LMFDB - Embedded newform 6019.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33786 q^{2} -0.380371 q^{3} +3.46560 q^{4} -3.85216 q^{5} +0.889254 q^{6} -3.60381 q^{7} -3.42637 q^{8} -2.85532 q^{9} +O(q^{10})$	\(q-2.33786 q^{2} -0.380371 q^{3} +3.46560 q^{4} -3.85216 q^{5} +0.889254 q^{6} -3.60381 q^{7} -3.42637 q^{8} -2.85532 q^{9} +9.00581 q^{10} +0.800740 q^{11} -1.31821 q^{12} +1.00000 q^{13} +8.42521 q^{14} +1.46525 q^{15} +1.07918 q^{16} -6.29140 q^{17} +6.67534 q^{18} +4.11095 q^{19} -13.3500 q^{20} +1.37078 q^{21} -1.87202 q^{22} +0.116752 q^{23} +1.30329 q^{24} +9.83911 q^{25} -2.33786 q^{26} +2.22719 q^{27} -12.4894 q^{28} -7.18253 q^{29} -3.42554 q^{30} -7.37578 q^{31} +4.32977 q^{32} -0.304578 q^{33} +14.7084 q^{34} +13.8824 q^{35} -9.89539 q^{36} +1.51148 q^{37} -9.61083 q^{38} -0.380371 q^{39} +13.1989 q^{40} -5.77533 q^{41} -3.20470 q^{42} +0.157824 q^{43} +2.77504 q^{44} +10.9991 q^{45} -0.272949 q^{46} +7.95096 q^{47} -0.410487 q^{48} +5.98746 q^{49} -23.0025 q^{50} +2.39306 q^{51} +3.46560 q^{52} -11.5369 q^{53} -5.20686 q^{54} -3.08458 q^{55} +12.3480 q^{56} -1.56368 q^{57} +16.7918 q^{58} -2.85585 q^{59} +5.07796 q^{60} +2.11275 q^{61} +17.2436 q^{62} +10.2900 q^{63} -12.2808 q^{64} -3.85216 q^{65} +0.712061 q^{66} +9.20004 q^{67} -21.8035 q^{68} -0.0444089 q^{69} -32.4552 q^{70} -4.45804 q^{71} +9.78337 q^{72} +5.14109 q^{73} -3.53364 q^{74} -3.74251 q^{75} +14.2469 q^{76} -2.88572 q^{77} +0.889254 q^{78} +5.75802 q^{79} -4.15715 q^{80} +7.71880 q^{81} +13.5019 q^{82} +1.56462 q^{83} +4.75059 q^{84} +24.2355 q^{85} -0.368970 q^{86} +2.73202 q^{87} -2.74363 q^{88} +14.9108 q^{89} -25.7145 q^{90} -3.60381 q^{91} +0.404614 q^{92} +2.80553 q^{93} -18.5882 q^{94} -15.8360 q^{95} -1.64692 q^{96} +12.7727 q^{97} -13.9979 q^{98} -2.28637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.33786	−1.65312	−0.826559	−	0.562850i	$-0.809705\pi$
$2$	−2.33786	−1.65312	−0.826559	+	0.562850i	$0.809705\pi$
$3$	−0.380371	−0.219607	−0.109804	−	0.993953i	$-0.535022\pi$
$3$	−0.380371	−0.219607	−0.109804	+	0.993953i	$0.535022\pi$
$4$	3.46560	1.73280
$5$	−3.85216	−1.72274	−0.861368	−	0.507981i	$-0.830392\pi$
$5$	−3.85216	−1.72274	−0.861368	+	0.507981i	$0.830392\pi$
$6$	0.889254	0.363036
$7$	−3.60381	−1.36211	−0.681056	−	0.732231i	$-0.738479\pi$
$7$	−3.60381	−1.36211	−0.681056	+	0.732231i	$0.738479\pi$
$8$	−3.42637	−1.21140
$9$	−2.85532	−0.951773
$10$	9.00581	2.84789
$11$	0.800740	0.241432	0.120716	−	0.992687i	$-0.461481\pi$
$11$	0.800740	0.241432	0.120716	+	0.992687i	$0.461481\pi$
$12$	−1.31821	−0.380535
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.42521	2.25173
$15$	1.46525	0.378325
$16$	1.07918	0.269794
$17$	−6.29140	−1.52589	−0.762944	−	0.646464i	$-0.776247\pi$
$17$	−6.29140	−1.52589	−0.762944	+	0.646464i	$0.776247\pi$
$18$	6.67534	1.57339
$19$	4.11095	0.943117	0.471558	−	0.881835i	$-0.343692\pi$
$19$	4.11095	0.943117	0.471558	+	0.881835i	$0.343692\pi$
$20$	−13.3500	−2.98516
$21$	1.37078	0.299130
$22$	−1.87202	−0.399116
$23$	0.116752	0.0243444	0.0121722	−	0.999926i	$-0.496125\pi$
$23$	0.116752	0.0243444	0.0121722	+	0.999926i	$0.496125\pi$
$24$	1.30329	0.266033
$25$	9.83911	1.96782
$26$	−2.33786	−0.458492
$27$	2.22719	0.428623
$28$	−12.4894	−2.36027
$29$	−7.18253	−1.33376	−0.666882	−	0.745164i	$-0.732371\pi$
$29$	−7.18253	−1.33376	−0.666882	+	0.745164i	$0.732371\pi$
$30$	−3.42554	−0.625416
$31$	−7.37578	−1.32473	−0.662365	−	0.749182i	$-0.730447\pi$
$31$	−7.37578	−1.32473	−0.662365	+	0.749182i	$0.730447\pi$
$32$	4.32977	0.765402
$33$	−0.304578	−0.0530202
$34$	14.7084	2.52247
$35$	13.8824	2.34656
$36$	−9.89539	−1.64923
$37$	1.51148	0.248486	0.124243	−	0.992252i	$-0.460350\pi$
$37$	1.51148	0.248486	0.124243	+	0.992252i	$0.460350\pi$
$38$	−9.61083	−1.55908
$39$	−0.380371	−0.0609080
$40$	13.1989	2.08693
$41$	−5.77533	−0.901954	−0.450977	−	0.892535i	$-0.648924\pi$
$41$	−5.77533	−0.901954	−0.450977	+	0.892535i	$0.648924\pi$
$42$	−3.20470	−0.494496
$43$	0.157824	0.0240679	0.0120340	−	0.999928i	$-0.496169\pi$
$43$	0.157824	0.0240679	0.0120340	+	0.999928i	$0.496169\pi$
$44$	2.77504	0.418353
$45$	10.9991	1.63965
$46$	−0.272949	−0.0402442
$47$	7.95096	1.15977	0.579883	−	0.814700i	$-0.303098\pi$
$47$	7.95096	1.15977	0.579883	+	0.814700i	$0.303098\pi$
$48$	−0.410487	−0.0592486
$49$	5.98746	0.855351
$50$	−23.0025	−3.25304
$51$	2.39306	0.335096
$52$	3.46560	0.480592
$53$	−11.5369	−1.58472	−0.792358	−	0.610056i	$-0.791147\pi$
$53$	−11.5369	−1.58472	−0.792358	+	0.610056i	$0.791147\pi$
$54$	−5.20686	−0.708564
$55$	−3.08458	−0.415924
$56$	12.3480	1.65007
$57$	−1.56368	−0.207115
$58$	16.7918	2.20487
$59$	−2.85585	−0.371801	−0.185900	−	0.982569i	$-0.559520\pi$
$59$	−2.85585	−0.371801	−0.185900	+	0.982569i	$0.559520\pi$
$60$	5.07796	0.655561
$61$	2.11275	0.270510	0.135255	−	0.990811i	$-0.456815\pi$
$61$	2.11275	0.270510	0.135255	+	0.990811i	$0.456815\pi$
$62$	17.2436	2.18993
$63$	10.2900	1.29642
$64$	−12.2808	−1.53509
$65$	−3.85216	−0.477801
$66$	0.712061	0.0876486
$67$	9.20004	1.12396	0.561982	−	0.827150i	$-0.310039\pi$
$67$	9.20004	1.12396	0.561982	+	0.827150i	$0.310039\pi$
$68$	−21.8035	−2.64406
$69$	−0.0444089	−0.00534620
$70$	−32.4552	−3.87914
$71$	−4.45804	−0.529072	−0.264536	−	0.964376i	$-0.585219\pi$
$71$	−4.45804	−0.529072	−0.264536	+	0.964376i	$0.585219\pi$
$72$	9.78337	1.15298
$73$	5.14109	0.601719	0.300860	−	0.953668i	$-0.402726\pi$
$73$	5.14109	0.601719	0.300860	+	0.953668i	$0.402726\pi$
$74$	−3.53364	−0.410777
$75$	−3.74251	−0.432147
$76$	14.2469	1.63423
$77$	−2.88572	−0.328858
$78$	0.889254	0.100688
$79$	5.75802	0.647828	0.323914	−	0.946087i	$-0.395001\pi$
$79$	5.75802	0.647828	0.323914	+	0.946087i	$0.395001\pi$
$80$	−4.15715	−0.464784
$81$	7.71880	0.857644
$82$	13.5019	1.49104
$83$	1.56462	0.171739	0.0858694	−	0.996306i	$-0.472633\pi$
$83$	1.56462	0.171739	0.0858694	+	0.996306i	$0.472633\pi$
$84$	4.75059	0.518331
$85$	24.2355	2.62870
$86$	−0.368970	−0.0397871
$87$	2.73202	0.292904
$88$	−2.74363	−0.292472
$89$	14.9108	1.58055	0.790273	−	0.612755i	$-0.209939\pi$
$89$	14.9108	1.58055	0.790273	+	0.612755i	$0.209939\pi$
$90$	−25.7145	−2.71054
$91$	−3.60381	−0.377782
$92$	0.404614	0.0421839
$93$	2.80553	0.290920
$94$	−18.5882	−1.91723
$95$	−15.8360	−1.62474
$96$	−1.64692	−0.168088
$97$	12.7727	1.29688	0.648438	−	0.761267i	$-0.275423\pi$
$97$	12.7727	1.29688	0.648438	+	0.761267i	$0.275423\pi$
$98$	−13.9979	−1.41400
$99$	−2.28637	−0.229789
$100$	34.0984	3.40984
$101$	10.2755	1.02245	0.511226	−	0.859447i	$-0.329192\pi$
$101$	10.2755	1.02245	0.511226	+	0.859447i	$0.329192\pi$
$102$	−5.59465	−0.553953
$103$	−7.95287	−0.783619	−0.391810	−	0.920046i	$-0.628151\pi$
$103$	−7.95287	−0.783619	−0.391810	+	0.920046i	$0.628151\pi$
$104$	−3.42637	−0.335983
$105$	−5.28047	−0.515321
$106$	26.9717	2.61972
$107$	7.49018	0.724103	0.362052	−	0.932158i	$-0.382076\pi$
$107$	7.49018	0.724103	0.362052	+	0.932158i	$0.382076\pi$
$108$	7.71855	0.742718
$109$	18.0540	1.72926	0.864628	−	0.502413i	$-0.167554\pi$
$109$	18.0540	1.72926	0.864628	+	0.502413i	$0.167554\pi$
$110$	7.21131	0.687572
$111$	−0.574923	−0.0545693
$112$	−3.88914	−0.367490
$113$	10.8213	1.01798	0.508990	−	0.860772i	$-0.330019\pi$
$113$	10.8213	1.01798	0.508990	+	0.860772i	$0.330019\pi$
$114$	3.65568	0.342386
$115$	−0.449745	−0.0419390
$116$	−24.8918	−2.31114
$117$	−2.85532	−0.263974
$118$	6.67659	0.614630
$119$	22.6730	2.07843
$120$	−5.02047	−0.458304
$121$	−10.3588	−0.941711
$122$	−4.93933	−0.447186
$123$	2.19676	0.198076
$124$	−25.5615	−2.29549
$125$	−18.6410	−1.66730
$126$	−24.0567	−2.14314
$127$	0.493898	0.0438264	0.0219132	−	0.999760i	$-0.493024\pi$
$127$	0.493898	0.0438264	0.0219132	+	0.999760i	$0.493024\pi$
$128$	20.0512	1.77229
$129$	−0.0600315	−0.00528548
$130$	9.00581	0.789862
$131$	−16.2498	−1.41975	−0.709876	−	0.704327i	$-0.751249\pi$
$131$	−16.2498	−1.41975	−0.709876	+	0.704327i	$0.751249\pi$
$132$	−1.05554	−0.0918734
$133$	−14.8151	−1.28463
$134$	−21.5084	−1.85804
$135$	−8.57949	−0.738405
$136$	21.5566	1.84847
$137$	22.2848	1.90392	0.951961	−	0.306220i	$-0.0990645\pi$
$137$	22.2848	1.90392	0.951961	+	0.306220i	$0.0990645\pi$
$138$	0.103822	0.00883790
$139$	7.09579	0.601857	0.300928	−	0.953647i	$-0.402703\pi$
$139$	7.09579	0.601857	0.300928	+	0.953647i	$0.402703\pi$
$140$	48.1110	4.06612
$141$	−3.02431	−0.254693
$142$	10.4223	0.874618
$143$	0.800740	0.0669612
$144$	−3.08139	−0.256782
$145$	27.6682	2.29772
$146$	−12.0192	−0.994713
$147$	−2.27745	−0.187841
$148$	5.23819	0.430576
$149$	21.6140	1.77069	0.885345	−	0.464935i	$-0.153922\pi$
$149$	21.6140	1.77069	0.885345	+	0.464935i	$0.153922\pi$
$150$	8.74946	0.714391
$151$	−23.8772	−1.94310	−0.971548	−	0.236842i	$-0.923888\pi$
$151$	−23.8772	−1.94310	−0.971548	+	0.236842i	$0.923888\pi$
$152$	−14.0856	−1.14249
$153$	17.9639	1.45230
$154$	6.74640	0.543641
$155$	28.4127	2.28216
$156$	−1.31821	−0.105541
$157$	−13.3738	−1.06735	−0.533674	−	0.845691i	$-0.679189\pi$
$157$	−13.3738	−1.06735	−0.533674	+	0.845691i	$0.679189\pi$
$158$	−13.4615	−1.07094
$159$	4.38830	0.348015
$160$	−16.6790	−1.31859
$161$	−0.420751	−0.0331598
$162$	−18.0455	−1.41779
$163$	15.6835	1.22843	0.614213	−	0.789141i	$-0.289474\pi$
$163$	15.6835	1.22843	0.614213	+	0.789141i	$0.289474\pi$
$164$	−20.0150	−1.56291
$165$	1.17328	0.0913398
$166$	−3.65785	−0.283905
$167$	21.1370	1.63563	0.817817	−	0.575479i	$-0.195184\pi$
$167$	21.1370	1.63563	0.817817	+	0.575479i	$0.195184\pi$
$168$	−4.69681	−0.362367
$169$	1.00000	0.0769231
$170$	−56.6591	−4.34556
$171$	−11.7381	−0.897633
$172$	0.546954	0.0417048
$173$	2.31186	0.175768	0.0878839	−	0.996131i	$-0.471990\pi$
$173$	2.31186	0.175768	0.0878839	+	0.996131i	$0.471990\pi$
$174$	−6.38710	−0.484204
$175$	−35.4583	−2.68040
$176$	0.864139	0.0651369
$177$	1.08628	0.0816500
$178$	−34.8595	−2.61283
$179$	−17.2778	−1.29140	−0.645702	−	0.763589i	$-0.723435\pi$
$179$	−17.2778	−1.29140	−0.645702	+	0.763589i	$0.723435\pi$
$180$	38.1186	2.84119
$181$	20.8776	1.55182	0.775910	−	0.630844i	$-0.217291\pi$
$181$	20.8776	1.55182	0.775910	+	0.630844i	$0.217291\pi$
$182$	8.42521	0.624518
$183$	−0.803629	−0.0594060
$184$	−0.400034	−0.0294909
$185$	−5.82246	−0.428076
$186$	−6.55894	−0.480925
$187$	−5.03777	−0.368398
$188$	27.5548	2.00964
$189$	−8.02637	−0.583833
$190$	37.0224	2.68589
$191$	−23.6106	−1.70841	−0.854203	−	0.519940i	$-0.825954\pi$
$191$	−23.6106	−1.70841	−0.854203	+	0.519940i	$0.825954\pi$
$192$	4.67124	0.337118
$193$	−15.4762	−1.11400	−0.557002	−	0.830511i	$-0.688048\pi$
$193$	−15.4762	−1.11400	−0.557002	+	0.830511i	$0.688048\pi$
$194$	−29.8609	−2.14389
$195$	1.46525	0.104928
$196$	20.7501	1.48215
$197$	−26.8796	−1.91509	−0.957546	−	0.288280i	$-0.906917\pi$
$197$	−26.8796	−1.91509	−0.957546	+	0.288280i	$0.906917\pi$
$198$	5.34521	0.379868
$199$	−19.8021	−1.40373	−0.701866	−	0.712309i	$-0.747650\pi$
$199$	−19.8021	−1.40373	−0.701866	+	0.712309i	$0.747650\pi$
$200$	−33.7124	−2.38383
$201$	−3.49942	−0.246830
$202$	−24.0227	−1.69023
$203$	25.8845	1.81674
$204$	8.29339	0.580654
$205$	22.2475	1.55383
$206$	18.5927	1.29542
$207$	−0.333363	−0.0231703
$208$	1.07918	0.0748274
$209$	3.29180	0.227699
$210$	12.3450	0.851887
$211$	23.5743	1.62292	0.811459	−	0.584409i	$-0.198674\pi$
$211$	23.5743	1.62292	0.811459	+	0.584409i	$0.198674\pi$
$212$	−39.9823	−2.74600
$213$	1.69571	0.116188
$214$	−17.5110	−1.19703
$215$	−0.607962	−0.0414627
$216$	−7.63117	−0.519235
$217$	26.5809	1.80443
$218$	−42.2077	−2.85866
$219$	−1.95552	−0.132142
$220$	−10.6899	−0.720713
$221$	−6.29140	−0.423205
$222$	1.34409	0.0902095
$223$	3.73435	0.250071	0.125035	−	0.992152i	$-0.460096\pi$
$223$	3.73435	0.250071	0.125035	+	0.992152i	$0.460096\pi$
$224$	−15.6037	−1.04256
$225$	−28.0938	−1.87292
$226$	−25.2987	−1.68284
$227$	5.37023	0.356435	0.178217	−	0.983991i	$-0.442967\pi$
$227$	5.37023	0.356435	0.178217	+	0.983991i	$0.442967\pi$
$228$	−5.41910	−0.358889
$229$	−9.18721	−0.607108	−0.303554	−	0.952814i	$-0.598173\pi$
$229$	−9.18721	−0.607108	−0.303554	+	0.952814i	$0.598173\pi$
$230$	1.05144	0.0693301
$231$	1.09764	0.0722195
$232$	24.6100	1.61573
$233$	13.0663	0.856000	0.428000	−	0.903779i	$-0.359218\pi$
$233$	13.0663	0.856000	0.428000	+	0.903779i	$0.359218\pi$
$234$	6.67534	0.436381
$235$	−30.6283	−1.99797
$236$	−9.89725	−0.644256
$237$	−2.19018	−0.142268
$238$	−53.0064	−3.43589
$239$	−1.63749	−0.105921	−0.0529603	−	0.998597i	$-0.516866\pi$
$239$	−1.63749	−0.105921	−0.0529603	+	0.998597i	$0.516866\pi$
$240$	1.58126	0.102070
$241$	−12.6882	−0.817318	−0.408659	−	0.912687i	$-0.634004\pi$
$241$	−12.6882	−0.817318	−0.408659	+	0.912687i	$0.634004\pi$
$242$	24.2175	1.55676
$243$	−9.61757	−0.616968
$244$	7.32196	0.468740
$245$	−23.0646	−1.47354
$246$	−5.13573	−0.327442
$247$	4.11095	0.261573
$248$	25.2721	1.60478
$249$	−0.595134	−0.0377151
$250$	43.5801	2.75625
$251$	14.9467	0.943427	0.471713	−	0.881752i	$-0.343636\pi$
$251$	14.9467	0.943427	0.471713	+	0.881752i	$0.343636\pi$
$252$	35.6611	2.24644
$253$	0.0934877	0.00587752
$254$	−1.15467	−0.0724501
$255$	−9.21845	−0.577282
$256$	−22.3154	−1.39471
$257$	−22.2557	−1.38827	−0.694136	−	0.719844i	$-0.744213\pi$
$257$	−22.2557	−1.38827	−0.694136	+	0.719844i	$0.744213\pi$
$258$	0.140345	0.00873752
$259$	−5.44710	−0.338466
$260$	−13.3500	−0.827934
$261$	20.5084	1.26944
$262$	37.9898	2.34702
$263$	−29.5773	−1.82381	−0.911906	−	0.410399i	$-0.865390\pi$
$263$	−29.5773	−1.82381	−0.911906	+	0.410399i	$0.865390\pi$
$264$	1.04360	0.0642289
$265$	44.4420	2.73005
$266$	34.6356	2.12365
$267$	−5.67164	−0.347099
$268$	31.8836	1.94760
$269$	−13.1148	−0.799621	−0.399810	−	0.916598i	$-0.630924\pi$
$269$	−13.1148	−0.799621	−0.399810	+	0.916598i	$0.630924\pi$
$270$	20.0577	1.22067
$271$	−25.6328	−1.55708	−0.778541	−	0.627593i	$-0.784040\pi$
$271$	−25.6328	−1.55708	−0.778541	+	0.627593i	$0.784040\pi$
$272$	−6.78952	−0.411675
$273$	1.37078	0.0829636
$274$	−52.0988	−3.14741
$275$	7.87857	0.475095
$276$	−0.153903	−0.00926389
$277$	29.8354	1.79263	0.896317	−	0.443415i	$-0.146233\pi$
$277$	29.8354	1.79263	0.896317	+	0.443415i	$0.146233\pi$
$278$	−16.5890	−0.994941
$279$	21.0602	1.26084
$280$	−47.5664	−2.84263
$281$	−26.2951	−1.56863	−0.784317	−	0.620360i	$-0.786986\pi$
$281$	−26.2951	−1.56863	−0.784317	+	0.620360i	$0.786986\pi$
$282$	7.07042	0.421037
$283$	16.7618	0.996388	0.498194	−	0.867065i	$-0.333997\pi$
$283$	16.7618	0.996388	0.498194	+	0.867065i	$0.333997\pi$
$284$	−15.4498	−0.916775
$285$	6.02356	0.356805
$286$	−1.87202	−0.110695
$287$	20.8132	1.22856
$288$	−12.3629	−0.728489
$289$	22.5817	1.32833
$290$	−64.6845	−3.79841
$291$	−4.85838	−0.284803
$292$	17.8170	1.04266
$293$	−5.20046	−0.303814	−0.151907	−	0.988395i	$-0.548541\pi$
$293$	−5.20046	−0.303814	−0.151907	+	0.988395i	$0.548541\pi$
$294$	5.32437	0.310524
$295$	11.0012	0.640515
$296$	−5.17889	−0.301017
$297$	1.78340	0.103483
$298$	−50.5306	−2.92716
$299$	0.116752	0.00675192
$300$	−12.9700	−0.748825
$301$	−0.568767	−0.0327832
$302$	55.8215	3.21217
$303$	−3.90850	−0.224537
$304$	4.43644	0.254447
$305$	−8.13866	−0.466018
$306$	−41.9972	−2.40082
$307$	−3.71689	−0.212134	−0.106067	−	0.994359i	$-0.533826\pi$
$307$	−3.71689	−0.212134	−0.106067	+	0.994359i	$0.533826\pi$
$308$	−10.0007	−0.569845
$309$	3.02504	0.172088
$310$	−66.4249	−3.77268
$311$	22.1481	1.25591	0.627953	−	0.778252i	$-0.283893\pi$
$311$	22.1481	1.25591	0.627953	+	0.778252i	$0.283893\pi$
$312$	1.30329	0.0737842
$313$	24.1012	1.36228	0.681140	−	0.732153i	$-0.261484\pi$
$313$	24.1012	1.36228	0.681140	+	0.732153i	$0.261484\pi$
$314$	31.2661	1.76445
$315$	−39.6388	−2.23339
$316$	19.9550	1.12256
$317$	1.33919	0.0752167	0.0376083	−	0.999293i	$-0.488026\pi$
$317$	1.33919	0.0752167	0.0376083	+	0.999293i	$0.488026\pi$
$318$	−10.2592	−0.575310
$319$	−5.75134	−0.322013
$320$	47.3074	2.64456
$321$	−2.84904	−0.159018
$322$	0.983657	0.0548171
$323$	−25.8636	−1.43909
$324$	26.7503	1.48613
$325$	9.83911	0.545776
$326$	−36.6658	−2.03073
$327$	−6.86719	−0.379757
$328$	19.7884	1.09263
$329$	−28.6538	−1.57973
$330$	−2.74297	−0.150996
$331$	13.3079	0.731467	0.365733	−	0.930720i	$-0.380818\pi$
$331$	13.3079	0.731467	0.365733	+	0.930720i	$0.380818\pi$
$332$	5.42233	0.297589
$333$	−4.31576	−0.236502
$334$	−49.4155	−2.70390
$335$	−35.4400	−1.93629
$336$	1.47932	0.0807033
$337$	17.5819	0.957749	0.478875	−	0.877883i	$-0.341045\pi$
$337$	17.5819	0.957749	0.478875	+	0.877883i	$0.341045\pi$
$338$	−2.33786	−0.127163
$339$	−4.11609	−0.223556
$340$	83.9903	4.55502
$341$	−5.90608	−0.319832
$342$	27.4420	1.48389
$343$	3.64901	0.197028
$344$	−0.540762	−0.0291559
$345$	0.171070	0.00921009
$346$	−5.40482	−0.290565
$347$	−21.9293	−1.17722	−0.588612	−	0.808416i	$-0.700325\pi$
$347$	−21.9293	−1.17722	−0.588612	+	0.808416i	$0.700325\pi$
$348$	9.46810	0.507543
$349$	8.96491	0.479881	0.239940	−	0.970788i	$-0.422872\pi$
$349$	8.96491	0.479881	0.239940	+	0.970788i	$0.422872\pi$
$350$	82.8966	4.43101
$351$	2.22719	0.118879
$352$	3.46702	0.184793
$353$	6.03308	0.321108	0.160554	−	0.987027i	$-0.448672\pi$
$353$	6.03308	0.321108	0.160554	+	0.987027i	$0.448672\pi$
$354$	−2.53958	−0.134977
$355$	17.1731	0.911451
$356$	51.6750	2.73877
$357$	−8.62415	−0.456438
$358$	40.3931	2.13484
$359$	−20.8381	−1.09979	−0.549897	−	0.835232i	$-0.685333\pi$
$359$	−20.8381	−1.09979	−0.549897	+	0.835232i	$0.685333\pi$
$360$	−37.6871	−1.98628
$361$	−2.10009	−0.110531
$362$	−48.8089	−2.56534
$363$	3.94019	0.206806
$364$	−12.4894	−0.654621
$365$	−19.8043	−1.03660
$366$	1.87877	0.0982051
$367$	−2.62664	−0.137110	−0.0685548	−	0.997647i	$-0.521839\pi$
$367$	−2.62664	−0.137110	−0.0685548	+	0.997647i	$0.521839\pi$
$368$	0.125995	0.00656797
$369$	16.4904	0.858456
$370$	13.6121	0.707660
$371$	41.5768	2.15856
$372$	9.72284	0.504106
$373$	24.8226	1.28527	0.642633	−	0.766174i	$-0.277842\pi$
$373$	24.8226	1.28527	0.642633	+	0.766174i	$0.277842\pi$
$374$	11.7776	0.609006
$375$	7.09049	0.366151
$376$	−27.2429	−1.40495
$377$	−7.18253	−0.369919
$378$	18.7646	0.965145
$379$	18.4088	0.945599	0.472799	−	0.881170i	$-0.343244\pi$
$379$	18.4088	0.945599	0.472799	+	0.881170i	$0.343244\pi$
$380$	−54.8813	−2.81535
$381$	−0.187864	−0.00962458
$382$	55.1984	2.82420
$383$	20.6286	1.05407	0.527036	−	0.849843i	$-0.323303\pi$
$383$	20.6286	1.05407	0.527036	+	0.849843i	$0.323303\pi$
$384$	−7.62687	−0.389207
$385$	11.1162	0.566535
$386$	36.1813	1.84158
$387$	−0.450637	−0.0229072
$388$	44.2652	2.24723
$389$	−25.2524	−1.28035	−0.640175	−	0.768229i	$-0.721138\pi$
$389$	−25.2524	−1.28035	−0.640175	+	0.768229i	$0.721138\pi$
$390$	−3.42554	−0.173459
$391$	−0.734531	−0.0371468
$392$	−20.5152	−1.03618
$393$	6.18095	0.311787
$394$	62.8408	3.16587
$395$	−22.1808	−1.11604
$396$	−7.92363	−0.398177
$397$	−12.4026	−0.622466	−0.311233	−	0.950334i	$-0.600742\pi$
$397$	−12.4026	−0.622466	−0.311233	+	0.950334i	$0.600742\pi$
$398$	46.2945	2.32054
$399$	5.63522	0.282114
$400$	10.6181	0.530906
$401$	−16.1133	−0.804658	−0.402329	−	0.915495i	$-0.631799\pi$
$401$	−16.1133	−0.804658	−0.402329	+	0.915495i	$0.631799\pi$
$402$	8.18117	0.408040
$403$	−7.37578	−0.367414
$404$	35.6108	1.77170
$405$	−29.7340	−1.47750
$406$	−60.5144	−3.00328
$407$	1.21030	0.0599925
$408$	−8.19951	−0.405936
$409$	−21.6906	−1.07253	−0.536264	−	0.844050i	$-0.680165\pi$
$409$	−21.6906	−1.07253	−0.536264	+	0.844050i	$0.680165\pi$
$410$	−52.0115	−2.56866
$411$	−8.47649	−0.418114
$412$	−27.5614	−1.35785
$413$	10.2920	0.506434
$414$	0.779357	0.0383033
$415$	−6.02714	−0.295861
$416$	4.32977	0.212284
$417$	−2.69903	−0.132172
$418$	−7.69578	−0.376413
$419$	−22.7262	−1.11025	−0.555123	−	0.831768i	$-0.687329\pi$
$419$	−22.7262	−1.11025	−0.555123	+	0.831768i	$0.687329\pi$
$420$	−18.3000	−0.892949
$421$	29.8990	1.45719	0.728593	−	0.684946i	$-0.240174\pi$
$421$	29.8990	1.45719	0.728593	+	0.684946i	$0.240174\pi$
$422$	−55.1134	−2.68288
$423$	−22.7025	−1.10383
$424$	39.5297	1.91973
$425$	−61.9018	−3.00268
$426$	−3.96433	−0.192072
$427$	−7.61397	−0.368466
$428$	25.9580	1.25473
$429$	−0.304578	−0.0147052
$430$	1.42133	0.0685427
$431$	17.0929	0.823335	0.411668	−	0.911334i	$-0.364946\pi$
$431$	17.0929	0.823335	0.411668	+	0.911334i	$0.364946\pi$
$432$	2.40353	0.115640
$433$	3.23329	0.155382	0.0776909	−	0.996977i	$-0.475245\pi$
$433$	3.23329	0.155382	0.0776909	+	0.996977i	$0.475245\pi$
$434$	−62.1425	−2.98294
$435$	−10.5242	−0.504596
$436$	62.5678	2.99645
$437$	0.479960	0.0229596
$438$	4.57173	0.218446
$439$	31.8194	1.51866	0.759329	−	0.650707i	$-0.225527\pi$
$439$	31.8194	1.51866	0.759329	+	0.650707i	$0.225527\pi$
$440$	10.5689	0.503852
$441$	−17.0961	−0.814100
$442$	14.7084	0.699608
$443$	−2.46275	−0.117009	−0.0585043	−	0.998287i	$-0.518633\pi$
$443$	−2.46275	−0.117009	−0.0585043	+	0.998287i	$0.518633\pi$
$444$	−1.99245	−0.0945576
$445$	−57.4389	−2.72286
$446$	−8.73040	−0.413396
$447$	−8.22134	−0.388856
$448$	44.2575	2.09097
$449$	−39.0129	−1.84113	−0.920567	−	0.390586i	$-0.872272\pi$
$449$	−39.0129	−1.84113	−0.920567	+	0.390586i	$0.872272\pi$
$450$	65.6794	3.09616
$451$	−4.62453	−0.217761
$452$	37.5022	1.76396
$453$	9.08217	0.426718
$454$	−12.5549	−0.589229
$455$	13.8824	0.650819
$456$	5.35776	0.250900
$457$	−32.0252	−1.49807	−0.749037	−	0.662528i	$-0.769483\pi$
$457$	−32.0252	−1.49807	−0.749037	+	0.662528i	$0.769483\pi$
$458$	21.4784	1.00362
$459$	−14.0121	−0.654031
$460$	−1.55864	−0.0726718
$461$	31.1090	1.44889	0.724444	−	0.689333i	$-0.242096\pi$
$461$	31.1090	1.44889	0.724444	+	0.689333i	$0.242096\pi$
$462$	−2.56613	−0.119387
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−7.75121	−0.359841
$465$	−10.8073	−0.501178
$466$	−30.5471	−1.41507
$467$	10.6604	0.493302	0.246651	−	0.969104i	$-0.420670\pi$
$467$	10.6604	0.493302	0.246651	+	0.969104i	$0.420670\pi$
$468$	−9.89539	−0.457414
$469$	−33.1552	−1.53097
$470$	71.6048	3.30288
$471$	5.08701	0.234397
$472$	9.78520	0.450401
$473$	0.126376	0.00581077
$474$	5.12034	0.235185
$475$	40.4481	1.85589
$476$	78.5756	3.60150
$477$	32.9415	1.50829
$478$	3.82823	0.175099
$479$	−9.93655	−0.454012	−0.227006	−	0.973893i	$-0.572894\pi$
$479$	−9.93655	−0.454012	−0.227006	+	0.973893i	$0.572894\pi$
$480$	6.34418	0.289571
$481$	1.51148	0.0689176
$482$	29.6632	1.35112
$483$	0.160041	0.00728213
$484$	−35.8995	−1.63180
$485$	−49.2026	−2.23418
$486$	22.4846	1.01992
$487$	0.534156	0.0242049	0.0121025	−	0.999927i	$-0.496148\pi$
$487$	0.534156	0.0242049	0.0121025	+	0.999927i	$0.496148\pi$
$488$	−7.23907	−0.327697
$489$	−5.96553	−0.269771
$490$	53.9219	2.43594
$491$	30.9822	1.39821	0.699103	−	0.715021i	$-0.253583\pi$
$491$	30.9822	1.39821	0.699103	+	0.715021i	$0.253583\pi$
$492$	7.61310	0.343225
$493$	45.1882	2.03517
$494$	−9.61083	−0.432412
$495$	8.80744	0.395865
$496$	−7.95976	−0.357404
$497$	16.0659	0.720655
$498$	1.39134	0.0623474
$499$	−33.4256	−1.49634	−0.748168	−	0.663509i	$-0.769066\pi$
$499$	−33.4256	−1.49634	−0.748168	+	0.663509i	$0.769066\pi$
$500$	−64.6022	−2.88910
$501$	−8.03991	−0.359197
$502$	−34.9433	−1.55960
$503$	−23.3307	−1.04026	−0.520132	−	0.854086i	$-0.674117\pi$
$503$	−23.3307	−1.04026	−0.520132	+	0.854086i	$0.674117\pi$
$504$	−35.2574	−1.57049
$505$	−39.5829	−1.76141
$506$	−0.218561	−0.00971623
$507$	−0.380371	−0.0168928
$508$	1.71165	0.0759423
$509$	−4.23757	−0.187827	−0.0939134	−	0.995580i	$-0.529938\pi$
$509$	−4.23757	−0.187827	−0.0939134	+	0.995580i	$0.529938\pi$
$510$	21.5515	0.954315
$511$	−18.5275	−0.819609
$512$	12.0679	0.533330
$513$	9.15587	0.404241
$514$	52.0307	2.29498
$515$	30.6357	1.34997
$516$	−0.208045	−0.00915868
$517$	6.36665	0.280005
$518$	12.7346	0.559524
$519$	−0.879365	−0.0385998
$520$	13.1989	0.578810
$521$	34.1467	1.49599	0.747997	−	0.663703i	$-0.231016\pi$
$521$	34.1467	1.49599	0.747997	+	0.663703i	$0.231016\pi$
$522$	−47.9459	−2.09853
$523$	−10.2269	−0.447190	−0.223595	−	0.974682i	$-0.571779\pi$
$523$	−10.2269	−0.447190	−0.223595	+	0.974682i	$0.571779\pi$
$524$	−56.3153	−2.46015
$525$	13.4873	0.588634
$526$	69.1476	3.01498
$527$	46.4040	2.02139
$528$	−0.328693	−0.0143045
$529$	−22.9864	−0.999407
$530$	−103.899	−4.51309
$531$	8.15437	0.353870
$532$	−51.3432	−2.22601
$533$	−5.77533	−0.250157
$534$	13.2595	0.573796
$535$	−28.8534	−1.24744
$536$	−31.5227	−1.36157
$537$	6.57197	0.283601
$538$	30.6605	1.32187
$539$	4.79440	0.206509
$540$	−29.7331	−1.27951
$541$	14.4061	0.619366	0.309683	−	0.950840i	$-0.399777\pi$
$541$	14.4061	0.619366	0.309683	+	0.950840i	$0.399777\pi$
$542$	59.9260	2.57404
$543$	−7.94122	−0.340790
$544$	−27.2403	−1.16792
$545$	−69.5467	−2.97905
$546$	−3.20470	−0.137149
$547$	16.6509	0.711940	0.355970	−	0.934497i	$-0.384150\pi$
$547$	16.6509	0.711940	0.355970	+	0.934497i	$0.384150\pi$
$548$	77.2303	3.29911
$549$	−6.03258	−0.257464
$550$	−18.4190	−0.785389
$551$	−29.5270	−1.25789
$552$	0.152161	0.00647641
$553$	−20.7508	−0.882414
$554$	−69.7510	−2.96343
$555$	2.21469	0.0940085
$556$	24.5912	1.04290
$557$	6.87407	0.291264	0.145632	−	0.989339i	$-0.453478\pi$
$557$	6.87407	0.291264	0.145632	+	0.989339i	$0.453478\pi$
$558$	−49.2358	−2.08432
$559$	0.157824	0.00667524
$560$	14.9816	0.633088
$561$	1.91622	0.0809029
$562$	61.4743	2.59314
$563$	7.60867	0.320667	0.160334	−	0.987063i	$-0.448743\pi$
$563$	7.60867	0.320667	0.160334	+	0.987063i	$0.448743\pi$
$564$	−10.4810	−0.441332
$565$	−41.6853	−1.75371
$566$	−39.1869	−1.64715
$567$	−27.8171	−1.16821
$568$	15.2749	0.640919
$569$	−5.47907	−0.229695	−0.114847	−	0.993383i	$-0.536638\pi$
$569$	−5.47907	−0.229695	−0.114847	+	0.993383i	$0.536638\pi$
$570$	−14.0822	−0.589840
$571$	−22.5954	−0.945587	−0.472793	−	0.881173i	$-0.656754\pi$
$571$	−22.5954	−0.945587	−0.472793	+	0.881173i	$0.656754\pi$
$572$	2.77504	0.116030
$573$	8.98079	0.375178
$574$	−48.6584	−2.03096
$575$	1.14873	0.0479054
$576$	35.0655	1.46106
$577$	−5.99073	−0.249397	−0.124699	−	0.992195i	$-0.539796\pi$
$577$	−5.99073	−0.249397	−0.124699	+	0.992195i	$0.539796\pi$
$578$	−52.7929	−2.19589
$579$	5.88671	0.244643
$580$	95.8870	3.98149
$581$	−5.63858	−0.233928
$582$	11.3582	0.470813
$583$	−9.23806	−0.382601
$584$	−17.6153	−0.728925
$585$	10.9991	0.454758
$586$	12.1580	0.502241
$587$	2.91142	0.120167	0.0600835	−	0.998193i	$-0.480863\pi$
$587$	2.91142	0.120167	0.0600835	+	0.998193i	$0.480863\pi$
$588$	−7.89274	−0.325491
$589$	−30.3215	−1.24937
$590$	−25.7193	−1.05885
$591$	10.2242	0.420568
$592$	1.63115	0.0670400
$593$	4.38913	0.180240	0.0901199	−	0.995931i	$-0.471275\pi$
$593$	4.38913	0.180240	0.0901199	+	0.995931i	$0.471275\pi$
$594$	−4.16934	−0.171070
$595$	−87.3400	−3.58059
$596$	74.9055	3.06825
$597$	7.53213	0.308270
$598$	−0.272949	−0.0111617
$599$	−10.2457	−0.418629	−0.209314	−	0.977848i	$-0.567123\pi$
$599$	−10.2457	−0.418629	−0.209314	+	0.977848i	$0.567123\pi$
$600$	12.8232	0.523505
$601$	9.96388	0.406435	0.203218	−	0.979134i	$-0.434860\pi$
$601$	9.96388	0.406435	0.203218	+	0.979134i	$0.434860\pi$
$602$	1.32970	0.0541945
$603$	−26.2690	−1.06976
$604$	−82.7487	−3.36700
$605$	39.9038	1.62232
$606$	9.13753	0.371187
$607$	−11.3797	−0.461888	−0.230944	−	0.972967i	$-0.574181\pi$
$607$	−11.3797	−0.461888	−0.230944	+	0.972967i	$0.574181\pi$
$608$	17.7995	0.721864
$609$	−9.84570	−0.398968
$610$	19.0271	0.770383
$611$	7.95096	0.321661
$612$	62.2558	2.51654
$613$	−5.89478	−0.238088	−0.119044	−	0.992889i	$-0.537983\pi$
$613$	−5.89478	−0.238088	−0.119044	+	0.992889i	$0.537983\pi$
$614$	8.68956	0.350682
$615$	−8.46228	−0.341232
$616$	9.88752	0.398380
$617$	15.9440	0.641882	0.320941	−	0.947099i	$-0.396001\pi$
$617$	15.9440	0.641882	0.320941	+	0.947099i	$0.396001\pi$
$618$	−7.07212	−0.284482
$619$	−27.0849	−1.08863	−0.544317	−	0.838879i	$-0.683211\pi$
$619$	−27.0849	−1.08863	−0.544317	+	0.838879i	$0.683211\pi$
$620$	98.4669	3.95453
$621$	0.260028	0.0104346
$622$	−51.7793	−2.07616
$623$	−53.7359	−2.15288
$624$	−0.410487	−0.0164326
$625$	22.6125	0.904501
$626$	−56.3453	−2.25201
$627$	−1.25210	−0.0500042
$628$	−46.3483	−1.84950
$629$	−9.50933	−0.379162
$630$	92.6700	3.69206
$631$	42.9710	1.71065	0.855325	−	0.518092i	$-0.173358\pi$
$631$	42.9710	1.71065	0.855325	+	0.518092i	$0.173358\pi$
$632$	−19.7291	−0.784781
$633$	−8.96695	−0.356404
$634$	−3.13085	−0.124342
$635$	−1.90257	−0.0755013
$636$	15.2081	0.603040
$637$	5.98746	0.237232
$638$	13.4458	0.532326
$639$	12.7291	0.503556
$640$	−77.2402	−3.05319
$641$	−17.7387	−0.700635	−0.350318	−	0.936631i	$-0.613926\pi$
$641$	−17.7387	−0.700635	−0.350318	+	0.936631i	$0.613926\pi$
$642$	6.66067	0.262876
$643$	35.8406	1.41342	0.706708	−	0.707505i	$-0.250179\pi$
$643$	35.8406	1.41342	0.706708	+	0.707505i	$0.250179\pi$
$644$	−1.45815	−0.0574593
$645$	0.231251	0.00910549
$646$	60.4656	2.37899
$647$	−15.8481	−0.623053	−0.311527	−	0.950237i	$-0.600840\pi$
$647$	−15.8481	−0.623053	−0.311527	+	0.950237i	$0.600840\pi$
$648$	−26.4474	−1.03895
$649$	−2.28680	−0.0897646
$650$	−23.0025	−0.902231
$651$	−10.1106	−0.396266
$652$	54.3527	2.12861
$653$	31.2005	1.22097	0.610485	−	0.792028i	$-0.290974\pi$
$653$	31.2005	1.22097	0.610485	+	0.792028i	$0.290974\pi$
$654$	16.0546	0.627783
$655$	62.5968	2.44586
$656$	−6.23259	−0.243342
$657$	−14.6795	−0.572700
$658$	66.9885	2.61148
$659$	41.1108	1.60145	0.800725	−	0.599032i	$-0.204448\pi$
$659$	41.1108	1.60145	0.800725	+	0.599032i	$0.204448\pi$
$660$	4.06612	0.158274
$661$	−30.9755	−1.20481	−0.602404	−	0.798191i	$-0.705790\pi$
$661$	−30.9755	−1.20481	−0.602404	+	0.798191i	$0.705790\pi$
$662$	−31.1120	−1.20920
$663$	2.39306	0.0929388
$664$	−5.36095	−0.208045
$665$	57.0700	2.21308
$666$	10.0897	0.390966
$667$	−0.838572	−0.0324697
$668$	73.2525	2.83422
$669$	−1.42044	−0.0549173
$670$	82.8538	3.20092
$671$	1.69177	0.0653099
$672$	5.93518	0.228954
$673$	−7.56289	−0.291528	−0.145764	−	0.989319i	$-0.546564\pi$
$673$	−7.56289	−0.291528	−0.145764	+	0.989319i	$0.546564\pi$
$674$	−41.1042	−1.58327
$675$	21.9136	0.843454
$676$	3.46560	0.133292
$677$	11.8918	0.457038	0.228519	−	0.973539i	$-0.426612\pi$
$677$	11.8918	0.457038	0.228519	+	0.973539i	$0.426612\pi$
$678$	9.62286	0.369564
$679$	−46.0306	−1.76649
$680$	−83.0395	−3.18442
$681$	−2.04268	−0.0782756
$682$	13.8076	0.528721
$683$	−14.9331	−0.571398	−0.285699	−	0.958319i	$-0.592226\pi$
$683$	−14.9331	−0.571398	−0.285699	+	0.958319i	$0.592226\pi$
$684$	−40.6794	−1.55542
$685$	−85.8446	−3.27996
$686$	−8.53088	−0.325711
$687$	3.49454	0.133325
$688$	0.170320	0.00649337
$689$	−11.5369	−0.439521
$690$	−0.399938	−0.0152254
$691$	1.42136	0.0540711	0.0270356	−	0.999634i	$-0.491393\pi$
$691$	1.42136	0.0540711	0.0270356	+	0.999634i	$0.491393\pi$
$692$	8.01199	0.304570
$693$	8.23964	0.312998
$694$	51.2676	1.94609
$695$	−27.3341	−1.03684
$696$	−9.36092	−0.354825
$697$	36.3349	1.37628
$698$	−20.9587	−0.793299
$699$	−4.97002	−0.187984
$700$	−122.884	−4.64459
$701$	−27.1564	−1.02568	−0.512841	−	0.858483i	$-0.671407\pi$
$701$	−27.1564	−1.02568	−0.512841	+	0.858483i	$0.671407\pi$
$702$	−5.20686	−0.196520
$703$	6.21363	0.234351
$704$	−9.83369	−0.370621
$705$	11.6501	0.438769
$706$	−14.1045	−0.530830
$707$	−37.0310	−1.39269
$708$	3.76462	0.141483
$709$	29.6895	1.11501	0.557506	−	0.830173i	$-0.311758\pi$
$709$	29.6895	1.11501	0.557506	+	0.830173i	$0.311758\pi$
$710$	−40.1482	−1.50674
$711$	−16.4410	−0.616585
$712$	−51.0900	−1.91468
$713$	−0.861134	−0.0322497
$714$	20.1621	0.754546
$715$	−3.08458	−0.115357
$716$	−59.8779	−2.23774
$717$	0.622854	0.0232609
$718$	48.7167	1.81809
$719$	−44.3578	−1.65427	−0.827133	−	0.562006i	$-0.810030\pi$
$719$	−44.3578	−1.65427	−0.827133	+	0.562006i	$0.810030\pi$
$720$	11.8700	0.442369
$721$	28.6606	1.06738
$722$	4.90972	0.182721
$723$	4.82622	0.179489
$724$	72.3534	2.68899
$725$	−70.6697	−2.62461
$726$	−9.21162	−0.341875
$727$	−12.1591	−0.450957	−0.225478	−	0.974248i	$-0.572395\pi$
$727$	−12.1591	−0.450957	−0.225478	+	0.974248i	$0.572395\pi$
$728$	12.3480	0.457647
$729$	−19.4982	−0.722154
$730$	46.2997	1.71363
$731$	−0.992932	−0.0367249
$732$	−2.78506	−0.102939
$733$	17.8101	0.657830	0.328915	−	0.944360i	$-0.393317\pi$
$733$	17.8101	0.657830	0.328915	+	0.944360i	$0.393317\pi$
$734$	6.14073	0.226658
$735$	8.77310	0.323601
$736$	0.505508	0.0186333
$737$	7.36684	0.271361
$738$	−38.5523	−1.41913
$739$	6.72051	0.247218	0.123609	−	0.992331i	$-0.460553\pi$
$739$	6.72051	0.247218	0.123609	+	0.992331i	$0.460553\pi$
$740$	−20.1783	−0.741770
$741$	−1.56368	−0.0574434
$742$	−97.2009	−3.56836
$743$	−39.3660	−1.44420	−0.722099	−	0.691790i	$-0.756823\pi$
$743$	−39.3660	−1.44420	−0.722099	+	0.691790i	$0.756823\pi$
$744$	−9.61277	−0.352421
$745$	−83.2606	−3.05043
$746$	−58.0318	−2.12470
$747$	−4.46747	−0.163456
$748$	−17.4589	−0.638361
$749$	−26.9932	−0.986310
$750$	−16.5766	−0.605291
$751$	17.7845	0.648966	0.324483	−	0.945891i	$-0.394810\pi$
$751$	17.7845	0.648966	0.324483	+	0.945891i	$0.394810\pi$
$752$	8.58048	0.312898
$753$	−5.68528	−0.207183
$754$	16.7918	0.611520
$755$	91.9786	3.34744
$756$	−27.8162	−1.01167
$757$	−31.9852	−1.16252	−0.581261	−	0.813717i	$-0.697441\pi$
$757$	−31.9852	−1.16252	−0.581261	+	0.813717i	$0.697441\pi$
$758$	−43.0373	−1.56319
$759$	−0.0355600	−0.00129074
$760$	54.2600	1.96822
$761$	−11.2232	−0.406840	−0.203420	−	0.979092i	$-0.565206\pi$
$761$	−11.2232	−0.406840	−0.203420	+	0.979092i	$0.565206\pi$
$762$	0.439201	0.0159106
$763$	−65.0631	−2.35544
$764$	−81.8250	−2.96032
$765$	−69.1999	−2.50193
$766$	−48.2268	−1.74251
$767$	−2.85585	−0.103119
$768$	8.48810	0.306288
$769$	−15.7128	−0.566617	−0.283308	−	0.959029i	$-0.591432\pi$
$769$	−15.7128	−0.566617	−0.283308	+	0.959029i	$0.591432\pi$
$770$	−25.9882	−0.936550
$771$	8.46541	0.304874
$772$	−53.6344	−1.93035
$773$	−29.3120	−1.05428	−0.527140	−	0.849778i	$-0.676736\pi$
$773$	−29.3120	−1.05428	−0.527140	+	0.849778i	$0.676736\pi$
$774$	1.05353	0.0378683
$775$	−72.5711	−2.60683
$776$	−43.7641	−1.57104
$777$	2.07191	0.0743295
$778$	59.0367	2.11657
$779$	−23.7421	−0.850648
$780$	5.07796	0.181820
$781$	−3.56973	−0.127735
$782$	1.71723	0.0614081
$783$	−15.9969	−0.571682
$784$	6.46152	0.230768
$785$	51.5180	1.83876
$786$	−14.4502	−0.515422
$787$	5.80362	0.206877	0.103438	−	0.994636i	$-0.467016\pi$
$787$	5.80362	0.206877	0.103438	+	0.994636i	$0.467016\pi$
$788$	−93.1539	−3.31847
$789$	11.2503	0.400522
$790$	51.8556	1.84494
$791$	−38.9978	−1.38660
$792$	7.83393	0.278367
$793$	2.11275	0.0750261
$794$	28.9955	1.02901
$795$	−16.9044	−0.599538
$796$	−68.6261	−2.43239
$797$	0.258983	0.00917366	0.00458683	−	0.999989i	$-0.498540\pi$
$797$	0.258983	0.00917366	0.00458683	+	0.999989i	$0.498540\pi$
$798$	−13.1744	−0.466368
$799$	−50.0226	−1.76967
$800$	42.6011	1.50618
$801$	−42.5752	−1.50432
$802$	37.6706	1.33020
$803$	4.11668	0.145274
$804$	−12.1276	−0.427707
$805$	1.62080	0.0571256
$806$	17.2436	0.607378
$807$	4.98846	0.175602
$808$	−35.2077	−1.23860
$809$	14.0036	0.492340	0.246170	−	0.969227i	$-0.420828\pi$
$809$	14.0036	0.492340	0.246170	+	0.969227i	$0.420828\pi$
$810$	69.5140	2.44247
$811$	−45.5520	−1.59955	−0.799774	−	0.600301i	$-0.795047\pi$
$811$	−45.5520	−1.59955	−0.799774	+	0.600301i	$0.795047\pi$
$812$	89.7053	3.14804
$813$	9.74997	0.341946
$814$	−2.82952	−0.0991747
$815$	−60.4152	−2.11625
$816$	2.58253	0.0904068
$817$	0.648806	0.0226988
$818$	50.7095	1.77302
$819$	10.2900	0.359563
$820$	77.1008	2.69248
$821$	5.08297	0.177397	0.0886984	−	0.996059i	$-0.471729\pi$
$821$	5.08297	0.177397	0.0886984	+	0.996059i	$0.471729\pi$
$822$	19.8169	0.691193
$823$	0.271676	0.00947003	0.00473502	−	0.999989i	$-0.498493\pi$
$823$	0.271676	0.00947003	0.00473502	+	0.999989i	$0.498493\pi$
$824$	27.2494	0.949279
$825$	−2.99677	−0.104334
$826$	−24.0612	−0.837196
$827$	−36.1024	−1.25540	−0.627702	−	0.778454i	$-0.716004\pi$
$827$	−36.1024	−1.25540	−0.627702	+	0.778454i	$0.716004\pi$
$828$	−1.15530	−0.0401495
$829$	−1.66488	−0.0578238	−0.0289119	−	0.999582i	$-0.509204\pi$
$829$	−1.66488	−0.0578238	−0.0289119	+	0.999582i	$0.509204\pi$
$830$	14.0906	0.489093
$831$	−11.3485	−0.393675
$832$	−12.2808	−0.425759
$833$	−37.6695	−1.30517
$834$	6.30996	0.218496
$835$	−81.4232	−2.81777
$836$	11.4081	0.394556
$837$	−16.4273	−0.567810
$838$	53.1307	1.83537
$839$	22.1421	0.764431	0.382216	−	0.924073i	$-0.375161\pi$
$839$	22.1421	0.764431	0.382216	+	0.924073i	$0.375161\pi$
$840$	18.0928	0.624262
$841$	22.5888	0.778924
$842$	−69.8997	−2.40890
$843$	10.0019	0.344483
$844$	81.6989	2.81219
$845$	−3.85216	−0.132518
$846$	53.0753	1.82477
$847$	37.3312	1.28272
$848$	−12.4503	−0.427547
$849$	−6.37571	−0.218814
$850$	144.718	4.96378
$851$	0.176468	0.00604924
$852$	5.87663	0.201330
$853$	33.6934	1.15364	0.576821	−	0.816871i	$-0.304293\pi$
$853$	33.6934	1.15364	0.576821	+	0.816871i	$0.304293\pi$
$854$	17.8004	0.609117
$855$	45.2169	1.54638
$856$	−25.6641	−0.877181
$857$	−9.54738	−0.326132	−0.163066	−	0.986615i	$-0.552138\pi$
$857$	−9.54738	−0.326132	−0.163066	+	0.986615i	$0.552138\pi$
$858$	0.712061	0.0243094
$859$	15.0640	0.513977	0.256988	−	0.966415i	$-0.417270\pi$
$859$	15.0640	0.513977	0.256988	+	0.966415i	$0.417270\pi$
$860$	−2.10695	−0.0718465
$861$	−7.91672	−0.269801
$862$	−39.9608	−1.36107
$863$	2.92477	0.0995604	0.0497802	−	0.998760i	$-0.484148\pi$
$863$	2.92477	0.0995604	0.0497802	+	0.998760i	$0.484148\pi$
$864$	9.64322	0.328069
$865$	−8.90566	−0.302802
$866$	−7.55898	−0.256864
$867$	−8.58941	−0.291712
$868$	92.1188	3.12672
$869$	4.61068	0.156406
$870$	24.6041	0.834157
$871$	9.20004	0.311731
$872$	−61.8595	−2.09483
$873$	−36.4703	−1.23433
$874$	−1.12208	−0.0379549
$875$	67.1787	2.27105
$876$	−6.77705	−0.228975
$877$	2.43959	0.0823792	0.0411896	−	0.999151i	$-0.486885\pi$
$877$	2.43959	0.0823792	0.0411896	+	0.999151i	$0.486885\pi$
$878$	−74.3894	−2.51052
$879$	1.97810	0.0667198
$880$	−3.32880	−0.112214
$881$	−31.4646	−1.06007	−0.530035	−	0.847976i	$-0.677821\pi$
$881$	−31.4646	−1.06007	−0.530035	+	0.847976i	$0.677821\pi$
$882$	39.9683	1.34580
$883$	−25.6910	−0.864572	−0.432286	−	0.901736i	$-0.642293\pi$
$883$	−25.6910	−0.864572	−0.432286	+	0.901736i	$0.642293\pi$
$884$	−21.8035	−0.733330
$885$	−4.18453	−0.140661
$886$	5.75756	0.193429
$887$	23.5484	0.790678	0.395339	−	0.918535i	$-0.370627\pi$
$887$	23.5484	0.790678	0.395339	+	0.918535i	$0.370627\pi$
$888$	1.96990	0.0661054
$889$	−1.77992	−0.0596964
$890$	134.284	4.50122
$891$	6.18075	0.207063
$892$	12.9418	0.433322
$893$	32.6860	1.09379
$894$	19.2203	0.642825
$895$	66.5568	2.22475
$896$	−72.2606	−2.41406
$897$	−0.0444089	−0.00148277
$898$	91.2068	3.04361
$899$	52.9768	1.76688
$900$	−97.3618	−3.24539
$901$	72.5833	2.41810
$902$	10.8115	0.359984
$903$	0.216342	0.00719942
$904$	−37.0777	−1.23318
$905$	−80.4238	−2.67338
$906$	−21.2329	−0.705415
$907$	−33.0241	−1.09655	−0.548274	−	0.836299i	$-0.684715\pi$
$907$	−33.0241	−1.09655	−0.548274	+	0.836299i	$0.684715\pi$
$908$	18.6111	0.617630
$909$	−29.3398	−0.973141
$910$	−32.4552	−1.07588
$911$	−13.6479	−0.452175	−0.226088	−	0.974107i	$-0.572594\pi$
$911$	−13.6479	−0.452175	−0.226088	+	0.974107i	$0.572594\pi$
$912$	−1.68749	−0.0558784
$913$	1.25285	0.0414633
$914$	74.8704	2.47649
$915$	3.09571	0.102341
$916$	−31.8392	−1.05200
$917$	58.5612	1.93386
$918$	32.7585	1.08119
$919$	−9.44522	−0.311569	−0.155785	−	0.987791i	$-0.549791\pi$
$919$	−9.44522	−0.311569	−0.155785	+	0.987791i	$0.549791\pi$
$920$	1.54099	0.0508050
$921$	1.41379	0.0465861
$922$	−72.7284	−2.39518
$923$	−4.45804	−0.146738
$924$	3.80398	0.125142
$925$	14.8716	0.488976
$926$	−2.33786	−0.0768269
$927$	22.7080	0.745828
$928$	−31.0987	−1.02087
$929$	2.43175	0.0797833	0.0398916	−	0.999204i	$-0.487299\pi$
$929$	2.43175	0.0797833	0.0398916	+	0.999204i	$0.487299\pi$
$930$	25.2661	0.828507
$931$	24.6141	0.806696
$932$	45.2824	1.48328
$933$	−8.42450	−0.275806
$934$	−24.9224	−0.815487
$935$	19.4063	0.634654
$936$	9.78337	0.319779
$937$	14.2765	0.466392	0.233196	−	0.972430i	$-0.425082\pi$
$937$	14.2765	0.466392	0.233196	+	0.972430i	$0.425082\pi$
$938$	77.5123	2.53087
$939$	−9.16739	−0.299166
$940$	−106.145	−3.46208
$941$	−57.9963	−1.89063	−0.945313	−	0.326165i	$-0.894243\pi$
$941$	−57.9963	−1.89063	−0.945313	+	0.326165i	$0.894243\pi$
$942$	−11.8927	−0.387486
$943$	−0.674279	−0.0219575
$944$	−3.08197	−0.100310
$945$	30.9189	1.00579
$946$	−0.295449	−0.00960588
$947$	45.5776	1.48107	0.740537	−	0.672016i	$-0.234571\pi$
$947$	45.5776	1.48107	0.740537	+	0.672016i	$0.234571\pi$
$948$	−7.59029	−0.246521
$949$	5.14109	0.166887
$950$	−94.5620	−3.06800
$951$	−0.509390	−0.0165181
$952$	−77.6861	−2.51782
$953$	−20.4369	−0.662017	−0.331008	−	0.943628i	$-0.607389\pi$
$953$	−20.4369	−0.662017	−0.331008	+	0.943628i	$0.607389\pi$
$954$	−77.0128	−2.49338
$955$	90.9519	2.94313
$956$	−5.67489	−0.183539
$957$	2.18764	0.0707164
$958$	23.2303	0.750536
$959$	−80.3103	−2.59336
$960$	−17.9943	−0.580765
$961$	23.4022	0.754908
$962$	−3.53364	−0.113929
$963$	−21.3869	−0.689182
$964$	−43.9722	−1.41625
$965$	59.6169	1.91914
$966$	−0.374154	−0.0120382
$967$	14.4577	0.464927	0.232464	−	0.972605i	$-0.425321\pi$
$967$	14.4577	0.464927	0.232464	+	0.972605i	$0.425321\pi$
$968$	35.4931	1.14079
$969$	9.83776	0.316034
$970$	115.029	3.69336
$971$	−0.277719	−0.00891242	−0.00445621	−	0.999990i	$-0.501418\pi$
$971$	−0.277719	−0.00891242	−0.00445621	+	0.999990i	$0.501418\pi$
$972$	−33.3306	−1.06908
$973$	−25.5719	−0.819797
$974$	−1.24878	−0.0400136
$975$	−3.74251	−0.119856
$976$	2.28003	0.0729820
$977$	56.2860	1.80075	0.900374	−	0.435117i	$-0.143293\pi$
$977$	56.2860	1.80075	0.900374	+	0.435117i	$0.143293\pi$
$978$	13.9466	0.445963
$979$	11.9397	0.381595
$980$	−79.9327	−2.55336
$981$	−51.5498	−1.64586
$982$	−72.4320	−2.31140
$983$	60.1724	1.91920	0.959601	−	0.281363i	$-0.0907866\pi$
$983$	60.1724	1.91920	0.959601	+	0.281363i	$0.0907866\pi$
$984$	−7.52692	−0.239949
$985$	103.544	3.29920
$986$	−105.644	−3.36438
$987$	10.8990	0.346920
$988$	14.2469	0.453254
$989$	0.0184262	0.000585919 0
$990$	−20.5906	−0.654412
$991$	16.6751	0.529702	0.264851	−	0.964289i	$-0.414677\pi$
$991$	16.6751	0.529702	0.264851	+	0.964289i	$0.414677\pi$
$992$	−31.9354	−1.01395
$993$	−5.06192	−0.160635
$994$	−37.5599	−1.19133
$995$	76.2807	2.41826
$996$	−2.06249	−0.0653526
$997$	7.86235	0.249003	0.124502	−	0.992219i	$-0.460267\pi$
$997$	7.86235	0.249003	0.124502	+	0.992219i	$0.460267\pi$
$998$	78.1445	2.47362
$999$	3.36636	0.106507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.11	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.11	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33786 q^{2} -0.380371 q^{3} +3.46560 q^{4} -3.85216 q^{5} +0.889254 q^{6} -3.60381 q^{7} -3.42637 q^{8} -2.85532 q^{9} +O(q^{10})\)	\(q-2.33786 q^{2} -0.380371 q^{3} +3.46560 q^{4} -3.85216 q^{5} +0.889254 q^{6} -3.60381 q^{7} -3.42637 q^{8} -2.85532 q^{9} +9.00581 q^{10} +0.800740 q^{11} -1.31821 q^{12} +1.00000 q^{13} +8.42521 q^{14} +1.46525 q^{15} +1.07918 q^{16} -6.29140 q^{17} +6.67534 q^{18} +4.11095 q^{19} -13.3500 q^{20} +1.37078 q^{21} -1.87202 q^{22} +0.116752 q^{23} +1.30329 q^{24} +9.83911 q^{25} -2.33786 q^{26} +2.22719 q^{27} -12.4894 q^{28} -7.18253 q^{29} -3.42554 q^{30} -7.37578 q^{31} +4.32977 q^{32} -0.304578 q^{33} +14.7084 q^{34} +13.8824 q^{35} -9.89539 q^{36} +1.51148 q^{37} -9.61083 q^{38} -0.380371 q^{39} +13.1989 q^{40} -5.77533 q^{41} -3.20470 q^{42} +0.157824 q^{43} +2.77504 q^{44} +10.9991 q^{45} -0.272949 q^{46} +7.95096 q^{47} -0.410487 q^{48} +5.98746 q^{49} -23.0025 q^{50} +2.39306 q^{51} +3.46560 q^{52} -11.5369 q^{53} -5.20686 q^{54} -3.08458 q^{55} +12.3480 q^{56} -1.56368 q^{57} +16.7918 q^{58} -2.85585 q^{59} +5.07796 q^{60} +2.11275 q^{61} +17.2436 q^{62} +10.2900 q^{63} -12.2808 q^{64} -3.85216 q^{65} +0.712061 q^{66} +9.20004 q^{67} -21.8035 q^{68} -0.0444089 q^{69} -32.4552 q^{70} -4.45804 q^{71} +9.78337 q^{72} +5.14109 q^{73} -3.53364 q^{74} -3.74251 q^{75} +14.2469 q^{76} -2.88572 q^{77} +0.889254 q^{78} +5.75802 q^{79} -4.15715 q^{80} +7.71880 q^{81} +13.5019 q^{82} +1.56462 q^{83} +4.75059 q^{84} +24.2355 q^{85} -0.368970 q^{86} +2.73202 q^{87} -2.74363 q^{88} +14.9108 q^{89} -25.7145 q^{90} -3.60381 q^{91} +0.404614 q^{92} +2.80553 q^{93} -18.5882 q^{94} -15.8360 q^{95} -1.64692 q^{96} +12.7727 q^{97} -13.9979 q^{98} -2.28637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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