LMFDB - Embedded newform 6033.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11027 q^{2} +1.00000 q^{3} +2.45325 q^{4} -0.410067 q^{5} -2.11027 q^{6} +2.75939 q^{7} -0.956486 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11027 q^{2} +1.00000 q^{3} +2.45325 q^{4} -0.410067 q^{5} -2.11027 q^{6} +2.75939 q^{7} -0.956486 q^{8} +1.00000 q^{9} +0.865353 q^{10} -0.365645 q^{11} +2.45325 q^{12} -4.77576 q^{13} -5.82306 q^{14} -0.410067 q^{15} -2.88806 q^{16} +0.510667 q^{17} -2.11027 q^{18} -6.27345 q^{19} -1.00600 q^{20} +2.75939 q^{21} +0.771611 q^{22} -2.37530 q^{23} -0.956486 q^{24} -4.83185 q^{25} +10.0782 q^{26} +1.00000 q^{27} +6.76947 q^{28} +2.73353 q^{29} +0.865353 q^{30} +7.57085 q^{31} +8.00756 q^{32} -0.365645 q^{33} -1.07765 q^{34} -1.13153 q^{35} +2.45325 q^{36} +7.78065 q^{37} +13.2387 q^{38} -4.77576 q^{39} +0.392223 q^{40} -3.25071 q^{41} -5.82306 q^{42} +5.74426 q^{43} -0.897020 q^{44} -0.410067 q^{45} +5.01254 q^{46} +8.36747 q^{47} -2.88806 q^{48} +0.614207 q^{49} +10.1965 q^{50} +0.510667 q^{51} -11.7161 q^{52} +5.67723 q^{53} -2.11027 q^{54} +0.149939 q^{55} -2.63931 q^{56} -6.27345 q^{57} -5.76849 q^{58} -6.59086 q^{59} -1.00600 q^{60} -4.34004 q^{61} -15.9766 q^{62} +2.75939 q^{63} -11.1220 q^{64} +1.95838 q^{65} +0.771611 q^{66} +1.72294 q^{67} +1.25280 q^{68} -2.37530 q^{69} +2.38784 q^{70} +10.1193 q^{71} -0.956486 q^{72} -12.1352 q^{73} -16.4193 q^{74} -4.83185 q^{75} -15.3904 q^{76} -1.00896 q^{77} +10.0782 q^{78} -13.9201 q^{79} +1.18430 q^{80} +1.00000 q^{81} +6.85989 q^{82} -11.8786 q^{83} +6.76947 q^{84} -0.209408 q^{85} -12.1220 q^{86} +2.73353 q^{87} +0.349734 q^{88} -14.6254 q^{89} +0.865353 q^{90} -13.1782 q^{91} -5.82722 q^{92} +7.57085 q^{93} -17.6576 q^{94} +2.57253 q^{95} +8.00756 q^{96} +1.38864 q^{97} -1.29614 q^{98} -0.365645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−2.11027	−1.49219	−0.746094	−	0.665840i	$-0.768073\pi$
$2$	−2.11027	−1.49219	−0.746094	+	0.665840i	$0.768073\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.45325	1.22663
$5$	−0.410067	−0.183387	−0.0916937	−	0.995787i	$-0.529228\pi$
$5$	−0.410067	−0.183387	−0.0916937	+	0.995787i	$0.529228\pi$
$6$	−2.11027	−0.861515
$7$	2.75939	1.04295	0.521475	−	0.853267i	$-0.325382\pi$
$7$	2.75939	1.04295	0.521475	+	0.853267i	$0.325382\pi$
$8$	−0.956486	−0.338169
$9$	1.00000	0.333333
$10$	0.865353	0.273649
$11$	−0.365645	−0.110246	−0.0551231	−	0.998480i	$-0.517555\pi$
$11$	−0.365645	−0.110246	−0.0551231	+	0.998480i	$0.517555\pi$
$12$	2.45325	0.708193
$13$	−4.77576	−1.32456	−0.662278	−	0.749258i	$-0.730410\pi$
$13$	−4.77576	−1.32456	−0.662278	+	0.749258i	$0.730410\pi$
$14$	−5.82306	−1.55628
$15$	−0.410067	−0.105879
$16$	−2.88806	−0.722015
$17$	0.510667	0.123855	0.0619275	−	0.998081i	$-0.480275\pi$
$17$	0.510667	0.123855	0.0619275	+	0.998081i	$0.480275\pi$
$18$	−2.11027	−0.497396
$19$	−6.27345	−1.43923	−0.719614	−	0.694374i	$-0.755681\pi$
$19$	−6.27345	−1.43923	−0.719614	+	0.694374i	$0.755681\pi$
$20$	−1.00600	−0.224948
$21$	2.75939	0.602147
$22$	0.771611	0.164508
$23$	−2.37530	−0.495285	−0.247642	−	0.968851i	$-0.579656\pi$
$23$	−2.37530	−0.495285	−0.247642	+	0.968851i	$0.579656\pi$
$24$	−0.956486	−0.195242
$25$	−4.83185	−0.966369
$26$	10.0782	1.97649
$27$	1.00000	0.192450
$28$	6.76947	1.27931
$29$	2.73353	0.507603	0.253802	−	0.967256i	$-0.418319\pi$
$29$	2.73353	0.507603	0.253802	+	0.967256i	$0.418319\pi$
$30$	0.865353	0.157991
$31$	7.57085	1.35976	0.679882	−	0.733321i	$-0.262031\pi$
$31$	7.57085	1.35976	0.679882	+	0.733321i	$0.262031\pi$
$32$	8.00756	1.41555
$33$	−0.365645	−0.0636507
$34$	−1.07765	−0.184815
$35$	−1.13153	−0.191264
$36$	2.45325	0.408875
$37$	7.78065	1.27913	0.639566	−	0.768736i	$-0.279114\pi$
$37$	7.78065	1.27913	0.639566	+	0.768736i	$0.279114\pi$
$38$	13.2387	2.14760
$39$	−4.77576	−0.764733
$40$	0.392223	0.0620159
$41$	−3.25071	−0.507676	−0.253838	−	0.967247i	$-0.581693\pi$
$41$	−3.25071	−0.507676	−0.253838	+	0.967247i	$0.581693\pi$
$42$	−5.82306	−0.898517
$43$	5.74426	0.875991	0.437996	−	0.898977i	$-0.355689\pi$
$43$	5.74426	0.875991	0.437996	+	0.898977i	$0.355689\pi$
$44$	−0.897020	−0.135231
$45$	−0.410067	−0.0611291
$46$	5.01254	0.739058
$47$	8.36747	1.22052	0.610260	−	0.792201i	$-0.291065\pi$
$47$	8.36747	1.22052	0.610260	+	0.792201i	$0.291065\pi$
$48$	−2.88806	−0.416855
$49$	0.614207	0.0877438
$50$	10.1965	1.44200
$51$	0.510667	0.0715077
$52$	−11.7161	−1.62474
$53$	5.67723	0.779827	0.389914	−	0.920851i	$-0.372505\pi$
$53$	5.67723	0.779827	0.389914	+	0.920851i	$0.372505\pi$
$54$	−2.11027	−0.287172
$55$	0.149939	0.0202178
$56$	−2.63931	−0.352693
$57$	−6.27345	−0.830939
$58$	−5.76849	−0.757440
$59$	−6.59086	−0.858057	−0.429028	−	0.903291i	$-0.641144\pi$
$59$	−6.59086	−0.858057	−0.429028	+	0.903291i	$0.641144\pi$
$60$	−1.00600	−0.129874
$61$	−4.34004	−0.555685	−0.277843	−	0.960627i	$-0.589619\pi$
$61$	−4.34004	−0.555685	−0.277843	+	0.960627i	$0.589619\pi$
$62$	−15.9766	−2.02902
$63$	2.75939	0.347650
$64$	−11.1220	−1.39025
$65$	1.95838	0.242907
$66$	0.771611	0.0949788
$67$	1.72294	0.210491	0.105245	−	0.994446i	$-0.466437\pi$
$67$	1.72294	0.210491	0.105245	+	0.994446i	$0.466437\pi$
$68$	1.25280	0.151924
$69$	−2.37530	−0.285953
$70$	2.38784	0.285402
$71$	10.1193	1.20094	0.600468	−	0.799649i	$-0.294981\pi$
$71$	10.1193	1.20094	0.600468	+	0.799649i	$0.294981\pi$
$72$	−0.956486	−0.112723
$73$	−12.1352	−1.42032	−0.710160	−	0.704040i	$-0.751378\pi$
$73$	−12.1352	−1.42032	−0.710160	+	0.704040i	$0.751378\pi$
$74$	−16.4193	−1.90871
$75$	−4.83185	−0.557933
$76$	−15.3904	−1.76540
$77$	−1.00896	−0.114981
$78$	10.0782	1.14113
$79$	−13.9201	−1.56613	−0.783065	−	0.621940i	$-0.786345\pi$
$79$	−13.9201	−1.56613	−0.783065	+	0.621940i	$0.786345\pi$
$80$	1.18430	0.132408
$81$	1.00000	0.111111
$82$	6.85989	0.757548
$83$	−11.8786	−1.30384	−0.651922	−	0.758286i	$-0.726037\pi$
$83$	−11.8786	−1.30384	−0.651922	+	0.758286i	$0.726037\pi$
$84$	6.76947	0.738609
$85$	−0.209408	−0.0227135
$86$	−12.1220	−1.30714
$87$	2.73353	0.293065
$88$	0.349734	0.0372818
$89$	−14.6254	−1.55029	−0.775143	−	0.631786i	$-0.782322\pi$
$89$	−14.6254	−1.55029	−0.775143	+	0.631786i	$0.782322\pi$
$90$	0.865353	0.0912162
$91$	−13.1782	−1.38145
$92$	−5.82722	−0.607529
$93$	7.57085	0.785060
$94$	−17.6576	−1.82125
$95$	2.57253	0.263936
$96$	8.00756	0.817268
$97$	1.38864	0.140995	0.0704976	−	0.997512i	$-0.477541\pi$
$97$	1.38864	0.140995	0.0704976	+	0.997512i	$0.477541\pi$
$98$	−1.29614	−0.130930
$99$	−0.365645	−0.0367487
$100$	−11.8537	−1.18537
$101$	−0.538700	−0.0536027	−0.0268013	−	0.999641i	$-0.508532\pi$
$101$	−0.538700	−0.0536027	−0.0268013	+	0.999641i	$0.508532\pi$
$102$	−1.07765	−0.106703
$103$	2.34011	0.230578	0.115289	−	0.993332i	$-0.463221\pi$
$103$	2.34011	0.230578	0.115289	+	0.993332i	$0.463221\pi$
$104$	4.56794	0.447924
$105$	−1.13153	−0.110426
$106$	−11.9805	−1.16365
$107$	8.84933	0.855497	0.427749	−	0.903898i	$-0.359307\pi$
$107$	8.84933	0.855497	0.427749	+	0.903898i	$0.359307\pi$
$108$	2.45325	0.236064
$109$	−15.1835	−1.45432	−0.727159	−	0.686469i	$-0.759160\pi$
$109$	−15.1835	−1.45432	−0.727159	+	0.686469i	$0.759160\pi$
$110$	−0.316412	−0.0301687
$111$	7.78065	0.738507
$112$	−7.96927	−0.753025
$113$	−6.91923	−0.650906	−0.325453	−	0.945558i	$-0.605517\pi$
$113$	−6.91923	−0.650906	−0.325453	+	0.945558i	$0.605517\pi$
$114$	13.2387	1.23992
$115$	0.974033	0.0908290
$116$	6.70603	0.622640
$117$	−4.77576	−0.441519
$118$	13.9085	1.28038
$119$	1.40913	0.129175
$120$	0.392223	0.0358049
$121$	−10.8663	−0.987846
$122$	9.15867	0.829187
$123$	−3.25071	−0.293107
$124$	18.5732	1.66792
$125$	4.03171	0.360607
$126$	−5.82306	−0.518759
$127$	−0.182675	−0.0162097	−0.00810487	−	0.999967i	$-0.502580\pi$
$127$	−0.182675	−0.0162097	−0.00810487	+	0.999967i	$0.502580\pi$
$128$	7.45539	0.658969
$129$	5.74426	0.505754
$130$	−4.13272	−0.362463
$131$	20.3977	1.78216	0.891079	−	0.453849i	$-0.149949\pi$
$131$	20.3977	1.78216	0.891079	+	0.453849i	$0.149949\pi$
$132$	−0.897020	−0.0780756
$133$	−17.3109	−1.50104
$134$	−3.63587	−0.314092
$135$	−0.410067	−0.0352929
$136$	−0.488446	−0.0418839
$137$	2.58203	0.220598	0.110299	−	0.993898i	$-0.464819\pi$
$137$	2.58203	0.220598	0.110299	+	0.993898i	$0.464819\pi$
$138$	5.01254	0.426696
$139$	−21.4487	−1.81926	−0.909630	−	0.415420i	$-0.863635\pi$
$139$	−21.4487	−1.81926	−0.909630	+	0.415420i	$0.863635\pi$
$140$	−2.77593	−0.234609
$141$	8.36747	0.704668
$142$	−21.3544	−1.79202
$143$	1.74623	0.146027
$144$	−2.88806	−0.240672
$145$	−1.12093	−0.0930881
$146$	25.6086	2.11939
$147$	0.614207	0.0506589
$148$	19.0879	1.56902
$149$	18.8249	1.54220	0.771098	−	0.636717i	$-0.219708\pi$
$149$	18.8249	1.54220	0.771098	+	0.636717i	$0.219708\pi$
$150$	10.1965	0.832542
$151$	−8.25809	−0.672033	−0.336017	−	0.941856i	$-0.609080\pi$
$151$	−8.25809	−0.672033	−0.336017	+	0.941856i	$0.609080\pi$
$152$	6.00047	0.486702
$153$	0.510667	0.0412850
$154$	2.12917	0.171574
$155$	−3.10455	−0.249364
$156$	−11.7161	−0.938042
$157$	−1.60194	−0.127849	−0.0639244	−	0.997955i	$-0.520362\pi$
$157$	−1.60194	−0.127849	−0.0639244	+	0.997955i	$0.520362\pi$
$158$	29.3751	2.33696
$159$	5.67723	0.450234
$160$	−3.28364	−0.259594
$161$	−6.55438	−0.516557
$162$	−2.11027	−0.165799
$163$	−10.6676	−0.835555	−0.417777	−	0.908549i	$-0.637191\pi$
$163$	−10.6676	−0.835555	−0.417777	+	0.908549i	$0.637191\pi$
$164$	−7.97482	−0.622729
$165$	0.149939	0.0116727
$166$	25.0671	1.94558
$167$	5.15260	0.398721	0.199360	−	0.979926i	$-0.436114\pi$
$167$	5.15260	0.398721	0.199360	+	0.979926i	$0.436114\pi$
$168$	−2.63931	−0.203627
$169$	9.80786	0.754451
$170$	0.441907	0.0338928
$171$	−6.27345	−0.479743
$172$	14.0921	1.07451
$173$	−2.66855	−0.202886	−0.101443	−	0.994841i	$-0.532346\pi$
$173$	−2.66855	−0.202886	−0.101443	+	0.994841i	$0.532346\pi$
$174$	−5.76849	−0.437308
$175$	−13.3329	−1.00787
$176$	1.05600	0.0795994
$177$	−6.59086	−0.495399
$178$	30.8635	2.31332
$179$	−12.0894	−0.903604	−0.451802	−	0.892118i	$-0.649219\pi$
$179$	−12.0894	−0.903604	−0.451802	+	0.892118i	$0.649219\pi$
$180$	−1.00600	−0.0749826
$181$	18.1865	1.35179	0.675895	−	0.736998i	$-0.263757\pi$
$181$	18.1865	1.35179	0.675895	+	0.736998i	$0.263757\pi$
$182$	27.8095	2.06138
$183$	−4.34004	−0.320825
$184$	2.27194	0.167490
$185$	−3.19059	−0.234577
$186$	−15.9766	−1.17146
$187$	−0.186723	−0.0136545
$188$	20.5275	1.49712
$189$	2.75939	0.200716
$190$	−5.42875	−0.393843
$191$	1.39421	0.100881	0.0504407	−	0.998727i	$-0.483937\pi$
$191$	1.39421	0.100881	0.0504407	+	0.998727i	$0.483937\pi$
$192$	−11.1220	−0.802663
$193$	−13.8811	−0.999181	−0.499590	−	0.866262i	$-0.666516\pi$
$193$	−13.8811	−0.999181	−0.499590	+	0.866262i	$0.666516\pi$
$194$	−2.93041	−0.210391
$195$	1.95838	0.140242
$196$	1.50680	0.107629
$197$	18.6431	1.32827	0.664133	−	0.747614i	$-0.268801\pi$
$197$	18.6431	1.32827	0.664133	+	0.747614i	$0.268801\pi$
$198$	0.771611	0.0548360
$199$	4.34104	0.307728	0.153864	−	0.988092i	$-0.450828\pi$
$199$	4.34104	0.307728	0.153864	+	0.988092i	$0.450828\pi$
$200$	4.62159	0.326796
$201$	1.72294	0.121527
$202$	1.13680	0.0799853
$203$	7.54286	0.529405
$204$	1.25280	0.0877132
$205$	1.33301	0.0931014
$206$	−4.93827	−0.344065
$207$	−2.37530	−0.165095
$208$	13.7927	0.956349
$209$	2.29386	0.158669
$210$	2.38784	0.164777
$211$	11.7137	0.806405	0.403202	−	0.915111i	$-0.367897\pi$
$211$	11.7137	0.806405	0.403202	+	0.915111i	$0.367897\pi$
$212$	13.9277	0.956557
$213$	10.1193	0.693361
$214$	−18.6745	−1.27656
$215$	−2.35553	−0.160646
$216$	−0.956486	−0.0650806
$217$	20.8909	1.41817
$218$	32.0414	2.17012
$219$	−12.1352	−0.820022
$220$	0.367838	0.0247996
$221$	−2.43882	−0.164053
$222$	−16.4193	−1.10199
$223$	−24.0829	−1.61271	−0.806355	−	0.591432i	$-0.798563\pi$
$223$	−24.0829	−1.61271	−0.806355	+	0.591432i	$0.798563\pi$
$224$	22.0960	1.47635
$225$	−4.83185	−0.322123
$226$	14.6015	0.971275
$227$	−22.6981	−1.50652	−0.753262	−	0.657721i	$-0.771521\pi$
$227$	−22.6981	−1.50652	−0.753262	+	0.657721i	$0.771521\pi$
$228$	−15.3904	−1.01925
$229$	−25.3014	−1.67197	−0.835983	−	0.548755i	$-0.815102\pi$
$229$	−25.3014	−1.67197	−0.835983	+	0.548755i	$0.815102\pi$
$230$	−2.05548	−0.135534
$231$	−1.00896	−0.0663844
$232$	−2.61458	−0.171656
$233$	−14.4608	−0.947359	−0.473680	−	0.880697i	$-0.657075\pi$
$233$	−14.4608	−0.947359	−0.473680	+	0.880697i	$0.657075\pi$
$234$	10.0782	0.658829
$235$	−3.43122	−0.223828
$236$	−16.1690	−1.05251
$237$	−13.9201	−0.904205
$238$	−2.97364	−0.192753
$239$	2.34530	0.151705	0.0758525	−	0.997119i	$-0.475832\pi$
$239$	2.34530	0.151705	0.0758525	+	0.997119i	$0.475832\pi$
$240$	1.18430	0.0764460
$241$	−4.55946	−0.293701	−0.146850	−	0.989159i	$-0.546914\pi$
$241$	−4.55946	−0.293701	−0.146850	+	0.989159i	$0.546914\pi$
$242$	22.9309	1.47405
$243$	1.00000	0.0641500
$244$	−10.6472	−0.681618
$245$	−0.251866	−0.0160911
$246$	6.85989	0.437371
$247$	29.9605	1.90634
$248$	−7.24141	−0.459830
$249$	−11.8786	−0.752775
$250$	−8.50801	−0.538094
$251$	1.56554	0.0988163	0.0494082	−	0.998779i	$-0.484266\pi$
$251$	1.56554	0.0988163	0.0494082	+	0.998779i	$0.484266\pi$
$252$	6.76947	0.426436
$253$	0.868518	0.0546033
$254$	0.385493	0.0241880
$255$	−0.209408	−0.0131136
$256$	6.51115	0.406947
$257$	−14.3356	−0.894232	−0.447116	−	0.894476i	$-0.647549\pi$
$257$	−14.3356	−0.894232	−0.447116	+	0.894476i	$0.647549\pi$
$258$	−12.1220	−0.754680
$259$	21.4698	1.33407
$260$	4.80440	0.297956
$261$	2.73353	0.169201
$262$	−43.0448	−2.65931
$263$	5.76765	0.355649	0.177824	−	0.984062i	$-0.443094\pi$
$263$	5.76765	0.355649	0.177824	+	0.984062i	$0.443094\pi$
$264$	0.349734	0.0215247
$265$	−2.32804	−0.143011
$266$	36.5307	2.23984
$267$	−14.6254	−0.895058
$268$	4.22681	0.258193
$269$	13.3182	0.812026	0.406013	−	0.913867i	$-0.366919\pi$
$269$	13.3182	0.812026	0.406013	+	0.913867i	$0.366919\pi$
$270$	0.865353	0.0526637
$271$	20.0530	1.21813	0.609067	−	0.793119i	$-0.291544\pi$
$271$	20.0530	1.21813	0.609067	+	0.793119i	$0.291544\pi$
$272$	−1.47484	−0.0894251
$273$	−13.1782	−0.797578
$274$	−5.44879	−0.329174
$275$	1.76674	0.106538
$276$	−5.82722	−0.350757
$277$	−17.3138	−1.04029	−0.520144	−	0.854079i	$-0.674122\pi$
$277$	−17.3138	−1.04029	−0.520144	+	0.854079i	$0.674122\pi$
$278$	45.2627	2.71468
$279$	7.57085	0.453255
$280$	1.08229	0.0646795
$281$	−29.5517	−1.76290	−0.881452	−	0.472273i	$-0.843433\pi$
$281$	−29.5517	−1.76290	−0.881452	+	0.472273i	$0.843433\pi$
$282$	−17.6576	−1.05150
$283$	−29.3352	−1.74380	−0.871898	−	0.489688i	$-0.837111\pi$
$283$	−29.3352	−1.74380	−0.871898	+	0.489688i	$0.837111\pi$
$284$	24.8251	1.47310
$285$	2.57253	0.152384
$286$	−3.68503	−0.217900
$287$	−8.96997	−0.529481
$288$	8.00756	0.471850
$289$	−16.7392	−0.984660
$290$	2.36547	0.138905
$291$	1.38864	0.0814036
$292$	−29.7708	−1.74220
$293$	−17.7635	−1.03775	−0.518877	−	0.854849i	$-0.673650\pi$
$293$	−17.7635	−1.03775	−0.518877	+	0.854849i	$0.673650\pi$
$294$	−1.29614	−0.0755926
$295$	2.70269	0.157357
$296$	−7.44208	−0.432562
$297$	−0.365645	−0.0212169
$298$	−39.7257	−2.30125
$299$	11.3439	0.656033
$300$	−11.8537	−0.684376
$301$	15.8506	0.913615
$302$	17.4268	1.00280
$303$	−0.538700	−0.0309475
$304$	18.1181	1.03914
$305$	1.77971	0.101906
$306$	−1.07765	−0.0616050
$307$	−9.14388	−0.521869	−0.260934	−	0.965357i	$-0.584031\pi$
$307$	−9.14388	−0.521869	−0.260934	+	0.965357i	$0.584031\pi$
$308$	−2.47522	−0.141039
$309$	2.34011	0.133124
$310$	6.55146	0.372098
$311$	−5.06991	−0.287488	−0.143744	−	0.989615i	$-0.545914\pi$
$311$	−5.06991	−0.287488	−0.143744	+	0.989615i	$0.545914\pi$
$312$	4.56794	0.258609
$313$	20.8580	1.17896	0.589481	−	0.807782i	$-0.299332\pi$
$313$	20.8580	1.17896	0.589481	+	0.807782i	$0.299332\pi$
$314$	3.38053	0.190775
$315$	−1.13153	−0.0637546
$316$	−34.1494	−1.92106
$317$	−6.87933	−0.386382	−0.193191	−	0.981161i	$-0.561884\pi$
$317$	−6.87933	−0.386382	−0.193191	+	0.981161i	$0.561884\pi$
$318$	−11.9805	−0.671833
$319$	−0.999501	−0.0559613
$320$	4.56077	0.254955
$321$	8.84933	0.493921
$322$	13.8315	0.770801
$323$	−3.20365	−0.178256
$324$	2.45325	0.136292
$325$	23.0757	1.28001
$326$	22.5116	1.24680
$327$	−15.1835	−0.839650
$328$	3.10926	0.171680
$329$	23.0891	1.27294
$330$	−0.316412	−0.0174179
$331$	−19.9265	−1.09526	−0.547631	−	0.836720i	$-0.684470\pi$
$331$	−19.9265	−1.09526	−0.547631	+	0.836720i	$0.684470\pi$
$332$	−29.1412	−1.59933
$333$	7.78065	0.426377
$334$	−10.8734	−0.594966
$335$	−0.706521	−0.0386013
$336$	−7.96927	−0.434759
$337$	−15.6723	−0.853723	−0.426862	−	0.904317i	$-0.640381\pi$
$337$	−15.6723	−0.853723	−0.426862	+	0.904317i	$0.640381\pi$
$338$	−20.6973	−1.12578
$339$	−6.91923	−0.375801
$340$	−0.513730	−0.0278609
$341$	−2.76824	−0.149909
$342$	13.2387	0.715867
$343$	−17.6209	−0.951437
$344$	−5.49430	−0.296233
$345$	0.974033	0.0524402
$346$	5.63137	0.302744
$347$	5.69000	0.305455	0.152728	−	0.988268i	$-0.451194\pi$
$347$	5.69000	0.305455	0.152728	+	0.988268i	$0.451194\pi$
$348$	6.70603	0.359481
$349$	−0.485002	−0.0259615	−0.0129808	−	0.999916i	$-0.504132\pi$
$349$	−0.485002	−0.0259615	−0.0129808	+	0.999916i	$0.504132\pi$
$350$	28.1361	1.50394
$351$	−4.77576	−0.254911
$352$	−2.92793	−0.156059
$353$	2.95008	0.157017	0.0785084	−	0.996913i	$-0.474984\pi$
$353$	2.95008	0.157017	0.0785084	+	0.996913i	$0.474984\pi$
$354$	13.9085	0.739229
$355$	−4.14957	−0.220236
$356$	−35.8797	−1.90162
$357$	1.40913	0.0745790
$358$	25.5119	1.34835
$359$	−34.8501	−1.83932	−0.919659	−	0.392717i	$-0.871535\pi$
$359$	−34.8501	−1.83932	−0.919659	+	0.392717i	$0.871535\pi$
$360$	0.392223	0.0206720
$361$	20.3562	1.07138
$362$	−38.3784	−2.01712
$363$	−10.8663	−0.570333
$364$	−32.3293	−1.69452
$365$	4.97625	0.260469
$366$	9.15867	0.478731
$367$	−30.3686	−1.58523	−0.792615	−	0.609723i	$-0.791281\pi$
$367$	−30.3686	−1.58523	−0.792615	+	0.609723i	$0.791281\pi$
$368$	6.86001	0.357603
$369$	−3.25071	−0.169225
$370$	6.73301	0.350033
$371$	15.6657	0.813321
$372$	18.5732	0.962976
$373$	−24.4455	−1.26574	−0.632871	−	0.774257i	$-0.718124\pi$
$373$	−24.4455	−1.26574	−0.632871	+	0.774257i	$0.718124\pi$
$374$	0.394037	0.0203752
$375$	4.03171	0.208197
$376$	−8.00336	−0.412742
$377$	−13.0547	−0.672350
$378$	−5.82306	−0.299506
$379$	19.7058	1.01222	0.506109	−	0.862469i	$-0.331083\pi$
$379$	19.7058	1.01222	0.506109	+	0.862469i	$0.331083\pi$
$380$	6.31107	0.323751
$381$	−0.182675	−0.00935870
$382$	−2.94216	−0.150534
$383$	24.1901	1.23606	0.618029	−	0.786155i	$-0.287931\pi$
$383$	24.1901	1.23606	0.618029	+	0.786155i	$0.287931\pi$
$384$	7.45539	0.380456
$385$	0.413739	0.0210861
$386$	29.2928	1.49097
$387$	5.74426	0.291997
$388$	3.40669	0.172948
$389$	−17.4954	−0.887053	−0.443526	−	0.896261i	$-0.646273\pi$
$389$	−17.4954	−0.887053	−0.443526	+	0.896261i	$0.646273\pi$
$390$	−4.13272	−0.209268
$391$	−1.21299	−0.0613435
$392$	−0.587480	−0.0296722
$393$	20.3977	1.02893
$394$	−39.3420	−1.98202
$395$	5.70816	0.287209
$396$	−0.897020	−0.0450769
$397$	35.8845	1.80099	0.900495	−	0.434865i	$-0.143204\pi$
$397$	35.8845	1.80099	0.900495	+	0.434865i	$0.143204\pi$
$398$	−9.16078	−0.459188
$399$	−17.3109	−0.866628
$400$	13.9547	0.697733
$401$	2.09884	0.104811	0.0524055	−	0.998626i	$-0.483311\pi$
$401$	2.09884	0.104811	0.0524055	+	0.998626i	$0.483311\pi$
$402$	−3.63587	−0.181341
$403$	−36.1565	−1.80109
$404$	−1.32157	−0.0657505
$405$	−0.410067	−0.0203764
$406$	−15.9175	−0.789972
$407$	−2.84496	−0.141019
$408$	−0.488446	−0.0241817
$409$	0.0930490	0.00460098	0.00230049	−	0.999997i	$-0.499268\pi$
$409$	0.0930490	0.00460098	0.00230049	+	0.999997i	$0.499268\pi$
$410$	−2.81301	−0.138925
$411$	2.58203	0.127362
$412$	5.74087	0.282833
$413$	−18.1867	−0.894910
$414$	5.01254	0.246353
$415$	4.87101	0.239109
$416$	−38.2422	−1.87498
$417$	−21.4487	−1.05035
$418$	−4.84067	−0.236765
$419$	15.0215	0.733848	0.366924	−	0.930251i	$-0.380411\pi$
$419$	15.0215	0.733848	0.366924	+	0.930251i	$0.380411\pi$
$420$	−2.77593	−0.135452
$421$	−6.94383	−0.338422	−0.169211	−	0.985580i	$-0.554122\pi$
$421$	−6.94383	−0.338422	−0.169211	+	0.985580i	$0.554122\pi$
$422$	−24.7191	−1.20331
$423$	8.36747	0.406840
$424$	−5.43019	−0.263713
$425$	−2.46747	−0.119690
$426$	−21.3544	−1.03462
$427$	−11.9758	−0.579552
$428$	21.7096	1.04938
$429$	1.74623	0.0843089
$430$	4.97081	0.239714
$431$	−31.6484	−1.52445	−0.762225	−	0.647313i	$-0.775893\pi$
$431$	−31.6484	−1.52445	−0.762225	+	0.647313i	$0.775893\pi$
$432$	−2.88806	−0.138952
$433$	37.2230	1.78883	0.894413	−	0.447243i	$-0.147594\pi$
$433$	37.2230	1.78883	0.894413	+	0.447243i	$0.147594\pi$
$434$	−44.0855	−2.11617
$435$	−1.12093	−0.0537444
$436$	−37.2490	−1.78390
$437$	14.9013	0.712828
$438$	25.6086	1.22363
$439$	36.1815	1.72685	0.863425	−	0.504477i	$-0.168315\pi$
$439$	36.1815	1.72685	0.863425	+	0.504477i	$0.168315\pi$
$440$	−0.143414	−0.00683702
$441$	0.614207	0.0292479
$442$	5.14658	0.244798
$443$	−0.928659	−0.0441219	−0.0220610	−	0.999757i	$-0.507023\pi$
$443$	−0.928659	−0.0441219	−0.0220610	+	0.999757i	$0.507023\pi$
$444$	19.0879	0.905872
$445$	5.99738	0.284303
$446$	50.8215	2.40647
$447$	18.8249	0.890387
$448$	−30.6900	−1.44996
$449$	−24.9889	−1.17930	−0.589651	−	0.807658i	$-0.700735\pi$
$449$	−24.9889	−1.17930	−0.589651	+	0.807658i	$0.700735\pi$
$450$	10.1965	0.480668
$451$	1.18861	0.0559694
$452$	−16.9746	−0.798419
$453$	−8.25809	−0.387999
$454$	47.8991	2.24802
$455$	5.40392	0.253340
$456$	6.00047	0.280998
$457$	−2.00574	−0.0938247	−0.0469124	−	0.998899i	$-0.514938\pi$
$457$	−2.00574	−0.0938247	−0.0469124	+	0.998899i	$0.514938\pi$
$458$	53.3930	2.49489
$459$	0.510667	0.0238359
$460$	2.38955	0.111413
$461$	6.69736	0.311927	0.155964	−	0.987763i	$-0.450152\pi$
$461$	6.69736	0.311927	0.155964	+	0.987763i	$0.450152\pi$
$462$	2.12917	0.0990581
$463$	28.9660	1.34616	0.673082	−	0.739567i	$-0.264970\pi$
$463$	28.9660	1.34616	0.673082	+	0.739567i	$0.264970\pi$
$464$	−7.89459	−0.366497
$465$	−3.10455	−0.143970
$466$	30.5163	1.41364
$467$	16.4434	0.760908	0.380454	−	0.924800i	$-0.375768\pi$
$467$	16.4434	0.760908	0.380454	+	0.924800i	$0.375768\pi$
$468$	−11.7161	−0.541579
$469$	4.75426	0.219531
$470$	7.24081	0.333994
$471$	−1.60194	−0.0738136
$472$	6.30406	0.290168
$473$	−2.10036	−0.0965747
$474$	29.3751	1.34924
$475$	30.3124	1.39083
$476$	3.45695	0.158449
$477$	5.67723	0.259942
$478$	−4.94923	−0.226372
$479$	26.2531	1.19953	0.599767	−	0.800175i	$-0.295260\pi$
$479$	26.2531	1.19953	0.599767	+	0.800175i	$0.295260\pi$
$480$	−3.28364	−0.149877
$481$	−37.1585	−1.69428
$482$	9.62171	0.438257
$483$	−6.55438	−0.298234
$484$	−26.6578	−1.21172
$485$	−0.569436	−0.0258567
$486$	−2.11027	−0.0957239
$487$	5.10475	0.231318	0.115659	−	0.993289i	$-0.463102\pi$
$487$	5.10475	0.231318	0.115659	+	0.993289i	$0.463102\pi$
$488$	4.15119	0.187915
$489$	−10.6676	−0.482408
$490$	0.531506	0.0240110
$491$	−34.6506	−1.56376	−0.781881	−	0.623428i	$-0.785739\pi$
$491$	−34.6506	−1.56376	−0.781881	+	0.623428i	$0.785739\pi$
$492$	−7.97482	−0.359533
$493$	1.39592	0.0628692
$494$	−63.2248	−2.84462
$495$	0.149939	0.00673925
$496$	−21.8651	−0.981770
$497$	27.9229	1.25252
$498$	25.0671	1.12328
$499$	6.01580	0.269304	0.134652	−	0.990893i	$-0.457008\pi$
$499$	6.01580	0.269304	0.134652	+	0.990893i	$0.457008\pi$
$500$	9.89081	0.442330
$501$	5.15260	0.230201
$502$	−3.30373	−0.147453
$503$	26.6990	1.19045	0.595226	−	0.803559i	$-0.297063\pi$
$503$	26.6990	1.19045	0.595226	+	0.803559i	$0.297063\pi$
$504$	−2.63931	−0.117564
$505$	0.220903	0.00983006
$506$	−1.83281	−0.0814784
$507$	9.80786	0.435582
$508$	−0.448147	−0.0198833
$509$	−27.6496	−1.22555	−0.612774	−	0.790258i	$-0.709947\pi$
$509$	−27.6496	−1.22555	−0.612774	+	0.790258i	$0.709947\pi$
$510$	0.441907	0.0195680
$511$	−33.4858	−1.48132
$512$	−28.6511	−1.26621
$513$	−6.27345	−0.276980
$514$	30.2521	1.33436
$515$	−0.959601	−0.0422851
$516$	14.0921	0.620371
$517$	−3.05952	−0.134558
$518$	−45.3072	−1.99068
$519$	−2.66855	−0.117136
$520$	−1.87316	−0.0821436
$521$	−2.07551	−0.0909299	−0.0454649	−	0.998966i	$-0.514477\pi$
$521$	−2.07551	−0.0909299	−0.0454649	+	0.998966i	$0.514477\pi$
$522$	−5.76849	−0.252480
$523$	22.9507	1.00357	0.501783	−	0.864994i	$-0.332678\pi$
$523$	22.9507	1.00357	0.501783	+	0.864994i	$0.332678\pi$
$524$	50.0408	2.18604
$525$	−13.3329	−0.581896
$526$	−12.1713	−0.530695
$527$	3.86619	0.168414
$528$	1.05600	0.0459567
$529$	−17.3579	−0.754693
$530$	4.91281	0.213399
$531$	−6.59086	−0.286019
$532$	−42.4679	−1.84122
$533$	15.5246	0.672446
$534$	30.8635	1.33559
$535$	−3.62882	−0.156887
$536$	−1.64797	−0.0711814
$537$	−12.0894	−0.521696
$538$	−28.1051	−1.21170
$539$	−0.224582	−0.00967342
$540$	−1.00600	−0.0432912
$541$	−12.2389	−0.526192	−0.263096	−	0.964770i	$-0.584744\pi$
$541$	−12.2389	−0.526192	−0.263096	+	0.964770i	$0.584744\pi$
$542$	−42.3173	−1.81769
$543$	18.1865	0.780456
$544$	4.08920	0.175323
$545$	6.22626	0.266704
$546$	27.8095	1.19014
$547$	42.2359	1.80588	0.902938	−	0.429770i	$-0.141406\pi$
$547$	42.2359	1.80588	0.902938	+	0.429770i	$0.141406\pi$
$548$	6.33438	0.270591
$549$	−4.34004	−0.185228
$550$	−3.72831	−0.158975
$551$	−17.1487	−0.730557
$552$	2.27194	0.0967003
$553$	−38.4108	−1.63339
$554$	36.5369	1.55230
$555$	−3.19059	−0.135433
$556$	−52.6192	−2.23155
$557$	−12.8590	−0.544855	−0.272427	−	0.962176i	$-0.587826\pi$
$557$	−12.8590	−0.544855	−0.272427	+	0.962176i	$0.587826\pi$
$558$	−15.9766	−0.676342
$559$	−27.4332	−1.16030
$560$	3.26793	0.138095
$561$	−0.186723	−0.00788345
$562$	62.3621	2.63059
$563$	12.3989	0.522553	0.261276	−	0.965264i	$-0.415857\pi$
$563$	12.3989	0.522553	0.261276	+	0.965264i	$0.415857\pi$
$564$	20.5275	0.864364
$565$	2.83735	0.119368
$566$	61.9052	2.60207
$567$	2.75939	0.115883
$568$	−9.67893	−0.406119
$569$	−39.0067	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$569$	−39.0067	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$570$	−5.42875	−0.227385
$571$	17.0975	0.715509	0.357754	−	0.933816i	$-0.383542\pi$
$571$	17.0975	0.715509	0.357754	+	0.933816i	$0.383542\pi$
$572$	4.28395	0.179121
$573$	1.39421	0.0582439
$574$	18.9291	0.790085
$575$	11.4771	0.478628
$576$	−11.1220	−0.463418
$577$	14.2958	0.595140	0.297570	−	0.954700i	$-0.403824\pi$
$577$	14.2958	0.595140	0.297570	+	0.954700i	$0.403824\pi$
$578$	35.3243	1.46930
$579$	−13.8811	−0.576877
$580$	−2.74992	−0.114184
$581$	−32.7776	−1.35984
$582$	−2.93041	−0.121469
$583$	−2.07585	−0.0859730
$584$	11.6072	0.480308
$585$	1.95838	0.0809690
$586$	37.4858	1.54853
$587$	2.76252	0.114021	0.0570107	−	0.998374i	$-0.481843\pi$
$587$	2.76252	0.114021	0.0570107	+	0.998374i	$0.481843\pi$
$588$	1.50680	0.0621395
$589$	−47.4954	−1.95701
$590$	−5.70342	−0.234806
$591$	18.6431	0.766875
$592$	−22.4710	−0.923552
$593$	21.8882	0.898841	0.449421	−	0.893320i	$-0.351630\pi$
$593$	21.8882	0.898841	0.449421	+	0.893320i	$0.351630\pi$
$594$	0.771611	0.0316596
$595$	−0.577837	−0.0236890
$596$	46.1822	1.89170
$597$	4.34104	0.177667
$598$	−23.9387	−0.978925
$599$	−30.2503	−1.23599	−0.617997	−	0.786181i	$-0.712055\pi$
$599$	−30.2503	−1.23599	−0.617997	+	0.786181i	$0.712055\pi$
$600$	4.62159	0.188676
$601$	16.3700	0.667747	0.333874	−	0.942618i	$-0.391644\pi$
$601$	16.3700	0.667747	0.333874	+	0.942618i	$0.391644\pi$
$602$	−33.4491	−1.36329
$603$	1.72294	0.0701636
$604$	−20.2592	−0.824334
$605$	4.45591	0.181158
$606$	1.13680	0.0461795
$607$	−11.4287	−0.463876	−0.231938	−	0.972731i	$-0.574507\pi$
$607$	−11.4287	−0.463876	−0.231938	+	0.972731i	$0.574507\pi$
$608$	−50.2351	−2.03730
$609$	7.54286	0.305652
$610$	−3.75567	−0.152063
$611$	−39.9610	−1.61665
$612$	1.25280	0.0506413
$613$	−25.6369	−1.03546	−0.517732	−	0.855543i	$-0.673224\pi$
$613$	−25.6369	−1.03546	−0.517732	+	0.855543i	$0.673224\pi$
$614$	19.2961	0.778727
$615$	1.33301	0.0537521
$616$	0.965052	0.0388830
$617$	−41.5175	−1.67143	−0.835715	−	0.549164i	$-0.814946\pi$
$617$	−41.5175	−1.67143	−0.835715	+	0.549164i	$0.814946\pi$
$618$	−4.93827	−0.198646
$619$	−1.50688	−0.0605667	−0.0302834	−	0.999541i	$-0.509641\pi$
$619$	−1.50688	−0.0605667	−0.0302834	+	0.999541i	$0.509641\pi$
$620$	−7.61625	−0.305876
$621$	−2.37530	−0.0953176
$622$	10.6989	0.428987
$623$	−40.3570	−1.61687
$624$	13.7927	0.552149
$625$	22.5060	0.900238
$626$	−44.0160	−1.75923
$627$	2.29386	0.0916079
$628$	−3.92997	−0.156823
$629$	3.97333	0.158427
$630$	2.38784	0.0951339
$631$	6.52124	0.259606	0.129803	−	0.991540i	$-0.458565\pi$
$631$	6.52124	0.259606	0.129803	+	0.991540i	$0.458565\pi$
$632$	13.3143	0.529616
$633$	11.7137	0.465578
$634$	14.5173	0.576554
$635$	0.0749087	0.00297266
$636$	13.9277	0.552268
$637$	−2.93330	−0.116222
$638$	2.10922	0.0835049
$639$	10.1193	0.400312
$640$	−3.05721	−0.120847
$641$	−47.5432	−1.87784	−0.938922	−	0.344129i	$-0.888174\pi$
$641$	−47.5432	−1.87784	−0.938922	+	0.344129i	$0.888174\pi$
$642$	−18.6745	−0.737024
$643$	8.39645	0.331124	0.165562	−	0.986199i	$-0.447056\pi$
$643$	8.39645	0.331124	0.165562	+	0.986199i	$0.447056\pi$
$644$	−16.0795	−0.633622
$645$	−2.35553	−0.0927489
$646$	6.76057	0.265991
$647$	25.8296	1.01547	0.507733	−	0.861514i	$-0.330484\pi$
$647$	25.8296	1.01547	0.507733	+	0.861514i	$0.330484\pi$
$648$	−0.956486	−0.0375743
$649$	2.40992	0.0945975
$650$	−48.6961	−1.91002
$651$	20.8909	0.818778
$652$	−26.1704	−1.02491
$653$	0.744259	0.0291251	0.0145625	−	0.999894i	$-0.495364\pi$
$653$	0.744259	0.0291251	0.0145625	+	0.999894i	$0.495364\pi$
$654$	32.0414	1.25292
$655$	−8.36443	−0.326825
$656$	9.38825	0.366550
$657$	−12.1352	−0.473440
$658$	−48.7242	−1.89947
$659$	32.1331	1.25173	0.625863	−	0.779933i	$-0.284747\pi$
$659$	32.1331	1.25173	0.625863	+	0.779933i	$0.284747\pi$
$660$	0.367838	0.0143181
$661$	1.90087	0.0739352	0.0369676	−	0.999316i	$-0.488230\pi$
$661$	1.90087	0.0739352	0.0369676	+	0.999316i	$0.488230\pi$
$662$	42.0504	1.63434
$663$	−2.43882	−0.0947161
$664$	11.3617	0.440919
$665$	7.09861	0.275272
$666$	−16.4193	−0.636235
$667$	−6.49296	−0.251408
$668$	12.6406	0.489081
$669$	−24.0829	−0.931098
$670$	1.49095	0.0576005
$671$	1.58692	0.0612622
$672$	22.0960	0.852370
$673$	13.9191	0.536543	0.268272	−	0.963343i	$-0.413548\pi$
$673$	13.9191	0.536543	0.268272	+	0.963343i	$0.413548\pi$
$674$	33.0728	1.27392
$675$	−4.83185	−0.185978
$676$	24.0612	0.925429
$677$	31.6831	1.21768	0.608840	−	0.793293i	$-0.291635\pi$
$677$	31.6831	1.21768	0.608840	+	0.793293i	$0.291635\pi$
$678$	14.6015	0.560766
$679$	3.83180	0.147051
$680$	0.200295	0.00768098
$681$	−22.6981	−0.869792
$682$	5.84175	0.223692
$683$	−43.0381	−1.64681	−0.823404	−	0.567455i	$-0.807928\pi$
$683$	−43.0381	−1.64681	−0.823404	+	0.567455i	$0.807928\pi$
$684$	−15.3904	−0.588465
$685$	−1.05881	−0.0404549
$686$	37.1848	1.41972
$687$	−25.3014	−0.965310
$688$	−16.5898	−0.632478
$689$	−27.1131	−1.03293
$690$	−2.05548	−0.0782506
$691$	−45.0252	−1.71284	−0.856420	−	0.516280i	$-0.827317\pi$
$691$	−45.0252	−1.71284	−0.856420	+	0.516280i	$0.827317\pi$
$692$	−6.54663	−0.248866
$693$	−1.00896	−0.0383271
$694$	−12.0075	−0.455797
$695$	8.79542	0.333629
$696$	−2.61458	−0.0991054
$697$	−1.66003	−0.0628782
$698$	1.02349	0.0387395
$699$	−14.4608	−0.546958
$700$	−32.7090	−1.23628
$701$	−35.7152	−1.34894	−0.674472	−	0.738300i	$-0.735629\pi$
$701$	−35.7152	−1.34894	−0.674472	+	0.738300i	$0.735629\pi$
$702$	10.0782	0.380375
$703$	−48.8116	−1.84096
$704$	4.06672	0.153270
$705$	−3.43122	−0.129227
$706$	−6.22547	−0.234299
$707$	−1.48648	−0.0559049
$708$	−16.1690	−0.607670
$709$	51.3674	1.92914	0.964572	−	0.263819i	$-0.0849821\pi$
$709$	51.3674	1.92914	0.964572	+	0.263819i	$0.0849821\pi$
$710$	8.75673	0.328634
$711$	−13.9201	−0.522043
$712$	13.9889	0.524258
$713$	−17.9831	−0.673471
$714$	−2.97364	−0.111286
$715$	−0.716072	−0.0267796
$716$	−29.6584	−1.10838
$717$	2.34530	0.0875869
$718$	73.5433	2.74461
$719$	45.7086	1.70464	0.852322	−	0.523018i	$-0.175194\pi$
$719$	45.7086	1.70464	0.852322	+	0.523018i	$0.175194\pi$
$720$	1.18430	0.0441361
$721$	6.45726	0.240481
$722$	−42.9571	−1.59870
$723$	−4.55946	−0.169568
$724$	44.6160	1.65814
$725$	−13.2080	−0.490532
$726$	22.9309	0.851044
$727$	−29.0743	−1.07831	−0.539154	−	0.842207i	$-0.681256\pi$
$727$	−29.0743	−1.07831	−0.539154	+	0.842207i	$0.681256\pi$
$728$	12.6047	0.467162
$729$	1.00000	0.0370370
$730$	−10.5012	−0.388669
$731$	2.93341	0.108496
$732$	−10.6472	−0.393532
$733$	8.59036	0.317292	0.158646	−	0.987336i	$-0.449287\pi$
$733$	8.59036	0.317292	0.158646	+	0.987336i	$0.449287\pi$
$734$	64.0861	2.36546
$735$	−0.251866	−0.00929021
$736$	−19.0204	−0.701101
$737$	−0.629985	−0.0232058
$738$	6.85989	0.252516
$739$	16.0601	0.590780	0.295390	−	0.955377i	$-0.404550\pi$
$739$	16.0601	0.590780	0.295390	+	0.955377i	$0.404550\pi$
$740$	−7.82732	−0.287738
$741$	29.9605	1.10063
$742$	−33.0588	−1.21363
$743$	34.8445	1.27832	0.639160	−	0.769074i	$-0.279282\pi$
$743$	34.8445	1.27832	0.639160	+	0.769074i	$0.279282\pi$
$744$	−7.24141	−0.265483
$745$	−7.71946	−0.282819
$746$	51.5868	1.88873
$747$	−11.8786	−0.434615
$748$	−0.458079	−0.0167490
$749$	24.4187	0.892240
$750$	−8.50801	−0.310669
$751$	6.25131	0.228113	0.114057	−	0.993474i	$-0.463615\pi$
$751$	6.25131	0.228113	0.114057	+	0.993474i	$0.463615\pi$
$752$	−24.1657	−0.881234
$753$	1.56554	0.0570516
$754$	27.5489	1.00327
$755$	3.38637	0.123242
$756$	6.76947	0.246203
$757$	−23.4706	−0.853054	−0.426527	−	0.904475i	$-0.640263\pi$
$757$	−23.4706	−0.853054	−0.426527	+	0.904475i	$0.640263\pi$
$758$	−41.5846	−1.51042
$759$	0.868518	0.0315252
$760$	−2.46059	−0.0892551
$761$	39.3760	1.42738	0.713689	−	0.700463i	$-0.247023\pi$
$761$	39.3760	1.42738	0.713689	+	0.700463i	$0.247023\pi$
$762$	0.385493	0.0139649
$763$	−41.8972	−1.51678
$764$	3.42035	0.123744
$765$	−0.209408	−0.00757115
$766$	−51.0478	−1.84443
$767$	31.4763	1.13655
$768$	6.51115	0.234951
$769$	14.2237	0.512920	0.256460	−	0.966555i	$-0.417444\pi$
$769$	14.2237	0.512920	0.256460	+	0.966555i	$0.417444\pi$
$770$	−0.873103	−0.0314644
$771$	−14.3356	−0.516285
$772$	−34.0537	−1.22562
$773$	32.6661	1.17492	0.587459	−	0.809254i	$-0.300128\pi$
$773$	32.6661	1.17492	0.587459	+	0.809254i	$0.300128\pi$
$774$	−12.1220	−0.435715
$775$	−36.5812	−1.31403
$776$	−1.32822	−0.0476801
$777$	21.4698	0.770226
$778$	36.9201	1.32365
$779$	20.3932	0.730662
$780$	4.80440	0.172025
$781$	−3.70006	−0.132399
$782$	2.55974	0.0915361
$783$	2.73353	0.0976883
$784$	−1.77386	−0.0633523
$785$	0.656903	0.0234459
$786$	−43.0448	−1.53536
$787$	−34.7609	−1.23909	−0.619546	−	0.784961i	$-0.712683\pi$
$787$	−34.7609	−1.23909	−0.619546	+	0.784961i	$0.712683\pi$
$788$	45.7362	1.62929
$789$	5.76765	0.205334
$790$	−12.0458	−0.428569
$791$	−19.0928	−0.678862
$792$	0.349734	0.0124273
$793$	20.7270	0.736037
$794$	−75.7261	−2.68742
$795$	−2.32804	−0.0825672
$796$	10.6497	0.377467
$797$	−38.7619	−1.37302	−0.686509	−	0.727121i	$-0.740858\pi$
$797$	−38.7619	−1.37302	−0.686509	+	0.727121i	$0.740858\pi$
$798$	36.5307	1.29317
$799$	4.27299	0.151168
$800$	−38.6913	−1.36794
$801$	−14.6254	−0.516762
$802$	−4.42912	−0.156398
$803$	4.43719	0.156585
$804$	4.22681	0.149068
$805$	2.68773	0.0947301
$806$	76.3002	2.68756
$807$	13.3182	0.468824
$808$	0.515259	0.0181268
$809$	12.5600	0.441585	0.220792	−	0.975321i	$-0.429136\pi$
$809$	12.5600	0.441585	0.220792	+	0.975321i	$0.429136\pi$
$810$	0.865353	0.0304054
$811$	−3.85407	−0.135335	−0.0676673	−	0.997708i	$-0.521556\pi$
$811$	−3.85407	−0.135335	−0.0676673	+	0.997708i	$0.521556\pi$
$812$	18.5045	0.649382
$813$	20.0530	0.703290
$814$	6.00364	0.210427
$815$	4.37445	0.153230
$816$	−1.47484	−0.0516296
$817$	−36.0363	−1.26075
$818$	−0.196359	−0.00686553
$819$	−13.1782	−0.460482
$820$	3.27021	0.114201
$821$	33.3198	1.16287	0.581434	−	0.813593i	$-0.302492\pi$
$821$	33.3198	1.16287	0.581434	+	0.813593i	$0.302492\pi$
$822$	−5.44879	−0.190049
$823$	−8.24742	−0.287487	−0.143744	−	0.989615i	$-0.545914\pi$
$823$	−8.24742	−0.287487	−0.143744	+	0.989615i	$0.545914\pi$
$824$	−2.23828	−0.0779742
$825$	1.76674	0.0615100
$826$	38.3789	1.33537
$827$	6.10610	0.212330	0.106165	−	0.994349i	$-0.466143\pi$
$827$	6.10610	0.212330	0.106165	+	0.994349i	$0.466143\pi$
$828$	−5.82722	−0.202510
$829$	−29.6962	−1.03139	−0.515697	−	0.856771i	$-0.672467\pi$
$829$	−29.6962	−1.03139	−0.515697	+	0.856771i	$0.672467\pi$
$830$	−10.2792	−0.356795
$831$	−17.3138	−0.600610
$832$	53.1161	1.84147
$833$	0.313655	0.0108675
$834$	45.2627	1.56732
$835$	−2.11291	−0.0731203
$836$	5.62741	0.194628
$837$	7.57085	0.261687
$838$	−31.6995	−1.09504
$839$	1.02773	0.0354812	0.0177406	−	0.999843i	$-0.494353\pi$
$839$	1.02773	0.0354812	0.0177406	+	0.999843i	$0.494353\pi$
$840$	1.08229	0.0373427
$841$	−21.5278	−0.742339
$842$	14.6534	0.504989
$843$	−29.5517	−1.01781
$844$	28.7367	0.989157
$845$	−4.02188	−0.138357
$846$	−17.6576	−0.607082
$847$	−29.9843	−1.03027
$848$	−16.3962	−0.563047
$849$	−29.3352	−1.00678
$850$	5.20703	0.178600
$851$	−18.4814	−0.633535
$852$	24.8251	0.850494
$853$	43.2684	1.48148	0.740742	−	0.671790i	$-0.234474\pi$
$853$	43.2684	1.48148	0.740742	+	0.671790i	$0.234474\pi$
$854$	25.2723	0.864800
$855$	2.57253	0.0879788
$856$	−8.46426	−0.289302
$857$	−46.6609	−1.59391	−0.796953	−	0.604041i	$-0.793556\pi$
$857$	−46.6609	−1.59391	−0.796953	+	0.604041i	$0.793556\pi$
$858$	−3.68503	−0.125805
$859$	−4.59723	−0.156856	−0.0784278	−	0.996920i	$-0.524990\pi$
$859$	−4.59723	−0.156856	−0.0784278	+	0.996920i	$0.524990\pi$
$860$	−5.77871	−0.197052
$861$	−8.96997	−0.305696
$862$	66.7867	2.27477
$863$	−19.8446	−0.675519	−0.337759	−	0.941233i	$-0.609669\pi$
$863$	−19.8446	−0.675519	−0.337759	+	0.941233i	$0.609669\pi$
$864$	8.00756	0.272423
$865$	1.09428	0.0372068
$866$	−78.5508	−2.66926
$867$	−16.7392	−0.568494
$868$	51.2506	1.73956
$869$	5.08981	0.172660
$870$	2.36547	0.0801968
$871$	−8.22835	−0.278807
$872$	14.5228	0.491805
$873$	1.38864	0.0469984
$874$	−31.4459	−1.06367
$875$	11.1250	0.376095
$876$	−29.7708	−1.00586
$877$	−21.4859	−0.725527	−0.362763	−	0.931881i	$-0.618167\pi$
$877$	−21.4859	−0.725527	−0.362763	+	0.931881i	$0.618167\pi$
$878$	−76.3529	−2.57679
$879$	−17.7635	−0.599148
$880$	−0.433032	−0.0145975
$881$	27.0987	0.912979	0.456489	−	0.889729i	$-0.349107\pi$
$881$	27.0987	0.912979	0.456489	+	0.889729i	$0.349107\pi$
$882$	−1.29614	−0.0436434
$883$	−27.2750	−0.917876	−0.458938	−	0.888468i	$-0.651770\pi$
$883$	−27.2750	−0.917876	−0.458938	+	0.888468i	$0.651770\pi$
$884$	−5.98305	−0.201232
$885$	2.70269	0.0908500
$886$	1.95972	0.0658382
$887$	−28.6088	−0.960590	−0.480295	−	0.877107i	$-0.659470\pi$
$887$	−28.6088	−0.960590	−0.480295	+	0.877107i	$0.659470\pi$
$888$	−7.44208	−0.249740
$889$	−0.504069	−0.0169059
$890$	−12.6561	−0.424233
$891$	−0.365645	−0.0122496
$892$	−59.0814	−1.97819
$893$	−52.4929	−1.75661
$894$	−39.7257	−1.32862
$895$	4.95746	0.165710
$896$	20.5723	0.687272
$897$	11.3439	0.378761
$898$	52.7335	1.75974
$899$	20.6951	0.690221
$900$	−11.8537	−0.395124
$901$	2.89918	0.0965855
$902$	−2.50829	−0.0835168
$903$	15.8506	0.527476
$904$	6.61814	0.220116
$905$	−7.45767	−0.247901
$906$	17.4268	0.578967
$907$	37.8894	1.25810	0.629048	−	0.777366i	$-0.283445\pi$
$907$	37.8894	1.25810	0.629048	+	0.777366i	$0.283445\pi$
$908$	−55.6841	−1.84794
$909$	−0.538700	−0.0178676
$910$	−11.4038	−0.378031
$911$	8.51745	0.282196	0.141098	−	0.989996i	$-0.454937\pi$
$911$	8.51745	0.282196	0.141098	+	0.989996i	$0.454937\pi$
$912$	18.1181	0.599950
$913$	4.34335	0.143744
$914$	4.23267	0.140004
$915$	1.77971	0.0588353
$916$	−62.0708	−2.05088
$917$	56.2852	1.85870
$918$	−1.07765	−0.0355677
$919$	5.28628	0.174378	0.0871891	−	0.996192i	$-0.472212\pi$
$919$	5.28628	0.174378	0.0871891	+	0.996192i	$0.472212\pi$
$920$	−0.931648	−0.0307155
$921$	−9.14388	−0.301301
$922$	−14.1333	−0.465454
$923$	−48.3272	−1.59071
$924$	−2.47522	−0.0814289
$925$	−37.5949	−1.23611
$926$	−61.1262	−2.00873
$927$	2.34011	0.0768592
$928$	21.8889	0.718538
$929$	−25.5423	−0.838015	−0.419008	−	0.907983i	$-0.637622\pi$
$929$	−25.5423	−0.838015	−0.419008	+	0.907983i	$0.637622\pi$
$930$	6.55146	0.214831
$931$	−3.85320	−0.126283
$932$	−35.4760	−1.16206
$933$	−5.06991	−0.165981
$934$	−34.7000	−1.13542
$935$	0.0765689	0.00250407
$936$	4.56794	0.149308
$937$	−5.70920	−0.186511	−0.0932557	−	0.995642i	$-0.529727\pi$
$937$	−5.70920	−0.186511	−0.0932557	+	0.995642i	$0.529727\pi$
$938$	−10.0328	−0.327582
$939$	20.8580	0.680674
$940$	−8.41765	−0.274553
$941$	27.3440	0.891388	0.445694	−	0.895185i	$-0.352957\pi$
$941$	27.3440	0.891388	0.445694	+	0.895185i	$0.352957\pi$
$942$	3.38053	0.110144
$943$	7.72143	0.251444
$944$	19.0348	0.619530
$945$	−1.13153	−0.0368087
$946$	4.43233	0.144108
$947$	−30.3828	−0.987307	−0.493653	−	0.869659i	$-0.664339\pi$
$947$	−30.3828	−0.987307	−0.493653	+	0.869659i	$0.664339\pi$
$948$	−34.1494	−1.10912
$949$	57.9549	1.88130
$950$	−63.9673	−2.07537
$951$	−6.87933	−0.223077
$952$	−1.34781	−0.0436828
$953$	13.0252	0.421928	0.210964	−	0.977494i	$-0.432340\pi$
$953$	13.0252	0.421928	0.210964	+	0.977494i	$0.432340\pi$
$954$	−11.9805	−0.387883
$955$	−0.571719	−0.0185004
$956$	5.75362	0.186085
$957$	−0.999501	−0.0323093
$958$	−55.4011	−1.78993
$959$	7.12482	0.230073
$960$	4.56077	0.147198
$961$	26.3178	0.848960
$962$	78.4146	2.52819
$963$	8.84933	0.285166
$964$	−11.1855	−0.360261
$965$	5.69216	0.183237
$966$	13.8315	0.445022
$967$	−35.0532	−1.12724	−0.563618	−	0.826036i	$-0.690591\pi$
$967$	−35.0532	−1.12724	−0.563618	+	0.826036i	$0.690591\pi$
$968$	10.3935	0.334059
$969$	−3.20365	−0.102916
$970$	1.20166	0.0385831
$971$	41.5599	1.33372	0.666860	−	0.745183i	$-0.267638\pi$
$971$	41.5599	1.33372	0.666860	+	0.745183i	$0.267638\pi$
$972$	2.45325	0.0786881
$973$	−59.1854	−1.89740
$974$	−10.7724	−0.345171
$975$	23.0757	0.739015
$976$	12.5343	0.401213
$977$	18.3316	0.586478	0.293239	−	0.956039i	$-0.405267\pi$
$977$	18.3316	0.586478	0.293239	+	0.956039i	$0.405267\pi$
$978$	22.5116	0.719843
$979$	5.34769	0.170913
$980$	−0.617890	−0.0197378
$981$	−15.1835	−0.484772
$982$	73.1223	2.33343
$983$	25.5602	0.815243	0.407622	−	0.913151i	$-0.366358\pi$
$983$	25.5602	0.815243	0.407622	+	0.913151i	$0.366358\pi$
$984$	3.10926	0.0991196
$985$	−7.64492	−0.243587
$986$	−2.94578	−0.0938127
$987$	23.0891	0.734933
$988$	73.5006	2.33837
$989$	−13.6444	−0.433865
$990$	−0.316412	−0.0100562
$991$	−21.3083	−0.676879	−0.338440	−	0.940988i	$-0.609899\pi$
$991$	−21.3083	−0.676879	−0.338440	+	0.940988i	$0.609899\pi$
$992$	60.6240	1.92482
$993$	−19.9265	−0.632350
$994$	−58.9250	−1.86899
$995$	−1.78012	−0.0564335
$996$	−29.1412	−0.923373
$997$	−23.3539	−0.739626	−0.369813	−	0.929106i	$-0.620578\pi$
$997$	−23.3539	−0.739626	−0.369813	+	0.929106i	$0.620578\pi$
$998$	−12.6950	−0.401853
$999$	7.78065	0.246169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.12	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.12	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11027 q^{2} +1.00000 q^{3} +2.45325 q^{4} -0.410067 q^{5} -2.11027 q^{6} +2.75939 q^{7} -0.956486 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11027 q^{2} +1.00000 q^{3} +2.45325 q^{4} -0.410067 q^{5} -2.11027 q^{6} +2.75939 q^{7} -0.956486 q^{8} +1.00000 q^{9} +0.865353 q^{10} -0.365645 q^{11} +2.45325 q^{12} -4.77576 q^{13} -5.82306 q^{14} -0.410067 q^{15} -2.88806 q^{16} +0.510667 q^{17} -2.11027 q^{18} -6.27345 q^{19} -1.00600 q^{20} +2.75939 q^{21} +0.771611 q^{22} -2.37530 q^{23} -0.956486 q^{24} -4.83185 q^{25} +10.0782 q^{26} +1.00000 q^{27} +6.76947 q^{28} +2.73353 q^{29} +0.865353 q^{30} +7.57085 q^{31} +8.00756 q^{32} -0.365645 q^{33} -1.07765 q^{34} -1.13153 q^{35} +2.45325 q^{36} +7.78065 q^{37} +13.2387 q^{38} -4.77576 q^{39} +0.392223 q^{40} -3.25071 q^{41} -5.82306 q^{42} +5.74426 q^{43} -0.897020 q^{44} -0.410067 q^{45} +5.01254 q^{46} +8.36747 q^{47} -2.88806 q^{48} +0.614207 q^{49} +10.1965 q^{50} +0.510667 q^{51} -11.7161 q^{52} +5.67723 q^{53} -2.11027 q^{54} +0.149939 q^{55} -2.63931 q^{56} -6.27345 q^{57} -5.76849 q^{58} -6.59086 q^{59} -1.00600 q^{60} -4.34004 q^{61} -15.9766 q^{62} +2.75939 q^{63} -11.1220 q^{64} +1.95838 q^{65} +0.771611 q^{66} +1.72294 q^{67} +1.25280 q^{68} -2.37530 q^{69} +2.38784 q^{70} +10.1193 q^{71} -0.956486 q^{72} -12.1352 q^{73} -16.4193 q^{74} -4.83185 q^{75} -15.3904 q^{76} -1.00896 q^{77} +10.0782 q^{78} -13.9201 q^{79} +1.18430 q^{80} +1.00000 q^{81} +6.85989 q^{82} -11.8786 q^{83} +6.76947 q^{84} -0.209408 q^{85} -12.1220 q^{86} +2.73353 q^{87} +0.349734 q^{88} -14.6254 q^{89} +0.865353 q^{90} -13.1782 q^{91} -5.82722 q^{92} +7.57085 q^{93} -17.6576 q^{94} +2.57253 q^{95} +8.00756 q^{96} +1.38864 q^{97} -1.29614 q^{98} -0.365645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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