LMFDB - Embedded newform 7942.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 $ x^12 - 3x^11 - 21x^10 + 59x^9 + 162x^8 - 408x^7 - 581x^6 + 1236x^5 + 972x^4 - 1596x^3 - 621x^2 + 648*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.94662$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.94662 q^{3} +1.00000 q^{4} -2.95323 q^{5} +2.94662 q^{6} -2.07806 q^{7} -1.00000 q^{8} +5.68257 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.94662 q^{3} +1.00000 q^{4} -2.95323 q^{5} +2.94662 q^{6} -2.07806 q^{7} -1.00000 q^{8} +5.68257 q^{9} +2.95323 q^{10} +1.00000 q^{11} -2.94662 q^{12} +1.47738 q^{13} +2.07806 q^{14} +8.70205 q^{15} +1.00000 q^{16} -6.48427 q^{17} -5.68257 q^{18} -2.95323 q^{20} +6.12324 q^{21} -1.00000 q^{22} -0.228161 q^{23} +2.94662 q^{24} +3.72157 q^{25} -1.47738 q^{26} -7.90453 q^{27} -2.07806 q^{28} -1.39773 q^{29} -8.70205 q^{30} +3.32792 q^{31} -1.00000 q^{32} -2.94662 q^{33} +6.48427 q^{34} +6.13698 q^{35} +5.68257 q^{36} -9.42281 q^{37} -4.35329 q^{39} +2.95323 q^{40} +5.92333 q^{41} -6.12324 q^{42} -7.77010 q^{43} +1.00000 q^{44} -16.7819 q^{45} +0.228161 q^{46} -11.0954 q^{47} -2.94662 q^{48} -2.68168 q^{49} -3.72157 q^{50} +19.1067 q^{51} +1.47738 q^{52} -0.528294 q^{53} +7.90453 q^{54} -2.95323 q^{55} +2.07806 q^{56} +1.39773 q^{58} +11.5435 q^{59} +8.70205 q^{60} +11.8112 q^{61} -3.32792 q^{62} -11.8087 q^{63} +1.00000 q^{64} -4.36305 q^{65} +2.94662 q^{66} +9.02739 q^{67} -6.48427 q^{68} +0.672304 q^{69} -6.13698 q^{70} -11.5703 q^{71} -5.68257 q^{72} +10.2330 q^{73} +9.42281 q^{74} -10.9660 q^{75} -2.07806 q^{77} +4.35329 q^{78} +3.92377 q^{79} -2.95323 q^{80} +6.24392 q^{81} -5.92333 q^{82} -14.5456 q^{83} +6.12324 q^{84} +19.1495 q^{85} +7.77010 q^{86} +4.11857 q^{87} -1.00000 q^{88} -1.87207 q^{89} +16.7819 q^{90} -3.07009 q^{91} -0.228161 q^{92} -9.80613 q^{93} +11.0954 q^{94} +2.94662 q^{96} -10.4084 q^{97} +2.68168 q^{98} +5.68257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.94662	−1.70123	−0.850616	−	0.525787i	$-0.823771\pi$
$3$	−2.94662	−1.70123	−0.850616	+	0.525787i	$0.823771\pi$
$4$	1.00000	0.500000
$5$	−2.95323	−1.32072	−0.660362	−	0.750947i	$-0.729597\pi$
$5$	−2.95323	−1.32072	−0.660362	+	0.750947i	$0.729597\pi$
$6$	2.94662	1.20295
$7$	−2.07806	−0.785431	−0.392716	−	0.919660i	$-0.628464\pi$
$7$	−2.07806	−0.785431	−0.392716	+	0.919660i	$0.628464\pi$
$8$	−1.00000	−0.353553
$9$	5.68257	1.89419
$10$	2.95323	0.933893
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.94662	−0.850616
$13$	1.47738	0.409752	0.204876	−	0.978788i	$-0.434321\pi$
$13$	1.47738	0.409752	0.204876	+	0.978788i	$0.434321\pi$
$14$	2.07806	0.555384
$15$	8.70205	2.24686
$16$	1.00000	0.250000
$17$	−6.48427	−1.57267	−0.786333	−	0.617803i	$-0.788023\pi$
$17$	−6.48427	−1.57267	−0.786333	+	0.617803i	$0.788023\pi$
$18$	−5.68257	−1.33940
$19$	0	0
$19$	0	0
$20$	−2.95323	−0.660362
$21$	6.12324	1.33620
$22$	−1.00000	−0.213201
$23$	−0.228161	−0.0475748	−0.0237874	−	0.999717i	$-0.507572\pi$
$23$	−0.228161	−0.0475748	−0.0237874	+	0.999717i	$0.507572\pi$
$24$	2.94662	0.601476
$25$	3.72157	0.744313
$26$	−1.47738	−0.289739
$27$	−7.90453	−1.52123
$28$	−2.07806	−0.392716
$29$	−1.39773	−0.259551	−0.129776	−	0.991543i	$-0.541426\pi$
$29$	−1.39773	−0.259551	−0.129776	+	0.991543i	$0.541426\pi$
$30$	−8.70205	−1.58877
$31$	3.32792	0.597713	0.298856	−	0.954298i	$-0.403395\pi$
$31$	3.32792	0.597713	0.298856	+	0.954298i	$0.403395\pi$
$32$	−1.00000	−0.176777
$33$	−2.94662	−0.512941
$34$	6.48427	1.11204
$35$	6.13698	1.03734
$36$	5.68257	0.947096
$37$	−9.42281	−1.54910	−0.774551	−	0.632512i	$-0.782024\pi$
$37$	−9.42281	−1.54910	−0.774551	+	0.632512i	$0.782024\pi$
$38$	0	0
$39$	−4.35329	−0.697084
$40$	2.95323	0.466947
$41$	5.92333	0.925069	0.462535	−	0.886601i	$-0.346940\pi$
$41$	5.92333	0.925069	0.462535	+	0.886601i	$0.346940\pi$
$42$	−6.12324	−0.944837
$43$	−7.77010	−1.18493	−0.592465	−	0.805596i	$-0.701845\pi$
$43$	−7.77010	−1.18493	−0.592465	+	0.805596i	$0.701845\pi$
$44$	1.00000	0.150756
$45$	−16.7819	−2.50170
$46$	0.228161	0.0336405
$47$	−11.0954	−1.61843	−0.809214	−	0.587514i	$-0.800107\pi$
$47$	−11.0954	−1.61843	−0.809214	+	0.587514i	$0.800107\pi$
$48$	−2.94662	−0.425308
$49$	−2.68168	−0.383097
$50$	−3.72157	−0.526309
$51$	19.1067	2.67547
$52$	1.47738	0.204876
$53$	−0.528294	−0.0725667	−0.0362834	−	0.999342i	$-0.511552\pi$
$53$	−0.528294	−0.0725667	−0.0362834	+	0.999342i	$0.511552\pi$
$54$	7.90453	1.07567
$55$	−2.95323	−0.398213
$56$	2.07806	0.277692
$57$	0	0
$58$	1.39773	0.183531
$59$	11.5435	1.50284	0.751420	−	0.659824i	$-0.229369\pi$
$59$	11.5435	1.50284	0.751420	+	0.659824i	$0.229369\pi$
$60$	8.70205	1.12343
$61$	11.8112	1.51227	0.756137	−	0.654414i	$-0.227084\pi$
$61$	11.8112	1.51227	0.756137	+	0.654414i	$0.227084\pi$
$62$	−3.32792	−0.422647
$63$	−11.8087	−1.48776
$64$	1.00000	0.125000
$65$	−4.36305	−0.541170
$66$	2.94662	0.362704
$67$	9.02739	1.10287	0.551436	−	0.834217i	$-0.314080\pi$
$67$	9.02739	1.10287	0.551436	+	0.834217i	$0.314080\pi$
$68$	−6.48427	−0.786333
$69$	0.672304	0.0809358
$70$	−6.13698	−0.733509
$71$	−11.5703	−1.37314	−0.686571	−	0.727063i	$-0.740885\pi$
$71$	−11.5703	−1.37314	−0.686571	+	0.727063i	$0.740885\pi$
$72$	−5.68257	−0.669698
$73$	10.2330	1.19768	0.598842	−	0.800867i	$-0.295628\pi$
$73$	10.2330	1.19768	0.598842	+	0.800867i	$0.295628\pi$
$74$	9.42281	1.09538
$75$	−10.9660	−1.26625
$76$	0	0
$77$	−2.07806	−0.236816
$78$	4.35329	0.492913
$79$	3.92377	0.441459	0.220729	−	0.975335i	$-0.429156\pi$
$79$	3.92377	0.441459	0.220729	+	0.975335i	$0.429156\pi$
$80$	−2.95323	−0.330181
$81$	6.24392	0.693769
$82$	−5.92333	−0.654123
$83$	−14.5456	−1.59659	−0.798295	−	0.602267i	$-0.794264\pi$
$83$	−14.5456	−1.59659	−0.798295	+	0.602267i	$0.794264\pi$
$84$	6.12324	0.668101
$85$	19.1495	2.07706
$86$	7.77010	0.837871
$87$	4.11857	0.441557
$88$	−1.00000	−0.106600
$89$	−1.87207	−0.198439	−0.0992194	−	0.995066i	$-0.531635\pi$
$89$	−1.87207	−0.198439	−0.0992194	+	0.995066i	$0.531635\pi$
$90$	16.7819	1.76897
$91$	−3.07009	−0.321832
$92$	−0.228161	−0.0237874
$93$	−9.80613	−1.01685
$94$	11.0954	1.14440
$95$	0	0
$96$	2.94662	0.300738
$97$	−10.4084	−1.05681	−0.528407	−	0.848991i	$-0.677211\pi$
$97$	−10.4084	−1.05681	−0.528407	+	0.848991i	$0.677211\pi$
$98$	2.68168	0.270891
$99$	5.68257	0.571120
$100$	3.72157	0.372157
$101$	−7.83935	−0.780045	−0.390022	−	0.920805i	$-0.627533\pi$
$101$	−7.83935	−0.780045	−0.390022	+	0.920805i	$0.627533\pi$
$102$	−19.1067	−1.89184
$103$	4.65497	0.458668	0.229334	−	0.973348i	$-0.426345\pi$
$103$	4.65497	0.458668	0.229334	+	0.973348i	$0.426345\pi$
$104$	−1.47738	−0.144869
$105$	−18.0833	−1.76475
$106$	0.528294	0.0513124
$107$	13.1166	1.26803	0.634015	−	0.773321i	$-0.281406\pi$
$107$	13.1166	1.26803	0.634015	+	0.773321i	$0.281406\pi$
$108$	−7.90453	−0.760613
$109$	7.08421	0.678545	0.339272	−	0.940688i	$-0.389819\pi$
$109$	7.08421	0.678545	0.339272	+	0.940688i	$0.389819\pi$
$110$	2.95323	0.281579
$111$	27.7655	2.63538
$112$	−2.07806	−0.196358
$113$	18.3311	1.72444	0.862220	−	0.506534i	$-0.169073\pi$
$113$	18.3311	1.72444	0.862220	+	0.506534i	$0.169073\pi$
$114$	0	0
$115$	0.673811	0.0628332
$116$	−1.39773	−0.129776
$117$	8.39534	0.776149
$118$	−11.5435	−1.06267
$119$	13.4747	1.23522
$120$	−8.70205	−0.794385
$121$	1.00000	0.0909091
$122$	−11.8112	−1.06934
$123$	−17.4538	−1.57376
$124$	3.32792	0.298856
$125$	3.77551	0.337692
$126$	11.8087	1.05200
$127$	17.5091	1.55368	0.776839	−	0.629699i	$-0.216822\pi$
$127$	17.5091	1.55368	0.776839	+	0.629699i	$0.216822\pi$
$128$	−1.00000	−0.0883883
$129$	22.8955	2.01584
$130$	4.36305	0.382665
$131$	−11.9456	−1.04369	−0.521845	−	0.853040i	$-0.674756\pi$
$131$	−11.9456	−1.04369	−0.521845	+	0.853040i	$0.674756\pi$
$132$	−2.94662	−0.256470
$133$	0	0
$134$	−9.02739	−0.779848
$135$	23.3439	2.00912
$136$	6.48427	0.556022
$137$	7.99451	0.683017	0.341509	−	0.939879i	$-0.389062\pi$
$137$	7.99451	0.683017	0.341509	+	0.939879i	$0.389062\pi$
$138$	−0.672304	−0.0572303
$139$	11.5943	0.983414	0.491707	−	0.870761i	$-0.336373\pi$
$139$	11.5943	0.983414	0.491707	+	0.870761i	$0.336373\pi$
$140$	6.13698	0.518669
$141$	32.6939	2.75332
$142$	11.5703	0.970957
$143$	1.47738	0.123545
$144$	5.68257	0.473548
$145$	4.12781	0.342796
$146$	−10.2330	−0.846891
$147$	7.90190	0.651738
$148$	−9.42281	−0.774551
$149$	7.14505	0.585345	0.292672	−	0.956213i	$-0.405455\pi$
$149$	7.14505	0.585345	0.292672	+	0.956213i	$0.405455\pi$
$150$	10.9660	0.895373
$151$	8.69479	0.707572	0.353786	−	0.935326i	$-0.384894\pi$
$151$	8.69479	0.707572	0.353786	+	0.935326i	$0.384894\pi$
$152$	0	0
$153$	−36.8473	−2.97893
$154$	2.07806	0.167455
$155$	−9.82812	−0.789414
$156$	−4.35329	−0.348542
$157$	−3.55736	−0.283908	−0.141954	−	0.989873i	$-0.545339\pi$
$157$	−3.55736	−0.283908	−0.141954	+	0.989873i	$0.545339\pi$
$158$	−3.92377	−0.312159
$159$	1.55668	0.123453
$160$	2.95323	0.233473
$161$	0.474131	0.0373668
$162$	−6.24392	−0.490569
$163$	3.20938	0.251378	0.125689	−	0.992070i	$-0.459886\pi$
$163$	3.20938	0.251378	0.125689	+	0.992070i	$0.459886\pi$
$164$	5.92333	0.462535
$165$	8.70205	0.677453
$166$	14.5456	1.12896
$167$	−2.01829	−0.156180	−0.0780902	−	0.996946i	$-0.524882\pi$
$167$	−2.01829	−0.156180	−0.0780902	+	0.996946i	$0.524882\pi$
$168$	−6.12324	−0.472419
$169$	−10.8173	−0.832103
$170$	−19.1495	−1.46870
$171$	0	0
$172$	−7.77010	−0.592465
$173$	−2.37170	−0.180317	−0.0901585	−	0.995927i	$-0.528737\pi$
$173$	−2.37170	−0.180317	−0.0901585	+	0.995927i	$0.528737\pi$
$174$	−4.11857	−0.312228
$175$	−7.73362	−0.584607
$176$	1.00000	0.0753778
$177$	−34.0144	−2.55668
$178$	1.87207	0.140317
$179$	16.3824	1.22448	0.612240	−	0.790672i	$-0.290269\pi$
$179$	16.3824	1.22448	0.612240	+	0.790672i	$0.290269\pi$
$180$	−16.7819	−1.25085
$181$	−19.6899	−1.46354	−0.731770	−	0.681552i	$-0.761305\pi$
$181$	−19.6899	−1.46354	−0.731770	+	0.681552i	$0.761305\pi$
$182$	3.07009	0.227570
$183$	−34.8032	−2.57273
$184$	0.228161	0.0168202
$185$	27.8277	2.04594
$186$	9.80613	0.719020
$187$	−6.48427	−0.474177
$188$	−11.0954	−0.809214
$189$	16.4260	1.19482
$190$	0	0
$191$	22.1606	1.60349	0.801744	−	0.597668i	$-0.203906\pi$
$191$	22.1606	1.60349	0.801744	+	0.597668i	$0.203906\pi$
$192$	−2.94662	−0.212654
$193$	20.7035	1.49027	0.745137	−	0.666912i	$-0.232384\pi$
$193$	20.7035	1.49027	0.745137	+	0.666912i	$0.232384\pi$
$194$	10.4084	0.747281
$195$	12.8563	0.920656
$196$	−2.68168	−0.191549
$197$	1.11692	0.0795774	0.0397887	−	0.999208i	$-0.487332\pi$
$197$	1.11692	0.0795774	0.0397887	+	0.999208i	$0.487332\pi$
$198$	−5.68257	−0.403843
$199$	8.52674	0.604445	0.302222	−	0.953237i	$-0.402271\pi$
$199$	8.52674	0.604445	0.302222	+	0.953237i	$0.402271\pi$
$200$	−3.72157	−0.263154
$201$	−26.6003	−1.87624
$202$	7.83935	0.551575
$203$	2.90456	0.203860
$204$	19.1067	1.33774
$205$	−17.4930	−1.22176
$206$	−4.65497	−0.324327
$207$	−1.29654	−0.0901158
$208$	1.47738	0.102438
$209$	0	0
$210$	18.0833	1.24787
$211$	−11.4074	−0.785316	−0.392658	−	0.919684i	$-0.628444\pi$
$211$	−11.4074	−0.785316	−0.392658	+	0.919684i	$0.628444\pi$
$212$	−0.528294	−0.0362834
$213$	34.0933	2.33603
$214$	−13.1166	−0.896632
$215$	22.9469	1.56496
$216$	7.90453	0.537835
$217$	−6.91561	−0.469462
$218$	−7.08421	−0.479804
$219$	−30.1528	−2.03754
$220$	−2.95323	−0.199107
$221$	−9.57975	−0.644404
$222$	−27.7655	−1.86350
$223$	10.0347	0.671972	0.335986	−	0.941867i	$-0.390931\pi$
$223$	10.0347	0.671972	0.335986	+	0.941867i	$0.390931\pi$
$224$	2.07806	0.138846
$225$	21.1481	1.40987
$226$	−18.3311	−1.21936
$227$	−13.5501	−0.899353	−0.449676	−	0.893192i	$-0.648461\pi$
$227$	−13.5501	−0.899353	−0.449676	+	0.893192i	$0.648461\pi$
$228$	0	0
$229$	24.7339	1.63446	0.817229	−	0.576312i	$-0.195509\pi$
$229$	24.7339	1.63446	0.817229	+	0.576312i	$0.195509\pi$
$230$	−0.673811	−0.0444298
$231$	6.12324	0.402880
$232$	1.39773	0.0917653
$233$	17.2441	1.12970	0.564850	−	0.825194i	$-0.308934\pi$
$233$	17.2441	1.12970	0.564850	+	0.825194i	$0.308934\pi$
$234$	−8.39534	−0.548820
$235$	32.7672	2.13750
$236$	11.5435	0.751420
$237$	−11.5619	−0.751024
$238$	−13.4747	−0.873434
$239$	4.07684	0.263709	0.131855	−	0.991269i	$-0.457907\pi$
$239$	4.07684	0.263709	0.131855	+	0.991269i	$0.457907\pi$
$240$	8.70205	0.561715
$241$	−16.9143	−1.08955	−0.544773	−	0.838583i	$-0.683384\pi$
$241$	−16.9143	−1.08955	−0.544773	+	0.838583i	$0.683384\pi$
$242$	−1.00000	−0.0642824
$243$	5.31512	0.340965
$244$	11.8112	0.756137
$245$	7.91962	0.505966
$246$	17.4538	1.11281
$247$	0	0
$248$	−3.32792	−0.211323
$249$	42.8604	2.71617
$250$	−3.77551	−0.238784
$251$	2.37582	0.149960	0.0749802	−	0.997185i	$-0.476111\pi$
$251$	2.37582	0.149960	0.0749802	+	0.997185i	$0.476111\pi$
$252$	−11.8087	−0.743879
$253$	−0.228161	−0.0143444
$254$	−17.5091	−1.09862
$255$	−56.4264	−3.53356
$256$	1.00000	0.0625000
$257$	11.1728	0.696938	0.348469	−	0.937320i	$-0.386702\pi$
$257$	11.1728	0.696938	0.348469	+	0.937320i	$0.386702\pi$
$258$	−22.8955	−1.42541
$259$	19.5811	1.21671
$260$	−4.36305	−0.270585
$261$	−7.94269	−0.491640
$262$	11.9456	0.738001
$263$	8.64085	0.532818	0.266409	−	0.963860i	$-0.414163\pi$
$263$	8.64085	0.532818	0.266409	+	0.963860i	$0.414163\pi$
$264$	2.94662	0.181352
$265$	1.56017	0.0958406
$266$	0	0
$267$	5.51628	0.337591
$268$	9.02739	0.551436
$269$	−18.5716	−1.13233	−0.566166	−	0.824291i	$-0.691574\pi$
$269$	−18.5716	−1.13233	−0.566166	+	0.824291i	$0.691574\pi$
$270$	−23.3439	−1.42066
$271$	−15.0326	−0.913165	−0.456582	−	0.889681i	$-0.650927\pi$
$271$	−15.0326	−0.913165	−0.456582	+	0.889681i	$0.650927\pi$
$272$	−6.48427	−0.393167
$273$	9.04638	0.547512
$274$	−7.99451	−0.482966
$275$	3.72157	0.224419
$276$	0.672304	0.0404679
$277$	−12.2880	−0.738313	−0.369156	−	0.929367i	$-0.620353\pi$
$277$	−12.2880	−0.738313	−0.369156	+	0.929367i	$0.620353\pi$
$278$	−11.5943	−0.695378
$279$	18.9112	1.13218
$280$	−6.13698	−0.366755
$281$	−8.43609	−0.503255	−0.251627	−	0.967824i	$-0.580966\pi$
$281$	−8.43609	−0.503255	−0.251627	+	0.967824i	$0.580966\pi$
$282$	−32.6939	−1.94689
$283$	−7.07322	−0.420459	−0.210230	−	0.977652i	$-0.567421\pi$
$283$	−7.07322	−0.420459	−0.210230	+	0.977652i	$0.567421\pi$
$284$	−11.5703	−0.686571
$285$	0	0
$286$	−1.47738	−0.0873595
$287$	−12.3090	−0.726579
$288$	−5.68257	−0.334849
$289$	25.0458	1.47328
$290$	−4.12781	−0.242393
$291$	30.6697	1.79789
$292$	10.2330	0.598842
$293$	−11.9630	−0.698887	−0.349443	−	0.936958i	$-0.613629\pi$
$293$	−11.9630	−0.698887	−0.349443	+	0.936958i	$0.613629\pi$
$294$	−7.90190	−0.460848
$295$	−34.0907	−1.98484
$296$	9.42281	0.547690
$297$	−7.90453	−0.458667
$298$	−7.14505	−0.413901
$299$	−0.337081	−0.0194939
$300$	−10.9660	−0.633125
$301$	16.1467	0.930681
$302$	−8.69479	−0.500329
$303$	23.0996	1.32704
$304$	0	0
$305$	−34.8813	−1.99730
$306$	36.8473	2.10642
$307$	24.7128	1.41043	0.705216	−	0.708992i	$-0.250850\pi$
$307$	24.7128	1.41043	0.705216	+	0.708992i	$0.250850\pi$
$308$	−2.07806	−0.118408
$309$	−13.7164	−0.780301
$310$	9.82812	0.558200
$311$	−17.2082	−0.975790	−0.487895	−	0.872902i	$-0.662235\pi$
$311$	−17.2082	−0.975790	−0.487895	+	0.872902i	$0.662235\pi$
$312$	4.35329	0.246456
$313$	27.1885	1.53678	0.768391	−	0.639980i	$-0.221057\pi$
$313$	27.1885	1.53678	0.768391	+	0.639980i	$0.221057\pi$
$314$	3.55736	0.200754
$315$	34.8738	1.96492
$316$	3.92377	0.220729
$317$	−29.0996	−1.63440	−0.817198	−	0.576357i	$-0.804474\pi$
$317$	−29.0996	−1.63440	−0.817198	+	0.576357i	$0.804474\pi$
$318$	−1.55668	−0.0872943
$319$	−1.39773	−0.0782577
$320$	−2.95323	−0.165091
$321$	−38.6496	−2.15721
$322$	−0.474131	−0.0264223
$323$	0	0
$324$	6.24392	0.346884
$325$	5.49818	0.304984
$326$	−3.20938	−0.177751
$327$	−20.8745	−1.15436
$328$	−5.92333	−0.327061
$329$	23.0568	1.27116
$330$	−8.70205	−0.479032
$331$	27.4036	1.50624	0.753118	−	0.657886i	$-0.228549\pi$
$331$	27.4036	1.50624	0.753118	+	0.657886i	$0.228549\pi$
$332$	−14.5456	−0.798295
$333$	−53.5458	−2.93429
$334$	2.01829	0.110436
$335$	−26.6600	−1.45659
$336$	6.12324	0.334050
$337$	13.3290	0.726075	0.363037	−	0.931775i	$-0.381740\pi$
$337$	13.3290	0.726075	0.363037	+	0.931775i	$0.381740\pi$
$338$	10.8173	0.588386
$339$	−54.0147	−2.93367
$340$	19.1495	1.03853
$341$	3.32792	0.180217
$342$	0	0
$343$	20.1191	1.08633
$344$	7.77010	0.418936
$345$	−1.98547	−0.106894
$346$	2.37170	0.127503
$347$	−26.8283	−1.44022	−0.720110	−	0.693860i	$-0.755908\pi$
$347$	−26.8283	−1.44022	−0.720110	+	0.693860i	$0.755908\pi$
$348$	4.11857	0.220779
$349$	−9.24323	−0.494779	−0.247389	−	0.968916i	$-0.579573\pi$
$349$	−9.24323	−0.494779	−0.247389	+	0.968916i	$0.579573\pi$
$350$	7.73362	0.413379
$351$	−11.6780	−0.623326
$352$	−1.00000	−0.0533002
$353$	−9.30472	−0.495240	−0.247620	−	0.968857i	$-0.579649\pi$
$353$	−9.30472	−0.495240	−0.247620	+	0.968857i	$0.579649\pi$
$354$	34.0144	1.80785
$355$	34.1697	1.81354
$356$	−1.87207	−0.0992194
$357$	−39.7048	−2.10140
$358$	−16.3824	−0.865838
$359$	10.1211	0.534171	0.267086	−	0.963673i	$-0.413939\pi$
$359$	10.1211	0.534171	0.267086	+	0.963673i	$0.413939\pi$
$360$	16.7819	0.884486
$361$	0	0
$362$	19.6899	1.03488
$363$	−2.94662	−0.154657
$364$	−3.07009	−0.160916
$365$	−30.2205	−1.58181
$366$	34.8032	1.81919
$367$	0.314933	0.0164394	0.00821969	−	0.999966i	$-0.497384\pi$
$367$	0.314933	0.0164394	0.00821969	+	0.999966i	$0.497384\pi$
$368$	−0.228161	−0.0118937
$369$	33.6598	1.75226
$370$	−27.8277	−1.44669
$371$	1.09782	0.0569962
$372$	−9.80613	−0.508424
$373$	−12.8591	−0.665821	−0.332911	−	0.942958i	$-0.608031\pi$
$373$	−12.8591	−0.665821	−0.332911	+	0.942958i	$0.608031\pi$
$374$	6.48427	0.335294
$375$	−11.1250	−0.574493
$376$	11.0954	0.572201
$377$	−2.06498	−0.106352
$378$	−16.4260	−0.844865
$379$	0.421417	0.0216467	0.0108234	−	0.999941i	$-0.496555\pi$
$379$	0.421417	0.0216467	0.0108234	+	0.999941i	$0.496555\pi$
$380$	0	0
$381$	−51.5926	−2.64317
$382$	−22.1606	−1.13384
$383$	30.4242	1.55460	0.777302	−	0.629127i	$-0.216588\pi$
$383$	30.4242	1.55460	0.777302	+	0.629127i	$0.216588\pi$
$384$	2.94662	0.150369
$385$	6.13698	0.312769
$386$	−20.7035	−1.05378
$387$	−44.1542	−2.24448
$388$	−10.4084	−0.528407
$389$	−20.1361	−1.02094	−0.510472	−	0.859895i	$-0.670529\pi$
$389$	−20.1361	−1.02094	−0.510472	+	0.859895i	$0.670529\pi$
$390$	−12.8563	−0.651002
$391$	1.47946	0.0748193
$392$	2.68168	0.135445
$393$	35.1991	1.77556
$394$	−1.11692	−0.0562697
$395$	−11.5878	−0.583045
$396$	5.68257	0.285560
$397$	−2.42216	−0.121565	−0.0607825	−	0.998151i	$-0.519360\pi$
$397$	−2.42216	−0.121565	−0.0607825	+	0.998151i	$0.519360\pi$
$398$	−8.52674	−0.427407
$399$	0	0
$400$	3.72157	0.186078
$401$	−34.0761	−1.70168	−0.850838	−	0.525427i	$-0.823905\pi$
$401$	−34.0761	−1.70168	−0.850838	+	0.525427i	$0.823905\pi$
$402$	26.6003	1.32670
$403$	4.91662	0.244914
$404$	−7.83935	−0.390022
$405$	−18.4397	−0.916277
$406$	−2.90456	−0.144151
$407$	−9.42281	−0.467072
$408$	−19.1067	−0.945922
$409$	13.9246	0.688527	0.344264	−	0.938873i	$-0.388129\pi$
$409$	13.9246	0.688527	0.344264	+	0.938873i	$0.388129\pi$
$410$	17.4930	0.863916
$411$	−23.5568	−1.16197
$412$	4.65497	0.229334
$413$	−23.9881	−1.18038
$414$	1.29654	0.0637215
$415$	42.9566	2.10866
$416$	−1.47738	−0.0724347
$417$	−34.1639	−1.67301
$418$	0	0
$419$	−5.04606	−0.246516	−0.123258	−	0.992375i	$-0.539334\pi$
$419$	−5.04606	−0.246516	−0.123258	+	0.992375i	$0.539334\pi$
$420$	−18.0833	−0.882377
$421$	−2.69348	−0.131272	−0.0656361	−	0.997844i	$-0.520908\pi$
$421$	−2.69348	−0.131272	−0.0656361	+	0.997844i	$0.520908\pi$
$422$	11.4074	0.555303
$423$	−63.0503	−3.06561
$424$	0.528294	0.0256562
$425$	−24.1316	−1.17056
$426$	−34.0933	−1.65182
$427$	−24.5444	−1.18779
$428$	13.1166	0.634015
$429$	−4.35329	−0.210179
$430$	−22.9469	−1.10660
$431$	16.5684	0.798072	0.399036	−	0.916935i	$-0.369345\pi$
$431$	16.5684	0.798072	0.399036	+	0.916935i	$0.369345\pi$
$432$	−7.90453	−0.380307
$433$	−37.2669	−1.79093	−0.895466	−	0.445130i	$-0.853157\pi$
$433$	−37.2669	−1.79093	−0.895466	+	0.445130i	$0.853157\pi$
$434$	6.91561	0.331960
$435$	−12.1631	−0.583175
$436$	7.08421	0.339272
$437$	0	0
$438$	30.1528	1.44076
$439$	−32.9417	−1.57222	−0.786110	−	0.618087i	$-0.787908\pi$
$439$	−32.9417	−1.57222	−0.786110	+	0.618087i	$0.787908\pi$
$440$	2.95323	0.140790
$441$	−15.2389	−0.725660
$442$	9.57975	0.455662
$443$	35.9317	1.70717	0.853584	−	0.520956i	$-0.174424\pi$
$443$	35.9317	1.70717	0.853584	+	0.520956i	$0.174424\pi$
$444$	27.7655	1.31769
$445$	5.52865	0.262083
$446$	−10.0347	−0.475156
$447$	−21.0537	−0.995808
$448$	−2.07806	−0.0981789
$449$	−10.3098	−0.486550	−0.243275	−	0.969957i	$-0.578222\pi$
$449$	−10.3098	−0.486550	−0.243275	+	0.969957i	$0.578222\pi$
$450$	−21.1481	−0.996929
$451$	5.92333	0.278919
$452$	18.3311	0.862220
$453$	−25.6202	−1.20374
$454$	13.5501	0.635938
$455$	9.06667	0.425052
$456$	0	0
$457$	6.68451	0.312688	0.156344	−	0.987703i	$-0.450029\pi$
$457$	6.68451	0.312688	0.156344	+	0.987703i	$0.450029\pi$
$458$	−24.7339	−1.15574
$459$	51.2551	2.39238
$460$	0.673811	0.0314166
$461$	−39.7813	−1.85280	−0.926401	−	0.376540i	$-0.877114\pi$
$461$	−39.7813	−1.85280	−0.926401	+	0.376540i	$0.877114\pi$
$462$	−6.12324	−0.284879
$463$	25.5278	1.18638	0.593189	−	0.805064i	$-0.297869\pi$
$463$	25.5278	1.18638	0.593189	+	0.805064i	$0.297869\pi$
$464$	−1.39773	−0.0648878
$465$	28.9597	1.34298
$466$	−17.2441	−0.798819
$467$	−21.3277	−0.986930	−0.493465	−	0.869766i	$-0.664270\pi$
$467$	−21.3277	−0.986930	−0.493465	+	0.869766i	$0.664270\pi$
$468$	8.39534	0.388075
$469$	−18.7594	−0.866230
$470$	−32.7672	−1.51144
$471$	10.4822	0.482994
$472$	−11.5435	−0.531334
$473$	−7.77010	−0.357270
$474$	11.5619	0.531054
$475$	0	0
$476$	13.4747	0.617611
$477$	−3.00207	−0.137455
$478$	−4.07684	−0.186471
$479$	−29.8202	−1.36252	−0.681261	−	0.732041i	$-0.738568\pi$
$479$	−29.8202	−1.36252	−0.681261	+	0.732041i	$0.738568\pi$
$480$	−8.70205	−0.397192
$481$	−13.9211	−0.634748
$482$	16.9143	0.770426
$483$	−1.39708	−0.0635695
$484$	1.00000	0.0454545
$485$	30.7385	1.39576
$486$	−5.31512	−0.241099
$487$	−10.1155	−0.458379	−0.229190	−	0.973382i	$-0.573608\pi$
$487$	−10.1155	−0.458379	−0.229190	+	0.973382i	$0.573608\pi$
$488$	−11.8112	−0.534669
$489$	−9.45682	−0.427652
$490$	−7.91962	−0.357772
$491$	14.0903	0.635885	0.317943	−	0.948110i	$-0.397008\pi$
$491$	14.0903	0.635885	0.317943	+	0.948110i	$0.397008\pi$
$492$	−17.4538	−0.786879
$493$	9.06324	0.408188
$494$	0	0
$495$	−16.7819	−0.754292
$496$	3.32792	0.149428
$497$	24.0437	1.07851
$498$	−42.8604	−1.92062
$499$	38.7650	1.73536	0.867680	−	0.497124i	$-0.165611\pi$
$499$	38.7650	1.73536	0.867680	+	0.497124i	$0.165611\pi$
$500$	3.77551	0.168846
$501$	5.94715	0.265699
$502$	−2.37582	−0.106038
$503$	35.4119	1.57894	0.789469	−	0.613791i	$-0.210356\pi$
$503$	35.4119	1.57894	0.789469	+	0.613791i	$0.210356\pi$
$504$	11.8087	0.526002
$505$	23.1514	1.03022
$506$	0.228161	0.0101430
$507$	31.8746	1.41560
$508$	17.5091	0.776839
$509$	8.50194	0.376842	0.188421	−	0.982088i	$-0.439663\pi$
$509$	8.50194	0.376842	0.188421	+	0.982088i	$0.439663\pi$
$510$	56.4264	2.49860
$511$	−21.2648	−0.940699
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−11.1728	−0.492809
$515$	−13.7472	−0.605774
$516$	22.8955	1.00792
$517$	−11.0954	−0.487974
$518$	−19.5811	−0.860346
$519$	6.98850	0.306761
$520$	4.36305	0.191332
$521$	15.7448	0.689793	0.344896	−	0.938641i	$-0.387914\pi$
$521$	15.7448	0.689793	0.344896	+	0.938641i	$0.387914\pi$
$522$	7.94269	0.347642
$523$	19.7145	0.862056	0.431028	−	0.902339i	$-0.358151\pi$
$523$	19.7145	0.862056	0.431028	+	0.902339i	$0.358151\pi$
$524$	−11.9456	−0.521845
$525$	22.7880	0.994552
$526$	−8.64085	−0.376759
$527$	−21.5791	−0.940003
$528$	−2.94662	−0.128235
$529$	−22.9479	−0.997737
$530$	−1.56017	−0.0677696
$531$	65.5970	2.84667
$532$	0	0
$533$	8.75103	0.379049
$534$	−5.51628	−0.238713
$535$	−38.7363	−1.67472
$536$	−9.02739	−0.389924
$537$	−48.2728	−2.08312
$538$	18.5716	0.800680
$539$	−2.68168	−0.115508
$540$	23.3439	1.00456
$541$	28.5478	1.22737	0.613683	−	0.789553i	$-0.289687\pi$
$541$	28.5478	1.22737	0.613683	+	0.789553i	$0.289687\pi$
$542$	15.0326	0.645705
$543$	58.0187	2.48982
$544$	6.48427	0.278011
$545$	−20.9213	−0.896170
$546$	−9.04638	−0.387149
$547$	25.9423	1.10921	0.554607	−	0.832113i	$-0.312869\pi$
$547$	25.9423	1.10921	0.554607	+	0.832113i	$0.312869\pi$
$548$	7.99451	0.341509
$549$	67.1182	2.86453
$550$	−3.72157	−0.158688
$551$	0	0
$552$	−0.672304	−0.0286151
$553$	−8.15382	−0.346736
$554$	12.2880	0.522066
$555$	−81.9978	−3.48061
$556$	11.5943	0.491707
$557$	−21.8306	−0.924991	−0.462495	−	0.886622i	$-0.653046\pi$
$557$	−21.8306	−0.924991	−0.462495	+	0.886622i	$0.653046\pi$
$558$	−18.9112	−0.800573
$559$	−11.4794	−0.485528
$560$	6.13698	0.259335
$561$	19.1067	0.806685
$562$	8.43609	0.355855
$563$	−21.4158	−0.902570	−0.451285	−	0.892380i	$-0.649034\pi$
$563$	−21.4158	−0.902570	−0.451285	+	0.892380i	$0.649034\pi$
$564$	32.6939	1.37666
$565$	−54.1358	−2.27751
$566$	7.07322	0.297310
$567$	−12.9752	−0.544908
$568$	11.5703	0.485479
$569$	−7.76334	−0.325456	−0.162728	−	0.986671i	$-0.552029\pi$
$569$	−7.76334	−0.325456	−0.162728	+	0.986671i	$0.552029\pi$
$570$	0	0
$571$	−20.5327	−0.859269	−0.429634	−	0.903003i	$-0.641358\pi$
$571$	−20.5327	−0.859269	−0.429634	+	0.903003i	$0.641358\pi$
$572$	1.47738	0.0617725
$573$	−65.2990	−2.72791
$574$	12.3090	0.513769
$575$	−0.849116	−0.0354106
$576$	5.68257	0.236774
$577$	8.50006	0.353862	0.176931	−	0.984223i	$-0.443383\pi$
$577$	8.50006	0.353862	0.176931	+	0.984223i	$0.443383\pi$
$578$	−25.0458	−1.04177
$579$	−61.0055	−2.53530
$580$	4.12781	0.171398
$581$	30.2266	1.25401
$582$	−30.6697	−1.27130
$583$	−0.528294	−0.0218797
$584$	−10.2330	−0.423446
$585$	−24.7934	−1.02508
$586$	11.9630	0.494187
$587$	31.4150	1.29664	0.648318	−	0.761370i	$-0.275473\pi$
$587$	31.4150	1.29664	0.648318	+	0.761370i	$0.275473\pi$
$588$	7.90190	0.325869
$589$	0	0
$590$	34.0907	1.40349
$591$	−3.29114	−0.135380
$592$	−9.42281	−0.387275
$593$	−12.5289	−0.514500	−0.257250	−	0.966345i	$-0.582816\pi$
$593$	−12.5289	−0.514500	−0.257250	+	0.966345i	$0.582816\pi$
$594$	7.90453	0.324327
$595$	−39.7938	−1.63139
$596$	7.14505	0.292672
$597$	−25.1251	−1.02830
$598$	0.337081	0.0137843
$599$	−10.1484	−0.414653	−0.207326	−	0.978272i	$-0.566476\pi$
$599$	−10.1484	−0.414653	−0.207326	+	0.978272i	$0.566476\pi$
$600$	10.9660	0.447687
$601$	−5.47539	−0.223346	−0.111673	−	0.993745i	$-0.535621\pi$
$601$	−5.47539	−0.223346	−0.111673	+	0.993745i	$0.535621\pi$
$602$	−16.1467	−0.658091
$603$	51.2988	2.08905
$604$	8.69479	0.353786
$605$	−2.95323	−0.120066
$606$	−23.0996	−0.938357
$607$	47.1378	1.91326	0.956631	−	0.291301i	$-0.0940883\pi$
$607$	47.1378	1.91326	0.956631	+	0.291301i	$0.0940883\pi$
$608$	0	0
$609$	−8.55862	−0.346813
$610$	34.8813	1.41230
$611$	−16.3921	−0.663155
$612$	−36.8473	−1.48947
$613$	−23.7209	−0.958078	−0.479039	−	0.877794i	$-0.659015\pi$
$613$	−23.7209	−0.958078	−0.479039	+	0.877794i	$0.659015\pi$
$614$	−24.7128	−0.997326
$615$	51.5451	2.07850
$616$	2.07806	0.0837273
$617$	19.5372	0.786537	0.393269	−	0.919424i	$-0.371344\pi$
$617$	19.5372	0.786537	0.393269	+	0.919424i	$0.371344\pi$
$618$	13.7164	0.551756
$619$	−22.9019	−0.920505	−0.460253	−	0.887788i	$-0.652241\pi$
$619$	−22.9019	−0.920505	−0.460253	+	0.887788i	$0.652241\pi$
$620$	−9.82812	−0.394707
$621$	1.80350	0.0723721
$622$	17.2082	0.689988
$623$	3.89026	0.155860
$624$	−4.35329	−0.174271
$625$	−29.7578	−1.19031
$626$	−27.1885	−1.08667
$627$	0	0
$628$	−3.55736	−0.141954
$629$	61.1001	2.43622
$630$	−34.8738	−1.38941
$631$	38.0544	1.51492	0.757461	−	0.652881i	$-0.226440\pi$
$631$	38.0544	1.51492	0.757461	+	0.652881i	$0.226440\pi$
$632$	−3.92377	−0.156079
$633$	33.6132	1.33601
$634$	29.0996	1.15569
$635$	−51.7083	−2.05198
$636$	1.55668	0.0617264
$637$	−3.96187	−0.156975
$638$	1.39773	0.0553365
$639$	−65.7490	−2.60099
$640$	2.95323	0.116737
$641$	1.90082	0.0750780	0.0375390	−	0.999295i	$-0.488048\pi$
$641$	1.90082	0.0750780	0.0375390	+	0.999295i	$0.488048\pi$
$642$	38.6496	1.52538
$643$	−31.8165	−1.25472	−0.627361	−	0.778729i	$-0.715865\pi$
$643$	−31.8165	−1.25472	−0.627361	+	0.778729i	$0.715865\pi$
$644$	0.474131	0.0186834
$645$	−67.6158	−2.66237
$646$	0	0
$647$	−2.23771	−0.0879735	−0.0439868	−	0.999032i	$-0.514006\pi$
$647$	−2.23771	−0.0879735	−0.0439868	+	0.999032i	$0.514006\pi$
$648$	−6.24392	−0.245284
$649$	11.5435	0.453124
$650$	−5.49818	−0.215656
$651$	20.3777	0.798664
$652$	3.20938	0.125689
$653$	−40.4920	−1.58458	−0.792288	−	0.610148i	$-0.791110\pi$
$653$	−40.4920	−1.58458	−0.792288	+	0.610148i	$0.791110\pi$
$654$	20.8745	0.816257
$655$	35.2781	1.37843
$656$	5.92333	0.231267
$657$	58.1499	2.26864
$658$	−23.0568	−0.898849
$659$	−23.2188	−0.904476	−0.452238	−	0.891897i	$-0.649374\pi$
$659$	−23.2188	−0.904476	−0.452238	+	0.891897i	$0.649374\pi$
$660$	8.70205	0.338727
$661$	18.5200	0.720344	0.360172	−	0.932886i	$-0.382718\pi$
$661$	18.5200	0.720344	0.360172	+	0.932886i	$0.382718\pi$
$662$	−27.4036	−1.06507
$663$	28.2279	1.09628
$664$	14.5456	0.564480
$665$	0	0
$666$	53.5458	2.07486
$667$	0.318907	0.0123481
$668$	−2.01829	−0.0780902
$669$	−29.5684	−1.14318
$670$	26.6600	1.02996
$671$	11.8112	0.455968
$672$	−6.12324	−0.236209
$673$	−48.0170	−1.85092	−0.925460	−	0.378846i	$-0.876321\pi$
$673$	−48.0170	−1.85092	−0.925460	+	0.378846i	$0.876321\pi$
$674$	−13.3290	−0.513412
$675$	−29.4172	−1.13227
$676$	−10.8173	−0.416052
$677$	31.6110	1.21491	0.607455	−	0.794354i	$-0.292191\pi$
$677$	31.6110	1.21491	0.607455	+	0.794354i	$0.292191\pi$
$678$	54.0147	2.07442
$679$	21.6293	0.830056
$680$	−19.1495	−0.734351
$681$	39.9270	1.53001
$682$	−3.32792	−0.127433
$683$	−43.4101	−1.66104	−0.830522	−	0.556987i	$-0.811958\pi$
$683$	−43.4101	−1.66104	−0.830522	+	0.556987i	$0.811958\pi$
$684$	0	0
$685$	−23.6096	−0.902077
$686$	−20.1191	−0.768150
$687$	−72.8813	−2.78059
$688$	−7.77010	−0.296232
$689$	−0.780492	−0.0297344
$690$	1.98547	0.0755854
$691$	9.45256	0.359592	0.179796	−	0.983704i	$-0.442456\pi$
$691$	9.45256	0.359592	0.179796	+	0.983704i	$0.442456\pi$
$692$	−2.37170	−0.0901585
$693$	−11.8087	−0.448576
$694$	26.8283	1.01839
$695$	−34.2406	−1.29882
$696$	−4.11857	−0.156114
$697$	−38.4085	−1.45483
$698$	9.24323	0.349862
$699$	−50.8119	−1.92188
$700$	−7.73362	−0.292303
$701$	−22.2947	−0.842058	−0.421029	−	0.907047i	$-0.638331\pi$
$701$	−22.2947	−0.842058	−0.421029	+	0.907047i	$0.638331\pi$
$702$	11.6780	0.440758
$703$	0	0
$704$	1.00000	0.0376889
$705$	−96.5526	−3.63638
$706$	9.30472	0.350188
$707$	16.2906	0.612672
$708$	−34.0144	−1.27834
$709$	2.04482	0.0767949	0.0383975	−	0.999263i	$-0.487775\pi$
$709$	2.04482	0.0767949	0.0383975	+	0.999263i	$0.487775\pi$
$710$	−34.1697	−1.28237
$711$	22.2971	0.836207
$712$	1.87207	0.0701587
$713$	−0.759302	−0.0284361
$714$	39.7048	1.48591
$715$	−4.36305	−0.163169
$716$	16.3824	0.612240
$717$	−12.0129	−0.448631
$718$	−10.1211	−0.377716
$719$	−41.4716	−1.54663	−0.773314	−	0.634023i	$-0.781402\pi$
$719$	−41.4716	−1.54663	−0.773314	+	0.634023i	$0.781402\pi$
$720$	−16.7819	−0.625426
$721$	−9.67330	−0.360252
$722$	0	0
$723$	49.8401	1.85357
$724$	−19.6899	−0.731770
$725$	−5.20173	−0.193187
$726$	2.94662	0.109359
$727$	−4.21641	−0.156378	−0.0781890	−	0.996939i	$-0.524914\pi$
$727$	−4.21641	−0.156378	−0.0781890	+	0.996939i	$0.524914\pi$
$728$	3.07009	0.113785
$729$	−34.3934	−1.27383
$730$	30.2205	1.11851
$731$	50.3834	1.86350
$732$	−34.8032	−1.28636
$733$	−21.2074	−0.783312	−0.391656	−	0.920112i	$-0.628098\pi$
$733$	−21.2074	−0.783312	−0.391656	+	0.920112i	$0.628098\pi$
$734$	−0.314933	−0.0116244
$735$	−23.3361	−0.860766
$736$	0.228161	0.00841012
$737$	9.02739	0.332528
$738$	−33.6598	−1.23903
$739$	8.01575	0.294864	0.147432	−	0.989072i	$-0.452899\pi$
$739$	8.01575	0.294864	0.147432	+	0.989072i	$0.452899\pi$
$740$	27.8277	1.02297
$741$	0	0
$742$	−1.09782	−0.0403024
$743$	39.5220	1.44992	0.724960	−	0.688791i	$-0.241858\pi$
$743$	39.5220	1.44992	0.724960	+	0.688791i	$0.241858\pi$
$744$	9.80613	0.359510
$745$	−21.1010	−0.773079
$746$	12.8591	0.470807
$747$	−82.6566	−3.02425
$748$	−6.48427	−0.237088
$749$	−27.2570	−0.995950
$750$	11.1250	0.406228
$751$	12.4115	0.452902	0.226451	−	0.974023i	$-0.427288\pi$
$751$	12.4115	0.452902	0.226451	+	0.974023i	$0.427288\pi$
$752$	−11.0954	−0.404607
$753$	−7.00064	−0.255117
$754$	2.06498	0.0752021
$755$	−25.6777	−0.934507
$756$	16.4260	0.597410
$757$	45.5701	1.65627	0.828136	−	0.560527i	$-0.189401\pi$
$757$	45.5701	1.65627	0.828136	+	0.560527i	$0.189401\pi$
$758$	−0.421417	−0.0153066
$759$	0.672304	0.0244031
$760$	0	0
$761$	23.2399	0.842447	0.421224	−	0.906957i	$-0.361601\pi$
$761$	23.2399	0.842447	0.421224	+	0.906957i	$0.361601\pi$
$762$	51.5926	1.86900
$763$	−14.7214	−0.532950
$764$	22.1606	0.801744
$765$	108.819	3.93435
$766$	−30.4242	−1.09927
$767$	17.0542	0.615793
$768$	−2.94662	−0.106327
$769$	−4.89342	−0.176461	−0.0882307	−	0.996100i	$-0.528121\pi$
$769$	−4.89342	−0.176461	−0.0882307	+	0.996100i	$0.528121\pi$
$770$	−6.13698	−0.221161
$771$	−32.9219	−1.18565
$772$	20.7035	0.745137
$773$	−25.9075	−0.931827	−0.465914	−	0.884830i	$-0.654274\pi$
$773$	−25.9075	−0.931827	−0.465914	+	0.884830i	$0.654274\pi$
$774$	44.1542	1.58709
$775$	12.3851	0.444885
$776$	10.4084	0.373640
$777$	−57.6982	−2.06991
$778$	20.1361	0.721916
$779$	0	0
$780$	12.8563	0.460328
$781$	−11.5703	−0.414018
$782$	−1.47946	−0.0529053
$783$	11.0484	0.394836
$784$	−2.68168	−0.0957744
$785$	10.5057	0.374965
$786$	−35.1991	−1.25551
$787$	−20.8301	−0.742511	−0.371256	−	0.928531i	$-0.621073\pi$
$787$	−20.8301	−0.742511	−0.371256	+	0.928531i	$0.621073\pi$
$788$	1.11692	0.0397887
$789$	−25.4613	−0.906447
$790$	11.5878	0.412275
$791$	−38.0930	−1.35443
$792$	−5.68257	−0.201921
$793$	17.4497	0.619658
$794$	2.42216	0.0859594
$795$	−4.59724	−0.163047
$796$	8.52674	0.302222
$797$	23.3076	0.825598	0.412799	−	0.910822i	$-0.364551\pi$
$797$	23.3076	0.825598	0.412799	+	0.910822i	$0.364551\pi$
$798$	0	0
$799$	71.9455	2.54525
$800$	−3.72157	−0.131577
$801$	−10.6382	−0.375881
$802$	34.0761	1.20327
$803$	10.2330	0.361116
$804$	−26.6003	−0.938120
$805$	−1.40022	−0.0493512
$806$	−4.91662	−0.173180
$807$	54.7236	1.92636
$808$	7.83935	0.275788
$809$	27.2402	0.957714	0.478857	−	0.877893i	$-0.341051\pi$
$809$	27.2402	0.957714	0.478857	+	0.877893i	$0.341051\pi$
$810$	18.4397	0.647906
$811$	14.8734	0.522274	0.261137	−	0.965302i	$-0.415903\pi$
$811$	14.8734	0.522274	0.261137	+	0.965302i	$0.415903\pi$
$812$	2.90456	0.101930
$813$	44.2953	1.55351
$814$	9.42281	0.330269
$815$	−9.47803	−0.332001
$816$	19.1067	0.668868
$817$	0	0
$818$	−13.9246	−0.486862
$819$	−17.4460	−0.609612
$820$	−17.4930	−0.610881
$821$	0.719078	0.0250960	0.0125480	−	0.999921i	$-0.496006\pi$
$821$	0.719078	0.0250960	0.0125480	+	0.999921i	$0.496006\pi$
$822$	23.5568	0.821637
$823$	19.6396	0.684594	0.342297	−	0.939592i	$-0.388795\pi$
$823$	19.6396	0.684594	0.342297	+	0.939592i	$0.388795\pi$
$824$	−4.65497	−0.162164
$825$	−10.9660	−0.381789
$826$	23.9881	0.834654
$827$	−12.7948	−0.444920	−0.222460	−	0.974942i	$-0.571409\pi$
$827$	−12.7948	−0.444920	−0.222460	+	0.974942i	$0.571409\pi$
$828$	−1.29654	−0.0450579
$829$	−20.7761	−0.721585	−0.360793	−	0.932646i	$-0.617494\pi$
$829$	−20.7761	−0.721585	−0.360793	+	0.932646i	$0.617494\pi$
$830$	−42.9566	−1.49104
$831$	36.2080	1.25604
$832$	1.47738	0.0512190
$833$	17.3887	0.602484
$834$	34.1639	1.18300
$835$	5.96049	0.206271
$836$	0	0
$837$	−26.3056	−0.909256
$838$	5.04606	0.174313
$839$	37.8790	1.30773	0.653865	−	0.756612i	$-0.273147\pi$
$839$	37.8790	1.30773	0.653865	+	0.756612i	$0.273147\pi$
$840$	18.0833	0.623935
$841$	−27.0464	−0.932633
$842$	2.69348	0.0928234
$843$	24.8580	0.856153
$844$	−11.4074	−0.392658
$845$	31.9461	1.09898
$846$	63.0503	2.16771
$847$	−2.07806	−0.0714029
$848$	−0.528294	−0.0181417
$849$	20.8421	0.715299
$850$	24.1316	0.827708
$851$	2.14992	0.0736982
$852$	34.0933	1.16802
$853$	−29.3638	−1.00540	−0.502698	−	0.864462i	$-0.667659\pi$
$853$	−29.3638	−1.00540	−0.502698	+	0.864462i	$0.667659\pi$
$854$	24.5444	0.839892
$855$	0	0
$856$	−13.1166	−0.448316
$857$	−5.05739	−0.172757	−0.0863786	−	0.996262i	$-0.527529\pi$
$857$	−5.05739	−0.172757	−0.0863786	+	0.996262i	$0.527529\pi$
$858$	4.35329	0.148619
$859$	16.9599	0.578663	0.289332	−	0.957229i	$-0.406567\pi$
$859$	16.9599	0.578663	0.289332	+	0.957229i	$0.406567\pi$
$860$	22.9469	0.782482
$861$	36.2700	1.23608
$862$	−16.5684	−0.564322
$863$	−3.61937	−0.123205	−0.0616023	−	0.998101i	$-0.519621\pi$
$863$	−3.61937	−0.123205	−0.0616023	+	0.998101i	$0.519621\pi$
$864$	7.90453	0.268917
$865$	7.00417	0.238149
$866$	37.2669	1.26638
$867$	−73.8003	−2.50639
$868$	−6.91561	−0.234731
$869$	3.92377	0.133105
$870$	12.1631	0.412367
$871$	13.3369	0.451904
$872$	−7.08421	−0.239902
$873$	−59.1466	−2.00181
$874$	0	0
$875$	−7.84573	−0.265234
$876$	−30.1528	−1.01877
$877$	8.09441	0.273329	0.136664	−	0.990617i	$-0.456362\pi$
$877$	8.09441	0.273329	0.136664	+	0.990617i	$0.456362\pi$
$878$	32.9417	1.11173
$879$	35.2505	1.18897
$880$	−2.95323	−0.0995533
$881$	−34.7558	−1.17095	−0.585476	−	0.810690i	$-0.699092\pi$
$881$	−34.7558	−1.17095	−0.585476	+	0.810690i	$0.699092\pi$
$882$	15.2389	0.513119
$883$	−33.7929	−1.13722	−0.568611	−	0.822606i	$-0.692519\pi$
$883$	−33.7929	−1.13722	−0.568611	+	0.822606i	$0.692519\pi$
$884$	−9.57975	−0.322202
$885$	100.452	3.37667
$886$	−35.9317	−1.20715
$887$	−19.7965	−0.664700	−0.332350	−	0.943156i	$-0.607842\pi$
$887$	−19.7965	−0.664700	−0.332350	+	0.943156i	$0.607842\pi$
$888$	−27.7655	−0.931748
$889$	−36.3848	−1.22031
$890$	−5.52865	−0.185321
$891$	6.24392	0.209179
$892$	10.0347	0.335986
$893$	0	0
$894$	21.0537	0.704142
$895$	−48.3811	−1.61720
$896$	2.07806	0.0694230
$897$	0.993250	0.0331636
$898$	10.3098	0.344043
$899$	−4.65153	−0.155137
$900$	21.1481	0.704936
$901$	3.42560	0.114123
$902$	−5.92333	−0.197225
$903$	−47.5782	−1.58330
$904$	−18.3311	−0.609682
$905$	58.1488	1.93293
$906$	25.6202	0.851175
$907$	−4.76964	−0.158373	−0.0791866	−	0.996860i	$-0.525232\pi$
$907$	−4.76964	−0.158373	−0.0791866	+	0.996860i	$0.525232\pi$
$908$	−13.5501	−0.449676
$909$	−44.5477	−1.47755
$910$	−9.06667	−0.300557
$911$	−2.93295	−0.0971729	−0.0485865	−	0.998819i	$-0.515472\pi$
$911$	−2.93295	−0.0971729	−0.0485865	+	0.998819i	$0.515472\pi$
$912$	0	0
$913$	−14.5456	−0.481390
$914$	−6.68451	−0.221104
$915$	102.782	3.39787
$916$	24.7339	0.817229
$917$	24.8236	0.819747
$918$	−51.2551	−1.69167
$919$	5.24634	0.173061	0.0865304	−	0.996249i	$-0.472422\pi$
$919$	5.24634	0.173061	0.0865304	+	0.996249i	$0.472422\pi$
$920$	−0.673811	−0.0222149
$921$	−72.8192	−2.39947
$922$	39.7813	1.31013
$923$	−17.0938	−0.562648
$924$	6.12324	0.201440
$925$	−35.0676	−1.15302
$926$	−25.5278	−0.838895
$927$	26.4522	0.868805
$928$	1.39773	0.0458826
$929$	48.3723	1.58704	0.793522	−	0.608542i	$-0.208245\pi$
$929$	48.3723	1.58704	0.793522	+	0.608542i	$0.208245\pi$
$930$	−28.9597	−0.949627
$931$	0	0
$932$	17.2441	0.564850
$933$	50.7062	1.66005
$934$	21.3277	0.697865
$935$	19.1495	0.626257
$936$	−8.39534	−0.274410
$937$	−8.81965	−0.288125	−0.144063	−	0.989569i	$-0.546017\pi$
$937$	−8.81965	−0.288125	−0.144063	+	0.989569i	$0.546017\pi$
$938$	18.7594	0.612517
$939$	−80.1141	−2.61442
$940$	32.7672	1.06875
$941$	−39.9909	−1.30367	−0.651833	−	0.758363i	$-0.726000\pi$
$941$	−39.9909	−1.30367	−0.651833	+	0.758363i	$0.726000\pi$
$942$	−10.4822	−0.341528
$943$	−1.35147	−0.0440100
$944$	11.5435	0.375710
$945$	−48.5099	−1.57803
$946$	7.77010	0.252628
$947$	−36.5370	−1.18729	−0.593646	−	0.804726i	$-0.702312\pi$
$947$	−36.5370	−1.18729	−0.593646	+	0.804726i	$0.702312\pi$
$948$	−11.5619	−0.375512
$949$	15.1181	0.490754
$950$	0	0
$951$	85.7455	2.78049
$952$	−13.4747	−0.436717
$953$	−2.28184	−0.0739159	−0.0369580	−	0.999317i	$-0.511767\pi$
$953$	−2.28184	−0.0739159	−0.0369580	+	0.999317i	$0.511767\pi$
$954$	3.00207	0.0971955
$955$	−65.4455	−2.11777
$956$	4.07684	0.131855
$957$	4.11857	0.133134
$958$	29.8202	0.963448
$959$	−16.6130	−0.536463
$960$	8.70205	0.280857
$961$	−19.9249	−0.642740
$962$	13.9211	0.448834
$963$	74.5360	2.40189
$964$	−16.9143	−0.544773
$965$	−61.1423	−1.96824
$966$	1.39708	0.0449505
$967$	31.0645	0.998966	0.499483	−	0.866324i	$-0.333523\pi$
$967$	31.0645	0.998966	0.499483	+	0.866324i	$0.333523\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−30.7385	−0.986952
$971$	31.8113	1.02087	0.510437	−	0.859915i	$-0.329484\pi$
$971$	31.8113	1.02087	0.510437	+	0.859915i	$0.329484\pi$
$972$	5.31512	0.170483
$973$	−24.0936	−0.772404
$974$	10.1155	0.324123
$975$	−16.2010	−0.518849
$976$	11.8112	0.378068
$977$	59.6065	1.90698	0.953491	−	0.301421i	$-0.0974611\pi$
$977$	59.6065	1.90698	0.953491	+	0.301421i	$0.0974611\pi$
$978$	9.45682	0.302396
$979$	−1.87207	−0.0598316
$980$	7.91962	0.252983
$981$	40.2566	1.28529
$982$	−14.0903	−0.449639
$983$	−41.2146	−1.31454	−0.657270	−	0.753655i	$-0.728289\pi$
$983$	−41.2146	−1.31454	−0.657270	+	0.753655i	$0.728289\pi$
$984$	17.4538	0.556407
$985$	−3.29853	−0.105100
$986$	−9.06324	−0.288632
$987$	−67.9397	−2.16255
$988$	0	0
$989$	1.77283	0.0563728
$990$	16.7819	0.533365
$991$	−52.7804	−1.67662	−0.838312	−	0.545191i	$-0.816457\pi$
$991$	−52.7804	−1.67662	−0.838312	+	0.545191i	$0.816457\pi$
$992$	−3.32792	−0.105662
$993$	−80.7479	−2.56246
$994$	−24.0437	−0.762621
$995$	−25.1814	−0.798305
$996$	42.8604	1.35809
$997$	−57.4846	−1.82056	−0.910278	−	0.413996i	$-0.864133\pi$
$997$	−57.4846	−1.82056	−0.910278	+	0.413996i	$0.864133\pi$
$998$	−38.7650	−1.22708
$999$	74.4829	2.35653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bs.1.1		12
19.14	odd	18		418.2.j.b.177.1	yes	24
19.15	odd	18		418.2.j.b.111.1	✓	24
19.18	odd	2		7942.2.a.bw.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.b.111.1	✓	24	19.15	odd	18
418.2.j.b.177.1	yes	24	19.14	odd	18
7942.2.a.bs.1.1		12	1.1	even	1	trivial
7942.2.a.bw.1.12		12	19.18	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.94662 q^{3} +1.00000 q^{4} -2.95323 q^{5} +2.94662 q^{6} -2.07806 q^{7} -1.00000 q^{8} +5.68257 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.94662 q^{3} +1.00000 q^{4} -2.95323 q^{5} +2.94662 q^{6} -2.07806 q^{7} -1.00000 q^{8} +5.68257 q^{9} +2.95323 q^{10} +1.00000 q^{11} -2.94662 q^{12} +1.47738 q^{13} +2.07806 q^{14} +8.70205 q^{15} +1.00000 q^{16} -6.48427 q^{17} -5.68257 q^{18} -2.95323 q^{20} +6.12324 q^{21} -1.00000 q^{22} -0.228161 q^{23} +2.94662 q^{24} +3.72157 q^{25} -1.47738 q^{26} -7.90453 q^{27} -2.07806 q^{28} -1.39773 q^{29} -8.70205 q^{30} +3.32792 q^{31} -1.00000 q^{32} -2.94662 q^{33} +6.48427 q^{34} +6.13698 q^{35} +5.68257 q^{36} -9.42281 q^{37} -4.35329 q^{39} +2.95323 q^{40} +5.92333 q^{41} -6.12324 q^{42} -7.77010 q^{43} +1.00000 q^{44} -16.7819 q^{45} +0.228161 q^{46} -11.0954 q^{47} -2.94662 q^{48} -2.68168 q^{49} -3.72157 q^{50} +19.1067 q^{51} +1.47738 q^{52} -0.528294 q^{53} +7.90453 q^{54} -2.95323 q^{55} +2.07806 q^{56} +1.39773 q^{58} +11.5435 q^{59} +8.70205 q^{60} +11.8112 q^{61} -3.32792 q^{62} -11.8087 q^{63} +1.00000 q^{64} -4.36305 q^{65} +2.94662 q^{66} +9.02739 q^{67} -6.48427 q^{68} +0.672304 q^{69} -6.13698 q^{70} -11.5703 q^{71} -5.68257 q^{72} +10.2330 q^{73} +9.42281 q^{74} -10.9660 q^{75} -2.07806 q^{77} +4.35329 q^{78} +3.92377 q^{79} -2.95323 q^{80} +6.24392 q^{81} -5.92333 q^{82} -14.5456 q^{83} +6.12324 q^{84} +19.1495 q^{85} +7.77010 q^{86} +4.11857 q^{87} -1.00000 q^{88} -1.87207 q^{89} +16.7819 q^{90} -3.07009 q^{91} -0.228161 q^{92} -9.80613 q^{93} +11.0954 q^{94} +2.94662 q^{96} -10.4084 q^{97} +2.68168 q^{98} +5.68257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

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