LMFDB - Embedded newform 3997.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3997,2,Mod(1,3997)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3997, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3997.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3997.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:	$31.9162056879$
Analytic rank:	$1$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	3997.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53379 q^{2} +2.83648 q^{3} +4.42008 q^{4} -4.00855 q^{5} -7.18704 q^{6} +1.00000 q^{7} -6.13198 q^{8} +5.04562 q^{9} +O(q^{10})$	\(q-2.53379 q^{2} +2.83648 q^{3} +4.42008 q^{4} -4.00855 q^{5} -7.18704 q^{6} +1.00000 q^{7} -6.13198 q^{8} +5.04562 q^{9} +10.1568 q^{10} -2.39111 q^{11} +12.5375 q^{12} +1.78408 q^{13} -2.53379 q^{14} -11.3702 q^{15} +6.69696 q^{16} +2.53181 q^{17} -12.7845 q^{18} -4.95335 q^{19} -17.7181 q^{20} +2.83648 q^{21} +6.05855 q^{22} +4.11409 q^{23} -17.3932 q^{24} +11.0685 q^{25} -4.52047 q^{26} +5.80238 q^{27} +4.42008 q^{28} -7.01569 q^{29} +28.8096 q^{30} +1.58957 q^{31} -4.70474 q^{32} -6.78233 q^{33} -6.41506 q^{34} -4.00855 q^{35} +22.3021 q^{36} +3.65955 q^{37} +12.5507 q^{38} +5.06049 q^{39} +24.5803 q^{40} -9.36479 q^{41} -7.18704 q^{42} -0.218043 q^{43} -10.5689 q^{44} -20.2256 q^{45} -10.4242 q^{46} -11.0420 q^{47} +18.9958 q^{48} +1.00000 q^{49} -28.0451 q^{50} +7.18142 q^{51} +7.88576 q^{52} +9.36668 q^{53} -14.7020 q^{54} +9.58486 q^{55} -6.13198 q^{56} -14.0501 q^{57} +17.7763 q^{58} +1.22573 q^{59} -50.2571 q^{60} -2.44590 q^{61} -4.02764 q^{62} +5.04562 q^{63} -1.47312 q^{64} -7.15155 q^{65} +17.1850 q^{66} -3.66917 q^{67} +11.1908 q^{68} +11.6695 q^{69} +10.1568 q^{70} -7.74662 q^{71} -30.9397 q^{72} -6.27982 q^{73} -9.27252 q^{74} +31.3955 q^{75} -21.8942 q^{76} -2.39111 q^{77} -12.8222 q^{78} +1.56383 q^{79} -26.8451 q^{80} +1.32145 q^{81} +23.7284 q^{82} -3.55882 q^{83} +12.5375 q^{84} -10.1489 q^{85} +0.552475 q^{86} -19.8999 q^{87} +14.6622 q^{88} +18.2561 q^{89} +51.2475 q^{90} +1.78408 q^{91} +18.1846 q^{92} +4.50879 q^{93} +27.9781 q^{94} +19.8558 q^{95} -13.3449 q^{96} +17.6095 q^{97} -2.53379 q^{98} -12.0646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q - 21 q^{2} - 14 q^{3} + 57 q^{4} - 16 q^{5} - 3 q^{6} + 63 q^{7} - 54 q^{8} + 39 q^{9}+O(q^{10}) $ 63 * q - 21 * q^2 - 14 * q^3 + 57 * q^4 - 16 * q^5 - 3 * q^6 + 63 * q^7 - 54 * q^8 + 39 * q^9	\( 63 q - 21 q^{2} - 14 q^{3} + 57 q^{4} - 16 q^{5} - 3 q^{6} + 63 q^{7} - 54 q^{8} + 39 q^{9} - 8 q^{10} - 54 q^{11} - 27 q^{12} - 10 q^{13} - 21 q^{14} - 33 q^{15} + 53 q^{16} - 25 q^{17} - 37 q^{18} - 23 q^{19} - 36 q^{20} - 14 q^{21} - 8 q^{22} - 62 q^{23} - 6 q^{24} + 37 q^{25} - 4 q^{26} - 56 q^{27} + 57 q^{28} - 96 q^{29} - 9 q^{30} - 9 q^{31} - 119 q^{32} - 23 q^{33} - 16 q^{35} + 16 q^{36} - 21 q^{37} - 21 q^{38} - 36 q^{39} + 3 q^{40} - 34 q^{41} - 3 q^{42} - 36 q^{43} - 79 q^{44} - 28 q^{45} - 15 q^{46} - 71 q^{47} - 16 q^{48} + 63 q^{49} - 69 q^{50} - 59 q^{51} + 4 q^{52} - 118 q^{53} - 4 q^{54} - 6 q^{55} - 54 q^{56} - 55 q^{57} + 16 q^{58} - 67 q^{59} - 32 q^{60} + q^{61} - 16 q^{62} + 39 q^{63} + 58 q^{64} - 100 q^{65} + 80 q^{66} - 82 q^{67} - 60 q^{68} + 7 q^{69} - 8 q^{70} - 115 q^{71} - 74 q^{72} - 9 q^{73} - 29 q^{74} - 38 q^{75} - 34 q^{76} - 54 q^{77} - 44 q^{78} - 21 q^{79} - 25 q^{80} + 3 q^{81} - q^{82} - 139 q^{83} - 27 q^{84} - 21 q^{85} - 58 q^{86} - q^{87} + 15 q^{88} - 29 q^{89} + 59 q^{90} - 10 q^{91} - 79 q^{92} - 45 q^{93} + 21 q^{94} - 83 q^{95} + 65 q^{96} + 22 q^{97} - 21 q^{98} - 73 q^{99}+O(q^{100}) \) 63 * q - 21 * q^2 - 14 * q^3 + 57 * q^4 - 16 * q^5 - 3 * q^6 + 63 * q^7 - 54 * q^8 + 39 * q^9 - 8 * q^10 - 54 * q^11 - 27 * q^12 - 10 * q^13 - 21 * q^14 - 33 * q^15 + 53 * q^16 - 25 * q^17 - 37 * q^18 - 23 * q^19 - 36 * q^20 - 14 * q^21 - 8 * q^22 - 62 * q^23 - 6 * q^24 + 37 * q^25 - 4 * q^26 - 56 * q^27 + 57 * q^28 - 96 * q^29 - 9 * q^30 - 9 * q^31 - 119 * q^32 - 23 * q^33 - 16 * q^35 + 16 * q^36 - 21 * q^37 - 21 * q^38 - 36 * q^39 + 3 * q^40 - 34 * q^41 - 3 * q^42 - 36 * q^43 - 79 * q^44 - 28 * q^45 - 15 * q^46 - 71 * q^47 - 16 * q^48 + 63 * q^49 - 69 * q^50 - 59 * q^51 + 4 * q^52 - 118 * q^53 - 4 * q^54 - 6 * q^55 - 54 * q^56 - 55 * q^57 + 16 * q^58 - 67 * q^59 - 32 * q^60 + q^61 - 16 * q^62 + 39 * q^63 + 58 * q^64 - 100 * q^65 + 80 * q^66 - 82 * q^67 - 60 * q^68 + 7 * q^69 - 8 * q^70 - 115 * q^71 - 74 * q^72 - 9 * q^73 - 29 * q^74 - 38 * q^75 - 34 * q^76 - 54 * q^77 - 44 * q^78 - 21 * q^79 - 25 * q^80 + 3 * q^81 - q^82 - 139 * q^83 - 27 * q^84 - 21 * q^85 - 58 * q^86 - q^87 + 15 * q^88 - 29 * q^89 + 59 * q^90 - 10 * q^91 - 79 * q^92 - 45 * q^93 + 21 * q^94 - 83 * q^95 + 65 * q^96 + 22 * q^97 - 21 * q^98 - 73 * 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 $

$2$	−2.53379	−1.79166	−0.895829	−	0.444398i	$-0.853418\pi$
$2$	−2.53379	−1.79166	−0.895829	+	0.444398i	$0.853418\pi$
$3$	2.83648	1.63764	0.818822	−	0.574048i	$-0.194628\pi$
$3$	2.83648	1.63764	0.818822	+	0.574048i	$0.194628\pi$
$4$	4.42008	2.21004
$5$	−4.00855	−1.79268	−0.896338	−	0.443370i	$-0.853783\pi$
$5$	−4.00855	−1.79268	−0.896338	+	0.443370i	$0.853783\pi$
$6$	−7.18704	−2.93410
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.13198	−2.16798
$9$	5.04562	1.68187
$10$	10.1568	3.21187
$11$	−2.39111	−0.720945	−0.360473	−	0.932770i	$-0.617385\pi$
$11$	−2.39111	−0.720945	−0.360473	+	0.932770i	$0.617385\pi$
$12$	12.5375	3.61926
$13$	1.78408	0.494813	0.247407	−	0.968912i	$-0.420422\pi$
$13$	1.78408	0.494813	0.247407	+	0.968912i	$0.420422\pi$
$14$	−2.53379	−0.677183
$15$	−11.3702	−2.93577
$16$	6.69696	1.67424
$17$	2.53181	0.614053	0.307027	−	0.951701i	$-0.400666\pi$
$17$	2.53181	0.614053	0.307027	+	0.951701i	$0.400666\pi$
$18$	−12.7845	−3.01335
$19$	−4.95335	−1.13638	−0.568189	−	0.822898i	$-0.692356\pi$
$19$	−4.95335	−1.13638	−0.568189	+	0.822898i	$0.692356\pi$
$20$	−17.7181	−3.96189
$21$	2.83648	0.618971
$22$	6.05855	1.29169
$23$	4.11409	0.857847	0.428924	−	0.903341i	$-0.358893\pi$
$23$	4.11409	0.857847	0.428924	+	0.903341i	$0.358893\pi$
$24$	−17.3932	−3.55038
$25$	11.0685	2.21369
$26$	−4.52047	−0.886537
$27$	5.80238	1.11667
$28$	4.42008	0.835317
$29$	−7.01569	−1.30278	−0.651391	−	0.758743i	$-0.725814\pi$
$29$	−7.01569	−1.30278	−0.651391	+	0.758743i	$0.725814\pi$
$30$	28.8096	5.25989
$31$	1.58957	0.285495	0.142748	−	0.989759i	$-0.454406\pi$
$31$	1.58957	0.285495	0.142748	+	0.989759i	$0.454406\pi$
$32$	−4.70474	−0.831688
$33$	−6.78233	−1.18065
$34$	−6.41506	−1.10017
$35$	−4.00855	−0.677568
$36$	22.3021	3.71701
$37$	3.65955	0.601626	0.300813	−	0.953683i	$-0.402742\pi$
$37$	3.65955	0.601626	0.300813	+	0.953683i	$0.402742\pi$
$38$	12.5507	2.03600
$39$	5.06049	0.810328
$40$	24.5803	3.88649
$41$	−9.36479	−1.46253	−0.731267	−	0.682091i	$-0.761071\pi$
$41$	−9.36479	−1.46253	−0.731267	+	0.682091i	$0.761071\pi$
$42$	−7.18704	−1.10898
$43$	−0.218043	−0.0332513	−0.0166256	−	0.999862i	$-0.505292\pi$
$43$	−0.218043	−0.0332513	−0.0166256	+	0.999862i	$0.505292\pi$
$44$	−10.5689	−1.59332
$45$	−20.2256	−3.01506
$46$	−10.4242	−1.53697
$47$	−11.0420	−1.61064	−0.805321	−	0.592839i	$-0.798007\pi$
$47$	−11.0420	−1.61064	−0.805321	+	0.592839i	$0.798007\pi$
$48$	18.9958	2.74181
$49$	1.00000	0.142857
$50$	−28.0451	−3.96618
$51$	7.18142	1.00560
$52$	7.88576	1.09356
$53$	9.36668	1.28661	0.643306	−	0.765609i	$-0.277562\pi$
$53$	9.36668	1.28661	0.643306	+	0.765609i	$0.277562\pi$
$54$	−14.7020	−2.00069
$55$	9.58486	1.29242
$56$	−6.13198	−0.819420
$57$	−14.0501	−1.86098
$58$	17.7763	2.33414
$59$	1.22573	0.159577	0.0797885	−	0.996812i	$-0.474576\pi$
$59$	1.22573	0.159577	0.0797885	+	0.996812i	$0.474576\pi$
$60$	−50.2571	−6.48816
$61$	−2.44590	−0.313165	−0.156582	−	0.987665i	$-0.550048\pi$
$61$	−2.44590	−0.313165	−0.156582	+	0.987665i	$0.550048\pi$
$62$	−4.02764	−0.511510
$63$	5.04562	0.635689
$64$	−1.47312	−0.184140
$65$	−7.15155	−0.887041
$66$	17.1850	2.11532
$67$	−3.66917	−0.448261	−0.224130	−	0.974559i	$-0.571954\pi$
$67$	−3.66917	−0.448261	−0.224130	+	0.974559i	$0.571954\pi$
$68$	11.1908	1.35708
$69$	11.6695	1.40485
$70$	10.1568	1.21397
$71$	−7.74662	−0.919355	−0.459677	−	0.888086i	$-0.652035\pi$
$71$	−7.74662	−0.919355	−0.459677	+	0.888086i	$0.652035\pi$
$72$	−30.9397	−3.64627
$73$	−6.27982	−0.734998	−0.367499	−	0.930024i	$-0.619786\pi$
$73$	−6.27982	−0.734998	−0.367499	+	0.930024i	$0.619786\pi$
$74$	−9.27252	−1.07791
$75$	31.3955	3.62524
$76$	−21.8942	−2.51144
$77$	−2.39111	−0.272492
$78$	−12.8222	−1.45183
$79$	1.56383	0.175945	0.0879725	−	0.996123i	$-0.471961\pi$
$79$	1.56383	0.175945	0.0879725	+	0.996123i	$0.471961\pi$
$80$	−26.8451	−3.00137
$81$	1.32145	0.146828
$82$	23.7284	2.62036
$83$	−3.55882	−0.390632	−0.195316	−	0.980740i	$-0.562573\pi$
$83$	−3.55882	−0.390632	−0.195316	+	0.980740i	$0.562573\pi$
$84$	12.5375	1.36795
$85$	−10.1489	−1.10080
$86$	0.552475	0.0595749
$87$	−19.8999	−2.13349
$88$	14.6622	1.56300
$89$	18.2561	1.93514	0.967569	−	0.252606i	$-0.0812878\pi$
$89$	18.2561	1.93514	0.967569	+	0.252606i	$0.0812878\pi$
$90$	51.2475	5.40196
$91$	1.78408	0.187022
$92$	18.1846	1.89588
$93$	4.50879	0.467539
$94$	27.9781	2.88572
$95$	19.8558	2.03716
$96$	−13.3449	−1.36201
$97$	17.6095	1.78798	0.893988	−	0.448091i	$-0.147896\pi$
$97$	17.6095	1.78798	0.893988	+	0.448091i	$0.147896\pi$
$98$	−2.53379	−0.255951
$99$	−12.0646	−1.21254
$100$	48.9235	4.89235
$101$	15.1416	1.50665	0.753323	−	0.657651i	$-0.228450\pi$
$101$	15.1416	1.50665	0.753323	+	0.657651i	$0.228450\pi$
$102$	−18.1962	−1.80169
$103$	9.84685	0.970239	0.485119	−	0.874448i	$-0.338776\pi$
$103$	9.84685	0.970239	0.485119	+	0.874448i	$0.338776\pi$
$104$	−10.9399	−1.07275
$105$	−11.3702	−1.10961
$106$	−23.7332	−2.30517
$107$	−2.55144	−0.246657	−0.123329	−	0.992366i	$-0.539357\pi$
$107$	−2.55144	−0.246657	−0.123329	+	0.992366i	$0.539357\pi$
$108$	25.6470	2.46788
$109$	−11.4541	−1.09711	−0.548553	−	0.836116i	$-0.684821\pi$
$109$	−11.4541	−1.09711	−0.548553	+	0.836116i	$0.684821\pi$
$110$	−24.2860	−2.31558
$111$	10.3802	0.985248
$112$	6.69696	0.632804
$113$	−14.1350	−1.32971	−0.664854	−	0.746974i	$-0.731506\pi$
$113$	−14.1350	−1.32971	−0.664854	+	0.746974i	$0.731506\pi$
$114$	35.6000	3.33424
$115$	−16.4915	−1.53784
$116$	−31.0099	−2.87920
$117$	9.00177	0.832214
$118$	−3.10575	−0.285908
$119$	2.53181	0.232090
$120$	69.7216	6.36468
$121$	−5.28261	−0.480238
$122$	6.19738	0.561085
$123$	−26.5631	−2.39511
$124$	7.02603	0.630957
$125$	−24.3257	−2.17576
$126$	−12.7845	−1.13894
$127$	9.14581	0.811560	0.405780	−	0.913971i	$-0.367000\pi$
$127$	9.14581	0.811560	0.405780	+	0.913971i	$0.367000\pi$
$128$	13.1421	1.16160
$129$	−0.618475	−0.0544537
$130$	18.1205	1.58927
$131$	−22.4279	−1.95953	−0.979766	−	0.200147i	$-0.935858\pi$
$131$	−22.4279	−1.95953	−0.979766	+	0.200147i	$0.935858\pi$
$132$	−29.9784	−2.60929
$133$	−4.95335	−0.429510
$134$	9.29690	0.803130
$135$	−23.2591	−2.00182
$136$	−15.5250	−1.33126
$137$	−4.55609	−0.389253	−0.194627	−	0.980877i	$-0.562350\pi$
$137$	−4.55609	−0.389253	−0.194627	+	0.980877i	$0.562350\pi$
$138$	−29.5681	−2.51701
$139$	−21.6910	−1.83981	−0.919903	−	0.392146i	$-0.871733\pi$
$139$	−21.6910	−1.83981	−0.919903	+	0.392146i	$0.871733\pi$
$140$	−17.7181	−1.49745
$141$	−31.3204	−2.63766
$142$	19.6283	1.64717
$143$	−4.26591	−0.356733
$144$	33.7904	2.81586
$145$	28.1227	2.33547
$146$	15.9117	1.31687
$147$	2.83648	0.233949
$148$	16.1755	1.32962
$149$	−10.9709	−0.898768	−0.449384	−	0.893339i	$-0.648356\pi$
$149$	−10.9709	−0.898768	−0.449384	+	0.893339i	$0.648356\pi$
$150$	−79.5494	−6.49518
$151$	−20.8448	−1.69633	−0.848165	−	0.529732i	$-0.822292\pi$
$151$	−20.8448	−1.69633	−0.848165	+	0.529732i	$0.822292\pi$
$152$	30.3738	2.46364
$153$	12.7745	1.03276
$154$	6.05855	0.488212
$155$	−6.37187	−0.511801
$156$	22.3678	1.79086
$157$	−3.89385	−0.310763	−0.155381	−	0.987855i	$-0.549661\pi$
$157$	−3.89385	−0.310763	−0.155381	+	0.987855i	$0.549661\pi$
$158$	−3.96242	−0.315234
$159$	26.5684	2.10701
$160$	18.8592	1.49095
$161$	4.11409	0.324236
$162$	−3.34829	−0.263066
$163$	−14.6486	−1.14737	−0.573684	−	0.819077i	$-0.694486\pi$
$163$	−14.6486	−1.14737	−0.573684	+	0.819077i	$0.694486\pi$
$164$	−41.3932	−3.23226
$165$	27.1873	2.11653
$166$	9.01730	0.699879
$167$	14.3793	1.11270	0.556352	−	0.830947i	$-0.312201\pi$
$167$	14.3793	1.11270	0.556352	+	0.830947i	$0.312201\pi$
$168$	−17.3932	−1.34192
$169$	−9.81708	−0.755160
$170$	25.7151	1.97226
$171$	−24.9928	−1.91124
$172$	−0.963768	−0.0734866
$173$	−0.129982	−0.00988232	−0.00494116	−	0.999988i	$-0.501573\pi$
$173$	−0.129982	−0.00988232	−0.00494116	+	0.999988i	$0.501573\pi$
$174$	50.4221	3.82249
$175$	11.0685	0.836696
$176$	−16.0131	−1.20704
$177$	3.47677	0.261330
$178$	−46.2570	−3.46711
$179$	−5.85921	−0.437938	−0.218969	−	0.975732i	$-0.570269\pi$
$179$	−5.85921	−0.437938	−0.218969	+	0.975732i	$0.570269\pi$
$180$	−89.3989	−6.66340
$181$	4.28531	0.318525	0.159262	−	0.987236i	$-0.449088\pi$
$181$	4.28531	0.318525	0.159262	+	0.987236i	$0.449088\pi$
$182$	−4.52047	−0.335079
$183$	−6.93774	−0.512852
$184$	−25.2275	−1.85980
$185$	−14.6695	−1.07852
$186$	−11.4243	−0.837671
$187$	−6.05382	−0.442699
$188$	−48.8066	−3.55959
$189$	5.80238	0.422061
$190$	−50.3103	−3.64989
$191$	−22.9940	−1.66379	−0.831895	−	0.554933i	$-0.812744\pi$
$191$	−22.9940	−1.66379	−0.831895	+	0.554933i	$0.812744\pi$
$192$	−4.17848	−0.301556
$193$	12.7721	0.919358	0.459679	−	0.888085i	$-0.347964\pi$
$193$	12.7721	0.919358	0.459679	+	0.888085i	$0.347964\pi$
$194$	−44.6188	−3.20344
$195$	−20.2852	−1.45266
$196$	4.42008	0.315720
$197$	16.8013	1.19705	0.598523	−	0.801106i	$-0.295755\pi$
$197$	16.8013	1.19705	0.598523	+	0.801106i	$0.295755\pi$
$198$	30.5692	2.17246
$199$	−18.6665	−1.32323	−0.661616	−	0.749843i	$-0.730129\pi$
$199$	−18.6665	−1.32323	−0.661616	+	0.749843i	$0.730129\pi$
$200$	−67.8715	−4.79924
$201$	−10.4075	−0.734091
$202$	−38.3656	−2.69940
$203$	−7.01569	−0.492405
$204$	31.7425	2.22242
$205$	37.5392	2.62185
$206$	−24.9498	−1.73834
$207$	20.7582	1.44279
$208$	11.9479	0.828437
$209$	11.8440	0.819266
$210$	28.8096	1.98805
$211$	6.49739	0.447299	0.223649	−	0.974670i	$-0.428203\pi$
$211$	6.49739	0.447299	0.223649	+	0.974670i	$0.428203\pi$
$212$	41.4015	2.84347
$213$	−21.9731	−1.50557
$214$	6.46482	0.441926
$215$	0.874036	0.0596088
$216$	−35.5800	−2.42091
$217$	1.58957	0.107907
$218$	29.0223	1.96564
$219$	−17.8126	−1.20366
$220$	42.3659	2.85631
$221$	4.51693	0.303842
$222$	−26.3013	−1.76523
$223$	−5.78444	−0.387355	−0.193677	−	0.981065i	$-0.562041\pi$
$223$	−5.78444	−0.387355	−0.193677	+	0.981065i	$0.562041\pi$
$224$	−4.70474	−0.314348
$225$	55.8473	3.72315
$226$	35.8150	2.38238
$227$	4.83065	0.320622	0.160311	−	0.987067i	$-0.448750\pi$
$227$	4.83065	0.320622	0.160311	+	0.987067i	$0.448750\pi$
$228$	−62.1026	−4.11284
$229$	−14.4328	−0.953743	−0.476872	−	0.878973i	$-0.658229\pi$
$229$	−14.4328	−0.953743	−0.476872	+	0.878973i	$0.658229\pi$
$230$	41.7860	2.75529
$231$	−6.78233	−0.446244
$232$	43.0201	2.82441
$233$	−4.62061	−0.302706	−0.151353	−	0.988480i	$-0.548363\pi$
$233$	−4.62061	−0.302706	−0.151353	+	0.988480i	$0.548363\pi$
$234$	−22.8086	−1.49104
$235$	44.2624	2.88736
$236$	5.41785	0.352672
$237$	4.43579	0.288135
$238$	−6.41506	−0.415827
$239$	−23.5232	−1.52159	−0.760796	−	0.648991i	$-0.775191\pi$
$239$	−23.5232	−1.52159	−0.760796	+	0.648991i	$0.775191\pi$
$240$	−76.1456	−4.91518
$241$	22.7729	1.46693	0.733466	−	0.679726i	$-0.237901\pi$
$241$	22.7729	1.46693	0.733466	+	0.679726i	$0.237901\pi$
$242$	13.3850	0.860422
$243$	−13.6588	−0.876215
$244$	−10.8111	−0.692107
$245$	−4.00855	−0.256097
$246$	67.3052	4.29122
$247$	−8.83715	−0.562295
$248$	−9.74721	−0.618949
$249$	−10.0945	−0.639715
$250$	61.6361	3.89821
$251$	−12.1842	−0.769059	−0.384529	−	0.923113i	$-0.625636\pi$
$251$	−12.1842	−0.769059	−0.384529	+	0.923113i	$0.625636\pi$
$252$	22.3021	1.40490
$253$	−9.83723	−0.618461
$254$	−23.1736	−1.45404
$255$	−28.7871	−1.80272
$256$	−30.3529	−1.89706
$257$	7.03743	0.438983	0.219491	−	0.975614i	$-0.429560\pi$
$257$	7.03743	0.438983	0.219491	+	0.975614i	$0.429560\pi$
$258$	1.56708	0.0975624
$259$	3.65955	0.227393
$260$	−31.6104	−1.96040
$261$	−35.3985	−2.19112
$262$	56.8275	3.51081
$263$	−8.58804	−0.529561	−0.264781	−	0.964309i	$-0.585300\pi$
$263$	−8.58804	−0.529561	−0.264781	+	0.964309i	$0.585300\pi$
$264$	41.5891	2.55963
$265$	−37.5468	−2.30648
$266$	12.5507	0.769536
$267$	51.7830	3.16907
$268$	−16.2180	−0.990674
$269$	16.9607	1.03411	0.517056	−	0.855952i	$-0.327028\pi$
$269$	16.9607	1.03411	0.517056	+	0.855952i	$0.327028\pi$
$270$	58.9336	3.58659
$271$	1.29923	0.0789228	0.0394614	−	0.999221i	$-0.487436\pi$
$271$	1.29923	0.0789228	0.0394614	+	0.999221i	$0.487436\pi$
$272$	16.9554	1.02807
$273$	5.06049	0.306275
$274$	11.5442	0.697409
$275$	−26.4658	−1.59595
$276$	51.5803	3.10477
$277$	−8.44034	−0.507131	−0.253566	−	0.967318i	$-0.581603\pi$
$277$	−8.44034	−0.507131	−0.253566	+	0.967318i	$0.581603\pi$
$278$	54.9604	3.29630
$279$	8.02038	0.480167
$280$	24.5803	1.46896
$281$	11.5178	0.687093	0.343547	−	0.939136i	$-0.388372\pi$
$281$	11.5178	0.687093	0.343547	+	0.939136i	$0.388372\pi$
$282$	79.3594	4.72578
$283$	−22.8520	−1.35841	−0.679206	−	0.733947i	$-0.737676\pi$
$283$	−22.8520	−1.35841	−0.679206	+	0.733947i	$0.737676\pi$
$284$	−34.2407	−2.03181
$285$	56.3205	3.33614
$286$	10.8089	0.639145
$287$	−9.36479	−0.552786
$288$	−23.7383	−1.39879
$289$	−10.5900	−0.622939
$290$	−71.2570	−4.18436
$291$	49.9491	2.92807
$292$	−27.7573	−1.62438
$293$	9.34997	0.546231	0.273115	−	0.961981i	$-0.411946\pi$
$293$	9.34997	0.546231	0.273115	+	0.961981i	$0.411946\pi$
$294$	−7.18704	−0.419157
$295$	−4.91341	−0.286070
$296$	−22.4403	−1.30431
$297$	−13.8741	−0.805057
$298$	27.7978	1.61029
$299$	7.33985	0.424474
$300$	138.771	8.01192
$301$	−0.218043	−0.0125678
$302$	52.8164	3.03924
$303$	42.9489	2.46735
$304$	−33.1724	−1.90257
$305$	9.80449	0.561403
$306$	−32.3680	−1.85035
$307$	−6.63711	−0.378800	−0.189400	−	0.981900i	$-0.560654\pi$
$307$	−6.63711	−0.378800	−0.189400	+	0.981900i	$0.560654\pi$
$308$	−10.5689	−0.602218
$309$	27.9304	1.58891
$310$	16.1450	0.916973
$311$	13.8567	0.785739	0.392870	−	0.919594i	$-0.371482\pi$
$311$	13.8567	0.785739	0.392870	+	0.919594i	$0.371482\pi$
$312$	−31.0308	−1.75678
$313$	−7.06964	−0.399600	−0.199800	−	0.979837i	$-0.564029\pi$
$313$	−7.06964	−0.399600	−0.199800	+	0.979837i	$0.564029\pi$
$314$	9.86618	0.556781
$315$	−20.2256	−1.13958
$316$	6.91228	0.388846
$317$	−5.75357	−0.323153	−0.161576	−	0.986860i	$-0.551658\pi$
$317$	−5.75357	−0.323153	−0.161576	+	0.986860i	$0.551658\pi$
$318$	−67.3187	−3.77505
$319$	16.7753	0.939234
$320$	5.90508	0.330104
$321$	−7.23712	−0.403937
$322$	−10.4242	−0.580920
$323$	−12.5409	−0.697796
$324$	5.84094	0.324497
$325$	19.7470	1.09536
$326$	37.1165	2.05569
$327$	−32.4894	−1.79667
$328$	57.4247	3.17075
$329$	−11.0420	−0.608766
$330$	−68.8868	−3.79209
$331$	26.9392	1.48071	0.740356	−	0.672215i	$-0.234657\pi$
$331$	26.9392	1.48071	0.740356	+	0.672215i	$0.234657\pi$
$332$	−15.7303	−0.863312
$333$	18.4647	1.01186
$334$	−36.4341	−1.99359
$335$	14.7080	0.803586
$336$	18.9958	1.03631
$337$	−16.9315	−0.922316	−0.461158	−	0.887318i	$-0.652566\pi$
$337$	−16.9315	−0.922316	−0.461158	+	0.887318i	$0.652566\pi$
$338$	24.8744	1.35299
$339$	−40.0936	−2.17759
$340$	−44.8588	−2.43281
$341$	−3.80083	−0.205827
$342$	63.3264	3.42430
$343$	1.00000	0.0539949
$344$	1.33703	0.0720881
$345$	−46.7779	−2.51844
$346$	0.329346	0.0177057
$347$	−19.6513	−1.05494	−0.527469	−	0.849574i	$-0.676859\pi$
$347$	−19.6513	−1.05494	−0.527469	+	0.849574i	$0.676859\pi$
$348$	−87.9591	−4.71510
$349$	14.3074	0.765860	0.382930	−	0.923777i	$-0.374915\pi$
$349$	14.3074	0.765860	0.382930	+	0.923777i	$0.374915\pi$
$350$	−28.0451	−1.49907
$351$	10.3519	0.552542
$352$	11.2495	0.599602
$353$	−5.88610	−0.313286	−0.156643	−	0.987655i	$-0.550067\pi$
$353$	−5.88610	−0.313286	−0.156643	+	0.987655i	$0.550067\pi$
$354$	−8.80940	−0.468215
$355$	31.0527	1.64811
$356$	80.6933	4.27674
$357$	7.18142	0.380081
$358$	14.8460	0.784635
$359$	−31.2155	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$359$	−31.2155	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$360$	124.023	6.53659
$361$	5.53571	0.291353
$362$	−10.8581	−0.570687
$363$	−14.9840	−0.786458
$364$	7.88576	0.413326
$365$	25.1730	1.31761
$366$	17.5788	0.918856
$367$	−15.2091	−0.793907	−0.396953	−	0.917839i	$-0.629933\pi$
$367$	−15.2091	−0.793907	−0.396953	+	0.917839i	$0.629933\pi$
$368$	27.5519	1.43624
$369$	−47.2512	−2.45980
$370$	37.1693	1.93234
$371$	9.36668	0.486294
$372$	19.9292	1.03328
$373$	−1.75415	−0.0908264	−0.0454132	−	0.998968i	$-0.514460\pi$
$373$	−1.75415	−0.0908264	−0.0454132	+	0.998968i	$0.514460\pi$
$374$	15.3391	0.793165
$375$	−68.9993	−3.56311
$376$	67.7093	3.49184
$377$	−12.5165	−0.644634
$378$	−14.7020	−0.756189
$379$	2.24001	0.115062	0.0575308	−	0.998344i	$-0.481677\pi$
$379$	2.24001	0.115062	0.0575308	+	0.998344i	$0.481677\pi$
$380$	87.7641	4.50220
$381$	25.9419	1.32905
$382$	58.2620	2.98094
$383$	−12.2223	−0.624530	−0.312265	−	0.949995i	$-0.601088\pi$
$383$	−12.2223	−0.624530	−0.312265	+	0.949995i	$0.601088\pi$
$384$	37.2772	1.90229
$385$	9.58486	0.488490
$386$	−32.3619	−1.64718
$387$	−1.10016	−0.0559244
$388$	77.8355	3.95150
$389$	4.30782	0.218415	0.109208	−	0.994019i	$-0.465169\pi$
$389$	4.30782	0.218415	0.109208	+	0.994019i	$0.465169\pi$
$390$	51.3985	2.60266
$391$	10.4161	0.526764
$392$	−6.13198	−0.309712
$393$	−63.6162	−3.20901
$394$	−42.5710	−2.14470
$395$	−6.26870	−0.315413
$396$	−53.3266	−2.67976
$397$	13.6889	0.687024	0.343512	−	0.939148i	$-0.388383\pi$
$397$	13.6889	0.687024	0.343512	+	0.939148i	$0.388383\pi$
$398$	47.2969	2.37078
$399$	−14.0501	−0.703384
$400$	74.1250	3.70625
$401$	−8.96419	−0.447650	−0.223825	−	0.974629i	$-0.571854\pi$
$401$	−8.96419	−0.447650	−0.223825	+	0.974629i	$0.571854\pi$
$402$	26.3705	1.31524
$403$	2.83591	0.141267
$404$	66.9271	3.32975
$405$	−5.29711	−0.263216
$406$	17.7763	0.882222
$407$	−8.75036	−0.433739
$408$	−44.0363	−2.18012
$409$	−16.6605	−0.823807	−0.411903	−	0.911227i	$-0.635136\pi$
$409$	−16.6605	−0.823807	−0.411903	+	0.911227i	$0.635136\pi$
$410$	−95.1164	−4.69746
$411$	−12.9233	−0.637458
$412$	43.5239	2.14427
$413$	1.22573	0.0603144
$414$	−52.5968	−2.58499
$415$	14.2657	0.700276
$416$	−8.39360	−0.411530
$417$	−61.5261	−3.01295
$418$	−30.0102	−1.46785
$419$	1.28422	0.0627383	0.0313692	−	0.999508i	$-0.490013\pi$
$419$	1.28422	0.0627383	0.0313692	+	0.999508i	$0.490013\pi$
$420$	−50.2571	−2.45229
$421$	−3.44415	−0.167858	−0.0839288	−	0.996472i	$-0.526747\pi$
$421$	−3.44415	−0.167858	−0.0839288	+	0.996472i	$0.526747\pi$
$422$	−16.4630	−0.801406
$423$	−55.7138	−2.70890
$424$	−57.4363	−2.78935
$425$	28.0232	1.35932
$426$	55.6753	2.69748
$427$	−2.44590	−0.118365
$428$	−11.2776	−0.545123
$429$	−12.1002	−0.584202
$430$	−2.21462	−0.106799
$431$	8.30455	0.400016	0.200008	−	0.979794i	$-0.435903\pi$
$431$	8.30455	0.400016	0.200008	+	0.979794i	$0.435903\pi$
$432$	38.8583	1.86957
$433$	25.2261	1.21229	0.606144	−	0.795355i	$-0.292715\pi$
$433$	25.2261	1.21229	0.606144	+	0.795355i	$0.292715\pi$
$434$	−4.02764	−0.193333
$435$	79.7696	3.82466
$436$	−50.6282	−2.42465
$437$	−20.3785	−0.974838
$438$	45.1334	2.15656
$439$	20.7512	0.990401	0.495201	−	0.868779i	$-0.335095\pi$
$439$	20.7512	0.990401	0.495201	+	0.868779i	$0.335095\pi$
$440$	−58.7741	−2.80195
$441$	5.04562	0.240268
$442$	−11.4449	−0.544381
$443$	−22.9997	−1.09275	−0.546374	−	0.837542i	$-0.683992\pi$
$443$	−22.9997	−1.09275	−0.546374	+	0.837542i	$0.683992\pi$
$444$	45.8815	2.17744
$445$	−73.1803	−3.46908
$446$	14.6565	0.694007
$447$	−31.1186	−1.47186
$448$	−1.47312	−0.0695985
$449$	21.3651	1.00828	0.504140	−	0.863622i	$-0.331810\pi$
$449$	21.3651	1.00828	0.504140	+	0.863622i	$0.331810\pi$
$450$	−141.505	−6.67062
$451$	22.3922	1.05441
$452$	−62.4778	−2.93871
$453$	−59.1260	−2.77798
$454$	−12.2399	−0.574445
$455$	−7.15155	−0.335270
$456$	86.1548	4.03457
$457$	2.91221	0.136227	0.0681136	−	0.997678i	$-0.478302\pi$
$457$	2.91221	0.136227	0.0681136	+	0.997678i	$0.478302\pi$
$458$	36.5695	1.70878
$459$	14.6905	0.685693
$460$	−72.8939	−3.39870
$461$	−9.87025	−0.459703	−0.229852	−	0.973226i	$-0.573824\pi$
$461$	−9.87025	−0.459703	−0.229852	+	0.973226i	$0.573824\pi$
$462$	17.1850	0.799517
$463$	−13.7056	−0.636955	−0.318478	−	0.947930i	$-0.603172\pi$
$463$	−13.7056	−0.636955	−0.318478	+	0.947930i	$0.603172\pi$
$464$	−46.9838	−2.18117
$465$	−18.0737	−0.838147
$466$	11.7077	0.542347
$467$	−33.4227	−1.54662	−0.773308	−	0.634030i	$-0.781400\pi$
$467$	−33.4227	−1.54662	−0.773308	+	0.634030i	$0.781400\pi$
$468$	39.7886	1.83923
$469$	−3.66917	−0.169427
$470$	−112.152	−5.17317
$471$	−11.0448	−0.508919
$472$	−7.51617	−0.345960
$473$	0.521364	0.0239723
$474$	−11.2393	−0.516240
$475$	−54.8260	−2.51559
$476$	11.1908	0.512929
$477$	47.2608	2.16392
$478$	59.6029	2.72617
$479$	23.5530	1.07616	0.538082	−	0.842892i	$-0.319149\pi$
$479$	23.5530	1.07616	0.538082	+	0.842892i	$0.319149\pi$
$480$	53.4937	2.44164
$481$	6.52891	0.297693
$482$	−57.7017	−2.62824
$483$	11.6695	0.530982
$484$	−23.3496	−1.06135
$485$	−70.5886	−3.20526
$486$	34.6086	1.56988
$487$	16.6979	0.756653	0.378327	−	0.925672i	$-0.376500\pi$
$487$	16.6979	0.756653	0.378327	+	0.925672i	$0.376500\pi$
$488$	14.9982	0.678936
$489$	−41.5505	−1.87898
$490$	10.1568	0.458838
$491$	−8.79655	−0.396983	−0.198491	−	0.980103i	$-0.563604\pi$
$491$	−8.79655	−0.396983	−0.198491	+	0.980103i	$0.563604\pi$
$492$	−117.411	−5.29329
$493$	−17.7624	−0.799977
$494$	22.3915	1.00744
$495$	48.3616	2.17369
$496$	10.6453	0.477988
$497$	−7.74662	−0.347483
$498$	25.5774	1.14615
$499$	−35.7290	−1.59945	−0.799726	−	0.600366i	$-0.795022\pi$
$499$	−35.7290	−1.59945	−0.799726	+	0.600366i	$0.795022\pi$
$500$	−107.522	−4.80851
$501$	40.7866	1.82221
$502$	30.8721	1.37789
$503$	−12.7586	−0.568876	−0.284438	−	0.958694i	$-0.591807\pi$
$503$	−12.7586	−0.568876	−0.284438	+	0.958694i	$0.591807\pi$
$504$	−30.9397	−1.37816
$505$	−60.6958	−2.70093
$506$	24.9254	1.10807
$507$	−27.8460	−1.23668
$508$	40.4252	1.79358
$509$	28.9116	1.28149	0.640743	−	0.767755i	$-0.278626\pi$
$509$	28.9116	1.28149	0.640743	+	0.767755i	$0.278626\pi$
$510$	72.9403	3.22985
$511$	−6.27982	−0.277803
$512$	50.6238	2.23728
$513$	−28.7412	−1.26896
$514$	−17.8314	−0.786507
$515$	−39.4716	−1.73933
$516$	−2.73371	−0.120345
$517$	26.4026	1.16119
$518$	−9.27252	−0.407411
$519$	−0.368690	−0.0161837
$520$	43.8531	1.92309
$521$	−20.5926	−0.902176	−0.451088	−	0.892479i	$-0.648964\pi$
$521$	−20.5926	−0.902176	−0.451088	+	0.892479i	$0.648964\pi$
$522$	89.6924	3.92573
$523$	−3.77257	−0.164963	−0.0824815	−	0.996593i	$-0.526285\pi$
$523$	−3.77257	−0.164963	−0.0824815	+	0.996593i	$0.526285\pi$
$524$	−99.1330	−4.33065
$525$	31.3955	1.37021
$526$	21.7603	0.948793
$527$	4.02448	0.175309
$528$	−45.4210	−1.97670
$529$	−6.07426	−0.264098
$530$	95.1356	4.13243
$531$	6.18460	0.268389
$532$	−21.8942	−0.949235
$533$	−16.7075	−0.723682
$534$	−131.207	−5.67788
$535$	10.2276	0.442177
$536$	22.4993	0.971820
$537$	−16.6195	−0.717186
$538$	−42.9748	−1.85278
$539$	−2.39111	−0.102992
$540$	−102.807	−4.42411
$541$	44.8739	1.92928	0.964640	−	0.263572i	$-0.0849006\pi$
$541$	44.8739	1.92928	0.964640	+	0.263572i	$0.0849006\pi$
$542$	−3.29198	−0.141403
$543$	12.1552	0.521630
$544$	−11.9115	−0.510701
$545$	45.9144	1.96676
$546$	−12.8222	−0.548740
$547$	1.97198	0.0843159	0.0421580	−	0.999111i	$-0.486577\pi$
$547$	1.97198	0.0843159	0.0421580	+	0.999111i	$0.486577\pi$
$548$	−20.1383	−0.860266
$549$	−12.3411	−0.526704
$550$	67.0588	2.85940
$551$	34.7512	1.48045
$552$	−71.5573	−3.04568
$553$	1.56383	0.0665010
$554$	21.3860	0.908606
$555$	−41.6097	−1.76623
$556$	−95.8760	−4.06605
$557$	38.2791	1.62194	0.810970	−	0.585088i	$-0.198940\pi$
$557$	38.2791	1.62194	0.810970	+	0.585088i	$0.198940\pi$
$558$	−20.3219	−0.860296
$559$	−0.389005	−0.0164532
$560$	−26.8451	−1.13441
$561$	−17.1715	−0.724983
$562$	−29.1836	−1.23104
$563$	−29.5459	−1.24521	−0.622606	−	0.782535i	$-0.713926\pi$
$563$	−29.5459	−1.24521	−0.622606	+	0.782535i	$0.713926\pi$
$564$	−138.439	−5.82933
$565$	56.6607	2.38374
$566$	57.9022	2.43381
$567$	1.32145	0.0554959
$568$	47.5021	1.99314
$569$	4.75495	0.199338	0.0996690	−	0.995021i	$-0.468222\pi$
$569$	4.75495	0.199338	0.0996690	+	0.995021i	$0.468222\pi$
$570$	−142.704	−5.97722
$571$	1.00000	0.0418487
$571$	1.00000	0.0418487
$572$	−18.8557	−0.788396
$573$	−65.2222	−2.72469
$574$	23.7284	0.990404
$575$	45.5366	1.89901
$576$	−7.43282	−0.309701
$577$	11.8872	0.494869	0.247435	−	0.968905i	$-0.420412\pi$
$577$	11.8872	0.494869	0.247435	+	0.968905i	$0.420412\pi$
$578$	26.8327	1.11609
$579$	36.2279	1.50558
$580$	124.305	5.16148
$581$	−3.55882	−0.147645
$582$	−126.560	−5.24610
$583$	−22.3967	−0.927578
$584$	38.5077	1.59346
$585$	−36.0840	−1.49189
$586$	−23.6908	−0.978659
$587$	24.5460	1.01312	0.506561	−	0.862204i	$-0.330917\pi$
$587$	24.5460	1.01312	0.506561	+	0.862204i	$0.330917\pi$
$588$	12.5375	0.517037
$589$	−7.87371	−0.324430
$590$	12.4496	0.512540
$591$	47.6566	1.96033
$592$	24.5079	1.00727
$593$	−31.1878	−1.28073	−0.640365	−	0.768071i	$-0.721217\pi$
$593$	−31.1878	−1.28073	−0.640365	+	0.768071i	$0.721217\pi$
$594$	35.1540	1.44239
$595$	−10.1489	−0.416063
$596$	−48.4921	−1.98631
$597$	−52.9471	−2.16698
$598$	−18.5976	−0.760513
$599$	47.1656	1.92713	0.963566	−	0.267469i	$-0.0861873\pi$
$599$	47.1656	1.92713	0.963566	+	0.267469i	$0.0861873\pi$
$600$	−192.516	−7.85944
$601$	−20.3203	−0.828884	−0.414442	−	0.910076i	$-0.636023\pi$
$601$	−20.3203	−0.828884	−0.414442	+	0.910076i	$0.636023\pi$
$602$	0.552475	0.0225172
$603$	−18.5133	−0.753918
$604$	−92.1359	−3.74896
$605$	21.1756	0.860911
$606$	−108.823	−4.42065
$607$	−1.10968	−0.0450406	−0.0225203	−	0.999746i	$-0.507169\pi$
$607$	−1.10968	−0.0450406	−0.0225203	+	0.999746i	$0.507169\pi$
$608$	23.3042	0.945111
$609$	−19.8999	−0.806384
$610$	−24.8425	−1.00584
$611$	−19.6998	−0.796967
$612$	56.4645	2.28244
$613$	−40.8876	−1.65143	−0.825717	−	0.564085i	$-0.809229\pi$
$613$	−40.8876	−1.65143	−0.825717	+	0.564085i	$0.809229\pi$
$614$	16.8170	0.678680
$615$	106.479	4.29366
$616$	14.6622	0.590757
$617$	40.3459	1.62427	0.812133	−	0.583472i	$-0.198306\pi$
$617$	40.3459	1.62427	0.812133	+	0.583472i	$0.198306\pi$
$618$	−70.7697	−2.84678
$619$	−20.5673	−0.826671	−0.413336	−	0.910579i	$-0.635636\pi$
$619$	−20.5673	−0.826671	−0.413336	+	0.910579i	$0.635636\pi$
$620$	−28.1642	−1.13110
$621$	23.8715	0.957930
$622$	−35.1098	−1.40778
$623$	18.2561	0.731413
$624$	33.8900	1.35668
$625$	42.1684	1.68674
$626$	17.9130	0.715947
$627$	33.5953	1.34167
$628$	−17.2111	−0.686799
$629$	9.26526	0.369430
$630$	51.2475	2.04175
$631$	21.5058	0.856133	0.428067	−	0.903747i	$-0.359195\pi$
$631$	21.5058	0.856133	0.428067	+	0.903747i	$0.359195\pi$
$632$	−9.58939	−0.381446
$633$	18.4297	0.732515
$634$	14.5783	0.578979
$635$	−36.6614	−1.45486
$636$	117.435	4.65658
$637$	1.78408	0.0706876
$638$	−42.5050	−1.68279
$639$	−39.0865	−1.54624
$640$	−52.6806	−2.08238
$641$	−45.0244	−1.77836	−0.889179	−	0.457560i	$-0.848723\pi$
$641$	−45.0244	−1.77836	−0.889179	+	0.457560i	$0.848723\pi$
$642$	18.3373	0.723717
$643$	23.2651	0.917485	0.458743	−	0.888569i	$-0.348300\pi$
$643$	23.2651	0.917485	0.458743	+	0.888569i	$0.348300\pi$
$644$	18.1846	0.716574
$645$	2.47919	0.0976179
$646$	31.7761	1.25021
$647$	23.5206	0.924692	0.462346	−	0.886700i	$-0.347008\pi$
$647$	23.5206	0.924692	0.462346	+	0.886700i	$0.347008\pi$
$648$	−8.10313	−0.318321
$649$	−2.93086	−0.115046
$650$	−50.0346	−1.96252
$651$	4.50879	0.176713
$652$	−64.7481	−2.53573
$653$	13.8013	0.540087	0.270044	−	0.962848i	$-0.412962\pi$
$653$	13.8013	0.540087	0.270044	+	0.962848i	$0.412962\pi$
$654$	82.3213	3.21902
$655$	89.9032	3.51281
$656$	−62.7157	−2.44864
$657$	−31.6856	−1.23617
$658$	27.9781	1.09070
$659$	−43.5923	−1.69811	−0.849057	−	0.528301i	$-0.822829\pi$
$659$	−43.5923	−1.69811	−0.849057	+	0.528301i	$0.822829\pi$
$660$	120.170	4.67761
$661$	−37.5799	−1.46169	−0.730845	−	0.682543i	$-0.760874\pi$
$661$	−37.5799	−1.46169	−0.730845	+	0.682543i	$0.760874\pi$
$662$	−68.2582	−2.65293
$663$	12.8122	0.497584
$664$	21.8226	0.846882
$665$	19.8558	0.769973
$666$	−46.7856	−1.81291
$667$	−28.8632	−1.11759
$668$	63.5577	2.45912
$669$	−16.4074	−0.634349
$670$	−37.2671	−1.43975
$671$	5.84839	0.225775
$672$	−13.3449	−0.514791
$673$	−9.06354	−0.349374	−0.174687	−	0.984624i	$-0.555891\pi$
$673$	−9.06354	−0.349374	−0.174687	+	0.984624i	$0.555891\pi$
$674$	42.9008	1.65248
$675$	64.2233	2.47196
$676$	−43.3923	−1.66893
$677$	21.2128	0.815274	0.407637	−	0.913144i	$-0.366353\pi$
$677$	21.2128	0.815274	0.407637	+	0.913144i	$0.366353\pi$
$678$	101.589	3.90149
$679$	17.6095	0.675791
$680$	62.2326	2.38651
$681$	13.7021	0.525064
$682$	9.63050	0.368771
$683$	34.4170	1.31693	0.658464	−	0.752612i	$-0.271206\pi$
$683$	34.4170	1.31693	0.658464	+	0.752612i	$0.271206\pi$
$684$	−110.470	−4.22393
$685$	18.2633	0.697806
$686$	−2.53379	−0.0967405
$687$	−40.9382	−1.56189
$688$	−1.46023	−0.0556706
$689$	16.7109	0.636633
$690$	118.525	4.51218
$691$	28.3598	1.07886	0.539428	−	0.842031i	$-0.318640\pi$
$691$	28.3598	1.07886	0.539428	+	0.842031i	$0.318640\pi$
$692$	−0.574530	−0.0218403
$693$	−12.0646	−0.458297
$694$	49.7923	1.89009
$695$	86.9494	3.29818
$696$	122.026	4.62537
$697$	−23.7098	−0.898074
$698$	−36.2520	−1.37216
$699$	−13.1063	−0.495725
$700$	48.9235	1.84913
$701$	−7.31129	−0.276144	−0.138072	−	0.990422i	$-0.544090\pi$
$701$	−7.31129	−0.276144	−0.138072	+	0.990422i	$0.544090\pi$
$702$	−26.2295	−0.989967
$703$	−18.1270	−0.683674
$704$	3.52239	0.132755
$705$	125.549	4.72847
$706$	14.9141	0.561301
$707$	15.1416	0.569459
$708$	15.3676	0.577551
$709$	−39.8557	−1.49681	−0.748407	−	0.663240i	$-0.769181\pi$
$709$	−39.8557	−1.49681	−0.748407	+	0.663240i	$0.769181\pi$
$710$	−78.6810	−2.95284
$711$	7.89052	0.295918
$712$	−111.946	−4.19534
$713$	6.53964	0.244911
$714$	−18.1962	−0.680976
$715$	17.1001	0.639508
$716$	−25.8982	−0.967860
$717$	−66.7232	−2.49182
$718$	79.0934	2.95174
$719$	14.4707	0.539666	0.269833	−	0.962907i	$-0.413031\pi$
$719$	14.4707	0.539666	0.269833	+	0.962907i	$0.413031\pi$
$720$	−135.450	−5.04793
$721$	9.84685	0.366716
$722$	−14.0263	−0.522005
$723$	64.5949	2.40231
$724$	18.9414	0.703952
$725$	−77.6529	−2.88395
$726$	37.9664	1.40906
$727$	13.2744	0.492322	0.246161	−	0.969229i	$-0.420831\pi$
$727$	13.2744	0.492322	0.246161	+	0.969229i	$0.420831\pi$
$728$	−10.9399	−0.405460
$729$	−42.7074	−1.58176
$730$	−63.7830	−2.36071
$731$	−0.552043	−0.0204180
$732$	−30.6654	−1.13342
$733$	−39.9945	−1.47723	−0.738615	−	0.674127i	$-0.764520\pi$
$733$	−39.9945	−1.47723	−0.738615	+	0.674127i	$0.764520\pi$
$734$	38.5366	1.42241
$735$	−11.3702	−0.419395
$736$	−19.3557	−0.713461
$737$	8.77337	0.323171
$738$	119.725	4.40712
$739$	18.6002	0.684219	0.342109	−	0.939660i	$-0.388859\pi$
$739$	18.6002	0.684219	0.342109	+	0.939660i	$0.388859\pi$
$740$	−64.8403	−2.38358
$741$	−25.0664	−0.920838
$742$	−23.7332	−0.871273
$743$	8.54400	0.313449	0.156725	−	0.987642i	$-0.449907\pi$
$743$	8.54400	0.313449	0.156725	+	0.987642i	$0.449907\pi$
$744$	−27.6478	−1.01362
$745$	43.9772	1.61120
$746$	4.44464	0.162730
$747$	−17.9565	−0.656993
$748$	−26.7584	−0.978383
$749$	−2.55144	−0.0932277
$750$	174.830	6.38388
$751$	1.27756	0.0466190	0.0233095	−	0.999728i	$-0.492580\pi$
$751$	1.27756	0.0466190	0.0233095	+	0.999728i	$0.492580\pi$
$752$	−73.9479	−2.69660
$753$	−34.5602	−1.25944
$754$	31.7142	1.15496
$755$	83.5576	3.04097
$756$	25.6470	0.932772
$757$	−44.2954	−1.60994	−0.804971	−	0.593314i	$-0.797819\pi$
$757$	−44.2954	−1.60994	−0.804971	+	0.593314i	$0.797819\pi$
$758$	−5.67571	−0.206151
$759$	−27.9031	−1.01282
$760$	−121.755	−4.41652
$761$	31.8054	1.15294	0.576472	−	0.817117i	$-0.304429\pi$
$761$	31.8054	1.15294	0.576472	+	0.817117i	$0.304429\pi$
$762$	−65.7313	−2.38120
$763$	−11.4541	−0.414667
$764$	−101.636	−3.67705
$765$	−51.2074	−1.85141
$766$	30.9687	1.11894
$767$	2.18680	0.0789608
$768$	−86.0955	−3.10670
$769$	−5.65288	−0.203848	−0.101924	−	0.994792i	$-0.532500\pi$
$769$	−5.65288	−0.203848	−0.101924	+	0.994792i	$0.532500\pi$
$770$	−24.2860	−0.875207
$771$	19.9615	0.718897
$772$	56.4539	2.03182
$773$	−23.9069	−0.859871	−0.429935	−	0.902860i	$-0.641464\pi$
$773$	−23.9069	−0.859871	−0.429935	+	0.902860i	$0.641464\pi$
$774$	2.78758	0.100198
$775$	17.5941	0.631998
$776$	−107.981	−3.87630
$777$	10.3802	0.372389
$778$	−10.9151	−0.391326
$779$	46.3871	1.66199
$780$	−89.6624	−3.21043
$781$	18.5230	0.662805
$782$	−26.3921	−0.943781
$783$	−40.7077	−1.45477
$784$	6.69696	0.239177
$785$	15.6087	0.557097
$786$	161.190	5.74946
$787$	−21.0668	−0.750952	−0.375476	−	0.926832i	$-0.622521\pi$
$787$	−21.0668	−0.750952	−0.375476	+	0.926832i	$0.622521\pi$
$788$	74.2633	2.64552
$789$	−24.3598	−0.867232
$790$	15.8836	0.565112
$791$	−14.1350	−0.502582
$792$	73.9800	2.62876
$793$	−4.36366	−0.154958
$794$	−34.6847	−1.23091
$795$	−106.501	−3.77719
$796$	−82.5074	−2.92440
$797$	14.7524	0.522558	0.261279	−	0.965263i	$-0.415856\pi$
$797$	14.7524	0.522558	0.261279	+	0.965263i	$0.415856\pi$
$798$	35.6000	1.26022
$799$	−27.9562	−0.989020
$800$	−52.0742	−1.84110
$801$	92.1132	3.25466
$802$	22.7133	0.802036
$803$	15.0157	0.529893
$804$	−46.0022	−1.62237
$805$	−16.4915	−0.581250
$806$	−7.18560	−0.253102
$807$	48.1087	1.69351
$808$	−92.8480	−3.26638
$809$	−23.8653	−0.839058	−0.419529	−	0.907742i	$-0.637805\pi$
$809$	−23.8653	−0.839058	−0.419529	+	0.907742i	$0.637805\pi$
$810$	13.4218	0.471593
$811$	−0.123654	−0.00434206	−0.00217103	−	0.999998i	$-0.500691\pi$
$811$	−0.123654	−0.00434206	−0.00217103	+	0.999998i	$0.500691\pi$
$812$	−31.0099	−1.08824
$813$	3.68525	0.129247
$814$	22.1716	0.777113
$815$	58.7197	2.05686
$816$	48.0937	1.68362
$817$	1.08004	0.0377860
$818$	42.2141	1.47598
$819$	9.00177	0.314547
$820$	165.926	5.79440
$821$	21.4486	0.748560	0.374280	−	0.927316i	$-0.377890\pi$
$821$	21.4486	0.748560	0.374280	+	0.927316i	$0.377890\pi$
$822$	32.7448	1.14211
$823$	50.1794	1.74914	0.874572	−	0.484895i	$-0.161142\pi$
$823$	50.1794	1.74914	0.874572	+	0.484895i	$0.161142\pi$
$824$	−60.3807	−2.10346
$825$	−75.0699	−2.61360
$826$	−3.10575	−0.108063
$827$	19.1680	0.666537	0.333269	−	0.942832i	$-0.391848\pi$
$827$	19.1680	0.666537	0.333269	+	0.942832i	$0.391848\pi$
$828$	91.7528	3.18863
$829$	18.9152	0.656954	0.328477	−	0.944512i	$-0.393465\pi$
$829$	18.9152	0.656954	0.328477	+	0.944512i	$0.393465\pi$
$830$	−36.1463	−1.25466
$831$	−23.9409	−0.830500
$832$	−2.62816	−0.0911151
$833$	2.53181	0.0877219
$834$	155.894	5.39817
$835$	−57.6401	−1.99472
$836$	52.3514	1.81061
$837$	9.22329	0.318803
$838$	−3.25395	−0.112406
$839$	13.7385	0.474307	0.237154	−	0.971472i	$-0.423786\pi$
$839$	13.7385	0.474307	0.237154	+	0.971472i	$0.423786\pi$
$840$	69.7216	2.40562
$841$	20.2199	0.697239
$842$	8.72675	0.300744
$843$	32.6700	1.12521
$844$	28.7190	0.988548
$845$	39.3522	1.35376
$846$	141.167	4.85342
$847$	−5.28261	−0.181513
$848$	62.7283	2.15410
$849$	−64.8194	−2.22460
$850$	−71.0048	−2.43544
$851$	15.0557	0.516103
$852$	−97.1231	−3.32738
$853$	15.0786	0.516280	0.258140	−	0.966107i	$-0.416890\pi$
$853$	15.0786	0.516280	0.258140	+	0.966107i	$0.416890\pi$
$854$	6.19738	0.212070
$855$	100.185	3.42624
$856$	15.6454	0.534749
$857$	−13.1595	−0.449519	−0.224760	−	0.974414i	$-0.572160\pi$
$857$	−13.1595	−0.449519	−0.224760	+	0.974414i	$0.572160\pi$
$858$	30.6593	1.04669
$859$	−11.7934	−0.402385	−0.201193	−	0.979552i	$-0.564482\pi$
$859$	−11.7934	−0.402385	−0.201193	+	0.979552i	$0.564482\pi$
$860$	3.86331	0.131738
$861$	−26.5631	−0.905266
$862$	−21.0420	−0.716692
$863$	42.3876	1.44289	0.721445	−	0.692472i	$-0.243478\pi$
$863$	42.3876	1.44289	0.721445	+	0.692472i	$0.243478\pi$
$864$	−27.2987	−0.928719
$865$	0.521038	0.0177158
$866$	−63.9176	−2.17201
$867$	−30.0382	−1.02015
$868$	7.02603	0.238479
$869$	−3.73929	−0.126847
$870$	−202.119	−6.85248
$871$	−6.54608	−0.221805
$872$	70.2364	2.37851
$873$	88.8510	3.00715
$874$	51.6349	1.74658
$875$	−24.3257	−0.822358
$876$	−78.7332	−2.66015
$877$	−38.6744	−1.30594	−0.652971	−	0.757382i	$-0.726478\pi$
$877$	−38.6744	−1.30594	−0.652971	+	0.757382i	$0.726478\pi$
$878$	−52.5792	−1.77446
$879$	26.5210	0.894531
$880$	64.1895	2.16383
$881$	−38.8993	−1.31055	−0.655275	−	0.755391i	$-0.727447\pi$
$881$	−38.8993	−1.31055	−0.655275	+	0.755391i	$0.727447\pi$
$882$	−12.7845	−0.430478
$883$	−40.9471	−1.37798	−0.688990	−	0.724771i	$-0.741945\pi$
$883$	−40.9471	−1.37798	−0.688990	+	0.724771i	$0.741945\pi$
$884$	19.9652	0.671503
$885$	−13.9368	−0.468481
$886$	58.2763	1.95783
$887$	20.9479	0.703361	0.351680	−	0.936120i	$-0.385610\pi$
$887$	20.9479	0.703361	0.351680	+	0.936120i	$0.385610\pi$
$888$	−63.6514	−2.13600
$889$	9.14581	0.306741
$890$	185.423	6.21540
$891$	−3.15974	−0.105855
$892$	−25.5677	−0.856070
$893$	54.6950	1.83030
$894$	78.8480	2.63707
$895$	23.4869	0.785081
$896$	13.1421	0.439045
$897$	20.8193	0.695137
$898$	−54.1345	−1.80649
$899$	−11.1519	−0.371938
$900$	246.850	8.22832
$901$	23.7146	0.790049
$902$	−56.7371	−1.88914
$903$	−0.618475	−0.0205816
$904$	86.6754	2.88278
$905$	−17.1779	−0.571012
$906$	149.813	4.97720
$907$	6.61550	0.219664	0.109832	−	0.993950i	$-0.464969\pi$
$907$	6.61550	0.219664	0.109832	+	0.993950i	$0.464969\pi$
$908$	21.3519	0.708587
$909$	76.3988	2.53399
$910$	18.1205	0.600689
$911$	−24.1942	−0.801590	−0.400795	−	0.916168i	$-0.631266\pi$
$911$	−24.1942	−0.801590	−0.400795	+	0.916168i	$0.631266\pi$
$912$	−94.0930	−3.11573
$913$	8.50952	0.281624
$914$	−7.37891	−0.244073
$915$	27.8102	0.919378
$916$	−63.7940	−2.10781
$917$	−22.4279	−0.740633
$918$	−37.2226	−1.22853
$919$	48.3660	1.59545	0.797723	−	0.603024i	$-0.206038\pi$
$919$	48.3660	1.59545	0.797723	+	0.603024i	$0.206038\pi$
$920$	101.126	3.33401
$921$	−18.8260	−0.620339
$922$	25.0091	0.823632
$923$	−13.8206	−0.454909
$924$	−29.9784	−0.986218
$925$	40.5055	1.33181
$926$	34.7272	1.14121
$927$	49.6835	1.63182
$928$	33.0070	1.08351
$929$	−6.59404	−0.216343	−0.108172	−	0.994132i	$-0.534500\pi$
$929$	−6.59404	−0.216343	−0.108172	+	0.994132i	$0.534500\pi$
$930$	45.7949	1.50167
$931$	−4.95335	−0.162340
$932$	−20.4235	−0.668994
$933$	39.3042	1.28676
$934$	84.6860	2.77101
$935$	24.2670	0.793616
$936$	−55.1987	−1.80422
$937$	−47.6512	−1.55670	−0.778349	−	0.627832i	$-0.783942\pi$
$937$	−47.6512	−1.55670	−0.778349	+	0.627832i	$0.783942\pi$
$938$	9.29690	0.303555
$939$	−20.0529	−0.654402
$940$	195.644	6.38119
$941$	2.71365	0.0884626	0.0442313	−	0.999021i	$-0.485916\pi$
$941$	2.71365	0.0884626	0.0442313	+	0.999021i	$0.485916\pi$
$942$	27.9852	0.911809
$943$	−38.5276	−1.25463
$944$	8.20870	0.267170
$945$	−23.2591	−0.756619
$946$	−1.32103	−0.0429503
$947$	−4.37151	−0.142055	−0.0710276	−	0.997474i	$-0.522628\pi$
$947$	−4.37151	−0.142055	−0.0710276	+	0.997474i	$0.522628\pi$
$948$	19.6065	0.636791
$949$	−11.2037	−0.363687
$950$	138.917	4.50707
$951$	−16.3199	−0.529209
$952$	−15.5250	−0.503167
$953$	56.1621	1.81927	0.909634	−	0.415410i	$-0.136362\pi$
$953$	56.1621	1.81927	0.909634	+	0.415410i	$0.136362\pi$
$954$	−119.749	−3.87701
$955$	92.1727	2.98264
$956$	−103.975	−3.36278
$957$	47.5827	1.53813
$958$	−59.6783	−1.92812
$959$	−4.55609	−0.147124
$960$	16.7497	0.540593
$961$	−28.4733	−0.918492
$962$	−16.5429	−0.533363
$963$	−12.8736	−0.414847
$964$	100.658	3.24198
$965$	−51.1977	−1.64811
$966$	−29.5681	−0.951339
$967$	−43.8305	−1.40949	−0.704747	−	0.709459i	$-0.748939\pi$
$967$	−43.8305	−1.40949	−0.704747	+	0.709459i	$0.748939\pi$
$968$	32.3929	1.04115
$969$	−35.5721	−1.14274
$970$	178.857	5.74274
$971$	49.8241	1.59893	0.799466	−	0.600712i	$-0.205116\pi$
$971$	49.8241	1.59893	0.799466	+	0.600712i	$0.205116\pi$
$972$	−60.3732	−1.93647
$973$	−21.6910	−0.695381
$974$	−42.3089	−1.35566
$975$	56.0119	1.79381
$976$	−16.3801	−0.524314
$977$	54.0150	1.72809	0.864046	−	0.503413i	$-0.167923\pi$
$977$	54.0150	1.72809	0.864046	+	0.503413i	$0.167923\pi$
$978$	105.280	3.36649
$979$	−43.6522	−1.39513
$980$	−17.7181	−0.565984
$981$	−57.7932	−1.84520
$982$	22.2886	0.711258
$983$	−55.7029	−1.77665	−0.888323	−	0.459220i	$-0.848129\pi$
$983$	−55.7029	−1.77665	−0.888323	+	0.459220i	$0.848129\pi$
$984$	162.884	5.19255
$985$	−67.3489	−2.14591
$986$	45.0061	1.43329
$987$	−31.3204	−0.996941
$988$	−39.0609	−1.24269
$989$	−0.897049	−0.0285245
$990$	−122.538	−3.89452
$991$	−0.877482	−0.0278741	−0.0139371	−	0.999903i	$-0.504436\pi$
$991$	−0.877482	−0.0278741	−0.0139371	+	0.999903i	$0.504436\pi$
$992$	−7.47851	−0.237443
$993$	76.4125	2.42488
$994$	19.6283	0.622572
$995$	74.8255	2.37213
$996$	−44.6187	−1.41380
$997$	36.2472	1.14796	0.573980	−	0.818869i	$-0.305399\pi$
$997$	36.2472	1.14796	0.573980	+	0.818869i	$0.305399\pi$
$998$	90.5298	2.86567
$999$	21.2341	0.671816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.2.a.c.1.8	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.2.a.c.1.8	✓	63	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:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3997.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53379 q^{2} +2.83648 q^{3} +4.42008 q^{4} -4.00855 q^{5} -7.18704 q^{6} +1.00000 q^{7} -6.13198 q^{8} +5.04562 q^{9} +O(q^{10})\)	\(q-2.53379 q^{2} +2.83648 q^{3} +4.42008 q^{4} -4.00855 q^{5} -7.18704 q^{6} +1.00000 q^{7} -6.13198 q^{8} +5.04562 q^{9} +10.1568 q^{10} -2.39111 q^{11} +12.5375 q^{12} +1.78408 q^{13} -2.53379 q^{14} -11.3702 q^{15} +6.69696 q^{16} +2.53181 q^{17} -12.7845 q^{18} -4.95335 q^{19} -17.7181 q^{20} +2.83648 q^{21} +6.05855 q^{22} +4.11409 q^{23} -17.3932 q^{24} +11.0685 q^{25} -4.52047 q^{26} +5.80238 q^{27} +4.42008 q^{28} -7.01569 q^{29} +28.8096 q^{30} +1.58957 q^{31} -4.70474 q^{32} -6.78233 q^{33} -6.41506 q^{34} -4.00855 q^{35} +22.3021 q^{36} +3.65955 q^{37} +12.5507 q^{38} +5.06049 q^{39} +24.5803 q^{40} -9.36479 q^{41} -7.18704 q^{42} -0.218043 q^{43} -10.5689 q^{44} -20.2256 q^{45} -10.4242 q^{46} -11.0420 q^{47} +18.9958 q^{48} +1.00000 q^{49} -28.0451 q^{50} +7.18142 q^{51} +7.88576 q^{52} +9.36668 q^{53} -14.7020 q^{54} +9.58486 q^{55} -6.13198 q^{56} -14.0501 q^{57} +17.7763 q^{58} +1.22573 q^{59} -50.2571 q^{60} -2.44590 q^{61} -4.02764 q^{62} +5.04562 q^{63} -1.47312 q^{64} -7.15155 q^{65} +17.1850 q^{66} -3.66917 q^{67} +11.1908 q^{68} +11.6695 q^{69} +10.1568 q^{70} -7.74662 q^{71} -30.9397 q^{72} -6.27982 q^{73} -9.27252 q^{74} +31.3955 q^{75} -21.8942 q^{76} -2.39111 q^{77} -12.8222 q^{78} +1.56383 q^{79} -26.8451 q^{80} +1.32145 q^{81} +23.7284 q^{82} -3.55882 q^{83} +12.5375 q^{84} -10.1489 q^{85} +0.552475 q^{86} -19.8999 q^{87} +14.6622 q^{88} +18.2561 q^{89} +51.2475 q^{90} +1.78408 q^{91} +18.1846 q^{92} +4.50879 q^{93} +27.9781 q^{94} +19.8558 q^{95} -13.3449 q^{96} +17.6095 q^{97} -2.53379 q^{98} -12.0646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q - 21 q^{2} - 14 q^{3} + 57 q^{4} - 16 q^{5} - 3 q^{6} + 63 q^{7} - 54 q^{8} + 39 q^{9}+O(q^{10}) \) 63 * q - 21 * q^2 - 14 * q^3 + 57 * q^4 - 16 * q^5 - 3 * q^6 + 63 * q^7 - 54 * q^8 + 39 * q^9	\( 63 q - 21 q^{2} - 14 q^{3} + 57 q^{4} - 16 q^{5} - 3 q^{6} + 63 q^{7} - 54 q^{8} + 39 q^{9} - 8 q^{10} - 54 q^{11} - 27 q^{12} - 10 q^{13} - 21 q^{14} - 33 q^{15} + 53 q^{16} - 25 q^{17} - 37 q^{18} - 23 q^{19} - 36 q^{20} - 14 q^{21} - 8 q^{22} - 62 q^{23} - 6 q^{24} + 37 q^{25} - 4 q^{26} - 56 q^{27} + 57 q^{28} - 96 q^{29} - 9 q^{30} - 9 q^{31} - 119 q^{32} - 23 q^{33} - 16 q^{35} + 16 q^{36} - 21 q^{37} - 21 q^{38} - 36 q^{39} + 3 q^{40} - 34 q^{41} - 3 q^{42} - 36 q^{43} - 79 q^{44} - 28 q^{45} - 15 q^{46} - 71 q^{47} - 16 q^{48} + 63 q^{49} - 69 q^{50} - 59 q^{51} + 4 q^{52} - 118 q^{53} - 4 q^{54} - 6 q^{55} - 54 q^{56} - 55 q^{57} + 16 q^{58} - 67 q^{59} - 32 q^{60} + q^{61} - 16 q^{62} + 39 q^{63} + 58 q^{64} - 100 q^{65} + 80 q^{66} - 82 q^{67} - 60 q^{68} + 7 q^{69} - 8 q^{70} - 115 q^{71} - 74 q^{72} - 9 q^{73} - 29 q^{74} - 38 q^{75} - 34 q^{76} - 54 q^{77} - 44 q^{78} - 21 q^{79} - 25 q^{80} + 3 q^{81} - q^{82} - 139 q^{83} - 27 q^{84} - 21 q^{85} - 58 q^{86} - q^{87} + 15 q^{88} - 29 q^{89} + 59 q^{90} - 10 q^{91} - 79 q^{92} - 45 q^{93} + 21 q^{94} - 83 q^{95} + 65 q^{96} + 22 q^{97} - 21 q^{98} - 73 q^{99}+O(q^{100}) \) 63 * q - 21 * q^2 - 14 * q^3 + 57 * q^4 - 16 * q^5 - 3 * q^6 + 63 * q^7 - 54 * q^8 + 39 * q^9 - 8 * q^10 - 54 * q^11 - 27 * q^12 - 10 * q^13 - 21 * q^14 - 33 * q^15 + 53 * q^16 - 25 * q^17 - 37 * q^18 - 23 * q^19 - 36 * q^20 - 14 * q^21 - 8 * q^22 - 62 * q^23 - 6 * q^24 + 37 * q^25 - 4 * q^26 - 56 * q^27 + 57 * q^28 - 96 * q^29 - 9 * q^30 - 9 * q^31 - 119 * q^32 - 23 * q^33 - 16 * q^35 + 16 * q^36 - 21 * q^37 - 21 * q^38 - 36 * q^39 + 3 * q^40 - 34 * q^41 - 3 * q^42 - 36 * q^43 - 79 * q^44 - 28 * q^45 - 15 * q^46 - 71 * q^47 - 16 * q^48 + 63 * q^49 - 69 * q^50 - 59 * q^51 + 4 * q^52 - 118 * q^53 - 4 * q^54 - 6 * q^55 - 54 * q^56 - 55 * q^57 + 16 * q^58 - 67 * q^59 - 32 * q^60 + q^61 - 16 * q^62 + 39 * q^63 + 58 * q^64 - 100 * q^65 + 80 * q^66 - 82 * q^67 - 60 * q^68 + 7 * q^69 - 8 * q^70 - 115 * q^71 - 74 * q^72 - 9 * q^73 - 29 * q^74 - 38 * q^75 - 34 * q^76 - 54 * q^77 - 44 * q^78 - 21 * q^79 - 25 * q^80 + 3 * q^81 - q^82 - 139 * q^83 - 27 * q^84 - 21 * q^85 - 58 * q^86 - q^87 + 15 * q^88 - 29 * q^89 + 59 * q^90 - 10 * q^91 - 79 * q^92 - 45 * q^93 + 21 * q^94 - 83 * q^95 + 65 * q^96 + 22 * q^97 - 21 * q^98 - 73 * q^99

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