LMFDB - Embedded newform 6033.2.a.d.1.10

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:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.42494 q^{2} -1.00000 q^{3} +3.88033 q^{4} -3.57030 q^{5} +2.42494 q^{6} +1.93625 q^{7} -4.55968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42494 q^{2} -1.00000 q^{3} +3.88033 q^{4} -3.57030 q^{5} +2.42494 q^{6} +1.93625 q^{7} -4.55968 q^{8} +1.00000 q^{9} +8.65775 q^{10} -0.760801 q^{11} -3.88033 q^{12} +4.96794 q^{13} -4.69529 q^{14} +3.57030 q^{15} +3.29630 q^{16} -1.65697 q^{17} -2.42494 q^{18} -3.79849 q^{19} -13.8539 q^{20} -1.93625 q^{21} +1.84490 q^{22} +8.00124 q^{23} +4.55968 q^{24} +7.74703 q^{25} -12.0469 q^{26} -1.00000 q^{27} +7.51329 q^{28} -6.50138 q^{29} -8.65775 q^{30} -4.68116 q^{31} +1.12605 q^{32} +0.760801 q^{33} +4.01806 q^{34} -6.91299 q^{35} +3.88033 q^{36} +8.73739 q^{37} +9.21110 q^{38} -4.96794 q^{39} +16.2794 q^{40} +0.688724 q^{41} +4.69529 q^{42} -2.55636 q^{43} -2.95216 q^{44} -3.57030 q^{45} -19.4025 q^{46} -6.78041 q^{47} -3.29630 q^{48} -3.25094 q^{49} -18.7861 q^{50} +1.65697 q^{51} +19.2772 q^{52} -1.50354 q^{53} +2.42494 q^{54} +2.71628 q^{55} -8.82869 q^{56} +3.79849 q^{57} +15.7655 q^{58} -1.26893 q^{59} +13.8539 q^{60} +10.9843 q^{61} +11.3515 q^{62} +1.93625 q^{63} -9.32319 q^{64} -17.7370 q^{65} -1.84490 q^{66} -2.40247 q^{67} -6.42960 q^{68} -8.00124 q^{69} +16.7636 q^{70} +4.19086 q^{71} -4.55968 q^{72} -6.01407 q^{73} -21.1876 q^{74} -7.74703 q^{75} -14.7394 q^{76} -1.47310 q^{77} +12.0469 q^{78} -12.5878 q^{79} -11.7688 q^{80} +1.00000 q^{81} -1.67011 q^{82} -9.04918 q^{83} -7.51329 q^{84} +5.91589 q^{85} +6.19901 q^{86} +6.50138 q^{87} +3.46901 q^{88} +1.79969 q^{89} +8.65775 q^{90} +9.61916 q^{91} +31.0475 q^{92} +4.68116 q^{93} +16.4421 q^{94} +13.5617 q^{95} -1.12605 q^{96} +4.34061 q^{97} +7.88333 q^{98} -0.760801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * 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 $

$2$	−2.42494	−1.71469	−0.857345	−	0.514742i	$-0.827888\pi$
$2$	−2.42494	−1.71469	−0.857345	+	0.514742i	$0.827888\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.88033	1.94016
$5$	−3.57030	−1.59669	−0.798343	−	0.602203i	$-0.794290\pi$
$5$	−3.57030	−1.59669	−0.798343	+	0.602203i	$0.794290\pi$
$6$	2.42494	0.989977
$7$	1.93625	0.731833	0.365917	−	0.930648i	$-0.380755\pi$
$7$	1.93625	0.731833	0.365917	+	0.930648i	$0.380755\pi$
$8$	−4.55968	−1.61209
$9$	1.00000	0.333333
$10$	8.65775	2.73782
$11$	−0.760801	−0.229390	−0.114695	−	0.993401i	$-0.536589\pi$
$11$	−0.760801	−0.229390	−0.114695	+	0.993401i	$0.536589\pi$
$12$	−3.88033	−1.12015
$13$	4.96794	1.37786	0.688929	−	0.724829i	$-0.258081\pi$
$13$	4.96794	1.37786	0.688929	+	0.724829i	$0.258081\pi$
$14$	−4.69529	−1.25487
$15$	3.57030	0.921847
$16$	3.29630	0.824074
$17$	−1.65697	−0.401875	−0.200938	−	0.979604i	$-0.564399\pi$
$17$	−1.65697	−0.401875	−0.200938	+	0.979604i	$0.564399\pi$
$18$	−2.42494	−0.571564
$19$	−3.79849	−0.871433	−0.435717	−	0.900084i	$-0.643505\pi$
$19$	−3.79849	−0.871433	−0.435717	+	0.900084i	$0.643505\pi$
$20$	−13.8539	−3.09783
$21$	−1.93625	−0.422524
$22$	1.84490	0.393333
$23$	8.00124	1.66837	0.834187	−	0.551482i	$-0.185937\pi$
$23$	8.00124	1.66837	0.834187	+	0.551482i	$0.185937\pi$
$24$	4.55968	0.930742
$25$	7.74703	1.54941
$26$	−12.0469	−2.36260
$27$	−1.00000	−0.192450
$28$	7.51329	1.41988
$29$	−6.50138	−1.20728	−0.603638	−	0.797258i	$-0.706283\pi$
$29$	−6.50138	−1.20728	−0.603638	+	0.797258i	$0.706283\pi$
$30$	−8.65775	−1.58068
$31$	−4.68116	−0.840761	−0.420380	−	0.907348i	$-0.638103\pi$
$31$	−4.68116	−0.840761	−0.420380	+	0.907348i	$0.638103\pi$
$32$	1.12605	0.199059
$33$	0.760801	0.132438
$34$	4.01806	0.689092
$35$	−6.91299	−1.16851
$36$	3.88033	0.646722
$37$	8.73739	1.43642	0.718209	−	0.695827i	$-0.244962\pi$
$37$	8.73739	1.43642	0.718209	+	0.695827i	$0.244962\pi$
$38$	9.21110	1.49424
$39$	−4.96794	−0.795506
$40$	16.2794	2.57400
$41$	0.688724	0.107561	0.0537803	−	0.998553i	$-0.482873\pi$
$41$	0.688724	0.107561	0.0537803	+	0.998553i	$0.482873\pi$
$42$	4.69529	0.724498
$43$	−2.55636	−0.389841	−0.194920	−	0.980819i	$-0.562445\pi$
$43$	−2.55636	−0.389841	−0.194920	+	0.980819i	$0.562445\pi$
$44$	−2.95216	−0.445054
$45$	−3.57030	−0.532229
$46$	−19.4025	−2.86075
$47$	−6.78041	−0.989024	−0.494512	−	0.869171i	$-0.664653\pi$
$47$	−6.78041	−0.989024	−0.494512	+	0.869171i	$0.664653\pi$
$48$	−3.29630	−0.475779
$49$	−3.25094	−0.464420
$50$	−18.7861	−2.65675
$51$	1.65697	0.232023
$52$	19.2772	2.67327
$53$	−1.50354	−0.206528	−0.103264	−	0.994654i	$-0.532929\pi$
$53$	−1.50354	−0.206528	−0.103264	+	0.994654i	$0.532929\pi$
$54$	2.42494	0.329992
$55$	2.71628	0.366264
$56$	−8.82869	−1.17978
$57$	3.79849	0.503122
$58$	15.7655	2.07011
$59$	−1.26893	−0.165201	−0.0826003	−	0.996583i	$-0.526322\pi$
$59$	−1.26893	−0.165201	−0.0826003	+	0.996583i	$0.526322\pi$
$60$	13.8539	1.78853
$61$	10.9843	1.40640	0.703201	−	0.710992i	$-0.251754\pi$
$61$	10.9843	1.40640	0.703201	+	0.710992i	$0.251754\pi$
$62$	11.3515	1.44164
$63$	1.93625	0.243944
$64$	−9.32319	−1.16540
$65$	−17.7370	−2.20001
$66$	−1.84490	−0.227091
$67$	−2.40247	−0.293509	−0.146754	−	0.989173i	$-0.546883\pi$
$67$	−2.40247	−0.293509	−0.146754	+	0.989173i	$0.546883\pi$
$68$	−6.42960	−0.779704
$69$	−8.00124	−0.963236
$70$	16.7636	2.00363
$71$	4.19086	0.497364	0.248682	−	0.968585i	$-0.420003\pi$
$71$	4.19086	0.497364	0.248682	+	0.968585i	$0.420003\pi$
$72$	−4.55968	−0.537364
$73$	−6.01407	−0.703894	−0.351947	−	0.936020i	$-0.614480\pi$
$73$	−6.01407	−0.703894	−0.351947	+	0.936020i	$0.614480\pi$
$74$	−21.1876	−2.46301
$75$	−7.74703	−0.894550
$76$	−14.7394	−1.69072
$77$	−1.47310	−0.167875
$78$	12.0469	1.36405
$79$	−12.5878	−1.41624	−0.708121	−	0.706091i	$-0.750457\pi$
$79$	−12.5878	−1.41624	−0.708121	+	0.706091i	$0.750457\pi$
$80$	−11.7688	−1.31579
$81$	1.00000	0.111111
$82$	−1.67011	−0.184433
$83$	−9.04918	−0.993276	−0.496638	−	0.867958i	$-0.665432\pi$
$83$	−9.04918	−0.993276	−0.496638	+	0.867958i	$0.665432\pi$
$84$	−7.51329	−0.819767
$85$	5.91589	0.641668
$86$	6.19901	0.668456
$87$	6.50138	0.697021
$88$	3.46901	0.369798
$89$	1.79969	0.190767	0.0953833	−	0.995441i	$-0.469592\pi$
$89$	1.79969	0.190767	0.0953833	+	0.995441i	$0.469592\pi$
$90$	8.65775	0.912607
$91$	9.61916	1.00836
$92$	31.0475	3.23692
$93$	4.68116	0.485413
$94$	16.4421	1.69587
$95$	13.5617	1.39140
$96$	−1.12605	−0.114927
$97$	4.34061	0.440722	0.220361	−	0.975418i	$-0.429276\pi$
$97$	4.34061	0.440722	0.220361	+	0.975418i	$0.429276\pi$
$98$	7.88333	0.796336
$99$	−0.760801	−0.0764633
$100$	30.0610	3.00610
$101$	8.00338	0.796366	0.398183	−	0.917306i	$-0.369641\pi$
$101$	8.00338	0.796366	0.398183	+	0.917306i	$0.369641\pi$
$102$	−4.01806	−0.397847
$103$	−2.53942	−0.250217	−0.125108	−	0.992143i	$-0.539928\pi$
$103$	−2.53942	−0.250217	−0.125108	+	0.992143i	$0.539928\pi$
$104$	−22.6522	−2.22123
$105$	6.91299	0.674638
$106$	3.64600	0.354131
$107$	−12.2062	−1.18002	−0.590010	−	0.807396i	$-0.700876\pi$
$107$	−12.2062	−1.18002	−0.590010	+	0.807396i	$0.700876\pi$
$108$	−3.88033	−0.373385
$109$	8.96883	0.859058	0.429529	−	0.903053i	$-0.358680\pi$
$109$	8.96883	0.859058	0.429529	+	0.903053i	$0.358680\pi$
$110$	−6.58683	−0.628029
$111$	−8.73739	−0.829317
$112$	6.38245	0.603085
$113$	−7.17879	−0.675324	−0.337662	−	0.941267i	$-0.609636\pi$
$113$	−7.17879	−0.675324	−0.337662	+	0.941267i	$0.609636\pi$
$114$	−9.21110	−0.862699
$115$	−28.5668	−2.66387
$116$	−25.2275	−2.34231
$117$	4.96794	0.459286
$118$	3.07708	0.283268
$119$	−3.20831	−0.294106
$120$	−16.2794	−1.48610
$121$	−10.4212	−0.947380
$122$	−26.6364	−2.41154
$123$	−0.688724	−0.0621002
$124$	−18.1644	−1.63121
$125$	−9.80770	−0.877228
$126$	−4.69529	−0.418289
$127$	17.9460	1.59245	0.796224	−	0.605001i	$-0.206827\pi$
$127$	17.9460	1.59245	0.796224	+	0.605001i	$0.206827\pi$
$128$	20.3561	1.79924
$129$	2.55636	0.225075
$130$	43.0112	3.77233
$131$	4.14801	0.362414	0.181207	−	0.983445i	$-0.442000\pi$
$131$	4.14801	0.362414	0.181207	+	0.983445i	$0.442000\pi$
$132$	2.95216	0.256952
$133$	−7.35482	−0.637744
$134$	5.82585	0.503277
$135$	3.57030	0.307282
$136$	7.55528	0.647860
$137$	14.6018	1.24752	0.623759	−	0.781617i	$-0.285605\pi$
$137$	14.6018	1.24752	0.623759	+	0.781617i	$0.285605\pi$
$138$	19.4025	1.65165
$139$	10.5539	0.895167	0.447584	−	0.894242i	$-0.352285\pi$
$139$	10.5539	0.895167	0.447584	+	0.894242i	$0.352285\pi$
$140$	−26.8247	−2.26710
$141$	6.78041	0.571013
$142$	−10.1626	−0.852825
$143$	−3.77961	−0.316067
$144$	3.29630	0.274691
$145$	23.2119	1.92764
$146$	14.5838	1.20696
$147$	3.25094	0.268133
$148$	33.9040	2.78689
$149$	8.15137	0.667786	0.333893	−	0.942611i	$-0.391638\pi$
$149$	8.15137	0.667786	0.333893	+	0.942611i	$0.391638\pi$
$150$	18.7861	1.53388
$151$	−8.96403	−0.729483	−0.364741	−	0.931109i	$-0.618843\pi$
$151$	−8.96403	−0.729483	−0.364741	+	0.931109i	$0.618843\pi$
$152$	17.3199	1.40483
$153$	−1.65697	−0.133958
$154$	3.57218	0.287854
$155$	16.7131	1.34243
$156$	−19.2772	−1.54341
$157$	−8.49427	−0.677916	−0.338958	−	0.940801i	$-0.610074\pi$
$157$	−8.49427	−0.677916	−0.338958	+	0.940801i	$0.610074\pi$
$158$	30.5247	2.42842
$159$	1.50354	0.119239
$160$	−4.02033	−0.317835
$161$	15.4924	1.22097
$162$	−2.42494	−0.190521
$163$	23.8719	1.86979	0.934897	−	0.354919i	$-0.115492\pi$
$163$	23.8719	1.86979	0.934897	+	0.354919i	$0.115492\pi$
$164$	2.67248	0.208685
$165$	−2.71628	−0.211462
$166$	21.9437	1.70316
$167$	8.68413	0.671998	0.335999	−	0.941862i	$-0.390926\pi$
$167$	8.68413	0.671998	0.335999	+	0.941862i	$0.390926\pi$
$168$	8.82869	0.681148
$169$	11.6804	0.898491
$170$	−14.3457	−1.10026
$171$	−3.79849	−0.290478
$172$	−9.91950	−0.756355
$173$	−5.13894	−0.390706	−0.195353	−	0.980733i	$-0.562585\pi$
$173$	−5.13894	−0.390706	−0.195353	+	0.980733i	$0.562585\pi$
$174$	−15.7655	−1.19518
$175$	15.0002	1.13391
$176$	−2.50782	−0.189034
$177$	1.26893	0.0953786
$178$	−4.36413	−0.327106
$179$	4.35330	0.325381	0.162690	−	0.986677i	$-0.447983\pi$
$179$	4.35330	0.325381	0.162690	+	0.986677i	$0.447983\pi$
$180$	−13.8539	−1.03261
$181$	25.0306	1.86051	0.930254	−	0.366916i	$-0.119586\pi$
$181$	25.0306	1.86051	0.930254	+	0.366916i	$0.119586\pi$
$182$	−23.3259	−1.72903
$183$	−10.9843	−0.811986
$184$	−36.4831	−2.68957
$185$	−31.1951	−2.29351
$186$	−11.3515	−0.832334
$187$	1.26063	0.0921861
$188$	−26.3102	−1.91887
$189$	−1.93625	−0.140841
$190$	−32.8864	−2.38583
$191$	−4.48016	−0.324173	−0.162086	−	0.986777i	$-0.551822\pi$
$191$	−4.48016	−0.324173	−0.162086	+	0.986777i	$0.551822\pi$
$192$	9.32319	0.672844
$193$	−17.1863	−1.23710	−0.618550	−	0.785745i	$-0.712280\pi$
$193$	−17.1863	−1.23710	−0.618550	+	0.785745i	$0.712280\pi$
$194$	−10.5257	−0.755702
$195$	17.7370	1.27017
$196$	−12.6147	−0.901051
$197$	−15.5560	−1.10832	−0.554160	−	0.832410i	$-0.686960\pi$
$197$	−15.5560	−1.10832	−0.554160	+	0.832410i	$0.686960\pi$
$198$	1.84490	0.131111
$199$	−14.8188	−1.05048	−0.525239	−	0.850955i	$-0.676024\pi$
$199$	−14.8188	−1.05048	−0.525239	+	0.850955i	$0.676024\pi$
$200$	−35.3240	−2.49778
$201$	2.40247	0.169457
$202$	−19.4077	−1.36552
$203$	−12.5883	−0.883525
$204$	6.42960	0.450162
$205$	−2.45895	−0.171741
$206$	6.15795	0.429045
$207$	8.00124	0.556125
$208$	16.3758	1.13546
$209$	2.88989	0.199898
$210$	−16.7636	−1.15680
$211$	−18.5990	−1.28040	−0.640202	−	0.768206i	$-0.721150\pi$
$211$	−18.5990	−1.28040	−0.640202	+	0.768206i	$0.721150\pi$
$212$	−5.83425	−0.400698
$213$	−4.19086	−0.287153
$214$	29.5994	2.02337
$215$	9.12695	0.622453
$216$	4.55968	0.310247
$217$	−9.06389	−0.615297
$218$	−21.7489	−1.47302
$219$	6.01407	0.406393
$220$	10.5401	0.710612
$221$	−8.23174	−0.553727
$222$	21.1876	1.42202
$223$	6.27658	0.420311	0.210156	−	0.977668i	$-0.432603\pi$
$223$	6.27658	0.420311	0.210156	+	0.977668i	$0.432603\pi$
$224$	2.18031	0.145678
$225$	7.74703	0.516468
$226$	17.4081	1.15797
$227$	12.0336	0.798698	0.399349	−	0.916799i	$-0.369236\pi$
$227$	12.0336	0.798698	0.399349	+	0.916799i	$0.369236\pi$
$228$	14.7394	0.976140
$229$	25.6497	1.69498	0.847490	−	0.530811i	$-0.178112\pi$
$229$	25.6497	1.69498	0.847490	+	0.530811i	$0.178112\pi$
$230$	69.2728	4.56771
$231$	1.47310	0.0969229
$232$	29.6442	1.94624
$233$	−23.4661	−1.53731	−0.768657	−	0.639662i	$-0.779074\pi$
$233$	−23.4661	−1.53731	−0.768657	+	0.639662i	$0.779074\pi$
$234$	−12.0469	−0.787533
$235$	24.2081	1.57916
$236$	−4.92387	−0.320516
$237$	12.5878	0.817667
$238$	7.77997	0.504300
$239$	3.95728	0.255975	0.127988	−	0.991776i	$-0.459148\pi$
$239$	3.95728	0.255975	0.127988	+	0.991776i	$0.459148\pi$
$240$	11.7688	0.759670
$241$	−9.56506	−0.616140	−0.308070	−	0.951364i	$-0.599683\pi$
$241$	−9.56506	−0.616140	−0.308070	+	0.951364i	$0.599683\pi$
$242$	25.2707	1.62446
$243$	−1.00000	−0.0641500
$244$	42.6229	2.72865
$245$	11.6068	0.741532
$246$	1.67011	0.106483
$247$	−18.8707	−1.20071
$248$	21.3446	1.35538
$249$	9.04918	0.573468
$250$	23.7831	1.50417
$251$	23.8401	1.50478	0.752388	−	0.658720i	$-0.228902\pi$
$251$	23.8401	1.50478	0.752388	+	0.658720i	$0.228902\pi$
$252$	7.51329	0.473292
$253$	−6.08735	−0.382708
$254$	−43.5179	−2.73056
$255$	−5.91589	−0.370467
$256$	−30.7159	−1.91974
$257$	16.5418	1.03185	0.515926	−	0.856633i	$-0.327448\pi$
$257$	16.5418	1.03185	0.515926	+	0.856633i	$0.327448\pi$
$258$	−6.19901	−0.385933
$259$	16.9178	1.05122
$260$	−68.8254	−4.26837
$261$	−6.50138	−0.402425
$262$	−10.0587	−0.621427
$263$	−28.0637	−1.73048	−0.865241	−	0.501356i	$-0.832835\pi$
$263$	−28.0637	−1.73048	−0.865241	+	0.501356i	$0.832835\pi$
$264$	−3.46901	−0.213503
$265$	5.36810	0.329760
$266$	17.8350	1.09353
$267$	−1.79969	−0.110139
$268$	−9.32238	−0.569455
$269$	15.6557	0.954546	0.477273	−	0.878755i	$-0.341625\pi$
$269$	15.6557	0.954546	0.477273	+	0.878755i	$0.341625\pi$
$270$	−8.65775	−0.526894
$271$	3.16554	0.192293	0.0961464	−	0.995367i	$-0.469348\pi$
$271$	3.16554	0.192293	0.0961464	+	0.995367i	$0.469348\pi$
$272$	−5.46188	−0.331175
$273$	−9.61916	−0.582178
$274$	−35.4085	−2.13911
$275$	−5.89394	−0.355418
$276$	−31.0475	−1.86884
$277$	−11.1678	−0.671010	−0.335505	−	0.942038i	$-0.608907\pi$
$277$	−11.1678	−0.671010	−0.335505	+	0.942038i	$0.608907\pi$
$278$	−25.5925	−1.53494
$279$	−4.68116	−0.280254
$280$	31.5210	1.88374
$281$	−6.02116	−0.359193	−0.179596	−	0.983740i	$-0.557479\pi$
$281$	−6.02116	−0.359193	−0.179596	+	0.983740i	$0.557479\pi$
$282$	−16.4421	−0.979111
$283$	−10.5110	−0.624816	−0.312408	−	0.949948i	$-0.601136\pi$
$283$	−10.5110	−0.624816	−0.312408	+	0.949948i	$0.601136\pi$
$284$	16.2619	0.964968
$285$	−13.5617	−0.803328
$286$	9.16532	0.541957
$287$	1.33354	0.0787165
$288$	1.12605	0.0663531
$289$	−14.2544	−0.838496
$290$	−56.2874	−3.30531
$291$	−4.34061	−0.254451
$292$	−23.3366	−1.36567
$293$	24.9220	1.45596	0.727979	−	0.685600i	$-0.240460\pi$
$293$	24.9220	1.45596	0.727979	+	0.685600i	$0.240460\pi$
$294$	−7.88333	−0.459765
$295$	4.53046	0.263773
$296$	−39.8398	−2.31564
$297$	0.760801	0.0441461
$298$	−19.7666	−1.14505
$299$	39.7497	2.29878
$300$	−30.0610	−1.73557
$301$	−4.94974	−0.285298
$302$	21.7372	1.25084
$303$	−8.00338	−0.459782
$304$	−12.5209	−0.718126
$305$	−39.2174	−2.24558
$306$	4.01806	0.229697
$307$	−6.27330	−0.358036	−0.179018	−	0.983846i	$-0.557292\pi$
$307$	−6.27330	−0.358036	−0.179018	+	0.983846i	$0.557292\pi$
$308$	−5.71611	−0.325706
$309$	2.53942	0.144463
$310$	−40.5283	−2.30185
$311$	33.0086	1.87174	0.935872	−	0.352339i	$-0.114614\pi$
$311$	33.0086	1.87174	0.935872	+	0.352339i	$0.114614\pi$
$312$	22.6522	1.28243
$313$	−17.6929	−1.00006	−0.500031	−	0.866008i	$-0.666678\pi$
$313$	−17.6929	−1.00006	−0.500031	+	0.866008i	$0.666678\pi$
$314$	20.5981	1.16242
$315$	−6.91299	−0.389503
$316$	−48.8449	−2.74774
$317$	20.7920	1.16780	0.583898	−	0.811827i	$-0.301527\pi$
$317$	20.7920	1.16780	0.583898	+	0.811827i	$0.301527\pi$
$318$	−3.64600	−0.204458
$319$	4.94625	0.276937
$320$	33.2866	1.86078
$321$	12.2062	0.681285
$322$	−37.5681	−2.09359
$323$	6.29400	0.350207
$324$	3.88033	0.215574
$325$	38.4867	2.13486
$326$	−57.8880	−3.20612
$327$	−8.96883	−0.495977
$328$	−3.14036	−0.173398
$329$	−13.1286	−0.723801
$330$	6.58683	0.362593
$331$	−19.0179	−1.04532	−0.522660	−	0.852541i	$-0.675060\pi$
$331$	−19.0179	−1.04532	−0.522660	+	0.852541i	$0.675060\pi$
$332$	−35.1138	−1.92712
$333$	8.73739	0.478806
$334$	−21.0585	−1.15227
$335$	8.57754	0.468641
$336$	−6.38245	−0.348191
$337$	5.62634	0.306486	0.153243	−	0.988189i	$-0.451028\pi$
$337$	5.62634	0.306486	0.153243	+	0.988189i	$0.451028\pi$
$338$	−28.3242	−1.54064
$339$	7.17879	0.389898
$340$	22.9556	1.24494
$341$	3.56143	0.192862
$342$	9.21110	0.498079
$343$	−19.8484	−1.07171
$344$	11.6562	0.628459
$345$	28.5668	1.53799
$346$	12.4616	0.669940
$347$	18.7918	1.00880	0.504398	−	0.863471i	$-0.331714\pi$
$347$	18.7918	1.00880	0.504398	+	0.863471i	$0.331714\pi$
$348$	25.2275	1.35234
$349$	19.4434	1.04078	0.520390	−	0.853929i	$-0.325787\pi$
$349$	19.4434	1.04078	0.520390	+	0.853929i	$0.325787\pi$
$350$	−36.3745	−1.94430
$351$	−4.96794	−0.265169
$352$	−0.856699	−0.0456622
$353$	−29.3393	−1.56157	−0.780786	−	0.624799i	$-0.785181\pi$
$353$	−29.3393	−1.56157	−0.780786	+	0.624799i	$0.785181\pi$
$354$	−3.07708	−0.163545
$355$	−14.9626	−0.794134
$356$	6.98338	0.370119
$357$	3.20831	0.169802
$358$	−10.5565	−0.557928
$359$	−11.5969	−0.612059	−0.306030	−	0.952022i	$-0.599001\pi$
$359$	−11.5969	−0.612059	−0.306030	+	0.952022i	$0.599001\pi$
$360$	16.2794	0.858001
$361$	−4.57148	−0.240604
$362$	−60.6976	−3.19020
$363$	10.4212	0.546970
$364$	37.3255	1.95639
$365$	21.4720	1.12390
$366$	26.6364	1.39231
$367$	−19.7608	−1.03151	−0.515754	−	0.856737i	$-0.672488\pi$
$367$	−19.7608	−1.03151	−0.515754	+	0.856737i	$0.672488\pi$
$368$	26.3745	1.37486
$369$	0.688724	0.0358535
$370$	75.6462	3.93266
$371$	−2.91124	−0.151144
$372$	18.1644	0.941782
$373$	−9.86831	−0.510962	−0.255481	−	0.966814i	$-0.582234\pi$
$373$	−9.86831	−0.510962	−0.255481	+	0.966814i	$0.582234\pi$
$374$	−3.05694	−0.158071
$375$	9.80770	0.506468
$376$	30.9165	1.59440
$377$	−32.2984	−1.66345
$378$	4.69529	0.241499
$379$	−17.4375	−0.895704	−0.447852	−	0.894108i	$-0.647811\pi$
$379$	−17.4375	−0.895704	−0.447852	+	0.894108i	$0.647811\pi$
$380$	52.6240	2.69955
$381$	−17.9460	−0.919401
$382$	10.8641	0.555856
$383$	3.15465	0.161195	0.0805975	−	0.996747i	$-0.474317\pi$
$383$	3.15465	0.161195	0.0805975	+	0.996747i	$0.474317\pi$
$384$	−20.3561	−1.03879
$385$	5.25941	0.268044
$386$	41.6758	2.12124
$387$	−2.55636	−0.129947
$388$	16.8430	0.855074
$389$	13.4655	0.682728	0.341364	−	0.939931i	$-0.389111\pi$
$389$	13.4655	0.682728	0.341364	+	0.939931i	$0.389111\pi$
$390$	−43.0112	−2.17796
$391$	−13.2578	−0.670478
$392$	14.8233	0.748687
$393$	−4.14801	−0.209240
$394$	37.7224	1.90043
$395$	44.9423	2.26129
$396$	−2.95216	−0.148351
$397$	15.6943	0.787674	0.393837	−	0.919180i	$-0.371147\pi$
$397$	15.6943	0.787674	0.393837	+	0.919180i	$0.371147\pi$
$398$	35.9347	1.80125
$399$	7.35482	0.368202
$400$	25.5365	1.27682
$401$	−25.0279	−1.24983	−0.624917	−	0.780691i	$-0.714867\pi$
$401$	−25.0279	−1.24983	−0.624917	+	0.780691i	$0.714867\pi$
$402$	−5.82585	−0.290567
$403$	−23.2557	−1.15845
$404$	31.0557	1.54508
$405$	−3.57030	−0.177410
$406$	30.5258	1.51497
$407$	−6.64741	−0.329500
$408$	−7.55528	−0.374042
$409$	−12.7472	−0.630306	−0.315153	−	0.949041i	$-0.602056\pi$
$409$	−12.7472	−0.630306	−0.315153	+	0.949041i	$0.602056\pi$
$410$	5.96280	0.294482
$411$	−14.6018	−0.720255
$412$	−9.85380	−0.485462
$413$	−2.45696	−0.120899
$414$	−19.4025	−0.953582
$415$	32.3083	1.58595
$416$	5.59414	0.274275
$417$	−10.5539	−0.516825
$418$	−7.00781	−0.342763
$419$	26.1350	1.27678	0.638390	−	0.769713i	$-0.279601\pi$
$419$	26.1350	1.27678	0.638390	+	0.769713i	$0.279601\pi$
$420$	26.8247	1.30891
$421$	16.5537	0.806780	0.403390	−	0.915028i	$-0.367832\pi$
$421$	16.5537	0.806780	0.403390	+	0.915028i	$0.367832\pi$
$422$	45.1013	2.19550
$423$	−6.78041	−0.329675
$424$	6.85569	0.332942
$425$	−12.8366	−0.622667
$426$	10.1626	0.492379
$427$	21.2684	1.02925
$428$	−47.3642	−2.28943
$429$	3.77961	0.182481
$430$	−22.1323	−1.06731
$431$	0.598159	0.0288123	0.0144061	−	0.999896i	$-0.495414\pi$
$431$	0.598159	0.0288123	0.0144061	+	0.999896i	$0.495414\pi$
$432$	−3.29630	−0.158593
$433$	11.0114	0.529173	0.264586	−	0.964362i	$-0.414765\pi$
$433$	11.0114	0.529173	0.264586	+	0.964362i	$0.414765\pi$
$434$	21.9794	1.05504
$435$	−23.2119	−1.11292
$436$	34.8020	1.66671
$437$	−30.3926	−1.45388
$438$	−14.5838	−0.696839
$439$	−1.99475	−0.0952041	−0.0476020	−	0.998866i	$-0.515158\pi$
$439$	−1.99475	−0.0952041	−0.0476020	+	0.998866i	$0.515158\pi$
$440$	−12.3854	−0.590451
$441$	−3.25094	−0.154807
$442$	19.9615	0.949470
$443$	7.36979	0.350149	0.175075	−	0.984555i	$-0.443983\pi$
$443$	7.36979	0.350149	0.175075	+	0.984555i	$0.443983\pi$
$444$	−33.9040	−1.60901
$445$	−6.42542	−0.304594
$446$	−15.2203	−0.720704
$447$	−8.15137	−0.385547
$448$	−18.0520	−0.852878
$449$	−20.8583	−0.984366	−0.492183	−	0.870492i	$-0.663801\pi$
$449$	−20.8583	−0.984366	−0.492183	+	0.870492i	$0.663801\pi$
$450$	−18.7861	−0.885584
$451$	−0.523982	−0.0246733
$452$	−27.8561	−1.31024
$453$	8.96403	0.421167
$454$	−29.1808	−1.36952
$455$	−34.3433	−1.61004
$456$	−17.3199	−0.811079
$457$	24.9318	1.16626	0.583129	−	0.812379i	$-0.301828\pi$
$457$	24.9318	1.16626	0.583129	+	0.812379i	$0.301828\pi$
$458$	−62.1990	−2.90637
$459$	1.65697	0.0773409
$460$	−110.849	−5.16834
$461$	40.2991	1.87691	0.938457	−	0.345395i	$-0.112255\pi$
$461$	40.2991	1.87691	0.938457	+	0.345395i	$0.112255\pi$
$462$	−3.57218	−0.166193
$463$	−23.0793	−1.07259	−0.536294	−	0.844031i	$-0.680176\pi$
$463$	−23.0793	−1.07259	−0.536294	+	0.844031i	$0.680176\pi$
$464$	−21.4305	−0.994885
$465$	−16.7131	−0.775053
$466$	56.9038	2.63602
$467$	−29.2526	−1.35365	−0.676824	−	0.736145i	$-0.736644\pi$
$467$	−29.2526	−1.35365	−0.676824	+	0.736145i	$0.736644\pi$
$468$	19.2772	0.891090
$469$	−4.65179	−0.214800
$470$	−58.7031	−2.70777
$471$	8.49427	0.391395
$472$	5.78592	0.266319
$473$	1.94488	0.0894255
$474$	−30.5247	−1.40205
$475$	−29.4270	−1.35020
$476$	−12.4493	−0.570613
$477$	−1.50354	−0.0688426
$478$	−9.59617	−0.438919
$479$	−0.121654	−0.00555850	−0.00277925	−	0.999996i	$-0.500885\pi$
$479$	−0.121654	−0.00555850	−0.00277925	+	0.999996i	$0.500885\pi$
$480$	4.02033	0.183502
$481$	43.4068	1.97918
$482$	23.1947	1.05649
$483$	−15.4924	−0.704929
$484$	−40.4376	−1.83807
$485$	−15.4973	−0.703695
$486$	2.42494	0.109997
$487$	25.4062	1.15127	0.575634	−	0.817708i	$-0.304755\pi$
$487$	25.4062	1.15127	0.575634	+	0.817708i	$0.304755\pi$
$488$	−50.0851	−2.26725
$489$	−23.8719	−1.07953
$490$	−28.1458	−1.27150
$491$	8.19647	0.369901	0.184951	−	0.982748i	$-0.440787\pi$
$491$	8.19647	0.369901	0.184951	+	0.982748i	$0.440787\pi$
$492$	−2.67248	−0.120485
$493$	10.7726	0.485174
$494$	45.7602	2.05885
$495$	2.71628	0.122088
$496$	−15.4305	−0.692849
$497$	8.11455	0.363988
$498$	−21.9437	−0.983321
$499$	−31.5756	−1.41352	−0.706759	−	0.707454i	$-0.749843\pi$
$499$	−31.5756	−1.41352	−0.706759	+	0.707454i	$0.749843\pi$
$500$	−38.0571	−1.70197
$501$	−8.68413	−0.387978
$502$	−57.8109	−2.58023
$503$	2.37882	0.106066	0.0530331	−	0.998593i	$-0.483111\pi$
$503$	2.37882	0.106066	0.0530331	+	0.998593i	$0.483111\pi$
$504$	−8.82869	−0.393261
$505$	−28.5744	−1.27155
$506$	14.7615	0.656227
$507$	−11.6804	−0.518744
$508$	69.6363	3.08961
$509$	−8.14632	−0.361079	−0.180540	−	0.983568i	$-0.557784\pi$
$509$	−8.14632	−0.361079	−0.180540	+	0.983568i	$0.557784\pi$
$510$	14.3457	0.635237
$511$	−11.6447	−0.515133
$512$	33.7719	1.49252
$513$	3.79849	0.167707
$514$	−40.1129	−1.76931
$515$	9.06650	0.399518
$516$	9.91950	0.436682
$517$	5.15854	0.226872
$518$	−41.0246	−1.80252
$519$	5.13894	0.225574
$520$	80.8752	3.54661
$521$	−25.5329	−1.11862	−0.559308	−	0.828960i	$-0.688933\pi$
$521$	−25.5329	−1.11862	−0.559308	+	0.828960i	$0.688933\pi$
$522$	15.7655	0.690035
$523$	−10.5304	−0.460461	−0.230231	−	0.973136i	$-0.573948\pi$
$523$	−10.5304	−0.460461	−0.230231	+	0.973136i	$0.573948\pi$
$524$	16.0957	0.703142
$525$	−15.0002	−0.654661
$526$	68.0528	2.96724
$527$	7.75655	0.337881
$528$	2.50782	0.109139
$529$	41.0199	1.78347
$530$	−13.0173	−0.565436
$531$	−1.26893	−0.0550669
$532$	−28.5391	−1.23733
$533$	3.42154	0.148203
$534$	4.36413	0.188855
$535$	43.5799	1.88412
$536$	10.9545	0.473163
$537$	−4.35330	−0.187859
$538$	−37.9641	−1.63675
$539$	2.47332	0.106533
$540$	13.8539	0.596178
$541$	−31.7291	−1.36414	−0.682071	−	0.731286i	$-0.738921\pi$
$541$	−31.7291	−1.36414	−0.682071	+	0.731286i	$0.738921\pi$
$542$	−7.67624	−0.329723
$543$	−25.0306	−1.07417
$544$	−1.86583	−0.0799970
$545$	−32.0214	−1.37165
$546$	23.3259	0.998256
$547$	−21.8365	−0.933663	−0.466832	−	0.884346i	$-0.654605\pi$
$547$	−21.8365	−0.933663	−0.466832	+	0.884346i	$0.654605\pi$
$548$	56.6599	2.42039
$549$	10.9843	0.468800
$550$	14.2925	0.609432
$551$	24.6954	1.05206
$552$	36.4831	1.55283
$553$	−24.3732	−1.03645
$554$	27.0813	1.15057
$555$	31.1951	1.32416
$556$	40.9525	1.73677
$557$	−33.0770	−1.40152	−0.700758	−	0.713399i	$-0.747155\pi$
$557$	−33.0770	−1.40152	−0.700758	+	0.713399i	$0.747155\pi$
$558$	11.3515	0.480548
$559$	−12.6998	−0.537145
$560$	−22.7873	−0.962937
$561$	−1.26063	−0.0532237
$562$	14.6010	0.615904
$563$	−45.6954	−1.92583	−0.962915	−	0.269806i	$-0.913041\pi$
$563$	−45.6954	−1.92583	−0.962915	+	0.269806i	$0.913041\pi$
$564$	26.3102	1.10786
$565$	25.6304	1.07828
$566$	25.4886	1.07137
$567$	1.93625	0.0813148
$568$	−19.1090	−0.801796
$569$	−4.86790	−0.204073	−0.102036	−	0.994781i	$-0.532536\pi$
$569$	−4.86790	−0.204073	−0.102036	+	0.994781i	$0.532536\pi$
$570$	32.8864	1.37746
$571$	−12.5753	−0.526259	−0.263130	−	0.964761i	$-0.584755\pi$
$571$	−12.5753	−0.526259	−0.263130	+	0.964761i	$0.584755\pi$
$572$	−14.6661	−0.613222
$573$	4.48016	0.187161
$574$	−3.23376	−0.134974
$575$	61.9858	2.58499
$576$	−9.32319	−0.388466
$577$	4.44596	0.185088	0.0925438	−	0.995709i	$-0.470500\pi$
$577$	4.44596	0.185088	0.0925438	+	0.995709i	$0.470500\pi$
$578$	34.5661	1.43776
$579$	17.1863	0.714240
$580$	90.0697	3.73994
$581$	−17.5215	−0.726913
$582$	10.5257	0.436305
$583$	1.14390	0.0473754
$584$	27.4223	1.13474
$585$	−17.7370	−0.733335
$586$	−60.4343	−2.49652
$587$	−26.5822	−1.09717	−0.548583	−	0.836096i	$-0.684832\pi$
$587$	−26.5822	−1.09717	−0.548583	+	0.836096i	$0.684832\pi$
$588$	12.6147	0.520222
$589$	17.7813	0.732667
$590$	−10.9861	−0.452290
$591$	15.5560	0.639889
$592$	28.8010	1.18372
$593$	31.3516	1.28746	0.643728	−	0.765254i	$-0.277387\pi$
$593$	31.3516	1.28746	0.643728	+	0.765254i	$0.277387\pi$
$594$	−1.84490	−0.0756970
$595$	11.4546	0.469594
$596$	31.6300	1.29562
$597$	14.8188	0.606494
$598$	−96.3905	−3.94170
$599$	−12.4912	−0.510378	−0.255189	−	0.966891i	$-0.582138\pi$
$599$	−12.4912	−0.510378	−0.255189	+	0.966891i	$0.582138\pi$
$600$	35.3240	1.44210
$601$	−39.5454	−1.61309	−0.806545	−	0.591173i	$-0.798665\pi$
$601$	−39.5454	−1.61309	−0.806545	+	0.591173i	$0.798665\pi$
$602$	12.0028	0.489199
$603$	−2.40247	−0.0978362
$604$	−34.7834	−1.41532
$605$	37.2067	1.51267
$606$	19.4077	0.788384
$607$	−2.04917	−0.0831734	−0.0415867	−	0.999135i	$-0.513241\pi$
$607$	−2.04917	−0.0831734	−0.0415867	+	0.999135i	$0.513241\pi$
$608$	−4.27729	−0.173467
$609$	12.5883	0.510103
$610$	95.0998	3.85048
$611$	−33.6846	−1.36273
$612$	−6.42960	−0.259901
$613$	−33.5615	−1.35554	−0.677768	−	0.735276i	$-0.737053\pi$
$613$	−33.5615	−1.35554	−0.677768	+	0.735276i	$0.737053\pi$
$614$	15.2124	0.613921
$615$	2.45895	0.0991544
$616$	6.71687	0.270630
$617$	21.0818	0.848722	0.424361	−	0.905493i	$-0.360499\pi$
$617$	21.0818	0.848722	0.424361	+	0.905493i	$0.360499\pi$
$618$	−6.15795	−0.247709
$619$	−10.5662	−0.424692	−0.212346	−	0.977195i	$-0.568110\pi$
$619$	−10.5662	−0.424692	−0.212346	+	0.977195i	$0.568110\pi$
$620$	64.8524	2.60454
$621$	−8.00124	−0.321079
$622$	−80.0438	−3.20946
$623$	3.48465	0.139609
$624$	−16.3758	−0.655556
$625$	−3.71872	−0.148749
$626$	42.9042	1.71480
$627$	−2.88989	−0.115411
$628$	−32.9605	−1.31527
$629$	−14.4776	−0.577261
$630$	16.7636	0.667877
$631$	7.65094	0.304579	0.152289	−	0.988336i	$-0.451335\pi$
$631$	7.65094	0.304579	0.152289	+	0.988336i	$0.451335\pi$
$632$	57.3965	2.28311
$633$	18.5990	0.739242
$634$	−50.4194	−2.00241
$635$	−64.0725	−2.54264
$636$	5.83425	0.231343
$637$	−16.1505	−0.639904
$638$	−11.9944	−0.474862
$639$	4.19086	0.165788
$640$	−72.6773	−2.87282
$641$	−40.8288	−1.61264	−0.806320	−	0.591480i	$-0.798544\pi$
$641$	−40.8288	−1.61264	−0.806320	+	0.591480i	$0.798544\pi$
$642$	−29.5994	−1.16819
$643$	19.7229	0.777794	0.388897	−	0.921281i	$-0.372856\pi$
$643$	19.7229	0.777794	0.388897	+	0.921281i	$0.372856\pi$
$644$	60.1156	2.36889
$645$	−9.12695	−0.359373
$646$	−15.2626	−0.600497
$647$	−26.4422	−1.03955	−0.519776	−	0.854303i	$-0.673985\pi$
$647$	−26.4422	−1.03955	−0.519776	+	0.854303i	$0.673985\pi$
$648$	−4.55968	−0.179121
$649$	0.965403	0.0378954
$650$	−93.3280	−3.66062
$651$	9.06389	0.355242
$652$	92.6310	3.62771
$653$	−36.3943	−1.42422	−0.712109	−	0.702069i	$-0.752260\pi$
$653$	−36.3943	−1.42422	−0.712109	+	0.702069i	$0.752260\pi$
$654$	21.7489	0.850448
$655$	−14.8096	−0.578661
$656$	2.27024	0.0886379
$657$	−6.01407	−0.234631
$658$	31.8360	1.24109
$659$	15.6680	0.610337	0.305168	−	0.952298i	$-0.401287\pi$
$659$	15.6680	0.610337	0.305168	+	0.952298i	$0.401287\pi$
$660$	−10.5401	−0.410272
$661$	−22.5675	−0.877772	−0.438886	−	0.898543i	$-0.644627\pi$
$661$	−22.5675	−0.877772	−0.438886	+	0.898543i	$0.644627\pi$
$662$	46.1173	1.79240
$663$	8.23174	0.319694
$664$	41.2614	1.60125
$665$	26.2589	1.01828
$666$	−21.1876	−0.821005
$667$	−52.0191	−2.01419
$668$	33.6973	1.30379
$669$	−6.27658	−0.242667
$670$	−20.8000	−0.803575
$671$	−8.35690	−0.322614
$672$	−2.18031	−0.0841074
$673$	−19.5193	−0.752413	−0.376207	−	0.926536i	$-0.622772\pi$
$673$	−19.5193	−0.752413	−0.376207	+	0.926536i	$0.622772\pi$
$674$	−13.6435	−0.525529
$675$	−7.74703	−0.298183
$676$	45.3238	1.74322
$677$	−10.5077	−0.403846	−0.201923	−	0.979401i	$-0.564719\pi$
$677$	−10.5077	−0.403846	−0.201923	+	0.979401i	$0.564719\pi$
$678$	−17.4081	−0.668555
$679$	8.40450	0.322535
$680$	−26.9746	−1.03443
$681$	−12.0336	−0.461129
$682$	−8.63625	−0.330699
$683$	−8.84142	−0.338308	−0.169154	−	0.985590i	$-0.554103\pi$
$683$	−8.84142	−0.338308	−0.169154	+	0.985590i	$0.554103\pi$
$684$	−14.7394	−0.563575
$685$	−52.1328	−1.99189
$686$	48.1311	1.83765
$687$	−25.6497	−0.978598
$688$	−8.42651	−0.321258
$689$	−7.46951	−0.284566
$690$	−69.2728	−2.63717
$691$	28.0062	1.06541	0.532704	−	0.846302i	$-0.321176\pi$
$691$	28.0062	1.06541	0.532704	+	0.846302i	$0.321176\pi$
$692$	−19.9408	−0.758034
$693$	−1.47310	−0.0559584
$694$	−45.5690	−1.72977
$695$	−37.6804	−1.42930
$696$	−29.6442	−1.12366
$697$	−1.14120	−0.0432259
$698$	−47.1490	−1.78461
$699$	23.4661	0.887568
$700$	58.2056	2.19997
$701$	−19.5299	−0.737633	−0.368817	−	0.929502i	$-0.620237\pi$
$701$	−19.5299	−0.737633	−0.368817	+	0.929502i	$0.620237\pi$
$702$	12.0469	0.454683
$703$	−33.1889	−1.25174
$704$	7.09309	0.267331
$705$	−24.2081	−0.911729
$706$	71.1459	2.67761
$707$	15.4965	0.582807
$708$	4.92387	0.185050
$709$	−44.0937	−1.65597	−0.827987	−	0.560747i	$-0.810514\pi$
$709$	−44.0937	−1.65597	−0.827987	+	0.560747i	$0.810514\pi$
$710$	36.2835	1.36169
$711$	−12.5878	−0.472080
$712$	−8.20601	−0.307533
$713$	−37.4551	−1.40270
$714$	−7.77997	−0.291158
$715$	13.4943	0.504659
$716$	16.8922	0.631293
$717$	−3.95728	−0.147787
$718$	28.1217	1.04949
$719$	7.93534	0.295938	0.147969	−	0.988992i	$-0.452726\pi$
$719$	7.93534	0.295938	0.147969	+	0.988992i	$0.452726\pi$
$720$	−11.7688	−0.438596
$721$	−4.91696	−0.183117
$722$	11.0856	0.412562
$723$	9.56506	0.355728
$724$	97.1269	3.60969
$725$	−50.3664	−1.87056
$726$	−25.2707	−0.937885
$727$	−14.8846	−0.552038	−0.276019	−	0.961152i	$-0.589015\pi$
$727$	−14.8846	−0.552038	−0.276019	+	0.961152i	$0.589015\pi$
$728$	−43.8603	−1.62557
$729$	1.00000	0.0370370
$730$	−52.0684	−1.92714
$731$	4.23581	0.156667
$732$	−42.6229	−1.57539
$733$	35.9591	1.32818	0.664090	−	0.747653i	$-0.268819\pi$
$733$	35.9591	1.32818	0.664090	+	0.747653i	$0.268819\pi$
$734$	47.9188	1.76872
$735$	−11.6068	−0.428124
$736$	9.00979	0.332105
$737$	1.82780	0.0673280
$738$	−1.67011	−0.0614777
$739$	23.7750	0.874578	0.437289	−	0.899321i	$-0.355939\pi$
$739$	23.7750	0.874578	0.437289	+	0.899321i	$0.355939\pi$
$740$	−121.047	−4.44979
$741$	18.8707	0.693231
$742$	7.05957	0.259165
$743$	−31.9885	−1.17354	−0.586771	−	0.809753i	$-0.699601\pi$
$743$	−31.9885	−1.17354	−0.586771	+	0.809753i	$0.699601\pi$
$744$	−21.3446	−0.782531
$745$	−29.1028	−1.06624
$746$	23.9300	0.876141
$747$	−9.04918	−0.331092
$748$	4.89165	0.178856
$749$	−23.6343	−0.863579
$750$	−23.7831	−0.868435
$751$	−10.4613	−0.381738	−0.190869	−	0.981616i	$-0.561131\pi$
$751$	−10.4613	−0.381738	−0.190869	+	0.981616i	$0.561131\pi$
$752$	−22.3502	−0.815029
$753$	−23.8401	−0.868783
$754$	78.3218	2.85231
$755$	32.0043	1.16475
$756$	−7.51329	−0.273256
$757$	−39.0930	−1.42086	−0.710430	−	0.703768i	$-0.751500\pi$
$757$	−39.0930	−1.42086	−0.710430	+	0.703768i	$0.751500\pi$
$758$	42.2849	1.53586
$759$	6.08735	0.220957
$760$	−61.8372	−2.24307
$761$	−13.4040	−0.485896	−0.242948	−	0.970039i	$-0.578114\pi$
$761$	−13.4040	−0.485896	−0.242948	+	0.970039i	$0.578114\pi$
$762$	43.5179	1.57649
$763$	17.3659	0.628688
$764$	−17.3845	−0.628949
$765$	5.91589	0.213889
$766$	−7.64983	−0.276400
$767$	−6.30396	−0.227623
$768$	30.7159	1.10836
$769$	−8.57846	−0.309347	−0.154674	−	0.987966i	$-0.549433\pi$
$769$	−8.57846	−0.309347	−0.154674	+	0.987966i	$0.549433\pi$
$770$	−12.7537	−0.459613
$771$	−16.5418	−0.595740
$772$	−66.6887	−2.40018
$773$	−27.7237	−0.997154	−0.498577	−	0.866845i	$-0.666144\pi$
$773$	−27.7237	−0.997154	−0.498577	+	0.866845i	$0.666144\pi$
$774$	6.19901	0.222819
$775$	−36.2651	−1.30268
$776$	−19.7918	−0.710485
$777$	−16.9178	−0.606922
$778$	−32.6530	−1.17067
$779$	−2.61611	−0.0937319
$780$	68.8254	2.46435
$781$	−3.18841	−0.114090
$782$	32.1495	1.14966
$783$	6.50138	0.232340
$784$	−10.7161	−0.382716
$785$	30.3271	1.08242
$786$	10.0587	0.358781
$787$	−1.62659	−0.0579816	−0.0289908	−	0.999580i	$-0.509229\pi$
$787$	−1.62659	−0.0579816	−0.0289908	+	0.999580i	$0.509229\pi$
$788$	−60.3625	−2.15032
$789$	28.0637	0.999094
$790$	−108.982	−3.87742
$791$	−13.8999	−0.494225
$792$	3.46901	0.123266
$793$	54.5695	1.93782
$794$	−38.0577	−1.35062
$795$	−5.36810	−0.190387
$796$	−57.5019	−2.03810
$797$	46.0561	1.63139	0.815696	−	0.578481i	$-0.196354\pi$
$797$	46.0561	1.63139	0.815696	+	0.578481i	$0.196354\pi$
$798$	−17.8350	−0.631352
$799$	11.2350	0.397464
$800$	8.72353	0.308423
$801$	1.79969	0.0635889
$802$	60.6912	2.14308
$803$	4.57551	0.161466
$804$	9.32238	0.328775
$805$	−55.3125	−1.94951
$806$	56.3936	1.98638
$807$	−15.6557	−0.551107
$808$	−36.4929	−1.28381
$809$	−46.9075	−1.64918	−0.824591	−	0.565730i	$-0.808595\pi$
$809$	−46.9075	−1.64918	−0.824591	+	0.565730i	$0.808595\pi$
$810$	8.65775	0.304202
$811$	−35.9457	−1.26222	−0.631112	−	0.775692i	$-0.717401\pi$
$811$	−35.9457	−1.26222	−0.631112	+	0.775692i	$0.717401\pi$
$812$	−48.8467	−1.71418
$813$	−3.16554	−0.111020
$814$	16.1196	0.564991
$815$	−85.2299	−2.98547
$816$	5.46188	0.191204
$817$	9.71029	0.339720
$818$	30.9111	1.08078
$819$	9.61916	0.336121
$820$	−9.54154	−0.333205
$821$	−27.5332	−0.960915	−0.480458	−	0.877018i	$-0.659529\pi$
$821$	−27.5332	−0.960915	−0.480458	+	0.877018i	$0.659529\pi$
$822$	35.4085	1.23501
$823$	50.4079	1.75711	0.878555	−	0.477642i	$-0.158508\pi$
$823$	50.4079	1.75711	0.878555	+	0.477642i	$0.158508\pi$
$824$	11.5790	0.403373
$825$	5.89394	0.205201
$826$	5.95799	0.207305
$827$	9.46104	0.328993	0.164496	−	0.986378i	$-0.447400\pi$
$827$	9.46104	0.328993	0.164496	+	0.986378i	$0.447400\pi$
$828$	31.0475	1.07897
$829$	−28.0433	−0.973985	−0.486993	−	0.873406i	$-0.661906\pi$
$829$	−28.0433	−0.973985	−0.486993	+	0.873406i	$0.661906\pi$
$830$	−78.3455	−2.71941
$831$	11.1678	0.387408
$832$	−46.3170	−1.60575
$833$	5.38672	0.186639
$834$	25.5925	0.886195
$835$	−31.0049	−1.07297
$836$	11.2137	0.387835
$837$	4.68116	0.161804
$838$	−63.3758	−2.18928
$839$	26.9334	0.929844	0.464922	−	0.885352i	$-0.346082\pi$
$839$	26.9334	0.929844	0.464922	+	0.885352i	$0.346082\pi$
$840$	−31.5210	−1.08758
$841$	13.2680	0.457516
$842$	−40.1418	−1.38338
$843$	6.02116	0.207380
$844$	−72.1701	−2.48420
$845$	−41.7025	−1.43461
$846$	16.4421	0.565290
$847$	−20.1780	−0.693325
$848$	−4.95613	−0.170194
$849$	10.5110	0.360738
$850$	31.1280	1.06768
$851$	69.9100	2.39648
$852$	−16.2619	−0.557124
$853$	38.8568	1.33043	0.665216	−	0.746651i	$-0.268339\pi$
$853$	38.8568	1.33043	0.665216	+	0.746651i	$0.268339\pi$
$854$	−51.5746	−1.76485
$855$	13.5617	0.463802
$856$	55.6565	1.90230
$857$	6.06651	0.207228	0.103614	−	0.994618i	$-0.466959\pi$
$857$	6.06651	0.207228	0.103614	+	0.994618i	$0.466959\pi$
$858$	−9.16532	−0.312899
$859$	13.1561	0.448881	0.224441	−	0.974488i	$-0.427944\pi$
$859$	13.1561	0.448881	0.224441	+	0.974488i	$0.427944\pi$
$860$	35.4156	1.20766
$861$	−1.33354	−0.0454470
$862$	−1.45050	−0.0494042
$863$	−1.67792	−0.0571170	−0.0285585	−	0.999592i	$-0.509092\pi$
$863$	−1.67792	−0.0571170	−0.0285585	+	0.999592i	$0.509092\pi$
$864$	−1.12605	−0.0383090
$865$	18.3475	0.623835
$866$	−26.7019	−0.907368
$867$	14.2544	0.484106
$868$	−35.1709	−1.19378
$869$	9.57683	0.324872
$870$	56.2874	1.90832
$871$	−11.9353	−0.404413
$872$	−40.8950	−1.38488
$873$	4.34061	0.146907
$874$	73.7003	2.49295
$875$	−18.9902	−0.641984
$876$	23.3366	0.788470
$877$	19.3174	0.652302	0.326151	−	0.945318i	$-0.394248\pi$
$877$	19.3174	0.652302	0.326151	+	0.945318i	$0.394248\pi$
$878$	4.83714	0.163246
$879$	−24.9220	−0.840598
$880$	8.95368	0.301829
$881$	−12.8232	−0.432025	−0.216013	−	0.976391i	$-0.569305\pi$
$881$	−12.8232	−0.432025	−0.216013	+	0.976391i	$0.569305\pi$
$882$	7.88333	0.265445
$883$	−28.7107	−0.966191	−0.483096	−	0.875568i	$-0.660488\pi$
$883$	−28.7107	−0.966191	−0.483096	+	0.875568i	$0.660488\pi$
$884$	−31.9419	−1.07432
$885$	−4.53046	−0.152290
$886$	−17.8713	−0.600398
$887$	2.70193	0.0907219	0.0453610	−	0.998971i	$-0.485556\pi$
$887$	2.70193	0.0907219	0.0453610	+	0.998971i	$0.485556\pi$
$888$	39.8398	1.33693
$889$	34.7479	1.16541
$890$	15.5813	0.522285
$891$	−0.760801	−0.0254878
$892$	24.3552	0.815473
$893$	25.7553	0.861868
$894$	19.7666	0.661093
$895$	−15.5426	−0.519531
$896$	39.4144	1.31674
$897$	−39.7497	−1.32720
$898$	50.5802	1.68788
$899$	30.4340	1.01503
$900$	30.0610	1.00203
$901$	2.49133	0.0829984
$902$	1.27062	0.0423071
$903$	4.94974	0.164717
$904$	32.7330	1.08868
$905$	−89.3666	−2.97065
$906$	−21.7372	−0.722171
$907$	2.01753	0.0669911	0.0334956	−	0.999439i	$-0.489336\pi$
$907$	2.01753	0.0669911	0.0334956	+	0.999439i	$0.489336\pi$
$908$	46.6944	1.54961
$909$	8.00338	0.265455
$910$	83.2804	2.76072
$911$	36.6792	1.21523	0.607617	−	0.794230i	$-0.292125\pi$
$911$	36.6792	1.21523	0.607617	+	0.794230i	$0.292125\pi$
$912$	12.5209	0.414610
$913$	6.88462	0.227848
$914$	−60.4580	−1.99977
$915$	39.2174	1.29649
$916$	99.5293	3.28854
$917$	8.03159	0.265226
$918$	−4.01806	−0.132616
$919$	26.2160	0.864785	0.432392	−	0.901686i	$-0.357670\pi$
$919$	26.2160	0.864785	0.432392	+	0.901686i	$0.357670\pi$
$920$	130.256	4.29440
$921$	6.27330	0.206712
$922$	−97.7228	−3.21833
$923$	20.8199	0.685297
$924$	5.71611	0.188046
$925$	67.6888	2.22559
$926$	55.9660	1.83916
$927$	−2.53942	−0.0834056
$928$	−7.32087	−0.240319
$929$	−5.00329	−0.164153	−0.0820763	−	0.996626i	$-0.526155\pi$
$929$	−5.00329	−0.164153	−0.0820763	+	0.996626i	$0.526155\pi$
$930$	40.5283	1.32898
$931$	12.3487	0.404711
$932$	−91.0561	−2.98264
$933$	−33.0086	−1.08065
$934$	70.9358	2.32109
$935$	−4.50081	−0.147192
$936$	−22.6522	−0.740411
$937$	−7.62553	−0.249115	−0.124558	−	0.992212i	$-0.539751\pi$
$937$	−7.62553	−0.249115	−0.124558	+	0.992212i	$0.539751\pi$
$938$	11.2803	0.368315
$939$	17.6929	0.577386
$940$	93.9353	3.06383
$941$	9.41810	0.307021	0.153511	−	0.988147i	$-0.450942\pi$
$941$	9.41810	0.307021	0.153511	+	0.988147i	$0.450942\pi$
$942$	−20.5981	−0.671122
$943$	5.51065	0.179451
$944$	−4.18277	−0.136138
$945$	6.91299	0.224879
$946$	−4.71621	−0.153337
$947$	−50.8253	−1.65160	−0.825800	−	0.563963i	$-0.809276\pi$
$947$	−50.8253	−1.65160	−0.825800	+	0.563963i	$0.809276\pi$
$948$	48.8449	1.58641
$949$	−29.8775	−0.969866
$950$	71.3587	2.31518
$951$	−20.7920	−0.674227
$952$	14.6289	0.474125
$953$	−36.7491	−1.19042	−0.595210	−	0.803570i	$-0.702931\pi$
$953$	−36.7491	−1.19042	−0.595210	+	0.803570i	$0.702931\pi$
$954$	3.64600	0.118044
$955$	15.9955	0.517602
$956$	15.3556	0.496634
$957$	−4.94625	−0.159890
$958$	0.295003	0.00953112
$959$	28.2728	0.912975
$960$	−33.2866	−1.07432
$961$	−9.08676	−0.293121
$962$	−105.259	−3.39368
$963$	−12.2062	−0.393340
$964$	−37.1156	−1.19541
$965$	61.3604	1.97526
$966$	37.5681	1.20873
$967$	−24.4691	−0.786872	−0.393436	−	0.919352i	$-0.628714\pi$
$967$	−24.4691	−0.786872	−0.393436	+	0.919352i	$0.628714\pi$
$968$	47.5173	1.52726
$969$	−6.29400	−0.202192
$970$	37.5799	1.20662
$971$	−17.9426	−0.575805	−0.287903	−	0.957660i	$-0.592958\pi$
$971$	−17.9426	−0.575805	−0.287903	+	0.957660i	$0.592958\pi$
$972$	−3.88033	−0.124462
$973$	20.4349	0.655113
$974$	−61.6086	−1.97407
$975$	−38.4867	−1.23256
$976$	36.2077	1.15898
$977$	45.3612	1.45123	0.725617	−	0.688098i	$-0.241554\pi$
$977$	45.3612	1.45123	0.725617	+	0.688098i	$0.241554\pi$
$978$	57.8880	1.85105
$979$	−1.36920	−0.0437599
$980$	45.0383	1.43869
$981$	8.96883	0.286353
$982$	−19.8759	−0.634267
$983$	−50.9128	−1.62387	−0.811934	−	0.583750i	$-0.801585\pi$
$983$	−50.9128	−1.62387	−0.811934	+	0.583750i	$0.801585\pi$
$984$	3.14036	0.100111
$985$	55.5396	1.76964
$986$	−26.1229	−0.831924
$987$	13.1286	0.417887
$988$	−73.2243	−2.32958
$989$	−20.4540	−0.650400
$990$	−6.58683	−0.209343
$991$	−19.2161	−0.610420	−0.305210	−	0.952285i	$-0.598727\pi$
$991$	−19.2161	−0.610420	−0.305210	+	0.952285i	$0.598727\pi$
$992$	−5.27121	−0.167361
$993$	19.0179	0.603516
$994$	−19.6773	−0.624126
$995$	52.9076	1.67728
$996$	35.1138	1.11262
$997$	−56.4014	−1.78625	−0.893125	−	0.449809i	$-0.851492\pi$
$997$	−56.4014	−1.78625	−0.893125	+	0.449809i	$0.851492\pi$
$998$	76.5689	2.42375
$999$	−8.73739	−0.276439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.10	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.10	✓	84	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)

\(f(q)\)	\(=\)	\(q-2.42494 q^{2} -1.00000 q^{3} +3.88033 q^{4} -3.57030 q^{5} +2.42494 q^{6} +1.93625 q^{7} -4.55968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42494 q^{2} -1.00000 q^{3} +3.88033 q^{4} -3.57030 q^{5} +2.42494 q^{6} +1.93625 q^{7} -4.55968 q^{8} +1.00000 q^{9} +8.65775 q^{10} -0.760801 q^{11} -3.88033 q^{12} +4.96794 q^{13} -4.69529 q^{14} +3.57030 q^{15} +3.29630 q^{16} -1.65697 q^{17} -2.42494 q^{18} -3.79849 q^{19} -13.8539 q^{20} -1.93625 q^{21} +1.84490 q^{22} +8.00124 q^{23} +4.55968 q^{24} +7.74703 q^{25} -12.0469 q^{26} -1.00000 q^{27} +7.51329 q^{28} -6.50138 q^{29} -8.65775 q^{30} -4.68116 q^{31} +1.12605 q^{32} +0.760801 q^{33} +4.01806 q^{34} -6.91299 q^{35} +3.88033 q^{36} +8.73739 q^{37} +9.21110 q^{38} -4.96794 q^{39} +16.2794 q^{40} +0.688724 q^{41} +4.69529 q^{42} -2.55636 q^{43} -2.95216 q^{44} -3.57030 q^{45} -19.4025 q^{46} -6.78041 q^{47} -3.29630 q^{48} -3.25094 q^{49} -18.7861 q^{50} +1.65697 q^{51} +19.2772 q^{52} -1.50354 q^{53} +2.42494 q^{54} +2.71628 q^{55} -8.82869 q^{56} +3.79849 q^{57} +15.7655 q^{58} -1.26893 q^{59} +13.8539 q^{60} +10.9843 q^{61} +11.3515 q^{62} +1.93625 q^{63} -9.32319 q^{64} -17.7370 q^{65} -1.84490 q^{66} -2.40247 q^{67} -6.42960 q^{68} -8.00124 q^{69} +16.7636 q^{70} +4.19086 q^{71} -4.55968 q^{72} -6.01407 q^{73} -21.1876 q^{74} -7.74703 q^{75} -14.7394 q^{76} -1.47310 q^{77} +12.0469 q^{78} -12.5878 q^{79} -11.7688 q^{80} +1.00000 q^{81} -1.67011 q^{82} -9.04918 q^{83} -7.51329 q^{84} +5.91589 q^{85} +6.19901 q^{86} +6.50138 q^{87} +3.46901 q^{88} +1.79969 q^{89} +8.65775 q^{90} +9.61916 q^{91} +31.0475 q^{92} +4.68116 q^{93} +16.4421 q^{94} +13.5617 q^{95} -1.12605 q^{96} +4.34061 q^{97} +7.88333 q^{98} -0.760801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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