LMFDB - Embedded newform 4001.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.43211 q^{2} +0.645473 q^{3} +3.91518 q^{4} -1.15456 q^{5} -1.56986 q^{6} +1.52754 q^{7} -4.65795 q^{8} -2.58336 q^{9} +O(q^{10})$	\(q-2.43211 q^{2} +0.645473 q^{3} +3.91518 q^{4} -1.15456 q^{5} -1.56986 q^{6} +1.52754 q^{7} -4.65795 q^{8} -2.58336 q^{9} +2.80801 q^{10} -3.11685 q^{11} +2.52715 q^{12} +4.55740 q^{13} -3.71516 q^{14} -0.745234 q^{15} +3.49829 q^{16} -2.58969 q^{17} +6.28304 q^{18} -7.28248 q^{19} -4.52030 q^{20} +0.985988 q^{21} +7.58053 q^{22} -6.08960 q^{23} -3.00658 q^{24} -3.66700 q^{25} -11.0841 q^{26} -3.60391 q^{27} +5.98061 q^{28} -10.5062 q^{29} +1.81250 q^{30} +7.22937 q^{31} +0.807642 q^{32} -2.01184 q^{33} +6.29842 q^{34} -1.76363 q^{35} -10.1143 q^{36} +10.7652 q^{37} +17.7118 q^{38} +2.94168 q^{39} +5.37786 q^{40} +5.88882 q^{41} -2.39804 q^{42} -4.57214 q^{43} -12.2030 q^{44} +2.98264 q^{45} +14.8106 q^{46} +10.7979 q^{47} +2.25805 q^{48} -4.66661 q^{49} +8.91857 q^{50} -1.67157 q^{51} +17.8431 q^{52} -2.00845 q^{53} +8.76513 q^{54} +3.59857 q^{55} -7.11521 q^{56} -4.70065 q^{57} +25.5523 q^{58} -5.67677 q^{59} -2.91773 q^{60} -3.17694 q^{61} -17.5827 q^{62} -3.94620 q^{63} -8.96086 q^{64} -5.26177 q^{65} +4.89303 q^{66} -1.68173 q^{67} -10.1391 q^{68} -3.93067 q^{69} +4.28936 q^{70} -13.0240 q^{71} +12.0332 q^{72} +14.1461 q^{73} -26.1821 q^{74} -2.36695 q^{75} -28.5123 q^{76} -4.76112 q^{77} -7.15450 q^{78} +15.4580 q^{79} -4.03897 q^{80} +5.42387 q^{81} -14.3223 q^{82} +11.0513 q^{83} +3.86032 q^{84} +2.98994 q^{85} +11.1200 q^{86} -6.78148 q^{87} +14.5181 q^{88} +15.1818 q^{89} -7.25412 q^{90} +6.96162 q^{91} -23.8419 q^{92} +4.66637 q^{93} -26.2617 q^{94} +8.40803 q^{95} +0.521311 q^{96} +1.72861 q^{97} +11.3497 q^{98} +8.05195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.43211	−1.71976	−0.859882	−	0.510492i	$-0.829463\pi$
$2$	−2.43211	−1.71976	−0.859882	+	0.510492i	$0.829463\pi$
$3$	0.645473	0.372664	0.186332	−	0.982487i	$-0.440340\pi$
$3$	0.645473	0.372664	0.186332	+	0.982487i	$0.440340\pi$
$4$	3.91518	1.95759
$5$	−1.15456	−0.516333	−0.258166	−	0.966100i	$-0.583118\pi$
$5$	−1.15456	−0.516333	−0.258166	+	0.966100i	$0.583118\pi$
$6$	−1.56986	−0.640895
$7$	1.52754	0.577357	0.288679	−	0.957426i	$-0.406784\pi$
$7$	1.52754	0.577357	0.288679	+	0.957426i	$0.406784\pi$
$8$	−4.65795	−1.64683
$9$	−2.58336	−0.861121
$10$	2.80801	0.887971
$11$	−3.11685	−0.939764	−0.469882	−	0.882729i	$-0.655704\pi$
$11$	−3.11685	−0.939764	−0.469882	+	0.882729i	$0.655704\pi$
$12$	2.52715	0.729524
$13$	4.55740	1.26400	0.631998	−	0.774970i	$-0.282235\pi$
$13$	4.55740	1.26400	0.631998	+	0.774970i	$0.282235\pi$
$14$	−3.71516	−0.992918
$15$	−0.745234	−0.192419
$16$	3.49829	0.874573
$17$	−2.58969	−0.628092	−0.314046	−	0.949408i	$-0.601685\pi$
$17$	−2.58969	−0.628092	−0.314046	+	0.949408i	$0.601685\pi$
$18$	6.28304	1.48093
$19$	−7.28248	−1.67072	−0.835358	−	0.549706i	$-0.814740\pi$
$19$	−7.28248	−1.67072	−0.835358	+	0.549706i	$0.814740\pi$
$20$	−4.52030	−1.01077
$21$	0.985988	0.215160
$22$	7.58053	1.61617
$23$	−6.08960	−1.26977	−0.634885	−	0.772607i	$-0.718952\pi$
$23$	−6.08960	−1.26977	−0.634885	+	0.772607i	$0.718952\pi$
$24$	−3.00658	−0.613715
$25$	−3.66700	−0.733400
$26$	−11.0841	−2.17377
$27$	−3.60391	−0.693573
$28$	5.98061	1.13023
$29$	−10.5062	−1.95096	−0.975478	−	0.220097i	$-0.929362\pi$
$29$	−10.5062	−1.95096	−0.975478	+	0.220097i	$0.929362\pi$
$30$	1.81250	0.330915
$31$	7.22937	1.29843	0.649217	−	0.760603i	$-0.275097\pi$
$31$	7.22937	1.29843	0.649217	+	0.760603i	$0.275097\pi$
$32$	0.807642	0.142772
$33$	−2.01184	−0.350216
$34$	6.29842	1.08017
$35$	−1.76363	−0.298108
$36$	−10.1143	−1.68572
$37$	10.7652	1.76978	0.884890	−	0.465800i	$-0.154233\pi$
$37$	10.7652	1.76978	0.884890	+	0.465800i	$0.154233\pi$
$38$	17.7118	2.87324
$39$	2.94168	0.471046
$40$	5.37786	0.850314
$41$	5.88882	0.919679	0.459839	−	0.888002i	$-0.347907\pi$
$41$	5.88882	0.919679	0.459839	+	0.888002i	$0.347907\pi$
$42$	−2.39804	−0.370025
$43$	−4.57214	−0.697245	−0.348622	−	0.937263i	$-0.613350\pi$
$43$	−4.57214	−0.697245	−0.348622	+	0.937263i	$0.613350\pi$
$44$	−12.2030	−1.83967
$45$	2.98264	0.444625
$46$	14.8106	2.18371
$47$	10.7979	1.57503	0.787516	−	0.616294i	$-0.211367\pi$
$47$	10.7979	1.57503	0.787516	+	0.616294i	$0.211367\pi$
$48$	2.25805	0.325922
$49$	−4.66661	−0.666659
$50$	8.91857	1.26128
$51$	−1.67157	−0.234067
$52$	17.8431	2.47439
$53$	−2.00845	−0.275882	−0.137941	−	0.990440i	$-0.544048\pi$
$53$	−2.00845	−0.275882	−0.137941	+	0.990440i	$0.544048\pi$
$54$	8.76513	1.19278
$55$	3.59857	0.485231
$56$	−7.11521	−0.950810
$57$	−4.70065	−0.622616
$58$	25.5523	3.35519
$59$	−5.67677	−0.739053	−0.369526	−	0.929220i	$-0.620480\pi$
$59$	−5.67677	−0.739053	−0.369526	+	0.929220i	$0.620480\pi$
$60$	−2.91773	−0.376677
$61$	−3.17694	−0.406766	−0.203383	−	0.979099i	$-0.565194\pi$
$61$	−3.17694	−0.406766	−0.203383	+	0.979099i	$0.565194\pi$
$62$	−17.5827	−2.23300
$63$	−3.94620	−0.497175
$64$	−8.96086	−1.12011
$65$	−5.26177	−0.652642
$66$	4.89303	0.602290
$67$	−1.68173	−0.205456	−0.102728	−	0.994709i	$-0.532757\pi$
$67$	−1.68173	−0.205456	−0.102728	+	0.994709i	$0.532757\pi$
$68$	−10.1391	−1.22955
$69$	−3.93067	−0.473198
$70$	4.28936	0.512676
$71$	−13.0240	−1.54566	−0.772830	−	0.634613i	$-0.781159\pi$
$71$	−13.0240	−1.54566	−0.772830	+	0.634613i	$0.781159\pi$
$72$	12.0332	1.41812
$73$	14.1461	1.65567	0.827836	−	0.560969i	$-0.189572\pi$
$73$	14.1461	1.65567	0.827836	+	0.560969i	$0.189572\pi$
$74$	−26.1821	−3.04361
$75$	−2.36695	−0.273312
$76$	−28.5123	−3.27058
$77$	−4.76112	−0.542580
$78$	−7.15450	−0.810088
$79$	15.4580	1.73916	0.869579	−	0.493793i	$-0.164390\pi$
$79$	15.4580	1.73916	0.869579	+	0.493793i	$0.164390\pi$
$80$	−4.03897	−0.451571
$81$	5.42387	0.602652
$82$	−14.3223	−1.58163
$83$	11.0513	1.21304	0.606520	−	0.795068i	$-0.292565\pi$
$83$	11.0513	1.21304	0.606520	+	0.795068i	$0.292565\pi$
$84$	3.86032	0.421196
$85$	2.98994	0.324305
$86$	11.1200	1.19910
$87$	−6.78148	−0.727051
$88$	14.5181	1.54763
$89$	15.1818	1.60927	0.804634	−	0.593771i	$-0.202362\pi$
$89$	15.1818	1.60927	0.804634	+	0.593771i	$0.202362\pi$
$90$	−7.25412	−0.764651
$91$	6.96162	0.729776
$92$	−23.8419	−2.48569
$93$	4.66637	0.483880
$94$	−26.2617	−2.70869
$95$	8.40803	0.862646
$96$	0.521311	0.0532061
$97$	1.72861	0.175513	0.0877567	−	0.996142i	$-0.472030\pi$
$97$	1.72861	0.175513	0.0877567	+	0.996142i	$0.472030\pi$
$98$	11.3497	1.14650
$99$	8.05195	0.809251
$100$	−14.3570	−1.43570
$101$	−7.28648	−0.725031	−0.362516	−	0.931978i	$-0.618082\pi$
$101$	−7.28648	−0.725031	−0.362516	+	0.931978i	$0.618082\pi$
$102$	4.06546	0.402541
$103$	10.3976	1.02451	0.512255	−	0.858833i	$-0.328810\pi$
$103$	10.3976	1.02451	0.512255	+	0.858833i	$0.328810\pi$
$104$	−21.2281	−2.08159
$105$	−1.13838	−0.111094
$106$	4.88478	0.474452
$107$	17.3744	1.67965	0.839825	−	0.542857i	$-0.182657\pi$
$107$	17.3744	1.67965	0.839825	+	0.542857i	$0.182657\pi$
$108$	−14.1100	−1.35773
$109$	−13.3440	−1.27812	−0.639062	−	0.769155i	$-0.720677\pi$
$109$	−13.3440	−1.27812	−0.639062	+	0.769155i	$0.720677\pi$
$110$	−8.75214	−0.834484
$111$	6.94862	0.659534
$112$	5.34379	0.504941
$113$	8.23117	0.774323	0.387162	−	0.922012i	$-0.373456\pi$
$113$	8.23117	0.774323	0.387162	+	0.922012i	$0.373456\pi$
$114$	11.4325	1.07075
$115$	7.03078	0.655624
$116$	−41.1338	−3.81917
$117$	−11.7734	−1.08845
$118$	13.8066	1.27100
$119$	−3.95586	−0.362633
$120$	3.47126	0.316881
$121$	−1.28527	−0.116843
$122$	7.72669	0.699541
$123$	3.80107	0.342731
$124$	28.3043	2.54180
$125$	10.0065	0.895012
$126$	9.59761	0.855023
$127$	10.7225	0.951467	0.475733	−	0.879590i	$-0.342183\pi$
$127$	10.7225	0.951467	0.475733	+	0.879590i	$0.342183\pi$
$128$	20.1786	1.78355
$129$	−2.95119	−0.259838
$130$	12.7972	1.12239
$131$	14.2495	1.24499	0.622494	−	0.782624i	$-0.286119\pi$
$131$	14.2495	1.24499	0.622494	+	0.782624i	$0.286119\pi$
$132$	−7.87672	−0.685581
$133$	−11.1243	−0.964600
$134$	4.09016	0.353336
$135$	4.16092	0.358115
$136$	12.0626	1.03436
$137$	5.55305	0.474429	0.237215	−	0.971457i	$-0.423766\pi$
$137$	5.55305	0.474429	0.237215	+	0.971457i	$0.423766\pi$
$138$	9.55985	0.813789
$139$	−14.4613	−1.22659	−0.613295	−	0.789854i	$-0.710156\pi$
$139$	−14.4613	−1.22659	−0.613295	+	0.789854i	$0.710156\pi$
$140$	−6.90495	−0.583575
$141$	6.96974	0.586958
$142$	31.6758	2.65817
$143$	−14.2047	−1.18786
$144$	−9.03736	−0.753114
$145$	12.1300	1.00734
$146$	−34.4049	−2.84737
$147$	−3.01217	−0.248440
$148$	42.1476	3.46451
$149$	15.3515	1.25765	0.628824	−	0.777548i	$-0.283537\pi$
$149$	15.3515	1.25765	0.628824	+	0.777548i	$0.283537\pi$
$150$	5.75670	0.470032
$151$	−7.56074	−0.615284	−0.307642	−	0.951502i	$-0.599540\pi$
$151$	−7.56074	−0.615284	−0.307642	+	0.951502i	$0.599540\pi$
$152$	33.9214	2.75139
$153$	6.69011	0.540863
$154$	11.5796	0.933109
$155$	−8.34671	−0.670424
$156$	11.5172	0.922115
$157$	−7.90927	−0.631228	−0.315614	−	0.948888i	$-0.602211\pi$
$157$	−7.90927	−0.631228	−0.315614	+	0.948888i	$0.602211\pi$
$158$	−37.5956	−2.99094
$159$	−1.29640	−0.102811
$160$	−0.932467	−0.0737180
$161$	−9.30213	−0.733110
$162$	−13.1915	−1.03642
$163$	1.26126	0.0987894	0.0493947	−	0.998779i	$-0.484271\pi$
$163$	1.26126	0.0987894	0.0493947	+	0.998779i	$0.484271\pi$
$164$	23.0558	1.80036
$165$	2.32278	0.180828
$166$	−26.8781	−2.08614
$167$	−19.5673	−1.51416	−0.757081	−	0.653321i	$-0.773375\pi$
$167$	−19.5673	−1.51416	−0.757081	+	0.653321i	$0.773375\pi$
$168$	−4.59268	−0.354333
$169$	7.76989	0.597684
$170$	−7.27188	−0.557728
$171$	18.8133	1.43869
$172$	−17.9008	−1.36492
$173$	−9.55639	−0.726559	−0.363280	−	0.931680i	$-0.618343\pi$
$173$	−9.55639	−0.726559	−0.363280	+	0.931680i	$0.618343\pi$
$174$	16.4933	1.25036
$175$	−5.60150	−0.423434
$176$	−10.9036	−0.821893
$177$	−3.66420	−0.275418
$178$	−36.9239	−2.76756
$179$	−17.9694	−1.34309	−0.671547	−	0.740962i	$-0.734370\pi$
$179$	−17.9694	−1.34309	−0.671547	+	0.740962i	$0.734370\pi$
$180$	11.6776	0.870395
$181$	17.0818	1.26968	0.634840	−	0.772644i	$-0.281066\pi$
$181$	17.0818	1.26968	0.634840	+	0.772644i	$0.281066\pi$
$182$	−16.9315	−1.25504
$183$	−2.05063	−0.151587
$184$	28.3650	2.09110
$185$	−12.4290	−0.913796
$186$	−11.3491	−0.832159
$187$	8.07166	0.590258
$188$	42.2757	3.08327
$189$	−5.50513	−0.400439
$190$	−20.4493	−1.48355
$191$	18.1692	1.31468	0.657338	−	0.753596i	$-0.271682\pi$
$191$	18.1692	1.31468	0.657338	+	0.753596i	$0.271682\pi$
$192$	−5.78400	−0.417424
$193$	−15.3613	−1.10573	−0.552866	−	0.833270i	$-0.686466\pi$
$193$	−15.3613	−1.10573	−0.552866	+	0.833270i	$0.686466\pi$
$194$	−4.20417	−0.301842
$195$	−3.39633	−0.243216
$196$	−18.2706	−1.30505
$197$	−23.1797	−1.65149	−0.825743	−	0.564047i	$-0.809244\pi$
$197$	−23.1797	−1.65149	−0.825743	+	0.564047i	$0.809244\pi$
$198$	−19.5833	−1.39172
$199$	0.480964	0.0340947	0.0170473	−	0.999855i	$-0.494573\pi$
$199$	0.480964	0.0340947	0.0170473	+	0.999855i	$0.494573\pi$
$200$	17.0807	1.20779
$201$	−1.08551	−0.0765661
$202$	17.7215	1.24688
$203$	−16.0487	−1.12640
$204$	−6.54452	−0.458208
$205$	−6.79897	−0.474860
$206$	−25.2883	−1.76192
$207$	15.7317	1.09343
$208$	15.9431	1.10546
$209$	22.6984	1.57008
$210$	2.76867	0.191056
$211$	17.8074	1.22591	0.612957	−	0.790116i	$-0.289980\pi$
$211$	17.8074	1.22591	0.612957	+	0.790116i	$0.289980\pi$
$212$	−7.86345	−0.540064
$213$	−8.40661	−0.576012
$214$	−42.2566	−2.88860
$215$	5.27879	0.360010
$216$	16.7868	1.14220
$217$	11.0432	0.749660
$218$	32.4542	2.19807
$219$	9.13091	0.617010
$220$	14.0891	0.949885
$221$	−11.8022	−0.793905
$222$	−16.8998	−1.13424
$223$	16.8863	1.13079	0.565397	−	0.824819i	$-0.308723\pi$
$223$	16.8863	1.13079	0.565397	+	0.824819i	$0.308723\pi$
$224$	1.23371	0.0824306
$225$	9.47320	0.631547
$226$	−20.0192	−1.33165
$227$	−0.761850	−0.0505657	−0.0252829	−	0.999680i	$-0.508049\pi$
$227$	−0.761850	−0.0505657	−0.0252829	+	0.999680i	$0.508049\pi$
$228$	−18.4039	−1.21883
$229$	−16.2642	−1.07477	−0.537383	−	0.843338i	$-0.680587\pi$
$229$	−16.2642	−1.07477	−0.537383	+	0.843338i	$0.680587\pi$
$230$	−17.0997	−1.12752
$231$	−3.07317	−0.202200
$232$	48.9374	3.21290
$233$	−16.2417	−1.06403	−0.532016	−	0.846734i	$-0.678565\pi$
$233$	−16.2417	−1.06403	−0.532016	+	0.846734i	$0.678565\pi$
$234$	28.6343	1.87188
$235$	−12.4667	−0.813241
$236$	−22.2256	−1.44676
$237$	9.97771	0.648122
$238$	9.62111	0.623644
$239$	22.3547	1.44601	0.723003	−	0.690845i	$-0.242761\pi$
$239$	22.3547	1.44601	0.723003	+	0.690845i	$0.242761\pi$
$240$	−2.60705	−0.168284
$241$	8.80312	0.567059	0.283529	−	0.958964i	$-0.408495\pi$
$241$	8.80312	0.567059	0.283529	+	0.958964i	$0.408495\pi$
$242$	3.12592	0.200942
$243$	14.3127	0.918160
$244$	−12.4383	−0.796281
$245$	5.38786	0.344218
$246$	−9.24465	−0.589417
$247$	−33.1892	−2.11178
$248$	−33.6740	−2.13830
$249$	7.13333	0.452057
$250$	−24.3370	−1.53921
$251$	−9.80716	−0.619022	−0.309511	−	0.950896i	$-0.600165\pi$
$251$	−9.80716	−0.619022	−0.309511	+	0.950896i	$0.600165\pi$
$252$	−15.4501	−0.973265
$253$	18.9804	1.19328
$254$	−26.0783	−1.63630
$255$	1.92993	0.120857
$256$	−31.1549	−1.94718
$257$	10.5111	0.655666	0.327833	−	0.944736i	$-0.393682\pi$
$257$	10.5111	0.655666	0.327833	+	0.944736i	$0.393682\pi$
$258$	7.17764	0.446860
$259$	16.4442	1.02180
$260$	−20.6008	−1.27761
$261$	27.1414	1.68001
$262$	−34.6565	−2.14109
$263$	18.1048	1.11639	0.558194	−	0.829710i	$-0.311494\pi$
$263$	18.1048	1.11639	0.558194	+	0.829710i	$0.311494\pi$
$264$	9.37104	0.576748
$265$	2.31887	0.142447
$266$	27.0556	1.65889
$267$	9.79945	0.599716
$268$	−6.58428	−0.402199
$269$	−27.4809	−1.67554	−0.837769	−	0.546025i	$-0.816141\pi$
$269$	−27.4809	−1.67554	−0.837769	+	0.546025i	$0.816141\pi$
$270$	−10.1198	−0.615873
$271$	1.10081	0.0668695	0.0334348	−	0.999441i	$-0.489355\pi$
$271$	1.10081	0.0668695	0.0334348	+	0.999441i	$0.489355\pi$
$272$	−9.05949	−0.549312
$273$	4.49354	0.271961
$274$	−13.5057	−0.815907
$275$	11.4295	0.689224
$276$	−15.3893	−0.926327
$277$	12.0008	0.721059	0.360529	−	0.932748i	$-0.382596\pi$
$277$	12.0008	0.721059	0.360529	+	0.932748i	$0.382596\pi$
$278$	35.1715	2.10945
$279$	−18.6761	−1.11811
$280$	8.21491	0.490935
$281$	−0.656951	−0.0391904	−0.0195952	−	0.999808i	$-0.506238\pi$
$281$	−0.656951	−0.0391904	−0.0195952	+	0.999808i	$0.506238\pi$
$282$	−16.9512	−1.00943
$283$	−11.2492	−0.668698	−0.334349	−	0.942449i	$-0.608516\pi$
$283$	−11.2492	−0.668698	−0.334349	+	0.942449i	$0.608516\pi$
$284$	−50.9912	−3.02577
$285$	5.42716	0.321477
$286$	34.5475	2.04284
$287$	8.99542	0.530983
$288$	−2.08643	−0.122944
$289$	−10.2935	−0.605501
$290$	−29.5016	−1.73239
$291$	1.11577	0.0654075
$292$	55.3845	3.24113
$293$	0.841654	0.0491700	0.0245850	−	0.999698i	$-0.492174\pi$
$293$	0.841654	0.0491700	0.0245850	+	0.999698i	$0.492174\pi$
$294$	7.32595	0.427258
$295$	6.55415	0.381597
$296$	−50.1435	−2.91453
$297$	11.2328	0.651795
$298$	−37.3367	−2.16286
$299$	−27.7527	−1.60498
$300$	−9.26705	−0.535033
$301$	−6.98414	−0.402559
$302$	18.3886	1.05814
$303$	−4.70322	−0.270193
$304$	−25.4763	−1.46116
$305$	3.66796	0.210026
$306$	−16.2711	−0.930158
$307$	−8.74998	−0.499388	−0.249694	−	0.968325i	$-0.580330\pi$
$307$	−8.74998	−0.499388	−0.249694	+	0.968325i	$0.580330\pi$
$308$	−18.6406	−1.06215
$309$	6.71140	0.381798
$310$	20.3002	1.15297
$311$	−19.6026	−1.11156	−0.555780	−	0.831330i	$-0.687580\pi$
$311$	−19.6026	−1.11156	−0.555780	+	0.831330i	$0.687580\pi$
$312$	−13.7022	−0.775733
$313$	23.3542	1.32006	0.660028	−	0.751241i	$-0.270545\pi$
$313$	23.3542	1.32006	0.660028	+	0.751241i	$0.270545\pi$
$314$	19.2362	1.08556
$315$	4.55611	0.256708
$316$	60.5208	3.40456
$317$	28.1719	1.58229	0.791147	−	0.611626i	$-0.209484\pi$
$317$	28.1719	1.58229	0.791147	+	0.611626i	$0.209484\pi$
$318$	3.15300	0.176811
$319$	32.7463	1.83344
$320$	10.3458	0.578348
$321$	11.2147	0.625945
$322$	22.6238	1.26078
$323$	18.8594	1.04936
$324$	21.2354	1.17975
$325$	−16.7120	−0.927015
$326$	−3.06752	−0.169894
$327$	−8.61320	−0.476311
$328$	−27.4298	−1.51456
$329$	16.4942	0.909356
$330$	−5.64927	−0.310982
$331$	4.91670	0.270246	0.135123	−	0.990829i	$-0.456857\pi$
$331$	4.91670	0.270246	0.135123	+	0.990829i	$0.456857\pi$
$332$	43.2680	2.37464
$333$	−27.8103	−1.52400
$334$	47.5899	2.60400
$335$	1.94165	0.106084
$336$	3.44927	0.188173
$337$	−10.2561	−0.558685	−0.279342	−	0.960192i	$-0.590116\pi$
$337$	−10.2561	−0.558685	−0.279342	+	0.960192i	$0.590116\pi$
$338$	−18.8973	−1.02788
$339$	5.31300	0.288563
$340$	11.7062	0.634856
$341$	−22.5328	−1.22022
$342$	−45.7561	−2.47421
$343$	−17.8213	−0.962257
$344$	21.2968	1.14825
$345$	4.53818	0.244327
$346$	23.2422	1.24951
$347$	27.1915	1.45972	0.729858	−	0.683598i	$-0.239586\pi$
$347$	27.1915	1.45972	0.729858	+	0.683598i	$0.239586\pi$
$348$	−26.5507	−1.42327
$349$	28.0209	1.49993	0.749963	−	0.661480i	$-0.230071\pi$
$349$	28.0209	1.49993	0.749963	+	0.661480i	$0.230071\pi$
$350$	13.6235	0.728207
$351$	−16.4245	−0.876673
$352$	−2.51730	−0.134172
$353$	−5.62984	−0.299646	−0.149823	−	0.988713i	$-0.547870\pi$
$353$	−5.62984	−0.299646	−0.149823	+	0.988713i	$0.547870\pi$
$354$	8.91176	0.473655
$355$	15.0369	0.798075
$356$	59.4395	3.15029
$357$	−2.55340	−0.135140
$358$	43.7036	2.30981
$359$	14.4913	0.764821	0.382411	−	0.923993i	$-0.375094\pi$
$359$	14.4913	0.764821	0.382411	+	0.923993i	$0.375094\pi$
$360$	−13.8930	−0.732223
$361$	34.0346	1.79129
$362$	−41.5449	−2.18355
$363$	−0.829607	−0.0435431
$364$	27.2560	1.42860
$365$	−16.3324	−0.854878
$366$	4.98737	0.260694
$367$	−1.35810	−0.0708920	−0.0354460	−	0.999372i	$-0.511285\pi$
$367$	−1.35810	−0.0708920	−0.0354460	+	0.999372i	$0.511285\pi$
$368$	−21.3032	−1.11051
$369$	−15.2130	−0.791955
$370$	30.2287	1.57151
$371$	−3.06799	−0.159282
$372$	18.2697	0.947239
$373$	−15.7366	−0.814812	−0.407406	−	0.913247i	$-0.633567\pi$
$373$	−15.7366	−0.814812	−0.407406	+	0.913247i	$0.633567\pi$
$374$	−19.6312	−1.01511
$375$	6.45895	0.333539
$376$	−50.2959	−2.59381
$377$	−47.8810	−2.46600
$378$	13.3891	0.688661
$379$	−13.0196	−0.668769	−0.334385	−	0.942437i	$-0.608528\pi$
$379$	−13.0196	−0.668769	−0.334385	+	0.942437i	$0.608528\pi$
$380$	32.9190	1.68871
$381$	6.92108	0.354577
$382$	−44.1895	−2.26093
$383$	−36.4198	−1.86096	−0.930481	−	0.366339i	$-0.880611\pi$
$383$	−36.4198	−1.86096	−0.930481	+	0.366339i	$0.880611\pi$
$384$	13.0247	0.664665
$385$	5.49697	0.280152
$386$	37.3605	1.90160
$387$	11.8115	0.600412
$388$	6.76781	0.343583
$389$	19.1461	0.970748	0.485374	−	0.874307i	$-0.338683\pi$
$389$	19.1461	0.970748	0.485374	+	0.874307i	$0.338683\pi$
$390$	8.26027	0.418275
$391$	15.7702	0.797532
$392$	21.7368	1.09788
$393$	9.19770	0.463962
$394$	56.3757	2.84017
$395$	−17.8471	−0.897985
$396$	31.5249	1.58418
$397$	24.7506	1.24220	0.621098	−	0.783733i	$-0.286687\pi$
$397$	24.7506	1.24220	0.621098	+	0.783733i	$0.286687\pi$
$398$	−1.16976	−0.0586348
$399$	−7.18044	−0.359472
$400$	−12.8282	−0.641412
$401$	14.7769	0.737925	0.368962	−	0.929444i	$-0.379713\pi$
$401$	14.7769	0.737925	0.368962	+	0.929444i	$0.379713\pi$
$402$	2.64009	0.131676
$403$	32.9471	1.64121
$404$	−28.5279	−1.41932
$405$	−6.26215	−0.311169
$406$	39.0323	1.93714
$407$	−33.5533	−1.66318
$408$	7.78610	0.385470
$409$	13.0927	0.647395	0.323697	−	0.946161i	$-0.395074\pi$
$409$	13.0927	0.647395	0.323697	+	0.946161i	$0.395074\pi$
$410$	16.5359	0.816648
$411$	3.58435	0.176803
$412$	40.7087	2.00557
$413$	−8.67151	−0.426697
$414$	−38.2612	−1.88044
$415$	−12.7594	−0.626333
$416$	3.68075	0.180463
$417$	−9.33437	−0.457106
$418$	−55.2051	−2.70017
$419$	−12.8884	−0.629641	−0.314820	−	0.949151i	$-0.601944\pi$
$419$	−12.8884	−0.629641	−0.314820	+	0.949151i	$0.601944\pi$
$420$	−4.45696	−0.217477
$421$	−19.7637	−0.963224	−0.481612	−	0.876385i	$-0.659949\pi$
$421$	−19.7637	−0.963224	−0.481612	+	0.876385i	$0.659949\pi$
$422$	−43.3097	−2.10828
$423$	−27.8949	−1.35629
$424$	9.35525	0.454331
$425$	9.49640	0.460643
$426$	20.4459	0.990605
$427$	−4.85291	−0.234849
$428$	68.0241	3.28807
$429$	−9.16876	−0.442672
$430$	−12.8386	−0.619133
$431$	13.9622	0.672534	0.336267	−	0.941767i	$-0.390836\pi$
$431$	13.9622	0.672534	0.336267	+	0.941767i	$0.390836\pi$
$432$	−12.6075	−0.606580
$433$	−20.0748	−0.964732	−0.482366	−	0.875970i	$-0.660222\pi$
$433$	−20.0748	−0.964732	−0.482366	+	0.875970i	$0.660222\pi$
$434$	−26.8583	−1.28924
$435$	7.82960	0.375400
$436$	−52.2442	−2.50205
$437$	44.3474	2.12143
$438$	−22.2074	−1.06111
$439$	1.24281	0.0593161	0.0296581	−	0.999560i	$-0.490558\pi$
$439$	1.24281	0.0593161	0.0296581	+	0.999560i	$0.490558\pi$
$440$	−16.7619	−0.799095
$441$	12.0556	0.574074
$442$	28.7044	1.36533
$443$	32.2202	1.53083	0.765414	−	0.643538i	$-0.222534\pi$
$443$	32.2202	1.53083	0.765414	+	0.643538i	$0.222534\pi$
$444$	27.2051	1.29110
$445$	−17.5282	−0.830918
$446$	−41.0695	−1.94470
$447$	9.90901	0.468680
$448$	−13.6881	−0.646702
$449$	34.5170	1.62896	0.814480	−	0.580192i	$-0.197023\pi$
$449$	34.5170	1.62896	0.814480	+	0.580192i	$0.197023\pi$
$450$	−23.0399	−1.08611
$451$	−18.3545	−0.864281
$452$	32.2265	1.51581
$453$	−4.88025	−0.229294
$454$	1.85291	0.0869612
$455$	−8.03758	−0.376808
$456$	21.8954	1.02534
$457$	17.1639	0.802895	0.401447	−	0.915882i	$-0.368507\pi$
$457$	17.1639	0.802895	0.401447	+	0.915882i	$0.368507\pi$
$458$	39.5563	1.84834
$459$	9.33301	0.435628
$460$	27.5268	1.28344
$461$	−26.4631	−1.23251	−0.616255	−	0.787547i	$-0.711351\pi$
$461$	−26.4631	−1.23251	−0.616255	+	0.787547i	$0.711351\pi$
$462$	7.47431	0.347736
$463$	18.7911	0.873295	0.436647	−	0.899633i	$-0.356166\pi$
$463$	18.7911	0.873295	0.436647	+	0.899633i	$0.356166\pi$
$464$	−36.7538	−1.70625
$465$	−5.38758	−0.249843
$466$	39.5018	1.82989
$467$	9.56827	0.442767	0.221383	−	0.975187i	$-0.428943\pi$
$467$	9.56827	0.442767	0.221383	+	0.975187i	$0.428943\pi$
$468$	−46.0951	−2.13075
$469$	−2.56891	−0.118621
$470$	30.3206	1.39858
$471$	−5.10522	−0.235236
$472$	26.4421	1.21710
$473$	14.2507	0.655246
$474$	−24.2669	−1.11462
$475$	26.7049	1.22530
$476$	−15.4879	−0.709888
$477$	5.18856	0.237568
$478$	−54.3692	−2.48679
$479$	−1.62505	−0.0742503	−0.0371252	−	0.999311i	$-0.511820\pi$
$479$	−1.62505	−0.0742503	−0.0371252	+	0.999311i	$0.511820\pi$
$480$	−0.601883	−0.0274721
$481$	49.0611	2.23699
$482$	−21.4102	−0.975207
$483$	−6.00427	−0.273204
$484$	−5.03207	−0.228730
$485$	−1.99577	−0.0906233
$486$	−34.8101	−1.57902
$487$	−4.76734	−0.216029	−0.108014	−	0.994149i	$-0.534449\pi$
$487$	−4.76734	−0.216029	−0.108014	+	0.994149i	$0.534449\pi$
$488$	14.7980	0.669875
$489$	0.814108	0.0368152
$490$	−13.1039	−0.591974
$491$	17.6701	0.797439	0.398719	−	0.917073i	$-0.369455\pi$
$491$	17.6701	0.797439	0.398719	+	0.917073i	$0.369455\pi$
$492$	14.8819	0.670928
$493$	27.2078	1.22538
$494$	80.7199	3.63176
$495$	−9.29642	−0.417843
$496$	25.2905	1.13558
$497$	−19.8947	−0.892397
$498$	−17.3491	−0.777431
$499$	15.2443	0.682430	0.341215	−	0.939985i	$-0.389162\pi$
$499$	15.2443	0.682430	0.341215	+	0.939985i	$0.389162\pi$
$500$	39.1774	1.75207
$501$	−12.6302	−0.564274
$502$	23.8521	1.06457
$503$	−10.7891	−0.481062	−0.240531	−	0.970641i	$-0.577322\pi$
$503$	−10.7891	−0.481062	−0.240531	+	0.970641i	$0.577322\pi$
$504$	18.3812	0.818763
$505$	8.41264	0.374358
$506$	−46.1624	−2.05217
$507$	5.01525	0.222735
$508$	41.9805	1.86258
$509$	−17.6960	−0.784361	−0.392181	−	0.919888i	$-0.628279\pi$
$509$	−17.6960	−0.784361	−0.392181	+	0.919888i	$0.628279\pi$
$510$	−4.69380	−0.207845
$511$	21.6087	0.955914
$512$	35.4151	1.56514
$513$	26.2454	1.15876
$514$	−25.5643	−1.12759
$515$	−12.0047	−0.528988
$516$	−11.5545	−0.508657
$517$	−33.6553	−1.48016
$518$	−39.9943	−1.75725
$519$	−6.16840	−0.270763
$520$	24.5090	1.07479
$521$	20.1694	0.883638	0.441819	−	0.897104i	$-0.354333\pi$
$521$	20.1694	0.883638	0.441819	+	0.897104i	$0.354333\pi$
$522$	−66.0110	−2.88922
$523$	0.427646	0.0186997	0.00934983	−	0.999956i	$-0.497024\pi$
$523$	0.427646	0.0186997	0.00934983	+	0.999956i	$0.497024\pi$
$524$	55.7896	2.43718
$525$	−3.61562	−0.157799
$526$	−44.0329	−1.91993
$527$	−18.7218	−0.815536
$528$	−7.03801	−0.306290
$529$	14.0832	0.612315
$530$	−5.63975	−0.244975
$531$	14.6652	0.636414
$532$	−43.5537	−1.88829
$533$	26.8377	1.16247
$534$	−23.8334	−1.03137
$535$	−20.0598	−0.867259
$536$	7.83340	0.338352
$537$	−11.5988	−0.500523
$538$	66.8366	2.88153
$539$	14.5451	0.626502
$540$	16.2907	0.701042
$541$	−4.42440	−0.190220	−0.0951099	−	0.995467i	$-0.530320\pi$
$541$	−4.42440	−0.190220	−0.0951099	+	0.995467i	$0.530320\pi$
$542$	−2.67730	−0.115000
$543$	11.0258	0.473164
$544$	−2.09154	−0.0896741
$545$	15.4064	0.659938
$546$	−10.9288	−0.467710
$547$	−4.91191	−0.210018	−0.105009	−	0.994471i	$-0.533487\pi$
$547$	−4.91191	−0.210018	−0.105009	+	0.994471i	$0.533487\pi$
$548$	21.7412	0.928739
$549$	8.20720	0.350275
$550$	−27.7978	−1.18530
$551$	76.5114	3.25949
$552$	18.3089	0.779277
$553$	23.6127	1.00412
$554$	−29.1873	−1.24005
$555$	−8.02256	−0.340539
$556$	−56.6186	−2.40116
$557$	34.3666	1.45616	0.728080	−	0.685492i	$-0.240413\pi$
$557$	34.3666	1.45616	0.728080	+	0.685492i	$0.240413\pi$
$558$	45.4224	1.92289
$559$	−20.8371	−0.881314
$560$	−6.16970	−0.260718
$561$	5.21004	0.219968
$562$	1.59778	0.0673983
$563$	19.1235	0.805959	0.402979	−	0.915209i	$-0.367975\pi$
$563$	19.1235	0.805959	0.402979	+	0.915209i	$0.367975\pi$
$564$	27.2878	1.14902
$565$	−9.50334	−0.399809
$566$	27.3595	1.15000
$567$	8.28519	0.347945
$568$	60.6649	2.54544
$569$	2.32776	0.0975846	0.0487923	−	0.998809i	$-0.484463\pi$
$569$	2.32776	0.0975846	0.0487923	+	0.998809i	$0.484463\pi$
$570$	−13.1995	−0.552865
$571$	13.9983	0.585813	0.292906	−	0.956141i	$-0.405378\pi$
$571$	13.9983	0.585813	0.292906	+	0.956141i	$0.405378\pi$
$572$	−55.6141	−2.32534
$573$	11.7277	0.489932
$574$	−21.8779	−0.913166
$575$	22.3306	0.931250
$576$	23.1492	0.964549
$577$	6.89108	0.286879	0.143440	−	0.989659i	$-0.454184\pi$
$577$	6.89108	0.286879	0.143440	+	0.989659i	$0.454184\pi$
$578$	25.0350	1.04132
$579$	−9.91532	−0.412067
$580$	47.4912	1.97197
$581$	16.8814	0.700358
$582$	−2.71368	−0.112486
$583$	6.26003	0.259264
$584$	−65.8916	−2.72662
$585$	13.5931	0.562004
$586$	−2.04700	−0.0845608
$587$	−20.4979	−0.846040	−0.423020	−	0.906120i	$-0.639030\pi$
$587$	−20.4979	−0.846040	−0.423020	+	0.906120i	$0.639030\pi$
$588$	−11.7932	−0.486344
$589$	−52.6478	−2.16932
$590$	−15.9404	−0.656257
$591$	−14.9619	−0.615449
$592$	37.6597	1.54780
$593$	−7.52526	−0.309025	−0.154513	−	0.987991i	$-0.549381\pi$
$593$	−7.52526	−0.309025	−0.154513	+	0.987991i	$0.549381\pi$
$594$	−27.3196	−1.12093
$595$	4.56726	0.187239
$596$	60.1041	2.46196
$597$	0.310450	0.0127059
$598$	67.4979	2.76019
$599$	−19.9136	−0.813648	−0.406824	−	0.913507i	$-0.633364\pi$
$599$	−19.9136	−0.813648	−0.406824	+	0.913507i	$0.633364\pi$
$600$	11.0251	0.450099
$601$	−9.38960	−0.383010	−0.191505	−	0.981492i	$-0.561337\pi$
$601$	−9.38960	−0.383010	−0.191505	+	0.981492i	$0.561337\pi$
$602$	16.9862	0.692307
$603$	4.34452	0.176923
$604$	−29.6017	−1.20448
$605$	1.48392	0.0603297
$606$	11.4388	0.464669
$607$	18.3155	0.743403	0.371702	−	0.928352i	$-0.378774\pi$
$607$	18.3155	0.743403	0.371702	+	0.928352i	$0.378774\pi$
$608$	−5.88164	−0.238532
$609$	−10.3590	−0.419768
$610$	−8.92089	−0.361196
$611$	49.2102	1.99083
$612$	26.1930	1.05879
$613$	−35.2297	−1.42292	−0.711458	−	0.702729i	$-0.751965\pi$
$613$	−35.2297	−1.42292	−0.711458	+	0.702729i	$0.751965\pi$
$614$	21.2810	0.858830
$615$	−4.38855	−0.176963
$616$	22.1770	0.893538
$617$	42.0795	1.69406	0.847028	−	0.531548i	$-0.178390\pi$
$617$	42.0795	1.69406	0.847028	+	0.531548i	$0.178390\pi$
$618$	−16.3229	−0.656603
$619$	−17.4446	−0.701156	−0.350578	−	0.936534i	$-0.614015\pi$
$619$	−17.4446	−0.701156	−0.350578	+	0.936534i	$0.614015\pi$
$620$	−32.6789	−1.31242
$621$	21.9464	0.880678
$622$	47.6757	1.91162
$623$	23.1909	0.929122
$624$	10.2909	0.411964
$625$	6.78191	0.271276
$626$	−56.8000	−2.27018
$627$	14.6512	0.585112
$628$	−30.9662	−1.23569
$629$	−27.8784	−1.11158
$630$	−11.0810	−0.441477
$631$	22.2204	0.884582	0.442291	−	0.896872i	$-0.354166\pi$
$631$	22.2204	0.884582	0.442291	+	0.896872i	$0.354166\pi$
$632$	−72.0024	−2.86410
$633$	11.4942	0.456854
$634$	−68.5174	−2.72117
$635$	−12.3797	−0.491274
$636$	−5.07565	−0.201262
$637$	−21.2676	−0.842654
$638$	−79.6427	−3.15308
$639$	33.6456	1.33100
$640$	−23.2973	−0.920905
$641$	−15.3088	−0.604661	−0.302330	−	0.953203i	$-0.597765\pi$
$641$	−15.3088	−0.604661	−0.302330	+	0.953203i	$0.597765\pi$
$642$	−27.2755	−1.07648
$643$	48.0449	1.89470	0.947352	−	0.320193i	$-0.103748\pi$
$643$	48.0449	1.89470	0.947352	+	0.320193i	$0.103748\pi$
$644$	−36.4195	−1.43513
$645$	3.40732	0.134163
$646$	−45.8682	−1.80466
$647$	−16.5753	−0.651642	−0.325821	−	0.945431i	$-0.605641\pi$
$647$	−16.5753	−0.651642	−0.325821	+	0.945431i	$0.605641\pi$
$648$	−25.2641	−0.992466
$649$	17.6936	0.694535
$650$	40.6455	1.59425
$651$	7.12808	0.279371
$652$	4.93806	0.193389
$653$	−27.4086	−1.07258	−0.536290	−	0.844034i	$-0.680175\pi$
$653$	−27.4086	−1.07258	−0.536290	+	0.844034i	$0.680175\pi$
$654$	20.9483	0.819143
$655$	−16.4519	−0.642828
$656$	20.6008	0.804326
$657$	−36.5445	−1.42574
$658$	−40.1158	−1.56388
$659$	15.2920	0.595691	0.297845	−	0.954614i	$-0.403732\pi$
$659$	15.2920	0.595691	0.297845	+	0.954614i	$0.403732\pi$
$660$	9.09411	0.353988
$661$	−19.0840	−0.742283	−0.371142	−	0.928576i	$-0.621034\pi$
$661$	−19.0840	−0.742283	−0.371142	+	0.928576i	$0.621034\pi$
$662$	−11.9580	−0.464760
$663$	−7.61803	−0.295860
$664$	−51.4765	−1.99767
$665$	12.8436	0.498055
$666$	67.6379	2.62092
$667$	63.9787	2.47726
$668$	−76.6095	−2.96411
$669$	10.8997	0.421406
$670$	−4.72232	−0.182439
$671$	9.90204	0.382264
$672$	0.796325	0.0307189
$673$	24.1822	0.932157	0.466078	−	0.884743i	$-0.345666\pi$
$673$	24.1822	0.932157	0.466078	+	0.884743i	$0.345666\pi$
$674$	24.9440	0.960806
$675$	13.2155	0.508667
$676$	30.4205	1.17002
$677$	45.2097	1.73755	0.868775	−	0.495207i	$-0.164908\pi$
$677$	45.2097	1.73755	0.868775	+	0.495207i	$0.164908\pi$
$678$	−12.9218	−0.496260
$679$	2.64052	0.101334
$680$	−13.9270	−0.534075
$681$	−0.491753	−0.0188440
$682$	54.8025	2.09850
$683$	−18.2710	−0.699121	−0.349561	−	0.936914i	$-0.613669\pi$
$683$	−18.2710	−0.699121	−0.349561	+	0.936914i	$0.613669\pi$
$684$	73.6576	2.81637
$685$	−6.41131	−0.244964
$686$	43.3433	1.65486
$687$	−10.4981	−0.400527
$688$	−15.9947	−0.609791
$689$	−9.15331	−0.348713
$690$	−11.0374	−0.420186
$691$	−20.2785	−0.771430	−0.385715	−	0.922618i	$-0.626045\pi$
$691$	−20.2785	−0.771430	−0.385715	+	0.922618i	$0.626045\pi$
$692$	−37.4150	−1.42231
$693$	12.2997	0.467227
$694$	−66.1329	−2.51037
$695$	16.6963	0.633329
$696$	31.5878	1.19733
$697$	−15.2502	−0.577643
$698$	−68.1501	−2.57952
$699$	−10.4836	−0.396527
$700$	−21.9309	−0.828910
$701$	−1.81957	−0.0687242	−0.0343621	−	0.999409i	$-0.510940\pi$
$701$	−1.81957	−0.0687242	−0.0343621	+	0.999409i	$0.510940\pi$
$702$	39.9462	1.50767
$703$	−78.3971	−2.95680
$704$	27.9296	1.05264
$705$	−8.04695	−0.303066
$706$	13.6924	0.515321
$707$	−11.1304	−0.418602
$708$	−14.3460	−0.539157
$709$	0.972273	0.0365145	0.0182572	−	0.999833i	$-0.494188\pi$
$709$	0.972273	0.0365145	0.0182572	+	0.999833i	$0.494188\pi$
$710$	−36.5714	−1.37250
$711$	−39.9336	−1.49763
$712$	−70.7160	−2.65019
$713$	−44.0240	−1.64871
$714$	6.21017	0.232410
$715$	16.4001	0.613330
$716$	−70.3534	−2.62923
$717$	14.4294	0.538874
$718$	−35.2445	−1.31531
$719$	−11.6015	−0.432664	−0.216332	−	0.976320i	$-0.569409\pi$
$719$	−11.6015	−0.432664	−0.216332	+	0.976320i	$0.569409\pi$
$720$	10.4341	0.388857
$721$	15.8828	0.591508
$722$	−82.7760	−3.08060
$723$	5.68217	0.211322
$724$	66.8783	2.48551
$725$	38.5263	1.43083
$726$	2.01770	0.0748839
$727$	27.8767	1.03389	0.516946	−	0.856018i	$-0.327069\pi$
$727$	27.8767	1.03389	0.516946	+	0.856018i	$0.327069\pi$
$728$	−32.4269	−1.20182
$729$	−7.03314	−0.260487
$730$	39.7223	1.47019
$731$	11.8404	0.437934
$732$	−8.02859	−0.296745
$733$	13.6023	0.502414	0.251207	−	0.967933i	$-0.419173\pi$
$733$	13.6023	0.502414	0.251207	+	0.967933i	$0.419173\pi$
$734$	3.30304	0.121918
$735$	3.47772	0.128278
$736$	−4.91822	−0.181288
$737$	5.24169	0.193080
$738$	36.9997	1.36198
$739$	−12.6441	−0.465120	−0.232560	−	0.972582i	$-0.574710\pi$
$739$	−12.6441	−0.465120	−0.232560	+	0.972582i	$0.574710\pi$
$740$	−48.6617	−1.78884
$741$	−21.4227	−0.786984
$742$	7.46172	0.273928
$743$	−0.383303	−0.0140620	−0.00703102	−	0.999975i	$-0.502238\pi$
$743$	−0.383303	−0.0140620	−0.00703102	+	0.999975i	$0.502238\pi$
$744$	−21.7357	−0.796869
$745$	−17.7242	−0.649365
$746$	38.2733	1.40128
$747$	−28.5496	−1.04458
$748$	31.6020	1.15549
$749$	26.5402	0.969758
$750$	−15.7089	−0.573608
$751$	−26.4984	−0.966939	−0.483469	−	0.875361i	$-0.660624\pi$
$751$	−26.4984	−0.966939	−0.483469	+	0.875361i	$0.660624\pi$
$752$	37.7741	1.37748
$753$	−6.33026	−0.230687
$754$	116.452	4.24094
$755$	8.72929	0.317691
$756$	−21.5536	−0.783897
$757$	−14.0794	−0.511724	−0.255862	−	0.966713i	$-0.582359\pi$
$757$	−14.0794	−0.511724	−0.255862	+	0.966713i	$0.582359\pi$
$758$	31.6650	1.15013
$759$	12.2513	0.444694
$760$	−39.1642	−1.42063
$761$	−28.0204	−1.01574	−0.507869	−	0.861435i	$-0.669566\pi$
$761$	−28.0204	−1.01574	−0.507869	+	0.861435i	$0.669566\pi$
$762$	−16.8329	−0.609790
$763$	−20.3835	−0.737934
$764$	71.1357	2.57360
$765$	−7.72410	−0.279266
$766$	88.5770	3.20042
$767$	−25.8713	−0.934159
$768$	−20.1096	−0.725644
$769$	26.1648	0.943527	0.471764	−	0.881725i	$-0.343618\pi$
$769$	26.1648	0.943527	0.471764	+	0.881725i	$0.343618\pi$
$770$	−13.3693	−0.481795
$771$	6.78465	0.244343
$772$	−60.1424	−2.16457
$773$	−12.6876	−0.456343	−0.228171	−	0.973621i	$-0.573275\pi$
$773$	−12.6876	−0.456343	−0.228171	+	0.973621i	$0.573275\pi$
$774$	−28.7269	−1.03257
$775$	−26.5101	−0.952272
$776$	−8.05175	−0.289041
$777$	10.6143	0.380786
$778$	−46.5656	−1.66946
$779$	−42.8852	−1.53652
$780$	−13.2973	−0.476118
$781$	40.5937	1.45256
$782$	−38.3549	−1.37157
$783$	37.8635	1.35313
$784$	−16.3252	−0.583042
$785$	9.13169	0.325924
$786$	−22.3699	−0.797906
$787$	8.78531	0.313162	0.156581	−	0.987665i	$-0.449953\pi$
$787$	8.78531	0.313162	0.156581	+	0.987665i	$0.449953\pi$
$788$	−90.7528	−3.23293
$789$	11.6861	0.416038
$790$	43.4062	1.54432
$791$	12.5735	0.447061
$792$	−37.5055	−1.33270
$793$	−14.4786	−0.514150
$794$	−60.1962	−2.13628
$795$	1.49677	0.0530848
$796$	1.88306	0.0667434
$797$	−9.63111	−0.341151	−0.170576	−	0.985345i	$-0.554563\pi$
$797$	−9.63111	−0.341151	−0.170576	+	0.985345i	$0.554563\pi$
$798$	17.4637	0.618207
$799$	−27.9631	−0.989265
$800$	−2.96162	−0.104709
$801$	−39.2201	−1.38578
$802$	−35.9392	−1.26906
$803$	−44.0911	−1.55594
$804$	−4.24997	−0.149885
$805$	10.7398	0.378529
$806$	−80.1313	−2.82250
$807$	−17.7382	−0.624413
$808$	33.9400	1.19401
$809$	34.4424	1.21093	0.605465	−	0.795872i	$-0.292987\pi$
$809$	34.4424	1.21093	0.605465	+	0.795872i	$0.292987\pi$
$810$	15.2303	0.535137
$811$	0.359968	0.0126402	0.00632008	−	0.999980i	$-0.497988\pi$
$811$	0.359968	0.0126402	0.00632008	+	0.999980i	$0.497988\pi$
$812$	−62.8336	−2.20503
$813$	0.710544	0.0249199
$814$	81.6056	2.86027
$815$	−1.45619	−0.0510082
$816$	−5.84766	−0.204709
$817$	33.2965	1.16490
$818$	−31.8431	−1.11337
$819$	−17.9844	−0.628426
$820$	−26.6192	−0.929583
$821$	13.8438	0.483150	0.241575	−	0.970382i	$-0.422336\pi$
$821$	13.8438	0.483150	0.241575	+	0.970382i	$0.422336\pi$
$822$	−8.71754	−0.304059
$823$	−1.09143	−0.0380448	−0.0190224	−	0.999819i	$-0.506055\pi$
$823$	−1.09143	−0.0380448	−0.0190224	+	0.999819i	$0.506055\pi$
$824$	−48.4316	−1.68720
$825$	7.37742	0.256849
$826$	21.0901	0.733819
$827$	−31.4499	−1.09362	−0.546810	−	0.837257i	$-0.684158\pi$
$827$	−31.4499	−1.09362	−0.546810	+	0.837257i	$0.684158\pi$
$828$	61.5923	2.14048
$829$	−0.0453522	−0.00157515	−0.000787574	−	1.00000i	$-0.500251\pi$
$829$	−0.0453522	−0.00157515	−0.000787574		1.00000i	$0.500251\pi$
$830$	31.0323	1.07715
$831$	7.74620	0.268713
$832$	−40.8382	−1.41581
$833$	12.0851	0.418723
$834$	22.7023	0.786115
$835$	22.5915	0.781812
$836$	88.8683	3.07358
$837$	−26.0540	−0.900559
$838$	31.3461	1.08283
$839$	29.2535	1.00994	0.504971	−	0.863136i	$-0.331503\pi$
$839$	29.2535	1.00994	0.504971	+	0.863136i	$0.331503\pi$
$840$	5.30250	0.182954
$841$	81.3806	2.80623
$842$	48.0676	1.65652
$843$	−0.424045	−0.0146049
$844$	69.7193	2.39984
$845$	−8.97077	−0.308604
$846$	67.8435	2.33251
$847$	−1.96331	−0.0674600
$848$	−7.02615	−0.241279
$849$	−7.26108	−0.249200
$850$	−23.0963	−0.792197
$851$	−65.5555	−2.24721
$852$	−32.9134	−1.12760
$853$	−9.13158	−0.312659	−0.156330	−	0.987705i	$-0.549966\pi$
$853$	−9.13158	−0.312659	−0.156330	+	0.987705i	$0.549966\pi$
$854$	11.8028	0.403885
$855$	−21.7210	−0.742843
$856$	−80.9292	−2.76610
$857$	20.4151	0.697366	0.348683	−	0.937241i	$-0.386629\pi$
$857$	20.4151	0.697366	0.348683	+	0.937241i	$0.386629\pi$
$858$	22.2995	0.761292
$859$	42.3734	1.44576	0.722880	−	0.690973i	$-0.242818\pi$
$859$	42.3734	1.44576	0.722880	+	0.690973i	$0.242818\pi$
$860$	20.6674	0.704753
$861$	5.80630	0.197878
$862$	−33.9576	−1.15660
$863$	−23.4335	−0.797687	−0.398843	−	0.917019i	$-0.630588\pi$
$863$	−23.4335	−0.797687	−0.398843	+	0.917019i	$0.630588\pi$
$864$	−2.91067	−0.0990230
$865$	11.0334	0.375146
$866$	48.8241	1.65911
$867$	−6.64418	−0.225648
$868$	43.2361	1.46753
$869$	−48.1801	−1.63440
$870$	−19.0425	−0.645600
$871$	−7.66431	−0.259695
$872$	62.1557	2.10486
$873$	−4.46562	−0.151138
$874$	−107.858	−3.64835
$875$	15.2854	0.516741
$876$	35.7492	1.20785
$877$	24.9935	0.843971	0.421985	−	0.906603i	$-0.361333\pi$
$877$	24.9935	0.843971	0.421985	+	0.906603i	$0.361333\pi$
$878$	−3.02266	−0.102010
$879$	0.543265	0.0183239
$880$	12.5889	0.424370
$881$	−6.27974	−0.211570	−0.105785	−	0.994389i	$-0.533736\pi$
$881$	−6.27974	−0.211570	−0.105785	+	0.994389i	$0.533736\pi$
$882$	−29.3205	−0.987273
$883$	20.2342	0.680936	0.340468	−	0.940256i	$-0.389414\pi$
$883$	20.2342	0.680936	0.340468	+	0.940256i	$0.389414\pi$
$884$	−46.2080	−1.55414
$885$	4.23053	0.142208
$886$	−78.3633	−2.63267
$887$	9.55250	0.320741	0.160371	−	0.987057i	$-0.448731\pi$
$887$	9.55250	0.320741	0.160371	+	0.987057i	$0.448731\pi$
$888$	−32.3663	−1.08614
$889$	16.3791	0.549336
$890$	42.6307	1.42898
$891$	−16.9054	−0.566351
$892$	66.1131	2.21363
$893$	−78.6354	−2.63143
$894$	−24.0999	−0.806020
$895$	20.7466	0.693484
$896$	30.8236	1.02975
$897$	−17.9137	−0.598119
$898$	−83.9494	−2.80143
$899$	−75.9534	−2.53319
$900$	37.0893	1.23631
$901$	5.20126	0.173279
$902$	44.6403	1.48636
$903$	−4.50807	−0.150019
$904$	−38.3403	−1.27518
$905$	−19.7219	−0.655577
$906$	11.8693	0.394332
$907$	−32.5589	−1.08110	−0.540550	−	0.841312i	$-0.681784\pi$
$907$	−32.5589	−1.08110	−0.540550	+	0.841312i	$0.681784\pi$
$908$	−2.98278	−0.0989871
$909$	18.8236	0.624340
$910$	19.5483	0.648021
$911$	−31.8059	−1.05378	−0.526888	−	0.849935i	$-0.676641\pi$
$911$	−31.8059	−1.05378	−0.526888	+	0.849935i	$0.676641\pi$
$912$	−16.4442	−0.544523
$913$	−34.4453	−1.13997
$914$	−41.7447	−1.38079
$915$	2.36757	0.0782693
$916$	−63.6771	−2.10395
$917$	21.7668	0.718803
$918$	−22.6990	−0.749177
$919$	−41.9102	−1.38249	−0.691245	−	0.722620i	$-0.742938\pi$
$919$	−41.9102	−1.38249	−0.691245	+	0.722620i	$0.742938\pi$
$920$	−32.7490	−1.07970
$921$	−5.64788	−0.186104
$922$	64.3613	2.11963
$923$	−59.3554	−1.95371
$924$	−12.0320	−0.395825
$925$	−39.4758	−1.29796
$926$	−45.7020	−1.50186
$927$	−26.8609	−0.882228
$928$	−8.48526	−0.278542
$929$	0.330378	0.0108394	0.00541968	−	0.999985i	$-0.498275\pi$
$929$	0.330378	0.0108394	0.00541968	+	0.999985i	$0.498275\pi$
$930$	13.1032	0.429671
$931$	33.9845	1.11380
$932$	−63.5894	−2.08294
$933$	−12.6529	−0.414238
$934$	−23.2711	−0.761455
$935$	−9.31918	−0.304770
$936$	54.8400	1.79250
$937$	−29.4541	−0.962224	−0.481112	−	0.876659i	$-0.659767\pi$
$937$	−29.4541	−0.962224	−0.481112	+	0.876659i	$0.659767\pi$
$938$	6.24789	0.204001
$939$	15.0745	0.491937
$940$	−48.8096	−1.59199
$941$	58.4243	1.90458	0.952289	−	0.305199i	$-0.0987230\pi$
$941$	58.4243	1.90458	0.952289	+	0.305199i	$0.0987230\pi$
$942$	12.4165	0.404551
$943$	−35.8606	−1.16778
$944$	−19.8590	−0.646356
$945$	6.35598	0.206760
$946$	−34.6592	−1.12687
$947$	−15.6187	−0.507540	−0.253770	−	0.967265i	$-0.581671\pi$
$947$	−15.6187	−0.507540	−0.253770	+	0.967265i	$0.581671\pi$
$948$	39.0646	1.26876
$949$	64.4693	2.09276
$950$	−64.9493	−2.10724
$951$	18.1842	0.589664
$952$	18.4262	0.597196
$953$	−47.4160	−1.53595	−0.767977	−	0.640478i	$-0.778736\pi$
$953$	−47.4160	−1.53595	−0.767977	+	0.640478i	$0.778736\pi$
$954$	−12.6192	−0.408561
$955$	−20.9773	−0.678810
$956$	87.5227	2.83069
$957$	21.1368	0.683257
$958$	3.95230	0.127693
$959$	8.48253	0.273915
$960$	6.67794	0.215530
$961$	21.2639	0.685931
$962$	−119.322	−3.84710
$963$	−44.8845	−1.44638
$964$	34.4658	1.11007
$965$	17.7355	0.570926
$966$	14.6031	0.469847
$967$	−22.9487	−0.737979	−0.368989	−	0.929434i	$-0.620296\pi$
$967$	−22.9487	−0.737979	−0.368989	+	0.929434i	$0.620296\pi$
$968$	5.98672	0.192420
$969$	12.1732	0.391060
$970$	4.85395	0.155851
$971$	37.5179	1.20401	0.602003	−	0.798494i	$-0.294370\pi$
$971$	37.5179	1.20401	0.602003	+	0.798494i	$0.294370\pi$
$972$	56.0368	1.79738
$973$	−22.0902	−0.708180
$974$	11.5947	0.371519
$975$	−10.7871	−0.345465
$976$	−11.1139	−0.355746
$977$	42.0988	1.34686	0.673430	−	0.739251i	$-0.264820\pi$
$977$	42.0988	1.34686	0.673430	+	0.739251i	$0.264820\pi$
$978$	−1.98000	−0.0633136
$979$	−47.3193	−1.51233
$980$	21.0945	0.673838
$981$	34.4724	1.10062
$982$	−42.9756	−1.37141
$983$	−35.1126	−1.11992	−0.559959	−	0.828520i	$-0.689183\pi$
$983$	−35.1126	−1.11992	−0.559959	+	0.828520i	$0.689183\pi$
$984$	−17.7052	−0.564421
$985$	26.7623	0.852716
$986$	−66.1726	−2.10736
$987$	10.6466	0.338884
$988$	−129.942	−4.13400
$989$	27.8425	0.885340
$990$	22.6100	0.718592
$991$	43.7046	1.38832	0.694161	−	0.719819i	$-0.255775\pi$
$991$	43.7046	1.38832	0.694161	+	0.719819i	$0.255775\pi$
$992$	5.83875	0.185380
$993$	3.17359	0.100711
$994$	48.3861	1.53471
$995$	−0.555300	−0.0176042
$996$	27.9283	0.884942
$997$	20.3466	0.644383	0.322192	−	0.946674i	$-0.395580\pi$
$997$	20.3466	0.644383	0.322192	+	0.946674i	$0.395580\pi$
$998$	−37.0760	−1.17362
$999$	−38.7967	−1.22747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.16	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.43211 q^{2} +0.645473 q^{3} +3.91518 q^{4} -1.15456 q^{5} -1.56986 q^{6} +1.52754 q^{7} -4.65795 q^{8} -2.58336 q^{9} +O(q^{10})\)	\(q-2.43211 q^{2} +0.645473 q^{3} +3.91518 q^{4} -1.15456 q^{5} -1.56986 q^{6} +1.52754 q^{7} -4.65795 q^{8} -2.58336 q^{9} +2.80801 q^{10} -3.11685 q^{11} +2.52715 q^{12} +4.55740 q^{13} -3.71516 q^{14} -0.745234 q^{15} +3.49829 q^{16} -2.58969 q^{17} +6.28304 q^{18} -7.28248 q^{19} -4.52030 q^{20} +0.985988 q^{21} +7.58053 q^{22} -6.08960 q^{23} -3.00658 q^{24} -3.66700 q^{25} -11.0841 q^{26} -3.60391 q^{27} +5.98061 q^{28} -10.5062 q^{29} +1.81250 q^{30} +7.22937 q^{31} +0.807642 q^{32} -2.01184 q^{33} +6.29842 q^{34} -1.76363 q^{35} -10.1143 q^{36} +10.7652 q^{37} +17.7118 q^{38} +2.94168 q^{39} +5.37786 q^{40} +5.88882 q^{41} -2.39804 q^{42} -4.57214 q^{43} -12.2030 q^{44} +2.98264 q^{45} +14.8106 q^{46} +10.7979 q^{47} +2.25805 q^{48} -4.66661 q^{49} +8.91857 q^{50} -1.67157 q^{51} +17.8431 q^{52} -2.00845 q^{53} +8.76513 q^{54} +3.59857 q^{55} -7.11521 q^{56} -4.70065 q^{57} +25.5523 q^{58} -5.67677 q^{59} -2.91773 q^{60} -3.17694 q^{61} -17.5827 q^{62} -3.94620 q^{63} -8.96086 q^{64} -5.26177 q^{65} +4.89303 q^{66} -1.68173 q^{67} -10.1391 q^{68} -3.93067 q^{69} +4.28936 q^{70} -13.0240 q^{71} +12.0332 q^{72} +14.1461 q^{73} -26.1821 q^{74} -2.36695 q^{75} -28.5123 q^{76} -4.76112 q^{77} -7.15450 q^{78} +15.4580 q^{79} -4.03897 q^{80} +5.42387 q^{81} -14.3223 q^{82} +11.0513 q^{83} +3.86032 q^{84} +2.98994 q^{85} +11.1200 q^{86} -6.78148 q^{87} +14.5181 q^{88} +15.1818 q^{89} -7.25412 q^{90} +6.96162 q^{91} -23.8419 q^{92} +4.66637 q^{93} -26.2617 q^{94} +8.40803 q^{95} +0.521311 q^{96} +1.72861 q^{97} +11.3497 q^{98} +8.05195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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