LMFDB - Embedded newform 6045.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 7x^{7} + 20x^{6} + 20x^{5} - 38x^{4} - 27x^{3} + 13x^{2} + 6x - 1 $ x^9 - 3x^8 - 7x^7 + 20x^6 + 20x^5 - 38x^4 - 27x^3 + 13x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.67506$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67506 q^{2} +1.00000 q^{3} +5.15596 q^{4} +1.00000 q^{5} -2.67506 q^{6} +1.28643 q^{7} -8.44238 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.67506 q^{2} +1.00000 q^{3} +5.15596 q^{4} +1.00000 q^{5} -2.67506 q^{6} +1.28643 q^{7} -8.44238 q^{8} +1.00000 q^{9} -2.67506 q^{10} -2.54775 q^{11} +5.15596 q^{12} -1.00000 q^{13} -3.44127 q^{14} +1.00000 q^{15} +12.2720 q^{16} -4.64645 q^{17} -2.67506 q^{18} +6.87263 q^{19} +5.15596 q^{20} +1.28643 q^{21} +6.81538 q^{22} -4.10982 q^{23} -8.44238 q^{24} +1.00000 q^{25} +2.67506 q^{26} +1.00000 q^{27} +6.63276 q^{28} -2.94149 q^{29} -2.67506 q^{30} -1.00000 q^{31} -15.9436 q^{32} -2.54775 q^{33} +12.4295 q^{34} +1.28643 q^{35} +5.15596 q^{36} -7.94192 q^{37} -18.3847 q^{38} -1.00000 q^{39} -8.44238 q^{40} +1.41245 q^{41} -3.44127 q^{42} -4.87142 q^{43} -13.1361 q^{44} +1.00000 q^{45} +10.9940 q^{46} +0.154540 q^{47} +12.2720 q^{48} -5.34511 q^{49} -2.67506 q^{50} -4.64645 q^{51} -5.15596 q^{52} +10.5663 q^{53} -2.67506 q^{54} -2.54775 q^{55} -10.8605 q^{56} +6.87263 q^{57} +7.86866 q^{58} -0.0417225 q^{59} +5.15596 q^{60} +9.68747 q^{61} +2.67506 q^{62} +1.28643 q^{63} +18.1060 q^{64} -1.00000 q^{65} +6.81538 q^{66} +9.78142 q^{67} -23.9569 q^{68} -4.10982 q^{69} -3.44127 q^{70} +1.01077 q^{71} -8.44238 q^{72} -4.64082 q^{73} +21.2451 q^{74} +1.00000 q^{75} +35.4350 q^{76} -3.27749 q^{77} +2.67506 q^{78} -0.226367 q^{79} +12.2720 q^{80} +1.00000 q^{81} -3.77838 q^{82} +1.23085 q^{83} +6.63276 q^{84} -4.64645 q^{85} +13.0314 q^{86} -2.94149 q^{87} +21.5091 q^{88} -13.3931 q^{89} -2.67506 q^{90} -1.28643 q^{91} -21.1901 q^{92} -1.00000 q^{93} -0.413405 q^{94} +6.87263 q^{95} -15.9436 q^{96} +7.38014 q^{97} +14.2985 q^{98} -2.54775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9} - 3 q^{10} + 5 q^{12} - 9 q^{13} + 11 q^{14} + 9 q^{15} + 9 q^{16} - 5 q^{17} - 3 q^{18} - 12 q^{19} + 5 q^{20} - 5 q^{21} - 17 q^{22} - 21 q^{23} - 18 q^{24} + 9 q^{25} + 3 q^{26} + 9 q^{27} - 8 q^{28} - 15 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} + 9 q^{34} - 5 q^{35} + 5 q^{36} - 13 q^{37} - 24 q^{38} - 9 q^{39} - 18 q^{40} - 11 q^{41} + 11 q^{42} - 26 q^{43} + 5 q^{44} + 9 q^{45} + 14 q^{46} - 21 q^{47} + 9 q^{48} - 26 q^{49} - 3 q^{50} - 5 q^{51} - 5 q^{52} + 18 q^{53} - 3 q^{54} - 19 q^{56} - 12 q^{57} - 16 q^{58} - 24 q^{59} + 5 q^{60} - 4 q^{61} + 3 q^{62} - 5 q^{63} + 2 q^{64} - 9 q^{65} - 17 q^{66} - 20 q^{67} - 19 q^{68} - 21 q^{69} + 11 q^{70} - 13 q^{71} - 18 q^{72} + 15 q^{73} + 12 q^{74} + 9 q^{75} + 54 q^{76} - 28 q^{77} + 3 q^{78} - 15 q^{79} + 9 q^{80} + 9 q^{81} - 21 q^{82} - 5 q^{83} - 8 q^{84} - 5 q^{85} + 36 q^{86} - 15 q^{87} + 23 q^{88} + 31 q^{89} - 3 q^{90} + 5 q^{91} - 7 q^{92} - 9 q^{93} - 12 q^{95} - 9 q^{96} - 11 q^{97} - 23 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9 - 3 * q^10 + 5 * q^12 - 9 * q^13 + 11 * q^14 + 9 * q^15 + 9 * q^16 - 5 * q^17 - 3 * q^18 - 12 * q^19 + 5 * q^20 - 5 * q^21 - 17 * q^22 - 21 * q^23 - 18 * q^24 + 9 * q^25 + 3 * q^26 + 9 * q^27 - 8 * q^28 - 15 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 + 9 * q^34 - 5 * q^35 + 5 * q^36 - 13 * q^37 - 24 * q^38 - 9 * q^39 - 18 * q^40 - 11 * q^41 + 11 * q^42 - 26 * q^43 + 5 * q^44 + 9 * q^45 + 14 * q^46 - 21 * q^47 + 9 * q^48 - 26 * q^49 - 3 * q^50 - 5 * q^51 - 5 * q^52 + 18 * q^53 - 3 * q^54 - 19 * q^56 - 12 * q^57 - 16 * q^58 - 24 * q^59 + 5 * q^60 - 4 * q^61 + 3 * q^62 - 5 * q^63 + 2 * q^64 - 9 * q^65 - 17 * q^66 - 20 * q^67 - 19 * q^68 - 21 * q^69 + 11 * q^70 - 13 * q^71 - 18 * q^72 + 15 * q^73 + 12 * q^74 + 9 * q^75 + 54 * q^76 - 28 * q^77 + 3 * q^78 - 15 * q^79 + 9 * q^80 + 9 * q^81 - 21 * q^82 - 5 * q^83 - 8 * q^84 - 5 * q^85 + 36 * q^86 - 15 * q^87 + 23 * q^88 + 31 * q^89 - 3 * q^90 + 5 * q^91 - 7 * q^92 - 9 * q^93 - 12 * q^95 - 9 * q^96 - 11 * q^97 - 23 * q^98

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 $

$2$	−2.67506	−1.89155	−0.945777	−	0.324816i	$-0.894698\pi$
$2$	−2.67506	−1.89155	−0.945777	+	0.324816i	$0.894698\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.15596	2.57798
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.67506	−1.09209
$7$	1.28643	0.486223	0.243112	−	0.969998i	$-0.421832\pi$
$7$	1.28643	0.486223	0.243112	+	0.969998i	$0.421832\pi$
$8$	−8.44238	−2.98483
$9$	1.00000	0.333333
$10$	−2.67506	−0.845929
$11$	−2.54775	−0.768175	−0.384087	−	0.923297i	$-0.625484\pi$
$11$	−2.54775	−0.768175	−0.384087	+	0.923297i	$0.625484\pi$
$12$	5.15596	1.48840
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.44127	−0.919718
$15$	1.00000	0.258199
$16$	12.2720	3.06800
$17$	−4.64645	−1.12693	−0.563464	−	0.826140i	$-0.690532\pi$
$17$	−4.64645	−1.12693	−0.563464	+	0.826140i	$0.690532\pi$
$18$	−2.67506	−0.630518
$19$	6.87263	1.57669	0.788344	−	0.615234i	$-0.210939\pi$
$19$	6.87263	1.57669	0.788344	+	0.615234i	$0.210939\pi$
$20$	5.15596	1.15291
$21$	1.28643	0.280721
$22$	6.81538	1.45304
$23$	−4.10982	−0.856957	−0.428479	−	0.903552i	$-0.640950\pi$
$23$	−4.10982	−0.856957	−0.428479	+	0.903552i	$0.640950\pi$
$24$	−8.44238	−1.72329
$25$	1.00000	0.200000
$26$	2.67506	0.524623
$27$	1.00000	0.192450
$28$	6.63276	1.25347
$29$	−2.94149	−0.546220	−0.273110	−	0.961983i	$-0.588052\pi$
$29$	−2.94149	−0.546220	−0.273110	+	0.961983i	$0.588052\pi$
$30$	−2.67506	−0.488397
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−15.9436	−2.81845
$33$	−2.54775	−0.443506
$34$	12.4295	2.13165
$35$	1.28643	0.217446
$36$	5.15596	0.859326
$37$	−7.94192	−1.30564	−0.652822	−	0.757511i	$-0.726415\pi$
$37$	−7.94192	−1.30564	−0.652822	+	0.757511i	$0.726415\pi$
$38$	−18.3847	−2.98239
$39$	−1.00000	−0.160128
$40$	−8.44238	−1.33486
$41$	1.41245	0.220587	0.110294	−	0.993899i	$-0.464821\pi$
$41$	1.41245	0.220587	0.110294	+	0.993899i	$0.464821\pi$
$42$	−3.44127	−0.530999
$43$	−4.87142	−0.742885	−0.371443	−	0.928456i	$-0.621137\pi$
$43$	−4.87142	−0.742885	−0.371443	+	0.928456i	$0.621137\pi$
$44$	−13.1361	−1.98034
$45$	1.00000	0.149071
$46$	10.9940	1.62098
$47$	0.154540	0.0225420	0.0112710	−	0.999936i	$-0.496412\pi$
$47$	0.154540	0.0225420	0.0112710	+	0.999936i	$0.496412\pi$
$48$	12.2720	1.77131
$49$	−5.34511	−0.763587
$50$	−2.67506	−0.378311
$51$	−4.64645	−0.650633
$52$	−5.15596	−0.715003
$53$	10.5663	1.45139	0.725697	−	0.688014i	$-0.241517\pi$
$53$	10.5663	1.45139	0.725697	+	0.688014i	$0.241517\pi$
$54$	−2.67506	−0.364030
$55$	−2.54775	−0.343538
$56$	−10.8605	−1.45130
$57$	6.87263	0.910302
$58$	7.86866	1.03321
$59$	−0.0417225	−0.00543180	−0.00271590	−	0.999996i	$-0.500864\pi$
$59$	−0.0417225	−0.00543180	−0.00271590	+	0.999996i	$0.500864\pi$
$60$	5.15596	0.665631
$61$	9.68747	1.24035	0.620176	−	0.784462i	$-0.287061\pi$
$61$	9.68747	1.24035	0.620176	+	0.784462i	$0.287061\pi$
$62$	2.67506	0.339733
$63$	1.28643	0.162074
$64$	18.1060	2.26326
$65$	−1.00000	−0.124035
$66$	6.81538	0.838916
$67$	9.78142	1.19499	0.597496	−	0.801872i	$-0.296163\pi$
$67$	9.78142	1.19499	0.597496	+	0.801872i	$0.296163\pi$
$68$	−23.9569	−2.90520
$69$	−4.10982	−0.494765
$70$	−3.44127	−0.411310
$71$	1.01077	0.119956	0.0599779	−	0.998200i	$-0.480897\pi$
$71$	1.01077	0.119956	0.0599779	+	0.998200i	$0.480897\pi$
$72$	−8.44238	−0.994944
$73$	−4.64082	−0.543167	−0.271584	−	0.962415i	$-0.587547\pi$
$73$	−4.64082	−0.543167	−0.271584	+	0.962415i	$0.587547\pi$
$74$	21.2451	2.46970
$75$	1.00000	0.115470
$76$	35.4350	4.06467
$77$	−3.27749	−0.373505
$78$	2.67506	0.302891
$79$	−0.226367	−0.0254683	−0.0127341	−	0.999919i	$-0.504054\pi$
$79$	−0.226367	−0.0254683	−0.0127341	+	0.999919i	$0.504054\pi$
$80$	12.2720	1.37205
$81$	1.00000	0.111111
$82$	−3.77838	−0.417252
$83$	1.23085	0.135103	0.0675514	−	0.997716i	$-0.478481\pi$
$83$	1.23085	0.135103	0.0675514	+	0.997716i	$0.478481\pi$
$84$	6.63276	0.723693
$85$	−4.64645	−0.503978
$86$	13.0314	1.40521
$87$	−2.94149	−0.315360
$88$	21.5091	2.29287
$89$	−13.3931	−1.41966	−0.709831	−	0.704372i	$-0.751229\pi$
$89$	−13.3931	−1.41966	−0.709831	+	0.704372i	$0.751229\pi$
$90$	−2.67506	−0.281976
$91$	−1.28643	−0.134854
$92$	−21.1901	−2.20922
$93$	−1.00000	−0.103695
$94$	−0.413405	−0.0426395
$95$	6.87263	0.705117
$96$	−15.9436	−1.62723
$97$	7.38014	0.749340	0.374670	−	0.927158i	$-0.377756\pi$
$97$	7.38014	0.749340	0.374670	+	0.927158i	$0.377756\pi$
$98$	14.2985	1.44437
$99$	−2.54775	−0.256058
$100$	5.15596	0.515596
$101$	−5.60828	−0.558045	−0.279022	−	0.960285i	$-0.590010\pi$
$101$	−5.60828	−0.558045	−0.279022	+	0.960285i	$0.590010\pi$
$102$	12.4295	1.23071
$103$	−17.3615	−1.71068	−0.855338	−	0.518070i	$-0.826651\pi$
$103$	−17.3615	−1.71068	−0.855338	+	0.518070i	$0.826651\pi$
$104$	8.44238	0.827844
$105$	1.28643	0.125542
$106$	−28.2655	−2.74539
$107$	0.813978	0.0786902	0.0393451	−	0.999226i	$-0.487473\pi$
$107$	0.813978	0.0786902	0.0393451	+	0.999226i	$0.487473\pi$
$108$	5.15596	0.496132
$109$	−1.66572	−0.159547	−0.0797734	−	0.996813i	$-0.525420\pi$
$109$	−1.66572	−0.159547	−0.0797734	+	0.996813i	$0.525420\pi$
$110$	6.81538	0.649821
$111$	−7.94192	−0.753814
$112$	15.7870	1.49173
$113$	−16.1490	−1.51917	−0.759585	−	0.650408i	$-0.774598\pi$
$113$	−16.1490	−1.51917	−0.759585	+	0.650408i	$0.774598\pi$
$114$	−18.3847	−1.72189
$115$	−4.10982	−0.383243
$116$	−15.1662	−1.40814
$117$	−1.00000	−0.0924500
$118$	0.111610	0.0102745
$119$	−5.97731	−0.547939
$120$	−8.44238	−0.770681
$121$	−4.50898	−0.409907
$122$	−25.9146	−2.34620
$123$	1.41245	0.127356
$124$	−5.15596	−0.463019
$125$	1.00000	0.0894427
$126$	−3.44127	−0.306573
$127$	−11.2992	−1.00265	−0.501323	−	0.865260i	$-0.667153\pi$
$127$	−11.2992	−1.00265	−0.501323	+	0.865260i	$0.667153\pi$
$128$	−16.5477	−1.46262
$129$	−4.87142	−0.428905
$130$	2.67506	0.234618
$131$	19.3014	1.68637	0.843186	−	0.537622i	$-0.180677\pi$
$131$	19.3014	1.68637	0.843186	+	0.537622i	$0.180677\pi$
$132$	−13.1361	−1.14335
$133$	8.84113	0.766623
$134$	−26.1659	−2.26039
$135$	1.00000	0.0860663
$136$	39.2271	3.36369
$137$	−14.1160	−1.20601	−0.603005	−	0.797738i	$-0.706030\pi$
$137$	−14.1160	−1.20601	−0.603005	+	0.797738i	$0.706030\pi$
$138$	10.9940	0.935874
$139$	−12.4544	−1.05637	−0.528186	−	0.849129i	$-0.677128\pi$
$139$	−12.4544	−1.05637	−0.528186	+	0.849129i	$0.677128\pi$
$140$	6.63276	0.560570
$141$	0.154540	0.0130146
$142$	−2.70386	−0.226903
$143$	2.54775	0.213053
$144$	12.2720	1.02267
$145$	−2.94149	−0.244277
$146$	12.4145	1.02743
$147$	−5.34511	−0.440857
$148$	−40.9482	−3.36592
$149$	19.3280	1.58341	0.791704	−	0.610905i	$-0.209194\pi$
$149$	19.3280	1.58341	0.791704	+	0.610905i	$0.209194\pi$
$150$	−2.67506	−0.218418
$151$	2.01886	0.164292	0.0821461	−	0.996620i	$-0.473823\pi$
$151$	2.01886	0.164292	0.0821461	+	0.996620i	$0.473823\pi$
$152$	−58.0214	−4.70615
$153$	−4.64645	−0.375643
$154$	8.76749	0.706504
$155$	−1.00000	−0.0803219
$156$	−5.15596	−0.412807
$157$	−10.8170	−0.863292	−0.431646	−	0.902043i	$-0.642067\pi$
$157$	−10.8170	−0.863292	−0.431646	+	0.902043i	$0.642067\pi$
$158$	0.605546	0.0481747
$159$	10.5663	0.837963
$160$	−15.9436	−1.26045
$161$	−5.28698	−0.416673
$162$	−2.67506	−0.210173
$163$	21.8283	1.70972	0.854861	−	0.518857i	$-0.173642\pi$
$163$	21.8283	1.70972	0.854861	+	0.518857i	$0.173642\pi$
$164$	7.28251	0.568669
$165$	−2.54775	−0.198342
$166$	−3.29259	−0.255554
$167$	−13.3985	−1.03681	−0.518405	−	0.855135i	$-0.673474\pi$
$167$	−13.3985	−1.03681	−0.518405	+	0.855135i	$0.673474\pi$
$168$	−10.8605	−0.837906
$169$	1.00000	0.0769231
$170$	12.4295	0.953301
$171$	6.87263	0.525563
$172$	−25.1169	−1.91514
$173$	12.0652	0.917297	0.458649	−	0.888618i	$-0.348334\pi$
$173$	12.0652	0.917297	0.458649	+	0.888618i	$0.348334\pi$
$174$	7.86866	0.596521
$175$	1.28643	0.0972447
$176$	−31.2659	−2.35676
$177$	−0.0417225	−0.00313605
$178$	35.8273	2.68537
$179$	−15.8174	−1.18225	−0.591123	−	0.806581i	$-0.701315\pi$
$179$	−15.8174	−1.18225	−0.591123	+	0.806581i	$0.701315\pi$
$180$	5.15596	0.384302
$181$	−4.49783	−0.334321	−0.167160	−	0.985930i	$-0.553460\pi$
$181$	−4.49783	−0.334321	−0.167160	+	0.985930i	$0.553460\pi$
$182$	3.44127	0.255084
$183$	9.68747	0.716118
$184$	34.6967	2.55788
$185$	−7.94192	−0.583902
$186$	2.67506	0.196145
$187$	11.8380	0.865678
$188$	0.796804	0.0581129
$189$	1.28643	0.0935737
$190$	−18.3847	−1.33377
$191$	−22.3987	−1.62071	−0.810357	−	0.585937i	$-0.800727\pi$
$191$	−22.3987	−1.62071	−0.810357	+	0.585937i	$0.800727\pi$
$192$	18.1060	1.30669
$193$	1.21765	0.0876482	0.0438241	−	0.999039i	$-0.486046\pi$
$193$	1.21765	0.0876482	0.0438241	+	0.999039i	$0.486046\pi$
$194$	−19.7423	−1.41742
$195$	−1.00000	−0.0716115
$196$	−27.5592	−1.96851
$197$	−15.8380	−1.12841	−0.564206	−	0.825634i	$-0.690817\pi$
$197$	−15.8380	−1.12841	−0.564206	+	0.825634i	$0.690817\pi$
$198$	6.81538	0.484348
$199$	−7.73934	−0.548627	−0.274314	−	0.961640i	$-0.588451\pi$
$199$	−7.73934	−0.548627	−0.274314	+	0.961640i	$0.588451\pi$
$200$	−8.44238	−0.596967
$201$	9.78142	0.689928
$202$	15.0025	1.05557
$203$	−3.78400	−0.265585
$204$	−23.9569	−1.67732
$205$	1.41245	0.0986495
$206$	46.4430	3.23584
$207$	−4.10982	−0.285652
$208$	−12.2720	−0.850909
$209$	−17.5097	−1.21117
$210$	−3.44127	−0.237470
$211$	−17.5201	−1.20613	−0.603067	−	0.797691i	$-0.706055\pi$
$211$	−17.5201	−1.20613	−0.603067	+	0.797691i	$0.706055\pi$
$212$	54.4795	3.74167
$213$	1.01077	0.0692565
$214$	−2.17744	−0.148847
$215$	−4.87142	−0.332228
$216$	−8.44238	−0.574431
$217$	−1.28643	−0.0873283
$218$	4.45590	0.301792
$219$	−4.64082	−0.313598
$220$	−13.1361	−0.885634
$221$	4.64645	0.312554
$222$	21.2451	1.42588
$223$	−22.6073	−1.51390	−0.756948	−	0.653475i	$-0.773310\pi$
$223$	−22.6073	−1.51390	−0.756948	+	0.653475i	$0.773310\pi$
$224$	−20.5102	−1.37040
$225$	1.00000	0.0666667
$226$	43.1996	2.87359
$227$	−20.7111	−1.37464	−0.687321	−	0.726354i	$-0.741213\pi$
$227$	−20.7111	−1.37464	−0.687321	+	0.726354i	$0.741213\pi$
$228$	35.4350	2.34674
$229$	−21.0350	−1.39003	−0.695015	−	0.718995i	$-0.744602\pi$
$229$	−21.0350	−1.39003	−0.695015	+	0.718995i	$0.744602\pi$
$230$	10.9940	0.724925
$231$	−3.27749	−0.215643
$232$	24.8332	1.63038
$233$	−14.3570	−0.940560	−0.470280	−	0.882517i	$-0.655847\pi$
$233$	−14.3570	−0.940560	−0.470280	+	0.882517i	$0.655847\pi$
$234$	2.67506	0.174874
$235$	0.154540	0.0100811
$236$	−0.215119	−0.0140031
$237$	−0.226367	−0.0147041
$238$	15.9897	1.03646
$239$	17.5459	1.13495	0.567474	−	0.823391i	$-0.307921\pi$
$239$	17.5459	1.13495	0.567474	+	0.823391i	$0.307921\pi$
$240$	12.2720	0.792153
$241$	−17.2179	−1.10911	−0.554553	−	0.832149i	$-0.687111\pi$
$241$	−17.2179	−1.10911	−0.554553	+	0.832149i	$0.687111\pi$
$242$	12.0618	0.775362
$243$	1.00000	0.0641500
$244$	49.9482	3.19760
$245$	−5.34511	−0.341486
$246$	−3.77838	−0.240901
$247$	−6.87263	−0.437295
$248$	8.44238	0.536092
$249$	1.23085	0.0780017
$250$	−2.67506	−0.169186
$251$	22.1303	1.39685	0.698427	−	0.715682i	$-0.253884\pi$
$251$	22.1303	1.39685	0.698427	+	0.715682i	$0.253884\pi$
$252$	6.63276	0.417824
$253$	10.4708	0.658293
$254$	30.2262	1.89656
$255$	−4.64645	−0.290972
$256$	8.05396	0.503373
$257$	−26.1459	−1.63094	−0.815468	−	0.578802i	$-0.803521\pi$
$257$	−26.1459	−1.63094	−0.815468	+	0.578802i	$0.803521\pi$
$258$	13.0314	0.811297
$259$	−10.2167	−0.634835
$260$	−5.15596	−0.319759
$261$	−2.94149	−0.182073
$262$	−51.6325	−3.18987
$263$	−19.0205	−1.17285	−0.586427	−	0.810002i	$-0.699466\pi$
$263$	−19.0205	−1.17285	−0.586427	+	0.810002i	$0.699466\pi$
$264$	21.5091	1.32379
$265$	10.5663	0.649084
$266$	−23.6506	−1.45011
$267$	−13.3931	−0.819642
$268$	50.4326	3.08066
$269$	13.0307	0.794496	0.397248	−	0.917711i	$-0.369965\pi$
$269$	13.0307	0.794496	0.397248	+	0.917711i	$0.369965\pi$
$270$	−2.67506	−0.162799
$271$	27.8906	1.69423	0.847117	−	0.531407i	$-0.178337\pi$
$271$	27.8906	1.69423	0.847117	+	0.531407i	$0.178337\pi$
$272$	−57.0211	−3.45741
$273$	−1.28643	−0.0778580
$274$	37.7611	2.28123
$275$	−2.54775	−0.153635
$276$	−21.1901	−1.27549
$277$	−10.9798	−0.659712	−0.329856	−	0.944031i	$-0.607000\pi$
$277$	−10.9798	−0.659712	−0.329856	+	0.944031i	$0.607000\pi$
$278$	33.3164	1.99819
$279$	−1.00000	−0.0598684
$280$	−10.8605	−0.649039
$281$	0.172144	0.0102693	0.00513464	−	0.999987i	$-0.498366\pi$
$281$	0.172144	0.0102693	0.00513464	+	0.999987i	$0.498366\pi$
$282$	−0.413405	−0.0246179
$283$	9.85607	0.585882	0.292941	−	0.956130i	$-0.405366\pi$
$283$	9.85607	0.585882	0.292941	+	0.956130i	$0.405366\pi$
$284$	5.21146	0.309244
$285$	6.87263	0.407099
$286$	−6.81538	−0.403002
$287$	1.81701	0.107255
$288$	−15.9436	−0.939483
$289$	4.58946	0.269968
$290$	7.86866	0.462064
$291$	7.38014	0.432632
$292$	−23.9279	−1.40027
$293$	28.0239	1.63717	0.818586	−	0.574384i	$-0.194759\pi$
$293$	28.0239	1.63717	0.818586	+	0.574384i	$0.194759\pi$
$294$	14.2985	0.833905
$295$	−0.0417225	−0.00242918
$296$	67.0488	3.89713
$297$	−2.54775	−0.147835
$298$	−51.7035	−2.99510
$299$	4.10982	0.237677
$300$	5.15596	0.297679
$301$	−6.26673	−0.361208
$302$	−5.40057	−0.310768
$303$	−5.60828	−0.322187
$304$	84.3408	4.83728
$305$	9.68747	0.554703
$306$	12.4295	0.710549
$307$	30.1557	1.72108	0.860538	−	0.509387i	$-0.170128\pi$
$307$	30.1557	1.72108	0.860538	+	0.509387i	$0.170128\pi$
$308$	−16.8986	−0.962887
$309$	−17.3615	−0.987660
$310$	2.67506	0.151933
$311$	−3.58605	−0.203346	−0.101673	−	0.994818i	$-0.532420\pi$
$311$	−3.58605	−0.203346	−0.101673	+	0.994818i	$0.532420\pi$
$312$	8.44238	0.477956
$313$	4.28239	0.242055	0.121028	−	0.992649i	$-0.461381\pi$
$313$	4.28239	0.242055	0.121028	+	0.992649i	$0.461381\pi$
$314$	28.9362	1.63296
$315$	1.28643	0.0724819
$316$	−1.16714	−0.0656567
$317$	4.95184	0.278123	0.139062	−	0.990284i	$-0.455591\pi$
$317$	4.95184	0.278123	0.139062	+	0.990284i	$0.455591\pi$
$318$	−28.2655	−1.58505
$319$	7.49416	0.419593
$320$	18.1060	1.01216
$321$	0.813978	0.0454318
$322$	14.1430	0.788159
$323$	−31.9333	−1.77682
$324$	5.15596	0.286442
$325$	−1.00000	−0.0554700
$326$	−58.3920	−3.23403
$327$	−1.66572	−0.0921144
$328$	−11.9244	−0.658416
$329$	0.198805	0.0109605
$330$	6.81538	0.375175
$331$	16.0731	0.883456	0.441728	−	0.897149i	$-0.354366\pi$
$331$	16.0731	0.883456	0.441728	+	0.897149i	$0.354366\pi$
$332$	6.34619	0.348292
$333$	−7.94192	−0.435215
$334$	35.8419	1.96118
$335$	9.78142	0.534416
$336$	15.7870	0.861252
$337$	4.54915	0.247808	0.123904	−	0.992294i	$-0.460458\pi$
$337$	4.54915	0.247808	0.123904	+	0.992294i	$0.460458\pi$
$338$	−2.67506	−0.145504
$339$	−16.1490	−0.877094
$340$	−23.9569	−1.29924
$341$	2.54775	0.137968
$342$	−18.3847	−0.994131
$343$	−15.8811	−0.857497
$344$	41.1264	2.21739
$345$	−4.10982	−0.221265
$346$	−32.2751	−1.73512
$347$	13.4999	0.724710	0.362355	−	0.932040i	$-0.381973\pi$
$347$	13.4999	0.724710	0.362355	+	0.932040i	$0.381973\pi$
$348$	−15.1662	−0.812993
$349$	−1.93756	−0.103715	−0.0518575	−	0.998654i	$-0.516514\pi$
$349$	−1.93756	−0.103715	−0.0518575	+	0.998654i	$0.516514\pi$
$350$	−3.44127	−0.183944
$351$	−1.00000	−0.0533761
$352$	40.6202	2.16506
$353$	−16.2601	−0.865438	−0.432719	−	0.901529i	$-0.642446\pi$
$353$	−16.2601	−0.865438	−0.432719	+	0.901529i	$0.642446\pi$
$354$	0.111610	0.00593201
$355$	1.01077	0.0536459
$356$	−69.0541	−3.65986
$357$	−5.97731	−0.316353
$358$	42.3125	2.23628
$359$	−1.01705	−0.0536776	−0.0268388	−	0.999640i	$-0.508544\pi$
$359$	−1.01705	−0.0536776	−0.0268388	+	0.999640i	$0.508544\pi$
$360$	−8.44238	−0.444953
$361$	28.2330	1.48595
$362$	12.0320	0.632386
$363$	−4.50898	−0.236660
$364$	−6.63276	−0.347651
$365$	−4.64082	−0.242912
$366$	−25.9146	−1.35458
$367$	−0.128170	−0.00669040	−0.00334520	−	0.999994i	$-0.501065\pi$
$367$	−0.128170	−0.00669040	−0.00334520	+	0.999994i	$0.501065\pi$
$368$	−50.4357	−2.62914
$369$	1.41245	0.0735290
$370$	21.2451	1.10448
$371$	13.5928	0.705702
$372$	−5.15596	−0.267324
$373$	−0.419240	−0.0217074	−0.0108537	−	0.999941i	$-0.503455\pi$
$373$	−0.419240	−0.0217074	−0.0108537	+	0.999941i	$0.503455\pi$
$374$	−31.6673	−1.63748
$375$	1.00000	0.0516398
$376$	−1.30469	−0.0672842
$377$	2.94149	0.151494
$378$	−3.44127	−0.177000
$379$	35.3628	1.81646	0.908232	−	0.418466i	$-0.137432\pi$
$379$	35.3628	1.81646	0.908232	+	0.418466i	$0.137432\pi$
$380$	35.4350	1.81778
$381$	−11.2992	−0.578878
$382$	59.9179	3.06567
$383$	24.1722	1.23514	0.617570	−	0.786516i	$-0.288117\pi$
$383$	24.1722	1.23514	0.617570	+	0.786516i	$0.288117\pi$
$384$	−16.5477	−0.844445
$385$	−3.27749	−0.167036
$386$	−3.25728	−0.165791
$387$	−4.87142	−0.247628
$388$	38.0517	1.93178
$389$	10.4910	0.531915	0.265957	−	0.963985i	$-0.414312\pi$
$389$	10.4910	0.531915	0.265957	+	0.963985i	$0.414312\pi$
$390$	2.67506	0.135457
$391$	19.0961	0.965730
$392$	45.1255	2.27918
$393$	19.3014	0.973628
$394$	42.3676	2.13445
$395$	−0.226367	−0.0113898
$396$	−13.1361	−0.660113
$397$	−11.8928	−0.596884	−0.298442	−	0.954428i	$-0.596467\pi$
$397$	−11.8928	−0.596884	−0.298442	+	0.954428i	$0.596467\pi$
$398$	20.7032	1.03776
$399$	8.84113	0.442610
$400$	12.2720	0.613599
$401$	6.33429	0.316319	0.158160	−	0.987414i	$-0.449444\pi$
$401$	6.33429	0.316319	0.158160	+	0.987414i	$0.449444\pi$
$402$	−26.1659	−1.30504
$403$	1.00000	0.0498135
$404$	−28.9160	−1.43863
$405$	1.00000	0.0496904
$406$	10.1224	0.502369
$407$	20.2340	1.00296
$408$	39.2271	1.94203
$409$	7.61599	0.376587	0.188293	−	0.982113i	$-0.439704\pi$
$409$	7.61599	0.376587	0.188293	+	0.982113i	$0.439704\pi$
$410$	−3.77838	−0.186601
$411$	−14.1160	−0.696290
$412$	−89.5150	−4.41009
$413$	−0.0536728	−0.00264107
$414$	10.9940	0.540327
$415$	1.23085	0.0604198
$416$	15.9436	0.781697
$417$	−12.4544	−0.609897
$418$	46.8396	2.29100
$419$	−27.1961	−1.32862	−0.664309	−	0.747458i	$-0.731274\pi$
$419$	−27.1961	−1.32862	−0.664309	+	0.747458i	$0.731274\pi$
$420$	6.63276	0.323645
$421$	−0.601937	−0.0293366	−0.0146683	−	0.999892i	$-0.504669\pi$
$421$	−0.601937	−0.0293366	−0.0146683	+	0.999892i	$0.504669\pi$
$422$	46.8674	2.28147
$423$	0.154540	0.00751401
$424$	−89.2049	−4.33217
$425$	−4.64645	−0.225386
$426$	−2.70386	−0.131002
$427$	12.4622	0.603089
$428$	4.19683	0.202862
$429$	2.54775	0.123006
$430$	13.0314	0.628428
$431$	−34.6539	−1.66922	−0.834610	−	0.550841i	$-0.814307\pi$
$431$	−34.6539	−1.66922	−0.834610	+	0.550841i	$0.814307\pi$
$432$	12.2720	0.590436
$433$	−12.5437	−0.602812	−0.301406	−	0.953496i	$-0.597456\pi$
$433$	−12.5437	−0.602812	−0.301406	+	0.953496i	$0.597456\pi$
$434$	3.44127	0.165186
$435$	−2.94149	−0.141033
$436$	−8.58837	−0.411308
$437$	−28.2453	−1.35116
$438$	12.4145	0.593187
$439$	8.98148	0.428662	0.214331	−	0.976761i	$-0.431243\pi$
$439$	8.98148	0.428662	0.214331	+	0.976761i	$0.431243\pi$
$440$	21.5091	1.02540
$441$	−5.34511	−0.254529
$442$	−12.4295	−0.591212
$443$	−31.0730	−1.47632	−0.738161	−	0.674625i	$-0.764305\pi$
$443$	−31.0730	−1.47632	−0.738161	+	0.674625i	$0.764305\pi$
$444$	−40.9482	−1.94332
$445$	−13.3931	−0.634892
$446$	60.4759	2.86362
$447$	19.3280	0.914181
$448$	23.2921	1.10045
$449$	−2.65710	−0.125396	−0.0626981	−	0.998033i	$-0.519971\pi$
$449$	−2.65710	−0.125396	−0.0626981	+	0.998033i	$0.519971\pi$
$450$	−2.67506	−0.126104
$451$	−3.59856	−0.169449
$452$	−83.2636	−3.91639
$453$	2.01886	0.0948542
$454$	55.4034	2.60021
$455$	−1.28643	−0.0603086
$456$	−58.0214	−2.71710
$457$	−0.655589	−0.0306671	−0.0153336	−	0.999882i	$-0.504881\pi$
$457$	−0.655589	−0.0306671	−0.0153336	+	0.999882i	$0.504881\pi$
$458$	56.2699	2.62932
$459$	−4.64645	−0.216878
$460$	−21.1901	−0.987992
$461$	4.05053	0.188652	0.0943260	−	0.995541i	$-0.469930\pi$
$461$	4.05053	0.188652	0.0943260	+	0.995541i	$0.469930\pi$
$462$	8.76749	0.407900
$463$	25.3174	1.17660	0.588301	−	0.808642i	$-0.299797\pi$
$463$	25.3174	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$464$	−36.0979	−1.67580
$465$	−1.00000	−0.0463739
$466$	38.4059	1.77912
$467$	−33.9972	−1.57320	−0.786602	−	0.617460i	$-0.788162\pi$
$467$	−33.9972	−1.57320	−0.786602	+	0.617460i	$0.788162\pi$
$468$	−5.15596	−0.238334
$469$	12.5831	0.581033
$470$	−0.413405	−0.0190690
$471$	−10.8170	−0.498422
$472$	0.352237	0.0162130
$473$	12.4112	0.570666
$474$	0.605546	0.0278137
$475$	6.87263	0.315338
$476$	−30.8187	−1.41258
$477$	10.5663	0.483798
$478$	−46.9363	−2.14682
$479$	23.9543	1.09450	0.547249	−	0.836970i	$-0.315675\pi$
$479$	23.9543	1.09450	0.547249	+	0.836970i	$0.315675\pi$
$480$	−15.9436	−0.727721
$481$	7.94192	0.362121
$482$	46.0591	2.09793
$483$	−5.28698	−0.240566
$484$	−23.2481	−1.05673
$485$	7.38014	0.335115
$486$	−2.67506	−0.121343
$487$	14.0138	0.635025	0.317512	−	0.948254i	$-0.397153\pi$
$487$	14.0138	0.635025	0.317512	+	0.948254i	$0.397153\pi$
$488$	−81.7853	−3.70225
$489$	21.8283	0.987109
$490$	14.2985	0.645940
$491$	25.3631	1.14462	0.572311	−	0.820036i	$-0.306047\pi$
$491$	25.3631	1.14462	0.572311	+	0.820036i	$0.306047\pi$
$492$	7.28251	0.328321
$493$	13.6675	0.615551
$494$	18.3847	0.827167
$495$	−2.54775	−0.114513
$496$	−12.2720	−0.551028
$497$	1.30028	0.0583253
$498$	−3.29259	−0.147544
$499$	25.9762	1.16286	0.581428	−	0.813598i	$-0.302494\pi$
$499$	25.9762	1.16286	0.581428	+	0.813598i	$0.302494\pi$
$500$	5.15596	0.230581
$501$	−13.3985	−0.598602
$502$	−59.2000	−2.64222
$503$	−24.7685	−1.10437	−0.552185	−	0.833721i	$-0.686206\pi$
$503$	−24.7685	−1.10437	−0.552185	+	0.833721i	$0.686206\pi$
$504$	−10.8605	−0.483765
$505$	−5.60828	−0.249565
$506$	−28.0100	−1.24520
$507$	1.00000	0.0444116
$508$	−58.2585	−2.58480
$509$	1.38823	0.0615322	0.0307661	−	0.999527i	$-0.490205\pi$
$509$	1.38823	0.0615322	0.0307661	+	0.999527i	$0.490205\pi$
$510$	12.4295	0.550389
$511$	−5.97008	−0.264101
$512$	11.5505	0.510464
$513$	6.87263	0.303434
$514$	69.9419	3.08501
$515$	−17.3615	−0.765038
$516$	−25.1169	−1.10571
$517$	−0.393730	−0.0173162
$518$	27.3303	1.20082
$519$	12.0652	0.529602
$520$	8.44238	0.370223
$521$	−15.6045	−0.683645	−0.341823	−	0.939764i	$-0.611044\pi$
$521$	−15.6045	−0.683645	−0.341823	+	0.939764i	$0.611044\pi$
$522$	7.86866	0.344402
$523$	−32.1659	−1.40652	−0.703258	−	0.710934i	$-0.748272\pi$
$523$	−32.1659	−1.40652	−0.703258	+	0.710934i	$0.748272\pi$
$524$	99.5173	4.34743
$525$	1.28643	0.0561442
$526$	50.8810	2.21852
$527$	4.64645	0.202402
$528$	−31.2659	−1.36067
$529$	−6.10935	−0.265624
$530$	−28.2655	−1.22778
$531$	−0.0417225	−0.00181060
$532$	45.5845	1.97634
$533$	−1.41245	−0.0611798
$534$	35.8273	1.55040
$535$	0.813978	0.0351913
$536$	−82.5785	−3.56685
$537$	−15.8174	−0.682570
$538$	−34.8579	−1.50283
$539$	13.6180	0.586568
$540$	5.15596	0.221877
$541$	−34.6655	−1.49039	−0.745194	−	0.666848i	$-0.767643\pi$
$541$	−34.6655	−1.49039	−0.745194	+	0.666848i	$0.767643\pi$
$542$	−74.6091	−3.20473
$543$	−4.49783	−0.193020
$544$	74.0809	3.17619
$545$	−1.66572	−0.0713515
$546$	3.44127	0.147273
$547$	−17.2935	−0.739418	−0.369709	−	0.929148i	$-0.620543\pi$
$547$	−17.2935	−0.739418	−0.369709	+	0.929148i	$0.620543\pi$
$548$	−72.7814	−3.10907
$549$	9.68747	0.413451
$550$	6.81538	0.290609
$551$	−20.2157	−0.861219
$552$	34.6967	1.47679
$553$	−0.291205	−0.0123833
$554$	29.3716	1.24788
$555$	−7.94192	−0.337116
$556$	−64.2146	−2.72331
$557$	−11.8138	−0.500567	−0.250283	−	0.968173i	$-0.580524\pi$
$557$	−11.8138	−0.500567	−0.250283	+	0.968173i	$0.580524\pi$
$558$	2.67506	0.113244
$559$	4.87142	0.206039
$560$	15.7870	0.667123
$561$	11.8380	0.499800
$562$	−0.460497	−0.0194249
$563$	−2.56665	−0.108172	−0.0540858	−	0.998536i	$-0.517224\pi$
$563$	−2.56665	−0.108172	−0.0540858	+	0.998536i	$0.517224\pi$
$564$	0.796804	0.0335515
$565$	−16.1490	−0.679394
$566$	−26.3656	−1.10823
$567$	1.28643	0.0540248
$568$	−8.53327	−0.358048
$569$	36.3125	1.52230	0.761149	−	0.648577i	$-0.224636\pi$
$569$	36.3125	1.52230	0.761149	+	0.648577i	$0.224636\pi$
$570$	−18.3847	−0.770051
$571$	3.22382	0.134913	0.0674564	−	0.997722i	$-0.478512\pi$
$571$	3.22382	0.134913	0.0674564	+	0.997722i	$0.478512\pi$
$572$	13.1361	0.549247
$573$	−22.3987	−0.935720
$574$	−4.86061	−0.202878
$575$	−4.10982	−0.171391
$576$	18.1060	0.754418
$577$	−36.0603	−1.50121	−0.750606	−	0.660750i	$-0.770238\pi$
$577$	−36.0603	−1.50121	−0.750606	+	0.660750i	$0.770238\pi$
$578$	−12.2771	−0.510659
$579$	1.21765	0.0506037
$580$	−15.1662	−0.629741
$581$	1.58339	0.0656902
$582$	−19.7423	−0.818346
$583$	−26.9203	−1.11493
$584$	39.1796	1.62126
$585$	−1.00000	−0.0413449
$586$	−74.9656	−3.09680
$587$	−22.8532	−0.943254	−0.471627	−	0.881798i	$-0.656333\pi$
$587$	−22.8532	−0.943254	−0.471627	+	0.881798i	$0.656333\pi$
$588$	−27.5592	−1.13652
$589$	−6.87263	−0.283182
$590$	0.111610	0.00459492
$591$	−15.8380	−0.651488
$592$	−97.4632	−4.00571
$593$	32.8813	1.35027	0.675137	−	0.737692i	$-0.264084\pi$
$593$	32.8813	1.35027	0.675137	+	0.737692i	$0.264084\pi$
$594$	6.81538	0.279639
$595$	−5.97731	−0.245046
$596$	99.6541	4.08199
$597$	−7.73934	−0.316750
$598$	−10.9940	−0.449579
$599$	46.2199	1.88849	0.944247	−	0.329237i	$-0.106791\pi$
$599$	46.2199	1.88849	0.944247	+	0.329237i	$0.106791\pi$
$600$	−8.44238	−0.344659
$601$	−12.5790	−0.513106	−0.256553	−	0.966530i	$-0.582587\pi$
$601$	−12.5790	−0.513106	−0.256553	+	0.966530i	$0.582587\pi$
$602$	16.7639	0.683245
$603$	9.78142	0.398330
$604$	10.4091	0.423542
$605$	−4.50898	−0.183316
$606$	15.0025	0.609435
$607$	2.71965	0.110387	0.0551936	−	0.998476i	$-0.482422\pi$
$607$	2.71965	0.110387	0.0551936	+	0.998476i	$0.482422\pi$
$608$	−109.574	−4.44382
$609$	−3.78400	−0.153336
$610$	−25.9146	−1.04925
$611$	−0.154540	−0.00625203
$612$	−23.9569	−0.968399
$613$	−14.6971	−0.593609	−0.296804	−	0.954938i	$-0.595921\pi$
$613$	−14.6971	−0.593609	−0.296804	+	0.954938i	$0.595921\pi$
$614$	−80.6683	−3.25551
$615$	1.41245	0.0569553
$616$	27.6698	1.11485
$617$	−21.5419	−0.867243	−0.433621	−	0.901095i	$-0.642764\pi$
$617$	−21.5419	−0.867243	−0.433621	+	0.901095i	$0.642764\pi$
$618$	46.4430	1.86821
$619$	−36.8862	−1.48258	−0.741291	−	0.671184i	$-0.765786\pi$
$619$	−36.8862	−1.48258	−0.741291	+	0.671184i	$0.765786\pi$
$620$	−5.15596	−0.207068
$621$	−4.10982	−0.164922
$622$	9.59291	0.384640
$623$	−17.2292	−0.690273
$624$	−12.2720	−0.491273
$625$	1.00000	0.0400000
$626$	−11.4557	−0.457860
$627$	−17.5097	−0.699271
$628$	−55.7721	−2.22555
$629$	36.9017	1.47137
$630$	−3.44127	−0.137103
$631$	−19.2285	−0.765474	−0.382737	−	0.923857i	$-0.625018\pi$
$631$	−19.2285	−0.765474	−0.382737	+	0.923857i	$0.625018\pi$
$632$	1.91108	0.0760186
$633$	−17.5201	−0.696361
$634$	−13.2465	−0.526085
$635$	−11.2992	−0.448397
$636$	54.4795	2.16025
$637$	5.34511	0.211781
$638$	−20.0474	−0.793682
$639$	1.01077	0.0399853
$640$	−16.5477	−0.654104
$641$	5.52324	0.218155	0.109077	−	0.994033i	$-0.465210\pi$
$641$	5.52324	0.218155	0.109077	+	0.994033i	$0.465210\pi$
$642$	−2.17744	−0.0859367
$643$	−6.97942	−0.275241	−0.137621	−	0.990485i	$-0.543945\pi$
$643$	−6.97942	−0.275241	−0.137621	+	0.990485i	$0.543945\pi$
$644$	−27.2595	−1.07417
$645$	−4.87142	−0.191812
$646$	85.4235	3.36094
$647$	−5.88010	−0.231171	−0.115585	−	0.993298i	$-0.536874\pi$
$647$	−5.88010	−0.231171	−0.115585	+	0.993298i	$0.536874\pi$
$648$	−8.44238	−0.331648
$649$	0.106298	0.00417257
$650$	2.67506	0.104925
$651$	−1.28643	−0.0504190
$652$	112.546	4.40763
$653$	−3.53309	−0.138260	−0.0691302	−	0.997608i	$-0.522022\pi$
$653$	−3.53309	−0.138260	−0.0691302	+	0.997608i	$0.522022\pi$
$654$	4.45590	0.174239
$655$	19.3014	0.754169
$656$	17.3335	0.676760
$657$	−4.64082	−0.181056
$658$	−0.531815	−0.0207323
$659$	4.96642	0.193464	0.0967322	−	0.995310i	$-0.469161\pi$
$659$	4.96642	0.193464	0.0967322	+	0.995310i	$0.469161\pi$
$660$	−13.1361	−0.511321
$661$	26.1147	1.01574	0.507871	−	0.861433i	$-0.330432\pi$
$661$	26.1147	1.01574	0.507871	+	0.861433i	$0.330432\pi$
$662$	−42.9965	−1.67110
$663$	4.64645	0.180453
$664$	−10.3913	−0.403260
$665$	8.84113	0.342844
$666$	21.2451	0.823232
$667$	12.0890	0.468088
$668$	−69.0823	−2.67287
$669$	−22.6073	−0.874048
$670$	−26.1659	−1.01088
$671$	−24.6812	−0.952808
$672$	−20.5102	−0.791199
$673$	−23.4945	−0.905646	−0.452823	−	0.891600i	$-0.649583\pi$
$673$	−23.4945	−0.905646	−0.452823	+	0.891600i	$0.649583\pi$
$674$	−12.1693	−0.468743
$675$	1.00000	0.0384900
$676$	5.15596	0.198306
$677$	32.0141	1.23040	0.615201	−	0.788370i	$-0.289075\pi$
$677$	32.0141	1.23040	0.615201	+	0.788370i	$0.289075\pi$
$678$	43.1996	1.65907
$679$	9.49401	0.364347
$680$	39.2271	1.50429
$681$	−20.7111	−0.793650
$682$	−6.81538	−0.260975
$683$	5.73692	0.219517	0.109759	−	0.993958i	$-0.464992\pi$
$683$	5.73692	0.219517	0.109759	+	0.993958i	$0.464992\pi$
$684$	35.4350	1.35489
$685$	−14.1160	−0.539344
$686$	42.4828	1.62200
$687$	−21.0350	−0.802534
$688$	−59.7820	−2.27917
$689$	−10.5663	−0.402545
$690$	10.9940	0.418536
$691$	−42.5919	−1.62027	−0.810136	−	0.586242i	$-0.800607\pi$
$691$	−42.5919	−1.62027	−0.810136	+	0.586242i	$0.800607\pi$
$692$	62.2075	2.36477
$693$	−3.27749	−0.124502
$694$	−36.1130	−1.37083
$695$	−12.4544	−0.472424
$696$	24.8332	0.941298
$697$	−6.56285	−0.248586
$698$	5.18308	0.196183
$699$	−14.3570	−0.543033
$700$	6.63276	0.250695
$701$	−20.2765	−0.765831	−0.382916	−	0.923783i	$-0.625080\pi$
$701$	−20.2765	−0.765831	−0.382916	+	0.923783i	$0.625080\pi$
$702$	2.67506	0.100964
$703$	−54.5819	−2.05859
$704$	−46.1296	−1.73858
$705$	0.154540	0.00582033
$706$	43.4968	1.63702
$707$	−7.21463	−0.271334
$708$	−0.215119	−0.00808468
$709$	−26.9918	−1.01370	−0.506850	−	0.862034i	$-0.669190\pi$
$709$	−26.9918	−1.01370	−0.506850	+	0.862034i	$0.669190\pi$
$710$	−2.70386	−0.101474
$711$	−0.226367	−0.00848943
$712$	113.069	4.23746
$713$	4.10982	0.153914
$714$	15.9897	0.598398
$715$	2.54775	0.0952804
$716$	−81.5538	−3.04781
$717$	17.5459	0.655263
$718$	2.72066	0.101534
$719$	−28.0397	−1.04570	−0.522852	−	0.852424i	$-0.675132\pi$
$719$	−28.0397	−1.04570	−0.522852	+	0.852424i	$0.675132\pi$
$720$	12.2720	0.457350
$721$	−22.3343	−0.831771
$722$	−75.5250	−2.81075
$723$	−17.2179	−0.640342
$724$	−23.1906	−0.861872
$725$	−2.94149	−0.109244
$726$	12.0618	0.447656
$727$	39.9223	1.48064	0.740318	−	0.672257i	$-0.234675\pi$
$727$	39.9223	1.48064	0.740318	+	0.672257i	$0.234675\pi$
$728$	10.8605	0.402517
$729$	1.00000	0.0370370
$730$	12.4145	0.459481
$731$	22.6348	0.837178
$732$	49.9482	1.84614
$733$	42.3426	1.56396	0.781981	−	0.623303i	$-0.214210\pi$
$733$	42.3426	1.56396	0.781981	+	0.623303i	$0.214210\pi$
$734$	0.342862	0.0126553
$735$	−5.34511	−0.197157
$736$	65.5252	2.41529
$737$	−24.9206	−0.917962
$738$	−3.77838	−0.139084
$739$	13.9131	0.511802	0.255901	−	0.966703i	$-0.417628\pi$
$739$	13.9131	0.511802	0.255901	+	0.966703i	$0.417628\pi$
$740$	−40.9482	−1.50529
$741$	−6.87263	−0.252472
$742$	−36.3615	−1.33487
$743$	9.93486	0.364475	0.182237	−	0.983255i	$-0.441666\pi$
$743$	9.93486	0.364475	0.182237	+	0.983255i	$0.441666\pi$
$744$	8.44238	0.309513
$745$	19.3280	0.708122
$746$	1.12149	0.0410608
$747$	1.23085	0.0450343
$748$	61.0361	2.23170
$749$	1.04712	0.0382610
$750$	−2.67506	−0.0976795
$751$	−2.90189	−0.105891	−0.0529457	−	0.998597i	$-0.516861\pi$
$751$	−2.90189	−0.105891	−0.0529457	+	0.998597i	$0.516861\pi$
$752$	1.89652	0.0691589
$753$	22.1303	0.806474
$754$	−7.86866	−0.286560
$755$	2.01886	0.0734737
$756$	6.63276	0.241231
$757$	14.3527	0.521657	0.260829	−	0.965385i	$-0.416004\pi$
$757$	14.3527	0.521657	0.260829	+	0.965385i	$0.416004\pi$
$758$	−94.5977	−3.43594
$759$	10.4708	0.380066
$760$	−58.0214	−2.10466
$761$	7.28850	0.264208	0.132104	−	0.991236i	$-0.457827\pi$
$761$	7.28850	0.264208	0.132104	+	0.991236i	$0.457827\pi$
$762$	30.2262	1.09498
$763$	−2.14282	−0.0775754
$764$	−115.487	−4.17817
$765$	−4.64645	−0.167993
$766$	−64.6620	−2.33633
$767$	0.0417225	0.00150651
$768$	8.05396	0.290622
$769$	−0.224035	−0.00807890	−0.00403945	−	0.999992i	$-0.501286\pi$
$769$	−0.224035	−0.00807890	−0.00403945	+	0.999992i	$0.501286\pi$
$770$	8.76749	0.315958
$771$	−26.1459	−0.941622
$772$	6.27814	0.225955
$773$	53.4560	1.92268	0.961339	−	0.275369i	$-0.0888001\pi$
$773$	53.4560	1.92268	0.961339	+	0.275369i	$0.0888001\pi$
$774$	13.0314	0.468403
$775$	−1.00000	−0.0359211
$776$	−62.3060	−2.23665
$777$	−10.2167	−0.366522
$778$	−28.0641	−1.00615
$779$	9.70722	0.347797
$780$	−5.15596	−0.184613
$781$	−2.57518	−0.0921470
$782$	−51.0832	−1.82673
$783$	−2.94149	−0.105120
$784$	−65.5951	−2.34268
$785$	−10.8170	−0.386076
$786$	−51.6325	−1.84167
$787$	24.1781	0.861857	0.430929	−	0.902386i	$-0.358186\pi$
$787$	24.1781	0.861857	0.430929	+	0.902386i	$0.358186\pi$
$788$	−81.6601	−2.90902
$789$	−19.0205	−0.677148
$790$	0.605546	0.0215444
$791$	−20.7745	−0.738656
$792$	21.5091	0.764291
$793$	−9.68747	−0.344012
$794$	31.8141	1.12904
$795$	10.5663	0.374749
$796$	−39.9037	−1.41435
$797$	28.3062	1.00266	0.501328	−	0.865257i	$-0.332845\pi$
$797$	28.3062	1.00266	0.501328	+	0.865257i	$0.332845\pi$
$798$	−23.6506	−0.837221
$799$	−0.718063	−0.0254033
$800$	−15.9436	−0.563690
$801$	−13.3931	−0.473221
$802$	−16.9446	−0.598335
$803$	11.8236	0.417247
$804$	50.4326	1.77862
$805$	−5.28698	−0.186342
$806$	−2.67506	−0.0942250
$807$	13.0307	0.458702
$808$	47.3472	1.66567
$809$	−5.46569	−0.192164	−0.0960818	−	0.995373i	$-0.530631\pi$
$809$	−5.46569	−0.192164	−0.0960818	+	0.995373i	$0.530631\pi$
$810$	−2.67506	−0.0939921
$811$	−43.4440	−1.52553	−0.762763	−	0.646678i	$-0.776158\pi$
$811$	−43.4440	−1.52553	−0.762763	+	0.646678i	$0.776158\pi$
$812$	−19.5102	−0.684673
$813$	27.8906	0.978166
$814$	−54.1273	−1.89716
$815$	21.8283	0.764611
$816$	−57.0211	−1.99614
$817$	−33.4795	−1.17130
$818$	−20.3733	−0.712334
$819$	−1.28643	−0.0449514
$820$	7.28251	0.254316
$821$	4.50201	0.157121	0.0785607	−	0.996909i	$-0.474968\pi$
$821$	4.50201	0.157121	0.0785607	+	0.996909i	$0.474968\pi$
$822$	37.7611	1.31707
$823$	0.709685	0.0247381	0.0123690	−	0.999924i	$-0.496063\pi$
$823$	0.709685	0.0247381	0.0123690	+	0.999924i	$0.496063\pi$
$824$	146.572	5.10609
$825$	−2.54775	−0.0887012
$826$	0.143578	0.00499572
$827$	8.65313	0.300899	0.150449	−	0.988618i	$-0.451928\pi$
$827$	8.65313	0.300899	0.150449	+	0.988618i	$0.451928\pi$
$828$	−21.1901	−0.736406
$829$	−6.19713	−0.215235	−0.107618	−	0.994192i	$-0.534322\pi$
$829$	−6.19713	−0.215235	−0.107618	+	0.994192i	$0.534322\pi$
$830$	−3.29259	−0.114287
$831$	−10.9798	−0.380885
$832$	−18.1060	−0.627714
$833$	24.8358	0.860508
$834$	33.3164	1.15365
$835$	−13.3985	−0.463675
$836$	−90.2794	−3.12238
$837$	−1.00000	−0.0345651
$838$	72.7513	2.51315
$839$	−35.3610	−1.22080	−0.610399	−	0.792094i	$-0.708991\pi$
$839$	−35.3610	−1.22080	−0.610399	+	0.792094i	$0.708991\pi$
$840$	−10.8605	−0.374723
$841$	−20.3477	−0.701643
$842$	1.61022	0.0554918
$843$	0.172144	0.00592897
$844$	−90.3329	−3.10939
$845$	1.00000	0.0344010
$846$	−0.413405	−0.0142132
$847$	−5.80047	−0.199307
$848$	129.670	4.45287
$849$	9.85607	0.338259
$850$	12.4295	0.426329
$851$	32.6399	1.11888
$852$	5.21146	0.178542
$853$	−20.1772	−0.690853	−0.345427	−	0.938446i	$-0.612266\pi$
$853$	−20.1772	−0.690853	−0.345427	+	0.938446i	$0.612266\pi$
$854$	−33.3372	−1.14077
$855$	6.87263	0.235039
$856$	−6.87191	−0.234877
$857$	23.3220	0.796664	0.398332	−	0.917241i	$-0.369589\pi$
$857$	23.3220	0.796664	0.398332	+	0.917241i	$0.369589\pi$
$858$	−6.81538	−0.232673
$859$	−9.77470	−0.333508	−0.166754	−	0.985998i	$-0.553329\pi$
$859$	−9.77470	−0.333508	−0.166754	+	0.985998i	$0.553329\pi$
$860$	−25.1169	−0.856478
$861$	1.81701	0.0619234
$862$	92.7014	3.15742
$863$	−36.9323	−1.25719	−0.628594	−	0.777733i	$-0.716369\pi$
$863$	−36.9323	−1.25719	−0.628594	+	0.777733i	$0.716369\pi$
$864$	−15.9436	−0.542411
$865$	12.0652	0.410228
$866$	33.5552	1.14025
$867$	4.58946	0.155866
$868$	−6.63276	−0.225130
$869$	0.576726	0.0195641
$870$	7.86866	0.266773
$871$	−9.78142	−0.331431
$872$	14.0626	0.476221
$873$	7.38014	0.249780
$874$	75.5579	2.55578
$875$	1.28643	0.0434891
$876$	−23.9279	−0.808449
$877$	−30.8437	−1.04152	−0.520758	−	0.853704i	$-0.674351\pi$
$877$	−30.8437	−1.04152	−0.520758	+	0.853704i	$0.674351\pi$
$878$	−24.0260	−0.810838
$879$	28.0239	0.945221
$880$	−31.2659	−1.05397
$881$	37.9002	1.27689	0.638445	−	0.769668i	$-0.279578\pi$
$881$	37.9002	1.27689	0.638445	+	0.769668i	$0.279578\pi$
$882$	14.2985	0.481455
$883$	−55.0359	−1.85211	−0.926053	−	0.377394i	$-0.876820\pi$
$883$	−55.0359	−1.85211	−0.926053	+	0.377394i	$0.876820\pi$
$884$	23.9569	0.805757
$885$	−0.0417225	−0.00140248
$886$	83.1221	2.79254
$887$	59.3356	1.99229	0.996147	−	0.0877025i	$-0.0279525\pi$
$887$	59.3356	1.99229	0.996147	+	0.0877025i	$0.0279525\pi$
$888$	67.0488	2.25001
$889$	−14.5356	−0.487510
$890$	35.8273	1.20093
$891$	−2.54775	−0.0853528
$892$	−116.562	−3.90279
$893$	1.06210	0.0355418
$894$	−51.7035	−1.72922
$895$	−15.8174	−0.528717
$896$	−21.2874	−0.711160
$897$	4.10982	0.137223
$898$	7.10790	0.237194
$899$	2.94149	0.0981041
$900$	5.15596	0.171865
$901$	−49.0958	−1.63562
$902$	9.62636	0.320523
$903$	−6.26673	−0.208544
$904$	136.336	4.53447
$905$	−4.49783	−0.149513
$906$	−5.40057	−0.179422
$907$	28.3120	0.940086	0.470043	−	0.882644i	$-0.344238\pi$
$907$	28.3120	0.940086	0.470043	+	0.882644i	$0.344238\pi$
$908$	−106.785	−3.54380
$909$	−5.60828	−0.186015
$910$	3.44127	0.114077
$911$	−59.8221	−1.98199	−0.990997	−	0.133887i	$-0.957254\pi$
$911$	−59.8221	−1.98199	−0.990997	+	0.133887i	$0.957254\pi$
$912$	84.3408	2.79280
$913$	−3.13588	−0.103783
$914$	1.75374	0.0580086
$915$	9.68747	0.320258
$916$	−108.455	−3.58347
$917$	24.8298	0.819954
$918$	12.4295	0.410236
$919$	−11.3644	−0.374875	−0.187438	−	0.982276i	$-0.560018\pi$
$919$	−11.3644	−0.374875	−0.187438	+	0.982276i	$0.560018\pi$
$920$	34.6967	1.14392
$921$	30.1557	0.993663
$922$	−10.8354	−0.356846
$923$	−1.01077	−0.0332698
$924$	−16.8986	−0.555923
$925$	−7.94192	−0.261129
$926$	−67.7257	−2.22561
$927$	−17.3615	−0.570226
$928$	46.8978	1.53949
$929$	13.2456	0.434574	0.217287	−	0.976108i	$-0.430279\pi$
$929$	13.2456	0.434574	0.217287	+	0.976108i	$0.430279\pi$
$930$	2.67506	0.0877187
$931$	−36.7349	−1.20394
$932$	−74.0242	−2.42474
$933$	−3.58605	−0.117402
$934$	90.9447	2.97580
$935$	11.8380	0.387143
$936$	8.44238	0.275948
$937$	29.5421	0.965099	0.482549	−	0.875869i	$-0.339711\pi$
$937$	29.5421	0.965099	0.482549	+	0.875869i	$0.339711\pi$
$938$	−33.6605	−1.09905
$939$	4.28239	0.139751
$940$	0.796804	0.0259889
$941$	9.28566	0.302704	0.151352	−	0.988480i	$-0.451637\pi$
$941$	9.28566	0.302704	0.151352	+	0.988480i	$0.451637\pi$
$942$	28.9362	0.942792
$943$	−5.80490	−0.189034
$944$	−0.512017	−0.0166647
$945$	1.28643	0.0418474
$946$	−33.2006	−1.07945
$947$	12.4652	0.405066	0.202533	−	0.979275i	$-0.435083\pi$
$947$	12.4652	0.405066	0.202533	+	0.979275i	$0.435083\pi$
$948$	−1.16714	−0.0379069
$949$	4.64082	0.150648
$950$	−18.3847	−0.596479
$951$	4.95184	0.160574
$952$	50.4627	1.63551
$953$	−27.0818	−0.877264	−0.438632	−	0.898667i	$-0.644537\pi$
$953$	−27.0818	−0.877264	−0.438632	+	0.898667i	$0.644537\pi$
$954$	−28.2655	−0.915131
$955$	−22.3987	−0.724805
$956$	90.4658	2.92587
$957$	7.49416	0.242252
$958$	−64.0791	−2.07030
$959$	−18.1592	−0.586390
$960$	18.1060	0.584370
$961$	1.00000	0.0322581
$962$	−21.2451	−0.684971
$963$	0.813978	0.0262301
$964$	−88.7750	−2.85925
$965$	1.21765	0.0391975
$966$	14.1430	0.455044
$967$	−33.3913	−1.07379	−0.536896	−	0.843649i	$-0.680403\pi$
$967$	−33.3913	−1.07379	−0.536896	+	0.843649i	$0.680403\pi$
$968$	38.0666	1.22351
$969$	−31.9333	−1.02584
$970$	−19.7423	−0.633888
$971$	12.2337	0.392597	0.196298	−	0.980544i	$-0.437108\pi$
$971$	12.2337	0.392597	0.196298	+	0.980544i	$0.437108\pi$
$972$	5.15596	0.165377
$973$	−16.0217	−0.513633
$974$	−37.4877	−1.20118
$975$	−1.00000	−0.0320256
$976$	118.884	3.80540
$977$	30.1900	0.965864	0.482932	−	0.875658i	$-0.339572\pi$
$977$	30.1900	0.965864	0.482932	+	0.875658i	$0.339572\pi$
$978$	−58.3920	−1.86717
$979$	34.1222	1.09055
$980$	−27.5592	−0.880345
$981$	−1.66572	−0.0531823
$982$	−67.8480	−2.16512
$983$	−14.4105	−0.459624	−0.229812	−	0.973235i	$-0.573811\pi$
$983$	−14.4105	−0.459624	−0.229812	+	0.973235i	$0.573811\pi$
$984$	−11.9244	−0.380136
$985$	−15.8380	−0.504641
$986$	−36.5613	−1.16435
$987$	0.198805	0.00632802
$988$	−35.4350	−1.12734
$989$	20.0207	0.636621
$990$	6.81538	0.216607
$991$	−47.2167	−1.49989	−0.749944	−	0.661501i	$-0.769920\pi$
$991$	−47.2167	−1.49989	−0.749944	+	0.661501i	$0.769920\pi$
$992$	15.9436	0.506209
$993$	16.0731	0.510063
$994$	−3.47832	−0.110326
$995$	−7.73934	−0.245354
$996$	6.34619	0.201087
$997$	−9.48975	−0.300544	−0.150272	−	0.988645i	$-0.548015\pi$
$997$	−9.48975	−0.300544	−0.150272	+	0.988645i	$0.548015\pi$
$998$	−69.4881	−2.19961
$999$	−7.94192	−0.251271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.u.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.u.1.1	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67506 q^{2} +1.00000 q^{3} +5.15596 q^{4} +1.00000 q^{5} -2.67506 q^{6} +1.28643 q^{7} -8.44238 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.67506 q^{2} +1.00000 q^{3} +5.15596 q^{4} +1.00000 q^{5} -2.67506 q^{6} +1.28643 q^{7} -8.44238 q^{8} +1.00000 q^{9} -2.67506 q^{10} -2.54775 q^{11} +5.15596 q^{12} -1.00000 q^{13} -3.44127 q^{14} +1.00000 q^{15} +12.2720 q^{16} -4.64645 q^{17} -2.67506 q^{18} +6.87263 q^{19} +5.15596 q^{20} +1.28643 q^{21} +6.81538 q^{22} -4.10982 q^{23} -8.44238 q^{24} +1.00000 q^{25} +2.67506 q^{26} +1.00000 q^{27} +6.63276 q^{28} -2.94149 q^{29} -2.67506 q^{30} -1.00000 q^{31} -15.9436 q^{32} -2.54775 q^{33} +12.4295 q^{34} +1.28643 q^{35} +5.15596 q^{36} -7.94192 q^{37} -18.3847 q^{38} -1.00000 q^{39} -8.44238 q^{40} +1.41245 q^{41} -3.44127 q^{42} -4.87142 q^{43} -13.1361 q^{44} +1.00000 q^{45} +10.9940 q^{46} +0.154540 q^{47} +12.2720 q^{48} -5.34511 q^{49} -2.67506 q^{50} -4.64645 q^{51} -5.15596 q^{52} +10.5663 q^{53} -2.67506 q^{54} -2.54775 q^{55} -10.8605 q^{56} +6.87263 q^{57} +7.86866 q^{58} -0.0417225 q^{59} +5.15596 q^{60} +9.68747 q^{61} +2.67506 q^{62} +1.28643 q^{63} +18.1060 q^{64} -1.00000 q^{65} +6.81538 q^{66} +9.78142 q^{67} -23.9569 q^{68} -4.10982 q^{69} -3.44127 q^{70} +1.01077 q^{71} -8.44238 q^{72} -4.64082 q^{73} +21.2451 q^{74} +1.00000 q^{75} +35.4350 q^{76} -3.27749 q^{77} +2.67506 q^{78} -0.226367 q^{79} +12.2720 q^{80} +1.00000 q^{81} -3.77838 q^{82} +1.23085 q^{83} +6.63276 q^{84} -4.64645 q^{85} +13.0314 q^{86} -2.94149 q^{87} +21.5091 q^{88} -13.3931 q^{89} -2.67506 q^{90} -1.28643 q^{91} -21.1901 q^{92} -1.00000 q^{93} -0.413405 q^{94} +6.87263 q^{95} -15.9436 q^{96} +7.38014 q^{97} +14.2985 q^{98} -2.54775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9} - 3 q^{10} + 5 q^{12} - 9 q^{13} + 11 q^{14} + 9 q^{15} + 9 q^{16} - 5 q^{17} - 3 q^{18} - 12 q^{19} + 5 q^{20} - 5 q^{21} - 17 q^{22} - 21 q^{23} - 18 q^{24} + 9 q^{25} + 3 q^{26} + 9 q^{27} - 8 q^{28} - 15 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} + 9 q^{34} - 5 q^{35} + 5 q^{36} - 13 q^{37} - 24 q^{38} - 9 q^{39} - 18 q^{40} - 11 q^{41} + 11 q^{42} - 26 q^{43} + 5 q^{44} + 9 q^{45} + 14 q^{46} - 21 q^{47} + 9 q^{48} - 26 q^{49} - 3 q^{50} - 5 q^{51} - 5 q^{52} + 18 q^{53} - 3 q^{54} - 19 q^{56} - 12 q^{57} - 16 q^{58} - 24 q^{59} + 5 q^{60} - 4 q^{61} + 3 q^{62} - 5 q^{63} + 2 q^{64} - 9 q^{65} - 17 q^{66} - 20 q^{67} - 19 q^{68} - 21 q^{69} + 11 q^{70} - 13 q^{71} - 18 q^{72} + 15 q^{73} + 12 q^{74} + 9 q^{75} + 54 q^{76} - 28 q^{77} + 3 q^{78} - 15 q^{79} + 9 q^{80} + 9 q^{81} - 21 q^{82} - 5 q^{83} - 8 q^{84} - 5 q^{85} + 36 q^{86} - 15 q^{87} + 23 q^{88} + 31 q^{89} - 3 q^{90} + 5 q^{91} - 7 q^{92} - 9 q^{93} - 12 q^{95} - 9 q^{96} - 11 q^{97} - 23 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9 - 3 * q^10 + 5 * q^12 - 9 * q^13 + 11 * q^14 + 9 * q^15 + 9 * q^16 - 5 * q^17 - 3 * q^18 - 12 * q^19 + 5 * q^20 - 5 * q^21 - 17 * q^22 - 21 * q^23 - 18 * q^24 + 9 * q^25 + 3 * q^26 + 9 * q^27 - 8 * q^28 - 15 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 + 9 * q^34 - 5 * q^35 + 5 * q^36 - 13 * q^37 - 24 * q^38 - 9 * q^39 - 18 * q^40 - 11 * q^41 + 11 * q^42 - 26 * q^43 + 5 * q^44 + 9 * q^45 + 14 * q^46 - 21 * q^47 + 9 * q^48 - 26 * q^49 - 3 * q^50 - 5 * q^51 - 5 * q^52 + 18 * q^53 - 3 * q^54 - 19 * q^56 - 12 * q^57 - 16 * q^58 - 24 * q^59 + 5 * q^60 - 4 * q^61 + 3 * q^62 - 5 * q^63 + 2 * q^64 - 9 * q^65 - 17 * q^66 - 20 * q^67 - 19 * q^68 - 21 * q^69 + 11 * q^70 - 13 * q^71 - 18 * q^72 + 15 * q^73 + 12 * q^74 + 9 * q^75 + 54 * q^76 - 28 * q^77 + 3 * q^78 - 15 * q^79 + 9 * q^80 + 9 * q^81 - 21 * q^82 - 5 * q^83 - 8 * q^84 - 5 * q^85 + 36 * q^86 - 15 * q^87 + 23 * q^88 + 31 * q^89 - 3 * q^90 + 5 * q^91 - 7 * q^92 - 9 * q^93 - 12 * q^95 - 9 * q^96 - 11 * q^97 - 23 * q^98

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