LMFDB - Embedded newform 8007.2.a.g.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.65517 q^{2} -1.00000 q^{3} +5.04993 q^{4} -2.53504 q^{5} +2.65517 q^{6} +2.76662 q^{7} -8.09809 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65517 q^{2} -1.00000 q^{3} +5.04993 q^{4} -2.53504 q^{5} +2.65517 q^{6} +2.76662 q^{7} -8.09809 q^{8} +1.00000 q^{9} +6.73097 q^{10} -2.96244 q^{11} -5.04993 q^{12} +2.35875 q^{13} -7.34584 q^{14} +2.53504 q^{15} +11.4019 q^{16} -1.00000 q^{17} -2.65517 q^{18} +4.22861 q^{19} -12.8018 q^{20} -2.76662 q^{21} +7.86579 q^{22} +6.95555 q^{23} +8.09809 q^{24} +1.42643 q^{25} -6.26287 q^{26} -1.00000 q^{27} +13.9712 q^{28} -7.92503 q^{29} -6.73097 q^{30} +1.98645 q^{31} -14.0779 q^{32} +2.96244 q^{33} +2.65517 q^{34} -7.01349 q^{35} +5.04993 q^{36} +3.65226 q^{37} -11.2277 q^{38} -2.35875 q^{39} +20.5290 q^{40} +12.2521 q^{41} +7.34584 q^{42} -6.21120 q^{43} -14.9601 q^{44} -2.53504 q^{45} -18.4682 q^{46} +11.8067 q^{47} -11.4019 q^{48} +0.654174 q^{49} -3.78743 q^{50} +1.00000 q^{51} +11.9115 q^{52} -8.96243 q^{53} +2.65517 q^{54} +7.50991 q^{55} -22.4043 q^{56} -4.22861 q^{57} +21.0423 q^{58} +4.83509 q^{59} +12.8018 q^{60} +10.7572 q^{61} -5.27435 q^{62} +2.76662 q^{63} +14.5754 q^{64} -5.97952 q^{65} -7.86579 q^{66} -1.75201 q^{67} -5.04993 q^{68} -6.95555 q^{69} +18.6220 q^{70} +12.5026 q^{71} -8.09809 q^{72} -15.8588 q^{73} -9.69738 q^{74} -1.42643 q^{75} +21.3542 q^{76} -8.19595 q^{77} +6.26287 q^{78} +1.92266 q^{79} -28.9044 q^{80} +1.00000 q^{81} -32.5315 q^{82} +2.56979 q^{83} -13.9712 q^{84} +2.53504 q^{85} +16.4918 q^{86} +7.92503 q^{87} +23.9901 q^{88} -11.2238 q^{89} +6.73097 q^{90} +6.52575 q^{91} +35.1251 q^{92} -1.98645 q^{93} -31.3488 q^{94} -10.7197 q^{95} +14.0779 q^{96} +1.70016 q^{97} -1.73694 q^{98} -2.96244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65517	−1.87749	−0.938745	−	0.344614i	$-0.888010\pi$
$2$	−2.65517	−1.87749	−0.938745	+	0.344614i	$0.888010\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.04993	2.52497
$5$	−2.53504	−1.13370	−0.566852	−	0.823819i	$-0.691839\pi$
$5$	−2.53504	−1.13370	−0.566852	+	0.823819i	$0.691839\pi$
$6$	2.65517	1.08397
$7$	2.76662	1.04568	0.522842	−	0.852430i	$-0.324872\pi$
$7$	2.76662	1.04568	0.522842	+	0.852430i	$0.324872\pi$
$8$	−8.09809	−2.86311
$9$	1.00000	0.333333
$10$	6.73097	2.12852
$11$	−2.96244	−0.893210	−0.446605	−	0.894731i	$-0.647367\pi$
$11$	−2.96244	−0.893210	−0.446605	+	0.894731i	$0.647367\pi$
$12$	−5.04993	−1.45779
$13$	2.35875	0.654198	0.327099	−	0.944990i	$-0.393929\pi$
$13$	2.35875	0.654198	0.327099	+	0.944990i	$0.393929\pi$
$14$	−7.34584	−1.96326
$15$	2.53504	0.654545
$16$	11.4019	2.85049
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.65517	−0.625830
$19$	4.22861	0.970110	0.485055	−	0.874484i	$-0.338800\pi$
$19$	4.22861	0.970110	0.485055	+	0.874484i	$0.338800\pi$
$20$	−12.8018	−2.86257
$21$	−2.76662	−0.603725
$22$	7.86579	1.67699
$23$	6.95555	1.45033	0.725166	−	0.688574i	$-0.241763\pi$
$23$	6.95555	1.45033	0.725166	+	0.688574i	$0.241763\pi$
$24$	8.09809	1.65302
$25$	1.42643	0.285287
$26$	−6.26287	−1.22825
$27$	−1.00000	−0.192450
$28$	13.9712	2.64031
$29$	−7.92503	−1.47164	−0.735820	−	0.677177i	$-0.763203\pi$
$29$	−7.92503	−1.47164	−0.735820	+	0.677177i	$0.763203\pi$
$30$	−6.73097	−1.22890
$31$	1.98645	0.356776	0.178388	−	0.983960i	$-0.442912\pi$
$31$	1.98645	0.356776	0.178388	+	0.983960i	$0.442912\pi$
$32$	−14.0779	−2.48865
$33$	2.96244	0.515695
$34$	2.65517	0.455358
$35$	−7.01349	−1.18550
$36$	5.04993	0.841655
$37$	3.65226	0.600428	0.300214	−	0.953872i	$-0.402942\pi$
$37$	3.65226	0.600428	0.300214	+	0.953872i	$0.402942\pi$
$38$	−11.2277	−1.82137
$39$	−2.35875	−0.377702
$40$	20.5290	3.24592
$41$	12.2521	1.91346	0.956732	−	0.290971i	$-0.0939782\pi$
$41$	12.2521	1.91346	0.956732	+	0.290971i	$0.0939782\pi$
$42$	7.34584	1.13349
$43$	−6.21120	−0.947200	−0.473600	−	0.880740i	$-0.657046\pi$
$43$	−6.21120	−0.947200	−0.473600	+	0.880740i	$0.657046\pi$
$44$	−14.9601	−2.25532
$45$	−2.53504	−0.377902
$46$	−18.4682	−2.72298
$47$	11.8067	1.72218	0.861092	−	0.508449i	$-0.169781\pi$
$47$	11.8067	1.72218	0.861092	+	0.508449i	$0.169781\pi$
$48$	−11.4019	−1.64573
$49$	0.654174	0.0934534
$50$	−3.78743	−0.535623
$51$	1.00000	0.140028
$52$	11.9115	1.65183
$53$	−8.96243	−1.23108	−0.615542	−	0.788104i	$-0.711063\pi$
$53$	−8.96243	−1.23108	−0.615542	+	0.788104i	$0.711063\pi$
$54$	2.65517	0.361323
$55$	7.50991	1.01264
$56$	−22.4043	−2.99390
$57$	−4.22861	−0.560093
$58$	21.0423	2.76299
$59$	4.83509	0.629475	0.314737	−	0.949179i	$-0.398084\pi$
$59$	4.83509	0.629475	0.314737	+	0.949179i	$0.398084\pi$
$60$	12.8018	1.65270
$61$	10.7572	1.37731	0.688657	−	0.725087i	$-0.258201\pi$
$61$	10.7572	1.37731	0.688657	+	0.725087i	$0.258201\pi$
$62$	−5.27435	−0.669844
$63$	2.76662	0.348561
$64$	14.5754	1.82193
$65$	−5.97952	−0.741668
$66$	−7.86579	−0.968212
$67$	−1.75201	−0.214042	−0.107021	−	0.994257i	$-0.534131\pi$
$67$	−1.75201	−0.214042	−0.107021	+	0.994257i	$0.534131\pi$
$68$	−5.04993	−0.612394
$69$	−6.95555	−0.837350
$70$	18.6220	2.22576
$71$	12.5026	1.48379	0.741895	−	0.670516i	$-0.233927\pi$
$71$	12.5026	1.48379	0.741895	+	0.670516i	$0.233927\pi$
$72$	−8.09809	−0.954369
$73$	−15.8588	−1.85614	−0.928068	−	0.372410i	$-0.878531\pi$
$73$	−15.8588	−1.85614	−0.928068	+	0.372410i	$0.878531\pi$
$74$	−9.69738	−1.12730
$75$	−1.42643	−0.164711
$76$	21.3542	2.44949
$77$	−8.19595	−0.934015
$78$	6.26287	0.709131
$79$	1.92266	0.216316	0.108158	−	0.994134i	$-0.465505\pi$
$79$	1.92266	0.216316	0.108158	+	0.994134i	$0.465505\pi$
$80$	−28.9044	−3.23161
$81$	1.00000	0.111111
$82$	−32.5315	−3.59251
$83$	2.56979	0.282071	0.141035	−	0.990005i	$-0.454957\pi$
$83$	2.56979	0.282071	0.141035	+	0.990005i	$0.454957\pi$
$84$	−13.9712	−1.52439
$85$	2.53504	0.274964
$86$	16.4918	1.77836
$87$	7.92503	0.849652
$88$	23.9901	2.55735
$89$	−11.2238	−1.18972	−0.594861	−	0.803828i	$-0.702793\pi$
$89$	−11.2238	−1.18972	−0.594861	+	0.803828i	$0.702793\pi$
$90$	6.73097	0.709506
$91$	6.52575	0.684084
$92$	35.1251	3.66204
$93$	−1.98645	−0.205985
$94$	−31.3488	−3.23338
$95$	−10.7197	−1.09982
$96$	14.0779	1.43682
$97$	1.70016	0.172625	0.0863124	−	0.996268i	$-0.472492\pi$
$97$	1.70016	0.172625	0.0863124	+	0.996268i	$0.472492\pi$
$98$	−1.73694	−0.175458
$99$	−2.96244	−0.297737
$100$	7.20340	0.720340
$101$	12.2914	1.22304	0.611521	−	0.791229i	$-0.290558\pi$
$101$	12.2914	1.22304	0.611521	+	0.791229i	$0.290558\pi$
$102$	−2.65517	−0.262901
$103$	4.80313	0.473267	0.236633	−	0.971599i	$-0.423956\pi$
$103$	4.80313	0.473267	0.236633	+	0.971599i	$0.423956\pi$
$104$	−19.1013	−1.87304
$105$	7.01349	0.684447
$106$	23.7968	2.31135
$107$	3.17316	0.306761	0.153380	−	0.988167i	$-0.450984\pi$
$107$	3.17316	0.306761	0.153380	+	0.988167i	$0.450984\pi$
$108$	−5.04993	−0.485930
$109$	−17.9645	−1.72069	−0.860345	−	0.509712i	$-0.829752\pi$
$109$	−17.9645	−1.72069	−0.860345	+	0.509712i	$0.829752\pi$
$110$	−19.9401	−1.90121
$111$	−3.65226	−0.346657
$112$	31.5448	2.98070
$113$	2.93180	0.275800	0.137900	−	0.990446i	$-0.455965\pi$
$113$	2.93180	0.275800	0.137900	+	0.990446i	$0.455965\pi$
$114$	11.2277	1.05157
$115$	−17.6326	−1.64425
$116$	−40.0208	−3.71584
$117$	2.35875	0.218066
$118$	−12.8380	−1.18183
$119$	−2.76662	−0.253615
$120$	−20.5290	−1.87403
$121$	−2.22394	−0.202176
$122$	−28.5621	−2.58589
$123$	−12.2521	−1.10474
$124$	10.0314	0.900848
$125$	9.05914	0.810274
$126$	−7.34584	−0.654420
$127$	2.12683	0.188726	0.0943629	−	0.995538i	$-0.469919\pi$
$127$	2.12683	0.188726	0.0943629	+	0.995538i	$0.469919\pi$
$128$	−10.5444	−0.931998
$129$	6.21120	0.546866
$130$	15.8766	1.39247
$131$	−9.93165	−0.867732	−0.433866	−	0.900977i	$-0.642851\pi$
$131$	−9.93165	−0.867732	−0.433866	+	0.900977i	$0.642851\pi$
$132$	14.9601	1.30211
$133$	11.6990	1.01443
$134$	4.65189	0.401862
$135$	2.53504	0.218182
$136$	8.09809	0.694405
$137$	17.5286	1.49757	0.748783	−	0.662815i	$-0.230638\pi$
$137$	17.5286	1.49757	0.748783	+	0.662815i	$0.230638\pi$
$138$	18.4682	1.57212
$139$	−1.23930	−0.105116	−0.0525581	−	0.998618i	$-0.516737\pi$
$139$	−1.23930	−0.105116	−0.0525581	+	0.998618i	$0.516737\pi$
$140$	−35.4176	−2.99334
$141$	−11.8067	−0.994304
$142$	−33.1966	−2.78580
$143$	−6.98765	−0.584336
$144$	11.4019	0.950162
$145$	20.0903	1.66841
$146$	42.1079	3.48488
$147$	−0.654174	−0.0539554
$148$	18.4437	1.51606
$149$	6.07607	0.497771	0.248886	−	0.968533i	$-0.419936\pi$
$149$	6.07607	0.497771	0.248886	+	0.968533i	$0.419936\pi$
$150$	3.78743	0.309242
$151$	4.28967	0.349089	0.174544	−	0.984649i	$-0.444155\pi$
$151$	4.28967	0.349089	0.174544	+	0.984649i	$0.444155\pi$
$152$	−34.2437	−2.77753
$153$	−1.00000	−0.0808452
$154$	21.7616	1.75360
$155$	−5.03572	−0.404479
$156$	−11.9115	−0.953683
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−5.10500	−0.406132
$159$	8.96243	0.710767
$160$	35.6881	2.82139
$161$	19.2434	1.51659
$162$	−2.65517	−0.208610
$163$	8.78230	0.687883	0.343942	−	0.938991i	$-0.388238\pi$
$163$	8.78230	0.687883	0.343942	+	0.938991i	$0.388238\pi$
$164$	61.8725	4.83143
$165$	−7.50991	−0.584646
$166$	−6.82323	−0.529585
$167$	18.5750	1.43737	0.718687	−	0.695334i	$-0.244743\pi$
$167$	18.5750	1.43737	0.718687	+	0.695334i	$0.244743\pi$
$168$	22.4043	1.72853
$169$	−7.43632	−0.572025
$170$	−6.73097	−0.516242
$171$	4.22861	0.323370
$172$	−31.3662	−2.39165
$173$	−5.02637	−0.382148	−0.191074	−	0.981576i	$-0.561197\pi$
$173$	−5.02637	−0.382148	−0.191074	+	0.981576i	$0.561197\pi$
$174$	−21.0423	−1.59521
$175$	3.94640	0.298320
$176$	−33.7776	−2.54608
$177$	−4.83509	−0.363427
$178$	29.8012	2.23369
$179$	−15.0989	−1.12855	−0.564273	−	0.825588i	$-0.690843\pi$
$179$	−15.0989	−1.12855	−0.564273	+	0.825588i	$0.690843\pi$
$180$	−12.8018	−0.954189
$181$	13.0813	0.972325	0.486163	−	0.873868i	$-0.338396\pi$
$181$	13.0813	0.972325	0.486163	+	0.873868i	$0.338396\pi$
$182$	−17.3270	−1.28436
$183$	−10.7572	−0.795192
$184$	−56.3267	−4.15246
$185$	−9.25863	−0.680708
$186$	5.27435	0.386734
$187$	2.96244	0.216635
$188$	59.6230	4.34846
$189$	−2.76662	−0.201242
$190$	28.4627	2.06490
$191$	21.7532	1.57401	0.787003	−	0.616949i	$-0.211632\pi$
$191$	21.7532	1.57401	0.787003	+	0.616949i	$0.211632\pi$
$192$	−14.5754	−1.05189
$193$	−20.7006	−1.49006	−0.745032	−	0.667028i	$-0.767566\pi$
$193$	−20.7006	−1.49006	−0.745032	+	0.667028i	$0.767566\pi$
$194$	−4.51421	−0.324101
$195$	5.97952	0.428202
$196$	3.30353	0.235967
$197$	−3.37641	−0.240559	−0.120280	−	0.992740i	$-0.538379\pi$
$197$	−3.37641	−0.240559	−0.120280	+	0.992740i	$0.538379\pi$
$198$	7.86579	0.558997
$199$	2.43776	0.172809	0.0864043	−	0.996260i	$-0.472462\pi$
$199$	2.43776	0.172809	0.0864043	+	0.996260i	$0.472462\pi$
$200$	−11.5514	−0.816807
$201$	1.75201	0.123577
$202$	−32.6358	−2.29625
$203$	−21.9255	−1.53887
$204$	5.04993	0.353566
$205$	−31.0597	−2.16930
$206$	−12.7531	−0.888554
$207$	6.95555	0.483444
$208$	26.8943	1.86478
$209$	−12.5270	−0.866512
$210$	−18.6220	−1.28504
$211$	−17.4038	−1.19813	−0.599065	−	0.800700i	$-0.704461\pi$
$211$	−17.4038	−1.19813	−0.599065	+	0.800700i	$0.704461\pi$
$212$	−45.2596	−3.10845
$213$	−12.5026	−0.856667
$214$	−8.42528	−0.575940
$215$	15.7457	1.07385
$216$	8.09809	0.551005
$217$	5.49574	0.373075
$218$	47.6989	3.23058
$219$	15.8588	1.07164
$220$	37.9245	2.55687
$221$	−2.35875	−0.158666
$222$	9.69738	0.650845
$223$	22.4073	1.50051	0.750253	−	0.661151i	$-0.229932\pi$
$223$	22.4073	1.50051	0.750253	+	0.661151i	$0.229932\pi$
$224$	−38.9482	−2.60234
$225$	1.42643	0.0950957
$226$	−7.78442	−0.517812
$227$	4.96128	0.329292	0.164646	−	0.986353i	$-0.447352\pi$
$227$	4.96128	0.329292	0.164646	+	0.986353i	$0.447352\pi$
$228$	−21.3542	−1.41422
$229$	−27.2713	−1.80214	−0.901068	−	0.433678i	$-0.857216\pi$
$229$	−27.2713	−1.80214	−0.901068	+	0.433678i	$0.857216\pi$
$230$	46.8176	3.08706
$231$	8.19595	0.539254
$232$	64.1776	4.21346
$233$	−15.9332	−1.04382	−0.521909	−	0.853001i	$-0.674780\pi$
$233$	−15.9332	−1.04382	−0.521909	+	0.853001i	$0.674780\pi$
$234$	−6.26287	−0.409417
$235$	−29.9305	−1.95245
$236$	24.4169	1.58940
$237$	−1.92266	−0.124890
$238$	7.34584	0.476160
$239$	−23.2137	−1.50157	−0.750785	−	0.660547i	$-0.770324\pi$
$239$	−23.2137	−1.50157	−0.750785	+	0.660547i	$0.770324\pi$
$240$	28.9044	1.86577
$241$	1.83838	0.118421	0.0592104	−	0.998246i	$-0.481142\pi$
$241$	1.83838	0.118421	0.0592104	+	0.998246i	$0.481142\pi$
$242$	5.90493	0.379583
$243$	−1.00000	−0.0641500
$244$	54.3229	3.47767
$245$	−1.65836	−0.105949
$246$	32.5315	2.07414
$247$	9.97422	0.634644
$248$	−16.0864	−1.02149
$249$	−2.56979	−0.162854
$250$	−24.0536	−1.52128
$251$	−12.0927	−0.763287	−0.381643	−	0.924310i	$-0.624642\pi$
$251$	−12.0927	−0.763287	−0.381643	+	0.924310i	$0.624642\pi$
$252$	13.9712	0.880105
$253$	−20.6054	−1.29545
$254$	−5.64710	−0.354331
$255$	−2.53504	−0.158750
$256$	−1.15377	−0.0721105
$257$	24.8159	1.54797	0.773987	−	0.633201i	$-0.218259\pi$
$257$	24.8159	1.54797	0.773987	+	0.633201i	$0.218259\pi$
$258$	−16.4918	−1.02673
$259$	10.1044	0.627857
$260$	−30.1962	−1.87269
$261$	−7.92503	−0.490547
$262$	26.3702	1.62916
$263$	−12.8990	−0.795389	−0.397694	−	0.917518i	$-0.630190\pi$
$263$	−12.8990	−0.795389	−0.397694	+	0.917518i	$0.630190\pi$
$264$	−23.9901	−1.47649
$265$	22.7201	1.39569
$266$	−31.0627	−1.90458
$267$	11.2238	0.686887
$268$	−8.84754	−0.540450
$269$	17.3196	1.05600	0.527998	−	0.849246i	$-0.322943\pi$
$269$	17.3196	1.05600	0.527998	+	0.849246i	$0.322943\pi$
$270$	−6.73097	−0.409634
$271$	15.4231	0.936886	0.468443	−	0.883494i	$-0.344815\pi$
$271$	15.4231	0.936886	0.468443	+	0.883494i	$0.344815\pi$
$272$	−11.4019	−0.691344
$273$	−6.52575	−0.394956
$274$	−46.5413	−2.81167
$275$	−4.22573	−0.254821
$276$	−35.1251	−2.11428
$277$	16.7984	1.00932	0.504660	−	0.863318i	$-0.331618\pi$
$277$	16.7984	1.00932	0.504660	+	0.863318i	$0.331618\pi$
$278$	3.29056	0.197354
$279$	1.98645	0.118925
$280$	56.7959	3.39420
$281$	−30.8929	−1.84292	−0.921458	−	0.388477i	$-0.873001\pi$
$281$	−30.8929	−1.84292	−0.921458	+	0.388477i	$0.873001\pi$
$282$	31.3488	1.86679
$283$	27.2550	1.62014	0.810071	−	0.586331i	$-0.199428\pi$
$283$	27.2550	1.62014	0.810071	+	0.586331i	$0.199428\pi$
$284$	63.1375	3.74652
$285$	10.7197	0.634981
$286$	18.5534	1.09709
$287$	33.8970	2.00088
$288$	−14.0779	−0.829550
$289$	1.00000	0.0588235
$290$	−53.3431	−3.13241
$291$	−1.70016	−0.0996650
$292$	−80.0860	−4.68668
$293$	−15.7632	−0.920899	−0.460449	−	0.887686i	$-0.652312\pi$
$293$	−15.7632	−0.920899	−0.460449	+	0.887686i	$0.652312\pi$
$294$	1.73694	0.101301
$295$	−12.2571	−0.713639
$296$	−29.5763	−1.71909
$297$	2.96244	0.171898
$298$	−16.1330	−0.934560
$299$	16.4064	0.948805
$300$	−7.20340	−0.415888
$301$	−17.1840	−0.990471
$302$	−11.3898	−0.655410
$303$	−12.2914	−0.706123
$304$	48.2144	2.76528
$305$	−27.2699	−1.56147
$306$	2.65517	0.151786
$307$	5.20882	0.297283	0.148641	−	0.988891i	$-0.452510\pi$
$307$	5.20882	0.297283	0.148641	+	0.988891i	$0.452510\pi$
$308$	−41.3890	−2.35835
$309$	−4.80313	−0.273241
$310$	13.3707	0.759405
$311$	4.15409	0.235557	0.117778	−	0.993040i	$-0.462423\pi$
$311$	4.15409	0.235557	0.117778	+	0.993040i	$0.462423\pi$
$312$	19.1013	1.08140
$313$	−15.4256	−0.871904	−0.435952	−	0.899970i	$-0.643588\pi$
$313$	−15.4256	−0.871904	−0.435952	+	0.899970i	$0.643588\pi$
$314$	−2.65517	−0.149840
$315$	−7.01349	−0.395165
$316$	9.70931	0.546191
$317$	−21.8291	−1.22604	−0.613022	−	0.790066i	$-0.710046\pi$
$317$	−21.8291	−1.22604	−0.613022	+	0.790066i	$0.710046\pi$
$318$	−23.7968	−1.33446
$319$	23.4774	1.31448
$320$	−36.9493	−2.06553
$321$	−3.17316	−0.177108
$322$	−51.0944	−2.84738
$323$	−4.22861	−0.235286
$324$	5.04993	0.280552
$325$	3.36460	0.186634
$326$	−23.3185	−1.29149
$327$	17.9645	0.993441
$328$	−99.2190	−5.47845
$329$	32.6646	1.80086
$330$	19.9401	1.09767
$331$	−13.5552	−0.745062	−0.372531	−	0.928020i	$-0.621510\pi$
$331$	−13.5552	−0.745062	−0.372531	+	0.928020i	$0.621510\pi$
$332$	12.9773	0.712220
$333$	3.65226	0.200143
$334$	−49.3197	−2.69865
$335$	4.44142	0.242661
$336$	−31.5448	−1.72091
$337$	−15.3359	−0.835400	−0.417700	−	0.908585i	$-0.637164\pi$
$337$	−15.3359	−0.835400	−0.417700	+	0.908585i	$0.637164\pi$
$338$	19.7447	1.07397
$339$	−2.93180	−0.159233
$340$	12.8018	0.694274
$341$	−5.88473	−0.318676
$342$	−11.2277	−0.607124
$343$	−17.5565	−0.947961
$344$	50.2989	2.71193
$345$	17.6326	0.949308
$346$	13.3459	0.717478
$347$	7.97432	0.428084	0.214042	−	0.976824i	$-0.431337\pi$
$347$	7.97432	0.428084	0.214042	+	0.976824i	$0.431337\pi$
$348$	40.0208	2.14534
$349$	−15.8749	−0.849765	−0.424882	−	0.905249i	$-0.639685\pi$
$349$	−15.8749	−0.849765	−0.424882	+	0.905249i	$0.639685\pi$
$350$	−10.4784	−0.560092
$351$	−2.35875	−0.125901
$352$	41.7050	2.22289
$353$	14.4743	0.770387	0.385193	−	0.922836i	$-0.374135\pi$
$353$	14.4743	0.770387	0.385193	+	0.922836i	$0.374135\pi$
$354$	12.8380	0.682331
$355$	−31.6947	−1.68218
$356$	−56.6795	−3.00401
$357$	2.76662	0.146425
$358$	40.0902	2.11883
$359$	7.05443	0.372319	0.186159	−	0.982520i	$-0.440396\pi$
$359$	7.05443	0.372319	0.186159	+	0.982520i	$0.440396\pi$
$360$	20.5290	1.08197
$361$	−1.11884	−0.0588863
$362$	−34.7331	−1.82553
$363$	2.22394	0.116726
$364$	32.9546	1.72729
$365$	40.2028	2.10431
$366$	28.5621	1.49297
$367$	2.56287	0.133781	0.0668904	−	0.997760i	$-0.478692\pi$
$367$	2.56287	0.133781	0.0668904	+	0.997760i	$0.478692\pi$
$368$	79.3068	4.13415
$369$	12.2521	0.637821
$370$	24.5832	1.27802
$371$	−24.7956	−1.28732
$372$	−10.0314	−0.520105
$373$	10.7248	0.555311	0.277656	−	0.960681i	$-0.410443\pi$
$373$	10.7248	0.555311	0.277656	+	0.960681i	$0.410443\pi$
$374$	−7.86579	−0.406730
$375$	−9.05914	−0.467812
$376$	−95.6117	−4.93080
$377$	−18.6931	−0.962745
$378$	7.34584	0.377829
$379$	2.08101	0.106894	0.0534472	−	0.998571i	$-0.482979\pi$
$379$	2.08101	0.106894	0.0534472	+	0.998571i	$0.482979\pi$
$380$	−54.1338	−2.77700
$381$	−2.12683	−0.108961
$382$	−57.7584	−2.95518
$383$	−1.15255	−0.0588923	−0.0294462	−	0.999566i	$-0.509374\pi$
$383$	−1.15255	−0.0588923	−0.0294462	+	0.999566i	$0.509374\pi$
$384$	10.5444	0.538089
$385$	20.7771	1.05890
$386$	54.9637	2.79758
$387$	−6.21120	−0.315733
$388$	8.58568	0.435872
$389$	24.9325	1.26413	0.632064	−	0.774916i	$-0.282208\pi$
$389$	24.9325	1.26413	0.632064	+	0.774916i	$0.282208\pi$
$390$	−15.8766	−0.803945
$391$	−6.95555	−0.351757
$392$	−5.29756	−0.267567
$393$	9.93165	0.500985
$394$	8.96495	0.451648
$395$	−4.87403	−0.245239
$396$	−14.9601	−0.751775
$397$	4.64394	0.233073	0.116536	−	0.993186i	$-0.462821\pi$
$397$	4.64394	0.233073	0.116536	+	0.993186i	$0.462821\pi$
$398$	−6.47268	−0.324446
$399$	−11.6990	−0.585680
$400$	16.2641	0.813206
$401$	1.48051	0.0739331	0.0369666	−	0.999317i	$-0.488230\pi$
$401$	1.48051	0.0739331	0.0369666	+	0.999317i	$0.488230\pi$
$402$	−4.65189	−0.232015
$403$	4.68552	0.233402
$404$	62.0708	3.08814
$405$	−2.53504	−0.125967
$406$	58.2160	2.88921
$407$	−10.8196	−0.536308
$408$	−8.09809	−0.400915
$409$	−36.1673	−1.78836	−0.894179	−	0.447710i	$-0.852240\pi$
$409$	−36.1673	−1.78836	−0.894179	+	0.447710i	$0.852240\pi$
$410$	82.4688	4.07284
$411$	−17.5286	−0.864621
$412$	24.2555	1.19498
$413$	13.3768	0.658231
$414$	−18.4682	−0.907661
$415$	−6.51452	−0.319785
$416$	−33.2062	−1.62807
$417$	1.23930	0.0606888
$418$	33.2614	1.62687
$419$	−28.9805	−1.41579	−0.707895	−	0.706318i	$-0.750355\pi$
$419$	−28.9805	−1.41579	−0.707895	+	0.706318i	$0.750355\pi$
$420$	35.4176	1.72820
$421$	−22.4576	−1.09452	−0.547259	−	0.836964i	$-0.684329\pi$
$421$	−22.4576	−1.09452	−0.547259	+	0.836964i	$0.684329\pi$
$422$	46.2102	2.24948
$423$	11.8067	0.574062
$424$	72.5785	3.52473
$425$	−1.42643	−0.0691923
$426$	33.1966	1.60838
$427$	29.7610	1.44023
$428$	16.0242	0.774560
$429$	6.98765	0.337367
$430$	−41.8074	−2.01613
$431$	−24.8090	−1.19501	−0.597503	−	0.801866i	$-0.703841\pi$
$431$	−24.8090	−1.19501	−0.597503	+	0.801866i	$0.703841\pi$
$432$	−11.4019	−0.548576
$433$	15.9159	0.764869	0.382434	−	0.923983i	$-0.375086\pi$
$433$	15.9159	0.764869	0.382434	+	0.923983i	$0.375086\pi$
$434$	−14.5921	−0.700444
$435$	−20.0903	−0.963255
$436$	−90.7197	−4.34468
$437$	29.4123	1.40698
$438$	−42.1079	−2.01199
$439$	6.55859	0.313024	0.156512	−	0.987676i	$-0.449975\pi$
$439$	6.55859	0.313024	0.156512	+	0.987676i	$0.449975\pi$
$440$	−60.8159	−2.89929
$441$	0.654174	0.0311511
$442$	6.26287	0.297894
$443$	−19.1658	−0.910593	−0.455297	−	0.890340i	$-0.650467\pi$
$443$	−19.1658	−0.910593	−0.455297	+	0.890340i	$0.650467\pi$
$444$	−18.4437	−0.875298
$445$	28.4529	1.34879
$446$	−59.4953	−2.81718
$447$	−6.07607	−0.287388
$448$	40.3246	1.90516
$449$	−36.9011	−1.74147	−0.870736	−	0.491751i	$-0.836357\pi$
$449$	−36.9011	−1.74147	−0.870736	+	0.491751i	$0.836357\pi$
$450$	−3.78743	−0.178541
$451$	−36.2963	−1.70913
$452$	14.8054	0.696386
$453$	−4.28967	−0.201546
$454$	−13.1731	−0.618242
$455$	−16.5430	−0.775550
$456$	34.2437	1.60361
$457$	36.9916	1.73039	0.865196	−	0.501434i	$-0.167194\pi$
$457$	36.9916	1.73039	0.865196	+	0.501434i	$0.167194\pi$
$458$	72.4099	3.38349
$459$	1.00000	0.0466760
$460$	−89.0435	−4.15167
$461$	24.9663	1.16280	0.581398	−	0.813619i	$-0.302506\pi$
$461$	24.9663	1.16280	0.581398	+	0.813619i	$0.302506\pi$
$462$	−21.7616	−1.01244
$463$	11.6232	0.540176	0.270088	−	0.962836i	$-0.412947\pi$
$463$	11.6232	0.540176	0.270088	+	0.962836i	$0.412947\pi$
$464$	−90.3607	−4.19489
$465$	5.03572	0.233526
$466$	42.3054	1.95976
$467$	−11.8904	−0.550220	−0.275110	−	0.961413i	$-0.588714\pi$
$467$	−11.8904	−0.550220	−0.275110	+	0.961413i	$0.588714\pi$
$468$	11.9115	0.550609
$469$	−4.84715	−0.223821
$470$	79.4705	3.66570
$471$	−1.00000	−0.0460776
$472$	−39.1550	−1.80225
$473$	18.4003	0.846048
$474$	5.10500	0.234480
$475$	6.03184	0.276760
$476$	−13.9712	−0.640370
$477$	−8.96243	−0.410361
$478$	61.6363	2.81918
$479$	15.7903	0.721475	0.360738	−	0.932667i	$-0.382525\pi$
$479$	15.7903	0.721475	0.360738	+	0.932667i	$0.382525\pi$
$480$	−35.6881	−1.62893
$481$	8.61475	0.392799
$482$	−4.88122	−0.222334
$483$	−19.2434	−0.875603
$484$	−11.2307	−0.510487
$485$	−4.30997	−0.195706
$486$	2.65517	0.120441
$487$	−4.41035	−0.199852	−0.0999260	−	0.994995i	$-0.531861\pi$
$487$	−4.41035	−0.199852	−0.0999260	+	0.994995i	$0.531861\pi$
$488$	−87.1124	−3.94340
$489$	−8.78230	−0.397149
$490$	4.40322	0.198917
$491$	17.8836	0.807073	0.403537	−	0.914963i	$-0.367781\pi$
$491$	17.8836	0.807073	0.403537	+	0.914963i	$0.367781\pi$
$492$	−61.8725	−2.78943
$493$	7.92503	0.356925
$494$	−26.4833	−1.19154
$495$	7.50991	0.337546
$496$	22.6493	1.01699
$497$	34.5900	1.55157
$498$	6.82323	0.305756
$499$	28.8815	1.29291	0.646457	−	0.762950i	$-0.276250\pi$
$499$	28.8815	1.29291	0.646457	+	0.762950i	$0.276250\pi$
$500$	45.7480	2.04591
$501$	−18.5750	−0.829868
$502$	32.1083	1.43306
$503$	−15.0468	−0.670905	−0.335453	−	0.942057i	$-0.608889\pi$
$503$	−15.0468	−0.670905	−0.335453	+	0.942057i	$0.608889\pi$
$504$	−22.4043	−0.997967
$505$	−31.1592	−1.38657
$506$	54.7109	2.43220
$507$	7.43632	0.330259
$508$	10.7404	0.476526
$509$	−31.4427	−1.39367	−0.696836	−	0.717231i	$-0.745409\pi$
$509$	−31.4427	−1.39367	−0.696836	+	0.717231i	$0.745409\pi$
$510$	6.73097	0.298052
$511$	−43.8753	−1.94093
$512$	24.1522	1.06738
$513$	−4.22861	−0.186698
$514$	−65.8905	−2.90631
$515$	−12.1761	−0.536545
$516$	31.3662	1.38082
$517$	−34.9767	−1.53827
$518$	−26.8289	−1.17880
$519$	5.02637	0.220633
$520$	48.4227	2.12347
$521$	−14.9769	−0.656148	−0.328074	−	0.944652i	$-0.606400\pi$
$521$	−14.9769	−0.656148	−0.328074	+	0.944652i	$0.606400\pi$
$522$	21.0423	0.920996
$523$	28.9370	1.26533	0.632663	−	0.774427i	$-0.281962\pi$
$523$	28.9370	1.26533	0.632663	+	0.774427i	$0.281962\pi$
$524$	−50.1541	−2.19099
$525$	−3.94640	−0.172235
$526$	34.2491	1.49333
$527$	−1.98645	−0.0865309
$528$	33.7776	1.46998
$529$	25.3797	1.10347
$530$	−60.3258	−2.62039
$531$	4.83509	0.209825
$532$	59.0789	2.56140
$533$	28.8997	1.25178
$534$	−29.8012	−1.28962
$535$	−8.04409	−0.347776
$536$	14.1880	0.612826
$537$	15.0989	0.651566
$538$	−45.9865	−1.98262
$539$	−1.93795	−0.0834735
$540$	12.8018	0.550901
$541$	38.6564	1.66197	0.830984	−	0.556296i	$-0.187778\pi$
$541$	38.6564	1.66197	0.830984	+	0.556296i	$0.187778\pi$
$542$	−40.9509	−1.75899
$543$	−13.0813	−0.561372
$544$	14.0779	0.603586
$545$	45.5408	1.95076
$546$	17.3270	0.741526
$547$	−43.1881	−1.84659	−0.923295	−	0.384093i	$-0.874514\pi$
$547$	−43.1881	−1.84659	−0.923295	+	0.384093i	$0.874514\pi$
$548$	88.5181	3.78130
$549$	10.7572	0.459105
$550$	11.2200	0.478424
$551$	−33.5119	−1.42765
$552$	56.3267	2.39742
$553$	5.31927	0.226198
$554$	−44.6027	−1.89499
$555$	9.25863	0.393007
$556$	−6.25838	−0.265415
$557$	−23.7808	−1.00762	−0.503811	−	0.863814i	$-0.668069\pi$
$557$	−23.7808	−1.00762	−0.503811	+	0.863814i	$0.668069\pi$
$558$	−5.27435	−0.223281
$559$	−14.6506	−0.619656
$560$	−79.9674	−3.37924
$561$	−2.96244	−0.125074
$562$	82.0260	3.46006
$563$	29.8220	1.25685	0.628424	−	0.777871i	$-0.283700\pi$
$563$	29.8220	1.25685	0.628424	+	0.777871i	$0.283700\pi$
$564$	−59.6230	−2.51058
$565$	−7.43223	−0.312676
$566$	−72.3667	−3.04180
$567$	2.76662	0.116187
$568$	−101.247	−4.24825
$569$	5.91952	0.248159	0.124080	−	0.992272i	$-0.460402\pi$
$569$	5.91952	0.248159	0.124080	+	0.992272i	$0.460402\pi$
$570$	−28.4627	−1.19217
$571$	−12.1333	−0.507763	−0.253881	−	0.967235i	$-0.581707\pi$
$571$	−12.1333	−0.507763	−0.253881	+	0.967235i	$0.581707\pi$
$572$	−35.2871	−1.47543
$573$	−21.7532	−0.908753
$574$	−90.0023	−3.75663
$575$	9.92164	0.413761
$576$	14.5754	0.607309
$577$	34.6120	1.44092	0.720458	−	0.693499i	$-0.243932\pi$
$577$	34.6120	1.44092	0.720458	+	0.693499i	$0.243932\pi$
$578$	−2.65517	−0.110441
$579$	20.7006	0.860289
$580$	101.454	4.21267
$581$	7.10962	0.294957
$582$	4.51421	0.187120
$583$	26.5507	1.09962
$584$	128.426	5.31432
$585$	−5.97952	−0.247223
$586$	41.8541	1.72898
$587$	−14.1948	−0.585883	−0.292941	−	0.956130i	$-0.594634\pi$
$587$	−14.1948	−0.585883	−0.292941	+	0.956130i	$0.594634\pi$
$588$	−3.30353	−0.136235
$589$	8.39991	0.346112
$590$	32.5448	1.33985
$591$	3.37641	0.138887
$592$	41.6429	1.71151
$593$	2.59127	0.106411	0.0532054	−	0.998584i	$-0.483056\pi$
$593$	2.59127	0.106411	0.0532054	+	0.998584i	$0.483056\pi$
$594$	−7.86579	−0.322737
$595$	7.01349	0.287525
$596$	30.6837	1.25685
$597$	−2.43776	−0.0997711
$598$	−43.5617	−1.78137
$599$	17.0164	0.695272	0.347636	−	0.937630i	$-0.386985\pi$
$599$	17.0164	0.695272	0.347636	+	0.937630i	$0.386985\pi$
$600$	11.5514	0.471584
$601$	15.4179	0.628911	0.314455	−	0.949272i	$-0.398178\pi$
$601$	15.4179	0.628911	0.314455	+	0.949272i	$0.398178\pi$
$602$	45.6265	1.85960
$603$	−1.75201	−0.0713475
$604$	21.6625	0.881437
$605$	5.63777	0.229208
$606$	32.6358	1.32574
$607$	31.7318	1.28795	0.643977	−	0.765045i	$-0.277283\pi$
$607$	31.7318	1.28795	0.643977	+	0.765045i	$0.277283\pi$
$608$	−59.5301	−2.41426
$609$	21.9255	0.888467
$610$	72.4061	2.93164
$611$	27.8490	1.12665
$612$	−5.04993	−0.204131
$613$	30.6219	1.23681	0.618403	−	0.785861i	$-0.287780\pi$
$613$	30.6219	1.23681	0.618403	+	0.785861i	$0.287780\pi$
$614$	−13.8303	−0.558146
$615$	31.0597	1.25245
$616$	66.3715	2.67418
$617$	−4.81934	−0.194020	−0.0970098	−	0.995283i	$-0.530928\pi$
$617$	−4.81934	−0.194020	−0.0970098	+	0.995283i	$0.530928\pi$
$618$	12.7531	0.513007
$619$	7.83502	0.314916	0.157458	−	0.987526i	$-0.449670\pi$
$619$	7.83502	0.314916	0.157458	+	0.987526i	$0.449670\pi$
$620$	−25.4301	−1.02130
$621$	−6.95555	−0.279117
$622$	−11.0298	−0.442256
$623$	−31.0520	−1.24407
$624$	−26.8943	−1.07663
$625$	−30.0975	−1.20390
$626$	40.9575	1.63699
$627$	12.5270	0.500281
$628$	5.04993	0.201514
$629$	−3.65226	−0.145625
$630$	18.6220	0.741919
$631$	28.3593	1.12897	0.564483	−	0.825445i	$-0.309076\pi$
$631$	28.3593	1.12897	0.564483	+	0.825445i	$0.309076\pi$
$632$	−15.5699	−0.619337
$633$	17.4038	0.691741
$634$	57.9599	2.30188
$635$	−5.39161	−0.213959
$636$	45.2596	1.79466
$637$	1.54303	0.0611371
$638$	−62.3366	−2.46793
$639$	12.5026	0.494597
$640$	26.7304	1.05661
$641$	14.3029	0.564931	0.282465	−	0.959277i	$-0.408848\pi$
$641$	14.3029	0.564931	0.282465	+	0.959277i	$0.408848\pi$
$642$	8.42528	0.332519
$643$	−20.3616	−0.802981	−0.401491	−	0.915863i	$-0.631508\pi$
$643$	−20.3616	−0.802981	−0.401491	+	0.915863i	$0.631508\pi$
$644$	97.1776	3.82933
$645$	−15.7457	−0.619985
$646$	11.2277	0.441747
$647$	−34.6119	−1.36074	−0.680368	−	0.732871i	$-0.738180\pi$
$647$	−34.6119	−1.36074	−0.680368	+	0.732871i	$0.738180\pi$
$648$	−8.09809	−0.318123
$649$	−14.3237	−0.562253
$650$	−8.93358	−0.350404
$651$	−5.49574	−0.215395
$652$	44.3500	1.73688
$653$	10.1347	0.396603	0.198301	−	0.980141i	$-0.436458\pi$
$653$	10.1347	0.396603	0.198301	+	0.980141i	$0.436458\pi$
$654$	−47.6989	−1.86518
$655$	25.1771	0.983752
$656$	139.698	5.45430
$657$	−15.8588	−0.618712
$658$	−86.7302	−3.38109
$659$	−40.0027	−1.55829	−0.779143	−	0.626846i	$-0.784345\pi$
$659$	−40.0027	−1.55829	−0.779143	+	0.626846i	$0.784345\pi$
$660$	−37.9245	−1.47621
$661$	22.6894	0.882515	0.441257	−	0.897381i	$-0.354533\pi$
$661$	22.6894	0.882515	0.441257	+	0.897381i	$0.354533\pi$
$662$	35.9914	1.39884
$663$	2.35875	0.0916061
$664$	−20.8104	−0.807599
$665$	−29.6573	−1.15006
$666$	−9.69738	−0.375766
$667$	−55.1229	−2.13437
$668$	93.8023	3.62932
$669$	−22.4073	−0.866318
$670$	−11.7927	−0.455593
$671$	−31.8675	−1.23023
$672$	38.9482	1.50246
$673$	13.3577	0.514902	0.257451	−	0.966291i	$-0.417117\pi$
$673$	13.3577	0.514902	0.257451	+	0.966291i	$0.417117\pi$
$674$	40.7195	1.56846
$675$	−1.42643	−0.0549035
$676$	−37.5529	−1.44434
$677$	−9.54646	−0.366900	−0.183450	−	0.983029i	$-0.558727\pi$
$677$	−9.54646	−0.366900	−0.183450	+	0.983029i	$0.558727\pi$
$678$	7.78442	0.298959
$679$	4.70369	0.180511
$680$	−20.5290	−0.787251
$681$	−4.96128	−0.190117
$682$	15.6250	0.598311
$683$	−6.96059	−0.266340	−0.133170	−	0.991093i	$-0.542516\pi$
$683$	−6.96059	−0.266340	−0.133170	+	0.991093i	$0.542516\pi$
$684$	21.3542	0.816498
$685$	−44.4357	−1.69780
$686$	46.6154	1.77979
$687$	27.2713	1.04046
$688$	−70.8198	−2.69998
$689$	−21.1401	−0.805373
$690$	−46.8176	−1.78232
$691$	25.7640	0.980111	0.490055	−	0.871691i	$-0.336977\pi$
$691$	25.7640	0.980111	0.490055	+	0.871691i	$0.336977\pi$
$692$	−25.3828	−0.964910
$693$	−8.19595	−0.311338
$694$	−21.1732	−0.803723
$695$	3.14168	0.119171
$696$	−64.1776	−2.43264
$697$	−12.2521	−0.464083
$698$	42.1506	1.59542
$699$	15.9332	0.602649
$700$	19.9290	0.753247
$701$	−27.3353	−1.03244	−0.516219	−	0.856456i	$-0.672661\pi$
$701$	−27.3353	−1.03244	−0.516219	+	0.856456i	$0.672661\pi$
$702$	6.26287	0.236377
$703$	15.4440	0.582481
$704$	−43.1788	−1.62736
$705$	29.9305	1.12725
$706$	−38.4316	−1.44639
$707$	34.0056	1.27891
$708$	−24.4169	−0.917642
$709$	−34.6085	−1.29975	−0.649874	−	0.760042i	$-0.725178\pi$
$709$	−34.6085	−1.29975	−0.649874	+	0.760042i	$0.725178\pi$
$710$	84.1549	3.15828
$711$	1.92266	0.0721055
$712$	90.8915	3.40630
$713$	13.8168	0.517444
$714$	−7.34584	−0.274911
$715$	17.7140	0.662465
$716$	−76.2485	−2.84954
$717$	23.2137	0.866931
$718$	−18.7307	−0.699024
$719$	−19.2458	−0.717749	−0.358874	−	0.933386i	$-0.616839\pi$
$719$	−19.2458	−0.717749	−0.358874	+	0.933386i	$0.616839\pi$
$720$	−28.9044	−1.07720
$721$	13.2884	0.494887
$722$	2.97071	0.110558
$723$	−1.83838	−0.0683703
$724$	66.0596	2.45509
$725$	−11.3045	−0.419840
$726$	−5.90493	−0.219153
$727$	50.2817	1.86485	0.932423	−	0.361370i	$-0.117691\pi$
$727$	50.2817	1.86485	0.932423	+	0.361370i	$0.117691\pi$
$728$	−52.8461	−1.95861
$729$	1.00000	0.0370370
$730$	−106.745	−3.95082
$731$	6.21120	0.229730
$732$	−54.3229	−2.00783
$733$	−1.49154	−0.0550912	−0.0275456	−	0.999621i	$-0.508769\pi$
$733$	−1.49154	−0.0550912	−0.0275456	+	0.999621i	$0.508769\pi$
$734$	−6.80486	−0.251172
$735$	1.65836	0.0611695
$736$	−97.9197	−3.60937
$737$	5.19024	0.191185
$738$	−32.5315	−1.19750
$739$	4.05371	0.149118	0.0745590	−	0.997217i	$-0.476245\pi$
$739$	4.05371	0.149118	0.0745590	+	0.997217i	$0.476245\pi$
$740$	−46.7555	−1.71876
$741$	−9.97422	−0.366412
$742$	65.8366	2.41694
$743$	29.0081	1.06420	0.532102	−	0.846680i	$-0.321402\pi$
$743$	29.0081	1.06420	0.532102	+	0.846680i	$0.321402\pi$
$744$	16.0864	0.589757
$745$	−15.4031	−0.564326
$746$	−28.4763	−1.04259
$747$	2.56979	0.0940237
$748$	14.9601	0.546996
$749$	8.77892	0.320775
$750$	24.0536	0.878311
$751$	50.7467	1.85178	0.925888	−	0.377799i	$-0.123319\pi$
$751$	50.7467	1.85178	0.925888	+	0.377799i	$0.123319\pi$
$752$	134.619	4.90906
$753$	12.0927	0.440684
$754$	49.6334	1.80754
$755$	−10.8745	−0.395763
$756$	−13.9712	−0.508129
$757$	13.7793	0.500818	0.250409	−	0.968140i	$-0.419435\pi$
$757$	13.7793	0.500818	0.250409	+	0.968140i	$0.419435\pi$
$758$	−5.52544	−0.200693
$759$	20.6054	0.747929
$760$	86.8091	3.14890
$761$	−45.9251	−1.66478	−0.832392	−	0.554188i	$-0.813029\pi$
$761$	−45.9251	−1.66478	−0.832392	+	0.554188i	$0.813029\pi$
$762$	5.64710	0.204573
$763$	−49.7010	−1.79930
$764$	109.852	3.97431
$765$	2.53504	0.0916546
$766$	3.06020	0.110570
$767$	11.4047	0.411801
$768$	1.15377	0.0416330
$769$	−33.3742	−1.20350	−0.601752	−	0.798683i	$-0.705530\pi$
$769$	−33.3742	−1.20350	−0.601752	+	0.798683i	$0.705530\pi$
$770$	−55.1666	−1.98807
$771$	−24.8159	−0.893724
$772$	−104.537	−3.76236
$773$	31.3998	1.12937	0.564686	−	0.825306i	$-0.308997\pi$
$773$	31.3998	1.12937	0.564686	+	0.825306i	$0.308997\pi$
$774$	16.4918	0.592786
$775$	2.83354	0.101784
$776$	−13.7680	−0.494243
$777$	−10.1044	−0.362494
$778$	−66.2000	−2.37339
$779$	51.8096	1.85627
$780$	30.1962	1.08120
$781$	−37.0384	−1.32534
$782$	18.4682	0.660421
$783$	7.92503	0.283217
$784$	7.45885	0.266388
$785$	−2.53504	−0.0904795
$786$	−26.3702	−0.940595
$787$	−2.11931	−0.0755452	−0.0377726	−	0.999286i	$-0.512026\pi$
$787$	−2.11931	−0.0755452	−0.0377726	+	0.999286i	$0.512026\pi$
$788$	−17.0506	−0.607404
$789$	12.8990	0.459218
$790$	12.9414	0.460434
$791$	8.11116	0.288400
$792$	23.9901	0.852452
$793$	25.3734	0.901036
$794$	−12.3305	−0.437591
$795$	−22.7201	−0.805800
$796$	12.3105	0.436336
$797$	36.2971	1.28571	0.642855	−	0.765988i	$-0.277750\pi$
$797$	36.2971	1.28571	0.642855	+	0.765988i	$0.277750\pi$
$798$	31.0627	1.09961
$799$	−11.8067	−0.417691
$800$	−20.0812	−0.709979
$801$	−11.2238	−0.396574
$802$	−3.93101	−0.138809
$803$	46.9809	1.65792
$804$	8.84754	0.312029
$805$	−48.7827	−1.71936
$806$	−12.4409	−0.438210
$807$	−17.3196	−0.609679
$808$	−99.5369	−3.50170
$809$	52.4749	1.84492	0.922460	−	0.386093i	$-0.126175\pi$
$809$	52.4749	1.84492	0.922460	+	0.386093i	$0.126175\pi$
$810$	6.73097	0.236502
$811$	18.5692	0.652054	0.326027	−	0.945360i	$-0.394290\pi$
$811$	18.5692	0.652054	0.326027	+	0.945360i	$0.394290\pi$
$812$	−110.722	−3.88559
$813$	−15.4231	−0.540911
$814$	28.7279	1.00691
$815$	−22.2635	−0.779856
$816$	11.4019	0.399148
$817$	−26.2648	−0.918888
$818$	96.0303	3.35762
$819$	6.52575	0.228028
$820$	−156.849	−5.47742
$821$	−2.04995	−0.0715437	−0.0357719	−	0.999360i	$-0.511389\pi$
$821$	−2.04995	−0.0715437	−0.0357719	+	0.999360i	$0.511389\pi$
$822$	46.5413	1.62332
$823$	7.29160	0.254169	0.127085	−	0.991892i	$-0.459438\pi$
$823$	7.29160	0.254169	0.127085	+	0.991892i	$0.459438\pi$
$824$	−38.8962	−1.35501
$825$	4.22573	0.147121
$826$	−35.5178	−1.23582
$827$	19.1838	0.667087	0.333543	−	0.942735i	$-0.391756\pi$
$827$	19.1838	0.667087	0.333543	+	0.942735i	$0.391756\pi$
$828$	35.1251	1.22068
$829$	43.0291	1.49446	0.747232	−	0.664563i	$-0.231382\pi$
$829$	43.0291	1.49446	0.747232	+	0.664563i	$0.231382\pi$
$830$	17.2972	0.600393
$831$	−16.7984	−0.582732
$832$	34.3797	1.19190
$833$	−0.654174	−0.0226658
$834$	−3.29056	−0.113943
$835$	−47.0883	−1.62956
$836$	−63.2606	−2.18791
$837$	−1.98645	−0.0686616
$838$	76.9482	2.65813
$839$	4.79803	0.165646	0.0828232	−	0.996564i	$-0.473606\pi$
$839$	4.79803	0.165646	0.0828232	+	0.996564i	$0.473606\pi$
$840$	−56.7959	−1.95964
$841$	33.8061	1.16573
$842$	59.6288	2.05494
$843$	30.8929	1.06401
$844$	−87.8882	−3.02524
$845$	18.8514	0.648507
$846$	−31.3488	−1.07779
$847$	−6.15278	−0.211412
$848$	−102.189	−3.50919
$849$	−27.2550	−0.935390
$850$	3.78743	0.129908
$851$	25.4035	0.870820
$852$	−63.1375	−2.16305
$853$	33.3619	1.14229	0.571144	−	0.820850i	$-0.306500\pi$
$853$	33.3619	1.14229	0.571144	+	0.820850i	$0.306500\pi$
$854$	−79.0204	−2.70402
$855$	−10.7197	−0.366606
$856$	−25.6965	−0.878289
$857$	47.1254	1.60977	0.804886	−	0.593429i	$-0.202226\pi$
$857$	47.1254	1.60977	0.804886	+	0.593429i	$0.202226\pi$
$858$	−18.5534	−0.633402
$859$	−5.04734	−0.172213	−0.0861064	−	0.996286i	$-0.527443\pi$
$859$	−5.04734	−0.172213	−0.0861064	+	0.996286i	$0.527443\pi$
$860$	79.5145	2.71142
$861$	−33.8970	−1.15521
$862$	65.8721	2.24361
$863$	49.9495	1.70030	0.850150	−	0.526541i	$-0.176511\pi$
$863$	49.9495	1.70030	0.850150	+	0.526541i	$0.176511\pi$
$864$	14.0779	0.478941
$865$	12.7421	0.433243
$866$	−42.2594	−1.43603
$867$	−1.00000	−0.0339618
$868$	27.7531	0.942001
$869$	−5.69578	−0.193216
$870$	53.3431	1.80850
$871$	−4.13255	−0.140026
$872$	145.478	4.92652
$873$	1.70016	0.0575416
$874$	−78.0948	−2.64159
$875$	25.0632	0.847290
$876$	80.0860	2.70586
$877$	56.7532	1.91642	0.958209	−	0.286069i	$-0.0923486\pi$
$877$	56.7532	1.91642	0.958209	+	0.286069i	$0.0923486\pi$
$878$	−17.4142	−0.587700
$879$	15.7632	0.531681
$880$	85.6276	2.88651
$881$	−10.2759	−0.346203	−0.173102	−	0.984904i	$-0.555379\pi$
$881$	−10.2759	−0.346203	−0.173102	+	0.984904i	$0.555379\pi$
$882$	−1.73694	−0.0584859
$883$	12.0454	0.405360	0.202680	−	0.979245i	$-0.435035\pi$
$883$	12.0454	0.405360	0.202680	+	0.979245i	$0.435035\pi$
$884$	−11.9115	−0.400627
$885$	12.2571	0.412019
$886$	50.8884	1.70963
$887$	−18.6774	−0.627127	−0.313563	−	0.949567i	$-0.601523\pi$
$887$	−18.6774	−0.627127	−0.313563	+	0.949567i	$0.601523\pi$
$888$	29.5763	0.992516
$889$	5.88413	0.197347
$890$	−75.5472	−2.53235
$891$	−2.96244	−0.0992455
$892$	113.155	3.78873
$893$	49.9260	1.67071
$894$	16.1330	0.539568
$895$	38.2764	1.27944
$896$	−29.1722	−0.974575
$897$	−16.4064	−0.547793
$898$	97.9788	3.26959
$899$	−15.7426	−0.525046
$900$	7.20340	0.240113
$901$	8.96243	0.298582
$902$	96.3728	3.20886
$903$	17.1840	0.571849
$904$	−23.7419	−0.789645
$905$	−33.1616	−1.10233
$906$	11.3898	0.378401
$907$	25.7806	0.856031	0.428016	−	0.903771i	$-0.359213\pi$
$907$	25.7806	0.856031	0.428016	+	0.903771i	$0.359213\pi$
$908$	25.0541	0.831451
$909$	12.2914	0.407680
$910$	43.9246	1.45609
$911$	22.2717	0.737896	0.368948	−	0.929450i	$-0.379718\pi$
$911$	22.2717	0.737896	0.368948	+	0.929450i	$0.379718\pi$
$912$	−48.2144	−1.59654
$913$	−7.61285	−0.251949
$914$	−98.2189	−3.24879
$915$	27.2699	0.901514
$916$	−137.718	−4.55033
$917$	−27.4771	−0.907373
$918$	−2.65517	−0.0876337
$919$	14.9821	0.494213	0.247107	−	0.968988i	$-0.420520\pi$
$919$	14.9821	0.494213	0.247107	+	0.968988i	$0.420520\pi$
$920$	142.790	4.70766
$921$	−5.20882	−0.171636
$922$	−66.2897	−2.18314
$923$	29.4906	0.970693
$924$	41.3890	1.36160
$925$	5.20971	0.171294
$926$	−30.8616	−1.01418
$927$	4.80313	0.157756
$928$	111.568	3.66240
$929$	−8.34337	−0.273737	−0.136868	−	0.990589i	$-0.543704\pi$
$929$	−8.34337	−0.273737	−0.136868	+	0.990589i	$0.543704\pi$
$930$	−13.3707	−0.438443
$931$	2.76625	0.0906601
$932$	−80.4616	−2.63561
$933$	−4.15409	−0.135999
$934$	31.5709	1.03303
$935$	−7.50991	−0.245600
$936$	−19.1013	−0.624346
$937$	−25.9083	−0.846387	−0.423193	−	0.906039i	$-0.639091\pi$
$937$	−25.9083	−0.846387	−0.423193	+	0.906039i	$0.639091\pi$
$938$	12.8700	0.420221
$939$	15.4256	0.503394
$940$	−151.147	−4.92987
$941$	29.5803	0.964291	0.482146	−	0.876091i	$-0.339858\pi$
$941$	29.5803	0.964291	0.482146	+	0.876091i	$0.339858\pi$
$942$	2.65517	0.0865101
$943$	85.2205	2.77516
$944$	55.1294	1.79431
$945$	7.01349	0.228149
$946$	−48.8560	−1.58845
$947$	41.7597	1.35701	0.678503	−	0.734597i	$-0.262629\pi$
$947$	41.7597	1.35701	0.678503	+	0.734597i	$0.262629\pi$
$948$	−9.70931	−0.315344
$949$	−37.4070	−1.21428
$950$	−16.0156	−0.519613
$951$	21.8291	0.707856
$952$	22.4043	0.726128
$953$	43.9666	1.42422	0.712110	−	0.702068i	$-0.247740\pi$
$953$	43.9666	1.42422	0.712110	+	0.702068i	$0.247740\pi$
$954$	23.7968	0.770449
$955$	−55.1452	−1.78446
$956$	−117.228	−3.79141
$957$	−23.4774	−0.758918
$958$	−41.9258	−1.35456
$959$	48.4949	1.56598
$960$	36.9493	1.19253
$961$	−27.0540	−0.872711
$962$	−22.8736	−0.737476
$963$	3.17316	0.102254
$964$	9.28371	0.299008
$965$	52.4770	1.68929
$966$	51.0944	1.64394
$967$	−27.4589	−0.883019	−0.441510	−	0.897257i	$-0.645557\pi$
$967$	−27.4589	−0.883019	−0.441510	+	0.897257i	$0.645557\pi$
$968$	18.0096	0.578851
$969$	4.22861	0.135843
$970$	11.4437	0.367435
$971$	29.8984	0.959484	0.479742	−	0.877410i	$-0.340730\pi$
$971$	29.8984	0.959484	0.479742	+	0.877410i	$0.340730\pi$
$972$	−5.04993	−0.161977
$973$	−3.42867	−0.109918
$974$	11.7102	0.375220
$975$	−3.36460	−0.107753
$976$	122.653	3.92601
$977$	−14.2681	−0.456475	−0.228238	−	0.973605i	$-0.573296\pi$
$977$	−14.2681	−0.456475	−0.228238	+	0.973605i	$0.573296\pi$
$978$	23.3185	0.745644
$979$	33.2499	1.06267
$980$	−8.37459	−0.267517
$981$	−17.9645	−0.573564
$982$	−47.4839	−1.51527
$983$	23.2724	0.742273	0.371137	−	0.928578i	$-0.378968\pi$
$983$	23.2724	0.742273	0.371137	+	0.928578i	$0.378968\pi$
$984$	99.2190	3.16298
$985$	8.55934	0.272723
$986$	−21.0423	−0.670123
$987$	−32.6646	−1.03973
$988$	50.3691	1.60246
$989$	−43.2024	−1.37375
$990$	−19.9401	−0.633738
$991$	59.7609	1.89837	0.949183	−	0.314724i	$-0.101912\pi$
$991$	59.7609	1.89837	0.949183	+	0.314724i	$0.101912\pi$
$992$	−27.9650	−0.887891
$993$	13.5552	0.430161
$994$	−91.8424	−2.91307
$995$	−6.17983	−0.195914
$996$	−12.9773	−0.411200
$997$	45.3328	1.43570	0.717852	−	0.696196i	$-0.245125\pi$
$997$	45.3328	1.43570	0.717852	+	0.696196i	$0.245125\pi$
$998$	−76.6853	−2.42743
$999$	−3.65226	−0.115552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.65517 q^{2} -1.00000 q^{3} +5.04993 q^{4} -2.53504 q^{5} +2.65517 q^{6} +2.76662 q^{7} -8.09809 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65517 q^{2} -1.00000 q^{3} +5.04993 q^{4} -2.53504 q^{5} +2.65517 q^{6} +2.76662 q^{7} -8.09809 q^{8} +1.00000 q^{9} +6.73097 q^{10} -2.96244 q^{11} -5.04993 q^{12} +2.35875 q^{13} -7.34584 q^{14} +2.53504 q^{15} +11.4019 q^{16} -1.00000 q^{17} -2.65517 q^{18} +4.22861 q^{19} -12.8018 q^{20} -2.76662 q^{21} +7.86579 q^{22} +6.95555 q^{23} +8.09809 q^{24} +1.42643 q^{25} -6.26287 q^{26} -1.00000 q^{27} +13.9712 q^{28} -7.92503 q^{29} -6.73097 q^{30} +1.98645 q^{31} -14.0779 q^{32} +2.96244 q^{33} +2.65517 q^{34} -7.01349 q^{35} +5.04993 q^{36} +3.65226 q^{37} -11.2277 q^{38} -2.35875 q^{39} +20.5290 q^{40} +12.2521 q^{41} +7.34584 q^{42} -6.21120 q^{43} -14.9601 q^{44} -2.53504 q^{45} -18.4682 q^{46} +11.8067 q^{47} -11.4019 q^{48} +0.654174 q^{49} -3.78743 q^{50} +1.00000 q^{51} +11.9115 q^{52} -8.96243 q^{53} +2.65517 q^{54} +7.50991 q^{55} -22.4043 q^{56} -4.22861 q^{57} +21.0423 q^{58} +4.83509 q^{59} +12.8018 q^{60} +10.7572 q^{61} -5.27435 q^{62} +2.76662 q^{63} +14.5754 q^{64} -5.97952 q^{65} -7.86579 q^{66} -1.75201 q^{67} -5.04993 q^{68} -6.95555 q^{69} +18.6220 q^{70} +12.5026 q^{71} -8.09809 q^{72} -15.8588 q^{73} -9.69738 q^{74} -1.42643 q^{75} +21.3542 q^{76} -8.19595 q^{77} +6.26287 q^{78} +1.92266 q^{79} -28.9044 q^{80} +1.00000 q^{81} -32.5315 q^{82} +2.56979 q^{83} -13.9712 q^{84} +2.53504 q^{85} +16.4918 q^{86} +7.92503 q^{87} +23.9901 q^{88} -11.2238 q^{89} +6.73097 q^{90} +6.52575 q^{91} +35.1251 q^{92} -1.98645 q^{93} -31.3488 q^{94} -10.7197 q^{95} +14.0779 q^{96} +1.70016 q^{97} -1.73694 q^{98} -2.96244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 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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