LMFDB - Embedded newform 1511.2.a.b.1.83

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$0$
Dimension:	$87$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.83
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68714 q^{2} +2.06594 q^{3} +5.22072 q^{4} -2.35624 q^{5} +5.55146 q^{6} +2.71656 q^{7} +8.65451 q^{8} +1.26810 q^{9} +O(q^{10})$	\(q+2.68714 q^{2} +2.06594 q^{3} +5.22072 q^{4} -2.35624 q^{5} +5.55146 q^{6} +2.71656 q^{7} +8.65451 q^{8} +1.26810 q^{9} -6.33154 q^{10} +2.34351 q^{11} +10.7857 q^{12} -0.971773 q^{13} +7.29978 q^{14} -4.86785 q^{15} +12.8144 q^{16} -8.03816 q^{17} +3.40756 q^{18} -3.96434 q^{19} -12.3013 q^{20} +5.61225 q^{21} +6.29733 q^{22} -3.12416 q^{23} +17.8797 q^{24} +0.551865 q^{25} -2.61129 q^{26} -3.57800 q^{27} +14.1824 q^{28} +8.28977 q^{29} -13.0806 q^{30} -6.34382 q^{31} +17.1252 q^{32} +4.84154 q^{33} -21.5997 q^{34} -6.40087 q^{35} +6.62040 q^{36} +6.95558 q^{37} -10.6527 q^{38} -2.00762 q^{39} -20.3921 q^{40} +1.99198 q^{41} +15.0809 q^{42} +6.70277 q^{43} +12.2348 q^{44} -2.98795 q^{45} -8.39506 q^{46} -2.14592 q^{47} +26.4738 q^{48} +0.379716 q^{49} +1.48294 q^{50} -16.6063 q^{51} -5.07335 q^{52} -8.26913 q^{53} -9.61457 q^{54} -5.52187 q^{55} +23.5105 q^{56} -8.19008 q^{57} +22.2758 q^{58} -1.30841 q^{59} -25.4136 q^{60} +6.53278 q^{61} -17.0467 q^{62} +3.44488 q^{63} +20.3888 q^{64} +2.28973 q^{65} +13.0099 q^{66} +6.16638 q^{67} -41.9650 q^{68} -6.45433 q^{69} -17.2000 q^{70} +2.66229 q^{71} +10.9748 q^{72} +2.54185 q^{73} +18.6906 q^{74} +1.14012 q^{75} -20.6967 q^{76} +6.36629 q^{77} -5.39476 q^{78} +3.03168 q^{79} -30.1939 q^{80} -11.1962 q^{81} +5.35274 q^{82} +15.4232 q^{83} +29.3000 q^{84} +18.9398 q^{85} +18.0113 q^{86} +17.1262 q^{87} +20.2819 q^{88} -2.78084 q^{89} -8.02904 q^{90} -2.63988 q^{91} -16.3104 q^{92} -13.1059 q^{93} -5.76639 q^{94} +9.34094 q^{95} +35.3795 q^{96} +5.77281 q^{97} +1.02035 q^{98} +2.97181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) $ 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * 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 $

$2$	2.68714	1.90009	0.950047	−	0.312107i	$-0.101035\pi$
$2$	2.68714	1.90009	0.950047	+	0.312107i	$0.101035\pi$
$3$	2.06594	1.19277	0.596385	−	0.802699i	$-0.296603\pi$
$3$	2.06594	1.19277	0.596385	+	0.802699i	$0.296603\pi$
$4$	5.22072	2.61036
$5$	−2.35624	−1.05374	−0.526871	−	0.849945i	$-0.676635\pi$
$5$	−2.35624	−1.05374	−0.526871	+	0.849945i	$0.676635\pi$
$6$	5.55146	2.26638
$7$	2.71656	1.02676	0.513382	−	0.858160i	$-0.328392\pi$
$7$	2.71656	1.02676	0.513382	+	0.858160i	$0.328392\pi$
$8$	8.65451	3.05983
$9$	1.26810	0.422700
$10$	−6.33154	−2.00221
$11$	2.34351	0.706595	0.353297	−	0.935511i	$-0.385060\pi$
$11$	2.34351	0.706595	0.353297	+	0.935511i	$0.385060\pi$
$12$	10.7857	3.11356
$13$	−0.971773	−0.269521	−0.134761	−	0.990878i	$-0.543027\pi$
$13$	−0.971773	−0.269521	−0.134761	+	0.990878i	$0.543027\pi$
$14$	7.29978	1.95095
$15$	−4.86785	−1.25687
$16$	12.8144	3.20361
$17$	−8.03816	−1.94954	−0.974770	−	0.223211i	$-0.928346\pi$
$17$	−8.03816	−1.94954	−0.974770	+	0.223211i	$0.928346\pi$
$18$	3.40756	0.803170
$19$	−3.96434	−0.909482	−0.454741	−	0.890624i	$-0.650268\pi$
$19$	−3.96434	−0.909482	−0.454741	+	0.890624i	$0.650268\pi$
$20$	−12.3013	−2.75064
$21$	5.61225	1.22469
$22$	6.29733	1.34260
$23$	−3.12416	−0.651433	−0.325716	−	0.945467i	$-0.605605\pi$
$23$	−3.12416	−0.651433	−0.325716	+	0.945467i	$0.605605\pi$
$24$	17.8797	3.64968
$25$	0.551865	0.110373
$26$	−2.61129	−0.512116
$27$	−3.57800	−0.688586
$28$	14.1824	2.68022
$29$	8.28977	1.53937	0.769686	−	0.638422i	$-0.220413\pi$
$29$	8.28977	1.53937	0.769686	+	0.638422i	$0.220413\pi$
$30$	−13.0806	−2.38818
$31$	−6.34382	−1.13938	−0.569691	−	0.821859i	$-0.692937\pi$
$31$	−6.34382	−1.13938	−0.569691	+	0.821859i	$0.692937\pi$
$32$	17.1252	3.02733
$33$	4.84154	0.842805
$34$	−21.5997	−3.70431
$35$	−6.40087	−1.08195
$36$	6.62040	1.10340
$37$	6.95558	1.14349	0.571745	−	0.820431i	$-0.306267\pi$
$37$	6.95558	1.14349	0.571745	+	0.820431i	$0.306267\pi$
$38$	−10.6527	−1.72810
$39$	−2.00762	−0.321477
$40$	−20.3921	−3.22427
$41$	1.99198	0.311096	0.155548	−	0.987828i	$-0.450286\pi$
$41$	1.99198	0.311096	0.155548	+	0.987828i	$0.450286\pi$
$42$	15.0809	2.32703
$43$	6.70277	1.02216	0.511082	−	0.859532i	$-0.329245\pi$
$43$	6.70277	1.02216	0.511082	+	0.859532i	$0.329245\pi$
$44$	12.2348	1.84446
$45$	−2.98795	−0.445417
$46$	−8.39506	−1.23778
$47$	−2.14592	−0.313015	−0.156507	−	0.987677i	$-0.550024\pi$
$47$	−2.14592	−0.313015	−0.156507	+	0.987677i	$0.550024\pi$
$48$	26.4738	3.82117
$49$	0.379716	0.0542451
$50$	1.48294	0.209719
$51$	−16.6063	−2.32535
$52$	−5.07335	−0.703547
$53$	−8.26913	−1.13585	−0.567926	−	0.823079i	$-0.692254\pi$
$53$	−8.26913	−1.13585	−0.567926	+	0.823079i	$0.692254\pi$
$54$	−9.61457	−1.30838
$55$	−5.52187	−0.744569
$56$	23.5105	3.14173
$57$	−8.19008	−1.08480
$58$	22.2758	2.92495
$59$	−1.30841	−0.170340	−0.0851702	−	0.996366i	$-0.527143\pi$
$59$	−1.30841	−0.170340	−0.0851702	+	0.996366i	$0.527143\pi$
$60$	−25.4136	−3.28089
$61$	6.53278	0.836437	0.418218	−	0.908347i	$-0.362655\pi$
$61$	6.53278	0.836437	0.418218	+	0.908347i	$0.362655\pi$
$62$	−17.0467	−2.16493
$63$	3.44488	0.434014
$64$	20.3888	2.54860
$65$	2.28973	0.284006
$66$	13.0099	1.60141
$67$	6.16638	0.753343	0.376672	−	0.926347i	$-0.377068\pi$
$67$	6.16638	0.753343	0.376672	+	0.926347i	$0.377068\pi$
$68$	−41.9650	−5.08900
$69$	−6.45433	−0.777010
$70$	−17.2000	−2.05580
$71$	2.66229	0.315956	0.157978	−	0.987443i	$-0.449502\pi$
$71$	2.66229	0.315956	0.157978	+	0.987443i	$0.449502\pi$
$72$	10.9748	1.29339
$73$	2.54185	0.297501	0.148751	−	0.988875i	$-0.452475\pi$
$73$	2.54185	0.297501	0.148751	+	0.988875i	$0.452475\pi$
$74$	18.6906	2.17274
$75$	1.14012	0.131650
$76$	−20.6967	−2.37407
$77$	6.36629	0.725506
$78$	−5.39476	−0.610836
$79$	3.03168	0.341090	0.170545	−	0.985350i	$-0.445447\pi$
$79$	3.03168	0.341090	0.170545	+	0.985350i	$0.445447\pi$
$80$	−30.1939	−3.37578
$81$	−11.1962	−1.24402
$82$	5.35274	0.591111
$83$	15.4232	1.69291	0.846456	−	0.532458i	$-0.178732\pi$
$83$	15.4232	1.69291	0.846456	+	0.532458i	$0.178732\pi$
$84$	29.3000	3.19689
$85$	18.9398	2.05431
$86$	18.0113	1.94221
$87$	17.1262	1.83612
$88$	20.2819	2.16206
$89$	−2.78084	−0.294768	−0.147384	−	0.989079i	$-0.547085\pi$
$89$	−2.78084	−0.294768	−0.147384	+	0.989079i	$0.547085\pi$
$90$	−8.02904	−0.846335
$91$	−2.63988	−0.276735
$92$	−16.3104	−1.70047
$93$	−13.1059	−1.35902
$94$	−5.76639	−0.594758
$95$	9.34094	0.958360
$96$	35.3795	3.61091
$97$	5.77281	0.586140	0.293070	−	0.956091i	$-0.405323\pi$
$97$	5.77281	0.586140	0.293070	+	0.956091i	$0.405323\pi$
$98$	1.02035	0.103071
$99$	2.97181	0.298678
$100$	2.88113	0.288113
$101$	−15.9099	−1.58310	−0.791549	−	0.611105i	$-0.790725\pi$
$101$	−15.9099	−1.58310	−0.791549	+	0.611105i	$0.790725\pi$
$102$	−44.6236	−4.41839
$103$	4.37551	0.431132	0.215566	−	0.976489i	$-0.430840\pi$
$103$	4.37551	0.431132	0.215566	+	0.976489i	$0.430840\pi$
$104$	−8.41022	−0.824690
$105$	−13.2238	−1.29051
$106$	−22.2203	−2.15823
$107$	−0.646179	−0.0624684	−0.0312342	−	0.999512i	$-0.509944\pi$
$107$	−0.646179	−0.0624684	−0.0312342	+	0.999512i	$0.509944\pi$
$108$	−18.6797	−1.79746
$109$	−7.34567	−0.703587	−0.351794	−	0.936078i	$-0.614428\pi$
$109$	−7.34567	−0.703587	−0.351794	+	0.936078i	$0.614428\pi$
$110$	−14.8380	−1.41475
$111$	14.3698	1.36392
$112$	34.8112	3.28935
$113$	0.549423	0.0516854	0.0258427	−	0.999666i	$-0.491773\pi$
$113$	0.549423	0.0516854	0.0258427	+	0.999666i	$0.491773\pi$
$114$	−22.0079	−2.06123
$115$	7.36128	0.686442
$116$	43.2786	4.01831
$117$	−1.23231	−0.113927
$118$	−3.51588	−0.323663
$119$	−21.8362	−2.00172
$120$	−42.1288	−3.84582
$121$	−5.50797	−0.500724
$122$	17.5545	1.58931
$123$	4.11532	0.371065
$124$	−33.1193	−2.97420
$125$	10.4809	0.937438
$126$	9.25686	0.824667
$127$	−9.80685	−0.870217	−0.435109	−	0.900378i	$-0.643290\pi$
$127$	−9.80685	−0.870217	−0.435109	+	0.900378i	$0.643290\pi$
$128$	20.5372	1.81525
$129$	13.8475	1.21921
$130$	6.15282	0.539638
$131$	−13.5405	−1.18304	−0.591518	−	0.806292i	$-0.701471\pi$
$131$	−13.5405	−1.18304	−0.591518	+	0.806292i	$0.701471\pi$
$132$	25.2763	2.20002
$133$	−10.7694	−0.933824
$134$	16.5699	1.43142
$135$	8.43062	0.725592
$136$	−69.5664	−5.96527
$137$	−1.08511	−0.0927072	−0.0463536	−	0.998925i	$-0.514760\pi$
$137$	−1.08511	−0.0927072	−0.0463536	+	0.998925i	$0.514760\pi$
$138$	−17.3437	−1.47639
$139$	15.8512	1.34448	0.672240	−	0.740333i	$-0.265332\pi$
$139$	15.8512	1.34448	0.672240	+	0.740333i	$0.265332\pi$
$140$	−33.4171	−2.82426
$141$	−4.43334	−0.373355
$142$	7.15395	0.600346
$143$	−2.27736	−0.190442
$144$	16.2500	1.35417
$145$	−19.5327	−1.62210
$146$	6.83031	0.565280
$147$	0.784469	0.0647019
$148$	36.3131	2.98492
$149$	17.4783	1.43188	0.715941	−	0.698161i	$-0.245998\pi$
$149$	17.4783	1.43188	0.715941	+	0.698161i	$0.245998\pi$
$150$	3.06366	0.250147
$151$	14.9353	1.21542	0.607708	−	0.794161i	$-0.292089\pi$
$151$	14.9353	1.21542	0.607708	+	0.794161i	$0.292089\pi$
$152$	−34.3094	−2.78286
$153$	−10.1932	−0.824071
$154$	17.1071	1.37853
$155$	14.9475	1.20062
$156$	−10.4812	−0.839170
$157$	−12.1623	−0.970654	−0.485327	−	0.874333i	$-0.661299\pi$
$157$	−12.1623	−0.970654	−0.485327	+	0.874333i	$0.661299\pi$
$158$	8.14654	0.648104
$159$	−17.0835	−1.35481
$160$	−40.3510	−3.19003
$161$	−8.48698	−0.668868
$162$	−30.0858	−2.36376
$163$	9.23831	0.723600	0.361800	−	0.932256i	$-0.382162\pi$
$163$	9.23831	0.723600	0.361800	+	0.932256i	$0.382162\pi$
$164$	10.3996	0.812071
$165$	−11.4078	−0.888099
$166$	41.4442	3.21669
$167$	−8.31898	−0.643742	−0.321871	−	0.946784i	$-0.604312\pi$
$167$	−8.31898	−0.643742	−0.321871	+	0.946784i	$0.604312\pi$
$168$	48.5713	3.74736
$169$	−12.0557	−0.927358
$170$	50.8940	3.90339
$171$	−5.02718	−0.384438
$172$	34.9933	2.66821
$173$	−15.0593	−1.14494	−0.572468	−	0.819927i	$-0.694014\pi$
$173$	−15.0593	−1.14494	−0.572468	+	0.819927i	$0.694014\pi$
$174$	46.0204	3.48880
$175$	1.49918	0.113327
$176$	30.0308	2.26365
$177$	−2.70309	−0.203177
$178$	−7.47250	−0.560087
$179$	17.0012	1.27073	0.635363	−	0.772214i	$-0.280851\pi$
$179$	17.0012	1.27073	0.635363	+	0.772214i	$0.280851\pi$
$180$	−15.5992	−1.16270
$181$	−12.2816	−0.912882	−0.456441	−	0.889754i	$-0.650876\pi$
$181$	−12.2816	−0.912882	−0.456441	+	0.889754i	$0.650876\pi$
$182$	−7.09373	−0.525822
$183$	13.4963	0.997677
$184$	−27.0381	−1.99328
$185$	−16.3890	−1.20494
$186$	−35.2175	−2.58227
$187$	−18.8375	−1.37753
$188$	−11.2033	−0.817081
$189$	−9.71985	−0.707015
$190$	25.1004	1.82097
$191$	21.8735	1.58271	0.791354	−	0.611358i	$-0.209376\pi$
$191$	21.8735	1.58271	0.791354	+	0.611358i	$0.209376\pi$
$192$	42.1220	3.03990
$193$	−16.9365	−1.21911	−0.609557	−	0.792742i	$-0.708653\pi$
$193$	−16.9365	−1.21911	−0.609557	+	0.792742i	$0.708653\pi$
$194$	15.5123	1.11372
$195$	4.73044	0.338754
$196$	1.98239	0.141599
$197$	−20.1110	−1.43285	−0.716426	−	0.697663i	$-0.754223\pi$
$197$	−20.1110	−1.43285	−0.716426	+	0.697663i	$0.754223\pi$
$198$	7.98566	0.567516
$199$	10.5341	0.746745	0.373373	−	0.927681i	$-0.378201\pi$
$199$	10.5341	0.746745	0.373373	+	0.927681i	$0.378201\pi$
$200$	4.77612	0.337723
$201$	12.7394	0.898566
$202$	−42.7522	−3.00804
$203$	22.5197	1.58057
$204$	−86.6970	−6.07000
$205$	−4.69359	−0.327815
$206$	11.7576	0.819191
$207$	−3.96175	−0.275361
$208$	−12.4527	−0.863441
$209$	−9.29047	−0.642635
$210$	−35.5342	−2.45209
$211$	−18.5537	−1.27729	−0.638645	−	0.769501i	$-0.720505\pi$
$211$	−18.5537	−1.27729	−0.638645	+	0.769501i	$0.720505\pi$
$212$	−43.1708	−2.96498
$213$	5.50014	0.376863
$214$	−1.73637	−0.118696
$215$	−15.7933	−1.07710
$216$	−30.9658	−2.10696
$217$	−17.2334	−1.16988
$218$	−19.7388	−1.33688
$219$	5.25131	0.354850
$220$	−28.8281	−1.94359
$221$	7.81126	0.525442
$222$	38.6136	2.59158
$223$	6.36769	0.426412	0.213206	−	0.977007i	$-0.431609\pi$
$223$	6.36769	0.426412	0.213206	+	0.977007i	$0.431609\pi$
$224$	46.5216	3.10835
$225$	0.699820	0.0466547
$226$	1.47638	0.0982070
$227$	23.3767	1.55156	0.775782	−	0.631001i	$-0.217356\pi$
$227$	23.3767	1.55156	0.775782	+	0.631001i	$0.217356\pi$
$228$	−42.7581	−2.83172
$229$	26.7989	1.77092	0.885462	−	0.464712i	$-0.153842\pi$
$229$	26.7989	1.77092	0.885462	+	0.464712i	$0.153842\pi$
$230$	19.7808	1.30431
$231$	13.1524	0.865362
$232$	71.7439	4.71022
$233$	−29.4063	−1.92647	−0.963234	−	0.268662i	$-0.913418\pi$
$233$	−29.4063	−1.92647	−0.963234	+	0.268662i	$0.913418\pi$
$234$	−3.31138	−0.216471
$235$	5.05631	0.329837
$236$	−6.83083	−0.444649
$237$	6.26326	0.406842
$238$	−58.6768	−3.80345
$239$	−21.4499	−1.38748	−0.693740	−	0.720226i	$-0.744038\pi$
$239$	−21.4499	−1.38748	−0.693740	+	0.720226i	$0.744038\pi$
$240$	−62.3787	−4.02653
$241$	27.3863	1.76410	0.882052	−	0.471152i	$-0.156162\pi$
$241$	27.3863	1.76410	0.882052	+	0.471152i	$0.156162\pi$
$242$	−14.8007	−0.951423
$243$	−12.3967	−0.795250
$244$	34.1058	2.18340
$245$	−0.894701	−0.0571603
$246$	11.0584	0.705059
$247$	3.85244	0.245125
$248$	−54.9026	−3.48632
$249$	31.8633	2.01926
$250$	28.1636	1.78122
$251$	−14.1291	−0.891822	−0.445911	−	0.895077i	$-0.647120\pi$
$251$	−14.1291	−0.891822	−0.445911	+	0.895077i	$0.647120\pi$
$252$	17.9847	1.13293
$253$	−7.32150	−0.460299
$254$	−26.3524	−1.65349
$255$	39.1285	2.45032
$256$	14.4088	0.900550
$257$	1.27296	0.0794048	0.0397024	−	0.999212i	$-0.487359\pi$
$257$	1.27296	0.0794048	0.0397024	+	0.999212i	$0.487359\pi$
$258$	37.2102	2.31661
$259$	18.8953	1.17409
$260$	11.9540	0.741357
$261$	10.5123	0.650693
$262$	−36.3851	−2.24788
$263$	−30.8596	−1.90288	−0.951441	−	0.307831i	$-0.900397\pi$
$263$	−30.8596	−1.90288	−0.951441	+	0.307831i	$0.900397\pi$
$264$	41.9012	2.57884
$265$	19.4841	1.19690
$266$	−28.9388	−1.77435
$267$	−5.74504	−0.351591
$268$	32.1929	1.96650
$269$	9.03862	0.551095	0.275547	−	0.961288i	$-0.411141\pi$
$269$	9.03862	0.551095	0.275547	+	0.961288i	$0.411141\pi$
$270$	22.6542	1.37869
$271$	−11.2239	−0.681805	−0.340903	−	0.940099i	$-0.610733\pi$
$271$	−11.2239	−0.681805	−0.340903	+	0.940099i	$0.610733\pi$
$272$	−103.005	−6.24557
$273$	−5.45383	−0.330081
$274$	−2.91584	−0.176152
$275$	1.29330	0.0779889
$276$	−33.6962	−2.02827
$277$	24.2910	1.45950	0.729752	−	0.683712i	$-0.239636\pi$
$277$	24.2910	1.45950	0.729752	+	0.683712i	$0.239636\pi$
$278$	42.5943	2.55464
$279$	−8.04460	−0.481618
$280$	−55.3964	−3.31057
$281$	−0.286107	−0.0170677	−0.00853387	−	0.999964i	$-0.502716\pi$
$281$	−0.286107	−0.0170677	−0.00853387	+	0.999964i	$0.502716\pi$
$282$	−11.9130	−0.709409
$283$	12.2030	0.725395	0.362698	−	0.931907i	$-0.381856\pi$
$283$	12.2030	0.725395	0.362698	+	0.931907i	$0.381856\pi$
$284$	13.8991	0.824759
$285$	19.2978	1.14310
$286$	−6.11958	−0.361858
$287$	5.41135	0.319422
$288$	21.7164	1.27965
$289$	47.6120	2.80071
$290$	−52.4871	−3.08215
$291$	11.9263	0.699130
$292$	13.2703	0.776584
$293$	4.85335	0.283536	0.141768	−	0.989900i	$-0.454721\pi$
$293$	4.85335	0.283536	0.141768	+	0.989900i	$0.454721\pi$
$294$	2.10798	0.122940
$295$	3.08293	0.179495
$296$	60.1971	3.49889
$297$	−8.38507	−0.486551
$298$	46.9667	2.72071
$299$	3.03598	0.175575
$300$	5.95224	0.343652
$301$	18.2085	1.04952
$302$	40.1331	2.30940
$303$	−32.8690	−1.88827
$304$	−50.8008	−2.91363
$305$	−15.3928	−0.881389
$306$	−27.3905	−1.56581
$307$	26.8644	1.53323	0.766616	−	0.642106i	$-0.221939\pi$
$307$	26.8644	1.53323	0.766616	+	0.642106i	$0.221939\pi$
$308$	33.2366	1.89383
$309$	9.03954	0.514241
$310$	40.1661	2.28128
$311$	33.9033	1.92248	0.961241	−	0.275710i	$-0.0889130\pi$
$311$	33.9033	1.92248	0.961241	+	0.275710i	$0.0889130\pi$
$312$	−17.3750	−0.983665
$313$	24.7013	1.39620	0.698101	−	0.716000i	$-0.254029\pi$
$313$	24.7013	1.39620	0.698101	+	0.716000i	$0.254029\pi$
$314$	−32.6817	−1.84433
$315$	−8.11695	−0.457339
$316$	15.8275	0.890368
$317$	−18.0239	−1.01232	−0.506162	−	0.862438i	$-0.668936\pi$
$317$	−18.0239	−1.01232	−0.506162	+	0.862438i	$0.668936\pi$
$318$	−45.9058	−2.57427
$319$	19.4272	1.08771
$320$	−48.0409	−2.68557
$321$	−1.33497	−0.0745105
$322$	−22.8057	−1.27091
$323$	31.8660	1.77307
$324$	−58.4523	−3.24735
$325$	−0.536287	−0.0297479
$326$	24.8246	1.37491
$327$	−15.1757	−0.839218
$328$	17.2396	0.951900
$329$	−5.82953	−0.321393
$330$	−30.6544	−1.68747
$331$	−0.870956	−0.0478721	−0.0239360	−	0.999713i	$-0.507620\pi$
$331$	−0.870956	−0.0478721	−0.0239360	+	0.999713i	$0.507620\pi$
$332$	80.5200	4.41911
$333$	8.82038	0.483354
$334$	−22.3543	−1.22317
$335$	−14.5295	−0.793830
$336$	71.9179	3.92344
$337$	25.8269	1.40688	0.703440	−	0.710755i	$-0.251646\pi$
$337$	25.8269	1.40688	0.703440	+	0.710755i	$0.251646\pi$
$338$	−32.3952	−1.76207
$339$	1.13507	0.0616487
$340$	98.8795	5.36249
$341$	−14.8668	−0.805082
$342$	−13.5087	−0.730469
$343$	−17.9844	−0.971067
$344$	58.0092	3.12765
$345$	15.2079	0.818768
$346$	−40.4664	−2.17549
$347$	10.7060	0.574726	0.287363	−	0.957822i	$-0.407221\pi$
$347$	10.7060	0.574726	0.287363	+	0.957822i	$0.407221\pi$
$348$	89.4108	4.79292
$349$	8.52117	0.456128	0.228064	−	0.973646i	$-0.426760\pi$
$349$	8.52117	0.456128	0.228064	+	0.973646i	$0.426760\pi$
$350$	4.02849	0.215332
$351$	3.47700	0.185588
$352$	40.1330	2.13909
$353$	−6.62108	−0.352404	−0.176202	−	0.984354i	$-0.556381\pi$
$353$	−6.62108	−0.352404	−0.176202	+	0.984354i	$0.556381\pi$
$354$	−7.26359	−0.386055
$355$	−6.27300	−0.332936
$356$	−14.5180	−0.769451
$357$	−45.1122	−2.38759
$358$	45.6845	2.41450
$359$	−19.9218	−1.05143	−0.525716	−	0.850660i	$-0.676203\pi$
$359$	−19.9218	−1.05143	−0.525716	+	0.850660i	$0.676203\pi$
$360$	−25.8592	−1.36290
$361$	−3.28400	−0.172842
$362$	−33.0023	−1.73456
$363$	−11.3791	−0.597249
$364$	−13.7821	−0.722377
$365$	−5.98921	−0.313490
$366$	36.2665	1.89568
$367$	10.9479	0.571475	0.285737	−	0.958308i	$-0.407762\pi$
$367$	10.9479	0.571475	0.285737	+	0.958308i	$0.407762\pi$
$368$	−40.0344	−2.08694
$369$	2.52604	0.131500
$370$	−44.0395	−2.28951
$371$	−22.4636	−1.16625
$372$	−68.4223	−3.54753
$373$	−1.42592	−0.0738313	−0.0369157	−	0.999318i	$-0.511753\pi$
$373$	−1.42592	−0.0738313	−0.0369157	+	0.999318i	$0.511753\pi$
$374$	−50.6190	−2.61745
$375$	21.6528	1.11815
$376$	−18.5719	−0.957773
$377$	−8.05577	−0.414894
$378$	−26.1186	−1.34340
$379$	−12.9171	−0.663505	−0.331752	−	0.943366i	$-0.607640\pi$
$379$	−12.9171	−0.663505	−0.331752	+	0.943366i	$0.607640\pi$
$380$	48.7664	2.50166
$381$	−20.2604	−1.03797
$382$	58.7770	3.00730
$383$	28.5352	1.45808	0.729040	−	0.684471i	$-0.239967\pi$
$383$	28.5352	1.45808	0.729040	+	0.684471i	$0.239967\pi$
$384$	42.4287	2.16518
$385$	−15.0005	−0.764496
$386$	−45.5107	−2.31643
$387$	8.49979	0.432069
$388$	30.1382	1.53004
$389$	−23.2575	−1.17920	−0.589601	−	0.807694i	$-0.700715\pi$
$389$	−23.2575	−1.17920	−0.589601	+	0.807694i	$0.700715\pi$
$390$	12.7113	0.643664
$391$	25.1125	1.26999
$392$	3.28625	0.165981
$393$	−27.9738	−1.41109
$394$	−54.0411	−2.72255
$395$	−7.14336	−0.359421
$396$	15.5150	0.779656
$397$	16.3638	0.821273	0.410637	−	0.911799i	$-0.365306\pi$
$397$	16.3638	0.821273	0.410637	+	0.911799i	$0.365306\pi$
$398$	28.3067	1.41889
$399$	−22.2489	−1.11384
$400$	7.07184	0.353592
$401$	21.6804	1.08267	0.541333	−	0.840808i	$-0.317920\pi$
$401$	21.6804	1.08267	0.541333	+	0.840808i	$0.317920\pi$
$402$	34.2324	1.70736
$403$	6.16475	0.307088
$404$	−83.0613	−4.13245
$405$	26.3810	1.31088
$406$	60.5136	3.00324
$407$	16.3005	0.807984
$408$	−143.720	−7.11519
$409$	−12.9883	−0.642229	−0.321114	−	0.947040i	$-0.604057\pi$
$409$	−12.9883	−0.642229	−0.321114	+	0.947040i	$0.604057\pi$
$410$	−12.6123	−0.622879
$411$	−2.24177	−0.110578
$412$	22.8433	1.12541
$413$	−3.55438	−0.174899
$414$	−10.6458	−0.523212
$415$	−36.3407	−1.78389
$416$	−16.6418	−0.815930
$417$	32.7476	1.60366
$418$	−24.9648	−1.22107
$419$	10.2593	0.501201	0.250601	−	0.968091i	$-0.419372\pi$
$419$	10.2593	0.501201	0.250601	+	0.968091i	$0.419372\pi$
$420$	−69.0378	−3.36870
$421$	31.7272	1.54629	0.773144	−	0.634230i	$-0.218683\pi$
$421$	31.7272	1.54629	0.773144	+	0.634230i	$0.218683\pi$
$422$	−49.8564	−2.42697
$423$	−2.72125	−0.132312
$424$	−71.5653	−3.47552
$425$	−4.43598	−0.215177
$426$	14.7796	0.716075
$427$	17.7467	0.858823
$428$	−3.37351	−0.163065
$429$	−4.70488	−0.227154
$430$	−42.4389	−2.04659
$431$	−17.5311	−0.844443	−0.422221	−	0.906493i	$-0.638749\pi$
$431$	−17.5311	−0.844443	−0.422221	+	0.906493i	$0.638749\pi$
$432$	−45.8500	−2.20596
$433$	−13.6166	−0.654370	−0.327185	−	0.944960i	$-0.606100\pi$
$433$	−13.6166	−0.654370	−0.327185	+	0.944960i	$0.606100\pi$
$434$	−46.3085	−2.22288
$435$	−40.3533	−1.93479
$436$	−38.3496	−1.83661
$437$	12.3852	0.592467
$438$	14.1110	0.674249
$439$	16.9446	0.808724	0.404362	−	0.914599i	$-0.367494\pi$
$439$	16.9446	0.808724	0.404362	+	0.914599i	$0.367494\pi$
$440$	−47.7891	−2.27825
$441$	0.481518	0.0229294
$442$	20.9900	0.998390
$443$	1.25001	0.0593896	0.0296948	−	0.999559i	$-0.490546\pi$
$443$	1.25001	0.0593896	0.0296948	+	0.999559i	$0.490546\pi$
$444$	75.0206	3.56032
$445$	6.55232	0.310610
$446$	17.1109	0.810223
$447$	36.1092	1.70790
$448$	55.3875	2.61681
$449$	32.4688	1.53230	0.766150	−	0.642662i	$-0.222170\pi$
$449$	32.4688	1.53230	0.766150	+	0.642662i	$0.222170\pi$
$450$	1.88051	0.0886483
$451$	4.66823	0.219818
$452$	2.86838	0.134917
$453$	30.8553	1.44971
$454$	62.8164	2.94812
$455$	6.22019	0.291607
$456$	−70.8812	−3.31932
$457$	−7.41838	−0.347017	−0.173509	−	0.984832i	$-0.555510\pi$
$457$	−7.41838	−0.347017	−0.173509	+	0.984832i	$0.555510\pi$
$458$	72.0125	3.36492
$459$	28.7605	1.34243
$460$	38.4311	1.79186
$461$	−2.00601	−0.0934294	−0.0467147	−	0.998908i	$-0.514875\pi$
$461$	−2.00601	−0.0934294	−0.0467147	+	0.998908i	$0.514875\pi$
$462$	35.3422	1.64427
$463$	−36.9352	−1.71653	−0.858263	−	0.513210i	$-0.828456\pi$
$463$	−36.9352	−1.71653	−0.858263	+	0.513210i	$0.828456\pi$
$464$	106.229	4.93155
$465$	30.8807	1.43206
$466$	−79.0187	−3.66047
$467$	−25.3401	−1.17260	−0.586300	−	0.810094i	$-0.699416\pi$
$467$	−25.3401	−1.17260	−0.586300	+	0.810094i	$0.699416\pi$
$468$	−6.43352	−0.297389
$469$	16.7514	0.773506
$470$	13.5870	0.626722
$471$	−25.1265	−1.15777
$472$	−11.3236	−0.521213
$473$	15.7080	0.722255
$474$	16.8302	0.773039
$475$	−2.18778	−0.100382
$476$	−114.000	−5.22520
$477$	−10.4861	−0.480125
$478$	−57.6389	−2.63634
$479$	−8.62990	−0.394310	−0.197155	−	0.980372i	$-0.563170\pi$
$479$	−8.62990	−0.394310	−0.197155	+	0.980372i	$0.563170\pi$
$480$	−83.3627	−3.80497
$481$	−6.75924	−0.308195
$482$	73.5907	3.35196
$483$	−17.5336	−0.797806
$484$	−28.7555	−1.30707
$485$	−13.6021	−0.617641
$486$	−33.3117	−1.51105
$487$	−26.1987	−1.18718	−0.593588	−	0.804769i	$-0.702289\pi$
$487$	−26.1987	−1.18718	−0.593588	+	0.804769i	$0.702289\pi$
$488$	56.5380	2.55936
$489$	19.0858	0.863089
$490$	−2.40419	−0.108610
$491$	25.8606	1.16707	0.583536	−	0.812087i	$-0.301669\pi$
$491$	25.8606	1.16707	0.583536	+	0.812087i	$0.301669\pi$
$492$	21.4849	0.968614
$493$	−66.6345	−3.00107
$494$	10.3520	0.465760
$495$	−7.00229	−0.314729
$496$	−81.2925	−3.65014
$497$	7.23229	0.324413
$498$	85.6211	3.83678
$499$	12.3334	0.552117	0.276058	−	0.961141i	$-0.410972\pi$
$499$	12.3334	0.552117	0.276058	+	0.961141i	$0.410972\pi$
$500$	54.7177	2.44705
$501$	−17.1865	−0.767836
$502$	−37.9669	−1.69455
$503$	−12.8205	−0.571637	−0.285818	−	0.958284i	$-0.592265\pi$
$503$	−12.8205	−0.571637	−0.285818	+	0.958284i	$0.592265\pi$
$504$	29.8137	1.32801
$505$	37.4876	1.66818
$506$	−19.6739	−0.874611
$507$	−24.9062	−1.10613
$508$	−51.1988	−2.27158
$509$	−19.8587	−0.880222	−0.440111	−	0.897943i	$-0.645061\pi$
$509$	−19.8587	−0.880222	−0.440111	+	0.897943i	$0.645061\pi$
$510$	105.144	4.65585
$511$	6.90510	0.305464
$512$	−2.35602	−0.104123
$513$	14.1844	0.626256
$514$	3.42061	0.150877
$515$	−10.3098	−0.454302
$516$	72.2939	3.18256
$517$	−5.02899	−0.221175
$518$	50.7742	2.23089
$519$	−31.1115	−1.36565
$520$	19.8165	0.869010
$521$	−37.2929	−1.63383	−0.816916	−	0.576757i	$-0.804318\pi$
$521$	−37.2929	−1.63383	−0.816916	+	0.576757i	$0.804318\pi$
$522$	28.2479	1.23638
$523$	36.4528	1.59397	0.796984	−	0.604000i	$-0.206427\pi$
$523$	36.4528	1.59397	0.796984	+	0.604000i	$0.206427\pi$
$524$	−70.6909	−3.08815
$525$	3.09720	0.135173
$526$	−82.9239	−3.61565
$527$	50.9926	2.22127
$528$	62.0417	2.70002
$529$	−13.2396	−0.575635
$530$	52.3564	2.27422
$531$	−1.65920	−0.0720029
$532$	−56.2239	−2.43761
$533$	−1.93575	−0.0838469
$534$	−15.4377	−0.668056
$535$	1.52255	0.0658256
$536$	53.3670	2.30510
$537$	35.1233	1.51568
$538$	24.2880	1.04713
$539$	0.889867	0.0383293
$540$	44.0139	1.89405
$541$	−4.37558	−0.188121	−0.0940605	−	0.995566i	$-0.529985\pi$
$541$	−4.37558	−0.188121	−0.0940605	+	0.995566i	$0.529985\pi$
$542$	−30.1603	−1.29549
$543$	−25.3730	−1.08886
$544$	−137.655	−5.90190
$545$	17.3082	0.741400
$546$	−14.6552	−0.627185
$547$	2.52672	0.108035	0.0540174	−	0.998540i	$-0.482797\pi$
$547$	2.52672	0.108035	0.0540174	+	0.998540i	$0.482797\pi$
$548$	−5.66505	−0.241999
$549$	8.28422	0.353562
$550$	3.47528	0.148186
$551$	−32.8635	−1.40003
$552$	−55.8590	−2.37752
$553$	8.23574	0.350219
$554$	65.2732	2.77319
$555$	−33.8587	−1.43722
$556$	82.7546	3.50957
$557$	−5.18861	−0.219848	−0.109924	−	0.993940i	$-0.535061\pi$
$557$	−5.18861	−0.219848	−0.109924	+	0.993940i	$0.535061\pi$
$558$	−21.6170	−0.915119
$559$	−6.51357	−0.275495
$560$	−82.0236	−3.46613
$561$	−38.9171	−1.64308
$562$	−0.768810	−0.0324303
$563$	4.65678	0.196260	0.0981300	−	0.995174i	$-0.468714\pi$
$563$	4.65678	0.196260	0.0981300	+	0.995174i	$0.468714\pi$
$564$	−23.1452	−0.974590
$565$	−1.29457	−0.0544630
$566$	32.7913	1.37832
$567$	−30.4152	−1.27732
$568$	23.0409	0.966773
$569$	−38.7755	−1.62555	−0.812777	−	0.582574i	$-0.802045\pi$
$569$	−38.7755	−1.62555	−0.812777	+	0.582574i	$0.802045\pi$
$570$	51.8559	2.17200
$571$	−36.0282	−1.50773	−0.753866	−	0.657028i	$-0.771813\pi$
$571$	−36.0282	−1.50773	−0.753866	+	0.657028i	$0.771813\pi$
$572$	−11.8894	−0.497122
$573$	45.1892	1.88781
$574$	14.5410	0.606932
$575$	−1.72412	−0.0719006
$576$	25.8551	1.07729
$577$	30.0048	1.24912	0.624558	−	0.780979i	$-0.285279\pi$
$577$	30.0048	1.24912	0.624558	+	0.780979i	$0.285279\pi$
$578$	127.940	5.32161
$579$	−34.9897	−1.45412
$580$	−101.975	−4.23427
$581$	41.8980	1.73822
$582$	32.0475	1.32841
$583$	−19.3788	−0.802587
$584$	21.9985	0.910303
$585$	2.90361	0.120049
$586$	13.0416	0.538745
$587$	−5.49683	−0.226879	−0.113439	−	0.993545i	$-0.536187\pi$
$587$	−5.49683	−0.226879	−0.113439	+	0.993545i	$0.536187\pi$
$588$	4.09549	0.168895
$589$	25.1490	1.03625
$590$	8.28425	0.341057
$591$	−41.5481	−1.70906
$592$	89.1319	3.66330
$593$	35.6649	1.46458	0.732291	−	0.680991i	$-0.238451\pi$
$593$	35.6649	1.46458	0.732291	+	0.680991i	$0.238451\pi$
$594$	−22.5318	−0.924493
$595$	51.4513	2.10930
$596$	91.2494	3.73772
$597$	21.7629	0.890695
$598$	8.15809	0.333609
$599$	19.7600	0.807372	0.403686	−	0.914898i	$-0.367729\pi$
$599$	19.7600	0.807372	0.403686	+	0.914898i	$0.367729\pi$
$600$	9.86717	0.402826
$601$	4.03716	0.164679	0.0823395	−	0.996604i	$-0.473761\pi$
$601$	4.03716	0.164679	0.0823395	+	0.996604i	$0.473761\pi$
$602$	48.9288	1.99419
$603$	7.81960	0.318439
$604$	77.9728	3.17267
$605$	12.9781	0.527634
$606$	−88.3235	−3.58790
$607$	14.9545	0.606984	0.303492	−	0.952834i	$-0.401847\pi$
$607$	14.9545	0.606984	0.303492	+	0.952834i	$0.401847\pi$
$608$	−67.8900	−2.75330
$609$	46.5243	1.88526
$610$	−41.3626	−1.67472
$611$	2.08535	0.0843642
$612$	−53.2158	−2.15112
$613$	−46.5361	−1.87958	−0.939788	−	0.341758i	$-0.888978\pi$
$613$	−46.5361	−1.87958	−0.939788	+	0.341758i	$0.888978\pi$
$614$	72.1883	2.91328
$615$	−9.69667	−0.391007
$616$	55.0971	2.21993
$617$	−30.5658	−1.23053	−0.615266	−	0.788320i	$-0.710951\pi$
$617$	−30.5658	−1.23053	−0.615266	+	0.788320i	$0.710951\pi$
$618$	24.2905	0.977107
$619$	−13.4745	−0.541586	−0.270793	−	0.962638i	$-0.587286\pi$
$619$	−13.4745	−0.541586	−0.270793	+	0.962638i	$0.587286\pi$
$620$	78.0369	3.13404
$621$	11.1782	0.448567
$622$	91.1030	3.65290
$623$	−7.55432	−0.302658
$624$	−25.7266	−1.02989
$625$	−27.4548	−1.09819
$626$	66.3759	2.65291
$627$	−19.1935	−0.766516
$628$	−63.4957	−2.53375
$629$	−55.9101	−2.22928
$630$	−21.8114	−0.868986
$631$	26.5687	1.05768	0.528841	−	0.848721i	$-0.322627\pi$
$631$	26.5687	1.05768	0.528841	+	0.848721i	$0.322627\pi$
$632$	26.2377	1.04368
$633$	−38.3308	−1.52351
$634$	−48.4328	−1.92351
$635$	23.1073	0.916985
$636$	−89.1882	−3.53654
$637$	−0.368997	−0.0146202
$638$	52.2035	2.06676
$639$	3.37606	0.133555
$640$	−48.3907	−1.91281
$641$	−36.0773	−1.42497	−0.712483	−	0.701689i	$-0.752430\pi$
$641$	−36.0773	−1.42497	−0.712483	+	0.701689i	$0.752430\pi$
$642$	−3.58724	−0.141577
$643$	−25.9588	−1.02372	−0.511858	−	0.859070i	$-0.671043\pi$
$643$	−25.9588	−1.02372	−0.511858	+	0.859070i	$0.671043\pi$
$644$	−44.3081	−1.74599
$645$	−32.6281	−1.28473
$646$	85.6284	3.36900
$647$	17.3246	0.681102	0.340551	−	0.940226i	$-0.389386\pi$
$647$	17.3246	0.681102	0.340551	+	0.940226i	$0.389386\pi$
$648$	−96.8978	−3.80651
$649$	−3.06627	−0.120362
$650$	−1.44108	−0.0565237
$651$	−35.6031	−1.39540
$652$	48.2306	1.88886
$653$	−24.5831	−0.962011	−0.481005	−	0.876718i	$-0.659728\pi$
$653$	−24.5831	−0.962011	−0.481005	+	0.876718i	$0.659728\pi$
$654$	−40.7792	−1.59459
$655$	31.9046	1.24662
$656$	25.5262	0.996629
$657$	3.22332	0.125754
$658$	−15.6648	−0.610676
$659$	38.9669	1.51793	0.758967	−	0.651130i	$-0.225705\pi$
$659$	38.9669	1.51793	0.758967	+	0.651130i	$0.225705\pi$
$660$	−59.5571	−2.31826
$661$	−35.9894	−1.39983	−0.699913	−	0.714228i	$-0.746778\pi$
$661$	−35.9894	−1.39983	−0.699913	+	0.714228i	$0.746778\pi$
$662$	−2.34038	−0.0909615
$663$	16.1376	0.626732
$664$	133.480	5.18003
$665$	25.3752	0.984010
$666$	23.7016	0.918417
$667$	−25.8986	−1.00280
$668$	−43.4310	−1.68040
$669$	13.1553	0.508612
$670$	−39.0427	−1.50835
$671$	15.3096	0.591022
$672$	96.1107	3.70755
$673$	18.1262	0.698715	0.349358	−	0.936989i	$-0.386400\pi$
$673$	18.1262	0.698715	0.349358	+	0.936989i	$0.386400\pi$
$674$	69.4004	2.67320
$675$	−1.97457	−0.0760013
$676$	−62.9392	−2.42074
$677$	−25.3201	−0.973131	−0.486566	−	0.873644i	$-0.661751\pi$
$677$	−25.3201	−0.973131	−0.486566	+	0.873644i	$0.661751\pi$
$678$	3.05010	0.117138
$679$	15.6822	0.601828
$680$	163.915	6.28585
$681$	48.2948	1.85066
$682$	−39.9491	−1.52973
$683$	−2.20652	−0.0844302	−0.0422151	−	0.999109i	$-0.513441\pi$
$683$	−2.20652	−0.0844302	−0.0422151	+	0.999109i	$0.513441\pi$
$684$	−26.2455	−1.00352
$685$	2.55678	0.0976895
$686$	−48.3266	−1.84512
$687$	55.3649	2.11230
$688$	85.8923	3.27461
$689$	8.03572	0.306136
$690$	40.8658	1.55574
$691$	39.1546	1.48951	0.744755	−	0.667338i	$-0.232566\pi$
$691$	39.1546	1.48951	0.744755	+	0.667338i	$0.232566\pi$
$692$	−78.6202	−2.98869
$693$	8.07310	0.306672
$694$	28.7684	1.09203
$695$	−37.3492	−1.41674
$696$	148.219	5.61821
$697$	−16.0119	−0.606493
$698$	22.8976	0.866686
$699$	−60.7515	−2.29783
$700$	7.82677	0.295824
$701$	−0.407947	−0.0154079	−0.00770397	−	0.999970i	$-0.502452\pi$
$701$	−0.407947	−0.0154079	−0.00770397	+	0.999970i	$0.502452\pi$
$702$	9.34318	0.352636
$703$	−27.5743	−1.03998
$704$	47.7814	1.80083
$705$	10.4460	0.393420
$706$	−17.7918	−0.669601
$707$	−43.2204	−1.62547
$708$	−14.1121	−0.530364
$709$	24.3181	0.913286	0.456643	−	0.889650i	$-0.349052\pi$
$709$	24.3181	0.913286	0.456643	+	0.889650i	$0.349052\pi$
$710$	−16.8564	−0.632611
$711$	3.84447	0.144179
$712$	−24.0668	−0.901941
$713$	19.8191	0.742231
$714$	−121.223	−4.53665
$715$	5.36600	0.200677
$716$	88.7582	3.31705
$717$	−44.3142	−1.65494
$718$	−53.5326	−1.99782
$719$	−21.7864	−0.812495	−0.406247	−	0.913763i	$-0.633163\pi$
$719$	−21.7864	−0.812495	−0.406247	+	0.913763i	$0.633163\pi$
$720$	−38.2889	−1.42694
$721$	11.8864	0.442671
$722$	−8.82456	−0.328416
$723$	56.5783	2.10417
$724$	−64.1186	−2.38295
$725$	4.57484	0.169905
$726$	−30.5773	−1.13483
$727$	18.5635	0.688483	0.344242	−	0.938881i	$-0.388136\pi$
$727$	18.5635	0.688483	0.344242	+	0.938881i	$0.388136\pi$
$728$	−22.8469	−0.846762
$729$	7.97782	0.295475
$730$	−16.0938	−0.595660
$731$	−53.8780	−1.99275
$732$	70.4604	2.60429
$733$	−7.53016	−0.278133	−0.139066	−	0.990283i	$-0.544410\pi$
$733$	−7.53016	−0.278133	−0.139066	+	0.990283i	$0.544410\pi$
$734$	29.4185	1.08586
$735$	−1.84840	−0.0681791
$736$	−53.5018	−1.97210
$737$	14.4510	0.532308
$738$	6.78781	0.249863
$739$	2.09125	0.0769280	0.0384640	−	0.999260i	$-0.487754\pi$
$739$	2.09125	0.0769280	0.0384640	+	0.999260i	$0.487754\pi$
$740$	−85.5624	−3.14534
$741$	7.95890	0.292377
$742$	−60.3629	−2.21599
$743$	17.8715	0.655643	0.327822	−	0.944740i	$-0.393685\pi$
$743$	17.8715	0.655643	0.327822	+	0.944740i	$0.393685\pi$
$744$	−113.425	−4.15838
$745$	−41.1831	−1.50883
$746$	−3.83164	−0.140286
$747$	19.5581	0.715595
$748$	−98.3452	−3.59586
$749$	−1.75539	−0.0641404
$750$	58.1842	2.12459
$751$	17.9905	0.656482	0.328241	−	0.944594i	$-0.393544\pi$
$751$	17.9905	0.656482	0.328241	+	0.944594i	$0.393544\pi$
$752$	−27.4988	−1.00278
$753$	−29.1899	−1.06374
$754$	−21.6470	−0.788337
$755$	−35.1911	−1.28073
$756$	−50.7446	−1.84556
$757$	−9.83269	−0.357375	−0.178688	−	0.983906i	$-0.557185\pi$
$757$	−9.83269	−0.357375	−0.178688	+	0.983906i	$0.557185\pi$
$758$	−34.7099	−1.26072
$759$	−15.1258	−0.549031
$760$	80.8412	2.93242
$761$	16.5977	0.601667	0.300833	−	0.953677i	$-0.402735\pi$
$761$	16.5977	0.601667	0.300833	+	0.953677i	$0.402735\pi$
$762$	−54.4424	−1.97224
$763$	−19.9550	−0.722418
$764$	114.195	4.13144
$765$	24.0176	0.868359
$766$	76.6780	2.77049
$767$	1.27148	0.0459104
$768$	29.7677	1.07415
$769$	−32.2696	−1.16367	−0.581836	−	0.813306i	$-0.697665\pi$
$769$	−32.2696	−1.16367	−0.581836	+	0.813306i	$0.697665\pi$
$770$	−40.3084	−1.45262
$771$	2.62985	0.0947116
$772$	−88.4205	−3.18233
$773$	−9.08645	−0.326817	−0.163408	−	0.986559i	$-0.552249\pi$
$773$	−9.08645	−0.326817	−0.163408	+	0.986559i	$0.552249\pi$
$774$	22.8401	0.820971
$775$	−3.50093	−0.125757
$776$	49.9608	1.79349
$777$	39.0365	1.40043
$778$	−62.4962	−2.24060
$779$	−7.89690	−0.282936
$780$	24.6963	0.884269
$781$	6.23911	0.223253
$782$	67.4808	2.41311
$783$	−29.6608	−1.05999
$784$	4.86584	0.173780
$785$	28.6572	1.02282
$786$	−75.1694	−2.68120
$787$	18.6907	0.666250	0.333125	−	0.942883i	$-0.391897\pi$
$787$	18.6907	0.666250	0.333125	+	0.942883i	$0.391897\pi$
$788$	−104.994	−3.74026
$789$	−63.7539	−2.26970
$790$	−19.1952	−0.682934
$791$	1.49254	0.0530687
$792$	25.7195	0.913904
$793$	−6.34838	−0.225437
$794$	43.9717	1.56050
$795$	40.2529	1.42762
$796$	54.9958	1.94927
$797$	40.9387	1.45012	0.725062	−	0.688683i	$-0.241811\pi$
$797$	40.9387	1.45012	0.725062	+	0.688683i	$0.241811\pi$
$798$	−59.7858	−2.11640
$799$	17.2493	0.610235
$800$	9.45078	0.334135
$801$	−3.52638	−0.124599
$802$	58.2582	2.05717
$803$	5.95685	0.210213
$804$	66.5086	2.34558
$805$	19.9974	0.704815
$806$	16.5655	0.583496
$807$	18.6732	0.657329
$808$	−137.693	−4.84402
$809$	24.7014	0.868455	0.434227	−	0.900803i	$-0.357021\pi$
$809$	24.7014	0.868455	0.434227	+	0.900803i	$0.357021\pi$
$810$	70.8894	2.49080
$811$	−22.2796	−0.782342	−0.391171	−	0.920318i	$-0.627930\pi$
$811$	−22.2796	−0.782342	−0.391171	+	0.920318i	$0.627930\pi$
$812$	117.569	4.12586
$813$	−23.1880	−0.813237
$814$	43.8016	1.53525
$815$	−21.7677	−0.762488
$816$	−212.801	−7.44953
$817$	−26.5721	−0.929639
$818$	−34.9013	−1.22029
$819$	−3.34764	−0.116976
$820$	−24.5039	−0.855713
$821$	−29.1680	−1.01797	−0.508986	−	0.860775i	$-0.669979\pi$
$821$	−29.1680	−1.01797	−0.508986	+	0.860775i	$0.669979\pi$
$822$	−6.02395	−0.210109
$823$	−46.3218	−1.61468	−0.807339	−	0.590088i	$-0.799093\pi$
$823$	−46.3218	−1.61468	−0.807339	+	0.590088i	$0.799093\pi$
$824$	37.8679	1.31919
$825$	2.67188	0.0930229
$826$	−9.55110	−0.332325
$827$	−6.29514	−0.218903	−0.109452	−	0.993992i	$-0.534909\pi$
$827$	−6.29514	−0.218903	−0.109452	+	0.993992i	$0.534909\pi$
$828$	−20.6832	−0.718791
$829$	−34.6079	−1.20198	−0.600991	−	0.799256i	$-0.705227\pi$
$829$	−34.6079	−1.20198	−0.600991	+	0.799256i	$0.705227\pi$
$830$	−97.6524	−3.38957
$831$	50.1837	1.74085
$832$	−19.8133	−0.686902
$833$	−3.05221	−0.105753
$834$	87.9973	3.04710
$835$	19.6015	0.678338
$836$	−48.5029	−1.67751
$837$	22.6981	0.784563
$838$	27.5683	0.952330
$839$	1.60024	0.0552463	0.0276231	−	0.999618i	$-0.491206\pi$
$839$	1.60024	0.0552463	0.0276231	+	0.999618i	$0.491206\pi$
$840$	−114.446	−3.94875
$841$	39.7204	1.36967
$842$	85.2554	2.93809
$843$	−0.591080	−0.0203579
$844$	−96.8637	−3.33418
$845$	28.4060	0.977197
$846$	−7.31237	−0.251404
$847$	−14.9627	−0.514126
$848$	−105.964	−3.63883
$849$	25.2107	0.865230
$850$	−11.9201	−0.408856
$851$	−21.7304	−0.744907
$852$	28.7146	0.983747
$853$	−39.8319	−1.36382	−0.681908	−	0.731438i	$-0.738850\pi$
$853$	−39.8319	−1.36382	−0.681908	+	0.731438i	$0.738850\pi$
$854$	47.6879	1.63185
$855$	11.8453	0.405099
$856$	−5.59236	−0.191143
$857$	−55.9530	−1.91132	−0.955659	−	0.294477i	$-0.904855\pi$
$857$	−55.9530	−1.91132	−0.955659	+	0.294477i	$0.904855\pi$
$858$	−12.6427	−0.431614
$859$	54.1405	1.84725	0.923625	−	0.383298i	$-0.125212\pi$
$859$	54.1405	1.84725	0.923625	+	0.383298i	$0.125212\pi$
$860$	−82.4525	−2.81161
$861$	11.1795	0.380997
$862$	−47.1085	−1.60452
$863$	−4.42195	−0.150525	−0.0752625	−	0.997164i	$-0.523979\pi$
$863$	−4.42195	−0.150525	−0.0752625	+	0.997164i	$0.523979\pi$
$864$	−61.2738	−2.08458
$865$	35.4833	1.20647
$866$	−36.5896	−1.24336
$867$	98.3635	3.34060
$868$	−89.9706	−3.05380
$869$	7.10476	0.241012
$870$	−108.435	−3.67629
$871$	−5.99232	−0.203042
$872$	−63.5732	−2.15286
$873$	7.32051	0.247762
$874$	33.2809	1.12574
$875$	28.4720	0.962528
$876$	27.4156	0.926287
$877$	−3.73624	−0.126164	−0.0630820	−	0.998008i	$-0.520093\pi$
$877$	−3.73624	−0.126164	−0.0630820	+	0.998008i	$0.520093\pi$
$878$	45.5326	1.53665
$879$	10.0267	0.338193
$880$	−70.7597	−2.38531
$881$	27.6835	0.932680	0.466340	−	0.884605i	$-0.345572\pi$
$881$	27.6835	0.932680	0.466340	+	0.884605i	$0.345572\pi$
$882$	1.29390	0.0435680
$883$	16.0363	0.539663	0.269831	−	0.962908i	$-0.413032\pi$
$883$	16.0363	0.539663	0.269831	+	0.962908i	$0.413032\pi$
$884$	40.7804	1.37159
$885$	6.36914	0.214096
$886$	3.35894	0.112846
$887$	−2.96454	−0.0995396	−0.0497698	−	0.998761i	$-0.515849\pi$
$887$	−2.96454	−0.0995396	−0.0497698	+	0.998761i	$0.515849\pi$
$888$	124.364	4.17337
$889$	−26.6409	−0.893508
$890$	17.6070	0.590188
$891$	−26.2384	−0.879021
$892$	33.2439	1.11309
$893$	8.50717	0.284682
$894$	97.0303	3.24518
$895$	−40.0588	−1.33902
$896$	55.7907	1.86384
$897$	6.27214	0.209421
$898$	87.2483	2.91151
$899$	−52.5888	−1.75393
$900$	3.65356	0.121785
$901$	66.4686	2.21439
$902$	12.5442	0.417676
$903$	37.6176	1.25184
$904$	4.75499	0.158148
$905$	28.9383	0.961942
$906$	82.9126	2.75459
$907$	20.9715	0.696347	0.348173	−	0.937430i	$-0.386802\pi$
$907$	20.9715	0.696347	0.348173	+	0.937430i	$0.386802\pi$
$908$	122.043	4.05014
$909$	−20.1754	−0.669176
$910$	16.7145	0.554081
$911$	−6.32193	−0.209455	−0.104727	−	0.994501i	$-0.533397\pi$
$911$	−6.32193	−0.209455	−0.104727	+	0.994501i	$0.533397\pi$
$912$	−104.951	−3.47529
$913$	36.1443	1.19620
$914$	−19.9342	−0.659366
$915$	−31.8006	−1.05129
$916$	139.910	4.62274
$917$	−36.7835	−1.21470
$918$	77.2835	2.55074
$919$	−30.8451	−1.01749	−0.508744	−	0.860918i	$-0.669890\pi$
$919$	−30.8451	−1.01749	−0.508744	+	0.860918i	$0.669890\pi$
$920$	63.7082	2.10040
$921$	55.5002	1.82879
$922$	−5.39044	−0.177525
$923$	−2.58714	−0.0851569
$924$	68.6647	2.25890
$925$	3.83854	0.126210
$926$	−99.2501	−3.26156
$927$	5.54859	0.182240
$928$	141.964	4.66019
$929$	42.2551	1.38634	0.693172	−	0.720772i	$-0.256213\pi$
$929$	42.2551	1.38634	0.693172	+	0.720772i	$0.256213\pi$
$930$	82.9808	2.72105
$931$	−1.50532	−0.0493349
$932$	−153.522	−5.02877
$933$	70.0422	2.29308
$934$	−68.0924	−2.22805
$935$	44.3857	1.45157
$936$	−10.6650	−0.348597
$937$	8.13886	0.265885	0.132942	−	0.991124i	$-0.457557\pi$
$937$	8.13886	0.265885	0.132942	+	0.991124i	$0.457557\pi$
$938$	45.0132	1.46973
$939$	51.0314	1.66535
$940$	26.3975	0.860993
$941$	−21.7935	−0.710447	−0.355223	−	0.934781i	$-0.615595\pi$
$941$	−21.7935	−0.710447	−0.355223	+	0.934781i	$0.615595\pi$
$942$	−67.5183	−2.19987
$943$	−6.22328	−0.202658
$944$	−16.7665	−0.545704
$945$	22.9023	0.745012
$946$	42.2096	1.37235
$947$	41.2484	1.34039	0.670197	−	0.742183i	$-0.266210\pi$
$947$	41.2484	1.34039	0.670197	+	0.742183i	$0.266210\pi$
$948$	32.6987	1.06200
$949$	−2.47010	−0.0801829
$950$	−5.87887	−0.190736
$951$	−37.2363	−1.20747
$952$	−188.981	−6.12492
$953$	10.0833	0.326630	0.163315	−	0.986574i	$-0.447781\pi$
$953$	10.0833	0.326630	0.163315	+	0.986574i	$0.447781\pi$
$954$	−28.1776	−0.912283
$955$	−51.5391	−1.66777
$956$	−111.984	−3.62182
$957$	40.1353	1.29739
$958$	−23.1897	−0.749227
$959$	−2.94777	−0.0951884
$960$	−99.2496	−3.20327
$961$	9.24399	0.298193
$962$	−18.1630	−0.585599
$963$	−0.819420	−0.0264054
$964$	142.976	4.60494
$965$	39.9064	1.28463
$966$	−47.1152	−1.51591
$967$	15.4752	0.497648	0.248824	−	0.968549i	$-0.419956\pi$
$967$	15.4752	0.497648	0.248824	+	0.968549i	$0.419956\pi$
$968$	−47.6688	−1.53213
$969$	65.8332	2.11487
$970$	−36.5508	−1.17358
$971$	22.0136	0.706451	0.353225	−	0.935538i	$-0.385085\pi$
$971$	22.0136	0.706451	0.353225	+	0.935538i	$0.385085\pi$
$972$	−64.7197	−2.07589
$973$	43.0608	1.38046
$974$	−70.3996	−2.25575
$975$	−1.10794	−0.0354824
$976$	83.7139	2.67962
$977$	38.9495	1.24611	0.623053	−	0.782180i	$-0.285892\pi$
$977$	38.9495	1.24611	0.623053	+	0.782180i	$0.285892\pi$
$978$	51.2861	1.63995
$979$	−6.51692	−0.208282
$980$	−4.67098	−0.149209
$981$	−9.31505	−0.297407
$982$	69.4910	2.21755
$983$	−46.6856	−1.48904	−0.744520	−	0.667600i	$-0.767322\pi$
$983$	−46.6856	−1.48904	−0.744520	+	0.667600i	$0.767322\pi$
$984$	35.6160	1.13540
$985$	47.3864	1.50986
$986$	−179.056	−5.70231
$987$	−12.0435	−0.383348
$988$	20.1125	0.639863
$989$	−20.9406	−0.665871
$990$	−18.8161	−0.598015
$991$	−27.5882	−0.876369	−0.438185	−	0.898885i	$-0.644378\pi$
$991$	−27.5882	−0.876369	−0.438185	+	0.898885i	$0.644378\pi$
$992$	−108.639	−3.44929
$993$	−1.79934	−0.0571004
$994$	19.4342	0.616414
$995$	−24.8210	−0.786877
$996$	166.349	5.27098
$997$	−30.3556	−0.961372	−0.480686	−	0.876893i	$-0.659612\pi$
$997$	−30.3556	−0.961372	−0.480686	+	0.876893i	$0.659612\pi$
$998$	33.1414	1.04907
$999$	−24.8870	−0.787391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.b.1.83	✓	87

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.b.1.83	✓	87	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:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68714 q^{2} +2.06594 q^{3} +5.22072 q^{4} -2.35624 q^{5} +5.55146 q^{6} +2.71656 q^{7} +8.65451 q^{8} +1.26810 q^{9} +O(q^{10})\)	\(q+2.68714 q^{2} +2.06594 q^{3} +5.22072 q^{4} -2.35624 q^{5} +5.55146 q^{6} +2.71656 q^{7} +8.65451 q^{8} +1.26810 q^{9} -6.33154 q^{10} +2.34351 q^{11} +10.7857 q^{12} -0.971773 q^{13} +7.29978 q^{14} -4.86785 q^{15} +12.8144 q^{16} -8.03816 q^{17} +3.40756 q^{18} -3.96434 q^{19} -12.3013 q^{20} +5.61225 q^{21} +6.29733 q^{22} -3.12416 q^{23} +17.8797 q^{24} +0.551865 q^{25} -2.61129 q^{26} -3.57800 q^{27} +14.1824 q^{28} +8.28977 q^{29} -13.0806 q^{30} -6.34382 q^{31} +17.1252 q^{32} +4.84154 q^{33} -21.5997 q^{34} -6.40087 q^{35} +6.62040 q^{36} +6.95558 q^{37} -10.6527 q^{38} -2.00762 q^{39} -20.3921 q^{40} +1.99198 q^{41} +15.0809 q^{42} +6.70277 q^{43} +12.2348 q^{44} -2.98795 q^{45} -8.39506 q^{46} -2.14592 q^{47} +26.4738 q^{48} +0.379716 q^{49} +1.48294 q^{50} -16.6063 q^{51} -5.07335 q^{52} -8.26913 q^{53} -9.61457 q^{54} -5.52187 q^{55} +23.5105 q^{56} -8.19008 q^{57} +22.2758 q^{58} -1.30841 q^{59} -25.4136 q^{60} +6.53278 q^{61} -17.0467 q^{62} +3.44488 q^{63} +20.3888 q^{64} +2.28973 q^{65} +13.0099 q^{66} +6.16638 q^{67} -41.9650 q^{68} -6.45433 q^{69} -17.2000 q^{70} +2.66229 q^{71} +10.9748 q^{72} +2.54185 q^{73} +18.6906 q^{74} +1.14012 q^{75} -20.6967 q^{76} +6.36629 q^{77} -5.39476 q^{78} +3.03168 q^{79} -30.1939 q^{80} -11.1962 q^{81} +5.35274 q^{82} +15.4232 q^{83} +29.3000 q^{84} +18.9398 q^{85} +18.0113 q^{86} +17.1262 q^{87} +20.2819 q^{88} -2.78084 q^{89} -8.02904 q^{90} -2.63988 q^{91} -16.3104 q^{92} -13.1059 q^{93} -5.76639 q^{94} +9.34094 q^{95} +35.3795 q^{96} +5.77281 q^{97} +1.02035 q^{98} +2.97181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * q^99

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