LMFDB - Embedded newform 4017.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0759064919$
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} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
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			1.14
Root			$-0.929067$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.929067 q^{2} +1.00000 q^{3} -1.13683 q^{4} +3.14855 q^{5} +0.929067 q^{6} -4.69509 q^{7} -2.91433 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.929067 q^{2} +1.00000 q^{3} -1.13683 q^{4} +3.14855 q^{5} +0.929067 q^{6} -4.69509 q^{7} -2.91433 q^{8} +1.00000 q^{9} +2.92521 q^{10} +3.66597 q^{11} -1.13683 q^{12} +1.00000 q^{13} -4.36205 q^{14} +3.14855 q^{15} -0.433937 q^{16} -1.38480 q^{17} +0.929067 q^{18} -7.63793 q^{19} -3.57938 q^{20} -4.69509 q^{21} +3.40593 q^{22} -6.10802 q^{23} -2.91433 q^{24} +4.91335 q^{25} +0.929067 q^{26} +1.00000 q^{27} +5.33754 q^{28} +7.71613 q^{29} +2.92521 q^{30} -8.72267 q^{31} +5.42550 q^{32} +3.66597 q^{33} -1.28658 q^{34} -14.7827 q^{35} -1.13683 q^{36} -6.63202 q^{37} -7.09614 q^{38} +1.00000 q^{39} -9.17590 q^{40} -5.87940 q^{41} -4.36205 q^{42} -5.93091 q^{43} -4.16760 q^{44} +3.14855 q^{45} -5.67476 q^{46} -4.57272 q^{47} -0.433937 q^{48} +15.0439 q^{49} +4.56483 q^{50} -1.38480 q^{51} -1.13683 q^{52} +3.98915 q^{53} +0.929067 q^{54} +11.5425 q^{55} +13.6830 q^{56} -7.63793 q^{57} +7.16880 q^{58} -3.82765 q^{59} -3.57938 q^{60} +5.46665 q^{61} -8.10394 q^{62} -4.69509 q^{63} +5.90853 q^{64} +3.14855 q^{65} +3.40593 q^{66} +2.19183 q^{67} +1.57429 q^{68} -6.10802 q^{69} -13.7341 q^{70} -1.33567 q^{71} -2.91433 q^{72} -0.304325 q^{73} -6.16159 q^{74} +4.91335 q^{75} +8.68306 q^{76} -17.2121 q^{77} +0.929067 q^{78} +7.29124 q^{79} -1.36627 q^{80} +1.00000 q^{81} -5.46236 q^{82} -16.2167 q^{83} +5.33754 q^{84} -4.36012 q^{85} -5.51021 q^{86} +7.71613 q^{87} -10.6838 q^{88} +0.821486 q^{89} +2.92521 q^{90} -4.69509 q^{91} +6.94381 q^{92} -8.72267 q^{93} -4.24837 q^{94} -24.0484 q^{95} +5.42550 q^{96} -16.2461 q^{97} +13.9768 q^{98} +3.66597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * 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 $

$2$	0.929067	0.656949	0.328475	−	0.944513i	$-0.393465\pi$
$2$	0.929067	0.656949	0.328475	+	0.944513i	$0.393465\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.13683	−0.568417
$5$	3.14855	1.40807	0.704037	−	0.710164i	$-0.251379\pi$
$5$	3.14855	1.40807	0.704037	+	0.710164i	$0.251379\pi$
$6$	0.929067	0.379290
$7$	−4.69509	−1.77458	−0.887289	−	0.461215i	$-0.847414\pi$
$7$	−4.69509	−1.77458	−0.887289	+	0.461215i	$0.847414\pi$
$8$	−2.91433	−1.03037
$9$	1.00000	0.333333
$10$	2.92521	0.925033
$11$	3.66597	1.10533	0.552666	−	0.833403i	$-0.313610\pi$
$11$	3.66597	1.10533	0.552666	+	0.833403i	$0.313610\pi$
$12$	−1.13683	−0.328176
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.36205	−1.16581
$15$	3.14855	0.812951
$16$	−0.433937	−0.108484
$17$	−1.38480	−0.335864	−0.167932	−	0.985799i	$-0.553709\pi$
$17$	−1.38480	−0.335864	−0.167932	+	0.985799i	$0.553709\pi$
$18$	0.929067	0.218983
$19$	−7.63793	−1.75226	−0.876130	−	0.482074i	$-0.839884\pi$
$19$	−7.63793	−1.75226	−0.876130	+	0.482074i	$0.839884\pi$
$20$	−3.57938	−0.800373
$21$	−4.69509	−1.02455
$22$	3.40593	0.726147
$23$	−6.10802	−1.27361	−0.636805	−	0.771025i	$-0.719744\pi$
$23$	−6.10802	−1.27361	−0.636805	+	0.771025i	$0.719744\pi$
$24$	−2.91433	−0.594885
$25$	4.91335	0.982670
$26$	0.929067	0.182205
$27$	1.00000	0.192450
$28$	5.33754	1.00870
$29$	7.71613	1.43285	0.716424	−	0.697665i	$-0.245777\pi$
$29$	7.71613	1.43285	0.716424	+	0.697665i	$0.245777\pi$
$30$	2.92521	0.534068
$31$	−8.72267	−1.56664	−0.783319	−	0.621620i	$-0.786475\pi$
$31$	−8.72267	−1.56664	−0.783319	+	0.621620i	$0.786475\pi$
$32$	5.42550	0.959102
$33$	3.66597	0.638164
$34$	−1.28658	−0.220646
$35$	−14.7827	−2.49873
$36$	−1.13683	−0.189472
$37$	−6.63202	−1.09030	−0.545149	−	0.838339i	$-0.683527\pi$
$37$	−6.63202	−1.09030	−0.545149	+	0.838339i	$0.683527\pi$
$38$	−7.09614	−1.15115
$39$	1.00000	0.160128
$40$	−9.17590	−1.45084
$41$	−5.87940	−0.918208	−0.459104	−	0.888383i	$-0.651829\pi$
$41$	−5.87940	−0.918208	−0.459104	+	0.888383i	$0.651829\pi$
$42$	−4.36205	−0.673079
$43$	−5.93091	−0.904455	−0.452227	−	0.891903i	$-0.649370\pi$
$43$	−5.93091	−0.904455	−0.452227	+	0.891903i	$0.649370\pi$
$44$	−4.16760	−0.628290
$45$	3.14855	0.469358
$46$	−5.67476	−0.836697
$47$	−4.57272	−0.667000	−0.333500	−	0.942750i	$-0.608230\pi$
$47$	−4.57272	−0.667000	−0.333500	+	0.942750i	$0.608230\pi$
$48$	−0.433937	−0.0626334
$49$	15.0439	2.14912
$50$	4.56483	0.645565
$51$	−1.38480	−0.193911
$52$	−1.13683	−0.157651
$53$	3.98915	0.547952	0.273976	−	0.961737i	$-0.411661\pi$
$53$	3.98915	0.547952	0.273976	+	0.961737i	$0.411661\pi$
$54$	0.929067	0.126430
$55$	11.5425	1.55639
$56$	13.6830	1.82847
$57$	−7.63793	−1.01167
$58$	7.16880	0.941309
$59$	−3.82765	−0.498317	−0.249159	−	0.968463i	$-0.580154\pi$
$59$	−3.82765	−0.498317	−0.249159	+	0.968463i	$0.580154\pi$
$60$	−3.57938	−0.462096
$61$	5.46665	0.699933	0.349967	−	0.936762i	$-0.386193\pi$
$61$	5.46665	0.699933	0.349967	+	0.936762i	$0.386193\pi$
$62$	−8.10394	−1.02920
$63$	−4.69509	−0.591526
$64$	5.90853	0.738566
$65$	3.14855	0.390529
$66$	3.40593	0.419241
$67$	2.19183	0.267774	0.133887	−	0.990997i	$-0.457254\pi$
$67$	2.19183	0.267774	0.133887	+	0.990997i	$0.457254\pi$
$68$	1.57429	0.190911
$69$	−6.10802	−0.735319
$70$	−13.7341	−1.64154
$71$	−1.33567	−0.158514	−0.0792572	−	0.996854i	$-0.525255\pi$
$71$	−1.33567	−0.158514	−0.0792572	+	0.996854i	$0.525255\pi$
$72$	−2.91433	−0.343457
$73$	−0.304325	−0.0356185	−0.0178093	−	0.999841i	$-0.505669\pi$
$73$	−0.304325	−0.0356185	−0.0178093	+	0.999841i	$0.505669\pi$
$74$	−6.16159	−0.716270
$75$	4.91335	0.567345
$76$	8.68306	0.996015
$77$	−17.2121	−1.96150
$78$	0.929067	0.105196
$79$	7.29124	0.820329	0.410164	−	0.912012i	$-0.365471\pi$
$79$	7.29124	0.820329	0.410164	+	0.912012i	$0.365471\pi$
$80$	−1.36627	−0.152754
$81$	1.00000	0.111111
$82$	−5.46236	−0.603216
$83$	−16.2167	−1.78001	−0.890005	−	0.455951i	$-0.849299\pi$
$83$	−16.2167	−1.78001	−0.890005	+	0.455951i	$0.849299\pi$
$84$	5.33754	0.582374
$85$	−4.36012	−0.472921
$86$	−5.51021	−0.594181
$87$	7.71613	0.827256
$88$	−10.6838	−1.13890
$89$	0.821486	0.0870773	0.0435386	−	0.999052i	$-0.486137\pi$
$89$	0.821486	0.0870773	0.0435386	+	0.999052i	$0.486137\pi$
$90$	2.92521	0.308344
$91$	−4.69509	−0.492179
$92$	6.94381	0.723942
$93$	−8.72267	−0.904499
$94$	−4.24837	−0.438186
$95$	−24.0484	−2.46731
$96$	5.42550	0.553738
$97$	−16.2461	−1.64954	−0.824769	−	0.565470i	$-0.808695\pi$
$97$	−16.2461	−1.64954	−0.824769	+	0.565470i	$0.808695\pi$
$98$	13.9768	1.41187
$99$	3.66597	0.368444
$100$	−5.58567	−0.558567
$101$	17.1465	1.70614	0.853072	−	0.521794i	$-0.174737\pi$
$101$	17.1465	1.70614	0.853072	+	0.521794i	$0.174737\pi$
$102$	−1.28658	−0.127390
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.91433	−0.285773
$105$	−14.7827	−1.44265
$106$	3.70619	0.359977
$107$	4.70211	0.454570	0.227285	−	0.973828i	$-0.427015\pi$
$107$	4.70211	0.454570	0.227285	+	0.973828i	$0.427015\pi$
$108$	−1.13683	−0.109392
$109$	15.9579	1.52849	0.764246	−	0.644925i	$-0.223112\pi$
$109$	15.9579	1.52849	0.764246	+	0.644925i	$0.223112\pi$
$110$	10.7237	1.02247
$111$	−6.63202	−0.629484
$112$	2.03737	0.192514
$113$	−5.02418	−0.472635	−0.236318	−	0.971676i	$-0.575941\pi$
$113$	−5.02418	−0.472635	−0.236318	+	0.971676i	$0.575941\pi$
$114$	−7.09614	−0.664615
$115$	−19.2314	−1.79334
$116$	−8.77196	−0.814456
$117$	1.00000	0.0924500
$118$	−3.55614	−0.327369
$119$	6.50178	0.596017
$120$	−9.17590	−0.837642
$121$	2.43935	0.221759
$122$	5.07888	0.459821
$123$	−5.87940	−0.530128
$124$	9.91623	0.890504
$125$	−0.272822	−0.0244020
$126$	−4.36205	−0.388603
$127$	−12.7035	−1.12726	−0.563629	−	0.826028i	$-0.690595\pi$
$127$	−12.7035	−1.12726	−0.563629	+	0.826028i	$0.690595\pi$
$128$	−5.36159	−0.473902
$129$	−5.93091	−0.522187
$130$	2.92521	0.256558
$131$	−21.2131	−1.85340	−0.926701	−	0.375800i	$-0.877368\pi$
$131$	−21.2131	−1.85340	−0.926701	+	0.375800i	$0.877368\pi$
$132$	−4.16760	−0.362743
$133$	35.8608	3.10952
$134$	2.03636	0.175914
$135$	3.14855	0.270984
$136$	4.03577	0.346065
$137$	−17.0264	−1.45466	−0.727331	−	0.686287i	$-0.759240\pi$
$137$	−17.0264	−1.45466	−0.727331	+	0.686287i	$0.759240\pi$
$138$	−5.67476	−0.483067
$139$	14.2045	1.20481	0.602406	−	0.798190i	$-0.294209\pi$
$139$	14.2045	1.20481	0.602406	+	0.798190i	$0.294209\pi$
$140$	16.8055	1.42032
$141$	−4.57272	−0.385093
$142$	−1.24092	−0.104136
$143$	3.66597	0.306564
$144$	−0.433937	−0.0361614
$145$	24.2946	2.01756
$146$	−0.282738	−0.0233996
$147$	15.0439	1.24080
$148$	7.53951	0.619744
$149$	−15.1983	−1.24509	−0.622547	−	0.782582i	$-0.713902\pi$
$149$	−15.1983	−1.24509	−0.622547	+	0.782582i	$0.713902\pi$
$150$	4.56483	0.372717
$151$	−0.494727	−0.0402603	−0.0201302	−	0.999797i	$-0.506408\pi$
$151$	−0.494727	−0.0402603	−0.0201302	+	0.999797i	$0.506408\pi$
$152$	22.2594	1.80548
$153$	−1.38480	−0.111955
$154$	−15.9912	−1.28860
$155$	−27.4637	−2.20594
$156$	−1.13683	−0.0910196
$157$	8.59300	0.685796	0.342898	−	0.939373i	$-0.388592\pi$
$157$	8.59300	0.685796	0.342898	+	0.939373i	$0.388592\pi$
$158$	6.77405	0.538914
$159$	3.98915	0.316360
$160$	17.0824	1.35049
$161$	28.6777	2.26012
$162$	0.929067	0.0729944
$163$	−1.70884	−0.133847	−0.0669235	−	0.997758i	$-0.521318\pi$
$163$	−1.70884	−0.133847	−0.0669235	+	0.997758i	$0.521318\pi$
$164$	6.68391	0.521925
$165$	11.5425	0.898581
$166$	−15.0664	−1.16938
$167$	−14.8814	−1.15155	−0.575777	−	0.817607i	$-0.695300\pi$
$167$	−14.8814	−1.15155	−0.575777	+	0.817607i	$0.695300\pi$
$168$	13.6830	1.05567
$169$	1.00000	0.0769231
$170$	−4.05084	−0.310686
$171$	−7.63793	−0.584087
$172$	6.74246	0.514108
$173$	−13.6698	−1.03929	−0.519647	−	0.854381i	$-0.673936\pi$
$173$	−13.6698	−1.03929	−0.519647	+	0.854381i	$0.673936\pi$
$174$	7.16880	0.543465
$175$	−23.0686	−1.74382
$176$	−1.59080	−0.119911
$177$	−3.82765	−0.287704
$178$	0.763215	0.0572054
$179$	−0.579218	−0.0432928	−0.0216464	−	0.999766i	$-0.506891\pi$
$179$	−0.579218	−0.0432928	−0.0216464	+	0.999766i	$0.506891\pi$
$180$	−3.57938	−0.266791
$181$	−11.7579	−0.873956	−0.436978	−	0.899472i	$-0.643951\pi$
$181$	−11.7579	−0.873956	−0.436978	+	0.899472i	$0.643951\pi$
$182$	−4.36205	−0.323337
$183$	5.46665	0.404107
$184$	17.8008	1.31229
$185$	−20.8812	−1.53522
$186$	−8.10394	−0.594210
$187$	−5.07665	−0.371242
$188$	5.19843	0.379135
$189$	−4.69509	−0.341518
$190$	−22.3425	−1.62090
$191$	−16.9560	−1.22689	−0.613445	−	0.789737i	$-0.710217\pi$
$191$	−16.9560	−1.22689	−0.613445	+	0.789737i	$0.710217\pi$
$192$	5.90853	0.426411
$193$	−21.4512	−1.54409	−0.772046	−	0.635566i	$-0.780767\pi$
$193$	−21.4512	−1.54409	−0.772046	+	0.635566i	$0.780767\pi$
$194$	−15.0937	−1.08366
$195$	3.14855	0.225472
$196$	−17.1024	−1.22160
$197$	18.6368	1.32781	0.663907	−	0.747815i	$-0.268897\pi$
$197$	18.6368	1.32781	0.663907	+	0.747815i	$0.268897\pi$
$198$	3.40593	0.242049
$199$	10.9977	0.779603	0.389802	−	0.920899i	$-0.372544\pi$
$199$	10.9977	0.779603	0.389802	+	0.920899i	$0.372544\pi$
$200$	−14.3191	−1.01251
$201$	2.19183	0.154600
$202$	15.9303	1.12085
$203$	−36.2279	−2.54270
$204$	1.57429	0.110223
$205$	−18.5116	−1.29290
$206$	−0.929067	−0.0647312
$207$	−6.10802	−0.424537
$208$	−0.433937	−0.0300881
$209$	−28.0004	−1.93683
$210$	−13.7341	−0.947745
$211$	−2.35793	−0.162327	−0.0811633	−	0.996701i	$-0.525864\pi$
$211$	−2.35793	−0.162327	−0.0811633	+	0.996701i	$0.525864\pi$
$212$	−4.53500	−0.311465
$213$	−1.33567	−0.0915183
$214$	4.36858	0.298630
$215$	−18.6737	−1.27354
$216$	−2.91433	−0.198295
$217$	40.9537	2.78012
$218$	14.8260	1.00414
$219$	−0.304325	−0.0205644
$220$	−13.1219	−0.884678
$221$	−1.38480	−0.0931520
$222$	−6.16159	−0.413539
$223$	3.34234	0.223820	0.111910	−	0.993718i	$-0.464303\pi$
$223$	3.34234	0.223820	0.111910	+	0.993718i	$0.464303\pi$
$224$	−25.4732	−1.70200
$225$	4.91335	0.327557
$226$	−4.66780	−0.310498
$227$	13.3109	0.883473	0.441737	−	0.897145i	$-0.354363\pi$
$227$	13.3109	0.883473	0.441737	+	0.897145i	$0.354363\pi$
$228$	8.68306	0.575050
$229$	7.85378	0.518992	0.259496	−	0.965744i	$-0.416443\pi$
$229$	7.85378	0.518992	0.259496	+	0.965744i	$0.416443\pi$
$230$	−17.8672	−1.17813
$231$	−17.2121	−1.13247
$232$	−22.4873	−1.47637
$233$	−13.6606	−0.894937	−0.447469	−	0.894300i	$-0.647674\pi$
$233$	−13.6606	−0.894937	−0.447469	+	0.894300i	$0.647674\pi$
$234$	0.929067	0.0607350
$235$	−14.3974	−0.939185
$236$	4.35140	0.283252
$237$	7.29124	0.473617
$238$	6.04059	0.391553
$239$	27.7402	1.79436	0.897182	−	0.441661i	$-0.145611\pi$
$239$	27.7402	1.79436	0.897182	+	0.441661i	$0.145611\pi$
$240$	−1.36627	−0.0881924
$241$	1.77288	0.114201	0.0571005	−	0.998368i	$-0.481814\pi$
$241$	1.77288	0.114201	0.0571005	+	0.998368i	$0.481814\pi$
$242$	2.26632	0.145685
$243$	1.00000	0.0641500
$244$	−6.21468	−0.397854
$245$	47.3663	3.02612
$246$	−5.46236	−0.348267
$247$	−7.63793	−0.485990
$248$	25.4207	1.61422
$249$	−16.2167	−1.02769
$250$	−0.253470	−0.0160309
$251$	16.9616	1.07061	0.535303	−	0.844660i	$-0.320197\pi$
$251$	16.9616	1.07061	0.535303	+	0.844660i	$0.320197\pi$
$252$	5.33754	0.336234
$253$	−22.3918	−1.40776
$254$	−11.8024	−0.740551
$255$	−4.36012	−0.273041
$256$	−16.7983	−1.04990
$257$	15.2020	0.948273	0.474137	−	0.880451i	$-0.342760\pi$
$257$	15.2020	0.948273	0.474137	+	0.880451i	$0.342760\pi$
$258$	−5.51021	−0.343051
$259$	31.1379	1.93482
$260$	−3.57938	−0.221984
$261$	7.71613	0.477616
$262$	−19.7084	−1.21759
$263$	−3.95883	−0.244112	−0.122056	−	0.992523i	$-0.538949\pi$
$263$	−3.95883	−0.244112	−0.122056	+	0.992523i	$0.538949\pi$
$264$	−10.6838	−0.657545
$265$	12.5600	0.771556
$266$	33.3170	2.04280
$267$	0.821486	0.0502741
$268$	−2.49175	−0.152208
$269$	19.8598	1.21087	0.605436	−	0.795894i	$-0.292999\pi$
$269$	19.8598	1.21087	0.605436	+	0.795894i	$0.292999\pi$
$270$	2.92521	0.178023
$271$	−1.84369	−0.111996	−0.0559982	−	0.998431i	$-0.517834\pi$
$271$	−1.84369	−0.111996	−0.0559982	+	0.998431i	$0.517834\pi$
$272$	0.600918	0.0364360
$273$	−4.69509	−0.284160
$274$	−15.8187	−0.955640
$275$	18.0122	1.08618
$276$	6.94381	0.417968
$277$	3.74630	0.225093	0.112547	−	0.993646i	$-0.464099\pi$
$277$	3.74630	0.225093	0.112547	+	0.993646i	$0.464099\pi$
$278$	13.1969	0.791500
$279$	−8.72267	−0.522213
$280$	43.0817	2.57462
$281$	6.65439	0.396967	0.198484	−	0.980104i	$-0.436398\pi$
$281$	6.65439	0.396967	0.198484	+	0.980104i	$0.436398\pi$
$282$	−4.24837	−0.252987
$283$	27.2685	1.62094	0.810472	−	0.585778i	$-0.199211\pi$
$283$	27.2685	1.62094	0.810472	+	0.585778i	$0.199211\pi$
$284$	1.51843	0.0901024
$285$	−24.0484	−1.42450
$286$	3.40593	0.201397
$287$	27.6043	1.62943
$288$	5.42550	0.319701
$289$	−15.0823	−0.887195
$290$	22.5713	1.32543
$291$	−16.2461	−0.952361
$292$	0.345967	0.0202462
$293$	14.1387	0.825992	0.412996	−	0.910733i	$-0.364482\pi$
$293$	14.1387	0.825992	0.412996	+	0.910733i	$0.364482\pi$
$294$	13.9768	0.815141
$295$	−12.0515	−0.701667
$296$	19.3279	1.12341
$297$	3.66597	0.212721
$298$	−14.1202	−0.817964
$299$	−6.10802	−0.353236
$300$	−5.58567	−0.322489
$301$	27.8461	1.60502
$302$	−0.459634	−0.0264490
$303$	17.1465	0.985042
$304$	3.31438	0.190093
$305$	17.2120	0.985557
$306$	−1.28658	−0.0735486
$307$	34.9776	1.99628	0.998138	−	0.0610040i	$-0.0194302\pi$
$307$	34.9776	1.99628	0.998138	+	0.0610040i	$0.0194302\pi$
$308$	19.5673	1.11495
$309$	−1.00000	−0.0568880
$310$	−25.5156	−1.44919
$311$	−18.7670	−1.06418	−0.532091	−	0.846687i	$-0.678593\pi$
$311$	−18.7670	−1.06418	−0.532091	+	0.846687i	$0.678593\pi$
$312$	−2.91433	−0.164991
$313$	24.3119	1.37419	0.687095	−	0.726567i	$-0.258885\pi$
$313$	24.3119	1.37419	0.687095	+	0.726567i	$0.258885\pi$
$314$	7.98347	0.450533
$315$	−14.7827	−0.832912
$316$	−8.28893	−0.466289
$317$	−18.0304	−1.01269	−0.506344	−	0.862331i	$-0.669004\pi$
$317$	−18.0304	−1.01269	−0.506344	+	0.862331i	$0.669004\pi$
$318$	3.70619	0.207833
$319$	28.2871	1.58377
$320$	18.6033	1.03995
$321$	4.70211	0.262446
$322$	26.6435	1.48478
$323$	10.5770	0.588522
$324$	−1.13683	−0.0631575
$325$	4.91335	0.272544
$326$	−1.58763	−0.0879307
$327$	15.9579	0.882475
$328$	17.1345	0.946095
$329$	21.4694	1.18364
$330$	10.7237	0.590323
$331$	29.4701	1.61982	0.809912	−	0.586552i	$-0.199515\pi$
$331$	29.4701	1.61982	0.809912	+	0.586552i	$0.199515\pi$
$332$	18.4357	1.01179
$333$	−6.63202	−0.363433
$334$	−13.8258	−0.756513
$335$	6.90108	0.377046
$336$	2.03737	0.111148
$337$	8.30639	0.452478	0.226239	−	0.974072i	$-0.427357\pi$
$337$	8.30639	0.452478	0.226239	+	0.974072i	$0.427357\pi$
$338$	0.929067	0.0505346
$339$	−5.02418	−0.272876
$340$	4.95674	0.268817
$341$	−31.9771	−1.73165
$342$	−7.09614	−0.383716
$343$	−37.7667	−2.03921
$344$	17.2846	0.931924
$345$	−19.2314	−1.03538
$346$	−12.7001	−0.682763
$347$	7.18591	0.385760	0.192880	−	0.981222i	$-0.438217\pi$
$347$	7.18591	0.385760	0.192880	+	0.981222i	$0.438217\pi$
$348$	−8.77196	−0.470226
$349$	−23.3022	−1.24734	−0.623670	−	0.781688i	$-0.714359\pi$
$349$	−23.3022	−1.24734	−0.623670	+	0.781688i	$0.714359\pi$
$350$	−21.4323	−1.14560
$351$	1.00000	0.0533761
$352$	19.8897	1.06013
$353$	8.21791	0.437395	0.218697	−	0.975793i	$-0.429819\pi$
$353$	8.21791	0.437395	0.218697	+	0.975793i	$0.429819\pi$
$354$	−3.55614	−0.189007
$355$	−4.20541	−0.223200
$356$	−0.933893	−0.0494962
$357$	6.50178	0.344111
$358$	−0.538132	−0.0284412
$359$	−30.3345	−1.60099	−0.800497	−	0.599336i	$-0.795431\pi$
$359$	−30.3345	−1.60099	−0.800497	+	0.599336i	$0.795431\pi$
$360$	−9.17590	−0.483613
$361$	39.3379	2.07042
$362$	−10.9239	−0.574145
$363$	2.43935	0.128033
$364$	5.33754	0.279763
$365$	−0.958181	−0.0501535
$366$	5.07888	0.265478
$367$	6.73011	0.351309	0.175654	−	0.984452i	$-0.443796\pi$
$367$	6.73011	0.351309	0.175654	+	0.984452i	$0.443796\pi$
$368$	2.65049	0.138167
$369$	−5.87940	−0.306069
$370$	−19.4001	−1.00856
$371$	−18.7294	−0.972383
$372$	9.91623	0.514133
$373$	−13.6857	−0.708621	−0.354310	−	0.935128i	$-0.615284\pi$
$373$	−13.6857	−0.708621	−0.354310	+	0.935128i	$0.615284\pi$
$374$	−4.71655	−0.243887
$375$	−0.272822	−0.0140885
$376$	13.3264	0.687258
$377$	7.71613	0.397401
$378$	−4.36205	−0.224360
$379$	0.374197	0.0192212	0.00961061	−	0.999954i	$-0.496941\pi$
$379$	0.374197	0.0192212	0.00961061	+	0.999954i	$0.496941\pi$
$380$	27.3390	1.40246
$381$	−12.7035	−0.650822
$382$	−15.7532	−0.806005
$383$	16.3288	0.834363	0.417182	−	0.908823i	$-0.363018\pi$
$383$	16.3288	0.834363	0.417182	+	0.908823i	$0.363018\pi$
$384$	−5.36159	−0.273607
$385$	−54.1930	−2.76193
$386$	−19.9296	−1.01439
$387$	−5.93091	−0.301485
$388$	18.4691	0.937626
$389$	−13.5414	−0.686577	−0.343289	−	0.939230i	$-0.611541\pi$
$389$	−13.5414	−0.686577	−0.343289	+	0.939230i	$0.611541\pi$
$390$	2.92521	0.148124
$391$	8.45841	0.427760
$392$	−43.8428	−2.21440
$393$	−21.2131	−1.07006
$394$	17.3148	0.872307
$395$	22.9568	1.15508
$396$	−4.16760	−0.209430
$397$	−29.0674	−1.45885	−0.729425	−	0.684061i	$-0.760212\pi$
$397$	−29.0674	−1.45885	−0.729425	+	0.684061i	$0.760212\pi$
$398$	10.2176	0.512160
$399$	35.8608	1.79528
$400$	−2.13208	−0.106604
$401$	−23.6137	−1.17921	−0.589606	−	0.807691i	$-0.700717\pi$
$401$	−23.6137	−1.17921	−0.589606	+	0.807691i	$0.700717\pi$
$402$	2.03636	0.101564
$403$	−8.72267	−0.434507
$404$	−19.4928	−0.969802
$405$	3.14855	0.156453
$406$	−33.6581	−1.67043
$407$	−24.3128	−1.20514
$408$	4.03577	0.199801
$409$	−9.27005	−0.458374	−0.229187	−	0.973382i	$-0.573607\pi$
$409$	−9.27005	−0.458374	−0.229187	+	0.973382i	$0.573607\pi$
$410$	−17.1985	−0.849373
$411$	−17.0264	−0.839850
$412$	1.13683	0.0560078
$413$	17.9711	0.884302
$414$	−5.67476	−0.278899
$415$	−51.0589	−2.50638
$416$	5.42550	0.266007
$417$	14.2045	0.695598
$418$	−26.0143	−1.27240
$419$	29.5869	1.44541	0.722706	−	0.691155i	$-0.242898\pi$
$419$	29.5869	1.44541	0.722706	+	0.691155i	$0.242898\pi$
$420$	16.8055	0.820025
$421$	−22.1064	−1.07740	−0.538700	−	0.842498i	$-0.681084\pi$
$421$	−22.1064	−1.07740	−0.538700	+	0.842498i	$0.681084\pi$
$422$	−2.19067	−0.106640
$423$	−4.57272	−0.222333
$424$	−11.6257	−0.564594
$425$	−6.80403	−0.330044
$426$	−1.24092	−0.0601229
$427$	−25.6664	−1.24209
$428$	−5.34553	−0.258386
$429$	3.66597	0.176995
$430$	−17.3492	−0.836650
$431$	24.2430	1.16774	0.583871	−	0.811846i	$-0.301537\pi$
$431$	24.2430	1.16774	0.583871	+	0.811846i	$0.301537\pi$
$432$	−0.433937	−0.0208778
$433$	−4.61462	−0.221764	−0.110882	−	0.993834i	$-0.535368\pi$
$433$	−4.61462	−0.221764	−0.110882	+	0.993834i	$0.535368\pi$
$434$	38.0487	1.82640
$435$	24.2946	1.16484
$436$	−18.1415	−0.868821
$437$	46.6526	2.23170
$438$	−0.282738	−0.0135097
$439$	26.4932	1.26445	0.632227	−	0.774783i	$-0.282141\pi$
$439$	26.4932	1.26445	0.632227	+	0.774783i	$0.282141\pi$
$440$	−33.6386	−1.60366
$441$	15.0439	0.716375
$442$	−1.28658	−0.0611962
$443$	21.5883	1.02569	0.512846	−	0.858480i	$-0.328591\pi$
$443$	21.5883	1.02569	0.512846	+	0.858480i	$0.328591\pi$
$444$	7.53951	0.357809
$445$	2.58649	0.122611
$446$	3.10526	0.147038
$447$	−15.1983	−0.718855
$448$	−27.7411	−1.31064
$449$	18.6259	0.879010	0.439505	−	0.898240i	$-0.355154\pi$
$449$	18.6259	0.879010	0.439505	+	0.898240i	$0.355154\pi$
$450$	4.56483	0.215188
$451$	−21.5537	−1.01492
$452$	5.71167	0.268654
$453$	−0.494727	−0.0232443
$454$	12.3667	0.580397
$455$	−14.7827	−0.693024
$456$	22.2594	1.04239
$457$	−7.94707	−0.371748	−0.185874	−	0.982574i	$-0.559512\pi$
$457$	−7.94707	−0.371748	−0.185874	+	0.982574i	$0.559512\pi$
$458$	7.29669	0.340952
$459$	−1.38480	−0.0646371
$460$	21.8629	1.01936
$461$	31.0672	1.44694	0.723471	−	0.690355i	$-0.242546\pi$
$461$	31.0672	1.44694	0.723471	+	0.690355i	$0.242546\pi$
$462$	−15.9912	−0.743976
$463$	−29.4215	−1.36734	−0.683668	−	0.729793i	$-0.739616\pi$
$463$	−29.4215	−1.36734	−0.683668	+	0.729793i	$0.739616\pi$
$464$	−3.34831	−0.155442
$465$	−27.4637	−1.27360
$466$	−12.6916	−0.587929
$467$	14.1749	0.655935	0.327967	−	0.944689i	$-0.393636\pi$
$467$	14.1749	0.655935	0.327967	+	0.944689i	$0.393636\pi$
$468$	−1.13683	−0.0525502
$469$	−10.2908	−0.475186
$470$	−13.3762	−0.616997
$471$	8.59300	0.395944
$472$	11.1550	0.513452
$473$	−21.7425	−0.999723
$474$	6.77405	0.311142
$475$	−37.5278	−1.72189
$476$	−7.39145	−0.338786
$477$	3.98915	0.182651
$478$	25.7725	1.17881
$479$	36.3637	1.66150	0.830751	−	0.556644i	$-0.187911\pi$
$479$	36.3637	1.66150	0.830751	+	0.556644i	$0.187911\pi$
$480$	17.0824	0.779704
$481$	−6.63202	−0.302394
$482$	1.64712	0.0750243
$483$	28.6777	1.30488
$484$	−2.77314	−0.126052
$485$	−51.1515	−2.32267
$486$	0.929067	0.0421433
$487$	0.341820	0.0154894	0.00774468	−	0.999970i	$-0.497535\pi$
$487$	0.341820	0.0154894	0.00774468	+	0.999970i	$0.497535\pi$
$488$	−15.9316	−0.721191
$489$	−1.70884	−0.0772766
$490$	44.0065	1.98801
$491$	−10.9861	−0.495795	−0.247897	−	0.968786i	$-0.579740\pi$
$491$	−10.9861	−0.495795	−0.247897	+	0.968786i	$0.579740\pi$
$492$	6.68391	0.301334
$493$	−10.6853	−0.481243
$494$	−7.09614	−0.319271
$495$	11.5425	0.518796
$496$	3.78509	0.169956
$497$	6.27107	0.281296
$498$	−15.0664	−0.675140
$499$	15.1965	0.680289	0.340145	−	0.940373i	$-0.389524\pi$
$499$	15.1965	0.680289	0.340145	+	0.940373i	$0.389524\pi$
$500$	0.310154	0.0138705
$501$	−14.8814	−0.664850
$502$	15.7585	0.703335
$503$	−9.09217	−0.405400	−0.202700	−	0.979241i	$-0.564972\pi$
$503$	−9.09217	−0.405400	−0.202700	+	0.979241i	$0.564972\pi$
$504$	13.6830	0.609491
$505$	53.9867	2.40237
$506$	−20.8035	−0.924828
$507$	1.00000	0.0444116
$508$	14.4418	0.640753
$509$	−25.9006	−1.14802	−0.574012	−	0.818847i	$-0.694614\pi$
$509$	−25.9006	−1.14802	−0.574012	+	0.818847i	$0.694614\pi$
$510$	−4.05084	−0.179374
$511$	1.42883	0.0632078
$512$	−4.88360	−0.215827
$513$	−7.63793	−0.337223
$514$	14.1237	0.622968
$515$	−3.14855	−0.138742
$516$	6.74246	0.296820
$517$	−16.7635	−0.737257
$518$	28.9292	1.27108
$519$	−13.6698	−0.600037
$520$	−9.17590	−0.402390
$521$	−20.4680	−0.896718	−0.448359	−	0.893853i	$-0.647991\pi$
$521$	−20.4680	−0.896718	−0.448359	+	0.893853i	$0.647991\pi$
$522$	7.16880	0.313770
$523$	−12.4803	−0.545725	−0.272862	−	0.962053i	$-0.587970\pi$
$523$	−12.4803	−0.545725	−0.272862	+	0.962053i	$0.587970\pi$
$524$	24.1158	1.05351
$525$	−23.0686	−1.00680
$526$	−3.67802	−0.160369
$527$	12.0792	0.526178
$528$	−1.59080	−0.0692307
$529$	14.3079	0.622081
$530$	11.6691	0.506873
$531$	−3.82765	−0.166106
$532$	−40.7678	−1.76751
$533$	−5.87940	−0.254665
$534$	0.763215	0.0330275
$535$	14.8048	0.640068
$536$	−6.38771	−0.275907
$537$	−0.579218	−0.0249951
$538$	18.4511	0.795482
$539$	55.1504	2.37550
$540$	−3.57938	−0.154032
$541$	−27.7287	−1.19215	−0.596074	−	0.802929i	$-0.703274\pi$
$541$	−27.7287	−1.19215	−0.596074	+	0.802929i	$0.703274\pi$
$542$	−1.71291	−0.0735760
$543$	−11.7579	−0.504579
$544$	−7.51326	−0.322128
$545$	50.2443	2.15223
$546$	−4.36205	−0.186679
$547$	−8.58270	−0.366970	−0.183485	−	0.983023i	$-0.558738\pi$
$547$	−8.58270	−0.366970	−0.183485	+	0.983023i	$0.558738\pi$
$548$	19.3562	0.826855
$549$	5.46665	0.233311
$550$	16.7345	0.713563
$551$	−58.9352	−2.51072
$552$	17.8008	0.757651
$553$	−34.2330	−1.45574
$554$	3.48056	0.147875
$555$	−20.8812	−0.886359
$556$	−16.1482	−0.684836
$557$	2.10505	0.0891939	0.0445970	−	0.999005i	$-0.485800\pi$
$557$	2.10505	0.0891939	0.0445970	+	0.999005i	$0.485800\pi$
$558$	−8.10394	−0.343067
$559$	−5.93091	−0.250851
$560$	6.41477	0.271073
$561$	−5.07665	−0.214336
$562$	6.18237	0.260788
$563$	−26.5316	−1.11818	−0.559088	−	0.829108i	$-0.688849\pi$
$563$	−26.5316	−1.11818	−0.559088	+	0.829108i	$0.688849\pi$
$564$	5.19843	0.218894
$565$	−15.8189	−0.665505
$566$	25.3342	1.06488
$567$	−4.69509	−0.197175
$568$	3.89257	0.163329
$569$	18.7496	0.786026	0.393013	−	0.919533i	$-0.371433\pi$
$569$	18.7496	0.786026	0.393013	+	0.919533i	$0.371433\pi$
$570$	−22.3425	−0.935826
$571$	16.0827	0.673040	0.336520	−	0.941676i	$-0.390750\pi$
$571$	16.0827	0.673040	0.336520	+	0.941676i	$0.390750\pi$
$572$	−4.16760	−0.174256
$573$	−16.9560	−0.708346
$574$	25.6463	1.07045
$575$	−30.0108	−1.25154
$576$	5.90853	0.246189
$577$	13.8339	0.575911	0.287955	−	0.957644i	$-0.407024\pi$
$577$	13.8339	0.575911	0.287955	+	0.957644i	$0.407024\pi$
$578$	−14.0125	−0.582842
$579$	−21.4512	−0.891482
$580$	−27.6189	−1.14681
$581$	76.1387	3.15876
$582$	−15.0937	−0.625653
$583$	14.6241	0.605669
$584$	0.886902	0.0367003
$585$	3.14855	0.130176
$586$	13.1358	0.542635
$587$	23.1993	0.957538	0.478769	−	0.877941i	$-0.341083\pi$
$587$	23.1993	0.957538	0.478769	+	0.877941i	$0.341083\pi$
$588$	−17.1024	−0.705291
$589$	66.6231	2.74516
$590$	−11.1967	−0.460960
$591$	18.6368	0.766614
$592$	2.87788	0.118280
$593$	28.3939	1.16600	0.582999	−	0.812473i	$-0.301879\pi$
$593$	28.3939	1.16600	0.582999	+	0.812473i	$0.301879\pi$
$594$	3.40593	0.139747
$595$	20.4712	0.839236
$596$	17.2780	0.707733
$597$	10.9977	0.450104
$598$	−5.67476	−0.232058
$599$	−31.8665	−1.30203	−0.651015	−	0.759065i	$-0.725657\pi$
$599$	−31.8665	−1.30203	−0.651015	+	0.759065i	$0.725657\pi$
$600$	−14.3191	−0.584576
$601$	−37.2545	−1.51964	−0.759821	−	0.650132i	$-0.774713\pi$
$601$	−37.2545	−1.51964	−0.759821	+	0.650132i	$0.774713\pi$
$602$	25.8709	1.05442
$603$	2.19183	0.0892582
$604$	0.562423	0.0228847
$605$	7.68041	0.312253
$606$	15.9303	0.647123
$607$	45.5927	1.85055	0.925275	−	0.379297i	$-0.123834\pi$
$607$	45.5927	1.85055	0.925275	+	0.379297i	$0.123834\pi$
$608$	−41.4396	−1.68060
$609$	−36.2279	−1.46803
$610$	15.9911	0.647461
$611$	−4.57272	−0.184993
$612$	1.57429	0.0636370
$613$	−38.1880	−1.54240	−0.771199	−	0.636594i	$-0.780343\pi$
$613$	−38.1880	−1.54240	−0.771199	+	0.636594i	$0.780343\pi$
$614$	32.4965	1.31145
$615$	−18.5116	−0.746458
$616$	50.1616	2.02107
$617$	17.1804	0.691656	0.345828	−	0.938298i	$-0.387598\pi$
$617$	17.1804	0.691656	0.345828	+	0.938298i	$0.387598\pi$
$618$	−0.929067	−0.0373725
$619$	38.3666	1.54208	0.771041	−	0.636785i	$-0.219736\pi$
$619$	38.3666	1.54208	0.771041	+	0.636785i	$0.219736\pi$
$620$	31.2217	1.25389
$621$	−6.10802	−0.245106
$622$	−17.4358	−0.699113
$623$	−3.85695	−0.154525
$624$	−0.433937	−0.0173714
$625$	−25.4257	−1.01703
$626$	22.5874	0.902774
$627$	−28.0004	−1.11823
$628$	−9.76882	−0.389818
$629$	9.18405	0.366192
$630$	−13.7341	−0.547181
$631$	−7.53014	−0.299770	−0.149885	−	0.988703i	$-0.547890\pi$
$631$	−7.53014	−0.299770	−0.149885	+	0.988703i	$0.547890\pi$
$632$	−21.2491	−0.845243
$633$	−2.35793	−0.0937193
$634$	−16.7515	−0.665285
$635$	−39.9977	−1.58726
$636$	−4.53500	−0.179825
$637$	15.0439	0.596060
$638$	26.2806	1.04046
$639$	−1.33567	−0.0528381
$640$	−16.8812	−0.667288
$641$	−15.8114	−0.624513	−0.312257	−	0.949998i	$-0.601085\pi$
$641$	−15.8114	−0.624513	−0.312257	+	0.949998i	$0.601085\pi$
$642$	4.36858	0.172414
$643$	−14.1819	−0.559278	−0.279639	−	0.960105i	$-0.590215\pi$
$643$	−14.1819	−0.559278	−0.279639	+	0.960105i	$0.590215\pi$
$644$	−32.6018	−1.28469
$645$	−18.6737	−0.735278
$646$	9.82677	0.386629
$647$	−43.6847	−1.71742	−0.858711	−	0.512460i	$-0.828734\pi$
$647$	−43.6847	−1.71742	−0.858711	+	0.512460i	$0.828734\pi$
$648$	−2.91433	−0.114486
$649$	−14.0320	−0.550806
$650$	4.56483	0.179047
$651$	40.9537	1.60510
$652$	1.94267	0.0760810
$653$	1.62995	0.0637849	0.0318925	−	0.999491i	$-0.489847\pi$
$653$	1.62995	0.0637849	0.0318925	+	0.999491i	$0.489847\pi$
$654$	14.8260	0.579741
$655$	−66.7906	−2.60972
$656$	2.55129	0.0996111
$657$	−0.304325	−0.0118728
$658$	19.9465	0.777594
$659$	19.4373	0.757169	0.378585	−	0.925567i	$-0.376411\pi$
$659$	19.4373	0.757169	0.378585	+	0.925567i	$0.376411\pi$
$660$	−13.1219	−0.510769
$661$	−6.47907	−0.252007	−0.126003	−	0.992030i	$-0.540215\pi$
$661$	−6.47907	−0.252007	−0.126003	+	0.992030i	$0.540215\pi$
$662$	27.3797	1.06414
$663$	−1.38480	−0.0537813
$664$	47.2607	1.83407
$665$	112.909	4.37843
$666$	−6.16159	−0.238757
$667$	−47.1302	−1.82489
$668$	16.9176	0.654563
$669$	3.34234	0.129222
$670$	6.41156	0.247700
$671$	20.0406	0.773659
$672$	−25.4732	−0.982651
$673$	−14.4547	−0.557188	−0.278594	−	0.960409i	$-0.589868\pi$
$673$	−14.4547	−0.557188	−0.278594	+	0.960409i	$0.589868\pi$
$674$	7.71719	0.297255
$675$	4.91335	0.189115
$676$	−1.13683	−0.0437244
$677$	11.7456	0.451418	0.225709	−	0.974195i	$-0.427530\pi$
$677$	11.7456	0.451418	0.225709	+	0.974195i	$0.427530\pi$
$678$	−4.66780	−0.179266
$679$	76.2767	2.92723
$680$	12.7068	0.487285
$681$	13.3109	0.510074
$682$	−29.7088	−1.13761
$683$	−18.6400	−0.713241	−0.356620	−	0.934249i	$-0.616071\pi$
$683$	−18.6400	−0.713241	−0.356620	+	0.934249i	$0.616071\pi$
$684$	8.68306	0.332005
$685$	−53.6084	−2.04827
$686$	−35.0878	−1.33966
$687$	7.85378	0.299640
$688$	2.57364	0.0981191
$689$	3.98915	0.151975
$690$	−17.8672	−0.680194
$691$	−37.5801	−1.42961	−0.714807	−	0.699322i	$-0.753486\pi$
$691$	−37.5801	−1.42961	−0.714807	+	0.699322i	$0.753486\pi$
$692$	15.5403	0.590753
$693$	−17.2121	−0.653832
$694$	6.67619	0.253425
$695$	44.7236	1.69646
$696$	−22.4873	−0.852380
$697$	8.14182	0.308393
$698$	−21.6493	−0.819439
$699$	−13.6606	−0.516692
$700$	26.2252	0.991220
$701$	−44.6994	−1.68827	−0.844136	−	0.536129i	$-0.819886\pi$
$701$	−44.6994	−1.68827	−0.844136	+	0.536129i	$0.819886\pi$
$702$	0.929067	0.0350654
$703$	50.6549	1.91049
$704$	21.6605	0.816361
$705$	−14.3974	−0.542239
$706$	7.63498	0.287346
$707$	−80.5045	−3.02768
$708$	4.35140	0.163536
$709$	13.6404	0.512274	0.256137	−	0.966640i	$-0.417550\pi$
$709$	13.6404	0.512274	0.256137	+	0.966640i	$0.417550\pi$
$710$	−3.90711	−0.146631
$711$	7.29124	0.273443
$712$	−2.39408	−0.0897219
$713$	53.2782	1.99528
$714$	6.04059	0.226063
$715$	11.5425	0.431665
$716$	0.658475	0.0246084
$717$	27.7402	1.03598
$718$	−28.1828	−1.05177
$719$	−26.5627	−0.990621	−0.495311	−	0.868716i	$-0.664946\pi$
$719$	−26.5627	−0.990621	−0.495311	+	0.868716i	$0.664946\pi$
$720$	−1.36627	−0.0509179
$721$	4.69509	0.174854
$722$	36.5476	1.36016
$723$	1.77288	0.0659340
$724$	13.3668	0.496772
$725$	37.9120	1.40802
$726$	2.26632	0.0841110
$727$	−36.1108	−1.33927	−0.669637	−	0.742688i	$-0.733550\pi$
$727$	−36.1108	−1.33927	−0.669637	+	0.742688i	$0.733550\pi$
$728$	13.6830	0.507127
$729$	1.00000	0.0370370
$730$	−0.890214	−0.0329483
$731$	8.21314	0.303774
$732$	−6.21468	−0.229701
$733$	39.2898	1.45120	0.725602	−	0.688115i	$-0.241561\pi$
$733$	39.2898	1.45120	0.725602	+	0.688115i	$0.241561\pi$
$734$	6.25272	0.230792
$735$	47.3663	1.74713
$736$	−33.1391	−1.22152
$737$	8.03518	0.295980
$738$	−5.46236	−0.201072
$739$	46.9341	1.72650	0.863249	−	0.504778i	$-0.168426\pi$
$739$	46.9341	1.72650	0.863249	+	0.504778i	$0.168426\pi$
$740$	23.7385	0.872645
$741$	−7.63793	−0.280586
$742$	−17.4009	−0.638806
$743$	−23.8962	−0.876666	−0.438333	−	0.898813i	$-0.644431\pi$
$743$	−23.8962	−0.876666	−0.438333	+	0.898813i	$0.644431\pi$
$744$	25.4207	0.931969
$745$	−47.8526	−1.75318
$746$	−12.7150	−0.465528
$747$	−16.2167	−0.593337
$748$	5.77132	0.211020
$749$	−22.0768	−0.806670
$750$	−0.253470	−0.00925542
$751$	10.5346	0.384413	0.192206	−	0.981355i	$-0.438436\pi$
$751$	10.5346	0.384413	0.192206	+	0.981355i	$0.438436\pi$
$752$	1.98427	0.0723591
$753$	16.9616	0.618115
$754$	7.16880	0.261072
$755$	−1.55767	−0.0566895
$756$	5.33754	0.194125
$757$	−49.2377	−1.78958	−0.894788	−	0.446492i	$-0.852673\pi$
$757$	−49.2377	−1.78958	−0.894788	+	0.446492i	$0.852673\pi$
$758$	0.347654	0.0126274
$759$	−22.3918	−0.812772
$760$	70.0849	2.54225
$761$	46.1843	1.67418	0.837090	−	0.547065i	$-0.184255\pi$
$761$	46.1843	1.67418	0.837090	+	0.547065i	$0.184255\pi$
$762$	−11.8024	−0.427557
$763$	−74.9239	−2.71243
$764$	19.2761	0.697386
$765$	−4.36012	−0.157640
$766$	15.1706	0.548134
$767$	−3.82765	−0.138208
$768$	−16.7983	−0.606157
$769$	31.4511	1.13415	0.567077	−	0.823665i	$-0.308074\pi$
$769$	31.4511	1.13415	0.567077	+	0.823665i	$0.308074\pi$
$770$	−50.3489	−1.81445
$771$	15.2020	0.547486
$772$	24.3865	0.877689
$773$	27.1044	0.974879	0.487440	−	0.873157i	$-0.337931\pi$
$773$	27.1044	0.974879	0.487440	+	0.873157i	$0.337931\pi$
$774$	−5.51021	−0.198060
$775$	−42.8575	−1.53949
$776$	47.3464	1.69964
$777$	31.1379	1.11707
$778$	−12.5809	−0.451047
$779$	44.9064	1.60894
$780$	−3.57938	−0.128162
$781$	−4.89652	−0.175211
$782$	7.85842	0.281017
$783$	7.71613	0.275752
$784$	−6.52809	−0.233146
$785$	27.0555	0.965651
$786$	−19.7084	−0.702976
$787$	18.6737	0.665647	0.332823	−	0.942989i	$-0.391999\pi$
$787$	18.6737	0.665647	0.332823	+	0.942989i	$0.391999\pi$
$788$	−21.1869	−0.754753
$789$	−3.95883	−0.140938
$790$	21.3284	0.758831
$791$	23.5890	0.838728
$792$	−10.6838	−0.379634
$793$	5.46665	0.194126
$794$	−27.0055	−0.958390
$795$	12.5600	0.445458
$796$	−12.5025	−0.443140
$797$	18.8959	0.669325	0.334663	−	0.942338i	$-0.391378\pi$
$797$	18.8959	0.669325	0.334663	+	0.942338i	$0.391378\pi$
$798$	33.3170	1.17941
$799$	6.33233	0.224022
$800$	26.6574	0.942481
$801$	0.821486	0.0290258
$802$	−21.9387	−0.774683
$803$	−1.11565	−0.0393703
$804$	−2.49175	−0.0878771
$805$	90.2931	3.18241
$806$	−8.10394	−0.285449
$807$	19.8598	0.699097
$808$	−49.9706	−1.75796
$809$	36.0760	1.26836	0.634182	−	0.773184i	$-0.281337\pi$
$809$	36.0760	1.26836	0.634182	+	0.773184i	$0.281337\pi$
$810$	2.92521	0.102781
$811$	−15.4598	−0.542866	−0.271433	−	0.962457i	$-0.587498\pi$
$811$	−15.4598	−0.542866	−0.271433	+	0.962457i	$0.587498\pi$
$812$	41.1851	1.44532
$813$	−1.84369	−0.0646612
$814$	−22.5882	−0.791717
$815$	−5.38038	−0.188466
$816$	0.600918	0.0210363
$817$	45.2998	1.58484
$818$	−8.61250	−0.301129
$819$	−4.69509	−0.164060
$820$	21.0446	0.734909
$821$	−34.1701	−1.19255	−0.596273	−	0.802782i	$-0.703352\pi$
$821$	−34.1701	−1.19255	−0.596273	+	0.802782i	$0.703352\pi$
$822$	−15.8187	−0.551739
$823$	−50.3955	−1.75668	−0.878339	−	0.478038i	$-0.841348\pi$
$823$	−50.3955	−1.75668	−0.878339	+	0.478038i	$0.841348\pi$
$824$	2.91433	0.101525
$825$	18.0122	0.627104
$826$	16.6964	0.580942
$827$	−6.01657	−0.209217	−0.104608	−	0.994513i	$-0.533359\pi$
$827$	−6.01657	−0.209217	−0.104608	+	0.994513i	$0.533359\pi$
$828$	6.94381	0.241314
$829$	−32.5108	−1.12915	−0.564573	−	0.825383i	$-0.690959\pi$
$829$	−32.5108	−1.12915	−0.564573	+	0.825383i	$0.690959\pi$
$830$	−47.4371	−1.64657
$831$	3.74630	0.129958
$832$	5.90853	0.204841
$833$	−20.8328	−0.721814
$834$	13.1969	0.456973
$835$	−46.8547	−1.62147
$836$	31.8319	1.10093
$837$	−8.72267	−0.301500
$838$	27.4882	0.949563
$839$	−50.0947	−1.72946	−0.864730	−	0.502236i	$-0.832511\pi$
$839$	−50.0947	−1.72946	−0.864730	+	0.502236i	$0.832511\pi$
$840$	43.0817	1.48646
$841$	30.5386	1.05306
$842$	−20.5383	−0.707797
$843$	6.65439	0.229189
$844$	2.68058	0.0922693
$845$	3.14855	0.108313
$846$	−4.24837	−0.146062
$847$	−11.4530	−0.393529
$848$	−1.73104	−0.0594442
$849$	27.2685	0.935852
$850$	−6.32140	−0.216822
$851$	40.5085	1.38861
$852$	1.51843	0.0520206
$853$	42.4941	1.45497	0.727486	−	0.686123i	$-0.240689\pi$
$853$	42.4941	1.45497	0.727486	+	0.686123i	$0.240689\pi$
$854$	−23.8458	−0.815987
$855$	−24.0484	−0.822437
$856$	−13.7035	−0.468376
$857$	6.24420	0.213298	0.106649	−	0.994297i	$-0.465988\pi$
$857$	6.24420	0.213298	0.106649	+	0.994297i	$0.465988\pi$
$858$	3.40593	0.116277
$859$	11.8174	0.403204	0.201602	−	0.979467i	$-0.435385\pi$
$859$	11.8174	0.403204	0.201602	+	0.979467i	$0.435385\pi$
$860$	21.2290	0.723901
$861$	27.6043	0.940752
$862$	22.5233	0.767148
$863$	37.3811	1.27247	0.636233	−	0.771497i	$-0.280492\pi$
$863$	37.3811	1.27247	0.636233	+	0.771497i	$0.280492\pi$
$864$	5.42550	0.184579
$865$	−43.0399	−1.46340
$866$	−4.28729	−0.145688
$867$	−15.0823	−0.512222
$868$	−46.5576	−1.58027
$869$	26.7295	0.906736
$870$	22.5713	0.765239
$871$	2.19183	0.0742673
$872$	−46.5066	−1.57491
$873$	−16.2461	−0.549846
$874$	43.3434	1.46611
$875$	1.28093	0.0433032
$876$	0.345967	0.0116891
$877$	28.9790	0.978550	0.489275	−	0.872130i	$-0.337261\pi$
$877$	28.9790	0.978550	0.489275	+	0.872130i	$0.337261\pi$
$878$	24.6140	0.830682
$879$	14.1387	0.476887
$880$	−5.00871	−0.168844
$881$	−56.3130	−1.89723	−0.948617	−	0.316426i	$-0.897517\pi$
$881$	−56.3130	−1.89723	−0.948617	+	0.316426i	$0.897517\pi$
$882$	13.9768	0.470622
$883$	29.1387	0.980596	0.490298	−	0.871555i	$-0.336888\pi$
$883$	29.1387	0.980596	0.490298	+	0.871555i	$0.336888\pi$
$884$	1.57429	0.0529492
$885$	−12.0515	−0.405108
$886$	20.0570	0.673828
$887$	16.7639	0.562877	0.281438	−	0.959579i	$-0.409188\pi$
$887$	16.7639	0.562877	0.281438	+	0.959579i	$0.409188\pi$
$888$	19.3279	0.648602
$889$	59.6443	2.00041
$890$	2.40302	0.0805494
$891$	3.66597	0.122815
$892$	−3.79969	−0.127223
$893$	34.9261	1.16876
$894$	−14.1202	−0.472252
$895$	−1.82370	−0.0609594
$896$	25.1731	0.840975
$897$	−6.10802	−0.203941
$898$	17.3047	0.577465
$899$	−67.3052	−2.24475
$900$	−5.58567	−0.186189
$901$	−5.52419	−0.184037
$902$	−20.0248	−0.666754
$903$	27.8461	0.926662
$904$	14.6421	0.486990
$905$	−37.0202	−1.23059
$906$	−0.459634	−0.0152703
$907$	45.8173	1.52134	0.760669	−	0.649140i	$-0.224871\pi$
$907$	45.8173	1.52134	0.760669	+	0.649140i	$0.224871\pi$
$908$	−15.1323	−0.502182
$909$	17.1465	0.568715
$910$	−13.7341	−0.455282
$911$	18.9879	0.629097	0.314548	−	0.949241i	$-0.398147\pi$
$911$	18.9879	0.629097	0.314548	+	0.949241i	$0.398147\pi$
$912$	3.31438	0.109750
$913$	−59.4498	−1.96750
$914$	−7.38336	−0.244220
$915$	17.2120	0.569012
$916$	−8.92845	−0.295004
$917$	99.5976	3.28900
$918$	−1.28658	−0.0424633
$919$	32.9904	1.08825	0.544127	−	0.839003i	$-0.316861\pi$
$919$	32.9904	1.08825	0.544127	+	0.839003i	$0.316861\pi$
$920$	56.0466	1.84780
$921$	34.9776	1.15255
$922$	28.8635	0.950568
$923$	−1.33567	−0.0439640
$924$	19.5673	0.643716
$925$	−32.5854	−1.07140
$926$	−27.3346	−0.898270
$927$	−1.00000	−0.0328443
$928$	41.8639	1.37425
$929$	−16.1133	−0.528660	−0.264330	−	0.964432i	$-0.585151\pi$
$929$	−16.1133	−0.528660	−0.264330	+	0.964432i	$0.585151\pi$
$930$	−25.5156	−0.836691
$931$	−114.904	−3.76583
$932$	15.5299	0.508698
$933$	−18.7670	−0.614405
$934$	13.1694	0.430916
$935$	−15.9841	−0.522735
$936$	−2.91433	−0.0952578
$937$	0.173319	0.00566207	0.00283103	−	0.999996i	$-0.499099\pi$
$937$	0.173319	0.00566207	0.00283103	+	0.999996i	$0.499099\pi$
$938$	−9.56087	−0.312173
$939$	24.3119	0.793390
$940$	16.3675	0.533849
$941$	5.52136	0.179991	0.0899956	−	0.995942i	$-0.471315\pi$
$941$	5.52136	0.179991	0.0899956	+	0.995942i	$0.471315\pi$
$942$	7.98347	0.260115
$943$	35.9115	1.16944
$944$	1.66096	0.0540596
$945$	−14.7827	−0.480882
$946$	−20.2003	−0.656768
$947$	−51.7119	−1.68041	−0.840206	−	0.542267i	$-0.817566\pi$
$947$	−51.7119	−1.68041	−0.840206	+	0.542267i	$0.817566\pi$
$948$	−8.28893	−0.269212
$949$	−0.304325	−0.00987880
$950$	−34.8658	−1.13120
$951$	−18.0304	−0.584676
$952$	−18.9483	−0.614119
$953$	25.6040	0.829394	0.414697	−	0.909959i	$-0.363888\pi$
$953$	25.6040	0.829394	0.414697	+	0.909959i	$0.363888\pi$
$954$	3.70619	0.119992
$955$	−53.3867	−1.72755
$956$	−31.5360	−1.01995
$957$	28.2871	0.914392
$958$	33.7844	1.09152
$959$	79.9404	2.58141
$960$	18.6033	0.600418
$961$	45.0850	1.45435
$962$	−6.16159	−0.198658
$963$	4.70211	0.151523
$964$	−2.01547	−0.0649138
$965$	−67.5402	−2.17419
$966$	26.6435	0.857240
$967$	−23.3263	−0.750124	−0.375062	−	0.927000i	$-0.622379\pi$
$967$	−23.3263	−0.750124	−0.375062	+	0.927000i	$0.622379\pi$
$968$	−7.10907	−0.228494
$969$	10.5770	0.339783
$970$	−47.5231	−1.52588
$971$	−1.90017	−0.0609793	−0.0304896	−	0.999535i	$-0.509707\pi$
$971$	−1.90017	−0.0609793	−0.0304896	+	0.999535i	$0.509707\pi$
$972$	−1.13683	−0.0364640
$973$	−66.6915	−2.13803
$974$	0.317574	0.0101757
$975$	4.91335	0.157353
$976$	−2.37218	−0.0759317
$977$	−7.66118	−0.245103	−0.122551	−	0.992462i	$-0.539108\pi$
$977$	−7.66118	−0.245103	−0.122551	+	0.992462i	$0.539108\pi$
$978$	−1.58763	−0.0507668
$979$	3.01154	0.0962493
$980$	−53.8477	−1.72010
$981$	15.9579	0.509497
$982$	−10.2068	−0.325712
$983$	9.05108	0.288685	0.144342	−	0.989528i	$-0.453893\pi$
$983$	9.05108	0.288685	0.144342	+	0.989528i	$0.453893\pi$
$984$	17.1345	0.546228
$985$	58.6787	1.86966
$986$	−9.92738	−0.316152
$987$	21.4694	0.683377
$988$	8.68306	0.276245
$989$	36.2261	1.15192
$990$	10.7237	0.340823
$991$	57.7773	1.83536	0.917678	−	0.397326i	$-0.130062\pi$
$991$	57.7773	1.83536	0.917678	+	0.397326i	$0.130062\pi$
$992$	−47.3249	−1.50257
$993$	29.4701	0.935206
$994$	5.82625	0.184797
$995$	34.6266	1.09774
$996$	18.4357	0.584156
$997$	−47.4482	−1.50270	−0.751349	−	0.659905i	$-0.770597\pi$
$997$	−47.4482	−1.50270	−0.751349	+	0.659905i	$0.770597\pi$
$998$	14.1186	0.446916
$999$	−6.63202	−0.209828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.14	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.14	✓	19	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.929067 q^{2} +1.00000 q^{3} -1.13683 q^{4} +3.14855 q^{5} +0.929067 q^{6} -4.69509 q^{7} -2.91433 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.929067 q^{2} +1.00000 q^{3} -1.13683 q^{4} +3.14855 q^{5} +0.929067 q^{6} -4.69509 q^{7} -2.91433 q^{8} +1.00000 q^{9} +2.92521 q^{10} +3.66597 q^{11} -1.13683 q^{12} +1.00000 q^{13} -4.36205 q^{14} +3.14855 q^{15} -0.433937 q^{16} -1.38480 q^{17} +0.929067 q^{18} -7.63793 q^{19} -3.57938 q^{20} -4.69509 q^{21} +3.40593 q^{22} -6.10802 q^{23} -2.91433 q^{24} +4.91335 q^{25} +0.929067 q^{26} +1.00000 q^{27} +5.33754 q^{28} +7.71613 q^{29} +2.92521 q^{30} -8.72267 q^{31} +5.42550 q^{32} +3.66597 q^{33} -1.28658 q^{34} -14.7827 q^{35} -1.13683 q^{36} -6.63202 q^{37} -7.09614 q^{38} +1.00000 q^{39} -9.17590 q^{40} -5.87940 q^{41} -4.36205 q^{42} -5.93091 q^{43} -4.16760 q^{44} +3.14855 q^{45} -5.67476 q^{46} -4.57272 q^{47} -0.433937 q^{48} +15.0439 q^{49} +4.56483 q^{50} -1.38480 q^{51} -1.13683 q^{52} +3.98915 q^{53} +0.929067 q^{54} +11.5425 q^{55} +13.6830 q^{56} -7.63793 q^{57} +7.16880 q^{58} -3.82765 q^{59} -3.57938 q^{60} +5.46665 q^{61} -8.10394 q^{62} -4.69509 q^{63} +5.90853 q^{64} +3.14855 q^{65} +3.40593 q^{66} +2.19183 q^{67} +1.57429 q^{68} -6.10802 q^{69} -13.7341 q^{70} -1.33567 q^{71} -2.91433 q^{72} -0.304325 q^{73} -6.16159 q^{74} +4.91335 q^{75} +8.68306 q^{76} -17.2121 q^{77} +0.929067 q^{78} +7.29124 q^{79} -1.36627 q^{80} +1.00000 q^{81} -5.46236 q^{82} -16.2167 q^{83} +5.33754 q^{84} -4.36012 q^{85} -5.51021 q^{86} +7.71613 q^{87} -10.6838 q^{88} +0.821486 q^{89} +2.92521 q^{90} -4.69509 q^{91} +6.94381 q^{92} -8.72267 q^{93} -4.24837 q^{94} -24.0484 q^{95} +5.42550 q^{96} -16.2461 q^{97} +13.9768 q^{98} +3.66597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

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