LMFDB - Embedded newform 6009.2.a.d.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.26328 q^{2} -1.00000 q^{3} +3.12245 q^{4} +3.34447 q^{5} +2.26328 q^{6} -1.47338 q^{7} -2.54043 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.26328 q^{2} -1.00000 q^{3} +3.12245 q^{4} +3.34447 q^{5} +2.26328 q^{6} -1.47338 q^{7} -2.54043 q^{8} +1.00000 q^{9} -7.56947 q^{10} +4.92962 q^{11} -3.12245 q^{12} -5.83705 q^{13} +3.33468 q^{14} -3.34447 q^{15} -0.495193 q^{16} -1.24322 q^{17} -2.26328 q^{18} +1.97603 q^{19} +10.4429 q^{20} +1.47338 q^{21} -11.1571 q^{22} -1.72326 q^{23} +2.54043 q^{24} +6.18545 q^{25} +13.2109 q^{26} -1.00000 q^{27} -4.60057 q^{28} +3.34169 q^{29} +7.56947 q^{30} -5.76008 q^{31} +6.20162 q^{32} -4.92962 q^{33} +2.81375 q^{34} -4.92768 q^{35} +3.12245 q^{36} -7.22061 q^{37} -4.47231 q^{38} +5.83705 q^{39} -8.49638 q^{40} +3.20882 q^{41} -3.33468 q^{42} -8.29945 q^{43} +15.3925 q^{44} +3.34447 q^{45} +3.90023 q^{46} -1.73358 q^{47} +0.495193 q^{48} -4.82914 q^{49} -13.9994 q^{50} +1.24322 q^{51} -18.2259 q^{52} -5.89753 q^{53} +2.26328 q^{54} +16.4869 q^{55} +3.74303 q^{56} -1.97603 q^{57} -7.56319 q^{58} +0.137770 q^{59} -10.4429 q^{60} +8.78137 q^{61} +13.0367 q^{62} -1.47338 q^{63} -13.0456 q^{64} -19.5218 q^{65} +11.1571 q^{66} +14.2826 q^{67} -3.88189 q^{68} +1.72326 q^{69} +11.1527 q^{70} +4.58262 q^{71} -2.54043 q^{72} +6.71170 q^{73} +16.3423 q^{74} -6.18545 q^{75} +6.17005 q^{76} -7.26321 q^{77} -13.2109 q^{78} +1.84943 q^{79} -1.65616 q^{80} +1.00000 q^{81} -7.26246 q^{82} -8.25180 q^{83} +4.60057 q^{84} -4.15790 q^{85} +18.7840 q^{86} -3.34169 q^{87} -12.5233 q^{88} +14.2361 q^{89} -7.56947 q^{90} +8.60021 q^{91} -5.38081 q^{92} +5.76008 q^{93} +3.92359 q^{94} +6.60875 q^{95} -6.20162 q^{96} -4.73060 q^{97} +10.9297 q^{98} +4.92962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26328	−1.60038	−0.800192	−	0.599744i	$-0.795269\pi$
$2$	−2.26328	−1.60038	−0.800192	+	0.599744i	$0.795269\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.12245	1.56123
$5$	3.34447	1.49569	0.747845	−	0.663873i	$-0.231089\pi$
$5$	3.34447	1.49569	0.747845	+	0.663873i	$0.231089\pi$
$6$	2.26328	0.923982
$7$	−1.47338	−0.556886	−0.278443	−	0.960453i	$-0.589818\pi$
$7$	−1.47338	−0.556886	−0.278443	+	0.960453i	$0.589818\pi$
$8$	−2.54043	−0.898178
$9$	1.00000	0.333333
$10$	−7.56947	−2.39368
$11$	4.92962	1.48634	0.743168	−	0.669105i	$-0.233322\pi$
$11$	4.92962	1.48634	0.743168	+	0.669105i	$0.233322\pi$
$12$	−3.12245	−0.901375
$13$	−5.83705	−1.61891	−0.809454	−	0.587184i	$-0.800237\pi$
$13$	−5.83705	−1.61891	−0.809454	+	0.587184i	$0.800237\pi$
$14$	3.33468	0.891232
$15$	−3.34447	−0.863537
$16$	−0.495193	−0.123798
$17$	−1.24322	−0.301524	−0.150762	−	0.988570i	$-0.548173\pi$
$17$	−1.24322	−0.301524	−0.150762	+	0.988570i	$0.548173\pi$
$18$	−2.26328	−0.533461
$19$	1.97603	0.453332	0.226666	−	0.973973i	$-0.427217\pi$
$19$	1.97603	0.453332	0.226666	+	0.973973i	$0.427217\pi$
$20$	10.4429	2.33511
$21$	1.47338	0.321519
$22$	−11.1571	−2.37871
$23$	−1.72326	−0.359325	−0.179663	−	0.983728i	$-0.557501\pi$
$23$	−1.72326	−0.359325	−0.179663	+	0.983728i	$0.557501\pi$
$24$	2.54043	0.518563
$25$	6.18545	1.23709
$26$	13.2109	2.59087
$27$	−1.00000	−0.192450
$28$	−4.60057	−0.869426
$29$	3.34169	0.620536	0.310268	−	0.950649i	$-0.399581\pi$
$29$	3.34169	0.620536	0.310268	+	0.950649i	$0.399581\pi$
$30$	7.56947	1.38199
$31$	−5.76008	−1.03454	−0.517271	−	0.855822i	$-0.673052\pi$
$31$	−5.76008	−1.03454	−0.517271	+	0.855822i	$0.673052\pi$
$32$	6.20162	1.09630
$33$	−4.92962	−0.858136
$34$	2.81375	0.482555
$35$	−4.92768	−0.832930
$36$	3.12245	0.520409
$37$	−7.22061	−1.18706	−0.593531	−	0.804811i	$-0.702266\pi$
$37$	−7.22061	−1.18706	−0.593531	+	0.804811i	$0.702266\pi$
$38$	−4.47231	−0.725504
$39$	5.83705	0.934676
$40$	−8.49638	−1.34340
$41$	3.20882	0.501133	0.250567	−	0.968099i	$-0.419383\pi$
$41$	3.20882	0.501133	0.250567	+	0.968099i	$0.419383\pi$
$42$	−3.33468	−0.514553
$43$	−8.29945	−1.26565	−0.632827	−	0.774293i	$-0.718106\pi$
$43$	−8.29945	−1.26565	−0.632827	+	0.774293i	$0.718106\pi$
$44$	15.3925	2.32051
$45$	3.34447	0.498563
$46$	3.90023	0.575058
$47$	−1.73358	−0.252869	−0.126434	−	0.991975i	$-0.540353\pi$
$47$	−1.73358	−0.252869	−0.126434	+	0.991975i	$0.540353\pi$
$48$	0.495193	0.0714749
$49$	−4.82914	−0.689877
$50$	−13.9994	−1.97982
$51$	1.24322	0.174085
$52$	−18.2259	−2.52748
$53$	−5.89753	−0.810089	−0.405044	−	0.914297i	$-0.632744\pi$
$53$	−5.89753	−0.810089	−0.405044	+	0.914297i	$0.632744\pi$
$54$	2.26328	0.307994
$55$	16.4869	2.22310
$56$	3.74303	0.500183
$57$	−1.97603	−0.261731
$58$	−7.56319	−0.993095
$59$	0.137770	0.0179361	0.00896804	−	0.999960i	$-0.497145\pi$
$59$	0.137770	0.0179361	0.00896804	+	0.999960i	$0.497145\pi$
$60$	−10.4429	−1.34818
$61$	8.78137	1.12434	0.562170	−	0.827022i	$-0.309967\pi$
$61$	8.78137	1.12434	0.562170	+	0.827022i	$0.309967\pi$
$62$	13.0367	1.65566
$63$	−1.47338	−0.185629
$64$	−13.0456	−1.63071
$65$	−19.5218	−2.42138
$66$	11.1571	1.37335
$67$	14.2826	1.74490	0.872451	−	0.488702i	$-0.162529\pi$
$67$	14.2826	1.74490	0.872451	+	0.488702i	$0.162529\pi$
$68$	−3.88189	−0.470748
$69$	1.72326	0.207456
$70$	11.1527	1.33301
$71$	4.58262	0.543857	0.271929	−	0.962317i	$-0.412339\pi$
$71$	4.58262	0.543857	0.271929	+	0.962317i	$0.412339\pi$
$72$	−2.54043	−0.299393
$73$	6.71170	0.785545	0.392773	−	0.919636i	$-0.371516\pi$
$73$	6.71170	0.785545	0.392773	+	0.919636i	$0.371516\pi$
$74$	16.3423	1.89975
$75$	−6.18545	−0.714234
$76$	6.17005	0.707753
$77$	−7.26321	−0.827720
$78$	−13.2109	−1.49584
$79$	1.84943	0.208077	0.104038	−	0.994573i	$-0.466823\pi$
$79$	1.84943	0.208077	0.104038	+	0.994573i	$0.466823\pi$
$80$	−1.65616	−0.185164
$81$	1.00000	0.111111
$82$	−7.26246	−0.802005
$83$	−8.25180	−0.905752	−0.452876	−	0.891573i	$-0.649602\pi$
$83$	−8.25180	−0.905752	−0.452876	+	0.891573i	$0.649602\pi$
$84$	4.60057	0.501963
$85$	−4.15790	−0.450987
$86$	18.7840	2.02553
$87$	−3.34169	−0.358267
$88$	−12.5233	−1.33499
$89$	14.2361	1.50902	0.754510	−	0.656289i	$-0.227875\pi$
$89$	14.2361	1.50902	0.754510	+	0.656289i	$0.227875\pi$
$90$	−7.56947	−0.797893
$91$	8.60021	0.901547
$92$	−5.38081	−0.560988
$93$	5.76008	0.597293
$94$	3.92359	0.404687
$95$	6.60875	0.678044
$96$	−6.20162	−0.632950
$97$	−4.73060	−0.480319	−0.240160	−	0.970733i	$-0.577200\pi$
$97$	−4.73060	−0.480319	−0.240160	+	0.970733i	$0.577200\pi$
$98$	10.9297	1.10407
$99$	4.92962	0.495445
$100$	19.3138	1.93138
$101$	−1.89808	−0.188866	−0.0944331	−	0.995531i	$-0.530104\pi$
$101$	−1.89808	−0.188866	−0.0944331	+	0.995531i	$0.530104\pi$
$102$	−2.81375	−0.278603
$103$	14.1624	1.39546	0.697729	−	0.716362i	$-0.254194\pi$
$103$	14.1624	1.39546	0.697729	+	0.716362i	$0.254194\pi$
$104$	14.8286	1.45407
$105$	4.92768	0.480892
$106$	13.3478	1.29645
$107$	11.7232	1.13333	0.566664	−	0.823949i	$-0.308234\pi$
$107$	11.7232	1.13333	0.566664	+	0.823949i	$0.308234\pi$
$108$	−3.12245	−0.300458
$109$	14.7905	1.41668	0.708339	−	0.705873i	$-0.249445\pi$
$109$	14.7905	1.41668	0.708339	+	0.705873i	$0.249445\pi$
$110$	−37.3146	−3.55781
$111$	7.22061	0.685350
$112$	0.729609	0.0689416
$113$	8.68514	0.817029	0.408514	−	0.912752i	$-0.366047\pi$
$113$	8.68514	0.817029	0.408514	+	0.912752i	$0.366047\pi$
$114$	4.47231	0.418870
$115$	−5.76339	−0.537439
$116$	10.4343	0.968797
$117$	−5.83705	−0.539636
$118$	−0.311812	−0.0287046
$119$	1.83173	0.167915
$120$	8.49638	0.775610
$121$	13.3011	1.20919
$122$	−19.8747	−1.79937
$123$	−3.20882	−0.289329
$124$	−17.9856	−1.61515
$125$	3.96469	0.354613
$126$	3.33468	0.297077
$127$	5.44700	0.483343	0.241671	−	0.970358i	$-0.422304\pi$
$127$	5.44700	0.483343	0.241671	+	0.970358i	$0.422304\pi$
$128$	17.1227	1.51345
$129$	8.29945	0.730726
$130$	44.1834	3.87514
$131$	−1.69961	−0.148495	−0.0742476	−	0.997240i	$-0.523656\pi$
$131$	−1.69961	−0.148495	−0.0742476	+	0.997240i	$0.523656\pi$
$132$	−15.3925	−1.33974
$133$	−2.91144	−0.252454
$134$	−32.3257	−2.79251
$135$	−3.34447	−0.287846
$136$	3.15831	0.270822
$137$	11.8312	1.01081	0.505403	−	0.862884i	$-0.331344\pi$
$137$	11.8312	1.01081	0.505403	+	0.862884i	$0.331344\pi$
$138$	−3.90023	−0.332010
$139$	−20.6755	−1.75368	−0.876838	−	0.480787i	$-0.840351\pi$
$139$	−20.6755	−1.75368	−0.876838	+	0.480787i	$0.840351\pi$
$140$	−15.3864	−1.30039
$141$	1.73358	0.145994
$142$	−10.3718	−0.870380
$143$	−28.7744	−2.40624
$144$	−0.495193	−0.0412661
$145$	11.1762	0.928130
$146$	−15.1905	−1.25717
$147$	4.82914	0.398301
$148$	−22.5460	−1.85327
$149$	16.7362	1.37108	0.685542	−	0.728034i	$-0.259565\pi$
$149$	16.7362	1.37108	0.685542	+	0.728034i	$0.259565\pi$
$150$	13.9994	1.14305
$151$	11.1093	0.904060	0.452030	−	0.892003i	$-0.350700\pi$
$151$	11.1093	0.904060	0.452030	+	0.892003i	$0.350700\pi$
$152$	−5.01996	−0.407172
$153$	−1.24322	−0.100508
$154$	16.4387	1.32467
$155$	−19.2644	−1.54735
$156$	18.2259	1.45924
$157$	−0.0914859	−0.00730137	−0.00365069	−	0.999993i	$-0.501162\pi$
$157$	−0.0914859	−0.00730137	−0.00365069	+	0.999993i	$0.501162\pi$
$158$	−4.18578	−0.333003
$159$	5.89753	0.467705
$160$	20.7411	1.63973
$161$	2.53903	0.200103
$162$	−2.26328	−0.177820
$163$	13.4183	1.05100	0.525500	−	0.850794i	$-0.323878\pi$
$163$	13.4183	1.05100	0.525500	+	0.850794i	$0.323878\pi$
$164$	10.0194	0.782382
$165$	−16.4869	−1.28351
$166$	18.6762	1.44955
$167$	19.3379	1.49641	0.748207	−	0.663466i	$-0.230915\pi$
$167$	19.3379	1.49641	0.748207	+	0.663466i	$0.230915\pi$
$168$	−3.74303	−0.288781
$169$	21.0712	1.62086
$170$	9.41050	0.721752
$171$	1.97603	0.151111
$172$	−25.9146	−1.97597
$173$	14.7274	1.11971	0.559853	−	0.828592i	$-0.310858\pi$
$173$	14.7274	1.11971	0.559853	+	0.828592i	$0.310858\pi$
$174$	7.56319	0.573364
$175$	−9.11354	−0.688919
$176$	−2.44111	−0.184006
$177$	−0.137770	−0.0103554
$178$	−32.2202	−2.41501
$179$	−15.0238	−1.12293	−0.561464	−	0.827501i	$-0.689762\pi$
$179$	−15.0238	−1.12293	−0.561464	+	0.827501i	$0.689762\pi$
$180$	10.4429	0.778370
$181$	16.7605	1.24580	0.622898	−	0.782303i	$-0.285955\pi$
$181$	16.7605	1.24580	0.622898	+	0.782303i	$0.285955\pi$
$182$	−19.4647	−1.44282
$183$	−8.78137	−0.649138
$184$	4.37783	0.322738
$185$	−24.1491	−1.77548
$186$	−13.0367	−0.955897
$187$	−6.12858	−0.448166
$188$	−5.41303	−0.394786
$189$	1.47338	0.107173
$190$	−14.9575	−1.08513
$191$	−0.969424	−0.0701450	−0.0350725	−	0.999385i	$-0.511166\pi$
$191$	−0.969424	−0.0701450	−0.0350725	+	0.999385i	$0.511166\pi$
$192$	13.0456	0.941488
$193$	−10.2351	−0.736742	−0.368371	−	0.929679i	$-0.620084\pi$
$193$	−10.2351	−0.736742	−0.368371	+	0.929679i	$0.620084\pi$
$194$	10.7067	0.768695
$195$	19.5218	1.39799
$196$	−15.0788	−1.07705
$197$	−25.3281	−1.80455	−0.902275	−	0.431162i	$-0.858104\pi$
$197$	−25.3281	−1.80455	−0.902275	+	0.431162i	$0.858104\pi$
$198$	−11.1571	−0.792902
$199$	16.9202	1.19944	0.599720	−	0.800210i	$-0.295279\pi$
$199$	16.9202	1.19944	0.599720	+	0.800210i	$0.295279\pi$
$200$	−15.7137	−1.11113
$201$	−14.2826	−1.00742
$202$	4.29590	0.302258
$203$	−4.92359	−0.345568
$204$	3.88189	0.271786
$205$	10.7318	0.749540
$206$	−32.0534	−2.23327
$207$	−1.72326	−0.119775
$208$	2.89047	0.200418
$209$	9.74105	0.673803
$210$	−11.1527	−0.769612
$211$	21.0468	1.44892	0.724462	−	0.689315i	$-0.242088\pi$
$211$	21.0468	1.44892	0.724462	+	0.689315i	$0.242088\pi$
$212$	−18.4148	−1.26473
$213$	−4.58262	−0.313996
$214$	−26.5330	−1.81376
$215$	−27.7572	−1.89303
$216$	2.54043	0.172854
$217$	8.48681	0.576122
$218$	−33.4752	−2.26723
$219$	−6.71170	−0.453535
$220$	51.4797	3.47076
$221$	7.25672	0.488140
$222$	−16.3423	−1.09682
$223$	−8.23412	−0.551398	−0.275699	−	0.961244i	$-0.588909\pi$
$223$	−8.23412	−0.551398	−0.275699	+	0.961244i	$0.588909\pi$
$224$	−9.13736	−0.610516
$225$	6.18545	0.412363
$226$	−19.6569	−1.30756
$227$	17.8966	1.18784	0.593921	−	0.804524i	$-0.297579\pi$
$227$	17.8966	1.18784	0.593921	+	0.804524i	$0.297579\pi$
$228$	−6.17005	−0.408622
$229$	−15.0850	−0.996843	−0.498422	−	0.866935i	$-0.666087\pi$
$229$	−15.0850	−0.996843	−0.498422	+	0.866935i	$0.666087\pi$
$230$	13.0442	0.860108
$231$	7.26321	0.477884
$232$	−8.48932	−0.557351
$233$	−30.1432	−1.97474	−0.987372	−	0.158420i	$-0.949360\pi$
$233$	−30.1432	−1.97474	−0.987372	+	0.158420i	$0.949360\pi$
$234$	13.2109	0.863624
$235$	−5.79790	−0.378214
$236$	0.430179	0.0280023
$237$	−1.84943	−0.120133
$238$	−4.14574	−0.268728
$239$	12.5378	0.811003	0.405501	−	0.914094i	$-0.367097\pi$
$239$	12.5378	0.811003	0.405501	+	0.914094i	$0.367097\pi$
$240$	1.65616	0.106904
$241$	−19.5998	−1.26254	−0.631268	−	0.775565i	$-0.717465\pi$
$241$	−19.5998	−1.26254	−0.631268	+	0.775565i	$0.717465\pi$
$242$	−30.1042	−1.93517
$243$	−1.00000	−0.0641500
$244$	27.4194	1.75535
$245$	−16.1509	−1.03184
$246$	7.26246	0.463038
$247$	−11.5342	−0.733902
$248$	14.6331	0.929202
$249$	8.25180	0.522936
$250$	−8.97322	−0.567516
$251$	8.90936	0.562354	0.281177	−	0.959656i	$-0.409275\pi$
$251$	8.90936	0.562354	0.281177	+	0.959656i	$0.409275\pi$
$252$	−4.60057	−0.289809
$253$	−8.49502	−0.534078
$254$	−12.3281	−0.773534
$255$	4.15790	0.260378
$256$	−12.6624	−0.791397
$257$	6.17563	0.385225	0.192613	−	0.981275i	$-0.438304\pi$
$257$	6.17563	0.385225	0.192613	+	0.981275i	$0.438304\pi$
$258$	−18.7840	−1.16944
$259$	10.6387	0.661058
$260$	−60.9560	−3.78033
$261$	3.34169	0.206845
$262$	3.84669	0.237649
$263$	21.1105	1.30173	0.650863	−	0.759195i	$-0.274407\pi$
$263$	21.1105	1.30173	0.650863	+	0.759195i	$0.274407\pi$
$264$	12.5233	0.770759
$265$	−19.7241	−1.21164
$266$	6.58942	0.404024
$267$	−14.2361	−0.871233
$268$	44.5969	2.72419
$269$	−29.0768	−1.77285	−0.886423	−	0.462876i	$-0.846817\pi$
$269$	−29.0768	−1.77285	−0.886423	+	0.462876i	$0.846817\pi$
$270$	7.56947	0.460664
$271$	−18.2436	−1.10822	−0.554111	−	0.832443i	$-0.686942\pi$
$271$	−18.2436	−1.10822	−0.554111	+	0.832443i	$0.686942\pi$
$272$	0.615632	0.0373282
$273$	−8.60021	−0.520509
$274$	−26.7773	−1.61768
$275$	30.4919	1.83873
$276$	5.38081	0.323886
$277$	11.5226	0.692327	0.346164	−	0.938174i	$-0.387484\pi$
$277$	11.5226	0.692327	0.346164	+	0.938174i	$0.387484\pi$
$278$	46.7946	2.80655
$279$	−5.76008	−0.344847
$280$	12.5184	0.748119
$281$	25.6600	1.53075	0.765374	−	0.643586i	$-0.222554\pi$
$281$	25.6600	1.53075	0.765374	+	0.643586i	$0.222554\pi$
$282$	−3.92359	−0.233646
$283$	14.4229	0.857351	0.428675	−	0.903459i	$-0.358980\pi$
$283$	14.4229	0.857351	0.428675	+	0.903459i	$0.358980\pi$
$284$	14.3090	0.849084
$285$	−6.60875	−0.391469
$286$	65.1247	3.85090
$287$	−4.72782	−0.279074
$288$	6.20162	0.365434
$289$	−15.4544	−0.909083
$290$	−25.2948	−1.48536
$291$	4.73060	0.277312
$292$	20.9570	1.22641
$293$	8.62350	0.503790	0.251895	−	0.967755i	$-0.418946\pi$
$293$	8.62350	0.503790	0.251895	+	0.967755i	$0.418946\pi$
$294$	−10.9297	−0.637434
$295$	0.460766	0.0268268
$296$	18.3435	1.06619
$297$	−4.92962	−0.286045
$298$	−37.8788	−2.19426
$299$	10.0588	0.581714
$300$	−19.3138	−1.11508
$301$	12.2283	0.704826
$302$	−25.1434	−1.44684
$303$	1.89808	0.109042
$304$	−0.978514	−0.0561217
$305$	29.3690	1.68166
$306$	2.81375	0.160852
$307$	3.07514	0.175508	0.0877538	−	0.996142i	$-0.472031\pi$
$307$	3.07514	0.175508	0.0877538	+	0.996142i	$0.472031\pi$
$308$	−22.6790	−1.29226
$309$	−14.1624	−0.805668
$310$	43.6008	2.47636
$311$	−30.8141	−1.74730	−0.873652	−	0.486551i	$-0.838255\pi$
$311$	−30.8141	−1.74730	−0.873652	+	0.486551i	$0.838255\pi$
$312$	−14.8286	−0.839505
$313$	9.89152	0.559102	0.279551	−	0.960131i	$-0.409814\pi$
$313$	9.89152	0.559102	0.279551	+	0.960131i	$0.409814\pi$
$314$	0.207059	0.0116850
$315$	−4.92768	−0.277643
$316$	5.77475	0.324855
$317$	3.88497	0.218202	0.109101	−	0.994031i	$-0.465203\pi$
$317$	3.88497	0.218202	0.109101	+	0.994031i	$0.465203\pi$
$318$	−13.3478	−0.748507
$319$	16.4732	0.922324
$320$	−43.6307	−2.43903
$321$	−11.7232	−0.654327
$322$	−5.74654	−0.320242
$323$	−2.45663	−0.136691
$324$	3.12245	0.173470
$325$	−36.1048	−2.00273
$326$	−30.3694	−1.68200
$327$	−14.7905	−0.817919
$328$	−8.15178	−0.450107
$329$	2.55423	0.140819
$330$	37.3146	2.05410
$331$	−1.43152	−0.0786834	−0.0393417	−	0.999226i	$-0.512526\pi$
$331$	−1.43152	−0.0786834	−0.0393417	+	0.999226i	$0.512526\pi$
$332$	−25.7658	−1.41408
$333$	−7.22061	−0.395687
$334$	−43.7672	−2.39483
$335$	47.7678	2.60983
$336$	−0.729609	−0.0398034
$337$	−19.3199	−1.05242	−0.526210	−	0.850355i	$-0.676387\pi$
$337$	−19.3199	−1.05242	−0.526210	+	0.850355i	$0.676387\pi$
$338$	−47.6901	−2.59400
$339$	−8.68514	−0.471712
$340$	−12.9828	−0.704093
$341$	−28.3950	−1.53768
$342$	−4.47231	−0.241835
$343$	17.4289	0.941070
$344$	21.0842	1.13678
$345$	5.76339	0.310291
$346$	−33.3324	−1.79196
$347$	−8.97280	−0.481685	−0.240843	−	0.970564i	$-0.577424\pi$
$347$	−8.97280	−0.481685	−0.240843	+	0.970564i	$0.577424\pi$
$348$	−10.4343	−0.559335
$349$	−12.7482	−0.682397	−0.341199	−	0.939991i	$-0.610833\pi$
$349$	−12.7482	−0.682397	−0.341199	+	0.939991i	$0.610833\pi$
$350$	20.6265	1.10253
$351$	5.83705	0.311559
$352$	30.5716	1.62947
$353$	−12.5960	−0.670420	−0.335210	−	0.942143i	$-0.608807\pi$
$353$	−12.5960	−0.670420	−0.335210	+	0.942143i	$0.608807\pi$
$354$	0.311812	0.0165726
$355$	15.3264	0.813442
$356$	44.4514	2.35592
$357$	−1.83173	−0.0969457
$358$	34.0030	1.79711
$359$	34.6800	1.83034	0.915170	−	0.403069i	$-0.132057\pi$
$359$	34.6800	1.83034	0.915170	+	0.403069i	$0.132057\pi$
$360$	−8.49638	−0.447799
$361$	−15.0953	−0.794490
$362$	−37.9337	−1.99375
$363$	−13.3011	−0.698128
$364$	26.8538	1.40752
$365$	22.4470	1.17493
$366$	19.8747	1.03887
$367$	21.3397	1.11392	0.556962	−	0.830538i	$-0.311967\pi$
$367$	21.3397	1.11392	0.556962	+	0.830538i	$0.311967\pi$
$368$	0.853347	0.0444838
$369$	3.20882	0.167044
$370$	54.6562	2.84144
$371$	8.68933	0.451127
$372$	17.9856	0.932509
$373$	8.30806	0.430175	0.215088	−	0.976595i	$-0.430996\pi$
$373$	8.30806	0.430175	0.215088	+	0.976595i	$0.430996\pi$
$374$	13.8707	0.717238
$375$	−3.96469	−0.204736
$376$	4.40404	0.227121
$377$	−19.5056	−1.00459
$378$	−3.33468	−0.171518
$379$	19.3031	0.991531	0.495766	−	0.868456i	$-0.334887\pi$
$379$	19.3031	0.991531	0.495766	+	0.868456i	$0.334887\pi$
$380$	20.6355	1.05858
$381$	−5.44700	−0.279058
$382$	2.19408	0.112259
$383$	18.2477	0.932416	0.466208	−	0.884675i	$-0.345620\pi$
$383$	18.2477	0.932416	0.466208	+	0.884675i	$0.345620\pi$
$384$	−17.1227	−0.873792
$385$	−24.2916	−1.23801
$386$	23.1650	1.17907
$387$	−8.29945	−0.421885
$388$	−14.7711	−0.749887
$389$	−2.44467	−0.123950	−0.0619749	−	0.998078i	$-0.519740\pi$
$389$	−2.44467	−0.123950	−0.0619749	+	0.998078i	$0.519740\pi$
$390$	−44.1834	−2.23731
$391$	2.14239	0.108345
$392$	12.2681	0.619632
$393$	1.69961	0.0857338
$394$	57.3246	2.88797
$395$	6.18535	0.311219
$396$	15.3925	0.773502
$397$	−5.41303	−0.271672	−0.135836	−	0.990731i	$-0.543372\pi$
$397$	−5.41303	−0.271672	−0.135836	+	0.990731i	$0.543372\pi$
$398$	−38.2951	−1.91956
$399$	2.91144	0.145755
$400$	−3.06299	−0.153150
$401$	−7.97718	−0.398361	−0.199181	−	0.979963i	$-0.563828\pi$
$401$	−7.97718	−0.398361	−0.199181	+	0.979963i	$0.563828\pi$
$402$	32.3257	1.61226
$403$	33.6219	1.67483
$404$	−5.92667	−0.294863
$405$	3.34447	0.166188
$406$	11.1435	0.553041
$407$	−35.5948	−1.76437
$408$	−3.15831	−0.156359
$409$	33.8438	1.67347	0.836735	−	0.547608i	$-0.184462\pi$
$409$	33.8438	1.67347	0.836735	+	0.547608i	$0.184462\pi$
$410$	−24.2891	−1.19955
$411$	−11.8312	−0.583589
$412$	44.2213	2.17863
$413$	−0.202987	−0.00998836
$414$	3.90023	0.191686
$415$	−27.5978	−1.35473
$416$	−36.1992	−1.77481
$417$	20.6755	1.01248
$418$	−22.0468	−1.07834
$419$	−31.3472	−1.53141	−0.765704	−	0.643193i	$-0.777609\pi$
$419$	−31.3472	−1.53141	−0.765704	+	0.643193i	$0.777609\pi$
$420$	15.3864	0.750782
$421$	−22.7440	−1.10847	−0.554237	−	0.832359i	$-0.686990\pi$
$421$	−22.7440	−1.10847	−0.554237	+	0.832359i	$0.686990\pi$
$422$	−47.6349	−2.31883
$423$	−1.73358	−0.0842896
$424$	14.9823	0.727603
$425$	−7.68985	−0.373013
$426$	10.3718	0.502514
$427$	−12.9383	−0.626129
$428$	36.6052	1.76938
$429$	28.7744	1.38924
$430$	62.8225	3.02957
$431$	−5.46332	−0.263159	−0.131580	−	0.991306i	$-0.542005\pi$
$431$	−5.46332	−0.263159	−0.131580	+	0.991306i	$0.542005\pi$
$432$	0.495193	0.0238250
$433$	−7.71986	−0.370993	−0.185496	−	0.982645i	$-0.559389\pi$
$433$	−7.71986	−0.370993	−0.185496	+	0.982645i	$0.559389\pi$
$434$	−19.2081	−0.922016
$435$	−11.1762	−0.535856
$436$	46.1828	2.21175
$437$	−3.40521	−0.162893
$438$	15.1905	0.725829
$439$	18.5177	0.883800	0.441900	−	0.897064i	$-0.354305\pi$
$439$	18.5177	0.883800	0.441900	+	0.897064i	$0.354305\pi$
$440$	−41.8839	−1.99674
$441$	−4.82914	−0.229959
$442$	−16.4240	−0.781211
$443$	24.1678	1.14825	0.574123	−	0.818769i	$-0.305343\pi$
$443$	24.1678	1.14825	0.574123	+	0.818769i	$0.305343\pi$
$444$	22.5460	1.06999
$445$	47.6120	2.25703
$446$	18.6362	0.882448
$447$	−16.7362	−0.791595
$448$	19.2212	0.908118
$449$	−11.1483	−0.526119	−0.263060	−	0.964780i	$-0.584732\pi$
$449$	−11.1483	−0.526119	−0.263060	+	0.964780i	$0.584732\pi$
$450$	−13.9994	−0.659939
$451$	15.8182	0.744852
$452$	27.1189	1.27557
$453$	−11.1093	−0.521959
$454$	−40.5052	−1.90100
$455$	28.7631	1.34844
$456$	5.01996	0.235081
$457$	2.17213	0.101608	0.0508039	−	0.998709i	$-0.483822\pi$
$457$	2.17213	0.101608	0.0508039	+	0.998709i	$0.483822\pi$
$458$	34.1416	1.59533
$459$	1.24322	0.0580284
$460$	−17.9959	−0.839064
$461$	−12.7656	−0.594552	−0.297276	−	0.954792i	$-0.596078\pi$
$461$	−12.7656	−0.594552	−0.297276	+	0.954792i	$0.596078\pi$
$462$	−16.4387	−0.764798
$463$	−22.6682	−1.05348	−0.526740	−	0.850027i	$-0.676586\pi$
$463$	−22.6682	−1.05348	−0.526740	+	0.850027i	$0.676586\pi$
$464$	−1.65478	−0.0768213
$465$	19.2644	0.893365
$466$	68.2225	3.16035
$467$	−2.07022	−0.0957982	−0.0478991	−	0.998852i	$-0.515253\pi$
$467$	−2.07022	−0.0957982	−0.0478991	+	0.998852i	$0.515253\pi$
$468$	−18.2259	−0.842494
$469$	−21.0438	−0.971712
$470$	13.1223	0.605287
$471$	0.0914859	0.00421545
$472$	−0.349994	−0.0161098
$473$	−40.9131	−1.88119
$474$	4.18578	0.192259
$475$	12.2226	0.560812
$476$	5.71951	0.262153
$477$	−5.89753	−0.270030
$478$	−28.3766	−1.29792
$479$	19.0388	0.869904	0.434952	−	0.900454i	$-0.356765\pi$
$479$	19.0388	0.869904	0.434952	+	0.900454i	$0.356765\pi$
$480$	−20.7411	−0.946698
$481$	42.1471	1.92174
$482$	44.3600	2.02054
$483$	−2.53903	−0.115530
$484$	41.5321	1.88782
$485$	−15.8213	−0.718409
$486$	2.26328	0.102665
$487$	−5.16621	−0.234103	−0.117052	−	0.993126i	$-0.537344\pi$
$487$	−5.16621	−0.234103	−0.117052	+	0.993126i	$0.537344\pi$
$488$	−22.3085	−1.00986
$489$	−13.4183	−0.606795
$490$	36.5541	1.65134
$491$	−9.88448	−0.446080	−0.223040	−	0.974809i	$-0.571598\pi$
$491$	−9.88448	−0.446080	−0.223040	+	0.974809i	$0.571598\pi$
$492$	−10.0194	−0.451709
$493$	−4.15444	−0.187107
$494$	26.1051	1.17452
$495$	16.4869	0.741033
$496$	2.85235	0.128074
$497$	−6.75196	−0.302867
$498$	−18.6762	−0.836899
$499$	15.1509	0.678245	0.339123	−	0.940742i	$-0.389870\pi$
$499$	15.1509	0.678245	0.339123	+	0.940742i	$0.389870\pi$
$500$	12.3796	0.553631
$501$	−19.3379	−0.863955
$502$	−20.1644	−0.899981
$503$	−10.5095	−0.468597	−0.234299	−	0.972165i	$-0.575279\pi$
$503$	−10.5095	−0.468597	−0.234299	+	0.972165i	$0.575279\pi$
$504$	3.74303	0.166728
$505$	−6.34807	−0.282485
$506$	19.2266	0.854729
$507$	−21.0712	−0.935804
$508$	17.0080	0.754608
$509$	15.0314	0.666257	0.333128	−	0.942882i	$-0.391896\pi$
$509$	15.0314	0.666257	0.333128	+	0.942882i	$0.391896\pi$
$510$	−9.41050	−0.416704
$511$	−9.88891	−0.437459
$512$	−5.58701	−0.246913
$513$	−1.97603	−0.0872437
$514$	−13.9772	−0.616508
$515$	47.3655	2.08717
$516$	25.9146	1.14083
$517$	−8.54589	−0.375848
$518$	−24.0785	−1.05795
$519$	−14.7274	−0.646463
$520$	49.5938	2.17483
$521$	8.64826	0.378887	0.189443	−	0.981892i	$-0.439332\pi$
$521$	8.64826	0.378887	0.189443	+	0.981892i	$0.439332\pi$
$522$	−7.56319	−0.331032
$523$	−41.9969	−1.83640	−0.918199	−	0.396120i	$-0.870356\pi$
$523$	−41.9969	−1.83640	−0.918199	+	0.396120i	$0.870356\pi$
$524$	−5.30694	−0.231835
$525$	9.11354	0.397747
$526$	−47.7790	−2.08326
$527$	7.16103	0.311940
$528$	2.44111	0.106236
$529$	−20.0304	−0.870886
$530$	44.6412	1.93909
$531$	0.137770	0.00597869
$532$	−9.09085	−0.394138
$533$	−18.7300	−0.811288
$534$	32.2202	1.39431
$535$	39.2079	1.69511
$536$	−36.2840	−1.56723
$537$	15.0238	0.648323
$538$	65.8091	2.83723
$539$	−23.8058	−1.02539
$540$	−10.4429	−0.449392
$541$	35.8460	1.54114	0.770569	−	0.637356i	$-0.219972\pi$
$541$	35.8460	1.54114	0.770569	+	0.637356i	$0.219972\pi$
$542$	41.2906	1.77358
$543$	−16.7605	−0.719260
$544$	−7.70996	−0.330562
$545$	49.4665	2.11891
$546$	19.4647	0.833013
$547$	−3.75161	−0.160407	−0.0802036	−	0.996779i	$-0.525557\pi$
$547$	−3.75161	−0.160407	−0.0802036	+	0.996779i	$0.525557\pi$
$548$	36.9423	1.57810
$549$	8.78137	0.374780
$550$	−69.0118	−2.94267
$551$	6.60326	0.281309
$552$	−4.37783	−0.186333
$553$	−2.72492	−0.115875
$554$	−26.0790	−1.10799
$555$	24.1491	1.02507
$556$	−64.5584	−2.73788
$557$	22.5643	0.956078	0.478039	−	0.878339i	$-0.341348\pi$
$557$	22.5643	0.956078	0.478039	+	0.878339i	$0.341348\pi$
$558$	13.0367	0.551888
$559$	48.4443	2.04898
$560$	2.44015	0.103115
$561$	6.12858	0.258749
$562$	−58.0759	−2.44978
$563$	−14.3757	−0.605863	−0.302932	−	0.953012i	$-0.597965\pi$
$563$	−14.3757	−0.605863	−0.302932	+	0.953012i	$0.597965\pi$
$564$	5.41303	0.227930
$565$	29.0471	1.22202
$566$	−32.6431	−1.37209
$567$	−1.47338	−0.0618763
$568$	−11.6418	−0.488480
$569$	−17.2282	−0.722245	−0.361123	−	0.932518i	$-0.617606\pi$
$569$	−17.2282	−0.722245	−0.361123	+	0.932518i	$0.617606\pi$
$570$	14.9575	0.626500
$571$	3.00505	0.125757	0.0628787	−	0.998021i	$-0.479972\pi$
$571$	3.00505	0.125757	0.0628787	+	0.998021i	$0.479972\pi$
$572$	−89.8468	−3.75668
$573$	0.969424	0.0404982
$574$	10.7004	0.446626
$575$	−10.6591	−0.444517
$576$	−13.0456	−0.543568
$577$	36.3064	1.51146	0.755728	−	0.654886i	$-0.227283\pi$
$577$	36.3064	1.51146	0.755728	+	0.654886i	$0.227283\pi$
$578$	34.9777	1.45488
$579$	10.2351	0.425358
$580$	34.8970	1.44902
$581$	12.1581	0.504401
$582$	−10.7067	−0.443806
$583$	−29.0726	−1.20406
$584$	−17.0506	−0.705559
$585$	−19.5218	−0.807128
$586$	−19.5174	−0.806257
$587$	−8.52354	−0.351804	−0.175902	−	0.984408i	$-0.556284\pi$
$587$	−8.52354	−0.351804	−0.175902	+	0.984408i	$0.556284\pi$
$588$	15.0788	0.621838
$589$	−11.3821	−0.468990
$590$	−1.04284	−0.0429332
$591$	25.3281	1.04186
$592$	3.57560	0.146956
$593$	40.0327	1.64394	0.821972	−	0.569527i	$-0.192874\pi$
$593$	40.0327	1.64394	0.821972	+	0.569527i	$0.192874\pi$
$594$	11.1571	0.457782
$595$	6.12617	0.251149
$596$	52.2580	2.14057
$597$	−16.9202	−0.692497
$598$	−22.7659	−0.930965
$599$	11.4049	0.465992	0.232996	−	0.972478i	$-0.425147\pi$
$599$	11.4049	0.465992	0.232996	+	0.972478i	$0.425147\pi$
$600$	15.7137	0.641509
$601$	19.2228	0.784114	0.392057	−	0.919941i	$-0.371764\pi$
$601$	19.2228	0.784114	0.392057	+	0.919941i	$0.371764\pi$
$602$	−27.6760	−1.12799
$603$	14.2826	0.581634
$604$	34.6882	1.41144
$605$	44.4851	1.80858
$606$	−4.29590	−0.174509
$607$	31.2675	1.26911	0.634555	−	0.772878i	$-0.281184\pi$
$607$	31.2675	1.26911	0.634555	+	0.772878i	$0.281184\pi$
$608$	12.2546	0.496988
$609$	4.92359	0.199514
$610$	−66.4704	−2.69131
$611$	10.1190	0.409371
$612$	−3.88189	−0.156916
$613$	35.6953	1.44172	0.720861	−	0.693080i	$-0.243747\pi$
$613$	35.6953	1.44172	0.720861	+	0.693080i	$0.243747\pi$
$614$	−6.95992	−0.280879
$615$	−10.7318	−0.432747
$616$	18.4517	0.743440
$617$	15.2687	0.614693	0.307346	−	0.951598i	$-0.400559\pi$
$617$	15.2687	0.614693	0.307346	+	0.951598i	$0.400559\pi$
$618$	32.0534	1.28938
$619$	40.2167	1.61645	0.808224	−	0.588876i	$-0.200429\pi$
$619$	40.2167	1.61645	0.808224	+	0.588876i	$0.200429\pi$
$620$	−60.1522	−2.41577
$621$	1.72326	0.0691521
$622$	69.7409	2.79636
$623$	−20.9752	−0.840352
$624$	−2.89047	−0.115711
$625$	−17.6675	−0.706699
$626$	−22.3873	−0.894777
$627$	−9.74105	−0.389020
$628$	−0.285660	−0.0113991
$629$	8.97679	0.357928
$630$	11.1527	0.444336
$631$	11.8085	0.470089	0.235045	−	0.971985i	$-0.424476\pi$
$631$	11.8085	0.470089	0.235045	+	0.971985i	$0.424476\pi$
$632$	−4.69834	−0.186890
$633$	−21.0468	−0.836536
$634$	−8.79279	−0.349206
$635$	18.2173	0.722931
$636$	18.4148	0.730193
$637$	28.1880	1.11685
$638$	−37.2836	−1.47607
$639$	4.58262	0.181286
$640$	57.2664	2.26365
$641$	4.32349	0.170767	0.0853837	−	0.996348i	$-0.472788\pi$
$641$	4.32349	0.170767	0.0853837	+	0.996348i	$0.472788\pi$
$642$	26.5330	1.04717
$643$	−5.07795	−0.200255	−0.100127	−	0.994975i	$-0.531925\pi$
$643$	−5.07795	−0.200255	−0.100127	+	0.994975i	$0.531925\pi$
$644$	7.92799	0.312406
$645$	27.7572	1.09294
$646$	5.56005	0.218757
$647$	7.78198	0.305941	0.152971	−	0.988231i	$-0.451116\pi$
$647$	7.78198	0.305941	0.152971	+	0.988231i	$0.451116\pi$
$648$	−2.54043	−0.0997975
$649$	0.679152	0.0266590
$650$	81.7154	3.20514
$651$	−8.48681	−0.332624
$652$	41.8979	1.64085
$653$	19.8766	0.777832	0.388916	−	0.921273i	$-0.372850\pi$
$653$	19.8766	0.777832	0.388916	+	0.921273i	$0.372850\pi$
$654$	33.4752	1.30898
$655$	−5.68427	−0.222103
$656$	−1.58898	−0.0620394
$657$	6.71170	0.261848
$658$	−5.78095	−0.225365
$659$	−8.91036	−0.347098	−0.173549	−	0.984825i	$-0.555524\pi$
$659$	−8.91036	−0.347098	−0.173549	+	0.984825i	$0.555524\pi$
$660$	−51.4797	−2.00384
$661$	3.51930	0.136885	0.0684425	−	0.997655i	$-0.478197\pi$
$661$	3.51930	0.136885	0.0684425	+	0.997655i	$0.478197\pi$
$662$	3.23993	0.125924
$663$	−7.25672	−0.281828
$664$	20.9631	0.813526
$665$	−9.73722	−0.377593
$666$	16.3423	0.633251
$667$	−5.75861	−0.222974
$668$	60.3818	2.33624
$669$	8.23412	0.318350
$670$	−108.112	−4.17673
$671$	43.2888	1.67115
$672$	9.13736	0.352481
$673$	−29.3661	−1.13198	−0.565991	−	0.824412i	$-0.691506\pi$
$673$	−29.3661	−1.13198	−0.565991	+	0.824412i	$0.691506\pi$
$674$	43.7263	1.68428
$675$	−6.18545	−0.238078
$676$	65.7938	2.53053
$677$	22.9952	0.883777	0.441889	−	0.897070i	$-0.354309\pi$
$677$	22.9952	0.883777	0.441889	+	0.897070i	$0.354309\pi$
$678$	19.6569	0.754920
$679$	6.96998	0.267483
$680$	10.5628	0.405067
$681$	−17.8966	−0.685801
$682$	64.2660	2.46087
$683$	32.0344	1.22576	0.612881	−	0.790175i	$-0.290011\pi$
$683$	32.0344	1.22576	0.612881	+	0.790175i	$0.290011\pi$
$684$	6.17005	0.235918
$685$	39.5689	1.51185
$686$	−39.4465	−1.50607
$687$	15.0850	0.575528
$688$	4.10983	0.156686
$689$	34.4242	1.31146
$690$	−13.0442	−0.496584
$691$	13.7736	0.523972	0.261986	−	0.965072i	$-0.415623\pi$
$691$	13.7736	0.523972	0.261986	+	0.965072i	$0.415623\pi$
$692$	45.9857	1.74811
$693$	−7.26321	−0.275907
$694$	20.3080	0.770881
$695$	−69.1486	−2.62296
$696$	8.48932	0.321787
$697$	−3.98926	−0.151104
$698$	28.8529	1.09210
$699$	30.1432	1.14012
$700$	−28.4566	−1.07556
$701$	4.71046	0.177911	0.0889557	−	0.996036i	$-0.471647\pi$
$701$	4.71046	0.177911	0.0889557	+	0.996036i	$0.471647\pi$
$702$	−13.2109	−0.498614
$703$	−14.2681	−0.538132
$704$	−64.3100	−2.42378
$705$	5.79790	0.218362
$706$	28.5084	1.07293
$707$	2.79660	0.105177
$708$	−0.430179	−0.0161671
$709$	−9.91394	−0.372326	−0.186163	−	0.982519i	$-0.559605\pi$
$709$	−9.91394	−0.372326	−0.186163	+	0.982519i	$0.559605\pi$
$710$	−34.6880	−1.30182
$711$	1.84943	0.0693590
$712$	−36.1657	−1.35537
$713$	9.92613	0.371737
$714$	4.14574	0.155150
$715$	−96.2351	−3.59899
$716$	−46.9110	−1.75314
$717$	−12.5378	−0.468233
$718$	−78.4906	−2.92924
$719$	15.0336	0.560659	0.280330	−	0.959904i	$-0.409556\pi$
$719$	15.0336	0.560659	0.280330	+	0.959904i	$0.409556\pi$
$720$	−1.65616	−0.0617213
$721$	−20.8666	−0.777112
$722$	34.1650	1.27149
$723$	19.5998	0.728926
$724$	52.3338	1.94497
$725$	20.6698	0.767659
$726$	30.1042	1.11727
$727$	28.4267	1.05429	0.527144	−	0.849776i	$-0.323263\pi$
$727$	28.4267	1.05429	0.527144	+	0.849776i	$0.323263\pi$
$728$	−21.8482	−0.809750
$729$	1.00000	0.0370370
$730$	−50.8040	−1.88034
$731$	10.3180	0.381626
$732$	−27.4194	−1.01345
$733$	45.5021	1.68066	0.840329	−	0.542076i	$-0.182362\pi$
$733$	45.5021	1.68066	0.840329	+	0.542076i	$0.182362\pi$
$734$	−48.2978	−1.78270
$735$	16.1509	0.595735
$736$	−10.6870	−0.393929
$737$	70.4079	2.59351
$738$	−7.26246	−0.267335
$739$	37.5039	1.37960	0.689802	−	0.723998i	$-0.257698\pi$
$739$	37.5039	1.37960	0.689802	+	0.723998i	$0.257698\pi$
$740$	−75.4044	−2.77192
$741$	11.5342	0.423718
$742$	−19.6664	−0.721977
$743$	0.389541	0.0142909	0.00714543	−	0.999974i	$-0.497726\pi$
$743$	0.389541	0.0142909	0.00714543	+	0.999974i	$0.497726\pi$
$744$	−14.6331	−0.536475
$745$	55.9736	2.05072
$746$	−18.8035	−0.688445
$747$	−8.25180	−0.301917
$748$	−19.1362	−0.699689
$749$	−17.2728	−0.631135
$750$	8.97322	0.327656
$751$	−10.9206	−0.398498	−0.199249	−	0.979949i	$-0.563850\pi$
$751$	−10.9206	−0.398498	−0.199249	+	0.979949i	$0.563850\pi$
$752$	0.858457	0.0313047
$753$	−8.90936	−0.324675
$754$	44.1467	1.60773
$755$	37.1546	1.35219
$756$	4.60057	0.167321
$757$	3.66474	0.133197	0.0665986	−	0.997780i	$-0.478785\pi$
$757$	3.66474	0.133197	0.0665986	+	0.997780i	$0.478785\pi$
$758$	−43.6883	−1.58683
$759$	8.49502	0.308350
$760$	−16.7891	−0.609004
$761$	−45.8836	−1.66328	−0.831640	−	0.555316i	$-0.812597\pi$
$761$	−45.8836	−1.66328	−0.831640	+	0.555316i	$0.812597\pi$
$762$	12.3281	0.446600
$763$	−21.7921	−0.788928
$764$	−3.02698	−0.109512
$765$	−4.15790	−0.150329
$766$	−41.2998	−1.49222
$767$	−0.804169	−0.0290369
$768$	12.6624	0.456913
$769$	−37.3651	−1.34742	−0.673709	−	0.738997i	$-0.735300\pi$
$769$	−37.3651	−1.34742	−0.673709	+	0.738997i	$0.735300\pi$
$770$	54.9787	1.98130
$771$	−6.17563	−0.222410
$772$	−31.9588	−1.15022
$773$	14.8768	0.535080	0.267540	−	0.963547i	$-0.413789\pi$
$773$	14.8768	0.535080	0.267540	+	0.963547i	$0.413789\pi$
$774$	18.7840	0.675177
$775$	−35.6287	−1.27982
$776$	12.0177	0.431412
$777$	−10.6387	−0.381662
$778$	5.53299	0.198367
$779$	6.34071	0.227179
$780$	60.9560	2.18257
$781$	22.5906	0.808354
$782$	−4.84883	−0.173394
$783$	−3.34169	−0.119422
$784$	2.39136	0.0854056
$785$	−0.305971	−0.0109206
$786$	−3.84669	−0.137207
$787$	−48.9501	−1.74488	−0.872442	−	0.488718i	$-0.837465\pi$
$787$	−48.9501	−1.74488	−0.872442	+	0.488718i	$0.837465\pi$
$788$	−79.0857	−2.81731
$789$	−21.1105	−0.751552
$790$	−13.9992	−0.498069
$791$	−12.7965	−0.454992
$792$	−12.5233	−0.444998
$793$	−51.2573	−1.82020
$794$	12.2512	0.434779
$795$	19.7241	0.699542
$796$	52.8324	1.87260
$797$	−7.23008	−0.256102	−0.128051	−	0.991768i	$-0.540872\pi$
$797$	−7.23008	−0.256102	−0.128051	+	0.991768i	$0.540872\pi$
$798$	−6.58942	−0.233263
$799$	2.15522	0.0762461
$800$	38.3598	1.35622
$801$	14.2361	0.503006
$802$	18.0546	0.637530
$803$	33.0861	1.16758
$804$	−44.5969	−1.57281
$805$	8.49168	0.299292
$806$	−76.0959	−2.68036
$807$	29.0768	1.02355
$808$	4.82194	0.169635
$809$	−38.7215	−1.36138	−0.680688	−	0.732573i	$-0.738319\pi$
$809$	−38.7215	−1.36138	−0.680688	+	0.732573i	$0.738319\pi$
$810$	−7.56947	−0.265964
$811$	12.8093	0.449796	0.224898	−	0.974382i	$-0.427795\pi$
$811$	12.8093	0.449796	0.224898	+	0.974382i	$0.427795\pi$
$812$	−15.3737	−0.539510
$813$	18.2436	0.639833
$814$	80.5612	2.82367
$815$	44.8770	1.57197
$816$	−0.615632	−0.0215514
$817$	−16.3999	−0.573761
$818$	−76.5982	−2.67819
$819$	8.60021	0.300516
$820$	33.5095	1.17020
$821$	8.24282	0.287676	0.143838	−	0.989601i	$-0.454056\pi$
$821$	8.24282	0.287676	0.143838	+	0.989601i	$0.454056\pi$
$822$	26.7773	0.933966
$823$	−9.21740	−0.321298	−0.160649	−	0.987012i	$-0.551359\pi$
$823$	−9.21740	−0.321298	−0.160649	+	0.987012i	$0.551359\pi$
$824$	−35.9785	−1.25337
$825$	−30.4919	−1.06159
$826$	0.459418	0.0159852
$827$	−8.28507	−0.288100	−0.144050	−	0.989570i	$-0.546013\pi$
$827$	−8.28507	−0.288100	−0.144050	+	0.989570i	$0.546013\pi$
$828$	−5.38081	−0.186996
$829$	−24.9232	−0.865618	−0.432809	−	0.901486i	$-0.642478\pi$
$829$	−24.9232	−0.865618	−0.432809	+	0.901486i	$0.642478\pi$
$830$	62.4618	2.16808
$831$	−11.5226	−0.399715
$832$	76.1481	2.63996
$833$	6.00367	0.208015
$834$	−46.7946	−1.62036
$835$	64.6750	2.23817
$836$	30.4160	1.05196
$837$	5.76008	0.199098
$838$	70.9475	2.45084
$839$	18.9315	0.653588	0.326794	−	0.945096i	$-0.394032\pi$
$839$	18.9315	0.653588	0.326794	+	0.945096i	$0.394032\pi$
$840$	−12.5184	−0.431927
$841$	−17.8331	−0.614935
$842$	51.4761	1.77398
$843$	−25.6600	−0.883777
$844$	65.7177	2.26210
$845$	70.4718	2.42431
$846$	3.92359	0.134896
$847$	−19.5976	−0.673383
$848$	2.92042	0.100288
$849$	−14.4229	−0.494992
$850$	17.4043	0.596963
$851$	12.4430	0.426541
$852$	−14.3090	−0.490219
$853$	−15.8127	−0.541415	−0.270708	−	0.962662i	$-0.587258\pi$
$853$	−15.8127	−0.541415	−0.270708	+	0.962662i	$0.587258\pi$
$854$	29.2831	1.00205
$855$	6.60875	0.226015
$856$	−29.7820	−1.01793
$857$	4.85184	0.165736	0.0828679	−	0.996561i	$-0.473592\pi$
$857$	4.85184	0.165736	0.0828679	+	0.996561i	$0.473592\pi$
$858$	−65.1247	−2.22332
$859$	−5.02733	−0.171530	−0.0857651	−	0.996315i	$-0.527333\pi$
$859$	−5.02733	−0.171530	−0.0857651	+	0.996315i	$0.527333\pi$
$860$	−86.6706	−2.95544
$861$	4.72782	0.161124
$862$	12.3651	0.421155
$863$	10.4975	0.357339	0.178669	−	0.983909i	$-0.442821\pi$
$863$	10.4975	0.357339	0.178669	+	0.983909i	$0.442821\pi$
$864$	−6.20162	−0.210983
$865$	49.2554	1.67473
$866$	17.4722	0.593731
$867$	15.4544	0.524859
$868$	26.4997	0.899457
$869$	9.11697	0.309272
$870$	25.2948	0.857575
$871$	−83.3685	−2.82483
$872$	−37.5743	−1.27243
$873$	−4.73060	−0.160106
$874$	7.70696	0.260692
$875$	−5.84151	−0.197479
$876$	−20.9570	−0.708070
$877$	1.76643	0.0596481	0.0298241	−	0.999555i	$-0.490505\pi$
$877$	1.76643	0.0596481	0.0298241	+	0.999555i	$0.490505\pi$
$878$	−41.9107	−1.41442
$879$	−8.62350	−0.290863
$880$	−8.16421	−0.275216
$881$	−4.40040	−0.148253	−0.0741266	−	0.997249i	$-0.523617\pi$
$881$	−4.40040	−0.148253	−0.0741266	+	0.997249i	$0.523617\pi$
$882$	10.9297	0.368023
$883$	−21.6219	−0.727634	−0.363817	−	0.931470i	$-0.618527\pi$
$883$	−21.6219	−0.727634	−0.363817	+	0.931470i	$0.618527\pi$
$884$	22.6588	0.762097
$885$	−0.460766	−0.0154885
$886$	−54.6985	−1.83763
$887$	23.7407	0.797134	0.398567	−	0.917139i	$-0.369508\pi$
$887$	23.7407	0.797134	0.398567	+	0.917139i	$0.369508\pi$
$888$	−18.3435	−0.615566
$889$	−8.02551	−0.269167
$890$	−107.759	−3.61211
$891$	4.92962	0.165148
$892$	−25.7107	−0.860857
$893$	−3.42560	−0.114633
$894$	37.8788	1.26686
$895$	−50.2464	−1.67955
$896$	−25.2284	−0.842821
$897$	−10.0588	−0.335853
$898$	25.2317	0.841992
$899$	−19.2484	−0.641970
$900$	19.3138	0.643792
$901$	7.33192	0.244262
$902$	−35.8012	−1.19205
$903$	−12.2283	−0.406931
$904$	−22.0640	−0.733837
$905$	56.0548	1.86332
$906$	25.1434	0.835335
$907$	14.8764	0.493962	0.246981	−	0.969020i	$-0.420561\pi$
$907$	14.8764	0.493962	0.246981	+	0.969020i	$0.420561\pi$
$908$	55.8814	1.85449
$909$	−1.89808	−0.0629554
$910$	−65.0991	−2.15801
$911$	47.4147	1.57092	0.785459	−	0.618913i	$-0.212427\pi$
$911$	47.4147	1.57092	0.785459	+	0.618913i	$0.212427\pi$
$912$	0.978514	0.0324019
$913$	−40.6782	−1.34625
$914$	−4.91614	−0.162612
$915$	−29.3690	−0.970909
$916$	−47.1021	−1.55630
$917$	2.50417	0.0826950
$918$	−2.81375	−0.0928677
$919$	−4.00411	−0.132084	−0.0660418	−	0.997817i	$-0.521037\pi$
$919$	−4.00411	−0.132084	−0.0660418	+	0.997817i	$0.521037\pi$
$920$	14.6415	0.482716
$921$	−3.07514	−0.101329
$922$	28.8921	0.951511
$923$	−26.7490	−0.880454
$924$	22.6790	0.746086
$925$	−44.6627	−1.46850
$926$	51.3045	1.68597
$927$	14.1624	0.465153
$928$	20.7239	0.680295
$929$	−51.0381	−1.67451	−0.837253	−	0.546815i	$-0.815840\pi$
$929$	−51.0381	−1.67451	−0.837253	+	0.546815i	$0.815840\pi$
$930$	−43.6008	−1.42973
$931$	−9.54251	−0.312743
$932$	−94.1206	−3.08302
$933$	30.8141	1.00881
$934$	4.68549	0.153314
$935$	−20.4968	−0.670318
$936$	14.8286	0.484689
$937$	−32.6659	−1.06715	−0.533573	−	0.845754i	$-0.679151\pi$
$937$	−32.6659	−1.06715	−0.533573	+	0.845754i	$0.679151\pi$
$938$	47.6281	1.55511
$939$	−9.89152	−0.322798
$940$	−18.1037	−0.590477
$941$	−35.6514	−1.16220	−0.581101	−	0.813831i	$-0.697378\pi$
$941$	−35.6514	−1.16220	−0.581101	+	0.813831i	$0.697378\pi$
$942$	−0.207059	−0.00674633
$943$	−5.52963	−0.180070
$944$	−0.0682226	−0.00222046
$945$	4.92768	0.160297
$946$	92.5980	3.01062
$947$	−3.17277	−0.103101	−0.0515506	−	0.998670i	$-0.516416\pi$
$947$	−3.17277	−0.103101	−0.0515506	+	0.998670i	$0.516416\pi$
$948$	−5.77475	−0.187555
$949$	−39.1765	−1.27172
$950$	−27.6632	−0.897514
$951$	−3.88497	−0.125979
$952$	−4.65339	−0.150817
$953$	30.2466	0.979784	0.489892	−	0.871783i	$-0.337036\pi$
$953$	30.2466	0.979784	0.489892	+	0.871783i	$0.337036\pi$
$954$	13.3478	0.432151
$955$	−3.24220	−0.104915
$956$	39.1487	1.26616
$957$	−16.4732	−0.532504
$958$	−43.0901	−1.39218
$959$	−17.4318	−0.562904
$960$	43.6307	1.40817
$961$	2.17856	0.0702762
$962$	−95.3908	−3.07552
$963$	11.7232	0.377776
$964$	−61.1996	−1.97111
$965$	−34.2311	−1.10194
$966$	5.74654	0.184892
$967$	40.5659	1.30451	0.652255	−	0.757999i	$-0.273823\pi$
$967$	40.5659	1.30451	0.652255	+	0.757999i	$0.273823\pi$
$968$	−33.7906	−1.08607
$969$	2.45663	0.0789183
$970$	35.8081	1.14973
$971$	−21.9199	−0.703443	−0.351722	−	0.936105i	$-0.614404\pi$
$971$	−21.9199	−0.703443	−0.351722	+	0.936105i	$0.614404\pi$
$972$	−3.12245	−0.100153
$973$	30.4630	0.976598
$974$	11.6926	0.374655
$975$	36.1048	1.15628
$976$	−4.34847	−0.139191
$977$	13.7365	0.439468	0.219734	−	0.975560i	$-0.429481\pi$
$977$	13.7365	0.439468	0.219734	+	0.975560i	$0.429481\pi$
$978$	30.3694	0.971105
$979$	70.1783	2.24291
$980$	−50.4304	−1.61094
$981$	14.7905	0.472226
$982$	22.3714	0.713899
$983$	30.6988	0.979141	0.489570	−	0.871964i	$-0.337154\pi$
$983$	30.6988	0.979141	0.489570	+	0.871964i	$0.337154\pi$
$984$	8.15178	0.259869
$985$	−84.7088	−2.69905
$986$	9.40268	0.299442
$987$	−2.55423	−0.0813020
$988$	−36.0149	−1.14579
$989$	14.3021	0.454781
$990$	−37.3146	−1.18594
$991$	−2.91690	−0.0926584	−0.0463292	−	0.998926i	$-0.514752\pi$
$991$	−2.91690	−0.0926584	−0.0463292	+	0.998926i	$0.514752\pi$
$992$	−35.7219	−1.13417
$993$	1.43152	0.0454279
$994$	15.2816	0.484703
$995$	56.5889	1.79399
$996$	25.7658	0.816422
$997$	17.3287	0.548804	0.274402	−	0.961615i	$-0.411520\pi$
$997$	17.3287	0.548804	0.274402	+	0.961615i	$0.411520\pi$
$998$	−34.2907	−1.08545
$999$	7.22061	0.228450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.14	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.26328 q^{2} -1.00000 q^{3} +3.12245 q^{4} +3.34447 q^{5} +2.26328 q^{6} -1.47338 q^{7} -2.54043 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.26328 q^{2} -1.00000 q^{3} +3.12245 q^{4} +3.34447 q^{5} +2.26328 q^{6} -1.47338 q^{7} -2.54043 q^{8} +1.00000 q^{9} -7.56947 q^{10} +4.92962 q^{11} -3.12245 q^{12} -5.83705 q^{13} +3.33468 q^{14} -3.34447 q^{15} -0.495193 q^{16} -1.24322 q^{17} -2.26328 q^{18} +1.97603 q^{19} +10.4429 q^{20} +1.47338 q^{21} -11.1571 q^{22} -1.72326 q^{23} +2.54043 q^{24} +6.18545 q^{25} +13.2109 q^{26} -1.00000 q^{27} -4.60057 q^{28} +3.34169 q^{29} +7.56947 q^{30} -5.76008 q^{31} +6.20162 q^{32} -4.92962 q^{33} +2.81375 q^{34} -4.92768 q^{35} +3.12245 q^{36} -7.22061 q^{37} -4.47231 q^{38} +5.83705 q^{39} -8.49638 q^{40} +3.20882 q^{41} -3.33468 q^{42} -8.29945 q^{43} +15.3925 q^{44} +3.34447 q^{45} +3.90023 q^{46} -1.73358 q^{47} +0.495193 q^{48} -4.82914 q^{49} -13.9994 q^{50} +1.24322 q^{51} -18.2259 q^{52} -5.89753 q^{53} +2.26328 q^{54} +16.4869 q^{55} +3.74303 q^{56} -1.97603 q^{57} -7.56319 q^{58} +0.137770 q^{59} -10.4429 q^{60} +8.78137 q^{61} +13.0367 q^{62} -1.47338 q^{63} -13.0456 q^{64} -19.5218 q^{65} +11.1571 q^{66} +14.2826 q^{67} -3.88189 q^{68} +1.72326 q^{69} +11.1527 q^{70} +4.58262 q^{71} -2.54043 q^{72} +6.71170 q^{73} +16.3423 q^{74} -6.18545 q^{75} +6.17005 q^{76} -7.26321 q^{77} -13.2109 q^{78} +1.84943 q^{79} -1.65616 q^{80} +1.00000 q^{81} -7.26246 q^{82} -8.25180 q^{83} +4.60057 q^{84} -4.15790 q^{85} +18.7840 q^{86} -3.34169 q^{87} -12.5233 q^{88} +14.2361 q^{89} -7.56947 q^{90} +8.60021 q^{91} -5.38081 q^{92} +5.76008 q^{93} +3.92359 q^{94} +6.60875 q^{95} -6.20162 q^{96} -4.73060 q^{97} +10.9297 q^{98} +4.92962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 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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