LMFDB - Embedded newform 4017.2.a.f.1.10

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			1.10
Root			$0.116858$ 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)

$f(q)$	$=$	$q-0.116858 q^{2} +1.00000 q^{3} -1.98634 q^{4} -1.39349 q^{5} -0.116858 q^{6} -4.81215 q^{7} +0.465837 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.116858 q^{2} +1.00000 q^{3} -1.98634 q^{4} -1.39349 q^{5} -0.116858 q^{6} -4.81215 q^{7} +0.465837 q^{8} +1.00000 q^{9} +0.162841 q^{10} +1.77929 q^{11} -1.98634 q^{12} +1.00000 q^{13} +0.562339 q^{14} -1.39349 q^{15} +3.91825 q^{16} -0.422486 q^{17} -0.116858 q^{18} +1.32976 q^{19} +2.76795 q^{20} -4.81215 q^{21} -0.207924 q^{22} +7.34590 q^{23} +0.465837 q^{24} -3.05819 q^{25} -0.116858 q^{26} +1.00000 q^{27} +9.55858 q^{28} -1.65563 q^{29} +0.162841 q^{30} +8.80975 q^{31} -1.38955 q^{32} +1.77929 q^{33} +0.0493709 q^{34} +6.70568 q^{35} -1.98634 q^{36} +0.494655 q^{37} -0.155393 q^{38} +1.00000 q^{39} -0.649139 q^{40} +5.35869 q^{41} +0.562339 q^{42} +1.57793 q^{43} -3.53427 q^{44} -1.39349 q^{45} -0.858429 q^{46} -11.4812 q^{47} +3.91825 q^{48} +16.1568 q^{49} +0.357374 q^{50} -0.422486 q^{51} -1.98634 q^{52} -8.41172 q^{53} -0.116858 q^{54} -2.47942 q^{55} -2.24168 q^{56} +1.32976 q^{57} +0.193474 q^{58} -8.75532 q^{59} +2.76795 q^{60} -3.98372 q^{61} -1.02949 q^{62} -4.81215 q^{63} -7.67412 q^{64} -1.39349 q^{65} -0.207924 q^{66} -2.56492 q^{67} +0.839202 q^{68} +7.34590 q^{69} -0.783613 q^{70} -10.8094 q^{71} +0.465837 q^{72} -10.5596 q^{73} -0.0578045 q^{74} -3.05819 q^{75} -2.64136 q^{76} -8.56218 q^{77} -0.116858 q^{78} +12.6272 q^{79} -5.46004 q^{80} +1.00000 q^{81} -0.626207 q^{82} +3.36857 q^{83} +9.55858 q^{84} +0.588730 q^{85} -0.184394 q^{86} -1.65563 q^{87} +0.828857 q^{88} +10.1717 q^{89} +0.162841 q^{90} -4.81215 q^{91} -14.5915 q^{92} +8.80975 q^{93} +1.34168 q^{94} -1.85301 q^{95} -1.38955 q^{96} -10.2822 q^{97} -1.88805 q^{98} +1.77929 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.116858	−0.0826312	−0.0413156	−	0.999146i	$-0.513155\pi$
$2$	−0.116858	−0.0826312	−0.0413156	+	0.999146i	$0.513155\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98634	−0.993172
$5$	−1.39349	−0.623188	−0.311594	−	0.950215i	$-0.600863\pi$
$5$	−1.39349	−0.623188	−0.311594	+	0.950215i	$0.600863\pi$
$6$	−0.116858	−0.0477072
$7$	−4.81215	−1.81882	−0.909410	−	0.415900i	$-0.863467\pi$
$7$	−4.81215	−1.81882	−0.909410	+	0.415900i	$0.863467\pi$
$8$	0.465837	0.164698
$9$	1.00000	0.333333
$10$	0.162841	0.0514948
$11$	1.77929	0.536475	0.268237	−	0.963353i	$-0.413559\pi$
$11$	1.77929	0.536475	0.268237	+	0.963353i	$0.413559\pi$
$12$	−1.98634	−0.573408
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.562339	0.150291
$15$	−1.39349	−0.359798
$16$	3.91825	0.979563
$17$	−0.422486	−0.102468	−0.0512339	−	0.998687i	$-0.516315\pi$
$17$	−0.422486	−0.102468	−0.0512339	+	0.998687i	$0.516315\pi$
$18$	−0.116858	−0.0275437
$19$	1.32976	0.305068	0.152534	−	0.988298i	$-0.451257\pi$
$19$	1.32976	0.305068	0.152534	+	0.988298i	$0.451257\pi$
$20$	2.76795	0.618933
$21$	−4.81215	−1.05010
$22$	−0.207924	−0.0443296
$23$	7.34590	1.53173	0.765863	−	0.643003i	$-0.222312\pi$
$23$	7.34590	1.53173	0.765863	+	0.643003i	$0.222312\pi$
$24$	0.465837	0.0950886
$25$	−3.05819	−0.611637
$26$	−0.116858	−0.0229178
$27$	1.00000	0.192450
$28$	9.55858	1.80640
$29$	−1.65563	−0.307443	−0.153721	−	0.988114i	$-0.549126\pi$
$29$	−1.65563	−0.307443	−0.153721	+	0.988114i	$0.549126\pi$
$30$	0.162841	0.0297305
$31$	8.80975	1.58228	0.791139	−	0.611637i	$-0.209488\pi$
$31$	8.80975	1.58228	0.791139	+	0.611637i	$0.209488\pi$
$32$	−1.38955	−0.245641
$33$	1.77929	0.309734
$34$	0.0493709	0.00846704
$35$	6.70568	1.13347
$36$	−1.98634	−0.331057
$37$	0.494655	0.0813208	0.0406604	−	0.999173i	$-0.487054\pi$
$37$	0.494655	0.0813208	0.0406604	+	0.999173i	$0.487054\pi$
$38$	−0.155393	−0.0252081
$39$	1.00000	0.160128
$40$	−0.649139	−0.102638
$41$	5.35869	0.836887	0.418444	−	0.908243i	$-0.362576\pi$
$41$	5.35869	0.836887	0.418444	+	0.908243i	$0.362576\pi$
$42$	0.562339	0.0867708
$43$	1.57793	0.240632	0.120316	−	0.992736i	$-0.461609\pi$
$43$	1.57793	0.240632	0.120316	+	0.992736i	$0.461609\pi$
$44$	−3.53427	−0.532812
$45$	−1.39349	−0.207729
$46$	−0.858429	−0.126568
$47$	−11.4812	−1.67471	−0.837356	−	0.546658i	$-0.815900\pi$
$47$	−11.4812	−1.67471	−0.837356	+	0.546658i	$0.815900\pi$
$48$	3.91825	0.565551
$49$	16.1568	2.30811
$50$	0.357374	0.0505403
$51$	−0.422486	−0.0591598
$52$	−1.98634	−0.275456
$53$	−8.41172	−1.15544	−0.577720	−	0.816235i	$-0.696057\pi$
$53$	−8.41172	−1.15544	−0.577720	+	0.816235i	$0.696057\pi$
$54$	−0.116858	−0.0159024
$55$	−2.47942	−0.334324
$56$	−2.24168	−0.299557
$57$	1.32976	0.176131
$58$	0.193474	0.0254044
$59$	−8.75532	−1.13985	−0.569923	−	0.821698i	$-0.693027\pi$
$59$	−8.75532	−1.13985	−0.569923	+	0.821698i	$0.693027\pi$
$60$	2.76795	0.357341
$61$	−3.98372	−0.510062	−0.255031	−	0.966933i	$-0.582086\pi$
$61$	−3.98372	−0.510062	−0.255031	+	0.966933i	$0.582086\pi$
$62$	−1.02949	−0.130746
$63$	−4.81215	−0.606274
$64$	−7.67412	−0.959265
$65$	−1.39349	−0.172841
$66$	−0.207924	−0.0255937
$67$	−2.56492	−0.313355	−0.156678	−	0.987650i	$-0.550078\pi$
$67$	−2.56492	−0.313355	−0.156678	+	0.987650i	$0.550078\pi$
$68$	0.839202	0.101768
$69$	7.34590	0.884343
$70$	−0.783613	−0.0936597
$71$	−10.8094	−1.28283	−0.641417	−	0.767192i	$-0.721653\pi$
$71$	−10.8094	−1.28283	−0.641417	+	0.767192i	$0.721653\pi$
$72$	0.465837	0.0548994
$73$	−10.5596	−1.23590	−0.617952	−	0.786216i	$-0.712037\pi$
$73$	−10.5596	−1.23590	−0.617952	+	0.786216i	$0.712037\pi$
$74$	−0.0578045	−0.00671964
$75$	−3.05819	−0.353129
$76$	−2.64136	−0.302985
$77$	−8.56218	−0.975751
$78$	−0.116858	−0.0132316
$79$	12.6272	1.42067	0.710333	−	0.703866i	$-0.248544\pi$
$79$	12.6272	1.42067	0.710333	+	0.703866i	$0.248544\pi$
$80$	−5.46004	−0.610452
$81$	1.00000	0.111111
$82$	−0.626207	−0.0691530
$83$	3.36857	0.369749	0.184875	−	0.982762i	$-0.440812\pi$
$83$	3.36857	0.369749	0.184875	+	0.982762i	$0.440812\pi$
$84$	9.55858	1.04293
$85$	0.588730	0.0638567
$86$	−0.184394	−0.0198837
$87$	−1.65563	−0.177502
$88$	0.828857	0.0883564
$89$	10.1717	1.07820	0.539101	−	0.842241i	$-0.318764\pi$
$89$	10.1717	1.07820	0.539101	+	0.842241i	$0.318764\pi$
$90$	0.162841	0.0171649
$91$	−4.81215	−0.504450
$92$	−14.5915	−1.52127
$93$	8.80975	0.913529
$94$	1.34168	0.138384
$95$	−1.85301	−0.190114
$96$	−1.38955	−0.141821
$97$	−10.2822	−1.04400	−0.522000	−	0.852945i	$-0.674814\pi$
$97$	−10.2822	−1.04400	−0.522000	+	0.852945i	$0.674814\pi$
$98$	−1.88805	−0.190722
$99$	1.77929	0.178825
$100$	6.07461	0.607461
$101$	8.64965	0.860673	0.430336	−	0.902669i	$-0.358395\pi$
$101$	8.64965	0.860673	0.430336	+	0.902669i	$0.358395\pi$
$102$	0.0493709	0.00488845
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	0.465837	0.0456791
$105$	6.70568	0.654407
$106$	0.982979	0.0954753
$107$	−0.872688	−0.0843659	−0.0421830	−	0.999110i	$-0.513431\pi$
$107$	−0.872688	−0.0843659	−0.0421830	+	0.999110i	$0.513431\pi$
$108$	−1.98634	−0.191136
$109$	−1.33197	−0.127580	−0.0637900	−	0.997963i	$-0.520319\pi$
$109$	−1.33197	−0.127580	−0.0637900	+	0.997963i	$0.520319\pi$
$110$	0.289740	0.0276256
$111$	0.494655	0.0469506
$112$	−18.8552	−1.78165
$113$	−15.5055	−1.45864	−0.729318	−	0.684175i	$-0.760162\pi$
$113$	−15.5055	−1.45864	−0.729318	+	0.684175i	$0.760162\pi$
$114$	−0.155393	−0.0145539
$115$	−10.2364	−0.954553
$116$	3.28865	0.305344
$117$	1.00000	0.0924500
$118$	1.02313	0.0941868
$119$	2.03306	0.186371
$120$	−0.649139	−0.0592580
$121$	−7.83414	−0.712195
$122$	0.465530	0.0421471
$123$	5.35869	0.483177
$124$	−17.4992	−1.57147
$125$	11.2290	1.00435
$126$	0.562339	0.0500971
$127$	−2.43320	−0.215912	−0.107956	−	0.994156i	$-0.534430\pi$
$127$	−2.43320	−0.215912	−0.107956	+	0.994156i	$0.534430\pi$
$128$	3.67589	0.324906
$129$	1.57793	0.138929
$130$	0.162841	0.0142821
$131$	−2.04123	−0.178343	−0.0891714	−	0.996016i	$-0.528422\pi$
$131$	−2.04123	−0.178343	−0.0891714	+	0.996016i	$0.528422\pi$
$132$	−3.53427	−0.307619
$133$	−6.39900	−0.554863
$134$	0.299732	0.0258929
$135$	−1.39349	−0.119933
$136$	−0.196809	−0.0168763
$137$	−8.78362	−0.750435	−0.375218	−	0.926937i	$-0.622432\pi$
$137$	−8.78362	−0.750435	−0.375218	+	0.926937i	$0.622432\pi$
$138$	−0.858429	−0.0730743
$139$	−9.82806	−0.833605	−0.416802	−	0.908997i	$-0.636849\pi$
$139$	−9.82806	−0.833605	−0.416802	+	0.908997i	$0.636849\pi$
$140$	−13.3198	−1.12573
$141$	−11.4812	−0.966896
$142$	1.26316	0.106002
$143$	1.77929	0.148791
$144$	3.91825	0.326521
$145$	2.30710	0.191595
$146$	1.23397	0.102124
$147$	16.1568	1.33259
$148$	−0.982556	−0.0807656
$149$	−3.54934	−0.290774	−0.145387	−	0.989375i	$-0.546443\pi$
$149$	−3.54934	−0.290774	−0.145387	+	0.989375i	$0.546443\pi$
$150$	0.357374	0.0291795
$151$	2.61550	0.212846	0.106423	−	0.994321i	$-0.466060\pi$
$151$	2.61550	0.212846	0.106423	+	0.994321i	$0.466060\pi$
$152$	0.619451	0.0502441
$153$	−0.422486	−0.0341559
$154$	1.00056	0.0806275
$155$	−12.2763	−0.986056
$156$	−1.98634	−0.159035
$157$	−6.63499	−0.529530	−0.264765	−	0.964313i	$-0.585294\pi$
$157$	−6.63499	−0.529530	−0.264765	+	0.964313i	$0.585294\pi$
$158$	−1.47559	−0.117391
$159$	−8.41172	−0.667093
$160$	1.93633	0.153080
$161$	−35.3496	−2.78594
$162$	−0.116858	−0.00918125
$163$	7.81917	0.612445	0.306222	−	0.951960i	$-0.400935\pi$
$163$	7.81917	0.612445	0.306222	+	0.951960i	$0.400935\pi$
$164$	−10.6442	−0.831173
$165$	−2.47942	−0.193022
$166$	−0.393645	−0.0305528
$167$	0.0202363	0.00156593	0.000782965	−	1.00000i	$-0.499751\pi$
$167$	0.0202363	0.00156593	0.000782965		1.00000i	$0.499751\pi$
$168$	−2.24168	−0.172949
$169$	1.00000	0.0769231
$170$	−0.0687979	−0.00527656
$171$	1.32976	0.101689
$172$	−3.13431	−0.238989
$173$	−7.73211	−0.587862	−0.293931	−	0.955827i	$-0.594964\pi$
$173$	−7.73211	−0.587862	−0.293931	+	0.955827i	$0.594964\pi$
$174$	0.193474	0.0146672
$175$	14.7164	1.11246
$176$	6.97169	0.525511
$177$	−8.75532	−0.658090
$178$	−1.18865	−0.0890931
$179$	17.0578	1.27496	0.637482	−	0.770466i	$-0.279976\pi$
$179$	17.0578	1.27496	0.637482	+	0.770466i	$0.279976\pi$
$180$	2.76795	0.206311
$181$	−5.39092	−0.400704	−0.200352	−	0.979724i	$-0.564209\pi$
$181$	−5.39092	−0.400704	−0.200352	+	0.979724i	$0.564209\pi$
$182$	0.562339	0.0416833
$183$	−3.98372	−0.294485
$184$	3.42199	0.252273
$185$	−0.689297	−0.0506781
$186$	−1.02949	−0.0754860
$187$	−0.751723	−0.0549714
$188$	22.8057	1.66328
$189$	−4.81215	−0.350032
$190$	0.216539	0.0157094
$191$	−2.97334	−0.215143	−0.107572	−	0.994197i	$-0.534308\pi$
$191$	−2.97334	−0.215143	−0.107572	+	0.994197i	$0.534308\pi$
$192$	−7.67412	−0.553832
$193$	11.4832	0.826582	0.413291	−	0.910599i	$-0.364379\pi$
$193$	11.4832	0.826582	0.413291	+	0.910599i	$0.364379\pi$
$194$	1.20156	0.0862670
$195$	−1.39349	−0.0997899
$196$	−32.0929	−2.29235
$197$	−14.6673	−1.04500	−0.522500	−	0.852639i	$-0.675000\pi$
$197$	−14.6673	−1.04500	−0.522500	+	0.852639i	$0.675000\pi$
$198$	−0.207924	−0.0147765
$199$	4.55244	0.322714	0.161357	−	0.986896i	$-0.448413\pi$
$199$	4.55244	0.322714	0.161357	+	0.986896i	$0.448413\pi$
$200$	−1.42462	−0.100736
$201$	−2.56492	−0.180916
$202$	−1.01078	−0.0711184
$203$	7.96713	0.559183
$204$	0.839202	0.0587559
$205$	−7.46729	−0.521538
$206$	0.116858	0.00814190
$207$	7.34590	0.510576
$208$	3.91825	0.271682
$209$	2.36602	0.163661
$210$	−0.783613	−0.0540745
$211$	−4.76508	−0.328041	−0.164021	−	0.986457i	$-0.552446\pi$
$211$	−4.76508	−0.328041	−0.164021	+	0.986457i	$0.552446\pi$
$212$	16.7086	1.14755
$213$	−10.8094	−0.740645
$214$	0.101981	0.00697126
$215$	−2.19883	−0.149959
$216$	0.465837	0.0316962
$217$	−42.3938	−2.87788
$218$	0.155652	0.0105421
$219$	−10.5596	−0.713549
$220$	4.92497	0.332042
$221$	−0.422486	−0.0284195
$222$	−0.0578045	−0.00387959
$223$	−18.2320	−1.22090	−0.610451	−	0.792054i	$-0.709012\pi$
$223$	−18.2320	−1.22090	−0.610451	+	0.792054i	$0.709012\pi$
$224$	6.68674	0.446776
$225$	−3.05819	−0.203879
$226$	1.81195	0.120529
$227$	1.71695	0.113958	0.0569789	−	0.998375i	$-0.481853\pi$
$227$	1.71695	0.113958	0.0569789	+	0.998375i	$0.481853\pi$
$228$	−2.64136	−0.174928
$229$	−8.24688	−0.544969	−0.272484	−	0.962160i	$-0.587845\pi$
$229$	−8.24688	−0.544969	−0.272484	+	0.962160i	$0.587845\pi$
$230$	1.19621	0.0788759
$231$	−8.56218	−0.563350
$232$	−0.771253	−0.0506353
$233$	3.35942	0.220083	0.110041	−	0.993927i	$-0.464902\pi$
$233$	3.35942	0.220083	0.110041	+	0.993927i	$0.464902\pi$
$234$	−0.116858	−0.00763926
$235$	15.9990	1.04366
$236$	17.3911	1.13206
$237$	12.6272	0.820222
$238$	−0.237580	−0.0154000
$239$	−22.3797	−1.44762	−0.723810	−	0.689999i	$-0.757611\pi$
$239$	−22.3797	−1.44762	−0.723810	+	0.689999i	$0.757611\pi$
$240$	−5.46004	−0.352444
$241$	−18.7100	−1.20522	−0.602608	−	0.798038i	$-0.705872\pi$
$241$	−18.7100	−1.20522	−0.602608	+	0.798038i	$0.705872\pi$
$242$	0.915484	0.0588495
$243$	1.00000	0.0641500
$244$	7.91303	0.506580
$245$	−22.5143	−1.43838
$246$	−0.626207	−0.0399255
$247$	1.32976	0.0846106
$248$	4.10391	0.260598
$249$	3.36857	0.213475
$250$	−1.31220	−0.0829909
$251$	10.3909	0.655866	0.327933	−	0.944701i	$-0.393648\pi$
$251$	10.3909	0.655866	0.327933	+	0.944701i	$0.393648\pi$
$252$	9.55858	0.602134
$253$	13.0705	0.821733
$254$	0.284339	0.0178410
$255$	0.588730	0.0368677
$256$	14.9187	0.932418
$257$	22.4910	1.40295	0.701475	−	0.712694i	$-0.252525\pi$
$257$	22.4910	1.40295	0.701475	+	0.712694i	$0.252525\pi$
$258$	−0.184394	−0.0114799
$259$	−2.38035	−0.147908
$260$	2.76795	0.171661
$261$	−1.65563	−0.102481
$262$	0.238534	0.0147367
$263$	−10.5012	−0.647534	−0.323767	−	0.946137i	$-0.604949\pi$
$263$	−10.5012	−0.647534	−0.323767	+	0.946137i	$0.604949\pi$
$264$	0.828857	0.0510126
$265$	11.7217	0.720055
$266$	0.747775	0.0458490
$267$	10.1717	0.622500
$268$	5.09482	0.311216
$269$	16.2909	0.993276	0.496638	−	0.867958i	$-0.334568\pi$
$269$	16.2909	0.993276	0.496638	+	0.867958i	$0.334568\pi$
$270$	0.162841	0.00991017
$271$	−23.8669	−1.44981	−0.724906	−	0.688848i	$-0.758117\pi$
$271$	−23.8669	−1.44981	−0.724906	+	0.688848i	$0.758117\pi$
$272$	−1.65540	−0.100374
$273$	−4.81215	−0.291244
$274$	1.02644	0.0620094
$275$	−5.44138	−0.328128
$276$	−14.5915	−0.878305
$277$	22.8978	1.37579	0.687897	−	0.725809i	$-0.258534\pi$
$277$	22.8978	1.37579	0.687897	+	0.725809i	$0.258534\pi$
$278$	1.14849	0.0688818
$279$	8.80975	0.527426
$280$	3.12375	0.186680
$281$	−6.01797	−0.359002	−0.179501	−	0.983758i	$-0.557448\pi$
$281$	−6.01797	−0.359002	−0.179501	+	0.983758i	$0.557448\pi$
$282$	1.34168	0.0798958
$283$	7.15170	0.425125	0.212562	−	0.977148i	$-0.431819\pi$
$283$	7.15170	0.425125	0.212562	+	0.977148i	$0.431819\pi$
$284$	21.4711	1.27408
$285$	−1.85301	−0.109763
$286$	−0.207924	−0.0122948
$287$	−25.7868	−1.52215
$288$	−1.38955	−0.0818802
$289$	−16.8215	−0.989500
$290$	−0.269604	−0.0158317
$291$	−10.2822	−0.602754
$292$	20.9749	1.22746
$293$	−16.8469	−0.984207	−0.492103	−	0.870537i	$-0.663772\pi$
$293$	−16.8469	−0.984207	−0.492103	+	0.870537i	$0.663772\pi$
$294$	−1.88805	−0.110113
$295$	12.2005	0.710338
$296$	0.230429	0.0133934
$297$	1.77929	0.103245
$298$	0.414770	0.0240270
$299$	7.34590	0.424825
$300$	6.07461	0.350718
$301$	−7.59322	−0.437666
$302$	−0.305642	−0.0175877
$303$	8.64965	0.496910
$304$	5.21033	0.298833
$305$	5.55127	0.317865
$306$	0.0493709	0.00282235
$307$	−17.0692	−0.974193	−0.487097	−	0.873348i	$-0.661944\pi$
$307$	−17.0692	−0.974193	−0.487097	+	0.873348i	$0.661944\pi$
$308$	17.0074	0.969089
$309$	−1.00000	−0.0568880
$310$	1.43459	0.0814790
$311$	−1.92307	−0.109047	−0.0545237	−	0.998512i	$-0.517364\pi$
$311$	−1.92307	−0.109047	−0.0545237	+	0.998512i	$0.517364\pi$
$312$	0.465837	0.0263728
$313$	26.0569	1.47282	0.736412	−	0.676533i	$-0.236519\pi$
$313$	26.0569	1.47282	0.736412	+	0.676533i	$0.236519\pi$
$314$	0.775353	0.0437557
$315$	6.70568	0.377822
$316$	−25.0819	−1.41097
$317$	−2.38463	−0.133934	−0.0669670	−	0.997755i	$-0.521332\pi$
$317$	−2.38463	−0.133934	−0.0669670	+	0.997755i	$0.521332\pi$
$318$	0.982979	0.0551227
$319$	−2.94584	−0.164935
$320$	10.6938	0.597802
$321$	−0.872688	−0.0487087
$322$	4.13089	0.230205
$323$	−0.561804	−0.0312596
$324$	−1.98634	−0.110352
$325$	−3.05819	−0.169638
$326$	−0.913734	−0.0506071
$327$	−1.33197	−0.0736583
$328$	2.49628	0.137834
$329$	55.2495	3.04600
$330$	0.289740	0.0159497
$331$	7.90274	0.434374	0.217187	−	0.976130i	$-0.430312\pi$
$331$	7.90274	0.434374	0.217187	+	0.976130i	$0.430312\pi$
$332$	−6.69115	−0.367224
$333$	0.494655	0.0271069
$334$	−0.00236477	−0.000129395 0
$335$	3.57419	0.195279
$336$	−18.8552	−1.02864
$337$	28.6905	1.56287	0.781436	−	0.623985i	$-0.214487\pi$
$337$	28.6905	1.56287	0.781436	+	0.623985i	$0.214487\pi$
$338$	−0.116858	−0.00635625
$339$	−15.5055	−0.842143
$340$	−1.16942	−0.0634207
$341$	15.6751	0.848852
$342$	−0.155393	−0.00840270
$343$	−44.0637	−2.37921
$344$	0.735057	0.0396316
$345$	−10.2364	−0.551112
$346$	0.903561	0.0485757
$347$	−24.4140	−1.31061	−0.655306	−	0.755363i	$-0.727461\pi$
$347$	−24.4140	−1.31061	−0.655306	+	0.755363i	$0.727461\pi$
$348$	3.28865	0.176290
$349$	−8.06869	−0.431907	−0.215954	−	0.976404i	$-0.569286\pi$
$349$	−8.06869	−0.431907	−0.215954	+	0.976404i	$0.569286\pi$
$350$	−1.71974	−0.0919238
$351$	1.00000	0.0533761
$352$	−2.47241	−0.131780
$353$	32.1076	1.70892	0.854459	−	0.519519i	$-0.173889\pi$
$353$	32.1076	1.70892	0.854459	+	0.519519i	$0.173889\pi$
$354$	1.02313	0.0543788
$355$	15.0627	0.799447
$356$	−20.2046	−1.07084
$357$	2.03306	0.107601
$358$	−1.99335	−0.105352
$359$	27.9770	1.47657	0.738284	−	0.674490i	$-0.235636\pi$
$359$	27.9770	1.47657	0.738284	+	0.674490i	$0.235636\pi$
$360$	−0.649139	−0.0342126
$361$	−17.2317	−0.906934
$362$	0.629973	0.0331107
$363$	−7.83414	−0.411186
$364$	9.55858	0.501006
$365$	14.7146	0.770200
$366$	0.465530	0.0243336
$367$	−37.8726	−1.97693	−0.988467	−	0.151439i	$-0.951609\pi$
$367$	−37.8726	−1.97693	−0.988467	+	0.151439i	$0.951609\pi$
$368$	28.7831	1.50042
$369$	5.35869	0.278962
$370$	0.0805500	0.00418760
$371$	40.4785	2.10154
$372$	−17.4992	−0.907291
$373$	−14.0427	−0.727104	−0.363552	−	0.931574i	$-0.618436\pi$
$373$	−14.0427	−0.727104	−0.363552	+	0.931574i	$0.618436\pi$
$374$	0.0878449	0.00454235
$375$	11.2290	0.579863
$376$	−5.34839	−0.275822
$377$	−1.65563	−0.0852693
$378$	0.562339	0.0289236
$379$	−0.111717	−0.00573850	−0.00286925	−	0.999996i	$-0.500913\pi$
$379$	−0.111717	−0.00573850	−0.00286925	+	0.999996i	$0.500913\pi$
$380$	3.68071	0.188816
$381$	−2.43320	−0.124657
$382$	0.347459	0.0177776
$383$	−23.1833	−1.18461	−0.592305	−	0.805714i	$-0.701782\pi$
$383$	−23.1833	−1.18461	−0.592305	+	0.805714i	$0.701782\pi$
$384$	3.67589	0.187585
$385$	11.9313	0.608076
$386$	−1.34191	−0.0683014
$387$	1.57793	0.0802106
$388$	20.4240	1.03687
$389$	16.1072	0.816669	0.408335	−	0.912832i	$-0.366110\pi$
$389$	16.1072	0.816669	0.408335	+	0.912832i	$0.366110\pi$
$390$	0.162841	0.00824576
$391$	−3.10354	−0.156953
$392$	7.52641	0.380141
$393$	−2.04123	−0.102966
$394$	1.71399	0.0863496
$395$	−17.5958	−0.885342
$396$	−3.53427	−0.177604
$397$	−29.8219	−1.49672	−0.748359	−	0.663294i	$-0.769158\pi$
$397$	−29.8219	−1.49672	−0.748359	+	0.663294i	$0.769158\pi$
$398$	−0.531990	−0.0266662
$399$	−6.39900	−0.320351
$400$	−11.9827	−0.599137
$401$	−1.90646	−0.0952041	−0.0476021	−	0.998866i	$-0.515158\pi$
$401$	−1.90646	−0.0952041	−0.0476021	+	0.998866i	$0.515158\pi$
$402$	0.299732	0.0149493
$403$	8.80975	0.438845
$404$	−17.1812	−0.854796
$405$	−1.39349	−0.0692431
$406$	−0.931025	−0.0462060
$407$	0.880133	0.0436266
$408$	−0.196809	−0.00974352
$409$	21.7899	1.07744	0.538720	−	0.842485i	$-0.318908\pi$
$409$	21.7899	1.07744	0.538720	+	0.842485i	$0.318908\pi$
$410$	0.872614	0.0430953
$411$	−8.78362	−0.433264
$412$	1.98634	0.0978602
$413$	42.1319	2.07317
$414$	−0.858429	−0.0421895
$415$	−4.69407	−0.230423
$416$	−1.38955	−0.0681285
$417$	−9.82806	−0.481282
$418$	−0.276489	−0.0135235
$419$	34.0432	1.66312	0.831560	−	0.555435i	$-0.187448\pi$
$419$	34.0432	1.66312	0.831560	+	0.555435i	$0.187448\pi$
$420$	−13.3198	−0.649939
$421$	−18.8085	−0.916669	−0.458334	−	0.888780i	$-0.651554\pi$
$421$	−18.8085	−0.916669	−0.458334	+	0.888780i	$0.651554\pi$
$422$	0.556838	0.0271065
$423$	−11.4812	−0.558237
$424$	−3.91849	−0.190299
$425$	1.29204	0.0626731
$426$	1.26316	0.0612004
$427$	19.1702	0.927712
$428$	1.73346	0.0837899
$429$	1.77929	0.0859047
$430$	0.256951	0.0123913
$431$	−20.7644	−1.00019	−0.500093	−	0.865972i	$-0.666701\pi$
$431$	−20.7644	−1.00019	−0.500093	+	0.865972i	$0.666701\pi$
$432$	3.91825	0.188517
$433$	−24.1627	−1.16119	−0.580593	−	0.814194i	$-0.697179\pi$
$433$	−24.1627	−1.16119	−0.580593	+	0.814194i	$0.697179\pi$
$434$	4.95406	0.237803
$435$	2.30710	0.110617
$436$	2.64576	0.126709
$437$	9.76828	0.467280
$438$	1.23397	0.0589614
$439$	−13.5640	−0.647373	−0.323686	−	0.946164i	$-0.604922\pi$
$439$	−13.5640	−0.647373	−0.323686	+	0.946164i	$0.604922\pi$
$440$	−1.15500	−0.0550626
$441$	16.1568	0.769369
$442$	0.0493709	0.00234833
$443$	8.75855	0.416131	0.208066	−	0.978115i	$-0.433283\pi$
$443$	8.75855	0.416131	0.208066	+	0.978115i	$0.433283\pi$
$444$	−0.982556	−0.0466300
$445$	−14.1742	−0.671922
$446$	2.13055	0.100885
$447$	−3.54934	−0.167878
$448$	36.9290	1.74473
$449$	−6.13733	−0.289638	−0.144819	−	0.989458i	$-0.546260\pi$
$449$	−6.13733	−0.289638	−0.144819	+	0.989458i	$0.546260\pi$
$450$	0.357374	0.0168468
$451$	9.53465	0.448969
$452$	30.7993	1.44868
$453$	2.61550	0.122887
$454$	−0.200639	−0.00941647
$455$	6.70568	0.314367
$456$	0.619451	0.0290084
$457$	−16.5815	−0.775648	−0.387824	−	0.921733i	$-0.626773\pi$
$457$	−16.5815	−0.775648	−0.387824	+	0.921733i	$0.626773\pi$
$458$	0.963715	0.0450314
$459$	−0.422486	−0.0197199
$460$	20.3331	0.948036
$461$	19.3497	0.901207	0.450604	−	0.892724i	$-0.351209\pi$
$461$	19.3497	0.901207	0.450604	+	0.892724i	$0.351209\pi$
$462$	1.00056	0.0465503
$463$	30.2145	1.40419	0.702093	−	0.712085i	$-0.252249\pi$
$463$	30.2145	1.40419	0.702093	+	0.712085i	$0.252249\pi$
$464$	−6.48717	−0.301159
$465$	−12.2763	−0.569300
$466$	−0.392576	−0.0181857
$467$	−22.8581	−1.05774	−0.528872	−	0.848701i	$-0.677385\pi$
$467$	−22.8581	−1.05774	−0.528872	+	0.848701i	$0.677385\pi$
$468$	−1.98634	−0.0918188
$469$	12.3428	0.569937
$470$	−1.86961	−0.0862389
$471$	−6.63499	−0.305724
$472$	−4.07855	−0.187731
$473$	2.80759	0.129093
$474$	−1.47559	−0.0677759
$475$	−4.06665	−0.186591
$476$	−4.03836	−0.185098
$477$	−8.41172	−0.385146
$478$	2.61525	0.119619
$479$	−14.2821	−0.652565	−0.326282	−	0.945272i	$-0.605796\pi$
$479$	−14.2821	−0.652565	−0.326282	+	0.945272i	$0.605796\pi$
$480$	1.93633	0.0883809
$481$	0.494655	0.0225543
$482$	2.18641	0.0995884
$483$	−35.3496	−1.60846
$484$	15.5613	0.707332
$485$	14.3282	0.650608
$486$	−0.116858	−0.00530079
$487$	−32.7635	−1.48465	−0.742327	−	0.670038i	$-0.766278\pi$
$487$	−32.7635	−1.48465	−0.742327	+	0.670038i	$0.766278\pi$
$488$	−1.85576	−0.0840064
$489$	7.81917	0.353595
$490$	2.63098	0.118855
$491$	14.5560	0.656902	0.328451	−	0.944521i	$-0.393473\pi$
$491$	14.5560	0.656902	0.328451	+	0.944521i	$0.393473\pi$
$492$	−10.6442	−0.479878
$493$	0.699480	0.0315030
$494$	−0.155393	−0.00699147
$495$	−2.47942	−0.111441
$496$	34.5188	1.54994
$497$	52.0162	2.33325
$498$	−0.393645	−0.0176397
$499$	−10.6365	−0.476154	−0.238077	−	0.971246i	$-0.576517\pi$
$499$	−10.6365	−0.476154	−0.238077	+	0.971246i	$0.576517\pi$
$500$	−22.3047	−0.997495
$501$	0.0202363	0.000904090 0
$502$	−1.21426	−0.0541950
$503$	−23.6781	−1.05575	−0.527877	−	0.849321i	$-0.677012\pi$
$503$	−23.6781	−1.05575	−0.527877	+	0.849321i	$0.677012\pi$
$504$	−2.24168	−0.0998522
$505$	−12.0532	−0.536361
$506$	−1.52739	−0.0679008
$507$	1.00000	0.0444116
$508$	4.83317	0.214437
$509$	−30.2953	−1.34282	−0.671409	−	0.741087i	$-0.734310\pi$
$509$	−30.2953	−1.34282	−0.671409	+	0.741087i	$0.734310\pi$
$510$	−0.0687979	−0.00304642
$511$	50.8142	2.24789
$512$	−9.09515	−0.401953
$513$	1.32976	0.0587103
$514$	−2.62826	−0.115927
$515$	1.39349	0.0614045
$516$	−3.13431	−0.137980
$517$	−20.4284	−0.898441
$518$	0.278164	0.0122218
$519$	−7.73211	−0.339402
$520$	−0.649139	−0.0284666
$521$	27.5866	1.20859	0.604296	−	0.796760i	$-0.293454\pi$
$521$	27.5866	1.20859	0.604296	+	0.796760i	$0.293454\pi$
$522$	0.193474	0.00846812
$523$	−28.3545	−1.23986	−0.619928	−	0.784659i	$-0.712838\pi$
$523$	−28.3545	−1.23986	−0.619928	+	0.784659i	$0.712838\pi$
$524$	4.05458	0.177125
$525$	14.7164	0.642278
$526$	1.22716	0.0535065
$527$	−3.72199	−0.162133
$528$	6.97169	0.303404
$529$	30.9623	1.34619
$530$	−1.36977	−0.0594991
$531$	−8.75532	−0.379949
$532$	12.7106	0.551075
$533$	5.35869	0.232111
$534$	−1.18865	−0.0514379
$535$	1.21608	0.0525758
$536$	−1.19484	−0.0516090
$537$	17.0578	0.736100
$538$	−1.90373	−0.0820756
$539$	28.7475	1.23824
$540$	2.76795	0.119114
$541$	−44.0757	−1.89496	−0.947482	−	0.319810i	$-0.896381\pi$
$541$	−44.0757	−1.89496	−0.947482	+	0.319810i	$0.896381\pi$
$542$	2.78904	0.119800
$543$	−5.39092	−0.231347
$544$	0.587066	0.0251703
$545$	1.85609	0.0795063
$546$	0.562339	0.0240659
$547$	−19.0915	−0.816295	−0.408147	−	0.912916i	$-0.633825\pi$
$547$	−19.0915	−0.816295	−0.408147	+	0.912916i	$0.633825\pi$
$548$	17.4473	0.745311
$549$	−3.98372	−0.170021
$550$	0.635870	0.0271136
$551$	−2.20159	−0.0937908
$552$	3.42199	0.145650
$553$	−60.7637	−2.58394
$554$	−2.67579	−0.113683
$555$	−0.689297	−0.0292590
$556$	19.5219	0.827913
$557$	0.591202	0.0250500	0.0125250	−	0.999922i	$-0.496013\pi$
$557$	0.591202	0.0250500	0.0125250	+	0.999922i	$0.496013\pi$
$558$	−1.02949	−0.0435818
$559$	1.57793	0.0667393
$560$	26.2745	1.11030
$561$	−0.751723	−0.0317377
$562$	0.703250	0.0296648
$563$	24.4996	1.03254	0.516268	−	0.856427i	$-0.327321\pi$
$563$	24.4996	1.03254	0.516268	+	0.856427i	$0.327321\pi$
$564$	22.8057	0.960294
$565$	21.6068	0.909004
$566$	−0.835735	−0.0351286
$567$	−4.81215	−0.202091
$568$	−5.03540	−0.211281
$569$	9.32414	0.390888	0.195444	−	0.980715i	$-0.437385\pi$
$569$	9.32414	0.390888	0.195444	+	0.980715i	$0.437385\pi$
$570$	0.216539	0.00906982
$571$	−5.05663	−0.211613	−0.105807	−	0.994387i	$-0.533742\pi$
$571$	−5.05663	−0.211613	−0.105807	+	0.994387i	$0.533742\pi$
$572$	−3.53427	−0.147775
$573$	−2.97334	−0.124213
$574$	3.01340	0.125777
$575$	−22.4651	−0.936861
$576$	−7.67412	−0.319755
$577$	12.8427	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$577$	12.8427	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$578$	1.96573	0.0817636
$579$	11.4832	0.477227
$580$	−4.58270	−0.190286
$581$	−16.2101	−0.672507
$582$	1.20156	0.0498063
$583$	−14.9669	−0.619864
$584$	−4.91903	−0.203551
$585$	−1.39349	−0.0576137
$586$	1.96870	0.0813262
$587$	−11.3776	−0.469604	−0.234802	−	0.972043i	$-0.575444\pi$
$587$	−11.3776	−0.469604	−0.234802	+	0.972043i	$0.575444\pi$
$588$	−32.0929	−1.32349
$589$	11.7148	0.482702
$590$	−1.42572	−0.0586961
$591$	−14.6673	−0.603331
$592$	1.93818	0.0796589
$593$	−16.7426	−0.687538	−0.343769	−	0.939054i	$-0.611704\pi$
$593$	−16.7426	−0.687538	−0.343769	+	0.939054i	$0.611704\pi$
$594$	−0.207924	−0.00853123
$595$	−2.83305	−0.116144
$596$	7.05022	0.288788
$597$	4.55244	0.186319
$598$	−0.858429	−0.0351038
$599$	9.60175	0.392317	0.196158	−	0.980572i	$-0.437153\pi$
$599$	9.60175	0.392317	0.196158	+	0.980572i	$0.437153\pi$
$600$	−1.42462	−0.0581597
$601$	31.8630	1.29972	0.649859	−	0.760055i	$-0.274828\pi$
$601$	31.8630	1.29972	0.649859	+	0.760055i	$0.274828\pi$
$602$	0.887330	0.0361649
$603$	−2.56492	−0.104452
$604$	−5.19528	−0.211393
$605$	10.9168	0.443831
$606$	−1.01078	−0.0410602
$607$	−21.4685	−0.871380	−0.435690	−	0.900097i	$-0.643496\pi$
$607$	−21.4685	−0.871380	−0.435690	+	0.900097i	$0.643496\pi$
$608$	−1.84777	−0.0749370
$609$	7.96713	0.322845
$610$	−0.648711	−0.0262655
$611$	−11.4812	−0.464482
$612$	0.839202	0.0339227
$613$	−11.9214	−0.481502	−0.240751	−	0.970587i	$-0.577394\pi$
$613$	−11.9214	−0.481502	−0.240751	+	0.970587i	$0.577394\pi$
$614$	1.99468	0.0804988
$615$	−7.46729	−0.301110
$616$	−3.98858	−0.160705
$617$	0.0130435	0.000525112 0	0.000262556	−	1.00000i	$-0.499916\pi$
$617$	0.0130435	0.000525112 0	0.000262556		1.00000i	$0.499916\pi$
$618$	0.116858	0.00470073
$619$	−38.7865	−1.55896	−0.779480	−	0.626427i	$-0.784517\pi$
$619$	−38.7865	−1.55896	−0.779480	+	0.626427i	$0.784517\pi$
$620$	24.3850	0.979323
$621$	7.34590	0.294781
$622$	0.224727	0.00901072
$623$	−48.9479	−1.96105
$624$	3.91825	0.156856
$625$	−0.356574	−0.0142630
$626$	−3.04496	−0.121701
$627$	2.36602	0.0944898
$628$	13.1794	0.525915
$629$	−0.208985	−0.00833277
$630$	−0.783613	−0.0312199
$631$	−4.65558	−0.185336	−0.0926679	−	0.995697i	$-0.529539\pi$
$631$	−4.65558	−0.185336	−0.0926679	+	0.995697i	$0.529539\pi$
$632$	5.88220	0.233981
$633$	−4.76508	−0.189395
$634$	0.278663	0.0110671
$635$	3.39064	0.134553
$636$	16.7086	0.662538
$637$	16.1568	0.640154
$638$	0.344245	0.0136288
$639$	−10.8094	−0.427611
$640$	−5.12232	−0.202477
$641$	19.7418	0.779753	0.389876	−	0.920867i	$-0.372518\pi$
$641$	19.7418	0.779753	0.389876	+	0.920867i	$0.372518\pi$
$642$	0.101981	0.00402486
$643$	41.5140	1.63715	0.818576	−	0.574398i	$-0.194764\pi$
$643$	41.5140	1.63715	0.818576	+	0.574398i	$0.194764\pi$
$644$	70.2164	2.76691
$645$	−2.19883	−0.0865788
$646$	0.0656514	0.00258302
$647$	−42.1621	−1.65756	−0.828782	−	0.559572i	$-0.810966\pi$
$647$	−42.1621	−1.65756	−0.828782	+	0.559572i	$0.810966\pi$
$648$	0.465837	0.0182998
$649$	−15.5782	−0.611498
$650$	0.357374	0.0140174
$651$	−42.3938	−1.66154
$652$	−15.5316	−0.608263
$653$	−5.98773	−0.234318	−0.117159	−	0.993113i	$-0.537379\pi$
$653$	−5.98773	−0.234318	−0.117159	+	0.993113i	$0.537379\pi$
$654$	0.155652	0.00608648
$655$	2.84443	0.111141
$656$	20.9967	0.819784
$657$	−10.5596	−0.411968
$658$	−6.45635	−0.251695
$659$	−0.560020	−0.0218153	−0.0109076	−	0.999941i	$-0.503472\pi$
$659$	−0.560020	−0.0218153	−0.0109076	+	0.999941i	$0.503472\pi$
$660$	4.92497	0.191704
$661$	−38.7835	−1.50850	−0.754252	−	0.656586i	$-0.772000\pi$
$661$	−38.7835	−1.50850	−0.754252	+	0.656586i	$0.772000\pi$
$662$	−0.923499	−0.0358928
$663$	−0.422486	−0.0164080
$664$	1.56921	0.0608970
$665$	8.91694	0.345784
$666$	−0.0578045	−0.00223988
$667$	−12.1621	−0.470918
$668$	−0.0401962	−0.00155524
$669$	−18.2320	−0.704889
$670$	−0.417674	−0.0161361
$671$	−7.08817	−0.273636
$672$	6.68674	0.257946
$673$	−18.4934	−0.712869	−0.356434	−	0.934320i	$-0.616008\pi$
$673$	−18.4934	−0.712869	−0.356434	+	0.934320i	$0.616008\pi$
$674$	−3.35272	−0.129142
$675$	−3.05819	−0.117710
$676$	−1.98634	−0.0763979
$677$	17.8887	0.687520	0.343760	−	0.939058i	$-0.388299\pi$
$677$	17.8887	0.687520	0.343760	+	0.939058i	$0.388299\pi$
$678$	1.81195	0.0695873
$679$	49.4795	1.89885
$680$	0.274252	0.0105171
$681$	1.71695	0.0657936
$682$	−1.83176	−0.0701417
$683$	29.2157	1.11791	0.558954	−	0.829199i	$-0.311203\pi$
$683$	29.2157	1.11791	0.558954	+	0.829199i	$0.311203\pi$
$684$	−2.64136	−0.100995
$685$	12.2399	0.467662
$686$	5.14920	0.196597
$687$	−8.24688	−0.314638
$688$	6.18272	0.235714
$689$	−8.41172	−0.320461
$690$	1.19621	0.0455390
$691$	5.96252	0.226825	0.113412	−	0.993548i	$-0.463822\pi$
$691$	5.96252	0.226825	0.113412	+	0.993548i	$0.463822\pi$
$692$	15.3586	0.583848
$693$	−8.56218	−0.325250
$694$	2.85298	0.108298
$695$	13.6953	0.519492
$696$	−0.771253	−0.0292343
$697$	−2.26397	−0.0857540
$698$	0.942893	0.0356890
$699$	3.35942	0.127065
$700$	−29.2319	−1.10486
$701$	−13.2418	−0.500136	−0.250068	−	0.968228i	$-0.580453\pi$
$701$	−13.2418	−0.500136	−0.250068	+	0.968228i	$0.580453\pi$
$702$	−0.116858	−0.00441053
$703$	0.657772	0.0248084
$704$	−13.6545	−0.514622
$705$	15.9990	0.602557
$706$	−3.75204	−0.141210
$707$	−41.6234	−1.56541
$708$	17.3911	0.653597
$709$	−12.5713	−0.472124	−0.236062	−	0.971738i	$-0.575857\pi$
$709$	−12.5713	−0.472124	−0.236062	+	0.971738i	$0.575857\pi$
$710$	−1.76020	−0.0660592
$711$	12.6272	0.473555
$712$	4.73837	0.177578
$713$	64.7156	2.42362
$714$	−0.237580	−0.00889121
$715$	−2.47942	−0.0927249
$716$	−33.8828	−1.26626
$717$	−22.3797	−0.835784
$718$	−3.26934	−0.122011
$719$	−31.3084	−1.16761	−0.583804	−	0.811895i	$-0.698436\pi$
$719$	−31.3084	−1.16761	−0.583804	+	0.811895i	$0.698436\pi$
$720$	−5.46004	−0.203484
$721$	4.81215	0.179214
$722$	2.01367	0.0749410
$723$	−18.7100	−0.695831
$724$	10.7082	0.397968
$725$	5.06322	0.188043
$726$	0.915484	0.0339768
$727$	13.7216	0.508907	0.254453	−	0.967085i	$-0.418104\pi$
$727$	13.7216	0.508907	0.254453	+	0.967085i	$0.418104\pi$
$728$	−2.24168	−0.0830820
$729$	1.00000	0.0370370
$730$	−1.71953	−0.0636425
$731$	−0.666652	−0.0246570
$732$	7.91303	0.292474
$733$	36.9544	1.36494	0.682471	−	0.730913i	$-0.260905\pi$
$733$	36.9544	1.36494	0.682471	+	0.730913i	$0.260905\pi$
$734$	4.42572	0.163356
$735$	−22.5143	−0.830452
$736$	−10.2075	−0.376254
$737$	−4.56373	−0.168107
$738$	−0.626207	−0.0230510
$739$	−35.5507	−1.30775	−0.653877	−	0.756601i	$-0.726859\pi$
$739$	−35.5507	−1.30775	−0.653877	+	0.756601i	$0.726859\pi$
$740$	1.36918	0.0503321
$741$	1.32976	0.0488499
$742$	−4.73024	−0.173653
$743$	−15.8216	−0.580438	−0.290219	−	0.956960i	$-0.593728\pi$
$743$	−15.8216	−0.580438	−0.290219	+	0.956960i	$0.593728\pi$
$744$	4.10391	0.150457
$745$	4.94598	0.181207
$746$	1.64100	0.0600815
$747$	3.36857	0.123250
$748$	1.49318	0.0545961
$749$	4.19950	0.153446
$750$	−1.31220	−0.0479148
$751$	2.19342	0.0800390	0.0400195	−	0.999199i	$-0.487258\pi$
$751$	2.19342	0.0800390	0.0400195	+	0.999199i	$0.487258\pi$
$752$	−44.9864	−1.64049
$753$	10.3909	0.378664
$754$	0.193474	0.00704590
$755$	−3.64467	−0.132643
$756$	9.55858	0.347642
$757$	21.0338	0.764486	0.382243	−	0.924062i	$-0.375152\pi$
$757$	21.0338	0.764486	0.382243	+	0.924062i	$0.375152\pi$
$758$	0.0130550	0.000474179 0
$759$	13.0705	0.474428
$760$	−0.863199	−0.0313115
$761$	46.7886	1.69608	0.848042	−	0.529929i	$-0.177781\pi$
$761$	46.7886	1.69608	0.848042	+	0.529929i	$0.177781\pi$
$762$	0.284339	0.0103005
$763$	6.40966	0.232045
$764$	5.90608	0.213674
$765$	0.588730	0.0212856
$766$	2.70915	0.0978857
$767$	−8.75532	−0.316136
$768$	14.9187	0.538332
$769$	−2.92074	−0.105325	−0.0526624	−	0.998612i	$-0.516771\pi$
$769$	−2.92074	−0.105325	−0.0526624	+	0.998612i	$0.516771\pi$
$770$	−1.39427	−0.0502461
$771$	22.4910	0.809993
$772$	−22.8097	−0.820938
$773$	20.7785	0.747349	0.373675	−	0.927560i	$-0.378098\pi$
$773$	20.7785	0.747349	0.373675	+	0.927560i	$0.378098\pi$
$774$	−0.184394	−0.00662790
$775$	−26.9418	−0.967780
$776$	−4.78983	−0.171945
$777$	−2.38035	−0.0853947
$778$	−1.88226	−0.0674824
$779$	7.12577	0.255307
$780$	2.76795	0.0991085
$781$	−19.2329	−0.688208
$782$	0.362674	0.0129692
$783$	−1.65563	−0.0591674
$784$	63.3062	2.26094
$785$	9.24580	0.329997
$786$	0.238534	0.00850823
$787$	34.6445	1.23494	0.617471	−	0.786594i	$-0.288157\pi$
$787$	34.6445	1.23494	0.617471	+	0.786594i	$0.288157\pi$
$788$	29.1342	1.03786
$789$	−10.5012	−0.373854
$790$	2.05622	0.0731568
$791$	74.6148	2.65300
$792$	0.828857	0.0294521
$793$	−3.98372	−0.141466
$794$	3.48493	0.123676
$795$	11.7217	0.415724
$796$	−9.04271	−0.320510
$797$	−31.0103	−1.09844	−0.549220	−	0.835678i	$-0.685075\pi$
$797$	−31.0103	−1.09844	−0.549220	+	0.835678i	$0.685075\pi$
$798$	0.747775	0.0264710
$799$	4.85066	0.171604
$800$	4.24951	0.150243
$801$	10.1717	0.359400
$802$	0.222786	0.00786683
$803$	−18.7885	−0.663031
$804$	5.09482	0.179680
$805$	49.2593	1.73616
$806$	−1.02949	−0.0362623
$807$	16.2909	0.573468
$808$	4.02933	0.141751
$809$	−32.9103	−1.15707	−0.578533	−	0.815659i	$-0.696375\pi$
$809$	−32.9103	−1.15707	−0.578533	+	0.815659i	$0.696375\pi$
$810$	0.162841	0.00572164
$811$	14.3377	0.503466	0.251733	−	0.967797i	$-0.419000\pi$
$811$	14.3377	0.503466	0.251733	+	0.967797i	$0.419000\pi$
$812$	−15.8255	−0.555365
$813$	−23.8669	−0.837049
$814$	−0.102851	−0.00360492
$815$	−10.8959	−0.381668
$816$	−1.65540	−0.0579508
$817$	2.09827	0.0734090
$818$	−2.54633	−0.0890302
$819$	−4.81215	−0.168150
$820$	14.8326	0.517977
$821$	56.0474	1.95607	0.978034	−	0.208444i	$-0.0668399\pi$
$821$	56.0474	1.95607	0.978034	+	0.208444i	$0.0668399\pi$
$822$	1.02644	0.0358011
$823$	−14.0858	−0.490999	−0.245500	−	0.969397i	$-0.578952\pi$
$823$	−14.0858	−0.490999	−0.245500	+	0.969397i	$0.578952\pi$
$824$	−0.465837	−0.0162282
$825$	−5.44138	−0.189445
$826$	−4.92346	−0.171309
$827$	−27.1193	−0.943029	−0.471515	−	0.881858i	$-0.656293\pi$
$827$	−27.1193	−0.943029	−0.471515	+	0.881858i	$0.656293\pi$
$828$	−14.5915	−0.507089
$829$	−8.82440	−0.306484	−0.153242	−	0.988189i	$-0.548971\pi$
$829$	−8.82440	−0.306484	−0.153242	+	0.988189i	$0.548971\pi$
$830$	0.548541	0.0190401
$831$	22.8978	0.794314
$832$	−7.67412	−0.266052
$833$	−6.82600	−0.236507
$834$	1.14849	0.0397689
$835$	−0.0281990	−0.000975868 0
$836$	−4.69973	−0.162544
$837$	8.80975	0.304510
$838$	−3.97823	−0.137426
$839$	−1.17546	−0.0405816	−0.0202908	−	0.999794i	$-0.506459\pi$
$839$	−1.17546	−0.0405816	−0.0202908	+	0.999794i	$0.506459\pi$
$840$	3.12375	0.107780
$841$	−26.2589	−0.905479
$842$	2.19792	0.0757454
$843$	−6.01797	−0.207270
$844$	9.46508	0.325802
$845$	−1.39349	−0.0479375
$846$	1.34168	0.0461278
$847$	37.6990	1.29535
$848$	−32.9593	−1.13183
$849$	7.15170	0.245446
$850$	−0.150985	−0.00517876
$851$	3.63369	0.124561
$852$	21.4711	0.735588
$853$	−31.2649	−1.07049	−0.535245	−	0.844697i	$-0.679781\pi$
$853$	−31.2649	−1.07049	−0.535245	+	0.844697i	$0.679781\pi$
$854$	−2.24020	−0.0766580
$855$	−1.85301	−0.0633715
$856$	−0.406530	−0.0138949
$857$	−31.7642	−1.08505	−0.542523	−	0.840041i	$-0.682531\pi$
$857$	−31.7642	−1.08505	−0.542523	+	0.840041i	$0.682531\pi$
$858$	−0.207924	−0.00709841
$859$	−20.0582	−0.684376	−0.342188	−	0.939631i	$-0.611168\pi$
$859$	−20.0582	−0.684376	−0.342188	+	0.939631i	$0.611168\pi$
$860$	4.36763	0.148935
$861$	−25.7868	−0.878813
$862$	2.42649	0.0826465
$863$	8.77730	0.298783	0.149391	−	0.988778i	$-0.452269\pi$
$863$	8.77730	0.298783	0.149391	+	0.988778i	$0.452269\pi$
$864$	−1.38955	−0.0472736
$865$	10.7746	0.366348
$866$	2.82361	0.0959503
$867$	−16.8215	−0.571288
$868$	84.2087	2.85823
$869$	22.4673	0.762151
$870$	−0.269604	−0.00914043
$871$	−2.56492	−0.0869091
$872$	−0.620483	−0.0210122
$873$	−10.2822	−0.348000
$874$	−1.14150	−0.0386119
$875$	−54.0356	−1.82674
$876$	20.9749	0.708677
$877$	−9.60909	−0.324476	−0.162238	−	0.986752i	$-0.551871\pi$
$877$	−9.60909	−0.324476	−0.162238	+	0.986752i	$0.551871\pi$
$878$	1.58506	0.0534932
$879$	−16.8469	−0.568232
$880$	−9.71498	−0.327492
$881$	−15.8766	−0.534898	−0.267449	−	0.963572i	$-0.586181\pi$
$881$	−15.8766	−0.534898	−0.267449	+	0.963572i	$0.586181\pi$
$882$	−1.88805	−0.0635739
$883$	−40.1706	−1.35185	−0.675924	−	0.736971i	$-0.736255\pi$
$883$	−40.1706	−1.35185	−0.675924	+	0.736971i	$0.736255\pi$
$884$	0.839202	0.0282254
$885$	12.2005	0.410114
$886$	−1.02351	−0.0343854
$887$	−15.0215	−0.504372	−0.252186	−	0.967679i	$-0.581150\pi$
$887$	−15.0215	−0.504372	−0.252186	+	0.967679i	$0.581150\pi$
$888$	0.230429	0.00773268
$889$	11.7089	0.392704
$890$	1.65637	0.0555217
$891$	1.77929	0.0596083
$892$	36.2150	1.21257
$893$	−15.2673	−0.510901
$894$	0.414770	0.0138720
$895$	−23.7699	−0.794541
$896$	−17.6889	−0.590946
$897$	7.34590	0.245273
$898$	0.717197	0.0239332
$899$	−14.5857	−0.486460
$900$	6.07461	0.202487
$901$	3.55383	0.118395
$902$	−1.11420	−0.0370989
$903$	−7.59322	−0.252687
$904$	−7.22304	−0.240235
$905$	7.51220	0.249714
$906$	−0.305642	−0.0101543
$907$	43.0364	1.42900	0.714501	−	0.699635i	$-0.246654\pi$
$907$	43.0364	1.42900	0.714501	+	0.699635i	$0.246654\pi$
$908$	−3.41045	−0.113180
$909$	8.64965	0.286891
$910$	−0.783613	−0.0259765
$911$	8.04108	0.266413	0.133206	−	0.991088i	$-0.457473\pi$
$911$	8.04108	0.266413	0.133206	+	0.991088i	$0.457473\pi$
$912$	5.21033	0.172531
$913$	5.99366	0.198361
$914$	1.93768	0.0640927
$915$	5.55127	0.183519
$916$	16.3811	0.541248
$917$	9.82268	0.324374
$918$	0.0493709	0.00162948
$919$	24.4005	0.804898	0.402449	−	0.915442i	$-0.368159\pi$
$919$	24.4005	0.804898	0.402449	+	0.915442i	$0.368159\pi$
$920$	−4.76851	−0.157213
$921$	−17.0692	−0.562451
$922$	−2.26117	−0.0744678
$923$	−10.8094	−0.355794
$924$	17.0074	0.559504
$925$	−1.51275	−0.0497388
$926$	−3.53081	−0.116030
$927$	−1.00000	−0.0328443
$928$	2.30059	0.0755204
$929$	35.7768	1.17380	0.586899	−	0.809660i	$-0.300349\pi$
$929$	35.7768	1.17380	0.586899	+	0.809660i	$0.300349\pi$
$930$	1.43459	0.0470419
$931$	21.4846	0.704129
$932$	−6.67296	−0.218580
$933$	−1.92307	−0.0629585
$934$	2.67115	0.0874027
$935$	1.04752	0.0342575
$936$	0.465837	0.0152264
$937$	46.1370	1.50723	0.753615	−	0.657316i	$-0.228308\pi$
$937$	46.1370	1.50723	0.753615	+	0.657316i	$0.228308\pi$
$938$	−1.44236	−0.0470946
$939$	26.0569	0.850335
$940$	−31.7795	−1.03653
$941$	5.35443	0.174550	0.0872748	−	0.996184i	$-0.472184\pi$
$941$	5.35443	0.174550	0.0872748	+	0.996184i	$0.472184\pi$
$942$	0.775353	0.0252624
$943$	39.3644	1.28188
$944$	−34.3055	−1.11655
$945$	6.70568	0.218136
$946$	−0.328089	−0.0106671
$947$	2.50694	0.0814647	0.0407324	−	0.999170i	$-0.487031\pi$
$947$	2.50694	0.0814647	0.0407324	+	0.999170i	$0.487031\pi$
$948$	−25.0819	−0.814621
$949$	−10.5596	−0.342778
$950$	0.475221	0.0154182
$951$	−2.38463	−0.0773268
$952$	0.947076	0.0306949
$953$	11.8481	0.383797	0.191899	−	0.981415i	$-0.438536\pi$
$953$	11.8481	0.383797	0.191899	+	0.981415i	$0.438536\pi$
$954$	0.982979	0.0318251
$955$	4.14332	0.134075
$956$	44.4537	1.43774
$957$	−2.94584	−0.0952254
$958$	1.66898	0.0539222
$959$	42.2681	1.36491
$960$	10.6938	0.345141
$961$	46.6117	1.50360
$962$	−0.0578045	−0.00186369
$963$	−0.872688	−0.0281220
$964$	37.1644	1.19699
$965$	−16.0018	−0.515115
$966$	4.13089	0.132909
$967$	59.8113	1.92340	0.961701	−	0.274101i	$-0.0883802\pi$
$967$	59.8113	1.92340	0.961701	+	0.274101i	$0.0883802\pi$
$968$	−3.64943	−0.117297
$969$	−0.561804	−0.0180478
$970$	−1.67436	−0.0537605
$971$	−8.99386	−0.288627	−0.144313	−	0.989532i	$-0.546097\pi$
$971$	−8.99386	−0.288627	−0.144313	+	0.989532i	$0.546097\pi$
$972$	−1.98634	−0.0637120
$973$	47.2940	1.51618
$974$	3.82868	0.122679
$975$	−3.05819	−0.0979403
$976$	−15.6092	−0.499638
$977$	−13.4745	−0.431086	−0.215543	−	0.976494i	$-0.569152\pi$
$977$	−13.4745	−0.431086	−0.215543	+	0.976494i	$0.569152\pi$
$978$	−0.913734	−0.0292180
$979$	18.0984	0.578428
$980$	44.7211	1.42856
$981$	−1.33197	−0.0425267
$982$	−1.70098	−0.0542806
$983$	35.9998	1.14822	0.574108	−	0.818779i	$-0.305349\pi$
$983$	35.9998	1.14822	0.574108	+	0.818779i	$0.305349\pi$
$984$	2.49628	0.0795784
$985$	20.4387	0.651231
$986$	−0.0817399	−0.00260313
$987$	55.2495	1.75861
$988$	−2.64136	−0.0840328
$989$	11.5913	0.368582
$990$	0.289740	0.00920855
$991$	−24.0162	−0.762899	−0.381450	−	0.924390i	$-0.624575\pi$
$991$	−24.0162	−0.762899	−0.381450	+	0.924390i	$0.624575\pi$
$992$	−12.2416	−0.388672
$993$	7.90274	0.250786
$994$	−6.07852	−0.192799
$995$	−6.34378	−0.201111
$996$	−6.69115	−0.212017
$997$	19.7276	0.624780	0.312390	−	0.949954i	$-0.398870\pi$
$997$	19.7276	0.624780	0.312390	+	0.949954i	$0.398870\pi$
$998$	1.24296	0.0393452
$999$	0.494655	0.0156502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.10	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-0.116858 q^{2} +1.00000 q^{3} -1.98634 q^{4} -1.39349 q^{5} -0.116858 q^{6} -4.81215 q^{7} +0.465837 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.116858 q^{2} +1.00000 q^{3} -1.98634 q^{4} -1.39349 q^{5} -0.116858 q^{6} -4.81215 q^{7} +0.465837 q^{8} +1.00000 q^{9} +0.162841 q^{10} +1.77929 q^{11} -1.98634 q^{12} +1.00000 q^{13} +0.562339 q^{14} -1.39349 q^{15} +3.91825 q^{16} -0.422486 q^{17} -0.116858 q^{18} +1.32976 q^{19} +2.76795 q^{20} -4.81215 q^{21} -0.207924 q^{22} +7.34590 q^{23} +0.465837 q^{24} -3.05819 q^{25} -0.116858 q^{26} +1.00000 q^{27} +9.55858 q^{28} -1.65563 q^{29} +0.162841 q^{30} +8.80975 q^{31} -1.38955 q^{32} +1.77929 q^{33} +0.0493709 q^{34} +6.70568 q^{35} -1.98634 q^{36} +0.494655 q^{37} -0.155393 q^{38} +1.00000 q^{39} -0.649139 q^{40} +5.35869 q^{41} +0.562339 q^{42} +1.57793 q^{43} -3.53427 q^{44} -1.39349 q^{45} -0.858429 q^{46} -11.4812 q^{47} +3.91825 q^{48} +16.1568 q^{49} +0.357374 q^{50} -0.422486 q^{51} -1.98634 q^{52} -8.41172 q^{53} -0.116858 q^{54} -2.47942 q^{55} -2.24168 q^{56} +1.32976 q^{57} +0.193474 q^{58} -8.75532 q^{59} +2.76795 q^{60} -3.98372 q^{61} -1.02949 q^{62} -4.81215 q^{63} -7.67412 q^{64} -1.39349 q^{65} -0.207924 q^{66} -2.56492 q^{67} +0.839202 q^{68} +7.34590 q^{69} -0.783613 q^{70} -10.8094 q^{71} +0.465837 q^{72} -10.5596 q^{73} -0.0578045 q^{74} -3.05819 q^{75} -2.64136 q^{76} -8.56218 q^{77} -0.116858 q^{78} +12.6272 q^{79} -5.46004 q^{80} +1.00000 q^{81} -0.626207 q^{82} +3.36857 q^{83} +9.55858 q^{84} +0.588730 q^{85} -0.184394 q^{86} -1.65563 q^{87} +0.828857 q^{88} +10.1717 q^{89} +0.162841 q^{90} -4.81215 q^{91} -14.5915 q^{92} +8.80975 q^{93} +1.34168 q^{94} -1.85301 q^{95} -1.38955 q^{96} -10.2822 q^{97} -1.88805 q^{98} +1.77929 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 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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