LMFDB - Embedded newform 4001.2.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +O(q^{10})$	\(q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +5.80197 q^{10} -0.661784 q^{11} -7.23197 q^{12} +3.28103 q^{13} +4.69118 q^{14} +4.63691 q^{15} +2.66109 q^{16} -6.82644 q^{17} -1.64277 q^{18} +3.26699 q^{19} -9.10256 q^{20} +3.74918 q^{21} +1.58937 q^{22} -6.36815 q^{23} +8.14927 q^{24} +0.836275 q^{25} -7.87984 q^{26} +4.44525 q^{27} -7.35988 q^{28} -1.41430 q^{29} -11.1362 q^{30} -3.18044 q^{31} +2.10057 q^{32} +1.27022 q^{33} +16.3946 q^{34} +4.71892 q^{35} +2.57730 q^{36} +5.91293 q^{37} -7.84612 q^{38} -6.29753 q^{39} +10.2571 q^{40} +0.877003 q^{41} -9.00417 q^{42} +4.37063 q^{43} -2.49351 q^{44} -1.65248 q^{45} +15.2940 q^{46} -10.3864 q^{47} -5.10765 q^{48} -3.18452 q^{49} -2.00843 q^{50} +13.1025 q^{51} +12.3625 q^{52} -6.93570 q^{53} -10.6759 q^{54} +1.59876 q^{55} +8.29340 q^{56} -6.27059 q^{57} +3.39664 q^{58} -7.14427 q^{59} +17.4713 q^{60} +2.14088 q^{61} +7.63827 q^{62} -1.33612 q^{63} -10.3670 q^{64} -7.92643 q^{65} -3.05060 q^{66} -11.2787 q^{67} -25.7211 q^{68} +12.2229 q^{69} -11.3331 q^{70} +7.19157 q^{71} -2.90420 q^{72} -9.65095 q^{73} -14.2007 q^{74} -1.60513 q^{75} +12.3096 q^{76} +1.29268 q^{77} +15.1244 q^{78} -0.353871 q^{79} -6.42877 q^{80} -10.5842 q^{81} -2.10624 q^{82} +0.410926 q^{83} +14.1264 q^{84} +16.4916 q^{85} -10.4967 q^{86} +2.71458 q^{87} +2.80979 q^{88} +1.94551 q^{89} +3.96867 q^{90} -6.40891 q^{91} -23.9943 q^{92} +6.10448 q^{93} +24.9444 q^{94} -7.89251 q^{95} -4.03180 q^{96} -12.5183 q^{97} +7.64806 q^{98} -0.452674 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40164	−1.69821	−0.849107	−	0.528220i	$-0.822860\pi$
$2$	−2.40164	−1.69821	−0.849107	+	0.528220i	$0.822860\pi$
$3$	−1.91938	−1.10815	−0.554077	−	0.832465i	$-0.686929\pi$
$3$	−1.91938	−1.10815	−0.554077	+	0.832465i	$0.686929\pi$
$4$	3.76787	1.88393
$5$	−2.41584	−1.08040	−0.540198	−	0.841538i	$-0.681651\pi$
$5$	−2.41584	−1.08040	−0.540198	+	0.841538i	$0.681651\pi$
$6$	4.60966	1.88188
$7$	−1.95333	−0.738288	−0.369144	−	0.929372i	$-0.620349\pi$
$7$	−1.95333	−0.738288	−0.369144	+	0.929372i	$0.620349\pi$
$8$	−4.24578	−1.50111
$9$	0.684021	0.228007
$10$	5.80197	1.83474
$11$	−0.661784	−0.199535	−0.0997677	−	0.995011i	$-0.531810\pi$
$11$	−0.661784	−0.199535	−0.0997677	+	0.995011i	$0.531810\pi$
$12$	−7.23197	−2.08769
$13$	3.28103	0.909993	0.454996	−	0.890493i	$-0.349641\pi$
$13$	3.28103	0.909993	0.454996	+	0.890493i	$0.349641\pi$
$14$	4.69118	1.25377
$15$	4.63691	1.19725
$16$	2.66109	0.665274
$17$	−6.82644	−1.65565	−0.827827	−	0.560984i	$-0.810423\pi$
$17$	−6.82644	−1.65565	−0.827827	+	0.560984i	$0.810423\pi$
$18$	−1.64277	−0.387205
$19$	3.26699	0.749498	0.374749	−	0.927126i	$-0.377729\pi$
$19$	3.26699	0.749498	0.374749	+	0.927126i	$0.377729\pi$
$20$	−9.10256	−2.03539
$21$	3.74918	0.818137
$22$	1.58937	0.338854
$23$	−6.36815	−1.32785	−0.663925	−	0.747799i	$-0.731111\pi$
$23$	−6.36815	−1.32785	−0.663925	+	0.747799i	$0.731111\pi$
$24$	8.14927	1.66346
$25$	0.836275	0.167255
$26$	−7.87984	−1.54536
$27$	4.44525	0.855488
$28$	−7.35988	−1.39089
$29$	−1.41430	−0.262629	−0.131315	−	0.991341i	$-0.541920\pi$
$29$	−1.41430	−0.262629	−0.131315	+	0.991341i	$0.541920\pi$
$30$	−11.1362	−2.03318
$31$	−3.18044	−0.571224	−0.285612	−	0.958345i	$-0.592197\pi$
$31$	−3.18044	−0.571224	−0.285612	+	0.958345i	$0.592197\pi$
$32$	2.10057	0.371333
$33$	1.27022	0.221116
$34$	16.3946	2.81166
$35$	4.71892	0.797643
$36$	2.57730	0.429550
$37$	5.91293	0.972080	0.486040	−	0.873937i	$-0.338441\pi$
$37$	5.91293	0.972080	0.486040	+	0.873937i	$0.338441\pi$
$38$	−7.84612	−1.27281
$39$	−6.29753	−1.00841
$40$	10.2571	1.62179
$41$	0.877003	0.136965	0.0684824	−	0.997652i	$-0.478184\pi$
$41$	0.877003	0.136965	0.0684824	+	0.997652i	$0.478184\pi$
$42$	−9.00417	−1.38937
$43$	4.37063	0.666515	0.333258	−	0.942836i	$-0.391852\pi$
$43$	4.37063	0.666515	0.333258	+	0.942836i	$0.391852\pi$
$44$	−2.49351	−0.375912
$45$	−1.65248	−0.246338
$46$	15.2940	2.25498
$47$	−10.3864	−1.51501	−0.757505	−	0.652829i	$-0.773582\pi$
$47$	−10.3864	−1.51501	−0.757505	+	0.652829i	$0.773582\pi$
$48$	−5.10765	−0.737226
$49$	−3.18452	−0.454931
$50$	−2.00843	−0.284035
$51$	13.1025	1.83472
$52$	12.3625	1.71437
$53$	−6.93570	−0.952691	−0.476346	−	0.879258i	$-0.658039\pi$
$53$	−6.93570	−0.952691	−0.476346	+	0.879258i	$0.658039\pi$
$54$	−10.6759	−1.45280
$55$	1.59876	0.215577
$56$	8.29340	1.10825
$57$	−6.27059	−0.830560
$58$	3.39664	0.446001
$59$	−7.14427	−0.930104	−0.465052	−	0.885283i	$-0.653964\pi$
$59$	−7.14427	−0.930104	−0.465052	+	0.885283i	$0.653964\pi$
$60$	17.4713	2.25553
$61$	2.14088	0.274112	0.137056	−	0.990563i	$-0.456236\pi$
$61$	2.14088	0.274112	0.137056	+	0.990563i	$0.456236\pi$
$62$	7.63827	0.970062
$63$	−1.33612	−0.168335
$64$	−10.3670	−1.29588
$65$	−7.92643	−0.983152
$66$	−3.05060	−0.375503
$67$	−11.2787	−1.37791	−0.688956	−	0.724803i	$-0.741931\pi$
$67$	−11.2787	−1.37791	−0.688956	+	0.724803i	$0.741931\pi$
$68$	−25.7211	−3.11914
$69$	12.2229	1.47146
$70$	−11.3331	−1.35457
$71$	7.19157	0.853482	0.426741	−	0.904374i	$-0.359662\pi$
$71$	7.19157	0.853482	0.426741	+	0.904374i	$0.359662\pi$
$72$	−2.90420	−0.342263
$73$	−9.65095	−1.12956	−0.564779	−	0.825242i	$-0.691039\pi$
$73$	−9.65095	−1.12956	−0.564779	+	0.825242i	$0.691039\pi$
$74$	−14.2007	−1.65080
$75$	−1.60513	−0.185344
$76$	12.3096	1.41201
$77$	1.29268	0.147315
$78$	15.1244	1.71250
$79$	−0.353871	−0.0398136	−0.0199068	−	0.999802i	$-0.506337\pi$
$79$	−0.353871	−0.0398136	−0.0199068	+	0.999802i	$0.506337\pi$
$80$	−6.42877	−0.718759
$81$	−10.5842	−1.17602
$82$	−2.10624	−0.232596
$83$	0.410926	0.0451050	0.0225525	−	0.999746i	$-0.492821\pi$
$83$	0.410926	0.0451050	0.0225525	+	0.999746i	$0.492821\pi$
$84$	14.1264	1.54132
$85$	16.4916	1.78876
$86$	−10.4967	−1.13189
$87$	2.71458	0.291034
$88$	2.80979	0.299525
$89$	1.94551	0.206223	0.103112	−	0.994670i	$-0.467120\pi$
$89$	1.94551	0.206223	0.103112	+	0.994670i	$0.467120\pi$
$90$	3.96867	0.418334
$91$	−6.40891	−0.671837
$92$	−23.9943	−2.50158
$93$	6.10448	0.633005
$94$	24.9444	2.57281
$95$	−7.89251	−0.809755
$96$	−4.03180	−0.411494
$97$	−12.5183	−1.27104	−0.635519	−	0.772085i	$-0.719214\pi$
$97$	−12.5183	−1.27104	−0.635519	+	0.772085i	$0.719214\pi$
$98$	7.64806	0.772570
$99$	−0.452674	−0.0454954
$100$	3.15097	0.315097
$101$	3.68698	0.366868	0.183434	−	0.983032i	$-0.441279\pi$
$101$	3.68698	0.366868	0.183434	+	0.983032i	$0.441279\pi$
$102$	−31.4675	−3.11575
$103$	−9.34932	−0.921216	−0.460608	−	0.887604i	$-0.652369\pi$
$103$	−9.34932	−0.921216	−0.460608	+	0.887604i	$0.652369\pi$
$104$	−13.9305	−1.36600
$105$	−9.05740	−0.883912
$106$	16.6570	1.61787
$107$	1.71192	0.165498	0.0827489	−	0.996570i	$-0.473630\pi$
$107$	1.71192	0.165498	0.0827489	+	0.996570i	$0.473630\pi$
$108$	16.7491	1.61168
$109$	−7.64974	−0.732712	−0.366356	−	0.930475i	$-0.619395\pi$
$109$	−7.64974	−0.732712	−0.366356	+	0.930475i	$0.619395\pi$
$110$	−3.83965	−0.366096
$111$	−11.3492	−1.07722
$112$	−5.19799	−0.491164
$113$	−15.0525	−1.41602	−0.708011	−	0.706201i	$-0.750407\pi$
$113$	−15.0525	−1.41602	−0.708011	+	0.706201i	$0.750407\pi$
$114$	15.0597	1.41047
$115$	15.3844	1.43460
$116$	−5.32890	−0.494776
$117$	2.24429	0.207485
$118$	17.1580	1.57952
$119$	13.3343	1.22235
$120$	−19.6873	−1.79720
$121$	−10.5620	−0.960186
$122$	−5.14162	−0.465501
$123$	−1.68330	−0.151778
$124$	−11.9835	−1.07615
$125$	10.0589	0.899694
$126$	3.20887	0.285869
$127$	−11.8598	−1.05239	−0.526193	−	0.850365i	$-0.676381\pi$
$127$	−11.8598	−1.05239	−0.526193	+	0.850365i	$0.676381\pi$
$128$	20.6967	1.82934
$129$	−8.38890	−0.738602
$130$	19.0364	1.66960
$131$	−6.50084	−0.567981	−0.283991	−	0.958827i	$-0.591658\pi$
$131$	−6.50084	−0.567981	−0.283991	+	0.958827i	$0.591658\pi$
$132$	4.78600	0.416568
$133$	−6.38149	−0.553346
$134$	27.0873	2.33999
$135$	−10.7390	−0.924265
$136$	28.9835	2.48532
$137$	−1.46698	−0.125333	−0.0626663	−	0.998035i	$-0.519960\pi$
$137$	−1.46698	−0.125333	−0.0626663	+	0.998035i	$0.519960\pi$
$138$	−29.3550	−2.49886
$139$	15.2297	1.29177	0.645885	−	0.763435i	$-0.276489\pi$
$139$	15.2297	1.29177	0.645885	+	0.763435i	$0.276489\pi$
$140$	17.7803	1.50271
$141$	19.9354	1.67887
$142$	−17.2715	−1.44940
$143$	−2.17133	−0.181576
$144$	1.82024	0.151687
$145$	3.41673	0.283744
$146$	23.1781	1.91823
$147$	6.11230	0.504134
$148$	22.2791	1.83133
$149$	5.26037	0.430946	0.215473	−	0.976510i	$-0.430871\pi$
$149$	5.26037	0.430946	0.215473	+	0.976510i	$0.430871\pi$
$150$	3.85494	0.314755
$151$	−2.08132	−0.169376	−0.0846879	−	0.996408i	$-0.526989\pi$
$151$	−2.08132	−0.169376	−0.0846879	+	0.996408i	$0.526989\pi$
$152$	−13.8709	−1.12508
$153$	−4.66942	−0.377500
$154$	−3.10455	−0.250172
$155$	7.68343	0.617148
$156$	−23.7283	−1.89978
$157$	−0.112095	−0.00894618	−0.00447309	−	0.999990i	$-0.501424\pi$
$157$	−0.112095	−0.00894618	−0.00447309	+	0.999990i	$0.501424\pi$
$158$	0.849871	0.0676121
$159$	13.3122	1.05573
$160$	−5.07465	−0.401186
$161$	12.4391	0.980336
$162$	25.4194	1.99713
$163$	−12.9707	−1.01594	−0.507970	−	0.861375i	$-0.669604\pi$
$163$	−12.9707	−1.01594	−0.507970	+	0.861375i	$0.669604\pi$
$164$	3.30443	0.258033
$165$	−3.06863	−0.238893
$166$	−0.986897	−0.0765981
$167$	−20.1266	−1.55745	−0.778723	−	0.627367i	$-0.784132\pi$
$167$	−20.1266	−1.55745	−0.778723	+	0.627367i	$0.784132\pi$
$168$	−15.9182	−1.22811
$169$	−2.23487	−0.171913
$170$	−39.6068	−3.03770
$171$	2.23469	0.170891
$172$	16.4680	1.25567
$173$	−8.09988	−0.615822	−0.307911	−	0.951415i	$-0.599630\pi$
$173$	−8.09988	−0.615822	−0.307911	+	0.951415i	$0.599630\pi$
$174$	−6.51945	−0.494238
$175$	−1.63352	−0.123482
$176$	−1.76107	−0.132746
$177$	13.7126	1.03070
$178$	−4.67240	−0.350211
$179$	−3.91190	−0.292389	−0.146194	−	0.989256i	$-0.546703\pi$
$179$	−3.91190	−0.292389	−0.146194	+	0.989256i	$0.546703\pi$
$180$	−6.22634	−0.464084
$181$	−19.4450	−1.44533	−0.722666	−	0.691197i	$-0.757084\pi$
$181$	−19.4450	−1.44533	−0.722666	+	0.691197i	$0.757084\pi$
$182$	15.3919	1.14092
$183$	−4.10916	−0.303758
$184$	27.0378	1.99325
$185$	−14.2847	−1.05023
$186$	−14.6607	−1.07498
$187$	4.51763	0.330361
$188$	−39.1346	−2.85418
$189$	−8.68302	−0.631596
$190$	18.9550	1.37514
$191$	−6.89866	−0.499169	−0.249585	−	0.968353i	$-0.580294\pi$
$191$	−6.89866	−0.499169	−0.249585	+	0.968353i	$0.580294\pi$
$192$	19.8982	1.43603
$193$	−5.56850	−0.400829	−0.200415	−	0.979711i	$-0.564229\pi$
$193$	−5.56850	−0.400829	−0.200415	+	0.979711i	$0.564229\pi$
$194$	30.0644	2.15850
$195$	15.2138	1.08948
$196$	−11.9988	−0.857060
$197$	−11.2946	−0.804707	−0.402354	−	0.915484i	$-0.631808\pi$
$197$	−11.2946	−0.804707	−0.402354	+	0.915484i	$0.631808\pi$
$198$	1.08716	0.0772610
$199$	−23.3799	−1.65736	−0.828679	−	0.559724i	$-0.810907\pi$
$199$	−23.3799	−1.65736	−0.828679	+	0.559724i	$0.810907\pi$
$200$	−3.55064	−0.251068
$201$	21.6481	1.52694
$202$	−8.85478	−0.623020
$203$	2.76259	0.193896
$204$	49.3686	3.45649
$205$	−2.11870	−0.147976
$206$	22.4537	1.56442
$207$	−4.35594	−0.302759
$208$	8.73112	0.605394
$209$	−2.16204	−0.149551
$210$	21.7526	1.50107
$211$	17.2283	1.18605	0.593023	−	0.805185i	$-0.297934\pi$
$211$	17.2283	1.18605	0.593023	+	0.805185i	$0.297934\pi$
$212$	−26.1328	−1.79481
$213$	−13.8034	−0.945790
$214$	−4.11142	−0.281051
$215$	−10.5587	−0.720100
$216$	−18.8735	−1.28418
$217$	6.21244	0.421728
$218$	18.3719	1.24430
$219$	18.5238	1.25173
$220$	6.02393	0.406133
$221$	−22.3977	−1.50663
$222$	27.2566	1.82934
$223$	−10.6011	−0.709903	−0.354951	−	0.934885i	$-0.615503\pi$
$223$	−10.6011	−0.709903	−0.354951	+	0.934885i	$0.615503\pi$
$224$	−4.10311	−0.274150
$225$	0.572029	0.0381353
$226$	36.1507	2.40471
$227$	9.03942	0.599968	0.299984	−	0.953944i	$-0.403019\pi$
$227$	9.03942	0.599968	0.299984	+	0.953944i	$0.403019\pi$
$228$	−23.6268	−1.56472
$229$	0.468543	0.0309622	0.0154811	−	0.999880i	$-0.495072\pi$
$229$	0.468543	0.0309622	0.0154811	+	0.999880i	$0.495072\pi$
$230$	−36.9478	−2.43627
$231$	−2.48114	−0.163247
$232$	6.00482	0.394236
$233$	−8.82531	−0.578165	−0.289082	−	0.957304i	$-0.593350\pi$
$233$	−8.82531	−0.578165	−0.289082	+	0.957304i	$0.593350\pi$
$234$	−5.38997	−0.352353
$235$	25.0918	1.63681
$236$	−26.9187	−1.75226
$237$	0.679213	0.0441197
$238$	−32.0241	−2.07581
$239$	−16.2907	−1.05376	−0.526878	−	0.849941i	$-0.676638\pi$
$239$	−16.2907	−1.05376	−0.526878	+	0.849941i	$0.676638\pi$
$240$	12.3393	0.796496
$241$	2.78334	0.179291	0.0896454	−	0.995974i	$-0.471427\pi$
$241$	2.78334	0.179291	0.0896454	+	0.995974i	$0.471427\pi$
$242$	25.3662	1.63060
$243$	6.97933	0.447724
$244$	8.06656	0.516408
$245$	7.69327	0.491505
$246$	4.04268	0.257752
$247$	10.7191	0.682038
$248$	13.5035	0.857470
$249$	−0.788724	−0.0499834
$250$	−24.1578	−1.52787
$251$	1.46310	0.0923501	0.0461750	−	0.998933i	$-0.485297\pi$
$251$	1.46310	0.0923501	0.0461750	+	0.998933i	$0.485297\pi$
$252$	−5.03431	−0.317132
$253$	4.21434	0.264953
$254$	28.4829	1.78718
$255$	−31.6536	−1.98222
$256$	−28.9719	−1.81074
$257$	−9.95063	−0.620703	−0.310352	−	0.950622i	$-0.600447\pi$
$257$	−9.95063	−0.620703	−0.310352	+	0.950622i	$0.600447\pi$
$258$	20.1471	1.25430
$259$	−11.5499	−0.717675
$260$	−29.8657	−1.85219
$261$	−0.967412	−0.0598813
$262$	15.6127	0.964554
$263$	−14.9582	−0.922359	−0.461180	−	0.887307i	$-0.652574\pi$
$263$	−14.9582	−0.922359	−0.461180	+	0.887307i	$0.652574\pi$
$264$	−5.39305	−0.331920
$265$	16.7555	1.02928
$266$	15.3260	0.939700
$267$	−3.73416	−0.228527
$268$	−42.4966	−2.59590
$269$	−5.04541	−0.307624	−0.153812	−	0.988100i	$-0.549155\pi$
$269$	−5.04541	−0.307624	−0.153812	+	0.988100i	$0.549155\pi$
$270$	25.7912	1.56960
$271$	28.3487	1.72206	0.861030	−	0.508555i	$-0.169820\pi$
$271$	28.3487	1.72206	0.861030	+	0.508555i	$0.169820\pi$
$272$	−18.1658	−1.10146
$273$	12.3011	0.744499
$274$	3.52316	0.212842
$275$	−0.553433	−0.0333733
$276$	46.0543	2.77214
$277$	23.1036	1.38816	0.694080	−	0.719898i	$-0.255811\pi$
$277$	23.1036	1.38816	0.694080	+	0.719898i	$0.255811\pi$
$278$	−36.5763	−2.19370
$279$	−2.17549	−0.130243
$280$	−20.0355	−1.19735
$281$	6.86479	0.409519	0.204760	−	0.978812i	$-0.434359\pi$
$281$	6.86479	0.409519	0.204760	+	0.978812i	$0.434359\pi$
$282$	−47.8777	−2.85108
$283$	1.80221	0.107130	0.0535651	−	0.998564i	$-0.482942\pi$
$283$	1.80221	0.107130	0.0535651	+	0.998564i	$0.482942\pi$
$284$	27.0969	1.60790
$285$	15.1487	0.897333
$286$	5.21475	0.308355
$287$	−1.71307	−0.101119
$288$	1.43684	0.0846664
$289$	29.6002	1.74119
$290$	−8.20574	−0.481858
$291$	24.0273	1.40851
$292$	−36.3635	−2.12801
$293$	7.23580	0.422720	0.211360	−	0.977408i	$-0.432211\pi$
$293$	7.23580	0.422720	0.211360	+	0.977408i	$0.432211\pi$
$294$	−14.6795	−0.856127
$295$	17.2594	1.00488
$296$	−25.1050	−1.45920
$297$	−2.94179	−0.170700
$298$	−12.6335	−0.731839
$299$	−20.8941	−1.20833
$300$	−6.04791	−0.349177
$301$	−8.53727	−0.492080
$302$	4.99859	0.287637
$303$	−7.07671	−0.406546
$304$	8.69376	0.498621
$305$	−5.17202	−0.296149
$306$	11.2143	0.641077
$307$	24.1293	1.37713	0.688565	−	0.725174i	$-0.258241\pi$
$307$	24.1293	1.37713	0.688565	+	0.725174i	$0.258241\pi$
$308$	4.87065	0.277531
$309$	17.9449	1.02085
$310$	−18.4528	−1.04805
$311$	2.09617	0.118863	0.0594314	−	0.998232i	$-0.481071\pi$
$311$	2.09617	0.118863	0.0594314	+	0.998232i	$0.481071\pi$
$312$	26.7380	1.51374
$313$	9.93427	0.561518	0.280759	−	0.959778i	$-0.409414\pi$
$313$	9.93427	0.561518	0.280759	+	0.959778i	$0.409414\pi$
$314$	0.269212	0.0151925
$315$	3.22784	0.181868
$316$	−1.33334	−0.0750062
$317$	5.38850	0.302648	0.151324	−	0.988484i	$-0.451646\pi$
$317$	5.38850	0.302648	0.151324	+	0.988484i	$0.451646\pi$
$318$	−31.9712	−1.79286
$319$	0.935963	0.0524038
$320$	25.0450	1.40006
$321$	−3.28583	−0.183397
$322$	−29.8742	−1.66482
$323$	−22.3019	−1.24091
$324$	−39.8798	−2.21554
$325$	2.74384	0.152201
$326$	31.1508	1.72529
$327$	14.6828	0.811958
$328$	−3.72356	−0.205599
$329$	20.2880	1.11851
$330$	7.36975	0.405691
$331$	16.5480	0.909559	0.454779	−	0.890604i	$-0.349718\pi$
$331$	16.5480	0.909559	0.454779	+	0.890604i	$0.349718\pi$
$332$	1.54832	0.0849749
$333$	4.04457	0.221641
$334$	48.3369	2.64488
$335$	27.2475	1.48869
$336$	9.97691	0.544285
$337$	15.5503	0.847079	0.423539	−	0.905878i	$-0.360788\pi$
$337$	15.5503	0.847079	0.423539	+	0.905878i	$0.360788\pi$
$338$	5.36736	0.291946
$339$	28.8915	1.56917
$340$	62.1380	3.36991
$341$	2.10477	0.113979
$342$	−5.36691	−0.290209
$343$	19.8937	1.07416
$344$	−18.5567	−1.00051
$345$	−29.5285	−1.58976
$346$	19.4530	1.04580
$347$	0.237153	0.0127310	0.00636551	−	0.999980i	$-0.497974\pi$
$347$	0.237153	0.0127310	0.00636551	+	0.999980i	$0.497974\pi$
$348$	10.2282	0.548289
$349$	−12.1902	−0.652525	−0.326263	−	0.945279i	$-0.605789\pi$
$349$	−12.1902	−0.652525	−0.326263	+	0.945279i	$0.605789\pi$
$350$	3.92312	0.209700
$351$	14.5850	0.778488
$352$	−1.39013	−0.0740940
$353$	−14.5713	−0.775551	−0.387775	−	0.921754i	$-0.626756\pi$
$353$	−14.5713	−0.775551	−0.387775	+	0.921754i	$0.626756\pi$
$354$	−32.9326	−1.75035
$355$	−17.3737	−0.922098
$356$	7.33041	0.388511
$357$	−25.5935	−1.35455
$358$	9.39497	0.496539
$359$	19.9049	1.05054	0.525270	−	0.850936i	$-0.323964\pi$
$359$	19.9049	1.05054	0.525270	+	0.850936i	$0.323964\pi$
$360$	7.01608	0.369780
$361$	−8.32680	−0.438252
$362$	46.6998	2.45449
$363$	20.2726	1.06403
$364$	−24.1479	−1.26570
$365$	23.3151	1.22037
$366$	9.86873	0.515847
$367$	10.6854	0.557775	0.278887	−	0.960324i	$-0.410034\pi$
$367$	10.6854	0.557775	0.278887	+	0.960324i	$0.410034\pi$
$368$	−16.9462	−0.883384
$369$	0.599888	0.0312289
$370$	34.3067	1.78352
$371$	13.5477	0.703360
$372$	23.0009	1.19254
$373$	−11.8408	−0.613092	−0.306546	−	0.951856i	$-0.599173\pi$
$373$	−11.8408	−0.613092	−0.306546	+	0.951856i	$0.599173\pi$
$374$	−10.8497	−0.561025
$375$	−19.3068	−0.997000
$376$	44.0983	2.27420
$377$	−4.64036	−0.238991
$378$	20.8535	1.07259
$379$	−1.89434	−0.0973059	−0.0486530	−	0.998816i	$-0.515493\pi$
$379$	−1.89434	−0.0973059	−0.0486530	+	0.998816i	$0.515493\pi$
$380$	−29.7379	−1.52552
$381$	22.7635	1.16621
$382$	16.5681	0.847697
$383$	12.8909	0.658696	0.329348	−	0.944209i	$-0.393171\pi$
$383$	12.8909	0.658696	0.329348	+	0.944209i	$0.393171\pi$
$384$	−39.7248	−2.02720
$385$	−3.12291	−0.159158
$386$	13.3735	0.680694
$387$	2.98960	0.151970
$388$	−47.1672	−2.39455
$389$	−14.7884	−0.749800	−0.374900	−	0.927065i	$-0.622323\pi$
$389$	−14.7884	−0.749800	−0.374900	+	0.927065i	$0.622323\pi$
$390$	−36.5381	−1.85018
$391$	43.4718	2.19846
$392$	13.5208	0.682901
$393$	12.4776	0.629411
$394$	27.1256	1.36657
$395$	0.854896	0.0430145
$396$	−1.70562	−0.0857104
$397$	−3.24499	−0.162861	−0.0814306	−	0.996679i	$-0.525949\pi$
$397$	−3.24499	−0.162861	−0.0814306	+	0.996679i	$0.525949\pi$
$398$	56.1501	2.81455
$399$	12.2485	0.613193
$400$	2.22541	0.111270
$401$	24.0365	1.20032	0.600162	−	0.799878i	$-0.295103\pi$
$401$	24.0365	1.20032	0.600162	+	0.799878i	$0.295103\pi$
$402$	−51.9909	−2.59307
$403$	−10.4351	−0.519810
$404$	13.8920	0.691155
$405$	25.5697	1.27057
$406$	−6.63475	−0.329277
$407$	−3.91308	−0.193964
$408$	−55.6304	−2.75412
$409$	−0.423743	−0.0209527	−0.0104764	−	0.999945i	$-0.503335\pi$
$409$	−0.423743	−0.0209527	−0.0104764	+	0.999945i	$0.503335\pi$
$410$	5.08834	0.251295
$411$	2.81569	0.138888
$412$	−35.2270	−1.73551
$413$	13.9551	0.686685
$414$	10.4614	0.514150
$415$	−0.992732	−0.0487313
$416$	6.89204	0.337910
$417$	−29.2317	−1.43148
$418$	5.19244	0.253970
$419$	−10.3485	−0.505556	−0.252778	−	0.967524i	$-0.581344\pi$
$419$	−10.3485	−0.505556	−0.252778	+	0.967524i	$0.581344\pi$
$420$	−34.1271	−1.66523
$421$	−19.2110	−0.936288	−0.468144	−	0.883652i	$-0.655077\pi$
$421$	−19.2110	−0.936288	−0.468144	+	0.883652i	$0.655077\pi$
$422$	−41.3762	−2.01416
$423$	−7.10451	−0.345433
$424$	29.4474	1.43009
$425$	−5.70877	−0.276916
$426$	33.1507	1.60616
$427$	−4.18184	−0.202373
$428$	6.45030	0.311787
$429$	4.16761	0.201214
$430$	25.3583	1.22288
$431$	−5.96194	−0.287177	−0.143588	−	0.989637i	$-0.545864\pi$
$431$	−5.96194	−0.287177	−0.143588	+	0.989637i	$0.545864\pi$
$432$	11.8292	0.569134
$433$	−12.7289	−0.611713	−0.305857	−	0.952078i	$-0.598943\pi$
$433$	−12.7289	−0.611713	−0.305857	+	0.952078i	$0.598943\pi$
$434$	−14.9200	−0.716185
$435$	−6.55800	−0.314432
$436$	−28.8232	−1.38038
$437$	−20.8047	−0.995222
$438$	−44.4876	−2.12570
$439$	35.8163	1.70942	0.854709	−	0.519108i	$-0.173736\pi$
$439$	35.8163	1.70942	0.854709	+	0.519108i	$0.173736\pi$
$440$	−6.78800	−0.323605
$441$	−2.17827	−0.103727
$442$	53.7912	2.55859
$443$	4.99409	0.237276	0.118638	−	0.992938i	$-0.462147\pi$
$443$	4.99409	0.237276	0.118638	+	0.992938i	$0.462147\pi$
$444$	−42.7622	−2.02940
$445$	−4.70003	−0.222803
$446$	25.4600	1.20557
$447$	−10.0966	−0.477555
$448$	20.2502	0.956730
$449$	16.8464	0.795031	0.397515	−	0.917595i	$-0.369873\pi$
$449$	16.8464	0.795031	0.397515	+	0.917595i	$0.369873\pi$
$450$	−1.37381	−0.0647619
$451$	−0.580386	−0.0273293
$452$	−56.7159	−2.66769
$453$	3.99485	0.187695
$454$	−21.7094	−1.01887
$455$	15.4829	0.725849
$456$	26.6236	1.24676
$457$	34.6162	1.61928	0.809639	−	0.586928i	$-0.199663\pi$
$457$	34.6162	1.61928	0.809639	+	0.586928i	$0.199663\pi$
$458$	−1.12527	−0.0525804
$459$	−30.3452	−1.41639
$460$	57.9665	2.70270
$461$	17.6626	0.822630	0.411315	−	0.911493i	$-0.365070\pi$
$461$	17.6626	0.822630	0.411315	+	0.911493i	$0.365070\pi$
$462$	5.95881	0.277229
$463$	19.9329	0.926361	0.463181	−	0.886264i	$-0.346708\pi$
$463$	19.9329	0.926361	0.463181	+	0.886264i	$0.346708\pi$
$464$	−3.76359	−0.174720
$465$	−14.7474	−0.683896
$466$	21.1952	0.981848
$467$	4.76380	0.220442	0.110221	−	0.993907i	$-0.464844\pi$
$467$	4.76380	0.220442	0.110221	+	0.993907i	$0.464844\pi$
$468$	8.45618	0.390887
$469$	22.0310	1.01730
$470$	−60.2615	−2.77966
$471$	0.215153	0.00991375
$472$	30.3330	1.39619
$473$	−2.89241	−0.132993
$474$	−1.63123	−0.0749247
$475$	2.73210	0.125357
$476$	50.2417	2.30283
$477$	−4.74416	−0.217220
$478$	39.1243	1.78951
$479$	26.7735	1.22331	0.611657	−	0.791123i	$-0.290503\pi$
$479$	26.7735	1.22331	0.611657	+	0.791123i	$0.290503\pi$
$480$	9.74018	0.444576
$481$	19.4005	0.884586
$482$	−6.68458	−0.304474
$483$	−23.8753	−1.08636
$484$	−39.7964	−1.80893
$485$	30.2421	1.37323
$486$	−16.7618	−0.760332
$487$	−22.1954	−1.00577	−0.502884	−	0.864354i	$-0.667728\pi$
$487$	−22.1954	−1.00577	−0.502884	+	0.864354i	$0.667728\pi$
$488$	−9.08971	−0.411472
$489$	24.8956	1.12582
$490$	−18.4765	−0.834682
$491$	22.1242	0.998452	0.499226	−	0.866472i	$-0.333618\pi$
$491$	22.1242	0.998452	0.499226	+	0.866472i	$0.333618\pi$
$492$	−6.34246	−0.285940
$493$	9.65464	0.434823
$494$	−25.7433	−1.15825
$495$	1.09359	0.0491531
$496$	−8.46346	−0.380020
$497$	−14.0475	−0.630116
$498$	1.89423	0.0848825
$499$	−40.8792	−1.83000	−0.915001	−	0.403450i	$-0.867811\pi$
$499$	−40.8792	−1.83000	−0.915001	+	0.403450i	$0.867811\pi$
$500$	37.9006	1.69496
$501$	38.6307	1.72589
$502$	−3.51384	−0.156830
$503$	−21.5219	−0.959613	−0.479807	−	0.877374i	$-0.659293\pi$
$503$	−21.5219	−0.959613	−0.479807	+	0.877374i	$0.659293\pi$
$504$	5.67285	0.252689
$505$	−8.90714	−0.396362
$506$	−10.1213	−0.449948
$507$	4.28957	0.190507
$508$	−44.6862	−1.98263
$509$	−13.5703	−0.601494	−0.300747	−	0.953704i	$-0.597236\pi$
$509$	−13.5703	−0.601494	−0.300747	+	0.953704i	$0.597236\pi$
$510$	76.0205	3.36624
$511$	18.8515	0.833939
$512$	28.1867	1.24569
$513$	14.5226	0.641187
$514$	23.8978	1.05409
$515$	22.5864	0.995278
$516$	−31.6083	−1.39148
$517$	6.87355	0.302298
$518$	27.7387	1.21877
$519$	15.5467	0.682426
$520$	33.6539	1.47582
$521$	17.3415	0.759744	0.379872	−	0.925039i	$-0.375968\pi$
$521$	17.3415	0.759744	0.379872	+	0.925039i	$0.375968\pi$
$522$	2.32337	0.101691
$523$	13.1524	0.575115	0.287558	−	0.957763i	$-0.407157\pi$
$523$	13.1524	0.575115	0.287558	+	0.957763i	$0.407157\pi$
$524$	−24.4943	−1.07004
$525$	3.13534	0.136838
$526$	35.9241	1.56636
$527$	21.7111	0.945750
$528$	3.38016	0.147103
$529$	17.5533	0.763188
$530$	−40.2407	−1.74794
$531$	−4.88683	−0.212070
$532$	−24.0446	−1.04247
$533$	2.87747	0.124637
$534$	8.96811	0.388088
$535$	−4.13573	−0.178803
$536$	47.8869	2.06840
$537$	7.50842	0.324012
$538$	12.1172	0.522411
$539$	2.10746	0.0907748
$540$	−40.4631	−1.74126
$541$	34.9176	1.50122	0.750612	−	0.660743i	$-0.229759\pi$
$541$	34.9176	1.50122	0.750612	+	0.660743i	$0.229759\pi$
$542$	−68.0833	−2.92443
$543$	37.3223	1.60165
$544$	−14.3394	−0.614798
$545$	18.4805	0.791619
$546$	−29.5429	−1.26432
$547$	37.3153	1.59549	0.797744	−	0.602996i	$-0.206027\pi$
$547$	37.3153	1.59549	0.797744	+	0.602996i	$0.206027\pi$
$548$	−5.52739	−0.236118
$549$	1.46441	0.0624994
$550$	1.32915	0.0566750
$551$	−4.62051	−0.196840
$552$	−51.8958	−2.20883
$553$	0.691226	0.0293939
$554$	−55.4865	−2.35739
$555$	27.4177	1.16382
$556$	57.3837	2.43361
$557$	−39.1178	−1.65748	−0.828738	−	0.559637i	$-0.810941\pi$
$557$	−39.1178	−1.65748	−0.828738	+	0.559637i	$0.810941\pi$
$558$	5.22474	0.221181
$559$	14.3402	0.606524
$560$	12.5575	0.530651
$561$	−8.67104	−0.366092
$562$	−16.4868	−0.695452
$563$	−41.5306	−1.75031	−0.875153	−	0.483846i	$-0.839240\pi$
$563$	−41.5306	−1.75031	−0.875153	+	0.483846i	$0.839240\pi$
$564$	75.1141	3.16287
$565$	36.3645	1.52986
$566$	−4.32825	−0.181930
$567$	20.6744	0.868241
$568$	−30.5338	−1.28117
$569$	−9.13224	−0.382844	−0.191422	−	0.981508i	$-0.561310\pi$
$569$	−9.13224	−0.382844	−0.191422	+	0.981508i	$0.561310\pi$
$570$	−36.3818	−1.52387
$571$	−7.11507	−0.297756	−0.148878	−	0.988856i	$-0.547566\pi$
$571$	−7.11507	−0.297756	−0.148878	+	0.988856i	$0.547566\pi$
$572$	−8.18128	−0.342077
$573$	13.2411	0.553157
$574$	4.11418	0.171723
$575$	−5.32552	−0.222090
$576$	−7.09125	−0.295469
$577$	−44.1924	−1.83975	−0.919877	−	0.392207i	$-0.871712\pi$
$577$	−44.1924	−1.83975	−0.919877	+	0.392207i	$0.871712\pi$
$578$	−71.0890	−2.95691
$579$	10.6881	0.444181
$580$	12.8738	0.534554
$581$	−0.802674	−0.0333005
$582$	−57.7050	−2.39195
$583$	4.58993	0.190096
$584$	40.9758	1.69559
$585$	−5.42184	−0.224165
$586$	−17.3778	−0.717869
$587$	30.8270	1.27237	0.636183	−	0.771538i	$-0.280512\pi$
$587$	30.8270	1.27237	0.636183	+	0.771538i	$0.280512\pi$
$588$	23.0303	0.949755
$589$	−10.3905	−0.428132
$590$	−41.4508	−1.70650
$591$	21.6786	0.891740
$592$	15.7349	0.646699
$593$	−26.1364	−1.07329	−0.536646	−	0.843807i	$-0.680309\pi$
$593$	−26.1364	−1.07329	−0.536646	+	0.843807i	$0.680309\pi$
$594$	7.06512	0.289885
$595$	−32.2134	−1.32062
$596$	19.8204	0.811874
$597$	44.8749	1.83661
$598$	50.1800	2.05201
$599$	−42.9686	−1.75565	−0.877824	−	0.478983i	$-0.841005\pi$
$599$	−42.9686	−1.75565	−0.877824	+	0.478983i	$0.841005\pi$
$600$	6.81503	0.278222
$601$	−12.3714	−0.504638	−0.252319	−	0.967644i	$-0.581193\pi$
$601$	−12.3714	−0.504638	−0.252319	+	0.967644i	$0.581193\pi$
$602$	20.5034	0.835658
$603$	−7.71486	−0.314173
$604$	−7.84216	−0.319093
$605$	25.5162	1.03738
$606$	16.9957	0.690403
$607$	−17.9270	−0.727635	−0.363817	−	0.931470i	$-0.618527\pi$
$607$	−17.9270	−0.727635	−0.363817	+	0.931470i	$0.618527\pi$
$608$	6.86255	0.278313
$609$	−5.30247	−0.214867
$610$	12.4213	0.502925
$611$	−34.0780	−1.37865
$612$	−17.5938	−0.711186
$613$	−9.50776	−0.384015	−0.192007	−	0.981393i	$-0.561500\pi$
$613$	−9.50776	−0.384015	−0.192007	+	0.981393i	$0.561500\pi$
$614$	−57.9498	−2.33866
$615$	4.06658	0.163981
$616$	−5.48844	−0.221135
$617$	−38.4300	−1.54713	−0.773566	−	0.633715i	$-0.781529\pi$
$617$	−38.4300	−1.54713	−0.773566	+	0.633715i	$0.781529\pi$
$618$	−43.0972	−1.73362
$619$	15.3425	0.616669	0.308334	−	0.951278i	$-0.400228\pi$
$619$	15.3425	0.616669	0.308334	+	0.951278i	$0.400228\pi$
$620$	28.9502	1.16267
$621$	−28.3080	−1.13596
$622$	−5.03424	−0.201855
$623$	−3.80021	−0.152252
$624$	−16.7583	−0.670870
$625$	−28.4820	−1.13928
$626$	−23.8585	−0.953578
$627$	4.14978	0.165726
$628$	−0.422360	−0.0168540
$629$	−40.3642	−1.60943
$630$	−7.75210	−0.308851
$631$	2.60971	0.103891	0.0519455	−	0.998650i	$-0.483458\pi$
$631$	2.60971	0.103891	0.0519455	+	0.998650i	$0.483458\pi$
$632$	1.50246	0.0597646
$633$	−33.0677	−1.31432
$634$	−12.9412	−0.513962
$635$	28.6514	1.13699
$636$	50.1588	1.98892
$637$	−10.4485	−0.413984
$638$	−2.24784	−0.0889930
$639$	4.91918	0.194600
$640$	−49.9998	−1.97642
$641$	25.5763	1.01020	0.505101	−	0.863060i	$-0.331455\pi$
$641$	25.5763	1.01020	0.505101	+	0.863060i	$0.331455\pi$
$642$	7.89138	0.311448
$643$	28.9415	1.14134	0.570671	−	0.821179i	$-0.306683\pi$
$643$	28.9415	1.14134	0.570671	+	0.821179i	$0.306683\pi$
$644$	46.8688	1.84689
$645$	20.2662	0.797982
$646$	53.5610	2.10733
$647$	47.9062	1.88339	0.941694	−	0.336470i	$-0.109233\pi$
$647$	47.9062	1.88339	0.941694	+	0.336470i	$0.109233\pi$
$648$	44.9381	1.76534
$649$	4.72796	0.185589
$650$	−6.58971	−0.258470
$651$	−11.9240	−0.467340
$652$	−48.8717	−1.91396
$653$	23.3821	0.915013	0.457507	−	0.889206i	$-0.348743\pi$
$653$	23.3821	0.915013	0.457507	+	0.889206i	$0.348743\pi$
$654$	−35.2627	−1.37888
$655$	15.7050	0.613644
$656$	2.33379	0.0911191
$657$	−6.60145	−0.257547
$658$	−48.7245	−1.89948
$659$	6.71032	0.261397	0.130699	−	0.991422i	$-0.458278\pi$
$659$	6.71032	0.261397	0.130699	+	0.991422i	$0.458278\pi$
$660$	−11.5622	−0.450058
$661$	9.78504	0.380594	0.190297	−	0.981727i	$-0.439055\pi$
$661$	9.78504	0.380594	0.190297	+	0.981727i	$0.439055\pi$
$662$	−39.7422	−1.54463
$663$	42.9897	1.66958
$664$	−1.74470	−0.0677076
$665$	15.4167	0.597832
$666$	−9.71359	−0.376394
$667$	9.00649	0.348733
$668$	−75.8346	−2.93413
$669$	20.3476	0.786682
$670$	−65.4387	−2.52812
$671$	−1.41680	−0.0546950
$672$	7.87542	0.303801
$673$	−45.2457	−1.74409	−0.872047	−	0.489421i	$-0.837208\pi$
$673$	−45.2457	−1.74409	−0.872047	+	0.489421i	$0.837208\pi$
$674$	−37.3462	−1.43852
$675$	3.71745	0.143085
$676$	−8.42071	−0.323874
$677$	−0.600190	−0.0230672	−0.0115336	−	0.999933i	$-0.503671\pi$
$677$	−0.600190	−0.0230672	−0.0115336	+	0.999933i	$0.503671\pi$
$678$	−69.3870	−2.66479
$679$	24.4523	0.938393
$680$	−70.0196	−2.68513
$681$	−17.3501	−0.664857
$682$	−5.05489	−0.193562
$683$	−16.1530	−0.618079	−0.309039	−	0.951049i	$-0.600007\pi$
$683$	−16.1530	−0.618079	−0.309039	+	0.951049i	$0.600007\pi$
$684$	8.42000	0.321947
$685$	3.54399	0.135409
$686$	−47.7774	−1.82415
$687$	−0.899312	−0.0343109
$688$	11.6307	0.443415
$689$	−22.7562	−0.866942
$690$	70.9169	2.69976
$691$	−45.3242	−1.72421	−0.862106	−	0.506727i	$-0.830855\pi$
$691$	−45.3242	−1.72421	−0.862106	+	0.506727i	$0.830855\pi$
$692$	−30.5193	−1.16017
$693$	0.884220	0.0335887
$694$	−0.569555	−0.0216200
$695$	−36.7926	−1.39562
$696$	−11.5255	−0.436874
$697$	−5.98680	−0.226766
$698$	29.2764	1.10813
$699$	16.9391	0.640696
$700$	−6.15488	−0.232633
$701$	25.1855	0.951243	0.475621	−	0.879650i	$-0.342223\pi$
$701$	25.1855	0.951243	0.475621	+	0.879650i	$0.342223\pi$
$702$	−35.0278	−1.32204
$703$	19.3175	0.728572
$704$	6.86072	0.258573
$705$	−48.1608	−1.81384
$706$	34.9949	1.31705
$707$	−7.20187	−0.270854
$708$	51.6671	1.94177
$709$	−31.2398	−1.17323	−0.586617	−	0.809864i	$-0.699541\pi$
$709$	−31.2398	−1.17323	−0.586617	+	0.809864i	$0.699541\pi$
$710$	41.7253	1.56592
$711$	−0.242055	−0.00907778
$712$	−8.26019	−0.309564
$713$	20.2535	0.758501
$714$	61.4664	2.30032
$715$	5.24558	0.196174
$716$	−14.7395	−0.550842
$717$	31.2680	1.16773
$718$	−47.8043	−1.78404
$719$	35.8470	1.33687	0.668434	−	0.743771i	$-0.266965\pi$
$719$	35.8470	1.33687	0.668434	+	0.743771i	$0.266965\pi$
$720$	−4.39741	−0.163882
$721$	18.2623	0.680123
$722$	19.9980	0.744247
$723$	−5.34229	−0.198682
$724$	−73.2660	−2.72291
$725$	−1.18275	−0.0439261
$726$	−48.6874	−1.80696
$727$	29.3426	1.08826	0.544129	−	0.839002i	$-0.316860\pi$
$727$	29.3426	1.08826	0.544129	+	0.839002i	$0.316860\pi$
$728$	27.2108	1.00850
$729$	18.3566	0.679872
$730$	−55.9945	−2.07245
$731$	−29.8358	−1.10352
$732$	−15.4828	−0.572260
$733$	5.96577	0.220351	0.110175	−	0.993912i	$-0.464859\pi$
$733$	5.96577	0.220351	0.110175	+	0.993912i	$0.464859\pi$
$734$	−25.6625	−0.947221
$735$	−14.7663	−0.544664
$736$	−13.3768	−0.493074
$737$	7.46406	0.274942
$738$	−1.44071	−0.0530334
$739$	14.3069	0.526287	0.263144	−	0.964757i	$-0.415241\pi$
$739$	14.3069	0.526287	0.263144	+	0.964757i	$0.415241\pi$
$740$	−53.8228	−1.97857
$741$	−20.5740	−0.755803
$742$	−32.5366	−1.19446
$743$	3.57676	0.131219	0.0656093	−	0.997845i	$-0.479101\pi$
$743$	3.57676	0.131219	0.0656093	+	0.997845i	$0.479101\pi$
$744$	−25.9183	−0.950210
$745$	−12.7082	−0.465592
$746$	28.4373	1.04116
$747$	0.281082	0.0102843
$748$	17.0218	0.622379
$749$	−3.34394	−0.122185
$750$	46.3680	1.69312
$751$	17.9465	0.654878	0.327439	−	0.944872i	$-0.393814\pi$
$751$	17.9465	0.654878	0.327439	+	0.944872i	$0.393814\pi$
$752$	−27.6392	−1.00790
$753$	−2.80825	−0.102338
$754$	11.1445	0.405858
$755$	5.02814	0.182993
$756$	−32.7165	−1.18989
$757$	17.9786	0.653442	0.326721	−	0.945121i	$-0.394056\pi$
$757$	17.9786	0.653442	0.326721	+	0.945121i	$0.394056\pi$
$758$	4.54953	0.165246
$759$	−8.08892	−0.293609
$760$	33.5099	1.21553
$761$	2.63730	0.0956020	0.0478010	−	0.998857i	$-0.484779\pi$
$761$	2.63730	0.0956020	0.0478010	+	0.998857i	$0.484779\pi$
$762$	−54.6696	−1.98047
$763$	14.9424	0.540952
$764$	−25.9932	−0.940402
$765$	11.2806	0.407850
$766$	−30.9594	−1.11861
$767$	−23.4405	−0.846388
$768$	55.6081	2.00658
$769$	−44.4599	−1.60326	−0.801632	−	0.597817i	$-0.796035\pi$
$769$	−44.4599	−1.60326	−0.801632	+	0.597817i	$0.796035\pi$
$770$	7.50009	0.270285
$771$	19.0990	0.687835
$772$	−20.9814	−0.755136
$773$	27.6340	0.993927	0.496964	−	0.867771i	$-0.334448\pi$
$773$	27.6340	0.993927	0.496964	+	0.867771i	$0.334448\pi$
$774$	−7.17994	−0.258078
$775$	−2.65972	−0.0955401
$776$	53.1499	1.90797
$777$	22.1686	0.795295
$778$	35.5163	1.27332
$779$	2.86516	0.102655
$780$	57.3237	2.05252
$781$	−4.75926	−0.170300
$782$	−104.403	−3.73346
$783$	−6.28692	−0.224676
$784$	−8.47430	−0.302653
$785$	0.270804	0.00966541
$786$	−29.9667	−1.06888
$787$	33.5212	1.19490	0.597451	−	0.801905i	$-0.296180\pi$
$787$	33.5212	1.19490	0.597451	+	0.801905i	$0.296180\pi$
$788$	−42.5566	−1.51602
$789$	28.7104	1.02212
$790$	−2.05315	−0.0730478
$791$	29.4025	1.04543
$792$	1.92195	0.0682937
$793$	7.02428	0.249440
$794$	7.79328	0.276573
$795$	−32.1602	−1.14061
$796$	−88.0924	−3.12235
$797$	13.9337	0.493556	0.246778	−	0.969072i	$-0.420628\pi$
$797$	13.9337	0.493556	0.246778	+	0.969072i	$0.420628\pi$
$798$	−29.4165	−1.04133
$799$	70.9020	2.50833
$800$	1.75666	0.0621072
$801$	1.33077	0.0470203
$802$	−57.7269	−2.03841
$803$	6.38684	0.225387
$804$	81.5672	2.87665
$805$	−30.0508	−1.05915
$806$	25.0614	0.882749
$807$	9.68405	0.340895
$808$	−15.6541	−0.550709
$809$	36.6018	1.28685	0.643425	−	0.765509i	$-0.277513\pi$
$809$	36.6018	1.28685	0.643425	+	0.765509i	$0.277513\pi$
$810$	−61.4091	−2.15770
$811$	−41.5592	−1.45934	−0.729671	−	0.683798i	$-0.760327\pi$
$811$	−41.5592	−1.45934	−0.729671	+	0.683798i	$0.760327\pi$
$812$	10.4091	0.365287
$813$	−54.4119	−1.90831
$814$	9.39781	0.329393
$815$	31.3350	1.09762
$816$	34.8671	1.22059
$817$	14.2788	0.499552
$818$	1.01768	0.0355822
$819$	−4.38383	−0.153183
$820$	−7.98297	−0.278777
$821$	−10.9706	−0.382876	−0.191438	−	0.981505i	$-0.561315\pi$
$821$	−10.9706	−0.382876	−0.191438	+	0.981505i	$0.561315\pi$
$822$	−6.76228	−0.235861
$823$	−28.1758	−0.982146	−0.491073	−	0.871118i	$-0.663395\pi$
$823$	−28.1758	−0.982146	−0.491073	+	0.871118i	$0.663395\pi$
$824$	39.6952	1.38285
$825$	1.06225	0.0369828
$826$	−33.5151	−1.16614
$827$	−53.1178	−1.84709	−0.923544	−	0.383493i	$-0.874721\pi$
$827$	−53.1178	−1.84709	−0.923544	+	0.383493i	$0.874721\pi$
$828$	−16.4126	−0.570378
$829$	−42.9561	−1.49193	−0.745964	−	0.665986i	$-0.768011\pi$
$829$	−42.9561	−1.49193	−0.745964	+	0.665986i	$0.768011\pi$
$830$	2.38418	0.0827562
$831$	−44.3446	−1.53830
$832$	−34.0144	−1.17924
$833$	21.7389	0.753208
$834$	70.2039	2.43096
$835$	48.6227	1.68266
$836$	−8.14628	−0.281745
$837$	−14.1378	−0.488675
$838$	24.8533	0.858542
$839$	33.6731	1.16252	0.581262	−	0.813717i	$-0.302559\pi$
$839$	33.6731	1.16252	0.581262	+	0.813717i	$0.302559\pi$
$840$	38.4558	1.32685
$841$	−26.9997	−0.931026
$842$	46.1379	1.59002
$843$	−13.1762	−0.453811
$844$	64.9141	2.23443
$845$	5.39910	0.185735
$846$	17.0625	0.586619
$847$	20.6311	0.708894
$848$	−18.4565	−0.633800
$849$	−3.45912	−0.118717
$850$	13.7104	0.470263
$851$	−37.6544	−1.29078
$852$	−52.0092	−1.78181
$853$	17.2295	0.589928	0.294964	−	0.955508i	$-0.404692\pi$
$853$	17.2295	0.589928	0.294964	+	0.955508i	$0.404692\pi$
$854$	10.0433	0.343674
$855$	−5.39864	−0.184630
$856$	−7.26845	−0.248430
$857$	22.5237	0.769394	0.384697	−	0.923043i	$-0.374306\pi$
$857$	22.5237	0.769394	0.384697	+	0.923043i	$0.374306\pi$
$858$	−10.0091	−0.341705
$859$	−35.6082	−1.21494	−0.607468	−	0.794344i	$-0.707815\pi$
$859$	−35.6082	−1.21494	−0.607468	+	0.794344i	$0.707815\pi$
$860$	−39.7839	−1.35662
$861$	3.28804	0.112056
$862$	14.3184	0.487688
$863$	−53.5774	−1.82379	−0.911897	−	0.410418i	$-0.865383\pi$
$863$	−53.5774	−1.82379	−0.911897	+	0.410418i	$0.865383\pi$
$864$	9.33757	0.317670
$865$	19.5680	0.665332
$866$	30.5703	1.03882
$867$	−56.8141	−1.92951
$868$	23.4077	0.794508
$869$	0.234186	0.00794423
$870$	15.7499	0.533973
$871$	−37.0057	−1.25389
$872$	32.4791	1.09988
$873$	−8.56276	−0.289806
$874$	49.9653	1.69010
$875$	−19.6483	−0.664233
$876$	69.7954	2.35817
$877$	0.600351	0.0202724	0.0101362	−	0.999949i	$-0.496773\pi$
$877$	0.600351	0.0202724	0.0101362	+	0.999949i	$0.496773\pi$
$878$	−86.0177	−2.90296
$879$	−13.8883	−0.468439
$880$	4.25446	0.143418
$881$	−19.2905	−0.649915	−0.324958	−	0.945729i	$-0.605350\pi$
$881$	−19.2905	−0.649915	−0.324958	+	0.945729i	$0.605350\pi$
$882$	5.23143	0.176151
$883$	9.00751	0.303127	0.151563	−	0.988448i	$-0.451569\pi$
$883$	9.00751	0.303127	0.151563	+	0.988448i	$0.451569\pi$
$884$	−84.3916	−2.83840
$885$	−33.1273	−1.11356
$886$	−11.9940	−0.402946
$887$	−2.58077	−0.0866539	−0.0433269	−	0.999061i	$-0.513796\pi$
$887$	−2.58077	−0.0866539	−0.0433269	+	0.999061i	$0.513796\pi$
$888$	48.1861	1.61702
$889$	23.1661	0.776965
$890$	11.2878	0.378367
$891$	7.00444	0.234658
$892$	−39.9436	−1.33741
$893$	−33.9322	−1.13550
$894$	24.2485	0.810991
$895$	9.45051	0.315896
$896$	−40.4273	−1.35058
$897$	40.1036	1.33902
$898$	−40.4590	−1.35013
$899$	4.49811	0.150020
$900$	2.15533	0.0718443
$901$	47.3461	1.57733
$902$	1.39388	0.0464111
$903$	16.3863	0.545301
$904$	63.9097	2.12561
$905$	46.9759	1.56153
$906$	−9.59419	−0.318746
$907$	6.34947	0.210831	0.105415	−	0.994428i	$-0.466383\pi$
$907$	6.34947	0.210831	0.105415	+	0.994428i	$0.466383\pi$
$908$	34.0594	1.13030
$909$	2.52197	0.0836484
$910$	−37.1843	−1.23265
$911$	52.1970	1.72936	0.864682	−	0.502319i	$-0.167520\pi$
$911$	52.1970	1.72936	0.864682	+	0.502319i	$0.167520\pi$
$912$	−16.6866	−0.552550
$913$	−0.271945	−0.00900005
$914$	−83.1356	−2.74988
$915$	9.92708	0.328179
$916$	1.76541	0.0583307
$917$	12.6983	0.419334
$918$	72.8782	2.40534
$919$	24.2446	0.799755	0.399877	−	0.916569i	$-0.369053\pi$
$919$	24.2446	0.799755	0.399877	+	0.916569i	$0.369053\pi$
$920$	−65.3189	−2.15350
$921$	−46.3133	−1.52607
$922$	−42.4192	−1.39700
$923$	23.5957	0.776662
$924$	−9.34863	−0.307547
$925$	4.94484	0.162585
$926$	−47.8717	−1.57316
$927$	−6.39513	−0.210044
$928$	−2.97085	−0.0975228
$929$	9.67059	0.317282	0.158641	−	0.987336i	$-0.449289\pi$
$929$	9.67059	0.317282	0.158641	+	0.987336i	$0.449289\pi$
$930$	35.4180	1.16140
$931$	−10.4038	−0.340970
$932$	−33.2526	−1.08922
$933$	−4.02334	−0.131718
$934$	−11.4409	−0.374359
$935$	−10.9139	−0.356921
$936$	−9.52876	−0.311457
$937$	−34.0517	−1.11242	−0.556210	−	0.831042i	$-0.687745\pi$
$937$	−34.0517	−1.11242	−0.556210	+	0.831042i	$0.687745\pi$
$938$	−52.9104	−1.72759
$939$	−19.0676	−0.622249
$940$	94.5428	3.08364
$941$	5.38602	0.175579	0.0877896	−	0.996139i	$-0.472020\pi$
$941$	5.38602	0.175579	0.0877896	+	0.996139i	$0.472020\pi$
$942$	−0.516721	−0.0168357
$943$	−5.58488	−0.181869
$944$	−19.0116	−0.618774
$945$	20.9768	0.682374
$946$	6.94653	0.225851
$947$	51.0898	1.66020	0.830098	−	0.557617i	$-0.188284\pi$
$947$	51.0898	1.66020	0.830098	+	0.557617i	$0.188284\pi$
$948$	2.55919	0.0831185
$949$	−31.6650	−1.02789
$950$	−6.56151	−0.212884
$951$	−10.3426	−0.335381
$952$	−56.6143	−1.83488
$953$	1.43687	0.0465448	0.0232724	−	0.999729i	$-0.492591\pi$
$953$	1.43687	0.0465448	0.0232724	+	0.999729i	$0.492591\pi$
$954$	11.3938	0.368886
$955$	16.6660	0.539301
$956$	−61.3811	−1.98521
$957$	−1.79647	−0.0580716
$958$	−64.3004	−2.07745
$959$	2.86549	0.0925315
$960$	−48.0709	−1.55148
$961$	−20.8848	−0.673703
$962$	−46.5929	−1.50222
$963$	1.17099	0.0377346
$964$	10.4873	0.337772
$965$	13.4526	0.433054
$966$	57.3399	1.84488
$967$	−22.1536	−0.712411	−0.356205	−	0.934408i	$-0.615930\pi$
$967$	−22.1536	−0.712411	−0.356205	+	0.934408i	$0.615930\pi$
$968$	44.8441	1.44134
$969$	42.8058	1.37512
$970$	−72.6307	−2.33203
$971$	0.788995	0.0253201	0.0126600	−	0.999920i	$-0.495970\pi$
$971$	0.788995	0.0253201	0.0126600	+	0.999920i	$0.495970\pi$
$972$	26.2972	0.843482
$973$	−29.7487	−0.953698
$974$	53.3052	1.70801
$975$	−5.26647	−0.168662
$976$	5.69709	0.182359
$977$	−42.9843	−1.37519	−0.687594	−	0.726095i	$-0.741333\pi$
$977$	−42.9843	−1.37519	−0.687594	+	0.726095i	$0.741333\pi$
$978$	−59.7903	−1.91188
$979$	−1.28750	−0.0411488
$980$	28.9872	0.925964
$981$	−5.23258	−0.167063
$982$	−53.1344	−1.69559
$983$	32.5447	1.03801	0.519007	−	0.854770i	$-0.326302\pi$
$983$	32.5447	1.03801	0.519007	+	0.854770i	$0.326302\pi$
$984$	7.14693	0.227836
$985$	27.2859	0.869402
$986$	−23.1870	−0.738423
$987$	−38.9404	−1.23949
$988$	40.3880	1.28491
$989$	−27.8328	−0.885033
$990$	−2.62640	−0.0834725
$991$	−28.1564	−0.894418	−0.447209	−	0.894430i	$-0.647582\pi$
$991$	−28.1564	−0.894418	−0.447209	+	0.894430i	$0.647582\pi$
$992$	−6.68075	−0.212114
$993$	−31.7619	−1.00793
$994$	33.7370	1.07007
$995$	56.4821	1.79060
$996$	−2.97181	−0.0941654
$997$	−1.49681	−0.0474044	−0.0237022	−	0.999719i	$-0.507545\pi$
$997$	−1.49681	−0.0474044	−0.0237022	+	0.999719i	$0.507545\pi$
$998$	98.1770	3.10774
$999$	26.2844	0.831603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.18	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +O(q^{10})\)	\(q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +5.80197 q^{10} -0.661784 q^{11} -7.23197 q^{12} +3.28103 q^{13} +4.69118 q^{14} +4.63691 q^{15} +2.66109 q^{16} -6.82644 q^{17} -1.64277 q^{18} +3.26699 q^{19} -9.10256 q^{20} +3.74918 q^{21} +1.58937 q^{22} -6.36815 q^{23} +8.14927 q^{24} +0.836275 q^{25} -7.87984 q^{26} +4.44525 q^{27} -7.35988 q^{28} -1.41430 q^{29} -11.1362 q^{30} -3.18044 q^{31} +2.10057 q^{32} +1.27022 q^{33} +16.3946 q^{34} +4.71892 q^{35} +2.57730 q^{36} +5.91293 q^{37} -7.84612 q^{38} -6.29753 q^{39} +10.2571 q^{40} +0.877003 q^{41} -9.00417 q^{42} +4.37063 q^{43} -2.49351 q^{44} -1.65248 q^{45} +15.2940 q^{46} -10.3864 q^{47} -5.10765 q^{48} -3.18452 q^{49} -2.00843 q^{50} +13.1025 q^{51} +12.3625 q^{52} -6.93570 q^{53} -10.6759 q^{54} +1.59876 q^{55} +8.29340 q^{56} -6.27059 q^{57} +3.39664 q^{58} -7.14427 q^{59} +17.4713 q^{60} +2.14088 q^{61} +7.63827 q^{62} -1.33612 q^{63} -10.3670 q^{64} -7.92643 q^{65} -3.05060 q^{66} -11.2787 q^{67} -25.7211 q^{68} +12.2229 q^{69} -11.3331 q^{70} +7.19157 q^{71} -2.90420 q^{72} -9.65095 q^{73} -14.2007 q^{74} -1.60513 q^{75} +12.3096 q^{76} +1.29268 q^{77} +15.1244 q^{78} -0.353871 q^{79} -6.42877 q^{80} -10.5842 q^{81} -2.10624 q^{82} +0.410926 q^{83} +14.1264 q^{84} +16.4916 q^{85} -10.4967 q^{86} +2.71458 q^{87} +2.80979 q^{88} +1.94551 q^{89} +3.96867 q^{90} -6.40891 q^{91} -23.9943 q^{92} +6.10448 q^{93} +24.9444 q^{94} -7.89251 q^{95} -4.03180 q^{96} -12.5183 q^{97} +7.64806 q^{98} -0.452674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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