LMFDB - Embedded newform 6014.2.a.j.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.676893 q^{3} +1.00000 q^{4} -1.03316 q^{5} +0.676893 q^{6} -4.68414 q^{7} -1.00000 q^{8} -2.54182 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.676893 q^{3} +1.00000 q^{4} -1.03316 q^{5} +0.676893 q^{6} -4.68414 q^{7} -1.00000 q^{8} -2.54182 q^{9} +1.03316 q^{10} +2.09740 q^{11} -0.676893 q^{12} -1.94293 q^{13} +4.68414 q^{14} +0.699341 q^{15} +1.00000 q^{16} -6.82829 q^{17} +2.54182 q^{18} +6.24007 q^{19} -1.03316 q^{20} +3.17066 q^{21} -2.09740 q^{22} +1.71772 q^{23} +0.676893 q^{24} -3.93258 q^{25} +1.94293 q^{26} +3.75122 q^{27} -4.68414 q^{28} -9.13307 q^{29} -0.699341 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.41971 q^{33} +6.82829 q^{34} +4.83947 q^{35} -2.54182 q^{36} -9.78807 q^{37} -6.24007 q^{38} +1.31516 q^{39} +1.03316 q^{40} +1.10064 q^{41} -3.17066 q^{42} -2.63096 q^{43} +2.09740 q^{44} +2.62611 q^{45} -1.71772 q^{46} -7.44970 q^{47} -0.676893 q^{48} +14.9411 q^{49} +3.93258 q^{50} +4.62203 q^{51} -1.94293 q^{52} -4.00354 q^{53} -3.75122 q^{54} -2.16695 q^{55} +4.68414 q^{56} -4.22386 q^{57} +9.13307 q^{58} -5.02353 q^{59} +0.699341 q^{60} -7.97165 q^{61} +1.00000 q^{62} +11.9062 q^{63} +1.00000 q^{64} +2.00736 q^{65} +1.41971 q^{66} -13.7779 q^{67} -6.82829 q^{68} -1.16272 q^{69} -4.83947 q^{70} -4.07104 q^{71} +2.54182 q^{72} -9.43471 q^{73} +9.78807 q^{74} +2.66193 q^{75} +6.24007 q^{76} -9.82450 q^{77} -1.31516 q^{78} +3.37471 q^{79} -1.03316 q^{80} +5.08627 q^{81} -1.10064 q^{82} -8.51126 q^{83} +3.17066 q^{84} +7.05474 q^{85} +2.63096 q^{86} +6.18211 q^{87} -2.09740 q^{88} -14.7939 q^{89} -2.62611 q^{90} +9.10095 q^{91} +1.71772 q^{92} +0.676893 q^{93} +7.44970 q^{94} -6.44701 q^{95} +0.676893 q^{96} +1.00000 q^{97} -14.9411 q^{98} -5.33120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.676893	−0.390804	−0.195402	−	0.980723i	$-0.562601\pi$
$3$	−0.676893	−0.390804	−0.195402	+	0.980723i	$0.562601\pi$
$4$	1.00000	0.500000
$5$	−1.03316	−0.462044	−0.231022	−	0.972948i	$-0.574207\pi$
$5$	−1.03316	−0.462044	−0.231022	+	0.972948i	$0.574207\pi$
$6$	0.676893	0.276340
$7$	−4.68414	−1.77044	−0.885218	−	0.465176i	$-0.845991\pi$
$7$	−4.68414	−1.77044	−0.885218	+	0.465176i	$0.845991\pi$
$8$	−1.00000	−0.353553
$9$	−2.54182	−0.847272
$10$	1.03316	0.326715
$11$	2.09740	0.632389	0.316195	−	0.948694i	$-0.397595\pi$
$11$	2.09740	0.632389	0.316195	+	0.948694i	$0.397595\pi$
$12$	−0.676893	−0.195402
$13$	−1.94293	−0.538872	−0.269436	−	0.963018i	$-0.586837\pi$
$13$	−1.94293	−0.538872	−0.269436	+	0.963018i	$0.586837\pi$
$14$	4.68414	1.25189
$15$	0.699341	0.180569
$16$	1.00000	0.250000
$17$	−6.82829	−1.65610	−0.828052	−	0.560651i	$-0.810551\pi$
$17$	−6.82829	−1.65610	−0.828052	+	0.560651i	$0.810551\pi$
$18$	2.54182	0.599112
$19$	6.24007	1.43157	0.715785	−	0.698321i	$-0.246069\pi$
$19$	6.24007	1.43157	0.715785	+	0.698321i	$0.246069\pi$
$20$	−1.03316	−0.231022
$21$	3.17066	0.691895
$22$	−2.09740	−0.447167
$23$	1.71772	0.358170	0.179085	−	0.983834i	$-0.442686\pi$
$23$	1.71772	0.358170	0.179085	+	0.983834i	$0.442686\pi$
$24$	0.676893	0.138170
$25$	−3.93258	−0.786515
$26$	1.94293	0.381040
$27$	3.75122	0.721922
$28$	−4.68414	−0.885218
$29$	−9.13307	−1.69597	−0.847984	−	0.530021i	$-0.822184\pi$
$29$	−9.13307	−1.69597	−0.847984	+	0.530021i	$0.822184\pi$
$30$	−0.699341	−0.127682
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−1.41971	−0.247141
$34$	6.82829	1.17104
$35$	4.83947	0.818020
$36$	−2.54182	−0.423636
$37$	−9.78807	−1.60915	−0.804574	−	0.593852i	$-0.797606\pi$
$37$	−9.78807	−1.60915	−0.804574	+	0.593852i	$0.797606\pi$
$38$	−6.24007	−1.01227
$39$	1.31516	0.210594
$40$	1.03316	0.163357
$41$	1.10064	0.171891	0.0859453	−	0.996300i	$-0.472609\pi$
$41$	1.10064	0.171891	0.0859453	+	0.996300i	$0.472609\pi$
$42$	−3.17066	−0.489243
$43$	−2.63096	−0.401218	−0.200609	−	0.979671i	$-0.564292\pi$
$43$	−2.63096	−0.401218	−0.200609	+	0.979671i	$0.564292\pi$
$44$	2.09740	0.316195
$45$	2.62611	0.391477
$46$	−1.71772	−0.253265
$47$	−7.44970	−1.08665	−0.543325	−	0.839522i	$-0.682835\pi$
$47$	−7.44970	−1.08665	−0.543325	+	0.839522i	$0.682835\pi$
$48$	−0.676893	−0.0977011
$49$	14.9411	2.13445
$50$	3.93258	0.556150
$51$	4.62203	0.647213
$52$	−1.94293	−0.269436
$53$	−4.00354	−0.549929	−0.274964	−	0.961454i	$-0.588666\pi$
$53$	−4.00354	−0.549929	−0.274964	+	0.961454i	$0.588666\pi$
$54$	−3.75122	−0.510476
$55$	−2.16695	−0.292192
$56$	4.68414	0.625944
$57$	−4.22386	−0.559464
$58$	9.13307	1.19923
$59$	−5.02353	−0.654008	−0.327004	−	0.945023i	$-0.606039\pi$
$59$	−5.02353	−0.654008	−0.327004	+	0.945023i	$0.606039\pi$
$60$	0.699341	0.0902845
$61$	−7.97165	−1.02067	−0.510333	−	0.859977i	$-0.670478\pi$
$61$	−7.97165	−1.02067	−0.510333	+	0.859977i	$0.670478\pi$
$62$	1.00000	0.127000
$63$	11.9062	1.50004
$64$	1.00000	0.125000
$65$	2.00736	0.248983
$66$	1.41971	0.174755
$67$	−13.7779	−1.68324	−0.841622	−	0.540067i	$-0.818399\pi$
$67$	−13.7779	−1.68324	−0.841622	+	0.540067i	$0.818399\pi$
$68$	−6.82829	−0.828052
$69$	−1.16272	−0.139975
$70$	−4.83947	−0.578428
$71$	−4.07104	−0.483144	−0.241572	−	0.970383i	$-0.577663\pi$
$71$	−4.07104	−0.483144	−0.241572	+	0.970383i	$0.577663\pi$
$72$	2.54182	0.299556
$73$	−9.43471	−1.10425	−0.552125	−	0.833762i	$-0.686183\pi$
$73$	−9.43471	−1.10425	−0.552125	+	0.833762i	$0.686183\pi$
$74$	9.78807	1.13784
$75$	2.66193	0.307374
$76$	6.24007	0.715785
$77$	−9.82450	−1.11961
$78$	−1.31516	−0.148912
$79$	3.37471	0.379684	0.189842	−	0.981815i	$-0.439202\pi$
$79$	3.37471	0.379684	0.189842	+	0.981815i	$0.439202\pi$
$80$	−1.03316	−0.115511
$81$	5.08627	0.565142
$82$	−1.10064	−0.121545
$83$	−8.51126	−0.934233	−0.467116	−	0.884196i	$-0.654707\pi$
$83$	−8.51126	−0.934233	−0.467116	+	0.884196i	$0.654707\pi$
$84$	3.17066	0.345947
$85$	7.05474	0.765194
$86$	2.63096	0.283704
$87$	6.18211	0.662792
$88$	−2.09740	−0.223583
$89$	−14.7939	−1.56815	−0.784073	−	0.620669i	$-0.786861\pi$
$89$	−14.7939	−1.56815	−0.784073	+	0.620669i	$0.786861\pi$
$90$	−2.62611	−0.276816
$91$	9.10095	0.954039
$92$	1.71772	0.179085
$93$	0.676893	0.0701906
$94$	7.44970	0.768378
$95$	−6.44701	−0.661449
$96$	0.676893	0.0690851
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−14.9411	−1.50928
$99$	−5.33120	−0.535806
$100$	−3.93258	−0.393258
$101$	−5.72953	−0.570110	−0.285055	−	0.958511i	$-0.592012\pi$
$101$	−5.72953	−0.570110	−0.285055	+	0.958511i	$0.592012\pi$
$102$	−4.62203	−0.457649
$103$	−17.8400	−1.75782	−0.878912	−	0.476984i	$-0.841730\pi$
$103$	−17.8400	−1.75782	−0.878912	+	0.476984i	$0.841730\pi$
$104$	1.94293	0.190520
$105$	−3.27581	−0.319686
$106$	4.00354	0.388858
$107$	−3.67900	−0.355662	−0.177831	−	0.984061i	$-0.556908\pi$
$107$	−3.67900	−0.355662	−0.177831	+	0.984061i	$0.556908\pi$
$108$	3.75122	0.360961
$109$	8.05773	0.771790	0.385895	−	0.922543i	$-0.373893\pi$
$109$	8.05773	0.771790	0.385895	+	0.922543i	$0.373893\pi$
$110$	2.16695	0.206611
$111$	6.62548	0.628862
$112$	−4.68414	−0.442609
$113$	−11.2510	−1.05841	−0.529203	−	0.848495i	$-0.677509\pi$
$113$	−11.2510	−1.05841	−0.529203	+	0.848495i	$0.677509\pi$
$114$	4.22386	0.395601
$115$	−1.77469	−0.165491
$116$	−9.13307	−0.847984
$117$	4.93857	0.456571
$118$	5.02353	0.462454
$119$	31.9846	2.93203
$120$	−0.699341	−0.0638408
$121$	−6.60092	−0.600084
$122$	7.97165	0.721719
$123$	−0.745014	−0.0671756
$124$	−1.00000	−0.0898027
$125$	9.22880	0.825449
$126$	−11.9062	−1.06069
$127$	12.9459	1.14876	0.574380	−	0.818589i	$-0.305243\pi$
$127$	12.9459	1.14876	0.574380	+	0.818589i	$0.305243\pi$
$128$	−1.00000	−0.0883883
$129$	1.78088	0.156798
$130$	−2.00736	−0.176057
$131$	19.0446	1.66393	0.831966	−	0.554826i	$-0.187215\pi$
$131$	19.0446	1.66393	0.831966	+	0.554826i	$0.187215\pi$
$132$	−1.41971	−0.123570
$133$	−29.2293	−2.53450
$134$	13.7779	1.19023
$135$	−3.87562	−0.333560
$136$	6.82829	0.585521
$137$	7.98441	0.682155	0.341077	−	0.940035i	$-0.389208\pi$
$137$	7.98441	0.682155	0.341077	+	0.940035i	$0.389208\pi$
$138$	1.16272	0.0989769
$139$	8.18254	0.694034	0.347017	−	0.937859i	$-0.387195\pi$
$139$	8.18254	0.694034	0.347017	+	0.937859i	$0.387195\pi$
$140$	4.83947	0.409010
$141$	5.04265	0.424668
$142$	4.07104	0.341634
$143$	−4.07510	−0.340777
$144$	−2.54182	−0.211818
$145$	9.43594	0.783613
$146$	9.43471	0.780822
$147$	−10.1135	−0.834151
$148$	−9.78807	−0.804574
$149$	13.6294	1.11657	0.558283	−	0.829651i	$-0.311460\pi$
$149$	13.6294	1.11657	0.558283	+	0.829651i	$0.311460\pi$
$150$	−2.66193	−0.217346
$151$	−4.39230	−0.357441	−0.178720	−	0.983900i	$-0.557196\pi$
$151$	−4.39230	−0.357441	−0.178720	+	0.983900i	$0.557196\pi$
$152$	−6.24007	−0.506136
$153$	17.3563	1.40317
$154$	9.82450	0.791681
$155$	1.03316	0.0829856
$156$	1.31516	0.105297
$157$	0.212538	0.0169624	0.00848120	−	0.999964i	$-0.497300\pi$
$157$	0.212538	0.0169624	0.00848120	+	0.999964i	$0.497300\pi$
$158$	−3.37471	−0.268477
$159$	2.70997	0.214915
$160$	1.03316	0.0816787
$161$	−8.04605	−0.634118
$162$	−5.08627	−0.399615
$163$	24.3992	1.91109	0.955547	−	0.294839i	$-0.0952659\pi$
$163$	24.3992	1.91109	0.955547	+	0.294839i	$0.0952659\pi$
$164$	1.10064	0.0859453
$165$	1.46680	0.114190
$166$	8.51126	0.660602
$167$	16.0251	1.24006	0.620029	−	0.784579i	$-0.287121\pi$
$167$	16.0251	1.24006	0.620029	+	0.784579i	$0.287121\pi$
$168$	−3.17066	−0.244622
$169$	−9.22502	−0.709617
$170$	−7.05474	−0.541074
$171$	−15.8611	−1.21293
$172$	−2.63096	−0.200609
$173$	8.93933	0.679645	0.339822	−	0.940490i	$-0.389633\pi$
$173$	8.93933	0.679645	0.339822	+	0.940490i	$0.389633\pi$
$174$	−6.18211	−0.468665
$175$	18.4207	1.39248
$176$	2.09740	0.158097
$177$	3.40039	0.255589
$178$	14.7939	1.10885
$179$	17.1178	1.27944	0.639721	−	0.768607i	$-0.279050\pi$
$179$	17.1178	1.27944	0.639721	+	0.768607i	$0.279050\pi$
$180$	2.62611	0.195739
$181$	−3.79844	−0.282336	−0.141168	−	0.989986i	$-0.545086\pi$
$181$	−3.79844	−0.282336	−0.141168	+	0.989986i	$0.545086\pi$
$182$	−9.10095	−0.674607
$183$	5.39596	0.398881
$184$	−1.71772	−0.126632
$185$	10.1127	0.743498
$186$	−0.676893	−0.0496322
$187$	−14.3217	−1.04730
$188$	−7.44970	−0.543325
$189$	−17.5712	−1.27812
$190$	6.44701	0.467715
$191$	−24.2047	−1.75139	−0.875696	−	0.482862i	$-0.839597\pi$
$191$	−24.2047	−1.75139	−0.875696	+	0.482862i	$0.839597\pi$
$192$	−0.676893	−0.0488506
$193$	−22.7547	−1.63792	−0.818960	−	0.573851i	$-0.805449\pi$
$193$	−22.7547	−1.63792	−0.818960	+	0.573851i	$0.805449\pi$
$194$	−1.00000	−0.0717958
$195$	−1.35877	−0.0973036
$196$	14.9411	1.06722
$197$	13.1965	0.940215	0.470108	−	0.882609i	$-0.344215\pi$
$197$	13.1965	0.940215	0.470108	+	0.882609i	$0.344215\pi$
$198$	5.33120	0.378872
$199$	5.97376	0.423468	0.211734	−	0.977327i	$-0.432089\pi$
$199$	5.97376	0.423468	0.211734	+	0.977327i	$0.432089\pi$
$200$	3.93258	0.278075
$201$	9.32619	0.657819
$202$	5.72953	0.403129
$203$	42.7805	3.00260
$204$	4.62203	0.323606
$205$	−1.13714	−0.0794211
$206$	17.8400	1.24297
$207$	−4.36614	−0.303468
$208$	−1.94293	−0.134718
$209$	13.0879	0.905310
$210$	3.27581	0.226052
$211$	−3.49845	−0.240843	−0.120422	−	0.992723i	$-0.538425\pi$
$211$	−3.49845	−0.240843	−0.120422	+	0.992723i	$0.538425\pi$
$212$	−4.00354	−0.274964
$213$	2.75566	0.188815
$214$	3.67900	0.251491
$215$	2.71821	0.185380
$216$	−3.75122	−0.255238
$217$	4.68414	0.317980
$218$	−8.05773	−0.545738
$219$	6.38629	0.431545
$220$	−2.16695	−0.146096
$221$	13.2669	0.892428
$222$	−6.62548	−0.444673
$223$	0.296483	0.0198539	0.00992697	−	0.999951i	$-0.496840\pi$
$223$	0.296483	0.0198539	0.00992697	+	0.999951i	$0.496840\pi$
$224$	4.68414	0.312972
$225$	9.99588	0.666392
$226$	11.2510	0.748406
$227$	−4.61006	−0.305980	−0.152990	−	0.988228i	$-0.548890\pi$
$227$	−4.61006	−0.305980	−0.152990	+	0.988228i	$0.548890\pi$
$228$	−4.22386	−0.279732
$229$	12.5511	0.829400	0.414700	−	0.909958i	$-0.363887\pi$
$229$	12.5511	0.829400	0.414700	+	0.909958i	$0.363887\pi$
$230$	1.77469	0.117019
$231$	6.65014	0.437547
$232$	9.13307	0.599615
$233$	21.1750	1.38722	0.693611	−	0.720350i	$-0.256019\pi$
$233$	21.1750	1.38722	0.693611	+	0.720350i	$0.256019\pi$
$234$	−4.93857	−0.322845
$235$	7.69675	0.502080
$236$	−5.02353	−0.327004
$237$	−2.28432	−0.148382
$238$	−31.9846	−2.07326
$239$	−14.3853	−0.930508	−0.465254	−	0.885177i	$-0.654037\pi$
$239$	−14.3853	−0.930508	−0.465254	+	0.885177i	$0.654037\pi$
$240$	0.699341	0.0451422
$241$	−14.8831	−0.958705	−0.479352	−	0.877623i	$-0.659128\pi$
$241$	−14.8831	−0.958705	−0.479352	+	0.877623i	$0.659128\pi$
$242$	6.60092	0.424323
$243$	−14.6965	−0.942782
$244$	−7.97165	−0.510333
$245$	−15.4366	−0.986209
$246$	0.745014	0.0475004
$247$	−12.1240	−0.771433
$248$	1.00000	0.0635001
$249$	5.76122	0.365102
$250$	−9.22880	−0.583681
$251$	−13.2219	−0.834560	−0.417280	−	0.908778i	$-0.637017\pi$
$251$	−13.2219	−0.834560	−0.417280	+	0.908778i	$0.637017\pi$
$252$	11.9062	0.750021
$253$	3.60275	0.226503
$254$	−12.9459	−0.812296
$255$	−4.77530	−0.299041
$256$	1.00000	0.0625000
$257$	−10.0408	−0.626325	−0.313162	−	0.949700i	$-0.601388\pi$
$257$	−10.0408	−0.626325	−0.313162	+	0.949700i	$0.601388\pi$
$258$	−1.78088	−0.110873
$259$	45.8486	2.84890
$260$	2.00736	0.124491
$261$	23.2146	1.43695
$262$	−19.0446	−1.17658
$263$	−18.0985	−1.11600	−0.558000	−	0.829841i	$-0.688431\pi$
$263$	−18.0985	−1.11600	−0.558000	+	0.829841i	$0.688431\pi$
$264$	1.41971	0.0873774
$265$	4.13631	0.254092
$266$	29.2293	1.79217
$267$	10.0139	0.612838
$268$	−13.7779	−0.841622
$269$	−11.6703	−0.711551	−0.355776	−	0.934571i	$-0.615783\pi$
$269$	−11.6703	−0.711551	−0.355776	+	0.934571i	$0.615783\pi$
$270$	3.87562	0.235863
$271$	8.38919	0.509607	0.254804	−	0.966993i	$-0.417989\pi$
$271$	8.38919	0.509607	0.254804	+	0.966993i	$0.417989\pi$
$272$	−6.82829	−0.414026
$273$	−6.16037	−0.372843
$274$	−7.98441	−0.482356
$275$	−8.24818	−0.497384
$276$	−1.16272	−0.0699873
$277$	0.0834203	0.00501224	0.00250612	−	0.999997i	$-0.499202\pi$
$277$	0.0834203	0.00501224	0.00250612	+	0.999997i	$0.499202\pi$
$278$	−8.18254	−0.490756
$279$	2.54182	0.152175
$280$	−4.83947	−0.289214
$281$	−17.4241	−1.03943	−0.519716	−	0.854339i	$-0.673962\pi$
$281$	−17.4241	−1.03943	−0.519716	+	0.854339i	$0.673962\pi$
$282$	−5.04265	−0.300285
$283$	−2.54318	−0.151176	−0.0755882	−	0.997139i	$-0.524083\pi$
$283$	−2.54318	−0.151176	−0.0755882	+	0.997139i	$0.524083\pi$
$284$	−4.07104	−0.241572
$285$	4.36393	0.258497
$286$	4.07510	0.240966
$287$	−5.15553	−0.304322
$288$	2.54182	0.149778
$289$	29.6256	1.74268
$290$	−9.43594	−0.554098
$291$	−0.676893	−0.0396802
$292$	−9.43471	−0.552125
$293$	−19.5176	−1.14023	−0.570114	−	0.821566i	$-0.693101\pi$
$293$	−19.5176	−1.14023	−0.570114	+	0.821566i	$0.693101\pi$
$294$	10.1135	0.589834
$295$	5.19013	0.302181
$296$	9.78807	0.568920
$297$	7.86780	0.456536
$298$	−13.6294	−0.789531
$299$	−3.33742	−0.193008
$300$	2.66193	0.153687
$301$	12.3238	0.710331
$302$	4.39230	0.252749
$303$	3.87828	0.222802
$304$	6.24007	0.357893
$305$	8.23601	0.471593
$306$	−17.3563	−0.992191
$307$	33.4564	1.90946	0.954729	−	0.297476i	$-0.0961450\pi$
$307$	33.4564	1.90946	0.954729	+	0.297476i	$0.0961450\pi$
$308$	−9.82450	−0.559803
$309$	12.0758	0.686966
$310$	−1.03316	−0.0586797
$311$	−33.0997	−1.87691	−0.938457	−	0.345396i	$-0.887744\pi$
$311$	−33.0997	−1.87691	−0.938457	+	0.345396i	$0.887744\pi$
$312$	−1.31516	−0.0744561
$313$	14.9703	0.846172	0.423086	−	0.906090i	$-0.360947\pi$
$313$	14.9703	0.846172	0.423086	+	0.906090i	$0.360947\pi$
$314$	−0.212538	−0.0119942
$315$	−12.3010	−0.693085
$316$	3.37471	0.189842
$317$	−10.4540	−0.587156	−0.293578	−	0.955935i	$-0.594846\pi$
$317$	−10.4540	−0.587156	−0.293578	+	0.955935i	$0.594846\pi$
$318$	−2.70997	−0.151968
$319$	−19.1557	−1.07251
$320$	−1.03316	−0.0577555
$321$	2.49029	0.138994
$322$	8.04605	0.448389
$323$	−42.6090	−2.37083
$324$	5.08627	0.282571
$325$	7.64072	0.423831
$326$	−24.3992	−1.35135
$327$	−5.45422	−0.301619
$328$	−1.10064	−0.0607725
$329$	34.8954	1.92384
$330$	−1.46680	−0.0807445
$331$	18.0120	0.990027	0.495014	−	0.868885i	$-0.335163\pi$
$331$	18.0120	0.990027	0.495014	+	0.868885i	$0.335163\pi$
$332$	−8.51126	−0.467116
$333$	24.8795	1.36339
$334$	−16.0251	−0.876854
$335$	14.2349	0.777733
$336$	3.17066	0.172974
$337$	1.87629	0.102208	0.0511041	−	0.998693i	$-0.483726\pi$
$337$	1.87629	0.102208	0.0511041	+	0.998693i	$0.483726\pi$
$338$	9.22502	0.501775
$339$	7.61573	0.413630
$340$	7.05474	0.382597
$341$	−2.09740	−0.113580
$342$	15.8611	0.857670
$343$	−37.1973	−2.00846
$344$	2.63096	0.141852
$345$	1.20127	0.0646744
$346$	−8.93933	−0.480581
$347$	25.3191	1.35920	0.679602	−	0.733581i	$-0.262153\pi$
$347$	25.3191	1.35920	0.679602	+	0.733581i	$0.262153\pi$
$348$	6.18211	0.331396
$349$	−20.3148	−1.08743	−0.543714	−	0.839271i	$-0.682982\pi$
$349$	−20.3148	−1.08743	−0.543714	+	0.839271i	$0.682982\pi$
$350$	−18.4207	−0.984629
$351$	−7.28836	−0.389024
$352$	−2.09740	−0.111792
$353$	36.2634	1.93011	0.965053	−	0.262055i	$-0.0844002\pi$
$353$	36.2634	1.93011	0.965053	+	0.262055i	$0.0844002\pi$
$354$	−3.40039	−0.180729
$355$	4.20605	0.223234
$356$	−14.7939	−0.784073
$357$	−21.6502	−1.14585
$358$	−17.1178	−0.904702
$359$	−1.15786	−0.0611093	−0.0305546	−	0.999533i	$-0.509727\pi$
$359$	−1.15786	−0.0611093	−0.0305546	+	0.999533i	$0.509727\pi$
$360$	−2.62611	−0.138408
$361$	19.9385	1.04939
$362$	3.79844	0.199642
$363$	4.46812	0.234515
$364$	9.10095	0.477019
$365$	9.74759	0.510212
$366$	−5.39596	−0.282051
$367$	24.4430	1.27591	0.637957	−	0.770072i	$-0.279780\pi$
$367$	24.4430	1.27591	0.637957	+	0.770072i	$0.279780\pi$
$368$	1.71772	0.0895426
$369$	−2.79762	−0.145638
$370$	−10.1127	−0.525732
$371$	18.7531	0.973614
$372$	0.676893	0.0350953
$373$	−2.20531	−0.114186	−0.0570932	−	0.998369i	$-0.518183\pi$
$373$	−2.20531	−0.114186	−0.0570932	+	0.998369i	$0.518183\pi$
$374$	14.3217	0.740555
$375$	−6.24691	−0.322589
$376$	7.44970	0.384189
$377$	17.7449	0.913910
$378$	17.5712	0.903765
$379$	9.96658	0.511949	0.255974	−	0.966684i	$-0.417604\pi$
$379$	9.96658	0.511949	0.255974	+	0.966684i	$0.417604\pi$
$380$	−6.44701	−0.330724
$381$	−8.76297	−0.448940
$382$	24.2047	1.23842
$383$	−29.7602	−1.52067	−0.760336	−	0.649530i	$-0.774966\pi$
$383$	−29.7602	−1.52067	−0.760336	+	0.649530i	$0.774966\pi$
$384$	0.676893	0.0345426
$385$	10.1503	0.517307
$386$	22.7547	1.15818
$387$	6.68742	0.339941
$388$	1.00000	0.0507673
$389$	26.8800	1.36287	0.681436	−	0.731877i	$-0.261356\pi$
$389$	26.8800	1.36287	0.681436	+	0.731877i	$0.261356\pi$
$390$	1.35877	0.0688040
$391$	−11.7291	−0.593167
$392$	−14.9411	−0.754641
$393$	−12.8911	−0.650272
$394$	−13.1965	−0.664833
$395$	−3.48662	−0.175431
$396$	−5.33120	−0.267903
$397$	4.94101	0.247982	0.123991	−	0.992283i	$-0.460431\pi$
$397$	4.94101	0.247982	0.123991	+	0.992283i	$0.460431\pi$
$398$	−5.97376	−0.299437
$399$	19.7851	0.990496
$400$	−3.93258	−0.196629
$401$	3.77305	0.188417	0.0942085	−	0.995552i	$-0.469968\pi$
$401$	3.77305	0.188417	0.0942085	+	0.995552i	$0.469968\pi$
$402$	−9.32619	−0.465148
$403$	1.94293	0.0967843
$404$	−5.72953	−0.285055
$405$	−5.25495	−0.261120
$406$	−42.7805	−2.12316
$407$	−20.5295	−1.01761
$408$	−4.62203	−0.228824
$409$	32.3535	1.59978	0.799888	−	0.600150i	$-0.204892\pi$
$409$	32.3535	1.59978	0.799888	+	0.600150i	$0.204892\pi$
$410$	1.13714	0.0561592
$411$	−5.40460	−0.266589
$412$	−17.8400	−0.878912
$413$	23.5309	1.15788
$414$	4.36614	0.214584
$415$	8.79352	0.431657
$416$	1.94293	0.0952600
$417$	−5.53870	−0.271231
$418$	−13.0879	−0.640151
$419$	−5.97027	−0.291667	−0.145833	−	0.989309i	$-0.546586\pi$
$419$	−5.97027	−0.291667	−0.145833	+	0.989309i	$0.546586\pi$
$420$	−3.27581	−0.159843
$421$	−21.2212	−1.03426	−0.517130	−	0.855907i	$-0.672999\pi$
$421$	−21.2212	−1.03426	−0.517130	+	0.855907i	$0.672999\pi$
$422$	3.49845	0.170302
$423$	18.9358	0.920688
$424$	4.00354	0.194429
$425$	26.8528	1.30255
$426$	−2.75566	−0.133512
$427$	37.3403	1.80702
$428$	−3.67900	−0.177831
$429$	2.75841	0.133177
$430$	−2.71821	−0.131084
$431$	−23.9704	−1.15461	−0.577306	−	0.816528i	$-0.695896\pi$
$431$	−23.9704	−1.15461	−0.577306	+	0.816528i	$0.695896\pi$
$432$	3.75122	0.180481
$433$	−37.1314	−1.78442	−0.892210	−	0.451620i	$-0.850846\pi$
$433$	−37.1314	−1.78442	−0.892210	+	0.451620i	$0.850846\pi$
$434$	−4.68414	−0.224846
$435$	−6.38713	−0.306239
$436$	8.05773	0.385895
$437$	10.7187	0.512746
$438$	−6.38629	−0.305149
$439$	−14.4956	−0.691839	−0.345920	−	0.938264i	$-0.612433\pi$
$439$	−14.4956	−0.691839	−0.345920	+	0.938264i	$0.612433\pi$
$440$	2.16695	0.103305
$441$	−37.9776	−1.80846
$442$	−13.2669	−0.631042
$443$	−31.9470	−1.51785	−0.758925	−	0.651178i	$-0.774275\pi$
$443$	−31.9470	−1.51785	−0.758925	+	0.651178i	$0.774275\pi$
$444$	6.62548	0.314431
$445$	15.2845	0.724553
$446$	−0.296483	−0.0140389
$447$	−9.22566	−0.436359
$448$	−4.68414	−0.221305
$449$	10.0337	0.473521	0.236760	−	0.971568i	$-0.423914\pi$
$449$	10.0337	0.473521	0.236760	+	0.971568i	$0.423914\pi$
$450$	−9.99588	−0.471210
$451$	2.30848	0.108702
$452$	−11.2510	−0.529203
$453$	2.97312	0.139689
$454$	4.61006	0.216361
$455$	−9.40276	−0.440808
$456$	4.22386	0.197800
$457$	−12.6100	−0.589873	−0.294937	−	0.955517i	$-0.595299\pi$
$457$	−12.6100	−0.589873	−0.294937	+	0.955517i	$0.595299\pi$
$458$	−12.5511	−0.586474
$459$	−25.6144	−1.19558
$460$	−1.77469	−0.0827453
$461$	0.0588823	0.00274242	0.00137121	−	0.999999i	$-0.499564\pi$
$461$	0.0588823	0.00274242	0.00137121	+	0.999999i	$0.499564\pi$
$462$	−6.65014	−0.309392
$463$	−12.1185	−0.563194	−0.281597	−	0.959533i	$-0.590864\pi$
$463$	−12.1185	−0.563194	−0.281597	+	0.959533i	$0.590864\pi$
$464$	−9.13307	−0.423992
$465$	−0.699341	−0.0324311
$466$	−21.1750	−0.980914
$467$	22.1054	1.02292	0.511458	−	0.859308i	$-0.329106\pi$
$467$	22.1054	1.02292	0.511458	+	0.859308i	$0.329106\pi$
$468$	4.93857	0.228286
$469$	64.5377	2.98008
$470$	−7.69675	−0.355024
$471$	−0.143866	−0.00662898
$472$	5.02353	0.231227
$473$	−5.51818	−0.253726
$474$	2.28432	0.104922
$475$	−24.5395	−1.12595
$476$	31.9846	1.46601
$477$	10.1763	0.465939
$478$	14.3853	0.657969
$479$	−36.0782	−1.64845	−0.824227	−	0.566259i	$-0.808390\pi$
$479$	−36.0782	−1.64845	−0.824227	+	0.566259i	$0.808390\pi$
$480$	−0.699341	−0.0319204
$481$	19.0175	0.867125
$482$	14.8831	0.677907
$483$	5.44632	0.247816
$484$	−6.60092	−0.300042
$485$	−1.03316	−0.0469135
$486$	14.6965	0.666647
$487$	−33.6702	−1.52574	−0.762872	−	0.646549i	$-0.776211\pi$
$487$	−33.6702	−1.52574	−0.762872	+	0.646549i	$0.776211\pi$
$488$	7.97165	0.360860
$489$	−16.5157	−0.746864
$490$	15.4366	0.697355
$491$	−24.8322	−1.12066	−0.560330	−	0.828269i	$-0.689326\pi$
$491$	−24.8322	−1.12066	−0.560330	+	0.828269i	$0.689326\pi$
$492$	−0.745014	−0.0335878
$493$	62.3633	2.80870
$494$	12.1240	0.545486
$495$	5.50800	0.247566
$496$	−1.00000	−0.0449013
$497$	19.0693	0.855375
$498$	−5.76122	−0.258166
$499$	−5.41033	−0.242200	−0.121100	−	0.992640i	$-0.538642\pi$
$499$	−5.41033	−0.242200	−0.121100	+	0.992640i	$0.538642\pi$
$500$	9.22880	0.412725
$501$	−10.8473	−0.484621
$502$	13.2219	0.590123
$503$	22.7385	1.01386	0.506929	−	0.861988i	$-0.330781\pi$
$503$	22.7385	1.01386	0.506929	+	0.861988i	$0.330781\pi$
$504$	−11.9062	−0.530345
$505$	5.91954	0.263416
$506$	−3.60275	−0.160162
$507$	6.24435	0.277321
$508$	12.9459	0.574380
$509$	−11.8182	−0.523832	−0.261916	−	0.965091i	$-0.584354\pi$
$509$	−11.8182	−0.523832	−0.261916	+	0.965091i	$0.584354\pi$
$510$	4.77530	0.211454
$511$	44.1934	1.95500
$512$	−1.00000	−0.0441942
$513$	23.4079	1.03348
$514$	10.0408	0.442879
$515$	18.4316	0.812193
$516$	1.78088	0.0783989
$517$	−15.6250	−0.687186
$518$	−45.8486	−2.01447
$519$	−6.05097	−0.265608
$520$	−2.00736	−0.0880287
$521$	42.1205	1.84533	0.922667	−	0.385598i	$-0.126005\pi$
$521$	42.1205	1.84533	0.922667	+	0.385598i	$0.126005\pi$
$522$	−23.2146	−1.01607
$523$	−26.3845	−1.15372	−0.576858	−	0.816845i	$-0.695721\pi$
$523$	−26.3845	−1.15372	−0.576858	+	0.816845i	$0.695721\pi$
$524$	19.0446	0.831966
$525$	−12.4689	−0.544185
$526$	18.0985	0.789131
$527$	6.82829	0.297445
$528$	−1.41971	−0.0617852
$529$	−20.0494	−0.871714
$530$	−4.13631	−0.179670
$531$	12.7689	0.554123
$532$	−29.2293	−1.26725
$533$	−2.13846	−0.0926271
$534$	−10.0139	−0.433342
$535$	3.80101	0.164332
$536$	13.7779	0.595116
$537$	−11.5869	−0.500012
$538$	11.6703	0.503143
$539$	31.3375	1.34980
$540$	−3.87562	−0.166780
$541$	20.9637	0.901299	0.450650	−	0.892701i	$-0.351192\pi$
$541$	20.9637	0.901299	0.450650	+	0.892701i	$0.351192\pi$
$542$	−8.38919	−0.360347
$543$	2.57114	0.110338
$544$	6.82829	0.292761
$545$	−8.32494	−0.356601
$546$	6.16037	0.263640
$547$	43.0463	1.84052	0.920262	−	0.391302i	$-0.127975\pi$
$547$	43.0463	1.84052	0.920262	+	0.391302i	$0.127975\pi$
$548$	7.98441	0.341077
$549$	20.2625	0.864781
$550$	8.24818	0.351703
$551$	−56.9910	−2.42790
$552$	1.16272	0.0494885
$553$	−15.8076	−0.672207
$554$	−0.0834203	−0.00354419
$555$	−6.84519	−0.290562
$556$	8.18254	0.347017
$557$	−13.8990	−0.588919	−0.294460	−	0.955664i	$-0.595140\pi$
$557$	−13.8990	−0.588919	−0.294460	+	0.955664i	$0.595140\pi$
$558$	−2.54182	−0.107604
$559$	5.11178	0.216205
$560$	4.83947	0.204505
$561$	9.69423	0.409291
$562$	17.4241	0.734990
$563$	18.1531	0.765062	0.382531	−	0.923943i	$-0.375052\pi$
$563$	18.1531	0.765062	0.382531	+	0.923943i	$0.375052\pi$
$564$	5.04265	0.212334
$565$	11.6241	0.489030
$566$	2.54318	0.106898
$567$	−23.8248	−1.00055
$568$	4.07104	0.170817
$569$	−16.6979	−0.700011	−0.350006	−	0.936748i	$-0.613820\pi$
$569$	−16.6979	−0.700011	−0.350006	+	0.936748i	$0.613820\pi$
$570$	−4.36393	−0.182785
$571$	−28.8645	−1.20794	−0.603971	−	0.797006i	$-0.706416\pi$
$571$	−28.8645	−1.20794	−0.603971	+	0.797006i	$0.706416\pi$
$572$	−4.07510	−0.170389
$573$	16.3840	0.684452
$574$	5.15553	0.215188
$575$	−6.75508	−0.281706
$576$	−2.54182	−0.105909
$577$	17.1412	0.713596	0.356798	−	0.934182i	$-0.383868\pi$
$577$	17.1412	0.713596	0.356798	+	0.934182i	$0.383868\pi$
$578$	−29.6256	−1.23226
$579$	15.4025	0.640106
$580$	9.43594	0.391806
$581$	39.8679	1.65400
$582$	0.676893	0.0280581
$583$	−8.39703	−0.347769
$584$	9.43471	0.390411
$585$	−5.10235	−0.210956
$586$	19.5176	0.806263
$587$	−21.9411	−0.905608	−0.452804	−	0.891610i	$-0.649576\pi$
$587$	−21.9411	−0.905608	−0.452804	+	0.891610i	$0.649576\pi$
$588$	−10.1135	−0.417075
$589$	−6.24007	−0.257118
$590$	−5.19013	−0.213674
$591$	−8.93265	−0.367440
$592$	−9.78807	−0.402287
$593$	−21.0609	−0.864866	−0.432433	−	0.901666i	$-0.642345\pi$
$593$	−21.0609	−0.864866	−0.432433	+	0.901666i	$0.642345\pi$
$594$	−7.86780	−0.322820
$595$	−33.0453	−1.35473
$596$	13.6294	0.558283
$597$	−4.04360	−0.165493
$598$	3.33742	0.136477
$599$	−0.0587268	−0.00239951	−0.00119976	−	0.999999i	$-0.500382\pi$
$599$	−0.0587268	−0.00239951	−0.00119976	+	0.999999i	$0.500382\pi$
$600$	−2.66193	−0.108673
$601$	−29.2120	−1.19158	−0.595790	−	0.803140i	$-0.703161\pi$
$601$	−29.2120	−1.19158	−0.595790	+	0.803140i	$0.703161\pi$
$602$	−12.3238	−0.502280
$603$	35.0210	1.42616
$604$	−4.39230	−0.178720
$605$	6.81982	0.277265
$606$	−3.87828	−0.157544
$607$	−45.1146	−1.83114	−0.915572	−	0.402153i	$-0.868262\pi$
$607$	−45.1146	−1.83114	−0.915572	+	0.402153i	$0.868262\pi$
$608$	−6.24007	−0.253068
$609$	−28.9579	−1.17343
$610$	−8.23601	−0.333466
$611$	14.4742	0.585565
$612$	17.3563	0.701585
$613$	−2.74621	−0.110918	−0.0554592	−	0.998461i	$-0.517662\pi$
$613$	−2.74621	−0.110918	−0.0554592	+	0.998461i	$0.517662\pi$
$614$	−33.4564	−1.35019
$615$	0.769720	0.0310381
$616$	9.82450	0.395840
$617$	11.2926	0.454625	0.227312	−	0.973822i	$-0.427006\pi$
$617$	11.2926	0.454625	0.227312	+	0.973822i	$0.427006\pi$
$618$	−12.0758	−0.485758
$619$	−6.40589	−0.257474	−0.128737	−	0.991679i	$-0.541092\pi$
$619$	−6.40589	−0.257474	−0.128737	+	0.991679i	$0.541092\pi$
$620$	1.03316	0.0414928
$621$	6.44356	0.258571
$622$	33.0997	1.32718
$623$	69.2964	2.77630
$624$	1.31516	0.0526484
$625$	10.1280	0.405121
$626$	−14.9703	−0.598334
$627$	−8.85912	−0.353799
$628$	0.212538	0.00848120
$629$	66.8358	2.66492
$630$	12.3010	0.490085
$631$	42.1399	1.67756	0.838781	−	0.544469i	$-0.183269\pi$
$631$	42.1399	1.67756	0.838781	+	0.544469i	$0.183269\pi$
$632$	−3.37471	−0.134239
$633$	2.36808	0.0941226
$634$	10.4540	0.415182
$635$	−13.3752	−0.530778
$636$	2.70997	0.107457
$637$	−29.0296	−1.15019
$638$	19.1557	0.758381
$639$	10.3478	0.409354
$640$	1.03316	0.0408393
$641$	−31.3929	−1.23995	−0.619973	−	0.784623i	$-0.712856\pi$
$641$	−31.3929	−1.23995	−0.619973	+	0.784623i	$0.712856\pi$
$642$	−2.49029	−0.0982839
$643$	−0.318715	−0.0125689	−0.00628444	−	0.999980i	$-0.502000\pi$
$643$	−0.318715	−0.0125689	−0.00628444	+	0.999980i	$0.502000\pi$
$644$	−8.04605	−0.317059
$645$	−1.83994	−0.0724475
$646$	42.6090	1.67643
$647$	−20.0730	−0.789152	−0.394576	−	0.918863i	$-0.629109\pi$
$647$	−20.0730	−0.789152	−0.394576	+	0.918863i	$0.629109\pi$
$648$	−5.08627	−0.199808
$649$	−10.5363	−0.413588
$650$	−7.64072	−0.299694
$651$	−3.17066	−0.124268
$652$	24.3992	0.955547
$653$	38.3716	1.50160	0.750798	−	0.660531i	$-0.229669\pi$
$653$	38.3716	1.50160	0.750798	+	0.660531i	$0.229669\pi$
$654$	5.45422	0.213277
$655$	−19.6761	−0.768811
$656$	1.10064	0.0429727
$657$	23.9813	0.935599
$658$	−34.8954	−1.36036
$659$	11.8031	0.459784	0.229892	−	0.973216i	$-0.426163\pi$
$659$	11.8031	0.459784	0.229892	+	0.973216i	$0.426163\pi$
$660$	1.46680	0.0570950
$661$	−15.5433	−0.604564	−0.302282	−	0.953219i	$-0.597748\pi$
$661$	−15.5433	−0.604564	−0.302282	+	0.953219i	$0.597748\pi$
$662$	−18.0120	−0.700055
$663$	−8.98028	−0.348765
$664$	8.51126	0.330301
$665$	30.1986	1.17105
$666$	−24.8795	−0.964060
$667$	−15.6881	−0.607445
$668$	16.0251	0.620029
$669$	−0.200687	−0.00775901
$670$	−14.2349	−0.549940
$671$	−16.7197	−0.645458
$672$	−3.17066	−0.122311
$673$	39.3394	1.51642	0.758211	−	0.652009i	$-0.226074\pi$
$673$	39.3394	1.51642	0.758211	+	0.652009i	$0.226074\pi$
$674$	−1.87629	−0.0722721
$675$	−14.7519	−0.567803
$676$	−9.22502	−0.354808
$677$	−40.0084	−1.53765	−0.768823	−	0.639461i	$-0.779157\pi$
$677$	−40.0084	−1.53765	−0.768823	+	0.639461i	$0.779157\pi$
$678$	−7.61573	−0.292480
$679$	−4.68414	−0.179761
$680$	−7.05474	−0.270537
$681$	3.12052	0.119579
$682$	2.09740	0.0803135
$683$	−6.25247	−0.239244	−0.119622	−	0.992819i	$-0.538168\pi$
$683$	−6.25247	−0.239244	−0.119622	+	0.992819i	$0.538168\pi$
$684$	−15.8611	−0.606465
$685$	−8.24920	−0.315186
$686$	37.1973	1.42020
$687$	−8.49575	−0.324133
$688$	−2.63096	−0.100304
$689$	7.77861	0.296341
$690$	−1.20127	−0.0457317
$691$	43.6307	1.65979	0.829895	−	0.557919i	$-0.188400\pi$
$691$	43.6307	1.65979	0.829895	+	0.557919i	$0.188400\pi$
$692$	8.93933	0.339822
$693$	24.9721	0.948610
$694$	−25.3191	−0.961102
$695$	−8.45389	−0.320674
$696$	−6.18211	−0.234332
$697$	−7.51548	−0.284669
$698$	20.3148	0.768927
$699$	−14.3332	−0.542132
$700$	18.4207	0.696238
$701$	−10.2072	−0.385520	−0.192760	−	0.981246i	$-0.561744\pi$
$701$	−10.2072	−0.385520	−0.192760	+	0.981246i	$0.561744\pi$
$702$	7.28836	0.275081
$703$	−61.0782	−2.30361
$704$	2.09740	0.0790487
$705$	−5.20988	−0.196215
$706$	−36.2634	−1.36479
$707$	26.8379	1.00934
$708$	3.40039	0.127795
$709$	−37.0222	−1.39040	−0.695199	−	0.718817i	$-0.744684\pi$
$709$	−37.0222	−1.39040	−0.695199	+	0.718817i	$0.744684\pi$
$710$	−4.20605	−0.157850
$711$	−8.57789	−0.321696
$712$	14.7939	0.554423
$713$	−1.71772	−0.0643293
$714$	21.6502	0.810238
$715$	4.21024	0.157454
$716$	17.1178	0.639721
$717$	9.73732	0.363647
$718$	1.15786	0.0432108
$719$	35.1336	1.31026	0.655132	−	0.755515i	$-0.272613\pi$
$719$	35.1336	1.31026	0.655132	+	0.755515i	$0.272613\pi$
$720$	2.62611	0.0978693
$721$	83.5648	3.11212
$722$	−19.9385	−0.742033
$723$	10.0743	0.374666
$724$	−3.79844	−0.141168
$725$	35.9165	1.33390
$726$	−4.46812	−0.165827
$727$	19.5710	0.725849	0.362925	−	0.931819i	$-0.381778\pi$
$727$	19.5710	0.725849	0.362925	+	0.931819i	$0.381778\pi$
$728$	−9.10095	−0.337304
$729$	−5.31085	−0.196698
$730$	−9.74759	−0.360774
$731$	17.9650	0.664459
$732$	5.39596	0.199440
$733$	41.2972	1.52535	0.762674	−	0.646784i	$-0.223886\pi$
$733$	41.2972	1.52535	0.762674	+	0.646784i	$0.223886\pi$
$734$	−24.4430	−0.902207
$735$	10.4489	0.385415
$736$	−1.71772	−0.0633162
$737$	−28.8978	−1.06447
$738$	2.79762	0.102982
$739$	46.9223	1.72606	0.863032	−	0.505149i	$-0.168563\pi$
$739$	46.9223	1.72606	0.863032	+	0.505149i	$0.168563\pi$
$740$	10.1127	0.371749
$741$	8.20667	0.301480
$742$	−18.7531	−0.688449
$743$	−21.4536	−0.787056	−0.393528	−	0.919313i	$-0.628746\pi$
$743$	−21.4536	−0.787056	−0.393528	+	0.919313i	$0.628746\pi$
$744$	−0.676893	−0.0248161
$745$	−14.0814	−0.515903
$746$	2.20531	0.0807420
$747$	21.6341	0.791549
$748$	−14.3217	−0.523651
$749$	17.2329	0.629678
$750$	6.24691	0.228105
$751$	44.6098	1.62783	0.813917	−	0.580981i	$-0.197331\pi$
$751$	44.6098	1.62783	0.813917	+	0.580981i	$0.197331\pi$
$752$	−7.44970	−0.271662
$753$	8.94983	0.326150
$754$	−17.7449	−0.646232
$755$	4.53796	0.165153
$756$	−17.5712	−0.639059
$757$	35.8959	1.30466	0.652329	−	0.757936i	$-0.273792\pi$
$757$	35.8959	1.30466	0.652329	+	0.757936i	$0.273792\pi$
$758$	−9.96658	−0.362003
$759$	−2.43868	−0.0885184
$760$	6.44701	0.233857
$761$	−18.8956	−0.684967	−0.342483	−	0.939524i	$-0.611268\pi$
$761$	−18.8956	−0.684967	−0.342483	+	0.939524i	$0.611268\pi$
$762$	8.76297	0.317449
$763$	−37.7435	−1.36641
$764$	−24.2047	−0.875696
$765$	−17.9318	−0.648327
$766$	29.7602	1.07528
$767$	9.76038	0.352427
$768$	−0.676893	−0.0244253
$769$	48.0110	1.73132	0.865660	−	0.500632i	$-0.166899\pi$
$769$	48.0110	1.73132	0.865660	+	0.500632i	$0.166899\pi$
$770$	−10.1503	−0.365791
$771$	6.79652	0.244771
$772$	−22.7547	−0.818960
$773$	−0.570789	−0.0205299	−0.0102649	−	0.999947i	$-0.503267\pi$
$773$	−0.570789	−0.0205299	−0.0102649	+	0.999947i	$0.503267\pi$
$774$	−6.68742	−0.240374
$775$	3.93258	0.141262
$776$	−1.00000	−0.0358979
$777$	−31.0346	−1.11336
$778$	−26.8800	−0.963696
$779$	6.86805	0.246074
$780$	−1.35877	−0.0486518
$781$	−8.53859	−0.305535
$782$	11.7291	0.419433
$783$	−34.2601	−1.22436
$784$	14.9411	0.533611
$785$	−0.219587	−0.00783738
$786$	12.8911	0.459812
$787$	−31.4231	−1.12011	−0.560057	−	0.828454i	$-0.689221\pi$
$787$	−31.4231	−1.12011	−0.560057	+	0.828454i	$0.689221\pi$
$788$	13.1965	0.470108
$789$	12.2507	0.436138
$790$	3.48662	0.124048
$791$	52.7012	1.87384
$792$	5.33120	0.189436
$793$	15.4884	0.550008
$794$	−4.94101	−0.175350
$795$	−2.79984	−0.0993001
$796$	5.97376	0.211734
$797$	23.7882	0.842622	0.421311	−	0.906916i	$-0.361570\pi$
$797$	23.7882	0.842622	0.421311	+	0.906916i	$0.361570\pi$
$798$	−19.7851	−0.700386
$799$	50.8687	1.79961
$800$	3.93258	0.139038
$801$	37.6033	1.32865
$802$	−3.77305	−0.133231
$803$	−19.7883	−0.698315
$804$	9.32619	0.328910
$805$	8.31288	0.292991
$806$	−1.94293	−0.0684368
$807$	7.89955	0.278077
$808$	5.72953	0.201564
$809$	25.2907	0.889174	0.444587	−	0.895736i	$-0.353350\pi$
$809$	25.2907	0.889174	0.444587	+	0.895736i	$0.353350\pi$
$810$	5.25495	0.184640
$811$	−37.1723	−1.30530	−0.652648	−	0.757662i	$-0.726342\pi$
$811$	−37.1723	−1.30530	−0.652648	+	0.757662i	$0.726342\pi$
$812$	42.7805	1.50130
$813$	−5.67859	−0.199157
$814$	20.5295	0.719558
$815$	−25.2084	−0.883010
$816$	4.62203	0.161803
$817$	−16.4174	−0.574372
$818$	−32.3535	−1.13121
$819$	−23.1329	−0.808330
$820$	−1.13714	−0.0397106
$821$	−28.8451	−1.00670	−0.503350	−	0.864083i	$-0.667899\pi$
$821$	−28.8451	−1.00670	−0.503350	+	0.864083i	$0.667899\pi$
$822$	5.40460	0.188507
$823$	23.4352	0.816900	0.408450	−	0.912781i	$-0.366069\pi$
$823$	23.4352	0.816900	0.408450	+	0.912781i	$0.366069\pi$
$824$	17.8400	0.621485
$825$	5.58313	0.194380
$826$	−23.5309	−0.818745
$827$	4.12670	0.143499	0.0717497	−	0.997423i	$-0.477142\pi$
$827$	4.12670	0.143499	0.0717497	+	0.997423i	$0.477142\pi$
$828$	−4.36614	−0.151734
$829$	−3.36211	−0.116771	−0.0583854	−	0.998294i	$-0.518595\pi$
$829$	−3.36211	−0.116771	−0.0583854	+	0.998294i	$0.518595\pi$
$830$	−8.79352	−0.305228
$831$	−0.0564666	−0.00195881
$832$	−1.94293	−0.0673590
$833$	−102.022	−3.53487
$834$	5.53870	0.191790
$835$	−16.5565	−0.572962
$836$	13.0879	0.452655
$837$	−3.75122	−0.129661
$838$	5.97027	0.206239
$839$	−40.1227	−1.38519	−0.692594	−	0.721328i	$-0.743532\pi$
$839$	−40.1227	−1.38519	−0.692594	+	0.721328i	$0.743532\pi$
$840$	3.27581	0.113026
$841$	54.4130	1.87631
$842$	21.2212	0.731332
$843$	11.7942	0.406215
$844$	−3.49845	−0.120422
$845$	9.53094	0.327874
$846$	−18.9358	−0.651025
$847$	30.9196	1.06241
$848$	−4.00354	−0.137482
$849$	1.72146	0.0590804
$850$	−26.8528	−0.921043
$851$	−16.8132	−0.576349
$852$	2.75566	0.0944073
$853$	7.15606	0.245019	0.122509	−	0.992467i	$-0.460906\pi$
$853$	7.15606	0.245019	0.122509	+	0.992467i	$0.460906\pi$
$854$	−37.3403	−1.27776
$855$	16.3871	0.560427
$856$	3.67900	0.125746
$857$	−6.07400	−0.207484	−0.103742	−	0.994604i	$-0.533082\pi$
$857$	−6.07400	−0.207484	−0.103742	+	0.994604i	$0.533082\pi$
$858$	−2.75841	−0.0941705
$859$	45.2608	1.54428	0.772140	−	0.635453i	$-0.219187\pi$
$859$	45.2608	1.54428	0.772140	+	0.635453i	$0.219187\pi$
$860$	2.71821	0.0926902
$861$	3.48975	0.118930
$862$	23.9704	0.816434
$863$	−31.3445	−1.06698	−0.533490	−	0.845806i	$-0.679120\pi$
$863$	−31.3445	−1.06698	−0.533490	+	0.845806i	$0.679120\pi$
$864$	−3.75122	−0.127619
$865$	−9.23578	−0.314026
$866$	37.1314	1.26178
$867$	−20.0534	−0.681048
$868$	4.68414	0.158990
$869$	7.07811	0.240108
$870$	6.38713	0.216544
$871$	26.7696	0.907053
$872$	−8.05773	−0.272869
$873$	−2.54182	−0.0860274
$874$	−10.7187	−0.362566
$875$	−43.2290	−1.46141
$876$	6.38629	0.215773
$877$	−11.0974	−0.374731	−0.187366	−	0.982290i	$-0.559995\pi$
$877$	−11.0974	−0.374731	−0.187366	+	0.982290i	$0.559995\pi$
$878$	14.4956	0.489204
$879$	13.2113	0.445606
$880$	−2.16695	−0.0730480
$881$	20.4220	0.688036	0.344018	−	0.938963i	$-0.388212\pi$
$881$	20.4220	0.688036	0.344018	+	0.938963i	$0.388212\pi$
$882$	37.9776	1.27877
$883$	39.6185	1.33327	0.666634	−	0.745386i	$-0.267735\pi$
$883$	39.6185	1.33327	0.666634	+	0.745386i	$0.267735\pi$
$884$	13.2669	0.446214
$885$	−3.51316	−0.118094
$886$	31.9470	1.07328
$887$	−49.6923	−1.66850	−0.834252	−	0.551383i	$-0.814100\pi$
$887$	−49.6923	−1.66850	−0.834252	+	0.551383i	$0.814100\pi$
$888$	−6.62548	−0.222336
$889$	−60.6402	−2.03381
$890$	−15.2845	−0.512336
$891$	10.6679	0.357390
$892$	0.296483	0.00992697
$893$	−46.4866	−1.55562
$894$	9.22566	0.308552
$895$	−17.6854	−0.591159
$896$	4.68414	0.156486
$897$	2.25908	0.0754284
$898$	−10.0337	−0.334830
$899$	9.13307	0.304605
$900$	9.99588	0.333196
$901$	27.3374	0.910740
$902$	−2.30848	−0.0768638
$903$	−8.34188	−0.277600
$904$	11.2510	0.374203
$905$	3.92441	0.130452
$906$	−2.97312	−0.0987753
$907$	45.2674	1.50308	0.751539	−	0.659689i	$-0.229312\pi$
$907$	45.2674	1.50308	0.751539	+	0.659689i	$0.229312\pi$
$908$	−4.61006	−0.152990
$909$	14.5634	0.483038
$910$	9.40276	0.311698
$911$	−34.0776	−1.12904	−0.564521	−	0.825419i	$-0.690939\pi$
$911$	−34.0776	−1.12904	−0.564521	+	0.825419i	$0.690939\pi$
$912$	−4.22386	−0.139866
$913$	−17.8515	−0.590799
$914$	12.6100	0.417103
$915$	−5.57490	−0.184301
$916$	12.5511	0.414700
$917$	−89.2074	−2.94589
$918$	25.6144	0.845402
$919$	−7.93532	−0.261762	−0.130881	−	0.991398i	$-0.541781\pi$
$919$	−7.93532	−0.261762	−0.130881	+	0.991398i	$0.541781\pi$
$920$	1.77469	0.0585097
$921$	−22.6464	−0.746225
$922$	−0.0588823	−0.00193919
$923$	7.90975	0.260353
$924$	6.65014	0.218773
$925$	38.4923	1.26562
$926$	12.1185	0.398238
$927$	45.3459	1.48935
$928$	9.13307	0.299808
$929$	0.335365	0.0110030	0.00550148	−	0.999985i	$-0.498249\pi$
$929$	0.335365	0.0110030	0.00550148	+	0.999985i	$0.498249\pi$
$930$	0.699341	0.0229323
$931$	93.2336	3.05561
$932$	21.1750	0.693611
$933$	22.4050	0.733506
$934$	−22.1054	−0.723311
$935$	14.7966	0.483900
$936$	−4.93857	−0.161422
$937$	−48.7517	−1.59265	−0.796324	−	0.604870i	$-0.793225\pi$
$937$	−48.7517	−1.59265	−0.796324	+	0.604870i	$0.793225\pi$
$938$	−64.5377	−2.10723
$939$	−10.1333	−0.330688
$940$	7.69675	0.251040
$941$	−17.0015	−0.554233	−0.277116	−	0.960836i	$-0.589379\pi$
$941$	−17.0015	−0.554233	−0.277116	+	0.960836i	$0.589379\pi$
$942$	0.143866	0.00468740
$943$	1.89059	0.0615661
$944$	−5.02353	−0.163502
$945$	18.1539	0.590547
$946$	5.51818	0.179411
$947$	37.7269	1.22596	0.612979	−	0.790099i	$-0.289971\pi$
$947$	37.7269	1.22596	0.612979	+	0.790099i	$0.289971\pi$
$948$	−2.28432	−0.0741912
$949$	18.3310	0.595049
$950$	24.5395	0.796168
$951$	7.07625	0.229463
$952$	−31.9846	−1.03663
$953$	−2.79575	−0.0905632	−0.0452816	−	0.998974i	$-0.514419\pi$
$953$	−2.79575	−0.0905632	−0.0452816	+	0.998974i	$0.514419\pi$
$954$	−10.1763	−0.329469
$955$	25.0074	0.809221
$956$	−14.3853	−0.465254
$957$	12.9664	0.419143
$958$	36.0782	1.16563
$959$	−37.4001	−1.20771
$960$	0.699341	0.0225711
$961$	1.00000	0.0322581
$962$	−19.0175	−0.613150
$963$	9.35134	0.301343
$964$	−14.8831	−0.479352
$965$	23.5093	0.756792
$966$	−5.44632	−0.175232
$967$	2.59102	0.0833217	0.0416608	−	0.999132i	$-0.486735\pi$
$967$	2.59102	0.0833217	0.0416608	+	0.999132i	$0.486735\pi$
$968$	6.60092	0.212162
$969$	28.8418	0.926531
$970$	1.03316	0.0331728
$971$	−27.8661	−0.894265	−0.447132	−	0.894468i	$-0.647555\pi$
$971$	−27.8661	−0.894265	−0.447132	+	0.894468i	$0.647555\pi$
$972$	−14.6965	−0.471391
$973$	−38.3281	−1.22874
$974$	33.6702	1.07886
$975$	−5.17195	−0.165635
$976$	−7.97165	−0.255166
$977$	1.67270	0.0535144	0.0267572	−	0.999642i	$-0.491482\pi$
$977$	1.67270	0.0535144	0.0267572	+	0.999642i	$0.491482\pi$
$978$	16.5157	0.528113
$979$	−31.0286	−0.991679
$980$	−15.4366	−0.493104
$981$	−20.4813	−0.653916
$982$	24.8322	0.792427
$983$	−7.97457	−0.254349	−0.127175	−	0.991880i	$-0.540591\pi$
$983$	−7.97457	−0.254349	−0.127175	+	0.991880i	$0.540591\pi$
$984$	0.745014	0.0237502
$985$	−13.6342	−0.434421
$986$	−62.3633	−1.98605
$987$	−23.6204	−0.751847
$988$	−12.1240	−0.385717
$989$	−4.51927	−0.143704
$990$	−5.50800	−0.175056
$991$	25.9571	0.824555	0.412277	−	0.911058i	$-0.364733\pi$
$991$	25.9571	0.824555	0.412277	+	0.911058i	$0.364733\pi$
$992$	1.00000	0.0317500
$993$	−12.1922	−0.386907
$994$	−19.0693	−0.604841
$995$	−6.17186	−0.195661
$996$	5.76122	0.182551
$997$	31.3493	0.992842	0.496421	−	0.868082i	$-0.334647\pi$
$997$	31.3493	0.992842	0.496421	+	0.868082i	$0.334647\pi$
$998$	5.41033	0.171261
$999$	−36.7172	−1.16168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.13	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.676893 q^{3} +1.00000 q^{4} -1.03316 q^{5} +0.676893 q^{6} -4.68414 q^{7} -1.00000 q^{8} -2.54182 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.676893 q^{3} +1.00000 q^{4} -1.03316 q^{5} +0.676893 q^{6} -4.68414 q^{7} -1.00000 q^{8} -2.54182 q^{9} +1.03316 q^{10} +2.09740 q^{11} -0.676893 q^{12} -1.94293 q^{13} +4.68414 q^{14} +0.699341 q^{15} +1.00000 q^{16} -6.82829 q^{17} +2.54182 q^{18} +6.24007 q^{19} -1.03316 q^{20} +3.17066 q^{21} -2.09740 q^{22} +1.71772 q^{23} +0.676893 q^{24} -3.93258 q^{25} +1.94293 q^{26} +3.75122 q^{27} -4.68414 q^{28} -9.13307 q^{29} -0.699341 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.41971 q^{33} +6.82829 q^{34} +4.83947 q^{35} -2.54182 q^{36} -9.78807 q^{37} -6.24007 q^{38} +1.31516 q^{39} +1.03316 q^{40} +1.10064 q^{41} -3.17066 q^{42} -2.63096 q^{43} +2.09740 q^{44} +2.62611 q^{45} -1.71772 q^{46} -7.44970 q^{47} -0.676893 q^{48} +14.9411 q^{49} +3.93258 q^{50} +4.62203 q^{51} -1.94293 q^{52} -4.00354 q^{53} -3.75122 q^{54} -2.16695 q^{55} +4.68414 q^{56} -4.22386 q^{57} +9.13307 q^{58} -5.02353 q^{59} +0.699341 q^{60} -7.97165 q^{61} +1.00000 q^{62} +11.9062 q^{63} +1.00000 q^{64} +2.00736 q^{65} +1.41971 q^{66} -13.7779 q^{67} -6.82829 q^{68} -1.16272 q^{69} -4.83947 q^{70} -4.07104 q^{71} +2.54182 q^{72} -9.43471 q^{73} +9.78807 q^{74} +2.66193 q^{75} +6.24007 q^{76} -9.82450 q^{77} -1.31516 q^{78} +3.37471 q^{79} -1.03316 q^{80} +5.08627 q^{81} -1.10064 q^{82} -8.51126 q^{83} +3.17066 q^{84} +7.05474 q^{85} +2.63096 q^{86} +6.18211 q^{87} -2.09740 q^{88} -14.7939 q^{89} -2.62611 q^{90} +9.10095 q^{91} +1.71772 q^{92} +0.676893 q^{93} +7.44970 q^{94} -6.44701 q^{95} +0.676893 q^{96} +1.00000 q^{97} -14.9411 q^{98} -5.33120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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