LMFDB - Embedded newform 3021.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3021,2,Mod(1,3021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3021 = 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3021.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:	$24.1228064506$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 24 x^{17} + 48 x^{16} + 231 x^{15} - 463 x^{14} - 1142 x^{13} + 2298 x^{12} + \cdots + 46 $ x^19 - 2x^18 - 24x^17 + 48x^16 + 231x^15 - 463x^14 - 1142x^13 + 2298x^12 + 3104x^11 - 6271x^10 - 4677x^9 + 9436x^8 + 3854x^7 - 7629x^6 - 1682x^5 + 3195x^4 + 338x^3 - 638x^2 - 21x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.703145$ of defining polynomial
Character	$\chi$	$=$	3021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.703145 q^{2} -1.00000 q^{3} -1.50559 q^{4} +3.71667 q^{5} +0.703145 q^{6} -3.12787 q^{7} +2.46494 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.703145 q^{2} -1.00000 q^{3} -1.50559 q^{4} +3.71667 q^{5} +0.703145 q^{6} -3.12787 q^{7} +2.46494 q^{8} +1.00000 q^{9} -2.61336 q^{10} -3.84987 q^{11} +1.50559 q^{12} -2.00721 q^{13} +2.19935 q^{14} -3.71667 q^{15} +1.27797 q^{16} +6.50916 q^{17} -0.703145 q^{18} -1.00000 q^{19} -5.59578 q^{20} +3.12787 q^{21} +2.70702 q^{22} -4.31219 q^{23} -2.46494 q^{24} +8.81367 q^{25} +1.41136 q^{26} -1.00000 q^{27} +4.70929 q^{28} +2.74154 q^{29} +2.61336 q^{30} +7.80165 q^{31} -5.82847 q^{32} +3.84987 q^{33} -4.57688 q^{34} -11.6253 q^{35} -1.50559 q^{36} +3.35458 q^{37} +0.703145 q^{38} +2.00721 q^{39} +9.16136 q^{40} -5.28746 q^{41} -2.19935 q^{42} -8.22999 q^{43} +5.79632 q^{44} +3.71667 q^{45} +3.03209 q^{46} -4.37983 q^{47} -1.27797 q^{48} +2.78358 q^{49} -6.19728 q^{50} -6.50916 q^{51} +3.02204 q^{52} -1.00000 q^{53} +0.703145 q^{54} -14.3087 q^{55} -7.71000 q^{56} +1.00000 q^{57} -1.92770 q^{58} -10.8691 q^{59} +5.59578 q^{60} +0.726001 q^{61} -5.48569 q^{62} -3.12787 q^{63} +1.54232 q^{64} -7.46016 q^{65} -2.70702 q^{66} -2.75890 q^{67} -9.80011 q^{68} +4.31219 q^{69} +8.17425 q^{70} +3.64804 q^{71} +2.46494 q^{72} +11.5547 q^{73} -2.35875 q^{74} -8.81367 q^{75} +1.50559 q^{76} +12.0419 q^{77} -1.41136 q^{78} +5.72772 q^{79} +4.74980 q^{80} +1.00000 q^{81} +3.71785 q^{82} +14.4704 q^{83} -4.70929 q^{84} +24.1924 q^{85} +5.78687 q^{86} -2.74154 q^{87} -9.48968 q^{88} -5.86496 q^{89} -2.61336 q^{90} +6.27831 q^{91} +6.49238 q^{92} -7.80165 q^{93} +3.07966 q^{94} -3.71667 q^{95} +5.82847 q^{96} -9.43858 q^{97} -1.95726 q^{98} -3.84987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} - 19 q^{3} + 14 q^{4} + 2 q^{5} - 2 q^{6} - 7 q^{7} + 19 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 - 19 * q^3 + 14 * q^4 + 2 * q^5 - 2 * q^6 - 7 * q^7 + 19 * q^9	\( 19 q + 2 q^{2} - 19 q^{3} + 14 q^{4} + 2 q^{5} - 2 q^{6} - 7 q^{7} + 19 q^{9} - 12 q^{10} - 10 q^{11} - 14 q^{12} - 14 q^{13} - 16 q^{14} - 2 q^{15} + 8 q^{16} + 11 q^{17} + 2 q^{18} - 19 q^{19} + 8 q^{20} + 7 q^{21} - 3 q^{22} + 13 q^{23} + 9 q^{25} - 7 q^{26} - 19 q^{27} - 24 q^{28} - 18 q^{29} + 12 q^{30} - 21 q^{31} - 3 q^{32} + 10 q^{33} - 10 q^{34} - 7 q^{35} + 14 q^{36} - 26 q^{37} - 2 q^{38} + 14 q^{39} - 27 q^{40} - 7 q^{41} + 16 q^{42} - 25 q^{43} - 5 q^{44} + 2 q^{45} - 11 q^{46} - 10 q^{47} - 8 q^{48} - 6 q^{49} - 16 q^{50} - 11 q^{51} - 37 q^{52} - 19 q^{53} - 2 q^{54} - 20 q^{55} - 33 q^{56} + 19 q^{57} - 27 q^{58} - 42 q^{59} - 8 q^{60} - 16 q^{61} - 6 q^{62} - 7 q^{63} - 32 q^{64} - q^{65} + 3 q^{66} - 40 q^{67} + 6 q^{68} - 13 q^{69} - 29 q^{70} - 23 q^{71} + 7 q^{73} + 15 q^{74} - 9 q^{75} - 14 q^{76} + 42 q^{77} + 7 q^{78} - 26 q^{79} + 7 q^{80} + 19 q^{81} - 19 q^{82} - 14 q^{83} + 24 q^{84} - 37 q^{85} - 24 q^{86} + 18 q^{87} - 50 q^{88} - 3 q^{89} - 12 q^{90} - 60 q^{91} + 44 q^{92} + 21 q^{93} - 62 q^{94} - 2 q^{95} + 3 q^{96} - 44 q^{97} + 52 q^{98} - 10 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 - 19 * q^3 + 14 * q^4 + 2 * q^5 - 2 * q^6 - 7 * q^7 + 19 * q^9 - 12 * q^10 - 10 * q^11 - 14 * q^12 - 14 * q^13 - 16 * q^14 - 2 * q^15 + 8 * q^16 + 11 * q^17 + 2 * q^18 - 19 * q^19 + 8 * q^20 + 7 * q^21 - 3 * q^22 + 13 * q^23 + 9 * q^25 - 7 * q^26 - 19 * q^27 - 24 * q^28 - 18 * q^29 + 12 * q^30 - 21 * q^31 - 3 * q^32 + 10 * q^33 - 10 * q^34 - 7 * q^35 + 14 * q^36 - 26 * q^37 - 2 * q^38 + 14 * q^39 - 27 * q^40 - 7 * q^41 + 16 * q^42 - 25 * q^43 - 5 * q^44 + 2 * q^45 - 11 * q^46 - 10 * q^47 - 8 * q^48 - 6 * q^49 - 16 * q^50 - 11 * q^51 - 37 * q^52 - 19 * q^53 - 2 * q^54 - 20 * q^55 - 33 * q^56 + 19 * q^57 - 27 * q^58 - 42 * q^59 - 8 * q^60 - 16 * q^61 - 6 * q^62 - 7 * q^63 - 32 * q^64 - q^65 + 3 * q^66 - 40 * q^67 + 6 * q^68 - 13 * q^69 - 29 * q^70 - 23 * q^71 + 7 * q^73 + 15 * q^74 - 9 * q^75 - 14 * q^76 + 42 * q^77 + 7 * q^78 - 26 * q^79 + 7 * q^80 + 19 * q^81 - 19 * q^82 - 14 * q^83 + 24 * q^84 - 37 * q^85 - 24 * q^86 + 18 * q^87 - 50 * q^88 - 3 * q^89 - 12 * q^90 - 60 * q^91 + 44 * q^92 + 21 * q^93 - 62 * q^94 - 2 * q^95 + 3 * q^96 - 44 * q^97 + 52 * q^98 - 10 * 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 $

$2$	−0.703145	−0.497198	−0.248599	−	0.968606i	$-0.579970\pi$
$2$	−0.703145	−0.497198	−0.248599	+	0.968606i	$0.579970\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.50559	−0.752794
$5$	3.71667	1.66215	0.831074	−	0.556162i	$-0.187727\pi$
$5$	3.71667	1.66215	0.831074	+	0.556162i	$0.187727\pi$
$6$	0.703145	0.287058
$7$	−3.12787	−1.18222	−0.591112	−	0.806589i	$-0.701311\pi$
$7$	−3.12787	−1.18222	−0.591112	+	0.806589i	$0.701311\pi$
$8$	2.46494	0.871486
$9$	1.00000	0.333333
$10$	−2.61336	−0.826417
$11$	−3.84987	−1.16078	−0.580390	−	0.814339i	$-0.697100\pi$
$11$	−3.84987	−1.16078	−0.580390	+	0.814339i	$0.697100\pi$
$12$	1.50559	0.434626
$13$	−2.00721	−0.556701	−0.278351	−	0.960480i	$-0.589788\pi$
$13$	−2.00721	−0.556701	−0.278351	+	0.960480i	$0.589788\pi$
$14$	2.19935	0.587800
$15$	−3.71667	−0.959641
$16$	1.27797	0.319492
$17$	6.50916	1.57870	0.789352	−	0.613941i	$-0.210417\pi$
$17$	6.50916	1.57870	0.789352	+	0.613941i	$0.210417\pi$
$18$	−0.703145	−0.165733
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−5.59578	−1.25125
$21$	3.12787	0.682558
$22$	2.70702	0.577138
$23$	−4.31219	−0.899153	−0.449577	−	0.893242i	$-0.648425\pi$
$23$	−4.31219	−0.899153	−0.449577	+	0.893242i	$0.648425\pi$
$24$	−2.46494	−0.503153
$25$	8.81367	1.76273
$26$	1.41136	0.276791
$27$	−1.00000	−0.192450
$28$	4.70929	0.889971
$29$	2.74154	0.509091	0.254545	−	0.967061i	$-0.418074\pi$
$29$	2.74154	0.509091	0.254545	+	0.967061i	$0.418074\pi$
$30$	2.61336	0.477132
$31$	7.80165	1.40122	0.700609	−	0.713545i	$-0.252912\pi$
$31$	7.80165	1.40122	0.700609	+	0.713545i	$0.252912\pi$
$32$	−5.82847	−1.03034
$33$	3.84987	0.670176
$34$	−4.57688	−0.784929
$35$	−11.6253	−1.96503
$36$	−1.50559	−0.250931
$37$	3.35458	0.551489	0.275745	−	0.961231i	$-0.411076\pi$
$37$	3.35458	0.551489	0.275745	+	0.961231i	$0.411076\pi$
$38$	0.703145	0.114065
$39$	2.00721	0.321411
$40$	9.16136	1.44854
$41$	−5.28746	−0.825762	−0.412881	−	0.910785i	$-0.635478\pi$
$41$	−5.28746	−0.825762	−0.412881	+	0.910785i	$0.635478\pi$
$42$	−2.19935	−0.339366
$43$	−8.22999	−1.25506	−0.627531	−	0.778592i	$-0.715934\pi$
$43$	−8.22999	−1.25506	−0.627531	+	0.778592i	$0.715934\pi$
$44$	5.79632	0.873828
$45$	3.71667	0.554049
$46$	3.03209	0.447057
$47$	−4.37983	−0.638864	−0.319432	−	0.947609i	$-0.603492\pi$
$47$	−4.37983	−0.638864	−0.319432	+	0.947609i	$0.603492\pi$
$48$	−1.27797	−0.184459
$49$	2.78358	0.397655
$50$	−6.19728	−0.876428
$51$	−6.50916	−0.911465
$52$	3.02204	0.419081
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	0.703145	0.0956859
$55$	−14.3087	−1.92939
$56$	−7.71000	−1.03029
$57$	1.00000	0.132453
$58$	−1.92770	−0.253119
$59$	−10.8691	−1.41504	−0.707520	−	0.706694i	$-0.750186\pi$
$59$	−10.8691	−1.41504	−0.707520	+	0.706694i	$0.750186\pi$
$60$	5.59578	0.722412
$61$	0.726001	0.0929549	0.0464775	−	0.998919i	$-0.485200\pi$
$61$	0.726001	0.0929549	0.0464775	+	0.998919i	$0.485200\pi$
$62$	−5.48569	−0.696683
$63$	−3.12787	−0.394075
$64$	1.54232	0.192790
$65$	−7.46016	−0.925319
$66$	−2.70702	−0.333211
$67$	−2.75890	−0.337054	−0.168527	−	0.985697i	$-0.553901\pi$
$67$	−2.75890	−0.337054	−0.168527	+	0.985697i	$0.553901\pi$
$68$	−9.80011	−1.18844
$69$	4.31219	0.519126
$70$	8.17425	0.977010
$71$	3.64804	0.432943	0.216471	−	0.976289i	$-0.430545\pi$
$71$	3.64804	0.432943	0.216471	+	0.976289i	$0.430545\pi$
$72$	2.46494	0.290495
$73$	11.5547	1.35237	0.676187	−	0.736730i	$-0.263631\pi$
$73$	11.5547	1.35237	0.676187	+	0.736730i	$0.263631\pi$
$74$	−2.35875	−0.274199
$75$	−8.81367	−1.01771
$76$	1.50559	0.172703
$77$	12.0419	1.37230
$78$	−1.41136	−0.159805
$79$	5.72772	0.644419	0.322209	−	0.946668i	$-0.395575\pi$
$79$	5.72772	0.644419	0.322209	+	0.946668i	$0.395575\pi$
$80$	4.74980	0.531043
$81$	1.00000	0.111111
$82$	3.71785	0.410568
$83$	14.4704	1.58834	0.794169	−	0.607697i	$-0.207907\pi$
$83$	14.4704	1.58834	0.794169	+	0.607697i	$0.207907\pi$
$84$	−4.70929	−0.513825
$85$	24.1924	2.62404
$86$	5.78687	0.624015
$87$	−2.74154	−0.293924
$88$	−9.48968	−1.01160
$89$	−5.86496	−0.621684	−0.310842	−	0.950462i	$-0.600611\pi$
$89$	−5.86496	−0.621684	−0.310842	+	0.950462i	$0.600611\pi$
$90$	−2.61336	−0.275472
$91$	6.27831	0.658146
$92$	6.49238	0.676877
$93$	−7.80165	−0.808994
$94$	3.07966	0.317642
$95$	−3.71667	−0.381323
$96$	5.82847	0.594865
$97$	−9.43858	−0.958342	−0.479171	−	0.877721i	$-0.659063\pi$
$97$	−9.43858	−0.958342	−0.479171	+	0.877721i	$0.659063\pi$
$98$	−1.95726	−0.197713
$99$	−3.84987	−0.386927
$100$	−13.2697	−1.32697
$101$	−11.0567	−1.10019	−0.550094	−	0.835103i	$-0.685408\pi$
$101$	−11.0567	−1.10019	−0.550094	+	0.835103i	$0.685408\pi$
$102$	4.57688	0.453179
$103$	−2.25460	−0.222153	−0.111076	−	0.993812i	$-0.535430\pi$
$103$	−2.25460	−0.222153	−0.111076	+	0.993812i	$0.535430\pi$
$104$	−4.94765	−0.485157
$105$	11.6253	1.13451
$106$	0.703145	0.0682954
$107$	−1.76544	−0.170671	−0.0853356	−	0.996352i	$-0.527196\pi$
$107$	−1.76544	−0.170671	−0.0853356	+	0.996352i	$0.527196\pi$
$108$	1.50559	0.144875
$109$	−8.61904	−0.825554	−0.412777	−	0.910832i	$-0.635441\pi$
$109$	−8.61904	−0.825554	−0.412777	+	0.910832i	$0.635441\pi$
$110$	10.0611	0.959288
$111$	−3.35458	−0.318402
$112$	−3.99732	−0.377712
$113$	11.4535	1.07745	0.538726	−	0.842481i	$-0.318906\pi$
$113$	11.4535	1.07745	0.538726	+	0.842481i	$0.318906\pi$
$114$	−0.703145	−0.0658555
$115$	−16.0270	−1.49453
$116$	−4.12763	−0.383240
$117$	−2.00721	−0.185567
$118$	7.64256	0.703555
$119$	−20.3598	−1.86638
$120$	−9.16136	−0.836314
$121$	3.82150	0.347409
$122$	−0.510484	−0.0462170
$123$	5.28746	0.476754
$124$	−11.7461	−1.05483
$125$	14.1742	1.26778
$126$	2.19935	0.195933
$127$	−2.97327	−0.263835	−0.131918	−	0.991261i	$-0.542113\pi$
$127$	−2.97327	−0.263835	−0.131918	+	0.991261i	$0.542113\pi$
$128$	10.5725	0.934483
$129$	8.22999	0.724610
$130$	5.24557	0.460067
$131$	−16.5563	−1.44653	−0.723265	−	0.690571i	$-0.757359\pi$
$131$	−16.5563	−1.44653	−0.723265	+	0.690571i	$0.757359\pi$
$132$	−5.79632	−0.504505
$133$	3.12787	0.271221
$134$	1.93991	0.167582
$135$	−3.71667	−0.319880
$136$	16.0447	1.37582
$137$	2.77472	0.237060	0.118530	−	0.992950i	$-0.462182\pi$
$137$	2.77472	0.237060	0.118530	+	0.992950i	$0.462182\pi$
$138$	−3.03209	−0.258109
$139$	11.1511	0.945826	0.472913	−	0.881109i	$-0.343202\pi$
$139$	11.1511	0.945826	0.472913	+	0.881109i	$0.343202\pi$
$140$	17.5029	1.47926
$141$	4.37983	0.368849
$142$	−2.56510	−0.215258
$143$	7.72751	0.646207
$144$	1.27797	0.106497
$145$	10.1894	0.846184
$146$	−8.12462	−0.672398
$147$	−2.78358	−0.229586
$148$	−5.05061	−0.415158
$149$	−13.9784	−1.14516	−0.572580	−	0.819849i	$-0.694057\pi$
$149$	−13.9784	−1.14516	−0.572580	+	0.819849i	$0.694057\pi$
$150$	6.19728	0.506006
$151$	−2.21136	−0.179958	−0.0899791	−	0.995944i	$-0.528680\pi$
$151$	−2.21136	−0.179958	−0.0899791	+	0.995944i	$0.528680\pi$
$152$	−2.46494	−0.199933
$153$	6.50916	0.526234
$154$	−8.46720	−0.682306
$155$	28.9962	2.32903
$156$	−3.02204	−0.241957
$157$	−18.9094	−1.50914	−0.754569	−	0.656221i	$-0.772154\pi$
$157$	−18.9094	−1.50914	−0.754569	+	0.656221i	$0.772154\pi$
$158$	−4.02741	−0.320404
$159$	1.00000	0.0793052
$160$	−21.6625	−1.71257
$161$	13.4880	1.06300
$162$	−0.703145	−0.0552443
$163$	−1.90351	−0.149094	−0.0745470	−	0.997217i	$-0.523751\pi$
$163$	−1.90351	−0.149094	−0.0745470	+	0.997217i	$0.523751\pi$
$164$	7.96073	0.621629
$165$	14.3087	1.11393
$166$	−10.1748	−0.789719
$167$	5.26675	0.407554	0.203777	−	0.979017i	$-0.434678\pi$
$167$	5.26675	0.407554	0.203777	+	0.979017i	$0.434678\pi$
$168$	7.71000	0.594839
$169$	−8.97109	−0.690084
$170$	−17.0108	−1.30467
$171$	−1.00000	−0.0764719
$172$	12.3910	0.944803
$173$	−19.6165	−1.49142	−0.745709	−	0.666272i	$-0.767889\pi$
$173$	−19.6165	−1.49142	−0.745709	+	0.666272i	$0.767889\pi$
$174$	1.92770	0.146138
$175$	−27.5680	−2.08395
$176$	−4.92002	−0.370860
$177$	10.8691	0.816973
$178$	4.12391	0.309100
$179$	−9.33319	−0.697595	−0.348798	−	0.937198i	$-0.613410\pi$
$179$	−9.33319	−0.697595	−0.348798	+	0.937198i	$0.613410\pi$
$180$	−5.59578	−0.417085
$181$	−10.9469	−0.813680	−0.406840	−	0.913500i	$-0.633369\pi$
$181$	−10.9469	−0.813680	−0.406840	+	0.913500i	$0.633369\pi$
$182$	−4.41456	−0.327229
$183$	−0.726001	−0.0536676
$184$	−10.6293	−0.783600
$185$	12.4679	0.916656
$186$	5.48569	0.402230
$187$	−25.0594	−1.83253
$188$	6.59422	0.480933
$189$	3.12787	0.227519
$190$	2.61336	0.189593
$191$	−9.58677	−0.693674	−0.346837	−	0.937925i	$-0.612744\pi$
$191$	−9.58677	−0.693674	−0.346837	+	0.937925i	$0.612744\pi$
$192$	−1.54232	−0.111307
$193$	−23.5190	−1.69293	−0.846467	−	0.532442i	$-0.821275\pi$
$193$	−23.5190	−1.69293	−0.846467	+	0.532442i	$0.821275\pi$
$194$	6.63669	0.476486
$195$	7.46016	0.534233
$196$	−4.19093	−0.299352
$197$	14.2925	1.01830	0.509148	−	0.860679i	$-0.329961\pi$
$197$	14.2925	1.01830	0.509148	+	0.860679i	$0.329961\pi$
$198$	2.70702	0.192379
$199$	−12.3610	−0.876250	−0.438125	−	0.898914i	$-0.644357\pi$
$199$	−12.3610	−0.876250	−0.438125	+	0.898914i	$0.644357\pi$
$200$	21.7251	1.53620
$201$	2.75890	0.194598
$202$	7.77449	0.547011
$203$	−8.57518	−0.601860
$204$	9.80011	0.686145
$205$	−19.6518	−1.37254
$206$	1.58531	0.110454
$207$	−4.31219	−0.299718
$208$	−2.56516	−0.177862
$209$	3.84987	0.266301
$210$	−8.17425	−0.564077
$211$	−6.88959	−0.474299	−0.237149	−	0.971473i	$-0.576213\pi$
$211$	−6.88959	−0.474299	−0.237149	+	0.971473i	$0.576213\pi$
$212$	1.50559	0.103404
$213$	−3.64804	−0.249960
$214$	1.24136	0.0848575
$215$	−30.5882	−2.08610
$216$	−2.46494	−0.167718
$217$	−24.4026	−1.65655
$218$	6.06043	0.410464
$219$	−11.5547	−0.780794
$220$	21.5430	1.45243
$221$	−13.0653	−0.878866
$222$	2.35875	0.158309
$223$	3.44896	0.230959	0.115480	−	0.993310i	$-0.463159\pi$
$223$	3.44896	0.230959	0.115480	+	0.993310i	$0.463159\pi$
$224$	18.2307	1.21809
$225$	8.81367	0.587578
$226$	−8.05345	−0.535708
$227$	−1.53057	−0.101588	−0.0507939	−	0.998709i	$-0.516175\pi$
$227$	−1.53057	−0.101588	−0.0507939	+	0.998709i	$0.516175\pi$
$228$	−1.50559	−0.0997100
$229$	1.52593	0.100836	0.0504180	−	0.998728i	$-0.483945\pi$
$229$	1.52593	0.100836	0.0504180	+	0.998728i	$0.483945\pi$
$230$	11.2693	0.743075
$231$	−12.0419	−0.792299
$232$	6.75771	0.443666
$233$	−29.3636	−1.92367	−0.961837	−	0.273621i	$-0.911778\pi$
$233$	−29.3636	−1.92367	−0.961837	+	0.273621i	$0.911778\pi$
$234$	1.41136	0.0922636
$235$	−16.2784	−1.06189
$236$	16.3644	1.06523
$237$	−5.72772	−0.372055
$238$	14.3159	0.927962
$239$	25.0690	1.62158	0.810789	−	0.585338i	$-0.199038\pi$
$239$	25.0690	1.62158	0.810789	+	0.585338i	$0.199038\pi$
$240$	−4.74980	−0.306598
$241$	17.5109	1.12797	0.563987	−	0.825784i	$-0.309267\pi$
$241$	17.5109	1.12797	0.563987	+	0.825784i	$0.309267\pi$
$242$	−2.68707	−0.172731
$243$	−1.00000	−0.0641500
$244$	−1.09306	−0.0699759
$245$	10.3457	0.660960
$246$	−3.71785	−0.237041
$247$	2.00721	0.127716
$248$	19.2306	1.22114
$249$	−14.4704	−0.917027
$250$	−9.96648	−0.630336
$251$	−0.101447	−0.00640325	−0.00320163	−	0.999995i	$-0.501019\pi$
$251$	−0.101447	−0.00640325	−0.00320163	+	0.999995i	$0.501019\pi$
$252$	4.70929	0.296657
$253$	16.6014	1.04372
$254$	2.09064	0.131178
$255$	−24.1924	−1.51499
$256$	−10.5186	−0.657413
$257$	24.8479	1.54997	0.774985	−	0.631980i	$-0.217757\pi$
$257$	24.8479	1.54997	0.774985	+	0.631980i	$0.217757\pi$
$258$	−5.78687	−0.360275
$259$	−10.4927	−0.651984
$260$	11.2319	0.696574
$261$	2.74154	0.169697
$262$	11.6415	0.719212
$263$	−21.5537	−1.32906	−0.664529	−	0.747262i	$-0.731368\pi$
$263$	−21.5537	−1.32906	−0.664529	+	0.747262i	$0.731368\pi$
$264$	9.48968	0.584049
$265$	−3.71667	−0.228313
$266$	−2.19935	−0.134851
$267$	5.86496	0.358930
$268$	4.15377	0.253732
$269$	−29.0497	−1.77119	−0.885596	−	0.464457i	$-0.846250\pi$
$269$	−29.0497	−1.77119	−0.885596	+	0.464457i	$0.846250\pi$
$270$	2.61336	0.159044
$271$	9.75510	0.592580	0.296290	−	0.955098i	$-0.404251\pi$
$271$	9.75510	0.592580	0.296290	+	0.955098i	$0.404251\pi$
$272$	8.31851	0.504384
$273$	−6.27831	−0.379980
$274$	−1.95103	−0.117866
$275$	−33.9315	−2.04614
$276$	−6.49238	−0.390795
$277$	−22.8049	−1.37022	−0.685108	−	0.728441i	$-0.740245\pi$
$277$	−22.8049	−1.37022	−0.685108	+	0.728441i	$0.740245\pi$
$278$	−7.84085	−0.470263
$279$	7.80165	0.467073
$280$	−28.6556	−1.71250
$281$	−23.4690	−1.40004	−0.700022	−	0.714121i	$-0.746827\pi$
$281$	−23.4690	−1.40004	−0.700022	+	0.714121i	$0.746827\pi$
$282$	−3.07966	−0.183391
$283$	−5.11312	−0.303943	−0.151972	−	0.988385i	$-0.548562\pi$
$283$	−5.11312	−0.303943	−0.151972	+	0.988385i	$0.548562\pi$
$284$	−5.49244	−0.325917
$285$	3.71667	0.220157
$286$	−5.43356	−0.321293
$287$	16.5385	0.976236
$288$	−5.82847	−0.343446
$289$	25.3692	1.49230
$290$	−7.16462	−0.420721
$291$	9.43858	0.553299
$292$	−17.3966	−1.01806
$293$	−27.2135	−1.58983	−0.794914	−	0.606722i	$-0.792484\pi$
$293$	−27.2135	−1.58983	−0.794914	+	0.606722i	$0.792484\pi$
$294$	1.95726	0.114150
$295$	−40.3970	−2.35200
$296$	8.26881	0.480615
$297$	3.84987	0.223392
$298$	9.82887	0.569371
$299$	8.65548	0.500560
$300$	13.2697	0.766129
$301$	25.7424	1.48376
$302$	1.55491	0.0894749
$303$	11.0567	0.635193
$304$	−1.27797	−0.0732966
$305$	2.69831	0.154505
$306$	−4.57688	−0.261643
$307$	15.6140	0.891136	0.445568	−	0.895248i	$-0.353002\pi$
$307$	15.6140	0.891136	0.445568	+	0.895248i	$0.353002\pi$
$308$	−18.1301	−1.03306
$309$	2.25460	0.128260
$310$	−20.3885	−1.15799
$311$	32.7805	1.85881	0.929405	−	0.369061i	$-0.120321\pi$
$311$	32.7805	1.85881	0.929405	+	0.369061i	$0.120321\pi$
$312$	4.94765	0.280106
$313$	−24.3091	−1.37403	−0.687016	−	0.726642i	$-0.741080\pi$
$313$	−24.3091	−1.37403	−0.687016	+	0.726642i	$0.741080\pi$
$314$	13.2961	0.750341
$315$	−11.6253	−0.655010
$316$	−8.62358	−0.485114
$317$	−11.2557	−0.632184	−0.316092	−	0.948729i	$-0.602371\pi$
$317$	−11.2557	−0.632184	−0.316092	+	0.948729i	$0.602371\pi$
$318$	−0.703145	−0.0394304
$319$	−10.5546	−0.590942
$320$	5.73229	0.320445
$321$	1.76544	0.0985371
$322$	−9.48399	−0.528522
$323$	−6.50916	−0.362179
$324$	−1.50559	−0.0836438
$325$	−17.6909	−0.981316
$326$	1.33844	0.0741293
$327$	8.61904	0.476634
$328$	−13.0332	−0.719641
$329$	13.6996	0.755281
$330$	−10.0611	−0.553845
$331$	−14.0731	−0.773529	−0.386764	−	0.922179i	$-0.626407\pi$
$331$	−14.0731	−0.773529	−0.386764	+	0.922179i	$0.626407\pi$
$332$	−21.7865	−1.19569
$333$	3.35458	0.183830
$334$	−3.70329	−0.202635
$335$	−10.2539	−0.560233
$336$	3.99732	0.218072
$337$	6.72243	0.366194	0.183097	−	0.983095i	$-0.441388\pi$
$337$	6.72243	0.366194	0.183097	+	0.983095i	$0.441388\pi$
$338$	6.30797	0.343109
$339$	−11.4535	−0.622067
$340$	−36.4238	−1.97536
$341$	−30.0354	−1.62651
$342$	0.703145	0.0380217
$343$	13.1884	0.712108
$344$	−20.2864	−1.09377
$345$	16.0270	0.862864
$346$	13.7933	0.741531
$347$	8.74182	0.469286	0.234643	−	0.972082i	$-0.424608\pi$
$347$	8.74182	0.469286	0.234643	+	0.972082i	$0.424608\pi$
$348$	4.12763	0.221264
$349$	16.9695	0.908356	0.454178	−	0.890911i	$-0.349933\pi$
$349$	16.9695	0.908356	0.454178	+	0.890911i	$0.349933\pi$
$350$	19.3843	1.03613
$351$	2.00721	0.107137
$352$	22.4388	1.19599
$353$	8.70638	0.463394	0.231697	−	0.972788i	$-0.425572\pi$
$353$	8.70638	0.463394	0.231697	+	0.972788i	$0.425572\pi$
$354$	−7.64256	−0.406198
$355$	13.5586	0.719614
$356$	8.83021	0.468000
$357$	20.3598	1.07756
$358$	6.56258	0.346843
$359$	15.6294	0.824887	0.412443	−	0.910983i	$-0.364675\pi$
$359$	15.6294	0.824887	0.412443	+	0.910983i	$0.364675\pi$
$360$	9.16136	0.482846
$361$	1.00000	0.0526316
$362$	7.69728	0.404560
$363$	−3.82150	−0.200577
$364$	−9.45254	−0.495448
$365$	42.9450	2.24785
$366$	0.510484	0.0266834
$367$	−32.1349	−1.67743	−0.838714	−	0.544572i	$-0.816692\pi$
$367$	−32.1349	−1.67743	−0.838714	+	0.544572i	$0.816692\pi$
$368$	−5.51084	−0.287273
$369$	−5.28746	−0.275254
$370$	−8.76672	−0.455760
$371$	3.12787	0.162391
$372$	11.7461	0.609006
$373$	−27.5355	−1.42574	−0.712868	−	0.701298i	$-0.752604\pi$
$373$	−27.5355	−1.42574	−0.712868	+	0.701298i	$0.752604\pi$
$374$	17.6204	0.911129
$375$	−14.1742	−0.731950
$376$	−10.7960	−0.556762
$377$	−5.50285	−0.283411
$378$	−2.19935	−0.113122
$379$	−27.5407	−1.41467	−0.707337	−	0.706877i	$-0.750103\pi$
$379$	−27.5407	−1.41467	−0.707337	+	0.706877i	$0.750103\pi$
$380$	5.59578	0.287057
$381$	2.97327	0.152325
$382$	6.74088	0.344894
$383$	−28.2279	−1.44238	−0.721188	−	0.692739i	$-0.756404\pi$
$383$	−28.2279	−1.44238	−0.721188	+	0.692739i	$0.756404\pi$
$384$	−10.5725	−0.539524
$385$	44.7558	2.28097
$386$	16.5372	0.841724
$387$	−8.22999	−0.418354
$388$	14.2106	0.721434
$389$	−12.2742	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$389$	−12.2742	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$390$	−5.24557	−0.265620
$391$	−28.0687	−1.41950
$392$	6.86135	0.346550
$393$	16.5563	0.835154
$394$	−10.0497	−0.506295
$395$	21.2881	1.07112
$396$	5.79632	0.291276
$397$	34.7125	1.74217	0.871085	−	0.491132i	$-0.163417\pi$
$397$	34.7125	1.74217	0.871085	+	0.491132i	$0.163417\pi$
$398$	8.69159	0.435670
$399$	−3.12787	−0.156589
$400$	11.2636	0.563180
$401$	−29.1138	−1.45387	−0.726936	−	0.686706i	$-0.759056\pi$
$401$	−29.1138	−1.45387	−0.726936	+	0.686706i	$0.759056\pi$
$402$	−1.93991	−0.0967538
$403$	−15.6596	−0.780060
$404$	16.6469	0.828214
$405$	3.71667	0.184683
$406$	6.02959	0.299244
$407$	−12.9147	−0.640157
$408$	−16.0447	−0.794329
$409$	10.4090	0.514690	0.257345	−	0.966320i	$-0.417152\pi$
$409$	10.4090	0.514690	0.257345	+	0.966320i	$0.417152\pi$
$410$	13.8180	0.682424
$411$	−2.77472	−0.136867
$412$	3.39450	0.167235
$413$	33.9972	1.67289
$414$	3.03209	0.149019
$415$	53.7819	2.64005
$416$	11.6990	0.573590
$417$	−11.1511	−0.546073
$418$	−2.70702	−0.132404
$419$	14.6928	0.717790	0.358895	−	0.933378i	$-0.383154\pi$
$419$	14.6928	0.717790	0.358895	+	0.933378i	$0.383154\pi$
$420$	−17.5029	−0.854053
$421$	−8.21807	−0.400524	−0.200262	−	0.979742i	$-0.564179\pi$
$421$	−8.21807	−0.400524	−0.200262	+	0.979742i	$0.564179\pi$
$422$	4.84437	0.235820
$423$	−4.37983	−0.212955
$424$	−2.46494	−0.119708
$425$	57.3696	2.78283
$426$	2.56510	0.124279
$427$	−2.27084	−0.109894
$428$	2.65802	0.128480
$429$	−7.72751	−0.373088
$430$	21.5079	1.03720
$431$	33.4822	1.61278	0.806391	−	0.591382i	$-0.201418\pi$
$431$	33.4822	1.61278	0.806391	+	0.591382i	$0.201418\pi$
$432$	−1.27797	−0.0614863
$433$	−3.36956	−0.161931	−0.0809654	−	0.996717i	$-0.525800\pi$
$433$	−3.36956	−0.161931	−0.0809654	+	0.996717i	$0.525800\pi$
$434$	17.1585	0.823636
$435$	−10.1894	−0.488544
$436$	12.9767	0.621472
$437$	4.31219	0.206280
$438$	8.12462	0.388209
$439$	−22.9786	−1.09671	−0.548355	−	0.836245i	$-0.684746\pi$
$439$	−22.9786	−1.09671	−0.548355	+	0.836245i	$0.684746\pi$
$440$	−35.2700	−1.68143
$441$	2.78358	0.132552
$442$	9.18678	0.436971
$443$	24.6137	1.16943	0.584717	−	0.811237i	$-0.301206\pi$
$443$	24.6137	1.16943	0.584717	+	0.811237i	$0.301206\pi$
$444$	5.05061	0.239691
$445$	−21.7981	−1.03333
$446$	−2.42512	−0.114833
$447$	13.9784	0.661158
$448$	−4.82417	−0.227921
$449$	28.0930	1.32579	0.662895	−	0.748713i	$-0.269328\pi$
$449$	28.0930	1.32579	0.662895	+	0.748713i	$0.269328\pi$
$450$	−6.19728	−0.292143
$451$	20.3560	0.958528
$452$	−17.2442	−0.811099
$453$	2.21136	0.103899
$454$	1.07622	0.0505093
$455$	23.3344	1.09393
$456$	2.46494	0.115431
$457$	0.116254	0.00543814	0.00271907	−	0.999996i	$-0.499134\pi$
$457$	0.116254	0.00543814	0.00271907	+	0.999996i	$0.499134\pi$
$458$	−1.07295	−0.0501355
$459$	−6.50916	−0.303822
$460$	24.1300	1.12507
$461$	−18.2299	−0.849052	−0.424526	−	0.905416i	$-0.639559\pi$
$461$	−18.2299	−0.849052	−0.424526	+	0.905416i	$0.639559\pi$
$462$	8.46720	0.393930
$463$	4.73817	0.220202	0.110101	−	0.993920i	$-0.464883\pi$
$463$	4.73817	0.220202	0.110101	+	0.993920i	$0.464883\pi$
$464$	3.50360	0.162651
$465$	−28.9962	−1.34467
$466$	20.6469	0.956448
$467$	20.8797	0.966196	0.483098	−	0.875566i	$-0.339512\pi$
$467$	20.8797	0.966196	0.483098	+	0.875566i	$0.339512\pi$
$468$	3.02204	0.139694
$469$	8.62949	0.398473
$470$	11.4461	0.527968
$471$	18.9094	0.871301
$472$	−26.7917	−1.23319
$473$	31.6844	1.45685
$474$	4.02741	0.184985
$475$	−8.81367	−0.404399
$476$	30.6535	1.40500
$477$	−1.00000	−0.0457869
$478$	−17.6271	−0.806246
$479$	31.3283	1.43142	0.715712	−	0.698395i	$-0.246102\pi$
$479$	31.3283	1.43142	0.715712	+	0.698395i	$0.246102\pi$
$480$	21.6625	0.988754
$481$	−6.73335	−0.307015
$482$	−12.3127	−0.560827
$483$	−13.4880	−0.613724
$484$	−5.75360	−0.261527
$485$	−35.0801	−1.59291
$486$	0.703145	0.0318953
$487$	4.18533	0.189655	0.0948276	−	0.995494i	$-0.469770\pi$
$487$	4.18533	0.189655	0.0948276	+	0.995494i	$0.469770\pi$
$488$	1.78955	0.0810089
$489$	1.90351	0.0860795
$490$	−7.27450	−0.328628
$491$	−12.7732	−0.576448	−0.288224	−	0.957563i	$-0.593065\pi$
$491$	−12.7732	−0.576448	−0.288224	+	0.957563i	$0.593065\pi$
$492$	−7.96073	−0.358898
$493$	17.8451	0.803703
$494$	−1.41136	−0.0635002
$495$	−14.3087	−0.643129
$496$	9.97027	0.447679
$497$	−11.4106	−0.511835
$498$	10.1748	0.455944
$499$	−16.7727	−0.750851	−0.375426	−	0.926853i	$-0.622503\pi$
$499$	−16.7727	−0.750851	−0.375426	+	0.926853i	$0.622503\pi$
$500$	−21.3404	−0.954374
$501$	−5.26675	−0.235301
$502$	0.0713316	0.00318369
$503$	−17.5506	−0.782544	−0.391272	−	0.920275i	$-0.627965\pi$
$503$	−17.5506	−0.782544	−0.391272	+	0.920275i	$0.627965\pi$
$504$	−7.71000	−0.343431
$505$	−41.0943	−1.82867
$506$	−11.6732	−0.518935
$507$	8.97109	0.398420
$508$	4.47652	0.198614
$509$	−12.1489	−0.538490	−0.269245	−	0.963072i	$-0.586774\pi$
$509$	−12.1489	−0.538490	−0.269245	+	0.963072i	$0.586774\pi$
$510$	17.0108	0.753250
$511$	−36.1416	−1.59881
$512$	−13.7488	−0.607618
$513$	1.00000	0.0441511
$514$	−17.4717	−0.770642
$515$	−8.37962	−0.369250
$516$	−12.3910	−0.545482
$517$	16.8618	0.741581
$518$	7.37788	0.324165
$519$	19.6165	0.861071
$520$	−18.3888	−0.806403
$521$	−4.60586	−0.201786	−0.100893	−	0.994897i	$-0.532170\pi$
$521$	−4.60586	−0.201786	−0.100893	+	0.994897i	$0.532170\pi$
$522$	−1.92770	−0.0843730
$523$	−9.96712	−0.435832	−0.217916	−	0.975968i	$-0.569926\pi$
$523$	−9.96712	−0.435832	−0.217916	+	0.975968i	$0.569926\pi$
$524$	24.9269	1.08894
$525$	27.5680	1.20317
$526$	15.1554	0.660806
$527$	50.7822	2.21211
$528$	4.92002	0.214116
$529$	−4.40504	−0.191524
$530$	2.61336	0.113517
$531$	−10.8691	−0.471680
$532$	−4.70929	−0.204173
$533$	10.6131	0.459703
$534$	−4.12391	−0.178459
$535$	−6.56155	−0.283681
$536$	−6.80051	−0.293737
$537$	9.33319	0.402757
$538$	20.4261	0.880634
$539$	−10.7164	−0.461589
$540$	5.59578	0.240804
$541$	41.3720	1.77872	0.889360	−	0.457207i	$-0.151150\pi$
$541$	41.3720	1.77872	0.889360	+	0.457207i	$0.151150\pi$
$542$	−6.85924	−0.294630
$543$	10.9469	0.469778
$544$	−37.9384	−1.62660
$545$	−32.0342	−1.37219
$546$	4.41456	0.188926
$547$	−10.0448	−0.429485	−0.214743	−	0.976671i	$-0.568891\pi$
$547$	−10.0448	−0.429485	−0.214743	+	0.976671i	$0.568891\pi$
$548$	−4.17758	−0.178457
$549$	0.726001	0.0309850
$550$	23.8587	1.01734
$551$	−2.74154	−0.116793
$552$	10.6293	0.452411
$553$	−17.9156	−0.761847
$554$	16.0352	0.681269
$555$	−12.4679	−0.529232
$556$	−16.7890	−0.712012
$557$	18.2282	0.772353	0.386177	−	0.922425i	$-0.373796\pi$
$557$	18.2282	0.772353	0.386177	+	0.922425i	$0.373796\pi$
$558$	−5.48569	−0.232228
$559$	16.5194	0.698694
$560$	−14.8568	−0.627812
$561$	25.0594	1.05801
$562$	16.5021	0.696100
$563$	38.6781	1.63009	0.815044	−	0.579399i	$-0.196713\pi$
$563$	38.6781	1.63009	0.815044	+	0.579399i	$0.196713\pi$
$564$	−6.59422	−0.277667
$565$	42.5688	1.79088
$566$	3.59526	0.151120
$567$	−3.12787	−0.131358
$568$	8.99218	0.377304
$569$	35.2148	1.47628	0.738141	−	0.674646i	$-0.235704\pi$
$569$	35.2148	1.47628	0.738141	+	0.674646i	$0.235704\pi$
$570$	−2.61336	−0.109462
$571$	−5.97071	−0.249866	−0.124933	−	0.992165i	$-0.539872\pi$
$571$	−5.97071	−0.249866	−0.124933	+	0.992165i	$0.539872\pi$
$572$	−11.6344	−0.486461
$573$	9.58677	0.400493
$574$	−11.6290	−0.485383
$575$	−38.0062	−1.58497
$576$	1.54232	0.0642632
$577$	24.9728	1.03963	0.519815	−	0.854279i	$-0.326001\pi$
$577$	24.9728	1.03963	0.519815	+	0.854279i	$0.326001\pi$
$578$	−17.8382	−0.741971
$579$	23.5190	0.977415
$580$	−15.3410	−0.637002
$581$	−45.2617	−1.87777
$582$	−6.63669	−0.275099
$583$	3.84987	0.159445
$584$	28.4816	1.17858
$585$	−7.46016	−0.308440
$586$	19.1350	0.790460
$587$	14.1460	0.583869	0.291935	−	0.956438i	$-0.405701\pi$
$587$	14.1460	0.583869	0.291935	+	0.956438i	$0.405701\pi$
$588$	4.19093	0.172831
$589$	−7.80165	−0.321462
$590$	28.4049	1.16941
$591$	−14.2925	−0.587913
$592$	4.28705	0.176197
$593$	−7.30252	−0.299879	−0.149939	−	0.988695i	$-0.547908\pi$
$593$	−7.30252	−0.299879	−0.149939	+	0.988695i	$0.547908\pi$
$594$	−2.70702	−0.111070
$595$	−75.6708	−3.10220
$596$	21.0458	0.862069
$597$	12.3610	0.505903
$598$	−6.08606	−0.248877
$599$	−21.1586	−0.864516	−0.432258	−	0.901750i	$-0.642283\pi$
$599$	−21.1586	−0.864516	−0.432258	+	0.901750i	$0.642283\pi$
$600$	−21.7251	−0.886924
$601$	−19.4858	−0.794842	−0.397421	−	0.917636i	$-0.630095\pi$
$601$	−19.4858	−0.794842	−0.397421	+	0.917636i	$0.630095\pi$
$602$	−18.1006	−0.737725
$603$	−2.75890	−0.112351
$604$	3.32940	0.135471
$605$	14.2033	0.577445
$606$	−7.77449	−0.315817
$607$	21.4698	0.871432	0.435716	−	0.900084i	$-0.356495\pi$
$607$	21.4698	0.871432	0.435716	+	0.900084i	$0.356495\pi$
$608$	5.82847	0.236376
$609$	8.57518	0.347484
$610$	−1.89730	−0.0768195
$611$	8.79126	0.355657
$612$	−9.80011	−0.396146
$613$	33.4102	1.34943	0.674713	−	0.738080i	$-0.264267\pi$
$613$	33.4102	1.34943	0.674713	+	0.738080i	$0.264267\pi$
$614$	−10.9789	−0.443071
$615$	19.6518	0.792436
$616$	29.6825	1.19594
$617$	7.92248	0.318947	0.159474	−	0.987202i	$-0.449020\pi$
$617$	7.92248	0.318947	0.159474	+	0.987202i	$0.449020\pi$
$618$	−1.58531	−0.0637706
$619$	−10.1965	−0.409832	−0.204916	−	0.978780i	$-0.565692\pi$
$619$	−10.1965	−0.409832	−0.204916	+	0.978780i	$0.565692\pi$
$620$	−43.6563	−1.75328
$621$	4.31219	0.173042
$622$	−23.0494	−0.924197
$623$	18.3448	0.734971
$624$	2.56516	0.102689
$625$	8.61240	0.344496
$626$	17.0928	0.683167
$627$	−3.84987	−0.153749
$628$	28.4698	1.13607
$629$	21.8355	0.870638
$630$	8.17425	0.325670
$631$	34.8090	1.38572	0.692862	−	0.721070i	$-0.256349\pi$
$631$	34.8090	1.38572	0.692862	+	0.721070i	$0.256349\pi$
$632$	14.1185	0.561602
$633$	6.88959	0.273836
$634$	7.91440	0.314321
$635$	−11.0507	−0.438533
$636$	−1.50559	−0.0597004
$637$	−5.58724	−0.221375
$638$	7.42139	0.293815
$639$	3.64804	0.144314
$640$	39.2944	1.55325
$641$	−14.3407	−0.566424	−0.283212	−	0.959057i	$-0.591400\pi$
$641$	−14.3407	−0.566424	−0.283212	+	0.959057i	$0.591400\pi$
$642$	−1.24136	−0.0489925
$643$	19.4433	0.766769	0.383385	−	0.923589i	$-0.374758\pi$
$643$	19.4433	0.766769	0.383385	+	0.923589i	$0.374758\pi$
$644$	−20.3073	−0.800220
$645$	30.5882	1.20441
$646$	4.57688	0.180075
$647$	−32.0988	−1.26193	−0.630967	−	0.775809i	$-0.717342\pi$
$647$	−32.0988	−1.26193	−0.630967	+	0.775809i	$0.717342\pi$
$648$	2.46494	0.0968318
$649$	41.8447	1.64255
$650$	12.4393	0.487908
$651$	24.4026	0.956412
$652$	2.86589	0.112237
$653$	28.4016	1.11144	0.555721	−	0.831369i	$-0.312442\pi$
$653$	28.4016	1.11144	0.555721	+	0.831369i	$0.312442\pi$
$654$	−6.06043	−0.236982
$655$	−61.5343	−2.40434
$656$	−6.75721	−0.263825
$657$	11.5547	0.450791
$658$	−9.63277	−0.375525
$659$	−30.3088	−1.18066	−0.590332	−	0.807161i	$-0.701003\pi$
$659$	−30.3088	−1.18066	−0.590332	+	0.807161i	$0.701003\pi$
$660$	−21.5430	−0.838561
$661$	−41.4321	−1.61152	−0.805761	−	0.592241i	$-0.798243\pi$
$661$	−41.4321	−1.61152	−0.805761	+	0.592241i	$0.798243\pi$
$662$	9.89544	0.384597
$663$	13.0653	0.507413
$664$	35.6687	1.38421
$665$	11.6253	0.450809
$666$	−2.35875	−0.0913998
$667$	−11.8220	−0.457751
$668$	−7.92956	−0.306804
$669$	−3.44896	−0.133344
$670$	7.21000	0.278547
$671$	−2.79501	−0.107900
$672$	−18.2307	−0.703264
$673$	19.9889	0.770515	0.385258	−	0.922809i	$-0.374113\pi$
$673$	19.9889	0.770515	0.385258	+	0.922809i	$0.374113\pi$
$674$	−4.72684	−0.182071
$675$	−8.81367	−0.339238
$676$	13.5068	0.519491
$677$	29.9814	1.15228	0.576139	−	0.817352i	$-0.304559\pi$
$677$	29.9814	1.15228	0.576139	+	0.817352i	$0.304559\pi$
$678$	8.05345	0.309291
$679$	29.5227	1.13298
$680$	59.6328	2.28681
$681$	1.53057	0.0586517
$682$	21.1192	0.808696
$683$	−30.6732	−1.17368	−0.586839	−	0.809703i	$-0.699628\pi$
$683$	−30.6732	−1.17368	−0.586839	+	0.809703i	$0.699628\pi$
$684$	1.50559	0.0575676
$685$	10.3127	0.394029
$686$	−9.27336	−0.354059
$687$	−1.52593	−0.0582177
$688$	−10.5177	−0.400983
$689$	2.00721	0.0764688
$690$	−11.2693	−0.429015
$691$	3.99537	0.151991	0.0759955	−	0.997108i	$-0.475787\pi$
$691$	3.99537	0.151991	0.0759955	+	0.997108i	$0.475787\pi$
$692$	29.5344	1.12273
$693$	12.0419	0.457434
$694$	−6.14677	−0.233328
$695$	41.4451	1.57210
$696$	−6.75771	−0.256150
$697$	−34.4169	−1.30363
$698$	−11.9320	−0.451633
$699$	29.3636	1.11063
$700$	41.5061	1.56878
$701$	−5.93238	−0.224063	−0.112031	−	0.993705i	$-0.535736\pi$
$701$	−5.93238	−0.224063	−0.112031	+	0.993705i	$0.535736\pi$
$702$	−1.41136	−0.0532684
$703$	−3.35458	−0.126520
$704$	−5.93772	−0.223786
$705$	16.2784	0.613081
$706$	−6.12184	−0.230399
$707$	34.5841	1.30067
$708$	−16.3644	−0.615012
$709$	−38.8136	−1.45768	−0.728838	−	0.684686i	$-0.759939\pi$
$709$	−38.8136	−1.45768	−0.728838	+	0.684686i	$0.759939\pi$
$710$	−9.53364	−0.357791
$711$	5.72772	0.214806
$712$	−14.4567	−0.541789
$713$	−33.6422	−1.25991
$714$	−14.3159	−0.535759
$715$	28.7207	1.07409
$716$	14.0519	0.525145
$717$	−25.0690	−0.936219
$718$	−10.9897	−0.410132
$719$	35.8985	1.33879	0.669394	−	0.742908i	$-0.266554\pi$
$719$	35.8985	1.33879	0.669394	+	0.742908i	$0.266554\pi$
$720$	4.74980	0.177014
$721$	7.05211	0.262634
$722$	−0.703145	−0.0261683
$723$	−17.5109	−0.651236
$724$	16.4816	0.612533
$725$	24.1630	0.897391
$726$	2.68707	0.0997264
$727$	12.3049	0.456364	0.228182	−	0.973619i	$-0.426722\pi$
$727$	12.3049	0.456364	0.228182	+	0.973619i	$0.426722\pi$
$728$	15.4756	0.573565
$729$	1.00000	0.0370370
$730$	−30.1966	−1.11762
$731$	−53.5703	−1.98137
$732$	1.09306	0.0404006
$733$	−2.06787	−0.0763786	−0.0381893	−	0.999271i	$-0.512159\pi$
$733$	−2.06787	−0.0763786	−0.0381893	+	0.999271i	$0.512159\pi$
$734$	22.5955	0.834015
$735$	−10.3457	−0.381606
$736$	25.1334	0.926431
$737$	10.6214	0.391245
$738$	3.71785	0.136856
$739$	−35.8428	−1.31850	−0.659249	−	0.751925i	$-0.729126\pi$
$739$	−35.8428	−1.31850	−0.659249	+	0.751925i	$0.729126\pi$
$740$	−18.7715	−0.690053
$741$	−2.00721	−0.0737369
$742$	−2.19935	−0.0807405
$743$	33.7388	1.23776	0.618878	−	0.785487i	$-0.287588\pi$
$743$	33.7388	1.23776	0.618878	+	0.785487i	$0.287588\pi$
$744$	−19.2306	−0.705027
$745$	−51.9533	−1.90342
$746$	19.3615	0.708874
$747$	14.4704	0.529446
$748$	37.7292	1.37951
$749$	5.52206	0.201772
$750$	9.96648	0.363925
$751$	1.25409	0.0457625	0.0228812	−	0.999738i	$-0.492716\pi$
$751$	1.25409	0.0457625	0.0228812	+	0.999738i	$0.492716\pi$
$752$	−5.59729	−0.204112
$753$	0.101447	0.00369692
$754$	3.86930	0.140912
$755$	−8.21892	−0.299117
$756$	−4.70929	−0.171275
$757$	−6.90251	−0.250876	−0.125438	−	0.992101i	$-0.540034\pi$
$757$	−6.90251	−0.250876	−0.125438	+	0.992101i	$0.540034\pi$
$758$	19.3651	0.703373
$759$	−16.6014	−0.602591
$760$	−9.16136	−0.332317
$761$	−15.1142	−0.547890	−0.273945	−	0.961745i	$-0.588329\pi$
$761$	−15.1142	−0.547890	−0.273945	+	0.961745i	$0.588329\pi$
$762$	−2.09064	−0.0757359
$763$	26.9592	0.975990
$764$	14.4337	0.522194
$765$	24.1924	0.874679
$766$	19.8483	0.717147
$767$	21.8167	0.787754
$768$	10.5186	0.379557
$769$	−28.0963	−1.01318	−0.506589	−	0.862188i	$-0.669094\pi$
$769$	−28.0963	−1.01318	−0.506589	+	0.862188i	$0.669094\pi$
$770$	−31.4698	−1.13409
$771$	−24.8479	−0.894876
$772$	35.4099	1.27443
$773$	−42.4633	−1.52730	−0.763649	−	0.645632i	$-0.776594\pi$
$773$	−42.4633	−1.52730	−0.763649	+	0.645632i	$0.776594\pi$
$774$	5.78687	0.208005
$775$	68.7612	2.46997
$776$	−23.2655	−0.835182
$777$	10.4927	0.376423
$778$	8.63056	0.309420
$779$	5.28746	0.189443
$780$	−11.2319	−0.402167
$781$	−14.0445	−0.502551
$782$	19.7364	0.705771
$783$	−2.74154	−0.0979746
$784$	3.55733	0.127048
$785$	−70.2803	−2.50841
$786$	−11.6415	−0.415237
$787$	8.30910	0.296187	0.148094	−	0.988973i	$-0.452686\pi$
$787$	8.30910	0.296187	0.148094	+	0.988973i	$0.452686\pi$
$788$	−21.5186	−0.766567
$789$	21.5537	0.767332
$790$	−14.9686	−0.532558
$791$	−35.8250	−1.27379
$792$	−9.48968	−0.337201
$793$	−1.45724	−0.0517481
$794$	−24.4079	−0.866204
$795$	3.71667	0.131817
$796$	18.6106	0.659636
$797$	−1.63522	−0.0579224	−0.0289612	−	0.999581i	$-0.509220\pi$
$797$	−1.63522	−0.0579224	−0.0289612	+	0.999581i	$0.509220\pi$
$798$	2.19935	0.0778560
$799$	−28.5090	−1.00858
$800$	−51.3702	−1.81621
$801$	−5.86496	−0.207228
$802$	20.4712	0.722862
$803$	−44.4841	−1.56981
$804$	−4.15377	−0.146492
$805$	50.1304	1.76686
$806$	11.0110	0.387844
$807$	29.0497	1.02260
$808$	−27.2542	−0.958798
$809$	−13.4362	−0.472391	−0.236196	−	0.971706i	$-0.575901\pi$
$809$	−13.4362	−0.472391	−0.236196	+	0.971706i	$0.575901\pi$
$810$	−2.61336	−0.0918241
$811$	−1.23625	−0.0434107	−0.0217053	−	0.999764i	$-0.506910\pi$
$811$	−1.23625	−0.0434107	−0.0217053	+	0.999764i	$0.506910\pi$
$812$	12.9107	0.453076
$813$	−9.75510	−0.342126
$814$	9.08089	0.318285
$815$	−7.07471	−0.247816
$816$	−8.31851	−0.291206
$817$	8.22999	0.287931
$818$	−7.31900	−0.255903
$819$	6.27831	0.219382
$820$	29.5875	1.03324
$821$	−38.3799	−1.33947	−0.669733	−	0.742602i	$-0.733592\pi$
$821$	−38.3799	−1.33947	−0.669733	+	0.742602i	$0.733592\pi$
$822$	1.95103	0.0680499
$823$	24.6357	0.858748	0.429374	−	0.903127i	$-0.358734\pi$
$823$	24.6357	0.858748	0.429374	+	0.903127i	$0.358734\pi$
$824$	−5.55745	−0.193603
$825$	33.9315	1.18134
$826$	−23.9050	−0.831760
$827$	−17.2116	−0.598507	−0.299254	−	0.954174i	$-0.596738\pi$
$827$	−17.2116	−0.598507	−0.299254	+	0.954174i	$0.596738\pi$
$828$	6.49238	0.225626
$829$	51.8135	1.79956	0.899779	−	0.436347i	$-0.143728\pi$
$829$	51.8135	1.79956	0.899779	+	0.436347i	$0.143728\pi$
$830$	−37.8165	−1.31263
$831$	22.8049	0.791095
$832$	−3.09576	−0.107326
$833$	18.1188	0.627778
$834$	7.84085	0.271507
$835$	19.5748	0.677414
$836$	−5.79632	−0.200470
$837$	−7.80165	−0.269665
$838$	−10.3312	−0.356884
$839$	−14.5613	−0.502712	−0.251356	−	0.967895i	$-0.580877\pi$
$839$	−14.5613	−0.502712	−0.251356	+	0.967895i	$0.580877\pi$
$840$	28.6556	0.988711
$841$	−21.4840	−0.740827
$842$	5.77849	0.199140
$843$	23.4690	0.808316
$844$	10.3729	0.357049
$845$	−33.3426	−1.14702
$846$	3.07966	0.105881
$847$	−11.9532	−0.410716
$848$	−1.27797	−0.0438856
$849$	5.11312	0.175482
$850$	−40.3391	−1.38362
$851$	−14.4656	−0.495873
$852$	5.49244	0.188168
$853$	10.9710	0.375640	0.187820	−	0.982203i	$-0.439858\pi$
$853$	10.9710	0.375640	0.187820	+	0.982203i	$0.439858\pi$
$854$	1.59673	0.0546389
$855$	−3.71667	−0.127108
$856$	−4.35169	−0.148738
$857$	37.7189	1.28845	0.644226	−	0.764835i	$-0.277180\pi$
$857$	37.7189	1.28845	0.644226	+	0.764835i	$0.277180\pi$
$858$	5.43356	0.185499
$859$	13.0074	0.443808	0.221904	−	0.975069i	$-0.428773\pi$
$859$	13.0074	0.443808	0.221904	+	0.975069i	$0.428773\pi$
$860$	46.0532	1.57040
$861$	−16.5385	−0.563630
$862$	−23.5429	−0.801873
$863$	0.407929	0.0138861	0.00694303	−	0.999976i	$-0.497790\pi$
$863$	0.407929	0.0138861	0.00694303	+	0.999976i	$0.497790\pi$
$864$	5.82847	0.198288
$865$	−72.9083	−2.47896
$866$	2.36929	0.0805117
$867$	−25.3692	−0.861582
$868$	36.7402	1.24704
$869$	−22.0510	−0.748028
$870$	7.16462	0.242903
$871$	5.53771	0.187638
$872$	−21.2454	−0.719459
$873$	−9.43858	−0.319447
$874$	−3.03209	−0.102562
$875$	−44.3350	−1.49880
$876$	17.3966	0.587777
$877$	41.5441	1.40284	0.701422	−	0.712747i	$-0.252549\pi$
$877$	41.5441	1.40284	0.701422	+	0.712747i	$0.252549\pi$
$878$	16.1573	0.545283
$879$	27.2135	0.917887
$880$	−18.2861	−0.616424
$881$	17.0898	0.575769	0.287884	−	0.957665i	$-0.407048\pi$
$881$	17.0898	0.575769	0.287884	+	0.957665i	$0.407048\pi$
$882$	−1.95726	−0.0659044
$883$	1.67765	0.0564576	0.0282288	−	0.999601i	$-0.491013\pi$
$883$	1.67765	0.0564576	0.0282288	+	0.999601i	$0.491013\pi$
$884$	19.6709	0.661605
$885$	40.3970	1.35793
$886$	−17.3070	−0.581441
$887$	−20.9497	−0.703422	−0.351711	−	0.936109i	$-0.614400\pi$
$887$	−20.9497	−0.703422	−0.351711	+	0.936109i	$0.614400\pi$
$888$	−8.26881	−0.277483
$889$	9.30002	0.311913
$890$	15.3272	0.513771
$891$	−3.84987	−0.128976
$892$	−5.19271	−0.173865
$893$	4.37983	0.146566
$894$	−9.82887	−0.328727
$895$	−34.6884	−1.15951
$896$	−33.0693	−1.10477
$897$	−8.65548	−0.288998
$898$	−19.7534	−0.659180
$899$	21.3885	0.713347
$900$	−13.2697	−0.442325
$901$	−6.50916	−0.216852
$902$	−14.3132	−0.476579
$903$	−25.7424	−0.856652
$904$	28.2321	0.938985
$905$	−40.6862	−1.35246
$906$	−1.55491	−0.0516584
$907$	30.7432	1.02081	0.510405	−	0.859934i	$-0.329495\pi$
$907$	30.7432	1.02081	0.510405	+	0.859934i	$0.329495\pi$
$908$	2.30441	0.0764747
$909$	−11.0567	−0.366729
$910$	−16.4075	−0.543903
$911$	32.3237	1.07093	0.535465	−	0.844557i	$-0.320136\pi$
$911$	32.3237	1.07093	0.535465	+	0.844557i	$0.320136\pi$
$912$	1.27797	0.0423178
$913$	−55.7093	−1.84371
$914$	−0.0817435	−0.00270383
$915$	−2.69831	−0.0892034
$916$	−2.29741	−0.0759087
$917$	51.7859	1.71012
$918$	4.57688	0.151060
$919$	50.5404	1.66717	0.833587	−	0.552388i	$-0.186283\pi$
$919$	50.5404	1.66717	0.833587	+	0.552388i	$0.186283\pi$
$920$	−39.5055	−1.30246
$921$	−15.6140	−0.514498
$922$	12.8183	0.422147
$923$	−7.32240	−0.241020
$924$	18.1301	0.596438
$925$	29.5661	0.972128
$926$	−3.33162	−0.109484
$927$	−2.25460	−0.0740509
$928$	−15.9790	−0.524535
$929$	3.04667	0.0999579	0.0499790	−	0.998750i	$-0.484085\pi$
$929$	3.04667	0.0999579	0.0499790	+	0.998750i	$0.484085\pi$
$930$	20.3885	0.668566
$931$	−2.78358	−0.0912282
$932$	44.2095	1.44813
$933$	−32.7805	−1.07318
$934$	−14.6814	−0.480391
$935$	−93.1377	−3.04593
$936$	−4.94765	−0.161719
$937$	39.8160	1.30073	0.650366	−	0.759621i	$-0.274615\pi$
$937$	39.8160	1.30073	0.650366	+	0.759621i	$0.274615\pi$
$938$	−6.06778	−0.198120
$939$	24.3091	0.793298
$940$	24.5086	0.799382
$941$	0.118742	0.00387088	0.00193544	−	0.999998i	$-0.499384\pi$
$941$	0.118742	0.00387088	0.00193544	+	0.999998i	$0.499384\pi$
$942$	−13.2961	−0.433210
$943$	22.8005	0.742487
$944$	−13.8904	−0.452094
$945$	11.6253	0.378170
$946$	−22.2787	−0.724343
$947$	55.6348	1.80789	0.903944	−	0.427650i	$-0.140658\pi$
$947$	55.6348	1.80789	0.903944	+	0.427650i	$0.140658\pi$
$948$	8.62358	0.280081
$949$	−23.1927	−0.752868
$950$	6.19728	0.201066
$951$	11.2557	0.364992
$952$	−50.1856	−1.62653
$953$	32.1146	1.04030	0.520148	−	0.854076i	$-0.325877\pi$
$953$	32.1146	1.04030	0.520148	+	0.854076i	$0.325877\pi$
$954$	0.703145	0.0227651
$955$	−35.6309	−1.15299
$956$	−37.7436	−1.22071
$957$	10.5546	0.341181
$958$	−22.0283	−0.711702
$959$	−8.67895	−0.280258
$960$	−5.73229	−0.185009
$961$	29.8658	0.963413
$962$	4.73452	0.152647
$963$	−1.76544	−0.0568904
$964$	−26.3641	−0.849132
$965$	−87.4124	−2.81390
$966$	9.48399	0.305142
$967$	−12.2045	−0.392470	−0.196235	−	0.980557i	$-0.562872\pi$
$967$	−12.2045	−0.392470	−0.196235	+	0.980557i	$0.562872\pi$
$968$	9.41975	0.302762
$969$	6.50916	0.209104
$970$	24.6664	0.791990
$971$	28.6033	0.917922	0.458961	−	0.888456i	$-0.348222\pi$
$971$	28.6033	0.917922	0.458961	+	0.888456i	$0.348222\pi$
$972$	1.50559	0.0482917
$973$	−34.8793	−1.11818
$974$	−2.94289	−0.0942963
$975$	17.6909	0.566563
$976$	0.927807	0.0296984
$977$	−37.5915	−1.20266	−0.601330	−	0.799001i	$-0.705362\pi$
$977$	−37.5915	−1.20266	−0.601330	+	0.799001i	$0.705362\pi$
$978$	−1.33844	−0.0427986
$979$	22.5793	0.721639
$980$	−15.5763	−0.497567
$981$	−8.61904	−0.275185
$982$	8.98142	0.286609
$983$	−8.52975	−0.272057	−0.136028	−	0.990705i	$-0.543434\pi$
$983$	−8.52975	−0.272057	−0.136028	+	0.990705i	$0.543434\pi$
$984$	13.0332	0.415485
$985$	53.1204	1.69256
$986$	−12.5477	−0.399600
$987$	−13.6996	−0.436062
$988$	−3.02204	−0.0961438
$989$	35.4893	1.12849
$990$	10.0611	0.319763
$991$	−27.2034	−0.864143	−0.432072	−	0.901839i	$-0.642217\pi$
$991$	−27.2034	−0.864143	−0.432072	+	0.901839i	$0.642217\pi$
$992$	−45.4717	−1.44373
$993$	14.0731	0.446597
$994$	8.02330	0.254484
$995$	−45.9419	−1.45646
$996$	21.7865	0.690332
$997$	46.5085	1.47294	0.736470	−	0.676470i	$-0.236491\pi$
$997$	46.5085	1.47294	0.736470	+	0.676470i	$0.236491\pi$
$998$	11.7937	0.373322
$999$	−3.35458	−0.106134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3021.2.a.i.1.7	✓	19
3.2	odd	2		9063.2.a.m.1.13		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3021.2.a.i.1.7	✓	19	1.1	even	1	trivial
9063.2.a.m.1.13		19	3.2	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:	\( N \)	\(=\)	\( 3021 = 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3021.a (trivial)

\(f(q)\)	\(=\)	\(q-0.703145 q^{2} -1.00000 q^{3} -1.50559 q^{4} +3.71667 q^{5} +0.703145 q^{6} -3.12787 q^{7} +2.46494 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.703145 q^{2} -1.00000 q^{3} -1.50559 q^{4} +3.71667 q^{5} +0.703145 q^{6} -3.12787 q^{7} +2.46494 q^{8} +1.00000 q^{9} -2.61336 q^{10} -3.84987 q^{11} +1.50559 q^{12} -2.00721 q^{13} +2.19935 q^{14} -3.71667 q^{15} +1.27797 q^{16} +6.50916 q^{17} -0.703145 q^{18} -1.00000 q^{19} -5.59578 q^{20} +3.12787 q^{21} +2.70702 q^{22} -4.31219 q^{23} -2.46494 q^{24} +8.81367 q^{25} +1.41136 q^{26} -1.00000 q^{27} +4.70929 q^{28} +2.74154 q^{29} +2.61336 q^{30} +7.80165 q^{31} -5.82847 q^{32} +3.84987 q^{33} -4.57688 q^{34} -11.6253 q^{35} -1.50559 q^{36} +3.35458 q^{37} +0.703145 q^{38} +2.00721 q^{39} +9.16136 q^{40} -5.28746 q^{41} -2.19935 q^{42} -8.22999 q^{43} +5.79632 q^{44} +3.71667 q^{45} +3.03209 q^{46} -4.37983 q^{47} -1.27797 q^{48} +2.78358 q^{49} -6.19728 q^{50} -6.50916 q^{51} +3.02204 q^{52} -1.00000 q^{53} +0.703145 q^{54} -14.3087 q^{55} -7.71000 q^{56} +1.00000 q^{57} -1.92770 q^{58} -10.8691 q^{59} +5.59578 q^{60} +0.726001 q^{61} -5.48569 q^{62} -3.12787 q^{63} +1.54232 q^{64} -7.46016 q^{65} -2.70702 q^{66} -2.75890 q^{67} -9.80011 q^{68} +4.31219 q^{69} +8.17425 q^{70} +3.64804 q^{71} +2.46494 q^{72} +11.5547 q^{73} -2.35875 q^{74} -8.81367 q^{75} +1.50559 q^{76} +12.0419 q^{77} -1.41136 q^{78} +5.72772 q^{79} +4.74980 q^{80} +1.00000 q^{81} +3.71785 q^{82} +14.4704 q^{83} -4.70929 q^{84} +24.1924 q^{85} +5.78687 q^{86} -2.74154 q^{87} -9.48968 q^{88} -5.86496 q^{89} -2.61336 q^{90} +6.27831 q^{91} +6.49238 q^{92} -7.80165 q^{93} +3.07966 q^{94} -3.71667 q^{95} +5.82847 q^{96} -9.43858 q^{97} -1.95726 q^{98} -3.84987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} - 19 q^{3} + 14 q^{4} + 2 q^{5} - 2 q^{6} - 7 q^{7} + 19 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 - 19 * q^3 + 14 * q^4 + 2 * q^5 - 2 * q^6 - 7 * q^7 + 19 * q^9	\( 19 q + 2 q^{2} - 19 q^{3} + 14 q^{4} + 2 q^{5} - 2 q^{6} - 7 q^{7} + 19 q^{9} - 12 q^{10} - 10 q^{11} - 14 q^{12} - 14 q^{13} - 16 q^{14} - 2 q^{15} + 8 q^{16} + 11 q^{17} + 2 q^{18} - 19 q^{19} + 8 q^{20} + 7 q^{21} - 3 q^{22} + 13 q^{23} + 9 q^{25} - 7 q^{26} - 19 q^{27} - 24 q^{28} - 18 q^{29} + 12 q^{30} - 21 q^{31} - 3 q^{32} + 10 q^{33} - 10 q^{34} - 7 q^{35} + 14 q^{36} - 26 q^{37} - 2 q^{38} + 14 q^{39} - 27 q^{40} - 7 q^{41} + 16 q^{42} - 25 q^{43} - 5 q^{44} + 2 q^{45} - 11 q^{46} - 10 q^{47} - 8 q^{48} - 6 q^{49} - 16 q^{50} - 11 q^{51} - 37 q^{52} - 19 q^{53} - 2 q^{54} - 20 q^{55} - 33 q^{56} + 19 q^{57} - 27 q^{58} - 42 q^{59} - 8 q^{60} - 16 q^{61} - 6 q^{62} - 7 q^{63} - 32 q^{64} - q^{65} + 3 q^{66} - 40 q^{67} + 6 q^{68} - 13 q^{69} - 29 q^{70} - 23 q^{71} + 7 q^{73} + 15 q^{74} - 9 q^{75} - 14 q^{76} + 42 q^{77} + 7 q^{78} - 26 q^{79} + 7 q^{80} + 19 q^{81} - 19 q^{82} - 14 q^{83} + 24 q^{84} - 37 q^{85} - 24 q^{86} + 18 q^{87} - 50 q^{88} - 3 q^{89} - 12 q^{90} - 60 q^{91} + 44 q^{92} + 21 q^{93} - 62 q^{94} - 2 q^{95} + 3 q^{96} - 44 q^{97} + 52 q^{98} - 10 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 - 19 * q^3 + 14 * q^4 + 2 * q^5 - 2 * q^6 - 7 * q^7 + 19 * q^9 - 12 * q^10 - 10 * q^11 - 14 * q^12 - 14 * q^13 - 16 * q^14 - 2 * q^15 + 8 * q^16 + 11 * q^17 + 2 * q^18 - 19 * q^19 + 8 * q^20 + 7 * q^21 - 3 * q^22 + 13 * q^23 + 9 * q^25 - 7 * q^26 - 19 * q^27 - 24 * q^28 - 18 * q^29 + 12 * q^30 - 21 * q^31 - 3 * q^32 + 10 * q^33 - 10 * q^34 - 7 * q^35 + 14 * q^36 - 26 * q^37 - 2 * q^38 + 14 * q^39 - 27 * q^40 - 7 * q^41 + 16 * q^42 - 25 * q^43 - 5 * q^44 + 2 * q^45 - 11 * q^46 - 10 * q^47 - 8 * q^48 - 6 * q^49 - 16 * q^50 - 11 * q^51 - 37 * q^52 - 19 * q^53 - 2 * q^54 - 20 * q^55 - 33 * q^56 + 19 * q^57 - 27 * q^58 - 42 * q^59 - 8 * q^60 - 16 * q^61 - 6 * q^62 - 7 * q^63 - 32 * q^64 - q^65 + 3 * q^66 - 40 * q^67 + 6 * q^68 - 13 * q^69 - 29 * q^70 - 23 * q^71 + 7 * q^73 + 15 * q^74 - 9 * q^75 - 14 * q^76 + 42 * q^77 + 7 * q^78 - 26 * q^79 + 7 * q^80 + 19 * q^81 - 19 * q^82 - 14 * q^83 + 24 * q^84 - 37 * q^85 - 24 * q^86 + 18 * q^87 - 50 * q^88 - 3 * q^89 - 12 * q^90 - 60 * q^91 + 44 * q^92 + 21 * q^93 - 62 * q^94 - 2 * q^95 + 3 * q^96 - 44 * q^97 + 52 * q^98 - 10 * q^99

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