LMFDB - Embedded newform 619.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.642946 q^{2} +1.06499 q^{3} -1.58662 q^{4} -0.849273 q^{5} +0.684732 q^{6} -0.754832 q^{7} -2.30600 q^{8} -1.86579 q^{9} +O(q^{10})$	\(q+0.642946 q^{2} +1.06499 q^{3} -1.58662 q^{4} -0.849273 q^{5} +0.684732 q^{6} -0.754832 q^{7} -2.30600 q^{8} -1.86579 q^{9} -0.546037 q^{10} -5.48239 q^{11} -1.68974 q^{12} +6.40779 q^{13} -0.485316 q^{14} -0.904468 q^{15} +1.69060 q^{16} -5.81407 q^{17} -1.19960 q^{18} -1.45134 q^{19} +1.34747 q^{20} -0.803890 q^{21} -3.52488 q^{22} -5.24561 q^{23} -2.45587 q^{24} -4.27874 q^{25} +4.11986 q^{26} -5.18203 q^{27} +1.19763 q^{28} -2.02459 q^{29} -0.581524 q^{30} +8.10514 q^{31} +5.69897 q^{32} -5.83869 q^{33} -3.73813 q^{34} +0.641058 q^{35} +2.96031 q^{36} +2.11237 q^{37} -0.933131 q^{38} +6.82424 q^{39} +1.95843 q^{40} -11.5613 q^{41} -0.516858 q^{42} +11.1749 q^{43} +8.69847 q^{44} +1.58457 q^{45} -3.37264 q^{46} +3.15061 q^{47} +1.80048 q^{48} -6.43023 q^{49} -2.75100 q^{50} -6.19193 q^{51} -10.1667 q^{52} +3.12967 q^{53} -3.33176 q^{54} +4.65604 q^{55} +1.74065 q^{56} -1.54566 q^{57} -1.30170 q^{58} +0.334022 q^{59} +1.43505 q^{60} +8.07978 q^{61} +5.21117 q^{62} +1.40836 q^{63} +0.282924 q^{64} -5.44196 q^{65} -3.75397 q^{66} -10.5272 q^{67} +9.22472 q^{68} -5.58653 q^{69} +0.412166 q^{70} -2.31568 q^{71} +4.30253 q^{72} -5.54601 q^{73} +1.35814 q^{74} -4.55682 q^{75} +2.30272 q^{76} +4.13828 q^{77} +4.38762 q^{78} +14.4975 q^{79} -1.43578 q^{80} +0.0785685 q^{81} -7.43332 q^{82} +0.466639 q^{83} +1.27547 q^{84} +4.93773 q^{85} +7.18486 q^{86} -2.15617 q^{87} +12.6424 q^{88} +6.92646 q^{89} +1.01879 q^{90} -4.83681 q^{91} +8.32279 q^{92} +8.63190 q^{93} +2.02567 q^{94} +1.23258 q^{95} +6.06936 q^{96} -13.2025 q^{97} -4.13429 q^{98} +10.2290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) $ 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * 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 $

$2$	0.642946	0.454632	0.227316	−	0.973821i	$-0.427005\pi$
$2$	0.642946	0.454632	0.227316	+	0.973821i	$0.427005\pi$
$3$	1.06499	0.614873	0.307436	−	0.951569i	$-0.400529\pi$
$3$	1.06499	0.614873	0.307436	+	0.951569i	$0.400529\pi$
$4$	−1.58662	−0.793310
$5$	−0.849273	−0.379806	−0.189903	−	0.981803i	$-0.560817\pi$
$5$	−0.849273	−0.379806	−0.189903	+	0.981803i	$0.560817\pi$
$6$	0.684732	0.279541
$7$	−0.754832	−0.285300	−0.142650	−	0.989773i	$-0.545562\pi$
$7$	−0.754832	−0.285300	−0.142650	+	0.989773i	$0.545562\pi$
$8$	−2.30600	−0.815295
$9$	−1.86579	−0.621931
$10$	−0.546037	−0.172672
$11$	−5.48239	−1.65300	−0.826501	−	0.562935i	$-0.809672\pi$
$11$	−5.48239	−1.65300	−0.826501	+	0.562935i	$0.809672\pi$
$12$	−1.68974	−0.487785
$13$	6.40779	1.77720	0.888601	−	0.458682i	$-0.151678\pi$
$13$	6.40779	1.77720	0.888601	+	0.458682i	$0.151678\pi$
$14$	−0.485316	−0.129706
$15$	−0.904468	−0.233533
$16$	1.69060	0.422651
$17$	−5.81407	−1.41012	−0.705059	−	0.709148i	$-0.749080\pi$
$17$	−5.81407	−1.41012	−0.705059	+	0.709148i	$0.749080\pi$
$18$	−1.19960	−0.282750
$19$	−1.45134	−0.332960	−0.166480	−	0.986045i	$-0.553240\pi$
$19$	−1.45134	−0.332960	−0.166480	+	0.986045i	$0.553240\pi$
$20$	1.34747	0.301304
$21$	−0.803890	−0.175423
$22$	−3.52488	−0.751507
$23$	−5.24561	−1.09379	−0.546893	−	0.837203i	$-0.684189\pi$
$23$	−5.24561	−1.09379	−0.546893	+	0.837203i	$0.684189\pi$
$24$	−2.45587	−0.501303
$25$	−4.27874	−0.855747
$26$	4.11986	0.807972
$27$	−5.18203	−0.997282
$28$	1.19763	0.226331
$29$	−2.02459	−0.375957	−0.187979	−	0.982173i	$-0.560194\pi$
$29$	−2.02459	−0.375957	−0.187979	+	0.982173i	$0.560194\pi$
$30$	−0.581524	−0.106171
$31$	8.10514	1.45573	0.727863	−	0.685723i	$-0.240514\pi$
$31$	8.10514	1.45573	0.727863	+	0.685723i	$0.240514\pi$
$32$	5.69897	1.00745
$33$	−5.83869	−1.01639
$34$	−3.73813	−0.641084
$35$	0.641058	0.108359
$36$	2.96031	0.493384
$37$	2.11237	0.347271	0.173635	−	0.984810i	$-0.444449\pi$
$37$	2.11237	0.347271	0.173635	+	0.984810i	$0.444449\pi$
$38$	−0.933131	−0.151374
$39$	6.82424	1.09275
$40$	1.95843	0.309654
$41$	−11.5613	−1.80558	−0.902789	−	0.430084i	$-0.858484\pi$
$41$	−11.5613	−1.80558	−0.902789	+	0.430084i	$0.858484\pi$
$42$	−0.516858	−0.0797529
$43$	11.1749	1.70416	0.852078	−	0.523415i	$-0.175342\pi$
$43$	11.1749	1.70416	0.852078	+	0.523415i	$0.175342\pi$
$44$	8.69847	1.31134
$45$	1.58457	0.236213
$46$	−3.37264	−0.497269
$47$	3.15061	0.459563	0.229782	−	0.973242i	$-0.426199\pi$
$47$	3.15061	0.459563	0.229782	+	0.973242i	$0.426199\pi$
$48$	1.80048	0.259877
$49$	−6.43023	−0.918604
$50$	−2.75100	−0.389050
$51$	−6.19193	−0.867044
$52$	−10.1667	−1.40987
$53$	3.12967	0.429893	0.214947	−	0.976626i	$-0.431042\pi$
$53$	3.12967	0.429893	0.214947	+	0.976626i	$0.431042\pi$
$54$	−3.33176	−0.453396
$55$	4.65604	0.627821
$56$	1.74065	0.232604
$57$	−1.54566	−0.204728
$58$	−1.30170	−0.170922
$59$	0.334022	0.0434859	0.0217429	−	0.999764i	$-0.493078\pi$
$59$	0.334022	0.0434859	0.0217429	+	0.999764i	$0.493078\pi$
$60$	1.43505	0.185264
$61$	8.07978	1.03451	0.517255	−	0.855832i	$-0.326954\pi$
$61$	8.07978	1.03451	0.517255	+	0.855832i	$0.326954\pi$
$62$	5.21117	0.661819
$63$	1.40836	0.177437
$64$	0.282924	0.0353655
$65$	−5.44196	−0.674992
$66$	−3.75397	−0.462081
$67$	−10.5272	−1.28610	−0.643050	−	0.765824i	$-0.722331\pi$
$67$	−10.5272	−1.28610	−0.643050	+	0.765824i	$0.722331\pi$
$68$	9.22472	1.11866
$69$	−5.58653	−0.672539
$70$	0.412166	0.0492633
$71$	−2.31568	−0.274821	−0.137410	−	0.990514i	$-0.543878\pi$
$71$	−2.31568	−0.274821	−0.137410	+	0.990514i	$0.543878\pi$
$72$	4.30253	0.507058
$73$	−5.54601	−0.649112	−0.324556	−	0.945867i	$-0.605215\pi$
$73$	−5.54601	−0.649112	−0.324556	+	0.945867i	$0.605215\pi$
$74$	1.35814	0.157880
$75$	−4.55682	−0.526176
$76$	2.30272	0.264140
$77$	4.13828	0.471601
$78$	4.38762	0.496800
$79$	14.4975	1.63110	0.815551	−	0.578685i	$-0.196434\pi$
$79$	14.4975	1.63110	0.815551	+	0.578685i	$0.196434\pi$
$80$	−1.43578	−0.160526
$81$	0.0785685	0.00872983
$82$	−7.43332	−0.820872
$83$	0.466639	0.0512202	0.0256101	−	0.999672i	$-0.491847\pi$
$83$	0.466639	0.0512202	0.0256101	+	0.999672i	$0.491847\pi$
$84$	1.27547	0.139165
$85$	4.93773	0.535572
$86$	7.18486	0.774763
$87$	−2.15617	−0.231166
$88$	12.6424	1.34768
$89$	6.92646	0.734204	0.367102	−	0.930181i	$-0.380350\pi$
$89$	6.92646	0.734204	0.367102	+	0.930181i	$0.380350\pi$
$90$	1.01879	0.107390
$91$	−4.83681	−0.507035
$92$	8.32279	0.867711
$93$	8.63190	0.895087
$94$	2.02567	0.208932
$95$	1.23258	0.126460
$96$	6.06936	0.619451
$97$	−13.2025	−1.34051	−0.670255	−	0.742130i	$-0.733815\pi$
$97$	−13.2025	−1.34051	−0.670255	+	0.742130i	$0.733815\pi$
$98$	−4.13429	−0.417626
$99$	10.2290	1.02805
$100$	6.78873	0.678873
$101$	2.31108	0.229961	0.114981	−	0.993368i	$-0.463319\pi$
$101$	2.31108	0.229961	0.114981	+	0.993368i	$0.463319\pi$
$102$	−3.98108	−0.394185
$103$	−19.7751	−1.94850	−0.974250	−	0.225468i	$-0.927609\pi$
$103$	−19.7751	−1.94850	−0.974250	+	0.225468i	$0.927609\pi$
$104$	−14.7764	−1.44894
$105$	0.682722	0.0666268
$106$	2.01221	0.195443
$107$	11.5088	1.11259	0.556297	−	0.830984i	$-0.312222\pi$
$107$	11.5088	1.11259	0.556297	+	0.830984i	$0.312222\pi$
$108$	8.22191	0.791154
$109$	−8.70844	−0.834117	−0.417058	−	0.908880i	$-0.636939\pi$
$109$	−8.70844	−0.834117	−0.417058	+	0.908880i	$0.636939\pi$
$110$	2.99358	0.285427
$111$	2.24965	0.213527
$112$	−1.27612	−0.120582
$113$	0.961456	0.0904462	0.0452231	−	0.998977i	$-0.485600\pi$
$113$	0.961456	0.0904462	0.0452231	+	0.998977i	$0.485600\pi$
$114$	−0.993777	−0.0930757
$115$	4.45495	0.415426
$116$	3.21226	0.298251
$117$	−11.9556	−1.10530
$118$	0.214758	0.0197701
$119$	4.38865	0.402306
$120$	2.08571	0.190398
$121$	19.0566	1.73242
$122$	5.19486	0.470321
$123$	−12.3127	−1.11020
$124$	−12.8598	−1.15484
$125$	7.88018	0.704824
$126$	0.905500	0.0806684
$127$	−5.41817	−0.480784	−0.240392	−	0.970676i	$-0.577276\pi$
$127$	−5.41817	−0.480784	−0.240392	+	0.970676i	$0.577276\pi$
$128$	−11.2160	−0.991368
$129$	11.9012	1.04784
$130$	−3.49889	−0.306873
$131$	3.74962	0.327606	0.163803	−	0.986493i	$-0.447624\pi$
$131$	3.74962	0.327606	0.163803	+	0.986493i	$0.447624\pi$
$132$	9.26379	0.806310
$133$	1.09552	0.0949933
$134$	−6.76841	−0.584701
$135$	4.40095	0.378774
$136$	13.4073	1.14966
$137$	−5.76083	−0.492181	−0.246090	−	0.969247i	$-0.579146\pi$
$137$	−5.76083	−0.492181	−0.246090	+	0.969247i	$0.579146\pi$
$138$	−3.59184	−0.305757
$139$	−15.7109	−1.33258	−0.666290	−	0.745693i	$-0.732119\pi$
$139$	−15.7109	−1.33258	−0.666290	+	0.745693i	$0.732119\pi$
$140$	−1.01712	−0.0859620
$141$	3.35537	0.282573
$142$	−1.48886	−0.124942
$143$	−35.1300	−2.93772
$144$	−3.15432	−0.262860
$145$	1.71943	0.142791
$146$	−3.56579	−0.295107
$147$	−6.84814	−0.564825
$148$	−3.35152	−0.275493
$149$	14.8973	1.22043	0.610216	−	0.792235i	$-0.291083\pi$
$149$	14.8973	1.22043	0.610216	+	0.792235i	$0.291083\pi$
$150$	−2.92979	−0.239216
$151$	−21.4832	−1.74828	−0.874140	−	0.485674i	$-0.838574\pi$
$151$	−21.4832	−1.74828	−0.874140	+	0.485674i	$0.838574\pi$
$152$	3.34679	0.271460
$153$	10.8479	0.876997
$154$	2.66069	0.214405
$155$	−6.88347	−0.552894
$156$	−10.8275	−0.866892
$157$	−8.75325	−0.698585	−0.349293	−	0.937014i	$-0.613578\pi$
$157$	−8.75325	−0.698585	−0.349293	+	0.937014i	$0.613578\pi$
$158$	9.32114	0.741550
$159$	3.33307	0.264330
$160$	−4.83998	−0.382634
$161$	3.95956	0.312057
$162$	0.0505153	0.00396886
$163$	22.5233	1.76416	0.882079	−	0.471101i	$-0.156143\pi$
$163$	22.5233	1.76416	0.882079	+	0.471101i	$0.156143\pi$
$164$	18.3435	1.43238
$165$	4.95864	0.386030
$166$	0.300023	0.0232863
$167$	11.4573	0.886595	0.443297	−	0.896375i	$-0.353809\pi$
$167$	11.4573	0.886595	0.443297	+	0.896375i	$0.353809\pi$
$168$	1.85377	0.143022
$169$	28.0598	2.15844
$170$	3.17469	0.243488
$171$	2.70790	0.207078
$172$	−17.7303	−1.35192
$173$	−4.33120	−0.329295	−0.164647	−	0.986352i	$-0.552649\pi$
$173$	−4.33120	−0.329295	−0.164647	+	0.986352i	$0.552649\pi$
$174$	−1.38630	−0.105095
$175$	3.22973	0.244144
$176$	−9.26855	−0.698643
$177$	0.355730	0.0267383
$178$	4.45334	0.333792
$179$	−5.10405	−0.381495	−0.190747	−	0.981639i	$-0.561091\pi$
$179$	−5.10405	−0.381495	−0.190747	+	0.981639i	$0.561091\pi$
$180$	−2.51411	−0.187391
$181$	−8.17536	−0.607669	−0.303835	−	0.952725i	$-0.598267\pi$
$181$	−8.17536	−0.607669	−0.303835	+	0.952725i	$0.598267\pi$
$182$	−3.10981	−0.230514
$183$	8.60489	0.636092
$184$	12.0964	0.891758
$185$	−1.79397	−0.131896
$186$	5.54985	0.406935
$187$	31.8750	2.33093
$188$	−4.99882	−0.364576
$189$	3.91156	0.284524
$190$	0.792483	0.0574928
$191$	1.89427	0.137064	0.0685322	−	0.997649i	$-0.478168\pi$
$191$	1.89427	0.137064	0.0685322	+	0.997649i	$0.478168\pi$
$192$	0.301311	0.0217453
$193$	−1.81858	−0.130904	−0.0654522	−	0.997856i	$-0.520849\pi$
$193$	−1.81858	−0.130904	−0.0654522	+	0.997856i	$0.520849\pi$
$194$	−8.48850	−0.609438
$195$	−5.79564	−0.415034
$196$	10.2023	0.728738
$197$	−26.6304	−1.89734	−0.948669	−	0.316271i	$-0.897569\pi$
$197$	−26.6304	−1.89734	−0.948669	+	0.316271i	$0.897569\pi$
$198$	6.57670	0.467386
$199$	4.85873	0.344426	0.172213	−	0.985060i	$-0.444908\pi$
$199$	4.85873	0.344426	0.172213	+	0.985060i	$0.444908\pi$
$200$	9.86678	0.697687
$201$	−11.2113	−0.790788
$202$	1.48590	0.104548
$203$	1.52823	0.107261
$204$	9.82424	0.687835
$205$	9.81873	0.685770
$206$	−12.7143	−0.885850
$207$	9.78723	0.680259
$208$	10.8330	0.751136
$209$	7.95679	0.550383
$210$	0.438953	0.0302906
$211$	5.61077	0.386261	0.193131	−	0.981173i	$-0.438136\pi$
$211$	5.61077	0.386261	0.193131	+	0.981173i	$0.438136\pi$
$212$	−4.96560	−0.341039
$213$	−2.46618	−0.168980
$214$	7.39951	0.505820
$215$	−9.49054	−0.647249
$216$	11.9498	0.813079
$217$	−6.11802	−0.415318
$218$	−5.59906	−0.379216
$219$	−5.90645	−0.399121
$220$	−7.38737	−0.498056
$221$	−37.2553	−2.50606
$222$	1.44640	0.0970763
$223$	−2.25031	−0.150692	−0.0753460	−	0.997157i	$-0.524006\pi$
$223$	−2.25031	−0.150692	−0.0753460	+	0.997157i	$0.524006\pi$
$224$	−4.30177	−0.287424
$225$	7.98324	0.532216
$226$	0.618164	0.0411197
$227$	−9.98554	−0.662764	−0.331382	−	0.943497i	$-0.607515\pi$
$227$	−9.98554	−0.662764	−0.331382	+	0.943497i	$0.607515\pi$
$228$	2.45238	0.162413
$229$	11.8202	0.781103	0.390551	−	0.920581i	$-0.372284\pi$
$229$	11.8202	0.781103	0.390551	+	0.920581i	$0.372284\pi$
$230$	2.86429	0.188866
$231$	4.40724	0.289975
$232$	4.66872	0.306516
$233$	−20.8798	−1.36788	−0.683941	−	0.729537i	$-0.739736\pi$
$233$	−20.8798	−1.36788	−0.683941	+	0.729537i	$0.739736\pi$
$234$	−7.68682	−0.502503
$235$	−2.67573	−0.174545
$236$	−0.529965	−0.0344978
$237$	15.4398	1.00292
$238$	2.82166	0.182901
$239$	6.78174	0.438674	0.219337	−	0.975649i	$-0.429611\pi$
$239$	6.78174	0.438674	0.219337	+	0.975649i	$0.429611\pi$
$240$	−1.52910	−0.0987028
$241$	−18.1338	−1.16810	−0.584050	−	0.811718i	$-0.698533\pi$
$241$	−18.1338	−1.16810	−0.584050	+	0.811718i	$0.698533\pi$
$242$	12.2524	0.787611
$243$	15.6298	1.00265
$244$	−12.8195	−0.820687
$245$	5.46102	0.348892
$246$	−7.91642	−0.504732
$247$	−9.29986	−0.591736
$248$	−18.6905	−1.18685
$249$	0.496966	0.0314939
$250$	5.06653	0.320435
$251$	−12.3104	−0.777026	−0.388513	−	0.921443i	$-0.627011\pi$
$251$	−12.3104	−0.777026	−0.388513	+	0.921443i	$0.627011\pi$
$252$	−2.23453	−0.140762
$253$	28.7585	1.80803
$254$	−3.48359	−0.218580
$255$	5.25864	0.329309
$256$	−7.77716	−0.486072
$257$	−25.4814	−1.58949	−0.794743	−	0.606946i	$-0.792394\pi$
$257$	−25.4814	−1.58949	−0.794743	+	0.606946i	$0.792394\pi$
$258$	7.65181	0.476381
$259$	−1.59448	−0.0990763
$260$	8.63433	0.535478
$261$	3.77747	0.233820
$262$	2.41081	0.148940
$263$	9.23102	0.569209	0.284605	−	0.958645i	$-0.408138\pi$
$263$	9.23102	0.569209	0.284605	+	0.958645i	$0.408138\pi$
$264$	13.4640	0.828655
$265$	−2.65794	−0.163276
$266$	0.704358	0.0431869
$267$	7.37662	0.451442
$268$	16.7026	1.02028
$269$	7.11008	0.433509	0.216755	−	0.976226i	$-0.430453\pi$
$269$	7.11008	0.433509	0.216755	+	0.976226i	$0.430453\pi$
$270$	2.82958	0.172203
$271$	2.72149	0.165318	0.0826592	−	0.996578i	$-0.473659\pi$
$271$	2.72149	0.165318	0.0826592	+	0.996578i	$0.473659\pi$
$272$	−9.82929	−0.595988
$273$	−5.15116	−0.311762
$274$	−3.70390	−0.223761
$275$	23.4577	1.41455
$276$	8.86370	0.533532
$277$	−20.2039	−1.21393	−0.606966	−	0.794728i	$-0.707614\pi$
$277$	−20.2039	−1.21393	−0.606966	+	0.794728i	$0.707614\pi$
$278$	−10.1013	−0.605833
$279$	−15.1225	−0.905362
$280$	−1.47828	−0.0883443
$281$	−3.17223	−0.189239	−0.0946196	−	0.995513i	$-0.530163\pi$
$281$	−3.17223	−0.189239	−0.0946196	+	0.995513i	$0.530163\pi$
$282$	2.15732	0.128467
$283$	−6.12902	−0.364332	−0.182166	−	0.983268i	$-0.558311\pi$
$283$	−6.12902	−0.364332	−0.182166	+	0.983268i	$0.558311\pi$
$284$	3.67410	0.218018
$285$	1.31269	0.0777569
$286$	−22.5867	−1.33558
$287$	8.72687	0.515131
$288$	−10.6331	−0.626562
$289$	16.8034	0.988434
$290$	1.10550	0.0649173
$291$	−14.0605	−0.824244
$292$	8.79942	0.514947
$293$	2.50155	0.146142	0.0730710	−	0.997327i	$-0.476720\pi$
$293$	2.50155	0.146142	0.0730710	+	0.997327i	$0.476720\pi$
$294$	−4.40298	−0.256787
$295$	−0.283675	−0.0165162
$296$	−4.87112	−0.283128
$297$	28.4099	1.64851
$298$	9.57814	0.554847
$299$	−33.6128	−1.94388
$300$	7.22994	0.417421
$301$	−8.43518	−0.486195
$302$	−13.8126	−0.794823
$303$	2.46128	0.141397
$304$	−2.45364	−0.140726
$305$	−6.86193	−0.392913
$306$	6.97458	0.398710
$307$	6.80714	0.388504	0.194252	−	0.980952i	$-0.437772\pi$
$307$	6.80714	0.388504	0.194252	+	0.980952i	$0.437772\pi$
$308$	−6.56588	−0.374126
$309$	−21.0603	−1.19808
$310$	−4.42570	−0.251363
$311$	−11.8458	−0.671716	−0.335858	−	0.941913i	$-0.609026\pi$
$311$	−11.8458	−0.671716	−0.335858	+	0.941913i	$0.609026\pi$
$312$	−15.7367	−0.890916
$313$	−23.0422	−1.30242	−0.651212	−	0.758896i	$-0.725739\pi$
$313$	−23.0422	−1.30242	−0.651212	+	0.758896i	$0.725739\pi$
$314$	−5.62787	−0.317599
$315$	−1.19608	−0.0673916
$316$	−23.0021	−1.29397
$317$	−29.1060	−1.63476	−0.817379	−	0.576101i	$-0.804574\pi$
$317$	−29.1060	−1.63476	−0.817379	+	0.576101i	$0.804574\pi$
$318$	2.14298	0.120173
$319$	11.0996	0.621458
$320$	−0.240279	−0.0134320
$321$	12.2567	0.684104
$322$	2.54578	0.141871
$323$	8.43817	0.469512
$324$	−0.124658	−0.00692547
$325$	−27.4172	−1.52084
$326$	14.4812	0.802042
$327$	−9.27441	−0.512876
$328$	26.6605	1.47208
$329$	−2.37818	−0.131113
$330$	3.18814	0.175501
$331$	−11.2658	−0.619226	−0.309613	−	0.950863i	$-0.600199\pi$
$331$	−11.2658	−0.619226	−0.309613	+	0.950863i	$0.600199\pi$
$332$	−0.740378	−0.0406335
$333$	−3.94124	−0.215979
$334$	7.36644	0.403074
$335$	8.94044	0.488469
$336$	−1.35906	−0.0741428
$337$	−8.92153	−0.485987	−0.242993	−	0.970028i	$-0.578129\pi$
$337$	−8.92153	−0.485987	−0.242993	+	0.970028i	$0.578129\pi$
$338$	18.0409	0.981297
$339$	1.02394	0.0556129
$340$	−7.83430	−0.424875
$341$	−44.4355	−2.40632
$342$	1.74103	0.0941442
$343$	10.1376	0.547377
$344$	−25.7694	−1.38939
$345$	4.74449	0.255434
$346$	−2.78473	−0.149708
$347$	16.6198	0.892196	0.446098	−	0.894984i	$-0.352813\pi$
$347$	16.6198	0.892196	0.446098	+	0.894984i	$0.352813\pi$
$348$	3.42103	0.183386
$349$	−11.4121	−0.610876	−0.305438	−	0.952212i	$-0.598803\pi$
$349$	−11.4121	−0.610876	−0.305438	+	0.952212i	$0.598803\pi$
$350$	2.07654	0.110996
$351$	−33.2053	−1.77237
$352$	−31.2440	−1.66531
$353$	7.94567	0.422906	0.211453	−	0.977388i	$-0.432181\pi$
$353$	7.94567	0.422906	0.211453	+	0.977388i	$0.432181\pi$
$354$	0.228715	0.0121561
$355$	1.96664	0.104379
$356$	−10.9897	−0.582451
$357$	4.67387	0.247367
$358$	−3.28163	−0.173439
$359$	30.0575	1.58637	0.793186	−	0.608980i	$-0.208421\pi$
$359$	30.0575	1.58637	0.793186	+	0.608980i	$0.208421\pi$
$360$	−3.65402	−0.192584
$361$	−16.8936	−0.889138
$362$	−5.25631	−0.276266
$363$	20.2951	1.06522
$364$	7.67418	0.402236
$365$	4.71008	0.246537
$366$	5.53248	0.289187
$367$	−17.3211	−0.904152	−0.452076	−	0.891979i	$-0.649316\pi$
$367$	−17.3211	−0.904152	−0.452076	+	0.891979i	$0.649316\pi$
$368$	−8.86825	−0.462290
$369$	21.5711	1.12295
$370$	−1.15343	−0.0599639
$371$	−2.36238	−0.122648
$372$	−13.6956	−0.710081
$373$	12.6853	0.656819	0.328409	−	0.944535i	$-0.393487\pi$
$373$	12.6853	0.656819	0.328409	+	0.944535i	$0.393487\pi$
$374$	20.4939	1.05971
$375$	8.39232	0.433377
$376$	−7.26531	−0.374680
$377$	−12.9732	−0.668152
$378$	2.51492	0.129354
$379$	−1.89256	−0.0972141	−0.0486071	−	0.998818i	$-0.515478\pi$
$379$	−1.89256	−0.0972141	−0.0486071	+	0.998818i	$0.515478\pi$
$380$	−1.95564	−0.100322
$381$	−5.77030	−0.295621
$382$	1.21791	0.0623138
$383$	−2.66054	−0.135947	−0.0679736	−	0.997687i	$-0.521653\pi$
$383$	−2.66054	−0.135947	−0.0679736	+	0.997687i	$0.521653\pi$
$384$	−11.9450	−0.609565
$385$	−3.51453	−0.179117
$386$	−1.16925	−0.0595133
$387$	−20.8501	−1.05987
$388$	20.9474	1.06344
$389$	24.2772	1.23090	0.615452	−	0.788174i	$-0.288973\pi$
$389$	24.2772	1.23090	0.615452	+	0.788174i	$0.288973\pi$
$390$	−3.72628	−0.188688
$391$	30.4983	1.54237
$392$	14.8281	0.748934
$393$	3.99332	0.201436
$394$	−17.1219	−0.862590
$395$	−12.3124	−0.619503
$396$	−16.2295	−0.815566
$397$	28.1600	1.41331	0.706655	−	0.707559i	$-0.250203\pi$
$397$	28.1600	1.41331	0.706655	+	0.707559i	$0.250203\pi$
$398$	3.12390	0.156587
$399$	1.16671	0.0584088
$400$	−7.23365	−0.361683
$401$	16.3857	0.818262	0.409131	−	0.912476i	$-0.365832\pi$
$401$	16.3857	0.818262	0.409131	+	0.912476i	$0.365832\pi$
$402$	−7.20829	−0.359517
$403$	51.9360	2.58712
$404$	−3.66681	−0.182431
$405$	−0.0667261	−0.00331565
$406$	0.982568	0.0487640
$407$	−11.5808	−0.574039
$408$	14.2786	0.706897
$409$	22.8880	1.13174	0.565869	−	0.824495i	$-0.308541\pi$
$409$	22.8880	1.13174	0.565869	+	0.824495i	$0.308541\pi$
$410$	6.31291	0.311773
$411$	−6.13523	−0.302629
$412$	31.3756	1.54577
$413$	−0.252130	−0.0124065
$414$	6.29266	0.309267
$415$	−0.396303	−0.0194538
$416$	36.5178	1.79043
$417$	−16.7320	−0.819367
$418$	5.11579	0.250221
$419$	−6.73859	−0.329202	−0.164601	−	0.986360i	$-0.552634\pi$
$419$	−6.73859	−0.329202	−0.164601	+	0.986360i	$0.552634\pi$
$420$	−1.08322	−0.0528557
$421$	−21.5414	−1.04986	−0.524931	−	0.851145i	$-0.675909\pi$
$421$	−21.5414	−1.04986	−0.524931	+	0.851145i	$0.675909\pi$
$422$	3.60742	0.175606
$423$	−5.87839	−0.285817
$424$	−7.21703	−0.350490
$425$	24.8769	1.20670
$426$	−1.58562	−0.0768235
$427$	−6.09888	−0.295145
$428$	−18.2600	−0.882632
$429$	−37.4131	−1.80632
$430$	−6.10190	−0.294260
$431$	23.0568	1.11061	0.555304	−	0.831647i	$-0.312602\pi$
$431$	23.0568	1.11061	0.555304	+	0.831647i	$0.312602\pi$
$432$	−8.76076	−0.421502
$433$	26.1349	1.25596	0.627982	−	0.778228i	$-0.283881\pi$
$433$	26.1349	1.25596	0.627982	+	0.778228i	$0.283881\pi$
$434$	−3.93356	−0.188817
$435$	1.83118	0.0877983
$436$	13.8170	0.661713
$437$	7.61315	0.364186
$438$	−3.79753	−0.181453
$439$	−33.6677	−1.60687	−0.803436	−	0.595391i	$-0.796997\pi$
$439$	−33.6677	−1.60687	−0.803436	+	0.595391i	$0.796997\pi$
$440$	−10.7368	−0.511859
$441$	11.9975	0.571309
$442$	−23.9532	−1.13934
$443$	−20.2677	−0.962947	−0.481474	−	0.876461i	$-0.659898\pi$
$443$	−20.2677	−0.962947	−0.481474	+	0.876461i	$0.659898\pi$
$444$	−3.56934	−0.169393
$445$	−5.88245	−0.278855
$446$	−1.44683	−0.0685093
$447$	15.8655	0.750411
$448$	−0.213560	−0.0100898
$449$	−40.9542	−1.93275	−0.966375	−	0.257137i	$-0.917221\pi$
$449$	−40.9542	−1.93275	−0.966375	+	0.257137i	$0.917221\pi$
$450$	5.13279	0.241962
$451$	63.3837	2.98462
$452$	−1.52547	−0.0717519
$453$	−22.8794	−1.07497
$454$	−6.42016	−0.301313
$455$	4.10777	0.192575
$456$	3.56430	0.166914
$457$	−4.05260	−0.189573	−0.0947863	−	0.995498i	$-0.530217\pi$
$457$	−4.05260	−0.189573	−0.0947863	+	0.995498i	$0.530217\pi$
$458$	7.59977	0.355114
$459$	30.1287	1.40629
$460$	−7.06832	−0.329562
$461$	5.86929	0.273360	0.136680	−	0.990615i	$-0.456357\pi$
$461$	5.86929	0.273360	0.136680	+	0.990615i	$0.456357\pi$
$462$	2.83361	0.131832
$463$	−22.5390	−1.04748	−0.523738	−	0.851879i	$-0.675463\pi$
$463$	−22.5390	−1.04748	−0.523738	+	0.851879i	$0.675463\pi$
$464$	−3.42279	−0.158899
$465$	−7.33084	−0.339959
$466$	−13.4246	−0.621883
$467$	8.00593	0.370470	0.185235	−	0.982694i	$-0.440695\pi$
$467$	8.00593	0.370470	0.185235	+	0.982694i	$0.440695\pi$
$468$	18.9690	0.876843
$469$	7.94625	0.366924
$470$	−1.72035	−0.0793537
$471$	−9.32213	−0.429541
$472$	−0.770255	−0.0354539
$473$	−61.2651	−2.81697
$474$	9.92693	0.455959
$475$	6.20989	0.284929
$476$	−6.96311	−0.319154
$477$	−5.83932	−0.267364
$478$	4.36029	0.199435
$479$	37.6786	1.72158	0.860789	−	0.508961i	$-0.169970\pi$
$479$	37.6786	1.72158	0.860789	+	0.508961i	$0.169970\pi$
$480$	−5.15454	−0.235271
$481$	13.5356	0.617170
$482$	−11.6590	−0.531055
$483$	4.21689	0.191875
$484$	−30.2356	−1.37434
$485$	11.2125	0.509134
$486$	10.0491	0.455836
$487$	27.7309	1.25661	0.628304	−	0.777968i	$-0.283750\pi$
$487$	27.7309	1.25661	0.628304	+	0.777968i	$0.283750\pi$
$488$	−18.6320	−0.843431
$489$	23.9871	1.08473
$490$	3.51114	0.158617
$491$	34.1728	1.54220	0.771099	−	0.636715i	$-0.219707\pi$
$491$	34.1728	1.54220	0.771099	+	0.636715i	$0.219707\pi$
$492$	19.5356	0.880734
$493$	11.7711	0.530144
$494$	−5.97931	−0.269022
$495$	−8.68721	−0.390461
$496$	13.7026	0.615264
$497$	1.74795	0.0784063
$498$	0.319522	0.0143181
$499$	−44.6511	−1.99886	−0.999428	−	0.0338067i	$-0.989237\pi$
$499$	−44.6511	−1.99886	−0.999428	+	0.0338067i	$0.989237\pi$
$500$	−12.5028	−0.559144
$501$	12.2020	0.545143
$502$	−7.91493	−0.353260
$503$	32.2310	1.43711	0.718555	−	0.695470i	$-0.244804\pi$
$503$	32.2310	1.43711	0.718555	+	0.695470i	$0.244804\pi$
$504$	−3.24769	−0.144663
$505$	−1.96274	−0.0873407
$506$	18.4901	0.821987
$507$	29.8834	1.32717
$508$	8.59657	0.381411
$509$	−13.4141	−0.594569	−0.297284	−	0.954789i	$-0.596081\pi$
$509$	−13.4141	−0.594569	−0.297284	+	0.954789i	$0.596081\pi$
$510$	3.38102	0.149714
$511$	4.18631	0.185191
$512$	17.4318	0.770384
$513$	7.52087	0.332054
$514$	−16.3832	−0.722630
$515$	16.7945	0.740053
$516$	−18.8826	−0.831262
$517$	−17.2729	−0.759659
$518$	−1.02517	−0.0450432
$519$	−4.61268	−0.202474
$520$	12.5492	0.550318
$521$	−34.6010	−1.51590	−0.757948	−	0.652315i	$-0.773798\pi$
$521$	−34.6010	−1.51590	−0.757948	+	0.652315i	$0.773798\pi$
$522$	2.42871	0.106302
$523$	−7.94238	−0.347296	−0.173648	−	0.984808i	$-0.555556\pi$
$523$	−7.94238	−0.347296	−0.173648	+	0.984808i	$0.555556\pi$
$524$	−5.94923	−0.259893
$525$	3.43963	0.150118
$526$	5.93505	0.258780
$527$	−47.1238	−2.05275
$528$	−9.87093	−0.429577
$529$	4.51642	0.196366
$530$	−1.70891	−0.0742305
$531$	−0.623215	−0.0270452
$532$	−1.73817	−0.0753591
$533$	−74.0826	−3.20887
$534$	4.74277	0.205240
$535$	−9.77407	−0.422570
$536$	24.2757	1.04855
$537$	−5.43577	−0.234571
$538$	4.57140	0.197087
$539$	35.2530	1.51845
$540$	−6.98264	−0.300485
$541$	−5.14278	−0.221105	−0.110553	−	0.993870i	$-0.535262\pi$
$541$	−5.14278	−0.221105	−0.110553	+	0.993870i	$0.535262\pi$
$542$	1.74977	0.0751590
$543$	−8.70668	−0.373639
$544$	−33.1342	−1.42062
$545$	7.39584	0.316803
$546$	−3.31192	−0.141737
$547$	−6.69283	−0.286165	−0.143082	−	0.989711i	$-0.545701\pi$
$547$	−6.69283	−0.286165	−0.143082	+	0.989711i	$0.545701\pi$
$548$	9.14025	0.390452
$549$	−15.0752	−0.643394
$550$	15.0820	0.643100
$551$	2.93837	0.125179
$552$	12.8826	0.548318
$553$	−10.9432	−0.465353
$554$	−12.9900	−0.551892
$555$	−1.91057	−0.0810990
$556$	24.9272	1.05715
$557$	−1.17015	−0.0495810	−0.0247905	−	0.999693i	$-0.507892\pi$
$557$	−1.17015	−0.0495810	−0.0247905	+	0.999693i	$0.507892\pi$
$558$	−9.72296	−0.411606
$559$	71.6064	3.02863
$560$	1.08378	0.0457979
$561$	33.9466	1.43323
$562$	−2.03957	−0.0860341
$563$	25.9841	1.09510	0.547549	−	0.836774i	$-0.315561\pi$
$563$	25.9841	1.09510	0.547549	+	0.836774i	$0.315561\pi$
$564$	−5.32370	−0.224168
$565$	−0.816538	−0.0343520
$566$	−3.94063	−0.165637
$567$	−0.0593060	−0.00249062
$568$	5.33997	0.224060
$569$	−30.7014	−1.28707	−0.643535	−	0.765417i	$-0.722533\pi$
$569$	−30.7014	−1.28707	−0.643535	+	0.765417i	$0.722533\pi$
$570$	0.843987	0.0353507
$571$	−11.0167	−0.461035	−0.230518	−	0.973068i	$-0.574042\pi$
$571$	−11.0167	−0.461035	−0.230518	+	0.973068i	$0.574042\pi$
$572$	55.7380	2.33052
$573$	2.01738	0.0842772
$574$	5.61091	0.234195
$575$	22.4446	0.936004
$576$	−0.527877	−0.0219949
$577$	35.4007	1.47375	0.736875	−	0.676029i	$-0.236301\pi$
$577$	35.4007	1.47375	0.736875	+	0.676029i	$0.236301\pi$
$578$	10.8037	0.449373
$579$	−1.93677	−0.0804896
$580$	−2.72808	−0.113278
$581$	−0.352234	−0.0146131
$582$	−9.04017	−0.374727
$583$	−17.1581	−0.710614
$584$	12.7891	0.529218
$585$	10.1536	0.419799
$586$	1.60836	0.0664408
$587$	20.1357	0.831090	0.415545	−	0.909573i	$-0.363591\pi$
$587$	20.1357	0.831090	0.415545	+	0.909573i	$0.363591\pi$
$588$	10.8654	0.448081
$589$	−11.7633	−0.484698
$590$	−0.182388	−0.00750879
$591$	−28.3611	−1.16662
$592$	3.57118	0.146774
$593$	31.6032	1.29779	0.648894	−	0.760879i	$-0.275232\pi$
$593$	31.6032	1.29779	0.648894	+	0.760879i	$0.275232\pi$
$594$	18.2660	0.749464
$595$	−3.72716	−0.152799
$596$	−23.6363	−0.968181
$597$	5.17450	0.211778
$598$	−21.6112	−0.883748
$599$	−16.8099	−0.686833	−0.343417	−	0.939183i	$-0.611584\pi$
$599$	−16.8099	−0.686833	−0.343417	+	0.939183i	$0.611584\pi$
$600$	10.5080	0.428989
$601$	2.27808	0.0929250	0.0464625	−	0.998920i	$-0.485205\pi$
$601$	2.27808	0.0929250	0.0464625	+	0.998920i	$0.485205\pi$
$602$	−5.42336	−0.221040
$603$	19.6415	0.799865
$604$	34.0857	1.38693
$605$	−16.1842	−0.657983
$606$	1.58247	0.0642835
$607$	29.0018	1.17715	0.588574	−	0.808444i	$-0.299690\pi$
$607$	29.0018	1.17715	0.588574	+	0.808444i	$0.299690\pi$
$608$	−8.27113	−0.335439
$609$	1.62755	0.0659516
$610$	−4.41185	−0.178631
$611$	20.1884	0.816737
$612$	−17.2114	−0.695730
$613$	−12.2778	−0.495897	−0.247948	−	0.968773i	$-0.579756\pi$
$613$	−12.2778	−0.495897	−0.247948	+	0.968773i	$0.579756\pi$
$614$	4.37662	0.176626
$615$	10.4569	0.421661
$616$	−9.54290	−0.384494
$617$	20.9586	0.843760	0.421880	−	0.906652i	$-0.361370\pi$
$617$	20.9586	0.843760	0.421880	+	0.906652i	$0.361370\pi$
$618$	−13.5407	−0.544685
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	10.9215	0.438616
$621$	27.1829	1.09081
$622$	−7.61623	−0.305383
$623$	−5.22832	−0.209468
$624$	11.5371	0.461853
$625$	14.7013	0.588050
$626$	−14.8149	−0.592123
$627$	8.47391	0.338416
$628$	13.8881	0.554195
$629$	−12.2814	−0.489693
$630$	−0.769017	−0.0306384
$631$	36.9483	1.47089	0.735445	−	0.677584i	$-0.236973\pi$
$631$	36.9483	1.47089	0.735445	+	0.677584i	$0.236973\pi$
$632$	−33.4314	−1.32983
$633$	5.97542	0.237501
$634$	−18.7136	−0.743212
$635$	4.60150	0.182605
$636$	−5.28832	−0.209695
$637$	−41.2036	−1.63254
$638$	7.13644	0.282535
$639$	4.32058	0.170920
$640$	9.52548	0.376528
$641$	31.8759	1.25902	0.629512	−	0.776991i	$-0.283255\pi$
$641$	31.8759	1.25902	0.629512	+	0.776991i	$0.283255\pi$
$642$	7.88041	0.311015
$643$	−18.7122	−0.737935	−0.368968	−	0.929442i	$-0.620289\pi$
$643$	−18.7122	−0.737935	−0.368968	+	0.929442i	$0.620289\pi$
$644$	−6.28231	−0.247558
$645$	−10.1073	−0.397976
$646$	5.42529	0.213455
$647$	−38.2561	−1.50400	−0.752000	−	0.659163i	$-0.770911\pi$
$647$	−38.2561	−1.50400	−0.752000	+	0.659163i	$0.770911\pi$
$648$	−0.181179	−0.00711739
$649$	−1.83124	−0.0718823
$650$	−17.6278	−0.691420
$651$	−6.51564	−0.255368
$652$	−35.7359	−1.39952
$653$	41.0674	1.60709	0.803545	−	0.595244i	$-0.202945\pi$
$653$	41.0674	1.60709	0.803545	+	0.595244i	$0.202945\pi$
$654$	−5.96294	−0.233170
$655$	−3.18445	−0.124427
$656$	−19.5457	−0.763130
$657$	10.3477	0.403703
$658$	−1.52904	−0.0596083
$659$	16.7619	0.652952	0.326476	−	0.945206i	$-0.394139\pi$
$659$	16.7619	0.652952	0.326476	+	0.945206i	$0.394139\pi$
$660$	−7.86748	−0.306241
$661$	−24.1598	−0.939709	−0.469855	−	0.882744i	$-0.655694\pi$
$661$	−24.1598	−0.939709	−0.469855	+	0.882744i	$0.655694\pi$
$662$	−7.24332	−0.281520
$663$	−39.6766	−1.54091
$664$	−1.07607	−0.0417596
$665$	−0.930392	−0.0360790
$666$	−2.53400	−0.0981907
$667$	10.6202	0.411217
$668$	−18.1784	−0.703345
$669$	−2.39656	−0.0926565
$670$	5.74822	0.222073
$671$	−44.2965	−1.71005
$672$	−4.58135	−0.176729
$673$	33.1615	1.27828	0.639141	−	0.769089i	$-0.279290\pi$
$673$	33.1615	1.27828	0.639141	+	0.769089i	$0.279290\pi$
$674$	−5.73606	−0.220945
$675$	22.1725	0.853421
$676$	−44.5202	−1.71232
$677$	−14.0342	−0.539379	−0.269689	−	0.962947i	$-0.586921\pi$
$677$	−14.0342	−0.539379	−0.269689	+	0.962947i	$0.586921\pi$
$678$	0.658340	0.0252834
$679$	9.96567	0.382447
$680$	−11.3864	−0.436649
$681$	−10.6345	−0.407515
$682$	−28.5696	−1.09399
$683$	−2.54743	−0.0974748	−0.0487374	−	0.998812i	$-0.515520\pi$
$683$	−2.54743	−0.0974748	−0.0487374	+	0.998812i	$0.515520\pi$
$684$	−4.29640	−0.164277
$685$	4.89251	0.186933
$686$	6.51791	0.248855
$687$	12.5884	0.480279
$688$	18.8923	0.720264
$689$	20.0543	0.764007
$690$	3.05045	0.116129
$691$	40.7076	1.54859	0.774296	−	0.632824i	$-0.218104\pi$
$691$	40.7076	1.54859	0.774296	+	0.632824i	$0.218104\pi$
$692$	6.87196	0.261233
$693$	−7.72118	−0.293304
$694$	10.6856	0.405620
$695$	13.3428	0.506122
$696$	4.97214	0.188469
$697$	67.2184	2.54608
$698$	−7.33737	−0.277724
$699$	−22.2368	−0.841074
$700$	−5.12435	−0.193682
$701$	34.8659	1.31687	0.658433	−	0.752640i	$-0.271220\pi$
$701$	34.8659	1.31687	0.658433	+	0.752640i	$0.271220\pi$
$702$	−21.3492	−0.805775
$703$	−3.06575	−0.115627
$704$	−1.55110	−0.0584592
$705$	−2.84962	−0.107323
$706$	5.10864	0.192266
$707$	−1.74448	−0.0656079
$708$	−0.564408	−0.0212118
$709$	19.4924	0.732054	0.366027	−	0.930604i	$-0.380718\pi$
$709$	19.4924	0.732054	0.366027	+	0.930604i	$0.380718\pi$
$710$	1.26445	0.0474538
$711$	−27.0494	−1.01443
$712$	−15.9724	−0.598593
$713$	−42.5164	−1.59225
$714$	3.00505	0.112461
$715$	29.8349	1.11576
$716$	8.09819	0.302644
$717$	7.22249	0.269729
$718$	19.3253	0.721215
$719$	39.9392	1.48948	0.744740	−	0.667355i	$-0.232574\pi$
$719$	39.9392	1.48948	0.744740	+	0.667355i	$0.232574\pi$
$720$	2.67888	0.0998359
$721$	14.9269	0.555907
$722$	−10.8617	−0.404230
$723$	−19.3123	−0.718232
$724$	12.9712	0.482070
$725$	8.66270	0.321724
$726$	13.0486	0.484281
$727$	22.2711	0.825989	0.412994	−	0.910734i	$-0.364483\pi$
$727$	22.2711	0.825989	0.412994	+	0.910734i	$0.364483\pi$
$728$	11.1537	0.413383
$729$	16.4098	0.607772
$730$	3.02833	0.112083
$731$	−64.9716	−2.40306
$732$	−13.6527	−0.504618
$733$	11.1884	0.413252	0.206626	−	0.978420i	$-0.433752\pi$
$733$	11.1884	0.413252	0.206626	+	0.978420i	$0.433752\pi$
$734$	−11.1365	−0.411056
$735$	5.81593	0.214524
$736$	−29.8946	−1.10193
$737$	57.7141	2.12592
$738$	13.8690	0.510526
$739$	18.6407	0.685711	0.342855	−	0.939388i	$-0.388606\pi$
$739$	18.6407	0.685711	0.342855	+	0.939388i	$0.388606\pi$
$740$	2.84636	0.104634
$741$	−9.90427	−0.363843
$742$	−1.51888	−0.0557598
$743$	43.0789	1.58041	0.790207	−	0.612841i	$-0.209973\pi$
$743$	43.0789	1.58041	0.790207	+	0.612841i	$0.209973\pi$
$744$	−19.9052	−0.729760
$745$	−12.6518	−0.463528
$746$	8.15595	0.298611
$747$	−0.870652	−0.0318555
$748$	−50.5735	−1.84915
$749$	−8.68718	−0.317423
$750$	5.39581	0.197027
$751$	24.1955	0.882905	0.441453	−	0.897285i	$-0.354463\pi$
$751$	24.1955	0.882905	0.441453	+	0.897285i	$0.354463\pi$
$752$	5.32643	0.194235
$753$	−13.1105	−0.477772
$754$	−8.34105	−0.303763
$755$	18.2451	0.664008
$756$	−6.20616	−0.225716
$757$	−11.1857	−0.406551	−0.203276	−	0.979122i	$-0.565159\pi$
$757$	−11.1857	−0.406551	−0.203276	+	0.979122i	$0.565159\pi$
$758$	−1.21681	−0.0441966
$759$	30.6275	1.11171
$760$	−2.84234	−0.103102
$761$	−30.7935	−1.11627	−0.558133	−	0.829752i	$-0.688482\pi$
$761$	−30.7935	−1.11627	−0.558133	+	0.829752i	$0.688482\pi$
$762$	−3.70999	−0.134399
$763$	6.57341	0.237973
$764$	−3.00548	−0.108735
$765$	−9.21278	−0.333089
$766$	−1.71058	−0.0618059
$767$	2.14034	0.0772832
$768$	−8.28261	−0.298873
$769$	−32.2850	−1.16423	−0.582113	−	0.813108i	$-0.697774\pi$
$769$	−32.2850	−1.16423	−0.582113	+	0.813108i	$0.697774\pi$
$770$	−2.25965	−0.0814323
$771$	−27.1375	−0.977332
$772$	2.88540	0.103848
$773$	38.6654	1.39070	0.695348	−	0.718673i	$-0.255250\pi$
$773$	38.6654	1.39070	0.695348	+	0.718673i	$0.255250\pi$
$774$	−13.4055	−0.481849
$775$	−34.6798	−1.24573
$776$	30.4450	1.09291
$777$	−1.69811	−0.0609193
$778$	15.6090	0.559608
$779$	16.7794	0.601184
$780$	9.19548	0.329251
$781$	12.6955	0.454279
$782$	19.6088	0.701209
$783$	10.4915	0.374935
$784$	−10.8710	−0.388249
$785$	7.43390	0.265327
$786$	2.56749	0.0915792
$787$	−24.8868	−0.887118	−0.443559	−	0.896245i	$-0.646284\pi$
$787$	−24.8868	−0.887118	−0.443559	+	0.896245i	$0.646284\pi$
$788$	42.2523	1.50518
$789$	9.83095	0.349991
$790$	−7.91619	−0.281645
$791$	−0.725738	−0.0258043
$792$	−23.5881	−0.838167
$793$	51.7735	1.83853
$794$	18.1054	0.642535
$795$	−2.83068	−0.100394
$796$	−7.70896	−0.273237
$797$	41.7054	1.47728	0.738640	−	0.674100i	$-0.235468\pi$
$797$	41.7054	1.47728	0.738640	+	0.674100i	$0.235468\pi$
$798$	0.750135	0.0265545
$799$	−18.3178	−0.648039
$800$	−24.3844	−0.862119
$801$	−12.9234	−0.456624
$802$	10.5351	0.372008
$803$	30.4054	1.07298
$804$	17.7882	0.627340
$805$	−3.36274	−0.118521
$806$	33.3921	1.17619
$807$	7.57217	0.266553
$808$	−5.32936	−0.187486
$809$	−29.0464	−1.02122	−0.510609	−	0.859813i	$-0.670580\pi$
$809$	−29.0464	−1.02122	−0.510609	+	0.859813i	$0.670580\pi$
$810$	−0.0429013	−0.00150740
$811$	17.4717	0.613516	0.306758	−	0.951788i	$-0.400756\pi$
$811$	17.4717	0.613516	0.306758	+	0.951788i	$0.400756\pi$
$812$	−2.42472	−0.0850909
$813$	2.89836	0.101650
$814$	−7.44583	−0.260976
$815$	−19.1284	−0.670038
$816$	−10.4681	−0.366457
$817$	−16.2185	−0.567415
$818$	14.7157	0.514524
$819$	9.02449	0.315341
$820$	−15.5786	−0.544028
$821$	−37.8389	−1.32059	−0.660293	−	0.751008i	$-0.729568\pi$
$821$	−37.8389	−1.32059	−0.660293	+	0.751008i	$0.729568\pi$
$822$	−3.94462	−0.137584
$823$	−43.8035	−1.52689	−0.763447	−	0.645871i	$-0.776494\pi$
$823$	−43.8035	−1.52689	−0.763447	+	0.645871i	$0.776494\pi$
$824$	45.6015	1.58860
$825$	24.9822	0.869770
$826$	−0.162106	−0.00564039
$827$	−30.2280	−1.05113	−0.525565	−	0.850753i	$-0.676146\pi$
$827$	−30.2280	−1.05113	−0.525565	+	0.850753i	$0.676146\pi$
$828$	−15.5286	−0.539657
$829$	54.5538	1.89473	0.947365	−	0.320155i	$-0.103735\pi$
$829$	54.5538	1.89473	0.947365	+	0.320155i	$0.103735\pi$
$830$	−0.254802	−0.00884430
$831$	−21.5169	−0.746414
$832$	1.81292	0.0628515
$833$	37.3858	1.29534
$834$	−10.7577	−0.372510
$835$	−9.73040	−0.336734
$836$	−12.6244	−0.436624
$837$	−42.0011	−1.45177
$838$	−4.33255	−0.149665
$839$	−4.44615	−0.153498	−0.0767491	−	0.997050i	$-0.524454\pi$
$839$	−4.44615	−0.153498	−0.0767491	+	0.997050i	$0.524454\pi$
$840$	−1.57436	−0.0543205
$841$	−24.9010	−0.858656
$842$	−13.8499	−0.477301
$843$	−3.37840	−0.116358
$844$	−8.90216	−0.306425
$845$	−23.8304	−0.819791
$846$	−3.77949	−0.129941
$847$	−14.3845	−0.494258
$848$	5.29103	0.181695
$849$	−6.52735	−0.224018
$850$	15.9945	0.548606
$851$	−11.0806	−0.379840
$852$	3.91289	0.134053
$853$	−30.6312	−1.04879	−0.524397	−	0.851474i	$-0.675709\pi$
$853$	−30.6312	−1.04879	−0.524397	+	0.851474i	$0.675709\pi$
$854$	−3.92125	−0.134182
$855$	−2.29974	−0.0786495
$856$	−26.5392	−0.907092
$857$	−30.4338	−1.03960	−0.519799	−	0.854289i	$-0.673993\pi$
$857$	−30.4338	−1.03960	−0.519799	+	0.854289i	$0.673993\pi$
$858$	−24.0546	−0.821211
$859$	−33.7811	−1.15260	−0.576298	−	0.817240i	$-0.695503\pi$
$859$	−33.7811	−1.15260	−0.576298	+	0.817240i	$0.695503\pi$
$860$	15.0579	0.513469
$861$	9.29404	0.316740
$862$	14.8243	0.504918
$863$	4.08552	0.139073	0.0695364	−	0.997579i	$-0.477848\pi$
$863$	4.08552	0.139073	0.0695364	+	0.997579i	$0.477848\pi$
$864$	−29.5322	−1.00471
$865$	3.67837	0.125068
$866$	16.8034	0.571001
$867$	17.8954	0.607761
$868$	9.70698	0.329476
$869$	−79.4812	−2.69621
$870$	1.17735	0.0399159
$871$	−67.4559	−2.28566
$872$	20.0817	0.680052
$873$	24.6331	0.833706
$874$	4.89484	0.165571
$875$	−5.94821	−0.201086
$876$	9.37130	0.316627
$877$	−22.9344	−0.774438	−0.387219	−	0.921988i	$-0.626564\pi$
$877$	−22.9344	−0.774438	−0.387219	+	0.921988i	$0.626564\pi$
$878$	−21.6465	−0.730534
$879$	2.66413	0.0898588
$880$	7.87153	0.265349
$881$	8.35631	0.281531	0.140766	−	0.990043i	$-0.455044\pi$
$881$	8.35631	0.281531	0.140766	+	0.990043i	$0.455044\pi$
$882$	7.71373	0.259735
$883$	10.4102	0.350331	0.175166	−	0.984539i	$-0.443954\pi$
$883$	10.4102	0.350331	0.175166	+	0.984539i	$0.443954\pi$
$884$	59.1101	1.98809
$885$	−0.302112	−0.0101554
$886$	−13.0310	−0.437786
$887$	1.25062	0.0419917	0.0209958	−	0.999780i	$-0.493316\pi$
$887$	1.25062	0.0419917	0.0209958	+	0.999780i	$0.493316\pi$
$888$	−5.18770	−0.174088
$889$	4.08981	0.137168
$890$	−3.78210	−0.126776
$891$	−0.430743	−0.0144304
$892$	3.57039	0.119546
$893$	−4.57259	−0.153016
$894$	10.2006	0.341160
$895$	4.33473	0.144894
$896$	8.46623	0.282837
$897$	−35.7973	−1.19524
$898$	−26.3314	−0.878689
$899$	−16.4096	−0.547291
$900$	−12.6664	−0.422212
$901$	−18.1961	−0.606200
$902$	40.7523	1.35690
$903$	−8.98339	−0.298948
$904$	−2.21712	−0.0737404
$905$	6.94311	0.230797
$906$	−14.7102	−0.488715
$907$	−43.5104	−1.44474	−0.722370	−	0.691506i	$-0.756947\pi$
$907$	−43.5104	−1.44474	−0.722370	+	0.691506i	$0.756947\pi$
$908$	15.8433	0.525777
$909$	−4.31200	−0.143020
$910$	2.64107	0.0875507
$911$	−19.5566	−0.647938	−0.323969	−	0.946068i	$-0.605017\pi$
$911$	−19.5566	−0.647938	−0.323969	+	0.946068i	$0.605017\pi$
$912$	−2.61310	−0.0865285
$913$	−2.55829	−0.0846672
$914$	−2.60560	−0.0861857
$915$	−7.30790	−0.241592
$916$	−18.7542	−0.619657
$917$	−2.83034	−0.0934659
$918$	19.3711	0.639342
$919$	29.6834	0.979163	0.489582	−	0.871957i	$-0.337149\pi$
$919$	29.6834	0.979163	0.489582	+	0.871957i	$0.337149\pi$
$920$	−10.2731	−0.338695
$921$	7.24954	0.238881
$922$	3.77364	0.124278
$923$	−14.8384	−0.488412
$924$	−6.99261	−0.230040
$925$	−9.03825	−0.297176
$926$	−14.4914	−0.476216
$927$	36.8963	1.21183
$928$	−11.5381	−0.378757
$929$	−33.3293	−1.09350	−0.546749	−	0.837297i	$-0.684135\pi$
$929$	−33.3293	−1.09350	−0.546749	+	0.837297i	$0.684135\pi$
$930$	−4.71333	−0.154556
$931$	9.33243	0.305858
$932$	33.1284	1.08516
$933$	−12.6157	−0.413020
$934$	5.14738	0.168428
$935$	−27.0705	−0.885301
$936$	27.5697	0.901144
$937$	43.8274	1.43178	0.715890	−	0.698213i	$-0.246021\pi$
$937$	43.8274	1.43178	0.715890	+	0.698213i	$0.246021\pi$
$938$	5.10901	0.166815
$939$	−24.5398	−0.800826
$940$	4.24536	0.138468
$941$	−31.8948	−1.03974	−0.519871	−	0.854245i	$-0.674020\pi$
$941$	−31.8948	−1.03974	−0.519871	+	0.854245i	$0.674020\pi$
$942$	−5.99363	−0.195283
$943$	60.6463	1.97491
$944$	0.564698	0.0183794
$945$	−3.32198	−0.108064
$946$	−39.3902	−1.28069
$947$	13.8478	0.449994	0.224997	−	0.974359i	$-0.427763\pi$
$947$	13.8478	0.449994	0.224997	+	0.974359i	$0.427763\pi$
$948$	−24.4970	−0.795627
$949$	−35.5377	−1.15360
$950$	3.99262	0.129538
$951$	−30.9977	−1.00517
$952$	−10.1202	−0.327999
$953$	32.8708	1.06479	0.532394	−	0.846496i	$-0.321292\pi$
$953$	32.8708	1.06479	0.532394	+	0.846496i	$0.321292\pi$
$954$	−3.75437	−0.121552
$955$	−1.60875	−0.0520579
$956$	−10.7600	−0.348005
$957$	11.8210	0.382118
$958$	24.2253	0.782684
$959$	4.34846	0.140419
$960$	−0.255895	−0.00825899
$961$	34.6933	1.11914
$962$	8.70266	0.280585
$963$	−21.4730	−0.691957
$964$	28.7714	0.926665
$965$	1.54447	0.0497183
$966$	2.71123	0.0872325
$967$	−1.46267	−0.0470362	−0.0235181	−	0.999723i	$-0.507487\pi$
$967$	−1.46267	−0.0470362	−0.0235181	+	0.999723i	$0.507487\pi$
$968$	−43.9445	−1.41243
$969$	8.98658	0.288690
$970$	7.20905	0.231469
$971$	−14.7154	−0.472240	−0.236120	−	0.971724i	$-0.575876\pi$
$971$	−14.7154	−0.472240	−0.236120	+	0.971724i	$0.575876\pi$
$972$	−24.7985	−0.795412
$973$	11.8591	0.380185
$974$	17.8295	0.571293
$975$	−29.1991	−0.935120
$976$	13.6597	0.437237
$977$	15.0790	0.482419	0.241209	−	0.970473i	$-0.422456\pi$
$977$	15.0790	0.482419	0.241209	+	0.970473i	$0.422456\pi$
$978$	15.4224	0.493154
$979$	−37.9736	−1.21364
$980$	−8.66456	−0.276779
$981$	16.2481	0.518763
$982$	21.9713	0.701132
$983$	−31.1093	−0.992232	−0.496116	−	0.868256i	$-0.665241\pi$
$983$	−31.1093	−0.992232	−0.496116	+	0.868256i	$0.665241\pi$
$984$	28.3932	0.905141
$985$	22.6165	0.720621
$986$	7.56819	0.241020
$987$	−2.53274	−0.0806181
$988$	14.7554	0.469430
$989$	−58.6192	−1.86398
$990$	−5.58541	−0.177516
$991$	23.9234	0.759952	0.379976	−	0.924996i	$-0.375932\pi$
$991$	23.9234	0.759952	0.379976	+	0.924996i	$0.375932\pi$
$992$	46.1910	1.46657
$993$	−11.9980	−0.380745
$994$	1.12384	0.0356460
$995$	−4.12639	−0.130815
$996$	−0.788496	−0.0249845
$997$	−34.6598	−1.09769	−0.548843	−	0.835925i	$-0.684932\pi$
$997$	−34.6598	−1.09769	−0.548843	+	0.835925i	$0.684932\pi$
$998$	−28.7082	−0.908743
$999$	−10.9463	−0.346327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.a.1.15	✓	21
3.2	odd	2		5571.2.a.e.1.7		21
4.3	odd	2		9904.2.a.j.1.6		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.a.1.15	✓	21	1.1	even	1	trivial
5571.2.a.e.1.7		21	3.2	odd	2
9904.2.a.j.1.6		21	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+0.642946 q^{2} +1.06499 q^{3} -1.58662 q^{4} -0.849273 q^{5} +0.684732 q^{6} -0.754832 q^{7} -2.30600 q^{8} -1.86579 q^{9} +O(q^{10})\)	\(q+0.642946 q^{2} +1.06499 q^{3} -1.58662 q^{4} -0.849273 q^{5} +0.684732 q^{6} -0.754832 q^{7} -2.30600 q^{8} -1.86579 q^{9} -0.546037 q^{10} -5.48239 q^{11} -1.68974 q^{12} +6.40779 q^{13} -0.485316 q^{14} -0.904468 q^{15} +1.69060 q^{16} -5.81407 q^{17} -1.19960 q^{18} -1.45134 q^{19} +1.34747 q^{20} -0.803890 q^{21} -3.52488 q^{22} -5.24561 q^{23} -2.45587 q^{24} -4.27874 q^{25} +4.11986 q^{26} -5.18203 q^{27} +1.19763 q^{28} -2.02459 q^{29} -0.581524 q^{30} +8.10514 q^{31} +5.69897 q^{32} -5.83869 q^{33} -3.73813 q^{34} +0.641058 q^{35} +2.96031 q^{36} +2.11237 q^{37} -0.933131 q^{38} +6.82424 q^{39} +1.95843 q^{40} -11.5613 q^{41} -0.516858 q^{42} +11.1749 q^{43} +8.69847 q^{44} +1.58457 q^{45} -3.37264 q^{46} +3.15061 q^{47} +1.80048 q^{48} -6.43023 q^{49} -2.75100 q^{50} -6.19193 q^{51} -10.1667 q^{52} +3.12967 q^{53} -3.33176 q^{54} +4.65604 q^{55} +1.74065 q^{56} -1.54566 q^{57} -1.30170 q^{58} +0.334022 q^{59} +1.43505 q^{60} +8.07978 q^{61} +5.21117 q^{62} +1.40836 q^{63} +0.282924 q^{64} -5.44196 q^{65} -3.75397 q^{66} -10.5272 q^{67} +9.22472 q^{68} -5.58653 q^{69} +0.412166 q^{70} -2.31568 q^{71} +4.30253 q^{72} -5.54601 q^{73} +1.35814 q^{74} -4.55682 q^{75} +2.30272 q^{76} +4.13828 q^{77} +4.38762 q^{78} +14.4975 q^{79} -1.43578 q^{80} +0.0785685 q^{81} -7.43332 q^{82} +0.466639 q^{83} +1.27547 q^{84} +4.93773 q^{85} +7.18486 q^{86} -2.15617 q^{87} +12.6424 q^{88} +6.92646 q^{89} +1.01879 q^{90} -4.83681 q^{91} +8.32279 q^{92} +8.63190 q^{93} +2.02567 q^{94} +1.23258 q^{95} +6.06936 q^{96} -13.2025 q^{97} -4.13429 q^{98} +10.2290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * q^99

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