LMFDB - Embedded newform 4033.2.a.d.1.7

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:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.60105 q^{2} +3.31359 q^{3} +4.76544 q^{4} -1.17110 q^{5} -8.61880 q^{6} +2.01510 q^{7} -7.19305 q^{8} +7.97988 q^{9} +O(q^{10})$	\(q-2.60105 q^{2} +3.31359 q^{3} +4.76544 q^{4} -1.17110 q^{5} -8.61880 q^{6} +2.01510 q^{7} -7.19305 q^{8} +7.97988 q^{9} +3.04608 q^{10} -2.35764 q^{11} +15.7907 q^{12} -1.55402 q^{13} -5.24137 q^{14} -3.88054 q^{15} +9.17857 q^{16} -5.14771 q^{17} -20.7560 q^{18} +1.38186 q^{19} -5.58080 q^{20} +6.67721 q^{21} +6.13233 q^{22} -7.77240 q^{23} -23.8348 q^{24} -3.62853 q^{25} +4.04207 q^{26} +16.5013 q^{27} +9.60284 q^{28} +0.340737 q^{29} +10.0935 q^{30} -5.28638 q^{31} -9.48779 q^{32} -7.81225 q^{33} +13.3894 q^{34} -2.35988 q^{35} +38.0277 q^{36} -1.00000 q^{37} -3.59428 q^{38} -5.14937 q^{39} +8.42377 q^{40} +2.43498 q^{41} -17.3677 q^{42} -11.7440 q^{43} -11.2352 q^{44} -9.34522 q^{45} +20.2164 q^{46} -8.86853 q^{47} +30.4140 q^{48} -2.93938 q^{49} +9.43797 q^{50} -17.0574 q^{51} -7.40558 q^{52} -12.4091 q^{53} -42.9206 q^{54} +2.76103 q^{55} -14.4947 q^{56} +4.57891 q^{57} -0.886273 q^{58} +2.65306 q^{59} -18.4925 q^{60} +4.90042 q^{61} +13.7501 q^{62} +16.0802 q^{63} +6.32104 q^{64} +1.81991 q^{65} +20.3200 q^{66} -2.27072 q^{67} -24.5311 q^{68} -25.7545 q^{69} +6.13815 q^{70} -1.52159 q^{71} -57.3996 q^{72} +13.1359 q^{73} +2.60105 q^{74} -12.0235 q^{75} +6.58517 q^{76} -4.75088 q^{77} +13.3938 q^{78} +5.42043 q^{79} -10.7490 q^{80} +30.7388 q^{81} -6.33348 q^{82} -10.4900 q^{83} +31.8199 q^{84} +6.02848 q^{85} +30.5466 q^{86} +1.12906 q^{87} +16.9586 q^{88} +9.49778 q^{89} +24.3073 q^{90} -3.13150 q^{91} -37.0389 q^{92} -17.5169 q^{93} +23.0675 q^{94} -1.61829 q^{95} -31.4386 q^{96} +0.204257 q^{97} +7.64546 q^{98} -18.8137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−2.60105	−1.83922	−0.919609	−	0.392835i	$-0.871494\pi$
$2$	−2.60105	−1.83922	−0.919609	+	0.392835i	$0.871494\pi$
$3$	3.31359	1.91310	0.956551	−	0.291565i	$-0.0941761\pi$
$3$	3.31359	1.91310	0.956551	+	0.291565i	$0.0941761\pi$
$4$	4.76544	2.38272
$5$	−1.17110	−0.523731	−0.261866	−	0.965104i	$-0.584338\pi$
$5$	−1.17110	−0.523731	−0.261866	+	0.965104i	$0.584338\pi$
$6$	−8.61880	−3.51861
$7$	2.01510	0.761636	0.380818	−	0.924650i	$-0.375642\pi$
$7$	2.01510	0.761636	0.380818	+	0.924650i	$0.375642\pi$
$8$	−7.19305	−2.54313
$9$	7.97988	2.65996
$10$	3.04608	0.963255
$11$	−2.35764	−0.710856	−0.355428	−	0.934704i	$-0.615665\pi$
$11$	−2.35764	−0.710856	−0.355428	+	0.934704i	$0.615665\pi$
$12$	15.7907	4.55839
$13$	−1.55402	−0.431007	−0.215503	−	0.976503i	$-0.569139\pi$
$13$	−1.55402	−0.431007	−0.215503	+	0.976503i	$0.569139\pi$
$14$	−5.24137	−1.40081
$15$	−3.88054	−1.00195
$16$	9.17857	2.29464
$17$	−5.14771	−1.24850	−0.624252	−	0.781223i	$-0.714596\pi$
$17$	−5.14771	−1.24850	−0.624252	+	0.781223i	$0.714596\pi$
$18$	−20.7560	−4.89224
$19$	1.38186	0.317020	0.158510	−	0.987357i	$-0.449331\pi$
$19$	1.38186	0.317020	0.158510	+	0.987357i	$0.449331\pi$
$20$	−5.58080	−1.24791
$21$	6.67721	1.45709
$22$	6.13233	1.30742
$23$	−7.77240	−1.62066	−0.810329	−	0.585976i	$-0.800711\pi$
$23$	−7.77240	−1.62066	−0.810329	+	0.585976i	$0.800711\pi$
$24$	−23.8348	−4.86526
$25$	−3.62853	−0.725706
$26$	4.04207	0.792715
$27$	16.5013	3.17567
$28$	9.60284	1.81477
$29$	0.340737	0.0632733	0.0316366	−	0.999499i	$-0.489928\pi$
$29$	0.340737	0.0632733	0.0316366	+	0.999499i	$0.489928\pi$
$30$	10.0935	1.84281
$31$	−5.28638	−0.949462	−0.474731	−	0.880131i	$-0.657455\pi$
$31$	−5.28638	−0.949462	−0.474731	+	0.880131i	$0.657455\pi$
$32$	−9.48779	−1.67722
$33$	−7.81225	−1.35994
$34$	13.3894	2.29627
$35$	−2.35988	−0.398892
$36$	38.0277	6.33794
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.59428	−0.583069
$39$	−5.14937	−0.824559
$40$	8.42377	1.33191
$41$	2.43498	0.380279	0.190140	−	0.981757i	$-0.439106\pi$
$41$	2.43498	0.380279	0.190140	+	0.981757i	$0.439106\pi$
$42$	−17.3677	−2.67990
$43$	−11.7440	−1.79094	−0.895469	−	0.445125i	$-0.853159\pi$
$43$	−11.7440	−1.79094	−0.895469	+	0.445125i	$0.853159\pi$
$44$	−11.2352	−1.69377
$45$	−9.34522	−1.39310
$46$	20.2164	2.98074
$47$	−8.86853	−1.29361	−0.646804	−	0.762656i	$-0.723895\pi$
$47$	−8.86853	−1.29361	−0.646804	+	0.762656i	$0.723895\pi$
$48$	30.4140	4.38988
$49$	−2.93938	−0.419911
$50$	9.43797	1.33473
$51$	−17.0574	−2.38851
$52$	−7.40558	−1.02697
$53$	−12.4091	−1.70452	−0.852262	−	0.523115i	$-0.824770\pi$
$53$	−12.4091	−1.70452	−0.852262	+	0.523115i	$0.824770\pi$
$54$	−42.9206	−5.84075
$55$	2.76103	0.372297
$56$	−14.4947	−1.93694
$57$	4.57891	0.606491
$58$	−0.886273	−0.116373
$59$	2.65306	0.345399	0.172700	−	0.984975i	$-0.444751\pi$
$59$	2.65306	0.345399	0.172700	+	0.984975i	$0.444751\pi$
$60$	−18.4925	−2.38737
$61$	4.90042	0.627434	0.313717	−	0.949516i	$-0.398426\pi$
$61$	4.90042	0.627434	0.313717	+	0.949516i	$0.398426\pi$
$62$	13.7501	1.74627
$63$	16.0802	2.02592
$64$	6.32104	0.790130
$65$	1.81991	0.225731
$66$	20.3200	2.50122
$67$	−2.27072	−0.277413	−0.138706	−	0.990334i	$-0.544294\pi$
$67$	−2.27072	−0.277413	−0.138706	+	0.990334i	$0.544294\pi$
$68$	−24.5311	−2.97484
$69$	−25.7545	−3.10048
$70$	6.13815	0.733650
$71$	−1.52159	−0.180580	−0.0902899	−	0.995916i	$-0.528779\pi$
$71$	−1.52159	−0.180580	−0.0902899	+	0.995916i	$0.528779\pi$
$72$	−57.3996	−6.76461
$73$	13.1359	1.53744	0.768720	−	0.639586i	$-0.220894\pi$
$73$	13.1359	1.53744	0.768720	+	0.639586i	$0.220894\pi$
$74$	2.60105	0.302366
$75$	−12.0235	−1.38835
$76$	6.58517	0.755370
$77$	−4.75088	−0.541413
$78$	13.3938	1.51654
$79$	5.42043	0.609846	0.304923	−	0.952377i	$-0.401369\pi$
$79$	5.42043	0.609846	0.304923	+	0.952377i	$0.401369\pi$
$80$	−10.7490	−1.20178
$81$	30.7388	3.41542
$82$	−6.33348	−0.699416
$83$	−10.4900	−1.15143	−0.575713	−	0.817652i	$-0.695275\pi$
$83$	−10.4900	−1.15143	−0.575713	+	0.817652i	$0.695275\pi$
$84$	31.8199	3.47183
$85$	6.02848	0.653880
$86$	30.5466	3.29392
$87$	1.12906	0.121048
$88$	16.9586	1.80780
$89$	9.49778	1.00676	0.503381	−	0.864065i	$-0.332089\pi$
$89$	9.49778	1.00676	0.503381	+	0.864065i	$0.332089\pi$
$90$	24.3073	2.56222
$91$	−3.13150	−0.328270
$92$	−37.0389	−3.86158
$93$	−17.5169	−1.81642
$94$	23.0675	2.37923
$95$	−1.61829	−0.166033
$96$	−31.4386	−3.20869
$97$	0.204257	0.0207392	0.0103696	−	0.999946i	$-0.496699\pi$
$97$	0.204257	0.0207392	0.0103696	+	0.999946i	$0.496699\pi$
$98$	7.64546	0.772308
$99$	−18.8137	−1.89085
$100$	−17.2916	−1.72916
$101$	7.08007	0.704493	0.352247	−	0.935907i	$-0.385418\pi$
$101$	7.08007	0.704493	0.352247	+	0.935907i	$0.385418\pi$
$102$	44.3671	4.39300
$103$	−12.9537	−1.27637	−0.638183	−	0.769885i	$-0.720314\pi$
$103$	−12.9537	−1.27637	−0.638183	+	0.769885i	$0.720314\pi$
$104$	11.1781	1.09610
$105$	−7.81967	−0.763122
$106$	32.2767	3.13499
$107$	−17.1427	−1.65725	−0.828624	−	0.559806i	$-0.810876\pi$
$107$	−17.1427	−1.65725	−0.828624	+	0.559806i	$0.810876\pi$
$108$	78.6359	7.56674
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−7.18157	−0.684735
$111$	−3.31359	−0.314512
$112$	18.4957	1.74768
$113$	8.74945	0.823079	0.411539	−	0.911392i	$-0.364991\pi$
$113$	8.74945	0.823079	0.411539	+	0.911392i	$0.364991\pi$
$114$	−11.9100	−1.11547
$115$	9.10224	0.848788
$116$	1.62376	0.150763
$117$	−12.4009	−1.14646
$118$	−6.90074	−0.635264
$119$	−10.3731	−0.950905
$120$	27.9129	2.54809
$121$	−5.44153	−0.494684
$122$	−12.7462	−1.15399
$123$	8.06851	0.727513
$124$	−25.1919	−2.26230
$125$	10.1049	0.903806
$126$	−41.8255	−3.72611
$127$	10.3941	0.922323	0.461162	−	0.887316i	$-0.347433\pi$
$127$	10.3941	0.922323	0.461162	+	0.887316i	$0.347433\pi$
$128$	2.53425	0.223998
$129$	−38.9147	−3.42625
$130$	−4.73366	−0.415169
$131$	7.19472	0.628605	0.314303	−	0.949323i	$-0.398229\pi$
$131$	7.19472	0.628605	0.314303	+	0.949323i	$0.398229\pi$
$132$	−37.2289	−3.24036
$133$	2.78458	0.241454
$134$	5.90625	0.510222
$135$	−19.3246	−1.66320
$136$	37.0277	3.17510
$137$	−3.87169	−0.330781	−0.165390	−	0.986228i	$-0.552888\pi$
$137$	−3.87169	−0.330781	−0.165390	+	0.986228i	$0.552888\pi$
$138$	66.9888	5.70246
$139$	4.52603	0.383893	0.191946	−	0.981405i	$-0.438520\pi$
$139$	4.52603	0.383893	0.191946	+	0.981405i	$0.438520\pi$
$140$	−11.2459	−0.950449
$141$	−29.3867	−2.47480
$142$	3.95773	0.332126
$143$	3.66381	0.306383
$144$	73.2438	6.10365
$145$	−0.399037	−0.0331382
$146$	−34.1671	−2.82769
$147$	−9.73989	−0.803332
$148$	−4.76544	−0.391717
$149$	−19.2671	−1.57842	−0.789210	−	0.614123i	$-0.789510\pi$
$149$	−19.2671	−1.57842	−0.789210	+	0.614123i	$0.789510\pi$
$150$	31.2736	2.55348
$151$	11.8631	0.965403	0.482702	−	0.875785i	$-0.339656\pi$
$151$	11.8631	0.965403	0.482702	+	0.875785i	$0.339656\pi$
$152$	−9.93977	−0.806222
$153$	−41.0781	−3.32097
$154$	12.3573	0.995776
$155$	6.19087	0.497263
$156$	−24.5390	−1.96470
$157$	0.972753	0.0776341	0.0388171	−	0.999246i	$-0.487641\pi$
$157$	0.972753	0.0776341	0.0388171	+	0.999246i	$0.487641\pi$
$158$	−14.0988	−1.12164
$159$	−41.1187	−3.26093
$160$	11.1111	0.878412
$161$	−15.6622	−1.23435
$162$	−79.9530	−6.28170
$163$	21.1239	1.65455	0.827275	−	0.561797i	$-0.189890\pi$
$163$	21.1239	1.65455	0.827275	+	0.561797i	$0.189890\pi$
$164$	11.6037	0.906100
$165$	9.14892	0.712242
$166$	27.2849	2.11772
$167$	−5.59785	−0.433175	−0.216587	−	0.976263i	$-0.569493\pi$
$167$	−5.59785	−0.433175	−0.216587	+	0.976263i	$0.569493\pi$
$168$	−48.0295	−3.70556
$169$	−10.5850	−0.814233
$170$	−15.6803	−1.20263
$171$	11.0271	0.843260
$172$	−55.9652	−4.26731
$173$	−13.4509	−1.02265	−0.511325	−	0.859387i	$-0.670845\pi$
$173$	−13.4509	−1.02265	−0.511325	+	0.859387i	$0.670845\pi$
$174$	−2.93675	−0.222634
$175$	−7.31184	−0.552724
$176$	−21.6398	−1.63116
$177$	8.79116	0.660784
$178$	−24.7042	−1.85165
$179$	12.0761	0.902607	0.451304	−	0.892370i	$-0.350959\pi$
$179$	12.0761	0.902607	0.451304	+	0.892370i	$0.350959\pi$
$180$	−44.5341	−3.31938
$181$	18.3471	1.36373	0.681863	−	0.731480i	$-0.261170\pi$
$181$	18.3471	1.36373	0.681863	+	0.731480i	$0.261170\pi$
$182$	8.14517	0.603760
$183$	16.2380	1.20035
$184$	55.9072	4.12154
$185$	1.17110	0.0861009
$186$	45.5623	3.34079
$187$	12.1365	0.887506
$188$	−42.2625	−3.08231
$189$	33.2517	2.41870
$190$	4.20925	0.305371
$191$	−6.32726	−0.457824	−0.228912	−	0.973447i	$-0.573517\pi$
$191$	−6.32726	−0.457824	−0.228912	+	0.973447i	$0.573517\pi$
$192$	20.9453	1.51160
$193$	11.7279	0.844192	0.422096	−	0.906551i	$-0.361295\pi$
$193$	11.7279	0.844192	0.422096	+	0.906551i	$0.361295\pi$
$194$	−0.531283	−0.0381439
$195$	6.03042	0.431847
$196$	−14.0074	−1.00053
$197$	13.6565	0.972984	0.486492	−	0.873685i	$-0.338276\pi$
$197$	13.6565	0.972984	0.486492	+	0.873685i	$0.338276\pi$
$198$	48.9353	3.47768
$199$	−26.2231	−1.85890	−0.929452	−	0.368944i	$-0.879720\pi$
$199$	−26.2231	−1.85890	−0.929452	+	0.368944i	$0.879720\pi$
$200$	26.1002	1.84556
$201$	−7.52423	−0.530718
$202$	−18.4156	−1.29572
$203$	0.686619	0.0481912
$204$	−81.2861	−5.69117
$205$	−2.85160	−0.199164
$206$	33.6932	2.34751
$207$	−62.0228	−4.31088
$208$	−14.2636	−0.989006
$209$	−3.25792	−0.225355
$210$	20.3393	1.40355
$211$	−27.5009	−1.89324	−0.946620	−	0.322352i	$-0.895526\pi$
$211$	−27.5009	−1.89324	−0.946620	+	0.322352i	$0.895526\pi$
$212$	−59.1350	−4.06141
$213$	−5.04193	−0.345468
$214$	44.5890	3.04804
$215$	13.7533	0.937969
$216$	−118.694	−8.07613
$217$	−10.6526	−0.723144
$218$	2.60105	0.176165
$219$	43.5269	2.94128
$220$	13.1575	0.887080
$221$	7.99963	0.538113
$222$	8.61880	0.578456
$223$	−1.12091	−0.0750615	−0.0375308	−	0.999295i	$-0.511949\pi$
$223$	−1.12091	−0.0750615	−0.0375308	+	0.999295i	$0.511949\pi$
$224$	−19.1188	−1.27743
$225$	−28.9552	−1.93035
$226$	−22.7577	−1.51382
$227$	−7.85794	−0.521550	−0.260775	−	0.965400i	$-0.583978\pi$
$227$	−7.85794	−0.521550	−0.260775	+	0.965400i	$0.583978\pi$
$228$	21.8205	1.44510
$229$	−1.03088	−0.0681226	−0.0340613	−	0.999420i	$-0.510844\pi$
$229$	−1.03088	−0.0681226	−0.0340613	+	0.999420i	$0.510844\pi$
$230$	−23.6754	−1.56111
$231$	−15.7425	−1.03578
$232$	−2.45094	−0.160912
$233$	19.9886	1.30950	0.654748	−	0.755847i	$-0.272775\pi$
$233$	19.9886	1.30950	0.654748	+	0.755847i	$0.272775\pi$
$234$	32.2552	2.10859
$235$	10.3859	0.677503
$236$	12.6430	0.822990
$237$	17.9611	1.16670
$238$	26.9810	1.74892
$239$	18.3141	1.18464	0.592321	−	0.805702i	$-0.298212\pi$
$239$	18.3141	1.18464	0.592321	+	0.805702i	$0.298212\pi$
$240$	−35.6178	−2.29912
$241$	29.0472	1.87109	0.935547	−	0.353202i	$-0.114907\pi$
$241$	29.0472	1.87109	0.935547	+	0.353202i	$0.114907\pi$
$242$	14.1537	0.909832
$243$	52.3520	3.35838
$244$	23.3527	1.49500
$245$	3.44230	0.219920
$246$	−20.9866	−1.33805
$247$	−2.14743	−0.136638
$248$	38.0252	2.41460
$249$	−34.7595	−2.20279
$250$	−26.2832	−1.66230
$251$	17.8973	1.12967	0.564834	−	0.825205i	$-0.308940\pi$
$251$	17.8973	1.12967	0.564834	+	0.825205i	$0.308940\pi$
$252$	76.6295	4.82720
$253$	18.3245	1.15205
$254$	−27.0354	−1.69635
$255$	19.9759	1.25094
$256$	−19.2338	−1.20211
$257$	19.8595	1.23880	0.619402	−	0.785074i	$-0.287375\pi$
$257$	19.8595	1.23880	0.619402	+	0.785074i	$0.287375\pi$
$258$	101.219	6.30161
$259$	−2.01510	−0.125212
$260$	8.67266	0.537855
$261$	2.71904	0.168304
$262$	−18.7138	−1.15614
$263$	−15.6347	−0.964075	−0.482038	−	0.876150i	$-0.660103\pi$
$263$	−15.6347	−0.964075	−0.482038	+	0.876150i	$0.660103\pi$
$264$	56.1939	3.45850
$265$	14.5323	0.892712
$266$	−7.24282	−0.444086
$267$	31.4717	1.92604
$268$	−10.8210	−0.660997
$269$	14.9388	0.910834	0.455417	−	0.890278i	$-0.349490\pi$
$269$	14.9388	0.910834	0.455417	+	0.890278i	$0.349490\pi$
$270$	50.2642	3.05898
$271$	5.92517	0.359929	0.179964	−	0.983673i	$-0.442402\pi$
$271$	5.92517	0.359929	0.179964	+	0.983673i	$0.442402\pi$
$272$	−47.2486	−2.86487
$273$	−10.3765	−0.628014
$274$	10.0704	0.608378
$275$	8.55477	0.515872
$276$	−122.732	−7.38759
$277$	−4.94849	−0.297326	−0.148663	−	0.988888i	$-0.547497\pi$
$277$	−4.94849	−0.297326	−0.148663	+	0.988888i	$0.547497\pi$
$278$	−11.7724	−0.706063
$279$	−42.1847	−2.52553
$280$	16.9747	1.01443
$281$	13.0469	0.778310	0.389155	−	0.921172i	$-0.372767\pi$
$281$	13.0469	0.778310	0.389155	+	0.921172i	$0.372767\pi$
$282$	76.4361	4.55170
$283$	6.21184	0.369255	0.184628	−	0.982809i	$-0.440892\pi$
$283$	6.21184	0.369255	0.184628	+	0.982809i	$0.440892\pi$
$284$	−7.25107	−0.430272
$285$	−5.36235	−0.317638
$286$	−9.52975	−0.563506
$287$	4.90672	0.289634
$288$	−75.7114	−4.46134
$289$	9.49893	0.558761
$290$	1.03791	0.0609483
$291$	0.676825	0.0396762
$292$	62.5983	3.66329
$293$	18.0544	1.05475	0.527374	−	0.849633i	$-0.323177\pi$
$293$	18.0544	1.05475	0.527374	+	0.849633i	$0.323177\pi$
$294$	25.3339	1.47750
$295$	−3.10700	−0.180896
$296$	7.19305	0.418087
$297$	−38.9041	−2.25744
$298$	50.1146	2.90306
$299$	12.0784	0.698514
$300$	−57.2971	−3.30805
$301$	−23.6652	−1.36404
$302$	−30.8564	−1.77559
$303$	23.4604	1.34777
$304$	12.6835	0.727447
$305$	−5.73887	−0.328607
$306$	106.846	6.10798
$307$	−19.4518	−1.11017	−0.555087	−	0.831792i	$-0.687315\pi$
$307$	−19.4518	−1.11017	−0.555087	+	0.831792i	$0.687315\pi$
$308$	−22.6401	−1.29004
$309$	−42.9232	−2.44182
$310$	−16.1027	−0.914574
$311$	−11.2484	−0.637837	−0.318918	−	0.947782i	$-0.603320\pi$
$311$	−11.2484	−0.637837	−0.318918	+	0.947782i	$0.603320\pi$
$312$	37.0397	2.09696
$313$	5.87260	0.331939	0.165969	−	0.986131i	$-0.446925\pi$
$313$	5.87260	0.331939	0.165969	+	0.986131i	$0.446925\pi$
$314$	−2.53018	−0.142786
$315$	−18.8315	−1.06104
$316$	25.8308	1.45309
$317$	33.9138	1.90479	0.952395	−	0.304867i	$-0.0986120\pi$
$317$	33.9138	1.90479	0.952395	+	0.304867i	$0.0986120\pi$
$318$	106.952	5.99756
$319$	−0.803336	−0.0449782
$320$	−7.40256	−0.413816
$321$	−56.8039	−3.17048
$322$	40.7380	2.27024
$323$	−7.11340	−0.395800
$324$	146.484	8.13800
$325$	5.63879	0.312784
$326$	−54.9442	−3.04308
$327$	−3.31359	−0.183242
$328$	−17.5149	−0.967098
$329$	−17.8710	−0.985259
$330$	−23.7968	−1.30997
$331$	11.6242	0.638926	0.319463	−	0.947599i	$-0.396497\pi$
$331$	11.6242	0.638926	0.319463	+	0.947599i	$0.396497\pi$
$332$	−49.9894	−2.74353
$333$	−7.97988	−0.437295
$334$	14.5603	0.796703
$335$	2.65924	0.145290
$336$	61.2872	3.34349
$337$	1.15699	0.0630252	0.0315126	−	0.999503i	$-0.489968\pi$
$337$	1.15699	0.0630252	0.0315126	+	0.999503i	$0.489968\pi$
$338$	27.5322	1.49755
$339$	28.9921	1.57463
$340$	28.7284	1.55801
$341$	12.4634	0.674930
$342$	−28.6819	−1.55094
$343$	−20.0288	−1.08145
$344$	84.4749	4.55458
$345$	30.1611	1.62382
$346$	34.9864	1.88088
$347$	−3.98509	−0.213931	−0.106966	−	0.994263i	$-0.534113\pi$
$347$	−3.98509	−0.213931	−0.106966	+	0.994263i	$0.534113\pi$
$348$	5.38049	0.288424
$349$	31.2330	1.67186	0.835932	−	0.548833i	$-0.184928\pi$
$349$	31.2330	1.67186	0.835932	+	0.548833i	$0.184928\pi$
$350$	19.0184	1.01658
$351$	−25.6432	−1.36873
$352$	22.3688	1.19226
$353$	−19.8095	−1.05436	−0.527178	−	0.849755i	$-0.676750\pi$
$353$	−19.8095	−1.05436	−0.527178	+	0.849755i	$0.676750\pi$
$354$	−22.8662	−1.21533
$355$	1.78193	0.0945753
$356$	45.2611	2.39883
$357$	−34.3724	−1.81918
$358$	−31.4104	−1.66009
$359$	22.2377	1.17366	0.586830	−	0.809710i	$-0.300376\pi$
$359$	22.2377	1.17366	0.586830	+	0.809710i	$0.300376\pi$
$360$	67.2206	3.54284
$361$	−17.0905	−0.899498
$362$	−47.7215	−2.50819
$363$	−18.0310	−0.946382
$364$	−14.9230	−0.782176
$365$	−15.3834	−0.805205
$366$	−42.2357	−2.20770
$367$	−36.7255	−1.91706	−0.958529	−	0.284996i	$-0.908008\pi$
$367$	−36.7255	−1.91706	−0.958529	+	0.284996i	$0.908008\pi$
$368$	−71.3395	−3.71883
$369$	19.4308	1.01153
$370$	−3.04608	−0.158358
$371$	−25.0056	−1.29823
$372$	−83.4758	−4.32802
$373$	6.15603	0.318747	0.159374	−	0.987218i	$-0.449053\pi$
$373$	6.15603	0.318747	0.159374	+	0.987218i	$0.449053\pi$
$374$	−31.5675	−1.63232
$375$	33.4833	1.72907
$376$	63.7918	3.28981
$377$	−0.529511	−0.0272712
$378$	−86.4892	−4.44852
$379$	−20.8972	−1.07341	−0.536707	−	0.843768i	$-0.680332\pi$
$379$	−20.8972	−1.07341	−0.536707	+	0.843768i	$0.680332\pi$
$380$	−7.71188	−0.395611
$381$	34.4416	1.76450
$382$	16.4575	0.842039
$383$	4.65311	0.237763	0.118881	−	0.992908i	$-0.462069\pi$
$383$	4.65311	0.237763	0.118881	+	0.992908i	$0.462069\pi$
$384$	8.39746	0.428531
$385$	5.56375	0.283555
$386$	−30.5048	−1.55265
$387$	−93.7154	−4.76382
$388$	0.973377	0.0494157
$389$	−5.22504	−0.264920	−0.132460	−	0.991188i	$-0.542288\pi$
$389$	−5.22504	−0.264920	−0.132460	+	0.991188i	$0.542288\pi$
$390$	−15.6854	−0.794261
$391$	40.0101	2.02340
$392$	21.1431	1.06789
$393$	23.8403	1.20259
$394$	−35.5211	−1.78953
$395$	−6.34785	−0.319395
$396$	−89.6556	−4.50536
$397$	−2.91895	−0.146498	−0.0732490	−	0.997314i	$-0.523337\pi$
$397$	−2.91895	−0.146498	−0.0732490	+	0.997314i	$0.523337\pi$
$398$	68.2074	3.41893
$399$	9.22695	0.461926
$400$	−33.3047	−1.66524
$401$	−20.5757	−1.02750	−0.513751	−	0.857939i	$-0.671745\pi$
$401$	−20.5757	−1.02750	−0.513751	+	0.857939i	$0.671745\pi$
$402$	19.5709	0.976107
$403$	8.21512	0.409224
$404$	33.7397	1.67861
$405$	−35.9981	−1.78876
$406$	−1.78593	−0.0886341
$407$	2.35764	0.116864
$408$	122.695	6.07429
$409$	6.93499	0.342913	0.171457	−	0.985192i	$-0.445153\pi$
$409$	6.93499	0.342913	0.171457	+	0.985192i	$0.445153\pi$
$410$	7.41713	0.366306
$411$	−12.8292	−0.632817
$412$	−61.7301	−3.04123
$413$	5.34618	0.263068
$414$	161.324	7.92865
$415$	12.2848	0.603037
$416$	14.7442	0.722893
$417$	14.9974	0.734426
$418$	8.47401	0.414478
$419$	−25.9334	−1.26693	−0.633464	−	0.773772i	$-0.718367\pi$
$419$	−25.9334	−1.26693	−0.633464	+	0.773772i	$0.718367\pi$
$420$	−37.2642	−1.81831
$421$	−10.8959	−0.531033	−0.265516	−	0.964106i	$-0.585542\pi$
$421$	−10.8959	−0.531033	−0.265516	+	0.964106i	$0.585542\pi$
$422$	71.5311	3.48208
$423$	−70.7698	−3.44095
$424$	89.2594	4.33482
$425$	18.6786	0.906046
$426$	13.1143	0.635390
$427$	9.87483	0.477876
$428$	−81.6926	−3.94876
$429$	12.1404	0.586143
$430$	−35.7731	−1.72513
$431$	4.17511	0.201108	0.100554	−	0.994932i	$-0.467938\pi$
$431$	4.17511	0.201108	0.100554	+	0.994932i	$0.467938\pi$
$432$	151.458	7.28703
$433$	−10.3484	−0.497311	−0.248656	−	0.968592i	$-0.579989\pi$
$433$	−10.3484	−0.497311	−0.248656	+	0.968592i	$0.579989\pi$
$434$	27.7079	1.33002
$435$	−1.32224	−0.0633967
$436$	−4.76544	−0.228223
$437$	−10.7403	−0.513781
$438$	−113.216	−5.40965
$439$	4.36848	0.208496	0.104248	−	0.994551i	$-0.466756\pi$
$439$	4.36848	0.208496	0.104248	+	0.994551i	$0.466756\pi$
$440$	−19.8602	−0.946799
$441$	−23.4559	−1.11695
$442$	−20.8074	−0.989707
$443$	29.3371	1.39385	0.696924	−	0.717145i	$-0.254551\pi$
$443$	29.3371	1.39385	0.696924	+	0.717145i	$0.254551\pi$
$444$	−15.7907	−0.749395
$445$	−11.1228	−0.527273
$446$	2.91553	0.138055
$447$	−63.8432	−3.01968
$448$	12.7375	0.601792
$449$	−20.4087	−0.963147	−0.481573	−	0.876406i	$-0.659934\pi$
$449$	−20.4087	−0.963147	−0.481573	+	0.876406i	$0.659934\pi$
$450$	75.3139	3.55033
$451$	−5.74080	−0.270324
$452$	41.6950	1.96117
$453$	39.3094	1.84691
$454$	20.4389	0.959244
$455$	3.66729	0.171925
$456$	−32.9363	−1.54238
$457$	35.4834	1.65985	0.829923	−	0.557878i	$-0.188384\pi$
$457$	35.4834	1.65985	0.829923	+	0.557878i	$0.188384\pi$
$458$	2.68137	0.125292
$459$	−84.9438	−3.96483
$460$	43.3762	2.02243
$461$	−21.2896	−0.991555	−0.495777	−	0.868450i	$-0.665117\pi$
$461$	−21.2896	−0.991555	−0.495777	+	0.868450i	$0.665117\pi$
$462$	40.9469	1.90502
$463$	−35.3079	−1.64090	−0.820449	−	0.571720i	$-0.806276\pi$
$463$	−35.3079	−1.64090	−0.820449	+	0.571720i	$0.806276\pi$
$464$	3.12748	0.145190
$465$	20.5140	0.951314
$466$	−51.9913	−2.40845
$467$	−7.82770	−0.362223	−0.181111	−	0.983463i	$-0.557969\pi$
$467$	−7.82770	−0.362223	−0.181111	+	0.983463i	$0.557969\pi$
$468$	−59.0956	−2.73169
$469$	−4.57572	−0.211287
$470$	−27.0143	−1.24608
$471$	3.22330	0.148522
$472$	−19.0836	−0.878394
$473$	27.6880	1.27310
$474$	−46.7176	−2.14581
$475$	−5.01411	−0.230063
$476$	−49.4327	−2.26574
$477$	−99.0233	−4.53396
$478$	−47.6359	−2.17881
$479$	8.66092	0.395728	0.197864	−	0.980230i	$-0.436600\pi$
$479$	8.66092	0.395728	0.197864	+	0.980230i	$0.436600\pi$
$480$	36.8177	1.68049
$481$	1.55402	0.0708570
$482$	−75.5531	−3.44135
$483$	−51.8979	−2.36144
$484$	−25.9313	−1.17870
$485$	−0.239205	−0.0108618
$486$	−136.170	−6.17679
$487$	−10.5472	−0.477939	−0.238970	−	0.971027i	$-0.576810\pi$
$487$	−10.5472	−0.477939	−0.238970	+	0.971027i	$0.576810\pi$
$488$	−35.2490	−1.59565
$489$	69.9959	3.16532
$490$	−8.95358	−0.404481
$491$	26.1954	1.18218	0.591091	−	0.806605i	$-0.298697\pi$
$491$	26.1954	1.18218	0.591091	+	0.806605i	$0.298697\pi$
$492$	38.4500	1.73346
$493$	−1.75402	−0.0789969
$494$	5.58556	0.251306
$495$	22.0327	0.990295
$496$	−48.5214	−2.17868
$497$	−3.06616	−0.137536
$498$	90.4111	4.05142
$499$	9.86402	0.441574	0.220787	−	0.975322i	$-0.429137\pi$
$499$	9.86402	0.441574	0.220787	+	0.975322i	$0.429137\pi$
$500$	48.1541	2.15352
$501$	−18.5490	−0.828708
$502$	−46.5517	−2.07770
$503$	−28.1812	−1.25654	−0.628269	−	0.777996i	$-0.716236\pi$
$503$	−28.1812	−1.25654	−0.628269	+	0.777996i	$0.716236\pi$
$504$	−115.666	−5.15217
$505$	−8.29145	−0.368965
$506$	−47.6629	−2.11888
$507$	−35.0745	−1.55771
$508$	49.5323	2.19764
$509$	−34.2811	−1.51949	−0.759743	−	0.650224i	$-0.774675\pi$
$509$	−34.2811	−1.51949	−0.759743	+	0.650224i	$0.774675\pi$
$510$	−51.9582	−2.30075
$511$	26.4701	1.17097
$512$	44.9595	1.98695
$513$	22.8024	1.00675
$514$	−51.6556	−2.27843
$515$	15.1701	0.668472
$516$	−185.446	−8.16379
$517$	20.9088	0.919569
$518$	5.24137	0.230292
$519$	−44.5707	−1.95644
$520$	−13.0907	−0.574064
$521$	−3.03895	−0.133139	−0.0665694	−	0.997782i	$-0.521205\pi$
$521$	−3.03895	−0.133139	−0.0665694	+	0.997782i	$0.521205\pi$
$522$	−7.07235	−0.309548
$523$	−3.06818	−0.134162	−0.0670812	−	0.997748i	$-0.521369\pi$
$523$	−3.06818	−0.134162	−0.0670812	+	0.997748i	$0.521369\pi$
$524$	34.2860	1.49779
$525$	−24.2285	−1.05742
$526$	40.6665	1.77314
$527$	27.2128	1.18541
$528$	−71.7053	−3.12057
$529$	37.4102	1.62653
$530$	−37.7992	−1.64189
$531$	21.1711	0.918747
$532$	13.2698	0.575317
$533$	−3.78399	−0.163903
$534$	−81.8594	−3.54240
$535$	20.0758	0.867952
$536$	16.3334	0.705495
$537$	40.0151	1.72678
$538$	−38.8565	−1.67522
$539$	6.92999	0.298496
$540$	−92.0903	−3.96294
$541$	−30.9230	−1.32949	−0.664743	−	0.747072i	$-0.731459\pi$
$541$	−30.9230	−1.32949	−0.664743	+	0.747072i	$0.731459\pi$
$542$	−15.4117	−0.661987
$543$	60.7946	2.60895
$544$	48.8404	2.09401
$545$	1.17110	0.0501643
$546$	26.9897	1.15505
$547$	−15.2506	−0.652068	−0.326034	−	0.945358i	$-0.605712\pi$
$547$	−15.2506	−0.652068	−0.326034	+	0.945358i	$0.605712\pi$
$548$	−18.4503	−0.788158
$549$	39.1047	1.66895
$550$	−22.2514	−0.948801
$551$	0.470850	0.0200589
$552$	185.254	7.88492
$553$	10.9227	0.464480
$554$	12.8712	0.546847
$555$	3.88054	0.164720
$556$	21.5685	0.914710
$557$	−11.3654	−0.481568	−0.240784	−	0.970579i	$-0.577405\pi$
$557$	−11.3654	−0.481568	−0.240784	+	0.970579i	$0.577405\pi$
$558$	109.724	4.64500
$559$	18.2503	0.771906
$560$	−21.6603	−0.915315
$561$	40.2152	1.69789
$562$	−33.9355	−1.43148
$563$	29.6159	1.24816	0.624081	−	0.781359i	$-0.285473\pi$
$563$	29.6159	1.24816	0.624081	+	0.781359i	$0.285473\pi$
$564$	−140.041	−5.89677
$565$	−10.2465	−0.431072
$566$	−16.1573	−0.679141
$567$	61.9417	2.60131
$568$	10.9449	0.459237
$569$	1.60709	0.0673729	0.0336864	−	0.999432i	$-0.489275\pi$
$569$	1.60709	0.0673729	0.0336864	+	0.999432i	$0.489275\pi$
$570$	13.9477	0.584206
$571$	3.23101	0.135213	0.0676067	−	0.997712i	$-0.478464\pi$
$571$	3.23101	0.135213	0.0676067	+	0.997712i	$0.478464\pi$
$572$	17.4597	0.730026
$573$	−20.9659	−0.875865
$574$	−12.7626	−0.532701
$575$	28.2024	1.17612
$576$	50.4411	2.10171
$577$	−21.1213	−0.879293	−0.439646	−	0.898171i	$-0.644896\pi$
$577$	−21.1213	−0.879293	−0.439646	+	0.898171i	$0.644896\pi$
$578$	−24.7072	−1.02768
$579$	38.8614	1.61502
$580$	−1.90159	−0.0789591
$581$	−21.1384	−0.876967
$582$	−1.76045	−0.0729731
$583$	29.2563	1.21167
$584$	−94.4871	−3.90990
$585$	14.5226	0.600436
$586$	−46.9603	−1.93991
$587$	−10.6658	−0.440224	−0.220112	−	0.975475i	$-0.570642\pi$
$587$	−10.6658	−0.440224	−0.220112	+	0.975475i	$0.570642\pi$
$588$	−46.4149	−1.91412
$589$	−7.30502	−0.300998
$590$	8.08144	0.332708
$591$	45.2520	1.86142
$592$	−9.17857	−0.377237
$593$	−5.11354	−0.209988	−0.104994	−	0.994473i	$-0.533482\pi$
$593$	−5.11354	−0.209988	−0.104994	+	0.994473i	$0.533482\pi$
$594$	101.191	4.15193
$595$	12.1480	0.498018
$596$	−91.8162	−3.76094
$597$	−86.8925	−3.55627
$598$	−31.4166	−1.28472
$599$	−13.1369	−0.536760	−0.268380	−	0.963313i	$-0.586488\pi$
$599$	−13.1369	−0.536760	−0.268380	+	0.963313i	$0.586488\pi$
$600$	86.4853	3.53075
$601$	10.9783	0.447813	0.223907	−	0.974611i	$-0.428119\pi$
$601$	10.9783	0.447813	0.223907	+	0.974611i	$0.428119\pi$
$602$	61.5544	2.50877
$603$	−18.1201	−0.737906
$604$	56.5328	2.30029
$605$	6.37256	0.259082
$606$	−61.0217	−2.47884
$607$	21.1662	0.859108	0.429554	−	0.903041i	$-0.358671\pi$
$607$	21.1662	0.859108	0.429554	+	0.903041i	$0.358671\pi$
$608$	−13.1108	−0.531712
$609$	2.27517	0.0921947
$610$	14.9271	0.604380
$611$	13.7818	0.557554
$612$	−195.755	−7.91294
$613$	−20.7641	−0.838656	−0.419328	−	0.907835i	$-0.637734\pi$
$613$	−20.7641	−0.838656	−0.419328	+	0.907835i	$0.637734\pi$
$614$	50.5951	2.04185
$615$	−9.44902	−0.381021
$616$	34.1733	1.37688
$617$	0.876748	0.0352966	0.0176483	−	0.999844i	$-0.494382\pi$
$617$	0.876748	0.0352966	0.0176483	+	0.999844i	$0.494382\pi$
$618$	111.645	4.49104
$619$	−15.0009	−0.602936	−0.301468	−	0.953476i	$-0.597477\pi$
$619$	−15.0009	−0.602936	−0.301468	+	0.953476i	$0.597477\pi$
$620$	29.5022	1.18484
$621$	−128.254	−5.14667
$622$	29.2575	1.17312
$623$	19.1390	0.766786
$624$	−47.2639	−1.89207
$625$	6.30887	0.252355
$626$	−15.2749	−0.610508
$627$	−10.7954	−0.431128
$628$	4.63560	0.184981
$629$	5.14771	0.205253
$630$	48.9817	1.95148
$631$	−25.4666	−1.01381	−0.506905	−	0.862002i	$-0.669210\pi$
$631$	−25.4666	−1.01381	−0.506905	+	0.862002i	$0.669210\pi$
$632$	−38.9894	−1.55092
$633$	−91.1267	−3.62196
$634$	−88.2114	−3.50332
$635$	−12.1725	−0.483049
$636$	−195.949	−7.76989
$637$	4.56784	0.180984
$638$	2.08951	0.0827247
$639$	−12.1421	−0.480335
$640$	−2.96785	−0.117315
$641$	−39.2307	−1.54952	−0.774760	−	0.632256i	$-0.782129\pi$
$641$	−39.2307	−1.54952	−0.774760	+	0.632256i	$0.782129\pi$
$642$	147.750	5.83121
$643$	22.5283	0.888431	0.444216	−	0.895920i	$-0.353482\pi$
$643$	22.5283	0.888431	0.444216	+	0.895920i	$0.353482\pi$
$644$	−74.6371	−2.94111
$645$	45.5729	1.79443
$646$	18.5023	0.727963
$647$	4.50467	0.177097	0.0885485	−	0.996072i	$-0.471777\pi$
$647$	4.50467	0.177097	0.0885485	+	0.996072i	$0.471777\pi$
$648$	−221.106	−8.68585
$649$	−6.25497	−0.245529
$650$	−14.6668	−0.575278
$651$	−35.2983	−1.38345
$652$	100.665	3.94233
$653$	−11.4086	−0.446454	−0.223227	−	0.974766i	$-0.571659\pi$
$653$	−11.4086	−0.446454	−0.223227	+	0.974766i	$0.571659\pi$
$654$	8.61880	0.337022
$655$	−8.42572	−0.329220
$656$	22.3496	0.872605
$657$	104.823	4.08953
$658$	46.4832	1.81210
$659$	−36.7225	−1.43051	−0.715253	−	0.698865i	$-0.753689\pi$
$659$	−36.7225	−1.43051	−0.715253	+	0.698865i	$0.753689\pi$
$660$	43.5987	1.69708
$661$	−44.5905	−1.73437	−0.867184	−	0.497987i	$-0.834073\pi$
$661$	−44.5905	−1.73437	−0.867184	+	0.497987i	$0.834073\pi$
$662$	−30.2352	−1.17512
$663$	26.5075	1.02947
$664$	75.4550	2.92822
$665$	−3.26102	−0.126457
$666$	20.7560	0.804280
$667$	−2.64834	−0.102544
$668$	−26.6763	−1.03214
$669$	−3.71423	−0.143600
$670$	−6.91680	−0.267219
$671$	−11.5534	−0.446015
$672$	−63.3520	−2.44385
$673$	−38.8733	−1.49846	−0.749228	−	0.662312i	$-0.769576\pi$
$673$	−38.8733	−1.49846	−0.749228	+	0.662312i	$0.769576\pi$
$674$	−3.00938	−0.115917
$675$	−59.8753	−2.30460
$676$	−50.4424	−1.94009
$677$	46.0772	1.77089	0.885446	−	0.464742i	$-0.153853\pi$
$677$	46.0772	1.77089	0.885446	+	0.464742i	$0.153853\pi$
$678$	−75.4098	−2.89609
$679$	0.411599	0.0157957
$680$	−43.3631	−1.66290
$681$	−26.0380	−0.997778
$682$	−32.4178	−1.24134
$683$	−22.8501	−0.874336	−0.437168	−	0.899380i	$-0.644018\pi$
$683$	−22.8501	−0.874336	−0.437168	+	0.899380i	$0.644018\pi$
$684$	52.5488	2.00925
$685$	4.53413	0.173240
$686$	52.0959	1.98903
$687$	−3.41592	−0.130326
$688$	−107.793	−4.10956
$689$	19.2840	0.734661
$690$	−78.4504	−2.98656
$691$	−1.11427	−0.0423887	−0.0211944	−	0.999775i	$-0.506747\pi$
$691$	−1.11427	−0.0423887	−0.0211944	+	0.999775i	$0.506747\pi$
$692$	−64.0994	−2.43669
$693$	−37.9114	−1.44014
$694$	10.3654	0.393466
$695$	−5.30043	−0.201057
$696$	−8.12141	−0.307841
$697$	−12.5346	−0.474780
$698$	−81.2385	−3.07492
$699$	66.2340	2.50520
$700$	−34.8442	−1.31699
$701$	−29.7925	−1.12525	−0.562624	−	0.826713i	$-0.690208\pi$
$701$	−29.7925	−1.12525	−0.562624	+	0.826713i	$0.690208\pi$
$702$	66.6992	2.51740
$703$	−1.38186	−0.0521177
$704$	−14.9028	−0.561669
$705$	34.4147	1.29613
$706$	51.5256	1.93919
$707$	14.2670	0.536567
$708$	41.8938	1.57446
$709$	−2.06602	−0.0775908	−0.0387954	−	0.999247i	$-0.512352\pi$
$709$	−2.06602	−0.0775908	−0.0387954	+	0.999247i	$0.512352\pi$
$710$	−4.63489	−0.173945
$711$	43.2544	1.62217
$712$	−68.3180	−2.56032
$713$	41.0878	1.53875
$714$	89.4041	3.34586
$715$	−4.29068	−0.160462
$716$	57.5478	2.15066
$717$	60.6855	2.26634
$718$	−57.8412	−2.15861
$719$	−20.1793	−0.752561	−0.376281	−	0.926506i	$-0.622797\pi$
$719$	−20.1793	−0.752561	−0.376281	+	0.926506i	$0.622797\pi$
$720$	−85.7757	−3.19667
$721$	−26.1030	−0.972126
$722$	44.4531	1.65437
$723$	96.2505	3.57959
$724$	87.4319	3.24938
$725$	−1.23637	−0.0459178
$726$	46.8995	1.74060
$727$	0.633812	0.0235068	0.0117534	−	0.999931i	$-0.496259\pi$
$727$	0.633812	0.0235068	0.0117534	+	0.999931i	$0.496259\pi$
$728$	22.5250	0.834832
$729$	81.2565	3.00950
$730$	40.0130	1.48095
$731$	60.4545	2.23599
$732$	77.3812	2.86009
$733$	−1.78868	−0.0660664	−0.0330332	−	0.999454i	$-0.510517\pi$
$733$	−1.78868	−0.0660664	−0.0330332	+	0.999454i	$0.510517\pi$
$734$	95.5248	3.52589
$735$	11.4064	0.420730
$736$	73.7429	2.71820
$737$	5.35354	0.197200
$738$	−50.5404	−1.86042
$739$	−8.68464	−0.319470	−0.159735	−	0.987160i	$-0.551064\pi$
$739$	−8.68464	−0.319470	−0.159735	+	0.987160i	$0.551064\pi$
$740$	5.58080	0.205154
$741$	−7.11570	−0.261402
$742$	65.0408	2.38772
$743$	14.1827	0.520314	0.260157	−	0.965566i	$-0.416226\pi$
$743$	14.1827	0.520314	0.260157	+	0.965566i	$0.416226\pi$
$744$	126.000	4.61938
$745$	22.5636	0.826668
$746$	−16.0121	−0.586246
$747$	−83.7088	−3.06274
$748$	57.8356	2.11468
$749$	−34.5442	−1.26222
$750$	−87.0917	−3.18014
$751$	18.0447	0.658461	0.329230	−	0.944250i	$-0.393211\pi$
$751$	18.0447	0.658461	0.329230	+	0.944250i	$0.393211\pi$
$752$	−81.4004	−2.96837
$753$	59.3043	2.16117
$754$	1.37728	0.0501577
$755$	−13.8928	−0.505612
$756$	158.459	5.76310
$757$	−23.2227	−0.844042	−0.422021	−	0.906586i	$-0.638679\pi$
$757$	−23.2227	−0.844042	−0.422021	+	0.906586i	$0.638679\pi$
$758$	54.3545	1.97424
$759$	60.7200	2.20399
$760$	11.6404	0.422243
$761$	−4.21127	−0.152658	−0.0763292	−	0.997083i	$-0.524320\pi$
$761$	−4.21127	−0.152658	−0.0763292	+	0.997083i	$0.524320\pi$
$762$	−89.5843	−3.24530
$763$	−2.01510	−0.0729515
$764$	−30.1522	−1.09087
$765$	48.1065	1.73929
$766$	−12.1029	−0.437297
$767$	−4.12290	−0.148869
$768$	−63.7329	−2.29976
$769$	−31.8961	−1.15020	−0.575101	−	0.818083i	$-0.695037\pi$
$769$	−31.8961	−1.15020	−0.575101	+	0.818083i	$0.695037\pi$
$770$	−14.4716	−0.521519
$771$	65.8064	2.36996
$772$	55.8886	2.01147
$773$	−36.7766	−1.32276	−0.661382	−	0.750050i	$-0.730030\pi$
$773$	−36.7766	−1.32276	−0.661382	+	0.750050i	$0.730030\pi$
$774$	243.758	8.76170
$775$	19.1818	0.689030
$776$	−1.46923	−0.0527424
$777$	−6.67721	−0.239544
$778$	13.5906	0.487245
$779$	3.36479	0.120556
$780$	28.7376	1.02897
$781$	3.58737	0.128366
$782$	−104.068	−3.72147
$783$	5.62259	0.200935
$784$	−26.9793	−0.963545
$785$	−1.13919	−0.0406594
$786$	−62.0098	−2.21182
$787$	17.4528	0.622126	0.311063	−	0.950389i	$-0.399315\pi$
$787$	17.4528	0.622126	0.311063	+	0.950389i	$0.399315\pi$
$788$	65.0792	2.31835
$789$	−51.8069	−1.84437
$790$	16.5111	0.587437
$791$	17.6310	0.626886
$792$	135.328	4.80866
$793$	−7.61533	−0.270428
$794$	7.59233	0.269442
$795$	48.1541	1.70785
$796$	−124.965	−4.42925
$797$	20.3278	0.720049	0.360024	−	0.932943i	$-0.382768\pi$
$797$	20.3278	0.720049	0.360024	+	0.932943i	$0.382768\pi$
$798$	−23.9997	−0.849582
$799$	45.6526	1.61507
$800$	34.4267	1.21717
$801$	75.7911	2.67795
$802$	53.5184	1.88980
$803$	−30.9697	−1.09290
$804$	−35.8563	−1.26455
$805$	18.3419	0.646468
$806$	−21.3679	−0.752652
$807$	49.5010	1.74252
$808$	−50.9273	−1.79162
$809$	−24.8228	−0.872722	−0.436361	−	0.899772i	$-0.643733\pi$
$809$	−24.8228	−0.872722	−0.436361	+	0.899772i	$0.643733\pi$
$810$	93.6329	3.28992
$811$	37.3397	1.31118	0.655588	−	0.755119i	$-0.272421\pi$
$811$	37.3397	1.31118	0.655588	+	0.755119i	$0.272421\pi$
$812$	3.27204	0.114826
$813$	19.6336	0.688580
$814$	−6.13233	−0.214938
$815$	−24.7381	−0.866539
$816$	−156.563	−5.48079
$817$	−16.2285	−0.567763
$818$	−18.0382	−0.630692
$819$	−24.9890	−0.873185
$820$	−13.5891	−0.474553
$821$	3.33407	0.116360	0.0581800	−	0.998306i	$-0.481470\pi$
$821$	3.33407	0.116360	0.0581800	+	0.998306i	$0.481470\pi$
$822$	33.3693	1.16389
$823$	−5.27587	−0.183905	−0.0919526	−	0.995763i	$-0.529311\pi$
$823$	−5.27587	−0.183905	−0.0919526	+	0.995763i	$0.529311\pi$
$824$	93.1766	3.24596
$825$	28.3470	0.986916
$826$	−13.9057	−0.483840
$827$	−12.0864	−0.420285	−0.210143	−	0.977671i	$-0.567393\pi$
$827$	−12.0864	−0.420285	−0.210143	+	0.977671i	$0.567393\pi$
$828$	−295.566	−10.2716
$829$	−8.73730	−0.303459	−0.151730	−	0.988422i	$-0.548484\pi$
$829$	−8.73730	−0.303459	−0.151730	+	0.988422i	$0.548484\pi$
$830$	−31.9533	−1.10912
$831$	−16.3973	−0.568815
$832$	−9.82300	−0.340551
$833$	15.1311	0.524260
$834$	−39.0090	−1.35077
$835$	6.55564	0.226867
$836$	−15.5255	−0.536959
$837$	−87.2320	−3.01518
$838$	67.4539	2.33016
$839$	12.3880	0.427682	0.213841	−	0.976868i	$-0.431402\pi$
$839$	12.3880	0.427682	0.213841	+	0.976868i	$0.431402\pi$
$840$	56.2473	1.94072
$841$	−28.8839	−0.995996
$842$	28.3407	0.976685
$843$	43.2319	1.48899
$844$	−131.054	−4.51106
$845$	12.3961	0.426439
$846$	184.076	6.32865
$847$	−10.9652	−0.376769
$848$	−113.898	−3.91127
$849$	20.5835	0.706423
$850$	−48.5840	−1.66642
$851$	7.77240	0.266434
$852$	−24.0271	−0.823153
$853$	−16.6881	−0.571390	−0.285695	−	0.958321i	$-0.592225\pi$
$853$	−16.6881	−0.571390	−0.285695	+	0.958321i	$0.592225\pi$
$854$	−25.6849	−0.878919
$855$	−12.9138	−0.441641
$856$	123.308	4.21459
$857$	−13.1614	−0.449586	−0.224793	−	0.974407i	$-0.572171\pi$
$857$	−13.1614	−0.449586	−0.224793	+	0.974407i	$0.572171\pi$
$858$	−31.5777	−1.07804
$859$	−13.3957	−0.457054	−0.228527	−	0.973538i	$-0.573391\pi$
$859$	−13.3957	−0.457054	−0.228527	+	0.973538i	$0.573391\pi$
$860$	65.5407	2.23492
$861$	16.2588	0.554100
$862$	−10.8597	−0.369882
$863$	1.35740	0.0462066	0.0231033	−	0.999733i	$-0.492645\pi$
$863$	1.35740	0.0462066	0.0231033	+	0.999733i	$0.492645\pi$
$864$	−156.561	−5.32630
$865$	15.7523	0.535594
$866$	26.9166	0.914664
$867$	31.4756	1.06897
$868$	−50.7643	−1.72305
$869$	−12.7794	−0.433512
$870$	3.43922	0.116600
$871$	3.52873	0.119567
$872$	7.19305	0.243587
$873$	1.62995	0.0551654
$874$	27.9361	0.944954
$875$	20.3623	0.688371
$876$	207.425	7.00825
$877$	−18.2859	−0.617472	−0.308736	−	0.951148i	$-0.599906\pi$
$877$	−18.2859	−0.617472	−0.308736	+	0.951148i	$0.599906\pi$
$878$	−11.3626	−0.383470
$879$	59.8248	2.01784
$880$	25.3423	0.854289
$881$	29.2080	0.984041	0.492020	−	0.870584i	$-0.336259\pi$
$881$	29.2080	0.984041	0.492020	+	0.870584i	$0.336259\pi$
$882$	61.0098	2.05431
$883$	−3.73447	−0.125675	−0.0628375	−	0.998024i	$-0.520015\pi$
$883$	−3.73447	−0.125675	−0.0628375	+	0.998024i	$0.520015\pi$
$884$	38.1218	1.28217
$885$	−10.2953	−0.346073
$886$	−76.3072	−2.56359
$887$	−13.9402	−0.468065	−0.234032	−	0.972229i	$-0.575192\pi$
$887$	−13.9402	−0.468065	−0.234032	+	0.972229i	$0.575192\pi$
$888$	23.8348	0.799844
$889$	20.9450	0.702474
$890$	28.9310	0.969769
$891$	−72.4710	−2.42787
$892$	−5.34162	−0.178851
$893$	−12.2551	−0.410100
$894$	166.059	5.55385
$895$	−14.1423	−0.472724
$896$	5.10676	0.170605
$897$	40.0230	1.33633
$898$	53.0840	1.77144
$899$	−1.80127	−0.0600756
$900$	−137.984	−4.59948
$901$	63.8786	2.12810
$902$	14.9321	0.497184
$903$	−78.4169	−2.60955
$904$	−62.9352	−2.09319
$905$	−21.4862	−0.714225
$906$	−102.245	−3.39688
$907$	23.5667	0.782520	0.391260	−	0.920280i	$-0.372039\pi$
$907$	23.5667	0.782520	0.391260	+	0.920280i	$0.372039\pi$
$908$	−37.4466	−1.24271
$909$	56.4981	1.87392
$910$	−9.53879	−0.316208
$911$	−41.9131	−1.38864	−0.694322	−	0.719665i	$-0.744295\pi$
$911$	−41.9131	−1.38864	−0.694322	+	0.719665i	$0.744295\pi$
$912$	42.0278	1.39168
$913$	24.7316	0.818497
$914$	−92.2941	−3.05282
$915$	−19.0163	−0.628658
$916$	−4.91261	−0.162317
$917$	14.4981	0.478768
$918$	220.943	7.29219
$919$	12.4132	0.409472	0.204736	−	0.978817i	$-0.434366\pi$
$919$	12.4132	0.409472	0.204736	+	0.978817i	$0.434366\pi$
$920$	−65.4729	−2.15858
$921$	−64.4553	−2.12388
$922$	55.3752	1.82369
$923$	2.36458	0.0778311
$924$	−75.0198	−2.46797
$925$	3.62853	0.119305
$926$	91.8375	3.01797
$927$	−103.369	−3.39508
$928$	−3.23284	−0.106123
$929$	39.0517	1.28124	0.640622	−	0.767856i	$-0.278677\pi$
$929$	39.0517	1.28124	0.640622	+	0.767856i	$0.278677\pi$
$930$	−53.3579	−1.74967
$931$	−4.06180	−0.133120
$932$	95.2545	3.12016
$933$	−37.2725	−1.22025
$934$	20.3602	0.666206
$935$	−14.2130	−0.464814
$936$	89.2000	2.91559
$937$	−1.48337	−0.0484597	−0.0242299	−	0.999706i	$-0.507713\pi$
$937$	−1.48337	−0.0484597	−0.0242299	+	0.999706i	$0.507713\pi$
$938$	11.9017	0.388603
$939$	19.4594	0.635033
$940$	49.4935	1.61430
$941$	−43.1849	−1.40779	−0.703894	−	0.710305i	$-0.748557\pi$
$941$	−43.1849	−1.40779	−0.703894	+	0.710305i	$0.748557\pi$
$942$	−8.38396	−0.273164
$943$	−18.9256	−0.616302
$944$	24.3513	0.792567
$945$	−38.9410	−1.26675
$946$	−72.0179	−2.34150
$947$	−58.3054	−1.89467	−0.947336	−	0.320242i	$-0.896236\pi$
$947$	−58.3054	−1.89467	−0.947336	+	0.320242i	$0.896236\pi$
$948$	85.5925	2.77992
$949$	−20.4134	−0.662646
$950$	13.0419	0.423136
$951$	112.376	3.64406
$952$	74.6146	2.41827
$953$	9.81020	0.317783	0.158892	−	0.987296i	$-0.449208\pi$
$953$	9.81020	0.317783	0.158892	+	0.987296i	$0.449208\pi$
$954$	257.564	8.33895
$955$	7.40984	0.239777
$956$	87.2749	2.82267
$957$	−2.66193	−0.0860478
$958$	−22.5275	−0.727829
$959$	−7.80184	−0.251934
$960$	−24.5291	−0.791672
$961$	−3.05419	−0.0985224
$962$	−4.04207	−0.130322
$963$	−136.797	−4.40821
$964$	138.423	4.45830
$965$	−13.7345	−0.442129
$966$	134.989	4.34320
$967$	−60.6263	−1.94961	−0.974805	−	0.223059i	$-0.928396\pi$
$967$	−60.6263	−1.94961	−0.974805	+	0.223059i	$0.928396\pi$
$968$	39.1412	1.25805
$969$	−23.5709	−0.757207
$970$	0.622184	0.0199771
$971$	38.4076	1.23256	0.616280	−	0.787527i	$-0.288639\pi$
$971$	38.4076	1.23256	0.616280	+	0.787527i	$0.288639\pi$
$972$	249.480	8.00208
$973$	9.12040	0.292387
$974$	27.4337	0.879034
$975$	18.6846	0.598388
$976$	44.9788	1.43974
$977$	54.7936	1.75300	0.876501	−	0.481400i	$-0.159872\pi$
$977$	54.7936	1.75300	0.876501	+	0.481400i	$0.159872\pi$
$978$	−182.063	−5.82172
$979$	−22.3923	−0.715662
$980$	16.4041	0.524009
$981$	−7.97988	−0.254778
$982$	−68.1355	−2.17429
$983$	60.2024	1.92016	0.960079	−	0.279729i	$-0.0902446\pi$
$983$	60.2024	1.92016	0.960079	+	0.279729i	$0.0902446\pi$
$984$	−58.0372	−1.85016
$985$	−15.9931	−0.509582
$986$	4.56228	0.145293
$987$	−59.2171	−1.88490
$988$	−10.2335	−0.325570
$989$	91.2787	2.90250
$990$	−57.3080	−1.82137
$991$	8.66741	0.275329	0.137665	−	0.990479i	$-0.456040\pi$
$991$	8.66741	0.275329	0.137665	+	0.990479i	$0.456040\pi$
$992$	50.1560	1.59246
$993$	38.5180	1.22233
$994$	7.97522	0.252959
$995$	30.7098	0.973566
$996$	−165.644	−5.24865
$997$	41.6409	1.31878	0.659390	−	0.751801i	$-0.270815\pi$
$997$	41.6409	1.31878	0.659390	+	0.751801i	$0.270815\pi$
$998$	−25.6568	−0.812151
$999$	−16.5013	−0.522077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.7	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.7	✓	79	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)

\(f(q)\)	\(=\)	\(q-2.60105 q^{2} +3.31359 q^{3} +4.76544 q^{4} -1.17110 q^{5} -8.61880 q^{6} +2.01510 q^{7} -7.19305 q^{8} +7.97988 q^{9} +O(q^{10})\)	\(q-2.60105 q^{2} +3.31359 q^{3} +4.76544 q^{4} -1.17110 q^{5} -8.61880 q^{6} +2.01510 q^{7} -7.19305 q^{8} +7.97988 q^{9} +3.04608 q^{10} -2.35764 q^{11} +15.7907 q^{12} -1.55402 q^{13} -5.24137 q^{14} -3.88054 q^{15} +9.17857 q^{16} -5.14771 q^{17} -20.7560 q^{18} +1.38186 q^{19} -5.58080 q^{20} +6.67721 q^{21} +6.13233 q^{22} -7.77240 q^{23} -23.8348 q^{24} -3.62853 q^{25} +4.04207 q^{26} +16.5013 q^{27} +9.60284 q^{28} +0.340737 q^{29} +10.0935 q^{30} -5.28638 q^{31} -9.48779 q^{32} -7.81225 q^{33} +13.3894 q^{34} -2.35988 q^{35} +38.0277 q^{36} -1.00000 q^{37} -3.59428 q^{38} -5.14937 q^{39} +8.42377 q^{40} +2.43498 q^{41} -17.3677 q^{42} -11.7440 q^{43} -11.2352 q^{44} -9.34522 q^{45} +20.2164 q^{46} -8.86853 q^{47} +30.4140 q^{48} -2.93938 q^{49} +9.43797 q^{50} -17.0574 q^{51} -7.40558 q^{52} -12.4091 q^{53} -42.9206 q^{54} +2.76103 q^{55} -14.4947 q^{56} +4.57891 q^{57} -0.886273 q^{58} +2.65306 q^{59} -18.4925 q^{60} +4.90042 q^{61} +13.7501 q^{62} +16.0802 q^{63} +6.32104 q^{64} +1.81991 q^{65} +20.3200 q^{66} -2.27072 q^{67} -24.5311 q^{68} -25.7545 q^{69} +6.13815 q^{70} -1.52159 q^{71} -57.3996 q^{72} +13.1359 q^{73} +2.60105 q^{74} -12.0235 q^{75} +6.58517 q^{76} -4.75088 q^{77} +13.3938 q^{78} +5.42043 q^{79} -10.7490 q^{80} +30.7388 q^{81} -6.33348 q^{82} -10.4900 q^{83} +31.8199 q^{84} +6.02848 q^{85} +30.5466 q^{86} +1.12906 q^{87} +16.9586 q^{88} +9.49778 q^{89} +24.3073 q^{90} -3.13150 q^{91} -37.0389 q^{92} -17.5169 q^{93} +23.0675 q^{94} -1.61829 q^{95} -31.4386 q^{96} +0.204257 q^{97} +7.64546 q^{98} -18.8137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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