LMFDB - Embedded newform 4001.2.a.b.1.40

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			1.40
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)

$f(q)$	$=$	$q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +O(q^{10})$	\(q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +7.52990 q^{10} -3.00578 q^{11} +3.54720 q^{12} +0.487304 q^{13} -9.43134 q^{14} -11.0993 q^{15} -4.89722 q^{16} +1.27456 q^{17} -7.68061 q^{18} +5.37940 q^{19} -5.45697 q^{20} +13.9021 q^{21} +5.47728 q^{22} -0.0884748 q^{23} +3.32545 q^{24} +12.0751 q^{25} -0.887990 q^{26} +3.26329 q^{27} +6.83496 q^{28} +2.32622 q^{29} +20.2257 q^{30} +7.57211 q^{31} +6.44788 q^{32} -8.07369 q^{33} -2.32256 q^{34} -21.3868 q^{35} +5.56619 q^{36} -4.84346 q^{37} -9.80261 q^{38} +1.30893 q^{39} -5.11583 q^{40} -1.44912 q^{41} -25.3331 q^{42} -10.7400 q^{43} -3.96943 q^{44} -17.4168 q^{45} +0.161223 q^{46} +1.02412 q^{47} -13.1542 q^{48} +19.7874 q^{49} -22.0038 q^{50} +3.42353 q^{51} +0.643532 q^{52} +2.55300 q^{53} -5.94654 q^{54} +12.4205 q^{55} +6.40767 q^{56} +14.4494 q^{57} -4.23896 q^{58} -0.415687 q^{59} -14.6577 q^{60} -4.77911 q^{61} -13.7983 q^{62} +21.8149 q^{63} -1.95521 q^{64} -2.01364 q^{65} +14.7123 q^{66} -3.55935 q^{67} +1.68318 q^{68} -0.237648 q^{69} +38.9721 q^{70} -5.50177 q^{71} +5.21822 q^{72} +4.20006 q^{73} +8.82599 q^{74} +32.4343 q^{75} +7.10402 q^{76} -15.5569 q^{77} -2.38519 q^{78} +16.6252 q^{79} +20.2363 q^{80} -3.87931 q^{81} +2.64065 q^{82} +11.0604 q^{83} +18.3591 q^{84} -5.26672 q^{85} +19.5710 q^{86} +6.24836 q^{87} -3.72128 q^{88} +7.34281 q^{89} +31.7378 q^{90} +2.52212 q^{91} -0.116840 q^{92} +20.3391 q^{93} -1.86621 q^{94} -22.2287 q^{95} +17.3194 q^{96} -16.7412 q^{97} -36.0576 q^{98} -12.6691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.82225	−1.28853	−0.644263	−	0.764804i	$-0.722836\pi$
$2$	−1.82225	−1.28853	−0.644263	+	0.764804i	$0.722836\pi$
$3$	2.68606	1.55080	0.775398	−	0.631473i	$-0.217549\pi$
$3$	2.68606	1.55080	0.775398	+	0.631473i	$0.217549\pi$
$4$	1.32060	0.660299
$5$	−4.13220	−1.84797	−0.923987	−	0.382423i	$-0.875090\pi$
$5$	−4.13220	−1.84797	−0.923987	+	0.382423i	$0.875090\pi$
$6$	−4.89467	−1.99824
$7$	5.17565	1.95621	0.978107	−	0.208105i	$-0.0667294\pi$
$7$	5.17565	1.95621	0.978107	+	0.208105i	$0.0667294\pi$
$8$	1.23804	0.437714
$9$	4.21490	1.40497
$10$	7.52990	2.38116
$11$	−3.00578	−0.906277	−0.453138	−	0.891440i	$-0.649696\pi$
$11$	−3.00578	−0.906277	−0.453138	+	0.891440i	$0.649696\pi$
$12$	3.54720	1.02399
$13$	0.487304	0.135154	0.0675769	−	0.997714i	$-0.478473\pi$
$13$	0.487304	0.135154	0.0675769	+	0.997714i	$0.478473\pi$
$14$	−9.43134	−2.52063
$15$	−11.0993	−2.86583
$16$	−4.89722	−1.22430
$17$	1.27456	0.309125	0.154563	−	0.987983i	$-0.450603\pi$
$17$	1.27456	0.309125	0.154563	+	0.987983i	$0.450603\pi$
$18$	−7.68061	−1.81034
$19$	5.37940	1.23412	0.617059	−	0.786917i	$-0.288324\pi$
$19$	5.37940	1.23412	0.617059	+	0.786917i	$0.288324\pi$
$20$	−5.45697	−1.22022
$21$	13.9021	3.03369
$22$	5.47728	1.16776
$23$	−0.0884748	−0.0184483	−0.00922413	−	0.999957i	$-0.502936\pi$
$23$	−0.0884748	−0.0184483	−0.00922413	+	0.999957i	$0.502936\pi$
$24$	3.32545	0.678804
$25$	12.0751	2.41501
$26$	−0.887990	−0.174149
$27$	3.26329	0.628021
$28$	6.83496	1.29169
$29$	2.32622	0.431968	0.215984	−	0.976397i	$-0.430704\pi$
$29$	2.32622	0.431968	0.215984	+	0.976397i	$0.430704\pi$
$30$	20.2257	3.69270
$31$	7.57211	1.35999	0.679996	−	0.733216i	$-0.261982\pi$
$31$	7.57211	1.35999	0.679996	+	0.733216i	$0.261982\pi$
$32$	6.44788	1.13983
$33$	−8.07369	−1.40545
$34$	−2.32256	−0.398316
$35$	−21.3868	−3.61503
$36$	5.56619	0.927698
$37$	−4.84346	−0.796259	−0.398130	−	0.917329i	$-0.630341\pi$
$37$	−4.84346	−0.796259	−0.398130	+	0.917329i	$0.630341\pi$
$38$	−9.80261	−1.59019
$39$	1.30893	0.209596
$40$	−5.11583	−0.808884
$41$	−1.44912	−0.226314	−0.113157	−	0.993577i	$-0.536096\pi$
$41$	−1.44912	−0.226314	−0.113157	+	0.993577i	$0.536096\pi$
$42$	−25.3331	−3.90898
$43$	−10.7400	−1.63784	−0.818919	−	0.573909i	$-0.805426\pi$
$43$	−10.7400	−1.63784	−0.818919	+	0.573909i	$0.805426\pi$
$44$	−3.96943	−0.598413
$45$	−17.4168	−2.59634
$46$	0.161223	0.0237711
$47$	1.02412	0.149384	0.0746920	−	0.997207i	$-0.476203\pi$
$47$	1.02412	0.149384	0.0746920	+	0.997207i	$0.476203\pi$
$48$	−13.1542	−1.89865
$49$	19.7874	2.82677
$50$	−22.0038	−3.11180
$51$	3.42353	0.479390
$52$	0.643532	0.0892419
$53$	2.55300	0.350681	0.175341	−	0.984508i	$-0.443897\pi$
$53$	2.55300	0.350681	0.175341	+	0.984508i	$0.443897\pi$
$54$	−5.94654	−0.809222
$55$	12.4205	1.67478
$56$	6.40767	0.856261
$57$	14.4494	1.91387
$58$	−4.23896	−0.556602
$59$	−0.415687	−0.0541178	−0.0270589	−	0.999634i	$-0.508614\pi$
$59$	−0.415687	−0.0541178	−0.0270589	+	0.999634i	$0.508614\pi$
$60$	−14.6577	−1.89231
$61$	−4.77911	−0.611902	−0.305951	−	0.952047i	$-0.598974\pi$
$61$	−4.77911	−0.611902	−0.305951	+	0.952047i	$0.598974\pi$
$62$	−13.7983	−1.75238
$63$	21.8149	2.74842
$64$	−1.95521	−0.244401
$65$	−2.01364	−0.249761
$66$	14.7123	1.81096
$67$	−3.55935	−0.434844	−0.217422	−	0.976078i	$-0.569765\pi$
$67$	−3.55935	−0.434844	−0.217422	+	0.976078i	$0.569765\pi$
$68$	1.68318	0.204115
$69$	−0.237648	−0.0286095
$70$	38.9721	4.65806
$71$	−5.50177	−0.652940	−0.326470	−	0.945208i	$-0.605859\pi$
$71$	−5.50177	−0.652940	−0.326470	+	0.945208i	$0.605859\pi$
$72$	5.21822	0.614973
$73$	4.20006	0.491580	0.245790	−	0.969323i	$-0.420953\pi$
$73$	4.20006	0.491580	0.245790	+	0.969323i	$0.420953\pi$
$74$	8.82599	1.02600
$75$	32.4343	3.74519
$76$	7.10402	0.814887
$77$	−15.5569	−1.77287
$78$	−2.38519	−0.270070
$79$	16.6252	1.87048	0.935239	−	0.354016i	$-0.115184\pi$
$79$	16.6252	1.87048	0.935239	+	0.354016i	$0.115184\pi$
$80$	20.2363	2.26248
$81$	−3.87931	−0.431034
$82$	2.64065	0.291611
$83$	11.0604	1.21403	0.607017	−	0.794689i	$-0.292366\pi$
$83$	11.0604	1.21403	0.607017	+	0.794689i	$0.292366\pi$
$84$	18.3591	2.00314
$85$	−5.26672	−0.571256
$86$	19.5710	2.11040
$87$	6.24836	0.669894
$88$	−3.72128	−0.396690
$89$	7.34281	0.778336	0.389168	−	0.921167i	$-0.372762\pi$
$89$	7.34281	0.778336	0.389168	+	0.921167i	$0.372762\pi$
$90$	31.7378	3.34546
$91$	2.52212	0.264390
$92$	−0.116840	−0.0121814
$93$	20.3391	2.10907
$94$	−1.86621	−0.192485
$95$	−22.2287	−2.28062
$96$	17.3194	1.76765
$97$	−16.7412	−1.69981	−0.849906	−	0.526934i	$-0.823342\pi$
$97$	−16.7412	−1.69981	−0.849906	+	0.526934i	$0.823342\pi$
$98$	−36.0576	−3.64237
$99$	−12.6691	−1.27329
$100$	15.9463	1.59463
$101$	−7.01632	−0.698150	−0.349075	−	0.937095i	$-0.613504\pi$
$101$	−7.01632	−0.698150	−0.349075	+	0.937095i	$0.613504\pi$
$102$	−6.23853	−0.617707
$103$	−0.948146	−0.0934236	−0.0467118	−	0.998908i	$-0.514874\pi$
$103$	−0.948146	−0.0934236	−0.0467118	+	0.998908i	$0.514874\pi$
$104$	0.603302	0.0591586
$105$	−57.4462	−5.60618
$106$	−4.65220	−0.451862
$107$	1.51759	0.146711	0.0733554	−	0.997306i	$-0.476629\pi$
$107$	1.51759	0.146711	0.0733554	+	0.997306i	$0.476629\pi$
$108$	4.30950	0.414682
$109$	14.3328	1.37283	0.686416	−	0.727209i	$-0.259183\pi$
$109$	14.3328	1.37283	0.686416	+	0.727209i	$0.259183\pi$
$110$	−22.6332	−2.15799
$111$	−13.0098	−1.23484
$112$	−25.3463	−2.39500
$113$	13.4796	1.26806	0.634028	−	0.773310i	$-0.281401\pi$
$113$	13.4796	1.26806	0.634028	+	0.773310i	$0.281401\pi$
$114$	−26.3304	−2.46607
$115$	0.365595	0.0340919
$116$	3.07200	0.285228
$117$	2.05394	0.189887
$118$	0.757486	0.0697322
$119$	6.59666	0.604715
$120$	−13.7414	−1.25441
$121$	−1.96529	−0.178663
$122$	8.70873	0.788452
$123$	−3.89241	−0.350967
$124$	9.99971	0.898001
$125$	−29.2355	−2.61490
$126$	−39.7522	−3.54140
$127$	3.88226	0.344495	0.172248	−	0.985054i	$-0.444897\pi$
$127$	3.88226	0.344495	0.172248	+	0.985054i	$0.444897\pi$
$128$	−9.33286	−0.824916
$129$	−28.8483	−2.53995
$130$	3.66935	0.321823
$131$	11.6225	1.01547	0.507733	−	0.861515i	$-0.330484\pi$
$131$	11.6225	1.01547	0.507733	+	0.861515i	$0.330484\pi$
$132$	−10.6621	−0.928017
$133$	27.8419	2.41420
$134$	6.48602	0.560307
$135$	−13.4846	−1.16057
$136$	1.57795	0.135308
$137$	−13.7634	−1.17589	−0.587945	−	0.808901i	$-0.700063\pi$
$137$	−13.7634	−1.17589	−0.587945	+	0.808901i	$0.700063\pi$
$138$	0.433055	0.0368641
$139$	18.7351	1.58909	0.794545	−	0.607205i	$-0.207709\pi$
$139$	18.7351	1.58909	0.794545	+	0.607205i	$0.207709\pi$
$140$	−28.2434	−2.38700
$141$	2.75086	0.231664
$142$	10.0256	0.841330
$143$	−1.46473	−0.122487
$144$	−20.6413	−1.72011
$145$	−9.61240	−0.798266
$146$	−7.65356	−0.633413
$147$	53.1501	4.38374
$148$	−6.39626	−0.525769
$149$	17.0987	1.40078	0.700390	−	0.713760i	$-0.253009\pi$
$149$	17.0987	1.40078	0.700390	+	0.713760i	$0.253009\pi$
$150$	−59.1034	−4.82577
$151$	0.102087	0.00830775	0.00415387	−	0.999991i	$-0.498678\pi$
$151$	0.102087	0.00830775	0.00415387	+	0.999991i	$0.498678\pi$
$152$	6.65992	0.540191
$153$	5.37213	0.434311
$154$	28.3485	2.28439
$155$	−31.2895	−2.51323
$156$	1.72856	0.138396
$157$	6.49465	0.518329	0.259165	−	0.965833i	$-0.416553\pi$
$157$	6.49465	0.518329	0.259165	+	0.965833i	$0.416553\pi$
$158$	−30.2952	−2.41016
$159$	6.85750	0.543835
$160$	−26.6439	−2.10638
$161$	−0.457915	−0.0360887
$162$	7.06908	0.555399
$163$	6.35927	0.498096	0.249048	−	0.968491i	$-0.419882\pi$
$163$	6.35927	0.498096	0.249048	+	0.968491i	$0.419882\pi$
$164$	−1.91370	−0.149435
$165$	33.3621	2.59724
$166$	−20.1548	−1.56431
$167$	−6.02781	−0.466446	−0.233223	−	0.972423i	$-0.574927\pi$
$167$	−6.02781	−0.466446	−0.233223	+	0.972423i	$0.574927\pi$
$168$	17.2114	1.32789
$169$	−12.7625	−0.981733
$170$	9.59728	0.736078
$171$	22.6736	1.73390
$172$	−14.1833	−1.08146
$173$	−21.1629	−1.60898	−0.804491	−	0.593965i	$-0.797562\pi$
$173$	−21.1629	−1.60898	−0.804491	+	0.593965i	$0.797562\pi$
$174$	−11.3861	−0.863176
$175$	62.4963	4.72427
$176$	14.7200	1.10956
$177$	−1.11656	−0.0839257
$178$	−13.3804	−1.00291
$179$	15.5515	1.16237	0.581186	−	0.813771i	$-0.302589\pi$
$179$	15.5515	1.16237	0.581186	+	0.813771i	$0.302589\pi$
$180$	−23.0006	−1.71436
$181$	−6.44125	−0.478774	−0.239387	−	0.970924i	$-0.576946\pi$
$181$	−6.44125	−0.478774	−0.239387	+	0.970924i	$0.576946\pi$
$182$	−4.59593	−0.340673
$183$	−12.8370	−0.948935
$184$	−0.109535	−0.00807506
$185$	20.0141	1.47147
$186$	−37.0630	−2.71759
$187$	−3.83103	−0.280153
$188$	1.35246	0.0986381
$189$	16.8897	1.22854
$190$	40.5063	2.93864
$191$	5.65605	0.409257	0.204629	−	0.978840i	$-0.434401\pi$
$191$	5.65605	0.409257	0.204629	+	0.978840i	$0.434401\pi$
$192$	−5.25181	−0.379017
$193$	−8.10006	−0.583055	−0.291528	−	0.956562i	$-0.594163\pi$
$193$	−8.10006	−0.583055	−0.291528	+	0.956562i	$0.594163\pi$
$194$	30.5067	2.19025
$195$	−5.40874	−0.387328
$196$	26.1312	1.86651
$197$	−10.5838	−0.754062	−0.377031	−	0.926201i	$-0.623055\pi$
$197$	−10.5838	−0.754062	−0.377031	+	0.926201i	$0.623055\pi$
$198$	23.0862	1.64067
$199$	−21.1551	−1.49964	−0.749822	−	0.661640i	$-0.769861\pi$
$199$	−21.1551	−1.49964	−0.749822	+	0.661640i	$0.769861\pi$
$200$	14.9494	1.05708
$201$	−9.56061	−0.674353
$202$	12.7855	0.899585
$203$	12.0397	0.845022
$204$	4.52111	0.316541
$205$	5.98803	0.418222
$206$	1.72776	0.120379
$207$	−0.372913	−0.0259192
$208$	−2.38643	−0.165469
$209$	−16.1693	−1.11845
$210$	104.681	7.22370
$211$	−0.592362	−0.0407799	−0.0203899	−	0.999792i	$-0.506491\pi$
$211$	−0.592362	−0.0407799	−0.0203899	+	0.999792i	$0.506491\pi$
$212$	3.37148	0.231554
$213$	−14.7781	−1.01258
$214$	−2.76543	−0.189041
$215$	44.3799	3.02668
$216$	4.04009	0.274893
$217$	39.1906	2.66043
$218$	−26.1179	−1.76893
$219$	11.2816	0.762340
$220$	16.4024	1.10585
$221$	0.621096	0.0417794
$222$	23.7071	1.59112
$223$	12.4349	0.832705	0.416352	−	0.909203i	$-0.363308\pi$
$223$	12.4349	0.832705	0.416352	+	0.909203i	$0.363308\pi$
$224$	33.3720	2.22976
$225$	50.8952	3.39301
$226$	−24.5632	−1.63392
$227$	15.8638	1.05292	0.526458	−	0.850201i	$-0.323520\pi$
$227$	15.8638	1.05292	0.526458	+	0.850201i	$0.323520\pi$
$228$	19.0818	1.26372
$229$	9.32802	0.616413	0.308206	−	0.951320i	$-0.400271\pi$
$229$	9.32802	0.616413	0.308206	+	0.951320i	$0.400271\pi$
$230$	−0.666206	−0.0439283
$231$	−41.7866	−2.74936
$232$	2.87996	0.189078
$233$	21.0202	1.37708	0.688540	−	0.725199i	$-0.258252\pi$
$233$	21.0202	1.37708	0.688540	+	0.725199i	$0.258252\pi$
$234$	−3.74279	−0.244674
$235$	−4.23188	−0.276058
$236$	−0.548955	−0.0357339
$237$	44.6562	2.90073
$238$	−12.0208	−0.779191
$239$	−8.07536	−0.522352	−0.261176	−	0.965291i	$-0.584110\pi$
$239$	−8.07536	−0.522352	−0.261176	+	0.965291i	$0.584110\pi$
$240$	54.3558	3.50865
$241$	16.0756	1.03552	0.517760	−	0.855526i	$-0.326766\pi$
$241$	16.0756	1.03552	0.517760	+	0.855526i	$0.326766\pi$
$242$	3.58125	0.230212
$243$	−20.2099	−1.29647
$244$	−6.31128	−0.404038
$245$	−81.7654	−5.22380
$246$	7.09294	0.452230
$247$	2.62140	0.166796
$248$	9.37458	0.595287
$249$	29.7088	1.88272
$250$	53.2744	3.36937
$251$	3.30727	0.208753	0.104377	−	0.994538i	$-0.466715\pi$
$251$	3.30727	0.208753	0.104377	+	0.994538i	$0.466715\pi$
$252$	28.8087	1.81478
$253$	0.265936	0.0167192
$254$	−7.07446	−0.443891
$255$	−14.1467	−0.885901
$256$	20.9172	1.30733
$257$	−2.73397	−0.170541	−0.0852703	−	0.996358i	$-0.527175\pi$
$257$	−2.73397	−0.170541	−0.0852703	+	0.996358i	$0.527175\pi$
$258$	52.5689	3.27280
$259$	−25.0681	−1.55765
$260$	−2.65920	−0.164917
$261$	9.80479	0.606901
$262$	−21.1792	−1.30845
$263$	23.8280	1.46930	0.734648	−	0.678448i	$-0.237347\pi$
$263$	23.8280	1.46930	0.734648	+	0.678448i	$0.237347\pi$
$264$	−9.99556	−0.615184
$265$	−10.5495	−0.648050
$266$	−50.7349	−3.11076
$267$	19.7232	1.20704
$268$	−4.70047	−0.287127
$269$	12.1682	0.741910	0.370955	−	0.928651i	$-0.379030\pi$
$269$	12.1682	0.741910	0.370955	+	0.928651i	$0.379030\pi$
$270$	24.5723	1.49542
$271$	−20.3384	−1.23547	−0.617736	−	0.786386i	$-0.711950\pi$
$271$	−20.3384	−1.23547	−0.617736	+	0.786386i	$0.711950\pi$
$272$	−6.24178	−0.378463
$273$	6.77455	0.410014
$274$	25.0804	1.51516
$275$	−36.2949	−2.18867
$276$	−0.313838	−0.0188908
$277$	9.70253	0.582968	0.291484	−	0.956576i	$-0.405851\pi$
$277$	9.70253	0.582968	0.291484	+	0.956576i	$0.405851\pi$
$278$	−34.1400	−2.04758
$279$	31.9157	1.91074
$280$	−26.4778	−1.58235
$281$	26.2637	1.56676	0.783380	−	0.621544i	$-0.213494\pi$
$281$	26.2637	1.56676	0.783380	+	0.621544i	$0.213494\pi$
$282$	−5.01275	−0.298505
$283$	8.58208	0.510152	0.255076	−	0.966921i	$-0.417900\pi$
$283$	8.58208	0.510152	0.255076	+	0.966921i	$0.417900\pi$
$284$	−7.26563	−0.431136
$285$	−59.7076	−3.53678
$286$	2.66910	0.157827
$287$	−7.50012	−0.442718
$288$	27.1772	1.60143
$289$	−15.3755	−0.904442
$290$	17.5162	1.02859
$291$	−44.9679	−2.63606
$292$	5.54659	0.324589
$293$	−0.133318	−0.00778854	−0.00389427	−	0.999992i	$-0.501240\pi$
$293$	−0.133318	−0.00778854	−0.00389427	+	0.999992i	$0.501240\pi$
$294$	−96.8527	−5.64857
$295$	1.71770	0.100008
$296$	−5.99640	−0.348534
$297$	−9.80874	−0.569161
$298$	−31.1581	−1.80494
$299$	−0.0431141	−0.00249335
$300$	42.8326	2.47294
$301$	−55.5867	−3.20396
$302$	−0.186029	−0.0107047
$303$	−18.8462	−1.08269
$304$	−26.3441	−1.51094
$305$	19.7482	1.13078
$306$	−9.78937	−0.559621
$307$	−26.5823	−1.51713	−0.758567	−	0.651595i	$-0.774100\pi$
$307$	−26.5823	−1.51713	−0.758567	+	0.651595i	$0.774100\pi$
$308$	−20.5444	−1.17062
$309$	−2.54678	−0.144881
$310$	57.0172	3.23836
$311$	19.4255	1.10152	0.550759	−	0.834664i	$-0.314338\pi$
$311$	19.4255	1.10152	0.550759	+	0.834664i	$0.314338\pi$
$312$	1.62050	0.0917430
$313$	−5.80086	−0.327884	−0.163942	−	0.986470i	$-0.552421\pi$
$313$	−5.80086	−0.327884	−0.163942	+	0.986470i	$0.552421\pi$
$314$	−11.8349	−0.667881
$315$	−90.1433	−5.07900
$316$	21.9552	1.23508
$317$	31.4424	1.76598	0.882990	−	0.469392i	$-0.155527\pi$
$317$	31.4424	1.76598	0.882990	+	0.469392i	$0.155527\pi$
$318$	−12.4961	−0.700745
$319$	−6.99210	−0.391483
$320$	8.07932	0.451648
$321$	4.07633	0.227518
$322$	0.834436	0.0465013
$323$	6.85635	0.381497
$324$	−5.12301	−0.284612
$325$	5.88422	0.326398
$326$	−11.5882	−0.641810
$327$	38.4987	2.12898
$328$	−1.79407	−0.0990607
$329$	5.30051	0.292227
$330$	−60.7941	−3.34661
$331$	11.4177	0.627575	0.313788	−	0.949493i	$-0.398402\pi$
$331$	11.4177	0.627575	0.313788	+	0.949493i	$0.398402\pi$
$332$	14.6063	0.801625
$333$	−20.4147	−1.11872
$334$	10.9842	0.601027
$335$	14.7079	0.803580
$336$	−68.0816	−3.71416
$337$	26.1871	1.42650	0.713251	−	0.700909i	$-0.247222\pi$
$337$	26.1871	1.42650	0.713251	+	0.700909i	$0.247222\pi$
$338$	23.2565	1.26499
$339$	36.2070	1.96649
$340$	−6.95521	−0.377199
$341$	−22.7601	−1.23253
$342$	−41.3171	−2.23417
$343$	66.1831	3.57355
$344$	−13.2966	−0.716904
$345$	0.982010	0.0528696
$346$	38.5640	2.07321
$347$	−28.5805	−1.53428	−0.767142	−	0.641478i	$-0.778322\pi$
$347$	−28.5805	−1.53428	−0.767142	+	0.641478i	$0.778322\pi$
$348$	8.25157	0.442330
$349$	24.1301	1.29165	0.645826	−	0.763484i	$-0.276513\pi$
$349$	24.1301	1.29165	0.645826	+	0.763484i	$0.276513\pi$
$350$	−113.884	−6.08735
$351$	1.59022	0.0848794
$352$	−19.3809	−1.03300
$353$	−33.3389	−1.77445	−0.887224	−	0.461338i	$-0.847369\pi$
$353$	−33.3389	−1.77445	−0.887224	+	0.461338i	$0.847369\pi$
$354$	2.03465	0.108140
$355$	22.7344	1.20662
$356$	9.69690	0.513935
$357$	17.7190	0.937789
$358$	−28.3387	−1.49775
$359$	21.5536	1.13755	0.568777	−	0.822492i	$-0.307417\pi$
$359$	21.5536	1.13755	0.568777	+	0.822492i	$0.307417\pi$
$360$	−21.5627	−1.13645
$361$	9.93793	0.523049
$362$	11.7376	0.616913
$363$	−5.27888	−0.277070
$364$	3.33070	0.174576
$365$	−17.3555	−0.908427
$366$	23.3922	1.22273
$367$	17.4807	0.912487	0.456244	−	0.889855i	$-0.349195\pi$
$367$	17.4807	0.912487	0.456244	+	0.889855i	$0.349195\pi$
$368$	0.433280	0.0225863
$369$	−6.10788	−0.317964
$370$	−36.4707	−1.89602
$371$	13.2134	0.686007
$372$	26.8598	1.39262
$373$	4.90780	0.254116	0.127058	−	0.991895i	$-0.459447\pi$
$373$	4.90780	0.254116	0.127058	+	0.991895i	$0.459447\pi$
$374$	6.98111	0.360984
$375$	−78.5282	−4.05518
$376$	1.26791	0.0653874
$377$	1.13358	0.0583821
$378$	−30.7772	−1.58301
$379$	−22.6574	−1.16383	−0.581917	−	0.813248i	$-0.697697\pi$
$379$	−22.6574	−1.16383	−0.581917	+	0.813248i	$0.697697\pi$
$380$	−29.3552	−1.50589
$381$	10.4280	0.534242
$382$	−10.3067	−0.527339
$383$	−5.15569	−0.263443	−0.131722	−	0.991287i	$-0.542051\pi$
$383$	−5.15569	−0.263443	−0.131722	+	0.991287i	$0.542051\pi$
$384$	−25.0686	−1.27928
$385$	64.2841	3.27622
$386$	14.7603	0.751282
$387$	−45.2682	−2.30111
$388$	−22.1084	−1.12238
$389$	−27.0339	−1.37067	−0.685336	−	0.728227i	$-0.740345\pi$
$389$	−27.0339	−1.37067	−0.685336	+	0.728227i	$0.740345\pi$
$390$	9.85608	0.499082
$391$	−0.112766	−0.00570283
$392$	24.4976	1.23732
$393$	31.2188	1.57478
$394$	19.2863	0.971629
$395$	−68.6985	−3.45660
$396$	−16.7307	−0.840751
$397$	20.3480	1.02124	0.510619	−	0.859807i	$-0.329416\pi$
$397$	20.3480	1.02124	0.510619	+	0.859807i	$0.329416\pi$
$398$	38.5499	1.93233
$399$	74.7849	3.74393
$400$	−59.1341	−2.95671
$401$	−37.3694	−1.86614	−0.933068	−	0.359699i	$-0.882879\pi$
$401$	−37.3694	−1.86614	−0.933068	+	0.359699i	$0.882879\pi$
$402$	17.4218	0.868922
$403$	3.68992	0.183808
$404$	−9.26574	−0.460988
$405$	16.0301	0.796541
$406$	−21.9394	−1.08883
$407$	14.5584	0.721631
$408$	4.23847	0.209836
$409$	30.4801	1.50715	0.753573	−	0.657364i	$-0.228329\pi$
$409$	30.4801	1.50715	0.753573	+	0.657364i	$0.228329\pi$
$410$	−10.9117	−0.538890
$411$	−36.9694	−1.82356
$412$	−1.25212	−0.0616875
$413$	−2.15145	−0.105866
$414$	0.679540	0.0333976
$415$	−45.7036	−2.24350
$416$	3.14207	0.154053
$417$	50.3235	2.46435
$418$	29.4645	1.44116
$419$	21.6303	1.05671	0.528354	−	0.849024i	$-0.322809\pi$
$419$	21.6303	1.05671	0.528354	+	0.849024i	$0.322809\pi$
$420$	−75.8633	−3.70175
$421$	−22.1290	−1.07850	−0.539251	−	0.842145i	$-0.681293\pi$
$421$	−22.1290	−1.07850	−0.539251	+	0.842145i	$0.681293\pi$
$422$	1.07943	0.0525459
$423$	4.31658	0.209880
$424$	3.16072	0.153498
$425$	15.3903	0.746541
$426$	26.9294	1.30473
$427$	−24.7350	−1.19701
$428$	2.00412	0.0968730
$429$	−3.93434	−0.189952
$430$	−80.8713	−3.89996
$431$	30.4676	1.46757	0.733786	−	0.679380i	$-0.237751\pi$
$431$	30.4676	1.46757	0.733786	+	0.679380i	$0.237751\pi$
$432$	−15.9811	−0.768889
$433$	20.3753	0.979175	0.489588	−	0.871954i	$-0.337147\pi$
$433$	20.3753	0.979175	0.489588	+	0.871954i	$0.337147\pi$
$434$	−71.4151	−3.42804
$435$	−25.8194	−1.23795
$436$	18.9278	0.906479
$437$	−0.475941	−0.0227674
$438$	−20.5579	−0.982294
$439$	27.8037	1.32700	0.663499	−	0.748177i	$-0.269071\pi$
$439$	27.8037	1.32700	0.663499	+	0.748177i	$0.269071\pi$
$440$	15.3771	0.733072
$441$	83.4019	3.97152
$442$	−1.13179	−0.0538339
$443$	−13.0379	−0.619450	−0.309725	−	0.950826i	$-0.600237\pi$
$443$	−13.0379	−0.619450	−0.309725	+	0.950826i	$0.600237\pi$
$444$	−17.1807	−0.815360
$445$	−30.3419	−1.43835
$446$	−22.6596	−1.07296
$447$	45.9281	2.17232
$448$	−10.1195	−0.478101
$449$	2.12159	0.100124	0.0500620	−	0.998746i	$-0.484058\pi$
$449$	2.12159	0.100124	0.0500620	+	0.998746i	$0.484058\pi$
$450$	−92.7437	−4.37198
$451$	4.35572	0.205103
$452$	17.8011	0.837296
$453$	0.274212	0.0128836
$454$	−28.9078	−1.35671
$455$	−10.4219	−0.488585
$456$	17.8889	0.837725
$457$	31.2174	1.46029	0.730144	−	0.683294i	$-0.239453\pi$
$457$	31.2174	1.46029	0.730144	+	0.683294i	$0.239453\pi$
$458$	−16.9980	−0.794264
$459$	4.15925	0.194137
$460$	0.482804	0.0225109
$461$	15.8163	0.736636	0.368318	−	0.929700i	$-0.379934\pi$
$461$	15.8163	0.736636	0.368318	+	0.929700i	$0.379934\pi$
$462$	76.1457	3.54262
$463$	−2.89470	−0.134528	−0.0672640	−	0.997735i	$-0.521427\pi$
$463$	−2.89470	−0.134528	−0.0672640	+	0.997735i	$0.521427\pi$
$464$	−11.3920	−0.528860
$465$	−84.0452	−3.89750
$466$	−38.3041	−1.77440
$467$	8.96153	0.414690	0.207345	−	0.978268i	$-0.433518\pi$
$467$	8.96153	0.414690	0.207345	+	0.978268i	$0.433518\pi$
$468$	2.71243	0.125382
$469$	−18.4220	−0.850647
$470$	7.71156	0.355708
$471$	17.4450	0.803823
$472$	−0.514637	−0.0236881
$473$	32.2821	1.48433
$474$	−81.3747	−3.73767
$475$	64.9565	2.98041
$476$	8.71154	0.399293
$477$	10.7606	0.492696
$478$	14.7153	0.673064
$479$	−35.2623	−1.61117	−0.805587	−	0.592477i	$-0.798150\pi$
$479$	−35.2623	−1.61117	−0.805587	+	0.592477i	$0.798150\pi$
$480$	−71.5670	−3.26657
$481$	−2.36023	−0.107617
$482$	−29.2938	−1.33430
$483$	−1.22999	−0.0559663
$484$	−2.59536	−0.117971
$485$	69.1780	3.14121
$486$	36.8276	1.67053
$487$	−9.78816	−0.443544	−0.221772	−	0.975099i	$-0.571184\pi$
$487$	−9.78816	−0.443544	−0.221772	+	0.975099i	$0.571184\pi$
$488$	−5.91673	−0.267838
$489$	17.0814	0.772445
$490$	148.997	6.73100
$491$	10.2068	0.460628	0.230314	−	0.973116i	$-0.426025\pi$
$491$	10.2068	0.460628	0.230314	+	0.973116i	$0.426025\pi$
$492$	−5.14031	−0.231743
$493$	2.96490	0.133532
$494$	−4.77685	−0.214921
$495$	52.3511	2.35301
$496$	−37.0823	−1.66504
$497$	−28.4753	−1.27729
$498$	−54.1369	−2.42593
$499$	−7.89886	−0.353601	−0.176801	−	0.984247i	$-0.556575\pi$
$499$	−7.89886	−0.353601	−0.176801	+	0.984247i	$0.556575\pi$
$500$	−38.6083	−1.72662
$501$	−16.1910	−0.723362
$502$	−6.02668	−0.268984
$503$	42.0662	1.87564	0.937821	−	0.347120i	$-0.112840\pi$
$503$	42.0662	1.87564	0.937821	+	0.347120i	$0.112840\pi$
$504$	27.0077	1.20302
$505$	28.9928	1.29016
$506$	−0.484602	−0.0215432
$507$	−34.2809	−1.52247
$508$	5.12691	0.227470
$509$	−20.1333	−0.892394	−0.446197	−	0.894935i	$-0.647222\pi$
$509$	−20.1333	−0.892394	−0.446197	+	0.894935i	$0.647222\pi$
$510$	25.7788	1.14151
$511$	21.7380	0.961634
$512$	−19.4507	−0.859609
$513$	17.5546	0.775053
$514$	4.98198	0.219746
$515$	3.91793	0.172645
$516$	−38.0970	−1.67713
$517$	−3.07829	−0.135383
$518$	45.6803	2.00708
$519$	−56.8446	−2.49520
$520$	−2.49296	−0.109324
$521$	−16.0105	−0.701434	−0.350717	−	0.936482i	$-0.614062\pi$
$521$	−16.0105	−0.701434	−0.350717	+	0.936482i	$0.614062\pi$
$522$	−17.8668	−0.782008
$523$	1.35515	0.0592564	0.0296282	−	0.999561i	$-0.490568\pi$
$523$	1.35515	0.0592564	0.0296282	+	0.999561i	$0.490568\pi$
$524$	15.3487	0.670511
$525$	167.869	7.32638
$526$	−43.4206	−1.89323
$527$	9.65108	0.420408
$528$	39.5386	1.72070
$529$	−22.9922	−0.999660
$530$	19.2238	0.835029
$531$	−1.75208	−0.0760338
$532$	36.7680	1.59409
$533$	−0.706160	−0.0305872
$534$	−35.9406	−1.55530
$535$	−6.27097	−0.271118
$536$	−4.40662	−0.190337
$537$	41.7722	1.80260
$538$	−22.1736	−0.955970
$539$	−59.4765	−2.56184
$540$	−17.8077	−0.766321
$541$	33.1080	1.42343	0.711713	−	0.702471i	$-0.247920\pi$
$541$	33.1080	1.42343	0.711713	+	0.702471i	$0.247920\pi$
$542$	37.0617	1.59194
$543$	−17.3016	−0.742481
$544$	8.21818	0.352352
$545$	−59.2259	−2.53696
$546$	−12.3449	−0.528314
$547$	−26.3531	−1.12678	−0.563388	−	0.826192i	$-0.690502\pi$
$547$	−26.3531	−1.12678	−0.563388	+	0.826192i	$0.690502\pi$
$548$	−18.1760	−0.776439
$549$	−20.1435	−0.859702
$550$	66.1385	2.82015
$551$	12.5137	0.533100
$552$	−0.294218	−0.0125228
$553$	86.0462	3.65906
$554$	−17.6804	−0.751170
$555$	53.7590	2.28194
$556$	24.7415	1.04927
$557$	24.1858	1.02478	0.512392	−	0.858752i	$-0.328760\pi$
$557$	24.1858	1.02478	0.512392	+	0.858752i	$0.328760\pi$
$558$	−58.1584	−2.46204
$559$	−5.23366	−0.221360
$560$	104.736	4.42590
$561$	−10.2904	−0.434460
$562$	−47.8590	−2.01881
$563$	−19.5434	−0.823657	−0.411828	−	0.911261i	$-0.635110\pi$
$563$	−19.5434	−0.823657	−0.411828	+	0.911261i	$0.635110\pi$
$564$	3.63278	0.152967
$565$	−55.7004	−2.34333
$566$	−15.6387	−0.657344
$567$	−20.0780	−0.843195
$568$	−6.81142	−0.285801
$569$	−10.0091	−0.419603	−0.209802	−	0.977744i	$-0.567282\pi$
$569$	−10.0091	−0.419603	−0.209802	+	0.977744i	$0.567282\pi$
$570$	108.802	4.55723
$571$	−8.28534	−0.346731	−0.173365	−	0.984858i	$-0.555464\pi$
$571$	−8.28534	−0.346731	−0.173365	+	0.984858i	$0.555464\pi$
$572$	−1.93432	−0.0808778
$573$	15.1925	0.634674
$574$	13.6671	0.570454
$575$	−1.06834	−0.0445528
$576$	−8.24102	−0.343376
$577$	9.42953	0.392556	0.196278	−	0.980548i	$-0.437114\pi$
$577$	9.42953	0.392556	0.196278	+	0.980548i	$0.437114\pi$
$578$	28.0180	1.16540
$579$	−21.7572	−0.904199
$580$	−12.6941	−0.527094
$581$	57.2447	2.37491
$582$	81.9427	3.39663
$583$	−7.67375	−0.317814
$584$	5.19984	0.215171
$585$	−8.48727	−0.350906
$586$	0.242939	0.0100357
$587$	−21.8257	−0.900844	−0.450422	−	0.892816i	$-0.648727\pi$
$587$	−21.8257	−0.900844	−0.450422	+	0.892816i	$0.648727\pi$
$588$	70.1898	2.89458
$589$	40.7334	1.67839
$590$	−3.13008	−0.128863
$591$	−28.4286	−1.16940
$592$	23.7195	0.974864
$593$	39.5962	1.62602	0.813010	−	0.582250i	$-0.197828\pi$
$593$	39.5962	1.62602	0.813010	+	0.582250i	$0.197828\pi$
$594$	17.8740	0.733379
$595$	−27.2587	−1.11750
$596$	22.5805	0.924934
$597$	−56.8237	−2.32564
$598$	0.0785647	0.00321275
$599$	29.4004	1.20127	0.600634	−	0.799524i	$-0.294915\pi$
$599$	29.4004	1.20127	0.600634	+	0.799524i	$0.294915\pi$
$600$	40.1550	1.63932
$601$	−24.8580	−1.01398	−0.506989	−	0.861953i	$-0.669241\pi$
$601$	−24.8580	−1.01398	−0.506989	+	0.861953i	$0.669241\pi$
$602$	101.293	4.12839
$603$	−15.0023	−0.610941
$604$	0.134816	0.00548560
$605$	8.12097	0.330164
$606$	34.3426	1.39507
$607$	24.2523	0.984372	0.492186	−	0.870490i	$-0.336198\pi$
$607$	24.2523	0.984372	0.492186	+	0.870490i	$0.336198\pi$
$608$	34.6857	1.40669
$609$	32.3393	1.31046
$610$	−35.9862	−1.45704
$611$	0.499060	0.0201898
$612$	7.09442	0.286775
$613$	−17.9999	−0.727009	−0.363504	−	0.931593i	$-0.618420\pi$
$613$	−17.9999	−0.727009	−0.363504	+	0.931593i	$0.618420\pi$
$614$	48.4397	1.95487
$615$	16.0842	0.648577
$616$	−19.2600	−0.776009
$617$	−30.0696	−1.21056	−0.605278	−	0.796014i	$-0.706938\pi$
$617$	−30.0696	−1.21056	−0.605278	+	0.796014i	$0.706938\pi$
$618$	4.64086	0.186683
$619$	−43.5036	−1.74856	−0.874279	−	0.485425i	$-0.838665\pi$
$619$	−43.5036	−1.74856	−0.874279	+	0.485425i	$0.838665\pi$
$620$	−41.3208	−1.65948
$621$	−0.288719	−0.0115859
$622$	−35.3981	−1.41934
$623$	38.0038	1.52259
$624$	−6.41009	−0.256609
$625$	60.4316	2.41726
$626$	10.5706	0.422487
$627$	−43.4316	−1.73449
$628$	8.57682	0.342252
$629$	−6.17326	−0.246144
$630$	164.264	6.54443
$631$	−32.6888	−1.30132	−0.650660	−	0.759369i	$-0.725508\pi$
$631$	−32.6888	−1.30132	−0.650660	+	0.759369i	$0.725508\pi$
$632$	20.5827	0.818734
$633$	−1.59112	−0.0632412
$634$	−57.2959	−2.27551
$635$	−16.0423	−0.636618
$636$	9.05600	0.359094
$637$	9.64247	0.382049
$638$	12.7414	0.504435
$639$	−23.1894	−0.917360
$640$	38.5652	1.52442
$641$	28.3515	1.11982	0.559908	−	0.828555i	$-0.310837\pi$
$641$	28.3515	1.11982	0.559908	+	0.828555i	$0.310837\pi$
$642$	−7.42809	−0.293163
$643$	−5.78843	−0.228273	−0.114137	−	0.993465i	$-0.536410\pi$
$643$	−5.78843	−0.228273	−0.114137	+	0.993465i	$0.536410\pi$
$644$	−0.604721	−0.0238294
$645$	119.207	4.69377
$646$	−12.4940	−0.491569
$647$	25.4787	1.00167	0.500836	−	0.865542i	$-0.333026\pi$
$647$	25.4787	1.00167	0.500836	+	0.865542i	$0.333026\pi$
$648$	−4.80274	−0.188670
$649$	1.24946	0.0490457
$650$	−10.7225	−0.420572
$651$	105.268	4.12579
$652$	8.39803	0.328892
$653$	23.0587	0.902355	0.451178	−	0.892434i	$-0.351004\pi$
$653$	23.0587	0.902355	0.451178	+	0.892434i	$0.351004\pi$
$654$	−70.1542	−2.74325
$655$	−48.0266	−1.87655
$656$	7.09664	0.277077
$657$	17.7028	0.690653
$658$	−9.65887	−0.376542
$659$	−24.6113	−0.958721	−0.479360	−	0.877618i	$-0.659131\pi$
$659$	−24.6113	−0.958721	−0.479360	+	0.877618i	$0.659131\pi$
$660$	44.0579	1.71495
$661$	−19.8608	−0.772497	−0.386249	−	0.922395i	$-0.626229\pi$
$661$	−19.8608	−0.772497	−0.386249	+	0.922395i	$0.626229\pi$
$662$	−20.8060	−0.808647
$663$	1.66830	0.0647914
$664$	13.6932	0.531399
$665$	−115.048	−4.46138
$666$	37.2007	1.44150
$667$	−0.205812	−0.00796906
$668$	−7.96031	−0.307994
$669$	33.4009	1.29135
$670$	−26.8015	−1.03543
$671$	14.3649	0.554552
$672$	89.6390	3.45790
$673$	−26.9327	−1.03818	−0.519090	−	0.854719i	$-0.673729\pi$
$673$	−26.9327	−1.03818	−0.519090	+	0.854719i	$0.673729\pi$
$674$	−47.7195	−1.83809
$675$	39.4044	1.51668
$676$	−16.8542	−0.648238
$677$	−18.9289	−0.727496	−0.363748	−	0.931497i	$-0.618503\pi$
$677$	−18.9289	−0.727496	−0.363748	+	0.931497i	$0.618503\pi$
$678$	−65.9782	−2.53388
$679$	−86.6467	−3.32520
$680$	−6.52041	−0.250046
$681$	42.6110	1.63286
$682$	41.4746	1.58814
$683$	−38.8590	−1.48690	−0.743448	−	0.668794i	$-0.766811\pi$
$683$	−38.8590	−1.48690	−0.743448	+	0.668794i	$0.766811\pi$
$684$	29.9428	1.14489
$685$	56.8732	2.17301
$686$	−120.602	−4.60461
$687$	25.0556	0.955930
$688$	52.5962	2.00521
$689$	1.24409	0.0473959
$690$	−1.78947	−0.0681239
$691$	−43.6266	−1.65964	−0.829818	−	0.558034i	$-0.811556\pi$
$691$	−43.6266	−1.65964	−0.829818	+	0.558034i	$0.811556\pi$
$692$	−27.9476	−1.06241
$693$	−65.5707	−2.49082
$694$	52.0809	1.97696
$695$	−77.4171	−2.93660
$696$	7.73572	0.293222
$697$	−1.84698	−0.0699593
$698$	−43.9710	−1.66433
$699$	56.4615	2.13557
$700$	82.5325	3.11943
$701$	−46.1568	−1.74332	−0.871660	−	0.490111i	$-0.836956\pi$
$701$	−46.1568	−1.74332	−0.871660	+	0.490111i	$0.836956\pi$
$702$	−2.89777	−0.109369
$703$	−26.0549	−0.982678
$704$	5.87693	0.221495
$705$	−11.3671	−0.428109
$706$	60.7518	2.28642
$707$	−36.3141	−1.36573
$708$	−1.47452	−0.0554160
$709$	−8.25597	−0.310060	−0.155030	−	0.987910i	$-0.549547\pi$
$709$	−8.25597	−0.310060	−0.155030	+	0.987910i	$0.549547\pi$
$710$	−41.4278	−1.55476
$711$	70.0735	2.62796
$712$	9.09070	0.340688
$713$	−0.669941	−0.0250895
$714$	−32.2885	−1.20837
$715$	6.05254	0.226352
$716$	20.5373	0.767513
$717$	−21.6909	−0.810061
$718$	−39.2760	−1.46577
$719$	8.86749	0.330702	0.165351	−	0.986235i	$-0.447124\pi$
$719$	8.86749	0.330702	0.165351	+	0.986235i	$0.447124\pi$
$720$	85.2939	3.17871
$721$	−4.90728	−0.182757
$722$	−18.1094	−0.673962
$723$	43.1800	1.60588
$724$	−8.50630	−0.316134
$725$	28.0892	1.04321
$726$	9.61945	0.357011
$727$	−31.0127	−1.15020	−0.575098	−	0.818085i	$-0.695036\pi$
$727$	−31.0127	−1.15020	−0.575098	+	0.818085i	$0.695036\pi$
$728$	3.12248	0.115727
$729$	−42.6471	−1.57952
$730$	31.6260	1.17053
$731$	−13.6888	−0.506297
$732$	−16.9525	−0.626581
$733$	−6.91323	−0.255346	−0.127673	−	0.991816i	$-0.540751\pi$
$733$	−6.91323	−0.255346	−0.127673	+	0.991816i	$0.540751\pi$
$734$	−31.8543	−1.17576
$735$	−219.626	−8.10105
$736$	−0.570474	−0.0210280
$737$	10.6986	0.394088
$738$	11.1301	0.409704
$739$	32.2320	1.18568	0.592838	−	0.805322i	$-0.298008\pi$
$739$	32.2320	1.18568	0.592838	+	0.805322i	$0.298008\pi$
$740$	26.4306	0.971608
$741$	7.04123	0.258666
$742$	−24.0782	−0.883938
$743$	−46.5143	−1.70644	−0.853222	−	0.521547i	$-0.825355\pi$
$743$	−46.5143	−1.70644	−0.853222	+	0.521547i	$0.825355\pi$
$744$	25.1807	0.923168
$745$	−70.6552	−2.58861
$746$	−8.94324	−0.327435
$747$	46.6184	1.70568
$748$	−5.05926	−0.184985
$749$	7.85451	0.286998
$750$	143.098	5.22520
$751$	41.3671	1.50951	0.754754	−	0.656008i	$-0.227756\pi$
$751$	41.3671	1.50951	0.754754	+	0.656008i	$0.227756\pi$
$752$	−5.01536	−0.182891
$753$	8.88352	0.323733
$754$	−2.06566	−0.0752269
$755$	−0.421845	−0.0153525
$756$	22.3045	0.811206
$757$	−3.99613	−0.145242	−0.0726208	−	0.997360i	$-0.523136\pi$
$757$	−3.99613	−0.145242	−0.0726208	+	0.997360i	$0.523136\pi$
$758$	41.2875	1.49963
$759$	0.714318	0.0259281
$760$	−27.5201	−0.998258
$761$	18.3632	0.665666	0.332833	−	0.942986i	$-0.391996\pi$
$761$	18.3632	0.665666	0.332833	+	0.942986i	$0.391996\pi$
$762$	−19.0024	−0.688384
$763$	74.1815	2.68555
$764$	7.46937	0.270232
$765$	−22.1987	−0.802595
$766$	9.39496	0.339454
$767$	−0.202566	−0.00731423
$768$	56.1849	2.02740
$769$	−18.2658	−0.658683	−0.329341	−	0.944211i	$-0.606827\pi$
$769$	−18.2658	−0.658683	−0.329341	+	0.944211i	$0.606827\pi$
$770$	−117.142	−4.22149
$771$	−7.34361	−0.264474
$772$	−10.6969	−0.384991
$773$	−13.0559	−0.469588	−0.234794	−	0.972045i	$-0.575442\pi$
$773$	−13.0559	−0.469588	−0.234794	+	0.972045i	$0.575442\pi$
$774$	82.4899	2.96504
$775$	91.4336	3.28439
$776$	−20.7263	−0.744031
$777$	−67.3342	−2.41560
$778$	49.2625	1.76615
$779$	−7.79537	−0.279298
$780$	−7.14277	−0.255752
$781$	16.5371	0.591744
$782$	0.205488	0.00734824
$783$	7.59114	0.271285
$784$	−96.9031	−3.46083
$785$	−26.8372	−0.957859
$786$	−56.8885	−2.02914
$787$	−42.3411	−1.50930	−0.754648	−	0.656130i	$-0.772192\pi$
$787$	−42.3411	−1.50930	−0.754648	+	0.656130i	$0.772192\pi$
$788$	−13.9769	−0.497906
$789$	64.0033	2.27858
$790$	125.186	4.45391
$791$	69.7658	2.48059
$792$	−15.6848	−0.557336
$793$	−2.32888	−0.0827008
$794$	−37.0792	−1.31589
$795$	−28.3365	−1.00499
$796$	−27.9373	−0.990213
$797$	54.0030	1.91288	0.956442	−	0.291921i	$-0.0942945\pi$
$797$	54.0030	1.91288	0.956442	+	0.291921i	$0.0942945\pi$
$798$	−136.277	−4.82415
$799$	1.30530	0.0461784
$800$	77.8584	2.75271
$801$	30.9492	1.09354
$802$	68.0963	2.40457
$803$	−12.6244	−0.445507
$804$	−12.6257	−0.445275
$805$	1.89219	0.0666911
$806$	−6.72396	−0.236841
$807$	32.6846	1.15055
$808$	−8.68650	−0.305590
$809$	18.9901	0.667655	0.333828	−	0.942634i	$-0.391660\pi$
$809$	18.9901	0.667655	0.333828	+	0.942634i	$0.391660\pi$
$810$	−29.2108	−1.02636
$811$	−1.99008	−0.0698810	−0.0349405	−	0.999389i	$-0.511124\pi$
$811$	−1.99008	−0.0698810	−0.0349405	+	0.999389i	$0.511124\pi$
$812$	15.8996	0.557967
$813$	−54.6302	−1.91596
$814$	−26.5290	−0.929840
$815$	−26.2777	−0.920469
$816$	−16.7658	−0.586919
$817$	−57.7749	−2.02129
$818$	−55.5424	−1.94200
$819$	10.6305	0.371459
$820$	7.90778	0.276152
$821$	−13.6320	−0.475759	−0.237879	−	0.971295i	$-0.576452\pi$
$821$	−13.6320	−0.475759	−0.237879	+	0.971295i	$0.576452\pi$
$822$	67.3675	2.34971
$823$	−21.4172	−0.746557	−0.373279	−	0.927719i	$-0.621766\pi$
$823$	−21.4172	−0.746557	−0.373279	+	0.927719i	$0.621766\pi$
$824$	−1.17384	−0.0408928
$825$	−97.4903	−3.39418
$826$	3.92048	0.136411
$827$	−9.71569	−0.337848	−0.168924	−	0.985629i	$-0.554029\pi$
$827$	−9.71569	−0.337848	−0.168924	+	0.985629i	$0.554029\pi$
$828$	−0.492467	−0.0171144
$829$	−32.0851	−1.11436	−0.557181	−	0.830391i	$-0.688117\pi$
$829$	−32.0851	−1.11436	−0.557181	+	0.830391i	$0.688117\pi$
$830$	83.2835	2.89081
$831$	26.0615	0.904065
$832$	−0.952782	−0.0330318
$833$	25.2201	0.873826
$834$	−91.7021	−3.17538
$835$	24.9081	0.861980
$836$	−21.3531	−0.738513
$837$	24.7100	0.854103
$838$	−39.4158	−1.36160
$839$	2.52233	0.0870804	0.0435402	−	0.999052i	$-0.486136\pi$
$839$	2.52233	0.0870804	0.0435402	+	0.999052i	$0.486136\pi$
$840$	−71.1208	−2.45390
$841$	−23.5887	−0.813404
$842$	40.3246	1.38968
$843$	70.5457	2.42972
$844$	−0.782272	−0.0269269
$845$	52.7373	1.81422
$846$	−7.86590	−0.270435
$847$	−10.1717	−0.349503
$848$	−12.5026	−0.429340
$849$	23.0520	0.791141
$850$	−28.0450	−0.961937
$851$	0.428524	0.0146896
$852$	−19.5159	−0.668603
$853$	−28.3783	−0.971654	−0.485827	−	0.874055i	$-0.661482\pi$
$853$	−28.3783	−0.971654	−0.485827	+	0.874055i	$0.661482\pi$
$854$	45.0734	1.54238
$855$	−93.6919	−3.20420
$856$	1.87884	0.0642173
$857$	20.0013	0.683231	0.341616	−	0.939840i	$-0.389026\pi$
$857$	20.0013	0.683231	0.341616	+	0.939840i	$0.389026\pi$
$858$	7.16936	0.244758
$859$	−55.8459	−1.90544	−0.952719	−	0.303853i	$-0.901727\pi$
$859$	−55.8459	−1.90544	−0.952719	+	0.303853i	$0.901727\pi$
$860$	58.6080	1.99852
$861$	−20.1458	−0.686565
$862$	−55.5196	−1.89101
$863$	−10.7654	−0.366457	−0.183229	−	0.983070i	$-0.558655\pi$
$863$	−10.7654	−0.366457	−0.183229	+	0.983070i	$0.558655\pi$
$864$	21.0413	0.715840
$865$	87.4491	2.97336
$866$	−37.1289	−1.26169
$867$	−41.2995	−1.40260
$868$	51.7551	1.75668
$869$	−49.9716	−1.69517
$870$	47.0495	1.59513
$871$	−1.73448	−0.0587707
$872$	17.7446	0.600907
$873$	−70.5626	−2.38818
$874$	0.867284	0.0293363
$875$	−151.313	−5.11531
$876$	14.8984	0.503372
$877$	−13.8207	−0.466692	−0.233346	−	0.972394i	$-0.574968\pi$
$877$	−13.8207	−0.466692	−0.233346	+	0.972394i	$0.574968\pi$
$878$	−50.6653	−1.70987
$879$	−0.358101	−0.0120784
$880$	−60.8257	−2.05044
$881$	−5.26645	−0.177431	−0.0887157	−	0.996057i	$-0.528276\pi$
$881$	−5.26645	−0.177431	−0.0887157	+	0.996057i	$0.528276\pi$
$882$	−151.979	−5.11741
$883$	−5.43937	−0.183049	−0.0915247	−	0.995803i	$-0.529174\pi$
$883$	−5.43937	−0.183049	−0.0915247	+	0.995803i	$0.529174\pi$
$884$	0.820218	0.0275869
$885$	4.61384	0.155093
$886$	23.7583	0.798177
$887$	25.5993	0.859542	0.429771	−	0.902938i	$-0.358594\pi$
$887$	25.5993	0.859542	0.429771	+	0.902938i	$0.358594\pi$
$888$	−16.1067	−0.540504
$889$	20.0932	0.673906
$890$	55.2906	1.85335
$891$	11.6603	0.390636
$892$	16.4215	0.549834
$893$	5.50918	0.184358
$894$	−83.6925	−2.79910
$895$	−64.2618	−2.14804
$896$	−48.3037	−1.61371
$897$	−0.115807	−0.00386668
$898$	−3.86607	−0.129012
$899$	17.6144	0.587473
$900$	67.2120	2.24040
$901$	3.25394	0.108404
$902$	−7.93722	−0.264280
$903$	−149.309	−4.96869
$904$	16.6883	0.555045
$905$	26.6165	0.884763
$906$	−0.499684	−0.0166009
$907$	−22.5912	−0.750129	−0.375064	−	0.926999i	$-0.622379\pi$
$907$	−22.5912	−0.750129	−0.375064	+	0.926999i	$0.622379\pi$
$908$	20.9497	0.695239
$909$	−29.5731	−0.980878
$910$	18.9913	0.629555
$911$	40.5238	1.34261	0.671307	−	0.741179i	$-0.265733\pi$
$911$	40.5238	1.34261	0.671307	+	0.741179i	$0.265733\pi$
$912$	−70.7617	−2.34315
$913$	−33.2450	−1.10025
$914$	−56.8859	−1.88162
$915$	53.0448	1.75361
$916$	12.3186	0.407017
$917$	60.1542	1.98647
$918$	−7.57920	−0.250151
$919$	56.5294	1.86473	0.932367	−	0.361514i	$-0.117740\pi$
$919$	56.5294	1.86473	0.932367	+	0.361514i	$0.117740\pi$
$920$	0.452622	0.0149225
$921$	−71.4017	−2.35277
$922$	−28.8212	−0.949175
$923$	−2.68103	−0.0882473
$924$	−55.1834	−1.81540
$925$	−58.4850	−1.92297
$926$	5.27486	0.173343
$927$	−3.99634	−0.131257
$928$	14.9992	0.492372
$929$	−24.7082	−0.810650	−0.405325	−	0.914173i	$-0.632842\pi$
$929$	−24.7082	−0.810650	−0.405325	+	0.914173i	$0.632842\pi$
$930$	153.152	5.02204
$931$	106.444	3.48857
$932$	27.7592	0.909284
$933$	52.1780	1.70823
$934$	−16.3301	−0.534339
$935$	15.8306	0.517716
$936$	2.54286	0.0831159
$937$	40.6915	1.32933	0.664667	−	0.747139i	$-0.268573\pi$
$937$	40.6915	1.32933	0.664667	+	0.747139i	$0.268573\pi$
$938$	33.5694	1.09608
$939$	−15.5814	−0.508481
$940$	−5.58862	−0.182281
$941$	25.7501	0.839429	0.419715	−	0.907656i	$-0.362130\pi$
$941$	25.7501	0.839429	0.419715	+	0.907656i	$0.362130\pi$
$942$	−31.7892	−1.03575
$943$	0.128210	0.00417510
$944$	2.03571	0.0662567
$945$	−69.7915	−2.27032
$946$	−58.8262	−1.91260
$947$	53.0653	1.72439	0.862196	−	0.506575i	$-0.169089\pi$
$947$	53.0653	1.72439	0.862196	+	0.506575i	$0.169089\pi$
$948$	58.9728	1.91535
$949$	2.04670	0.0664388
$950$	−118.367	−3.84033
$951$	84.4560	2.73867
$952$	8.16694	0.264692
$953$	17.7978	0.576528	0.288264	−	0.957551i	$-0.406922\pi$
$953$	17.7978	0.576528	0.288264	+	0.957551i	$0.406922\pi$
$954$	−19.6086	−0.634851
$955$	−23.3719	−0.756297
$956$	−10.6643	−0.344908
$957$	−18.7812	−0.607109
$958$	64.2567	2.07604
$959$	−71.2348	−2.30029
$960$	21.7015	0.700413
$961$	26.3369	0.849576
$962$	4.30094	0.138668
$963$	6.39648	0.206124
$964$	21.2294	0.683753
$965$	33.4710	1.07747
$966$	2.24134	0.0721140
$967$	−33.3758	−1.07329	−0.536647	−	0.843807i	$-0.680309\pi$
$967$	−33.3758	−1.07329	−0.536647	+	0.843807i	$0.680309\pi$
$968$	−2.43311	−0.0782031
$969$	18.4165	0.591624
$970$	−126.060	−4.04753
$971$	−18.5427	−0.595064	−0.297532	−	0.954712i	$-0.596163\pi$
$971$	−18.5427	−0.595064	−0.297532	+	0.954712i	$0.596163\pi$
$972$	−26.6892	−0.856056
$973$	96.9664	3.10860
$974$	17.8365	0.571518
$975$	15.8053	0.506176
$976$	23.4043	0.749154
$977$	32.6089	1.04325	0.521626	−	0.853174i	$-0.325326\pi$
$977$	32.6089	1.04325	0.521626	+	0.853174i	$0.325326\pi$
$978$	−31.1265	−0.995316
$979$	−22.0709	−0.705388
$980$	−107.979	−3.44927
$981$	60.4112	1.92878
$982$	−18.5994	−0.593531
$983$	−59.8324	−1.90836	−0.954179	−	0.299237i	$-0.903268\pi$
$983$	−59.8324	−1.90836	−0.954179	+	0.299237i	$0.903268\pi$
$984$	−4.81896	−0.153623
$985$	43.7342	1.39349
$986$	−5.40279	−0.172060
$987$	14.2375	0.453184
$988$	3.46182	0.110135
$989$	0.950222	0.0302153
$990$	−95.3968	−3.03191
$991$	−28.0661	−0.891551	−0.445775	−	0.895145i	$-0.647072\pi$
$991$	−28.0661	−0.891551	−0.445775	+	0.895145i	$0.647072\pi$
$992$	48.8240	1.55016
$993$	30.6687	0.973241
$994$	51.8891	1.64582
$995$	87.4169	2.77130
$996$	39.2334	1.24316
$997$	−40.7160	−1.28949	−0.644744	−	0.764399i	$-0.723036\pi$
$997$	−40.7160	−1.28949	−0.644744	+	0.764399i	$0.723036\pi$
$998$	14.3937	0.455625
$999$	−15.8056	−0.500068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.40	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.40	✓	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)

\(f(q)\)	\(=\)	\(q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +O(q^{10})\)	\(q-1.82225 q^{2} +2.68606 q^{3} +1.32060 q^{4} -4.13220 q^{5} -4.89467 q^{6} +5.17565 q^{7} +1.23804 q^{8} +4.21490 q^{9} +7.52990 q^{10} -3.00578 q^{11} +3.54720 q^{12} +0.487304 q^{13} -9.43134 q^{14} -11.0993 q^{15} -4.89722 q^{16} +1.27456 q^{17} -7.68061 q^{18} +5.37940 q^{19} -5.45697 q^{20} +13.9021 q^{21} +5.47728 q^{22} -0.0884748 q^{23} +3.32545 q^{24} +12.0751 q^{25} -0.887990 q^{26} +3.26329 q^{27} +6.83496 q^{28} +2.32622 q^{29} +20.2257 q^{30} +7.57211 q^{31} +6.44788 q^{32} -8.07369 q^{33} -2.32256 q^{34} -21.3868 q^{35} +5.56619 q^{36} -4.84346 q^{37} -9.80261 q^{38} +1.30893 q^{39} -5.11583 q^{40} -1.44912 q^{41} -25.3331 q^{42} -10.7400 q^{43} -3.96943 q^{44} -17.4168 q^{45} +0.161223 q^{46} +1.02412 q^{47} -13.1542 q^{48} +19.7874 q^{49} -22.0038 q^{50} +3.42353 q^{51} +0.643532 q^{52} +2.55300 q^{53} -5.94654 q^{54} +12.4205 q^{55} +6.40767 q^{56} +14.4494 q^{57} -4.23896 q^{58} -0.415687 q^{59} -14.6577 q^{60} -4.77911 q^{61} -13.7983 q^{62} +21.8149 q^{63} -1.95521 q^{64} -2.01364 q^{65} +14.7123 q^{66} -3.55935 q^{67} +1.68318 q^{68} -0.237648 q^{69} +38.9721 q^{70} -5.50177 q^{71} +5.21822 q^{72} +4.20006 q^{73} +8.82599 q^{74} +32.4343 q^{75} +7.10402 q^{76} -15.5569 q^{77} -2.38519 q^{78} +16.6252 q^{79} +20.2363 q^{80} -3.87931 q^{81} +2.64065 q^{82} +11.0604 q^{83} +18.3591 q^{84} -5.26672 q^{85} +19.5710 q^{86} +6.24836 q^{87} -3.72128 q^{88} +7.34281 q^{89} +31.7378 q^{90} +2.52212 q^{91} -0.116840 q^{92} +20.3391 q^{93} -1.86621 q^{94} -22.2287 q^{95} +17.3194 q^{96} -16.7412 q^{97} -36.0576 q^{98} -12.6691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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