855$	0.00872767	0.000298480 0
$856$	−50.6069	−1.72971
$857$	5.32626	0.181942	0.0909708	−	0.995854i	$-0.471003\pi$
$857$	5.32626	0.181942	0.0909708	+	0.995854i	$0.471003\pi$
$858$	−37.9056	−1.29407
$859$	−30.0169	−1.02416	−0.512082	−	0.858936i	$-0.671126\pi$
$859$	−30.0169	−1.02416	−0.512082	+	0.858936i	$0.671126\pi$
$860$	0.636068	0.0216897
$861$	−14.2945	−0.487155
$862$	−47.4896	−1.61750
$863$	36.6007	1.24590	0.622951	−	0.782260i	$-0.285933\pi$
$863$	36.6007	1.24590	0.622951	+	0.782260i	$0.285933\pi$
$864$	19.6979	0.670135
$865$	−0.0384207	−0.00130634
$866$	8.08249	0.274654
$867$	16.9255	0.574821
$868$	−38.0412	−1.29120
$869$	21.6531	0.734531
$870$	−0.0670420	−0.00227294
$871$	−13.9428	−0.472432
$872$	−112.956	−3.82518
$873$	15.3644	0.520006
$874$	14.1837	0.479771
$875$	0.345903	0.0116937
$876$	64.0341	2.16351
$877$	6.44729	0.217709	0.108855	−	0.994058i	$-0.465282\pi$
$877$	6.44729	0.217709	0.108855	+	0.994058i	$0.465282\pi$
$878$	−27.9667	−0.943831
$879$	−3.95271	−0.133322
$880$	0.555114	0.0187129
$881$	−19.3414	−0.651629	−0.325814	−	0.945434i	$-0.605638\pi$
$881$	−19.3414	−0.651629	−0.325814	+	0.945434i	$0.605638\pi$
$882$	1.56130	0.0525718
$883$	−11.6132	−0.390816	−0.195408	−	0.980722i	$-0.562603\pi$
$883$	−11.6132	−0.390816	−0.195408	+	0.980722i	$0.562603\pi$
$884$	7.01841	0.236055
$885$	0.139399	0.00468585
$886$	−61.9839	−2.08239
$887$	37.0347	1.24350	0.621752	−	0.783214i	$-0.286421\pi$
$887$	37.0347	1.24350	0.621752	+	0.783214i	$0.286421\pi$
$888$	21.0531	0.706496
$889$	−11.2731	−0.378089
$890$	0.510488	0.0171116
$891$	2.91066	0.0975108
$892$	−127.134	−4.25675
$893$	−5.79326	−0.193864
$894$	36.2965	1.21394
$895$	0.170535	0.00570036
$896$	75.2721	2.51466
$897$	−39.2653	−1.31103
$898$	89.6276	2.99091
$899$	−5.07548	−0.169277
$900$	−26.7790	−0.892633
$901$	−1.79548	−0.0598160
$902$	44.5212	1.48239
$903$	22.0561	0.733982
$904$	−45.0795	−1.49932
$905$	−0.327406	−0.0108833
$906$	9.61269	0.319360
$907$	−34.5716	−1.14793	−0.573966	−	0.818879i	$-0.694596\pi$
$907$	−34.5716	−1.14793	−0.573966	+	0.818879i	$0.694596\pi$
$908$	34.6872	1.15113
$909$	3.88445	0.128839
$910$	−0.450478	−0.0149332
$911$	−43.5857	−1.44406	−0.722030	−	0.691862i	$-0.756791\pi$
$911$	−43.5857	−1.44406	−0.722030	+	0.691862i	$0.756791\pi$
$912$	−8.93701	−0.295934
$913$	−33.9470	−1.12348
$914$	−37.3685	−1.23604
$915$	−0.0117872	−0.000389674 0
$916$	97.3990	3.21815
$917$	7.92344	0.261655
$918$	−0.740166	−0.0244291
$919$	8.53590	0.281573	0.140787	−	0.990040i	$-0.455037\pi$
$919$	8.53590	0.281573	0.140787	+	0.990040i	$0.455037\pi$
$920$	1.01580	0.0334900
$921$	−17.6968	−0.583128
$922$	−89.9037	−2.96082
$923$	29.2264	0.962000
$924$	39.5136	1.29990
$925$	−11.5645	−0.380239
$926$	23.0979	0.759044
$927$	−9.47246	−0.311116
$928$	35.6777	1.17118
$929$	−18.8456	−0.618303	−0.309151	−	0.951013i	$-0.600045\pi$
$929$	−18.8456	−0.618303	−0.309151	+	0.951013i	$0.600045\pi$
$930$	0.103721	0.00340116
$931$	−0.368143	−0.0120654
$932$	−46.1682	−1.51229
$933$	18.6461	0.610447
$934$	−53.1311	−1.73850
$935$	−0.0108405	−0.000354521 0
$936$	43.7051	1.42855
$937$	−39.4358	−1.28831	−0.644155	−	0.764895i	$-0.722791\pi$
$937$	−39.4358	−1.28831	−0.644155	+	0.764895i	$0.722791\pi$
$938$	19.9615	0.651766
$939$	5.34429	0.174404
$940$	−0.662158	−0.0215972
$941$	−16.5150	−0.538372	−0.269186	−	0.963088i	$-0.586755\pi$
$941$	−16.5150	−0.538372	−0.269186	+	0.963088i	$0.586755\pi$
$942$	62.1609	2.02531
$943$	46.1183	1.50182
$944$	−142.743	−4.64588
$945$	0.0345910	0.00112524
$946$	−68.6954	−2.23348
$947$	31.0225	1.00809	0.504047	−	0.863676i	$-0.331844\pi$
$947$	31.0225	1.00809	0.504047	+	0.863676i	$0.331844\pi$
$948$	−39.8445	−1.29409
$949$	57.4066	1.86350
$950$	8.67211	0.281360
$951$	7.93872	0.257431
$952$	−6.29600	−0.204054
$953$	−12.2500	−0.396818	−0.198409	−	0.980119i	$-0.563577\pi$
$953$	−12.2500	−0.396818	−0.198409	+	0.980119i	$0.563577\pi$
$954$	−17.8440	−0.577721
$955$	0.129560	0.00419248
$956$	−18.0049	−0.582321
$957$	5.27193	0.170417
$958$	−31.8096	−1.02772
$959$	18.7216	0.604552
$960$	−0.347667	−0.0112209
$961$	−23.1477	−0.746699
$962$	30.1221	0.971175
$963$	5.55990	0.179165
$964$	−129.338	−4.16569
$965$	0.103930	0.00334562
$966$	56.2152	1.80869
$967$	30.5841	0.983518	0.491759	−	0.870731i	$-0.336354\pi$
$967$	30.5841	0.983518	0.491759	+	0.870731i	$0.336354\pi$
$968$	23.0106	0.739588
$969$	0.174525	0.00560656
$970$	−0.568701	−0.0182599
$971$	47.5229	1.52508	0.762541	−	0.646939i	$-0.223951\pi$
$971$	47.5229	1.52508	0.762541	+	0.646939i	$0.223951\pi$
$972$	−5.35600	−0.171794
$973$	−9.78718	−0.313763
$974$	14.8012	0.474261
$975$	−24.0074	−0.768851
$976$	12.0700	0.386350
$977$	−7.88620	−0.252302	−0.126151	−	0.992011i	$-0.540262\pi$
$977$	−7.88620	−0.252302	−0.126151	+	0.992011i	$0.540262\pi$
$978$	−23.4241	−0.749019
$979$	−40.1429	−1.28297
$980$	−0.0420780	−0.00134413
$981$	12.4099	0.396218
$982$	40.0451	1.27789
$983$	−33.4806	−1.06786	−0.533932	−	0.845527i	$-0.679286\pi$
$983$	−33.4806	−1.06786	−0.533932	+	0.845527i	$0.679286\pi$
$984$	−51.3330	−1.63644
$985$	0.235617	0.00750740
$986$	−1.34062	−0.0426942
$987$	−22.9608	−0.730851
$988$	−16.4468	−0.523242
$989$	−71.1597	−2.26275
$990$	−0.107736	−0.00342407
$991$	44.7834	1.42259	0.711296	−	0.702893i	$-0.248109\pi$
$991$	44.7834	1.42259	0.711296	+	0.702893i	$0.248109\pi$
$992$	−55.1974	−1.75252
$993$	−26.6923	−0.847054
$994$	−41.8428	−1.32717
$995$	−0.0948203	−0.00300601
$996$	62.4669	1.97934
$997$	28.3937	0.899236	0.449618	−	0.893221i	$-0.351560\pi$
$997$	28.3937	0.899236	0.449618	+	0.893221i	$0.351560\pi$
$998$	105.677	3.34516
$999$	−2.31299	−0.0731798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.3	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.3	✓	93	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71219 q^{2} -1.00000 q^{3} +5.35600 q^{4} +0.0136473 q^{5} +2.71219 q^{6} -2.53463 q^{7} -9.10211 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.71219 q^{2} -1.00000 q^{3} +5.35600 q^{4} +0.0136473 q^{5} +2.71219 q^{6} -2.53463 q^{7} -9.10211 q^{8} +1.00000 q^{9} -0.0370143 q^{10} +2.91066 q^{11} -5.35600 q^{12} -4.80165 q^{13} +6.87440 q^{14} -0.0136473 q^{15} +13.9747 q^{16} -0.272903 q^{17} -2.71219 q^{18} +0.639514 q^{19} +0.0730951 q^{20} +2.53463 q^{21} -7.89428 q^{22} -8.17747 q^{23} +9.10211 q^{24} -4.99981 q^{25} +13.0230 q^{26} -1.00000 q^{27} -13.5755 q^{28} -1.81125 q^{29} +0.0370143 q^{30} +2.80220 q^{31} -19.6979 q^{32} -2.91066 q^{33} +0.740166 q^{34} -0.0345910 q^{35} +5.35600 q^{36} +2.31299 q^{37} -1.73449 q^{38} +4.80165 q^{39} -0.124220 q^{40} -5.63968 q^{41} -6.87440 q^{42} +8.70192 q^{43} +15.5895 q^{44} +0.0136473 q^{45} +22.1789 q^{46} -9.05885 q^{47} -13.9747 q^{48} -0.575661 q^{49} +13.5605 q^{50} +0.272903 q^{51} -25.7176 q^{52} +6.57917 q^{53} +2.71219 q^{54} +0.0397228 q^{55} +23.0705 q^{56} -0.639514 q^{57} +4.91246 q^{58} -10.2144 q^{59} -0.0730951 q^{60} +0.863702 q^{61} -7.60011 q^{62} -2.53463 q^{63} +25.4750 q^{64} -0.0655298 q^{65} +7.89428 q^{66} +2.90374 q^{67} -1.46167 q^{68} +8.17747 q^{69} +0.0938174 q^{70} -6.08675 q^{71} -9.10211 q^{72} -11.9556 q^{73} -6.27328 q^{74} +4.99981 q^{75} +3.42523 q^{76} -7.37744 q^{77} -13.0230 q^{78} +7.43924 q^{79} +0.190718 q^{80} +1.00000 q^{81} +15.2959 q^{82} -11.6630 q^{83} +13.5755 q^{84} -0.00372440 q^{85} -23.6013 q^{86} +1.81125 q^{87} -26.4932 q^{88} -13.7917 q^{89} -0.0370143 q^{90} +12.1704 q^{91} -43.7985 q^{92} -2.80220 q^{93} +24.5693 q^{94} +0.00872767 q^{95} +19.6979 q^{96} +15.3644 q^{97} +1.56130 q^{98} +2.91066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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