LMFDB - Embedded newform 4033.2.a.f.1.3

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:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.66672 q^{2} -1.32046 q^{3} +5.11137 q^{4} +0.282486 q^{5} +3.52128 q^{6} -2.11170 q^{7} -8.29715 q^{8} -1.25639 q^{9} +O(q^{10})$	\(q-2.66672 q^{2} -1.32046 q^{3} +5.11137 q^{4} +0.282486 q^{5} +3.52128 q^{6} -2.11170 q^{7} -8.29715 q^{8} -1.25639 q^{9} -0.753309 q^{10} -3.12811 q^{11} -6.74935 q^{12} +0.585254 q^{13} +5.63131 q^{14} -0.373010 q^{15} +11.9034 q^{16} +2.84963 q^{17} +3.35044 q^{18} +2.44831 q^{19} +1.44389 q^{20} +2.78841 q^{21} +8.34178 q^{22} +7.78873 q^{23} +10.9560 q^{24} -4.92020 q^{25} -1.56071 q^{26} +5.62038 q^{27} -10.7937 q^{28} +5.73527 q^{29} +0.994712 q^{30} -6.47507 q^{31} -15.1487 q^{32} +4.13054 q^{33} -7.59914 q^{34} -0.596526 q^{35} -6.42189 q^{36} +1.00000 q^{37} -6.52895 q^{38} -0.772803 q^{39} -2.34382 q^{40} -10.9864 q^{41} -7.43591 q^{42} -3.71535 q^{43} -15.9889 q^{44} -0.354913 q^{45} -20.7703 q^{46} -2.88172 q^{47} -15.7179 q^{48} -2.54071 q^{49} +13.1208 q^{50} -3.76281 q^{51} +2.99145 q^{52} -2.19641 q^{53} -14.9880 q^{54} -0.883646 q^{55} +17.5211 q^{56} -3.23289 q^{57} -15.2943 q^{58} +5.22603 q^{59} -1.90659 q^{60} +5.20577 q^{61} +17.2672 q^{62} +2.65313 q^{63} +16.5904 q^{64} +0.165326 q^{65} -11.0150 q^{66} -10.7881 q^{67} +14.5655 q^{68} -10.2847 q^{69} +1.59077 q^{70} +6.53403 q^{71} +10.4245 q^{72} -3.02260 q^{73} -2.66672 q^{74} +6.49692 q^{75} +12.5142 q^{76} +6.60564 q^{77} +2.06085 q^{78} -7.81238 q^{79} +3.36253 q^{80} -3.65230 q^{81} +29.2975 q^{82} +0.0341406 q^{83} +14.2526 q^{84} +0.804978 q^{85} +9.90779 q^{86} -7.57318 q^{87} +25.9544 q^{88} -8.92098 q^{89} +0.946452 q^{90} -1.23588 q^{91} +39.8111 q^{92} +8.55005 q^{93} +7.68473 q^{94} +0.691612 q^{95} +20.0031 q^{96} +0.398466 q^{97} +6.77534 q^{98} +3.93013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−2.66672	−1.88565	−0.942826	−	0.333284i	$-0.891843\pi$
$2$	−2.66672	−1.88565	−0.942826	+	0.333284i	$0.891843\pi$
$3$	−1.32046	−0.762366	−0.381183	−	0.924500i	$-0.624483\pi$
$3$	−1.32046	−0.762366	−0.381183	+	0.924500i	$0.624483\pi$
$4$	5.11137	2.55569
$5$	0.282486	0.126331	0.0631657	−	0.998003i	$-0.479880\pi$
$5$	0.282486	0.126331	0.0631657	+	0.998003i	$0.479880\pi$
$6$	3.52128	1.43756
$7$	−2.11170	−0.798149	−0.399075	−	0.916918i	$-0.630669\pi$
$7$	−2.11170	−0.798149	−0.399075	+	0.916918i	$0.630669\pi$
$8$	−8.29715	−2.93348
$9$	−1.25639	−0.418798
$10$	−0.753309	−0.238217
$11$	−3.12811	−0.943161	−0.471580	−	0.881823i	$-0.656316\pi$
$11$	−3.12811	−0.943161	−0.471580	+	0.881823i	$0.656316\pi$
$12$	−6.74935	−1.94837
$13$	0.585254	0.162320	0.0811602	−	0.996701i	$-0.474137\pi$
$13$	0.585254	0.162320	0.0811602	+	0.996701i	$0.474137\pi$
$14$	5.63131	1.50503
$15$	−0.373010	−0.0963108
$16$	11.9034	2.97585
$17$	2.84963	0.691136	0.345568	−	0.938394i	$-0.387686\pi$
$17$	2.84963	0.691136	0.345568	+	0.938394i	$0.387686\pi$
$18$	3.35044	0.789707
$19$	2.44831	0.561681	0.280840	−	0.959754i	$-0.409387\pi$
$19$	2.44831	0.561681	0.280840	+	0.959754i	$0.409387\pi$
$20$	1.44389	0.322863
$21$	2.78841	0.608482
$22$	8.34178	1.77847
$23$	7.78873	1.62406	0.812032	−	0.583613i	$-0.198362\pi$
$23$	7.78873	1.62406	0.812032	+	0.583613i	$0.198362\pi$
$24$	10.9560	2.23639
$25$	−4.92020	−0.984040
$26$	−1.56071	−0.306080
$27$	5.62038	1.08164
$28$	−10.7937	−2.03982
$29$	5.73527	1.06501	0.532506	−	0.846426i	$-0.321250\pi$
$29$	5.73527	1.06501	0.532506	+	0.846426i	$0.321250\pi$
$30$	0.994712	0.181609
$31$	−6.47507	−1.16296	−0.581478	−	0.813562i	$-0.697525\pi$
$31$	−6.47507	−1.16296	−0.581478	+	0.813562i	$0.697525\pi$
$32$	−15.1487	−2.67793
$33$	4.13054	0.719034
$34$	−7.59914	−1.30324
$35$	−0.596526	−0.100831
$36$	−6.42189	−1.07032
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−6.52895	−1.05914
$39$	−0.772803	−0.123748
$40$	−2.34382	−0.370591
$41$	−10.9864	−1.71578	−0.857890	−	0.513833i	$-0.828225\pi$
$41$	−10.9864	−1.71578	−0.857890	+	0.513833i	$0.828225\pi$
$42$	−7.43591	−1.14739
$43$	−3.71535	−0.566586	−0.283293	−	0.959033i	$-0.591427\pi$
$43$	−3.71535	−0.566586	−0.283293	+	0.959033i	$0.591427\pi$
$44$	−15.9889	−2.41042
$45$	−0.354913	−0.0529073
$46$	−20.7703	−3.06242
$47$	−2.88172	−0.420342	−0.210171	−	0.977665i	$-0.567402\pi$
$47$	−2.88172	−0.420342	−0.210171	+	0.977665i	$0.567402\pi$
$48$	−15.7179	−2.26868
$49$	−2.54071	−0.362958
$50$	13.1208	1.85556
$51$	−3.76281	−0.526899
$52$	2.99145	0.414840
$53$	−2.19641	−0.301700	−0.150850	−	0.988557i	$-0.548201\pi$
$53$	−2.19641	−0.301700	−0.150850	+	0.988557i	$0.548201\pi$
$54$	−14.9880	−2.03960
$55$	−0.883646	−0.119151
$56$	17.5211	2.34136
$57$	−3.23289	−0.428207
$58$	−15.2943	−2.00824
$59$	5.22603	0.680372	0.340186	−	0.940358i	$-0.389510\pi$
$59$	5.22603	0.680372	0.340186	+	0.940358i	$0.389510\pi$
$60$	−1.90659	−0.246140
$61$	5.20577	0.666531	0.333265	−	0.942833i	$-0.391850\pi$
$61$	5.20577	0.666531	0.333265	+	0.942833i	$0.391850\pi$
$62$	17.2672	2.19293
$63$	2.65313	0.334263
$64$	16.5904	2.07380
$65$	0.165326	0.0205062
$66$	−11.0150	−1.35585
$67$	−10.7881	−1.31797	−0.658987	−	0.752154i	$-0.729015\pi$
$67$	−10.7881	−1.31797	−0.658987	+	0.752154i	$0.729015\pi$
$68$	14.5655	1.76633
$69$	−10.2847	−1.23813
$70$	1.59077	0.190133
$71$	6.53403	0.775446	0.387723	−	0.921776i	$-0.373262\pi$
$71$	6.53403	0.775446	0.387723	+	0.921776i	$0.373262\pi$
$72$	10.4245	1.22854
$73$	−3.02260	−0.353769	−0.176884	−	0.984232i	$-0.556602\pi$
$73$	−3.02260	−0.353769	−0.176884	+	0.984232i	$0.556602\pi$
$74$	−2.66672	−0.309999
$75$	6.49692	0.750199
$76$	12.5142	1.43548
$77$	6.60564	0.752783
$78$	2.06085	0.233345
$79$	−7.81238	−0.878962	−0.439481	−	0.898252i	$-0.644838\pi$
$79$	−7.81238	−0.878962	−0.439481	+	0.898252i	$0.644838\pi$
$80$	3.36253	0.375943
$81$	−3.65230	−0.405811
$82$	29.2975	3.23537
$83$	0.0341406	0.00374742	0.00187371	−	0.999998i	$-0.499404\pi$
$83$	0.0341406	0.00374742	0.00187371	+	0.999998i	$0.499404\pi$
$84$	14.2526	1.55509
$85$	0.804978	0.0873121
$86$	9.90779	1.06838
$87$	−7.57318	−0.811930
$88$	25.9544	2.76675
$89$	−8.92098	−0.945622	−0.472811	−	0.881164i	$-0.656761\pi$
$89$	−8.92098	−0.945622	−0.472811	+	0.881164i	$0.656761\pi$
$90$	0.946452	0.0997648
$91$	−1.23588	−0.129556
$92$	39.8111	4.15060
$93$	8.55005	0.886599
$94$	7.68473	0.792620
$95$	0.691612	0.0709579
$96$	20.0031	2.04156
$97$	0.398466	0.0404580	0.0202290	−	0.999795i	$-0.493560\pi$
$97$	0.398466	0.0404580	0.0202290	+	0.999795i	$0.493560\pi$
$98$	6.77534	0.684413
$99$	3.93013	0.394993
$100$	−25.1490	−2.51490
$101$	−10.9169	−1.08627	−0.543137	−	0.839644i	$-0.682764\pi$
$101$	−10.9169	−1.08627	−0.543137	+	0.839644i	$0.682764\pi$
$102$	10.0343	0.993548
$103$	−6.64691	−0.654940	−0.327470	−	0.944862i	$-0.606196\pi$
$103$	−6.64691	−0.654940	−0.327470	+	0.944862i	$0.606196\pi$
$104$	−4.85594	−0.476164
$105$	0.787687	0.0768704
$106$	5.85721	0.568902
$107$	14.4923	1.40103	0.700513	−	0.713640i	$-0.252955\pi$
$107$	14.4923	1.40103	0.700513	+	0.713640i	$0.252955\pi$
$108$	28.7279	2.76434
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	2.35643	0.224677
$111$	−1.32046	−0.125332
$112$	−25.1364	−2.37517
$113$	−3.81063	−0.358474	−0.179237	−	0.983806i	$-0.557363\pi$
$113$	−3.81063	−0.358474	−0.179237	+	0.983806i	$0.557363\pi$
$114$	8.62120	0.807449
$115$	2.20021	0.205170
$116$	29.3151	2.72184
$117$	−0.735310	−0.0679794
$118$	−13.9363	−1.28294
$119$	−6.01757	−0.551629
$120$	3.09492	0.282526
$121$	−1.21493	−0.110448
$122$	−13.8823	−1.25685
$123$	14.5070	1.30805
$124$	−33.0965	−2.97215
$125$	−2.80231	−0.250647
$126$	−7.07514	−0.630304
$127$	1.33653	0.118598	0.0592988	−	0.998240i	$-0.481114\pi$
$127$	1.33653	0.118598	0.0592988	+	0.998240i	$0.481114\pi$
$128$	−13.9445	−1.23253
$129$	4.90597	0.431946
$130$	−0.440877	−0.0386675
$131$	19.6894	1.72027	0.860136	−	0.510064i	$-0.170378\pi$
$131$	19.6894	1.72027	0.860136	+	0.510064i	$0.170378\pi$
$132$	21.1127	1.83762
$133$	−5.17011	−0.448305
$134$	28.7687	2.48524
$135$	1.58768	0.136646
$136$	−23.6438	−2.02744
$137$	6.73024	0.575004	0.287502	−	0.957780i	$-0.407175\pi$
$137$	6.73024	0.575004	0.287502	+	0.957780i	$0.407175\pi$
$138$	27.4263	2.33469
$139$	−13.6558	−1.15827	−0.579137	−	0.815231i	$-0.696610\pi$
$139$	−13.6558	−1.15827	−0.579137	+	0.815231i	$0.696610\pi$
$140$	−3.04907	−0.257693
$141$	3.80519	0.320455
$142$	−17.4244	−1.46222
$143$	−1.83074	−0.153094
$144$	−14.9553	−1.24628
$145$	1.62013	0.134545
$146$	8.06041	0.667085
$147$	3.35489	0.276707
$148$	5.11137	0.420152
$149$	−21.4240	−1.75512	−0.877562	−	0.479464i	$-0.840831\pi$
$149$	−21.4240	−1.75512	−0.877562	+	0.479464i	$0.840831\pi$
$150$	−17.3254	−1.41462
$151$	−18.8277	−1.53218	−0.766089	−	0.642734i	$-0.777800\pi$
$151$	−18.8277	−1.53218	−0.766089	+	0.642734i	$0.777800\pi$
$152$	−20.3140	−1.64768
$153$	−3.58025	−0.289446
$154$	−17.6154	−1.41949
$155$	−1.82911	−0.146918
$156$	−3.95009	−0.316260
$157$	4.51224	0.360116	0.180058	−	0.983656i	$-0.442371\pi$
$157$	4.51224	0.360116	0.180058	+	0.983656i	$0.442371\pi$
$158$	20.8334	1.65742
$159$	2.90027	0.230006
$160$	−4.27928	−0.338306
$161$	−16.4475	−1.29624
$162$	9.73964	0.765218
$163$	12.5702	0.984577	0.492288	−	0.870432i	$-0.336161\pi$
$163$	12.5702	0.984577	0.492288	+	0.870432i	$0.336161\pi$
$164$	−56.1553	−4.38500
$165$	1.16682	0.0908366
$166$	−0.0910432	−0.00706632
$167$	17.8598	1.38203	0.691016	−	0.722840i	$-0.257164\pi$
$167$	17.8598	1.38203	0.691016	+	0.722840i	$0.257164\pi$
$168$	−23.1359	−1.78497
$169$	−12.6575	−0.973652
$170$	−2.14665	−0.164640
$171$	−3.07604	−0.235231
$172$	−18.9906	−1.44802
$173$	9.45773	0.719058	0.359529	−	0.933134i	$-0.382937\pi$
$173$	9.45773	0.719058	0.359529	+	0.933134i	$0.382937\pi$
$174$	20.1955	1.53102
$175$	10.3900	0.785411
$176$	−37.2351	−2.80670
$177$	−6.90075	−0.518692
$178$	23.7897	1.78311
$179$	−0.235481	−0.0176006	−0.00880032	−	0.999961i	$-0.502801\pi$
$179$	−0.235481	−0.0176006	−0.00880032	+	0.999961i	$0.502801\pi$
$180$	−1.81409	−0.135214
$181$	7.88157	0.585832	0.292916	−	0.956138i	$-0.405374\pi$
$181$	7.88157	0.585832	0.292916	+	0.956138i	$0.405374\pi$
$182$	3.29575	0.244297
$183$	−6.87400	−0.508140
$184$	−64.6243	−4.76416
$185$	0.282486	0.0207688
$186$	−22.8005	−1.67182
$187$	−8.91394	−0.651852
$188$	−14.7296	−1.07426
$189$	−11.8686	−0.863313
$190$	−1.84433	−0.133802
$191$	22.0817	1.59778	0.798888	−	0.601479i	$-0.205422\pi$
$191$	22.0817	1.59778	0.798888	+	0.601479i	$0.205422\pi$
$192$	−21.9069	−1.58099
$193$	13.3583	0.961549	0.480774	−	0.876844i	$-0.340356\pi$
$193$	13.3583	0.961549	0.480774	+	0.876844i	$0.340356\pi$
$194$	−1.06259	−0.0762898
$195$	−0.218306	−0.0156332
$196$	−12.9865	−0.927607
$197$	−5.84967	−0.416772	−0.208386	−	0.978047i	$-0.566821\pi$
$197$	−5.84967	−0.416772	−0.208386	+	0.978047i	$0.566821\pi$
$198$	−10.4806	−0.744820
$199$	16.9420	1.20099	0.600493	−	0.799630i	$-0.294971\pi$
$199$	16.9420	1.20099	0.600493	+	0.799630i	$0.294971\pi$
$200$	40.8236	2.88667
$201$	14.2452	1.00478
$202$	29.1123	2.04834
$203$	−12.1112	−0.850039
$204$	−19.2331	−1.34659
$205$	−3.10349	−0.216757
$206$	17.7254	1.23499
$207$	−9.78571	−0.680154
$208$	6.96651	0.483040
$209$	−7.65858	−0.529755
$210$	−2.10054	−0.144951
$211$	8.97733	0.618025	0.309012	−	0.951058i	$-0.400002\pi$
$211$	8.97733	0.618025	0.309012	+	0.951058i	$0.400002\pi$
$212$	−11.2267	−0.771052
$213$	−8.62790	−0.591174
$214$	−38.6469	−2.64185
$215$	−1.04953	−0.0715776
$216$	−46.6332	−3.17298
$217$	13.6734	0.928213
$218$	2.66672	0.180613
$219$	3.99121	0.269701
$220$	−4.51664	−0.304512
$221$	1.66776	0.112185
$222$	3.52128	0.236333
$223$	−4.98364	−0.333729	−0.166864	−	0.985980i	$-0.553364\pi$
$223$	−4.98364	−0.333729	−0.166864	+	0.985980i	$0.553364\pi$
$224$	31.9895	2.13739
$225$	6.18171	0.412114
$226$	10.1619	0.675957
$227$	−4.94560	−0.328251	−0.164125	−	0.986439i	$-0.552480\pi$
$227$	−4.94560	−0.328251	−0.164125	+	0.986439i	$0.552480\pi$
$228$	−16.5245	−1.09436
$229$	14.5668	0.962602	0.481301	−	0.876555i	$-0.340164\pi$
$229$	14.5668	0.962602	0.481301	+	0.876555i	$0.340164\pi$
$230$	−5.86732	−0.386880
$231$	−8.72247	−0.573896
$232$	−47.5864	−3.12420
$233$	−0.487090	−0.0319103	−0.0159552	−	0.999873i	$-0.505079\pi$
$233$	−0.487090	−0.0319103	−0.0159552	+	0.999873i	$0.505079\pi$
$234$	1.96086	0.128186
$235$	−0.814045	−0.0531024
$236$	26.7122	1.73882
$237$	10.3159	0.670091
$238$	16.0471	1.04018
$239$	−18.6924	−1.20911	−0.604556	−	0.796563i	$-0.706650\pi$
$239$	−18.6924	−1.20911	−0.604556	+	0.796563i	$0.706650\pi$
$240$	−4.44008	−0.286606
$241$	14.6817	0.945734	0.472867	−	0.881134i	$-0.343219\pi$
$241$	14.6817	0.945734	0.472867	+	0.881134i	$0.343219\pi$
$242$	3.23987	0.208267
$243$	−12.0384	−0.772267
$244$	26.6086	1.70344
$245$	−0.717713	−0.0458530
$246$	−38.6861	−2.46653
$247$	1.43288	0.0911723
$248$	53.7246	3.41151
$249$	−0.0450812	−0.00285690
$250$	7.47298	0.472632
$251$	14.6712	0.926037	0.463019	−	0.886349i	$-0.346766\pi$
$251$	14.6712	0.926037	0.463019	+	0.886349i	$0.346766\pi$
$252$	13.5611	0.854271
$253$	−24.3640	−1.53175
$254$	−3.56414	−0.223634
$255$	−1.06294	−0.0665638
$256$	4.00530	0.250331
$257$	7.71964	0.481538	0.240769	−	0.970582i	$-0.422600\pi$
$257$	7.71964	0.481538	0.240769	+	0.970582i	$0.422600\pi$
$258$	−13.0828	−0.814501
$259$	−2.11170	−0.131215
$260$	0.845043	0.0524073
$261$	−7.20575	−0.446025
$262$	−52.5061	−3.24384
$263$	−6.70759	−0.413608	−0.206804	−	0.978382i	$-0.566306\pi$
$263$	−6.70759	−0.413608	−0.206804	+	0.978382i	$0.566306\pi$
$264$	−34.2717	−2.10927
$265$	−0.620455	−0.0381142
$266$	13.7872	0.845348
$267$	11.7798	0.720910
$268$	−55.1419	−3.36833
$269$	−12.4120	−0.756774	−0.378387	−	0.925647i	$-0.623521\pi$
$269$	−12.4120	−0.756774	−0.378387	+	0.925647i	$0.623521\pi$
$270$	−4.23388	−0.257666
$271$	−25.6953	−1.56088	−0.780439	−	0.625232i	$-0.785004\pi$
$271$	−25.6953	−1.56088	−0.780439	+	0.625232i	$0.785004\pi$
$272$	33.9202	2.05671
$273$	1.63193	0.0987690
$274$	−17.9476	−1.08426
$275$	15.3909	0.928108
$276$	−52.5689	−3.16428
$277$	13.2777	0.797782	0.398891	−	0.916998i	$-0.369395\pi$
$277$	13.2777	0.797782	0.398891	+	0.916998i	$0.369395\pi$
$278$	36.4162	2.18410
$279$	8.13523	0.487043
$280$	4.94946	0.295787
$281$	−17.2384	−1.02836	−0.514178	−	0.857683i	$-0.671903\pi$
$281$	−17.2384	−1.02836	−0.514178	+	0.857683i	$0.671903\pi$
$282$	−10.1474	−0.604267
$283$	2.17497	0.129289	0.0646444	−	0.997908i	$-0.479409\pi$
$283$	2.17497	0.129289	0.0646444	+	0.997908i	$0.479409\pi$
$284$	33.3978	1.98180
$285$	−0.913245	−0.0540959
$286$	4.88206	0.288682
$287$	23.1999	1.36945
$288$	19.0327	1.12151
$289$	−8.87963	−0.522331
$290$	−4.32043	−0.253704
$291$	−0.526157	−0.0308439
$292$	−15.4496	−0.904121
$293$	20.2592	1.18355	0.591777	−	0.806102i	$-0.298427\pi$
$293$	20.2592	1.18355	0.591777	+	0.806102i	$0.298427\pi$
$294$	−8.94655	−0.521773
$295$	1.47628	0.0859523
$296$	−8.29715	−0.482262
$297$	−17.5812	−1.02016
$298$	57.1317	3.30955
$299$	4.55839	0.263619
$300$	33.2082	1.91727
$301$	7.84573	0.452220
$302$	50.2082	2.88916
$303$	14.4153	0.828139
$304$	29.1432	1.67148
$305$	1.47055	0.0842037
$306$	9.54751	0.545795
$307$	7.81015	0.445749	0.222875	−	0.974847i	$-0.428456\pi$
$307$	7.81015	0.445749	0.222875	+	0.974847i	$0.428456\pi$
$308$	33.7639	1.92388
$309$	8.77697	0.499304
$310$	4.87772	0.277036
$311$	−7.67064	−0.434962	−0.217481	−	0.976065i	$-0.569784\pi$
$311$	−7.67064	−0.434962	−0.217481	+	0.976065i	$0.569784\pi$
$312$	6.41206	0.363012
$313$	−17.4415	−0.985851	−0.492926	−	0.870071i	$-0.664073\pi$
$313$	−17.4415	−0.985851	−0.492926	+	0.870071i	$0.664073\pi$
$314$	−12.0329	−0.679054
$315$	0.749471	0.0422279
$316$	−39.9320	−2.24635
$317$	7.93855	0.445873	0.222937	−	0.974833i	$-0.428436\pi$
$317$	7.93855	0.445873	0.222937	+	0.974833i	$0.428436\pi$
$318$	−7.73419	−0.433712
$319$	−17.9406	−1.00448
$320$	4.68654	0.261986
$321$	−19.1365	−1.06809
$322$	43.8608	2.44427
$323$	6.97677	0.388198
$324$	−18.6683	−1.03713
$325$	−2.87957	−0.159730
$326$	−33.5212	−1.85657
$327$	1.32046	0.0730214
$328$	91.1554	5.03321
$329$	6.08535	0.335496
$330$	−3.11157	−0.171286
$331$	24.9422	1.37095	0.685475	−	0.728096i	$-0.259595\pi$
$331$	24.9422	1.37095	0.685475	+	0.728096i	$0.259595\pi$
$332$	0.174505	0.00957722
$333$	−1.25639	−0.0688499
$334$	−47.6270	−2.60603
$335$	−3.04748	−0.166501
$336$	33.1916	1.81075
$337$	27.5242	1.49934	0.749669	−	0.661813i	$-0.230213\pi$
$337$	27.5242	1.49934	0.749669	+	0.661813i	$0.230213\pi$
$338$	33.7539	1.83597
$339$	5.03177	0.273288
$340$	4.11454	0.223142
$341$	20.2547	1.09685
$342$	8.20292	0.443563
$343$	20.1471	1.08784
$344$	30.8268	1.66207
$345$	−2.90528	−0.156415
$346$	−25.2211	−1.35589
$347$	27.3134	1.46626	0.733129	−	0.680089i	$-0.238059\pi$
$347$	27.3134	1.46626	0.733129	+	0.680089i	$0.238059\pi$
$348$	−38.7093	−2.07504
$349$	−15.6535	−0.837914	−0.418957	−	0.908006i	$-0.637604\pi$
$349$	−15.6535	−0.837914	−0.418957	+	0.908006i	$0.637604\pi$
$350$	−27.7072	−1.48101
$351$	3.28936	0.175573
$352$	47.3866	2.52572
$353$	29.4434	1.56712	0.783558	−	0.621319i	$-0.213403\pi$
$353$	29.4434	1.56712	0.783558	+	0.621319i	$0.213403\pi$
$354$	18.4023	0.978074
$355$	1.84577	0.0979632
$356$	−45.5985	−2.41671
$357$	7.94594	0.420544
$358$	0.627960	0.0331887
$359$	10.1877	0.537687	0.268843	−	0.963184i	$-0.413359\pi$
$359$	10.1877	0.537687	0.268843	+	0.963184i	$0.413359\pi$
$360$	2.94476	0.155203
$361$	−13.0058	−0.684515
$362$	−21.0179	−1.10468
$363$	1.60426	0.0842019
$364$	−6.31707	−0.331104
$365$	−0.853841	−0.0446921
$366$	18.3310	0.958176
$367$	−5.63779	−0.294290	−0.147145	−	0.989115i	$-0.547008\pi$
$367$	−5.63779	−0.294290	−0.147145	+	0.989115i	$0.547008\pi$
$368$	92.7123	4.83296
$369$	13.8032	0.718565
$370$	−0.753309	−0.0391627
$371$	4.63817	0.240802
$372$	43.7025	2.26587
$373$	−10.9166	−0.565238	−0.282619	−	0.959232i	$-0.591203\pi$
$373$	−10.9166	−0.565238	−0.282619	+	0.959232i	$0.591203\pi$
$374$	23.7709	1.22917
$375$	3.70034	0.191085
$376$	23.9101	1.23307
$377$	3.35659	0.172873
$378$	31.6502	1.62791
$379$	30.1883	1.55067	0.775334	−	0.631551i	$-0.217582\pi$
$379$	30.1883	1.55067	0.775334	+	0.631551i	$0.217582\pi$
$380$	3.53509	0.181346
$381$	−1.76483	−0.0904148
$382$	−58.8857	−3.01285
$383$	−13.5349	−0.691599	−0.345799	−	0.938308i	$-0.612392\pi$
$383$	−13.5349	−0.691599	−0.345799	+	0.938308i	$0.612392\pi$
$384$	18.4131	0.939641
$385$	1.86600	0.0951001
$386$	−35.6227	−1.81315
$387$	4.66794	0.237285
$388$	2.03671	0.103398
$389$	8.36783	0.424266	0.212133	−	0.977241i	$-0.431959\pi$
$389$	8.36783	0.424266	0.212133	+	0.977241i	$0.431959\pi$
$390$	0.582160	0.0294788
$391$	22.1950	1.12245
$392$	21.0806	1.06473
$393$	−25.9990	−1.31148
$394$	15.5994	0.785887
$395$	−2.20689	−0.111040
$396$	20.0884	1.00948
$397$	4.24958	0.213281	0.106640	−	0.994298i	$-0.465991\pi$
$397$	4.24958	0.213281	0.106640	+	0.994298i	$0.465991\pi$
$398$	−45.1795	−2.26464
$399$	6.82690	0.341773
$400$	−58.5671	−2.92835
$401$	3.72419	0.185977	0.0929885	−	0.995667i	$-0.470358\pi$
$401$	3.72419	0.185977	0.0929885	+	0.995667i	$0.470358\pi$
$402$	−37.9879	−1.89466
$403$	−3.78956	−0.188772
$404$	−55.8005	−2.77618
$405$	−1.03172	−0.0512667
$406$	32.2971	1.60288
$407$	−3.12811	−0.155055
$408$	31.2206	1.54565
$409$	12.9227	0.638984	0.319492	−	0.947589i	$-0.396488\pi$
$409$	12.9227	0.638984	0.319492	+	0.947589i	$0.396488\pi$
$410$	8.27612	0.408728
$411$	−8.88700	−0.438363
$412$	−33.9749	−1.67382
$413$	−11.0358	−0.543038
$414$	26.0957	1.28253
$415$	0.00964422	0.000473416 0
$416$	−8.86582	−0.434682
$417$	18.0320	0.883028
$418$	20.4233	0.998934
$419$	23.5784	1.15188	0.575940	−	0.817492i	$-0.304636\pi$
$419$	23.5784	1.15188	0.575940	+	0.817492i	$0.304636\pi$
$420$	4.02616	0.196457
$421$	−13.2193	−0.644268	−0.322134	−	0.946694i	$-0.604400\pi$
$421$	−13.2193	−0.644268	−0.322134	+	0.946694i	$0.604400\pi$
$422$	−23.9400	−1.16538
$423$	3.62058	0.176038
$424$	18.2240	0.885034
$425$	−14.0207	−0.680105
$426$	23.0082	1.11475
$427$	−10.9930	−0.531991
$428$	74.0757	3.58058
$429$	2.41741	0.116714
$430$	2.79881	0.134971
$431$	30.0175	1.44589	0.722947	−	0.690904i	$-0.242787\pi$
$431$	30.0175	1.44589	0.722947	+	0.690904i	$0.242787\pi$
$432$	66.9016	3.21880
$433$	31.0488	1.49211	0.746056	−	0.665883i	$-0.231945\pi$
$433$	31.0488	1.49211	0.746056	+	0.665883i	$0.231945\pi$
$434$	−36.4631	−1.75029
$435$	−2.13931	−0.102572
$436$	−5.11137	−0.244790
$437$	19.0692	0.912205
$438$	−10.6434	−0.508563
$439$	−16.5762	−0.791137	−0.395569	−	0.918436i	$-0.629452\pi$
$439$	−16.5762	−0.791137	−0.395569	+	0.918436i	$0.629452\pi$
$440$	7.33174	0.349527
$441$	3.19212	0.152006
$442$	−4.44743	−0.211543
$443$	5.52690	0.262591	0.131295	−	0.991343i	$-0.458086\pi$
$443$	5.52690	0.262591	0.131295	+	0.991343i	$0.458086\pi$
$444$	−6.74935	−0.320310
$445$	−2.52005	−0.119462
$446$	13.2899	0.629297
$447$	28.2895	1.33805
$448$	−35.0340	−1.65520
$449$	−38.5165	−1.81770	−0.908852	−	0.417119i	$-0.863040\pi$
$449$	−38.5165	−1.81770	−0.908852	+	0.417119i	$0.863040\pi$
$450$	−16.4849	−0.777103
$451$	34.3665	1.61826
$452$	−19.4776	−0.916147
$453$	24.8612	1.16808
$454$	13.1885	0.618967
$455$	−0.349120	−0.0163670
$456$	26.8238	1.25614
$457$	14.1776	0.663201	0.331601	−	0.943420i	$-0.392411\pi$
$457$	14.1776	0.663201	0.331601	+	0.943420i	$0.392411\pi$
$458$	−38.8456	−1.81513
$459$	16.0160	0.747562
$460$	11.2461	0.524351
$461$	−37.5338	−1.74812	−0.874061	−	0.485816i	$-0.838523\pi$
$461$	−37.5338	−1.74812	−0.874061	+	0.485816i	$0.838523\pi$
$462$	23.2603	1.08217
$463$	−14.8066	−0.688123	−0.344061	−	0.938947i	$-0.611803\pi$
$463$	−14.8066	−0.688123	−0.344061	+	0.938947i	$0.611803\pi$
$464$	68.2691	3.16931
$465$	2.41527	0.112005
$466$	1.29893	0.0601718
$467$	11.5446	0.534218	0.267109	−	0.963666i	$-0.413932\pi$
$467$	11.5446	0.534218	0.267109	+	0.963666i	$0.413932\pi$
$468$	−3.75844	−0.173734
$469$	22.7812	1.05194
$470$	2.17083	0.100133
$471$	−5.95822	−0.274540
$472$	−43.3612	−1.99586
$473$	11.6220	0.534382
$474$	−27.5096	−1.26356
$475$	−12.0462	−0.552717
$476$	−30.7580	−1.40979
$477$	2.75956	0.126351
$478$	49.8474	2.27997
$479$	33.7500	1.54207	0.771037	−	0.636790i	$-0.219738\pi$
$479$	33.7500	1.54207	0.771037	+	0.636790i	$0.219738\pi$
$480$	5.65060	0.257913
$481$	0.585254	0.0266853
$482$	−39.1520	−1.78333
$483$	21.7182	0.988213
$484$	−6.20995	−0.282271
$485$	0.112561	0.00511112
$486$	32.1031	1.45623
$487$	33.5691	1.52116	0.760581	−	0.649243i	$-0.224914\pi$
$487$	33.5691	1.52116	0.760581	+	0.649243i	$0.224914\pi$
$488$	−43.1930	−1.95526
$489$	−16.5985	−0.750608
$490$	1.91394	0.0864628
$491$	9.22414	0.416279	0.208140	−	0.978099i	$-0.433259\pi$
$491$	9.22414	0.416279	0.208140	+	0.978099i	$0.433259\pi$
$492$	74.1507	3.34297
$493$	16.3434	0.736068
$494$	−3.82110	−0.171919
$495$	1.11021	0.0499001
$496$	−77.0752	−3.46078
$497$	−13.7979	−0.618922
$498$	0.120219	0.00538713
$499$	26.6585	1.19340	0.596698	−	0.802466i	$-0.296479\pi$
$499$	26.6585	1.19340	0.596698	+	0.802466i	$0.296479\pi$
$500$	−14.3237	−0.640574
$501$	−23.5831	−1.05361
$502$	−39.1239	−1.74618
$503$	−17.0258	−0.759144	−0.379572	−	0.925162i	$-0.623929\pi$
$503$	−17.0258	−0.759144	−0.379572	+	0.925162i	$0.623929\pi$
$504$	−22.0134	−0.980555
$505$	−3.08387	−0.137231
$506$	64.9719	2.88835
$507$	16.7137	0.742280
$508$	6.83149	0.303098
$509$	−6.59566	−0.292347	−0.146174	−	0.989259i	$-0.546696\pi$
$509$	−6.59566	−0.292347	−0.146174	+	0.989259i	$0.546696\pi$
$510$	2.83456	0.125516
$511$	6.38284	0.282360
$512$	17.2080	0.760495
$513$	13.7604	0.607538
$514$	−20.5861	−0.908013
$515$	−1.87766	−0.0827395
$516$	25.0762	1.10392
$517$	9.01434	0.396450
$518$	5.63131	0.247426
$519$	−12.4885	−0.548185
$520$	−1.37173	−0.0601545
$521$	−17.9292	−0.785495	−0.392747	−	0.919646i	$-0.628475\pi$
$521$	−17.9292	−0.785495	−0.392747	+	0.919646i	$0.628475\pi$
$522$	19.2157	0.841048
$523$	−29.4305	−1.28691	−0.643454	−	0.765485i	$-0.722499\pi$
$523$	−29.4305	−1.28691	−0.643454	+	0.765485i	$0.722499\pi$
$524$	100.640	4.39648
$525$	−13.7196	−0.598771
$526$	17.8872	0.779921
$527$	−18.4515	−0.803761
$528$	49.1673	2.13973
$529$	37.6644	1.63758
$530$	1.65458	0.0718702
$531$	−6.56595	−0.284938
$532$	−26.4263	−1.14573
$533$	−6.42981	−0.278506
$534$	−31.4133	−1.35939
$535$	4.09387	0.176994
$536$	89.5103	3.86626
$537$	0.310942	0.0134181
$538$	33.0993	1.42701
$539$	7.94761	0.342328
$540$	8.11521	0.349223
$541$	−5.63290	−0.242177	−0.121089	−	0.992642i	$-0.538639\pi$
$541$	−5.63290	−0.242177	−0.121089	+	0.992642i	$0.538639\pi$
$542$	68.5221	2.94327
$543$	−10.4073	−0.446619
$544$	−43.1680	−1.85081
$545$	−0.282486	−0.0121004
$546$	−4.35190	−0.186244
$547$	−12.2042	−0.521812	−0.260906	−	0.965364i	$-0.584021\pi$
$547$	−12.2042	−0.521812	−0.260906	+	0.965364i	$0.584021\pi$
$548$	34.4008	1.46953
$549$	−6.54049	−0.279141
$550$	−41.0432	−1.75009
$551$	14.0417	0.598197
$552$	85.3336	3.63204
$553$	16.4974	0.701542
$554$	−35.4079	−1.50434
$555$	−0.373010	−0.0158334
$556$	−69.8001	−2.96018
$557$	−39.0490	−1.65456	−0.827279	−	0.561791i	$-0.810112\pi$
$557$	−39.0490	−1.65456	−0.827279	+	0.561791i	$0.810112\pi$
$558$	−21.6943	−0.918395
$559$	−2.17443	−0.0919685
$560$	−7.10068	−0.300058
$561$	11.7705	0.496950
$562$	45.9699	1.93912
$563$	5.69860	0.240167	0.120084	−	0.992764i	$-0.461684\pi$
$563$	5.69860	0.240167	0.120084	+	0.992764i	$0.461684\pi$
$564$	19.4497	0.818982
$565$	−1.07645	−0.0452865
$566$	−5.80004	−0.243794
$567$	7.71257	0.323898
$568$	−54.2138	−2.27476
$569$	19.5106	0.817925	0.408962	−	0.912551i	$-0.365891\pi$
$569$	19.5106	0.817925	0.408962	+	0.912551i	$0.365891\pi$
$570$	2.43536	0.102006
$571$	26.1481	1.09427	0.547133	−	0.837046i	$-0.315719\pi$
$571$	26.1481	1.09427	0.547133	+	0.837046i	$0.315719\pi$
$572$	−9.35760	−0.391261
$573$	−29.1580	−1.21809
$574$	−61.8676	−2.58230
$575$	−38.3221	−1.59814
$576$	−20.8440	−0.868501
$577$	−35.5889	−1.48158	−0.740792	−	0.671734i	$-0.765550\pi$
$577$	−35.5889	−1.48158	−0.740792	+	0.671734i	$0.765550\pi$
$578$	23.6795	0.984936
$579$	−17.6390	−0.733052
$580$	8.28109	0.343854
$581$	−0.0720948	−0.00299100
$582$	1.40311	0.0581608
$583$	6.87062	0.284552
$584$	25.0790	1.03777
$585$	−0.207714	−0.00858793
$586$	−54.0255	−2.23177
$587$	8.67563	0.358082	0.179041	−	0.983842i	$-0.442701\pi$
$587$	8.67563	0.358082	0.179041	+	0.983842i	$0.442701\pi$
$588$	17.1481	0.707176
$589$	−15.8530	−0.653210
$590$	−3.93682	−0.162076
$591$	7.72424	0.317733
$592$	11.9034	0.489226
$593$	45.8131	1.88132	0.940660	−	0.339352i	$-0.110208\pi$
$593$	45.8131	1.88132	0.940660	+	0.339352i	$0.110208\pi$
$594$	46.8840	1.92367
$595$	−1.69988	−0.0696881
$596$	−109.506	−4.48554
$597$	−22.3712	−0.915592
$598$	−12.1559	−0.497093
$599$	15.4604	0.631695	0.315847	−	0.948810i	$-0.397711\pi$
$599$	15.4604	0.631695	0.315847	+	0.948810i	$0.397711\pi$
$600$	−53.9059	−2.20070
$601$	−10.3946	−0.424003	−0.212001	−	0.977269i	$-0.567998\pi$
$601$	−10.3946	−0.424003	−0.212001	+	0.977269i	$0.567998\pi$
$602$	−20.9223	−0.852730
$603$	13.5541	0.551964
$604$	−96.2355	−3.91577
$605$	−0.343200	−0.0139531
$606$	−38.4416	−1.56158
$607$	7.48731	0.303900	0.151950	−	0.988388i	$-0.451445\pi$
$607$	7.48731	0.303900	0.151950	+	0.988388i	$0.451445\pi$
$608$	−37.0886	−1.50414
$609$	15.9923	0.648041
$610$	−3.92155	−0.158779
$611$	−1.68654	−0.0682301
$612$	−18.3000	−0.739733
$613$	3.85021	0.155509	0.0777543	−	0.996973i	$-0.475225\pi$
$613$	3.85021	0.155509	0.0777543	+	0.996973i	$0.475225\pi$
$614$	−20.8275	−0.840528
$615$	4.09802	0.165248
$616$	−54.8080	−2.20828
$617$	7.29444	0.293663	0.146831	−	0.989162i	$-0.453092\pi$
$617$	7.29444	0.293663	0.146831	+	0.989162i	$0.453092\pi$
$618$	−23.4057	−0.941514
$619$	−34.2151	−1.37522	−0.687610	−	0.726081i	$-0.741340\pi$
$619$	−34.2151	−1.37522	−0.687610	+	0.726081i	$0.741340\pi$
$620$	−9.34928	−0.375476
$621$	43.7757	1.75666
$622$	20.4554	0.820187
$623$	18.8385	0.754747
$624$	−9.19898	−0.368254
$625$	23.8094	0.952376
$626$	46.5115	1.85897
$627$	10.1128	0.403868
$628$	23.0637	0.920343
$629$	2.84963	0.113622
$630$	−1.99863	−0.0796272
$631$	−22.3144	−0.888324	−0.444162	−	0.895947i	$-0.646498\pi$
$631$	−22.3144	−0.888324	−0.444162	+	0.895947i	$0.646498\pi$
$632$	64.8205	2.57842
$633$	−11.8542	−0.471161
$634$	−21.1698	−0.840762
$635$	0.377550	0.0149826
$636$	14.8244	0.587824
$637$	−1.48696	−0.0589155
$638$	47.8423	1.89410
$639$	−8.20930	−0.324755
$640$	−3.93912	−0.155708
$641$	27.0793	1.06957	0.534783	−	0.844989i	$-0.320393\pi$
$641$	27.0793	1.06957	0.534783	+	0.844989i	$0.320393\pi$
$642$	51.0316	2.01406
$643$	12.4365	0.490448	0.245224	−	0.969466i	$-0.421139\pi$
$643$	12.4365	0.490448	0.245224	+	0.969466i	$0.421139\pi$
$644$	−84.0693	−3.31280
$645$	1.38586	0.0545684
$646$	−18.6051	−0.732006
$647$	37.0323	1.45589	0.727944	−	0.685636i	$-0.240476\pi$
$647$	37.0323	1.45589	0.727944	+	0.685636i	$0.240476\pi$
$648$	30.3037	1.19044
$649$	−16.3476	−0.641700
$650$	7.67899	0.301195
$651$	−18.0552	−0.707638
$652$	64.2512	2.51627
$653$	17.8963	0.700335	0.350167	−	0.936687i	$-0.386125\pi$
$653$	17.8963	0.700335	0.350167	+	0.936687i	$0.386125\pi$
$654$	−3.52128	−0.137693
$655$	5.56198	0.217324
$656$	−130.775	−5.10590
$657$	3.79757	0.148157
$658$	−16.2279	−0.632629
$659$	0.450954	0.0175667	0.00878333	−	0.999961i	$-0.497204\pi$
$659$	0.450954	0.0175667	0.00878333	+	0.999961i	$0.497204\pi$
$660$	5.96403	0.232150
$661$	37.5598	1.46091	0.730454	−	0.682962i	$-0.239309\pi$
$661$	37.5598	1.46091	0.730454	+	0.682962i	$0.239309\pi$
$662$	−66.5139	−2.58514
$663$	−2.20220	−0.0855264
$664$	−0.283269	−0.0109930
$665$	−1.46048	−0.0566350
$666$	3.35044	0.129827
$667$	44.6705	1.72965
$668$	91.2880	3.53204
$669$	6.58068	0.254424
$670$	8.12676	0.313964
$671$	−16.2842	−0.628645
$672$	−42.2407	−1.62947
$673$	14.0539	0.541738	0.270869	−	0.962616i	$-0.412689\pi$
$673$	14.0539	0.541738	0.270869	+	0.962616i	$0.412689\pi$
$674$	−73.3992	−2.82723
$675$	−27.6534	−1.06438
$676$	−64.6971	−2.48835
$677$	3.39839	0.130611	0.0653053	−	0.997865i	$-0.479198\pi$
$677$	3.39839	0.130611	0.0653053	+	0.997865i	$0.479198\pi$
$678$	−13.4183	−0.515327
$679$	−0.841441	−0.0322916
$680$	−6.67902	−0.256129
$681$	6.53045	0.250247
$682$	−54.0136	−2.06829
$683$	−32.1149	−1.22884	−0.614421	−	0.788978i	$-0.710611\pi$
$683$	−32.1149	−1.22884	−0.614421	+	0.788978i	$0.710611\pi$
$684$	−15.7228	−0.601176
$685$	1.90120	0.0726410
$686$	−53.7267	−2.05130
$687$	−19.2349	−0.733855
$688$	−44.2253	−1.68607
$689$	−1.28546	−0.0489721
$690$	7.74755	0.294944
$691$	−6.53753	−0.248699	−0.124350	−	0.992238i	$-0.539684\pi$
$691$	−6.53753	−0.248699	−0.124350	+	0.992238i	$0.539684\pi$
$692$	48.3420	1.83769
$693$	−8.29928	−0.315264
$694$	−72.8370	−2.76485
$695$	−3.85758	−0.146326
$696$	62.8358	2.38178
$697$	−31.3070	−1.18584
$698$	41.7435	1.58001
$699$	0.643181	0.0243274
$700$	53.1072	2.00726
$701$	−44.2499	−1.67130	−0.835648	−	0.549266i	$-0.814907\pi$
$701$	−44.2499	−1.67130	−0.835648	+	0.549266i	$0.814907\pi$
$702$	−8.77177	−0.331069
$703$	2.44831	0.0923398
$704$	−51.8965	−1.95592
$705$	1.07491	0.0404835
$706$	−78.5173	−2.95504
$707$	23.0533	0.867009
$708$	−35.2723	−1.32562
$709$	−0.275455	−0.0103449	−0.00517247	−	0.999987i	$-0.501646\pi$
$709$	−0.275455	−0.0103449	−0.00517247	+	0.999987i	$0.501646\pi$
$710$	−4.92214	−0.184725
$711$	9.81542	0.368107
$712$	74.0187	2.77397
$713$	−50.4326	−1.88871
$714$	−21.1896	−0.792999
$715$	−0.517158	−0.0193406
$716$	−1.20363	−0.0449817
$717$	24.6825	0.921787
$718$	−27.1677	−1.01389
$719$	34.6886	1.29366	0.646832	−	0.762632i	$-0.276093\pi$
$719$	34.6886	1.29366	0.646832	+	0.762632i	$0.276093\pi$
$720$	−4.22466	−0.157444
$721$	14.0363	0.522740
$722$	34.6827	1.29076
$723$	−19.3866	−0.720996
$724$	40.2856	1.49720
$725$	−28.2187	−1.04802
$726$	−4.27811	−0.158776
$727$	34.3683	1.27465	0.637325	−	0.770595i	$-0.280041\pi$
$727$	34.3683	1.27465	0.637325	+	0.770595i	$0.280041\pi$
$728$	10.2543	0.380050
$729$	26.8532	0.994561
$730$	2.27695	0.0842737
$731$	−10.5874	−0.391588
$732$	−35.1356	−1.29865
$733$	13.3248	0.492164	0.246082	−	0.969249i	$-0.420857\pi$
$733$	13.3248	0.492164	0.246082	+	0.969249i	$0.420857\pi$
$734$	15.0344	0.554929
$735$	0.947709	0.0349568
$736$	−117.989	−4.34913
$737$	33.7463	1.24306
$738$	−36.8091	−1.35496
$739$	39.6322	1.45789	0.728947	−	0.684570i	$-0.240010\pi$
$739$	39.6322	1.45789	0.728947	+	0.684570i	$0.240010\pi$
$740$	1.44389	0.0530784
$741$	−1.89206	−0.0695067
$742$	−12.3687	−0.454069
$743$	14.6256	0.536563	0.268281	−	0.963341i	$-0.413544\pi$
$743$	14.6256	0.536563	0.268281	+	0.963341i	$0.413544\pi$
$744$	−70.9410	−2.60082
$745$	−6.05197	−0.221727
$746$	29.1114	1.06584
$747$	−0.0428940	−0.00156941
$748$	−45.5625	−1.66593
$749$	−30.6035	−1.11823
$750$	−9.86774	−0.360319
$751$	23.8520	0.870373	0.435186	−	0.900340i	$-0.356682\pi$
$751$	23.8520	0.870373	0.435186	+	0.900340i	$0.356682\pi$
$752$	−34.3023	−1.25087
$753$	−19.3727	−0.705980
$754$	−8.95108	−0.325979
$755$	−5.31856	−0.193562
$756$	−60.6648	−2.20636
$757$	−33.3624	−1.21258	−0.606289	−	0.795245i	$-0.707342\pi$
$757$	−33.3624	−1.21258	−0.606289	+	0.795245i	$0.707342\pi$
$758$	−80.5036	−2.92402
$759$	32.1716	1.16776
$760$	−5.73841	−0.208154
$761$	10.3425	0.374914	0.187457	−	0.982273i	$-0.439976\pi$
$761$	10.3425	0.374914	0.187457	+	0.982273i	$0.439976\pi$
$762$	4.70629	0.170491
$763$	2.11170	0.0764488
$764$	112.868	4.08342
$765$	−1.01137	−0.0365661
$766$	36.0936	1.30412
$767$	3.05856	0.110438
$768$	−5.28882	−0.190844
$769$	−37.6772	−1.35868	−0.679338	−	0.733826i	$-0.737733\pi$
$769$	−37.6772	−1.35868	−0.679338	+	0.733826i	$0.737733\pi$
$770$	−4.97609	−0.179326
$771$	−10.1935	−0.367108
$772$	68.2790	2.45742
$773$	10.0205	0.360414	0.180207	−	0.983629i	$-0.442323\pi$
$773$	10.0205	0.360414	0.180207	+	0.983629i	$0.442323\pi$
$774$	−12.4481	−0.447437
$775$	31.8586	1.14440
$776$	−3.30613	−0.118683
$777$	2.78841	0.100034
$778$	−22.3146	−0.800018
$779$	−26.8980	−0.963721
$780$	−1.11584	−0.0399536
$781$	−20.4392	−0.731370
$782$	−59.1877	−2.11655
$783$	32.2344	1.15196
$784$	−30.2430	−1.08011
$785$	1.27464	0.0454940
$786$	69.3321	2.47299
$787$	−6.49592	−0.231555	−0.115777	−	0.993275i	$-0.536936\pi$
$787$	−6.49592	−0.231555	−0.115777	+	0.993275i	$0.536936\pi$
$788$	−29.8999	−1.06514
$789$	8.85709	0.315321
$790$	5.88514	0.209384
$791$	8.04692	0.286116
$792$	−32.6089	−1.15871
$793$	3.04670	0.108191
$794$	−11.3324	−0.402173
$795$	0.819284	0.0290570
$796$	86.5969	3.06935
$797$	36.6040	1.29658	0.648290	−	0.761393i	$-0.275484\pi$
$797$	36.6040	1.29658	0.648290	+	0.761393i	$0.275484\pi$
$798$	−18.2054	−0.644465
$799$	−8.21183	−0.290514
$800$	74.5344	2.63519
$801$	11.2083	0.396024
$802$	−9.93135	−0.350688
$803$	9.45502	0.333661
$804$	72.8125	2.56790
$805$	−4.64618	−0.163756
$806$	10.1057	0.355958
$807$	16.3895	0.576939
$808$	90.5793	3.18657
$809$	12.9219	0.454311	0.227155	−	0.973859i	$-0.427058\pi$
$809$	12.9219	0.454311	0.227155	+	0.973859i	$0.427058\pi$
$810$	2.75131	0.0966711
$811$	−1.96637	−0.0690487	−0.0345244	−	0.999404i	$-0.510992\pi$
$811$	−1.96637	−0.0690487	−0.0345244	+	0.999404i	$0.510992\pi$
$812$	−61.9048	−2.17243
$813$	33.9295	1.18996
$814$	8.34178	0.292379
$815$	3.55091	0.124383
$816$	−44.7902	−1.56797
$817$	−9.09634	−0.318241
$818$	−34.4611	−1.20490
$819$	1.55276	0.0542577
$820$	−15.8631	−0.553963
$821$	29.4988	1.02952	0.514758	−	0.857336i	$-0.327882\pi$
$821$	29.4988	1.02952	0.514758	+	0.857336i	$0.327882\pi$
$822$	23.6991	0.826601
$823$	11.8907	0.414484	0.207242	−	0.978290i	$-0.433551\pi$
$823$	11.8907	0.414484	0.207242	+	0.978290i	$0.433551\pi$
$824$	55.1504	1.92126
$825$	−20.3231	−0.707558
$826$	29.4294	1.02398
$827$	−11.2458	−0.391054	−0.195527	−	0.980698i	$-0.562642\pi$
$827$	−11.2458	−0.391054	−0.195527	+	0.980698i	$0.562642\pi$
$828$	−50.0184	−1.73826
$829$	−17.7578	−0.616753	−0.308376	−	0.951264i	$-0.599786\pi$
$829$	−17.7578	−0.616753	−0.308376	+	0.951264i	$0.599786\pi$
$830$	−0.0257184	−0.000892699 0
$831$	−17.5327	−0.608202
$832$	9.70959	0.336619
$833$	−7.24006	−0.250853
$834$	−48.0861	−1.66509
$835$	5.04513	0.174594
$836$	−39.1459	−1.35389
$837$	−36.3924	−1.25790
$838$	−62.8769	−2.17205
$839$	−5.36417	−0.185192	−0.0925958	−	0.995704i	$-0.529516\pi$
$839$	−5.36417	−0.185192	−0.0925958	+	0.995704i	$0.529516\pi$
$840$	−6.53555	−0.225498
$841$	3.89331	0.134252
$842$	35.2521	1.21487
$843$	22.7626	0.783984
$844$	45.8865	1.57948
$845$	−3.57555	−0.123003
$846$	−9.65505	−0.331947
$847$	2.56557	0.0881541
$848$	−26.1447	−0.897814
$849$	−2.87196	−0.0985655
$850$	37.3893	1.28244
$851$	7.78873	0.266994
$852$	−44.1004	−1.51086
$853$	−10.0531	−0.344212	−0.172106	−	0.985078i	$-0.555057\pi$
$853$	−10.0531	−0.344212	−0.172106	+	0.985078i	$0.555057\pi$
$854$	29.3153	1.00315
$855$	−0.868937	−0.0297170
$856$	−120.245	−4.10989
$857$	−48.6023	−1.66022	−0.830111	−	0.557598i	$-0.811723\pi$
$857$	−48.6023	−1.66022	−0.830111	+	0.557598i	$0.811723\pi$
$858$	−6.44656	−0.220082
$859$	18.0666	0.616426	0.308213	−	0.951317i	$-0.400269\pi$
$859$	18.0666	0.616426	0.308213	+	0.951317i	$0.400269\pi$
$860$	−5.36456	−0.182930
$861$	−30.6345	−1.04402
$862$	−80.0482	−2.72645
$863$	44.5630	1.51694	0.758471	−	0.651707i	$-0.225947\pi$
$863$	44.5630	1.51694	0.758471	+	0.651707i	$0.225947\pi$
$864$	−85.1412	−2.89656
$865$	2.67167	0.0908395
$866$	−82.7984	−2.81360
$867$	11.7252	0.398208
$868$	69.8900	2.37222
$869$	24.4380	0.829002
$870$	5.70494	0.193416
$871$	−6.31377	−0.213934
$872$	8.29715	0.280977
$873$	−0.500629	−0.0169437
$874$	−50.8522	−1.72010
$875$	5.91766	0.200053
$876$	20.4006	0.689272
$877$	6.73318	0.227363	0.113682	−	0.993517i	$-0.463736\pi$
$877$	6.73318	0.227363	0.113682	+	0.993517i	$0.463736\pi$
$878$	44.2039	1.49181
$879$	−26.7514	−0.902302
$880$	−10.5184	−0.354574
$881$	27.2479	0.918004	0.459002	−	0.888435i	$-0.348207\pi$
$881$	27.2479	0.918004	0.459002	+	0.888435i	$0.348207\pi$
$882$	−8.51249	−0.286630
$883$	−8.70316	−0.292885	−0.146442	−	0.989219i	$-0.546782\pi$
$883$	−8.70316	−0.292885	−0.146442	+	0.989219i	$0.546782\pi$
$884$	8.52452	0.286711
$885$	−1.94936	−0.0655271
$886$	−14.7387	−0.495155
$887$	−46.2493	−1.55290	−0.776450	−	0.630179i	$-0.782981\pi$
$887$	−46.2493	−1.55290	−0.776450	+	0.630179i	$0.782981\pi$
$888$	10.9560	0.367660
$889$	−2.82235	−0.0946586
$890$	6.72025	0.225263
$891$	11.4248	0.382745
$892$	−25.4732	−0.852907
$893$	−7.05535	−0.236098
$894$	−75.4400	−2.52309
$895$	−0.0665199	−0.00222351
$896$	29.4467	0.983745
$897$	−6.01916	−0.200974
$898$	102.712	3.42756
$899$	−37.1363	−1.23856
$900$	31.5970	1.05323
$901$	−6.25895	−0.208516
$902$	−91.6457	−3.05147
$903$	−10.3599	−0.344757
$904$	31.6174	1.05158
$905$	2.22643	0.0740090
$906$	−66.2978	−2.20260
$907$	16.4131	0.544987	0.272494	−	0.962158i	$-0.412152\pi$
$907$	16.4131	0.544987	0.272494	+	0.962158i	$0.412152\pi$
$908$	−25.2788	−0.838907
$909$	13.7160	0.454929
$910$	0.931002	0.0308624
$911$	−4.28492	−0.141966	−0.0709829	−	0.997478i	$-0.522614\pi$
$911$	−4.28492	−0.141966	−0.0709829	+	0.997478i	$0.522614\pi$
$912$	−38.4823	−1.27428
$913$	−0.106795	−0.00353441
$914$	−37.8077	−1.25057
$915$	−1.94180	−0.0641941
$916$	74.4564	2.46011
$917$	−41.5782	−1.37303
$918$	−42.7101	−1.40964
$919$	25.2287	0.832218	0.416109	−	0.909315i	$-0.363394\pi$
$919$	25.2287	0.832218	0.416109	+	0.909315i	$0.363394\pi$
$920$	−18.2554	−0.601864
$921$	−10.3130	−0.339824
$922$	100.092	3.29635
$923$	3.82407	0.125871
$924$	−44.5838	−1.46670
$925$	−4.92020	−0.161775
$926$	39.4851	1.29756
$927$	8.35114	0.274287
$928$	−86.8816	−2.85203
$929$	4.31329	0.141514	0.0707571	−	0.997494i	$-0.477458\pi$
$929$	4.31329	0.141514	0.0707571	+	0.997494i	$0.477458\pi$
$930$	−6.44083	−0.211203
$931$	−6.22044	−0.203867
$932$	−2.48970	−0.0815528
$933$	10.1287	0.331600
$934$	−30.7860	−1.00735
$935$	−2.51806	−0.0823494
$936$	6.10097	0.199416
$937$	23.4464	0.765959	0.382980	−	0.923757i	$-0.374898\pi$
$937$	23.4464	0.765959	0.382980	+	0.923757i	$0.374898\pi$
$938$	−60.7511	−1.98359
$939$	23.0307	0.751580
$940$	−4.16089	−0.135713
$941$	−26.1473	−0.852379	−0.426189	−	0.904634i	$-0.640144\pi$
$941$	−26.1473	−0.852379	−0.426189	+	0.904634i	$0.640144\pi$
$942$	15.8889	0.517688
$943$	−85.5698	−2.78654
$944$	62.2075	2.02468
$945$	−3.35271	−0.109064
$946$	−30.9927	−1.00766
$947$	20.3697	0.661928	0.330964	−	0.943643i	$-0.392626\pi$
$947$	20.3697	0.661928	0.330964	+	0.943643i	$0.392626\pi$
$948$	52.7285	1.71254
$949$	−1.76899	−0.0574238
$950$	32.1237	1.04223
$951$	−10.4825	−0.339919
$952$	49.9286	1.61820
$953$	−53.3495	−1.72816	−0.864080	−	0.503354i	$-0.832099\pi$
$953$	−53.3495	−1.72816	−0.864080	+	0.503354i	$0.832099\pi$
$954$	−7.35895	−0.238255
$955$	6.23777	0.201849
$956$	−95.5439	−3.09011
$957$	23.6897	0.765780
$958$	−90.0015	−2.90782
$959$	−14.2123	−0.458939
$960$	−6.18838	−0.199729
$961$	10.9265	0.352468
$962$	−1.56071	−0.0503192
$963$	−18.2081	−0.586746
$964$	75.0438	2.41700
$965$	3.77352	0.121474
$966$	−57.9163	−1.86343
$967$	−15.5422	−0.499802	−0.249901	−	0.968271i	$-0.580398\pi$
$967$	−15.5422	−0.499802	−0.249901	+	0.968271i	$0.580398\pi$
$968$	10.0804	0.323998
$969$	−9.21252	−0.295949
$970$	−0.300168	−0.00963780
$971$	−40.5433	−1.30110	−0.650548	−	0.759465i	$-0.725461\pi$
$971$	−40.5433	−1.30110	−0.650548	+	0.759465i	$0.725461\pi$
$972$	−61.5330	−1.97367
$973$	28.8371	0.924475
$974$	−89.5193	−2.86838
$975$	3.80235	0.121773
$976$	61.9663	1.98349
$977$	8.40900	0.269028	0.134514	−	0.990912i	$-0.457053\pi$
$977$	8.40900	0.269028	0.134514	+	0.990912i	$0.457053\pi$
$978$	44.2634	1.41539
$979$	27.9058	0.891873
$980$	−3.66850	−0.117186
$981$	1.25639	0.0401135
$982$	−24.5982	−0.784959
$983$	25.0169	0.797916	0.398958	−	0.916969i	$-0.369372\pi$
$983$	25.0169	0.797916	0.398958	+	0.916969i	$0.369372\pi$
$984$	−120.367	−3.83715
$985$	−1.65245	−0.0526514
$986$	−43.5831	−1.38797
$987$	−8.03544	−0.255771
$988$	7.32401	0.233008
$989$	−28.9379	−0.920172
$990$	−2.96061	−0.0940942
$991$	50.3166	1.59836	0.799180	−	0.601091i	$-0.205267\pi$
$991$	50.3166	1.59836	0.799180	+	0.601091i	$0.205267\pi$
$992$	98.0885	3.11431
$993$	−32.9352	−1.04517
$994$	36.7952	1.16707
$995$	4.78587	0.151722
$996$	−0.230427	−0.00730135
$997$	−42.2446	−1.33790	−0.668949	−	0.743308i	$-0.733256\pi$
$997$	−42.2446	−1.33790	−0.668949	+	0.743308i	$0.733256\pi$
$998$	−71.0905	−2.25033
$999$	5.62038	0.177821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.3	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.3	✓	85	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)

\(f(q)\)	\(=\)	\(q-2.66672 q^{2} -1.32046 q^{3} +5.11137 q^{4} +0.282486 q^{5} +3.52128 q^{6} -2.11170 q^{7} -8.29715 q^{8} -1.25639 q^{9} +O(q^{10})\)	\(q-2.66672 q^{2} -1.32046 q^{3} +5.11137 q^{4} +0.282486 q^{5} +3.52128 q^{6} -2.11170 q^{7} -8.29715 q^{8} -1.25639 q^{9} -0.753309 q^{10} -3.12811 q^{11} -6.74935 q^{12} +0.585254 q^{13} +5.63131 q^{14} -0.373010 q^{15} +11.9034 q^{16} +2.84963 q^{17} +3.35044 q^{18} +2.44831 q^{19} +1.44389 q^{20} +2.78841 q^{21} +8.34178 q^{22} +7.78873 q^{23} +10.9560 q^{24} -4.92020 q^{25} -1.56071 q^{26} +5.62038 q^{27} -10.7937 q^{28} +5.73527 q^{29} +0.994712 q^{30} -6.47507 q^{31} -15.1487 q^{32} +4.13054 q^{33} -7.59914 q^{34} -0.596526 q^{35} -6.42189 q^{36} +1.00000 q^{37} -6.52895 q^{38} -0.772803 q^{39} -2.34382 q^{40} -10.9864 q^{41} -7.43591 q^{42} -3.71535 q^{43} -15.9889 q^{44} -0.354913 q^{45} -20.7703 q^{46} -2.88172 q^{47} -15.7179 q^{48} -2.54071 q^{49} +13.1208 q^{50} -3.76281 q^{51} +2.99145 q^{52} -2.19641 q^{53} -14.9880 q^{54} -0.883646 q^{55} +17.5211 q^{56} -3.23289 q^{57} -15.2943 q^{58} +5.22603 q^{59} -1.90659 q^{60} +5.20577 q^{61} +17.2672 q^{62} +2.65313 q^{63} +16.5904 q^{64} +0.165326 q^{65} -11.0150 q^{66} -10.7881 q^{67} +14.5655 q^{68} -10.2847 q^{69} +1.59077 q^{70} +6.53403 q^{71} +10.4245 q^{72} -3.02260 q^{73} -2.66672 q^{74} +6.49692 q^{75} +12.5142 q^{76} +6.60564 q^{77} +2.06085 q^{78} -7.81238 q^{79} +3.36253 q^{80} -3.65230 q^{81} +29.2975 q^{82} +0.0341406 q^{83} +14.2526 q^{84} +0.804978 q^{85} +9.90779 q^{86} -7.57318 q^{87} +25.9544 q^{88} -8.92098 q^{89} +0.946452 q^{90} -1.23588 q^{91} +39.8111 q^{92} +8.55005 q^{93} +7.68473 q^{94} +0.691612 q^{95} +20.0031 q^{96} +0.398466 q^{97} +6.77534 q^{98} +3.93013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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