LMFDB - Embedded newform 671.2.a.d.1.12

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			1.12
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)

$f(q)$	$=$	$q+0.543169 q^{2} -1.77928 q^{3} -1.70497 q^{4} -0.382346 q^{5} -0.966447 q^{6} -4.84691 q^{7} -2.01242 q^{8} +0.165824 q^{9} +O(q^{10})$	\(q+0.543169 q^{2} -1.77928 q^{3} -1.70497 q^{4} -0.382346 q^{5} -0.966447 q^{6} -4.84691 q^{7} -2.01242 q^{8} +0.165824 q^{9} -0.207678 q^{10} -1.00000 q^{11} +3.03361 q^{12} +6.63881 q^{13} -2.63269 q^{14} +0.680299 q^{15} +2.31685 q^{16} +4.99283 q^{17} +0.0900705 q^{18} +7.01598 q^{19} +0.651888 q^{20} +8.62399 q^{21} -0.543169 q^{22} -7.26609 q^{23} +3.58066 q^{24} -4.85381 q^{25} +3.60599 q^{26} +5.04278 q^{27} +8.26382 q^{28} +1.46741 q^{29} +0.369517 q^{30} -1.13218 q^{31} +5.28329 q^{32} +1.77928 q^{33} +2.71195 q^{34} +1.85320 q^{35} -0.282725 q^{36} -8.90479 q^{37} +3.81086 q^{38} -11.8123 q^{39} +0.769442 q^{40} +2.75714 q^{41} +4.68428 q^{42} -0.438418 q^{43} +1.70497 q^{44} -0.0634022 q^{45} -3.94671 q^{46} -9.41958 q^{47} -4.12232 q^{48} +16.4925 q^{49} -2.63644 q^{50} -8.88362 q^{51} -11.3190 q^{52} +8.67499 q^{53} +2.73908 q^{54} +0.382346 q^{55} +9.75403 q^{56} -12.4834 q^{57} +0.797050 q^{58} +9.48074 q^{59} -1.15989 q^{60} +1.00000 q^{61} -0.614967 q^{62} -0.803734 q^{63} -1.76398 q^{64} -2.53832 q^{65} +0.966447 q^{66} +6.48857 q^{67} -8.51261 q^{68} +12.9284 q^{69} +1.00660 q^{70} -3.31654 q^{71} -0.333708 q^{72} +6.10854 q^{73} -4.83681 q^{74} +8.63627 q^{75} -11.9620 q^{76} +4.84691 q^{77} -6.41606 q^{78} -2.55910 q^{79} -0.885838 q^{80} -9.46997 q^{81} +1.49759 q^{82} +14.7949 q^{83} -14.7036 q^{84} -1.90899 q^{85} -0.238135 q^{86} -2.61092 q^{87} +2.01242 q^{88} +10.4506 q^{89} -0.0344381 q^{90} -32.1777 q^{91} +12.3884 q^{92} +2.01447 q^{93} -5.11642 q^{94} -2.68253 q^{95} -9.40043 q^{96} +9.14364 q^{97} +8.95822 q^{98} -0.165824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.543169	0.384078	0.192039	−	0.981387i	$-0.438490\pi$
$2$	0.543169	0.384078	0.192039	+	0.981387i	$0.438490\pi$
$3$	−1.77928	−1.02727	−0.513633	−	0.858010i	$-0.671701\pi$
$3$	−1.77928	−1.02727	−0.513633	+	0.858010i	$0.671701\pi$
$4$	−1.70497	−0.852484
$5$	−0.382346	−0.170990	−0.0854952	−	0.996339i	$-0.527247\pi$
$5$	−0.382346	−0.170990	−0.0854952	+	0.996339i	$0.527247\pi$
$6$	−0.966447	−0.394551
$7$	−4.84691	−1.83196	−0.915979	−	0.401225i	$-0.868585\pi$
$7$	−4.84691	−1.83196	−0.915979	+	0.401225i	$0.868585\pi$
$8$	−2.01242	−0.711499
$9$	0.165824	0.0552747
$10$	−0.207678	−0.0656737
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.03361	0.875727
$13$	6.63881	1.84127	0.920637	−	0.390419i	$-0.127670\pi$
$13$	6.63881	1.84127	0.920637	+	0.390419i	$0.127670\pi$
$14$	−2.63269	−0.703616
$15$	0.680299	0.175653
$16$	2.31685	0.579212
$17$	4.99283	1.21094	0.605469	−	0.795869i	$-0.292985\pi$
$17$	4.99283	1.21094	0.605469	+	0.795869i	$0.292985\pi$
$18$	0.0900705	0.0212298
$19$	7.01598	1.60958	0.804789	−	0.593562i	$-0.202279\pi$
$19$	7.01598	1.60958	0.804789	+	0.593562i	$0.202279\pi$
$20$	0.651888	0.145766
$21$	8.62399	1.88191
$22$	−0.543169	−0.115804
$23$	−7.26609	−1.51508	−0.757542	−	0.652786i	$-0.773600\pi$
$23$	−7.26609	−1.51508	−0.757542	+	0.652786i	$0.773600\pi$
$24$	3.58066	0.730898
$25$	−4.85381	−0.970762
$26$	3.60599	0.707194
$27$	5.04278	0.970484
$28$	8.26382	1.56172
$29$	1.46741	0.272491	0.136245	−	0.990675i	$-0.456496\pi$
$29$	1.46741	0.272491	0.136245	+	0.990675i	$0.456496\pi$
$30$	0.369517	0.0674643
$31$	−1.13218	−0.203346	−0.101673	−	0.994818i	$-0.532420\pi$
$31$	−1.13218	−0.203346	−0.101673	+	0.994818i	$0.532420\pi$
$32$	5.28329	0.933962
$33$	1.77928	0.309732
$34$	2.71195	0.465095
$35$	1.85320	0.313247
$36$	−0.282725	−0.0471208
$37$	−8.90479	−1.46394	−0.731969	−	0.681337i	$-0.761399\pi$
$37$	−8.90479	−1.46394	−0.731969	+	0.681337i	$0.761399\pi$
$38$	3.81086	0.618204
$39$	−11.8123	−1.89148
$40$	0.769442	0.121659
$41$	2.75714	0.430594	0.215297	−	0.976549i	$-0.430928\pi$
$41$	2.75714	0.430594	0.215297	+	0.976549i	$0.430928\pi$
$42$	4.68428	0.722800
$43$	−0.438418	−0.0668582	−0.0334291	−	0.999441i	$-0.510643\pi$
$43$	−0.438418	−0.0668582	−0.0334291	+	0.999441i	$0.510643\pi$
$44$	1.70497	0.257034
$45$	−0.0634022	−0.00945144
$46$	−3.94671	−0.581911
$47$	−9.41958	−1.37399	−0.686994	−	0.726664i	$-0.741070\pi$
$47$	−9.41958	−1.37399	−0.686994	+	0.726664i	$0.741070\pi$
$48$	−4.12232	−0.595005
$49$	16.4925	2.35607
$50$	−2.63644	−0.372849
$51$	−8.88362	−1.24396
$52$	−11.3190	−1.56966
$53$	8.67499	1.19160	0.595801	−	0.803132i	$-0.296835\pi$
$53$	8.67499	1.19160	0.595801	+	0.803132i	$0.296835\pi$
$54$	2.73908	0.372742
$55$	0.382346	0.0515555
$56$	9.75403	1.30344
$57$	−12.4834	−1.65346
$58$	0.797050	0.104658
$59$	9.48074	1.23429	0.617143	−	0.786851i	$-0.288290\pi$
$59$	9.48074	1.23429	0.617143	+	0.786851i	$0.288290\pi$
$60$	−1.15989	−0.149741
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−0.614967	−0.0781009
$63$	−0.803734	−0.101261
$64$	−1.76398	−0.220498
$65$	−2.53832	−0.314840
$66$	0.966447	0.118961
$67$	6.48857	0.792705	0.396353	−	0.918098i	$-0.370276\pi$
$67$	6.48857	0.792705	0.396353	+	0.918098i	$0.370276\pi$
$68$	−8.51261	−1.03231
$69$	12.9284	1.55639
$70$	1.00660	0.120312
$71$	−3.31654	−0.393601	−0.196800	−	0.980444i	$-0.563055\pi$
$71$	−3.31654	−0.393601	−0.196800	+	0.980444i	$0.563055\pi$
$72$	−0.333708	−0.0393279
$73$	6.10854	0.714950	0.357475	−	0.933923i	$-0.383638\pi$
$73$	6.10854	0.714950	0.357475	+	0.933923i	$0.383638\pi$
$74$	−4.83681	−0.562267
$75$	8.63627	0.997231
$76$	−11.9620	−1.37214
$77$	4.84691	0.552356
$78$	−6.41606	−0.726476
$79$	−2.55910	−0.287922	−0.143961	−	0.989583i	$-0.545984\pi$
$79$	−2.55910	−0.287922	−0.143961	+	0.989583i	$0.545984\pi$
$80$	−0.885838	−0.0990397
$81$	−9.46997	−1.05222
$82$	1.49759	0.165382
$83$	14.7949	1.62395	0.811974	−	0.583693i	$-0.198393\pi$
$83$	14.7949	1.62395	0.811974	+	0.583693i	$0.198393\pi$
$84$	−14.7036	−1.60430
$85$	−1.90899	−0.207059
$86$	−0.238135	−0.0256788
$87$	−2.61092	−0.279920
$88$	2.01242	0.214525
$89$	10.4506	1.10776	0.553879	−	0.832597i	$-0.313147\pi$
$89$	10.4506	1.10776	0.553879	+	0.832597i	$0.313147\pi$
$90$	−0.0344381	−0.00363009
$91$	−32.1777	−3.37314
$92$	12.3884	1.29158
$93$	2.01447	0.208891
$94$	−5.11642	−0.527719
$95$	−2.68253	−0.275222
$96$	−9.40043	−0.959427
$97$	9.14364	0.928396	0.464198	−	0.885731i	$-0.346343\pi$
$97$	9.14364	0.928396	0.464198	+	0.885731i	$0.346343\pi$
$98$	8.95822	0.904917
$99$	−0.165824	−0.0166660
$100$	8.27559	0.827559
$101$	4.96054	0.493592	0.246796	−	0.969067i	$-0.420622\pi$
$101$	4.96054	0.493592	0.246796	+	0.969067i	$0.420622\pi$
$102$	−4.82531	−0.477776
$103$	−11.2088	−1.10444	−0.552220	−	0.833698i	$-0.686219\pi$
$103$	−11.2088	−1.10444	−0.552220	+	0.833698i	$0.686219\pi$
$104$	−13.3601	−1.31007
$105$	−3.29735	−0.321788
$106$	4.71198	0.457668
$107$	11.3950	1.10160	0.550798	−	0.834638i	$-0.314323\pi$
$107$	11.3950	1.10160	0.550798	+	0.834638i	$0.314323\pi$
$108$	−8.59778	−0.827322
$109$	8.81005	0.843850	0.421925	−	0.906631i	$-0.361355\pi$
$109$	8.81005	0.843850	0.421925	+	0.906631i	$0.361355\pi$
$110$	0.207678	0.0198014
$111$	15.8441	1.50385
$112$	−11.2296	−1.06109
$113$	−5.60704	−0.527466	−0.263733	−	0.964596i	$-0.584954\pi$
$113$	−5.60704	−0.527466	−0.263733	+	0.964596i	$0.584954\pi$
$114$	−6.78058	−0.635059
$115$	2.77816	0.259065
$116$	−2.50188	−0.232294
$117$	1.10088	0.101776
$118$	5.14964	0.474063
$119$	−24.1998	−2.21839
$120$	−1.36905	−0.124977
$121$	1.00000	0.0909091
$122$	0.543169	0.0491762
$123$	−4.90572	−0.442334
$124$	1.93034	0.173349
$125$	3.76757	0.336981
$126$	−0.436563	−0.0388922
$127$	9.96922	0.884625	0.442313	−	0.896861i	$-0.354158\pi$
$127$	9.96922	0.884625	0.442313	+	0.896861i	$0.354158\pi$
$128$	−11.5247	−1.01865
$129$	0.780068	0.0686811
$130$	−1.37874	−0.120923
$131$	−10.9236	−0.954398	−0.477199	−	0.878795i	$-0.658348\pi$
$131$	−10.9236	−0.954398	−0.477199	+	0.878795i	$0.658348\pi$
$132$	−3.03361	−0.264042
$133$	−34.0058	−2.94868
$134$	3.52439	0.304461
$135$	−1.92809	−0.165943
$136$	−10.0477	−0.861582
$137$	−20.4682	−1.74871	−0.874357	−	0.485283i	$-0.838717\pi$
$137$	−20.4682	−1.74871	−0.874357	+	0.485283i	$0.838717\pi$
$138$	7.02229	0.597777
$139$	3.67439	0.311658	0.155829	−	0.987784i	$-0.450195\pi$
$139$	3.67439	0.311658	0.155829	+	0.987784i	$0.450195\pi$
$140$	−3.15964	−0.267038
$141$	16.7600	1.41145
$142$	−1.80144	−0.151174
$143$	−6.63881	−0.555165
$144$	0.384190	0.0320158
$145$	−0.561057	−0.0465933
$146$	3.31797	0.274597
$147$	−29.3447	−2.42031
$148$	15.1824	1.24798
$149$	−16.2675	−1.33269	−0.666343	−	0.745645i	$-0.732141\pi$
$149$	−16.2675	−1.33269	−0.666343	+	0.745645i	$0.732141\pi$
$150$	4.69095	0.383015
$151$	8.76278	0.713105	0.356552	−	0.934275i	$-0.383952\pi$
$151$	8.76278	0.713105	0.356552	+	0.934275i	$0.383952\pi$
$152$	−14.1191	−1.14521
$153$	0.827931	0.0669343
$154$	2.63269	0.212148
$155$	0.432886	0.0347702
$156$	20.1396	1.61245
$157$	9.66814	0.771601	0.385801	−	0.922582i	$-0.373925\pi$
$157$	9.66814	0.771601	0.385801	+	0.922582i	$0.373925\pi$
$158$	−1.39002	−0.110584
$159$	−15.4352	−1.22409
$160$	−2.02004	−0.159698
$161$	35.2181	2.77557
$162$	−5.14380	−0.404135
$163$	9.13632	0.715612	0.357806	−	0.933796i	$-0.383525\pi$
$163$	9.13632	0.715612	0.357806	+	0.933796i	$0.383525\pi$
$164$	−4.70084	−0.367074
$165$	−0.680299	−0.0529612
$166$	8.03612	0.623724
$167$	−0.383938	−0.0297100	−0.0148550	−	0.999890i	$-0.504729\pi$
$167$	−0.383938	−0.0297100	−0.0148550	+	0.999890i	$0.504729\pi$
$168$	−17.3551	−1.33898
$169$	31.0738	2.39029
$170$	−1.03690	−0.0795268
$171$	1.16342	0.0889689
$172$	0.747489	0.0569955
$173$	7.59080	0.577118	0.288559	−	0.957462i	$-0.406824\pi$
$173$	7.59080	0.577118	0.288559	+	0.957462i	$0.406824\pi$
$174$	−1.41817	−0.107511
$175$	23.5260	1.77840
$176$	−2.31685	−0.174639
$177$	−16.8688	−1.26794
$178$	5.67642	0.425466
$179$	23.7154	1.77257	0.886287	−	0.463136i	$-0.153276\pi$
$179$	23.7154	1.77257	0.886287	+	0.463136i	$0.153276\pi$
$180$	0.108099	0.00805720
$181$	0.0185149	0.00137620	0.000688100	−	1.00000i	$-0.499781\pi$
$181$	0.0185149	0.00137620	0.000688100		1.00000i	$0.499781\pi$
$182$	−17.4779	−1.29555
$183$	−1.77928	−0.131528
$184$	14.6224	1.07798
$185$	3.40471	0.250319
$186$	1.09420	0.0802303
$187$	−4.99283	−0.365112
$188$	16.0601	1.17130
$189$	−24.4419	−1.77789
$190$	−1.45707	−0.105707
$191$	−6.18153	−0.447280	−0.223640	−	0.974672i	$-0.571794\pi$
$191$	−6.18153	−0.447280	−0.223640	+	0.974672i	$0.571794\pi$
$192$	3.13861	0.226510
$193$	−7.73036	−0.556443	−0.278222	−	0.960517i	$-0.589745\pi$
$193$	−7.73036	−0.556443	−0.278222	+	0.960517i	$0.589745\pi$
$194$	4.96654	0.356577
$195$	4.51638	0.323425
$196$	−28.1192	−2.00851
$197$	0.334691	0.0238457	0.0119229	−	0.999929i	$-0.496205\pi$
$197$	0.334691	0.0238457	0.0119229	+	0.999929i	$0.496205\pi$
$198$	−0.0900705	−0.00640103
$199$	22.7898	1.61553	0.807763	−	0.589507i	$-0.200678\pi$
$199$	22.7898	1.61553	0.807763	+	0.589507i	$0.200678\pi$
$200$	9.76792	0.690696
$201$	−11.5450	−0.814319
$202$	2.69441	0.189578
$203$	−7.11239	−0.499192
$204$	15.1463	1.06045
$205$	−1.05418	−0.0736273
$206$	−6.08830	−0.424192
$207$	−1.20489	−0.0837459
$208$	15.3811	1.06649
$209$	−7.01598	−0.485306
$210$	−1.79102	−0.123592
$211$	3.08674	0.212500	0.106250	−	0.994339i	$-0.466116\pi$
$211$	3.08674	0.212500	0.106250	+	0.994339i	$0.466116\pi$
$212$	−14.7906	−1.01582
$213$	5.90104	0.404333
$214$	6.18941	0.423099
$215$	0.167628	0.0114321
$216$	−10.1482	−0.690498
$217$	5.48759	0.372522
$218$	4.78535	0.324105
$219$	−10.8688	−0.734444
$220$	−0.651888	−0.0439503
$221$	33.1464	2.22967
$222$	8.60601	0.577598
$223$	−13.6000	−0.910723	−0.455361	−	0.890307i	$-0.650490\pi$
$223$	−13.6000	−0.910723	−0.455361	+	0.890307i	$0.650490\pi$
$224$	−25.6076	−1.71098
$225$	−0.804879	−0.0536586
$226$	−3.04557	−0.202588
$227$	0.745926	0.0495089	0.0247544	−	0.999694i	$-0.492120\pi$
$227$	0.745926	0.0495089	0.0247544	+	0.999694i	$0.492120\pi$
$228$	21.2837	1.40955
$229$	14.2486	0.941574	0.470787	−	0.882247i	$-0.343970\pi$
$229$	14.2486	0.941574	0.470787	+	0.882247i	$0.343970\pi$
$230$	1.50901	0.0995012
$231$	−8.62399	−0.567417
$232$	−2.95304	−0.193877
$233$	−24.4434	−1.60134	−0.800670	−	0.599105i	$-0.795523\pi$
$233$	−24.4434	−1.60134	−0.800670	+	0.599105i	$0.795523\pi$
$234$	0.597961	0.0390899
$235$	3.60154	0.234939
$236$	−16.1643	−1.05221
$237$	4.55335	0.295772
$238$	−13.1446	−0.852036
$239$	12.1455	0.785629	0.392814	−	0.919618i	$-0.371501\pi$
$239$	12.1455	0.785629	0.392814	+	0.919618i	$0.371501\pi$
$240$	1.57615	0.101740
$241$	0.928093	0.0597837	0.0298918	−	0.999553i	$-0.490484\pi$
$241$	0.928093	0.0597837	0.0298918	+	0.999553i	$0.490484\pi$
$242$	0.543169	0.0349162
$243$	1.72136	0.110425
$244$	−1.70497	−0.109149
$245$	−6.30585	−0.402866
$246$	−2.66463	−0.169891
$247$	46.5778	2.96367
$248$	2.27843	0.144681
$249$	−26.3242	−1.66823
$250$	2.04642	0.129427
$251$	−2.41807	−0.152627	−0.0763136	−	0.997084i	$-0.524315\pi$
$251$	−2.41807	−0.152627	−0.0763136	+	0.997084i	$0.524315\pi$
$252$	1.37034	0.0863234
$253$	7.26609	0.456815
$254$	5.41497	0.339765
$255$	3.39662	0.212704
$256$	−2.73190	−0.170744
$257$	−6.27947	−0.391703	−0.195851	−	0.980634i	$-0.562747\pi$
$257$	−6.27947	−0.391703	−0.195851	+	0.980634i	$0.562747\pi$
$258$	0.423708	0.0263789
$259$	43.1607	2.68188
$260$	4.32776	0.268396
$261$	0.243332	0.0150618
$262$	−5.93335	−0.366563
$263$	−3.85746	−0.237861	−0.118931	−	0.992903i	$-0.537947\pi$
$263$	−3.85746	−0.237861	−0.118931	+	0.992903i	$0.537947\pi$
$264$	−3.58066	−0.220374
$265$	−3.31685	−0.203752
$266$	−18.4709	−1.13252
$267$	−18.5944	−1.13796
$268$	−11.0628	−0.675768
$269$	−3.12253	−0.190384	−0.0951921	−	0.995459i	$-0.530347\pi$
$269$	−3.12253	−0.190384	−0.0951921	+	0.995459i	$0.530347\pi$
$270$	−1.04728	−0.0637353
$271$	14.4266	0.876355	0.438177	−	0.898889i	$-0.355624\pi$
$271$	14.4266	0.876355	0.438177	+	0.898889i	$0.355624\pi$
$272$	11.5676	0.701391
$273$	57.2530	3.46511
$274$	−11.1177	−0.671643
$275$	4.85381	0.292696
$276$	−22.0425	−1.32680
$277$	5.31864	0.319566	0.159783	−	0.987152i	$-0.448921\pi$
$277$	5.31864	0.319566	0.159783	+	0.987152i	$0.448921\pi$
$278$	1.99581	0.119701
$279$	−0.187743	−0.0112399
$280$	−3.72941	−0.222875
$281$	−17.4272	−1.03962	−0.519809	−	0.854282i	$-0.673997\pi$
$281$	−17.4272	−1.03962	−0.519809	+	0.854282i	$0.673997\pi$
$282$	9.10353	0.542107
$283$	0.559072	0.0332334	0.0166167	−	0.999862i	$-0.494711\pi$
$283$	0.559072	0.0332334	0.0166167	+	0.999862i	$0.494711\pi$
$284$	5.65459	0.335538
$285$	4.77297	0.282726
$286$	−3.60599	−0.213227
$287$	−13.3636	−0.788830
$288$	0.876096	0.0516245
$289$	7.92833	0.466372
$290$	−0.304749	−0.0178955
$291$	−16.2691	−0.953709
$292$	−10.4149	−0.609483
$293$	−1.57569	−0.0920530	−0.0460265	−	0.998940i	$-0.514656\pi$
$293$	−1.57569	−0.0920530	−0.0460265	+	0.998940i	$0.514656\pi$
$294$	−15.9392	−0.929590
$295$	−3.62492	−0.211051
$296$	17.9202	1.04159
$297$	−5.04278	−0.292612
$298$	−8.83600	−0.511856
$299$	−48.2382	−2.78969
$300$	−14.7246	−0.850123
$301$	2.12497	0.122481
$302$	4.75967	0.273888
$303$	−8.82617	−0.507050
$304$	16.2550	0.932287
$305$	−0.382346	−0.0218931
$306$	0.449707	0.0257080
$307$	−19.7291	−1.12600	−0.563001	−	0.826456i	$-0.690353\pi$
$307$	−19.7291	−1.12600	−0.563001	+	0.826456i	$0.690353\pi$
$308$	−8.26382	−0.470875
$309$	19.9436	1.13455
$310$	0.235130	0.0133545
$311$	−8.10368	−0.459518	−0.229759	−	0.973248i	$-0.573794\pi$
$311$	−8.10368	−0.459518	−0.229759	+	0.973248i	$0.573794\pi$
$312$	23.7713	1.34578
$313$	−3.29020	−0.185973	−0.0929865	−	0.995667i	$-0.529641\pi$
$313$	−3.29020	−0.185973	−0.0929865	+	0.995667i	$0.529641\pi$
$314$	5.25143	0.296355
$315$	0.307305	0.0173147
$316$	4.36319	0.245448
$317$	−9.56197	−0.537054	−0.268527	−	0.963272i	$-0.586537\pi$
$317$	−9.56197	−0.537054	−0.268527	+	0.963272i	$0.586537\pi$
$318$	−8.38392	−0.470147
$319$	−1.46741	−0.0821590
$320$	0.674452	0.0377030
$321$	−20.2749	−1.13163
$322$	19.1294	1.06604
$323$	35.0296	1.94910
$324$	16.1460	0.897000
$325$	−32.2235	−1.78744
$326$	4.96257	0.274851
$327$	−15.6755	−0.866858
$328$	−5.54854	−0.306367
$329$	45.6558	2.51709
$330$	−0.369517	−0.0203413
$331$	−31.5705	−1.73527	−0.867636	−	0.497200i	$-0.834361\pi$
$331$	−31.5705	−1.73527	−0.867636	+	0.497200i	$0.834361\pi$
$332$	−25.2248	−1.38439
$333$	−1.47663	−0.0809188
$334$	−0.208543	−0.0114110
$335$	−2.48088	−0.135545
$336$	19.9805	1.09002
$337$	2.48834	0.135548	0.0677742	−	0.997701i	$-0.478410\pi$
$337$	2.48834	0.135548	0.0677742	+	0.997701i	$0.478410\pi$
$338$	16.8783	0.918060
$339$	9.97648	0.541848
$340$	3.25476	0.176514
$341$	1.13218	0.0613112
$342$	0.631933	0.0341710
$343$	−46.0094	−2.48427
$344$	0.882283	0.0475695
$345$	−4.94312	−0.266128
$346$	4.12309	0.221659
$347$	0.0808406	0.00433975	0.00216987	−	0.999998i	$-0.499309\pi$
$347$	0.0808406	0.00433975	0.00216987	+	0.999998i	$0.499309\pi$
$348$	4.45154	0.238628
$349$	24.9294	1.33444	0.667219	−	0.744862i	$-0.267485\pi$
$349$	24.9294	1.33444	0.667219	+	0.744862i	$0.267485\pi$
$350$	12.7786	0.683044
$351$	33.4781	1.78693
$352$	−5.28329	−0.281600
$353$	24.0803	1.28167	0.640833	−	0.767680i	$-0.278589\pi$
$353$	24.0803	1.28167	0.640833	+	0.767680i	$0.278589\pi$
$354$	−9.16263	−0.486988
$355$	1.26807	0.0673019
$356$	−17.8179	−0.944345
$357$	43.0581	2.27888
$358$	12.8815	0.680808
$359$	7.77746	0.410478	0.205239	−	0.978712i	$-0.434203\pi$
$359$	7.77746	0.410478	0.205239	+	0.978712i	$0.434203\pi$
$360$	0.127592	0.00672469
$361$	30.2240	1.59074
$362$	0.0100567	0.000528568 0
$363$	−1.77928	−0.0933878
$364$	54.8619	2.87555
$365$	−2.33557	−0.122250
$366$	−0.966447	−0.0505170
$367$	−0.661468	−0.0345283	−0.0172642	−	0.999851i	$-0.505496\pi$
$367$	−0.661468	−0.0345283	−0.0172642	+	0.999851i	$0.505496\pi$
$368$	−16.8344	−0.877556
$369$	0.457201	0.0238009
$370$	1.84933	0.0961423
$371$	−42.0469	−2.18297
$372$	−3.43460	−0.178076
$373$	16.7512	0.867346	0.433673	−	0.901070i	$-0.357217\pi$
$373$	16.7512	0.867346	0.433673	+	0.901070i	$0.357217\pi$
$374$	−2.71195	−0.140232
$375$	−6.70354	−0.346169
$376$	18.9562	0.977590
$377$	9.74184	0.501730
$378$	−13.2761	−0.682848
$379$	14.6827	0.754200	0.377100	−	0.926173i	$-0.376921\pi$
$379$	14.6827	0.754200	0.377100	+	0.926173i	$0.376921\pi$
$380$	4.57363	0.234622
$381$	−17.7380	−0.908745
$382$	−3.35761	−0.171790
$383$	−19.4800	−0.995384	−0.497692	−	0.867354i	$-0.665819\pi$
$383$	−19.4800	−0.995384	−0.497692	+	0.867354i	$0.665819\pi$
$384$	20.5056	1.04642
$385$	−1.85320	−0.0944476
$386$	−4.19889	−0.213718
$387$	−0.0727004	−0.00369557
$388$	−15.5896	−0.791443
$389$	−2.50398	−0.126957	−0.0634784	−	0.997983i	$-0.520219\pi$
$389$	−2.50398	−0.126957	−0.0634784	+	0.997983i	$0.520219\pi$
$390$	2.45316	0.124220
$391$	−36.2783	−1.83467
$392$	−33.1899	−1.67634
$393$	19.4361	0.980420
$394$	0.181794	0.00915862
$395$	0.978463	0.0492318
$396$	0.282725	0.0142075
$397$	−20.8712	−1.04749	−0.523747	−	0.851874i	$-0.675466\pi$
$397$	−20.8712	−1.04749	−0.523747	+	0.851874i	$0.675466\pi$
$398$	12.3787	0.620489
$399$	60.5058	3.02908
$400$	−11.2456	−0.562278
$401$	16.2136	0.809669	0.404834	−	0.914390i	$-0.367329\pi$
$401$	16.2136	0.809669	0.404834	+	0.914390i	$0.367329\pi$
$402$	−6.27086	−0.312762
$403$	−7.51635	−0.374416
$404$	−8.45756	−0.420779
$405$	3.62081	0.179919
$406$	−3.86323	−0.191729
$407$	8.90479	0.441394
$408$	17.8776	0.885073
$409$	26.6015	1.31536	0.657680	−	0.753298i	$-0.271538\pi$
$409$	26.6015	1.31536	0.657680	+	0.753298i	$0.271538\pi$
$410$	−0.572599	−0.0282787
$411$	36.4185	1.79639
$412$	19.1107	0.941518
$413$	−45.9523	−2.26116
$414$	−0.654460	−0.0321650
$415$	−5.65676	−0.277680
$416$	35.0747	1.71968
$417$	−6.53776	−0.320155
$418$	−3.81086	−0.186395
$419$	2.09758	0.102474	0.0512368	−	0.998687i	$-0.483684\pi$
$419$	2.09758	0.102474	0.0512368	+	0.998687i	$0.483684\pi$
$420$	5.62187	0.274319
$421$	−1.48575	−0.0724108	−0.0362054	−	0.999344i	$-0.511527\pi$
$421$	−1.48575	−0.0724108	−0.0362054	+	0.999344i	$0.511527\pi$
$422$	1.67662	0.0816168
$423$	−1.56199	−0.0759467
$424$	−17.4578	−0.847823
$425$	−24.2342	−1.17553
$426$	3.20526	0.155295
$427$	−4.84691	−0.234558
$428$	−19.4281	−0.939093
$429$	11.8123	0.570302
$430$	0.0910501	0.00439082
$431$	34.7087	1.67186	0.835928	−	0.548838i	$-0.184930\pi$
$431$	34.7087	1.67186	0.835928	+	0.548838i	$0.184930\pi$
$432$	11.6834	0.562116
$433$	31.4962	1.51361	0.756806	−	0.653639i	$-0.226759\pi$
$433$	31.4962	1.51361	0.756806	+	0.653639i	$0.226759\pi$
$434$	2.98069	0.143078
$435$	0.998276	0.0478637
$436$	−15.0209	−0.719369
$437$	−50.9788	−2.43865
$438$	−5.90358	−0.282084
$439$	35.4239	1.69069	0.845344	−	0.534222i	$-0.179395\pi$
$439$	35.4239	1.69069	0.845344	+	0.534222i	$0.179395\pi$
$440$	−0.769442	−0.0366817
$441$	2.73486	0.130231
$442$	18.0041	0.856368
$443$	8.39721	0.398964	0.199482	−	0.979902i	$-0.436074\pi$
$443$	8.39721	0.398964	0.199482	+	0.979902i	$0.436074\pi$
$444$	−27.0137	−1.28201
$445$	−3.99573	−0.189416
$446$	−7.38709	−0.349789
$447$	28.9444	1.36902
$448$	8.54986	0.403943
$449$	−2.16357	−0.102105	−0.0510525	−	0.998696i	$-0.516258\pi$
$449$	−2.16357	−0.102105	−0.0510525	+	0.998696i	$0.516258\pi$
$450$	−0.437185	−0.0206091
$451$	−2.75714	−0.129829
$452$	9.55982	0.449656
$453$	−15.5914	−0.732548
$454$	0.405164	0.0190153
$455$	12.3030	0.576774
$456$	25.1218	1.17644
$457$	10.3573	0.484496	0.242248	−	0.970214i	$-0.422115\pi$
$457$	10.3573	0.484496	0.242248	+	0.970214i	$0.422115\pi$
$458$	7.73940	0.361638
$459$	25.1777	1.17520
$460$	−4.73667	−0.220849
$461$	−3.38383	−0.157601	−0.0788004	−	0.996890i	$-0.525109\pi$
$461$	−3.38383	−0.157601	−0.0788004	+	0.996890i	$0.525109\pi$
$462$	−4.68428	−0.217933
$463$	−11.3541	−0.527668	−0.263834	−	0.964568i	$-0.584987\pi$
$463$	−11.3541	−0.527668	−0.263834	+	0.964568i	$0.584987\pi$
$464$	3.39976	0.157830
$465$	−0.770224	−0.0357183
$466$	−13.2769	−0.615040
$467$	−24.1374	−1.11694	−0.558472	−	0.829523i	$-0.688612\pi$
$467$	−24.1374	−1.11694	−0.558472	+	0.829523i	$0.688612\pi$
$468$	−1.87696	−0.0867623
$469$	−31.4495	−1.45220
$470$	1.95624	0.0902348
$471$	−17.2023	−0.792639
$472$	−19.0793	−0.878194
$473$	0.438418	0.0201585
$474$	2.47324	0.113600
$475$	−34.0543	−1.56252
$476$	41.2598	1.89114
$477$	1.43852	0.0658654
$478$	6.59707	0.301743
$479$	2.16493	0.0989181	0.0494591	−	0.998776i	$-0.484250\pi$
$479$	2.16493	0.0989181	0.0494591	+	0.998776i	$0.484250\pi$
$480$	3.59422	0.164053
$481$	−59.1172	−2.69551
$482$	0.504111	0.0229616
$483$	−62.6627	−2.85125
$484$	−1.70497	−0.0774985
$485$	−3.49603	−0.158747
$486$	0.934987	0.0424119
$487$	−42.2450	−1.91430	−0.957151	−	0.289590i	$-0.906481\pi$
$487$	−42.2450	−1.91430	−0.957151	+	0.289590i	$0.906481\pi$
$488$	−2.01242	−0.0910981
$489$	−16.2560	−0.735124
$490$	−3.42514	−0.154732
$491$	6.16680	0.278304	0.139152	−	0.990271i	$-0.455562\pi$
$491$	6.16680	0.278304	0.139152	+	0.990271i	$0.455562\pi$
$492$	8.36409	0.377082
$493$	7.32651	0.329969
$494$	25.2996	1.13828
$495$	0.0634022	0.00284972
$496$	−2.62310	−0.117781
$497$	16.0750	0.721061
$498$	−14.2985	−0.640730
$499$	31.3774	1.40465	0.702323	−	0.711859i	$-0.252146\pi$
$499$	31.3774	1.40465	0.702323	+	0.711859i	$0.252146\pi$
$500$	−6.42358	−0.287271
$501$	0.683133	0.0305201
$502$	−1.31342	−0.0586208
$503$	−0.489122	−0.0218089	−0.0109044	−	0.999941i	$-0.503471\pi$
$503$	−0.489122	−0.0218089	−0.0109044	+	0.999941i	$0.503471\pi$
$504$	1.61745	0.0720471
$505$	−1.89664	−0.0843995
$506$	3.94671	0.175453
$507$	−55.2889	−2.45547
$508$	−16.9972	−0.754129
$509$	−13.6789	−0.606306	−0.303153	−	0.952942i	$-0.598039\pi$
$509$	−13.6789	−0.606306	−0.303153	+	0.952942i	$0.598039\pi$
$510$	1.84494	0.0816952
$511$	−29.6075	−1.30976
$512$	21.5655	0.953071
$513$	35.3801	1.56207
$514$	−3.41081	−0.150445
$515$	4.28566	0.188849
$516$	−1.32999	−0.0585495
$517$	9.41958	0.414273
$518$	23.4436	1.03005
$519$	−13.5061	−0.592853
$520$	5.10818	0.224008
$521$	21.1576	0.926933	0.463466	−	0.886114i	$-0.346605\pi$
$521$	21.1576	0.926933	0.463466	+	0.886114i	$0.346605\pi$
$522$	0.132170	0.00578493
$523$	27.5811	1.20604	0.603019	−	0.797727i	$-0.293964\pi$
$523$	27.5811	1.20604	0.603019	+	0.797727i	$0.293964\pi$
$524$	18.6244	0.813609
$525$	−41.8592	−1.82689
$526$	−2.09525	−0.0913573
$527$	−5.65280	−0.246240
$528$	4.12232	0.179401
$529$	29.7961	1.29548
$530$	−1.80161	−0.0782569
$531$	1.57213	0.0682248
$532$	57.9788	2.51370
$533$	18.3042	0.792841
$534$	−10.0999	−0.437066
$535$	−4.35683	−0.188362
$536$	−13.0578	−0.564009
$537$	−42.1963	−1.82091
$538$	−1.69606	−0.0731224
$539$	−16.4925	−0.710383
$540$	3.28733	0.141464
$541$	18.8555	0.810662	0.405331	−	0.914170i	$-0.367156\pi$
$541$	18.8555	0.810662	0.405331	+	0.914170i	$0.367156\pi$
$542$	7.83609	0.336589
$543$	−0.0329431	−0.00141372
$544$	26.3785	1.13097
$545$	−3.36849	−0.144290
$546$	31.0981	1.33087
$547$	−11.5604	−0.494289	−0.247144	−	0.968979i	$-0.579492\pi$
$547$	−11.5604	−0.494289	−0.247144	+	0.968979i	$0.579492\pi$
$548$	34.8976	1.49075
$549$	0.165824	0.00707720
$550$	2.63644	0.112418
$551$	10.2953	0.438595
$552$	−26.0174	−1.10737
$553$	12.4037	0.527460
$554$	2.88892	0.122738
$555$	−6.05792	−0.257145
$556$	−6.26472	−0.265683
$557$	1.65640	0.0701838	0.0350919	−	0.999384i	$-0.488828\pi$
$557$	1.65640	0.0701838	0.0350919	+	0.999384i	$0.488828\pi$
$558$	−0.101976	−0.00431700
$559$	−2.91058	−0.123104
$560$	4.29358	0.181437
$561$	8.88362	0.375067
$562$	−9.46590	−0.399295
$563$	8.71228	0.367179	0.183589	−	0.983003i	$-0.441228\pi$
$563$	8.71228	0.367179	0.183589	+	0.983003i	$0.441228\pi$
$564$	−28.5753	−1.20324
$565$	2.14383	0.0901916
$566$	0.303670	0.0127642
$567$	45.9001	1.92762
$568$	6.67428	0.280047
$569$	−32.6564	−1.36903	−0.684514	−	0.729000i	$-0.739985\pi$
$569$	−32.6564	−1.36903	−0.684514	+	0.729000i	$0.739985\pi$
$570$	2.59253	0.108589
$571$	−27.7851	−1.16277	−0.581385	−	0.813628i	$-0.697489\pi$
$571$	−27.7851	−1.16277	−0.581385	+	0.813628i	$0.697489\pi$
$572$	11.3190	0.473269
$573$	10.9986	0.459475
$574$	−7.25870	−0.302972
$575$	35.2682	1.47079
$576$	−0.292511	−0.0121880
$577$	18.0541	0.751600	0.375800	−	0.926701i	$-0.377368\pi$
$577$	18.0541	0.751600	0.375800	+	0.926701i	$0.377368\pi$
$578$	4.30642	0.179123
$579$	13.7544	0.571615
$580$	0.956584	0.0397200
$581$	−71.7094	−2.97501
$582$	−8.83685	−0.366299
$583$	−8.67499	−0.359281
$584$	−12.2930	−0.508686
$585$	−0.420915	−0.0174027
$586$	−0.855868	−0.0353556
$587$	30.6820	1.26638	0.633191	−	0.773996i	$-0.281745\pi$
$587$	30.6820	1.26638	0.633191	+	0.773996i	$0.281745\pi$
$588$	50.0318	2.06328
$589$	−7.94338	−0.327301
$590$	−1.96894	−0.0810602
$591$	−0.595507	−0.0244959
$592$	−20.6311	−0.847932
$593$	−25.9352	−1.06503	−0.532515	−	0.846420i	$-0.678753\pi$
$593$	−25.9352	−1.06503	−0.532515	+	0.846420i	$0.678753\pi$
$594$	−2.73908	−0.112386
$595$	9.25269	0.379323
$596$	27.7356	1.13609
$597$	−40.5494	−1.65958
$598$	−26.2015	−1.07146
$599$	0.490442	0.0200389	0.0100195	−	0.999950i	$-0.496811\pi$
$599$	0.490442	0.0200389	0.0100195	+	0.999950i	$0.496811\pi$
$600$	−17.3798	−0.709529
$601$	32.3923	1.32131	0.660654	−	0.750690i	$-0.270279\pi$
$601$	32.3923	1.32131	0.660654	+	0.750690i	$0.270279\pi$
$602$	1.15422	0.0470425
$603$	1.07596	0.0438166
$604$	−14.9403	−0.607910
$605$	−0.382346	−0.0155446
$606$	−4.79410	−0.194747
$607$	8.19359	0.332567	0.166284	−	0.986078i	$-0.446823\pi$
$607$	8.19359	0.332567	0.166284	+	0.986078i	$0.446823\pi$
$608$	37.0675	1.50328
$609$	12.6549	0.512802
$610$	−0.207678	−0.00840865
$611$	−62.5348	−2.52989
$612$	−1.41160	−0.0570604
$613$	−12.4348	−0.502236	−0.251118	−	0.967957i	$-0.580798\pi$
$613$	−12.4348	−0.502236	−0.251118	+	0.967957i	$0.580798\pi$
$614$	−10.7163	−0.432473
$615$	1.87568	0.0756348
$616$	−9.75403	−0.393001
$617$	3.32280	0.133771	0.0668854	−	0.997761i	$-0.478694\pi$
$617$	3.32280	0.133771	0.0668854	+	0.997761i	$0.478694\pi$
$618$	10.8328	0.435758
$619$	8.67691	0.348755	0.174377	−	0.984679i	$-0.444209\pi$
$619$	8.67691	0.348755	0.174377	+	0.984679i	$0.444209\pi$
$620$	−0.738056	−0.0296411
$621$	−36.6413	−1.47036
$622$	−4.40167	−0.176491
$623$	−50.6529	−2.02937
$624$	−27.3673	−1.09557
$625$	22.8285	0.913142
$626$	−1.78713	−0.0714282
$627$	12.4834	0.498538
$628$	−16.4839	−0.657778
$629$	−44.4601	−1.77274
$630$	0.166918	0.00665018
$631$	−11.6248	−0.462777	−0.231388	−	0.972861i	$-0.574327\pi$
$631$	−11.6248	−0.462777	−0.231388	+	0.972861i	$0.574327\pi$
$632$	5.15000	0.204856
$633$	−5.49217	−0.218294
$634$	−5.19377	−0.206271
$635$	−3.81169	−0.151262
$636$	26.3165	1.04352
$637$	109.491	4.33818
$638$	−0.797050	−0.0315555
$639$	−0.549962	−0.0217562
$640$	4.40643	0.174179
$641$	−49.6826	−1.96235	−0.981173	−	0.193131i	$-0.938136\pi$
$641$	−49.6826	−1.96235	−0.981173	+	0.193131i	$0.938136\pi$
$642$	−11.0127	−0.434636
$643$	−11.9840	−0.472604	−0.236302	−	0.971680i	$-0.575935\pi$
$643$	−11.9840	−0.472604	−0.236302	+	0.971680i	$0.575935\pi$
$644$	−60.0457	−2.36613
$645$	−0.298256	−0.0117438
$646$	19.0270	0.748607
$647$	−8.19183	−0.322054	−0.161027	−	0.986950i	$-0.551481\pi$
$647$	−8.19183	−0.322054	−0.161027	+	0.986950i	$0.551481\pi$
$648$	19.0576	0.748653
$649$	−9.48074	−0.372151
$650$	−17.5028	−0.686517
$651$	−9.76394	−0.382679
$652$	−15.5771	−0.610048
$653$	43.5568	1.70451	0.852255	−	0.523127i	$-0.175235\pi$
$653$	43.5568	1.70451	0.852255	+	0.523127i	$0.175235\pi$
$654$	−8.51445	−0.332942
$655$	4.17659	0.163193
$656$	6.38789	0.249405
$657$	1.01294	0.0395187
$658$	24.7988	0.966759
$659$	−41.1666	−1.60362	−0.801811	−	0.597578i	$-0.796130\pi$
$659$	−41.1666	−1.60362	−0.801811	+	0.597578i	$0.796130\pi$
$660$	1.15989	0.0451486
$661$	−10.8706	−0.422819	−0.211409	−	0.977398i	$-0.567805\pi$
$661$	−10.8706	−0.422819	−0.211409	+	0.977398i	$0.567805\pi$
$662$	−17.1481	−0.666480
$663$	−58.9767	−2.29046
$664$	−29.7736	−1.15544
$665$	13.0020	0.504196
$666$	−0.802059	−0.0310792
$667$	−10.6623	−0.412846
$668$	0.654603	0.0253273
$669$	24.1981	0.935554
$670$	−1.34754	−0.0520599
$671$	−1.00000	−0.0386046
$672$	45.5630	1.75763
$673$	0.548928	0.0211596	0.0105798	−	0.999944i	$-0.496632\pi$
$673$	0.548928	0.0211596	0.0105798	+	0.999944i	$0.496632\pi$
$674$	1.35159	0.0520612
$675$	−24.4767	−0.942109
$676$	−52.9798	−2.03769
$677$	−44.4999	−1.71027	−0.855135	−	0.518405i	$-0.826526\pi$
$677$	−44.4999	−1.71027	−0.855135	+	0.518405i	$0.826526\pi$
$678$	5.41891	0.208112
$679$	−44.3184	−1.70078
$680$	3.84169	0.147322
$681$	−1.32721	−0.0508588
$682$	0.614967	0.0235483
$683$	17.8878	0.684456	0.342228	−	0.939617i	$-0.388819\pi$
$683$	17.8878	0.684456	0.342228	+	0.939617i	$0.388819\pi$
$684$	−1.98359	−0.0758446
$685$	7.82593	0.299013
$686$	−24.9908	−0.954155
$687$	−25.3522	−0.967247
$688$	−1.01575	−0.0387251
$689$	57.5916	2.19407
$690$	−2.68495	−0.102214
$691$	20.7703	0.790140	0.395070	−	0.918651i	$-0.370720\pi$
$691$	20.7703	0.790140	0.395070	+	0.918651i	$0.370720\pi$
$692$	−12.9421	−0.491984
$693$	0.803734	0.0305313
$694$	0.0439101	0.00166680
$695$	−1.40489	−0.0532905
$696$	5.25428	0.199163
$697$	13.7659	0.521422
$698$	13.5409	0.512529
$699$	43.4916	1.64500
$700$	−40.1110	−1.51605
$701$	−44.6060	−1.68474	−0.842372	−	0.538896i	$-0.818842\pi$
$701$	−44.6060	−1.68474	−0.842372	+	0.538896i	$0.818842\pi$
$702$	18.1842	0.686320
$703$	−62.4759	−2.35632
$704$	1.76398	0.0664826
$705$	−6.40813	−0.241344
$706$	13.0797	0.492260
$707$	−24.0433	−0.904240
$708$	28.7608	1.08090
$709$	28.2143	1.05961	0.529806	−	0.848119i	$-0.322265\pi$
$709$	28.2143	1.05961	0.529806	+	0.848119i	$0.322265\pi$
$710$	0.688774	0.0258492
$711$	−0.424361	−0.0159148
$712$	−21.0310	−0.788168
$713$	8.22655	0.308087
$714$	23.3878	0.875267
$715$	2.53832	0.0949279
$716$	−40.4341	−1.51109
$717$	−21.6102	−0.807050
$718$	4.22447	0.157656
$719$	46.9913	1.75248	0.876241	−	0.481874i	$-0.160044\pi$
$719$	46.9913	1.75248	0.876241	+	0.481874i	$0.160044\pi$
$720$	−0.146893	−0.00547439
$721$	54.3282	2.02329
$722$	16.4168	0.610968
$723$	−1.65133	−0.0614137
$724$	−0.0315672	−0.00117319
$725$	−7.12252	−0.264524
$726$	−0.966447	−0.0358682
$727$	32.3241	1.19883	0.599417	−	0.800437i	$-0.295399\pi$
$727$	32.3241	1.19883	0.599417	+	0.800437i	$0.295399\pi$
$728$	64.7551	2.39999
$729$	25.3472	0.938784
$730$	−1.26861	−0.0469534
$731$	−2.18895	−0.0809612
$732$	3.03361	0.112125
$733$	36.5957	1.35169	0.675846	−	0.737043i	$-0.263779\pi$
$733$	36.5957	1.35169	0.675846	+	0.737043i	$0.263779\pi$
$734$	−0.359289	−0.0132616
$735$	11.2198	0.413850
$736$	−38.3888	−1.41503
$737$	−6.48857	−0.239010
$738$	0.248337	0.00914142
$739$	−39.6416	−1.45824	−0.729120	−	0.684386i	$-0.760070\pi$
$739$	−39.6416	−1.45824	−0.729120	+	0.684386i	$0.760070\pi$
$740$	−5.80492	−0.213393
$741$	−82.8748	−3.04448
$742$	−22.8386	−0.838430
$743$	−2.00195	−0.0734442	−0.0367221	−	0.999326i	$-0.511692\pi$
$743$	−2.00195	−0.0734442	−0.0367221	+	0.999326i	$0.511692\pi$
$744$	−4.05396	−0.148625
$745$	6.21981	0.227876
$746$	9.09874	0.333129
$747$	2.45335	0.0897633
$748$	8.51261	0.311252
$749$	−55.2305	−2.01808
$750$	−3.64115	−0.132956
$751$	35.5941	1.29885	0.649423	−	0.760427i	$-0.275010\pi$
$751$	35.5941	1.29885	0.649423	+	0.760427i	$0.275010\pi$
$752$	−21.8238	−0.795830
$753$	4.30242	0.156789
$754$	5.29146	0.192704
$755$	−3.35041	−0.121934
$756$	41.6726	1.51562
$757$	−34.5632	−1.25622	−0.628110	−	0.778124i	$-0.716171\pi$
$757$	−34.5632	−1.25622	−0.628110	+	0.778124i	$0.716171\pi$
$758$	7.97519	0.289672
$759$	−12.9284	−0.469271
$760$	5.39839	0.195820
$761$	23.6216	0.856282	0.428141	−	0.903712i	$-0.359169\pi$
$761$	23.6216	0.856282	0.428141	+	0.903712i	$0.359169\pi$
$762$	−9.63473	−0.349029
$763$	−42.7015	−1.54590
$764$	10.5393	0.381299
$765$	−0.316556	−0.0114451
$766$	−10.5810	−0.382305
$767$	62.9408	2.27266
$768$	4.86080	0.175399
$769$	43.1853	1.55730	0.778651	−	0.627457i	$-0.215904\pi$
$769$	43.1853	1.55730	0.778651	+	0.627457i	$0.215904\pi$
$770$	−1.00660	−0.0362753
$771$	11.1729	0.402383
$772$	13.1800	0.474359
$773$	15.2209	0.547457	0.273729	−	0.961807i	$-0.411743\pi$
$773$	15.2209	0.547457	0.273729	+	0.961807i	$0.411743\pi$
$774$	−0.0394886	−0.00141939
$775$	5.49541	0.197401
$776$	−18.4009	−0.660553
$777$	−76.7948	−2.75500
$778$	−1.36008	−0.0487614
$779$	19.3441	0.693073
$780$	−7.70028	−0.275714
$781$	3.31654	0.118675
$782$	−19.7053	−0.704659
$783$	7.39981	0.264448
$784$	38.2107	1.36467
$785$	−3.69657	−0.131936
$786$	10.5571	0.376558
$787$	−42.0410	−1.49860	−0.749300	−	0.662231i	$-0.769610\pi$
$787$	−42.0410	−1.49860	−0.749300	+	0.662231i	$0.769610\pi$
$788$	−0.570637	−0.0203281
$789$	6.86349	0.244347
$790$	0.531470	0.0189089
$791$	27.1768	0.966296
$792$	0.333708	0.0118578
$793$	6.63881	0.235751
$794$	−11.3366	−0.402320
$795$	5.90159	0.209308
$796$	−38.8559	−1.37721
$797$	19.2573	0.682128	0.341064	−	0.940040i	$-0.389213\pi$
$797$	19.2573	0.682128	0.341064	+	0.940040i	$0.389213\pi$
$798$	32.8648	1.16340
$799$	−47.0303	−1.66381
$800$	−25.6441	−0.906655
$801$	1.73296	0.0612310
$802$	8.80672	0.310976
$803$	−6.10854	−0.215566
$804$	19.6838	0.694194
$805$	−13.4655	−0.474596
$806$	−4.08265	−0.143805
$807$	5.55585	0.195575
$808$	−9.98270	−0.351190
$809$	−38.0646	−1.33828	−0.669139	−	0.743137i	$-0.733337\pi$
$809$	−38.0646	−1.33828	−0.669139	+	0.743137i	$0.733337\pi$
$810$	1.96671	0.0691031
$811$	45.5995	1.60121	0.800607	−	0.599190i	$-0.204511\pi$
$811$	45.5995	1.60121	0.800607	+	0.599190i	$0.204511\pi$
$812$	12.1264	0.425553
$813$	−25.6689	−0.900249
$814$	4.83681	0.169530
$815$	−3.49324	−0.122363
$816$	−20.5820	−0.720515
$817$	−3.07594	−0.107613
$818$	14.4491	0.505201
$819$	−5.33584	−0.186449
$820$	1.79735	0.0627661
$821$	28.3822	0.990544	0.495272	−	0.868738i	$-0.335068\pi$
$821$	28.3822	0.990544	0.495272	+	0.868738i	$0.335068\pi$
$822$	19.7814	0.689956
$823$	5.50235	0.191800	0.0958999	−	0.995391i	$-0.469427\pi$
$823$	5.50235	0.191800	0.0958999	+	0.995391i	$0.469427\pi$
$824$	22.5569	0.785808
$825$	−8.63627	−0.300676
$826$	−24.9598	−0.868464
$827$	−20.3520	−0.707707	−0.353854	−	0.935301i	$-0.615129\pi$
$827$	−20.3520	−0.707707	−0.353854	+	0.935301i	$0.615129\pi$
$828$	2.05430	0.0713920
$829$	4.27755	0.148565	0.0742827	−	0.997237i	$-0.476333\pi$
$829$	4.27755	0.148565	0.0742827	+	0.997237i	$0.476333\pi$
$830$	−3.07258	−0.106651
$831$	−9.46333	−0.328279
$832$	−11.7107	−0.405997
$833$	82.3443	2.85306
$834$	−3.55111	−0.122965
$835$	0.146797	0.00508013
$836$	11.9620	0.413715
$837$	−5.70935	−0.197344
$838$	1.13934	0.0393579
$839$	−42.2443	−1.45844	−0.729218	−	0.684281i	$-0.760116\pi$
$839$	−42.2443	−1.45844	−0.729218	+	0.684281i	$0.760116\pi$
$840$	6.63566	0.228952
$841$	−26.8467	−0.925749
$842$	−0.807011	−0.0278114
$843$	31.0078	1.06796
$844$	−5.26280	−0.181153
$845$	−11.8809	−0.408717
$846$	−0.848426	−0.0291695
$847$	−4.84691	−0.166542
$848$	20.0986	0.690190
$849$	−0.994743	−0.0341395
$850$	−13.1633	−0.451497
$851$	64.7030	2.21799
$852$	−10.0611	−0.344687
$853$	34.5772	1.18390	0.591950	−	0.805975i	$-0.298358\pi$
$853$	34.5772	1.18390	0.591950	+	0.805975i	$0.298358\pi$
$854$	−2.63269	−0.0900888
$855$	−0.444829	−0.0152128
$856$	−22.9316	−0.783785
$857$	−11.1524	−0.380959	−0.190480	−	0.981691i	$-0.561004\pi$
$857$	−11.1524	−0.380959	−0.190480	+	0.981691i	$0.561004\pi$
$858$	6.41606	0.219041
$859$	16.8745	0.575751	0.287876	−	0.957668i	$-0.407051\pi$
$859$	16.8745	0.575751	0.287876	+	0.957668i	$0.407051\pi$
$860$	−0.285800	−0.00974568
$861$	23.7776	0.810338
$862$	18.8527	0.642124
$863$	−45.4420	−1.54686	−0.773432	−	0.633879i	$-0.781462\pi$
$863$	−45.4420	−1.54686	−0.773432	+	0.633879i	$0.781462\pi$
$864$	26.6425	0.906395
$865$	−2.90231	−0.0986816
$866$	17.1078	0.581346
$867$	−14.1067	−0.479088
$868$	−9.35616	−0.317569
$869$	2.55910	0.0868116
$870$	0.542232	0.0183834
$871$	43.0764	1.45959
$872$	−17.7296	−0.600399
$873$	1.51624	0.0513168
$874$	−27.6901	−0.936631
$875$	−18.2610	−0.617336
$876$	18.5309	0.626101
$877$	24.3604	0.822593	0.411296	−	0.911502i	$-0.365076\pi$
$877$	24.3604	0.822593	0.411296	+	0.911502i	$0.365076\pi$
$878$	19.2411	0.649357
$879$	2.80360	0.0945629
$880$	0.885838	0.0298616
$881$	−32.4348	−1.09276	−0.546379	−	0.837538i	$-0.683994\pi$
$881$	−32.4348	−1.09276	−0.546379	+	0.837538i	$0.683994\pi$
$882$	1.48549	0.0500190
$883$	−26.0372	−0.876220	−0.438110	−	0.898921i	$-0.644352\pi$
$883$	−26.0372	−0.876220	−0.438110	+	0.898921i	$0.644352\pi$
$884$	−56.5136	−1.90076
$885$	6.44974	0.216806
$886$	4.56110	0.153233
$887$	−14.7623	−0.495668	−0.247834	−	0.968803i	$-0.579719\pi$
$887$	−14.7623	−0.495668	−0.247834	+	0.968803i	$0.579719\pi$
$888$	−31.8850	−1.06999
$889$	−48.3199	−1.62060
$890$	−2.17036	−0.0727505
$891$	9.46997	0.317256
$892$	23.1875	0.776376
$893$	−66.0876	−2.21154
$894$	15.7217	0.525812
$895$	−9.06750	−0.303093
$896$	55.8592	1.86613
$897$	85.8291	2.86575
$898$	−1.17518	−0.0392163
$899$	−1.66137	−0.0554099
$900$	1.37229	0.0457431
$901$	43.3127	1.44296
$902$	−1.49759	−0.0498644
$903$	−3.78092	−0.125821
$904$	11.2837	0.375292
$905$	−0.00707908	−0.000235317 0
$906$	−8.46876	−0.281356
$907$	42.1811	1.40060	0.700300	−	0.713849i	$-0.253050\pi$
$907$	42.1811	1.40060	0.700300	+	0.713849i	$0.253050\pi$
$908$	−1.27178	−0.0422055
$909$	0.822577	0.0272832
$910$	6.68262	0.221527
$911$	57.2649	1.89727	0.948635	−	0.316373i	$-0.102465\pi$
$911$	57.2649	1.89727	0.948635	+	0.316373i	$0.102465\pi$
$912$	−28.9221	−0.957707
$913$	−14.7949	−0.489639
$914$	5.62578	0.186084
$915$	0.680299	0.0224900
$916$	−24.2934	−0.802677
$917$	52.9456	1.74842
$918$	13.6758	0.451367
$919$	1.86371	0.0614780	0.0307390	−	0.999527i	$-0.490214\pi$
$919$	1.86371	0.0614780	0.0307390	+	0.999527i	$0.490214\pi$
$920$	−5.59083	−0.184324
$921$	35.1036	1.15670
$922$	−1.83799	−0.0605310
$923$	−22.0179	−0.724727
$924$	14.7036	0.483714
$925$	43.2222	1.42114
$926$	−6.16717	−0.202666
$927$	−1.85870	−0.0610476
$928$	7.75273	0.254496
$929$	−36.0486	−1.18272	−0.591358	−	0.806409i	$-0.701408\pi$
$929$	−36.0486	−1.18272	−0.591358	+	0.806409i	$0.701408\pi$
$930$	−0.418361	−0.0137186
$931$	115.711	3.79228
$932$	41.6752	1.36512
$933$	14.4187	0.472047
$934$	−13.1107	−0.428994
$935$	1.90899	0.0624306
$936$	−2.21543	−0.0724135
$937$	−16.1499	−0.527596	−0.263798	−	0.964578i	$-0.584975\pi$
$937$	−16.1499	−0.527596	−0.263798	+	0.964578i	$0.584975\pi$
$938$	−17.0824	−0.557760
$939$	5.85417	0.191044
$940$	−6.14051	−0.200281
$941$	54.6806	1.78254	0.891268	−	0.453476i	$-0.149816\pi$
$941$	54.6806	1.78254	0.891268	+	0.453476i	$0.149816\pi$
$942$	−9.34374	−0.304436
$943$	−20.0337	−0.652386
$944$	21.9654	0.714914
$945$	9.34526	0.304001
$946$	0.238135	0.00774244
$947$	30.3263	0.985472	0.492736	−	0.870179i	$-0.335997\pi$
$947$	30.3263	0.985472	0.492736	+	0.870179i	$0.335997\pi$
$948$	−7.76332	−0.252141
$949$	40.5534	1.31642
$950$	−18.4972	−0.600129
$951$	17.0134	0.551697
$952$	48.7002	1.57838
$953$	−46.0196	−1.49072	−0.745361	−	0.666662i	$-0.767723\pi$
$953$	−46.0196	−1.49072	−0.745361	+	0.666662i	$0.767723\pi$
$954$	0.781361	0.0252975
$955$	2.36348	0.0764805
$956$	−20.7077	−0.669736
$957$	2.61092	0.0843991
$958$	1.17592	0.0379923
$959$	99.2074	3.20357
$960$	−1.20004	−0.0387310
$961$	−29.7182	−0.958650
$962$	−32.1106	−1.03529
$963$	1.88957	0.0608904
$964$	−1.58237	−0.0509646
$965$	2.95567	0.0951465
$966$	−34.0364	−1.09510
$967$	55.9407	1.79893	0.899466	−	0.436991i	$-0.143956\pi$
$967$	55.9407	1.79893	0.899466	+	0.436991i	$0.143956\pi$
$968$	−2.01242	−0.0646817
$969$	−62.3273	−2.00224
$970$	−1.89894	−0.0609712
$971$	0.422452	0.0135571	0.00677856	−	0.999977i	$-0.497842\pi$
$971$	0.422452	0.0135571	0.00677856	+	0.999977i	$0.497842\pi$
$972$	−2.93486	−0.0941356
$973$	−17.8094	−0.570944
$974$	−22.9461	−0.735242
$975$	57.3346	1.83618
$976$	2.31685	0.0741606
$977$	−20.1876	−0.645858	−0.322929	−	0.946423i	$-0.604667\pi$
$977$	−20.1876	−0.645858	−0.322929	+	0.946423i	$0.604667\pi$
$978$	−8.82978	−0.282345
$979$	−10.4506	−0.334001
$980$	10.7513	0.343437
$981$	1.46092	0.0466436
$982$	3.34962	0.106891
$983$	−25.6609	−0.818457	−0.409228	−	0.912432i	$-0.634202\pi$
$983$	−25.6609	−0.818457	−0.409228	+	0.912432i	$0.634202\pi$
$984$	9.87238	0.314720
$985$	−0.127968	−0.00407739
$986$	3.97953	0.126734
$987$	−81.2344	−2.58572
$988$	−79.4136	−2.52648
$989$	3.18559	0.101296
$990$	0.0344381	0.00109451
$991$	−47.8468	−1.51991	−0.759953	−	0.649978i	$-0.774778\pi$
$991$	−47.8468	−1.51991	−0.759953	+	0.649978i	$0.774778\pi$
$992$	−5.98165	−0.189918
$993$	56.1726	1.78259
$994$	8.73142	0.276944
$995$	−8.71359	−0.276239
$996$	44.8819	1.42214
$997$	−25.9634	−0.822268	−0.411134	−	0.911575i	$-0.634867\pi$
$997$	−25.9634	−0.822268	−0.411134	+	0.911575i	$0.634867\pi$
$998$	17.0432	0.539494
$999$	−44.9049	−1.42073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.12	✓	21
3.2	odd	2		6039.2.a.l.1.10		21
11.10	odd	2		7381.2.a.j.1.10		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.12	✓	21	1.1	even	1	trivial
6039.2.a.l.1.10		21	3.2	odd	2
7381.2.a.j.1.10		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)

\(f(q)\)	\(=\)	\(q+0.543169 q^{2} -1.77928 q^{3} -1.70497 q^{4} -0.382346 q^{5} -0.966447 q^{6} -4.84691 q^{7} -2.01242 q^{8} +0.165824 q^{9} +O(q^{10})\)	\(q+0.543169 q^{2} -1.77928 q^{3} -1.70497 q^{4} -0.382346 q^{5} -0.966447 q^{6} -4.84691 q^{7} -2.01242 q^{8} +0.165824 q^{9} -0.207678 q^{10} -1.00000 q^{11} +3.03361 q^{12} +6.63881 q^{13} -2.63269 q^{14} +0.680299 q^{15} +2.31685 q^{16} +4.99283 q^{17} +0.0900705 q^{18} +7.01598 q^{19} +0.651888 q^{20} +8.62399 q^{21} -0.543169 q^{22} -7.26609 q^{23} +3.58066 q^{24} -4.85381 q^{25} +3.60599 q^{26} +5.04278 q^{27} +8.26382 q^{28} +1.46741 q^{29} +0.369517 q^{30} -1.13218 q^{31} +5.28329 q^{32} +1.77928 q^{33} +2.71195 q^{34} +1.85320 q^{35} -0.282725 q^{36} -8.90479 q^{37} +3.81086 q^{38} -11.8123 q^{39} +0.769442 q^{40} +2.75714 q^{41} +4.68428 q^{42} -0.438418 q^{43} +1.70497 q^{44} -0.0634022 q^{45} -3.94671 q^{46} -9.41958 q^{47} -4.12232 q^{48} +16.4925 q^{49} -2.63644 q^{50} -8.88362 q^{51} -11.3190 q^{52} +8.67499 q^{53} +2.73908 q^{54} +0.382346 q^{55} +9.75403 q^{56} -12.4834 q^{57} +0.797050 q^{58} +9.48074 q^{59} -1.15989 q^{60} +1.00000 q^{61} -0.614967 q^{62} -0.803734 q^{63} -1.76398 q^{64} -2.53832 q^{65} +0.966447 q^{66} +6.48857 q^{67} -8.51261 q^{68} +12.9284 q^{69} +1.00660 q^{70} -3.31654 q^{71} -0.333708 q^{72} +6.10854 q^{73} -4.83681 q^{74} +8.63627 q^{75} -11.9620 q^{76} +4.84691 q^{77} -6.41606 q^{78} -2.55910 q^{79} -0.885838 q^{80} -9.46997 q^{81} +1.49759 q^{82} +14.7949 q^{83} -14.7036 q^{84} -1.90899 q^{85} -0.238135 q^{86} -2.61092 q^{87} +2.01242 q^{88} +10.4506 q^{89} -0.0344381 q^{90} -32.1777 q^{91} +12.3884 q^{92} +2.01447 q^{93} -5.11642 q^{94} -2.68253 q^{95} -9.40043 q^{96} +9.14364 q^{97} +8.95822 q^{98} -0.165824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 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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