LMFDB - Embedded newform 4033.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64408 q^{2} -3.27443 q^{3} +4.99114 q^{4} -3.17028 q^{5} +8.65784 q^{6} +2.13489 q^{7} -7.90879 q^{8} +7.72189 q^{9} +O(q^{10})$	\(q-2.64408 q^{2} -3.27443 q^{3} +4.99114 q^{4} -3.17028 q^{5} +8.65784 q^{6} +2.13489 q^{7} -7.90879 q^{8} +7.72189 q^{9} +8.38246 q^{10} -0.824221 q^{11} -16.3431 q^{12} +6.19334 q^{13} -5.64482 q^{14} +10.3809 q^{15} +10.9292 q^{16} +3.88533 q^{17} -20.4173 q^{18} +1.88197 q^{19} -15.8233 q^{20} -6.99056 q^{21} +2.17930 q^{22} -7.15939 q^{23} +25.8968 q^{24} +5.05067 q^{25} -16.3757 q^{26} -15.4615 q^{27} +10.6555 q^{28} +8.66616 q^{29} -27.4478 q^{30} -3.30763 q^{31} -13.0800 q^{32} +2.69885 q^{33} -10.2731 q^{34} -6.76821 q^{35} +38.5410 q^{36} +1.00000 q^{37} -4.97606 q^{38} -20.2797 q^{39} +25.0731 q^{40} +4.17874 q^{41} +18.4836 q^{42} -10.2211 q^{43} -4.11380 q^{44} -24.4805 q^{45} +18.9300 q^{46} -8.41525 q^{47} -35.7868 q^{48} -2.44223 q^{49} -13.3544 q^{50} -12.7222 q^{51} +30.9118 q^{52} -2.20528 q^{53} +40.8813 q^{54} +2.61301 q^{55} -16.8844 q^{56} -6.16237 q^{57} -22.9140 q^{58} -3.19155 q^{59} +51.8123 q^{60} +10.4500 q^{61} +8.74562 q^{62} +16.4854 q^{63} +12.7261 q^{64} -19.6346 q^{65} -7.13597 q^{66} +4.04557 q^{67} +19.3922 q^{68} +23.4429 q^{69} +17.8957 q^{70} +0.151426 q^{71} -61.0708 q^{72} -5.98785 q^{73} -2.64408 q^{74} -16.5381 q^{75} +9.39315 q^{76} -1.75962 q^{77} +53.6210 q^{78} -13.9394 q^{79} -34.6485 q^{80} +27.4619 q^{81} -11.0489 q^{82} +5.15412 q^{83} -34.8908 q^{84} -12.3176 q^{85} +27.0252 q^{86} -28.3767 q^{87} +6.51859 q^{88} -5.19580 q^{89} +64.7284 q^{90} +13.2221 q^{91} -35.7335 q^{92} +10.8306 q^{93} +22.2506 q^{94} -5.96636 q^{95} +42.8294 q^{96} +9.95594 q^{97} +6.45744 q^{98} -6.36454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) $ 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * 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 $

$2$	−2.64408	−1.86964	−0.934822	−	0.355117i	$-0.884441\pi$
$2$	−2.64408	−1.86964	−0.934822	+	0.355117i	$0.884441\pi$
$3$	−3.27443	−1.89049	−0.945246	−	0.326358i	$-0.894179\pi$
$3$	−3.27443	−1.89049	−0.945246	+	0.326358i	$0.894179\pi$
$4$	4.99114	2.49557
$5$	−3.17028	−1.41779	−0.708896	−	0.705313i	$-0.750806\pi$
$5$	−3.17028	−1.41779	−0.708896	+	0.705313i	$0.750806\pi$
$6$	8.65784	3.53455
$7$	2.13489	0.806914	0.403457	−	0.914999i	$-0.367809\pi$
$7$	2.13489	0.806914	0.403457	+	0.914999i	$0.367809\pi$
$8$	−7.90879	−2.79618
$9$	7.72189	2.57396
$10$	8.38246	2.65077
$11$	−0.824221	−0.248512	−0.124256	−	0.992250i	$-0.539654\pi$
$11$	−0.824221	−0.248512	−0.124256	+	0.992250i	$0.539654\pi$
$12$	−16.3431	−4.71785
$13$	6.19334	1.71772	0.858862	−	0.512206i	$-0.171172\pi$
$13$	6.19334	1.71772	0.858862	+	0.512206i	$0.171172\pi$
$14$	−5.64482	−1.50864
$15$	10.3809	2.68033
$16$	10.9292	2.73229
$17$	3.88533	0.942331	0.471165	−	0.882045i	$-0.343834\pi$
$17$	3.88533	0.942331	0.471165	+	0.882045i	$0.343834\pi$
$18$	−20.4173	−4.81239
$19$	1.88197	0.431753	0.215876	−	0.976421i	$-0.430739\pi$
$19$	1.88197	0.431753	0.215876	+	0.976421i	$0.430739\pi$
$20$	−15.8233	−3.53820
$21$	−6.99056	−1.52546
$22$	2.17930	0.464629
$23$	−7.15939	−1.49284	−0.746418	−	0.665478i	$-0.768228\pi$
$23$	−7.15939	−1.49284	−0.746418	+	0.665478i	$0.768228\pi$
$24$	25.8968	5.28616
$25$	5.05067	1.01013
$26$	−16.3757	−3.21153
$27$	−15.4615	−2.97556
$28$	10.6555	2.01371
$29$	8.66616	1.60926	0.804632	−	0.593773i	$-0.202362\pi$
$29$	8.66616	1.60926	0.804632	+	0.593773i	$0.202362\pi$
$30$	−27.4478	−5.01125
$31$	−3.30763	−0.594068	−0.297034	−	0.954867i	$-0.595997\pi$
$31$	−3.30763	−0.594068	−0.297034	+	0.954867i	$0.595997\pi$
$32$	−13.0800	−2.31223
$33$	2.69885	0.469810
$34$	−10.2731	−1.76182
$35$	−6.76821	−1.14404
$36$	38.5410	6.42350
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−4.97606	−0.807224
$39$	−20.2797	−3.24735
$40$	25.0731	3.96440
$41$	4.17874	0.652610	0.326305	−	0.945265i	$-0.394196\pi$
$41$	4.17874	0.652610	0.326305	+	0.945265i	$0.394196\pi$
$42$	18.4836	2.85208
$43$	−10.2211	−1.55870	−0.779348	−	0.626591i	$-0.784450\pi$
$43$	−10.2211	−1.55870	−0.779348	+	0.626591i	$0.784450\pi$
$44$	−4.11380	−0.620179
$45$	−24.4805	−3.64934
$46$	18.9300	2.79107
$47$	−8.41525	−1.22749	−0.613745	−	0.789504i	$-0.710338\pi$
$47$	−8.41525	−1.22749	−0.613745	+	0.789504i	$0.710338\pi$
$48$	−35.7868	−5.16538
$49$	−2.44223	−0.348890
$50$	−13.3544	−1.88859
$51$	−12.7222	−1.78147
$52$	30.9118	4.28670
$53$	−2.20528	−0.302918	−0.151459	−	0.988464i	$-0.548397\pi$
$53$	−2.20528	−0.302918	−0.151459	+	0.988464i	$0.548397\pi$
$54$	40.8813	5.56325
$55$	2.61301	0.352338
$56$	−16.8844	−2.25628
$57$	−6.16237	−0.816226
$58$	−22.9140	−3.00875
$59$	−3.19155	−0.415504	−0.207752	−	0.978182i	$-0.566615\pi$
$59$	−3.19155	−0.415504	−0.207752	+	0.978182i	$0.566615\pi$
$60$	51.8123	6.68893
$61$	10.4500	1.33799	0.668994	−	0.743268i	$-0.266725\pi$
$61$	10.4500	1.33799	0.668994	+	0.743268i	$0.266725\pi$
$62$	8.74562	1.11070
$63$	16.4854	2.07697
$64$	12.7261	1.59076
$65$	−19.6346	−2.43538
$66$	−7.13597	−0.878378
$67$	4.04557	0.494245	0.247123	−	0.968984i	$-0.420515\pi$
$67$	4.04557	0.494245	0.247123	+	0.968984i	$0.420515\pi$
$68$	19.3922	2.35165
$69$	23.4429	2.82219
$70$	17.8957	2.13894
$71$	0.151426	0.0179710	0.00898550	−	0.999960i	$-0.497140\pi$
$71$	0.151426	0.0179710	0.00898550	+	0.999960i	$0.497140\pi$
$72$	−61.0708	−7.19726
$73$	−5.98785	−0.700825	−0.350412	−	0.936595i	$-0.613959\pi$
$73$	−5.98785	−0.700825	−0.350412	+	0.936595i	$0.613959\pi$
$74$	−2.64408	−0.307368
$75$	−16.5381	−1.90965
$76$	9.39315	1.07747
$77$	−1.75962	−0.200528
$78$	53.6210	6.07138
$79$	−13.9394	−1.56830	−0.784152	−	0.620569i	$-0.786902\pi$
$79$	−13.9394	−1.56830	−0.784152	+	0.620569i	$0.786902\pi$
$80$	−34.6485	−3.87382
$81$	27.4619	3.05132
$82$	−11.0489	−1.22015
$83$	5.15412	0.565738	0.282869	−	0.959158i	$-0.408714\pi$
$83$	5.15412	0.565738	0.282869	+	0.959158i	$0.408714\pi$
$84$	−34.8908	−3.80690
$85$	−12.3176	−1.33603
$86$	27.0252	2.91421
$87$	−28.3767	−3.04230
$88$	6.51859	0.694884
$89$	−5.19580	−0.550754	−0.275377	−	0.961336i	$-0.588803\pi$
$89$	−5.19580	−0.550754	−0.275377	+	0.961336i	$0.588803\pi$
$90$	64.7284	6.82297
$91$	13.2221	1.38606
$92$	−35.7335	−3.72547
$93$	10.8306	1.12308
$94$	22.2506	2.29497
$95$	−5.96636	−0.612136
$96$	42.8294	4.37126
$97$	9.95594	1.01087	0.505436	−	0.862864i	$-0.331332\pi$
$97$	9.95594	1.01087	0.505436	+	0.862864i	$0.331332\pi$
$98$	6.45744	0.652300
$99$	−6.36454	−0.639661
$100$	25.2086	2.52086
$101$	4.20359	0.418273	0.209137	−	0.977886i	$-0.432935\pi$
$101$	4.20359	0.418273	0.209137	+	0.977886i	$0.432935\pi$
$102$	33.6385	3.33071
$103$	−16.0068	−1.57719	−0.788597	−	0.614910i	$-0.789192\pi$
$103$	−16.0068	−1.57719	−0.788597	+	0.614910i	$0.789192\pi$
$104$	−48.9819	−4.80307
$105$	22.1620	2.16279
$106$	5.83093	0.566350
$107$	−4.78269	−0.462360	−0.231180	−	0.972911i	$-0.574259\pi$
$107$	−4.78269	−0.462360	−0.231180	+	0.972911i	$0.574259\pi$
$108$	−77.1704	−7.42572
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−6.90900	−0.658747
$111$	−3.27443	−0.310795
$112$	23.3326	2.20472
$113$	2.20057	0.207012	0.103506	−	0.994629i	$-0.466994\pi$
$113$	2.20057	0.207012	0.103506	+	0.994629i	$0.466994\pi$
$114$	16.2938	1.52605
$115$	22.6972	2.11653
$116$	43.2540	4.01603
$117$	47.8243	4.42136
$118$	8.43870	0.776845
$119$	8.29476	0.760380
$120$	−82.1000	−7.49467
$121$	−10.3207	−0.938242
$122$	−27.6306	−2.50156
$123$	−13.6830	−1.23375
$124$	−16.5088	−1.48254
$125$	−0.160634	−0.0143675
$126$	−43.5887	−3.88319
$127$	1.32906	0.117935	0.0589673	−	0.998260i	$-0.481219\pi$
$127$	1.32906	0.117935	0.0589673	+	0.998260i	$0.481219\pi$
$128$	−7.48880	−0.661923
$129$	33.4681	2.94670
$130$	51.9155	4.55329
$131$	11.0890	0.968850	0.484425	−	0.874833i	$-0.339029\pi$
$131$	11.0890	0.968850	0.484425	+	0.874833i	$0.339029\pi$
$132$	13.4703	1.17244
$133$	4.01780	0.348387
$134$	−10.6968	−0.924063
$135$	49.0172	4.21873
$136$	−30.7282	−2.63493
$137$	−21.7805	−1.86083	−0.930416	−	0.366506i	$-0.880554\pi$
$137$	−21.7805	−1.86083	−0.930416	+	0.366506i	$0.880554\pi$
$138$	−61.9848	−5.27650
$139$	5.25674	0.445871	0.222936	−	0.974833i	$-0.428436\pi$
$139$	5.25674	0.445871	0.222936	+	0.974833i	$0.428436\pi$
$140$	−33.7810	−2.85502
$141$	27.5551	2.32056
$142$	−0.400382	−0.0335994
$143$	−5.10469	−0.426875
$144$	84.3938	7.03282
$145$	−27.4741	−2.28160
$146$	15.8323	1.31029
$147$	7.99691	0.659574
$148$	4.99114	0.410269
$149$	16.4061	1.34404	0.672020	−	0.740533i	$-0.265427\pi$
$149$	16.4061	1.34404	0.672020	+	0.740533i	$0.265427\pi$
$150$	43.7279	3.57037
$151$	−8.79541	−0.715761	−0.357880	−	0.933767i	$-0.616500\pi$
$151$	−8.79541	−0.715761	−0.357880	+	0.933767i	$0.616500\pi$
$152$	−14.8841	−1.20726
$153$	30.0021	2.42552
$154$	4.65258	0.374916
$155$	10.4861	0.842265
$156$	−101.219	−8.10397
$157$	−8.72247	−0.696129	−0.348065	−	0.937471i	$-0.613161\pi$
$157$	−8.72247	−0.696129	−0.348065	+	0.937471i	$0.613161\pi$
$158$	36.8568	2.93217
$159$	7.22103	0.572665
$160$	41.4671	3.27827
$161$	−15.2845	−1.20459
$162$	−72.6113	−5.70488
$163$	18.5347	1.45175	0.725873	−	0.687828i	$-0.241436\pi$
$163$	18.5347	1.45175	0.725873	+	0.687828i	$0.241436\pi$
$164$	20.8567	1.62863
$165$	−8.55612	−0.666093
$166$	−13.6279	−1.05773
$167$	13.7771	1.06611	0.533054	−	0.846081i	$-0.321044\pi$
$167$	13.7771	1.06611	0.533054	+	0.846081i	$0.321044\pi$
$168$	55.2869	4.26547
$169$	25.3575	1.95058
$170$	32.5686	2.49790
$171$	14.5323	1.11132
$172$	−51.0147	−3.88983
$173$	−14.2695	−1.08489	−0.542445	−	0.840092i	$-0.682501\pi$
$173$	−14.2695	−1.08489	−0.542445	+	0.840092i	$0.682501\pi$
$174$	75.0302	5.68802
$175$	10.7826	0.815091
$176$	−9.00805	−0.679007
$177$	10.4505	0.785508
$178$	13.7381	1.02971
$179$	12.3995	0.926785	0.463392	−	0.886153i	$-0.346632\pi$
$179$	12.3995	0.926785	0.463392	+	0.886153i	$0.346632\pi$
$180$	−122.186	−9.10718
$181$	−19.9955	−1.48625	−0.743127	−	0.669151i	$-0.766658\pi$
$181$	−19.9955	−1.48625	−0.743127	+	0.669151i	$0.766658\pi$
$182$	−34.9603	−2.59143
$183$	−34.2178	−2.52946
$184$	56.6221	4.17424
$185$	−3.17028	−0.233084
$186$	−28.6369	−2.09976
$187$	−3.20237	−0.234180
$188$	−42.0017	−3.06329
$189$	−33.0086	−2.40102
$190$	15.7755	1.14448
$191$	−12.1733	−0.880830	−0.440415	−	0.897794i	$-0.645169\pi$
$191$	−12.1733	−0.880830	−0.440415	+	0.897794i	$0.645169\pi$
$192$	−41.6707	−3.00732
$193$	1.87798	0.135180	0.0675898	−	0.997713i	$-0.478469\pi$
$193$	1.87798	0.135180	0.0675898	+	0.997713i	$0.478469\pi$
$194$	−26.3243	−1.88997
$195$	64.2922	4.60406
$196$	−12.1895	−0.870679
$197$	−17.2258	−1.22729	−0.613644	−	0.789582i	$-0.710297\pi$
$197$	−17.2258	−1.22729	−0.613644	+	0.789582i	$0.710297\pi$
$198$	16.8283	1.19594
$199$	15.9244	1.12885	0.564424	−	0.825485i	$-0.309098\pi$
$199$	15.9244	1.12885	0.564424	+	0.825485i	$0.309098\pi$
$200$	−39.9447	−2.82452
$201$	−13.2469	−0.934367
$202$	−11.1146	−0.782022
$203$	18.5013	1.29854
$204$	−63.4984	−4.44578
$205$	−13.2478	−0.925265
$206$	42.3231	2.94879
$207$	−55.2840	−3.84250
$208$	67.6881	4.69333
$209$	−1.55116	−0.107296
$210$	−58.5980	−4.04365
$211$	8.28769	0.570548	0.285274	−	0.958446i	$-0.407915\pi$
$211$	8.28769	0.570548	0.285274	+	0.958446i	$0.407915\pi$
$212$	−11.0069	−0.755954
$213$	−0.495835	−0.0339740
$214$	12.6458	0.864448
$215$	32.4036	2.20991
$216$	122.282	8.32021
$217$	−7.06144	−0.479362
$218$	−2.64408	−0.179079
$219$	19.6068	1.32490
$220$	13.0419	0.879284
$221$	24.0632	1.61866
$222$	8.65784	0.581076
$223$	6.20462	0.415492	0.207746	−	0.978183i	$-0.433387\pi$
$223$	6.20462	0.415492	0.207746	+	0.978183i	$0.433387\pi$
$224$	−27.9243	−1.86577
$225$	39.0007	2.60005
$226$	−5.81847	−0.387039
$227$	−25.0538	−1.66288	−0.831439	−	0.555617i	$-0.812482\pi$
$227$	−25.0538	−1.66288	−0.831439	+	0.555617i	$0.812482\pi$
$228$	−30.7572	−2.03695
$229$	−4.25007	−0.280853	−0.140426	−	0.990091i	$-0.544847\pi$
$229$	−4.25007	−0.280853	−0.140426	+	0.990091i	$0.544847\pi$
$230$	−60.0132	−3.95716
$231$	5.76176	0.379096
$232$	−68.5388	−4.49979
$233$	27.6966	1.81447	0.907234	−	0.420627i	$-0.138190\pi$
$233$	27.6966	1.81447	0.907234	+	0.420627i	$0.138190\pi$
$234$	−126.451	−8.26637
$235$	26.6787	1.74033
$236$	−15.9295	−1.03692
$237$	45.6435	2.96487
$238$	−21.9320	−1.42164
$239$	8.02150	0.518867	0.259434	−	0.965761i	$-0.416464\pi$
$239$	8.02150	0.518867	0.259434	+	0.965761i	$0.416464\pi$
$240$	113.454	7.32343
$241$	−0.760848	−0.0490105	−0.0245053	−	0.999700i	$-0.507801\pi$
$241$	−0.760848	−0.0490105	−0.0245053	+	0.999700i	$0.507801\pi$
$242$	27.2886	1.75418
$243$	−43.5375	−2.79293
$244$	52.1575	3.33904
$245$	7.74255	0.494653
$246$	36.1789	2.30668
$247$	11.6557	0.741633
$248$	26.1594	1.66112
$249$	−16.8768	−1.06952
$250$	0.424728	0.0268621
$251$	−1.48843	−0.0939487	−0.0469744	−	0.998896i	$-0.514958\pi$
$251$	−1.48843	−0.0939487	−0.0469744	+	0.998896i	$0.514958\pi$
$252$	82.2809	5.18321
$253$	5.90092	0.370987
$254$	−3.51413	−0.220496
$255$	40.3330	2.52575
$256$	−5.65121	−0.353201
$257$	−20.9502	−1.30684	−0.653419	−	0.756997i	$-0.726666\pi$
$257$	−20.9502	−1.30684	−0.653419	+	0.756997i	$0.726666\pi$
$258$	−88.4922	−5.50929
$259$	2.13489	0.132656
$260$	−97.9991	−6.07765
$261$	66.9191	4.14219
$262$	−29.3202	−1.81141
$263$	19.2513	1.18709	0.593544	−	0.804802i	$-0.297728\pi$
$263$	19.2513	1.18709	0.593544	+	0.804802i	$0.297728\pi$
$264$	−21.3447	−1.31367
$265$	6.99135	0.429475
$266$	−10.6234	−0.651360
$267$	17.0133	1.04120
$268$	20.1920	1.23342
$269$	6.49374	0.395930	0.197965	−	0.980209i	$-0.436567\pi$
$269$	6.49374	0.395930	0.197965	+	0.980209i	$0.436567\pi$
$270$	−129.605	−7.88752
$271$	−1.56934	−0.0953306	−0.0476653	−	0.998863i	$-0.515178\pi$
$271$	−1.56934	−0.0953306	−0.0476653	+	0.998863i	$0.515178\pi$
$272$	42.4634	2.57472
$273$	−43.2949	−2.62033
$274$	57.5892	3.47909
$275$	−4.16287	−0.251030
$276$	117.007	7.04298
$277$	32.2049	1.93501	0.967504	−	0.252856i	$-0.0813700\pi$
$277$	32.2049	1.93501	0.967504	+	0.252856i	$0.0813700\pi$
$278$	−13.8992	−0.833620
$279$	−25.5411	−1.52911
$280$	53.5283	3.19893
$281$	13.3550	0.796692	0.398346	−	0.917235i	$-0.369584\pi$
$281$	13.3550	0.796692	0.398346	+	0.917235i	$0.369584\pi$
$282$	−72.8579	−4.33862
$283$	−31.6614	−1.88208	−0.941038	−	0.338300i	$-0.890148\pi$
$283$	−31.6614	−1.88208	−0.941038	+	0.338300i	$0.890148\pi$
$284$	0.755789	0.0448478
$285$	19.5364	1.15724
$286$	13.4972	0.798105
$287$	8.92117	0.526600
$288$	−101.002	−5.95160
$289$	−1.90422	−0.112013
$290$	72.6437	4.26578
$291$	−32.6000	−1.91105
$292$	−29.8862	−1.74896
$293$	−24.7721	−1.44720	−0.723600	−	0.690220i	$-0.757514\pi$
$293$	−24.7721	−1.44720	−0.723600	+	0.690220i	$0.757514\pi$
$294$	−21.1444	−1.23317
$295$	10.1181	0.589099
$296$	−7.90879	−0.459689
$297$	12.7437	0.739463
$298$	−43.3789	−2.51287
$299$	−44.3405	−2.56428
$300$	−82.5437	−4.76566
$301$	−21.8209	−1.25773
$302$	23.2557	1.33822
$303$	−13.7644	−0.790742
$304$	20.5683	1.17967
$305$	−33.1295	−1.89699
$306$	−79.3277	−4.53486
$307$	−15.7035	−0.896246	−0.448123	−	0.893972i	$-0.647907\pi$
$307$	−15.7035	−0.896246	−0.448123	+	0.893972i	$0.647907\pi$
$308$	−8.78252	−0.500431
$309$	52.4131	2.98168
$310$	−27.7261	−1.57473
$311$	16.2056	0.918935	0.459467	−	0.888195i	$-0.348040\pi$
$311$	16.2056	0.918935	0.459467	+	0.888195i	$0.348040\pi$
$312$	160.388	9.08016
$313$	−16.1043	−0.910271	−0.455136	−	0.890422i	$-0.650409\pi$
$313$	−16.1043	−0.910271	−0.455136	+	0.890422i	$0.650409\pi$
$314$	23.0629	1.30151
$315$	−52.2633	−2.94471
$316$	−69.5734	−3.91381
$317$	−31.5204	−1.77036	−0.885181	−	0.465247i	$-0.845965\pi$
$317$	−31.5204	−1.77036	−0.885181	+	0.465247i	$0.845965\pi$
$318$	−19.0930	−1.07068
$319$	−7.14283	−0.399922
$320$	−40.3452	−2.25537
$321$	15.6606	0.874088
$322$	40.4134	2.25215
$323$	7.31206	0.406854
$324$	137.066	7.61478
$325$	31.2805	1.73513
$326$	−49.0070	−2.71425
$327$	−3.27443	−0.181076
$328$	−33.0488	−1.82481
$329$	−17.9657	−0.990479
$330$	22.6230	1.24536
$331$	−12.6259	−0.693982	−0.346991	−	0.937868i	$-0.612797\pi$
$331$	−12.6259	−0.693982	−0.346991	+	0.937868i	$0.612797\pi$
$332$	25.7249	1.41184
$333$	7.72189	0.423157
$334$	−36.4278	−1.99324
$335$	−12.8256	−0.700737
$336$	−76.4010	−4.16802
$337$	−24.9554	−1.35941	−0.679704	−	0.733486i	$-0.737892\pi$
$337$	−24.9554	−1.35941	−0.679704	+	0.733486i	$0.737892\pi$
$338$	−67.0472	−3.64689
$339$	−7.20560	−0.391355
$340$	−61.4787	−3.33415
$341$	2.72622	0.147633
$342$	−38.4246	−2.07776
$343$	−20.1582	−1.08844
$344$	80.8362	4.35839
$345$	−74.3205	−4.00128
$346$	37.7296	2.02836
$347$	−11.5686	−0.621035	−0.310518	−	0.950568i	$-0.600502\pi$
$347$	−11.5686	−0.621035	−0.310518	+	0.950568i	$0.600502\pi$
$348$	−141.632	−7.59228
$349$	−15.7032	−0.840571	−0.420285	−	0.907392i	$-0.638070\pi$
$349$	−15.7032	−0.840571	−0.420285	+	0.907392i	$0.638070\pi$
$350$	−28.5101	−1.52393
$351$	−95.7583	−5.11120
$352$	10.7808	0.574618
$353$	2.18741	0.116424	0.0582121	−	0.998304i	$-0.481460\pi$
$353$	2.18741	0.116424	0.0582121	+	0.998304i	$0.481460\pi$
$354$	−27.6319	−1.46862
$355$	−0.480063	−0.0254791
$356$	−25.9330	−1.37444
$357$	−27.1606	−1.43749
$358$	−32.7853	−1.73276
$359$	−7.50078	−0.395876	−0.197938	−	0.980215i	$-0.563424\pi$
$359$	−7.50078	−0.395876	−0.197938	+	0.980215i	$0.563424\pi$
$360$	193.611	10.2042
$361$	−15.4582	−0.813589
$362$	52.8696	2.77876
$363$	33.7943	1.77374
$364$	65.9935	3.45900
$365$	18.9832	0.993624
$366$	90.4746	4.72918
$367$	−11.3622	−0.593101	−0.296551	−	0.955017i	$-0.595836\pi$
$367$	−11.3622	−0.593101	−0.296551	+	0.955017i	$0.595836\pi$
$368$	−78.2461	−4.07886
$369$	32.2678	1.67979
$370$	8.38246	0.435783
$371$	−4.70804	−0.244429
$372$	54.0570	2.80272
$373$	34.9003	1.80707	0.903535	−	0.428514i	$-0.140963\pi$
$373$	34.9003	1.80707	0.903535	+	0.428514i	$0.140963\pi$
$374$	8.46731	0.437834
$375$	0.525984	0.0271617
$376$	66.5545	3.43228
$377$	53.6725	2.76427
$378$	87.2773	4.48906
$379$	20.5290	1.05450	0.527252	−	0.849709i	$-0.323222\pi$
$379$	20.5290	1.05450	0.527252	+	0.849709i	$0.323222\pi$
$380$	−29.7789	−1.52763
$381$	−4.35190	−0.222955
$382$	32.1872	1.64684
$383$	26.9669	1.37794	0.688972	−	0.724788i	$-0.258062\pi$
$383$	26.9669	1.37794	0.688972	+	0.724788i	$0.258062\pi$
$384$	24.5216	1.25136
$385$	5.57850	0.284307
$386$	−4.96551	−0.252738
$387$	−78.9258	−4.01203
$388$	49.6915	2.52270
$389$	−27.9044	−1.41481	−0.707406	−	0.706808i	$-0.750135\pi$
$389$	−27.9044	−1.41481	−0.707406	+	0.706808i	$0.750135\pi$
$390$	−169.993	−8.60795
$391$	−27.8166	−1.40674
$392$	19.3151	0.975559
$393$	−36.3101	−1.83160
$394$	45.5464	2.29459
$395$	44.1918	2.22353
$396$	−31.7663	−1.59632
$397$	−9.37019	−0.470276	−0.235138	−	0.971962i	$-0.575554\pi$
$397$	−9.37019	−0.470276	−0.235138	+	0.971962i	$0.575554\pi$
$398$	−42.1053	−2.11055
$399$	−13.1560	−0.658624
$400$	55.1996	2.75998
$401$	27.2918	1.36289	0.681444	−	0.731870i	$-0.261352\pi$
$401$	27.2918	1.36289	0.681444	+	0.731870i	$0.261352\pi$
$402$	35.0259	1.74693
$403$	−20.4853	−1.02045
$404$	20.9807	1.04383
$405$	−87.0618	−4.32614
$406$	−48.9189	−2.42780
$407$	−0.824221	−0.0408551
$408$	100.617	4.98131
$409$	−34.9145	−1.72641	−0.863206	−	0.504852i	$-0.831547\pi$
$409$	−34.9145	−1.72641	−0.863206	+	0.504852i	$0.831547\pi$
$410$	35.0281	1.72992
$411$	71.3186	3.51789
$412$	−79.8920	−3.93600
$413$	−6.81362	−0.335276
$414$	146.175	7.18411
$415$	−16.3400	−0.802099
$416$	−81.0088	−3.97178
$417$	−17.2128	−0.842916
$418$	4.10138	0.200605
$419$	30.3031	1.48040	0.740202	−	0.672385i	$-0.234730\pi$
$419$	30.3031	1.48040	0.740202	+	0.672385i	$0.234730\pi$
$420$	110.614	5.39739
$421$	−9.66613	−0.471098	−0.235549	−	0.971862i	$-0.575689\pi$
$421$	−9.66613	−0.471098	−0.235549	+	0.971862i	$0.575689\pi$
$422$	−21.9133	−1.06672
$423$	−64.9816	−3.15951
$424$	17.4411	0.847014
$425$	19.6235	0.951880
$426$	1.31102	0.0635193
$427$	22.3097	1.07964
$428$	−23.8710	−1.15385
$429$	16.7149	0.807004
$430$	−85.6775	−4.13174
$431$	−36.8248	−1.77379	−0.886895	−	0.461971i	$-0.847142\pi$
$431$	−36.8248	−1.77379	−0.886895	+	0.461971i	$0.847142\pi$
$432$	−168.981	−8.13011
$433$	−1.13275	−0.0544367	−0.0272184	−	0.999630i	$-0.508665\pi$
$433$	−1.13275	−0.0544367	−0.0272184	+	0.999630i	$0.508665\pi$
$434$	18.6710	0.896235
$435$	89.9621	4.31335
$436$	4.99114	0.239032
$437$	−13.4737	−0.644536
$438$	−51.8418	−2.47710
$439$	4.89934	0.233833	0.116916	−	0.993142i	$-0.462699\pi$
$439$	4.89934	0.233833	0.116916	+	0.993142i	$0.462699\pi$
$440$	−20.6658	−0.985201
$441$	−18.8586	−0.898030
$442$	−63.6249	−3.02633
$443$	36.0102	1.71090	0.855449	−	0.517887i	$-0.173281\pi$
$443$	36.0102	1.71090	0.855449	+	0.517887i	$0.173281\pi$
$444$	−16.3431	−0.775610
$445$	16.4721	0.780854
$446$	−16.4055	−0.776822
$447$	−53.7206	−2.54090
$448$	27.1688	1.28361
$449$	−3.87046	−0.182658	−0.0913291	−	0.995821i	$-0.529112\pi$
$449$	−3.87046	−0.182658	−0.0913291	+	0.995821i	$0.529112\pi$
$450$	−103.121	−4.86116
$451$	−3.44421	−0.162181
$452$	10.9833	0.516613
$453$	28.8000	1.35314
$454$	66.2441	3.10899
$455$	−41.9178	−1.96514
$456$	48.7369	2.28231
$457$	−13.8332	−0.647091	−0.323545	−	0.946213i	$-0.604875\pi$
$457$	−13.8332	−0.647091	−0.323545	+	0.946213i	$0.604875\pi$
$458$	11.2375	0.525094
$459$	−60.0730	−2.80397
$460$	113.285	5.28194
$461$	−12.6634	−0.589792	−0.294896	−	0.955529i	$-0.595285\pi$
$461$	−12.6634	−0.589792	−0.294896	+	0.955529i	$0.595285\pi$
$462$	−15.2345	−0.708775
$463$	6.44705	0.299620	0.149810	−	0.988715i	$-0.452134\pi$
$463$	6.44705	0.299620	0.149810	+	0.988715i	$0.452134\pi$
$464$	94.7139	4.39698
$465$	−34.3360	−1.59229
$466$	−73.2320	−3.39241
$467$	−9.83077	−0.454914	−0.227457	−	0.973788i	$-0.573041\pi$
$467$	−9.83077	−0.454914	−0.227457	+	0.973788i	$0.573041\pi$
$468$	238.698	11.0338
$469$	8.63687	0.398813
$470$	−70.5405	−3.25379
$471$	28.5611	1.31603
$472$	25.2413	1.16182
$473$	8.42441	0.387355
$474$	−120.685	−5.54325
$475$	9.50519	0.436128
$476$	41.4003	1.89758
$477$	−17.0289	−0.779701
$478$	−21.2094	−0.970097
$479$	14.1471	0.646396	0.323198	−	0.946331i	$-0.395242\pi$
$479$	14.1471	0.646396	0.323198	+	0.946331i	$0.395242\pi$
$480$	−135.781	−6.19754
$481$	6.19334	0.282392
$482$	2.01174	0.0916323
$483$	50.0481	2.27727
$484$	−51.5118	−2.34145
$485$	−31.5631	−1.43321
$486$	115.117	5.22179
$487$	9.14238	0.414281	0.207140	−	0.978311i	$-0.433584\pi$
$487$	9.14238	0.414281	0.207140	+	0.978311i	$0.433584\pi$
$488$	−82.6470	−3.74125
$489$	−60.6904	−2.74452
$490$	−20.4719	−0.924826
$491$	−37.8399	−1.70769	−0.853846	−	0.520526i	$-0.825736\pi$
$491$	−37.8399	−1.70769	−0.853846	+	0.520526i	$0.825736\pi$
$492$	−68.2937	−3.07892
$493$	33.6709	1.51646
$494$	−30.8185	−1.38659
$495$	20.1774	0.906906
$496$	−36.1496	−1.62317
$497$	0.323279	0.0145010
$498$	44.6236	1.99963
$499$	27.3131	1.22270	0.611351	−	0.791360i	$-0.290626\pi$
$499$	27.3131	1.22270	0.611351	+	0.791360i	$0.290626\pi$
$500$	−0.801745	−0.0358551
$501$	−45.1123	−2.01547
$502$	3.93552	0.175651
$503$	−30.1340	−1.34361	−0.671803	−	0.740730i	$-0.734480\pi$
$503$	−30.1340	−1.34361	−0.671803	+	0.740730i	$0.734480\pi$
$504$	−130.380	−5.80757
$505$	−13.3266	−0.593024
$506$	−15.6025	−0.693614
$507$	−83.0314	−3.68755
$508$	6.63350	0.294314
$509$	−29.5854	−1.31135	−0.655675	−	0.755043i	$-0.727616\pi$
$509$	−29.5854	−1.31135	−0.655675	+	0.755043i	$0.727616\pi$
$510$	−106.644	−4.72226
$511$	−12.7834	−0.565505
$512$	29.9198	1.32228
$513$	−29.0980	−1.28471
$514$	55.3939	2.44332
$515$	50.7460	2.23613
$516$	167.044	7.35370
$517$	6.93603	0.305046
$518$	−5.64482	−0.248019
$519$	46.7244	2.05098
$520$	155.286	6.80975
$521$	−8.57638	−0.375738	−0.187869	−	0.982194i	$-0.560158\pi$
$521$	−8.57638	−0.375738	−0.187869	+	0.982194i	$0.560158\pi$
$522$	−176.939	−7.74442
$523$	0.373074	0.0163134	0.00815670	−	0.999967i	$-0.497404\pi$
$523$	0.373074	0.0163134	0.00815670	+	0.999967i	$0.497404\pi$
$524$	55.3467	2.41783
$525$	−35.3070	−1.54092
$526$	−50.9020	−2.21943
$527$	−12.8512	−0.559808
$528$	29.4962	1.28366
$529$	28.2568	1.22856
$530$	−18.4857	−0.802966
$531$	−24.6448	−1.06949
$532$	20.0534	0.869424
$533$	25.8804	1.12100
$534$	−44.9844	−1.94667
$535$	15.1625	0.655530
$536$	−31.9956	−1.38200
$537$	−40.6014	−1.75208
$538$	−17.1699	−0.740249
$539$	2.01294	0.0867034
$540$	244.652	10.5281
$541$	18.9937	0.816602	0.408301	−	0.912847i	$-0.366121\pi$
$541$	18.9937	0.816602	0.408301	+	0.912847i	$0.366121\pi$
$542$	4.14945	0.178234
$543$	65.4738	2.80975
$544$	−50.8200	−2.17889
$545$	−3.17028	−0.135800
$546$	114.475	4.89908
$547$	18.7551	0.801909	0.400955	−	0.916098i	$-0.368678\pi$
$547$	18.7551	0.801909	0.400955	+	0.916098i	$0.368678\pi$
$548$	−108.709	−4.64383
$549$	80.6939	3.44393
$550$	11.0069	0.469337
$551$	16.3094	0.694805
$552$	−185.405	−7.89136
$553$	−29.7591	−1.26549
$554$	−85.1523	−3.61778
$555$	10.3809	0.440643
$556$	26.2371	1.11270
$557$	36.9453	1.56542	0.782711	−	0.622386i	$-0.213836\pi$
$557$	36.9453	1.56542	0.782711	+	0.622386i	$0.213836\pi$
$558$	67.5327	2.85889
$559$	−63.3025	−2.67741
$560$	−73.9709	−3.12584
$561$	10.4859	0.442716
$562$	−35.3116	−1.48953
$563$	1.46919	0.0619189	0.0309594	−	0.999521i	$-0.490144\pi$
$563$	1.46919	0.0619189	0.0309594	+	0.999521i	$0.490144\pi$
$564$	137.531	5.79112
$565$	−6.97641	−0.293500
$566$	83.7152	3.51881
$567$	58.6282	2.46215
$568$	−1.19760	−0.0502501
$569$	−20.9968	−0.880231	−0.440115	−	0.897941i	$-0.645062\pi$
$569$	−20.9968	−0.880231	−0.440115	+	0.897941i	$0.645062\pi$
$570$	−51.6558	−2.16362
$571$	13.6662	0.571913	0.285957	−	0.958243i	$-0.407689\pi$
$571$	13.6662	0.571913	0.285957	+	0.958243i	$0.407689\pi$
$572$	−25.4782	−1.06530
$573$	39.8606	1.66520
$574$	−23.5882	−0.984554
$575$	−36.1597	−1.50796
$576$	98.2694	4.09456
$577$	−13.3513	−0.555822	−0.277911	−	0.960607i	$-0.589642\pi$
$577$	−13.3513	−0.555822	−0.277911	+	0.960607i	$0.589642\pi$
$578$	5.03491	0.209425
$579$	−6.14930	−0.255556
$580$	−137.127	−5.69389
$581$	11.0035	0.456502
$582$	86.1970	3.57298
$583$	1.81764	0.0752789
$584$	47.3567	1.95963
$585$	−151.616	−6.26857
$586$	65.4992	2.70575
$587$	41.6912	1.72078	0.860389	−	0.509637i	$-0.170220\pi$
$587$	41.6912	1.72078	0.860389	+	0.509637i	$0.170220\pi$
$588$	39.9137	1.64601
$589$	−6.22485	−0.256490
$590$	−26.7530	−1.10140
$591$	56.4047	2.32018
$592$	10.9292	0.449186
$593$	10.5274	0.432309	0.216154	−	0.976359i	$-0.430649\pi$
$593$	10.5274	0.432309	0.216154	+	0.976359i	$0.430649\pi$
$594$	−33.6953	−1.38253
$595$	−26.2967	−1.07806
$596$	81.8850	3.35414
$597$	−52.1432	−2.13408
$598$	117.240	4.79429
$599$	−12.3447	−0.504391	−0.252195	−	0.967676i	$-0.581153\pi$
$599$	−12.3447	−0.504391	−0.252195	+	0.967676i	$0.581153\pi$
$600$	130.796	5.33973
$601$	−18.5676	−0.757389	−0.378695	−	0.925522i	$-0.623627\pi$
$601$	−18.5676	−0.757389	−0.378695	+	0.925522i	$0.623627\pi$
$602$	57.6960	2.35151
$603$	31.2395	1.27217
$604$	−43.8991	−1.78623
$605$	32.7194	1.33023
$606$	36.3940	1.47841
$607$	−22.0509	−0.895017	−0.447508	−	0.894280i	$-0.647689\pi$
$607$	−22.0509	−0.895017	−0.447508	+	0.894280i	$0.647689\pi$
$608$	−24.6161	−0.998313
$609$	−60.5813	−2.45488
$610$	87.5968	3.54669
$611$	−52.1186	−2.10849
$612$	149.744	6.05306
$613$	32.0673	1.29519	0.647594	−	0.761986i	$-0.275775\pi$
$613$	32.0673	1.29519	0.647594	+	0.761986i	$0.275775\pi$
$614$	41.5212	1.67566
$615$	43.3789	1.74921
$616$	13.9165	0.560712
$617$	30.7988	1.23991	0.619956	−	0.784637i	$-0.287150\pi$
$617$	30.7988	1.23991	0.619956	+	0.784637i	$0.287150\pi$
$618$	−138.584	−5.57467
$619$	−0.834315	−0.0335339	−0.0167670	−	0.999859i	$-0.505337\pi$
$619$	−0.834315	−0.0335339	−0.0167670	+	0.999859i	$0.505337\pi$
$620$	52.3376	2.10193
$621$	110.695	4.44203
$622$	−42.8488	−1.71808
$623$	−11.0925	−0.444411
$624$	−221.640	−8.87270
$625$	−24.7441	−0.989764
$626$	42.5811	1.70188
$627$	5.07915	0.202842
$628$	−43.5351	−1.73724
$629$	3.88533	0.154918
$630$	138.188	5.50555
$631$	38.8706	1.54742	0.773708	−	0.633543i	$-0.218400\pi$
$631$	38.8706	1.54742	0.773708	+	0.633543i	$0.218400\pi$
$632$	110.244	4.38526
$633$	−27.1375	−1.07862
$634$	83.3423	3.30995
$635$	−4.21348	−0.167207
$636$	36.0412	1.42912
$637$	−15.1256	−0.599297
$638$	18.8862	0.747711
$639$	1.16930	0.0462567
$640$	23.7416	0.938469
$641$	21.5425	0.850877	0.425439	−	0.904987i	$-0.360120\pi$
$641$	21.5425	0.850877	0.425439	+	0.904987i	$0.360120\pi$
$642$	−41.4077	−1.63423
$643$	9.52345	0.375568	0.187784	−	0.982210i	$-0.439869\pi$
$643$	9.52345	0.375568	0.187784	+	0.982210i	$0.439869\pi$
$644$	−76.2871	−3.00613
$645$	−106.103	−4.17781
$646$	−19.3336	−0.760672
$647$	14.1709	0.557114	0.278557	−	0.960420i	$-0.410144\pi$
$647$	14.1709	0.557114	0.278557	+	0.960420i	$0.410144\pi$
$648$	−217.190	−8.53204
$649$	2.63054	0.103258
$650$	−82.7081	−3.24408
$651$	23.1222	0.906229
$652$	92.5090	3.62293
$653$	−20.4560	−0.800504	−0.400252	−	0.916405i	$-0.631077\pi$
$653$	−20.4560	−0.800504	−0.400252	+	0.916405i	$0.631077\pi$
$654$	8.65784	0.338548
$655$	−35.1552	−1.37363
$656$	45.6702	1.78312
$657$	−46.2375	−1.80390
$658$	47.5026	1.85184
$659$	−2.66258	−0.103720	−0.0518598	−	0.998654i	$-0.516515\pi$
$659$	−2.66258	−0.103720	−0.0518598	+	0.998654i	$0.516515\pi$
$660$	−42.7048	−1.66228
$661$	10.4695	0.407217	0.203609	−	0.979052i	$-0.434733\pi$
$661$	10.4695	0.407217	0.203609	+	0.979052i	$0.434733\pi$
$662$	33.3838	1.29750
$663$	−78.7932	−3.06007
$664$	−40.7629	−1.58191
$665$	−12.7375	−0.493941
$666$	−20.4173	−0.791153
$667$	−62.0444	−2.40237
$668$	68.7636	2.66054
$669$	−20.3166	−0.785485
$670$	33.9118	1.31013
$671$	−8.61313	−0.332506
$672$	91.4363	3.52723
$673$	−5.31397	−0.204838	−0.102419	−	0.994741i	$-0.532658\pi$
$673$	−5.31397	−0.204838	−0.102419	+	0.994741i	$0.532658\pi$
$674$	65.9840	2.54161
$675$	−78.0908	−3.00572
$676$	126.563	4.86780
$677$	−1.10229	−0.0423644	−0.0211822	−	0.999776i	$-0.506743\pi$
$677$	−1.10229	−0.0423644	−0.0211822	+	0.999776i	$0.506743\pi$
$678$	19.0522	0.731694
$679$	21.2549	0.815687
$680$	97.4171	3.73578
$681$	82.0368	3.14366
$682$	−7.20833	−0.276021
$683$	35.5521	1.36036	0.680182	−	0.733044i	$-0.261901\pi$
$683$	35.5521	1.36036	0.680182	+	0.733044i	$0.261901\pi$
$684$	72.5329	2.77336
$685$	69.0502	2.63827
$686$	53.2997	2.03499
$687$	13.9166	0.530950
$688$	−111.708	−4.25881
$689$	−13.6581	−0.520331
$690$	196.509	7.48097
$691$	−20.4475	−0.777861	−0.388931	−	0.921267i	$-0.627155\pi$
$691$	−20.4475	−0.777861	−0.388931	+	0.921267i	$0.627155\pi$
$692$	−71.2210	−2.70742
$693$	−13.5876	−0.516151
$694$	30.5883	1.16111
$695$	−16.6653	−0.632153
$696$	224.426	8.50683
$697$	16.2358	0.614974
$698$	41.5203	1.57157
$699$	−90.6907	−3.43024
$700$	53.8176	2.03411
$701$	31.4512	1.18789	0.593947	−	0.804504i	$-0.297569\pi$
$701$	31.4512	1.18789	0.593947	+	0.804504i	$0.297569\pi$
$702$	253.192	9.55613
$703$	1.88197	0.0709797
$704$	−10.4891	−0.395323
$705$	−87.3575	−3.29007
$706$	−5.78368	−0.217672
$707$	8.97422	0.337510
$708$	52.1599	1.96029
$709$	11.9634	0.449294	0.224647	−	0.974440i	$-0.427877\pi$
$709$	11.9634	0.449294	0.224647	+	0.974440i	$0.427877\pi$
$710$	1.26932	0.0476369
$711$	−107.638	−4.03676
$712$	41.0925	1.54001
$713$	23.6806	0.886845
$714$	71.8147	2.68760
$715$	16.1833	0.605220
$716$	61.8878	2.31285
$717$	−26.2658	−0.980915
$718$	19.8326	0.740147
$719$	−46.5827	−1.73724	−0.868620	−	0.495478i	$-0.834993\pi$
$719$	−46.5827	−1.73724	−0.868620	+	0.495478i	$0.834993\pi$
$720$	−267.552	−9.97107
$721$	−34.1728	−1.27266
$722$	40.8727	1.52112
$723$	2.49134	0.0926541
$724$	−99.8002	−3.70905
$725$	43.7699	1.62557
$726$	−89.3546	−3.31626
$727$	−29.5504	−1.09596	−0.547981	−	0.836491i	$-0.684603\pi$
$727$	−29.5504	−1.09596	−0.547981	+	0.836491i	$0.684603\pi$
$728$	−104.571	−3.87566
$729$	60.1749	2.22870
$730$	−50.1929	−1.85772
$731$	−39.7121	−1.46881
$732$	−170.786	−6.31243
$733$	−43.4774	−1.60588	−0.802938	−	0.596063i	$-0.796731\pi$
$733$	−43.4774	−1.60588	−0.802938	+	0.596063i	$0.796731\pi$
$734$	30.0425	1.10889
$735$	−25.3524	−0.935139
$736$	93.6445	3.45178
$737$	−3.33445	−0.122826
$738$	−85.3184	−3.14062
$739$	−11.3346	−0.416951	−0.208475	−	0.978028i	$-0.566850\pi$
$739$	−11.3346	−0.416951	−0.208475	+	0.978028i	$0.566850\pi$
$740$	−15.8233	−0.581676
$741$	−38.1657	−1.40205
$742$	12.4484	0.456995
$743$	36.3342	1.33297	0.666487	−	0.745517i	$-0.267797\pi$
$743$	36.3342	1.33297	0.666487	+	0.745517i	$0.267797\pi$
$744$	−85.6569	−3.14034
$745$	−52.0119	−1.90557
$746$	−92.2791	−3.37858
$747$	39.7995	1.45619
$748$	−15.9835	−0.584413
$749$	−10.2105	−0.373085
$750$	−1.39074	−0.0507827
$751$	25.8926	0.944835	0.472417	−	0.881375i	$-0.343381\pi$
$751$	25.8926	0.944835	0.472417	+	0.881375i	$0.343381\pi$
$752$	−91.9717	−3.35386
$753$	4.87375	0.177609
$754$	−141.914	−5.16821
$755$	27.8839	1.01480
$756$	−164.751	−5.99192
$757$	−42.0653	−1.52889	−0.764444	−	0.644690i	$-0.776986\pi$
$757$	−42.0653	−1.52889	−0.764444	+	0.644690i	$0.776986\pi$
$758$	−54.2802	−1.97155
$759$	−19.3221	−0.701349
$760$	47.1867	1.71164
$761$	−7.46783	−0.270708	−0.135354	−	0.990797i	$-0.543217\pi$
$761$	−7.46783	−0.270708	−0.135354	+	0.990797i	$0.543217\pi$
$762$	11.5068	0.416846
$763$	2.13489	0.0772883
$764$	−60.7586	−2.19817
$765$	−95.1149	−3.43889
$766$	−71.3026	−2.57627
$767$	−19.7664	−0.713722
$768$	18.5045	0.667724
$769$	9.36486	0.337706	0.168853	−	0.985641i	$-0.445994\pi$
$769$	9.36486	0.337706	0.168853	+	0.985641i	$0.445994\pi$
$770$	−14.7500	−0.531552
$771$	68.6000	2.47057
$772$	9.37323	0.337350
$773$	44.5572	1.60261	0.801305	−	0.598256i	$-0.204140\pi$
$773$	44.5572	1.60261	0.801305	+	0.598256i	$0.204140\pi$
$774$	208.686	7.50106
$775$	−16.7057	−0.600088
$776$	−78.7395	−2.82658
$777$	−6.99056	−0.250785
$778$	73.7815	2.64519
$779$	7.86426	0.281766
$780$	320.891	11.4897
$781$	−0.124809	−0.00446601
$782$	73.5491	2.63011
$783$	−133.992	−4.78847
$784$	−26.6915	−0.953270
$785$	27.6527	0.986966
$786$	96.0068	3.42445
$787$	12.4181	0.442659	0.221329	−	0.975199i	$-0.428960\pi$
$787$	12.4181	0.442659	0.221329	+	0.975199i	$0.428960\pi$
$788$	−85.9764	−3.06278
$789$	−63.0371	−2.24418
$790$	−116.846	−4.15721
$791$	4.69798	0.167041
$792$	50.3358	1.78861
$793$	64.7206	2.29829
$794$	24.7755	0.879249
$795$	−22.8927	−0.811920
$796$	79.4807	2.81712
$797$	−11.2583	−0.398790	−0.199395	−	0.979919i	$-0.563898\pi$
$797$	−11.2583	−0.398790	−0.199395	+	0.979919i	$0.563898\pi$
$798$	34.7855	1.23139
$799$	−32.6960	−1.15670
$800$	−66.0626	−2.33566
$801$	−40.1214	−1.41762
$802$	−72.1616	−2.54811
$803$	4.93531	0.174163
$804$	−66.1173	−2.33178
$805$	48.4562	1.70786
$806$	54.1647	1.90787
$807$	−21.2633	−0.748504
$808$	−33.2453	−1.16957
$809$	−46.5709	−1.63735	−0.818673	−	0.574260i	$-0.805290\pi$
$809$	−46.5709	−1.63735	−0.818673	+	0.574260i	$0.805290\pi$
$810$	230.198	8.08834
$811$	7.06308	0.248018	0.124009	−	0.992281i	$-0.460425\pi$
$811$	7.06308	0.248018	0.124009	+	0.992281i	$0.460425\pi$
$812$	92.3426	3.24059
$813$	5.13869	0.180222
$814$	2.17930	0.0763845
$815$	−58.7600	−2.05827
$816$	−139.043	−4.86749
$817$	−19.2357	−0.672971
$818$	92.3166	3.22778
$819$	102.100	3.56766
$820$	−66.1215	−2.30906
$821$	−1.85501	−0.0647401	−0.0323701	−	0.999476i	$-0.510306\pi$
$821$	−1.85501	−0.0647401	−0.0323701	+	0.999476i	$0.510306\pi$
$822$	−188.572	−6.57720
$823$	2.51833	0.0877836	0.0438918	−	0.999036i	$-0.486024\pi$
$823$	2.51833	0.0877836	0.0438918	+	0.999036i	$0.486024\pi$
$824$	126.594	4.41012
$825$	13.6310	0.474571
$826$	18.0157	0.626847
$827$	48.3493	1.68127	0.840635	−	0.541602i	$-0.182182\pi$
$827$	48.3493	1.68127	0.840635	+	0.541602i	$0.182182\pi$
$828$	−275.930	−9.58922
$829$	48.4150	1.68152	0.840761	−	0.541407i	$-0.182108\pi$
$829$	48.4150	1.68152	0.840761	+	0.541407i	$0.182108\pi$
$830$	43.2042	1.49964
$831$	−105.453	−3.65812
$832$	78.8170	2.73249
$833$	−9.48887	−0.328770
$834$	45.5120	1.57595
$835$	−43.6774	−1.51152
$836$	−7.74203	−0.267764
$837$	51.1409	1.76769
$838$	−80.1237	−2.76783
$839$	−25.8727	−0.893226	−0.446613	−	0.894727i	$-0.647370\pi$
$839$	−25.8727	−0.893226	−0.446613	+	0.894727i	$0.647370\pi$
$840$	−175.275	−6.04755
$841$	46.1023	1.58973
$842$	25.5580	0.880786
$843$	−43.7300	−1.50614
$844$	41.3650	1.42384
$845$	−80.3904	−2.76551
$846$	171.816	5.90717
$847$	−22.0335	−0.757080
$848$	−24.1019	−0.827662
$849$	103.673	3.55805
$850$	−51.8860	−1.77968
$851$	−7.15939	−0.245421
$852$	−2.47478	−0.0847845
$853$	35.4688	1.21443	0.607214	−	0.794538i	$-0.292287\pi$
$853$	35.4688	1.21443	0.607214	+	0.794538i	$0.292287\pi$
$854$	−58.9885	−2.01854
$855$	−46.0716	−1.57561
$856$	37.8253	1.29284
$857$	−16.7679	−0.572780	−0.286390	−	0.958113i	$-0.592455\pi$
$857$	−16.7679	−0.572780	−0.286390	+	0.958113i	$0.592455\pi$
$858$	−44.1955	−1.50881
$859$	−4.72875	−0.161343	−0.0806714	−	0.996741i	$-0.525706\pi$
$859$	−4.72875	−0.161343	−0.0806714	+	0.996741i	$0.525706\pi$
$860$	161.731	5.51497
$861$	−29.2117	−0.995533
$862$	97.3677	3.31636
$863$	13.6033	0.463061	0.231531	−	0.972828i	$-0.425627\pi$
$863$	13.6033	0.463061	0.231531	+	0.972828i	$0.425627\pi$
$864$	202.236	6.88020
$865$	45.2383	1.53815
$866$	2.99509	0.101777
$867$	6.23524	0.211760
$868$	−35.2446	−1.19628
$869$	11.4891	0.389742
$870$	−237.867	−8.06443
$871$	25.0556	0.848978
$872$	−7.90879	−0.267825
$873$	76.8787	2.60195
$874$	35.6256	1.20505
$875$	−0.342936	−0.0115933
$876$	97.8602	3.30639
$877$	−35.3828	−1.19479	−0.597396	−	0.801946i	$-0.703798\pi$
$877$	−35.3828	−1.19479	−0.597396	+	0.801946i	$0.703798\pi$
$878$	−12.9542	−0.437184
$879$	81.1144	2.73592
$880$	28.5580	0.962691
$881$	−8.05943	−0.271529	−0.135764	−	0.990741i	$-0.543349\pi$
$881$	−8.05943	−0.271529	−0.135764	+	0.990741i	$0.543349\pi$
$882$	49.8636	1.67900
$883$	−20.4408	−0.687888	−0.343944	−	0.938990i	$-0.611763\pi$
$883$	−20.4408	−0.687888	−0.343944	+	0.938990i	$0.611763\pi$
$884$	120.103	4.03949
$885$	−33.1310	−1.11369
$886$	−95.2138	−3.19877
$887$	−38.4039	−1.28948	−0.644739	−	0.764403i	$-0.723034\pi$
$887$	−38.4039	−1.28948	−0.644739	+	0.764403i	$0.723034\pi$
$888$	25.8968	0.869039
$889$	2.83739	0.0951631
$890$	−43.5536	−1.45992
$891$	−22.6347	−0.758290
$892$	30.9681	1.03689
$893$	−15.8372	−0.529972
$894$	142.041	4.75057
$895$	−39.3100	−1.31399
$896$	−15.9878	−0.534115
$897$	145.190	4.84775
$898$	10.2338	0.341506
$899$	−28.6644	−0.956012
$900$	194.658	6.48859
$901$	−8.56824	−0.285449
$902$	9.10675	0.303221
$903$	71.4509	2.37774
$904$	−17.4038	−0.578843
$905$	63.3913	2.10720
$906$	−76.1493	−2.52989
$907$	49.0298	1.62801	0.814004	−	0.580859i	$-0.197283\pi$
$907$	49.0298	1.62801	0.814004	+	0.580859i	$0.197283\pi$
$908$	−125.047	−4.14982
$909$	32.4597	1.07662
$910$	110.834	3.67411
$911$	−9.34740	−0.309693	−0.154847	−	0.987939i	$-0.549488\pi$
$911$	−9.34740	−0.309693	−0.154847	+	0.987939i	$0.549488\pi$
$912$	−67.3496	−2.23017
$913$	−4.24814	−0.140593
$914$	36.5761	1.20983
$915$	108.480	3.58624
$916$	−21.2127	−0.700887
$917$	23.6738	0.781779
$918$	158.837	5.24242
$919$	38.1410	1.25815	0.629077	−	0.777343i	$-0.283433\pi$
$919$	38.1410	1.25815	0.629077	+	0.777343i	$0.283433\pi$
$920$	−179.508	−5.91820
$921$	51.4200	1.69435
$922$	33.4829	1.10270
$923$	0.937835	0.0308692
$924$	28.7578	0.946061
$925$	5.05067	0.166065
$926$	−17.0465	−0.560182
$927$	−123.603	−4.05964
$928$	−113.353	−3.72100
$929$	−33.1736	−1.08839	−0.544196	−	0.838958i	$-0.683165\pi$
$929$	−33.1736	−1.08839	−0.544196	+	0.838958i	$0.683165\pi$
$930$	90.7870	2.97702
$931$	−4.59620	−0.150634
$932$	138.238	4.52813
$933$	−53.0641	−1.73724
$934$	25.9933	0.850526
$935$	10.1524	0.332019
$936$	−378.232	−12.3629
$937$	33.6645	1.09977	0.549886	−	0.835240i	$-0.314671\pi$
$937$	33.6645	1.09977	0.549886	+	0.835240i	$0.314671\pi$
$938$	−22.8365	−0.745639
$939$	52.7325	1.72086
$940$	133.157	4.34310
$941$	−3.78986	−0.123546	−0.0617730	−	0.998090i	$-0.519675\pi$
$941$	−3.78986	−0.123546	−0.0617730	+	0.998090i	$0.519675\pi$
$942$	−75.5178	−2.46050
$943$	−29.9172	−0.974239
$944$	−34.8810	−1.13528
$945$	104.647	3.40415
$946$	−22.2748	−0.724215
$947$	25.5402	0.829943	0.414972	−	0.909834i	$-0.363791\pi$
$947$	25.5402	0.829943	0.414972	+	0.909834i	$0.363791\pi$
$948$	227.813	7.39903
$949$	−37.0848	−1.20382
$950$	−25.1324	−0.815404
$951$	103.211	3.34686
$952$	−65.6015	−2.12616
$953$	−22.8300	−0.739538	−0.369769	−	0.929124i	$-0.620563\pi$
$953$	−22.8300	−0.739538	−0.369769	+	0.929124i	$0.620563\pi$
$954$	45.0258	1.45776
$955$	38.5928	1.24883
$956$	40.0364	1.29487
$957$	23.3887	0.756049
$958$	−37.4059	−1.20853
$959$	−46.4990	−1.50153
$960$	132.108	4.26376
$961$	−20.0596	−0.647083
$962$	−16.3757	−0.527973
$963$	−36.9314	−1.19010
$964$	−3.79750	−0.122309
$965$	−5.95371	−0.191657
$966$	−132.331	−4.25768
$967$	2.62655	0.0844640	0.0422320	−	0.999108i	$-0.486553\pi$
$967$	2.62655	0.0844640	0.0422320	+	0.999108i	$0.486553\pi$
$968$	81.6239	2.62349
$969$	−23.9428	−0.769154
$970$	83.4553	2.67959
$971$	−30.7575	−0.987054	−0.493527	−	0.869731i	$-0.664293\pi$
$971$	−30.7575	−0.987054	−0.493527	+	0.869731i	$0.664293\pi$
$972$	−217.302	−6.96996
$973$	11.2226	0.359780
$974$	−24.1732	−0.774558
$975$	−102.426	−3.28025
$976$	114.210	3.65577
$977$	−42.9079	−1.37274	−0.686372	−	0.727250i	$-0.740798\pi$
$977$	−42.9079	−1.37274	−0.686372	+	0.727250i	$0.740798\pi$
$978$	160.470	5.13127
$979$	4.28249	0.136869
$980$	38.6441	1.23444
$981$	7.72189	0.246541
$982$	100.052	3.19278
$983$	−46.7375	−1.49069	−0.745347	−	0.666677i	$-0.767716\pi$
$983$	−46.7375	−1.49069	−0.745347	+	0.666677i	$0.767716\pi$
$984$	108.216	3.44980
$985$	54.6107	1.74004
$986$	−89.0283	−2.83524
$987$	58.8273	1.87249
$988$	58.1750	1.85079
$989$	73.1765	2.32688
$990$	−53.3505	−1.69559
$991$	−21.8623	−0.694478	−0.347239	−	0.937777i	$-0.612881\pi$
$991$	−21.8623	−0.694478	−0.347239	+	0.937777i	$0.612881\pi$
$992$	43.2637	1.37362
$993$	41.3426	1.31197
$994$	−0.854774	−0.0271118
$995$	−50.4847	−1.60047
$996$	−84.2344	−2.66907
$997$	44.2809	1.40239	0.701195	−	0.712970i	$-0.252650\pi$
$997$	44.2809	1.40239	0.701195	+	0.712970i	$0.252650\pi$
$998$	−72.2179	−2.28602
$999$	−15.4615	−0.489180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.4	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.4	✓	77	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64408 q^{2} -3.27443 q^{3} +4.99114 q^{4} -3.17028 q^{5} +8.65784 q^{6} +2.13489 q^{7} -7.90879 q^{8} +7.72189 q^{9} +O(q^{10})\)	\(q-2.64408 q^{2} -3.27443 q^{3} +4.99114 q^{4} -3.17028 q^{5} +8.65784 q^{6} +2.13489 q^{7} -7.90879 q^{8} +7.72189 q^{9} +8.38246 q^{10} -0.824221 q^{11} -16.3431 q^{12} +6.19334 q^{13} -5.64482 q^{14} +10.3809 q^{15} +10.9292 q^{16} +3.88533 q^{17} -20.4173 q^{18} +1.88197 q^{19} -15.8233 q^{20} -6.99056 q^{21} +2.17930 q^{22} -7.15939 q^{23} +25.8968 q^{24} +5.05067 q^{25} -16.3757 q^{26} -15.4615 q^{27} +10.6555 q^{28} +8.66616 q^{29} -27.4478 q^{30} -3.30763 q^{31} -13.0800 q^{32} +2.69885 q^{33} -10.2731 q^{34} -6.76821 q^{35} +38.5410 q^{36} +1.00000 q^{37} -4.97606 q^{38} -20.2797 q^{39} +25.0731 q^{40} +4.17874 q^{41} +18.4836 q^{42} -10.2211 q^{43} -4.11380 q^{44} -24.4805 q^{45} +18.9300 q^{46} -8.41525 q^{47} -35.7868 q^{48} -2.44223 q^{49} -13.3544 q^{50} -12.7222 q^{51} +30.9118 q^{52} -2.20528 q^{53} +40.8813 q^{54} +2.61301 q^{55} -16.8844 q^{56} -6.16237 q^{57} -22.9140 q^{58} -3.19155 q^{59} +51.8123 q^{60} +10.4500 q^{61} +8.74562 q^{62} +16.4854 q^{63} +12.7261 q^{64} -19.6346 q^{65} -7.13597 q^{66} +4.04557 q^{67} +19.3922 q^{68} +23.4429 q^{69} +17.8957 q^{70} +0.151426 q^{71} -61.0708 q^{72} -5.98785 q^{73} -2.64408 q^{74} -16.5381 q^{75} +9.39315 q^{76} -1.75962 q^{77} +53.6210 q^{78} -13.9394 q^{79} -34.6485 q^{80} +27.4619 q^{81} -11.0489 q^{82} +5.15412 q^{83} -34.8908 q^{84} -12.3176 q^{85} +27.0252 q^{86} -28.3767 q^{87} +6.51859 q^{88} -5.19580 q^{89} +64.7284 q^{90} +13.2221 q^{91} -35.7335 q^{92} +10.8306 q^{93} +22.2506 q^{94} -5.96636 q^{95} +42.8294 q^{96} +9.95594 q^{97} +6.45744 q^{98} -6.36454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

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