LMFDB - Embedded newform 4033.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37004 q^{2} +2.31466 q^{3} +3.61710 q^{4} +2.16488 q^{5} -5.48585 q^{6} -1.68976 q^{7} -3.83259 q^{8} +2.35766 q^{9} +O(q^{10})$	\(q-2.37004 q^{2} +2.31466 q^{3} +3.61710 q^{4} +2.16488 q^{5} -5.48585 q^{6} -1.68976 q^{7} -3.83259 q^{8} +2.35766 q^{9} -5.13086 q^{10} -2.35742 q^{11} +8.37236 q^{12} -1.96496 q^{13} +4.00481 q^{14} +5.01097 q^{15} +1.84920 q^{16} +2.88498 q^{17} -5.58776 q^{18} -2.74095 q^{19} +7.83059 q^{20} -3.91123 q^{21} +5.58717 q^{22} +0.0476245 q^{23} -8.87115 q^{24} -0.313280 q^{25} +4.65704 q^{26} -1.48679 q^{27} -6.11204 q^{28} -2.72434 q^{29} -11.8762 q^{30} -6.57126 q^{31} +3.28250 q^{32} -5.45662 q^{33} -6.83751 q^{34} -3.65814 q^{35} +8.52790 q^{36} +1.00000 q^{37} +6.49616 q^{38} -4.54822 q^{39} -8.29711 q^{40} +5.62708 q^{41} +9.26978 q^{42} -3.47896 q^{43} -8.52700 q^{44} +5.10407 q^{45} -0.112872 q^{46} +2.04241 q^{47} +4.28027 q^{48} -4.14470 q^{49} +0.742486 q^{50} +6.67775 q^{51} -7.10746 q^{52} +5.86345 q^{53} +3.52376 q^{54} -5.10353 q^{55} +6.47617 q^{56} -6.34437 q^{57} +6.45680 q^{58} -13.6784 q^{59} +18.1252 q^{60} +15.1143 q^{61} +15.5742 q^{62} -3.98389 q^{63} -11.4781 q^{64} -4.25391 q^{65} +12.9324 q^{66} -3.96873 q^{67} +10.4352 q^{68} +0.110235 q^{69} +8.66995 q^{70} -7.71757 q^{71} -9.03595 q^{72} +16.0022 q^{73} -2.37004 q^{74} -0.725137 q^{75} -9.91427 q^{76} +3.98347 q^{77} +10.7795 q^{78} -1.45482 q^{79} +4.00330 q^{80} -10.5144 q^{81} -13.3364 q^{82} -10.9619 q^{83} -14.1473 q^{84} +6.24564 q^{85} +8.24528 q^{86} -6.30593 q^{87} +9.03500 q^{88} -4.27834 q^{89} -12.0968 q^{90} +3.32032 q^{91} +0.172263 q^{92} -15.2102 q^{93} -4.84059 q^{94} -5.93383 q^{95} +7.59787 q^{96} +5.25498 q^{97} +9.82311 q^{98} -5.55799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) $ 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.37004	−1.67587	−0.837936	−	0.545768i	$-0.816238\pi$
$2$	−2.37004	−1.67587	−0.837936	+	0.545768i	$0.816238\pi$
$3$	2.31466	1.33637	0.668186	−	0.743995i	$-0.267071\pi$
$3$	2.31466	1.33637	0.668186	+	0.743995i	$0.267071\pi$
$4$	3.61710	1.80855
$5$	2.16488	0.968165	0.484083	−	0.875022i	$-0.339153\pi$
$5$	2.16488	0.968165	0.484083	+	0.875022i	$0.339153\pi$
$6$	−5.48585	−2.23959
$7$	−1.68976	−0.638671	−0.319335	−	0.947642i	$-0.603460\pi$
$7$	−1.68976	−0.638671	−0.319335	+	0.947642i	$0.603460\pi$
$8$	−3.83259	−1.35502
$9$	2.35766	0.785888
$10$	−5.13086	−1.62252
$11$	−2.35742	−0.710787	−0.355394	−	0.934717i	$-0.615653\pi$
$11$	−2.35742	−0.710787	−0.355394	+	0.934717i	$0.615653\pi$
$12$	8.37236	2.41689
$13$	−1.96496	−0.544982	−0.272491	−	0.962158i	$-0.587848\pi$
$13$	−1.96496	−0.544982	−0.272491	+	0.962158i	$0.587848\pi$
$14$	4.00481	1.07033
$15$	5.01097	1.29383
$16$	1.84920	0.462300
$17$	2.88498	0.699709	0.349855	−	0.936804i	$-0.386231\pi$
$17$	2.88498	0.699709	0.349855	+	0.936804i	$0.386231\pi$
$18$	−5.58776	−1.31705
$19$	−2.74095	−0.628816	−0.314408	−	0.949288i	$-0.601806\pi$
$19$	−2.74095	−0.628816	−0.314408	+	0.949288i	$0.601806\pi$
$20$	7.83059	1.75097
$21$	−3.91123	−0.853501
$22$	5.58717	1.19119
$23$	0.0476245	0.00993040	0.00496520	−	0.999988i	$-0.498420\pi$
$23$	0.0476245	0.00993040	0.00496520	+	0.999988i	$0.498420\pi$
$24$	−8.87115	−1.81082
$25$	−0.313280	−0.0626559
$26$	4.65704	0.913321
$27$	−1.48679	−0.286133
$28$	−6.11204	−1.15507
$29$	−2.72434	−0.505897	−0.252949	−	0.967480i	$-0.581400\pi$
$29$	−2.72434	−0.505897	−0.252949	+	0.967480i	$0.581400\pi$
$30$	−11.8762	−2.16829
$31$	−6.57126	−1.18023	−0.590116	−	0.807318i	$-0.700918\pi$
$31$	−6.57126	−1.18023	−0.590116	+	0.807318i	$0.700918\pi$
$32$	3.28250	0.580269
$33$	−5.45662	−0.949876
$34$	−6.83751	−1.17262
$35$	−3.65814	−0.618339
$36$	8.52790	1.42132
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	6.49616	1.05382
$39$	−4.54822	−0.728298
$40$	−8.29711	−1.31189
$41$	5.62708	0.878803	0.439401	−	0.898291i	$-0.355191\pi$
$41$	5.62708	0.878803	0.439401	+	0.898291i	$0.355191\pi$
$42$	9.26978	1.43036
$43$	−3.47896	−0.530536	−0.265268	−	0.964175i	$-0.585460\pi$
$43$	−3.47896	−0.530536	−0.265268	+	0.964175i	$0.585460\pi$
$44$	−8.52700	−1.28549
$45$	5.10407	0.760869
$46$	−0.112872	−0.0166421
$47$	2.04241	0.297916	0.148958	−	0.988844i	$-0.452408\pi$
$47$	2.04241	0.297916	0.148958	+	0.988844i	$0.452408\pi$
$48$	4.28027	0.617804
$49$	−4.14470	−0.592100
$50$	0.742486	0.105003
$51$	6.67775	0.935071
$52$	−7.10746	−0.985627
$53$	5.86345	0.805407	0.402704	−	0.915330i	$-0.368070\pi$
$53$	5.86345	0.805407	0.402704	+	0.915330i	$0.368070\pi$
$54$	3.52376	0.479523
$55$	−5.10353	−0.688160
$56$	6.47617	0.865414
$57$	−6.34437	−0.840332
$58$	6.45680	0.847819
$59$	−13.6784	−1.78077	−0.890387	−	0.455204i	$-0.849566\pi$
$59$	−13.6784	−1.78077	−0.890387	+	0.455204i	$0.849566\pi$
$60$	18.1252	2.33995
$61$	15.1143	1.93518	0.967591	−	0.252524i	$-0.0812605\pi$
$61$	15.1143	1.93518	0.967591	+	0.252524i	$0.0812605\pi$
$62$	15.5742	1.97792
$63$	−3.98389	−0.501923
$64$	−11.4781	−1.43476
$65$	−4.25391	−0.527633
$66$	12.9324	1.59187
$67$	−3.96873	−0.484857	−0.242428	−	0.970169i	$-0.577944\pi$
$67$	−3.96873	−0.484857	−0.242428	+	0.970169i	$0.577944\pi$
$68$	10.4352	1.26546
$69$	0.110235	0.0132707
$70$	8.66995	1.03626
$71$	−7.71757	−0.915907	−0.457954	−	0.888976i	$-0.651417\pi$
$71$	−7.71757	−0.915907	−0.457954	+	0.888976i	$0.651417\pi$
$72$	−9.03595	−1.06490
$73$	16.0022	1.87291	0.936457	−	0.350784i	$-0.114085\pi$
$73$	16.0022	1.87291	0.936457	+	0.350784i	$0.114085\pi$
$74$	−2.37004	−0.275512
$75$	−0.725137	−0.0837316
$76$	−9.91427	−1.13725
$77$	3.98347	0.453959
$78$	10.7795	1.22054
$79$	−1.45482	−0.163680	−0.0818402	−	0.996645i	$-0.526080\pi$
$79$	−1.45482	−0.163680	−0.0818402	+	0.996645i	$0.526080\pi$
$80$	4.00330	0.447583
$81$	−10.5144	−1.16827
$82$	−13.3364	−1.47276
$83$	−10.9619	−1.20323	−0.601615	−	0.798786i	$-0.705476\pi$
$83$	−10.9619	−1.20323	−0.601615	+	0.798786i	$0.705476\pi$
$84$	−14.1473	−1.54360
$85$	6.24564	0.677434
$86$	8.24528	0.889111
$87$	−6.30593	−0.676067
$88$	9.03500	0.963135
$89$	−4.27834	−0.453503	−0.226751	−	0.973953i	$-0.572811\pi$
$89$	−4.27834	−0.453503	−0.226751	+	0.973953i	$0.572811\pi$
$90$	−12.0968	−1.27512
$91$	3.32032	0.348064
$92$	0.172263	0.0179596
$93$	−15.2102	−1.57723
$94$	−4.84059	−0.499269
$95$	−5.93383	−0.608798
$96$	7.59787	0.775455
$97$	5.25498	0.533563	0.266781	−	0.963757i	$-0.414040\pi$
$97$	5.25498	0.533563	0.266781	+	0.963757i	$0.414040\pi$
$98$	9.82311	0.992284
$99$	−5.55799	−0.558599
$100$	−1.13316	−0.113316
$101$	−6.57903	−0.654638	−0.327319	−	0.944914i	$-0.606145\pi$
$101$	−6.57903	−0.654638	−0.327319	+	0.944914i	$0.606145\pi$
$102$	−15.8265	−1.56706
$103$	−10.0440	−0.989663	−0.494832	−	0.868989i	$-0.664770\pi$
$103$	−10.0440	−0.989663	−0.494832	+	0.868989i	$0.664770\pi$
$104$	7.53089	0.738464
$105$	−8.46736	−0.826330
$106$	−13.8966	−1.34976
$107$	−4.37826	−0.423262	−0.211631	−	0.977350i	$-0.567878\pi$
$107$	−4.37826	−0.423262	−0.211631	+	0.977350i	$0.567878\pi$
$108$	−5.37787	−0.517486
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	12.0956	1.15327
$111$	2.31466	0.219698
$112$	−3.12471	−0.295257
$113$	−17.7545	−1.67020	−0.835101	−	0.550097i	$-0.814591\pi$
$113$	−17.7545	−1.67020	−0.835101	+	0.550097i	$0.814591\pi$
$114$	15.0364	1.40829
$115$	0.103102	0.00961427
$116$	−9.85421	−0.914940
$117$	−4.63272	−0.428295
$118$	32.4183	2.98435
$119$	−4.87493	−0.446884
$120$	−19.2050	−1.75317
$121$	−5.44259	−0.494781
$122$	−35.8214	−3.24312
$123$	13.0248	1.17441
$124$	−23.7689	−2.13451
$125$	−11.5026	−1.02883
$126$	9.44199	0.841160
$127$	−16.4600	−1.46059	−0.730294	−	0.683133i	$-0.760617\pi$
$127$	−16.4600	−1.46059	−0.730294	+	0.683133i	$0.760617\pi$
$128$	20.6385	1.82420
$129$	−8.05262	−0.708993
$130$	10.0819	0.884245
$131$	−3.98666	−0.348316	−0.174158	−	0.984718i	$-0.555720\pi$
$131$	−3.98666	−0.348316	−0.174158	+	0.984718i	$0.555720\pi$
$132$	−19.7371	−1.71790
$133$	4.63155	0.401607
$134$	9.40604	0.812558
$135$	−3.21873	−0.277024
$136$	−11.0569	−0.948124
$137$	16.9442	1.44764	0.723819	−	0.689990i	$-0.242385\pi$
$137$	16.9442	1.44764	0.723819	+	0.689990i	$0.242385\pi$
$138$	−0.261261	−0.0222400
$139$	5.95390	0.505003	0.252501	−	0.967597i	$-0.418747\pi$
$139$	5.95390	0.505003	0.252501	+	0.967597i	$0.418747\pi$
$140$	−13.2319	−1.11830
$141$	4.72749	0.398126
$142$	18.2910	1.53494
$143$	4.63223	0.387366
$144$	4.35979	0.363316
$145$	−5.89788	−0.489792
$146$	−37.9258	−3.13876
$147$	−9.59358	−0.791265
$148$	3.61710	0.297324
$149$	9.63941	0.789691	0.394846	−	0.918748i	$-0.370798\pi$
$149$	9.63941	0.789691	0.394846	+	0.918748i	$0.370798\pi$
$150$	1.71860	0.140323
$151$	1.62055	0.131878	0.0659392	−	0.997824i	$-0.478996\pi$
$151$	1.62055	0.131878	0.0659392	+	0.997824i	$0.478996\pi$
$152$	10.5049	0.852062
$153$	6.80180	0.549893
$154$	−9.44100	−0.760777
$155$	−14.2260	−1.14266
$156$	−16.4514	−1.31716
$157$	−20.1281	−1.60639	−0.803197	−	0.595714i	$-0.796869\pi$
$157$	−20.1281	−1.60639	−0.803197	+	0.595714i	$0.796869\pi$
$158$	3.44799	0.274307
$159$	13.5719	1.07632
$160$	7.10622	0.561796
$161$	−0.0804742	−0.00634225
$162$	24.9196	1.95787
$163$	−5.56602	−0.435964	−0.217982	−	0.975953i	$-0.569947\pi$
$163$	−5.56602	−0.435964	−0.217982	+	0.975953i	$0.569947\pi$
$164$	20.3537	1.58936
$165$	−11.8129	−0.919637
$166$	25.9803	2.01646
$167$	0.358081	0.0277092	0.0138546	−	0.999904i	$-0.495590\pi$
$167$	0.358081	0.0277092	0.0138546	+	0.999904i	$0.495590\pi$
$168$	14.9901	1.15651
$169$	−9.13893	−0.702995
$170$	−14.8024	−1.13529
$171$	−6.46223	−0.494179
$172$	−12.5837	−0.959501
$173$	−4.38910	−0.333697	−0.166849	−	0.985983i	$-0.553359\pi$
$173$	−4.38910	−0.333697	−0.166849	+	0.985983i	$0.553359\pi$
$174$	14.9453	1.13300
$175$	0.529368	0.0400165
$176$	−4.35933	−0.328597
$177$	−31.6608	−2.37977
$178$	10.1398	0.760013
$179$	−9.78456	−0.731333	−0.365666	−	0.930746i	$-0.619159\pi$
$179$	−9.78456	−0.731333	−0.365666	+	0.930746i	$0.619159\pi$
$180$	18.4619	1.37607
$181$	−7.92794	−0.589279	−0.294640	−	0.955608i	$-0.595200\pi$
$181$	−7.92794	−0.589279	−0.294640	+	0.955608i	$0.595200\pi$
$182$	−7.86929	−0.583311
$183$	34.9844	2.58612
$184$	−0.182525	−0.0134559
$185$	2.16488	0.159165
$186$	36.0489	2.64323
$187$	−6.80109	−0.497345
$188$	7.38759	0.538795
$189$	2.51233	0.182745
$190$	14.0634	1.02027
$191$	−10.1186	−0.732157	−0.366078	−	0.930584i	$-0.619300\pi$
$191$	−10.1186	−0.732157	−0.366078	+	0.930584i	$0.619300\pi$
$192$	−26.5678	−1.91737
$193$	16.2733	1.17138	0.585690	−	0.810535i	$-0.300823\pi$
$193$	16.2733	1.17138	0.585690	+	0.810535i	$0.300823\pi$
$194$	−12.4545	−0.894183
$195$	−9.84637	−0.705113
$196$	−14.9918	−1.07084
$197$	−26.1062	−1.85999	−0.929995	−	0.367572i	$-0.880189\pi$
$197$	−26.1062	−1.85999	−0.929995	+	0.367572i	$0.880189\pi$
$198$	13.1727	0.936141
$199$	7.78902	0.552149	0.276075	−	0.961136i	$-0.410966\pi$
$199$	7.78902	0.552149	0.276075	+	0.961136i	$0.410966\pi$
$200$	1.20067	0.0849003
$201$	−9.18626	−0.647949
$202$	15.5926	1.09709
$203$	4.60349	0.323102
$204$	24.1541	1.69112
$205$	12.1820	0.850826
$206$	23.8047	1.65855
$207$	0.112283	0.00780418
$208$	−3.63361	−0.251945
$209$	6.46155	0.446955
$210$	20.0680	1.38482
$211$	−14.2141	−0.978538	−0.489269	−	0.872133i	$-0.662736\pi$
$211$	−14.2141	−0.978538	−0.489269	+	0.872133i	$0.662736\pi$
$212$	21.2087	1.45662
$213$	−17.8636	−1.22399
$214$	10.3767	0.709333
$215$	−7.53154	−0.513647
$216$	5.69827	0.387718
$217$	11.1039	0.753780
$218$	−2.37004	−0.160519
$219$	37.0396	2.50291
$220$	−18.4600	−1.24457
$221$	−5.66886	−0.381329
$222$	−5.48585	−0.368186
$223$	22.2004	1.48665	0.743325	−	0.668930i	$-0.233247\pi$
$223$	22.2004	1.48665	0.743325	+	0.668930i	$0.233247\pi$
$224$	−5.54664	−0.370601
$225$	−0.738608	−0.0492405
$226$	42.0789	2.79905
$227$	9.31882	0.618512	0.309256	−	0.950979i	$-0.399920\pi$
$227$	9.31882	0.618512	0.309256	+	0.950979i	$0.399920\pi$
$228$	−22.9482	−1.51978
$229$	16.4221	1.08520	0.542602	−	0.839990i	$-0.317439\pi$
$229$	16.4221	1.08520	0.542602	+	0.839990i	$0.317439\pi$
$230$	−0.244355	−0.0161123
$231$	9.22040	0.606658
$232$	10.4413	0.685503
$233$	−8.18218	−0.536032	−0.268016	−	0.963414i	$-0.586368\pi$
$233$	−8.18218	−0.536032	−0.268016	+	0.963414i	$0.586368\pi$
$234$	10.9797	0.717767
$235$	4.42158	0.288432
$236$	−49.4761	−3.22062
$237$	−3.36742	−0.218738
$238$	11.5538	0.748920
$239$	9.71326	0.628299	0.314149	−	0.949374i	$-0.398281\pi$
$239$	9.71326	0.628299	0.314149	+	0.949374i	$0.398281\pi$
$240$	9.26629	0.598137
$241$	23.7117	1.52740	0.763701	−	0.645570i	$-0.223380\pi$
$241$	23.7117	1.52740	0.763701	+	0.645570i	$0.223380\pi$
$242$	12.8992	0.829190
$243$	−19.8769	−1.27511
$244$	54.6697	3.49987
$245$	−8.97279	−0.573251
$246$	−30.8693	−1.96816
$247$	5.38585	0.342694
$248$	25.1849	1.59924
$249$	−25.3732	−1.60796
$250$	27.2617	1.72418
$251$	−11.0777	−0.699218	−0.349609	−	0.936896i	$-0.613686\pi$
$251$	−11.0777	−0.699218	−0.349609	+	0.936896i	$0.613686\pi$
$252$	−14.4101	−0.907753
$253$	−0.112271	−0.00705840
$254$	39.0108	2.44776
$255$	14.4565	0.905304
$256$	−25.9579	−1.62237
$257$	19.3107	1.20457	0.602283	−	0.798283i	$-0.294258\pi$
$257$	19.3107	1.20457	0.602283	+	0.798283i	$0.294258\pi$
$258$	19.0850	1.18818
$259$	−1.68976	−0.104997
$260$	−15.3868	−0.954250
$261$	−6.42308	−0.397579
$262$	9.44855	0.583734
$263$	−6.16767	−0.380315	−0.190157	−	0.981754i	$-0.560900\pi$
$263$	−6.16767	−0.380315	−0.190157	+	0.981754i	$0.560900\pi$
$264$	20.9130	1.28711
$265$	12.6937	0.779768
$266$	−10.9770	−0.673041
$267$	−9.90291	−0.606048
$268$	−14.3553	−0.876887
$269$	14.8995	0.908441	0.454221	−	0.890889i	$-0.349918\pi$
$269$	14.8995	0.908441	0.454221	+	0.890889i	$0.349918\pi$
$270$	7.62853	0.464258
$271$	4.49695	0.273170	0.136585	−	0.990628i	$-0.456387\pi$
$271$	4.49695	0.273170	0.136585	+	0.990628i	$0.456387\pi$
$272$	5.33490	0.323476
$273$	7.68542	0.465143
$274$	−40.1584	−2.42606
$275$	0.738530	0.0445350
$276$	0.398730	0.0240007
$277$	25.1197	1.50930	0.754649	−	0.656128i	$-0.227807\pi$
$277$	25.1197	1.50930	0.754649	+	0.656128i	$0.227807\pi$
$278$	−14.1110	−0.846321
$279$	−15.4928	−0.927530
$280$	14.0201	0.837864
$281$	−4.56077	−0.272073	−0.136036	−	0.990704i	$-0.543436\pi$
$281$	−4.56077	−0.272073	−0.136036	+	0.990704i	$0.543436\pi$
$282$	−11.2043	−0.667209
$283$	15.7269	0.934866	0.467433	−	0.884029i	$-0.345179\pi$
$283$	15.7269	0.934866	0.467433	+	0.884029i	$0.345179\pi$
$284$	−27.9152	−1.65646
$285$	−13.7348	−0.813580
$286$	−10.9786	−0.649177
$287$	−9.50844	−0.561265
$288$	7.73902	0.456026
$289$	−8.67692	−0.510407
$290$	13.9782	0.820829
$291$	12.1635	0.713038
$292$	57.8814	3.38725
$293$	−14.8955	−0.870203	−0.435102	−	0.900381i	$-0.643288\pi$
$293$	−14.8955	−0.870203	−0.435102	+	0.900381i	$0.643288\pi$
$294$	22.7372	1.32606
$295$	−29.6121	−1.72408
$296$	−3.83259	−0.222765
$297$	3.50499	0.203380
$298$	−22.8458	−1.32342
$299$	−0.0935803	−0.00541189
$300$	−2.62289	−0.151433
$301$	5.87862	0.338838
$302$	−3.84077	−0.221012
$303$	−15.2282	−0.874839
$304$	−5.06856	−0.290702
$305$	32.7206	1.87358
$306$	−16.1206	−0.921551
$307$	6.76770	0.386253	0.193126	−	0.981174i	$-0.438137\pi$
$307$	6.76770	0.386253	0.193126	+	0.981174i	$0.438137\pi$
$308$	14.4086	0.821007
$309$	−23.2484	−1.32256
$310$	33.7162	1.91495
$311$	13.1885	0.747854	0.373927	−	0.927458i	$-0.378011\pi$
$311$	13.1885	0.747854	0.373927	+	0.927458i	$0.378011\pi$
$312$	17.4315	0.986862
$313$	−27.8960	−1.57677	−0.788387	−	0.615180i	$-0.789083\pi$
$313$	−27.8960	−1.57677	−0.788387	+	0.615180i	$0.789083\pi$
$314$	47.7043	2.69211
$315$	−8.62466	−0.485945
$316$	−5.26224	−0.296024
$317$	−28.3260	−1.59095	−0.795473	−	0.605989i	$-0.792778\pi$
$317$	−28.3260	−1.59095	−0.795473	+	0.605989i	$0.792778\pi$
$318$	−32.1660	−1.80378
$319$	6.42240	0.359585
$320$	−24.8486	−1.38908
$321$	−10.1342	−0.565635
$322$	0.190727	0.0106288
$323$	−7.90757	−0.439989
$324$	−38.0317	−2.11287
$325$	0.615582	0.0341464
$326$	13.1917	0.730620
$327$	2.31466	0.128001
$328$	−21.5663	−1.19080
$329$	−3.45119	−0.190270
$330$	27.9972	1.54119
$331$	26.6662	1.46571	0.732853	−	0.680387i	$-0.238188\pi$
$331$	26.6662	1.46571	0.732853	+	0.680387i	$0.238188\pi$
$332$	−39.6504	−2.17610
$333$	2.35766	0.129199
$334$	−0.848668	−0.0464370
$335$	−8.59183	−0.469422
$336$	−7.23265	−0.394573
$337$	−9.39360	−0.511702	−0.255851	−	0.966716i	$-0.582356\pi$
$337$	−9.39360	−0.511702	−0.255851	+	0.966716i	$0.582356\pi$
$338$	21.6596	1.17813
$339$	−41.0957	−2.23201
$340$	22.5911	1.22517
$341$	15.4912	0.838894
$342$	15.3158	0.828181
$343$	18.8319	1.01683
$344$	13.3334	0.718890
$345$	0.238645	0.0128482
$346$	10.4024	0.559234
$347$	−10.5776	−0.567836	−0.283918	−	0.958849i	$-0.591634\pi$
$347$	−10.5776	−0.567836	−0.283918	+	0.958849i	$0.591634\pi$
$348$	−22.8092	−1.22270
$349$	20.9428	1.12104	0.560522	−	0.828140i	$-0.310601\pi$
$349$	20.9428	1.12104	0.560522	+	0.828140i	$0.310601\pi$
$350$	−1.25463	−0.0670625
$351$	2.92149	0.155938
$352$	−7.73821	−0.412448
$353$	33.7855	1.79822	0.899110	−	0.437723i	$-0.144215\pi$
$353$	33.7855	1.79822	0.899110	+	0.437723i	$0.144215\pi$
$354$	75.0375	3.98820
$355$	−16.7076	−0.886749
$356$	−15.4752	−0.820182
$357$	−11.2838	−0.597203
$358$	23.1898	1.22562
$359$	−10.7581	−0.567792	−0.283896	−	0.958855i	$-0.591627\pi$
$359$	−10.7581	−0.567792	−0.283896	+	0.958855i	$0.591627\pi$
$360$	−19.5618	−1.03100
$361$	−11.4872	−0.604590
$362$	18.7895	0.987557
$363$	−12.5978	−0.661211
$364$	12.0099	0.629491
$365$	34.6428	1.81329
$366$	−82.9145	−4.33401
$367$	8.19945	0.428008	0.214004	−	0.976833i	$-0.431349\pi$
$367$	8.19945	0.428008	0.214004	+	0.976833i	$0.431349\pi$
$368$	0.0880673	0.00459082
$369$	13.2668	0.690640
$370$	−5.13086	−0.266741
$371$	−9.90785	−0.514390
$372$	−55.0169	−2.85249
$373$	−13.8625	−0.717773	−0.358886	−	0.933381i	$-0.616843\pi$
$373$	−13.8625	−0.717773	−0.358886	+	0.933381i	$0.616843\pi$
$374$	16.1189	0.833486
$375$	−26.6247	−1.37489
$376$	−7.82771	−0.403683
$377$	5.35322	0.275705
$378$	−5.95432	−0.306257
$379$	38.7775	1.99187	0.995933	−	0.0900940i	$-0.0287167\pi$
$379$	38.7775	1.99187	0.995933	+	0.0900940i	$0.0287167\pi$
$380$	−21.4632	−1.10104
$381$	−38.0993	−1.95189
$382$	23.9815	1.22700
$383$	−28.3499	−1.44861	−0.724306	−	0.689479i	$-0.757839\pi$
$383$	−28.3499	−1.44861	−0.724306	+	0.689479i	$0.757839\pi$
$384$	47.7711	2.43781
$385$	8.62376	0.439507
$386$	−38.5685	−1.96309
$387$	−8.20221	−0.416942
$388$	19.0078	0.964974
$389$	25.1206	1.27367	0.636833	−	0.771002i	$-0.280244\pi$
$389$	25.1206	1.27367	0.636833	+	0.771002i	$0.280244\pi$
$390$	23.3363	1.18168
$391$	0.137396	0.00694839
$392$	15.8849	0.802310
$393$	−9.22778	−0.465480
$394$	61.8728	3.11711
$395$	−3.14952	−0.158470
$396$	−20.1038	−1.01025
$397$	13.4199	0.673525	0.336762	−	0.941590i	$-0.390668\pi$
$397$	13.4199	0.673525	0.336762	+	0.941590i	$0.390668\pi$
$398$	−18.4603	−0.925331
$399$	10.7205	0.536695
$400$	−0.579317	−0.0289658
$401$	−13.0704	−0.652707	−0.326353	−	0.945248i	$-0.605820\pi$
$401$	−13.0704	−0.652707	−0.326353	+	0.945248i	$0.605820\pi$
$402$	21.7718	1.08588
$403$	12.9123	0.643206
$404$	−23.7970	−1.18394
$405$	−22.7625	−1.13108
$406$	−10.9105	−0.541477
$407$	−2.35742	−0.116853
$408$	−25.5931	−1.26704
$409$	−36.3736	−1.79856	−0.899280	−	0.437374i	$-0.855908\pi$
$409$	−36.3736	−1.79856	−0.899280	+	0.437374i	$0.855908\pi$
$410$	−28.8718	−1.42588
$411$	39.2200	1.93458
$412$	−36.3301	−1.78985
$413$	23.1132	1.13733
$414$	−0.266114	−0.0130788
$415$	−23.7313	−1.16493
$416$	−6.44998	−0.316236
$417$	13.7813	0.674871
$418$	−15.3141	−0.749039
$419$	18.9324	0.924906	0.462453	−	0.886644i	$-0.346969\pi$
$419$	18.9324	0.924906	0.462453	+	0.886644i	$0.346969\pi$
$420$	−30.6273	−1.49446
$421$	−16.1665	−0.787906	−0.393953	−	0.919131i	$-0.628893\pi$
$421$	−16.1665	−0.787906	−0.393953	+	0.919131i	$0.628893\pi$
$422$	33.6880	1.63990
$423$	4.81531	0.234128
$424$	−22.4722	−1.09135
$425$	−0.903804	−0.0438409
$426$	42.3374	2.05125
$427$	−25.5395	−1.23594
$428$	−15.8366	−0.765490
$429$	10.7220	0.517665
$430$	17.8501	0.860806
$431$	−0.784183	−0.0377728	−0.0188864	−	0.999822i	$-0.506012\pi$
$431$	−0.784183	−0.0377728	−0.0188864	+	0.999822i	$0.506012\pi$
$432$	−2.74938	−0.132279
$433$	−16.8390	−0.809231	−0.404616	−	0.914487i	$-0.632595\pi$
$433$	−16.8390	−0.809231	−0.404616	+	0.914487i	$0.632595\pi$
$434$	−26.3166	−1.26324
$435$	−13.6516	−0.654544
$436$	3.61710	0.173228
$437$	−0.130536	−0.00624440
$438$	−87.7855	−4.19455
$439$	9.00646	0.429855	0.214928	−	0.976630i	$-0.431048\pi$
$439$	9.00646	0.429855	0.214928	+	0.976630i	$0.431048\pi$
$440$	19.5597	0.932473
$441$	−9.77181	−0.465324
$442$	13.4354	0.639059
$443$	−17.6612	−0.839108	−0.419554	−	0.907730i	$-0.637814\pi$
$443$	−17.6612	−0.839108	−0.419554	+	0.907730i	$0.637814\pi$
$444$	8.37236	0.397335
$445$	−9.26210	−0.439066
$446$	−52.6159	−2.49144
$447$	22.3120	1.05532
$448$	19.3952	0.916337
$449$	38.5912	1.82123	0.910616	−	0.413254i	$-0.135608\pi$
$449$	38.5912	1.82123	0.910616	+	0.413254i	$0.135608\pi$
$450$	1.75053	0.0825209
$451$	−13.2654	−0.624642
$452$	−64.2197	−3.02064
$453$	3.75103	0.176239
$454$	−22.0860	−1.03655
$455$	7.18810	0.336983
$456$	24.3154	1.13867
$457$	9.19059	0.429918	0.214959	−	0.976623i	$-0.431038\pi$
$457$	9.19059	0.429918	0.214959	+	0.976623i	$0.431038\pi$
$458$	−38.9211	−1.81866
$459$	−4.28936	−0.200210
$460$	0.372928	0.0173879
$461$	11.6102	0.540739	0.270369	−	0.962757i	$-0.412854\pi$
$461$	11.6102	0.540739	0.270369	+	0.962757i	$0.412854\pi$
$462$	−21.8527	−1.01668
$463$	−28.7003	−1.33382	−0.666908	−	0.745140i	$-0.732383\pi$
$463$	−28.7003	−1.33382	−0.666908	+	0.745140i	$0.732383\pi$
$464$	−5.03785	−0.233876
$465$	−32.9284	−1.52702
$466$	19.3921	0.898322
$467$	28.0550	1.29823	0.649115	−	0.760690i	$-0.275139\pi$
$467$	28.0550	1.29823	0.649115	+	0.760690i	$0.275139\pi$
$468$	−16.7570	−0.774592
$469$	6.70621	0.309664
$470$	−10.4793	−0.483375
$471$	−46.5897	−2.14674
$472$	52.4236	2.41299
$473$	8.20135	0.377098
$474$	7.98094	0.366577
$475$	0.858683	0.0393991
$476$	−17.6331	−0.808211
$477$	13.8241	0.632960
$478$	−23.0208	−1.05295
$479$	−7.16007	−0.327152	−0.163576	−	0.986531i	$-0.552303\pi$
$479$	−7.16007	−0.327152	−0.163576	+	0.986531i	$0.552303\pi$
$480$	16.4485	0.750768
$481$	−1.96496	−0.0895945
$482$	−56.1976	−2.55973
$483$	−0.186271	−0.00847560
$484$	−19.6864	−0.894836
$485$	11.3764	0.516577
$486$	47.1092	2.13692
$487$	−11.7408	−0.532029	−0.266014	−	0.963969i	$-0.585707\pi$
$487$	−11.7408	−0.532029	−0.266014	+	0.963969i	$0.585707\pi$
$488$	−57.9267	−2.62222
$489$	−12.8834	−0.582610
$490$	21.2659	0.960695
$491$	−32.6337	−1.47274	−0.736369	−	0.676580i	$-0.763461\pi$
$491$	−32.6337	−1.47274	−0.736369	+	0.676580i	$0.763461\pi$
$492$	47.1120	2.12397
$493$	−7.85966	−0.353981
$494$	−12.7647	−0.574311
$495$	−12.0324	−0.540816
$496$	−12.1516	−0.545621
$497$	13.0409	0.584963
$498$	60.1356	2.69474
$499$	16.7893	0.751592	0.375796	−	0.926703i	$-0.377369\pi$
$499$	16.7893	0.751592	0.375796	+	0.926703i	$0.377369\pi$
$500$	−41.6061	−1.86068
$501$	0.828838	0.0370297
$502$	26.2546	1.17180
$503$	−1.99152	−0.0887974	−0.0443987	−	0.999014i	$-0.514137\pi$
$503$	−1.99152	−0.0887974	−0.0443987	+	0.999014i	$0.514137\pi$
$504$	15.2686	0.680119
$505$	−14.2428	−0.633798
$506$	0.266086	0.0118290
$507$	−21.1535	−0.939462
$508$	−59.5374	−2.64154
$509$	−34.6826	−1.53728	−0.768640	−	0.639681i	$-0.779066\pi$
$509$	−34.6826	−1.53728	−0.768640	+	0.639681i	$0.779066\pi$
$510$	−34.2626	−1.51717
$511$	−27.0399	−1.19617
$512$	20.2444	0.894686
$513$	4.07522	0.179925
$514$	−45.7671	−2.01870
$515$	−21.7441	−0.958157
$516$	−29.1271	−1.28225
$517$	−4.81480	−0.211755
$518$	4.00481	0.175961
$519$	−10.1593	−0.445943
$520$	16.3035	0.714955
$521$	−21.3626	−0.935912	−0.467956	−	0.883752i	$-0.655009\pi$
$521$	−21.3626	−0.935912	−0.467956	+	0.883752i	$0.655009\pi$
$522$	15.2230	0.666291
$523$	25.1574	1.10006	0.550028	−	0.835146i	$-0.314617\pi$
$523$	25.1574	1.10006	0.550028	+	0.835146i	$0.314617\pi$
$524$	−14.4201	−0.629947
$525$	1.22531	0.0534769
$526$	14.6176	0.637359
$527$	−18.9579	−0.825820
$528$	−10.0904	−0.439128
$529$	−22.9977	−0.999901
$530$	−30.0846	−1.30679
$531$	−32.2490	−1.39949
$532$	16.7528	0.726325
$533$	−11.0570	−0.478932
$534$	23.4703	1.01566
$535$	−9.47842	−0.409788
$536$	15.2105	0.656993
$537$	−22.6480	−0.977332
$538$	−35.3125	−1.52243
$539$	9.77078	0.420857
$540$	−11.6425	−0.501012
$541$	21.4819	0.923581	0.461790	−	0.886989i	$-0.347207\pi$
$541$	21.4819	0.923581	0.461790	+	0.886989i	$0.347207\pi$
$542$	−10.6580	−0.457798
$543$	−18.3505	−0.787496
$544$	9.46992	0.406020
$545$	2.16488	0.0927334
$546$	−18.2148	−0.779520
$547$	−31.4036	−1.34272	−0.671360	−	0.741131i	$-0.734290\pi$
$547$	−31.4036	−1.34272	−0.671360	+	0.741131i	$0.734290\pi$
$548$	61.2887	2.61812
$549$	35.6343	1.52084
$550$	−1.75035	−0.0746351
$551$	7.46727	0.318117
$552$	−0.422484	−0.0179821
$553$	2.45831	0.104538
$554$	−59.5348	−2.52939
$555$	5.01097	0.212704
$556$	21.5358	0.913323
$557$	−10.7217	−0.454292	−0.227146	−	0.973861i	$-0.572939\pi$
$557$	−10.7217	−0.454292	−0.227146	+	0.973861i	$0.572939\pi$
$558$	36.7186	1.55442
$559$	6.83602	0.289133
$560$	−6.76463	−0.285858
$561$	−15.7422	−0.664637
$562$	10.8092	0.455959
$563$	15.7026	0.661786	0.330893	−	0.943668i	$-0.392650\pi$
$563$	15.7026	0.661786	0.330893	+	0.943668i	$0.392650\pi$
$564$	17.0998	0.720031
$565$	−38.4364	−1.61703
$566$	−37.2734	−1.56672
$567$	17.7669	0.746138
$568$	29.5783	1.24108
$569$	21.4805	0.900511	0.450256	−	0.892900i	$-0.351333\pi$
$569$	21.4805	0.900511	0.450256	+	0.892900i	$0.351333\pi$
$570$	32.5521	1.36346
$571$	−8.56796	−0.358558	−0.179279	−	0.983798i	$-0.557376\pi$
$571$	−8.56796	−0.358558	−0.179279	+	0.983798i	$0.557376\pi$
$572$	16.7552	0.700571
$573$	−23.4212	−0.978433
$574$	22.5354	0.940609
$575$	−0.0149198	−0.000622198 0
$576$	−27.0614	−1.12756
$577$	24.7930	1.03214	0.516072	−	0.856545i	$-0.327394\pi$
$577$	24.7930	1.03214	0.516072	+	0.856545i	$0.327394\pi$
$578$	20.5647	0.855377
$579$	37.6673	1.56540
$580$	−21.3332	−0.885813
$581$	18.5231	0.768467
$582$	−28.8280	−1.19496
$583$	−13.8226	−0.572474
$584$	−61.3298	−2.53784
$585$	−10.0293	−0.414660
$586$	35.3029	1.45835
$587$	−6.23675	−0.257418	−0.128709	−	0.991682i	$-0.541083\pi$
$587$	−6.23675	−0.257418	−0.128709	+	0.991682i	$0.541083\pi$
$588$	−34.7009	−1.43104
$589$	18.0115	0.742150
$590$	70.1819	2.88934
$591$	−60.4271	−2.48564
$592$	1.84920	0.0760016
$593$	−22.3907	−0.919475	−0.459738	−	0.888055i	$-0.652057\pi$
$593$	−22.3907	−0.919475	−0.459738	+	0.888055i	$0.652057\pi$
$594$	−8.30697	−0.340839
$595$	−10.5536	−0.432657
$596$	34.8667	1.42819
$597$	18.0290	0.737876
$598$	0.221789	0.00906964
$599$	33.3572	1.36294	0.681469	−	0.731847i	$-0.261341\pi$
$599$	33.3572	1.36294	0.681469	+	0.731847i	$0.261341\pi$
$600$	2.77915	0.113458
$601$	16.4818	0.672305	0.336153	−	0.941808i	$-0.390874\pi$
$601$	16.4818	0.672305	0.336153	+	0.941808i	$0.390874\pi$
$602$	−13.9326	−0.567849
$603$	−9.35692	−0.381043
$604$	5.86169	0.238509
$605$	−11.7826	−0.479030
$606$	36.0916	1.46612
$607$	−13.4349	−0.545305	−0.272653	−	0.962113i	$-0.587901\pi$
$607$	−13.4349	−0.545305	−0.272653	+	0.962113i	$0.587901\pi$
$608$	−8.99715	−0.364883
$609$	10.6555	0.431784
$610$	−77.5492	−3.13987
$611$	−4.01325	−0.162359
$612$	24.6028	0.994508
$613$	2.32777	0.0940178	0.0470089	−	0.998894i	$-0.485031\pi$
$613$	2.32777	0.0940178	0.0470089	+	0.998894i	$0.485031\pi$
$614$	−16.0397	−0.647311
$615$	28.1972	1.13702
$616$	−15.2670	−0.615126
$617$	−37.8592	−1.52415	−0.762076	−	0.647487i	$-0.775820\pi$
$617$	−37.8592	−1.52415	−0.762076	+	0.647487i	$0.775820\pi$
$618$	55.0998	2.21644
$619$	−6.63899	−0.266843	−0.133422	−	0.991059i	$-0.542596\pi$
$619$	−6.63899	−0.266843	−0.133422	+	0.991059i	$0.542596\pi$
$620$	−51.4568	−2.06656
$621$	−0.0708078	−0.00284142
$622$	−31.2574	−1.25331
$623$	7.22938	0.289639
$624$	−8.41057	−0.336692
$625$	−23.3355	−0.933418
$626$	66.1146	2.64247
$627$	14.9563	0.597298
$628$	−72.8051	−2.90524
$629$	2.88498	0.115032
$630$	20.4408	0.814381
$631$	−46.6925	−1.85880	−0.929399	−	0.369078i	$-0.879674\pi$
$631$	−46.6925	−1.85880	−0.929399	+	0.369078i	$0.879674\pi$
$632$	5.57574	0.221791
$633$	−32.9008	−1.30769
$634$	67.1338	2.66622
$635$	−35.6339	−1.41409
$636$	49.0910	1.94658
$637$	8.14417	0.322684
$638$	−15.2214	−0.602619
$639$	−18.1954	−0.719800
$640$	44.6799	1.76613
$641$	7.14710	0.282294	0.141147	−	0.989989i	$-0.454921\pi$
$641$	7.14710	0.282294	0.141147	+	0.989989i	$0.454921\pi$
$642$	24.0185	0.947933
$643$	35.5556	1.40218	0.701088	−	0.713075i	$-0.252698\pi$
$643$	35.5556	1.40218	0.701088	+	0.713075i	$0.252698\pi$
$644$	−0.291083	−0.0114703
$645$	−17.4330	−0.686423
$646$	18.7413	0.737365
$647$	−22.9999	−0.904221	−0.452111	−	0.891962i	$-0.649329\pi$
$647$	−22.9999	−0.904221	−0.452111	+	0.891962i	$0.649329\pi$
$648$	40.2974	1.58303
$649$	32.2456	1.26575
$650$	−1.45896	−0.0572249
$651$	25.7017	1.00733
$652$	−20.1328	−0.788462
$653$	43.3226	1.69534	0.847671	−	0.530522i	$-0.178004\pi$
$653$	43.3226	1.69534	0.847671	+	0.530522i	$0.178004\pi$
$654$	−5.48585	−0.214514
$655$	−8.63066	−0.337228
$656$	10.4056	0.406271
$657$	37.7277	1.47190
$658$	8.17946	0.318868
$659$	42.4355	1.65305	0.826527	−	0.562898i	$-0.190314\pi$
$659$	42.4355	1.65305	0.826527	+	0.562898i	$0.190314\pi$
$660$	−42.7286	−1.66321
$661$	−22.7973	−0.886713	−0.443356	−	0.896345i	$-0.646212\pi$
$661$	−22.7973	−0.886713	−0.443356	+	0.896345i	$0.646212\pi$
$662$	−63.1999	−2.45634
$663$	−13.1215	−0.509597
$664$	42.0126	1.63041
$665$	10.0268	0.388822
$666$	−5.58776	−0.216521
$667$	−0.129745	−0.00502376
$668$	1.29522	0.0501134
$669$	51.3865	1.98672
$670$	20.3630	0.786691
$671$	−35.6306	−1.37550
$672$	−12.8386	−0.495260
$673$	15.4641	0.596099	0.298049	−	0.954550i	$-0.403664\pi$
$673$	15.4641	0.596099	0.298049	+	0.954550i	$0.403664\pi$
$674$	22.2632	0.857548
$675$	0.465782	0.0179280
$676$	−33.0564	−1.27140
$677$	−36.8011	−1.41438	−0.707191	−	0.707022i	$-0.750038\pi$
$677$	−36.8011	−1.41438	−0.707191	+	0.707022i	$0.750038\pi$
$678$	97.3984	3.74056
$679$	−8.87968	−0.340771
$680$	−23.9370	−0.917940
$681$	21.5699	0.826562
$682$	−36.7147	−1.40588
$683$	−2.79918	−0.107107	−0.0535537	−	0.998565i	$-0.517055\pi$
$683$	−2.79918	−0.107107	−0.0535537	+	0.998565i	$0.517055\pi$
$684$	−23.3745	−0.893747
$685$	36.6821	1.40155
$686$	−44.6324	−1.70407
$687$	38.0117	1.45024
$688$	−6.43329	−0.245267
$689$	−11.5215	−0.438933
$690$	−0.565599	−0.0215320
$691$	11.0504	0.420377	0.210189	−	0.977661i	$-0.432592\pi$
$691$	11.0504	0.420377	0.210189	+	0.977661i	$0.432592\pi$
$692$	−15.8758	−0.603508
$693$	9.39169	0.356761
$694$	25.0694	0.951621
$695$	12.8895	0.488926
$696$	24.1680	0.916087
$697$	16.2340	0.614907
$698$	−49.6354	−1.87873
$699$	−18.9390	−0.716338
$700$	1.91478	0.0723718
$701$	5.17566	0.195482	0.0977410	−	0.995212i	$-0.468838\pi$
$701$	5.17566	0.195482	0.0977410	+	0.995212i	$0.468838\pi$
$702$	−6.92405	−0.261332
$703$	−2.74095	−0.103377
$704$	27.0585	1.01981
$705$	10.2345	0.385452
$706$	−80.0730	−3.01359
$707$	11.1170	0.418098
$708$	−114.520	−4.30394
$709$	39.6425	1.48881	0.744403	−	0.667730i	$-0.232734\pi$
$709$	39.6425	1.48881	0.744403	+	0.667730i	$0.232734\pi$
$710$	39.5978	1.48608
$711$	−3.42998	−0.128634
$712$	16.3971	0.614508
$713$	−0.312953	−0.0117202
$714$	26.7431	1.00084
$715$	10.0282	0.375035
$716$	−35.3917	−1.32265
$717$	22.4829	0.839640
$718$	25.4972	0.951546
$719$	27.0869	1.01017	0.505085	−	0.863069i	$-0.331461\pi$
$719$	27.0869	1.01017	0.505085	+	0.863069i	$0.331461\pi$
$720$	9.43844	0.351750
$721$	16.9720	0.632069
$722$	27.2252	1.01322
$723$	54.8845	2.04118
$724$	−28.6761	−1.06574
$725$	0.853480	0.0316975
$726$	29.8572	1.10811
$727$	14.6645	0.543877	0.271938	−	0.962315i	$-0.412335\pi$
$727$	14.6645	0.543877	0.271938	+	0.962315i	$0.412335\pi$
$728$	−12.7254	−0.471635
$729$	−14.4652	−0.535747
$730$	−82.1050	−3.03884
$731$	−10.0367	−0.371221
$732$	126.542	4.67713
$733$	32.5685	1.20295	0.601473	−	0.798893i	$-0.294581\pi$
$733$	32.5685	1.20295	0.601473	+	0.798893i	$0.294581\pi$
$734$	−19.4330	−0.717287
$735$	−20.7690	−0.766076
$736$	0.156327	0.00576230
$737$	9.35593	0.344630
$738$	−31.4428	−1.15743
$739$	0.155802	0.00573127	0.00286564	−	0.999996i	$-0.499088\pi$
$739$	0.155802	0.00573127	0.00286564	+	0.999996i	$0.499088\pi$
$740$	7.83059	0.287858
$741$	12.4664	0.457966
$742$	23.4820	0.862052
$743$	−26.3048	−0.965031	−0.482516	−	0.875887i	$-0.660277\pi$
$743$	−26.3048	−0.965031	−0.482516	+	0.875887i	$0.660277\pi$
$744$	58.2946	2.13718
$745$	20.8682	0.764551
$746$	32.8547	1.20290
$747$	−25.8446	−0.945604
$748$	−24.6002	−0.899472
$749$	7.39822	0.270325
$750$	63.1017	2.30415
$751$	−36.6122	−1.33600	−0.668000	−	0.744162i	$-0.732849\pi$
$751$	−36.6122	−1.33600	−0.668000	+	0.744162i	$0.732849\pi$
$752$	3.77682	0.137726
$753$	−25.6411	−0.934415
$754$	−12.6874	−0.462046
$755$	3.50830	0.127680
$756$	9.08734	0.330503
$757$	25.4266	0.924146	0.462073	−	0.886842i	$-0.347106\pi$
$757$	25.4266	0.924146	0.462073	+	0.886842i	$0.347106\pi$
$758$	−91.9043	−3.33811
$759$	−0.259869	−0.00943265
$760$	22.7419	0.824937
$761$	−8.67347	−0.314413	−0.157207	−	0.987566i	$-0.550249\pi$
$761$	−8.67347	−0.314413	−0.157207	+	0.987566i	$0.550249\pi$
$762$	90.2969	3.27111
$763$	−1.68976	−0.0611735
$764$	−36.6000	−1.32414
$765$	14.7251	0.532387
$766$	67.1904	2.42769
$767$	26.8775	0.970490
$768$	−60.0839	−2.16809
$769$	7.92091	0.285635	0.142818	−	0.989749i	$-0.454384\pi$
$769$	7.92091	0.285635	0.142818	+	0.989749i	$0.454384\pi$
$770$	−20.4387	−0.736558
$771$	44.6977	1.60975
$772$	58.8623	2.11850
$773$	−40.8354	−1.46875	−0.734374	−	0.678745i	$-0.762524\pi$
$773$	−40.8354	−1.46875	−0.734374	+	0.678745i	$0.762524\pi$
$774$	19.4396	0.698741
$775$	2.05864	0.0739486
$776$	−20.1402	−0.722991
$777$	−3.91123	−0.140315
$778$	−59.5369	−2.13450
$779$	−15.4235	−0.552606
$780$	−35.6153	−1.27523
$781$	18.1935	0.651015
$782$	−0.325633	−0.0116446
$783$	4.05053	0.144754
$784$	−7.66438	−0.273728
$785$	−43.5749	−1.55525
$786$	21.8702	0.780085
$787$	−52.7076	−1.87882	−0.939412	−	0.342790i	$-0.888628\pi$
$787$	−52.7076	−1.87882	−0.939412	+	0.342790i	$0.888628\pi$
$788$	−94.4287	−3.36388
$789$	−14.2761	−0.508242
$790$	7.46450	0.265575
$791$	30.0009	1.06671
$792$	21.3015	0.756916
$793$	−29.6989	−1.05464
$794$	−31.8057	−1.12874
$795$	29.3816	1.04206
$796$	28.1736	0.998588
$797$	−19.7744	−0.700447	−0.350223	−	0.936666i	$-0.613894\pi$
$797$	−19.7744	−0.700447	−0.350223	+	0.936666i	$0.613894\pi$
$798$	−25.4080	−0.899433
$799$	5.89230	0.208455
$800$	−1.02834	−0.0363573
$801$	−10.0869	−0.356402
$802$	30.9775	1.09385
$803$	−37.7238	−1.33124
$804$	−33.2276	−1.17185
$805$	−0.174217	−0.00614035
$806$	−30.6026	−1.07793
$807$	34.4874	1.21401
$808$	25.2147	0.887051
$809$	−21.7693	−0.765369	−0.382685	−	0.923879i	$-0.625000\pi$
$809$	−21.7693	−0.765369	−0.382685	+	0.923879i	$0.625000\pi$
$810$	53.9480	1.89554
$811$	3.66953	0.128855	0.0644273	−	0.997922i	$-0.479478\pi$
$811$	3.66953	0.128855	0.0644273	+	0.997922i	$0.479478\pi$
$812$	16.6513	0.584345
$813$	10.4089	0.365057
$814$	5.58717	0.195830
$815$	−12.0498	−0.422085
$816$	12.3485	0.432283
$817$	9.53564	0.333610
$818$	86.2070	3.01416
$819$	7.82819	0.273539
$820$	44.0634	1.53876
$821$	−23.4296	−0.817699	−0.408850	−	0.912602i	$-0.634070\pi$
$821$	−23.4296	−0.817699	−0.408850	+	0.912602i	$0.634070\pi$
$822$	−92.9531	−3.24211
$823$	−6.22019	−0.216822	−0.108411	−	0.994106i	$-0.534576\pi$
$823$	−6.22019	−0.216822	−0.108411	+	0.994106i	$0.534576\pi$
$824$	38.4945	1.34102
$825$	1.70945	0.0595154
$826$	−54.7793	−1.90602
$827$	43.3179	1.50631	0.753156	−	0.657842i	$-0.228530\pi$
$827$	43.3179	1.50631	0.753156	+	0.657842i	$0.228530\pi$
$828$	0.406137	0.0141142
$829$	21.6761	0.752842	0.376421	−	0.926449i	$-0.377155\pi$
$829$	21.6761	0.752842	0.376421	+	0.926449i	$0.377155\pi$
$830$	56.2443	1.95227
$831$	58.1437	2.01698
$832$	22.5539	0.781917
$833$	−11.9574	−0.414298
$834$	−32.6622	−1.13100
$835$	0.775204	0.0268271
$836$	23.3721	0.808340
$837$	9.77010	0.337704
$838$	−44.8705	−1.55003
$839$	11.7373	0.405216	0.202608	−	0.979260i	$-0.435058\pi$
$839$	11.7373	0.405216	0.202608	+	0.979260i	$0.435058\pi$
$840$	32.4519	1.11970
$841$	−21.5780	−0.744068
$842$	38.3152	1.32043
$843$	−10.5566	−0.363590
$844$	−51.4137	−1.76973
$845$	−19.7847	−0.680615
$846$	−11.4125	−0.392369
$847$	9.19670	0.316002
$848$	10.8427	0.372340
$849$	36.4024	1.24933
$850$	2.14205	0.0734718
$851$	0.0476245	0.00163255
$852$	−64.6143	−2.21365
$853$	18.6776	0.639507	0.319754	−	0.947501i	$-0.396400\pi$
$853$	18.6776	0.639507	0.319754	+	0.947501i	$0.396400\pi$
$854$	60.5297	2.07128
$855$	−13.9900	−0.478447
$856$	16.7801	0.573531
$857$	−31.7085	−1.08314	−0.541571	−	0.840655i	$-0.682170\pi$
$857$	−31.7085	−1.08314	−0.541571	+	0.840655i	$0.682170\pi$
$858$	−25.4117	−0.867541
$859$	42.9560	1.46564	0.732819	−	0.680423i	$-0.238204\pi$
$859$	42.9560	1.46564	0.732819	+	0.680423i	$0.238204\pi$
$860$	−27.2423	−0.928955
$861$	−22.0088	−0.750059
$862$	1.85855	0.0633024
$863$	−24.5960	−0.837259	−0.418629	−	0.908157i	$-0.637489\pi$
$863$	−24.5960	−0.837259	−0.418629	+	0.908157i	$0.637489\pi$
$864$	−4.88039	−0.166034
$865$	−9.50189	−0.323074
$866$	39.9092	1.35617
$867$	−20.0841	−0.682093
$868$	40.1638	1.36325
$869$	3.42962	0.116342
$870$	32.3549	1.09693
$871$	7.79839	0.264238
$872$	−3.83259	−0.129788
$873$	12.3895	0.419320
$874$	0.309377	0.0104648
$875$	19.4367	0.657081
$876$	133.976	4.52663
$877$	−2.58847	−0.0874063	−0.0437031	−	0.999045i	$-0.513916\pi$
$877$	−2.58847	−0.0874063	−0.0437031	+	0.999045i	$0.513916\pi$
$878$	−21.3457	−0.720382
$879$	−34.4780	−1.16291
$880$	−9.43744	−0.318136
$881$	14.4982	0.488458	0.244229	−	0.969718i	$-0.421465\pi$
$881$	14.4982	0.488458	0.244229	+	0.969718i	$0.421465\pi$
$882$	23.1596	0.779824
$883$	23.0297	0.775011	0.387505	−	0.921867i	$-0.373337\pi$
$883$	23.0297	0.775011	0.387505	+	0.921867i	$0.373337\pi$
$884$	−20.5048	−0.689652
$885$	−68.5420	−2.30402
$886$	41.8577	1.40624
$887$	22.5055	0.755661	0.377830	−	0.925875i	$-0.376670\pi$
$887$	22.5055	0.755661	0.377830	+	0.925875i	$0.376670\pi$
$888$	−8.87115	−0.297696
$889$	27.8135	0.932834
$890$	21.9516	0.735818
$891$	24.7868	0.830390
$892$	80.3011	2.68868
$893$	−5.59813	−0.187334
$894$	−52.8803	−1.76858
$895$	−21.1824	−0.708051
$896$	−34.8741	−1.16506
$897$	−0.216607	−0.00723229
$898$	−91.4628	−3.05215
$899$	17.9023	0.597077
$900$	−2.67162	−0.0890539
$901$	16.9159	0.563551
$902$	31.4395	1.04682
$903$	13.6070	0.452813
$904$	68.0457	2.26317
$905$	−17.1631	−0.570520
$906$	−8.89009	−0.295353
$907$	20.1741	0.669869	0.334935	−	0.942241i	$-0.391286\pi$
$907$	20.1741	0.669869	0.334935	+	0.942241i	$0.391286\pi$
$908$	33.7071	1.11861
$909$	−15.5111	−0.514472
$910$	−17.0361	−0.564741
$911$	−43.8885	−1.45409	−0.727045	−	0.686590i	$-0.759107\pi$
$911$	−43.8885	−1.45409	−0.727045	+	0.686590i	$0.759107\pi$
$912$	−11.7320	−0.388486
$913$	25.8419	0.855241
$914$	−21.7821	−0.720487
$915$	75.7371	2.50379
$916$	59.4004	1.96265
$917$	6.73651	0.222459
$918$	10.1660	0.335527
$919$	−4.39603	−0.145012	−0.0725059	−	0.997368i	$-0.523100\pi$
$919$	−4.39603	−0.145012	−0.0725059	+	0.997368i	$0.523100\pi$
$920$	−0.395146	−0.0130276
$921$	15.6649	0.516177
$922$	−27.5165	−0.906209
$923$	15.1647	0.499153
$924$	33.3511	1.09717
$925$	−0.313280	−0.0103006
$926$	68.0209	2.23531
$927$	−23.6803	−0.777764
$928$	−8.94264	−0.293557
$929$	31.2767	1.02616	0.513078	−	0.858342i	$-0.328505\pi$
$929$	31.2767	1.02616	0.513078	+	0.858342i	$0.328505\pi$
$930$	78.0417	2.55909
$931$	11.3604	0.372322
$932$	−29.5957	−0.969440
$933$	30.5270	0.999410
$934$	−66.4915	−2.17567
$935$	−14.7236	−0.481512
$936$	17.7553	0.580350
$937$	41.2739	1.34836	0.674179	−	0.738568i	$-0.264498\pi$
$937$	41.2739	1.34836	0.674179	+	0.738568i	$0.264498\pi$
$938$	−15.8940	−0.518957
$939$	−64.5698	−2.10715
$940$	15.9933	0.521643
$941$	8.14720	0.265591	0.132796	−	0.991143i	$-0.457605\pi$
$941$	8.14720	0.265591	0.132796	+	0.991143i	$0.457605\pi$
$942$	110.419	3.59766
$943$	0.267987	0.00872686
$944$	−25.2941	−0.823252
$945$	5.43890	0.176927
$946$	−19.4375	−0.631969
$947$	−4.67084	−0.151782	−0.0758910	−	0.997116i	$-0.524180\pi$
$947$	−4.67084	−0.151782	−0.0758910	+	0.997116i	$0.524180\pi$
$948$	−12.1803	−0.395598
$949$	−31.4437	−1.02070
$950$	−2.03511	−0.0660278
$951$	−65.5651	−2.12609
$952$	18.6836	0.605539
$953$	12.4677	0.403870	0.201935	−	0.979399i	$-0.435277\pi$
$953$	12.4677	0.403870	0.201935	+	0.979399i	$0.435277\pi$
$954$	−32.7636	−1.06076
$955$	−21.9056	−0.708849
$956$	35.1338	1.13631
$957$	14.8657	0.480540
$958$	16.9697	0.548265
$959$	−28.6316	−0.924563
$960$	−57.5162	−1.85633
$961$	12.1814	0.392949
$962$	4.65704	0.150149
$963$	−10.3225	−0.332637
$964$	85.7674	2.76238
$965$	35.2299	1.13409
$966$	0.441469	0.0142040
$967$	20.3790	0.655345	0.327673	−	0.944791i	$-0.393736\pi$
$967$	20.3790	0.655345	0.327673	+	0.944791i	$0.393736\pi$
$968$	20.8592	0.670441
$969$	−18.3034	−0.587988
$970$	−26.9626	−0.865717
$971$	40.4440	1.29791	0.648955	−	0.760827i	$-0.275207\pi$
$971$	40.4440	1.29791	0.648955	+	0.760827i	$0.275207\pi$
$972$	−71.8968	−2.30609
$973$	−10.0607	−0.322531
$974$	27.8263	0.891612
$975$	1.42487	0.0456322
$976$	27.9493	0.894634
$977$	−9.55881	−0.305814	−0.152907	−	0.988241i	$-0.548863\pi$
$977$	−9.55881	−0.305814	−0.152907	+	0.988241i	$0.548863\pi$
$978$	30.5343	0.976380
$979$	10.0858	0.322344
$980$	−32.4555	−1.03675
$981$	2.35766	0.0752744
$982$	77.3432	2.46812
$983$	33.3010	1.06214	0.531069	−	0.847329i	$-0.321791\pi$
$983$	33.3010	1.06214	0.531069	+	0.847329i	$0.321791\pi$
$984$	−49.9187	−1.59135
$985$	−56.5169	−1.80078
$986$	18.6277	0.593227
$987$	−7.98833	−0.254271
$988$	19.4812	0.619778
$989$	−0.165684	−0.00526844
$990$	28.5173	0.906339
$991$	30.6258	0.972860	0.486430	−	0.873720i	$-0.338299\pi$
$991$	30.6258	0.972860	0.486430	+	0.873720i	$0.338299\pi$
$992$	−21.5701	−0.684852
$993$	61.7232	1.95873
$994$	−30.9074	−0.980323
$995$	16.8623	0.534572
$996$	−91.7774	−2.90808
$997$	−19.9255	−0.631046	−0.315523	−	0.948918i	$-0.602180\pi$
$997$	−19.9255	−0.631046	−0.315523	+	0.948918i	$0.602180\pi$
$998$	−39.7913	−1.25957
$999$	−1.48679	−0.0470400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.9	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.9	✓	77	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37004 q^{2} +2.31466 q^{3} +3.61710 q^{4} +2.16488 q^{5} -5.48585 q^{6} -1.68976 q^{7} -3.83259 q^{8} +2.35766 q^{9} +O(q^{10})\)	\(q-2.37004 q^{2} +2.31466 q^{3} +3.61710 q^{4} +2.16488 q^{5} -5.48585 q^{6} -1.68976 q^{7} -3.83259 q^{8} +2.35766 q^{9} -5.13086 q^{10} -2.35742 q^{11} +8.37236 q^{12} -1.96496 q^{13} +4.00481 q^{14} +5.01097 q^{15} +1.84920 q^{16} +2.88498 q^{17} -5.58776 q^{18} -2.74095 q^{19} +7.83059 q^{20} -3.91123 q^{21} +5.58717 q^{22} +0.0476245 q^{23} -8.87115 q^{24} -0.313280 q^{25} +4.65704 q^{26} -1.48679 q^{27} -6.11204 q^{28} -2.72434 q^{29} -11.8762 q^{30} -6.57126 q^{31} +3.28250 q^{32} -5.45662 q^{33} -6.83751 q^{34} -3.65814 q^{35} +8.52790 q^{36} +1.00000 q^{37} +6.49616 q^{38} -4.54822 q^{39} -8.29711 q^{40} +5.62708 q^{41} +9.26978 q^{42} -3.47896 q^{43} -8.52700 q^{44} +5.10407 q^{45} -0.112872 q^{46} +2.04241 q^{47} +4.28027 q^{48} -4.14470 q^{49} +0.742486 q^{50} +6.67775 q^{51} -7.10746 q^{52} +5.86345 q^{53} +3.52376 q^{54} -5.10353 q^{55} +6.47617 q^{56} -6.34437 q^{57} +6.45680 q^{58} -13.6784 q^{59} +18.1252 q^{60} +15.1143 q^{61} +15.5742 q^{62} -3.98389 q^{63} -11.4781 q^{64} -4.25391 q^{65} +12.9324 q^{66} -3.96873 q^{67} +10.4352 q^{68} +0.110235 q^{69} +8.66995 q^{70} -7.71757 q^{71} -9.03595 q^{72} +16.0022 q^{73} -2.37004 q^{74} -0.725137 q^{75} -9.91427 q^{76} +3.98347 q^{77} +10.7795 q^{78} -1.45482 q^{79} +4.00330 q^{80} -10.5144 q^{81} -13.3364 q^{82} -10.9619 q^{83} -14.1473 q^{84} +6.24564 q^{85} +8.24528 q^{86} -6.30593 q^{87} +9.03500 q^{88} -4.27834 q^{89} -12.0968 q^{90} +3.32032 q^{91} +0.172263 q^{92} -15.2102 q^{93} -4.84059 q^{94} -5.93383 q^{95} +7.59787 q^{96} +5.25498 q^{97} +9.82311 q^{98} -5.55799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

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