LMFDB - Embedded newform 717.2.a.d.1.2

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			1.2
Root			$-0.360520$ 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)

$f(q)$	$=$	$q-2.15574 q^{2} -1.00000 q^{3} +2.64721 q^{4} +3.41325 q^{5} +2.15574 q^{6} +0.201367 q^{7} -1.39522 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15574 q^{2} -1.00000 q^{3} +2.64721 q^{4} +3.41325 q^{5} +2.15574 q^{6} +0.201367 q^{7} -1.39522 q^{8} +1.00000 q^{9} -7.35809 q^{10} -5.35035 q^{11} -2.64721 q^{12} -5.86183 q^{13} -0.434095 q^{14} -3.41325 q^{15} -2.28669 q^{16} +4.05336 q^{17} -2.15574 q^{18} -2.42759 q^{19} +9.03561 q^{20} -0.201367 q^{21} +11.5340 q^{22} -4.58506 q^{23} +1.39522 q^{24} +6.65030 q^{25} +12.6366 q^{26} -1.00000 q^{27} +0.533062 q^{28} +3.44243 q^{29} +7.35809 q^{30} -7.68267 q^{31} +7.71995 q^{32} +5.35035 q^{33} -8.73799 q^{34} +0.687317 q^{35} +2.64721 q^{36} -0.781965 q^{37} +5.23326 q^{38} +5.86183 q^{39} -4.76224 q^{40} +5.87100 q^{41} +0.434095 q^{42} -8.05607 q^{43} -14.1635 q^{44} +3.41325 q^{45} +9.88419 q^{46} -3.12717 q^{47} +2.28669 q^{48} -6.95945 q^{49} -14.3363 q^{50} -4.05336 q^{51} -15.5175 q^{52} -11.6536 q^{53} +2.15574 q^{54} -18.2621 q^{55} -0.280952 q^{56} +2.42759 q^{57} -7.42099 q^{58} +9.93358 q^{59} -9.03561 q^{60} +5.67948 q^{61} +16.5618 q^{62} +0.201367 q^{63} -12.0688 q^{64} -20.0079 q^{65} -11.5340 q^{66} -6.84647 q^{67} +10.7301 q^{68} +4.58506 q^{69} -1.48168 q^{70} +12.8677 q^{71} -1.39522 q^{72} -7.37793 q^{73} +1.68571 q^{74} -6.65030 q^{75} -6.42636 q^{76} -1.07739 q^{77} -12.6366 q^{78} +14.6391 q^{79} -7.80506 q^{80} +1.00000 q^{81} -12.6564 q^{82} -15.8846 q^{83} -0.533062 q^{84} +13.8351 q^{85} +17.3668 q^{86} -3.44243 q^{87} +7.46492 q^{88} -5.12607 q^{89} -7.35809 q^{90} -1.18038 q^{91} -12.1376 q^{92} +7.68267 q^{93} +6.74135 q^{94} -8.28599 q^{95} -7.71995 q^{96} -11.8563 q^{97} +15.0028 q^{98} -5.35035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.15574	−1.52434	−0.762169	−	0.647378i	$-0.775865\pi$
$2$	−2.15574	−1.52434	−0.762169	+	0.647378i	$0.775865\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.64721	1.32361
$5$	3.41325	1.52645	0.763227	−	0.646131i	$-0.223614\pi$
$5$	3.41325	1.52645	0.763227	+	0.646131i	$0.223614\pi$
$6$	2.15574	0.880077
$7$	0.201367	0.0761096	0.0380548	−	0.999276i	$-0.487884\pi$
$7$	0.201367	0.0761096	0.0380548	+	0.999276i	$0.487884\pi$
$8$	−1.39522	−0.493285
$9$	1.00000	0.333333
$10$	−7.35809	−2.32683
$11$	−5.35035	−1.61319	−0.806596	−	0.591103i	$-0.798693\pi$
$11$	−5.35035	−1.61319	−0.806596	+	0.591103i	$0.798693\pi$
$12$	−2.64721	−0.764184
$13$	−5.86183	−1.62578	−0.812890	−	0.582417i	$-0.802107\pi$
$13$	−5.86183	−1.62578	−0.812890	+	0.582417i	$0.802107\pi$
$14$	−0.434095	−0.116017
$15$	−3.41325	−0.881298
$16$	−2.28669	−0.571673
$17$	4.05336	0.983084	0.491542	−	0.870854i	$-0.336433\pi$
$17$	4.05336	0.983084	0.491542	+	0.870854i	$0.336433\pi$
$18$	−2.15574	−0.508113
$19$	−2.42759	−0.556928	−0.278464	−	0.960447i	$-0.589825\pi$
$19$	−2.42759	−0.556928	−0.278464	+	0.960447i	$0.589825\pi$
$20$	9.03561	2.02042
$21$	−0.201367	−0.0439419
$22$	11.5340	2.45905
$23$	−4.58506	−0.956050	−0.478025	−	0.878346i	$-0.658647\pi$
$23$	−4.58506	−0.956050	−0.478025	+	0.878346i	$0.658647\pi$
$24$	1.39522	0.284798
$25$	6.65030	1.33006
$26$	12.6366	2.47824
$27$	−1.00000	−0.192450
$28$	0.533062	0.100739
$29$	3.44243	0.639244	0.319622	−	0.947545i	$-0.396444\pi$
$29$	3.44243	0.639244	0.319622	+	0.947545i	$0.396444\pi$
$30$	7.35809	1.34340
$31$	−7.68267	−1.37985	−0.689924	−	0.723881i	$-0.742356\pi$
$31$	−7.68267	−1.37985	−0.689924	+	0.723881i	$0.742356\pi$
$32$	7.71995	1.36471
$33$	5.35035	0.931377
$34$	−8.73799	−1.49855
$35$	0.687317	0.116178
$36$	2.64721	0.441202
$37$	−0.781965	−0.128554	−0.0642771	−	0.997932i	$-0.520474\pi$
$37$	−0.781965	−0.128554	−0.0642771	+	0.997932i	$0.520474\pi$
$38$	5.23326	0.848947
$39$	5.86183	0.938645
$40$	−4.76224	−0.752977
$41$	5.87100	0.916897	0.458448	−	0.888721i	$-0.348405\pi$
$41$	5.87100	0.916897	0.458448	+	0.888721i	$0.348405\pi$
$42$	0.434095	0.0669823
$43$	−8.05607	−1.22854	−0.614270	−	0.789096i	$-0.710549\pi$
$43$	−8.05607	−1.22854	−0.614270	+	0.789096i	$0.710549\pi$
$44$	−14.1635	−2.13523
$45$	3.41325	0.508818
$46$	9.88419	1.45734
$47$	−3.12717	−0.456144	−0.228072	−	0.973644i	$-0.573242\pi$
$47$	−3.12717	−0.456144	−0.228072	+	0.973644i	$0.573242\pi$
$48$	2.28669	0.330056
$49$	−6.95945	−0.994207
$50$	−14.3363	−2.02746
$51$	−4.05336	−0.567584
$52$	−15.5175	−2.15189
$53$	−11.6536	−1.60075	−0.800375	−	0.599499i	$-0.795366\pi$
$53$	−11.6536	−1.60075	−0.800375	+	0.599499i	$0.795366\pi$
$54$	2.15574	0.293359
$55$	−18.2621	−2.46246
$56$	−0.280952	−0.0375437
$57$	2.42759	0.321543
$58$	−7.42099	−0.974423
$59$	9.93358	1.29324	0.646621	−	0.762811i	$-0.276182\pi$
$59$	9.93358	1.29324	0.646621	+	0.762811i	$0.276182\pi$
$60$	−9.03561	−1.16649
$61$	5.67948	0.727183	0.363591	−	0.931559i	$-0.381550\pi$
$61$	5.67948	0.727183	0.363591	+	0.931559i	$0.381550\pi$
$62$	16.5618	2.10336
$63$	0.201367	0.0253699
$64$	−12.0688	−1.50860
$65$	−20.0079	−2.48168
$66$	−11.5340	−1.41973
$67$	−6.84647	−0.836429	−0.418215	−	0.908348i	$-0.637344\pi$
$67$	−6.84647	−0.836429	−0.418215	+	0.908348i	$0.637344\pi$
$68$	10.7301	1.30122
$69$	4.58506	0.551976
$70$	−1.48168	−0.177094
$71$	12.8677	1.52711	0.763555	−	0.645743i	$-0.223452\pi$
$71$	12.8677	1.52711	0.763555	+	0.645743i	$0.223452\pi$
$72$	−1.39522	−0.164428
$73$	−7.37793	−0.863521	−0.431761	−	0.901988i	$-0.642107\pi$
$73$	−7.37793	−0.863521	−0.431761	+	0.901988i	$0.642107\pi$
$74$	1.68571	0.195960
$75$	−6.65030	−0.767911
$76$	−6.42636	−0.737154
$77$	−1.07739	−0.122779
$78$	−12.6366	−1.43081
$79$	14.6391	1.64702	0.823512	−	0.567299i	$-0.192012\pi$
$79$	14.6391	1.64702	0.823512	+	0.567299i	$0.192012\pi$
$80$	−7.80506	−0.872632
$81$	1.00000	0.111111
$82$	−12.6564	−1.39766
$83$	−15.8846	−1.74357	−0.871783	−	0.489893i	$-0.837036\pi$
$83$	−15.8846	−1.74357	−0.871783	+	0.489893i	$0.837036\pi$
$84$	−0.533062	−0.0581618
$85$	13.8351	1.50063
$86$	17.3668	1.87271
$87$	−3.44243	−0.369067
$88$	7.46492	0.795763
$89$	−5.12607	−0.543362	−0.271681	−	0.962387i	$-0.587580\pi$
$89$	−5.12607	−0.543362	−0.271681	+	0.962387i	$0.587580\pi$
$90$	−7.35809	−0.775610
$91$	−1.18038	−0.123738
$92$	−12.1376	−1.26543
$93$	7.68267	0.796656
$94$	6.74135	0.695318
$95$	−8.28599	−0.850125
$96$	−7.71995	−0.787914
$97$	−11.8563	−1.20382	−0.601911	−	0.798563i	$-0.705594\pi$
$97$	−11.8563	−1.20382	−0.601911	+	0.798563i	$0.705594\pi$
$98$	15.0028	1.51551
$99$	−5.35035	−0.537731
$100$	17.6048	1.76048
$101$	−15.8321	−1.57535	−0.787677	−	0.616089i	$-0.788716\pi$
$101$	−15.8321	−1.57535	−0.787677	+	0.616089i	$0.788716\pi$
$102$	8.73799	0.865190
$103$	16.7153	1.64701	0.823505	−	0.567310i	$-0.192016\pi$
$103$	16.7153	1.64701	0.823505	+	0.567310i	$0.192016\pi$
$104$	8.17855	0.801973
$105$	−0.687317	−0.0670753
$106$	25.1222	2.44008
$107$	−3.25084	−0.314271	−0.157135	−	0.987577i	$-0.550226\pi$
$107$	−3.25084	−0.314271	−0.157135	+	0.987577i	$0.550226\pi$
$108$	−2.64721	−0.254728
$109$	−2.91908	−0.279597	−0.139799	−	0.990180i	$-0.544646\pi$
$109$	−2.91908	−0.279597	−0.139799	+	0.990180i	$0.544646\pi$
$110$	39.3684	3.75363
$111$	0.781965	0.0742208
$112$	−0.460465	−0.0435098
$113$	2.24561	0.211249	0.105625	−	0.994406i	$-0.466316\pi$
$113$	2.24561	0.211249	0.105625	+	0.994406i	$0.466316\pi$
$114$	−5.23326	−0.490140
$115$	−15.6500	−1.45937
$116$	9.11285	0.846107
$117$	−5.86183	−0.541927
$118$	−21.4142	−1.97134
$119$	0.816214	0.0748222
$120$	4.76224	0.434731
$121$	17.6263	1.60239
$122$	−12.2435	−1.10847
$123$	−5.87100	−0.529371
$124$	−20.3377	−1.82638
$125$	5.63289	0.503821
$126$	−0.434095	−0.0386723
$127$	−8.75323	−0.776724	−0.388362	−	0.921507i	$-0.626959\pi$
$127$	−8.75323	−0.776724	−0.388362	+	0.921507i	$0.626959\pi$
$128$	10.5773	0.934913
$129$	8.05607	0.709298
$130$	43.1319	3.78292
$131$	8.69454	0.759646	0.379823	−	0.925059i	$-0.375985\pi$
$131$	8.69454	0.759646	0.379823	+	0.925059i	$0.375985\pi$
$132$	14.1635	1.23278
$133$	−0.488838	−0.0423876
$134$	14.7592	1.27500
$135$	−3.41325	−0.293766
$136$	−5.65533	−0.484941
$137$	−8.49089	−0.725426	−0.362713	−	0.931901i	$-0.618149\pi$
$137$	−8.49089	−0.725426	−0.362713	+	0.931901i	$0.618149\pi$
$138$	−9.88419	−0.841398
$139$	−1.97577	−0.167582	−0.0837912	−	0.996483i	$-0.526703\pi$
$139$	−1.97577	−0.167582	−0.0837912	+	0.996483i	$0.526703\pi$
$140$	1.81947	0.153774
$141$	3.12717	0.263355
$142$	−27.7393	−2.32783
$143$	31.3629	2.62270
$144$	−2.28669	−0.190558
$145$	11.7499	0.975775
$146$	15.9049	1.31630
$147$	6.95945	0.574006
$148$	−2.07003	−0.170155
$149$	3.31898	0.271901	0.135951	−	0.990716i	$-0.456591\pi$
$149$	3.31898	0.271901	0.135951	+	0.990716i	$0.456591\pi$
$150$	14.3363	1.17056
$151$	−13.3688	−1.08794	−0.543968	−	0.839106i	$-0.683079\pi$
$151$	−13.3688	−1.08794	−0.543968	+	0.839106i	$0.683079\pi$
$152$	3.38703	0.274724
$153$	4.05336	0.327695
$154$	2.32256	0.187157
$155$	−26.2229	−2.10628
$156$	15.5175	1.24240
$157$	3.64757	0.291108	0.145554	−	0.989350i	$-0.453504\pi$
$157$	3.64757	0.291108	0.145554	+	0.989350i	$0.453504\pi$
$158$	−31.5580	−2.51062
$159$	11.6536	0.924194
$160$	26.3502	2.08316
$161$	−0.923280	−0.0727646
$162$	−2.15574	−0.169371
$163$	−14.8589	−1.16384	−0.581920	−	0.813246i	$-0.697698\pi$
$163$	−14.8589	−1.16384	−0.581920	+	0.813246i	$0.697698\pi$
$164$	15.5418	1.21361
$165$	18.2621	1.42170
$166$	34.2431	2.65778
$167$	12.1352	0.939049	0.469524	−	0.882919i	$-0.344425\pi$
$167$	12.1352	0.939049	0.469524	+	0.882919i	$0.344425\pi$
$168$	0.280952	0.0216759
$169$	21.3611	1.64316
$170$	−29.8250	−2.28747
$171$	−2.42759	−0.185643
$172$	−21.3261	−1.62610
$173$	−13.0426	−0.991610	−0.495805	−	0.868434i	$-0.665127\pi$
$173$	−13.0426	−0.991610	−0.495805	+	0.868434i	$0.665127\pi$
$174$	7.42099	0.562583
$175$	1.33915	0.101230
$176$	12.2346	0.922219
$177$	−9.93358	−0.746654
$178$	11.0505	0.828267
$179$	5.36036	0.400652	0.200326	−	0.979729i	$-0.435800\pi$
$179$	5.36036	0.400652	0.200326	+	0.979729i	$0.435800\pi$
$180$	9.03561	0.673474
$181$	5.12883	0.381223	0.190611	−	0.981666i	$-0.438953\pi$
$181$	5.12883	0.381223	0.190611	+	0.981666i	$0.438953\pi$
$182$	2.54459	0.188618
$183$	−5.67948	−0.419839
$184$	6.39716	0.471605
$185$	−2.66905	−0.196232
$186$	−16.5618	−1.21437
$187$	−21.6869	−1.58590
$188$	−8.27827	−0.603755
$189$	−0.201367	−0.0146473
$190$	17.8624	1.29588
$191$	−12.0807	−0.874130	−0.437065	−	0.899430i	$-0.643982\pi$
$191$	−12.0807	−0.874130	−0.437065	+	0.899430i	$0.643982\pi$
$192$	12.0688	0.870992
$193$	25.6877	1.84904	0.924519	−	0.381135i	$-0.124467\pi$
$193$	25.6877	1.84904	0.924519	+	0.381135i	$0.124467\pi$
$194$	25.5590	1.83503
$195$	20.0079	1.43280
$196$	−18.4231	−1.31594
$197$	−8.44159	−0.601439	−0.300719	−	0.953713i	$-0.597227\pi$
$197$	−8.44159	−0.601439	−0.300719	+	0.953713i	$0.597227\pi$
$198$	11.5340	0.819683
$199$	4.76581	0.337839	0.168920	−	0.985630i	$-0.445972\pi$
$199$	4.76581	0.337839	0.168920	+	0.985630i	$0.445972\pi$
$200$	−9.27864	−0.656099
$201$	6.84647	0.482913
$202$	34.1299	2.40137
$203$	0.693193	0.0486526
$204$	−10.7301	−0.751257
$205$	20.0392	1.39960
$206$	−36.0339	−2.51060
$207$	−4.58506	−0.318683
$208$	13.4042	0.929415
$209$	12.9885	0.898432
$210$	1.48168	0.102245
$211$	7.98569	0.549758	0.274879	−	0.961479i	$-0.411362\pi$
$211$	7.98569	0.549758	0.274879	+	0.961479i	$0.411362\pi$
$212$	−30.8497	−2.11876
$213$	−12.8677	−0.881677
$214$	7.00797	0.479055
$215$	−27.4974	−1.87531
$216$	1.39522	0.0949327
$217$	−1.54704	−0.105020
$218$	6.29278	0.426201
$219$	7.37793	0.498554
$220$	−48.3437	−3.25933
$221$	−23.7601	−1.59828
$222$	−1.68571	−0.113138
$223$	−24.9471	−1.67058	−0.835291	−	0.549808i	$-0.814701\pi$
$223$	−24.9471	−1.67058	−0.835291	+	0.549808i	$0.814701\pi$
$224$	1.55455	0.103867
$225$	6.65030	0.443353
$226$	−4.84095	−0.322015
$227$	25.4484	1.68907	0.844536	−	0.535499i	$-0.179877\pi$
$227$	25.4484	1.68907	0.844536	+	0.535499i	$0.179877\pi$
$228$	6.42636	0.425596
$229$	−8.84963	−0.584800	−0.292400	−	0.956296i	$-0.594454\pi$
$229$	−8.84963	−0.584800	−0.292400	+	0.956296i	$0.594454\pi$
$230$	33.7372	2.22457
$231$	1.07739	0.0708868
$232$	−4.80295	−0.315329
$233$	23.9242	1.56733	0.783665	−	0.621184i	$-0.213348\pi$
$233$	23.9242	1.56733	0.783665	+	0.621184i	$0.213348\pi$
$234$	12.6366	0.826079
$235$	−10.6738	−0.696283
$236$	26.2963	1.71174
$237$	−14.6391	−0.950910
$238$	−1.75954	−0.114054
$239$	−1.00000	−0.0646846
$239$	−1.00000	−0.0646846
$240$	7.80506	0.503815
$241$	−5.57115	−0.358870	−0.179435	−	0.983770i	$-0.557427\pi$
$241$	−5.57115	−0.358870	−0.179435	+	0.983770i	$0.557427\pi$
$242$	−37.9977	−2.44258
$243$	−1.00000	−0.0641500
$244$	15.0348	0.962503
$245$	−23.7544	−1.51761
$246$	12.6564	0.806940
$247$	14.2302	0.905443
$248$	10.7190	0.680659
$249$	15.8846	1.00665
$250$	−12.1430	−0.767994
$251$	−24.0752	−1.51961	−0.759806	−	0.650150i	$-0.774706\pi$
$251$	−24.0752	−1.51961	−0.759806	+	0.650150i	$0.774706\pi$
$252$	0.533062	0.0335797
$253$	24.5317	1.54229
$254$	18.8697	1.18399
$255$	−13.8351	−0.866390
$256$	1.33568	0.0834801
$257$	1.65551	0.103268	0.0516339	−	0.998666i	$-0.483557\pi$
$257$	1.65551	0.103268	0.0516339	+	0.998666i	$0.483557\pi$
$258$	−17.3668	−1.08121
$259$	−0.157462	−0.00978422
$260$	−52.9652	−3.28476
$261$	3.44243	0.213081
$262$	−18.7432	−1.15796
$263$	−13.7969	−0.850751	−0.425375	−	0.905017i	$-0.639858\pi$
$263$	−13.7969	−0.850751	−0.425375	+	0.905017i	$0.639858\pi$
$264$	−7.46492	−0.459434
$265$	−39.7768	−2.44347
$266$	1.05381	0.0646130
$267$	5.12607	0.313710
$268$	−18.1241	−1.10710
$269$	−2.37746	−0.144956	−0.0724782	−	0.997370i	$-0.523091\pi$
$269$	−2.37746	−0.144956	−0.0724782	+	0.997370i	$0.523091\pi$
$270$	7.35809	0.447799
$271$	3.47333	0.210990	0.105495	−	0.994420i	$-0.466357\pi$
$271$	3.47333	0.210990	0.105495	+	0.994420i	$0.466357\pi$
$272$	−9.26879	−0.562003
$273$	1.18038	0.0714399
$274$	18.3042	1.10579
$275$	−35.5815	−2.14564
$276$	12.1376	0.730599
$277$	−2.25803	−0.135672	−0.0678359	−	0.997696i	$-0.521609\pi$
$277$	−2.25803	−0.135672	−0.0678359	+	0.997696i	$0.521609\pi$
$278$	4.25924	0.255452
$279$	−7.68267	−0.459950
$280$	−0.958959	−0.0573088
$281$	−0.502713	−0.0299894	−0.0149947	−	0.999888i	$-0.504773\pi$
$281$	−0.502713	−0.0299894	−0.0149947	+	0.999888i	$0.504773\pi$
$282$	−6.74135	−0.401442
$283$	21.6234	1.28538	0.642690	−	0.766127i	$-0.277818\pi$
$283$	21.6234	1.28538	0.642690	+	0.766127i	$0.277818\pi$
$284$	34.0634	2.02129
$285$	8.28599	0.490820
$286$	−67.6102	−3.99787
$287$	1.18223	0.0697847
$288$	7.71995	0.454903
$289$	−0.570276	−0.0335456
$290$	−25.3297	−1.48741
$291$	11.8563	0.695027
$292$	−19.5309	−1.14296
$293$	18.7307	1.09426	0.547129	−	0.837048i	$-0.315721\pi$
$293$	18.7307	1.09426	0.547129	+	0.837048i	$0.315721\pi$
$294$	−15.0028	−0.874979
$295$	33.9058	1.97407
$296$	1.09101	0.0634139
$297$	5.35035	0.310459
$298$	−7.15485	−0.414469
$299$	26.8768	1.55433
$300$	−17.6048	−1.01641
$301$	−1.62223	−0.0935037
$302$	28.8196	1.65838
$303$	15.8321	0.909531
$304$	5.55116	0.318381
$305$	19.3855	1.11001
$306$	−8.73799	−0.499517
$307$	4.73274	0.270112	0.135056	−	0.990838i	$-0.456879\pi$
$307$	4.73274	0.270112	0.135056	+	0.990838i	$0.456879\pi$
$308$	−2.85207	−0.162512
$309$	−16.7153	−0.950901
$310$	56.5298	3.21067
$311$	−21.6404	−1.22711	−0.613556	−	0.789651i	$-0.710262\pi$
$311$	−21.6404	−1.22711	−0.613556	+	0.789651i	$0.710262\pi$
$312$	−8.17855	−0.463019
$313$	24.4364	1.38123	0.690615	−	0.723223i	$-0.257340\pi$
$313$	24.4364	1.38123	0.690615	+	0.723223i	$0.257340\pi$
$314$	−7.86321	−0.443747
$315$	0.687317	0.0387259
$316$	38.7527	2.18001
$317$	2.93779	0.165003	0.0825013	−	0.996591i	$-0.473709\pi$
$317$	2.93779	0.165003	0.0825013	+	0.996591i	$0.473709\pi$
$318$	−25.1222	−1.40878
$319$	−18.4182	−1.03122
$320$	−41.1940	−2.30281
$321$	3.25084	0.181444
$322$	1.99035	0.110918
$323$	−9.83991	−0.547507
$324$	2.64721	0.147067
$325$	−38.9830	−2.16239
$326$	32.0319	1.77408
$327$	2.91908	0.161426
$328$	−8.19135	−0.452291
$329$	−0.629709	−0.0347170
$330$	−39.3684	−2.16716
$331$	−13.2517	−0.728379	−0.364190	−	0.931325i	$-0.618654\pi$
$331$	−13.2517	−0.728379	−0.364190	+	0.931325i	$0.618654\pi$
$332$	−42.0500	−2.30779
$333$	−0.781965	−0.0428514
$334$	−26.1603	−1.43143
$335$	−23.3687	−1.27677
$336$	0.460465	0.0251204
$337$	−6.76419	−0.368469	−0.184234	−	0.982882i	$-0.558981\pi$
$337$	−6.76419	−0.368469	−0.184234	+	0.982882i	$0.558981\pi$
$338$	−46.0490	−2.50473
$339$	−2.24561	−0.121965
$340$	36.6246	1.98625
$341$	41.1050	2.22596
$342$	5.23326	0.282982
$343$	−2.81098	−0.151778
$344$	11.2400	0.606020
$345$	15.6500	0.842565
$346$	28.1164	1.51155
$347$	28.8872	1.55075	0.775374	−	0.631503i	$-0.217561\pi$
$347$	28.8872	1.55075	0.775374	+	0.631503i	$0.217561\pi$
$348$	−9.11285	−0.488500
$349$	8.86947	0.474772	0.237386	−	0.971415i	$-0.423709\pi$
$349$	8.86947	0.474772	0.237386	+	0.971415i	$0.423709\pi$
$350$	−2.88686	−0.154309
$351$	5.86183	0.312882
$352$	−41.3045	−2.20154
$353$	1.97699	0.105224	0.0526122	−	0.998615i	$-0.483245\pi$
$353$	1.97699	0.105224	0.0526122	+	0.998615i	$0.483245\pi$
$354$	21.4142	1.13815
$355$	43.9206	2.33106
$356$	−13.5698	−0.719197
$357$	−0.816214	−0.0431986
$358$	−11.5555	−0.610730
$359$	16.3404	0.862413	0.431206	−	0.902253i	$-0.358088\pi$
$359$	16.3404	0.862413	0.431206	+	0.902253i	$0.358088\pi$
$360$	−4.76224	−0.250992
$361$	−13.1068	−0.689831
$362$	−11.0564	−0.581112
$363$	−17.6263	−0.925140
$364$	−3.12472	−0.163780
$365$	−25.1827	−1.31812
$366$	12.2435	0.639977
$367$	−32.2353	−1.68267	−0.841333	−	0.540517i	$-0.818229\pi$
$367$	−32.2353	−1.68267	−0.841333	+	0.540517i	$0.818229\pi$
$368$	10.4846	0.546548
$369$	5.87100	0.305632
$370$	5.75377	0.299124
$371$	−2.34666	−0.121833
$372$	20.3377	1.05446
$373$	−0.382479	−0.0198040	−0.00990201	−	0.999951i	$-0.503152\pi$
$373$	−0.382479	−0.0198040	−0.00990201	+	0.999951i	$0.503152\pi$
$374$	46.7513	2.41745
$375$	−5.63289	−0.290881
$376$	4.36309	0.225009
$377$	−20.1790	−1.03927
$378$	0.434095	0.0223274
$379$	−3.06644	−0.157512	−0.0787562	−	0.996894i	$-0.525095\pi$
$379$	−3.06644	−0.157512	−0.0787562	+	0.996894i	$0.525095\pi$
$380$	−21.9348	−1.12523
$381$	8.75323	0.448442
$382$	26.0429	1.33247
$383$	−7.87059	−0.402168	−0.201084	−	0.979574i	$-0.564446\pi$
$383$	−7.87059	−0.402168	−0.201084	+	0.979574i	$0.564446\pi$
$384$	−10.5773	−0.539772
$385$	−3.67739	−0.187417
$386$	−55.3759	−2.81856
$387$	−8.05607	−0.409513
$388$	−31.3861	−1.59339
$389$	9.22062	0.467504	0.233752	−	0.972296i	$-0.424900\pi$
$389$	9.22062	0.467504	0.233752	+	0.972296i	$0.424900\pi$
$390$	−43.1319	−2.18407
$391$	−18.5849	−0.939878
$392$	9.70997	0.490428
$393$	−8.69454	−0.438582
$394$	18.1979	0.916796
$395$	49.9669	2.51411
$396$	−14.1635	−0.711744
$397$	29.5873	1.48495	0.742473	−	0.669876i	$-0.233653\pi$
$397$	29.5873	1.48495	0.742473	+	0.669876i	$0.233653\pi$
$398$	−10.2738	−0.514981
$399$	0.488838	0.0244725
$400$	−15.2072	−0.760360
$401$	33.1480	1.65533	0.827666	−	0.561221i	$-0.189668\pi$
$401$	33.1480	1.65533	0.827666	+	0.561221i	$0.189668\pi$
$402$	−14.7592	−0.736122
$403$	45.0346	2.24333
$404$	−41.9109	−2.08515
$405$	3.41325	0.169606
$406$	−1.49434	−0.0741630
$407$	4.18379	0.207383
$408$	5.65533	0.279981
$409$	−27.5969	−1.36458	−0.682290	−	0.731081i	$-0.739016\pi$
$409$	−27.5969	−1.36458	−0.682290	+	0.731081i	$0.739016\pi$
$410$	−43.1993	−2.13346
$411$	8.49089	0.418825
$412$	44.2490	2.17999
$413$	2.00030	0.0984282
$414$	9.88419	0.485781
$415$	−54.2183	−2.66147
$416$	−45.2531	−2.21872
$417$	1.97577	0.0967537
$418$	−27.9998	−1.36951
$419$	−23.6207	−1.15394	−0.576972	−	0.816764i	$-0.695766\pi$
$419$	−23.6207	−1.15394	−0.576972	+	0.816764i	$0.695766\pi$
$420$	−1.81947	−0.0887813
$421$	−19.6014	−0.955315	−0.477657	−	0.878546i	$-0.658514\pi$
$421$	−19.6014	−0.955315	−0.477657	+	0.878546i	$0.658514\pi$
$422$	−17.2151	−0.838017
$423$	−3.12717	−0.152048
$424$	16.2594	0.789626
$425$	26.9561	1.30756
$426$	27.7393	1.34397
$427$	1.14366	0.0553456
$428$	−8.60567	−0.415971
$429$	−31.3629	−1.51421
$430$	59.2773	2.85860
$431$	34.8589	1.67910	0.839548	−	0.543286i	$-0.182820\pi$
$431$	34.8589	1.67910	0.839548	+	0.543286i	$0.182820\pi$
$432$	2.28669	0.110019
$433$	−11.7316	−0.563787	−0.281893	−	0.959446i	$-0.590962\pi$
$433$	−11.7316	−0.563787	−0.281893	+	0.959446i	$0.590962\pi$
$434$	3.33501	0.160086
$435$	−11.7499	−0.563364
$436$	−7.72743	−0.370077
$437$	11.1307	0.532451
$438$	−15.9049	−0.759965
$439$	37.1023	1.77079	0.885397	−	0.464835i	$-0.153886\pi$
$439$	37.1023	1.77079	0.885397	+	0.464835i	$0.153886\pi$
$440$	25.4797	1.21470
$441$	−6.95945	−0.331402
$442$	51.2206	2.43632
$443$	5.25818	0.249824	0.124912	−	0.992168i	$-0.460135\pi$
$443$	5.25818	0.249824	0.124912	+	0.992168i	$0.460135\pi$
$444$	2.07003	0.0982392
$445$	−17.4966	−0.829417
$446$	53.7794	2.54653
$447$	−3.31898	−0.156982
$448$	−2.43026	−0.114819
$449$	21.0799	0.994822	0.497411	−	0.867515i	$-0.334284\pi$
$449$	21.0799	0.994822	0.497411	+	0.867515i	$0.334284\pi$
$450$	−14.3363	−0.675820
$451$	−31.4119	−1.47913
$452$	5.94460	0.279611
$453$	13.3688	0.628120
$454$	−54.8602	−2.57472
$455$	−4.02894	−0.188880
$456$	−3.38703	−0.158612
$457$	−31.7180	−1.48371	−0.741853	−	0.670563i	$-0.766053\pi$
$457$	−31.7180	−1.48371	−0.741853	+	0.670563i	$0.766053\pi$
$458$	19.0775	0.891433
$459$	−4.05336	−0.189195
$460$	−41.4288	−1.93163
$461$	14.1119	0.657258	0.328629	−	0.944459i	$-0.393413\pi$
$461$	14.1119	0.657258	0.328629	+	0.944459i	$0.393413\pi$
$462$	−2.32256	−0.108055
$463$	5.51783	0.256435	0.128218	−	0.991746i	$-0.459074\pi$
$463$	5.51783	0.256435	0.128218	+	0.991746i	$0.459074\pi$
$464$	−7.87178	−0.365438
$465$	26.2229	1.21606
$466$	−51.5744	−2.38914
$467$	−11.0132	−0.509630	−0.254815	−	0.966990i	$-0.582015\pi$
$467$	−11.0132	−0.509630	−0.254815	+	0.966990i	$0.582015\pi$
$468$	−15.5175	−0.717297
$469$	−1.37865	−0.0636603
$470$	23.0100	1.06137
$471$	−3.64757	−0.168071
$472$	−13.8595	−0.637937
$473$	43.1028	1.98187
$474$	31.5580	1.44951
$475$	−16.1442	−0.740748
$476$	2.16069	0.0990351
$477$	−11.6536	−0.533584
$478$	2.15574	0.0986012
$479$	18.8603	0.861747	0.430874	−	0.902412i	$-0.358205\pi$
$479$	18.8603	0.861747	0.430874	+	0.902412i	$0.358205\pi$
$480$	−26.3502	−1.20271
$481$	4.58375	0.209001
$482$	12.0100	0.547039
$483$	0.923280	0.0420107
$484$	46.6605	2.12093
$485$	−40.4685	−1.83758
$486$	2.15574	0.0977863
$487$	30.7402	1.39297	0.696485	−	0.717571i	$-0.254746\pi$
$487$	30.7402	1.39297	0.696485	+	0.717571i	$0.254746\pi$
$488$	−7.92412	−0.358708
$489$	14.8589	0.671943
$490$	51.2082	2.31335
$491$	31.9405	1.44146	0.720728	−	0.693218i	$-0.243808\pi$
$491$	31.9405	1.44146	0.720728	+	0.693218i	$0.243808\pi$
$492$	−15.5418	−0.700678
$493$	13.9534	0.628430
$494$	−30.6765	−1.38020
$495$	−18.2621	−0.820821
$496$	17.5679	0.788822
$497$	2.59112	0.116228
$498$	−34.2431	−1.53447
$499$	−21.7380	−0.973127	−0.486564	−	0.873645i	$-0.661750\pi$
$499$	−21.7380	−0.973127	−0.486564	+	0.873645i	$0.661750\pi$
$500$	14.9115	0.666861
$501$	−12.1352	−0.542160
$502$	51.8998	2.31640
$503$	−13.3905	−0.597052	−0.298526	−	0.954401i	$-0.596495\pi$
$503$	−13.3905	−0.597052	−0.298526	+	0.954401i	$0.596495\pi$
$504$	−0.280952	−0.0125146
$505$	−54.0390	−2.40470
$506$	−52.8839	−2.35098
$507$	−21.3611	−0.948680
$508$	−23.1717	−1.02808
$509$	−15.7825	−0.699547	−0.349774	−	0.936834i	$-0.613741\pi$
$509$	−15.7825	−0.699547	−0.349774	+	0.936834i	$0.613741\pi$
$510$	29.8250	1.32067
$511$	−1.48567	−0.0657223
$512$	−24.0340	−1.06216
$513$	2.42759	0.107181
$514$	−3.56884	−0.157415
$515$	57.0536	2.51408
$516$	21.3261	0.938831
$517$	16.7314	0.735848
$518$	0.339447	0.0149145
$519$	13.0426	0.572506
$520$	27.9155	1.22417
$521$	−3.01206	−0.131961	−0.0659803	−	0.997821i	$-0.521017\pi$
$521$	−3.01206	−0.131961	−0.0659803	+	0.997821i	$0.521017\pi$
$522$	−7.42099	−0.324808
$523$	21.0704	0.921342	0.460671	−	0.887571i	$-0.347609\pi$
$523$	21.0704	0.921342	0.460671	+	0.887571i	$0.347609\pi$
$524$	23.0163	1.00547
$525$	−1.33915	−0.0584454
$526$	29.7424	1.29683
$527$	−31.1406	−1.35651
$528$	−12.2346	−0.532443
$529$	−1.97726	−0.0859679
$530$	85.7485	3.72468
$531$	9.93358	0.431081
$532$	−1.29406	−0.0561045
$533$	−34.4148	−1.49067
$534$	−11.0505	−0.478200
$535$	−11.0960	−0.479720
$536$	9.55234	0.412598
$537$	−5.36036	−0.231317
$538$	5.12519	0.220963
$539$	37.2355	1.60385
$540$	−9.03561	−0.388831
$541$	34.6808	1.49104	0.745522	−	0.666481i	$-0.232200\pi$
$541$	34.6808	1.49104	0.745522	+	0.666481i	$0.232200\pi$
$542$	−7.48760	−0.321620
$543$	−5.12883	−0.220099
$544$	31.2917	1.34162
$545$	−9.96357	−0.426792
$546$	−2.54459	−0.108899
$547$	−26.6304	−1.13863	−0.569317	−	0.822118i	$-0.692792\pi$
$547$	−26.6304	−1.13863	−0.569317	+	0.822118i	$0.692792\pi$
$548$	−22.4772	−0.960178
$549$	5.67948	0.242394
$550$	76.7043	3.27068
$551$	−8.35683	−0.356013
$552$	−6.39716	−0.272281
$553$	2.94783	0.125354
$554$	4.86772	0.206810
$555$	2.66905	0.113295
$556$	−5.23027	−0.221813
$557$	−29.6425	−1.25599	−0.627996	−	0.778217i	$-0.716125\pi$
$557$	−29.6425	−1.25599	−0.627996	+	0.778217i	$0.716125\pi$
$558$	16.5618	0.701119
$559$	47.2234	1.99734
$560$	−1.57168	−0.0664157
$561$	21.6869	0.915622
$562$	1.08372	0.0457139
$563$	−11.2332	−0.473422	−0.236711	−	0.971580i	$-0.576069\pi$
$563$	−11.2332	−0.473422	−0.236711	+	0.971580i	$0.576069\pi$
$564$	8.27827	0.348578
$565$	7.66483	0.322462
$566$	−46.6145	−1.95935
$567$	0.201367	0.00845663
$568$	−17.9532	−0.753300
$569$	41.8311	1.75365	0.876825	−	0.480810i	$-0.159657\pi$
$569$	41.8311	1.75365	0.876825	+	0.480810i	$0.159657\pi$
$570$	−17.8624	−0.748175
$571$	10.8247	0.453001	0.226501	−	0.974011i	$-0.427271\pi$
$571$	10.8247	0.453001	0.226501	+	0.974011i	$0.427271\pi$
$572$	83.0242	3.47142
$573$	12.0807	0.504679
$574$	−2.54857	−0.106375
$575$	−30.4920	−1.27160
$576$	−12.0688	−0.502868
$577$	10.1277	0.421621	0.210810	−	0.977527i	$-0.432390\pi$
$577$	10.1277	0.421621	0.210810	+	0.977527i	$0.432390\pi$
$578$	1.22937	0.0511349
$579$	−25.6877	−1.06754
$580$	31.1045	1.29154
$581$	−3.19864	−0.132702
$582$	−25.5590	−1.05946
$583$	62.3511	2.58232
$584$	10.2938	0.425962
$585$	−20.0079	−0.827226
$586$	−40.3785	−1.66802
$587$	10.6488	0.439521	0.219761	−	0.975554i	$-0.429472\pi$
$587$	10.6488	0.439521	0.219761	+	0.975554i	$0.429472\pi$
$588$	18.4231	0.759758
$589$	18.6504	0.768477
$590$	−73.0921	−3.00915
$591$	8.44159	0.347241
$592$	1.78811	0.0734910
$593$	−16.3794	−0.672620	−0.336310	−	0.941751i	$-0.609179\pi$
$593$	−16.3794	−0.672620	−0.336310	+	0.941751i	$0.609179\pi$
$594$	−11.5340	−0.473244
$595$	2.78594	0.114213
$596$	8.78603	0.359890
$597$	−4.76581	−0.195052
$598$	−57.9395	−2.36932
$599$	36.6709	1.49833	0.749167	−	0.662381i	$-0.230454\pi$
$599$	36.6709	1.49833	0.749167	+	0.662381i	$0.230454\pi$
$600$	9.27864	0.378799
$601$	−31.4184	−1.28158	−0.640792	−	0.767714i	$-0.721394\pi$
$601$	−31.4184	−1.28158	−0.640792	+	0.767714i	$0.721394\pi$
$602$	3.49710	0.142531
$603$	−6.84647	−0.278810
$604$	−35.3900	−1.44000
$605$	60.1630	2.44597
$606$	−34.1299	−1.38643
$607$	−25.9196	−1.05204	−0.526021	−	0.850471i	$-0.676317\pi$
$607$	−25.9196	−1.05204	−0.526021	+	0.850471i	$0.676317\pi$
$608$	−18.7409	−0.760044
$609$	−0.693193	−0.0280896
$610$	−41.7901	−1.69203
$611$	18.3309	0.741590
$612$	10.7301	0.433739
$613$	42.5971	1.72048	0.860240	−	0.509890i	$-0.170314\pi$
$613$	42.5971	1.72048	0.860240	+	0.509890i	$0.170314\pi$
$614$	−10.2026	−0.411741
$615$	−20.0392	−0.808060
$616$	1.50319	0.0605653
$617$	−31.0455	−1.24984	−0.624922	−	0.780687i	$-0.714869\pi$
$617$	−31.0455	−1.24984	−0.624922	+	0.780687i	$0.714869\pi$
$618$	36.0339	1.44949
$619$	2.71096	0.108963	0.0544813	−	0.998515i	$-0.482649\pi$
$619$	2.71096	0.108963	0.0544813	+	0.998515i	$0.482649\pi$
$620$	−69.4176	−2.78788
$621$	4.58506	0.183992
$622$	46.6510	1.87053
$623$	−1.03222	−0.0413551
$624$	−13.4042	−0.536598
$625$	−14.0250	−0.561000
$626$	−52.6786	−2.10546
$627$	−12.9885	−0.518710
$628$	9.65589	0.385312
$629$	−3.16959	−0.126380
$630$	−1.48168	−0.0590314
$631$	−22.5598	−0.898093	−0.449047	−	0.893508i	$-0.648236\pi$
$631$	−22.5598	−0.898093	−0.449047	+	0.893508i	$0.648236\pi$
$632$	−20.4247	−0.812452
$633$	−7.98569	−0.317403
$634$	−6.33311	−0.251520
$635$	−29.8770	−1.18563
$636$	30.8497	1.22327
$637$	40.7951	1.61636
$638$	39.7049	1.57193
$639$	12.8677	0.509037
$640$	36.1031	1.42710
$641$	45.7883	1.80853	0.904265	−	0.426971i	$-0.140420\pi$
$641$	45.7883	1.80853	0.904265	+	0.426971i	$0.140420\pi$
$642$	−7.00797	−0.276583
$643$	−16.8011	−0.662571	−0.331285	−	0.943531i	$-0.607482\pi$
$643$	−16.8011	−0.662571	−0.331285	+	0.943531i	$0.607482\pi$
$644$	−2.44412	−0.0963117
$645$	27.4974	1.08271
$646$	21.2123	0.834586
$647$	30.7434	1.20865	0.604323	−	0.796739i	$-0.293443\pi$
$647$	30.7434	1.20865	0.604323	+	0.796739i	$0.293443\pi$
$648$	−1.39522	−0.0548094
$649$	−53.1482	−2.08625
$650$	84.0371	3.29621
$651$	1.54704	0.0606332
$652$	−39.3347	−1.54046
$653$	18.9143	0.740172	0.370086	−	0.928997i	$-0.379328\pi$
$653$	18.9143	0.740172	0.370086	+	0.928997i	$0.379328\pi$
$654$	−6.29278	−0.246067
$655$	29.6767	1.15956
$656$	−13.4252	−0.524165
$657$	−7.37793	−0.287840
$658$	1.35749	0.0529204
$659$	−29.5539	−1.15126	−0.575629	−	0.817711i	$-0.695243\pi$
$659$	−29.5539	−1.15126	−0.575629	+	0.817711i	$0.695243\pi$
$660$	48.3437	1.88178
$661$	16.6977	0.649465	0.324733	−	0.945806i	$-0.394726\pi$
$661$	16.6977	0.649465	0.324733	+	0.945806i	$0.394726\pi$
$662$	28.5672	1.11030
$663$	23.7601	0.922767
$664$	22.1626	0.860075
$665$	−1.66853	−0.0647027
$666$	1.68571	0.0653200
$667$	−15.7837	−0.611149
$668$	32.1244	1.24293
$669$	24.9471	0.964511
$670$	50.3769	1.94623
$671$	−30.3872	−1.17309
$672$	−1.55455	−0.0599679
$673$	45.9061	1.76955	0.884775	−	0.466018i	$-0.154312\pi$
$673$	45.9061	1.76955	0.884775	+	0.466018i	$0.154312\pi$
$674$	14.5818	0.561671
$675$	−6.65030	−0.255970
$676$	56.5473	2.17490
$677$	12.4084	0.476892	0.238446	−	0.971156i	$-0.423362\pi$
$677$	12.4084	0.476892	0.238446	+	0.971156i	$0.423362\pi$
$678$	4.84095	0.185915
$679$	−2.38746	−0.0916225
$680$	−19.3031	−0.740239
$681$	−25.4484	−0.975186
$682$	−88.6117	−3.39312
$683$	−12.9318	−0.494820	−0.247410	−	0.968911i	$-0.579579\pi$
$683$	−12.9318	−0.494820	−0.247410	+	0.968911i	$0.579579\pi$
$684$	−6.42636	−0.245718
$685$	−28.9816	−1.10733
$686$	6.05973	0.231362
$687$	8.84963	0.337634
$688$	18.4218	0.702323
$689$	68.3117	2.60247
$690$	−33.7372	−1.28435
$691$	7.42986	0.282645	0.141323	−	0.989964i	$-0.454865\pi$
$691$	7.42986	0.282645	0.141323	+	0.989964i	$0.454865\pi$
$692$	−34.5265	−1.31250
$693$	−1.07739	−0.0409265
$694$	−62.2733	−2.36386
$695$	−6.74379	−0.255807
$696$	4.80295	0.182055
$697$	23.7973	0.901387
$698$	−19.1203	−0.723713
$699$	−23.9242	−0.904898
$700$	3.54502	0.133989
$701$	−13.2033	−0.498682	−0.249341	−	0.968416i	$-0.580214\pi$
$701$	−13.2033	−0.498682	−0.249341	+	0.968416i	$0.580214\pi$
$702$	−12.6366	−0.476937
$703$	1.89829	0.0715955
$704$	64.5725	2.43367
$705$	10.6738	0.401999
$706$	−4.26187	−0.160398
$707$	−3.18807	−0.119900
$708$	−26.2963	−0.988275
$709$	−38.7599	−1.45566	−0.727830	−	0.685758i	$-0.759471\pi$
$709$	−38.7599	−1.45566	−0.727830	+	0.685758i	$0.759471\pi$
$710$	−94.6813	−3.55333
$711$	14.6391	0.549008
$712$	7.15199	0.268032
$713$	35.2255	1.31920
$714$	1.75954	0.0658493
$715$	107.049	4.00342
$716$	14.1900	0.530306
$717$	1.00000	0.0373457
$718$	−35.2256	−1.31461
$719$	37.8102	1.41008	0.705041	−	0.709167i	$-0.250929\pi$
$719$	37.8102	1.41008	0.705041	+	0.709167i	$0.250929\pi$
$720$	−7.80506	−0.290877
$721$	3.36592	0.125353
$722$	28.2548	1.05154
$723$	5.57115	0.207193
$724$	13.5771	0.504589
$725$	22.8932	0.850232
$726$	37.9977	1.41023
$727$	−7.34986	−0.272591	−0.136296	−	0.990668i	$-0.543520\pi$
$727$	−7.34986	−0.272591	−0.136296	+	0.990668i	$0.543520\pi$
$728$	1.64689	0.0610379
$729$	1.00000	0.0370370
$730$	54.2874	2.00927
$731$	−32.6542	−1.20776
$732$	−15.0348	−0.555702
$733$	−30.6192	−1.13095	−0.565473	−	0.824767i	$-0.691306\pi$
$733$	−30.6192	−1.13095	−0.565473	+	0.824767i	$0.691306\pi$
$734$	69.4908	2.56495
$735$	23.7544	0.876193
$736$	−35.3964	−1.30473
$737$	36.6310	1.34932
$738$	−12.6564	−0.465887
$739$	17.9779	0.661328	0.330664	−	0.943749i	$-0.392727\pi$
$739$	17.9779	0.661328	0.330664	+	0.943749i	$0.392727\pi$
$740$	−7.06553	−0.259734
$741$	−14.2302	−0.522758
$742$	5.05879	0.185714
$743$	−15.7997	−0.579634	−0.289817	−	0.957082i	$-0.593595\pi$
$743$	−15.7997	−0.579634	−0.289817	+	0.957082i	$0.593595\pi$
$744$	−10.7190	−0.392978
$745$	11.3285	0.415044
$746$	0.824525	0.0301880
$747$	−15.8846	−0.581189
$748$	−57.4098	−2.09911
$749$	−0.654613	−0.0239190
$750$	12.1430	0.443401
$751$	−18.1005	−0.660495	−0.330248	−	0.943894i	$-0.607132\pi$
$751$	−18.1005	−0.660495	−0.330248	+	0.943894i	$0.607132\pi$
$752$	7.15087	0.260765
$753$	24.0752	0.877348
$754$	43.5006	1.58420
$755$	−45.6310	−1.66068
$756$	−0.533062	−0.0193873
$757$	−29.8230	−1.08394	−0.541968	−	0.840399i	$-0.682321\pi$
$757$	−29.8230	−1.08394	−0.541968	+	0.840399i	$0.682321\pi$
$758$	6.61044	0.240102
$759$	−24.5317	−0.890443
$760$	11.5608	0.419354
$761$	−13.1033	−0.474996	−0.237498	−	0.971388i	$-0.576327\pi$
$761$	−13.1033	−0.474996	−0.237498	+	0.971388i	$0.576327\pi$
$762$	−18.8697	−0.683577
$763$	−0.587807	−0.0212801
$764$	−31.9802	−1.15700
$765$	13.8351	0.500211
$766$	16.9669	0.613040
$767$	−58.2290	−2.10253
$768$	−1.33568	−0.0481972
$769$	−23.6108	−0.851428	−0.425714	−	0.904858i	$-0.639977\pi$
$769$	−23.6108	−0.851428	−0.425714	+	0.904858i	$0.639977\pi$
$770$	7.92749	0.285687
$771$	−1.65551	−0.0596217
$772$	68.0007	2.44740
$773$	−35.3954	−1.27308	−0.636542	−	0.771242i	$-0.719636\pi$
$773$	−35.3954	−1.27308	−0.636542	+	0.771242i	$0.719636\pi$
$774$	17.3668	0.624237
$775$	−51.0921	−1.83528
$776$	16.5421	0.593828
$777$	0.157462	0.00564892
$778$	−19.8773	−0.712634
$779$	−14.2524	−0.510646
$780$	52.9652	1.89646
$781$	−68.8465	−2.46352
$782$	40.0642	1.43269
$783$	−3.44243	−0.123022
$784$	15.9141	0.568362
$785$	12.4501	0.444362
$786$	18.7432	0.668547
$787$	8.17427	0.291381	0.145691	−	0.989330i	$-0.453460\pi$
$787$	8.17427	0.291381	0.145691	+	0.989330i	$0.453460\pi$
$788$	−22.3467	−0.796068
$789$	13.7969	0.491181
$790$	−107.716	−3.83235
$791$	0.452192	0.0160781
$792$	7.46492	0.265254
$793$	−33.2922	−1.18224
$794$	−63.7826	−2.26356
$795$	39.7768	1.41074
$796$	12.6161	0.447166
$797$	−1.26503	−0.0448098	−0.0224049	−	0.999749i	$-0.507132\pi$
$797$	−1.26503	−0.0448098	−0.0224049	+	0.999749i	$0.507132\pi$
$798$	−1.05381	−0.0373043
$799$	−12.6755	−0.448428
$800$	51.3400	1.81514
$801$	−5.12607	−0.181121
$802$	−71.4584	−2.52328
$803$	39.4745	1.39303
$804$	18.1241	0.639186
$805$	−3.15139	−0.111072
$806$	−97.0828	−3.41959
$807$	2.37746	0.0836906
$808$	22.0893	0.777098
$809$	−43.0690	−1.51423	−0.757113	−	0.653284i	$-0.773391\pi$
$809$	−43.0690	−1.51423	−0.757113	+	0.653284i	$0.773391\pi$
$810$	−7.35809	−0.258537
$811$	−21.0119	−0.737829	−0.368914	−	0.929463i	$-0.620270\pi$
$811$	−21.0119	−0.737829	−0.368914	+	0.929463i	$0.620270\pi$
$812$	1.83503	0.0643969
$813$	−3.47333	−0.121815
$814$	−9.01916	−0.316121
$815$	−50.7172	−1.77655
$816$	9.26879	0.324472
$817$	19.5569	0.684208
$818$	59.4918	2.08008
$819$	−1.18038	−0.0412458
$820$	53.0481	1.85252
$821$	−39.9137	−1.39300	−0.696498	−	0.717559i	$-0.745260\pi$
$821$	−39.9137	−1.39300	−0.696498	+	0.717559i	$0.745260\pi$
$822$	−18.3042	−0.638431
$823$	−40.1020	−1.39787	−0.698934	−	0.715186i	$-0.746342\pi$
$823$	−40.1020	−1.39787	−0.698934	+	0.715186i	$0.746342\pi$
$824$	−23.3216	−0.812445
$825$	35.5815	1.23879
$826$	−4.31212	−0.150038
$827$	−12.4405	−0.432599	−0.216299	−	0.976327i	$-0.569399\pi$
$827$	−12.4405	−0.432599	−0.216299	+	0.976327i	$0.569399\pi$
$828$	−12.1376	−0.421811
$829$	−37.5224	−1.30321	−0.651603	−	0.758560i	$-0.725903\pi$
$829$	−37.5224	−1.30321	−0.651603	+	0.758560i	$0.725903\pi$
$830$	116.881	4.05698
$831$	2.25803	0.0783301
$832$	70.7454	2.45266
$833$	−28.2092	−0.977389
$834$	−4.25924	−0.147485
$835$	41.4205	1.43341
$836$	34.3833	1.18917
$837$	7.68267	0.265552
$838$	50.9200	1.75900
$839$	−16.9559	−0.585381	−0.292691	−	0.956207i	$-0.594551\pi$
$839$	−16.9559	−0.585381	−0.292691	+	0.956207i	$0.594551\pi$
$840$	0.958959	0.0330872
$841$	−17.1497	−0.591368
$842$	42.2556	1.45622
$843$	0.502713	0.0173144
$844$	21.1398	0.727663
$845$	72.9108	2.50821
$846$	6.74135	0.231773
$847$	3.54935	0.121957
$848$	26.6483	0.915106
$849$	−21.6234	−0.742114
$850$	−58.1102	−1.99316
$851$	3.58535	0.122904
$852$	−34.0634	−1.16699
$853$	7.61916	0.260875	0.130438	−	0.991457i	$-0.458362\pi$
$853$	7.61916	0.260875	0.130438	+	0.991457i	$0.458362\pi$
$854$	−2.46543	−0.0843654
$855$	−8.28599	−0.283375
$856$	4.53564	0.155025
$857$	−39.0722	−1.33468	−0.667341	−	0.744753i	$-0.732567\pi$
$857$	−39.0722	−1.33468	−0.667341	+	0.744753i	$0.732567\pi$
$858$	67.6102	2.30817
$859$	19.9870	0.681949	0.340974	−	0.940073i	$-0.389243\pi$
$859$	19.9870	0.681949	0.340974	+	0.940073i	$0.389243\pi$
$860$	−72.7915	−2.48217
$861$	−1.18223	−0.0402902
$862$	−75.1467	−2.55951
$863$	24.0312	0.818032	0.409016	−	0.912527i	$-0.365872\pi$
$863$	24.0312	0.818032	0.409016	+	0.912527i	$0.365872\pi$
$864$	−7.71995	−0.262638
$865$	−44.5177	−1.51365
$866$	25.2904	0.859402
$867$	0.570276	0.0193676
$868$	−4.09534	−0.139005
$869$	−78.3242	−2.65697
$870$	25.3297	0.858757
$871$	40.1329	1.35985
$872$	4.07276	0.137921
$873$	−11.8563	−0.401274
$874$	−23.9948	−0.811636
$875$	1.13428	0.0383457
$876$	19.5309	0.659889
$877$	−53.1210	−1.79377	−0.896884	−	0.442266i	$-0.854175\pi$
$877$	−53.1210	−1.79377	−0.896884	+	0.442266i	$0.854175\pi$
$878$	−79.9828	−2.69929
$879$	−18.7307	−0.631770
$880$	41.7598	1.40772
$881$	−22.0782	−0.743834	−0.371917	−	0.928266i	$-0.621299\pi$
$881$	−22.0782	−0.743834	−0.371917	+	0.928266i	$0.621299\pi$
$882$	15.0028	0.505169
$883$	34.6218	1.16512	0.582559	−	0.812789i	$-0.302052\pi$
$883$	34.6218	1.16512	0.582559	+	0.812789i	$0.302052\pi$
$884$	−62.8981	−2.11549
$885$	−33.9058	−1.13973
$886$	−11.3353	−0.380816
$887$	−19.0942	−0.641121	−0.320561	−	0.947228i	$-0.603871\pi$
$887$	−19.0942	−0.641121	−0.320561	+	0.947228i	$0.603871\pi$
$888$	−1.09101	−0.0366120
$889$	−1.76261	−0.0591162
$890$	37.7180	1.26431
$891$	−5.35035	−0.179244
$892$	−66.0403	−2.21119
$893$	7.59149	0.254039
$894$	7.15485	0.239294
$895$	18.2963	0.611577
$896$	2.12993	0.0711559
$897$	−26.8768	−0.897391
$898$	−45.4428	−1.51644
$899$	−26.4471	−0.882059
$900$	17.6048	0.586825
$901$	−47.2364	−1.57367
$902$	67.7160	2.25470
$903$	1.62223	0.0539844
$904$	−3.13312	−0.104206
$905$	17.5060	0.581919
$906$	−28.8196	−0.957467
$907$	−41.6275	−1.38222	−0.691109	−	0.722751i	$-0.742877\pi$
$907$	−41.6275	−1.38222	−0.691109	+	0.722751i	$0.742877\pi$
$908$	67.3674	2.23567
$909$	−15.8321	−0.525118
$910$	8.68534	0.287916
$911$	−21.5111	−0.712693	−0.356347	−	0.934354i	$-0.615978\pi$
$911$	−21.5111	−0.712693	−0.356347	+	0.934354i	$0.615978\pi$
$912$	−5.55116	−0.183817
$913$	84.9884	2.81271
$914$	68.3757	2.26167
$915$	−19.3855	−0.640865
$916$	−23.4269	−0.774045
$917$	1.75080	0.0578163
$918$	8.73799	0.288397
$919$	31.8930	1.05205	0.526027	−	0.850468i	$-0.323681\pi$
$919$	31.8930	1.05205	0.526027	+	0.850468i	$0.323681\pi$
$920$	21.8351	0.719883
$921$	−4.73274	−0.155949
$922$	−30.4216	−1.00188
$923$	−75.4281	−2.48275
$924$	2.85207	0.0938261
$925$	−5.20030	−0.170985
$926$	−11.8950	−0.390894
$927$	16.7153	0.549003
$928$	26.5754	0.872381
$929$	27.5226	0.902986	0.451493	−	0.892275i	$-0.350892\pi$
$929$	27.5226	0.902986	0.451493	+	0.892275i	$0.350892\pi$
$930$	−56.5298	−1.85368
$931$	16.8947	0.553702
$932$	63.3326	2.07453
$933$	21.6404	0.708474
$934$	23.7416	0.776848
$935$	−74.0229	−2.42081
$936$	8.17855	0.267324
$937$	−25.9600	−0.848076	−0.424038	−	0.905644i	$-0.639388\pi$
$937$	−25.9600	−0.848076	−0.424038	+	0.905644i	$0.639388\pi$
$938$	2.97202	0.0970399
$939$	−24.4364	−0.797453
$940$	−28.2558	−0.921604
$941$	11.4091	0.371925	0.185963	−	0.982557i	$-0.440460\pi$
$941$	11.4091	0.371925	0.185963	+	0.982557i	$0.440460\pi$
$942$	7.86321	0.256197
$943$	−26.9189	−0.876599
$944$	−22.7150	−0.739312
$945$	−0.687317	−0.0223584
$946$	−92.9185	−3.02104
$947$	41.0600	1.33427	0.667136	−	0.744936i	$-0.267520\pi$
$947$	41.0600	1.33427	0.667136	+	0.744936i	$0.267520\pi$
$948$	−38.7527	−1.25863
$949$	43.2482	1.40390
$950$	34.8027	1.12915
$951$	−2.93779	−0.0952643
$952$	−1.13880	−0.0369087
$953$	−1.67519	−0.0542647	−0.0271324	−	0.999632i	$-0.508638\pi$
$953$	−1.67519	−0.0542647	−0.0271324	+	0.999632i	$0.508638\pi$
$954$	25.1222	0.813362
$955$	−41.2346	−1.33432
$956$	−2.64721	−0.0856170
$957$	18.4182	0.595377
$958$	−40.6578	−1.31359
$959$	−1.70979	−0.0552119
$960$	41.1940	1.32953
$961$	28.0235	0.903983
$962$	−9.88137	−0.318588
$963$	−3.25084	−0.104757
$964$	−14.7480	−0.475002
$965$	87.6785	2.82247
$966$	−1.99035	−0.0640385
$967$	−5.42710	−0.174524	−0.0872618	−	0.996185i	$-0.527812\pi$
$967$	−5.42710	−0.174524	−0.0872618	+	0.996185i	$0.527812\pi$
$968$	−24.5925	−0.790434
$969$	9.83991	0.316103
$970$	87.2395	2.80109
$971$	20.7489	0.665865	0.332932	−	0.942951i	$-0.391962\pi$
$971$	20.7489	0.665865	0.332932	+	0.942951i	$0.391962\pi$
$972$	−2.64721	−0.0849094
$973$	−0.397854	−0.0127546
$974$	−66.2678	−2.12336
$975$	38.9830	1.24845
$976$	−12.9872	−0.415711
$977$	−4.41802	−0.141345	−0.0706725	−	0.997500i	$-0.522515\pi$
$977$	−4.41802	−0.141345	−0.0706725	+	0.997500i	$0.522515\pi$
$978$	−32.0319	−1.02427
$979$	27.4263	0.876547
$980$	−62.8829	−2.00872
$981$	−2.91908	−0.0931991
$982$	−68.8554	−2.19727
$983$	−10.9017	−0.347710	−0.173855	−	0.984771i	$-0.555622\pi$
$983$	−10.9017	−0.347710	−0.173855	+	0.984771i	$0.555622\pi$
$984$	8.19135	0.261131
$985$	−28.8133	−0.918068
$986$	−30.0799	−0.957940
$987$	0.629709	0.0200438
$988$	37.6702	1.19845
$989$	36.9375	1.17455
$990$	39.3684	1.25121
$991$	−2.15506	−0.0684576	−0.0342288	−	0.999414i	$-0.510897\pi$
$991$	−2.15506	−0.0684576	−0.0342288	+	0.999414i	$0.510897\pi$
$992$	−59.3099	−1.88309
$993$	13.2517	0.420530
$994$	−5.58579	−0.177170
$995$	16.2669	0.515696
$996$	42.0500	1.33241
$997$	36.3803	1.15217	0.576087	−	0.817388i	$-0.304579\pi$
$997$	36.3803	1.15217	0.576087	+	0.817388i	$0.304579\pi$
$998$	46.8615	1.48338
$999$	0.781965	0.0247403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.d.1.2	✓	6
3.2	odd	2		2151.2.a.e.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.d.1.2	✓	6	1.1	even	1	trivial
2151.2.a.e.1.5		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)

\(f(q)\)	\(=\)	\(q-2.15574 q^{2} -1.00000 q^{3} +2.64721 q^{4} +3.41325 q^{5} +2.15574 q^{6} +0.201367 q^{7} -1.39522 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15574 q^{2} -1.00000 q^{3} +2.64721 q^{4} +3.41325 q^{5} +2.15574 q^{6} +0.201367 q^{7} -1.39522 q^{8} +1.00000 q^{9} -7.35809 q^{10} -5.35035 q^{11} -2.64721 q^{12} -5.86183 q^{13} -0.434095 q^{14} -3.41325 q^{15} -2.28669 q^{16} +4.05336 q^{17} -2.15574 q^{18} -2.42759 q^{19} +9.03561 q^{20} -0.201367 q^{21} +11.5340 q^{22} -4.58506 q^{23} +1.39522 q^{24} +6.65030 q^{25} +12.6366 q^{26} -1.00000 q^{27} +0.533062 q^{28} +3.44243 q^{29} +7.35809 q^{30} -7.68267 q^{31} +7.71995 q^{32} +5.35035 q^{33} -8.73799 q^{34} +0.687317 q^{35} +2.64721 q^{36} -0.781965 q^{37} +5.23326 q^{38} +5.86183 q^{39} -4.76224 q^{40} +5.87100 q^{41} +0.434095 q^{42} -8.05607 q^{43} -14.1635 q^{44} +3.41325 q^{45} +9.88419 q^{46} -3.12717 q^{47} +2.28669 q^{48} -6.95945 q^{49} -14.3363 q^{50} -4.05336 q^{51} -15.5175 q^{52} -11.6536 q^{53} +2.15574 q^{54} -18.2621 q^{55} -0.280952 q^{56} +2.42759 q^{57} -7.42099 q^{58} +9.93358 q^{59} -9.03561 q^{60} +5.67948 q^{61} +16.5618 q^{62} +0.201367 q^{63} -12.0688 q^{64} -20.0079 q^{65} -11.5340 q^{66} -6.84647 q^{67} +10.7301 q^{68} +4.58506 q^{69} -1.48168 q^{70} +12.8677 q^{71} -1.39522 q^{72} -7.37793 q^{73} +1.68571 q^{74} -6.65030 q^{75} -6.42636 q^{76} -1.07739 q^{77} -12.6366 q^{78} +14.6391 q^{79} -7.80506 q^{80} +1.00000 q^{81} -12.6564 q^{82} -15.8846 q^{83} -0.533062 q^{84} +13.8351 q^{85} +17.3668 q^{86} -3.44243 q^{87} +7.46492 q^{88} -5.12607 q^{89} -7.35809 q^{90} -1.18038 q^{91} -12.1376 q^{92} +7.68267 q^{93} +6.74135 q^{94} -8.28599 q^{95} -7.71995 q^{96} -11.8563 q^{97} +15.0028 q^{98} -5.35035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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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