LMFDB - Embedded newform 4001.2.a.a.1.9

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:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.47526 q^{2} +2.78845 q^{3} +4.12689 q^{4} -0.919151 q^{5} -6.90213 q^{6} -1.88527 q^{7} -5.26460 q^{8} +4.77546 q^{9} +O(q^{10})$	\(q-2.47526 q^{2} +2.78845 q^{3} +4.12689 q^{4} -0.919151 q^{5} -6.90213 q^{6} -1.88527 q^{7} -5.26460 q^{8} +4.77546 q^{9} +2.27513 q^{10} -0.0993384 q^{11} +11.5076 q^{12} -1.32378 q^{13} +4.66652 q^{14} -2.56301 q^{15} +4.77744 q^{16} +3.44782 q^{17} -11.8205 q^{18} +4.91865 q^{19} -3.79323 q^{20} -5.25698 q^{21} +0.245888 q^{22} -4.32524 q^{23} -14.6801 q^{24} -4.15516 q^{25} +3.27669 q^{26} +4.95077 q^{27} -7.78030 q^{28} +2.14056 q^{29} +6.34410 q^{30} -1.24710 q^{31} -1.29619 q^{32} -0.277000 q^{33} -8.53423 q^{34} +1.73285 q^{35} +19.7078 q^{36} -6.56282 q^{37} -12.1749 q^{38} -3.69129 q^{39} +4.83896 q^{40} -8.90542 q^{41} +13.0124 q^{42} -12.2461 q^{43} -0.409959 q^{44} -4.38936 q^{45} +10.7061 q^{46} +0.653971 q^{47} +13.3217 q^{48} -3.44576 q^{49} +10.2851 q^{50} +9.61407 q^{51} -5.46308 q^{52} -4.85290 q^{53} -12.2544 q^{54} +0.0913070 q^{55} +9.92518 q^{56} +13.7154 q^{57} -5.29843 q^{58} +2.85733 q^{59} -10.5772 q^{60} -11.2634 q^{61} +3.08689 q^{62} -9.00302 q^{63} -6.34647 q^{64} +1.21675 q^{65} +0.685646 q^{66} +12.7127 q^{67} +14.2288 q^{68} -12.0607 q^{69} -4.28924 q^{70} +9.36488 q^{71} -25.1408 q^{72} +10.1227 q^{73} +16.2447 q^{74} -11.5865 q^{75} +20.2987 q^{76} +0.187280 q^{77} +9.13688 q^{78} +1.25081 q^{79} -4.39119 q^{80} -0.521391 q^{81} +22.0432 q^{82} +1.33964 q^{83} -21.6950 q^{84} -3.16907 q^{85} +30.3122 q^{86} +5.96884 q^{87} +0.522976 q^{88} -11.6815 q^{89} +10.8648 q^{90} +2.49568 q^{91} -17.8498 q^{92} -3.47748 q^{93} -1.61874 q^{94} -4.52098 q^{95} -3.61436 q^{96} +17.4539 q^{97} +8.52914 q^{98} -0.474386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.47526	−1.75027	−0.875135	−	0.483879i	$-0.839228\pi$
$2$	−2.47526	−1.75027	−0.875135	+	0.483879i	$0.839228\pi$
$3$	2.78845	1.60991	0.804956	−	0.593334i	$-0.202189\pi$
$3$	2.78845	1.60991	0.804956	+	0.593334i	$0.202189\pi$
$4$	4.12689	2.06344
$5$	−0.919151	−0.411057	−0.205528	−	0.978651i	$-0.565891\pi$
$5$	−0.919151	−0.411057	−0.205528	+	0.978651i	$0.565891\pi$
$6$	−6.90213	−2.81778
$7$	−1.88527	−0.712565	−0.356282	−	0.934378i	$-0.615956\pi$
$7$	−1.88527	−0.712565	−0.356282	+	0.934378i	$0.615956\pi$
$8$	−5.26460	−1.86132
$9$	4.77546	1.59182
$10$	2.27513	0.719460
$11$	−0.0993384	−0.0299516	−0.0149758	−	0.999888i	$-0.504767\pi$
$11$	−0.0993384	−0.0299516	−0.0149758	+	0.999888i	$0.504767\pi$
$12$	11.5076	3.32197
$13$	−1.32378	−0.367150	−0.183575	−	0.983006i	$-0.558767\pi$
$13$	−1.32378	−0.367150	−0.183575	+	0.983006i	$0.558767\pi$
$14$	4.66652	1.24718
$15$	−2.56301	−0.661766
$16$	4.77744	1.19436
$17$	3.44782	0.836219	0.418110	−	0.908397i	$-0.362693\pi$
$17$	3.44782	0.836219	0.418110	+	0.908397i	$0.362693\pi$
$18$	−11.8205	−2.78611
$19$	4.91865	1.12841	0.564207	−	0.825633i	$-0.309182\pi$
$19$	4.91865	1.12841	0.564207	+	0.825633i	$0.309182\pi$
$20$	−3.79323	−0.848193
$21$	−5.25698	−1.14717
$22$	0.245888	0.0524235
$23$	−4.32524	−0.901874	−0.450937	−	0.892556i	$-0.648910\pi$
$23$	−4.32524	−0.901874	−0.450937	+	0.892556i	$0.648910\pi$
$24$	−14.6801	−2.99656
$25$	−4.15516	−0.831032
$26$	3.27669	0.642611
$27$	4.95077	0.952776
$28$	−7.78030	−1.47034
$29$	2.14056	0.397492	0.198746	−	0.980051i	$-0.436313\pi$
$29$	2.14056	0.397492	0.198746	+	0.980051i	$0.436313\pi$
$30$	6.34410	1.15827
$31$	−1.24710	−0.223986	−0.111993	−	0.993709i	$-0.535723\pi$
$31$	−1.24710	−0.223986	−0.111993	+	0.993709i	$0.535723\pi$
$32$	−1.29619	−0.229136
$33$	−0.277000	−0.0482195
$34$	−8.53423	−1.46361
$35$	1.73285	0.292904
$36$	19.7078	3.28463
$37$	−6.56282	−1.07892	−0.539461	−	0.842011i	$-0.681372\pi$
$37$	−6.56282	−1.07892	−0.539461	+	0.842011i	$0.681372\pi$
$38$	−12.1749	−1.97503
$39$	−3.69129	−0.591079
$40$	4.83896	0.765106
$41$	−8.90542	−1.39079	−0.695396	−	0.718627i	$-0.744771\pi$
$41$	−8.90542	−1.39079	−0.695396	+	0.718627i	$0.744771\pi$
$42$	13.0124	2.00785
$43$	−12.2461	−1.86751	−0.933757	−	0.357908i	$-0.883490\pi$
$43$	−12.2461	−1.86751	−0.933757	+	0.357908i	$0.883490\pi$
$44$	−0.409959	−0.0618036
$45$	−4.38936	−0.654328
$46$	10.7061	1.57852
$47$	0.653971	0.0953915	0.0476957	−	0.998862i	$-0.484812\pi$
$47$	0.653971	0.0953915	0.0476957	+	0.998862i	$0.484812\pi$
$48$	13.3217	1.92281
$49$	−3.44576	−0.492252
$50$	10.2851	1.45453
$51$	9.61407	1.34624
$52$	−5.46308	−0.757593
$53$	−4.85290	−0.666597	−0.333299	−	0.942821i	$-0.608162\pi$
$53$	−4.85290	−0.666597	−0.333299	+	0.942821i	$0.608162\pi$
$54$	−12.2544	−1.66762
$55$	0.0913070	0.0123118
$56$	9.92518	1.32631
$57$	13.7154	1.81665
$58$	−5.29843	−0.695718
$59$	2.85733	0.371993	0.185996	−	0.982550i	$-0.440449\pi$
$59$	2.85733	0.371993	0.185996	+	0.982550i	$0.440449\pi$
$60$	−10.5772	−1.36552
$61$	−11.2634	−1.44213	−0.721064	−	0.692868i	$-0.756347\pi$
$61$	−11.2634	−1.44213	−0.721064	+	0.692868i	$0.756347\pi$
$62$	3.08689	0.392035
$63$	−9.00302	−1.13427
$64$	−6.34647	−0.793309
$65$	1.21675	0.150919
$66$	0.685646	0.0843972
$67$	12.7127	1.55311	0.776553	−	0.630053i	$-0.216967\pi$
$67$	12.7127	1.55311	0.776553	+	0.630053i	$0.216967\pi$
$68$	14.2288	1.72549
$69$	−12.0607	−1.45194
$70$	−4.28924	−0.512662
$71$	9.36488	1.11141	0.555704	−	0.831380i	$-0.312449\pi$
$71$	9.36488	1.11141	0.555704	+	0.831380i	$0.312449\pi$
$72$	−25.1408	−2.96288
$73$	10.1227	1.18477	0.592385	−	0.805655i	$-0.298187\pi$
$73$	10.1227	1.18477	0.592385	+	0.805655i	$0.298187\pi$
$74$	16.2447	1.88840
$75$	−11.5865	−1.33789
$76$	20.2987	2.32842
$77$	0.187280	0.0213425
$78$	9.13688	1.03455
$79$	1.25081	0.140728	0.0703638	−	0.997521i	$-0.477584\pi$
$79$	1.25081	0.140728	0.0703638	+	0.997521i	$0.477584\pi$
$80$	−4.39119	−0.490950
$81$	−0.521391	−0.0579323
$82$	22.0432	2.43426
$83$	1.33964	0.147044	0.0735220	−	0.997294i	$-0.476576\pi$
$83$	1.33964	0.147044	0.0735220	+	0.997294i	$0.476576\pi$
$84$	−21.6950	−2.36711
$85$	−3.16907	−0.343734
$86$	30.3122	3.26865
$87$	5.96884	0.639927
$88$	0.522976	0.0557495
$89$	−11.6815	−1.23824	−0.619120	−	0.785297i	$-0.712510\pi$
$89$	−11.6815	−1.23824	−0.619120	+	0.785297i	$0.712510\pi$
$90$	10.8648	1.14525
$91$	2.49568	0.261618
$92$	−17.8498	−1.86097
$93$	−3.47748	−0.360597
$94$	−1.61874	−0.166961
$95$	−4.52098	−0.463843
$96$	−3.61436	−0.368889
$97$	17.4539	1.77217	0.886087	−	0.463519i	$-0.153413\pi$
$97$	17.4539	1.77217	0.886087	+	0.463519i	$0.153413\pi$
$98$	8.52914	0.861573
$99$	−0.474386	−0.0476776
$100$	−17.1479	−1.71479
$101$	−11.0609	−1.10060	−0.550299	−	0.834968i	$-0.685486\pi$
$101$	−11.0609	−1.10060	−0.550299	+	0.834968i	$0.685486\pi$
$102$	−23.7973	−2.35628
$103$	5.18959	0.511345	0.255673	−	0.966763i	$-0.417703\pi$
$103$	5.18959	0.511345	0.255673	+	0.966763i	$0.417703\pi$
$104$	6.96915	0.683381
$105$	4.83196	0.471551
$106$	12.0122	1.16673
$107$	16.9974	1.64320	0.821602	−	0.570061i	$-0.193080\pi$
$107$	16.9974	1.64320	0.821602	+	0.570061i	$0.193080\pi$
$108$	20.4313	1.96600
$109$	−12.5530	−1.20236	−0.601178	−	0.799115i	$-0.705302\pi$
$109$	−12.5530	−1.20236	−0.601178	+	0.799115i	$0.705302\pi$
$110$	−0.226008	−0.0215490
$111$	−18.3001	−1.73697
$112$	−9.00675	−0.851058
$113$	13.8959	1.30722	0.653609	−	0.756833i	$-0.273254\pi$
$113$	13.8959	1.30722	0.653609	+	0.756833i	$0.273254\pi$
$114$	−33.9491	−3.17963
$115$	3.97554	0.370721
$116$	8.83385	0.820202
$117$	−6.32164	−0.584436
$118$	−7.07263	−0.651088
$119$	−6.50007	−0.595860
$120$	13.4932	1.23175
$121$	−10.9901	−0.999103
$122$	27.8798	2.52411
$123$	−24.8323	−2.23905
$124$	−5.14664	−0.462182
$125$	8.41498	0.752658
$126$	22.2848	1.98528
$127$	−16.4292	−1.45786	−0.728929	−	0.684589i	$-0.759982\pi$
$127$	−16.4292	−1.45786	−0.728929	+	0.684589i	$0.759982\pi$
$128$	18.3015	1.61764
$129$	−34.1477	−3.00653
$130$	−3.01177	−0.264150
$131$	−6.57955	−0.574858	−0.287429	−	0.957802i	$-0.592801\pi$
$131$	−6.57955	−0.574858	−0.287429	+	0.957802i	$0.592801\pi$
$132$	−1.14315	−0.0994983
$133$	−9.27297	−0.804068
$134$	−31.4672	−2.71835
$135$	−4.55050	−0.391645
$136$	−18.1514	−1.55647
$137$	−20.2687	−1.73167	−0.865835	−	0.500329i	$-0.833212\pi$
$137$	−20.2687	−1.73167	−0.865835	+	0.500329i	$0.833212\pi$
$138$	29.8533	2.54128
$139$	2.39514	0.203153	0.101577	−	0.994828i	$-0.467611\pi$
$139$	2.39514	0.203153	0.101577	+	0.994828i	$0.467611\pi$
$140$	7.15127	0.604392
$141$	1.82357	0.153572
$142$	−23.1805	−1.94526
$143$	0.131502	0.0109967
$144$	22.8144	1.90120
$145$	−1.96750	−0.163392
$146$	−25.0562	−2.07367
$147$	−9.60834	−0.792482
$148$	−27.0840	−2.22629
$149$	14.8596	1.21735	0.608675	−	0.793420i	$-0.291701\pi$
$149$	14.8596	1.21735	0.608675	+	0.793420i	$0.291701\pi$
$150$	28.6795	2.34167
$151$	−20.0438	−1.63114	−0.815570	−	0.578659i	$-0.803576\pi$
$151$	−20.0438	−1.63114	−0.815570	+	0.578659i	$0.803576\pi$
$152$	−25.8947	−2.10034
$153$	16.4649	1.33111
$154$	−0.463565	−0.0373551
$155$	1.14627	0.0920708
$156$	−15.2335	−1.21966
$157$	−14.3839	−1.14796	−0.573979	−	0.818870i	$-0.694601\pi$
$157$	−14.3839	−1.14796	−0.573979	+	0.818870i	$0.694601\pi$
$158$	−3.09609	−0.246311
$159$	−13.5321	−1.07316
$160$	1.19139	0.0941880
$161$	8.15423	0.642643
$162$	1.29057	0.101397
$163$	−7.99146	−0.625940	−0.312970	−	0.949763i	$-0.601324\pi$
$163$	−7.99146	−0.625940	−0.312970	+	0.949763i	$0.601324\pi$
$164$	−36.7517	−2.86982
$165$	0.254605	0.0198210
$166$	−3.31594	−0.257367
$167$	5.21537	0.403578	0.201789	−	0.979429i	$-0.435325\pi$
$167$	5.21537	0.403578	0.201789	+	0.979429i	$0.435325\pi$
$168$	27.6759	2.13524
$169$	−11.2476	−0.865201
$170$	7.84425	0.601626
$171$	23.4888	1.79623
$172$	−50.5383	−3.85351
$173$	15.2492	1.15938	0.579689	−	0.814838i	$-0.303174\pi$
$173$	15.2492	1.15938	0.579689	+	0.814838i	$0.303174\pi$
$174$	−14.7744	−1.12005
$175$	7.83360	0.592164
$176$	−0.474583	−0.0357730
$177$	7.96753	0.598876
$178$	28.9148	2.16725
$179$	−13.6712	−1.02183	−0.510916	−	0.859631i	$-0.670694\pi$
$179$	−13.6712	−1.02183	−0.510916	+	0.859631i	$0.670694\pi$
$180$	−18.1144	−1.35017
$181$	−4.12037	−0.306265	−0.153132	−	0.988206i	$-0.548936\pi$
$181$	−4.12037	−0.306265	−0.153132	+	0.988206i	$0.548936\pi$
$182$	−6.17743	−0.457902
$183$	−31.4074	−2.32170
$184$	22.7706	1.67867
$185$	6.03222	0.443498
$186$	8.60764	0.631143
$187$	−0.342501	−0.0250461
$188$	2.69887	0.196835
$189$	−9.33353	−0.678914
$190$	11.1906	0.811850
$191$	18.4663	1.33617	0.668086	−	0.744084i	$-0.267114\pi$
$191$	18.4663	1.33617	0.668086	+	0.744084i	$0.267114\pi$
$192$	−17.6968	−1.27716
$193$	3.20048	0.230375	0.115188	−	0.993344i	$-0.463253\pi$
$193$	3.20048	0.230375	0.115188	+	0.993344i	$0.463253\pi$
$194$	−43.2028	−3.10178
$195$	3.39285	0.242967
$196$	−14.2203	−1.01573
$197$	−1.05727	−0.0753277	−0.0376638	−	0.999290i	$-0.511992\pi$
$197$	−1.05727	−0.0753277	−0.0376638	+	0.999290i	$0.511992\pi$
$198$	1.17423	0.0834486
$199$	−15.6959	−1.11266	−0.556328	−	0.830963i	$-0.687790\pi$
$199$	−15.6959	−1.11266	−0.556328	+	0.830963i	$0.687790\pi$
$200$	21.8752	1.54681
$201$	35.4488	2.50036
$202$	27.3785	1.92634
$203$	−4.03553	−0.283239
$204$	39.6762	2.77789
$205$	8.18542	0.571695
$206$	−12.8456	−0.894993
$207$	−20.6550	−1.43562
$208$	−6.32426	−0.438509
$209$	−0.488610	−0.0337979
$210$	−11.9603	−0.825341
$211$	14.1496	0.974097	0.487049	−	0.873375i	$-0.338073\pi$
$211$	14.1496	0.974097	0.487049	+	0.873375i	$0.338073\pi$
$212$	−20.0274	−1.37549
$213$	26.1135	1.78927
$214$	−42.0730	−2.87605
$215$	11.2560	0.767654
$216$	−26.0638	−1.77342
$217$	2.35112	0.159604
$218$	31.0718	2.10445
$219$	28.2266	1.90737
$220$	0.376814	0.0254048
$221$	−4.56415	−0.307018
$222$	45.2974	3.04016
$223$	−22.2529	−1.49016	−0.745082	−	0.666973i	$-0.767589\pi$
$223$	−22.2529	−1.49016	−0.745082	+	0.666973i	$0.767589\pi$
$224$	2.44367	0.163274
$225$	−19.8428	−1.32285
$226$	−34.3959	−2.28798
$227$	16.1572	1.07239	0.536195	−	0.844094i	$-0.319861\pi$
$227$	16.1572	1.07239	0.536195	+	0.844094i	$0.319861\pi$
$228$	56.6019	3.74856
$229$	−28.1391	−1.85948	−0.929741	−	0.368215i	$-0.879969\pi$
$229$	−28.1391	−1.85948	−0.929741	+	0.368215i	$0.879969\pi$
$230$	−9.84049	−0.648863
$231$	0.522220	0.0343595
$232$	−11.2692	−0.739858
$233$	−0.327835	−0.0214772	−0.0107386	−	0.999942i	$-0.503418\pi$
$233$	−0.327835	−0.0214772	−0.0107386	+	0.999942i	$0.503418\pi$
$234$	15.6477	1.02292
$235$	−0.601098	−0.0392113
$236$	11.7919	0.767587
$237$	3.48783	0.226559
$238$	16.0893	1.04292
$239$	8.01739	0.518602	0.259301	−	0.965797i	$-0.416508\pi$
$239$	8.01739	0.518602	0.259301	+	0.965797i	$0.416508\pi$
$240$	−12.2446	−0.790386
$241$	−0.592648	−0.0381758	−0.0190879	−	0.999818i	$-0.506076\pi$
$241$	−0.592648	−0.0381758	−0.0190879	+	0.999818i	$0.506076\pi$
$242$	27.2034	1.74870
$243$	−16.3062	−1.04604
$244$	−46.4828	−2.97575
$245$	3.16718	0.202343
$246$	61.4663	3.91895
$247$	−6.51119	−0.414297
$248$	6.56547	0.416908
$249$	3.73551	0.236728
$250$	−20.8292	−1.31736
$251$	−29.2205	−1.84438	−0.922192	−	0.386733i	$-0.873603\pi$
$251$	−29.2205	−1.84438	−0.922192	+	0.386733i	$0.873603\pi$
$252$	−37.1545	−2.34051
$253$	0.429662	0.0270126
$254$	40.6665	2.55165
$255$	−8.83679	−0.553381
$256$	−32.6080	−2.03800
$257$	−4.26126	−0.265810	−0.132905	−	0.991129i	$-0.542431\pi$
$257$	−4.26126	−0.265810	−0.132905	+	0.991129i	$0.542431\pi$
$258$	84.5242	5.26225
$259$	12.3727	0.768801
$260$	5.02140	0.311414
$261$	10.2221	0.632735
$262$	16.2861	1.00616
$263$	−12.7560	−0.786567	−0.393283	−	0.919417i	$-0.628661\pi$
$263$	−12.7560	−0.786567	−0.393283	+	0.919417i	$0.628661\pi$
$264$	1.45829	0.0897518
$265$	4.46055	0.274009
$266$	22.9530	1.40734
$267$	−32.5734	−1.99346
$268$	52.4640	3.20475
$269$	−24.2979	−1.48147	−0.740736	−	0.671797i	$-0.765523\pi$
$269$	−24.2979	−1.48147	−0.740736	+	0.671797i	$0.765523\pi$
$270$	11.2637	0.685485
$271$	13.9106	0.845010	0.422505	−	0.906361i	$-0.361151\pi$
$271$	13.9106	0.845010	0.422505	+	0.906361i	$0.361151\pi$
$272$	16.4717	0.998746
$273$	6.95907	0.421182
$274$	50.1702	3.03089
$275$	0.412767	0.0248908
$276$	−49.7732	−2.99599
$277$	−0.769903	−0.0462590	−0.0231295	−	0.999732i	$-0.507363\pi$
$277$	−0.769903	−0.0462590	−0.0231295	+	0.999732i	$0.507363\pi$
$278$	−5.92858	−0.355573
$279$	−5.95547	−0.356545
$280$	−9.12273	−0.545188
$281$	6.41366	0.382607	0.191303	−	0.981531i	$-0.438729\pi$
$281$	6.41366	0.382607	0.191303	+	0.981531i	$0.438729\pi$
$282$	−4.51379	−0.268792
$283$	−9.74716	−0.579409	−0.289704	−	0.957116i	$-0.593557\pi$
$283$	−9.74716	−0.579409	−0.289704	+	0.957116i	$0.593557\pi$
$284$	38.6478	2.29333
$285$	−12.6065	−0.746746
$286$	−0.325501	−0.0192473
$287$	16.7891	0.991029
$288$	−6.18990	−0.364743
$289$	−5.11254	−0.300738
$290$	4.87006	0.285980
$291$	48.6693	2.85305
$292$	41.7752	2.44471
$293$	28.8235	1.68389	0.841944	−	0.539565i	$-0.181411\pi$
$293$	28.8235	1.68389	0.841944	+	0.539565i	$0.181411\pi$
$294$	23.7831	1.38706
$295$	−2.62632	−0.152910
$296$	34.5506	2.00821
$297$	−0.491801	−0.0285372
$298$	−36.7814	−2.13069
$299$	5.72565	0.331123
$300$	−47.8160	−2.76066
$301$	23.0872	1.33072
$302$	49.6135	2.85493
$303$	−30.8427	−1.77187
$304$	23.4985	1.34773
$305$	10.3528	0.592797
$306$	−40.7549	−2.32980
$307$	22.9538	1.31004	0.655020	−	0.755612i	$-0.272660\pi$
$307$	22.9538	1.31004	0.655020	+	0.755612i	$0.272660\pi$
$308$	0.772882	0.0440390
$309$	14.4709	0.823221
$310$	−2.83732	−0.161149
$311$	16.8380	0.954796	0.477398	−	0.878687i	$-0.341580\pi$
$311$	16.8380	0.954796	0.477398	+	0.878687i	$0.341580\pi$
$312$	19.4331	1.10018
$313$	−19.2504	−1.08810	−0.544048	−	0.839054i	$-0.683109\pi$
$313$	−19.2504	−1.08810	−0.544048	+	0.839054i	$0.683109\pi$
$314$	35.6038	2.00924
$315$	8.27513	0.466251
$316$	5.16197	0.290384
$317$	−6.57383	−0.369223	−0.184612	−	0.982812i	$-0.559103\pi$
$317$	−6.57383	−0.369223	−0.184612	+	0.982812i	$0.559103\pi$
$318$	33.4953	1.87833
$319$	−0.212640	−0.0119055
$320$	5.83337	0.326095
$321$	47.3965	2.64542
$322$	−20.1838	−1.12480
$323$	16.9586	0.943602
$324$	−2.15172	−0.119540
$325$	5.50051	0.305113
$326$	19.7809	1.09556
$327$	−35.0033	−1.93569
$328$	46.8834	2.58870
$329$	−1.23291	−0.0679726
$330$	−0.630212	−0.0346920
$331$	7.32558	0.402650	0.201325	−	0.979524i	$-0.435475\pi$
$331$	7.32558	0.402650	0.201325	+	0.979524i	$0.435475\pi$
$332$	5.52853	0.303417
$333$	−31.3405	−1.71745
$334$	−12.9094	−0.706370
$335$	−11.6849	−0.638414
$336$	−25.1149	−1.37013
$337$	−7.91903	−0.431377	−0.215688	−	0.976462i	$-0.569200\pi$
$337$	−7.91903	−0.431377	−0.215688	+	0.976462i	$0.569200\pi$
$338$	27.8407	1.51434
$339$	38.7481	2.10451
$340$	−13.0784	−0.709275
$341$	0.123885	0.00670874
$342$	−58.1407	−3.14389
$343$	19.6931	1.06333
$344$	64.4708	3.47603
$345$	11.0856	0.596829
$346$	−37.7457	−2.02922
$347$	−8.53192	−0.458017	−0.229009	−	0.973424i	$-0.573548\pi$
$347$	−8.53192	−0.458017	−0.229009	+	0.973424i	$0.573548\pi$
$348$	24.6328	1.32045
$349$	−22.3034	−1.19387	−0.596937	−	0.802288i	$-0.703616\pi$
$349$	−22.3034	−1.19387	−0.596937	+	0.802288i	$0.703616\pi$
$350$	−19.3902	−1.03645
$351$	−6.55372	−0.349811
$352$	0.128761	0.00686301
$353$	−11.8306	−0.629679	−0.314839	−	0.949145i	$-0.601951\pi$
$353$	−11.8306	−0.629679	−0.314839	+	0.949145i	$0.601951\pi$
$354$	−19.7217	−1.04819
$355$	−8.60774	−0.456852
$356$	−48.2084	−2.55504
$357$	−18.1251	−0.959283
$358$	33.8396	1.78848
$359$	−21.0628	−1.11165	−0.555825	−	0.831299i	$-0.687598\pi$
$359$	−21.0628	−1.11165	−0.555825	+	0.831299i	$0.687598\pi$
$360$	23.1082	1.21791
$361$	5.19308	0.273320
$362$	10.1990	0.536046
$363$	−30.6454	−1.60847
$364$	10.2994	0.539834
$365$	−9.30426	−0.487007
$366$	77.7413	4.06360
$367$	−7.03378	−0.367161	−0.183580	−	0.983005i	$-0.558769\pi$
$367$	−7.03378	−0.367161	−0.183580	+	0.983005i	$0.558769\pi$
$368$	−20.6635	−1.07716
$369$	−42.5274	−2.21389
$370$	−14.9313	−0.776241
$371$	9.14902	0.474994
$372$	−14.3512	−0.744073
$373$	8.32078	0.430834	0.215417	−	0.976522i	$-0.430889\pi$
$373$	8.32078	0.430834	0.215417	+	0.976522i	$0.430889\pi$
$374$	0.847777	0.0438375
$375$	23.4647	1.21171
$376$	−3.44289	−0.177554
$377$	−2.83362	−0.145939
$378$	23.1029	1.18828
$379$	6.45039	0.331334	0.165667	−	0.986182i	$-0.447022\pi$
$379$	6.45039	0.331334	0.165667	+	0.986182i	$0.447022\pi$
$380$	−18.6576	−0.957114
$381$	−45.8121	−2.34702
$382$	−45.7088	−2.33866
$383$	−18.5412	−0.947413	−0.473707	−	0.880683i	$-0.657084\pi$
$383$	−18.5412	−0.947413	−0.473707	+	0.880683i	$0.657084\pi$
$384$	51.0329	2.60426
$385$	−0.172138	−0.00877297
$386$	−7.92200	−0.403219
$387$	−58.4807	−2.97274
$388$	72.0303	3.65678
$389$	−3.28740	−0.166678	−0.0833389	−	0.996521i	$-0.526558\pi$
$389$	−3.28740	−0.166678	−0.0833389	+	0.996521i	$0.526558\pi$
$390$	−8.39817	−0.425258
$391$	−14.9126	−0.754164
$392$	18.1405	0.916236
$393$	−18.3468	−0.925472
$394$	2.61702	0.131844
$395$	−1.14969	−0.0578471
$396$	−1.95774	−0.0983801
$397$	14.5143	0.728450	0.364225	−	0.931311i	$-0.381334\pi$
$397$	14.5143	0.728450	0.364225	+	0.931311i	$0.381334\pi$
$398$	38.8515	1.94745
$399$	−25.8572	−1.29448
$400$	−19.8510	−0.992551
$401$	−24.6272	−1.22982	−0.614911	−	0.788597i	$-0.710808\pi$
$401$	−24.6272	−1.22982	−0.614911	+	0.788597i	$0.710808\pi$
$402$	−87.7448	−4.37631
$403$	1.65088	0.0822363
$404$	−45.6470	−2.27102
$405$	0.479237	0.0238135
$406$	9.98896	0.495744
$407$	0.651940	0.0323155
$408$	−50.6142	−2.50578
$409$	32.9459	1.62907	0.814535	−	0.580114i	$-0.196992\pi$
$409$	32.9459	1.62907	0.814535	+	0.580114i	$0.196992\pi$
$410$	−20.2610	−1.00062
$411$	−56.5182	−2.78784
$412$	21.4169	1.05513
$413$	−5.38684	−0.265069
$414$	51.1263	2.51272
$415$	−1.23133	−0.0604435
$416$	1.71587	0.0841273
$417$	6.67873	0.327059
$418$	1.20944	0.0591554
$419$	−18.5915	−0.908255	−0.454127	−	0.890937i	$-0.650049\pi$
$419$	−18.5915	−0.908255	−0.454127	+	0.890937i	$0.650049\pi$
$420$	19.9409	0.973019
$421$	0.735469	0.0358446	0.0179223	−	0.999839i	$-0.494295\pi$
$421$	0.735469	0.0358446	0.0179223	+	0.999839i	$0.494295\pi$
$422$	−35.0238	−1.70493
$423$	3.12301	0.151846
$424$	25.5486	1.24075
$425$	−14.3262	−0.694925
$426$	−64.6376	−3.13170
$427$	21.2345	1.02761
$428$	70.1466	3.39066
$429$	0.366686	0.0177038
$430$	−27.8615	−1.34360
$431$	−20.1292	−0.969588	−0.484794	−	0.874628i	$-0.661105\pi$
$431$	−20.1292	−0.969588	−0.484794	+	0.874628i	$0.661105\pi$
$432$	23.6520	1.13796
$433$	12.2449	0.588454	0.294227	−	0.955735i	$-0.404938\pi$
$433$	12.2449	0.588454	0.294227	+	0.955735i	$0.404938\pi$
$434$	−5.81962	−0.279351
$435$	−5.48627	−0.263046
$436$	−51.8047	−2.48100
$437$	−21.2743	−1.01769
$438$	−69.8680	−3.33842
$439$	14.8916	0.710739	0.355369	−	0.934726i	$-0.384355\pi$
$439$	14.8916	0.710739	0.355369	+	0.934726i	$0.384355\pi$
$440$	−0.480694	−0.0229162
$441$	−16.4551	−0.783575
$442$	11.2974	0.537364
$443$	16.7328	0.795002	0.397501	−	0.917602i	$-0.369878\pi$
$443$	16.7328	0.795002	0.397501	+	0.917602i	$0.369878\pi$
$444$	−75.5225	−3.58414
$445$	10.7371	0.508987
$446$	55.0816	2.60819
$447$	41.4354	1.95983
$448$	11.9648	0.565284
$449$	35.2871	1.66530	0.832650	−	0.553800i	$-0.186823\pi$
$449$	35.2871	1.66530	0.832650	+	0.553800i	$0.186823\pi$
$450$	49.1160	2.31535
$451$	0.884650	0.0416565
$452$	57.3469	2.69737
$453$	−55.8911	−2.62599
$454$	−39.9932	−1.87697
$455$	−2.29390	−0.107540
$456$	−72.2060	−3.38136
$457$	2.20982	0.103371	0.0516855	−	0.998663i	$-0.483541\pi$
$457$	2.20982	0.103371	0.0516855	+	0.998663i	$0.483541\pi$
$458$	69.6513	3.25459
$459$	17.0694	0.796730
$460$	16.4066	0.764963
$461$	29.1330	1.35686	0.678430	−	0.734665i	$-0.262661\pi$
$461$	29.1330	1.35686	0.678430	+	0.734665i	$0.262661\pi$
$462$	−1.29263	−0.0601385
$463$	−11.0694	−0.514440	−0.257220	−	0.966353i	$-0.582806\pi$
$463$	−11.0694	−0.514440	−0.257220	+	0.966353i	$0.582806\pi$
$464$	10.2264	0.474748
$465$	3.19632	0.148226
$466$	0.811475	0.0375908
$467$	−24.0317	−1.11205	−0.556027	−	0.831164i	$-0.687675\pi$
$467$	−24.0317	−1.11205	−0.556027	+	0.831164i	$0.687675\pi$
$468$	−26.0887	−1.20595
$469$	−23.9669	−1.10669
$470$	1.48787	0.0686304
$471$	−40.1087	−1.84811
$472$	−15.0427	−0.692396
$473$	1.21651	0.0559351
$474$	−8.63328	−0.396540
$475$	−20.4378	−0.937749
$476$	−26.8251	−1.22952
$477$	−23.1748	−1.06110
$478$	−19.8451	−0.907693
$479$	−26.7515	−1.22231	−0.611154	−	0.791512i	$-0.709294\pi$
$479$	−26.7515	−1.22231	−0.611154	+	0.791512i	$0.709294\pi$
$480$	3.32214	0.151634
$481$	8.68771	0.396126
$482$	1.46695	0.0668179
$483$	22.7377	1.03460
$484$	−45.3551	−2.06159
$485$	−16.0428	−0.728464
$486$	40.3620	1.83086
$487$	11.8841	0.538518	0.269259	−	0.963068i	$-0.413221\pi$
$487$	11.8841	0.538518	0.269259	+	0.963068i	$0.413221\pi$
$488$	59.2972	2.68426
$489$	−22.2838	−1.00771
$490$	−7.83957	−0.354156
$491$	16.4484	0.742308	0.371154	−	0.928571i	$-0.378962\pi$
$491$	16.4484	0.742308	0.371154	+	0.928571i	$0.378962\pi$
$492$	−102.480	−4.62016
$493$	7.38026	0.332390
$494$	16.1169	0.725132
$495$	0.436032	0.0195982
$496$	−5.95794	−0.267519
$497$	−17.6553	−0.791949
$498$	−9.24633	−0.414338
$499$	−23.1859	−1.03794	−0.518972	−	0.854792i	$-0.673685\pi$
$499$	−23.1859	−1.03794	−0.518972	+	0.854792i	$0.673685\pi$
$500$	34.7277	1.55307
$501$	14.5428	0.649725
$502$	72.3283	3.22817
$503$	−24.8361	−1.10739	−0.553694	−	0.832720i	$-0.686782\pi$
$503$	−24.8361	−1.10739	−0.553694	+	0.832720i	$0.686782\pi$
$504$	47.3972	2.11124
$505$	10.1666	0.452408
$506$	−1.06352	−0.0472794
$507$	−31.3634	−1.39290
$508$	−67.8016	−3.00821
$509$	20.1010	0.890961	0.445481	−	0.895292i	$-0.353033\pi$
$509$	20.1010	0.890961	0.445481	+	0.895292i	$0.353033\pi$
$510$	21.8733	0.968566
$511$	−19.0840	−0.844225
$512$	44.1101	1.94941
$513$	24.3511	1.07513
$514$	10.5477	0.465239
$515$	−4.77002	−0.210192
$516$	−140.924	−6.20382
$517$	−0.0649644	−0.00285713
$518$	−30.6256	−1.34561
$519$	42.5217	1.86650
$520$	−6.40570	−0.280909
$521$	15.1825	0.665155	0.332578	−	0.943076i	$-0.392082\pi$
$521$	15.1825	0.665155	0.332578	+	0.943076i	$0.392082\pi$
$522$	−25.3024	−1.10746
$523$	−13.5801	−0.593817	−0.296908	−	0.954906i	$-0.595956\pi$
$523$	−13.5801	−0.593817	−0.296908	+	0.954906i	$0.595956\pi$
$524$	−27.1531	−1.18619
$525$	21.8436	0.953333
$526$	31.5743	1.37670
$527$	−4.29977	−0.187301
$528$	−1.32335	−0.0575915
$529$	−4.29234	−0.186623
$530$	−11.0410	−0.479590
$531$	13.6451	0.592145
$532$	−38.2685	−1.65915
$533$	11.7888	0.510629
$534$	80.6274	3.48909
$535$	−15.6232	−0.675450
$536$	−66.9273	−2.89082
$537$	−38.1214	−1.64506
$538$	60.1436	2.59297
$539$	0.342296	0.0147438
$540$	−18.7794	−0.808138
$541$	−36.3313	−1.56200	−0.781002	−	0.624528i	$-0.785291\pi$
$541$	−36.3313	−1.56200	−0.781002	+	0.624528i	$0.785291\pi$
$542$	−34.4323	−1.47900
$543$	−11.4895	−0.493060
$544$	−4.46903	−0.191608
$545$	11.5381	0.494237
$546$	−17.2255	−0.737182
$547$	−3.90615	−0.167015	−0.0835074	−	0.996507i	$-0.526612\pi$
$547$	−3.90615	−0.167015	−0.0835074	+	0.996507i	$0.526612\pi$
$548$	−83.6466	−3.57321
$549$	−53.7878	−2.29561
$550$	−1.02170	−0.0435656
$551$	10.5287	0.448536
$552$	63.4947	2.70251
$553$	−2.35812	−0.100278
$554$	1.90571	0.0809657
$555$	16.8206	0.713993
$556$	9.88448	0.419195
$557$	−16.4313	−0.696215	−0.348107	−	0.937455i	$-0.613176\pi$
$557$	−16.4313	−0.696215	−0.348107	+	0.937455i	$0.613176\pi$
$558$	14.7413	0.624049
$559$	16.2111	0.685657
$560$	8.27857	0.349833
$561$	−0.955047	−0.0403221
$562$	−15.8754	−0.669665
$563$	−2.84105	−0.119736	−0.0598681	−	0.998206i	$-0.519068\pi$
$563$	−2.84105	−0.119736	−0.0598681	+	0.998206i	$0.519068\pi$
$564$	7.52565	0.316887
$565$	−12.7724	−0.537341
$566$	24.1267	1.01412
$567$	0.982961	0.0412805
$568$	−49.3023	−2.06868
$569$	7.06053	0.295993	0.147996	−	0.988988i	$-0.452718\pi$
$569$	7.06053	0.295993	0.147996	+	0.988988i	$0.452718\pi$
$570$	31.2044	1.30701
$571$	26.6916	1.11701	0.558504	−	0.829502i	$-0.311375\pi$
$571$	26.6916	1.11701	0.558504	+	0.829502i	$0.311375\pi$
$572$	0.542694	0.0226912
$573$	51.4923	2.15112
$574$	−41.5573	−1.73457
$575$	17.9721	0.749486
$576$	−30.3073	−1.26280
$577$	29.4046	1.22413	0.612064	−	0.790808i	$-0.290339\pi$
$577$	29.4046	1.22413	0.612064	+	0.790808i	$0.290339\pi$
$578$	12.6548	0.526372
$579$	8.92437	0.370884
$580$	−8.11964	−0.337150
$581$	−2.52557	−0.104778
$582$	−120.469	−4.99360
$583$	0.482079	0.0199657
$584$	−53.2918	−2.20523
$585$	5.81054	0.240236
$586$	−71.3456	−2.94726
$587$	−18.4890	−0.763121	−0.381560	−	0.924344i	$-0.624613\pi$
$587$	−18.4890	−0.763121	−0.381560	+	0.924344i	$0.624613\pi$
$588$	−39.6525	−1.63524
$589$	−6.13404	−0.252749
$590$	6.50081	0.267634
$591$	−2.94816	−0.121271
$592$	−31.3535	−1.28862
$593$	−5.29334	−0.217371	−0.108686	−	0.994076i	$-0.534664\pi$
$593$	−5.29334	−0.217371	−0.108686	+	0.994076i	$0.534664\pi$
$594$	1.21733	0.0499478
$595$	5.97454	0.244932
$596$	61.3241	2.51193
$597$	−43.7674	−1.79128
$598$	−14.1724	−0.579554
$599$	33.2375	1.35805	0.679023	−	0.734117i	$-0.262404\pi$
$599$	33.2375	1.35805	0.679023	+	0.734117i	$0.262404\pi$
$600$	60.9980	2.49023
$601$	18.7877	0.766367	0.383184	−	0.923672i	$-0.374828\pi$
$601$	18.7877	0.766367	0.383184	+	0.923672i	$0.374828\pi$
$602$	−57.1467	−2.32913
$603$	60.7090	2.47226
$604$	−82.7184	−3.36577
$605$	10.1016	0.410688
$606$	76.3436	3.10125
$607$	−45.8220	−1.85986	−0.929929	−	0.367740i	$-0.880132\pi$
$607$	−45.8220	−1.85986	−0.929929	+	0.367740i	$0.880132\pi$
$608$	−6.37550	−0.258561
$609$	−11.2529	−0.455989
$610$	−25.6257	−1.03755
$611$	−0.865712	−0.0350229
$612$	67.9489	2.74667
$613$	7.85283	0.317173	0.158586	−	0.987345i	$-0.449306\pi$
$613$	7.85283	0.317173	0.158586	+	0.987345i	$0.449306\pi$
$614$	−56.8164	−2.29292
$615$	22.8246	0.920378
$616$	−0.985951	−0.0397251
$617$	22.6488	0.911807	0.455904	−	0.890029i	$-0.349316\pi$
$617$	22.6488	0.911807	0.455904	+	0.890029i	$0.349316\pi$
$618$	−35.8192	−1.44086
$619$	−14.6419	−0.588506	−0.294253	−	0.955728i	$-0.595071\pi$
$619$	−14.6419	−0.588506	−0.294253	+	0.955728i	$0.595071\pi$
$620$	4.73054	0.189983
$621$	−21.4132	−0.859284
$622$	−41.6784	−1.67115
$623$	22.0228	0.882325
$624$	−17.6349	−0.705961
$625$	13.0412	0.521647
$626$	47.6496	1.90446
$627$	−1.36247	−0.0544116
$628$	−59.3606	−2.36875
$629$	−22.6274	−0.902215
$630$	−20.4831	−0.816065
$631$	−37.4022	−1.48896	−0.744479	−	0.667646i	$-0.767302\pi$
$631$	−37.4022	−1.48896	−0.744479	+	0.667646i	$0.767302\pi$
$632$	−6.58503	−0.261939
$633$	39.4554	1.56821
$634$	16.2719	0.646240
$635$	15.1009	0.599263
$636$	−55.8454	−2.21441
$637$	4.56142	0.180730
$638$	0.526337	0.0208379
$639$	44.7216	1.76916
$640$	−16.8219	−0.664943
$641$	−27.9140	−1.10254	−0.551269	−	0.834328i	$-0.685856\pi$
$641$	−27.9140	−1.10254	−0.551269	+	0.834328i	$0.685856\pi$
$642$	−117.318	−4.63019
$643$	8.58145	0.338419	0.169210	−	0.985580i	$-0.445878\pi$
$643$	8.58145	0.338419	0.169210	+	0.985580i	$0.445878\pi$
$644$	33.6516	1.32606
$645$	31.3869	1.23586
$646$	−41.9769	−1.65156
$647$	28.9865	1.13958	0.569788	−	0.821792i	$-0.307025\pi$
$647$	28.9865	1.13958	0.569788	+	0.821792i	$0.307025\pi$
$648$	2.74491	0.107830
$649$	−0.283843	−0.0111418
$650$	−13.6152	−0.534031
$651$	6.55597	0.256949
$652$	−32.9799	−1.29159
$653$	2.91288	0.113990	0.0569949	−	0.998374i	$-0.481848\pi$
$653$	2.91288	0.113990	0.0569949	+	0.998374i	$0.481848\pi$
$654$	86.6422	3.38798
$655$	6.04760	0.236299
$656$	−42.5451	−1.66111
$657$	48.3404	1.88594
$658$	3.05177	0.118970
$659$	3.16689	0.123364	0.0616822	−	0.998096i	$-0.480353\pi$
$659$	3.16689	0.123364	0.0616822	+	0.998096i	$0.480353\pi$
$660$	1.05073	0.0408995
$661$	−8.96793	−0.348812	−0.174406	−	0.984674i	$-0.555801\pi$
$661$	−8.96793	−0.348812	−0.174406	+	0.984674i	$0.555801\pi$
$662$	−18.1327	−0.704747
$663$	−12.7269	−0.494272
$664$	−7.05264	−0.273695
$665$	8.52326	0.330518
$666$	77.5757	3.00600
$667$	−9.25842	−0.358488
$668$	21.5233	0.832760
$669$	−62.0511	−2.39903
$670$	28.9231	1.11740
$671$	1.11889	0.0431941
$672$	6.81404	0.262857
$673$	45.8784	1.76848	0.884242	−	0.467029i	$-0.154676\pi$
$673$	45.8784	1.76848	0.884242	+	0.467029i	$0.154676\pi$
$674$	19.6016	0.755026
$675$	−20.5712	−0.791788
$676$	−46.4177	−1.78529
$677$	18.4266	0.708193	0.354097	−	0.935209i	$-0.384788\pi$
$677$	18.4266	0.708193	0.354097	+	0.935209i	$0.384788\pi$
$678$	−95.9113	−3.68345
$679$	−32.9053	−1.26279
$680$	16.6839	0.639797
$681$	45.0535	1.72645
$682$	−0.306647	−0.0117421
$683$	−28.8407	−1.10356	−0.551780	−	0.833990i	$-0.686051\pi$
$683$	−28.8407	−1.10356	−0.551780	+	0.833990i	$0.686051\pi$
$684$	96.9356	3.70643
$685$	18.6300	0.711815
$686$	−48.7454	−1.86111
$687$	−78.4644	−2.99360
$688$	−58.5050	−2.23048
$689$	6.42416	0.244741
$690$	−27.4397	−1.04461
$691$	−39.7290	−1.51136	−0.755680	−	0.654941i	$-0.772694\pi$
$691$	−39.7290	−1.51136	−0.755680	+	0.654941i	$0.772694\pi$
$692$	62.9319	2.39231
$693$	0.894345	0.0339734
$694$	21.1187	0.801654
$695$	−2.20149	−0.0835074
$696$	−31.4235	−1.19111
$697$	−30.7043	−1.16301
$698$	55.2066	2.08960
$699$	−0.914151	−0.0345764
$700$	32.3284	1.22190
$701$	31.1182	1.17532	0.587659	−	0.809109i	$-0.300050\pi$
$701$	31.1182	1.17532	0.587659	+	0.809109i	$0.300050\pi$
$702$	16.2221	0.612265
$703$	−32.2802	−1.21747
$704$	0.630448	0.0237609
$705$	−1.67613	−0.0631268
$706$	29.2837	1.10211
$707$	20.8527	0.784247
$708$	32.8811	1.23575
$709$	−12.5517	−0.471390	−0.235695	−	0.971827i	$-0.575737\pi$
$709$	−12.5517	−0.471390	−0.235695	+	0.971827i	$0.575737\pi$
$710$	21.3064	0.799613
$711$	5.97321	0.224013
$712$	61.4985	2.30475
$713$	5.39400	0.202007
$714$	44.8643	1.67900
$715$	−0.120870	−0.00452028
$716$	−56.4194	−2.10849
$717$	22.3561	0.834904
$718$	52.1357	1.94569
$719$	45.9380	1.71320	0.856600	−	0.515981i	$-0.172573\pi$
$719$	45.9380	1.71320	0.856600	+	0.515981i	$0.172573\pi$
$720$	−20.9699	−0.781503
$721$	−9.78377	−0.364367
$722$	−12.8542	−0.478384
$723$	−1.65257	−0.0614597
$724$	−17.0043	−0.631961
$725$	−8.89437	−0.330329
$726$	75.8553	2.81525
$727$	26.8915	0.997350	0.498675	−	0.866789i	$-0.333820\pi$
$727$	26.8915	0.997350	0.498675	+	0.866789i	$0.333820\pi$
$728$	−13.1387	−0.486953
$729$	−43.9048	−1.62610
$730$	23.0304	0.852395
$731$	−42.2224	−1.56165
$732$	−129.615	−4.79070
$733$	4.19541	0.154961	0.0774806	−	0.996994i	$-0.475312\pi$
$733$	4.19541	0.154961	0.0774806	+	0.996994i	$0.475312\pi$
$734$	17.4104	0.642630
$735$	8.83151	0.325755
$736$	5.60633	0.206652
$737$	−1.26286	−0.0465181
$738$	105.266	3.87490
$739$	39.3928	1.44909	0.724543	−	0.689230i	$-0.242051\pi$
$739$	39.3928	1.44909	0.724543	+	0.689230i	$0.242051\pi$
$740$	24.8943	0.915134
$741$	−18.1561	−0.666982
$742$	−22.6462	−0.831367
$743$	29.3464	1.07662	0.538308	−	0.842748i	$-0.319064\pi$
$743$	29.3464	1.07662	0.538308	+	0.842748i	$0.319064\pi$
$744$	18.3075	0.671185
$745$	−13.6583	−0.500400
$746$	−20.5961	−0.754075
$747$	6.39737	0.234067
$748$	−1.41346	−0.0516813
$749$	−32.0447	−1.17089
$750$	−58.0812	−2.12083
$751$	−16.0765	−0.586641	−0.293320	−	0.956014i	$-0.594760\pi$
$751$	−16.0765	−0.586641	−0.293320	+	0.956014i	$0.594760\pi$
$752$	3.12431	0.113932
$753$	−81.4800	−2.96930
$754$	7.01394	0.255433
$755$	18.4233	0.670491
$756$	−38.5185	−1.40090
$757$	−7.45653	−0.271012	−0.135506	−	0.990777i	$-0.543266\pi$
$757$	−7.45653	−0.271012	−0.135506	+	0.990777i	$0.543266\pi$
$758$	−15.9664	−0.579924
$759$	1.19809	0.0434879
$760$	23.8011	0.863357
$761$	40.1606	1.45582	0.727911	−	0.685672i	$-0.240492\pi$
$761$	40.1606	1.45582	0.727911	+	0.685672i	$0.240492\pi$
$762$	113.397	4.10793
$763$	23.6657	0.856756
$764$	76.2083	2.75712
$765$	−15.1337	−0.547161
$766$	45.8943	1.65823
$767$	−3.78247	−0.136577
$768$	−90.9258	−3.28100
$769$	26.8100	0.966795	0.483397	−	0.875401i	$-0.339403\pi$
$769$	26.8100	0.966795	0.483397	+	0.875401i	$0.339403\pi$
$770$	0.426086	0.0153551
$771$	−11.8823	−0.427931
$772$	13.2080	0.475367
$773$	9.53471	0.342940	0.171470	−	0.985189i	$-0.445148\pi$
$773$	9.53471	0.342940	0.171470	+	0.985189i	$0.445148\pi$
$774$	144.755	5.20310
$775$	5.18190	0.186139
$776$	−91.8877	−3.29857
$777$	34.5006	1.23770
$778$	8.13716	0.291731
$779$	−43.8026	−1.56939
$780$	14.0019	0.501349
$781$	−0.930292	−0.0332885
$782$	36.9126	1.31999
$783$	10.5974	0.378721
$784$	−16.4619	−0.587926
$785$	13.2209	0.471876
$786$	45.4129	1.61982
$787$	12.6911	0.452389	0.226194	−	0.974082i	$-0.427372\pi$
$787$	12.6911	0.452389	0.226194	+	0.974082i	$0.427372\pi$
$788$	−4.36325	−0.155434
$789$	−35.5694	−1.26630
$790$	2.84577	0.101248
$791$	−26.1975	−0.931477
$792$	2.49745	0.0887430
$793$	14.9102	0.529477
$794$	−35.9265	−1.27498
$795$	12.4380	0.441131
$796$	−64.7754	−2.29590
$797$	36.9422	1.30856	0.654280	−	0.756252i	$-0.272972\pi$
$797$	36.9422	1.30856	0.654280	+	0.756252i	$0.272972\pi$
$798$	64.0032	2.26569
$799$	2.25477	0.0797682
$800$	5.38588	0.190420
$801$	−55.7846	−1.97105
$802$	60.9585	2.15252
$803$	−1.00557	−0.0354858
$804$	146.293	5.15936
$805$	−7.49497	−0.264163
$806$	−4.08635	−0.143936
$807$	−67.7536	−2.38504
$808$	58.2310	2.04856
$809$	−14.1846	−0.498703	−0.249352	−	0.968413i	$-0.580218\pi$
$809$	−14.1846	−0.498703	−0.249352	+	0.968413i	$0.580218\pi$
$810$	−1.18623	−0.0416800
$811$	39.0807	1.37231	0.686154	−	0.727456i	$-0.259297\pi$
$811$	39.0807	1.37231	0.686154	+	0.727456i	$0.259297\pi$
$812$	−16.6542	−0.584447
$813$	38.7891	1.36039
$814$	−1.61372	−0.0565608
$815$	7.34536	0.257297
$816$	45.9306	1.60789
$817$	−60.2343	−2.10733
$818$	−81.5495	−2.85131
$819$	11.9180	0.416448
$820$	33.7803	1.17966
$821$	−32.1405	−1.12171	−0.560856	−	0.827914i	$-0.689528\pi$
$821$	−32.1405	−1.12171	−0.560856	+	0.827914i	$0.689528\pi$
$822$	139.897	4.87947
$823$	37.4497	1.30542	0.652708	−	0.757610i	$-0.273633\pi$
$823$	37.4497	1.30542	0.652708	+	0.757610i	$0.273633\pi$
$824$	−27.3211	−0.951775
$825$	1.15098	0.0400720
$826$	13.3338	0.463942
$827$	−10.6750	−0.371206	−0.185603	−	0.982625i	$-0.559424\pi$
$827$	−10.6750	−0.371206	−0.185603	+	0.982625i	$0.559424\pi$
$828$	−85.2408	−2.96232
$829$	15.9374	0.553528	0.276764	−	0.960938i	$-0.410738\pi$
$829$	15.9374	0.553528	0.276764	+	0.960938i	$0.410738\pi$
$830$	3.04785	0.105792
$831$	−2.14684	−0.0744729
$832$	8.40132	0.291263
$833$	−11.8804	−0.411630
$834$	−16.5316	−0.572441
$835$	−4.79371	−0.165893
$836$	−2.01644	−0.0697401
$837$	−6.17410	−0.213408
$838$	46.0187	1.58969
$839$	19.4832	0.672636	0.336318	−	0.941748i	$-0.390818\pi$
$839$	19.4832	0.672636	0.336318	+	0.941748i	$0.390818\pi$
$840$	−25.4383	−0.877704
$841$	−24.4180	−0.842000
$842$	−1.82047	−0.0627377
$843$	17.8842	0.615963
$844$	58.3937	2.01000
$845$	10.3383	0.355647
$846$	−7.73024	−0.265771
$847$	20.7194	0.711925
$848$	−23.1844	−0.796157
$849$	−27.1795	−0.932797
$850$	35.4611	1.21631
$851$	28.3858	0.973051
$852$	107.768	3.69206
$853$	−37.6147	−1.28790	−0.643952	−	0.765066i	$-0.722706\pi$
$853$	−37.6147	−1.28790	−0.643952	+	0.765066i	$0.722706\pi$
$854$	−52.5608	−1.79859
$855$	−21.5897	−0.738353
$856$	−89.4846	−3.05852
$857$	35.7417	1.22091	0.610457	−	0.792049i	$-0.290986\pi$
$857$	35.7417	1.22091	0.610457	+	0.792049i	$0.290986\pi$
$858$	−0.907643	−0.0309864
$859$	41.5877	1.41895	0.709477	−	0.704729i	$-0.248931\pi$
$859$	41.5877	1.41895	0.709477	+	0.704729i	$0.248931\pi$
$860$	46.4524	1.58401
$861$	46.8156	1.59547
$862$	49.8248	1.69704
$863$	−46.6987	−1.58964	−0.794821	−	0.606843i	$-0.792436\pi$
$863$	−46.6987	−1.58964	−0.794821	+	0.606843i	$0.792436\pi$
$864$	−6.41714	−0.218316
$865$	−14.0163	−0.476570
$866$	−30.3094	−1.02995
$867$	−14.2561	−0.484161
$868$	9.70280	0.329335
$869$	−0.124254	−0.00421502
$870$	13.5799	0.460402
$871$	−16.8288	−0.570222
$872$	66.0863	2.23796
$873$	83.3503	2.82098
$874$	52.6593	1.78123
$875$	−15.8645	−0.536318
$876$	116.488	3.93576
$877$	15.7910	0.533223	0.266611	−	0.963804i	$-0.414096\pi$
$877$	15.7910	0.533223	0.266611	+	0.963804i	$0.414096\pi$
$878$	−36.8606	−1.24398
$879$	80.3729	2.71091
$880$	0.436213	0.0147048
$881$	−30.4886	−1.02719	−0.513594	−	0.858033i	$-0.671686\pi$
$881$	−30.4886	−1.02719	−0.513594	+	0.858033i	$0.671686\pi$
$882$	40.7305	1.37147
$883$	24.1611	0.813087	0.406543	−	0.913631i	$-0.366734\pi$
$883$	24.1611	0.813087	0.406543	+	0.913631i	$0.366734\pi$
$884$	−18.8357	−0.633514
$885$	−7.32336	−0.246172
$886$	−41.4181	−1.39147
$887$	−1.55136	−0.0520897	−0.0260448	−	0.999661i	$-0.508291\pi$
$887$	−1.55136	−0.0520897	−0.0260448	+	0.999661i	$0.508291\pi$
$888$	96.3426	3.23305
$889$	30.9735	1.03882
$890$	−26.5770	−0.890864
$891$	0.0517941	0.00173517
$892$	−91.8352	−3.07487
$893$	3.21665	0.107641
$894$	−102.563	−3.43023
$895$	12.5659	0.420031
$896$	−34.5033	−1.15267
$897$	15.9657	0.533079
$898$	−87.3445	−2.91472
$899$	−2.66949	−0.0890325
$900$	−81.8890	−2.72963
$901$	−16.7319	−0.557421
$902$	−2.18973	−0.0729102
$903$	64.3775	2.14235
$904$	−73.1563	−2.43314
$905$	3.78724	0.125892
$906$	138.345	4.59619
$907$	−45.8752	−1.52326	−0.761630	−	0.648012i	$-0.775600\pi$
$907$	−45.8752	−1.52326	−0.761630	+	0.648012i	$0.775600\pi$
$908$	66.6789	2.21282
$909$	−52.8207	−1.75195
$910$	5.67799	0.188224
$911$	0.913274	0.0302581	0.0151291	−	0.999886i	$-0.495184\pi$
$911$	0.913274	0.0302581	0.0151291	+	0.999886i	$0.495184\pi$
$912$	65.5245	2.16973
$913$	−0.133077	−0.00440421
$914$	−5.46986	−0.180927
$915$	28.8681	0.954351
$916$	−116.127	−3.83694
$917$	12.4042	0.409624
$918$	−42.2510	−1.39449
$919$	34.9491	1.15287	0.576433	−	0.817145i	$-0.304444\pi$
$919$	34.9491	1.15287	0.576433	+	0.817145i	$0.304444\pi$
$920$	−20.9296	−0.690029
$921$	64.0054	2.10905
$922$	−72.1117	−2.37487
$923$	−12.3970	−0.408053
$924$	2.15514	0.0708990
$925$	27.2696	0.896619
$926$	27.3997	0.900409
$927$	24.7827	0.813969
$928$	−2.77457	−0.0910798
$929$	37.8230	1.24093	0.620465	−	0.784234i	$-0.286944\pi$
$929$	37.8230	1.24093	0.620465	+	0.784234i	$0.286944\pi$
$930$	−7.91172	−0.259436
$931$	−16.9485	−0.555464
$932$	−1.35294	−0.0443170
$933$	46.9520	1.53714
$934$	59.4846	1.94639
$935$	0.314810	0.0102954
$936$	33.2809	1.08782
$937$	−22.0068	−0.718931	−0.359466	−	0.933158i	$-0.617041\pi$
$937$	−22.0068	−0.718931	−0.359466	+	0.933158i	$0.617041\pi$
$938$	59.3241	1.93700
$939$	−53.6787	−1.75174
$940$	−2.48066	−0.0809104
$941$	−46.1969	−1.50598	−0.752988	−	0.658034i	$-0.771388\pi$
$941$	−46.1969	−1.50598	−0.752988	+	0.658034i	$0.771388\pi$
$942$	99.2793	3.23469
$943$	38.5180	1.25432
$944$	13.6507	0.444293
$945$	8.57892	0.279072
$946$	−3.01117	−0.0979016
$947$	54.1508	1.75967	0.879833	−	0.475284i	$-0.157655\pi$
$947$	54.1508	1.75967	0.879833	+	0.475284i	$0.157655\pi$
$948$	14.3939	0.467492
$949$	−13.4002	−0.434988
$950$	50.5887	1.64131
$951$	−18.3308	−0.594417
$952$	34.2202	1.10908
$953$	48.7345	1.57867	0.789333	−	0.613965i	$-0.210426\pi$
$953$	48.7345	1.57867	0.789333	+	0.613965i	$0.210426\pi$
$954$	57.3636	1.85721
$955$	−16.9733	−0.549243
$956$	33.0869	1.07011
$957$	−0.592935	−0.0191669
$958$	66.2169	2.13937
$959$	38.2119	1.23393
$960$	16.2661	0.524985
$961$	−29.4447	−0.949830
$962$	−21.5043	−0.693327
$963$	81.1705	2.61568
$964$	−2.44579	−0.0787736
$965$	−2.94172	−0.0946974
$966$	−56.2815	−1.81083
$967$	−12.4028	−0.398848	−0.199424	−	0.979913i	$-0.563907\pi$
$967$	−12.4028	−0.398848	−0.199424	+	0.979913i	$0.563907\pi$
$968$	57.8586	1.85965
$969$	47.2882	1.51912
$970$	39.7099	1.27501
$971$	20.8330	0.668562	0.334281	−	0.942474i	$-0.391507\pi$
$971$	20.8330	0.668562	0.334281	+	0.942474i	$0.391507\pi$
$972$	−67.2938	−2.15845
$973$	−4.51548	−0.144760
$974$	−29.4161	−0.942552
$975$	15.3379	0.491206
$976$	−53.8101	−1.72242
$977$	−51.9973	−1.66354	−0.831771	−	0.555119i	$-0.812673\pi$
$977$	−51.9973	−1.66354	−0.831771	+	0.555119i	$0.812673\pi$
$978$	55.1581	1.76376
$979$	1.16042	0.0370873
$980$	13.0706	0.417525
$981$	−59.9461	−1.91393
$982$	−40.7141	−1.29924
$983$	43.4633	1.38626	0.693131	−	0.720811i	$-0.256231\pi$
$983$	43.4633	1.38626	0.693131	+	0.720811i	$0.256231\pi$
$984$	130.732	4.16759
$985$	0.971795	0.0309639
$986$	−18.2680	−0.581773
$987$	−3.43791	−0.109430
$988$	−26.8710	−0.854879
$989$	52.9673	1.68426
$990$	−1.07929	−0.0343021
$991$	10.6781	0.339202	0.169601	−	0.985513i	$-0.445752\pi$
$991$	10.6781	0.339202	0.169601	+	0.985513i	$0.445752\pi$
$992$	1.61648	0.0513232
$993$	20.4270	0.648232
$994$	43.7014	1.38613
$995$	14.4269	0.457365
$996$	15.4160	0.488475
$997$	33.8106	1.07079	0.535397	−	0.844601i	$-0.320162\pi$
$997$	33.8106	1.07079	0.535397	+	0.844601i	$0.320162\pi$
$998$	57.3910	1.81668
$999$	−32.4910	−1.02797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.9	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.9	✓	149	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)

\(f(q)\)	\(=\)	\(q-2.47526 q^{2} +2.78845 q^{3} +4.12689 q^{4} -0.919151 q^{5} -6.90213 q^{6} -1.88527 q^{7} -5.26460 q^{8} +4.77546 q^{9} +O(q^{10})\)	\(q-2.47526 q^{2} +2.78845 q^{3} +4.12689 q^{4} -0.919151 q^{5} -6.90213 q^{6} -1.88527 q^{7} -5.26460 q^{8} +4.77546 q^{9} +2.27513 q^{10} -0.0993384 q^{11} +11.5076 q^{12} -1.32378 q^{13} +4.66652 q^{14} -2.56301 q^{15} +4.77744 q^{16} +3.44782 q^{17} -11.8205 q^{18} +4.91865 q^{19} -3.79323 q^{20} -5.25698 q^{21} +0.245888 q^{22} -4.32524 q^{23} -14.6801 q^{24} -4.15516 q^{25} +3.27669 q^{26} +4.95077 q^{27} -7.78030 q^{28} +2.14056 q^{29} +6.34410 q^{30} -1.24710 q^{31} -1.29619 q^{32} -0.277000 q^{33} -8.53423 q^{34} +1.73285 q^{35} +19.7078 q^{36} -6.56282 q^{37} -12.1749 q^{38} -3.69129 q^{39} +4.83896 q^{40} -8.90542 q^{41} +13.0124 q^{42} -12.2461 q^{43} -0.409959 q^{44} -4.38936 q^{45} +10.7061 q^{46} +0.653971 q^{47} +13.3217 q^{48} -3.44576 q^{49} +10.2851 q^{50} +9.61407 q^{51} -5.46308 q^{52} -4.85290 q^{53} -12.2544 q^{54} +0.0913070 q^{55} +9.92518 q^{56} +13.7154 q^{57} -5.29843 q^{58} +2.85733 q^{59} -10.5772 q^{60} -11.2634 q^{61} +3.08689 q^{62} -9.00302 q^{63} -6.34647 q^{64} +1.21675 q^{65} +0.685646 q^{66} +12.7127 q^{67} +14.2288 q^{68} -12.0607 q^{69} -4.28924 q^{70} +9.36488 q^{71} -25.1408 q^{72} +10.1227 q^{73} +16.2447 q^{74} -11.5865 q^{75} +20.2987 q^{76} +0.187280 q^{77} +9.13688 q^{78} +1.25081 q^{79} -4.39119 q^{80} -0.521391 q^{81} +22.0432 q^{82} +1.33964 q^{83} -21.6950 q^{84} -3.16907 q^{85} +30.3122 q^{86} +5.96884 q^{87} +0.522976 q^{88} -11.6815 q^{89} +10.8648 q^{90} +2.49568 q^{91} -17.8498 q^{92} -3.47748 q^{93} -1.61874 q^{94} -4.52098 q^{95} -3.61436 q^{96} +17.4539 q^{97} +8.52914 q^{98} -0.474386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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