LMFDB - Embedded newform 71.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(1,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("71.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.19869$ of defining polynomial
Character	$\chi$	$=$	71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19869 q^{2} +2.19869 q^{3} +2.83424 q^{4} -2.03293 q^{5} -4.83424 q^{6} +4.39738 q^{7} -1.83424 q^{8} +1.83424 q^{9} +O(q^{10})$	\(q-2.19869 q^{2} +2.19869 q^{3} +2.83424 q^{4} -2.03293 q^{5} -4.83424 q^{6} +4.39738 q^{7} -1.83424 q^{8} +1.83424 q^{9} +4.46980 q^{10} +3.66849 q^{11} +6.23163 q^{12} -5.66849 q^{13} -9.66849 q^{14} -4.46980 q^{15} -1.63555 q^{16} -0.728896 q^{17} -4.03293 q^{18} -1.56314 q^{19} -5.76183 q^{20} +9.66849 q^{21} -8.06587 q^{22} -4.00000 q^{23} -4.03293 q^{24} -0.867178 q^{25} +12.4633 q^{26} -2.56314 q^{27} +12.4633 q^{28} -1.86718 q^{29} +9.82770 q^{30} +4.00000 q^{31} +7.26456 q^{32} +8.06587 q^{33} +1.60262 q^{34} -8.93959 q^{35} +5.19869 q^{36} -6.83424 q^{37} +3.43686 q^{38} -12.4633 q^{39} +3.72890 q^{40} +6.79476 q^{41} -21.2580 q^{42} +4.36445 q^{43} +10.3974 q^{44} -3.72890 q^{45} +8.79476 q^{46} +1.27110 q^{47} -3.59607 q^{48} +12.3370 q^{49} +1.90666 q^{50} -1.60262 q^{51} -16.0659 q^{52} -13.3370 q^{53} +5.63555 q^{54} -7.45779 q^{55} -8.06587 q^{56} -3.43686 q^{57} +4.10535 q^{58} +6.06587 q^{59} -12.6685 q^{60} +12.7948 q^{61} -8.79476 q^{62} +8.06587 q^{63} -12.7014 q^{64} +11.5237 q^{65} -17.7344 q^{66} -7.66849 q^{67} -2.06587 q^{68} -8.79476 q^{69} +19.6554 q^{70} +1.00000 q^{71} -3.36445 q^{72} +5.23817 q^{73} +15.0264 q^{74} -1.90666 q^{75} -4.43032 q^{76} +16.1317 q^{77} +27.4028 q^{78} -8.43032 q^{79} +3.32497 q^{80} -11.1383 q^{81} -14.9396 q^{82} -0.768374 q^{83} +27.4028 q^{84} +1.48180 q^{85} -9.59607 q^{86} -4.10535 q^{87} -6.72890 q^{88} -1.46980 q^{89} +8.19869 q^{90} -24.9265 q^{91} -11.3370 q^{92} +8.79476 q^{93} -2.79476 q^{94} +3.17776 q^{95} +15.9725 q^{96} +3.60262 q^{97} -27.1252 q^{98} +6.72890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - 9 q^{6} + 2 q^{7}+O(q^{10}) $ 3 * q - q^2 + q^3 + 3 * q^4 + 5 * q^5 - 9 * q^6 + 2 * q^7	\( 3 q - q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - 9 q^{6} + 2 q^{7} + 8 q^{10} + 2 q^{12} - 6 q^{13} - 18 q^{14} - 8 q^{15} - 5 q^{16} - 2 q^{17} - q^{18} + q^{19} - 6 q^{20} + 18 q^{21} - 2 q^{22} - 12 q^{23} - q^{24} + 14 q^{25} + 4 q^{26} - 2 q^{27} + 4 q^{28} + 11 q^{29} - 4 q^{30} + 12 q^{31} - 6 q^{32} + 2 q^{33} + 16 q^{34} - 16 q^{35} + 10 q^{36} - 15 q^{37} + 16 q^{38} - 4 q^{39} + 11 q^{40} - 2 q^{41} - 8 q^{42} + 13 q^{43} + 20 q^{44} - 11 q^{45} + 4 q^{46} + 4 q^{47} + 6 q^{48} + 15 q^{49} + 6 q^{50} - 16 q^{51} - 26 q^{52} - 18 q^{53} + 17 q^{54} - 22 q^{55} - 2 q^{56} - 16 q^{57} + 7 q^{58} - 4 q^{59} - 27 q^{60} + 16 q^{61} - 4 q^{62} + 2 q^{63} - 16 q^{64} + 12 q^{65} - 20 q^{66} - 12 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 3 q^{71} - 10 q^{72} + 27 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 4 q^{77} + 38 q^{78} - 3 q^{79} - 7 q^{80} - 17 q^{81} - 34 q^{82} - 19 q^{83} + 38 q^{84} - 6 q^{85} - 12 q^{86} - 7 q^{87} - 20 q^{88} + q^{89} + 19 q^{90} - 8 q^{91} - 12 q^{92} + 4 q^{93} + 14 q^{94} + 10 q^{95} + 26 q^{96} + 22 q^{97} - 9 q^{98} + 20 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^3 + 3 * q^4 + 5 * q^5 - 9 * q^6 + 2 * q^7 + 8 * q^10 + 2 * q^12 - 6 * q^13 - 18 * q^14 - 8 * q^15 - 5 * q^16 - 2 * q^17 - q^18 + q^19 - 6 * q^20 + 18 * q^21 - 2 * q^22 - 12 * q^23 - q^24 + 14 * q^25 + 4 * q^26 - 2 * q^27 + 4 * q^28 + 11 * q^29 - 4 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 16 * q^34 - 16 * q^35 + 10 * q^36 - 15 * q^37 + 16 * q^38 - 4 * q^39 + 11 * q^40 - 2 * q^41 - 8 * q^42 + 13 * q^43 + 20 * q^44 - 11 * q^45 + 4 * q^46 + 4 * q^47 + 6 * q^48 + 15 * q^49 + 6 * q^50 - 16 * q^51 - 26 * q^52 - 18 * q^53 + 17 * q^54 - 22 * q^55 - 2 * q^56 - 16 * q^57 + 7 * q^58 - 4 * q^59 - 27 * q^60 + 16 * q^61 - 4 * q^62 + 2 * q^63 - 16 * q^64 + 12 * q^65 - 20 * q^66 - 12 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 3 * q^71 - 10 * q^72 + 27 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 4 * q^77 + 38 * q^78 - 3 * q^79 - 7 * q^80 - 17 * q^81 - 34 * q^82 - 19 * q^83 + 38 * q^84 - 6 * q^85 - 12 * q^86 - 7 * q^87 - 20 * q^88 + q^89 + 19 * q^90 - 8 * q^91 - 12 * q^92 + 4 * q^93 + 14 * q^94 + 10 * q^95 + 26 * q^96 + 22 * q^97 - 9 * q^98 + 20 * 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 $

$2$	−2.19869	−1.55471	−0.777355	−	0.629062i	$-0.783439\pi$
$2$	−2.19869	−1.55471	−0.777355	+	0.629062i	$0.783439\pi$
$3$	2.19869	1.26941	0.634707	−	0.772752i	$-0.281121\pi$
$3$	2.19869	1.26941	0.634707	+	0.772752i	$0.281121\pi$
$4$	2.83424	1.41712
$5$	−2.03293	−0.909156	−0.454578	−	0.890707i	$-0.650210\pi$
$5$	−2.03293	−0.909156	−0.454578	+	0.890707i	$0.650210\pi$
$6$	−4.83424	−1.97357
$7$	4.39738	1.66205	0.831027	−	0.556232i	$-0.187753\pi$
$7$	4.39738	1.66205	0.831027	+	0.556232i	$0.187753\pi$
$8$	−1.83424	−0.648503
$9$	1.83424	0.611414
$10$	4.46980	1.41347
$11$	3.66849	1.10609	0.553045	−	0.833151i	$-0.313466\pi$
$11$	3.66849	1.10609	0.553045	+	0.833151i	$0.313466\pi$
$12$	6.23163	1.79892
$13$	−5.66849	−1.57216	−0.786078	−	0.618128i	$-0.787891\pi$
$13$	−5.66849	−1.57216	−0.786078	+	0.618128i	$0.787891\pi$
$14$	−9.66849	−2.58401
$15$	−4.46980	−1.15410
$16$	−1.63555	−0.408888
$17$	−0.728896	−0.176783	−0.0883916	−	0.996086i	$-0.528173\pi$
$17$	−0.728896	−0.176783	−0.0883916	+	0.996086i	$0.528173\pi$
$18$	−4.03293	−0.950572
$19$	−1.56314	−0.358609	−0.179304	−	0.983794i	$-0.557385\pi$
$19$	−1.56314	−0.358609	−0.179304	+	0.983794i	$0.557385\pi$
$20$	−5.76183	−1.28838
$21$	9.66849	2.10984
$22$	−8.06587	−1.71965
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−4.03293	−0.823219
$25$	−0.867178	−0.173436
$26$	12.4633	2.44424
$27$	−2.56314	−0.493276
$28$	12.4633	2.35533
$29$	−1.86718	−0.346726	−0.173363	−	0.984858i	$-0.555463\pi$
$29$	−1.86718	−0.346726	−0.173363	+	0.984858i	$0.555463\pi$
$30$	9.82770	1.79428
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	7.26456	1.28420
$33$	8.06587	1.40409
$34$	1.60262	0.274847
$35$	−8.93959	−1.51107
$36$	5.19869	0.866449
$37$	−6.83424	−1.12354	−0.561771	−	0.827293i	$-0.689880\pi$
$37$	−6.83424	−1.12354	−0.561771	+	0.827293i	$0.689880\pi$
$38$	3.43686	0.557532
$39$	−12.4633	−1.99572
$40$	3.72890	0.589590
$41$	6.79476	1.06116	0.530582	−	0.847634i	$-0.321973\pi$
$41$	6.79476	1.06116	0.530582	+	0.847634i	$0.321973\pi$
$42$	−21.2580	−3.28018
$43$	4.36445	0.665572	0.332786	−	0.943002i	$-0.392011\pi$
$43$	4.36445	0.665572	0.332786	+	0.943002i	$0.392011\pi$
$44$	10.3974	1.56746
$45$	−3.72890	−0.555871
$46$	8.79476	1.29672
$47$	1.27110	0.185410	0.0927048	−	0.995694i	$-0.470449\pi$
$47$	1.27110	0.185410	0.0927048	+	0.995694i	$0.470449\pi$
$48$	−3.59607	−0.519049
$49$	12.3370	1.76242
$50$	1.90666	0.269642
$51$	−1.60262	−0.224411
$52$	−16.0659	−2.22794
$53$	−13.3370	−1.83197	−0.915987	−	0.401208i	$-0.868591\pi$
$53$	−13.3370	−1.83197	−0.915987	+	0.401208i	$0.868591\pi$
$54$	5.63555	0.766901
$55$	−7.45779	−1.00561
$56$	−8.06587	−1.07785
$57$	−3.43686	−0.455223
$58$	4.10535	0.539058
$59$	6.06587	0.789709	0.394854	−	0.918744i	$-0.370795\pi$
$59$	6.06587	0.789709	0.394854	+	0.918744i	$0.370795\pi$
$60$	−12.6685	−1.63549
$61$	12.7948	1.63820	0.819101	−	0.573649i	$-0.194473\pi$
$61$	12.7948	1.63820	0.819101	+	0.573649i	$0.194473\pi$
$62$	−8.79476	−1.11694
$63$	8.06587	1.01620
$64$	−12.7014	−1.58768
$65$	11.5237	1.42933
$66$	−17.7344	−2.18295
$67$	−7.66849	−0.936855	−0.468427	−	0.883502i	$-0.655179\pi$
$67$	−7.66849	−0.936855	−0.468427	+	0.883502i	$0.655179\pi$
$68$	−2.06587	−0.250523
$69$	−8.79476	−1.05877
$70$	19.6554	2.34927
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−3.36445	−0.396504
$73$	5.23817	0.613081	0.306541	−	0.951858i	$-0.400828\pi$
$73$	5.23817	0.613081	0.306541	+	0.951858i	$0.400828\pi$
$74$	15.0264	1.74678
$75$	−1.90666	−0.220162
$76$	−4.43032	−0.508192
$77$	16.1317	1.83838
$78$	27.4028	3.10276
$79$	−8.43032	−0.948485	−0.474242	−	0.880394i	$-0.657278\pi$
$79$	−8.43032	−0.948485	−0.474242	+	0.880394i	$0.657278\pi$
$80$	3.32497	0.371743
$81$	−11.1383	−1.23759
$82$	−14.9396	−1.64980
$83$	−0.768374	−0.0843400	−0.0421700	−	0.999110i	$-0.513427\pi$
$83$	−0.768374	−0.0843400	−0.0421700	+	0.999110i	$0.513427\pi$
$84$	27.4028	2.98990
$85$	1.48180	0.160724
$86$	−9.59607	−1.03477
$87$	−4.10535	−0.440139
$88$	−6.72890	−0.717303
$89$	−1.46980	−0.155798	−0.0778990	−	0.996961i	$-0.524821\pi$
$89$	−1.46980	−0.155798	−0.0778990	+	0.996961i	$0.524821\pi$
$90$	8.19869	0.864218
$91$	−24.9265	−2.61301
$92$	−11.3370	−1.18196
$93$	8.79476	0.911975
$94$	−2.79476	−0.288258
$95$	3.17776	0.326031
$96$	15.9725	1.63019
$97$	3.60262	0.365790	0.182895	−	0.983132i	$-0.441453\pi$
$97$	3.60262	0.365790	0.182895	+	0.983132i	$0.441453\pi$
$98$	−27.1252	−2.74006
$99$	6.72890	0.676280
$100$	−2.45779	−0.245779
$101$	1.16576	0.115997	0.0579986	−	0.998317i	$-0.481528\pi$
$101$	1.16576	0.115997	0.0579986	+	0.998317i	$0.481528\pi$
$102$	3.52366	0.348894
$103$	−0.343517	−0.0338477	−0.0169238	−	0.999857i	$-0.505387\pi$
$103$	−0.343517	−0.0338477	−0.0169238	+	0.999857i	$0.505387\pi$
$104$	10.3974	1.01955
$105$	−19.6554	−1.91817
$106$	29.3239	2.84819
$107$	16.7948	1.62361	0.811806	−	0.583928i	$-0.198485\pi$
$107$	16.7948	1.62361	0.811806	+	0.583928i	$0.198485\pi$
$108$	−7.26456	−0.699033
$109$	−5.86718	−0.561974	−0.280987	−	0.959712i	$-0.590662\pi$
$109$	−5.86718	−0.561974	−0.280987	+	0.959712i	$0.590662\pi$
$110$	16.3974	1.56343
$111$	−15.0264	−1.42624
$112$	−7.19215	−0.679594
$113$	−2.72890	−0.256713	−0.128356	−	0.991728i	$-0.540970\pi$
$113$	−2.72890	−0.256713	−0.128356	+	0.991728i	$0.540970\pi$
$114$	7.55660	0.707740
$115$	8.13174	0.758288
$116$	−5.29204	−0.491353
$117$	−10.3974	−0.961238
$118$	−13.3370	−1.22777
$119$	−3.20524	−0.293823
$120$	8.19869	0.748435
$121$	2.45779	0.223436
$122$	−28.1317	−2.54693
$123$	14.9396	1.34706
$124$	11.3370	1.01809
$125$	11.9276	1.06684
$126$	−17.7344	−1.57990
$127$	14.4633	1.28341	0.641703	−	0.766953i	$-0.278228\pi$
$127$	14.4633	1.28341	0.641703	+	0.766953i	$0.278228\pi$
$128$	13.3974	1.18417
$129$	9.59607	0.844887
$130$	−25.3370	−2.22220
$131$	10.2436	0.894990	0.447495	−	0.894286i	$-0.352316\pi$
$131$	10.2436	0.894990	0.447495	+	0.894286i	$0.352316\pi$
$132$	22.8606	1.98976
$133$	−6.87372	−0.596027
$134$	16.8606	1.45654
$135$	5.21069	0.448465
$136$	1.33697	0.114644
$137$	2.54221	0.217195	0.108598	−	0.994086i	$-0.465364\pi$
$137$	2.54221	0.217195	0.108598	+	0.994086i	$0.465364\pi$
$138$	19.3370	1.64607
$139$	−0.939590	−0.0796950	−0.0398475	−	0.999206i	$-0.512687\pi$
$139$	−0.939590	−0.0796950	−0.0398475	+	0.999206i	$0.512687\pi$
$140$	−25.3370	−2.14137
$141$	2.79476	0.235362
$142$	−2.19869	−0.184510
$143$	−20.7948	−1.73895
$144$	−3.00000	−0.250000
$145$	3.79585	0.315228
$146$	−11.5171	−0.953163
$147$	27.1252	2.23725
$148$	−19.3699	−1.59220
$149$	−4.93959	−0.404667	−0.202334	−	0.979317i	$-0.564852\pi$
$149$	−4.93959	−0.404667	−0.202334	+	0.979317i	$0.564852\pi$
$150$	4.19215	0.342287
$151$	13.8013	1.12313	0.561567	−	0.827431i	$-0.310199\pi$
$151$	13.8013	1.12313	0.561567	+	0.827431i	$0.310199\pi$
$152$	2.86718	0.232559
$153$	−1.33697	−0.108088
$154$	−35.4687	−2.85815
$155$	−8.13174	−0.653157
$156$	−35.3239	−2.82817
$157$	5.20415	0.415336	0.207668	−	0.978199i	$-0.433413\pi$
$157$	5.20415	0.415336	0.207668	+	0.978199i	$0.433413\pi$
$158$	18.5357	1.47462
$159$	−29.3239	−2.32554
$160$	−14.7684	−1.16754
$161$	−17.5895	−1.38625
$162$	24.4896	1.92409
$163$	−6.66303	−0.521889	−0.260944	−	0.965354i	$-0.584034\pi$
$163$	−6.66303	−0.521889	−0.260944	+	0.965354i	$0.584034\pi$
$164$	19.2580	1.50380
$165$	−16.3974	−1.27653
$166$	1.68942	0.131124
$167$	−4.43032	−0.342828	−0.171414	−	0.985199i	$-0.554834\pi$
$167$	−4.43032	−0.342828	−0.171414	+	0.985199i	$0.554834\pi$
$168$	−17.7344	−1.36824
$169$	19.1317	1.47167
$170$	−3.25802	−0.249878
$171$	−2.86718	−0.219259
$172$	12.3699	0.943197
$173$	−14.7948	−1.12483	−0.562413	−	0.826857i	$-0.690127\pi$
$173$	−14.7948	−1.12483	−0.562413	+	0.826857i	$0.690127\pi$
$174$	9.02639	0.684289
$175$	−3.81331	−0.288259
$176$	−6.00000	−0.452267
$177$	13.3370	1.00247
$178$	3.23163	0.242221
$179$	6.97252	0.521151	0.260575	−	0.965453i	$-0.416088\pi$
$179$	6.97252	0.521151	0.260575	+	0.965453i	$0.416088\pi$
$180$	−10.5686	−0.787737
$181$	−5.85517	−0.435212	−0.217606	−	0.976037i	$-0.569825\pi$
$181$	−5.85517	−0.435212	−0.217606	+	0.976037i	$0.569825\pi$
$182$	54.8057	4.06247
$183$	28.1317	2.07956
$184$	7.33697	0.540889
$185$	13.8936	1.02148
$186$	−19.3370	−1.41786
$187$	−2.67395	−0.195538
$188$	3.60262	0.262748
$189$	−11.2711	−0.819852
$190$	−6.98691	−0.506884
$191$	−4.07787	−0.295064	−0.147532	−	0.989057i	$-0.547133\pi$
$191$	−4.07787	−0.295064	−0.147532	+	0.989057i	$0.547133\pi$
$192$	−27.9265	−2.01542
$193$	15.0055	1.08012	0.540058	−	0.841628i	$-0.318402\pi$
$193$	15.0055	1.08012	0.540058	+	0.841628i	$0.318402\pi$
$194$	−7.92104	−0.568698
$195$	25.3370	1.81442
$196$	34.9660	2.49757
$197$	−14.0659	−1.00215	−0.501076	−	0.865403i	$-0.667062\pi$
$197$	−14.0659	−1.00215	−0.501076	+	0.865403i	$0.667062\pi$
$198$	−14.7948	−1.05142
$199$	10.4369	0.739849	0.369925	−	0.929062i	$-0.379383\pi$
$199$	10.4369	0.739849	0.369925	+	0.929062i	$0.379383\pi$
$200$	1.59061	0.112473
$201$	−16.8606	−1.18926
$202$	−2.56314	−0.180342
$203$	−8.21069	−0.576278
$204$	−4.54221	−0.318018
$205$	−13.8133	−0.964764
$206$	0.755287	0.0526233
$207$	−7.33697	−0.509955
$208$	9.27110	0.642835
$209$	−5.73436	−0.396654
$210$	43.2162	2.98220
$211$	−5.39192	−0.371195	−0.185598	−	0.982626i	$-0.559422\pi$
$211$	−5.39192	−0.371195	−0.185598	+	0.982626i	$0.559422\pi$
$212$	−37.8002	−2.59613
$213$	2.19869	0.150652
$214$	−36.9265	−2.52424
$215$	−8.87264	−0.605109
$216$	4.70142	0.319891
$217$	17.5895	1.19406
$218$	12.9001	0.873706
$219$	11.5171	0.778255
$220$	−21.1372	−1.42507
$221$	4.13174	0.277931
$222$	33.0384	2.21739
$223$	29.8266	1.99734	0.998669	−	0.0515788i	$-0.0164253\pi$
$223$	29.8266	1.99734	0.998669	+	0.0515788i	$0.0164253\pi$
$224$	31.9450	2.13442
$225$	−1.59061	−0.106041
$226$	6.00000	0.399114
$227$	−7.15028	−0.474581	−0.237291	−	0.971439i	$-0.576259\pi$
$227$	−7.15028	−0.474581	−0.237291	+	0.971439i	$0.576259\pi$
$228$	−9.74090	−0.645107
$229$	29.5016	1.94952	0.974762	−	0.223248i	$-0.0716658\pi$
$229$	29.5016	1.94952	0.974762	+	0.223248i	$0.0716658\pi$
$230$	−17.8792	−1.17892
$231$	35.4687	2.33367
$232$	3.42486	0.224853
$233$	−3.41831	−0.223941	−0.111971	−	0.993712i	$-0.535716\pi$
$233$	−3.41831	−0.223941	−0.111971	+	0.993712i	$0.535716\pi$
$234$	22.8606	1.49445
$235$	−2.58407	−0.168566
$236$	17.1921	1.11911
$237$	−18.5357	−1.20402
$238$	7.04732	0.456810
$239$	−17.0713	−1.10425	−0.552126	−	0.833761i	$-0.686183\pi$
$239$	−17.0713	−1.10425	−0.552126	+	0.833761i	$0.686183\pi$
$240$	7.31058	0.471896
$241$	0.807853	0.0520384	0.0260192	−	0.999661i	$-0.491717\pi$
$241$	0.807853	0.0520384	0.0260192	+	0.999661i	$0.491717\pi$
$242$	−5.40393	−0.347378
$243$	−16.8002	−1.07773
$244$	36.2635	2.32153
$245$	−25.0803	−1.60232
$246$	−32.8475	−2.09428
$247$	8.86063	0.563789
$248$	−7.33697	−0.465898
$249$	−1.68942	−0.107063
$250$	−26.2251	−1.65862
$251$	17.7738	1.12187	0.560937	−	0.827858i	$-0.310441\pi$
$251$	17.7738	1.12187	0.560937	+	0.827858i	$0.310441\pi$
$252$	22.8606	1.44008
$253$	−14.6739	−0.922543
$254$	−31.8002	−1.99532
$255$	3.25802	0.204025
$256$	−4.05387	−0.253367
$257$	−12.5422	−0.782361	−0.391181	−	0.920314i	$-0.627933\pi$
$257$	−12.5422	−0.782361	−0.391181	+	0.920314i	$0.627933\pi$
$258$	−21.0988	−1.31355
$259$	−30.0528	−1.86739
$260$	32.6609	2.02554
$261$	−3.42486	−0.211993
$262$	−22.5226	−1.39145
$263$	27.7673	1.71220	0.856102	−	0.516807i	$-0.172879\pi$
$263$	27.7673	1.71220	0.856102	+	0.516807i	$0.172879\pi$
$264$	−14.7948	−0.910555
$265$	27.1132	1.66555
$266$	15.1132	0.926649
$267$	−3.23163	−0.197772
$268$	−21.7344	−1.32764
$269$	3.40284	0.207475	0.103737	−	0.994605i	$-0.466920\pi$
$269$	3.40284	0.207475	0.103737	+	0.994605i	$0.466920\pi$
$270$	−11.4567	−0.697233
$271$	−25.2700	−1.53504	−0.767522	−	0.641022i	$-0.778511\pi$
$271$	−25.2700	−1.53504	−0.767522	+	0.641022i	$0.778511\pi$
$272$	1.19215	0.0722846
$273$	−54.8057	−3.31699
$274$	−5.58953	−0.337676
$275$	−3.18123	−0.191835
$276$	−24.9265	−1.50040
$277$	−11.6290	−0.698719	−0.349360	−	0.936989i	$-0.613601\pi$
$277$	−11.6290	−0.698719	−0.349360	+	0.936989i	$0.613601\pi$
$278$	2.06587	0.123903
$279$	7.33697	0.439253
$280$	16.3974	0.979931
$281$	4.06587	0.242549	0.121275	−	0.992619i	$-0.461302\pi$
$281$	4.06587	0.242549	0.121275	+	0.992619i	$0.461302\pi$
$282$	−6.14483	−0.365919
$283$	−13.1921	−0.784192	−0.392096	−	0.919924i	$-0.628250\pi$
$283$	−13.1921	−0.784192	−0.392096	+	0.919924i	$0.628250\pi$
$284$	2.83424	0.168181
$285$	6.98691	0.413869
$286$	45.7213	2.70356
$287$	29.8792	1.76371
$288$	13.3250	0.785181
$289$	−16.4687	−0.968748
$290$	−8.34590	−0.490088
$291$	7.92104	0.464340
$292$	14.8462	0.868811
$293$	−25.3370	−1.48020	−0.740101	−	0.672496i	$-0.765222\pi$
$293$	−25.3370	−1.48020	−0.740101	+	0.672496i	$0.765222\pi$
$294$	−59.6399	−3.47827
$295$	−12.3315	−0.717968
$296$	12.5357	0.728621
$297$	−9.40284	−0.545608
$298$	10.8606	0.629140
$299$	22.6739	1.31127
$300$	−5.40393	−0.311996
$301$	19.1921	1.10622
$302$	−30.3448	−1.74615
$303$	2.56314	0.147249
$304$	2.55660	0.146631
$305$	−26.0109	−1.48938
$306$	2.93959	0.168045
$307$	3.60262	0.205612	0.102806	−	0.994701i	$-0.467218\pi$
$307$	3.60262	0.205612	0.102806	+	0.994701i	$0.467218\pi$
$308$	45.7213	2.60521
$309$	−0.755287	−0.0429668
$310$	17.8792	1.01547
$311$	−4.31604	−0.244740	−0.122370	−	0.992485i	$-0.539049\pi$
$311$	−4.31604	−0.244740	−0.122370	+	0.992485i	$0.539049\pi$
$312$	22.8606	1.29423
$313$	9.96052	0.563002	0.281501	−	0.959561i	$-0.409168\pi$
$313$	9.96052	0.563002	0.281501	+	0.959561i	$0.409168\pi$
$314$	−11.4423	−0.645727
$315$	−16.3974	−0.923888
$316$	−23.8936	−1.34412
$317$	9.40284	0.528116	0.264058	−	0.964507i	$-0.414939\pi$
$317$	9.40284	0.528116	0.264058	+	0.964507i	$0.414939\pi$
$318$	64.4742	3.61553
$319$	−6.84972	−0.383510
$320$	25.8212	1.44345
$321$	36.9265	2.06104
$322$	38.6739	2.15521
$323$	1.13937	0.0633960
$324$	−31.5686	−1.75381
$325$	4.91558	0.272668
$326$	14.6499	0.811385
$327$	−12.9001	−0.713378
$328$	−12.4633	−0.688168
$329$	5.58953	0.308161
$330$	36.0528	1.98464
$331$	−31.9320	−1.75514	−0.877570	−	0.479449i	$-0.840837\pi$
$331$	−31.9320	−1.75514	−0.877570	+	0.479449i	$0.840837\pi$
$332$	−2.17776	−0.119520
$333$	−12.5357	−0.686950
$334$	9.74090	0.532998
$335$	15.5895	0.851747
$336$	−15.8133	−0.862687
$337$	−28.7817	−1.56784	−0.783919	−	0.620863i	$-0.786782\pi$
$337$	−28.7817	−1.56784	−0.783919	+	0.620863i	$0.786782\pi$
$338$	−42.0648	−2.28802
$339$	−6.00000	−0.325875
$340$	4.19978	0.227765
$341$	14.6739	0.794639
$342$	6.30404	0.340883
$343$	23.4687	1.26719
$344$	−8.00546	−0.431625
$345$	17.8792	0.962583
$346$	32.5291	1.74878
$347$	−20.1317	−1.08073	−0.540364	−	0.841431i	$-0.681714\pi$
$347$	−20.1317	−1.08073	−0.540364	+	0.841431i	$0.681714\pi$
$348$	−11.6356	−0.623731
$349$	34.1976	1.83056	0.915278	−	0.402823i	$-0.131971\pi$
$349$	34.1976	1.83056	0.915278	+	0.402823i	$0.131971\pi$
$350$	8.38429	0.448159
$351$	14.5291	0.775507
$352$	26.6499	1.42045
$353$	28.7398	1.52967	0.764833	−	0.644229i	$-0.222821\pi$
$353$	28.7398	1.52967	0.764833	+	0.644229i	$0.222821\pi$
$354$	−29.3239	−1.55855
$355$	−2.03293	−0.107897
$356$	−4.16576	−0.220785
$357$	−7.04732	−0.372984
$358$	−15.3304	−0.810238
$359$	16.4962	0.870635	0.435318	−	0.900277i	$-0.356636\pi$
$359$	16.4962	0.870635	0.435318	+	0.900277i	$0.356636\pi$
$360$	6.83970	0.360484
$361$	−16.5566	−0.871400
$362$	12.8737	0.676628
$363$	5.40393	0.283633
$364$	−70.6478	−3.70295
$365$	−10.6489	−0.557387
$366$	−61.8530	−3.23311
$367$	−4.56205	−0.238137	−0.119069	−	0.992886i	$-0.537991\pi$
$367$	−4.56205	−0.238137	−0.119069	+	0.992886i	$0.537991\pi$
$368$	6.54221	0.341036
$369$	12.4633	0.648811
$370$	−30.5477	−1.58810
$371$	−58.6478	−3.04484
$372$	24.9265	1.29238
$373$	−2.76183	−0.143002	−0.0715011	−	0.997441i	$-0.522779\pi$
$373$	−2.76183	−0.143002	−0.0715011	+	0.997441i	$0.522779\pi$
$374$	5.87918	0.304005
$375$	26.2251	1.35426
$376$	−2.33151	−0.120239
$377$	10.5841	0.545107
$378$	24.7817	1.27463
$379$	−30.9935	−1.59203	−0.796013	−	0.605279i	$-0.793062\pi$
$379$	−30.9935	−1.59203	−0.796013	+	0.605279i	$0.793062\pi$
$380$	9.00654	0.462026
$381$	31.8002	1.62917
$382$	8.96598	0.458739
$383$	−26.1317	−1.33527	−0.667635	−	0.744489i	$-0.732693\pi$
$383$	−26.1317	−1.33527	−0.667635	+	0.744489i	$0.732693\pi$
$384$	29.4567	1.50321
$385$	−32.7948	−1.67138
$386$	−32.9924	−1.67927
$387$	8.00546	0.406940
$388$	10.2107	0.518369
$389$	−4.81877	−0.244321	−0.122161	−	0.992510i	$-0.538982\pi$
$389$	−4.81877	−0.244321	−0.122161	+	0.992510i	$0.538982\pi$
$390$	−55.7082	−2.82089
$391$	2.91558	0.147447
$392$	−22.6290	−1.14294
$393$	22.5226	1.13611
$394$	30.9265	1.55805
$395$	17.1383	0.862321
$396$	19.0713	0.958370
$397$	−11.0055	−0.552348	−0.276174	−	0.961108i	$-0.589067\pi$
$397$	−11.0055	−0.552348	−0.276174	+	0.961108i	$0.589067\pi$
$398$	−22.9474	−1.15025
$399$	−15.1132	−0.756606
$400$	1.41831	0.0709157
$401$	13.1921	0.658784	0.329392	−	0.944193i	$-0.393156\pi$
$401$	13.1921	0.658784	0.329392	+	0.944193i	$0.393156\pi$
$402$	37.0713	1.84895
$403$	−22.6739	−1.12947
$404$	3.30404	0.164382
$405$	22.6434	1.12516
$406$	18.0528	0.895944
$407$	−25.0713	−1.24274
$408$	2.93959	0.145531
$409$	29.9749	1.48216	0.741082	−	0.671415i	$-0.234313\pi$
$409$	29.9749	1.48216	0.741082	+	0.671415i	$0.234313\pi$
$410$	30.3712	1.49993
$411$	5.58953	0.275711
$412$	−0.973609	−0.0479663
$413$	26.6739	1.31254
$414$	16.1317	0.792832
$415$	1.56205	0.0766782
$416$	−41.1791	−2.01897
$417$	−2.06587	−0.101166
$418$	12.6081	0.616681
$419$	−30.3304	−1.48174	−0.740869	−	0.671649i	$-0.765586\pi$
$419$	−30.3304	−1.48174	−0.740869	+	0.671649i	$0.765586\pi$
$420$	−55.7082	−2.71828
$421$	−9.15028	−0.445958	−0.222979	−	0.974823i	$-0.571578\pi$
$421$	−9.15028	−0.445958	−0.222979	+	0.974823i	$0.571578\pi$
$422$	11.8552	0.577101
$423$	2.33151	0.113362
$424$	24.4633	1.18804
$425$	0.632082	0.0306605
$426$	−4.83424	−0.234220
$427$	56.2635	2.72278
$428$	47.6004	2.30085
$429$	−45.7213	−2.20744
$430$	19.5082	0.940768
$431$	39.9474	1.92420	0.962100	−	0.272697i	$-0.0879155\pi$
$431$	39.9474	1.92420	0.962100	+	0.272697i	$0.0879155\pi$
$432$	4.19215	0.201695
$433$	4.35552	0.209313	0.104656	−	0.994508i	$-0.466626\pi$
$433$	4.35552	0.209313	0.104656	+	0.994508i	$0.466626\pi$
$434$	−38.6739	−1.85641
$435$	8.34590	0.400155
$436$	−16.6290	−0.796385
$437$	6.25256	0.299100
$438$	−25.3226	−1.20996
$439$	15.6135	0.745193	0.372597	−	0.927993i	$-0.378467\pi$
$439$	15.6135	0.745193	0.372597	+	0.927993i	$0.378467\pi$
$440$	13.6794	0.652140
$441$	22.6290	1.07757
$442$	−9.08442	−0.432102
$443$	4.86063	0.230936	0.115468	−	0.993311i	$-0.463163\pi$
$443$	4.86063	0.230936	0.115468	+	0.993311i	$0.463163\pi$
$444$	−42.5884	−2.02116
$445$	2.98800	0.141645
$446$	−65.5795	−3.10528
$447$	−10.8606	−0.513690
$448$	−55.8530	−2.63881
$449$	−7.86826	−0.371326	−0.185663	−	0.982613i	$-0.559443\pi$
$449$	−7.86826	−0.371326	−0.185663	+	0.982613i	$0.559443\pi$
$450$	3.49727	0.164863
$451$	24.9265	1.17374
$452$	−7.73436	−0.363793
$453$	30.3448	1.42572
$454$	15.7213	0.737836
$455$	50.6739	2.37563
$456$	6.30404	0.295214
$457$	23.0604	1.07872	0.539360	−	0.842075i	$-0.318666\pi$
$457$	23.0604	1.07872	0.539360	+	0.842075i	$0.318666\pi$
$458$	−64.8650	−3.03094
$459$	1.86826	0.0872030
$460$	23.0473	1.07459
$461$	−36.2635	−1.68896	−0.844479	−	0.535588i	$-0.820090\pi$
$461$	−36.2635	−1.68896	−0.844479	+	0.535588i	$0.820090\pi$
$462$	−77.9847	−3.62818
$463$	2.35790	0.109581	0.0547906	−	0.998498i	$-0.482551\pi$
$463$	2.35790	0.109581	0.0547906	+	0.998498i	$0.482551\pi$
$464$	3.05387	0.141772
$465$	−17.8792	−0.829127
$466$	7.51582	0.348164
$467$	5.62662	0.260369	0.130185	−	0.991490i	$-0.458443\pi$
$467$	5.62662	0.260369	0.130185	+	0.991490i	$0.458443\pi$
$468$	−29.4687	−1.36219
$469$	−33.7213	−1.55710
$470$	5.68157	0.262071
$471$	11.4423	0.527234
$472$	−11.1263	−0.512128
$473$	16.0109	0.736183
$474$	40.7542	1.87190
$475$	1.35552	0.0621955
$476$	−9.08442	−0.416384
$477$	−24.4633	−1.12010
$478$	37.5346	1.71679
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	−32.4711	−1.48210
$481$	38.7398	1.76638
$482$	−1.77622	−0.0809045
$483$	−38.6739	−1.75973
$484$	6.96598	0.316635
$485$	−7.32389	−0.332560
$486$	36.9385	1.67556
$487$	−3.12628	−0.141665	−0.0708326	−	0.997488i	$-0.522566\pi$
$487$	−3.12628	−0.141665	−0.0708326	+	0.997488i	$0.522566\pi$
$488$	−23.4687	−1.06238
$489$	−14.6499	−0.662493
$490$	55.1437	2.49114
$491$	−1.19215	−0.0538009	−0.0269004	−	0.999638i	$-0.508564\pi$
$491$	−1.19215	−0.0538009	−0.0269004	+	0.999638i	$0.508564\pi$
$492$	42.3424	1.90894
$493$	1.36098	0.0612954
$494$	−19.4818	−0.876528
$495$	−13.6794	−0.614844
$496$	−6.54221	−0.293754
$497$	4.39738	0.197250
$498$	3.71451	0.166451
$499$	−9.93305	−0.444664	−0.222332	−	0.974971i	$-0.571367\pi$
$499$	−9.93305	−0.444664	−0.222332	+	0.974971i	$0.571367\pi$
$500$	33.8057	1.51184
$501$	−9.74090	−0.435191
$502$	−39.0792	−1.74419
$503$	0.451248	0.0201202	0.0100601	−	0.999949i	$-0.496798\pi$
$503$	0.451248	0.0201202	0.0100601	+	0.999949i	$0.496798\pi$
$504$	−14.7948	−0.659011
$505$	−2.36991	−0.105459
$506$	32.2635	1.43429
$507$	42.0648	1.86816
$508$	40.9924	1.81874
$509$	10.1317	0.449081	0.224541	−	0.974465i	$-0.427912\pi$
$509$	10.1317	0.449081	0.224541	+	0.974465i	$0.427912\pi$
$510$	−7.16337	−0.317199
$511$	23.0342	1.01897
$512$	−17.8816	−0.790261
$513$	4.00654	0.176893
$514$	27.5764	1.21634
$515$	0.698347	0.0307728
$516$	27.1976	1.19731
$517$	4.66303	0.205080
$518$	66.0768	2.90325
$519$	−32.5291	−1.42787
$520$	−21.1372	−0.926927
$521$	−26.5202	−1.16187	−0.580935	−	0.813950i	$-0.697313\pi$
$521$	−26.5202	−1.16187	−0.580935	+	0.813950i	$0.697313\pi$
$522$	7.53020	0.329588
$523$	−26.7289	−1.16877	−0.584387	−	0.811475i	$-0.698665\pi$
$523$	−26.7289	−1.16877	−0.584387	+	0.811475i	$0.698665\pi$
$524$	29.0329	1.26831
$525$	−8.38429	−0.365921
$526$	−61.0517	−2.66198
$527$	−2.91558	−0.127005
$528$	−13.1921	−0.574115
$529$	−7.00000	−0.304348
$530$	−59.6135	−2.58945
$531$	11.1263	0.482839
$532$	−19.4818	−0.844643
$533$	−38.5160	−1.66831
$534$	7.10535	0.307478
$535$	−34.1427	−1.47612
$536$	14.0659	0.607553
$537$	15.3304	0.661557
$538$	−7.48180	−0.322563
$539$	45.2580	1.94940
$540$	14.7684	0.635530
$541$	34.7398	1.49358	0.746791	−	0.665059i	$-0.231594\pi$
$541$	34.7398	1.49358	0.746791	+	0.665059i	$0.231594\pi$
$542$	55.5610	2.38655
$543$	−12.8737	−0.552464
$544$	−5.29511	−0.227026
$545$	11.9276	0.510922
$546$	120.501	5.15696
$547$	−33.5631	−1.43506	−0.717528	−	0.696530i	$-0.754727\pi$
$547$	−33.5631	−1.43506	−0.717528	+	0.696530i	$0.754727\pi$
$548$	7.20524	0.307792
$549$	23.4687	1.00162
$550$	6.99454	0.298248
$551$	2.91866	0.124339
$552$	16.1317	0.686612
$553$	−37.0713	−1.57643
$554$	25.5686	1.08631
$555$	30.5477	1.29668
$556$	−2.66303	−0.112938
$557$	35.3490	1.49778	0.748892	−	0.662692i	$-0.230586\pi$
$557$	35.3490	1.49778	0.748892	+	0.662692i	$0.230586\pi$
$558$	−16.1317	−0.682911
$559$	−24.7398	−1.04638
$560$	14.6212	0.617857
$561$	−5.87918	−0.248219
$562$	−8.93959	−0.377094
$563$	−24.5291	−1.03378	−0.516890	−	0.856052i	$-0.672910\pi$
$563$	−24.5291	−1.03378	−0.516890	+	0.856052i	$0.672910\pi$
$564$	7.92104	0.333536
$565$	5.54767	0.233392
$566$	29.0055	1.21919
$567$	−48.9793	−2.05694
$568$	−1.83424	−0.0769631
$569$	17.8092	0.746599	0.373299	−	0.927711i	$-0.378226\pi$
$569$	17.8092	0.746599	0.373299	+	0.927711i	$0.378226\pi$
$570$	−15.3621	−0.643446
$571$	19.1527	0.801514	0.400757	−	0.916184i	$-0.368747\pi$
$571$	19.1527	0.801514	0.400757	+	0.916184i	$0.368747\pi$
$572$	−58.9374	−2.46430
$573$	−8.96598	−0.374559
$574$	−65.6951	−2.74206
$575$	3.46871	0.144655
$576$	−23.2975	−0.970729
$577$	−17.8092	−0.741405	−0.370702	−	0.928752i	$-0.620883\pi$
$577$	−17.8092	−0.741405	−0.370702	+	0.928752i	$0.620883\pi$
$578$	36.2096	1.50612
$579$	32.9924	1.37112
$580$	10.7584	0.446717
$581$	−3.37884	−0.140178
$582$	−17.4159	−0.721913
$583$	−48.9265	−2.02633
$584$	−9.60808	−0.397585
$585$	21.1372	0.873916
$586$	55.7082	2.30128
$587$	36.1856	1.49354	0.746770	−	0.665083i	$-0.231604\pi$
$587$	36.1856	1.49354	0.746770	+	0.665083i	$0.231604\pi$
$588$	76.8794	3.17045
$589$	−6.25256	−0.257632
$590$	27.1132	1.11623
$591$	−30.9265	−1.27215
$592$	11.1778	0.459403
$593$	−26.3963	−1.08397	−0.541983	−	0.840389i	$-0.682326\pi$
$593$	−26.3963	−1.08397	−0.541983	+	0.840389i	$0.682326\pi$
$594$	20.6739	0.848262
$595$	6.51603	0.267131
$596$	−14.0000	−0.573462
$597$	22.9474	0.939176
$598$	−49.8530	−2.03864
$599$	−23.5106	−0.960616	−0.480308	−	0.877100i	$-0.659475\pi$
$599$	−23.5106	−0.960616	−0.480308	+	0.877100i	$0.659475\pi$
$600$	3.49727	0.142775
$601$	7.95814	0.324619	0.162310	−	0.986740i	$-0.448106\pi$
$601$	7.95814	0.324619	0.162310	+	0.986740i	$0.448106\pi$
$602$	−42.1976	−1.71985
$603$	−14.0659	−0.572806
$604$	39.1163	1.59162
$605$	−4.99653	−0.203138
$606$	−5.63555	−0.228929
$607$	−36.9396	−1.49933	−0.749666	−	0.661817i	$-0.769786\pi$
$607$	−36.9396	−1.49933	−0.749666	+	0.661817i	$0.769786\pi$
$608$	−11.3555	−0.460527
$609$	−18.0528	−0.731536
$610$	57.1900	2.31555
$611$	−7.20524	−0.291493
$612$	−3.78931	−0.153174
$613$	34.5280	1.39457	0.697287	−	0.716792i	$-0.254390\pi$
$613$	34.5280	1.39457	0.697287	+	0.716792i	$0.254390\pi$
$614$	−7.92104	−0.319667
$615$	−30.3712	−1.22469
$616$	−29.5895	−1.19220
$617$	−31.5566	−1.27042	−0.635210	−	0.772339i	$-0.719087\pi$
$617$	−31.5566	−1.27042	−0.635210	+	0.772339i	$0.719087\pi$
$618$	1.66064	0.0668008
$619$	−17.7344	−0.712804	−0.356402	−	0.934333i	$-0.615997\pi$
$619$	−17.7344	−0.712804	−0.356402	+	0.934333i	$0.615997\pi$
$620$	−23.0473	−0.925603
$621$	10.2526	0.411421
$622$	9.48964	0.380500
$623$	−6.46325	−0.258945
$624$	20.3843	0.816025
$625$	−19.9121	−0.796485
$626$	−21.9001	−0.875305
$627$	−12.6081	−0.503518
$628$	14.7498	0.588582
$629$	4.98145	0.198624
$630$	36.0528	1.43638
$631$	10.2635	0.408583	0.204291	−	0.978910i	$-0.434511\pi$
$631$	10.2635	0.408583	0.204291	+	0.978910i	$0.434511\pi$
$632$	15.4633	0.615095
$633$	−11.8552	−0.471201
$634$	−20.6739	−0.821067
$635$	−29.4028	−1.16682
$636$	−83.1110	−3.29557
$637$	−69.9320	−2.77081
$638$	15.0604	0.596247
$639$	1.83424	0.0725615
$640$	−27.2360	−1.07660
$641$	−10.9132	−0.431045	−0.215523	−	0.976499i	$-0.569146\pi$
$641$	−10.9132	−0.431045	−0.215523	+	0.976499i	$0.569146\pi$
$642$	−81.1900	−3.20431
$643$	−24.9265	−0.983005	−0.491503	−	0.870876i	$-0.663552\pi$
$643$	−24.9265	−0.983005	−0.491503	+	0.870876i	$0.663552\pi$
$644$	−49.8530	−1.96448
$645$	−19.5082	−0.768134
$646$	−2.50511	−0.0985624
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	20.4303	0.802579
$649$	22.2526	0.873489
$650$	−10.8079	−0.423919
$651$	38.6739	1.51575
$652$	−18.8846	−0.739580
$653$	50.4633	1.97478	0.987390	−	0.158308i	$-0.0506038\pi$
$653$	50.4633	1.97478	0.987390	+	0.158308i	$0.0506038\pi$
$654$	28.3634	1.10910
$655$	−20.8246	−0.813685
$656$	−11.1132	−0.433897
$657$	9.60808	0.374847
$658$	−12.2897	−0.479100
$659$	28.3173	1.10309	0.551544	−	0.834146i	$-0.314039\pi$
$659$	28.3173	1.10309	0.551544	+	0.834146i	$0.314039\pi$
$660$	−46.4742	−1.80900
$661$	−42.2504	−1.64335	−0.821675	−	0.569957i	$-0.806960\pi$
$661$	−42.2504	−1.64335	−0.821675	+	0.569957i	$0.806960\pi$
$662$	70.2085	2.72873
$663$	9.08442	0.352809
$664$	1.40939	0.0546948
$665$	13.9738	0.541882
$666$	27.5621	1.06801
$667$	7.46871	0.289190
$668$	−12.5566	−0.485829
$669$	65.5795	2.53545
$670$	−34.2766	−1.32422
$671$	46.9374	1.81200
$672$	70.2373	2.70946
$673$	0.873721	0.0336795	0.0168397	−	0.999858i	$-0.494639\pi$
$673$	0.873721	0.0336795	0.0168397	+	0.999858i	$0.494639\pi$
$674$	63.2820	2.43753
$675$	2.22270	0.0855516
$676$	54.2240	2.08554
$677$	16.2515	0.624595	0.312297	−	0.949984i	$-0.398901\pi$
$677$	16.2515	0.624595	0.312297	+	0.949984i	$0.398901\pi$
$678$	13.1921	0.506641
$679$	15.8421	0.607964
$680$	−2.71798	−0.104230
$681$	−15.7213	−0.602440
$682$	−32.2635	−1.23543
$683$	−21.8242	−0.835081	−0.417540	−	0.908658i	$-0.637108\pi$
$683$	−21.8242	−0.835081	−0.417540	+	0.908658i	$0.637108\pi$
$684$	−8.12628	−0.310716
$685$	−5.16814	−0.197465
$686$	−51.6004	−1.97011
$687$	64.8650	2.47475
$688$	−7.13828	−0.272144
$689$	75.6004	2.88015
$690$	−39.3108	−1.49654
$691$	34.7158	1.32065	0.660326	−	0.750979i	$-0.270418\pi$
$691$	34.7158	1.32065	0.660326	+	0.750979i	$0.270418\pi$
$692$	−41.9320	−1.59401
$693$	29.5895	1.12401
$694$	44.2635	1.68022
$695$	1.91013	0.0724552
$696$	7.53020	0.285432
$697$	−4.95268	−0.187596
$698$	−75.1900	−2.84598
$699$	−7.51582	−0.284274
$700$	−10.8079	−0.408498
$701$	−34.8606	−1.31667	−0.658334	−	0.752726i	$-0.728739\pi$
$701$	−34.8606	−1.31667	−0.658334	+	0.752726i	$0.728739\pi$
$702$	−31.9450	−1.20569
$703$	10.6829	0.402912
$704$	−46.5950	−1.75611
$705$	−5.68157	−0.213980
$706$	−63.1900	−2.37819
$707$	5.12628	0.192794
$708$	37.8002	1.42062
$709$	26.0288	0.977531	0.488766	−	0.872415i	$-0.337447\pi$
$709$	26.0288	0.977531	0.488766	+	0.872415i	$0.337447\pi$
$710$	4.46980	0.167748
$711$	−15.4633	−0.579917
$712$	2.69596	0.101035
$713$	−16.0000	−0.599205
$714$	15.4949	0.579882
$715$	42.2744	1.58097
$716$	19.7618	0.738534
$717$	−37.5346	−1.40175
$718$	−36.2700	−1.35359
$719$	25.2425	0.941388	0.470694	−	0.882297i	$-0.344004\pi$
$719$	25.2425	0.941388	0.470694	+	0.882297i	$0.344004\pi$
$720$	6.09880	0.227289
$721$	−1.51057	−0.0562567
$722$	36.4028	1.35477
$723$	1.77622	0.0660583
$724$	−16.5950	−0.616748
$725$	1.61917	0.0601346
$726$	−11.8816	−0.440966
$727$	29.1263	1.08023	0.540117	−	0.841590i	$-0.318380\pi$
$727$	29.1263	1.08023	0.540117	+	0.841590i	$0.318380\pi$
$728$	45.7213	1.69454
$729$	−3.52366	−0.130506
$730$	23.4135	0.866574
$731$	−3.18123	−0.117662
$732$	79.7322	2.94699
$733$	−25.9080	−0.956932	−0.478466	−	0.878106i	$-0.658807\pi$
$733$	−25.9080	−0.956932	−0.478466	+	0.878106i	$0.658807\pi$
$734$	10.0305	0.370234
$735$	−55.1437	−2.03401
$736$	−29.0582	−1.07110
$737$	−28.1317	−1.03625
$738$	−27.4028	−1.00871
$739$	−29.2162	−1.07473	−0.537367	−	0.843349i	$-0.680581\pi$
$739$	−29.2162	−1.07473	−0.537367	+	0.843349i	$0.680581\pi$
$740$	39.3778	1.44755
$741$	19.4818	0.715682
$742$	128.948	4.73384
$743$	2.78385	0.102129	0.0510647	−	0.998695i	$-0.483739\pi$
$743$	2.78385	0.102129	0.0510647	+	0.998695i	$0.483739\pi$
$744$	−16.1317	−0.591418
$745$	10.0419	0.367905
$746$	6.07241	0.222327
$747$	−1.40939	−0.0515667
$748$	−7.57861	−0.277101
$749$	73.8530	2.69853
$750$	−57.6609	−2.10548
$751$	−35.3479	−1.28986	−0.644931	−	0.764240i	$-0.723114\pi$
$751$	−35.3479	−1.28986	−0.644931	+	0.764240i	$0.723114\pi$
$752$	−2.07896	−0.0758117
$753$	39.0792	1.42412
$754$	−23.2711	−0.847484
$755$	−28.0572	−1.02110
$756$	−31.9450	−1.16183
$757$	38.7926	1.40994	0.704970	−	0.709237i	$-0.250960\pi$
$757$	38.7926	1.40994	0.704970	+	0.709237i	$0.250960\pi$
$758$	68.1450	2.47514
$759$	−32.2635	−1.17109
$760$	−5.82878	−0.211432
$761$	−23.4687	−0.850740	−0.425370	−	0.905020i	$-0.639856\pi$
$761$	−23.4687	−0.850740	−0.425370	+	0.905020i	$0.639856\pi$
$762$	−69.9189	−2.53289
$763$	−25.8002	−0.934031
$764$	−11.5577	−0.418142
$765$	2.71798	0.0982687
$766$	57.4556	2.07596
$767$	−34.3843	−1.24154
$768$	−8.91320	−0.321627
$769$	1.94722	0.0702185	0.0351093	−	0.999383i	$-0.488822\pi$
$769$	1.94722	0.0702185	0.0351093	+	0.999383i	$0.488822\pi$
$770$	72.1056	2.59850
$771$	−27.5764	−0.993141
$772$	42.5291	1.53066
$773$	49.3479	1.77492	0.887460	−	0.460884i	$-0.152468\pi$
$773$	49.3479	1.77492	0.887460	+	0.460884i	$0.152468\pi$
$774$	−17.6015	−0.632674
$775$	−3.46871	−0.124600
$776$	−6.60808	−0.237216
$777$	−66.0768	−2.37049
$778$	10.5950	0.379849
$779$	−10.6212	−0.380543
$780$	71.8111	2.57125
$781$	3.66849	0.131269
$782$	−6.41047	−0.229238
$783$	4.78584	0.171032
$784$	−20.1778	−0.720634
$785$	−10.5797	−0.377606
$786$	−49.5202	−1.76633
$787$	41.6914	1.48614	0.743069	−	0.669215i	$-0.233369\pi$
$787$	41.6914	1.48614	0.743069	+	0.669215i	$0.233369\pi$
$788$	−39.8661	−1.42017
$789$	61.0517	2.17350
$790$	−37.6818	−1.34066
$791$	−12.0000	−0.426671
$792$	−12.3424	−0.438569
$793$	−72.5270	−2.57551
$794$	24.1976	0.858741
$795$	59.6135	2.11427
$796$	29.5806	1.04846
$797$	12.6654	0.448632	0.224316	−	0.974516i	$-0.427985\pi$
$797$	12.6654	0.448632	0.224316	+	0.974516i	$0.427985\pi$
$798$	33.2292	1.17630
$799$	−0.926503	−0.0327773
$800$	−6.29966	−0.222727
$801$	−2.69596	−0.0952571
$802$	−29.0055	−1.02422
$803$	19.2162	0.678123
$804$	−47.7871	−1.68532
$805$	35.7584	1.26032
$806$	49.8530	1.75600
$807$	7.48180	0.263372
$808$	−2.13828	−0.0752245
$809$	24.8737	0.874513	0.437257	−	0.899337i	$-0.355950\pi$
$809$	24.8737	0.874513	0.437257	+	0.899337i	$0.355950\pi$
$810$	−49.7858	−1.74930
$811$	−11.4118	−0.400721	−0.200361	−	0.979722i	$-0.564211\pi$
$811$	−11.4118	−0.400721	−0.200361	+	0.979722i	$0.564211\pi$
$812$	−23.2711	−0.816656
$813$	−55.5610	−1.94861
$814$	55.1241	1.93210
$815$	13.5455	0.474478
$816$	2.62116	0.0917591
$817$	−6.82224	−0.238680
$818$	−65.9056	−2.30433
$819$	−45.7213	−1.59763
$820$	−39.1503	−1.36719
$821$	−45.0078	−1.57078	−0.785392	−	0.618998i	$-0.787539\pi$
$821$	−45.0078	−1.57078	−0.785392	+	0.618998i	$0.787539\pi$
$822$	−12.2897	−0.428651
$823$	19.5477	0.681389	0.340694	−	0.940174i	$-0.389338\pi$
$823$	19.5477	0.681389	0.340694	+	0.940174i	$0.389338\pi$
$824$	0.630093	0.0219503
$825$	−6.99454	−0.243519
$826$	−58.6478	−2.04062
$827$	33.7893	1.17497	0.587485	−	0.809235i	$-0.300118\pi$
$827$	33.7893	1.17497	0.587485	+	0.809235i	$0.300118\pi$
$828$	−20.7948	−0.722668
$829$	−27.1767	−0.943885	−0.471942	−	0.881629i	$-0.656447\pi$
$829$	−27.1767	−0.943885	−0.471942	+	0.881629i	$0.656447\pi$
$830$	−3.43448	−0.119212
$831$	−25.5686	−0.886965
$832$	71.9978	2.49608
$833$	−8.99237	−0.311567
$834$	4.54221	0.157284
$835$	9.00654	0.311684
$836$	−16.2526	−0.562106
$837$	−10.2526	−0.354380
$838$	66.6872	2.30367
$839$	−31.7058	−1.09461	−0.547303	−	0.836935i	$-0.684345\pi$
$839$	−31.7058	−1.09461	−0.547303	+	0.836935i	$0.684345\pi$
$840$	36.0528	1.24394
$841$	−25.5136	−0.879781
$842$	20.1187	0.693334
$843$	8.93959	0.307896
$844$	−15.2820	−0.526029
$845$	−38.8936	−1.33798
$846$	−5.12628	−0.176245
$847$	10.8079	0.371362
$848$	21.8133	0.749072
$849$	−29.0055	−0.995465
$850$	−1.38975	−0.0476682
$851$	27.3370	0.937099
$852$	6.23163	0.213492
$853$	45.5754	1.56047	0.780235	−	0.625486i	$-0.215099\pi$
$853$	45.5754	1.56047	0.780235	+	0.625486i	$0.215099\pi$
$854$	−123.706	−4.23313
$855$	5.82878	0.199340
$856$	−30.8057	−1.05292
$857$	−27.4567	−0.937903	−0.468952	−	0.883224i	$-0.655368\pi$
$857$	−27.4567	−0.937903	−0.468952	+	0.883224i	$0.655368\pi$
$858$	100.527	3.43193
$859$	7.84209	0.267569	0.133784	−	0.991010i	$-0.457287\pi$
$859$	7.84209	0.267569	0.133784	+	0.991010i	$0.457287\pi$
$860$	−25.1472	−0.857513
$861$	65.6951	2.23888
$862$	−87.8321	−2.99157
$863$	−11.0185	−0.375076	−0.187538	−	0.982257i	$-0.560051\pi$
$863$	−11.0185	−0.375076	−0.187538	+	0.982257i	$0.560051\pi$
$864$	−18.6201	−0.633468
$865$	30.0768	1.02264
$866$	−9.57644	−0.325421
$867$	−36.2096	−1.22974
$868$	49.8530	1.69212
$869$	−30.9265	−1.04911
$870$	−18.3501	−0.622125
$871$	43.4687	1.47288
$872$	10.7618	0.364442
$873$	6.60808	0.223650
$874$	−13.7474	−0.465014
$875$	52.4502	1.77314
$876$	32.6423	1.10288
$877$	−8.31167	−0.280665	−0.140333	−	0.990104i	$-0.544817\pi$
$877$	−8.31167	−0.280665	−0.140333	+	0.990104i	$0.544817\pi$
$878$	−34.3293	−1.15856
$879$	−55.7082	−1.87899
$880$	12.1976	0.411181
$881$	−1.61155	−0.0542944	−0.0271472	−	0.999631i	$-0.508642\pi$
$881$	−1.61155	−0.0542944	−0.0271472	+	0.999631i	$0.508642\pi$
$882$	−49.7542	−1.67531
$883$	50.7267	1.70709	0.853545	−	0.521019i	$-0.174448\pi$
$883$	50.7267	1.70709	0.853545	+	0.521019i	$0.174448\pi$
$884$	11.7103	0.393862
$885$	−27.1132	−0.911400
$886$	−10.6870	−0.359038
$887$	−4.80785	−0.161432	−0.0807159	−	0.996737i	$-0.525721\pi$
$887$	−4.80785	−0.161432	−0.0807159	+	0.996737i	$0.525721\pi$
$888$	27.5621	0.924922
$889$	63.6004	2.13309
$890$	−6.56968	−0.220216
$891$	−40.8606	−1.36888
$892$	84.5359	2.83047
$893$	−1.98691	−0.0664895
$894$	23.8792	0.798639
$895$	−14.1747	−0.473807
$896$	58.9134	1.96816
$897$	49.8530	1.66454
$898$	17.2999	0.577304
$899$	−7.46871	−0.249095
$900$	−4.50819	−0.150273
$901$	9.72127	0.323862
$902$	−54.8057	−1.82483
$903$	42.1976	1.40425
$904$	5.00546	0.166479
$905$	11.9032	0.395675
$906$	−66.7189	−2.21659
$907$	−25.2031	−0.836854	−0.418427	−	0.908250i	$-0.637418\pi$
$907$	−25.2031	−0.836854	−0.418427	+	0.908250i	$0.637418\pi$
$908$	−20.2656	−0.672539
$909$	2.13828	0.0709223
$910$	−111.416	−3.69342
$911$	33.7213	1.11724	0.558618	−	0.829425i	$-0.311332\pi$
$911$	33.7213	1.11724	0.558618	+	0.829425i	$0.311332\pi$
$912$	5.62116	0.186135
$913$	−2.81877	−0.0932877
$914$	−50.7027	−1.67710
$915$	−57.1900	−1.89064
$916$	83.6148	2.76271
$917$	45.0452	1.48752
$918$	−4.10773	−0.135575
$919$	−7.19215	−0.237247	−0.118624	−	0.992939i	$-0.537848\pi$
$919$	−7.19215	−0.237247	−0.118624	+	0.992939i	$0.537848\pi$
$920$	−14.9156	−0.491752
$921$	7.92104	0.261007
$922$	79.7322	2.62584
$923$	−5.66849	−0.186581
$924$	100.527	3.30709
$925$	5.92650	0.194862
$926$	−5.18430	−0.170367
$927$	−0.630093	−0.0206950
$928$	−13.5642	−0.445267
$929$	−14.9660	−0.491018	−0.245509	−	0.969394i	$-0.578955\pi$
$929$	−14.9660	−0.491018	−0.245509	+	0.969394i	$0.578955\pi$
$930$	39.3108	1.28905
$931$	−19.2844	−0.632021
$932$	−9.68833	−0.317352
$933$	−9.48964	−0.310677
$934$	−12.3712	−0.404798
$935$	5.43596	0.177775
$936$	19.0713	0.623366
$937$	−34.5400	−1.12837	−0.564187	−	0.825647i	$-0.690810\pi$
$937$	−34.5400	−1.12837	−0.564187	+	0.825647i	$0.690810\pi$
$938$	74.1427	2.42084
$939$	21.9001	0.714683
$940$	−7.32389	−0.238879
$941$	42.7553	1.39378	0.696891	−	0.717177i	$-0.254566\pi$
$941$	42.7553	1.39378	0.696891	+	0.717177i	$0.254566\pi$
$942$	−25.1581	−0.819696
$943$	−27.1791	−0.885072
$944$	−9.92104	−0.322902
$945$	22.9134	0.745373
$946$	−35.2031	−1.14455
$947$	−59.1043	−1.92063	−0.960315	−	0.278917i	$-0.910025\pi$
$947$	−59.1043	−1.92063	−0.960315	+	0.278917i	$0.910025\pi$
$948$	−52.5346	−1.70624
$949$	−29.6925	−0.963859
$950$	−2.98037	−0.0966959
$951$	20.6739	0.670399
$952$	5.87918	0.190545
$953$	31.2011	1.01070	0.505351	−	0.862914i	$-0.331363\pi$
$953$	31.2011	1.01070	0.505351	+	0.862914i	$0.331363\pi$
$954$	53.7871	1.74142
$955$	8.29005	0.268260
$956$	−48.3843	−1.56486
$957$	−15.0604	−0.486834
$958$	52.7686	1.70488
$959$	11.1791	0.360991
$960$	56.7727	1.83233
$961$	−15.0000	−0.483871
$962$	−85.1769	−2.74621
$963$	30.8057	0.992699
$964$	2.28965	0.0737447
$965$	−30.5051	−0.981994
$966$	85.0321	2.73586
$967$	6.72890	0.216387	0.108193	−	0.994130i	$-0.465493\pi$
$967$	6.72890	0.216387	0.108193	+	0.994130i	$0.465493\pi$
$968$	−4.50819	−0.144899
$969$	2.50511	0.0804759
$970$	16.1030	0.517035
$971$	−10.6259	−0.341002	−0.170501	−	0.985357i	$-0.554539\pi$
$971$	−10.6259	−0.341002	−0.170501	+	0.985357i	$0.554539\pi$
$972$	−47.6159	−1.52728
$973$	−4.13174	−0.132457
$974$	6.87372	0.220248
$975$	10.8079	0.346128
$976$	−20.9265	−0.669841
$977$	−19.3010	−0.617493	−0.308746	−	0.951144i	$-0.599909\pi$
$977$	−19.3010	−0.617493	−0.308746	+	0.951144i	$0.599909\pi$
$978$	32.2107	1.02998
$979$	−5.39192	−0.172327
$980$	−71.0835	−2.27068
$981$	−10.7618	−0.343599
$982$	2.62116	0.0836447
$983$	−12.9529	−0.413133	−0.206567	−	0.978433i	$-0.566229\pi$
$983$	−12.9529	−0.413133	−0.206567	+	0.978433i	$0.566229\pi$
$984$	−27.4028	−0.873571
$985$	28.5950	0.911112
$986$	−2.99237	−0.0952965
$987$	12.2897	0.391184
$988$	25.1132	0.798957
$989$	−17.4578	−0.555125
$990$	30.0768	0.955903
$991$	−26.7398	−0.849418	−0.424709	−	0.905330i	$-0.639624\pi$
$991$	−26.7398	−0.849418	−0.424709	+	0.905330i	$0.639624\pi$
$992$	29.0582	0.922600
$993$	−70.2085	−2.22800
$994$	−9.66849	−0.306666
$995$	−21.2175	−0.672638
$996$	−4.78822	−0.151721
$997$	25.6596	0.812646	0.406323	−	0.913729i	$-0.366811\pi$
$997$	25.6596	0.812646	0.406323	+	0.913729i	$0.366811\pi$
$998$	21.8397	0.691324
$999$	17.5171	0.554217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.a.a.1.1	✓	3
3.2	odd	2		639.2.a.h.1.3		3
4.3	odd	2		1136.2.a.h.1.1		3
5.4	even	2		1775.2.a.f.1.3		3
7.6	odd	2		3479.2.a.k.1.1		3
8.3	odd	2		4544.2.a.u.1.3		3
8.5	even	2		4544.2.a.r.1.1		3
11.10	odd	2		8591.2.a.g.1.3		3
71.70	odd	2		5041.2.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.a.a.1.1	✓	3	1.1	even	1	trivial
639.2.a.h.1.3		3	3.2	odd	2
1136.2.a.h.1.1		3	4.3	odd	2
1775.2.a.f.1.3		3	5.4	even	2
3479.2.a.k.1.1		3	7.6	odd	2
4544.2.a.r.1.1		3	8.5	even	2
4544.2.a.u.1.3		3	8.3	odd	2
5041.2.a.a.1.1		3	71.70	odd	2
8591.2.a.g.1.3		3	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19869 q^{2} +2.19869 q^{3} +2.83424 q^{4} -2.03293 q^{5} -4.83424 q^{6} +4.39738 q^{7} -1.83424 q^{8} +1.83424 q^{9} +O(q^{10})\)	\(q-2.19869 q^{2} +2.19869 q^{3} +2.83424 q^{4} -2.03293 q^{5} -4.83424 q^{6} +4.39738 q^{7} -1.83424 q^{8} +1.83424 q^{9} +4.46980 q^{10} +3.66849 q^{11} +6.23163 q^{12} -5.66849 q^{13} -9.66849 q^{14} -4.46980 q^{15} -1.63555 q^{16} -0.728896 q^{17} -4.03293 q^{18} -1.56314 q^{19} -5.76183 q^{20} +9.66849 q^{21} -8.06587 q^{22} -4.00000 q^{23} -4.03293 q^{24} -0.867178 q^{25} +12.4633 q^{26} -2.56314 q^{27} +12.4633 q^{28} -1.86718 q^{29} +9.82770 q^{30} +4.00000 q^{31} +7.26456 q^{32} +8.06587 q^{33} +1.60262 q^{34} -8.93959 q^{35} +5.19869 q^{36} -6.83424 q^{37} +3.43686 q^{38} -12.4633 q^{39} +3.72890 q^{40} +6.79476 q^{41} -21.2580 q^{42} +4.36445 q^{43} +10.3974 q^{44} -3.72890 q^{45} +8.79476 q^{46} +1.27110 q^{47} -3.59607 q^{48} +12.3370 q^{49} +1.90666 q^{50} -1.60262 q^{51} -16.0659 q^{52} -13.3370 q^{53} +5.63555 q^{54} -7.45779 q^{55} -8.06587 q^{56} -3.43686 q^{57} +4.10535 q^{58} +6.06587 q^{59} -12.6685 q^{60} +12.7948 q^{61} -8.79476 q^{62} +8.06587 q^{63} -12.7014 q^{64} +11.5237 q^{65} -17.7344 q^{66} -7.66849 q^{67} -2.06587 q^{68} -8.79476 q^{69} +19.6554 q^{70} +1.00000 q^{71} -3.36445 q^{72} +5.23817 q^{73} +15.0264 q^{74} -1.90666 q^{75} -4.43032 q^{76} +16.1317 q^{77} +27.4028 q^{78} -8.43032 q^{79} +3.32497 q^{80} -11.1383 q^{81} -14.9396 q^{82} -0.768374 q^{83} +27.4028 q^{84} +1.48180 q^{85} -9.59607 q^{86} -4.10535 q^{87} -6.72890 q^{88} -1.46980 q^{89} +8.19869 q^{90} -24.9265 q^{91} -11.3370 q^{92} +8.79476 q^{93} -2.79476 q^{94} +3.17776 q^{95} +15.9725 q^{96} +3.60262 q^{97} -27.1252 q^{98} +6.72890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - 9 q^{6} + 2 q^{7}+O(q^{10}) \) 3 * q - q^2 + q^3 + 3 * q^4 + 5 * q^5 - 9 * q^6 + 2 * q^7	\( 3 q - q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - 9 q^{6} + 2 q^{7} + 8 q^{10} + 2 q^{12} - 6 q^{13} - 18 q^{14} - 8 q^{15} - 5 q^{16} - 2 q^{17} - q^{18} + q^{19} - 6 q^{20} + 18 q^{21} - 2 q^{22} - 12 q^{23} - q^{24} + 14 q^{25} + 4 q^{26} - 2 q^{27} + 4 q^{28} + 11 q^{29} - 4 q^{30} + 12 q^{31} - 6 q^{32} + 2 q^{33} + 16 q^{34} - 16 q^{35} + 10 q^{36} - 15 q^{37} + 16 q^{38} - 4 q^{39} + 11 q^{40} - 2 q^{41} - 8 q^{42} + 13 q^{43} + 20 q^{44} - 11 q^{45} + 4 q^{46} + 4 q^{47} + 6 q^{48} + 15 q^{49} + 6 q^{50} - 16 q^{51} - 26 q^{52} - 18 q^{53} + 17 q^{54} - 22 q^{55} - 2 q^{56} - 16 q^{57} + 7 q^{58} - 4 q^{59} - 27 q^{60} + 16 q^{61} - 4 q^{62} + 2 q^{63} - 16 q^{64} + 12 q^{65} - 20 q^{66} - 12 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 3 q^{71} - 10 q^{72} + 27 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 4 q^{77} + 38 q^{78} - 3 q^{79} - 7 q^{80} - 17 q^{81} - 34 q^{82} - 19 q^{83} + 38 q^{84} - 6 q^{85} - 12 q^{86} - 7 q^{87} - 20 q^{88} + q^{89} + 19 q^{90} - 8 q^{91} - 12 q^{92} + 4 q^{93} + 14 q^{94} + 10 q^{95} + 26 q^{96} + 22 q^{97} - 9 q^{98} + 20 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^3 + 3 * q^4 + 5 * q^5 - 9 * q^6 + 2 * q^7 + 8 * q^10 + 2 * q^12 - 6 * q^13 - 18 * q^14 - 8 * q^15 - 5 * q^16 - 2 * q^17 - q^18 + q^19 - 6 * q^20 + 18 * q^21 - 2 * q^22 - 12 * q^23 - q^24 + 14 * q^25 + 4 * q^26 - 2 * q^27 + 4 * q^28 + 11 * q^29 - 4 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 16 * q^34 - 16 * q^35 + 10 * q^36 - 15 * q^37 + 16 * q^38 - 4 * q^39 + 11 * q^40 - 2 * q^41 - 8 * q^42 + 13 * q^43 + 20 * q^44 - 11 * q^45 + 4 * q^46 + 4 * q^47 + 6 * q^48 + 15 * q^49 + 6 * q^50 - 16 * q^51 - 26 * q^52 - 18 * q^53 + 17 * q^54 - 22 * q^55 - 2 * q^56 - 16 * q^57 + 7 * q^58 - 4 * q^59 - 27 * q^60 + 16 * q^61 - 4 * q^62 + 2 * q^63 - 16 * q^64 + 12 * q^65 - 20 * q^66 - 12 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 3 * q^71 - 10 * q^72 + 27 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 4 * q^77 + 38 * q^78 - 3 * q^79 - 7 * q^80 - 17 * q^81 - 34 * q^82 - 19 * q^83 + 38 * q^84 - 6 * q^85 - 12 * q^86 - 7 * q^87 - 20 * q^88 + q^89 + 19 * q^90 - 8 * q^91 - 12 * q^92 + 4 * q^93 + 14 * q^94 + 10 * q^95 + 26 * q^96 + 22 * q^97 - 9 * q^98 + 20 * q^99

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