LMFDB - Embedded newform 7942.2.a.bo.1.4

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 14x^{6} + 29x^{5} + 64x^{4} - 50x^{3} - 36x^{2} + 30x - 5 $ x^8 - 3x^7 - 14x^6 + 29x^5 + 64x^4 - 50x^3 - 36x^2 + 30*x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.370513$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.629487 q^{3} +1.00000 q^{4} +1.24752 q^{5} -0.629487 q^{6} -2.54316 q^{7} -1.00000 q^{8} -2.60375 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.629487 q^{3} +1.00000 q^{4} +1.24752 q^{5} -0.629487 q^{6} -2.54316 q^{7} -1.00000 q^{8} -2.60375 q^{9} -1.24752 q^{10} -1.00000 q^{11} +0.629487 q^{12} -7.07204 q^{13} +2.54316 q^{14} +0.785299 q^{15} +1.00000 q^{16} -5.73296 q^{17} +2.60375 q^{18} +1.24752 q^{20} -1.60089 q^{21} +1.00000 q^{22} +1.76701 q^{23} -0.629487 q^{24} -3.44369 q^{25} +7.07204 q^{26} -3.52749 q^{27} -2.54316 q^{28} -5.47429 q^{29} -0.785299 q^{30} +6.26904 q^{31} -1.00000 q^{32} -0.629487 q^{33} +5.73296 q^{34} -3.17265 q^{35} -2.60375 q^{36} +0.519644 q^{37} -4.45176 q^{39} -1.24752 q^{40} +0.911921 q^{41} +1.60089 q^{42} +6.38929 q^{43} -1.00000 q^{44} -3.24823 q^{45} -1.76701 q^{46} +4.03673 q^{47} +0.629487 q^{48} -0.532320 q^{49} +3.44369 q^{50} -3.60883 q^{51} -7.07204 q^{52} -1.71467 q^{53} +3.52749 q^{54} -1.24752 q^{55} +2.54316 q^{56} +5.47429 q^{58} +4.00236 q^{59} +0.785299 q^{60} -12.6252 q^{61} -6.26904 q^{62} +6.62175 q^{63} +1.00000 q^{64} -8.82252 q^{65} +0.629487 q^{66} +10.5778 q^{67} -5.73296 q^{68} +1.11231 q^{69} +3.17265 q^{70} -9.10511 q^{71} +2.60375 q^{72} -17.0064 q^{73} -0.519644 q^{74} -2.16776 q^{75} +2.54316 q^{77} +4.45176 q^{78} +5.56025 q^{79} +1.24752 q^{80} +5.59073 q^{81} -0.911921 q^{82} +10.3053 q^{83} -1.60089 q^{84} -7.15199 q^{85} -6.38929 q^{86} -3.44600 q^{87} +1.00000 q^{88} +6.71159 q^{89} +3.24823 q^{90} +17.9853 q^{91} +1.76701 q^{92} +3.94628 q^{93} -4.03673 q^{94} -0.629487 q^{96} +5.06574 q^{97} +0.532320 q^{98} +2.60375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * 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
$3$	0.629487	0.363435	0.181717	−	0.983351i	$-0.441834\pi$
$3$	0.629487	0.363435	0.181717	+	0.983351i	$0.441834\pi$
$4$	1.00000	0.500000
$5$	1.24752	0.557909	0.278954	−	0.960304i	$-0.410012\pi$
$5$	1.24752	0.557909	0.278954	+	0.960304i	$0.410012\pi$
$6$	−0.629487	−0.256987
$7$	−2.54316	−0.961225	−0.480613	−	0.876933i	$-0.659586\pi$
$7$	−2.54316	−0.961225	−0.480613	+	0.876933i	$0.659586\pi$
$8$	−1.00000	−0.353553
$9$	−2.60375	−0.867915
$10$	−1.24752	−0.394501
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.629487	0.181717
$13$	−7.07204	−1.96143	−0.980715	−	0.195442i	$-0.937386\pi$
$13$	−7.07204	−1.96143	−0.980715	+	0.195442i	$0.937386\pi$
$14$	2.54316	0.679689
$15$	0.785299	0.202763
$16$	1.00000	0.250000
$17$	−5.73296	−1.39045	−0.695223	−	0.718794i	$-0.744695\pi$
$17$	−5.73296	−1.39045	−0.695223	+	0.718794i	$0.744695\pi$
$18$	2.60375	0.613709
$19$	0	0
$19$	0	0
$20$	1.24752	0.278954
$21$	−1.60089	−0.349343
$22$	1.00000	0.213201
$23$	1.76701	0.368448	0.184224	−	0.982884i	$-0.441023\pi$
$23$	1.76701	0.368448	0.184224	+	0.982884i	$0.441023\pi$
$24$	−0.629487	−0.128494
$25$	−3.44369	−0.688738
$26$	7.07204	1.38694
$27$	−3.52749	−0.678865
$28$	−2.54316	−0.480613
$29$	−5.47429	−1.01655	−0.508275	−	0.861195i	$-0.669717\pi$
$29$	−5.47429	−1.01655	−0.508275	+	0.861195i	$0.669717\pi$
$30$	−0.785299	−0.143375
$31$	6.26904	1.12595	0.562977	−	0.826473i	$-0.309656\pi$
$31$	6.26904	1.12595	0.562977	+	0.826473i	$0.309656\pi$
$32$	−1.00000	−0.176777
$33$	−0.629487	−0.109580
$34$	5.73296	0.983194
$35$	−3.17265	−0.536276
$36$	−2.60375	−0.433958
$37$	0.519644	0.0854289	0.0427145	−	0.999087i	$-0.486399\pi$
$37$	0.519644	0.0854289	0.0427145	+	0.999087i	$0.486399\pi$
$38$	0	0
$39$	−4.45176	−0.712852
$40$	−1.24752	−0.197250
$41$	0.911921	0.142418	0.0712091	−	0.997461i	$-0.477314\pi$
$41$	0.911921	0.142418	0.0712091	+	0.997461i	$0.477314\pi$
$42$	1.60089	0.247023
$43$	6.38929	0.974358	0.487179	−	0.873302i	$-0.338026\pi$
$43$	6.38929	0.974358	0.487179	+	0.873302i	$0.338026\pi$
$44$	−1.00000	−0.150756
$45$	−3.24823	−0.484217
$46$	−1.76701	−0.260532
$47$	4.03673	0.588817	0.294409	−	0.955680i	$-0.404877\pi$
$47$	4.03673	0.588817	0.294409	+	0.955680i	$0.404877\pi$
$48$	0.629487	0.0908587
$49$	−0.532320	−0.0760457
$50$	3.44369	0.487011
$51$	−3.60883	−0.505337
$52$	−7.07204	−0.980715
$53$	−1.71467	−0.235529	−0.117764	−	0.993042i	$-0.537573\pi$
$53$	−1.71467	−0.235529	−0.117764	+	0.993042i	$0.537573\pi$
$54$	3.52749	0.480030
$55$	−1.24752	−0.168216
$56$	2.54316	0.339845
$57$	0	0
$58$	5.47429	0.718809
$59$	4.00236	0.521064	0.260532	−	0.965465i	$-0.416102\pi$
$59$	4.00236	0.521064	0.260532	+	0.965465i	$0.416102\pi$
$60$	0.785299	0.101382
$61$	−12.6252	−1.61649	−0.808246	−	0.588845i	$-0.799583\pi$
$61$	−12.6252	−1.61649	−0.808246	+	0.588845i	$0.799583\pi$
$62$	−6.26904	−0.796169
$63$	6.62175	0.834262
$64$	1.00000	0.125000
$65$	−8.82252	−1.09430
$66$	0.629487	0.0774845
$67$	10.5778	1.29228	0.646140	−	0.763219i	$-0.276382\pi$
$67$	10.5778	1.29228	0.646140	+	0.763219i	$0.276382\pi$
$68$	−5.73296	−0.695223
$69$	1.11231	0.133907
$70$	3.17265	0.379204
$71$	−9.10511	−1.08058	−0.540289	−	0.841480i	$-0.681685\pi$
$71$	−9.10511	−1.08058	−0.540289	+	0.841480i	$0.681685\pi$
$72$	2.60375	0.306854
$73$	−17.0064	−1.99045	−0.995226	−	0.0975942i	$-0.968885\pi$
$73$	−17.0064	−1.99045	−0.995226	+	0.0975942i	$0.968885\pi$
$74$	−0.519644	−0.0604074
$75$	−2.16776	−0.250311
$76$	0	0
$77$	2.54316	0.289820
$78$	4.45176	0.504062
$79$	5.56025	0.625577	0.312788	−	0.949823i	$-0.398737\pi$
$79$	5.56025	0.625577	0.312788	+	0.949823i	$0.398737\pi$
$80$	1.24752	0.139477
$81$	5.59073	0.621192
$82$	−0.911921	−0.100705
$83$	10.3053	1.13116	0.565579	−	0.824694i	$-0.308653\pi$
$83$	10.3053	1.13116	0.565579	+	0.824694i	$0.308653\pi$
$84$	−1.60089	−0.174671
$85$	−7.15199	−0.775742
$86$	−6.38929	−0.688975
$87$	−3.44600	−0.369450
$88$	1.00000	0.106600
$89$	6.71159	0.711427	0.355714	−	0.934595i	$-0.384238\pi$
$89$	6.71159	0.711427	0.355714	+	0.934595i	$0.384238\pi$
$90$	3.24823	0.342393
$91$	17.9853	1.88538
$92$	1.76701	0.184224
$93$	3.94628	0.409211
$94$	−4.03673	−0.416357
$95$	0	0
$96$	−0.629487	−0.0642468
$97$	5.06574	0.514347	0.257174	−	0.966365i	$-0.417209\pi$
$97$	5.06574	0.514347	0.257174	+	0.966365i	$0.417209\pi$
$98$	0.532320	0.0537724
$99$	2.60375	0.261686
$100$	−3.44369	−0.344369
$101$	−1.09506	−0.108963	−0.0544814	−	0.998515i	$-0.517351\pi$
$101$	−1.09506	−0.108963	−0.0544814	+	0.998515i	$0.517351\pi$
$102$	3.60883	0.357327
$103$	8.01195	0.789441	0.394720	−	0.918801i	$-0.370841\pi$
$103$	8.01195	0.789441	0.394720	+	0.918801i	$0.370841\pi$
$104$	7.07204	0.693470
$105$	−1.99714	−0.194901
$106$	1.71467	0.166544
$107$	−1.13235	−0.109469	−0.0547344	−	0.998501i	$-0.517431\pi$
$107$	−1.13235	−0.109469	−0.0547344	+	0.998501i	$0.517431\pi$
$108$	−3.52749	−0.339433
$109$	−2.80777	−0.268936	−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80777	−0.268936	−0.134468	+	0.990918i	$0.542932\pi$
$110$	1.24752	0.118947
$111$	0.327109	0.0310478
$112$	−2.54316	−0.240306
$113$	−4.20350	−0.395432	−0.197716	−	0.980259i	$-0.563352\pi$
$113$	−4.20350	−0.395432	−0.197716	+	0.980259i	$0.563352\pi$
$114$	0	0
$115$	2.20439	0.205560
$116$	−5.47429	−0.508275
$117$	18.4138	1.70236
$118$	−4.00236	−0.368448
$119$	14.5799	1.33653
$120$	−0.785299	−0.0716877
$121$	1.00000	0.0909091
$122$	12.6252	1.14303
$123$	0.574043	0.0517597
$124$	6.26904	0.562977
$125$	−10.5337	−0.942161
$126$	−6.62175	−0.589912
$127$	3.94482	0.350046	0.175023	−	0.984564i	$-0.444000\pi$
$127$	3.94482	0.350046	0.175023	+	0.984564i	$0.444000\pi$
$128$	−1.00000	−0.0883883
$129$	4.02198	0.354116
$130$	8.82252	0.773786
$131$	−8.13753	−0.710979	−0.355490	−	0.934680i	$-0.615686\pi$
$131$	−8.13753	−0.710979	−0.355490	+	0.934680i	$0.615686\pi$
$132$	−0.629487	−0.0547898
$133$	0	0
$134$	−10.5778	−0.913779
$135$	−4.40062	−0.378745
$136$	5.73296	0.491597
$137$	−1.33653	−0.114187	−0.0570937	−	0.998369i	$-0.518183\pi$
$137$	−1.33653	−0.114187	−0.0570937	+	0.998369i	$0.518183\pi$
$138$	−1.11231	−0.0946864
$139$	−14.4332	−1.22421	−0.612105	−	0.790776i	$-0.709677\pi$
$139$	−14.4332	−1.22421	−0.612105	+	0.790776i	$0.709677\pi$
$140$	−3.17265	−0.268138
$141$	2.54107	0.213997
$142$	9.10511	0.764083
$143$	7.07204	0.591394
$144$	−2.60375	−0.216979
$145$	−6.82929	−0.567142
$146$	17.0064	1.40746
$147$	−0.335089	−0.0276377
$148$	0.519644	0.0427145
$149$	12.3807	1.01426	0.507132	−	0.861868i	$-0.330706\pi$
$149$	12.3807	1.01426	0.507132	+	0.861868i	$0.330706\pi$
$150$	2.16776	0.176997
$151$	15.6391	1.27269	0.636345	−	0.771404i	$-0.280445\pi$
$151$	15.6391	1.27269	0.636345	+	0.771404i	$0.280445\pi$
$152$	0	0
$153$	14.9272	1.20679
$154$	−2.54316	−0.204934
$155$	7.82077	0.628179
$156$	−4.45176	−0.356426
$157$	21.6670	1.72922	0.864609	−	0.502445i	$-0.167566\pi$
$157$	21.6670	1.72922	0.864609	+	0.502445i	$0.167566\pi$
$158$	−5.56025	−0.442349
$159$	−1.07937	−0.0855993
$160$	−1.24752	−0.0986252
$161$	−4.49381	−0.354162
$162$	−5.59073	−0.439249
$163$	−12.1901	−0.954805	−0.477403	−	0.878685i	$-0.658422\pi$
$163$	−12.1901	−0.954805	−0.477403	+	0.878685i	$0.658422\pi$
$164$	0.911921	0.0712091
$165$	−0.785299	−0.0611355
$166$	−10.3053	−0.799850
$167$	16.8627	1.30488	0.652438	−	0.757842i	$-0.273746\pi$
$167$	16.8627	1.30488	0.652438	+	0.757842i	$0.273746\pi$
$168$	1.60089	0.123511
$169$	37.0137	2.84721
$170$	7.15199	0.548533
$171$	0	0
$172$	6.38929	0.487179
$173$	19.8445	1.50875	0.754373	−	0.656446i	$-0.227941\pi$
$173$	19.8445	1.50875	0.754373	+	0.656446i	$0.227941\pi$
$174$	3.44600	0.261240
$175$	8.75787	0.662033
$176$	−1.00000	−0.0753778
$177$	2.51944	0.189373
$178$	−6.71159	−0.503055
$179$	−7.22486	−0.540012	−0.270006	−	0.962859i	$-0.587026\pi$
$179$	−7.22486	−0.540012	−0.270006	+	0.962859i	$0.587026\pi$
$180$	−3.24823	−0.242109
$181$	−23.1532	−1.72096	−0.860480	−	0.509484i	$-0.829836\pi$
$181$	−23.1532	−1.72096	−0.860480	+	0.509484i	$0.829836\pi$
$182$	−17.9853	−1.33316
$183$	−7.94741	−0.587490
$184$	−1.76701	−0.130266
$185$	0.648267	0.0476615
$186$	−3.94628	−0.289356
$187$	5.73296	0.419235
$188$	4.03673	0.294409
$189$	8.97098	0.652543
$190$	0	0
$191$	−26.3906	−1.90956	−0.954780	−	0.297313i	$-0.903910\pi$
$191$	−26.3906	−1.90956	−0.954780	+	0.297313i	$0.903910\pi$
$192$	0.629487	0.0454293
$193$	−6.66366	−0.479661	−0.239830	−	0.970815i	$-0.577092\pi$
$193$	−6.66366	−0.479661	−0.239830	+	0.970815i	$0.577092\pi$
$194$	−5.06574	−0.363699
$195$	−5.55367	−0.397706
$196$	−0.532320	−0.0380229
$197$	−14.6474	−1.04358	−0.521791	−	0.853073i	$-0.674736\pi$
$197$	−14.6474	−1.04358	−0.521791	+	0.853073i	$0.674736\pi$
$198$	−2.60375	−0.185040
$199$	−11.8064	−0.836930	−0.418465	−	0.908233i	$-0.637432\pi$
$199$	−11.8064	−0.836930	−0.418465	+	0.908233i	$0.637432\pi$
$200$	3.44369	0.243506
$201$	6.65857	0.469659
$202$	1.09506	0.0770484
$203$	13.9220	0.977134
$204$	−3.60883	−0.252668
$205$	1.13764	0.0794563
$206$	−8.01195	−0.558219
$207$	−4.60086	−0.319782
$208$	−7.07204	−0.490358
$209$	0	0
$210$	1.99714	0.137816
$211$	26.2927	1.81006	0.905032	−	0.425343i	$-0.139846\pi$
$211$	26.2927	1.81006	0.905032	+	0.425343i	$0.139846\pi$
$212$	−1.71467	−0.117764
$213$	−5.73155	−0.392719
$214$	1.13235	0.0774061
$215$	7.97078	0.543603
$216$	3.52749	0.240015
$217$	−15.9432	−1.08230
$218$	2.80777	0.190166
$219$	−10.7053	−0.723400
$220$	−1.24752	−0.0841079
$221$	40.5437	2.72726
$222$	−0.327109	−0.0219541
$223$	27.2252	1.82313	0.911567	−	0.411151i	$-0.134873\pi$
$223$	27.2252	1.82313	0.911567	+	0.411151i	$0.134873\pi$
$224$	2.54316	0.169922
$225$	8.96649	0.597766
$226$	4.20350	0.279612
$227$	25.4375	1.68835	0.844175	−	0.536068i	$-0.180091\pi$
$227$	25.4375	1.68835	0.844175	+	0.536068i	$0.180091\pi$
$228$	0	0
$229$	21.4833	1.41966	0.709830	−	0.704373i	$-0.248772\pi$
$229$	21.4833	1.41966	0.709830	+	0.704373i	$0.248772\pi$
$230$	−2.20439	−0.145353
$231$	1.60089	0.105331
$232$	5.47429	0.359405
$233$	1.74431	0.114274	0.0571368	−	0.998366i	$-0.481803\pi$
$233$	1.74431	0.114274	0.0571368	+	0.998366i	$0.481803\pi$
$234$	−18.4138	−1.20375
$235$	5.03590	0.328506
$236$	4.00236	0.260532
$237$	3.50011	0.227356
$238$	−14.5799	−0.945071
$239$	−19.7598	−1.27815	−0.639076	−	0.769143i	$-0.720683\pi$
$239$	−19.7598	−1.27815	−0.639076	+	0.769143i	$0.720683\pi$
$240$	0.785299	0.0506908
$241$	10.1904	0.656423	0.328211	−	0.944604i	$-0.393554\pi$
$241$	10.1904	0.656423	0.328211	+	0.944604i	$0.393554\pi$
$242$	−1.00000	−0.0642824
$243$	14.1018	0.904628
$244$	−12.6252	−0.808246
$245$	−0.664081	−0.0424265
$246$	−0.574043	−0.0365996
$247$	0	0
$248$	−6.26904	−0.398085
$249$	6.48709	0.411102
$250$	10.5337	0.666209
$251$	−4.59544	−0.290062	−0.145031	−	0.989427i	$-0.546328\pi$
$251$	−4.59544	−0.290062	−0.145031	+	0.989427i	$0.546328\pi$
$252$	6.62175	0.417131
$253$	−1.76701	−0.111091
$254$	−3.94482	−0.247520
$255$	−4.50209	−0.281932
$256$	1.00000	0.0625000
$257$	−1.86074	−0.116070	−0.0580349	−	0.998315i	$-0.518483\pi$
$257$	−1.86074	−0.116070	−0.0580349	+	0.998315i	$0.518483\pi$
$258$	−4.02198	−0.250397
$259$	−1.32154	−0.0821164
$260$	−8.82252	−0.547149
$261$	14.2537	0.882279
$262$	8.13753	0.502738
$263$	24.9962	1.54133	0.770667	−	0.637238i	$-0.219923\pi$
$263$	24.9962	1.54133	0.770667	+	0.637238i	$0.219923\pi$
$264$	0.629487	0.0387423
$265$	−2.13909	−0.131403
$266$	0	0
$267$	4.22486	0.258557
$268$	10.5778	0.646140
$269$	−8.31848	−0.507187	−0.253593	−	0.967311i	$-0.581612\pi$
$269$	−8.31848	−0.507187	−0.253593	+	0.967311i	$0.581612\pi$
$270$	4.40062	0.267813
$271$	−1.25327	−0.0761306	−0.0380653	−	0.999275i	$-0.512119\pi$
$271$	−1.25327	−0.0761306	−0.0380653	+	0.999275i	$0.512119\pi$
$272$	−5.73296	−0.347612
$273$	11.3216	0.685211
$274$	1.33653	0.0807427
$275$	3.44369	0.207662
$276$	1.11231	0.0669534
$277$	10.6847	0.641983	0.320992	−	0.947082i	$-0.395984\pi$
$277$	10.6847	0.641983	0.320992	+	0.947082i	$0.395984\pi$
$278$	14.4332	0.865648
$279$	−16.3230	−0.977232
$280$	3.17265	0.189602
$281$	3.90949	0.233220	0.116610	−	0.993178i	$-0.462797\pi$
$281$	3.90949	0.233220	0.116610	+	0.993178i	$0.462797\pi$
$282$	−2.54107	−0.151318
$283$	10.5118	0.624861	0.312430	−	0.949941i	$-0.398857\pi$
$283$	10.5118	0.624861	0.312430	+	0.949941i	$0.398857\pi$
$284$	−9.10511	−0.540289
$285$	0	0
$286$	−7.07204	−0.418178
$287$	−2.31916	−0.136896
$288$	2.60375	0.153427
$289$	15.8668	0.933342
$290$	6.82929	0.401030
$291$	3.18882	0.186932
$292$	−17.0064	−0.995226
$293$	−22.5190	−1.31557	−0.657787	−	0.753204i	$-0.728507\pi$
$293$	−22.5190	−1.31557	−0.657787	+	0.753204i	$0.728507\pi$
$294$	0.335089	0.0195428
$295$	4.99304	0.290706
$296$	−0.519644	−0.0302037
$297$	3.52749	0.204686
$298$	−12.3807	−0.717193
$299$	−12.4964	−0.722685
$300$	−2.16776	−0.125156
$301$	−16.2490	−0.936578
$302$	−15.6391	−0.899928
$303$	−0.689329	−0.0396009
$304$	0	0
$305$	−15.7502	−0.901855
$306$	−14.9272	−0.853329
$307$	−17.2192	−0.982749	−0.491375	−	0.870948i	$-0.663505\pi$
$307$	−17.2192	−0.982749	−0.491375	+	0.870948i	$0.663505\pi$
$308$	2.54316	0.144910
$309$	5.04342	0.286910
$310$	−7.82077	−0.444190
$311$	−14.3593	−0.814244	−0.407122	−	0.913374i	$-0.633468\pi$
$311$	−14.3593	−0.814244	−0.407122	+	0.913374i	$0.633468\pi$
$312$	4.45176	0.252031
$313$	−7.70390	−0.435450	−0.217725	−	0.976010i	$-0.569864\pi$
$313$	−7.70390	−0.435450	−0.217725	+	0.976010i	$0.569864\pi$
$314$	−21.6670	−1.22274
$315$	8.26078	0.465442
$316$	5.56025	0.312788
$317$	12.7933	0.718542	0.359271	−	0.933233i	$-0.383025\pi$
$317$	12.7933	0.718542	0.359271	+	0.933233i	$0.383025\pi$
$318$	1.07937	0.0605278
$319$	5.47429	0.306501
$320$	1.24752	0.0697386
$321$	−0.712803	−0.0397848
$322$	4.49381	0.250430
$323$	0	0
$324$	5.59073	0.310596
$325$	24.3539	1.35091
$326$	12.1901	0.675149
$327$	−1.76746	−0.0977405
$328$	−0.911921	−0.0503524
$329$	−10.2661	−0.565986
$330$	0.785299	0.0432293
$331$	−6.96567	−0.382868	−0.191434	−	0.981505i	$-0.561314\pi$
$331$	−6.96567	−0.382868	−0.191434	+	0.981505i	$0.561314\pi$
$332$	10.3053	0.565579
$333$	−1.35302	−0.0741450
$334$	−16.8627	−0.922687
$335$	13.1960	0.720974
$336$	−1.60089	−0.0873357
$337$	−19.8712	−1.08245	−0.541226	−	0.840877i	$-0.682039\pi$
$337$	−19.8712	−1.08245	−0.541226	+	0.840877i	$0.682039\pi$
$338$	−37.0137	−2.01328
$339$	−2.64605	−0.143714
$340$	−7.15199	−0.387871
$341$	−6.26904	−0.339488
$342$	0	0
$343$	19.1559	1.03432
$344$	−6.38929	−0.344488
$345$	1.38763	0.0747077
$346$	−19.8445	−1.06684
$347$	13.5930	0.729709	0.364855	−	0.931064i	$-0.381119\pi$
$347$	13.5930	0.729709	0.364855	+	0.931064i	$0.381119\pi$
$348$	−3.44600	−0.184725
$349$	−35.3835	−1.89404	−0.947018	−	0.321180i	$-0.895921\pi$
$349$	−35.3835	−1.89404	−0.947018	+	0.321180i	$0.895921\pi$
$350$	−8.75787	−0.468128
$351$	24.9465	1.33155
$352$	1.00000	0.0533002
$353$	9.25340	0.492509	0.246254	−	0.969205i	$-0.420800\pi$
$353$	9.25340	0.492509	0.246254	+	0.969205i	$0.420800\pi$
$354$	−2.51944	−0.133907
$355$	−11.3588	−0.602863
$356$	6.71159	0.355714
$357$	9.17783	0.485742
$358$	7.22486	0.381846
$359$	−1.78559	−0.0942398	−0.0471199	−	0.998889i	$-0.515004\pi$
$359$	−1.78559	−0.0942398	−0.0471199	+	0.998889i	$0.515004\pi$
$360$	3.24823	0.171197
$361$	0	0
$362$	23.1532	1.21690
$363$	0.629487	0.0330395
$364$	17.9853	0.942688
$365$	−21.2159	−1.11049
$366$	7.94741	0.415418
$367$	−8.84374	−0.461639	−0.230820	−	0.972997i	$-0.574141\pi$
$367$	−8.84374	−0.461639	−0.230820	+	0.972997i	$0.574141\pi$
$368$	1.76701	0.0921120
$369$	−2.37441	−0.123607
$370$	−0.648267	−0.0337018
$371$	4.36070	0.226396
$372$	3.94628	0.204605
$373$	15.5281	0.804013	0.402007	−	0.915637i	$-0.368313\pi$
$373$	15.5281	0.804013	0.402007	+	0.915637i	$0.368313\pi$
$374$	−5.73296	−0.296444
$375$	−6.63082	−0.342414
$376$	−4.03673	−0.208178
$377$	38.7144	1.99389
$378$	−8.97098	−0.461417
$379$	19.9305	1.02376	0.511879	−	0.859057i	$-0.328949\pi$
$379$	19.9305	1.02376	0.511879	+	0.859057i	$0.328949\pi$
$380$	0	0
$381$	2.48322	0.127219
$382$	26.3906	1.35026
$383$	−26.7922	−1.36902	−0.684509	−	0.729005i	$-0.739983\pi$
$383$	−26.7922	−1.36902	−0.684509	+	0.729005i	$0.739983\pi$
$384$	−0.629487	−0.0321234
$385$	3.17265	0.161693
$386$	6.66366	0.339171
$387$	−16.6361	−0.845660
$388$	5.06574	0.257174
$389$	−33.3676	−1.69181	−0.845903	−	0.533337i	$-0.820938\pi$
$389$	−33.3676	−1.69181	−0.845903	+	0.533337i	$0.820938\pi$
$390$	5.55367	0.281221
$391$	−10.1302	−0.512307
$392$	0.532320	0.0268862
$393$	−5.12247	−0.258395
$394$	14.6474	0.737924
$395$	6.93653	0.349015
$396$	2.60375	0.130843
$397$	3.84714	0.193082	0.0965412	−	0.995329i	$-0.469222\pi$
$397$	3.84714	0.193082	0.0965412	+	0.995329i	$0.469222\pi$
$398$	11.8064	0.591799
$399$	0	0
$400$	−3.44369	−0.172185
$401$	0.370021	0.0184780	0.00923899	−	0.999957i	$-0.497059\pi$
$401$	0.370021	0.0184780	0.00923899	+	0.999957i	$0.497059\pi$
$402$	−6.65857	−0.332099
$403$	−44.3349	−2.20848
$404$	−1.09506	−0.0544814
$405$	6.97455	0.346568
$406$	−13.9220	−0.690938
$407$	−0.519644	−0.0257578
$408$	3.60883	0.178663
$409$	−26.2887	−1.29989	−0.649947	−	0.759979i	$-0.725209\pi$
$409$	−26.2887	−1.29989	−0.649947	+	0.759979i	$0.725209\pi$
$410$	−1.13764	−0.0561841
$411$	−0.841328	−0.0414997
$412$	8.01195	0.394720
$413$	−10.1787	−0.500859
$414$	4.60086	0.226120
$415$	12.8561	0.631083
$416$	7.07204	0.346735
$417$	−9.08554	−0.444921
$418$	0	0
$419$	−3.93641	−0.192306	−0.0961531	−	0.995367i	$-0.530654\pi$
$419$	−3.93641	−0.192306	−0.0961531	+	0.995367i	$0.530654\pi$
$420$	−1.99714	−0.0974506
$421$	−8.39813	−0.409300	−0.204650	−	0.978835i	$-0.565606\pi$
$421$	−8.39813	−0.409300	−0.204650	+	0.978835i	$0.565606\pi$
$422$	−26.2927	−1.27991
$423$	−10.5106	−0.511043
$424$	1.71467	0.0832719
$425$	19.7425	0.957654
$426$	5.73155	0.277694
$427$	32.1080	1.55381
$428$	−1.13235	−0.0547344
$429$	4.45176	0.214933
$430$	−7.97078	−0.384385
$431$	29.9455	1.44242	0.721211	−	0.692715i	$-0.243586\pi$
$431$	29.9455	1.44242	0.721211	+	0.692715i	$0.243586\pi$
$432$	−3.52749	−0.169716
$433$	−19.2205	−0.923679	−0.461839	−	0.886964i	$-0.652810\pi$
$433$	−19.2205	−0.923679	−0.461839	+	0.886964i	$0.652810\pi$
$434$	15.9432	0.765298
$435$	−4.29895	−0.206119
$436$	−2.80777	−0.134468
$437$	0	0
$438$	10.7053	0.511521
$439$	−26.1541	−1.24827	−0.624133	−	0.781318i	$-0.714548\pi$
$439$	−26.1541	−1.24827	−0.624133	+	0.781318i	$0.714548\pi$
$440$	1.24752	0.0594733
$441$	1.38603	0.0660012
$442$	−40.5437	−1.92847
$443$	−28.0412	−1.33228	−0.666139	−	0.745828i	$-0.732054\pi$
$443$	−28.0412	−1.33228	−0.666139	+	0.745828i	$0.732054\pi$
$444$	0.327109	0.0155239
$445$	8.37285	0.396911
$446$	−27.2252	−1.28915
$447$	7.79348	0.368619
$448$	−2.54316	−0.120153
$449$	−15.9307	−0.751819	−0.375909	−	0.926656i	$-0.622670\pi$
$449$	−15.9307	−0.751819	−0.375909	+	0.926656i	$0.622670\pi$
$450$	−8.96649	−0.422685
$451$	−0.911921	−0.0429407
$452$	−4.20350	−0.197716
$453$	9.84461	0.462540
$454$	−25.4375	−1.19384
$455$	22.4371	1.05187
$456$	0	0
$457$	−0.264720	−0.0123831	−0.00619154	−	0.999981i	$-0.501971\pi$
$457$	−0.264720	−0.0123831	−0.00619154	+	0.999981i	$0.501971\pi$
$458$	−21.4833	−1.00385
$459$	20.2229	0.943926
$460$	2.20439	0.102780
$461$	34.2545	1.59539	0.797696	−	0.603060i	$-0.206052\pi$
$461$	34.2545	1.59539	0.797696	+	0.603060i	$0.206052\pi$
$462$	−1.60089	−0.0744801
$463$	20.0514	0.931866	0.465933	−	0.884820i	$-0.345719\pi$
$463$	20.0514	0.931866	0.465933	+	0.884820i	$0.345719\pi$
$464$	−5.47429	−0.254137
$465$	4.92307	0.228302
$466$	−1.74431	−0.0808037
$467$	1.07144	0.0495804	0.0247902	−	0.999693i	$-0.492108\pi$
$467$	1.07144	0.0495804	0.0247902	+	0.999693i	$0.492108\pi$
$468$	18.4138	0.851178
$469$	−26.9010	−1.24217
$470$	−5.03590	−0.232289
$471$	13.6391	0.628458
$472$	−4.00236	−0.184224
$473$	−6.38929	−0.293780
$474$	−3.50011	−0.160765
$475$	0	0
$476$	14.5799	0.668266
$477$	4.46458	0.204419
$478$	19.7598	0.903790
$479$	−40.1386	−1.83398	−0.916989	−	0.398913i	$-0.869387\pi$
$479$	−40.1386	−1.83398	−0.916989	+	0.398913i	$0.869387\pi$
$480$	−0.785299	−0.0358438
$481$	−3.67494	−0.167563
$482$	−10.1904	−0.464161
$483$	−2.82879	−0.128715
$484$	1.00000	0.0454545
$485$	6.31961	0.286959
$486$	−14.1018	−0.639669
$487$	−3.61501	−0.163812	−0.0819059	−	0.996640i	$-0.526101\pi$
$487$	−3.61501	−0.163812	−0.0819059	+	0.996640i	$0.526101\pi$
$488$	12.6252	0.571516
$489$	−7.67354	−0.347009
$490$	0.664081	0.0300001
$491$	−34.8719	−1.57374	−0.786872	−	0.617116i	$-0.788301\pi$
$491$	−34.8719	−1.57374	−0.786872	+	0.617116i	$0.788301\pi$
$492$	0.574043	0.0258799
$493$	31.3839	1.41346
$494$	0	0
$495$	3.24823	0.145997
$496$	6.26904	0.281488
$497$	23.1558	1.03868
$498$	−6.48709	−0.290693
$499$	18.5011	0.828222	0.414111	−	0.910226i	$-0.364093\pi$
$499$	18.5011	0.828222	0.414111	+	0.910226i	$0.364093\pi$
$500$	−10.5337	−0.471081
$501$	10.6149	0.474237
$502$	4.59544	0.205105
$503$	16.0870	0.717283	0.358641	−	0.933475i	$-0.383240\pi$
$503$	16.0870	0.717283	0.358641	+	0.933475i	$0.383240\pi$
$504$	−6.62175	−0.294956
$505$	−1.36612	−0.0607913
$506$	1.76701	0.0785534
$507$	23.2997	1.03477
$508$	3.94482	0.175023
$509$	26.4025	1.17027	0.585135	−	0.810936i	$-0.301041\pi$
$509$	26.4025	1.17027	0.585135	+	0.810936i	$0.301041\pi$
$510$	4.50209	0.199356
$511$	43.2501	1.91327
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	1.86074	0.0820738
$515$	9.99508	0.440436
$516$	4.02198	0.177058
$517$	−4.03673	−0.177535
$518$	1.32154	0.0580651
$519$	12.4918	0.548331
$520$	8.82252	0.386893
$521$	23.7648	1.04115	0.520576	−	0.853815i	$-0.325717\pi$
$521$	23.7648	1.04115	0.520576	+	0.853815i	$0.325717\pi$
$522$	−14.2537	−0.623866
$523$	43.4157	1.89843	0.949217	−	0.314622i	$-0.101878\pi$
$523$	43.4157	1.89843	0.949217	+	0.314622i	$0.101878\pi$
$524$	−8.13753	−0.355490
$525$	5.51297	0.240606
$526$	−24.9962	−1.08989
$527$	−35.9402	−1.56558
$528$	−0.629487	−0.0273949
$529$	−19.8777	−0.864246
$530$	2.13909	0.0929163
$531$	−10.4211	−0.452239
$532$	0	0
$533$	−6.44914	−0.279343
$534$	−4.22486	−0.182828
$535$	−1.41264	−0.0610736
$536$	−10.5778	−0.456890
$537$	−4.54796	−0.196259
$538$	8.31848	0.358635
$539$	0.532320	0.0229286
$540$	−4.40062	−0.189372
$541$	15.0805	0.648360	0.324180	−	0.945995i	$-0.394912\pi$
$541$	15.0805	0.648360	0.324180	+	0.945995i	$0.394912\pi$
$542$	1.25327	0.0538325
$543$	−14.5746	−0.625457
$544$	5.73296	0.245799
$545$	−3.50275	−0.150041
$546$	−11.3216	−0.484518
$547$	−1.83960	−0.0786555	−0.0393278	−	0.999226i	$-0.512522\pi$
$547$	−1.83960	−0.0786555	−0.0393278	+	0.999226i	$0.512522\pi$
$548$	−1.33653	−0.0570937
$549$	32.8728	1.40298
$550$	−3.44369	−0.146839
$551$	0	0
$552$	−1.11231	−0.0473432
$553$	−14.1406	−0.601320
$554$	−10.6847	−0.453951
$555$	0.408076	0.0173219
$556$	−14.4332	−0.612105
$557$	15.3553	0.650625	0.325312	−	0.945607i	$-0.394531\pi$
$557$	15.3553	0.650625	0.325312	+	0.945607i	$0.394531\pi$
$558$	16.3230	0.691007
$559$	−45.1853	−1.91114
$560$	−3.17265	−0.134069
$561$	3.60883	0.152365
$562$	−3.90949	−0.164912
$563$	−27.0806	−1.14131	−0.570655	−	0.821190i	$-0.693311\pi$
$563$	−27.0806	−1.14131	−0.570655	+	0.821190i	$0.693311\pi$
$564$	2.54107	0.106998
$565$	−5.24395	−0.220615
$566$	−10.5118	−0.441843
$567$	−14.2181	−0.597105
$568$	9.10511	0.382042
$569$	−25.4128	−1.06536	−0.532680	−	0.846317i	$-0.678815\pi$
$569$	−25.4128	−1.06536	−0.532680	+	0.846317i	$0.678815\pi$
$570$	0	0
$571$	−43.7967	−1.83283	−0.916417	−	0.400225i	$-0.868932\pi$
$571$	−43.7967	−1.83283	−0.916417	+	0.400225i	$0.868932\pi$
$572$	7.07204	0.295697
$573$	−16.6126	−0.694001
$574$	2.31916	0.0968001
$575$	−6.08505	−0.253764
$576$	−2.60375	−0.108489
$577$	19.0486	0.793005	0.396503	−	0.918034i	$-0.370224\pi$
$577$	19.0486	0.793005	0.396503	+	0.918034i	$0.370224\pi$
$578$	−15.8668	−0.659973
$579$	−4.19469	−0.174325
$580$	−6.82929	−0.283571
$581$	−26.2082	−1.08730
$582$	−3.18882	−0.132181
$583$	1.71467	0.0710146
$584$	17.0064	0.703731
$585$	22.9716	0.949759
$586$	22.5190	0.930251
$587$	9.49482	0.391893	0.195946	−	0.980615i	$-0.437222\pi$
$587$	9.49482	0.391893	0.195946	+	0.980615i	$0.437222\pi$
$588$	−0.335089	−0.0138188
$589$	0	0
$590$	−4.99304	−0.205560
$591$	−9.22034	−0.379274
$592$	0.519644	0.0213572
$593$	8.97059	0.368378	0.184189	−	0.982891i	$-0.441034\pi$
$593$	8.97059	0.368378	0.184189	+	0.982891i	$0.441034\pi$
$594$	−3.52749	−0.144735
$595$	18.1887	0.745663
$596$	12.3807	0.507132
$597$	−7.43195	−0.304170
$598$	12.4964	0.511016
$599$	26.0932	1.06614	0.533069	−	0.846072i	$-0.321039\pi$
$599$	26.0932	1.06614	0.533069	+	0.846072i	$0.321039\pi$
$600$	2.16776	0.0884984
$601$	−15.5593	−0.634679	−0.317340	−	0.948312i	$-0.602789\pi$
$601$	−15.5593	−0.634679	−0.317340	+	0.948312i	$0.602789\pi$
$602$	16.2490	0.662260
$603$	−27.5418	−1.12159
$604$	15.6391	0.636345
$605$	1.24752	0.0507190
$606$	0.689329	0.0280021
$607$	−22.5982	−0.917232	−0.458616	−	0.888635i	$-0.651655\pi$
$607$	−22.5982	−0.917232	−0.458616	+	0.888635i	$0.651655\pi$
$608$	0	0
$609$	8.76373	0.355124
$610$	15.7502	0.637708
$611$	−28.5479	−1.15492
$612$	14.9272	0.603395
$613$	−6.52493	−0.263539	−0.131770	−	0.991280i	$-0.542066\pi$
$613$	−6.52493	−0.263539	−0.131770	+	0.991280i	$0.542066\pi$
$614$	17.2192	0.694909
$615$	0.716131	0.0288772
$616$	−2.54316	−0.102467
$617$	40.3872	1.62593	0.812963	−	0.582315i	$-0.197853\pi$
$617$	40.3872	1.62593	0.812963	+	0.582315i	$0.197853\pi$
$618$	−5.04342	−0.202876
$619$	−25.2384	−1.01442	−0.507208	−	0.861824i	$-0.669323\pi$
$619$	−25.2384	−1.01442	−0.507208	+	0.861824i	$0.669323\pi$
$620$	7.82077	0.314090
$621$	−6.23312	−0.250127
$622$	14.3593	0.575757
$623$	−17.0687	−0.683842
$624$	−4.45176	−0.178213
$625$	4.07745	0.163098
$626$	7.70390	0.307910
$627$	0	0
$628$	21.6670	0.864609
$629$	−2.97910	−0.118784
$630$	−8.26078	−0.329117
$631$	−15.8965	−0.632829	−0.316414	−	0.948621i	$-0.602479\pi$
$631$	−15.8965	−0.632829	−0.316414	+	0.948621i	$0.602479\pi$
$632$	−5.56025	−0.221175
$633$	16.5509	0.657840
$634$	−12.7933	−0.508086
$635$	4.92125	0.195294
$636$	−1.07937	−0.0427996
$637$	3.76459	0.149158
$638$	−5.47429	−0.216729
$639$	23.7074	0.937849
$640$	−1.24752	−0.0493126
$641$	7.10217	0.280519	0.140259	−	0.990115i	$-0.455206\pi$
$641$	7.10217	0.280519	0.140259	+	0.990115i	$0.455206\pi$
$642$	0.712803	0.0281321
$643$	39.9759	1.57649	0.788247	−	0.615359i	$-0.210989\pi$
$643$	39.9759	1.57649	0.788247	+	0.615359i	$0.210989\pi$
$644$	−4.49381	−0.177081
$645$	5.01751	0.197564
$646$	0	0
$647$	32.7841	1.28888	0.644438	−	0.764656i	$-0.277091\pi$
$647$	32.7841	1.28888	0.644438	+	0.764656i	$0.277091\pi$
$648$	−5.59073	−0.219625
$649$	−4.00236	−0.157107
$650$	−24.3539	−0.955239
$651$	−10.0360	−0.393344
$652$	−12.1901	−0.477403
$653$	−5.69237	−0.222760	−0.111380	−	0.993778i	$-0.535527\pi$
$653$	−5.69237	−0.222760	−0.111380	+	0.993778i	$0.535527\pi$
$654$	1.76746	0.0691130
$655$	−10.1517	−0.396661
$656$	0.911921	0.0356045
$657$	44.2804	1.72754
$658$	10.2661	0.400212
$659$	−22.8856	−0.891496	−0.445748	−	0.895159i	$-0.647062\pi$
$659$	−22.8856	−0.891496	−0.445748	+	0.895159i	$0.647062\pi$
$660$	−0.785299	−0.0305677
$661$	19.0906	0.742538	0.371269	−	0.928525i	$-0.378923\pi$
$661$	19.0906	0.742538	0.371269	+	0.928525i	$0.378923\pi$
$662$	6.96567	0.270729
$663$	25.5218	0.991183
$664$	−10.3053	−0.399925
$665$	0	0
$666$	1.35302	0.0524285
$667$	−9.67315	−0.374546
$668$	16.8627	0.652438
$669$	17.1379	0.662590
$670$	−13.1960	−0.509805
$671$	12.6252	0.487391
$672$	1.60089	0.0617557
$673$	−43.4402	−1.67450	−0.837249	−	0.546822i	$-0.815838\pi$
$673$	−43.4402	−1.67450	−0.837249	+	0.546822i	$0.815838\pi$
$674$	19.8712	0.765408
$675$	12.1476	0.467560
$676$	37.0137	1.42360
$677$	38.0136	1.46098	0.730491	−	0.682922i	$-0.239291\pi$
$677$	38.0136	1.46098	0.730491	+	0.682922i	$0.239291\pi$
$678$	2.64605	0.101621
$679$	−12.8830	−0.494404
$680$	7.15199	0.274266
$681$	16.0126	0.613605
$682$	6.26904	0.240054
$683$	18.6169	0.712354	0.356177	−	0.934418i	$-0.384080\pi$
$683$	18.6169	0.712354	0.356177	+	0.934418i	$0.384080\pi$
$684$	0	0
$685$	−1.66735	−0.0637061
$686$	−19.1559	−0.731376
$687$	13.5235	0.515953
$688$	6.38929	0.243589
$689$	12.1262	0.461973
$690$	−1.38763	−0.0528264
$691$	13.5140	0.514095	0.257048	−	0.966399i	$-0.417250\pi$
$691$	13.5140	0.514095	0.257048	+	0.966399i	$0.417250\pi$
$692$	19.8445	0.754373
$693$	−6.62175	−0.251539
$694$	−13.5930	−0.515983
$695$	−18.0058	−0.682997
$696$	3.44600	0.130620
$697$	−5.22801	−0.198025
$698$	35.3835	1.33929
$699$	1.09802	0.0415310
$700$	8.75787	0.331016
$701$	29.3514	1.10859	0.554294	−	0.832321i	$-0.312988\pi$
$701$	29.3514	1.10859	0.554294	+	0.832321i	$0.312988\pi$
$702$	−24.9465	−0.941546
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	3.17004	0.119391
$706$	−9.25340	−0.348256
$707$	2.78493	0.104738
$708$	2.51944	0.0946863
$709$	17.6748	0.663791	0.331895	−	0.943316i	$-0.392312\pi$
$709$	17.6748	0.663791	0.331895	+	0.943316i	$0.392312\pi$
$710$	11.3588	0.426289
$711$	−14.4775	−0.542947
$712$	−6.71159	−0.251528
$713$	11.0775	0.414855
$714$	−9.17783	−0.343472
$715$	8.82252	0.329944
$716$	−7.22486	−0.270006
$717$	−12.4385	−0.464525
$718$	1.78559	0.0666376
$719$	−24.1432	−0.900390	−0.450195	−	0.892930i	$-0.648646\pi$
$719$	−24.1432	−0.900390	−0.450195	+	0.892930i	$0.648646\pi$
$720$	−3.24823	−0.121054
$721$	−20.3757	−0.758831
$722$	0	0
$723$	6.41474	0.238567
$724$	−23.1532	−0.860480
$725$	18.8518	0.700137
$726$	−0.629487	−0.0233625
$727$	−10.9357	−0.405584	−0.202792	−	0.979222i	$-0.565002\pi$
$727$	−10.9357	−0.405584	−0.202792	+	0.979222i	$0.565002\pi$
$728$	−17.9853	−0.666581
$729$	−7.89531	−0.292419
$730$	21.2159	0.785235
$731$	−36.6295	−1.35479
$732$	−7.94741	−0.293745
$733$	−28.8292	−1.06483	−0.532415	−	0.846483i	$-0.678715\pi$
$733$	−28.8292	−1.06483	−0.532415	+	0.846483i	$0.678715\pi$
$734$	8.84374	0.326428
$735$	−0.418030	−0.0154193
$736$	−1.76701	−0.0651330
$737$	−10.5778	−0.389637
$738$	2.37441	0.0874033
$739$	26.9388	0.990958	0.495479	−	0.868620i	$-0.334993\pi$
$739$	26.9388	0.990958	0.495479	+	0.868620i	$0.334993\pi$
$740$	0.648267	0.0238308
$741$	0	0
$742$	−4.36070	−0.160086
$743$	33.4242	1.22621	0.613107	−	0.790000i	$-0.289919\pi$
$743$	33.4242	1.22621	0.613107	+	0.790000i	$0.289919\pi$
$744$	−3.94628	−0.144678
$745$	15.4452	0.565867
$746$	−15.5281	−0.568523
$747$	−26.8325	−0.981750
$748$	5.73296	0.209618
$749$	2.87976	0.105224
$750$	6.63082	0.242123
$751$	−30.6337	−1.11784	−0.558920	−	0.829221i	$-0.688784\pi$
$751$	−30.6337	−1.11784	−0.558920	+	0.829221i	$0.688784\pi$
$752$	4.03673	0.147204
$753$	−2.89277	−0.105419
$754$	−38.7144	−1.40989
$755$	19.5101	0.710045
$756$	8.97098	0.326271
$757$	−50.5259	−1.83639	−0.918197	−	0.396124i	$-0.870355\pi$
$757$	−50.5259	−1.83639	−0.918197	+	0.396124i	$0.870355\pi$
$758$	−19.9305	−0.723907
$759$	−1.11231	−0.0403744
$760$	0	0
$761$	17.7313	0.642760	0.321380	−	0.946950i	$-0.395853\pi$
$761$	17.7313	0.642760	0.321380	+	0.946950i	$0.395853\pi$
$762$	−2.48322	−0.0899574
$763$	7.14062	0.258508
$764$	−26.3906	−0.954780
$765$	18.6220	0.673278
$766$	26.7922	0.968042
$767$	−28.3049	−1.02203
$768$	0.629487	0.0227147
$769$	51.2836	1.84933	0.924667	−	0.380776i	$-0.124343\pi$
$769$	51.2836	1.84933	0.924667	+	0.380776i	$0.124343\pi$
$770$	−3.17265	−0.114334
$771$	−1.17131	−0.0421838
$772$	−6.66366	−0.239830
$773$	−30.2742	−1.08889	−0.544444	−	0.838797i	$-0.683259\pi$
$773$	−30.2742	−1.08889	−0.544444	+	0.838797i	$0.683259\pi$
$774$	16.6361	0.597972
$775$	−21.5886	−0.775487
$776$	−5.06574	−0.181849
$777$	−0.831892	−0.0298440
$778$	33.3676	1.19629
$779$	0	0
$780$	−5.55367	−0.198853
$781$	9.10511	0.325806
$782$	10.1302	0.362256
$783$	19.3105	0.690100
$784$	−0.532320	−0.0190114
$785$	27.0301	0.964746
$786$	5.12247	0.182713
$787$	−8.07300	−0.287771	−0.143886	−	0.989594i	$-0.545960\pi$
$787$	−8.07300	−0.287771	−0.143886	+	0.989594i	$0.545960\pi$
$788$	−14.6474	−0.521791
$789$	15.7348	0.560174
$790$	−6.93653	−0.246791
$791$	10.6902	0.380099
$792$	−2.60375	−0.0925201
$793$	89.2860	3.17064
$794$	−3.84714	−0.136530
$795$	−1.34653	−0.0477566
$796$	−11.8064	−0.418465
$797$	24.7581	0.876975	0.438488	−	0.898737i	$-0.355514\pi$
$797$	24.7581	0.876975	0.438488	+	0.898737i	$0.355514\pi$
$798$	0	0
$799$	−23.1424	−0.818719
$800$	3.44369	0.121753
$801$	−17.4753	−0.617459
$802$	−0.370021	−0.0130659
$803$	17.0064	0.600144
$804$	6.65857	0.234830
$805$	−5.60612	−0.197590
$806$	44.3349	1.56163
$807$	−5.23638	−0.184329
$808$	1.09506	0.0385242
$809$	45.8041	1.61039	0.805193	−	0.593013i	$-0.202062\pi$
$809$	45.8041	1.61039	0.805193	+	0.593013i	$0.202062\pi$
$810$	−6.97455	−0.245061
$811$	25.7604	0.904570	0.452285	−	0.891873i	$-0.350609\pi$
$811$	25.7604	0.904570	0.452285	+	0.891873i	$0.350609\pi$
$812$	13.9220	0.488567
$813$	−0.788916	−0.0276685
$814$	0.519644	0.0182135
$815$	−15.2075	−0.532694
$816$	−3.60883	−0.126334
$817$	0	0
$818$	26.2887	0.919164
$819$	−46.8293	−1.63635
$820$	1.13764	0.0397282
$821$	−35.0704	−1.22397	−0.611983	−	0.790871i	$-0.709628\pi$
$821$	−35.0704	−1.22397	−0.611983	+	0.790871i	$0.709628\pi$
$822$	0.841328	0.0293447
$823$	−10.9017	−0.380009	−0.190004	−	0.981783i	$-0.560850\pi$
$823$	−10.9017	−0.380009	−0.190004	+	0.981783i	$0.560850\pi$
$824$	−8.01195	−0.279109
$825$	2.16776	0.0754717
$826$	10.1787	0.354161
$827$	2.01079	0.0699221	0.0349611	−	0.999389i	$-0.488869\pi$
$827$	2.01079	0.0699221	0.0349611	+	0.999389i	$0.488869\pi$
$828$	−4.60086	−0.159891
$829$	−8.33479	−0.289479	−0.144740	−	0.989470i	$-0.546234\pi$
$829$	−8.33479	−0.289479	−0.144740	+	0.989470i	$0.546234\pi$
$830$	−12.8561	−0.446243
$831$	6.72590	0.233319
$832$	−7.07204	−0.245179
$833$	3.05177	0.105738
$834$	9.08554	0.314606
$835$	21.0366	0.728002
$836$	0	0
$837$	−22.1140	−0.764371
$838$	3.93641	0.135981
$839$	−34.6396	−1.19589	−0.597947	−	0.801536i	$-0.704017\pi$
$839$	−34.6396	−1.19589	−0.597947	+	0.801536i	$0.704017\pi$
$840$	1.99714	0.0689080
$841$	0.967835	0.0333736
$842$	8.39813	0.289419
$843$	2.46097	0.0847604
$844$	26.2927	0.905032
$845$	46.1754	1.58848
$846$	10.5106	0.361362
$847$	−2.54316	−0.0873841
$848$	−1.71467	−0.0588822
$849$	6.61704	0.227096
$850$	−19.7425	−0.677163
$851$	0.918218	0.0314761
$852$	−5.73155	−0.196360
$853$	−18.5172	−0.634015	−0.317008	−	0.948423i	$-0.602678\pi$
$853$	−18.5172	−0.634015	−0.317008	+	0.948423i	$0.602678\pi$
$854$	−32.1080	−1.09871
$855$	0	0
$856$	1.13235	0.0387031
$857$	11.0124	0.376175	0.188087	−	0.982152i	$-0.439771\pi$
$857$	11.0124	0.376175	0.188087	+	0.982152i	$0.439771\pi$
$858$	−4.45176	−0.151981
$859$	23.6344	0.806395	0.403197	−	0.915113i	$-0.367899\pi$
$859$	23.6344	0.806395	0.403197	+	0.915113i	$0.367899\pi$
$860$	7.97078	0.271801
$861$	−1.45988	−0.0497527
$862$	−29.9455	−1.01995
$863$	−14.6313	−0.498056	−0.249028	−	0.968496i	$-0.580111\pi$
$863$	−14.6313	−0.498056	−0.249028	+	0.968496i	$0.580111\pi$
$864$	3.52749	0.120008
$865$	24.7564	0.841742
$866$	19.2205	0.653139
$867$	9.98796	0.339209
$868$	−15.9432	−0.541148
$869$	−5.56025	−0.188618
$870$	4.29895	0.145748
$871$	−74.8063	−2.53472
$872$	2.80777	0.0950831
$873$	−13.1899	−0.446410
$874$	0	0
$875$	26.7889	0.905629
$876$	−10.7053	−0.361700
$877$	−2.45537	−0.0829120	−0.0414560	−	0.999140i	$-0.513200\pi$
$877$	−2.45537	−0.0829120	−0.0414560	+	0.999140i	$0.513200\pi$
$878$	26.1541	0.882658
$879$	−14.1754	−0.478125
$880$	−1.24752	−0.0420539
$881$	−39.9862	−1.34717	−0.673585	−	0.739110i	$-0.735246\pi$
$881$	−39.9862	−1.34717	−0.673585	+	0.739110i	$0.735246\pi$
$882$	−1.38603	−0.0466699
$883$	−32.2749	−1.08614	−0.543068	−	0.839688i	$-0.682738\pi$
$883$	−32.2749	−1.08614	−0.543068	+	0.839688i	$0.682738\pi$
$884$	40.5437	1.36363
$885$	3.14305	0.105653
$886$	28.0412	0.942063
$887$	46.2997	1.55459	0.777295	−	0.629136i	$-0.216591\pi$
$887$	46.2997	1.55459	0.777295	+	0.629136i	$0.216591\pi$
$888$	−0.327109	−0.0109771
$889$	−10.0323	−0.336473
$890$	−8.37285	−0.280659
$891$	−5.59073	−0.187296
$892$	27.2252	0.911567
$893$	0	0
$894$	−7.79348	−0.260653
$895$	−9.01317	−0.301277
$896$	2.54316	0.0849611
$897$	−7.86632	−0.262649
$898$	15.9307	0.531616
$899$	−34.3186	−1.14459
$900$	8.96649	0.298883
$901$	9.83016	0.327490
$902$	0.911921	0.0303637
$903$	−10.2286	−0.340385
$904$	4.20350	0.139806
$905$	−28.8841	−0.960139
$906$	−9.84461	−0.327065
$907$	6.29268	0.208945	0.104472	−	0.994528i	$-0.466685\pi$
$907$	6.29268	0.208945	0.104472	+	0.994528i	$0.466685\pi$
$908$	25.4375	0.844175
$909$	2.85127	0.0945705
$910$	−22.4371	−0.743783
$911$	7.28219	0.241270	0.120635	−	0.992697i	$-0.461507\pi$
$911$	7.28219	0.241270	0.120635	+	0.992697i	$0.461507\pi$
$912$	0	0
$913$	−10.3053	−0.341057
$914$	0.264720	0.00875615
$915$	−9.91457	−0.327765
$916$	21.4833	0.709830
$917$	20.6951	0.683411
$918$	−20.2229	−0.667456
$919$	40.7729	1.34498	0.672488	−	0.740108i	$-0.265226\pi$
$919$	40.7729	1.34498	0.672488	+	0.740108i	$0.265226\pi$
$920$	−2.20439	−0.0726765
$921$	−10.8392	−0.357165
$922$	−34.2545	−1.12811
$923$	64.3917	2.11948
$924$	1.60089	0.0526654
$925$	−1.78949	−0.0588381
$926$	−20.0514	−0.658929
$927$	−20.8611	−0.685168
$928$	5.47429	0.179702
$929$	−0.941208	−0.0308800	−0.0154400	−	0.999881i	$-0.504915\pi$
$929$	−0.941208	−0.0308800	−0.0154400	+	0.999881i	$0.504915\pi$
$930$	−4.92307	−0.161434
$931$	0	0
$932$	1.74431	0.0571368
$933$	−9.03903	−0.295925
$934$	−1.07144	−0.0350586
$935$	7.15199	0.233895
$936$	−18.4138	−0.601874
$937$	−5.53288	−0.180751	−0.0903757	−	0.995908i	$-0.528807\pi$
$937$	−5.53288	−0.180751	−0.0903757	+	0.995908i	$0.528807\pi$
$938$	26.9010	0.878348
$939$	−4.84951	−0.158258
$940$	5.03590	0.164253
$941$	8.51069	0.277440	0.138720	−	0.990332i	$-0.455701\pi$
$941$	8.51069	0.277440	0.138720	+	0.990332i	$0.455701\pi$
$942$	−13.6391	−0.444387
$943$	1.61138	0.0524737
$944$	4.00236	0.130266
$945$	11.1915	0.364059
$946$	6.38929	0.207734
$947$	44.6062	1.44951	0.724754	−	0.689008i	$-0.241954\pi$
$947$	44.6062	1.44951	0.724754	+	0.689008i	$0.241954\pi$
$948$	3.50011	0.113678
$949$	120.270	3.90413
$950$	0	0
$951$	8.05321	0.261143
$952$	−14.5799	−0.472536
$953$	−12.5324	−0.405965	−0.202982	−	0.979182i	$-0.565063\pi$
$953$	−12.5324	−0.405965	−0.202982	+	0.979182i	$0.565063\pi$
$954$	−4.46458	−0.144546
$955$	−32.9229	−1.06536
$956$	−19.7598	−0.639076
$957$	3.44600	0.111393
$958$	40.1386	1.29682
$959$	3.39901	0.109760
$960$	0.785299	0.0253454
$961$	8.30091	0.267771
$962$	3.67494	0.118485
$963$	2.94836	0.0950096
$964$	10.1904	0.328211
$965$	−8.31306	−0.267607
$966$	2.82879	0.0910150
$967$	13.5922	0.437095	0.218547	−	0.975826i	$-0.429868\pi$
$967$	13.5922	0.437095	0.218547	+	0.975826i	$0.429868\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−6.31961	−0.202911
$971$	56.7409	1.82090	0.910451	−	0.413618i	$-0.135735\pi$
$971$	56.7409	1.82090	0.910451	+	0.413618i	$0.135735\pi$
$972$	14.1018	0.452314
$973$	36.7061	1.17674
$974$	3.61501	0.115832
$975$	15.3305	0.490968
$976$	−12.6252	−0.404123
$977$	51.5269	1.64849	0.824246	−	0.566231i	$-0.191599\pi$
$977$	51.5269	1.64849	0.824246	+	0.566231i	$0.191599\pi$
$978$	7.67354	0.245373
$979$	−6.71159	−0.214503
$980$	−0.664081	−0.0212133
$981$	7.31072	0.233413
$982$	34.8719	1.11281
$983$	43.9340	1.40128	0.700639	−	0.713516i	$-0.252899\pi$
$983$	43.9340	1.40128	0.700639	+	0.713516i	$0.252899\pi$
$984$	−0.574043	−0.0182998
$985$	−18.2729	−0.582223
$986$	−31.3839	−0.999466
$987$	−6.46235	−0.205699
$988$	0	0
$989$	11.2900	0.359000
$990$	−3.24823	−0.103235
$991$	−29.8055	−0.946803	−0.473401	−	0.880847i	$-0.656974\pi$
$991$	−29.8055	−0.946803	−0.473401	+	0.880847i	$0.656974\pi$
$992$	−6.26904	−0.199042
$993$	−4.38480	−0.139148
$994$	−23.1558	−0.734456
$995$	−14.7287	−0.466931
$996$	6.48709	0.205551
$997$	−19.8343	−0.628158	−0.314079	−	0.949397i	$-0.601696\pi$
$997$	−19.8343	−0.628158	−0.314079	+	0.949397i	$0.601696\pi$
$998$	−18.5011	−0.585641
$999$	−1.83304	−0.0579947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bo.1.4	✓	8
19.18	odd	2		7942.2.a.bp.1.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bo.1.4	✓	8	1.1	even	1	trivial
7942.2.a.bp.1.5	yes	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.629487 q^{3} +1.00000 q^{4} +1.24752 q^{5} -0.629487 q^{6} -2.54316 q^{7} -1.00000 q^{8} -2.60375 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.629487 q^{3} +1.00000 q^{4} +1.24752 q^{5} -0.629487 q^{6} -2.54316 q^{7} -1.00000 q^{8} -2.60375 q^{9} -1.24752 q^{10} -1.00000 q^{11} +0.629487 q^{12} -7.07204 q^{13} +2.54316 q^{14} +0.785299 q^{15} +1.00000 q^{16} -5.73296 q^{17} +2.60375 q^{18} +1.24752 q^{20} -1.60089 q^{21} +1.00000 q^{22} +1.76701 q^{23} -0.629487 q^{24} -3.44369 q^{25} +7.07204 q^{26} -3.52749 q^{27} -2.54316 q^{28} -5.47429 q^{29} -0.785299 q^{30} +6.26904 q^{31} -1.00000 q^{32} -0.629487 q^{33} +5.73296 q^{34} -3.17265 q^{35} -2.60375 q^{36} +0.519644 q^{37} -4.45176 q^{39} -1.24752 q^{40} +0.911921 q^{41} +1.60089 q^{42} +6.38929 q^{43} -1.00000 q^{44} -3.24823 q^{45} -1.76701 q^{46} +4.03673 q^{47} +0.629487 q^{48} -0.532320 q^{49} +3.44369 q^{50} -3.60883 q^{51} -7.07204 q^{52} -1.71467 q^{53} +3.52749 q^{54} -1.24752 q^{55} +2.54316 q^{56} +5.47429 q^{58} +4.00236 q^{59} +0.785299 q^{60} -12.6252 q^{61} -6.26904 q^{62} +6.62175 q^{63} +1.00000 q^{64} -8.82252 q^{65} +0.629487 q^{66} +10.5778 q^{67} -5.73296 q^{68} +1.11231 q^{69} +3.17265 q^{70} -9.10511 q^{71} +2.60375 q^{72} -17.0064 q^{73} -0.519644 q^{74} -2.16776 q^{75} +2.54316 q^{77} +4.45176 q^{78} +5.56025 q^{79} +1.24752 q^{80} +5.59073 q^{81} -0.911921 q^{82} +10.3053 q^{83} -1.60089 q^{84} -7.15199 q^{85} -6.38929 q^{86} -3.44600 q^{87} +1.00000 q^{88} +6.71159 q^{89} +3.24823 q^{90} +17.9853 q^{91} +1.76701 q^{92} +3.94628 q^{93} -4.03673 q^{94} -0.629487 q^{96} +5.06574 q^{97} +0.532320 q^{98} +2.60375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * q^98 - 15 * q^99

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