LMFDB - Embedded newform 6015.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12396 q^{2} -1.00000 q^{3} +2.51122 q^{4} +1.00000 q^{5} +2.12396 q^{6} -2.76942 q^{7} -1.08582 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12396 q^{2} -1.00000 q^{3} +2.51122 q^{4} +1.00000 q^{5} +2.12396 q^{6} -2.76942 q^{7} -1.08582 q^{8} +1.00000 q^{9} -2.12396 q^{10} -5.65008 q^{11} -2.51122 q^{12} -1.69789 q^{13} +5.88214 q^{14} -1.00000 q^{15} -2.71621 q^{16} -3.25979 q^{17} -2.12396 q^{18} -4.88904 q^{19} +2.51122 q^{20} +2.76942 q^{21} +12.0006 q^{22} +5.29434 q^{23} +1.08582 q^{24} +1.00000 q^{25} +3.60625 q^{26} -1.00000 q^{27} -6.95462 q^{28} -1.71407 q^{29} +2.12396 q^{30} +6.93186 q^{31} +7.94076 q^{32} +5.65008 q^{33} +6.92368 q^{34} -2.76942 q^{35} +2.51122 q^{36} -2.99583 q^{37} +10.3841 q^{38} +1.69789 q^{39} -1.08582 q^{40} +3.44527 q^{41} -5.88214 q^{42} +12.8452 q^{43} -14.1886 q^{44} +1.00000 q^{45} -11.2450 q^{46} +0.298867 q^{47} +2.71621 q^{48} +0.669677 q^{49} -2.12396 q^{50} +3.25979 q^{51} -4.26377 q^{52} +10.8318 q^{53} +2.12396 q^{54} -5.65008 q^{55} +3.00708 q^{56} +4.88904 q^{57} +3.64061 q^{58} +2.80718 q^{59} -2.51122 q^{60} +7.75331 q^{61} -14.7230 q^{62} -2.76942 q^{63} -11.4335 q^{64} -1.69789 q^{65} -12.0006 q^{66} +12.7331 q^{67} -8.18606 q^{68} -5.29434 q^{69} +5.88214 q^{70} +10.1251 q^{71} -1.08582 q^{72} +10.1146 q^{73} +6.36304 q^{74} -1.00000 q^{75} -12.2775 q^{76} +15.6474 q^{77} -3.60625 q^{78} +5.00218 q^{79} -2.71621 q^{80} +1.00000 q^{81} -7.31763 q^{82} -14.4015 q^{83} +6.95462 q^{84} -3.25979 q^{85} -27.2827 q^{86} +1.71407 q^{87} +6.13495 q^{88} -16.9242 q^{89} -2.12396 q^{90} +4.70215 q^{91} +13.2953 q^{92} -6.93186 q^{93} -0.634782 q^{94} -4.88904 q^{95} -7.94076 q^{96} -9.33647 q^{97} -1.42237 q^{98} -5.65008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	−2.12396	−1.50187	−0.750935	−	0.660377i	$-0.770397\pi$
$2$	−2.12396	−1.50187	−0.750935	+	0.660377i	$0.770397\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.51122	1.25561
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.12396	0.867105
$7$	−2.76942	−1.04674	−0.523371	−	0.852105i	$-0.675326\pi$
$7$	−2.76942	−1.04674	−0.523371	+	0.852105i	$0.675326\pi$
$8$	−1.08582	−0.383894
$9$	1.00000	0.333333
$10$	−2.12396	−0.671656
$11$	−5.65008	−1.70356	−0.851782	−	0.523897i	$-0.824478\pi$
$11$	−5.65008	−1.70356	−0.851782	+	0.523897i	$0.824478\pi$
$12$	−2.51122	−0.724927
$13$	−1.69789	−0.470909	−0.235454	−	0.971885i	$-0.575658\pi$
$13$	−1.69789	−0.470909	−0.235454	+	0.971885i	$0.575658\pi$
$14$	5.88214	1.57207
$15$	−1.00000	−0.258199
$16$	−2.71621	−0.679052
$17$	−3.25979	−0.790615	−0.395308	−	0.918549i	$-0.629362\pi$
$17$	−3.25979	−0.790615	−0.395308	+	0.918549i	$0.629362\pi$
$18$	−2.12396	−0.500623
$19$	−4.88904	−1.12162	−0.560811	−	0.827944i	$-0.689511\pi$
$19$	−4.88904	−1.12162	−0.560811	+	0.827944i	$0.689511\pi$
$20$	2.51122	0.561526
$21$	2.76942	0.604337
$22$	12.0006	2.55853
$23$	5.29434	1.10395	0.551973	−	0.833862i	$-0.313875\pi$
$23$	5.29434	1.10395	0.551973	+	0.833862i	$0.313875\pi$
$24$	1.08582	0.221641
$25$	1.00000	0.200000
$26$	3.60625	0.707243
$27$	−1.00000	−0.192450
$28$	−6.95462	−1.31430
$29$	−1.71407	−0.318294	−0.159147	−	0.987255i	$-0.550874\pi$
$29$	−1.71407	−0.318294	−0.159147	+	0.987255i	$0.550874\pi$
$30$	2.12396	0.387781
$31$	6.93186	1.24500	0.622499	−	0.782621i	$-0.286117\pi$
$31$	6.93186	1.24500	0.622499	+	0.782621i	$0.286117\pi$
$32$	7.94076	1.40374
$33$	5.65008	0.983553
$34$	6.92368	1.18740
$35$	−2.76942	−0.468117
$36$	2.51122	0.418537
$37$	−2.99583	−0.492512	−0.246256	−	0.969205i	$-0.579200\pi$
$37$	−2.99583	−0.492512	−0.246256	+	0.969205i	$0.579200\pi$
$38$	10.3841	1.68453
$39$	1.69789	0.271879
$40$	−1.08582	−0.171683
$41$	3.44527	0.538061	0.269030	−	0.963132i	$-0.413297\pi$
$41$	3.44527	0.538061	0.269030	+	0.963132i	$0.413297\pi$
$42$	−5.88214	−0.907634
$43$	12.8452	1.95887	0.979437	−	0.201750i	$-0.0646628\pi$
$43$	12.8452	1.95887	0.979437	+	0.201750i	$0.0646628\pi$
$44$	−14.1886	−2.13901
$45$	1.00000	0.149071
$46$	−11.2450	−1.65798
$47$	0.298867	0.0435942	0.0217971	−	0.999762i	$-0.493061\pi$
$47$	0.298867	0.0435942	0.0217971	+	0.999762i	$0.493061\pi$
$48$	2.71621	0.392051
$49$	0.669677	0.0956681
$50$	−2.12396	−0.300374
$51$	3.25979	0.456462
$52$	−4.26377	−0.591278
$53$	10.8318	1.48787	0.743934	−	0.668253i	$-0.232958\pi$
$53$	10.8318	1.48787	0.743934	+	0.668253i	$0.232958\pi$
$54$	2.12396	0.289035
$55$	−5.65008	−0.761857
$56$	3.00708	0.401838
$57$	4.88904	0.647569
$58$	3.64061	0.478036
$59$	2.80718	0.365464	0.182732	−	0.983163i	$-0.441506\pi$
$59$	2.80718	0.365464	0.182732	+	0.983163i	$0.441506\pi$
$60$	−2.51122	−0.324197
$61$	7.75331	0.992709	0.496355	−	0.868120i	$-0.334672\pi$
$61$	7.75331	0.992709	0.496355	+	0.868120i	$0.334672\pi$
$62$	−14.7230	−1.86982
$63$	−2.76942	−0.348914
$64$	−11.4335	−1.42918
$65$	−1.69789	−0.210597
$66$	−12.0006	−1.47717
$67$	12.7331	1.55560	0.777801	−	0.628511i	$-0.216335\pi$
$67$	12.7331	1.55560	0.777801	+	0.628511i	$0.216335\pi$
$68$	−8.18606	−0.992705
$69$	−5.29434	−0.637364
$70$	5.88214	0.703051
$71$	10.1251	1.20163	0.600814	−	0.799389i	$-0.294843\pi$
$71$	10.1251	1.20163	0.600814	+	0.799389i	$0.294843\pi$
$72$	−1.08582	−0.127965
$73$	10.1146	1.18382	0.591912	−	0.806003i	$-0.298373\pi$
$73$	10.1146	1.18382	0.591912	+	0.806003i	$0.298373\pi$
$74$	6.36304	0.739688
$75$	−1.00000	−0.115470
$76$	−12.2775	−1.40832
$77$	15.6474	1.78319
$78$	−3.60625	−0.408327
$79$	5.00218	0.562789	0.281395	−	0.959592i	$-0.409203\pi$
$79$	5.00218	0.562789	0.281395	+	0.959592i	$0.409203\pi$
$80$	−2.71621	−0.303681
$81$	1.00000	0.111111
$82$	−7.31763	−0.808097
$83$	−14.4015	−1.58077	−0.790385	−	0.612610i	$-0.790120\pi$
$83$	−14.4015	−1.58077	−0.790385	+	0.612610i	$0.790120\pi$
$84$	6.95462	0.758812
$85$	−3.25979	−0.353574
$86$	−27.2827	−2.94197
$87$	1.71407	0.183767
$88$	6.13495	0.653988
$89$	−16.9242	−1.79396	−0.896980	−	0.442071i	$-0.854244\pi$
$89$	−16.9242	−1.79396	−0.896980	+	0.442071i	$0.854244\pi$
$90$	−2.12396	−0.223885
$91$	4.70215	0.492920
$92$	13.2953	1.38613
$93$	−6.93186	−0.718800
$94$	−0.634782	−0.0654728
$95$	−4.88904	−0.501605
$96$	−7.94076	−0.810451
$97$	−9.33647	−0.947975	−0.473987	−	0.880532i	$-0.657186\pi$
$97$	−9.33647	−0.947975	−0.473987	+	0.880532i	$0.657186\pi$
$98$	−1.42237	−0.143681
$99$	−5.65008	−0.567855
$100$	2.51122	0.251122
$101$	−12.3387	−1.22775	−0.613873	−	0.789405i	$-0.710389\pi$
$101$	−12.3387	−1.22775	−0.613873	+	0.789405i	$0.710389\pi$
$102$	−6.92368	−0.685546
$103$	1.86070	0.183340	0.0916701	−	0.995789i	$-0.470779\pi$
$103$	1.86070	0.183340	0.0916701	+	0.995789i	$0.470779\pi$
$104$	1.84359	0.180779
$105$	2.76942	0.270268
$106$	−23.0064	−2.23458
$107$	16.8131	1.62538	0.812690	−	0.582696i	$-0.198002\pi$
$107$	16.8131	1.62538	0.812690	+	0.582696i	$0.198002\pi$
$108$	−2.51122	−0.241642
$109$	−11.8097	−1.13117	−0.565584	−	0.824691i	$-0.691349\pi$
$109$	−11.8097	−1.13117	−0.565584	+	0.824691i	$0.691349\pi$
$110$	12.0006	1.14421
$111$	2.99583	0.284352
$112$	7.52232	0.710792
$113$	−4.22567	−0.397518	−0.198759	−	0.980048i	$-0.563691\pi$
$113$	−4.22567	−0.397518	−0.198759	+	0.980048i	$0.563691\pi$
$114$	−10.3841	−0.972564
$115$	5.29434	0.493700
$116$	−4.30440	−0.399653
$117$	−1.69789	−0.156970
$118$	−5.96235	−0.548879
$119$	9.02772	0.827570
$120$	1.08582	0.0991210
$121$	20.9234	1.90213
$122$	−16.4677	−1.49092
$123$	−3.44527	−0.310650
$124$	17.4074	1.56323
$125$	1.00000	0.0894427
$126$	5.88214	0.524023
$127$	−11.3893	−1.01064	−0.505319	−	0.862933i	$-0.668625\pi$
$127$	−11.3893	−1.01064	−0.505319	+	0.862933i	$0.668625\pi$
$128$	8.40275	0.742706
$129$	−12.8452	−1.13096
$130$	3.60625	0.316289
$131$	3.77710	0.330007	0.165003	−	0.986293i	$-0.447236\pi$
$131$	3.77710	0.330007	0.165003	+	0.986293i	$0.447236\pi$
$132$	14.1886	1.23496
$133$	13.5398	1.17405
$134$	−27.0447	−2.33631
$135$	−1.00000	−0.0860663
$136$	3.53953	0.303512
$137$	−12.0610	−1.03044	−0.515219	−	0.857059i	$-0.672289\pi$
$137$	−12.0610	−1.03044	−0.515219	+	0.857059i	$0.672289\pi$
$138$	11.2450	0.957237
$139$	−8.75546	−0.742629	−0.371314	−	0.928507i	$-0.621093\pi$
$139$	−8.75546	−0.742629	−0.371314	+	0.928507i	$0.621093\pi$
$140$	−6.95462	−0.587773
$141$	−0.298867	−0.0251691
$142$	−21.5053	−1.80469
$143$	9.59319	0.802223
$144$	−2.71621	−0.226351
$145$	−1.71407	−0.142345
$146$	−21.4830	−1.77795
$147$	−0.669677	−0.0552340
$148$	−7.52320	−0.618403
$149$	−15.7933	−1.29384	−0.646918	−	0.762560i	$-0.723942\pi$
$149$	−15.7933	−1.29384	−0.646918	+	0.762560i	$0.723942\pi$
$150$	2.12396	0.173421
$151$	14.4151	1.17309	0.586543	−	0.809918i	$-0.300489\pi$
$151$	14.4151	1.17309	0.586543	+	0.809918i	$0.300489\pi$
$152$	5.30860	0.430584
$153$	−3.25979	−0.263538
$154$	−33.2346	−2.67812
$155$	6.93186	0.556780
$156$	4.26377	0.341374
$157$	−2.66342	−0.212564	−0.106282	−	0.994336i	$-0.533895\pi$
$157$	−2.66342	−0.212564	−0.106282	+	0.994336i	$0.533895\pi$
$158$	−10.6244	−0.845236
$159$	−10.8318	−0.859021
$160$	7.94076	0.627772
$161$	−14.6622	−1.15555
$162$	−2.12396	−0.166874
$163$	15.5366	1.21692	0.608461	−	0.793584i	$-0.291787\pi$
$163$	15.5366	1.21692	0.608461	+	0.793584i	$0.291787\pi$
$164$	8.65184	0.675595
$165$	5.65008	0.439858
$166$	30.5883	2.37411
$167$	11.1516	0.862938	0.431469	−	0.902128i	$-0.357995\pi$
$167$	11.1516	0.862938	0.431469	+	0.902128i	$0.357995\pi$
$168$	−3.00708	−0.232001
$169$	−10.1172	−0.778245
$170$	6.92368	0.531022
$171$	−4.88904	−0.373874
$172$	32.2571	2.45958
$173$	−1.60083	−0.121709	−0.0608545	−	0.998147i	$-0.519383\pi$
$173$	−1.60083	−0.121709	−0.0608545	+	0.998147i	$0.519383\pi$
$174$	−3.64061	−0.275994
$175$	−2.76942	−0.209348
$176$	15.3468	1.15681
$177$	−2.80718	−0.211001
$178$	35.9464	2.69429
$179$	−18.3836	−1.37406	−0.687028	−	0.726631i	$-0.741085\pi$
$179$	−18.3836	−1.37406	−0.687028	+	0.726631i	$0.741085\pi$
$180$	2.51122	0.187175
$181$	−6.08709	−0.452450	−0.226225	−	0.974075i	$-0.572638\pi$
$181$	−6.08709	−0.452450	−0.226225	+	0.974075i	$0.572638\pi$
$182$	−9.98720	−0.740301
$183$	−7.75331	−0.573141
$184$	−5.74868	−0.423798
$185$	−2.99583	−0.220258
$186$	14.7230	1.07954
$187$	18.4181	1.34686
$188$	0.750520	0.0547373
$189$	2.76942	0.201446
$190$	10.3841	0.753345
$191$	−16.2081	−1.17278	−0.586390	−	0.810029i	$-0.699451\pi$
$191$	−16.2081	−1.17278	−0.586390	+	0.810029i	$0.699451\pi$
$192$	11.4335	0.825140
$193$	24.2287	1.74402	0.872009	−	0.489490i	$-0.162817\pi$
$193$	24.2287	1.74402	0.872009	+	0.489490i	$0.162817\pi$
$194$	19.8303	1.42373
$195$	1.69789	0.121588
$196$	1.68171	0.120122
$197$	4.46828	0.318352	0.159176	−	0.987250i	$-0.449116\pi$
$197$	4.46828	0.318352	0.159176	+	0.987250i	$0.449116\pi$
$198$	12.0006	0.852843
$199$	−23.2513	−1.64824	−0.824122	−	0.566413i	$-0.808331\pi$
$199$	−23.2513	−1.64824	−0.824122	+	0.566413i	$0.808331\pi$
$200$	−1.08582	−0.0767788
$201$	−12.7331	−0.898127
$202$	26.2069	1.84391
$203$	4.74696	0.333172
$204$	8.18606	0.573138
$205$	3.44527	0.240628
$206$	−3.95206	−0.275353
$207$	5.29434	0.367982
$208$	4.61181	0.319772
$209$	27.6235	1.91076
$210$	−5.88214	−0.405906
$211$	21.8383	1.50341	0.751705	−	0.659499i	$-0.229232\pi$
$211$	21.8383	1.50341	0.751705	+	0.659499i	$0.229232\pi$
$212$	27.2012	1.86818
$213$	−10.1251	−0.693760
$214$	−35.7103	−2.44111
$215$	12.8452	0.876035
$216$	1.08582	0.0738804
$217$	−19.1972	−1.30319
$218$	25.0835	1.69887
$219$	−10.1146	−0.683481
$220$	−14.1886	−0.956596
$221$	5.53475	0.372308
$222$	−6.36304	−0.427059
$223$	12.9807	0.869250	0.434625	−	0.900612i	$-0.356881\pi$
$223$	12.9807	0.869250	0.434625	+	0.900612i	$0.356881\pi$
$224$	−21.9913	−1.46935
$225$	1.00000	0.0666667
$226$	8.97518	0.597020
$227$	−4.17972	−0.277417	−0.138709	−	0.990333i	$-0.544295\pi$
$227$	−4.17972	−0.277417	−0.138709	+	0.990333i	$0.544295\pi$
$228$	12.2775	0.813095
$229$	13.2684	0.876803	0.438401	−	0.898779i	$-0.355545\pi$
$229$	13.2684	0.876803	0.438401	+	0.898779i	$0.355545\pi$
$230$	−11.2450	−0.741472
$231$	−15.6474	−1.02953
$232$	1.86116	0.122191
$233$	−14.6995	−0.962996	−0.481498	−	0.876447i	$-0.659907\pi$
$233$	−14.6995	−0.962996	−0.481498	+	0.876447i	$0.659907\pi$
$234$	3.60625	0.235748
$235$	0.298867	0.0194959
$236$	7.04946	0.458881
$237$	−5.00218	−0.324927
$238$	−19.1746	−1.24290
$239$	3.58467	0.231873	0.115936	−	0.993257i	$-0.463013\pi$
$239$	3.58467	0.231873	0.115936	+	0.993257i	$0.463013\pi$
$240$	2.71621	0.175331
$241$	−7.57922	−0.488220	−0.244110	−	0.969747i	$-0.578496\pi$
$241$	−7.57922	−0.488220	−0.244110	+	0.969747i	$0.578496\pi$
$242$	−44.4406	−2.85675
$243$	−1.00000	−0.0641500
$244$	19.4703	1.24646
$245$	0.669677	0.0427841
$246$	7.31763	0.466555
$247$	8.30103	0.528182
$248$	−7.52672	−0.477947
$249$	14.4015	0.912658
$250$	−2.12396	−0.134331
$251$	1.77677	0.112149	0.0560743	−	0.998427i	$-0.482142\pi$
$251$	1.77677	0.112149	0.0560743	+	0.998427i	$0.482142\pi$
$252$	−6.95462	−0.438100
$253$	−29.9134	−1.88064
$254$	24.1905	1.51785
$255$	3.25979	0.204136
$256$	5.01980	0.313737
$257$	−13.6420	−0.850965	−0.425483	−	0.904967i	$-0.639896\pi$
$257$	−13.6420	−0.850965	−0.425483	+	0.904967i	$0.639896\pi$
$258$	27.2827	1.69855
$259$	8.29671	0.515533
$260$	−4.26377	−0.264428
$261$	−1.71407	−0.106098
$262$	−8.02243	−0.495627
$263$	−10.1619	−0.626609	−0.313305	−	0.949653i	$-0.601436\pi$
$263$	−10.1619	−0.626609	−0.313305	+	0.949653i	$0.601436\pi$
$264$	−6.13495	−0.377580
$265$	10.8318	0.665395
$266$	−28.7580	−1.76327
$267$	16.9242	1.03574
$268$	31.9757	1.95323
$269$	−21.8244	−1.33066	−0.665329	−	0.746550i	$-0.731709\pi$
$269$	−21.8244	−1.33066	−0.665329	+	0.746550i	$0.731709\pi$
$270$	2.12396	0.129260
$271$	−3.76925	−0.228966	−0.114483	−	0.993425i	$-0.536521\pi$
$271$	−3.76925	−0.228966	−0.114483	+	0.993425i	$0.536521\pi$
$272$	8.85427	0.536869
$273$	−4.70215	−0.284587
$274$	25.6170	1.54758
$275$	−5.65008	−0.340713
$276$	−13.2953	−0.800281
$277$	−3.07480	−0.184747	−0.0923736	−	0.995724i	$-0.529445\pi$
$277$	−3.07480	−0.184747	−0.0923736	+	0.995724i	$0.529445\pi$
$278$	18.5963	1.11533
$279$	6.93186	0.414999
$280$	3.00708	0.179707
$281$	−16.8528	−1.00535	−0.502677	−	0.864474i	$-0.667652\pi$
$281$	−16.8528	−1.00535	−0.502677	+	0.864474i	$0.667652\pi$
$282$	0.634782	0.0378007
$283$	−21.0335	−1.25031	−0.625156	−	0.780500i	$-0.714965\pi$
$283$	−21.0335	−1.25031	−0.625156	+	0.780500i	$0.714965\pi$
$284$	25.4263	1.50878
$285$	4.88904	0.289602
$286$	−20.3756	−1.20483
$287$	−9.54139	−0.563211
$288$	7.94076	0.467914
$289$	−6.37377	−0.374928
$290$	3.64061	0.213784
$291$	9.33647	0.547314
$292$	25.4000	1.48642
$293$	−1.27909	−0.0747255	−0.0373627	−	0.999302i	$-0.511896\pi$
$293$	−1.27909	−0.0747255	−0.0373627	+	0.999302i	$0.511896\pi$
$294$	1.42237	0.0829542
$295$	2.80718	0.163440
$296$	3.25292	0.189072
$297$	5.65008	0.327851
$298$	33.5443	1.94317
$299$	−8.98918	−0.519858
$300$	−2.51122	−0.144985
$301$	−35.5737	−2.05044
$302$	−30.6172	−1.76182
$303$	12.3387	0.708840
$304$	13.2797	0.761640
$305$	7.75331	0.443953
$306$	6.92368	0.395800
$307$	−3.15036	−0.179801	−0.0899004	−	0.995951i	$-0.528655\pi$
$307$	−3.15036	−0.179801	−0.0899004	+	0.995951i	$0.528655\pi$
$308$	39.2942	2.23899
$309$	−1.86070	−0.105851
$310$	−14.7230	−0.836211
$311$	−11.5439	−0.654593	−0.327296	−	0.944922i	$-0.606138\pi$
$311$	−11.5439	−0.654593	−0.327296	+	0.944922i	$0.606138\pi$
$312$	−1.84359	−0.104373
$313$	13.4017	0.757507	0.378754	−	0.925498i	$-0.376353\pi$
$313$	13.4017	0.757507	0.378754	+	0.925498i	$0.376353\pi$
$314$	5.65700	0.319243
$315$	−2.76942	−0.156039
$316$	12.5616	0.706644
$317$	14.1733	0.796053	0.398026	−	0.917374i	$-0.369695\pi$
$317$	14.1733	0.796053	0.398026	+	0.917374i	$0.369695\pi$
$318$	23.0064	1.29014
$319$	9.68461	0.542234
$320$	−11.4335	−0.639150
$321$	−16.8131	−0.938414
$322$	31.1421	1.73548
$323$	15.9372	0.886772
$324$	2.51122	0.139512
$325$	−1.69789	−0.0941817
$326$	−32.9992	−1.82766
$327$	11.8097	0.653080
$328$	−3.74093	−0.206558
$329$	−0.827687	−0.0456319
$330$	−12.0006	−0.660610
$331$	21.2543	1.16824	0.584120	−	0.811667i	$-0.301440\pi$
$331$	21.2543	1.16824	0.584120	+	0.811667i	$0.301440\pi$
$332$	−36.1654	−1.98483
$333$	−2.99583	−0.164171
$334$	−23.6856	−1.29602
$335$	12.7331	0.695686
$336$	−7.52232	−0.410376
$337$	−1.39693	−0.0760957	−0.0380478	−	0.999276i	$-0.512114\pi$
$337$	−1.39693	−0.0760957	−0.0380478	+	0.999276i	$0.512114\pi$
$338$	21.4885	1.16882
$339$	4.22567	0.229507
$340$	−8.18606	−0.443951
$341$	−39.1656	−2.12093
$342$	10.3841	0.561510
$343$	17.5313	0.946602
$344$	−13.9475	−0.752000
$345$	−5.29434	−0.285038
$346$	3.40011	0.182791
$347$	−11.2603	−0.604485	−0.302243	−	0.953231i	$-0.597735\pi$
$347$	−11.2603	−0.604485	−0.302243	+	0.953231i	$0.597735\pi$
$348$	4.30440	0.230740
$349$	14.0961	0.754545	0.377272	−	0.926102i	$-0.376862\pi$
$349$	14.0961	0.754545	0.377272	+	0.926102i	$0.376862\pi$
$350$	5.88214	0.314414
$351$	1.69789	0.0906264
$352$	−44.8660	−2.39136
$353$	4.72334	0.251398	0.125699	−	0.992068i	$-0.459883\pi$
$353$	4.72334	0.251398	0.125699	+	0.992068i	$0.459883\pi$
$354$	5.96235	0.316895
$355$	10.1251	0.537384
$356$	−42.5004	−2.25252
$357$	−9.02772	−0.477798
$358$	39.0462	2.06365
$359$	−2.60691	−0.137588	−0.0687938	−	0.997631i	$-0.521915\pi$
$359$	−2.60691	−0.137588	−0.0687938	+	0.997631i	$0.521915\pi$
$360$	−1.08582	−0.0572275
$361$	4.90270	0.258037
$362$	12.9288	0.679521
$363$	−20.9234	−1.09819
$364$	11.8082	0.618915
$365$	10.1146	0.529422
$366$	16.4677	0.860783
$367$	−24.9076	−1.30017	−0.650084	−	0.759862i	$-0.725266\pi$
$367$	−24.9076	−1.30017	−0.650084	+	0.759862i	$0.725266\pi$
$368$	−14.3805	−0.749637
$369$	3.44527	0.179354
$370$	6.36304	0.330799
$371$	−29.9979	−1.55741
$372$	−17.4074	−0.902533
$373$	−22.7303	−1.17693	−0.588466	−	0.808522i	$-0.700268\pi$
$373$	−22.7303	−1.17693	−0.588466	+	0.808522i	$0.700268\pi$
$374$	−39.1193	−2.02281
$375$	−1.00000	−0.0516398
$376$	−0.324514	−0.0167355
$377$	2.91029	0.149887
$378$	−5.88214	−0.302545
$379$	31.8666	1.63688	0.818439	−	0.574594i	$-0.194840\pi$
$379$	31.8666	1.63688	0.818439	+	0.574594i	$0.194840\pi$
$380$	−12.2775	−0.629820
$381$	11.3893	0.583492
$382$	34.4255	1.76136
$383$	1.34896	0.0689289	0.0344644	−	0.999406i	$-0.489027\pi$
$383$	1.34896	0.0689289	0.0344644	+	0.999406i	$0.489027\pi$
$384$	−8.40275	−0.428801
$385$	15.6474	0.797467
$386$	−51.4608	−2.61929
$387$	12.8452	0.652958
$388$	−23.4459	−1.19029
$389$	31.2350	1.58368	0.791838	−	0.610731i	$-0.209124\pi$
$389$	31.2350	1.58368	0.791838	+	0.610731i	$0.209124\pi$
$390$	−3.60625	−0.182609
$391$	−17.2584	−0.872796
$392$	−0.727146	−0.0367264
$393$	−3.77710	−0.190530
$394$	−9.49047	−0.478123
$395$	5.00218	0.251687
$396$	−14.1886	−0.713004
$397$	23.4109	1.17496	0.587480	−	0.809239i	$-0.300120\pi$
$397$	23.4109	1.17496	0.587480	+	0.809239i	$0.300120\pi$
$398$	49.3850	2.47545
$399$	−13.5398	−0.677837
$400$	−2.71621	−0.135810
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	27.0447	1.34887
$403$	−11.7695	−0.586280
$404$	−30.9852	−1.54157
$405$	1.00000	0.0496904
$406$	−10.0824	−0.500380
$407$	16.9267	0.839025
$408$	−3.53953	−0.175233
$409$	10.0570	0.497285	0.248642	−	0.968595i	$-0.420016\pi$
$409$	10.0570	0.497285	0.248642	+	0.968595i	$0.420016\pi$
$410$	−7.31763	−0.361392
$411$	12.0610	0.594923
$412$	4.67263	0.230204
$413$	−7.77426	−0.382546
$414$	−11.2450	−0.552661
$415$	−14.4015	−0.706942
$416$	−13.4825	−0.661034
$417$	8.75546	0.428757
$418$	−58.6712	−2.86970
$419$	−17.0685	−0.833852	−0.416926	−	0.908940i	$-0.636893\pi$
$419$	−17.0685	−0.833852	−0.416926	+	0.908940i	$0.636893\pi$
$420$	6.95462	0.339351
$421$	29.8006	1.45239	0.726197	−	0.687486i	$-0.241286\pi$
$421$	29.8006	1.45239	0.726197	+	0.687486i	$0.241286\pi$
$422$	−46.3837	−2.25793
$423$	0.298867	0.0145314
$424$	−11.7614	−0.571184
$425$	−3.25979	−0.158123
$426$	21.5053	1.04194
$427$	−21.4721	−1.03911
$428$	42.2213	2.04085
$429$	−9.59319	−0.463164
$430$	−27.2827	−1.31569
$431$	31.8867	1.53593	0.767963	−	0.640494i	$-0.221270\pi$
$431$	31.8867	1.53593	0.767963	+	0.640494i	$0.221270\pi$
$432$	2.71621	0.130684
$433$	9.94943	0.478139	0.239070	−	0.971002i	$-0.423158\pi$
$433$	9.94943	0.478139	0.239070	+	0.971002i	$0.423158\pi$
$434$	40.7742	1.95722
$435$	1.71407	0.0821831
$436$	−29.6569	−1.42031
$437$	−25.8842	−1.23821
$438$	21.4830	1.02650
$439$	−16.6585	−0.795065	−0.397533	−	0.917588i	$-0.630133\pi$
$439$	−16.6585	−0.795065	−0.397533	+	0.917588i	$0.630133\pi$
$440$	6.13495	0.292472
$441$	0.669677	0.0318894
$442$	−11.7556	−0.559157
$443$	20.2662	0.962878	0.481439	−	0.876480i	$-0.340114\pi$
$443$	20.2662	0.962878	0.481439	+	0.876480i	$0.340114\pi$
$444$	7.52320	0.357035
$445$	−16.9242	−0.802283
$446$	−27.5705	−1.30550
$447$	15.7933	0.746996
$448$	31.6641	1.49599
$449$	18.7614	0.885406	0.442703	−	0.896668i	$-0.354020\pi$
$449$	18.7614	0.885406	0.442703	+	0.896668i	$0.354020\pi$
$450$	−2.12396	−0.100125
$451$	−19.4661	−0.916621
$452$	−10.6116	−0.499128
$453$	−14.4151	−0.677281
$454$	8.87756	0.416645
$455$	4.70215	0.220440
$456$	−5.30860	−0.248598
$457$	−6.54535	−0.306179	−0.153089	−	0.988212i	$-0.548922\pi$
$457$	−6.54535	−0.306179	−0.153089	+	0.988212i	$0.548922\pi$
$458$	−28.1817	−1.31684
$459$	3.25979	0.152154
$460$	13.2953	0.619895
$461$	−14.0361	−0.653725	−0.326863	−	0.945072i	$-0.605991\pi$
$461$	−14.0361	−0.653725	−0.326863	+	0.945072i	$0.605991\pi$
$462$	33.2346	1.54621
$463$	40.5795	1.88589	0.942944	−	0.332952i	$-0.108045\pi$
$463$	40.5795	1.88589	0.942944	+	0.332952i	$0.108045\pi$
$464$	4.65576	0.216138
$465$	−6.93186	−0.321457
$466$	31.2212	1.44629
$467$	25.1266	1.16272	0.581360	−	0.813646i	$-0.302521\pi$
$467$	25.1266	1.16272	0.581360	+	0.813646i	$0.302521\pi$
$468$	−4.26377	−0.197093
$469$	−35.2634	−1.62831
$470$	−0.634782	−0.0292803
$471$	2.66342	0.122724
$472$	−3.04808	−0.140299
$473$	−72.5764	−3.33707
$474$	10.6244	0.487997
$475$	−4.88904	−0.224324
$476$	22.6706	1.03911
$477$	10.8318	0.495956
$478$	−7.61370	−0.348243
$479$	−42.4869	−1.94128	−0.970638	−	0.240546i	$-0.922673\pi$
$479$	−42.4869	−1.94128	−0.970638	+	0.240546i	$0.922673\pi$
$480$	−7.94076	−0.362445
$481$	5.08658	0.231928
$482$	16.0980	0.733243
$483$	14.6622	0.667155
$484$	52.5433	2.38833
$485$	−9.33647	−0.423947
$486$	2.12396	0.0963449
$487$	−41.7211	−1.89056	−0.945281	−	0.326258i	$-0.894212\pi$
$487$	−41.7211	−1.89056	−0.945281	+	0.326258i	$0.894212\pi$
$488$	−8.41867	−0.381095
$489$	−15.5366	−0.702590
$490$	−1.42237	−0.0642561
$491$	2.75961	0.124539	0.0622696	−	0.998059i	$-0.480166\pi$
$491$	2.75961	0.124539	0.0622696	+	0.998059i	$0.480166\pi$
$492$	−8.65184	−0.390055
$493$	5.58749	0.251648
$494$	−17.6311	−0.793260
$495$	−5.65008	−0.253952
$496$	−18.8284	−0.845419
$497$	−28.0406	−1.25779
$498$	−30.5883	−1.37069
$499$	5.29940	0.237234	0.118617	−	0.992940i	$-0.462154\pi$
$499$	5.29940	0.237234	0.118617	+	0.992940i	$0.462154\pi$
$500$	2.51122	0.112305
$501$	−11.1516	−0.498217
$502$	−3.77379	−0.168433
$503$	−41.9937	−1.87241	−0.936204	−	0.351457i	$-0.885686\pi$
$503$	−41.9937	−1.87241	−0.936204	+	0.351457i	$0.885686\pi$
$504$	3.00708	0.133946
$505$	−12.3387	−0.549065
$506$	63.5351	2.82448
$507$	10.1172	0.449320
$508$	−28.6011	−1.26897
$509$	−8.41363	−0.372928	−0.186464	−	0.982462i	$-0.559703\pi$
$509$	−8.41363	−0.372928	−0.186464	+	0.982462i	$0.559703\pi$
$510$	−6.92368	−0.306586
$511$	−28.0115	−1.23916
$512$	−27.4674	−1.21390
$513$	4.88904	0.215856
$514$	28.9751	1.27804
$515$	1.86070	0.0819922
$516$	−32.2571	−1.42004
$517$	−1.68862	−0.0742655
$518$	−17.6219	−0.774263
$519$	1.60083	0.0702687
$520$	1.84359	0.0808468
$521$	−36.5402	−1.60085	−0.800427	−	0.599430i	$-0.795394\pi$
$521$	−36.5402	−1.60085	−0.800427	+	0.599430i	$0.795394\pi$
$522$	3.64061	0.159345
$523$	−37.8083	−1.65324	−0.826622	−	0.562758i	$-0.809740\pi$
$523$	−37.8083	−1.65324	−0.826622	+	0.562758i	$0.809740\pi$
$524$	9.48514	0.414360
$525$	2.76942	0.120867
$526$	21.5835	0.941085
$527$	−22.5964	−0.984314
$528$	−15.3468	−0.667884
$529$	5.03002	0.218697
$530$	−23.0064	−0.999336
$531$	2.80718	0.121821
$532$	34.0014	1.47415
$533$	−5.84967	−0.253377
$534$	−35.9464	−1.55555
$535$	16.8131	0.726892
$536$	−13.8259	−0.597186
$537$	18.3836	0.793312
$538$	46.3543	1.99848
$539$	−3.78373	−0.162977
$540$	−2.51122	−0.108066
$541$	−24.0344	−1.03332	−0.516660	−	0.856191i	$-0.672825\pi$
$541$	−24.0344	−1.03332	−0.516660	+	0.856191i	$0.672825\pi$
$542$	8.00576	0.343877
$543$	6.08709	0.261222
$544$	−25.8852	−1.10982
$545$	−11.8097	−0.505874
$546$	9.98720	0.427413
$547$	28.4455	1.21624	0.608122	−	0.793844i	$-0.291923\pi$
$547$	28.4455	1.21624	0.608122	+	0.793844i	$0.291923\pi$
$548$	−30.2877	−1.29383
$549$	7.75331	0.330903
$550$	12.0006	0.511706
$551$	8.38013	0.357006
$552$	5.74868	0.244680
$553$	−13.8531	−0.589095
$554$	6.53077	0.277466
$555$	2.99583	0.127166
$556$	−21.9869	−0.932452
$557$	−3.54864	−0.150361	−0.0751804	−	0.997170i	$-0.523953\pi$
$557$	−3.54864	−0.150361	−0.0751804	+	0.997170i	$0.523953\pi$
$558$	−14.7230	−0.623275
$559$	−21.8097	−0.922451
$560$	7.52232	0.317876
$561$	−18.4181	−0.777612
$562$	35.7948	1.50991
$563$	23.1140	0.974137	0.487069	−	0.873364i	$-0.338066\pi$
$563$	23.1140	0.974137	0.487069	+	0.873364i	$0.338066\pi$
$564$	−0.750520	−0.0316026
$565$	−4.22567	−0.177775
$566$	44.6744	1.87781
$567$	−2.76942	−0.116305
$568$	−10.9940	−0.461297
$569$	−29.8376	−1.25086	−0.625429	−	0.780281i	$-0.715076\pi$
$569$	−29.8376	−1.25086	−0.625429	+	0.780281i	$0.715076\pi$
$570$	−10.3841	−0.434944
$571$	−40.2520	−1.68449	−0.842247	−	0.539092i	$-0.818767\pi$
$571$	−40.2520	−1.68449	−0.842247	+	0.539092i	$0.818767\pi$
$572$	24.0906	1.00728
$573$	16.2081	0.677105
$574$	20.2656	0.845869
$575$	5.29434	0.220789
$576$	−11.4335	−0.476395
$577$	27.5172	1.14555	0.572777	−	0.819711i	$-0.305866\pi$
$577$	27.5172	1.14555	0.572777	+	0.819711i	$0.305866\pi$
$578$	13.5377	0.563092
$579$	−24.2287	−1.00691
$580$	−4.30440	−0.178730
$581$	39.8838	1.65466
$582$	−19.8303	−0.821993
$583$	−61.2008	−2.53468
$584$	−10.9826	−0.454463
$585$	−1.69789	−0.0701989
$586$	2.71675	0.112228
$587$	−0.482016	−0.0198949	−0.00994746	−	0.999951i	$-0.503166\pi$
$587$	−0.482016	−0.0198949	−0.00994746	+	0.999951i	$0.503166\pi$
$588$	−1.68171	−0.0693524
$589$	−33.8901	−1.39642
$590$	−5.96235	−0.245466
$591$	−4.46828	−0.183801
$592$	8.13731	0.334441
$593$	−10.6320	−0.436603	−0.218301	−	0.975881i	$-0.570052\pi$
$593$	−10.6320	−0.436603	−0.218301	+	0.975881i	$0.570052\pi$
$594$	−12.0006	−0.492389
$595$	9.02772	0.370100
$596$	−39.6604	−1.62455
$597$	23.2513	0.951614
$598$	19.0927	0.780758
$599$	−2.03412	−0.0831119	−0.0415560	−	0.999136i	$-0.513231\pi$
$599$	−2.03412	−0.0831119	−0.0415560	+	0.999136i	$0.513231\pi$
$600$	1.08582	0.0443283
$601$	−36.7319	−1.49832	−0.749162	−	0.662387i	$-0.769543\pi$
$601$	−36.7319	−1.49832	−0.749162	+	0.662387i	$0.769543\pi$
$602$	75.5573	3.07949
$603$	12.7331	0.518534
$604$	36.1996	1.47294
$605$	20.9234	0.850658
$606$	−26.2069	−1.06458
$607$	−17.1258	−0.695115	−0.347557	−	0.937659i	$-0.612989\pi$
$607$	−17.1258	−0.695115	−0.347557	+	0.937659i	$0.612989\pi$
$608$	−38.8227	−1.57447
$609$	−4.74696	−0.192357
$610$	−16.4677	−0.666759
$611$	−0.507441	−0.0205289
$612$	−8.18606	−0.330902
$613$	23.1614	0.935479	0.467740	−	0.883866i	$-0.345069\pi$
$613$	23.1614	0.935479	0.467740	+	0.883866i	$0.345069\pi$
$614$	6.69126	0.270037
$615$	−3.44527	−0.138927
$616$	−16.9902	−0.684556
$617$	−37.1142	−1.49416	−0.747081	−	0.664733i	$-0.768545\pi$
$617$	−37.1142	−1.49416	−0.747081	+	0.664733i	$0.768545\pi$
$618$	3.95206	0.158975
$619$	7.36525	0.296034	0.148017	−	0.988985i	$-0.452711\pi$
$619$	7.36525	0.296034	0.148017	+	0.988985i	$0.452711\pi$
$620$	17.4074	0.699099
$621$	−5.29434	−0.212455
$622$	24.5188	0.983112
$623$	46.8701	1.87781
$624$	−4.61181	−0.184620
$625$	1.00000	0.0400000
$626$	−28.4647	−1.13768
$627$	−27.6235	−1.10318
$628$	−6.68843	−0.266897
$629$	9.76578	0.389387
$630$	5.88214	0.234350
$631$	29.6041	1.17852	0.589259	−	0.807944i	$-0.299420\pi$
$631$	29.6041	1.17852	0.589259	+	0.807944i	$0.299420\pi$
$632$	−5.43145	−0.216051
$633$	−21.8383	−0.867994
$634$	−30.1036	−1.19557
$635$	−11.3893	−0.451971
$636$	−27.2012	−1.07860
$637$	−1.13703	−0.0450509
$638$	−20.5698	−0.814365
$639$	10.1251	0.400542
$640$	8.40275	0.332148
$641$	−33.9299	−1.34015	−0.670076	−	0.742293i	$-0.733738\pi$
$641$	−33.9299	−1.34015	−0.670076	+	0.742293i	$0.733738\pi$
$642$	35.7103	1.40937
$643$	25.9164	1.02204	0.511021	−	0.859568i	$-0.329267\pi$
$643$	25.9164	1.02204	0.511021	+	0.859568i	$0.329267\pi$
$644$	−36.8201	−1.45092
$645$	−12.8452	−0.505779
$646$	−33.8501	−1.33182
$647$	−13.8118	−0.542999	−0.271500	−	0.962439i	$-0.587520\pi$
$647$	−13.8118	−0.542999	−0.271500	+	0.962439i	$0.587520\pi$
$648$	−1.08582	−0.0426549
$649$	−15.8608	−0.622591
$650$	3.60625	0.141449
$651$	19.1972	0.752398
$652$	39.0159	1.52798
$653$	5.27149	0.206289	0.103145	−	0.994666i	$-0.467110\pi$
$653$	5.27149	0.206289	0.103145	+	0.994666i	$0.467110\pi$
$654$	−25.0835	−0.980841
$655$	3.77710	0.147584
$656$	−9.35807	−0.365371
$657$	10.1146	0.394608
$658$	1.75798	0.0685331
$659$	41.8860	1.63165	0.815823	−	0.578302i	$-0.196285\pi$
$659$	41.8860	1.63165	0.815823	+	0.578302i	$0.196285\pi$
$660$	14.1886	0.552291
$661$	18.9366	0.736550	0.368275	−	0.929717i	$-0.379949\pi$
$661$	18.9366	0.736550	0.368275	+	0.929717i	$0.379949\pi$
$662$	−45.1433	−1.75454
$663$	−5.53475	−0.214952
$664$	15.6374	0.606848
$665$	13.5398	0.525051
$666$	6.36304	0.246563
$667$	−9.07484	−0.351379
$668$	28.0042	1.08351
$669$	−12.9807	−0.501861
$670$	−27.0447	−1.04483
$671$	−43.8068	−1.69114
$672$	21.9913	0.848332
$673$	−6.96566	−0.268506	−0.134253	−	0.990947i	$-0.542864\pi$
$673$	−6.96566	−0.268506	−0.134253	+	0.990947i	$0.542864\pi$
$674$	2.96703	0.114286
$675$	−1.00000	−0.0384900
$676$	−25.4065	−0.977173
$677$	−15.4910	−0.595366	−0.297683	−	0.954665i	$-0.596214\pi$
$677$	−15.4910	−0.595366	−0.297683	+	0.954665i	$0.596214\pi$
$678$	−8.97518	−0.344690
$679$	25.8566	0.992285
$680$	3.53953	0.135735
$681$	4.17972	0.160167
$682$	83.1862	3.18536
$683$	29.8813	1.14338	0.571688	−	0.820471i	$-0.306289\pi$
$683$	29.8813	1.14338	0.571688	+	0.820471i	$0.306289\pi$
$684$	−12.2775	−0.469440
$685$	−12.0610	−0.460826
$686$	−37.2359	−1.42167
$687$	−13.2684	−0.506222
$688$	−34.8902	−1.33018
$689$	−18.3912	−0.700650
$690$	11.2450	0.428089
$691$	14.2759	0.543080	0.271540	−	0.962427i	$-0.412467\pi$
$691$	14.2759	0.543080	0.271540	+	0.962427i	$0.412467\pi$
$692$	−4.02004	−0.152819
$693$	15.6474	0.594397
$694$	23.9165	0.907858
$695$	−8.75546	−0.332114
$696$	−1.86116	−0.0705471
$697$	−11.2309	−0.425399
$698$	−29.9395	−1.13323
$699$	14.6995	0.555986
$700$	−6.95462	−0.262860
$701$	7.85997	0.296867	0.148433	−	0.988922i	$-0.452577\pi$
$701$	7.85997	0.296867	0.148433	+	0.988922i	$0.452577\pi$
$702$	−3.60625	−0.136109
$703$	14.6467	0.552412
$704$	64.6000	2.43471
$705$	−0.298867	−0.0112560
$706$	−10.0322	−0.377567
$707$	34.1710	1.28513
$708$	−7.04946	−0.264935
$709$	41.1449	1.54523	0.772614	−	0.634876i	$-0.218949\pi$
$709$	41.1449	1.54523	0.772614	+	0.634876i	$0.218949\pi$
$710$	−21.5053	−0.807080
$711$	5.00218	0.187596
$712$	18.3766	0.688690
$713$	36.6996	1.37441
$714$	19.1746	0.717590
$715$	9.59319	0.358765
$716$	−46.1654	−1.72528
$717$	−3.58467	−0.133872
$718$	5.53699	0.206639
$719$	38.9677	1.45325	0.726625	−	0.687034i	$-0.241088\pi$
$719$	38.9677	1.45325	0.726625	+	0.687034i	$0.241088\pi$
$720$	−2.71621	−0.101227
$721$	−5.15305	−0.191910
$722$	−10.4132	−0.387538
$723$	7.57922	0.281874
$724$	−15.2860	−0.568101
$725$	−1.71407	−0.0636588
$726$	44.4406	1.64934
$727$	−29.4865	−1.09359	−0.546797	−	0.837265i	$-0.684153\pi$
$727$	−29.4865	−1.09359	−0.546797	+	0.837265i	$0.684153\pi$
$728$	−5.10567	−0.189229
$729$	1.00000	0.0370370
$730$	−21.4830	−0.795122
$731$	−41.8726	−1.54872
$732$	−19.4703	−0.719642
$733$	−50.2923	−1.85759	−0.928795	−	0.370595i	$-0.879154\pi$
$733$	−50.2923	−1.85759	−0.928795	+	0.370595i	$0.879154\pi$
$734$	52.9029	1.95268
$735$	−0.669677	−0.0247014
$736$	42.0411	1.54965
$737$	−71.9433	−2.65007
$738$	−7.31763	−0.269366
$739$	20.4380	0.751823	0.375911	−	0.926656i	$-0.377330\pi$
$739$	20.4380	0.751823	0.375911	+	0.926656i	$0.377330\pi$
$740$	−7.52320	−0.276558
$741$	−8.30103	−0.304946
$742$	63.7145	2.33903
$743$	−18.8746	−0.692441	−0.346220	−	0.938153i	$-0.612535\pi$
$743$	−18.8746	−0.692441	−0.346220	+	0.938153i	$0.612535\pi$
$744$	7.52672	0.275943
$745$	−15.7933	−0.578621
$746$	48.2784	1.76760
$747$	−14.4015	−0.526923
$748$	46.2519	1.69114
$749$	−46.5624	−1.70135
$750$	2.12396	0.0775562
$751$	12.7094	0.463773	0.231886	−	0.972743i	$-0.425510\pi$
$751$	12.7094	0.463773	0.231886	+	0.972743i	$0.425510\pi$
$752$	−0.811784	−0.0296027
$753$	−1.77677	−0.0647490
$754$	−6.18134	−0.225111
$755$	14.4151	0.524620
$756$	6.95462	0.252937
$757$	−28.0101	−1.01805	−0.509023	−	0.860753i	$-0.669993\pi$
$757$	−28.0101	−1.01805	−0.509023	+	0.860753i	$0.669993\pi$
$758$	−67.6835	−2.45838
$759$	29.9134	1.08579
$760$	5.30860	0.192563
$761$	−12.2785	−0.445096	−0.222548	−	0.974922i	$-0.571437\pi$
$761$	−12.2785	−0.445096	−0.222548	+	0.974922i	$0.571437\pi$
$762$	−24.1905	−0.876329
$763$	32.7061	1.18404
$764$	−40.7023	−1.47256
$765$	−3.25979	−0.117858
$766$	−2.86515	−0.103522
$767$	−4.76627	−0.172100
$768$	−5.01980	−0.181136
$769$	−33.3828	−1.20381	−0.601907	−	0.798566i	$-0.705592\pi$
$769$	−33.3828	−1.20381	−0.601907	+	0.798566i	$0.705592\pi$
$770$	−33.2346	−1.19769
$771$	13.6420	0.491305
$772$	60.8435	2.18981
$773$	−2.01768	−0.0725711	−0.0362855	−	0.999341i	$-0.511553\pi$
$773$	−2.01768	−0.0725711	−0.0362855	+	0.999341i	$0.511553\pi$
$774$	−27.2827	−0.980658
$775$	6.93186	0.249000
$776$	10.1377	0.363922
$777$	−8.29671	−0.297643
$778$	−66.3420	−2.37847
$779$	−16.8441	−0.603501
$780$	4.26377	0.152667
$781$	−57.2076	−2.04705
$782$	36.6563	1.31083
$783$	1.71407	0.0612557
$784$	−1.81898	−0.0649636
$785$	−2.66342	−0.0950614
$786$	8.02243	0.286150
$787$	−19.5470	−0.696777	−0.348388	−	0.937350i	$-0.613271\pi$
$787$	−19.5470	−0.696777	−0.348388	+	0.937350i	$0.613271\pi$
$788$	11.2209	0.399726
$789$	10.1619	0.361773
$790$	−10.6244	−0.378001
$791$	11.7027	0.416099
$792$	6.13495	0.217996
$793$	−13.1642	−0.467475
$794$	−49.7239	−1.76463
$795$	−10.8318	−0.384166
$796$	−58.3893	−2.06955
$797$	42.9127	1.52005	0.760023	−	0.649896i	$-0.225188\pi$
$797$	42.9127	1.52005	0.760023	+	0.649896i	$0.225188\pi$
$798$	28.7580	1.01802
$799$	−0.974243	−0.0344662
$800$	7.94076	0.280748
$801$	−16.9242	−0.597987
$802$	−2.12396	−0.0749998
$803$	−57.1483	−2.01672
$804$	−31.9757	−1.12770
$805$	−14.6622	−0.516776
$806$	24.9980	0.880516
$807$	21.8244	0.768256
$808$	13.3976	0.471324
$809$	−40.9307	−1.43905	−0.719523	−	0.694468i	$-0.755640\pi$
$809$	−40.9307	−1.43905	−0.719523	+	0.694468i	$0.755640\pi$
$810$	−2.12396	−0.0746285
$811$	6.25467	0.219631	0.109816	−	0.993952i	$-0.464974\pi$
$811$	6.25467	0.219631	0.109816	+	0.993952i	$0.464974\pi$
$812$	11.9207	0.418334
$813$	3.76925	0.132193
$814$	−35.9517	−1.26011
$815$	15.5366	0.544224
$816$	−8.85427	−0.309962
$817$	−62.8007	−2.19712
$818$	−21.3606	−0.746856
$819$	4.70215	0.164307
$820$	8.65184	0.302135
$821$	−37.8756	−1.32187	−0.660933	−	0.750445i	$-0.729839\pi$
$821$	−37.8756	−1.32187	−0.660933	+	0.750445i	$0.729839\pi$
$822$	−25.6170	−0.893497
$823$	−25.2591	−0.880478	−0.440239	−	0.897881i	$-0.645106\pi$
$823$	−25.2591	−0.880478	−0.440239	+	0.897881i	$0.645106\pi$
$824$	−2.02038	−0.0703832
$825$	5.65008	0.196711
$826$	16.5122	0.574535
$827$	6.39455	0.222360	0.111180	−	0.993800i	$-0.464537\pi$
$827$	6.39455	0.222360	0.111180	+	0.993800i	$0.464537\pi$
$828$	13.2953	0.462042
$829$	−44.4423	−1.54355	−0.771773	−	0.635899i	$-0.780630\pi$
$829$	−44.4423	−1.54355	−0.771773	+	0.635899i	$0.780630\pi$
$830$	30.5883	1.06173
$831$	3.07480	0.106664
$832$	19.4127	0.673015
$833$	−2.18301	−0.0756367
$834$	−18.5963	−0.643937
$835$	11.1516	0.385917
$836$	69.3687	2.39917
$837$	−6.93186	−0.239600
$838$	36.2529	1.25234
$839$	−26.5393	−0.916240	−0.458120	−	0.888890i	$-0.651477\pi$
$839$	−26.5393	−0.916240	−0.458120	+	0.888890i	$0.651477\pi$
$840$	−3.00708	−0.103754
$841$	−26.0620	−0.898689
$842$	−63.2955	−2.18131
$843$	16.8528	0.580442
$844$	54.8408	1.88770
$845$	−10.1172	−0.348042
$846$	−0.634782	−0.0218243
$847$	−57.9457	−1.99104
$848$	−29.4216	−1.01034
$849$	21.0335	0.721868
$850$	6.92368	0.237480
$851$	−15.8610	−0.543706
$852$	−25.4263	−0.871092
$853$	−41.7254	−1.42865	−0.714325	−	0.699814i	$-0.753266\pi$
$853$	−41.7254	−1.42865	−0.714325	+	0.699814i	$0.753266\pi$
$854$	45.6061	1.56061
$855$	−4.88904	−0.167202
$856$	−18.2559	−0.623974
$857$	32.0526	1.09490	0.547448	−	0.836839i	$-0.315599\pi$
$857$	32.0526	1.09490	0.547448	+	0.836839i	$0.315599\pi$
$858$	20.3756	0.695611
$859$	12.1299	0.413867	0.206933	−	0.978355i	$-0.433652\pi$
$859$	12.1299	0.413867	0.206933	+	0.978355i	$0.433652\pi$
$860$	32.2571	1.09996
$861$	9.54139	0.325170
$862$	−67.7261	−2.30676
$863$	−15.9295	−0.542247	−0.271124	−	0.962545i	$-0.587395\pi$
$863$	−15.9295	−0.542247	−0.271124	+	0.962545i	$0.587395\pi$
$864$	−7.94076	−0.270150
$865$	−1.60083	−0.0544299
$866$	−21.1322	−0.718102
$867$	6.37377	0.216465
$868$	−48.2084	−1.63630
$869$	−28.2627	−0.958747
$870$	−3.64061	−0.123428
$871$	−21.6194	−0.732546
$872$	12.8232	0.434249
$873$	−9.33647	−0.315992
$874$	54.9772	1.85963
$875$	−2.76942	−0.0936234
$876$	−25.4000	−0.858186
$877$	12.5379	0.423374	0.211687	−	0.977338i	$-0.432104\pi$
$877$	12.5379	0.423374	0.211687	+	0.977338i	$0.432104\pi$
$878$	35.3820	1.19408
$879$	1.27909	0.0431428
$880$	15.3468	0.517341
$881$	49.5890	1.67070	0.835349	−	0.549720i	$-0.185266\pi$
$881$	49.5890	1.67070	0.835349	+	0.549720i	$0.185266\pi$
$882$	−1.42237	−0.0478937
$883$	33.9004	1.14084	0.570420	−	0.821353i	$-0.306780\pi$
$883$	33.9004	1.14084	0.570420	+	0.821353i	$0.306780\pi$
$884$	13.8990	0.467473
$885$	−2.80718	−0.0943624
$886$	−43.0448	−1.44612
$887$	13.6907	0.459690	0.229845	−	0.973227i	$-0.426178\pi$
$887$	13.6907	0.459690	0.229845	+	0.973227i	$0.426178\pi$
$888$	−3.25292	−0.109161
$889$	31.5418	1.05788
$890$	35.9464	1.20492
$891$	−5.65008	−0.189285
$892$	32.5973	1.09144
$893$	−1.46117	−0.0488962
$894$	−33.5443	−1.12189
$895$	−18.3836	−0.614497
$896$	−23.2707	−0.777421
$897$	8.98918	0.300140
$898$	−39.8486	−1.32976
$899$	−11.8817	−0.396275
$900$	2.51122	0.0837074
$901$	−35.3095	−1.17633
$902$	41.3452	1.37664
$903$	35.5737	1.18382
$904$	4.58830	0.152605
$905$	−6.08709	−0.202342
$906$	30.6172	1.01719
$907$	11.2288	0.372846	0.186423	−	0.982470i	$-0.440311\pi$
$907$	11.2288	0.372846	0.186423	+	0.982470i	$0.440311\pi$
$908$	−10.4962	−0.348328
$909$	−12.3387	−0.409249
$910$	−9.98720	−0.331073
$911$	42.7441	1.41617	0.708087	−	0.706125i	$-0.249558\pi$
$911$	42.7441	1.41617	0.708087	+	0.706125i	$0.249558\pi$
$912$	−13.2797	−0.439733
$913$	81.3697	2.69294
$914$	13.9021	0.459840
$915$	−7.75331	−0.256316
$916$	33.3200	1.10092
$917$	−10.4604	−0.345432
$918$	−6.92368	−0.228515
$919$	46.7934	1.54357	0.771787	−	0.635882i	$-0.219363\pi$
$919$	46.7934	1.54357	0.771787	+	0.635882i	$0.219363\pi$
$920$	−5.74868	−0.189528
$921$	3.15036	0.103808
$922$	29.8121	0.981810
$923$	−17.1912	−0.565857
$924$	−39.2942	−1.29268
$925$	−2.99583	−0.0985024
$926$	−86.1893	−2.83236
$927$	1.86070	0.0611134
$928$	−13.6110	−0.446803
$929$	47.7010	1.56502	0.782509	−	0.622639i	$-0.213940\pi$
$929$	47.7010	1.56502	0.782509	+	0.622639i	$0.213940\pi$
$930$	14.7230	0.482787
$931$	−3.27408	−0.107303
$932$	−36.9137	−1.20915
$933$	11.5439	0.377929
$934$	−53.3680	−1.74625
$935$	18.4181	0.602336
$936$	1.84359	0.0602597
$937$	17.4957	0.571559	0.285779	−	0.958295i	$-0.407748\pi$
$937$	17.4957	0.571559	0.285779	+	0.958295i	$0.407748\pi$
$938$	74.8982	2.44551
$939$	−13.4017	−0.437347
$940$	0.750520	0.0244793
$941$	49.4030	1.61049	0.805245	−	0.592942i	$-0.202034\pi$
$941$	49.4030	1.61049	0.805245	+	0.592942i	$0.202034\pi$
$942$	−5.65700	−0.184315
$943$	18.2404	0.593990
$944$	−7.62489	−0.248169
$945$	2.76942	0.0900892
$946$	154.150	5.01184
$947$	1.06656	0.0346585	0.0173292	−	0.999850i	$-0.494484\pi$
$947$	1.06656	0.0346585	0.0173292	+	0.999850i	$0.494484\pi$
$948$	−12.5616	−0.407981
$949$	−17.1734	−0.557473
$950$	10.3841	0.336906
$951$	−14.1733	−0.459601
$952$	−9.80245	−0.317699
$953$	46.5371	1.50748	0.753742	−	0.657171i	$-0.228247\pi$
$953$	46.5371	1.50748	0.753742	+	0.657171i	$0.228247\pi$
$954$	−23.0064	−0.744861
$955$	−16.2081	−0.524483
$956$	9.00189	0.291142
$957$	−9.68461	−0.313059
$958$	90.2406	2.91554
$959$	33.4018	1.07860
$960$	11.4335	0.369014
$961$	17.0506	0.550020
$962$	−10.8037	−0.348326
$963$	16.8131	0.541793
$964$	−19.0331	−0.613015
$965$	24.2287	0.779948
$966$	−31.1421	−1.00198
$967$	−55.6655	−1.79008	−0.895041	−	0.445984i	$-0.852854\pi$
$967$	−55.6655	−1.79008	−0.895041	+	0.445984i	$0.852854\pi$
$968$	−22.7190	−0.730216
$969$	−15.9372	−0.511978
$970$	19.8303	0.636713
$971$	−20.3022	−0.651529	−0.325765	−	0.945451i	$-0.605622\pi$
$971$	−20.3022	−0.651529	−0.325765	+	0.945451i	$0.605622\pi$
$972$	−2.51122	−0.0805475
$973$	24.2475	0.777340
$974$	88.6140	2.83938
$975$	1.69789	0.0543758
$976$	−21.0596	−0.674102
$977$	6.67842	0.213662	0.106831	−	0.994277i	$-0.465930\pi$
$977$	6.67842	0.213662	0.106831	+	0.994277i	$0.465930\pi$
$978$	32.9992	1.05520
$979$	95.6230	3.05613
$980$	1.68171	0.0537202
$981$	−11.8097	−0.377056
$982$	−5.86130	−0.187042
$983$	−22.6862	−0.723578	−0.361789	−	0.932260i	$-0.617834\pi$
$983$	−22.6862	−0.723578	−0.361789	+	0.932260i	$0.617834\pi$
$984$	3.74093	0.119256
$985$	4.46828	0.142371
$986$	−11.8676	−0.377942
$987$	0.827687	0.0263456
$988$	20.8457	0.663191
$989$	68.0068	2.16249
$990$	12.0006	0.381403
$991$	−23.0067	−0.730833	−0.365416	−	0.930844i	$-0.619073\pi$
$991$	−23.0067	−0.730833	−0.365416	+	0.930844i	$0.619073\pi$
$992$	55.0442	1.74766
$993$	−21.2543	−0.674484
$994$	59.5572	1.88904
$995$	−23.2513	−0.737117
$996$	36.1654	1.14594
$997$	−0.899142	−0.0284761	−0.0142381	−	0.999899i	$-0.504532\pi$
$997$	−0.899142	−0.0284761	−0.0142381	+	0.999899i	$0.504532\pi$
$998$	−11.2557	−0.356294
$999$	2.99583	0.0947839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.6	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.6	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12396 q^{2} -1.00000 q^{3} +2.51122 q^{4} +1.00000 q^{5} +2.12396 q^{6} -2.76942 q^{7} -1.08582 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12396 q^{2} -1.00000 q^{3} +2.51122 q^{4} +1.00000 q^{5} +2.12396 q^{6} -2.76942 q^{7} -1.08582 q^{8} +1.00000 q^{9} -2.12396 q^{10} -5.65008 q^{11} -2.51122 q^{12} -1.69789 q^{13} +5.88214 q^{14} -1.00000 q^{15} -2.71621 q^{16} -3.25979 q^{17} -2.12396 q^{18} -4.88904 q^{19} +2.51122 q^{20} +2.76942 q^{21} +12.0006 q^{22} +5.29434 q^{23} +1.08582 q^{24} +1.00000 q^{25} +3.60625 q^{26} -1.00000 q^{27} -6.95462 q^{28} -1.71407 q^{29} +2.12396 q^{30} +6.93186 q^{31} +7.94076 q^{32} +5.65008 q^{33} +6.92368 q^{34} -2.76942 q^{35} +2.51122 q^{36} -2.99583 q^{37} +10.3841 q^{38} +1.69789 q^{39} -1.08582 q^{40} +3.44527 q^{41} -5.88214 q^{42} +12.8452 q^{43} -14.1886 q^{44} +1.00000 q^{45} -11.2450 q^{46} +0.298867 q^{47} +2.71621 q^{48} +0.669677 q^{49} -2.12396 q^{50} +3.25979 q^{51} -4.26377 q^{52} +10.8318 q^{53} +2.12396 q^{54} -5.65008 q^{55} +3.00708 q^{56} +4.88904 q^{57} +3.64061 q^{58} +2.80718 q^{59} -2.51122 q^{60} +7.75331 q^{61} -14.7230 q^{62} -2.76942 q^{63} -11.4335 q^{64} -1.69789 q^{65} -12.0006 q^{66} +12.7331 q^{67} -8.18606 q^{68} -5.29434 q^{69} +5.88214 q^{70} +10.1251 q^{71} -1.08582 q^{72} +10.1146 q^{73} +6.36304 q^{74} -1.00000 q^{75} -12.2775 q^{76} +15.6474 q^{77} -3.60625 q^{78} +5.00218 q^{79} -2.71621 q^{80} +1.00000 q^{81} -7.31763 q^{82} -14.4015 q^{83} +6.95462 q^{84} -3.25979 q^{85} -27.2827 q^{86} +1.71407 q^{87} +6.13495 q^{88} -16.9242 q^{89} -2.12396 q^{90} +4.70215 q^{91} +13.2953 q^{92} -6.93186 q^{93} -0.634782 q^{94} -4.88904 q^{95} -7.94076 q^{96} -9.33647 q^{97} -1.42237 q^{98} -5.65008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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