LMFDB - Embedded newform 8021.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42489 q^{2} +3.03758 q^{3} +3.88008 q^{4} +0.138091 q^{5} -7.36579 q^{6} +2.88225 q^{7} -4.55899 q^{8} +6.22689 q^{9} +O(q^{10})$	\(q-2.42489 q^{2} +3.03758 q^{3} +3.88008 q^{4} +0.138091 q^{5} -7.36579 q^{6} +2.88225 q^{7} -4.55899 q^{8} +6.22689 q^{9} -0.334855 q^{10} -5.02154 q^{11} +11.7861 q^{12} -1.00000 q^{13} -6.98914 q^{14} +0.419462 q^{15} +3.29487 q^{16} +5.56335 q^{17} -15.0995 q^{18} +7.89644 q^{19} +0.535803 q^{20} +8.75507 q^{21} +12.1767 q^{22} -5.18368 q^{23} -13.8483 q^{24} -4.98093 q^{25} +2.42489 q^{26} +9.80195 q^{27} +11.1834 q^{28} -8.73993 q^{29} -1.01715 q^{30} +5.25304 q^{31} +1.12828 q^{32} -15.2533 q^{33} -13.4905 q^{34} +0.398012 q^{35} +24.1609 q^{36} +1.11006 q^{37} -19.1480 q^{38} -3.03758 q^{39} -0.629554 q^{40} +6.09354 q^{41} -21.2301 q^{42} +4.80109 q^{43} -19.4840 q^{44} +0.859876 q^{45} +12.5698 q^{46} +4.34487 q^{47} +10.0084 q^{48} +1.30737 q^{49} +12.0782 q^{50} +16.8991 q^{51} -3.88008 q^{52} -1.03828 q^{53} -23.7686 q^{54} -0.693428 q^{55} -13.1401 q^{56} +23.9861 q^{57} +21.1934 q^{58} +1.27498 q^{59} +1.62755 q^{60} +1.49136 q^{61} -12.7380 q^{62} +17.9475 q^{63} -9.32570 q^{64} -0.138091 q^{65} +36.9876 q^{66} +9.48393 q^{67} +21.5862 q^{68} -15.7458 q^{69} -0.965135 q^{70} -1.93280 q^{71} -28.3883 q^{72} -0.0756784 q^{73} -2.69178 q^{74} -15.1300 q^{75} +30.6388 q^{76} -14.4733 q^{77} +7.36579 q^{78} +14.7474 q^{79} +0.454991 q^{80} +11.0935 q^{81} -14.7761 q^{82} +1.35773 q^{83} +33.9704 q^{84} +0.768246 q^{85} -11.6421 q^{86} -26.5482 q^{87} +22.8931 q^{88} +9.09802 q^{89} -2.08510 q^{90} -2.88225 q^{91} -20.1131 q^{92} +15.9565 q^{93} -10.5358 q^{94} +1.09043 q^{95} +3.42725 q^{96} -7.82669 q^{97} -3.17023 q^{98} -31.2686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.42489	−1.71465	−0.857327	−	0.514772i	$-0.827877\pi$
$2$	−2.42489	−1.71465	−0.857327	+	0.514772i	$0.827877\pi$
$3$	3.03758	1.75375	0.876874	−	0.480720i	$-0.159625\pi$
$3$	3.03758	1.75375	0.876874	+	0.480720i	$0.159625\pi$
$4$	3.88008	1.94004
$5$	0.138091	0.0617560	0.0308780	−	0.999523i	$-0.490170\pi$
$5$	0.138091	0.0617560	0.0308780	+	0.999523i	$0.490170\pi$
$6$	−7.36579	−3.00707
$7$	2.88225	1.08939	0.544694	−	0.838635i	$-0.316646\pi$
$7$	2.88225	1.08939	0.544694	+	0.838635i	$0.316646\pi$
$8$	−4.55899	−1.61185
$9$	6.22689	2.07563
$10$	−0.334855	−0.105890
$11$	−5.02154	−1.51405	−0.757025	−	0.653386i	$-0.773348\pi$
$11$	−5.02154	−1.51405	−0.757025	+	0.653386i	$0.773348\pi$
$12$	11.7861	3.40234
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−6.98914	−1.86793
$15$	0.419462	0.108305
$16$	3.29487	0.823718
$17$	5.56335	1.34931	0.674655	−	0.738133i	$-0.264292\pi$
$17$	5.56335	1.34931	0.674655	+	0.738133i	$0.264292\pi$
$18$	−15.0995	−3.55899
$19$	7.89644	1.81157	0.905784	−	0.423740i	$-0.139283\pi$
$19$	7.89644	1.81157	0.905784	+	0.423740i	$0.139283\pi$
$20$	0.535803	0.119809
$21$	8.75507	1.91051
$22$	12.1767	2.59607
$23$	−5.18368	−1.08087	−0.540436	−	0.841385i	$-0.681741\pi$
$23$	−5.18368	−1.08087	−0.540436	+	0.841385i	$0.681741\pi$
$24$	−13.8483	−2.82677
$25$	−4.98093	−0.996186
$26$	2.42489	0.475560
$27$	9.80195	1.88639
$28$	11.1834	2.11346
$29$	−8.73993	−1.62296	−0.811482	−	0.584377i	$-0.801339\pi$
$29$	−8.73993	−1.62296	−0.811482	+	0.584377i	$0.801339\pi$
$30$	−1.01715	−0.185705
$31$	5.25304	0.943473	0.471737	−	0.881740i	$-0.343627\pi$
$31$	5.25304	0.943473	0.471737	+	0.881740i	$0.343627\pi$
$32$	1.12828	0.199454
$33$	−15.2533	−2.65526
$34$	−13.4905	−2.31360
$35$	0.398012	0.0672763
$36$	24.1609	4.02681
$37$	1.11006	0.182493	0.0912467	−	0.995828i	$-0.470915\pi$
$37$	1.11006	0.182493	0.0912467	+	0.995828i	$0.470915\pi$
$38$	−19.1480	−3.10621
$39$	−3.03758	−0.486402
$40$	−0.629554	−0.0995412
$41$	6.09354	0.951651	0.475825	−	0.879540i	$-0.342149\pi$
$41$	6.09354	0.951651	0.475825	+	0.879540i	$0.342149\pi$
$42$	−21.2301	−3.27587
$43$	4.80109	0.732160	0.366080	−	0.930583i	$-0.380700\pi$
$43$	4.80109	0.732160	0.366080	+	0.930583i	$0.380700\pi$
$44$	−19.4840	−2.93732
$45$	0.859876	0.128183
$46$	12.5698	1.85332
$47$	4.34487	0.633764	0.316882	−	0.948465i	$-0.397364\pi$
$47$	4.34487	0.633764	0.316882	+	0.948465i	$0.397364\pi$
$48$	10.0084	1.44459
$49$	1.30737	0.186768
$50$	12.0782	1.70812
$51$	16.8991	2.36635
$52$	−3.88008	−0.538071
$53$	−1.03828	−0.142619	−0.0713093	−	0.997454i	$-0.522718\pi$
$53$	−1.03828	−0.142619	−0.0713093	+	0.997454i	$0.522718\pi$
$54$	−23.7686	−3.23450
$55$	−0.693428	−0.0935018
$56$	−13.1401	−1.75593
$57$	23.9861	3.17703
$58$	21.1934	2.78282
$59$	1.27498	0.165988	0.0829940	−	0.996550i	$-0.473552\pi$
$59$	1.27498	0.165988	0.0829940	+	0.996550i	$0.473552\pi$
$60$	1.62755	0.210115
$61$	1.49136	0.190949	0.0954745	−	0.995432i	$-0.469563\pi$
$61$	1.49136	0.190949	0.0954745	+	0.995432i	$0.469563\pi$
$62$	−12.7380	−1.61773
$63$	17.9475	2.26117
$64$	−9.32570	−1.16571
$65$	−0.138091	−0.0171280
$66$	36.9876	4.55286
$67$	9.48393	1.15865	0.579323	−	0.815098i	$-0.303317\pi$
$67$	9.48393	1.15865	0.579323	+	0.815098i	$0.303317\pi$
$68$	21.5862	2.61772
$69$	−15.7458	−1.89558
$70$	−0.965135	−0.115356
$71$	−1.93280	−0.229381	−0.114691	−	0.993401i	$-0.536588\pi$
$71$	−1.93280	−0.229381	−0.114691	+	0.993401i	$0.536588\pi$
$72$	−28.3883	−3.34560
$73$	−0.0756784	−0.00885749	−0.00442875	−	0.999990i	$-0.501410\pi$
$73$	−0.0756784	−0.00885749	−0.00442875	+	0.999990i	$0.501410\pi$
$74$	−2.69178	−0.312913
$75$	−15.1300	−1.74706
$76$	30.6388	3.51452
$77$	−14.4733	−1.64939
$78$	7.36579	0.834012
$79$	14.7474	1.65922	0.829609	−	0.558345i	$-0.188564\pi$
$79$	14.7474	1.65922	0.829609	+	0.558345i	$0.188564\pi$
$80$	0.454991	0.0508696
$81$	11.0935	1.23261
$82$	−14.7761	−1.63175
$83$	1.35773	0.149030	0.0745149	−	0.997220i	$-0.476259\pi$
$83$	1.35773	0.149030	0.0745149	+	0.997220i	$0.476259\pi$
$84$	33.9704	3.70647
$85$	0.768246	0.0833280
$86$	−11.6421	−1.25540
$87$	−26.5482	−2.84627
$88$	22.8931	2.44042
$89$	9.09802	0.964388	0.482194	−	0.876064i	$-0.339840\pi$
$89$	9.09802	0.964388	0.482194	+	0.876064i	$0.339840\pi$
$90$	−2.08510	−0.219789
$91$	−2.88225	−0.302142
$92$	−20.1131	−2.09693
$93$	15.9565	1.65461
$94$	−10.5358	−1.08669
$95$	1.09043	0.111875
$96$	3.42725	0.349792
$97$	−7.82669	−0.794680	−0.397340	−	0.917672i	$-0.630067\pi$
$97$	−7.82669	−0.794680	−0.397340	+	0.917672i	$0.630067\pi$
$98$	−3.17023	−0.320242
$99$	−31.2686	−3.14261
$100$	−19.3264	−1.93264
$101$	1.43402	0.142690	0.0713452	−	0.997452i	$-0.477271\pi$
$101$	1.43402	0.142690	0.0713452	+	0.997452i	$0.477271\pi$
$102$	−40.9785	−4.05747
$103$	−8.67009	−0.854290	−0.427145	−	0.904183i	$-0.640481\pi$
$103$	−8.67009	−0.854290	−0.427145	+	0.904183i	$0.640481\pi$
$104$	4.55899	0.447046
$105$	1.20899	0.117986
$106$	2.51771	0.244542
$107$	1.24713	0.120565	0.0602825	−	0.998181i	$-0.480800\pi$
$107$	1.24713	0.120565	0.0602825	+	0.998181i	$0.480800\pi$
$108$	38.0324	3.65967
$109$	5.59657	0.536054	0.268027	−	0.963411i	$-0.413628\pi$
$109$	5.59657	0.536054	0.268027	+	0.963411i	$0.413628\pi$
$110$	1.68148	0.160323
$111$	3.37191	0.320047
$112$	9.49665	0.897349
$113$	3.25743	0.306433	0.153216	−	0.988193i	$-0.451037\pi$
$113$	3.25743	0.306433	0.153216	+	0.988193i	$0.451037\pi$
$114$	−58.1635	−5.44752
$115$	−0.715818	−0.0667503
$116$	−33.9116	−3.14862
$117$	−6.22689	−0.575677
$118$	−3.09168	−0.284612
$119$	16.0350	1.46992
$120$	−1.91232	−0.174570
$121$	14.2158	1.29235
$122$	−3.61638	−0.327411
$123$	18.5096	1.66896
$124$	20.3822	1.83038
$125$	−1.37827	−0.123277
$126$	−43.5206	−3.87712
$127$	5.07341	0.450193	0.225096	−	0.974337i	$-0.427730\pi$
$127$	5.07341	0.450193	0.225096	+	0.974337i	$0.427730\pi$
$128$	20.3572	1.79934
$129$	14.5837	1.28402
$130$	0.334855	0.0293687
$131$	−21.8038	−1.90500	−0.952501	−	0.304534i	$-0.901499\pi$
$131$	−21.8038	−1.90500	−0.952501	+	0.304534i	$0.901499\pi$
$132$	−59.1841	−5.15132
$133$	22.7595	1.97350
$134$	−22.9975	−1.98668
$135$	1.35356	0.116496
$136$	−25.3632	−2.17488
$137$	13.5479	1.15747	0.578736	−	0.815515i	$-0.303546\pi$
$137$	13.5479	1.15747	0.578736	+	0.815515i	$0.303546\pi$
$138$	38.1819	3.25026
$139$	7.51472	0.637390	0.318695	−	0.947857i	$-0.396755\pi$
$139$	7.51472	0.637390	0.318695	+	0.947857i	$0.396755\pi$
$140$	1.54432	0.130519
$141$	13.1979	1.11146
$142$	4.68682	0.393309
$143$	5.02154	0.419922
$144$	20.5168	1.70973
$145$	−1.20690	−0.100228
$146$	0.183512	0.0151875
$147$	3.97125	0.327543
$148$	4.30714	0.354045
$149$	13.8573	1.13524	0.567618	−	0.823292i	$-0.307865\pi$
$149$	13.8573	1.13524	0.567618	+	0.823292i	$0.307865\pi$
$150$	36.6885	2.99560
$151$	−4.40492	−0.358467	−0.179233	−	0.983807i	$-0.557362\pi$
$151$	−4.40492	−0.358467	−0.179233	+	0.983807i	$0.557362\pi$
$152$	−35.9998	−2.91997
$153$	34.6424	2.80067
$154$	35.0962	2.82813
$155$	0.725395	0.0582652
$156$	−11.7861	−0.943640
$157$	−24.3067	−1.93988	−0.969941	−	0.243339i	$-0.921757\pi$
$157$	−24.3067	−1.93988	−0.969941	+	0.243339i	$0.921757\pi$
$158$	−35.7609	−2.84498
$159$	−3.15386	−0.250117
$160$	0.155805	0.0123175
$161$	−14.9407	−1.17749
$162$	−26.9006	−2.11351
$163$	23.9023	1.87217	0.936087	−	0.351768i	$-0.114419\pi$
$163$	23.9023	1.87217	0.936087	+	0.351768i	$0.114419\pi$
$164$	23.6434	1.84624
$165$	−2.10634	−0.163979
$166$	−3.29234	−0.255535
$167$	−6.39802	−0.495094	−0.247547	−	0.968876i	$-0.579624\pi$
$167$	−6.39802	−0.495094	−0.247547	+	0.968876i	$0.579624\pi$
$168$	−39.9143	−3.07945
$169$	1.00000	0.0769231
$170$	−1.86291	−0.142879
$171$	49.1703	3.76015
$172$	18.6286	1.42042
$173$	9.30534	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$173$	9.30534	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$174$	64.3765	4.88037
$175$	−14.3563	−1.08523
$176$	−16.5453	−1.24715
$177$	3.87285	0.291101
$178$	−22.0617	−1.65359
$179$	7.04014	0.526205	0.263102	−	0.964768i	$-0.415254\pi$
$179$	7.04014	0.526205	0.263102	+	0.964768i	$0.415254\pi$
$180$	3.33639	0.248680
$181$	24.8965	1.85054	0.925271	−	0.379306i	$-0.123837\pi$
$181$	24.8965	1.85054	0.925271	+	0.379306i	$0.123837\pi$
$182$	6.98914	0.518069
$183$	4.53012	0.334876
$184$	23.6323	1.74220
$185$	0.153290	0.0112701
$186$	−38.6928	−2.83709
$187$	−27.9366	−2.04292
$188$	16.8584	1.22953
$189$	28.2517	2.05501
$190$	−2.64416	−0.191827
$191$	−16.6830	−1.20714	−0.603570	−	0.797310i	$-0.706255\pi$
$191$	−16.6830	−1.20714	−0.603570	+	0.797310i	$0.706255\pi$
$192$	−28.3276	−2.04437
$193$	19.7948	1.42486	0.712430	−	0.701743i	$-0.247595\pi$
$193$	19.7948	1.42486	0.712430	+	0.701743i	$0.247595\pi$
$194$	18.9788	1.36260
$195$	−0.419462	−0.0300383
$196$	5.07272	0.362337
$197$	−22.3846	−1.59484	−0.797419	−	0.603426i	$-0.793802\pi$
$197$	−22.3846	−1.59484	−0.797419	+	0.603426i	$0.793802\pi$
$198$	75.8228	5.38849
$199$	5.50598	0.390309	0.195154	−	0.980773i	$-0.437479\pi$
$199$	5.50598	0.390309	0.195154	+	0.980773i	$0.437479\pi$
$200$	22.7080	1.60570
$201$	28.8082	2.03197
$202$	−3.47734	−0.244665
$203$	−25.1907	−1.76804
$204$	65.5699	4.59081
$205$	0.841461	0.0587702
$206$	21.0240	1.46481
$207$	−32.2782	−2.24349
$208$	−3.29487	−0.228458
$209$	−39.6523	−2.74281
$210$	−2.93167	−0.202305
$211$	−4.43328	−0.305199	−0.152600	−	0.988288i	$-0.548765\pi$
$211$	−4.43328	−0.305199	−0.152600	+	0.988288i	$0.548765\pi$
$212$	−4.02861	−0.276686
$213$	−5.87103	−0.402277
$214$	−3.02416	−0.206727
$215$	0.662986	0.0452153
$216$	−44.6870	−3.04056
$217$	15.1406	1.02781
$218$	−13.5711	−0.919148
$219$	−0.229879	−0.0155338
$220$	−2.69056	−0.181397
$221$	−5.56335	−0.374231
$222$	−8.17650	−0.548771
$223$	9.87839	0.661506	0.330753	−	0.943717i	$-0.392697\pi$
$223$	9.87839	0.661506	0.330753	+	0.943717i	$0.392697\pi$
$224$	3.25199	0.217283
$225$	−31.0157	−2.06772
$226$	−7.89889	−0.525426
$227$	−13.9293	−0.924520	−0.462260	−	0.886745i	$-0.652961\pi$
$227$	−13.9293	−0.924520	−0.462260	+	0.886745i	$0.652961\pi$
$228$	93.0679	6.16357
$229$	−14.5064	−0.958612	−0.479306	−	0.877648i	$-0.659112\pi$
$229$	−14.5064	−0.958612	−0.479306	+	0.877648i	$0.659112\pi$
$230$	1.73578	0.114454
$231$	−43.9639	−2.89261
$232$	39.8452	2.61597
$233$	26.3181	1.72415	0.862077	−	0.506778i	$-0.169163\pi$
$233$	26.3181	1.72415	0.862077	+	0.506778i	$0.169163\pi$
$234$	15.0995	0.987087
$235$	0.599986	0.0391388
$236$	4.94702	0.322023
$237$	44.7965	2.90985
$238$	−38.8830	−2.52041
$239$	−20.8878	−1.35112	−0.675559	−	0.737306i	$-0.736098\pi$
$239$	−20.8878	−1.35112	−0.675559	+	0.737306i	$0.736098\pi$
$240$	1.38207	0.0892124
$241$	−15.2599	−0.982978	−0.491489	−	0.870884i	$-0.663547\pi$
$241$	−15.2599	−0.982978	−0.491489	+	0.870884i	$0.663547\pi$
$242$	−34.4718	−2.21593
$243$	4.29164	0.275309
$244$	5.78659	0.370449
$245$	0.180536	0.0115340
$246$	−44.8837	−2.86168
$247$	−7.89644	−0.502439
$248$	−23.9485	−1.52073
$249$	4.12420	0.261361
$250$	3.34216	0.211377
$251$	3.46303	0.218584	0.109292	−	0.994010i	$-0.465142\pi$
$251$	3.46303	0.218584	0.109292	+	0.994010i	$0.465142\pi$
$252$	69.6377	4.38676
$253$	26.0300	1.63649
$254$	−12.3025	−0.771925
$255$	2.33361	0.146136
$256$	−30.7126	−1.91954
$257$	29.3133	1.82852	0.914258	−	0.405133i	$-0.132775\pi$
$257$	29.3133	1.82852	0.914258	+	0.405133i	$0.132775\pi$
$258$	−35.3639	−2.20166
$259$	3.19948	0.198806
$260$	−0.535803	−0.0332291
$261$	−54.4226	−3.36868
$262$	52.8717	3.26642
$263$	−0.738956	−0.0455660	−0.0227830	−	0.999740i	$-0.507253\pi$
$263$	−0.738956	−0.0455660	−0.0227830	+	0.999740i	$0.507253\pi$
$264$	69.5397	4.27987
$265$	−0.143377	−0.00880756
$266$	−55.1893	−3.38387
$267$	27.6360	1.69129
$268$	36.7984	2.24782
$269$	6.17049	0.376222	0.188111	−	0.982148i	$-0.439764\pi$
$269$	6.17049	0.376222	0.188111	+	0.982148i	$0.439764\pi$
$270$	−3.28223	−0.199750
$271$	−6.53751	−0.397125	−0.198563	−	0.980088i	$-0.563627\pi$
$271$	−6.53751	−0.397125	−0.198563	+	0.980088i	$0.563627\pi$
$272$	18.3305	1.11145
$273$	−8.75507	−0.529881
$274$	−32.8520	−1.98466
$275$	25.0119	1.50828
$276$	−61.0951	−3.67749
$277$	17.9307	1.07735	0.538677	−	0.842512i	$-0.318924\pi$
$277$	17.9307	1.07735	0.538677	+	0.842512i	$0.318924\pi$
$278$	−18.2224	−1.09290
$279$	32.7101	1.95830
$280$	−1.81453	−0.108439
$281$	7.43318	0.443426	0.221713	−	0.975112i	$-0.428835\pi$
$281$	7.43318	0.443426	0.221713	+	0.975112i	$0.428835\pi$
$282$	−32.0034	−1.90577
$283$	0.552823	0.0328619	0.0164309	−	0.999865i	$-0.494770\pi$
$283$	0.552823	0.0328619	0.0164309	+	0.999865i	$0.494770\pi$
$284$	−7.49942	−0.445009
$285$	3.31225	0.196201
$286$	−12.1767	−0.720021
$287$	17.5631	1.03672
$288$	7.02569	0.413993
$289$	13.9508	0.820637
$290$	2.92661	0.171856
$291$	−23.7742	−1.39367
$292$	−0.293639	−0.0171839
$293$	24.4595	1.42894	0.714471	−	0.699665i	$-0.246667\pi$
$293$	24.4595	1.42894	0.714471	+	0.699665i	$0.246667\pi$
$294$	−9.62984	−0.561624
$295$	0.176063	0.0102508
$296$	−5.06077	−0.294151
$297$	−49.2209	−2.85608
$298$	−33.6024	−1.94654
$299$	5.18368	0.299780
$300$	−58.7056	−3.38937
$301$	13.8380	0.797607
$302$	10.6814	0.614647
$303$	4.35595	0.250243
$304$	26.0178	1.49222
$305$	0.205943	0.0117922
$306$	−84.0039	−4.80218
$307$	25.2066	1.43862	0.719308	−	0.694691i	$-0.244459\pi$
$307$	25.2066	1.43862	0.719308	+	0.694691i	$0.244459\pi$
$308$	−56.1577	−3.19988
$309$	−26.3361	−1.49821
$310$	−1.75900	−0.0999046
$311$	7.48231	0.424283	0.212141	−	0.977239i	$-0.431956\pi$
$311$	7.48231	0.424283	0.212141	+	0.977239i	$0.431956\pi$
$312$	13.8483	0.784005
$313$	−3.68351	−0.208204	−0.104102	−	0.994567i	$-0.533197\pi$
$313$	−3.68351	−0.208204	−0.104102	+	0.994567i	$0.533197\pi$
$314$	58.9409	3.32623
$315$	2.47838	0.139641
$316$	57.2213	3.21895
$317$	29.4750	1.65548	0.827741	−	0.561110i	$-0.189626\pi$
$317$	29.4750	1.65548	0.827741	+	0.561110i	$0.189626\pi$
$318$	7.64775	0.428865
$319$	43.8879	2.45725
$320$	−1.28779	−0.0719898
$321$	3.78827	0.211440
$322$	36.2294	2.01899
$323$	43.9306	2.44437
$324$	43.0438	2.39132
$325$	4.98093	0.276292
$326$	−57.9605	−3.21013
$327$	17.0000	0.940104
$328$	−27.7804	−1.53391
$329$	12.5230	0.690415
$330$	5.10764	0.281167
$331$	8.09419	0.444897	0.222449	−	0.974944i	$-0.428595\pi$
$331$	8.09419	0.444897	0.222449	+	0.974944i	$0.428595\pi$
$332$	5.26809	0.289124
$333$	6.91225	0.378789
$334$	15.5145	0.848915
$335$	1.30964	0.0715534
$336$	28.8468	1.57372
$337$	−10.9379	−0.595828	−0.297914	−	0.954593i	$-0.596291\pi$
$337$	−10.9379	−0.595828	−0.297914	+	0.954593i	$0.596291\pi$
$338$	−2.42489	−0.131897
$339$	9.89469	0.537406
$340$	2.98086	0.161660
$341$	−26.3783	−1.42847
$342$	−119.232	−6.44735
$343$	−16.4076	−0.885926
$344$	−21.8881	−1.18013
$345$	−2.17435	−0.117063
$346$	−22.5644	−1.21307
$347$	−13.0695	−0.701606	−0.350803	−	0.936449i	$-0.614091\pi$
$347$	−13.0695	−0.701606	−0.350803	+	0.936449i	$0.614091\pi$
$348$	−103.009	−5.52188
$349$	−16.8875	−0.903965	−0.451983	−	0.892027i	$-0.649283\pi$
$349$	−16.8875	−0.903965	−0.451983	+	0.892027i	$0.649283\pi$
$350$	34.8124	1.86080
$351$	−9.80195	−0.523189
$352$	−5.66571	−0.301983
$353$	−3.99507	−0.212636	−0.106318	−	0.994332i	$-0.533906\pi$
$353$	−3.99507	−0.212636	−0.106318	+	0.994332i	$0.533906\pi$
$354$	−9.39122	−0.499138
$355$	−0.266902	−0.0141657
$356$	35.3011	1.87095
$357$	48.7075	2.57787
$358$	−17.0716	−0.902260
$359$	−7.09247	−0.374326	−0.187163	−	0.982329i	$-0.559929\pi$
$359$	−7.09247	−0.374326	−0.187163	+	0.982329i	$0.559929\pi$
$360$	−3.92017	−0.206611
$361$	43.3538	2.28178
$362$	−60.3712	−3.17304
$363$	43.1818	2.26645
$364$	−11.1834	−0.586168
$365$	−0.0104505	−0.000547004 0
$366$	−10.9850	−0.574197
$367$	−32.7733	−1.71075	−0.855377	−	0.518006i	$-0.826675\pi$
$367$	−32.7733	−1.71075	−0.855377	+	0.518006i	$0.826675\pi$
$368$	−17.0796	−0.890333
$369$	37.9438	1.97528
$370$	−0.371710	−0.0193243
$371$	−2.99258	−0.155367
$372$	61.9126	3.21002
$373$	−11.0268	−0.570945	−0.285473	−	0.958387i	$-0.592151\pi$
$373$	−11.0268	−0.570945	−0.285473	+	0.958387i	$0.592151\pi$
$374$	67.7430	3.50291
$375$	−4.18662	−0.216196
$376$	−19.8082	−1.02153
$377$	8.73993	0.450129
$378$	−68.5072	−3.52363
$379$	12.4991	0.642036	0.321018	−	0.947073i	$-0.395975\pi$
$379$	12.4991	0.642036	0.321018	+	0.947073i	$0.395975\pi$
$380$	4.23094	0.217043
$381$	15.4109	0.789525
$382$	40.4544	2.06983
$383$	−5.58164	−0.285209	−0.142604	−	0.989780i	$-0.545548\pi$
$383$	−5.58164	−0.285209	−0.142604	+	0.989780i	$0.545548\pi$
$384$	61.8367	3.15559
$385$	−1.99863	−0.101860
$386$	−48.0002	−2.44314
$387$	29.8959	1.51969
$388$	−30.3682	−1.54171
$389$	−5.54885	−0.281338	−0.140669	−	0.990057i	$-0.544925\pi$
$389$	−5.54885	−0.281338	−0.140669	+	0.990057i	$0.544925\pi$
$390$	1.01715	0.0515053
$391$	−28.8386	−1.45843
$392$	−5.96030	−0.301041
$393$	−66.2307	−3.34089
$394$	54.2802	2.73460
$395$	2.03649	0.102467
$396$	−121.325	−6.09679
$397$	11.9840	0.601461	0.300731	−	0.953709i	$-0.402769\pi$
$397$	11.9840	0.601461	0.300731	+	0.953709i	$0.402769\pi$
$398$	−13.3514	−0.669245
$399$	69.1339	3.46102
$400$	−16.4115	−0.820576
$401$	−23.1223	−1.15467	−0.577336	−	0.816507i	$-0.695908\pi$
$401$	−23.1223	−1.15467	−0.577336	+	0.816507i	$0.695908\pi$
$402$	−69.8567	−3.48413
$403$	−5.25304	−0.261672
$404$	5.56412	0.276825
$405$	1.53191	0.0761214
$406$	61.0846	3.03158
$407$	−5.57423	−0.276304
$408$	−77.0428	−3.81419
$409$	−38.3803	−1.89779	−0.948893	−	0.315598i	$-0.897795\pi$
$409$	−38.3803	−1.89779	−0.948893	+	0.315598i	$0.897795\pi$
$410$	−2.04045	−0.100771
$411$	41.1527	2.02991
$412$	−33.6407	−1.65736
$413$	3.67481	0.180825
$414$	78.2710	3.84681
$415$	0.187489	0.00920350
$416$	−1.12828	−0.0553185
$417$	22.8266	1.11782
$418$	96.1523	4.70296
$419$	24.0578	1.17530	0.587651	−	0.809115i	$-0.300053\pi$
$419$	24.0578	1.17530	0.587651	+	0.809115i	$0.300053\pi$
$420$	4.69100	0.228897
$421$	−6.24548	−0.304386	−0.152193	−	0.988351i	$-0.548634\pi$
$421$	−6.24548	−0.304386	−0.152193	+	0.988351i	$0.548634\pi$
$422$	10.7502	0.523311
$423$	27.0550	1.31546
$424$	4.73350	0.229879
$425$	−27.7106	−1.34416
$426$	14.2366	0.689765
$427$	4.29847	0.208018
$428$	4.83898	0.233901
$429$	15.2533	0.736437
$430$	−1.60767	−0.0775286
$431$	30.7286	1.48014	0.740072	−	0.672528i	$-0.234792\pi$
$431$	30.7286	1.48014	0.740072	+	0.672528i	$0.234792\pi$
$432$	32.2962	1.55385
$433$	1.91517	0.0920372	0.0460186	−	0.998941i	$-0.485347\pi$
$433$	1.91517	0.0920372	0.0460186	+	0.998941i	$0.485347\pi$
$434$	−36.7142	−1.76234
$435$	−3.66607	−0.175774
$436$	21.7152	1.03997
$437$	−40.9326	−1.95807
$438$	0.557432	0.0266351
$439$	0.556863	0.0265776	0.0132888	−	0.999912i	$-0.495770\pi$
$439$	0.556863	0.0265776	0.0132888	+	0.999912i	$0.495770\pi$
$440$	3.16133	0.150710
$441$	8.14088	0.387661
$442$	13.4905	0.641677
$443$	15.5409	0.738370	0.369185	−	0.929356i	$-0.379637\pi$
$443$	15.5409	0.738370	0.369185	+	0.929356i	$0.379637\pi$
$444$	13.0833	0.620905
$445$	1.25635	0.0595568
$446$	−23.9540	−1.13425
$447$	42.0927	1.99092
$448$	−26.8790	−1.26991
$449$	−11.8804	−0.560671	−0.280336	−	0.959902i	$-0.590446\pi$
$449$	−11.8804	−0.560671	−0.280336	+	0.959902i	$0.590446\pi$
$450$	75.2097	3.54542
$451$	−30.5989	−1.44085
$452$	12.6391	0.594492
$453$	−13.3803	−0.628661
$454$	33.7770	1.58523
$455$	−0.398012	−0.0186591
$456$	−109.352	−5.12089
$457$	−0.442734	−0.0207102	−0.0103551	−	0.999946i	$-0.503296\pi$
$457$	−0.442734	−0.0207102	−0.0103551	+	0.999946i	$0.503296\pi$
$458$	35.1765	1.64369
$459$	54.5317	2.54532
$460$	−2.77743	−0.129498
$461$	20.8643	0.971750	0.485875	−	0.874028i	$-0.338501\pi$
$461$	20.8643	0.971750	0.485875	+	0.874028i	$0.338501\pi$
$462$	106.608	4.95983
$463$	16.5247	0.767968	0.383984	−	0.923340i	$-0.374552\pi$
$463$	16.5247	0.767968	0.383984	+	0.923340i	$0.374552\pi$
$464$	−28.7970	−1.33686
$465$	2.20345	0.102182
$466$	−63.8184	−2.95633
$467$	6.50880	0.301191	0.150596	−	0.988595i	$-0.451881\pi$
$467$	6.50880	0.301191	0.150596	+	0.988595i	$0.451881\pi$
$468$	−24.1609	−1.11684
$469$	27.3351	1.26222
$470$	−1.45490	−0.0671095
$471$	−73.8334	−3.40207
$472$	−5.81261	−0.267547
$473$	−24.1089	−1.10853
$474$	−108.627	−4.98939
$475$	−39.3316	−1.80466
$476$	62.2170	2.85171
$477$	−6.46526	−0.296024
$478$	50.6505	2.31670
$479$	−36.7967	−1.68128	−0.840642	−	0.541591i	$-0.817822\pi$
$479$	−36.7967	−1.68128	−0.840642	+	0.541591i	$0.817822\pi$
$480$	0.473271	0.0216018
$481$	−1.11006	−0.0506146
$482$	37.0036	1.68547
$483$	−45.3835	−2.06502
$484$	55.1586	2.50721
$485$	−1.08079	−0.0490763
$486$	−10.4067	−0.472059
$487$	−34.5399	−1.56515	−0.782576	−	0.622555i	$-0.786095\pi$
$487$	−34.5399	−1.56515	−0.782576	+	0.622555i	$0.786095\pi$
$488$	−6.79909	−0.307780
$489$	72.6052	3.28332
$490$	−0.437780	−0.0197769
$491$	−22.8064	−1.02924	−0.514620	−	0.857419i	$-0.672067\pi$
$491$	−22.8064	−1.02924	−0.514620	+	0.857419i	$0.672067\pi$
$492$	71.8188	3.23784
$493$	−48.6233	−2.18988
$494$	19.1480	0.861509
$495$	−4.31790	−0.194075
$496$	17.3081	0.777156
$497$	−5.57081	−0.249885
$498$	−10.0007	−0.448144
$499$	−30.0837	−1.34673	−0.673366	−	0.739309i	$-0.735152\pi$
$499$	−30.0837	−1.34673	−0.673366	+	0.739309i	$0.735152\pi$
$500$	−5.34782	−0.239162
$501$	−19.4345	−0.868270
$502$	−8.39745	−0.374797
$503$	−13.4194	−0.598342	−0.299171	−	0.954200i	$-0.596710\pi$
$503$	−13.4194	−0.598342	−0.299171	+	0.954200i	$0.596710\pi$
$504$	−81.8223	−3.64466
$505$	0.198025	0.00881199
$506$	−63.1199	−2.80602
$507$	3.03758	0.134904
$508$	19.6853	0.873392
$509$	−36.0741	−1.59896	−0.799478	−	0.600695i	$-0.794890\pi$
$509$	−36.0741	−1.59896	−0.799478	+	0.600695i	$0.794890\pi$
$510$	−5.65874	−0.250573
$511$	−0.218124	−0.00964925
$512$	33.7601	1.49200
$513$	77.4005	3.41732
$514$	−71.0816	−3.13527
$515$	−1.19726	−0.0527576
$516$	56.5860	2.49106
$517$	−21.8179	−0.959551
$518$	−7.75839	−0.340884
$519$	28.2657	1.24073
$520$	0.629554	0.0276078
$521$	37.6632	1.65006	0.825028	−	0.565092i	$-0.191159\pi$
$521$	37.6632	1.65006	0.825028	+	0.565092i	$0.191159\pi$
$522$	131.969	5.77612
$523$	−29.0183	−1.26888	−0.634441	−	0.772971i	$-0.718770\pi$
$523$	−29.0183	−1.26888	−0.634441	+	0.772971i	$0.718770\pi$
$524$	−84.6004	−3.69578
$525$	−43.6084	−1.90323
$526$	1.79189	0.0781299
$527$	29.2245	1.27304
$528$	−50.2577	−2.18719
$529$	3.87051	0.168283
$530$	0.347673	0.0151019
$531$	7.93915	0.344530
$532$	88.3088	3.82867
$533$	−6.09354	−0.263940
$534$	−67.0141	−2.89998
$535$	0.172218	0.00744561
$536$	−43.2371	−1.86756
$537$	21.3850	0.922831
$538$	−14.9628	−0.645090
$539$	−6.56503	−0.282776
$540$	5.25192	0.226007
$541$	1.44451	0.0621044	0.0310522	−	0.999518i	$-0.490114\pi$
$541$	1.44451	0.0621044	0.0310522	+	0.999518i	$0.490114\pi$
$542$	15.8527	0.680933
$543$	75.6251	3.24538
$544$	6.27702	0.269125
$545$	0.772834	0.0331046
$546$	21.2301	0.908563
$547$	−6.77738	−0.289780	−0.144890	−	0.989448i	$-0.546283\pi$
$547$	−6.77738	−0.289780	−0.144890	+	0.989448i	$0.546283\pi$
$548$	52.5668	2.24554
$549$	9.28653	0.396340
$550$	−60.6511	−2.58617
$551$	−69.0144	−2.94011
$552$	71.7851	3.05538
$553$	42.5058	1.80753
$554$	−43.4800	−1.84729
$555$	0.465629	0.0197649
$556$	29.1577	1.23656
$557$	−26.0325	−1.10303	−0.551517	−	0.834164i	$-0.685951\pi$
$557$	−26.0325	−1.10303	−0.551517	+	0.834164i	$0.685951\pi$
$558$	−79.3183	−3.35781
$559$	−4.80109	−0.203065
$560$	1.31140	0.0554167
$561$	−84.8595	−3.58277
$562$	−18.0246	−0.760323
$563$	−5.36611	−0.226155	−0.113077	−	0.993586i	$-0.536071\pi$
$563$	−5.36611	−0.226155	−0.113077	+	0.993586i	$0.536071\pi$
$564$	51.2089	2.15628
$565$	0.449820	0.0189241
$566$	−1.34053	−0.0563468
$567$	31.9743	1.34280
$568$	8.81161	0.369727
$569$	−25.6715	−1.07621	−0.538103	−	0.842879i	$-0.680859\pi$
$569$	−25.6715	−1.07621	−0.538103	+	0.842879i	$0.680859\pi$
$570$	−8.03185	−0.336417
$571$	−0.209914	−0.00878462	−0.00439231	−	0.999990i	$-0.501398\pi$
$571$	−0.209914	−0.00878462	−0.00439231	+	0.999990i	$0.501398\pi$
$572$	19.4840	0.814666
$573$	−50.6759	−2.11702
$574$	−42.5886	−1.77761
$575$	25.8195	1.07675
$576$	−58.0701	−2.41959
$577$	−37.4971	−1.56102	−0.780512	−	0.625141i	$-0.785041\pi$
$577$	−37.4971	−1.56102	−0.780512	+	0.625141i	$0.785041\pi$
$578$	−33.8292	−1.40711
$579$	60.1283	2.49885
$580$	−4.68288	−0.194446
$581$	3.91331	0.162351
$582$	57.6497	2.38966
$583$	5.21376	0.215932
$584$	0.345017	0.0142769
$585$	−0.859876	−0.0355515
$586$	−59.3117	−2.45014
$587$	−15.5042	−0.639926	−0.319963	−	0.947430i	$-0.603670\pi$
$587$	−15.5042	−0.639926	−0.319963	+	0.947430i	$0.603670\pi$
$588$	15.4088	0.635448
$589$	41.4803	1.70917
$590$	−0.426932	−0.0175765
$591$	−67.9951	−2.79694
$592$	3.65752	0.150323
$593$	−44.5883	−1.83102	−0.915510	−	0.402295i	$-0.868213\pi$
$593$	−44.5883	−1.83102	−0.915510	+	0.402295i	$0.868213\pi$
$594$	119.355	4.89720
$595$	2.21428	0.0907766
$596$	53.7675	2.20240
$597$	16.7249	0.684503
$598$	−12.5698	−0.514019
$599$	−45.8748	−1.87439	−0.937197	−	0.348800i	$-0.886589\pi$
$599$	−45.8748	−1.87439	−0.937197	+	0.348800i	$0.886589\pi$
$600$	68.9774	2.81599
$601$	45.4705	1.85478	0.927390	−	0.374097i	$-0.122047\pi$
$601$	45.4705	1.85478	0.927390	+	0.374097i	$0.122047\pi$
$602$	−33.5555	−1.36762
$603$	59.0554	2.40492
$604$	−17.0914	−0.695441
$605$	1.96308	0.0798104
$606$	−10.5627	−0.429080
$607$	−32.6696	−1.32602	−0.663008	−	0.748612i	$-0.730721\pi$
$607$	−32.6696	−1.32602	−0.663008	+	0.748612i	$0.730721\pi$
$608$	8.90941	0.361324
$609$	−76.5187	−3.10069
$610$	−0.499388	−0.0202196
$611$	−4.34487	−0.175775
$612$	134.415	5.43341
$613$	29.2618	1.18187	0.590936	−	0.806718i	$-0.298759\pi$
$613$	29.2618	1.18187	0.590936	+	0.806718i	$0.298759\pi$
$614$	−61.1232	−2.46673
$615$	2.55600	0.103068
$616$	65.9838	2.65856
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	63.8621	2.56891
$619$	0.802544	0.0322570	0.0161285	−	0.999870i	$-0.494866\pi$
$619$	0.802544	0.0322570	0.0161285	+	0.999870i	$0.494866\pi$
$620$	2.81459	0.113037
$621$	−50.8102	−2.03894
$622$	−18.1438	−0.727498
$623$	26.2228	1.05059
$624$	−10.0084	−0.400658
$625$	24.7143	0.988573
$626$	8.93211	0.356999
$627$	−120.447	−4.81019
$628$	−94.3118	−3.76345
$629$	6.17567	0.246240
$630$	−6.00979	−0.239436
$631$	38.9968	1.55244	0.776220	−	0.630462i	$-0.217135\pi$
$631$	38.9968	1.55244	0.776220	+	0.630462i	$0.217135\pi$
$632$	−67.2334	−2.67440
$633$	−13.4664	−0.535243
$634$	−71.4736	−2.83858
$635$	0.700591	0.0278021
$636$	−12.2372	−0.485238
$637$	−1.30737	−0.0518000
$638$	−106.423	−4.21334
$639$	−12.0353	−0.476111
$640$	2.81114	0.111120
$641$	−17.2501	−0.681340	−0.340670	−	0.940183i	$-0.610654\pi$
$641$	−17.2501	−0.681340	−0.340670	+	0.940183i	$0.610654\pi$
$642$	−9.18613	−0.362547
$643$	7.27167	0.286767	0.143383	−	0.989667i	$-0.454202\pi$
$643$	7.27167	0.286767	0.143383	+	0.989667i	$0.454202\pi$
$644$	−57.9710	−2.28438
$645$	2.01387	0.0792962
$646$	−106.527	−4.19124
$647$	−22.1538	−0.870957	−0.435479	−	0.900199i	$-0.643421\pi$
$647$	−22.1538	−0.870957	−0.435479	+	0.900199i	$0.643421\pi$
$648$	−50.5753	−1.98678
$649$	−6.40235	−0.251314
$650$	−12.0782	−0.473746
$651$	45.9907	1.80252
$652$	92.7430	3.63210
$653$	−2.59620	−0.101597	−0.0507985	−	0.998709i	$-0.516177\pi$
$653$	−2.59620	−0.101597	−0.0507985	+	0.998709i	$0.516177\pi$
$654$	−41.2232	−1.61195
$655$	−3.01090	−0.117645
$656$	20.0774	0.783892
$657$	−0.471242	−0.0183849
$658$	−30.3669	−1.18382
$659$	35.6118	1.38724	0.693620	−	0.720341i	$-0.256015\pi$
$659$	35.6118	1.38724	0.693620	+	0.720341i	$0.256015\pi$
$660$	−8.17278	−0.318125
$661$	29.1106	1.13227	0.566136	−	0.824312i	$-0.308438\pi$
$661$	29.1106	1.13227	0.566136	+	0.824312i	$0.308438\pi$
$662$	−19.6275	−0.762845
$663$	−16.8991	−0.656307
$664$	−6.18986	−0.240213
$665$	3.14288	0.121876
$666$	−16.7614	−0.649493
$667$	45.3050	1.75422
$668$	−24.8249	−0.960502
$669$	30.0064	1.16012
$670$	−3.17574	−0.122689
$671$	−7.48891	−0.289106
$672$	9.87818	0.381059
$673$	−27.2791	−1.05153	−0.525766	−	0.850629i	$-0.676221\pi$
$673$	−27.2791	−1.05153	−0.525766	+	0.850629i	$0.676221\pi$
$674$	26.5233	1.02164
$675$	−48.8228	−1.87919
$676$	3.88008	0.149234
$677$	4.53154	0.174161	0.0870805	−	0.996201i	$-0.472246\pi$
$677$	4.53154	0.174161	0.0870805	+	0.996201i	$0.472246\pi$
$678$	−23.9935	−0.921465
$679$	−22.5585	−0.865715
$680$	−3.50243	−0.134312
$681$	−42.3114	−1.62137
$682$	63.9645	2.44933
$683$	13.7679	0.526815	0.263407	−	0.964685i	$-0.415154\pi$
$683$	13.7679	0.526815	0.263407	+	0.964685i	$0.415154\pi$
$684$	190.785	7.29484
$685$	1.87083	0.0714809
$686$	39.7865	1.51906
$687$	−44.0645	−1.68116
$688$	15.8190	0.603093
$689$	1.03828	0.0395553
$690$	5.27256	0.200723
$691$	11.4773	0.436617	0.218309	−	0.975880i	$-0.429946\pi$
$691$	11.4773	0.436617	0.218309	+	0.975880i	$0.429946\pi$
$692$	36.1055	1.37252
$693$	−90.1239	−3.42352
$694$	31.6920	1.20301
$695$	1.03771	0.0393627
$696$	121.033	4.58775
$697$	33.9005	1.28407
$698$	40.9502	1.54999
$699$	79.9432	3.02373
$700$	−55.7036	−2.10540
$701$	19.6352	0.741610	0.370805	−	0.928711i	$-0.379082\pi$
$701$	19.6352	0.741610	0.370805	+	0.928711i	$0.379082\pi$
$702$	23.7686	0.897089
$703$	8.76556	0.330599
$704$	46.8294	1.76495
$705$	1.82251	0.0686395
$706$	9.68760	0.364598
$707$	4.13321	0.155445
$708$	15.0270	0.564748
$709$	48.9098	1.83684	0.918422	−	0.395601i	$-0.129464\pi$
$709$	48.9098	1.83684	0.918422	+	0.395601i	$0.129464\pi$
$710$	0.647207	0.0242892
$711$	91.8308	3.44392
$712$	−41.4778	−1.55444
$713$	−27.2300	−1.01977
$714$	−118.110	−4.42016
$715$	0.693428	0.0259327
$716$	27.3163	1.02086
$717$	−63.4483	−2.36952
$718$	17.1984	0.641840
$719$	−40.1056	−1.49569	−0.747843	−	0.663876i	$-0.768910\pi$
$719$	−40.1056	−1.49569	−0.747843	+	0.663876i	$0.768910\pi$
$720$	2.83318	0.105586
$721$	−24.9894	−0.930654
$722$	−105.128	−3.91246
$723$	−46.3532	−1.72390
$724$	96.6005	3.59013
$725$	43.5330	1.61677
$726$	−104.711	−3.88619
$727$	39.1594	1.45234	0.726171	−	0.687514i	$-0.241298\pi$
$727$	39.1594	1.45234	0.726171	+	0.687514i	$0.241298\pi$
$728$	13.1401	0.487006
$729$	−20.2444	−0.749792
$730$	0.0253413	0.000937922 0
$731$	26.7101	0.987910
$732$	17.5772	0.649674
$733$	4.03553	0.149056	0.0745279	−	0.997219i	$-0.476255\pi$
$733$	4.03553	0.149056	0.0745279	+	0.997219i	$0.476255\pi$
$734$	79.4717	2.93335
$735$	0.548393	0.0202278
$736$	−5.84865	−0.215584
$737$	−47.6239	−1.75425
$738$	−92.0095	−3.38692
$739$	−44.4601	−1.63549	−0.817745	−	0.575580i	$-0.804776\pi$
$739$	−44.4601	−1.63549	−0.817745	+	0.575580i	$0.804776\pi$
$740$	0.594776	0.0218644
$741$	−23.9861	−0.881151
$742$	7.25668	0.266401
$743$	37.1580	1.36319	0.681597	−	0.731728i	$-0.261286\pi$
$743$	37.1580	1.36319	0.681597	+	0.731728i	$0.261286\pi$
$744$	−72.7456	−2.66698
$745$	1.91357	0.0701076
$746$	26.7387	0.978974
$747$	8.45442	0.309331
$748$	−108.396	−3.96335
$749$	3.59455	0.131342
$750$	10.1521	0.370702
$751$	−14.7911	−0.539733	−0.269867	−	0.962898i	$-0.586980\pi$
$751$	−14.7911	−0.539733	−0.269867	+	0.962898i	$0.586980\pi$
$752$	14.3158	0.522043
$753$	10.5192	0.383342
$754$	−21.1934	−0.771816
$755$	−0.608278	−0.0221375
$756$	109.619	3.98680
$757$	−35.3899	−1.28627	−0.643133	−	0.765754i	$-0.722366\pi$
$757$	−35.3899	−1.28627	−0.643133	+	0.765754i	$0.722366\pi$
$758$	−30.3089	−1.10087
$759$	79.0683	2.87000
$760$	−4.97124	−0.180326
$761$	−51.4713	−1.86583	−0.932917	−	0.360091i	$-0.882746\pi$
$761$	−51.4713	−1.86583	−0.932917	+	0.360091i	$0.882746\pi$
$762$	−37.3697	−1.35376
$763$	16.1307	0.583971
$764$	−64.7314	−2.34190
$765$	4.78379	0.172958
$766$	13.5349	0.489034
$767$	−1.27498	−0.0460368
$768$	−93.2919	−3.36638
$769$	−32.9261	−1.18734	−0.593672	−	0.804707i	$-0.702322\pi$
$769$	−32.9261	−1.18734	−0.593672	+	0.804707i	$0.702322\pi$
$770$	4.84646	0.174654
$771$	89.0416	3.20676
$772$	76.8054	2.76429
$773$	25.0555	0.901185	0.450592	−	0.892730i	$-0.351213\pi$
$773$	25.0555	0.901185	0.450592	+	0.892730i	$0.351213\pi$
$774$	−72.4942	−2.60575
$775$	−26.1650	−0.939875
$776$	35.6818	1.28090
$777$	9.71869	0.348656
$778$	13.4553	0.482397
$779$	48.1173	1.72398
$780$	−1.62755	−0.0582755
$781$	9.70562	0.347295
$782$	69.9304	2.50070
$783$	−85.6684	−3.06154
$784$	4.30763	0.153844
$785$	−3.35652	−0.119799
$786$	160.602	5.72848
$787$	40.7485	1.45253	0.726263	−	0.687417i	$-0.241255\pi$
$787$	40.7485	1.45253	0.726263	+	0.687417i	$0.241255\pi$
$788$	−86.8541	−3.09405
$789$	−2.24464	−0.0799112
$790$	−4.93825	−0.175695
$791$	9.38872	0.333824
$792$	142.553	5.06540
$793$	−1.49136	−0.0529597
$794$	−29.0599	−1.03130
$795$	−0.435518	−0.0154462
$796$	21.3637	0.757215
$797$	−8.07591	−0.286063	−0.143032	−	0.989718i	$-0.545685\pi$
$797$	−8.07591	−0.286063	−0.143032	+	0.989718i	$0.545685\pi$
$798$	−167.642	−5.93446
$799$	24.1720	0.855144
$800$	−5.61989	−0.198693
$801$	56.6524	2.00171
$802$	56.0689	1.97986
$803$	0.380022	0.0134107
$804$	111.778	3.94211
$805$	−2.06317	−0.0727171
$806$	12.7380	0.448678
$807$	18.7434	0.659798
$808$	−6.53768	−0.229995
$809$	22.6947	0.797904	0.398952	−	0.916972i	$-0.369374\pi$
$809$	22.6947	0.797904	0.398952	+	0.916972i	$0.369374\pi$
$810$	−3.71472	−0.130522
$811$	−15.5797	−0.547078	−0.273539	−	0.961861i	$-0.588194\pi$
$811$	−15.5797	−0.547078	−0.273539	+	0.961861i	$0.588194\pi$
$812$	−97.7419	−3.43007
$813$	−19.8582	−0.696458
$814$	13.5169	0.473766
$815$	3.30069	0.115618
$816$	55.6804	1.94920
$817$	37.9115	1.32636
$818$	93.0680	3.25405
$819$	−17.9475	−0.627136
$820$	3.26494	0.114017
$821$	−3.29249	−0.114909	−0.0574543	−	0.998348i	$-0.518298\pi$
$821$	−3.29249	−0.114909	−0.0574543	+	0.998348i	$0.518298\pi$
$822$	−99.7907	−3.48060
$823$	−43.3839	−1.51227	−0.756135	−	0.654416i	$-0.772914\pi$
$823$	−43.3839	−1.51227	−0.756135	+	0.654416i	$0.772914\pi$
$824$	39.5269	1.37698
$825$	75.9758	2.64514
$826$	−8.91099	−0.310053
$827$	−11.5481	−0.401565	−0.200783	−	0.979636i	$-0.564349\pi$
$827$	−11.5481	−0.401565	−0.200783	+	0.979636i	$0.564349\pi$
$828$	−125.242	−4.35246
$829$	−37.3413	−1.29692	−0.648459	−	0.761250i	$-0.724586\pi$
$829$	−37.3413	−1.29692	−0.648459	+	0.761250i	$0.724586\pi$
$830$	−0.454641	−0.0157808
$831$	54.4661	1.88941
$832$	9.32570	0.323310
$833$	7.27337	0.252007
$834$	−55.3519	−1.91668
$835$	−0.883508	−0.0305750
$836$	−153.854	−5.32116
$837$	51.4900	1.77975
$838$	−58.3375	−2.01524
$839$	−40.6330	−1.40281	−0.701404	−	0.712764i	$-0.747443\pi$
$839$	−40.6330	−1.40281	−0.701404	+	0.712764i	$0.747443\pi$
$840$	−5.51179	−0.190175
$841$	47.3864	1.63401
$842$	15.1446	0.521917
$843$	22.5789	0.777658
$844$	−17.2015	−0.592099
$845$	0.138091	0.00475046
$846$	−65.6054	−2.25556
$847$	40.9736	1.40787
$848$	−3.42100	−0.117478
$849$	1.67924	0.0576315
$850$	67.1952	2.30478
$851$	−5.75421	−0.197252
$852$	−22.7801	−0.780433
$853$	−27.5739	−0.944111	−0.472056	−	0.881569i	$-0.656488\pi$
$853$	−27.5739	−0.944111	−0.472056	+	0.881569i	$0.656488\pi$
$854$	−10.4233	−0.356678
$855$	6.78996	0.232212
$856$	−5.68567	−0.194332
$857$	−34.3517	−1.17343	−0.586717	−	0.809792i	$-0.699580\pi$
$857$	−34.3517	−1.17343	−0.586717	+	0.809792i	$0.699580\pi$
$858$	−36.9876	−1.26274
$859$	30.7086	1.04776	0.523881	−	0.851791i	$-0.324483\pi$
$859$	30.7086	1.04776	0.523881	+	0.851791i	$0.324483\pi$
$860$	2.57244	0.0877195
$861$	53.3493	1.81814
$862$	−74.5134	−2.53794
$863$	52.9434	1.80221	0.901106	−	0.433598i	$-0.142756\pi$
$863$	52.9434	1.80221	0.901106	+	0.433598i	$0.142756\pi$
$864$	11.0594	0.376247
$865$	1.28498	0.0436907
$866$	−4.64407	−0.157812
$867$	42.3768	1.43919
$868$	58.7467	1.99399
$869$	−74.0548	−2.51214
$870$	8.88980	0.301392
$871$	−9.48393	−0.321351
$872$	−25.5147	−0.864037
$873$	−48.7360	−1.64946
$874$	99.2570	3.35742
$875$	−3.97253	−0.134296
$876$	−0.891951	−0.0301362
$877$	1.81188	0.0611830	0.0305915	−	0.999532i	$-0.490261\pi$
$877$	1.81188	0.0611830	0.0305915	+	0.999532i	$0.490261\pi$
$878$	−1.35033	−0.0455715
$879$	74.2978	2.50600
$880$	−2.28476	−0.0770191
$881$	10.9737	0.369712	0.184856	−	0.982766i	$-0.440818\pi$
$881$	10.9737	0.369712	0.184856	+	0.982766i	$0.440818\pi$
$882$	−19.7407	−0.664705
$883$	29.4410	0.990769	0.495384	−	0.868674i	$-0.335027\pi$
$883$	29.4410	0.990769	0.495384	+	0.868674i	$0.335027\pi$
$884$	−21.5862	−0.726024
$885$	0.534804	0.0179772
$886$	−37.6849	−1.26605
$887$	4.50884	0.151392	0.0756959	−	0.997131i	$-0.475882\pi$
$887$	4.50884	0.151392	0.0756959	+	0.997131i	$0.475882\pi$
$888$	−15.3725	−0.515867
$889$	14.6229	0.490435
$890$	−3.04651	−0.102119
$891$	−55.7066	−1.86624
$892$	38.3290	1.28335
$893$	34.3090	1.14811
$894$	−102.070	−3.41373
$895$	0.972178	0.0324963
$896$	58.6746	1.96018
$897$	15.7458	0.525738
$898$	28.8087	0.961358
$899$	−45.9112	−1.53122
$900$	−120.344	−4.01145
$901$	−5.77631	−0.192437
$902$	74.1990	2.47056
$903$	42.0339	1.39880
$904$	−14.8506	−0.493922
$905$	3.43798	0.114282
$906$	32.4457	1.07794
$907$	−5.30593	−0.176181	−0.0880903	−	0.996112i	$-0.528076\pi$
$907$	−5.30593	−0.176181	−0.0880903	+	0.996112i	$0.528076\pi$
$908$	−54.0468	−1.79361
$909$	8.92949	0.296173
$910$	0.965135	0.0319939
$911$	6.05486	0.200606	0.100303	−	0.994957i	$-0.468019\pi$
$911$	6.05486	0.200606	0.100303	+	0.994957i	$0.468019\pi$
$912$	79.0310	2.61698
$913$	−6.81788	−0.225639
$914$	1.07358	0.0355109
$915$	0.625568	0.0206806
$916$	−56.2862	−1.85975
$917$	−62.8439	−2.07529
$918$	−132.233	−4.36434
$919$	22.9531	0.757152	0.378576	−	0.925570i	$-0.376414\pi$
$919$	22.9531	0.757152	0.378576	+	0.925570i	$0.376414\pi$
$920$	3.26340	0.107591
$921$	76.5671	2.52297
$922$	−50.5937	−1.66622
$923$	1.93280	0.0636189
$924$	−170.584	−5.61179
$925$	−5.52915	−0.181797
$926$	−40.0705	−1.31680
$927$	−53.9878	−1.77319
$928$	−9.86110	−0.323707
$929$	−1.68204	−0.0551860	−0.0275930	−	0.999619i	$-0.508784\pi$
$929$	−1.68204	−0.0551860	−0.0275930	+	0.999619i	$0.508784\pi$
$930$	−5.34311	−0.175208
$931$	10.3236	0.338342
$932$	102.116	3.34493
$933$	22.7281	0.744085
$934$	−15.7831	−0.516439
$935$	−3.85778	−0.126163
$936$	28.3883	0.927902
$937$	35.1459	1.14817	0.574083	−	0.818797i	$-0.305359\pi$
$937$	35.1459	1.14817	0.574083	+	0.818797i	$0.305359\pi$
$938$	−66.2845	−2.16427
$939$	−11.1890	−0.365138
$940$	2.32799	0.0759308
$941$	−29.8970	−0.974615	−0.487307	−	0.873231i	$-0.662021\pi$
$941$	−29.8970	−0.974615	−0.487307	+	0.873231i	$0.662021\pi$
$942$	179.038	5.83337
$943$	−31.5869	−1.02861
$944$	4.20089	0.136727
$945$	3.90130	0.126909
$946$	58.4613	1.90074
$947$	−5.78506	−0.187989	−0.0939947	−	0.995573i	$-0.529964\pi$
$947$	−5.78506	−0.187989	−0.0939947	+	0.995573i	$0.529964\pi$
$948$	173.814	5.64522
$949$	0.0756784	0.00245663
$950$	95.3748	3.09437
$951$	89.5327	2.90330
$952$	−73.1032	−2.36929
$953$	56.5249	1.83102	0.915511	−	0.402293i	$-0.131787\pi$
$953$	56.5249	1.83102	0.915511	+	0.402293i	$0.131787\pi$
$954$	15.6775	0.507579
$955$	−2.30377	−0.0745481
$956$	−81.0463	−2.62122
$957$	133.313	4.30940
$958$	89.2279	2.88282
$959$	39.0483	1.26094
$960$	−3.91177	−0.126252
$961$	−3.40562	−0.109859
$962$	2.69178	0.0867865
$963$	7.76577	0.250248
$964$	−59.2098	−1.90702
$965$	2.73348	0.0879937
$966$	110.050	3.54079
$967$	48.3142	1.55368	0.776840	−	0.629698i	$-0.216821\pi$
$967$	48.3142	1.55368	0.776840	+	0.629698i	$0.216821\pi$
$968$	−64.8099	−2.08307
$969$	133.443	4.28680
$970$	2.62080	0.0841489
$971$	−57.6326	−1.84952	−0.924759	−	0.380552i	$-0.875734\pi$
$971$	−57.6326	−1.84952	−0.924759	+	0.380552i	$0.875734\pi$
$972$	16.6519	0.534110
$973$	21.6593	0.694366
$974$	83.7554	2.68369
$975$	15.1300	0.484547
$976$	4.91384	0.157288
$977$	1.60710	0.0514156	0.0257078	−	0.999670i	$-0.491816\pi$
$977$	1.60710	0.0514156	0.0257078	+	0.999670i	$0.491816\pi$
$978$	−176.060	−5.62976
$979$	−45.6861	−1.46013
$980$	0.700495	0.0223765
$981$	34.8493	1.11265
$982$	55.3030	1.76479
$983$	44.4642	1.41819	0.709094	−	0.705114i	$-0.249104\pi$
$983$	44.4642	1.41819	0.709094	+	0.705114i	$0.249104\pi$
$984$	−84.3851	−2.69010
$985$	−3.09111	−0.0984909
$986$	117.906	3.75489
$987$	38.0396	1.21081
$988$	−30.6388	−0.974751
$989$	−24.8873	−0.791371
$990$	10.4704	0.332772
$991$	33.1668	1.05358	0.526789	−	0.849996i	$-0.323396\pi$
$991$	33.1668	1.05358	0.526789	+	0.849996i	$0.323396\pi$
$992$	5.92690	0.188179
$993$	24.5868	0.780237
$994$	13.5086	0.428467
$995$	0.760325	0.0241039
$996$	16.0023	0.507051
$997$	−58.5658	−1.85480	−0.927398	−	0.374076i	$-0.877960\pi$
$997$	−58.5658	−1.85480	−0.927398	+	0.374076i	$0.877960\pi$
$998$	72.9496	2.30918
$999$	10.8808	0.344253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.17	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.17	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42489 q^{2} +3.03758 q^{3} +3.88008 q^{4} +0.138091 q^{5} -7.36579 q^{6} +2.88225 q^{7} -4.55899 q^{8} +6.22689 q^{9} +O(q^{10})\)	\(q-2.42489 q^{2} +3.03758 q^{3} +3.88008 q^{4} +0.138091 q^{5} -7.36579 q^{6} +2.88225 q^{7} -4.55899 q^{8} +6.22689 q^{9} -0.334855 q^{10} -5.02154 q^{11} +11.7861 q^{12} -1.00000 q^{13} -6.98914 q^{14} +0.419462 q^{15} +3.29487 q^{16} +5.56335 q^{17} -15.0995 q^{18} +7.89644 q^{19} +0.535803 q^{20} +8.75507 q^{21} +12.1767 q^{22} -5.18368 q^{23} -13.8483 q^{24} -4.98093 q^{25} +2.42489 q^{26} +9.80195 q^{27} +11.1834 q^{28} -8.73993 q^{29} -1.01715 q^{30} +5.25304 q^{31} +1.12828 q^{32} -15.2533 q^{33} -13.4905 q^{34} +0.398012 q^{35} +24.1609 q^{36} +1.11006 q^{37} -19.1480 q^{38} -3.03758 q^{39} -0.629554 q^{40} +6.09354 q^{41} -21.2301 q^{42} +4.80109 q^{43} -19.4840 q^{44} +0.859876 q^{45} +12.5698 q^{46} +4.34487 q^{47} +10.0084 q^{48} +1.30737 q^{49} +12.0782 q^{50} +16.8991 q^{51} -3.88008 q^{52} -1.03828 q^{53} -23.7686 q^{54} -0.693428 q^{55} -13.1401 q^{56} +23.9861 q^{57} +21.1934 q^{58} +1.27498 q^{59} +1.62755 q^{60} +1.49136 q^{61} -12.7380 q^{62} +17.9475 q^{63} -9.32570 q^{64} -0.138091 q^{65} +36.9876 q^{66} +9.48393 q^{67} +21.5862 q^{68} -15.7458 q^{69} -0.965135 q^{70} -1.93280 q^{71} -28.3883 q^{72} -0.0756784 q^{73} -2.69178 q^{74} -15.1300 q^{75} +30.6388 q^{76} -14.4733 q^{77} +7.36579 q^{78} +14.7474 q^{79} +0.454991 q^{80} +11.0935 q^{81} -14.7761 q^{82} +1.35773 q^{83} +33.9704 q^{84} +0.768246 q^{85} -11.6421 q^{86} -26.5482 q^{87} +22.8931 q^{88} +9.09802 q^{89} -2.08510 q^{90} -2.88225 q^{91} -20.1131 q^{92} +15.9565 q^{93} -10.5358 q^{94} +1.09043 q^{95} +3.42725 q^{96} -7.82669 q^{97} -3.17023 q^{98} -31.2686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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