LMFDB - Embedded newform 8049.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22780 q^{2} -1.00000 q^{3} +2.96308 q^{4} +4.08366 q^{5} +2.22780 q^{6} +2.32778 q^{7} -2.14554 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22780 q^{2} -1.00000 q^{3} +2.96308 q^{4} +4.08366 q^{5} +2.22780 q^{6} +2.32778 q^{7} -2.14554 q^{8} +1.00000 q^{9} -9.09757 q^{10} -5.17618 q^{11} -2.96308 q^{12} -1.23569 q^{13} -5.18581 q^{14} -4.08366 q^{15} -1.14633 q^{16} +0.0659753 q^{17} -2.22780 q^{18} +3.64583 q^{19} +12.1002 q^{20} -2.32778 q^{21} +11.5315 q^{22} +2.98658 q^{23} +2.14554 q^{24} +11.6763 q^{25} +2.75287 q^{26} -1.00000 q^{27} +6.89738 q^{28} +9.03463 q^{29} +9.09757 q^{30} -8.97330 q^{31} +6.84487 q^{32} +5.17618 q^{33} -0.146979 q^{34} +9.50586 q^{35} +2.96308 q^{36} -3.00029 q^{37} -8.12216 q^{38} +1.23569 q^{39} -8.76165 q^{40} -4.81990 q^{41} +5.18581 q^{42} +10.3235 q^{43} -15.3374 q^{44} +4.08366 q^{45} -6.65349 q^{46} +3.64756 q^{47} +1.14633 q^{48} -1.58146 q^{49} -26.0124 q^{50} -0.0659753 q^{51} -3.66144 q^{52} -8.10566 q^{53} +2.22780 q^{54} -21.1378 q^{55} -4.99433 q^{56} -3.64583 q^{57} -20.1273 q^{58} +0.724895 q^{59} -12.1002 q^{60} -13.3939 q^{61} +19.9907 q^{62} +2.32778 q^{63} -12.9563 q^{64} -5.04614 q^{65} -11.5315 q^{66} +13.5288 q^{67} +0.195490 q^{68} -2.98658 q^{69} -21.1771 q^{70} +4.07801 q^{71} -2.14554 q^{72} +11.2996 q^{73} +6.68403 q^{74} -11.6763 q^{75} +10.8029 q^{76} -12.0490 q^{77} -2.75287 q^{78} -6.24094 q^{79} -4.68123 q^{80} +1.00000 q^{81} +10.7378 q^{82} +4.90107 q^{83} -6.89738 q^{84} +0.269421 q^{85} -22.9987 q^{86} -9.03463 q^{87} +11.1057 q^{88} +5.34755 q^{89} -9.09757 q^{90} -2.87641 q^{91} +8.84946 q^{92} +8.97330 q^{93} -8.12601 q^{94} +14.8883 q^{95} -6.84487 q^{96} -11.6709 q^{97} +3.52316 q^{98} -5.17618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.22780	−1.57529	−0.787645	−	0.616129i	$-0.788700\pi$
$2$	−2.22780	−1.57529	−0.787645	+	0.616129i	$0.788700\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.96308	1.48154
$5$	4.08366	1.82627	0.913135	−	0.407657i	$-0.133654\pi$
$5$	4.08366	1.82627	0.913135	+	0.407657i	$0.133654\pi$
$6$	2.22780	0.909494
$7$	2.32778	0.879817	0.439908	−	0.898043i	$-0.355011\pi$
$7$	2.32778	0.879817	0.439908	+	0.898043i	$0.355011\pi$
$8$	−2.14554	−0.758562
$9$	1.00000	0.333333
$10$	−9.09757	−2.87690
$11$	−5.17618	−1.56068	−0.780338	−	0.625357i	$-0.784953\pi$
$11$	−5.17618	−1.56068	−0.780338	+	0.625357i	$0.784953\pi$
$12$	−2.96308	−0.855366
$13$	−1.23569	−0.342719	−0.171359	−	0.985209i	$-0.554816\pi$
$13$	−1.23569	−0.342719	−0.171359	+	0.985209i	$0.554816\pi$
$14$	−5.18581	−1.38597
$15$	−4.08366	−1.05440
$16$	−1.14633	−0.286583
$17$	0.0659753	0.0160013	0.00800067	−	0.999968i	$-0.497453\pi$
$17$	0.0659753	0.0160013	0.00800067	+	0.999968i	$0.497453\pi$
$18$	−2.22780	−0.525097
$19$	3.64583	0.836410	0.418205	−	0.908353i	$-0.362659\pi$
$19$	3.64583	0.836410	0.418205	+	0.908353i	$0.362659\pi$
$20$	12.1002	2.70569
$21$	−2.32778	−0.507963
$22$	11.5315	2.45852
$23$	2.98658	0.622745	0.311372	−	0.950288i	$-0.399211\pi$
$23$	2.98658	0.622745	0.311372	+	0.950288i	$0.399211\pi$
$24$	2.14554	0.437956
$25$	11.6763	2.33526
$26$	2.75287	0.539881
$27$	−1.00000	−0.192450
$28$	6.89738	1.30348
$29$	9.03463	1.67769	0.838844	−	0.544371i	$-0.183232\pi$
$29$	9.03463	1.67769	0.838844	+	0.544371i	$0.183232\pi$
$30$	9.09757	1.66098
$31$	−8.97330	−1.61165	−0.805826	−	0.592153i	$-0.798278\pi$
$31$	−8.97330	−1.61165	−0.805826	+	0.592153i	$0.798278\pi$
$32$	6.84487	1.21001
$33$	5.17618	0.901057
$34$	−0.146979	−0.0252068
$35$	9.50586	1.60678
$36$	2.96308	0.493846
$37$	−3.00029	−0.493245	−0.246622	−	0.969112i	$-0.579321\pi$
$37$	−3.00029	−0.493245	−0.246622	+	0.969112i	$0.579321\pi$
$38$	−8.12216	−1.31759
$39$	1.23569	0.197869
$40$	−8.76165	−1.38534
$41$	−4.81990	−0.752742	−0.376371	−	0.926469i	$-0.622828\pi$
$41$	−4.81990	−0.752742	−0.376371	+	0.926469i	$0.622828\pi$
$42$	5.18581	0.800188
$43$	10.3235	1.57432	0.787162	−	0.616746i	$-0.211549\pi$
$43$	10.3235	1.57432	0.787162	+	0.616746i	$0.211549\pi$
$44$	−15.3374	−2.31220
$45$	4.08366	0.608757
$46$	−6.65349	−0.981003
$47$	3.64756	0.532051	0.266025	−	0.963966i	$-0.414289\pi$
$47$	3.64756	0.532051	0.266025	+	0.963966i	$0.414289\pi$
$48$	1.14633	0.165459
$49$	−1.58146	−0.225922
$50$	−26.0124	−3.67871
$51$	−0.0659753	−0.00923838
$52$	−3.66144	−0.507751
$53$	−8.10566	−1.11340	−0.556699	−	0.830714i	$-0.687932\pi$
$53$	−8.10566	−1.11340	−0.556699	+	0.830714i	$0.687932\pi$
$54$	2.22780	0.303165
$55$	−21.1378	−2.85022
$56$	−4.99433	−0.667396
$57$	−3.64583	−0.482902
$58$	−20.1273	−2.64285
$59$	0.724895	0.0943733	0.0471866	−	0.998886i	$-0.484974\pi$
$59$	0.724895	0.0943733	0.0471866	+	0.998886i	$0.484974\pi$
$60$	−12.1002	−1.56213
$61$	−13.3939	−1.71491	−0.857453	−	0.514562i	$-0.827955\pi$
$61$	−13.3939	−1.71491	−0.857453	+	0.514562i	$0.827955\pi$
$62$	19.9907	2.53882
$63$	2.32778	0.293272
$64$	−12.9563	−1.61954
$65$	−5.04614	−0.625897
$66$	−11.5315	−1.41943
$67$	13.5288	1.65281	0.826405	−	0.563076i	$-0.190382\pi$
$67$	13.5288	1.65281	0.826405	+	0.563076i	$0.190382\pi$
$68$	0.195490	0.0237066
$69$	−2.98658	−0.359542
$70$	−21.1771	−2.53115
$71$	4.07801	0.483971	0.241985	−	0.970280i	$-0.422201\pi$
$71$	4.07801	0.483971	0.241985	+	0.970280i	$0.422201\pi$
$72$	−2.14554	−0.252854
$73$	11.2996	1.32252	0.661260	−	0.750157i	$-0.270022\pi$
$73$	11.2996	1.32252	0.661260	+	0.750157i	$0.270022\pi$
$74$	6.68403	0.777003
$75$	−11.6763	−1.34826
$76$	10.8029	1.23917
$77$	−12.0490	−1.37311
$78$	−2.75287	−0.311701
$79$	−6.24094	−0.702161	−0.351080	−	0.936345i	$-0.614186\pi$
$79$	−6.24094	−0.702161	−0.351080	+	0.936345i	$0.614186\pi$
$80$	−4.68123	−0.523378
$81$	1.00000	0.111111
$82$	10.7378	1.18579
$83$	4.90107	0.537962	0.268981	−	0.963145i	$-0.413313\pi$
$83$	4.90107	0.537962	0.268981	+	0.963145i	$0.413313\pi$
$84$	−6.89738	−0.752566
$85$	0.269421	0.0292228
$86$	−22.9987	−2.48002
$87$	−9.03463	−0.968614
$88$	11.1057	1.18387
$89$	5.34755	0.566839	0.283419	−	0.958996i	$-0.408531\pi$
$89$	5.34755	0.566839	0.283419	+	0.958996i	$0.408531\pi$
$90$	−9.09757	−0.958968
$91$	−2.87641	−0.301530
$92$	8.84946	0.922620
$93$	8.97330	0.930488
$94$	−8.12601	−0.838134
$95$	14.8883	1.52751
$96$	−6.84487	−0.698602
$97$	−11.6709	−1.18500	−0.592502	−	0.805569i	$-0.701860\pi$
$97$	−11.6709	−1.18500	−0.592502	+	0.805569i	$0.701860\pi$
$98$	3.52316	0.355893
$99$	−5.17618	−0.520226
$100$	34.5978	3.45978
$101$	17.1227	1.70377	0.851886	−	0.523728i	$-0.175459\pi$
$101$	17.1227	1.70377	0.851886	+	0.523728i	$0.175459\pi$
$102$	0.146979	0.0145531
$103$	−1.04702	−0.103166	−0.0515832	−	0.998669i	$-0.516427\pi$
$103$	−1.04702	−0.103166	−0.0515832	+	0.998669i	$0.516427\pi$
$104$	2.65122	0.259974
$105$	−9.50586	−0.927677
$106$	18.0578	1.75393
$107$	0.759091	0.0733841	0.0366920	−	0.999327i	$-0.488318\pi$
$107$	0.759091	0.0733841	0.0366920	+	0.999327i	$0.488318\pi$
$108$	−2.96308	−0.285122
$109$	−11.9021	−1.14001	−0.570006	−	0.821640i	$-0.693059\pi$
$109$	−11.9021	−1.14001	−0.570006	+	0.821640i	$0.693059\pi$
$110$	47.0907	4.48992
$111$	3.00029	0.284775
$112$	−2.66840	−0.252141
$113$	3.41210	0.320983	0.160492	−	0.987037i	$-0.448692\pi$
$113$	3.41210	0.320983	0.160492	+	0.987037i	$0.448692\pi$
$114$	8.12216	0.760710
$115$	12.1962	1.13730
$116$	26.7703	2.48556
$117$	−1.23569	−0.114240
$118$	−1.61492	−0.148665
$119$	0.153576	0.0140783
$120$	8.76165	0.799826
$121$	15.7928	1.43571
$122$	29.8388	2.70148
$123$	4.81990	0.434596
$124$	−26.5886	−2.38772
$125$	27.2638	2.43855
$126$	−5.18581	−0.461989
$127$	7.04577	0.625211	0.312606	−	0.949883i	$-0.398798\pi$
$127$	7.04577	0.625211	0.312606	+	0.949883i	$0.398798\pi$
$128$	15.1743	1.34123
$129$	−10.3235	−0.908936
$130$	11.2418	0.985969
$131$	21.7273	1.89832	0.949161	−	0.314792i	$-0.101935\pi$
$131$	21.7273	1.89832	0.949161	+	0.314792i	$0.101935\pi$
$132$	15.3374	1.33495
$133$	8.48668	0.735888
$134$	−30.1395	−2.60366
$135$	−4.08366	−0.351466
$136$	−0.141552	−0.0121380
$137$	−11.3985	−0.973840	−0.486920	−	0.873447i	$-0.661880\pi$
$137$	−11.3985	−0.973840	−0.486920	+	0.873447i	$0.661880\pi$
$138$	6.65349	0.566383
$139$	14.5070	1.23047	0.615234	−	0.788345i	$-0.289062\pi$
$139$	14.5070	1.23047	0.615234	+	0.788345i	$0.289062\pi$
$140$	28.1666	2.38051
$141$	−3.64756	−0.307180
$142$	−9.08498	−0.762394
$143$	6.39615	0.534873
$144$	−1.14633	−0.0955277
$145$	36.8944	3.06391
$146$	−25.1732	−2.08335
$147$	1.58146	0.130436
$148$	−8.89009	−0.730761
$149$	−18.2158	−1.49230	−0.746148	−	0.665780i	$-0.768099\pi$
$149$	−18.2158	−1.49230	−0.746148	+	0.665780i	$0.768099\pi$
$150$	26.0124	2.12391
$151$	23.1304	1.88232	0.941161	−	0.337959i	$-0.109737\pi$
$151$	23.1304	1.88232	0.941161	+	0.337959i	$0.109737\pi$
$152$	−7.82226	−0.634469
$153$	0.0659753	0.00533378
$154$	26.8427	2.16305
$155$	−36.6439	−2.94331
$156$	3.66144	0.293150
$157$	9.99466	0.797661	0.398830	−	0.917025i	$-0.369416\pi$
$157$	9.99466	0.797661	0.398830	+	0.917025i	$0.369416\pi$
$158$	13.9035	1.10611
$159$	8.10566	0.642821
$160$	27.9521	2.20981
$161$	6.95209	0.547901
$162$	−2.22780	−0.175032
$163$	−1.72489	−0.135104	−0.0675518	−	0.997716i	$-0.521519\pi$
$163$	−1.72489	−0.135104	−0.0675518	+	0.997716i	$0.521519\pi$
$164$	−14.2817	−1.11522
$165$	21.1378	1.64557
$166$	−10.9186	−0.847447
$167$	−14.4421	−1.11756	−0.558781	−	0.829315i	$-0.688731\pi$
$167$	−14.4421	−1.11756	−0.558781	+	0.829315i	$0.688731\pi$
$168$	4.99433	0.385321
$169$	−11.4731	−0.882544
$170$	−0.600214	−0.0460343
$171$	3.64583	0.278803
$172$	30.5894	2.33242
$173$	−15.1521	−1.15199	−0.575995	−	0.817453i	$-0.695385\pi$
$173$	−15.1521	−1.15199	−0.575995	+	0.817453i	$0.695385\pi$
$174$	20.1273	1.52585
$175$	27.1798	2.05460
$176$	5.93362	0.447263
$177$	−0.724895	−0.0544864
$178$	−11.9132	−0.892935
$179$	16.6046	1.24109	0.620543	−	0.784173i	$-0.286912\pi$
$179$	16.6046	1.24109	0.620543	+	0.784173i	$0.286912\pi$
$180$	12.1002	0.901896
$181$	−5.67598	−0.421892	−0.210946	−	0.977498i	$-0.567654\pi$
$181$	−5.67598	−0.421892	−0.210946	+	0.977498i	$0.567654\pi$
$182$	6.40806	0.474997
$183$	13.3939	0.990102
$184$	−6.40782	−0.472391
$185$	−12.2522	−0.900798
$186$	−19.9907	−1.46579
$187$	−0.341500	−0.0249729
$188$	10.8080	0.788254
$189$	−2.32778	−0.169321
$190$	−33.1682	−2.40627
$191$	−0.820426	−0.0593639	−0.0296820	−	0.999559i	$-0.509449\pi$
$191$	−0.820426	−0.0593639	−0.0296820	+	0.999559i	$0.509449\pi$
$192$	12.9563	0.935041
$193$	1.60021	0.115186	0.0575930	−	0.998340i	$-0.481657\pi$
$193$	1.60021	0.115186	0.0575930	+	0.998340i	$0.481657\pi$
$194$	26.0005	1.86673
$195$	5.04614	0.361362
$196$	−4.68597	−0.334712
$197$	22.5809	1.60882	0.804411	−	0.594073i	$-0.202481\pi$
$197$	22.5809	1.60882	0.804411	+	0.594073i	$0.202481\pi$
$198$	11.5315	0.819506
$199$	0.691071	0.0489888	0.0244944	−	0.999700i	$-0.492202\pi$
$199$	0.691071	0.0489888	0.0244944	+	0.999700i	$0.492202\pi$
$200$	−25.0520	−1.77144
$201$	−13.5288	−0.954250
$202$	−38.1459	−2.68393
$203$	21.0306	1.47606
$204$	−0.195490	−0.0136870
$205$	−19.6829	−1.37471
$206$	2.33256	0.162517
$207$	2.98658	0.207582
$208$	1.41651	0.0982174
$209$	−18.8715	−1.30537
$210$	21.1771	1.46136
$211$	4.18934	0.288406	0.144203	−	0.989548i	$-0.453938\pi$
$211$	4.18934	0.288406	0.144203	+	0.989548i	$0.453938\pi$
$212$	−24.0177	−1.64954
$213$	−4.07801	−0.279421
$214$	−1.69110	−0.115601
$215$	42.1578	2.87514
$216$	2.14554	0.145985
$217$	−20.8878	−1.41796
$218$	26.5154	1.79585
$219$	−11.2996	−0.763557
$220$	−62.6328	−4.22271
$221$	−0.0815250	−0.00548396
$222$	−6.68403	−0.448603
$223$	18.9389	1.26824	0.634122	−	0.773233i	$-0.281362\pi$
$223$	18.9389	1.26824	0.634122	+	0.773233i	$0.281362\pi$
$224$	15.9333	1.06459
$225$	11.6763	0.778421
$226$	−7.60146	−0.505642
$227$	−16.6909	−1.10782	−0.553908	−	0.832578i	$-0.686864\pi$
$227$	−16.6909	−1.10782	−0.553908	+	0.832578i	$0.686864\pi$
$228$	−10.8029	−0.715437
$229$	−7.88751	−0.521222	−0.260611	−	0.965444i	$-0.583924\pi$
$229$	−7.88751	−0.521222	−0.260611	+	0.965444i	$0.583924\pi$
$230$	−27.1706	−1.79158
$231$	12.0490	0.792765
$232$	−19.3841	−1.27263
$233$	28.7208	1.88156	0.940781	−	0.339015i	$-0.110094\pi$
$233$	28.7208	1.88156	0.940781	+	0.339015i	$0.110094\pi$
$234$	2.75287	0.179960
$235$	14.8954	0.971668
$236$	2.14792	0.139818
$237$	6.24094	0.405393
$238$	−0.342135	−0.0221773
$239$	23.1029	1.49440	0.747202	−	0.664596i	$-0.231397\pi$
$239$	23.1029	1.49440	0.747202	+	0.664596i	$0.231397\pi$
$240$	4.68123	0.302172
$241$	−26.7625	−1.72393	−0.861963	−	0.506971i	$-0.830765\pi$
$241$	−26.7625	−1.72393	−0.861963	+	0.506971i	$0.830765\pi$
$242$	−35.1832	−2.26166
$243$	−1.00000	−0.0641500
$244$	−39.6870	−2.54070
$245$	−6.45813	−0.412595
$246$	−10.7378	−0.684615
$247$	−4.50512	−0.286654
$248$	19.2525	1.22254
$249$	−4.90107	−0.310593
$250$	−60.7382	−3.84142
$251$	20.0462	1.26531	0.632653	−	0.774435i	$-0.281966\pi$
$251$	20.0462	1.26531	0.632653	+	0.774435i	$0.281966\pi$
$252$	6.89738	0.434494
$253$	−15.4591	−0.971903
$254$	−15.6965	−0.984889
$255$	−0.269421	−0.0168718
$256$	−7.89259	−0.493287
$257$	−2.01933	−0.125962	−0.0629810	−	0.998015i	$-0.520061\pi$
$257$	−2.01933	−0.125962	−0.0629810	+	0.998015i	$0.520061\pi$
$258$	22.9987	1.43184
$259$	−6.98400	−0.433965
$260$	−14.9521	−0.927290
$261$	9.03463	0.559230
$262$	−48.4040	−2.99041
$263$	−2.67779	−0.165120	−0.0825598	−	0.996586i	$-0.526310\pi$
$263$	−2.67779	−0.165120	−0.0825598	+	0.996586i	$0.526310\pi$
$264$	−11.1057	−0.683508
$265$	−33.1008	−2.03337
$266$	−18.9066	−1.15924
$267$	−5.34755	−0.327265
$268$	40.0870	2.44870
$269$	19.9787	1.21812	0.609061	−	0.793123i	$-0.291546\pi$
$269$	19.9787	1.21812	0.609061	+	0.793123i	$0.291546\pi$
$270$	9.09757	0.553660
$271$	−12.8583	−0.781083	−0.390542	−	0.920585i	$-0.627712\pi$
$271$	−12.8583	−0.781083	−0.390542	+	0.920585i	$0.627712\pi$
$272$	−0.0756295	−0.00458571
$273$	2.87641	0.174088
$274$	25.3935	1.53408
$275$	−60.4387	−3.64459
$276$	−8.84946	−0.532675
$277$	−13.9401	−0.837582	−0.418791	−	0.908083i	$-0.637546\pi$
$277$	−13.9401	−0.837582	−0.418791	+	0.908083i	$0.637546\pi$
$278$	−32.3186	−1.93834
$279$	−8.97330	−0.537217
$280$	−20.3952	−1.21884
$281$	19.1097	1.13999	0.569995	−	0.821648i	$-0.306945\pi$
$281$	19.1097	1.13999	0.569995	+	0.821648i	$0.306945\pi$
$282$	8.12601	0.483897
$283$	−9.61841	−0.571755	−0.285877	−	0.958266i	$-0.592285\pi$
$283$	−9.61841	−0.571755	−0.285877	+	0.958266i	$0.592285\pi$
$284$	12.0835	0.717021
$285$	−14.8883	−0.881909
$286$	−14.2493	−0.842581
$287$	−11.2197	−0.662276
$288$	6.84487	0.403338
$289$	−16.9956	−0.999744
$290$	−82.1932	−4.82655
$291$	11.6709	0.684163
$292$	33.4816	1.95936
$293$	4.55521	0.266118	0.133059	−	0.991108i	$-0.457520\pi$
$293$	4.55521	0.266118	0.133059	+	0.991108i	$0.457520\pi$
$294$	−3.52316	−0.205475
$295$	2.96023	0.172351
$296$	6.43723	0.374157
$297$	5.17618	0.300352
$298$	40.5811	2.35080
$299$	−3.69049	−0.213426
$300$	−34.5978	−1.99750
$301$	24.0309	1.38512
$302$	−51.5297	−2.96520
$303$	−17.1227	−0.983673
$304$	−4.17933	−0.239701
$305$	−54.6960	−3.13188
$306$	−0.146979	−0.00840225
$307$	−10.5234	−0.600605	−0.300302	−	0.953844i	$-0.597088\pi$
$307$	−10.5234	−0.600605	−0.300302	+	0.953844i	$0.597088\pi$
$308$	−35.7021	−2.03431
$309$	1.04702	0.0595631
$310$	81.6352	4.63657
$311$	7.50526	0.425584	0.212792	−	0.977097i	$-0.431744\pi$
$311$	7.50526	0.425584	0.212792	+	0.977097i	$0.431744\pi$
$312$	−2.65122	−0.150096
$313$	19.9375	1.12693	0.563467	−	0.826138i	$-0.309467\pi$
$313$	19.9375	1.12693	0.563467	+	0.826138i	$0.309467\pi$
$314$	−22.2661	−1.25655
$315$	9.50586	0.535594
$316$	−18.4924	−1.04028
$317$	8.79483	0.493967	0.246984	−	0.969020i	$-0.420561\pi$
$317$	8.79483	0.493967	0.246984	+	0.969020i	$0.420561\pi$
$318$	−18.0578	−1.01263
$319$	−46.7649	−2.61833
$320$	−52.9092	−2.95771
$321$	−0.759091	−0.0423683
$322$	−15.4878	−0.863103
$323$	0.240534	0.0133837
$324$	2.96308	0.164615
$325$	−14.4283	−0.800338
$326$	3.84270	0.212827
$327$	11.9021	0.658186
$328$	10.3413	0.571002
$329$	8.49070	0.468107
$330$	−47.0907	−2.59226
$331$	10.2136	0.561389	0.280695	−	0.959797i	$-0.409435\pi$
$331$	10.2136	0.561389	0.280695	+	0.959797i	$0.409435\pi$
$332$	14.5222	0.797012
$333$	−3.00029	−0.164415
$334$	32.1740	1.76048
$335$	55.2472	3.01848
$336$	2.66840	0.145573
$337$	17.2380	0.939012	0.469506	−	0.882929i	$-0.344432\pi$
$337$	17.2380	0.939012	0.469506	+	0.882929i	$0.344432\pi$
$338$	25.5597	1.39026
$339$	−3.41210	−0.185320
$340$	0.798314	0.0432947
$341$	46.4474	2.51527
$342$	−8.12216	−0.439196
$343$	−19.9757	−1.07859
$344$	−22.1495	−1.19422
$345$	−12.1962	−0.656620
$346$	33.7557	1.81472
$347$	−15.2269	−0.817423	−0.408712	−	0.912664i	$-0.634022\pi$
$347$	−15.2269	−0.817423	−0.408712	+	0.912664i	$0.634022\pi$
$348$	−26.7703	−1.43504
$349$	29.1870	1.56234	0.781171	−	0.624317i	$-0.214622\pi$
$349$	29.1870	1.56234	0.781171	+	0.624317i	$0.214622\pi$
$350$	−60.5511	−3.23659
$351$	1.23569	0.0659563
$352$	−35.4303	−1.88844
$353$	16.8560	0.897157	0.448578	−	0.893743i	$-0.351930\pi$
$353$	16.8560	0.897157	0.448578	+	0.893743i	$0.351930\pi$
$354$	1.61492	0.0858319
$355$	16.6532	0.883861
$356$	15.8452	0.839793
$357$	−0.153576	−0.00812809
$358$	−36.9916	−1.95507
$359$	5.68501	0.300043	0.150022	−	0.988683i	$-0.452066\pi$
$359$	5.68501	0.300043	0.150022	+	0.988683i	$0.452066\pi$
$360$	−8.76165	−0.461780
$361$	−5.70793	−0.300418
$362$	12.6449	0.664603
$363$	−15.7928	−0.828909
$364$	−8.52303	−0.446728
$365$	46.1438	2.41528
$366$	−29.8388	−1.55970
$367$	−19.4091	−1.01315	−0.506573	−	0.862197i	$-0.669088\pi$
$367$	−19.4091	−1.01315	−0.506573	+	0.862197i	$0.669088\pi$
$368$	−3.42361	−0.178468
$369$	−4.81990	−0.250914
$370$	27.2953	1.41902
$371$	−18.8682	−0.979587
$372$	26.5886	1.37855
$373$	6.34358	0.328458	0.164229	−	0.986422i	$-0.447486\pi$
$373$	6.34358	0.328458	0.164229	+	0.986422i	$0.447486\pi$
$374$	0.760792	0.0393396
$375$	−27.2638	−1.40790
$376$	−7.82597	−0.403594
$377$	−11.1640	−0.574975
$378$	5.18581	0.266729
$379$	20.8050	1.06868	0.534341	−	0.845269i	$-0.320560\pi$
$379$	20.8050	1.06868	0.534341	+	0.845269i	$0.320560\pi$
$380$	44.1153	2.26307
$381$	−7.04577	−0.360966
$382$	1.82774	0.0935154
$383$	17.9338	0.916373	0.458186	−	0.888856i	$-0.348499\pi$
$383$	17.9338	0.916373	0.458186	+	0.888856i	$0.348499\pi$
$384$	−15.1743	−0.774359
$385$	−49.2040	−2.50767
$386$	−3.56495	−0.181451
$387$	10.3235	0.524775
$388$	−34.5819	−1.75563
$389$	−20.0962	−1.01892	−0.509458	−	0.860496i	$-0.670154\pi$
$389$	−20.0962	−1.01892	−0.509458	+	0.860496i	$0.670154\pi$
$390$	−11.2418	−0.569250
$391$	0.197040	0.00996476
$392$	3.39307	0.171376
$393$	−21.7273	−1.09600
$394$	−50.3056	−2.53436
$395$	−25.4859	−1.28234
$396$	−15.3374	−0.770734
$397$	−19.0198	−0.954577	−0.477288	−	0.878747i	$-0.658380\pi$
$397$	−19.0198	−0.954577	−0.477288	+	0.878747i	$0.658380\pi$
$398$	−1.53957	−0.0771715
$399$	−8.48668	−0.424865
$400$	−13.3849	−0.669246
$401$	16.0926	0.803625	0.401812	−	0.915722i	$-0.368380\pi$
$401$	16.0926	0.803625	0.401812	+	0.915722i	$0.368380\pi$
$402$	30.1395	1.50322
$403$	11.0882	0.552343
$404$	50.7358	2.52420
$405$	4.08366	0.202919
$406$	−46.8519	−2.32522
$407$	15.5300	0.769795
$408$	0.141552	0.00700789
$409$	−7.06363	−0.349274	−0.174637	−	0.984633i	$-0.555875\pi$
$409$	−7.06363	−0.349274	−0.174637	+	0.984633i	$0.555875\pi$
$410$	43.8494	2.16557
$411$	11.3985	0.562247
$412$	−3.10241	−0.152845
$413$	1.68739	0.0830312
$414$	−6.65349	−0.327001
$415$	20.0143	0.982464
$416$	−8.45814	−0.414694
$417$	−14.5070	−0.710411
$418$	42.0418	2.05633
$419$	11.0213	0.538425	0.269213	−	0.963081i	$-0.413237\pi$
$419$	11.0213	0.538425	0.269213	+	0.963081i	$0.413237\pi$
$420$	−28.1666	−1.37439
$421$	−33.6041	−1.63776	−0.818882	−	0.573962i	$-0.805406\pi$
$421$	−33.6041	−1.63776	−0.818882	+	0.573962i	$0.805406\pi$
$422$	−9.33300	−0.454323
$423$	3.64756	0.177350
$424$	17.3910	0.844582
$425$	0.770347	0.0373673
$426$	9.08498	0.440168
$427$	−31.1779	−1.50880
$428$	2.24924	0.108721
$429$	−6.39615	−0.308809
$430$	−93.9191	−4.52918
$431$	21.6980	1.04516	0.522579	−	0.852591i	$-0.324970\pi$
$431$	21.6980	1.04516	0.522579	+	0.852591i	$0.324970\pi$
$432$	1.14633	0.0551529
$433$	−26.0958	−1.25408	−0.627041	−	0.778986i	$-0.715734\pi$
$433$	−26.0958	−1.25408	−0.627041	+	0.778986i	$0.715734\pi$
$434$	46.5338	2.23370
$435$	−36.8944	−1.76895
$436$	−35.2668	−1.68897
$437$	10.8886	0.520870
$438$	25.1732	1.20282
$439$	−9.27092	−0.442477	−0.221238	−	0.975220i	$-0.571010\pi$
$439$	−9.27092	−0.442477	−0.221238	+	0.975220i	$0.571010\pi$
$440$	45.3519	2.16207
$441$	−1.58146	−0.0753074
$442$	0.181621	0.00863883
$443$	23.6950	1.12578	0.562891	−	0.826531i	$-0.309689\pi$
$443$	23.6950	1.12578	0.562891	+	0.826531i	$0.309689\pi$
$444$	8.89009	0.421905
$445$	21.8376	1.03520
$446$	−42.1920	−1.99785
$447$	18.2158	0.861578
$448$	−30.1594	−1.42490
$449$	17.0830	0.806197	0.403099	−	0.915157i	$-0.367933\pi$
$449$	17.0830	0.806197	0.403099	+	0.915157i	$0.367933\pi$
$450$	−26.0124	−1.22624
$451$	24.9487	1.17479
$452$	10.1103	0.475549
$453$	−23.1304	−1.08676
$454$	37.1840	1.74513
$455$	−11.7463	−0.550675
$456$	7.82226	0.366311
$457$	5.78546	0.270632	0.135316	−	0.990802i	$-0.456795\pi$
$457$	5.78546	0.270632	0.135316	+	0.990802i	$0.456795\pi$
$458$	17.5718	0.821075
$459$	−0.0659753	−0.00307946
$460$	36.1382	1.68495
$461$	−21.8969	−1.01984	−0.509921	−	0.860221i	$-0.670325\pi$
$461$	−21.8969	−1.01984	−0.509921	+	0.860221i	$0.670325\pi$
$462$	−26.8427	−1.24884
$463$	14.7872	0.687220	0.343610	−	0.939112i	$-0.388350\pi$
$463$	14.7872	0.687220	0.343610	+	0.939112i	$0.388350\pi$
$464$	−10.3567	−0.480797
$465$	36.6439	1.69932
$466$	−63.9841	−2.96400
$467$	−24.9511	−1.15460	−0.577299	−	0.816533i	$-0.695893\pi$
$467$	−24.9511	−1.15460	−0.577299	+	0.816533i	$0.695893\pi$
$468$	−3.66144	−0.169250
$469$	31.4921	1.45417
$470$	−33.1839	−1.53066
$471$	−9.99466	−0.460530
$472$	−1.55529	−0.0715880
$473$	−53.4365	−2.45701
$474$	−13.9035	−0.638611
$475$	42.5698	1.95324
$476$	0.455056	0.0208575
$477$	−8.10566	−0.371133
$478$	−51.4686	−2.35412
$479$	16.5172	0.754690	0.377345	−	0.926073i	$-0.376837\pi$
$479$	16.5172	0.754690	0.377345	+	0.926073i	$0.376837\pi$
$480$	−27.9521	−1.27583
$481$	3.70743	0.169044
$482$	59.6215	2.71568
$483$	−6.95209	−0.316331
$484$	46.7954	2.12706
$485$	−47.6602	−2.16414
$486$	2.22780	0.101055
$487$	18.4642	0.836695	0.418347	−	0.908287i	$-0.362610\pi$
$487$	18.4642	0.836695	0.418347	+	0.908287i	$0.362610\pi$
$488$	28.7370	1.30086
$489$	1.72489	0.0780021
$490$	14.3874	0.649956
$491$	12.1978	0.550481	0.275241	−	0.961375i	$-0.411242\pi$
$491$	12.1978	0.550481	0.275241	+	0.961375i	$0.411242\pi$
$492$	14.2817	0.643871
$493$	0.596062	0.0268453
$494$	10.0365	0.451563
$495$	−21.1378	−0.950072
$496$	10.2864	0.461872
$497$	9.49270	0.425806
$498$	10.9186	0.489273
$499$	24.9985	1.11909	0.559543	−	0.828801i	$-0.310977\pi$
$499$	24.9985	1.11909	0.559543	+	0.828801i	$0.310977\pi$
$500$	80.7847	3.61280
$501$	14.4421	0.645225
$502$	−44.6589	−1.99322
$503$	17.4078	0.776175	0.388087	−	0.921623i	$-0.373136\pi$
$503$	17.4078	0.776175	0.388087	+	0.921623i	$0.373136\pi$
$504$	−4.99433	−0.222465
$505$	69.9233	3.11155
$506$	34.4397	1.53103
$507$	11.4731	0.509537
$508$	20.8772	0.926274
$509$	20.7232	0.918539	0.459270	−	0.888297i	$-0.348111\pi$
$509$	20.7232	0.918539	0.459270	+	0.888297i	$0.348111\pi$
$510$	0.600214	0.0265779
$511$	26.3030	1.16357
$512$	−12.7655	−0.564160
$513$	−3.64583	−0.160967
$514$	4.49864	0.198427
$515$	−4.27569	−0.188410
$516$	−30.5894	−1.34662
$517$	−18.8804	−0.830359
$518$	15.5589	0.683620
$519$	15.1521	0.665102
$520$	10.8267	0.474782
$521$	−30.0637	−1.31711	−0.658557	−	0.752531i	$-0.728833\pi$
$521$	−30.0637	−1.31711	−0.658557	+	0.752531i	$0.728833\pi$
$522$	−20.1273	−0.880949
$523$	40.6196	1.77617	0.888086	−	0.459677i	$-0.152035\pi$
$523$	40.6196	1.77617	0.888086	+	0.459677i	$0.152035\pi$
$524$	64.3796	2.81244
$525$	−27.1798	−1.18623
$526$	5.96557	0.260111
$527$	−0.592016	−0.0257886
$528$	−5.93362	−0.258228
$529$	−14.0803	−0.612189
$530$	73.7418	3.20314
$531$	0.724895	0.0314578
$532$	25.1467	1.09025
$533$	5.95591	0.257979
$534$	11.9132	0.515536
$535$	3.09987	0.134019
$536$	−29.0266	−1.25376
$537$	−16.6046	−0.716541
$538$	−44.5085	−1.91890
$539$	8.18590	0.352592
$540$	−12.1002	−0.520710
$541$	−13.6391	−0.586392	−0.293196	−	0.956052i	$-0.594719\pi$
$541$	−13.6391	−0.586392	−0.293196	+	0.956052i	$0.594719\pi$
$542$	28.6456	1.23043
$543$	5.67598	0.243580
$544$	0.451592	0.0193618
$545$	−48.6041	−2.08197
$546$	−6.40806	−0.274240
$547$	−0.924926	−0.0395470	−0.0197735	−	0.999804i	$-0.506295\pi$
$547$	−0.924926	−0.0395470	−0.0197735	+	0.999804i	$0.506295\pi$
$548$	−33.7746	−1.44278
$549$	−13.3939	−0.571636
$550$	134.645	5.74128
$551$	32.9387	1.40324
$552$	6.40782	0.272735
$553$	−14.5275	−0.617773
$554$	31.0558	1.31943
$555$	12.2522	0.520076
$556$	42.9854	1.82299
$557$	37.6293	1.59441	0.797203	−	0.603711i	$-0.206312\pi$
$557$	37.6293	1.59441	0.797203	+	0.603711i	$0.206312\pi$
$558$	19.9907	0.846273
$559$	−12.7567	−0.539551
$560$	−10.8969	−0.460477
$561$	0.341500	0.0144181
$562$	−42.5726	−1.79581
$563$	3.62528	0.152787	0.0763937	−	0.997078i	$-0.475659\pi$
$563$	3.62528	0.152787	0.0763937	+	0.997078i	$0.475659\pi$
$564$	−10.8080	−0.455098
$565$	13.9339	0.586202
$566$	21.4278	0.900680
$567$	2.32778	0.0977574
$568$	−8.74952	−0.367122
$569$	−7.95433	−0.333463	−0.166731	−	0.986002i	$-0.553321\pi$
$569$	−7.95433	−0.333463	−0.166731	+	0.986002i	$0.553321\pi$
$570$	33.1682	1.38926
$571$	−36.3901	−1.52288	−0.761439	−	0.648237i	$-0.775507\pi$
$571$	−36.3901	−1.52288	−0.761439	+	0.648237i	$0.775507\pi$
$572$	18.9523	0.792435
$573$	0.820426	0.0342738
$574$	24.9951	1.04328
$575$	34.8722	1.45427
$576$	−12.9563	−0.539846
$577$	−39.9443	−1.66290	−0.831451	−	0.555598i	$-0.812489\pi$
$577$	−39.9443	−1.66290	−0.831451	+	0.555598i	$0.812489\pi$
$578$	37.8628	1.57489
$579$	−1.60021	−0.0665027
$580$	109.321	4.53930
$581$	11.4086	0.473308
$582$	−26.0005	−1.07775
$583$	41.9564	1.73766
$584$	−24.2437	−1.00321
$585$	−5.04614	−0.208632
$586$	−10.1481	−0.419214
$587$	17.0608	0.704173	0.352086	−	0.935967i	$-0.385472\pi$
$587$	17.0608	0.704173	0.352086	+	0.935967i	$0.385472\pi$
$588$	4.68597	0.193246
$589$	−32.7151	−1.34800
$590$	−6.59478	−0.271503
$591$	−22.5809	−0.928854
$592$	3.43933	0.141355
$593$	−23.8994	−0.981433	−0.490716	−	0.871319i	$-0.663265\pi$
$593$	−23.8994	−0.981433	−0.490716	+	0.871319i	$0.663265\pi$
$594$	−11.5315	−0.473142
$595$	0.627151	0.0257107
$596$	−53.9748	−2.21089
$597$	−0.691071	−0.0282837
$598$	8.22165	0.336208
$599$	−34.9542	−1.42819	−0.714095	−	0.700049i	$-0.753161\pi$
$599$	−34.9542	−1.42819	−0.714095	+	0.700049i	$0.753161\pi$
$600$	25.0520	1.02274
$601$	−33.8716	−1.38165	−0.690827	−	0.723021i	$-0.742753\pi$
$601$	−33.8716	−1.38165	−0.690827	+	0.723021i	$0.742753\pi$
$602$	−53.5359	−2.18196
$603$	13.5288	0.550937
$604$	68.5370	2.78873
$605$	64.4926	2.62200
$606$	38.1459	1.54957
$607$	−32.6307	−1.32444	−0.662220	−	0.749310i	$-0.730386\pi$
$607$	−32.6307	−1.32444	−0.662220	+	0.749310i	$0.730386\pi$
$608$	24.9552	1.01207
$609$	−21.0306	−0.852203
$610$	121.851	4.93362
$611$	−4.50725	−0.182344
$612$	0.195490	0.00790220
$613$	20.1498	0.813841	0.406921	−	0.913463i	$-0.366603\pi$
$613$	20.1498	0.813841	0.406921	+	0.913463i	$0.366603\pi$
$614$	23.4441	0.946126
$615$	19.6829	0.793690
$616$	25.8516	1.04159
$617$	−15.4470	−0.621872	−0.310936	−	0.950431i	$-0.600643\pi$
$617$	−15.4470	−0.621872	−0.310936	+	0.950431i	$0.600643\pi$
$618$	−2.33256	−0.0938291
$619$	−41.7819	−1.67936	−0.839678	−	0.543085i	$-0.817256\pi$
$619$	−41.7819	−1.67936	−0.839678	+	0.543085i	$0.817256\pi$
$620$	−108.579	−4.36063
$621$	−2.98658	−0.119847
$622$	−16.7202	−0.670419
$623$	12.4479	0.498714
$624$	−1.41651	−0.0567058
$625$	52.9546	2.11818
$626$	−44.4167	−1.77525
$627$	18.8715	0.753654
$628$	29.6149	1.18176
$629$	−0.197945	−0.00789258
$630$	−21.1771	−0.843716
$631$	45.6755	1.81831	0.909157	−	0.416454i	$-0.136727\pi$
$631$	45.6755	1.81831	0.909157	+	0.416454i	$0.136727\pi$
$632$	13.3902	0.532633
$633$	−4.18934	−0.166511
$634$	−19.5931	−0.778141
$635$	28.7726	1.14180
$636$	24.0177	0.952364
$637$	1.95419	0.0774278
$638$	104.183	4.12463
$639$	4.07801	0.161324
$640$	61.9667	2.44945
$641$	29.6277	1.17023	0.585113	−	0.810952i	$-0.301050\pi$
$641$	29.6277	1.17023	0.585113	+	0.810952i	$0.301050\pi$
$642$	1.69110	0.0667424
$643$	−20.7709	−0.819126	−0.409563	−	0.912282i	$-0.634319\pi$
$643$	−20.7709	−0.819126	−0.409563	+	0.912282i	$0.634319\pi$
$644$	20.5996	0.811737
$645$	−42.1578	−1.65996
$646$	−0.535862	−0.0210832
$647$	−29.2526	−1.15004	−0.575019	−	0.818140i	$-0.695005\pi$
$647$	−29.2526	−1.15004	−0.575019	+	0.818140i	$0.695005\pi$
$648$	−2.14554	−0.0842847
$649$	−3.75219	−0.147286
$650$	32.1433	1.26076
$651$	20.8878	0.818659
$652$	−5.11097	−0.200161
$653$	−7.24727	−0.283608	−0.141804	−	0.989895i	$-0.545290\pi$
$653$	−7.24727	−0.283608	−0.141804	+	0.989895i	$0.545290\pi$
$654$	−26.5154	−1.03683
$655$	88.7269	3.46685
$656$	5.52521	0.215723
$657$	11.2996	0.440840
$658$	−18.9155	−0.737405
$659$	−27.1667	−1.05827	−0.529133	−	0.848539i	$-0.677483\pi$
$659$	−27.1667	−1.05827	−0.529133	+	0.848539i	$0.677483\pi$
$660$	62.6328	2.43798
$661$	47.4611	1.84602	0.923011	−	0.384774i	$-0.125721\pi$
$661$	47.4611	1.84602	0.923011	+	0.384774i	$0.125721\pi$
$662$	−22.7538	−0.884351
$663$	0.0815250	0.00316617
$664$	−10.5154	−0.408078
$665$	34.6567	1.34393
$666$	6.68403	0.259001
$667$	26.9826	1.04477
$668$	−42.7930	−1.65571
$669$	−18.9389	−0.732221
$670$	−123.080	−4.75498
$671$	69.3290	2.67642
$672$	−15.9333	−0.614641
$673$	12.3184	0.474840	0.237420	−	0.971407i	$-0.423698\pi$
$673$	12.3184	0.474840	0.237420	+	0.971407i	$0.423698\pi$
$674$	−38.4027	−1.47922
$675$	−11.6763	−0.449421
$676$	−33.9956	−1.30752
$677$	8.80944	0.338574	0.169287	−	0.985567i	$-0.445854\pi$
$677$	8.80944	0.338574	0.169287	+	0.985567i	$0.445854\pi$
$678$	7.60146	0.291932
$679$	−27.1673	−1.04259
$680$	−0.578052	−0.0221673
$681$	16.6909	0.639598
$682$	−103.475	−3.96228
$683$	1.53499	0.0587348	0.0293674	−	0.999569i	$-0.490651\pi$
$683$	1.53499	0.0587348	0.0293674	+	0.999569i	$0.490651\pi$
$684$	10.8029	0.413058
$685$	−46.5476	−1.77849
$686$	44.5018	1.69909
$687$	7.88751	0.300927
$688$	−11.8342	−0.451174
$689$	10.0161	0.381583
$690$	27.1706	1.03437
$691$	13.4381	0.511210	0.255605	−	0.966781i	$-0.417725\pi$
$691$	13.4381	0.511210	0.255605	+	0.966781i	$0.417725\pi$
$692$	−44.8967	−1.70672
$693$	−12.0490	−0.457703
$694$	33.9225	1.28768
$695$	59.2417	2.24717
$696$	19.3841	0.734754
$697$	−0.317994	−0.0120449
$698$	−65.0226	−2.46114
$699$	−28.7208	−1.08632
$700$	80.5359	3.04397
$701$	16.0463	0.606059	0.303030	−	0.952981i	$-0.402002\pi$
$701$	16.0463	0.606059	0.303030	+	0.952981i	$0.402002\pi$
$702$	−2.75287	−0.103900
$703$	−10.9385	−0.412555
$704$	67.0642	2.52758
$705$	−14.8954	−0.560993
$706$	−37.5518	−1.41328
$707$	39.8578	1.49901
$708$	−2.14792	−0.0807237
$709$	4.00847	0.150541	0.0752706	−	0.997163i	$-0.476018\pi$
$709$	4.00847	0.150541	0.0752706	+	0.997163i	$0.476018\pi$
$710$	−37.1000	−1.39234
$711$	−6.24094	−0.234054
$712$	−11.4734	−0.429982
$713$	−26.7995	−1.00365
$714$	0.342135	0.0128041
$715$	26.1197	0.976823
$716$	49.2007	1.83872
$717$	−23.1029	−0.862795
$718$	−12.6650	−0.472655
$719$	8.53861	0.318437	0.159218	−	0.987243i	$-0.449103\pi$
$719$	8.53861	0.318437	0.159218	+	0.987243i	$0.449103\pi$
$720$	−4.68123	−0.174459
$721$	−2.43724	−0.0907675
$722$	12.7161	0.473245
$723$	26.7625	0.995309
$724$	−16.8184	−0.625050
$725$	105.491	3.91784
$726$	35.1832	1.30577
$727$	−34.9861	−1.29756	−0.648781	−	0.760975i	$-0.724721\pi$
$727$	−34.9861	−1.29756	−0.648781	+	0.760975i	$0.724721\pi$
$728$	6.17145	0.228729
$729$	1.00000	0.0370370
$730$	−102.799	−3.80476
$731$	0.681098	0.0251913
$732$	39.6870	1.46687
$733$	32.0028	1.18205	0.591026	−	0.806653i	$-0.298723\pi$
$733$	32.0028	1.18205	0.591026	+	0.806653i	$0.298723\pi$
$734$	43.2395	1.59600
$735$	6.45813	0.238212
$736$	20.4427	0.753529
$737$	−70.0277	−2.57950
$738$	10.7378	0.395263
$739$	1.44761	0.0532511	0.0266255	−	0.999645i	$-0.491524\pi$
$739$	1.44761	0.0532511	0.0266255	+	0.999645i	$0.491524\pi$
$740$	−36.3041	−1.33457
$741$	4.50512	0.165500
$742$	42.0345	1.54313
$743$	33.0700	1.21322	0.606609	−	0.795000i	$-0.292529\pi$
$743$	33.0700	1.21322	0.606609	+	0.795000i	$0.292529\pi$
$744$	−19.2525	−0.705833
$745$	−74.3872	−2.72534
$746$	−14.1322	−0.517416
$747$	4.90107	0.179321
$748$	−1.01189	−0.0369984
$749$	1.76699	0.0645645
$750$	60.7382	2.21784
$751$	22.7314	0.829481	0.414740	−	0.909940i	$-0.363872\pi$
$751$	22.7314	0.829481	0.414740	+	0.909940i	$0.363872\pi$
$752$	−4.18131	−0.152477
$753$	−20.0462	−0.730525
$754$	24.8711	0.905753
$755$	94.4566	3.43763
$756$	−6.89738	−0.250855
$757$	22.7073	0.825311	0.412656	−	0.910887i	$-0.364601\pi$
$757$	22.7073	0.825311	0.412656	+	0.910887i	$0.364601\pi$
$758$	−46.3494	−1.68348
$759$	15.4591	0.561129
$760$	−31.9435	−1.15871
$761$	−40.0269	−1.45097	−0.725486	−	0.688237i	$-0.758385\pi$
$761$	−40.0269	−1.45097	−0.725486	+	0.688237i	$0.758385\pi$
$762$	15.6965	0.568626
$763$	−27.7054	−1.00300
$764$	−2.43098	−0.0879499
$765$	0.269421	0.00974093
$766$	−39.9528	−1.44355
$767$	−0.895745	−0.0323435
$768$	7.89259	0.284799
$769$	−7.83647	−0.282590	−0.141295	−	0.989968i	$-0.545127\pi$
$769$	−7.83647	−0.282590	−0.141295	+	0.989968i	$0.545127\pi$
$770$	109.617	3.95031
$771$	2.01933	0.0727242
$772$	4.74156	0.170652
$773$	−48.5144	−1.74494	−0.872471	−	0.488665i	$-0.837484\pi$
$773$	−48.5144	−1.74494	−0.872471	+	0.488665i	$0.837484\pi$
$774$	−22.9987	−0.826672
$775$	−104.775	−3.76363
$776$	25.0404	0.898899
$777$	6.98400	0.250550
$778$	44.7701	1.60509
$779$	−17.5725	−0.629602
$780$	14.9521	0.535371
$781$	−21.1085	−0.755322
$782$	−0.438966	−0.0156974
$783$	−9.03463	−0.322871
$784$	1.81287	0.0647454
$785$	40.8148	1.45674
$786$	48.4040	1.72651
$787$	12.8916	0.459535	0.229768	−	0.973245i	$-0.426203\pi$
$787$	12.8916	0.459535	0.229768	+	0.973245i	$0.426203\pi$
$788$	66.9089	2.38353
$789$	2.67779	0.0953318
$790$	56.7774	2.02005
$791$	7.94261	0.282407
$792$	11.1057	0.394623
$793$	16.5507	0.587731
$794$	42.3723	1.50374
$795$	33.1008	1.17396
$796$	2.04770	0.0725787
$797$	0.579189	0.0205159	0.0102580	−	0.999947i	$-0.496735\pi$
$797$	0.579189	0.0205159	0.0102580	+	0.999947i	$0.496735\pi$
$798$	18.9066	0.669286
$799$	0.240648	0.00851353
$800$	79.9228	2.82570
$801$	5.34755	0.188946
$802$	−35.8510	−1.26594
$803$	−58.4888	−2.06403
$804$	−40.0870	−1.41376
$805$	28.3900	1.00062
$806$	−24.7023	−0.870101
$807$	−19.9787	−0.703284
$808$	−36.7374	−1.29242
$809$	−25.9722	−0.913135	−0.456567	−	0.889689i	$-0.650921\pi$
$809$	−25.9722	−0.913135	−0.456567	+	0.889689i	$0.650921\pi$
$810$	−9.09757	−0.319656
$811$	−52.4114	−1.84041	−0.920207	−	0.391432i	$-0.871980\pi$
$811$	−52.4114	−1.84041	−0.920207	+	0.391432i	$0.871980\pi$
$812$	62.3153	2.18684
$813$	12.8583	0.450959
$814$	−34.5978	−1.21265
$815$	−7.04386	−0.246736
$816$	0.0756295	0.00264756
$817$	37.6378	1.31678
$818$	15.7363	0.550208
$819$	−2.87641	−0.100510
$820$	−58.3218	−2.03669
$821$	36.1358	1.26115	0.630575	−	0.776129i	$-0.282819\pi$
$821$	36.1358	1.26115	0.630575	+	0.776129i	$0.282819\pi$
$822$	−25.3935	−0.885701
$823$	−27.5797	−0.961367	−0.480684	−	0.876894i	$-0.659611\pi$
$823$	−27.5797	−0.961367	−0.480684	+	0.876894i	$0.659611\pi$
$824$	2.24643	0.0782581
$825$	60.4387	2.10420
$826$	−3.75917	−0.130798
$827$	5.89999	0.205163	0.102581	−	0.994725i	$-0.467290\pi$
$827$	5.89999	0.205163	0.102581	+	0.994725i	$0.467290\pi$
$828$	8.84946	0.307540
$829$	−19.7408	−0.685625	−0.342812	−	0.939404i	$-0.611380\pi$
$829$	−19.7408	−0.685625	−0.342812	+	0.939404i	$0.611380\pi$
$830$	−44.5878	−1.54767
$831$	13.9401	0.483578
$832$	16.0100	0.555046
$833$	−0.104337	−0.00361506
$834$	32.3186	1.11910
$835$	−58.9766	−2.04097
$836$	−55.9176	−1.93395
$837$	8.97330	0.310163
$838$	−24.5532	−0.848176
$839$	14.0533	0.485173	0.242587	−	0.970130i	$-0.422004\pi$
$839$	14.0533	0.485173	0.242587	+	0.970130i	$0.422004\pi$
$840$	20.3952	0.703700
$841$	52.6245	1.81464
$842$	74.8631	2.57995
$843$	−19.1097	−0.658174
$844$	12.4133	0.427285
$845$	−46.8522	−1.61176
$846$	−8.12601	−0.279378
$847$	36.7622	1.26316
$848$	9.29178	0.319081
$849$	9.61841	0.330103
$850$	−1.71618	−0.0588644
$851$	−8.96060	−0.307165
$852$	−12.0835	−0.413972
$853$	26.5994	0.910746	0.455373	−	0.890301i	$-0.349506\pi$
$853$	26.5994	0.910746	0.455373	+	0.890301i	$0.349506\pi$
$854$	69.4580	2.37680
$855$	14.8883	0.509170
$856$	−1.62866	−0.0556664
$857$	17.4319	0.595461	0.297731	−	0.954650i	$-0.403770\pi$
$857$	17.4319	0.595461	0.297731	+	0.954650i	$0.403770\pi$
$858$	14.2493	0.486464
$859$	1.45208	0.0495442	0.0247721	−	0.999693i	$-0.492114\pi$
$859$	1.45208	0.0495442	0.0247721	+	0.999693i	$0.492114\pi$
$860$	124.917	4.25963
$861$	11.2197	0.382365
$862$	−48.3388	−1.64643
$863$	−32.6897	−1.11277	−0.556386	−	0.830924i	$-0.687812\pi$
$863$	−32.6897	−1.11277	−0.556386	+	0.830924i	$0.687812\pi$
$864$	−6.84487	−0.232867
$865$	−61.8760	−2.10385
$866$	58.1360	1.97554
$867$	16.9956	0.577202
$868$	−61.8922	−2.10076
$869$	32.3042	1.09585
$870$	82.1932	2.78661
$871$	−16.7175	−0.566449
$872$	25.5364	0.864770
$873$	−11.6709	−0.395001
$874$	−24.2575	−0.820522
$875$	63.4640	2.14548
$876$	−33.4816	−1.13124
$877$	−20.7311	−0.700039	−0.350020	−	0.936742i	$-0.613825\pi$
$877$	−20.7311	−0.700039	−0.350020	+	0.936742i	$0.613825\pi$
$878$	20.6537	0.697029
$879$	−4.55521	−0.153644
$880$	24.2309	0.816824
$881$	48.0578	1.61911	0.809555	−	0.587044i	$-0.199709\pi$
$881$	48.0578	1.61911	0.809555	+	0.587044i	$0.199709\pi$
$882$	3.52316	0.118631
$883$	−23.7634	−0.799703	−0.399851	−	0.916580i	$-0.630938\pi$
$883$	−23.7634	−0.799703	−0.399851	+	0.916580i	$0.630938\pi$
$884$	−0.241565	−0.00812470
$885$	−2.96023	−0.0995069
$886$	−52.7876	−1.77343
$887$	−26.4717	−0.888834	−0.444417	−	0.895820i	$-0.646589\pi$
$887$	−26.4717	−0.888834	−0.444417	+	0.895820i	$0.646589\pi$
$888$	−6.43723	−0.216019
$889$	16.4010	0.550071
$890$	−48.6497	−1.63074
$891$	−5.17618	−0.173409
$892$	56.1174	1.87895
$893$	13.2984	0.445013
$894$	−40.5811	−1.35723
$895$	67.8076	2.26656
$896$	35.3223	1.18004
$897$	3.69049	0.123222
$898$	−38.0575	−1.26999
$899$	−81.0704	−2.70385
$900$	34.5978	1.15326
$901$	−0.534773	−0.0178159
$902$	−55.5806	−1.85063
$903$	−24.0309	−0.799698
$904$	−7.32079	−0.243486
$905$	−23.1788	−0.770489
$906$	51.5297	1.71196
$907$	−56.5593	−1.87802	−0.939011	−	0.343887i	$-0.888256\pi$
$907$	−56.5593	−1.87802	−0.939011	+	0.343887i	$0.888256\pi$
$908$	−49.4565	−1.64127
$909$	17.1227	0.567924
$910$	26.1684	0.867472
$911$	−38.8732	−1.28793	−0.643963	−	0.765057i	$-0.722711\pi$
$911$	−38.8732	−1.28793	−0.643963	+	0.765057i	$0.722711\pi$
$912$	4.17933	0.138391
$913$	−25.3688	−0.839585
$914$	−12.8888	−0.426324
$915$	54.6960	1.80819
$916$	−23.3713	−0.772210
$917$	50.5763	1.67018
$918$	0.146979	0.00485104
$919$	−45.4844	−1.50039	−0.750195	−	0.661216i	$-0.770041\pi$
$919$	−45.4844	−1.50039	−0.750195	+	0.661216i	$0.770041\pi$
$920$	−26.1674	−0.862713
$921$	10.5234	0.346759
$922$	48.7819	1.60655
$923$	−5.03916	−0.165866
$924$	35.7021	1.17451
$925$	−35.0323	−1.15185
$926$	−32.9429	−1.08257
$927$	−1.04702	−0.0343888
$928$	61.8409	2.03003
$929$	21.1414	0.693628	0.346814	−	0.937934i	$-0.387264\pi$
$929$	21.1414	0.693628	0.346814	+	0.937934i	$0.387264\pi$
$930$	−81.6352	−2.67692
$931$	−5.76571	−0.188964
$932$	85.1019	2.78761
$933$	−7.50526	−0.245711
$934$	55.5859	1.81883
$935$	−1.39457	−0.0456073
$936$	2.65122	0.0866578
$937$	11.1735	0.365021	0.182510	−	0.983204i	$-0.441578\pi$
$937$	11.1735	0.365021	0.182510	+	0.983204i	$0.441578\pi$
$938$	−70.1580	−2.29074
$939$	−19.9375	−0.650636
$940$	44.1362	1.43956
$941$	2.29526	0.0748234	0.0374117	−	0.999300i	$-0.488089\pi$
$941$	2.29526	0.0748234	0.0374117	+	0.999300i	$0.488089\pi$
$942$	22.2661	0.725468
$943$	−14.3950	−0.468766
$944$	−0.830970	−0.0270458
$945$	−9.50586	−0.309226
$946$	119.046	3.87050
$947$	19.8639	0.645489	0.322745	−	0.946486i	$-0.395394\pi$
$947$	19.8639	0.645489	0.322745	+	0.946486i	$0.395394\pi$
$948$	18.4924	0.600605
$949$	−13.9628	−0.453252
$950$	−94.8369	−3.07691
$951$	−8.79483	−0.285192
$952$	−0.329502	−0.0106792
$953$	−21.3791	−0.692536	−0.346268	−	0.938136i	$-0.612551\pi$
$953$	−21.3791	−0.692536	−0.346268	+	0.938136i	$0.612551\pi$
$954$	18.0578	0.584642
$955$	−3.35034	−0.108415
$956$	68.4558	2.21402
$957$	46.7649	1.51169
$958$	−36.7969	−1.18886
$959$	−26.5332	−0.856801
$960$	52.9092	1.70764
$961$	49.5201	1.59742
$962$	−8.25940	−0.266294
$963$	0.759091	0.0244614
$964$	−79.2994	−2.55406
$965$	6.53474	0.210361
$966$	15.4878	0.498313
$967$	52.6180	1.69208	0.846041	−	0.533118i	$-0.178980\pi$
$967$	52.6180	1.69208	0.846041	+	0.533118i	$0.178980\pi$
$968$	−33.8841	−1.08908
$969$	−0.240534	−0.00772708
$970$	106.177	3.40914
$971$	59.7041	1.91600	0.957998	−	0.286776i	$-0.0925835\pi$
$971$	59.7041	1.91600	0.957998	+	0.286776i	$0.0925835\pi$
$972$	−2.96308	−0.0950407
$973$	33.7691	1.08259
$974$	−41.1346	−1.31804
$975$	14.4283	0.462075
$976$	15.3538	0.491463
$977$	−21.4957	−0.687707	−0.343853	−	0.939023i	$-0.611732\pi$
$977$	−21.4957	−0.687707	−0.343853	+	0.939023i	$0.611732\pi$
$978$	−3.84270	−0.122876
$979$	−27.6799	−0.884652
$980$	−19.1359	−0.611275
$981$	−11.9021	−0.380004
$982$	−27.1743	−0.867167
$983$	−22.5477	−0.719161	−0.359581	−	0.933114i	$-0.617080\pi$
$983$	−22.5477	−0.719161	−0.359581	+	0.933114i	$0.617080\pi$
$984$	−10.3413	−0.329668
$985$	92.2128	2.93814
$986$	−1.32790	−0.0422891
$987$	−8.49070	−0.270262
$988$	−13.3490	−0.424688
$989$	30.8320	0.980402
$990$	47.0907	1.49664
$991$	49.8018	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$991$	49.8018	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$992$	−61.4210	−1.95012
$993$	−10.2136	−0.324118
$994$	−21.1478	−0.670767
$995$	2.82210	0.0894667
$996$	−14.5222	−0.460155
$997$	−49.2414	−1.55949	−0.779745	−	0.626097i	$-0.784651\pi$
$997$	−49.2414	−1.55949	−0.779745	+	0.626097i	$0.784651\pi$
$998$	−55.6916	−1.76289
$999$	3.00029	0.0949250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.18	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.18	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22780 q^{2} -1.00000 q^{3} +2.96308 q^{4} +4.08366 q^{5} +2.22780 q^{6} +2.32778 q^{7} -2.14554 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22780 q^{2} -1.00000 q^{3} +2.96308 q^{4} +4.08366 q^{5} +2.22780 q^{6} +2.32778 q^{7} -2.14554 q^{8} +1.00000 q^{9} -9.09757 q^{10} -5.17618 q^{11} -2.96308 q^{12} -1.23569 q^{13} -5.18581 q^{14} -4.08366 q^{15} -1.14633 q^{16} +0.0659753 q^{17} -2.22780 q^{18} +3.64583 q^{19} +12.1002 q^{20} -2.32778 q^{21} +11.5315 q^{22} +2.98658 q^{23} +2.14554 q^{24} +11.6763 q^{25} +2.75287 q^{26} -1.00000 q^{27} +6.89738 q^{28} +9.03463 q^{29} +9.09757 q^{30} -8.97330 q^{31} +6.84487 q^{32} +5.17618 q^{33} -0.146979 q^{34} +9.50586 q^{35} +2.96308 q^{36} -3.00029 q^{37} -8.12216 q^{38} +1.23569 q^{39} -8.76165 q^{40} -4.81990 q^{41} +5.18581 q^{42} +10.3235 q^{43} -15.3374 q^{44} +4.08366 q^{45} -6.65349 q^{46} +3.64756 q^{47} +1.14633 q^{48} -1.58146 q^{49} -26.0124 q^{50} -0.0659753 q^{51} -3.66144 q^{52} -8.10566 q^{53} +2.22780 q^{54} -21.1378 q^{55} -4.99433 q^{56} -3.64583 q^{57} -20.1273 q^{58} +0.724895 q^{59} -12.1002 q^{60} -13.3939 q^{61} +19.9907 q^{62} +2.32778 q^{63} -12.9563 q^{64} -5.04614 q^{65} -11.5315 q^{66} +13.5288 q^{67} +0.195490 q^{68} -2.98658 q^{69} -21.1771 q^{70} +4.07801 q^{71} -2.14554 q^{72} +11.2996 q^{73} +6.68403 q^{74} -11.6763 q^{75} +10.8029 q^{76} -12.0490 q^{77} -2.75287 q^{78} -6.24094 q^{79} -4.68123 q^{80} +1.00000 q^{81} +10.7378 q^{82} +4.90107 q^{83} -6.89738 q^{84} +0.269421 q^{85} -22.9987 q^{86} -9.03463 q^{87} +11.1057 q^{88} +5.34755 q^{89} -9.09757 q^{90} -2.87641 q^{91} +8.84946 q^{92} +8.97330 q^{93} -8.12601 q^{94} +14.8883 q^{95} -6.84487 q^{96} -11.6709 q^{97} +3.52316 q^{98} -5.17618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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