LMFDB - Embedded newform 671.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55546 q^{2} +1.15142 q^{3} +4.53040 q^{4} +4.10969 q^{5} -2.94242 q^{6} -4.64385 q^{7} -6.46634 q^{8} -1.67423 q^{9} +O(q^{10})$	\(q-2.55546 q^{2} +1.15142 q^{3} +4.53040 q^{4} +4.10969 q^{5} -2.94242 q^{6} -4.64385 q^{7} -6.46634 q^{8} -1.67423 q^{9} -10.5022 q^{10} -1.00000 q^{11} +5.21640 q^{12} +0.666644 q^{13} +11.8672 q^{14} +4.73199 q^{15} +7.46372 q^{16} +4.42323 q^{17} +4.27843 q^{18} +6.64507 q^{19} +18.6186 q^{20} -5.34703 q^{21} +2.55546 q^{22} -1.40560 q^{23} -7.44549 q^{24} +11.8896 q^{25} -1.70358 q^{26} -5.38201 q^{27} -21.0385 q^{28} +5.66326 q^{29} -12.0924 q^{30} +5.31632 q^{31} -6.14057 q^{32} -1.15142 q^{33} -11.3034 q^{34} -19.0848 q^{35} -7.58492 q^{36} +4.06782 q^{37} -16.9812 q^{38} +0.767588 q^{39} -26.5747 q^{40} +6.02550 q^{41} +13.6641 q^{42} +10.4418 q^{43} -4.53040 q^{44} -6.88057 q^{45} +3.59197 q^{46} +1.84924 q^{47} +8.59388 q^{48} +14.5654 q^{49} -30.3834 q^{50} +5.09301 q^{51} +3.02016 q^{52} -11.3583 q^{53} +13.7535 q^{54} -4.10969 q^{55} +30.0287 q^{56} +7.65127 q^{57} -14.4723 q^{58} -2.44525 q^{59} +21.4378 q^{60} +1.00000 q^{61} -13.5857 q^{62} +7.77487 q^{63} +0.764583 q^{64} +2.73970 q^{65} +2.94242 q^{66} +7.44418 q^{67} +20.0390 q^{68} -1.61844 q^{69} +48.7706 q^{70} -3.85363 q^{71} +10.8261 q^{72} -8.62822 q^{73} -10.3952 q^{74} +13.6899 q^{75} +30.1048 q^{76} +4.64385 q^{77} -1.96154 q^{78} -4.96078 q^{79} +30.6736 q^{80} -1.17428 q^{81} -15.3980 q^{82} -12.6840 q^{83} -24.2242 q^{84} +18.1781 q^{85} -26.6835 q^{86} +6.52080 q^{87} +6.46634 q^{88} -0.290276 q^{89} +17.5830 q^{90} -3.09579 q^{91} -6.36794 q^{92} +6.12132 q^{93} -4.72566 q^{94} +27.3092 q^{95} -7.07039 q^{96} +8.07144 q^{97} -37.2213 q^{98} +1.67423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	−2.55546	−1.80699	−0.903493	−	0.428603i	$-0.859006\pi$
$2$	−2.55546	−1.80699	−0.903493	+	0.428603i	$0.859006\pi$
$3$	1.15142	0.664774	0.332387	−	0.943143i	$-0.392146\pi$
$3$	1.15142	0.664774	0.332387	+	0.943143i	$0.392146\pi$
$4$	4.53040	2.26520
$5$	4.10969	1.83791	0.918956	−	0.394361i	$-0.129034\pi$
$5$	4.10969	1.83791	0.918956	+	0.394361i	$0.129034\pi$
$6$	−2.94242	−1.20124
$7$	−4.64385	−1.75521	−0.877605	−	0.479384i	$-0.840860\pi$
$7$	−4.64385	−1.75521	−0.877605	+	0.479384i	$0.840860\pi$
$8$	−6.46634	−2.28620
$9$	−1.67423	−0.558076
$10$	−10.5022	−3.32108
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.21640	1.50584
$13$	0.666644	0.184894	0.0924468	−	0.995718i	$-0.470531\pi$
$13$	0.666644	0.184894	0.0924468	+	0.995718i	$0.470531\pi$
$14$	11.8672	3.17164
$15$	4.73199	1.22179
$16$	7.46372	1.86593
$17$	4.42323	1.07279	0.536396	−	0.843967i	$-0.319785\pi$
$17$	4.42323	1.07279	0.536396	+	0.843967i	$0.319785\pi$
$18$	4.27843	1.00844
$19$	6.64507	1.52448	0.762241	−	0.647293i	$-0.224099\pi$
$19$	6.64507	1.52448	0.762241	+	0.647293i	$0.224099\pi$
$20$	18.6186	4.16324
$21$	−5.34703	−1.16682
$22$	2.55546	0.544827
$23$	−1.40560	−0.293088	−0.146544	−	0.989204i	$-0.546815\pi$
$23$	−1.40560	−0.293088	−0.146544	+	0.989204i	$0.546815\pi$
$24$	−7.44549	−1.51980
$25$	11.8896	2.37792
$26$	−1.70358	−0.334100
$27$	−5.38201	−1.03577
$28$	−21.0385	−3.97590
$29$	5.66326	1.05164	0.525821	−	0.850595i	$-0.323758\pi$
$29$	5.66326	1.05164	0.525821	+	0.850595i	$0.323758\pi$
$30$	−12.0924	−2.20777
$31$	5.31632	0.954839	0.477420	−	0.878675i	$-0.341572\pi$
$31$	5.31632	0.954839	0.477420	+	0.878675i	$0.341572\pi$
$32$	−6.14057	−1.08551
$33$	−1.15142	−0.200437
$34$	−11.3034	−1.93852
$35$	−19.0848	−3.22592
$36$	−7.58492	−1.26415
$37$	4.06782	0.668745	0.334373	−	0.942441i	$-0.391476\pi$
$37$	4.06782	0.668745	0.334373	+	0.942441i	$0.391476\pi$
$38$	−16.9812	−2.75472
$39$	0.767588	0.122912
$40$	−26.5747	−4.20183
$41$	6.02550	0.941025	0.470513	−	0.882393i	$-0.344069\pi$
$41$	6.02550	0.941025	0.470513	+	0.882393i	$0.344069\pi$
$42$	13.6641	2.10842
$43$	10.4418	1.59235	0.796177	−	0.605064i	$-0.206853\pi$
$43$	10.4418	1.59235	0.796177	+	0.605064i	$0.206853\pi$
$44$	−4.53040	−0.682983
$45$	−6.88057	−1.02569
$46$	3.59197	0.529606
$47$	1.84924	0.269739	0.134869	−	0.990863i	$-0.456938\pi$
$47$	1.84924	0.269739	0.134869	+	0.990863i	$0.456938\pi$
$48$	8.59388	1.24042
$49$	14.5654	2.08077
$50$	−30.3834	−4.29686
$51$	5.09301	0.713164
$52$	3.02016	0.418821
$53$	−11.3583	−1.56018	−0.780092	−	0.625665i	$-0.784828\pi$
$53$	−11.3583	−1.56018	−0.780092	+	0.625665i	$0.784828\pi$
$54$	13.7535	1.87162
$55$	−4.10969	−0.554151
$56$	30.0287	4.01276
$57$	7.65127	1.01344
$58$	−14.4723	−1.90030
$59$	−2.44525	−0.318345	−0.159172	−	0.987251i	$-0.550883\pi$
$59$	−2.44525	−0.318345	−0.159172	+	0.987251i	$0.550883\pi$
$60$	21.4378	2.76761
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−13.5857	−1.72538
$63$	7.77487	0.979541
$64$	0.764583	0.0955729
$65$	2.73970	0.339818
$66$	2.94242	0.362187
$67$	7.44418	0.909451	0.454725	−	0.890632i	$-0.349737\pi$
$67$	7.44418	0.909451	0.454725	+	0.890632i	$0.349737\pi$
$68$	20.0390	2.43009
$69$	−1.61844	−0.194837
$70$	48.7706	5.82920
$71$	−3.85363	−0.457342	−0.228671	−	0.973504i	$-0.573438\pi$
$71$	−3.85363	−0.457342	−0.228671	+	0.973504i	$0.573438\pi$
$72$	10.8261	1.27587
$73$	−8.62822	−1.00986	−0.504929	−	0.863161i	$-0.668481\pi$
$73$	−8.62822	−1.00986	−0.504929	+	0.863161i	$0.668481\pi$
$74$	−10.3952	−1.20841
$75$	13.6899	1.58078
$76$	30.1048	3.45326
$77$	4.64385	0.529216
$78$	−1.96154	−0.222101
$79$	−4.96078	−0.558131	−0.279065	−	0.960272i	$-0.590025\pi$
$79$	−4.96078	−0.558131	−0.279065	+	0.960272i	$0.590025\pi$
$80$	30.6736	3.42941
$81$	−1.17428	−0.130475
$82$	−15.3980	−1.70042
$83$	−12.6840	−1.39225	−0.696123	−	0.717923i	$-0.745093\pi$
$83$	−12.6840	−1.39225	−0.696123	+	0.717923i	$0.745093\pi$
$84$	−24.2242	−2.64308
$85$	18.1781	1.97170
$86$	−26.6835	−2.87736
$87$	6.52080	0.699103
$88$	6.46634	0.689315
$89$	−0.290276	−0.0307692	−0.0153846	−	0.999882i	$-0.504897\pi$
$89$	−0.290276	−0.0307692	−0.0153846	+	0.999882i	$0.504897\pi$
$90$	17.5830	1.85342
$91$	−3.09579	−0.324527
$92$	−6.36794	−0.663903
$93$	6.12132	0.634752
$94$	−4.72566	−0.487414
$95$	27.3092	2.80186
$96$	−7.07039	−0.721619
$97$	8.07144	0.819531	0.409765	−	0.912191i	$-0.365611\pi$
$97$	8.07144	0.819531	0.409765	+	0.912191i	$0.365611\pi$
$98$	−37.2213	−3.75991
$99$	1.67423	0.168266
$100$	53.8646	5.38646
$101$	−8.17458	−0.813401	−0.406701	−	0.913561i	$-0.633321\pi$
$101$	−8.17458	−0.813401	−0.406701	+	0.913561i	$0.633321\pi$
$102$	−13.0150	−1.28868
$103$	−10.9265	−1.07662	−0.538309	−	0.842747i	$-0.680937\pi$
$103$	−10.9265	−1.07662	−0.538309	+	0.842747i	$0.680937\pi$
$104$	−4.31075	−0.422704
$105$	−21.9747	−2.14451
$106$	29.0258	2.81923
$107$	−17.6392	−1.70524	−0.852622	−	0.522529i	$-0.824989\pi$
$107$	−17.6392	−1.70524	−0.852622	+	0.522529i	$0.824989\pi$
$108$	−24.3826	−2.34622
$109$	9.09300	0.870951	0.435476	−	0.900200i	$-0.356580\pi$
$109$	9.09300	0.870951	0.435476	+	0.900200i	$0.356580\pi$
$110$	10.5022	1.00134
$111$	4.68378	0.444564
$112$	−34.6604	−3.27510
$113$	1.42046	0.133625	0.0668127	−	0.997766i	$-0.478717\pi$
$113$	1.42046	0.133625	0.0668127	+	0.997766i	$0.478717\pi$
$114$	−19.5526	−1.83127
$115$	−5.77659	−0.538670
$116$	25.6568	2.38218
$117$	−1.11611	−0.103185
$118$	6.24875	0.575244
$119$	−20.5408	−1.88298
$120$	−30.5987	−2.79327
$121$	1.00000	0.0909091
$122$	−2.55546	−0.231361
$123$	6.93789	0.625569
$124$	24.0850	2.16290
$125$	28.3141	2.53249
$126$	−19.8684	−1.77002
$127$	−14.4613	−1.28323	−0.641617	−	0.767025i	$-0.721736\pi$
$127$	−14.4613	−1.28323	−0.641617	+	0.767025i	$0.721736\pi$
$128$	10.3273	0.912811
$129$	12.0229	1.05855
$130$	−7.00121	−0.614047
$131$	−5.53968	−0.484004	−0.242002	−	0.970276i	$-0.577804\pi$
$131$	−5.53968	−0.484004	−0.242002	+	0.970276i	$0.577804\pi$
$132$	−5.21640	−0.454029
$133$	−30.8587	−2.67579
$134$	−19.0233	−1.64337
$135$	−22.1184	−1.90365
$136$	−28.6022	−2.45261
$137$	16.9200	1.44558	0.722788	−	0.691070i	$-0.242860\pi$
$137$	16.9200	1.44558	0.722788	+	0.691070i	$0.242860\pi$
$138$	4.13587	0.352068
$139$	6.73354	0.571132	0.285566	−	0.958359i	$-0.407818\pi$
$139$	6.73354	0.571132	0.285566	+	0.958359i	$0.407818\pi$
$140$	−86.4618	−7.30736
$141$	2.12925	0.179315
$142$	9.84782	0.826410
$143$	−0.666644	−0.0557475
$144$	−12.4960	−1.04133
$145$	23.2743	1.93282
$146$	22.0491	1.82480
$147$	16.7709	1.38324
$148$	18.4288	1.51484
$149$	3.20949	0.262932	0.131466	−	0.991321i	$-0.458032\pi$
$149$	3.20949	0.262932	0.131466	+	0.991321i	$0.458032\pi$
$150$	−34.9841	−2.85644
$151$	18.5000	1.50551	0.752753	−	0.658303i	$-0.228725\pi$
$151$	18.5000	1.50551	0.752753	+	0.658303i	$0.228725\pi$
$152$	−42.9693	−3.48527
$153$	−7.40550	−0.598699
$154$	−11.8672	−0.956286
$155$	21.8484	1.75491
$156$	3.47748	0.278421
$157$	2.76599	0.220750	0.110375	−	0.993890i	$-0.464795\pi$
$157$	2.76599	0.220750	0.110375	+	0.993890i	$0.464795\pi$
$158$	12.6771	1.00853
$159$	−13.0782	−1.03717
$160$	−25.2359	−1.99507
$161$	6.52741	0.514432
$162$	3.00082	0.235767
$163$	−3.05445	−0.239243	−0.119621	−	0.992820i	$-0.538168\pi$
$163$	−3.05445	−0.239243	−0.119621	+	0.992820i	$0.538168\pi$
$164$	27.2979	2.13161
$165$	−4.73199	−0.368385
$166$	32.4134	2.51577
$167$	−9.05972	−0.701062	−0.350531	−	0.936551i	$-0.613999\pi$
$167$	−9.05972	−0.701062	−0.350531	+	0.936551i	$0.613999\pi$
$168$	34.5757	2.66758
$169$	−12.5556	−0.965814
$170$	−46.4536	−3.56283
$171$	−11.1254	−0.850777
$172$	47.3053	3.60700
$173$	7.33280	0.557503	0.278751	−	0.960363i	$-0.410079\pi$
$173$	7.33280	0.557503	0.278751	+	0.960363i	$0.410079\pi$
$174$	−16.6637	−1.26327
$175$	−55.2135	−4.17375
$176$	−7.46372	−0.562599
$177$	−2.81552	−0.211627
$178$	0.741790	0.0555995
$179$	−2.46630	−0.184340	−0.0921698	−	0.995743i	$-0.529380\pi$
$179$	−2.46630	−0.184340	−0.0921698	+	0.995743i	$0.529380\pi$
$180$	−31.1717	−2.32340
$181$	−5.68151	−0.422303	−0.211152	−	0.977453i	$-0.567721\pi$
$181$	−5.68151	−0.422303	−0.211152	+	0.977453i	$0.567721\pi$
$182$	7.91119	0.586417
$183$	1.15142	0.0851155
$184$	9.08911	0.670058
$185$	16.7175	1.22909
$186$	−15.6428	−1.14699
$187$	−4.42323	−0.323459
$188$	8.37778	0.611012
$189$	24.9932	1.81799
$190$	−69.7877	−5.06293
$191$	−16.5871	−1.20020	−0.600101	−	0.799924i	$-0.704873\pi$
$191$	−16.5871	−1.20020	−0.600101	+	0.799924i	$0.704873\pi$
$192$	0.880358	0.0635344
$193$	−26.7259	−1.92377	−0.961886	−	0.273450i	$-0.911835\pi$
$193$	−26.7259	−1.92377	−0.961886	+	0.273450i	$0.911835\pi$
$194$	−20.6263	−1.48088
$195$	3.15455	0.225902
$196$	65.9869	4.71335
$197$	−6.55487	−0.467015	−0.233508	−	0.972355i	$-0.575020\pi$
$197$	−6.55487	−0.467015	−0.233508	+	0.972355i	$0.575020\pi$
$198$	−4.27843	−0.304055
$199$	0.207457	0.0147062	0.00735310	−	0.999973i	$-0.497659\pi$
$199$	0.207457	0.0147062	0.00735310	+	0.999973i	$0.497659\pi$
$200$	−76.8822	−5.43639
$201$	8.57139	0.604579
$202$	20.8899	1.46980
$203$	−26.2993	−1.84585
$204$	23.0734	1.61546
$205$	24.7630	1.72952
$206$	27.9222	1.94543
$207$	2.35330	0.163566
$208$	4.97564	0.344999
$209$	−6.64507	−0.459649
$210$	56.1555	3.87510
$211$	15.2259	1.04820	0.524098	−	0.851658i	$-0.324403\pi$
$211$	15.2259	1.04820	0.524098	+	0.851658i	$0.324403\pi$
$212$	−51.4577	−3.53413
$213$	−4.43715	−0.304029
$214$	45.0763	3.08135
$215$	42.9124	2.92660
$216$	34.8019	2.36797
$217$	−24.6882	−1.67594
$218$	−23.2368	−1.57380
$219$	−9.93472	−0.671326
$220$	−18.6186	−1.25526
$221$	2.94872	0.198352
$222$	−11.9692	−0.803322
$223$	−11.7887	−0.789428	−0.394714	−	0.918804i	$-0.629156\pi$
$223$	−11.7887	−0.789428	−0.394714	+	0.918804i	$0.629156\pi$
$224$	28.5159	1.90530
$225$	−19.9059	−1.32706
$226$	−3.62993	−0.241459
$227$	1.77042	0.117507	0.0587535	−	0.998273i	$-0.481287\pi$
$227$	1.77042	0.117507	0.0587535	+	0.998273i	$0.481287\pi$
$228$	34.6633	2.29563
$229$	−15.2622	−1.00856	−0.504279	−	0.863541i	$-0.668242\pi$
$229$	−15.2622	−1.00856	−0.504279	+	0.863541i	$0.668242\pi$
$230$	14.7619	0.973370
$231$	5.34703	0.351809
$232$	−36.6206	−2.40426
$233$	−12.7162	−0.833064	−0.416532	−	0.909121i	$-0.636755\pi$
$233$	−12.7162	−0.833064	−0.416532	+	0.909121i	$0.636755\pi$
$234$	2.85219	0.186453
$235$	7.59980	0.495756
$236$	−11.0780	−0.721114
$237$	−5.71195	−0.371031
$238$	52.4914	3.40251
$239$	2.15176	0.139186	0.0695930	−	0.997575i	$-0.477830\pi$
$239$	2.15176	0.139186	0.0695930	+	0.997575i	$0.477830\pi$
$240$	35.3182	2.27978
$241$	15.9652	1.02841	0.514205	−	0.857667i	$-0.328087\pi$
$241$	15.9652	1.02841	0.514205	+	0.857667i	$0.328087\pi$
$242$	−2.55546	−0.164271
$243$	14.7939	0.949031
$244$	4.53040	0.290029
$245$	59.8592	3.82426
$246$	−17.7295	−1.13039
$247$	4.42989	0.281867
$248$	−34.3771	−2.18295
$249$	−14.6046	−0.925528
$250$	−72.3557	−4.57617
$251$	−1.05335	−0.0664867	−0.0332433	−	0.999447i	$-0.510584\pi$
$251$	−1.05335	−0.0664867	−0.0332433	+	0.999447i	$0.510584\pi$
$252$	35.2232	2.21886
$253$	1.40560	0.0883694
$254$	36.9554	2.31879
$255$	20.9307	1.31073
$256$	−27.9202	−1.74501
$257$	2.08120	0.129822	0.0649109	−	0.997891i	$-0.479324\pi$
$257$	2.08120	0.129822	0.0649109	+	0.997891i	$0.479324\pi$
$258$	−30.7240	−1.91279
$259$	−18.8903	−1.17379
$260$	12.4119	0.769756
$261$	−9.48159	−0.586896
$262$	14.1565	0.874589
$263$	−10.6735	−0.658155	−0.329077	−	0.944303i	$-0.606738\pi$
$263$	−10.6735	−0.658155	−0.329077	+	0.944303i	$0.606738\pi$
$264$	7.44549	0.458238
$265$	−46.6792	−2.86748
$266$	78.8583	4.83511
$267$	−0.334230	−0.0204545
$268$	33.7251	2.06009
$269$	14.9995	0.914535	0.457267	−	0.889329i	$-0.348828\pi$
$269$	14.9995	0.914535	0.457267	+	0.889329i	$0.348828\pi$
$270$	56.5228	3.43987
$271$	14.3260	0.870244	0.435122	−	0.900372i	$-0.356705\pi$
$271$	14.3260	0.870244	0.435122	+	0.900372i	$0.356705\pi$
$272$	33.0138	2.00175
$273$	−3.56457	−0.215737
$274$	−43.2386	−2.61214
$275$	−11.8896	−0.716969
$276$	−7.33218	−0.441345
$277$	23.2753	1.39848	0.699238	−	0.714889i	$-0.253523\pi$
$277$	23.2753	1.39848	0.699238	+	0.714889i	$0.253523\pi$
$278$	−17.2073	−1.03203
$279$	−8.90073	−0.532873
$280$	123.409	7.37510
$281$	−29.5558	−1.76315	−0.881576	−	0.472042i	$-0.843517\pi$
$281$	−29.5558	−1.76315	−0.881576	+	0.472042i	$0.843517\pi$
$282$	−5.44123	−0.324020
$283$	14.7770	0.878402	0.439201	−	0.898389i	$-0.355262\pi$
$283$	14.7770	0.878402	0.439201	+	0.898389i	$0.355262\pi$
$284$	−17.4585	−1.03597
$285$	31.4444	1.86261
$286$	1.70358	0.100735
$287$	−27.9815	−1.65170
$288$	10.2807	0.605797
$289$	2.56499	0.150882
$290$	−59.4766	−3.49259
$291$	9.29363	0.544803
$292$	−39.0893	−2.28753
$293$	17.3480	1.01348	0.506741	−	0.862099i	$-0.330850\pi$
$293$	17.3480	1.01348	0.506741	+	0.862099i	$0.330850\pi$
$294$	−42.8574	−2.49949
$295$	−10.0492	−0.585089
$296$	−26.3039	−1.52888
$297$	5.38201	0.312296
$298$	−8.20174	−0.475114
$299$	−0.937036	−0.0541902
$300$	62.0208	3.58077
$301$	−48.4900	−2.79492
$302$	−47.2760	−2.72043
$303$	−9.41239	−0.540728
$304$	49.5969	2.84458
$305$	4.10969	0.235320
$306$	18.9245	1.08184
$307$	21.3713	1.21972	0.609861	−	0.792508i	$-0.291225\pi$
$307$	21.3713	1.21972	0.609861	+	0.792508i	$0.291225\pi$
$308$	21.0385	1.19878
$309$	−12.5810	−0.715707
$310$	−55.8329	−3.17110
$311$	17.5491	0.995121	0.497560	−	0.867429i	$-0.334229\pi$
$311$	17.5491	0.995121	0.497560	+	0.867429i	$0.334229\pi$
$312$	−4.96349	−0.281002
$313$	−6.04955	−0.341941	−0.170970	−	0.985276i	$-0.554690\pi$
$313$	−6.04955	−0.341941	−0.170970	+	0.985276i	$0.554690\pi$
$314$	−7.06839	−0.398892
$315$	31.9523	1.80031
$316$	−22.4743	−1.26428
$317$	4.99781	0.280705	0.140353	−	0.990102i	$-0.455176\pi$
$317$	4.99781	0.280705	0.140353	+	0.990102i	$0.455176\pi$
$318$	33.4209	1.87415
$319$	−5.66326	−0.317082
$320$	3.14220	0.175655
$321$	−20.3101	−1.13360
$322$	−16.6806	−0.929571
$323$	29.3927	1.63545
$324$	−5.31994	−0.295552
$325$	7.92612	0.439662
$326$	7.80554	0.432309
$327$	10.4699	0.578986
$328$	−38.9630	−2.15137
$329$	−8.58758	−0.473449
$330$	12.0924	0.665667
$331$	19.8112	1.08892	0.544462	−	0.838786i	$-0.316734\pi$
$331$	19.8112	1.08892	0.544462	+	0.838786i	$0.316734\pi$
$332$	−57.4634	−3.15371
$333$	−6.81046	−0.373211
$334$	23.1518	1.26681
$335$	30.5933	1.67149
$336$	−39.9087	−2.17720
$337$	−8.12725	−0.442720	−0.221360	−	0.975192i	$-0.571050\pi$
$337$	−8.12725	−0.442720	−0.221360	+	0.975192i	$0.571050\pi$
$338$	32.0854	1.74521
$339$	1.63555	0.0888307
$340$	82.3542	4.46628
$341$	−5.31632	−0.287895
$342$	28.4305	1.53734
$343$	−35.1324	−1.89697
$344$	−67.5200	−3.64044
$345$	−6.65130	−0.358094
$346$	−18.7387	−1.00740
$347$	−17.6978	−0.950067	−0.475034	−	0.879968i	$-0.657564\pi$
$347$	−17.6978	−0.950067	−0.475034	+	0.879968i	$0.657564\pi$
$348$	29.5418	1.58361
$349$	−31.7603	−1.70009	−0.850044	−	0.526712i	$-0.823425\pi$
$349$	−31.7603	−1.70009	−0.850044	+	0.526712i	$0.823425\pi$
$350$	141.096	7.54190
$351$	−3.58788	−0.191507
$352$	6.14057	0.327294
$353$	−5.73302	−0.305138	−0.152569	−	0.988293i	$-0.548755\pi$
$353$	−5.73302	−0.305138	−0.152569	+	0.988293i	$0.548755\pi$
$354$	7.19495	0.382407
$355$	−15.8372	−0.840554
$356$	−1.31507	−0.0696983
$357$	−23.6512	−1.25175
$358$	6.30253	0.333099
$359$	−4.65129	−0.245486	−0.122743	−	0.992438i	$-0.539169\pi$
$359$	−4.65129	−0.245486	−0.122743	+	0.992438i	$0.539169\pi$
$360$	44.4921	2.34494
$361$	25.1569	1.32405
$362$	14.5189	0.763096
$363$	1.15142	0.0604340
$364$	−14.0252	−0.735119
$365$	−35.4594	−1.85603
$366$	−2.94242	−0.153803
$367$	−16.4324	−0.857764	−0.428882	−	0.903360i	$-0.641092\pi$
$367$	−16.4324	−0.857764	−0.428882	+	0.903360i	$0.641092\pi$
$368$	−10.4910	−0.546882
$369$	−10.0881	−0.525163
$370$	−42.7210	−2.22096
$371$	52.7463	2.73845
$372$	27.7320	1.43784
$373$	−8.15729	−0.422368	−0.211184	−	0.977446i	$-0.567732\pi$
$373$	−8.15729	−0.422368	−0.211184	+	0.977446i	$0.567732\pi$
$374$	11.3034	0.584486
$375$	32.6015	1.68353
$376$	−11.9578	−0.616676
$377$	3.77538	0.194442
$378$	−63.8694	−3.28509
$379$	17.5944	0.903764	0.451882	−	0.892078i	$-0.350753\pi$
$379$	17.5944	0.903764	0.451882	+	0.892078i	$0.350753\pi$
$380$	123.722	6.34678
$381$	−16.6511	−0.853060
$382$	42.3878	2.16875
$383$	10.7199	0.547762	0.273881	−	0.961764i	$-0.411693\pi$
$383$	10.7199	0.547762	0.273881	+	0.961764i	$0.411693\pi$
$384$	11.8911	0.606813
$385$	19.0848	0.972652
$386$	68.2971	3.47623
$387$	−17.4819	−0.888654
$388$	36.5669	1.85640
$389$	−13.7433	−0.696811	−0.348406	−	0.937344i	$-0.613277\pi$
$389$	−13.7433	−0.696811	−0.348406	+	0.937344i	$0.613277\pi$
$390$	−8.06135	−0.408202
$391$	−6.21731	−0.314423
$392$	−94.1846	−4.75704
$393$	−6.37851	−0.321753
$394$	16.7507	0.843890
$395$	−20.3873	−1.02580
$396$	7.58492	0.381157
$397$	27.5986	1.38513	0.692567	−	0.721353i	$-0.256480\pi$
$397$	27.5986	1.38513	0.692567	+	0.721353i	$0.256480\pi$
$398$	−0.530148	−0.0265739
$399$	−35.5314	−1.77879
$400$	88.7405	4.43703
$401$	12.7201	0.635210	0.317605	−	0.948223i	$-0.397121\pi$
$401$	12.7201	0.635210	0.317605	+	0.948223i	$0.397121\pi$
$402$	−21.9039	−1.09247
$403$	3.54409	0.176544
$404$	−37.0341	−1.84252
$405$	−4.82592	−0.239802
$406$	67.2070	3.33543
$407$	−4.06782	−0.201634
$408$	−32.9331	−1.63043
$409$	−18.4882	−0.914180	−0.457090	−	0.889420i	$-0.651108\pi$
$409$	−18.4882	−0.914180	−0.457090	+	0.889420i	$0.651108\pi$
$410$	−63.2809	−3.12522
$411$	19.4821	0.960981
$412$	−49.5013	−2.43876
$413$	11.3554	0.558762
$414$	−6.01377	−0.295561
$415$	−52.1272	−2.55882
$416$	−4.09357	−0.200704
$417$	7.75315	0.379673
$418$	16.9812	0.830579
$419$	17.5999	0.859810	0.429905	−	0.902874i	$-0.358547\pi$
$419$	17.5999	0.859810	0.429905	+	0.902874i	$0.358547\pi$
$420$	−99.5540	−4.85774
$421$	30.1765	1.47071	0.735356	−	0.677681i	$-0.237015\pi$
$421$	30.1765	1.47071	0.735356	+	0.677681i	$0.237015\pi$
$422$	−38.9093	−1.89407
$423$	−3.09604	−0.150535
$424$	73.4467	3.56689
$425$	52.5904	2.55101
$426$	11.3390	0.549376
$427$	−4.64385	−0.224732
$428$	−79.9125	−3.86272
$429$	−0.767588	−0.0370595
$430$	−109.661	−5.28833
$431$	−25.7244	−1.23910	−0.619550	−	0.784957i	$-0.712685\pi$
$431$	−25.7244	−1.23910	−0.619550	+	0.784957i	$0.712685\pi$
$432$	−40.1698	−1.93267
$433$	4.10568	0.197306	0.0986532	−	0.995122i	$-0.468547\pi$
$433$	4.10568	0.197306	0.0986532	+	0.995122i	$0.468547\pi$
$434$	63.0898	3.02841
$435$	26.7985	1.28489
$436$	41.1949	1.97288
$437$	−9.34032	−0.446808
$438$	25.3878	1.21308
$439$	−25.9632	−1.23915	−0.619577	−	0.784936i	$-0.712696\pi$
$439$	−25.9632	−1.23915	−0.619577	+	0.784936i	$0.712696\pi$
$440$	26.5747	1.26690
$441$	−24.3857	−1.16123
$442$	−7.53535	−0.358420
$443$	31.5884	1.50081	0.750405	−	0.660979i	$-0.229859\pi$
$443$	31.5884	1.50081	0.750405	+	0.660979i	$0.229859\pi$
$444$	21.2194	1.00703
$445$	−1.19295	−0.0565510
$446$	30.1255	1.42649
$447$	3.69548	0.174790
$448$	−3.55061	−0.167751
$449$	−9.68232	−0.456937	−0.228468	−	0.973551i	$-0.573372\pi$
$449$	−9.68232	−0.456937	−0.228468	+	0.973551i	$0.573372\pi$
$450$	50.8688	2.39798
$451$	−6.02550	−0.283730
$452$	6.43524	0.302688
$453$	21.3013	1.00082
$454$	−4.52425	−0.212334
$455$	−12.7228	−0.596453
$456$	−49.4758	−2.31692
$457$	24.2305	1.13345	0.566727	−	0.823906i	$-0.308210\pi$
$457$	24.2305	1.13345	0.566727	+	0.823906i	$0.308210\pi$
$458$	39.0021	1.82245
$459$	−23.8059	−1.11116
$460$	−26.1703	−1.22020
$461$	−19.6817	−0.916667	−0.458334	−	0.888780i	$-0.651553\pi$
$461$	−19.6817	−0.916667	−0.458334	+	0.888780i	$0.651553\pi$
$462$	−13.6641	−0.635714
$463$	−29.3838	−1.36558	−0.682790	−	0.730615i	$-0.739234\pi$
$463$	−29.3838	−1.36558	−0.682790	+	0.730615i	$0.739234\pi$
$464$	42.2690	1.96229
$465$	25.1568	1.16662
$466$	32.4957	1.50534
$467$	−1.53420	−0.0709943	−0.0354971	−	0.999370i	$-0.511301\pi$
$467$	−1.53420	−0.0709943	−0.0354971	+	0.999370i	$0.511301\pi$
$468$	−5.05644	−0.233734
$469$	−34.5696	−1.59628
$470$	−19.4210	−0.895824
$471$	3.18482	0.146749
$472$	15.8118	0.727799
$473$	−10.4418	−0.480113
$474$	14.5967	0.670447
$475$	79.0071	3.62509
$476$	−93.0582	−4.26532
$477$	19.0164	0.870701
$478$	−5.49876	−0.251507
$479$	19.5431	0.892949	0.446474	−	0.894796i	$-0.352679\pi$
$479$	19.5431	0.892949	0.446474	+	0.894796i	$0.352679\pi$
$480$	−29.0571	−1.32627
$481$	2.71179	0.123647
$482$	−40.7985	−1.85832
$483$	7.51580	0.341981
$484$	4.53040	0.205927
$485$	33.1712	1.50622
$486$	−37.8054	−1.71489
$487$	15.7254	0.712585	0.356292	−	0.934375i	$-0.384041\pi$
$487$	15.7254	0.712585	0.356292	+	0.934375i	$0.384041\pi$
$488$	−6.46634	−0.292718
$489$	−3.51696	−0.159042
$490$	−152.968	−6.91039
$491$	−22.1504	−0.999635	−0.499817	−	0.866131i	$-0.666600\pi$
$491$	−22.1504	−0.999635	−0.499817	+	0.866131i	$0.666600\pi$
$492$	31.4314	1.41704
$493$	25.0499	1.12819
$494$	−11.3204	−0.509330
$495$	6.88057	0.309258
$496$	39.6795	1.78166
$497$	17.8957	0.802731
$498$	37.3215	1.67242
$499$	−11.7623	−0.526553	−0.263276	−	0.964720i	$-0.584803\pi$
$499$	−11.7623	−0.526553	−0.263276	+	0.964720i	$0.584803\pi$
$500$	128.274	5.73660
$501$	−10.4316	−0.466047
$502$	2.69179	0.120140
$503$	−28.1289	−1.25421	−0.627103	−	0.778936i	$-0.715760\pi$
$503$	−28.1289	−1.25421	−0.627103	+	0.778936i	$0.715760\pi$
$504$	−50.2750	−2.23943
$505$	−33.5950	−1.49496
$506$	−3.59197	−0.159682
$507$	−14.4568	−0.642048
$508$	−65.5155	−2.90678
$509$	−6.45547	−0.286134	−0.143067	−	0.989713i	$-0.545696\pi$
$509$	−6.45547	−0.286134	−0.143067	+	0.989713i	$0.545696\pi$
$510$	−53.4877	−2.36847
$511$	40.0682	1.77251
$512$	50.6944	2.24040
$513$	−35.7638	−1.57901
$514$	−5.31844	−0.234586
$515$	−44.9045	−1.97873
$516$	54.4684	2.39784
$517$	−1.84924	−0.0813293
$518$	48.2736	2.12102
$519$	8.44315	0.370613
$520$	−17.7159	−0.776892
$521$	−27.5801	−1.20830	−0.604152	−	0.796869i	$-0.706488\pi$
$521$	−27.5801	−1.20830	−0.604152	+	0.796869i	$0.706488\pi$
$522$	24.2299	1.06051
$523$	−26.3856	−1.15376	−0.576882	−	0.816828i	$-0.695731\pi$
$523$	−26.3856	−1.15376	−0.576882	+	0.816828i	$0.695731\pi$
$524$	−25.0970	−1.09637
$525$	−63.5740	−2.77460
$526$	27.2757	1.18928
$527$	23.5153	1.02434
$528$	−8.59388	−0.374001
$529$	−21.0243	−0.914099
$530$	119.287	5.18150
$531$	4.09391	0.177661
$532$	−139.802	−6.06120
$533$	4.01686	0.173990
$534$	0.854113	0.0369611
$535$	−72.4916	−3.13409
$536$	−48.1366	−2.07918
$537$	−2.83975	−0.122544
$538$	−38.3306	−1.65255
$539$	−14.5654	−0.627374
$540$	−100.205	−4.31215
$541$	12.1153	0.520877	0.260438	−	0.965491i	$-0.416133\pi$
$541$	12.1153	0.520877	0.260438	+	0.965491i	$0.416133\pi$
$542$	−36.6096	−1.57252
$543$	−6.54181	−0.280736
$544$	−27.1612	−1.16453
$545$	37.3695	1.60073
$546$	9.10912	0.389834
$547$	−21.7847	−0.931448	−0.465724	−	0.884930i	$-0.654206\pi$
$547$	−21.7847	−0.931448	−0.465724	+	0.884930i	$0.654206\pi$
$548$	76.6545	3.27452
$549$	−1.67423	−0.0714543
$550$	30.3834	1.29555
$551$	37.6328	1.60321
$552$	10.4654	0.445437
$553$	23.0371	0.979638
$554$	−59.4792	−2.52703
$555$	19.2489	0.817070
$556$	30.5056	1.29373
$557$	−38.1464	−1.61631	−0.808157	−	0.588968i	$-0.799535\pi$
$557$	−38.1464	−1.61631	−0.808157	+	0.588968i	$0.799535\pi$
$558$	22.7455	0.962894
$559$	6.96093	0.294416
$560$	−142.444	−6.01934
$561$	−5.09301	−0.215027
$562$	75.5288	3.18599
$563$	−12.7597	−0.537756	−0.268878	−	0.963174i	$-0.586653\pi$
$563$	−12.7597	−0.537756	−0.268878	+	0.963174i	$0.586653\pi$
$564$	9.64636	0.406185
$565$	5.83765	0.245592
$566$	−37.7621	−1.58726
$567$	5.45317	0.229011
$568$	24.9189	1.04557
$569$	45.2759	1.89806	0.949032	−	0.315179i	$-0.102064\pi$
$569$	45.2759	1.89806	0.949032	+	0.315179i	$0.102064\pi$
$570$	−80.3550	−3.36570
$571$	−1.77216	−0.0741627	−0.0370813	−	0.999312i	$-0.511806\pi$
$571$	−1.77216	−0.0741627	−0.0370813	+	0.999312i	$0.511806\pi$
$572$	−3.02016	−0.126279
$573$	−19.0988	−0.797863
$574$	71.5058	2.98459
$575$	−16.7120	−0.696940
$576$	−1.28009	−0.0533370
$577$	1.31236	0.0546341	0.0273170	−	0.999627i	$-0.491304\pi$
$577$	1.31236	0.0546341	0.0273170	+	0.999627i	$0.491304\pi$
$578$	−6.55475	−0.272642
$579$	−30.7728	−1.27887
$580$	105.442	4.37823
$581$	58.9024	2.44369
$582$	−23.7496	−0.984451
$583$	11.3583	0.470413
$584$	55.7931	2.30873
$585$	−4.58689	−0.189644
$586$	−44.3322	−1.83135
$587$	−21.1079	−0.871218	−0.435609	−	0.900136i	$-0.643467\pi$
$587$	−21.1079	−0.871218	−0.435609	+	0.900136i	$0.643467\pi$
$588$	75.9787	3.13331
$589$	35.3273	1.45564
$590$	25.6805	1.05725
$591$	−7.54742	−0.310459
$592$	30.3610	1.24783
$593$	23.0846	0.947972	0.473986	−	0.880532i	$-0.342815\pi$
$593$	23.0846	0.947972	0.473986	+	0.880532i	$0.342815\pi$
$594$	−13.7535	−0.564314
$595$	−84.4166	−3.46074
$596$	14.5403	0.595593
$597$	0.238870	0.00977630
$598$	2.39456	0.0979209
$599$	−31.8521	−1.30144	−0.650721	−	0.759317i	$-0.725533\pi$
$599$	−31.8521	−1.30144	−0.650721	+	0.759317i	$0.725533\pi$
$600$	−88.5238	−3.61397
$601$	−15.8717	−0.647421	−0.323711	−	0.946156i	$-0.604930\pi$
$601$	−15.8717	−0.647421	−0.323711	+	0.946156i	$0.604930\pi$
$602$	123.914	5.05038
$603$	−12.4632	−0.507543
$604$	83.8123	3.41027
$605$	4.10969	0.167083
$606$	24.0530	0.977088
$607$	38.9427	1.58063	0.790317	−	0.612698i	$-0.209916\pi$
$607$	38.9427	1.58063	0.790317	+	0.612698i	$0.209916\pi$
$608$	−40.8045	−1.65484
$609$	−30.2816	−1.22707
$610$	−10.5022	−0.425221
$611$	1.23278	0.0498730
$612$	−33.5499	−1.35617
$613$	−9.68199	−0.391052	−0.195526	−	0.980699i	$-0.562641\pi$
$613$	−9.68199	−0.391052	−0.195526	+	0.980699i	$0.562641\pi$
$614$	−54.6135	−2.20402
$615$	28.5126	1.14974
$616$	−30.0287	−1.20989
$617$	−21.1567	−0.851736	−0.425868	−	0.904785i	$-0.640031\pi$
$617$	−21.1567	−0.851736	−0.425868	+	0.904785i	$0.640031\pi$
$618$	32.1503	1.29327
$619$	15.5848	0.626405	0.313202	−	0.949686i	$-0.398598\pi$
$619$	15.5848	0.626405	0.313202	+	0.949686i	$0.398598\pi$
$620$	98.9822	3.97522
$621$	7.56496	0.303571
$622$	−44.8462	−1.79817
$623$	1.34800	0.0540064
$624$	5.72906	0.229346
$625$	56.9144	2.27657
$626$	15.4594	0.617883
$627$	−7.65127	−0.305562
$628$	12.5310	0.500043
$629$	17.9929	0.717424
$630$	−81.6530	−3.25313
$631$	−36.5302	−1.45425	−0.727123	−	0.686507i	$-0.759143\pi$
$631$	−36.5302	−1.45425	−0.727123	+	0.686507i	$0.759143\pi$
$632$	32.0781	1.27600
$633$	17.5315	0.696813
$634$	−12.7717	−0.507230
$635$	−59.4316	−2.35847
$636$	−59.2495	−2.34939
$637$	9.70991	0.384720
$638$	14.4723	0.572962
$639$	6.45186	0.255231
$640$	42.4420	1.67767
$641$	−21.4341	−0.846597	−0.423298	−	0.905990i	$-0.639128\pi$
$641$	−21.4341	−0.846597	−0.423298	+	0.905990i	$0.639128\pi$
$642$	51.9018	2.04840
$643$	21.0844	0.831488	0.415744	−	0.909482i	$-0.363521\pi$
$643$	21.0844	0.831488	0.415744	+	0.909482i	$0.363521\pi$
$644$	29.5718	1.16529
$645$	49.4103	1.94553
$646$	−75.1120	−2.95524
$647$	21.5720	0.848083	0.424041	−	0.905643i	$-0.360611\pi$
$647$	21.5720	0.848083	0.424041	+	0.905643i	$0.360611\pi$
$648$	7.59328	0.298292
$649$	2.44525	0.0959845
$650$	−20.2549	−0.794463
$651$	−28.4265	−1.11412
$652$	−13.8379	−0.541933
$653$	−12.2422	−0.479074	−0.239537	−	0.970887i	$-0.576996\pi$
$653$	−12.2422	−0.479074	−0.239537	+	0.970887i	$0.576996\pi$
$654$	−26.7554	−1.04622
$655$	−22.7664	−0.889557
$656$	44.9726	1.75589
$657$	14.4456	0.563577
$658$	21.9453	0.855515
$659$	−10.3699	−0.403952	−0.201976	−	0.979390i	$-0.564736\pi$
$659$	−10.3699	−0.403952	−0.201976	+	0.979390i	$0.564736\pi$
$660$	−21.4378	−0.834466
$661$	−15.9771	−0.621437	−0.310719	−	0.950502i	$-0.600570\pi$
$661$	−15.9771	−0.621437	−0.310719	+	0.950502i	$0.600570\pi$
$662$	−50.6269	−1.96767
$663$	3.39522	0.131859
$664$	82.0189	3.18295
$665$	−126.820	−4.91786
$666$	17.4039	0.674387
$667$	−7.96029	−0.308224
$668$	−41.0441	−1.58804
$669$	−13.5737	−0.524791
$670$	−78.1801	−3.02036
$671$	−1.00000	−0.0386046
$672$	32.8338	1.26659
$673$	7.29351	0.281144	0.140572	−	0.990070i	$-0.455106\pi$
$673$	7.29351	0.281144	0.140572	+	0.990070i	$0.455106\pi$
$674$	20.7689	0.799988
$675$	−63.9899	−2.46297
$676$	−56.8818	−2.18776
$677$	1.80650	0.0694294	0.0347147	−	0.999397i	$-0.488948\pi$
$677$	1.80650	0.0694294	0.0347147	+	0.999397i	$0.488948\pi$
$678$	−4.17958	−0.160516
$679$	−37.4826	−1.43845
$680$	−117.546	−4.50769
$681$	2.03850	0.0781156
$682$	13.5857	0.520222
$683$	28.5417	1.09212	0.546059	−	0.837747i	$-0.316128\pi$
$683$	28.5417	1.09212	0.546059	+	0.837747i	$0.316128\pi$
$684$	−50.4023	−1.92718
$685$	69.5362	2.65684
$686$	89.7796	3.42780
$687$	−17.5733	−0.670462
$688$	77.9343	2.97122
$689$	−7.57194	−0.288468
$690$	16.9972	0.647071
$691$	23.4829	0.893330	0.446665	−	0.894701i	$-0.352612\pi$
$691$	23.4829	0.893330	0.446665	+	0.894701i	$0.352612\pi$
$692$	33.2205	1.26285
$693$	−7.77487	−0.295343
$694$	45.2261	1.71676
$695$	27.6728	1.04969
$696$	−42.1658	−1.59829
$697$	26.6522	1.00952
$698$	81.1622	3.07203
$699$	−14.6417	−0.553799
$700$	−250.139	−9.45437
$701$	−11.2981	−0.426722	−0.213361	−	0.976973i	$-0.568441\pi$
$701$	−11.2981	−0.426722	−0.213361	+	0.976973i	$0.568441\pi$
$702$	9.16870	0.346050
$703$	27.0309	1.01949
$704$	−0.764583	−0.0288163
$705$	8.75057	0.329566
$706$	14.6505	0.551380
$707$	37.9615	1.42769
$708$	−12.7554	−0.479378
$709$	−18.1320	−0.680961	−0.340481	−	0.940252i	$-0.610590\pi$
$709$	−18.1320	−0.680961	−0.340481	+	0.940252i	$0.610590\pi$
$710$	40.4715	1.51887
$711$	8.30547	0.311479
$712$	1.87702	0.0703445
$713$	−7.47263	−0.279852
$714$	60.4397	2.26190
$715$	−2.73970	−0.102459
$716$	−11.1733	−0.417566
$717$	2.47759	0.0925272
$718$	11.8862	0.443590
$719$	41.2774	1.53939	0.769694	−	0.638414i	$-0.220409\pi$
$719$	41.2774	1.53939	0.769694	+	0.638414i	$0.220409\pi$
$720$	−51.3546	−1.91387
$721$	50.7410	1.88969
$722$	−64.2876	−2.39254
$723$	18.3827	0.683660
$724$	−25.7395	−0.956601
$725$	67.3338	2.50072
$726$	−2.94242	−0.109203
$727$	−24.7151	−0.916634	−0.458317	−	0.888789i	$-0.651547\pi$
$727$	−24.7151	−0.916634	−0.458317	+	0.888789i	$0.651547\pi$
$728$	20.0185	0.741934
$729$	20.5569	0.761366
$730$	90.6151	3.35382
$731$	46.1863	1.70826
$732$	5.21640	0.192804
$733$	28.0872	1.03742	0.518712	−	0.854949i	$-0.326412\pi$
$733$	28.0872	1.03742	0.518712	+	0.854949i	$0.326412\pi$
$734$	41.9924	1.54997
$735$	68.9232	2.54227
$736$	8.63120	0.318150
$737$	−7.44418	−0.274210
$738$	25.7797	0.948963
$739$	36.3266	1.33630	0.668148	−	0.744029i	$-0.267087\pi$
$739$	36.3266	1.33630	0.668148	+	0.744029i	$0.267087\pi$
$740$	75.7369	2.78414
$741$	5.10067	0.187378
$742$	−134.791	−4.94834
$743$	37.8239	1.38762	0.693812	−	0.720156i	$-0.255930\pi$
$743$	37.8239	1.38762	0.693812	+	0.720156i	$0.255930\pi$
$744$	−39.5826	−1.45117
$745$	13.1900	0.483245
$746$	20.8457	0.763214
$747$	21.2358	0.776979
$748$	−20.0390	−0.732699
$749$	81.9137	2.99306
$750$	−83.3119	−3.04212
$751$	−11.3714	−0.414948	−0.207474	−	0.978241i	$-0.566524\pi$
$751$	−11.3714	−0.414948	−0.207474	+	0.978241i	$0.566524\pi$
$752$	13.8022	0.503314
$753$	−1.21285	−0.0441986
$754$	−9.64784	−0.351354
$755$	76.0292	2.76699
$756$	113.229	4.11811
$757$	−42.1631	−1.53244	−0.766222	−	0.642576i	$-0.777866\pi$
$757$	−42.1631	−1.53244	−0.766222	+	0.642576i	$0.777866\pi$
$758$	−44.9619	−1.63309
$759$	1.61844	0.0587457
$760$	−176.591	−6.40562
$761$	−16.4116	−0.594920	−0.297460	−	0.954734i	$-0.596139\pi$
$761$	−16.4116	−0.594920	−0.297460	+	0.954734i	$0.596139\pi$
$762$	42.5512	1.54147
$763$	−42.2265	−1.52870
$764$	−75.1463	−2.71870
$765$	−30.4343	−1.10036
$766$	−27.3944	−0.989799
$767$	−1.63011	−0.0588599
$768$	−32.1479	−1.16004
$769$	9.09945	0.328134	0.164067	−	0.986449i	$-0.447539\pi$
$769$	9.09945	0.328134	0.164067	+	0.986449i	$0.447539\pi$
$770$	−48.7706	−1.75757
$771$	2.39634	0.0863021
$772$	−121.079	−4.35773
$773$	7.14478	0.256980	0.128490	−	0.991711i	$-0.458987\pi$
$773$	7.14478	0.256980	0.128490	+	0.991711i	$0.458987\pi$
$774$	44.6743	1.60579
$775$	63.2088	2.27053
$776$	−52.1927	−1.87361
$777$	−21.7508	−0.780304
$778$	35.1204	1.25913
$779$	40.0399	1.43458
$780$	14.2914	0.511713
$781$	3.85363	0.137894
$782$	15.8881	0.568157
$783$	−30.4797	−1.08926
$784$	108.712	3.88256
$785$	11.3674	0.405719
$786$	16.3001	0.581404
$787$	45.7797	1.63187	0.815936	−	0.578143i	$-0.196222\pi$
$787$	45.7797	1.63187	0.815936	+	0.578143i	$0.196222\pi$
$788$	−29.6962	−1.05788
$789$	−12.2897	−0.437524
$790$	52.0990	1.85360
$791$	−6.59640	−0.234541
$792$	−10.8261	−0.384690
$793$	0.666644	0.0236732
$794$	−70.5273	−2.50292
$795$	−53.7474	−1.90622
$796$	0.939861	0.0333125
$797$	48.6021	1.72157	0.860787	−	0.508965i	$-0.169972\pi$
$797$	48.6021	1.72157	0.860787	+	0.508965i	$0.169972\pi$
$798$	90.7992	3.21426
$799$	8.17960	0.289374
$800$	−73.0089	−2.58125
$801$	0.485988	0.0171715
$802$	−32.5057	−1.14782
$803$	8.62822	0.304483
$804$	38.8318	1.36949
$805$	26.8256	0.945480
$806$	−9.05680	−0.319012
$807$	17.2707	0.607959
$808$	52.8597	1.85960
$809$	−34.3381	−1.20726	−0.603632	−	0.797263i	$-0.706280\pi$
$809$	−34.3381	−1.20726	−0.603632	+	0.797263i	$0.706280\pi$
$810$	12.3325	0.433318
$811$	10.0089	0.351461	0.175731	−	0.984438i	$-0.443771\pi$
$811$	10.0089	0.351461	0.175731	+	0.984438i	$0.443771\pi$
$812$	−119.147	−4.18122
$813$	16.4953	0.578515
$814$	10.3952	0.364350
$815$	−12.5529	−0.439707
$816$	38.0128	1.33071
$817$	69.3862	2.42752
$818$	47.2458	1.65191
$819$	5.18307	0.181111
$820$	112.186	3.91771
$821$	−1.61559	−0.0563846	−0.0281923	−	0.999603i	$-0.508975\pi$
$821$	−1.61559	−0.0563846	−0.0281923	+	0.999603i	$0.508975\pi$
$822$	−49.7858	−1.73648
$823$	−47.3899	−1.65191	−0.825953	−	0.563739i	$-0.809363\pi$
$823$	−47.3899	−1.65191	−0.825953	+	0.563739i	$0.809363\pi$
$824$	70.6544	2.46136
$825$	−13.6899	−0.476622
$826$	−29.0183	−1.00968
$827$	−27.5468	−0.957896	−0.478948	−	0.877843i	$-0.658982\pi$
$827$	−27.5468	−0.957896	−0.478948	+	0.877843i	$0.658982\pi$
$828$	10.6614	0.370509
$829$	42.1510	1.46396	0.731982	−	0.681324i	$-0.238596\pi$
$829$	42.1510	1.46396	0.731982	+	0.681324i	$0.238596\pi$
$830$	133.209	4.62376
$831$	26.7997	0.929670
$832$	0.509705	0.0176708
$833$	64.4260	2.23223
$834$	−19.8129	−0.686064
$835$	−37.2327	−1.28849
$836$	−30.1048	−1.04120
$837$	−28.6125	−0.988992
$838$	−44.9758	−1.55366
$839$	−4.16582	−0.143820	−0.0719101	−	0.997411i	$-0.522909\pi$
$839$	−4.16582	−0.143820	−0.0719101	+	0.997411i	$0.522909\pi$
$840$	142.096	4.90277
$841$	3.07253	0.105949
$842$	−77.1150	−2.65756
$843$	−34.0312	−1.17210
$844$	68.9795	2.37437
$845$	−51.5996	−1.77508
$846$	7.91183	0.272014
$847$	−4.64385	−0.159565
$848$	−84.7752	−2.91119
$849$	17.0146	0.583939
$850$	−134.393	−4.60964
$851$	−5.71773	−0.196001
$852$	−20.1021	−0.688686
$853$	−49.3442	−1.68951	−0.844756	−	0.535152i	$-0.820254\pi$
$853$	−49.3442	−1.68951	−0.844756	+	0.535152i	$0.820254\pi$
$854$	11.8672	0.406087
$855$	−45.7218	−1.56365
$856$	114.061	3.89852
$857$	19.4233	0.663486	0.331743	−	0.943370i	$-0.392363\pi$
$857$	19.4233	0.663486	0.331743	+	0.943370i	$0.392363\pi$
$858$	1.96154	0.0669660
$859$	31.7807	1.08434	0.542171	−	0.840268i	$-0.317603\pi$
$859$	31.7807	1.08434	0.542171	+	0.840268i	$0.317603\pi$
$860$	194.410	6.62934
$861$	−32.2185	−1.09800
$862$	65.7378	2.23904
$863$	−5.84413	−0.198936	−0.0994682	−	0.995041i	$-0.531714\pi$
$863$	−5.84413	−0.198936	−0.0994682	+	0.995041i	$0.531714\pi$
$864$	33.0486	1.12434
$865$	30.1356	1.02464
$866$	−10.4919	−0.356530
$867$	2.95339	0.100302
$868$	−111.847	−3.79635
$869$	4.96078	0.168283
$870$	−68.4826	−2.32178
$871$	4.96261	0.168152
$872$	−58.7985	−1.99117
$873$	−13.5134	−0.457361
$874$	23.8689	0.807376
$875$	−131.486	−4.44505
$876$	−45.0083	−1.52069
$877$	−14.8060	−0.499962	−0.249981	−	0.968251i	$-0.580424\pi$
$877$	−14.8060	−0.499962	−0.249981	+	0.968251i	$0.580424\pi$
$878$	66.3479	2.23913
$879$	19.9749	0.673736
$880$	−30.6736	−1.03401
$881$	−41.4772	−1.39740	−0.698701	−	0.715414i	$-0.746238\pi$
$881$	−41.4772	−1.39740	−0.698701	+	0.715414i	$0.746238\pi$
$882$	62.3169	2.09832
$883$	−33.2315	−1.11833	−0.559164	−	0.829057i	$-0.688878\pi$
$883$	−33.2315	−1.11833	−0.559164	+	0.829057i	$0.688878\pi$
$884$	13.3589	0.449308
$885$	−11.5709	−0.388952
$886$	−80.7230	−2.71194
$887$	−16.9919	−0.570533	−0.285266	−	0.958448i	$-0.592082\pi$
$887$	−16.9919	−0.570533	−0.285266	+	0.958448i	$0.592082\pi$
$888$	−30.2869	−1.01636
$889$	67.1562	2.25235
$890$	3.04853	0.102187
$891$	1.17428	0.0393397
$892$	−53.4074	−1.78821
$893$	12.2883	0.411212
$894$	−9.44366	−0.315843
$895$	−10.1357	−0.338800
$896$	−47.9584	−1.60218
$897$	−1.07892	−0.0360242
$898$	24.7428	0.825678
$899$	30.1077	1.00415
$900$	−90.1816	−3.00605
$901$	−50.2404	−1.67375
$902$	15.3980	0.512696
$903$	−55.8324	−1.85799
$904$	−9.18517	−0.305494
$905$	−23.3493	−0.776156
$906$	−54.4346	−1.80847
$907$	5.14525	0.170845	0.0854226	−	0.996345i	$-0.472776\pi$
$907$	5.14525	0.170845	0.0854226	+	0.996345i	$0.472776\pi$
$908$	8.02072	0.266177
$909$	13.6861	0.453940
$910$	32.5126	1.07778
$911$	−23.1471	−0.766899	−0.383449	−	0.923562i	$-0.625264\pi$
$911$	−23.1471	−0.766899	−0.383449	+	0.923562i	$0.625264\pi$
$912$	57.1069	1.89100
$913$	12.6840	0.419778
$914$	−61.9201	−2.04814
$915$	4.73199	0.156435
$916$	−69.1441	−2.28458
$917$	25.7255	0.849529
$918$	60.8351	2.00786
$919$	55.6699	1.83638	0.918190	−	0.396141i	$-0.129651\pi$
$919$	55.6699	1.83638	0.918190	+	0.396141i	$0.129651\pi$
$920$	37.3535	1.23151
$921$	24.6073	0.810839
$922$	50.2958	1.65640
$923$	−2.56900	−0.0845596
$924$	24.2242	0.796917
$925$	48.3647	1.59022
$926$	75.0892	2.46758
$927$	18.2934	0.600835
$928$	−34.7757	−1.14157
$929$	−26.0308	−0.854044	−0.427022	−	0.904241i	$-0.640437\pi$
$929$	−26.0308	−0.854044	−0.427022	+	0.904241i	$0.640437\pi$
$930$	−64.2872	−2.10806
$931$	96.7878	3.17209
$932$	−57.6093	−1.88706
$933$	20.2065	0.661530
$934$	3.92059	0.128286
$935$	−18.1781	−0.594489
$936$	7.21717	0.235901
$937$	−36.2353	−1.18376	−0.591878	−	0.806027i	$-0.701613\pi$
$937$	−36.2353	−1.18376	−0.591878	+	0.806027i	$0.701613\pi$
$938$	88.3415	2.88445
$939$	−6.96559	−0.227313
$940$	34.4301	1.12299
$941$	−5.78164	−0.188476	−0.0942380	−	0.995550i	$-0.530041\pi$
$941$	−5.78164	−0.188476	−0.0942380	+	0.995550i	$0.530041\pi$
$942$	−8.13870	−0.265173
$943$	−8.46945	−0.275803
$944$	−18.2507	−0.594009
$945$	102.715	3.34131
$946$	26.6835	0.867557
$947$	5.19982	0.168972	0.0844858	−	0.996425i	$-0.473075\pi$
$947$	5.19982	0.168972	0.0844858	+	0.996425i	$0.473075\pi$
$948$	−25.8774	−0.840459
$949$	−5.75195	−0.186716
$950$	−201.900	−6.55050
$951$	5.75459	0.186605
$952$	132.824	4.30486
$953$	−5.45893	−0.176832	−0.0884160	−	0.996084i	$-0.528180\pi$
$953$	−5.45893	−0.176832	−0.0884160	+	0.996084i	$0.528180\pi$
$954$	−48.5957	−1.57334
$955$	−68.1681	−2.20587
$956$	9.74835	0.315284
$957$	−6.52080	−0.210788
$958$	−49.9418	−1.61355
$959$	−78.5741	−2.53729
$960$	3.61800	0.116771
$961$	−2.73675	−0.0882824
$962$	−6.92987	−0.223428
$963$	29.5320	0.951655
$964$	72.3288	2.32955
$965$	−109.835	−3.53572
$966$	−19.2064	−0.617954
$967$	52.8290	1.69887	0.849433	−	0.527697i	$-0.176944\pi$
$967$	52.8290	1.69887	0.849433	+	0.527697i	$0.176944\pi$
$968$	−6.46634	−0.207836
$969$	33.8434	1.08721
$970$	−84.7677	−2.72173
$971$	−47.3848	−1.52065	−0.760326	−	0.649542i	$-0.774961\pi$
$971$	−47.3848	−1.52065	−0.760326	+	0.649542i	$0.774961\pi$
$972$	67.0224	2.14975
$973$	−31.2696	−1.00246
$974$	−40.1856	−1.28763
$975$	9.12631	0.292276
$976$	7.46372	0.238908
$977$	49.1774	1.57332	0.786662	−	0.617384i	$-0.211808\pi$
$977$	49.1774	1.57332	0.786662	+	0.617384i	$0.211808\pi$
$978$	8.98746	0.287387
$979$	0.290276	0.00927726
$980$	271.186	8.66272
$981$	−15.2238	−0.486057
$982$	56.6046	1.80633
$983$	−30.5252	−0.973601	−0.486801	−	0.873513i	$-0.661836\pi$
$983$	−30.5252	−0.973601	−0.486801	+	0.873513i	$0.661836\pi$
$984$	−44.8628	−1.43017
$985$	−26.9385	−0.858332
$986$	−64.0142	−2.03863
$987$	−9.88793	−0.314736
$988$	20.0692	0.638486
$989$	−14.6770	−0.466700
$990$	−17.5830	−0.558826
$991$	−31.0393	−0.985997	−0.492999	−	0.870030i	$-0.664099\pi$
$991$	−31.0393	−0.985997	−0.492999	+	0.870030i	$0.664099\pi$
$992$	−32.6452	−1.03649
$993$	22.8111	0.723888
$994$	−45.7318	−1.45052
$995$	0.852583	0.0270287
$996$	−66.1646	−2.09651
$997$	27.6505	0.875700	0.437850	−	0.899048i	$-0.355740\pi$
$997$	27.6505	0.875700	0.437850	+	0.899048i	$0.355740\pi$
$998$	30.0581	0.951473
$999$	−21.8930	−0.692665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.3	✓	21
3.2	odd	2		6039.2.a.l.1.19		21
11.10	odd	2		7381.2.a.j.1.19		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.3	✓	21	1.1	even	1	trivial
6039.2.a.l.1.19		21	3.2	odd	2
7381.2.a.j.1.19		21	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55546 q^{2} +1.15142 q^{3} +4.53040 q^{4} +4.10969 q^{5} -2.94242 q^{6} -4.64385 q^{7} -6.46634 q^{8} -1.67423 q^{9} +O(q^{10})\)	\(q-2.55546 q^{2} +1.15142 q^{3} +4.53040 q^{4} +4.10969 q^{5} -2.94242 q^{6} -4.64385 q^{7} -6.46634 q^{8} -1.67423 q^{9} -10.5022 q^{10} -1.00000 q^{11} +5.21640 q^{12} +0.666644 q^{13} +11.8672 q^{14} +4.73199 q^{15} +7.46372 q^{16} +4.42323 q^{17} +4.27843 q^{18} +6.64507 q^{19} +18.6186 q^{20} -5.34703 q^{21} +2.55546 q^{22} -1.40560 q^{23} -7.44549 q^{24} +11.8896 q^{25} -1.70358 q^{26} -5.38201 q^{27} -21.0385 q^{28} +5.66326 q^{29} -12.0924 q^{30} +5.31632 q^{31} -6.14057 q^{32} -1.15142 q^{33} -11.3034 q^{34} -19.0848 q^{35} -7.58492 q^{36} +4.06782 q^{37} -16.9812 q^{38} +0.767588 q^{39} -26.5747 q^{40} +6.02550 q^{41} +13.6641 q^{42} +10.4418 q^{43} -4.53040 q^{44} -6.88057 q^{45} +3.59197 q^{46} +1.84924 q^{47} +8.59388 q^{48} +14.5654 q^{49} -30.3834 q^{50} +5.09301 q^{51} +3.02016 q^{52} -11.3583 q^{53} +13.7535 q^{54} -4.10969 q^{55} +30.0287 q^{56} +7.65127 q^{57} -14.4723 q^{58} -2.44525 q^{59} +21.4378 q^{60} +1.00000 q^{61} -13.5857 q^{62} +7.77487 q^{63} +0.764583 q^{64} +2.73970 q^{65} +2.94242 q^{66} +7.44418 q^{67} +20.0390 q^{68} -1.61844 q^{69} +48.7706 q^{70} -3.85363 q^{71} +10.8261 q^{72} -8.62822 q^{73} -10.3952 q^{74} +13.6899 q^{75} +30.1048 q^{76} +4.64385 q^{77} -1.96154 q^{78} -4.96078 q^{79} +30.6736 q^{80} -1.17428 q^{81} -15.3980 q^{82} -12.6840 q^{83} -24.2242 q^{84} +18.1781 q^{85} -26.6835 q^{86} +6.52080 q^{87} +6.46634 q^{88} -0.290276 q^{89} +17.5830 q^{90} -3.09579 q^{91} -6.36794 q^{92} +6.12132 q^{93} -4.72566 q^{94} +27.3092 q^{95} -7.07039 q^{96} +8.07144 q^{97} -37.2213 q^{98} +1.67423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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