LMFDB - Embedded newform 4033.2.a.d.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.24777 q^{2} -0.430015 q^{3} +3.05245 q^{4} -2.54923 q^{5} +0.966572 q^{6} -1.16281 q^{7} -2.36567 q^{8} -2.81509 q^{9} +O(q^{10})$	\(q-2.24777 q^{2} -0.430015 q^{3} +3.05245 q^{4} -2.54923 q^{5} +0.966572 q^{6} -1.16281 q^{7} -2.36567 q^{8} -2.81509 q^{9} +5.73008 q^{10} -4.74947 q^{11} -1.31260 q^{12} +7.05536 q^{13} +2.61373 q^{14} +1.09621 q^{15} -0.787431 q^{16} +0.294550 q^{17} +6.32766 q^{18} -2.10260 q^{19} -7.78141 q^{20} +0.500025 q^{21} +10.6757 q^{22} +0.0839506 q^{23} +1.01727 q^{24} +1.49858 q^{25} -15.8588 q^{26} +2.50057 q^{27} -3.54943 q^{28} +2.00176 q^{29} -2.46402 q^{30} -3.70206 q^{31} +6.50130 q^{32} +2.04234 q^{33} -0.662080 q^{34} +2.96427 q^{35} -8.59293 q^{36} -1.00000 q^{37} +4.72616 q^{38} -3.03391 q^{39} +6.03065 q^{40} -4.65519 q^{41} -1.12394 q^{42} +10.0771 q^{43} -14.4976 q^{44} +7.17631 q^{45} -0.188701 q^{46} +9.77592 q^{47} +0.338607 q^{48} -5.64787 q^{49} -3.36846 q^{50} -0.126661 q^{51} +21.5362 q^{52} -1.02973 q^{53} -5.62070 q^{54} +12.1075 q^{55} +2.75083 q^{56} +0.904149 q^{57} -4.49948 q^{58} -5.69236 q^{59} +3.34612 q^{60} +12.6845 q^{61} +8.32137 q^{62} +3.27341 q^{63} -13.0386 q^{64} -17.9858 q^{65} -4.59071 q^{66} +2.67338 q^{67} +0.899101 q^{68} -0.0361000 q^{69} -6.66299 q^{70} +1.82350 q^{71} +6.65957 q^{72} +2.80184 q^{73} +2.24777 q^{74} -0.644412 q^{75} -6.41810 q^{76} +5.52274 q^{77} +6.81952 q^{78} +10.8000 q^{79} +2.00734 q^{80} +7.36998 q^{81} +10.4638 q^{82} +3.88417 q^{83} +1.52630 q^{84} -0.750877 q^{85} -22.6510 q^{86} -0.860785 q^{87} +11.2357 q^{88} -0.146585 q^{89} -16.1307 q^{90} -8.20405 q^{91} +0.256255 q^{92} +1.59194 q^{93} -21.9740 q^{94} +5.36002 q^{95} -2.79566 q^{96} +16.0336 q^{97} +12.6951 q^{98} +13.3702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.24777	−1.58941	−0.794705	−	0.606995i	$-0.792375\pi$
$2$	−2.24777	−1.58941	−0.794705	+	0.606995i	$0.792375\pi$
$3$	−0.430015	−0.248269	−0.124135	−	0.992265i	$-0.539615\pi$
$3$	−0.430015	−0.248269	−0.124135	+	0.992265i	$0.539615\pi$
$4$	3.05245	1.52623
$5$	−2.54923	−1.14005	−0.570026	−	0.821627i	$-0.693067\pi$
$5$	−2.54923	−1.14005	−0.570026	+	0.821627i	$0.693067\pi$
$6$	0.966572	0.394601
$7$	−1.16281	−0.439501	−0.219750	−	0.975556i	$-0.570524\pi$
$7$	−1.16281	−0.439501	−0.219750	+	0.975556i	$0.570524\pi$
$8$	−2.36567	−0.836391
$9$	−2.81509	−0.938363
$10$	5.73008	1.81201
$11$	−4.74947	−1.43202	−0.716010	−	0.698090i	$-0.754034\pi$
$11$	−4.74947	−1.43202	−0.716010	+	0.698090i	$0.754034\pi$
$12$	−1.31260	−0.378915
$13$	7.05536	1.95681	0.978403	−	0.206709i	$-0.0662752\pi$
$13$	7.05536	1.95681	0.978403	+	0.206709i	$0.0662752\pi$
$14$	2.61373	0.698548
$15$	1.09621	0.283039
$16$	−0.787431	−0.196858
$17$	0.294550	0.0714389	0.0357195	−	0.999362i	$-0.488628\pi$
$17$	0.294550	0.0714389	0.0357195	+	0.999362i	$0.488628\pi$
$18$	6.32766	1.49144
$19$	−2.10260	−0.482370	−0.241185	−	0.970479i	$-0.577536\pi$
$19$	−2.10260	−0.482370	−0.241185	+	0.970479i	$0.577536\pi$
$20$	−7.78141	−1.73998
$21$	0.500025	0.109114
$22$	10.6757	2.27607
$23$	0.0839506	0.0175049	0.00875245	−	0.999962i	$-0.497214\pi$
$23$	0.0839506	0.0175049	0.00875245	+	0.999962i	$0.497214\pi$
$24$	1.01727	0.207650
$25$	1.49858	0.299716
$26$	−15.8588	−3.11017
$27$	2.50057	0.481235
$28$	−3.54943	−0.670778
$29$	2.00176	0.371717	0.185858	−	0.982577i	$-0.440493\pi$
$29$	2.00176	0.371717	0.185858	+	0.982577i	$0.440493\pi$
$30$	−2.46402	−0.449866
$31$	−3.70206	−0.664910	−0.332455	−	0.943119i	$-0.607877\pi$
$31$	−3.70206	−0.664910	−0.332455	+	0.943119i	$0.607877\pi$
$32$	6.50130	1.14928
$33$	2.04234	0.355526
$34$	−0.662080	−0.113546
$35$	2.96427	0.501054
$36$	−8.59293	−1.43215
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.72616	0.766684
$39$	−3.03391	−0.485814
$40$	6.03065	0.953529
$41$	−4.65519	−0.727019	−0.363509	−	0.931591i	$-0.618422\pi$
$41$	−4.65519	−0.727019	−0.363509	+	0.931591i	$0.618422\pi$
$42$	−1.12394	−0.173428
$43$	10.0771	1.53674	0.768372	−	0.640004i	$-0.221067\pi$
$43$	10.0771	1.53674	0.768372	+	0.640004i	$0.221067\pi$
$44$	−14.4976	−2.18559
$45$	7.17631	1.06978
$46$	−0.188701	−0.0278225
$47$	9.77592	1.42596	0.712982	−	0.701182i	$-0.247344\pi$
$47$	9.77592	1.42596	0.712982	+	0.701182i	$0.247344\pi$
$48$	0.338607	0.0488737
$49$	−5.64787	−0.806839
$50$	−3.36846	−0.476373
$51$	−0.126661	−0.0177361
$52$	21.5362	2.98653
$53$	−1.02973	−0.141444	−0.0707222	−	0.997496i	$-0.522530\pi$
$53$	−1.02973	−0.141444	−0.0707222	+	0.997496i	$0.522530\pi$
$54$	−5.62070	−0.764881
$55$	12.1075	1.63258
$56$	2.75083	0.367595
$57$	0.904149	0.119758
$58$	−4.49948	−0.590811
$59$	−5.69236	−0.741082	−0.370541	−	0.928816i	$-0.620828\pi$
$59$	−5.69236	−0.741082	−0.370541	+	0.928816i	$0.620828\pi$
$60$	3.34612	0.431982
$61$	12.6845	1.62408	0.812041	−	0.583600i	$-0.198357\pi$
$61$	12.6845	1.62408	0.812041	+	0.583600i	$0.198357\pi$
$62$	8.32137	1.05681
$63$	3.27341	0.412411
$64$	−13.0386	−1.62982
$65$	−17.9858	−2.23086
$66$	−4.59071	−0.565077
$67$	2.67338	0.326605	0.163302	−	0.986576i	$-0.447785\pi$
$67$	2.67338	0.326605	0.163302	+	0.986576i	$0.447785\pi$
$68$	0.899101	0.109032
$69$	−0.0361000	−0.00434593
$70$	−6.66299	−0.796380
$71$	1.82350	0.216410	0.108205	−	0.994129i	$-0.465490\pi$
$71$	1.82350	0.216410	0.108205	+	0.994129i	$0.465490\pi$
$72$	6.65957	0.784838
$73$	2.80184	0.327930	0.163965	−	0.986466i	$-0.447572\pi$
$73$	2.80184	0.327930	0.163965	+	0.986466i	$0.447572\pi$
$74$	2.24777	0.261298
$75$	−0.644412	−0.0744103
$76$	−6.41810	−0.736206
$77$	5.52274	0.629374
$78$	6.81952	0.772158
$79$	10.8000	1.21509	0.607545	−	0.794285i	$-0.292154\pi$
$79$	10.8000	1.21509	0.607545	+	0.794285i	$0.292154\pi$
$80$	2.00734	0.224428
$81$	7.36998	0.818887
$82$	10.4638	1.15553
$83$	3.88417	0.426343	0.213172	−	0.977015i	$-0.431621\pi$
$83$	3.88417	0.426343	0.213172	+	0.977015i	$0.431621\pi$
$84$	1.52630	0.166533
$85$	−0.750877	−0.0814440
$86$	−22.6510	−2.44252
$87$	−0.860785	−0.0922858
$88$	11.2357	1.19773
$89$	−0.146585	−0.0155380	−0.00776899	−	0.999970i	$-0.502473\pi$
$89$	−0.146585	−0.0155380	−0.00776899	+	0.999970i	$0.502473\pi$
$90$	−16.1307	−1.70032
$91$	−8.20405	−0.860018
$92$	0.256255	0.0267165
$93$	1.59194	0.165076
$94$	−21.9740	−2.26644
$95$	5.36002	0.549926
$96$	−2.79566	−0.285330
$97$	16.0336	1.62797	0.813985	−	0.580886i	$-0.197294\pi$
$97$	16.0336	1.62797	0.813985	+	0.580886i	$0.197294\pi$
$98$	12.6951	1.28240
$99$	13.3702	1.34375
$100$	4.57435	0.457435
$101$	−12.9748	−1.29104	−0.645522	−	0.763742i	$-0.723360\pi$
$101$	−12.9748	−1.29104	−0.645522	+	0.763742i	$0.723360\pi$
$102$	0.284704	0.0281899
$103$	2.59612	0.255804	0.127902	−	0.991787i	$-0.459176\pi$
$103$	2.59612	0.255804	0.127902	+	0.991787i	$0.459176\pi$
$104$	−16.6907	−1.63665
$105$	−1.27468	−0.124396
$106$	2.31460	0.224813
$107$	−19.0742	−1.84398	−0.921988	−	0.387217i	$-0.873436\pi$
$107$	−19.0742	−1.84398	−0.921988	+	0.387217i	$0.873436\pi$
$108$	7.63288	0.734474
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−27.2149	−2.59484
$111$	0.430015	0.0408152
$112$	0.915632	0.0865191
$113$	5.69733	0.535960	0.267980	−	0.963425i	$-0.413644\pi$
$113$	5.69733	0.535960	0.267980	+	0.963425i	$0.413644\pi$
$114$	−2.03232	−0.190344
$115$	−0.214009	−0.0199565
$116$	6.11027	0.567325
$117$	−19.8615	−1.83619
$118$	12.7951	1.17788
$119$	−0.342506	−0.0313975
$120$	−2.59327	−0.236732
$121$	11.5575	1.05068
$122$	−28.5118	−2.58133
$123$	2.00180	0.180496
$124$	−11.3004	−1.01480
$125$	8.92593	0.798359
$126$	−7.35787	−0.655491
$127$	−7.68914	−0.682301	−0.341150	−	0.940009i	$-0.610817\pi$
$127$	−7.68914	−0.682301	−0.341150	+	0.940009i	$0.610817\pi$
$128$	16.3050	1.44117
$129$	−4.33330	−0.381526
$130$	40.4278	3.54575
$131$	−10.1462	−0.886477	−0.443238	−	0.896404i	$-0.646170\pi$
$131$	−10.1462	−0.886477	−0.443238	+	0.896404i	$0.646170\pi$
$132$	6.23416	0.542614
$133$	2.44493	0.212002
$134$	−6.00912	−0.519109
$135$	−6.37454	−0.548633
$136$	−0.696809	−0.0597509
$137$	−10.8127	−0.923794	−0.461897	−	0.886934i	$-0.652831\pi$
$137$	−10.8127	−0.923794	−0.461897	+	0.886934i	$0.652831\pi$
$138$	0.0811443	0.00690746
$139$	−13.7521	−1.16644	−0.583218	−	0.812316i	$-0.698207\pi$
$139$	−13.7521	−1.16644	−0.583218	+	0.812316i	$0.698207\pi$
$140$	9.04831	0.764722
$141$	−4.20379	−0.354023
$142$	−4.09881	−0.343964
$143$	−33.5093	−2.80219
$144$	2.21669	0.184724
$145$	−5.10294	−0.423776
$146$	−6.29788	−0.521216
$147$	2.42867	0.200313
$148$	−3.05245	−0.250910
$149$	23.5174	1.92662	0.963309	−	0.268396i	$-0.0864935\pi$
$149$	23.5174	1.92662	0.963309	+	0.268396i	$0.0864935\pi$
$150$	1.44849	0.118269
$151$	5.90896	0.480864	0.240432	−	0.970666i	$-0.422711\pi$
$151$	5.90896	0.480864	0.240432	+	0.970666i	$0.422711\pi$
$152$	4.97407	0.403450
$153$	−0.829185	−0.0670356
$154$	−12.4138	−1.00033
$155$	9.43741	0.758031
$156$	−9.26087	−0.741463
$157$	−10.1050	−0.806464	−0.403232	−	0.915098i	$-0.632113\pi$
$157$	−10.1050	−0.806464	−0.403232	+	0.915098i	$0.632113\pi$
$158$	−24.2758	−1.93128
$159$	0.442799	0.0351163
$160$	−16.5733	−1.31024
$161$	−0.0976186	−0.00769342
$162$	−16.5660	−1.30155
$163$	16.7315	1.31051	0.655255	−	0.755408i	$-0.272561\pi$
$163$	16.7315	1.31051	0.655255	+	0.755408i	$0.272561\pi$
$164$	−14.2098	−1.10960
$165$	−5.20641	−0.405318
$166$	−8.73071	−0.677635
$167$	10.6026	0.820456	0.410228	−	0.911983i	$-0.365449\pi$
$167$	10.6026	0.820456	0.410228	+	0.911983i	$0.365449\pi$
$168$	−1.18290	−0.0912624
$169$	36.7781	2.82909
$170$	1.68780	0.129448
$171$	5.91901	0.452638
$172$	30.7599	2.34542
$173$	−11.7940	−0.896685	−0.448342	−	0.893862i	$-0.647985\pi$
$173$	−11.7940	−0.896685	−0.448342	+	0.893862i	$0.647985\pi$
$174$	1.93484	0.146680
$175$	−1.74257	−0.131726
$176$	3.73988	0.281904
$177$	2.44780	0.183988
$178$	0.329489	0.0246962
$179$	−15.1551	−1.13275	−0.566374	−	0.824148i	$-0.691654\pi$
$179$	−15.1551	−1.13275	−0.566374	+	0.824148i	$0.691654\pi$
$180$	21.9054	1.63273
$181$	−2.19847	−0.163411	−0.0817055	−	0.996657i	$-0.526037\pi$
$181$	−2.19847	−0.163411	−0.0817055	+	0.996657i	$0.526037\pi$
$182$	18.4408	1.36692
$183$	−5.45451	−0.403209
$184$	−0.198600	−0.0146410
$185$	2.54923	0.187423
$186$	−3.57831	−0.262374
$187$	−1.39896	−0.102302
$188$	29.8405	2.17635
$189$	−2.90769	−0.211503
$190$	−12.0481	−0.874059
$191$	−8.33547	−0.603134	−0.301567	−	0.953445i	$-0.597510\pi$
$191$	−8.33547	−0.603134	−0.301567	+	0.953445i	$0.597510\pi$
$192$	5.60677	0.404634
$193$	14.6536	1.05479	0.527395	−	0.849620i	$-0.323169\pi$
$193$	14.6536	1.05479	0.527395	+	0.849620i	$0.323169\pi$
$194$	−36.0399	−2.58751
$195$	7.73413	0.553853
$196$	−17.2399	−1.23142
$197$	24.7052	1.76018	0.880088	−	0.474811i	$-0.157484\pi$
$197$	24.7052	1.76018	0.880088	+	0.474811i	$0.157484\pi$
$198$	−30.0531	−2.13578
$199$	17.1851	1.21822	0.609111	−	0.793085i	$-0.291526\pi$
$199$	17.1851	1.21822	0.609111	+	0.793085i	$0.291526\pi$
$200$	−3.54515	−0.250680
$201$	−1.14959	−0.0810859
$202$	29.1644	2.05200
$203$	−2.32766	−0.163370
$204$	−0.386627	−0.0270693
$205$	11.8672	0.828838
$206$	−5.83548	−0.406577
$207$	−0.236328	−0.0164259
$208$	−5.55561	−0.385212
$209$	9.98625	0.690764
$210$	2.86518	0.197716
$211$	−14.0705	−0.968655	−0.484328	−	0.874887i	$-0.660936\pi$
$211$	−14.0705	−0.968655	−0.484328	+	0.874887i	$0.660936\pi$
$212$	−3.14321	−0.215876
$213$	−0.784133	−0.0537279
$214$	42.8745	2.93084
$215$	−25.6889	−1.75197
$216$	−5.91553	−0.402501
$217$	4.30479	0.292228
$218$	2.24777	0.152238
$219$	−1.20483	−0.0814150
$220$	36.9576	2.49168
$221$	2.07816	0.139792
$222$	−0.966572	−0.0648721
$223$	−18.9661	−1.27007	−0.635033	−	0.772485i	$-0.719014\pi$
$223$	−18.9661	−1.27007	−0.635033	+	0.772485i	$0.719014\pi$
$224$	−7.55978	−0.505109
$225$	−4.21864	−0.281243
$226$	−12.8063	−0.851860
$227$	−6.97613	−0.463022	−0.231511	−	0.972832i	$-0.574367\pi$
$227$	−6.97613	−0.463022	−0.231511	+	0.972832i	$0.574367\pi$
$228$	2.75987	0.182777
$229$	3.48427	0.230247	0.115123	−	0.993351i	$-0.463274\pi$
$229$	3.48427	0.230247	0.115123	+	0.993351i	$0.463274\pi$
$230$	0.481043	0.0317191
$231$	−2.37486	−0.156254
$232$	−4.73550	−0.310901
$233$	−10.6089	−0.695014	−0.347507	−	0.937677i	$-0.612972\pi$
$233$	−10.6089	−0.695014	−0.347507	+	0.937677i	$0.612972\pi$
$234$	44.6439	2.91846
$235$	−24.9211	−1.62567
$236$	−17.3757	−1.13106
$237$	−4.64414	−0.301669
$238$	0.769874	0.0499035
$239$	3.24797	0.210094	0.105047	−	0.994467i	$-0.466501\pi$
$239$	3.24797	0.210094	0.105047	+	0.994467i	$0.466501\pi$
$240$	−0.863187	−0.0557185
$241$	−10.8670	−0.700004	−0.350002	−	0.936749i	$-0.613819\pi$
$241$	−10.8670	−0.700004	−0.350002	+	0.936749i	$0.613819\pi$
$242$	−25.9786	−1.66997
$243$	−10.6709	−0.684540
$244$	38.7188	2.47872
$245$	14.3977	0.919838
$246$	−4.49958	−0.286883
$247$	−14.8346	−0.943904
$248$	8.75786	0.556125
$249$	−1.67025	−0.105848
$250$	−20.0634	−1.26892
$251$	0.598480	0.0377757	0.0188879	−	0.999822i	$-0.493987\pi$
$251$	0.598480	0.0377757	0.0188879	+	0.999822i	$0.493987\pi$
$252$	9.99194	0.629433
$253$	−0.398721	−0.0250674
$254$	17.2834	1.08446
$255$	0.322888	0.0202200
$256$	−10.5728	−0.660798
$257$	9.01116	0.562101	0.281050	−	0.959693i	$-0.409317\pi$
$257$	9.01116	0.562101	0.281050	+	0.959693i	$0.409317\pi$
$258$	9.74024	0.606401
$259$	1.16281	0.0722535
$260$	−54.9007	−3.40480
$261$	−5.63512	−0.348805
$262$	22.8063	1.40898
$263$	−23.4255	−1.44448	−0.722240	−	0.691642i	$-0.756887\pi$
$263$	−23.4255	−1.44448	−0.722240	+	0.691642i	$0.756887\pi$
$264$	−4.83151	−0.297359
$265$	2.62502	0.161254
$266$	−5.49562	−0.336958
$267$	0.0630337	0.00385760
$268$	8.16036	0.498473
$269$	15.8899	0.968823	0.484411	−	0.874840i	$-0.339034\pi$
$269$	15.8899	0.968823	0.484411	+	0.874840i	$0.339034\pi$
$270$	14.3285	0.872003
$271$	15.5382	0.943880	0.471940	−	0.881631i	$-0.343554\pi$
$271$	15.5382	0.943880	0.471940	+	0.881631i	$0.343554\pi$
$272$	−0.231938	−0.0140633
$273$	3.52786	0.213516
$274$	24.3045	1.46829
$275$	−7.11748	−0.429200
$276$	−0.110193	−0.00663287
$277$	−17.1127	−1.02820	−0.514101	−	0.857730i	$-0.671874\pi$
$277$	−17.1127	−1.02820	−0.514101	+	0.857730i	$0.671874\pi$
$278$	30.9115	1.85395
$279$	10.4216	0.623926
$280$	−7.01250	−0.419077
$281$	−16.0612	−0.958129	−0.479065	−	0.877780i	$-0.659024\pi$
$281$	−16.0612	−0.958129	−0.479065	+	0.877780i	$0.659024\pi$
$282$	9.44913	0.562688
$283$	−2.50329	−0.148805	−0.0744024	−	0.997228i	$-0.523705\pi$
$283$	−2.50329	−0.148805	−0.0744024	+	0.997228i	$0.523705\pi$
$284$	5.56616	0.330291
$285$	−2.30489	−0.136530
$286$	75.3210	4.45382
$287$	5.41310	0.319525
$288$	−18.3017	−1.07844
$289$	−16.9132	−0.994896
$290$	11.4702	0.673555
$291$	−6.89470	−0.404175
$292$	8.55249	0.500496
$293$	16.0100	0.935312	0.467656	−	0.883911i	$-0.345099\pi$
$293$	16.0100	0.935312	0.467656	+	0.883911i	$0.345099\pi$
$294$	−5.45908	−0.318380
$295$	14.5111	0.844872
$296$	2.36567	0.137502
$297$	−11.8764	−0.689139
$298$	−52.8615	−3.06219
$299$	0.592302	0.0342537
$300$	−1.96704	−0.113567
$301$	−11.7178	−0.675400
$302$	−13.2820	−0.764291
$303$	5.57937	0.320526
$304$	1.65565	0.0949582
$305$	−32.3357	−1.85154
$306$	1.86381	0.106547
$307$	−9.45518	−0.539636	−0.269818	−	0.962911i	$-0.586963\pi$
$307$	−9.45518	−0.539636	−0.269818	+	0.962911i	$0.586963\pi$
$308$	16.8579	0.960568
$309$	−1.11637	−0.0635081
$310$	−21.2131	−1.20482
$311$	−1.38739	−0.0786715	−0.0393357	−	0.999226i	$-0.512524\pi$
$311$	−1.38739	−0.0786715	−0.0393357	+	0.999226i	$0.512524\pi$
$312$	7.17723	0.406331
$313$	−12.6434	−0.714648	−0.357324	−	0.933980i	$-0.616311\pi$
$313$	−12.6434	−0.714648	−0.357324	+	0.933980i	$0.616311\pi$
$314$	22.7136	1.28180
$315$	−8.34469	−0.470170
$316$	32.9664	1.85450
$317$	8.34217	0.468543	0.234271	−	0.972171i	$-0.424730\pi$
$317$	8.34217	0.468543	0.234271	+	0.972171i	$0.424730\pi$
$318$	−0.995310	−0.0558142
$319$	−9.50729	−0.532306
$320$	33.2383	1.85808
$321$	8.20220	0.457802
$322$	0.219424	0.0122280
$323$	−0.619322	−0.0344600
$324$	22.4965	1.24981
$325$	10.5730	0.586487
$326$	−37.6084	−2.08294
$327$	0.430015	0.0237799
$328$	11.0127	0.608072
$329$	−11.3675	−0.626713
$330$	11.7028	0.644217
$331$	−16.9375	−0.930970	−0.465485	−	0.885056i	$-0.654120\pi$
$331$	−16.9375	−0.930970	−0.465485	+	0.885056i	$0.654120\pi$
$332$	11.8563	0.650697
$333$	2.81509	0.154266
$334$	−23.8322	−1.30404
$335$	−6.81505	−0.372346
$336$	−0.393735	−0.0214800
$337$	−29.5763	−1.61112	−0.805561	−	0.592512i	$-0.798136\pi$
$337$	−29.5763	−1.61112	−0.805561	+	0.592512i	$0.798136\pi$
$338$	−82.6686	−4.49658
$339$	−2.44993	−0.133062
$340$	−2.29202	−0.124302
$341$	17.5828	0.952164
$342$	−13.3045	−0.719428
$343$	14.7071	0.794107
$344$	−23.8391	−1.28532
$345$	0.0920272	0.00495458
$346$	26.5103	1.42520
$347$	−6.29530	−0.337949	−0.168975	−	0.985620i	$-0.554046\pi$
$347$	−6.29530	−0.337949	−0.168975	+	0.985620i	$0.554046\pi$
$348$	−2.62751	−0.140849
$349$	12.2184	0.654035	0.327018	−	0.945018i	$-0.393956\pi$
$349$	12.2184	0.654035	0.327018	+	0.945018i	$0.393956\pi$
$350$	3.91688	0.209366
$351$	17.6424	0.941684
$352$	−30.8778	−1.64579
$353$	−27.3453	−1.45545	−0.727723	−	0.685871i	$-0.759421\pi$
$353$	−27.3453	−1.45545	−0.727723	+	0.685871i	$0.759421\pi$
$354$	−5.50208	−0.292432
$355$	−4.64853	−0.246718
$356$	−0.447444	−0.0237145
$357$	0.147283	0.00779502
$358$	34.0652	1.80040
$359$	17.1295	0.904060	0.452030	−	0.892003i	$-0.350700\pi$
$359$	17.1295	0.904060	0.452030	+	0.892003i	$0.350700\pi$
$360$	−16.9768	−0.894756
$361$	−14.5791	−0.767319
$362$	4.94165	0.259727
$363$	−4.96990	−0.260852
$364$	−25.0425	−1.31258
$365$	−7.14254	−0.373857
$366$	12.2605	0.640865
$367$	26.6592	1.39160	0.695799	−	0.718236i	$-0.255050\pi$
$367$	26.6592	1.39160	0.695799	+	0.718236i	$0.255050\pi$
$368$	−0.0661052	−0.00344597
$369$	13.1048	0.682207
$370$	−5.73008	−0.297893
$371$	1.19738	0.0621650
$372$	4.85932	0.251944
$373$	1.17442	0.0608089	0.0304045	−	0.999538i	$-0.490320\pi$
$373$	1.17442	0.0608089	0.0304045	+	0.999538i	$0.490320\pi$
$374$	3.14453	0.162600
$375$	−3.83828	−0.198208
$376$	−23.1266	−1.19266
$377$	14.1231	0.727378
$378$	6.53581	0.336166
$379$	−16.5853	−0.851928	−0.425964	−	0.904740i	$-0.640065\pi$
$379$	−16.5853	−0.851928	−0.425964	+	0.904740i	$0.640065\pi$
$380$	16.3612	0.839313
$381$	3.30644	0.169394
$382$	18.7362	0.958627
$383$	−13.4128	−0.685364	−0.342682	−	0.939451i	$-0.611335\pi$
$383$	−13.4128	−0.685364	−0.342682	+	0.939451i	$0.611335\pi$
$384$	−7.01139	−0.357799
$385$	−14.0787	−0.717519
$386$	−32.9379	−1.67649
$387$	−28.3679	−1.44202
$388$	48.9420	2.48465
$389$	11.7260	0.594531	0.297265	−	0.954795i	$-0.403925\pi$
$389$	11.7260	0.594531	0.297265	+	0.954795i	$0.403925\pi$
$390$	−17.3845	−0.880300
$391$	0.0247277	0.00125053
$392$	13.3610	0.674833
$393$	4.36301	0.220085
$394$	−55.5316	−2.79764
$395$	−27.5316	−1.38527
$396$	40.8119	2.05087
$397$	3.57515	0.179431	0.0897157	−	0.995967i	$-0.471404\pi$
$397$	3.57515	0.179431	0.0897157	+	0.995967i	$0.471404\pi$
$398$	−38.6282	−1.93625
$399$	−1.05135	−0.0526335
$400$	−1.18003	−0.0590015
$401$	−9.37817	−0.468323	−0.234162	−	0.972198i	$-0.575235\pi$
$401$	−9.37817	−0.468323	−0.234162	+	0.972198i	$0.575235\pi$
$402$	2.58401	0.128879
$403$	−26.1194	−1.30110
$404$	−39.6051	−1.97043
$405$	−18.7878	−0.933573
$406$	5.23204	0.259662
$407$	4.74947	0.235423
$408$	0.299638	0.0148343
$409$	−9.26333	−0.458042	−0.229021	−	0.973421i	$-0.573552\pi$
$409$	−9.26333	−0.458042	−0.229021	+	0.973421i	$0.573552\pi$
$410$	−26.6746	−1.31736
$411$	4.64963	0.229349
$412$	7.92455	0.390414
$413$	6.61914	0.325706
$414$	0.531211	0.0261076
$415$	−9.90165	−0.486053
$416$	45.8690	2.24892
$417$	5.91359	0.289590
$418$	−22.4468	−1.09791
$419$	−24.2130	−1.18288	−0.591441	−	0.806348i	$-0.701441\pi$
$419$	−24.2130	−1.18288	−0.591441	+	0.806348i	$0.701441\pi$
$420$	−3.89090	−0.189857
$421$	−9.74620	−0.475001	−0.237500	−	0.971387i	$-0.576328\pi$
$421$	−9.74620	−0.475001	−0.237500	+	0.971387i	$0.576328\pi$
$422$	31.6273	1.53959
$423$	−27.5201	−1.33807
$424$	2.43601	0.118303
$425$	0.441408	0.0214114
$426$	1.76255	0.0853957
$427$	−14.7497	−0.713786
$428$	−58.2233	−2.81433
$429$	14.4095	0.695696
$430$	57.7426	2.78459
$431$	−2.88528	−0.138979	−0.0694896	−	0.997583i	$-0.522137\pi$
$431$	−2.88528	−0.138979	−0.0694896	+	0.997583i	$0.522137\pi$
$432$	−1.96903	−0.0947349
$433$	9.16473	0.440429	0.220214	−	0.975452i	$-0.429324\pi$
$433$	9.16473	0.440429	0.220214	+	0.975452i	$0.429324\pi$
$434$	−9.67617	−0.464471
$435$	2.19434	0.105211
$436$	−3.05245	−0.146186
$437$	−0.176515	−0.00844384
$438$	2.70818	0.129402
$439$	9.64524	0.460342	0.230171	−	0.973150i	$-0.426071\pi$
$439$	9.64524	0.460342	0.230171	+	0.973150i	$0.426071\pi$
$440$	−28.6424	−1.36547
$441$	15.8993	0.757107
$442$	−4.67122	−0.222187
$443$	−29.8736	−1.41934	−0.709669	−	0.704536i	$-0.751155\pi$
$443$	−29.8736	−1.41934	−0.709669	+	0.704536i	$0.751155\pi$
$444$	1.31260	0.0622932
$445$	0.373679	0.0177141
$446$	42.6315	2.01866
$447$	−10.1128	−0.478319
$448$	15.1614	0.716307
$449$	4.58987	0.216609	0.108305	−	0.994118i	$-0.465458\pi$
$449$	4.58987	0.216609	0.108305	+	0.994118i	$0.465458\pi$
$450$	9.48252	0.447010
$451$	22.1097	1.04111
$452$	17.3908	0.817996
$453$	−2.54094	−0.119384
$454$	15.6807	0.735932
$455$	20.9140	0.980464
$456$	−2.13892	−0.100164
$457$	−9.83523	−0.460073	−0.230036	−	0.973182i	$-0.573885\pi$
$457$	−9.83523	−0.460073	−0.230036	+	0.973182i	$0.573885\pi$
$458$	−7.83182	−0.365957
$459$	0.736544	0.0343789
$460$	−0.653254	−0.0304581
$461$	−14.4415	−0.672607	−0.336303	−	0.941754i	$-0.609177\pi$
$461$	−14.4415	−0.672607	−0.336303	+	0.941754i	$0.609177\pi$
$462$	5.33813	0.248352
$463$	3.42847	0.159334	0.0796672	−	0.996822i	$-0.474614\pi$
$463$	3.42847	0.159334	0.0796672	+	0.996822i	$0.474614\pi$
$464$	−1.57624	−0.0731753
$465$	−4.05822	−0.188196
$466$	23.8464	1.10466
$467$	7.08429	0.327822	0.163911	−	0.986475i	$-0.447589\pi$
$467$	7.08429	0.327822	0.163911	+	0.986475i	$0.447589\pi$
$468$	−60.6262	−2.80245
$469$	−3.10863	−0.143543
$470$	56.0168	2.58386
$471$	4.34528	0.200220
$472$	13.4663	0.619835
$473$	−47.8609	−2.20065
$474$	10.4389	0.479477
$475$	−3.15092	−0.144574
$476$	−1.04548	−0.0479197
$477$	2.89878	0.132726
$478$	−7.30068	−0.333925
$479$	−0.855569	−0.0390919	−0.0195460	−	0.999809i	$-0.506222\pi$
$479$	−0.855569	−0.0390919	−0.0195460	+	0.999809i	$0.506222\pi$
$480$	7.12677	0.325291
$481$	−7.05536	−0.321697
$482$	24.4264	1.11259
$483$	0.0419774	0.00191004
$484$	35.2788	1.60358
$485$	−40.8735	−1.85597
$486$	23.9857	1.08801
$487$	34.3690	1.55741	0.778704	−	0.627392i	$-0.215877\pi$
$487$	34.3690	1.55741	0.778704	+	0.627392i	$0.215877\pi$
$488$	−30.0073	−1.35837
$489$	−7.19478	−0.325359
$490$	−32.3627	−1.46200
$491$	−35.2937	−1.59278	−0.796392	−	0.604781i	$-0.793261\pi$
$491$	−35.2937	−1.59278	−0.796392	+	0.604781i	$0.793261\pi$
$492$	6.11040	0.275478
$493$	0.589618	0.0265551
$494$	33.3448	1.50025
$495$	−34.0837	−1.53195
$496$	2.91512	0.130893
$497$	−2.12039	−0.0951124
$498$	3.75433	0.168236
$499$	−33.3454	−1.49274	−0.746372	−	0.665529i	$-0.768206\pi$
$499$	−33.3454	−1.49274	−0.746372	+	0.665529i	$0.768206\pi$
$500$	27.2460	1.21848
$501$	−4.55929	−0.203694
$502$	−1.34524	−0.0600411
$503$	−20.5881	−0.917979	−0.458989	−	0.888442i	$-0.651788\pi$
$503$	−20.5881	−0.917979	−0.458989	+	0.888442i	$0.651788\pi$
$504$	−7.74382	−0.344937
$505$	33.0758	1.47186
$506$	0.896232	0.0398424
$507$	−15.8151	−0.702374
$508$	−23.4707	−1.04135
$509$	1.56105	0.0691925	0.0345963	−	0.999401i	$-0.488985\pi$
$509$	1.56105	0.0691925	0.0345963	+	0.999401i	$0.488985\pi$
$510$	−0.725777	−0.0321379
$511$	−3.25801	−0.144126
$512$	−8.84493	−0.390894
$513$	−5.25771	−0.232133
$514$	−20.2550	−0.893409
$515$	−6.61812	−0.291629
$516$	−13.2272	−0.582295
$517$	−46.4305	−2.04201
$518$	−2.61373	−0.114841
$519$	5.07161	0.222619
$520$	42.5484	1.86587
$521$	38.6568	1.69359	0.846793	−	0.531923i	$-0.178530\pi$
$521$	38.6568	1.69359	0.846793	+	0.531923i	$0.178530\pi$
$522$	12.6664	0.554395
$523$	−40.7829	−1.78331	−0.891655	−	0.452716i	$-0.850455\pi$
$523$	−40.7829	−1.78331	−0.891655	+	0.452716i	$0.850455\pi$
$524$	−30.9708	−1.35296
$525$	0.749329	0.0327034
$526$	52.6551	2.29587
$527$	−1.09044	−0.0475004
$528$	−1.60820	−0.0699881
$529$	−22.9930	−0.999694
$530$	−5.90044	−0.256299
$531$	16.0245	0.695404
$532$	7.46303	0.323563
$533$	−32.8441	−1.42263
$534$	−0.141685	−0.00613131
$535$	48.6247	2.10223
$536$	−6.32433	−0.273169
$537$	6.51693	0.281226
$538$	−35.7167	−1.53986
$539$	26.8244	1.15541
$540$	−19.4580	−0.837338
$541$	−26.3166	−1.13144	−0.565719	−	0.824598i	$-0.691401\pi$
$541$	−26.3166	−1.13144	−0.565719	+	0.824598i	$0.691401\pi$
$542$	−34.9263	−1.50021
$543$	0.945374	0.0405699
$544$	1.91496	0.0821033
$545$	2.54923	0.109197
$546$	−7.92980	−0.339364
$547$	−19.8536	−0.848877	−0.424439	−	0.905457i	$-0.639528\pi$
$547$	−19.8536	−0.848877	−0.424439	+	0.905457i	$0.639528\pi$
$548$	−33.0054	−1.40992
$549$	−35.7079	−1.52398
$550$	15.9984	0.682175
$551$	−4.20890	−0.179305
$552$	0.0854007	0.00363489
$553$	−12.5583	−0.534033
$554$	38.4653	1.63424
$555$	−1.09621	−0.0465314
$556$	−41.9776	−1.78025
$557$	−1.64757	−0.0698098	−0.0349049	−	0.999391i	$-0.511113\pi$
$557$	−1.64757	−0.0698098	−0.0349049	+	0.999391i	$0.511113\pi$
$558$	−23.4254	−0.991675
$559$	71.0976	3.00711
$560$	−2.33416	−0.0986362
$561$	0.601573	0.0253984
$562$	36.1018	1.52286
$563$	−3.61375	−0.152301	−0.0761507	−	0.997096i	$-0.524263\pi$
$563$	−3.61375	−0.152301	−0.0761507	+	0.997096i	$0.524263\pi$
$564$	−12.8319	−0.540319
$565$	−14.5238	−0.611021
$566$	5.62680	0.236512
$567$	−8.56989	−0.359901
$568$	−4.31381	−0.181003
$569$	−23.5827	−0.988638	−0.494319	−	0.869281i	$-0.664583\pi$
$569$	−23.5827	−0.988638	−0.494319	+	0.869281i	$0.664583\pi$
$570$	5.18085	0.217002
$571$	−42.5523	−1.78076	−0.890378	−	0.455221i	$-0.849560\pi$
$571$	−42.5523	−1.78076	−0.890378	+	0.455221i	$0.849560\pi$
$572$	−102.285	−4.27677
$573$	3.58437	0.149739
$574$	−12.1674	−0.507857
$575$	0.125807	0.00524651
$576$	36.7047	1.52936
$577$	−14.1166	−0.587682	−0.293841	−	0.955854i	$-0.594934\pi$
$577$	−14.1166	−0.587682	−0.293841	+	0.955854i	$0.594934\pi$
$578$	38.0170	1.58130
$579$	−6.30126	−0.261872
$580$	−15.5765	−0.646779
$581$	−4.51656	−0.187378
$582$	15.4977	0.642400
$583$	4.89068	0.202551
$584$	−6.62823	−0.274278
$585$	50.6315	2.09335
$586$	−35.9867	−1.48660
$587$	30.4626	1.25733	0.628664	−	0.777677i	$-0.283602\pi$
$587$	30.4626	1.25733	0.628664	+	0.777677i	$0.283602\pi$
$588$	7.41340	0.305723
$589$	7.78396	0.320732
$590$	−32.6177	−1.34285
$591$	−10.6236	−0.436997
$592$	0.787431	0.0323632
$593$	−12.6272	−0.518539	−0.259269	−	0.965805i	$-0.583482\pi$
$593$	−12.6272	−0.518539	−0.259269	+	0.965805i	$0.583482\pi$
$594$	26.6954	1.09532
$595$	0.873127	0.0357947
$596$	71.7857	2.94046
$597$	−7.38985	−0.302447
$598$	−1.33136	−0.0544432
$599$	−33.8513	−1.38313	−0.691564	−	0.722315i	$-0.743078\pi$
$599$	−33.8513	−1.38313	−0.691564	+	0.722315i	$0.743078\pi$
$600$	1.52447	0.0622361
$601$	14.0076	0.571380	0.285690	−	0.958322i	$-0.407777\pi$
$601$	14.0076	0.571380	0.285690	+	0.958322i	$0.407777\pi$
$602$	26.3388	1.07349
$603$	−7.52579	−0.306474
$604$	18.0368	0.733908
$605$	−29.4628	−1.19783
$606$	−12.5411	−0.509448
$607$	−7.10471	−0.288371	−0.144186	−	0.989551i	$-0.546056\pi$
$607$	−7.10471	−0.288371	−0.144186	+	0.989551i	$0.546056\pi$
$608$	−13.6697	−0.554378
$609$	1.00093	0.0405597
$610$	72.6831	2.94285
$611$	68.9726	2.79033
$612$	−2.53105	−0.102312
$613$	7.39456	0.298663	0.149332	−	0.988787i	$-0.452288\pi$
$613$	7.39456	0.298663	0.149332	+	0.988787i	$0.452288\pi$
$614$	21.2530	0.857703
$615$	−5.10305	−0.205775
$616$	−13.0650	−0.526403
$617$	40.6914	1.63818	0.819088	−	0.573668i	$-0.194480\pi$
$617$	40.6914	1.63818	0.819088	+	0.573668i	$0.194480\pi$
$618$	2.50934	0.100940
$619$	32.8933	1.32210	0.661048	−	0.750344i	$-0.270112\pi$
$619$	32.8933	1.32210	0.661048	+	0.750344i	$0.270112\pi$
$620$	28.8073	1.15693
$621$	0.209924	0.00842398
$622$	3.11852	0.125041
$623$	0.170451	0.00682896
$624$	2.38899	0.0956362
$625$	−30.2472	−1.20989
$626$	28.4195	1.13587
$627$	−4.29423	−0.171495
$628$	−30.8449	−1.23085
$629$	−0.294550	−0.0117445
$630$	18.7569	0.747293
$631$	−17.9048	−0.712778	−0.356389	−	0.934338i	$-0.615992\pi$
$631$	−17.9048	−0.712778	−0.356389	+	0.934338i	$0.615992\pi$
$632$	−25.5492	−1.01629
$633$	6.05053	0.240487
$634$	−18.7512	−0.744707
$635$	19.6014	0.777858
$636$	1.35162	0.0535954
$637$	−39.8478	−1.57883
$638$	21.3702	0.846053
$639$	−5.13332	−0.203071
$640$	−41.5653	−1.64301
$641$	−7.64672	−0.302027	−0.151014	−	0.988532i	$-0.548254\pi$
$641$	−7.64672	−0.302027	−0.151014	+	0.988532i	$0.548254\pi$
$642$	−18.4366	−0.727636
$643$	16.5325	0.651978	0.325989	−	0.945374i	$-0.394303\pi$
$643$	16.5325	0.651978	0.325989	+	0.945374i	$0.394303\pi$
$644$	−0.297976	−0.0117419
$645$	11.0466	0.434959
$646$	1.39209	0.0547711
$647$	15.2064	0.597826	0.298913	−	0.954280i	$-0.403376\pi$
$647$	15.2064	0.597826	0.298913	+	0.954280i	$0.403376\pi$
$648$	−17.4350	−0.684910
$649$	27.0357	1.06125
$650$	−23.7657	−0.932168
$651$	−1.85112	−0.0725513
$652$	51.0721	2.00014
$653$	18.6645	0.730399	0.365200	−	0.930929i	$-0.381001\pi$
$653$	18.6645	0.730399	0.365200	+	0.930929i	$0.381001\pi$
$654$	−0.966572	−0.0377960
$655$	25.8650	1.01063
$656$	3.66564	0.143119
$657$	−7.88742	−0.307718
$658$	25.5516	0.996104
$659$	12.9082	0.502833	0.251416	−	0.967879i	$-0.419104\pi$
$659$	12.9082	0.502833	0.251416	+	0.967879i	$0.419104\pi$
$660$	−15.8923	−0.618608
$661$	−39.8418	−1.54967	−0.774834	−	0.632165i	$-0.782167\pi$
$661$	−39.8418	−1.54967	−0.774834	+	0.632165i	$0.782167\pi$
$662$	38.0716	1.47969
$663$	−0.893638	−0.0347060
$664$	−9.18868	−0.356590
$665$	−6.23269	−0.241693
$666$	−6.32766	−0.245192
$667$	0.168049	0.00650687
$668$	32.3641	1.25220
$669$	8.15572	0.315318
$670$	15.3187	0.591811
$671$	−60.2446	−2.32572
$672$	3.25082	0.125403
$673$	−31.0630	−1.19739	−0.598695	−	0.800977i	$-0.704314\pi$
$673$	−31.0630	−1.19739	−0.598695	+	0.800977i	$0.704314\pi$
$674$	66.4806	2.56074
$675$	3.74731	0.144234
$676$	112.264	4.31783
$677$	21.9780	0.844682	0.422341	−	0.906437i	$-0.361208\pi$
$677$	21.9780	0.844682	0.422341	+	0.906437i	$0.361208\pi$
$678$	5.50688	0.211490
$679$	−18.6441	−0.715495
$680$	1.77633	0.0681191
$681$	2.99984	0.114954
$682$	−39.5221	−1.51338
$683$	37.3784	1.43025	0.715123	−	0.698999i	$-0.246371\pi$
$683$	37.3784	1.43025	0.715123	+	0.698999i	$0.246371\pi$
$684$	18.0675	0.690828
$685$	27.5642	1.05317
$686$	−33.0581	−1.26216
$687$	−1.49829	−0.0571632
$688$	−7.93502	−0.302520
$689$	−7.26513	−0.276779
$690$	−0.206856	−0.00787486
$691$	13.0529	0.496556	0.248278	−	0.968689i	$-0.420135\pi$
$691$	13.0529	0.496556	0.248278	+	0.968689i	$0.420135\pi$
$692$	−36.0008	−1.36854
$693$	−15.5470	−0.590581
$694$	14.1504	0.537141
$695$	35.0572	1.32980
$696$	2.03633	0.0771870
$697$	−1.37119	−0.0519374
$698$	−27.4641	−1.03953
$699$	4.56200	0.172551
$700$	−5.31911	−0.201043
$701$	−44.0974	−1.66554	−0.832769	−	0.553621i	$-0.813246\pi$
$701$	−44.0974	−1.66554	−0.832769	+	0.553621i	$0.813246\pi$
$702$	−39.6561	−1.49672
$703$	2.10260	0.0793011
$704$	61.9263	2.33393
$705$	10.7164	0.403604
$706$	61.4659	2.31330
$707$	15.0873	0.567415
$708$	7.47179	0.280807
$709$	−26.3781	−0.990651	−0.495326	−	0.868707i	$-0.664951\pi$
$709$	−26.3781	−0.990651	−0.495326	+	0.868707i	$0.664951\pi$
$710$	10.4488	0.392137
$711$	−30.4028	−1.14020
$712$	0.346772	0.0129958
$713$	−0.310790	−0.0116392
$714$	−0.331057	−0.0123895
$715$	85.4229	3.19463
$716$	−46.2603	−1.72883
$717$	−1.39667	−0.0521598
$718$	−38.5031	−1.43692
$719$	15.9648	0.595387	0.297693	−	0.954662i	$-0.403783\pi$
$719$	15.9648	0.595387	0.297693	+	0.954662i	$0.403783\pi$
$720$	−5.65085	−0.210595
$721$	−3.01880	−0.112426
$722$	32.7703	1.21959
$723$	4.67296	0.173789
$724$	−6.71073	−0.249402
$725$	2.99980	0.111410
$726$	11.1712	0.414601
$727$	−4.30426	−0.159636	−0.0798181	−	0.996809i	$-0.525434\pi$
$727$	−4.30426	−0.159636	−0.0798181	+	0.996809i	$0.525434\pi$
$728$	19.4081	0.719311
$729$	−17.5213	−0.648937
$730$	16.0548	0.594213
$731$	2.96821	0.109783
$732$	−16.6497	−0.615389
$733$	16.6432	0.614731	0.307365	−	0.951592i	$-0.400553\pi$
$733$	16.6432	0.614731	0.307365	+	0.951592i	$0.400553\pi$
$734$	−59.9236	−2.21182
$735$	−6.19124	−0.228367
$736$	0.545788	0.0201180
$737$	−12.6971	−0.467705
$738$	−29.4565	−1.08431
$739$	−2.54039	−0.0934498	−0.0467249	−	0.998908i	$-0.514878\pi$
$739$	−2.54039	−0.0934498	−0.0467249	+	0.998908i	$0.514878\pi$
$740$	7.78141	0.286050
$741$	6.37910	0.234342
$742$	−2.69144	−0.0988057
$743$	−7.43169	−0.272642	−0.136321	−	0.990665i	$-0.543528\pi$
$743$	−7.43169	−0.272642	−0.136321	+	0.990665i	$0.543528\pi$
$744$	−3.76601	−0.138069
$745$	−59.9512	−2.19644
$746$	−2.63981	−0.0966503
$747$	−10.9343	−0.400065
$748$	−4.27026	−0.156136
$749$	22.1797	0.810430
$750$	8.62755	0.315034
$751$	−8.16338	−0.297886	−0.148943	−	0.988846i	$-0.547587\pi$
$751$	−8.16338	−0.297886	−0.148943	+	0.988846i	$0.547587\pi$
$752$	−7.69786	−0.280712
$753$	−0.257355	−0.00937854
$754$	−31.7455	−1.15610
$755$	−15.0633	−0.548210
$756$	−8.87559	−0.322802
$757$	19.8339	0.720877	0.360438	−	0.932783i	$-0.382627\pi$
$757$	19.8339	0.720877	0.360438	+	0.932783i	$0.382627\pi$
$758$	37.2798	1.35406
$759$	0.171456	0.00622345
$760$	−12.6800	−0.459954
$761$	10.2965	0.373247	0.186624	−	0.982431i	$-0.440246\pi$
$761$	10.2965	0.373247	0.186624	+	0.982431i	$0.440246\pi$
$762$	−7.43211	−0.269237
$763$	1.16281	0.0420966
$764$	−25.4436	−0.920519
$765$	2.11378	0.0764240
$766$	30.1489	1.08933
$767$	−40.1617	−1.45015
$768$	4.54644	0.164056
$769$	−29.7110	−1.07141	−0.535703	−	0.844406i	$-0.679953\pi$
$769$	−29.7110	−1.07141	−0.535703	+	0.844406i	$0.679953\pi$
$770$	31.6457	1.14043
$771$	−3.87493	−0.139552
$772$	44.7295	1.60985
$773$	37.5946	1.35218	0.676092	−	0.736817i	$-0.263672\pi$
$773$	37.5946	1.35218	0.676092	+	0.736817i	$0.263672\pi$
$774$	63.7645	2.29197
$775$	−5.54784	−0.199284
$776$	−37.9304	−1.36162
$777$	−0.500025	−0.0179383
$778$	−26.3573	−0.944953
$779$	9.78801	0.350692
$780$	23.6081	0.845305
$781$	−8.66068	−0.309904
$782$	−0.0555820	−0.00198761
$783$	5.00554	0.178883
$784$	4.44731	0.158832
$785$	25.7599	0.919410
$786$	−9.80703	−0.349805
$787$	−48.6549	−1.73436	−0.867180	−	0.497994i	$-0.834070\pi$
$787$	−48.6549	−1.73436	−0.867180	+	0.497994i	$0.834070\pi$
$788$	75.4116	2.68643
$789$	10.0733	0.358620
$790$	61.8846	2.20176
$791$	−6.62491	−0.235555
$792$	−31.6295	−1.12390
$793$	89.4936	3.17801
$794$	−8.03609	−0.285190
$795$	−1.12880	−0.0400343
$796$	52.4568	1.85928
$797$	39.1366	1.38629	0.693144	−	0.720799i	$-0.256225\pi$
$797$	39.1366	1.38629	0.693144	+	0.720799i	$0.256225\pi$
$798$	2.36320	0.0836563
$799$	2.87950	0.101869
$800$	9.74274	0.344458
$801$	0.412650	0.0145803
$802$	21.0799	0.744358
$803$	−13.3073	−0.469603
$804$	−3.50907	−0.123755
$805$	0.248852	0.00877089
$806$	58.7103	2.06798
$807$	−6.83288	−0.240529
$808$	30.6942	1.07982
$809$	26.4619	0.930350	0.465175	−	0.885219i	$-0.345991\pi$
$809$	26.4619	0.930350	0.465175	+	0.885219i	$0.345991\pi$
$810$	42.2306	1.48383
$811$	27.6638	0.971408	0.485704	−	0.874123i	$-0.338563\pi$
$811$	27.6638	0.971408	0.485704	+	0.874123i	$0.338563\pi$
$812$	−7.10509	−0.249340
$813$	−6.68166	−0.234336
$814$	−10.6757	−0.374183
$815$	−42.6524	−1.49405
$816$	0.0997367	0.00349148
$817$	−21.1881	−0.741279
$818$	20.8218	0.728017
$819$	23.0951	0.807008
$820$	36.2240	1.26500
$821$	−2.02895	−0.0708107	−0.0354054	−	0.999373i	$-0.511272\pi$
$821$	−2.02895	−0.0708107	−0.0354054	+	0.999373i	$0.511272\pi$
$822$	−10.4513	−0.364531
$823$	25.8220	0.900097	0.450048	−	0.893004i	$-0.351407\pi$
$823$	25.8220	0.900097	0.450048	+	0.893004i	$0.351407\pi$
$824$	−6.14158	−0.213952
$825$	3.06062	0.106557
$826$	−14.8783	−0.517681
$827$	26.4839	0.920936	0.460468	−	0.887676i	$-0.347682\pi$
$827$	26.4839	0.920936	0.460468	+	0.887676i	$0.347682\pi$
$828$	−0.721381	−0.0250697
$829$	53.6005	1.86162	0.930812	−	0.365500i	$-0.119102\pi$
$829$	53.6005	1.86162	0.930812	+	0.365500i	$0.119102\pi$
$830$	22.2566	0.772538
$831$	7.35871	0.255271
$832$	−91.9917	−3.18924
$833$	−1.66358	−0.0576397
$834$	−13.2924	−0.460277
$835$	−27.0286	−0.935362
$836$	30.4826	1.05426
$837$	−9.25727	−0.319978
$838$	54.4252	1.88009
$839$	−52.5306	−1.81356	−0.906779	−	0.421607i	$-0.861466\pi$
$839$	−52.5306	−1.81356	−0.906779	+	0.421607i	$0.861466\pi$
$840$	3.01548	0.104044
$841$	−24.9930	−0.861827
$842$	21.9072	0.754971
$843$	6.90654	0.237874
$844$	−42.9496	−1.47839
$845$	−93.7560	−3.22530
$846$	61.8587	2.12675
$847$	−13.4392	−0.461776
$848$	0.810842	0.0278444
$849$	1.07645	0.0369436
$850$	−0.992182	−0.0340315
$851$	−0.0839506	−0.00287779
$852$	−2.39353	−0.0820010
$853$	10.3780	0.355338	0.177669	−	0.984090i	$-0.443144\pi$
$853$	10.3780	0.355338	0.177669	+	0.984090i	$0.443144\pi$
$854$	33.1538	1.13450
$855$	−15.0889	−0.516030
$856$	45.1234	1.54229
$857$	53.7916	1.83749	0.918744	−	0.394854i	$-0.129205\pi$
$857$	53.7916	1.83749	0.918744	+	0.394854i	$0.129205\pi$
$858$	−32.3891	−1.10575
$859$	−31.3370	−1.06920	−0.534602	−	0.845104i	$-0.679539\pi$
$859$	−31.3370	−1.06920	−0.534602	+	0.845104i	$0.679539\pi$
$860$	−78.4141	−2.67390
$861$	−2.32771	−0.0793282
$862$	6.48544	0.220895
$863$	−0.927314	−0.0315661	−0.0157831	−	0.999875i	$-0.505024\pi$
$863$	−0.927314	−0.0315661	−0.0157831	+	0.999875i	$0.505024\pi$
$864$	16.2570	0.553074
$865$	30.0658	1.02227
$866$	−20.6002	−0.700022
$867$	7.27294	0.247002
$868$	13.1402	0.446007
$869$	−51.2941	−1.74003
$870$	−4.93236	−0.167223
$871$	18.8616	0.639102
$872$	2.36567	0.0801118
$873$	−45.1361	−1.52763
$874$	0.396764	0.0134207
$875$	−10.3792	−0.350880
$876$	−3.67769	−0.124258
$877$	31.7024	1.07051	0.535257	−	0.844689i	$-0.320215\pi$
$877$	31.7024	1.07051	0.535257	+	0.844689i	$0.320215\pi$
$878$	−21.6802	−0.731673
$879$	−6.88452	−0.232209
$880$	−9.53383	−0.321385
$881$	39.2656	1.32289	0.661445	−	0.749993i	$-0.269943\pi$
$881$	39.2656	1.32289	0.661445	+	0.749993i	$0.269943\pi$
$882$	−35.7378	−1.20335
$883$	28.9049	0.972729	0.486364	−	0.873756i	$-0.338323\pi$
$883$	28.9049	0.972729	0.486364	+	0.873756i	$0.338323\pi$
$884$	6.34348	0.213354
$885$	−6.24000	−0.209755
$886$	67.1489	2.25591
$887$	−17.7689	−0.596620	−0.298310	−	0.954469i	$-0.596423\pi$
$887$	−17.7689	−0.596620	−0.298310	+	0.954469i	$0.596423\pi$
$888$	−1.01727	−0.0341375
$889$	8.94101	0.299872
$890$	−0.839944	−0.0281550
$891$	−35.0035	−1.17266
$892$	−57.8933	−1.93841
$893$	−20.5549	−0.687842
$894$	22.7312	0.760246
$895$	38.6339	1.29139
$896$	−18.9596	−0.633397
$897$	−0.254698	−0.00850413
$898$	−10.3169	−0.344281
$899$	−7.41063	−0.247158
$900$	−12.8772	−0.429240
$901$	−0.303308	−0.0101046
$902$	−49.6975	−1.65474
$903$	5.03880	0.167681
$904$	−13.4780	−0.448272
$905$	5.60441	0.186297
$906$	5.71144	0.189750
$907$	16.8000	0.557835	0.278918	−	0.960315i	$-0.410024\pi$
$907$	16.8000	0.557835	0.278918	+	0.960315i	$0.410024\pi$
$908$	−21.2943	−0.706676
$909$	36.5253	1.21147
$910$	−47.0098	−1.55836
$911$	11.8168	0.391507	0.195754	−	0.980653i	$-0.437285\pi$
$911$	11.8168	0.391507	0.195754	+	0.980653i	$0.437285\pi$
$912$	−0.711955	−0.0235752
$913$	−18.4478	−0.610532
$914$	22.1073	0.731245
$915$	13.9048	0.459679
$916$	10.6356	0.351409
$917$	11.7981	0.389607
$918$	−1.65558	−0.0546423
$919$	38.3081	1.26367	0.631834	−	0.775103i	$-0.282302\pi$
$919$	38.3081	1.26367	0.631834	+	0.775103i	$0.282302\pi$
$920$	0.506276	0.0166914
$921$	4.06586	0.133975
$922$	32.4611	1.06905
$923$	12.8655	0.423472
$924$	−7.24914	−0.238479
$925$	−1.49858	−0.0492731
$926$	−7.70639	−0.253248
$927$	−7.30831	−0.240036
$928$	13.0140	0.427206
$929$	21.7794	0.714557	0.357279	−	0.933998i	$-0.383705\pi$
$929$	21.7794	0.714557	0.357279	+	0.933998i	$0.383705\pi$
$930$	9.12194	0.299120
$931$	11.8752	0.389195
$932$	−32.3833	−1.06075
$933$	0.596597	0.0195317
$934$	−15.9238	−0.521044
$935$	3.56627	0.116630
$936$	46.9857	1.53578
$937$	−46.4791	−1.51840	−0.759202	−	0.650855i	$-0.774411\pi$
$937$	−46.4791	−1.51840	−0.759202	+	0.650855i	$0.774411\pi$
$938$	6.98747	0.228149
$939$	5.43685	0.177425
$940$	−76.0705	−2.48115
$941$	−5.60750	−0.182799	−0.0913996	−	0.995814i	$-0.529134\pi$
$941$	−5.60750	−0.182799	−0.0913996	+	0.995814i	$0.529134\pi$
$942$	−9.76717	−0.318232
$943$	−0.390806	−0.0127264
$944$	4.48234	0.145888
$945$	7.41238	0.241125
$946$	107.580	3.49773
$947$	−19.9986	−0.649868	−0.324934	−	0.945737i	$-0.605342\pi$
$947$	−19.9986	−0.649868	−0.324934	+	0.945737i	$0.605342\pi$
$948$	−14.1760	−0.460416
$949$	19.7680	0.641696
$950$	7.08254	0.229788
$951$	−3.58725	−0.116325
$952$	0.810257	0.0262606
$953$	−47.9112	−1.55199	−0.775997	−	0.630736i	$-0.782753\pi$
$953$	−47.9112	−1.55199	−0.775997	+	0.630736i	$0.782753\pi$
$954$	−6.51579	−0.210956
$955$	21.2490	0.687603
$956$	9.91428	0.320651
$957$	4.08827	0.132155
$958$	1.92312	0.0621331
$959$	12.5732	0.406008
$960$	−14.2929	−0.461303
$961$	−17.2947	−0.557895
$962$	15.8588	0.511308
$963$	53.6957	1.73032
$964$	−33.1710	−1.06837
$965$	−37.3554	−1.20251
$966$	−0.0943554	−0.00303584
$967$	6.65369	0.213968	0.106984	−	0.994261i	$-0.465881\pi$
$967$	6.65369	0.213968	0.106984	+	0.994261i	$0.465881\pi$
$968$	−27.3413	−0.878782
$969$	0.266317	0.00855535
$970$	91.8741	2.94990
$971$	31.1185	0.998640	0.499320	−	0.866418i	$-0.333583\pi$
$971$	31.1185	0.998640	0.499320	+	0.866418i	$0.333583\pi$
$972$	−32.5725	−1.04476
$973$	15.9911	0.512650
$974$	−77.2535	−2.47536
$975$	−4.54656	−0.145606
$976$	−9.98815	−0.319713
$977$	−9.70385	−0.310454	−0.155227	−	0.987879i	$-0.549611\pi$
$977$	−9.70385	−0.310454	−0.155227	+	0.987879i	$0.549611\pi$
$978$	16.1722	0.517129
$979$	0.696202	0.0222507
$980$	43.9484	1.40388
$981$	2.81509	0.0898788
$982$	79.3321	2.53159
$983$	22.6855	0.723554	0.361777	−	0.932265i	$-0.382170\pi$
$983$	22.6855	0.723554	0.361777	+	0.932265i	$0.382170\pi$
$984$	−4.73560	−0.150965
$985$	−62.9794	−2.00669
$986$	−1.32532	−0.0422069
$987$	4.88821	0.155593
$988$	−45.2820	−1.44061
$989$	0.845978	0.0269005
$990$	76.6122	2.43490
$991$	1.67284	0.0531396	0.0265698	−	0.999647i	$-0.491542\pi$
$991$	1.67284	0.0531396	0.0265698	+	0.999647i	$0.491542\pi$
$992$	−24.0682	−0.764167
$993$	7.28338	0.231131
$994$	4.76614	0.151173
$995$	−43.8089	−1.38883
$996$	−5.09836	−0.161548
$997$	6.58580	0.208575	0.104287	−	0.994547i	$-0.466744\pi$
$997$	6.58580	0.208575	0.104287	+	0.994547i	$0.466744\pi$
$998$	74.9526	2.37258
$999$	−2.50057	−0.0791146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.13	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.24777 q^{2} -0.430015 q^{3} +3.05245 q^{4} -2.54923 q^{5} +0.966572 q^{6} -1.16281 q^{7} -2.36567 q^{8} -2.81509 q^{9} +O(q^{10})\)	\(q-2.24777 q^{2} -0.430015 q^{3} +3.05245 q^{4} -2.54923 q^{5} +0.966572 q^{6} -1.16281 q^{7} -2.36567 q^{8} -2.81509 q^{9} +5.73008 q^{10} -4.74947 q^{11} -1.31260 q^{12} +7.05536 q^{13} +2.61373 q^{14} +1.09621 q^{15} -0.787431 q^{16} +0.294550 q^{17} +6.32766 q^{18} -2.10260 q^{19} -7.78141 q^{20} +0.500025 q^{21} +10.6757 q^{22} +0.0839506 q^{23} +1.01727 q^{24} +1.49858 q^{25} -15.8588 q^{26} +2.50057 q^{27} -3.54943 q^{28} +2.00176 q^{29} -2.46402 q^{30} -3.70206 q^{31} +6.50130 q^{32} +2.04234 q^{33} -0.662080 q^{34} +2.96427 q^{35} -8.59293 q^{36} -1.00000 q^{37} +4.72616 q^{38} -3.03391 q^{39} +6.03065 q^{40} -4.65519 q^{41} -1.12394 q^{42} +10.0771 q^{43} -14.4976 q^{44} +7.17631 q^{45} -0.188701 q^{46} +9.77592 q^{47} +0.338607 q^{48} -5.64787 q^{49} -3.36846 q^{50} -0.126661 q^{51} +21.5362 q^{52} -1.02973 q^{53} -5.62070 q^{54} +12.1075 q^{55} +2.75083 q^{56} +0.904149 q^{57} -4.49948 q^{58} -5.69236 q^{59} +3.34612 q^{60} +12.6845 q^{61} +8.32137 q^{62} +3.27341 q^{63} -13.0386 q^{64} -17.9858 q^{65} -4.59071 q^{66} +2.67338 q^{67} +0.899101 q^{68} -0.0361000 q^{69} -6.66299 q^{70} +1.82350 q^{71} +6.65957 q^{72} +2.80184 q^{73} +2.24777 q^{74} -0.644412 q^{75} -6.41810 q^{76} +5.52274 q^{77} +6.81952 q^{78} +10.8000 q^{79} +2.00734 q^{80} +7.36998 q^{81} +10.4638 q^{82} +3.88417 q^{83} +1.52630 q^{84} -0.750877 q^{85} -22.6510 q^{86} -0.860785 q^{87} +11.2357 q^{88} -0.146585 q^{89} -16.1307 q^{90} -8.20405 q^{91} +0.256255 q^{92} +1.59194 q^{93} -21.9740 q^{94} +5.36002 q^{95} -2.79566 q^{96} +16.0336 q^{97} +12.6951 q^{98} +13.3702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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