LMFDB - Embedded newform 4033.2.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.36112 q^{2} +2.69902 q^{3} +3.57489 q^{4} -1.67448 q^{5} -6.37271 q^{6} +0.928256 q^{7} -3.71850 q^{8} +4.28471 q^{9} +O(q^{10})$	\(q-2.36112 q^{2} +2.69902 q^{3} +3.57489 q^{4} -1.67448 q^{5} -6.37271 q^{6} +0.928256 q^{7} -3.71850 q^{8} +4.28471 q^{9} +3.95366 q^{10} -3.49980 q^{11} +9.64870 q^{12} -0.276549 q^{13} -2.19172 q^{14} -4.51946 q^{15} +1.63005 q^{16} +6.67158 q^{17} -10.1167 q^{18} -0.580059 q^{19} -5.98609 q^{20} +2.50538 q^{21} +8.26344 q^{22} -4.63275 q^{23} -10.0363 q^{24} -2.19611 q^{25} +0.652965 q^{26} +3.46747 q^{27} +3.31841 q^{28} -7.80804 q^{29} +10.6710 q^{30} +7.22903 q^{31} +3.58825 q^{32} -9.44602 q^{33} -15.7524 q^{34} -1.55435 q^{35} +15.3174 q^{36} +1.00000 q^{37} +1.36959 q^{38} -0.746411 q^{39} +6.22657 q^{40} -12.0930 q^{41} -5.91551 q^{42} +4.51509 q^{43} -12.5114 q^{44} -7.17468 q^{45} +10.9385 q^{46} -0.809109 q^{47} +4.39955 q^{48} -6.13834 q^{49} +5.18527 q^{50} +18.0067 q^{51} -0.988631 q^{52} -6.89448 q^{53} -8.18711 q^{54} +5.86035 q^{55} -3.45172 q^{56} -1.56559 q^{57} +18.4357 q^{58} +0.0301235 q^{59} -16.1566 q^{60} -5.72360 q^{61} -17.0686 q^{62} +3.97731 q^{63} -11.7324 q^{64} +0.463076 q^{65} +22.3032 q^{66} +13.5351 q^{67} +23.8502 q^{68} -12.5039 q^{69} +3.67000 q^{70} +2.72934 q^{71} -15.9327 q^{72} -14.5280 q^{73} -2.36112 q^{74} -5.92734 q^{75} -2.07365 q^{76} -3.24871 q^{77} +1.76237 q^{78} -1.73719 q^{79} -2.72950 q^{80} -3.49537 q^{81} +28.5529 q^{82} +11.3102 q^{83} +8.95646 q^{84} -11.1715 q^{85} -10.6607 q^{86} -21.0741 q^{87} +13.0140 q^{88} -8.45946 q^{89} +16.9403 q^{90} -0.256708 q^{91} -16.5616 q^{92} +19.5113 q^{93} +1.91040 q^{94} +0.971299 q^{95} +9.68477 q^{96} +13.4988 q^{97} +14.4934 q^{98} -14.9956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.36112	−1.66956	−0.834782	−	0.550580i	$-0.814406\pi$
$2$	−2.36112	−1.66956	−0.834782	+	0.550580i	$0.814406\pi$
$3$	2.69902	1.55828	0.779140	−	0.626850i	$-0.215656\pi$
$3$	2.69902	1.55828	0.779140	+	0.626850i	$0.215656\pi$
$4$	3.57489	1.78744
$5$	−1.67448	−0.748851	−0.374426	−	0.927257i	$-0.622160\pi$
$5$	−1.67448	−0.748851	−0.374426	+	0.927257i	$0.622160\pi$
$6$	−6.37271	−2.60165
$7$	0.928256	0.350848	0.175424	−	0.984493i	$-0.443870\pi$
$7$	0.928256	0.350848	0.175424	+	0.984493i	$0.443870\pi$
$8$	−3.71850	−1.31469
$9$	4.28471	1.42824
$10$	3.95366	1.25026
$11$	−3.49980	−1.05523	−0.527614	−	0.849484i	$-0.676913\pi$
$11$	−3.49980	−1.05523	−0.527614	+	0.849484i	$0.676913\pi$
$12$	9.64870	2.78534
$13$	−0.276549	−0.0767008	−0.0383504	−	0.999264i	$-0.512210\pi$
$13$	−0.276549	−0.0767008	−0.0383504	+	0.999264i	$0.512210\pi$
$14$	−2.19172	−0.585763
$15$	−4.51946	−1.16692
$16$	1.63005	0.407514
$17$	6.67158	1.61810	0.809048	−	0.587742i	$-0.199983\pi$
$17$	6.67158	1.61810	0.809048	+	0.587742i	$0.199983\pi$
$18$	−10.1167	−2.38453
$19$	−0.580059	−0.133075	−0.0665374	−	0.997784i	$-0.521195\pi$
$19$	−0.580059	−0.133075	−0.0665374	+	0.997784i	$0.521195\pi$
$20$	−5.98609	−1.33853
$21$	2.50538	0.546719
$22$	8.26344	1.76177
$23$	−4.63275	−0.965995	−0.482997	−	0.875622i	$-0.660452\pi$
$23$	−4.63275	−0.965995	−0.482997	+	0.875622i	$0.660452\pi$
$24$	−10.0363	−2.04865
$25$	−2.19611	−0.439222
$26$	0.652965	0.128057
$27$	3.46747	0.667315
$28$	3.31841	0.627121
$29$	−7.80804	−1.44992	−0.724958	−	0.688793i	$-0.758141\pi$
$29$	−7.80804	−1.44992	−0.724958	+	0.688793i	$0.758141\pi$
$30$	10.6710	1.94825
$31$	7.22903	1.29837	0.649186	−	0.760630i	$-0.275110\pi$
$31$	7.22903	1.29837	0.649186	+	0.760630i	$0.275110\pi$
$32$	3.58825	0.634319
$33$	−9.44602	−1.64434
$34$	−15.7524	−2.70152
$35$	−1.55435	−0.262733
$36$	15.3174	2.55290
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	1.36959	0.222177
$39$	−0.746411	−0.119521
$40$	6.22657	0.984507
$41$	−12.0930	−1.88860	−0.944302	−	0.329081i	$-0.893261\pi$
$41$	−12.0930	−1.88860	−0.944302	+	0.329081i	$0.893261\pi$
$42$	−5.91551	−0.912783
$43$	4.51509	0.688545	0.344273	−	0.938870i	$-0.388126\pi$
$43$	4.51509	0.688545	0.344273	+	0.938870i	$0.388126\pi$
$44$	−12.5114	−1.88616
$45$	−7.17468	−1.06954
$46$	10.9385	1.61279
$47$	−0.809109	−0.118021	−0.0590103	−	0.998257i	$-0.518794\pi$
$47$	−0.809109	−0.118021	−0.0590103	+	0.998257i	$0.518794\pi$
$48$	4.39955	0.635020
$49$	−6.13834	−0.876906
$50$	5.18527	0.733308
$51$	18.0067	2.52145
$52$	−0.988631	−0.137098
$53$	−6.89448	−0.947030	−0.473515	−	0.880786i	$-0.657015\pi$
$53$	−6.89448	−0.947030	−0.473515	+	0.880786i	$0.657015\pi$
$54$	−8.18711	−1.11412
$55$	5.86035	0.790209
$56$	−3.45172	−0.461256
$57$	−1.56559	−0.207368
$58$	18.4357	2.42073
$59$	0.0301235	0.00392174	0.00196087	−	0.999998i	$-0.499376\pi$
$59$	0.0301235	0.00392174	0.00196087	+	0.999998i	$0.499376\pi$
$60$	−16.1566	−2.08581
$61$	−5.72360	−0.732832	−0.366416	−	0.930451i	$-0.619415\pi$
$61$	−5.72360	−0.732832	−0.366416	+	0.930451i	$0.619415\pi$
$62$	−17.0686	−2.16771
$63$	3.97731	0.501094
$64$	−11.7324	−1.46655
$65$	0.463076	0.0574375
$66$	22.3032	2.74533
$67$	13.5351	1.65358	0.826790	−	0.562511i	$-0.190165\pi$
$67$	13.5351	1.65358	0.826790	+	0.562511i	$0.190165\pi$
$68$	23.8502	2.89226
$69$	−12.5039	−1.50529
$70$	3.67000	0.438649
$71$	2.72934	0.323913	0.161957	−	0.986798i	$-0.448220\pi$
$71$	2.72934	0.323913	0.161957	+	0.986798i	$0.448220\pi$
$72$	−15.9327	−1.87769
$73$	−14.5280	−1.70037	−0.850186	−	0.526482i	$-0.823511\pi$
$73$	−14.5280	−1.70037	−0.850186	+	0.526482i	$0.823511\pi$
$74$	−2.36112	−0.274475
$75$	−5.92734	−0.684430
$76$	−2.07365	−0.237864
$77$	−3.24871	−0.370224
$78$	1.76237	0.199549
$79$	−1.73719	−0.195449	−0.0977246	−	0.995213i	$-0.531156\pi$
$79$	−1.73719	−0.195449	−0.0977246	+	0.995213i	$0.531156\pi$
$80$	−2.72950	−0.305167
$81$	−3.49537	−0.388375
$82$	28.5529	3.15314
$83$	11.3102	1.24146	0.620730	−	0.784024i	$-0.286836\pi$
$83$	11.3102	1.24146	0.620730	+	0.784024i	$0.286836\pi$
$84$	8.95646	0.977230
$85$	−11.1715	−1.21171
$86$	−10.6607	−1.14957
$87$	−21.0741	−2.25938
$88$	13.0140	1.38730
$89$	−8.45946	−0.896701	−0.448351	−	0.893858i	$-0.647988\pi$
$89$	−8.45946	−0.896701	−0.448351	+	0.893858i	$0.647988\pi$
$90$	16.9403	1.78566
$91$	−0.256708	−0.0269103
$92$	−16.5616	−1.72666
$93$	19.5113	2.02323
$94$	1.91040	0.197043
$95$	0.971299	0.0996532
$96$	9.68477	0.988447
$97$	13.4988	1.37060	0.685298	−	0.728263i	$-0.259672\pi$
$97$	13.4988	1.37060	0.685298	+	0.728263i	$0.259672\pi$
$98$	14.4934	1.46405
$99$	−14.9956	−1.50712
$100$	−7.85084	−0.785084
$101$	−7.04848	−0.701350	−0.350675	−	0.936497i	$-0.614048\pi$
$101$	−7.04848	−0.701350	−0.350675	+	0.936497i	$0.614048\pi$
$102$	−42.5161	−4.20972
$103$	5.65514	0.557217	0.278609	−	0.960405i	$-0.410127\pi$
$103$	5.65514	0.557217	0.278609	+	0.960405i	$0.410127\pi$
$104$	1.02835	0.100838
$105$	−4.19522	−0.409412
$106$	16.2787	1.58113
$107$	15.2608	1.47532	0.737658	−	0.675174i	$-0.235932\pi$
$107$	15.2608	1.47532	0.737658	+	0.675174i	$0.235932\pi$
$108$	12.3958	1.19279
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−13.8370	−1.31930
$111$	2.69902	0.256180
$112$	1.51311	0.142975
$113$	−14.2074	−1.33652	−0.668262	−	0.743926i	$-0.732961\pi$
$113$	−14.2074	−1.33652	−0.668262	+	0.743926i	$0.732961\pi$
$114$	3.69655	0.346214
$115$	7.75746	0.723387
$116$	−27.9129	−2.59164
$117$	−1.18493	−0.109547
$118$	−0.0711252	−0.00654760
$119$	6.19294	0.567706
$120$	16.8056	1.53414
$121$	1.24857	0.113506
$122$	13.5141	1.22351
$123$	−32.6392	−2.94297
$124$	25.8430	2.32077
$125$	12.0498	1.07776
$126$	−9.39091	−0.836609
$127$	−11.0459	−0.980163	−0.490081	−	0.871677i	$-0.663033\pi$
$127$	−11.0459	−0.980163	−0.490081	+	0.871677i	$0.663033\pi$
$128$	20.5251	1.81418
$129$	12.1863	1.07295
$130$	−1.09338	−0.0958956
$131$	−4.08619	−0.357012	−0.178506	−	0.983939i	$-0.557126\pi$
$131$	−4.08619	−0.357012	−0.178506	+	0.983939i	$0.557126\pi$
$132$	−33.7685	−2.93917
$133$	−0.538443	−0.0466890
$134$	−31.9581	−2.76076
$135$	−5.80622	−0.499719
$136$	−24.8083	−2.12729
$137$	−11.6153	−0.992363	−0.496182	−	0.868219i	$-0.665265\pi$
$137$	−11.6153	−0.992363	−0.496182	+	0.868219i	$0.665265\pi$
$138$	29.5232	2.51318
$139$	−14.3414	−1.21642	−0.608210	−	0.793776i	$-0.708112\pi$
$139$	−14.3414	−1.21642	−0.608210	+	0.793776i	$0.708112\pi$
$140$	−5.55662	−0.469620
$141$	−2.18380	−0.183909
$142$	−6.44430	−0.540794
$143$	0.967864	0.0809369
$144$	6.98432	0.582026
$145$	13.0744	1.08577
$146$	34.3023	2.83888
$147$	−16.5675	−1.36647
$148$	3.57489	0.293854
$149$	−8.82460	−0.722939	−0.361470	−	0.932384i	$-0.617725\pi$
$149$	−8.82460	−0.722939	−0.361470	+	0.932384i	$0.617725\pi$
$150$	13.9952	1.14270
$151$	11.5777	0.942180	0.471090	−	0.882085i	$-0.343861\pi$
$151$	11.5777	0.942180	0.471090	+	0.882085i	$0.343861\pi$
$152$	2.15695	0.174952
$153$	28.5858	2.31103
$154$	7.67059	0.618113
$155$	−12.1049	−0.972287
$156$	−2.66834	−0.213638
$157$	−23.5736	−1.88138	−0.940689	−	0.339270i	$-0.889820\pi$
$157$	−23.5736	−1.88138	−0.940689	+	0.339270i	$0.889820\pi$
$158$	4.10171	0.326315
$159$	−18.6083	−1.47574
$160$	−6.00847	−0.475011
$161$	−4.30038	−0.338917
$162$	8.25299	0.648416
$163$	8.00171	0.626742	0.313371	−	0.949631i	$-0.398542\pi$
$163$	8.00171	0.626742	0.313371	+	0.949631i	$0.398542\pi$
$164$	−43.2310	−3.37577
$165$	15.8172	1.23137
$166$	−26.7048	−2.07270
$167$	−12.6219	−0.976711	−0.488355	−	0.872645i	$-0.662403\pi$
$167$	−12.6219	−0.976711	−0.488355	+	0.872645i	$0.662403\pi$
$168$	−9.31627	−0.718766
$169$	−12.9235	−0.994117
$170$	26.3771	2.02303
$171$	−2.48539	−0.190062
$172$	16.1410	1.23074
$173$	3.23525	0.245971	0.122986	−	0.992408i	$-0.460753\pi$
$173$	3.23525	0.245971	0.122986	+	0.992408i	$0.460753\pi$
$174$	49.7584	3.77217
$175$	−2.03855	−0.154100
$176$	−5.70486	−0.430020
$177$	0.0813039	0.00611118
$178$	19.9738	1.49710
$179$	0.876035	0.0654779	0.0327390	−	0.999464i	$-0.489577\pi$
$179$	0.876035	0.0654779	0.0327390	+	0.999464i	$0.489577\pi$
$180$	−25.6487	−1.91174
$181$	4.25828	0.316515	0.158258	−	0.987398i	$-0.449412\pi$
$181$	4.25828	0.316515	0.158258	+	0.987398i	$0.449412\pi$
$182$	0.606119	0.0449285
$183$	−15.4481	−1.14196
$184$	17.2269	1.26998
$185$	−1.67448	−0.123110
$186$	−46.0685	−3.37791
$187$	−23.3492	−1.70746
$188$	−2.89248	−0.210955
$189$	3.21870	0.234126
$190$	−2.29335	−0.166377
$191$	−22.2730	−1.61162	−0.805809	−	0.592175i	$-0.798269\pi$
$191$	−22.2730	−1.61162	−0.805809	+	0.592175i	$0.798269\pi$
$192$	−31.6660	−2.28530
$193$	−12.5377	−0.902480	−0.451240	−	0.892403i	$-0.649018\pi$
$193$	−12.5377	−0.902480	−0.451240	+	0.892403i	$0.649018\pi$
$194$	−31.8723	−2.28830
$195$	1.24985	0.0895038
$196$	−21.9439	−1.56742
$197$	−14.4965	−1.03284	−0.516418	−	0.856337i	$-0.672735\pi$
$197$	−14.4965	−1.03284	−0.516418	+	0.856337i	$0.672735\pi$
$198$	35.4065	2.51623
$199$	20.4797	1.45176	0.725882	−	0.687819i	$-0.241432\pi$
$199$	20.4797	1.45176	0.725882	+	0.687819i	$0.241432\pi$
$200$	8.16623	0.577440
$201$	36.5316	2.57674
$202$	16.6423	1.17095
$203$	−7.24786	−0.508700
$204$	64.3721	4.50695
$205$	20.2495	1.41428
$206$	−13.3525	−0.930310
$207$	−19.8500	−1.37967
$208$	−0.450789	−0.0312566
$209$	2.03009	0.140424
$210$	9.90542	0.683539
$211$	−27.3726	−1.88440	−0.942202	−	0.335045i	$-0.891248\pi$
$211$	−27.3726	−1.88440	−0.942202	+	0.335045i	$0.891248\pi$
$212$	−24.6470	−1.69276
$213$	7.36655	0.504748
$214$	−36.0326	−2.46314
$215$	−7.56045	−0.515618
$216$	−12.8938	−0.877311
$217$	6.71039	0.455531
$218$	−2.36112	−0.159915
$219$	−39.2113	−2.64966
$220$	20.9501	1.41245
$221$	−1.84502	−0.124109
$222$	−6.37271	−0.427708
$223$	16.8295	1.12698	0.563492	−	0.826122i	$-0.309458\pi$
$223$	16.8295	1.12698	0.563492	+	0.826122i	$0.309458\pi$
$224$	3.33082	0.222550
$225$	−9.40969	−0.627313
$226$	33.5455	2.23141
$227$	19.2560	1.27806	0.639032	−	0.769180i	$-0.279335\pi$
$227$	19.2560	1.27806	0.639032	+	0.769180i	$0.279335\pi$
$228$	−5.59682	−0.370658
$229$	8.64869	0.571521	0.285761	−	0.958301i	$-0.407754\pi$
$229$	8.64869	0.571521	0.285761	+	0.958301i	$0.407754\pi$
$230$	−18.3163	−1.20774
$231$	−8.76833	−0.576913
$232$	29.0342	1.90619
$233$	17.3403	1.13600	0.568001	−	0.823028i	$-0.307717\pi$
$233$	17.3403	1.13600	0.568001	+	0.823028i	$0.307717\pi$
$234$	2.79777	0.182896
$235$	1.35484	0.0883800
$236$	0.107688	0.00700990
$237$	−4.68871	−0.304565
$238$	−14.6223	−0.947821
$239$	−9.09186	−0.588103	−0.294052	−	0.955790i	$-0.595004\pi$
$239$	−9.09186	−0.588103	−0.294052	+	0.955790i	$0.595004\pi$
$240$	−7.36697	−0.475536
$241$	16.2769	1.04849	0.524244	−	0.851568i	$-0.324348\pi$
$241$	16.2769	1.04849	0.524244	+	0.851568i	$0.324348\pi$
$242$	−2.94802	−0.189506
$243$	−19.8365	−1.27251
$244$	−20.4612	−1.30990
$245$	10.2785	0.656672
$246$	77.0650	4.91348
$247$	0.160415	0.0102069
$248$	−26.8812	−1.70696
$249$	30.5266	1.93454
$250$	−28.4509	−1.79939
$251$	−6.17917	−0.390026	−0.195013	−	0.980801i	$-0.562475\pi$
$251$	−6.17917	−0.390026	−0.195013	+	0.980801i	$0.562475\pi$
$252$	14.2184	0.895678
$253$	16.2137	1.01934
$254$	26.0806	1.63644
$255$	−30.1520	−1.88819
$256$	−24.9974	−1.56234
$257$	−17.6760	−1.10260	−0.551300	−	0.834307i	$-0.685868\pi$
$257$	−17.6760	−1.10260	−0.551300	+	0.834307i	$0.685868\pi$
$258$	−28.7734	−1.79135
$259$	0.928256	0.0576790
$260$	1.65545	0.102666
$261$	−33.4552	−2.07082
$262$	9.64798	0.596054
$263$	7.59593	0.468385	0.234193	−	0.972190i	$-0.424755\pi$
$263$	7.59593	0.468385	0.234193	+	0.972190i	$0.424755\pi$
$264$	35.1251	2.16180
$265$	11.5447	0.709185
$266$	1.27133	0.0779502
$267$	−22.8323	−1.39731
$268$	48.3866	2.95568
$269$	−8.27718	−0.504669	−0.252334	−	0.967640i	$-0.581198\pi$
$269$	−8.27718	−0.504669	−0.252334	+	0.967640i	$0.581198\pi$
$270$	13.7092	0.834314
$271$	2.78016	0.168883	0.0844415	−	0.996428i	$-0.473089\pi$
$271$	2.78016	0.168883	0.0844415	+	0.996428i	$0.473089\pi$
$272$	10.8750	0.659396
$273$	−0.692860	−0.0419338
$274$	27.4252	1.65681
$275$	7.68593	0.463479
$276$	−44.7000	−2.69062
$277$	−15.5075	−0.931755	−0.465878	−	0.884849i	$-0.654261\pi$
$277$	−15.5075	−0.931755	−0.465878	+	0.884849i	$0.654261\pi$
$278$	33.8617	2.03089
$279$	30.9743	1.85438
$280$	5.77985	0.345412
$281$	18.6545	1.11283	0.556417	−	0.830903i	$-0.312176\pi$
$281$	18.6545	1.11283	0.556417	+	0.830903i	$0.312176\pi$
$282$	5.15622	0.307048
$283$	22.5686	1.34156	0.670782	−	0.741655i	$-0.265959\pi$
$283$	22.5686	1.34156	0.670782	+	0.741655i	$0.265959\pi$
$284$	9.75709	0.578977
$285$	2.62156	0.155288
$286$	−2.28524	−0.135129
$287$	−11.2254	−0.662612
$288$	15.3746	0.905959
$289$	27.5100	1.61824
$290$	−30.8703	−1.81277
$291$	36.4335	2.13577
$292$	−51.9360	−3.03932
$293$	−13.8185	−0.807284	−0.403642	−	0.914917i	$-0.632256\pi$
$293$	−13.8185	−0.807284	−0.403642	+	0.914917i	$0.632256\pi$
$294$	39.1179	2.28140
$295$	−0.0504413	−0.00293680
$296$	−3.71850	−0.216134
$297$	−12.1354	−0.704169
$298$	20.8359	1.20699
$299$	1.28118	0.0740926
$300$	−21.1896	−1.22338
$301$	4.19116	0.241575
$302$	−27.3363	−1.57303
$303$	−19.0240	−1.09290
$304$	−0.945528	−0.0542297
$305$	9.58407	0.548782
$306$	−67.4946	−3.85841
$307$	27.8347	1.58861	0.794305	−	0.607519i	$-0.207835\pi$
$307$	27.8347	1.58861	0.794305	+	0.607519i	$0.207835\pi$
$308$	−11.6138	−0.661756
$309$	15.2633	0.868301
$310$	28.5811	1.62330
$311$	−6.08162	−0.344857	−0.172428	−	0.985022i	$-0.555161\pi$
$311$	−6.08162	−0.344857	−0.172428	+	0.985022i	$0.555161\pi$
$312$	2.77553	0.157133
$313$	28.7643	1.62585	0.812927	−	0.582366i	$-0.197873\pi$
$313$	28.7643	1.62585	0.812927	+	0.582366i	$0.197873\pi$
$314$	55.6601	3.14108
$315$	−6.65994	−0.375245
$316$	−6.21026	−0.349354
$317$	29.1930	1.63964	0.819821	−	0.572620i	$-0.194073\pi$
$317$	29.1930	1.63964	0.819821	+	0.572620i	$0.194073\pi$
$318$	43.9365	2.46384
$319$	27.3265	1.52999
$320$	19.6457	1.09823
$321$	41.1892	2.29896
$322$	10.1537	0.565844
$323$	−3.86991	−0.215328
$324$	−12.4956	−0.694198
$325$	0.607331	0.0336887
$326$	−18.8930	−1.04639
$327$	2.69902	0.149256
$328$	44.9677	2.48293
$329$	−0.751060	−0.0414073
$330$	−37.3463	−2.05585
$331$	−20.1566	−1.10790	−0.553952	−	0.832548i	$-0.686881\pi$
$331$	−20.1566	−1.10790	−0.553952	+	0.832548i	$0.686881\pi$
$332$	40.4329	2.21904
$333$	4.28471	0.234801
$334$	29.8018	1.63068
$335$	−22.6644	−1.23829
$336$	4.08391	0.222796
$337$	6.41476	0.349434	0.174717	−	0.984619i	$-0.444099\pi$
$337$	6.41476	0.349434	0.174717	+	0.984619i	$0.444099\pi$
$338$	30.5140	1.65974
$339$	−38.3462	−2.08268
$340$	−39.9367	−2.16587
$341$	−25.3001	−1.37008
$342$	5.86830	0.317321
$343$	−12.1957	−0.658508
$344$	−16.7894	−0.905223
$345$	20.9375	1.12724
$346$	−7.63881	−0.410665
$347$	20.9407	1.12416	0.562078	−	0.827084i	$-0.310002\pi$
$347$	20.9407	1.12416	0.562078	+	0.827084i	$0.310002\pi$
$348$	−75.3374	−4.03851
$349$	−30.6510	−1.64071	−0.820356	−	0.571853i	$-0.806225\pi$
$349$	−30.6510	−1.64071	−0.820356	+	0.571853i	$0.806225\pi$
$350$	4.81326	0.257280
$351$	−0.958924	−0.0511836
$352$	−12.5581	−0.669351
$353$	−28.6567	−1.52524	−0.762621	−	0.646846i	$-0.776088\pi$
$353$	−28.6567	−1.52524	−0.762621	+	0.646846i	$0.776088\pi$
$354$	−0.191968	−0.0102030
$355$	−4.57023	−0.242563
$356$	−30.2416	−1.60280
$357$	16.7149	0.884645
$358$	−2.06842	−0.109320
$359$	19.6105	1.03500	0.517500	−	0.855683i	$-0.326863\pi$
$359$	19.6105	1.03500	0.517500	+	0.855683i	$0.326863\pi$
$360$	26.6791	1.40611
$361$	−18.6635	−0.982291
$362$	−10.0543	−0.528442
$363$	3.36991	0.176874
$364$	−0.917703	−0.0481007
$365$	24.3269	1.27333
$366$	36.4749	1.90657
$367$	−15.0828	−0.787316	−0.393658	−	0.919257i	$-0.628791\pi$
$367$	−15.0828	−0.787316	−0.393658	+	0.919257i	$0.628791\pi$
$368$	−7.55163	−0.393656
$369$	−51.8149	−2.69737
$370$	3.95366	0.205541
$371$	−6.39984	−0.332263
$372$	69.7507	3.61641
$373$	10.3595	0.536393	0.268197	−	0.963364i	$-0.413572\pi$
$373$	10.3595	0.536393	0.268197	+	0.963364i	$0.413572\pi$
$374$	55.1302	2.85072
$375$	32.5225	1.67946
$376$	3.00867	0.155161
$377$	2.15930	0.111210
$378$	−7.59973	−0.390888
$379$	−21.7639	−1.11794	−0.558968	−	0.829189i	$-0.688802\pi$
$379$	−21.7639	−1.11794	−0.558968	+	0.829189i	$0.688802\pi$
$380$	3.47229	0.178125
$381$	−29.8130	−1.52737
$382$	52.5893	2.69070
$383$	−32.8782	−1.68000	−0.839999	−	0.542589i	$-0.817444\pi$
$383$	−32.8782	−1.68000	−0.839999	+	0.542589i	$0.817444\pi$
$384$	55.3977	2.82700
$385$	5.43990	0.277243
$386$	29.6029	1.50675
$387$	19.3459	0.983407
$388$	48.2567	2.44986
$389$	−33.3989	−1.69339	−0.846696	−	0.532077i	$-0.821412\pi$
$389$	−33.3989	−1.69339	−0.846696	+	0.532077i	$0.821412\pi$
$390$	−2.95105	−0.149432
$391$	−30.9078	−1.56307
$392$	22.8254	1.15286
$393$	−11.0287	−0.556325
$394$	34.2281	1.72438
$395$	2.90889	0.146362
$396$	−53.6077	−2.69389
$397$	−7.25031	−0.363883	−0.181941	−	0.983309i	$-0.558238\pi$
$397$	−7.25031	−0.363883	−0.181941	+	0.983309i	$0.558238\pi$
$398$	−48.3549	−2.42381
$399$	−1.45327	−0.0727545
$400$	−3.57977	−0.178989
$401$	18.2170	0.909712	0.454856	−	0.890565i	$-0.349691\pi$
$401$	18.2170	0.909712	0.454856	+	0.890565i	$0.349691\pi$
$402$	−86.2555	−4.30203
$403$	−1.99918	−0.0995862
$404$	−25.1975	−1.25362
$405$	5.85294	0.290835
$406$	17.1131	0.849307
$407$	−3.49980	−0.173478
$408$	−66.9581	−3.31492
$409$	32.5034	1.60719	0.803595	−	0.595176i	$-0.202918\pi$
$409$	32.5034	1.60719	0.803595	+	0.595176i	$0.202918\pi$
$410$	−47.8114	−2.36124
$411$	−31.3500	−1.54638
$412$	20.2165	0.995995
$413$	0.0279623	0.00137594
$414$	46.8682	2.30345
$415$	−18.9388	−0.929669
$416$	−0.992327	−0.0486528
$417$	−38.7077	−1.89552
$418$	−4.79328	−0.234447
$419$	−17.9282	−0.875849	−0.437925	−	0.899012i	$-0.644286\pi$
$419$	−17.9282	−0.875849	−0.437925	+	0.899012i	$0.644286\pi$
$420$	−14.9974	−0.731800
$421$	−16.6911	−0.813473	−0.406737	−	0.913545i	$-0.633333\pi$
$421$	−16.6911	−0.813473	−0.406737	+	0.913545i	$0.633333\pi$
$422$	64.6299	3.14613
$423$	−3.46680	−0.168562
$424$	25.6371	1.24505
$425$	−14.6515	−0.710703
$426$	−17.3933	−0.842708
$427$	−5.31297	−0.257113
$428$	54.5557	2.63705
$429$	2.61229	0.126122
$430$	17.8511	0.860858
$431$	−1.06289	−0.0511977	−0.0255988	−	0.999672i	$-0.508149\pi$
$431$	−1.06289	−0.0511977	−0.0255988	+	0.999672i	$0.508149\pi$
$432$	5.65216	0.271940
$433$	29.1650	1.40158	0.700790	−	0.713368i	$-0.252831\pi$
$433$	29.1650	1.40158	0.700790	+	0.713368i	$0.252831\pi$
$434$	−15.8440	−0.760538
$435$	35.2881	1.69194
$436$	3.57489	0.171206
$437$	2.68727	0.128549
$438$	92.5827	4.42377
$439$	−24.5631	−1.17233	−0.586167	−	0.810190i	$-0.699364\pi$
$439$	−24.5631	−1.17233	−0.586167	+	0.810190i	$0.699364\pi$
$440$	−21.7917	−1.03888
$441$	−26.3010	−1.25243
$442$	4.35631	0.207209
$443$	−12.5239	−0.595028	−0.297514	−	0.954717i	$-0.596157\pi$
$443$	−12.5239	−0.595028	−0.297514	+	0.954717i	$0.596157\pi$
$444$	9.64870	0.457907
$445$	14.1652	0.671496
$446$	−39.7364	−1.88157
$447$	−23.8178	−1.12654
$448$	−10.8907	−0.514536
$449$	−21.4659	−1.01304	−0.506520	−	0.862228i	$-0.669068\pi$
$449$	−21.4659	−1.01304	−0.506520	+	0.862228i	$0.669068\pi$
$450$	22.2174	1.04734
$451$	42.3229	1.99291
$452$	−50.7900	−2.38896
$453$	31.2485	1.46818
$454$	−45.4657	−2.13381
$455$	0.429853	0.0201518
$456$	5.82166	0.272624
$457$	−18.1821	−0.850524	−0.425262	−	0.905070i	$-0.639818\pi$
$457$	−18.1821	−0.850524	−0.425262	+	0.905070i	$0.639818\pi$
$458$	−20.4206	−0.954192
$459$	23.1335	1.07978
$460$	27.7321	1.29301
$461$	−23.7314	−1.10528	−0.552641	−	0.833419i	$-0.686380\pi$
$461$	−23.7314	−1.10528	−0.552641	+	0.833419i	$0.686380\pi$
$462$	20.7031	0.963194
$463$	−31.2688	−1.45318	−0.726592	−	0.687070i	$-0.758897\pi$
$463$	−31.2688	−1.45318	−0.726592	+	0.687070i	$0.758897\pi$
$464$	−12.7275	−0.590860
$465$	−32.6713	−1.51510
$466$	−40.9426	−1.89663
$467$	14.4689	0.669543	0.334772	−	0.942299i	$-0.391341\pi$
$467$	14.4689	0.669543	0.334772	+	0.942299i	$0.391341\pi$
$468$	−4.23600	−0.195809
$469$	12.5641	0.580155
$470$	−3.19894	−0.147556
$471$	−63.6256	−2.93171
$472$	−0.112014	−0.00515588
$473$	−15.8019	−0.726572
$474$	11.0706	0.508490
$475$	1.27387	0.0584493
$476$	22.1391	1.01474
$477$	−29.5409	−1.35258
$478$	21.4670	0.981876
$479$	18.2764	0.835070	0.417535	−	0.908661i	$-0.362894\pi$
$479$	18.2764	0.835070	0.417535	+	0.908661i	$0.362894\pi$
$480$	−16.2170	−0.740200
$481$	−0.276549	−0.0126095
$482$	−38.4317	−1.75052
$483$	−11.6068	−0.528128
$484$	4.46349	0.202886
$485$	−22.6035	−1.02637
$486$	46.8363	2.12454
$487$	24.5713	1.11343	0.556716	−	0.830703i	$-0.312061\pi$
$487$	24.5713	1.11343	0.556716	+	0.830703i	$0.312061\pi$
$488$	21.2832	0.963447
$489$	21.5968	0.976640
$490$	−24.2689	−1.09636
$491$	−9.69456	−0.437509	−0.218755	−	0.975780i	$-0.570199\pi$
$491$	−9.69456	−0.437509	−0.218755	+	0.975780i	$0.570199\pi$
$492$	−116.681	−5.26040
$493$	−52.0920	−2.34610
$494$	−0.378758	−0.0170411
$495$	25.1099	1.12861
$496$	11.7837	0.529104
$497$	2.53353	0.113644
$498$	−72.0769	−3.22984
$499$	38.8775	1.74040	0.870199	−	0.492701i	$-0.163990\pi$
$499$	38.8775	1.74040	0.870199	+	0.492701i	$0.163990\pi$
$500$	43.0765	1.92644
$501$	−34.0667	−1.52199
$502$	14.5898	0.651173
$503$	−40.1858	−1.79180	−0.895899	−	0.444258i	$-0.853467\pi$
$503$	−40.1858	−1.79180	−0.895899	+	0.444258i	$0.853467\pi$
$504$	−14.7896	−0.658783
$505$	11.8026	0.525207
$506$	−38.2824	−1.70186
$507$	−34.8809	−1.54911
$508$	−39.4878	−1.75199
$509$	3.34670	0.148340	0.0741699	−	0.997246i	$-0.476369\pi$
$509$	3.34670	0.148340	0.0741699	+	0.997246i	$0.476369\pi$
$510$	71.1924	3.15245
$511$	−13.4857	−0.596572
$512$	17.9718	0.794247
$513$	−2.01134	−0.0888027
$514$	41.7352	1.84086
$515$	−9.46943	−0.417273
$516$	43.5648	1.91783
$517$	2.83172	0.124539
$518$	−2.19172	−0.0962988
$519$	8.73200	0.383292
$520$	−1.72195	−0.0755125
$521$	5.84915	0.256256	0.128128	−	0.991758i	$-0.459103\pi$
$521$	5.84915	0.256256	0.128128	+	0.991758i	$0.459103\pi$
$522$	78.9918	3.45738
$523$	39.0983	1.70965	0.854824	−	0.518918i	$-0.173665\pi$
$523$	39.0983	1.70965	0.854824	+	0.518918i	$0.173665\pi$
$524$	−14.6077	−0.638139
$525$	−5.50209	−0.240131
$526$	−17.9349	−0.781999
$527$	48.2290	2.10089
$528$	−15.3975	−0.670091
$529$	−1.53764	−0.0668540
$530$	−27.2584	−1.18403
$531$	0.129071	0.00560118
$532$	−1.92488	−0.0834539
$533$	3.34429	0.144857
$534$	53.9097	2.33290
$535$	−25.5539	−1.10479
$536$	−50.3304	−2.17394
$537$	2.36444	0.102033
$538$	19.5434	0.842577
$539$	21.4829	0.925336
$540$	−20.7566	−0.893221
$541$	−0.413657	−0.0177845	−0.00889226	−	0.999960i	$-0.502831\pi$
$541$	−0.413657	−0.0177845	−0.00889226	+	0.999960i	$0.502831\pi$
$542$	−6.56430	−0.281961
$543$	11.4932	0.493219
$544$	23.9393	1.02639
$545$	−1.67448	−0.0717270
$546$	1.63593	0.0700112
$547$	0.141728	0.00605985	0.00302992	−	0.999995i	$-0.499036\pi$
$547$	0.141728	0.00605985	0.00302992	+	0.999995i	$0.499036\pi$
$548$	−41.5235	−1.77379
$549$	−24.5240	−1.04666
$550$	−18.1474	−0.773808
$551$	4.52912	0.192947
$552$	46.4957	1.97899
$553$	−1.61256	−0.0685729
$554$	36.6151	1.55562
$555$	−4.51946	−0.191841
$556$	−51.2689	−2.17428
$557$	10.7105	0.453817	0.226908	−	0.973916i	$-0.427138\pi$
$557$	10.7105	0.453817	0.226908	+	0.973916i	$0.427138\pi$
$558$	−73.1341	−3.09601
$559$	−1.24864	−0.0528120
$560$	−2.53367	−0.107067
$561$	−63.0199	−2.66070
$562$	−44.0455	−1.85795
$563$	−32.2990	−1.36124	−0.680619	−	0.732637i	$-0.738289\pi$
$563$	−32.2990	−1.36124	−0.680619	+	0.732637i	$0.738289\pi$
$564$	−7.80685	−0.328728
$565$	23.7901	1.00086
$566$	−53.2872	−2.23983
$567$	−3.24460	−0.136260
$568$	−10.1491	−0.425845
$569$	−8.07948	−0.338709	−0.169355	−	0.985555i	$-0.554168\pi$
$569$	−8.07948	−0.338709	−0.169355	+	0.985555i	$0.554168\pi$
$570$	−6.18981	−0.259263
$571$	−27.5882	−1.15453	−0.577266	−	0.816556i	$-0.695880\pi$
$571$	−27.5882	−1.15453	−0.577266	+	0.816556i	$0.695880\pi$
$572$	3.46001	0.144670
$573$	−60.1153	−2.51135
$574$	26.5044	1.10627
$575$	10.1740	0.424286
$576$	−50.2700	−2.09458
$577$	14.2679	0.593980	0.296990	−	0.954881i	$-0.404017\pi$
$577$	14.2679	0.593980	0.296990	+	0.954881i	$0.404017\pi$
$578$	−64.9545	−2.70175
$579$	−33.8394	−1.40632
$580$	46.7396	1.94076
$581$	10.4988	0.435564
$582$	−86.0240	−3.56581
$583$	24.1293	0.999332
$584$	54.0224	2.23546
$585$	1.98415	0.0820344
$586$	32.6271	1.34781
$587$	40.4027	1.66760	0.833798	−	0.552069i	$-0.186161\pi$
$587$	40.4027	1.66760	0.833798	+	0.552069i	$0.186161\pi$
$588$	−59.2270	−2.44248
$589$	−4.19326	−0.172780
$590$	0.119098	0.00490318
$591$	−39.1264	−1.60945
$592$	1.63005	0.0669948
$593$	20.0209	0.822160	0.411080	−	0.911599i	$-0.365152\pi$
$593$	20.0209	0.822160	0.411080	+	0.911599i	$0.365152\pi$
$594$	28.6532	1.17566
$595$	−10.3700	−0.425127
$596$	−31.5470	−1.29221
$597$	55.2750	2.26226
$598$	−3.02502	−0.123702
$599$	−23.2773	−0.951086	−0.475543	−	0.879692i	$-0.657748\pi$
$599$	−23.2773	−0.951086	−0.475543	+	0.879692i	$0.657748\pi$
$600$	22.0408	0.899813
$601$	19.3464	0.789156	0.394578	−	0.918862i	$-0.370891\pi$
$601$	19.3464	0.789156	0.394578	+	0.918862i	$0.370891\pi$
$602$	−9.89584	−0.403324
$603$	57.9942	2.36171
$604$	41.3890	1.68409
$605$	−2.09070	−0.0849992
$606$	44.9179	1.82467
$607$	−9.14144	−0.371040	−0.185520	−	0.982641i	$-0.559397\pi$
$607$	−9.14144	−0.371040	−0.185520	+	0.982641i	$0.559397\pi$
$608$	−2.08140	−0.0844118
$609$	−19.5621	−0.792697
$610$	−22.6292	−0.916228
$611$	0.223758	0.00905228
$612$	102.191	4.13083
$613$	−17.1933	−0.694431	−0.347216	−	0.937785i	$-0.612873\pi$
$613$	−17.1933	−0.694431	−0.347216	+	0.937785i	$0.612873\pi$
$614$	−65.7211	−2.65229
$615$	54.6537	2.20385
$616$	12.0803	0.486730
$617$	−28.7260	−1.15647	−0.578233	−	0.815872i	$-0.696257\pi$
$617$	−28.7260	−1.15647	−0.578233	+	0.815872i	$0.696257\pi$
$618$	−36.0386	−1.44968
$619$	−38.0921	−1.53105	−0.765526	−	0.643405i	$-0.777521\pi$
$619$	−38.0921	−1.53105	−0.765526	+	0.643405i	$0.777521\pi$
$620$	−43.2736	−1.73791
$621$	−16.0639	−0.644622
$622$	14.3594	0.575761
$623$	−7.85255	−0.314606
$624$	−1.21669	−0.0487066
$625$	−9.19657	−0.367863
$626$	−67.9159	−2.71447
$627$	5.47925	0.218820
$628$	−84.2730	−3.36286
$629$	6.67158	0.266013
$630$	15.7249	0.626496
$631$	25.4629	1.01366	0.506831	−	0.862045i	$-0.330817\pi$
$631$	25.4629	1.01366	0.506831	+	0.862045i	$0.330817\pi$
$632$	6.45975	0.256955
$633$	−73.8791	−2.93643
$634$	−68.9282	−2.73749
$635$	18.4961	0.733996
$636$	−66.5228	−2.63780
$637$	1.69755	0.0672594
$638$	−64.5212	−2.55442
$639$	11.6944	0.462625
$640$	−34.3689	−1.35855
$641$	34.2343	1.35217	0.676086	−	0.736823i	$-0.263675\pi$
$641$	34.2343	1.35217	0.676086	+	0.736823i	$0.263675\pi$
$642$	−97.2527	−3.83826
$643$	22.9706	0.905871	0.452936	−	0.891543i	$-0.350377\pi$
$643$	22.9706	0.905871	0.452936	+	0.891543i	$0.350377\pi$
$644$	−15.3734	−0.605796
$645$	−20.4058	−0.803478
$646$	9.13733	0.359503
$647$	−31.8653	−1.25275	−0.626377	−	0.779520i	$-0.715463\pi$
$647$	−31.8653	−1.25275	−0.626377	+	0.779520i	$0.715463\pi$
$648$	12.9975	0.510592
$649$	−0.105426	−0.00413833
$650$	−1.43398	−0.0562454
$651$	18.1115	0.709845
$652$	28.6052	1.12027
$653$	−34.6724	−1.35684	−0.678418	−	0.734676i	$-0.737334\pi$
$653$	−34.6724	−1.35684	−0.678418	+	0.734676i	$0.737334\pi$
$654$	−6.37271	−0.249193
$655$	6.84225	0.267349
$656$	−19.7122	−0.769631
$657$	−62.2483	−2.42854
$658$	1.77334	0.0691321
$659$	51.1373	1.99203	0.996013	−	0.0892123i	$-0.0284350\pi$
$659$	51.1373	1.99203	0.996013	+	0.0892123i	$0.0284350\pi$
$660$	56.5447	2.20100
$661$	−23.6508	−0.919910	−0.459955	−	0.887942i	$-0.652134\pi$
$661$	−23.6508	−0.919910	−0.459955	+	0.887942i	$0.652134\pi$
$662$	47.5921	1.84972
$663$	−4.97974	−0.193397
$664$	−42.0572	−1.63213
$665$	0.901614	0.0349631
$666$	−10.1167	−0.392015
$667$	36.1727	1.40061
$668$	−45.1218	−1.74582
$669$	45.4230	1.75616
$670$	53.5133	2.06740
$671$	20.0314	0.773305
$672$	8.98994	0.346795
$673$	27.6832	1.06711	0.533555	−	0.845765i	$-0.320856\pi$
$673$	27.6832	1.06711	0.533555	+	0.845765i	$0.320856\pi$
$674$	−15.1460	−0.583403
$675$	−7.61493	−0.293099
$676$	−46.2002	−1.77693
$677$	9.41147	0.361712	0.180856	−	0.983510i	$-0.442113\pi$
$677$	9.41147	0.361712	0.180856	+	0.983510i	$0.442113\pi$
$678$	90.5399	3.47716
$679$	12.5303	0.480870
$680$	41.5411	1.59303
$681$	51.9723	1.99158
$682$	59.7366	2.28743
$683$	−19.2569	−0.736843	−0.368422	−	0.929659i	$-0.620102\pi$
$683$	−19.2569	−0.736843	−0.368422	+	0.929659i	$0.620102\pi$
$684$	−8.88498	−0.339726
$685$	19.4496	0.743133
$686$	28.7956	1.09942
$687$	23.3430	0.890591
$688$	7.35985	0.280592
$689$	1.90666	0.0726380
$690$	−49.4360	−1.88200
$691$	−24.0123	−0.913470	−0.456735	−	0.889603i	$-0.650981\pi$
$691$	−24.0123	−0.913470	−0.456735	+	0.889603i	$0.650981\pi$
$692$	11.5657	0.439660
$693$	−13.9198	−0.528769
$694$	−49.4436	−1.87685
$695$	24.0144	0.910918
$696$	78.3639	2.97038
$697$	−80.6792	−3.05594
$698$	72.3708	2.73928
$699$	46.8019	1.77021
$700$	−7.28759	−0.275445
$701$	29.2560	1.10498	0.552492	−	0.833518i	$-0.313677\pi$
$701$	29.2560	1.10498	0.552492	+	0.833518i	$0.313677\pi$
$702$	2.26414	0.0854543
$703$	−0.580059	−0.0218773
$704$	41.0610	1.54754
$705$	3.65674	0.137721
$706$	67.6619	2.54649
$707$	−6.54279	−0.246067
$708$	0.290653	0.0109234
$709$	−6.98165	−0.262201	−0.131101	−	0.991369i	$-0.541851\pi$
$709$	−6.98165	−0.262201	−0.131101	+	0.991369i	$0.541851\pi$
$710$	10.7909	0.404974
$711$	−7.44336	−0.279148
$712$	31.4565	1.17888
$713$	−33.4903	−1.25422
$714$	−39.4658	−1.47697
$715$	−1.62067	−0.0606097
$716$	3.13173	0.117038
$717$	−24.5391	−0.916430
$718$	−46.3027	−1.72800
$719$	20.7957	0.775550	0.387775	−	0.921754i	$-0.373244\pi$
$719$	20.7957	0.775550	0.387775	+	0.921754i	$0.373244\pi$
$720$	−11.6951	−0.435851
$721$	5.24941	0.195498
$722$	44.0668	1.64000
$723$	43.9317	1.63384
$724$	15.2229	0.565753
$725$	17.1473	0.636834
$726$	−7.95676	−0.295303
$727$	−14.3639	−0.532726	−0.266363	−	0.963873i	$-0.585822\pi$
$727$	−14.3639	−0.532726	−0.266363	+	0.963873i	$0.585822\pi$
$728$	0.954570	0.0353787
$729$	−43.0530	−1.59455
$730$	−57.4387	−2.12590
$731$	30.1228	1.11413
$732$	−55.2253	−2.04119
$733$	−43.0595	−1.59044	−0.795220	−	0.606321i	$-0.792645\pi$
$733$	−43.0595	−1.59044	−0.795220	+	0.606321i	$0.792645\pi$
$734$	35.6123	1.31448
$735$	27.7420	1.02328
$736$	−16.6235	−0.612749
$737$	−47.3702	−1.74490
$738$	122.341	4.50344
$739$	13.8221	0.508454	0.254227	−	0.967145i	$-0.418179\pi$
$739$	13.8221	0.508454	0.254227	+	0.967145i	$0.418179\pi$
$740$	−5.98609	−0.220053
$741$	0.432963	0.0159053
$742$	15.1108	0.554735
$743$	9.87455	0.362262	0.181131	−	0.983459i	$-0.442024\pi$
$743$	9.87455	0.362262	0.181131	+	0.983459i	$0.442024\pi$
$744$	−72.5528	−2.65991
$745$	14.7766	0.541374
$746$	−24.4600	−0.895543
$747$	48.4611	1.77310
$748$	−83.4707	−3.05199
$749$	14.1659	0.517612
$750$	−76.7896	−2.80396
$751$	−31.6564	−1.15516	−0.577580	−	0.816334i	$-0.696003\pi$
$751$	−31.6564	−1.15516	−0.577580	+	0.816334i	$0.696003\pi$
$752$	−1.31889	−0.0480950
$753$	−16.6777	−0.607770
$754$	−5.09837	−0.185672
$755$	−19.3867	−0.705553
$756$	11.5065	0.418487
$757$	30.3159	1.10185	0.550925	−	0.834554i	$-0.314275\pi$
$757$	30.3159	1.10185	0.550925	+	0.834554i	$0.314275\pi$
$758$	51.3871	1.86647
$759$	43.7610	1.58842
$760$	−3.61178	−0.131013
$761$	22.5776	0.818436	0.409218	−	0.912437i	$-0.365802\pi$
$761$	22.5776	0.818436	0.409218	+	0.912437i	$0.365802\pi$
$762$	70.3922	2.55004
$763$	0.928256	0.0336051
$764$	−79.6235	−2.88068
$765$	−47.8665	−1.73062
$766$	77.6294	2.80486
$767$	−0.00833061	−0.000300801 0
$768$	−67.4686	−2.43456
$769$	3.07079	0.110735	0.0553677	−	0.998466i	$-0.482367\pi$
$769$	3.07079	0.110735	0.0553677	+	0.998466i	$0.482367\pi$
$770$	−12.8443	−0.462875
$771$	−47.7080	−1.71816
$772$	−44.8207	−1.61313
$773$	−21.4453	−0.771333	−0.385667	−	0.922638i	$-0.626029\pi$
$773$	−21.4453	−0.771333	−0.385667	+	0.922638i	$0.626029\pi$
$774$	−45.6780	−1.64186
$775$	−15.8757	−0.570273
$776$	−50.1953	−1.80191
$777$	2.50538	0.0898801
$778$	78.8589	2.82723
$779$	7.01463	0.251325
$780$	4.46808	0.159983
$781$	−9.55214	−0.341802
$782$	72.9770	2.60965
$783$	−27.0741	−0.967550
$784$	−10.0058	−0.357351
$785$	39.4736	1.40887
$786$	26.0401	0.928820
$787$	−17.3680	−0.619103	−0.309552	−	0.950883i	$-0.600179\pi$
$787$	−17.3680	−0.619103	−0.309552	+	0.950883i	$0.600179\pi$
$788$	−51.8235	−1.84614
$789$	20.5016	0.729876
$790$	−6.86825	−0.244361
$791$	−13.1881	−0.468916
$792$	55.7613	1.98139
$793$	1.58286	0.0562088
$794$	17.1189	0.607525
$795$	31.1594	1.10511
$796$	73.2125	2.59495
$797$	55.2668	1.95765	0.978825	−	0.204698i	$-0.0656214\pi$
$797$	55.2668	1.95765	0.978825	+	0.204698i	$0.0656214\pi$
$798$	3.43135	0.121468
$799$	−5.39804	−0.190969
$800$	−7.88019	−0.278607
$801$	−36.2464	−1.28070
$802$	−43.0124	−1.51882
$803$	50.8450	1.79428
$804$	130.596	4.60578
$805$	7.20091	0.253799
$806$	4.72030	0.166265
$807$	−22.3403	−0.786416
$808$	26.2098	0.922057
$809$	5.06803	0.178183	0.0890913	−	0.996023i	$-0.471604\pi$
$809$	5.06803	0.178183	0.0890913	+	0.996023i	$0.471604\pi$
$810$	−13.8195	−0.485567
$811$	−9.05874	−0.318095	−0.159048	−	0.987271i	$-0.550842\pi$
$811$	−9.05874	−0.318095	−0.159048	+	0.987271i	$0.550842\pi$
$812$	−25.9103	−0.909273
$813$	7.50372	0.263167
$814$	8.26344	0.289633
$815$	−13.3987	−0.469337
$816$	29.3520	1.02752
$817$	−2.61902	−0.0916280
$818$	−76.7445	−2.68331
$819$	−1.09992	−0.0384343
$820$	72.3896	2.52795
$821$	39.4117	1.37548	0.687739	−	0.725958i	$-0.258603\pi$
$821$	39.4117	1.37548	0.687739	+	0.725958i	$0.258603\pi$
$822$	74.0211	2.58178
$823$	12.9510	0.451442	0.225721	−	0.974192i	$-0.427526\pi$
$823$	12.9510	0.451442	0.225721	+	0.974192i	$0.427526\pi$
$824$	−21.0286	−0.732567
$825$	20.7445	0.722230
$826$	−0.0660224	−0.00229721
$827$	15.0364	0.522868	0.261434	−	0.965221i	$-0.415805\pi$
$827$	15.0364	0.522868	0.261434	+	0.965221i	$0.415805\pi$
$828$	−70.9615	−2.46608
$829$	14.6124	0.507511	0.253755	−	0.967268i	$-0.418334\pi$
$829$	14.6124	0.507511	0.253755	+	0.967268i	$0.418334\pi$
$830$	44.7168	1.55214
$831$	−41.8551	−1.45194
$832$	3.24458	0.112486
$833$	−40.9524	−1.41892
$834$	91.3935	3.16470
$835$	21.1351	0.731411
$836$	7.25734	0.251000
$837$	25.0664	0.866422
$838$	42.3306	1.46229
$839$	33.2113	1.14658	0.573290	−	0.819353i	$-0.305667\pi$
$839$	33.2113	1.14658	0.573290	+	0.819353i	$0.305667\pi$
$840$	15.5999	0.538249
$841$	31.9654	1.10226
$842$	39.4096	1.35815
$843$	50.3489	1.73411
$844$	−97.8538	−3.36827
$845$	21.6402	0.744446
$846$	8.18553	0.281424
$847$	1.15899	0.0398234
$848$	−11.2384	−0.385927
$849$	60.9131	2.09053
$850$	34.5940	1.18656
$851$	−4.63275	−0.158809
$852$	26.3346	0.902208
$853$	−15.9817	−0.547202	−0.273601	−	0.961843i	$-0.588215\pi$
$853$	−15.9817	−0.547202	−0.273601	+	0.961843i	$0.588215\pi$
$854$	12.5446	0.429266
$855$	4.16174	0.142328
$856$	−56.7473	−1.93958
$857$	−17.0856	−0.583632	−0.291816	−	0.956475i	$-0.594259\pi$
$857$	−17.0856	−0.583632	−0.291816	+	0.956475i	$0.594259\pi$
$858$	−6.16792	−0.210569
$859$	−36.5182	−1.24599	−0.622993	−	0.782228i	$-0.714083\pi$
$859$	−36.5182	−1.24599	−0.622993	+	0.782228i	$0.714083\pi$
$860$	−27.0278	−0.921639
$861$	−30.2975	−1.03254
$862$	2.50961	0.0854778
$863$	−24.6267	−0.838301	−0.419151	−	0.907917i	$-0.637672\pi$
$863$	−24.6267	−0.838301	−0.419151	+	0.907917i	$0.637672\pi$
$864$	12.4421	0.423290
$865$	−5.41737	−0.184196
$866$	−68.8620	−2.34003
$867$	74.2501	2.52167
$868$	23.9889	0.814236
$869$	6.07981	0.206243
$870$	−83.3195	−2.82480
$871$	−3.74312	−0.126831
$872$	−3.71850	−0.125924
$873$	57.8385	1.95754
$874$	−6.34496	−0.214622
$875$	11.1853	0.378131
$876$	−140.176	−4.73612
$877$	−8.05631	−0.272042	−0.136021	−	0.990706i	$-0.543432\pi$
$877$	−8.05631	−0.272042	−0.136021	+	0.990706i	$0.543432\pi$
$878$	57.9965	1.95729
$879$	−37.2964	−1.25797
$880$	9.55268	0.322021
$881$	−33.7605	−1.13742	−0.568711	−	0.822538i	$-0.692558\pi$
$881$	−33.7605	−1.13742	−0.568711	+	0.822538i	$0.692558\pi$
$882$	62.0999	2.09101
$883$	−15.1013	−0.508200	−0.254100	−	0.967178i	$-0.581779\pi$
$883$	−15.1013	−0.508200	−0.254100	+	0.967178i	$0.581779\pi$
$884$	−6.59573	−0.221839
$885$	−0.136142	−0.00457636
$886$	29.5704	0.993437
$887$	22.8054	0.765731	0.382866	−	0.923804i	$-0.374937\pi$
$887$	22.8054	0.765731	0.382866	+	0.923804i	$0.374937\pi$
$888$	−10.0363	−0.336797
$889$	−10.2534	−0.343888
$890$	−33.4458	−1.12111
$891$	12.2331	0.409824
$892$	60.1634	2.01442
$893$	0.469331	0.0157056
$894$	56.2366	1.88083
$895$	−1.46690	−0.0490332
$896$	19.0526	0.636501
$897$	3.45793	0.115457
$898$	50.6837	1.69134
$899$	−56.4445	−1.88253
$900$	−33.6386	−1.12129
$901$	−45.9971	−1.53239
$902$	−99.9294	−3.32729
$903$	11.3120	0.376441
$904$	52.8304	1.75711
$905$	−7.13041	−0.237023
$906$	−73.7814	−2.45122
$907$	−46.7710	−1.55300	−0.776502	−	0.630114i	$-0.783008\pi$
$907$	−46.7710	−1.55300	−0.776502	+	0.630114i	$0.783008\pi$
$908$	68.8380	2.28447
$909$	−30.2007	−1.00169
$910$	−1.01494	−0.0336448
$911$	18.8829	0.625620	0.312810	−	0.949816i	$-0.398730\pi$
$911$	18.8829	0.625620	0.312810	+	0.949816i	$0.398730\pi$
$912$	−2.55200	−0.0845052
$913$	−39.5835	−1.31002
$914$	42.9302	1.42000
$915$	25.8676	0.855157
$916$	30.9181	1.02156
$917$	−3.79303	−0.125257
$918$	−54.6210	−1.80276
$919$	48.0869	1.58624	0.793120	−	0.609066i	$-0.208456\pi$
$919$	48.0869	1.58624	0.793120	+	0.609066i	$0.208456\pi$
$920$	−28.8461	−0.951029
$921$	75.1264	2.47550
$922$	56.0327	1.84534
$923$	−0.754796	−0.0248444
$924$	−31.3458	−1.03120
$925$	−2.19611	−0.0722076
$926$	73.8293	2.42618
$927$	24.2306	0.795839
$928$	−28.0172	−0.919710
$929$	−18.1909	−0.596823	−0.298412	−	0.954437i	$-0.596457\pi$
$929$	−18.1909	−0.596823	−0.298412	+	0.954437i	$0.596457\pi$
$930$	77.1409	2.52955
$931$	3.56060	0.116694
$932$	61.9897	2.03054
$933$	−16.4144	−0.537384
$934$	−34.1629	−1.11785
$935$	39.0978	1.27863
$936$	4.40617	0.144020
$937$	38.8486	1.26913	0.634564	−	0.772871i	$-0.281180\pi$
$937$	38.8486	1.26913	0.634564	+	0.772871i	$0.281180\pi$
$938$	−29.6653	−0.968606
$939$	77.6354	2.53354
$940$	4.84340	0.157974
$941$	−33.0016	−1.07582	−0.537911	−	0.843002i	$-0.680786\pi$
$941$	−33.0016	−1.07582	−0.537911	+	0.843002i	$0.680786\pi$
$942$	150.228	4.89469
$943$	56.0237	1.82438
$944$	0.0491029	0.00159816
$945$	−5.38965	−0.175325
$946$	37.3102	1.21306
$947$	−32.1803	−1.04572	−0.522860	−	0.852419i	$-0.675135\pi$
$947$	−32.1803	−1.04572	−0.522860	+	0.852419i	$0.675135\pi$
$948$	−16.7616	−0.544392
$949$	4.01770	0.130420
$950$	−3.00777	−0.0975848
$951$	78.7925	2.55502
$952$	−23.0285	−0.746356
$953$	48.6488	1.57589	0.787945	−	0.615745i	$-0.211145\pi$
$953$	48.6488	1.57589	0.787945	+	0.615745i	$0.211145\pi$
$954$	69.7496	2.25823
$955$	37.2958	1.20686
$956$	−32.5024	−1.05120
$957$	73.7549	2.38416
$958$	−43.1528	−1.39420
$959$	−10.7820	−0.348168
$960$	53.0242	1.71135
$961$	21.2588	0.685769
$962$	0.652965	0.0210524
$963$	65.3881	2.10710
$964$	58.1881	1.87411
$965$	20.9941	0.675824
$966$	27.4051	0.881744
$967$	−27.4082	−0.881389	−0.440694	−	0.897657i	$-0.645268\pi$
$967$	−27.4082	−0.881389	−0.440694	+	0.897657i	$0.645268\pi$
$968$	−4.64280	−0.149225
$969$	−10.4450	−0.335541
$970$	53.3696	1.71359
$971$	56.1553	1.80211	0.901055	−	0.433706i	$-0.142794\pi$
$971$	56.1553	1.80211	0.901055	+	0.433706i	$0.142794\pi$
$972$	−70.9132	−2.27454
$973$	−13.3125	−0.426778
$974$	−58.0158	−1.85895
$975$	1.63920	0.0524964
$976$	−9.32978	−0.298639
$977$	39.6301	1.26788	0.633939	−	0.773383i	$-0.281437\pi$
$977$	39.6301	1.26788	0.633939	+	0.773383i	$0.281437\pi$
$978$	−50.9926	−1.63056
$979$	29.6064	0.946224
$980$	36.7447	1.17377
$981$	4.28471	0.136800
$982$	22.8900	0.730450
$983$	−14.5686	−0.464666	−0.232333	−	0.972636i	$-0.574636\pi$
$983$	−14.5686	−0.464666	−0.232333	+	0.972636i	$0.574636\pi$
$984$	121.369	3.86910
$985$	24.2742	0.773440
$986$	122.995	3.91697
$987$	−2.02713	−0.0645242
$988$	0.573465	0.0182443
$989$	−20.9173	−0.665131
$990$	−59.2875	−1.88428
$991$	−50.9140	−1.61734	−0.808669	−	0.588264i	$-0.799812\pi$
$991$	−50.9140	−1.61734	−0.808669	+	0.588264i	$0.799812\pi$
$992$	25.9396	0.823582
$993$	−54.4030	−1.72643
$994$	−5.98196	−0.189736
$995$	−34.2928	−1.08716
$996$	109.129	3.45789
$997$	49.1931	1.55796	0.778981	−	0.627048i	$-0.215737\pi$
$997$	49.1931	1.55796	0.778981	+	0.627048i	$0.215737\pi$
$998$	−91.7945	−2.90571
$999$	3.46747	0.109706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.10	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.36112 q^{2} +2.69902 q^{3} +3.57489 q^{4} -1.67448 q^{5} -6.37271 q^{6} +0.928256 q^{7} -3.71850 q^{8} +4.28471 q^{9} +O(q^{10})\)	\(q-2.36112 q^{2} +2.69902 q^{3} +3.57489 q^{4} -1.67448 q^{5} -6.37271 q^{6} +0.928256 q^{7} -3.71850 q^{8} +4.28471 q^{9} +3.95366 q^{10} -3.49980 q^{11} +9.64870 q^{12} -0.276549 q^{13} -2.19172 q^{14} -4.51946 q^{15} +1.63005 q^{16} +6.67158 q^{17} -10.1167 q^{18} -0.580059 q^{19} -5.98609 q^{20} +2.50538 q^{21} +8.26344 q^{22} -4.63275 q^{23} -10.0363 q^{24} -2.19611 q^{25} +0.652965 q^{26} +3.46747 q^{27} +3.31841 q^{28} -7.80804 q^{29} +10.6710 q^{30} +7.22903 q^{31} +3.58825 q^{32} -9.44602 q^{33} -15.7524 q^{34} -1.55435 q^{35} +15.3174 q^{36} +1.00000 q^{37} +1.36959 q^{38} -0.746411 q^{39} +6.22657 q^{40} -12.0930 q^{41} -5.91551 q^{42} +4.51509 q^{43} -12.5114 q^{44} -7.17468 q^{45} +10.9385 q^{46} -0.809109 q^{47} +4.39955 q^{48} -6.13834 q^{49} +5.18527 q^{50} +18.0067 q^{51} -0.988631 q^{52} -6.89448 q^{53} -8.18711 q^{54} +5.86035 q^{55} -3.45172 q^{56} -1.56559 q^{57} +18.4357 q^{58} +0.0301235 q^{59} -16.1566 q^{60} -5.72360 q^{61} -17.0686 q^{62} +3.97731 q^{63} -11.7324 q^{64} +0.463076 q^{65} +22.3032 q^{66} +13.5351 q^{67} +23.8502 q^{68} -12.5039 q^{69} +3.67000 q^{70} +2.72934 q^{71} -15.9327 q^{72} -14.5280 q^{73} -2.36112 q^{74} -5.92734 q^{75} -2.07365 q^{76} -3.24871 q^{77} +1.76237 q^{78} -1.73719 q^{79} -2.72950 q^{80} -3.49537 q^{81} +28.5529 q^{82} +11.3102 q^{83} +8.95646 q^{84} -11.1715 q^{85} -10.6607 q^{86} -21.0741 q^{87} +13.0140 q^{88} -8.45946 q^{89} +16.9403 q^{90} -0.256708 q^{91} -16.5616 q^{92} +19.5113 q^{93} +1.91040 q^{94} +0.971299 q^{95} +9.68477 q^{96} +13.4988 q^{97} +14.4934 q^{98} -14.9956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 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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