LMFDB - Embedded newform 6034.2.a.m.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.28514 q^{3} +1.00000 q^{4} -4.30862 q^{5} +2.28514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.22188 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.28514 q^{3} +1.00000 q^{4} -4.30862 q^{5} +2.28514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.22188 q^{9} -4.30862 q^{10} -3.90640 q^{11} +2.28514 q^{12} +1.04416 q^{13} +1.00000 q^{14} -9.84581 q^{15} +1.00000 q^{16} +3.45057 q^{17} +2.22188 q^{18} +0.429457 q^{19} -4.30862 q^{20} +2.28514 q^{21} -3.90640 q^{22} -8.52666 q^{23} +2.28514 q^{24} +13.5642 q^{25} +1.04416 q^{26} -1.77811 q^{27} +1.00000 q^{28} +1.66401 q^{29} -9.84581 q^{30} +1.67646 q^{31} +1.00000 q^{32} -8.92669 q^{33} +3.45057 q^{34} -4.30862 q^{35} +2.22188 q^{36} +9.17995 q^{37} +0.429457 q^{38} +2.38604 q^{39} -4.30862 q^{40} -9.18843 q^{41} +2.28514 q^{42} -11.8899 q^{43} -3.90640 q^{44} -9.57324 q^{45} -8.52666 q^{46} -6.15729 q^{47} +2.28514 q^{48} +1.00000 q^{49} +13.5642 q^{50} +7.88504 q^{51} +1.04416 q^{52} -2.74939 q^{53} -1.77811 q^{54} +16.8312 q^{55} +1.00000 q^{56} +0.981370 q^{57} +1.66401 q^{58} +7.43093 q^{59} -9.84581 q^{60} -5.78287 q^{61} +1.67646 q^{62} +2.22188 q^{63} +1.00000 q^{64} -4.49887 q^{65} -8.92669 q^{66} -16.0929 q^{67} +3.45057 q^{68} -19.4846 q^{69} -4.30862 q^{70} -6.97934 q^{71} +2.22188 q^{72} -9.42436 q^{73} +9.17995 q^{74} +30.9961 q^{75} +0.429457 q^{76} -3.90640 q^{77} +2.38604 q^{78} +11.8854 q^{79} -4.30862 q^{80} -10.7289 q^{81} -9.18843 q^{82} -12.8683 q^{83} +2.28514 q^{84} -14.8672 q^{85} -11.8899 q^{86} +3.80250 q^{87} -3.90640 q^{88} +3.01955 q^{89} -9.57324 q^{90} +1.04416 q^{91} -8.52666 q^{92} +3.83095 q^{93} -6.15729 q^{94} -1.85037 q^{95} +2.28514 q^{96} -1.79982 q^{97} +1.00000 q^{98} -8.67956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.28514	1.31933	0.659664	−	0.751560i	$-0.270699\pi$
$3$	2.28514	1.31933	0.659664	+	0.751560i	$0.270699\pi$
$4$	1.00000	0.500000
$5$	−4.30862	−1.92687	−0.963437	−	0.267937i	$-0.913658\pi$
$5$	−4.30862	−1.92687	−0.963437	+	0.267937i	$0.913658\pi$
$6$	2.28514	0.932906
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	2.22188	0.740627
$10$	−4.30862	−1.36251
$11$	−3.90640	−1.17782	−0.588912	−	0.808197i	$-0.700444\pi$
$11$	−3.90640	−1.17782	−0.588912	+	0.808197i	$0.700444\pi$
$12$	2.28514	0.659664
$13$	1.04416	0.289597	0.144798	−	0.989461i	$-0.453747\pi$
$13$	1.04416	0.289597	0.144798	+	0.989461i	$0.453747\pi$
$14$	1.00000	0.267261
$15$	−9.84581	−2.54218
$16$	1.00000	0.250000
$17$	3.45057	0.836885	0.418443	−	0.908243i	$-0.362576\pi$
$17$	3.45057	0.836885	0.418443	+	0.908243i	$0.362576\pi$
$18$	2.22188	0.523703
$19$	0.429457	0.0985241	0.0492621	−	0.998786i	$-0.484313\pi$
$19$	0.429457	0.0985241	0.0492621	+	0.998786i	$0.484313\pi$
$20$	−4.30862	−0.963437
$21$	2.28514	0.498659
$22$	−3.90640	−0.832847
$23$	−8.52666	−1.77793	−0.888965	−	0.457975i	$-0.848575\pi$
$23$	−8.52666	−1.77793	−0.888965	+	0.457975i	$0.848575\pi$
$24$	2.28514	0.466453
$25$	13.5642	2.71284
$26$	1.04416	0.204776
$27$	−1.77811	−0.342198
$28$	1.00000	0.188982
$29$	1.66401	0.308999	0.154499	−	0.987993i	$-0.450624\pi$
$29$	1.66401	0.308999	0.154499	+	0.987993i	$0.450624\pi$
$30$	−9.84581	−1.79759
$31$	1.67646	0.301101	0.150550	−	0.988602i	$-0.451895\pi$
$31$	1.67646	0.301101	0.150550	+	0.988602i	$0.451895\pi$
$32$	1.00000	0.176777
$33$	−8.92669	−1.55394
$34$	3.45057	0.591767
$35$	−4.30862	−0.728290
$36$	2.22188	0.370314
$37$	9.17995	1.50918	0.754588	−	0.656199i	$-0.227837\pi$
$37$	9.17995	1.50918	0.754588	+	0.656199i	$0.227837\pi$
$38$	0.429457	0.0696671
$39$	2.38604	0.382073
$40$	−4.30862	−0.681253
$41$	−9.18843	−1.43499	−0.717496	−	0.696563i	$-0.754712\pi$
$41$	−9.18843	−1.43499	−0.717496	+	0.696563i	$0.754712\pi$
$42$	2.28514	0.352605
$43$	−11.8899	−1.81319	−0.906593	−	0.422006i	$-0.861326\pi$
$43$	−11.8899	−1.81319	−0.906593	+	0.422006i	$0.861326\pi$
$44$	−3.90640	−0.588912
$45$	−9.57324	−1.42709
$46$	−8.52666	−1.25719
$47$	−6.15729	−0.898133	−0.449066	−	0.893498i	$-0.648243\pi$
$47$	−6.15729	−0.898133	−0.449066	+	0.893498i	$0.648243\pi$
$48$	2.28514	0.329832
$49$	1.00000	0.142857
$50$	13.5642	1.91827
$51$	7.88504	1.10413
$52$	1.04416	0.144798
$53$	−2.74939	−0.377658	−0.188829	−	0.982010i	$-0.560469\pi$
$53$	−2.74939	−0.377658	−0.188829	+	0.982010i	$0.560469\pi$
$54$	−1.77811	−0.241970
$55$	16.8312	2.26952
$56$	1.00000	0.133631
$57$	0.981370	0.129986
$58$	1.66401	0.218495
$59$	7.43093	0.967424	0.483712	−	0.875227i	$-0.339288\pi$
$59$	7.43093	0.967424	0.483712	+	0.875227i	$0.339288\pi$
$60$	−9.84581	−1.27109
$61$	−5.78287	−0.740420	−0.370210	−	0.928948i	$-0.620714\pi$
$61$	−5.78287	−0.740420	−0.370210	+	0.928948i	$0.620714\pi$
$62$	1.67646	0.212910
$63$	2.22188	0.279931
$64$	1.00000	0.125000
$65$	−4.49887	−0.558016
$66$	−8.92669	−1.09880
$67$	−16.0929	−1.96607	−0.983033	−	0.183430i	$-0.941280\pi$
$67$	−16.0929	−1.96607	−0.983033	+	0.183430i	$0.941280\pi$
$68$	3.45057	0.418443
$69$	−19.4846	−2.34567
$70$	−4.30862	−0.514979
$71$	−6.97934	−0.828296	−0.414148	−	0.910210i	$-0.635920\pi$
$71$	−6.97934	−0.828296	−0.414148	+	0.910210i	$0.635920\pi$
$72$	2.22188	0.261851
$73$	−9.42436	−1.10304	−0.551519	−	0.834162i	$-0.685952\pi$
$73$	−9.42436	−1.10304	−0.551519	+	0.834162i	$0.685952\pi$
$74$	9.17995	1.06715
$75$	30.9961	3.57913
$76$	0.429457	0.0492621
$77$	−3.90640	−0.445176
$78$	2.38604	0.270166
$79$	11.8854	1.33722	0.668608	−	0.743615i	$-0.266890\pi$
$79$	11.8854	1.33722	0.668608	+	0.743615i	$0.266890\pi$
$80$	−4.30862	−0.481718
$81$	−10.7289	−1.19210
$82$	−9.18843	−1.01469
$83$	−12.8683	−1.41248	−0.706240	−	0.707973i	$-0.749610\pi$
$83$	−12.8683	−1.41248	−0.706240	+	0.707973i	$0.749610\pi$
$84$	2.28514	0.249330
$85$	−14.8672	−1.61257
$86$	−11.8899	−1.28212
$87$	3.80250	0.407671
$88$	−3.90640	−0.416424
$89$	3.01955	0.320072	0.160036	−	0.987111i	$-0.448839\pi$
$89$	3.01955	0.320072	0.160036	+	0.987111i	$0.448839\pi$
$90$	−9.57324	−1.00911
$91$	1.04416	0.109457
$92$	−8.52666	−0.888965
$93$	3.83095	0.397251
$94$	−6.15729	−0.635076
$95$	−1.85037	−0.189843
$96$	2.28514	0.233227
$97$	−1.79982	−0.182744	−0.0913719	−	0.995817i	$-0.529125\pi$
$97$	−1.79982	−0.182744	−0.0913719	+	0.995817i	$0.529125\pi$
$98$	1.00000	0.101015
$99$	−8.67956	−0.872329
$100$	13.5642	1.35642
$101$	−13.4889	−1.34220	−0.671099	−	0.741368i	$-0.734178\pi$
$101$	−13.4889	−1.34220	−0.671099	+	0.741368i	$0.734178\pi$
$102$	7.88504	0.780735
$103$	0.328063	0.0323250	0.0161625	−	0.999869i	$-0.494855\pi$
$103$	0.328063	0.0323250	0.0161625	+	0.999869i	$0.494855\pi$
$104$	1.04416	0.102388
$105$	−9.84581	−0.960853
$106$	−2.74939	−0.267044
$107$	18.2297	1.76233	0.881165	−	0.472809i	$-0.156760\pi$
$107$	18.2297	1.76233	0.881165	+	0.472809i	$0.156760\pi$
$108$	−1.77811	−0.171099
$109$	−12.4259	−1.19018	−0.595091	−	0.803659i	$-0.702884\pi$
$109$	−12.4259	−1.19018	−0.595091	+	0.803659i	$0.702884\pi$
$110$	16.8312	1.60479
$111$	20.9775	1.99110
$112$	1.00000	0.0944911
$113$	−10.4924	−0.987044	−0.493522	−	0.869733i	$-0.664291\pi$
$113$	−10.4924	−0.987044	−0.493522	+	0.869733i	$0.664291\pi$
$114$	0.981370	0.0919137
$115$	36.7381	3.42585
$116$	1.66401	0.154499
$117$	2.31999	0.214483
$118$	7.43093	0.684072
$119$	3.45057	0.316313
$120$	−9.84581	−0.898796
$121$	4.25997	0.387270
$122$	−5.78287	−0.523556
$123$	−20.9969	−1.89323
$124$	1.67646	0.150550
$125$	−36.8999	−3.30043
$126$	2.22188	0.197941
$127$	−1.86786	−0.165746	−0.0828729	−	0.996560i	$-0.526410\pi$
$127$	−1.86786	−0.165746	−0.0828729	+	0.996560i	$0.526410\pi$
$128$	1.00000	0.0883883
$129$	−27.1700	−2.39219
$130$	−4.49887	−0.394577
$131$	−8.46487	−0.739579	−0.369790	−	0.929115i	$-0.620570\pi$
$131$	−8.46487	−0.739579	−0.369790	+	0.929115i	$0.620570\pi$
$132$	−8.92669	−0.776968
$133$	0.429457	0.0372386
$134$	−16.0929	−1.39022
$135$	7.66121	0.659372
$136$	3.45057	0.295884
$137$	15.9858	1.36576	0.682880	−	0.730531i	$-0.260727\pi$
$137$	15.9858	1.36576	0.682880	+	0.730531i	$0.260727\pi$
$138$	−19.4846	−1.65864
$139$	1.03140	0.0874819	0.0437409	−	0.999043i	$-0.486072\pi$
$139$	1.03140	0.0874819	0.0437409	+	0.999043i	$0.486072\pi$
$140$	−4.30862	−0.364145
$141$	−14.0703	−1.18493
$142$	−6.97934	−0.585694
$143$	−4.07889	−0.341094
$144$	2.22188	0.185157
$145$	−7.16959	−0.595402
$146$	−9.42436	−0.779966
$147$	2.28514	0.188475
$148$	9.17995	0.754588
$149$	−10.1972	−0.835391	−0.417695	−	0.908587i	$-0.637162\pi$
$149$	−10.1972	−0.835391	−0.417695	+	0.908587i	$0.637162\pi$
$150$	30.9961	2.53082
$151$	4.04239	0.328965	0.164483	−	0.986380i	$-0.447405\pi$
$151$	4.04239	0.328965	0.164483	+	0.986380i	$0.447405\pi$
$152$	0.429457	0.0348335
$153$	7.66675	0.619820
$154$	−3.90640	−0.314787
$155$	−7.22322	−0.580183
$156$	2.38604	0.191036
$157$	6.57595	0.524818	0.262409	−	0.964957i	$-0.415483\pi$
$157$	6.57595	0.524818	0.262409	+	0.964957i	$0.415483\pi$
$158$	11.8854	0.945555
$159$	−6.28275	−0.498255
$160$	−4.30862	−0.340626
$161$	−8.52666	−0.671995
$162$	−10.7289	−0.842941
$163$	−11.1703	−0.874926	−0.437463	−	0.899237i	$-0.644123\pi$
$163$	−11.1703	−0.874926	−0.437463	+	0.899237i	$0.644123\pi$
$164$	−9.18843	−0.717496
$165$	38.4617	2.99424
$166$	−12.8683	−0.998774
$167$	7.00801	0.542296	0.271148	−	0.962538i	$-0.412597\pi$
$167$	7.00801	0.542296	0.271148	+	0.962538i	$0.412597\pi$
$168$	2.28514	0.176303
$169$	−11.9097	−0.916134
$170$	−14.8672	−1.14026
$171$	0.954202	0.0729696
$172$	−11.8899	−0.906593
$173$	−3.99309	−0.303589	−0.151794	−	0.988412i	$-0.548505\pi$
$173$	−3.99309	−0.303589	−0.151794	+	0.988412i	$0.548505\pi$
$174$	3.80250	0.288267
$175$	13.5642	1.02536
$176$	−3.90640	−0.294456
$177$	16.9807	1.27635
$178$	3.01955	0.226325
$179$	−21.3317	−1.59440	−0.797202	−	0.603713i	$-0.793687\pi$
$179$	−21.3317	−1.59440	−0.797202	+	0.603713i	$0.793687\pi$
$180$	−9.57324	−0.713547
$181$	19.6656	1.46173	0.730867	−	0.682520i	$-0.239116\pi$
$181$	19.6656	1.46173	0.730867	+	0.682520i	$0.239116\pi$
$182$	1.04416	0.0773979
$183$	−13.2147	−0.976857
$184$	−8.52666	−0.628593
$185$	−39.5529	−2.90799
$186$	3.83095	0.280899
$187$	−13.4793	−0.985704
$188$	−6.15729	−0.449066
$189$	−1.77811	−0.129339
$190$	−1.85037	−0.134240
$191$	4.82792	0.349336	0.174668	−	0.984627i	$-0.444115\pi$
$191$	4.82792	0.349336	0.174668	+	0.984627i	$0.444115\pi$
$192$	2.28514	0.164916
$193$	1.26389	0.0909769	0.0454884	−	0.998965i	$-0.485516\pi$
$193$	1.26389	0.0909769	0.0454884	+	0.998965i	$0.485516\pi$
$194$	−1.79982	−0.129219
$195$	−10.2806	−0.736206
$196$	1.00000	0.0714286
$197$	7.70645	0.549062	0.274531	−	0.961578i	$-0.411477\pi$
$197$	7.70645	0.549062	0.274531	+	0.961578i	$0.411477\pi$
$198$	−8.67956	−0.616830
$199$	19.7135	1.39745	0.698726	−	0.715390i	$-0.253751\pi$
$199$	19.7135	1.39745	0.698726	+	0.715390i	$0.253751\pi$
$200$	13.5642	0.959134
$201$	−36.7747	−2.59389
$202$	−13.4889	−0.949077
$203$	1.66401	0.116791
$204$	7.88504	0.552063
$205$	39.5895	2.76505
$206$	0.328063	0.0228572
$207$	−18.9452	−1.31678
$208$	1.04416	0.0723991
$209$	−1.67763	−0.116044
$210$	−9.84581	−0.679426
$211$	18.0569	1.24309	0.621543	−	0.783380i	$-0.286506\pi$
$211$	18.0569	1.24309	0.621543	+	0.783380i	$0.286506\pi$
$212$	−2.74939	−0.188829
$213$	−15.9488	−1.09279
$214$	18.2297	1.24616
$215$	51.2289	3.49378
$216$	−1.77811	−0.120985
$217$	1.67646	0.113805
$218$	−12.4259	−0.841585
$219$	−21.5360	−1.45527
$220$	16.8312	1.13476
$221$	3.60293	0.242359
$222$	20.9775	1.40792
$223$	20.9945	1.40590	0.702949	−	0.711240i	$-0.251866\pi$
$223$	20.9945	1.40590	0.702949	+	0.711240i	$0.251866\pi$
$224$	1.00000	0.0668153
$225$	30.1381	2.00920
$226$	−10.4924	−0.697946
$227$	14.8307	0.984348	0.492174	−	0.870497i	$-0.336202\pi$
$227$	14.8307	0.984348	0.492174	+	0.870497i	$0.336202\pi$
$228$	0.981370	0.0649928
$229$	−17.9530	−1.18637	−0.593185	−	0.805066i	$-0.702130\pi$
$229$	−17.9530	−1.18637	−0.593185	+	0.805066i	$0.702130\pi$
$230$	36.7381	2.42244
$231$	−8.92669	−0.587333
$232$	1.66401	0.109248
$233$	17.2881	1.13258	0.566290	−	0.824206i	$-0.308378\pi$
$233$	17.2881	1.13258	0.566290	+	0.824206i	$0.308378\pi$
$234$	2.31999	0.151662
$235$	26.5294	1.73059
$236$	7.43093	0.483712
$237$	27.1599	1.76423
$238$	3.45057	0.223667
$239$	23.0049	1.48806	0.744031	−	0.668145i	$-0.232911\pi$
$239$	23.0049	1.48806	0.744031	+	0.668145i	$0.232911\pi$
$240$	−9.84581	−0.635545
$241$	−0.356635	−0.0229729	−0.0114864	−	0.999934i	$-0.503656\pi$
$241$	−0.356635	−0.0229729	−0.0114864	+	0.999934i	$0.503656\pi$
$242$	4.25997	0.273841
$243$	−19.1827	−1.23057
$244$	−5.78287	−0.370210
$245$	−4.30862	−0.275268
$246$	−20.9969	−1.33871
$247$	0.448419	0.0285322
$248$	1.67646	0.106455
$249$	−29.4059	−1.86352
$250$	−36.8999	−2.33375
$251$	−25.3561	−1.60046	−0.800232	−	0.599691i	$-0.795290\pi$
$251$	−25.3561	−1.60046	−0.800232	+	0.599691i	$0.795290\pi$
$252$	2.22188	0.139965
$253$	33.3085	2.09409
$254$	−1.86786	−0.117200
$255$	−33.9736	−2.12751
$256$	1.00000	0.0625000
$257$	16.1827	1.00945	0.504724	−	0.863281i	$-0.331594\pi$
$257$	16.1827	1.00945	0.504724	+	0.863281i	$0.331594\pi$
$258$	−27.1700	−1.69153
$259$	9.17995	0.570415
$260$	−4.49887	−0.279008
$261$	3.69723	0.228853
$262$	−8.46487	−0.522962
$263$	−5.90848	−0.364333	−0.182166	−	0.983268i	$-0.558311\pi$
$263$	−5.90848	−0.364333	−0.182166	+	0.983268i	$0.558311\pi$
$264$	−8.92669	−0.549400
$265$	11.8461	0.727698
$266$	0.429457	0.0263317
$267$	6.90010	0.422279
$268$	−16.0929	−0.983033
$269$	24.0541	1.46660	0.733302	−	0.679903i	$-0.237978\pi$
$269$	24.0541	1.46660	0.733302	+	0.679903i	$0.237978\pi$
$270$	7.66121	0.466246
$271$	29.0266	1.76324	0.881620	−	0.471959i	$-0.156453\pi$
$271$	29.0266	1.76324	0.881620	+	0.471959i	$0.156453\pi$
$272$	3.45057	0.209221
$273$	2.38604	0.144410
$274$	15.9858	0.965738
$275$	−52.9872	−3.19525
$276$	−19.4846	−1.17284
$277$	15.9435	0.957954	0.478977	−	0.877827i	$-0.341008\pi$
$277$	15.9435	0.957954	0.478977	+	0.877827i	$0.341008\pi$
$278$	1.03140	0.0618590
$279$	3.72489	0.223004
$280$	−4.30862	−0.257489
$281$	−24.9332	−1.48739	−0.743694	−	0.668520i	$-0.766928\pi$
$281$	−24.9332	−1.48739	−0.743694	+	0.668520i	$0.766928\pi$
$282$	−14.0703	−0.837874
$283$	−1.42289	−0.0845818	−0.0422909	−	0.999105i	$-0.513466\pi$
$283$	−1.42289	−0.0845818	−0.0422909	+	0.999105i	$0.513466\pi$
$284$	−6.97934	−0.414148
$285$	−4.22835	−0.250466
$286$	−4.07889	−0.241190
$287$	−9.18843	−0.542376
$288$	2.22188	0.130926
$289$	−5.09359	−0.299623
$290$	−7.16959	−0.421013
$291$	−4.11284	−0.241099
$292$	−9.42436	−0.551519
$293$	−10.8181	−0.632003	−0.316001	−	0.948759i	$-0.602340\pi$
$293$	−10.8181	−0.632003	−0.316001	+	0.948759i	$0.602340\pi$
$294$	2.28514	0.133272
$295$	−32.0170	−1.86410
$296$	9.17995	0.533574
$297$	6.94602	0.403049
$298$	−10.1972	−0.590710
$299$	−8.90315	−0.514883
$300$	30.9961	1.78956
$301$	−11.8899	−0.685320
$302$	4.04239	0.232614
$303$	−30.8241	−1.77080
$304$	0.429457	0.0246310
$305$	24.9162	1.42670
$306$	7.66675	0.438279
$307$	10.0623	0.574288	0.287144	−	0.957887i	$-0.407294\pi$
$307$	10.0623	0.574288	0.287144	+	0.957887i	$0.407294\pi$
$308$	−3.90640	−0.222588
$309$	0.749672	0.0426473
$310$	−7.22322	−0.410251
$311$	−31.6755	−1.79615	−0.898077	−	0.439839i	$-0.855035\pi$
$311$	−31.6755	−1.79615	−0.898077	+	0.439839i	$0.855035\pi$
$312$	2.38604	0.135083
$313$	1.56321	0.0883579	0.0441790	−	0.999024i	$-0.485933\pi$
$313$	1.56321	0.0883579	0.0441790	+	0.999024i	$0.485933\pi$
$314$	6.57595	0.371102
$315$	−9.57324	−0.539391
$316$	11.8854	0.668608
$317$	−8.52542	−0.478835	−0.239418	−	0.970917i	$-0.576957\pi$
$317$	−8.52542	−0.478835	−0.239418	+	0.970917i	$0.576957\pi$
$318$	−6.28275	−0.352319
$319$	−6.50029	−0.363946
$320$	−4.30862	−0.240859
$321$	41.6574	2.32509
$322$	−8.52666	−0.475172
$323$	1.48187	0.0824534
$324$	−10.7289	−0.596049
$325$	14.1631	0.785629
$326$	−11.1703	−0.618666
$327$	−28.3949	−1.57024
$328$	−9.18843	−0.507346
$329$	−6.15729	−0.339462
$330$	38.4617	2.11725
$331$	−0.716421	−0.0393781	−0.0196890	−	0.999806i	$-0.506268\pi$
$331$	−0.716421	−0.0393781	−0.0196890	+	0.999806i	$0.506268\pi$
$332$	−12.8683	−0.706240
$333$	20.3968	1.11774
$334$	7.00801	0.383461
$335$	69.3384	3.78836
$336$	2.28514	0.124665
$337$	−13.8756	−0.755850	−0.377925	−	0.925836i	$-0.623362\pi$
$337$	−13.8756	−0.755850	−0.377925	+	0.925836i	$0.623362\pi$
$338$	−11.9097	−0.647804
$339$	−23.9767	−1.30224
$340$	−14.8672	−0.806286
$341$	−6.54892	−0.354644
$342$	0.954202	0.0515973
$343$	1.00000	0.0539949
$344$	−11.8899	−0.641058
$345$	83.9519	4.51982
$346$	−3.99309	−0.214670
$347$	10.3309	0.554590	0.277295	−	0.960785i	$-0.410562\pi$
$347$	10.3309	0.554590	0.277295	+	0.960785i	$0.410562\pi$
$348$	3.80250	0.203836
$349$	17.6657	0.945623	0.472811	−	0.881164i	$-0.343239\pi$
$349$	17.6657	0.945623	0.472811	+	0.881164i	$0.343239\pi$
$350$	13.5642	0.725037
$351$	−1.85662	−0.0990993
$352$	−3.90640	−0.208212
$353$	−18.7110	−0.995885	−0.497943	−	0.867210i	$-0.665911\pi$
$353$	−18.7110	−0.995885	−0.497943	+	0.867210i	$0.665911\pi$
$354$	16.9807	0.902516
$355$	30.0713	1.59602
$356$	3.01955	0.160036
$357$	7.88504	0.417321
$358$	−21.3317	−1.12741
$359$	36.0647	1.90342	0.951711	−	0.306995i	$-0.0993235\pi$
$359$	36.0647	1.90342	0.951711	+	0.306995i	$0.0993235\pi$
$360$	−9.57324	−0.504554
$361$	−18.8156	−0.990293
$362$	19.6656	1.03360
$363$	9.73464	0.510936
$364$	1.04416	0.0547286
$365$	40.6060	2.12541
$366$	−13.2147	−0.690742
$367$	−1.53861	−0.0803146	−0.0401573	−	0.999193i	$-0.512786\pi$
$367$	−1.53861	−0.0803146	−0.0401573	+	0.999193i	$0.512786\pi$
$368$	−8.52666	−0.444483
$369$	−20.4156	−1.06279
$370$	−39.5529	−2.05626
$371$	−2.74939	−0.142741
$372$	3.83095	0.198625
$373$	−32.4346	−1.67940	−0.839699	−	0.543051i	$-0.817269\pi$
$373$	−32.4346	−1.67940	−0.839699	+	0.543051i	$0.817269\pi$
$374$	−13.4793	−0.696998
$375$	−84.3215	−4.35434
$376$	−6.15729	−0.317538
$377$	1.73749	0.0894850
$378$	−1.77811	−0.0914562
$379$	−30.0024	−1.54112	−0.770559	−	0.637369i	$-0.780023\pi$
$379$	−30.0024	−1.54112	−0.770559	+	0.637369i	$0.780023\pi$
$380$	−1.85037	−0.0949217
$381$	−4.26833	−0.218673
$382$	4.82792	0.247018
$383$	13.4952	0.689571	0.344786	−	0.938681i	$-0.387952\pi$
$383$	13.4952	0.689571	0.344786	+	0.938681i	$0.387952\pi$
$384$	2.28514	0.116613
$385$	16.8312	0.857797
$386$	1.26389	0.0643304
$387$	−26.4179	−1.34290
$388$	−1.79982	−0.0913719
$389$	−2.78700	−0.141306	−0.0706532	−	0.997501i	$-0.522508\pi$
$389$	−2.78700	−0.141306	−0.0706532	+	0.997501i	$0.522508\pi$
$390$	−10.2806	−0.520576
$391$	−29.4218	−1.48792
$392$	1.00000	0.0505076
$393$	−19.3435	−0.975748
$394$	7.70645	0.388246
$395$	−51.2098	−2.57665
$396$	−8.67956	−0.436164
$397$	14.5134	0.728408	0.364204	−	0.931319i	$-0.381341\pi$
$397$	14.5134	0.728408	0.364204	+	0.931319i	$0.381341\pi$
$398$	19.7135	0.988147
$399$	0.981370	0.0491300
$400$	13.5642	0.678210
$401$	−19.2954	−0.963565	−0.481783	−	0.876291i	$-0.660011\pi$
$401$	−19.2954	−0.963565	−0.481783	+	0.876291i	$0.660011\pi$
$402$	−36.7747	−1.83415
$403$	1.75048	0.0871978
$404$	−13.4889	−0.671099
$405$	46.2267	2.29702
$406$	1.66401	0.0825834
$407$	−35.8606	−1.77754
$408$	7.88504	0.390368
$409$	−0.892037	−0.0441084	−0.0220542	−	0.999757i	$-0.507021\pi$
$409$	−0.892037	−0.0441084	−0.0220542	+	0.999757i	$0.507021\pi$
$410$	39.5895	1.95518
$411$	36.5299	1.80189
$412$	0.328063	0.0161625
$413$	7.43093	0.365652
$414$	−18.9452	−0.931107
$415$	55.4446	2.72167
$416$	1.04416	0.0511939
$417$	2.35689	0.115417
$418$	−1.67763	−0.0820556
$419$	33.5335	1.63822	0.819109	−	0.573639i	$-0.194469\pi$
$419$	33.5335	1.63822	0.819109	+	0.573639i	$0.194469\pi$
$420$	−9.84581	−0.480427
$421$	−40.7511	−1.98609	−0.993043	−	0.117756i	$-0.962430\pi$
$421$	−40.7511	−1.98609	−0.993043	+	0.117756i	$0.962430\pi$
$422$	18.0569	0.878995
$423$	−13.6808	−0.665182
$424$	−2.74939	−0.133522
$425$	46.8042	2.27034
$426$	−15.9488	−0.772722
$427$	−5.78287	−0.279852
$428$	18.2297	0.881165
$429$	−9.32085	−0.450015
$430$	51.2289	2.47048
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−1.77811	−0.0855494
$433$	26.4494	1.27108	0.635538	−	0.772070i	$-0.280778\pi$
$433$	26.4494	1.27108	0.635538	+	0.772070i	$0.280778\pi$
$434$	1.67646	0.0804726
$435$	−16.3835	−0.785530
$436$	−12.4259	−0.595091
$437$	−3.66183	−0.175169
$438$	−21.5360	−1.02903
$439$	6.19767	0.295798	0.147899	−	0.989002i	$-0.452749\pi$
$439$	6.19767	0.295798	0.147899	+	0.989002i	$0.452749\pi$
$440$	16.8312	0.802396
$441$	2.22188	0.105804
$442$	3.60293	0.171374
$443$	2.84810	0.135317	0.0676587	−	0.997709i	$-0.478447\pi$
$443$	2.84810	0.135317	0.0676587	+	0.997709i	$0.478447\pi$
$444$	20.9775	0.995549
$445$	−13.0101	−0.616737
$446$	20.9945	0.994121
$447$	−23.3022	−1.10215
$448$	1.00000	0.0472456
$449$	2.63403	0.124307	0.0621537	−	0.998067i	$-0.480203\pi$
$449$	2.63403	0.124307	0.0621537	+	0.998067i	$0.480203\pi$
$450$	30.1381	1.42072
$451$	35.8937	1.69017
$452$	−10.4924	−0.493522
$453$	9.23745	0.434013
$454$	14.8307	0.696039
$455$	−4.49887	−0.210910
$456$	0.981370	0.0459569
$457$	−41.6061	−1.94625	−0.973126	−	0.230274i	$-0.926038\pi$
$457$	−41.6061	−1.94625	−0.973126	+	0.230274i	$0.926038\pi$
$458$	−17.9530	−0.838890
$459$	−6.13549	−0.286380
$460$	36.7381	1.71292
$461$	21.1655	0.985777	0.492889	−	0.870092i	$-0.335941\pi$
$461$	21.1655	0.985777	0.492889	+	0.870092i	$0.335941\pi$
$462$	−8.92669	−0.415307
$463$	−11.9152	−0.553748	−0.276874	−	0.960906i	$-0.589298\pi$
$463$	−11.9152	−0.553748	−0.276874	+	0.960906i	$0.589298\pi$
$464$	1.66401	0.0772497
$465$	−16.5061	−0.765452
$466$	17.2881	0.800856
$467$	24.7014	1.14304	0.571522	−	0.820586i	$-0.306353\pi$
$467$	24.7014	1.14304	0.571522	+	0.820586i	$0.306353\pi$
$468$	2.31999	0.107242
$469$	−16.0929	−0.743103
$470$	26.5294	1.22371
$471$	15.0270	0.692407
$472$	7.43093	0.342036
$473$	46.4466	2.13561
$474$	27.1599	1.24750
$475$	5.82524	0.267280
$476$	3.45057	0.158156
$477$	−6.10882	−0.279704
$478$	23.0049	1.05222
$479$	−20.5894	−0.940753	−0.470376	−	0.882466i	$-0.655882\pi$
$479$	−20.5894	−0.940753	−0.470376	+	0.882466i	$0.655882\pi$
$480$	−9.84581	−0.449398
$481$	9.58530	0.437052
$482$	−0.356635	−0.0162443
$483$	−19.4846	−0.886582
$484$	4.25997	0.193635
$485$	7.75473	0.352124
$486$	−19.1827	−0.870146
$487$	−1.50149	−0.0680391	−0.0340196	−	0.999421i	$-0.510831\pi$
$487$	−1.50149	−0.0680391	−0.0340196	+	0.999421i	$0.510831\pi$
$488$	−5.78287	−0.261778
$489$	−25.5257	−1.15431
$490$	−4.30862	−0.194644
$491$	11.5335	0.520498	0.260249	−	0.965542i	$-0.416195\pi$
$491$	11.5335	0.520498	0.260249	+	0.965542i	$0.416195\pi$
$492$	−20.9969	−0.946613
$493$	5.74178	0.258597
$494$	0.448419	0.0201753
$495$	37.3969	1.68087
$496$	1.67646	0.0752752
$497$	−6.97934	−0.313066
$498$	−29.4059	−1.31771
$499$	−9.00283	−0.403022	−0.201511	−	0.979486i	$-0.564585\pi$
$499$	−9.00283	−0.403022	−0.201511	+	0.979486i	$0.564585\pi$
$500$	−36.8999	−1.65021
$501$	16.0143	0.715466
$502$	−25.3561	−1.13170
$503$	11.2774	0.502836	0.251418	−	0.967879i	$-0.419103\pi$
$503$	11.2774	0.502836	0.251418	+	0.967879i	$0.419103\pi$
$504$	2.22188	0.0989705
$505$	58.1186	2.58625
$506$	33.3085	1.48074
$507$	−27.2155	−1.20868
$508$	−1.86786	−0.0828729
$509$	−10.3332	−0.458013	−0.229006	−	0.973425i	$-0.573548\pi$
$509$	−10.3332	−0.458013	−0.229006	+	0.973425i	$0.573548\pi$
$510$	−33.9736	−1.50438
$511$	−9.42436	−0.416909
$512$	1.00000	0.0441942
$513$	−0.763622	−0.0337147
$514$	16.1827	0.713788
$515$	−1.41350	−0.0622862
$516$	−27.1700	−1.19609
$517$	24.0528	1.05784
$518$	9.17995	0.403344
$519$	−9.12478	−0.400534
$520$	−4.49887	−0.197288
$521$	−5.94815	−0.260593	−0.130297	−	0.991475i	$-0.541593\pi$
$521$	−5.94815	−0.260593	−0.130297	+	0.991475i	$0.541593\pi$
$522$	3.69723	0.161824
$523$	14.9666	0.654442	0.327221	−	0.944948i	$-0.393888\pi$
$523$	14.9666	0.654442	0.327221	+	0.944948i	$0.393888\pi$
$524$	−8.46487	−0.369790
$525$	30.9961	1.35278
$526$	−5.90848	−0.257622
$527$	5.78473	0.251987
$528$	−8.92669	−0.388484
$529$	49.7039	2.16104
$530$	11.8461	0.514561
$531$	16.5106	0.716501
$532$	0.429457	0.0186193
$533$	−9.59415	−0.415569
$534$	6.90010	0.298597
$535$	−78.5447	−3.39579
$536$	−16.0929	−0.695109
$537$	−48.7459	−2.10354
$538$	24.0541	1.03705
$539$	−3.90640	−0.168261
$540$	7.66121	0.329686
$541$	−2.89579	−0.124500	−0.0622499	−	0.998061i	$-0.519828\pi$
$541$	−2.89579	−0.124500	−0.0622499	+	0.998061i	$0.519828\pi$
$542$	29.0266	1.24680
$543$	44.9387	1.92851
$544$	3.45057	0.147942
$545$	53.5383	2.29333
$546$	2.38604	0.102113
$547$	−4.09402	−0.175048	−0.0875238	−	0.996162i	$-0.527895\pi$
$547$	−4.09402	−0.175048	−0.0875238	+	0.996162i	$0.527895\pi$
$548$	15.9858	0.682880
$549$	−12.8488	−0.548375
$550$	−52.9872	−2.25938
$551$	0.714620	0.0304438
$552$	−19.4846	−0.829321
$553$	11.8854	0.505420
$554$	15.9435	0.677376
$555$	−90.3841	−3.83659
$556$	1.03140	0.0437409
$557$	−24.6159	−1.04301	−0.521504	−	0.853249i	$-0.674629\pi$
$557$	−24.6159	−1.04301	−0.521504	+	0.853249i	$0.674629\pi$
$558$	3.72489	0.157687
$559$	−12.4149	−0.525093
$560$	−4.30862	−0.182072
$561$	−30.8021	−1.30047
$562$	−24.9332	−1.05174
$563$	−16.2713	−0.685752	−0.342876	−	0.939381i	$-0.611401\pi$
$563$	−16.2713	−0.685752	−0.342876	+	0.939381i	$0.611401\pi$
$564$	−14.0703	−0.592466
$565$	45.2079	1.90191
$566$	−1.42289	−0.0598084
$567$	−10.7289	−0.450571
$568$	−6.97934	−0.292847
$569$	−27.5061	−1.15312	−0.576559	−	0.817056i	$-0.695605\pi$
$569$	−27.5061	−1.15312	−0.576559	+	0.817056i	$0.695605\pi$
$570$	−4.22835	−0.177106
$571$	−10.7794	−0.451105	−0.225553	−	0.974231i	$-0.572419\pi$
$571$	−10.7794	−0.451105	−0.225553	+	0.974231i	$0.572419\pi$
$572$	−4.07889	−0.170547
$573$	11.0325	0.460889
$574$	−9.18843	−0.383518
$575$	−115.657	−4.82324
$576$	2.22188	0.0925784
$577$	31.9821	1.33143	0.665716	−	0.746205i	$-0.268126\pi$
$577$	31.9821	1.33143	0.665716	+	0.746205i	$0.268126\pi$
$578$	−5.09359	−0.211865
$579$	2.88817	0.120028
$580$	−7.16959	−0.297701
$581$	−12.8683	−0.533867
$582$	−4.11284	−0.170483
$583$	10.7402	0.444814
$584$	−9.42436	−0.389983
$585$	−9.99595	−0.413282
$586$	−10.8181	−0.446894
$587$	29.4609	1.21598	0.607992	−	0.793943i	$-0.291975\pi$
$587$	29.4609	1.21598	0.607992	+	0.793943i	$0.291975\pi$
$588$	2.28514	0.0942377
$589$	0.719966	0.0296657
$590$	−32.0170	−1.31812
$591$	17.6104	0.724393
$592$	9.17995	0.377294
$593$	10.6710	0.438207	0.219104	−	0.975702i	$-0.429687\pi$
$593$	10.6710	0.438207	0.219104	+	0.975702i	$0.429687\pi$
$594$	6.94602	0.284998
$595$	−14.8672	−0.609495
$596$	−10.1972	−0.417695
$597$	45.0481	1.84370
$598$	−8.90315	−0.364077
$599$	14.9675	0.611556	0.305778	−	0.952103i	$-0.401083\pi$
$599$	14.9675	0.611556	0.305778	+	0.952103i	$0.401083\pi$
$600$	30.9961	1.26541
$601$	−5.45981	−0.222710	−0.111355	−	0.993781i	$-0.535519\pi$
$601$	−5.45981	−0.222710	−0.111355	+	0.993781i	$0.535519\pi$
$602$	−11.8899	−0.484594
$603$	−35.7566	−1.45612
$604$	4.04239	0.164483
$605$	−18.3546	−0.746220
$606$	−30.8241	−1.25214
$607$	13.6838	0.555408	0.277704	−	0.960667i	$-0.410427\pi$
$607$	13.6838	0.555408	0.277704	+	0.960667i	$0.410427\pi$
$608$	0.429457	0.0174168
$609$	3.80250	0.154085
$610$	24.9162	1.00883
$611$	−6.42917	−0.260096
$612$	7.66675	0.309910
$613$	−5.40720	−0.218395	−0.109197	−	0.994020i	$-0.534828\pi$
$613$	−5.40720	−0.218395	−0.109197	+	0.994020i	$0.534828\pi$
$614$	10.0623	0.406083
$615$	90.4676	3.64801
$616$	−3.90640	−0.157393
$617$	−19.9587	−0.803505	−0.401753	−	0.915748i	$-0.631599\pi$
$617$	−19.9587	−0.803505	−0.401753	+	0.915748i	$0.631599\pi$
$618$	0.749672	0.0301562
$619$	37.8844	1.52270	0.761352	−	0.648339i	$-0.224536\pi$
$619$	37.8844	1.52270	0.761352	+	0.648339i	$0.224536\pi$
$620$	−7.22322	−0.290092
$621$	15.1613	0.608404
$622$	−31.6755	−1.27007
$623$	3.01955	0.120976
$624$	2.38604	0.0955182
$625$	91.1665	3.64666
$626$	1.56321	0.0624785
$627$	−3.83363	−0.153100
$628$	6.57595	0.262409
$629$	31.6760	1.26301
$630$	−9.57324	−0.381407
$631$	−19.9304	−0.793415	−0.396707	−	0.917945i	$-0.629847\pi$
$631$	−19.9304	−0.793415	−0.396707	+	0.917945i	$0.629847\pi$
$632$	11.8854	0.472777
$633$	41.2626	1.64004
$634$	−8.52542	−0.338588
$635$	8.04789	0.319371
$636$	−6.28275	−0.249127
$637$	1.04416	0.0413709
$638$	−6.50029	−0.257349
$639$	−15.5073	−0.613458
$640$	−4.30862	−0.170313
$641$	−22.9503	−0.906480	−0.453240	−	0.891388i	$-0.649732\pi$
$641$	−22.9503	−0.906480	−0.453240	+	0.891388i	$0.649732\pi$
$642$	41.6574	1.64409
$643$	10.9253	0.430851	0.215425	−	0.976520i	$-0.430886\pi$
$643$	10.9253	0.430851	0.215425	+	0.976520i	$0.430886\pi$
$644$	−8.52666	−0.335997
$645$	117.065	4.60944
$646$	1.48187	0.0583034
$647$	42.5802	1.67400	0.837000	−	0.547203i	$-0.184307\pi$
$647$	42.5802	1.67400	0.837000	+	0.547203i	$0.184307\pi$
$648$	−10.7289	−0.421470
$649$	−29.0282	−1.13946
$650$	14.1631	0.555524
$651$	3.83095	0.150147
$652$	−11.1703	−0.437463
$653$	−5.27968	−0.206610	−0.103305	−	0.994650i	$-0.532942\pi$
$653$	−5.27968	−0.206610	−0.103305	+	0.994650i	$0.532942\pi$
$654$	−28.3949	−1.11033
$655$	36.4719	1.42508
$656$	−9.18843	−0.358748
$657$	−20.9398	−0.816940
$658$	−6.15729	−0.240036
$659$	34.1095	1.32872	0.664358	−	0.747415i	$-0.268705\pi$
$659$	34.1095	1.32872	0.664358	+	0.747415i	$0.268705\pi$
$660$	38.4617	1.49712
$661$	31.5917	1.22877	0.614387	−	0.789005i	$-0.289404\pi$
$661$	31.5917	1.22877	0.614387	+	0.789005i	$0.289404\pi$
$662$	−0.716421	−0.0278445
$663$	8.23321	0.319751
$664$	−12.8683	−0.499387
$665$	−1.85037	−0.0717541
$666$	20.3968	0.790359
$667$	−14.1884	−0.549379
$668$	7.00801	0.271148
$669$	47.9756	1.85484
$670$	69.3384	2.67877
$671$	22.5902	0.872085
$672$	2.28514	0.0881513
$673$	33.3080	1.28393	0.641964	−	0.766735i	$-0.278120\pi$
$673$	33.3080	1.28393	0.641964	+	0.766735i	$0.278120\pi$
$674$	−13.8756	−0.534466
$675$	−24.1187	−0.928328
$676$	−11.9097	−0.458067
$677$	44.8300	1.72296	0.861478	−	0.507795i	$-0.169539\pi$
$677$	44.8300	1.72296	0.861478	+	0.507795i	$0.169539\pi$
$678$	−23.9767	−0.920819
$679$	−1.79982	−0.0690707
$680$	−14.8672	−0.570130
$681$	33.8903	1.29868
$682$	−6.54892	−0.250771
$683$	−5.40323	−0.206749	−0.103374	−	0.994643i	$-0.532964\pi$
$683$	−5.40323	−0.206749	−0.103374	+	0.994643i	$0.532964\pi$
$684$	0.954202	0.0364848
$685$	−68.8768	−2.63165
$686$	1.00000	0.0381802
$687$	−41.0252	−1.56521
$688$	−11.8899	−0.453297
$689$	−2.87079	−0.109368
$690$	83.9519	3.19599
$691$	0.873907	0.0332450	0.0166225	−	0.999862i	$-0.494709\pi$
$691$	0.873907	0.0332450	0.0166225	+	0.999862i	$0.494709\pi$
$692$	−3.99309	−0.151794
$693$	−8.67956	−0.329709
$694$	10.3309	0.392154
$695$	−4.44389	−0.168566
$696$	3.80250	0.144134
$697$	−31.7053	−1.20092
$698$	17.6657	0.668656
$699$	39.5058	1.49425
$700$	13.5642	0.512679
$701$	−9.61822	−0.363275	−0.181638	−	0.983366i	$-0.558140\pi$
$701$	−9.61822	−0.363275	−0.181638	+	0.983366i	$0.558140\pi$
$702$	−1.85662	−0.0700738
$703$	3.94239	0.148690
$704$	−3.90640	−0.147228
$705$	60.6235	2.28321
$706$	−18.7110	−0.704197
$707$	−13.4889	−0.507303
$708$	16.9807	0.638175
$709$	28.1228	1.05617	0.528087	−	0.849190i	$-0.322909\pi$
$709$	28.1228	1.05617	0.528087	+	0.849190i	$0.322909\pi$
$710$	30.0713	1.12856
$711$	26.4080	0.990379
$712$	3.01955	0.113162
$713$	−14.2946	−0.535336
$714$	7.88504	0.295090
$715$	17.5744	0.657245
$716$	−21.3317	−0.797202
$717$	52.5695	1.96324
$718$	36.0647	1.34592
$719$	−15.8762	−0.592081	−0.296041	−	0.955175i	$-0.595666\pi$
$719$	−15.8762	−0.592081	−0.296041	+	0.955175i	$0.595666\pi$
$720$	−9.57324	−0.356774
$721$	0.328063	0.0122177
$722$	−18.8156	−0.700243
$723$	−0.814962	−0.0303088
$724$	19.6656	0.730867
$725$	22.5710	0.838265
$726$	9.73464	0.361286
$727$	−22.3182	−0.827735	−0.413867	−	0.910337i	$-0.635822\pi$
$727$	−22.3182	−0.827735	−0.413867	+	0.910337i	$0.635822\pi$
$728$	1.04416	0.0386990
$729$	−11.6486	−0.431430
$730$	40.6060	1.50290
$731$	−41.0268	−1.51743
$732$	−13.2147	−0.488429
$733$	−37.3967	−1.38128	−0.690639	−	0.723200i	$-0.742671\pi$
$733$	−37.3967	−1.38128	−0.690639	+	0.723200i	$0.742671\pi$
$734$	−1.53861	−0.0567910
$735$	−9.84581	−0.363168
$736$	−8.52666	−0.314297
$737$	62.8655	2.31568
$738$	−20.4156	−0.751509
$739$	−18.8450	−0.693223	−0.346612	−	0.938009i	$-0.612668\pi$
$739$	−18.8450	−0.693223	−0.346612	+	0.938009i	$0.612668\pi$
$740$	−39.5529	−1.45399
$741$	1.02470	0.0376434
$742$	−2.74939	−0.100933
$743$	−32.3786	−1.18785	−0.593927	−	0.804519i	$-0.702423\pi$
$743$	−32.3786	−1.18785	−0.593927	+	0.804519i	$0.702423\pi$
$744$	3.83095	0.140449
$745$	43.9360	1.60969
$746$	−32.4346	−1.18751
$747$	−28.5918	−1.04612
$748$	−13.4793	−0.492852
$749$	18.2297	0.666098
$750$	−84.3215	−3.07899
$751$	50.0307	1.82565	0.912823	−	0.408356i	$-0.133898\pi$
$751$	50.0307	1.82565	0.912823	+	0.408356i	$0.133898\pi$
$752$	−6.15729	−0.224533
$753$	−57.9423	−2.11154
$754$	1.73749	0.0632755
$755$	−17.4171	−0.633875
$756$	−1.77811	−0.0646693
$757$	−26.7577	−0.972526	−0.486263	−	0.873813i	$-0.661640\pi$
$757$	−26.7577	−0.972526	−0.486263	+	0.873813i	$0.661640\pi$
$758$	−30.0024	−1.08973
$759$	76.1148	2.76279
$760$	−1.85037	−0.0671198
$761$	34.0178	1.23315	0.616573	−	0.787298i	$-0.288521\pi$
$761$	34.0178	1.23315	0.616573	+	0.787298i	$0.288521\pi$
$762$	−4.26833	−0.154625
$763$	−12.4259	−0.449846
$764$	4.82792	0.174668
$765$	−33.0331	−1.19431
$766$	13.4952	0.487601
$767$	7.75904	0.280163
$768$	2.28514	0.0824580
$769$	−46.5799	−1.67972	−0.839858	−	0.542806i	$-0.817362\pi$
$769$	−46.5799	−1.67972	−0.839858	+	0.542806i	$0.817362\pi$
$770$	16.8312	0.606554
$771$	36.9798	1.33179
$772$	1.26389	0.0454884
$773$	−34.9880	−1.25843	−0.629216	−	0.777230i	$-0.716624\pi$
$773$	−34.9880	−1.25843	−0.629216	+	0.777230i	$0.716624\pi$
$774$	−26.4179	−0.949570
$775$	22.7398	0.816838
$776$	−1.79982	−0.0646097
$777$	20.9775	0.752564
$778$	−2.78700	−0.0999187
$779$	−3.94603	−0.141381
$780$	−10.2806	−0.368103
$781$	27.2641	0.975587
$782$	−29.4218	−1.05212
$783$	−2.95880	−0.105739
$784$	1.00000	0.0357143
$785$	−28.3332	−1.01126
$786$	−19.3435	−0.689958
$787$	−18.0976	−0.645109	−0.322554	−	0.946551i	$-0.604542\pi$
$787$	−18.0976	−0.645109	−0.322554	+	0.946551i	$0.604542\pi$
$788$	7.70645	0.274531
$789$	−13.5017	−0.480674
$790$	−51.2098	−1.82196
$791$	−10.4924	−0.373068
$792$	−8.67956	−0.308415
$793$	−6.03821	−0.214423
$794$	14.5134	0.515062
$795$	27.0700	0.960073
$796$	19.7135	0.698726
$797$	−20.4308	−0.723696	−0.361848	−	0.932237i	$-0.617854\pi$
$797$	−20.4308	−0.723696	−0.361848	+	0.932237i	$0.617854\pi$
$798$	0.981370	0.0347401
$799$	−21.2461	−0.751634
$800$	13.5642	0.479567
$801$	6.70908	0.237054
$802$	−19.2954	−0.681344
$803$	36.8153	1.29918
$804$	−36.7747	−1.29694
$805$	36.7381	1.29485
$806$	1.75048	0.0616581
$807$	54.9670	1.93493
$808$	−13.4889	−0.474539
$809$	−46.7076	−1.64215	−0.821075	−	0.570820i	$-0.806625\pi$
$809$	−46.7076	−1.64215	−0.821075	+	0.570820i	$0.806625\pi$
$810$	46.2267	1.62424
$811$	−9.99395	−0.350935	−0.175468	−	0.984485i	$-0.556144\pi$
$811$	−9.99395	−0.350935	−0.175468	+	0.984485i	$0.556144\pi$
$812$	1.66401	0.0583953
$813$	66.3300	2.32629
$814$	−35.8606	−1.25691
$815$	48.1286	1.68587
$816$	7.88504	0.276032
$817$	−5.10618	−0.178643
$818$	−0.892037	−0.0311893
$819$	2.31999	0.0810670
$820$	39.5895	1.38252
$821$	40.8788	1.42668	0.713340	−	0.700818i	$-0.247182\pi$
$821$	40.8788	1.42668	0.713340	+	0.700818i	$0.247182\pi$
$822$	36.5299	1.27413
$823$	−3.06424	−0.106813	−0.0534064	−	0.998573i	$-0.517008\pi$
$823$	−3.06424	−0.106813	−0.0534064	+	0.998573i	$0.517008\pi$
$824$	0.328063	0.0114286
$825$	−121.083	−4.21558
$826$	7.43093	0.258555
$827$	−20.8491	−0.724993	−0.362497	−	0.931985i	$-0.618076\pi$
$827$	−20.8491	−0.724993	−0.362497	+	0.931985i	$0.618076\pi$
$828$	−18.9452	−0.658392
$829$	−0.274528	−0.00953475	−0.00476737	−	0.999989i	$-0.501518\pi$
$829$	−0.274528	−0.00953475	−0.00476737	+	0.999989i	$0.501518\pi$
$830$	55.4446	1.92451
$831$	36.4333	1.26386
$832$	1.04416	0.0361996
$833$	3.45057	0.119555
$834$	2.35689	0.0816123
$835$	−30.1948	−1.04494
$836$	−1.67763	−0.0580220
$837$	−2.98093	−0.103036
$838$	33.5335	1.15839
$839$	−10.3754	−0.358197	−0.179099	−	0.983831i	$-0.557318\pi$
$839$	−10.3754	−0.358197	−0.179099	+	0.983831i	$0.557318\pi$
$840$	−9.84581	−0.339713
$841$	−26.2311	−0.904520
$842$	−40.7511	−1.40437
$843$	−56.9759	−1.96235
$844$	18.0569	0.621543
$845$	51.3145	1.76527
$846$	−13.6808	−0.470354
$847$	4.25997	0.146374
$848$	−2.74939	−0.0944144
$849$	−3.25150	−0.111591
$850$	46.8042	1.60537
$851$	−78.2743	−2.68321
$852$	−15.9488	−0.546397
$853$	−39.8082	−1.36301	−0.681503	−	0.731816i	$-0.738673\pi$
$853$	−39.8082	−1.36301	−0.681503	+	0.731816i	$0.738673\pi$
$854$	−5.78287	−0.197886
$855$	−4.11129	−0.140603
$856$	18.2297	0.623078
$857$	−18.1099	−0.618621	−0.309310	−	0.950961i	$-0.600098\pi$
$857$	−18.1099	−0.618621	−0.309310	+	0.950961i	$0.600098\pi$
$858$	−9.32085	−0.318209
$859$	25.6335	0.874602	0.437301	−	0.899315i	$-0.355934\pi$
$859$	25.6335	0.874602	0.437301	+	0.899315i	$0.355934\pi$
$860$	51.2289	1.74689
$861$	−20.9969	−0.715572
$862$	−1.00000	−0.0340601
$863$	−46.9906	−1.59958	−0.799789	−	0.600281i	$-0.795055\pi$
$863$	−46.9906	−1.59958	−0.799789	+	0.600281i	$0.795055\pi$
$864$	−1.77811	−0.0604926
$865$	17.2047	0.584977
$866$	26.4494	0.898786
$867$	−11.6396	−0.395301
$868$	1.67646	0.0569027
$869$	−46.4293	−1.57501
$870$	−16.3835	−0.555454
$871$	−16.8035	−0.569366
$872$	−12.4259	−0.420793
$873$	−3.99898	−0.135345
$874$	−3.66183	−0.123863
$875$	−36.8999	−1.24744
$876$	−21.5360	−0.727635
$877$	10.3472	0.349401	0.174700	−	0.984622i	$-0.444104\pi$
$877$	10.3472	0.349401	0.174700	+	0.984622i	$0.444104\pi$
$878$	6.19767	0.209161
$879$	−24.7210	−0.833819
$880$	16.8312	0.567379
$881$	−5.51738	−0.185885	−0.0929427	−	0.995671i	$-0.529627\pi$
$881$	−5.51738	−0.185885	−0.0929427	+	0.995671i	$0.529627\pi$
$882$	2.22188	0.0748147
$883$	39.3213	1.32327	0.661633	−	0.749828i	$-0.269864\pi$
$883$	39.3213	1.32327	0.661633	+	0.749828i	$0.269864\pi$
$884$	3.60293	0.121180
$885$	−73.1635	−2.45937
$886$	2.84810	0.0956839
$887$	−18.8080	−0.631512	−0.315756	−	0.948840i	$-0.602258\pi$
$887$	−18.8080	−0.631512	−0.315756	+	0.948840i	$0.602258\pi$
$888$	20.9775	0.703959
$889$	−1.86786	−0.0626460
$890$	−13.0101	−0.436099
$891$	41.9113	1.40408
$892$	20.9945	0.702949
$893$	−2.64429	−0.0884877
$894$	−23.3022	−0.779341
$895$	91.9101	3.07221
$896$	1.00000	0.0334077
$897$	−20.3450	−0.679299
$898$	2.63403	0.0878986
$899$	2.78964	0.0930399
$900$	30.1381	1.00460
$901$	−9.48695	−0.316056
$902$	35.8937	1.19513
$903$	−27.1700	−0.904162
$904$	−10.4924	−0.348973
$905$	−84.7316	−2.81657
$906$	9.23745	0.306894
$907$	−56.6226	−1.88012	−0.940061	−	0.341007i	$-0.889232\pi$
$907$	−56.6226	−1.88012	−0.940061	+	0.341007i	$0.889232\pi$
$908$	14.8307	0.492174
$909$	−29.9708	−0.994069
$910$	−4.49887	−0.149136
$911$	40.2920	1.33493	0.667466	−	0.744640i	$-0.267379\pi$
$911$	40.2920	1.33493	0.667466	+	0.744640i	$0.267379\pi$
$912$	0.981370	0.0324964
$913$	50.2687	1.66365
$914$	−41.6061	−1.37621
$915$	56.9370	1.88228
$916$	−17.9530	−0.593185
$917$	−8.46487	−0.279535
$918$	−6.13549	−0.202501
$919$	44.1052	1.45490	0.727449	−	0.686162i	$-0.240706\pi$
$919$	44.1052	1.45490	0.727449	+	0.686162i	$0.240706\pi$
$920$	36.7381	1.21122
$921$	22.9939	0.757675
$922$	21.1655	0.697050
$923$	−7.28752	−0.239872
$924$	−8.92669	−0.293666
$925$	124.519	4.09415
$926$	−11.9152	−0.391559
$927$	0.728918	0.0239408
$928$	1.66401	0.0546238
$929$	28.4009	0.931804	0.465902	−	0.884836i	$-0.345730\pi$
$929$	28.4009	0.931804	0.465902	+	0.884836i	$0.345730\pi$
$930$	−16.5061	−0.541256
$931$	0.429457	0.0140749
$932$	17.2881	0.566290
$933$	−72.3831	−2.36972
$934$	24.7014	0.808255
$935$	58.0772	1.89933
$936$	2.31999	0.0758312
$937$	−8.78192	−0.286893	−0.143446	−	0.989658i	$-0.545818\pi$
$937$	−8.78192	−0.286893	−0.143446	+	0.989658i	$0.545818\pi$
$938$	−16.0929	−0.525453
$939$	3.57216	0.116573
$940$	26.5294	0.865294
$941$	25.3603	0.826722	0.413361	−	0.910567i	$-0.364355\pi$
$941$	25.3603	0.826722	0.413361	+	0.910567i	$0.364355\pi$
$942$	15.0270	0.489606
$943$	78.3466	2.55132
$944$	7.43093	0.241856
$945$	7.66121	0.249219
$946$	46.4466	1.51011
$947$	−2.56474	−0.0833430	−0.0416715	−	0.999131i	$-0.513268\pi$
$947$	−2.56474	−0.0833430	−0.0416715	+	0.999131i	$0.513268\pi$
$948$	27.1599	0.882114
$949$	−9.84050	−0.319436
$950$	5.82524	0.188996
$951$	−19.4818	−0.631741
$952$	3.45057	0.111834
$953$	−30.8696	−0.999964	−0.499982	−	0.866036i	$-0.666660\pi$
$953$	−30.8696	−0.999964	−0.499982	+	0.866036i	$0.666660\pi$
$954$	−6.10882	−0.197780
$955$	−20.8017	−0.673127
$956$	23.0049	0.744031
$957$	−14.8541	−0.480165
$958$	−20.5894	−0.665213
$959$	15.9858	0.516209
$960$	−9.84581	−0.317772
$961$	−28.1895	−0.909338
$962$	9.58530	0.309042
$963$	40.5042	1.30523
$964$	−0.356635	−0.0114864
$965$	−5.44563	−0.175301
$966$	−19.4846	−0.626908
$967$	23.7956	0.765216	0.382608	−	0.923911i	$-0.375026\pi$
$967$	23.7956	0.765216	0.382608	+	0.923911i	$0.375026\pi$
$968$	4.25997	0.136921
$969$	3.38628	0.108783
$970$	7.75473	0.248989
$971$	−16.3578	−0.524945	−0.262473	−	0.964939i	$-0.584538\pi$
$971$	−16.3578	−0.524945	−0.262473	+	0.964939i	$0.584538\pi$
$972$	−19.1827	−0.615286
$973$	1.03140	0.0330650
$974$	−1.50149	−0.0481109
$975$	32.3648	1.03650
$976$	−5.78287	−0.185105
$977$	29.5393	0.945047	0.472524	−	0.881318i	$-0.343343\pi$
$977$	29.5393	0.945047	0.472524	+	0.881318i	$0.343343\pi$
$978$	−25.5257	−0.816223
$979$	−11.7956	−0.376988
$980$	−4.30862	−0.137634
$981$	−27.6088	−0.881481
$982$	11.5335	0.368048
$983$	43.8605	1.39893	0.699466	−	0.714666i	$-0.253421\pi$
$983$	43.8605	1.39893	0.699466	+	0.714666i	$0.253421\pi$
$984$	−20.9969	−0.669356
$985$	−33.2042	−1.05797
$986$	5.74178	0.182856
$987$	−14.0703	−0.447862
$988$	0.448419	0.0142661
$989$	101.381	3.22372
$990$	37.3969	1.18855
$991$	0.347308	0.0110326	0.00551631	−	0.999985i	$-0.498244\pi$
$991$	0.347308	0.0110326	0.00551631	+	0.999985i	$0.498244\pi$
$992$	1.67646	0.0532276
$993$	−1.63713	−0.0519526
$994$	−6.97934	−0.221371
$995$	−84.9379	−2.69271
$996$	−29.4059	−0.931762
$997$	−56.1650	−1.77876	−0.889382	−	0.457164i	$-0.848865\pi$
$997$	−56.1650	−1.77876	−0.889382	+	0.457164i	$0.848865\pi$
$998$	−9.00283	−0.284980
$999$	−16.3230	−0.516436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.20	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.20	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.28514 q^{3} +1.00000 q^{4} -4.30862 q^{5} +2.28514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.22188 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.28514 q^{3} +1.00000 q^{4} -4.30862 q^{5} +2.28514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.22188 q^{9} -4.30862 q^{10} -3.90640 q^{11} +2.28514 q^{12} +1.04416 q^{13} +1.00000 q^{14} -9.84581 q^{15} +1.00000 q^{16} +3.45057 q^{17} +2.22188 q^{18} +0.429457 q^{19} -4.30862 q^{20} +2.28514 q^{21} -3.90640 q^{22} -8.52666 q^{23} +2.28514 q^{24} +13.5642 q^{25} +1.04416 q^{26} -1.77811 q^{27} +1.00000 q^{28} +1.66401 q^{29} -9.84581 q^{30} +1.67646 q^{31} +1.00000 q^{32} -8.92669 q^{33} +3.45057 q^{34} -4.30862 q^{35} +2.22188 q^{36} +9.17995 q^{37} +0.429457 q^{38} +2.38604 q^{39} -4.30862 q^{40} -9.18843 q^{41} +2.28514 q^{42} -11.8899 q^{43} -3.90640 q^{44} -9.57324 q^{45} -8.52666 q^{46} -6.15729 q^{47} +2.28514 q^{48} +1.00000 q^{49} +13.5642 q^{50} +7.88504 q^{51} +1.04416 q^{52} -2.74939 q^{53} -1.77811 q^{54} +16.8312 q^{55} +1.00000 q^{56} +0.981370 q^{57} +1.66401 q^{58} +7.43093 q^{59} -9.84581 q^{60} -5.78287 q^{61} +1.67646 q^{62} +2.22188 q^{63} +1.00000 q^{64} -4.49887 q^{65} -8.92669 q^{66} -16.0929 q^{67} +3.45057 q^{68} -19.4846 q^{69} -4.30862 q^{70} -6.97934 q^{71} +2.22188 q^{72} -9.42436 q^{73} +9.17995 q^{74} +30.9961 q^{75} +0.429457 q^{76} -3.90640 q^{77} +2.38604 q^{78} +11.8854 q^{79} -4.30862 q^{80} -10.7289 q^{81} -9.18843 q^{82} -12.8683 q^{83} +2.28514 q^{84} -14.8672 q^{85} -11.8899 q^{86} +3.80250 q^{87} -3.90640 q^{88} +3.01955 q^{89} -9.57324 q^{90} +1.04416 q^{91} -8.52666 q^{92} +3.83095 q^{93} -6.15729 q^{94} -1.85037 q^{95} +2.28514 q^{96} -1.79982 q^{97} +1.00000 q^{98} -8.67956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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