LMFDB - Embedded newform 6001.2.a.c.1.3

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:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.69106 q^{2} +2.90048 q^{3} +5.24179 q^{4} +1.92081 q^{5} -7.80536 q^{6} -1.20204 q^{7} -8.72383 q^{8} +5.41280 q^{9} +O(q^{10})$	\(q-2.69106 q^{2} +2.90048 q^{3} +5.24179 q^{4} +1.92081 q^{5} -7.80536 q^{6} -1.20204 q^{7} -8.72383 q^{8} +5.41280 q^{9} -5.16901 q^{10} +4.39826 q^{11} +15.2037 q^{12} +4.89889 q^{13} +3.23477 q^{14} +5.57128 q^{15} +12.9927 q^{16} -1.00000 q^{17} -14.5661 q^{18} +3.36389 q^{19} +10.0685 q^{20} -3.48651 q^{21} -11.8360 q^{22} +6.09901 q^{23} -25.3033 q^{24} -1.31049 q^{25} -13.1832 q^{26} +6.99827 q^{27} -6.30086 q^{28} -2.39114 q^{29} -14.9926 q^{30} -2.86035 q^{31} -17.5166 q^{32} +12.7571 q^{33} +2.69106 q^{34} -2.30890 q^{35} +28.3727 q^{36} -2.46495 q^{37} -9.05243 q^{38} +14.2092 q^{39} -16.7568 q^{40} -0.624351 q^{41} +9.38239 q^{42} +3.46842 q^{43} +23.0547 q^{44} +10.3970 q^{45} -16.4128 q^{46} +0.226662 q^{47} +37.6852 q^{48} -5.55509 q^{49} +3.52659 q^{50} -2.90048 q^{51} +25.6790 q^{52} +8.30118 q^{53} -18.8327 q^{54} +8.44822 q^{55} +10.4864 q^{56} +9.75691 q^{57} +6.43469 q^{58} +1.38614 q^{59} +29.2034 q^{60} +2.20597 q^{61} +7.69736 q^{62} -6.50642 q^{63} +21.1525 q^{64} +9.40985 q^{65} -34.3300 q^{66} +13.6842 q^{67} -5.24179 q^{68} +17.6901 q^{69} +6.21338 q^{70} +4.40197 q^{71} -47.2203 q^{72} -2.25729 q^{73} +6.63332 q^{74} -3.80104 q^{75} +17.6328 q^{76} -5.28690 q^{77} -38.2376 q^{78} -14.3401 q^{79} +24.9566 q^{80} +4.05997 q^{81} +1.68016 q^{82} -14.9957 q^{83} -18.2755 q^{84} -1.92081 q^{85} -9.33372 q^{86} -6.93545 q^{87} -38.3697 q^{88} +6.54082 q^{89} -27.9788 q^{90} -5.88869 q^{91} +31.9697 q^{92} -8.29639 q^{93} -0.609961 q^{94} +6.46140 q^{95} -50.8064 q^{96} -4.22487 q^{97} +14.9491 q^{98} +23.8069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.69106	−1.90286	−0.951432	−	0.307858i	$-0.900388\pi$
$2$	−2.69106	−1.90286	−0.951432	+	0.307858i	$0.900388\pi$
$3$	2.90048	1.67459	0.837297	−	0.546748i	$-0.184135\pi$
$3$	2.90048	1.67459	0.837297	+	0.546748i	$0.184135\pi$
$4$	5.24179	2.62089
$5$	1.92081	0.859013	0.429506	−	0.903064i	$-0.358688\pi$
$5$	1.92081	0.859013	0.429506	+	0.903064i	$0.358688\pi$
$6$	−7.80536	−3.18653
$7$	−1.20204	−0.454330	−0.227165	−	0.973856i	$-0.572946\pi$
$7$	−1.20204	−0.454330	−0.227165	+	0.973856i	$0.572946\pi$
$8$	−8.72383	−3.08434
$9$	5.41280	1.80427
$10$	−5.16901	−1.63458
$11$	4.39826	1.32613	0.663063	−	0.748564i	$-0.269256\pi$
$11$	4.39826	1.32613	0.663063	+	0.748564i	$0.269256\pi$
$12$	15.2037	4.38893
$13$	4.89889	1.35871	0.679354	−	0.733810i	$-0.262260\pi$
$13$	4.89889	1.35871	0.679354	+	0.733810i	$0.262260\pi$
$14$	3.23477	0.864528
$15$	5.57128	1.43850
$16$	12.9927	3.24819
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−14.5661	−3.43327
$19$	3.36389	0.771730	0.385865	−	0.922555i	$-0.373903\pi$
$19$	3.36389	0.771730	0.385865	+	0.922555i	$0.373903\pi$
$20$	10.0685	2.25138
$21$	−3.48651	−0.760818
$22$	−11.8360	−2.52344
$23$	6.09901	1.27173	0.635866	−	0.771800i	$-0.280643\pi$
$23$	6.09901	1.27173	0.635866	+	0.771800i	$0.280643\pi$
$24$	−25.3033	−5.16502
$25$	−1.31049	−0.262097
$26$	−13.1832	−2.58544
$27$	6.99827	1.34682
$28$	−6.30086	−1.19075
$29$	−2.39114	−0.444023	−0.222012	−	0.975044i	$-0.571262\pi$
$29$	−2.39114	−0.444023	−0.222012	+	0.975044i	$0.571262\pi$
$30$	−14.9926	−2.73727
$31$	−2.86035	−0.513734	−0.256867	−	0.966447i	$-0.582690\pi$
$31$	−2.86035	−0.513734	−0.256867	+	0.966447i	$0.582690\pi$
$32$	−17.5166	−3.09652
$33$	12.7571	2.22072
$34$	2.69106	0.461512
$35$	−2.30890	−0.390275
$36$	28.3727	4.72879
$37$	−2.46495	−0.405235	−0.202618	−	0.979258i	$-0.564945\pi$
$37$	−2.46495	−0.405235	−0.202618	+	0.979258i	$0.564945\pi$
$38$	−9.05243	−1.46850
$39$	14.2092	2.27529
$40$	−16.7568	−2.64949
$41$	−0.624351	−0.0975072	−0.0487536	−	0.998811i	$-0.515525\pi$
$41$	−0.624351	−0.0975072	−0.0487536	+	0.998811i	$0.515525\pi$
$42$	9.38239	1.44773
$43$	3.46842	0.528929	0.264465	−	0.964395i	$-0.414805\pi$
$43$	3.46842	0.528929	0.264465	+	0.964395i	$0.414805\pi$
$44$	23.0547	3.47563
$45$	10.3970	1.54989
$46$	−16.4128	−2.41993
$47$	0.226662	0.0330621	0.0165310	−	0.999863i	$-0.494738\pi$
$47$	0.226662	0.0330621	0.0165310	+	0.999863i	$0.494738\pi$
$48$	37.6852	5.43939
$49$	−5.55509	−0.793584
$50$	3.52659	0.498736
$51$	−2.90048	−0.406149
$52$	25.6790	3.56103
$53$	8.30118	1.14025	0.570127	−	0.821556i	$-0.306894\pi$
$53$	8.30118	1.14025	0.570127	+	0.821556i	$0.306894\pi$
$54$	−18.8327	−2.56281
$55$	8.44822	1.13916
$56$	10.4864	1.40131
$57$	9.75691	1.29233
$58$	6.43469	0.844916
$59$	1.38614	0.180460	0.0902302	−	0.995921i	$-0.471240\pi$
$59$	1.38614	0.180460	0.0902302	+	0.995921i	$0.471240\pi$
$60$	29.2034	3.77015
$61$	2.20597	0.282446	0.141223	−	0.989978i	$-0.454897\pi$
$61$	2.20597	0.282446	0.141223	+	0.989978i	$0.454897\pi$
$62$	7.69736	0.977566
$63$	−6.50642	−0.819732
$64$	21.1525	2.64407
$65$	9.40985	1.16715
$66$	−34.3300	−4.22573
$67$	13.6842	1.67179	0.835896	−	0.548888i	$-0.184949\pi$
$67$	13.6842	1.67179	0.835896	+	0.548888i	$0.184949\pi$
$68$	−5.24179	−0.635660
$69$	17.6901	2.12963
$70$	6.21338	0.742640
$71$	4.40197	0.522418	0.261209	−	0.965282i	$-0.415879\pi$
$71$	4.40197	0.522418	0.261209	+	0.965282i	$0.415879\pi$
$72$	−47.2203	−5.56497
$73$	−2.25729	−0.264195	−0.132098	−	0.991237i	$-0.542171\pi$
$73$	−2.25729	−0.264195	−0.132098	+	0.991237i	$0.542171\pi$
$74$	6.63332	0.771108
$75$	−3.80104	−0.438907
$76$	17.6328	2.02262
$77$	−5.28690	−0.602498
$78$	−38.2376	−4.32956
$79$	−14.3401	−1.61339	−0.806695	−	0.590968i	$-0.798746\pi$
$79$	−14.3401	−1.61339	−0.806695	+	0.590968i	$0.798746\pi$
$80$	24.9566	2.79023
$81$	4.05997	0.451108
$82$	1.68016	0.185543
$83$	−14.9957	−1.64599	−0.822997	−	0.568046i	$-0.807700\pi$
$83$	−14.9957	−1.64599	−0.822997	+	0.568046i	$0.807700\pi$
$84$	−18.2755	−1.99402
$85$	−1.92081	−0.208341
$86$	−9.33372	−1.00648
$87$	−6.93545	−0.743558
$88$	−38.3697	−4.09022
$89$	6.54082	0.693325	0.346663	−	0.937990i	$-0.387315\pi$
$89$	6.54082	0.693325	0.346663	+	0.937990i	$0.387315\pi$
$90$	−27.9788	−2.94922
$91$	−5.88869	−0.617302
$92$	31.9697	3.33307
$93$	−8.29639	−0.860296
$94$	−0.609961	−0.0629126
$95$	6.46140	0.662926
$96$	−50.8064	−5.18541
$97$	−4.22487	−0.428971	−0.214485	−	0.976727i	$-0.568807\pi$
$97$	−4.22487	−0.428971	−0.214485	+	0.976727i	$0.568807\pi$
$98$	14.9491	1.51008
$99$	23.8069	2.39268
$100$	−6.86929	−0.686929
$101$	−6.17947	−0.614880	−0.307440	−	0.951568i	$-0.599472\pi$
$101$	−6.17947	−0.614880	−0.307440	+	0.951568i	$0.599472\pi$
$102$	7.80536	0.772846
$103$	16.3056	1.60664	0.803320	−	0.595548i	$-0.203065\pi$
$103$	16.3056	1.60664	0.803320	+	0.595548i	$0.203065\pi$
$104$	−42.7371	−4.19072
$105$	−6.69692	−0.653552
$106$	−22.3389	−2.16975
$107$	−1.50670	−0.145658	−0.0728291	−	0.997344i	$-0.523203\pi$
$107$	−1.50670	−0.145658	−0.0728291	+	0.997344i	$0.523203\pi$
$108$	36.6834	3.52987
$109$	3.81157	0.365082	0.182541	−	0.983198i	$-0.441568\pi$
$109$	3.81157	0.365082	0.182541	+	0.983198i	$0.441568\pi$
$110$	−22.7346	−2.16766
$111$	−7.14954	−0.678604
$112$	−15.6178	−1.47575
$113$	−7.36741	−0.693067	−0.346534	−	0.938038i	$-0.612641\pi$
$113$	−7.36741	−0.693067	−0.346534	+	0.938038i	$0.612641\pi$
$114$	−26.2564	−2.45914
$115$	11.7150	1.09243
$116$	−12.5338	−1.16374
$117$	26.5167	2.45147
$118$	−3.73019	−0.343392
$119$	1.20204	0.110191
$120$	−48.6029	−4.43681
$121$	8.34468	0.758608
$122$	−5.93640	−0.537457
$123$	−1.81092	−0.163285
$124$	−14.9933	−1.34644
$125$	−12.1212	−1.08416
$126$	17.5091	1.55984
$127$	−16.9619	−1.50513	−0.752564	−	0.658519i	$-0.771183\pi$
$127$	−16.9619	−1.50513	−0.752564	+	0.658519i	$0.771183\pi$
$128$	−21.8896	−1.93478
$129$	10.0601	0.885742
$130$	−25.3224	−2.22092
$131$	8.19958	0.716400	0.358200	−	0.933645i	$-0.383391\pi$
$131$	8.19958	0.716400	0.358200	+	0.933645i	$0.383391\pi$
$132$	66.8698	5.82027
$133$	−4.04355	−0.350620
$134$	−36.8250	−3.18119
$135$	13.4424	1.15693
$136$	8.72383	0.748062
$137$	13.7469	1.17448	0.587240	−	0.809413i	$-0.300215\pi$
$137$	13.7469	1.17448	0.587240	+	0.809413i	$0.300215\pi$
$138$	−47.6050	−4.05240
$139$	−13.0318	−1.10534	−0.552670	−	0.833400i	$-0.686391\pi$
$139$	−13.0318	−1.10534	−0.552670	+	0.833400i	$0.686391\pi$
$140$	−12.1027	−1.02287
$141$	0.657429	0.0553656
$142$	−11.8460	−0.994091
$143$	21.5466	1.80182
$144$	70.3271	5.86059
$145$	−4.59292	−0.381421
$146$	6.07448	0.502728
$147$	−16.1124	−1.32893
$148$	−12.9207	−1.06208
$149$	8.55049	0.700484	0.350242	−	0.936659i	$-0.386099\pi$
$149$	8.55049	0.700484	0.350242	+	0.936659i	$0.386099\pi$
$150$	10.2288	0.835180
$151$	−3.43388	−0.279445	−0.139722	−	0.990191i	$-0.544621\pi$
$151$	−3.43388	−0.279445	−0.139722	+	0.990191i	$0.544621\pi$
$152$	−29.3460	−2.38028
$153$	−5.41280	−0.437599
$154$	14.2273	1.14647
$155$	−5.49419	−0.441304
$156$	74.4813	5.96328
$157$	−5.57839	−0.445204	−0.222602	−	0.974909i	$-0.571455\pi$
$157$	−5.57839	−0.445204	−0.222602	+	0.974909i	$0.571455\pi$
$158$	38.5901	3.07006
$159$	24.0774	1.90946
$160$	−33.6460	−2.65995
$161$	−7.33128	−0.577786
$162$	−10.9256	−0.858397
$163$	−21.8811	−1.71386	−0.856931	−	0.515432i	$-0.827631\pi$
$163$	−21.8811	−1.71386	−0.856931	+	0.515432i	$0.827631\pi$
$164$	−3.27271	−0.255556
$165$	24.5039	1.90763
$166$	40.3543	3.13210
$167$	−16.0258	−1.24011	−0.620056	−	0.784557i	$-0.712890\pi$
$167$	−16.0258	−1.24011	−0.620056	+	0.784557i	$0.712890\pi$
$168$	30.4157	2.34662
$169$	10.9992	0.846090
$170$	5.16901	0.396445
$171$	18.2081	1.39241
$172$	18.1807	1.38627
$173$	6.20892	0.472056	0.236028	−	0.971746i	$-0.424154\pi$
$173$	6.20892	0.472056	0.236028	+	0.971746i	$0.424154\pi$
$174$	18.6637	1.41489
$175$	1.57526	0.119079
$176$	57.1455	4.30750
$177$	4.02048	0.302198
$178$	−17.6017	−1.31930
$179$	11.6436	0.870283	0.435142	−	0.900362i	$-0.356698\pi$
$179$	11.6436	0.870283	0.435142	+	0.900362i	$0.356698\pi$
$180$	54.4986	4.06209
$181$	−10.8377	−0.805557	−0.402778	−	0.915298i	$-0.631955\pi$
$181$	−10.8377	−0.805557	−0.402778	+	0.915298i	$0.631955\pi$
$182$	15.8468	1.17464
$183$	6.39839	0.472982
$184$	−53.2067	−3.92245
$185$	−4.73470	−0.348102
$186$	22.3261	1.63703
$187$	−4.39826	−0.321633
$188$	1.18811	0.0866521
$189$	−8.41223	−0.611900
$190$	−17.3880	−1.26146
$191$	13.1941	0.954690	0.477345	−	0.878716i	$-0.341599\pi$
$191$	13.1941	0.954690	0.477345	+	0.878716i	$0.341599\pi$
$192$	61.3526	4.42774
$193$	23.6843	1.70483	0.852417	−	0.522863i	$-0.175136\pi$
$193$	23.6843	1.70483	0.852417	+	0.522863i	$0.175136\pi$
$194$	11.3694	0.816274
$195$	27.2931	1.95450
$196$	−29.1186	−2.07990
$197$	−6.49194	−0.462531	−0.231266	−	0.972891i	$-0.574287\pi$
$197$	−6.49194	−0.462531	−0.231266	+	0.972891i	$0.574287\pi$
$198$	−64.0657	−4.55295
$199$	−13.2163	−0.936880	−0.468440	−	0.883495i	$-0.655184\pi$
$199$	−13.2163	−0.936880	−0.468440	+	0.883495i	$0.655184\pi$
$200$	11.4325	0.808397
$201$	39.6908	2.79957
$202$	16.6293	1.17003
$203$	2.87425	0.201733
$204$	−15.2037	−1.06447
$205$	−1.19926	−0.0837599
$206$	−43.8793	−3.05722
$207$	33.0127	2.29454
$208$	63.6501	4.41334
$209$	14.7953	1.02341
$210$	18.0218	1.24362
$211$	−20.0203	−1.37825	−0.689127	−	0.724641i	$-0.742006\pi$
$211$	−20.0203	−1.37825	−0.689127	+	0.724641i	$0.742006\pi$
$212$	43.5130	2.98848
$213$	12.7678	0.874838
$214$	4.05462	0.277168
$215$	6.66218	0.454357
$216$	−61.0517	−4.15404
$217$	3.43827	0.233405
$218$	−10.2571	−0.694702
$219$	−6.54722	−0.442420
$220$	44.2838	2.98561
$221$	−4.89889	−0.329535
$222$	19.2398	1.29129
$223$	−19.1718	−1.28384	−0.641918	−	0.766773i	$-0.721861\pi$
$223$	−19.1718	−1.28384	−0.641918	+	0.766773i	$0.721861\pi$
$224$	21.0557	1.40684
$225$	−7.09340	−0.472893
$226$	19.8261	1.31881
$227$	−1.81912	−0.120740	−0.0603698	−	0.998176i	$-0.519228\pi$
$227$	−1.81912	−0.120740	−0.0603698	+	0.998176i	$0.519228\pi$
$228$	51.1436	3.38707
$229$	22.9613	1.51733	0.758663	−	0.651483i	$-0.225853\pi$
$229$	22.9613	1.51733	0.758663	+	0.651483i	$0.225853\pi$
$230$	−31.5258	−2.07875
$231$	−15.3346	−1.00894
$232$	20.8599	1.36952
$233$	−12.1118	−0.793469	−0.396734	−	0.917933i	$-0.629857\pi$
$233$	−12.1118	−0.793469	−0.396734	+	0.917933i	$0.629857\pi$
$234$	−71.3580	−4.66482
$235$	0.435375	0.0284007
$236$	7.26586	0.472967
$237$	−41.5933	−2.70177
$238$	−3.23477	−0.209679
$239$	−3.85778	−0.249539	−0.124769	−	0.992186i	$-0.539819\pi$
$239$	−3.85778	−0.249539	−0.124769	+	0.992186i	$0.539819\pi$
$240$	72.3862	4.67251
$241$	9.80258	0.631440	0.315720	−	0.948852i	$-0.397754\pi$
$241$	9.80258	0.631440	0.315720	+	0.948852i	$0.397754\pi$
$242$	−22.4560	−1.44353
$243$	−9.21894	−0.591395
$244$	11.5632	0.740261
$245$	−10.6703	−0.681699
$246$	4.87328	0.310709
$247$	16.4794	1.04856
$248$	24.9532	1.58453
$249$	−43.4948	−2.75637
$250$	32.6190	2.06300
$251$	13.0580	0.824215	0.412107	−	0.911135i	$-0.364793\pi$
$251$	13.0580	0.824215	0.412107	+	0.911135i	$0.364793\pi$
$252$	−34.1052	−2.14843
$253$	26.8250	1.68647
$254$	45.6455	2.86406
$255$	−5.57128	−0.348887
$256$	16.6010	1.03757
$257$	−14.2587	−0.889436	−0.444718	−	0.895671i	$-0.646696\pi$
$257$	−14.2587	−0.889436	−0.444718	+	0.895671i	$0.646696\pi$
$258$	−27.0723	−1.68545
$259$	2.96298	0.184110
$260$	49.3244	3.05897
$261$	−12.9427	−0.801135
$262$	−22.0655	−1.36321
$263$	3.43706	0.211938	0.105969	−	0.994369i	$-0.466206\pi$
$263$	3.43706	0.211938	0.105969	+	0.994369i	$0.466206\pi$
$264$	−111.290	−6.84946
$265$	15.9450	0.979493
$266$	10.8814	0.667182
$267$	18.9715	1.16104
$268$	71.7297	4.38159
$269$	29.7162	1.81183	0.905913	−	0.423464i	$-0.139186\pi$
$269$	29.7162	1.81183	0.905913	+	0.423464i	$0.139186\pi$
$270$	−36.1741	−2.20149
$271$	0.593779	0.0360695	0.0180347	−	0.999837i	$-0.494259\pi$
$271$	0.593779	0.0360695	0.0180347	+	0.999837i	$0.494259\pi$
$272$	−12.9927	−0.787801
$273$	−17.0800	−1.03373
$274$	−36.9938	−2.23488
$275$	−5.76386	−0.347574
$276$	92.7275	5.58154
$277$	−0.816584	−0.0490638	−0.0245319	−	0.999699i	$-0.507810\pi$
$277$	−0.816584	−0.0490638	−0.0245319	+	0.999699i	$0.507810\pi$
$278$	35.0692	2.10331
$279$	−15.4825	−0.926912
$280$	20.1424	1.20374
$281$	26.2515	1.56603	0.783016	−	0.622002i	$-0.213680\pi$
$281$	26.2515	1.56603	0.783016	+	0.622002i	$0.213680\pi$
$282$	−1.76918	−0.105353
$283$	−20.2555	−1.20406	−0.602032	−	0.798472i	$-0.705642\pi$
$283$	−20.2555	−1.20406	−0.602032	+	0.798472i	$0.705642\pi$
$284$	23.0742	1.36920
$285$	18.7412	1.11013
$286$	−57.9831	−3.42862
$287$	0.750497	0.0443004
$288$	−94.8135	−5.58694
$289$	1.00000	0.0588235
$290$	12.3598	0.725793
$291$	−12.2542	−0.718352
$292$	−11.8322	−0.692427
$293$	−8.96731	−0.523876	−0.261938	−	0.965085i	$-0.584362\pi$
$293$	−8.96731	−0.523876	−0.261938	+	0.965085i	$0.584362\pi$
$294$	43.3595	2.52878
$295$	2.66252	0.155018
$296$	21.5038	1.24988
$297$	30.7802	1.78605
$298$	−23.0099	−1.33293
$299$	29.8784	1.72791
$300$	−19.9243	−1.15033
$301$	−4.16919	−0.240308
$302$	9.24075	0.531746
$303$	−17.9234	−1.02967
$304$	43.7062	2.50672
$305$	4.23726	0.242625
$306$	14.5661	0.832691
$307$	−16.7943	−0.958503	−0.479251	−	0.877678i	$-0.659092\pi$
$307$	−16.7943	−0.958503	−0.479251	+	0.877678i	$0.659092\pi$
$308$	−27.7128	−1.57908
$309$	47.2941	2.69047
$310$	14.7852	0.839742
$311$	−10.1794	−0.577219	−0.288609	−	0.957447i	$-0.593193\pi$
$311$	−10.1794	−0.577219	−0.288609	+	0.957447i	$0.593193\pi$
$312$	−123.958	−7.01775
$313$	−8.26962	−0.467426	−0.233713	−	0.972306i	$-0.575088\pi$
$313$	−8.26962	−0.467426	−0.233713	+	0.972306i	$0.575088\pi$
$314$	15.0118	0.847162
$315$	−12.4976	−0.704160
$316$	−75.1678	−4.22852
$317$	11.8427	0.665152	0.332576	−	0.943076i	$-0.392082\pi$
$317$	11.8427	0.665152	0.332576	+	0.943076i	$0.392082\pi$
$318$	−64.7937	−3.63345
$319$	−10.5168	−0.588830
$320$	40.6300	2.27129
$321$	−4.37016	−0.243918
$322$	19.7289	1.09945
$323$	−3.36389	−0.187172
$324$	21.2815	1.18231
$325$	−6.41994	−0.356114
$326$	58.8833	3.26125
$327$	11.0554	0.611364
$328$	5.44673	0.300745
$329$	−0.272458	−0.0150211
$330$	−65.9414	−3.62996
$331$	−18.7361	−1.02983	−0.514916	−	0.857241i	$-0.672177\pi$
$331$	−18.7361	−1.02983	−0.514916	+	0.857241i	$0.672177\pi$
$332$	−78.6043	−4.31397
$333$	−13.3423	−0.731152
$334$	43.1263	2.35977
$335$	26.2848	1.43609
$336$	−45.2993	−2.47128
$337$	−13.2141	−0.719817	−0.359908	−	0.932988i	$-0.617192\pi$
$337$	−13.2141	−0.719817	−0.359908	+	0.932988i	$0.617192\pi$
$338$	−29.5994	−1.60999
$339$	−21.3690	−1.16061
$340$	−10.0685	−0.546040
$341$	−12.5806	−0.681275
$342$	−48.9989	−2.64956
$343$	15.0918	0.814879
$344$	−30.2579	−1.63140
$345$	33.9793	1.82938
$346$	−16.7086	−0.898258
$347$	−15.6025	−0.837585	−0.418793	−	0.908082i	$-0.637547\pi$
$347$	−15.6025	−0.837585	−0.418793	+	0.908082i	$0.637547\pi$
$348$	−36.3541	−1.94879
$349$	18.4997	0.990266	0.495133	−	0.868817i	$-0.335119\pi$
$349$	18.4997	0.990266	0.495133	+	0.868817i	$0.335119\pi$
$350$	−4.23912	−0.226591
$351$	34.2838	1.82993
$352$	−77.0423	−4.10637
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−10.8193	−0.575042
$355$	8.45536	0.448764
$356$	34.2856	1.81713
$357$	3.48651	0.184525
$358$	−31.3336	−1.65603
$359$	23.1293	1.22072	0.610358	−	0.792125i	$-0.291025\pi$
$359$	23.1293	1.22072	0.610358	+	0.792125i	$0.291025\pi$
$360$	−90.7013	−4.78038
$361$	−7.68422	−0.404433
$362$	29.1648	1.53287
$363$	24.2036	1.27036
$364$	−30.8672	−1.61788
$365$	−4.33582	−0.226947
$366$	−17.2184	−0.900022
$367$	−14.5218	−0.758030	−0.379015	−	0.925390i	$-0.623737\pi$
$367$	−14.5218	−0.758030	−0.379015	+	0.925390i	$0.623737\pi$
$368$	79.2429	4.13082
$369$	−3.37948	−0.175929
$370$	12.7413	0.662391
$371$	−9.97838	−0.518052
$372$	−43.4879	−2.25474
$373$	−36.6352	−1.89690	−0.948449	−	0.316930i	$-0.897348\pi$
$373$	−36.6352	−1.89690	−0.948449	+	0.316930i	$0.897348\pi$
$374$	11.8360	0.612023
$375$	−35.1575	−1.81552
$376$	−1.97736	−0.101975
$377$	−11.7139	−0.603298
$378$	22.6378	1.16436
$379$	9.70768	0.498650	0.249325	−	0.968420i	$-0.419791\pi$
$379$	9.70768	0.498650	0.249325	+	0.968420i	$0.419791\pi$
$380$	33.8693	1.73746
$381$	−49.1978	−2.52048
$382$	−35.5060	−1.81665
$383$	−36.2394	−1.85175	−0.925873	−	0.377834i	$-0.876669\pi$
$383$	−36.2394	−1.85175	−0.925873	+	0.377834i	$0.876669\pi$
$384$	−63.4904	−3.23998
$385$	−10.1551	−0.517554
$386$	−63.7358	−3.24407
$387$	18.7739	0.954329
$388$	−22.1459	−1.12429
$389$	13.1059	0.664494	0.332247	−	0.943192i	$-0.392193\pi$
$389$	13.1059	0.664494	0.332247	+	0.943192i	$0.392193\pi$
$390$	−73.4473	−3.71915
$391$	−6.09901	−0.308440
$392$	48.4617	2.44768
$393$	23.7827	1.19968
$394$	17.4702	0.880135
$395$	−27.5447	−1.38592
$396$	124.791	6.27096
$397$	−2.95577	−0.148346	−0.0741730	−	0.997245i	$-0.523632\pi$
$397$	−2.95577	−0.148346	−0.0741730	+	0.997245i	$0.523632\pi$
$398$	35.5659	1.78276
$399$	−11.7282	−0.587146
$400$	−17.0268	−0.851341
$401$	−21.1258	−1.05497	−0.527486	−	0.849564i	$-0.676865\pi$
$401$	−21.1258	−1.05497	−0.527486	+	0.849564i	$0.676865\pi$
$402$	−106.810	−5.32721
$403$	−14.0126	−0.698015
$404$	−32.3914	−1.61153
$405$	7.79844	0.387507
$406$	−7.73478	−0.383870
$407$	−10.8415	−0.537392
$408$	25.3033	1.25270
$409$	31.1820	1.54185	0.770926	−	0.636925i	$-0.219794\pi$
$409$	31.1820	1.54185	0.770926	+	0.636925i	$0.219794\pi$
$410$	3.22728	0.159384
$411$	39.8727	1.96678
$412$	85.4705	4.21083
$413$	−1.66620	−0.0819886
$414$	−88.8390	−4.36620
$415$	−28.8039	−1.41393
$416$	−85.8117	−4.20727
$417$	−37.7984	−1.85100
$418$	−39.8149	−1.94741
$419$	6.47319	0.316236	0.158118	−	0.987420i	$-0.449457\pi$
$419$	6.47319	0.316236	0.158118	+	0.987420i	$0.449457\pi$
$420$	−35.1038	−1.71289
$421$	18.0188	0.878183	0.439092	−	0.898442i	$-0.355300\pi$
$421$	18.0188	0.878183	0.439092	+	0.898442i	$0.355300\pi$
$422$	53.8757	2.62263
$423$	1.22688	0.0596527
$424$	−72.4180	−3.51693
$425$	1.31049	0.0635680
$426$	−34.3590	−1.66470
$427$	−2.65168	−0.128324
$428$	−7.89780	−0.381755
$429$	62.4956	3.01731
$430$	−17.9283	−0.864579
$431$	8.51488	0.410147	0.205074	−	0.978747i	$-0.434257\pi$
$431$	8.51488	0.410147	0.205074	+	0.978747i	$0.434257\pi$
$432$	90.9267	4.37472
$433$	−22.0775	−1.06098	−0.530489	−	0.847692i	$-0.677991\pi$
$433$	−22.0775	−1.06098	−0.530489	+	0.847692i	$0.677991\pi$
$434$	−9.25257	−0.444137
$435$	−13.3217	−0.638726
$436$	19.9794	0.956841
$437$	20.5164	0.981433
$438$	17.6189	0.841865
$439$	17.9418	0.856314	0.428157	−	0.903704i	$-0.359163\pi$
$439$	17.9418	0.856314	0.428157	+	0.903704i	$0.359163\pi$
$440$	−73.7008	−3.51355
$441$	−30.0686	−1.43184
$442$	13.1832	0.627061
$443$	37.1678	1.76590	0.882948	−	0.469471i	$-0.155556\pi$
$443$	37.1678	1.76590	0.882948	+	0.469471i	$0.155556\pi$
$444$	−37.4764	−1.77855
$445$	12.5637	0.595575
$446$	51.5923	2.44297
$447$	24.8006	1.17303
$448$	−25.4263	−1.20128
$449$	−39.4880	−1.86355	−0.931777	−	0.363032i	$-0.881742\pi$
$449$	−39.4880	−1.86355	−0.931777	+	0.363032i	$0.881742\pi$
$450$	19.0887	0.899852
$451$	−2.74606	−0.129307
$452$	−38.6184	−1.81646
$453$	−9.95989	−0.467957
$454$	4.89537	0.229751
$455$	−11.3111	−0.530270
$456$	−85.1176	−3.98600
$457$	1.81284	0.0848009	0.0424004	−	0.999101i	$-0.486499\pi$
$457$	1.81284	0.0848009	0.0424004	+	0.999101i	$0.486499\pi$
$458$	−61.7902	−2.88726
$459$	−6.99827	−0.326651
$460$	61.4077	2.86315
$461$	6.15990	0.286895	0.143448	−	0.989658i	$-0.454181\pi$
$461$	6.15990	0.286895	0.143448	+	0.989658i	$0.454181\pi$
$462$	41.2662	1.91988
$463$	−18.6539	−0.866920	−0.433460	−	0.901173i	$-0.642707\pi$
$463$	−18.6539	−0.866920	−0.433460	+	0.901173i	$0.642707\pi$
$464$	−31.0674	−1.44227
$465$	−15.9358	−0.739005
$466$	32.5935	1.50986
$467$	14.1399	0.654316	0.327158	−	0.944970i	$-0.393909\pi$
$467$	14.1399	0.654316	0.327158	+	0.944970i	$0.393909\pi$
$468$	138.995	6.42504
$469$	−16.4490	−0.759545
$470$	−1.17162	−0.0540427
$471$	−16.1800	−0.745536
$472$	−12.0925	−0.556601
$473$	15.2550	0.701426
$474$	111.930	5.14111
$475$	−4.40834	−0.202268
$476$	6.30086	0.288799
$477$	44.9326	2.05732
$478$	10.3815	0.474838
$479$	3.01688	0.137845	0.0689223	−	0.997622i	$-0.478044\pi$
$479$	3.01688	0.137845	0.0689223	+	0.997622i	$0.478044\pi$
$480$	−97.5896	−4.45433
$481$	−12.0755	−0.550597
$482$	−26.3793	−1.20154
$483$	−21.2642	−0.967556
$484$	43.7410	1.98823
$485$	−8.11518	−0.368491
$486$	24.8087	1.12534
$487$	10.1444	0.459688	0.229844	−	0.973227i	$-0.426178\pi$
$487$	10.1444	0.459688	0.229844	+	0.973227i	$0.426178\pi$
$488$	−19.2445	−0.871159
$489$	−63.4658	−2.87002
$490$	28.7143	1.29718
$491$	−16.9218	−0.763669	−0.381835	−	0.924231i	$-0.624708\pi$
$491$	−16.9218	−0.763669	−0.381835	+	0.924231i	$0.624708\pi$
$492$	−9.49244	−0.427952
$493$	2.39114	0.107691
$494$	−44.3469	−1.99526
$495$	45.7285	2.05534
$496$	−37.1638	−1.66870
$497$	−5.29136	−0.237350
$498$	117.047	5.24500
$499$	25.9639	1.16231	0.581153	−	0.813795i	$-0.302602\pi$
$499$	25.9639	1.16231	0.581153	+	0.813795i	$0.302602\pi$
$500$	−63.5370	−2.84146
$501$	−46.4825	−2.07669
$502$	−35.1399	−1.56837
$503$	−11.2133	−0.499977	−0.249988	−	0.968249i	$-0.580427\pi$
$503$	−11.2133	−0.499977	−0.249988	+	0.968249i	$0.580427\pi$
$504$	56.7609	2.52833
$505$	−11.8696	−0.528189
$506$	−72.1877	−3.20913
$507$	31.9029	1.41686
$508$	−88.9108	−3.94478
$509$	32.0976	1.42270	0.711351	−	0.702837i	$-0.248084\pi$
$509$	32.0976	1.42270	0.711351	+	0.702837i	$0.248084\pi$
$510$	14.9926	0.663884
$511$	2.71336	0.120032
$512$	−0.895154	−0.0395606
$513$	23.5414	1.03938
$514$	38.3711	1.69248
$515$	31.3200	1.38012
$516$	52.7328	2.32143
$517$	0.996919	0.0438444
$518$	−7.97354	−0.350337
$519$	18.0089	0.790502
$520$	−82.0899	−3.59988
$521$	30.9918	1.35778	0.678888	−	0.734242i	$-0.262462\pi$
$521$	30.9918	1.35778	0.678888	+	0.734242i	$0.262462\pi$
$522$	34.8296	1.52445
$523$	38.2633	1.67314	0.836569	−	0.547862i	$-0.184558\pi$
$523$	38.2633	1.67314	0.836569	+	0.547862i	$0.184558\pi$
$524$	42.9804	1.87761
$525$	4.56902	0.199408
$526$	−9.24931	−0.403289
$527$	2.86035	0.124599
$528$	165.749	7.21332
$529$	14.1979	0.617301
$530$	−42.9089	−1.86384
$531$	7.50291	0.325598
$532$	−21.1954	−0.918937
$533$	−3.05863	−0.132484
$534$	−51.0535	−2.20930
$535$	−2.89409	−0.125122
$536$	−119.379	−5.15637
$537$	33.7720	1.45737
$538$	−79.9679	−3.44766
$539$	−24.4327	−1.05239
$540$	70.4619	3.03220
$541$	−11.5836	−0.498019	−0.249010	−	0.968501i	$-0.580105\pi$
$541$	−11.5836	−0.498019	−0.249010	+	0.968501i	$0.580105\pi$
$542$	−1.59789	−0.0686353
$543$	−31.4344	−1.34898
$544$	17.5166	0.751016
$545$	7.32130	0.313610
$546$	45.9633	1.96705
$547$	−29.4274	−1.25822	−0.629112	−	0.777314i	$-0.716581\pi$
$547$	−29.4274	−1.25822	−0.629112	+	0.777314i	$0.716581\pi$
$548$	72.0585	3.07819
$549$	11.9405	0.509608
$550$	15.5109	0.661386
$551$	−8.04353	−0.342666
$552$	−154.325	−6.56851
$553$	17.2375	0.733011
$554$	2.19747	0.0933617
$555$	−13.7329	−0.582930
$556$	−68.3097	−2.89698
$557$	39.8952	1.69041	0.845206	−	0.534440i	$-0.179478\pi$
$557$	39.8952	1.69041	0.845206	+	0.534440i	$0.179478\pi$
$558$	41.6643	1.76379
$559$	16.9914	0.718661
$560$	−29.9989	−1.26769
$561$	−12.7571	−0.538604
$562$	−70.6442	−2.97995
$563$	12.2858	0.517786	0.258893	−	0.965906i	$-0.416642\pi$
$563$	12.2858	0.517786	0.258893	+	0.965906i	$0.416642\pi$
$564$	3.44610	0.145107
$565$	−14.1514	−0.595354
$566$	54.5087	2.29117
$567$	−4.88026	−0.204952
$568$	−38.4021	−1.61131
$569$	−1.66539	−0.0698167	−0.0349084	−	0.999391i	$-0.511114\pi$
$569$	−1.66539	−0.0698167	−0.0349084	+	0.999391i	$0.511114\pi$
$570$	−50.4336	−2.11243
$571$	3.37725	0.141333	0.0706667	−	0.997500i	$-0.477487\pi$
$571$	3.37725	0.141333	0.0706667	+	0.997500i	$0.477487\pi$
$572$	112.943	4.72237
$573$	38.2692	1.59872
$574$	−2.01963	−0.0842977
$575$	−7.99267	−0.333318
$576$	114.494	4.77060
$577$	−0.820741	−0.0341679	−0.0170840	−	0.999854i	$-0.505438\pi$
$577$	−0.820741	−0.0341679	−0.0170840	+	0.999854i	$0.505438\pi$
$578$	−2.69106	−0.111933
$579$	68.6959	2.85491
$580$	−24.0751	−0.999665
$581$	18.0255	0.747824
$582$	32.9767	1.36693
$583$	36.5107	1.51212
$584$	19.6922	0.814868
$585$	50.9336	2.10584
$586$	24.1315	0.996865
$587$	−7.04367	−0.290724	−0.145362	−	0.989379i	$-0.546435\pi$
$587$	−7.04367	−0.290724	−0.145362	+	0.989379i	$0.546435\pi$
$588$	−84.4580	−3.48299
$589$	−9.62191	−0.396464
$590$	−7.16499	−0.294978
$591$	−18.8297	−0.774552
$592$	−32.0265	−1.31628
$593$	20.0308	0.822567	0.411283	−	0.911508i	$-0.365081\pi$
$593$	20.0308	0.822567	0.411283	+	0.911508i	$0.365081\pi$
$594$	−82.8313	−3.39861
$595$	2.30890	0.0946556
$596$	44.8199	1.83589
$597$	−38.3337	−1.56889
$598$	−80.4045	−3.28798
$599$	16.4679	0.672861	0.336431	−	0.941708i	$-0.390780\pi$
$599$	16.4679	0.672861	0.336431	+	0.941708i	$0.390780\pi$
$600$	33.1597	1.35374
$601$	33.8627	1.38129	0.690644	−	0.723195i	$-0.257327\pi$
$601$	33.8627	1.38129	0.690644	+	0.723195i	$0.257327\pi$
$602$	11.2195	0.457274
$603$	74.0698	3.01636
$604$	−17.9996	−0.732395
$605$	16.0286	0.651653
$606$	48.2330	1.95933
$607$	−2.08919	−0.0847975	−0.0423987	−	0.999101i	$-0.513500\pi$
$607$	−2.08919	−0.0847975	−0.0423987	+	0.999101i	$0.513500\pi$
$608$	−58.9238	−2.38968
$609$	8.33672	0.337821
$610$	−11.4027	−0.461682
$611$	1.11039	0.0449217
$612$	−28.3727	−1.14690
$613$	3.75332	0.151595	0.0757976	−	0.997123i	$-0.475850\pi$
$613$	3.75332	0.151595	0.0757976	+	0.997123i	$0.475850\pi$
$614$	45.1945	1.82390
$615$	−3.47843	−0.140264
$616$	46.1220	1.85831
$617$	6.96339	0.280335	0.140168	−	0.990128i	$-0.455236\pi$
$617$	6.96339	0.280335	0.140168	+	0.990128i	$0.455236\pi$
$618$	−127.271	−5.11960
$619$	47.9655	1.92790	0.963948	−	0.266092i	$-0.0857323\pi$
$619$	47.9655	1.92790	0.963948	+	0.266092i	$0.0857323\pi$
$620$	−28.7994	−1.15661
$621$	42.6825	1.71279
$622$	27.3932	1.09837
$623$	−7.86235	−0.314998
$624$	184.616	7.39055
$625$	−16.7302	−0.669208
$626$	22.2540	0.889449
$627$	42.9134	1.71380
$628$	−29.2407	−1.16683
$629$	2.46495	0.0982840
$630$	33.6317	1.33992
$631$	43.0562	1.71404	0.857019	−	0.515284i	$-0.172314\pi$
$631$	43.0562	1.71404	0.857019	+	0.515284i	$0.172314\pi$
$632$	125.101	4.97624
$633$	−58.0685	−2.30802
$634$	−31.8694	−1.26569
$635$	−32.5807	−1.29292
$636$	126.209	5.00450
$637$	−27.2138	−1.07825
$638$	28.3014	1.12046
$639$	23.8270	0.942581
$640$	−42.0458	−1.66200
$641$	4.35494	0.172010	0.0860049	−	0.996295i	$-0.472590\pi$
$641$	4.35494	0.172010	0.0860049	+	0.996295i	$0.472590\pi$
$642$	11.7603	0.464144
$643$	−45.1405	−1.78017	−0.890084	−	0.455796i	$-0.849355\pi$
$643$	−45.1405	−1.78017	−0.890084	+	0.455796i	$0.849355\pi$
$644$	−38.4290	−1.51431
$645$	19.3235	0.760863
$646$	9.05243	0.356163
$647$	27.2706	1.07212	0.536058	−	0.844181i	$-0.319913\pi$
$647$	27.2706	1.07212	0.536058	+	0.844181i	$0.319913\pi$
$648$	−35.4185	−1.39137
$649$	6.09662	0.239313
$650$	17.2764	0.677637
$651$	9.97263	0.390858
$652$	−114.696	−4.49185
$653$	−14.0796	−0.550976	−0.275488	−	0.961304i	$-0.588839\pi$
$653$	−14.0796	−0.550976	−0.275488	+	0.961304i	$0.588839\pi$
$654$	−29.7507	−1.16334
$655$	15.7498	0.615397
$656$	−8.11203	−0.316722
$657$	−12.2182	−0.476678
$658$	0.733199	0.0285831
$659$	−34.2811	−1.33540	−0.667701	−	0.744430i	$-0.732721\pi$
$659$	−34.2811	−1.33540	−0.667701	+	0.744430i	$0.732721\pi$
$660$	128.444	4.99969
$661$	−38.6634	−1.50383	−0.751915	−	0.659260i	$-0.770870\pi$
$661$	−38.6634	−1.50383	−0.751915	+	0.659260i	$0.770870\pi$
$662$	50.4200	1.95963
$663$	−14.2092	−0.551838
$664$	130.820	5.07680
$665$	−7.76689	−0.301187
$666$	35.9048	1.39128
$667$	−14.5836	−0.564678
$668$	−84.0038	−3.25020
$669$	−55.6073	−2.14990
$670$	−70.7338	−2.73269
$671$	9.70245	0.374559
$672$	61.0716	2.35589
$673$	−36.2554	−1.39754	−0.698772	−	0.715344i	$-0.746270\pi$
$673$	−36.2554	−1.39754	−0.698772	+	0.715344i	$0.746270\pi$
$674$	35.5598	1.36971
$675$	−9.17114	−0.352997
$676$	57.6553	2.21751
$677$	−27.1883	−1.04493	−0.522466	−	0.852660i	$-0.674988\pi$
$677$	−27.1883	−1.04493	−0.522466	+	0.852660i	$0.674988\pi$
$678$	57.5053	2.20848
$679$	5.07848	0.194894
$680$	16.7568	0.642595
$681$	−5.27634	−0.202190
$682$	33.8550	1.29637
$683$	−32.0455	−1.22619	−0.613093	−	0.790011i	$-0.710075\pi$
$683$	−32.0455	−1.22619	−0.613093	+	0.790011i	$0.710075\pi$
$684$	95.4428	3.64935
$685$	26.4053	1.00889
$686$	−40.6128	−1.55060
$687$	66.5988	2.54090
$688$	45.0643	1.71806
$689$	40.6666	1.54927
$690$	−91.4401	−3.48107
$691$	16.6336	0.632772	0.316386	−	0.948631i	$-0.397530\pi$
$691$	16.6336	0.632772	0.316386	+	0.948631i	$0.397530\pi$
$692$	32.5458	1.23721
$693$	−28.6169	−1.08707
$694$	41.9872	1.59381
$695$	−25.0315	−0.949501
$696$	60.5037	2.29339
$697$	0.624351	0.0236490
$698$	−49.7837	−1.88434
$699$	−35.1300	−1.32874
$700$	8.25719	0.312092
$701$	−12.0401	−0.454750	−0.227375	−	0.973807i	$-0.573014\pi$
$701$	−12.0401	−0.454750	−0.227375	+	0.973807i	$0.573014\pi$
$702$	−92.2596	−3.48212
$703$	−8.29183	−0.312732
$704$	93.0344	3.50637
$705$	1.26280	0.0475597
$706$	−2.69106	−0.101279
$707$	7.42799	0.279358
$708$	21.0745	0.792028
$709$	17.6381	0.662413	0.331206	−	0.943558i	$-0.392544\pi$
$709$	17.6381	0.662413	0.331206	+	0.943558i	$0.392544\pi$
$710$	−22.7538	−0.853937
$711$	−77.6201	−2.91098
$712$	−57.0610	−2.13845
$713$	−17.4453	−0.653332
$714$	−9.38239	−0.351127
$715$	41.3870	1.54778
$716$	61.0332	2.28092
$717$	−11.1894	−0.417876
$718$	−62.2422	−2.32286
$719$	−19.4731	−0.726224	−0.363112	−	0.931745i	$-0.618286\pi$
$719$	−19.4731	−0.726224	−0.363112	+	0.931745i	$0.618286\pi$
$720$	135.085	5.03432
$721$	−19.6001	−0.729944
$722$	20.6787	0.769581
$723$	28.4322	1.05740
$724$	−56.8087	−2.11128
$725$	3.13355	0.116377
$726$	−65.1333	−2.41732
$727$	33.6703	1.24876	0.624381	−	0.781120i	$-0.285351\pi$
$727$	33.6703	1.24876	0.624381	+	0.781120i	$0.285351\pi$
$728$	51.3719	1.90397
$729$	−38.9193	−1.44145
$730$	11.6679	0.431849
$731$	−3.46842	−0.128284
$732$	33.5390	1.23964
$733$	−38.0867	−1.40677	−0.703383	−	0.710811i	$-0.748328\pi$
$733$	−38.0867	−1.40677	−0.703383	+	0.710811i	$0.748328\pi$
$734$	39.0789	1.44243
$735$	−30.9489	−1.14157
$736$	−106.834	−3.93794
$737$	60.1867	2.21701
$738$	9.09438	0.334769
$739$	29.7132	1.09302	0.546509	−	0.837454i	$-0.315957\pi$
$739$	29.7132	1.09302	0.546509	+	0.837454i	$0.315957\pi$
$740$	−24.8183	−0.912338
$741$	47.7981	1.75591
$742$	26.8524	0.985782
$743$	3.54189	0.129939	0.0649696	−	0.997887i	$-0.479305\pi$
$743$	3.54189	0.129939	0.0649696	+	0.997887i	$0.479305\pi$
$744$	72.3763	2.65344
$745$	16.4239	0.601724
$746$	98.5874	3.60954
$747$	−81.1688	−2.96981
$748$	−23.0547	−0.842964
$749$	1.81112	0.0661769
$750$	94.6107	3.45470
$751$	25.9971	0.948648	0.474324	−	0.880350i	$-0.342693\pi$
$751$	25.9971	0.948648	0.474324	+	0.880350i	$0.342693\pi$
$752$	2.94496	0.107392
$753$	37.8746	1.38023
$754$	31.5229	1.14799
$755$	−6.59582	−0.240047
$756$	−44.0951	−1.60372
$757$	−18.0526	−0.656134	−0.328067	−	0.944654i	$-0.606397\pi$
$757$	−18.0526	−0.656134	−0.328067	+	0.944654i	$0.606397\pi$
$758$	−26.1239	−0.948863
$759$	77.8055	2.82416
$760$	−56.3682	−2.04469
$761$	−21.9526	−0.795781	−0.397890	−	0.917433i	$-0.630258\pi$
$761$	−21.9526	−0.795781	−0.397890	+	0.917433i	$0.630258\pi$
$762$	132.394	4.79613
$763$	−4.58167	−0.165868
$764$	69.1605	2.50214
$765$	−10.3970	−0.375903
$766$	97.5223	3.52362
$767$	6.79057	0.245193
$768$	48.1510	1.73750
$769$	−26.7659	−0.965203	−0.482602	−	0.875840i	$-0.660308\pi$
$769$	−26.7659	−0.965203	−0.482602	+	0.875840i	$0.660308\pi$
$770$	27.3280	0.984834
$771$	−41.3572	−1.48944
$772$	124.148	4.46819
$773$	−25.4690	−0.916057	−0.458028	−	0.888938i	$-0.651444\pi$
$773$	−25.4690	−0.916057	−0.458028	+	0.888938i	$0.651444\pi$
$774$	−50.5215	−1.81596
$775$	3.74845	0.134648
$776$	36.8571	1.32309
$777$	8.59406	0.308310
$778$	−35.2687	−1.26444
$779$	−2.10025	−0.0752492
$780$	143.065	5.12253
$781$	19.3610	0.692792
$782$	16.4128	0.586920
$783$	−16.7338	−0.598018
$784$	−72.1759	−2.57771
$785$	−10.7150	−0.382436
$786$	−64.0007	−2.28283
$787$	−24.0000	−0.855507	−0.427753	−	0.903895i	$-0.640695\pi$
$787$	−24.0000	−0.855507	−0.427753	+	0.903895i	$0.640695\pi$
$788$	−34.0293	−1.21225
$789$	9.96912	0.354910
$790$	74.1242	2.63722
$791$	8.85595	0.314881
$792$	−207.687	−7.37984
$793$	10.8068	0.383762
$794$	7.95416	0.282282
$795$	46.2482	1.64025
$796$	−69.2771	−2.45546
$797$	3.33823	0.118246	0.0591230	−	0.998251i	$-0.481170\pi$
$797$	3.33823	0.118246	0.0591230	+	0.998251i	$0.481170\pi$
$798$	31.5613	1.11726
$799$	−0.226662	−0.00801873
$800$	22.9552	0.811589
$801$	35.4041	1.25094
$802$	56.8507	2.00747
$803$	−9.92813	−0.350356
$804$	208.051	7.33738
$805$	−14.0820	−0.496325
$806$	37.7086	1.32823
$807$	86.1912	3.03407
$808$	53.9086	1.89650
$809$	−14.2290	−0.500265	−0.250132	−	0.968212i	$-0.580474\pi$
$809$	−14.2290	−0.500265	−0.250132	+	0.968212i	$0.580474\pi$
$810$	−20.9860	−0.737374
$811$	26.6437	0.935586	0.467793	−	0.883838i	$-0.345049\pi$
$811$	26.6437	0.935586	0.467793	+	0.883838i	$0.345049\pi$
$812$	15.0662	0.528720
$813$	1.72224	0.0604017
$814$	29.1751	1.02259
$815$	−42.0295	−1.47223
$816$	−37.6852	−1.31925
$817$	11.6674	0.408191
$818$	−83.9126	−2.93394
$819$	−31.8743	−1.11378
$820$	−6.28626	−0.219526
$821$	−40.3933	−1.40974	−0.704868	−	0.709338i	$-0.748994\pi$
$821$	−40.3933	−1.40974	−0.704868	+	0.709338i	$0.748994\pi$
$822$	−107.300	−3.74251
$823$	−49.8945	−1.73921	−0.869606	−	0.493746i	$-0.835627\pi$
$823$	−49.8945	−1.73921	−0.869606	+	0.493746i	$0.835627\pi$
$824$	−142.247	−4.95542
$825$	−16.7180	−0.582045
$826$	4.48385	0.156013
$827$	−49.5658	−1.72357	−0.861787	−	0.507271i	$-0.830654\pi$
$827$	−49.5658	−1.72357	−0.861787	+	0.507271i	$0.830654\pi$
$828$	173.045	6.01375
$829$	19.5213	0.678001	0.339001	−	0.940786i	$-0.389911\pi$
$829$	19.5213	0.678001	0.339001	+	0.940786i	$0.389911\pi$
$830$	77.5130	2.69052
$831$	−2.36849	−0.0821619
$832$	103.624	3.59252
$833$	5.55509	0.192472
$834$	101.718	3.52219
$835$	−30.7825	−1.06527
$836$	77.5536	2.68225
$837$	−20.0175	−0.691906
$838$	−17.4197	−0.601755
$839$	34.3423	1.18563	0.592814	−	0.805339i	$-0.298017\pi$
$839$	34.3423	1.18563	0.592814	+	0.805339i	$0.298017\pi$
$840$	58.4228	2.01578
$841$	−23.2825	−0.802843
$842$	−48.4896	−1.67106
$843$	76.1419	2.62247
$844$	−104.942	−3.61226
$845$	21.1273	0.726802
$846$	−3.30159	−0.113511
$847$	−10.0307	−0.344658
$848$	107.855	3.70376
$849$	−58.7507	−2.01632
$850$	−3.52659	−0.120961
$851$	−15.0338	−0.515350
$852$	66.9263	2.29286
$853$	−47.5573	−1.62833	−0.814165	−	0.580634i	$-0.802805\pi$
$853$	−47.5573	−1.62833	−0.814165	+	0.580634i	$0.802805\pi$
$854$	7.13581	0.244183
$855$	34.9742	1.19609
$856$	13.1442	0.449260
$857$	−23.5476	−0.804370	−0.402185	−	0.915558i	$-0.631749\pi$
$857$	−23.5476	−0.804370	−0.402185	+	0.915558i	$0.631749\pi$
$858$	−168.179	−5.74154
$859$	−25.2565	−0.861740	−0.430870	−	0.902414i	$-0.641793\pi$
$859$	−25.2565	−0.861740	−0.430870	+	0.902414i	$0.641793\pi$
$860$	34.9217	1.19082
$861$	2.17680	0.0741852
$862$	−22.9140	−0.780455
$863$	49.9706	1.70102	0.850509	−	0.525961i	$-0.176294\pi$
$863$	49.9706	1.70102	0.850509	+	0.525961i	$0.176294\pi$
$864$	−122.586	−4.17045
$865$	11.9262	0.405502
$866$	59.4118	2.01890
$867$	2.90048	0.0985055
$868$	18.0227	0.611729
$869$	−63.0716	−2.13956
$870$	35.8494	1.21541
$871$	67.0375	2.27148
$872$	−33.2515	−1.12604
$873$	−22.8684	−0.773977
$874$	−55.2108	−1.86753
$875$	14.5703	0.492565
$876$	−34.3191	−1.15953
$877$	31.8087	1.07410	0.537051	−	0.843550i	$-0.319538\pi$
$877$	31.8087	1.07410	0.537051	+	0.843550i	$0.319538\pi$
$878$	−48.2823	−1.62945
$879$	−26.0095	−0.877280
$880$	109.766	3.70020
$881$	5.53431	0.186456	0.0932278	−	0.995645i	$-0.470282\pi$
$881$	5.53431	0.186456	0.0932278	+	0.995645i	$0.470282\pi$
$882$	80.9162	2.72459
$883$	3.01957	0.101617	0.0508083	−	0.998708i	$-0.483820\pi$
$883$	3.01957	0.101617	0.0508083	+	0.998708i	$0.483820\pi$
$884$	−25.6790	−0.863677
$885$	7.72258	0.259592
$886$	−100.021	−3.36026
$887$	48.4724	1.62754	0.813772	−	0.581185i	$-0.197411\pi$
$887$	48.4724	1.62754	0.813772	+	0.581185i	$0.197411\pi$
$888$	62.3714	2.09305
$889$	20.3890	0.683825
$890$	−33.8096	−1.13330
$891$	17.8568	0.598226
$892$	−100.494	−3.36480
$893$	0.762467	0.0255150
$894$	−66.7397	−2.23211
$895$	22.3651	0.747584
$896$	26.3122	0.879031
$897$	86.6618	2.89355
$898$	106.264	3.54609
$899$	6.83949	0.228110
$900$	−37.1821	−1.23940
$901$	−8.30118	−0.276552
$902$	7.38979	0.246053
$903$	−12.0927	−0.402419
$904$	64.2720	2.13765
$905$	−20.8171	−0.691984
$906$	26.8026	0.890458
$907$	6.89493	0.228942	0.114471	−	0.993427i	$-0.463483\pi$
$907$	6.89493	0.228942	0.114471	+	0.993427i	$0.463483\pi$
$908$	−9.53546	−0.316445
$909$	−33.4482	−1.10941
$910$	30.4387	1.00903
$911$	39.4785	1.30798	0.653990	−	0.756503i	$-0.273094\pi$
$911$	39.4785	1.30798	0.653990	+	0.756503i	$0.273094\pi$
$912$	126.769	4.19774
$913$	−65.9550	−2.18279
$914$	−4.87844	−0.161365
$915$	12.2901	0.406298
$916$	120.358	3.97675
$917$	−9.85625	−0.325482
$918$	18.8327	0.621573
$919$	−28.8588	−0.951964	−0.475982	−	0.879455i	$-0.657907\pi$
$919$	−28.8588	−0.951964	−0.475982	+	0.879455i	$0.657907\pi$
$920$	−102.200	−3.36943
$921$	−48.7116	−1.60510
$922$	−16.5766	−0.545923
$923$	21.5648	0.709814
$924$	−80.3805	−2.64432
$925$	3.23028	0.106211
$926$	50.1987	1.64963
$927$	88.2589	2.89880
$928$	41.8845	1.37493
$929$	10.1700	0.333667	0.166833	−	0.985985i	$-0.446646\pi$
$929$	10.1700	0.333667	0.166833	+	0.985985i	$0.446646\pi$
$930$	42.8841	1.40623
$931$	−18.6867	−0.612433
$932$	−63.4873	−2.07960
$933$	−29.5251	−0.966607
$934$	−38.0513	−1.24508
$935$	−8.44822	−0.276286
$936$	−231.327	−7.56117
$937$	44.7573	1.46216	0.731078	−	0.682294i	$-0.239017\pi$
$937$	44.7573	1.46216	0.731078	+	0.682294i	$0.239017\pi$
$938$	44.2652	1.44531
$939$	−23.9859	−0.782750
$940$	2.28214	0.0744353
$941$	−1.69114	−0.0551295	−0.0275648	−	0.999620i	$-0.508775\pi$
$941$	−1.69114	−0.0551295	−0.0275648	+	0.999620i	$0.508775\pi$
$942$	43.5413	1.41865
$943$	−3.80792	−0.124003
$944$	18.0098	0.586169
$945$	−16.1583	−0.525629
$946$	−41.0521	−1.33472
$947$	46.0489	1.49639	0.748194	−	0.663480i	$-0.230921\pi$
$947$	46.0489	1.49639	0.748194	+	0.663480i	$0.230921\pi$
$948$	−218.023	−7.08106
$949$	−11.0582	−0.358964
$950$	11.8631	0.384889
$951$	34.3495	1.11386
$952$	−10.4864	−0.339867
$953$	54.9546	1.78015	0.890076	−	0.455811i	$-0.150651\pi$
$953$	54.9546	1.78015	0.890076	+	0.455811i	$0.150651\pi$
$954$	−120.916	−3.91480
$955$	25.3433	0.820091
$956$	−20.2216	−0.654014
$957$	−30.5039	−0.986051
$958$	−8.11858	−0.262299
$959$	−16.5244	−0.533601
$960$	117.847	3.80349
$961$	−22.8184	−0.736077
$962$	32.4959	1.04771
$963$	−8.15546	−0.262806
$964$	51.3830	1.65494
$965$	45.4931	1.46447
$966$	57.2233	1.84113
$967$	32.6323	1.04938	0.524692	−	0.851292i	$-0.324181\pi$
$967$	32.6323	1.04938	0.524692	+	0.851292i	$0.324181\pi$
$968$	−72.7976	−2.33980
$969$	−9.75691	−0.313437
$970$	21.8384	0.701189
$971$	−1.66266	−0.0533574	−0.0266787	−	0.999644i	$-0.508493\pi$
$971$	−1.66266	−0.0533574	−0.0266787	+	0.999644i	$0.508493\pi$
$972$	−48.3237	−1.54998
$973$	15.6647	0.502189
$974$	−27.2993	−0.874725
$975$	−18.6209	−0.596347
$976$	28.6617	0.917437
$977$	−24.6012	−0.787062	−0.393531	−	0.919311i	$-0.628747\pi$
$977$	−24.6012	−0.787062	−0.393531	+	0.919311i	$0.628747\pi$
$978$	170.790	5.46126
$979$	28.7682	0.919436
$980$	−55.9313	−1.78666
$981$	20.6312	0.658705
$982$	45.5375	1.45316
$983$	−47.7874	−1.52418	−0.762091	−	0.647470i	$-0.775827\pi$
$983$	−47.7874	−1.52418	−0.762091	+	0.647470i	$0.775827\pi$
$984$	15.7981	0.503626
$985$	−12.4698	−0.397320
$986$	−6.43469	−0.204922
$987$	−0.790259	−0.0251542
$988$	86.3813	2.74815
$989$	21.1539	0.672656
$990$	−123.058	−3.91104
$991$	−6.69788	−0.212765	−0.106383	−	0.994325i	$-0.533927\pi$
$991$	−6.69788	−0.212765	−0.106383	+	0.994325i	$0.533927\pi$
$992$	50.1035	1.59079
$993$	−54.3438	−1.72455
$994$	14.2394	0.451645
$995$	−25.3860	−0.804792
$996$	−227.990	−7.22415
$997$	20.3575	0.644729	0.322365	−	0.946616i	$-0.395522\pi$
$997$	20.3575	0.644729	0.322365	+	0.946616i	$0.395522\pi$
$998$	−69.8704	−2.21171
$999$	−17.2504	−0.545778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.3	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.3	✓	121	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)

\(f(q)\)	\(=\)	\(q-2.69106 q^{2} +2.90048 q^{3} +5.24179 q^{4} +1.92081 q^{5} -7.80536 q^{6} -1.20204 q^{7} -8.72383 q^{8} +5.41280 q^{9} +O(q^{10})\)	\(q-2.69106 q^{2} +2.90048 q^{3} +5.24179 q^{4} +1.92081 q^{5} -7.80536 q^{6} -1.20204 q^{7} -8.72383 q^{8} +5.41280 q^{9} -5.16901 q^{10} +4.39826 q^{11} +15.2037 q^{12} +4.89889 q^{13} +3.23477 q^{14} +5.57128 q^{15} +12.9927 q^{16} -1.00000 q^{17} -14.5661 q^{18} +3.36389 q^{19} +10.0685 q^{20} -3.48651 q^{21} -11.8360 q^{22} +6.09901 q^{23} -25.3033 q^{24} -1.31049 q^{25} -13.1832 q^{26} +6.99827 q^{27} -6.30086 q^{28} -2.39114 q^{29} -14.9926 q^{30} -2.86035 q^{31} -17.5166 q^{32} +12.7571 q^{33} +2.69106 q^{34} -2.30890 q^{35} +28.3727 q^{36} -2.46495 q^{37} -9.05243 q^{38} +14.2092 q^{39} -16.7568 q^{40} -0.624351 q^{41} +9.38239 q^{42} +3.46842 q^{43} +23.0547 q^{44} +10.3970 q^{45} -16.4128 q^{46} +0.226662 q^{47} +37.6852 q^{48} -5.55509 q^{49} +3.52659 q^{50} -2.90048 q^{51} +25.6790 q^{52} +8.30118 q^{53} -18.8327 q^{54} +8.44822 q^{55} +10.4864 q^{56} +9.75691 q^{57} +6.43469 q^{58} +1.38614 q^{59} +29.2034 q^{60} +2.20597 q^{61} +7.69736 q^{62} -6.50642 q^{63} +21.1525 q^{64} +9.40985 q^{65} -34.3300 q^{66} +13.6842 q^{67} -5.24179 q^{68} +17.6901 q^{69} +6.21338 q^{70} +4.40197 q^{71} -47.2203 q^{72} -2.25729 q^{73} +6.63332 q^{74} -3.80104 q^{75} +17.6328 q^{76} -5.28690 q^{77} -38.2376 q^{78} -14.3401 q^{79} +24.9566 q^{80} +4.05997 q^{81} +1.68016 q^{82} -14.9957 q^{83} -18.2755 q^{84} -1.92081 q^{85} -9.33372 q^{86} -6.93545 q^{87} -38.3697 q^{88} +6.54082 q^{89} -27.9788 q^{90} -5.88869 q^{91} +31.9697 q^{92} -8.29639 q^{93} -0.609961 q^{94} +6.46140 q^{95} -50.8064 q^{96} -4.22487 q^{97} +14.9491 q^{98} +23.8069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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