LMFDB - Embedded newform 8007.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71794 q^{2} -1.00000 q^{3} +5.38720 q^{4} +2.54834 q^{5} +2.71794 q^{6} +4.22064 q^{7} -9.20622 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.71794 q^{2} -1.00000 q^{3} +5.38720 q^{4} +2.54834 q^{5} +2.71794 q^{6} +4.22064 q^{7} -9.20622 q^{8} +1.00000 q^{9} -6.92625 q^{10} -2.27721 q^{11} -5.38720 q^{12} -4.46154 q^{13} -11.4715 q^{14} -2.54834 q^{15} +14.2476 q^{16} -1.00000 q^{17} -2.71794 q^{18} +3.01583 q^{19} +13.7284 q^{20} -4.22064 q^{21} +6.18931 q^{22} +4.52885 q^{23} +9.20622 q^{24} +1.49405 q^{25} +12.1262 q^{26} -1.00000 q^{27} +22.7375 q^{28} -0.921501 q^{29} +6.92625 q^{30} +9.72534 q^{31} -20.3116 q^{32} +2.27721 q^{33} +2.71794 q^{34} +10.7556 q^{35} +5.38720 q^{36} -10.7066 q^{37} -8.19684 q^{38} +4.46154 q^{39} -23.4606 q^{40} -2.71723 q^{41} +11.4715 q^{42} +9.58550 q^{43} -12.2678 q^{44} +2.54834 q^{45} -12.3091 q^{46} +8.77859 q^{47} -14.2476 q^{48} +10.8138 q^{49} -4.06074 q^{50} +1.00000 q^{51} -24.0352 q^{52} +7.08094 q^{53} +2.71794 q^{54} -5.80310 q^{55} -38.8562 q^{56} -3.01583 q^{57} +2.50459 q^{58} -10.1901 q^{59} -13.7284 q^{60} -5.11953 q^{61} -26.4329 q^{62} +4.22064 q^{63} +26.7106 q^{64} -11.3695 q^{65} -6.18931 q^{66} +7.24240 q^{67} -5.38720 q^{68} -4.52885 q^{69} -29.2332 q^{70} -16.3060 q^{71} -9.20622 q^{72} +8.60850 q^{73} +29.0998 q^{74} -1.49405 q^{75} +16.2469 q^{76} -9.61128 q^{77} -12.1262 q^{78} +12.8720 q^{79} +36.3077 q^{80} +1.00000 q^{81} +7.38526 q^{82} -4.75131 q^{83} -22.7375 q^{84} -2.54834 q^{85} -26.0528 q^{86} +0.921501 q^{87} +20.9645 q^{88} -6.81203 q^{89} -6.92625 q^{90} -18.8306 q^{91} +24.3978 q^{92} -9.72534 q^{93} -23.8597 q^{94} +7.68536 q^{95} +20.3116 q^{96} -2.48629 q^{97} -29.3914 q^{98} -2.27721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.71794	−1.92187	−0.960937	−	0.276766i	$-0.910737\pi$
$2$	−2.71794	−1.92187	−0.960937	+	0.276766i	$0.910737\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.38720	2.69360
$5$	2.54834	1.13965	0.569827	−	0.821765i	$-0.307010\pi$
$5$	2.54834	1.13965	0.569827	+	0.821765i	$0.307010\pi$
$6$	2.71794	1.10959
$7$	4.22064	1.59525	0.797627	−	0.603152i	$-0.206089\pi$
$7$	4.22064	1.59525	0.797627	+	0.603152i	$0.206089\pi$
$8$	−9.20622	−3.25489
$9$	1.00000	0.333333
$10$	−6.92625	−2.19027
$11$	−2.27721	−0.686604	−0.343302	−	0.939225i	$-0.611545\pi$
$11$	−2.27721	−0.686604	−0.343302	+	0.939225i	$0.611545\pi$
$12$	−5.38720	−1.55515
$13$	−4.46154	−1.23741	−0.618705	−	0.785624i	$-0.712342\pi$
$13$	−4.46154	−1.23741	−0.618705	+	0.785624i	$0.712342\pi$
$14$	−11.4715	−3.06588
$15$	−2.54834	−0.657979
$16$	14.2476	3.56189
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.71794	−0.640625
$19$	3.01583	0.691878	0.345939	−	0.938257i	$-0.387560\pi$
$19$	3.01583	0.691878	0.345939	+	0.938257i	$0.387560\pi$
$20$	13.7284	3.06977
$21$	−4.22064	−0.921020
$22$	6.18931	1.31957
$23$	4.52885	0.944331	0.472165	−	0.881510i	$-0.343473\pi$
$23$	4.52885	0.944331	0.472165	+	0.881510i	$0.343473\pi$
$24$	9.20622	1.87921
$25$	1.49405	0.298810
$26$	12.1262	2.37815
$27$	−1.00000	−0.192450
$28$	22.7375	4.29698
$29$	−0.921501	−0.171118	−0.0855592	−	0.996333i	$-0.527268\pi$
$29$	−0.921501	−0.171118	−0.0855592	+	0.996333i	$0.527268\pi$
$30$	6.92625	1.26455
$31$	9.72534	1.74672	0.873361	−	0.487073i	$-0.161935\pi$
$31$	9.72534	1.74672	0.873361	+	0.487073i	$0.161935\pi$
$32$	−20.3116	−3.59062
$33$	2.27721	0.396411
$34$	2.71794	0.466123
$35$	10.7556	1.81804
$36$	5.38720	0.897867
$37$	−10.7066	−1.76015	−0.880075	−	0.474834i	$-0.842508\pi$
$37$	−10.7066	−1.76015	−0.880075	+	0.474834i	$0.842508\pi$
$38$	−8.19684	−1.32970
$39$	4.46154	0.714419
$40$	−23.4606	−3.70945
$41$	−2.71723	−0.424360	−0.212180	−	0.977231i	$-0.568056\pi$
$41$	−2.71723	−0.424360	−0.212180	+	0.977231i	$0.568056\pi$
$42$	11.4715	1.77008
$43$	9.58550	1.46177	0.730887	−	0.682498i	$-0.239107\pi$
$43$	9.58550	1.46177	0.730887	+	0.682498i	$0.239107\pi$
$44$	−12.2678	−1.84944
$45$	2.54834	0.379885
$46$	−12.3091	−1.81488
$47$	8.77859	1.28049	0.640245	−	0.768171i	$-0.278833\pi$
$47$	8.77859	1.28049	0.640245	+	0.768171i	$0.278833\pi$
$48$	−14.2476	−2.05646
$49$	10.8138	1.54483
$50$	−4.06074	−0.574276
$51$	1.00000	0.140028
$52$	−24.0352	−3.33309
$53$	7.08094	0.972641	0.486321	−	0.873780i	$-0.338339\pi$
$53$	7.08094	0.972641	0.486321	+	0.873780i	$0.338339\pi$
$54$	2.71794	0.369865
$55$	−5.80310	−0.782490
$56$	−38.8562	−5.19238
$57$	−3.01583	−0.399456
$58$	2.50459	0.328868
$59$	−10.1901	−1.32663	−0.663317	−	0.748339i	$-0.730852\pi$
$59$	−10.1901	−1.32663	−0.663317	+	0.748339i	$0.730852\pi$
$60$	−13.7284	−1.77233
$61$	−5.11953	−0.655488	−0.327744	−	0.944767i	$-0.606288\pi$
$61$	−5.11953	−0.655488	−0.327744	+	0.944767i	$0.606288\pi$
$62$	−26.4329	−3.35698
$63$	4.22064	0.531751
$64$	26.7106	3.33882
$65$	−11.3695	−1.41022
$66$	−6.18931	−0.761852
$67$	7.24240	0.884800	0.442400	−	0.896818i	$-0.354127\pi$
$67$	7.24240	0.884800	0.442400	+	0.896818i	$0.354127\pi$
$68$	−5.38720	−0.653294
$69$	−4.52885	−0.545209
$70$	−29.2332	−3.49404
$71$	−16.3060	−1.93517	−0.967586	−	0.252543i	$-0.918733\pi$
$71$	−16.3060	−1.93517	−0.967586	+	0.252543i	$0.918733\pi$
$72$	−9.20622	−1.08496
$73$	8.60850	1.00755	0.503775	−	0.863835i	$-0.331944\pi$
$73$	8.60850	1.00755	0.503775	+	0.863835i	$0.331944\pi$
$74$	29.0998	3.38279
$75$	−1.49405	−0.172518
$76$	16.2469	1.86365
$77$	−9.61128	−1.09531
$78$	−12.1262	−1.37302
$79$	12.8720	1.44822	0.724108	−	0.689687i	$-0.242252\pi$
$79$	12.8720	1.44822	0.724108	+	0.689687i	$0.242252\pi$
$80$	36.3077	4.05932
$81$	1.00000	0.111111
$82$	7.38526	0.815566
$83$	−4.75131	−0.521524	−0.260762	−	0.965403i	$-0.583974\pi$
$83$	−4.75131	−0.521524	−0.260762	+	0.965403i	$0.583974\pi$
$84$	−22.7375	−2.48086
$85$	−2.54834	−0.276407
$86$	−26.0528	−2.80935
$87$	0.921501	0.0987953
$88$	20.9645	2.23482
$89$	−6.81203	−0.722074	−0.361037	−	0.932552i	$-0.617577\pi$
$89$	−6.81203	−0.722074	−0.361037	+	0.932552i	$0.617577\pi$
$90$	−6.92625	−0.730090
$91$	−18.8306	−1.97398
$92$	24.3978	2.54365
$93$	−9.72534	−1.00847
$94$	−23.8597	−2.46094
$95$	7.68536	0.788502
$96$	20.3116	2.07304
$97$	−2.48629	−0.252444	−0.126222	−	0.992002i	$-0.540285\pi$
$97$	−2.48629	−0.252444	−0.126222	+	0.992002i	$0.540285\pi$
$98$	−29.3914	−2.96898
$99$	−2.27721	−0.228868
$100$	8.04876	0.804876
$101$	−12.8018	−1.27382	−0.636912	−	0.770937i	$-0.719788\pi$
$101$	−12.8018	−1.27382	−0.636912	+	0.770937i	$0.719788\pi$
$102$	−2.71794	−0.269116
$103$	0.566586	0.0558274	0.0279137	−	0.999610i	$-0.491114\pi$
$103$	0.566586	0.0558274	0.0279137	+	0.999610i	$0.491114\pi$
$104$	41.0740	4.02763
$105$	−10.7556	−1.04964
$106$	−19.2456	−1.86929
$107$	7.97736	0.771200	0.385600	−	0.922666i	$-0.373994\pi$
$107$	7.97736	0.771200	0.385600	+	0.922666i	$0.373994\pi$
$108$	−5.38720	−0.518384
$109$	−4.42093	−0.423448	−0.211724	−	0.977329i	$-0.567908\pi$
$109$	−4.42093	−0.423448	−0.211724	+	0.977329i	$0.567908\pi$
$110$	15.7725	1.50385
$111$	10.7066	1.01622
$112$	60.1339	5.68212
$113$	20.8976	1.96588	0.982940	−	0.183927i	$-0.0588810\pi$
$113$	20.8976	1.96588	0.982940	+	0.183927i	$0.0588810\pi$
$114$	8.19684	0.767705
$115$	11.5411	1.07621
$116$	−4.96431	−0.460925
$117$	−4.46154	−0.412470
$118$	27.6960	2.54962
$119$	−4.22064	−0.386906
$120$	23.4606	2.14165
$121$	−5.81433	−0.528576
$122$	13.9146	1.25977
$123$	2.71723	0.245004
$124$	52.3924	4.70498
$125$	−8.93436	−0.799113
$126$	−11.4715	−1.02196
$127$	17.7440	1.57453	0.787263	−	0.616618i	$-0.211498\pi$
$127$	17.7440	1.57453	0.787263	+	0.616618i	$0.211498\pi$
$128$	−31.9746	−2.82618
$129$	−9.58550	−0.843956
$130$	30.9017	2.71026
$131$	3.69546	0.322874	0.161437	−	0.986883i	$-0.448387\pi$
$131$	3.69546	0.322874	0.161437	+	0.986883i	$0.448387\pi$
$132$	12.2678	1.06777
$133$	12.7287	1.10372
$134$	−19.6844	−1.70047
$135$	−2.54834	−0.219326
$136$	9.20622	0.789427
$137$	−0.888691	−0.0759260	−0.0379630	−	0.999279i	$-0.512087\pi$
$137$	−0.888691	−0.0759260	−0.0379630	+	0.999279i	$0.512087\pi$
$138$	12.3091	1.04782
$139$	21.0381	1.78443	0.892215	−	0.451611i	$-0.149150\pi$
$139$	21.0381	1.78443	0.892215	+	0.451611i	$0.149150\pi$
$140$	57.9429	4.89707
$141$	−8.77859	−0.739291
$142$	44.3189	3.71916
$143$	10.1599	0.849610
$144$	14.2476	1.18730
$145$	−2.34830	−0.195016
$146$	−23.3974	−1.93638
$147$	−10.8138	−0.891910
$148$	−57.6785	−4.74115
$149$	9.14136	0.748890	0.374445	−	0.927249i	$-0.377833\pi$
$149$	9.14136	0.748890	0.374445	+	0.927249i	$0.377833\pi$
$150$	4.06074	0.331558
$151$	−19.5812	−1.59350	−0.796748	−	0.604312i	$-0.793448\pi$
$151$	−19.5812	−1.59350	−0.796748	+	0.604312i	$0.793448\pi$
$152$	−27.7644	−2.25199
$153$	−1.00000	−0.0808452
$154$	26.1229	2.10504
$155$	24.7835	1.99066
$156$	24.0352	1.92436
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−34.9854	−2.78329
$159$	−7.08094	−0.561555
$160$	−51.7609	−4.09206
$161$	19.1147	1.50645
$162$	−2.71794	−0.213542
$163$	−1.15737	−0.0906525	−0.0453262	−	0.998972i	$-0.514433\pi$
$163$	−1.15737	−0.0906525	−0.0453262	+	0.998972i	$0.514433\pi$
$164$	−14.6383	−1.14306
$165$	5.80310	0.451771
$166$	12.9138	1.00230
$167$	10.5626	0.817355	0.408678	−	0.912679i	$-0.365990\pi$
$167$	10.5626	0.817355	0.408678	+	0.912679i	$0.365990\pi$
$168$	38.8562	2.99782
$169$	6.90537	0.531182
$170$	6.92625	0.531219
$171$	3.01583	0.230626
$172$	51.6390	3.93744
$173$	−17.6388	−1.34105	−0.670527	−	0.741885i	$-0.733932\pi$
$173$	−17.6388	−1.34105	−0.670527	+	0.741885i	$0.733932\pi$
$174$	−2.50459	−0.189872
$175$	6.30586	0.476678
$176$	−32.4446	−2.44561
$177$	10.1901	0.765932
$178$	18.5147	1.38774
$179$	22.4340	1.67680	0.838399	−	0.545057i	$-0.183492\pi$
$179$	22.4340	1.67680	0.838399	+	0.545057i	$0.183492\pi$
$180$	13.7284	1.02326
$181$	1.09936	0.0817150	0.0408575	−	0.999165i	$-0.486991\pi$
$181$	1.09936	0.0817150	0.0408575	+	0.999165i	$0.486991\pi$
$182$	51.1804	3.79374
$183$	5.11953	0.378446
$184$	−41.6936	−3.07369
$185$	−27.2840	−2.00596
$186$	26.4329	1.93815
$187$	2.27721	0.166526
$188$	47.2921	3.44913
$189$	−4.22064	−0.307007
$190$	−20.8884	−1.51540
$191$	1.19196	0.0862469	0.0431234	−	0.999070i	$-0.486269\pi$
$191$	1.19196	0.0862469	0.0431234	+	0.999070i	$0.486269\pi$
$192$	−26.7106	−1.92767
$193$	18.3725	1.32248	0.661241	−	0.750173i	$-0.270030\pi$
$193$	18.3725	1.32248	0.661241	+	0.750173i	$0.270030\pi$
$194$	6.75758	0.485166
$195$	11.3695	0.814190
$196$	58.2563	4.16117
$197$	12.5153	0.891677	0.445839	−	0.895113i	$-0.352906\pi$
$197$	12.5153	0.891677	0.445839	+	0.895113i	$0.352906\pi$
$198$	6.18931	0.439855
$199$	−11.1344	−0.789296	−0.394648	−	0.918832i	$-0.629133\pi$
$199$	−11.1344	−0.789296	−0.394648	+	0.918832i	$0.629133\pi$
$200$	−13.7546	−0.972595
$201$	−7.24240	−0.510840
$202$	34.7945	2.44813
$203$	−3.88933	−0.272977
$204$	5.38720	0.377180
$205$	−6.92443	−0.483623
$206$	−1.53995	−0.107293
$207$	4.52885	0.314777
$208$	−63.5661	−4.40752
$209$	−6.86766	−0.475046
$210$	29.2332	2.01728
$211$	29.0438	1.99946	0.999730	−	0.0232171i	$-0.00739091\pi$
$211$	29.0438	1.99946	0.999730	+	0.0232171i	$0.00739091\pi$
$212$	38.1465	2.61991
$213$	16.3060	1.11727
$214$	−21.6820	−1.48215
$215$	24.4271	1.66592
$216$	9.20622	0.626404
$217$	41.0472	2.78646
$218$	12.0158	0.813814
$219$	−8.60850	−0.581709
$220$	−31.2625	−2.10772
$221$	4.46154	0.300116
$222$	−29.0998	−1.95305
$223$	−7.73873	−0.518224	−0.259112	−	0.965847i	$-0.583430\pi$
$223$	−7.73873	−0.518224	−0.259112	+	0.965847i	$0.583430\pi$
$224$	−85.7280	−5.72794
$225$	1.49405	0.0996034
$226$	−56.7984	−3.77817
$227$	−25.2467	−1.67568	−0.837842	−	0.545913i	$-0.816183\pi$
$227$	−25.2467	−1.67568	−0.837842	+	0.545913i	$0.816183\pi$
$228$	−16.2469	−1.07598
$229$	20.3490	1.34470	0.672351	−	0.740233i	$-0.265285\pi$
$229$	20.3490	1.34470	0.672351	+	0.740233i	$0.265285\pi$
$230$	−31.3679	−2.06834
$231$	9.61128	0.632376
$232$	8.48354	0.556972
$233$	7.96514	0.521814	0.260907	−	0.965364i	$-0.415978\pi$
$233$	7.96514	0.521814	0.260907	+	0.965364i	$0.415978\pi$
$234$	12.1262	0.792715
$235$	22.3709	1.45931
$236$	−54.8960	−3.57342
$237$	−12.8720	−0.836128
$238$	11.4715	0.743584
$239$	−7.84880	−0.507696	−0.253848	−	0.967244i	$-0.581696\pi$
$239$	−7.84880	−0.507696	−0.253848	+	0.967244i	$0.581696\pi$
$240$	−36.3077	−2.34365
$241$	−14.3167	−0.922223	−0.461111	−	0.887342i	$-0.652549\pi$
$241$	−14.3167	−0.922223	−0.461111	+	0.887342i	$0.652549\pi$
$242$	15.8030	1.01586
$243$	−1.00000	−0.0641500
$244$	−27.5799	−1.76562
$245$	27.5573	1.76057
$246$	−7.38526	−0.470867
$247$	−13.4552	−0.856137
$248$	−89.5336	−5.68539
$249$	4.75131	0.301102
$250$	24.2831	1.53580
$251$	−27.2705	−1.72130	−0.860649	−	0.509199i	$-0.829942\pi$
$251$	−27.2705	−1.72130	−0.860649	+	0.509199i	$0.829942\pi$
$252$	22.7375	1.43233
$253$	−10.3131	−0.648381
$254$	−48.2272	−3.02604
$255$	2.54834	0.159583
$256$	33.4840	2.09275
$257$	20.1023	1.25394	0.626972	−	0.779042i	$-0.284294\pi$
$257$	20.1023	1.25394	0.626972	+	0.779042i	$0.284294\pi$
$258$	26.0528	1.62198
$259$	−45.1886	−2.80789
$260$	−61.2500	−3.79857
$261$	−0.921501	−0.0570395
$262$	−10.0441	−0.620524
$263$	11.2304	0.692499	0.346249	−	0.938143i	$-0.387455\pi$
$263$	11.2304	0.692499	0.346249	+	0.938143i	$0.387455\pi$
$264$	−20.9645	−1.29027
$265$	18.0447	1.10847
$266$	−34.5960	−2.12121
$267$	6.81203	0.416890
$268$	39.0163	2.38330
$269$	15.6771	0.955852	0.477926	−	0.878400i	$-0.341389\pi$
$269$	15.6771	0.955852	0.477926	+	0.878400i	$0.341389\pi$
$270$	6.92625	0.421518
$271$	−10.8169	−0.657082	−0.328541	−	0.944490i	$-0.606557\pi$
$271$	−10.8169	−0.657082	−0.328541	+	0.944490i	$0.606557\pi$
$272$	−14.2476	−0.863885
$273$	18.8306	1.13968
$274$	2.41541	0.145920
$275$	−3.40226	−0.205164
$276$	−24.3978	−1.46858
$277$	−26.2568	−1.57762	−0.788808	−	0.614639i	$-0.789302\pi$
$277$	−26.2568	−1.57762	−0.788808	+	0.614639i	$0.789302\pi$
$278$	−57.1804	−3.42945
$279$	9.72534	0.582241
$280$	−99.0189	−5.91751
$281$	14.5070	0.865416	0.432708	−	0.901534i	$-0.357558\pi$
$281$	14.5070	0.865416	0.432708	+	0.901534i	$0.357558\pi$
$282$	23.8597	1.42082
$283$	22.6576	1.34685	0.673427	−	0.739253i	$-0.264821\pi$
$283$	22.6576	1.34685	0.673427	+	0.739253i	$0.264821\pi$
$284$	−87.8440	−5.21258
$285$	−7.68536	−0.455242
$286$	−27.6139	−1.63284
$287$	−11.4684	−0.676961
$288$	−20.3116	−1.19687
$289$	1.00000	0.0588235
$290$	6.38254	0.374796
$291$	2.48629	0.145749
$292$	46.3758	2.71394
$293$	−14.5991	−0.852888	−0.426444	−	0.904514i	$-0.640234\pi$
$293$	−14.5991	−0.852888	−0.426444	+	0.904514i	$0.640234\pi$
$294$	29.3914	1.71414
$295$	−25.9678	−1.51190
$296$	98.5671	5.72910
$297$	2.27721	0.132137
$298$	−24.8457	−1.43927
$299$	−20.2057	−1.16852
$300$	−8.04876	−0.464695
$301$	40.4570	2.33190
$302$	53.2206	3.06250
$303$	12.8018	0.735442
$304$	42.9682	2.46440
$305$	−13.0463	−0.747030
$306$	2.71794	0.155374
$307$	−26.6295	−1.51983	−0.759914	−	0.650024i	$-0.774759\pi$
$307$	−26.6295	−1.51983	−0.759914	+	0.650024i	$0.774759\pi$
$308$	−51.7779	−2.95032
$309$	−0.566586	−0.0322320
$310$	−67.3601	−3.82580
$311$	20.5542	1.16552	0.582761	−	0.812643i	$-0.301972\pi$
$311$	20.5542	1.16552	0.582761	+	0.812643i	$0.301972\pi$
$312$	−41.0740	−2.32535
$313$	−1.32010	−0.0746163	−0.0373082	−	0.999304i	$-0.511878\pi$
$313$	−1.32010	−0.0746163	−0.0373082	+	0.999304i	$0.511878\pi$
$314$	−2.71794	−0.153382
$315$	10.7556	0.606012
$316$	69.3442	3.90092
$317$	−3.67704	−0.206523	−0.103262	−	0.994654i	$-0.532928\pi$
$317$	−3.67704	−0.206523	−0.103262	+	0.994654i	$0.532928\pi$
$318$	19.2456	1.07924
$319$	2.09845	0.117491
$320$	68.0677	3.80510
$321$	−7.97736	−0.445253
$322$	−51.9525	−2.89520
$323$	−3.01583	−0.167805
$324$	5.38720	0.299289
$325$	−6.66578	−0.369751
$326$	3.14567	0.174223
$327$	4.42093	0.244478
$328$	25.0154	1.38124
$329$	37.0513	2.04270
$330$	−15.7725	−0.868247
$331$	23.9905	1.31864	0.659318	−	0.751864i	$-0.270845\pi$
$331$	23.9905	1.31864	0.659318	+	0.751864i	$0.270845\pi$
$332$	−25.5963	−1.40478
$333$	−10.7066	−0.586717
$334$	−28.7084	−1.57085
$335$	18.4561	1.00837
$336$	−60.1339	−3.28057
$337$	3.91250	0.213128	0.106564	−	0.994306i	$-0.466015\pi$
$337$	3.91250	0.213128	0.106564	+	0.994306i	$0.466015\pi$
$338$	−18.7684	−1.02087
$339$	−20.8976	−1.13500
$340$	−13.7284	−0.744529
$341$	−22.1466	−1.19931
$342$	−8.19684	−0.443235
$343$	16.0968	0.869147
$344$	−88.2462	−4.75792
$345$	−11.5411	−0.621350
$346$	47.9412	2.57734
$347$	−21.7114	−1.16553	−0.582763	−	0.812642i	$-0.698029\pi$
$347$	−21.7114	−1.16553	−0.582763	+	0.812642i	$0.698029\pi$
$348$	4.96431	0.266115
$349$	−17.2990	−0.925994	−0.462997	−	0.886360i	$-0.653226\pi$
$349$	−17.2990	−0.925994	−0.462997	+	0.886360i	$0.653226\pi$
$350$	−17.1390	−0.916116
$351$	4.46154	0.238140
$352$	46.2537	2.46533
$353$	19.6188	1.04420	0.522102	−	0.852883i	$-0.325148\pi$
$353$	19.6188	1.04420	0.522102	+	0.852883i	$0.325148\pi$
$354$	−27.6960	−1.47203
$355$	−41.5534	−2.20543
$356$	−36.6978	−1.94498
$357$	4.22064	0.223380
$358$	−60.9743	−3.22259
$359$	13.1841	0.695831	0.347915	−	0.937526i	$-0.386890\pi$
$359$	13.1841	0.695831	0.347915	+	0.937526i	$0.386890\pi$
$360$	−23.4606	−1.23648
$361$	−9.90478	−0.521304
$362$	−2.98800	−0.157046
$363$	5.81433	0.305173
$364$	−101.444	−5.31712
$365$	21.9374	1.14826
$366$	−13.9146	−0.727327
$367$	22.0931	1.15325	0.576625	−	0.817009i	$-0.304369\pi$
$367$	22.0931	1.15325	0.576625	+	0.817009i	$0.304369\pi$
$368$	64.5251	3.36360
$369$	−2.71723	−0.141453
$370$	74.1564	3.85521
$371$	29.8861	1.55161
$372$	−52.3924	−2.71642
$373$	−3.77332	−0.195375	−0.0976876	−	0.995217i	$-0.531145\pi$
$373$	−3.77332	−0.195375	−0.0976876	+	0.995217i	$0.531145\pi$
$374$	−6.18931	−0.320042
$375$	8.93436	0.461368
$376$	−80.8177	−4.16785
$377$	4.11132	0.211744
$378$	11.4715	0.590028
$379$	22.0667	1.13349	0.566745	−	0.823893i	$-0.308203\pi$
$379$	22.0667	1.13349	0.566745	+	0.823893i	$0.308203\pi$
$380$	41.4026	2.12391
$381$	−17.7440	−0.909053
$382$	−3.23967	−0.165756
$383$	3.65052	0.186533	0.0932663	−	0.995641i	$-0.470269\pi$
$383$	3.65052	0.186533	0.0932663	+	0.995641i	$0.470269\pi$
$384$	31.9746	1.63170
$385$	−24.4928	−1.24827
$386$	−49.9354	−2.54165
$387$	9.58550	0.487258
$388$	−13.3941	−0.679984
$389$	3.76962	0.191127	0.0955636	−	0.995423i	$-0.469535\pi$
$389$	3.76962	0.191127	0.0955636	+	0.995423i	$0.469535\pi$
$390$	−30.9017	−1.56477
$391$	−4.52885	−0.229034
$392$	−99.5545	−5.02826
$393$	−3.69546	−0.186412
$394$	−34.0158	−1.71369
$395$	32.8023	1.65046
$396$	−12.2678	−0.616479
$397$	18.7183	0.939445	0.469723	−	0.882814i	$-0.344354\pi$
$397$	18.7183	0.939445	0.469723	+	0.882814i	$0.344354\pi$
$398$	30.2626	1.51693
$399$	−12.7287	−0.637234
$400$	21.2866	1.06433
$401$	−7.49813	−0.374439	−0.187219	−	0.982318i	$-0.559948\pi$
$401$	−7.49813	−0.374439	−0.187219	+	0.982318i	$0.559948\pi$
$402$	19.6844	0.981770
$403$	−43.3900	−2.16141
$404$	−68.9657	−3.43117
$405$	2.54834	0.126628
$406$	10.5710	0.524628
$407$	24.3811	1.20853
$408$	−9.20622	−0.455776
$409$	−16.5661	−0.819139	−0.409569	−	0.912279i	$-0.634321\pi$
$409$	−16.5661	−0.819139	−0.409569	+	0.912279i	$0.634321\pi$
$410$	18.8202	0.929463
$411$	0.888691	0.0438359
$412$	3.05231	0.150377
$413$	−43.0086	−2.11632
$414$	−12.3091	−0.604962
$415$	−12.1080	−0.594356
$416$	90.6210	4.44306
$417$	−21.0381	−1.03024
$418$	18.6659	0.912979
$419$	13.2039	0.645051	0.322525	−	0.946561i	$-0.395468\pi$
$419$	13.2039	0.645051	0.322525	+	0.946561i	$0.395468\pi$
$420$	−57.9429	−2.82732
$421$	−8.08536	−0.394056	−0.197028	−	0.980398i	$-0.563129\pi$
$421$	−8.08536	−0.394056	−0.197028	+	0.980398i	$0.563129\pi$
$422$	−78.9395	−3.84271
$423$	8.77859	0.426830
$424$	−65.1887	−3.16584
$425$	−1.49405	−0.0724722
$426$	−44.3189	−2.14726
$427$	−21.6077	−1.04567
$428$	42.9757	2.07731
$429$	−10.1599	−0.490522
$430$	−66.3915	−3.20168
$431$	1.17668	0.0566788	0.0283394	−	0.999598i	$-0.490978\pi$
$431$	1.17668	0.0566788	0.0283394	+	0.999598i	$0.490978\pi$
$432$	−14.2476	−0.685486
$433$	17.4859	0.840317	0.420158	−	0.907451i	$-0.361975\pi$
$433$	17.4859	0.840317	0.420158	+	0.907451i	$0.361975\pi$
$434$	−111.564	−5.35524
$435$	2.34830	0.112592
$436$	−23.8164	−1.14060
$437$	13.6582	0.653362
$438$	23.3974	1.11797
$439$	1.81125	0.0864464	0.0432232	−	0.999065i	$-0.486237\pi$
$439$	1.81125	0.0864464	0.0432232	+	0.999065i	$0.486237\pi$
$440$	53.4247	2.54692
$441$	10.8138	0.514944
$442$	−12.1262	−0.576785
$443$	31.2542	1.48493	0.742466	−	0.669884i	$-0.233656\pi$
$443$	31.2542	1.48493	0.742466	+	0.669884i	$0.233656\pi$
$444$	57.6785	2.73730
$445$	−17.3594	−0.822914
$446$	21.0334	0.995961
$447$	−9.14136	−0.432372
$448$	112.736	5.32627
$449$	40.3562	1.90453	0.952263	−	0.305280i	$-0.0987500\pi$
$449$	40.3562	1.90453	0.952263	+	0.305280i	$0.0987500\pi$
$450$	−4.06074	−0.191425
$451$	6.18769	0.291367
$452$	112.580	5.29530
$453$	19.5812	0.920005
$454$	68.6191	3.22046
$455$	−47.9868	−2.24965
$456$	27.7644	1.30019
$457$	−2.70555	−0.126560	−0.0632801	−	0.997996i	$-0.520156\pi$
$457$	−2.70555	−0.126560	−0.0632801	+	0.997996i	$0.520156\pi$
$458$	−55.3075	−2.58435
$459$	1.00000	0.0466760
$460$	62.1741	2.89888
$461$	−4.34730	−0.202474	−0.101237	−	0.994862i	$-0.532280\pi$
$461$	−4.34730	−0.202474	−0.101237	+	0.994862i	$0.532280\pi$
$462$	−26.1229	−1.21535
$463$	32.5762	1.51394	0.756971	−	0.653448i	$-0.226678\pi$
$463$	32.5762	1.51394	0.756971	+	0.653448i	$0.226678\pi$
$464$	−13.1291	−0.609505
$465$	−24.7835	−1.14931
$466$	−21.6488	−1.00286
$467$	0.0127955	0.000592105 0	0.000296053	−	1.00000i	$-0.499906\pi$
$467$	0.0127955	0.000592105 0	0.000296053		1.00000i	$0.499906\pi$
$468$	−24.0352	−1.11103
$469$	30.5676	1.41148
$470$	−60.8027	−2.80462
$471$	−1.00000	−0.0460776
$472$	93.8120	4.31805
$473$	−21.8282	−1.00366
$474$	34.9854	1.60693
$475$	4.50580	0.206740
$476$	−22.7375	−1.04217
$477$	7.08094	0.324214
$478$	21.3326	0.975729
$479$	−10.1516	−0.463839	−0.231920	−	0.972735i	$-0.574501\pi$
$479$	−10.1516	−0.463839	−0.231920	+	0.972735i	$0.574501\pi$
$480$	51.7609	2.36255
$481$	47.7679	2.17803
$482$	38.9121	1.77240
$483$	−19.1147	−0.869747
$484$	−31.3230	−1.42377
$485$	−6.33591	−0.287699
$486$	2.71794	0.123288
$487$	−41.1178	−1.86323	−0.931613	−	0.363451i	$-0.881599\pi$
$487$	−41.1178	−1.86323	−0.931613	+	0.363451i	$0.881599\pi$
$488$	47.1315	2.13354
$489$	1.15737	0.0523382
$490$	−74.8993	−3.38360
$491$	40.7909	1.84087	0.920433	−	0.390900i	$-0.127836\pi$
$491$	40.7909	1.84087	0.920433	+	0.390900i	$0.127836\pi$
$492$	14.6383	0.659944
$493$	0.921501	0.0415023
$494$	36.5706	1.64539
$495$	−5.80310	−0.260830
$496$	138.562	6.22163
$497$	−68.8220	−3.08709
$498$	−12.9138	−0.578680
$499$	7.95009	0.355895	0.177947	−	0.984040i	$-0.443054\pi$
$499$	7.95009	0.355895	0.177947	+	0.984040i	$0.443054\pi$
$500$	−48.1312	−2.15249
$501$	−10.5626	−0.471900
$502$	74.1196	3.30812
$503$	−6.83827	−0.304904	−0.152452	−	0.988311i	$-0.548717\pi$
$503$	−6.83827	−0.304904	−0.152452	+	0.988311i	$0.548717\pi$
$504$	−38.8562	−1.73079
$505$	−32.6233	−1.45172
$506$	28.0305	1.24611
$507$	−6.90537	−0.306678
$508$	95.5906	4.24115
$509$	−42.9266	−1.90269	−0.951344	−	0.308130i	$-0.900297\pi$
$509$	−42.9266	−1.90269	−0.951344	+	0.308130i	$0.900297\pi$
$510$	−6.92625	−0.306699
$511$	36.3334	1.60730
$512$	−27.0582	−1.19582
$513$	−3.01583	−0.133152
$514$	−54.6368	−2.40992
$515$	1.44386	0.0636239
$516$	−51.6390	−2.27328
$517$	−19.9907	−0.879189
$518$	122.820	5.39640
$519$	17.6388	0.774258
$520$	104.671	4.59011
$521$	−11.3482	−0.497174	−0.248587	−	0.968610i	$-0.579966\pi$
$521$	−11.3482	−0.497174	−0.248587	+	0.968610i	$0.579966\pi$
$522$	2.50459	0.109623
$523$	−3.03382	−0.132660	−0.0663299	−	0.997798i	$-0.521129\pi$
$523$	−3.03382	−0.132660	−0.0663299	+	0.997798i	$0.521129\pi$
$524$	19.9082	0.869695
$525$	−6.30586	−0.275210
$526$	−30.5237	−1.33090
$527$	−9.72534	−0.423642
$528$	32.4446	1.41197
$529$	−2.48952	−0.108240
$530$	−49.0443	−2.13035
$531$	−10.1901	−0.442211
$532$	68.5723	2.97299
$533$	12.1230	0.525107
$534$	−18.5147	−0.801209
$535$	20.3290	0.878901
$536$	−66.6752	−2.87993
$537$	−22.4340	−0.968099
$538$	−42.6096	−1.83703
$539$	−24.6253	−1.06069
$540$	−13.7284	−0.590778
$541$	−27.0371	−1.16242	−0.581208	−	0.813755i	$-0.697420\pi$
$541$	−27.0371	−1.16242	−0.581208	+	0.813755i	$0.697420\pi$
$542$	29.3998	1.26283
$543$	−1.09936	−0.0471782
$544$	20.3116	0.870852
$545$	−11.2660	−0.482584
$546$	−51.1804	−2.19032
$547$	1.93121	0.0825724	0.0412862	−	0.999147i	$-0.486854\pi$
$547$	1.93121	0.0825724	0.0412862	+	0.999147i	$0.486854\pi$
$548$	−4.78756	−0.204514
$549$	−5.11953	−0.218496
$550$	9.24715	0.394300
$551$	−2.77909	−0.118393
$552$	41.6936	1.77460
$553$	54.3282	2.31027
$554$	71.3644	3.03198
$555$	27.2840	1.15814
$556$	113.337	4.80654
$557$	41.4363	1.75571	0.877857	−	0.478923i	$-0.158973\pi$
$557$	41.4363	1.75571	0.877857	+	0.478923i	$0.158973\pi$
$558$	−26.4329	−1.11899
$559$	−42.7661	−1.80881
$560$	153.242	6.47565
$561$	−2.27721	−0.0961437
$562$	−39.4292	−1.66322
$563$	−0.0368888	−0.00155468	−0.000777340	−	1.00000i	$-0.500247\pi$
$563$	−0.0368888	−0.00155468	−0.000777340		1.00000i	$0.500247\pi$
$564$	−47.2921	−1.99136
$565$	53.2542	2.24042
$566$	−61.5820	−2.58849
$567$	4.22064	0.177250
$568$	150.117	6.29877
$569$	8.25762	0.346177	0.173089	−	0.984906i	$-0.444625\pi$
$569$	8.25762	0.346177	0.173089	+	0.984906i	$0.444625\pi$
$570$	20.8884	0.874917
$571$	17.6637	0.739204	0.369602	−	0.929190i	$-0.379494\pi$
$571$	17.6637	0.739204	0.369602	+	0.929190i	$0.379494\pi$
$572$	54.7332	2.28851
$573$	−1.19196	−0.0497947
$574$	31.1706	1.30103
$575$	6.76634	0.282176
$576$	26.7106	1.11294
$577$	44.2431	1.84187	0.920933	−	0.389721i	$-0.127428\pi$
$577$	44.2431	1.84187	0.920933	+	0.389721i	$0.127428\pi$
$578$	−2.71794	−0.113051
$579$	−18.3725	−0.763536
$580$	−12.6508	−0.525295
$581$	−20.0536	−0.831962
$582$	−6.75758	−0.280111
$583$	−16.1248	−0.667819
$584$	−79.2518	−3.27946
$585$	−11.3695	−0.470073
$586$	39.6795	1.63914
$587$	8.97172	0.370303	0.185151	−	0.982710i	$-0.440722\pi$
$587$	8.97172	0.370303	0.185151	+	0.982710i	$0.440722\pi$
$588$	−58.2563	−2.40245
$589$	29.3300	1.20852
$590$	70.5789	2.90569
$591$	−12.5153	−0.514810
$592$	−152.543	−6.26946
$593$	−28.3066	−1.16241	−0.581206	−	0.813757i	$-0.697419\pi$
$593$	−28.3066	−1.16241	−0.581206	+	0.813757i	$0.697419\pi$
$594$	−6.18931	−0.253951
$595$	−10.7556	−0.440939
$596$	49.2464	2.01721
$597$	11.1344	0.455700
$598$	54.9178	2.24576
$599$	−15.7065	−0.641750	−0.320875	−	0.947122i	$-0.603977\pi$
$599$	−15.7065	−0.641750	−0.320875	+	0.947122i	$0.603977\pi$
$600$	13.7546	0.561528
$601$	33.3722	1.36128	0.680640	−	0.732618i	$-0.261702\pi$
$601$	33.3722	1.36128	0.680640	+	0.732618i	$0.261702\pi$
$602$	−109.960	−4.48162
$603$	7.24240	0.294933
$604$	−105.488	−4.29224
$605$	−14.8169	−0.602393
$606$	−34.7945	−1.41343
$607$	−12.7456	−0.517330	−0.258665	−	0.965967i	$-0.583283\pi$
$607$	−12.7456	−0.517330	−0.258665	+	0.965967i	$0.583283\pi$
$608$	−61.2563	−2.48427
$609$	3.88933	0.157603
$610$	35.4591	1.43570
$611$	−39.1661	−1.58449
$612$	−5.38720	−0.217765
$613$	−38.2217	−1.54376	−0.771879	−	0.635769i	$-0.780683\pi$
$613$	−38.2217	−1.54376	−0.771879	+	0.635769i	$0.780683\pi$
$614$	72.3775	2.92092
$615$	6.92443	0.279220
$616$	88.4836	3.56510
$617$	41.2945	1.66245	0.831227	−	0.555933i	$-0.187639\pi$
$617$	41.2945	1.66245	0.831227	+	0.555933i	$0.187639\pi$
$618$	1.53995	0.0619458
$619$	11.6813	0.469512	0.234756	−	0.972054i	$-0.424571\pi$
$619$	11.6813	0.469512	0.234756	+	0.972054i	$0.424571\pi$
$620$	133.514	5.36204
$621$	−4.52885	−0.181736
$622$	−55.8652	−2.23999
$623$	−28.7512	−1.15189
$624$	63.5661	2.54468
$625$	−30.2381	−1.20952
$626$	3.58795	0.143403
$627$	6.86766	0.274268
$628$	5.38720	0.214973
$629$	10.7066	0.426899
$630$	−29.2332	−1.16468
$631$	26.1727	1.04192	0.520960	−	0.853581i	$-0.325574\pi$
$631$	26.1727	1.04192	0.520960	+	0.853581i	$0.325574\pi$
$632$	−118.503	−4.71379
$633$	−29.0438	−1.15439
$634$	9.99398	0.396912
$635$	45.2178	1.79441
$636$	−38.1465	−1.51261
$637$	−48.2464	−1.91159
$638$	−5.70346	−0.225802
$639$	−16.3060	−0.645057
$640$	−81.4823	−3.22087
$641$	18.6131	0.735172	0.367586	−	0.929990i	$-0.380184\pi$
$641$	18.6131	0.735172	0.367586	+	0.929990i	$0.380184\pi$
$642$	21.6820	0.855720
$643$	17.2151	0.678899	0.339449	−	0.940624i	$-0.389759\pi$
$643$	17.2151	0.678899	0.339449	+	0.940624i	$0.389759\pi$
$644$	102.975	4.05777
$645$	−24.4271	−0.961817
$646$	8.19684	0.322500
$647$	−8.04640	−0.316337	−0.158168	−	0.987412i	$-0.550559\pi$
$647$	−8.04640	−0.316337	−0.158168	+	0.987412i	$0.550559\pi$
$648$	−9.20622	−0.361655
$649$	23.2049	0.910871
$650$	18.1172	0.710615
$651$	−41.0472	−1.60877
$652$	−6.23501	−0.244182
$653$	−20.1541	−0.788690	−0.394345	−	0.918962i	$-0.629029\pi$
$653$	−20.1541	−0.788690	−0.394345	+	0.918962i	$0.629029\pi$
$654$	−12.0158	−0.469856
$655$	9.41731	0.367965
$656$	−38.7139	−1.51152
$657$	8.60850	0.335850
$658$	−100.703	−3.92582
$659$	−31.6137	−1.23150	−0.615748	−	0.787943i	$-0.711146\pi$
$659$	−31.6137	−1.23150	−0.615748	+	0.787943i	$0.711146\pi$
$660$	31.2625	1.21689
$661$	35.5438	1.38249	0.691246	−	0.722619i	$-0.257062\pi$
$661$	35.5438	1.38249	0.691246	+	0.722619i	$0.257062\pi$
$662$	−65.2047	−2.53425
$663$	−4.46154	−0.173272
$664$	43.7416	1.69750
$665$	32.4372	1.25786
$666$	29.0998	1.12760
$667$	−4.17334	−0.161592
$668$	56.9027	2.20163
$669$	7.73873	0.299197
$670$	−50.1627	−1.93795
$671$	11.6582	0.450061
$672$	85.7280	3.30703
$673$	13.3264	0.513695	0.256847	−	0.966452i	$-0.417316\pi$
$673$	13.3264	0.513695	0.256847	+	0.966452i	$0.417316\pi$
$674$	−10.6340	−0.409604
$675$	−1.49405	−0.0575061
$676$	37.2006	1.43079
$677$	−19.4695	−0.748275	−0.374137	−	0.927373i	$-0.622061\pi$
$677$	−19.4695	−0.748275	−0.374137	+	0.927373i	$0.622061\pi$
$678$	56.7984	2.18133
$679$	−10.4937	−0.402713
$680$	23.4606	0.899673
$681$	25.2467	0.967457
$682$	60.1932	2.30492
$683$	−22.5054	−0.861145	−0.430572	−	0.902556i	$-0.641688\pi$
$683$	−22.5054	−0.861145	−0.430572	+	0.902556i	$0.641688\pi$
$684$	16.2469	0.621215
$685$	−2.26469	−0.0865293
$686$	−43.7502	−1.67039
$687$	−20.3490	−0.776364
$688$	136.570	5.20668
$689$	−31.5919	−1.20356
$690$	31.3679	1.19416
$691$	−46.4036	−1.76527	−0.882637	−	0.470055i	$-0.844234\pi$
$691$	−46.4036	−1.76527	−0.882637	+	0.470055i	$0.844234\pi$
$692$	−95.0238	−3.61226
$693$	−9.61128	−0.365102
$694$	59.0102	2.24000
$695$	53.6123	2.03363
$696$	−8.48354	−0.321568
$697$	2.71723	0.102922
$698$	47.0177	1.77965
$699$	−7.96514	−0.301269
$700$	33.9710	1.28398
$701$	−9.93949	−0.375409	−0.187705	−	0.982226i	$-0.560105\pi$
$701$	−9.93949	−0.375409	−0.187705	+	0.982226i	$0.560105\pi$
$702$	−12.1262	−0.457674
$703$	−32.2892	−1.21781
$704$	−60.8255	−2.29245
$705$	−22.3709	−0.842536
$706$	−53.3228	−2.00683
$707$	−54.0317	−2.03207
$708$	54.8960	2.06312
$709$	−9.90373	−0.371942	−0.185971	−	0.982555i	$-0.559543\pi$
$709$	−9.90373	−0.371942	−0.185971	+	0.982555i	$0.559543\pi$
$710$	112.940	4.23855
$711$	12.8720	0.482739
$712$	62.7131	2.35027
$713$	44.0446	1.64948
$714$	−11.4715	−0.429309
$715$	25.8908	0.968261
$716$	120.857	4.51663
$717$	7.84880	0.293119
$718$	−35.8337	−1.33730
$719$	22.9446	0.855688	0.427844	−	0.903853i	$-0.359273\pi$
$719$	22.9446	0.855688	0.427844	+	0.903853i	$0.359273\pi$
$720$	36.3077	1.35311
$721$	2.39136	0.0890588
$722$	26.9206	1.00188
$723$	14.3167	0.532445
$724$	5.92249	0.220108
$725$	−1.37677	−0.0511320
$726$	−15.8030	−0.586505
$727$	0.665120	0.0246679	0.0123340	−	0.999924i	$-0.496074\pi$
$727$	0.665120	0.0246679	0.0123340	+	0.999924i	$0.496074\pi$
$728$	173.359	6.42509
$729$	1.00000	0.0370370
$730$	−59.6246	−2.20681
$731$	−9.58550	−0.354532
$732$	27.5799	1.01938
$733$	27.1826	1.00401	0.502007	−	0.864864i	$-0.332595\pi$
$733$	27.1826	1.00401	0.502007	+	0.864864i	$0.332595\pi$
$734$	−60.0478	−2.21640
$735$	−27.5573	−1.01647
$736$	−91.9882	−3.39073
$737$	−16.4924	−0.607507
$738$	7.38526	0.271855
$739$	21.5065	0.791129	0.395564	−	0.918438i	$-0.370549\pi$
$739$	21.5065	0.791129	0.395564	+	0.918438i	$0.370549\pi$
$740$	−146.985	−5.40326
$741$	13.4552	0.494291
$742$	−81.2287	−2.98200
$743$	−23.0476	−0.845533	−0.422766	−	0.906239i	$-0.638941\pi$
$743$	−23.0476	−0.845533	−0.422766	+	0.906239i	$0.638941\pi$
$744$	89.5336	3.28246
$745$	23.2953	0.853475
$746$	10.2557	0.375487
$747$	−4.75131	−0.173841
$748$	12.2678	0.448554
$749$	33.6696	1.23026
$750$	−24.2831	−0.886692
$751$	−33.8794	−1.23628	−0.618139	−	0.786069i	$-0.712113\pi$
$751$	−33.8794	−1.23628	−0.618139	+	0.786069i	$0.712113\pi$
$752$	125.074	4.56096
$753$	27.2705	0.993792
$754$	−11.1743	−0.406945
$755$	−49.8996	−1.81603
$756$	−22.7375	−0.826954
$757$	28.9149	1.05093	0.525466	−	0.850815i	$-0.323891\pi$
$757$	28.9149	1.05093	0.525466	+	0.850815i	$0.323891\pi$
$758$	−59.9760	−2.17843
$759$	10.3131	0.374343
$760$	−70.7532	−2.56649
$761$	3.29226	0.119344	0.0596721	−	0.998218i	$-0.480994\pi$
$761$	3.29226	0.119344	0.0596721	+	0.998218i	$0.480994\pi$
$762$	48.2272	1.74709
$763$	−18.6592	−0.675507
$764$	6.42131	0.232315
$765$	−2.54834	−0.0921355
$766$	−9.92189	−0.358492
$767$	45.4634	1.64159
$768$	−33.4840	−1.20825
$769$	−38.8629	−1.40143	−0.700716	−	0.713441i	$-0.747136\pi$
$769$	−38.8629	−1.40143	−0.700716	+	0.713441i	$0.747136\pi$
$770$	66.5701	2.39902
$771$	−20.1023	−0.723965
$772$	98.9765	3.56224
$773$	25.1140	0.903287	0.451643	−	0.892199i	$-0.350838\pi$
$773$	25.1140	0.903287	0.451643	+	0.892199i	$0.350838\pi$
$774$	−26.0528	−0.936449
$775$	14.5302	0.521939
$776$	22.8893	0.821679
$777$	45.1886	1.62113
$778$	−10.2456	−0.367323
$779$	−8.19469	−0.293605
$780$	61.2500	2.19310
$781$	37.1322	1.32870
$782$	12.3091	0.440174
$783$	0.921501	0.0329318
$784$	154.071	5.50253
$785$	2.54834	0.0909543
$786$	10.0441	0.358260
$787$	−33.3383	−1.18838	−0.594191	−	0.804324i	$-0.702528\pi$
$787$	−33.3383	−1.18838	−0.594191	+	0.804324i	$0.702528\pi$
$788$	67.4224	2.40182
$789$	−11.2304	−0.399814
$790$	−89.1548	−3.17199
$791$	88.2013	3.13608
$792$	20.9645	0.744940
$793$	22.8410	0.811107
$794$	−50.8753	−1.80550
$795$	−18.0447	−0.639978
$796$	−59.9833	−2.12605
$797$	18.1500	0.642907	0.321454	−	0.946925i	$-0.395829\pi$
$797$	18.1500	0.642907	0.321454	+	0.946925i	$0.395829\pi$
$798$	34.5960	1.22468
$799$	−8.77859	−0.310564
$800$	−30.3466	−1.07291
$801$	−6.81203	−0.240691
$802$	20.3795	0.719624
$803$	−19.6033	−0.691787
$804$	−39.0163	−1.37600
$805$	48.7107	1.71683
$806$	117.932	4.15396
$807$	−15.6771	−0.551862
$808$	117.856	4.14616
$809$	−9.80367	−0.344679	−0.172339	−	0.985038i	$-0.555133\pi$
$809$	−9.80367	−0.344679	−0.172339	+	0.985038i	$0.555133\pi$
$810$	−6.92625	−0.243363
$811$	−45.8694	−1.61069	−0.805346	−	0.592805i	$-0.798020\pi$
$811$	−45.8694	−1.61069	−0.805346	+	0.592805i	$0.798020\pi$
$812$	−20.9526	−0.735292
$813$	10.8169	0.379367
$814$	−66.2664	−2.32263
$815$	−2.94938	−0.103312
$816$	14.2476	0.498764
$817$	28.9082	1.01137
$818$	45.0256	1.57428
$819$	−18.8306	−0.657994
$820$	−37.3033	−1.30269
$821$	−8.02859	−0.280200	−0.140100	−	0.990137i	$-0.544742\pi$
$821$	−8.02859	−0.280200	−0.140100	+	0.990137i	$0.544742\pi$
$822$	−2.41541	−0.0842471
$823$	−19.6631	−0.685412	−0.342706	−	0.939443i	$-0.611343\pi$
$823$	−19.6631	−0.685412	−0.342706	+	0.939443i	$0.611343\pi$
$824$	−5.21612	−0.181712
$825$	3.40226	0.118452
$826$	116.895	4.06729
$827$	−28.1795	−0.979897	−0.489949	−	0.871751i	$-0.662984\pi$
$827$	−28.1795	−0.979897	−0.489949	+	0.871751i	$0.662984\pi$
$828$	24.3978	0.847884
$829$	−17.1239	−0.594737	−0.297369	−	0.954763i	$-0.596109\pi$
$829$	−17.1239	−0.594737	−0.297369	+	0.954763i	$0.596109\pi$
$830$	32.9087	1.14228
$831$	26.2568	0.910838
$832$	−119.170	−4.13149
$833$	−10.8138	−0.374677
$834$	57.1804	1.97999
$835$	26.9170	0.931502
$836$	−36.9975	−1.27959
$837$	−9.72534	−0.336157
$838$	−35.8873	−1.23971
$839$	23.9774	0.827791	0.413896	−	0.910324i	$-0.364168\pi$
$839$	23.9774	0.827791	0.413896	+	0.910324i	$0.364168\pi$
$840$	99.0189	3.41648
$841$	−28.1508	−0.970718
$842$	21.9755	0.757327
$843$	−14.5070	−0.499648
$844$	156.465	5.38575
$845$	17.5972	0.605363
$846$	−23.8597	−0.820313
$847$	−24.5402	−0.843212
$848$	100.886	3.46444
$849$	−22.6576	−0.777607
$850$	4.06074	0.139282
$851$	−48.4885	−1.66216
$852$	87.8440	3.00949
$853$	−28.8190	−0.986744	−0.493372	−	0.869818i	$-0.664236\pi$
$853$	−28.8190	−0.986744	−0.493372	+	0.869818i	$0.664236\pi$
$854$	58.7285	2.00965
$855$	7.68536	0.262834
$856$	−73.4413	−2.51017
$857$	4.86515	0.166190	0.0830951	−	0.996542i	$-0.473519\pi$
$857$	4.86515	0.166190	0.0830951	+	0.996542i	$0.473519\pi$
$858$	27.6139	0.942723
$859$	−46.6232	−1.59076	−0.795381	−	0.606109i	$-0.792729\pi$
$859$	−46.6232	−1.59076	−0.795381	+	0.606109i	$0.792729\pi$
$860$	131.594	4.48732
$861$	11.4684	0.390844
$862$	−3.19816	−0.108930
$863$	33.9422	1.15541	0.577703	−	0.816247i	$-0.303949\pi$
$863$	33.9422	1.15541	0.577703	+	0.816247i	$0.303949\pi$
$864$	20.3116	0.691014
$865$	−44.9497	−1.52834
$866$	−47.5255	−1.61498
$867$	−1.00000	−0.0339618
$868$	221.130	7.50563
$869$	−29.3123	−0.994350
$870$	−6.38254	−0.216388
$871$	−32.3123	−1.09486
$872$	40.7000	1.37828
$873$	−2.48629	−0.0841481
$874$	−37.1223	−1.25568
$875$	−37.7087	−1.27479
$876$	−46.3758	−1.56689
$877$	1.41520	0.0477880	0.0238940	−	0.999714i	$-0.492394\pi$
$877$	1.41520	0.0477880	0.0238940	+	0.999714i	$0.492394\pi$
$878$	−4.92288	−0.166139
$879$	14.5991	0.492415
$880$	−82.6801	−2.78714
$881$	−13.2123	−0.445135	−0.222568	−	0.974917i	$-0.571444\pi$
$881$	−13.2123	−0.445135	−0.222568	+	0.974917i	$0.571444\pi$
$882$	−29.3914	−0.989658
$883$	47.8840	1.61142	0.805712	−	0.592308i	$-0.201783\pi$
$883$	47.8840	1.61142	0.805712	+	0.592308i	$0.201783\pi$
$884$	24.0352	0.808393
$885$	25.9678	0.872897
$886$	−84.9471	−2.85385
$887$	10.2418	0.343885	0.171942	−	0.985107i	$-0.444996\pi$
$887$	10.2418	0.343885	0.171942	+	0.985107i	$0.444996\pi$
$888$	−98.5671	−3.30770
$889$	74.8911	2.51177
$890$	47.1818	1.58154
$891$	−2.27721	−0.0762893
$892$	−41.6901	−1.39589
$893$	26.4747	0.885943
$894$	24.8457	0.830964
$895$	57.1696	1.91097
$896$	−134.954	−4.50848
$897$	20.2057	0.674647
$898$	−109.686	−3.66026
$899$	−8.96191	−0.298896
$900$	8.04876	0.268292
$901$	−7.08094	−0.235900
$902$	−16.8178	−0.559971
$903$	−40.4570	−1.34632
$904$	−192.388	−6.39872
$905$	2.80155	0.0931268
$906$	−53.2206	−1.76814
$907$	14.3348	0.475979	0.237990	−	0.971268i	$-0.423512\pi$
$907$	14.3348	0.475979	0.237990	+	0.971268i	$0.423512\pi$
$908$	−136.009	−4.51363
$909$	−12.8018	−0.424608
$910$	130.425	4.32355
$911$	23.1503	0.767004	0.383502	−	0.923540i	$-0.374718\pi$
$911$	23.1503	0.767004	0.383502	+	0.923540i	$0.374718\pi$
$912$	−42.9682	−1.42282
$913$	10.8197	0.358080
$914$	7.35352	0.243233
$915$	13.0463	0.431298
$916$	109.624	3.62209
$917$	15.5972	0.515066
$918$	−2.71794	−0.0897054
$919$	−32.9349	−1.08642	−0.543211	−	0.839596i	$-0.682792\pi$
$919$	−32.9349	−1.08642	−0.543211	+	0.839596i	$0.682792\pi$
$920$	−106.250	−3.50295
$921$	26.6295	0.877473
$922$	11.8157	0.389130
$923$	72.7501	2.39460
$924$	51.7779	1.70337
$925$	−15.9962	−0.525951
$926$	−88.5401	−2.90961
$927$	0.566586	0.0186091
$928$	18.7172	0.614421
$929$	19.4146	0.636974	0.318487	−	0.947927i	$-0.396825\pi$
$929$	19.4146	0.636974	0.318487	+	0.947927i	$0.396825\pi$
$930$	67.3601	2.20882
$931$	32.6127	1.06884
$932$	42.9099	1.40556
$933$	−20.5542	−0.672915
$934$	−0.0347774	−0.00113795
$935$	5.80310	0.189782
$936$	41.0740	1.34254
$937$	54.7978	1.79017	0.895084	−	0.445898i	$-0.147116\pi$
$937$	54.7978	1.79017	0.895084	+	0.445898i	$0.147116\pi$
$938$	−83.0809	−2.71269
$939$	1.32010	0.0430797
$940$	120.516	3.93081
$941$	−34.4831	−1.12412	−0.562059	−	0.827097i	$-0.689990\pi$
$941$	−34.4831	−1.12412	−0.562059	+	0.827097i	$0.689990\pi$
$942$	2.71794	0.0885553
$943$	−12.3059	−0.400736
$944$	−145.184	−4.72532
$945$	−10.7556	−0.349881
$946$	59.3276	1.92891
$947$	26.1599	0.850082	0.425041	−	0.905174i	$-0.360260\pi$
$947$	26.1599	0.850082	0.425041	+	0.905174i	$0.360260\pi$
$948$	−69.3442	−2.25220
$949$	−38.4072	−1.24675
$950$	−12.2465	−0.397329
$951$	3.67704	0.119236
$952$	38.8562	1.25934
$953$	36.1032	1.16950	0.584748	−	0.811215i	$-0.301193\pi$
$953$	36.1032	1.16950	0.584748	+	0.811215i	$0.301193\pi$
$954$	−19.2456	−0.623098
$955$	3.03751	0.0982916
$956$	−42.2831	−1.36753
$957$	−2.09845	−0.0678332
$958$	27.5915	0.891441
$959$	−3.75085	−0.121121
$960$	−68.0677	−2.19688
$961$	63.5822	2.05104
$962$	−129.830	−4.18589
$963$	7.97736	0.257067
$964$	−77.1272	−2.48410
$965$	46.8195	1.50717
$966$	51.9525	1.67155
$967$	−42.6562	−1.37173	−0.685865	−	0.727728i	$-0.740576\pi$
$967$	−42.6562	−1.37173	−0.685865	+	0.727728i	$0.740576\pi$
$968$	53.5280	1.72046
$969$	3.01583	0.0968824
$970$	17.2206	0.552921
$971$	−2.18297	−0.0700549	−0.0350274	−	0.999386i	$-0.511152\pi$
$971$	−2.18297	−0.0700549	−0.0350274	+	0.999386i	$0.511152\pi$
$972$	−5.38720	−0.172795
$973$	88.7944	2.84662
$974$	111.756	3.58089
$975$	6.66578	0.213476
$976$	−72.9408	−2.33478
$977$	3.25951	0.104281	0.0521404	−	0.998640i	$-0.483396\pi$
$977$	3.25951	0.104281	0.0521404	+	0.998640i	$0.483396\pi$
$978$	−3.14567	−0.100588
$979$	15.5124	0.495779
$980$	148.457	4.74229
$981$	−4.42093	−0.141149
$982$	−110.867	−3.53791
$983$	−6.48035	−0.206691	−0.103346	−	0.994646i	$-0.532955\pi$
$983$	−6.48035	−0.206691	−0.103346	+	0.994646i	$0.532955\pi$
$984$	−25.0154	−0.797462
$985$	31.8932	1.01620
$986$	−2.50459	−0.0797622
$987$	−37.0513	−1.17936
$988$	−72.4862	−2.30609
$989$	43.4113	1.38040
$990$	15.7725	0.501283
$991$	26.0625	0.827904	0.413952	−	0.910299i	$-0.364148\pi$
$991$	26.0625	0.827904	0.413952	+	0.910299i	$0.364148\pi$
$992$	−197.537	−6.27181
$993$	−23.9905	−0.761314
$994$	187.054	5.93300
$995$	−28.3743	−0.899524
$996$	25.5963	0.811049
$997$	39.4235	1.24855	0.624277	−	0.781203i	$-0.285394\pi$
$997$	39.4235	1.24855	0.624277	+	0.781203i	$0.285394\pi$
$998$	−21.6079	−0.683985
$999$	10.7066	0.338741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.2	✓	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71794 q^{2} -1.00000 q^{3} +5.38720 q^{4} +2.54834 q^{5} +2.71794 q^{6} +4.22064 q^{7} -9.20622 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.71794 q^{2} -1.00000 q^{3} +5.38720 q^{4} +2.54834 q^{5} +2.71794 q^{6} +4.22064 q^{7} -9.20622 q^{8} +1.00000 q^{9} -6.92625 q^{10} -2.27721 q^{11} -5.38720 q^{12} -4.46154 q^{13} -11.4715 q^{14} -2.54834 q^{15} +14.2476 q^{16} -1.00000 q^{17} -2.71794 q^{18} +3.01583 q^{19} +13.7284 q^{20} -4.22064 q^{21} +6.18931 q^{22} +4.52885 q^{23} +9.20622 q^{24} +1.49405 q^{25} +12.1262 q^{26} -1.00000 q^{27} +22.7375 q^{28} -0.921501 q^{29} +6.92625 q^{30} +9.72534 q^{31} -20.3116 q^{32} +2.27721 q^{33} +2.71794 q^{34} +10.7556 q^{35} +5.38720 q^{36} -10.7066 q^{37} -8.19684 q^{38} +4.46154 q^{39} -23.4606 q^{40} -2.71723 q^{41} +11.4715 q^{42} +9.58550 q^{43} -12.2678 q^{44} +2.54834 q^{45} -12.3091 q^{46} +8.77859 q^{47} -14.2476 q^{48} +10.8138 q^{49} -4.06074 q^{50} +1.00000 q^{51} -24.0352 q^{52} +7.08094 q^{53} +2.71794 q^{54} -5.80310 q^{55} -38.8562 q^{56} -3.01583 q^{57} +2.50459 q^{58} -10.1901 q^{59} -13.7284 q^{60} -5.11953 q^{61} -26.4329 q^{62} +4.22064 q^{63} +26.7106 q^{64} -11.3695 q^{65} -6.18931 q^{66} +7.24240 q^{67} -5.38720 q^{68} -4.52885 q^{69} -29.2332 q^{70} -16.3060 q^{71} -9.20622 q^{72} +8.60850 q^{73} +29.0998 q^{74} -1.49405 q^{75} +16.2469 q^{76} -9.61128 q^{77} -12.1262 q^{78} +12.8720 q^{79} +36.3077 q^{80} +1.00000 q^{81} +7.38526 q^{82} -4.75131 q^{83} -22.7375 q^{84} -2.54834 q^{85} -26.0528 q^{86} +0.921501 q^{87} +20.9645 q^{88} -6.81203 q^{89} -6.92625 q^{90} -18.8306 q^{91} +24.3978 q^{92} -9.72534 q^{93} -23.8597 q^{94} +7.68536 q^{95} +20.3116 q^{96} -2.48629 q^{97} -29.3914 q^{98} -2.27721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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