LMFDB - Embedded newform 4017.2.a.f.1.16

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			1.16
Root			$-1.49588$ 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)

$f(q)$	$=$	$q+1.49588 q^{2} +1.00000 q^{3} +0.237660 q^{4} -0.502630 q^{5} +1.49588 q^{6} -1.16688 q^{7} -2.63625 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.49588 q^{2} +1.00000 q^{3} +0.237660 q^{4} -0.502630 q^{5} +1.49588 q^{6} -1.16688 q^{7} -2.63625 q^{8} +1.00000 q^{9} -0.751875 q^{10} +2.95834 q^{11} +0.237660 q^{12} +1.00000 q^{13} -1.74551 q^{14} -0.502630 q^{15} -4.41884 q^{16} -7.31263 q^{17} +1.49588 q^{18} +0.915876 q^{19} -0.119455 q^{20} -1.16688 q^{21} +4.42533 q^{22} -2.85855 q^{23} -2.63625 q^{24} -4.74736 q^{25} +1.49588 q^{26} +1.00000 q^{27} -0.277319 q^{28} +0.163533 q^{29} -0.751875 q^{30} +9.20427 q^{31} -1.33755 q^{32} +2.95834 q^{33} -10.9388 q^{34} +0.586507 q^{35} +0.237660 q^{36} -7.57145 q^{37} +1.37004 q^{38} +1.00000 q^{39} +1.32506 q^{40} -1.38513 q^{41} -1.74551 q^{42} -9.31640 q^{43} +0.703078 q^{44} -0.502630 q^{45} -4.27604 q^{46} -0.624016 q^{47} -4.41884 q^{48} -5.63840 q^{49} -7.10149 q^{50} -7.31263 q^{51} +0.237660 q^{52} -5.00002 q^{53} +1.49588 q^{54} -1.48695 q^{55} +3.07618 q^{56} +0.915876 q^{57} +0.244626 q^{58} +11.8203 q^{59} -0.119455 q^{60} -11.5224 q^{61} +13.7685 q^{62} -1.16688 q^{63} +6.83686 q^{64} -0.502630 q^{65} +4.42533 q^{66} +15.0041 q^{67} -1.73792 q^{68} -2.85855 q^{69} +0.877345 q^{70} -4.99042 q^{71} -2.63625 q^{72} -12.4704 q^{73} -11.3260 q^{74} -4.74736 q^{75} +0.217667 q^{76} -3.45202 q^{77} +1.49588 q^{78} -14.4688 q^{79} +2.22104 q^{80} +1.00000 q^{81} -2.07199 q^{82} +3.35502 q^{83} -0.277319 q^{84} +3.67555 q^{85} -13.9362 q^{86} +0.163533 q^{87} -7.79893 q^{88} -11.5306 q^{89} -0.751875 q^{90} -1.16688 q^{91} -0.679361 q^{92} +9.20427 q^{93} -0.933453 q^{94} -0.460347 q^{95} -1.33755 q^{96} -7.39984 q^{97} -8.43438 q^{98} +2.95834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.49588	1.05775	0.528874	−	0.848700i	$-0.322614\pi$
$2$	1.49588	1.05775	0.528874	+	0.848700i	$0.322614\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.237660	0.118830
$5$	−0.502630	−0.224783	−0.112392	−	0.993664i	$-0.535851\pi$
$5$	−0.502630	−0.224783	−0.112392	+	0.993664i	$0.535851\pi$
$6$	1.49588	0.610691
$7$	−1.16688	−0.441038	−0.220519	−	0.975383i	$-0.570775\pi$
$7$	−1.16688	−0.441038	−0.220519	+	0.975383i	$0.570775\pi$
$8$	−2.63625	−0.932056
$9$	1.00000	0.333333
$10$	−0.751875	−0.237764
$11$	2.95834	0.891973	0.445987	−	0.895040i	$-0.352853\pi$
$11$	2.95834	0.891973	0.445987	+	0.895040i	$0.352853\pi$
$12$	0.237660	0.0686064
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.74551	−0.466506
$15$	−0.502630	−0.129779
$16$	−4.41884	−1.10471
$17$	−7.31263	−1.77357	−0.886786	−	0.462180i	$-0.847068\pi$
$17$	−7.31263	−1.77357	−0.886786	+	0.462180i	$0.847068\pi$
$18$	1.49588	0.352583
$19$	0.915876	0.210116	0.105058	−	0.994466i	$-0.466497\pi$
$19$	0.915876	0.210116	0.105058	+	0.994466i	$0.466497\pi$
$20$	−0.119455	−0.0267109
$21$	−1.16688	−0.254633
$22$	4.42533	0.943483
$23$	−2.85855	−0.596048	−0.298024	−	0.954558i	$-0.596328\pi$
$23$	−2.85855	−0.596048	−0.298024	+	0.954558i	$0.596328\pi$
$24$	−2.63625	−0.538123
$25$	−4.74736	−0.949473
$26$	1.49588	0.293366
$27$	1.00000	0.192450
$28$	−0.277319	−0.0524084
$29$	0.163533	0.0303673	0.0151836	−	0.999885i	$-0.495167\pi$
$29$	0.163533	0.0303673	0.0151836	+	0.999885i	$0.495167\pi$
$30$	−0.751875	−0.137273
$31$	9.20427	1.65314	0.826568	−	0.562836i	$-0.190290\pi$
$31$	9.20427	1.65314	0.826568	+	0.562836i	$0.190290\pi$
$32$	−1.33755	−0.236448
$33$	2.95834	0.514981
$34$	−10.9388	−1.87599
$35$	0.586507	0.0991378
$36$	0.237660	0.0396099
$37$	−7.57145	−1.24474	−0.622369	−	0.782724i	$-0.713830\pi$
$37$	−7.57145	−1.24474	−0.622369	+	0.782724i	$0.713830\pi$
$38$	1.37004	0.222250
$39$	1.00000	0.160128
$40$	1.32506	0.209510
$41$	−1.38513	−0.216321	−0.108161	−	0.994133i	$-0.534496\pi$
$41$	−1.38513	−0.216321	−0.108161	+	0.994133i	$0.534496\pi$
$42$	−1.74551	−0.269338
$43$	−9.31640	−1.42074	−0.710369	−	0.703830i	$-0.751472\pi$
$43$	−9.31640	−1.42074	−0.710369	+	0.703830i	$0.751472\pi$
$44$	0.703078	0.105993
$45$	−0.502630	−0.0749277
$46$	−4.27604	−0.630468
$47$	−0.624016	−0.0910221	−0.0455110	−	0.998964i	$-0.514492\pi$
$47$	−0.624016	−0.0910221	−0.0455110	+	0.998964i	$0.514492\pi$
$48$	−4.41884	−0.637804
$49$	−5.63840	−0.805486
$50$	−7.10149	−1.00430
$51$	−7.31263	−1.02397
$52$	0.237660	0.0329575
$53$	−5.00002	−0.686806	−0.343403	−	0.939188i	$-0.611580\pi$
$53$	−5.00002	−0.686806	−0.343403	+	0.939188i	$0.611580\pi$
$54$	1.49588	0.203564
$55$	−1.48695	−0.200501
$56$	3.07618	0.411071
$57$	0.915876	0.121311
$58$	0.244626	0.0321209
$59$	11.8203	1.53888	0.769439	−	0.638721i	$-0.220536\pi$
$59$	11.8203	1.53888	0.769439	+	0.638721i	$0.220536\pi$
$60$	−0.119455	−0.0154216
$61$	−11.5224	−1.47529	−0.737644	−	0.675190i	$-0.764061\pi$
$61$	−11.5224	−1.47529	−0.737644	+	0.675190i	$0.764061\pi$
$62$	13.7685	1.74860
$63$	−1.16688	−0.147013
$64$	6.83686	0.854607
$65$	−0.502630	−0.0623436
$66$	4.42533	0.544720
$67$	15.0041	1.83304	0.916521	−	0.399986i	$-0.130985\pi$
$67$	15.0041	1.83304	0.916521	+	0.399986i	$0.130985\pi$
$68$	−1.73792	−0.210753
$69$	−2.85855	−0.344128
$70$	0.877345	0.104863
$71$	−4.99042	−0.592253	−0.296127	−	0.955149i	$-0.595695\pi$
$71$	−4.99042	−0.592253	−0.296127	+	0.955149i	$0.595695\pi$
$72$	−2.63625	−0.310685
$73$	−12.4704	−1.45955	−0.729776	−	0.683687i	$-0.760376\pi$
$73$	−12.4704	−1.45955	−0.729776	+	0.683687i	$0.760376\pi$
$74$	−11.3260	−1.31662
$75$	−4.74736	−0.548178
$76$	0.217667	0.0249681
$77$	−3.45202	−0.393394
$78$	1.49588	0.169375
$79$	−14.4688	−1.62787	−0.813934	−	0.580958i	$-0.802678\pi$
$79$	−14.4688	−1.62787	−0.813934	+	0.580958i	$0.802678\pi$
$80$	2.22104	0.248320
$81$	1.00000	0.111111
$82$	−2.07199	−0.228813
$83$	3.35502	0.368261	0.184131	−	0.982902i	$-0.441053\pi$
$83$	3.35502	0.368261	0.184131	+	0.982902i	$0.441053\pi$
$84$	−0.277319	−0.0302580
$85$	3.67555	0.398669
$86$	−13.9362	−1.50278
$87$	0.163533	0.0175326
$88$	−7.79893	−0.831369
$89$	−11.5306	−1.22224	−0.611122	−	0.791537i	$-0.709281\pi$
$89$	−11.5306	−1.22224	−0.611122	+	0.791537i	$0.709281\pi$
$90$	−0.751875	−0.0792546
$91$	−1.16688	−0.122322
$92$	−0.679361	−0.0708283
$93$	9.20427	0.954439
$94$	−0.933453	−0.0962784
$95$	−0.460347	−0.0472306
$96$	−1.33755	−0.136513
$97$	−7.39984	−0.751340	−0.375670	−	0.926754i	$-0.622587\pi$
$97$	−7.39984	−0.751340	−0.375670	+	0.926754i	$0.622587\pi$
$98$	−8.43438	−0.852001
$99$	2.95834	0.297324
$100$	−1.12826	−0.112826
$101$	−13.5298	−1.34627	−0.673133	−	0.739522i	$-0.735052\pi$
$101$	−13.5298	−1.34627	−0.673133	+	0.739522i	$0.735052\pi$
$102$	−10.9388	−1.08310
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.63625	−0.258506
$105$	0.586507	0.0572372
$106$	−7.47943	−0.726467
$107$	−9.20834	−0.890204	−0.445102	−	0.895480i	$-0.646833\pi$
$107$	−9.20834	−0.890204	−0.445102	+	0.895480i	$0.646833\pi$
$108$	0.237660	0.0228688
$109$	10.8856	1.04265	0.521327	−	0.853357i	$-0.325437\pi$
$109$	10.8856	1.04265	0.521327	+	0.853357i	$0.325437\pi$
$110$	−2.22430	−0.212079
$111$	−7.57145	−0.718650
$112$	5.15623	0.487218
$113$	10.7461	1.01091	0.505453	−	0.862854i	$-0.331325\pi$
$113$	10.7461	1.01091	0.505453	+	0.862854i	$0.331325\pi$
$114$	1.37004	0.128316
$115$	1.43679	0.133982
$116$	0.0388652	0.00360854
$117$	1.00000	0.0924500
$118$	17.6818	1.62774
$119$	8.53293	0.782212
$120$	1.32506	0.120961
$121$	−2.24822	−0.204383
$122$	−17.2361	−1.56048
$123$	−1.38513	−0.124893
$124$	2.18749	0.196442
$125$	4.89932	0.438209
$126$	−1.74551	−0.155502
$127$	21.7967	1.93414	0.967071	−	0.254506i	$-0.0819130\pi$
$127$	21.7967	1.93414	0.967071	+	0.254506i	$0.0819130\pi$
$128$	12.9022	1.14041
$129$	−9.31640	−0.820263
$130$	−0.751875	−0.0659438
$131$	10.0569	0.878673	0.439336	−	0.898323i	$-0.355214\pi$
$131$	10.0569	0.878673	0.439336	+	0.898323i	$0.355214\pi$
$132$	0.703078	0.0611951
$133$	−1.06871	−0.0926692
$134$	22.4444	1.93890
$135$	−0.502630	−0.0432595
$136$	19.2779	1.65307
$137$	13.1206	1.12097	0.560483	−	0.828166i	$-0.310616\pi$
$137$	13.1206	1.12097	0.560483	+	0.828166i	$0.310616\pi$
$138$	−4.27604	−0.364001
$139$	−6.52635	−0.553558	−0.276779	−	0.960934i	$-0.589267\pi$
$139$	−6.52635	−0.553558	−0.276779	+	0.960934i	$0.589267\pi$
$140$	0.139389	0.0117805
$141$	−0.624016	−0.0525516
$142$	−7.46507	−0.626455
$143$	2.95834	0.247389
$144$	−4.41884	−0.368236
$145$	−0.0821966	−0.00682605
$146$	−18.6543	−1.54384
$147$	−5.63840	−0.465047
$148$	−1.79943	−0.147912
$149$	−8.22715	−0.673994	−0.336997	−	0.941506i	$-0.609411\pi$
$149$	−8.22715	−0.673994	−0.336997	+	0.941506i	$0.609411\pi$
$150$	−7.10149	−0.579834
$151$	9.53503	0.775950	0.387975	−	0.921670i	$-0.373175\pi$
$151$	9.53503	0.775950	0.387975	+	0.921670i	$0.373175\pi$
$152$	−2.41448	−0.195840
$153$	−7.31263	−0.591191
$154$	−5.16381	−0.416111
$155$	−4.62635	−0.371597
$156$	0.237660	0.0190280
$157$	7.48552	0.597409	0.298705	−	0.954346i	$-0.403445\pi$
$157$	7.48552	0.597409	0.298705	+	0.954346i	$0.403445\pi$
$158$	−21.6436	−1.72187
$159$	−5.00002	−0.396527
$160$	0.672294	0.0531495
$161$	3.33557	0.262879
$162$	1.49588	0.117528
$163$	−11.8541	−0.928486	−0.464243	−	0.885708i	$-0.653673\pi$
$163$	−11.8541	−0.928486	−0.464243	+	0.885708i	$0.653673\pi$
$164$	−0.329190	−0.0257054
$165$	−1.48695	−0.115759
$166$	5.01871	0.389528
$167$	−6.07120	−0.469804	−0.234902	−	0.972019i	$-0.575477\pi$
$167$	−6.07120	−0.469804	−0.234902	+	0.972019i	$0.575477\pi$
$168$	3.07618	0.237332
$169$	1.00000	0.0769231
$170$	5.49818	0.421691
$171$	0.915876	0.0700388
$172$	−2.21413	−0.168826
$173$	−19.9715	−1.51840	−0.759202	−	0.650855i	$-0.774410\pi$
$173$	−19.9715	−1.51840	−0.759202	+	0.650855i	$0.774410\pi$
$174$	0.244626	0.0185450
$175$	5.53958	0.418753
$176$	−13.0724	−0.985371
$177$	11.8203	0.888471
$178$	−17.2484	−1.29282
$179$	19.0378	1.42295	0.711474	−	0.702712i	$-0.248028\pi$
$179$	19.0378	1.42295	0.711474	+	0.702712i	$0.248028\pi$
$180$	−0.119455	−0.00890365
$181$	−12.9367	−0.961577	−0.480788	−	0.876837i	$-0.659649\pi$
$181$	−12.9367	−0.961577	−0.480788	+	0.876837i	$0.659649\pi$
$182$	−1.74551	−0.129386
$183$	−11.5224	−0.851757
$184$	7.53584	0.555550
$185$	3.80564	0.279796
$186$	13.7685	1.00956
$187$	−21.6332	−1.58198
$188$	−0.148303	−0.0108161
$189$	−1.16688	−0.0848777
$190$	−0.688625	−0.0499581
$191$	−20.7712	−1.50295	−0.751475	−	0.659761i	$-0.770657\pi$
$191$	−20.7712	−1.50295	−0.751475	+	0.659761i	$0.770657\pi$
$192$	6.83686	0.493408
$193$	−6.87826	−0.495108	−0.247554	−	0.968874i	$-0.579627\pi$
$193$	−6.87826	−0.495108	−0.247554	+	0.968874i	$0.579627\pi$
$194$	−11.0693	−0.794728
$195$	−0.502630	−0.0359941
$196$	−1.34002	−0.0957158
$197$	−16.3320	−1.16360	−0.581802	−	0.813331i	$-0.697652\pi$
$197$	−16.3320	−1.16360	−0.581802	+	0.813331i	$0.697652\pi$
$198$	4.42533	0.314494
$199$	12.7314	0.902508	0.451254	−	0.892396i	$-0.350977\pi$
$199$	12.7314	0.902508	0.451254	+	0.892396i	$0.350977\pi$
$200$	12.5152	0.884961
$201$	15.0041	1.05831
$202$	−20.2390	−1.42401
$203$	−0.190822	−0.0133931
$204$	−1.73792	−0.121679
$205$	0.696209	0.0486254
$206$	−1.49588	−0.104223
$207$	−2.85855	−0.198683
$208$	−4.41884	−0.306391
$209$	2.70948	0.187418
$210$	0.877345	0.0605426
$211$	0.935515	0.0644035	0.0322018	−	0.999481i	$-0.489748\pi$
$211$	0.935515	0.0644035	0.0322018	+	0.999481i	$0.489748\pi$
$212$	−1.18830	−0.0816130
$213$	−4.99042	−0.341938
$214$	−13.7746	−0.941611
$215$	4.68271	0.319358
$216$	−2.63625	−0.179374
$217$	−10.7402	−0.729095
$218$	16.2836	1.10286
$219$	−12.4704	−0.842672
$220$	−0.353389	−0.0238255
$221$	−7.31263	−0.491901
$222$	−11.3260	−0.760150
$223$	−11.2953	−0.756388	−0.378194	−	0.925726i	$-0.623455\pi$
$223$	−11.2953	−0.756388	−0.378194	+	0.925726i	$0.623455\pi$
$224$	1.56076	0.104282
$225$	−4.74736	−0.316491
$226$	16.0749	1.06928
$227$	22.4402	1.48941	0.744703	−	0.667396i	$-0.232591\pi$
$227$	22.4402	1.48941	0.744703	+	0.667396i	$0.232591\pi$
$228$	0.217667	0.0144153
$229$	−1.21949	−0.0805863	−0.0402932	−	0.999188i	$-0.512829\pi$
$229$	−1.21949	−0.0805863	−0.0402932	+	0.999188i	$0.512829\pi$
$230$	2.14927	0.141719
$231$	−3.45202	−0.227126
$232$	−0.431114	−0.0283040
$233$	10.3028	0.674960	0.337480	−	0.941333i	$-0.390425\pi$
$233$	10.3028	0.674960	0.337480	+	0.941333i	$0.390425\pi$
$234$	1.49588	0.0977888
$235$	0.313649	0.0204602
$236$	2.80922	0.182865
$237$	−14.4688	−0.939850
$238$	12.7642	0.827383
$239$	9.77089	0.632026	0.316013	−	0.948755i	$-0.397656\pi$
$239$	9.77089	0.632026	0.316013	+	0.948755i	$0.397656\pi$
$240$	2.22104	0.143368
$241$	−0.220147	−0.0141809	−0.00709047	−	0.999975i	$-0.502257\pi$
$241$	−0.220147	−0.0141809	−0.00709047	+	0.999975i	$0.502257\pi$
$242$	−3.36306	−0.216186
$243$	1.00000	0.0641500
$244$	−2.73840	−0.175308
$245$	2.83403	0.181060
$246$	−2.07199	−0.132105
$247$	0.915876	0.0582758
$248$	−24.2648	−1.54082
$249$	3.35502	0.212616
$250$	7.32880	0.463514
$251$	−14.3355	−0.904851	−0.452425	−	0.891802i	$-0.649441\pi$
$251$	−14.3355	−0.904851	−0.452425	+	0.891802i	$0.649441\pi$
$252$	−0.277319	−0.0174695
$253$	−8.45655	−0.531659
$254$	32.6052	2.04583
$255$	3.67555	0.230172
$256$	5.62648	0.351655
$257$	2.70580	0.168783	0.0843915	−	0.996433i	$-0.473105\pi$
$257$	2.70580	0.168783	0.0843915	+	0.996433i	$0.473105\pi$
$258$	−13.9362	−0.867631
$259$	8.83494	0.548976
$260$	−0.119455	−0.00740828
$261$	0.163533	0.0101224
$262$	15.0439	0.929414
$263$	18.9445	1.16817	0.584083	−	0.811694i	$-0.301454\pi$
$263$	18.9445	1.16817	0.584083	+	0.811694i	$0.301454\pi$
$264$	−7.79893	−0.479991
$265$	2.51316	0.154382
$266$	−1.59867	−0.0980207
$267$	−11.5306	−0.705662
$268$	3.56587	0.217820
$269$	−1.47665	−0.0900330	−0.0450165	−	0.998986i	$-0.514334\pi$
$269$	−1.47665	−0.0900330	−0.0450165	+	0.998986i	$0.514334\pi$
$270$	−0.751875	−0.0457577
$271$	9.56884	0.581266	0.290633	−	0.956835i	$-0.406134\pi$
$271$	9.56884	0.581266	0.290633	+	0.956835i	$0.406134\pi$
$272$	32.3133	1.95928
$273$	−1.16688	−0.0706225
$274$	19.6268	1.18570
$275$	−14.0443	−0.846904
$276$	−0.679361	−0.0408927
$277$	8.16508	0.490592	0.245296	−	0.969448i	$-0.421115\pi$
$277$	8.16508	0.490592	0.245296	+	0.969448i	$0.421115\pi$
$278$	−9.76264	−0.585524
$279$	9.20427	0.551046
$280$	−1.54618	−0.0924019
$281$	24.1909	1.44311	0.721554	−	0.692358i	$-0.243428\pi$
$281$	24.1909	1.44311	0.721554	+	0.692358i	$0.243428\pi$
$282$	−0.933453	−0.0555863
$283$	10.5806	0.628953	0.314476	−	0.949265i	$-0.398171\pi$
$283$	10.5806	0.628953	0.314476	+	0.949265i	$0.398171\pi$
$284$	−1.18602	−0.0703774
$285$	−0.460347	−0.0272686
$286$	4.42533	0.261675
$287$	1.61628	0.0954058
$288$	−1.33755	−0.0788160
$289$	36.4745	2.14556
$290$	−0.122956	−0.00722024
$291$	−7.39984	−0.433786
$292$	−2.96371	−0.173438
$293$	9.53889	0.557268	0.278634	−	0.960397i	$-0.410118\pi$
$293$	9.53889	0.557268	0.278634	+	0.960397i	$0.410118\pi$
$294$	−8.43438	−0.491903
$295$	−5.94126	−0.345914
$296$	19.9602	1.16017
$297$	2.95834	0.171660
$298$	−12.3068	−0.712916
$299$	−2.85855	−0.165314
$300$	−1.12826	−0.0651399
$301$	10.8711	0.626599
$302$	14.2633	0.820759
$303$	−13.5298	−0.777267
$304$	−4.04711	−0.232118
$305$	5.79149	0.331620
$306$	−10.9388	−0.625331
$307$	−26.6002	−1.51815	−0.759077	−	0.651001i	$-0.774349\pi$
$307$	−26.6002	−1.51815	−0.759077	+	0.651001i	$0.774349\pi$
$308$	−0.820405	−0.0467469
$309$	−1.00000	−0.0568880
$310$	−6.92047	−0.393056
$311$	−20.3769	−1.15547	−0.577734	−	0.816225i	$-0.696063\pi$
$311$	−20.3769	−1.15547	−0.577734	+	0.816225i	$0.696063\pi$
$312$	−2.63625	−0.149248
$313$	−10.8993	−0.616067	−0.308034	−	0.951375i	$-0.599671\pi$
$313$	−10.8993	−0.616067	−0.308034	+	0.951375i	$0.599671\pi$
$314$	11.1974	0.631908
$315$	0.586507	0.0330459
$316$	−3.43865	−0.193439
$317$	−1.63045	−0.0915755	−0.0457877	−	0.998951i	$-0.514580\pi$
$317$	−1.63045	−0.0915755	−0.0457877	+	0.998951i	$0.514580\pi$
$318$	−7.47943	−0.419426
$319$	0.483786	0.0270868
$320$	−3.43641	−0.192101
$321$	−9.20834	−0.513960
$322$	4.98961	0.278060
$323$	−6.69746	−0.372657
$324$	0.237660	0.0132033
$325$	−4.74736	−0.263336
$326$	−17.7323	−0.982103
$327$	10.8856	0.601977
$328$	3.65156	0.201623
$329$	0.728149	0.0401441
$330$	−2.22430	−0.122444
$331$	−22.7062	−1.24805	−0.624024	−	0.781405i	$-0.714503\pi$
$331$	−22.7062	−1.24805	−0.624024	+	0.781405i	$0.714503\pi$
$332$	0.797353	0.0437605
$333$	−7.57145	−0.414913
$334$	−9.08180	−0.496934
$335$	−7.54152	−0.412037
$336$	5.15623	0.281296
$337$	−15.3502	−0.836181	−0.418091	−	0.908405i	$-0.637301\pi$
$337$	−15.3502	−0.836181	−0.418091	+	0.908405i	$0.637301\pi$
$338$	1.49588	0.0813652
$339$	10.7461	0.583647
$340$	0.873530	0.0473738
$341$	27.2294	1.47455
$342$	1.37004	0.0740834
$343$	14.7474	0.796287
$344$	24.5604	1.32421
$345$	1.43679	0.0773543
$346$	−29.8750	−1.60609
$347$	12.3637	0.663720	0.331860	−	0.943329i	$-0.392324\pi$
$347$	12.3637	0.663720	0.331860	+	0.943329i	$0.392324\pi$
$348$	0.0388652	0.00208339
$349$	30.2055	1.61686	0.808432	−	0.588589i	$-0.200317\pi$
$349$	30.2055	1.61686	0.808432	+	0.588589i	$0.200317\pi$
$350$	8.28655	0.442935
$351$	1.00000	0.0533761
$352$	−3.95693	−0.210905
$353$	−9.39304	−0.499941	−0.249970	−	0.968253i	$-0.580421\pi$
$353$	−9.39304	−0.499941	−0.249970	+	0.968253i	$0.580421\pi$
$354$	17.6818	0.939778
$355$	2.50833	0.133129
$356$	−2.74036	−0.145239
$357$	8.53293	0.451610
$358$	28.4782	1.50512
$359$	23.5567	1.24327	0.621637	−	0.783306i	$-0.286468\pi$
$359$	23.5567	1.24327	0.621637	+	0.783306i	$0.286468\pi$
$360$	1.32506	0.0698368
$361$	−18.1612	−0.955851
$362$	−19.3517	−1.01711
$363$	−2.24822	−0.118001
$364$	−0.277319	−0.0145355
$365$	6.26801	0.328083
$366$	−17.2361	−0.900944
$367$	6.01381	0.313918	0.156959	−	0.987605i	$-0.449831\pi$
$367$	6.01381	0.313918	0.156959	+	0.987605i	$0.449831\pi$
$368$	12.6314	0.658460
$369$	−1.38513	−0.0721071
$370$	5.69278	0.295954
$371$	5.83440	0.302907
$372$	2.18749	0.113416
$373$	33.9967	1.76028	0.880142	−	0.474711i	$-0.157447\pi$
$373$	33.9967	1.76028	0.880142	+	0.474711i	$0.157447\pi$
$374$	−32.3608	−1.67334
$375$	4.89932	0.253000
$376$	1.64506	0.0848376
$377$	0.163533	0.00842237
$378$	−1.74551	−0.0897792
$379$	15.9566	0.819637	0.409819	−	0.912167i	$-0.365592\pi$
$379$	15.9566	0.819637	0.409819	+	0.912167i	$0.365592\pi$
$380$	−0.109406	−0.00561241
$381$	21.7967	1.11668
$382$	−31.0712	−1.58974
$383$	33.3442	1.70381	0.851904	−	0.523698i	$-0.175448\pi$
$383$	33.3442	1.70381	0.851904	+	0.523698i	$0.175448\pi$
$384$	12.9022	0.658414
$385$	1.73509	0.0884283
$386$	−10.2891	−0.523699
$387$	−9.31640	−0.473579
$388$	−1.75864	−0.0892816
$389$	−12.5316	−0.635379	−0.317689	−	0.948195i	$-0.602907\pi$
$389$	−12.5316	−0.635379	−0.317689	+	0.948195i	$0.602907\pi$
$390$	−0.751875	−0.0380727
$391$	20.9035	1.05713
$392$	14.8642	0.750758
$393$	10.0569	0.507302
$394$	−24.4307	−1.23080
$395$	7.27246	0.365917
$396$	0.703078	0.0353310
$397$	−24.6591	−1.23760	−0.618801	−	0.785547i	$-0.712381\pi$
$397$	−24.6591	−1.23760	−0.618801	+	0.785547i	$0.712381\pi$
$398$	19.0447	0.954625
$399$	−1.06871	−0.0535026
$400$	20.9778	1.04889
$401$	28.4982	1.42313	0.711566	−	0.702620i	$-0.247986\pi$
$401$	28.4982	1.42313	0.711566	+	0.702620i	$0.247986\pi$
$402$	22.4444	1.11942
$403$	9.20427	0.458498
$404$	−3.21549	−0.159977
$405$	−0.502630	−0.0249759
$406$	−0.285448	−0.0141665
$407$	−22.3989	−1.11027
$408$	19.2779	0.954399
$409$	19.1897	0.948871	0.474436	−	0.880290i	$-0.342652\pi$
$409$	19.1897	0.948871	0.474436	+	0.880290i	$0.342652\pi$
$410$	1.04145	0.0514334
$411$	13.1206	0.647190
$412$	−0.237660	−0.0117087
$413$	−13.7929	−0.678703
$414$	−4.27604	−0.210156
$415$	−1.68634	−0.0827790
$416$	−1.33755	−0.0655789
$417$	−6.52635	−0.319597
$418$	4.05305	0.198241
$419$	0.437456	0.0213711	0.0106856	−	0.999943i	$-0.496599\pi$
$419$	0.437456	0.0213711	0.0106856	+	0.999943i	$0.496599\pi$
$420$	0.139389	0.00680149
$421$	−9.87931	−0.481488	−0.240744	−	0.970589i	$-0.577391\pi$
$421$	−9.87931	−0.481488	−0.240744	+	0.970589i	$0.577391\pi$
$422$	1.39942	0.0681227
$423$	−0.624016	−0.0303407
$424$	13.1813	0.640141
$425$	34.7157	1.68396
$426$	−7.46507	−0.361684
$427$	13.4452	0.650657
$428$	−2.18845	−0.105783
$429$	2.95834	0.142830
$430$	7.00477	0.337800
$431$	−6.76233	−0.325730	−0.162865	−	0.986648i	$-0.552074\pi$
$431$	−6.76233	−0.325730	−0.162865	+	0.986648i	$0.552074\pi$
$432$	−4.41884	−0.212601
$433$	−20.4171	−0.981183	−0.490592	−	0.871390i	$-0.663219\pi$
$433$	−20.4171	−0.981183	−0.490592	+	0.871390i	$0.663219\pi$
$434$	−16.0661	−0.771199
$435$	−0.0821966	−0.00394102
$436$	2.58707	0.123898
$437$	−2.61807	−0.125239
$438$	−18.6543	−0.891335
$439$	28.8696	1.37787	0.688936	−	0.724822i	$-0.258078\pi$
$439$	28.8696	1.37787	0.688936	+	0.724822i	$0.258078\pi$
$440$	3.91998	0.186878
$441$	−5.63840	−0.268495
$442$	−10.9388	−0.520307
$443$	−32.4706	−1.54273	−0.771363	−	0.636396i	$-0.780425\pi$
$443$	−32.4706	−1.54273	−0.771363	+	0.636396i	$0.780425\pi$
$444$	−1.79943	−0.0853971
$445$	5.79564	0.274740
$446$	−16.8964	−0.800067
$447$	−8.22715	−0.389131
$448$	−7.97776	−0.376914
$449$	−37.9540	−1.79116	−0.895581	−	0.444899i	$-0.853240\pi$
$449$	−37.9540	−1.79116	−0.895581	+	0.444899i	$0.853240\pi$
$450$	−7.10149	−0.334767
$451$	−4.09769	−0.192953
$452$	2.55391	0.120126
$453$	9.53503	0.447995
$454$	33.5678	1.57542
$455$	0.586507	0.0274959
$456$	−2.41448	−0.113068
$457$	29.0493	1.35887	0.679435	−	0.733736i	$-0.262225\pi$
$457$	29.0493	1.35887	0.679435	+	0.733736i	$0.262225\pi$
$458$	−1.82422	−0.0852400
$459$	−7.31263	−0.341324
$460$	0.341467	0.0159210
$461$	22.2169	1.03474	0.517371	−	0.855761i	$-0.326911\pi$
$461$	22.2169	1.03474	0.517371	+	0.855761i	$0.326911\pi$
$462$	−5.16381	−0.240242
$463$	−33.1546	−1.54083	−0.770414	−	0.637545i	$-0.779950\pi$
$463$	−33.1546	−1.54083	−0.770414	+	0.637545i	$0.779950\pi$
$464$	−0.722625	−0.0335470
$465$	−4.62635	−0.214542
$466$	15.4118	0.713938
$467$	17.3575	0.803209	0.401605	−	0.915813i	$-0.368453\pi$
$467$	17.3575	0.803209	0.401605	+	0.915813i	$0.368453\pi$
$468$	0.237660	0.0109858
$469$	−17.5079	−0.808441
$470$	0.469182	0.0216418
$471$	7.48552	0.344915
$472$	−31.1614	−1.43432
$473$	−27.5611	−1.26726
$474$	−21.6436	−0.994124
$475$	−4.34800	−0.199500
$476$	2.02793	0.0929501
$477$	−5.00002	−0.228935
$478$	14.6161	0.668524
$479$	−16.9323	−0.773657	−0.386828	−	0.922152i	$-0.626429\pi$
$479$	−16.9323	−0.773657	−0.386828	+	0.922152i	$0.626429\pi$
$480$	0.672294	0.0306859
$481$	−7.57145	−0.345228
$482$	−0.329314	−0.0149999
$483$	3.33557	0.151774
$484$	−0.534311	−0.0242868
$485$	3.71938	0.168888
$486$	1.49588	0.0678545
$487$	4.97097	0.225256	0.112628	−	0.993637i	$-0.464073\pi$
$487$	4.97097	0.225256	0.112628	+	0.993637i	$0.464073\pi$
$488$	30.3758	1.37505
$489$	−11.8541	−0.536061
$490$	4.23937	0.191515
$491$	27.4068	1.23685	0.618425	−	0.785844i	$-0.287771\pi$
$491$	27.4068	1.23685	0.618425	+	0.785844i	$0.287771\pi$
$492$	−0.329190	−0.0148410
$493$	−1.19585	−0.0538586
$494$	1.37004	0.0616411
$495$	−1.48695	−0.0668335
$496$	−40.6722	−1.82624
$497$	5.82319	0.261206
$498$	5.01871	0.224894
$499$	−25.7598	−1.15317	−0.576583	−	0.817039i	$-0.695614\pi$
$499$	−25.7598	−1.15317	−0.576583	+	0.817039i	$0.695614\pi$
$500$	1.16437	0.0520723
$501$	−6.07120	−0.271241
$502$	−21.4443	−0.957104
$503$	30.2522	1.34888	0.674439	−	0.738331i	$-0.264386\pi$
$503$	30.2522	1.34888	0.674439	+	0.738331i	$0.264386\pi$
$504$	3.07618	0.137024
$505$	6.80049	0.302618
$506$	−12.6500	−0.562361
$507$	1.00000	0.0444116
$508$	5.18019	0.229834
$509$	−13.0135	−0.576811	−0.288406	−	0.957508i	$-0.593125\pi$
$509$	−13.0135	−0.576811	−0.288406	+	0.957508i	$0.593125\pi$
$510$	5.49818	0.243464
$511$	14.5514	0.643717
$512$	−17.3879	−0.768444
$513$	0.915876	0.0404369
$514$	4.04755	0.178530
$515$	0.502630	0.0221485
$516$	−2.21413	−0.0974718
$517$	−1.84605	−0.0811893
$518$	13.2160	0.580678
$519$	−19.9715	−0.876651
$520$	1.32506	0.0581077
$521$	21.0674	0.922980	0.461490	−	0.887145i	$-0.347315\pi$
$521$	21.0674	0.922980	0.461490	+	0.887145i	$0.347315\pi$
$522$	0.244626	0.0107070
$523$	29.7801	1.30219	0.651096	−	0.758995i	$-0.274310\pi$
$523$	29.7801	1.30219	0.651096	+	0.758995i	$0.274310\pi$
$524$	2.39011	0.104413
$525$	5.53958	0.241767
$526$	28.3387	1.23562
$527$	−67.3074	−2.93196
$528$	−13.0724	−0.568904
$529$	−14.8287	−0.644727
$530$	3.75939	0.163298
$531$	11.8203	0.512959
$532$	−0.253990	−0.0110119
$533$	−1.38513	−0.0599967
$534$	−17.2484	−0.746413
$535$	4.62839	0.200103
$536$	−39.5546	−1.70850
$537$	19.0378	0.821540
$538$	−2.20889	−0.0952321
$539$	−16.6803	−0.718472
$540$	−0.119455	−0.00514052
$541$	−7.66263	−0.329442	−0.164721	−	0.986340i	$-0.552672\pi$
$541$	−7.66263	−0.329442	−0.164721	+	0.986340i	$0.552672\pi$
$542$	14.3138	0.614832
$543$	−12.9367	−0.555167
$544$	9.78102	0.419358
$545$	−5.47145	−0.234371
$546$	−1.74551	−0.0747008
$547$	31.0741	1.32863	0.664317	−	0.747451i	$-0.268723\pi$
$547$	31.0741	1.32863	0.664317	+	0.747451i	$0.268723\pi$
$548$	3.11823	0.133204
$549$	−11.5224	−0.491762
$550$	−21.0086	−0.895811
$551$	0.149776	0.00638067
$552$	7.53584	0.320747
$553$	16.8833	0.717951
$554$	12.2140	0.518923
$555$	3.80564	0.161540
$556$	−1.55105	−0.0657792
$557$	28.1833	1.19417	0.597083	−	0.802180i	$-0.296326\pi$
$557$	28.1833	1.19417	0.597083	+	0.802180i	$0.296326\pi$
$558$	13.7685	0.582867
$559$	−9.31640	−0.394042
$560$	−2.59168	−0.109518
$561$	−21.6332	−0.913356
$562$	36.1867	1.52644
$563$	−3.00105	−0.126479	−0.0632396	−	0.997998i	$-0.520143\pi$
$563$	−3.00105	−0.126479	−0.0632396	+	0.997998i	$0.520143\pi$
$564$	−0.148303	−0.00624470
$565$	−5.40131	−0.227235
$566$	15.8274	0.665273
$567$	−1.16688	−0.0490042
$568$	13.1560	0.552013
$569$	27.3995	1.14865	0.574323	−	0.818629i	$-0.305265\pi$
$569$	27.3995	1.14865	0.574323	+	0.818629i	$0.305265\pi$
$570$	−0.688625	−0.0288433
$571$	−19.0484	−0.797149	−0.398575	−	0.917136i	$-0.630495\pi$
$571$	−19.0484	−0.797149	−0.398575	+	0.917136i	$0.630495\pi$
$572$	0.703078	0.0293972
$573$	−20.7712	−0.867729
$574$	2.41776	0.100915
$575$	13.5706	0.565931
$576$	6.83686	0.284869
$577$	−15.5982	−0.649360	−0.324680	−	0.945824i	$-0.605257\pi$
$577$	−15.5982	−0.649360	−0.324680	+	0.945824i	$0.605257\pi$
$578$	54.5615	2.26946
$579$	−6.87826	−0.285851
$580$	−0.0195348	−0.000811139 0
$581$	−3.91489	−0.162417
$582$	−11.0693	−0.458836
$583$	−14.7918	−0.612612
$584$	32.8751	1.36038
$585$	−0.502630	−0.0207812
$586$	14.2691	0.589449
$587$	1.06659	0.0440230	0.0220115	−	0.999758i	$-0.492993\pi$
$587$	1.06659	0.0440230	0.0220115	+	0.999758i	$0.492993\pi$
$588$	−1.34002	−0.0552615
$589$	8.42998	0.347351
$590$	−8.88742	−0.365889
$591$	−16.3320	−0.671807
$592$	33.4570	1.37507
$593$	−30.7876	−1.26429	−0.632147	−	0.774848i	$-0.717826\pi$
$593$	−30.7876	−1.26429	−0.632147	+	0.774848i	$0.717826\pi$
$594$	4.42533	0.181573
$595$	−4.28891	−0.175828
$596$	−1.95526	−0.0800906
$597$	12.7314	0.521063
$598$	−4.27604	−0.174860
$599$	−11.0979	−0.453446	−0.226723	−	0.973959i	$-0.572801\pi$
$599$	−11.0979	−0.453446	−0.226723	+	0.973959i	$0.572801\pi$
$600$	12.5152	0.510933
$601$	7.08826	0.289136	0.144568	−	0.989495i	$-0.453821\pi$
$601$	7.08826	0.289136	0.144568	+	0.989495i	$0.453821\pi$
$602$	16.2618	0.662783
$603$	15.0041	0.611014
$604$	2.26609	0.0922060
$605$	1.13002	0.0459419
$606$	−20.2390	−0.822152
$607$	−23.2987	−0.945664	−0.472832	−	0.881153i	$-0.656768\pi$
$607$	−23.2987	−0.945664	−0.472832	+	0.881153i	$0.656768\pi$
$608$	−1.22503	−0.0496816
$609$	−0.190822	−0.00773252
$610$	8.66338	0.350770
$611$	−0.624016	−0.0252450
$612$	−1.73792	−0.0702511
$613$	−36.9742	−1.49337	−0.746686	−	0.665177i	$-0.768356\pi$
$613$	−36.9742	−1.49337	−0.746686	+	0.665177i	$0.768356\pi$
$614$	−39.7907	−1.60582
$615$	0.696209	0.0280739
$616$	9.10038	0.366665
$617$	13.3667	0.538122	0.269061	−	0.963123i	$-0.413287\pi$
$617$	13.3667	0.538122	0.269061	+	0.963123i	$0.413287\pi$
$618$	−1.49588	−0.0601732
$619$	19.2573	0.774015	0.387008	−	0.922077i	$-0.373509\pi$
$619$	19.2573	0.774015	0.387008	+	0.922077i	$0.373509\pi$
$620$	−1.09950	−0.0441568
$621$	−2.85855	−0.114709
$622$	−30.4814	−1.22219
$623$	13.4548	0.539055
$624$	−4.41884	−0.176895
$625$	21.2743	0.850971
$626$	−16.3041	−0.651644
$627$	2.70948	0.108206
$628$	1.77901	0.0709901
$629$	55.3672	2.20763
$630$	0.877345	0.0349543
$631$	9.08691	0.361744	0.180872	−	0.983507i	$-0.442108\pi$
$631$	9.08691	0.361744	0.180872	+	0.983507i	$0.442108\pi$
$632$	38.1434	1.51726
$633$	0.935515	0.0371834
$634$	−2.43897	−0.0968637
$635$	−10.9557	−0.434763
$636$	−1.18830	−0.0471193
$637$	−5.63840	−0.223402
$638$	0.723686	0.0286510
$639$	−4.99042	−0.197418
$640$	−6.48505	−0.256344
$641$	−26.2358	−1.03625	−0.518127	−	0.855304i	$-0.673371\pi$
$641$	−26.2358	−1.03625	−0.518127	+	0.855304i	$0.673371\pi$
$642$	−13.7746	−0.543639
$643$	−28.9517	−1.14175	−0.570873	−	0.821039i	$-0.693395\pi$
$643$	−28.9517	−1.14175	−0.570873	+	0.821039i	$0.693395\pi$
$644$	0.792730	0.0312379
$645$	4.68271	0.184381
$646$	−10.0186	−0.394177
$647$	−7.91298	−0.311091	−0.155546	−	0.987829i	$-0.549714\pi$
$647$	−7.91298	−0.311091	−0.155546	+	0.987829i	$0.549714\pi$
$648$	−2.63625	−0.103562
$649$	34.9686	1.37264
$650$	−7.10149	−0.278543
$651$	−10.7402	−0.420943
$652$	−2.81724	−0.110332
$653$	−18.5191	−0.724710	−0.362355	−	0.932040i	$-0.618027\pi$
$653$	−18.5191	−0.724710	−0.362355	+	0.932040i	$0.618027\pi$
$654$	16.2836	0.636739
$655$	−5.05489	−0.197511
$656$	6.12067	0.238972
$657$	−12.4704	−0.486517
$658$	1.08922	0.0424624
$659$	4.57697	0.178293	0.0891467	−	0.996019i	$-0.471586\pi$
$659$	4.57697	0.178293	0.0891467	+	0.996019i	$0.471586\pi$
$660$	−0.353389	−0.0137556
$661$	14.0949	0.548227	0.274114	−	0.961697i	$-0.411616\pi$
$661$	14.0949	0.548227	0.274114	+	0.961697i	$0.411616\pi$
$662$	−33.9658	−1.32012
$663$	−7.31263	−0.283999
$664$	−8.84468	−0.343240
$665$	0.537168	0.0208305
$666$	−11.3260	−0.438873
$667$	−0.467466	−0.0181004
$668$	−1.44288	−0.0558267
$669$	−11.2953	−0.436701
$670$	−11.2812	−0.435831
$671$	−34.0871	−1.31592
$672$	1.56076	0.0602075
$673$	−22.4548	−0.865569	−0.432784	−	0.901497i	$-0.642469\pi$
$673$	−22.4548	−0.865569	−0.432784	+	0.901497i	$0.642469\pi$
$674$	−22.9621	−0.884468
$675$	−4.74736	−0.182726
$676$	0.237660	0.00914076
$677$	−2.34096	−0.0899705	−0.0449852	−	0.998988i	$-0.514324\pi$
$677$	−2.34096	−0.0899705	−0.0449852	+	0.998988i	$0.514324\pi$
$678$	16.0749	0.617352
$679$	8.63469	0.331369
$680$	−9.68967	−0.371582
$681$	22.4402	0.859909
$682$	40.7319	1.55971
$683$	−34.6502	−1.32585	−0.662926	−	0.748685i	$-0.730686\pi$
$683$	−34.6502	−1.32585	−0.662926	+	0.748685i	$0.730686\pi$
$684$	0.217667	0.00832270
$685$	−6.59480	−0.251974
$686$	22.0604	0.842271
$687$	−1.21949	−0.0465265
$688$	41.1677	1.56950
$689$	−5.00002	−0.190486
$690$	2.14927	0.0818213
$691$	−22.0698	−0.839576	−0.419788	−	0.907622i	$-0.637896\pi$
$691$	−22.0698	−0.839576	−0.419788	+	0.907622i	$0.637896\pi$
$692$	−4.74642	−0.180432
$693$	−3.45202	−0.131131
$694$	18.4947	0.702048
$695$	3.28034	0.124430
$696$	−0.431114	−0.0163413
$697$	10.1290	0.383661
$698$	45.1839	1.71023
$699$	10.3028	0.389689
$700$	1.31654	0.0497604
$701$	39.6992	1.49942	0.749708	−	0.661768i	$-0.230194\pi$
$701$	39.6992	1.49942	0.749708	+	0.661768i	$0.230194\pi$
$702$	1.49588	0.0564584
$703$	−6.93451	−0.261540
$704$	20.2258	0.762287
$705$	0.313649	0.0118127
$706$	−14.0509	−0.528811
$707$	15.7876	0.593754
$708$	2.80922	0.105577
$709$	−24.8331	−0.932626	−0.466313	−	0.884620i	$-0.654418\pi$
$709$	−24.8331	−0.932626	−0.466313	+	0.884620i	$0.654418\pi$
$710$	3.75217	0.140816
$711$	−14.4688	−0.542623
$712$	30.3976	1.13920
$713$	−26.3108	−0.985348
$714$	12.7642	0.477690
$715$	−1.48695	−0.0556089
$716$	4.52451	0.169089
$717$	9.77089	0.364900
$718$	35.2380	1.31507
$719$	19.4049	0.723681	0.361841	−	0.932240i	$-0.382148\pi$
$719$	19.4049	0.723681	0.361841	+	0.932240i	$0.382148\pi$
$720$	2.22104	0.0827733
$721$	1.16688	0.0434567
$722$	−27.1669	−1.01105
$723$	−0.220147	−0.00818737
$724$	−3.07453	−0.114264
$725$	−0.776350	−0.0288329
$726$	−3.36306	−0.124815
$727$	−2.92561	−0.108505	−0.0542524	−	0.998527i	$-0.517278\pi$
$727$	−2.92561	−0.108505	−0.0542524	+	0.998527i	$0.517278\pi$
$728$	3.07618	0.114011
$729$	1.00000	0.0370370
$730$	9.37620	0.347029
$731$	68.1274	2.51978
$732$	−2.73840	−0.101214
$733$	−24.3501	−0.899391	−0.449696	−	0.893182i	$-0.648468\pi$
$733$	−24.3501	−0.899391	−0.449696	+	0.893182i	$0.648468\pi$
$734$	8.99595	0.332046
$735$	2.83403	0.104535
$736$	3.82345	0.140934
$737$	44.3873	1.63503
$738$	−2.07199	−0.0762711
$739$	−6.81902	−0.250842	−0.125421	−	0.992104i	$-0.540028\pi$
$739$	−6.81902	−0.250842	−0.125421	+	0.992104i	$0.540028\pi$
$740$	0.904447	0.0332481
$741$	0.915876	0.0336456
$742$	8.72757	0.320399
$743$	−11.0218	−0.404351	−0.202176	−	0.979349i	$-0.564801\pi$
$743$	−11.0218	−0.404351	−0.202176	+	0.979349i	$0.564801\pi$
$744$	−24.2648	−0.889590
$745$	4.13522	0.151503
$746$	50.8550	1.86194
$747$	3.35502	0.122754
$748$	−5.14135	−0.187986
$749$	10.7450	0.392613
$750$	7.32880	0.267610
$751$	42.1117	1.53668	0.768339	−	0.640043i	$-0.221084\pi$
$751$	42.1117	1.53668	0.768339	+	0.640043i	$0.221084\pi$
$752$	2.75742	0.100553
$753$	−14.3355	−0.522416
$754$	0.244626	0.00890874
$755$	−4.79260	−0.174420
$756$	−0.277319	−0.0100860
$757$	−36.7263	−1.33484	−0.667421	−	0.744681i	$-0.732602\pi$
$757$	−36.7263	−1.33484	−0.667421	+	0.744681i	$0.732602\pi$
$758$	23.8692	0.866969
$759$	−8.45655	−0.306953
$760$	1.21359	0.0440216
$761$	−2.16894	−0.0786241	−0.0393121	−	0.999227i	$-0.512517\pi$
$761$	−2.16894	−0.0786241	−0.0393121	+	0.999227i	$0.512517\pi$
$762$	32.6052	1.18116
$763$	−12.7022	−0.459850
$764$	−4.93647	−0.178595
$765$	3.67555	0.132890
$766$	49.8789	1.80220
$767$	11.8203	0.426808
$768$	5.62648	0.203028
$769$	0.00853953	0.000307943 0	0.000153972	−	1.00000i	$-0.499951\pi$
$769$	0.00853953	0.000307943 0	0.000153972		1.00000i	$0.499951\pi$
$770$	2.59549	0.0935348
$771$	2.70580	0.0974469
$772$	−1.63469	−0.0588336
$773$	10.8299	0.389524	0.194762	−	0.980851i	$-0.437607\pi$
$773$	10.8299	0.389524	0.194762	+	0.980851i	$0.437607\pi$
$774$	−13.9362	−0.500927
$775$	−43.6960	−1.56961
$776$	19.5078	0.700290
$777$	8.83494	0.316952
$778$	−18.7458	−0.672071
$779$	−1.26861	−0.0454527
$780$	−0.119455	−0.00427717
$781$	−14.7634	−0.528274
$782$	31.2691	1.11818
$783$	0.163533	0.00584419
$784$	24.9152	0.889828
$785$	−3.76245	−0.134288
$786$	15.0439	0.536597
$787$	−19.9263	−0.710297	−0.355148	−	0.934810i	$-0.615570\pi$
$787$	−19.9263	−0.710297	−0.355148	+	0.934810i	$0.615570\pi$
$788$	−3.88145	−0.138271
$789$	18.9445	0.674441
$790$	10.8787	0.387048
$791$	−12.5393	−0.445848
$792$	−7.79893	−0.277123
$793$	−11.5224	−0.409171
$794$	−36.8870	−1.30907
$795$	2.51316	0.0891327
$796$	3.02575	0.107245
$797$	4.71207	0.166910	0.0834550	−	0.996512i	$-0.473405\pi$
$797$	4.71207	0.166910	0.0834550	+	0.996512i	$0.473405\pi$
$798$	−1.59867	−0.0565923
$799$	4.56320	0.161434
$800$	6.34984	0.224501
$801$	−11.5306	−0.407414
$802$	42.6299	1.50531
$803$	−36.8917	−1.30188
$804$	3.56587	0.125759
$805$	−1.67656	−0.0590909
$806$	13.7685	0.484975
$807$	−1.47665	−0.0519806
$808$	35.6680	1.25479
$809$	8.65692	0.304361	0.152181	−	0.988353i	$-0.451370\pi$
$809$	8.65692	0.304361	0.152181	+	0.988353i	$0.451370\pi$
$810$	−0.751875	−0.0264182
$811$	−2.89682	−0.101721	−0.0508606	−	0.998706i	$-0.516196\pi$
$811$	−2.89682	−0.101721	−0.0508606	+	0.998706i	$0.516196\pi$
$812$	−0.0453508	−0.00159150
$813$	9.56884	0.335594
$814$	−33.5061	−1.17439
$815$	5.95824	0.208708
$816$	32.3133	1.13119
$817$	−8.53267	−0.298520
$818$	28.7056	1.00367
$819$	−1.16688	−0.0407739
$820$	0.165461	0.00577815
$821$	30.8410	1.07636	0.538179	−	0.842830i	$-0.319112\pi$
$821$	30.8410	1.07636	0.538179	+	0.842830i	$0.319112\pi$
$822$	19.6268	0.684563
$823$	−41.7366	−1.45485	−0.727423	−	0.686189i	$-0.759282\pi$
$823$	−41.7366	−1.45485	−0.727423	+	0.686189i	$0.759282\pi$
$824$	2.63625	0.0918382
$825$	−14.0443	−0.488960
$826$	−20.6325	−0.717896
$827$	−24.0897	−0.837681	−0.418840	−	0.908060i	$-0.637563\pi$
$827$	−24.0897	−0.837681	−0.418840	+	0.908060i	$0.637563\pi$
$828$	−0.679361	−0.0236094
$829$	−25.1884	−0.874829	−0.437414	−	0.899260i	$-0.644106\pi$
$829$	−25.1884	−0.874829	−0.437414	+	0.899260i	$0.644106\pi$
$830$	−2.52256	−0.0875593
$831$	8.16508	0.283244
$832$	6.83686	0.237025
$833$	41.2315	1.42859
$834$	−9.76264	−0.338053
$835$	3.05157	0.105604
$836$	0.643933	0.0222709
$837$	9.20427	0.318146
$838$	0.654382	0.0226053
$839$	−4.88183	−0.168540	−0.0842698	−	0.996443i	$-0.526856\pi$
$839$	−4.88183	−0.168540	−0.0842698	+	0.996443i	$0.526856\pi$
$840$	−1.54618	−0.0533483
$841$	−28.9733	−0.999078
$842$	−14.7783	−0.509293
$843$	24.1909	0.833179
$844$	0.222334	0.00765306
$845$	−0.502630	−0.0172910
$846$	−0.933453	−0.0320928
$847$	2.62339	0.0901407
$848$	22.0943	0.758721
$849$	10.5806	0.363126
$850$	51.9305	1.78120
$851$	21.6433	0.741924
$852$	−1.18602	−0.0406324
$853$	−32.7499	−1.12134	−0.560668	−	0.828041i	$-0.689456\pi$
$853$	−32.7499	−1.12134	−0.560668	+	0.828041i	$0.689456\pi$
$854$	20.1124	0.688231
$855$	−0.460347	−0.0157435
$856$	24.2755	0.829720
$857$	7.27262	0.248428	0.124214	−	0.992255i	$-0.460359\pi$
$857$	7.27262	0.248428	0.124214	+	0.992255i	$0.460359\pi$
$858$	4.42533	0.151078
$859$	34.5000	1.17712	0.588562	−	0.808452i	$-0.299694\pi$
$859$	34.5000	1.17712	0.588562	+	0.808452i	$0.299694\pi$
$860$	1.11289	0.0379492
$861$	1.61628	0.0550826
$862$	−10.1156	−0.344540
$863$	−15.7451	−0.535969	−0.267984	−	0.963423i	$-0.586358\pi$
$863$	−15.7451	−0.535969	−0.267984	+	0.963423i	$0.586358\pi$
$864$	−1.33755	−0.0455044
$865$	10.0383	0.341312
$866$	−30.5416	−1.03784
$867$	36.4745	1.23874
$868$	−2.55252	−0.0866383
$869$	−42.8037	−1.45201
$870$	−0.122956	−0.00416861
$871$	15.0041	0.508395
$872$	−28.6972	−0.971811
$873$	−7.39984	−0.250447
$874$	−3.91633	−0.132472
$875$	−5.71690	−0.193266
$876$	−2.96371	−0.100135
$877$	−29.2283	−0.986969	−0.493484	−	0.869755i	$-0.664277\pi$
$877$	−29.2283	−0.986969	−0.493484	+	0.869755i	$0.664277\pi$
$878$	43.1855	1.45744
$879$	9.53889	0.321739
$880$	6.57060	0.221495
$881$	29.9312	1.00841	0.504204	−	0.863585i	$-0.331786\pi$
$881$	29.9312	1.00841	0.504204	+	0.863585i	$0.331786\pi$
$882$	−8.43438	−0.284000
$883$	−44.3133	−1.49126	−0.745630	−	0.666360i	$-0.767851\pi$
$883$	−44.3133	−1.49126	−0.745630	+	0.666360i	$0.767851\pi$
$884$	−1.73792	−0.0584525
$885$	−5.94126	−0.199713
$886$	−48.5722	−1.63181
$887$	50.6496	1.70065	0.850324	−	0.526260i	$-0.176406\pi$
$887$	50.6496	1.70065	0.850324	+	0.526260i	$0.176406\pi$
$888$	19.9602	0.669822
$889$	−25.4340	−0.853029
$890$	8.66959	0.290605
$891$	2.95834	0.0991082
$892$	−2.68443	−0.0898815
$893$	−0.571521	−0.0191252
$894$	−12.3068	−0.411602
$895$	−9.56895	−0.319855
$896$	−15.0553	−0.502962
$897$	−2.85855	−0.0954440
$898$	−56.7747	−1.89460
$899$	1.50520	0.0502013
$900$	−1.12826	−0.0376086
$901$	36.5633	1.21810
$902$	−6.12966	−0.204095
$903$	10.8711	0.361767
$904$	−28.3294	−0.942221
$905$	6.50237	0.216146
$906$	14.2633	0.473865
$907$	25.4483	0.844997	0.422499	−	0.906364i	$-0.361153\pi$
$907$	25.4483	0.844997	0.422499	+	0.906364i	$0.361153\pi$
$908$	5.33312	0.176986
$909$	−13.5298	−0.448755
$910$	0.877345	0.0290837
$911$	−49.0906	−1.62644	−0.813222	−	0.581953i	$-0.802289\pi$
$911$	−49.0906	−1.62644	−0.813222	+	0.581953i	$0.802289\pi$
$912$	−4.04711	−0.134013
$913$	9.92530	0.328479
$914$	43.4543	1.43734
$915$	5.79149	0.191461
$916$	−0.289824	−0.00957606
$917$	−11.7351	−0.387528
$918$	−10.9388	−0.361035
$919$	−14.9502	−0.493160	−0.246580	−	0.969122i	$-0.579307\pi$
$919$	−14.9502	−0.493160	−0.246580	+	0.969122i	$0.579307\pi$
$920$	−3.78774	−0.124878
$921$	−26.6002	−0.876506
$922$	33.2338	1.09450
$923$	−4.99042	−0.164262
$924$	−0.820405	−0.0269893
$925$	35.9444	1.18184
$926$	−49.5954	−1.62981
$927$	−1.00000	−0.0328443
$928$	−0.218734	−0.00718028
$929$	24.7380	0.811628	0.405814	−	0.913956i	$-0.366988\pi$
$929$	24.7380	0.811628	0.405814	+	0.913956i	$0.366988\pi$
$930$	−6.92047	−0.226931
$931$	−5.16408	−0.169246
$932$	2.44857	0.0802054
$933$	−20.3769	−0.667110
$934$	25.9648	0.849593
$935$	10.8735	0.355602
$936$	−2.63625	−0.0861686
$937$	−16.1921	−0.528973	−0.264486	−	0.964389i	$-0.585202\pi$
$937$	−16.1921	−0.528973	−0.264486	+	0.964389i	$0.585202\pi$
$938$	−26.1898	−0.855126
$939$	−10.8993	−0.355687
$940$	0.0745418	0.00243129
$941$	45.3240	1.47752	0.738760	−	0.673968i	$-0.235412\pi$
$941$	45.3240	1.47752	0.738760	+	0.673968i	$0.235412\pi$
$942$	11.1974	0.364832
$943$	3.95946	0.128938
$944$	−52.2322	−1.70001
$945$	0.586507	0.0190791
$946$	−41.2281	−1.34044
$947$	−35.0957	−1.14046	−0.570229	−	0.821486i	$-0.693145\pi$
$947$	−35.0957	−1.14046	−0.570229	+	0.821486i	$0.693145\pi$
$948$	−3.43865	−0.111682
$949$	−12.4704	−0.404807
$950$	−6.50409	−0.211020
$951$	−1.63045	−0.0528711
$952$	−22.4949	−0.729065
$953$	−59.7737	−1.93626	−0.968130	−	0.250446i	$-0.919423\pi$
$953$	−59.7737	−1.93626	−0.968130	+	0.250446i	$0.919423\pi$
$954$	−7.47943	−0.242156
$955$	10.4402	0.337838
$956$	2.32215	0.0751036
$957$	0.483786	0.0156386
$958$	−25.3287	−0.818334
$959$	−15.3101	−0.494388
$960$	−3.43641	−0.110910
$961$	53.7187	1.73286
$962$	−11.3260	−0.365164
$963$	−9.20834	−0.296735
$964$	−0.0523202	−0.00168512
$965$	3.45722	0.111292
$966$	4.98961	0.160538
$967$	−21.4280	−0.689077	−0.344539	−	0.938772i	$-0.611965\pi$
$967$	−21.4280	−0.689077	−0.344539	+	0.938772i	$0.611965\pi$
$968$	5.92686	0.190497
$969$	−6.69746	−0.215154
$970$	5.56375	0.178641
$971$	−55.3889	−1.77751	−0.888757	−	0.458378i	$-0.848431\pi$
$971$	−55.3889	−1.77751	−0.888757	+	0.458378i	$0.848431\pi$
$972$	0.237660	0.00762294
$973$	7.61544	0.244140
$974$	7.43597	0.238264
$975$	−4.74736	−0.152037
$976$	50.9154	1.62976
$977$	59.1114	1.89114	0.945571	−	0.325416i	$-0.105504\pi$
$977$	59.1114	1.89114	0.945571	+	0.325416i	$0.105504\pi$
$978$	−17.7323	−0.567018
$979$	−34.1115	−1.09021
$980$	0.673535	0.0215153
$981$	10.8856	0.347551
$982$	40.9972	1.30827
$983$	−17.2762	−0.551025	−0.275513	−	0.961297i	$-0.588848\pi$
$983$	−17.2762	−0.551025	−0.275513	+	0.961297i	$0.588848\pi$
$984$	3.65156	0.116407
$985$	8.20894	0.261559
$986$	−1.78886	−0.0569688
$987$	0.728149	0.0231772
$988$	0.217667	0.00692491
$989$	26.6313	0.846828
$990$	−2.22430	−0.0706930
$991$	−14.5711	−0.462865	−0.231432	−	0.972851i	$-0.574341\pi$
$991$	−14.5711	−0.462865	−0.231432	+	0.972851i	$0.574341\pi$
$992$	−12.3112	−0.390881
$993$	−22.7062	−0.720561
$994$	8.71080	0.276290
$995$	−6.39921	−0.202869
$996$	0.797353	0.0252651
$997$	−39.7122	−1.25770	−0.628849	−	0.777527i	$-0.716474\pi$
$997$	−39.7122	−1.25770	−0.628849	+	0.777527i	$0.716474\pi$
$998$	−38.5335	−1.21976
$999$	−7.57145	−0.239550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.16	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.49588 q^{2} +1.00000 q^{3} +0.237660 q^{4} -0.502630 q^{5} +1.49588 q^{6} -1.16688 q^{7} -2.63625 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.49588 q^{2} +1.00000 q^{3} +0.237660 q^{4} -0.502630 q^{5} +1.49588 q^{6} -1.16688 q^{7} -2.63625 q^{8} +1.00000 q^{9} -0.751875 q^{10} +2.95834 q^{11} +0.237660 q^{12} +1.00000 q^{13} -1.74551 q^{14} -0.502630 q^{15} -4.41884 q^{16} -7.31263 q^{17} +1.49588 q^{18} +0.915876 q^{19} -0.119455 q^{20} -1.16688 q^{21} +4.42533 q^{22} -2.85855 q^{23} -2.63625 q^{24} -4.74736 q^{25} +1.49588 q^{26} +1.00000 q^{27} -0.277319 q^{28} +0.163533 q^{29} -0.751875 q^{30} +9.20427 q^{31} -1.33755 q^{32} +2.95834 q^{33} -10.9388 q^{34} +0.586507 q^{35} +0.237660 q^{36} -7.57145 q^{37} +1.37004 q^{38} +1.00000 q^{39} +1.32506 q^{40} -1.38513 q^{41} -1.74551 q^{42} -9.31640 q^{43} +0.703078 q^{44} -0.502630 q^{45} -4.27604 q^{46} -0.624016 q^{47} -4.41884 q^{48} -5.63840 q^{49} -7.10149 q^{50} -7.31263 q^{51} +0.237660 q^{52} -5.00002 q^{53} +1.49588 q^{54} -1.48695 q^{55} +3.07618 q^{56} +0.915876 q^{57} +0.244626 q^{58} +11.8203 q^{59} -0.119455 q^{60} -11.5224 q^{61} +13.7685 q^{62} -1.16688 q^{63} +6.83686 q^{64} -0.502630 q^{65} +4.42533 q^{66} +15.0041 q^{67} -1.73792 q^{68} -2.85855 q^{69} +0.877345 q^{70} -4.99042 q^{71} -2.63625 q^{72} -12.4704 q^{73} -11.3260 q^{74} -4.74736 q^{75} +0.217667 q^{76} -3.45202 q^{77} +1.49588 q^{78} -14.4688 q^{79} +2.22104 q^{80} +1.00000 q^{81} -2.07199 q^{82} +3.35502 q^{83} -0.277319 q^{84} +3.67555 q^{85} -13.9362 q^{86} +0.163533 q^{87} -7.79893 q^{88} -11.5306 q^{89} -0.751875 q^{90} -1.16688 q^{91} -0.679361 q^{92} +9.20427 q^{93} -0.933453 q^{94} -0.460347 q^{95} -1.33755 q^{96} -7.39984 q^{97} -8.43438 q^{98} +2.95834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 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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