LMFDB - Embedded newform 4001.2.a.b.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.38517 q^{2} +0.919938 q^{3} +3.68905 q^{4} +3.44498 q^{5} -2.19421 q^{6} -3.87561 q^{7} -4.02868 q^{8} -2.15371 q^{9} +O(q^{10})$	\(q-2.38517 q^{2} +0.919938 q^{3} +3.68905 q^{4} +3.44498 q^{5} -2.19421 q^{6} -3.87561 q^{7} -4.02868 q^{8} -2.15371 q^{9} -8.21687 q^{10} -2.95884 q^{11} +3.39370 q^{12} -7.06133 q^{13} +9.24401 q^{14} +3.16917 q^{15} +2.23100 q^{16} +5.48855 q^{17} +5.13698 q^{18} -1.68327 q^{19} +12.7087 q^{20} -3.56532 q^{21} +7.05734 q^{22} +1.14696 q^{23} -3.70614 q^{24} +6.86788 q^{25} +16.8425 q^{26} -4.74110 q^{27} -14.2973 q^{28} +7.01474 q^{29} -7.55901 q^{30} +10.3580 q^{31} +2.73604 q^{32} -2.72195 q^{33} -13.0911 q^{34} -13.3514 q^{35} -7.94517 q^{36} -10.6986 q^{37} +4.01490 q^{38} -6.49598 q^{39} -13.8787 q^{40} -6.98313 q^{41} +8.50391 q^{42} -4.35611 q^{43} -10.9153 q^{44} -7.41950 q^{45} -2.73570 q^{46} +0.995509 q^{47} +2.05238 q^{48} +8.02038 q^{49} -16.3811 q^{50} +5.04912 q^{51} -26.0496 q^{52} +14.3843 q^{53} +11.3083 q^{54} -10.1931 q^{55} +15.6136 q^{56} -1.54851 q^{57} -16.7314 q^{58} +1.51056 q^{59} +11.6912 q^{60} +3.59272 q^{61} -24.7057 q^{62} +8.34696 q^{63} -10.9879 q^{64} -24.3261 q^{65} +6.49232 q^{66} +1.34754 q^{67} +20.2475 q^{68} +1.05513 q^{69} +31.8454 q^{70} +2.71774 q^{71} +8.67663 q^{72} -13.8312 q^{73} +25.5181 q^{74} +6.31803 q^{75} -6.20968 q^{76} +11.4673 q^{77} +15.4940 q^{78} +2.81997 q^{79} +7.68576 q^{80} +2.09963 q^{81} +16.6560 q^{82} +12.1277 q^{83} -13.1527 q^{84} +18.9079 q^{85} +10.3901 q^{86} +6.45312 q^{87} +11.9202 q^{88} +14.7548 q^{89} +17.6968 q^{90} +27.3670 q^{91} +4.23120 q^{92} +9.52873 q^{93} -2.37446 q^{94} -5.79884 q^{95} +2.51698 q^{96} -16.0606 q^{97} -19.1300 q^{98} +6.37249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.38517	−1.68657	−0.843286	−	0.537465i	$-0.819382\pi$
$2$	−2.38517	−1.68657	−0.843286	+	0.537465i	$0.819382\pi$
$3$	0.919938	0.531126	0.265563	−	0.964093i	$-0.414442\pi$
$3$	0.919938	0.531126	0.265563	+	0.964093i	$0.414442\pi$
$4$	3.68905	1.84453
$5$	3.44498	1.54064	0.770321	−	0.637657i	$-0.220096\pi$
$5$	3.44498	1.54064	0.770321	+	0.637657i	$0.220096\pi$
$6$	−2.19421	−0.895783
$7$	−3.87561	−1.46484	−0.732422	−	0.680851i	$-0.761610\pi$
$7$	−3.87561	−1.46484	−0.732422	+	0.680851i	$0.761610\pi$
$8$	−4.02868	−1.42435
$9$	−2.15371	−0.717905
$10$	−8.21687	−2.59840
$11$	−2.95884	−0.892123	−0.446062	−	0.895002i	$-0.647174\pi$
$11$	−2.95884	−0.892123	−0.446062	+	0.895002i	$0.647174\pi$
$12$	3.39370	0.979676
$13$	−7.06133	−1.95846	−0.979230	−	0.202751i	$-0.935012\pi$
$13$	−7.06133	−1.95846	−0.979230	+	0.202751i	$0.935012\pi$
$14$	9.24401	2.47057
$15$	3.16917	0.818275
$16$	2.23100	0.557751
$17$	5.48855	1.33117	0.665584	−	0.746323i	$-0.268183\pi$
$17$	5.48855	1.33117	0.665584	+	0.746323i	$0.268183\pi$
$18$	5.13698	1.21080
$19$	−1.68327	−0.386169	−0.193085	−	0.981182i	$-0.561849\pi$
$19$	−1.68327	−0.386169	−0.193085	+	0.981182i	$0.561849\pi$
$20$	12.7087	2.84175
$21$	−3.56532	−0.778017
$22$	7.05734	1.50463
$23$	1.14696	0.239158	0.119579	−	0.992825i	$-0.461846\pi$
$23$	1.14696	0.239158	0.119579	+	0.992825i	$0.461846\pi$
$24$	−3.70614	−0.756512
$25$	6.86788	1.37358
$26$	16.8425	3.30309
$27$	−4.74110	−0.912424
$28$	−14.2973	−2.70194
$29$	7.01474	1.30260	0.651302	−	0.758819i	$-0.274223\pi$
$29$	7.01474	1.30260	0.651302	+	0.758819i	$0.274223\pi$
$30$	−7.55901	−1.38008
$31$	10.3580	1.86036	0.930178	−	0.367110i	$-0.119653\pi$
$31$	10.3580	1.86036	0.930178	+	0.367110i	$0.119653\pi$
$32$	2.73604	0.483668
$33$	−2.72195	−0.473830
$34$	−13.0911	−2.24511
$35$	−13.3514	−2.25680
$36$	−7.94517	−1.32419
$37$	−10.6986	−1.75884	−0.879421	−	0.476045i	$-0.842070\pi$
$37$	−10.6986	−1.75884	−0.879421	+	0.476045i	$0.842070\pi$
$38$	4.01490	0.651302
$39$	−6.49598	−1.04019
$40$	−13.8787	−2.19442
$41$	−6.98313	−1.09058	−0.545291	−	0.838247i	$-0.683581\pi$
$41$	−6.98313	−1.09058	−0.545291	+	0.838247i	$0.683581\pi$
$42$	8.50391	1.31218
$43$	−4.35611	−0.664300	−0.332150	−	0.943227i	$-0.607774\pi$
$43$	−4.35611	−0.664300	−0.332150	+	0.943227i	$0.607774\pi$
$44$	−10.9153	−1.64554
$45$	−7.41950	−1.10603
$46$	−2.73570	−0.403357
$47$	0.995509	0.145210	0.0726049	−	0.997361i	$-0.476869\pi$
$47$	0.995509	0.145210	0.0726049	+	0.997361i	$0.476869\pi$
$48$	2.05238	0.296236
$49$	8.02038	1.14577
$50$	−16.3811	−2.31664
$51$	5.04912	0.707018
$52$	−26.0496	−3.61243
$53$	14.3843	1.97583	0.987916	−	0.154991i	$-0.0495349\pi$
$53$	14.3843	1.97583	0.987916	+	0.154991i	$0.0495349\pi$
$54$	11.3083	1.53887
$55$	−10.1931	−1.37444
$56$	15.6136	2.08646
$57$	−1.54851	−0.205105
$58$	−16.7314	−2.19694
$59$	1.51056	0.196658	0.0983291	−	0.995154i	$-0.468650\pi$
$59$	1.51056	0.196658	0.0983291	+	0.995154i	$0.468650\pi$
$60$	11.6912	1.50933
$61$	3.59272	0.460001	0.230000	−	0.973191i	$-0.426127\pi$
$61$	3.59272	0.460001	0.230000	+	0.973191i	$0.426127\pi$
$62$	−24.7057	−3.13762
$63$	8.34696	1.05162
$64$	−10.9879	−1.37349
$65$	−24.3261	−3.01729
$66$	6.49232	0.799149
$67$	1.34754	0.164628	0.0823139	−	0.996606i	$-0.473769\pi$
$67$	1.34754	0.164628	0.0823139	+	0.996606i	$0.473769\pi$
$68$	20.2475	2.45537
$69$	1.05513	0.127023
$70$	31.8454	3.80626
$71$	2.71774	0.322537	0.161268	−	0.986911i	$-0.448442\pi$
$71$	2.71774	0.322537	0.161268	+	0.986911i	$0.448442\pi$
$72$	8.67663	1.02255
$73$	−13.8312	−1.61882	−0.809409	−	0.587245i	$-0.800213\pi$
$73$	−13.8312	−1.61882	−0.809409	+	0.587245i	$0.800213\pi$
$74$	25.5181	2.96641
$75$	6.31803	0.729543
$76$	−6.20968	−0.712299
$77$	11.4673	1.30682
$78$	15.4940	1.75436
$79$	2.81997	0.317271	0.158636	−	0.987337i	$-0.449291\pi$
$79$	2.81997	0.317271	0.158636	+	0.987337i	$0.449291\pi$
$80$	7.68576	0.859294
$81$	2.09963	0.233292
$82$	16.6560	1.83935
$83$	12.1277	1.33118	0.665592	−	0.746316i	$-0.268179\pi$
$83$	12.1277	1.33118	0.665592	+	0.746316i	$0.268179\pi$
$84$	−13.1527	−1.43507
$85$	18.9079	2.05085
$86$	10.3901	1.12039
$87$	6.45312	0.691847
$88$	11.9202	1.27070
$89$	14.7548	1.56400	0.782000	−	0.623278i	$-0.214199\pi$
$89$	14.7548	1.56400	0.782000	+	0.623278i	$0.214199\pi$
$90$	17.6968	1.86541
$91$	27.3670	2.86884
$92$	4.23120	0.441133
$93$	9.52873	0.988084
$94$	−2.37446	−0.244907
$95$	−5.79884	−0.594948
$96$	2.51698	0.256889
$97$	−16.0606	−1.63071	−0.815353	−	0.578964i	$-0.803457\pi$
$97$	−16.0606	−1.63071	−0.815353	+	0.578964i	$0.803457\pi$
$98$	−19.1300	−1.93242
$99$	6.37249	0.640460
$100$	25.3360	2.53360
$101$	−13.2655	−1.31996	−0.659981	−	0.751282i	$-0.729436\pi$
$101$	−13.2655	−1.31996	−0.659981	+	0.751282i	$0.729436\pi$
$102$	−12.0430	−1.19244
$103$	5.62495	0.554243	0.277121	−	0.960835i	$-0.410620\pi$
$103$	5.62495	0.554243	0.277121	+	0.960835i	$0.410620\pi$
$104$	28.4479	2.78954
$105$	−12.2825	−1.19865
$106$	−34.3090	−3.33238
$107$	13.1839	1.27454	0.637270	−	0.770641i	$-0.280064\pi$
$107$	13.1839	1.27454	0.637270	+	0.770641i	$0.280064\pi$
$108$	−17.4902	−1.68299
$109$	−6.15206	−0.589260	−0.294630	−	0.955611i	$-0.595196\pi$
$109$	−6.15206	−0.589260	−0.294630	+	0.955611i	$0.595196\pi$
$110$	24.3124	2.31810
$111$	−9.84206	−0.934167
$112$	−8.64650	−0.817018
$113$	0.726324	0.0683268	0.0341634	−	0.999416i	$-0.489123\pi$
$113$	0.726324	0.0683268	0.0341634	+	0.999416i	$0.489123\pi$
$114$	3.69346	0.345924
$115$	3.95125	0.368456
$116$	25.8777	2.40269
$117$	15.2081	1.40599
$118$	−3.60295	−0.331678
$119$	−21.2715	−1.94995
$120$	−12.7676	−1.16551
$121$	−2.24527	−0.204116
$122$	−8.56927	−0.775825
$123$	−6.42405	−0.579237
$124$	38.2113	3.43147
$125$	6.43482	0.575548
$126$	−19.9090	−1.77363
$127$	−6.85413	−0.608206	−0.304103	−	0.952639i	$-0.598357\pi$
$127$	−6.85413	−0.608206	−0.304103	+	0.952639i	$0.598357\pi$
$128$	20.7360	1.83282
$129$	−4.00735	−0.352827
$130$	58.0221	5.08887
$131$	20.4690	1.78839	0.894193	−	0.447682i	$-0.147750\pi$
$131$	20.4690	1.78839	0.894193	+	0.447682i	$0.147750\pi$
$132$	−10.0414	−0.873992
$133$	6.52371	0.565678
$134$	−3.21411	−0.277657
$135$	−16.3330	−1.40572
$136$	−22.1116	−1.89605
$137$	7.37733	0.630288	0.315144	−	0.949044i	$-0.397947\pi$
$137$	7.37733	0.630288	0.315144	+	0.949044i	$0.397947\pi$
$138$	−2.51667	−0.214233
$139$	4.48704	0.380586	0.190293	−	0.981727i	$-0.439056\pi$
$139$	4.48704	0.380586	0.190293	+	0.981727i	$0.439056\pi$
$140$	−49.2540	−4.16273
$141$	0.915806	0.0771248
$142$	−6.48229	−0.543981
$143$	20.8933	1.74719
$144$	−4.80494	−0.400412
$145$	24.1656	2.00685
$146$	32.9898	2.73026
$147$	7.37825	0.608548
$148$	−39.4678	−3.24423
$149$	2.66554	0.218369	0.109185	−	0.994021i	$-0.465176\pi$
$149$	2.66554	0.218369	0.109185	+	0.994021i	$0.465176\pi$
$150$	−15.0696	−1.23043
$151$	11.3160	0.920886	0.460443	−	0.887689i	$-0.347691\pi$
$151$	11.3160	0.920886	0.460443	+	0.887689i	$0.347691\pi$
$152$	6.78137	0.550042
$153$	−11.8208	−0.955652
$154$	−27.3515	−2.20405
$155$	35.6832	2.86614
$156$	−23.9640	−1.91866
$157$	20.1845	1.61090	0.805450	−	0.592664i	$-0.201924\pi$
$157$	20.1845	1.61090	0.805450	+	0.592664i	$0.201924\pi$
$158$	−6.72611	−0.535101
$159$	13.2326	1.04942
$160$	9.42560	0.745159
$161$	−4.44517	−0.350329
$162$	−5.00798	−0.393464
$163$	10.3022	0.806933	0.403467	−	0.914994i	$-0.367805\pi$
$163$	10.3022	0.806933	0.403467	+	0.914994i	$0.367805\pi$
$164$	−25.7611	−2.01161
$165$	−9.37705	−0.730003
$166$	−28.9266	−2.24514
$167$	−8.22506	−0.636474	−0.318237	−	0.948011i	$-0.603091\pi$
$167$	−8.22506	−0.636474	−0.318237	+	0.948011i	$0.603091\pi$
$168$	14.3636	1.10817
$169$	36.8624	2.83557
$170$	−45.0987	−3.45891
$171$	3.62529	0.277233
$172$	−16.0699	−1.22532
$173$	−4.98538	−0.379032	−0.189516	−	0.981878i	$-0.560692\pi$
$173$	−4.98538	−0.379032	−0.189516	+	0.981878i	$0.560692\pi$
$174$	−15.3918	−1.16685
$175$	−26.6173	−2.01208
$176$	−6.60118	−0.497582
$177$	1.38962	0.104450
$178$	−35.1927	−2.63780
$179$	8.42514	0.629724	0.314862	−	0.949137i	$-0.398042\pi$
$179$	8.42514	0.629724	0.314862	+	0.949137i	$0.398042\pi$
$180$	−27.3709	−2.04011
$181$	−9.11980	−0.677870	−0.338935	−	0.940810i	$-0.610067\pi$
$181$	−9.11980	−0.677870	−0.338935	+	0.940810i	$0.610067\pi$
$182$	−65.2750	−4.83851
$183$	3.30508	0.244319
$184$	−4.62074	−0.340645
$185$	−36.8565	−2.70975
$186$	−22.7277	−1.66647
$187$	−16.2397	−1.18757
$188$	3.67248	0.267843
$189$	18.3747	1.33656
$190$	13.8312	1.00342
$191$	8.99307	0.650716	0.325358	−	0.945591i	$-0.394515\pi$
$191$	8.99307	0.650716	0.325358	+	0.945591i	$0.394515\pi$
$192$	−10.1082	−0.729497
$193$	−7.20174	−0.518393	−0.259196	−	0.965825i	$-0.583458\pi$
$193$	−7.20174	−0.518393	−0.259196	+	0.965825i	$0.583458\pi$
$194$	38.3073	2.75030
$195$	−22.3785	−1.60256
$196$	29.5876	2.11340
$197$	−11.0169	−0.784920	−0.392460	−	0.919769i	$-0.628376\pi$
$197$	−11.0169	−0.784920	−0.392460	+	0.919769i	$0.628376\pi$
$198$	−15.1995	−1.08018
$199$	25.0009	1.77226	0.886132	−	0.463433i	$-0.153383\pi$
$199$	25.0009	1.77226	0.886132	+	0.463433i	$0.153383\pi$
$200$	−27.6685	−1.95646
$201$	1.23965	0.0874381
$202$	31.6404	2.22621
$203$	−27.1864	−1.90811
$204$	18.6265	1.30411
$205$	−24.0568	−1.68020
$206$	−13.4165	−0.934770
$207$	−2.47023	−0.171693
$208$	−15.7538	−1.09233
$209$	4.98053	0.344511
$210$	29.2958	2.02160
$211$	11.2138	0.771989	0.385994	−	0.922501i	$-0.373858\pi$
$211$	11.2138	0.771989	0.385994	+	0.922501i	$0.373858\pi$
$212$	53.0643	3.64447
$213$	2.50015	0.171308
$214$	−31.4460	−2.14960
$215$	−15.0067	−1.02345
$216$	19.1004	1.29962
$217$	−40.1437	−2.72513
$218$	14.6737	0.993830
$219$	−12.7238	−0.859797
$220$	−37.6030	−2.53520
$221$	−38.7564	−2.60704
$222$	23.4750	1.57554
$223$	14.4478	0.967497	0.483749	−	0.875207i	$-0.339275\pi$
$223$	14.4478	0.967497	0.483749	+	0.875207i	$0.339275\pi$
$224$	−10.6038	−0.708498
$225$	−14.7915	−0.986097
$226$	−1.73241	−0.115238
$227$	20.0752	1.33244	0.666218	−	0.745757i	$-0.267912\pi$
$227$	20.0752	1.33244	0.666218	+	0.745757i	$0.267912\pi$
$228$	−5.71252	−0.378321
$229$	−9.32123	−0.615964	−0.307982	−	0.951392i	$-0.599654\pi$
$229$	−9.32123	−0.615964	−0.307982	+	0.951392i	$0.599654\pi$
$230$	−9.42443	−0.621428
$231$	10.5492	0.694087
$232$	−28.2601	−1.85537
$233$	12.4891	0.818187	0.409094	−	0.912492i	$-0.365845\pi$
$233$	12.4891	0.818187	0.409094	+	0.912492i	$0.365845\pi$
$234$	−36.2739	−2.37130
$235$	3.42951	0.223716
$236$	5.57254	0.362741
$237$	2.59419	0.168511
$238$	50.7362	3.28874
$239$	−7.75431	−0.501584	−0.250792	−	0.968041i	$-0.580691\pi$
$239$	−7.75431	−0.501584	−0.250792	+	0.968041i	$0.580691\pi$
$240$	7.07042	0.456393
$241$	15.3284	0.987390	0.493695	−	0.869635i	$-0.335646\pi$
$241$	15.3284	0.987390	0.493695	+	0.869635i	$0.335646\pi$
$242$	5.35537	0.344256
$243$	16.1548	1.03633
$244$	13.2537	0.848484
$245$	27.6300	1.76522
$246$	15.3225	0.976925
$247$	11.8861	0.756297
$248$	−41.7292	−2.64981
$249$	11.1567	0.707026
$250$	−15.3482	−0.970703
$251$	−18.1003	−1.14248	−0.571242	−	0.820782i	$-0.693538\pi$
$251$	−18.1003	−1.14248	−0.571242	+	0.820782i	$0.693538\pi$
$252$	30.7924	1.93974
$253$	−3.39367	−0.213358
$254$	16.3483	1.02578
$255$	17.3941	1.08926
$256$	−27.4832	−1.71770
$257$	9.91405	0.618421	0.309211	−	0.950994i	$-0.399935\pi$
$257$	9.91405	0.618421	0.309211	+	0.950994i	$0.399935\pi$
$258$	9.55822	0.595069
$259$	41.4637	2.57643
$260$	−89.7404	−5.56546
$261$	−15.1077	−0.935146
$262$	−48.8221	−3.01624
$263$	−27.4873	−1.69494	−0.847470	−	0.530844i	$-0.821875\pi$
$263$	−27.4873	−1.69494	−0.847470	+	0.530844i	$0.821875\pi$
$264$	10.9659	0.674902
$265$	49.5535	3.04405
$266$	−15.5602	−0.954056
$267$	13.5735	0.830682
$268$	4.97113	0.303660
$269$	−19.7128	−1.20191	−0.600954	−	0.799284i	$-0.705213\pi$
$269$	−19.7128	−1.20191	−0.600954	+	0.799284i	$0.705213\pi$
$270$	38.9570	2.37085
$271$	−8.83538	−0.536711	−0.268356	−	0.963320i	$-0.586480\pi$
$271$	−8.83538	−0.536711	−0.268356	+	0.963320i	$0.586480\pi$
$272$	12.2450	0.742459
$273$	25.1759	1.52372
$274$	−17.5962	−1.06303
$275$	−20.3210	−1.22540
$276$	3.89244	0.234297
$277$	13.5529	0.814312	0.407156	−	0.913359i	$-0.366521\pi$
$277$	13.5529	0.814312	0.407156	+	0.913359i	$0.366521\pi$
$278$	−10.7024	−0.641885
$279$	−22.3082	−1.33556
$280$	53.7886	3.21448
$281$	6.81637	0.406630	0.203315	−	0.979113i	$-0.434828\pi$
$281$	6.81637	0.406630	0.203315	+	0.979113i	$0.434828\pi$
$282$	−2.18436	−0.130077
$283$	5.25860	0.312591	0.156296	−	0.987710i	$-0.450045\pi$
$283$	5.25860	0.312591	0.156296	+	0.987710i	$0.450045\pi$
$284$	10.0259	0.594927
$285$	−5.33457	−0.315993
$286$	−49.8342	−2.94676
$287$	27.0639	1.59753
$288$	−5.89265	−0.347227
$289$	13.1241	0.772008
$290$	−57.6392	−3.38469
$291$	−14.7747	−0.866111
$292$	−51.0240	−2.98595
$293$	−28.6122	−1.67154	−0.835771	−	0.549078i	$-0.814979\pi$
$293$	−28.6122	−1.67154	−0.835771	+	0.549078i	$0.814979\pi$
$294$	−17.5984	−1.02636
$295$	5.20385	0.302980
$296$	43.1013	2.50521
$297$	14.0281	0.813995
$298$	−6.35776	−0.368295
$299$	−8.09907	−0.468381
$300$	23.3075	1.34566
$301$	16.8826	0.973096
$302$	−26.9907	−1.55314
$303$	−12.2034	−0.701067
$304$	−3.75538	−0.215386
$305$	12.3769	0.708697
$306$	28.1946	1.61178
$307$	22.0597	1.25902	0.629508	−	0.776994i	$-0.283257\pi$
$307$	22.0597	1.25902	0.629508	+	0.776994i	$0.283257\pi$
$308$	42.3035	2.41047
$309$	5.17460	0.294373
$310$	−85.1105	−4.83395
$311$	20.7875	1.17875	0.589375	−	0.807859i	$-0.299374\pi$
$311$	20.7875	1.17875	0.589375	+	0.807859i	$0.299374\pi$
$312$	26.1703	1.48160
$313$	2.43463	0.137613	0.0688066	−	0.997630i	$-0.478081\pi$
$313$	2.43463	0.137613	0.0688066	+	0.997630i	$0.478081\pi$
$314$	−48.1436	−2.71690
$315$	28.7551	1.62017
$316$	10.4030	0.585215
$317$	0.489184	0.0274753	0.0137377	−	0.999906i	$-0.495627\pi$
$317$	0.489184	0.0274753	0.0137377	+	0.999906i	$0.495627\pi$
$318$	−31.5621	−1.76992
$319$	−20.7555	−1.16208
$320$	−37.8532	−2.11606
$321$	12.1284	0.676942
$322$	10.6025	0.590855
$323$	−9.23872	−0.514056
$324$	7.74565	0.430314
$325$	−48.4964	−2.69010
$326$	−24.5726	−1.36095
$327$	−5.65951	−0.312972
$328$	28.1328	1.55338
$329$	−3.85821	−0.212710
$330$	22.3659	1.23120
$331$	6.09099	0.334791	0.167396	−	0.985890i	$-0.446464\pi$
$331$	6.09099	0.334791	0.167396	+	0.985890i	$0.446464\pi$
$332$	44.7396	2.45540
$333$	23.0418	1.26268
$334$	19.6182	1.07346
$335$	4.64224	0.253632
$336$	−7.95424	−0.433940
$337$	−7.24223	−0.394510	−0.197255	−	0.980352i	$-0.563203\pi$
$337$	−7.24223	−0.394510	−0.197255	+	0.980352i	$0.563203\pi$
$338$	−87.9232	−4.78239
$339$	0.668173	0.0362901
$340$	69.7523	3.78285
$341$	−30.6477	−1.65967
$342$	−8.64694	−0.467573
$343$	−3.95459	−0.213528
$344$	17.5494	0.946199
$345$	3.63491	0.195697
$346$	11.8910	0.639264
$347$	22.5941	1.21291	0.606457	−	0.795116i	$-0.292590\pi$
$347$	22.5941	1.21291	0.606457	+	0.795116i	$0.292590\pi$
$348$	23.8059	1.27613
$349$	25.3100	1.35481	0.677406	−	0.735609i	$-0.263104\pi$
$349$	25.3100	1.35481	0.677406	+	0.735609i	$0.263104\pi$
$350$	63.4868	3.39351
$351$	33.4784	1.78695
$352$	−8.09550	−0.431491
$353$	8.87134	0.472174	0.236087	−	0.971732i	$-0.424135\pi$
$353$	8.87134	0.472174	0.236087	+	0.971732i	$0.424135\pi$
$354$	−3.31449	−0.176163
$355$	9.36257	0.496913
$356$	54.4311	2.88484
$357$	−19.5684	−1.03567
$358$	−20.0954	−1.06208
$359$	22.0661	1.16461	0.582303	−	0.812972i	$-0.302152\pi$
$359$	22.0661	1.16461	0.582303	+	0.812972i	$0.302152\pi$
$360$	29.8908	1.57538
$361$	−16.1666	−0.850873
$362$	21.7523	1.14328
$363$	−2.06551	−0.108411
$364$	100.958	5.29165
$365$	−47.6482	−2.49402
$366$	−7.88319	−0.412061
$367$	30.9559	1.61589	0.807943	−	0.589261i	$-0.200581\pi$
$367$	30.9559	1.61589	0.807943	+	0.589261i	$0.200581\pi$
$368$	2.55887	0.133390
$369$	15.0397	0.782934
$370$	87.9092	4.57018
$371$	−55.7479	−2.89429
$372$	35.1520	1.82255
$373$	−0.825192	−0.0427268	−0.0213634	−	0.999772i	$-0.506801\pi$
$373$	−0.825192	−0.0427268	−0.0213634	+	0.999772i	$0.506801\pi$
$374$	38.7345	2.00292
$375$	5.91963	0.305689
$376$	−4.01059	−0.206830
$377$	−49.5334	−2.55110
$378$	−43.8267	−2.25420
$379$	−37.6837	−1.93568	−0.967842	−	0.251560i	$-0.919056\pi$
$379$	−37.6837	−1.93568	−0.967842	+	0.251560i	$0.919056\pi$
$380$	−21.3922	−1.09740
$381$	−6.30538	−0.323034
$382$	−21.4500	−1.09748
$383$	−19.9505	−1.01942	−0.509710	−	0.860346i	$-0.670247\pi$
$383$	−19.9505	−1.01942	−0.509710	+	0.860346i	$0.670247\pi$
$384$	19.0759	0.973461
$385$	39.5047	2.01334
$386$	17.1774	0.874307
$387$	9.38181	0.476904
$388$	−59.2484	−3.00788
$389$	35.2492	1.78721	0.893603	−	0.448859i	$-0.148169\pi$
$389$	35.2492	1.78721	0.893603	+	0.448859i	$0.148169\pi$
$390$	53.3767	2.70283
$391$	6.29514	0.318359
$392$	−32.3116	−1.63198
$393$	18.8302	0.949859
$394$	26.2772	1.32382
$395$	9.71473	0.488801
$396$	23.5085	1.18134
$397$	−8.29365	−0.416246	−0.208123	−	0.978103i	$-0.566736\pi$
$397$	−8.29365	−0.416246	−0.208123	+	0.978103i	$0.566736\pi$
$398$	−59.6314	−2.98905
$399$	6.00141	0.300446
$400$	15.3223	0.766113
$401$	10.6733	0.533002	0.266501	−	0.963835i	$-0.414132\pi$
$401$	10.6733	0.533002	0.266501	+	0.963835i	$0.414132\pi$
$402$	−2.95678	−0.147471
$403$	−73.1414	−3.64343
$404$	−48.9370	−2.43471
$405$	7.23318	0.359420
$406$	64.8443	3.21817
$407$	31.6555	1.56910
$408$	−20.3413	−1.00704
$409$	17.1692	0.848964	0.424482	−	0.905436i	$-0.360456\pi$
$409$	17.1692	0.848964	0.424482	+	0.905436i	$0.360456\pi$
$410$	57.3795	2.83377
$411$	6.78669	0.334763
$412$	20.7507	1.02231
$413$	−5.85435	−0.288074
$414$	5.89192	0.289572
$415$	41.7795	2.05088
$416$	−19.3201	−0.947244
$417$	4.12780	0.202139
$418$	−11.8794	−0.581042
$419$	15.9313	0.778296	0.389148	−	0.921175i	$-0.372770\pi$
$419$	15.9313	0.778296	0.389148	+	0.921175i	$0.372770\pi$
$420$	−45.3107	−2.21093
$421$	23.8058	1.16022	0.580112	−	0.814537i	$-0.303009\pi$
$421$	23.8058	1.16022	0.580112	+	0.814537i	$0.303009\pi$
$422$	−26.7468	−1.30201
$423$	−2.14404	−0.104247
$424$	−57.9497	−2.81428
$425$	37.6947	1.82846
$426$	−5.96330	−0.288923
$427$	−13.9240	−0.673830
$428$	48.6363	2.35092
$429$	19.2206	0.927978
$430$	35.7936	1.72612
$431$	−5.94187	−0.286210	−0.143105	−	0.989708i	$-0.545709\pi$
$431$	−5.94187	−0.286210	−0.143105	+	0.989708i	$0.545709\pi$
$432$	−10.5774	−0.508905
$433$	−22.0815	−1.06117	−0.530584	−	0.847633i	$-0.678027\pi$
$433$	−22.0815	−1.06117	−0.530584	+	0.847633i	$0.678027\pi$
$434$	95.7496	4.59613
$435$	22.2309	1.06589
$436$	−22.6953	−1.08691
$437$	−1.93065	−0.0923554
$438$	30.3486	1.45011
$439$	−21.3795	−1.02039	−0.510194	−	0.860059i	$-0.670427\pi$
$439$	−21.3795	−1.02039	−0.510194	+	0.860059i	$0.670427\pi$
$440$	41.0649	1.95769
$441$	−17.2736	−0.822553
$442$	92.4408	4.39696
$443$	−33.8298	−1.60730	−0.803650	−	0.595102i	$-0.797112\pi$
$443$	−33.8298	−1.60730	−0.803650	+	0.595102i	$0.797112\pi$
$444$	−36.3079	−1.72310
$445$	50.8298	2.40957
$446$	−34.4605	−1.63175
$447$	2.45213	0.115982
$448$	42.5850	2.01195
$449$	3.48225	0.164337	0.0821687	−	0.996618i	$-0.473815\pi$
$449$	3.48225	0.164337	0.0821687	+	0.996618i	$0.473815\pi$
$450$	35.2802	1.66312
$451$	20.6620	0.972934
$452$	2.67945	0.126031
$453$	10.4101	0.489107
$454$	−47.8828	−2.24725
$455$	94.2787	4.41985
$456$	6.23844	0.292142
$457$	34.1437	1.59717	0.798587	−	0.601879i	$-0.205581\pi$
$457$	34.1437	1.59717	0.798587	+	0.601879i	$0.205581\pi$
$458$	22.2327	1.03887
$459$	−26.0217	−1.21459
$460$	14.5764	0.679628
$461$	16.4780	0.767456	0.383728	−	0.923446i	$-0.374640\pi$
$461$	16.4780	0.767456	0.383728	+	0.923446i	$0.374640\pi$
$462$	−25.1617	−1.17063
$463$	−14.8724	−0.691180	−0.345590	−	0.938386i	$-0.612321\pi$
$463$	−14.8724	−0.691180	−0.345590	+	0.938386i	$0.612321\pi$
$464$	15.6499	0.726528
$465$	32.8263	1.52228
$466$	−29.7886	−1.37993
$467$	23.7337	1.09826	0.549132	−	0.835735i	$-0.314958\pi$
$467$	23.7337	1.09826	0.549132	+	0.835735i	$0.314958\pi$
$468$	56.1034	2.59338
$469$	−5.22253	−0.241154
$470$	−8.17997	−0.377314
$471$	18.5685	0.855591
$472$	−6.08557	−0.280111
$473$	12.8890	0.592638
$474$	−6.18760	−0.284206
$475$	−11.5605	−0.530433
$476$	−78.4716	−3.59674
$477$	−30.9796	−1.41846
$478$	18.4954	0.845958
$479$	−7.03361	−0.321374	−0.160687	−	0.987005i	$-0.551371\pi$
$479$	−7.03361	−0.321374	−0.160687	+	0.987005i	$0.551371\pi$
$480$	8.67096	0.395773
$481$	75.5465	3.44462
$482$	−36.5609	−1.66530
$483$	−4.08928	−0.186069
$484$	−8.28293	−0.376497
$485$	−55.3284	−2.51233
$486$	−38.5320	−1.74785
$487$	−25.6843	−1.16387	−0.581933	−	0.813237i	$-0.697703\pi$
$487$	−25.6843	−1.16387	−0.581933	+	0.813237i	$0.697703\pi$
$488$	−14.4739	−0.655204
$489$	9.47741	0.428583
$490$	−65.9024	−2.97717
$491$	−10.9719	−0.495155	−0.247577	−	0.968868i	$-0.579634\pi$
$491$	−10.9719	−0.495155	−0.247577	+	0.968868i	$0.579634\pi$
$492$	−23.6987	−1.06842
$493$	38.5007	1.73398
$494$	−28.3505	−1.27555
$495$	21.9531	0.986719
$496$	23.1088	1.03761
$497$	−10.5329	−0.472466
$498$	−26.6106	−1.19245
$499$	17.8819	0.800502	0.400251	−	0.916405i	$-0.368923\pi$
$499$	17.8819	0.800502	0.400251	+	0.916405i	$0.368923\pi$
$500$	23.7384	1.06161
$501$	−7.56654	−0.338048
$502$	43.1724	1.92688
$503$	−32.2881	−1.43966	−0.719828	−	0.694153i	$-0.755779\pi$
$503$	−32.2881	−1.43966	−0.719828	+	0.694153i	$0.755779\pi$
$504$	−33.6273	−1.49788
$505$	−45.6992	−2.03359
$506$	8.09449	0.359844
$507$	33.9111	1.50604
$508$	−25.2853	−1.12185
$509$	−39.2698	−1.74060	−0.870302	−	0.492518i	$-0.836077\pi$
$509$	−39.2698	−1.74060	−0.870302	+	0.492518i	$0.836077\pi$
$510$	−41.4880	−1.83712
$511$	53.6044	2.37132
$512$	24.0801	1.06420
$513$	7.98056	0.352350
$514$	−23.6467	−1.04301
$515$	19.3778	0.853889
$516$	−14.7833	−0.650799
$517$	−2.94555	−0.129545
$518$	−98.8981	−4.34533
$519$	−4.58624	−0.201314
$520$	98.0023	4.29768
$521$	41.4068	1.81407	0.907033	−	0.421059i	$-0.138341\pi$
$521$	41.4068	1.81407	0.907033	+	0.421059i	$0.138341\pi$
$522$	36.0346	1.57719
$523$	−6.51882	−0.285048	−0.142524	−	0.989791i	$-0.545522\pi$
$523$	−6.51882	−0.285048	−0.142524	+	0.989791i	$0.545522\pi$
$524$	75.5113	3.29872
$525$	−24.4862	−1.06867
$526$	65.5620	2.85864
$527$	56.8505	2.47645
$528$	−6.07267	−0.264279
$529$	−21.6845	−0.942804
$530$	−118.194	−5.13401
$531$	−3.25332	−0.141182
$532$	24.0663	1.04341
$533$	49.3102	2.13586
$534$	−32.3750	−1.40101
$535$	45.4184	1.96361
$536$	−5.42880	−0.234488
$537$	7.75060	0.334463
$538$	47.0183	2.02710
$539$	−23.7310	−1.02217
$540$	−60.2532	−2.59289
$541$	−26.9278	−1.15772	−0.578858	−	0.815429i	$-0.696501\pi$
$541$	−26.9278	−1.15772	−0.578858	+	0.815429i	$0.696501\pi$
$542$	21.0739	0.905202
$543$	−8.38965	−0.360034
$544$	15.0169	0.643843
$545$	−21.1937	−0.907839
$546$	−60.0489	−2.56986
$547$	−32.7115	−1.39864	−0.699321	−	0.714808i	$-0.746514\pi$
$547$	−32.7115	−1.39864	−0.699321	+	0.714808i	$0.746514\pi$
$548$	27.2154	1.16258
$549$	−7.73770	−0.330237
$550$	48.4690	2.06673
$551$	−11.8077	−0.503025
$552$	−4.25079	−0.180926
$553$	−10.9291	−0.464753
$554$	−32.3259	−1.37340
$555$	−33.9057	−1.43922
$556$	16.5529	0.702000
$557$	23.3466	0.989228	0.494614	−	0.869113i	$-0.335309\pi$
$557$	23.3466	0.989228	0.494614	+	0.869113i	$0.335309\pi$
$558$	53.2090	2.25252
$559$	30.7599	1.30101
$560$	−29.7870	−1.25873
$561$	−14.9395	−0.630747
$562$	−16.2582	−0.685812
$563$	4.56015	0.192187	0.0960937	−	0.995372i	$-0.469365\pi$
$563$	4.56015	0.192187	0.0960937	+	0.995372i	$0.469365\pi$
$564$	3.37846	0.142259
$565$	2.50217	0.105267
$566$	−12.5427	−0.527207
$567$	−8.13735	−0.341737
$568$	−10.9489	−0.459407
$569$	34.5145	1.44692	0.723462	−	0.690364i	$-0.242550\pi$
$569$	34.5145	1.44692	0.723462	+	0.690364i	$0.242550\pi$
$570$	12.7239	0.532945
$571$	−25.2619	−1.05718	−0.528589	−	0.848878i	$-0.677279\pi$
$571$	−25.2619	−1.05718	−0.528589	+	0.848878i	$0.677279\pi$
$572$	77.0766	3.22273
$573$	8.27307	0.345612
$574$	−64.5522	−2.69436
$575$	7.87719	0.328502
$576$	23.6649	0.986036
$577$	−15.0159	−0.625120	−0.312560	−	0.949898i	$-0.601187\pi$
$577$	−15.0159	−0.625120	−0.312560	+	0.949898i	$0.601187\pi$
$578$	−31.3033	−1.30205
$579$	−6.62515	−0.275332
$580$	89.1482	3.70168
$581$	−47.0021	−1.94998
$582$	35.2403	1.46076
$583$	−42.5607	−1.76269
$584$	55.7215	2.30577
$585$	52.3916	2.16612
$586$	68.2450	2.81918
$587$	24.9292	1.02894	0.514469	−	0.857509i	$-0.327989\pi$
$587$	24.9292	1.02894	0.514469	+	0.857509i	$0.327989\pi$
$588$	27.2187	1.12248
$589$	−17.4354	−0.718412
$590$	−12.4121	−0.510997
$591$	−10.1348	−0.416892
$592$	−23.8686	−0.980995
$593$	−46.2621	−1.89976	−0.949879	−	0.312617i	$-0.898794\pi$
$593$	−46.2621	−1.89976	−0.949879	+	0.312617i	$0.898794\pi$
$594$	−33.4595	−1.37286
$595$	−73.2798	−3.00418
$596$	9.83330	0.402788
$597$	22.9992	0.941296
$598$	19.3177	0.789959
$599$	43.2281	1.76625	0.883127	−	0.469134i	$-0.155434\pi$
$599$	43.2281	1.76625	0.883127	+	0.469134i	$0.155434\pi$
$600$	−25.4533	−1.03913
$601$	−2.56879	−0.104783	−0.0523916	−	0.998627i	$-0.516684\pi$
$601$	−2.56879	−0.104783	−0.0523916	+	0.998627i	$0.516684\pi$
$602$	−40.2679	−1.64120
$603$	−2.90221	−0.118187
$604$	41.7455	1.69860
$605$	−7.73492	−0.314469
$606$	29.1072	1.18240
$607$	13.7290	0.557243	0.278622	−	0.960401i	$-0.410122\pi$
$607$	13.7290	0.557243	0.278622	+	0.960401i	$0.410122\pi$
$608$	−4.60550	−0.186778
$609$	−25.0098	−1.01345
$610$	−29.5209	−1.19527
$611$	−7.02962	−0.284388
$612$	−43.6074	−1.76272
$613$	34.0785	1.37642	0.688208	−	0.725513i	$-0.258397\pi$
$613$	34.0785	1.37642	0.688208	+	0.725513i	$0.258397\pi$
$614$	−52.6163	−2.12342
$615$	−22.1307	−0.892397
$616$	−46.1982	−1.86138
$617$	−31.6656	−1.27481	−0.637404	−	0.770530i	$-0.719992\pi$
$617$	−31.6656	−1.27481	−0.637404	+	0.770530i	$0.719992\pi$
$618$	−12.3423	−0.496481
$619$	−28.2460	−1.13530	−0.567650	−	0.823270i	$-0.692147\pi$
$619$	−28.2460	−1.13530	−0.567650	+	0.823270i	$0.692147\pi$
$620$	131.637	5.28667
$621$	−5.43785	−0.218213
$622$	−49.5818	−1.98805
$623$	−57.1837	−2.29102
$624$	−14.4926	−0.580166
$625$	−12.1716	−0.486864
$626$	−5.80701	−0.232095
$627$	4.58178	0.182979
$628$	74.4617	2.97135
$629$	−58.7199	−2.34131
$630$	−68.5860	−2.73253
$631$	15.4405	0.614677	0.307338	−	0.951600i	$-0.400562\pi$
$631$	15.4405	0.614677	0.307338	+	0.951600i	$0.400562\pi$
$632$	−11.3608	−0.451907
$633$	10.3160	0.410023
$634$	−1.16679	−0.0463391
$635$	−23.6124	−0.937028
$636$	48.8159	1.93568
$637$	−56.6345	−2.24394
$638$	49.5054	1.95994
$639$	−5.85324	−0.231551
$640$	71.4352	2.82373
$641$	−7.43140	−0.293523	−0.146761	−	0.989172i	$-0.546885\pi$
$641$	−7.43140	−0.293523	−0.146761	+	0.989172i	$0.546885\pi$
$642$	−28.9284	−1.14171
$643$	22.1881	0.875014	0.437507	−	0.899215i	$-0.355862\pi$
$643$	22.1881	0.875014	0.437507	+	0.899215i	$0.355862\pi$
$644$	−16.3985	−0.646191
$645$	−13.8052	−0.543580
$646$	22.0359	0.866993
$647$	−22.7674	−0.895078	−0.447539	−	0.894264i	$-0.647699\pi$
$647$	−22.7674	−0.895078	−0.447539	+	0.894264i	$0.647699\pi$
$648$	−8.45874	−0.332291
$649$	−4.46951	−0.175443
$650$	115.672	4.53704
$651$	−36.9297	−1.44739
$652$	38.0055	1.48841
$653$	−9.26530	−0.362579	−0.181290	−	0.983430i	$-0.558027\pi$
$653$	−9.26530	−0.362579	−0.181290	+	0.983430i	$0.558027\pi$
$654$	13.4989	0.527849
$655$	70.5153	2.75526
$656$	−15.5794	−0.608273
$657$	29.7884	1.16216
$658$	9.20249	0.358750
$659$	34.4367	1.34146	0.670732	−	0.741700i	$-0.265980\pi$
$659$	34.4367	1.34146	0.670732	+	0.741700i	$0.265980\pi$
$660$	−34.5924	−1.34651
$661$	−3.58711	−0.139522	−0.0697612	−	0.997564i	$-0.522224\pi$
$661$	−3.58711	−0.139522	−0.0697612	+	0.997564i	$0.522224\pi$
$662$	−14.5281	−0.564649
$663$	−35.6535	−1.38467
$664$	−48.8585	−1.89608
$665$	22.4741	0.871507
$666$	−54.9586	−2.12960
$667$	8.04562	0.311528
$668$	−30.3427	−1.17399
$669$	13.2911	0.513863
$670$	−11.0725	−0.427769
$671$	−10.6303	−0.410378
$672$	−9.75486	−0.376302
$673$	−4.26607	−0.164445	−0.0822225	−	0.996614i	$-0.526202\pi$
$673$	−4.26607	−0.164445	−0.0822225	+	0.996614i	$0.526202\pi$
$674$	17.2740	0.665369
$675$	−32.5613	−1.25328
$676$	135.987	5.23028
$677$	−26.7235	−1.02707	−0.513533	−	0.858070i	$-0.671664\pi$
$677$	−26.7235	−1.02707	−0.513533	+	0.858070i	$0.671664\pi$
$678$	−1.59371	−0.0612060
$679$	62.2446	2.38873
$680$	−76.1740	−2.92114
$681$	18.4679	0.707692
$682$	73.1001	2.79915
$683$	−12.8006	−0.489802	−0.244901	−	0.969548i	$-0.578755\pi$
$683$	−12.8006	−0.489802	−0.244901	+	0.969548i	$0.578755\pi$
$684$	13.3739	0.511363
$685$	25.4148	0.971048
$686$	9.43239	0.360130
$687$	−8.57495	−0.327155
$688$	−9.71848	−0.370514
$689$	−101.572	−3.86959
$690$	−8.66989	−0.330057
$691$	25.3653	0.964940	0.482470	−	0.875913i	$-0.339740\pi$
$691$	25.3653	0.964940	0.482470	+	0.875913i	$0.339740\pi$
$692$	−18.3913	−0.699134
$693$	−24.6973	−0.938174
$694$	−53.8908	−2.04567
$695$	15.4578	0.586346
$696$	−25.9976	−0.985435
$697$	−38.3272	−1.45175
$698$	−60.3687	−2.28499
$699$	11.4892	0.434561
$700$	−98.1925	−3.71133
$701$	6.26945	0.236794	0.118397	−	0.992966i	$-0.462224\pi$
$701$	6.26945	0.236794	0.118397	+	0.992966i	$0.462224\pi$
$702$	−79.8519	−3.01382
$703$	18.0087	0.679211
$704$	32.5115	1.22532
$705$	3.15493	0.118822
$706$	−21.1597	−0.796356
$707$	51.4118	1.93354
$708$	5.12639	0.192661
$709$	−23.2815	−0.874354	−0.437177	−	0.899376i	$-0.644022\pi$
$709$	−23.2815	−0.874354	−0.437177	+	0.899376i	$0.644022\pi$
$710$	−22.3313	−0.838080
$711$	−6.07341	−0.227771
$712$	−59.4422	−2.22769
$713$	11.8802	0.444918
$714$	46.6741	1.74673
$715$	71.9771	2.69179
$716$	31.0808	1.16154
$717$	−7.13348	−0.266405
$718$	−52.6315	−1.96419
$719$	36.0213	1.34337	0.671684	−	0.740838i	$-0.265571\pi$
$719$	36.0213	1.34337	0.671684	+	0.740838i	$0.265571\pi$
$720$	−16.5529	−0.616891
$721$	−21.8001	−0.811879
$722$	38.5601	1.43506
$723$	14.1012	0.524429
$724$	−33.6434	−1.25035
$725$	48.1764	1.78923
$726$	4.92660	0.182843
$727$	−25.1945	−0.934411	−0.467206	−	0.884149i	$-0.654739\pi$
$727$	−25.1945	−0.934411	−0.467206	+	0.884149i	$0.654739\pi$
$728$	−110.253	−4.08624
$729$	8.56254	0.317131
$730$	113.649	4.20634
$731$	−23.9087	−0.884295
$732$	12.1926	0.450652
$733$	−24.7606	−0.914555	−0.457277	−	0.889324i	$-0.651175\pi$
$733$	−24.7606	−0.914555	−0.457277	+	0.889324i	$0.651175\pi$
$734$	−73.8352	−2.72531
$735$	25.4179	0.937554
$736$	3.13813	0.115673
$737$	−3.98714	−0.146868
$738$	−35.8722	−1.32048
$739$	−6.02063	−0.221472	−0.110736	−	0.993850i	$-0.535321\pi$
$739$	−6.02063	−0.221472	−0.110736	+	0.993850i	$0.535321\pi$
$740$	−135.966	−4.99820
$741$	10.9345	0.401689
$742$	132.968	4.88142
$743$	4.05351	0.148709	0.0743545	−	0.997232i	$-0.476310\pi$
$743$	4.05351	0.148709	0.0743545	+	0.997232i	$0.476310\pi$
$744$	−38.3882	−1.40738
$745$	9.18272	0.336429
$746$	1.96823	0.0720619
$747$	−26.1195	−0.955663
$748$	−59.9092	−2.19050
$749$	−51.0959	−1.86700
$750$	−14.1194	−0.515566
$751$	15.3833	0.561344	0.280672	−	0.959804i	$-0.409443\pi$
$751$	15.3833	0.561344	0.280672	+	0.959804i	$0.409443\pi$
$752$	2.22098	0.0809909
$753$	−16.6512	−0.606803
$754$	118.146	4.30261
$755$	38.9835	1.41876
$756$	67.7851	2.46532
$757$	−45.2575	−1.64491	−0.822456	−	0.568829i	$-0.807397\pi$
$757$	−45.2575	−1.64491	−0.822456	+	0.568829i	$0.807397\pi$
$758$	89.8822	3.26467
$759$	−3.12197	−0.113320
$760$	23.3617	0.847417
$761$	15.1241	0.548248	0.274124	−	0.961694i	$-0.411612\pi$
$761$	15.1241	0.548248	0.274124	+	0.961694i	$0.411612\pi$
$762$	15.0394	0.544821
$763$	23.8430	0.863174
$764$	33.1759	1.20026
$765$	−40.7223	−1.47232
$766$	47.5853	1.71933
$767$	−10.6666	−0.385147
$768$	−25.2828	−0.912316
$769$	3.26777	0.117839	0.0589193	−	0.998263i	$-0.481235\pi$
$769$	3.26777	0.117839	0.0589193	+	0.998263i	$0.481235\pi$
$770$	−94.2255	−3.39565
$771$	9.12031	0.328460
$772$	−26.5676	−0.956189
$773$	22.0600	0.793442	0.396721	−	0.917939i	$-0.370148\pi$
$773$	22.0600	0.793442	0.396721	+	0.917939i	$0.370148\pi$
$774$	−22.3772	−0.804334
$775$	71.1377	2.55534
$776$	64.7030	2.32270
$777$	38.1440	1.36841
$778$	−84.0755	−3.01425
$779$	11.7545	0.421149
$780$	−82.5556	−2.95596
$781$	−8.04136	−0.287743
$782$	−15.0150	−0.536936
$783$	−33.2575	−1.18853
$784$	17.8935	0.639053
$785$	69.5352	2.48182
$786$	−44.9133	−1.60201
$787$	−10.7240	−0.382271	−0.191135	−	0.981564i	$-0.561217\pi$
$787$	−10.7240	−0.382271	−0.191135	+	0.981564i	$0.561217\pi$
$788$	−40.6418	−1.44781
$789$	−25.2866	−0.900227
$790$	−23.1713	−0.824399
$791$	−2.81495	−0.100088
$792$	−25.6728	−0.912242
$793$	−25.3694	−0.900894
$794$	19.7818	0.702030
$795$	45.5862	1.61677
$796$	92.2295	3.26899
$797$	−11.0115	−0.390047	−0.195023	−	0.980799i	$-0.562478\pi$
$797$	−11.0115	−0.390047	−0.195023	+	0.980799i	$0.562478\pi$
$798$	−14.3144	−0.506724
$799$	5.46389	0.193299
$800$	18.7908	0.664355
$801$	−31.7775	−1.12280
$802$	−25.4578	−0.898946
$803$	40.9243	1.44419
$804$	4.57313	0.161282
$805$	−15.3135	−0.539731
$806$	174.455	6.14491
$807$	−18.1345	−0.638365
$808$	53.4423	1.88010
$809$	−32.4502	−1.14089	−0.570443	−	0.821337i	$-0.693229\pi$
$809$	−32.4502	−1.14089	−0.570443	+	0.821337i	$0.693229\pi$
$810$	−17.2524	−0.606187
$811$	−48.7845	−1.71306	−0.856528	−	0.516101i	$-0.827383\pi$
$811$	−48.7845	−1.71306	−0.856528	+	0.516101i	$0.827383\pi$
$812$	−100.292	−3.51956
$813$	−8.12800	−0.285061
$814$	−75.5038	−2.64641
$815$	35.4910	1.24320
$816$	11.2646	0.394340
$817$	7.33252	0.256532
$818$	−40.9516	−1.43184
$819$	−58.9407	−2.05955
$820$	−88.7466	−3.09917
$821$	20.5173	0.716058	0.358029	−	0.933710i	$-0.383449\pi$
$821$	20.5173	0.716058	0.358029	+	0.933710i	$0.383449\pi$
$822$	−16.1874	−0.564601
$823$	−21.6999	−0.756411	−0.378206	−	0.925722i	$-0.623459\pi$
$823$	−21.6999	−0.756411	−0.378206	+	0.925722i	$0.623459\pi$
$824$	−22.6611	−0.789438
$825$	−18.6940	−0.650842
$826$	13.9636	0.485857
$827$	−29.7106	−1.03314	−0.516570	−	0.856245i	$-0.672791\pi$
$827$	−29.7106	−1.03314	−0.516570	+	0.856245i	$0.672791\pi$
$828$	−9.11279	−0.316691
$829$	−6.34953	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$829$	−6.34953	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$830$	−99.6514	−3.45895
$831$	12.4678	0.432503
$832$	77.5894	2.68993
$833$	44.0202	1.52521
$834$	−9.84551	−0.340922
$835$	−28.3352	−0.980578
$836$	18.3734	0.635459
$837$	−49.1084	−1.69743
$838$	−37.9989	−1.31265
$839$	38.9219	1.34373	0.671867	−	0.740672i	$-0.265493\pi$
$839$	38.9219	1.34373	0.671867	+	0.740672i	$0.265493\pi$
$840$	49.4821	1.70730
$841$	20.2065	0.696776
$842$	−56.7810	−1.95680
$843$	6.27063	0.215972
$844$	41.3682	1.42395
$845$	126.990	4.36859
$846$	5.11391	0.175820
$847$	8.70181	0.298998
$848$	32.0913	1.10202
$849$	4.83758	0.166025
$850$	−89.9084	−3.08383
$851$	−12.2709	−0.420641
$852$	9.22320	0.315982
$853$	3.54324	0.121318	0.0606591	−	0.998159i	$-0.480680\pi$
$853$	3.54324	0.121318	0.0606591	+	0.998159i	$0.480680\pi$
$854$	33.2112	1.13646
$855$	12.4890	0.427116
$856$	−53.1139	−1.81540
$857$	16.0792	0.549256	0.274628	−	0.961551i	$-0.411445\pi$
$857$	16.0792	0.549256	0.274628	+	0.961551i	$0.411445\pi$
$858$	−45.8444	−1.56510
$859$	−13.6311	−0.465087	−0.232544	−	0.972586i	$-0.574705\pi$
$859$	−13.6311	−0.465087	−0.232544	+	0.972586i	$0.574705\pi$
$860$	−55.3605	−1.88778
$861$	24.8971	0.848492
$862$	14.1724	0.482713
$863$	3.08603	0.105050	0.0525249	−	0.998620i	$-0.483273\pi$
$863$	3.08603	0.105050	0.0525249	+	0.998620i	$0.483273\pi$
$864$	−12.9718	−0.441310
$865$	−17.1745	−0.583952
$866$	52.6681	1.78974
$867$	12.0734	0.410033
$868$	−148.092	−5.02657
$869$	−8.34383	−0.283045
$870$	−53.0245	−1.79770
$871$	−9.51540	−0.322417
$872$	24.7847	0.839315
$873$	34.5899	1.17069
$874$	4.60493	0.155764
$875$	−24.9389	−0.843088
$876$	−46.9389	−1.58592
$877$	−16.2778	−0.549661	−0.274831	−	0.961493i	$-0.588622\pi$
$877$	−16.2778	−0.549661	−0.274831	+	0.961493i	$0.588622\pi$
$878$	50.9939	1.72096
$879$	−26.3214	−0.887800
$880$	−22.7409	−0.766596
$881$	−28.8275	−0.971222	−0.485611	−	0.874175i	$-0.661403\pi$
$881$	−28.8275	−0.971222	−0.485611	+	0.874175i	$0.661403\pi$
$882$	41.2005	1.38729
$883$	−0.673378	−0.0226610	−0.0113305	−	0.999936i	$-0.503607\pi$
$883$	−0.673378	−0.0226610	−0.0113305	+	0.999936i	$0.503607\pi$
$884$	−142.974	−4.80875
$885$	4.78722	0.160921
$886$	80.6899	2.71083
$887$	44.5006	1.49418	0.747092	−	0.664720i	$-0.231449\pi$
$887$	44.5006	1.49418	0.747092	+	0.664720i	$0.231449\pi$
$888$	39.6506	1.33059
$889$	26.5640	0.890927
$890$	−121.238	−4.06391
$891$	−6.21247	−0.208125
$892$	53.2987	1.78457
$893$	−1.67571	−0.0560756
$894$	−5.84875	−0.195611
$895$	29.0244	0.970180
$896$	−80.3649	−2.68480
$897$	−7.45064	−0.248769
$898$	−8.30576	−0.277167
$899$	72.6588	2.42331
$900$	−54.5665	−1.81888
$901$	78.9487	2.63016
$902$	−49.2824	−1.64092
$903$	15.5309	0.516837
$904$	−2.92613	−0.0973215
$905$	−31.4175	−1.04435
$906$	−24.8298	−0.824914
$907$	−5.20869	−0.172952	−0.0864758	−	0.996254i	$-0.527561\pi$
$907$	−5.20869	−0.172952	−0.0864758	+	0.996254i	$0.527561\pi$
$908$	74.0584	2.45771
$909$	28.5700	0.947608
$910$	−224.871	−7.45440
$911$	41.7412	1.38295	0.691474	−	0.722402i	$-0.256962\pi$
$911$	41.7412	1.38295	0.691474	+	0.722402i	$0.256962\pi$
$912$	−3.45472	−0.114397
$913$	−35.8838	−1.18758
$914$	−81.4386	−2.69375
$915$	11.3859	0.376407
$916$	−34.3865	−1.13616
$917$	−79.3300	−2.61971
$918$	62.0663	2.04849
$919$	9.01916	0.297515	0.148757	−	0.988874i	$-0.452473\pi$
$919$	9.01916	0.297515	0.148757	+	0.988874i	$0.452473\pi$
$920$	−15.9184	−0.524813
$921$	20.2936	0.668696
$922$	−39.3029	−1.29437
$923$	−19.1909	−0.631675
$924$	38.9166	1.28026
$925$	−73.4769	−2.41590
$926$	35.4733	1.16573
$927$	−12.1145	−0.397893
$928$	19.1926	0.630028
$929$	2.71168	0.0889674	0.0444837	−	0.999010i	$-0.485836\pi$
$929$	2.71168	0.0889674	0.0444837	+	0.999010i	$0.485836\pi$
$930$	−78.2964	−2.56744
$931$	−13.5005	−0.442460
$932$	46.0729	1.50917
$933$	19.1232	0.626065
$934$	−56.6090	−1.85230
$935$	−55.9455	−1.82961
$936$	−61.2686	−2.00263
$937$	9.16025	0.299252	0.149626	−	0.988743i	$-0.452193\pi$
$937$	9.16025	0.299252	0.149626	+	0.988743i	$0.452193\pi$
$938$	12.4566	0.406724
$939$	2.23971	0.0730900
$940$	12.6516	0.412651
$941$	22.6781	0.739285	0.369643	−	0.929174i	$-0.379480\pi$
$941$	22.6781	0.739285	0.369643	+	0.929174i	$0.379480\pi$
$942$	−44.2891	−1.44302
$943$	−8.00938	−0.260821
$944$	3.37006	0.109686
$945$	63.3003	2.05916
$946$	−30.7425	−0.999526
$947$	−31.6352	−1.02801	−0.514003	−	0.857789i	$-0.671838\pi$
$947$	−31.6352	−1.02801	−0.514003	+	0.857789i	$0.671838\pi$
$948$	9.57012	0.310823
$949$	97.6666	3.17039
$950$	27.5738	0.894614
$951$	0.450019	0.0145929
$952$	85.6960	2.77742
$953$	−29.4439	−0.953782	−0.476891	−	0.878962i	$-0.658236\pi$
$953$	−29.4439	−0.953782	−0.476891	+	0.878962i	$0.658236\pi$
$954$	73.8918	2.39233
$955$	30.9809	1.00252
$956$	−28.6060	−0.925185
$957$	−19.0937	−0.617213
$958$	16.7764	0.542020
$959$	−28.5917	−0.923274
$960$	−34.8226	−1.12389
$961$	76.2886	2.46092
$962$	−180.191	−5.80961
$963$	−28.3944	−0.914998
$964$	56.5473	1.82127
$965$	−24.8099	−0.798657
$966$	9.75365	0.313819
$967$	−29.3556	−0.944013	−0.472006	−	0.881595i	$-0.656470\pi$
$967$	−29.3556	−0.944013	−0.472006	+	0.881595i	$0.656470\pi$
$968$	9.04549	0.290733
$969$	−8.49904	−0.273029
$970$	131.968	4.23723
$971$	−33.1433	−1.06362	−0.531809	−	0.846864i	$-0.678488\pi$
$971$	−33.1433	−1.06362	−0.531809	+	0.846864i	$0.678488\pi$
$972$	59.5960	1.91154
$973$	−17.3900	−0.557499
$974$	61.2614	1.96294
$975$	−44.6137	−1.42878
$976$	8.01537	0.256566
$977$	36.9476	1.18206	0.591030	−	0.806650i	$-0.298722\pi$
$977$	36.9476	1.18206	0.591030	+	0.806650i	$0.298722\pi$
$978$	−22.6053	−0.722837
$979$	−43.6569	−1.39528
$980$	101.929	3.25599
$981$	13.2498	0.423033
$982$	26.1699	0.835115
$983$	14.9759	0.477657	0.238828	−	0.971062i	$-0.423237\pi$
$983$	14.9759	0.477657	0.238828	+	0.971062i	$0.423237\pi$
$984$	25.8805	0.825039
$985$	−37.9529	−1.20928
$986$	−91.8308	−2.92449
$987$	−3.54931	−0.112976
$988$	43.8486	1.39501
$989$	−4.99628	−0.158873
$990$	−52.3620	−1.66417
$991$	−8.36649	−0.265770	−0.132885	−	0.991131i	$-0.542424\pi$
$991$	−8.36649	−0.265770	−0.132885	+	0.991131i	$0.542424\pi$
$992$	28.3399	0.899794
$993$	5.60333	0.177816
$994$	25.1228	0.796848
$995$	86.1274	2.73042
$996$	41.1576	1.30413
$997$	−0.519309	−0.0164467	−0.00822334	−	0.999966i	$-0.502618\pi$
$997$	−0.519309	−0.0164467	−0.00822334	+	0.999966i	$0.502618\pi$
$998$	−42.6514	−1.35011
$999$	50.7232	1.60481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.20	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.38517 q^{2} +0.919938 q^{3} +3.68905 q^{4} +3.44498 q^{5} -2.19421 q^{6} -3.87561 q^{7} -4.02868 q^{8} -2.15371 q^{9} +O(q^{10})\)	\(q-2.38517 q^{2} +0.919938 q^{3} +3.68905 q^{4} +3.44498 q^{5} -2.19421 q^{6} -3.87561 q^{7} -4.02868 q^{8} -2.15371 q^{9} -8.21687 q^{10} -2.95884 q^{11} +3.39370 q^{12} -7.06133 q^{13} +9.24401 q^{14} +3.16917 q^{15} +2.23100 q^{16} +5.48855 q^{17} +5.13698 q^{18} -1.68327 q^{19} +12.7087 q^{20} -3.56532 q^{21} +7.05734 q^{22} +1.14696 q^{23} -3.70614 q^{24} +6.86788 q^{25} +16.8425 q^{26} -4.74110 q^{27} -14.2973 q^{28} +7.01474 q^{29} -7.55901 q^{30} +10.3580 q^{31} +2.73604 q^{32} -2.72195 q^{33} -13.0911 q^{34} -13.3514 q^{35} -7.94517 q^{36} -10.6986 q^{37} +4.01490 q^{38} -6.49598 q^{39} -13.8787 q^{40} -6.98313 q^{41} +8.50391 q^{42} -4.35611 q^{43} -10.9153 q^{44} -7.41950 q^{45} -2.73570 q^{46} +0.995509 q^{47} +2.05238 q^{48} +8.02038 q^{49} -16.3811 q^{50} +5.04912 q^{51} -26.0496 q^{52} +14.3843 q^{53} +11.3083 q^{54} -10.1931 q^{55} +15.6136 q^{56} -1.54851 q^{57} -16.7314 q^{58} +1.51056 q^{59} +11.6912 q^{60} +3.59272 q^{61} -24.7057 q^{62} +8.34696 q^{63} -10.9879 q^{64} -24.3261 q^{65} +6.49232 q^{66} +1.34754 q^{67} +20.2475 q^{68} +1.05513 q^{69} +31.8454 q^{70} +2.71774 q^{71} +8.67663 q^{72} -13.8312 q^{73} +25.5181 q^{74} +6.31803 q^{75} -6.20968 q^{76} +11.4673 q^{77} +15.4940 q^{78} +2.81997 q^{79} +7.68576 q^{80} +2.09963 q^{81} +16.6560 q^{82} +12.1277 q^{83} -13.1527 q^{84} +18.9079 q^{85} +10.3901 q^{86} +6.45312 q^{87} +11.9202 q^{88} +14.7548 q^{89} +17.6968 q^{90} +27.3670 q^{91} +4.23120 q^{92} +9.52873 q^{93} -2.37446 q^{94} -5.79884 q^{95} +2.51698 q^{96} -16.0606 q^{97} -19.1300 q^{98} +6.37249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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