LMFDB - Embedded newform 4017.2.a.k.1.4

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:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.23055 q^{2} +1.00000 q^{3} +2.97534 q^{4} +2.00994 q^{5} -2.23055 q^{6} -4.12307 q^{7} -2.17553 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23055 q^{2} +1.00000 q^{3} +2.97534 q^{4} +2.00994 q^{5} -2.23055 q^{6} -4.12307 q^{7} -2.17553 q^{8} +1.00000 q^{9} -4.48326 q^{10} +3.38236 q^{11} +2.97534 q^{12} +1.00000 q^{13} +9.19669 q^{14} +2.00994 q^{15} -1.09805 q^{16} -1.97817 q^{17} -2.23055 q^{18} -5.67965 q^{19} +5.98025 q^{20} -4.12307 q^{21} -7.54450 q^{22} +5.94102 q^{23} -2.17553 q^{24} -0.960144 q^{25} -2.23055 q^{26} +1.00000 q^{27} -12.2675 q^{28} -1.35263 q^{29} -4.48326 q^{30} +4.45900 q^{31} +6.80031 q^{32} +3.38236 q^{33} +4.41239 q^{34} -8.28712 q^{35} +2.97534 q^{36} +8.00141 q^{37} +12.6687 q^{38} +1.00000 q^{39} -4.37269 q^{40} -4.07269 q^{41} +9.19669 q^{42} +1.59312 q^{43} +10.0636 q^{44} +2.00994 q^{45} -13.2517 q^{46} -5.33059 q^{47} -1.09805 q^{48} +9.99968 q^{49} +2.14164 q^{50} -1.97817 q^{51} +2.97534 q^{52} -5.08905 q^{53} -2.23055 q^{54} +6.79833 q^{55} +8.96986 q^{56} -5.67965 q^{57} +3.01711 q^{58} +7.57340 q^{59} +5.98025 q^{60} -6.90100 q^{61} -9.94599 q^{62} -4.12307 q^{63} -12.9723 q^{64} +2.00994 q^{65} -7.54450 q^{66} +14.1171 q^{67} -5.88571 q^{68} +5.94102 q^{69} +18.4848 q^{70} +5.77774 q^{71} -2.17553 q^{72} +5.76602 q^{73} -17.8475 q^{74} -0.960144 q^{75} -16.8989 q^{76} -13.9457 q^{77} -2.23055 q^{78} -8.56830 q^{79} -2.20701 q^{80} +1.00000 q^{81} +9.08432 q^{82} -1.02947 q^{83} -12.2675 q^{84} -3.97600 q^{85} -3.55353 q^{86} -1.35263 q^{87} -7.35843 q^{88} +15.6289 q^{89} -4.48326 q^{90} -4.12307 q^{91} +17.6765 q^{92} +4.45900 q^{93} +11.8901 q^{94} -11.4158 q^{95} +6.80031 q^{96} +2.26693 q^{97} -22.3048 q^{98} +3.38236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−2.23055	−1.57723	−0.788617	−	0.614885i	$-0.789203\pi$
$2$	−2.23055	−1.57723	−0.788617	+	0.614885i	$0.789203\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.97534	1.48767
$5$	2.00994	0.898872	0.449436	−	0.893312i	$-0.351625\pi$
$5$	2.00994	0.898872	0.449436	+	0.893312i	$0.351625\pi$
$6$	−2.23055	−0.910617
$7$	−4.12307	−1.55837	−0.779186	−	0.626792i	$-0.784368\pi$
$7$	−4.12307	−1.55837	−0.779186	+	0.626792i	$0.784368\pi$
$8$	−2.17553	−0.769167
$9$	1.00000	0.333333
$10$	−4.48326	−1.41773
$11$	3.38236	1.01982	0.509909	−	0.860228i	$-0.329679\pi$
$11$	3.38236	1.01982	0.509909	+	0.860228i	$0.329679\pi$
$12$	2.97534	0.858906
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	9.19669	2.45792
$15$	2.00994	0.518964
$16$	−1.09805	−0.274512
$17$	−1.97817	−0.479776	−0.239888	−	0.970801i	$-0.577111\pi$
$17$	−1.97817	−0.479776	−0.239888	+	0.970801i	$0.577111\pi$
$18$	−2.23055	−0.525745
$19$	−5.67965	−1.30300	−0.651501	−	0.758648i	$-0.725860\pi$
$19$	−5.67965	−1.30300	−0.651501	+	0.758648i	$0.725860\pi$
$20$	5.98025	1.33722
$21$	−4.12307	−0.899727
$22$	−7.54450	−1.60849
$23$	5.94102	1.23879	0.619394	−	0.785080i	$-0.287378\pi$
$23$	5.94102	1.23879	0.619394	+	0.785080i	$0.287378\pi$
$24$	−2.17553	−0.444079
$25$	−0.960144	−0.192029
$26$	−2.23055	−0.437446
$27$	1.00000	0.192450
$28$	−12.2675	−2.31834
$29$	−1.35263	−0.251178	−0.125589	−	0.992082i	$-0.540082\pi$
$29$	−1.35263	−0.251178	−0.125589	+	0.992082i	$0.540082\pi$
$30$	−4.48326	−0.818528
$31$	4.45900	0.800859	0.400430	−	0.916328i	$-0.368861\pi$
$31$	4.45900	0.800859	0.400430	+	0.916328i	$0.368861\pi$
$32$	6.80031	1.20214
$33$	3.38236	0.588793
$34$	4.41239	0.756719
$35$	−8.28712	−1.40078
$36$	2.97534	0.495889
$37$	8.00141	1.31542	0.657712	−	0.753270i	$-0.271524\pi$
$37$	8.00141	1.31542	0.657712	+	0.753270i	$0.271524\pi$
$38$	12.6687	2.05514
$39$	1.00000	0.160128
$40$	−4.37269	−0.691383
$41$	−4.07269	−0.636047	−0.318023	−	0.948083i	$-0.603019\pi$
$41$	−4.07269	−0.636047	−0.318023	+	0.948083i	$0.603019\pi$
$42$	9.19669	1.41908
$43$	1.59312	0.242949	0.121474	−	0.992595i	$-0.461238\pi$
$43$	1.59312	0.242949	0.121474	+	0.992595i	$0.461238\pi$
$44$	10.0636	1.51715
$45$	2.00994	0.299624
$46$	−13.2517	−1.95386
$47$	−5.33059	−0.777547	−0.388773	−	0.921333i	$-0.627101\pi$
$47$	−5.33059	−0.777547	−0.388773	+	0.921333i	$0.627101\pi$
$48$	−1.09805	−0.158490
$49$	9.99968	1.42853
$50$	2.14164	0.302874
$51$	−1.97817	−0.276999
$52$	2.97534	0.412605
$53$	−5.08905	−0.699035	−0.349518	−	0.936930i	$-0.613654\pi$
$53$	−5.08905	−0.699035	−0.349518	+	0.936930i	$0.613654\pi$
$54$	−2.23055	−0.303539
$55$	6.79833	0.916687
$56$	8.96986	1.19865
$57$	−5.67965	−0.752288
$58$	3.01711	0.396166
$59$	7.57340	0.985973	0.492987	−	0.870037i	$-0.335905\pi$
$59$	7.57340	0.985973	0.492987	+	0.870037i	$0.335905\pi$
$60$	5.98025	0.772046
$61$	−6.90100	−0.883583	−0.441791	−	0.897118i	$-0.645657\pi$
$61$	−6.90100	−0.883583	−0.441791	+	0.897118i	$0.645657\pi$
$62$	−9.94599	−1.26314
$63$	−4.12307	−0.519458
$64$	−12.9723	−1.62154
$65$	2.00994	0.249302
$66$	−7.54450	−0.928664
$67$	14.1171	1.72468	0.862338	−	0.506333i	$-0.168999\pi$
$67$	14.1171	1.72468	0.862338	+	0.506333i	$0.168999\pi$
$68$	−5.88571	−0.713747
$69$	5.94102	0.715215
$70$	18.4848	2.20936
$71$	5.77774	0.685692	0.342846	−	0.939392i	$-0.388609\pi$
$71$	5.77774	0.685692	0.342846	+	0.939392i	$0.388609\pi$
$72$	−2.17553	−0.256389
$73$	5.76602	0.674862	0.337431	−	0.941350i	$-0.390442\pi$
$73$	5.76602	0.674862	0.337431	+	0.941350i	$0.390442\pi$
$74$	−17.8475	−2.07473
$75$	−0.960144	−0.110868
$76$	−16.8989	−1.93843
$77$	−13.9457	−1.58926
$78$	−2.23055	−0.252560
$79$	−8.56830	−0.964009	−0.482004	−	0.876169i	$-0.660091\pi$
$79$	−8.56830	−0.964009	−0.482004	+	0.876169i	$0.660091\pi$
$80$	−2.20701	−0.246751
$81$	1.00000	0.111111
$82$	9.08432	1.00319
$83$	−1.02947	−0.112999	−0.0564995	−	0.998403i	$-0.517994\pi$
$83$	−1.02947	−0.112999	−0.0564995	+	0.998403i	$0.517994\pi$
$84$	−12.2675	−1.33850
$85$	−3.97600	−0.431257
$86$	−3.55353	−0.383187
$87$	−1.35263	−0.145017
$88$	−7.35843	−0.784411
$89$	15.6289	1.65666	0.828330	−	0.560240i	$-0.189291\pi$
$89$	15.6289	1.65666	0.828330	+	0.560240i	$0.189291\pi$
$90$	−4.48326	−0.472577
$91$	−4.12307	−0.432215
$92$	17.6765	1.84291
$93$	4.45900	0.462376
$94$	11.8901	1.22637
$95$	−11.4158	−1.17123
$96$	6.80031	0.694054
$97$	2.26693	0.230172	0.115086	−	0.993356i	$-0.463286\pi$
$97$	2.26693	0.230172	0.115086	+	0.993356i	$0.463286\pi$
$98$	−22.3048	−2.25312
$99$	3.38236	0.339940
$100$	−2.85675	−0.285675
$101$	−8.42998	−0.838815	−0.419407	−	0.907798i	$-0.637762\pi$
$101$	−8.42998	−0.838815	−0.419407	+	0.907798i	$0.637762\pi$
$102$	4.41239	0.436892
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.17553	−0.213328
$105$	−8.28712	−0.808740
$106$	11.3514	1.10254
$107$	−1.52130	−0.147069	−0.0735347	−	0.997293i	$-0.523428\pi$
$107$	−1.52130	−0.147069	−0.0735347	+	0.997293i	$0.523428\pi$
$108$	2.97534	0.286302
$109$	18.1272	1.73627	0.868136	−	0.496326i	$-0.165318\pi$
$109$	18.1272	1.73627	0.868136	+	0.496326i	$0.165318\pi$
$110$	−15.1640	−1.44583
$111$	8.00141	0.759460
$112$	4.52732	0.427792
$113$	14.6743	1.38044	0.690219	−	0.723600i	$-0.257514\pi$
$113$	14.6743	1.38044	0.690219	+	0.723600i	$0.257514\pi$
$114$	12.6687	1.18653
$115$	11.9411	1.11351
$116$	−4.02454	−0.373669
$117$	1.00000	0.0924500
$118$	−16.8928	−1.55511
$119$	8.15612	0.747670
$120$	−4.37269	−0.399170
$121$	0.440338	0.0400308
$122$	15.3930	1.39362
$123$	−4.07269	−0.367222
$124$	13.2670	1.19141
$125$	−11.9795	−1.07148
$126$	9.19669	0.819306
$127$	9.48166	0.841361	0.420680	−	0.907209i	$-0.361791\pi$
$127$	9.48166	0.841361	0.420680	+	0.907209i	$0.361791\pi$
$128$	15.3347	1.35541
$129$	1.59312	0.140266
$130$	−4.48326	−0.393208
$131$	−1.36723	−0.119455	−0.0597276	−	0.998215i	$-0.519023\pi$
$131$	−1.36723	−0.119455	−0.0597276	+	0.998215i	$0.519023\pi$
$132$	10.0636	0.875928
$133$	23.4176	2.03056
$134$	−31.4888	−2.72022
$135$	2.00994	0.172988
$136$	4.30357	0.369028
$137$	−18.1425	−1.55002	−0.775010	−	0.631948i	$-0.782255\pi$
$137$	−18.1425	−1.55002	−0.775010	+	0.631948i	$0.782255\pi$
$138$	−13.2517	−1.12806
$139$	14.0392	1.19079	0.595395	−	0.803433i	$-0.296995\pi$
$139$	14.0392	1.19079	0.595395	+	0.803433i	$0.296995\pi$
$140$	−24.6570	−2.08389
$141$	−5.33059	−0.448917
$142$	−12.8875	−1.08150
$143$	3.38236	0.282847
$144$	−1.09805	−0.0915040
$145$	−2.71871	−0.225776
$146$	−12.8614	−1.06442
$147$	9.99968	0.824760
$148$	23.8069	1.95691
$149$	13.5606	1.11093	0.555464	−	0.831540i	$-0.312541\pi$
$149$	13.5606	1.11093	0.555464	+	0.831540i	$0.312541\pi$
$150$	2.14164	0.174865
$151$	14.2213	1.15731	0.578655	−	0.815573i	$-0.303578\pi$
$151$	14.2213	1.15731	0.578655	+	0.815573i	$0.303578\pi$
$152$	12.3563	1.00223
$153$	−1.97817	−0.159925
$154$	31.1065	2.50663
$155$	8.96231	0.719870
$156$	2.97534	0.238218
$157$	15.5774	1.24321	0.621605	−	0.783330i	$-0.286481\pi$
$157$	15.5774	1.24321	0.621605	+	0.783330i	$0.286481\pi$
$158$	19.1120	1.52047
$159$	−5.08905	−0.403588
$160$	13.6682	1.08057
$161$	−24.4952	−1.93049
$162$	−2.23055	−0.175248
$163$	−16.8348	−1.31861	−0.659303	−	0.751877i	$-0.729149\pi$
$163$	−16.8348	−1.31861	−0.659303	+	0.751877i	$0.729149\pi$
$164$	−12.1176	−0.946227
$165$	6.79833	0.529249
$166$	2.29628	0.178226
$167$	2.25314	0.174354	0.0871768	−	0.996193i	$-0.472215\pi$
$167$	2.25314	0.174354	0.0871768	+	0.996193i	$0.472215\pi$
$168$	8.96986	0.692040
$169$	1.00000	0.0769231
$170$	8.86864	0.680194
$171$	−5.67965	−0.434334
$172$	4.74007	0.361427
$173$	18.6654	1.41910	0.709552	−	0.704653i	$-0.248897\pi$
$173$	18.6654	1.41910	0.709552	+	0.704653i	$0.248897\pi$
$174$	3.01711	0.228726
$175$	3.95874	0.299252
$176$	−3.71399	−0.279952
$177$	7.57340	0.569252
$178$	−34.8610	−2.61294
$179$	−10.9462	−0.818159	−0.409079	−	0.912499i	$-0.634150\pi$
$179$	−10.9462	−0.818159	−0.409079	+	0.912499i	$0.634150\pi$
$180$	5.98025	0.445741
$181$	−14.0458	−1.04401	−0.522007	−	0.852941i	$-0.674817\pi$
$181$	−14.0458	−1.04401	−0.522007	+	0.852941i	$0.674817\pi$
$182$	9.19669	0.681704
$183$	−6.90100	−0.510137
$184$	−12.9249	−0.952835
$185$	16.0824	1.18240
$186$	−9.94599	−0.729276
$187$	−6.69087	−0.489285
$188$	−15.8603	−1.15673
$189$	−4.12307	−0.299909
$190$	25.4634	1.84731
$191$	8.09245	0.585549	0.292774	−	0.956182i	$-0.405422\pi$
$191$	8.09245	0.585549	0.292774	+	0.956182i	$0.405422\pi$
$192$	−12.9723	−0.936196
$193$	26.5628	1.91203	0.956017	−	0.293311i	$-0.0947572\pi$
$193$	26.5628	1.91203	0.956017	+	0.293311i	$0.0947572\pi$
$194$	−5.05649	−0.363035
$195$	2.00994	0.143935
$196$	29.7524	2.12517
$197$	−17.5535	−1.25064	−0.625319	−	0.780369i	$-0.715031\pi$
$197$	−17.5535	−1.25064	−0.625319	+	0.780369i	$0.715031\pi$
$198$	−7.54450	−0.536164
$199$	1.27605	0.0904567	0.0452283	−	0.998977i	$-0.485598\pi$
$199$	1.27605	0.0904567	0.0452283	+	0.998977i	$0.485598\pi$
$200$	2.08882	0.147702
$201$	14.1171	0.995742
$202$	18.8035	1.32301
$203$	5.57699	0.391428
$204$	−5.88571	−0.412082
$205$	−8.18585	−0.571725
$206$	−2.23055	−0.155410
$207$	5.94102	0.412929
$208$	−1.09805	−0.0761359
$209$	−19.2106	−1.32883
$210$	18.4848	1.27557
$211$	5.78927	0.398550	0.199275	−	0.979944i	$-0.436141\pi$
$211$	5.78927	0.398550	0.199275	+	0.979944i	$0.436141\pi$
$212$	−15.1416	−1.03993
$213$	5.77774	0.395884
$214$	3.39333	0.231963
$215$	3.20208	0.218380
$216$	−2.17553	−0.148026
$217$	−18.3847	−1.24804
$218$	−40.4336	−2.73851
$219$	5.76602	0.389632
$220$	20.2273	1.36373
$221$	−1.97817	−0.133066
$222$	−17.8475	−1.19785
$223$	10.9670	0.734403	0.367202	−	0.930141i	$-0.380316\pi$
$223$	10.9670	0.734403	0.367202	+	0.930141i	$0.380316\pi$
$224$	−28.0381	−1.87338
$225$	−0.960144	−0.0640096
$226$	−32.7316	−2.17727
$227$	1.83518	0.121805	0.0609026	−	0.998144i	$-0.480602\pi$
$227$	1.83518	0.121805	0.0609026	+	0.998144i	$0.480602\pi$
$228$	−16.8989	−1.11915
$229$	−25.5147	−1.68606	−0.843031	−	0.537865i	$-0.819231\pi$
$229$	−25.5147	−1.68606	−0.843031	+	0.537865i	$0.819231\pi$
$230$	−26.6352	−1.75627
$231$	−13.9457	−0.917559
$232$	2.94269	0.193197
$233$	−8.39178	−0.549764	−0.274882	−	0.961478i	$-0.588639\pi$
$233$	−8.39178	−0.549764	−0.274882	+	0.961478i	$0.588639\pi$
$234$	−2.23055	−0.145815
$235$	−10.7142	−0.698915
$236$	22.5334	1.46680
$237$	−8.56830	−0.556571
$238$	−18.1926	−1.17925
$239$	−0.902351	−0.0583682	−0.0291841	−	0.999574i	$-0.509291\pi$
$239$	−0.902351	−0.0583682	−0.0291841	+	0.999574i	$0.509291\pi$
$240$	−2.20701	−0.142462
$241$	−4.55419	−0.293361	−0.146681	−	0.989184i	$-0.546859\pi$
$241$	−4.55419	−0.293361	−0.146681	+	0.989184i	$0.546859\pi$
$242$	−0.982195	−0.0631379
$243$	1.00000	0.0641500
$244$	−20.5328	−1.31448
$245$	20.0988	1.28406
$246$	9.08432	0.579195
$247$	−5.67965	−0.361387
$248$	−9.70069	−0.615994
$249$	−1.02947	−0.0652400
$250$	26.7209	1.68998
$251$	−1.90161	−0.120029	−0.0600144	−	0.998198i	$-0.519115\pi$
$251$	−1.90161	−0.120029	−0.0600144	+	0.998198i	$0.519115\pi$
$252$	−12.2675	−0.772781
$253$	20.0947	1.26334
$254$	−21.1493	−1.32702
$255$	−3.97600	−0.248987
$256$	−8.26017	−0.516261
$257$	−2.14166	−0.133593	−0.0667966	−	0.997767i	$-0.521278\pi$
$257$	−2.14166	−0.133593	−0.0667966	+	0.997767i	$0.521278\pi$
$258$	−3.55353	−0.221233
$259$	−32.9904	−2.04992
$260$	5.98025	0.370879
$261$	−1.35263	−0.0837258
$262$	3.04966	0.188409
$263$	5.37548	0.331467	0.165733	−	0.986171i	$-0.447001\pi$
$263$	5.37548	0.331467	0.165733	+	0.986171i	$0.447001\pi$
$264$	−7.35843	−0.452880
$265$	−10.2287	−0.628343
$266$	−52.2340	−3.20267
$267$	15.6289	0.956474
$268$	42.0031	2.56575
$269$	1.67358	0.102040	0.0510201	−	0.998698i	$-0.483753\pi$
$269$	1.67358	0.102040	0.0510201	+	0.998698i	$0.483753\pi$
$270$	−4.48326	−0.272843
$271$	4.57325	0.277805	0.138903	−	0.990306i	$-0.455642\pi$
$271$	4.57325	0.277805	0.138903	+	0.990306i	$0.455642\pi$
$272$	2.17212	0.131704
$273$	−4.12307	−0.249539
$274$	40.4677	2.44475
$275$	−3.24755	−0.195835
$276$	17.6765	1.06400
$277$	−6.67570	−0.401104	−0.200552	−	0.979683i	$-0.564274\pi$
$277$	−6.67570	−0.401104	−0.200552	+	0.979683i	$0.564274\pi$
$278$	−31.3151	−1.87816
$279$	4.45900	0.266953
$280$	18.0289	1.07743
$281$	−12.5168	−0.746690	−0.373345	−	0.927692i	$-0.621789\pi$
$281$	−12.5168	−0.746690	−0.373345	+	0.927692i	$0.621789\pi$
$282$	11.8901	0.708047
$283$	−29.6457	−1.76226	−0.881128	−	0.472877i	$-0.843215\pi$
$283$	−29.6457	−1.76226	−0.881128	+	0.472877i	$0.843215\pi$
$284$	17.1907	1.02008
$285$	−11.4158	−0.676211
$286$	−7.54450	−0.446116
$287$	16.7920	0.991198
$288$	6.80031	0.400712
$289$	−13.0869	−0.769815
$290$	6.06421	0.356102
$291$	2.26693	0.132890
$292$	17.1559	1.00397
$293$	3.48296	0.203477	0.101738	−	0.994811i	$-0.467560\pi$
$293$	3.48296	0.203477	0.101738	+	0.994811i	$0.467560\pi$
$294$	−22.3048	−1.30084
$295$	15.2221	0.886264
$296$	−17.4073	−1.01178
$297$	3.38236	0.196264
$298$	−30.2476	−1.75219
$299$	5.94102	0.343578
$300$	−2.85675	−0.164935
$301$	−6.56854	−0.378605
$302$	−31.7212	−1.82535
$303$	−8.42998	−0.484290
$304$	6.23653	0.357689
$305$	−13.8706	−0.794228
$306$	4.41239	0.252240
$307$	21.4649	1.22507	0.612533	−	0.790445i	$-0.290151\pi$
$307$	21.4649	1.22507	0.612533	+	0.790445i	$0.290151\pi$
$308$	−41.4931	−2.36429
$309$	1.00000	0.0568880
$310$	−19.9908	−1.13540
$311$	13.4673	0.763661	0.381831	−	0.924232i	$-0.375294\pi$
$311$	13.4673	0.763661	0.381831	+	0.924232i	$0.375294\pi$
$312$	−2.17553	−0.123165
$313$	17.9955	1.01717	0.508584	−	0.861012i	$-0.330169\pi$
$313$	17.9955	1.01717	0.508584	+	0.861012i	$0.330169\pi$
$314$	−34.7461	−1.96083
$315$	−8.28712	−0.466926
$316$	−25.4936	−1.43412
$317$	9.18968	0.516144	0.258072	−	0.966126i	$-0.416913\pi$
$317$	9.18968	0.516144	0.258072	+	0.966126i	$0.416913\pi$
$318$	11.3514	0.636553
$319$	−4.57509	−0.256156
$320$	−26.0736	−1.45756
$321$	−1.52130	−0.0849106
$322$	54.6377	3.04484
$323$	11.2353	0.625149
$324$	2.97534	0.165296
$325$	−0.960144	−0.0532592
$326$	37.5509	2.07975
$327$	18.1272	1.00244
$328$	8.86026	0.489226
$329$	21.9784	1.21171
$330$	−15.1640	−0.834750
$331$	−27.7532	−1.52545	−0.762727	−	0.646720i	$-0.776140\pi$
$331$	−27.7532	−1.52545	−0.762727	+	0.646720i	$0.776140\pi$
$332$	−3.06302	−0.168105
$333$	8.00141	0.438475
$334$	−5.02574	−0.274996
$335$	28.3745	1.55026
$336$	4.52732	0.246986
$337$	20.2709	1.10423	0.552114	−	0.833769i	$-0.313821\pi$
$337$	20.2709	1.10423	0.552114	+	0.833769i	$0.313821\pi$
$338$	−2.23055	−0.121326
$339$	14.6743	0.796996
$340$	−11.8299	−0.641568
$341$	15.0819	0.816731
$342$	12.6687	0.685046
$343$	−12.3679	−0.667804
$344$	−3.46589	−0.186868
$345$	11.9411	0.642887
$346$	−41.6340	−2.23826
$347$	26.2661	1.41004	0.705018	−	0.709189i	$-0.250939\pi$
$347$	26.2661	1.41004	0.705018	+	0.709189i	$0.250939\pi$
$348$	−4.02454	−0.215738
$349$	1.03998	0.0556690	0.0278345	−	0.999613i	$-0.491139\pi$
$349$	1.03998	0.0556690	0.0278345	+	0.999613i	$0.491139\pi$
$350$	−8.83015	−0.471991
$351$	1.00000	0.0533761
$352$	23.0011	1.22596
$353$	2.27684	0.121184	0.0605919	−	0.998163i	$-0.480701\pi$
$353$	2.27684	0.121184	0.0605919	+	0.998163i	$0.480701\pi$
$354$	−16.8928	−0.897844
$355$	11.6129	0.616349
$356$	46.5013	2.46456
$357$	8.15612	0.431667
$358$	24.4160	1.29043
$359$	−4.83609	−0.255239	−0.127620	−	0.991823i	$-0.540734\pi$
$359$	−4.83609	−0.255239	−0.127620	+	0.991823i	$0.540734\pi$
$360$	−4.37269	−0.230461
$361$	13.2584	0.697812
$362$	31.3298	1.64666
$363$	0.440338	0.0231118
$364$	−12.2675	−0.642992
$365$	11.5894	0.606615
$366$	15.3930	0.804605
$367$	0.878090	0.0458359	0.0229180	−	0.999737i	$-0.492704\pi$
$367$	0.878090	0.0458359	0.0229180	+	0.999737i	$0.492704\pi$
$368$	−6.52352	−0.340062
$369$	−4.07269	−0.212016
$370$	−35.8724	−1.86492
$371$	20.9825	1.08936
$372$	13.2670	0.687862
$373$	−12.2561	−0.634594	−0.317297	−	0.948326i	$-0.602775\pi$
$373$	−12.2561	−0.634594	−0.317297	+	0.948326i	$0.602775\pi$
$374$	14.9243	0.771717
$375$	−11.9795	−0.618620
$376$	11.5969	0.598063
$377$	−1.35263	−0.0696641
$378$	9.19669	0.473027
$379$	37.1929	1.91047	0.955236	−	0.295846i	$-0.0956014\pi$
$379$	37.1929	1.91047	0.955236	+	0.295846i	$0.0956014\pi$
$380$	−33.9657	−1.74240
$381$	9.48166	0.485760
$382$	−18.0506	−0.923548
$383$	18.1069	0.925221	0.462610	−	0.886562i	$-0.346913\pi$
$383$	18.1069	0.925221	0.462610	+	0.886562i	$0.346913\pi$
$384$	15.3347	0.782546
$385$	−28.0300	−1.42854
$386$	−59.2496	−3.01573
$387$	1.59312	0.0809829
$388$	6.74487	0.342419
$389$	−3.39316	−0.172040	−0.0860200	−	0.996293i	$-0.527415\pi$
$389$	−3.39316	−0.172040	−0.0860200	+	0.996293i	$0.527415\pi$
$390$	−4.48326	−0.227019
$391$	−11.7523	−0.594341
$392$	−21.7546	−1.09877
$393$	−1.36723	−0.0689675
$394$	39.1540	1.97255
$395$	−17.2218	−0.866520
$396$	10.0636	0.505717
$397$	19.0033	0.953749	0.476875	−	0.878971i	$-0.341770\pi$
$397$	19.0033	0.953749	0.476875	+	0.878971i	$0.341770\pi$
$398$	−2.84629	−0.142671
$399$	23.4176	1.17235
$400$	1.05428	0.0527142
$401$	30.3229	1.51425	0.757126	−	0.653269i	$-0.226603\pi$
$401$	30.3229	1.51425	0.757126	+	0.653269i	$0.226603\pi$
$402$	−31.4888	−1.57052
$403$	4.45900	0.222118
$404$	−25.0820	−1.24788
$405$	2.00994	0.0998747
$406$	−12.4397	−0.617374
$407$	27.0636	1.34149
$408$	4.30357	0.213058
$409$	1.61264	0.0797401	0.0398700	−	0.999205i	$-0.487306\pi$
$409$	1.61264	0.0797401	0.0398700	+	0.999205i	$0.487306\pi$
$410$	18.2589	0.901744
$411$	−18.1425	−0.894905
$412$	2.97534	0.146584
$413$	−31.2257	−1.53651
$414$	−13.2517	−0.651286
$415$	−2.06917	−0.101572
$416$	6.80031	0.333413
$417$	14.0392	0.687503
$418$	42.8501	2.09587
$419$	−3.21679	−0.157150	−0.0785752	−	0.996908i	$-0.525037\pi$
$419$	−3.21679	−0.157150	−0.0785752	+	0.996908i	$0.525037\pi$
$420$	−24.6570	−1.20314
$421$	−12.8252	−0.625060	−0.312530	−	0.949908i	$-0.601177\pi$
$421$	−12.8252	−0.625060	−0.312530	+	0.949908i	$0.601177\pi$
$422$	−12.9132	−0.628606
$423$	−5.33059	−0.259182
$424$	11.0714	0.537675
$425$	1.89932	0.0921308
$426$	−12.8875	−0.624402
$427$	28.4533	1.37695
$428$	−4.52637	−0.218791
$429$	3.38236	0.163302
$430$	−7.14238	−0.344436
$431$	−12.4510	−0.599743	−0.299871	−	0.953980i	$-0.596944\pi$
$431$	−12.4510	−0.599743	−0.299871	+	0.953980i	$0.596944\pi$
$432$	−1.09805	−0.0528298
$433$	40.1788	1.93087	0.965435	−	0.260642i	$-0.0839343\pi$
$433$	40.1788	1.93087	0.965435	+	0.260642i	$0.0839343\pi$
$434$	41.0080	1.96845
$435$	−2.71871	−0.130352
$436$	53.9346	2.58300
$437$	−33.7429	−1.61414
$438$	−12.8614	−0.614541
$439$	−7.29132	−0.347996	−0.173998	−	0.984746i	$-0.555669\pi$
$439$	−7.29132	−0.347996	−0.173998	+	0.984746i	$0.555669\pi$
$440$	−14.7900	−0.705085
$441$	9.99968	0.476175
$442$	4.41239	0.209876
$443$	28.8800	1.37213	0.686065	−	0.727540i	$-0.259336\pi$
$443$	28.8800	1.37213	0.686065	+	0.727540i	$0.259336\pi$
$444$	23.8069	1.12982
$445$	31.4132	1.48913
$446$	−24.4624	−1.15833
$447$	13.5606	0.641395
$448$	53.4857	2.52696
$449$	−6.49074	−0.306317	−0.153158	−	0.988202i	$-0.548944\pi$
$449$	−6.49074	−0.306317	−0.153158	+	0.988202i	$0.548944\pi$
$450$	2.14164	0.100958
$451$	−13.7753	−0.648653
$452$	43.6608	2.05363
$453$	14.2213	0.668173
$454$	−4.09345	−0.192115
$455$	−8.28712	−0.388506
$456$	12.3563	0.578635
$457$	19.9347	0.932508	0.466254	−	0.884651i	$-0.345603\pi$
$457$	19.9347	0.932508	0.466254	+	0.884651i	$0.345603\pi$
$458$	56.9118	2.65931
$459$	−1.97817	−0.0923329
$460$	35.5288	1.65654
$461$	4.96179	0.231094	0.115547	−	0.993302i	$-0.463138\pi$
$461$	4.96179	0.231094	0.115547	+	0.993302i	$0.463138\pi$
$462$	31.1065	1.44721
$463$	−16.0119	−0.744138	−0.372069	−	0.928205i	$-0.621351\pi$
$463$	−16.0119	−0.744138	−0.372069	+	0.928205i	$0.621351\pi$
$464$	1.48525	0.0689512
$465$	8.96231	0.415617
$466$	18.7183	0.867107
$467$	8.46488	0.391708	0.195854	−	0.980633i	$-0.437252\pi$
$467$	8.46488	0.391708	0.195854	+	0.980633i	$0.437252\pi$
$468$	2.97534	0.137535
$469$	−58.2057	−2.68769
$470$	23.8984	1.10235
$471$	15.5774	0.717768
$472$	−16.4762	−0.758378
$473$	5.38850	0.247764
$474$	19.1120	0.877842
$475$	5.45328	0.250214
$476$	24.2672	1.11228
$477$	−5.08905	−0.233012
$478$	2.01274	0.0920604
$479$	21.6261	0.988122	0.494061	−	0.869427i	$-0.335512\pi$
$479$	21.6261	0.988122	0.494061	+	0.869427i	$0.335512\pi$
$480$	13.6682	0.623866
$481$	8.00141	0.364833
$482$	10.1583	0.462700
$483$	−24.4952	−1.11457
$484$	1.31015	0.0595525
$485$	4.55639	0.206895
$486$	−2.23055	−0.101180
$487$	36.9177	1.67290	0.836450	−	0.548044i	$-0.184627\pi$
$487$	36.9177	1.67290	0.836450	+	0.548044i	$0.184627\pi$
$488$	15.0133	0.679622
$489$	−16.8348	−0.761298
$490$	−44.8312	−2.02527
$491$	−20.3841	−0.919920	−0.459960	−	0.887940i	$-0.652136\pi$
$491$	−20.3841	−0.919920	−0.459960	+	0.887940i	$0.652136\pi$
$492$	−12.1176	−0.546304
$493$	2.67573	0.120509
$494$	12.6687	0.569993
$495$	6.79833	0.305562
$496$	−4.89619	−0.219845
$497$	−23.8220	−1.06856
$498$	2.29628	0.102899
$499$	32.3853	1.44977	0.724883	−	0.688872i	$-0.241894\pi$
$499$	32.3853	1.44977	0.724883	+	0.688872i	$0.241894\pi$
$500$	−35.6431	−1.59401
$501$	2.25314	0.100663
$502$	4.24164	0.189314
$503$	25.4295	1.13385	0.566923	−	0.823771i	$-0.308134\pi$
$503$	25.4295	1.13385	0.566923	+	0.823771i	$0.308134\pi$
$504$	8.96986	0.399550
$505$	−16.9438	−0.753987
$506$	−44.8220	−1.99258
$507$	1.00000	0.0444116
$508$	28.2111	1.25167
$509$	7.80278	0.345852	0.172926	−	0.984935i	$-0.444678\pi$
$509$	7.80278	0.345852	0.172926	+	0.984935i	$0.444678\pi$
$510$	8.86864	0.392710
$511$	−23.7737	−1.05169
$512$	−12.2447	−0.541146
$513$	−5.67965	−0.250763
$514$	4.77707	0.210708
$515$	2.00994	0.0885685
$516$	4.74007	0.208670
$517$	−18.0300	−0.792957
$518$	73.5865	3.23321
$519$	18.6654	0.819320
$520$	−4.37269	−0.191755
$521$	−36.2009	−1.58599	−0.792996	−	0.609227i	$-0.791480\pi$
$521$	−36.2009	−1.58599	−0.792996	+	0.609227i	$0.791480\pi$
$522$	3.01711	0.132055
$523$	7.37153	0.322335	0.161167	−	0.986927i	$-0.448474\pi$
$523$	7.37153	0.322335	0.161167	+	0.986927i	$0.448474\pi$
$524$	−4.06796	−0.177710
$525$	3.95874	0.172773
$526$	−11.9903	−0.522800
$527$	−8.82064	−0.384233
$528$	−3.71399	−0.161631
$529$	12.2957	0.534597
$530$	22.8156	0.991044
$531$	7.57340	0.328658
$532$	69.6752	3.02080
$533$	−4.07269	−0.176408
$534$	−34.8610	−1.50858
$535$	−3.05772	−0.132197
$536$	−30.7122	−1.32656
$537$	−10.9462	−0.472364
$538$	−3.73300	−0.160941
$539$	33.8225	1.45684
$540$	5.98025	0.257349
$541$	4.16669	0.179140	0.0895699	−	0.995981i	$-0.471451\pi$
$541$	4.16669	0.179140	0.0895699	+	0.995981i	$0.471451\pi$
$542$	−10.2008	−0.438164
$543$	−14.0458	−0.602762
$544$	−13.4522	−0.576756
$545$	36.4346	1.56069
$546$	9.19669	0.393582
$547$	22.9638	0.981862	0.490931	−	0.871198i	$-0.336657\pi$
$547$	22.9638	0.981862	0.490931	+	0.871198i	$0.336657\pi$
$548$	−53.9801	−2.30592
$549$	−6.90100	−0.294528
$550$	7.24381	0.308877
$551$	7.68248	0.327285
$552$	−12.9249	−0.550119
$553$	35.3277	1.50228
$554$	14.8905	0.632635
$555$	16.0824	0.682658
$556$	41.7714	1.77150
$557$	27.2070	1.15280	0.576399	−	0.817169i	$-0.304457\pi$
$557$	27.2070	1.15280	0.576399	+	0.817169i	$0.304457\pi$
$558$	−9.94599	−0.421048
$559$	1.59312	0.0673818
$560$	9.09965	0.384530
$561$	−6.69087	−0.282489
$562$	27.9193	1.17771
$563$	−31.9632	−1.34709	−0.673544	−	0.739147i	$-0.735229\pi$
$563$	−31.9632	−1.34709	−0.673544	+	0.739147i	$0.735229\pi$
$564$	−15.8603	−0.667839
$565$	29.4944	1.24084
$566$	66.1262	2.77949
$567$	−4.12307	−0.173153
$568$	−12.5697	−0.527411
$569$	−12.4912	−0.523660	−0.261830	−	0.965114i	$-0.584326\pi$
$569$	−12.4912	−0.523660	−0.261830	+	0.965114i	$0.584326\pi$
$570$	25.4634	1.06654
$571$	−14.6591	−0.613465	−0.306733	−	0.951796i	$-0.599236\pi$
$571$	−14.6591	−0.613465	−0.306733	+	0.951796i	$0.599236\pi$
$572$	10.0636	0.420782
$573$	8.09245	0.338067
$574$	−37.4552	−1.56335
$575$	−5.70423	−0.237883
$576$	−12.9723	−0.540513
$577$	30.5605	1.27225	0.636125	−	0.771586i	$-0.280536\pi$
$577$	30.5605	1.27225	0.636125	+	0.771586i	$0.280536\pi$
$578$	29.1908	1.21418
$579$	26.5628	1.10391
$580$	−8.08907	−0.335880
$581$	4.24457	0.176095
$582$	−5.05649	−0.209598
$583$	−17.2130	−0.712889
$584$	−12.5442	−0.519081
$585$	2.00994	0.0831008
$586$	−7.76891	−0.320931
$587$	−2.90949	−0.120087	−0.0600437	−	0.998196i	$-0.519124\pi$
$587$	−2.90949	−0.120087	−0.0600437	+	0.998196i	$0.519124\pi$
$588$	29.7524	1.22697
$589$	−25.3255	−1.04352
$590$	−33.9536	−1.39785
$591$	−17.5535	−0.722056
$592$	−8.78593	−0.361099
$593$	−47.7260	−1.95987	−0.979936	−	0.199313i	$-0.936129\pi$
$593$	−47.7260	−1.95987	−0.979936	+	0.199313i	$0.936129\pi$
$594$	−7.54450	−0.309555
$595$	16.3933	0.672060
$596$	40.3474	1.65269
$597$	1.27605	0.0522252
$598$	−13.2517	−0.541903
$599$	19.9418	0.814800	0.407400	−	0.913250i	$-0.366435\pi$
$599$	19.9418	0.814800	0.407400	+	0.913250i	$0.366435\pi$
$600$	2.08882	0.0852759
$601$	−23.5009	−0.958621	−0.479311	−	0.877645i	$-0.659113\pi$
$601$	−23.5009	−0.958621	−0.479311	+	0.877645i	$0.659113\pi$
$602$	14.6514	0.597148
$603$	14.1171	0.574892
$604$	42.3130	1.72169
$605$	0.885054	0.0359825
$606$	18.8035	0.763839
$607$	22.8831	0.928795	0.464398	−	0.885627i	$-0.346271\pi$
$607$	22.8831	0.928795	0.464398	+	0.885627i	$0.346271\pi$
$608$	−38.6234	−1.56638
$609$	5.57699	0.225991
$610$	30.9390	1.25268
$611$	−5.33059	−0.215653
$612$	−5.88571	−0.237916
$613$	7.65104	0.309023	0.154511	−	0.987991i	$-0.450620\pi$
$613$	7.65104	0.309023	0.154511	+	0.987991i	$0.450620\pi$
$614$	−47.8784	−1.93222
$615$	−8.18585	−0.330085
$616$	30.3393	1.22240
$617$	−16.4454	−0.662069	−0.331034	−	0.943619i	$-0.607398\pi$
$617$	−16.4454	−0.662069	−0.331034	+	0.943619i	$0.607398\pi$
$618$	−2.23055	−0.0897257
$619$	−13.4790	−0.541768	−0.270884	−	0.962612i	$-0.587316\pi$
$619$	−13.4790	−0.541768	−0.270884	+	0.962612i	$0.587316\pi$
$620$	26.6659	1.07093
$621$	5.94102	0.238405
$622$	−30.0395	−1.20447
$623$	−64.4390	−2.58170
$624$	−1.09805	−0.0439571
$625$	−19.2774	−0.771096
$626$	−40.1399	−1.60431
$627$	−19.2106	−0.767198
$628$	46.3480	1.84949
$629$	−15.8281	−0.631109
$630$	18.4848	0.736452
$631$	8.97380	0.357242	0.178621	−	0.983918i	$-0.442836\pi$
$631$	8.97380	0.357242	0.178621	+	0.983918i	$0.442836\pi$
$632$	18.6406	0.741483
$633$	5.78927	0.230103
$634$	−20.4980	−0.814080
$635$	19.0576	0.756276
$636$	−15.1416	−0.600405
$637$	9.99968	0.396202
$638$	10.2049	0.404017
$639$	5.77774	0.228564
$640$	30.8218	1.21834
$641$	−22.8361	−0.901972	−0.450986	−	0.892531i	$-0.648928\pi$
$641$	−22.8361	−0.901972	−0.450986	+	0.892531i	$0.648928\pi$
$642$	3.39333	0.133924
$643$	9.26754	0.365476	0.182738	−	0.983162i	$-0.441504\pi$
$643$	9.26754	0.365476	0.182738	+	0.983162i	$0.441504\pi$
$644$	−72.8815	−2.87193
$645$	3.20208	0.126082
$646$	−25.0609	−0.986006
$647$	32.9107	1.29385	0.646926	−	0.762552i	$-0.276054\pi$
$647$	32.9107	1.29385	0.646926	+	0.762552i	$0.276054\pi$
$648$	−2.17553	−0.0854630
$649$	25.6160	1.00551
$650$	2.14164	0.0840022
$651$	−18.3847	−0.720555
$652$	−50.0893	−1.96165
$653$	−40.4211	−1.58180	−0.790900	−	0.611945i	$-0.790387\pi$
$653$	−40.4211	−1.58180	−0.790900	+	0.611945i	$0.790387\pi$
$654$	−40.4336	−1.58108
$655$	−2.74804	−0.107375
$656$	4.47200	0.174602
$657$	5.76602	0.224954
$658$	−49.0238	−1.91115
$659$	7.62441	0.297005	0.148502	−	0.988912i	$-0.452555\pi$
$659$	7.62441	0.297005	0.148502	+	0.988912i	$0.452555\pi$
$660$	20.2273	0.787347
$661$	−2.25233	−0.0876054	−0.0438027	−	0.999040i	$-0.513947\pi$
$661$	−2.25233	−0.0876054	−0.0438027	+	0.999040i	$0.513947\pi$
$662$	61.9048	2.40600
$663$	−1.97817	−0.0768257
$664$	2.23964	0.0869150
$665$	47.0679	1.82522
$666$	−17.8475	−0.691577
$667$	−8.03602	−0.311156
$668$	6.70386	0.259380
$669$	10.9670	0.424008
$670$	−63.2906	−2.44513
$671$	−23.3416	−0.901094
$672$	−28.0381	−1.08159
$673$	−24.5903	−0.947887	−0.473944	−	0.880555i	$-0.657170\pi$
$673$	−24.5903	−0.947887	−0.473944	+	0.880555i	$0.657170\pi$
$674$	−45.2152	−1.74163
$675$	−0.960144	−0.0369559
$676$	2.97534	0.114436
$677$	−11.1628	−0.429021	−0.214510	−	0.976722i	$-0.568816\pi$
$677$	−11.1628	−0.429021	−0.214510	+	0.976722i	$0.568816\pi$
$678$	−32.7316	−1.25705
$679$	−9.34669	−0.358693
$680$	8.64991	0.331709
$681$	1.83518	0.0703243
$682$	−33.6409	−1.28818
$683$	41.4943	1.58774	0.793869	−	0.608089i	$-0.208064\pi$
$683$	41.4943	1.58774	0.793869	+	0.608089i	$0.208064\pi$
$684$	−16.8989	−0.646144
$685$	−36.4654	−1.39327
$686$	27.5872	1.05328
$687$	−25.5147	−0.973448
$688$	−1.74932	−0.0666923
$689$	−5.08905	−0.193877
$690$	−26.6352	−1.01398
$691$	−34.8828	−1.32701	−0.663503	−	0.748174i	$-0.730931\pi$
$691$	−34.8828	−1.32701	−0.663503	+	0.748174i	$0.730931\pi$
$692$	55.5358	2.11116
$693$	−13.9457	−0.529753
$694$	−58.5877	−2.22396
$695$	28.2180	1.07037
$696$	2.94269	0.111543
$697$	8.05646	0.305160
$698$	−2.31973	−0.0878031
$699$	−8.39178	−0.317406
$700$	11.7786	0.445188
$701$	−24.0407	−0.908004	−0.454002	−	0.891001i	$-0.650004\pi$
$701$	−24.0407	−0.908004	−0.454002	+	0.891001i	$0.650004\pi$
$702$	−2.23055	−0.0841865
$703$	−45.4452	−1.71400
$704$	−43.8770	−1.65368
$705$	−10.7142	−0.403519
$706$	−5.07859	−0.191135
$707$	34.7574	1.30719
$708$	22.5334	0.846858
$709$	−43.6837	−1.64057	−0.820287	−	0.571952i	$-0.806186\pi$
$709$	−43.6837	−1.64057	−0.820287	+	0.571952i	$0.806186\pi$
$710$	−25.9031	−0.972127
$711$	−8.56830	−0.321336
$712$	−34.0012	−1.27425
$713$	26.4910	0.992095
$714$	−18.1926	−0.680841
$715$	6.79833	0.254243
$716$	−32.5687	−1.21715
$717$	−0.902351	−0.0336989
$718$	10.7871	0.402572
$719$	−28.5737	−1.06562	−0.532809	−	0.846235i	$-0.678864\pi$
$719$	−28.5737	−1.06562	−0.532809	+	0.846235i	$0.678864\pi$
$720$	−2.20701	−0.0822504
$721$	−4.12307	−0.153551
$722$	−29.5735	−1.10061
$723$	−4.55419	−0.169372
$724$	−41.7909	−1.55315
$725$	1.29872	0.0482333
$726$	−0.982195	−0.0364527
$727$	13.2293	0.490647	0.245323	−	0.969441i	$-0.421106\pi$
$727$	13.2293	0.490647	0.245323	+	0.969441i	$0.421106\pi$
$728$	8.96986	0.332445
$729$	1.00000	0.0370370
$730$	−25.8506	−0.956773
$731$	−3.15146	−0.116561
$732$	−20.5328	−0.758914
$733$	45.6547	1.68629	0.843147	−	0.537684i	$-0.180701\pi$
$733$	45.6547	1.68629	0.843147	+	0.537684i	$0.180701\pi$
$734$	−1.95862	−0.0722940
$735$	20.0988	0.741354
$736$	40.4008	1.48919
$737$	47.7490	1.75886
$738$	9.08432	0.334398
$739$	43.4283	1.59754	0.798768	−	0.601640i	$-0.205486\pi$
$739$	43.4283	1.59754	0.798768	+	0.601640i	$0.205486\pi$
$740$	47.8504	1.75902
$741$	−5.67965	−0.208647
$742$	−46.8024	−1.71817
$743$	46.4244	1.70315	0.851573	−	0.524236i	$-0.175649\pi$
$743$	46.4244	1.70315	0.851573	+	0.524236i	$0.175649\pi$
$744$	−9.70069	−0.355644
$745$	27.2560	0.998583
$746$	27.3377	1.00090
$747$	−1.02947	−0.0376663
$748$	−19.9076	−0.727893
$749$	6.27242	0.229189
$750$	26.7209	0.975709
$751$	−20.0873	−0.732996	−0.366498	−	0.930419i	$-0.619443\pi$
$751$	−20.0873	−0.732996	−0.366498	+	0.930419i	$0.619443\pi$
$752$	5.85324	0.213446
$753$	−1.90161	−0.0692987
$754$	3.01711	0.109877
$755$	28.5839	1.04027
$756$	−12.2675	−0.446165
$757$	−22.5716	−0.820379	−0.410189	−	0.912000i	$-0.634537\pi$
$757$	−22.5716	−0.820379	−0.410189	+	0.912000i	$0.634537\pi$
$758$	−82.9605	−3.01326
$759$	20.0947	0.729390
$760$	24.8353	0.900872
$761$	−44.7677	−1.62283	−0.811413	−	0.584473i	$-0.801301\pi$
$761$	−44.7677	−1.62283	−0.811413	+	0.584473i	$0.801301\pi$
$762$	−21.1493	−0.766157
$763$	−74.7398	−2.70576
$764$	24.0777	0.871102
$765$	−3.97600	−0.143752
$766$	−40.3883	−1.45929
$767$	7.57340	0.273460
$768$	−8.26017	−0.298063
$769$	−10.2412	−0.369307	−0.184654	−	0.982804i	$-0.559116\pi$
$769$	−10.2412	−0.369307	−0.184654	+	0.982804i	$0.559116\pi$
$770$	62.5222	2.25314
$771$	−2.14166	−0.0771300
$772$	79.0333	2.84447
$773$	−39.9504	−1.43691	−0.718457	−	0.695571i	$-0.755151\pi$
$773$	−39.9504	−1.43691	−0.718457	+	0.695571i	$0.755151\pi$
$774$	−3.55353	−0.127729
$775$	−4.28128	−0.153788
$776$	−4.93177	−0.177040
$777$	−32.9904	−1.18352
$778$	7.56860	0.271347
$779$	23.1314	0.828770
$780$	5.98025	0.214127
$781$	19.5424	0.699281
$782$	26.2141	0.937415
$783$	−1.35263	−0.0483391
$784$	−10.9801	−0.392147
$785$	31.3096	1.11749
$786$	3.04966	0.108778
$787$	−8.55285	−0.304876	−0.152438	−	0.988313i	$-0.548712\pi$
$787$	−8.55285	−0.304876	−0.152438	+	0.988313i	$0.548712\pi$
$788$	−52.2277	−1.86053
$789$	5.37548	0.191372
$790$	38.4139	1.36671
$791$	−60.5030	−2.15124
$792$	−7.35843	−0.261470
$793$	−6.90100	−0.245062
$794$	−42.3878	−1.50429
$795$	−10.2287	−0.362774
$796$	3.79667	0.134570
$797$	−26.2335	−0.929238	−0.464619	−	0.885511i	$-0.653809\pi$
$797$	−26.2335	−0.929238	−0.464619	+	0.885511i	$0.653809\pi$
$798$	−52.2340	−1.84906
$799$	10.5448	0.373048
$800$	−6.52927	−0.230845
$801$	15.6289	0.552220
$802$	−67.6366	−2.38833
$803$	19.5027	0.688237
$804$	42.0031	1.48133
$805$	−49.2339	−1.73527
$806$	−9.94599	−0.350333
$807$	1.67358	0.0589129
$808$	18.3397	0.645188
$809$	21.6086	0.759717	0.379858	−	0.925045i	$-0.375973\pi$
$809$	21.6086	0.759717	0.379858	+	0.925045i	$0.375973\pi$
$810$	−4.48326	−0.157526
$811$	47.7635	1.67720	0.838602	−	0.544744i	$-0.183373\pi$
$811$	47.7635	1.67720	0.838602	+	0.544744i	$0.183373\pi$
$812$	16.5934	0.582315
$813$	4.57325	0.160391
$814$	−60.3667	−2.11585
$815$	−33.8370	−1.18526
$816$	2.17212	0.0760395
$817$	−9.04837	−0.316562
$818$	−3.59708	−0.125769
$819$	−4.12307	−0.144072
$820$	−24.3557	−0.850537
$821$	32.8032	1.14484	0.572420	−	0.819960i	$-0.306005\pi$
$821$	32.8032	1.14484	0.572420	+	0.819960i	$0.306005\pi$
$822$	40.4677	1.41147
$823$	50.9673	1.77661	0.888304	−	0.459257i	$-0.151884\pi$
$823$	50.9673	1.77661	0.888304	+	0.459257i	$0.151884\pi$
$824$	−2.17553	−0.0757882
$825$	−3.24755	−0.113065
$826$	69.6503	2.42344
$827$	46.8313	1.62849	0.814243	−	0.580525i	$-0.197153\pi$
$827$	46.8313	1.62849	0.814243	+	0.580525i	$0.197153\pi$
$828$	17.6765	0.614302
$829$	24.1189	0.837685	0.418842	−	0.908059i	$-0.362436\pi$
$829$	24.1189	0.837685	0.418842	+	0.908059i	$0.362436\pi$
$830$	4.61538	0.160202
$831$	−6.67570	−0.231577
$832$	−12.9723	−0.449734
$833$	−19.7810	−0.685373
$834$	−31.3151	−1.08435
$835$	4.52868	0.156722
$836$	−57.1580	−1.97685
$837$	4.45900	0.154125
$838$	7.17519	0.247863
$839$	−0.821245	−0.0283525	−0.0141763	−	0.999900i	$-0.504513\pi$
$839$	−0.821245	−0.0283525	−0.0141763	+	0.999900i	$0.504513\pi$
$840$	18.0289	0.622056
$841$	−27.1704	−0.936910
$842$	28.6071	0.985866
$843$	−12.5168	−0.431102
$844$	17.2250	0.592909
$845$	2.00994	0.0691440
$846$	11.8901	0.408791
$847$	−1.81555	−0.0623829
$848$	5.58802	0.191893
$849$	−29.6457	−1.01744
$850$	−4.23653	−0.145312
$851$	47.5365	1.62953
$852$	17.1907	0.588944
$853$	26.3511	0.902245	0.451122	−	0.892462i	$-0.351024\pi$
$853$	26.3511	0.902245	0.451122	+	0.892462i	$0.351024\pi$
$854$	−63.4664	−2.17177
$855$	−11.4158	−0.390411
$856$	3.30963	0.113121
$857$	−29.3274	−1.00181	−0.500903	−	0.865504i	$-0.666999\pi$
$857$	−29.3274	−1.00181	−0.500903	+	0.865504i	$0.666999\pi$
$858$	−7.54450	−0.257565
$859$	6.13524	0.209332	0.104666	−	0.994507i	$-0.466623\pi$
$859$	6.13524	0.209332	0.104666	+	0.994507i	$0.466623\pi$
$860$	9.52725	0.324877
$861$	16.7920	0.572269
$862$	27.7725	0.945935
$863$	31.9077	1.08615	0.543075	−	0.839684i	$-0.317260\pi$
$863$	31.9077	1.08615	0.543075	+	0.839684i	$0.317260\pi$
$864$	6.80031	0.231351
$865$	37.5163	1.27559
$866$	−89.6207	−3.04544
$867$	−13.0869	−0.444453
$868$	−54.7008	−1.85667
$869$	−28.9810	−0.983114
$870$	6.06421	0.205596
$871$	14.1171	0.478339
$872$	−39.4364	−1.33548
$873$	2.26693	0.0767239
$874$	75.2651	2.54588
$875$	49.3924	1.66977
$876$	17.1559	0.579643
$877$	−24.9058	−0.841010	−0.420505	−	0.907290i	$-0.638147\pi$
$877$	−24.9058	−0.841010	−0.420505	+	0.907290i	$0.638147\pi$
$878$	16.2636	0.548871
$879$	3.48296	0.117477
$880$	−7.46489	−0.251641
$881$	7.68219	0.258820	0.129410	−	0.991591i	$-0.458692\pi$
$881$	7.68219	0.258820	0.129410	+	0.991591i	$0.458692\pi$
$882$	−22.3048	−0.751040
$883$	−39.6809	−1.33537	−0.667685	−	0.744444i	$-0.732715\pi$
$883$	−39.6809	−1.33537	−0.667685	+	0.744444i	$0.732715\pi$
$884$	−5.88571	−0.197958
$885$	15.2221	0.511685
$886$	−64.4182	−2.16417
$887$	5.71008	0.191726	0.0958629	−	0.995395i	$-0.469439\pi$
$887$	5.71008	0.191726	0.0958629	+	0.995395i	$0.469439\pi$
$888$	−17.4073	−0.584152
$889$	−39.0935	−1.31115
$890$	−70.0685	−2.34870
$891$	3.38236	0.113313
$892$	32.6305	1.09255
$893$	30.2759	1.01314
$894$	−30.2476	−1.01163
$895$	−22.0012	−0.735420
$896$	−63.2261	−2.11223
$897$	5.94102	0.198365
$898$	14.4779	0.483134
$899$	−6.03138	−0.201158
$900$	−2.85675	−0.0952250
$901$	10.0670	0.335380
$902$	30.7264	1.02308
$903$	−6.56854	−0.218587
$904$	−31.9243	−1.06179
$905$	−28.2312	−0.938435
$906$	−31.7212	−1.05387
$907$	−24.3513	−0.808573	−0.404287	−	0.914632i	$-0.632480\pi$
$907$	−24.3513	−0.808573	−0.404287	+	0.914632i	$0.632480\pi$
$908$	5.46028	0.181206
$909$	−8.42998	−0.279605
$910$	18.4848	0.612765
$911$	4.93320	0.163444	0.0817222	−	0.996655i	$-0.473958\pi$
$911$	4.93320	0.163444	0.0817222	+	0.996655i	$0.473958\pi$
$912$	6.23653	0.206512
$913$	−3.48203	−0.115238
$914$	−44.4653	−1.47078
$915$	−13.8706	−0.458548
$916$	−75.9150	−2.50830
$917$	5.63717	0.186156
$918$	4.41239	0.145631
$919$	42.3555	1.39718	0.698590	−	0.715523i	$-0.253811\pi$
$919$	42.3555	1.39718	0.698590	+	0.715523i	$0.253811\pi$
$920$	−25.9782	−0.856477
$921$	21.4649	0.707292
$922$	−11.0675	−0.364489
$923$	5.77774	0.190177
$924$	−41.4931	−1.36502
$925$	−7.68250	−0.252599
$926$	35.7154	1.17368
$927$	1.00000	0.0328443
$928$	−9.19832	−0.301950
$929$	21.3645	0.700947	0.350473	−	0.936573i	$-0.386021\pi$
$929$	21.3645	0.700947	0.350473	+	0.936573i	$0.386021\pi$
$930$	−19.9908	−0.655526
$931$	−56.7947	−1.86137
$932$	−24.9684	−0.817866
$933$	13.4673	0.440900
$934$	−18.8813	−0.617815
$935$	−13.4482	−0.439804
$936$	−2.17553	−0.0711095
$937$	−31.0432	−1.01414	−0.507069	−	0.861906i	$-0.669271\pi$
$937$	−31.0432	−1.01414	−0.507069	+	0.861906i	$0.669271\pi$
$938$	129.830	4.23911
$939$	17.9955	0.587262
$940$	−31.8782	−1.03975
$941$	−13.1047	−0.427203	−0.213601	−	0.976921i	$-0.568519\pi$
$941$	−13.1047	−0.427203	−0.213601	+	0.976921i	$0.568519\pi$
$942$	−34.7461	−1.13209
$943$	−24.1959	−0.787927
$944$	−8.31596	−0.270661
$945$	−8.28712	−0.269580
$946$	−12.0193	−0.390781
$947$	−15.8297	−0.514396	−0.257198	−	0.966359i	$-0.582799\pi$
$947$	−15.8297	−0.514396	−0.257198	+	0.966359i	$0.582799\pi$
$948$	−25.4936	−0.827992
$949$	5.76602	0.187173
$950$	−12.1638	−0.394646
$951$	9.18968	0.297996
$952$	−17.7439	−0.575083
$953$	−25.2535	−0.818042	−0.409021	−	0.912525i	$-0.634130\pi$
$953$	−25.2535	−0.818042	−0.409021	+	0.912525i	$0.634130\pi$
$954$	11.3514	0.367514
$955$	16.2653	0.526334
$956$	−2.68480	−0.0868325
$957$	−4.57509	−0.147892
$958$	−48.2380	−1.55850
$959$	74.8029	2.41551
$960$	−26.0736	−0.841520
$961$	−11.1174	−0.358625
$962$	−17.8475	−0.575427
$963$	−1.52130	−0.0490232
$964$	−13.5503	−0.436424
$965$	53.3897	1.71867
$966$	54.6377	1.75794
$967$	5.17577	0.166441	0.0832207	−	0.996531i	$-0.473479\pi$
$967$	5.17577	0.166441	0.0832207	+	0.996531i	$0.473479\pi$
$968$	−0.957970	−0.0307903
$969$	11.2353	0.360930
$970$	−10.1632	−0.326322
$971$	48.4606	1.55517	0.777587	−	0.628775i	$-0.216443\pi$
$971$	48.4606	1.55517	0.777587	+	0.628775i	$0.216443\pi$
$972$	2.97534	0.0954339
$973$	−57.8846	−1.85570
$974$	−82.3466	−2.63855
$975$	−0.960144	−0.0307492
$976$	7.57763	0.242554
$977$	−24.7714	−0.792507	−0.396253	−	0.918141i	$-0.629690\pi$
$977$	−24.7714	−0.792507	−0.396253	+	0.918141i	$0.629690\pi$
$978$	37.5509	1.20075
$979$	52.8625	1.68949
$980$	59.8006	1.91026
$981$	18.1272	0.578758
$982$	45.4676	1.45093
$983$	−62.6423	−1.99798	−0.998989	−	0.0449566i	$-0.985685\pi$
$983$	−62.6423	−1.99798	−0.998989	+	0.0449566i	$0.985685\pi$
$984$	8.86026	0.282455
$985$	−35.2816	−1.12416
$986$	−5.96835	−0.190071
$987$	21.9784	0.699580
$988$	−16.8989	−0.537625
$989$	9.46476	0.300962
$990$	−15.1640	−0.481943
$991$	−49.8832	−1.58459	−0.792295	−	0.610138i	$-0.791114\pi$
$991$	−49.8832	−1.58459	−0.792295	+	0.610138i	$0.791114\pi$
$992$	30.3225	0.962742
$993$	−27.7532	−0.880722
$994$	53.1361	1.68537
$995$	2.56478	0.0813090
$996$	−3.06302	−0.0970554
$997$	−5.47668	−0.173448	−0.0867241	−	0.996232i	$-0.527640\pi$
$997$	−5.47668	−0.173448	−0.0867241	+	0.996232i	$0.527640\pi$
$998$	−72.2369	−2.28662
$999$	8.00141	0.253153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.4	✓	32	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)

\(f(q)\)	\(=\)	\(q-2.23055 q^{2} +1.00000 q^{3} +2.97534 q^{4} +2.00994 q^{5} -2.23055 q^{6} -4.12307 q^{7} -2.17553 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23055 q^{2} +1.00000 q^{3} +2.97534 q^{4} +2.00994 q^{5} -2.23055 q^{6} -4.12307 q^{7} -2.17553 q^{8} +1.00000 q^{9} -4.48326 q^{10} +3.38236 q^{11} +2.97534 q^{12} +1.00000 q^{13} +9.19669 q^{14} +2.00994 q^{15} -1.09805 q^{16} -1.97817 q^{17} -2.23055 q^{18} -5.67965 q^{19} +5.98025 q^{20} -4.12307 q^{21} -7.54450 q^{22} +5.94102 q^{23} -2.17553 q^{24} -0.960144 q^{25} -2.23055 q^{26} +1.00000 q^{27} -12.2675 q^{28} -1.35263 q^{29} -4.48326 q^{30} +4.45900 q^{31} +6.80031 q^{32} +3.38236 q^{33} +4.41239 q^{34} -8.28712 q^{35} +2.97534 q^{36} +8.00141 q^{37} +12.6687 q^{38} +1.00000 q^{39} -4.37269 q^{40} -4.07269 q^{41} +9.19669 q^{42} +1.59312 q^{43} +10.0636 q^{44} +2.00994 q^{45} -13.2517 q^{46} -5.33059 q^{47} -1.09805 q^{48} +9.99968 q^{49} +2.14164 q^{50} -1.97817 q^{51} +2.97534 q^{52} -5.08905 q^{53} -2.23055 q^{54} +6.79833 q^{55} +8.96986 q^{56} -5.67965 q^{57} +3.01711 q^{58} +7.57340 q^{59} +5.98025 q^{60} -6.90100 q^{61} -9.94599 q^{62} -4.12307 q^{63} -12.9723 q^{64} +2.00994 q^{65} -7.54450 q^{66} +14.1171 q^{67} -5.88571 q^{68} +5.94102 q^{69} +18.4848 q^{70} +5.77774 q^{71} -2.17553 q^{72} +5.76602 q^{73} -17.8475 q^{74} -0.960144 q^{75} -16.8989 q^{76} -13.9457 q^{77} -2.23055 q^{78} -8.56830 q^{79} -2.20701 q^{80} +1.00000 q^{81} +9.08432 q^{82} -1.02947 q^{83} -12.2675 q^{84} -3.97600 q^{85} -3.55353 q^{86} -1.35263 q^{87} -7.35843 q^{88} +15.6289 q^{89} -4.48326 q^{90} -4.12307 q^{91} +17.6765 q^{92} +4.45900 q^{93} +11.8901 q^{94} -11.4158 q^{95} +6.80031 q^{96} +2.26693 q^{97} -22.3048 q^{98} +3.38236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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