LMFDB - Embedded newform 4001.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61467 q^{2} +2.84813 q^{3} +4.83651 q^{4} +0.542328 q^{5} -7.44692 q^{6} +4.00529 q^{7} -7.41654 q^{8} +5.11183 q^{9} +O(q^{10})$	\(q-2.61467 q^{2} +2.84813 q^{3} +4.83651 q^{4} +0.542328 q^{5} -7.44692 q^{6} +4.00529 q^{7} -7.41654 q^{8} +5.11183 q^{9} -1.41801 q^{10} +4.26836 q^{11} +13.7750 q^{12} +5.82628 q^{13} -10.4725 q^{14} +1.54462 q^{15} +9.71880 q^{16} -4.23240 q^{17} -13.3658 q^{18} +6.94781 q^{19} +2.62298 q^{20} +11.4076 q^{21} -11.1604 q^{22} -5.99682 q^{23} -21.1232 q^{24} -4.70588 q^{25} -15.2338 q^{26} +6.01477 q^{27} +19.3716 q^{28} -3.54923 q^{29} -4.03868 q^{30} +9.01083 q^{31} -10.5784 q^{32} +12.1568 q^{33} +11.0663 q^{34} +2.17218 q^{35} +24.7234 q^{36} -5.38722 q^{37} -18.1663 q^{38} +16.5940 q^{39} -4.02220 q^{40} +5.31155 q^{41} -29.8271 q^{42} +2.25132 q^{43} +20.6440 q^{44} +2.77229 q^{45} +15.6797 q^{46} +3.58041 q^{47} +27.6804 q^{48} +9.04234 q^{49} +12.3043 q^{50} -12.0544 q^{51} +28.1789 q^{52} -13.1494 q^{53} -15.7266 q^{54} +2.31485 q^{55} -29.7054 q^{56} +19.7883 q^{57} +9.28008 q^{58} -7.82877 q^{59} +7.47057 q^{60} +1.46293 q^{61} -23.5604 q^{62} +20.4744 q^{63} +8.22141 q^{64} +3.15976 q^{65} -31.7861 q^{66} -4.09795 q^{67} -20.4700 q^{68} -17.0797 q^{69} -5.67954 q^{70} +13.6342 q^{71} -37.9121 q^{72} -9.91788 q^{73} +14.0858 q^{74} -13.4029 q^{75} +33.6032 q^{76} +17.0960 q^{77} -43.3879 q^{78} -4.77574 q^{79} +5.27078 q^{80} +1.79533 q^{81} -13.8880 q^{82} -12.5684 q^{83} +55.1728 q^{84} -2.29535 q^{85} -5.88647 q^{86} -10.1087 q^{87} -31.6565 q^{88} +17.5147 q^{89} -7.24863 q^{90} +23.3359 q^{91} -29.0037 q^{92} +25.6640 q^{93} -9.36159 q^{94} +3.76800 q^{95} -30.1286 q^{96} -11.9961 q^{97} -23.6428 q^{98} +21.8191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	−2.61467	−1.84885	−0.924426	−	0.381361i	$-0.875455\pi$
$2$	−2.61467	−1.84885	−0.924426	+	0.381361i	$0.875455\pi$
$3$	2.84813	1.64437	0.822184	−	0.569222i	$-0.192756\pi$
$3$	2.84813	1.64437	0.822184	+	0.569222i	$0.192756\pi$
$4$	4.83651	2.41825
$5$	0.542328	0.242537	0.121268	−	0.992620i	$-0.461304\pi$
$5$	0.542328	0.242537	0.121268	+	0.992620i	$0.461304\pi$
$6$	−7.44692	−3.04019
$7$	4.00529	1.51386	0.756929	−	0.653498i	$-0.226699\pi$
$7$	4.00529	1.51386	0.756929	+	0.653498i	$0.226699\pi$
$8$	−7.41654	−2.62214
$9$	5.11183	1.70394
$10$	−1.41801	−0.448414
$11$	4.26836	1.28696	0.643479	−	0.765463i	$-0.277490\pi$
$11$	4.26836	1.28696	0.643479	+	0.765463i	$0.277490\pi$
$12$	13.7750	3.97650
$13$	5.82628	1.61592	0.807960	−	0.589237i	$-0.200572\pi$
$13$	5.82628	1.61592	0.807960	+	0.589237i	$0.200572\pi$
$14$	−10.4725	−2.79890
$15$	1.54462	0.398819
$16$	9.71880	2.42970
$17$	−4.23240	−1.02651	−0.513253	−	0.858237i	$-0.671560\pi$
$17$	−4.23240	−1.02651	−0.513253	+	0.858237i	$0.671560\pi$
$18$	−13.3658	−3.15034
$19$	6.94781	1.59394	0.796969	−	0.604020i	$-0.206435\pi$
$19$	6.94781	1.59394	0.796969	+	0.604020i	$0.206435\pi$
$20$	2.62298	0.586515
$21$	11.4076	2.48934
$22$	−11.1604	−2.37940
$23$	−5.99682	−1.25042	−0.625212	−	0.780455i	$-0.714987\pi$
$23$	−5.99682	−1.25042	−0.625212	+	0.780455i	$0.714987\pi$
$24$	−21.1232	−4.31177
$25$	−4.70588	−0.941176
$26$	−15.2338	−2.98760
$27$	6.01477	1.15754
$28$	19.3716	3.66089
$29$	−3.54923	−0.659076	−0.329538	−	0.944142i	$-0.606893\pi$
$29$	−3.54923	−0.659076	−0.329538	+	0.944142i	$0.606893\pi$
$30$	−4.03868	−0.737358
$31$	9.01083	1.61839	0.809197	−	0.587538i	$-0.199903\pi$
$31$	9.01083	1.61839	0.809197	+	0.587538i	$0.199903\pi$
$32$	−10.5784	−1.87001
$33$	12.1568	2.11623
$34$	11.0663	1.89786
$35$	2.17218	0.367166
$36$	24.7234	4.12057
$37$	−5.38722	−0.885654	−0.442827	−	0.896607i	$-0.646024\pi$
$37$	−5.38722	−0.885654	−0.442827	+	0.896607i	$0.646024\pi$
$38$	−18.1663	−2.94696
$39$	16.5940	2.65717
$40$	−4.02220	−0.635966
$41$	5.31155	0.829525	0.414763	−	0.909930i	$-0.363865\pi$
$41$	5.31155	0.829525	0.414763	+	0.909930i	$0.363865\pi$
$42$	−29.8271	−4.60242
$43$	2.25132	0.343323	0.171662	−	0.985156i	$-0.445086\pi$
$43$	2.25132	0.343323	0.171662	+	0.985156i	$0.445086\pi$
$44$	20.6440	3.11219
$45$	2.77229	0.413269
$46$	15.6797	2.31185
$47$	3.58041	0.522256	0.261128	−	0.965304i	$-0.415905\pi$
$47$	3.58041	0.522256	0.261128	+	0.965304i	$0.415905\pi$
$48$	27.6804	3.99532
$49$	9.04234	1.29176
$50$	12.3043	1.74010
$51$	−12.0544	−1.68795
$52$	28.1789	3.90771
$53$	−13.1494	−1.80621	−0.903103	−	0.429424i	$-0.858716\pi$
$53$	−13.1494	−1.80621	−0.903103	+	0.429424i	$0.858716\pi$
$54$	−15.7266	−2.14013
$55$	2.31485	0.312135
$56$	−29.7054	−3.96955
$57$	19.7883	2.62102
$58$	9.28008	1.21853
$59$	−7.82877	−1.01922	−0.509609	−	0.860406i	$-0.670210\pi$
$59$	−7.82877	−1.01922	−0.509609	+	0.860406i	$0.670210\pi$
$60$	7.47057	0.964447
$61$	1.46293	0.187309	0.0936547	−	0.995605i	$-0.470145\pi$
$61$	1.46293	0.187309	0.0936547	+	0.995605i	$0.470145\pi$
$62$	−23.5604	−2.99217
$63$	20.4744	2.57953
$64$	8.22141	1.02768
$65$	3.15976	0.391920
$66$	−31.7861	−3.91260
$67$	−4.09795	−0.500644	−0.250322	−	0.968163i	$-0.580536\pi$
$67$	−4.09795	−0.500644	−0.250322	+	0.968163i	$0.580536\pi$
$68$	−20.4700	−2.48235
$69$	−17.0797	−2.05616
$70$	−5.67954	−0.678835
$71$	13.6342	1.61809	0.809043	−	0.587749i	$-0.199986\pi$
$71$	13.6342	1.61809	0.809043	+	0.587749i	$0.199986\pi$
$72$	−37.9121	−4.46798
$73$	−9.91788	−1.16080	−0.580400	−	0.814332i	$-0.697104\pi$
$73$	−9.91788	−1.16080	−0.580400	+	0.814332i	$0.697104\pi$
$74$	14.0858	1.63744
$75$	−13.4029	−1.54764
$76$	33.6032	3.85455
$77$	17.0960	1.94827
$78$	−43.3879	−4.91271
$79$	−4.77574	−0.537312	−0.268656	−	0.963236i	$-0.586580\pi$
$79$	−4.77574	−0.537312	−0.268656	+	0.963236i	$0.586580\pi$
$80$	5.27078	0.589291
$81$	1.79533	0.199481
$82$	−13.8880	−1.53367
$83$	−12.5684	−1.37956	−0.689781	−	0.724018i	$-0.742293\pi$
$83$	−12.5684	−1.37956	−0.689781	+	0.724018i	$0.742293\pi$
$84$	55.1728	6.01985
$85$	−2.29535	−0.248966
$86$	−5.88647	−0.634754
$87$	−10.1087	−1.08376
$88$	−31.6565	−3.37459
$89$	17.5147	1.85656	0.928278	−	0.371888i	$-0.121289\pi$
$89$	17.5147	1.85656	0.928278	+	0.371888i	$0.121289\pi$
$90$	−7.24863	−0.764073
$91$	23.3359	2.44627
$92$	−29.0037	−3.02384
$93$	25.6640	2.66123
$94$	−9.36159	−0.965575
$95$	3.76800	0.386588
$96$	−30.1286	−3.07499
$97$	−11.9961	−1.21802	−0.609011	−	0.793161i	$-0.708434\pi$
$97$	−11.9961	−1.21802	−0.609011	+	0.793161i	$0.708434\pi$
$98$	−23.6428	−2.38828
$99$	21.8191	2.19291
$100$	−22.7600	−2.27600
$101$	10.4377	1.03859	0.519295	−	0.854595i	$-0.326194\pi$
$101$	10.4377	1.03859	0.519295	+	0.854595i	$0.326194\pi$
$102$	31.5183	3.12078
$103$	−13.2358	−1.30417	−0.652083	−	0.758148i	$-0.726105\pi$
$103$	−13.2358	−1.30417	−0.652083	+	0.758148i	$0.726105\pi$
$104$	−43.2108	−4.23717
$105$	6.18665	0.603755
$106$	34.3813	3.33941
$107$	−8.43017	−0.814975	−0.407488	−	0.913211i	$-0.633595\pi$
$107$	−8.43017	−0.814975	−0.407488	+	0.913211i	$0.633595\pi$
$108$	29.0905	2.79923
$109$	−11.7541	−1.12584	−0.562921	−	0.826511i	$-0.690322\pi$
$109$	−11.7541	−1.12584	−0.562921	+	0.826511i	$0.690322\pi$
$110$	−6.05258	−0.577091
$111$	−15.3435	−1.45634
$112$	38.9266	3.67822
$113$	8.22147	0.773411	0.386705	−	0.922203i	$-0.373613\pi$
$113$	8.22147	0.773411	0.386705	+	0.922203i	$0.373613\pi$
$114$	−51.7398	−4.84588
$115$	−3.25225	−0.303274
$116$	−17.1659	−1.59381
$117$	29.7830	2.75344
$118$	20.4697	1.88438
$119$	−16.9520	−1.55398
$120$	−11.4557	−1.04576
$121$	7.21890	0.656263
$122$	−3.82509	−0.346307
$123$	15.1280	1.36404
$124$	43.5810	3.91369
$125$	−5.26377	−0.470806
$126$	−53.5338	−4.76917
$127$	−6.36973	−0.565222	−0.282611	−	0.959235i	$-0.591201\pi$
$127$	−6.36973	−0.565222	−0.282611	+	0.959235i	$0.591201\pi$
$128$	−0.339528	−0.0300103
$129$	6.41205	0.564550
$130$	−8.26173	−0.724602
$131$	−6.54581	−0.571910	−0.285955	−	0.958243i	$-0.592311\pi$
$131$	−6.54581	−0.571910	−0.285955	+	0.958243i	$0.592311\pi$
$132$	58.7966	5.11759
$133$	27.8280	2.41299
$134$	10.7148	0.925617
$135$	3.26198	0.280747
$136$	31.3897	2.69165
$137$	12.3365	1.05398	0.526990	−	0.849871i	$-0.323320\pi$
$137$	12.3365	1.05398	0.526990	+	0.849871i	$0.323320\pi$
$138$	44.6578	3.80153
$139$	−13.9825	−1.18598	−0.592989	−	0.805210i	$-0.702052\pi$
$139$	−13.9825	−1.18598	−0.592989	+	0.805210i	$0.702052\pi$
$140$	10.5058	0.887900
$141$	10.1975	0.858781
$142$	−35.6491	−2.99160
$143$	24.8687	2.07962
$144$	49.6809	4.14007
$145$	−1.92485	−0.159850
$146$	25.9320	2.14615
$147$	25.7538	2.12413
$148$	−26.0553	−2.14174
$149$	−11.7810	−0.965133	−0.482567	−	0.875859i	$-0.660295\pi$
$149$	−11.7810	−0.965133	−0.482567	+	0.875859i	$0.660295\pi$
$150$	35.0443	2.86136
$151$	−8.93697	−0.727280	−0.363640	−	0.931539i	$-0.618466\pi$
$151$	−8.93697	−0.727280	−0.363640	+	0.931539i	$0.618466\pi$
$152$	−51.5287	−4.17953
$153$	−21.6353	−1.74911
$154$	−44.7005	−3.60207
$155$	4.88683	0.392520
$156$	80.2570	6.42570
$157$	−10.6270	−0.848126	−0.424063	−	0.905633i	$-0.639397\pi$
$157$	−10.6270	−0.848126	−0.424063	+	0.905633i	$0.639397\pi$
$158$	12.4870	0.993411
$159$	−37.4511	−2.97007
$160$	−5.73696	−0.453546
$161$	−24.0190	−1.89296
$162$	−4.69420	−0.368812
$163$	10.6263	0.832315	0.416158	−	0.909292i	$-0.363376\pi$
$163$	10.6263	0.832315	0.416158	+	0.909292i	$0.363376\pi$
$164$	25.6894	2.00600
$165$	6.59300	0.513264
$166$	32.8623	2.55061
$167$	15.6588	1.21171	0.605856	−	0.795574i	$-0.292831\pi$
$167$	15.6588	1.21171	0.605856	+	0.795574i	$0.292831\pi$
$168$	−84.6047	−6.52740
$169$	20.9456	1.61120
$170$	6.00158	0.460300
$171$	35.5161	2.71598
$172$	10.8885	0.830243
$173$	−10.5339	−0.800878	−0.400439	−	0.916323i	$-0.631142\pi$
$173$	−10.5339	−0.800878	−0.400439	+	0.916323i	$0.631142\pi$
$174$	26.4309	2.00372
$175$	−18.8484	−1.42481
$176$	41.4833	3.12692
$177$	−22.2973	−1.67597
$178$	−45.7952	−3.43250
$179$	−1.41524	−0.105780	−0.0528899	−	0.998600i	$-0.516843\pi$
$179$	−1.41524	−0.105780	−0.0528899	+	0.998600i	$0.516843\pi$
$180$	13.4082	0.999389
$181$	−8.79067	−0.653406	−0.326703	−	0.945127i	$-0.605938\pi$
$181$	−8.79067	−0.653406	−0.326703	+	0.945127i	$0.605938\pi$
$182$	−61.0158	−4.52280
$183$	4.16662	0.308005
$184$	44.4757	3.27879
$185$	−2.92164	−0.214803
$186$	−67.1029	−4.92023
$187$	−18.0654	−1.32107
$188$	17.3167	1.26295
$189$	24.0909	1.75235
$190$	−9.85207	−0.714745
$191$	−4.51368	−0.326599	−0.163299	−	0.986577i	$-0.552214\pi$
$191$	−4.51368	−0.326599	−0.163299	+	0.986577i	$0.552214\pi$
$192$	23.4156	1.68988
$193$	5.40613	0.389142	0.194571	−	0.980888i	$-0.437669\pi$
$193$	5.40613	0.389142	0.194571	+	0.980888i	$0.437669\pi$
$194$	31.3660	2.25194
$195$	8.99940	0.644460
$196$	43.7334	3.12381
$197$	−4.95467	−0.353005	−0.176503	−	0.984300i	$-0.556478\pi$
$197$	−4.95467	−0.353005	−0.176503	+	0.984300i	$0.556478\pi$
$198$	−57.0499	−4.05436
$199$	11.8654	0.841116	0.420558	−	0.907266i	$-0.361834\pi$
$199$	11.8654	0.841116	0.420558	+	0.907266i	$0.361834\pi$
$200$	34.9013	2.46790
$201$	−11.6715	−0.823243
$202$	−27.2912	−1.92020
$203$	−14.2157	−0.997747
$204$	−58.3012	−4.08190
$205$	2.88061	0.201190
$206$	34.6074	2.41121
$207$	−30.6547	−2.13065
$208$	56.6245	3.92620
$209$	29.6558	2.05133
$210$	−16.1761	−1.11625
$211$	−7.51728	−0.517511	−0.258756	−	0.965943i	$-0.583312\pi$
$211$	−7.51728	−0.517511	−0.258756	+	0.965943i	$0.583312\pi$
$212$	−63.5971	−4.36786
$213$	38.8320	2.66073
$214$	22.0421	1.50677
$215$	1.22096	0.0832685
$216$	−44.6088	−3.03524
$217$	36.0910	2.45002
$218$	30.7332	2.08151
$219$	−28.2474	−1.90878
$220$	11.1958	0.754821
$221$	−24.6591	−1.65875
$222$	40.1182	2.69256
$223$	−20.8419	−1.39568	−0.697840	−	0.716254i	$-0.745855\pi$
$223$	−20.8419	−1.39568	−0.697840	+	0.716254i	$0.745855\pi$
$224$	−42.3695	−2.83093
$225$	−24.0557	−1.60371
$226$	−21.4964	−1.42992
$227$	13.2383	0.878659	0.439330	−	0.898326i	$-0.355216\pi$
$227$	13.2383	0.878659	0.439330	+	0.898326i	$0.355216\pi$
$228$	95.7061	6.33829
$229$	15.3539	1.01461	0.507307	−	0.861766i	$-0.330641\pi$
$229$	15.3539	1.01461	0.507307	+	0.861766i	$0.330641\pi$
$230$	8.50356	0.560708
$231$	48.6916	3.20367
$232$	26.3230	1.72819
$233$	−26.4713	−1.73419	−0.867097	−	0.498139i	$-0.834017\pi$
$233$	−26.4713	−1.73419	−0.867097	+	0.498139i	$0.834017\pi$
$234$	−77.8727	−5.09070
$235$	1.94176	0.126666
$236$	−37.8639	−2.46473
$237$	−13.6019	−0.883539
$238$	44.3238	2.87309
$239$	−0.152615	−0.00987184	−0.00493592	−	0.999988i	$-0.501571\pi$
$239$	−0.152615	−0.00987184	−0.00493592	+	0.999988i	$0.501571\pi$
$240$	15.0119	0.969011
$241$	−9.85704	−0.634948	−0.317474	−	0.948267i	$-0.602835\pi$
$241$	−9.85704	−0.634948	−0.317474	+	0.948267i	$0.602835\pi$
$242$	−18.8750	−1.21333
$243$	−12.9310	−0.829522
$244$	7.07549	0.452962
$245$	4.90392	0.313300
$246$	−39.5547	−2.52192
$247$	40.4799	2.57568
$248$	−66.8292	−4.24366
$249$	−35.7964	−2.26851
$250$	13.7630	0.870451
$251$	−13.4971	−0.851929	−0.425964	−	0.904740i	$-0.640065\pi$
$251$	−13.4971	−0.851929	−0.425964	+	0.904740i	$0.640065\pi$
$252$	99.0245	6.23795
$253$	−25.5966	−1.60924
$254$	16.6547	1.04501
$255$	−6.53745	−0.409391
$256$	−15.5551	−0.972192
$257$	9.73490	0.607246	0.303623	−	0.952792i	$-0.401804\pi$
$257$	9.73490	0.607246	0.303623	+	0.952792i	$0.401804\pi$
$258$	−16.7654	−1.04377
$259$	−21.5774	−1.34075
$260$	15.2822	0.947762
$261$	−18.1431	−1.12303
$262$	17.1152	1.05738
$263$	−13.7807	−0.849754	−0.424877	−	0.905251i	$-0.639683\pi$
$263$	−13.7807	−0.849754	−0.424877	+	0.905251i	$0.639683\pi$
$264$	−90.1616	−5.54906
$265$	−7.13128	−0.438071
$266$	−72.7611	−4.46127
$267$	49.8841	3.05286
$268$	−19.8198	−1.21068
$269$	4.10945	0.250558	0.125279	−	0.992122i	$-0.460017\pi$
$269$	4.10945	0.250558	0.125279	+	0.992122i	$0.460017\pi$
$270$	−8.52901	−0.519059
$271$	−2.64167	−0.160470	−0.0802349	−	0.996776i	$-0.525567\pi$
$271$	−2.64167	−0.160470	−0.0802349	+	0.996776i	$0.525567\pi$
$272$	−41.1338	−2.49410
$273$	66.4638	4.02257
$274$	−32.2560	−1.94865
$275$	−20.0864	−1.21125
$276$	−82.6062	−4.97231
$277$	14.3608	0.862855	0.431428	−	0.902148i	$-0.358010\pi$
$277$	14.3608	0.862855	0.431428	+	0.902148i	$0.358010\pi$
$278$	36.5596	2.19270
$279$	46.0619	2.75765
$280$	−16.1101	−0.962761
$281$	−22.5221	−1.34356	−0.671778	−	0.740753i	$-0.734469\pi$
$281$	−22.5221	−1.34356	−0.671778	+	0.740753i	$0.734469\pi$
$282$	−26.6630	−1.58776
$283$	−3.53773	−0.210296	−0.105148	−	0.994457i	$-0.533532\pi$
$283$	−3.53773	−0.210296	−0.105148	+	0.994457i	$0.533532\pi$
$284$	65.9421	3.91294
$285$	10.7317	0.635693
$286$	−65.0234	−3.84491
$287$	21.2743	1.25578
$288$	−54.0749	−3.18640
$289$	0.913182	0.0537166
$290$	5.03285	0.295539
$291$	−34.1665	−2.00288
$292$	−47.9679	−2.80711
$293$	0.539130	0.0314963	0.0157482	−	0.999876i	$-0.494987\pi$
$293$	0.539130	0.0314963	0.0157482	+	0.999876i	$0.494987\pi$
$294$	−67.3376	−3.92721
$295$	−4.24576	−0.247198
$296$	39.9545	2.32231
$297$	25.6732	1.48971
$298$	30.8033	1.78439
$299$	−34.9392	−2.02058
$300$	−64.8235	−3.74258
$301$	9.01719	0.519742
$302$	23.3672	1.34463
$303$	29.7279	1.70782
$304$	67.5244	3.87279
$305$	0.793390	0.0454294
$306$	56.5692	3.23385
$307$	−26.5372	−1.51456	−0.757279	−	0.653091i	$-0.773472\pi$
$307$	−26.5372	−1.51456	−0.757279	+	0.653091i	$0.773472\pi$
$308$	82.6850	4.71142
$309$	−37.6974	−2.14453
$310$	−12.7775	−0.725711
$311$	32.5889	1.84795	0.923973	−	0.382457i	$-0.124922\pi$
$311$	32.5889	1.84795	0.923973	+	0.382457i	$0.124922\pi$
$312$	−123.070	−6.96747
$313$	0.462968	0.0261685	0.0130843	−	0.999914i	$-0.495835\pi$
$313$	0.462968	0.0261685	0.0130843	+	0.999914i	$0.495835\pi$
$314$	27.7861	1.56806
$315$	11.1038	0.625630
$316$	−23.0979	−1.29936
$317$	−20.6826	−1.16165	−0.580824	−	0.814029i	$-0.697270\pi$
$317$	−20.6826	−1.16165	−0.580824	+	0.814029i	$0.697270\pi$
$318$	97.9223	5.49121
$319$	−15.1494	−0.848204
$320$	4.45871	0.249249
$321$	−24.0102	−1.34012
$322$	62.8018	3.49981
$323$	−29.4059	−1.63619
$324$	8.68314	0.482397
$325$	−27.4178	−1.52087
$326$	−27.7843	−1.53883
$327$	−33.4773	−1.85130
$328$	−39.3933	−2.17513
$329$	14.3406	0.790621
$330$	−17.2385	−0.948949
$331$	−29.5928	−1.62657	−0.813283	−	0.581868i	$-0.802322\pi$
$331$	−29.5928	−1.62657	−0.813283	+	0.581868i	$0.802322\pi$
$332$	−60.7872	−3.33613
$333$	−27.5386	−1.50910
$334$	−40.9426	−2.24028
$335$	−2.22243	−0.121425
$336$	110.868	6.04834
$337$	16.4939	0.898479	0.449239	−	0.893411i	$-0.351695\pi$
$337$	16.4939	0.898479	0.449239	+	0.893411i	$0.351695\pi$
$338$	−54.7658	−2.97887
$339$	23.4158	1.27177
$340$	−11.1015	−0.602062
$341$	38.4615	2.08281
$342$	−92.8628	−5.02145
$343$	8.18018	0.441688
$344$	−16.6970	−0.900242
$345$	−9.26281	−0.498693
$346$	27.5427	1.48070
$347$	22.6691	1.21694	0.608471	−	0.793576i	$-0.291783\pi$
$347$	22.6691	1.21694	0.608471	+	0.793576i	$0.291783\pi$
$348$	−48.8907	−2.62082
$349$	6.37177	0.341073	0.170536	−	0.985351i	$-0.445450\pi$
$349$	6.37177	0.341073	0.170536	+	0.985351i	$0.445450\pi$
$350$	49.2824	2.63426
$351$	35.0437	1.87050
$352$	−45.1524	−2.40663
$353$	14.5419	0.773986	0.386993	−	0.922083i	$-0.373514\pi$
$353$	14.5419	0.773986	0.386993	+	0.922083i	$0.373514\pi$
$354$	58.3002	3.09862
$355$	7.39423	0.392445
$356$	84.7100	4.48962
$357$	−48.2814	−2.55532
$358$	3.70038	0.195571
$359$	16.9338	0.893731	0.446865	−	0.894601i	$-0.352540\pi$
$359$	16.9338	0.893731	0.446865	+	0.894601i	$0.352540\pi$
$360$	−20.5608	−1.08365
$361$	29.2721	1.54064
$362$	22.9847	1.20805
$363$	20.5603	1.07914
$364$	112.865	5.91571
$365$	−5.37875	−0.281536
$366$	−10.8943	−0.569457
$367$	28.7192	1.49913	0.749564	−	0.661932i	$-0.230263\pi$
$367$	28.7192	1.49913	0.749564	+	0.661932i	$0.230263\pi$
$368$	−58.2819	−3.03815
$369$	27.1518	1.41346
$370$	7.63914	0.397140
$371$	−52.6671	−2.73434
$372$	124.124	6.43554
$373$	−0.0494638	−0.00256114	−0.00128057	−	0.999999i	$-0.500408\pi$
$373$	−0.0494638	−0.00256114	−0.00128057	+	0.999999i	$0.500408\pi$
$374$	47.2351	2.44247
$375$	−14.9919	−0.774178
$376$	−26.5542	−1.36943
$377$	−20.6788	−1.06501
$378$	−62.9898	−3.23984
$379$	−6.63209	−0.340667	−0.170334	−	0.985386i	$-0.554485\pi$
$379$	−6.63209	−0.340667	−0.170334	+	0.985386i	$0.554485\pi$
$380$	18.2239	0.934869
$381$	−18.1418	−0.929432
$382$	11.8018	0.603832
$383$	22.3632	1.14271	0.571353	−	0.820704i	$-0.306419\pi$
$383$	22.3632	1.14271	0.571353	+	0.820704i	$0.306419\pi$
$384$	−0.967020	−0.0493480
$385$	9.27166	0.472527
$386$	−14.1352	−0.719465
$387$	11.5084	0.585004
$388$	−58.0194	−2.94549
$389$	−23.4494	−1.18893	−0.594466	−	0.804121i	$-0.702636\pi$
$389$	−23.4494	−1.18893	−0.594466	+	0.804121i	$0.702636\pi$
$390$	−23.5305	−1.19151
$391$	25.3809	1.28357
$392$	−67.0629	−3.38719
$393$	−18.6433	−0.940431
$394$	12.9548	0.652655
$395$	−2.59002	−0.130318
$396$	105.528	5.30300
$397$	26.9076	1.35045	0.675227	−	0.737610i	$-0.264046\pi$
$397$	26.9076	1.35045	0.675227	+	0.737610i	$0.264046\pi$
$398$	−31.0241	−1.55510
$399$	79.2577	3.96785
$400$	−45.7355	−2.28677
$401$	6.93141	0.346138	0.173069	−	0.984910i	$-0.444632\pi$
$401$	6.93141	0.346138	0.173069	+	0.984910i	$0.444632\pi$
$402$	30.5171	1.52205
$403$	52.4996	2.61519
$404$	50.4821	2.51158
$405$	0.973660	0.0483815
$406$	37.1694	1.84469
$407$	−22.9946	−1.13980
$408$	89.4020	4.42606
$409$	17.9931	0.889702	0.444851	−	0.895605i	$-0.353257\pi$
$409$	17.9931	0.889702	0.444851	+	0.895605i	$0.353257\pi$
$410$	−7.53184	−0.371971
$411$	35.1360	1.73313
$412$	−64.0152	−3.15380
$413$	−31.3565	−1.54295
$414$	80.1521	3.93926
$415$	−6.81620	−0.334594
$416$	−61.6327	−3.02179
$417$	−39.8239	−1.95018
$418$	−77.5401	−3.79261
$419$	14.0505	0.686414	0.343207	−	0.939260i	$-0.388487\pi$
$419$	14.0505	0.686414	0.343207	+	0.939260i	$0.388487\pi$
$420$	29.9218	1.46003
$421$	12.2106	0.595106	0.297553	−	0.954705i	$-0.403830\pi$
$421$	12.2106	0.595106	0.297553	+	0.954705i	$0.403830\pi$
$422$	19.6552	0.956802
$423$	18.3024	0.889895
$424$	97.5228	4.73613
$425$	19.9172	0.966124
$426$	−101.533	−4.91929
$427$	5.85947	0.283560
$428$	−40.7726	−1.97082
$429$	70.8292	3.41966
$430$	−3.19240	−0.153951
$431$	−27.7443	−1.33639	−0.668197	−	0.743985i	$-0.732934\pi$
$431$	−27.7443	−1.33639	−0.668197	+	0.743985i	$0.732934\pi$
$432$	58.4563	2.81248
$433$	−5.90175	−0.283620	−0.141810	−	0.989894i	$-0.545292\pi$
$433$	−5.90175	−0.283620	−0.141810	+	0.989894i	$0.545292\pi$
$434$	−94.3661	−4.52972
$435$	−5.48222	−0.262852
$436$	−56.8490	−2.72257
$437$	−41.6648	−1.99310
$438$	73.8576	3.52905
$439$	15.6517	0.747016	0.373508	−	0.927627i	$-0.378155\pi$
$439$	15.6517	0.747016	0.373508	+	0.927627i	$0.378155\pi$
$440$	−17.1682	−0.818462
$441$	46.2229	2.20109
$442$	64.4756	3.06679
$443$	5.46485	0.259643	0.129822	−	0.991537i	$-0.458560\pi$
$443$	5.46485	0.259643	0.129822	+	0.991537i	$0.458560\pi$
$444$	−74.2089	−3.52180
$445$	9.49872	0.450283
$446$	54.4948	2.58040
$447$	−33.5537	−1.58703
$448$	32.9291	1.55576
$449$	25.2078	1.18963	0.594815	−	0.803863i	$-0.297225\pi$
$449$	25.2078	1.18963	0.594815	+	0.803863i	$0.297225\pi$
$450$	62.8977	2.96502
$451$	22.6716	1.06757
$452$	39.7632	1.87030
$453$	−25.4536	−1.19592
$454$	−34.6139	−1.62451
$455$	12.6557	0.593311
$456$	−146.760	−6.87269
$457$	10.8555	0.507797	0.253899	−	0.967231i	$-0.418287\pi$
$457$	10.8555	0.507797	0.253899	+	0.967231i	$0.418287\pi$
$458$	−40.1454	−1.87587
$459$	−25.4569	−1.18823
$460$	−15.7295	−0.733393
$461$	−4.91271	−0.228808	−0.114404	−	0.993434i	$-0.536496\pi$
$461$	−4.91271	−0.228808	−0.114404	+	0.993434i	$0.536496\pi$
$462$	−127.313	−5.92312
$463$	−24.2465	−1.12683	−0.563416	−	0.826174i	$-0.690513\pi$
$463$	−24.2465	−1.12683	−0.563416	+	0.826174i	$0.690513\pi$
$464$	−34.4943	−1.60136
$465$	13.9183	0.645446
$466$	69.2139	3.20627
$467$	−16.5552	−0.766082	−0.383041	−	0.923731i	$-0.625123\pi$
$467$	−16.5552	−0.766082	−0.383041	+	0.923731i	$0.625123\pi$
$468$	144.046	6.65851
$469$	−16.4135	−0.757904
$470$	−5.07706	−0.234187
$471$	−30.2670	−1.39463
$472$	58.0624	2.67254
$473$	9.60945	0.441843
$474$	35.5645	1.63353
$475$	−32.6956	−1.50018
$476$	−81.9884	−3.75793
$477$	−67.2174	−3.07767
$478$	0.399038	0.0182516
$479$	−27.3320	−1.24883	−0.624415	−	0.781093i	$-0.714663\pi$
$479$	−27.3320	−1.24883	−0.624415	+	0.781093i	$0.714663\pi$
$480$	−16.3396	−0.745797
$481$	−31.3875	−1.43115
$482$	25.7729	1.17392
$483$	−68.4092	−3.11273
$484$	34.9143	1.58701
$485$	−6.50584	−0.295415
$486$	33.8102	1.53366
$487$	39.1599	1.77451	0.887253	−	0.461284i	$-0.152611\pi$
$487$	39.1599	1.77451	0.887253	+	0.461284i	$0.152611\pi$
$488$	−10.8499	−0.491152
$489$	30.2650	1.36863
$490$	−12.8221	−0.579245
$491$	23.8327	1.07555	0.537777	−	0.843087i	$-0.319264\pi$
$491$	23.8327	1.07555	0.537777	+	0.843087i	$0.319264\pi$
$492$	73.1666	3.29861
$493$	15.0218	0.676546
$494$	−105.842	−4.76204
$495$	11.8331	0.531860
$496$	87.5744	3.93221
$497$	54.6091	2.44955
$498$	93.5959	4.19413
$499$	24.0920	1.07850	0.539252	−	0.842144i	$-0.318707\pi$
$499$	24.0920	1.07850	0.539252	+	0.842144i	$0.318707\pi$
$500$	−25.4583	−1.13853
$501$	44.5982	1.99250
$502$	35.2905	1.57509
$503$	−26.2144	−1.16884	−0.584420	−	0.811451i	$-0.698678\pi$
$503$	−26.2144	−1.16884	−0.584420	+	0.811451i	$0.698678\pi$
$504$	−151.849	−6.76389
$505$	5.66066	0.251896
$506$	66.9267	2.97525
$507$	59.6557	2.64940
$508$	−30.8072	−1.36685
$509$	20.4537	0.906594	0.453297	−	0.891360i	$-0.350248\pi$
$509$	20.4537	0.906594	0.453297	+	0.891360i	$0.350248\pi$
$510$	17.0933	0.756903
$511$	−39.7240	−1.75729
$512$	41.3505	1.82745
$513$	41.7895	1.84505
$514$	−25.4536	−1.12271
$515$	−7.17817	−0.316308
$516$	31.0119	1.36522
$517$	15.2825	0.672122
$518$	56.4178	2.47885
$519$	−30.0019	−1.31694
$520$	−23.4345	−1.02767
$521$	−10.9743	−0.480791	−0.240396	−	0.970675i	$-0.577277\pi$
$521$	−10.9743	−0.480791	−0.240396	+	0.970675i	$0.577277\pi$
$522$	47.4382	2.07631
$523$	−0.449791	−0.0196680	−0.00983399	−	0.999952i	$-0.503130\pi$
$523$	−0.449791	−0.0196680	−0.00983399	+	0.999952i	$0.503130\pi$
$524$	−31.6589	−1.38302
$525$	−53.6827	−2.34290
$526$	36.0320	1.57107
$527$	−38.1374	−1.66129
$528$	118.150	5.14181
$529$	12.9619	0.563560
$530$	18.6460	0.809929
$531$	−40.0193	−1.73669
$532$	134.590	5.83523
$533$	30.9466	1.34045
$534$	−130.431	−5.64429
$535$	−4.57192	−0.197661
$536$	30.3926	1.31276
$537$	−4.03077	−0.173941
$538$	−10.7449	−0.463244
$539$	38.5960	1.66245
$540$	15.7766	0.678916
$541$	10.3137	0.443422	0.221711	−	0.975112i	$-0.428836\pi$
$541$	10.3137	0.443422	0.221711	+	0.975112i	$0.428836\pi$
$542$	6.90709	0.296685
$543$	−25.0370	−1.07444
$544$	44.7719	1.91958
$545$	−6.37460	−0.273058
$546$	−173.781	−7.43714
$547$	26.5023	1.13316	0.566578	−	0.824008i	$-0.308267\pi$
$547$	26.5023	1.13316	0.566578	+	0.824008i	$0.308267\pi$
$548$	59.6657	2.54879
$549$	7.47827	0.319165
$550$	52.5193	2.23943
$551$	−24.6594	−1.05053
$552$	126.672	5.39153
$553$	−19.1282	−0.813414
$554$	−37.5487	−1.59529
$555$	−8.32121	−0.353216
$556$	−67.6264	−2.86800
$557$	−0.506713	−0.0214701	−0.0107351	−	0.999942i	$-0.503417\pi$
$557$	−0.506713	−0.0214701	−0.0107351	+	0.999942i	$0.503417\pi$
$558$	−120.437	−5.09849
$559$	13.1168	0.554783
$560$	21.1110	0.892102
$561$	−51.4525	−2.17233
$562$	58.8879	2.48404
$563$	33.3229	1.40439	0.702197	−	0.711982i	$-0.252202\pi$
$563$	33.3229	1.40439	0.702197	+	0.711982i	$0.252202\pi$
$564$	49.3201	2.07675
$565$	4.45874	0.187580
$566$	9.25001	0.388807
$567$	7.19083	0.301986
$568$	−101.119	−4.24285
$569$	4.56793	0.191498	0.0957488	−	0.995406i	$-0.469475\pi$
$569$	4.56793	0.191498	0.0957488	+	0.995406i	$0.469475\pi$
$570$	−28.0600	−1.17530
$571$	−35.9343	−1.50380	−0.751901	−	0.659276i	$-0.770863\pi$
$571$	−35.9343	−1.50380	−0.751901	+	0.659276i	$0.770863\pi$
$572$	120.278	5.02906
$573$	−12.8555	−0.537048
$574$	−55.6253	−2.32176
$575$	28.2203	1.17687
$576$	42.0265	1.75110
$577$	37.7682	1.57231	0.786156	−	0.618028i	$-0.212068\pi$
$577$	37.7682	1.57231	0.786156	+	0.618028i	$0.212068\pi$
$578$	−2.38767	−0.0993141
$579$	15.3973	0.639892
$580$	−9.30955	−0.386558
$581$	−50.3401	−2.08846
$582$	89.3342	3.70302
$583$	−56.1263	−2.32451
$584$	73.5563	3.04378
$585$	16.1522	0.667809
$586$	−1.40965	−0.0582321
$587$	18.3586	0.757739	0.378869	−	0.925450i	$-0.376313\pi$
$587$	18.3586	0.757739	0.378869	+	0.925450i	$0.376313\pi$
$588$	124.558	5.13670
$589$	62.6056	2.57962
$590$	11.1013	0.457032
$591$	−14.1115	−0.580471
$592$	−52.3573	−2.15187
$593$	26.7101	1.09685	0.548426	−	0.836199i	$-0.315227\pi$
$593$	26.7101	1.09685	0.548426	+	0.836199i	$0.315227\pi$
$594$	−67.1270	−2.75425
$595$	−9.19354	−0.376898
$596$	−56.9787	−2.33394
$597$	33.7942	1.38310
$598$	91.3545	3.73576
$599$	30.8037	1.25860	0.629302	−	0.777161i	$-0.283341\pi$
$599$	30.8037	1.25860	0.629302	+	0.777161i	$0.283341\pi$
$600$	99.4035	4.05813
$601$	37.4560	1.52786	0.763930	−	0.645299i	$-0.223267\pi$
$601$	37.4560	1.52786	0.763930	+	0.645299i	$0.223267\pi$
$602$	−23.5770	−0.960927
$603$	−20.9480	−0.853070
$604$	−43.2237	−1.75875
$605$	3.91501	0.159168
$606$	−77.7288	−3.15752
$607$	40.6594	1.65031	0.825157	−	0.564903i	$-0.191086\pi$
$607$	40.6594	1.65031	0.825157	+	0.564903i	$0.191086\pi$
$608$	−73.4967	−2.98068
$609$	−40.4882	−1.64066
$610$	−2.07445	−0.0839922
$611$	20.8605	0.843924
$612$	−104.639	−4.22979
$613$	4.41352	0.178260	0.0891302	−	0.996020i	$-0.471591\pi$
$613$	4.41352	0.178260	0.0891302	+	0.996020i	$0.471591\pi$
$614$	69.3861	2.80019
$615$	8.20434	0.330831
$616$	−126.793	−5.10865
$617$	33.9212	1.36562	0.682808	−	0.730598i	$-0.260759\pi$
$617$	33.9212	1.36562	0.682808	+	0.730598i	$0.260759\pi$
$618$	98.5662	3.96492
$619$	1.57393	0.0632614	0.0316307	−	0.999500i	$-0.489930\pi$
$619$	1.57393	0.0632614	0.0316307	+	0.999500i	$0.489930\pi$
$620$	23.6352	0.949212
$621$	−36.0695	−1.44742
$622$	−85.2093	−3.41658
$623$	70.1515	2.81056
$624$	161.274	6.45611
$625$	20.6747	0.826988
$626$	−1.21051	−0.0483817
$627$	84.4634	3.37314
$628$	−51.3975	−2.05099
$629$	22.8009	0.909130
$630$	−29.0329	−1.15670
$631$	0.354094	0.0140962	0.00704812	−	0.999975i	$-0.497756\pi$
$631$	0.354094	0.0140962	0.00704812	+	0.999975i	$0.497756\pi$
$632$	35.4194	1.40891
$633$	−21.4102	−0.850978
$634$	54.0781	2.14771
$635$	−3.45448	−0.137087
$636$	−181.133	−7.18237
$637$	52.6833	2.08739
$638$	39.6107	1.56820
$639$	69.6959	2.75713
$640$	−0.184136	−0.00727860
$641$	−17.1152	−0.676009	−0.338004	−	0.941145i	$-0.609752\pi$
$641$	−17.1152	−0.676009	−0.338004	+	0.941145i	$0.609752\pi$
$642$	62.7788	2.47768
$643$	−40.6890	−1.60462	−0.802308	−	0.596910i	$-0.796395\pi$
$643$	−40.6890	−1.60462	−0.802308	+	0.596910i	$0.796395\pi$
$644$	−116.168	−4.57767
$645$	3.47744	0.136924
$646$	76.8868	3.02507
$647$	−44.8977	−1.76511	−0.882555	−	0.470209i	$-0.844178\pi$
$647$	−44.8977	−1.76511	−0.882555	+	0.470209i	$0.844178\pi$
$648$	−13.3152	−0.523069
$649$	−33.4160	−1.31169
$650$	71.6885	2.81185
$651$	102.792	4.02873
$652$	51.3942	2.01275
$653$	24.5648	0.961295	0.480648	−	0.876914i	$-0.340402\pi$
$653$	24.5648	0.961295	0.480648	+	0.876914i	$0.340402\pi$
$654$	87.5321	3.42278
$655$	−3.54998	−0.138709
$656$	51.6219	2.01550
$657$	−50.6985	−1.97794
$658$	−37.4959	−1.46174
$659$	28.6528	1.11615	0.558076	−	0.829790i	$-0.311540\pi$
$659$	28.6528	1.11615	0.558076	+	0.829790i	$0.311540\pi$
$660$	31.8871	1.24120
$661$	42.4063	1.64942	0.824708	−	0.565559i	$-0.191340\pi$
$661$	42.4063	1.64942	0.824708	+	0.565559i	$0.191340\pi$
$662$	77.3754	3.00728
$663$	−70.2324	−2.72760
$664$	93.2141	3.61741
$665$	15.0919	0.585239
$666$	72.0043	2.79011
$667$	21.2841	0.824125
$668$	75.7338	2.93023
$669$	−59.3605	−2.29501
$670$	5.81093	0.224496
$671$	6.24432	0.241059
$672$	−120.674	−4.65509
$673$	−30.6046	−1.17972	−0.589861	−	0.807505i	$-0.700817\pi$
$673$	−30.6046	−1.17972	−0.589861	+	0.807505i	$0.700817\pi$
$674$	−43.1261	−1.66115
$675$	−28.3048	−1.08945
$676$	101.303	3.89629
$677$	37.1259	1.42687	0.713433	−	0.700724i	$-0.247140\pi$
$677$	37.1259	1.42687	0.713433	+	0.700724i	$0.247140\pi$
$678$	−61.2246	−2.35132
$679$	−48.0480	−1.84391
$680$	17.0235	0.652823
$681$	37.7045	1.44484
$682$	−100.564	−3.85080
$683$	−13.3506	−0.510846	−0.255423	−	0.966829i	$-0.582215\pi$
$683$	−13.3506	−0.510846	−0.255423	+	0.966829i	$0.582215\pi$
$684$	171.774	6.56793
$685$	6.69045	0.255629
$686$	−21.3885	−0.816616
$687$	43.7298	1.66840
$688$	21.8801	0.834172
$689$	−76.6120	−2.91868
$690$	24.2192	0.922010
$691$	23.7035	0.901725	0.450863	−	0.892593i	$-0.351116\pi$
$691$	23.7035	0.901725	0.450863	+	0.892593i	$0.351116\pi$
$692$	−50.9473	−1.93673
$693$	87.3920	3.31975
$694$	−59.2723	−2.24994
$695$	−7.58309	−0.287643
$696$	74.9714	2.84178
$697$	−22.4806	−0.851514
$698$	−16.6601	−0.630593
$699$	−75.3937	−2.85165
$700$	−91.1605	−3.44554
$701$	−35.9658	−1.35841	−0.679204	−	0.733949i	$-0.737675\pi$
$701$	−35.9658	−1.35841	−0.679204	+	0.733949i	$0.737675\pi$
$702$	−91.6279	−3.45827
$703$	−37.4294	−1.41168
$704$	35.0920	1.32258
$705$	5.53037	0.208286
$706$	−38.0223	−1.43099
$707$	41.8060	1.57228
$708$	−107.841	−4.05292
$709$	43.4966	1.63355	0.816774	−	0.576957i	$-0.195760\pi$
$709$	43.4966	1.63355	0.816774	+	0.576957i	$0.195760\pi$
$710$	−19.3335	−0.725573
$711$	−24.4128	−0.915550
$712$	−129.899	−4.86815
$713$	−54.0363	−2.02368
$714$	126.240	4.72441
$715$	13.4870	0.504385
$716$	−6.84480	−0.255802
$717$	−0.434667	−0.0162329
$718$	−44.2763	−1.65238
$719$	−20.3475	−0.758832	−0.379416	−	0.925226i	$-0.623875\pi$
$719$	−20.3475	−0.758832	−0.379416	+	0.925226i	$0.623875\pi$
$720$	26.9433	1.00412
$721$	−53.0134	−1.97432
$722$	−76.5370	−2.84841
$723$	−28.0741	−1.04409
$724$	−42.5162	−1.58010
$725$	16.7023	0.620307
$726$	−53.7585	−1.99517
$727$	−6.12057	−0.227000	−0.113500	−	0.993538i	$-0.536206\pi$
$727$	−6.12057	−0.227000	−0.113500	+	0.993538i	$0.536206\pi$
$728$	−173.072	−6.41447
$729$	−42.2150	−1.56352
$730$	14.0637	0.520519
$731$	−9.52848	−0.352424
$732$	20.1519	0.744835
$733$	3.12572	0.115451	0.0577255	−	0.998332i	$-0.481615\pi$
$733$	3.12572	0.115451	0.0577255	+	0.998332i	$0.481615\pi$
$734$	−75.0912	−2.77167
$735$	13.9670	0.515180
$736$	63.4367	2.33831
$737$	−17.4915	−0.644308
$738$	−70.9930	−2.61329
$739$	−41.2416	−1.51710	−0.758548	−	0.651617i	$-0.774091\pi$
$739$	−41.2416	−1.51710	−0.758548	+	0.651617i	$0.774091\pi$
$740$	−14.1306	−0.519449
$741$	115.292	4.23536
$742$	137.707	5.05539
$743$	−29.3865	−1.07809	−0.539043	−	0.842278i	$-0.681214\pi$
$743$	−29.3865	−1.07809	−0.539043	+	0.842278i	$0.681214\pi$
$744$	−190.338	−6.97813
$745$	−6.38915	−0.234080
$746$	0.129332	0.00473516
$747$	−64.2476	−2.35070
$748$	−87.3734	−3.19469
$749$	−33.7653	−1.23376
$750$	39.1989	1.43134
$751$	2.83523	0.103459	0.0517296	−	0.998661i	$-0.483527\pi$
$751$	2.83523	0.103459	0.0517296	+	0.998661i	$0.483527\pi$
$752$	34.7973	1.26893
$753$	−38.4414	−1.40088
$754$	54.0684	1.96905
$755$	−4.84677	−0.176392
$756$	116.516	4.23764
$757$	7.75085	0.281709	0.140855	−	0.990030i	$-0.455015\pi$
$757$	7.75085	0.281709	0.140855	+	0.990030i	$0.455015\pi$
$758$	17.3407	0.629844
$759$	−72.9024	−2.64619
$760$	−27.9455	−1.01369
$761$	−8.86280	−0.321276	−0.160638	−	0.987013i	$-0.551355\pi$
$761$	−8.86280	−0.321276	−0.160638	+	0.987013i	$0.551355\pi$
$762$	47.4348	1.71838
$763$	−47.0787	−1.70436
$764$	−21.8305	−0.789798
$765$	−11.7334	−0.424223
$766$	−58.4725	−2.11270
$767$	−45.6126	−1.64698
$768$	−44.3028	−1.59864
$769$	6.98504	0.251887	0.125944	−	0.992037i	$-0.459804\pi$
$769$	6.98504	0.251887	0.125944	+	0.992037i	$0.459804\pi$
$770$	−24.2423	−0.873633
$771$	27.7262	0.998536
$772$	26.1468	0.941043
$773$	12.3434	0.443962	0.221981	−	0.975051i	$-0.428748\pi$
$773$	12.3434	0.443962	0.221981	+	0.975051i	$0.428748\pi$
$774$	−30.0906	−1.08159
$775$	−42.4039	−1.52319
$776$	88.9698	3.19383
$777$	−61.4551	−2.20469
$778$	61.3125	2.19816
$779$	36.9037	1.32221
$780$	43.5257	1.55847
$781$	58.1958	2.08241
$782$	−66.3628	−2.37313
$783$	−21.3478	−0.762909
$784$	87.8807	3.13860
$785$	−5.76332	−0.205702
$786$	48.7461	1.73872
$787$	9.81160	0.349746	0.174873	−	0.984591i	$-0.444049\pi$
$787$	9.81160	0.349746	0.174873	+	0.984591i	$0.444049\pi$
$788$	−23.9633	−0.853657
$789$	−39.2492	−1.39731
$790$	6.77205	0.240939
$791$	32.9294	1.17083
$792$	−161.822	−5.75011
$793$	8.52346	0.302677
$794$	−70.3546	−2.49679
$795$	−20.3108	−0.720350
$796$	57.3871	2.03403
$797$	53.6826	1.90153	0.950767	−	0.309906i	$-0.100298\pi$
$797$	53.6826	1.90153	0.950767	+	0.309906i	$0.100298\pi$
$798$	−207.233	−7.33597
$799$	−15.1537	−0.536100
$800$	49.7806	1.76001
$801$	89.5323	3.16347
$802$	−18.1234	−0.639959
$803$	−42.3331	−1.49390
$804$	−56.4492	−1.99081
$805$	−13.0262	−0.459113
$806$	−137.269	−4.83511
$807$	11.7042	0.412009
$808$	−77.4117	−2.72333
$809$	47.1234	1.65677	0.828385	−	0.560159i	$-0.189260\pi$
$809$	47.1234	1.65677	0.828385	+	0.560159i	$0.189260\pi$
$810$	−2.54580	−0.0894503
$811$	−39.1308	−1.37407	−0.687034	−	0.726626i	$-0.741088\pi$
$811$	−39.1308	−1.37407	−0.687034	+	0.726626i	$0.741088\pi$
$812$	−68.7544	−2.41281
$813$	−7.52380	−0.263871
$814$	60.1233	2.10732
$815$	5.76294	0.201867
$816$	−117.154	−4.10122
$817$	15.6418	0.547236
$818$	−47.0461	−1.64493
$819$	119.289	4.16831
$820$	13.9321	0.486529
$821$	−10.5481	−0.368130	−0.184065	−	0.982914i	$-0.558926\pi$
$821$	−10.5481	−0.368130	−0.184065	+	0.982914i	$0.558926\pi$
$822$	−91.8691	−3.20430
$823$	28.4328	0.991104	0.495552	−	0.868578i	$-0.334966\pi$
$823$	28.4328	0.991104	0.495552	+	0.868578i	$0.334966\pi$
$824$	98.1641	3.41971
$825$	−57.2086	−1.99175
$826$	81.9869	2.85269
$827$	22.9908	0.799467	0.399733	−	0.916631i	$-0.369103\pi$
$827$	22.9908	0.799467	0.399733	+	0.916631i	$0.369103\pi$
$828$	−148.262	−5.15246
$829$	−48.9838	−1.70128	−0.850638	−	0.525751i	$-0.823784\pi$
$829$	−48.9838	−1.70128	−0.850638	+	0.525751i	$0.823784\pi$
$830$	17.8221	0.618615
$831$	40.9013	1.41885
$832$	47.9003	1.66064
$833$	−38.2708	−1.32600
$834$	104.126	3.60560
$835$	8.49220	0.293885
$836$	143.430	4.96064
$837$	54.1981	1.87336
$838$	−36.7376	−1.26908
$839$	9.31047	0.321433	0.160717	−	0.987001i	$-0.448620\pi$
$839$	9.31047	0.321433	0.160717	+	0.987001i	$0.448620\pi$
$840$	−45.8835	−1.58313
$841$	−16.4029	−0.565619
$842$	−31.9266	−1.10026
$843$	−64.1458	−2.20930
$844$	−36.3574	−1.25147
$845$	11.3594	0.390774
$846$	−47.8549	−1.64529
$847$	28.9138	0.993489
$848$	−127.796	−4.38854
$849$	−10.0759	−0.345805
$850$	−52.0768	−1.78622
$851$	32.3062	1.10744
$852$	187.812	6.43432
$853$	−18.5047	−0.633588	−0.316794	−	0.948494i	$-0.602606\pi$
$853$	−18.5047	−0.633588	−0.316794	+	0.948494i	$0.602606\pi$
$854$	−15.3206	−0.524260
$855$	19.2614	0.658725
$856$	62.5227	2.13698
$857$	−48.7635	−1.66573	−0.832865	−	0.553475i	$-0.813301\pi$
$857$	−48.7635	−1.66573	−0.832865	+	0.553475i	$0.813301\pi$
$858$	−185.195	−6.32245
$859$	−5.64541	−0.192619	−0.0963094	−	0.995351i	$-0.530704\pi$
$859$	−5.64541	−0.192619	−0.0963094	+	0.995351i	$0.530704\pi$
$860$	5.90516	0.201364
$861$	60.5920	2.06497
$862$	72.5421	2.47079
$863$	55.7674	1.89834	0.949172	−	0.314757i	$-0.101923\pi$
$863$	55.7674	1.89834	0.949172	+	0.314757i	$0.101923\pi$
$864$	−63.6265	−2.16462
$865$	−5.71284	−0.194242
$866$	15.4311	0.524372
$867$	2.60086	0.0883298
$868$	174.554	5.92476
$869$	−20.3846	−0.691499
$870$	14.3342	0.485975
$871$	−23.8758	−0.809001
$872$	87.1750	2.95212
$873$	−61.3222	−2.07544
$874$	108.940	3.68494
$875$	−21.0829	−0.712733
$876$	−136.619	−4.61592
$877$	35.9469	1.21384	0.606921	−	0.794762i	$-0.292404\pi$
$877$	35.9469	1.21384	0.606921	+	0.794762i	$0.292404\pi$
$878$	−40.9241	−1.38112
$879$	1.53551	0.0517915
$880$	22.4976	0.758393
$881$	20.6552	0.695890	0.347945	−	0.937515i	$-0.386880\pi$
$881$	20.6552	0.695890	0.347945	+	0.937515i	$0.386880\pi$
$882$	−120.858	−4.06949
$883$	−4.10460	−0.138131	−0.0690655	−	0.997612i	$-0.522002\pi$
$883$	−4.10460	−0.138131	−0.0690655	+	0.997612i	$0.522002\pi$
$884$	−119.264	−4.01129
$885$	−12.0925	−0.406484
$886$	−14.2888	−0.480042
$887$	40.1728	1.34887	0.674435	−	0.738334i	$-0.264387\pi$
$887$	40.1728	1.34887	0.674435	+	0.738334i	$0.264387\pi$
$888$	113.796	3.81873
$889$	−25.5126	−0.855665
$890$	−24.8360	−0.832506
$891$	7.66312	0.256724
$892$	−100.802	−3.37511
$893$	24.8760	0.832444
$894$	87.7318	2.93419
$895$	−0.767523	−0.0256555
$896$	−1.35991	−0.0454314
$897$	−99.5112	−3.32258
$898$	−65.9102	−2.19945
$899$	−31.9815	−1.06664
$900$	−116.345	−3.87818
$901$	55.6534	1.85408
$902$	−59.2789	−1.97377
$903$	25.6821	0.854647
$904$	−60.9748	−2.02799
$905$	−4.76743	−0.158475
$906$	66.5529	2.21107
$907$	−24.7404	−0.821491	−0.410746	−	0.911750i	$-0.634732\pi$
$907$	−24.7404	−0.821491	−0.410746	+	0.911750i	$0.634732\pi$
$908$	64.0273	2.12482
$909$	53.3558	1.76970
$910$	−33.0906	−1.09694
$911$	−57.3142	−1.89890	−0.949451	−	0.313914i	$-0.898360\pi$
$911$	−57.3142	−1.89890	−0.949451	+	0.313914i	$0.898360\pi$
$912$	192.318	6.36829
$913$	−53.6465	−1.77544
$914$	−28.3835	−0.938842
$915$	2.25968	0.0747026
$916$	74.2592	2.45359
$917$	−26.2179	−0.865791
$918$	66.5614	2.19685
$919$	0.727751	0.0240063	0.0120032	−	0.999928i	$-0.496179\pi$
$919$	0.727751	0.0240063	0.0120032	+	0.999928i	$0.496179\pi$
$920$	24.1204	0.795226
$921$	−75.5814	−2.49049
$922$	12.8451	0.423032
$923$	79.4369	2.61470
$924$	235.498	7.74730
$925$	25.3516	0.833556
$926$	63.3967	2.08334
$927$	−67.6594	−2.22223
$928$	37.5452	1.23248
$929$	13.5069	0.443146	0.221573	−	0.975144i	$-0.428881\pi$
$929$	13.5069	0.443146	0.221573	+	0.975144i	$0.428881\pi$
$930$	−36.3918	−1.19334
$931$	62.8245	2.05899
$932$	−128.029	−4.19372
$933$	92.8173	3.03870
$934$	43.2863	1.41637
$935$	−9.79738	−0.320408
$936$	−220.887	−7.21990
$937$	15.7011	0.512934	0.256467	−	0.966553i	$-0.417442\pi$
$937$	15.7011	0.512934	0.256467	+	0.966553i	$0.417442\pi$
$938$	42.9158	1.40125
$939$	1.31859	0.0430306
$940$	9.39132	0.306311
$941$	−59.3929	−1.93615	−0.968076	−	0.250657i	$-0.919353\pi$
$941$	−59.3929	−1.93615	−0.968076	+	0.250657i	$0.919353\pi$
$942$	79.1384	2.57847
$943$	−31.8524	−1.03726
$944$	−76.0862	−2.47639
$945$	13.0652	0.425010
$946$	−25.1256	−0.816902
$947$	26.8911	0.873843	0.436921	−	0.899500i	$-0.356069\pi$
$947$	26.8911	0.873843	0.436921	+	0.899500i	$0.356069\pi$
$948$	−65.7857	−2.13662
$949$	−57.7844	−1.87576
$950$	85.4882	2.77360
$951$	−58.9065	−1.91018
$952$	125.725	4.07477
$953$	3.70183	0.119914	0.0599569	−	0.998201i	$-0.480904\pi$
$953$	3.70183	0.119914	0.0599569	+	0.998201i	$0.480904\pi$
$954$	175.751	5.69016
$955$	−2.44790	−0.0792121
$956$	−0.738124	−0.0238726
$957$	−43.1474	−1.39476
$958$	71.4641	2.30890
$959$	49.4113	1.59558
$960$	12.6990	0.409857
$961$	50.1951	1.61920
$962$	82.0679	2.64598
$963$	−43.0936	−1.38867
$964$	−47.6737	−1.53547
$965$	2.93190	0.0943811
$966$	178.868	5.75497
$967$	−34.5614	−1.11142	−0.555710	−	0.831376i	$-0.687554\pi$
$967$	−34.5614	−1.11142	−0.555710	+	0.831376i	$0.687554\pi$
$968$	−53.5392	−1.72082
$969$	−83.7518	−2.69049
$970$	17.0106	0.546179
$971$	−41.1825	−1.32161	−0.660805	−	0.750558i	$-0.729785\pi$
$971$	−41.1825	−1.32161	−0.660805	+	0.750558i	$0.729785\pi$
$972$	−62.5407	−2.00600
$973$	−56.0039	−1.79540
$974$	−102.390	−3.28080
$975$	−78.0894	−2.50086
$976$	14.2179	0.455105
$977$	−0.278734	−0.00891748	−0.00445874	−	0.999990i	$-0.501419\pi$
$977$	−0.278734	−0.00891748	−0.00445874	+	0.999990i	$0.501419\pi$
$978$	−79.1331	−2.53040
$979$	74.7591	2.38931
$980$	23.7178	0.757639
$981$	−60.0852	−1.91837
$982$	−62.3147	−1.98854
$983$	21.2937	0.679162	0.339581	−	0.940577i	$-0.389715\pi$
$983$	21.2937	0.679162	0.339581	+	0.940577i	$0.389715\pi$
$984$	−112.197	−3.57672
$985$	−2.68706	−0.0856167
$986$	−39.2770	−1.25083
$987$	40.8438	1.30007
$988$	195.782	6.22864
$989$	−13.5008	−0.429300
$990$	−30.9398	−0.983331
$991$	54.9212	1.74463	0.872314	−	0.488946i	$-0.162618\pi$
$991$	54.9212	1.74463	0.872314	+	0.488946i	$0.162618\pi$
$992$	−95.3201	−3.02641
$993$	−84.2841	−2.67467
$994$	−142.785	−4.52886
$995$	6.43494	0.204001
$996$	−173.130	−5.48583
$997$	−20.6319	−0.653418	−0.326709	−	0.945125i	$-0.605940\pi$
$997$	−20.6319	−0.653418	−0.326709	+	0.945125i	$0.605940\pi$
$998$	−62.9926	−1.99399
$999$	−32.4029	−1.02518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.13	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.13	✓	184	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61467 q^{2} +2.84813 q^{3} +4.83651 q^{4} +0.542328 q^{5} -7.44692 q^{6} +4.00529 q^{7} -7.41654 q^{8} +5.11183 q^{9} +O(q^{10})\)	\(q-2.61467 q^{2} +2.84813 q^{3} +4.83651 q^{4} +0.542328 q^{5} -7.44692 q^{6} +4.00529 q^{7} -7.41654 q^{8} +5.11183 q^{9} -1.41801 q^{10} +4.26836 q^{11} +13.7750 q^{12} +5.82628 q^{13} -10.4725 q^{14} +1.54462 q^{15} +9.71880 q^{16} -4.23240 q^{17} -13.3658 q^{18} +6.94781 q^{19} +2.62298 q^{20} +11.4076 q^{21} -11.1604 q^{22} -5.99682 q^{23} -21.1232 q^{24} -4.70588 q^{25} -15.2338 q^{26} +6.01477 q^{27} +19.3716 q^{28} -3.54923 q^{29} -4.03868 q^{30} +9.01083 q^{31} -10.5784 q^{32} +12.1568 q^{33} +11.0663 q^{34} +2.17218 q^{35} +24.7234 q^{36} -5.38722 q^{37} -18.1663 q^{38} +16.5940 q^{39} -4.02220 q^{40} +5.31155 q^{41} -29.8271 q^{42} +2.25132 q^{43} +20.6440 q^{44} +2.77229 q^{45} +15.6797 q^{46} +3.58041 q^{47} +27.6804 q^{48} +9.04234 q^{49} +12.3043 q^{50} -12.0544 q^{51} +28.1789 q^{52} -13.1494 q^{53} -15.7266 q^{54} +2.31485 q^{55} -29.7054 q^{56} +19.7883 q^{57} +9.28008 q^{58} -7.82877 q^{59} +7.47057 q^{60} +1.46293 q^{61} -23.5604 q^{62} +20.4744 q^{63} +8.22141 q^{64} +3.15976 q^{65} -31.7861 q^{66} -4.09795 q^{67} -20.4700 q^{68} -17.0797 q^{69} -5.67954 q^{70} +13.6342 q^{71} -37.9121 q^{72} -9.91788 q^{73} +14.0858 q^{74} -13.4029 q^{75} +33.6032 q^{76} +17.0960 q^{77} -43.3879 q^{78} -4.77574 q^{79} +5.27078 q^{80} +1.79533 q^{81} -13.8880 q^{82} -12.5684 q^{83} +55.1728 q^{84} -2.29535 q^{85} -5.88647 q^{86} -10.1087 q^{87} -31.6565 q^{88} +17.5147 q^{89} -7.24863 q^{90} +23.3359 q^{91} -29.0037 q^{92} +25.6640 q^{93} -9.36159 q^{94} +3.76800 q^{95} -30.1286 q^{96} -11.9961 q^{97} -23.6428 q^{98} +21.8191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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