LMFDB - Embedded newform 6001.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28982 q^{2} -3.10307 q^{3} +3.24328 q^{4} +2.16467 q^{5} +7.10548 q^{6} -1.63956 q^{7} -2.84688 q^{8} +6.62906 q^{9} +O(q^{10})$	\(q-2.28982 q^{2} -3.10307 q^{3} +3.24328 q^{4} +2.16467 q^{5} +7.10548 q^{6} -1.63956 q^{7} -2.84688 q^{8} +6.62906 q^{9} -4.95671 q^{10} -5.86219 q^{11} -10.0641 q^{12} +1.80761 q^{13} +3.75431 q^{14} -6.71713 q^{15} +0.0322975 q^{16} +1.00000 q^{17} -15.1794 q^{18} -2.74943 q^{19} +7.02063 q^{20} +5.08769 q^{21} +13.4234 q^{22} -3.48732 q^{23} +8.83409 q^{24} -0.314198 q^{25} -4.13911 q^{26} -11.2612 q^{27} -5.31756 q^{28} +5.15263 q^{29} +15.3810 q^{30} +3.45994 q^{31} +5.61981 q^{32} +18.1908 q^{33} -2.28982 q^{34} -3.54912 q^{35} +21.4999 q^{36} +5.57495 q^{37} +6.29570 q^{38} -5.60916 q^{39} -6.16257 q^{40} -4.42454 q^{41} -11.6499 q^{42} +3.95099 q^{43} -19.0127 q^{44} +14.3497 q^{45} +7.98534 q^{46} +1.39132 q^{47} -0.100222 q^{48} -4.31183 q^{49} +0.719456 q^{50} -3.10307 q^{51} +5.86259 q^{52} -4.72508 q^{53} +25.7862 q^{54} -12.6897 q^{55} +4.66765 q^{56} +8.53168 q^{57} -11.7986 q^{58} +5.75199 q^{59} -21.7855 q^{60} -5.18024 q^{61} -7.92265 q^{62} -10.8688 q^{63} -12.9330 q^{64} +3.91289 q^{65} -41.6537 q^{66} +14.6590 q^{67} +3.24328 q^{68} +10.8214 q^{69} +8.12684 q^{70} +7.70835 q^{71} -18.8722 q^{72} +11.4341 q^{73} -12.7656 q^{74} +0.974978 q^{75} -8.91717 q^{76} +9.61144 q^{77} +12.8440 q^{78} -2.92339 q^{79} +0.0699136 q^{80} +15.0572 q^{81} +10.1314 q^{82} -7.63267 q^{83} +16.5008 q^{84} +2.16467 q^{85} -9.04706 q^{86} -15.9890 q^{87} +16.6890 q^{88} -8.20182 q^{89} -32.8583 q^{90} -2.96370 q^{91} -11.3104 q^{92} -10.7365 q^{93} -3.18587 q^{94} -5.95161 q^{95} -17.4387 q^{96} -15.6624 q^{97} +9.87331 q^{98} -38.8608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.28982	−1.61915	−0.809574	−	0.587018i	$-0.800302\pi$
$2$	−2.28982	−1.61915	−0.809574	+	0.587018i	$0.800302\pi$
$3$	−3.10307	−1.79156	−0.895780	−	0.444498i	$-0.853382\pi$
$3$	−3.10307	−1.79156	−0.895780	+	0.444498i	$0.853382\pi$
$4$	3.24328	1.62164
$5$	2.16467	0.968070	0.484035	−	0.875049i	$-0.339171\pi$
$5$	2.16467	0.968070	0.484035	+	0.875049i	$0.339171\pi$
$6$	7.10548	2.90080
$7$	−1.63956	−0.619697	−0.309849	−	0.950786i	$-0.600278\pi$
$7$	−1.63956	−0.619697	−0.309849	+	0.950786i	$0.600278\pi$
$8$	−2.84688	−1.00653
$9$	6.62906	2.20969
$10$	−4.95671	−1.56745
$11$	−5.86219	−1.76752	−0.883759	−	0.467943i	$-0.844995\pi$
$11$	−5.86219	−1.76752	−0.883759	+	0.467943i	$0.844995\pi$
$12$	−10.0641	−2.90526
$13$	1.80761	0.501342	0.250671	−	0.968072i	$-0.419349\pi$
$13$	1.80761	0.501342	0.250671	+	0.968072i	$0.419349\pi$
$14$	3.75431	1.00338
$15$	−6.71713	−1.73436
$16$	0.0322975	0.00807439
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−15.1794	−3.57781
$19$	−2.74943	−0.630763	−0.315381	−	0.948965i	$-0.602132\pi$
$19$	−2.74943	−0.630763	−0.315381	+	0.948965i	$0.602132\pi$
$20$	7.02063	1.56986
$21$	5.08769	1.11022
$22$	13.4234	2.86187
$23$	−3.48732	−0.727157	−0.363579	−	0.931564i	$-0.618445\pi$
$23$	−3.48732	−0.727157	−0.363579	+	0.931564i	$0.618445\pi$
$24$	8.83409	1.80325
$25$	−0.314198	−0.0628395
$26$	−4.13911	−0.811746
$27$	−11.2612	−2.16722
$28$	−5.31756	−1.00493
$29$	5.15263	0.956820	0.478410	−	0.878137i	$-0.341213\pi$
$29$	5.15263	0.956820	0.478410	+	0.878137i	$0.341213\pi$
$30$	15.3810	2.80818
$31$	3.45994	0.621424	0.310712	−	0.950504i	$-0.399432\pi$
$31$	3.45994	0.621424	0.310712	+	0.950504i	$0.399432\pi$
$32$	5.61981	0.993452
$33$	18.1908	3.16661
$34$	−2.28982	−0.392701
$35$	−3.54912	−0.599911
$36$	21.4999	3.58331
$37$	5.57495	0.916516	0.458258	−	0.888819i	$-0.348474\pi$
$37$	5.57495	0.916516	0.458258	+	0.888819i	$0.348474\pi$
$38$	6.29570	1.02130
$39$	−5.60916	−0.898184
$40$	−6.16257	−0.974388
$41$	−4.42454	−0.690998	−0.345499	−	0.938419i	$-0.612290\pi$
$41$	−4.42454	−0.690998	−0.345499	+	0.938419i	$0.612290\pi$
$42$	−11.6499	−1.79762
$43$	3.95099	0.602521	0.301260	−	0.953542i	$-0.402593\pi$
$43$	3.95099	0.602521	0.301260	+	0.953542i	$0.402593\pi$
$44$	−19.0127	−2.86628
$45$	14.3497	2.13913
$46$	7.98534	1.17737
$47$	1.39132	0.202945	0.101472	−	0.994838i	$-0.467645\pi$
$47$	1.39132	0.202945	0.101472	+	0.994838i	$0.467645\pi$
$48$	−0.100222	−0.0144657
$49$	−4.31183	−0.615975
$50$	0.719456	0.101746
$51$	−3.10307	−0.434517
$52$	5.86259	0.812995
$53$	−4.72508	−0.649039	−0.324520	−	0.945879i	$-0.605203\pi$
$53$	−4.72508	−0.649039	−0.324520	+	0.945879i	$0.605203\pi$
$54$	25.7862	3.50906
$55$	−12.6897	−1.71108
$56$	4.66765	0.623741
$57$	8.53168	1.13005
$58$	−11.7986	−1.54923
$59$	5.75199	0.748846	0.374423	−	0.927258i	$-0.377841\pi$
$59$	5.75199	0.748846	0.374423	+	0.927258i	$0.377841\pi$
$60$	−21.7855	−2.81250
$61$	−5.18024	−0.663261	−0.331631	−	0.943409i	$-0.607599\pi$
$61$	−5.18024	−0.663261	−0.331631	+	0.943409i	$0.607599\pi$
$62$	−7.92265	−1.00618
$63$	−10.8688	−1.36934
$64$	−12.9330	−1.61662
$65$	3.91289	0.485334
$66$	−41.6537	−5.12721
$67$	14.6590	1.79088	0.895440	−	0.445182i	$-0.146861\pi$
$67$	14.6590	1.79088	0.895440	+	0.445182i	$0.146861\pi$
$68$	3.24328	0.393305
$69$	10.8214	1.30275
$70$	8.12684	0.971344
$71$	7.70835	0.914812	0.457406	−	0.889258i	$-0.348779\pi$
$71$	7.70835	0.914812	0.457406	+	0.889258i	$0.348779\pi$
$72$	−18.8722	−2.22411
$73$	11.4341	1.33826	0.669130	−	0.743146i	$-0.266667\pi$
$73$	11.4341	1.33826	0.669130	+	0.743146i	$0.266667\pi$
$74$	−12.7656	−1.48398
$75$	0.974978	0.112581
$76$	−8.91717	−1.02287
$77$	9.61144	1.09533
$78$	12.8440	1.45429
$79$	−2.92339	−0.328907	−0.164453	−	0.986385i	$-0.552586\pi$
$79$	−2.92339	−0.328907	−0.164453	+	0.986385i	$0.552586\pi$
$80$	0.0699136	0.00781658
$81$	15.0572	1.67303
$82$	10.1314	1.11883
$83$	−7.63267	−0.837794	−0.418897	−	0.908034i	$-0.637583\pi$
$83$	−7.63267	−0.837794	−0.418897	+	0.908034i	$0.637583\pi$
$84$	16.5008	1.80038
$85$	2.16467	0.234792
$86$	−9.04706	−0.975570
$87$	−15.9890	−1.71420
$88$	16.6890	1.77905
$89$	−8.20182	−0.869391	−0.434695	−	0.900578i	$-0.643144\pi$
$89$	−8.20182	−0.869391	−0.434695	+	0.900578i	$0.643144\pi$
$90$	−32.8583	−3.46357
$91$	−2.96370	−0.310680
$92$	−11.3104	−1.17919
$93$	−10.7365	−1.11332
$94$	−3.18587	−0.328598
$95$	−5.95161	−0.610623
$96$	−17.4387	−1.77983
$97$	−15.6624	−1.59027	−0.795136	−	0.606431i	$-0.792601\pi$
$97$	−15.6624	−1.59027	−0.795136	+	0.606431i	$0.792601\pi$
$98$	9.87331	0.997355
$99$	−38.8608	−3.90566
$100$	−1.01903	−0.101903
$101$	3.90949	0.389009	0.194504	−	0.980902i	$-0.437690\pi$
$101$	3.90949	0.389009	0.194504	+	0.980902i	$0.437690\pi$
$102$	7.10548	0.703547
$103$	−9.67545	−0.953351	−0.476675	−	0.879079i	$-0.658158\pi$
$103$	−9.67545	−0.953351	−0.476675	+	0.879079i	$0.658158\pi$
$104$	−5.14607	−0.504613
$105$	11.0132	1.07478
$106$	10.8196	1.05089
$107$	−12.4229	−1.20097	−0.600486	−	0.799636i	$-0.705026\pi$
$107$	−12.4229	−1.20097	−0.600486	+	0.799636i	$0.705026\pi$
$108$	−36.5233	−3.51446
$109$	−11.9630	−1.14585	−0.572925	−	0.819608i	$-0.694191\pi$
$109$	−11.9630	−1.14585	−0.572925	+	0.819608i	$0.694191\pi$
$110$	29.0572	2.77049
$111$	−17.2995	−1.64199
$112$	−0.0529539	−0.00500367
$113$	15.3475	1.44377	0.721885	−	0.692013i	$-0.243276\pi$
$113$	15.3475	1.44377	0.721885	+	0.692013i	$0.243276\pi$
$114$	−19.5360	−1.82972
$115$	−7.54891	−0.703939
$116$	16.7114	1.55162
$117$	11.9828	1.10781
$118$	−13.1710	−1.21249
$119$	−1.63956	−0.150299
$120$	19.1229	1.74567
$121$	23.3653	2.12412
$122$	11.8618	1.07392
$123$	13.7297	1.23796
$124$	11.2216	1.00773
$125$	−11.5035	−1.02890
$126$	24.8875	2.21716
$127$	18.1190	1.60780	0.803900	−	0.594765i	$-0.202755\pi$
$127$	18.1190	1.60780	0.803900	+	0.594765i	$0.202755\pi$
$128$	18.3745	1.62409
$129$	−12.2602	−1.07945
$130$	−8.95981	−0.785828
$131$	−14.3850	−1.25682	−0.628410	−	0.777883i	$-0.716294\pi$
$131$	−14.3850	−1.25682	−0.628410	+	0.777883i	$0.716294\pi$
$132$	58.9978	5.13510
$133$	4.50787	0.390882
$134$	−33.5665	−2.89970
$135$	−24.3769	−2.09803
$136$	−2.84688	−0.244118
$137$	3.19856	0.273272	0.136636	−	0.990621i	$-0.456371\pi$
$137$	3.19856	0.273272	0.136636	+	0.990621i	$0.456371\pi$
$138$	−24.7791	−2.10934
$139$	7.68335	0.651693	0.325847	−	0.945423i	$-0.394351\pi$
$139$	7.68335	0.651693	0.325847	+	0.945423i	$0.394351\pi$
$140$	−11.5108	−0.972838
$141$	−4.31737	−0.363588
$142$	−17.6507	−1.48122
$143$	−10.5966	−0.886130
$144$	0.214102	0.0178419
$145$	11.1538	0.926269
$146$	−26.1820	−2.16684
$147$	13.3799	1.10356
$148$	18.0811	1.48626
$149$	6.25294	0.512261	0.256131	−	0.966642i	$-0.417552\pi$
$149$	6.25294	0.512261	0.256131	+	0.966642i	$0.417552\pi$
$150$	−2.23253	−0.182285
$151$	−7.95551	−0.647410	−0.323705	−	0.946158i	$-0.604929\pi$
$151$	−7.95551	−0.647410	−0.323705	+	0.946158i	$0.604929\pi$
$152$	7.82731	0.634879
$153$	6.62906	0.535928
$154$	−22.0085	−1.77349
$155$	7.48964	0.601583
$156$	−18.1921	−1.45653
$157$	14.2546	1.13764	0.568821	−	0.822462i	$-0.307400\pi$
$157$	14.2546	1.13764	0.568821	+	0.822462i	$0.307400\pi$
$158$	6.69403	0.532548
$159$	14.6623	1.16279
$160$	12.1650	0.961732
$161$	5.71769	0.450617
$162$	−34.4784	−2.70888
$163$	1.93799	0.151795	0.0758977	−	0.997116i	$-0.475818\pi$
$163$	1.93799	0.151795	0.0758977	+	0.997116i	$0.475818\pi$
$164$	−14.3500	−1.12055
$165$	39.3771	3.06550
$166$	17.4774	1.35651
$167$	0.380152	0.0294170	0.0147085	−	0.999892i	$-0.495318\pi$
$167$	0.380152	0.0294170	0.0147085	+	0.999892i	$0.495318\pi$
$168$	−14.4841	−1.11747
$169$	−9.73253	−0.748656
$170$	−4.95671	−0.380162
$171$	−18.2261	−1.39379
$172$	12.8142	0.977071
$173$	6.39594	0.486274	0.243137	−	0.969992i	$-0.421823\pi$
$173$	6.39594	0.486274	0.243137	+	0.969992i	$0.421823\pi$
$174$	36.6119	2.77554
$175$	0.515147	0.0389415
$176$	−0.189334	−0.0142716
$177$	−17.8489	−1.34160
$178$	18.7807	1.40767
$179$	19.2048	1.43543	0.717715	−	0.696337i	$-0.245188\pi$
$179$	19.2048	1.43543	0.717715	+	0.696337i	$0.245188\pi$
$180$	46.5402	3.46890
$181$	12.3052	0.914641	0.457321	−	0.889302i	$-0.348809\pi$
$181$	12.3052	0.914641	0.457321	+	0.889302i	$0.348809\pi$
$182$	6.78634	0.503037
$183$	16.0746	1.18827
$184$	9.92800	0.731902
$185$	12.0679	0.887252
$186$	24.5846	1.80263
$187$	−5.86219	−0.428686
$188$	4.51244	0.329104
$189$	18.4635	1.34302
$190$	13.6281	0.988688
$191$	5.24140	0.379254	0.189627	−	0.981856i	$-0.439272\pi$
$191$	5.24140	0.379254	0.189627	+	0.981856i	$0.439272\pi$
$192$	40.1319	2.89627
$193$	21.9020	1.57654	0.788268	−	0.615331i	$-0.210978\pi$
$193$	21.9020	1.57654	0.788268	+	0.615331i	$0.210978\pi$
$194$	35.8640	2.57489
$195$	−12.1420	−0.869505
$196$	−13.9845	−0.998890
$197$	−1.49958	−0.106841	−0.0534205	−	0.998572i	$-0.517012\pi$
$197$	−1.49958	−0.106841	−0.0534205	+	0.998572i	$0.517012\pi$
$198$	88.9843	6.32384
$199$	4.14343	0.293720	0.146860	−	0.989157i	$-0.453083\pi$
$199$	4.14343	0.293720	0.146860	+	0.989157i	$0.453083\pi$
$200$	0.894485	0.0632496
$201$	−45.4879	−3.20847
$202$	−8.95203	−0.629863
$203$	−8.44807	−0.592939
$204$	−10.0641	−0.704630
$205$	−9.57768	−0.668934
$206$	22.1551	1.54362
$207$	−23.1177	−1.60679
$208$	0.0583815	0.00404803
$209$	16.1177	1.11488
$210$	−25.2182	−1.74022
$211$	−6.44986	−0.444027	−0.222013	−	0.975044i	$-0.571263\pi$
$211$	−6.44986	−0.444027	−0.222013	+	0.975044i	$0.571263\pi$
$212$	−15.3247	−1.05251
$213$	−23.9196	−1.63894
$214$	28.4463	1.94455
$215$	8.55260	0.583282
$216$	32.0594	2.18137
$217$	−5.67280	−0.385095
$218$	27.3932	1.85530
$219$	−35.4808	−2.39757
$220$	−41.1563	−2.77476
$221$	1.80761	0.121593
$222$	39.6127	2.65863
$223$	14.7174	0.985553	0.492777	−	0.870156i	$-0.335982\pi$
$223$	14.7174	0.985553	0.492777	+	0.870156i	$0.335982\pi$
$224$	−9.21405	−0.615639
$225$	−2.08283	−0.138856
$226$	−35.1430	−2.33768
$227$	−14.6991	−0.975614	−0.487807	−	0.872952i	$-0.662203\pi$
$227$	−14.6991	−0.975614	−0.487807	+	0.872952i	$0.662203\pi$
$228$	27.6706	1.83253
$229$	−7.14899	−0.472418	−0.236209	−	0.971702i	$-0.575905\pi$
$229$	−7.14899	−0.472418	−0.236209	+	0.971702i	$0.575905\pi$
$230$	17.2856	1.13978
$231$	−29.8250	−1.96234
$232$	−14.6689	−0.963064
$233$	4.61616	0.302415	0.151207	−	0.988502i	$-0.451684\pi$
$233$	4.61616	0.302415	0.151207	+	0.988502i	$0.451684\pi$
$234$	−27.4384	−1.79370
$235$	3.01175	0.196465
$236$	18.6553	1.21436
$237$	9.07148	0.589256
$238$	3.75431	0.243356
$239$	7.50613	0.485531	0.242766	−	0.970085i	$-0.421945\pi$
$239$	7.50613	0.485531	0.242766	+	0.970085i	$0.421945\pi$
$240$	−0.216947	−0.0140039
$241$	23.5152	1.51474	0.757372	−	0.652983i	$-0.226483\pi$
$241$	23.5152	1.51474	0.757372	+	0.652983i	$0.226483\pi$
$242$	−53.5023	−3.43926
$243$	−12.9400	−0.830102
$244$	−16.8009	−1.07557
$245$	−9.33369	−0.596308
$246$	−31.4385	−2.00445
$247$	−4.96991	−0.316228
$248$	−9.85006	−0.625479
$249$	23.6847	1.50096
$250$	26.3409	1.66595
$251$	12.8679	0.812216	0.406108	−	0.913825i	$-0.366886\pi$
$251$	12.8679	0.812216	0.406108	+	0.913825i	$0.366886\pi$
$252$	−35.2504	−2.22057
$253$	20.4434	1.28526
$254$	−41.4892	−2.60326
$255$	−6.71713	−0.420643
$256$	−16.2085	−1.01303
$257$	8.19234	0.511024	0.255512	−	0.966806i	$-0.417756\pi$
$257$	8.19234	0.511024	0.255512	+	0.966806i	$0.417756\pi$
$258$	28.0737	1.74779
$259$	−9.14049	−0.567963
$260$	12.6906	0.787037
$261$	34.1571	2.11427
$262$	32.9390	2.03498
$263$	−26.0121	−1.60397	−0.801987	−	0.597342i	$-0.796223\pi$
$263$	−26.0121	−1.60397	−0.801987	+	0.597342i	$0.796223\pi$
$264$	−51.7871	−3.18728
$265$	−10.2282	−0.628316
$266$	−10.3222	−0.632895
$267$	25.4508	1.55757
$268$	47.5432	2.90416
$269$	−24.5396	−1.49620	−0.748102	−	0.663584i	$-0.769034\pi$
$269$	−24.5396	−1.49620	−0.748102	+	0.663584i	$0.769034\pi$
$270$	55.8186	3.39701
$271$	−16.1897	−0.983455	−0.491728	−	0.870749i	$-0.663634\pi$
$271$	−16.1897	−0.983455	−0.491728	+	0.870749i	$0.663634\pi$
$272$	0.0322975	0.00195833
$273$	9.19657	0.556602
$274$	−7.32414	−0.442467
$275$	1.84189	0.111070
$276$	35.0969	2.11258
$277$	−10.8813	−0.653792	−0.326896	−	0.945060i	$-0.606003\pi$
$277$	−10.8813	−0.653792	−0.326896	+	0.945060i	$0.606003\pi$
$278$	−17.5935	−1.05519
$279$	22.9362	1.37315
$280$	10.1039	0.603825
$281$	−3.39666	−0.202628	−0.101314	−	0.994855i	$-0.532305\pi$
$281$	−3.39666	−0.202628	−0.101314	+	0.994855i	$0.532305\pi$
$282$	9.88600	0.588703
$283$	26.5397	1.57762	0.788809	−	0.614638i	$-0.210698\pi$
$283$	26.5397	1.57762	0.788809	+	0.614638i	$0.210698\pi$
$284$	25.0003	1.48350
$285$	18.4683	1.09397
$286$	24.2643	1.43478
$287$	7.25432	0.428209
$288$	37.2541	2.19522
$289$	1.00000	0.0588235
$290$	−25.5401	−1.49977
$291$	48.6015	2.84907
$292$	37.0839	2.17017
$293$	−13.2203	−0.772340	−0.386170	−	0.922428i	$-0.626202\pi$
$293$	−13.2203	−0.772340	−0.386170	+	0.922428i	$0.626202\pi$
$294$	−30.6376	−1.78682
$295$	12.4512	0.724935
$296$	−15.8712	−0.922497
$297$	66.0155	3.83061
$298$	−14.3181	−0.829426
$299$	−6.30373	−0.364554
$300$	3.16213	0.182565
$301$	−6.47791	−0.373380
$302$	18.2167	1.04825
$303$	−12.1314	−0.696933
$304$	−0.0887999	−0.00509302
$305$	−11.2135	−0.642084
$306$	−15.1794	−0.867746
$307$	12.8149	0.731384	0.365692	−	0.930736i	$-0.380832\pi$
$307$	12.8149	0.731384	0.365692	+	0.930736i	$0.380832\pi$
$308$	31.1726	1.77622
$309$	30.0236	1.70798
$310$	−17.1499	−0.974051
$311$	−27.3211	−1.54924	−0.774620	−	0.632427i	$-0.782059\pi$
$311$	−27.3211	−1.54924	−0.774620	+	0.632427i	$0.782059\pi$
$312$	15.9686	0.904045
$313$	−19.6826	−1.11252	−0.556262	−	0.831007i	$-0.687765\pi$
$313$	−19.6826	−1.11252	−0.556262	+	0.831007i	$0.687765\pi$
$314$	−32.6405	−1.84201
$315$	−23.5273	−1.32561
$316$	−9.48135	−0.533368
$317$	−12.4788	−0.700879	−0.350439	−	0.936585i	$-0.613968\pi$
$317$	−12.4788	−0.700879	−0.350439	+	0.936585i	$0.613968\pi$
$318$	−33.5739	−1.88273
$319$	−30.2057	−1.69120
$320$	−27.9956	−1.56500
$321$	38.5493	2.15161
$322$	−13.0925	−0.729616
$323$	−2.74943	−0.152982
$324$	48.8348	2.71305
$325$	−0.567948	−0.0315041
$326$	−4.43766	−0.245779
$327$	37.1221	2.05286
$328$	12.5962	0.695507
$329$	−2.28116	−0.125764
$330$	−90.1665	−4.96350
$331$	−35.1738	−1.93333	−0.966663	−	0.256051i	$-0.917579\pi$
$331$	−35.1738	−1.93333	−0.966663	+	0.256051i	$0.917579\pi$
$332$	−24.7549	−1.35860
$333$	36.9567	2.02521
$334$	−0.870479	−0.0476305
$335$	31.7319	1.73370
$336$	0.164320	0.00896438
$337$	22.2053	1.20960	0.604801	−	0.796376i	$-0.293253\pi$
$337$	22.2053	1.20960	0.604801	+	0.796376i	$0.293253\pi$
$338$	22.2858	1.21219
$339$	−47.6244	−2.58660
$340$	7.02063	0.380747
$341$	−20.2829	−1.09838
$342$	41.7346	2.25675
$343$	18.5465	1.00142
$344$	−11.2480	−0.606452
$345$	23.4248	1.26115
$346$	−14.6456	−0.787350
$347$	19.3508	1.03880	0.519402	−	0.854530i	$-0.326155\pi$
$347$	19.3508	1.03880	0.519402	+	0.854530i	$0.326155\pi$
$348$	−51.8567	−2.77981
$349$	29.0833	1.55679	0.778397	−	0.627772i	$-0.216033\pi$
$349$	29.0833	1.55679	0.778397	+	0.627772i	$0.216033\pi$
$350$	−1.17960	−0.0630520
$351$	−20.3560	−1.08652
$352$	−32.9444	−1.75594
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	40.8707	2.17225
$355$	16.6860	0.885603
$356$	−26.6008	−1.40984
$357$	5.08769	0.269269
$358$	−43.9754	−2.32417
$359$	19.5261	1.03055	0.515275	−	0.857025i	$-0.327690\pi$
$359$	19.5261	1.03055	0.515275	+	0.857025i	$0.327690\pi$
$360$	−40.8520	−2.15309
$361$	−11.4406	−0.602139
$362$	−28.1768	−1.48094
$363$	−72.5042	−3.80548
$364$	−9.61210	−0.503811
$365$	24.7510	1.29553
$366$	−36.8081	−1.92399
$367$	−12.1543	−0.634449	−0.317224	−	0.948351i	$-0.602751\pi$
$367$	−12.1543	−0.634449	−0.317224	+	0.948351i	$0.602751\pi$
$368$	−0.112632	−0.00587135
$369$	−29.3306	−1.52689
$370$	−27.6334	−1.43659
$371$	7.74707	0.402208
$372$	−34.8213	−1.80540
$373$	32.6220	1.68910	0.844552	−	0.535474i	$-0.179867\pi$
$373$	32.6220	1.68910	0.844552	+	0.535474i	$0.179867\pi$
$374$	13.4234	0.694106
$375$	35.6962	1.84334
$376$	−3.96093	−0.204269
$377$	9.31397	0.479694
$378$	−42.2781	−2.17455
$379$	−29.0424	−1.49181	−0.745904	−	0.666053i	$-0.767982\pi$
$379$	−29.0424	−1.49181	−0.745904	+	0.666053i	$0.767982\pi$
$380$	−19.3027	−0.990210
$381$	−56.2245	−2.88047
$382$	−12.0019	−0.614069
$383$	25.1560	1.28541	0.642705	−	0.766114i	$-0.277812\pi$
$383$	25.1560	1.28541	0.642705	+	0.766114i	$0.277812\pi$
$384$	−57.0175	−2.90966
$385$	20.8056	1.06035
$386$	−50.1515	−2.55265
$387$	26.1914	1.33138
$388$	−50.7974	−2.57885
$389$	−7.50894	−0.380718	−0.190359	−	0.981715i	$-0.560965\pi$
$389$	−7.50894	−0.380718	−0.190359	+	0.981715i	$0.560965\pi$
$390$	27.8030	1.40786
$391$	−3.48732	−0.176361
$392$	12.2753	0.619995
$393$	44.6375	2.25167
$394$	3.43378	0.172991
$395$	−6.32817	−0.318405
$396$	−126.036	−6.33357
$397$	2.44727	0.122825	0.0614124	−	0.998112i	$-0.480440\pi$
$397$	2.44727	0.122825	0.0614124	+	0.998112i	$0.480440\pi$
$398$	−9.48770	−0.475576
$399$	−13.9882	−0.700288
$400$	−0.0101478	−0.000507391 0
$401$	30.4357	1.51989	0.759944	−	0.649989i	$-0.225226\pi$
$401$	30.4357	1.51989	0.759944	+	0.649989i	$0.225226\pi$
$402$	104.159	5.19499
$403$	6.25424	0.311546
$404$	12.6796	0.630832
$405$	32.5940	1.61961
$406$	19.3446	0.960055
$407$	−32.6814	−1.61996
$408$	8.83409	0.437353
$409$	−9.48210	−0.468860	−0.234430	−	0.972133i	$-0.575322\pi$
$409$	−9.48210	−0.468860	−0.234430	+	0.972133i	$0.575322\pi$
$410$	21.9312	1.08310
$411$	−9.92537	−0.489583
$412$	−31.3802	−1.54599
$413$	−9.43076	−0.464058
$414$	52.9353	2.60163
$415$	−16.5222	−0.811044
$416$	10.1584	0.498059
$417$	−23.8420	−1.16755
$418$	−36.9066	−1.80516
$419$	16.9282	0.826999	0.413499	−	0.910504i	$-0.364306\pi$
$419$	16.9282	0.826999	0.413499	+	0.910504i	$0.364306\pi$
$420$	35.7188	1.74290
$421$	−8.23088	−0.401148	−0.200574	−	0.979679i	$-0.564281\pi$
$421$	−8.23088	−0.401148	−0.200574	+	0.979679i	$0.564281\pi$
$422$	14.7690	0.718945
$423$	9.22315	0.448445
$424$	13.4517	0.653275
$425$	−0.314198	−0.0152408
$426$	54.7715	2.65369
$427$	8.49333	0.411021
$428$	−40.2911	−1.94754
$429$	32.8819	1.58756
$430$	−19.5839	−0.944420
$431$	−30.8601	−1.48648	−0.743240	−	0.669024i	$-0.766712\pi$
$431$	−30.8601	−1.48648	−0.743240	+	0.669024i	$0.766712\pi$
$432$	−0.363710	−0.0174990
$433$	20.8714	1.00301	0.501507	−	0.865154i	$-0.332779\pi$
$433$	20.8714	1.00301	0.501507	+	0.865154i	$0.332779\pi$
$434$	12.9897	0.623525
$435$	−34.6109	−1.65947
$436$	−38.7994	−1.85816
$437$	9.58815	0.458663
$438$	81.2447	3.88202
$439$	−34.6886	−1.65560	−0.827798	−	0.561026i	$-0.810407\pi$
$439$	−34.6886	−1.65560	−0.827798	+	0.561026i	$0.810407\pi$
$440$	36.1262	1.72225
$441$	−28.5834	−1.36111
$442$	−4.13911	−0.196877
$443$	1.00722	0.0478547	0.0239273	−	0.999714i	$-0.492383\pi$
$443$	1.00722	0.0478547	0.0239273	+	0.999714i	$0.492383\pi$
$444$	−56.1070	−2.66272
$445$	−17.7542	−0.841632
$446$	−33.7003	−1.59576
$447$	−19.4033	−0.917746
$448$	21.2044	1.00181
$449$	−21.5134	−1.01528	−0.507639	−	0.861570i	$-0.669482\pi$
$449$	−21.5134	−1.01528	−0.507639	+	0.861570i	$0.669482\pi$
$450$	4.76932	0.224828
$451$	25.9375	1.22135
$452$	49.7762	2.34127
$453$	24.6865	1.15987
$454$	33.6583	1.57966
$455$	−6.41543	−0.300760
$456$	−24.2887	−1.13742
$457$	−3.93775	−0.184200	−0.0921001	−	0.995750i	$-0.529358\pi$
$457$	−3.93775	−0.184200	−0.0921001	+	0.995750i	$0.529358\pi$
$458$	16.3699	0.764915
$459$	−11.2612	−0.525629
$460$	−24.4832	−1.14154
$461$	10.4642	0.487368	0.243684	−	0.969855i	$-0.421644\pi$
$461$	10.4642	0.487368	0.243684	+	0.969855i	$0.421644\pi$
$462$	68.2939	3.17732
$463$	31.1162	1.44609	0.723046	−	0.690800i	$-0.242742\pi$
$463$	31.1162	1.44609	0.723046	+	0.690800i	$0.242742\pi$
$464$	0.166417	0.00772573
$465$	−23.2409	−1.07777
$466$	−10.5702	−0.489654
$467$	−36.1286	−1.67183	−0.835916	−	0.548857i	$-0.815063\pi$
$467$	−36.1286	−1.67183	−0.835916	+	0.548857i	$0.815063\pi$
$468$	38.8635	1.79646
$469$	−24.0344	−1.10980
$470$	−6.89637	−0.318106
$471$	−44.2331	−2.03815
$472$	−16.3753	−0.753732
$473$	−23.1615	−1.06497
$474$	−20.7721	−0.954092
$475$	0.863865	0.0396368
$476$	−5.31756	−0.243730
$477$	−31.3228	−1.43417
$478$	−17.1877	−0.786147
$479$	−37.9593	−1.73440	−0.867202	−	0.497957i	$-0.834084\pi$
$479$	−37.9593	−1.73440	−0.867202	+	0.497957i	$0.834084\pi$
$480$	−37.7490	−1.72300
$481$	10.0774	0.459488
$482$	−53.8455	−2.45260
$483$	−17.7424	−0.807307
$484$	75.7801	3.44455
$485$	−33.9039	−1.53950
$486$	29.6303	1.34406
$487$	0.521664	0.0236388	0.0118194	−	0.999930i	$-0.496238\pi$
$487$	0.521664	0.0236388	0.0118194	+	0.999930i	$0.496238\pi$
$488$	14.7475	0.667590
$489$	−6.01374	−0.271951
$490$	21.3725	0.965510
$491$	−5.88766	−0.265707	−0.132853	−	0.991136i	$-0.542414\pi$
$491$	−5.88766	−0.265707	−0.132853	+	0.991136i	$0.542414\pi$
$492$	44.5292	2.00753
$493$	5.15263	0.232063
$494$	11.3802	0.512019
$495$	−84.1209	−3.78095
$496$	0.111748	0.00501762
$497$	−12.6383	−0.566907
$498$	−54.2338	−2.43027
$499$	−28.2572	−1.26497	−0.632483	−	0.774574i	$-0.717964\pi$
$499$	−28.2572	−1.26497	−0.632483	+	0.774574i	$0.717964\pi$
$500$	−37.3090	−1.66851
$501$	−1.17964	−0.0527023
$502$	−29.4652	−1.31510
$503$	−9.16788	−0.408776	−0.204388	−	0.978890i	$-0.565520\pi$
$503$	−9.16788	−0.408776	−0.204388	+	0.978890i	$0.565520\pi$
$504$	30.9421	1.37827
$505$	8.46276	0.376588
$506$	−46.8116	−2.08103
$507$	30.2008	1.34126
$508$	58.7649	2.60727
$509$	−15.4289	−0.683872	−0.341936	−	0.939723i	$-0.611083\pi$
$509$	−15.4289	−0.683872	−0.341936	+	0.939723i	$0.611083\pi$
$510$	15.3810	0.681083
$511$	−18.7469	−0.829315
$512$	0.365401	0.0161486
$513$	30.9620	1.36700
$514$	−18.7590	−0.827423
$515$	−20.9442	−0.922911
$516$	−39.7633	−1.75048
$517$	−8.15619	−0.358709
$518$	20.9301	0.919615
$519$	−19.8471	−0.871190
$520$	−11.1395	−0.488501
$521$	8.81733	0.386294	0.193147	−	0.981170i	$-0.438131\pi$
$521$	8.81733	0.386294	0.193147	+	0.981170i	$0.438131\pi$
$522$	−78.2136	−3.42332
$523$	11.0698	0.484047	0.242024	−	0.970270i	$-0.422189\pi$
$523$	11.0698	0.484047	0.242024	+	0.970270i	$0.422189\pi$
$524$	−46.6544	−2.03811
$525$	−1.59854	−0.0697660
$526$	59.5630	2.59707
$527$	3.45994	0.150718
$528$	0.587518	0.0255685
$529$	−10.8386	−0.471243
$530$	23.4208	1.01734
$531$	38.1303	1.65471
$532$	14.6203	0.633869
$533$	−7.99786	−0.346426
$534$	−58.2778	−2.52193
$535$	−26.8916	−1.16262
$536$	−41.7324	−1.80257
$537$	−59.5937	−2.57166
$538$	56.1912	2.42257
$539$	25.2768	1.08875
$540$	−79.0610	−3.40224
$541$	7.71937	0.331881	0.165941	−	0.986136i	$-0.446934\pi$
$541$	7.71937	0.331881	0.165941	+	0.986136i	$0.446934\pi$
$542$	37.0716	1.59236
$543$	−38.1840	−1.63863
$544$	5.61981	0.240947
$545$	−25.8960	−1.10926
$546$	−21.0585	−0.901221
$547$	9.14422	0.390979	0.195489	−	0.980706i	$-0.437370\pi$
$547$	9.14422	0.390979	0.195489	+	0.980706i	$0.437370\pi$
$548$	10.3738	0.443148
$549$	−34.3401	−1.46560
$550$	−4.21759	−0.179839
$551$	−14.1668	−0.603526
$552$	−30.8073	−1.31125
$553$	4.79308	0.203822
$554$	24.9161	1.05859
$555$	−37.4477	−1.58957
$556$	24.9192	1.05681
$557$	−18.1052	−0.767143	−0.383572	−	0.923511i	$-0.625306\pi$
$557$	−18.1052	−0.767143	−0.383572	+	0.923511i	$0.625306\pi$
$558$	−52.5197	−2.22334
$559$	7.14187	0.302069
$560$	−0.114628	−0.00484391
$561$	18.1908	0.768016
$562$	7.77775	0.328084
$563$	−7.17913	−0.302564	−0.151282	−	0.988491i	$-0.548340\pi$
$563$	−7.17913	−0.302564	−0.151282	+	0.988491i	$0.548340\pi$
$564$	−14.0024	−0.589609
$565$	33.2223	1.39767
$566$	−60.7711	−2.55440
$567$	−24.6873	−1.03677
$568$	−21.9448	−0.920782
$569$	−6.48243	−0.271757	−0.135879	−	0.990725i	$-0.543386\pi$
$569$	−6.48243	−0.271757	−0.135879	+	0.990725i	$0.543386\pi$
$570$	−42.2891	−1.77129
$571$	−23.7470	−0.993782	−0.496891	−	0.867813i	$-0.665525\pi$
$571$	−23.7470	−0.993782	−0.496891	+	0.867813i	$0.665525\pi$
$572$	−34.3676	−1.43698
$573$	−16.2644	−0.679457
$574$	−16.6111	−0.693334
$575$	1.09571	0.0456942
$576$	−85.7333	−3.57222
$577$	−12.8455	−0.534767	−0.267384	−	0.963590i	$-0.586159\pi$
$577$	−12.8455	−0.534767	−0.267384	+	0.963590i	$0.586159\pi$
$578$	−2.28982	−0.0952440
$579$	−67.9633	−2.82446
$580$	36.1747	1.50207
$581$	12.5143	0.519179
$582$	−111.289	−4.61306
$583$	27.6993	1.14719
$584$	−32.5515	−1.34699
$585$	25.9388	1.07244
$586$	30.2722	1.25053
$587$	5.58519	0.230525	0.115263	−	0.993335i	$-0.463229\pi$
$587$	5.58519	0.230525	0.115263	+	0.993335i	$0.463229\pi$
$588$	43.3948	1.78957
$589$	−9.51288	−0.391971
$590$	−28.5110	−1.17378
$591$	4.65332	0.191412
$592$	0.180057	0.00740031
$593$	8.88240	0.364757	0.182378	−	0.983228i	$-0.441620\pi$
$593$	8.88240	0.364757	0.182378	+	0.983228i	$0.441620\pi$
$594$	−151.164	−6.20232
$595$	−3.54912	−0.145500
$596$	20.2800	0.830703
$597$	−12.8574	−0.526216
$598$	14.4344	0.590267
$599$	10.1605	0.415145	0.207573	−	0.978220i	$-0.433444\pi$
$599$	10.1605	0.415145	0.207573	+	0.978220i	$0.433444\pi$
$600$	−2.77565	−0.113315
$601$	45.5495	1.85800	0.929002	−	0.370075i	$-0.120668\pi$
$601$	45.5495	1.85800	0.929002	+	0.370075i	$0.120668\pi$
$602$	14.8332	0.604558
$603$	97.1753	3.95728
$604$	−25.8019	−1.04987
$605$	50.5782	2.05630
$606$	27.7788	1.12844
$607$	−31.9655	−1.29744	−0.648719	−	0.761028i	$-0.724695\pi$
$607$	−31.9655	−1.29744	−0.648719	+	0.761028i	$0.724695\pi$
$608$	−15.4513	−0.626632
$609$	26.2150	1.06228
$610$	25.6769	1.03963
$611$	2.51497	0.101745
$612$	21.4999	0.869081
$613$	25.5826	1.03327	0.516636	−	0.856205i	$-0.327184\pi$
$613$	25.5826	1.03327	0.516636	+	0.856205i	$0.327184\pi$
$614$	−29.3438	−1.18422
$615$	29.7202	1.19844
$616$	−27.3627	−1.10247
$617$	−7.30124	−0.293937	−0.146968	−	0.989141i	$-0.546952\pi$
$617$	−7.30124	−0.293937	−0.146968	+	0.989141i	$0.546952\pi$
$618$	−68.7487	−2.76548
$619$	−9.01014	−0.362148	−0.181074	−	0.983469i	$-0.557957\pi$
$619$	−9.01014	−0.362148	−0.181074	+	0.983469i	$0.557957\pi$
$620$	24.2910	0.975550
$621$	39.2715	1.57591
$622$	62.5605	2.50845
$623$	13.4474	0.538759
$624$	−0.181162	−0.00725228
$625$	−23.3303	−0.933212
$626$	45.0695	1.80134
$627$	−50.0144	−1.99738
$628$	46.2317	1.84484
$629$	5.57495	0.222288
$630$	53.8733	2.14636
$631$	24.1078	0.959714	0.479857	−	0.877347i	$-0.340688\pi$
$631$	24.1078	0.959714	0.479857	+	0.877347i	$0.340688\pi$
$632$	8.32254	0.331053
$633$	20.0144	0.795501
$634$	28.5742	1.13483
$635$	39.2216	1.55646
$636$	47.5538	1.88563
$637$	−7.79412	−0.308814
$638$	69.1657	2.73830
$639$	51.0991	2.02145
$640$	39.7748	1.57224
$641$	−44.4722	−1.75655	−0.878273	−	0.478160i	$-0.841304\pi$
$641$	−44.4722	−1.75655	−0.878273	+	0.478160i	$0.841304\pi$
$642$	−88.2710	−3.48378
$643$	6.46535	0.254968	0.127484	−	0.991841i	$-0.459310\pi$
$643$	6.46535	0.254968	0.127484	+	0.991841i	$0.459310\pi$
$644$	18.5441	0.730738
$645$	−26.5393	−1.04499
$646$	6.29570	0.247701
$647$	−24.9539	−0.981039	−0.490520	−	0.871430i	$-0.663193\pi$
$647$	−24.9539	−0.981039	−0.490520	+	0.871430i	$0.663193\pi$
$648$	−42.8662	−1.68394
$649$	−33.7193	−1.32360
$650$	1.30050	0.0510098
$651$	17.6031	0.689920
$652$	6.28546	0.246157
$653$	−11.5147	−0.450606	−0.225303	−	0.974289i	$-0.572337\pi$
$653$	−11.5147	−0.450606	−0.225303	+	0.974289i	$0.572337\pi$
$654$	−85.0030	−3.32388
$655$	−31.1387	−1.21669
$656$	−0.142902	−0.00557938
$657$	75.7973	2.95713
$658$	5.22345	0.203631
$659$	−24.8784	−0.969124	−0.484562	−	0.874757i	$-0.661021\pi$
$659$	−24.8784	−0.969124	−0.484562	+	0.874757i	$0.661021\pi$
$660$	127.711	4.97114
$661$	33.2052	1.29153	0.645766	−	0.763535i	$-0.276538\pi$
$661$	33.2052	1.29153	0.645766	+	0.763535i	$0.276538\pi$
$662$	80.5417	3.13034
$663$	−5.60916	−0.217842
$664$	21.7293	0.843261
$665$	9.75805	0.378401
$666$	−84.6242	−3.27912
$667$	−17.9689	−0.695758
$668$	1.23294	0.0477038
$669$	−45.6693	−1.76568
$670$	−72.6603	−2.80711
$671$	30.3675	1.17233
$672$	28.5919	1.10295
$673$	−43.4556	−1.67509	−0.837546	−	0.546367i	$-0.816010\pi$
$673$	−43.4556	−1.67509	−0.837546	+	0.546367i	$0.816010\pi$
$674$	−50.8463	−1.95852
$675$	3.53825	0.136187
$676$	−31.5653	−1.21405
$677$	−2.59030	−0.0995535	−0.0497767	−	0.998760i	$-0.515851\pi$
$677$	−2.59030	−0.0995535	−0.0497767	+	0.998760i	$0.515851\pi$
$678$	109.051	4.18809
$679$	25.6795	0.985487
$680$	−6.16257	−0.236324
$681$	45.6124	1.74787
$682$	46.4441	1.77844
$683$	18.4685	0.706678	0.353339	−	0.935495i	$-0.385046\pi$
$683$	18.4685	0.706678	0.353339	+	0.935495i	$0.385046\pi$
$684$	−59.1124	−2.26022
$685$	6.92384	0.264546
$686$	−42.4681	−1.62144
$687$	22.1838	0.846366
$688$	0.127607	0.00486499
$689$	−8.54111	−0.325390
$690$	−53.6386	−2.04199
$691$	−21.9046	−0.833291	−0.416645	−	0.909069i	$-0.636794\pi$
$691$	−21.9046	−0.833291	−0.416645	+	0.909069i	$0.636794\pi$
$692$	20.7438	0.788562
$693$	63.7148	2.42033
$694$	−44.3098	−1.68198
$695$	16.6319	0.630885
$696$	45.5188	1.72539
$697$	−4.42454	−0.167592
$698$	−66.5956	−2.52068
$699$	−14.3243	−0.541794
$700$	1.67077	0.0631490
$701$	−14.8084	−0.559305	−0.279652	−	0.960101i	$-0.590219\pi$
$701$	−14.8084	−0.559305	−0.279652	+	0.960101i	$0.590219\pi$
$702$	46.6115	1.75924
$703$	−15.3279	−0.578104
$704$	75.8155	2.85740
$705$	−9.34569	−0.351979
$706$	−2.28982	−0.0861785
$707$	−6.40986	−0.241068
$708$	−57.8888	−2.17559
$709$	17.9391	0.673718	0.336859	−	0.941555i	$-0.390635\pi$
$709$	17.9391	0.673718	0.336859	+	0.941555i	$0.390635\pi$
$710$	−38.2080	−1.43392
$711$	−19.3793	−0.726780
$712$	23.3496	0.875064
$713$	−12.0659	−0.451873
$714$	−11.6499	−0.435986
$715$	−22.9381	−0.857837
$716$	62.2864	2.32775
$717$	−23.2921	−0.869858
$718$	−44.7113	−1.66861
$719$	26.8367	1.00084	0.500420	−	0.865783i	$-0.333179\pi$
$719$	26.8367	1.00084	0.500420	+	0.865783i	$0.333179\pi$
$720$	0.463461	0.0172722
$721$	15.8635	0.590789
$722$	26.1970	0.974951
$723$	−72.9692	−2.71376
$724$	39.9093	1.48322
$725$	−1.61895	−0.0601261
$726$	166.022	6.16164
$727$	46.7658	1.73445	0.867223	−	0.497919i	$-0.165902\pi$
$727$	46.7658	1.73445	0.867223	+	0.497919i	$0.165902\pi$
$728$	8.43731	0.312707
$729$	−5.01792	−0.185849
$730$	−56.6755	−2.09765
$731$	3.95099	0.146133
$732$	52.1346	1.92695
$733$	23.1772	0.856068	0.428034	−	0.903763i	$-0.359206\pi$
$733$	23.1772	0.856068	0.428034	+	0.903763i	$0.359206\pi$
$734$	27.8311	1.02727
$735$	28.9631	1.06832
$736$	−19.5981	−0.722396
$737$	−85.9338	−3.16541
$738$	67.1617	2.47226
$739$	31.8635	1.17212	0.586060	−	0.810268i	$-0.300678\pi$
$739$	31.8635	1.17212	0.586060	+	0.810268i	$0.300678\pi$
$740$	39.1397	1.43880
$741$	15.4220	0.566541
$742$	−17.7394	−0.651234
$743$	−13.1801	−0.483531	−0.241765	−	0.970335i	$-0.577726\pi$
$743$	−13.1801	−0.483531	−0.241765	+	0.970335i	$0.577726\pi$
$744$	30.5655	1.12058
$745$	13.5356	0.495905
$746$	−74.6985	−2.73491
$747$	−50.5974	−1.85126
$748$	−19.0127	−0.695174
$749$	20.3682	0.744238
$750$	−81.7378	−2.98464
$751$	−18.4561	−0.673474	−0.336737	−	0.941599i	$-0.609323\pi$
$751$	−18.4561	−0.673474	−0.336737	+	0.941599i	$0.609323\pi$
$752$	0.0449363	0.00163866
$753$	−39.9301	−1.45513
$754$	−21.3273	−0.776695
$755$	−17.2211	−0.626739
$756$	59.8823	2.17790
$757$	40.4243	1.46925	0.734623	−	0.678475i	$-0.237359\pi$
$757$	40.4243	1.46925	0.734623	+	0.678475i	$0.237359\pi$
$758$	66.5019	2.41546
$759$	−63.4372	−2.30262
$760$	16.9436	0.614607
$761$	2.22807	0.0807673	0.0403837	−	0.999184i	$-0.487142\pi$
$761$	2.22807	0.0807673	0.0403837	+	0.999184i	$0.487142\pi$
$762$	128.744	4.66390
$763$	19.6142	0.710080
$764$	16.9993	0.615014
$765$	14.3497	0.518816
$766$	−57.6027	−2.08127
$767$	10.3974	0.375428
$768$	50.2960	1.81490
$769$	−36.6919	−1.32315	−0.661573	−	0.749881i	$-0.730111\pi$
$769$	−36.6919	−1.32315	−0.661573	+	0.749881i	$0.730111\pi$
$770$	−47.6411	−1.71687
$771$	−25.4214	−0.915530
$772$	71.0341	2.55657
$773$	−39.3543	−1.41548	−0.707738	−	0.706475i	$-0.750284\pi$
$773$	−39.3543	−1.41548	−0.707738	+	0.706475i	$0.750284\pi$
$774$	−59.9735	−2.15570
$775$	−1.08711	−0.0390500
$776$	44.5889	1.60065
$777$	28.3636	1.01754
$778$	17.1941	0.616439
$779$	12.1650	0.435855
$780$	−39.3798	−1.41002
$781$	−45.1878	−1.61695
$782$	7.98534	0.285555
$783$	−58.0250	−2.07364
$784$	−0.139261	−0.00497362
$785$	30.8565	1.10132
$786$	−102.212	−3.64578
$787$	29.5706	1.05408	0.527040	−	0.849841i	$-0.323302\pi$
$787$	29.5706	1.05408	0.527040	+	0.849841i	$0.323302\pi$
$788$	−4.86357	−0.173257
$789$	80.7173	2.87361
$790$	14.4904	0.515544
$791$	−25.1632	−0.894700
$792$	110.632	3.93115
$793$	−9.36387	−0.332521
$794$	−5.60381	−0.198872
$795$	31.7390	1.12567
$796$	13.4383	0.476307
$797$	−43.2642	−1.53250	−0.766249	−	0.642544i	$-0.777879\pi$
$797$	−43.2642	−1.53250	−0.766249	+	0.642544i	$0.777879\pi$
$798$	32.0306	1.13387
$799$	1.39132	0.0492214
$800$	−1.76573	−0.0624281
$801$	−54.3703	−1.92108
$802$	−69.6924	−2.46092
$803$	−67.0288	−2.36540
$804$	−147.530	−5.20298
$805$	12.3769	0.436229
$806$	−14.3211	−0.504439
$807$	76.1480	2.68054
$808$	−11.1299	−0.391547
$809$	−17.6419	−0.620257	−0.310128	−	0.950695i	$-0.600372\pi$
$809$	−17.6419	−0.620257	−0.310128	+	0.950695i	$0.600372\pi$
$810$	−74.6344	−2.62238
$811$	35.9134	1.26109	0.630545	−	0.776153i	$-0.282831\pi$
$811$	35.9134	1.26109	0.630545	+	0.776153i	$0.282831\pi$
$812$	−27.3995	−0.961532
$813$	50.2379	1.76192
$814$	74.8346	2.62295
$815$	4.19512	0.146949
$816$	−0.100222	−0.00350846
$817$	−10.8630	−0.380047
$818$	21.7123	0.759153
$819$	−19.6465	−0.686505
$820$	−31.0631	−1.08477
$821$	−5.58470	−0.194907	−0.0974537	−	0.995240i	$-0.531070\pi$
$821$	−5.58470	−0.194907	−0.0974537	+	0.995240i	$0.531070\pi$
$822$	22.7273	0.792706
$823$	−15.1723	−0.528874	−0.264437	−	0.964403i	$-0.585186\pi$
$823$	−15.1723	−0.528874	−0.264437	+	0.964403i	$0.585186\pi$
$824$	27.5449	0.959572
$825$	−5.71551	−0.198989
$826$	21.5948	0.751378
$827$	−44.5791	−1.55017	−0.775084	−	0.631859i	$-0.782292\pi$
$827$	−44.5791	−1.55017	−0.775084	+	0.631859i	$0.782292\pi$
$828$	−74.9770	−2.60563
$829$	8.86584	0.307923	0.153962	−	0.988077i	$-0.450797\pi$
$829$	8.86584	0.307923	0.153962	+	0.988077i	$0.450797\pi$
$830$	37.8329	1.31320
$831$	33.7653	1.17131
$832$	−23.3778	−0.810479
$833$	−4.31183	−0.149396
$834$	54.5939	1.89043
$835$	0.822903	0.0284777
$836$	52.2741	1.80794
$837$	−38.9632	−1.34677
$838$	−38.7626	−1.33903
$839$	15.7591	0.544066	0.272033	−	0.962288i	$-0.412304\pi$
$839$	15.7591	0.544066	0.272033	+	0.962288i	$0.412304\pi$
$840$	−31.3532	−1.08179
$841$	−2.45038	−0.0844958
$842$	18.8472	0.649519
$843$	10.5401	0.363020
$844$	−20.9187	−0.720051
$845$	−21.0677	−0.724752
$846$	−21.1194	−0.726098
$847$	−38.3089	−1.31631
$848$	−0.152608	−0.00524059
$849$	−82.3545	−2.82640
$850$	0.719456	0.0246772
$851$	−19.4417	−0.666451
$852$	−77.5778	−2.65777
$853$	−15.0212	−0.514316	−0.257158	−	0.966369i	$-0.582786\pi$
$853$	−15.0212	−0.514316	−0.257158	+	0.966369i	$0.582786\pi$
$854$	−19.4482	−0.665504
$855$	−39.4536	−1.34928
$856$	35.3667	1.20881
$857$	0.675325	0.0230687	0.0115343	−	0.999933i	$-0.496328\pi$
$857$	0.675325	0.0230687	0.0115343	+	0.999933i	$0.496328\pi$
$858$	−75.2938	−2.57049
$859$	29.4941	1.00632	0.503162	−	0.864192i	$-0.332170\pi$
$859$	29.4941	1.00632	0.503162	+	0.864192i	$0.332170\pi$
$860$	27.7385	0.945874
$861$	−22.5107	−0.767162
$862$	70.6642	2.40683
$863$	−39.3274	−1.33872	−0.669360	−	0.742938i	$-0.733432\pi$
$863$	−39.3274	−1.33872	−0.669360	+	0.742938i	$0.733432\pi$
$864$	−63.2860	−2.15303
$865$	13.8451	0.470748
$866$	−47.7917	−1.62403
$867$	−3.10307	−0.105386
$868$	−18.3985	−0.624485
$869$	17.1374	0.581348
$870$	79.2528	2.68692
$871$	26.4978	0.897843
$872$	34.0573	1.15333
$873$	−103.827	−3.51400
$874$	−21.9551	−0.742644
$875$	18.8607	0.637609
$876$	−115.074	−3.88800
$877$	−38.1546	−1.28839	−0.644195	−	0.764862i	$-0.722807\pi$
$877$	−38.1546	−1.28839	−0.644195	+	0.764862i	$0.722807\pi$
$878$	79.4306	2.68065
$879$	41.0236	1.38369
$880$	−0.409847	−0.0138159
$881$	−29.7310	−1.00166	−0.500832	−	0.865545i	$-0.666973\pi$
$881$	−29.7310	−1.00166	−0.500832	+	0.865545i	$0.666973\pi$
$882$	65.4508	2.20384
$883$	49.5281	1.66675	0.833376	−	0.552707i	$-0.186405\pi$
$883$	49.5281	1.66675	0.833376	+	0.552707i	$0.186405\pi$
$884$	5.86259	0.197180
$885$	−38.6369	−1.29877
$886$	−2.30636	−0.0774838
$887$	−36.2354	−1.21667	−0.608333	−	0.793682i	$-0.708161\pi$
$887$	−36.2354	−1.21667	−0.608333	+	0.793682i	$0.708161\pi$
$888$	49.2496	1.65271
$889$	−29.7072	−0.996349
$890$	40.6540	1.36273
$891$	−88.2684	−2.95710
$892$	47.7328	1.59821
$893$	−3.82534	−0.128010
$894$	44.4302	1.48597
$895$	41.5720	1.38960
$896$	−30.1262	−1.00645
$897$	19.5609	0.653121
$898$	49.2617	1.64389
$899$	17.8278	0.594591
$900$	−6.75521	−0.225174
$901$	−4.72508	−0.157415
$902$	−59.3923	−1.97755
$903$	20.1014	0.668933
$904$	−43.6925	−1.45319
$905$	26.6368	0.885437
$906$	−56.5277	−1.87801
$907$	−44.8820	−1.49028	−0.745141	−	0.666907i	$-0.767618\pi$
$907$	−44.8820	−1.49028	−0.745141	+	0.666907i	$0.767618\pi$
$908$	−47.6733	−1.58209
$909$	25.9162	0.859588
$910$	14.6902	0.486975
$911$	−10.9670	−0.363353	−0.181676	−	0.983358i	$-0.558152\pi$
$911$	−10.9670	−0.363353	−0.181676	+	0.983358i	$0.558152\pi$
$912$	0.275552	0.00912445
$913$	44.7442	1.48082
$914$	9.01674	0.298247
$915$	34.7963	1.15033
$916$	−23.1862	−0.766092
$917$	23.5851	0.778847
$918$	25.7862	0.851071
$919$	−26.8394	−0.885350	−0.442675	−	0.896682i	$-0.645970\pi$
$919$	−26.8394	−0.885350	−0.442675	+	0.896682i	$0.645970\pi$
$920$	21.4909	0.708533
$921$	−39.7655	−1.31032
$922$	−23.9612	−0.789121
$923$	13.9337	0.458634
$924$	−96.7308	−3.18221
$925$	−1.75164	−0.0575935
$926$	−71.2504	−2.34143
$927$	−64.1391	−2.10661
$928$	28.9568	0.950555
$929$	−28.4767	−0.934290	−0.467145	−	0.884181i	$-0.654717\pi$
$929$	−28.4767	−0.934290	−0.467145	+	0.884181i	$0.654717\pi$
$930$	53.2175	1.74507
$931$	11.8551	0.388534
$932$	14.9715	0.490408
$933$	84.7795	2.77556
$934$	82.7280	2.70694
$935$	−12.6897	−0.414998
$936$	−34.1136	−1.11504
$937$	−45.5528	−1.48815	−0.744073	−	0.668098i	$-0.767109\pi$
$937$	−45.5528	−1.48815	−0.744073	+	0.668098i	$0.767109\pi$
$938$	55.0344	1.79694
$939$	61.0764	1.99315
$940$	9.76795	0.318595
$941$	25.2451	0.822966	0.411483	−	0.911417i	$-0.365011\pi$
$941$	25.2451	0.822966	0.411483	+	0.911417i	$0.365011\pi$
$942$	101.286	3.30007
$943$	15.4298	0.502464
$944$	0.185775	0.00604647
$945$	39.9674	1.30014
$946$	53.0356	1.72434
$947$	−10.3089	−0.334995	−0.167497	−	0.985873i	$-0.553569\pi$
$947$	−10.3089	−0.334995	−0.167497	+	0.985873i	$0.553569\pi$
$948$	29.4213	0.955560
$949$	20.6684	0.670925
$950$	−1.97810	−0.0641779
$951$	38.7226	1.25567
$952$	4.66765	0.151279
$953$	−40.8731	−1.32401	−0.662005	−	0.749499i	$-0.730294\pi$
$953$	−40.8731	−1.32401	−0.662005	+	0.749499i	$0.730294\pi$
$954$	71.7236	2.32214
$955$	11.3459	0.367145
$956$	24.3445	0.787356
$957$	93.7305	3.02988
$958$	86.9199	2.80825
$959$	−5.24425	−0.169346
$960$	86.8724	2.80379
$961$	−19.0288	−0.613832
$962$	−23.0753	−0.743979
$963$	−82.3524	−2.65377
$964$	76.2662	2.45637
$965$	47.4105	1.52620
$966$	40.6269	1.30715
$967$	6.84739	0.220197	0.110099	−	0.993921i	$-0.464883\pi$
$967$	6.84739	0.220197	0.110099	+	0.993921i	$0.464883\pi$
$968$	−66.5183	−2.13798
$969$	8.53168	0.274077
$970$	77.6338	2.49267
$971$	−1.16064	−0.0372467	−0.0186234	−	0.999827i	$-0.505928\pi$
$971$	−1.16064	−0.0372467	−0.0186234	+	0.999827i	$0.505928\pi$
$972$	−41.9681	−1.34613
$973$	−12.5974	−0.403853
$974$	−1.19452	−0.0382748
$975$	1.76238	0.0564415
$976$	−0.167309	−0.00535543
$977$	11.1284	0.356030	0.178015	−	0.984028i	$-0.443033\pi$
$977$	11.1284	0.356030	0.178015	+	0.984028i	$0.443033\pi$
$978$	13.7704	0.440328
$979$	48.0806	1.53666
$980$	−30.2718	−0.966996
$981$	−79.3036	−2.53197
$982$	13.4817	0.430218
$983$	−19.2942	−0.615388	−0.307694	−	0.951485i	$-0.599557\pi$
$983$	−19.2942	−0.615388	−0.307694	+	0.951485i	$0.599557\pi$
$984$	−39.0868	−1.24604
$985$	−3.24611	−0.103430
$986$	−11.7986	−0.375744
$987$	7.07861	0.225314
$988$	−16.1188	−0.512807
$989$	−13.7784	−0.438127
$990$	192.622	6.12192
$991$	55.0091	1.74742	0.873710	−	0.486447i	$-0.161707\pi$
$991$	55.0091	1.74742	0.873710	+	0.486447i	$0.161707\pi$
$992$	19.4442	0.617355
$993$	109.147	3.46367
$994$	28.9395	0.917906
$995$	8.96916	0.284341
$996$	76.8162	2.43401
$997$	13.4964	0.427436	0.213718	−	0.976895i	$-0.431443\pi$
$997$	13.4964	0.427436	0.213718	+	0.976895i	$0.431443\pi$
$998$	64.7039	2.04817
$999$	−62.7808	−1.98630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.16	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.16	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28982 q^{2} -3.10307 q^{3} +3.24328 q^{4} +2.16467 q^{5} +7.10548 q^{6} -1.63956 q^{7} -2.84688 q^{8} +6.62906 q^{9} +O(q^{10})\)	\(q-2.28982 q^{2} -3.10307 q^{3} +3.24328 q^{4} +2.16467 q^{5} +7.10548 q^{6} -1.63956 q^{7} -2.84688 q^{8} +6.62906 q^{9} -4.95671 q^{10} -5.86219 q^{11} -10.0641 q^{12} +1.80761 q^{13} +3.75431 q^{14} -6.71713 q^{15} +0.0322975 q^{16} +1.00000 q^{17} -15.1794 q^{18} -2.74943 q^{19} +7.02063 q^{20} +5.08769 q^{21} +13.4234 q^{22} -3.48732 q^{23} +8.83409 q^{24} -0.314198 q^{25} -4.13911 q^{26} -11.2612 q^{27} -5.31756 q^{28} +5.15263 q^{29} +15.3810 q^{30} +3.45994 q^{31} +5.61981 q^{32} +18.1908 q^{33} -2.28982 q^{34} -3.54912 q^{35} +21.4999 q^{36} +5.57495 q^{37} +6.29570 q^{38} -5.60916 q^{39} -6.16257 q^{40} -4.42454 q^{41} -11.6499 q^{42} +3.95099 q^{43} -19.0127 q^{44} +14.3497 q^{45} +7.98534 q^{46} +1.39132 q^{47} -0.100222 q^{48} -4.31183 q^{49} +0.719456 q^{50} -3.10307 q^{51} +5.86259 q^{52} -4.72508 q^{53} +25.7862 q^{54} -12.6897 q^{55} +4.66765 q^{56} +8.53168 q^{57} -11.7986 q^{58} +5.75199 q^{59} -21.7855 q^{60} -5.18024 q^{61} -7.92265 q^{62} -10.8688 q^{63} -12.9330 q^{64} +3.91289 q^{65} -41.6537 q^{66} +14.6590 q^{67} +3.24328 q^{68} +10.8214 q^{69} +8.12684 q^{70} +7.70835 q^{71} -18.8722 q^{72} +11.4341 q^{73} -12.7656 q^{74} +0.974978 q^{75} -8.91717 q^{76} +9.61144 q^{77} +12.8440 q^{78} -2.92339 q^{79} +0.0699136 q^{80} +15.0572 q^{81} +10.1314 q^{82} -7.63267 q^{83} +16.5008 q^{84} +2.16467 q^{85} -9.04706 q^{86} -15.9890 q^{87} +16.6890 q^{88} -8.20182 q^{89} -32.8583 q^{90} -2.96370 q^{91} -11.3104 q^{92} -10.7365 q^{93} -3.18587 q^{94} -5.95161 q^{95} -17.4387 q^{96} -15.6624 q^{97} +9.87331 q^{98} -38.8608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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