LMFDB - Embedded newform 6009.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.15308 q^{2} -1.00000 q^{3} +2.63577 q^{4} -3.48527 q^{5} +2.15308 q^{6} +4.31227 q^{7} -1.36887 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15308 q^{2} -1.00000 q^{3} +2.63577 q^{4} -3.48527 q^{5} +2.15308 q^{6} +4.31227 q^{7} -1.36887 q^{8} +1.00000 q^{9} +7.50407 q^{10} -1.99927 q^{11} -2.63577 q^{12} +6.01332 q^{13} -9.28468 q^{14} +3.48527 q^{15} -2.32425 q^{16} -5.48114 q^{17} -2.15308 q^{18} -6.76739 q^{19} -9.18637 q^{20} -4.31227 q^{21} +4.30460 q^{22} +6.48700 q^{23} +1.36887 q^{24} +7.14709 q^{25} -12.9472 q^{26} -1.00000 q^{27} +11.3662 q^{28} +8.10553 q^{29} -7.50407 q^{30} -0.800706 q^{31} +7.74205 q^{32} +1.99927 q^{33} +11.8014 q^{34} -15.0294 q^{35} +2.63577 q^{36} +3.82135 q^{37} +14.5708 q^{38} -6.01332 q^{39} +4.77088 q^{40} -5.52467 q^{41} +9.28468 q^{42} -9.61058 q^{43} -5.26963 q^{44} -3.48527 q^{45} -13.9671 q^{46} +5.20278 q^{47} +2.32425 q^{48} +11.5957 q^{49} -15.3883 q^{50} +5.48114 q^{51} +15.8497 q^{52} +5.64131 q^{53} +2.15308 q^{54} +6.96800 q^{55} -5.90294 q^{56} +6.76739 q^{57} -17.4519 q^{58} -11.8493 q^{59} +9.18637 q^{60} +0.0876535 q^{61} +1.72399 q^{62} +4.31227 q^{63} -12.0208 q^{64} -20.9580 q^{65} -4.30460 q^{66} +14.6458 q^{67} -14.4470 q^{68} -6.48700 q^{69} +32.3596 q^{70} -1.98346 q^{71} -1.36887 q^{72} +2.83611 q^{73} -8.22768 q^{74} -7.14709 q^{75} -17.8373 q^{76} -8.62141 q^{77} +12.9472 q^{78} +10.4598 q^{79} +8.10064 q^{80} +1.00000 q^{81} +11.8951 q^{82} +12.8557 q^{83} -11.3662 q^{84} +19.1032 q^{85} +20.6924 q^{86} -8.10553 q^{87} +2.73675 q^{88} -6.18776 q^{89} +7.50407 q^{90} +25.9311 q^{91} +17.0983 q^{92} +0.800706 q^{93} -11.2020 q^{94} +23.5862 q^{95} -7.74205 q^{96} +13.9295 q^{97} -24.9665 q^{98} -1.99927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.15308	−1.52246	−0.761230	−	0.648482i	$-0.775404\pi$
$2$	−2.15308	−1.52246	−0.761230	+	0.648482i	$0.775404\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.63577	1.31789
$5$	−3.48527	−1.55866	−0.779329	−	0.626614i	$-0.784440\pi$
$5$	−3.48527	−1.55866	−0.779329	+	0.626614i	$0.784440\pi$
$6$	2.15308	0.878993
$7$	4.31227	1.62989	0.814943	−	0.579542i	$-0.196768\pi$
$7$	4.31227	1.62989	0.814943	+	0.579542i	$0.196768\pi$
$8$	−1.36887	−0.483969
$9$	1.00000	0.333333
$10$	7.50407	2.37300
$11$	−1.99927	−0.602804	−0.301402	−	0.953497i	$-0.597455\pi$
$11$	−1.99927	−0.602804	−0.301402	+	0.953497i	$0.597455\pi$
$12$	−2.63577	−0.760882
$13$	6.01332	1.66780	0.833898	−	0.551919i	$-0.186104\pi$
$13$	6.01332	1.66780	0.833898	+	0.551919i	$0.186104\pi$
$14$	−9.28468	−2.48144
$15$	3.48527	0.899892
$16$	−2.32425	−0.581063
$17$	−5.48114	−1.32937	−0.664686	−	0.747123i	$-0.731435\pi$
$17$	−5.48114	−1.32937	−0.664686	+	0.747123i	$0.731435\pi$
$18$	−2.15308	−0.507487
$19$	−6.76739	−1.55255	−0.776273	−	0.630396i	$-0.782892\pi$
$19$	−6.76739	−1.55255	−0.776273	+	0.630396i	$0.782892\pi$
$20$	−9.18637	−2.05413
$21$	−4.31227	−0.941015
$22$	4.30460	0.917745
$23$	6.48700	1.35263	0.676317	−	0.736611i	$-0.263575\pi$
$23$	6.48700	1.35263	0.676317	+	0.736611i	$0.263575\pi$
$24$	1.36887	0.279419
$25$	7.14709	1.42942
$26$	−12.9472	−2.53915
$27$	−1.00000	−0.192450
$28$	11.3662	2.14800
$29$	8.10553	1.50516	0.752579	−	0.658502i	$-0.228810\pi$
$29$	8.10553	1.50516	0.752579	+	0.658502i	$0.228810\pi$
$30$	−7.50407	−1.37005
$31$	−0.800706	−0.143811	−0.0719056	−	0.997411i	$-0.522908\pi$
$31$	−0.800706	−0.143811	−0.0719056	+	0.997411i	$0.522908\pi$
$32$	7.74205	1.36861
$33$	1.99927	0.348029
$34$	11.8014	2.02392
$35$	−15.0294	−2.54043
$36$	2.63577	0.439295
$37$	3.82135	0.628226	0.314113	−	0.949386i	$-0.398293\pi$
$37$	3.82135	0.628226	0.314113	+	0.949386i	$0.398293\pi$
$38$	14.5708	2.36369
$39$	−6.01332	−0.962902
$40$	4.77088	0.754342
$41$	−5.52467	−0.862809	−0.431405	−	0.902159i	$-0.641982\pi$
$41$	−5.52467	−0.862809	−0.431405	+	0.902159i	$0.641982\pi$
$42$	9.28468	1.43266
$43$	−9.61058	−1.46560	−0.732800	−	0.680444i	$-0.761787\pi$
$43$	−9.61058	−1.46560	−0.732800	+	0.680444i	$0.761787\pi$
$44$	−5.26963	−0.794426
$45$	−3.48527	−0.519553
$46$	−13.9671	−2.05933
$47$	5.20278	0.758904	0.379452	−	0.925212i	$-0.376113\pi$
$47$	5.20278	0.758904	0.379452	+	0.925212i	$0.376113\pi$
$48$	2.32425	0.335477
$49$	11.5957	1.65653
$50$	−15.3883	−2.17623
$51$	5.48114	0.767513
$52$	15.8497	2.19796
$53$	5.64131	0.774894	0.387447	−	0.921892i	$-0.373357\pi$
$53$	5.64131	0.774894	0.387447	+	0.921892i	$0.373357\pi$
$54$	2.15308	0.292998
$55$	6.96800	0.939565
$56$	−5.90294	−0.788813
$57$	6.76739	0.896363
$58$	−17.4519	−2.29154
$59$	−11.8493	−1.54265	−0.771325	−	0.636442i	$-0.780406\pi$
$59$	−11.8493	−1.54265	−0.771325	+	0.636442i	$0.780406\pi$
$60$	9.18637	1.18596
$61$	0.0876535	0.0112229	0.00561144	−	0.999984i	$-0.498214\pi$
$61$	0.0876535	0.0112229	0.00561144	+	0.999984i	$0.498214\pi$
$62$	1.72399	0.218947
$63$	4.31227	0.543295
$64$	−12.0208	−1.50260
$65$	−20.9580	−2.59952
$66$	−4.30460	−0.529860
$67$	14.6458	1.78927	0.894636	−	0.446797i	$-0.147435\pi$
$67$	14.6458	1.78927	0.894636	+	0.446797i	$0.147435\pi$
$68$	−14.4470	−1.75196
$69$	−6.48700	−0.780943
$70$	32.3596	3.86771
$71$	−1.98346	−0.235393	−0.117697	−	0.993050i	$-0.537551\pi$
$71$	−1.98346	−0.235393	−0.117697	+	0.993050i	$0.537551\pi$
$72$	−1.36887	−0.161323
$73$	2.83611	0.331942	0.165971	−	0.986131i	$-0.446924\pi$
$73$	2.83611	0.331942	0.165971	+	0.986131i	$0.446924\pi$
$74$	−8.22768	−0.956449
$75$	−7.14709	−0.825275
$76$	−17.8373	−2.04608
$77$	−8.62141	−0.982501
$78$	12.9472	1.46598
$79$	10.4598	1.17681	0.588407	−	0.808565i	$-0.299755\pi$
$79$	10.4598	1.17681	0.588407	+	0.808565i	$0.299755\pi$
$80$	8.10064	0.905679
$81$	1.00000	0.111111
$82$	11.8951	1.31359
$83$	12.8557	1.41110	0.705550	−	0.708660i	$-0.250700\pi$
$83$	12.8557	1.41110	0.705550	+	0.708660i	$0.250700\pi$
$84$	−11.3662	−1.24015
$85$	19.1032	2.07204
$86$	20.6924	2.23132
$87$	−8.10553	−0.869004
$88$	2.73675	0.291738
$89$	−6.18776	−0.655901	−0.327951	−	0.944695i	$-0.606358\pi$
$89$	−6.18776	−0.655901	−0.327951	+	0.944695i	$0.606358\pi$
$90$	7.50407	0.790999
$91$	25.9311	2.71832
$92$	17.0983	1.78262
$93$	0.800706	0.0830294
$94$	−11.2020	−1.15540
$95$	23.5862	2.41989
$96$	−7.74205	−0.790169
$97$	13.9295	1.41433	0.707163	−	0.707051i	$-0.249975\pi$
$97$	13.9295	1.41433	0.707163	+	0.707051i	$0.249975\pi$
$98$	−24.9665	−2.52199
$99$	−1.99927	−0.200935
$100$	18.8381	1.88381
$101$	−11.6521	−1.15943	−0.579713	−	0.814821i	$-0.696835\pi$
$101$	−11.6521	−1.15943	−0.579713	+	0.814821i	$0.696835\pi$
$102$	−11.8014	−1.16851
$103$	15.4512	1.52245	0.761225	−	0.648488i	$-0.224598\pi$
$103$	15.4512	1.52245	0.761225	+	0.648488i	$0.224598\pi$
$104$	−8.23146	−0.807161
$105$	15.0294	1.46672
$106$	−12.1462	−1.17975
$107$	3.42031	0.330654	0.165327	−	0.986239i	$-0.447132\pi$
$107$	3.42031	0.330654	0.165327	+	0.986239i	$0.447132\pi$
$108$	−2.63577	−0.253627
$109$	−19.1015	−1.82959	−0.914797	−	0.403914i	$-0.867650\pi$
$109$	−19.1015	−1.82959	−0.914797	+	0.403914i	$0.867650\pi$
$110$	−15.0027	−1.43045
$111$	−3.82135	−0.362706
$112$	−10.0228	−0.947065
$113$	−1.76882	−0.166397	−0.0831983	−	0.996533i	$-0.526514\pi$
$113$	−1.76882	−0.166397	−0.0831983	+	0.996533i	$0.526514\pi$
$114$	−14.5708	−1.36468
$115$	−22.6089	−2.10829
$116$	21.3643	1.98363
$117$	6.01332	0.555932
$118$	25.5126	2.34862
$119$	−23.6362	−2.16672
$120$	−4.77088	−0.435520
$121$	−7.00290	−0.636628
$122$	−0.188725	−0.0170864
$123$	5.52467	0.498143
$124$	−2.11048	−0.189527
$125$	−7.48318	−0.669316
$126$	−9.28468	−0.827145
$127$	−3.76338	−0.333946	−0.166973	−	0.985961i	$-0.553399\pi$
$127$	−3.76338	−0.333946	−0.166973	+	0.985961i	$0.553399\pi$
$128$	10.3977	0.919032
$129$	9.61058	0.846164
$130$	45.1244	3.95767
$131$	17.3776	1.51829	0.759145	−	0.650922i	$-0.225618\pi$
$131$	17.3776	1.51829	0.759145	+	0.650922i	$0.225618\pi$
$132$	5.26963	0.458662
$133$	−29.1828	−2.53047
$134$	−31.5337	−2.72409
$135$	3.48527	0.299964
$136$	7.50297	0.643374
$137$	−21.4231	−1.83030	−0.915150	−	0.403114i	$-0.867928\pi$
$137$	−21.4231	−1.83030	−0.915150	+	0.403114i	$0.867928\pi$
$138$	13.9671	1.18896
$139$	7.86329	0.666955	0.333478	−	0.942758i	$-0.391778\pi$
$139$	7.86329	0.666955	0.333478	+	0.942758i	$0.391778\pi$
$140$	−39.6141	−3.34800
$141$	−5.20278	−0.438153
$142$	4.27056	0.358377
$143$	−12.0223	−1.00535
$144$	−2.32425	−0.193688
$145$	−28.2499	−2.34603
$146$	−6.10638	−0.505368
$147$	−11.5957	−0.956395
$148$	10.0722	0.827930
$149$	−9.10230	−0.745689	−0.372845	−	0.927894i	$-0.621618\pi$
$149$	−9.10230	−0.745689	−0.372845	+	0.927894i	$0.621618\pi$
$150$	15.3883	1.25645
$151$	−6.58555	−0.535925	−0.267962	−	0.963429i	$-0.586350\pi$
$151$	−6.58555	−0.535925	−0.267962	+	0.963429i	$0.586350\pi$
$152$	9.26368	0.751384
$153$	−5.48114	−0.443124
$154$	18.5626	1.49582
$155$	2.79068	0.224153
$156$	−15.8497	−1.26900
$157$	−9.11622	−0.727553	−0.363777	−	0.931486i	$-0.618513\pi$
$157$	−9.11622	−0.727553	−0.363777	+	0.931486i	$0.618513\pi$
$158$	−22.5207	−1.79165
$159$	−5.64131	−0.447385
$160$	−26.9831	−2.13320
$161$	27.9737	2.20464
$162$	−2.15308	−0.169162
$163$	−8.56355	−0.670749	−0.335375	−	0.942085i	$-0.608863\pi$
$163$	−8.56355	−0.670749	−0.335375	+	0.942085i	$0.608863\pi$
$164$	−14.5618	−1.13708
$165$	−6.96800	−0.542458
$166$	−27.6795	−2.14834
$167$	−11.2999	−0.874415	−0.437207	−	0.899361i	$-0.644032\pi$
$167$	−11.2999	−0.874415	−0.437207	+	0.899361i	$0.644032\pi$
$168$	5.90294	0.455422
$169$	23.1600	1.78154
$170$	−41.1309	−3.15460
$171$	−6.76739	−0.517516
$172$	−25.3313	−1.93149
$173$	10.3934	0.790198	0.395099	−	0.918639i	$-0.370710\pi$
$173$	10.3934	0.790198	0.395099	+	0.918639i	$0.370710\pi$
$174$	17.4519	1.32302
$175$	30.8202	2.32979
$176$	4.64681	0.350267
$177$	11.8493	0.890649
$178$	13.3228	0.998584
$179$	−15.7445	−1.17680	−0.588401	−	0.808569i	$-0.700242\pi$
$179$	−15.7445	−1.17680	−0.588401	+	0.808569i	$0.700242\pi$
$180$	−9.18637	−0.684712
$181$	−8.15782	−0.606366	−0.303183	−	0.952932i	$-0.598049\pi$
$181$	−8.15782	−0.606366	−0.303183	+	0.952932i	$0.598049\pi$
$182$	−55.8318	−4.13853
$183$	−0.0876535	−0.00647953
$184$	−8.87986	−0.654632
$185$	−13.3184	−0.979189
$186$	−1.72399	−0.126409
$187$	10.9583	0.801350
$188$	13.7133	1.00015
$189$	−4.31227	−0.313672
$190$	−50.7830	−3.68419
$191$	15.3212	1.10860	0.554301	−	0.832316i	$-0.312986\pi$
$191$	15.3212	1.10860	0.554301	+	0.832316i	$0.312986\pi$
$192$	12.0208	0.867525
$193$	19.8008	1.42529	0.712645	−	0.701524i	$-0.247497\pi$
$193$	19.8008	1.42529	0.712645	+	0.701524i	$0.247497\pi$
$194$	−29.9914	−2.15325
$195$	20.9580	1.50084
$196$	30.5636	2.18311
$197$	11.0168	0.784912	0.392456	−	0.919771i	$-0.371626\pi$
$197$	11.0168	0.784912	0.392456	+	0.919771i	$0.371626\pi$
$198$	4.30460	0.305915
$199$	−20.0272	−1.41969	−0.709845	−	0.704357i	$-0.751235\pi$
$199$	−20.0272	−1.41969	−0.709845	+	0.704357i	$0.751235\pi$
$200$	−9.78344	−0.691793
$201$	−14.6458	−1.03304
$202$	25.0879	1.76518
$203$	34.9532	2.45323
$204$	14.4470	1.01149
$205$	19.2550	1.34483
$206$	−33.2677	−2.31787
$207$	6.48700	0.450878
$208$	−13.9765	−0.969094
$209$	13.5299	0.935881
$210$	−32.3596	−2.23302
$211$	−19.5737	−1.34751	−0.673755	−	0.738955i	$-0.735320\pi$
$211$	−19.5737	−1.34751	−0.673755	+	0.738955i	$0.735320\pi$
$212$	14.8692	1.02122
$213$	1.98346	0.135904
$214$	−7.36421	−0.503407
$215$	33.4954	2.28437
$216$	1.36887	0.0931398
$217$	−3.45286	−0.234396
$218$	41.1272	2.78548
$219$	−2.83611	−0.191647
$220$	18.3661	1.23824
$221$	−32.9599	−2.21712
$222$	8.22768	0.552206
$223$	−7.99299	−0.535250	−0.267625	−	0.963523i	$-0.586239\pi$
$223$	−7.99299	−0.535250	−0.267625	+	0.963523i	$0.586239\pi$
$224$	33.3858	2.23068
$225$	7.14709	0.476473
$226$	3.80842	0.253332
$227$	−15.9380	−1.05784	−0.528921	−	0.848671i	$-0.677403\pi$
$227$	−15.9380	−1.05784	−0.528921	+	0.848671i	$0.677403\pi$
$228$	17.8373	1.18130
$229$	−3.16691	−0.209275	−0.104638	−	0.994510i	$-0.533368\pi$
$229$	−3.16691	−0.209275	−0.104638	+	0.994510i	$0.533368\pi$
$230$	48.6789	3.20979
$231$	8.62141	0.567247
$232$	−11.0954	−0.728449
$233$	2.88792	0.189194	0.0945971	−	0.995516i	$-0.469844\pi$
$233$	2.88792	0.189194	0.0945971	+	0.995516i	$0.469844\pi$
$234$	−12.9472	−0.846384
$235$	−18.1331	−1.18287
$236$	−31.2321	−2.03304
$237$	−10.4598	−0.679434
$238$	50.8907	3.29875
$239$	18.5052	1.19700	0.598500	−	0.801122i	$-0.295763\pi$
$239$	18.5052	1.19700	0.598500	+	0.801122i	$0.295763\pi$
$240$	−8.10064	−0.522894
$241$	−21.2547	−1.36914	−0.684569	−	0.728948i	$-0.740010\pi$
$241$	−21.2547	−1.36914	−0.684569	+	0.728948i	$0.740010\pi$
$242$	15.0778	0.969240
$243$	−1.00000	−0.0641500
$244$	0.231035	0.0147905
$245$	−40.4140	−2.58196
$246$	−11.8951	−0.758403
$247$	−40.6945	−2.58933
$248$	1.09606	0.0696001
$249$	−12.8557	−0.814699
$250$	16.1119	1.01901
$251$	−8.07934	−0.509964	−0.254982	−	0.966946i	$-0.582069\pi$
$251$	−8.07934	−0.509964	−0.254982	+	0.966946i	$0.582069\pi$
$252$	11.3662	0.716001
$253$	−12.9693	−0.815372
$254$	8.10287	0.508419
$255$	−19.1032	−1.19629
$256$	1.65453	0.103408
$257$	15.8053	0.985906	0.492953	−	0.870056i	$-0.335917\pi$
$257$	15.8053	0.985906	0.492953	+	0.870056i	$0.335917\pi$
$258$	−20.6924	−1.28825
$259$	16.4787	1.02394
$260$	−55.2406	−3.42588
$261$	8.10553	0.501719
$262$	−37.4155	−2.31154
$263$	−7.09567	−0.437538	−0.218769	−	0.975777i	$-0.570204\pi$
$263$	−7.09567	−0.437538	−0.218769	+	0.975777i	$0.570204\pi$
$264$	−2.73675	−0.168435
$265$	−19.6615	−1.20780
$266$	62.8331	3.85254
$267$	6.18776	0.378685
$268$	38.6030	2.35806
$269$	−0.637677	−0.0388798	−0.0194399	−	0.999811i	$-0.506188\pi$
$269$	−0.637677	−0.0388798	−0.0194399	+	0.999811i	$0.506188\pi$
$270$	−7.50407	−0.456683
$271$	−5.76846	−0.350409	−0.175204	−	0.984532i	$-0.556059\pi$
$271$	−5.76846	−0.350409	−0.175204	+	0.984532i	$0.556059\pi$
$272$	12.7395	0.772449
$273$	−25.9311	−1.56942
$274$	46.1258	2.78656
$275$	−14.2890	−0.861658
$276$	−17.0983	−1.02919
$277$	11.3662	0.682929	0.341465	−	0.939895i	$-0.389077\pi$
$277$	11.3662	0.682929	0.341465	+	0.939895i	$0.389077\pi$
$278$	−16.9303	−1.01541
$279$	−0.800706	−0.0479370
$280$	20.5733	1.22949
$281$	16.0409	0.956918	0.478459	−	0.878110i	$-0.341195\pi$
$281$	16.0409	0.956918	0.478459	+	0.878110i	$0.341195\pi$
$282$	11.2020	0.667071
$283$	3.43113	0.203959	0.101980	−	0.994786i	$-0.467482\pi$
$283$	3.43113	0.203959	0.101980	+	0.994786i	$0.467482\pi$
$284$	−5.22795	−0.310222
$285$	−23.5862	−1.39712
$286$	25.8850	1.53061
$287$	−23.8239	−1.40628
$288$	7.74205	0.456205
$289$	13.0429	0.767230
$290$	60.8245	3.57174
$291$	−13.9295	−0.816561
$292$	7.47534	0.437461
$293$	21.3014	1.24444	0.622220	−	0.782842i	$-0.286231\pi$
$293$	21.3014	1.24444	0.622220	+	0.782842i	$0.286231\pi$
$294$	24.9665	1.45607
$295$	41.2980	2.40447
$296$	−5.23093	−0.304041
$297$	1.99927	0.116010
$298$	19.5980	1.13528
$299$	39.0084	2.25592
$300$	−18.8381	−1.08762
$301$	−41.4434	−2.38876
$302$	14.1792	0.815924
$303$	11.6521	0.669395
$304$	15.7291	0.902127
$305$	−0.305496	−0.0174926
$306$	11.8014	0.674639
$307$	−30.2449	−1.72617	−0.863083	−	0.505062i	$-0.831469\pi$
$307$	−30.2449	−1.72617	−0.863083	+	0.505062i	$0.831469\pi$
$308$	−22.7241	−1.29482
$309$	−15.4512	−0.878987
$310$	−6.00856	−0.341263
$311$	16.7513	0.949879	0.474940	−	0.880018i	$-0.342470\pi$
$311$	16.7513	0.949879	0.474940	+	0.880018i	$0.342470\pi$
$312$	8.23146	0.466014
$313$	−9.75796	−0.551553	−0.275776	−	0.961222i	$-0.588935\pi$
$313$	−9.75796	−0.551553	−0.275776	+	0.961222i	$0.588935\pi$
$314$	19.6280	1.10767
$315$	−15.0294	−0.846812
$316$	27.5695	1.55091
$317$	−12.6711	−0.711678	−0.355839	−	0.934547i	$-0.615805\pi$
$317$	−12.6711	−0.711678	−0.355839	+	0.934547i	$0.615805\pi$
$318$	12.1462	0.681126
$319$	−16.2052	−0.907315
$320$	41.8956	2.34204
$321$	−3.42031	−0.190903
$322$	−60.2297	−3.35647
$323$	37.0930	2.06391
$324$	2.63577	0.146432
$325$	42.9778	2.38398
$326$	18.4380	1.02119
$327$	19.1015	1.05632
$328$	7.56256	0.417573
$329$	22.4358	1.23693
$330$	15.0027	0.825871
$331$	10.4876	0.576449	0.288224	−	0.957563i	$-0.406935\pi$
$331$	10.4876	0.576449	0.288224	+	0.957563i	$0.406935\pi$
$332$	33.8848	1.85967
$333$	3.82135	0.209409
$334$	24.3297	1.33126
$335$	−51.0446	−2.78886
$336$	10.0228	0.546789
$337$	28.8172	1.56977	0.784886	−	0.619640i	$-0.212721\pi$
$337$	28.8172	1.56977	0.784886	+	0.619640i	$0.212721\pi$
$338$	−49.8655	−2.71233
$339$	1.76882	0.0960692
$340$	50.3518	2.73071
$341$	1.60083	0.0866899
$342$	14.5708	0.787897
$343$	19.8178	1.07006
$344$	13.1556	0.709304
$345$	22.6089	1.21722
$346$	−22.3779	−1.20304
$347$	−9.19501	−0.493614	−0.246807	−	0.969065i	$-0.579381\pi$
$347$	−9.19501	−0.493614	−0.246807	+	0.969065i	$0.579381\pi$
$348$	−21.3643	−1.14525
$349$	25.3286	1.35581	0.677904	−	0.735151i	$-0.262889\pi$
$349$	25.3286	1.35581	0.677904	+	0.735151i	$0.262889\pi$
$350$	−66.3584	−3.54701
$351$	−6.01332	−0.320967
$352$	−15.4785	−0.825005
$353$	5.74802	0.305936	0.152968	−	0.988231i	$-0.451117\pi$
$353$	5.74802	0.305936	0.152968	+	0.988231i	$0.451117\pi$
$354$	−25.5126	−1.35598
$355$	6.91289	0.366898
$356$	−16.3095	−0.864403
$357$	23.6362	1.25096
$358$	33.8993	1.79163
$359$	35.6254	1.88024	0.940118	−	0.340850i	$-0.110715\pi$
$359$	35.6254	1.88024	0.940118	+	0.340850i	$0.110715\pi$
$360$	4.77088	0.251447
$361$	26.7976	1.41040
$362$	17.5645	0.923169
$363$	7.00290	0.367557
$364$	68.3484	3.58243
$365$	−9.88460	−0.517384
$366$	0.188725	0.00986483
$367$	−25.3627	−1.32392	−0.661962	−	0.749537i	$-0.730276\pi$
$367$	−25.3627	−1.32392	−0.661962	+	0.749537i	$0.730276\pi$
$368$	−15.0774	−0.785965
$369$	−5.52467	−0.287603
$370$	28.6757	1.49078
$371$	24.3269	1.26299
$372$	2.11048	0.109423
$373$	0.494014	0.0255791	0.0127895	−	0.999918i	$-0.495929\pi$
$373$	0.494014	0.0255791	0.0127895	+	0.999918i	$0.495929\pi$
$374$	−23.5941	−1.22002
$375$	7.48318	0.386430
$376$	−7.12193	−0.367285
$377$	48.7411	2.51030
$378$	9.28468	0.477552
$379$	23.2382	1.19367	0.596833	−	0.802366i	$-0.296426\pi$
$379$	23.2382	1.19367	0.596833	+	0.802366i	$0.296426\pi$
$380$	62.1678	3.18914
$381$	3.76338	0.192804
$382$	−32.9878	−1.68780
$383$	11.8774	0.606908	0.303454	−	0.952846i	$-0.401860\pi$
$383$	11.8774	0.606908	0.303454	+	0.952846i	$0.401860\pi$
$384$	−10.3977	−0.530603
$385$	30.0479	1.53138
$386$	−42.6327	−2.16995
$387$	−9.61058	−0.488533
$388$	36.7150	1.86392
$389$	24.9772	1.26639	0.633196	−	0.773991i	$-0.281743\pi$
$389$	24.9772	1.26639	0.633196	+	0.773991i	$0.281743\pi$
$390$	−45.1244	−2.28496
$391$	−35.5562	−1.79815
$392$	−15.8730	−0.801706
$393$	−17.3776	−0.876585
$394$	−23.7200	−1.19500
$395$	−36.4550	−1.83425
$396$	−5.26963	−0.264809
$397$	14.2267	0.714017	0.357009	−	0.934101i	$-0.383797\pi$
$397$	14.2267	0.714017	0.357009	+	0.934101i	$0.383797\pi$
$398$	43.1203	2.16142
$399$	29.1828	1.46097
$400$	−16.6116	−0.830581
$401$	−23.1273	−1.15492	−0.577461	−	0.816419i	$-0.695956\pi$
$401$	−23.1273	−1.15492	−0.577461	+	0.816419i	$0.695956\pi$
$402$	31.5337	1.57276
$403$	−4.81491	−0.239848
$404$	−30.7122	−1.52799
$405$	−3.48527	−0.173184
$406$	−75.2572	−3.73495
$407$	−7.63992	−0.378697
$408$	−7.50297	−0.371452
$409$	−24.7792	−1.22525	−0.612625	−	0.790373i	$-0.709887\pi$
$409$	−24.7792	−1.22525	−0.612625	+	0.790373i	$0.709887\pi$
$410$	−41.4576	−2.04744
$411$	21.4231	1.05672
$412$	40.7258	2.00642
$413$	−51.0975	−2.51434
$414$	−13.9671	−0.686444
$415$	−44.8057	−2.19942
$416$	46.5554	2.28257
$417$	−7.86329	−0.385067
$418$	−29.1310	−1.42484
$419$	−27.8188	−1.35904	−0.679518	−	0.733659i	$-0.737811\pi$
$419$	−27.8188	−1.35904	−0.679518	+	0.733659i	$0.737811\pi$
$420$	39.6141	1.93297
$421$	−7.74439	−0.377439	−0.188719	−	0.982031i	$-0.560434\pi$
$421$	−7.74439	−0.377439	−0.188719	+	0.982031i	$0.560434\pi$
$422$	42.1439	2.05153
$423$	5.20278	0.252968
$424$	−7.72222	−0.375024
$425$	−39.1742	−1.90023
$426$	−4.27056	−0.206909
$427$	0.377986	0.0182920
$428$	9.01515	0.435764
$429$	12.0223	0.580441
$430$	−72.1185	−3.47786
$431$	0.919399	0.0442859	0.0221430	−	0.999755i	$-0.492951\pi$
$431$	0.919399	0.0442859	0.0221430	+	0.999755i	$0.492951\pi$
$432$	2.32425	0.111826
$433$	13.0384	0.626584	0.313292	−	0.949657i	$-0.398568\pi$
$433$	13.0384	0.626584	0.313292	+	0.949657i	$0.398568\pi$
$434$	7.43430	0.356858
$435$	28.2499	1.35448
$436$	−50.3473	−2.41120
$437$	−43.9001	−2.10003
$438$	6.10638	0.291774
$439$	13.4723	0.642999	0.321499	−	0.946910i	$-0.395813\pi$
$439$	13.4723	0.642999	0.321499	+	0.946910i	$0.395813\pi$
$440$	−9.53829	−0.454720
$441$	11.5957	0.552175
$442$	70.9654	3.37548
$443$	11.6036	0.551305	0.275652	−	0.961257i	$-0.411106\pi$
$443$	11.6036	0.551305	0.275652	+	0.961257i	$0.411106\pi$
$444$	−10.0722	−0.478005
$445$	21.5660	1.02233
$446$	17.2096	0.814897
$447$	9.10230	0.430524
$448$	−51.8369	−2.44906
$449$	25.1164	1.18532	0.592659	−	0.805453i	$-0.298078\pi$
$449$	25.1164	1.18532	0.592659	+	0.805453i	$0.298078\pi$
$450$	−15.3883	−0.725411
$451$	11.0453	0.520105
$452$	−4.66221	−0.219292
$453$	6.58555	0.309416
$454$	34.3159	1.61052
$455$	−90.3767	−4.23693
$456$	−9.26368	−0.433812
$457$	28.8017	1.34728	0.673642	−	0.739058i	$-0.264729\pi$
$457$	28.8017	1.34728	0.673642	+	0.739058i	$0.264729\pi$
$458$	6.81862	0.318613
$459$	5.48114	0.255838
$460$	−59.5920	−2.77849
$461$	−26.3446	−1.22699	−0.613496	−	0.789698i	$-0.710237\pi$
$461$	−26.3446	−1.22699	−0.613496	+	0.789698i	$0.710237\pi$
$462$	−18.5626	−0.863611
$463$	36.4895	1.69581	0.847906	−	0.530147i	$-0.177863\pi$
$463$	36.4895	1.69581	0.847906	+	0.530147i	$0.177863\pi$
$464$	−18.8393	−0.874591
$465$	−2.79068	−0.129415
$466$	−6.21794	−0.288041
$467$	14.8630	0.687776	0.343888	−	0.939011i	$-0.388256\pi$
$467$	14.8630	0.687776	0.343888	+	0.939011i	$0.388256\pi$
$468$	15.8497	0.732655
$469$	63.1567	2.91631
$470$	39.0421	1.80088
$471$	9.11622	0.420053
$472$	16.2202	0.746594
$473$	19.2142	0.883469
$474$	22.5207	1.03441
$475$	−48.3672	−2.21924
$476$	−62.2995	−2.85549
$477$	5.64131	0.258298
$478$	−39.8432	−1.82239
$479$	8.90482	0.406872	0.203436	−	0.979088i	$-0.434789\pi$
$479$	8.90482	0.406872	0.203436	+	0.979088i	$0.434789\pi$
$480$	26.9831	1.23160
$481$	22.9790	1.04775
$482$	45.7632	2.08446
$483$	−27.9737	−1.27285
$484$	−18.4581	−0.839003
$485$	−48.5480	−2.20445
$486$	2.15308	0.0976659
$487$	−23.9631	−1.08587	−0.542937	−	0.839774i	$-0.682688\pi$
$487$	−23.9631	−1.08587	−0.542937	+	0.839774i	$0.682688\pi$
$488$	−0.119986	−0.00543152
$489$	8.56355	0.387257
$490$	87.0148	3.93093
$491$	5.14796	0.232324	0.116162	−	0.993230i	$-0.462941\pi$
$491$	5.14796	0.232324	0.116162	+	0.993230i	$0.462941\pi$
$492$	14.5618	0.656496
$493$	−44.4275	−2.00092
$494$	87.6187	3.94215
$495$	6.96800	0.313188
$496$	1.86104	0.0835633
$497$	−8.55322	−0.383664
$498$	27.6795	1.24035
$499$	−24.6255	−1.10239	−0.551195	−	0.834377i	$-0.685828\pi$
$499$	−24.6255	−1.10239	−0.551195	+	0.834377i	$0.685828\pi$
$500$	−19.7240	−0.882082
$501$	11.2999	0.504844
$502$	17.3955	0.776399
$503$	36.9354	1.64687	0.823435	−	0.567411i	$-0.192055\pi$
$503$	36.9354	1.64687	0.823435	+	0.567411i	$0.192055\pi$
$504$	−5.90294	−0.262938
$505$	40.6106	1.80715
$506$	27.9240	1.24137
$507$	−23.1600	−1.02857
$508$	−9.91941	−0.440102
$509$	−19.4118	−0.860415	−0.430207	−	0.902730i	$-0.641560\pi$
$509$	−19.4118	−0.860415	−0.430207	+	0.902730i	$0.641560\pi$
$510$	41.1309	1.82131
$511$	12.2301	0.541026
$512$	−24.3577	−1.07647
$513$	6.76739	0.298788
$514$	−34.0301	−1.50100
$515$	−53.8515	−2.37298
$516$	25.3313	1.11515
$517$	−10.4018	−0.457470
$518$	−35.4800	−1.55890
$519$	−10.3934	−0.456221
$520$	28.6888	1.25809
$521$	45.5963	1.99761	0.998804	−	0.0488922i	$-0.0155691\pi$
$521$	45.5963	1.99761	0.998804	+	0.0488922i	$0.0155691\pi$
$522$	−17.4519	−0.763848
$523$	22.7090	0.992994	0.496497	−	0.868038i	$-0.334619\pi$
$523$	22.7090	0.992994	0.496497	+	0.868038i	$0.334619\pi$
$524$	45.8034	2.00093
$525$	−30.8202	−1.34510
$526$	15.2776	0.666134
$527$	4.38879	0.191179
$528$	−4.64681	−0.202227
$529$	19.0812	0.829617
$530$	42.3328	1.83882
$531$	−11.8493	−0.514217
$532$	−76.9193	−3.33487
$533$	−33.2217	−1.43899
$534$	−13.3228	−0.576533
$535$	−11.9207	−0.515376
$536$	−20.0482	−0.865951
$537$	15.7445	0.679427
$538$	1.37297	0.0591930
$539$	−23.1829	−0.998560
$540$	9.18637	0.395318
$541$	28.1426	1.20994	0.604972	−	0.796247i	$-0.293184\pi$
$541$	28.1426	1.20994	0.604972	+	0.796247i	$0.293184\pi$
$542$	12.4200	0.533484
$543$	8.15782	0.350086
$544$	−42.4353	−1.81940
$545$	66.5739	2.85171
$546$	55.8318	2.38938
$547$	−23.9180	−1.02266	−0.511330	−	0.859384i	$-0.670847\pi$
$547$	−23.9180	−1.02266	−0.511330	+	0.859384i	$0.670847\pi$
$548$	−56.4664	−2.41213
$549$	0.0876535	0.00374096
$550$	30.7654	1.31184
$551$	−54.8533	−2.33683
$552$	8.87986	0.377952
$553$	45.1053	1.91807
$554$	−24.4724	−1.03973
$555$	13.3184	0.565335
$556$	20.7258	0.878971
$557$	9.26289	0.392481	0.196241	−	0.980556i	$-0.437127\pi$
$557$	9.26289	0.392481	0.196241	+	0.980556i	$0.437127\pi$
$558$	1.72399	0.0729823
$559$	−57.7915	−2.44432
$560$	34.9321	1.47615
$561$	−10.9583	−0.462660
$562$	−34.5373	−1.45687
$563$	−3.04101	−0.128163	−0.0640817	−	0.997945i	$-0.520412\pi$
$563$	−3.04101	−0.128163	−0.0640817	+	0.997945i	$0.520412\pi$
$564$	−13.7133	−0.577436
$565$	6.16481	0.259356
$566$	−7.38750	−0.310520
$567$	4.31227	0.181098
$568$	2.71510	0.113923
$569$	−4.75044	−0.199149	−0.0995743	−	0.995030i	$-0.531748\pi$
$569$	−4.75044	−0.199149	−0.0995743	+	0.995030i	$0.531748\pi$
$570$	50.7830	2.12707
$571$	32.3289	1.35292	0.676460	−	0.736479i	$-0.263513\pi$
$571$	32.3289	1.35292	0.676460	+	0.736479i	$0.263513\pi$
$572$	−31.6880	−1.32494
$573$	−15.3212	−0.640051
$574$	51.2948	2.14101
$575$	46.3632	1.93348
$576$	−12.0208	−0.500866
$577$	−14.5754	−0.606783	−0.303391	−	0.952866i	$-0.598119\pi$
$577$	−14.5754	−0.606783	−0.303391	+	0.952866i	$0.598119\pi$
$578$	−28.0825	−1.16808
$579$	−19.8008	−0.822892
$580$	−74.4603	−3.09180
$581$	55.4374	2.29993
$582$	29.9914	1.24318
$583$	−11.2785	−0.467109
$584$	−3.88226	−0.160649
$585$	−20.9580	−0.866508
$586$	−45.8637	−1.89461
$587$	8.10101	0.334364	0.167182	−	0.985926i	$-0.446533\pi$
$587$	8.10101	0.334364	0.167182	+	0.985926i	$0.446533\pi$
$588$	−30.5636	−1.26042
$589$	5.41870	0.223274
$590$	−88.9182	−3.66070
$591$	−11.0168	−0.453169
$592$	−8.88177	−0.365038
$593$	34.4370	1.41416	0.707078	−	0.707135i	$-0.250013\pi$
$593$	34.4370	1.41416	0.707078	+	0.707135i	$0.250013\pi$
$594$	−4.30460	−0.176620
$595$	82.3784	3.37718
$596$	−23.9916	−0.982733
$597$	20.0272	0.819659
$598$	−83.9884	−3.43454
$599$	15.6638	0.640007	0.320004	−	0.947416i	$-0.396316\pi$
$599$	15.6638	0.640007	0.320004	+	0.947416i	$0.396316\pi$
$600$	9.78344	0.399407
$601$	−0.765369	−0.0312201	−0.0156100	−	0.999878i	$-0.504969\pi$
$601$	−0.765369	−0.0312201	−0.0156100	+	0.999878i	$0.504969\pi$
$602$	89.2312	3.63679
$603$	14.6458	0.596424
$604$	−17.3580	−0.706288
$605$	24.4070	0.992285
$606$	−25.0879	−1.01913
$607$	40.0156	1.62418	0.812091	−	0.583531i	$-0.198329\pi$
$607$	40.0156	1.62418	0.812091	+	0.583531i	$0.198329\pi$
$608$	−52.3935	−2.12484
$609$	−34.9532	−1.41638
$610$	0.657758	0.0266319
$611$	31.2860	1.26570
$612$	−14.4470	−0.583987
$613$	13.0648	0.527681	0.263840	−	0.964566i	$-0.415011\pi$
$613$	13.0648	0.527681	0.263840	+	0.964566i	$0.415011\pi$
$614$	65.1197	2.62802
$615$	−19.2550	−0.776435
$616$	11.8016	0.475500
$617$	22.8941	0.921681	0.460840	−	0.887483i	$-0.347548\pi$
$617$	22.8941	0.921681	0.460840	+	0.887483i	$0.347548\pi$
$618$	33.2677	1.33822
$619$	5.02739	0.202068	0.101034	−	0.994883i	$-0.467785\pi$
$619$	5.02739	0.202068	0.101034	+	0.994883i	$0.467785\pi$
$620$	7.35559	0.295407
$621$	−6.48700	−0.260314
$622$	−36.0670	−1.44615
$623$	−26.6833	−1.06904
$624$	13.9765	0.559507
$625$	−9.65456	−0.386182
$626$	21.0097	0.839717
$627$	−13.5299	−0.540331
$628$	−24.0283	−0.958832
$629$	−20.9453	−0.835146
$630$	32.3596	1.28924
$631$	−49.2222	−1.95951	−0.979753	−	0.200210i	$-0.935838\pi$
$631$	−49.2222	−1.95951	−0.979753	+	0.200210i	$0.935838\pi$
$632$	−14.3180	−0.569541
$633$	19.5737	0.777986
$634$	27.2819	1.08350
$635$	13.1164	0.520508
$636$	−14.8692	−0.589603
$637$	69.7285	2.76275
$638$	34.8911	1.38135
$639$	−1.98346	−0.0784645
$640$	−36.2386	−1.43246
$641$	29.9577	1.18326	0.591628	−	0.806211i	$-0.298485\pi$
$641$	29.9577	1.18326	0.591628	+	0.806211i	$0.298485\pi$
$642$	7.36421	0.290642
$643$	17.4351	0.687575	0.343787	−	0.939048i	$-0.388290\pi$
$643$	17.4351	0.687575	0.343787	+	0.939048i	$0.388290\pi$
$644$	73.7323	2.90546
$645$	−33.4954	−1.31888
$646$	−79.8645	−3.14222
$647$	44.4314	1.74678	0.873389	−	0.487023i	$-0.161917\pi$
$647$	44.4314	1.74678	0.873389	+	0.487023i	$0.161917\pi$
$648$	−1.36887	−0.0537743
$649$	23.6900	0.929915
$650$	−92.5347	−3.62951
$651$	3.45286	0.135328
$652$	−22.5716	−0.883971
$653$	−15.3695	−0.601454	−0.300727	−	0.953710i	$-0.597229\pi$
$653$	−15.3695	−0.601454	−0.300727	+	0.953710i	$0.597229\pi$
$654$	−41.1272	−1.60820
$655$	−60.5656	−2.36649
$656$	12.8407	0.501346
$657$	2.83611	0.110647
$658$	−48.3062	−1.88317
$659$	−10.3014	−0.401287	−0.200643	−	0.979664i	$-0.564303\pi$
$659$	−10.3014	−0.401287	−0.200643	+	0.979664i	$0.564303\pi$
$660$	−18.3661	−0.714898
$661$	0.674024	0.0262165	0.0131082	−	0.999914i	$-0.495827\pi$
$661$	0.674024	0.0262165	0.0131082	+	0.999914i	$0.495827\pi$
$662$	−22.5806	−0.877621
$663$	32.9599	1.28006
$664$	−17.5978	−0.682928
$665$	101.710	3.94414
$666$	−8.22768	−0.318816
$667$	52.5806	2.03593
$668$	−29.7840	−1.15238
$669$	7.99299	0.309027
$670$	109.903	4.24593
$671$	−0.175243	−0.00676519
$672$	−33.3858	−1.28789
$673$	−28.3084	−1.09121	−0.545604	−	0.838043i	$-0.683700\pi$
$673$	−28.3084	−1.09121	−0.545604	+	0.838043i	$0.683700\pi$
$674$	−62.0459	−2.38992
$675$	−7.14709	−0.275092
$676$	61.0446	2.34787
$677$	−44.9410	−1.72722	−0.863612	−	0.504157i	$-0.831803\pi$
$677$	−44.9410	−1.72722	−0.863612	+	0.504157i	$0.831803\pi$
$678$	−3.80842	−0.146262
$679$	60.0677	2.30519
$680$	−26.1499	−1.00280
$681$	15.9380	0.610746
$682$	−3.44672	−0.131982
$683$	−10.6616	−0.407956	−0.203978	−	0.978975i	$-0.565387\pi$
$683$	−10.6616	−0.407956	−0.203978	+	0.978975i	$0.565387\pi$
$684$	−17.8373	−0.682026
$685$	74.6653	2.85281
$686$	−42.6694	−1.62912
$687$	3.16691	0.120825
$688$	22.3374	0.851605
$689$	33.9230	1.29236
$690$	−48.6789	−1.85318
$691$	6.29996	0.239662	0.119831	−	0.992794i	$-0.461765\pi$
$691$	6.29996	0.239662	0.119831	+	0.992794i	$0.461765\pi$
$692$	27.3947	1.04139
$693$	−8.62141	−0.327500
$694$	19.7976	0.751507
$695$	−27.4057	−1.03956
$696$	11.0954	0.420570
$697$	30.2815	1.14699
$698$	−54.5346	−2.06416
$699$	−2.88792	−0.109231
$700$	81.2350	3.07039
$701$	31.9239	1.20575	0.602875	−	0.797835i	$-0.294022\pi$
$701$	31.9239	1.20575	0.602875	+	0.797835i	$0.294022\pi$
$702$	12.9472	0.488660
$703$	−25.8606	−0.975350
$704$	24.0328	0.905771
$705$	18.1331	0.682931
$706$	−12.3760	−0.465776
$707$	−50.2470	−1.88973
$708$	31.2321	1.17377
$709$	12.1319	0.455624	0.227812	−	0.973705i	$-0.426843\pi$
$709$	12.1319	0.455624	0.227812	+	0.973705i	$0.426843\pi$
$710$	−14.8840	−0.558588
$711$	10.4598	0.392271
$712$	8.47024	0.317436
$713$	−5.19418	−0.194524
$714$	−50.8907	−1.90453
$715$	41.9009	1.56700
$716$	−41.4990	−1.55089
$717$	−18.5052	−0.691089
$718$	−76.7044	−2.86258
$719$	30.8582	1.15082	0.575408	−	0.817866i	$-0.304843\pi$
$719$	30.8582	1.15082	0.575408	+	0.817866i	$0.304843\pi$
$720$	8.10064	0.301893
$721$	66.6297	2.48142
$722$	−57.6975	−2.14728
$723$	21.2547	0.790472
$724$	−21.5022	−0.799121
$725$	57.9309	2.15150
$726$	−15.0778	−0.559591
$727$	−7.38070	−0.273735	−0.136867	−	0.990589i	$-0.543703\pi$
$727$	−7.38070	−0.273735	−0.136867	+	0.990589i	$0.543703\pi$
$728$	−35.4963	−1.31558
$729$	1.00000	0.0370370
$730$	21.2824	0.787696
$731$	52.6769	1.94833
$732$	−0.231035	−0.00853928
$733$	−17.6057	−0.650280	−0.325140	−	0.945666i	$-0.605411\pi$
$733$	−17.6057	−0.650280	−0.325140	+	0.945666i	$0.605411\pi$
$734$	54.6081	2.01562
$735$	40.4140	1.49069
$736$	50.2227	1.85123
$737$	−29.2810	−1.07858
$738$	11.8951	0.437864
$739$	42.4481	1.56148	0.780739	−	0.624857i	$-0.214843\pi$
$739$	42.4481	1.56148	0.780739	+	0.624857i	$0.214843\pi$
$740$	−35.1043	−1.29046
$741$	40.6945	1.49495
$742$	−52.3778	−1.92285
$743$	8.38026	0.307442	0.153721	−	0.988114i	$-0.450874\pi$
$743$	8.38026	0.307442	0.153721	+	0.988114i	$0.450874\pi$
$744$	−1.09606	−0.0401836
$745$	31.7239	1.16228
$746$	−1.06365	−0.0389431
$747$	12.8557	0.470367
$748$	28.8836	1.05609
$749$	14.7493	0.538927
$750$	−16.1119	−0.588324
$751$	27.6850	1.01024	0.505121	−	0.863049i	$-0.331448\pi$
$751$	27.6850	1.01024	0.505121	+	0.863049i	$0.331448\pi$
$752$	−12.0926	−0.440971
$753$	8.07934	0.294428
$754$	−104.944	−3.82183
$755$	22.9524	0.835324
$756$	−11.3662	−0.413383
$757$	−23.8313	−0.866163	−0.433081	−	0.901355i	$-0.642574\pi$
$757$	−23.8313	−0.866163	−0.433081	+	0.901355i	$0.642574\pi$
$758$	−50.0338	−1.81731
$759$	12.9693	0.470755
$760$	−32.2864	−1.17115
$761$	−38.4933	−1.39538	−0.697690	−	0.716400i	$-0.745789\pi$
$761$	−38.4933	−1.39538	−0.697690	+	0.716400i	$0.745789\pi$
$762$	−8.10287	−0.293536
$763$	−82.3709	−2.98203
$764$	40.3831	1.46101
$765$	19.1032	0.690679
$766$	−25.5731	−0.923994
$767$	−71.2538	−2.57282
$768$	−1.65453	−0.0597028
$769$	−9.90602	−0.357220	−0.178610	−	0.983920i	$-0.557160\pi$
$769$	−9.90602	−0.357220	−0.178610	+	0.983920i	$0.557160\pi$
$770$	−64.6957	−2.33147
$771$	−15.8053	−0.569213
$772$	52.1903	1.87837
$773$	−44.3490	−1.59512	−0.797562	−	0.603237i	$-0.793877\pi$
$773$	−44.3490	−1.59512	−0.797562	+	0.603237i	$0.793877\pi$
$774$	20.6924	0.743772
$775$	−5.72272	−0.205566
$776$	−19.0677	−0.684489
$777$	−16.4787	−0.591169
$778$	−53.7780	−1.92803
$779$	37.3877	1.33955
$780$	55.2406	1.97793
$781$	3.96548	0.141896
$782$	76.5554	2.73762
$783$	−8.10553	−0.289668
$784$	−26.9513	−0.962545
$785$	31.7725	1.13401
$786$	37.4155	1.33457
$787$	−27.8897	−0.994159	−0.497079	−	0.867705i	$-0.665594\pi$
$787$	−27.8897	−0.994159	−0.497079	+	0.867705i	$0.665594\pi$
$788$	29.0377	1.03442
$789$	7.09567	0.252613
$790$	78.4908	2.79258
$791$	−7.62764	−0.271207
$792$	2.73675	0.0972460
$793$	0.527089	0.0187175
$794$	−30.6313	−1.08706
$795$	19.6615	0.697321
$796$	−52.7871	−1.87099
$797$	−11.0486	−0.391362	−0.195681	−	0.980668i	$-0.562692\pi$
$797$	−11.0486	−0.391362	−0.195681	+	0.980668i	$0.562692\pi$
$798$	−62.8331	−2.22427
$799$	−28.5172	−1.00887
$800$	55.3331	1.95632
$801$	−6.18776	−0.218634
$802$	49.7950	1.75832
$803$	−5.67016	−0.200096
$804$	−38.6030	−1.36142
$805$	−97.4958	−3.43628
$806$	10.3669	0.365158
$807$	0.637677	0.0224473
$808$	15.9502	0.561126
$809$	−46.7462	−1.64351	−0.821755	−	0.569841i	$-0.807005\pi$
$809$	−46.7462	−1.64351	−0.821755	+	0.569841i	$0.807005\pi$
$810$	7.50407	0.263666
$811$	−51.6174	−1.81253	−0.906267	−	0.422707i	$-0.861080\pi$
$811$	−51.6174	−1.81253	−0.906267	+	0.422707i	$0.861080\pi$
$812$	92.1287	3.23308
$813$	5.76846	0.202309
$814$	16.4494	0.576551
$815$	29.8463	1.04547
$816$	−12.7395	−0.445973
$817$	65.0386	2.27541
$818$	53.3516	1.86540
$819$	25.9311	0.906105
$820$	50.7517	1.77233
$821$	4.42463	0.154421	0.0772104	−	0.997015i	$-0.475399\pi$
$821$	4.42463	0.154421	0.0772104	+	0.997015i	$0.475399\pi$
$822$	−46.1258	−1.60882
$823$	−8.21259	−0.286273	−0.143136	−	0.989703i	$-0.545719\pi$
$823$	−8.21259	−0.286273	−0.143136	+	0.989703i	$0.545719\pi$
$824$	−21.1507	−0.736818
$825$	14.2890	0.497479
$826$	110.017	3.82799
$827$	34.7883	1.20971	0.604853	−	0.796337i	$-0.293232\pi$
$827$	34.7883	1.20971	0.604853	+	0.796337i	$0.293232\pi$
$828$	17.0983	0.594205
$829$	24.7072	0.858117	0.429059	−	0.903277i	$-0.358845\pi$
$829$	24.7072	0.858117	0.429059	+	0.903277i	$0.358845\pi$
$830$	96.4704	3.34854
$831$	−11.3662	−0.394289
$832$	−72.2848	−2.50603
$833$	−63.5575	−2.20214
$834$	16.9303	0.586249
$835$	39.3833	1.36291
$836$	35.6617	1.23338
$837$	0.800706	0.0276765
$838$	59.8962	2.06908
$839$	7.86148	0.271409	0.135704	−	0.990749i	$-0.456670\pi$
$839$	7.86148	0.271409	0.135704	+	0.990749i	$0.456670\pi$
$840$	−20.5733	−0.709847
$841$	36.6995	1.26550
$842$	16.6743	0.574635
$843$	−16.0409	−0.552477
$844$	−51.5919	−1.77587
$845$	−80.7190	−2.77682
$846$	−11.2020	−0.385134
$847$	−30.1984	−1.03763
$848$	−13.1118	−0.450262
$849$	−3.43113	−0.117756
$850$	84.3454	2.89302
$851$	24.7891	0.849759
$852$	5.22795	0.179107
$853$	28.5146	0.976322	0.488161	−	0.872754i	$-0.337668\pi$
$853$	28.5146	0.976322	0.488161	+	0.872754i	$0.337668\pi$
$854$	−0.813835	−0.0278488
$855$	23.5862	0.806630
$856$	−4.68196	−0.160026
$857$	49.9737	1.70707	0.853534	−	0.521037i	$-0.174455\pi$
$857$	49.9737	1.70707	0.853534	+	0.521037i	$0.174455\pi$
$858$	−25.8850	−0.883699
$859$	−30.3929	−1.03699	−0.518496	−	0.855080i	$-0.673508\pi$
$859$	−30.3929	−1.03699	−0.518496	+	0.855080i	$0.673508\pi$
$860$	88.2863	3.01054
$861$	23.8239	0.811916
$862$	−1.97954	−0.0674235
$863$	−15.8295	−0.538844	−0.269422	−	0.963022i	$-0.586833\pi$
$863$	−15.8295	−0.538844	−0.269422	+	0.963022i	$0.586833\pi$
$864$	−7.74205	−0.263390
$865$	−36.2239	−1.23165
$866$	−28.0727	−0.953949
$867$	−13.0429	−0.442961
$868$	−9.10096	−0.308907
$869$	−20.9119	−0.709388
$870$	−60.8245	−2.06214
$871$	88.0700	2.98414
$872$	26.1475	0.885466
$873$	13.9295	0.471442
$874$	94.5206	3.19721
$875$	−32.2695	−1.09091
$876$	−7.47534	−0.252568
$877$	−26.8745	−0.907489	−0.453745	−	0.891132i	$-0.649912\pi$
$877$	−26.8745	−0.907489	−0.453745	+	0.891132i	$0.649912\pi$
$878$	−29.0070	−0.978940
$879$	−21.3014	−0.718478
$880$	−16.1954	−0.545946
$881$	25.0501	0.843961	0.421980	−	0.906605i	$-0.361335\pi$
$881$	25.0501	0.843961	0.421980	+	0.906605i	$0.361335\pi$
$882$	−24.9665	−0.840665
$883$	4.51887	0.152072	0.0760361	−	0.997105i	$-0.475774\pi$
$883$	4.51887	0.152072	0.0760361	+	0.997105i	$0.475774\pi$
$884$	−86.8747	−2.92191
$885$	−41.2980	−1.38822
$886$	−24.9836	−0.839340
$887$	−22.9800	−0.771593	−0.385796	−	0.922584i	$-0.626073\pi$
$887$	−22.9800	−0.771593	−0.385796	+	0.922584i	$0.626073\pi$
$888$	5.23093	0.175538
$889$	−16.2287	−0.544293
$890$	−46.4334	−1.55645
$891$	−1.99927	−0.0669782
$892$	−21.0677	−0.705398
$893$	−35.2093	−1.17823
$894$	−19.5980	−0.655456
$895$	54.8739	1.83423
$896$	44.8375	1.49792
$897$	−39.0084	−1.30245
$898$	−54.0778	−1.80460
$899$	−6.49015	−0.216459
$900$	18.8381	0.627937
$901$	−30.9208	−1.03012
$902$	−23.7815	−0.791839
$903$	41.4434	1.37915
$904$	2.42129	0.0805308
$905$	28.4322	0.945118
$906$	−14.1792	−0.471074
$907$	27.2841	0.905954	0.452977	−	0.891522i	$-0.350362\pi$
$907$	27.2841	0.905954	0.452977	+	0.891522i	$0.350362\pi$
$908$	−42.0089	−1.39412
$909$	−11.6521	−0.386475
$910$	194.589	6.45055
$911$	15.2032	0.503704	0.251852	−	0.967766i	$-0.418960\pi$
$911$	15.2032	0.503704	0.251852	+	0.967766i	$0.418960\pi$
$912$	−15.7291	−0.520843
$913$	−25.7021	−0.850616
$914$	−62.0124	−2.05119
$915$	0.305496	0.0100994
$916$	−8.34724	−0.275801
$917$	74.9370	2.47464
$918$	−11.8014	−0.389503
$919$	13.0043	0.428973	0.214486	−	0.976727i	$-0.431192\pi$
$919$	13.0043	0.428973	0.214486	+	0.976727i	$0.431192\pi$
$920$	30.9487	1.02035
$921$	30.2449	0.996602
$922$	56.7222	1.86805
$923$	−11.9272	−0.392588
$924$	22.7241	0.747567
$925$	27.3115	0.897997
$926$	−78.5650	−2.58181
$927$	15.4512	0.507483
$928$	62.7534	2.05998
$929$	18.0802	0.593192	0.296596	−	0.955003i	$-0.404149\pi$
$929$	18.0802	0.593192	0.296596	+	0.955003i	$0.404149\pi$
$930$	6.00856	0.197028
$931$	−78.4725	−2.57183
$932$	7.61191	0.249336
$933$	−16.7513	−0.548413
$934$	−32.0012	−1.04711
$935$	−38.1926	−1.24903
$936$	−8.23146	−0.269054
$937$	5.04246	0.164730	0.0823650	−	0.996602i	$-0.473753\pi$
$937$	5.04246	0.164730	0.0823650	+	0.996602i	$0.473753\pi$
$938$	−135.982	−4.43996
$939$	9.75796	0.318439
$940$	−47.7947	−1.55889
$941$	−27.0907	−0.883132	−0.441566	−	0.897229i	$-0.645577\pi$
$941$	−27.0907	−0.883132	−0.441566	+	0.897229i	$0.645577\pi$
$942$	−19.6280	−0.639514
$943$	−35.8386	−1.16706
$944$	27.5408	0.896376
$945$	15.0294	0.488907
$946$	−41.3697	−1.34505
$947$	32.4973	1.05602	0.528011	−	0.849238i	$-0.322938\pi$
$947$	32.4973	1.05602	0.528011	+	0.849238i	$0.322938\pi$
$948$	−27.5695	−0.895417
$949$	17.0544	0.553611
$950$	104.139	3.37870
$951$	12.6711	0.410887
$952$	32.3548	1.04863
$953$	46.2515	1.49823	0.749116	−	0.662439i	$-0.230478\pi$
$953$	46.2515	1.49823	0.749116	+	0.662439i	$0.230478\pi$
$954$	−12.1462	−0.393248
$955$	−53.3984	−1.72793
$956$	48.7754	1.57751
$957$	16.2052	0.523839
$958$	−19.1728	−0.619446
$959$	−92.3822	−2.98318
$960$	−41.8956	−1.35218
$961$	−30.3589	−0.979318
$962$	−49.4757	−1.59516
$963$	3.42031	0.110218
$964$	−56.0226	−1.80437
$965$	−69.0110	−2.22154
$966$	60.2297	1.93786
$967$	37.1311	1.19406	0.597028	−	0.802220i	$-0.296348\pi$
$967$	37.1311	1.19406	0.597028	+	0.802220i	$0.296348\pi$
$968$	9.58607	0.308108
$969$	−37.0930	−1.19160
$970$	104.528	3.35619
$971$	−3.19884	−0.102656	−0.0513279	−	0.998682i	$-0.516345\pi$
$971$	−3.19884	−0.102656	−0.0513279	+	0.998682i	$0.516345\pi$
$972$	−2.63577	−0.0845424
$973$	33.9086	1.08706
$974$	51.5946	1.65320
$975$	−42.9778	−1.37639
$976$	−0.203729	−0.00652120
$977$	15.8452	0.506933	0.253467	−	0.967344i	$-0.418429\pi$
$977$	15.8452	0.506933	0.253467	+	0.967344i	$0.418429\pi$
$978$	−18.4380	−0.589584
$979$	12.3710	0.395380
$980$	−106.522	−3.40273
$981$	−19.1015	−0.609865
$982$	−11.0840	−0.353705
$983$	16.4987	0.526228	0.263114	−	0.964765i	$-0.415250\pi$
$983$	16.4987	0.526228	0.263114	+	0.964765i	$0.415250\pi$
$984$	−7.56256	−0.241086
$985$	−38.3964	−1.22341
$986$	95.6562	3.04631
$987$	−22.4358	−0.714139
$988$	−107.261	−3.41244
$989$	−62.3438	−1.98242
$990$	−15.0027	−0.476817
$991$	52.6832	1.67354	0.836769	−	0.547556i	$-0.184442\pi$
$991$	52.6832	1.67354	0.836769	+	0.547556i	$0.184442\pi$
$992$	−6.19911	−0.196822
$993$	−10.4876	−0.332813
$994$	18.4158	0.584114
$995$	69.8002	2.21281
$996$	−33.8848	−1.07368
$997$	4.20223	0.133086	0.0665429	−	0.997784i	$-0.478803\pi$
$997$	4.20223	0.133086	0.0665429	+	0.997784i	$0.478803\pi$
$998$	53.0208	1.67834
$999$	−3.82135	−0.120902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.15	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.15308 q^{2} -1.00000 q^{3} +2.63577 q^{4} -3.48527 q^{5} +2.15308 q^{6} +4.31227 q^{7} -1.36887 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15308 q^{2} -1.00000 q^{3} +2.63577 q^{4} -3.48527 q^{5} +2.15308 q^{6} +4.31227 q^{7} -1.36887 q^{8} +1.00000 q^{9} +7.50407 q^{10} -1.99927 q^{11} -2.63577 q^{12} +6.01332 q^{13} -9.28468 q^{14} +3.48527 q^{15} -2.32425 q^{16} -5.48114 q^{17} -2.15308 q^{18} -6.76739 q^{19} -9.18637 q^{20} -4.31227 q^{21} +4.30460 q^{22} +6.48700 q^{23} +1.36887 q^{24} +7.14709 q^{25} -12.9472 q^{26} -1.00000 q^{27} +11.3662 q^{28} +8.10553 q^{29} -7.50407 q^{30} -0.800706 q^{31} +7.74205 q^{32} +1.99927 q^{33} +11.8014 q^{34} -15.0294 q^{35} +2.63577 q^{36} +3.82135 q^{37} +14.5708 q^{38} -6.01332 q^{39} +4.77088 q^{40} -5.52467 q^{41} +9.28468 q^{42} -9.61058 q^{43} -5.26963 q^{44} -3.48527 q^{45} -13.9671 q^{46} +5.20278 q^{47} +2.32425 q^{48} +11.5957 q^{49} -15.3883 q^{50} +5.48114 q^{51} +15.8497 q^{52} +5.64131 q^{53} +2.15308 q^{54} +6.96800 q^{55} -5.90294 q^{56} +6.76739 q^{57} -17.4519 q^{58} -11.8493 q^{59} +9.18637 q^{60} +0.0876535 q^{61} +1.72399 q^{62} +4.31227 q^{63} -12.0208 q^{64} -20.9580 q^{65} -4.30460 q^{66} +14.6458 q^{67} -14.4470 q^{68} -6.48700 q^{69} +32.3596 q^{70} -1.98346 q^{71} -1.36887 q^{72} +2.83611 q^{73} -8.22768 q^{74} -7.14709 q^{75} -17.8373 q^{76} -8.62141 q^{77} +12.9472 q^{78} +10.4598 q^{79} +8.10064 q^{80} +1.00000 q^{81} +11.8951 q^{82} +12.8557 q^{83} -11.3662 q^{84} +19.1032 q^{85} +20.6924 q^{86} -8.10553 q^{87} +2.73675 q^{88} -6.18776 q^{89} +7.50407 q^{90} +25.9311 q^{91} +17.0983 q^{92} +0.800706 q^{93} -11.2020 q^{94} +23.5862 q^{95} -7.74205 q^{96} +13.9295 q^{97} -24.9665 q^{98} -1.99927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 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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