LMFDB - Embedded newform 671.2.a.d.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.45442 q^{2} -2.91272 q^{3} +0.115325 q^{4} +3.82594 q^{5} +4.23631 q^{6} +3.26042 q^{7} +2.74110 q^{8} +5.48395 q^{9} +O(q^{10})$	\(q-1.45442 q^{2} -2.91272 q^{3} +0.115325 q^{4} +3.82594 q^{5} +4.23631 q^{6} +3.26042 q^{7} +2.74110 q^{8} +5.48395 q^{9} -5.56450 q^{10} -1.00000 q^{11} -0.335911 q^{12} +5.15443 q^{13} -4.74201 q^{14} -11.1439 q^{15} -4.21735 q^{16} +1.81260 q^{17} -7.97594 q^{18} -6.25538 q^{19} +0.441227 q^{20} -9.49669 q^{21} +1.45442 q^{22} -3.26360 q^{23} -7.98406 q^{24} +9.63778 q^{25} -7.49668 q^{26} -7.23504 q^{27} +0.376009 q^{28} +9.11409 q^{29} +16.2078 q^{30} +9.69614 q^{31} +0.651580 q^{32} +2.91272 q^{33} -2.63628 q^{34} +12.4742 q^{35} +0.632438 q^{36} -11.3749 q^{37} +9.09792 q^{38} -15.0134 q^{39} +10.4873 q^{40} -1.74708 q^{41} +13.8121 q^{42} +1.82661 q^{43} -0.115325 q^{44} +20.9812 q^{45} +4.74662 q^{46} -3.66916 q^{47} +12.2840 q^{48} +3.63034 q^{49} -14.0173 q^{50} -5.27961 q^{51} +0.594436 q^{52} -6.16433 q^{53} +10.5228 q^{54} -3.82594 q^{55} +8.93714 q^{56} +18.2202 q^{57} -13.2557 q^{58} +8.95135 q^{59} -1.28517 q^{60} +1.00000 q^{61} -14.1022 q^{62} +17.8800 q^{63} +7.48703 q^{64} +19.7205 q^{65} -4.23631 q^{66} +4.57270 q^{67} +0.209039 q^{68} +9.50594 q^{69} -18.1426 q^{70} -5.54735 q^{71} +15.0320 q^{72} -7.91540 q^{73} +16.5438 q^{74} -28.0722 q^{75} -0.721404 q^{76} -3.26042 q^{77} +21.8357 q^{78} +6.29660 q^{79} -16.1353 q^{80} +4.62182 q^{81} +2.54098 q^{82} -2.81886 q^{83} -1.09521 q^{84} +6.93490 q^{85} -2.65665 q^{86} -26.5468 q^{87} -2.74110 q^{88} +5.92388 q^{89} -30.5154 q^{90} +16.8056 q^{91} -0.376375 q^{92} -28.2422 q^{93} +5.33648 q^{94} -23.9327 q^{95} -1.89787 q^{96} +10.3200 q^{97} -5.28002 q^{98} -5.48395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.45442	−1.02843	−0.514214	−	0.857662i	$-0.671916\pi$
$2$	−1.45442	−1.02843	−0.514214	+	0.857662i	$0.671916\pi$
$3$	−2.91272	−1.68166	−0.840830	−	0.541299i	$-0.817933\pi$
$3$	−2.91272	−1.68166	−0.840830	+	0.541299i	$0.817933\pi$
$4$	0.115325	0.0576627
$5$	3.82594	1.71101	0.855505	−	0.517794i	$-0.173247\pi$
$5$	3.82594	1.71101	0.855505	+	0.517794i	$0.173247\pi$
$6$	4.23631	1.72947
$7$	3.26042	1.23232	0.616161	−	0.787620i	$-0.288687\pi$
$7$	3.26042	1.23232	0.616161	+	0.787620i	$0.288687\pi$
$8$	2.74110	0.969125
$9$	5.48395	1.82798
$10$	−5.56450	−1.75965
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.335911	−0.0969690
$13$	5.15443	1.42958	0.714791	−	0.699339i	$-0.246522\pi$
$13$	5.15443	1.42958	0.714791	+	0.699339i	$0.246522\pi$
$14$	−4.74201	−1.26735
$15$	−11.1439	−2.87734
$16$	−4.21735	−1.05434
$17$	1.81260	0.439621	0.219810	−	0.975543i	$-0.429456\pi$
$17$	1.81260	0.439621	0.219810	+	0.975543i	$0.429456\pi$
$18$	−7.97594	−1.87995
$19$	−6.25538	−1.43508	−0.717541	−	0.696516i	$-0.754732\pi$
$19$	−6.25538	−1.43508	−0.717541	+	0.696516i	$0.754732\pi$
$20$	0.441227	0.0986614
$21$	−9.49669	−2.07235
$22$	1.45442	0.310082
$23$	−3.26360	−0.680507	−0.340253	−	0.940334i	$-0.610513\pi$
$23$	−3.26360	−0.680507	−0.340253	+	0.940334i	$0.610513\pi$
$24$	−7.98406	−1.62974
$25$	9.63778	1.92756
$26$	−7.49668	−1.47022
$27$	−7.23504	−1.39238
$28$	0.376009	0.0710590
$29$	9.11409	1.69244	0.846222	−	0.532830i	$-0.178872\pi$
$29$	9.11409	1.69244	0.846222	+	0.532830i	$0.178872\pi$
$30$	16.2078	2.95913
$31$	9.69614	1.74148	0.870739	−	0.491745i	$-0.163641\pi$
$31$	9.69614	1.74148	0.870739	+	0.491745i	$0.163641\pi$
$32$	0.651580	0.115184
$33$	2.91272	0.507040
$34$	−2.63628	−0.452118
$35$	12.4742	2.10852
$36$	0.632438	0.105406
$37$	−11.3749	−1.87002	−0.935010	−	0.354622i	$-0.884610\pi$
$37$	−11.3749	−1.87002	−0.935010	+	0.354622i	$0.884610\pi$
$38$	9.09792	1.47588
$39$	−15.0134	−2.40407
$40$	10.4873	1.65818
$41$	−1.74708	−0.272848	−0.136424	−	0.990651i	$-0.543561\pi$
$41$	−1.74708	−0.272848	−0.136424	+	0.990651i	$0.543561\pi$
$42$	13.8121	2.13126
$43$	1.82661	0.278555	0.139278	−	0.990253i	$-0.455522\pi$
$43$	1.82661	0.278555	0.139278	+	0.990253i	$0.455522\pi$
$44$	−0.115325	−0.0173860
$45$	20.9812	3.12770
$46$	4.74662	0.699852
$47$	−3.66916	−0.535202	−0.267601	−	0.963530i	$-0.586231\pi$
$47$	−3.66916	−0.535202	−0.267601	+	0.963530i	$0.586231\pi$
$48$	12.2840	1.77304
$49$	3.63034	0.518620
$50$	−14.0173	−1.98235
$51$	−5.27961	−0.739293
$52$	0.594436	0.0824335
$53$	−6.16433	−0.846735	−0.423368	−	0.905958i	$-0.639152\pi$
$53$	−6.16433	−0.846735	−0.423368	+	0.905958i	$0.639152\pi$
$54$	10.5228	1.43197
$55$	−3.82594	−0.515889
$56$	8.93714	1.19428
$57$	18.2202	2.41332
$58$	−13.2557	−1.74056
$59$	8.95135	1.16537	0.582683	−	0.812699i	$-0.302003\pi$
$59$	8.95135	1.16537	0.582683	+	0.812699i	$0.302003\pi$
$60$	−1.28517	−0.165915
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−14.1022	−1.79098
$63$	17.8800	2.25266
$64$	7.48703	0.935879
$65$	19.7205	2.44603
$66$	−4.23631	−0.521453
$67$	4.57270	0.558644	0.279322	−	0.960197i	$-0.409890\pi$
$67$	4.57270	0.558644	0.279322	+	0.960197i	$0.409890\pi$
$68$	0.209039	0.0253497
$69$	9.50594	1.14438
$70$	−18.1426	−2.16846
$71$	−5.54735	−0.658350	−0.329175	−	0.944269i	$-0.606771\pi$
$71$	−5.54735	−0.658350	−0.329175	+	0.944269i	$0.606771\pi$
$72$	15.0320	1.77154
$73$	−7.91540	−0.926427	−0.463214	−	0.886247i	$-0.653304\pi$
$73$	−7.91540	−0.926427	−0.463214	+	0.886247i	$0.653304\pi$
$74$	16.5438	1.92318
$75$	−28.0722	−3.24150
$76$	−0.721404	−0.0827507
$77$	−3.26042	−0.371559
$78$	21.8357	2.47241
$79$	6.29660	0.708422	0.354211	−	0.935165i	$-0.384749\pi$
$79$	6.29660	0.708422	0.354211	+	0.935165i	$0.384749\pi$
$80$	−16.1353	−1.80398
$81$	4.62182	0.513535
$82$	2.54098	0.280604
$83$	−2.81886	−0.309410	−0.154705	−	0.987961i	$-0.549443\pi$
$83$	−2.81886	−0.309410	−0.154705	+	0.987961i	$0.549443\pi$
$84$	−1.09521	−0.119497
$85$	6.93490	0.752196
$86$	−2.65665	−0.286474
$87$	−26.5468	−2.84612
$88$	−2.74110	−0.292202
$89$	5.92388	0.627930	0.313965	−	0.949435i	$-0.398343\pi$
$89$	5.92388	0.627930	0.313965	+	0.949435i	$0.398343\pi$
$90$	−30.5154	−3.21661
$91$	16.8056	1.76171
$92$	−0.376375	−0.0392398
$93$	−28.2422	−2.92858
$94$	5.33648	0.550416
$95$	−23.9327	−2.45544
$96$	−1.89787	−0.193701
$97$	10.3200	1.04784	0.523919	−	0.851768i	$-0.324469\pi$
$97$	10.3200	1.04784	0.523919	+	0.851768i	$0.324469\pi$
$98$	−5.28002	−0.533362
$99$	−5.48395	−0.551157
$100$	1.11148	0.111148
$101$	−8.83521	−0.879136	−0.439568	−	0.898209i	$-0.644868\pi$
$101$	−8.83521	−0.879136	−0.439568	+	0.898209i	$0.644868\pi$
$102$	7.67875	0.760309
$103$	17.0024	1.67529	0.837646	−	0.546213i	$-0.183931\pi$
$103$	17.0024	1.67529	0.837646	+	0.546213i	$0.183931\pi$
$104$	14.1288	1.38544
$105$	−36.3337	−3.54581
$106$	8.96549	0.870806
$107$	−14.3578	−1.38802	−0.694010	−	0.719966i	$-0.744158\pi$
$107$	−14.3578	−1.38802	−0.694010	+	0.719966i	$0.744158\pi$
$108$	−0.834383	−0.0802886
$109$	12.6102	1.20784	0.603921	−	0.797044i	$-0.293604\pi$
$109$	12.6102	1.20784	0.603921	+	0.797044i	$0.293604\pi$
$110$	5.56450	0.530554
$111$	33.1319	3.14474
$112$	−13.7503	−1.29928
$113$	1.44813	0.136228	0.0681142	−	0.997678i	$-0.478302\pi$
$113$	1.44813	0.136228	0.0681142	+	0.997678i	$0.478302\pi$
$114$	−26.4997	−2.48192
$115$	−12.4863	−1.16435
$116$	1.05109	0.0975908
$117$	28.2666	2.61325
$118$	−13.0190	−1.19849
$119$	5.90985	0.541755
$120$	−30.5465	−2.78850
$121$	1.00000	0.0909091
$122$	−1.45442	−0.131677
$123$	5.08876	0.458838
$124$	1.11821	0.100418
$125$	17.7439	1.58706
$126$	−26.0049	−2.31670
$127$	1.73437	0.153901	0.0769503	−	0.997035i	$-0.475482\pi$
$127$	1.73437	0.153901	0.0769503	+	0.997035i	$0.475482\pi$
$128$	−12.1924	−1.07767
$129$	−5.32040	−0.468435
$130$	−28.6818	−2.51556
$131$	−8.63290	−0.754260	−0.377130	−	0.926160i	$-0.623089\pi$
$131$	−8.63290	−0.754260	−0.377130	+	0.926160i	$0.623089\pi$
$132$	0.335911	0.0292373
$133$	−20.3952	−1.76848
$134$	−6.65061	−0.574525
$135$	−27.6808	−2.38238
$136$	4.96853	0.426048
$137$	−6.05841	−0.517605	−0.258802	−	0.965930i	$-0.583328\pi$
$137$	−6.05841	−0.517605	−0.258802	+	0.965930i	$0.583328\pi$
$138$	−13.8256	−1.17691
$139$	12.8486	1.08981	0.544903	−	0.838499i	$-0.316566\pi$
$139$	12.8486	1.08981	0.544903	+	0.838499i	$0.316566\pi$
$140$	1.43859	0.121583
$141$	10.6872	0.900027
$142$	8.06816	0.677065
$143$	−5.15443	−0.431035
$144$	−23.1277	−1.92731
$145$	34.8699	2.89579
$146$	11.5123	0.952763
$147$	−10.5742	−0.872142
$148$	−1.31181	−0.107830
$149$	−6.70006	−0.548891	−0.274445	−	0.961603i	$-0.588494\pi$
$149$	−6.70006	−0.548891	−0.274445	+	0.961603i	$0.588494\pi$
$150$	40.8286	3.33364
$151$	7.94403	0.646476	0.323238	−	0.946318i	$-0.395229\pi$
$151$	7.94403	0.646476	0.323238	+	0.946318i	$0.395229\pi$
$152$	−17.1466	−1.39077
$153$	9.94022	0.803619
$154$	4.74201	0.382122
$155$	37.0968	2.97969
$156$	−1.73143	−0.138625
$157$	−18.5035	−1.47674	−0.738369	−	0.674397i	$-0.764404\pi$
$157$	−18.5035	−1.47674	−0.738369	+	0.674397i	$0.764404\pi$
$158$	−9.15787	−0.728561
$159$	17.9550	1.42392
$160$	2.49290	0.197081
$161$	−10.6407	−0.838604
$162$	−6.72205	−0.528134
$163$	10.4832	0.821105	0.410552	−	0.911837i	$-0.365336\pi$
$163$	10.4832	0.821105	0.410552	+	0.911837i	$0.365336\pi$
$164$	−0.201483	−0.0157331
$165$	11.1439	0.867550
$166$	4.09980	0.318206
$167$	5.69053	0.440346	0.220173	−	0.975461i	$-0.429338\pi$
$167$	5.69053	0.440346	0.220173	+	0.975461i	$0.429338\pi$
$168$	−26.0314	−2.00837
$169$	13.5681	1.04370
$170$	−10.0862	−0.773579
$171$	−34.3041	−2.62330
$172$	0.210654	0.0160622
$173$	2.76526	0.210239	0.105119	−	0.994460i	$-0.466478\pi$
$173$	2.76526	0.210239	0.105119	+	0.994460i	$0.466478\pi$
$174$	38.6101	2.92702
$175$	31.4232	2.37537
$176$	4.21735	0.317895
$177$	−26.0728	−1.95975
$178$	−8.61578	−0.645780
$179$	6.27826	0.469259	0.234630	−	0.972085i	$-0.424612\pi$
$179$	6.27826	0.469259	0.234630	+	0.972085i	$0.424612\pi$
$180$	2.41967	0.180351
$181$	4.88002	0.362729	0.181365	−	0.983416i	$-0.441949\pi$
$181$	4.88002	0.362729	0.181365	+	0.983416i	$0.441949\pi$
$182$	−24.4423	−1.81179
$183$	−2.91272	−0.215315
$184$	−8.94584	−0.659496
$185$	−43.5196	−3.19962
$186$	41.0759	3.01183
$187$	−1.81260	−0.132551
$188$	−0.423147	−0.0308612
$189$	−23.5893	−1.71587
$190$	34.8081	2.52524
$191$	−10.8614	−0.785906	−0.392953	−	0.919558i	$-0.628547\pi$
$191$	−10.8614	−0.785906	−0.392953	+	0.919558i	$0.628547\pi$
$192$	−21.8076	−1.57383
$193$	17.1678	1.23576	0.617882	−	0.786271i	$-0.287991\pi$
$193$	17.1678	1.23576	0.617882	+	0.786271i	$0.287991\pi$
$194$	−15.0096	−1.07763
$195$	−57.4403	−4.11339
$196$	0.418670	0.0299050
$197$	−1.25956	−0.0897399	−0.0448700	−	0.998993i	$-0.514287\pi$
$197$	−1.25956	−0.0897399	−0.0448700	+	0.998993i	$0.514287\pi$
$198$	7.97594	0.566825
$199$	5.80007	0.411156	0.205578	−	0.978641i	$-0.434093\pi$
$199$	5.80007	0.411156	0.205578	+	0.978641i	$0.434093\pi$
$200$	26.4181	1.86804
$201$	−13.3190	−0.939450
$202$	12.8501	0.904128
$203$	29.7158	2.08564
$204$	−0.608873	−0.0426296
$205$	−6.68421	−0.466846
$206$	−24.7285	−1.72292
$207$	−17.8974	−1.24395
$208$	−21.7380	−1.50726
$209$	6.25538	0.432694
$210$	52.8444	3.64661
$211$	−15.5879	−1.07312	−0.536559	−	0.843863i	$-0.680276\pi$
$211$	−15.5879	−1.07312	−0.536559	+	0.843863i	$0.680276\pi$
$212$	−0.710903	−0.0488250
$213$	16.1579	1.10712
$214$	20.8822	1.42748
$215$	6.98848	0.476611
$216$	−19.8320	−1.34939
$217$	31.6135	2.14606
$218$	−18.3405	−1.24218
$219$	23.0553	1.55794
$220$	−0.441227	−0.0297475
$221$	9.34293	0.628474
$222$	−48.1875	−3.23413
$223$	7.31670	0.489962	0.244981	−	0.969528i	$-0.421218\pi$
$223$	7.31670	0.489962	0.244981	+	0.969528i	$0.421218\pi$
$224$	2.12443	0.141944
$225$	52.8531	3.52354
$226$	−2.10618	−0.140101
$227$	−22.9379	−1.52244	−0.761220	−	0.648493i	$-0.775399\pi$
$227$	−22.9379	−1.52244	−0.761220	+	0.648493i	$0.775399\pi$
$228$	2.10125	0.139159
$229$	13.4703	0.890144	0.445072	−	0.895495i	$-0.353178\pi$
$229$	13.4703	0.890144	0.445072	+	0.895495i	$0.353178\pi$
$230$	18.1603	1.19745
$231$	9.49669	0.624837
$232$	24.9826	1.64019
$233$	−6.65333	−0.435874	−0.217937	−	0.975963i	$-0.569933\pi$
$233$	−6.65333	−0.435874	−0.217937	+	0.975963i	$0.569933\pi$
$234$	−41.1114	−2.68754
$235$	−14.0380	−0.915735
$236$	1.03232	0.0671982
$237$	−18.3402	−1.19133
$238$	−8.59538	−0.557156
$239$	3.00085	0.194109	0.0970545	−	0.995279i	$-0.469058\pi$
$239$	3.00085	0.194109	0.0970545	+	0.995279i	$0.469058\pi$
$240$	46.9977	3.03369
$241$	−19.4575	−1.25337	−0.626683	−	0.779274i	$-0.715588\pi$
$241$	−19.4575	−1.25337	−0.626683	+	0.779274i	$0.715588\pi$
$242$	−1.45442	−0.0934934
$243$	8.24305	0.528792
$244$	0.115325	0.00738295
$245$	13.8894	0.887363
$246$	−7.40117	−0.471881
$247$	−32.2429	−2.05157
$248$	26.5781	1.68771
$249$	8.21056	0.520323
$250$	−25.8069	−1.63217
$251$	21.7902	1.37538	0.687691	−	0.726003i	$-0.258624\pi$
$251$	21.7902	1.37538	0.687691	+	0.726003i	$0.258624\pi$
$252$	2.06201	0.129895
$253$	3.26360	0.205180
$254$	−2.52250	−0.158276
$255$	−20.1994	−1.26494
$256$	2.75878	0.172424
$257$	−5.38983	−0.336208	−0.168104	−	0.985769i	$-0.553765\pi$
$257$	−5.38983	−0.336208	−0.168104	+	0.985769i	$0.553765\pi$
$258$	7.73807	0.481751
$259$	−37.0869	−2.30447
$260$	2.27427	0.141045
$261$	49.9812	3.09376
$262$	12.5558	0.775701
$263$	6.98170	0.430510	0.215255	−	0.976558i	$-0.430942\pi$
$263$	6.98170	0.430510	0.215255	+	0.976558i	$0.430942\pi$
$264$	7.98406	0.491385
$265$	−23.5843	−1.44877
$266$	29.6630	1.81876
$267$	−17.2546	−1.05596
$268$	0.527348	0.0322129
$269$	15.9257	0.971009	0.485505	−	0.874234i	$-0.338636\pi$
$269$	15.9257	0.971009	0.485505	+	0.874234i	$0.338636\pi$
$270$	40.2594	2.45011
$271$	11.8128	0.717579	0.358789	−	0.933419i	$-0.383190\pi$
$271$	11.8128	0.717579	0.358789	+	0.933419i	$0.383190\pi$
$272$	−7.64439	−0.463509
$273$	−48.9500	−2.96259
$274$	8.81144	0.532319
$275$	−9.63778	−0.581180
$276$	1.09628	0.0659881
$277$	−18.2085	−1.09404	−0.547022	−	0.837118i	$-0.684239\pi$
$277$	−18.2085	−1.09404	−0.547022	+	0.837118i	$0.684239\pi$
$278$	−18.6873	−1.12079
$279$	53.1731	3.18339
$280$	34.1929	2.04342
$281$	10.6699	0.636515	0.318258	−	0.948004i	$-0.396902\pi$
$281$	10.6699	0.636515	0.318258	+	0.948004i	$0.396902\pi$
$282$	−15.5437	−0.925613
$283$	−2.57426	−0.153024	−0.0765119	−	0.997069i	$-0.524378\pi$
$283$	−2.57426	−0.153024	−0.0765119	+	0.997069i	$0.524378\pi$
$284$	−0.639750	−0.0379622
$285$	69.7092	4.12922
$286$	7.49668	0.443288
$287$	−5.69621	−0.336237
$288$	3.57323	0.210555
$289$	−13.7145	−0.806733
$290$	−50.7154	−2.97811
$291$	−30.0593	−1.76211
$292$	−0.912846	−0.0534203
$293$	−28.0168	−1.63676	−0.818379	−	0.574679i	$-0.805127\pi$
$293$	−28.0168	−1.63676	−0.818379	+	0.574679i	$0.805127\pi$
$294$	15.3792	0.896935
$295$	34.2473	1.99395
$296$	−31.1797	−1.81228
$297$	7.23504	0.419820
$298$	9.74468	0.564494
$299$	−16.8220	−0.972839
$300$	−3.23743	−0.186913
$301$	5.95551	0.343270
$302$	−11.5539	−0.664854
$303$	25.7345	1.47841
$304$	26.3811	1.51306
$305$	3.82594	0.219072
$306$	−14.4572	−0.826464
$307$	−20.1014	−1.14725	−0.573624	−	0.819119i	$-0.694463\pi$
$307$	−20.1014	−1.14725	−0.573624	+	0.819119i	$0.694463\pi$
$308$	−0.376009	−0.0214251
$309$	−49.5231	−2.81727
$310$	−53.9542	−3.06439
$311$	−11.4362	−0.648489	−0.324245	−	0.945973i	$-0.605110\pi$
$311$	−11.4362	−0.648489	−0.324245	+	0.945973i	$0.605110\pi$
$312$	−41.1533	−2.32985
$313$	22.3538	1.26351	0.631755	−	0.775168i	$-0.282335\pi$
$313$	22.3538	1.26351	0.631755	+	0.775168i	$0.282335\pi$
$314$	26.9118	1.51872
$315$	68.4076	3.85433
$316$	0.726157	0.0408495
$317$	7.92764	0.445261	0.222630	−	0.974903i	$-0.428536\pi$
$317$	7.92764	0.445261	0.222630	+	0.974903i	$0.428536\pi$
$318$	−26.1140	−1.46440
$319$	−9.11409	−0.510291
$320$	28.6449	1.60130
$321$	41.8202	2.33418
$322$	15.4760	0.862443
$323$	−11.3385	−0.630892
$324$	0.533013	0.0296118
$325$	49.6773	2.75560
$326$	−15.2469	−0.844447
$327$	−36.7301	−2.03118
$328$	−4.78892	−0.264424
$329$	−11.9630	−0.659541
$330$	−16.2078	−0.892212
$331$	4.99164	0.274365	0.137183	−	0.990546i	$-0.456195\pi$
$331$	4.99164	0.274365	0.137183	+	0.990546i	$0.456195\pi$
$332$	−0.325086	−0.0178414
$333$	−62.3792	−3.41836
$334$	−8.27640	−0.452864
$335$	17.4949	0.955846
$336$	40.0509	2.18496
$337$	2.19574	0.119609	0.0598047	−	0.998210i	$-0.480952\pi$
$337$	2.19574	0.119609	0.0598047	+	0.998210i	$0.480952\pi$
$338$	−19.7337	−1.07337
$339$	−4.21799	−0.229090
$340$	0.799770	0.0433736
$341$	−9.69614	−0.525076
$342$	49.8925	2.69788
$343$	−10.9865	−0.593216
$344$	5.00692	0.269955
$345$	36.3691	1.95805
$346$	−4.02184	−0.216215
$347$	−28.2253	−1.51521	−0.757606	−	0.652712i	$-0.773631\pi$
$347$	−28.2253	−1.51521	−0.757606	+	0.652712i	$0.773631\pi$
$348$	−3.06152	−0.164115
$349$	−7.90778	−0.423294	−0.211647	−	0.977346i	$-0.567883\pi$
$349$	−7.90778	−0.423294	−0.211647	+	0.977346i	$0.567883\pi$
$350$	−45.7024	−2.44290
$351$	−37.2925	−1.99053
$352$	−0.651580	−0.0347294
$353$	−3.84148	−0.204461	−0.102231	−	0.994761i	$-0.532598\pi$
$353$	−3.84148	−0.204461	−0.102231	+	0.994761i	$0.532598\pi$
$354$	37.9207	2.01546
$355$	−21.2238	−1.12644
$356$	0.683173	0.0362081
$357$	−17.2137	−0.911048
$358$	−9.13120	−0.482599
$359$	−16.0984	−0.849641	−0.424821	−	0.905278i	$-0.639663\pi$
$359$	−16.0984	−0.849641	−0.424821	+	0.905278i	$0.639663\pi$
$360$	57.5116	3.03113
$361$	20.1297	1.05946
$362$	−7.09758	−0.373041
$363$	−2.91272	−0.152878
$364$	1.93811	0.101585
$365$	−30.2838	−1.58513
$366$	4.23631	0.221435
$367$	26.0929	1.36204	0.681020	−	0.732264i	$-0.261536\pi$
$367$	26.0929	1.36204	0.681020	+	0.732264i	$0.261536\pi$
$368$	13.7637	0.717484
$369$	−9.58089	−0.498761
$370$	63.2956	3.29058
$371$	−20.0983	−1.04345
$372$	−3.25704	−0.168870
$373$	7.64383	0.395782	0.197891	−	0.980224i	$-0.436591\pi$
$373$	7.64383	0.395782	0.197891	+	0.980224i	$0.436591\pi$
$374$	2.63628	0.136319
$375$	−51.6829	−2.66889
$376$	−10.0575	−0.518677
$377$	46.9779	2.41949
$378$	34.3086	1.76464
$379$	−9.14079	−0.469531	−0.234765	−	0.972052i	$-0.575432\pi$
$379$	−9.14079	−0.469531	−0.234765	+	0.972052i	$0.575432\pi$
$380$	−2.76004	−0.141587
$381$	−5.05174	−0.258809
$382$	15.7971	0.808248
$383$	−16.8609	−0.861550	−0.430775	−	0.902459i	$-0.641760\pi$
$383$	−16.8609	−0.861550	−0.430775	+	0.902459i	$0.641760\pi$
$384$	35.5131	1.81227
$385$	−12.4742	−0.635742
$386$	−24.9691	−1.27089
$387$	10.0170	0.509194
$388$	1.19016	0.0604212
$389$	12.9794	0.658083	0.329041	−	0.944315i	$-0.393274\pi$
$389$	12.9794	0.658083	0.329041	+	0.944315i	$0.393274\pi$
$390$	83.5421	4.23032
$391$	−5.91560	−0.299165
$392$	9.95112	0.502607
$393$	25.1452	1.26841
$394$	1.83192	0.0922910
$395$	24.0904	1.21212
$396$	−0.632438	−0.0317812
$397$	−0.913635	−0.0458540	−0.0229270	−	0.999737i	$-0.507299\pi$
$397$	−0.913635	−0.0458540	−0.0229270	+	0.999737i	$0.507299\pi$
$398$	−8.43571	−0.422844
$399$	59.4054	2.97399
$400$	−40.6459	−2.03230
$401$	36.2175	1.80862	0.904309	−	0.426879i	$-0.140387\pi$
$401$	36.2175	1.80862	0.904309	+	0.426879i	$0.140387\pi$
$402$	19.3714	0.966156
$403$	49.9781	2.48959
$404$	−1.01892	−0.0506933
$405$	17.6828	0.878664
$406$	−43.2191	−2.14493
$407$	11.3749	0.563832
$408$	−14.4719	−0.716468
$409$	3.86996	0.191357	0.0956787	−	0.995412i	$-0.469498\pi$
$409$	3.86996	0.191357	0.0956787	+	0.995412i	$0.469498\pi$
$410$	9.72163	0.480117
$411$	17.6465	0.870435
$412$	1.96080	0.0966018
$413$	29.1852	1.43611
$414$	26.0302	1.27932
$415$	−10.7848	−0.529404
$416$	3.35852	0.164665
$417$	−37.4245	−1.83269
$418$	−9.09792	−0.444994
$419$	5.40560	0.264081	0.132040	−	0.991244i	$-0.457847\pi$
$419$	5.40560	0.264081	0.132040	+	0.991244i	$0.457847\pi$
$420$	−4.19020	−0.204461
$421$	20.8768	1.01748	0.508738	−	0.860922i	$-0.330112\pi$
$421$	20.8768	1.01748	0.508738	+	0.860922i	$0.330112\pi$
$422$	22.6713	1.10362
$423$	−20.1215	−0.978339
$424$	−16.8970	−0.820593
$425$	17.4695	0.847394
$426$	−23.5003	−1.13859
$427$	3.26042	0.157783
$428$	−1.65582	−0.0800369
$429$	15.0134	0.724854
$430$	−10.1642	−0.490159
$431$	−24.5720	−1.18359	−0.591796	−	0.806087i	$-0.701581\pi$
$431$	−24.5720	−1.18359	−0.591796	+	0.806087i	$0.701581\pi$
$432$	30.5127	1.46804
$433$	−39.3999	−1.89344	−0.946719	−	0.322061i	$-0.895624\pi$
$433$	−39.3999	−1.89344	−0.946719	+	0.322061i	$0.895624\pi$
$434$	−45.9792	−2.20707
$435$	−101.566	−4.86973
$436$	1.45428	0.0696474
$437$	20.4150	0.976583
$438$	−33.5321	−1.60222
$439$	8.87304	0.423487	0.211744	−	0.977325i	$-0.432086\pi$
$439$	8.87304	0.423487	0.211744	+	0.977325i	$0.432086\pi$
$440$	−10.4873	−0.499961
$441$	19.9086	0.948027
$442$	−13.5885	−0.646340
$443$	−0.994527	−0.0472514	−0.0236257	−	0.999721i	$-0.507521\pi$
$443$	−0.994527	−0.0472514	−0.0236257	+	0.999721i	$0.507521\pi$
$444$	3.82094	0.181334
$445$	22.6644	1.07439
$446$	−10.6415	−0.503891
$447$	19.5154	0.923047
$448$	24.4109	1.15331
$449$	−8.22095	−0.387971	−0.193985	−	0.981004i	$-0.562141\pi$
$449$	−8.22095	−0.387971	−0.193985	+	0.981004i	$0.562141\pi$
$450$	−76.8703	−3.62370
$451$	1.74708	0.0822668
$452$	0.167006	0.00785530
$453$	−23.1388	−1.08715
$454$	33.3612	1.56572
$455$	64.2971	3.01430
$456$	49.9433	2.33881
$457$	−39.5336	−1.84931	−0.924653	−	0.380811i	$-0.875645\pi$
$457$	−39.5336	−1.84931	−0.924653	+	0.380811i	$0.875645\pi$
$458$	−19.5915	−0.915449
$459$	−13.1143	−0.612121
$460$	−1.43999	−0.0671398
$461$	3.35525	0.156270	0.0781349	−	0.996943i	$-0.475104\pi$
$461$	3.35525	0.156270	0.0781349	+	0.996943i	$0.475104\pi$
$462$	−13.8121	−0.642599
$463$	3.96701	0.184363	0.0921814	−	0.995742i	$-0.470616\pi$
$463$	3.96701	0.184363	0.0921814	+	0.995742i	$0.470616\pi$
$464$	−38.4373	−1.78441
$465$	−108.053	−5.01082
$466$	9.67670	0.448265
$467$	−27.4883	−1.27201	−0.636004	−	0.771686i	$-0.719414\pi$
$467$	−27.4883	−1.27201	−0.636004	+	0.771686i	$0.719414\pi$
$468$	3.25986	0.150687
$469$	14.9089	0.688430
$470$	20.4170	0.941767
$471$	53.8955	2.48337
$472$	24.5366	1.12939
$473$	−1.82661	−0.0839875
$474$	26.6743	1.22519
$475$	−60.2880	−2.76620
$476$	0.681555	0.0312390
$477$	−33.8048	−1.54782
$478$	−4.36449	−0.199627
$479$	−11.9418	−0.545635	−0.272817	−	0.962066i	$-0.587955\pi$
$479$	−11.9418	−0.545635	−0.272817	+	0.962066i	$0.587955\pi$
$480$	−7.26114	−0.331424
$481$	−58.6310	−2.67334
$482$	28.2993	1.28900
$483$	30.9934	1.41025
$484$	0.115325	0.00524206
$485$	39.4837	1.79286
$486$	−11.9888	−0.543824
$487$	34.5789	1.56692	0.783460	−	0.621442i	$-0.213453\pi$
$487$	34.5789	1.56692	0.783460	+	0.621442i	$0.213453\pi$
$488$	2.74110	0.124084
$489$	−30.5345	−1.38082
$490$	−20.2010	−0.912589
$491$	−22.9030	−1.03360	−0.516799	−	0.856106i	$-0.672877\pi$
$491$	−22.9030	−1.03360	−0.516799	+	0.856106i	$0.672877\pi$
$492$	0.586862	0.0264578
$493$	16.5202	0.744034
$494$	46.8946	2.10989
$495$	−20.9812	−0.943036
$496$	−40.8920	−1.83611
$497$	−18.0867	−0.811299
$498$	−11.9416	−0.535114
$499$	−23.7634	−1.06380	−0.531898	−	0.846808i	$-0.678521\pi$
$499$	−23.7634	−1.06380	−0.531898	+	0.846808i	$0.678521\pi$
$500$	2.04632	0.0915141
$501$	−16.5749	−0.740513
$502$	−31.6920	−1.41448
$503$	19.3269	0.861744	0.430872	−	0.902413i	$-0.358206\pi$
$503$	19.3269	0.861744	0.430872	+	0.902413i	$0.358206\pi$
$504$	49.0108	2.18311
$505$	−33.8029	−1.50421
$506$	−4.74662	−0.211013
$507$	−39.5202	−1.75515
$508$	0.200017	0.00887432
$509$	16.3288	0.723763	0.361881	−	0.932224i	$-0.382135\pi$
$509$	16.3288	0.723763	0.361881	+	0.932224i	$0.382135\pi$
$510$	29.3784	1.30090
$511$	−25.8075	−1.14166
$512$	20.3724	0.900342
$513$	45.2579	1.99819
$514$	7.83906	0.345766
$515$	65.0499	2.86644
$516$	−0.613577	−0.0270112
$517$	3.66916	0.161369
$518$	53.9398	2.36998
$519$	−8.05443	−0.353550
$520$	54.0559	2.37051
$521$	−0.718142	−0.0314624	−0.0157312	−	0.999876i	$-0.505008\pi$
$521$	−0.718142	−0.0314624	−0.0157312	+	0.999876i	$0.505008\pi$
$522$	−72.6934	−3.18170
$523$	6.65017	0.290792	0.145396	−	0.989374i	$-0.453554\pi$
$523$	6.65017	0.290792	0.145396	+	0.989374i	$0.453554\pi$
$524$	−0.995592	−0.0434926
$525$	−91.5271	−3.99457
$526$	−10.1543	−0.442749
$527$	17.5753	0.765591
$528$	−12.2840	−0.534591
$529$	−12.3489	−0.536911
$530$	34.3014	1.48996
$531$	49.0887	2.13027
$532$	−2.35208	−0.101976
$533$	−9.00519	−0.390058
$534$	25.0954	1.08598
$535$	−54.9320	−2.37492
$536$	12.5342	0.541396
$537$	−18.2868	−0.789135
$538$	−23.1626	−0.998612
$539$	−3.63034	−0.156370
$540$	−3.19230	−0.137375
$541$	−14.3220	−0.615750	−0.307875	−	0.951427i	$-0.599618\pi$
$541$	−14.3220	−0.615750	−0.307875	+	0.951427i	$0.599618\pi$
$542$	−17.1808	−0.737978
$543$	−14.2141	−0.609988
$544$	1.18106	0.0506374
$545$	48.2459	2.06663
$546$	71.1937	3.04681
$547$	−6.09736	−0.260704	−0.130352	−	0.991468i	$-0.541611\pi$
$547$	−6.09736	−0.260704	−0.130352	+	0.991468i	$0.541611\pi$
$548$	−0.698688	−0.0298465
$549$	5.48395	0.234049
$550$	14.0173	0.597702
$551$	−57.0121	−2.42880
$552$	26.0567	1.10905
$553$	20.5295	0.873005
$554$	26.4828	1.12514
$555$	126.760	5.38068
$556$	1.48177	0.0628412
$557$	33.7124	1.42844	0.714219	−	0.699922i	$-0.246782\pi$
$557$	33.7124	1.42844	0.714219	+	0.699922i	$0.246782\pi$
$558$	−77.3358	−3.27389
$559$	9.41512	0.398217
$560$	−52.6079	−2.22309
$561$	5.27961	0.222905
$562$	−15.5185	−0.654610
$563$	−17.1856	−0.724285	−0.362142	−	0.932123i	$-0.617955\pi$
$563$	−17.1856	−0.724285	−0.362142	+	0.932123i	$0.617955\pi$
$564$	1.23251	0.0518980
$565$	5.54044	0.233088
$566$	3.74404	0.157374
$567$	15.0691	0.632841
$568$	−15.2059	−0.638023
$569$	−30.9151	−1.29603	−0.648015	−	0.761628i	$-0.724401\pi$
$569$	−30.9151	−1.29603	−0.648015	+	0.761628i	$0.724401\pi$
$570$	−101.386	−4.24660
$571$	−13.0403	−0.545718	−0.272859	−	0.962054i	$-0.587969\pi$
$571$	−13.0403	−0.545718	−0.272859	+	0.962054i	$0.587969\pi$
$572$	−0.594436	−0.0248546
$573$	31.6364	1.32163
$574$	8.28466	0.345795
$575$	−31.4538	−1.31171
$576$	41.0585	1.71077
$577$	−14.3202	−0.596157	−0.298078	−	0.954541i	$-0.596346\pi$
$577$	−14.3202	−0.596157	−0.298078	+	0.954541i	$0.596346\pi$
$578$	19.9465	0.829667
$579$	−50.0049	−2.07813
$580$	4.02139	0.166979
$581$	−9.19067	−0.381293
$582$	43.7188	1.81220
$583$	6.16433	0.255300
$584$	−21.6969	−0.897824
$585$	108.146	4.47129
$586$	40.7480	1.68329
$587$	−32.3428	−1.33493	−0.667466	−	0.744640i	$-0.732621\pi$
$587$	−32.3428	−1.33493	−0.667466	+	0.744640i	$0.732621\pi$
$588$	−1.21947	−0.0502900
$589$	−60.6530	−2.49917
$590$	−49.8098	−2.05064
$591$	3.66875	0.150912
$592$	47.9719	1.97163
$593$	7.57405	0.311029	0.155514	−	0.987834i	$-0.450296\pi$
$593$	7.57405	0.311029	0.155514	+	0.987834i	$0.450296\pi$
$594$	−10.5228	−0.431754
$595$	22.6107	0.926948
$596$	−0.772687	−0.0316505
$597$	−16.8940	−0.691425
$598$	24.4661	1.00049
$599$	−37.0706	−1.51466	−0.757332	−	0.653030i	$-0.773498\pi$
$599$	−37.0706	−1.51466	−0.757332	+	0.653030i	$0.773498\pi$
$600$	−76.9487	−3.14142
$601$	−34.1013	−1.39102	−0.695511	−	0.718515i	$-0.744822\pi$
$601$	−34.1013	−1.39102	−0.695511	+	0.718515i	$0.744822\pi$
$602$	−8.66178	−0.353028
$603$	25.0764	1.02119
$604$	0.916149	0.0372776
$605$	3.82594	0.155546
$606$	−37.4287	−1.52044
$607$	26.0356	1.05675	0.528375	−	0.849011i	$-0.322801\pi$
$607$	26.0356	1.05675	0.528375	+	0.849011i	$0.322801\pi$
$608$	−4.07588	−0.165299
$609$	−86.5537	−3.50733
$610$	−5.56450	−0.225300
$611$	−18.9124	−0.765114
$612$	1.14636	0.0463388
$613$	30.6659	1.23859	0.619293	−	0.785160i	$-0.287419\pi$
$613$	30.6659	1.23859	0.619293	+	0.785160i	$0.287419\pi$
$614$	29.2358	1.17986
$615$	19.4692	0.785076
$616$	−8.93714	−0.360088
$617$	15.6936	0.631801	0.315901	−	0.948792i	$-0.397693\pi$
$617$	15.6936	0.631801	0.315901	+	0.948792i	$0.397693\pi$
$618$	72.0272	2.89736
$619$	15.1794	0.610111	0.305055	−	0.952335i	$-0.401325\pi$
$619$	15.1794	0.610111	0.305055	+	0.952335i	$0.401325\pi$
$620$	4.27820	0.171817
$621$	23.6122	0.947527
$622$	16.6330	0.666924
$623$	19.3143	0.773812
$624$	63.3168	2.53470
$625$	19.6979	0.787917
$626$	−32.5117	−1.29943
$627$	−18.2202	−0.727644
$628$	−2.13392	−0.0851527
$629$	−20.6182	−0.822100
$630$	−99.4931	−3.96390
$631$	31.6400	1.25957	0.629784	−	0.776771i	$-0.283144\pi$
$631$	31.6400	1.25957	0.629784	+	0.776771i	$0.283144\pi$
$632$	17.2596	0.686550
$633$	45.4033	1.80462
$634$	−11.5301	−0.457918
$635$	6.63559	0.263326
$636$	2.07066	0.0821071
$637$	18.7123	0.741409
$638$	13.2557	0.524797
$639$	−30.4214	−1.20345
$640$	−46.6474	−1.84390
$641$	5.81111	0.229525	0.114762	−	0.993393i	$-0.463389\pi$
$641$	5.81111	0.229525	0.114762	+	0.993393i	$0.463389\pi$
$642$	−60.8240	−2.40053
$643$	−49.2787	−1.94336	−0.971680	−	0.236300i	$-0.924065\pi$
$643$	−49.2787	−1.94336	−0.971680	+	0.236300i	$0.924065\pi$
$644$	−1.22714	−0.0483561
$645$	−20.3555	−0.801497
$646$	16.4909	0.648827
$647$	0.304638	0.0119766	0.00598828	−	0.999982i	$-0.498094\pi$
$647$	0.304638	0.0119766	0.00598828	+	0.999982i	$0.498094\pi$
$648$	12.6689	0.497680
$649$	−8.95135	−0.351371
$650$	−72.2514	−2.83393
$651$	−92.0813	−3.60895
$652$	1.20897	0.0473471
$653$	3.17370	0.124196	0.0620981	−	0.998070i	$-0.480221\pi$
$653$	3.17370	0.124196	0.0620981	+	0.998070i	$0.480221\pi$
$654$	53.4208	2.08892
$655$	−33.0289	−1.29055
$656$	7.36805	0.287674
$657$	−43.4076	−1.69349
$658$	17.3992	0.678290
$659$	33.4416	1.30270	0.651349	−	0.758778i	$-0.274203\pi$
$659$	33.4416	1.30270	0.651349	+	0.758778i	$0.274203\pi$
$660$	1.28517	0.0500253
$661$	−18.6941	−0.727118	−0.363559	−	0.931571i	$-0.618438\pi$
$661$	−18.6941	−0.727118	−0.363559	+	0.931571i	$0.618438\pi$
$662$	−7.25991	−0.282165
$663$	−27.2134	−1.05688
$664$	−7.72678	−0.299857
$665$	−78.0306	−3.02590
$666$	90.7254	3.51554
$667$	−29.7447	−1.15172
$668$	0.656262	0.0253916
$669$	−21.3115	−0.823950
$670$	−25.4448	−0.983018
$671$	−1.00000	−0.0386046
$672$	−6.18786	−0.238702
$673$	8.20391	0.316237	0.158119	−	0.987420i	$-0.449457\pi$
$673$	8.20391	0.316237	0.158119	+	0.987420i	$0.449457\pi$
$674$	−3.19351	−0.123010
$675$	−69.7297	−2.68390
$676$	1.56475	0.0601826
$677$	−31.6490	−1.21637	−0.608185	−	0.793795i	$-0.708102\pi$
$677$	−31.6490	−1.21637	−0.608185	+	0.793795i	$0.708102\pi$
$678$	6.13472	0.235602
$679$	33.6476	1.29128
$680$	19.0093	0.728972
$681$	66.8116	2.56023
$682$	14.1022	0.540002
$683$	−34.5524	−1.32211	−0.661056	−	0.750337i	$-0.729891\pi$
$683$	−34.5524	−1.32211	−0.661056	+	0.750337i	$0.729891\pi$
$684$	−3.95614	−0.151267
$685$	−23.1791	−0.885627
$686$	15.9790	0.610080
$687$	−39.2353	−1.49692
$688$	−7.70345	−0.293691
$689$	−31.7736	−1.21048
$690$	−52.8958	−2.01371
$691$	−29.6034	−1.12617	−0.563083	−	0.826401i	$-0.690385\pi$
$691$	−29.6034	−1.12617	−0.563083	+	0.826401i	$0.690385\pi$
$692$	0.318904	0.0121229
$693$	−17.8800	−0.679204
$694$	41.0513	1.55829
$695$	49.1580	1.86467
$696$	−72.7675	−2.75824
$697$	−3.16676	−0.119950
$698$	11.5012	0.435327
$699$	19.3793	0.732992
$700$	3.62389	0.136970
$701$	22.7553	0.859455	0.429728	−	0.902959i	$-0.358610\pi$
$701$	22.7553	0.859455	0.429728	+	0.902959i	$0.358610\pi$
$702$	54.2388	2.04711
$703$	71.1542	2.68363
$704$	−7.48703	−0.282178
$705$	40.8887	1.53996
$706$	5.58710	0.210273
$707$	−28.8065	−1.08338
$708$	−3.00685	−0.113004
$709$	2.14817	0.0806762	0.0403381	−	0.999186i	$-0.487157\pi$
$709$	2.14817	0.0806762	0.0403381	+	0.999186i	$0.487157\pi$
$710$	30.8683	1.15846
$711$	34.5302	1.29498
$712$	16.2379	0.608543
$713$	−31.6443	−1.18509
$714$	25.0359	0.936946
$715$	−19.7205	−0.737505
$716$	0.724043	0.0270587
$717$	−8.74064	−0.326425
$718$	23.4138	0.873794
$719$	21.9828	0.819820	0.409910	−	0.912126i	$-0.365560\pi$
$719$	21.9828	0.819820	0.409910	+	0.912126i	$0.365560\pi$
$720$	−88.4852	−3.29765
$721$	55.4348	2.06450
$722$	−29.2770	−1.08958
$723$	56.6742	2.10774
$724$	0.562790	0.0209159
$725$	87.8396	3.26228
$726$	4.23631	0.157224
$727$	48.6664	1.80494	0.902468	−	0.430757i	$-0.141753\pi$
$727$	48.6664	1.80494	0.902468	+	0.430757i	$0.141753\pi$
$728$	46.0658	1.70731
$729$	−37.8752	−1.40278
$730$	44.0452	1.63019
$731$	3.31092	0.122459
$732$	−0.335911	−0.0124156
$733$	5.69436	0.210326	0.105163	−	0.994455i	$-0.466464\pi$
$733$	5.69436	0.210326	0.105163	+	0.994455i	$0.466464\pi$
$734$	−37.9500	−1.40076
$735$	−40.4560	−1.49224
$736$	−2.12649	−0.0783836
$737$	−4.57270	−0.168438
$738$	13.9346	0.512940
$739$	33.6899	1.23930	0.619652	−	0.784877i	$-0.287274\pi$
$739$	33.6899	1.23930	0.619652	+	0.784877i	$0.287274\pi$
$740$	−5.01891	−0.184499
$741$	93.9146	3.45004
$742$	29.2313	1.07311
$743$	25.4613	0.934083	0.467042	−	0.884235i	$-0.345320\pi$
$743$	25.4613	0.934083	0.467042	+	0.884235i	$0.345320\pi$
$744$	−77.4146	−2.83816
$745$	−25.6340	−0.939157
$746$	−11.1173	−0.407033
$747$	−15.4585	−0.565596
$748$	−0.209039	−0.00764323
$749$	−46.8124	−1.71049
$750$	75.1684	2.74476
$751$	11.6876	0.426485	0.213243	−	0.976999i	$-0.431598\pi$
$751$	11.6876	0.426485	0.213243	+	0.976999i	$0.431598\pi$
$752$	15.4741	0.564283
$753$	−63.4687	−2.31293
$754$	−68.3254	−2.48827
$755$	30.3934	1.10613
$756$	−2.72044	−0.0989415
$757$	−32.0082	−1.16336	−0.581678	−	0.813419i	$-0.697604\pi$
$757$	−32.0082	−1.16336	−0.581678	+	0.813419i	$0.697604\pi$
$758$	13.2945	0.482878
$759$	−9.50594	−0.345044
$760$	−65.6019	−2.37963
$761$	36.3035	1.31600	0.658001	−	0.753017i	$-0.271402\pi$
$761$	36.3035	1.31600	0.658001	+	0.753017i	$0.271402\pi$
$762$	7.34733	0.266166
$763$	41.1147	1.48845
$764$	−1.25260	−0.0453175
$765$	38.0306	1.37500
$766$	24.5227	0.886042
$767$	46.1391	1.66599
$768$	−8.03556	−0.289958
$769$	−30.3964	−1.09612	−0.548062	−	0.836438i	$-0.684634\pi$
$769$	−30.3964	−1.09612	−0.548062	+	0.836438i	$0.684634\pi$
$770$	18.1426	0.653814
$771$	15.6991	0.565389
$772$	1.97988	0.0712574
$773$	−8.45088	−0.303957	−0.151979	−	0.988384i	$-0.548564\pi$
$773$	−8.45088	−0.303957	−0.151979	+	0.988384i	$0.548564\pi$
$774$	−14.5689	−0.523669
$775$	93.4493	3.35680
$776$	28.2882	1.01549
$777$	108.024	3.87533
$778$	−18.8775	−0.676791
$779$	10.9286	0.391559
$780$	−6.62433	−0.237189
$781$	5.54735	0.198500
$782$	8.60375	0.307669
$783$	−65.9408	−2.35653
$784$	−15.3104	−0.546800
$785$	−70.7931	−2.52672
$786$	−36.5716	−1.30447
$787$	−24.9875	−0.890707	−0.445354	−	0.895355i	$-0.646922\pi$
$787$	−24.9875	−0.890707	−0.445354	+	0.895355i	$0.646922\pi$
$788$	−0.145259	−0.00517464
$789$	−20.3358	−0.723972
$790$	−35.0374	−1.24658
$791$	4.72151	0.167877
$792$	−15.0320	−0.534140
$793$	5.15443	0.183039
$794$	1.32881	0.0471576
$795$	68.6945	2.43634
$796$	0.668895	0.0237083
$797$	−18.0752	−0.640257	−0.320128	−	0.947374i	$-0.603726\pi$
$797$	−18.0752	−0.640257	−0.320128	+	0.947374i	$0.603726\pi$
$798$	−86.4002	−3.05853
$799$	−6.65073	−0.235286
$800$	6.27979	0.222024
$801$	32.4862	1.14784
$802$	−52.6754	−1.86003
$803$	7.91540	0.279328
$804$	−1.53602	−0.0541712
$805$	−40.7106	−1.43486
$806$	−72.6889	−2.56036
$807$	−46.3872	−1.63291
$808$	−24.2182	−0.851993
$809$	30.1014	1.05831	0.529154	−	0.848526i	$-0.322509\pi$
$809$	30.1014	1.05831	0.529154	+	0.848526i	$0.322509\pi$
$810$	−25.7181	−0.903642
$811$	−12.8525	−0.451311	−0.225656	−	0.974207i	$-0.572452\pi$
$811$	−12.8525	−0.451311	−0.225656	+	0.974207i	$0.572452\pi$
$812$	3.42698	0.120263
$813$	−34.4075	−1.20672
$814$	−16.5438	−0.579860
$815$	40.1079	1.40492
$816$	22.2660	0.779465
$817$	−11.4261	−0.399749
$818$	−5.62853	−0.196797
$819$	92.1610	3.22037
$820$	−0.770859	−0.0269196
$821$	32.8927	1.14796	0.573981	−	0.818869i	$-0.305398\pi$
$821$	32.8927	1.14796	0.573981	+	0.818869i	$0.305398\pi$
$822$	−25.6653	−0.895179
$823$	32.1184	1.11958	0.559789	−	0.828635i	$-0.310882\pi$
$823$	32.1184	1.11958	0.559789	+	0.828635i	$0.310882\pi$
$824$	46.6052	1.62357
$825$	28.0722	0.977348
$826$	−42.4474	−1.47693
$827$	−7.66041	−0.266378	−0.133189	−	0.991091i	$-0.542522\pi$
$827$	−7.66041	−0.266378	−0.133189	+	0.991091i	$0.542522\pi$
$828$	−2.06402	−0.0717297
$829$	−27.0956	−0.941068	−0.470534	−	0.882382i	$-0.655939\pi$
$829$	−27.0956	−0.941068	−0.470534	+	0.882382i	$0.655939\pi$
$830$	15.6856	0.544454
$831$	53.0363	1.83981
$832$	38.5914	1.33791
$833$	6.58036	0.227996
$834$	54.4308	1.88478
$835$	21.7716	0.753437
$836$	0.721404	0.0249503
$837$	−70.1520	−2.42481
$838$	−7.86199	−0.271588
$839$	57.2281	1.97573	0.987866	−	0.155307i	$-0.0496368\pi$
$839$	57.2281	1.97573	0.987866	+	0.155307i	$0.0496368\pi$
$840$	−99.5944	−3.43633
$841$	54.0666	1.86437
$842$	−30.3636	−1.04640
$843$	−31.0786	−1.07040
$844$	−1.79768	−0.0618788
$845$	51.9108	1.78578
$846$	29.2650	1.00615
$847$	3.26042	0.112029
$848$	25.9971	0.892745
$849$	7.49810	0.257334
$850$	−25.4079	−0.871483
$851$	37.1230	1.27256
$852$	1.86341	0.0638395
$853$	2.91211	0.0997089	0.0498544	−	0.998756i	$-0.484124\pi$
$853$	2.91211	0.0997089	0.0498544	+	0.998756i	$0.484124\pi$
$854$	−4.74201	−0.162268
$855$	−131.245	−4.48850
$856$	−39.3561	−1.34516
$857$	−11.9479	−0.408133	−0.204066	−	0.978957i	$-0.565416\pi$
$857$	−11.9479	−0.408133	−0.204066	+	0.978957i	$0.565416\pi$
$858$	−21.8357	−0.745460
$859$	−28.3977	−0.968917	−0.484459	−	0.874814i	$-0.660983\pi$
$859$	−28.3977	−0.968917	−0.484459	+	0.874814i	$0.660983\pi$
$860$	0.805949	0.0274826
$861$	16.5915	0.565436
$862$	35.7379	1.21724
$863$	−27.3821	−0.932097	−0.466049	−	0.884759i	$-0.654323\pi$
$863$	−27.3821	−0.932097	−0.466049	+	0.884759i	$0.654323\pi$
$864$	−4.71421	−0.160381
$865$	10.5797	0.359721
$866$	57.3038	1.94726
$867$	39.9464	1.35665
$868$	3.64584	0.123748
$869$	−6.29660	−0.213597
$870$	147.720	5.00817
$871$	23.5697	0.798627
$872$	34.5659	1.17055
$873$	56.5944	1.91543
$874$	−29.6919	−1.00434
$875$	57.8524	1.95577
$876$	2.65887	0.0898347
$877$	−11.0166	−0.372004	−0.186002	−	0.982549i	$-0.559553\pi$
$877$	−11.0166	−0.372004	−0.186002	+	0.982549i	$0.559553\pi$
$878$	−12.9051	−0.435526
$879$	81.6051	2.75247
$880$	16.1353	0.543921
$881$	−26.1108	−0.879695	−0.439848	−	0.898072i	$-0.644968\pi$
$881$	−26.1108	−0.879695	−0.439848	+	0.898072i	$0.644968\pi$
$882$	−28.9553	−0.974977
$883$	8.12745	0.273511	0.136755	−	0.990605i	$-0.456333\pi$
$883$	8.12745	0.273511	0.136755	+	0.990605i	$0.456333\pi$
$884$	1.07748	0.0362395
$885$	−99.7528	−3.35315
$886$	1.44646	0.0485946
$887$	32.6845	1.09744	0.548720	−	0.836006i	$-0.315115\pi$
$887$	32.6845	1.09744	0.548720	+	0.836006i	$0.315115\pi$
$888$	90.8178	3.04765
$889$	5.65478	0.189655
$890$	−32.9634	−1.10494
$891$	−4.62182	−0.154837
$892$	0.843801	0.0282525
$893$	22.9520	0.768058
$894$	−28.3835	−0.949287
$895$	24.0202	0.802907
$896$	−39.7524	−1.32803
$897$	48.9977	1.63599
$898$	11.9567	0.399000
$899$	88.3715	2.94736
$900$	6.09530	0.203177
$901$	−11.1735	−0.372243
$902$	−2.54098	−0.0846054
$903$	−17.3467	−0.577263
$904$	3.96946	0.132022
$905$	18.6707	0.620634
$906$	33.6534	1.11806
$907$	−37.3623	−1.24060	−0.620298	−	0.784366i	$-0.712988\pi$
$907$	−37.3623	−1.24060	−0.620298	+	0.784366i	$0.712988\pi$
$908$	−2.64532	−0.0877880
$909$	−48.4518	−1.60705
$910$	−93.5148	−3.09998
$911$	−0.782097	−0.0259120	−0.0129560	−	0.999916i	$-0.504124\pi$
$911$	−0.782097	−0.0259120	−0.0129560	+	0.999916i	$0.504124\pi$
$912$	−76.8409	−2.54445
$913$	2.81886	0.0932907
$914$	57.4984	1.90188
$915$	−11.1439	−0.368405
$916$	1.55347	0.0513281
$917$	−28.1469	−0.929491
$918$	19.0736	0.629522
$919$	3.64261	0.120159	0.0600793	−	0.998194i	$-0.480865\pi$
$919$	3.64261	0.120159	0.0600793	+	0.998194i	$0.480865\pi$
$920$	−34.2262	−1.12840
$921$	58.5498	1.92928
$922$	−4.87994	−0.160712
$923$	−28.5934	−0.941164
$924$	1.09521	0.0360297
$925$	−109.629	−3.60457
$926$	−5.76969	−0.189604
$927$	93.2400	3.06240
$928$	5.93856	0.194943
$929$	−6.85276	−0.224832	−0.112416	−	0.993661i	$-0.535859\pi$
$929$	−6.85276	−0.224832	−0.112416	+	0.993661i	$0.535859\pi$
$930$	157.154	5.15327
$931$	−22.7091	−0.744262
$932$	−0.767297	−0.0251337
$933$	33.3105	1.09054
$934$	39.9795	1.30817
$935$	−6.93490	−0.226796
$936$	77.4816	2.53257
$937$	−24.9476	−0.815002	−0.407501	−	0.913205i	$-0.633600\pi$
$937$	−24.9476	−0.815002	−0.407501	+	0.913205i	$0.633600\pi$
$938$	−21.6838	−0.708000
$939$	−65.1103	−2.12480
$940$	−1.61893	−0.0528038
$941$	−47.1630	−1.53747	−0.768735	−	0.639568i	$-0.779113\pi$
$941$	−47.1630	−1.53747	−0.768735	+	0.639568i	$0.779113\pi$
$942$	−78.3865	−2.55397
$943$	5.70176	0.185675
$944$	−37.7510	−1.22869
$945$	−90.2510	−2.93587
$946$	2.65665	0.0863750
$947$	−49.6803	−1.61439	−0.807196	−	0.590283i	$-0.799016\pi$
$947$	−49.6803	−1.61439	−0.807196	+	0.590283i	$0.799016\pi$
$948$	−2.11509	−0.0686950
$949$	−40.7993	−1.32440
$950$	87.6838	2.84484
$951$	−23.0910	−0.748777
$952$	16.1995	0.525028
$953$	−31.7621	−1.02887	−0.514437	−	0.857528i	$-0.671999\pi$
$953$	−31.7621	−1.02887	−0.514437	+	0.857528i	$0.671999\pi$
$954$	49.1663	1.59182
$955$	−41.5552	−1.34469
$956$	0.346074	0.0111928
$957$	26.5468	0.858136
$958$	17.3683	0.561146
$959$	−19.7529	−0.637856
$960$	−83.4346	−2.69284
$961$	63.0152	2.03275
$962$	85.2739	2.74934
$963$	−78.7373	−2.53727
$964$	−2.24394	−0.0722725
$965$	65.6828	2.11440
$966$	−45.0772	−1.45034
$967$	−9.66371	−0.310764	−0.155382	−	0.987854i	$-0.549661\pi$
$967$	−9.66371	−0.310764	−0.155382	+	0.987854i	$0.549661\pi$
$968$	2.74110	0.0881023
$969$	33.0259	1.06095
$970$	−57.4257	−1.84383
$971$	49.0323	1.57352	0.786760	−	0.617259i	$-0.211757\pi$
$971$	49.0323	1.57352	0.786760	+	0.617259i	$0.211757\pi$
$972$	0.950633	0.0304916
$973$	41.8919	1.34299
$974$	−50.2921	−1.61146
$975$	−144.696	−4.63398
$976$	−4.21735	−0.134994
$977$	26.3062	0.841610	0.420805	−	0.907151i	$-0.361748\pi$
$977$	26.3062	0.841610	0.420805	+	0.907151i	$0.361748\pi$
$978$	44.4099	1.42007
$979$	−5.92388	−0.189328
$980$	1.60180	0.0511677
$981$	69.1538	2.20791
$982$	33.3105	1.06298
$983$	−10.5887	−0.337728	−0.168864	−	0.985639i	$-0.554010\pi$
$983$	−10.5887	−0.337728	−0.168864	+	0.985639i	$0.554010\pi$
$984$	13.9488	0.444671
$985$	−4.81899	−0.153546
$986$	−24.0273	−0.765185
$987$	34.8449	1.10912
$988$	−3.71842	−0.118299
$989$	−5.96131	−0.189559
$990$	30.5154	0.969844
$991$	−14.3949	−0.457270	−0.228635	−	0.973512i	$-0.573426\pi$
$991$	−14.3949	−0.457270	−0.228635	+	0.973512i	$0.573426\pi$
$992$	6.31782	0.200591
$993$	−14.5392	−0.461389
$994$	26.3056	0.834362
$995$	22.1907	0.703492
$996$	0.946886	0.0300032
$997$	−56.8098	−1.79919	−0.899593	−	0.436730i	$-0.856137\pi$
$997$	−56.8098	−1.79919	−0.899593	+	0.436730i	$0.856137\pi$
$998$	34.5619	1.09404
$999$	82.2977	2.60379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.7	✓	21
3.2	odd	2		6039.2.a.l.1.15		21
11.10	odd	2		7381.2.a.j.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.7	✓	21	1.1	even	1	trivial
6039.2.a.l.1.15		21	3.2	odd	2
7381.2.a.j.1.15		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)

\(f(q)\)	\(=\)	\(q-1.45442 q^{2} -2.91272 q^{3} +0.115325 q^{4} +3.82594 q^{5} +4.23631 q^{6} +3.26042 q^{7} +2.74110 q^{8} +5.48395 q^{9} +O(q^{10})\)	\(q-1.45442 q^{2} -2.91272 q^{3} +0.115325 q^{4} +3.82594 q^{5} +4.23631 q^{6} +3.26042 q^{7} +2.74110 q^{8} +5.48395 q^{9} -5.56450 q^{10} -1.00000 q^{11} -0.335911 q^{12} +5.15443 q^{13} -4.74201 q^{14} -11.1439 q^{15} -4.21735 q^{16} +1.81260 q^{17} -7.97594 q^{18} -6.25538 q^{19} +0.441227 q^{20} -9.49669 q^{21} +1.45442 q^{22} -3.26360 q^{23} -7.98406 q^{24} +9.63778 q^{25} -7.49668 q^{26} -7.23504 q^{27} +0.376009 q^{28} +9.11409 q^{29} +16.2078 q^{30} +9.69614 q^{31} +0.651580 q^{32} +2.91272 q^{33} -2.63628 q^{34} +12.4742 q^{35} +0.632438 q^{36} -11.3749 q^{37} +9.09792 q^{38} -15.0134 q^{39} +10.4873 q^{40} -1.74708 q^{41} +13.8121 q^{42} +1.82661 q^{43} -0.115325 q^{44} +20.9812 q^{45} +4.74662 q^{46} -3.66916 q^{47} +12.2840 q^{48} +3.63034 q^{49} -14.0173 q^{50} -5.27961 q^{51} +0.594436 q^{52} -6.16433 q^{53} +10.5228 q^{54} -3.82594 q^{55} +8.93714 q^{56} +18.2202 q^{57} -13.2557 q^{58} +8.95135 q^{59} -1.28517 q^{60} +1.00000 q^{61} -14.1022 q^{62} +17.8800 q^{63} +7.48703 q^{64} +19.7205 q^{65} -4.23631 q^{66} +4.57270 q^{67} +0.209039 q^{68} +9.50594 q^{69} -18.1426 q^{70} -5.54735 q^{71} +15.0320 q^{72} -7.91540 q^{73} +16.5438 q^{74} -28.0722 q^{75} -0.721404 q^{76} -3.26042 q^{77} +21.8357 q^{78} +6.29660 q^{79} -16.1353 q^{80} +4.62182 q^{81} +2.54098 q^{82} -2.81886 q^{83} -1.09521 q^{84} +6.93490 q^{85} -2.65665 q^{86} -26.5468 q^{87} -2.74110 q^{88} +5.92388 q^{89} -30.5154 q^{90} +16.8056 q^{91} -0.376375 q^{92} -28.2422 q^{93} +5.33648 q^{94} -23.9327 q^{95} -1.89787 q^{96} +10.3200 q^{97} -5.28002 q^{98} -5.48395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 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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