LMFDB - Embedded newform 4034.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.41599 q^{3} +1.00000 q^{4} +1.09379 q^{5} -3.41599 q^{6} +4.04655 q^{7} +1.00000 q^{8} +8.66901 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.41599 q^{3} +1.00000 q^{4} +1.09379 q^{5} -3.41599 q^{6} +4.04655 q^{7} +1.00000 q^{8} +8.66901 q^{9} +1.09379 q^{10} +1.13342 q^{11} -3.41599 q^{12} -1.55276 q^{13} +4.04655 q^{14} -3.73637 q^{15} +1.00000 q^{16} -4.98060 q^{17} +8.66901 q^{18} -2.70861 q^{19} +1.09379 q^{20} -13.8230 q^{21} +1.13342 q^{22} -4.20260 q^{23} -3.41599 q^{24} -3.80363 q^{25} -1.55276 q^{26} -19.3653 q^{27} +4.04655 q^{28} -7.09742 q^{29} -3.73637 q^{30} -7.08192 q^{31} +1.00000 q^{32} -3.87176 q^{33} -4.98060 q^{34} +4.42607 q^{35} +8.66901 q^{36} -6.59627 q^{37} -2.70861 q^{38} +5.30423 q^{39} +1.09379 q^{40} +8.21349 q^{41} -13.8230 q^{42} +7.00495 q^{43} +1.13342 q^{44} +9.48205 q^{45} -4.20260 q^{46} +1.05696 q^{47} -3.41599 q^{48} +9.37458 q^{49} -3.80363 q^{50} +17.0137 q^{51} -1.55276 q^{52} -6.09949 q^{53} -19.3653 q^{54} +1.23972 q^{55} +4.04655 q^{56} +9.25260 q^{57} -7.09742 q^{58} -7.54428 q^{59} -3.73637 q^{60} -11.4723 q^{61} -7.08192 q^{62} +35.0796 q^{63} +1.00000 q^{64} -1.69839 q^{65} -3.87176 q^{66} +5.47712 q^{67} -4.98060 q^{68} +14.3561 q^{69} +4.42607 q^{70} -16.2111 q^{71} +8.66901 q^{72} -12.7058 q^{73} -6.59627 q^{74} +12.9932 q^{75} -2.70861 q^{76} +4.58645 q^{77} +5.30423 q^{78} -4.93886 q^{79} +1.09379 q^{80} +40.1446 q^{81} +8.21349 q^{82} +5.74803 q^{83} -13.8230 q^{84} -5.44772 q^{85} +7.00495 q^{86} +24.2447 q^{87} +1.13342 q^{88} -2.36834 q^{89} +9.48205 q^{90} -6.28334 q^{91} -4.20260 q^{92} +24.1918 q^{93} +1.05696 q^{94} -2.96265 q^{95} -3.41599 q^{96} -11.0614 q^{97} +9.37458 q^{98} +9.82563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.41599	−1.97222	−0.986112	−	0.166081i	$-0.946889\pi$
$3$	−3.41599	−1.97222	−0.986112	+	0.166081i	$0.946889\pi$
$4$	1.00000	0.500000
$5$	1.09379	0.489157	0.244578	−	0.969630i	$-0.421350\pi$
$5$	1.09379	0.489157	0.244578	+	0.969630i	$0.421350\pi$
$6$	−3.41599	−1.39457
$7$	4.04655	1.52945	0.764726	−	0.644355i	$-0.222874\pi$
$7$	4.04655	1.52945	0.764726	+	0.644355i	$0.222874\pi$
$8$	1.00000	0.353553
$9$	8.66901	2.88967
$10$	1.09379	0.345886
$11$	1.13342	0.341739	0.170870	−	0.985294i	$-0.445342\pi$
$11$	1.13342	0.341739	0.170870	+	0.985294i	$0.445342\pi$
$12$	−3.41599	−0.986112
$13$	−1.55276	−0.430659	−0.215330	−	0.976541i	$-0.569083\pi$
$13$	−1.55276	−0.430659	−0.215330	+	0.976541i	$0.569083\pi$
$14$	4.04655	1.08149
$15$	−3.73637	−0.964727
$16$	1.00000	0.250000
$17$	−4.98060	−1.20797	−0.603986	−	0.796995i	$-0.706422\pi$
$17$	−4.98060	−1.20797	−0.603986	+	0.796995i	$0.706422\pi$
$18$	8.66901	2.04330
$19$	−2.70861	−0.621399	−0.310699	−	0.950508i	$-0.600563\pi$
$19$	−2.70861	−0.621399	−0.310699	+	0.950508i	$0.600563\pi$
$20$	1.09379	0.244578
$21$	−13.8230	−3.01642
$22$	1.13342	0.241646
$23$	−4.20260	−0.876303	−0.438151	−	0.898901i	$-0.644367\pi$
$23$	−4.20260	−0.876303	−0.438151	+	0.898901i	$0.644367\pi$
$24$	−3.41599	−0.697287
$25$	−3.80363	−0.760726
$26$	−1.55276	−0.304522
$27$	−19.3653	−3.72685
$28$	4.04655	0.764726
$29$	−7.09742	−1.31796	−0.658979	−	0.752161i	$-0.729011\pi$
$29$	−7.09742	−1.31796	−0.658979	+	0.752161i	$0.729011\pi$
$30$	−3.73637	−0.682165
$31$	−7.08192	−1.27195	−0.635975	−	0.771710i	$-0.719402\pi$
$31$	−7.08192	−1.27195	−0.635975	+	0.771710i	$0.719402\pi$
$32$	1.00000	0.176777
$33$	−3.87176	−0.673986
$34$	−4.98060	−0.854165
$35$	4.42607	0.748142
$36$	8.66901	1.44483
$37$	−6.59627	−1.08442	−0.542210	−	0.840243i	$-0.682412\pi$
$37$	−6.59627	−1.08442	−0.542210	+	0.840243i	$0.682412\pi$
$38$	−2.70861	−0.439395
$39$	5.30423	0.849356
$40$	1.09379	0.172943
$41$	8.21349	1.28273	0.641366	−	0.767235i	$-0.278368\pi$
$41$	8.21349	1.28273	0.641366	+	0.767235i	$0.278368\pi$
$42$	−13.8230	−2.13293
$43$	7.00495	1.06825	0.534123	−	0.845407i	$-0.320642\pi$
$43$	7.00495	1.06825	0.534123	+	0.845407i	$0.320642\pi$
$44$	1.13342	0.170870
$45$	9.48205	1.41350
$46$	−4.20260	−0.619640
$47$	1.05696	0.154173	0.0770867	−	0.997024i	$-0.475438\pi$
$47$	1.05696	0.154173	0.0770867	+	0.997024i	$0.475438\pi$
$48$	−3.41599	−0.493056
$49$	9.37458	1.33923
$50$	−3.80363	−0.537914
$51$	17.0137	2.38239
$52$	−1.55276	−0.215330
$53$	−6.09949	−0.837829	−0.418915	−	0.908026i	$-0.637589\pi$
$53$	−6.09949	−0.837829	−0.418915	+	0.908026i	$0.637589\pi$
$54$	−19.3653	−2.63528
$55$	1.23972	0.167164
$56$	4.04655	0.540743
$57$	9.25260	1.22554
$58$	−7.09742	−0.931937
$59$	−7.54428	−0.982182	−0.491091	−	0.871108i	$-0.663402\pi$
$59$	−7.54428	−0.982182	−0.491091	+	0.871108i	$0.663402\pi$
$60$	−3.73637	−0.482364
$61$	−11.4723	−1.46887	−0.734437	−	0.678677i	$-0.762554\pi$
$61$	−11.4723	−1.46887	−0.734437	+	0.678677i	$0.762554\pi$
$62$	−7.08192	−0.899404
$63$	35.0796	4.41961
$64$	1.00000	0.125000
$65$	−1.69839	−0.210660
$66$	−3.87176	−0.476580
$67$	5.47712	0.669137	0.334569	−	0.942371i	$-0.391409\pi$
$67$	5.47712	0.669137	0.334569	+	0.942371i	$0.391409\pi$
$68$	−4.98060	−0.603986
$69$	14.3561	1.72827
$70$	4.42607	0.529017
$71$	−16.2111	−1.92391	−0.961953	−	0.273215i	$-0.911913\pi$
$71$	−16.2111	−1.92391	−0.961953	+	0.273215i	$0.911913\pi$
$72$	8.66901	1.02165
$73$	−12.7058	−1.48710	−0.743550	−	0.668680i	$-0.766860\pi$
$73$	−12.7058	−1.48710	−0.743550	+	0.668680i	$0.766860\pi$
$74$	−6.59627	−0.766801
$75$	12.9932	1.50032
$76$	−2.70861	−0.310699
$77$	4.58645	0.522674
$78$	5.30423	0.600586
$79$	−4.93886	−0.555666	−0.277833	−	0.960629i	$-0.589616\pi$
$79$	−4.93886	−0.555666	−0.277833	+	0.960629i	$0.589616\pi$
$80$	1.09379	0.122289
$81$	40.1446	4.46052
$82$	8.21349	0.907028
$83$	5.74803	0.630928	0.315464	−	0.948938i	$-0.397840\pi$
$83$	5.74803	0.630928	0.315464	+	0.948938i	$0.397840\pi$
$84$	−13.8230	−1.50821
$85$	−5.44772	−0.590888
$86$	7.00495	0.755363
$87$	24.2447	2.59931
$88$	1.13342	0.120823
$89$	−2.36834	−0.251044	−0.125522	−	0.992091i	$-0.540061\pi$
$89$	−2.36834	−0.251044	−0.125522	+	0.992091i	$0.540061\pi$
$90$	9.48205	0.999496
$91$	−6.28334	−0.658673
$92$	−4.20260	−0.438151
$93$	24.1918	2.50857
$94$	1.05696	0.109017
$95$	−2.96265	−0.303961
$96$	−3.41599	−0.348643
$97$	−11.0614	−1.12311	−0.561556	−	0.827439i	$-0.689797\pi$
$97$	−11.0614	−1.12311	−0.561556	+	0.827439i	$0.689797\pi$
$98$	9.37458	0.946976
$99$	9.82563	0.987513
$100$	−3.80363	−0.380363
$101$	13.6007	1.35332	0.676660	−	0.736296i	$-0.263427\pi$
$101$	13.6007	1.35332	0.676660	+	0.736296i	$0.263427\pi$
$102$	17.0137	1.68461
$103$	12.8885	1.26995	0.634973	−	0.772534i	$-0.281011\pi$
$103$	12.8885	1.26995	0.634973	+	0.772534i	$0.281011\pi$
$104$	−1.55276	−0.152261
$105$	−15.1194	−1.47550
$106$	−6.09949	−0.592435
$107$	10.9096	1.05467	0.527334	−	0.849658i	$-0.323192\pi$
$107$	10.9096	1.05467	0.527334	+	0.849658i	$0.323192\pi$
$108$	−19.3653	−1.86343
$109$	−3.76001	−0.360144	−0.180072	−	0.983653i	$-0.557633\pi$
$109$	−3.76001	−0.360144	−0.180072	+	0.983653i	$0.557633\pi$
$110$	1.23972	0.118203
$111$	22.5328	2.13872
$112$	4.04655	0.382363
$113$	14.1065	1.32703	0.663516	−	0.748162i	$-0.269064\pi$
$113$	14.1065	1.32703	0.663516	+	0.748162i	$0.269064\pi$
$114$	9.25260	0.866586
$115$	−4.59675	−0.428650
$116$	−7.09742	−0.658979
$117$	−13.4609	−1.24446
$118$	−7.54428	−0.694507
$119$	−20.1542	−1.84754
$120$	−3.73637	−0.341083
$121$	−9.71536	−0.883214
$122$	−11.4723	−1.03865
$123$	−28.0572	−2.52983
$124$	−7.08192	−0.635975
$125$	−9.62930	−0.861271
$126$	35.0796	3.12514
$127$	15.1083	1.34065	0.670323	−	0.742069i	$-0.266156\pi$
$127$	15.1083	1.34065	0.670323	+	0.742069i	$0.266156\pi$
$128$	1.00000	0.0883883
$129$	−23.9289	−2.10682
$130$	−1.69839	−0.148959
$131$	−3.00876	−0.262877	−0.131438	−	0.991324i	$-0.541960\pi$
$131$	−3.00876	−0.262877	−0.131438	+	0.991324i	$0.541960\pi$
$132$	−3.87176	−0.336993
$133$	−10.9605	−0.950400
$134$	5.47712	0.473151
$135$	−21.1815	−1.82301
$136$	−4.98060	−0.427083
$137$	4.53318	0.387295	0.193648	−	0.981071i	$-0.437968\pi$
$137$	4.53318	0.387295	0.193648	+	0.981071i	$0.437968\pi$
$138$	14.3561	1.22207
$139$	−7.15835	−0.607163	−0.303582	−	0.952805i	$-0.598183\pi$
$139$	−7.15835	−0.607163	−0.303582	+	0.952805i	$0.598183\pi$
$140$	4.42607	0.374071
$141$	−3.61057	−0.304064
$142$	−16.2111	−1.36041
$143$	−1.75993	−0.147173
$144$	8.66901	0.722417
$145$	−7.76308	−0.644688
$146$	−12.7058	−1.05154
$147$	−32.0235	−2.64125
$148$	−6.59627	−0.542210
$149$	−10.8796	−0.891294	−0.445647	−	0.895209i	$-0.647026\pi$
$149$	−10.8796	−0.891294	−0.445647	+	0.895209i	$0.647026\pi$
$150$	12.9932	1.06089
$151$	19.4245	1.58074	0.790370	−	0.612630i	$-0.209888\pi$
$151$	19.4245	1.58074	0.790370	+	0.612630i	$0.209888\pi$
$152$	−2.70861	−0.219698
$153$	−43.1768	−3.49064
$154$	4.58645	0.369586
$155$	−7.74612	−0.622183
$156$	5.30423	0.424678
$157$	12.5299	0.999997	0.499999	−	0.866026i	$-0.333334\pi$
$157$	12.5299	0.999997	0.499999	+	0.866026i	$0.333334\pi$
$158$	−4.93886	−0.392915
$159$	20.8358	1.65239
$160$	1.09379	0.0864715
$161$	−17.0060	−1.34026
$162$	40.1446	3.15406
$163$	−8.59053	−0.672863	−0.336431	−	0.941708i	$-0.609220\pi$
$163$	−8.59053	−0.672863	−0.336431	+	0.941708i	$0.609220\pi$
$164$	8.21349	0.641366
$165$	−4.23488	−0.329685
$166$	5.74803	0.446134
$167$	−13.9992	−1.08329	−0.541647	−	0.840606i	$-0.682199\pi$
$167$	−13.9992	−1.08329	−0.541647	+	0.840606i	$0.682199\pi$
$168$	−13.8230	−1.06647
$169$	−10.5889	−0.814533
$170$	−5.44772	−0.417821
$171$	−23.4810	−1.79564
$172$	7.00495	0.534123
$173$	−0.971312	−0.0738475	−0.0369237	−	0.999318i	$-0.511756\pi$
$173$	−0.971312	−0.0738475	−0.0369237	+	0.999318i	$0.511756\pi$
$174$	24.2447	1.83799
$175$	−15.3916	−1.16349
$176$	1.13342	0.0854348
$177$	25.7712	1.93708
$178$	−2.36834	−0.177515
$179$	−13.0292	−0.973845	−0.486923	−	0.873445i	$-0.661881\pi$
$179$	−13.0292	−0.973845	−0.486923	+	0.873445i	$0.661881\pi$
$180$	9.48205	0.706751
$181$	−21.3411	−1.58627	−0.793134	−	0.609047i	$-0.791552\pi$
$181$	−21.3411	−1.58627	−0.793134	+	0.609047i	$0.791552\pi$
$182$	−6.28334	−0.465752
$183$	39.1892	2.89695
$184$	−4.20260	−0.309820
$185$	−7.21492	−0.530452
$186$	24.1918	1.77383
$187$	−5.64511	−0.412811
$188$	1.05696	0.0770867
$189$	−78.3626	−5.70004
$190$	−2.96265	−0.214933
$191$	17.6029	1.27370	0.636850	−	0.770988i	$-0.280237\pi$
$191$	17.6029	1.27370	0.636850	+	0.770988i	$0.280237\pi$
$192$	−3.41599	−0.246528
$193$	−9.13554	−0.657590	−0.328795	−	0.944401i	$-0.606643\pi$
$193$	−9.13554	−0.657590	−0.328795	+	0.944401i	$0.606643\pi$
$194$	−11.0614	−0.794160
$195$	5.80170	0.415468
$196$	9.37458	0.669613
$197$	−4.55363	−0.324432	−0.162216	−	0.986755i	$-0.551864\pi$
$197$	−4.55363	−0.324432	−0.162216	+	0.986755i	$0.551864\pi$
$198$	9.82563	0.698277
$199$	−6.32261	−0.448198	−0.224099	−	0.974566i	$-0.571944\pi$
$199$	−6.32261	−0.448198	−0.224099	+	0.974566i	$0.571944\pi$
$200$	−3.80363	−0.268957
$201$	−18.7098	−1.31969
$202$	13.6007	0.956941
$203$	−28.7201	−2.01576
$204$	17.0137	1.19120
$205$	8.98382	0.627457
$206$	12.8885	0.897987
$207$	−36.4324	−2.53222
$208$	−1.55276	−0.107665
$209$	−3.07000	−0.212356
$210$	−15.1194	−1.04334
$211$	12.2105	0.840603	0.420302	−	0.907384i	$-0.361924\pi$
$211$	12.2105	0.840603	0.420302	+	0.907384i	$0.361924\pi$
$212$	−6.09949	−0.418915
$213$	55.3771	3.79437
$214$	10.9096	0.745763
$215$	7.66193	0.522539
$216$	−19.3653	−1.31764
$217$	−28.6573	−1.94539
$218$	−3.76001	−0.254660
$219$	43.4029	2.93290
$220$	1.23972	0.0835820
$221$	7.73369	0.520224
$222$	22.5328	1.51230
$223$	25.2779	1.69273	0.846367	−	0.532599i	$-0.178785\pi$
$223$	25.2779	1.69273	0.846367	+	0.532599i	$0.178785\pi$
$224$	4.04655	0.270372
$225$	−32.9737	−2.19824
$226$	14.1065	0.938353
$227$	1.47222	0.0977144	0.0488572	−	0.998806i	$-0.484442\pi$
$227$	1.47222	0.0977144	0.0488572	+	0.998806i	$0.484442\pi$
$228$	9.25260	0.612769
$229$	−28.1695	−1.86149	−0.930747	−	0.365664i	$-0.880842\pi$
$229$	−28.1695	−1.86149	−0.930747	+	0.365664i	$0.880842\pi$
$230$	−4.59675	−0.303101
$231$	−15.6673	−1.03083
$232$	−7.09742	−0.465969
$233$	18.4248	1.20705	0.603526	−	0.797343i	$-0.293762\pi$
$233$	18.4248	1.20705	0.603526	+	0.797343i	$0.293762\pi$
$234$	−13.4609	−0.879968
$235$	1.15609	0.0754150
$236$	−7.54428	−0.491091
$237$	16.8711	1.09590
$238$	−20.1542	−1.30641
$239$	20.3838	1.31852	0.659259	−	0.751916i	$-0.270870\pi$
$239$	20.3838	1.31852	0.659259	+	0.751916i	$0.270870\pi$
$240$	−3.73637	−0.241182
$241$	28.0107	1.80433	0.902164	−	0.431393i	$-0.141978\pi$
$241$	28.0107	1.80433	0.902164	+	0.431393i	$0.141978\pi$
$242$	−9.71536	−0.624527
$243$	−79.0380	−5.07029
$244$	−11.4723	−0.734437
$245$	10.2538	0.655092
$246$	−28.0572	−1.78886
$247$	4.20584	0.267611
$248$	−7.08192	−0.449702
$249$	−19.6352	−1.24433
$250$	−9.62930	−0.609011
$251$	7.10623	0.448541	0.224271	−	0.974527i	$-0.428000\pi$
$251$	7.10623	0.448541	0.224271	+	0.974527i	$0.428000\pi$
$252$	35.0796	2.20981
$253$	−4.76331	−0.299467
$254$	15.1083	0.947980
$255$	18.6094	1.16536
$256$	1.00000	0.0625000
$257$	20.4846	1.27779	0.638896	−	0.769293i	$-0.279391\pi$
$257$	20.4846	1.27779	0.638896	+	0.769293i	$0.279391\pi$
$258$	−23.9289	−1.48975
$259$	−26.6922	−1.65857
$260$	−1.69839	−0.105330
$261$	−61.5276	−3.80846
$262$	−3.00876	−0.185882
$263$	16.6743	1.02818	0.514090	−	0.857736i	$-0.328130\pi$
$263$	16.6743	1.02818	0.514090	+	0.857736i	$0.328130\pi$
$264$	−3.87176	−0.238290
$265$	−6.67155	−0.409830
$266$	−10.9605	−0.672034
$267$	8.09024	0.495115
$268$	5.47712	0.334569
$269$	−20.1248	−1.22703	−0.613515	−	0.789683i	$-0.710245\pi$
$269$	−20.1248	−1.22703	−0.613515	+	0.789683i	$0.710245\pi$
$270$	−21.1815	−1.28907
$271$	12.7646	0.775392	0.387696	−	0.921787i	$-0.373271\pi$
$271$	12.7646	0.775392	0.387696	+	0.921787i	$0.373271\pi$
$272$	−4.98060	−0.301993
$273$	21.4638	1.29905
$274$	4.53318	0.273859
$275$	−4.31111	−0.259970
$276$	14.3561	0.864133
$277$	23.0569	1.38535	0.692677	−	0.721248i	$-0.256431\pi$
$277$	23.0569	1.38535	0.692677	+	0.721248i	$0.256431\pi$
$278$	−7.15835	−0.429329
$279$	−61.3932	−3.67551
$280$	4.42607	0.264508
$281$	24.9672	1.48942	0.744710	−	0.667388i	$-0.232588\pi$
$281$	24.9672	1.48942	0.744710	+	0.667388i	$0.232588\pi$
$282$	−3.61057	−0.215006
$283$	−10.4072	−0.618641	−0.309320	−	0.950958i	$-0.600102\pi$
$283$	−10.4072	−0.618641	−0.309320	+	0.950958i	$0.600102\pi$
$284$	−16.2111	−0.961953
$285$	10.1204	0.599480
$286$	−1.75993	−0.104067
$287$	33.2363	1.96188
$288$	8.66901	0.510826
$289$	7.80635	0.459197
$290$	−7.76308	−0.455863
$291$	37.7856	2.21503
$292$	−12.7058	−0.743550
$293$	−26.4575	−1.54566	−0.772831	−	0.634612i	$-0.781160\pi$
$293$	−26.4575	−1.54566	−0.772831	+	0.634612i	$0.781160\pi$
$294$	−32.0235	−1.86765
$295$	−8.25184	−0.480441
$296$	−6.59627	−0.383400
$297$	−21.9490	−1.27361
$298$	−10.8796	−0.630240
$299$	6.52564	0.377388
$300$	12.9932	0.750161
$301$	28.3459	1.63383
$302$	19.4245	1.11775
$303$	−46.4599	−2.66905
$304$	−2.70861	−0.155350
$305$	−12.5482	−0.718510
$306$	−43.1768	−2.46825
$307$	−21.4235	−1.22270	−0.611352	−	0.791359i	$-0.709374\pi$
$307$	−21.4235	−1.22270	−0.611352	+	0.791359i	$0.709374\pi$
$308$	4.58645	0.261337
$309$	−44.0272	−2.50462
$310$	−7.74612	−0.439950
$311$	10.8681	0.616276	0.308138	−	0.951342i	$-0.400294\pi$
$311$	10.8681	0.616276	0.308138	+	0.951342i	$0.400294\pi$
$312$	5.30423	0.300293
$313$	10.1928	0.576134	0.288067	−	0.957610i	$-0.406987\pi$
$313$	10.1928	0.576134	0.288067	+	0.957610i	$0.406987\pi$
$314$	12.5299	0.707105
$315$	38.3696	2.16188
$316$	−4.93886	−0.277833
$317$	27.7028	1.55595	0.777973	−	0.628298i	$-0.216248\pi$
$317$	27.7028	1.55595	0.777973	+	0.628298i	$0.216248\pi$
$318$	20.8358	1.16841
$319$	−8.04436	−0.450398
$320$	1.09379	0.0611446
$321$	−37.2670	−2.08004
$322$	−17.0060	−0.947710
$323$	13.4905	0.750632
$324$	40.1446	2.23026
$325$	5.90613	0.327613
$326$	−8.59053	−0.475786
$327$	12.8442	0.710284
$328$	8.21349	0.453514
$329$	4.27704	0.235801
$330$	−4.23488	−0.233123
$331$	−0.635642	−0.0349381	−0.0174690	−	0.999847i	$-0.505561\pi$
$331$	−0.635642	−0.0349381	−0.0174690	+	0.999847i	$0.505561\pi$
$332$	5.74803	0.315464
$333$	−57.1831	−3.13362
$334$	−13.9992	−0.766004
$335$	5.99081	0.327313
$336$	−13.8230	−0.754106
$337$	−20.9115	−1.13912	−0.569562	−	0.821948i	$-0.692887\pi$
$337$	−20.9115	−1.13912	−0.569562	+	0.821948i	$0.692887\pi$
$338$	−10.5889	−0.575962
$339$	−48.1878	−2.61720
$340$	−5.44772	−0.295444
$341$	−8.02679	−0.434675
$342$	−23.4810	−1.26971
$343$	9.60887	0.518830
$344$	7.00495	0.377682
$345$	15.7025	0.845393
$346$	−0.971312	−0.0522180
$347$	29.8853	1.60433	0.802164	−	0.597103i	$-0.203682\pi$
$347$	29.8853	1.60433	0.802164	+	0.597103i	$0.203682\pi$
$348$	24.2447	1.29965
$349$	−20.5804	−1.10164	−0.550821	−	0.834623i	$-0.685685\pi$
$349$	−20.5804	−1.10164	−0.550821	+	0.834623i	$0.685685\pi$
$350$	−15.3916	−0.822714
$351$	30.0697	1.60500
$352$	1.13342	0.0604115
$353$	−12.0332	−0.640463	−0.320231	−	0.947339i	$-0.603761\pi$
$353$	−12.0332	−0.640463	−0.320231	+	0.947339i	$0.603761\pi$
$354$	25.7712	1.36972
$355$	−17.7315	−0.941092
$356$	−2.36834	−0.125522
$357$	68.8468	3.64376
$358$	−13.0292	−0.688612
$359$	−22.8012	−1.20340	−0.601699	−	0.798723i	$-0.705510\pi$
$359$	−22.8012	−1.20340	−0.601699	+	0.798723i	$0.705510\pi$
$360$	9.48205	0.499748
$361$	−11.6634	−0.613864
$362$	−21.3411	−1.12166
$363$	33.1876	1.74190
$364$	−6.28334	−0.329336
$365$	−13.8974	−0.727425
$366$	39.1892	2.04845
$367$	14.0527	0.733543	0.366772	−	0.930311i	$-0.380463\pi$
$367$	14.0527	0.733543	0.366772	+	0.930311i	$0.380463\pi$
$368$	−4.20260	−0.219076
$369$	71.2028	3.70667
$370$	−7.21492	−0.375086
$371$	−24.6819	−1.28142
$372$	24.1918	1.25429
$373$	14.3392	0.742457	0.371228	−	0.928542i	$-0.378937\pi$
$373$	14.3392	0.742457	0.371228	+	0.928542i	$0.378937\pi$
$374$	−5.64511	−0.291902
$375$	32.8936	1.69862
$376$	1.05696	0.0545085
$377$	11.0206	0.567591
$378$	−78.3626	−4.03054
$379$	−7.18333	−0.368983	−0.184491	−	0.982834i	$-0.559064\pi$
$379$	−7.18333	−0.368983	−0.184491	+	0.982834i	$0.559064\pi$
$380$	−2.96265	−0.151981
$381$	−51.6099	−2.64405
$382$	17.6029	0.900642
$383$	13.7133	0.700719	0.350359	−	0.936615i	$-0.386059\pi$
$383$	13.7133	0.700719	0.350359	+	0.936615i	$0.386059\pi$
$384$	−3.41599	−0.174322
$385$	5.01660	0.255670
$386$	−9.13554	−0.464987
$387$	60.7260	3.08687
$388$	−11.0614	−0.561556
$389$	1.22656	0.0621888	0.0310944	−	0.999516i	$-0.490101\pi$
$389$	1.22656	0.0621888	0.0310944	+	0.999516i	$0.490101\pi$
$390$	5.80170	0.293781
$391$	20.9315	1.05855
$392$	9.37458	0.473488
$393$	10.2779	0.518452
$394$	−4.55363	−0.229408
$395$	−5.40207	−0.271808
$396$	9.82563	0.493756
$397$	−8.04480	−0.403757	−0.201878	−	0.979411i	$-0.564705\pi$
$397$	−8.04480	−0.403757	−0.201878	+	0.979411i	$0.564705\pi$
$398$	−6.32261	−0.316924
$399$	37.4411	1.87440
$400$	−3.80363	−0.190181
$401$	−11.1712	−0.557862	−0.278931	−	0.960311i	$-0.589980\pi$
$401$	−11.1712	−0.557862	−0.278931	+	0.960311i	$0.589980\pi$
$402$	−18.7098	−0.933161
$403$	10.9965	0.547777
$404$	13.6007	0.676660
$405$	43.9097	2.18189
$406$	−28.7201	−1.42535
$407$	−7.47635	−0.370589
$408$	17.0137	0.842303
$409$	−28.8015	−1.42414	−0.712071	−	0.702108i	$-0.752243\pi$
$409$	−28.8015	−1.42414	−0.712071	+	0.702108i	$0.752243\pi$
$410$	8.98382	0.443679
$411$	−15.4853	−0.763834
$412$	12.8885	0.634973
$413$	−30.5283	−1.50220
$414$	−36.4324	−1.79055
$415$	6.28712	0.308623
$416$	−1.55276	−0.0761305
$417$	24.4529	1.19746
$418$	−3.07000	−0.150159
$419$	−16.8539	−0.823365	−0.411682	−	0.911327i	$-0.635059\pi$
$419$	−16.8539	−0.823365	−0.411682	+	0.911327i	$0.635059\pi$
$420$	−15.1194	−0.737752
$421$	−8.83940	−0.430806	−0.215403	−	0.976525i	$-0.569106\pi$
$421$	−8.83940	−0.430806	−0.215403	+	0.976525i	$0.569106\pi$
$422$	12.2105	0.594396
$423$	9.16279	0.445510
$424$	−6.09949	−0.296217
$425$	18.9443	0.918935
$426$	55.3771	2.68303
$427$	−46.4231	−2.24657
$428$	10.9096	0.527334
$429$	6.01192	0.290258
$430$	7.66193	0.369491
$431$	−13.1631	−0.634046	−0.317023	−	0.948418i	$-0.602683\pi$
$431$	−13.1631	−0.634046	−0.317023	+	0.948418i	$0.602683\pi$
$432$	−19.3653	−0.931713
$433$	−34.2473	−1.64582	−0.822911	−	0.568170i	$-0.807652\pi$
$433$	−34.2473	−1.64582	−0.822911	+	0.568170i	$0.807652\pi$
$434$	−28.6573	−1.37560
$435$	26.5186	1.27147
$436$	−3.76001	−0.180072
$437$	11.3832	0.544533
$438$	43.4029	2.07387
$439$	22.4881	1.07330	0.536650	−	0.843805i	$-0.319690\pi$
$439$	22.4881	1.07330	0.536650	+	0.843805i	$0.319690\pi$
$440$	1.23972	0.0591014
$441$	81.2683	3.86992
$442$	7.73369	0.367854
$443$	−14.9799	−0.711715	−0.355858	−	0.934540i	$-0.615811\pi$
$443$	−14.9799	−0.711715	−0.355858	+	0.934540i	$0.615811\pi$
$444$	22.5328	1.06936
$445$	−2.59047	−0.122800
$446$	25.2779	1.19694
$447$	37.1647	1.75783
$448$	4.04655	0.191182
$449$	32.2781	1.52330	0.761649	−	0.647990i	$-0.224390\pi$
$449$	32.2781	1.52330	0.761649	+	0.647990i	$0.224390\pi$
$450$	−32.9737	−1.55439
$451$	9.30934	0.438360
$452$	14.1065	0.663516
$453$	−66.3538	−3.11757
$454$	1.47222	0.0690945
$455$	−6.87264	−0.322194
$456$	9.25260	0.433293
$457$	26.9120	1.25889	0.629444	−	0.777046i	$-0.283283\pi$
$457$	26.9120	1.25889	0.629444	+	0.777046i	$0.283283\pi$
$458$	−28.1695	−1.31627
$459$	96.4507	4.50193
$460$	−4.59675	−0.214325
$461$	−7.22237	−0.336379	−0.168190	−	0.985755i	$-0.553792\pi$
$461$	−7.22237	−0.336379	−0.168190	+	0.985755i	$0.553792\pi$
$462$	−15.6673	−0.728907
$463$	15.8570	0.736937	0.368469	−	0.929640i	$-0.379882\pi$
$463$	15.8570	0.736937	0.368469	+	0.929640i	$0.379882\pi$
$464$	−7.09742	−0.329490
$465$	26.4607	1.22708
$466$	18.4248	0.853514
$467$	9.30631	0.430645	0.215322	−	0.976543i	$-0.430920\pi$
$467$	9.30631	0.430645	0.215322	+	0.976543i	$0.430920\pi$
$468$	−13.4609	−0.622231
$469$	22.1635	1.02341
$470$	1.15609	0.0533264
$471$	−42.8022	−1.97222
$472$	−7.54428	−0.347254
$473$	7.93956	0.365061
$474$	16.8711	0.774916
$475$	10.3026	0.472714
$476$	−20.1542	−0.923768
$477$	−52.8765	−2.42105
$478$	20.3838	0.932334
$479$	24.7599	1.13131	0.565655	−	0.824642i	$-0.308623\pi$
$479$	24.7599	1.13131	0.565655	+	0.824642i	$0.308623\pi$
$480$	−3.73637	−0.170541
$481$	10.2424	0.467015
$482$	28.0107	1.27585
$483$	58.0925	2.64330
$484$	−9.71536	−0.441607
$485$	−12.0988	−0.549378
$486$	−79.0380	−3.58523
$487$	−24.7018	−1.11935	−0.559673	−	0.828714i	$-0.689073\pi$
$487$	−24.7018	−1.11935	−0.559673	+	0.828714i	$0.689073\pi$
$488$	−11.4723	−0.519325
$489$	29.3452	1.32704
$490$	10.2538	0.463220
$491$	−27.1071	−1.22333	−0.611664	−	0.791118i	$-0.709499\pi$
$491$	−27.1071	−1.22333	−0.611664	+	0.791118i	$0.709499\pi$
$492$	−28.0572	−1.26492
$493$	35.3494	1.59206
$494$	4.20584	0.189230
$495$	10.7472	0.483049
$496$	−7.08192	−0.317987
$497$	−65.5991	−2.94252
$498$	−19.6352	−0.879875
$499$	31.3018	1.40126	0.700630	−	0.713525i	$-0.252903\pi$
$499$	31.3018	1.40126	0.700630	+	0.713525i	$0.252903\pi$
$500$	−9.62930	−0.430635
$501$	47.8213	2.13650
$502$	7.10623	0.317167
$503$	14.0311	0.625614	0.312807	−	0.949817i	$-0.398731\pi$
$503$	14.0311	0.625614	0.312807	+	0.949817i	$0.398731\pi$
$504$	35.0796	1.56257
$505$	14.8763	0.661986
$506$	−4.76331	−0.211755
$507$	36.1717	1.60644
$508$	15.1083	0.670323
$509$	−11.8872	−0.526892	−0.263446	−	0.964674i	$-0.584859\pi$
$509$	−11.8872	−0.526892	−0.263446	+	0.964674i	$0.584859\pi$
$510$	18.6094	0.824036
$511$	−51.4146	−2.27445
$512$	1.00000	0.0441942
$513$	52.4531	2.31586
$514$	20.4846	0.903536
$515$	14.0973	0.621203
$516$	−23.9289	−1.05341
$517$	1.19798	0.0526871
$518$	−26.6922	−1.17279
$519$	3.31799	0.145644
$520$	−1.69839	−0.0744795
$521$	−8.76885	−0.384170	−0.192085	−	0.981378i	$-0.561525\pi$
$521$	−8.76885	−0.384170	−0.192085	+	0.981378i	$0.561525\pi$
$522$	−61.5276	−2.69299
$523$	−15.6168	−0.682876	−0.341438	−	0.939904i	$-0.610914\pi$
$523$	−15.6168	−0.682876	−0.341438	+	0.939904i	$0.610914\pi$
$524$	−3.00876	−0.131438
$525$	52.5775	2.29467
$526$	16.6743	0.727033
$527$	35.2722	1.53648
$528$	−3.87176	−0.168497
$529$	−5.33815	−0.232093
$530$	−6.67155	−0.289793
$531$	−65.4014	−2.83818
$532$	−10.9605	−0.475200
$533$	−12.7536	−0.552420
$534$	8.09024	0.350099
$535$	11.9328	0.515898
$536$	5.47712	0.236576
$537$	44.5075	1.92064
$538$	−20.1248	−0.867642
$539$	10.6253	0.457666
$540$	−21.1815	−0.911507
$541$	18.2069	0.782777	0.391388	−	0.920226i	$-0.371995\pi$
$541$	18.2069	0.782777	0.391388	+	0.920226i	$0.371995\pi$
$542$	12.7646	0.548285
$543$	72.9009	3.12848
$544$	−4.98060	−0.213541
$545$	−4.11266	−0.176167
$546$	21.4638	0.918567
$547$	−40.2232	−1.71982	−0.859910	−	0.510445i	$-0.829481\pi$
$547$	−40.2232	−1.71982	−0.859910	+	0.510445i	$0.829481\pi$
$548$	4.53318	0.193648
$549$	−99.4532	−4.24456
$550$	−4.31111	−0.183826
$551$	19.2242	0.818977
$552$	14.3561	0.611034
$553$	−19.9854	−0.849864
$554$	23.0569	0.979593
$555$	24.6461	1.04617
$556$	−7.15835	−0.303582
$557$	10.4978	0.444808	0.222404	−	0.974955i	$-0.428610\pi$
$557$	10.4978	0.444808	0.222404	+	0.974955i	$0.428610\pi$
$558$	−61.3932	−2.59898
$559$	−10.8770	−0.460050
$560$	4.42607	0.187036
$561$	19.2837	0.814157
$562$	24.9672	1.05318
$563$	−29.5764	−1.24650	−0.623249	−	0.782024i	$-0.714188\pi$
$563$	−29.5764	−1.24650	−0.623249	+	0.782024i	$0.714188\pi$
$564$	−3.61057	−0.152032
$565$	15.4296	0.649126
$566$	−10.4072	−0.437445
$567$	162.447	6.82215
$568$	−16.2111	−0.680203
$569$	−24.2436	−1.01634	−0.508172	−	0.861256i	$-0.669678\pi$
$569$	−24.2436	−1.01634	−0.508172	+	0.861256i	$0.669678\pi$
$570$	10.1204	0.423896
$571$	7.69358	0.321966	0.160983	−	0.986957i	$-0.448534\pi$
$571$	7.69358	0.321966	0.160983	+	0.986957i	$0.448534\pi$
$572$	−1.75993	−0.0735865
$573$	−60.1313	−2.51202
$574$	33.2363	1.38726
$575$	15.9851	0.666626
$576$	8.66901	0.361209
$577$	1.72988	0.0720160	0.0360080	−	0.999352i	$-0.488536\pi$
$577$	1.72988	0.0720160	0.0360080	+	0.999352i	$0.488536\pi$
$578$	7.80635	0.324701
$579$	31.2069	1.29692
$580$	−7.76308	−0.322344
$581$	23.2597	0.964975
$582$	37.7856	1.56626
$583$	−6.91329	−0.286319
$584$	−12.7058	−0.525769
$585$	−14.7234	−0.608737
$586$	−26.4575	−1.09295
$587$	−21.5068	−0.887682	−0.443841	−	0.896105i	$-0.646385\pi$
$587$	−21.5068	−0.887682	−0.443841	+	0.896105i	$0.646385\pi$
$588$	−32.0235	−1.32063
$589$	19.1822	0.790388
$590$	−8.25184	−0.339723
$591$	15.5552	0.639854
$592$	−6.59627	−0.271105
$593$	−31.1657	−1.27982	−0.639911	−	0.768449i	$-0.721029\pi$
$593$	−31.1657	−1.27982	−0.639911	+	0.768449i	$0.721029\pi$
$594$	−21.9490	−0.900579
$595$	−22.0445	−0.903735
$596$	−10.8796	−0.445647
$597$	21.5980	0.883946
$598$	6.52564	0.266853
$599$	−4.27013	−0.174473	−0.0872363	−	0.996188i	$-0.527804\pi$
$599$	−4.27013	−0.174473	−0.0872363	+	0.996188i	$0.527804\pi$
$600$	12.9932	0.530444
$601$	−47.0374	−1.91869	−0.959347	−	0.282228i	$-0.908927\pi$
$601$	−47.0374	−1.91869	−0.959347	+	0.282228i	$0.908927\pi$
$602$	28.3459	1.15529
$603$	47.4812	1.93358
$604$	19.4245	0.790370
$605$	−10.6265	−0.432030
$606$	−46.4599	−1.88730
$607$	−35.1591	−1.42706	−0.713531	−	0.700623i	$-0.752905\pi$
$607$	−35.1591	−1.42706	−0.713531	+	0.700623i	$0.752905\pi$
$608$	−2.70861	−0.109849
$609$	98.1076	3.97552
$610$	−12.5482	−0.508063
$611$	−1.64121	−0.0663962
$612$	−43.1768	−1.74532
$613$	−19.9222	−0.804652	−0.402326	−	0.915496i	$-0.631798\pi$
$613$	−19.9222	−0.804652	−0.402326	+	0.915496i	$0.631798\pi$
$614$	−21.4235	−0.864583
$615$	−30.6887	−1.23749
$616$	4.58645	0.184793
$617$	0.913958	0.0367946	0.0183973	−	0.999831i	$-0.494144\pi$
$617$	0.913958	0.0367946	0.0183973	+	0.999831i	$0.494144\pi$
$618$	−44.0272	−1.77103
$619$	42.1797	1.69535	0.847673	−	0.530519i	$-0.178003\pi$
$619$	42.1797	1.69535	0.847673	+	0.530519i	$0.178003\pi$
$620$	−7.74612	−0.311092
$621$	81.3845	3.26585
$622$	10.8681	0.435773
$623$	−9.58362	−0.383960
$624$	5.30423	0.212339
$625$	8.48572	0.339429
$626$	10.1928	0.407388
$627$	10.4871	0.418814
$628$	12.5299	0.499999
$629$	32.8534	1.30995
$630$	38.3696	1.52868
$631$	−10.2561	−0.408288	−0.204144	−	0.978941i	$-0.565441\pi$
$631$	−10.2561	−0.408288	−0.204144	+	0.978941i	$0.565441\pi$
$632$	−4.93886	−0.196457
$633$	−41.7109	−1.65786
$634$	27.7028	1.10022
$635$	16.5253	0.655786
$636$	20.8358	0.826193
$637$	−14.5565	−0.576750
$638$	−8.04436	−0.318479
$639$	−140.534	−5.55945
$640$	1.09379	0.0432358
$641$	−2.17445	−0.0858857	−0.0429428	−	0.999078i	$-0.513673\pi$
$641$	−2.17445	−0.0858857	−0.0429428	+	0.999078i	$0.513673\pi$
$642$	−37.2670	−1.47081
$643$	−0.917471	−0.0361815	−0.0180908	−	0.999836i	$-0.505759\pi$
$643$	−0.917471	−0.0361815	−0.0180908	+	0.999836i	$0.505759\pi$
$644$	−17.0060	−0.670132
$645$	−26.1731	−1.03056
$646$	13.4905	0.530777
$647$	33.7090	1.32524	0.662619	−	0.748957i	$-0.269445\pi$
$647$	33.7090	1.32524	0.662619	+	0.748957i	$0.269445\pi$
$648$	40.1446	1.57703
$649$	−8.55084	−0.335650
$650$	5.90613	0.231658
$651$	97.8933	3.83674
$652$	−8.59053	−0.336431
$653$	−12.3529	−0.483406	−0.241703	−	0.970350i	$-0.577706\pi$
$653$	−12.3529	−0.483406	−0.241703	+	0.970350i	$0.577706\pi$
$654$	12.8442	0.502247
$655$	−3.29095	−0.128588
$656$	8.21349	0.320683
$657$	−110.147	−4.29723
$658$	4.27704	0.166736
$659$	7.25377	0.282567	0.141283	−	0.989969i	$-0.454877\pi$
$659$	7.25377	0.282567	0.141283	+	0.989969i	$0.454877\pi$
$660$	−4.23488	−0.164843
$661$	34.9994	1.36132	0.680660	−	0.732600i	$-0.261693\pi$
$661$	34.9994	1.36132	0.680660	+	0.732600i	$0.261693\pi$
$662$	−0.635642	−0.0247049
$663$	−26.4182	−1.02600
$664$	5.74803	0.223067
$665$	−11.9885	−0.464895
$666$	−57.1831	−2.21580
$667$	29.8276	1.15493
$668$	−13.9992	−0.541647
$669$	−86.3492	−3.33845
$670$	5.99081	0.231445
$671$	−13.0029	−0.501972
$672$	−13.8230	−0.533233
$673$	−19.5528	−0.753705	−0.376852	−	0.926273i	$-0.622994\pi$
$673$	−19.5528	−0.753705	−0.376852	+	0.926273i	$0.622994\pi$
$674$	−20.9115	−0.805483
$675$	73.6583	2.83511
$676$	−10.5889	−0.407266
$677$	−25.2986	−0.972305	−0.486153	−	0.873874i	$-0.661600\pi$
$677$	−25.2986	−0.972305	−0.486153	+	0.873874i	$0.661600\pi$
$678$	−48.1878	−1.85064
$679$	−44.7604	−1.71775
$680$	−5.44772	−0.208910
$681$	−5.02908	−0.192715
$682$	−8.02679	−0.307362
$683$	18.3962	0.703909	0.351955	−	0.936017i	$-0.385517\pi$
$683$	18.3962	0.703909	0.351955	+	0.936017i	$0.385517\pi$
$684$	−23.4810	−0.897818
$685$	4.95833	0.189448
$686$	9.60887	0.366868
$687$	96.2269	3.67128
$688$	7.00495	0.267061
$689$	9.47106	0.360819
$690$	15.7025	0.597783
$691$	−14.3491	−0.545864	−0.272932	−	0.962033i	$-0.587993\pi$
$691$	−14.3491	−0.545864	−0.272932	+	0.962033i	$0.587993\pi$
$692$	−0.971312	−0.0369237
$693$	39.7599	1.51035
$694$	29.8853	1.13443
$695$	−7.82972	−0.296998
$696$	24.2447	0.918995
$697$	−40.9081	−1.54950
$698$	−20.5804	−0.778978
$699$	−62.9391	−2.38058
$700$	−15.3916	−0.581747
$701$	−9.43385	−0.356311	−0.178156	−	0.984002i	$-0.557013\pi$
$701$	−9.43385	−0.356311	−0.178156	+	0.984002i	$0.557013\pi$
$702$	30.0697	1.13491
$703$	17.8667	0.673857
$704$	1.13342	0.0427174
$705$	−3.94919	−0.148735
$706$	−12.0332	−0.452876
$707$	55.0359	2.06984
$708$	25.7712	0.968541
$709$	49.8921	1.87374	0.936869	−	0.349680i	$-0.113710\pi$
$709$	49.8921	1.87374	0.936869	+	0.349680i	$0.113710\pi$
$710$	−17.7315	−0.665452
$711$	−42.8150	−1.60569
$712$	−2.36834	−0.0887574
$713$	29.7625	1.11461
$714$	68.8468	2.57652
$715$	−1.92499	−0.0719907
$716$	−13.0292	−0.486923
$717$	−69.6309	−2.60041
$718$	−22.8012	−0.850932
$719$	−8.06315	−0.300705	−0.150352	−	0.988632i	$-0.548041\pi$
$719$	−8.06315	−0.300705	−0.150352	+	0.988632i	$0.548041\pi$
$720$	9.48205	0.353375
$721$	52.1542	1.94232
$722$	−11.6634	−0.434067
$723$	−95.6843	−3.55854
$724$	−21.3411	−0.793134
$725$	26.9960	1.00260
$726$	33.1876	1.23171
$727$	−13.9705	−0.518136	−0.259068	−	0.965859i	$-0.583415\pi$
$727$	−13.9705	−0.518136	−0.259068	+	0.965859i	$0.583415\pi$
$728$	−6.28334	−0.232876
$729$	149.559	5.53923
$730$	−13.8974	−0.514367
$731$	−34.8888	−1.29041
$732$	39.1892	1.44847
$733$	6.14863	0.227105	0.113552	−	0.993532i	$-0.463777\pi$
$733$	6.14863	0.227105	0.113552	+	0.993532i	$0.463777\pi$
$734$	14.0527	0.518693
$735$	−35.0269	−1.29199
$736$	−4.20260	−0.154910
$737$	6.20789	0.228670
$738$	71.2028	2.62101
$739$	−23.8808	−0.878469	−0.439235	−	0.898372i	$-0.644750\pi$
$739$	−23.8808	−0.878469	−0.439235	+	0.898372i	$0.644750\pi$
$740$	−7.21492	−0.265226
$741$	−14.3671	−0.527789
$742$	−24.6819	−0.906101
$743$	13.1548	0.482604	0.241302	−	0.970450i	$-0.422426\pi$
$743$	13.1548	0.482604	0.241302	+	0.970450i	$0.422426\pi$
$744$	24.1918	0.886914
$745$	−11.9000	−0.435983
$746$	14.3392	0.524996
$747$	49.8297	1.82317
$748$	−5.64511	−0.206406
$749$	44.1461	1.61306
$750$	32.8936	1.20111
$751$	−9.47827	−0.345867	−0.172933	−	0.984934i	$-0.555325\pi$
$751$	−9.47827	−0.345867	−0.172933	+	0.984934i	$0.555325\pi$
$752$	1.05696	0.0385433
$753$	−24.2748	−0.884624
$754$	11.0206	0.401347
$755$	21.2462	0.773230
$756$	−78.3626	−2.85002
$757$	−26.2504	−0.954085	−0.477043	−	0.878880i	$-0.658291\pi$
$757$	−26.2504	−0.954085	−0.477043	+	0.878880i	$0.658291\pi$
$758$	−7.18333	−0.260910
$759$	16.2714	0.590616
$760$	−2.96265	−0.107467
$761$	28.2982	1.02581	0.512904	−	0.858446i	$-0.328570\pi$
$761$	28.2982	1.02581	0.512904	+	0.858446i	$0.328570\pi$
$762$	−51.6099	−1.86963
$763$	−15.2151	−0.550823
$764$	17.6029	0.636850
$765$	−47.2263	−1.70747
$766$	13.7133	0.495483
$767$	11.7145	0.422985
$768$	−3.41599	−0.123264
$769$	−34.1902	−1.23293	−0.616465	−	0.787382i	$-0.711436\pi$
$769$	−34.1902	−1.23293	−0.616465	+	0.787382i	$0.711436\pi$
$770$	5.01660	0.180786
$771$	−69.9751	−2.52009
$772$	−9.13554	−0.328795
$773$	39.8895	1.43473	0.717364	−	0.696699i	$-0.245349\pi$
$773$	39.8895	1.43473	0.717364	+	0.696699i	$0.245349\pi$
$774$	60.7260	2.18275
$775$	26.9370	0.967605
$776$	−11.0614	−0.397080
$777$	91.1802	3.27107
$778$	1.22656	0.0439742
$779$	−22.2472	−0.797088
$780$	5.80170	0.207734
$781$	−18.3740	−0.657474
$782$	20.9315	0.748507
$783$	137.444	4.91183
$784$	9.37458	0.334807
$785$	13.7051	0.489156
$786$	10.2779	0.366601
$787$	33.1707	1.18241	0.591203	−	0.806523i	$-0.298653\pi$
$787$	33.1707	1.18241	0.591203	+	0.806523i	$0.298653\pi$
$788$	−4.55363	−0.162216
$789$	−56.9592	−2.02780
$790$	−5.40207	−0.192197
$791$	57.0828	2.02963
$792$	9.82563	0.349139
$793$	17.8137	0.632584
$794$	−8.04480	−0.285499
$795$	22.7900	0.808276
$796$	−6.32261	−0.224099
$797$	3.27315	0.115941	0.0579705	−	0.998318i	$-0.481537\pi$
$797$	3.27315	0.115941	0.0579705	+	0.998318i	$0.481537\pi$
$798$	37.4411	1.32540
$799$	−5.26429	−0.186237
$800$	−3.80363	−0.134479
$801$	−20.5312	−0.725434
$802$	−11.1712	−0.394468
$803$	−14.4010	−0.508200
$804$	−18.7098	−0.659844
$805$	−18.6010	−0.655599
$806$	10.9965	0.387337
$807$	68.7462	2.41998
$808$	13.6007	0.478471
$809$	12.2151	0.429460	0.214730	−	0.976673i	$-0.431113\pi$
$809$	12.2151	0.429460	0.214730	+	0.976673i	$0.431113\pi$
$810$	43.9097	1.54283
$811$	−40.7592	−1.43125	−0.715625	−	0.698485i	$-0.753858\pi$
$811$	−40.7592	−1.43125	−0.715625	+	0.698485i	$0.753858\pi$
$812$	−28.7201	−1.00788
$813$	−43.6036	−1.52925
$814$	−7.47635	−0.262046
$815$	−9.39622	−0.329135
$816$	17.0137	0.595598
$817$	−18.9737	−0.663806
$818$	−28.8015	−1.00702
$819$	−54.4703	−1.90335
$820$	8.98382	0.313728
$821$	18.1488	0.633398	0.316699	−	0.948526i	$-0.397426\pi$
$821$	18.1488	0.633398	0.316699	+	0.948526i	$0.397426\pi$
$822$	−15.4853	−0.540112
$823$	39.3156	1.37046	0.685228	−	0.728328i	$-0.259702\pi$
$823$	39.3156	1.37046	0.685228	+	0.728328i	$0.259702\pi$
$824$	12.8885	0.448994
$825$	14.7267	0.512719
$826$	−30.5283	−1.06222
$827$	−38.5514	−1.34056	−0.670282	−	0.742107i	$-0.733827\pi$
$827$	−38.5514	−1.34056	−0.670282	+	0.742107i	$0.733827\pi$
$828$	−36.4324	−1.26611
$829$	3.15330	0.109519	0.0547594	−	0.998500i	$-0.482561\pi$
$829$	3.15330	0.109519	0.0547594	+	0.998500i	$0.482561\pi$
$830$	6.28712	0.218229
$831$	−78.7621	−2.73223
$832$	−1.55276	−0.0538324
$833$	−46.6910	−1.61775
$834$	24.4529	0.846734
$835$	−15.3122	−0.529901
$836$	−3.07000	−0.106178
$837$	137.143	4.74037
$838$	−16.8539	−0.582207
$839$	−11.7210	−0.404655	−0.202327	−	0.979318i	$-0.564850\pi$
$839$	−11.7210	−0.404655	−0.202327	+	0.979318i	$0.564850\pi$
$840$	−15.1194	−0.521670
$841$	21.3734	0.737014
$842$	−8.83940	−0.304626
$843$	−85.2879	−2.93747
$844$	12.2105	0.420302
$845$	−11.5820	−0.398434
$846$	9.16279	0.315023
$847$	−39.3137	−1.35083
$848$	−6.09949	−0.209457
$849$	35.5508	1.22010
$850$	18.9443	0.649785
$851$	27.7215	0.950280
$852$	55.3771	1.89719
$853$	−9.66093	−0.330784	−0.165392	−	0.986228i	$-0.552889\pi$
$853$	−9.66093	−0.330784	−0.165392	+	0.986228i	$0.552889\pi$
$854$	−46.4231	−1.58857
$855$	−25.6832	−0.878348
$856$	10.9096	0.372881
$857$	24.2694	0.829025	0.414513	−	0.910044i	$-0.363952\pi$
$857$	24.2694	0.829025	0.414513	+	0.910044i	$0.363952\pi$
$858$	6.01192	0.205244
$859$	5.09777	0.173934	0.0869668	−	0.996211i	$-0.472283\pi$
$859$	5.09777	0.173934	0.0869668	+	0.996211i	$0.472283\pi$
$860$	7.66193	0.261270
$861$	−113.535	−3.86926
$862$	−13.1631	−0.448338
$863$	−17.2683	−0.587819	−0.293909	−	0.955833i	$-0.594956\pi$
$863$	−17.2683	−0.587819	−0.293909	+	0.955833i	$0.594956\pi$
$864$	−19.3653	−0.658820
$865$	−1.06241	−0.0361230
$866$	−34.2473	−1.16377
$867$	−26.6664	−0.905639
$868$	−28.6573	−0.972694
$869$	−5.59781	−0.189893
$870$	26.5186	0.899065
$871$	−8.50468	−0.288170
$872$	−3.76001	−0.127330
$873$	−95.8911	−3.24542
$874$	11.3832	0.385043
$875$	−38.9655	−1.31727
$876$	43.4029	1.46645
$877$	−3.43646	−0.116041	−0.0580204	−	0.998315i	$-0.518479\pi$
$877$	−3.43646	−0.116041	−0.0580204	+	0.998315i	$0.518479\pi$
$878$	22.4881	0.758938
$879$	90.3785	3.04839
$880$	1.23972	0.0417910
$881$	−5.40612	−0.182137	−0.0910683	−	0.995845i	$-0.529028\pi$
$881$	−5.40612	−0.182137	−0.0910683	+	0.995845i	$0.529028\pi$
$882$	81.2683	2.73645
$883$	4.74549	0.159699	0.0798493	−	0.996807i	$-0.474556\pi$
$883$	4.74549	0.159699	0.0798493	+	0.996807i	$0.474556\pi$
$884$	7.73369	0.260112
$885$	28.1882	0.947537
$886$	−14.9799	−0.503259
$887$	12.2205	0.410324	0.205162	−	0.978728i	$-0.434228\pi$
$887$	12.2205	0.410324	0.205162	+	0.978728i	$0.434228\pi$
$888$	22.5328	0.756152
$889$	61.1366	2.05046
$890$	−2.59047	−0.0868326
$891$	45.5008	1.52433
$892$	25.2779	0.846367
$893$	−2.86289	−0.0958031
$894$	37.1647	1.24297
$895$	−14.2511	−0.476363
$896$	4.04655	0.135186
$897$	−22.2916	−0.744293
$898$	32.2781	1.07713
$899$	50.2634	1.67638
$900$	−32.9737	−1.09912
$901$	30.3791	1.01207
$902$	9.30934	0.309967
$903$	−96.8294	−3.22228
$904$	14.1065	0.469176
$905$	−23.3426	−0.775934
$906$	−66.3538	−2.20446
$907$	−0.152660	−0.00506898	−0.00253449	−	0.999997i	$-0.500807\pi$
$907$	−0.152660	−0.00506898	−0.00253449	+	0.999997i	$0.500807\pi$
$908$	1.47222	0.0488572
$909$	117.904	3.91065
$910$	−6.87264	−0.227826
$911$	−17.0109	−0.563597	−0.281799	−	0.959474i	$-0.590931\pi$
$911$	−17.0109	−0.563597	−0.281799	+	0.959474i	$0.590931\pi$
$912$	9.25260	0.306384
$913$	6.51493	0.215613
$914$	26.9120	0.890168
$915$	42.8647	1.41706
$916$	−28.1695	−0.930747
$917$	−12.1751	−0.402058
$918$	96.4507	3.18335
$919$	9.33837	0.308044	0.154022	−	0.988067i	$-0.450777\pi$
$919$	9.33837	0.308044	0.154022	+	0.988067i	$0.450777\pi$
$920$	−4.59675	−0.151550
$921$	73.1826	2.41145
$922$	−7.22237	−0.237856
$923$	25.1720	0.828548
$924$	−15.6673	−0.515415
$925$	25.0898	0.824946
$926$	15.8570	0.521093
$927$	111.731	3.66972
$928$	−7.09742	−0.232984
$929$	52.2351	1.71378	0.856889	−	0.515500i	$-0.172394\pi$
$929$	52.2351	1.71378	0.856889	+	0.515500i	$0.172394\pi$
$930$	26.4607	0.867680
$931$	−25.3921	−0.832193
$932$	18.4248	0.603526
$933$	−37.1255	−1.21543
$934$	9.30631	0.304512
$935$	−6.17455	−0.201930
$936$	−13.4609	−0.439984
$937$	−47.5098	−1.55208	−0.776038	−	0.630686i	$-0.782774\pi$
$937$	−47.5098	−1.55208	−0.776038	+	0.630686i	$0.782774\pi$
$938$	22.1635	0.723663
$939$	−34.8187	−1.13626
$940$	1.15609	0.0377075
$941$	30.1304	0.982224	0.491112	−	0.871096i	$-0.336591\pi$
$941$	30.1304	0.982224	0.491112	+	0.871096i	$0.336591\pi$
$942$	−42.8022	−1.39457
$943$	−34.5180	−1.12406
$944$	−7.54428	−0.245545
$945$	−85.7121	−2.78821
$946$	7.93956	0.258137
$947$	28.6745	0.931797	0.465899	−	0.884838i	$-0.345731\pi$
$947$	28.6745	0.931797	0.465899	+	0.884838i	$0.345731\pi$
$948$	16.8711	0.547949
$949$	19.7291	0.640433
$950$	10.3026	0.334259
$951$	−94.6327	−3.06867
$952$	−20.1542	−0.653203
$953$	−9.18281	−0.297460	−0.148730	−	0.988878i	$-0.547519\pi$
$953$	−9.18281	−0.297460	−0.148730	+	0.988878i	$0.547519\pi$
$954$	−52.8765	−1.71194
$955$	19.2538	0.623039
$956$	20.3838	0.659259
$957$	27.4795	0.888286
$958$	24.7599	0.799958
$959$	18.3437	0.592350
$960$	−3.73637	−0.120591
$961$	19.1536	0.617857
$962$	10.2424	0.330230
$963$	94.5751	3.04764
$964$	28.0107	0.902164
$965$	−9.99234	−0.321665
$966$	58.0925	1.86910
$967$	−13.5606	−0.436080	−0.218040	−	0.975940i	$-0.569966\pi$
$967$	−13.5606	−0.436080	−0.218040	+	0.975940i	$0.569966\pi$
$968$	−9.71536	−0.312263
$969$	−46.0835	−1.48042
$970$	−12.0988	−0.388469
$971$	32.8595	1.05451	0.527255	−	0.849707i	$-0.323221\pi$
$971$	32.8595	1.05451	0.527255	+	0.849707i	$0.323221\pi$
$972$	−79.0380	−2.53514
$973$	−28.9666	−0.928628
$974$	−24.7018	−0.791497
$975$	−20.1753	−0.646127
$976$	−11.4723	−0.367218
$977$	54.2616	1.73598	0.867990	−	0.496581i	$-0.165411\pi$
$977$	54.2616	1.73598	0.867990	+	0.496581i	$0.165411\pi$
$978$	29.3452	0.938356
$979$	−2.68433	−0.0857915
$980$	10.2538	0.327546
$981$	−32.5956	−1.04070
$982$	−27.1071	−0.865023
$983$	−4.60746	−0.146955	−0.0734775	−	0.997297i	$-0.523410\pi$
$983$	−4.60746	−0.146955	−0.0734775	+	0.997297i	$0.523410\pi$
$984$	−28.0572	−0.894432
$985$	−4.98070	−0.158698
$986$	35.3494	1.12575
$987$	−14.6103	−0.465052
$988$	4.20584	0.133805
$989$	−29.4390	−0.936106
$990$	10.7472	0.341567
$991$	16.5049	0.524296	0.262148	−	0.965028i	$-0.415569\pi$
$991$	16.5049	0.524296	0.262148	+	0.965028i	$0.415569\pi$
$992$	−7.08192	−0.224851
$993$	2.17135	0.0689057
$994$	−65.5991	−2.08068
$995$	−6.91559	−0.219239
$996$	−19.6352	−0.622166
$997$	54.4894	1.72570	0.862848	−	0.505464i	$-0.168679\pi$
$997$	54.4894	1.72570	0.862848	+	0.505464i	$0.168679\pi$
$998$	31.3018	0.990840
$999$	127.739	4.04147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.1	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.1	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.41599 q^{3} +1.00000 q^{4} +1.09379 q^{5} -3.41599 q^{6} +4.04655 q^{7} +1.00000 q^{8} +8.66901 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.41599 q^{3} +1.00000 q^{4} +1.09379 q^{5} -3.41599 q^{6} +4.04655 q^{7} +1.00000 q^{8} +8.66901 q^{9} +1.09379 q^{10} +1.13342 q^{11} -3.41599 q^{12} -1.55276 q^{13} +4.04655 q^{14} -3.73637 q^{15} +1.00000 q^{16} -4.98060 q^{17} +8.66901 q^{18} -2.70861 q^{19} +1.09379 q^{20} -13.8230 q^{21} +1.13342 q^{22} -4.20260 q^{23} -3.41599 q^{24} -3.80363 q^{25} -1.55276 q^{26} -19.3653 q^{27} +4.04655 q^{28} -7.09742 q^{29} -3.73637 q^{30} -7.08192 q^{31} +1.00000 q^{32} -3.87176 q^{33} -4.98060 q^{34} +4.42607 q^{35} +8.66901 q^{36} -6.59627 q^{37} -2.70861 q^{38} +5.30423 q^{39} +1.09379 q^{40} +8.21349 q^{41} -13.8230 q^{42} +7.00495 q^{43} +1.13342 q^{44} +9.48205 q^{45} -4.20260 q^{46} +1.05696 q^{47} -3.41599 q^{48} +9.37458 q^{49} -3.80363 q^{50} +17.0137 q^{51} -1.55276 q^{52} -6.09949 q^{53} -19.3653 q^{54} +1.23972 q^{55} +4.04655 q^{56} +9.25260 q^{57} -7.09742 q^{58} -7.54428 q^{59} -3.73637 q^{60} -11.4723 q^{61} -7.08192 q^{62} +35.0796 q^{63} +1.00000 q^{64} -1.69839 q^{65} -3.87176 q^{66} +5.47712 q^{67} -4.98060 q^{68} +14.3561 q^{69} +4.42607 q^{70} -16.2111 q^{71} +8.66901 q^{72} -12.7058 q^{73} -6.59627 q^{74} +12.9932 q^{75} -2.70861 q^{76} +4.58645 q^{77} +5.30423 q^{78} -4.93886 q^{79} +1.09379 q^{80} +40.1446 q^{81} +8.21349 q^{82} +5.74803 q^{83} -13.8230 q^{84} -5.44772 q^{85} +7.00495 q^{86} +24.2447 q^{87} +1.13342 q^{88} -2.36834 q^{89} +9.48205 q^{90} -6.28334 q^{91} -4.20260 q^{92} +24.1918 q^{93} +1.05696 q^{94} -2.96265 q^{95} -3.41599 q^{96} -11.0614 q^{97} +9.37458 q^{98} +9.82563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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