LMFDB - Embedded newform 717.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,2,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("717.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	717.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:	$5.72527382493$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1767625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1 $ x^6 - 7x^4 - x^3 + 11x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.267500$ of defining polynomial
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.12029 q^{2} -1.00000 q^{3} +2.49562 q^{4} -2.47082 q^{5} -2.12029 q^{6} -2.45271 q^{7} +1.05086 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.12029 q^{2} -1.00000 q^{3} +2.49562 q^{4} -2.47082 q^{5} -2.12029 q^{6} -2.45271 q^{7} +1.05086 q^{8} +1.00000 q^{9} -5.23885 q^{10} -4.01073 q^{11} -2.49562 q^{12} +1.62598 q^{13} -5.20045 q^{14} +2.47082 q^{15} -2.76312 q^{16} +4.89570 q^{17} +2.12029 q^{18} -6.28561 q^{19} -6.16623 q^{20} +2.45271 q^{21} -8.50391 q^{22} -3.83124 q^{23} -1.05086 q^{24} +1.10496 q^{25} +3.44755 q^{26} -1.00000 q^{27} -6.12103 q^{28} -0.357168 q^{29} +5.23885 q^{30} -8.44143 q^{31} -7.96032 q^{32} +4.01073 q^{33} +10.3803 q^{34} +6.06021 q^{35} +2.49562 q^{36} -1.81610 q^{37} -13.3273 q^{38} -1.62598 q^{39} -2.59648 q^{40} +10.7403 q^{41} +5.20045 q^{42} +9.09255 q^{43} -10.0093 q^{44} -2.47082 q^{45} -8.12332 q^{46} +11.0197 q^{47} +2.76312 q^{48} -0.984213 q^{49} +2.34284 q^{50} -4.89570 q^{51} +4.05783 q^{52} +5.78427 q^{53} -2.12029 q^{54} +9.90981 q^{55} -2.57745 q^{56} +6.28561 q^{57} -0.757299 q^{58} -1.43742 q^{59} +6.16623 q^{60} +2.21862 q^{61} -17.8983 q^{62} -2.45271 q^{63} -11.3519 q^{64} -4.01751 q^{65} +8.50391 q^{66} -14.2454 q^{67} +12.2178 q^{68} +3.83124 q^{69} +12.8494 q^{70} -4.12013 q^{71} +1.05086 q^{72} +2.78648 q^{73} -3.85066 q^{74} -1.10496 q^{75} -15.6865 q^{76} +9.83717 q^{77} -3.44755 q^{78} +7.84263 q^{79} +6.82718 q^{80} +1.00000 q^{81} +22.7725 q^{82} -9.91715 q^{83} +6.12103 q^{84} -12.0964 q^{85} +19.2788 q^{86} +0.357168 q^{87} -4.21471 q^{88} +0.978993 q^{89} -5.23885 q^{90} -3.98806 q^{91} -9.56131 q^{92} +8.44143 q^{93} +23.3649 q^{94} +15.5306 q^{95} +7.96032 q^{96} -16.8523 q^{97} -2.08682 q^{98} -4.01073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * 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 $

$2$	2.12029	1.49927	0.749635	−	0.661852i	$-0.230229\pi$
$2$	2.12029	1.49927	0.749635	+	0.661852i	$0.230229\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.49562	1.24781
$5$	−2.47082	−1.10499	−0.552493	−	0.833518i	$-0.686323\pi$
$5$	−2.47082	−1.10499	−0.552493	+	0.833518i	$0.686323\pi$
$6$	−2.12029	−0.865604
$7$	−2.45271	−0.927037	−0.463519	−	0.886087i	$-0.653413\pi$
$7$	−2.45271	−0.927037	−0.463519	+	0.886087i	$0.653413\pi$
$8$	1.05086	0.371534
$9$	1.00000	0.333333
$10$	−5.23885	−1.65667
$11$	−4.01073	−1.20928	−0.604641	−	0.796498i	$-0.706683\pi$
$11$	−4.01073	−1.20928	−0.604641	+	0.796498i	$0.706683\pi$
$12$	−2.49562	−0.720424
$13$	1.62598	0.450966	0.225483	−	0.974247i	$-0.427604\pi$
$13$	1.62598	0.450966	0.225483	+	0.974247i	$0.427604\pi$
$14$	−5.20045	−1.38988
$15$	2.47082	0.637964
$16$	−2.76312	−0.690780
$17$	4.89570	1.18738	0.593691	−	0.804693i	$-0.297670\pi$
$17$	4.89570	1.18738	0.593691	+	0.804693i	$0.297670\pi$
$18$	2.12029	0.499757
$19$	−6.28561	−1.44202	−0.721009	−	0.692926i	$-0.756321\pi$
$19$	−6.28561	−1.44202	−0.721009	+	0.692926i	$0.756321\pi$
$20$	−6.16623	−1.37881
$21$	2.45271	0.535225
$22$	−8.50391	−1.81304
$23$	−3.83124	−0.798868	−0.399434	−	0.916762i	$-0.630793\pi$
$23$	−3.83124	−0.798868	−0.399434	+	0.916762i	$0.630793\pi$
$24$	−1.05086	−0.214505
$25$	1.10496	0.220992
$26$	3.44755	0.676120
$27$	−1.00000	−0.192450
$28$	−6.12103	−1.15677
$29$	−0.357168	−0.0663244	−0.0331622	−	0.999450i	$-0.510558\pi$
$29$	−0.357168	−0.0663244	−0.0331622	+	0.999450i	$0.510558\pi$
$30$	5.23885	0.956479
$31$	−8.44143	−1.51613	−0.758063	−	0.652181i	$-0.773854\pi$
$31$	−8.44143	−1.51613	−0.758063	+	0.652181i	$0.773854\pi$
$32$	−7.96032	−1.40720
$33$	4.01073	0.698179
$34$	10.3803	1.78020
$35$	6.06021	1.02436
$36$	2.49562	0.415937
$37$	−1.81610	−0.298566	−0.149283	−	0.988795i	$-0.547696\pi$
$37$	−1.81610	−0.298566	−0.149283	+	0.988795i	$0.547696\pi$
$38$	−13.3273	−2.16197
$39$	−1.62598	−0.260365
$40$	−2.59648	−0.410540
$41$	10.7403	1.67735	0.838676	−	0.544630i	$-0.183330\pi$
$41$	10.7403	1.67735	0.838676	+	0.544630i	$0.183330\pi$
$42$	5.20045	0.802447
$43$	9.09255	1.38660	0.693301	−	0.720649i	$-0.256156\pi$
$43$	9.09255	1.38660	0.693301	+	0.720649i	$0.256156\pi$
$44$	−10.0093	−1.50895
$45$	−2.47082	−0.368328
$46$	−8.12332	−1.19772
$47$	11.0197	1.60739	0.803693	−	0.595044i	$-0.202866\pi$
$47$	11.0197	1.60739	0.803693	+	0.595044i	$0.202866\pi$
$48$	2.76312	0.398822
$49$	−0.984213	−0.140602
$50$	2.34284	0.331327
$51$	−4.89570	−0.685535
$52$	4.05783	0.562720
$53$	5.78427	0.794530	0.397265	−	0.917704i	$-0.369959\pi$
$53$	5.78427	0.794530	0.397265	+	0.917704i	$0.369959\pi$
$54$	−2.12029	−0.288535
$55$	9.90981	1.33624
$56$	−2.57745	−0.344426
$57$	6.28561	0.832550
$58$	−0.757299	−0.0994382
$59$	−1.43742	−0.187136	−0.0935678	−	0.995613i	$-0.529827\pi$
$59$	−1.43742	−0.187136	−0.0935678	+	0.995613i	$0.529827\pi$
$60$	6.16623	0.796057
$61$	2.21862	0.284065	0.142032	−	0.989862i	$-0.454636\pi$
$61$	2.21862	0.284065	0.142032	+	0.989862i	$0.454636\pi$
$62$	−17.8983	−2.27308
$63$	−2.45271	−0.309012
$64$	−11.3519	−1.41899
$65$	−4.01751	−0.498311
$66$	8.50391	1.04676
$67$	−14.2454	−1.74036	−0.870178	−	0.492738i	$-0.835996\pi$
$67$	−14.2454	−1.74036	−0.870178	+	0.492738i	$0.835996\pi$
$68$	12.2178	1.48163
$69$	3.83124	0.461227
$70$	12.8494	1.53580
$71$	−4.12013	−0.488969	−0.244485	−	0.969653i	$-0.578619\pi$
$71$	−4.12013	−0.488969	−0.244485	+	0.969653i	$0.578619\pi$
$72$	1.05086	0.123845
$73$	2.78648	0.326133	0.163067	−	0.986615i	$-0.447861\pi$
$73$	2.78648	0.326133	0.163067	+	0.986615i	$0.447861\pi$
$74$	−3.85066	−0.447630
$75$	−1.10496	−0.127590
$76$	−15.6865	−1.79936
$77$	9.83717	1.12105
$78$	−3.44755	−0.390358
$79$	7.84263	0.882365	0.441182	−	0.897417i	$-0.354559\pi$
$79$	7.84263	0.882365	0.441182	+	0.897417i	$0.354559\pi$
$80$	6.82718	0.763302
$81$	1.00000	0.111111
$82$	22.7725	2.51480
$83$	−9.91715	−1.08855	−0.544274	−	0.838907i	$-0.683195\pi$
$83$	−9.91715	−1.08855	−0.544274	+	0.838907i	$0.683195\pi$
$84$	6.12103	0.667859
$85$	−12.0964	−1.31204
$86$	19.2788	2.07889
$87$	0.357168	0.0382924
$88$	−4.21471	−0.449290
$89$	0.978993	0.103773	0.0518865	−	0.998653i	$-0.483477\pi$
$89$	0.978993	0.103773	0.0518865	+	0.998653i	$0.483477\pi$
$90$	−5.23885	−0.552224
$91$	−3.98806	−0.418062
$92$	−9.56131	−0.996836
$93$	8.44143	0.875336
$94$	23.3649	2.40991
$95$	15.5306	1.59341
$96$	7.96032	0.812447
$97$	−16.8523	−1.71109	−0.855545	−	0.517728i	$-0.826778\pi$
$97$	−16.8523	−1.71109	−0.855545	+	0.517728i	$0.826778\pi$
$98$	−2.08682	−0.210800
$99$	−4.01073	−0.403094
$100$	2.75756	0.275756
$101$	3.80431	0.378543	0.189271	−	0.981925i	$-0.439387\pi$
$101$	3.80431	0.378543	0.189271	+	0.981925i	$0.439387\pi$
$102$	−10.3803	−1.02780
$103$	8.01017	0.789266	0.394633	−	0.918839i	$-0.370872\pi$
$103$	8.01017	0.789266	0.394633	+	0.918839i	$0.370872\pi$
$104$	1.70867	0.167549
$105$	−6.06021	−0.591416
$106$	12.2643	1.19122
$107$	−12.6857	−1.22638	−0.613188	−	0.789937i	$-0.710113\pi$
$107$	−12.6857	−1.22638	−0.613188	+	0.789937i	$0.710113\pi$
$108$	−2.49562	−0.240141
$109$	−18.7766	−1.79847	−0.899237	−	0.437461i	$-0.855878\pi$
$109$	−18.7766	−1.79847	−0.899237	+	0.437461i	$0.855878\pi$
$110$	21.0116	2.00338
$111$	1.81610	0.172377
$112$	6.77713	0.640379
$113$	−7.61332	−0.716201	−0.358101	−	0.933683i	$-0.616575\pi$
$113$	−7.61332	−0.716201	−0.358101	+	0.933683i	$0.616575\pi$
$114$	13.3273	1.24822
$115$	9.46630	0.882737
$116$	−0.891355	−0.0827603
$117$	1.62598	0.150322
$118$	−3.04774	−0.280567
$119$	−12.0077	−1.10075
$120$	2.59648	0.237025
$121$	5.08598	0.462362
$122$	4.70410	0.425890
$123$	−10.7403	−0.968420
$124$	−21.0666	−1.89184
$125$	9.62395	0.860792
$126$	−5.20045	−0.463293
$127$	14.0067	1.24290	0.621448	−	0.783455i	$-0.286545\pi$
$127$	14.0067	1.24290	0.621448	+	0.783455i	$0.286545\pi$
$128$	−8.14873	−0.720253
$129$	−9.09255	−0.800555
$130$	−8.51828	−0.747102
$131$	−4.05565	−0.354344	−0.177172	−	0.984180i	$-0.556695\pi$
$131$	−4.05565	−0.354344	−0.177172	+	0.984180i	$0.556695\pi$
$132$	10.0093	0.871195
$133$	15.4168	1.33680
$134$	−30.2044	−2.60926
$135$	2.47082	0.212655
$136$	5.14468	0.441153
$137$	−15.5346	−1.32721	−0.663604	−	0.748084i	$-0.730974\pi$
$137$	−15.5346	−1.32721	−0.663604	+	0.748084i	$0.730974\pi$
$138$	8.12332	0.691503
$139$	1.09201	0.0926232	0.0463116	−	0.998927i	$-0.485253\pi$
$139$	1.09201	0.0926232	0.0463116	+	0.998927i	$0.485253\pi$
$140$	15.1240	1.27821
$141$	−11.0197	−0.928025
$142$	−8.73586	−0.733097
$143$	−6.52138	−0.545345
$144$	−2.76312	−0.230260
$145$	0.882498	0.0732875
$146$	5.90815	0.488962
$147$	0.984213	0.0811765
$148$	−4.53230	−0.372553
$149$	−15.9702	−1.30833	−0.654167	−	0.756350i	$-0.726981\pi$
$149$	−15.9702	−1.30833	−0.654167	+	0.756350i	$0.726981\pi$
$150$	−2.34284	−0.191292
$151$	−8.44617	−0.687339	−0.343670	−	0.939091i	$-0.611670\pi$
$151$	−8.44617	−0.687339	−0.343670	+	0.939091i	$0.611670\pi$
$152$	−6.60528	−0.535759
$153$	4.89570	0.395794
$154$	20.8576	1.68076
$155$	20.8573	1.67530
$156$	−4.05783	−0.324887
$157$	8.21810	0.655876	0.327938	−	0.944699i	$-0.393646\pi$
$157$	8.21810	0.655876	0.327938	+	0.944699i	$0.393646\pi$
$158$	16.6286	1.32290
$159$	−5.78427	−0.458722
$160$	19.6685	1.55494
$161$	9.39691	0.740580
$162$	2.12029	0.166586
$163$	3.58850	0.281073	0.140537	−	0.990075i	$-0.455117\pi$
$163$	3.58850	0.281073	0.140537	+	0.990075i	$0.455117\pi$
$164$	26.8037	2.09302
$165$	−9.90981	−0.771478
$166$	−21.0272	−1.63203
$167$	14.0773	1.08934	0.544668	−	0.838652i	$-0.316656\pi$
$167$	14.0773	1.08934	0.544668	+	0.838652i	$0.316656\pi$
$168$	2.57745	0.198855
$169$	−10.3562	−0.796630
$170$	−25.6478	−1.96710
$171$	−6.28561	−0.480673
$172$	22.6916	1.73021
$173$	5.90842	0.449208	0.224604	−	0.974450i	$-0.427891\pi$
$173$	5.90842	0.449208	0.224604	+	0.974450i	$0.427891\pi$
$174$	0.757299	0.0574107
$175$	−2.71015	−0.204868
$176$	11.0821	0.835348
$177$	1.43742	0.108043
$178$	2.07575	0.155584
$179$	18.5491	1.38642	0.693211	−	0.720735i	$-0.256195\pi$
$179$	18.5491	1.38642	0.693211	+	0.720735i	$0.256195\pi$
$180$	−6.16623	−0.459604
$181$	−0.921544	−0.0684978	−0.0342489	−	0.999413i	$-0.510904\pi$
$181$	−0.921544	−0.0684978	−0.0342489	+	0.999413i	$0.510904\pi$
$182$	−8.45584	−0.626788
$183$	−2.21862	−0.164005
$184$	−4.02608	−0.296807
$185$	4.48727	0.329911
$186$	17.8983	1.31236
$187$	−19.6353	−1.43588
$188$	27.5009	2.00571
$189$	2.45271	0.178408
$190$	32.9294	2.38895
$191$	15.1285	1.09466	0.547329	−	0.836918i	$-0.315645\pi$
$191$	15.1285	1.09466	0.547329	+	0.836918i	$0.315645\pi$
$192$	11.3519	0.819256
$193$	−22.7285	−1.63603	−0.818015	−	0.575197i	$-0.804925\pi$
$193$	−22.7285	−1.63603	−0.818015	+	0.575197i	$0.804925\pi$
$194$	−35.7317	−2.56539
$195$	4.01751	0.287700
$196$	−2.45622	−0.175444
$197$	−2.47078	−0.176036	−0.0880179	−	0.996119i	$-0.528053\pi$
$197$	−2.47078	−0.176036	−0.0880179	+	0.996119i	$0.528053\pi$
$198$	−8.50391	−0.604346
$199$	−5.34461	−0.378869	−0.189435	−	0.981893i	$-0.560666\pi$
$199$	−5.34461	−0.378869	−0.189435	+	0.981893i	$0.560666\pi$
$200$	1.16116	0.0821062
$201$	14.2454	1.00479
$202$	8.06622	0.567538
$203$	0.876029	0.0614852
$204$	−12.2178	−0.855417
$205$	−26.5374	−1.85345
$206$	16.9839	1.18332
$207$	−3.83124	−0.266289
$208$	−4.49278	−0.311518
$209$	25.2099	1.74381
$210$	−12.8494	−0.886692
$211$	−10.3377	−0.711676	−0.355838	−	0.934548i	$-0.615804\pi$
$211$	−10.3377	−0.711676	−0.355838	+	0.934548i	$0.615804\pi$
$212$	14.4353	0.991423
$213$	4.12013	0.282307
$214$	−26.8974	−1.83867
$215$	−22.4661	−1.53217
$216$	−1.05086	−0.0715018
$217$	20.7044	1.40551
$218$	−39.8119	−2.69640
$219$	−2.78648	−0.188293
$220$	24.7311	1.66737
$221$	7.96031	0.535469
$222$	3.85066	0.258440
$223$	−10.2702	−0.687745	−0.343873	−	0.939016i	$-0.611739\pi$
$223$	−10.2702	−0.687745	−0.343873	+	0.939016i	$0.611739\pi$
$224$	19.5244	1.30453
$225$	1.10496	0.0736641
$226$	−16.1424	−1.07378
$227$	−16.9467	−1.12479	−0.562396	−	0.826868i	$-0.690120\pi$
$227$	−16.9467	−1.12479	−0.562396	+	0.826868i	$0.690120\pi$
$228$	15.6865	1.03886
$229$	−29.0495	−1.91964	−0.959822	−	0.280609i	$-0.909464\pi$
$229$	−29.0495	−1.91964	−0.959822	+	0.280609i	$0.909464\pi$
$230$	20.0713	1.32346
$231$	−9.83717	−0.647238
$232$	−0.375332	−0.0246418
$233$	−19.7368	−1.29300	−0.646500	−	0.762914i	$-0.723768\pi$
$233$	−19.7368	−1.29300	−0.646500	+	0.762914i	$0.723768\pi$
$234$	3.44755	0.225373
$235$	−27.2277	−1.77614
$236$	−3.58725	−0.233510
$237$	−7.84263	−0.509434
$238$	−25.4598	−1.65032
$239$	−1.00000	−0.0646846
$239$	−1.00000	−0.0646846
$240$	−6.82718	−0.440692
$241$	10.4837	0.675311	0.337656	−	0.941270i	$-0.390366\pi$
$241$	10.4837	0.675311	0.337656	+	0.941270i	$0.390366\pi$
$242$	10.7837	0.693205
$243$	−1.00000	−0.0641500
$244$	5.53682	0.354459
$245$	2.43182	0.155363
$246$	−22.7725	−1.45192
$247$	−10.2203	−0.650301
$248$	−8.87074	−0.563293
$249$	9.91715	0.628474
$250$	20.4055	1.29056
$251$	12.1227	0.765177	0.382588	−	0.923919i	$-0.375033\pi$
$251$	12.1227	0.765177	0.382588	+	0.923919i	$0.375033\pi$
$252$	−6.12103	−0.385589
$253$	15.3661	0.966056
$254$	29.6983	1.86344
$255$	12.0964	0.757506
$256$	5.42623	0.339139
$257$	28.3873	1.77075	0.885377	−	0.464874i	$-0.153900\pi$
$257$	28.3873	1.77075	0.885377	+	0.464874i	$0.153900\pi$
$258$	−19.2788	−1.20025
$259$	4.45438	0.276781
$260$	−10.0262	−0.621797
$261$	−0.357168	−0.0221081
$262$	−8.59914	−0.531257
$263$	−14.0844	−0.868482	−0.434241	−	0.900797i	$-0.642983\pi$
$263$	−14.0844	−0.868482	−0.434241	+	0.900797i	$0.642983\pi$
$264$	4.21471	0.259397
$265$	−14.2919	−0.877944
$266$	32.6880	2.00423
$267$	−0.978993	−0.0599134
$268$	−35.5512	−2.17163
$269$	22.1224	1.34883	0.674415	−	0.738353i	$-0.264396\pi$
$269$	22.1224	1.34883	0.674415	+	0.738353i	$0.264396\pi$
$270$	5.23885	0.318826
$271$	−0.185181	−0.0112490	−0.00562449	−	0.999984i	$-0.501790\pi$
$271$	−0.185181	−0.0112490	−0.00562449	+	0.999984i	$0.501790\pi$
$272$	−13.5274	−0.820219
$273$	3.98806	0.241368
$274$	−32.9377	−1.98984
$275$	−4.43171	−0.267242
$276$	9.56131	0.575523
$277$	−15.8869	−0.954549	−0.477274	−	0.878754i	$-0.658375\pi$
$277$	−15.8869	−0.954549	−0.477274	+	0.878754i	$0.658375\pi$
$278$	2.31538	0.138867
$279$	−8.44143	−0.505375
$280$	6.36842	0.380586
$281$	19.9963	1.19288	0.596440	−	0.802658i	$-0.296581\pi$
$281$	19.9963	1.19288	0.596440	+	0.802658i	$0.296581\pi$
$282$	−23.3649	−1.39136
$283$	−30.1737	−1.79364	−0.896819	−	0.442398i	$-0.854128\pi$
$283$	−30.1737	−1.79364	−0.896819	+	0.442398i	$0.854128\pi$
$284$	−10.2823	−0.610141
$285$	−15.5306	−0.919955
$286$	−13.8272	−0.817619
$287$	−26.3428	−1.55497
$288$	−7.96032	−0.469067
$289$	6.96786	0.409874
$290$	1.87115	0.109878
$291$	16.8523	0.987898
$292$	6.95401	0.406953
$293$	−0.459157	−0.0268242	−0.0134121	−	0.999910i	$-0.504269\pi$
$293$	−0.459157	−0.0268242	−0.0134121	+	0.999910i	$0.504269\pi$
$294$	2.08682	0.121706
$295$	3.55160	0.206782
$296$	−1.90847	−0.110927
$297$	4.01073	0.232726
$298$	−33.8615	−1.96155
$299$	−6.22952	−0.360262
$300$	−2.75756	−0.159208
$301$	−22.3014	−1.28543
$302$	−17.9083	−1.03051
$303$	−3.80431	−0.218552
$304$	17.3679	0.996117
$305$	−5.48181	−0.313887
$306$	10.3803	0.593402
$307$	−11.2133	−0.639978	−0.319989	−	0.947421i	$-0.603679\pi$
$307$	−11.2133	−0.639978	−0.319989	+	0.947421i	$0.603679\pi$
$308$	24.5498	1.39886
$309$	−8.01017	−0.455683
$310$	44.2234	2.51172
$311$	12.1228	0.687423	0.343712	−	0.939075i	$-0.388316\pi$
$311$	12.1228	0.687423	0.343712	+	0.939075i	$0.388316\pi$
$312$	−1.70867	−0.0967347
$313$	12.8050	0.723782	0.361891	−	0.932220i	$-0.382131\pi$
$313$	12.8050	0.723782	0.361891	+	0.932220i	$0.382131\pi$
$314$	17.4247	0.983335
$315$	6.06021	0.341454
$316$	19.5722	1.10102
$317$	−2.96789	−0.166693	−0.0833467	−	0.996521i	$-0.526561\pi$
$317$	−2.96789	−0.166693	−0.0833467	+	0.996521i	$0.526561\pi$
$318$	−12.2643	−0.687748
$319$	1.43250	0.0802049
$320$	28.0486	1.56797
$321$	12.6857	0.708049
$322$	19.9242	1.11033
$323$	−30.7725	−1.71223
$324$	2.49562	0.138646
$325$	1.79665	0.0996600
$326$	7.60865	0.421404
$327$	18.7766	1.03835
$328$	11.2865	0.623194
$329$	−27.0281	−1.49011
$330$	−21.0116	−1.15665
$331$	35.0721	1.92773	0.963867	−	0.266383i	$-0.0858286\pi$
$331$	35.0721	1.92773	0.963867	+	0.266383i	$0.0858286\pi$
$332$	−24.7494	−1.35830
$333$	−1.81610	−0.0995219
$334$	29.8480	1.63321
$335$	35.1979	1.92307
$336$	−6.77713	−0.369723
$337$	12.4068	0.675840	0.337920	−	0.941175i	$-0.390277\pi$
$337$	12.4068	0.675840	0.337920	+	0.941175i	$0.390277\pi$
$338$	−21.9581	−1.19436
$339$	7.61332	0.413499
$340$	−30.1880	−1.63718
$341$	33.8563	1.83342
$342$	−13.3273	−0.720658
$343$	19.5830	1.05738
$344$	9.55498	0.515170
$345$	−9.46630	−0.509649
$346$	12.5275	0.673485
$347$	−25.6920	−1.37922	−0.689610	−	0.724181i	$-0.742218\pi$
$347$	−25.6920	−1.37922	−0.689610	+	0.724181i	$0.742218\pi$
$348$	0.891355	0.0477817
$349$	−16.4397	−0.879996	−0.439998	−	0.897999i	$-0.645021\pi$
$349$	−16.4397	−0.879996	−0.439998	+	0.897999i	$0.645021\pi$
$350$	−5.74630	−0.307153
$351$	−1.62598	−0.0867885
$352$	31.9267	1.70170
$353$	9.96346	0.530302	0.265151	−	0.964207i	$-0.414578\pi$
$353$	9.96346	0.530302	0.265151	+	0.964207i	$0.414578\pi$
$354$	3.04774	0.161985
$355$	10.1801	0.540304
$356$	2.44319	0.129489
$357$	12.0077	0.635516
$358$	39.3293	2.07862
$359$	5.08801	0.268535	0.134267	−	0.990945i	$-0.457132\pi$
$359$	5.08801	0.268535	0.134267	+	0.990945i	$0.457132\pi$
$360$	−2.59648	−0.136847
$361$	20.5089	1.07942
$362$	−1.95394	−0.102697
$363$	−5.08598	−0.266945
$364$	−9.95269	−0.521662
$365$	−6.88491	−0.360373
$366$	−4.70410	−0.245887
$367$	15.5615	0.812302	0.406151	−	0.913806i	$-0.366871\pi$
$367$	15.5615	0.812302	0.406151	+	0.913806i	$0.366871\pi$
$368$	10.5862	0.551842
$369$	10.7403	0.559117
$370$	9.51430	0.494625
$371$	−14.1871	−0.736559
$372$	21.0666	1.09225
$373$	−17.8554	−0.924519	−0.462259	−	0.886745i	$-0.652961\pi$
$373$	−17.8554	−0.924519	−0.462259	+	0.886745i	$0.652961\pi$
$374$	−41.6326	−2.15277
$375$	−9.62395	−0.496978
$376$	11.5801	0.597199
$377$	−0.580748	−0.0299101
$378$	5.20045	0.267482
$379$	25.1729	1.29304	0.646522	−	0.762896i	$-0.276223\pi$
$379$	25.1729	1.29304	0.646522	+	0.762896i	$0.276223\pi$
$380$	38.7586	1.98827
$381$	−14.0067	−0.717587
$382$	32.0767	1.64119
$383$	−21.4662	−1.09687	−0.548435	−	0.836194i	$-0.684776\pi$
$383$	−21.4662	−1.09687	−0.548435	+	0.836194i	$0.684776\pi$
$384$	8.14873	0.415838
$385$	−24.3059	−1.23874
$386$	−48.1909	−2.45285
$387$	9.09255	0.462200
$388$	−42.0569	−2.13512
$389$	14.1828	0.719096	0.359548	−	0.933127i	$-0.382931\pi$
$389$	14.1828	0.719096	0.359548	+	0.933127i	$0.382931\pi$
$390$	8.51828	0.431340
$391$	−18.7566	−0.948561
$392$	−1.03427	−0.0522384
$393$	4.05565	0.204580
$394$	−5.23877	−0.263925
$395$	−19.3777	−0.975000
$396$	−10.0093	−0.502985
$397$	−8.60119	−0.431681	−0.215841	−	0.976429i	$-0.569249\pi$
$397$	−8.60119	−0.431681	−0.215841	+	0.976429i	$0.569249\pi$
$398$	−11.3321	−0.568027
$399$	−15.4168	−0.771805
$400$	−3.05314	−0.152657
$401$	−13.5162	−0.674969	−0.337485	−	0.941331i	$-0.609576\pi$
$401$	−13.5162	−0.674969	−0.337485	+	0.941331i	$0.609576\pi$
$402$	30.2044	1.50646
$403$	−13.7256	−0.683721
$404$	9.49410	0.472349
$405$	−2.47082	−0.122776
$406$	1.85743	0.0921829
$407$	7.28391	0.361050
$408$	−5.14468	−0.254700
$409$	26.6663	1.31856	0.659281	−	0.751896i	$-0.270861\pi$
$409$	26.6663	1.31856	0.659281	+	0.751896i	$0.270861\pi$
$410$	−56.2668	−2.77882
$411$	15.5346	0.766263
$412$	19.9904	0.984854
$413$	3.52557	0.173482
$414$	−8.12332	−0.399240
$415$	24.5035	1.20283
$416$	−12.9433	−0.634599
$417$	−1.09201	−0.0534760
$418$	53.4523	2.61444
$419$	7.37267	0.360179	0.180089	−	0.983650i	$-0.442361\pi$
$419$	7.37267	0.360179	0.180089	+	0.983650i	$0.442361\pi$
$420$	−15.1240	−0.737975
$421$	36.1603	1.76235	0.881174	−	0.472793i	$-0.156754\pi$
$421$	36.1603	1.76235	0.881174	+	0.472793i	$0.156754\pi$
$422$	−21.9189	−1.06699
$423$	11.0197	0.535795
$424$	6.07844	0.295195
$425$	5.40956	0.262402
$426$	8.73586	0.423254
$427$	−5.44162	−0.263339
$428$	−31.6588	−1.53028
$429$	6.52138	0.314855
$430$	−47.6345	−2.29714
$431$	−13.4750	−0.649066	−0.324533	−	0.945874i	$-0.605207\pi$
$431$	−13.4750	−0.649066	−0.324533	+	0.945874i	$0.605207\pi$
$432$	2.76312	0.132941
$433$	−8.22943	−0.395481	−0.197741	−	0.980254i	$-0.563360\pi$
$433$	−8.22943	−0.395481	−0.197741	+	0.980254i	$0.563360\pi$
$434$	43.8992	2.10723
$435$	−0.882498	−0.0423125
$436$	−46.8593	−2.24416
$437$	24.0817	1.15198
$438$	−5.90815	−0.282302
$439$	−1.65529	−0.0790028	−0.0395014	−	0.999220i	$-0.512577\pi$
$439$	−1.65529	−0.0790028	−0.0395014	+	0.999220i	$0.512577\pi$
$440$	10.4138	0.496458
$441$	−0.984213	−0.0468673
$442$	16.8782	0.802812
$443$	−15.9770	−0.759092	−0.379546	−	0.925173i	$-0.623920\pi$
$443$	−15.9770	−0.759092	−0.379546	+	0.925173i	$0.623920\pi$
$444$	4.53230	0.215094
$445$	−2.41892	−0.114668
$446$	−21.7758	−1.03112
$447$	15.9702	0.755367
$448$	27.8430	1.31546
$449$	13.7005	0.646566	0.323283	−	0.946302i	$-0.395213\pi$
$449$	13.7005	0.646566	0.323283	+	0.946302i	$0.395213\pi$
$450$	2.34284	0.110442
$451$	−43.0765	−2.02839
$452$	−19.0000	−0.893683
$453$	8.44617	0.396836
$454$	−35.9319	−1.68637
$455$	9.85379	0.461953
$456$	6.60528	0.309321
$457$	34.4962	1.61367	0.806833	−	0.590779i	$-0.201180\pi$
$457$	34.4962	1.61367	0.806833	+	0.590779i	$0.201180\pi$
$458$	−61.5933	−2.87806
$459$	−4.89570	−0.228512
$460$	23.6243	1.10149
$461$	−30.3840	−1.41513	−0.707563	−	0.706651i	$-0.750205\pi$
$461$	−30.3840	−1.41513	−0.707563	+	0.706651i	$0.750205\pi$
$462$	−20.8576	−0.970384
$463$	−19.9606	−0.927648	−0.463824	−	0.885927i	$-0.653523\pi$
$463$	−19.9606	−0.927648	−0.463824	+	0.885927i	$0.653523\pi$
$464$	0.986897	0.0458156
$465$	−20.8573	−0.967233
$466$	−41.8477	−1.93856
$467$	8.39058	0.388270	0.194135	−	0.980975i	$-0.437810\pi$
$467$	8.39058	0.388270	0.194135	+	0.980975i	$0.437810\pi$
$468$	4.05783	0.187573
$469$	34.9399	1.61337
$470$	−57.7305	−2.66291
$471$	−8.21810	−0.378670
$472$	−1.51052	−0.0695273
$473$	−36.4678	−1.67679
$474$	−16.6286	−0.763778
$475$	−6.94536	−0.318675
$476$	−29.9667	−1.37352
$477$	5.78427	0.264843
$478$	−2.12029	−0.0969797
$479$	21.2295	0.969999	0.485000	−	0.874514i	$-0.338820\pi$
$479$	21.2295	0.969999	0.485000	+	0.874514i	$0.338820\pi$
$480$	−19.6685	−0.897742
$481$	−2.95295	−0.134643
$482$	22.2284	1.01247
$483$	−9.39691	−0.427574
$484$	12.6927	0.576940
$485$	41.6390	1.89073
$486$	−2.12029	−0.0961782
$487$	5.32666	0.241374	0.120687	−	0.992691i	$-0.461490\pi$
$487$	5.32666	0.241374	0.120687	+	0.992691i	$0.461490\pi$
$488$	2.33145	0.105540
$489$	−3.58850	−0.162278
$490$	5.15615	0.232931
$491$	24.0997	1.08760	0.543802	−	0.839213i	$-0.316984\pi$
$491$	24.0997	1.08760	0.543802	+	0.839213i	$0.316984\pi$
$492$	−26.8037	−1.20840
$493$	−1.74859	−0.0787523
$494$	−21.6700	−0.974977
$495$	9.90981	0.445413
$496$	23.3247	1.04731
$497$	10.1055	0.453293
$498$	21.0272	0.942252
$499$	−34.1034	−1.52668	−0.763339	−	0.645998i	$-0.776441\pi$
$499$	−34.1034	−1.52668	−0.763339	+	0.645998i	$0.776441\pi$
$500$	24.0177	1.07410
$501$	−14.0773	−0.628928
$502$	25.7036	1.14721
$503$	−10.6016	−0.472704	−0.236352	−	0.971667i	$-0.575952\pi$
$503$	−10.6016	−0.472704	−0.236352	+	0.971667i	$0.575952\pi$
$504$	−2.57745	−0.114809
$505$	−9.39976	−0.418284
$506$	32.5805	1.44838
$507$	10.3562	0.459934
$508$	34.9555	1.55090
$509$	20.2990	0.899736	0.449868	−	0.893095i	$-0.351471\pi$
$509$	20.2990	0.899736	0.449868	+	0.893095i	$0.351471\pi$
$510$	25.6478	1.13571
$511$	−6.83444	−0.302338
$512$	27.8026	1.22871
$513$	6.28561	0.277517
$514$	60.1893	2.65484
$515$	−19.7917	−0.872127
$516$	−22.6916	−0.998940
$517$	−44.1970	−1.94378
$518$	9.44456	0.414970
$519$	−5.90842	−0.259351
$520$	−4.22183	−0.185140
$521$	−1.16040	−0.0508378	−0.0254189	−	0.999677i	$-0.508092\pi$
$521$	−1.16040	−0.0508378	−0.0254189	+	0.999677i	$0.508092\pi$
$522$	−0.757299	−0.0331461
$523$	−19.3796	−0.847412	−0.423706	−	0.905800i	$-0.639271\pi$
$523$	−19.3796	−0.847412	−0.423706	+	0.905800i	$0.639271\pi$
$524$	−10.1214	−0.442154
$525$	2.71015	0.118281
$526$	−29.8630	−1.30209
$527$	−41.3267	−1.80022
$528$	−11.0821	−0.482288
$529$	−8.32163	−0.361810
$530$	−30.3029	−1.31628
$531$	−1.43742	−0.0623786
$532$	38.4744	1.66808
$533$	17.4635	0.756429
$534$	−2.07575	−0.0898264
$535$	31.3442	1.35513
$536$	−14.9699	−0.646602
$537$	−18.5491	−0.800451
$538$	46.9059	2.02226
$539$	3.94742	0.170027
$540$	6.16623	0.265352
$541$	−4.77487	−0.205288	−0.102644	−	0.994718i	$-0.532730\pi$
$541$	−4.77487	−0.205288	−0.102644	+	0.994718i	$0.532730\pi$
$542$	−0.392638	−0.0168652
$543$	0.921544	0.0395472
$544$	−38.9713	−1.67088
$545$	46.3937	1.98729
$546$	8.45584	0.361876
$547$	−12.9501	−0.553704	−0.276852	−	0.960913i	$-0.589291\pi$
$547$	−12.9501	−0.553704	−0.276852	+	0.960913i	$0.589291\pi$
$548$	−38.7684	−1.65610
$549$	2.21862	0.0946882
$550$	−9.39649	−0.400668
$551$	2.24502	0.0956410
$552$	4.02608	0.171362
$553$	−19.2357	−0.817985
$554$	−33.6847	−1.43113
$555$	−4.48727	−0.190474
$556$	2.72525	0.115576
$557$	15.2371	0.645618	0.322809	−	0.946464i	$-0.395373\pi$
$557$	15.2371	0.645618	0.322809	+	0.946464i	$0.395373\pi$
$558$	−17.8983	−0.757694
$559$	14.7843	0.625310
$560$	−16.7451	−0.707609
$561$	19.6353	0.829005
$562$	42.3979	1.78845
$563$	−44.4294	−1.87247	−0.936237	−	0.351368i	$-0.885716\pi$
$563$	−44.4294	−1.87247	−0.936237	+	0.351368i	$0.885716\pi$
$564$	−27.5009	−1.15800
$565$	18.8112	0.791392
$566$	−63.9768	−2.68915
$567$	−2.45271	−0.103004
$568$	−4.32967	−0.181669
$569$	−32.3049	−1.35429	−0.677146	−	0.735848i	$-0.736784\pi$
$569$	−32.3049	−1.35429	−0.677146	+	0.735848i	$0.736784\pi$
$570$	−32.9294	−1.37926
$571$	−17.6597	−0.739036	−0.369518	−	0.929224i	$-0.620477\pi$
$571$	−17.6597	−0.739036	−0.369518	+	0.929224i	$0.620477\pi$
$572$	−16.2749	−0.680487
$573$	−15.1285	−0.632001
$574$	−55.8544	−2.33132
$575$	−4.23337	−0.176544
$576$	−11.3519	−0.472997
$577$	−5.92655	−0.246726	−0.123363	−	0.992362i	$-0.539368\pi$
$577$	−5.92655	−0.246726	−0.123363	+	0.992362i	$0.539368\pi$
$578$	14.7739	0.614512
$579$	22.7285	0.944562
$580$	2.20238	0.0914489
$581$	24.3239	1.00913
$582$	35.7317	1.48113
$583$	−23.1992	−0.960811
$584$	2.92820	0.121170
$585$	−4.01751	−0.166104
$586$	−0.973544	−0.0402167
$587$	25.8268	1.06599	0.532993	−	0.846120i	$-0.321067\pi$
$587$	25.8268	1.06599	0.532993	+	0.846120i	$0.321067\pi$
$588$	2.45622	0.101293
$589$	53.0596	2.18628
$590$	7.53041	0.310022
$591$	2.47078	0.101634
$592$	5.01811	0.206243
$593$	−9.21060	−0.378234	−0.189117	−	0.981955i	$-0.560563\pi$
$593$	−9.21060	−0.378234	−0.189117	+	0.981955i	$0.560563\pi$
$594$	8.50391	0.348920
$595$	29.6690	1.21631
$596$	−39.8557	−1.63255
$597$	5.34461	0.218740
$598$	−13.2084	−0.540131
$599$	−43.4301	−1.77450	−0.887252	−	0.461285i	$-0.847389\pi$
$599$	−43.4301	−1.77450	−0.887252	+	0.461285i	$0.847389\pi$
$600$	−1.16116	−0.0474041
$601$	−10.2416	−0.417765	−0.208883	−	0.977941i	$-0.566983\pi$
$601$	−10.2416	−0.417765	−0.208883	+	0.977941i	$0.566983\pi$
$602$	−47.2854	−1.92721
$603$	−14.2454	−0.580118
$604$	−21.0784	−0.857669
$605$	−12.5666	−0.510903
$606$	−8.06622	−0.327668
$607$	45.2285	1.83577	0.917884	−	0.396849i	$-0.129896\pi$
$607$	45.2285	1.83577	0.917884	+	0.396849i	$0.129896\pi$
$608$	50.0355	2.02921
$609$	−0.876029	−0.0354985
$610$	−11.6230	−0.470602
$611$	17.9178	0.724876
$612$	12.2178	0.493875
$613$	20.4029	0.824064	0.412032	−	0.911169i	$-0.364819\pi$
$613$	20.4029	0.824064	0.412032	+	0.911169i	$0.364819\pi$
$614$	−23.7755	−0.959500
$615$	26.5374	1.07009
$616$	10.3375	0.416508
$617$	4.40978	0.177531	0.0887655	−	0.996053i	$-0.471708\pi$
$617$	4.40978	0.177531	0.0887655	+	0.996053i	$0.471708\pi$
$618$	−16.9839	−0.683192
$619$	20.8034	0.836160	0.418080	−	0.908410i	$-0.362703\pi$
$619$	20.8034	0.836160	0.418080	+	0.908410i	$0.362703\pi$
$620$	52.0518	2.09045
$621$	3.83124	0.153742
$622$	25.7039	1.03063
$623$	−2.40119	−0.0962015
$624$	4.49278	0.179855
$625$	−29.3039	−1.17215
$626$	27.1503	1.08514
$627$	−25.2099	−1.00679
$628$	20.5093	0.818409
$629$	−8.89109	−0.354511
$630$	12.8494	0.511932
$631$	33.5580	1.33592	0.667962	−	0.744196i	$-0.267167\pi$
$631$	33.5580	1.33592	0.667962	+	0.744196i	$0.267167\pi$
$632$	8.24149	0.327829
$633$	10.3377	0.410886
$634$	−6.29278	−0.249918
$635$	−34.6081	−1.37338
$636$	−14.4353	−0.572398
$637$	−1.60031	−0.0634067
$638$	3.03732	0.120249
$639$	−4.12013	−0.162990
$640$	20.1341	0.795869
$641$	24.5383	0.969206	0.484603	−	0.874734i	$-0.338964\pi$
$641$	24.5383	0.969206	0.484603	+	0.874734i	$0.338964\pi$
$642$	26.8974	1.06156
$643$	9.18123	0.362073	0.181036	−	0.983476i	$-0.442055\pi$
$643$	9.18123	0.362073	0.181036	+	0.983476i	$0.442055\pi$
$644$	23.4511	0.924104
$645$	22.4661	0.884601
$646$	−65.2465	−2.56709
$647$	33.3174	1.30984	0.654922	−	0.755697i	$-0.272702\pi$
$647$	33.3174	1.30984	0.654922	+	0.755697i	$0.272702\pi$
$648$	1.05086	0.0412816
$649$	5.76509	0.226300
$650$	3.80941	0.149417
$651$	−20.7044	−0.811469
$652$	8.95553	0.350726
$653$	−8.78496	−0.343782	−0.171891	−	0.985116i	$-0.554988\pi$
$653$	−8.78496	−0.343782	−0.171891	+	0.985116i	$0.554988\pi$
$654$	39.8119	1.55677
$655$	10.0208	0.391545
$656$	−29.6767	−1.15868
$657$	2.78648	0.108711
$658$	−57.3073	−2.23407
$659$	−27.9953	−1.09054	−0.545270	−	0.838260i	$-0.683573\pi$
$659$	−27.9953	−1.09054	−0.545270	+	0.838260i	$0.683573\pi$
$660$	−24.7311	−0.962657
$661$	−31.7412	−1.23459	−0.617294	−	0.786732i	$-0.711771\pi$
$661$	−31.7412	−1.23459	−0.617294	+	0.786732i	$0.711771\pi$
$662$	74.3628	2.89019
$663$	−7.96031	−0.309153
$664$	−10.4215	−0.404433
$665$	−38.0921	−1.47715
$666$	−3.85066	−0.149210
$667$	1.36839	0.0529844
$668$	35.1316	1.35928
$669$	10.2702	0.397070
$670$	74.6297	2.88320
$671$	−8.89828	−0.343514
$672$	−19.5244	−0.753169
$673$	−0.521763	−0.0201125	−0.0100562	−	0.999949i	$-0.503201\pi$
$673$	−0.521763	−0.0201125	−0.0100562	+	0.999949i	$0.503201\pi$
$674$	26.3059	1.01327
$675$	−1.10496	−0.0425300
$676$	−25.8451	−0.994042
$677$	−2.22663	−0.0855765	−0.0427882	−	0.999084i	$-0.513624\pi$
$677$	−2.22663	−0.0855765	−0.0427882	+	0.999084i	$0.513624\pi$
$678$	16.1424	0.619946
$679$	41.3338	1.58624
$680$	−12.7116	−0.487467
$681$	16.9467	0.649398
$682$	71.7852	2.74880
$683$	−18.9101	−0.723577	−0.361788	−	0.932260i	$-0.617834\pi$
$683$	−18.9101	−0.723577	−0.361788	+	0.932260i	$0.617834\pi$
$684$	−15.6865	−0.599788
$685$	38.3831	1.46654
$686$	41.5215	1.58530
$687$	29.0495	1.10831
$688$	−25.1238	−0.957836
$689$	9.40511	0.358306
$690$	−20.0713	−0.764101
$691$	−18.7431	−0.713022	−0.356511	−	0.934291i	$-0.616034\pi$
$691$	−18.7431	−0.713022	−0.356511	+	0.934291i	$0.616034\pi$
$692$	14.7452	0.560527
$693$	9.83717	0.373683
$694$	−54.4745	−2.06782
$695$	−2.69817	−0.102347
$696$	0.375332	0.0142269
$697$	52.5812	1.99166
$698$	−34.8568	−1.31935
$699$	19.7368	0.746514
$700$	−6.76351	−0.255637
$701$	16.1798	0.611102	0.305551	−	0.952176i	$-0.401159\pi$
$701$	16.1798	0.611102	0.305551	+	0.952176i	$0.401159\pi$
$702$	−3.44755	−0.130119
$703$	11.4153	0.430537
$704$	45.5296	1.71596
$705$	27.2277	1.02545
$706$	21.1254	0.795065
$707$	−9.33086	−0.350923
$708$	3.58725	0.134817
$709$	−8.57907	−0.322194	−0.161097	−	0.986939i	$-0.551503\pi$
$709$	−8.57907	−0.322194	−0.161097	+	0.986939i	$0.551503\pi$
$710$	21.5848	0.810062
$711$	7.84263	0.294122
$712$	1.02878	0.0385552
$713$	32.3411	1.21118
$714$	25.4598	0.952811
$715$	16.1132	0.602598
$716$	46.2914	1.72999
$717$	1.00000	0.0373457
$718$	10.7880	0.402606
$719$	−32.5343	−1.21333	−0.606663	−	0.794959i	$-0.707492\pi$
$719$	−32.5343	−1.21333	−0.606663	+	0.794959i	$0.707492\pi$
$720$	6.82718	0.254434
$721$	−19.6466	−0.731679
$722$	43.4848	1.61834
$723$	−10.4837	−0.389891
$724$	−2.29982	−0.0854723
$725$	−0.394657	−0.0146572
$726$	−10.7837	−0.400222
$727$	−4.65810	−0.172759	−0.0863797	−	0.996262i	$-0.527530\pi$
$727$	−4.65810	−0.172759	−0.0863797	+	0.996262i	$0.527530\pi$
$728$	−4.19088	−0.155325
$729$	1.00000	0.0370370
$730$	−14.5980	−0.540296
$731$	44.5144	1.64642
$732$	−5.53682	−0.204647
$733$	8.64374	0.319264	0.159632	−	0.987177i	$-0.448969\pi$
$733$	8.64374	0.319264	0.159632	+	0.987177i	$0.448969\pi$
$734$	32.9948	1.21786
$735$	−2.43182	−0.0896989
$736$	30.4979	1.12417
$737$	57.1346	2.10458
$738$	22.7725	0.838268
$739$	42.9217	1.57890	0.789450	−	0.613815i	$-0.210366\pi$
$739$	42.9217	1.57890	0.789450	+	0.613815i	$0.210366\pi$
$740$	11.1985	0.411666
$741$	10.2203	0.375452
$742$	−30.0808	−1.10430
$743$	39.0878	1.43399	0.716997	−	0.697076i	$-0.245516\pi$
$743$	39.0878	1.43399	0.716997	+	0.697076i	$0.245516\pi$
$744$	8.87074	0.325217
$745$	39.4596	1.44569
$746$	−37.8586	−1.38610
$747$	−9.91715	−0.362850
$748$	−49.0024	−1.79170
$749$	31.1144	1.13690
$750$	−20.4055	−0.745105
$751$	33.4998	1.22243	0.611213	−	0.791466i	$-0.290682\pi$
$751$	33.4998	1.22243	0.611213	+	0.791466i	$0.290682\pi$
$752$	−30.4487	−1.11035
$753$	−12.1227	−0.441775
$754$	−1.23135	−0.0448432
$755$	20.8690	0.759500
$756$	6.12103	0.222620
$757$	42.7926	1.55533	0.777663	−	0.628682i	$-0.216405\pi$
$757$	42.7926	1.55533	0.777663	+	0.628682i	$0.216405\pi$
$758$	53.3737	1.93862
$759$	−15.3661	−0.557753
$760$	16.3205	0.592006
$761$	3.50389	0.127016	0.0635079	−	0.997981i	$-0.479771\pi$
$761$	3.50389	0.127016	0.0635079	+	0.997981i	$0.479771\pi$
$762$	−29.6983	−1.07586
$763$	46.0536	1.66725
$764$	37.7549	1.36592
$765$	−12.0964	−0.437346
$766$	−45.5144	−1.64450
$767$	−2.33721	−0.0843919
$768$	−5.42623	−0.195802
$769$	−33.9827	−1.22545	−0.612724	−	0.790297i	$-0.709926\pi$
$769$	−33.9827	−1.22545	−0.612724	+	0.790297i	$0.709926\pi$
$770$	−51.5355	−1.85721
$771$	−28.3873	−1.02235
$772$	−56.7216	−2.04146
$773$	16.2523	0.584553	0.292277	−	0.956334i	$-0.405587\pi$
$773$	16.2523	0.584553	0.292277	+	0.956334i	$0.405587\pi$
$774$	19.2788	0.692963
$775$	−9.32746	−0.335052
$776$	−17.7094	−0.635729
$777$	−4.45438	−0.159800
$778$	30.0716	1.07812
$779$	−67.5093	−2.41877
$780$	10.0262	0.358995
$781$	16.5247	0.591302
$782$	−39.7693	−1.42215
$783$	0.357168	0.0127641
$784$	2.71950	0.0971250
$785$	−20.3055	−0.724733
$786$	8.59914	0.306721
$787$	−10.9298	−0.389606	−0.194803	−	0.980842i	$-0.562407\pi$
$787$	−10.9298	−0.389606	−0.194803	+	0.980842i	$0.562407\pi$
$788$	−6.16613	−0.219659
$789$	14.0844	0.501418
$790$	−41.0864	−1.46179
$791$	18.6733	0.663945
$792$	−4.21471	−0.149763
$793$	3.60743	0.128104
$794$	−18.2370	−0.647207
$795$	14.2919	0.506881
$796$	−13.3381	−0.472757
$797$	−17.4122	−0.616772	−0.308386	−	0.951261i	$-0.599789\pi$
$797$	−17.4122	−0.616772	−0.308386	+	0.951261i	$0.599789\pi$
$798$	−32.6880	−1.15714
$799$	53.9490	1.90858
$800$	−8.79585	−0.310980
$801$	0.978993	0.0345910
$802$	−28.6583	−1.01196
$803$	−11.1758	−0.394387
$804$	35.5512	1.25379
$805$	−23.2181	−0.818330
$806$	−29.1022	−1.02508
$807$	−22.1224	−0.778747
$808$	3.99778	0.140642
$809$	−21.8841	−0.769403	−0.384702	−	0.923041i	$-0.625696\pi$
$809$	−21.8841	−0.769403	−0.384702	+	0.923041i	$0.625696\pi$
$810$	−5.23885	−0.184075
$811$	41.8415	1.46925	0.734627	−	0.678471i	$-0.237357\pi$
$811$	41.8415	1.46925	0.734627	+	0.678471i	$0.237357\pi$
$812$	2.18624	0.0767218
$813$	0.185181	0.00649460
$814$	15.4440	0.541311
$815$	−8.86655	−0.310582
$816$	13.5274	0.473554
$817$	−57.1522	−1.99950
$818$	56.5402	1.97688
$819$	−3.98806	−0.139354
$820$	−66.2272	−2.31275
$821$	36.7094	1.28117	0.640584	−	0.767888i	$-0.278692\pi$
$821$	36.7094	1.28117	0.640584	+	0.767888i	$0.278692\pi$
$822$	32.9377	1.14884
$823$	−31.0617	−1.08274	−0.541371	−	0.840784i	$-0.682095\pi$
$823$	−31.0617	−1.08274	−0.541371	+	0.840784i	$0.682095\pi$
$824$	8.41755	0.293239
$825$	4.43171	0.154292
$826$	7.47521	0.260096
$827$	55.1422	1.91748	0.958741	−	0.284281i	$-0.0917550\pi$
$827$	55.1422	1.91748	0.958741	+	0.284281i	$0.0917550\pi$
$828$	−9.56131	−0.332279
$829$	11.6426	0.404366	0.202183	−	0.979348i	$-0.435196\pi$
$829$	11.6426	0.404366	0.202183	+	0.979348i	$0.435196\pi$
$830$	51.9545	1.80337
$831$	15.8869	0.551109
$832$	−18.4580	−0.639917
$833$	−4.81841	−0.166948
$834$	−2.31538	−0.0801750
$835$	−34.7825	−1.20370
$836$	62.9144	2.17594
$837$	8.44143	0.291779
$838$	15.6322	0.540005
$839$	9.99713	0.345139	0.172570	−	0.984997i	$-0.444793\pi$
$839$	9.99713	0.345139	0.172570	+	0.984997i	$0.444793\pi$
$840$	−6.36842	−0.219731
$841$	−28.8724	−0.995601
$842$	76.6703	2.64223
$843$	−19.9963	−0.688709
$844$	−25.7989	−0.888036
$845$	25.5883	0.880264
$846$	23.3649	0.803302
$847$	−12.4744	−0.428627
$848$	−15.9826	−0.548846
$849$	30.1737	1.03556
$850$	11.4698	0.393412
$851$	6.95792	0.238514
$852$	10.2823	0.352265
$853$	41.0682	1.40615	0.703073	−	0.711117i	$-0.251811\pi$
$853$	41.0682	1.40615	0.703073	+	0.711117i	$0.251811\pi$
$854$	−11.5378	−0.394816
$855$	15.5306	0.531136
$856$	−13.3309	−0.455641
$857$	−22.0503	−0.753224	−0.376612	−	0.926371i	$-0.622911\pi$
$857$	−22.0503	−0.753224	−0.376612	+	0.926371i	$0.622911\pi$
$858$	13.8272	0.472053
$859$	5.68153	0.193851	0.0969256	−	0.995292i	$-0.469099\pi$
$859$	5.68153	0.193851	0.0969256	+	0.995292i	$0.469099\pi$
$860$	−56.0668	−1.91186
$861$	26.3428	0.897761
$862$	−28.5708	−0.973125
$863$	27.0640	0.921269	0.460635	−	0.887590i	$-0.347622\pi$
$863$	27.0640	0.921269	0.460635	+	0.887590i	$0.347622\pi$
$864$	7.96032	0.270816
$865$	−14.5986	−0.496369
$866$	−17.4488	−0.592933
$867$	−6.96786	−0.236641
$868$	51.6703	1.75380
$869$	−31.4547	−1.06703
$870$	−1.87115	−0.0634379
$871$	−23.1628	−0.784841
$872$	−19.7316	−0.668195
$873$	−16.8523	−0.570363
$874$	51.0601	1.72713
$875$	−23.6048	−0.797986
$876$	−6.95401	−0.234954
$877$	−31.5393	−1.06501	−0.532503	−	0.846428i	$-0.678749\pi$
$877$	−31.5393	−1.06501	−0.532503	+	0.846428i	$0.678749\pi$
$878$	−3.50970	−0.118447
$879$	0.459157	0.0154870
$880$	−27.3820	−0.923047
$881$	−9.23845	−0.311251	−0.155626	−	0.987816i	$-0.549739\pi$
$881$	−9.23845	−0.311251	−0.155626	+	0.987816i	$0.549739\pi$
$882$	−2.08682	−0.0702667
$883$	−22.5049	−0.757350	−0.378675	−	0.925530i	$-0.623620\pi$
$883$	−22.5049	−0.757350	−0.378675	+	0.925530i	$0.623620\pi$
$884$	19.8659	0.668163
$885$	−3.55160	−0.119386
$886$	−33.8759	−1.13808
$887$	−30.2960	−1.01724	−0.508621	−	0.860991i	$-0.669844\pi$
$887$	−30.2960	−1.01724	−0.508621	+	0.860991i	$0.669844\pi$
$888$	1.90847	0.0640439
$889$	−34.3545	−1.15221
$890$	−5.12880	−0.171918
$891$	−4.01073	−0.134365
$892$	−25.6306	−0.858176
$893$	−69.2654	−2.31788
$894$	33.8615	1.13250
$895$	−45.8314	−1.53198
$896$	19.9865	0.667701
$897$	6.22952	0.207998
$898$	29.0490	0.969377
$899$	3.01501	0.100556
$900$	2.75756	0.0919188
$901$	28.3180	0.943410
$902$	−91.3345	−3.04111
$903$	22.3014	0.742144
$904$	−8.00052	−0.266093
$905$	2.27697	0.0756891
$906$	17.9083	0.594964
$907$	−34.6786	−1.15148	−0.575742	−	0.817632i	$-0.695287\pi$
$907$	−34.6786	−1.15148	−0.575742	+	0.817632i	$0.695287\pi$
$908$	−42.2925	−1.40353
$909$	3.80431	0.126181
$910$	20.8929	0.692592
$911$	−29.6688	−0.982970	−0.491485	−	0.870886i	$-0.663546\pi$
$911$	−29.6688	−0.982970	−0.491485	+	0.870886i	$0.663546\pi$
$912$	−17.3679	−0.575109
$913$	39.7750	1.31636
$914$	73.1420	2.41932
$915$	5.48181	0.181223
$916$	−72.4965	−2.39535
$917$	9.94733	0.328490
$918$	−10.3803	−0.342601
$919$	3.41218	0.112558	0.0562788	−	0.998415i	$-0.482076\pi$
$919$	3.41218	0.112558	0.0562788	+	0.998415i	$0.482076\pi$
$920$	9.94774	0.327967
$921$	11.2133	0.369492
$922$	−64.4229	−2.12165
$923$	−6.69925	−0.220509
$924$	−24.5498	−0.807630
$925$	−2.00672	−0.0659807
$926$	−42.3222	−1.39079
$927$	8.01017	0.263089
$928$	2.84317	0.0933317
$929$	−5.27469	−0.173057	−0.0865285	−	0.996249i	$-0.527577\pi$
$929$	−5.27469	−0.173057	−0.0865285	+	0.996249i	$0.527577\pi$
$930$	−44.2234	−1.45014
$931$	6.18638	0.202750
$932$	−49.2555	−1.61342
$933$	−12.1228	−0.396884
$934$	17.7905	0.582121
$935$	48.5154	1.58662
$936$	1.70867	0.0558498
$937$	−11.6027	−0.379043	−0.189521	−	0.981877i	$-0.560694\pi$
$937$	−11.6027	−0.379043	−0.189521	+	0.981877i	$0.560694\pi$
$938$	74.0826	2.41888
$939$	−12.8050	−0.417876
$940$	−67.9499	−2.21628
$941$	−28.2271	−0.920178	−0.460089	−	0.887873i	$-0.652182\pi$
$941$	−28.2271	−0.920178	−0.460089	+	0.887873i	$0.652182\pi$
$942$	−17.4247	−0.567729
$943$	−41.1486	−1.33998
$944$	3.97175	0.129270
$945$	−6.06021	−0.197139
$946$	−77.3222	−2.51396
$947$	−41.9537	−1.36331	−0.681657	−	0.731672i	$-0.738740\pi$
$947$	−41.9537	−1.36331	−0.681657	+	0.731672i	$0.738740\pi$
$948$	−19.5722	−0.635676
$949$	4.53077	0.147075
$950$	−14.7262	−0.477780
$951$	2.96789	0.0962404
$952$	−12.6184	−0.408965
$953$	−51.3228	−1.66251	−0.831255	−	0.555892i	$-0.812377\pi$
$953$	−51.3228	−1.66251	−0.831255	+	0.555892i	$0.812377\pi$
$954$	12.2643	0.397072
$955$	−37.3798	−1.20958
$956$	−2.49562	−0.0807141
$957$	−1.43250	−0.0463063
$958$	45.0126	1.45429
$959$	38.1018	1.23037
$960$	−28.0486	−0.905265
$961$	40.2578	1.29864
$962$	−6.26111	−0.201866
$963$	−12.6857	−0.408792
$964$	26.1632	0.842660
$965$	56.1580	1.80779
$966$	−19.9242	−0.641049
$967$	−15.0557	−0.484158	−0.242079	−	0.970257i	$-0.577829\pi$
$967$	−15.0557	−0.484158	−0.242079	+	0.970257i	$0.577829\pi$
$968$	5.34464	0.171783
$969$	30.7725	0.988554
$970$	88.2867	2.83471
$971$	18.2675	0.586232	0.293116	−	0.956077i	$-0.405308\pi$
$971$	18.2675	0.586232	0.293116	+	0.956077i	$0.405308\pi$
$972$	−2.49562	−0.0800471
$973$	−2.67839	−0.0858651
$974$	11.2940	0.361885
$975$	−1.79665	−0.0575388
$976$	−6.13030	−0.196226
$977$	11.8112	0.377873	0.188936	−	0.981989i	$-0.439496\pi$
$977$	11.8112	0.377873	0.188936	+	0.981989i	$0.439496\pi$
$978$	−7.60865	−0.243298
$979$	−3.92648	−0.125491
$980$	6.06889	0.193864
$981$	−18.7766	−0.599492
$982$	51.0983	1.63061
$983$	−30.4350	−0.970725	−0.485363	−	0.874313i	$-0.661312\pi$
$983$	−30.4350	−0.970725	−0.485363	+	0.874313i	$0.661312\pi$
$984$	−11.2865	−0.359801
$985$	6.10486	0.194517
$986$	−3.70750	−0.118071
$987$	27.0281	0.860313
$988$	−25.5060	−0.811453
$989$	−34.8357	−1.10771
$990$	21.0116	0.667794
$991$	54.3952	1.72792	0.863960	−	0.503561i	$-0.167977\pi$
$991$	54.3952	1.72792	0.863960	+	0.503561i	$0.167977\pi$
$992$	67.1965	2.13349
$993$	−35.0721	−1.11298
$994$	21.4265	0.679608
$995$	13.2056	0.418645
$996$	24.7494	0.784216
$997$	14.6453	0.463821	0.231910	−	0.972737i	$-0.425502\pi$
$997$	14.6453	0.463821	0.231910	+	0.972737i	$0.425502\pi$
$998$	−72.3090	−2.28890
$999$	1.81610	0.0574590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.d.1.6	✓	6
3.2	odd	2		2151.2.a.e.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.d.1.6	✓	6	1.1	even	1	trivial
2151.2.a.e.1.1		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q+2.12029 q^{2} -1.00000 q^{3} +2.49562 q^{4} -2.47082 q^{5} -2.12029 q^{6} -2.45271 q^{7} +1.05086 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.12029 q^{2} -1.00000 q^{3} +2.49562 q^{4} -2.47082 q^{5} -2.12029 q^{6} -2.45271 q^{7} +1.05086 q^{8} +1.00000 q^{9} -5.23885 q^{10} -4.01073 q^{11} -2.49562 q^{12} +1.62598 q^{13} -5.20045 q^{14} +2.47082 q^{15} -2.76312 q^{16} +4.89570 q^{17} +2.12029 q^{18} -6.28561 q^{19} -6.16623 q^{20} +2.45271 q^{21} -8.50391 q^{22} -3.83124 q^{23} -1.05086 q^{24} +1.10496 q^{25} +3.44755 q^{26} -1.00000 q^{27} -6.12103 q^{28} -0.357168 q^{29} +5.23885 q^{30} -8.44143 q^{31} -7.96032 q^{32} +4.01073 q^{33} +10.3803 q^{34} +6.06021 q^{35} +2.49562 q^{36} -1.81610 q^{37} -13.3273 q^{38} -1.62598 q^{39} -2.59648 q^{40} +10.7403 q^{41} +5.20045 q^{42} +9.09255 q^{43} -10.0093 q^{44} -2.47082 q^{45} -8.12332 q^{46} +11.0197 q^{47} +2.76312 q^{48} -0.984213 q^{49} +2.34284 q^{50} -4.89570 q^{51} +4.05783 q^{52} +5.78427 q^{53} -2.12029 q^{54} +9.90981 q^{55} -2.57745 q^{56} +6.28561 q^{57} -0.757299 q^{58} -1.43742 q^{59} +6.16623 q^{60} +2.21862 q^{61} -17.8983 q^{62} -2.45271 q^{63} -11.3519 q^{64} -4.01751 q^{65} +8.50391 q^{66} -14.2454 q^{67} +12.2178 q^{68} +3.83124 q^{69} +12.8494 q^{70} -4.12013 q^{71} +1.05086 q^{72} +2.78648 q^{73} -3.85066 q^{74} -1.10496 q^{75} -15.6865 q^{76} +9.83717 q^{77} -3.44755 q^{78} +7.84263 q^{79} +6.82718 q^{80} +1.00000 q^{81} +22.7725 q^{82} -9.91715 q^{83} +6.12103 q^{84} -12.0964 q^{85} +19.2788 q^{86} +0.357168 q^{87} -4.21471 q^{88} +0.978993 q^{89} -5.23885 q^{90} -3.98806 q^{91} -9.56131 q^{92} +8.44143 q^{93} +23.3649 q^{94} +15.5306 q^{95} +7.96032 q^{96} -16.8523 q^{97} -2.08682 q^{98} -4.01073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * q^99

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