LMFDB - Embedded newform 4017.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.89635$ 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)

$f(q)$	$=$	$q+1.89635 q^{2} +1.00000 q^{3} +1.59615 q^{4} +1.10443 q^{5} +1.89635 q^{6} -4.39855 q^{7} -0.765840 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.89635 q^{2} +1.00000 q^{3} +1.59615 q^{4} +1.10443 q^{5} +1.89635 q^{6} -4.39855 q^{7} -0.765840 q^{8} +1.00000 q^{9} +2.09438 q^{10} -0.990085 q^{11} +1.59615 q^{12} -1.00000 q^{13} -8.34120 q^{14} +1.10443 q^{15} -4.64460 q^{16} -2.20747 q^{17} +1.89635 q^{18} +2.67115 q^{19} +1.76283 q^{20} -4.39855 q^{21} -1.87755 q^{22} +2.38700 q^{23} -0.765840 q^{24} -3.78024 q^{25} -1.89635 q^{26} +1.00000 q^{27} -7.02075 q^{28} +3.69191 q^{29} +2.09438 q^{30} -3.35426 q^{31} -7.27612 q^{32} -0.990085 q^{33} -4.18613 q^{34} -4.85788 q^{35} +1.59615 q^{36} -8.54619 q^{37} +5.06545 q^{38} -1.00000 q^{39} -0.845813 q^{40} -6.01111 q^{41} -8.34120 q^{42} +3.59584 q^{43} -1.58032 q^{44} +1.10443 q^{45} +4.52660 q^{46} -6.31254 q^{47} -4.64460 q^{48} +12.3473 q^{49} -7.16867 q^{50} -2.20747 q^{51} -1.59615 q^{52} -9.57780 q^{53} +1.89635 q^{54} -1.09348 q^{55} +3.36859 q^{56} +2.67115 q^{57} +7.00117 q^{58} -7.08167 q^{59} +1.76283 q^{60} -5.63071 q^{61} -6.36086 q^{62} -4.39855 q^{63} -4.50889 q^{64} -1.10443 q^{65} -1.87755 q^{66} +2.02543 q^{67} -3.52345 q^{68} +2.38700 q^{69} -9.21224 q^{70} +2.39750 q^{71} -0.765840 q^{72} +7.49270 q^{73} -16.2066 q^{74} -3.78024 q^{75} +4.26356 q^{76} +4.35494 q^{77} -1.89635 q^{78} -14.9525 q^{79} -5.12962 q^{80} +1.00000 q^{81} -11.3992 q^{82} +6.40425 q^{83} -7.02075 q^{84} -2.43798 q^{85} +6.81897 q^{86} +3.69191 q^{87} +0.758246 q^{88} +7.77075 q^{89} +2.09438 q^{90} +4.39855 q^{91} +3.81002 q^{92} -3.35426 q^{93} -11.9708 q^{94} +2.95009 q^{95} -7.27612 q^{96} -3.98874 q^{97} +23.4147 q^{98} -0.990085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	1.89635	1.34092	0.670462	−	0.741944i	$-0.266096\pi$
$2$	1.89635	1.34092	0.670462	+	0.741944i	$0.266096\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.59615	0.798076
$5$	1.10443	0.493914	0.246957	−	0.969026i	$-0.420569\pi$
$5$	1.10443	0.493914	0.246957	+	0.969026i	$0.420569\pi$
$6$	1.89635	0.774182
$7$	−4.39855	−1.66250	−0.831248	−	0.555902i	$-0.812373\pi$
$7$	−4.39855	−1.66250	−0.831248	+	0.555902i	$0.812373\pi$
$8$	−0.765840	−0.270765
$9$	1.00000	0.333333
$10$	2.09438	0.662301
$11$	−0.990085	−0.298522	−0.149261	−	0.988798i	$-0.547689\pi$
$11$	−0.990085	−0.298522	−0.149261	+	0.988798i	$0.547689\pi$
$12$	1.59615	0.460769
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−8.34120	−2.22928
$15$	1.10443	0.285162
$16$	−4.64460	−1.16115
$17$	−2.20747	−0.535389	−0.267695	−	0.963504i	$-0.586262\pi$
$17$	−2.20747	−0.535389	−0.267695	+	0.963504i	$0.586262\pi$
$18$	1.89635	0.446974
$19$	2.67115	0.612804	0.306402	−	0.951902i	$-0.400875\pi$
$19$	2.67115	0.612804	0.306402	+	0.951902i	$0.400875\pi$
$20$	1.76283	0.394181
$21$	−4.39855	−0.959843
$22$	−1.87755	−0.400295
$23$	2.38700	0.497725	0.248862	−	0.968539i	$-0.419943\pi$
$23$	2.38700	0.497725	0.248862	+	0.968539i	$0.419943\pi$
$24$	−0.765840	−0.156326
$25$	−3.78024	−0.756049
$26$	−1.89635	−0.371905
$27$	1.00000	0.192450
$28$	−7.02075	−1.32680
$29$	3.69191	0.685571	0.342786	−	0.939414i	$-0.388630\pi$
$29$	3.69191	0.685571	0.342786	+	0.939414i	$0.388630\pi$
$30$	2.09438	0.382380
$31$	−3.35426	−0.602443	−0.301221	−	0.953554i	$-0.597394\pi$
$31$	−3.35426	−0.602443	−0.301221	+	0.953554i	$0.597394\pi$
$32$	−7.27612	−1.28625
$33$	−0.990085	−0.172352
$34$	−4.18613	−0.717916
$35$	−4.85788	−0.821131
$36$	1.59615	0.266025
$37$	−8.54619	−1.40498	−0.702492	−	0.711691i	$-0.747930\pi$
$37$	−8.54619	−1.40498	−0.702492	+	0.711691i	$0.747930\pi$
$38$	5.06545	0.821724
$39$	−1.00000	−0.160128
$40$	−0.845813	−0.133735
$41$	−6.01111	−0.938778	−0.469389	−	0.882991i	$-0.655526\pi$
$41$	−6.01111	−0.938778	−0.469389	+	0.882991i	$0.655526\pi$
$42$	−8.34120	−1.28708
$43$	3.59584	0.548360	0.274180	−	0.961678i	$-0.411594\pi$
$43$	3.59584	0.548360	0.274180	+	0.961678i	$0.411594\pi$
$44$	−1.58032	−0.238243
$45$	1.10443	0.164638
$46$	4.52660	0.667411
$47$	−6.31254	−0.920779	−0.460390	−	0.887717i	$-0.652290\pi$
$47$	−6.31254	−0.920779	−0.460390	+	0.887717i	$0.652290\pi$
$48$	−4.64460	−0.670391
$49$	12.3473	1.76389
$50$	−7.16867	−1.01380
$51$	−2.20747	−0.309107
$52$	−1.59615	−0.221346
$53$	−9.57780	−1.31561	−0.657806	−	0.753187i	$-0.728515\pi$
$53$	−9.57780	−1.31561	−0.657806	+	0.753187i	$0.728515\pi$
$54$	1.89635	0.258061
$55$	−1.09348	−0.147444
$56$	3.36859	0.450146
$57$	2.67115	0.353803
$58$	7.00117	0.919298
$59$	−7.08167	−0.921955	−0.460978	−	0.887412i	$-0.652501\pi$
$59$	−7.08167	−0.921955	−0.460978	+	0.887412i	$0.652501\pi$
$60$	1.76283	0.227581
$61$	−5.63071	−0.720938	−0.360469	−	0.932771i	$-0.617383\pi$
$61$	−5.63071	−0.720938	−0.360469	+	0.932771i	$0.617383\pi$
$62$	−6.36086	−0.807830
$63$	−4.39855	−0.554165
$64$	−4.50889	−0.563611
$65$	−1.10443	−0.136987
$66$	−1.87755	−0.231110
$67$	2.02543	0.247446	0.123723	−	0.992317i	$-0.460517\pi$
$67$	2.02543	0.247446	0.123723	+	0.992317i	$0.460517\pi$
$68$	−3.52345	−0.427281
$69$	2.38700	0.287362
$70$	−9.21224	−1.10107
$71$	2.39750	0.284531	0.142265	−	0.989829i	$-0.454561\pi$
$71$	2.39750	0.284531	0.142265	+	0.989829i	$0.454561\pi$
$72$	−0.765840	−0.0902551
$73$	7.49270	0.876954	0.438477	−	0.898742i	$-0.355518\pi$
$73$	7.49270	0.876954	0.438477	+	0.898742i	$0.355518\pi$
$74$	−16.2066	−1.88398
$75$	−3.78024	−0.436505
$76$	4.26356	0.489064
$77$	4.35494	0.496291
$78$	−1.89635	−0.214720
$79$	−14.9525	−1.68228	−0.841142	−	0.540815i	$-0.818116\pi$
$79$	−14.9525	−1.68228	−0.841142	+	0.540815i	$0.818116\pi$
$80$	−5.12962	−0.573509
$81$	1.00000	0.111111
$82$	−11.3992	−1.25883
$83$	6.40425	0.702958	0.351479	−	0.936196i	$-0.385679\pi$
$83$	6.40425	0.702958	0.351479	+	0.936196i	$0.385679\pi$
$84$	−7.02075	−0.766027
$85$	−2.43798	−0.264437
$86$	6.81897	0.735309
$87$	3.69191	0.395815
$88$	0.758246	0.0808293
$89$	7.77075	0.823698	0.411849	−	0.911252i	$-0.364883\pi$
$89$	7.77075	0.823698	0.411849	+	0.911252i	$0.364883\pi$
$90$	2.09438	0.220767
$91$	4.39855	0.461093
$92$	3.81002	0.397222
$93$	−3.35426	−0.347820
$94$	−11.9708	−1.23469
$95$	2.95009	0.302673
$96$	−7.27612	−0.742616
$97$	−3.98874	−0.404995	−0.202498	−	0.979283i	$-0.564906\pi$
$97$	−3.98874	−0.404995	−0.202498	+	0.979283i	$0.564906\pi$
$98$	23.4147	2.36525
$99$	−0.990085	−0.0995073
$100$	−6.03384	−0.603384
$101$	−13.9228	−1.38537	−0.692686	−	0.721239i	$-0.743573\pi$
$101$	−13.9228	−1.38537	−0.692686	+	0.721239i	$0.743573\pi$
$102$	−4.18613	−0.414489
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	0.765840	0.0750968
$105$	−4.85788	−0.474080
$106$	−18.1629	−1.76414
$107$	−10.8419	−1.04813	−0.524063	−	0.851679i	$-0.675584\pi$
$107$	−10.8419	−1.04813	−0.524063	+	0.851679i	$0.675584\pi$
$108$	1.59615	0.153590
$109$	11.7532	1.12575	0.562876	−	0.826542i	$-0.309695\pi$
$109$	11.7532	1.12575	0.562876	+	0.826542i	$0.309695\pi$
$110$	−2.07361	−0.197711
$111$	−8.54619	−0.811168
$112$	20.4295	1.93041
$113$	−6.93295	−0.652197	−0.326098	−	0.945336i	$-0.605734\pi$
$113$	−6.93295	−0.652197	−0.326098	+	0.945336i	$0.605734\pi$
$114$	5.06545	0.474422
$115$	2.63627	0.245833
$116$	5.89285	0.547138
$117$	−1.00000	−0.0924500
$118$	−13.4293	−1.23627
$119$	9.70966	0.890083
$120$	−0.845813	−0.0772119
$121$	−10.0197	−0.910885
$122$	−10.6778	−0.966723
$123$	−6.01111	−0.542004
$124$	−5.35390	−0.480795
$125$	−9.69713	−0.867338
$126$	−8.34120	−0.743093
$127$	−15.7553	−1.39806	−0.699029	−	0.715094i	$-0.746384\pi$
$127$	−15.7553	−1.39806	−0.699029	+	0.715094i	$0.746384\pi$
$128$	6.00181	0.530490
$129$	3.59584	0.316596
$130$	−2.09438	−0.183689
$131$	4.50402	0.393518	0.196759	−	0.980452i	$-0.436958\pi$
$131$	4.50402	0.393518	0.196759	+	0.980452i	$0.436958\pi$
$132$	−1.58032	−0.137550
$133$	−11.7492	−1.01878
$134$	3.84093	0.331806
$135$	1.10443	0.0950539
$136$	1.69057	0.144965
$137$	16.3156	1.39394	0.696968	−	0.717103i	$-0.254532\pi$
$137$	16.3156	1.39394	0.696968	+	0.717103i	$0.254532\pi$
$138$	4.52660	0.385330
$139$	12.5660	1.06583	0.532917	−	0.846167i	$-0.321096\pi$
$139$	12.5660	1.06583	0.532917	+	0.846167i	$0.321096\pi$
$140$	−7.75390	−0.655324
$141$	−6.31254	−0.531612
$142$	4.54650	0.381534
$143$	0.990085	0.0827950
$144$	−4.64460	−0.387050
$145$	4.07745	0.338613
$146$	14.2088	1.17593
$147$	12.3473	1.01838
$148$	−13.6410	−1.12128
$149$	19.4392	1.59252	0.796261	−	0.604953i	$-0.206808\pi$
$149$	19.4392	1.59252	0.796261	+	0.604953i	$0.206808\pi$
$150$	−7.16867	−0.585320
$151$	7.03454	0.572463	0.286231	−	0.958160i	$-0.407597\pi$
$151$	7.03454	0.572463	0.286231	+	0.958160i	$0.407597\pi$
$152$	−2.04567	−0.165926
$153$	−2.20747	−0.178463
$154$	8.25850	0.665489
$155$	−3.70453	−0.297555
$156$	−1.59615	−0.127794
$157$	3.14102	0.250681	0.125341	−	0.992114i	$-0.459998\pi$
$157$	3.14102	0.250681	0.125341	+	0.992114i	$0.459998\pi$
$158$	−28.3551	−2.25581
$159$	−9.57780	−0.759569
$160$	−8.03594	−0.635297
$161$	−10.4994	−0.827466
$162$	1.89635	0.148991
$163$	24.5025	1.91918	0.959591	−	0.281398i	$-0.0907982\pi$
$163$	24.5025	1.91918	0.959591	+	0.281398i	$0.0907982\pi$
$164$	−9.59464	−0.749216
$165$	−1.09348	−0.0851270
$166$	12.1447	0.942613
$167$	−6.48619	−0.501917	−0.250958	−	0.967998i	$-0.580746\pi$
$167$	−6.48619	−0.501917	−0.250958	+	0.967998i	$0.580746\pi$
$168$	3.36859	0.259892
$169$	1.00000	0.0769231
$170$	−4.62328	−0.354589
$171$	2.67115	0.204268
$172$	5.73950	0.437633
$173$	12.4086	0.943409	0.471704	−	0.881757i	$-0.343639\pi$
$173$	12.4086	0.943409	0.471704	+	0.881757i	$0.343639\pi$
$174$	7.00117	0.530757
$175$	16.6276	1.25693
$176$	4.59855	0.346629
$177$	−7.08167	−0.532291
$178$	14.7361	1.10452
$179$	5.15007	0.384934	0.192467	−	0.981303i	$-0.438351\pi$
$179$	5.15007	0.384934	0.192467	+	0.981303i	$0.438351\pi$
$180$	1.76283	0.131394
$181$	18.5639	1.37984	0.689921	−	0.723884i	$-0.257645\pi$
$181$	18.5639	1.37984	0.689921	+	0.723884i	$0.257645\pi$
$182$	8.34120	0.618291
$183$	−5.63071	−0.416234
$184$	−1.82806	−0.134767
$185$	−9.43864	−0.693942
$186$	−6.36086	−0.466401
$187$	2.18558	0.159825
$188$	−10.0758	−0.734851
$189$	−4.39855	−0.319948
$190$	5.59441	0.405861
$191$	2.35313	0.170267	0.0851333	−	0.996370i	$-0.472868\pi$
$191$	2.35313	0.170267	0.0851333	+	0.996370i	$0.472868\pi$
$192$	−4.50889	−0.325401
$193$	14.3452	1.03259	0.516293	−	0.856412i	$-0.327311\pi$
$193$	14.3452	1.03259	0.516293	+	0.856412i	$0.327311\pi$
$194$	−7.56406	−0.543068
$195$	−1.10443	−0.0790896
$196$	19.7081	1.40772
$197$	−2.63072	−0.187431	−0.0937154	−	0.995599i	$-0.529874\pi$
$197$	−2.63072	−0.187431	−0.0937154	+	0.995599i	$0.529874\pi$
$198$	−1.87755	−0.133432
$199$	−6.43291	−0.456017	−0.228009	−	0.973659i	$-0.573221\pi$
$199$	−6.43291	−0.456017	−0.228009	+	0.973659i	$0.573221\pi$
$200$	2.89506	0.204712
$201$	2.02543	0.142863
$202$	−26.4026	−1.85768
$203$	−16.2391	−1.13976
$204$	−3.52345	−0.246691
$205$	−6.63883	−0.463676
$206$	1.89635	0.132125
$207$	2.38700	0.165908
$208$	4.64460	0.322045
$209$	−2.64467	−0.182935
$210$	−9.21224	−0.635705
$211$	−7.67877	−0.528628	−0.264314	−	0.964437i	$-0.585146\pi$
$211$	−7.67877	−0.528628	−0.264314	+	0.964437i	$0.585146\pi$
$212$	−15.2876	−1.04996
$213$	2.39750	0.164274
$214$	−20.5601	−1.40546
$215$	3.97134	0.270843
$216$	−0.765840	−0.0521088
$217$	14.7539	1.00156
$218$	22.2882	1.50955
$219$	7.49270	0.506310
$220$	−1.74535	−0.117672
$221$	2.20747	0.148490
$222$	−16.2066	−1.08771
$223$	27.9316	1.87044	0.935218	−	0.354074i	$-0.115204\pi$
$223$	27.9316	1.87044	0.935218	+	0.354074i	$0.115204\pi$
$224$	32.0044	2.13838
$225$	−3.78024	−0.252016
$226$	−13.1473	−0.874546
$227$	−21.3824	−1.41920	−0.709598	−	0.704606i	$-0.751124\pi$
$227$	−21.3824	−1.41920	−0.709598	+	0.704606i	$0.751124\pi$
$228$	4.26356	0.282361
$229$	3.95484	0.261343	0.130671	−	0.991426i	$-0.458287\pi$
$229$	3.95484	0.261343	0.130671	+	0.991426i	$0.458287\pi$
$230$	4.99930	0.329644
$231$	4.35494	0.286534
$232$	−2.82741	−0.185629
$233$	−16.4130	−1.07525	−0.537627	−	0.843183i	$-0.680679\pi$
$233$	−16.4130	−1.07525	−0.537627	+	0.843183i	$0.680679\pi$
$234$	−1.89635	−0.123968
$235$	−6.97174	−0.454786
$236$	−11.3034	−0.735790
$237$	−14.9525	−0.971267
$238$	18.4129	1.19353
$239$	7.31462	0.473143	0.236572	−	0.971614i	$-0.423976\pi$
$239$	7.31462	0.473143	0.236572	+	0.971614i	$0.423976\pi$
$240$	−5.12962	−0.331116
$241$	24.7536	1.59452	0.797258	−	0.603638i	$-0.206283\pi$
$241$	24.7536	1.59452	0.797258	+	0.603638i	$0.206283\pi$
$242$	−19.0009	−1.22143
$243$	1.00000	0.0641500
$244$	−8.98746	−0.575363
$245$	13.6366	0.871213
$246$	−11.3992	−0.726785
$247$	−2.67115	−0.169961
$248$	2.56883	0.163121
$249$	6.40425	0.405853
$250$	−18.3892	−1.16303
$251$	−4.79776	−0.302832	−0.151416	−	0.988470i	$-0.548383\pi$
$251$	−4.79776	−0.302832	−0.151416	+	0.988470i	$0.548383\pi$
$252$	−7.02075	−0.442266
$253$	−2.36334	−0.148582
$254$	−29.8776	−1.87469
$255$	−2.43798	−0.152672
$256$	20.3993	1.27496
$257$	9.14654	0.570545	0.285273	−	0.958446i	$-0.407916\pi$
$257$	9.14654	0.570545	0.285273	+	0.958446i	$0.407916\pi$
$258$	6.81897	0.424531
$259$	37.5909	2.33578
$260$	−1.76283	−0.109326
$261$	3.69191	0.228524
$262$	8.54121	0.527678
$263$	−13.6221	−0.839973	−0.419987	−	0.907530i	$-0.637965\pi$
$263$	−13.6221	−0.839973	−0.419987	+	0.907530i	$0.637965\pi$
$264$	0.758246	0.0466668
$265$	−10.5780	−0.649800
$266$	−22.2806	−1.36611
$267$	7.77075	0.475562
$268$	3.23289	0.197480
$269$	−18.5298	−1.12978	−0.564889	−	0.825167i	$-0.691081\pi$
$269$	−18.5298	−1.12978	−0.564889	+	0.825167i	$0.691081\pi$
$270$	2.09438	0.127460
$271$	−23.2355	−1.41146	−0.705728	−	0.708483i	$-0.749380\pi$
$271$	−23.2355	−1.41146	−0.705728	+	0.708483i	$0.749380\pi$
$272$	10.2528	0.621668
$273$	4.39855	0.266212
$274$	30.9401	1.86916
$275$	3.74276	0.225697
$276$	3.81002	0.229336
$277$	−8.60887	−0.517257	−0.258628	−	0.965977i	$-0.583271\pi$
$277$	−8.60887	−0.517257	−0.258628	+	0.965977i	$0.583271\pi$
$278$	23.8296	1.42920
$279$	−3.35426	−0.200814
$280$	3.72035	0.222334
$281$	17.2701	1.03024	0.515122	−	0.857117i	$-0.327746\pi$
$281$	17.2701	1.03024	0.515122	+	0.857117i	$0.327746\pi$
$282$	−11.9708	−0.712851
$283$	7.51808	0.446903	0.223452	−	0.974715i	$-0.428268\pi$
$283$	7.51808	0.446903	0.223452	+	0.974715i	$0.428268\pi$
$284$	3.82677	0.227077
$285$	2.95009	0.174748
$286$	1.87755	0.111022
$287$	26.4402	1.56071
$288$	−7.27612	−0.428750
$289$	−12.1271	−0.713358
$290$	7.73227	0.454055
$291$	−3.98874	−0.233824
$292$	11.9595	0.699876
$293$	−16.8945	−0.986989	−0.493495	−	0.869749i	$-0.664281\pi$
$293$	−16.8945	−0.986989	−0.493495	+	0.869749i	$0.664281\pi$
$294$	23.4147	1.36558
$295$	−7.82118	−0.455367
$296$	6.54501	0.380421
$297$	−0.990085	−0.0574505
$298$	36.8636	2.13545
$299$	−2.38700	−0.138044
$300$	−6.03384	−0.348364
$301$	−15.8165	−0.911646
$302$	13.3400	0.767629
$303$	−13.9228	−0.799845
$304$	−12.4064	−0.711558
$305$	−6.21870	−0.356082
$306$	−4.18613	−0.239305
$307$	−32.6879	−1.86560	−0.932799	−	0.360397i	$-0.882641\pi$
$307$	−32.6879	−1.86560	−0.932799	+	0.360397i	$0.882641\pi$
$308$	6.95114	0.396078
$309$	1.00000	0.0568880
$310$	−7.02510	−0.398999
$311$	−8.53485	−0.483967	−0.241983	−	0.970280i	$-0.577798\pi$
$311$	−8.53485	−0.483967	−0.241983	+	0.970280i	$0.577798\pi$
$312$	0.765840	0.0433571
$313$	−4.54925	−0.257139	−0.128569	−	0.991701i	$-0.541038\pi$
$313$	−4.54925	−0.257139	−0.128569	+	0.991701i	$0.541038\pi$
$314$	5.95649	0.336144
$315$	−4.85788	−0.273710
$316$	−23.8664	−1.34259
$317$	−5.25998	−0.295430	−0.147715	−	0.989030i	$-0.547192\pi$
$317$	−5.25998	−0.295430	−0.147715	+	0.989030i	$0.547192\pi$
$318$	−18.1629	−1.01852
$319$	−3.65531	−0.204658
$320$	−4.97973	−0.278375
$321$	−10.8419	−0.605136
$322$	−19.9105	−1.10957
$323$	−5.89648	−0.328089
$324$	1.59615	0.0886751
$325$	3.78024	0.209690
$326$	46.4653	2.57348
$327$	11.7532	0.649953
$328$	4.60355	0.254188
$329$	27.7660	1.53079
$330$	−2.07361	−0.114149
$331$	19.1538	1.05279	0.526393	−	0.850242i	$-0.323544\pi$
$331$	19.1538	1.05279	0.526393	+	0.850242i	$0.323544\pi$
$332$	10.2222	0.561014
$333$	−8.54619	−0.468328
$334$	−12.3001	−0.673032
$335$	2.23694	0.122217
$336$	20.4295	1.11452
$337$	12.6461	0.688876	0.344438	−	0.938809i	$-0.388070\pi$
$337$	12.6461	0.688876	0.344438	+	0.938809i	$0.388070\pi$
$338$	1.89635	0.103148
$339$	−6.93295	−0.376546
$340$	−3.89139	−0.211040
$341$	3.32100	0.179842
$342$	5.06545	0.273908
$343$	−23.5202	−1.26997
$344$	−2.75383	−0.148477
$345$	2.63627	0.141932
$346$	23.5311	1.26504
$347$	22.4785	1.20671	0.603355	−	0.797473i	$-0.293830\pi$
$347$	22.4785	1.20671	0.603355	+	0.797473i	$0.293830\pi$
$348$	5.89285	0.315890
$349$	5.89878	0.315755	0.157877	−	0.987459i	$-0.449535\pi$
$349$	5.89878	0.315755	0.157877	+	0.987459i	$0.449535\pi$
$350$	31.5318	1.68544
$351$	−1.00000	−0.0533761
$352$	7.20398	0.383973
$353$	16.8038	0.894374	0.447187	−	0.894440i	$-0.352426\pi$
$353$	16.8038	0.894374	0.447187	+	0.894440i	$0.352426\pi$
$354$	−13.4293	−0.713762
$355$	2.64786	0.140534
$356$	12.4033	0.657373
$357$	9.70966	0.513890
$358$	9.76634	0.516167
$359$	0.960697	0.0507037	0.0253518	−	0.999679i	$-0.491929\pi$
$359$	0.960697	0.0507037	0.0253518	+	0.999679i	$0.491929\pi$
$360$	−0.845813	−0.0445783
$361$	−11.8649	−0.624471
$362$	35.2037	1.85026
$363$	−10.0197	−0.525900
$364$	7.02075	0.367987
$365$	8.27514	0.433140
$366$	−10.6778	−0.558138
$367$	−2.48358	−0.129642	−0.0648209	−	0.997897i	$-0.520648\pi$
$367$	−2.48358	−0.129642	−0.0648209	+	0.997897i	$0.520648\pi$
$368$	−11.0867	−0.577934
$369$	−6.01111	−0.312926
$370$	−17.8990	−0.930523
$371$	42.1285	2.18720
$372$	−5.35390	−0.277587
$373$	−20.8352	−1.07881	−0.539403	−	0.842047i	$-0.681350\pi$
$373$	−20.8352	−1.07881	−0.539403	+	0.842047i	$0.681350\pi$
$374$	4.14463	0.214314
$375$	−9.69713	−0.500758
$376$	4.83440	0.249315
$377$	−3.69191	−0.190143
$378$	−8.34120	−0.429025
$379$	−21.9458	−1.12728	−0.563640	−	0.826021i	$-0.690599\pi$
$379$	−21.9458	−1.12728	−0.563640	+	0.826021i	$0.690599\pi$
$380$	4.70879	0.241556
$381$	−15.7553	−0.807169
$382$	4.46236	0.228314
$383$	−30.9033	−1.57909	−0.789544	−	0.613694i	$-0.789683\pi$
$383$	−30.9033	−1.57909	−0.789544	+	0.613694i	$0.789683\pi$
$384$	6.00181	0.306279
$385$	4.80971	0.245125
$386$	27.2035	1.38462
$387$	3.59584	0.182787
$388$	−6.36663	−0.323217
$389$	32.3604	1.64074	0.820369	−	0.571834i	$-0.193768\pi$
$389$	32.3604	1.64074	0.820369	+	0.571834i	$0.193768\pi$
$390$	−2.09438	−0.106053
$391$	−5.26923	−0.266477
$392$	−9.45602	−0.477601
$393$	4.50402	0.227198
$394$	−4.98876	−0.251330
$395$	−16.5139	−0.830904
$396$	−1.58032	−0.0794143
$397$	39.0033	1.95752	0.978759	−	0.205014i	$-0.0657239\pi$
$397$	39.0033	1.95752	0.978759	+	0.205014i	$0.0657239\pi$
$398$	−12.1991	−0.611484
$399$	−11.7492	−0.588196
$400$	17.5577	0.877887
$401$	−27.4590	−1.37124	−0.685619	−	0.727960i	$-0.740469\pi$
$401$	−27.4590	−1.37124	−0.685619	+	0.727960i	$0.740469\pi$
$402$	3.84093	0.191568
$403$	3.35426	0.167088
$404$	−22.2229	−1.10563
$405$	1.10443	0.0548794
$406$	−30.7950	−1.52833
$407$	8.46145	0.419419
$408$	1.69057	0.0836955
$409$	23.0115	1.13784	0.568922	−	0.822391i	$-0.307361\pi$
$409$	23.0115	1.13784	0.568922	+	0.822391i	$0.307361\pi$
$410$	−12.5896	−0.621754
$411$	16.3156	0.804789
$412$	1.59615	0.0786367
$413$	31.1491	1.53275
$414$	4.52660	0.222470
$415$	7.07302	0.347201
$416$	7.27612	0.356741
$417$	12.5660	0.615360
$418$	−5.01522	−0.245302
$419$	−20.5273	−1.00282	−0.501412	−	0.865209i	$-0.667186\pi$
$419$	−20.5273	−1.00282	−0.501412	+	0.865209i	$0.667186\pi$
$420$	−7.75390	−0.378352
$421$	−6.46207	−0.314942	−0.157471	−	0.987524i	$-0.550334\pi$
$421$	−6.46207	−0.314942	−0.157471	+	0.987524i	$0.550334\pi$
$422$	−14.5616	−0.708850
$423$	−6.31254	−0.306926
$424$	7.33506	0.356222
$425$	8.34476	0.404780
$426$	4.54650	0.220279
$427$	24.7670	1.19856
$428$	−17.3053	−0.836484
$429$	0.990085	0.0478017
$430$	7.53105	0.363180
$431$	18.7731	0.904271	0.452135	−	0.891949i	$-0.350662\pi$
$431$	18.7731	0.904271	0.452135	+	0.891949i	$0.350662\pi$
$432$	−4.64460	−0.223464
$433$	10.7519	0.516705	0.258353	−	0.966051i	$-0.416820\pi$
$433$	10.7519	0.516705	0.258353	+	0.966051i	$0.416820\pi$
$434$	27.9786	1.34301
$435$	4.07745	0.195499
$436$	18.7599	0.898435
$437$	6.37605	0.305008
$438$	14.2088	0.678923
$439$	−29.5122	−1.40854	−0.704269	−	0.709933i	$-0.748725\pi$
$439$	−29.5122	−1.40854	−0.704269	+	0.709933i	$0.748725\pi$
$440$	0.837427	0.0399228
$441$	12.3473	0.587965
$442$	4.18613	0.199114
$443$	−25.4045	−1.20701	−0.603503	−	0.797361i	$-0.706229\pi$
$443$	−25.4045	−1.20701	−0.603503	+	0.797361i	$0.706229\pi$
$444$	−13.6410	−0.647374
$445$	8.58222	0.406836
$446$	52.9681	2.50811
$447$	19.4392	0.919443
$448$	19.8326	0.937001
$449$	3.87407	0.182828	0.0914142	−	0.995813i	$-0.470861\pi$
$449$	3.87407	0.182828	0.0914142	+	0.995813i	$0.470861\pi$
$450$	−7.16867	−0.337934
$451$	5.95151	0.280246
$452$	−11.0660	−0.520502
$453$	7.03454	0.330512
$454$	−40.5485	−1.90303
$455$	4.85788	0.227741
$456$	−2.04567	−0.0957975
$457$	9.61626	0.449829	0.224915	−	0.974378i	$-0.427790\pi$
$457$	9.61626	0.449829	0.224915	+	0.974378i	$0.427790\pi$
$458$	7.49976	0.350441
$459$	−2.20747	−0.103036
$460$	4.20789	0.196194
$461$	−16.5991	−0.773097	−0.386549	−	0.922269i	$-0.626333\pi$
$461$	−16.5991	−0.773097	−0.386549	+	0.922269i	$0.626333\pi$
$462$	8.25850	0.384220
$463$	−0.477144	−0.0221748	−0.0110874	−	0.999939i	$-0.503529\pi$
$463$	−0.477144	−0.0221748	−0.0110874	+	0.999939i	$0.503529\pi$
$464$	−17.1475	−0.796052
$465$	−3.70453	−0.171794
$466$	−31.1249	−1.44183
$467$	4.76464	0.220481	0.110241	−	0.993905i	$-0.464838\pi$
$467$	4.76464	0.220481	0.110241	+	0.993905i	$0.464838\pi$
$468$	−1.59615	−0.0737821
$469$	−8.90895	−0.411377
$470$	−13.2209	−0.609833
$471$	3.14102	0.144731
$472$	5.42343	0.249633
$473$	−3.56018	−0.163697
$474$	−28.3551	−1.30239
$475$	−10.0976	−0.463310
$476$	15.4981	0.710353
$477$	−9.57780	−0.438538
$478$	13.8711	0.634449
$479$	−9.60959	−0.439073	−0.219537	−	0.975604i	$-0.570455\pi$
$479$	−9.60959	−0.439073	−0.219537	+	0.975604i	$0.570455\pi$
$480$	−8.03594	−0.366789
$481$	8.54619	0.389673
$482$	46.9415	2.13812
$483$	−10.4994	−0.477738
$484$	−15.9930	−0.726955
$485$	−4.40527	−0.200033
$486$	1.89635	0.0860203
$487$	−36.4055	−1.64969	−0.824845	−	0.565359i	$-0.808738\pi$
$487$	−36.4055	−1.64969	−0.824845	+	0.565359i	$0.808738\pi$
$488$	4.31222	0.195205
$489$	24.5025	1.10804
$490$	25.8599	1.16823
$491$	−28.2482	−1.27482	−0.637412	−	0.770523i	$-0.719995\pi$
$491$	−28.2482	−1.27482	−0.637412	+	0.770523i	$0.719995\pi$
$492$	−9.59464	−0.432560
$493$	−8.14978	−0.367048
$494$	−5.06545	−0.227905
$495$	−1.09348	−0.0491481
$496$	15.5792	0.699527
$497$	−10.5455	−0.473031
$498$	12.1447	0.544218
$499$	−12.9688	−0.580564	−0.290282	−	0.956941i	$-0.593749\pi$
$499$	−12.9688	−0.580564	−0.290282	+	0.956941i	$0.593749\pi$
$500$	−15.4781	−0.692201
$501$	−6.48619	−0.289782
$502$	−9.09824	−0.406074
$503$	−20.4275	−0.910816	−0.455408	−	0.890283i	$-0.650507\pi$
$503$	−20.4275	−0.910816	−0.455408	+	0.890283i	$0.650507\pi$
$504$	3.36859	0.150049
$505$	−15.3767	−0.684255
$506$	−4.48172	−0.199237
$507$	1.00000	0.0444116
$508$	−25.1478	−1.11576
$509$	9.16497	0.406230	0.203115	−	0.979155i	$-0.434893\pi$
$509$	9.16497	0.406230	0.203115	+	0.979155i	$0.434893\pi$
$510$	−4.62328	−0.204722
$511$	−32.9570	−1.45793
$512$	26.6807	1.17913
$513$	2.67115	0.117934
$514$	17.3451	0.765058
$515$	1.10443	0.0486668
$516$	5.73950	0.252667
$517$	6.24995	0.274873
$518$	71.2855	3.13210
$519$	12.4086	0.544677
$520$	0.845813	0.0370914
$521$	−18.7624	−0.821998	−0.410999	−	0.911636i	$-0.634820\pi$
$521$	−18.7624	−0.821998	−0.410999	+	0.911636i	$0.634820\pi$
$522$	7.00117	0.306433
$523$	−35.2518	−1.54145	−0.770726	−	0.637167i	$-0.780106\pi$
$523$	−35.2518	−1.54145	−0.770726	+	0.637167i	$0.780106\pi$
$524$	7.18910	0.314057
$525$	16.6276	0.725688
$526$	−25.8323	−1.12634
$527$	7.40442	0.322541
$528$	4.59855	0.200126
$529$	−17.3022	−0.752270
$530$	−20.0596	−0.871332
$531$	−7.08167	−0.307318
$532$	−18.7535	−0.813067
$533$	6.01111	0.260370
$534$	14.7361	0.637693
$535$	−11.9741	−0.517685
$536$	−1.55115	−0.0669997
$537$	5.15007	0.222242
$538$	−35.1389	−1.51495
$539$	−12.2248	−0.526561
$540$	1.76283	0.0758602
$541$	12.1435	0.522088	0.261044	−	0.965327i	$-0.415933\pi$
$541$	12.1435	0.522088	0.261044	+	0.965327i	$0.415933\pi$
$542$	−44.0627	−1.89266
$543$	18.5639	0.796653
$544$	16.0618	0.688644
$545$	12.9805	0.556025
$546$	8.34120	0.356971
$547$	−29.3298	−1.25405	−0.627025	−	0.778999i	$-0.715728\pi$
$547$	−29.3298	−1.25405	−0.627025	+	0.778999i	$0.715728\pi$
$548$	26.0421	1.11247
$549$	−5.63071	−0.240313
$550$	7.09759	0.302642
$551$	9.86166	0.420121
$552$	−1.82806	−0.0778075
$553$	65.7692	2.79679
$554$	−16.3255	−0.693602
$555$	−9.43864	−0.400648
$556$	20.0572	0.850617
$557$	−3.28247	−0.139083	−0.0695413	−	0.997579i	$-0.522154\pi$
$557$	−3.28247	−0.139083	−0.0695413	+	0.997579i	$0.522154\pi$
$558$	−6.36086	−0.269277
$559$	−3.59584	−0.152088
$560$	22.5629	0.953457
$561$	2.18558	0.0922752
$562$	32.7501	1.38148
$563$	22.7881	0.960402	0.480201	−	0.877158i	$-0.340564\pi$
$563$	22.7881	0.960402	0.480201	+	0.877158i	$0.340564\pi$
$564$	−10.0758	−0.424267
$565$	−7.65693	−0.322129
$566$	14.2569	0.599263
$567$	−4.39855	−0.184722
$568$	−1.83610	−0.0770410
$569$	22.0380	0.923881	0.461940	−	0.886911i	$-0.347153\pi$
$569$	22.0380	0.923881	0.461940	+	0.886911i	$0.347153\pi$
$570$	5.59441	0.234324
$571$	−15.7941	−0.660962	−0.330481	−	0.943813i	$-0.607211\pi$
$571$	−15.7941	−0.660962	−0.330481	+	0.943813i	$0.607211\pi$
$572$	1.58032	0.0660767
$573$	2.35313	0.0983035
$574$	50.1399	2.09280
$575$	−9.02346	−0.376304
$576$	−4.50889	−0.187870
$577$	−40.7168	−1.69506	−0.847530	−	0.530747i	$-0.821911\pi$
$577$	−40.7168	−1.69506	−0.847530	+	0.530747i	$0.821911\pi$
$578$	−22.9972	−0.956559
$579$	14.3452	0.596164
$580$	6.50822	0.270239
$581$	−28.1694	−1.16866
$582$	−7.56406	−0.313540
$583$	9.48284	0.392739
$584$	−5.73821	−0.237449
$585$	−1.10443	−0.0456624
$586$	−32.0380	−1.32348
$587$	−34.0516	−1.40546	−0.702731	−	0.711456i	$-0.748036\pi$
$587$	−34.0516	−1.40546	−0.702731	+	0.711456i	$0.748036\pi$
$588$	19.7081	0.812748
$589$	−8.95974	−0.369180
$590$	−14.8317	−0.610612
$591$	−2.63072	−0.108213
$592$	39.6937	1.63140
$593$	2.17190	0.0891891	0.0445945	−	0.999005i	$-0.485800\pi$
$593$	2.17190	0.0891891	0.0445945	+	0.999005i	$0.485800\pi$
$594$	−1.87755	−0.0770368
$595$	10.7236	0.439625
$596$	31.0279	1.27095
$597$	−6.43291	−0.263282
$598$	−4.52660	−0.185106
$599$	22.5713	0.922239	0.461119	−	0.887338i	$-0.347448\pi$
$599$	22.5713	0.922239	0.461119	+	0.887338i	$0.347448\pi$
$600$	2.89506	0.118190
$601$	−37.2963	−1.52135	−0.760673	−	0.649135i	$-0.775131\pi$
$601$	−37.2963	−1.52135	−0.760673	+	0.649135i	$0.775131\pi$
$602$	−29.9936	−1.22245
$603$	2.02543	0.0824818
$604$	11.2282	0.456869
$605$	−11.0661	−0.449899
$606$	−26.4026	−1.07253
$607$	−8.59044	−0.348675	−0.174338	−	0.984686i	$-0.555778\pi$
$607$	−8.59044	−0.348675	−0.174338	+	0.984686i	$0.555778\pi$
$608$	−19.4356	−0.788219
$609$	−16.2391	−0.658040
$610$	−11.7928	−0.477478
$611$	6.31254	0.255378
$612$	−3.52345	−0.142427
$613$	19.1579	0.773781	0.386891	−	0.922126i	$-0.373549\pi$
$613$	19.1579	0.773781	0.386891	+	0.922126i	$0.373549\pi$
$614$	−61.9878	−2.50162
$615$	−6.63883	−0.267703
$616$	−3.33519	−0.134378
$617$	1.35892	0.0547081	0.0273540	−	0.999626i	$-0.491292\pi$
$617$	1.35892	0.0547081	0.0273540	+	0.999626i	$0.491292\pi$
$618$	1.89635	0.0762825
$619$	0.126035	0.00506577	0.00253289	−	0.999997i	$-0.499194\pi$
$619$	0.126035	0.00506577	0.00253289	+	0.999997i	$0.499194\pi$
$620$	−5.91299	−0.237471
$621$	2.38700	0.0957872
$622$	−16.1851	−0.648963
$623$	−34.1801	−1.36940
$624$	4.64460	0.185933
$625$	8.19145	0.327658
$626$	−8.62697	−0.344803
$627$	−2.64467	−0.105618
$628$	5.01355	0.200062
$629$	18.8654	0.752214
$630$	−9.21224	−0.367025
$631$	−34.5514	−1.37547	−0.687734	−	0.725963i	$-0.741394\pi$
$631$	−34.5514	−1.37547	−0.687734	+	0.725963i	$0.741394\pi$
$632$	11.4512	0.455504
$633$	−7.67877	−0.305204
$634$	−9.97477	−0.396149
$635$	−17.4006	−0.690521
$636$	−15.2876	−0.606194
$637$	−12.3473	−0.489216
$638$	−6.93175	−0.274431
$639$	2.39750	0.0948436
$640$	6.62856	0.262017
$641$	3.28800	0.129868	0.0649341	−	0.997890i	$-0.479316\pi$
$641$	3.28800	0.129868	0.0649341	+	0.997890i	$0.479316\pi$
$642$	−20.5601	−0.811441
$643$	−3.28871	−0.129694	−0.0648471	−	0.997895i	$-0.520656\pi$
$643$	−3.28871	−0.129694	−0.0648471	+	0.997895i	$0.520656\pi$
$644$	−16.7586	−0.660380
$645$	3.97134	0.156371
$646$	−11.1818	−0.439942
$647$	−20.4068	−0.802275	−0.401138	−	0.916018i	$-0.631385\pi$
$647$	−20.4068	−0.802275	−0.401138	+	0.916018i	$0.631385\pi$
$648$	−0.765840	−0.0300850
$649$	7.01146	0.275224
$650$	7.16867	0.281178
$651$	14.7539	0.578250
$652$	39.1097	1.53165
$653$	44.3511	1.73559	0.867797	−	0.496919i	$-0.165535\pi$
$653$	44.3511	1.73559	0.867797	+	0.496919i	$0.165535\pi$
$654$	22.2882	0.871537
$655$	4.97436	0.194364
$656$	27.9192	1.09006
$657$	7.49270	0.292318
$658$	52.6542	2.05267
$659$	−33.0722	−1.28831	−0.644155	−	0.764895i	$-0.722791\pi$
$659$	−33.0722	−1.28831	−0.644155	+	0.764895i	$0.722791\pi$
$660$	−1.74535	−0.0679377
$661$	−49.0275	−1.90695	−0.953475	−	0.301471i	$-0.902522\pi$
$661$	−49.0275	−1.90695	−0.953475	+	0.301471i	$0.902522\pi$
$662$	36.3223	1.41170
$663$	2.20747	0.0857309
$664$	−4.90463	−0.190337
$665$	−12.9761	−0.503193
$666$	−16.2066	−0.627992
$667$	8.81261	0.341226
$668$	−10.3529	−0.400567
$669$	27.9316	1.07990
$670$	4.24202	0.163884
$671$	5.57488	0.215216
$672$	32.0044	1.23460
$673$	−14.3109	−0.551646	−0.275823	−	0.961208i	$-0.588950\pi$
$673$	−14.3109	−0.551646	−0.275823	+	0.961208i	$0.588950\pi$
$674$	23.9814	0.923730
$675$	−3.78024	−0.145502
$676$	1.59615	0.0613904
$677$	33.9824	1.30605	0.653026	−	0.757336i	$-0.273499\pi$
$677$	33.9824	1.30605	0.653026	+	0.757336i	$0.273499\pi$
$678$	−13.1473	−0.504919
$679$	17.5447	0.673303
$680$	1.86711	0.0716002
$681$	−21.3824	−0.819374
$682$	6.29779	0.241155
$683$	−43.7255	−1.67311	−0.836554	−	0.547884i	$-0.815434\pi$
$683$	−43.7255	−1.67311	−0.836554	+	0.547884i	$0.815434\pi$
$684$	4.26356	0.163021
$685$	18.0194	0.688485
$686$	−44.6025	−1.70293
$687$	3.95484	0.150886
$688$	−16.7012	−0.636729
$689$	9.57780	0.364885
$690$	4.99930	0.190320
$691$	0.303099	0.0115304	0.00576522	−	0.999983i	$-0.498165\pi$
$691$	0.303099	0.0115304	0.00576522	+	0.999983i	$0.498165\pi$
$692$	19.8060	0.752912
$693$	4.35494	0.165430
$694$	42.6272	1.61811
$695$	13.8782	0.526431
$696$	−2.82741	−0.107173
$697$	13.2693	0.502612
$698$	11.1862	0.423403
$699$	−16.4130	−0.620798
$700$	26.5402	1.00312
$701$	23.9062	0.902926	0.451463	−	0.892290i	$-0.350902\pi$
$701$	23.9062	0.902926	0.451463	+	0.892290i	$0.350902\pi$
$702$	−1.89635	−0.0715732
$703$	−22.8282	−0.860981
$704$	4.46418	0.168250
$705$	−6.97174	−0.262571
$706$	31.8659	1.19929
$707$	61.2403	2.30318
$708$	−11.3034	−0.424809
$709$	−35.3341	−1.32700	−0.663500	−	0.748176i	$-0.730930\pi$
$709$	−35.3341	−1.32700	−0.663500	+	0.748176i	$0.730930\pi$
$710$	5.02128	0.188445
$711$	−14.9525	−0.560761
$712$	−5.95115	−0.223029
$713$	−8.00663	−0.299851
$714$	18.4129	0.689087
$715$	1.09348	0.0408937
$716$	8.22029	0.307207
$717$	7.31462	0.273169
$718$	1.82182	0.0679897
$719$	31.0580	1.15827	0.579133	−	0.815233i	$-0.303391\pi$
$719$	31.0580	1.15827	0.579133	+	0.815233i	$0.303391\pi$
$720$	−5.12962	−0.191170
$721$	−4.39855	−0.163811
$722$	−22.5001	−0.837367
$723$	24.7536	0.920595
$724$	29.6308	1.10122
$725$	−13.9563	−0.518325
$726$	−19.0009	−0.705191
$727$	−18.2681	−0.677525	−0.338762	−	0.940872i	$-0.610008\pi$
$727$	−18.2681	−0.677525	−0.338762	+	0.940872i	$0.610008\pi$
$728$	−3.36859	−0.124848
$729$	1.00000	0.0370370
$730$	15.6926	0.580808
$731$	−7.93769	−0.293586
$732$	−8.98746	−0.332186
$733$	5.95306	0.219881	0.109941	−	0.993938i	$-0.464934\pi$
$733$	5.95306	0.219881	0.109941	+	0.993938i	$0.464934\pi$
$734$	−4.70974	−0.173840
$735$	13.6366	0.502995
$736$	−17.3681	−0.640198
$737$	−2.00535	−0.0738679
$738$	−11.3992	−0.419610
$739$	7.75939	0.285434	0.142717	−	0.989764i	$-0.454416\pi$
$739$	7.75939	0.285434	0.142717	+	0.989764i	$0.454416\pi$
$740$	−15.0655	−0.553818
$741$	−2.67115	−0.0981272
$742$	79.8904	2.93287
$743$	24.8652	0.912215	0.456108	−	0.889925i	$-0.349243\pi$
$743$	24.8652	0.912215	0.456108	+	0.889925i	$0.349243\pi$
$744$	2.56883	0.0941777
$745$	21.4692	0.786570
$746$	−39.5109	−1.44660
$747$	6.40425	0.234319
$748$	3.48851	0.127553
$749$	47.6887	1.74251
$750$	−18.3892	−0.671478
$751$	5.68013	0.207271	0.103635	−	0.994615i	$-0.466953\pi$
$751$	5.68013	0.207271	0.103635	+	0.994615i	$0.466953\pi$
$752$	29.3193	1.06916
$753$	−4.79776	−0.174840
$754$	−7.00117	−0.254967
$755$	7.76913	0.282748
$756$	−7.02075	−0.255342
$757$	−3.42893	−0.124627	−0.0623133	−	0.998057i	$-0.519848\pi$
$757$	−3.42893	−0.124627	−0.0623133	+	0.998057i	$0.519848\pi$
$758$	−41.6170	−1.51160
$759$	−2.36334	−0.0857837
$760$	−2.25930	−0.0819533
$761$	29.0315	1.05239	0.526196	−	0.850363i	$-0.323618\pi$
$761$	29.0315	1.05239	0.526196	+	0.850363i	$0.323618\pi$
$762$	−29.8776	−1.08235
$763$	−51.6970	−1.87156
$764$	3.75595	0.135886
$765$	−2.43798	−0.0881455
$766$	−58.6036	−2.11744
$767$	7.08167	0.255704
$768$	20.3993	0.736097
$769$	27.1001	0.977254	0.488627	−	0.872493i	$-0.337498\pi$
$769$	27.1001	0.977254	0.488627	+	0.872493i	$0.337498\pi$
$770$	9.12090	0.328694
$771$	9.14654	0.329405
$772$	22.8970	0.824082
$773$	−30.1816	−1.08556	−0.542778	−	0.839876i	$-0.682627\pi$
$773$	−30.1816	−1.08556	−0.542778	+	0.839876i	$0.682627\pi$
$774$	6.81897	0.245103
$775$	12.6799	0.455476
$776$	3.05474	0.109659
$777$	37.5909	1.34856
$778$	61.3667	2.20010
$779$	−16.0566	−0.575287
$780$	−1.76283	−0.0631195
$781$	−2.37373	−0.0849386
$782$	−9.99232	−0.357325
$783$	3.69191	0.131938
$784$	−57.3481	−2.04815
$785$	3.46903	0.123815
$786$	8.54121	0.304655
$787$	−3.14045	−0.111945	−0.0559725	−	0.998432i	$-0.517826\pi$
$787$	−3.14045	−0.111945	−0.0559725	+	0.998432i	$0.517826\pi$
$788$	−4.19902	−0.149584
$789$	−13.6221	−0.484959
$790$	−31.3161	−1.11418
$791$	30.4949	1.08427
$792$	0.758246	0.0269431
$793$	5.63071	0.199952
$794$	73.9639	2.62488
$795$	−10.5780	−0.375162
$796$	−10.2679	−0.363936
$797$	−17.9228	−0.634857	−0.317429	−	0.948282i	$-0.602819\pi$
$797$	−17.9228	−0.634857	−0.317429	+	0.948282i	$0.602819\pi$
$798$	−22.2806	−0.788725
$799$	13.9347	0.492975
$800$	27.5055	0.972467
$801$	7.77075	0.274566
$802$	−52.0720	−1.83873
$803$	−7.41841	−0.261790
$804$	3.23289	0.114015
$805$	−11.5958	−0.408697
$806$	6.36086	0.224052
$807$	−18.5298	−0.652278
$808$	10.6627	0.375111
$809$	39.2274	1.37916	0.689580	−	0.724209i	$-0.257795\pi$
$809$	39.2274	1.37916	0.689580	+	0.724209i	$0.257795\pi$
$810$	2.09438	0.0735890
$811$	23.0795	0.810430	0.405215	−	0.914221i	$-0.367197\pi$
$811$	23.0795	0.810430	0.405215	+	0.914221i	$0.367197\pi$
$812$	−25.9200	−0.909614
$813$	−23.2355	−0.814905
$814$	16.0459	0.562408
$815$	27.0612	0.947912
$816$	10.2528	0.358920
$817$	9.60503	0.336037
$818$	43.6379	1.52576
$819$	4.39855	0.153698
$820$	−10.5966	−0.370048
$821$	29.8488	1.04173	0.520866	−	0.853639i	$-0.325609\pi$
$821$	29.8488	1.04173	0.520866	+	0.853639i	$0.325609\pi$
$822$	30.9401	1.07916
$823$	−20.8340	−0.726228	−0.363114	−	0.931745i	$-0.618286\pi$
$823$	−20.8340	−0.726228	−0.363114	+	0.931745i	$0.618286\pi$
$824$	−0.765840	−0.0266793
$825$	3.74276	0.130306
$826$	59.0697	2.05530
$827$	−47.9600	−1.66773	−0.833867	−	0.551966i	$-0.813878\pi$
$827$	−47.9600	−1.66773	−0.833867	+	0.551966i	$0.813878\pi$
$828$	3.81002	0.132407
$829$	−25.0496	−0.870009	−0.435005	−	0.900428i	$-0.643253\pi$
$829$	−25.0496	−0.870009	−0.435005	+	0.900428i	$0.643253\pi$
$830$	13.4129	0.465570
$831$	−8.60887	−0.298638
$832$	4.50889	0.156317
$833$	−27.2562	−0.944370
$834$	23.8296	0.825151
$835$	−7.16352	−0.247904
$836$	−4.22129	−0.145996
$837$	−3.35426	−0.115940
$838$	−38.9270	−1.34471
$839$	28.0678	0.969007	0.484504	−	0.874789i	$-0.339000\pi$
$839$	28.0678	0.969007	0.484504	+	0.874789i	$0.339000\pi$
$840$	3.72035	0.128364
$841$	−15.3698	−0.529992
$842$	−12.2544	−0.422313
$843$	17.2701	0.594812
$844$	−12.2565	−0.421885
$845$	1.10443	0.0379934
$846$	−11.9708	−0.411565
$847$	44.0723	1.51434
$848$	44.4851	1.52762
$849$	7.51808	0.258020
$850$	15.8246	0.542779
$851$	−20.3998	−0.699296
$852$	3.82677	0.131103
$853$	16.7323	0.572902	0.286451	−	0.958095i	$-0.407524\pi$
$853$	16.7323	0.572902	0.286451	+	0.958095i	$0.407524\pi$
$854$	46.9669	1.60717
$855$	2.95009	0.100891
$856$	8.30316	0.283796
$857$	2.40073	0.0820075	0.0410038	−	0.999159i	$-0.486944\pi$
$857$	2.40073	0.0820075	0.0410038	+	0.999159i	$0.486944\pi$
$858$	1.87755	0.0640985
$859$	11.6263	0.396685	0.198342	−	0.980133i	$-0.436444\pi$
$859$	11.6263	0.396685	0.198342	+	0.980133i	$0.436444\pi$
$860$	6.33885	0.216153
$861$	26.4402	0.901079
$862$	35.6005	1.21256
$863$	11.7265	0.399175	0.199587	−	0.979880i	$-0.436040\pi$
$863$	11.7265	0.399175	0.199587	+	0.979880i	$0.436040\pi$
$864$	−7.27612	−0.247539
$865$	13.7044	0.465963
$866$	20.3895	0.692862
$867$	−12.1271	−0.411858
$868$	23.5494	0.799320
$869$	14.8042	0.502198
$870$	7.73227	0.262149
$871$	−2.02543	−0.0686290
$872$	−9.00106	−0.304814
$873$	−3.98874	−0.134998
$874$	12.0912	0.408992
$875$	42.6533	1.44195
$876$	11.9595	0.404074
$877$	41.2502	1.39292	0.696459	−	0.717596i	$-0.254758\pi$
$877$	41.2502	1.39292	0.696459	+	0.717596i	$0.254758\pi$
$878$	−55.9654	−1.88874
$879$	−16.8945	−0.569839
$880$	5.07876	0.171205
$881$	11.2067	0.377564	0.188782	−	0.982019i	$-0.439546\pi$
$881$	11.2067	0.377564	0.188782	+	0.982019i	$0.439546\pi$
$882$	23.4147	0.788415
$883$	−7.02150	−0.236292	−0.118146	−	0.992996i	$-0.537695\pi$
$883$	−7.02150	−0.236292	−0.118146	+	0.992996i	$0.537695\pi$
$884$	3.52345	0.118506
$885$	−7.82118	−0.262906
$886$	−48.1760	−1.61850
$887$	−11.9291	−0.400539	−0.200270	−	0.979741i	$-0.564182\pi$
$887$	−11.9291	−0.400539	−0.200270	+	0.979741i	$0.564182\pi$
$888$	6.54501	0.219636
$889$	69.3005	2.32426
$890$	16.2749	0.545537
$891$	−0.990085	−0.0331691
$892$	44.5830	1.49275
$893$	−16.8618	−0.564257
$894$	36.8636	1.23290
$895$	5.68787	0.190125
$896$	−26.3993	−0.881938
$897$	−2.38700	−0.0796998
$898$	7.34659	0.245159
$899$	−12.3836	−0.413017
$900$	−6.03384	−0.201128
$901$	21.1427	0.704365
$902$	11.2862	0.375788
$903$	−15.8165	−0.526339
$904$	5.30953	0.176592
$905$	20.5024	0.681524
$906$	13.3400	0.443191
$907$	−48.3609	−1.60580	−0.802899	−	0.596115i	$-0.796710\pi$
$907$	−48.3609	−1.60580	−0.802899	+	0.596115i	$0.796710\pi$
$908$	−34.1295	−1.13263
$909$	−13.9228	−0.461791
$910$	9.21224	0.305383
$911$	24.9020	0.825039	0.412519	−	0.910949i	$-0.364649\pi$
$911$	24.9020	0.825039	0.412519	+	0.910949i	$0.364649\pi$
$912$	−12.4064	−0.410818
$913$	−6.34075	−0.209848
$914$	18.2358	0.603187
$915$	−6.21870	−0.205584
$916$	6.31252	0.208571
$917$	−19.8112	−0.654223
$918$	−4.18613	−0.138163
$919$	51.5264	1.69970	0.849850	−	0.527025i	$-0.176693\pi$
$919$	51.5264	1.69970	0.849850	+	0.527025i	$0.176693\pi$
$920$	−2.01896	−0.0665632
$921$	−32.6879	−1.07710
$922$	−31.4777	−1.03666
$923$	−2.39750	−0.0789146
$924$	6.95114	0.228676
$925$	32.3067	1.06224
$926$	−0.904833	−0.0297346
$927$	1.00000	0.0328443
$928$	−26.8628	−0.881815
$929$	−43.7077	−1.43400	−0.717001	−	0.697072i	$-0.754486\pi$
$929$	−43.7077	−1.43400	−0.717001	+	0.697072i	$0.754486\pi$
$930$	−7.02510	−0.230362
$931$	32.9814	1.08092
$932$	−26.1977	−0.858133
$933$	−8.53485	−0.279418
$934$	9.03543	0.295648
$935$	2.41381	0.0789401
$936$	0.765840	0.0250323
$937$	25.3835	0.829243	0.414621	−	0.909994i	$-0.363914\pi$
$937$	25.3835	0.829243	0.414621	+	0.909994i	$0.363914\pi$
$938$	−16.8945	−0.551625
$939$	−4.54925	−0.148459
$940$	−11.1279	−0.362954
$941$	−9.57231	−0.312048	−0.156024	−	0.987753i	$-0.549868\pi$
$941$	−9.57231	−0.312048	−0.156024	+	0.987753i	$0.549868\pi$
$942$	5.95649	0.194073
$943$	−14.3486	−0.467253
$944$	32.8916	1.07053
$945$	−4.85788	−0.158027
$946$	−6.75136	−0.219506
$947$	−5.41374	−0.175923	−0.0879614	−	0.996124i	$-0.528035\pi$
$947$	−5.41374	−0.175923	−0.0879614	+	0.996124i	$0.528035\pi$
$948$	−23.8664	−0.775144
$949$	−7.49270	−0.243223
$950$	−19.1486	−0.621263
$951$	−5.25998	−0.170566
$952$	−7.43604	−0.241003
$953$	−14.3588	−0.465127	−0.232563	−	0.972581i	$-0.574711\pi$
$953$	−14.3588	−0.465127	−0.232563	+	0.972581i	$0.574711\pi$
$954$	−18.1629	−0.588045
$955$	2.59886	0.0840971
$956$	11.6752	0.377604
$957$	−3.65531	−0.118159
$958$	−18.2232	−0.588764
$959$	−71.7650	−2.31741
$960$	−4.97973	−0.160720
$961$	−19.7489	−0.637063
$962$	16.2066	0.522521
$963$	−10.8419	−0.349375
$964$	39.5104	1.27254
$965$	15.8432	0.510009
$966$	−19.9105	−0.640609
$967$	21.9742	0.706643	0.353322	−	0.935502i	$-0.385052\pi$
$967$	21.9742	0.706643	0.353322	+	0.935502i	$0.385052\pi$
$968$	7.67351	0.246636
$969$	−5.89648	−0.189422
$970$	−8.35394	−0.268229
$971$	−10.7813	−0.345988	−0.172994	−	0.984923i	$-0.555344\pi$
$971$	−10.7813	−0.345988	−0.172994	+	0.984923i	$0.555344\pi$
$972$	1.59615	0.0511966
$973$	−55.2722	−1.77195
$974$	−69.0376	−2.21211
$975$	3.78024	0.121065
$976$	26.1524	0.837118
$977$	34.8145	1.11381	0.556907	−	0.830575i	$-0.311988\pi$
$977$	34.8145	1.11381	0.556907	+	0.830575i	$0.311988\pi$
$978$	46.4653	1.48580
$979$	−7.69371	−0.245892
$980$	21.7661	0.695293
$981$	11.7532	0.375251
$982$	−53.5685	−1.70944
$983$	1.08752	0.0346866	0.0173433	−	0.999850i	$-0.494479\pi$
$983$	1.08752	0.0346866	0.0173433	+	0.999850i	$0.494479\pi$
$984$	4.60355	0.146756
$985$	−2.90543	−0.0925748
$986$	−15.4548	−0.492183
$987$	27.7660	0.883803
$988$	−4.26356	−0.135642
$989$	8.58328	0.272932
$990$	−2.07361	−0.0659038
$991$	39.3497	1.24999	0.624993	−	0.780631i	$-0.285102\pi$
$991$	39.3497	1.24999	0.624993	+	0.780631i	$0.285102\pi$
$992$	24.4060	0.774892
$993$	19.1538	0.607826
$994$	−19.9980	−0.634299
$995$	−7.10468	−0.225233
$996$	10.2222	0.323901
$997$	−16.4039	−0.519516	−0.259758	−	0.965674i	$-0.583643\pi$
$997$	−16.4039	−0.519516	−0.259758	+	0.965674i	$0.583643\pi$
$998$	−24.5935	−0.778492
$999$	−8.54619	−0.270389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.14	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.14	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.89635 q^{2} +1.00000 q^{3} +1.59615 q^{4} +1.10443 q^{5} +1.89635 q^{6} -4.39855 q^{7} -0.765840 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.89635 q^{2} +1.00000 q^{3} +1.59615 q^{4} +1.10443 q^{5} +1.89635 q^{6} -4.39855 q^{7} -0.765840 q^{8} +1.00000 q^{9} +2.09438 q^{10} -0.990085 q^{11} +1.59615 q^{12} -1.00000 q^{13} -8.34120 q^{14} +1.10443 q^{15} -4.64460 q^{16} -2.20747 q^{17} +1.89635 q^{18} +2.67115 q^{19} +1.76283 q^{20} -4.39855 q^{21} -1.87755 q^{22} +2.38700 q^{23} -0.765840 q^{24} -3.78024 q^{25} -1.89635 q^{26} +1.00000 q^{27} -7.02075 q^{28} +3.69191 q^{29} +2.09438 q^{30} -3.35426 q^{31} -7.27612 q^{32} -0.990085 q^{33} -4.18613 q^{34} -4.85788 q^{35} +1.59615 q^{36} -8.54619 q^{37} +5.06545 q^{38} -1.00000 q^{39} -0.845813 q^{40} -6.01111 q^{41} -8.34120 q^{42} +3.59584 q^{43} -1.58032 q^{44} +1.10443 q^{45} +4.52660 q^{46} -6.31254 q^{47} -4.64460 q^{48} +12.3473 q^{49} -7.16867 q^{50} -2.20747 q^{51} -1.59615 q^{52} -9.57780 q^{53} +1.89635 q^{54} -1.09348 q^{55} +3.36859 q^{56} +2.67115 q^{57} +7.00117 q^{58} -7.08167 q^{59} +1.76283 q^{60} -5.63071 q^{61} -6.36086 q^{62} -4.39855 q^{63} -4.50889 q^{64} -1.10443 q^{65} -1.87755 q^{66} +2.02543 q^{67} -3.52345 q^{68} +2.38700 q^{69} -9.21224 q^{70} +2.39750 q^{71} -0.765840 q^{72} +7.49270 q^{73} -16.2066 q^{74} -3.78024 q^{75} +4.26356 q^{76} +4.35494 q^{77} -1.89635 q^{78} -14.9525 q^{79} -5.12962 q^{80} +1.00000 q^{81} -11.3992 q^{82} +6.40425 q^{83} -7.02075 q^{84} -2.43798 q^{85} +6.81897 q^{86} +3.69191 q^{87} +0.758246 q^{88} +7.77075 q^{89} +2.09438 q^{90} +4.39855 q^{91} +3.81002 q^{92} -3.35426 q^{93} -11.9708 q^{94} +2.95009 q^{95} -7.27612 q^{96} -3.98874 q^{97} +23.4147 q^{98} -0.990085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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