LMFDB - Embedded newform 4001.2.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.73134 q^{2} +2.60660 q^{3} +5.46019 q^{4} -2.78013 q^{5} -7.11951 q^{6} -4.77010 q^{7} -9.45095 q^{8} +3.79438 q^{9} +O(q^{10})$	\(q-2.73134 q^{2} +2.60660 q^{3} +5.46019 q^{4} -2.78013 q^{5} -7.11951 q^{6} -4.77010 q^{7} -9.45095 q^{8} +3.79438 q^{9} +7.59346 q^{10} -5.83664 q^{11} +14.2326 q^{12} -1.87301 q^{13} +13.0288 q^{14} -7.24669 q^{15} +14.8933 q^{16} -7.42699 q^{17} -10.3637 q^{18} -2.84199 q^{19} -15.1800 q^{20} -12.4338 q^{21} +15.9418 q^{22} +0.931598 q^{23} -24.6349 q^{24} +2.72912 q^{25} +5.11582 q^{26} +2.07064 q^{27} -26.0457 q^{28} -7.87193 q^{29} +19.7932 q^{30} +9.52117 q^{31} -21.7768 q^{32} -15.2138 q^{33} +20.2856 q^{34} +13.2615 q^{35} +20.7181 q^{36} -9.70110 q^{37} +7.76244 q^{38} -4.88220 q^{39} +26.2749 q^{40} +3.79143 q^{41} +33.9608 q^{42} +4.05023 q^{43} -31.8692 q^{44} -10.5489 q^{45} -2.54451 q^{46} +1.91568 q^{47} +38.8210 q^{48} +15.7539 q^{49} -7.45413 q^{50} -19.3592 q^{51} -10.2270 q^{52} +0.163432 q^{53} -5.65561 q^{54} +16.2266 q^{55} +45.0820 q^{56} -7.40795 q^{57} +21.5009 q^{58} -1.71736 q^{59} -39.5684 q^{60} -4.72755 q^{61} -26.0055 q^{62} -18.0996 q^{63} +29.6930 q^{64} +5.20721 q^{65} +41.5540 q^{66} -15.7470 q^{67} -40.5528 q^{68} +2.42831 q^{69} -36.2216 q^{70} -4.17639 q^{71} -35.8605 q^{72} -7.50657 q^{73} +26.4970 q^{74} +7.11372 q^{75} -15.5178 q^{76} +27.8414 q^{77} +13.3349 q^{78} +4.79640 q^{79} -41.4054 q^{80} -5.98581 q^{81} -10.3557 q^{82} +1.13275 q^{83} -67.8908 q^{84} +20.6480 q^{85} -11.0625 q^{86} -20.5190 q^{87} +55.1618 q^{88} -6.41276 q^{89} +28.8125 q^{90} +8.93446 q^{91} +5.08671 q^{92} +24.8179 q^{93} -5.23237 q^{94} +7.90111 q^{95} -56.7634 q^{96} -3.59427 q^{97} -43.0292 q^{98} -22.1464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.73134	−1.93135	−0.965673	−	0.259761i	$-0.916356\pi$
$2$	−2.73134	−1.93135	−0.965673	+	0.259761i	$0.916356\pi$
$3$	2.60660	1.50492	0.752462	−	0.658636i	$-0.228866\pi$
$3$	2.60660	1.50492	0.752462	+	0.658636i	$0.228866\pi$
$4$	5.46019	2.73010
$5$	−2.78013	−1.24331	−0.621656	−	0.783291i	$-0.713540\pi$
$5$	−2.78013	−1.24331	−0.621656	+	0.783291i	$0.713540\pi$
$6$	−7.11951	−2.90653
$7$	−4.77010	−1.80293	−0.901465	−	0.432852i	$-0.857507\pi$
$7$	−4.77010	−1.80293	−0.901465	+	0.432852i	$0.857507\pi$
$8$	−9.45095	−3.34142
$9$	3.79438	1.26479
$10$	7.59346	2.40126
$11$	−5.83664	−1.75981	−0.879907	−	0.475147i	$-0.842395\pi$
$11$	−5.83664	−1.75981	−0.879907	+	0.475147i	$0.842395\pi$
$12$	14.2326	4.10859
$13$	−1.87301	−0.519480	−0.259740	−	0.965679i	$-0.583637\pi$
$13$	−1.87301	−0.519480	−0.259740	+	0.965679i	$0.583637\pi$
$14$	13.0288	3.48208
$15$	−7.24669	−1.87109
$16$	14.8933	3.72333
$17$	−7.42699	−1.80131	−0.900655	−	0.434534i	$-0.856913\pi$
$17$	−7.42699	−1.80131	−0.900655	+	0.434534i	$0.856913\pi$
$18$	−10.3637	−2.44275
$19$	−2.84199	−0.651998	−0.325999	−	0.945370i	$-0.605701\pi$
$19$	−2.84199	−0.651998	−0.325999	+	0.945370i	$0.605701\pi$
$20$	−15.1800	−3.39436
$21$	−12.4338	−2.71327
$22$	15.9418	3.39881
$23$	0.931598	0.194252	0.0971258	−	0.995272i	$-0.469035\pi$
$23$	0.931598	0.194252	0.0971258	+	0.995272i	$0.469035\pi$
$24$	−24.6349	−5.02857
$25$	2.72912	0.545823
$26$	5.11582	1.00330
$27$	2.07064	0.398495
$28$	−26.0457	−4.92217
$29$	−7.87193	−1.46178	−0.730890	−	0.682495i	$-0.760895\pi$
$29$	−7.87193	−1.46178	−0.730890	+	0.682495i	$0.760895\pi$
$30$	19.7932	3.61372
$31$	9.52117	1.71005	0.855026	−	0.518585i	$-0.173541\pi$
$31$	9.52117	1.71005	0.855026	+	0.518585i	$0.173541\pi$
$32$	−21.7768	−3.84963
$33$	−15.2138	−2.64838
$34$	20.2856	3.47895
$35$	13.2615	2.24160
$36$	20.7181	3.45301
$37$	−9.70110	−1.59485	−0.797426	−	0.603417i	$-0.793806\pi$
$37$	−9.70110	−1.59485	−0.797426	+	0.603417i	$0.793806\pi$
$38$	7.76244	1.25923
$39$	−4.88220	−0.781777
$40$	26.2749	4.15442
$41$	3.79143	0.592122	0.296061	−	0.955169i	$-0.404327\pi$
$41$	3.79143	0.592122	0.296061	+	0.955169i	$0.404327\pi$
$42$	33.9608	5.24027
$43$	4.05023	0.617654	0.308827	−	0.951118i	$-0.400064\pi$
$43$	4.05023	0.617654	0.308827	+	0.951118i	$0.400064\pi$
$44$	−31.8692	−4.80446
$45$	−10.5489	−1.57253
$46$	−2.54451	−0.375167
$47$	1.91568	0.279431	0.139715	−	0.990192i	$-0.455381\pi$
$47$	1.91568	0.279431	0.139715	+	0.990192i	$0.455381\pi$
$48$	38.8210	5.60333
$49$	15.7539	2.25056
$50$	−7.45413	−1.05417
$51$	−19.3592	−2.71083
$52$	−10.2270	−1.41823
$53$	0.163432	0.0224492	0.0112246	−	0.999937i	$-0.496427\pi$
$53$	0.163432	0.0224492	0.0112246	+	0.999937i	$0.496427\pi$
$54$	−5.65561	−0.769631
$55$	16.2266	2.18800
$56$	45.0820	6.02434
$57$	−7.40795	−0.981207
$58$	21.5009	2.82320
$59$	−1.71736	−0.223581	−0.111791	−	0.993732i	$-0.535659\pi$
$59$	−1.71736	−0.223581	−0.111791	+	0.993732i	$0.535659\pi$
$60$	−39.5684	−5.10825
$61$	−4.72755	−0.605300	−0.302650	−	0.953102i	$-0.597871\pi$
$61$	−4.72755	−0.605300	−0.302650	+	0.953102i	$0.597871\pi$
$62$	−26.0055	−3.30270
$63$	−18.0996	−2.28034
$64$	29.6930	3.71163
$65$	5.20721	0.645875
$66$	41.5540	5.11495
$67$	−15.7470	−1.92380	−0.961900	−	0.273402i	$-0.911851\pi$
$67$	−15.7470	−1.92380	−0.961900	+	0.273402i	$0.911851\pi$
$68$	−40.5528	−4.91775
$69$	2.42831	0.292334
$70$	−36.2216	−4.32931
$71$	−4.17639	−0.495646	−0.247823	−	0.968805i	$-0.579715\pi$
$71$	−4.17639	−0.495646	−0.247823	+	0.968805i	$0.579715\pi$
$72$	−35.8605	−4.22620
$73$	−7.50657	−0.878578	−0.439289	−	0.898346i	$-0.644770\pi$
$73$	−7.50657	−0.878578	−0.439289	+	0.898346i	$0.644770\pi$
$74$	26.4970	3.08021
$75$	7.11372	0.821422
$76$	−15.5178	−1.78002
$77$	27.8414	3.17282
$78$	13.3349	1.50988
$79$	4.79640	0.539637	0.269818	−	0.962911i	$-0.413036\pi$
$79$	4.79640	0.539637	0.269818	+	0.962911i	$0.413036\pi$
$80$	−41.4054	−4.62926
$81$	−5.98581	−0.665090
$82$	−10.3557	−1.14359
$83$	1.13275	0.124335	0.0621677	−	0.998066i	$-0.480199\pi$
$83$	1.13275	0.124335	0.0621677	+	0.998066i	$0.480199\pi$
$84$	−67.8908	−7.40749
$85$	20.6480	2.23959
$86$	−11.0625	−1.19290
$87$	−20.5190	−2.19987
$88$	55.1618	5.88027
$89$	−6.41276	−0.679752	−0.339876	−	0.940470i	$-0.610385\pi$
$89$	−6.41276	−0.679752	−0.339876	+	0.940470i	$0.610385\pi$
$90$	28.8125	3.03710
$91$	8.93446	0.936586
$92$	5.08671	0.530326
$93$	24.8179	2.57350
$94$	−5.23237	−0.539677
$95$	7.90111	0.810636
$96$	−56.7634	−5.79339
$97$	−3.59427	−0.364942	−0.182471	−	0.983211i	$-0.558410\pi$
$97$	−3.59427	−0.364942	−0.182471	+	0.983211i	$0.558410\pi$
$98$	−43.0292	−4.34660
$99$	−22.1464	−2.22580
$100$	14.9015	1.49015
$101$	−1.72571	−0.171715	−0.0858573	−	0.996307i	$-0.527363\pi$
$101$	−1.72571	−0.171715	−0.0858573	+	0.996307i	$0.527363\pi$
$102$	52.8766	5.23556
$103$	3.97639	0.391805	0.195903	−	0.980623i	$-0.437236\pi$
$103$	3.97639	0.391805	0.195903	+	0.980623i	$0.437236\pi$
$104$	17.7017	1.73580
$105$	34.5675	3.37344
$106$	−0.446389	−0.0433571
$107$	−16.3046	−1.57622	−0.788112	−	0.615532i	$-0.788941\pi$
$107$	−16.3046	−1.57622	−0.788112	+	0.615532i	$0.788941\pi$
$108$	11.3061	1.08793
$109$	8.82823	0.845591	0.422796	−	0.906225i	$-0.361049\pi$
$109$	8.82823	0.845591	0.422796	+	0.906225i	$0.361049\pi$
$110$	−44.3203	−4.22578
$111$	−25.2869	−2.40013
$112$	−71.0428	−6.71291
$113$	12.1221	1.14035	0.570177	−	0.821522i	$-0.306875\pi$
$113$	12.1221	1.14035	0.570177	+	0.821522i	$0.306875\pi$
$114$	20.2336	1.89505
$115$	−2.58996	−0.241515
$116$	−42.9823	−3.99080
$117$	−7.10692	−0.657035
$118$	4.69068	0.431812
$119$	35.4275	3.24764
$120$	68.4881	6.25208
$121$	23.0664	2.09694
$122$	12.9125	1.16904
$123$	9.88275	0.891098
$124$	51.9874	4.66861
$125$	6.31335	0.564683
$126$	49.4361	4.40412
$127$	−9.71457	−0.862028	−0.431014	−	0.902345i	$-0.641844\pi$
$127$	−9.71457	−0.862028	−0.431014	+	0.902345i	$0.641844\pi$
$128$	−37.5481	−3.31881
$129$	10.5573	0.929521
$130$	−14.2226	−1.24741
$131$	−17.4431	−1.52401	−0.762007	−	0.647569i	$-0.775786\pi$
$131$	−17.4431	−1.52401	−0.762007	+	0.647569i	$0.775786\pi$
$132$	−83.0703	−7.23034
$133$	13.5566	1.17551
$134$	43.0103	3.71552
$135$	−5.75664	−0.495453
$136$	70.1922	6.01893
$137$	1.80600	0.154297	0.0771485	−	0.997020i	$-0.475418\pi$
$137$	1.80600	0.154297	0.0771485	+	0.997020i	$0.475418\pi$
$138$	−6.63252	−0.564598
$139$	3.54419	0.300615	0.150307	−	0.988639i	$-0.451974\pi$
$139$	3.54419	0.300615	0.150307	+	0.988639i	$0.451974\pi$
$140$	72.4104	6.11980
$141$	4.99342	0.420522
$142$	11.4071	0.957264
$143$	10.9321	0.914188
$144$	56.5110	4.70925
$145$	21.8850	1.81745
$146$	20.5030	1.69684
$147$	41.0642	3.38692
$148$	−52.9699	−4.35410
$149$	14.9176	1.22210	0.611050	−	0.791592i	$-0.290747\pi$
$149$	14.9176	1.22210	0.611050	+	0.791592i	$0.290747\pi$
$150$	−19.4300	−1.58645
$151$	14.3796	1.17019	0.585096	−	0.810964i	$-0.301057\pi$
$151$	14.3796	1.17019	0.585096	+	0.810964i	$0.301057\pi$
$152$	26.8595	2.17860
$153$	−28.1809	−2.27829
$154$	−76.0442	−6.12781
$155$	−26.4701	−2.12613
$156$	−26.6578	−2.13433
$157$	13.1225	1.04729	0.523644	−	0.851937i	$-0.324572\pi$
$157$	13.1225	1.04729	0.523644	+	0.851937i	$0.324572\pi$
$158$	−13.1006	−1.04223
$159$	0.426003	0.0337843
$160$	60.5423	4.78629
$161$	−4.44382	−0.350222
$162$	16.3493	1.28452
$163$	−13.4677	−1.05487	−0.527434	−	0.849596i	$-0.676846\pi$
$163$	−13.4677	−1.05487	−0.527434	+	0.849596i	$0.676846\pi$
$164$	20.7019	1.61655
$165$	42.2963	3.29277
$166$	−3.09392	−0.240135
$167$	16.0547	1.24235	0.621174	−	0.783673i	$-0.286656\pi$
$167$	16.0547	1.24235	0.621174	+	0.783673i	$0.286656\pi$
$168$	117.511	9.06617
$169$	−9.49183	−0.730141
$170$	−56.3966	−4.32542
$171$	−10.7836	−0.824643
$172$	22.1150	1.68625
$173$	−6.23749	−0.474227	−0.237114	−	0.971482i	$-0.576201\pi$
$173$	−6.23749	−0.474227	−0.237114	+	0.971482i	$0.576201\pi$
$174$	56.0443	4.24871
$175$	−13.0182	−0.984081
$176$	−86.9270	−6.55237
$177$	−4.47647	−0.336472
$178$	17.5154	1.31284
$179$	9.61699	0.718807	0.359404	−	0.933182i	$-0.382980\pi$
$179$	9.61699	0.718807	0.359404	+	0.933182i	$0.382980\pi$
$180$	−57.5989	−4.29317
$181$	6.13143	0.455746	0.227873	−	0.973691i	$-0.426823\pi$
$181$	6.13143	0.455746	0.227873	+	0.973691i	$0.426823\pi$
$182$	−24.4030	−1.80887
$183$	−12.3228	−0.910931
$184$	−8.80449	−0.649075
$185$	26.9703	1.98290
$186$	−67.7860	−4.97031
$187$	43.3487	3.16997
$188$	10.4600	0.762873
$189$	−9.87717	−0.718458
$190$	−21.5806	−1.56562
$191$	−9.95957	−0.720649	−0.360325	−	0.932827i	$-0.617334\pi$
$191$	−9.95957	−0.720649	−0.360325	+	0.932827i	$0.617334\pi$
$192$	77.3980	5.58572
$193$	23.7717	1.71113	0.855564	−	0.517697i	$-0.173211\pi$
$193$	23.7717	1.71113	0.855564	+	0.517697i	$0.173211\pi$
$194$	9.81714	0.704830
$195$	13.5731	0.971993
$196$	86.0193	6.14424
$197$	−9.82143	−0.699748	−0.349874	−	0.936797i	$-0.613776\pi$
$197$	−9.82143	−0.699748	−0.349874	+	0.936797i	$0.613776\pi$
$198$	60.4894	4.29879
$199$	−13.3408	−0.945701	−0.472851	−	0.881143i	$-0.656775\pi$
$199$	−13.3408	−0.945701	−0.472851	+	0.881143i	$0.656775\pi$
$200$	−25.7927	−1.82382
$201$	−41.0461	−2.89517
$202$	4.71349	0.331640
$203$	37.5499	2.63549
$204$	−105.705	−7.40084
$205$	−10.5407	−0.736192
$206$	−10.8609	−0.756712
$207$	3.53484	0.245688
$208$	−27.8954	−1.93420
$209$	16.5877	1.14739
$210$	−94.4154	−6.51528
$211$	−22.1764	−1.52669	−0.763343	−	0.645993i	$-0.776443\pi$
$211$	−22.1764	−1.52669	−0.763343	+	0.645993i	$0.776443\pi$
$212$	0.892372	0.0612884
$213$	−10.8862	−0.745909
$214$	44.5333	3.04423
$215$	−11.2601	−0.767936
$216$	−19.5695	−1.33154
$217$	−45.4170	−3.08310
$218$	−24.1129	−1.63313
$219$	−19.5667	−1.32219
$220$	88.6004	5.97344
$221$	13.9108	0.935745
$222$	69.0671	4.63548
$223$	−19.0799	−1.27768	−0.638842	−	0.769338i	$-0.720586\pi$
$223$	−19.0799	−1.27768	−0.638842	+	0.769338i	$0.720586\pi$
$224$	103.878	6.94061
$225$	10.3553	0.690354
$226$	−33.1096	−2.20242
$227$	4.06125	0.269555	0.134777	−	0.990876i	$-0.456968\pi$
$227$	4.06125	0.269555	0.134777	+	0.990876i	$0.456968\pi$
$228$	−40.4488	−2.67879
$229$	−8.86160	−0.585591	−0.292796	−	0.956175i	$-0.594586\pi$
$229$	−8.86160	−0.585591	−0.292796	+	0.956175i	$0.594586\pi$
$230$	7.07406	0.466449
$231$	72.5714	4.77485
$232$	74.3972	4.88442
$233$	10.1171	0.662792	0.331396	−	0.943492i	$-0.392480\pi$
$233$	10.1171	0.662792	0.331396	+	0.943492i	$0.392480\pi$
$234$	19.4114	1.26896
$235$	−5.32584	−0.347419
$236$	−9.37711	−0.610398
$237$	12.5023	0.812112
$238$	−96.7645	−6.27231
$239$	−12.3384	−0.798107	−0.399054	−	0.916928i	$-0.630661\pi$
$239$	−12.3384	−0.798107	−0.399054	+	0.916928i	$0.630661\pi$
$240$	−107.927	−6.96668
$241$	2.66044	0.171374	0.0856870	−	0.996322i	$-0.472691\pi$
$241$	2.66044	0.171374	0.0856870	+	0.996322i	$0.472691\pi$
$242$	−63.0020	−4.04992
$243$	−21.8146	−1.39940
$244$	−25.8133	−1.65253
$245$	−43.7979	−2.79814
$246$	−26.9931	−1.72102
$247$	5.32308	0.338700
$248$	−89.9841	−5.71400
$249$	2.95263	0.187115
$250$	−17.2439	−1.09060
$251$	−24.4886	−1.54571	−0.772854	−	0.634584i	$-0.781172\pi$
$251$	−24.4886	−1.54571	−0.772854	+	0.634584i	$0.781172\pi$
$252$	−98.8273	−6.22554
$253$	−5.43740	−0.341846
$254$	26.5337	1.66487
$255$	53.8212	3.37041
$256$	43.1704	2.69815
$257$	13.2520	0.826640	0.413320	−	0.910586i	$-0.364369\pi$
$257$	13.2520	0.826640	0.413320	+	0.910586i	$0.364369\pi$
$258$	−28.8356	−1.79523
$259$	46.2753	2.87541
$260$	28.4324	1.76330
$261$	−29.8691	−1.84885
$262$	47.6431	2.94340
$263$	−17.7529	−1.09469	−0.547345	−	0.836907i	$-0.684362\pi$
$263$	−17.7529	−1.09469	−0.547345	+	0.836907i	$0.684362\pi$
$264$	143.785	8.84935
$265$	−0.454363	−0.0279113
$266$	−37.0276	−2.27031
$267$	−16.7155	−1.02297
$268$	−85.9816	−5.25216
$269$	0.0317366	0.00193502	0.000967508	−	1.00000i	$-0.499692\pi$
$269$	0.0317366	0.00193502	0.000967508		1.00000i	$0.499692\pi$
$270$	15.7233	0.956891
$271$	22.1924	1.34809	0.674046	−	0.738689i	$-0.264555\pi$
$271$	22.1924	1.34809	0.674046	+	0.738689i	$0.264555\pi$
$272$	−110.613	−6.70688
$273$	23.2886	1.40949
$274$	−4.93279	−0.298001
$275$	−15.9289	−0.960547
$276$	13.2590	0.798099
$277$	−18.8718	−1.13390	−0.566948	−	0.823753i	$-0.691876\pi$
$277$	−18.8718	−1.13390	−0.566948	+	0.823753i	$0.691876\pi$
$278$	−9.68038	−0.580591
$279$	36.1270	2.16286
$280$	−125.334	−7.49013
$281$	5.70495	0.340329	0.170164	−	0.985416i	$-0.445570\pi$
$281$	5.70495	0.340329	0.170164	+	0.985416i	$0.445570\pi$
$282$	−13.6387	−0.812173
$283$	−0.730251	−0.0434089	−0.0217045	−	0.999764i	$-0.506909\pi$
$283$	−0.730251	−0.0434089	−0.0217045	+	0.999764i	$0.506909\pi$
$284$	−22.8039	−1.35316
$285$	20.5951	1.21995
$286$	−29.8592	−1.76561
$287$	−18.0855	−1.06755
$288$	−82.6294	−4.86899
$289$	38.1603	2.24472
$290$	−59.7752	−3.51012
$291$	−9.36882	−0.549210
$292$	−40.9873	−2.39860
$293$	−6.72388	−0.392813	−0.196407	−	0.980523i	$-0.562927\pi$
$293$	−6.72388	−0.392813	−0.196407	+	0.980523i	$0.562927\pi$
$294$	−112.160	−6.54131
$295$	4.77448	0.277981
$296$	91.6847	5.32906
$297$	−12.0856	−0.701276
$298$	−40.7451	−2.36030
$299$	−1.74489	−0.100910
$300$	38.8423	2.24256
$301$	−19.3200	−1.11359
$302$	−39.2754	−2.26005
$303$	−4.49824	−0.258417
$304$	−42.3267	−2.42761
$305$	13.1432	0.752577
$306$	76.9714	4.40016
$307$	12.1621	0.694125	0.347063	−	0.937842i	$-0.387179\pi$
$307$	12.1621	0.694125	0.347063	+	0.937842i	$0.387179\pi$
$308$	152.019	8.66211
$309$	10.3649	0.589637
$310$	72.2987	4.10629
$311$	18.9629	1.07529	0.537643	−	0.843173i	$-0.319315\pi$
$311$	18.9629	1.07529	0.537643	+	0.843173i	$0.319315\pi$
$312$	46.1414	2.61224
$313$	14.0730	0.795455	0.397727	−	0.917504i	$-0.369799\pi$
$313$	14.0730	0.795455	0.397727	+	0.917504i	$0.369799\pi$
$314$	−35.8419	−2.02268
$315$	50.3192	2.83517
$316$	26.1893	1.47326
$317$	1.46559	0.0823159	0.0411579	−	0.999153i	$-0.486895\pi$
$317$	1.46559	0.0823159	0.0411579	+	0.999153i	$0.486895\pi$
$318$	−1.16356	−0.0652491
$319$	45.9456	2.57246
$320$	−82.5505	−4.61471
$321$	−42.4996	−2.37210
$322$	12.1376	0.676400
$323$	21.1075	1.17445
$324$	−32.6837	−1.81576
$325$	−5.11166	−0.283544
$326$	36.7847	2.03732
$327$	23.0117	1.27255
$328$	−35.8326	−1.97853
$329$	−9.13800	−0.503794
$330$	−115.526	−6.35947
$331$	0.944701	0.0519254	0.0259627	−	0.999663i	$-0.491735\pi$
$331$	0.944701	0.0519254	0.0259627	+	0.999663i	$0.491735\pi$
$332$	6.18503	0.339448
$333$	−36.8097	−2.01716
$334$	−43.8507	−2.39940
$335$	43.7786	2.39188
$336$	−185.180	−10.1024
$337$	8.88167	0.483816	0.241908	−	0.970299i	$-0.422227\pi$
$337$	8.88167	0.483816	0.241908	+	0.970299i	$0.422227\pi$
$338$	25.9254	1.41015
$339$	31.5976	1.71614
$340$	112.742	6.11430
$341$	−55.5716	−3.00937
$342$	29.4536	1.59267
$343$	−41.7570	−2.25467
$344$	−38.2785	−2.06384
$345$	−6.75100	−0.363462
$346$	17.0367	0.915897
$347$	−16.0008	−0.858967	−0.429484	−	0.903075i	$-0.641304\pi$
$347$	−16.0008	−0.858967	−0.429484	+	0.903075i	$0.641304\pi$
$348$	−112.038	−6.00585
$349$	−31.4388	−1.68288	−0.841440	−	0.540350i	$-0.818292\pi$
$349$	−31.4388	−1.68288	−0.841440	+	0.540350i	$0.818292\pi$
$350$	35.5570	1.90060
$351$	−3.87833	−0.207010
$352$	127.103	6.77463
$353$	−16.5149	−0.878999	−0.439500	−	0.898243i	$-0.644844\pi$
$353$	−16.5149	−0.878999	−0.439500	+	0.898243i	$0.644844\pi$
$354$	12.2268	0.649845
$355$	11.6109	0.616242
$356$	−35.0149	−1.85579
$357$	92.3456	4.88745
$358$	−26.2672	−1.38827
$359$	16.0561	0.847411	0.423705	−	0.905800i	$-0.360729\pi$
$359$	16.0561	0.847411	0.423705	+	0.905800i	$0.360729\pi$
$360$	99.6969	5.25449
$361$	−10.9231	−0.574899
$362$	−16.7470	−0.880203
$363$	60.1249	3.15574
$364$	48.7839	2.55697
$365$	20.8692	1.09235
$366$	33.6578	1.75932
$367$	−31.9877	−1.66975	−0.834873	−	0.550443i	$-0.814459\pi$
$367$	−31.9877	−1.66975	−0.834873	+	0.550443i	$0.814459\pi$
$368$	13.8746	0.723263
$369$	14.3861	0.748912
$370$	−73.6650	−3.82966
$371$	−0.779589	−0.0404743
$372$	135.511	7.02590
$373$	2.80996	0.145494	0.0727472	−	0.997350i	$-0.476823\pi$
$373$	2.80996	0.145494	0.0727472	+	0.997350i	$0.476823\pi$
$374$	−118.400	−6.12231
$375$	16.4564	0.849805
$376$	−18.1050	−0.933694
$377$	14.7442	0.759366
$378$	26.9779	1.38759
$379$	−21.5280	−1.10582	−0.552908	−	0.833242i	$-0.686482\pi$
$379$	−21.5280	−1.10582	−0.552908	+	0.833242i	$0.686482\pi$
$380$	43.1416	2.21312
$381$	−25.3220	−1.29729
$382$	27.2029	1.39182
$383$	−19.1359	−0.977801	−0.488901	−	0.872340i	$-0.662602\pi$
$383$	−19.1359	−0.977801	−0.488901	+	0.872340i	$0.662602\pi$
$384$	−97.8730	−4.99456
$385$	−77.4026	−3.94480
$386$	−64.9286	−3.30478
$387$	15.3681	0.781205
$388$	−19.6254	−0.996328
$389$	10.4993	0.532338	0.266169	−	0.963926i	$-0.414242\pi$
$389$	10.4993	0.532338	0.266169	+	0.963926i	$0.414242\pi$
$390$	−37.0728	−1.87725
$391$	−6.91897	−0.349907
$392$	−148.889	−7.52005
$393$	−45.4674	−2.29352
$394$	26.8256	1.35146
$395$	−13.3346	−0.670937
$396$	−120.924	−6.07665
$397$	16.2459	0.815358	0.407679	−	0.913125i	$-0.366338\pi$
$397$	16.2459	0.815358	0.407679	+	0.913125i	$0.366338\pi$
$398$	36.4381	1.82648
$399$	35.3367	1.76905
$400$	40.6456	2.03228
$401$	−0.890388	−0.0444639	−0.0222319	−	0.999753i	$-0.507077\pi$
$401$	−0.890388	−0.0444639	−0.0222319	+	0.999753i	$0.507077\pi$
$402$	112.111	5.59158
$403$	−17.8333	−0.888338
$404$	−9.42271	−0.468797
$405$	16.6413	0.826914
$406$	−102.561	−5.09004
$407$	56.6219	2.80664
$408$	182.963	9.05803
$409$	−17.7442	−0.877395	−0.438698	−	0.898635i	$-0.644560\pi$
$409$	−17.7442	−0.877395	−0.438698	+	0.898635i	$0.644560\pi$
$410$	28.7901	1.42184
$411$	4.70753	0.232205
$412$	21.7119	1.06967
$413$	8.19198	0.403101
$414$	−9.65483	−0.474509
$415$	−3.14919	−0.154588
$416$	40.7882	1.99980
$417$	9.23831	0.452402
$418$	−45.3065	−2.21602
$419$	−15.0359	−0.734550	−0.367275	−	0.930112i	$-0.619709\pi$
$419$	−15.0359	−0.734550	−0.367275	+	0.930112i	$0.619709\pi$
$420$	188.745	9.20982
$421$	−16.6842	−0.813139	−0.406570	−	0.913620i	$-0.633275\pi$
$421$	−16.6842	−0.813139	−0.406570	+	0.913620i	$0.633275\pi$
$422$	60.5712	2.94856
$423$	7.26882	0.353422
$424$	−1.54459	−0.0750120
$425$	−20.2691	−0.983197
$426$	29.7338	1.44061
$427$	22.5509	1.09131
$428$	−89.0262	−4.30325
$429$	28.4956	1.37578
$430$	30.7552	1.48315
$431$	14.4538	0.696214	0.348107	−	0.937455i	$-0.386825\pi$
$431$	14.4538	0.696214	0.348107	+	0.937455i	$0.386825\pi$
$432$	30.8387	1.48373
$433$	−20.6568	−0.992704	−0.496352	−	0.868121i	$-0.665327\pi$
$433$	−20.6568	−0.992704	−0.496352	+	0.868121i	$0.665327\pi$
$434$	124.049	5.95454
$435$	57.0455	2.73512
$436$	48.2039	2.30855
$437$	−2.64759	−0.126652
$438$	53.4431	2.55361
$439$	30.3738	1.44966	0.724832	−	0.688925i	$-0.241917\pi$
$439$	30.3738	1.44966	0.724832	+	0.688925i	$0.241917\pi$
$440$	−153.357	−7.31100
$441$	59.7763	2.84649
$442$	−37.9952	−1.80725
$443$	15.2727	0.725629	0.362815	−	0.931861i	$-0.381816\pi$
$443$	15.2727	0.725629	0.362815	+	0.931861i	$0.381816\pi$
$444$	−138.072	−6.55259
$445$	17.8283	0.845143
$446$	52.1136	2.46765
$447$	38.8844	1.83917
$448$	−141.639	−6.69181
$449$	−4.62446	−0.218242	−0.109121	−	0.994028i	$-0.534804\pi$
$449$	−4.62446	−0.218242	−0.109121	+	0.994028i	$0.534804\pi$
$450$	−28.2838	−1.33331
$451$	−22.1292	−1.04202
$452$	66.1891	3.11328
$453$	37.4818	1.76105
$454$	−11.0926	−0.520604
$455$	−24.8390	−1.16447
$456$	70.0122	3.27862
$457$	−33.8593	−1.58387	−0.791935	−	0.610605i	$-0.790926\pi$
$457$	−33.8593	−1.58387	−0.791935	+	0.610605i	$0.790926\pi$
$458$	24.2040	1.13098
$459$	−15.3786	−0.717813
$460$	−14.1417	−0.659360
$461$	−26.0711	−1.21425	−0.607127	−	0.794605i	$-0.707678\pi$
$461$	−26.0711	−1.21425	−0.607127	+	0.794605i	$0.707678\pi$
$462$	−198.217	−9.22189
$463$	0.316975	0.0147311	0.00736553	−	0.999973i	$-0.497655\pi$
$463$	0.316975	0.0147311	0.00736553	+	0.999973i	$0.497655\pi$
$464$	−117.239	−5.44270
$465$	−68.9970	−3.19966
$466$	−27.6332	−1.28008
$467$	−41.5385	−1.92217	−0.961087	−	0.276247i	$-0.910909\pi$
$467$	−41.5385	−1.92217	−0.961087	+	0.276247i	$0.910909\pi$
$468$	−38.8052	−1.79377
$469$	75.1147	3.46848
$470$	14.5467	0.670987
$471$	34.2051	1.57609
$472$	16.2307	0.747077
$473$	−23.6397	−1.08696
$474$	−34.1480	−1.56847
$475$	−7.75613	−0.355876
$476$	193.441	8.86637
$477$	0.620125	0.0283936
$478$	33.7004	1.54142
$479$	7.33292	0.335050	0.167525	−	0.985868i	$-0.446423\pi$
$479$	7.33292	0.335050	0.167525	+	0.985868i	$0.446423\pi$
$480$	157.810	7.20299
$481$	18.1703	0.828493
$482$	−7.26655	−0.330982
$483$	−11.5833	−0.527057
$484$	125.947	5.72486
$485$	9.99252	0.453737
$486$	59.5829	2.70273
$487$	39.8709	1.80672	0.903361	−	0.428881i	$-0.141092\pi$
$487$	39.8709	1.80672	0.903361	+	0.428881i	$0.141092\pi$
$488$	44.6798	2.02256
$489$	−35.1049	−1.58750
$490$	119.627	5.40418
$491$	11.1987	0.505389	0.252695	−	0.967546i	$-0.418683\pi$
$491$	11.1987	0.505389	0.252695	+	0.967546i	$0.418683\pi$
$492$	53.9618	2.43278
$493$	58.4648	2.63312
$494$	−14.5391	−0.654146
$495$	61.5700	2.76736
$496$	141.802	6.36709
$497$	19.9218	0.893615
$498$	−8.06462	−0.361384
$499$	12.3475	0.552750	0.276375	−	0.961050i	$-0.410867\pi$
$499$	12.3475	0.552750	0.276375	+	0.961050i	$0.410867\pi$
$500$	34.4721	1.54164
$501$	41.8482	1.86964
$502$	66.8867	2.98530
$503$	36.0024	1.60527	0.802634	−	0.596472i	$-0.203431\pi$
$503$	36.0024	1.60527	0.802634	+	0.596472i	$0.203431\pi$
$504$	171.058	7.61955
$505$	4.79770	0.213495
$506$	14.8514	0.660224
$507$	−24.7414	−1.09881
$508$	−53.0434	−2.35342
$509$	−37.4150	−1.65839	−0.829196	−	0.558957i	$-0.811202\pi$
$509$	−37.4150	−1.65839	−0.829196	+	0.558957i	$0.811202\pi$
$510$	−147.004	−6.50943
$511$	35.8071	1.58401
$512$	−42.8166	−1.89224
$513$	−5.88474	−0.259818
$514$	−36.1958	−1.59653
$515$	−11.0549	−0.487136
$516$	57.6451	2.53768
$517$	−11.1811	−0.491746
$518$	−126.393	−5.55340
$519$	−16.2587	−0.713676
$520$	−49.2131	−2.15814
$521$	12.2483	0.536607	0.268304	−	0.963334i	$-0.413537\pi$
$521$	12.2483	0.536607	0.268304	+	0.963334i	$0.413537\pi$
$522$	81.5826	3.57077
$523$	−12.3772	−0.541219	−0.270609	−	0.962689i	$-0.587225\pi$
$523$	−12.3772	−0.541219	−0.270609	+	0.962689i	$0.587225\pi$
$524$	−95.2429	−4.16071
$525$	−33.9332	−1.48097
$526$	48.4891	2.11423
$527$	−70.7137	−3.08034
$528$	−226.584	−9.86081
$529$	−22.1321	−0.962266
$530$	1.24102	0.0539064
$531$	−6.51632	−0.282784
$532$	74.0217	3.20925
$533$	−7.10139	−0.307595
$534$	45.6557	1.97572
$535$	45.3289	1.95974
$536$	148.824	6.42821
$537$	25.0677	1.08175
$538$	−0.0866833	−0.00373718
$539$	−91.9498	−3.96056
$540$	−31.4324	−1.35263
$541$	−7.33608	−0.315403	−0.157701	−	0.987487i	$-0.550408\pi$
$541$	−7.33608	−0.315403	−0.157701	+	0.987487i	$0.550408\pi$
$542$	−60.6149	−2.60363
$543$	15.9822	0.685862
$544$	161.736	6.93438
$545$	−24.5436	−1.05133
$546$	−63.6090	−2.72221
$547$	−11.0541	−0.472638	−0.236319	−	0.971676i	$-0.575941\pi$
$547$	−11.0541	−0.472638	−0.236319	+	0.971676i	$0.575941\pi$
$548$	9.86111	0.421246
$549$	−17.9381	−0.765580
$550$	43.5071	1.85515
$551$	22.3720	0.953078
$552$	−22.9498	−0.976809
$553$	−22.8793	−0.972928
$554$	51.5452	2.18995
$555$	70.3009	2.98411
$556$	19.3520	0.820707
$557$	7.13102	0.302151	0.151075	−	0.988522i	$-0.451726\pi$
$557$	7.13102	0.302151	0.151075	+	0.988522i	$0.451726\pi$
$558$	−98.6748	−4.17724
$559$	−7.58612	−0.320859
$560$	197.508	8.34624
$561$	112.993	4.77056
$562$	−15.5821	−0.657293
$563$	−43.2792	−1.82400	−0.912000	−	0.410190i	$-0.865462\pi$
$563$	−43.2792	−1.82400	−0.912000	+	0.410190i	$0.865462\pi$
$564$	27.2650	1.14807
$565$	−33.7011	−1.41781
$566$	1.99456	0.0838376
$567$	28.5529	1.19911
$568$	39.4708	1.65616
$569$	32.4985	1.36241	0.681204	−	0.732094i	$-0.261457\pi$
$569$	32.4985	1.36241	0.681204	+	0.732094i	$0.261457\pi$
$570$	−56.2520	−2.35614
$571$	−1.94358	−0.0813365	−0.0406682	−	0.999173i	$-0.512949\pi$
$571$	−1.94358	−0.0813365	−0.0406682	+	0.999173i	$0.512949\pi$
$572$	59.6914	2.49582
$573$	−25.9607	−1.08452
$574$	49.3976	2.06182
$575$	2.54244	0.106027
$576$	112.667	4.69445
$577$	−10.8787	−0.452886	−0.226443	−	0.974024i	$-0.572710\pi$
$577$	−10.8787	−0.452886	−0.226443	+	0.974024i	$0.572710\pi$
$578$	−104.228	−4.33533
$579$	61.9635	2.57512
$580$	119.496	4.96181
$581$	−5.40333	−0.224168
$582$	25.5894	1.06071
$583$	−0.953896	−0.0395063
$584$	70.9443	2.93569
$585$	19.7582	0.816899
$586$	18.3652	0.758658
$587$	0.237692	0.00981058	0.00490529	−	0.999988i	$-0.498439\pi$
$587$	0.237692	0.00981058	0.00490529	+	0.999988i	$0.498439\pi$
$588$	224.218	9.24661
$589$	−27.0591	−1.11495
$590$	−13.0407	−0.536877
$591$	−25.6006	−1.05307
$592$	−144.482	−5.93816
$593$	−20.1547	−0.827654	−0.413827	−	0.910356i	$-0.635808\pi$
$593$	−20.1547	−0.827654	−0.413827	+	0.910356i	$0.635808\pi$
$594$	33.0098	1.35441
$595$	−98.4931	−4.03782
$596$	81.4532	3.33645
$597$	−34.7741	−1.42321
$598$	4.76589	0.194892
$599$	−15.8017	−0.645640	−0.322820	−	0.946460i	$-0.604631\pi$
$599$	−15.8017	−0.645640	−0.322820	+	0.946460i	$0.604631\pi$
$600$	−67.2314	−2.74471
$601$	27.4830	1.12105	0.560526	−	0.828137i	$-0.310599\pi$
$601$	27.4830	1.12105	0.560526	+	0.828137i	$0.310599\pi$
$602$	52.7694	2.15072
$603$	−59.7501	−2.43321
$604$	78.5152	3.19474
$605$	−64.1275	−2.60715
$606$	12.2862	0.499093
$607$	12.7863	0.518979	0.259490	−	0.965746i	$-0.416446\pi$
$607$	12.7863	0.518979	0.259490	+	0.965746i	$0.416446\pi$
$608$	61.8895	2.50995
$609$	97.8778	3.96621
$610$	−35.8985	−1.45349
$611$	−3.58809	−0.145159
$612$	−153.873	−6.21995
$613$	25.2825	1.02115	0.510575	−	0.859833i	$-0.329433\pi$
$613$	25.2825	1.02115	0.510575	+	0.859833i	$0.329433\pi$
$614$	−33.2187	−1.34060
$615$	−27.4753	−1.10791
$616$	−263.128	−10.6017
$617$	18.2444	0.734491	0.367245	−	0.930124i	$-0.380301\pi$
$617$	18.2444	0.734491	0.367245	+	0.930124i	$0.380301\pi$
$618$	−28.3099	−1.13879
$619$	−19.9628	−0.802374	−0.401187	−	0.915996i	$-0.631402\pi$
$619$	−19.9628	−0.802374	−0.401187	+	0.915996i	$0.631402\pi$
$620$	−144.532	−5.80453
$621$	1.92900	0.0774082
$622$	−51.7940	−2.07675
$623$	30.5896	1.22554
$624$	−72.7122	−2.91082
$625$	−31.1975	−1.24790
$626$	−38.4382	−1.53630
$627$	43.2375	1.72674
$628$	71.6513	2.85920
$629$	72.0501	2.87282
$630$	−137.439	−5.47569
$631$	11.3864	0.453286	0.226643	−	0.973978i	$-0.427225\pi$
$631$	11.3864	0.453286	0.226643	+	0.973978i	$0.427225\pi$
$632$	−45.3305	−1.80315
$633$	−57.8051	−2.29755
$634$	−4.00302	−0.158980
$635$	27.0077	1.07177
$636$	2.32606	0.0922343
$637$	−29.5072	−1.16912
$638$	−125.493	−4.96831
$639$	−15.8468	−0.626890
$640$	104.389	4.12632
$641$	−17.4366	−0.688703	−0.344352	−	0.938841i	$-0.611901\pi$
$641$	−17.4366	−0.688703	−0.344352	+	0.938841i	$0.611901\pi$
$642$	116.081	4.58134
$643$	−7.91919	−0.312302	−0.156151	−	0.987733i	$-0.549909\pi$
$643$	−7.91919	−0.312302	−0.156151	+	0.987733i	$0.549909\pi$
$644$	−24.2641	−0.956140
$645$	−29.3507	−1.15568
$646$	−57.6516	−2.26827
$647$	15.2537	0.599685	0.299842	−	0.953989i	$-0.403066\pi$
$647$	15.2537	0.599685	0.299842	+	0.953989i	$0.403066\pi$
$648$	56.5716	2.22234
$649$	10.0236	0.393461
$650$	13.9617	0.547622
$651$	−118.384	−4.63984
$652$	−73.5360	−2.87989
$653$	−12.8040	−0.501061	−0.250531	−	0.968109i	$-0.580605\pi$
$653$	−12.8040	−0.501061	−0.250531	+	0.968109i	$0.580605\pi$
$654$	−62.8527	−2.45773
$655$	48.4942	1.89482
$656$	56.4670	2.20467
$657$	−28.4828	−1.11122
$658$	24.9589	0.973001
$659$	−24.0091	−0.935263	−0.467631	−	0.883924i	$-0.654892\pi$
$659$	−24.0091	−0.935263	−0.467631	+	0.883924i	$0.654892\pi$
$660$	230.946	8.98957
$661$	−16.7021	−0.649635	−0.324817	−	0.945777i	$-0.605303\pi$
$661$	−16.7021	−0.649635	−0.324817	+	0.945777i	$0.605303\pi$
$662$	−2.58029	−0.100286
$663$	36.2601	1.40822
$664$	−10.7056	−0.415456
$665$	−37.6891	−1.46152
$666$	100.540	3.89583
$667$	−7.33347	−0.283953
$668$	87.6617	3.39173
$669$	−49.7337	−1.92282
$670$	−119.574	−4.61955
$671$	27.5930	1.06522
$672$	270.768	10.4451
$673$	−32.2352	−1.24258	−0.621289	−	0.783582i	$-0.713391\pi$
$673$	−32.2352	−1.24258	−0.621289	+	0.783582i	$0.713391\pi$
$674$	−24.2588	−0.934415
$675$	5.65101	0.217508
$676$	−51.8272	−1.99335
$677$	−23.7311	−0.912059	−0.456029	−	0.889965i	$-0.650729\pi$
$677$	−23.7311	−0.912059	−0.456029	+	0.889965i	$0.650729\pi$
$678$	−86.3036	−3.31447
$679$	17.1450	0.657966
$680$	−195.143	−7.48340
$681$	10.5861	0.405659
$682$	151.785	5.81214
$683$	−8.27589	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$683$	−8.27589	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$684$	−58.8806	−2.25136
$685$	−5.02091	−0.191839
$686$	114.052	4.35454
$687$	−23.0987	−0.881270
$688$	60.3214	2.29973
$689$	−0.306111	−0.0116619
$690$	18.4393	0.701971
$691$	−26.5703	−1.01078	−0.505391	−	0.862891i	$-0.668652\pi$
$691$	−26.5703	−1.01078	−0.505391	+	0.862891i	$0.668652\pi$
$692$	−34.0579	−1.29469
$693$	105.641	4.01296
$694$	43.7035	1.65896
$695$	−9.85331	−0.373757
$696$	193.924	7.35067
$697$	−28.1589	−1.06660
$698$	85.8699	3.25022
$699$	26.3712	0.997452
$700$	−71.0817	−2.68664
$701$	−36.8491	−1.39177	−0.695886	−	0.718153i	$-0.744988\pi$
$701$	−36.8491	−1.39177	−0.695886	+	0.718153i	$0.744988\pi$
$702$	10.5930	0.399808
$703$	27.5705	1.03984
$704$	−173.308	−6.53178
$705$	−13.8823	−0.522839
$706$	45.1077	1.69765
$707$	8.23182	0.309589
$708$	−24.4424	−0.918602
$709$	42.1359	1.58245	0.791223	−	0.611528i	$-0.209445\pi$
$709$	42.1359	1.58245	0.791223	+	0.611528i	$0.209445\pi$
$710$	−31.7133	−1.19018
$711$	18.1994	0.682530
$712$	60.6067	2.27133
$713$	8.86990	0.332180
$714$	−252.227	−9.43935
$715$	−30.3926	−1.13662
$716$	52.5106	1.96241
$717$	−32.1614	−1.20109
$718$	−43.8547	−1.63664
$719$	10.5054	0.391784	0.195892	−	0.980625i	$-0.437240\pi$
$719$	10.5054	0.391784	0.195892	+	0.980625i	$0.437240\pi$
$720$	−157.108	−5.85506
$721$	−18.9678	−0.706398
$722$	29.8346	1.11033
$723$	6.93471	0.257905
$724$	33.4788	1.24423
$725$	−21.4834	−0.797874
$726$	−164.221	−6.09482
$727$	−15.9051	−0.589887	−0.294944	−	0.955515i	$-0.595301\pi$
$727$	−15.9051	−0.589887	−0.294944	+	0.955515i	$0.595301\pi$
$728$	−84.4392	−3.12952
$729$	−38.9045	−1.44091
$730$	−57.0009	−2.10970
$731$	−30.0810	−1.11259
$732$	−67.2851	−2.48693
$733$	31.2736	1.15512	0.577559	−	0.816349i	$-0.304005\pi$
$733$	31.2736	1.15512	0.577559	+	0.816349i	$0.304005\pi$
$734$	87.3692	3.22486
$735$	−114.164	−4.21099
$736$	−20.2872	−0.747796
$737$	91.9094	3.38553
$738$	−39.2934	−1.44641
$739$	18.3752	0.675944	0.337972	−	0.941156i	$-0.390259\pi$
$739$	18.3752	0.675944	0.337972	+	0.941156i	$0.390259\pi$
$740$	147.263	5.41350
$741$	13.8752	0.509717
$742$	2.12932	0.0781698
$743$	−29.2402	−1.07272	−0.536359	−	0.843990i	$-0.680201\pi$
$743$	−29.2402	−1.07272	−0.536359	+	0.843990i	$0.680201\pi$
$744$	−234.553	−8.59913
$745$	−41.4729	−1.51945
$746$	−7.67495	−0.281000
$747$	4.29809	0.157259
$748$	236.692	8.65433
$749$	77.7746	2.84182
$750$	−44.9480	−1.64127
$751$	11.3146	0.412876	0.206438	−	0.978460i	$-0.433813\pi$
$751$	11.3146	0.412876	0.206438	+	0.978460i	$0.433813\pi$
$752$	28.5309	1.04041
$753$	−63.8321	−2.32617
$754$	−40.2714	−1.46660
$755$	−39.9770	−1.45491
$756$	−53.9313	−1.96146
$757$	−4.96074	−0.180301	−0.0901505	−	0.995928i	$-0.528735\pi$
$757$	−4.96074	−0.180301	−0.0901505	+	0.995928i	$0.528735\pi$
$758$	58.8001	2.13571
$759$	−14.1731	−0.514453
$760$	−74.6730	−2.70867
$761$	12.4174	0.450132	0.225066	−	0.974344i	$-0.427740\pi$
$761$	12.4174	0.450132	0.225066	+	0.974344i	$0.427740\pi$
$762$	69.1629	2.50551
$763$	−42.1116	−1.52454
$764$	−54.3812	−1.96744
$765$	78.3464	2.83262
$766$	52.2667	1.88847
$767$	3.21663	0.116146
$768$	112.528	4.06051
$769$	−1.48062	−0.0533925	−0.0266963	−	0.999644i	$-0.508499\pi$
$769$	−1.48062	−0.0533925	−0.0266963	+	0.999644i	$0.508499\pi$
$770$	211.413	7.61878
$771$	34.5428	1.24403
$772$	129.798	4.67154
$773$	12.0224	0.432417	0.216209	−	0.976347i	$-0.430631\pi$
$773$	12.0224	0.432417	0.216209	+	0.976347i	$0.430631\pi$
$774$	−41.9755	−1.50878
$775$	25.9844	0.933386
$776$	33.9692	1.21942
$777$	120.621	4.32727
$778$	−28.6772	−1.02813
$779$	−10.7752	−0.386062
$780$	74.1120	2.65363
$781$	24.3761	0.872245
$782$	18.8980	0.675792
$783$	−16.2999	−0.582512
$784$	234.628	8.37957
$785$	−36.4822	−1.30211
$786$	124.187	4.42959
$787$	−24.6853	−0.879935	−0.439968	−	0.898014i	$-0.645010\pi$
$787$	−24.6853	−0.879935	−0.439968	+	0.898014i	$0.645010\pi$
$788$	−53.6269	−1.91038
$789$	−46.2748	−1.64743
$790$	36.4213	1.29581
$791$	−57.8238	−2.05598
$792$	209.305	7.43733
$793$	8.85475	0.314441
$794$	−44.3730	−1.57474
$795$	−1.18434	−0.0420044
$796$	−72.8431	−2.58186
$797$	−37.4278	−1.32576	−0.662880	−	0.748726i	$-0.730666\pi$
$797$	−37.4278	−1.32576	−0.662880	+	0.748726i	$0.730666\pi$
$798$	−96.5164	−3.41664
$799$	−14.2277	−0.503342
$800$	−59.4314	−2.10122
$801$	−24.3325	−0.859746
$802$	2.43195	0.0858751
$803$	43.8132	1.54613
$804$	−224.120	−7.90410
$805$	12.3544	0.435435
$806$	48.7086	1.71569
$807$	0.0827248	0.00291205
$808$	16.3096	0.573770
$809$	14.0413	0.493664	0.246832	−	0.969058i	$-0.420610\pi$
$809$	14.0413	0.493664	0.246832	+	0.969058i	$0.420610\pi$
$810$	−45.4530	−1.59706
$811$	−16.7663	−0.588744	−0.294372	−	0.955691i	$-0.595110\pi$
$811$	−16.7663	−0.588744	−0.294372	+	0.955691i	$0.595110\pi$
$812$	205.030	7.19514
$813$	57.8468	2.02878
$814$	−154.653	−5.42059
$815$	37.4418	1.31153
$816$	−288.323	−10.0933
$817$	−11.5107	−0.402709
$818$	48.4654	1.69455
$819$	33.9008	1.18459
$820$	−57.5541	−2.00988
$821$	50.0647	1.74727	0.873634	−	0.486583i	$-0.161757\pi$
$821$	50.0647	1.74727	0.873634	+	0.486583i	$0.161757\pi$
$822$	−12.8578	−0.448469
$823$	−5.14747	−0.179429	−0.0897147	−	0.995968i	$-0.528596\pi$
$823$	−5.14747	−0.179429	−0.0897147	+	0.995968i	$0.528596\pi$
$824$	−37.5807	−1.30918
$825$	−41.5202	−1.44555
$826$	−22.3750	−0.778528
$827$	44.9547	1.56323	0.781614	−	0.623763i	$-0.214397\pi$
$827$	44.9547	1.56323	0.781614	+	0.623763i	$0.214397\pi$
$828$	19.3009	0.670753
$829$	2.56378	0.0890438	0.0445219	−	0.999008i	$-0.485824\pi$
$829$	2.56378	0.0890438	0.0445219	+	0.999008i	$0.485824\pi$
$830$	8.60149	0.298562
$831$	−49.1913	−1.70643
$832$	−55.6154	−1.92812
$833$	−117.004	−4.05395
$834$	−25.2329	−0.873744
$835$	−44.6341	−1.54463
$836$	90.5720	3.13250
$837$	19.7149	0.681447
$838$	41.0680	1.41867
$839$	45.9567	1.58660	0.793301	−	0.608830i	$-0.208361\pi$
$839$	45.9567	1.58660	0.793301	+	0.608830i	$0.208361\pi$
$840$	−326.696	−11.2721
$841$	32.9673	1.13680
$842$	45.5702	1.57045
$843$	14.8705	0.512169
$844$	−121.087	−4.16800
$845$	26.3885	0.907792
$846$	−19.8536	−0.682581
$847$	−110.029	−3.78064
$848$	2.43405	0.0835857
$849$	−1.90348	−0.0653271
$850$	55.3618	1.89889
$851$	−9.03753	−0.309802
$852$	−59.4407	−2.03641
$853$	−1.34073	−0.0459056	−0.0229528	−	0.999737i	$-0.507307\pi$
$853$	−1.34073	−0.0459056	−0.0229528	+	0.999737i	$0.507307\pi$
$854$	−61.5941	−2.10771
$855$	29.9798	1.02529
$856$	154.094	5.26682
$857$	8.40760	0.287198	0.143599	−	0.989636i	$-0.454132\pi$
$857$	8.40760	0.287198	0.143599	+	0.989636i	$0.454132\pi$
$858$	−77.8311	−2.65711
$859$	27.2127	0.928487	0.464243	−	0.885708i	$-0.346326\pi$
$859$	27.2127	0.928487	0.464243	+	0.885708i	$0.346326\pi$
$860$	−61.4826	−2.09654
$861$	−47.1418	−1.60659
$862$	−39.4781	−1.34463
$863$	52.1284	1.77447	0.887235	−	0.461318i	$-0.152623\pi$
$863$	52.1284	1.77447	0.887235	+	0.461318i	$0.152623\pi$
$864$	−45.0919	−1.53406
$865$	17.3410	0.589612
$866$	56.4207	1.91725
$867$	99.4686	3.37813
$868$	−247.985	−8.41718
$869$	−27.9948	−0.949660
$870$	−155.810	−5.28246
$871$	29.4943	0.999375
$872$	−83.4352	−2.82547
$873$	−13.6380	−0.461577
$874$	7.23147	0.244608
$875$	−30.1153	−1.01808
$876$	−106.838	−3.60971
$877$	−18.2570	−0.616495	−0.308247	−	0.951306i	$-0.599742\pi$
$877$	−18.2570	−0.616495	−0.308247	+	0.951306i	$0.599742\pi$
$878$	−82.9612	−2.79980
$879$	−17.5265	−0.591154
$880$	241.668	8.14664
$881$	−27.7907	−0.936292	−0.468146	−	0.883651i	$-0.655078\pi$
$881$	−27.7907	−0.936292	−0.468146	+	0.883651i	$0.655078\pi$
$882$	−163.269	−5.49756
$883$	−22.9546	−0.772484	−0.386242	−	0.922398i	$-0.626227\pi$
$883$	−22.9546	−0.772484	−0.386242	+	0.922398i	$0.626227\pi$
$884$	75.9559	2.55467
$885$	12.4452	0.418340
$886$	−41.7149	−1.40144
$887$	−20.7176	−0.695630	−0.347815	−	0.937563i	$-0.613076\pi$
$887$	−20.7176	−0.695630	−0.347815	+	0.937563i	$0.613076\pi$
$888$	238.986	8.01983
$889$	46.3395	1.55418
$890$	−48.6951	−1.63226
$891$	34.9370	1.17043
$892$	−104.180	−3.48820
$893$	−5.44435	−0.182188
$894$	−106.206	−3.55207
$895$	−26.7365	−0.893701
$896$	179.108	5.98359
$897$	−4.54825	−0.151861
$898$	12.6310	0.421500
$899$	−74.9500	−2.49972
$900$	56.5420	1.88473
$901$	−1.21381	−0.0404379
$902$	60.4423	2.01251
$903$	−50.3596	−1.67586
$904$	−114.566	−3.81039
$905$	−17.0462	−0.566634
$906$	−102.375	−3.40120
$907$	54.8192	1.82024	0.910121	−	0.414342i	$-0.135988\pi$
$907$	54.8192	1.82024	0.910121	+	0.414342i	$0.135988\pi$
$908$	22.1752	0.735911
$909$	−6.54800	−0.217184
$910$	67.8435	2.24899
$911$	−22.0016	−0.728944	−0.364472	−	0.931214i	$-0.618750\pi$
$911$	−22.0016	−0.728944	−0.364472	+	0.931214i	$0.618750\pi$
$912$	−110.329	−3.65336
$913$	−6.61145	−0.218807
$914$	92.4810	3.05900
$915$	34.2591	1.13257
$916$	−48.3861	−1.59872
$917$	83.2056	2.74769
$918$	42.0042	1.38635
$919$	0.705553	0.0232741	0.0116370	−	0.999932i	$-0.496296\pi$
$919$	0.705553	0.0232741	0.0116370	+	0.999932i	$0.496296\pi$
$920$	24.4776	0.807003
$921$	31.7017	1.04461
$922$	71.2090	2.34514
$923$	7.82242	0.257478
$924$	396.254	13.0358
$925$	−26.4754	−0.870507
$926$	−0.865764	−0.0284508
$927$	15.0879	0.495553
$928$	171.425	5.62731
$929$	8.18969	0.268695	0.134348	−	0.990934i	$-0.457106\pi$
$929$	8.18969	0.268695	0.134348	+	0.990934i	$0.457106\pi$
$930$	188.454	6.17965
$931$	−44.7725	−1.46736
$932$	55.2413	1.80949
$933$	49.4287	1.61822
$934$	113.456	3.71238
$935$	−120.515	−3.94126
$936$	67.1672	2.19543
$937$	−42.2173	−1.37918	−0.689589	−	0.724201i	$-0.742209\pi$
$937$	−42.2173	−1.37918	−0.689589	+	0.724201i	$0.742209\pi$
$938$	−205.164	−6.69883
$939$	36.6828	1.19710
$940$	−29.0801	−0.948489
$941$	22.7660	0.742151	0.371076	−	0.928603i	$-0.378989\pi$
$941$	22.7660	0.742151	0.371076	+	0.928603i	$0.378989\pi$
$942$	−93.4257	−3.04397
$943$	3.53209	0.115021
$944$	−25.5772	−0.832467
$945$	27.4598	0.893267
$946$	64.5680	2.09929
$947$	−20.9456	−0.680640	−0.340320	−	0.940310i	$-0.610535\pi$
$947$	−20.9456	−0.680640	−0.340320	+	0.940310i	$0.610535\pi$
$948$	68.2650	2.21714
$949$	14.0599	0.456404
$950$	21.1846	0.687319
$951$	3.82022	0.123879
$952$	−334.824	−10.8517
$953$	35.4665	1.14887	0.574436	−	0.818549i	$-0.305221\pi$
$953$	35.4665	1.14887	0.574436	+	0.818549i	$0.305221\pi$
$954$	−1.69377	−0.0548378
$955$	27.6889	0.895992
$956$	−67.3703	−2.17891
$957$	119.762	3.87136
$958$	−20.0287	−0.647097
$959$	−8.61481	−0.278187
$960$	−215.176	−6.94479
$961$	59.6526	1.92428
$962$	−49.6291	−1.60011
$963$	−61.8658	−1.99360
$964$	14.5265	0.467868
$965$	−66.0885	−2.12746
$966$	31.6378	1.01793
$967$	21.1302	0.679500	0.339750	−	0.940516i	$-0.389657\pi$
$967$	21.1302	0.679500	0.339750	+	0.940516i	$0.389657\pi$
$968$	−217.999	−7.00676
$969$	55.0188	1.76746
$970$	−27.2929	−0.876323
$971$	34.1694	1.09655	0.548274	−	0.836299i	$-0.315285\pi$
$971$	34.1694	1.09655	0.548274	+	0.836299i	$0.315285\pi$
$972$	−119.112	−3.82051
$973$	−16.9062	−0.541987
$974$	−108.901	−3.48940
$975$	−13.3241	−0.426712
$976$	−70.4089	−2.25373
$977$	2.83751	0.0907801	0.0453900	−	0.998969i	$-0.485547\pi$
$977$	2.83751	0.0907801	0.0453900	+	0.998969i	$0.485547\pi$
$978$	95.8831	3.06600
$979$	37.4290	1.19624
$980$	−239.145	−7.63920
$981$	33.4977	1.06950
$982$	−30.5874	−0.976082
$983$	−37.6787	−1.20176	−0.600882	−	0.799338i	$-0.705184\pi$
$983$	−37.6787	−1.20176	−0.600882	+	0.799338i	$0.705184\pi$
$984$	−93.4014	−2.97753
$985$	27.3048	0.870005
$986$	−159.687	−5.08547
$987$	−23.8191	−0.758171
$988$	29.0651	0.924683
$989$	3.77318	0.119980
$990$	−168.168	−5.34474
$991$	30.6901	0.974902	0.487451	−	0.873150i	$-0.337927\pi$
$991$	30.6901	0.974902	0.487451	+	0.873150i	$0.337927\pi$
$992$	−207.340	−6.58307
$993$	2.46246	0.0781438
$994$	−54.4131	−1.72588
$995$	37.0890	1.17580
$996$	16.1219	0.510843
$997$	50.7002	1.60569	0.802845	−	0.596188i	$-0.203319\pi$
$997$	50.7002	1.60569	0.802845	+	0.596188i	$0.203319\pi$
$998$	−33.7251	−1.06755
$999$	−20.0875	−0.635540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.5	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.73134 q^{2} +2.60660 q^{3} +5.46019 q^{4} -2.78013 q^{5} -7.11951 q^{6} -4.77010 q^{7} -9.45095 q^{8} +3.79438 q^{9} +O(q^{10})\)	\(q-2.73134 q^{2} +2.60660 q^{3} +5.46019 q^{4} -2.78013 q^{5} -7.11951 q^{6} -4.77010 q^{7} -9.45095 q^{8} +3.79438 q^{9} +7.59346 q^{10} -5.83664 q^{11} +14.2326 q^{12} -1.87301 q^{13} +13.0288 q^{14} -7.24669 q^{15} +14.8933 q^{16} -7.42699 q^{17} -10.3637 q^{18} -2.84199 q^{19} -15.1800 q^{20} -12.4338 q^{21} +15.9418 q^{22} +0.931598 q^{23} -24.6349 q^{24} +2.72912 q^{25} +5.11582 q^{26} +2.07064 q^{27} -26.0457 q^{28} -7.87193 q^{29} +19.7932 q^{30} +9.52117 q^{31} -21.7768 q^{32} -15.2138 q^{33} +20.2856 q^{34} +13.2615 q^{35} +20.7181 q^{36} -9.70110 q^{37} +7.76244 q^{38} -4.88220 q^{39} +26.2749 q^{40} +3.79143 q^{41} +33.9608 q^{42} +4.05023 q^{43} -31.8692 q^{44} -10.5489 q^{45} -2.54451 q^{46} +1.91568 q^{47} +38.8210 q^{48} +15.7539 q^{49} -7.45413 q^{50} -19.3592 q^{51} -10.2270 q^{52} +0.163432 q^{53} -5.65561 q^{54} +16.2266 q^{55} +45.0820 q^{56} -7.40795 q^{57} +21.5009 q^{58} -1.71736 q^{59} -39.5684 q^{60} -4.72755 q^{61} -26.0055 q^{62} -18.0996 q^{63} +29.6930 q^{64} +5.20721 q^{65} +41.5540 q^{66} -15.7470 q^{67} -40.5528 q^{68} +2.42831 q^{69} -36.2216 q^{70} -4.17639 q^{71} -35.8605 q^{72} -7.50657 q^{73} +26.4970 q^{74} +7.11372 q^{75} -15.5178 q^{76} +27.8414 q^{77} +13.3349 q^{78} +4.79640 q^{79} -41.4054 q^{80} -5.98581 q^{81} -10.3557 q^{82} +1.13275 q^{83} -67.8908 q^{84} +20.6480 q^{85} -11.0625 q^{86} -20.5190 q^{87} +55.1618 q^{88} -6.41276 q^{89} +28.8125 q^{90} +8.93446 q^{91} +5.08671 q^{92} +24.8179 q^{93} -5.23237 q^{94} +7.90111 q^{95} -56.7634 q^{96} -3.59427 q^{97} -43.0292 q^{98} -22.1464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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