LMFDB - Embedded newform 361.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(1,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("361.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^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			$1.61803$ of defining polynomial
Character	$\chi$	$=$	361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} +0.381966 q^{3} +0.618034 q^{4} +3.23607 q^{5} +0.618034 q^{6} +3.00000 q^{7} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} +0.381966 q^{3} +0.618034 q^{4} +3.23607 q^{5} +0.618034 q^{6} +3.00000 q^{7} -2.23607 q^{8} -2.85410 q^{9} +5.23607 q^{10} -1.61803 q^{11} +0.236068 q^{12} -1.00000 q^{13} +4.85410 q^{14} +1.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} -4.61803 q^{18} +2.00000 q^{20} +1.14590 q^{21} -2.61803 q^{22} +5.38197 q^{23} -0.854102 q^{24} +5.47214 q^{25} -1.61803 q^{26} -2.23607 q^{27} +1.85410 q^{28} -3.61803 q^{29} +2.00000 q^{30} -8.85410 q^{31} -3.38197 q^{32} -0.618034 q^{33} +1.23607 q^{34} +9.70820 q^{35} -1.76393 q^{36} +8.85410 q^{37} -0.381966 q^{39} -7.23607 q^{40} -3.00000 q^{41} +1.85410 q^{42} -0.145898 q^{43} -1.00000 q^{44} -9.23607 q^{45} +8.70820 q^{46} +3.00000 q^{47} -1.85410 q^{48} +2.00000 q^{49} +8.85410 q^{50} +0.291796 q^{51} -0.618034 q^{52} -6.32624 q^{53} -3.61803 q^{54} -5.23607 q^{55} -6.70820 q^{56} -5.85410 q^{58} +0.326238 q^{59} +0.763932 q^{60} -10.2361 q^{61} -14.3262 q^{62} -8.56231 q^{63} +4.23607 q^{64} -3.23607 q^{65} -1.00000 q^{66} -7.00000 q^{67} +0.472136 q^{68} +2.05573 q^{69} +15.7082 q^{70} -7.47214 q^{71} +6.38197 q^{72} -2.70820 q^{73} +14.3262 q^{74} +2.09017 q^{75} -4.85410 q^{77} -0.618034 q^{78} +13.4164 q^{79} -15.7082 q^{80} +7.70820 q^{81} -4.85410 q^{82} +8.47214 q^{83} +0.708204 q^{84} +2.47214 q^{85} -0.236068 q^{86} -1.38197 q^{87} +3.61803 q^{88} -7.76393 q^{89} -14.9443 q^{90} -3.00000 q^{91} +3.32624 q^{92} -3.38197 q^{93} +4.85410 q^{94} -1.29180 q^{96} +13.8541 q^{97} +3.23607 q^{98} +4.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - q^{6} + 6 q^{7} + q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 - q^6 + 6 * q^7 + q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - q^{6} + 6 q^{7} + q^{9} + 6 q^{10} - q^{11} - 4 q^{12} - 2 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - 7 q^{18} + 4 q^{20} + 9 q^{21} - 3 q^{22} + 13 q^{23} + 5 q^{24} + 2 q^{25} - q^{26} - 3 q^{28} - 5 q^{29} + 4 q^{30} - 11 q^{31} - 9 q^{32} + q^{33} - 2 q^{34} + 6 q^{35} - 8 q^{36} + 11 q^{37} - 3 q^{39} - 10 q^{40} - 6 q^{41} - 3 q^{42} - 7 q^{43} - 2 q^{44} - 14 q^{45} + 4 q^{46} + 6 q^{47} + 3 q^{48} + 4 q^{49} + 11 q^{50} + 14 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 6 q^{55} - 5 q^{58} - 15 q^{59} + 6 q^{60} - 16 q^{61} - 13 q^{62} + 3 q^{63} + 4 q^{64} - 2 q^{65} - 2 q^{66} - 14 q^{67} - 8 q^{68} + 22 q^{69} + 18 q^{70} - 6 q^{71} + 15 q^{72} + 8 q^{73} + 13 q^{74} - 7 q^{75} - 3 q^{77} + q^{78} - 18 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 12 q^{84} - 4 q^{85} + 4 q^{86} - 5 q^{87} + 5 q^{88} - 20 q^{89} - 12 q^{90} - 6 q^{91} - 9 q^{92} - 9 q^{93} + 3 q^{94} - 16 q^{96} + 21 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 - q^6 + 6 * q^7 + q^9 + 6 * q^10 - q^11 - 4 * q^12 - 2 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - 7 * q^18 + 4 * q^20 + 9 * q^21 - 3 * q^22 + 13 * q^23 + 5 * q^24 + 2 * q^25 - q^26 - 3 * q^28 - 5 * q^29 + 4 * q^30 - 11 * q^31 - 9 * q^32 + q^33 - 2 * q^34 + 6 * q^35 - 8 * q^36 + 11 * q^37 - 3 * q^39 - 10 * q^40 - 6 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 14 * q^45 + 4 * q^46 + 6 * q^47 + 3 * q^48 + 4 * q^49 + 11 * q^50 + 14 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 6 * q^55 - 5 * q^58 - 15 * q^59 + 6 * q^60 - 16 * q^61 - 13 * q^62 + 3 * q^63 + 4 * q^64 - 2 * q^65 - 2 * q^66 - 14 * q^67 - 8 * q^68 + 22 * q^69 + 18 * q^70 - 6 * q^71 + 15 * q^72 + 8 * q^73 + 13 * q^74 - 7 * q^75 - 3 * q^77 + q^78 - 18 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 12 * q^84 - 4 * q^85 + 4 * q^86 - 5 * q^87 + 5 * q^88 - 20 * q^89 - 12 * q^90 - 6 * q^91 - 9 * q^92 - 9 * q^93 + 3 * q^94 - 16 * q^96 + 21 * q^97 + 2 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	0.618034	0.309017
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	0.618034	0.252311
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−2.23607	−0.790569
$9$	−2.85410	−0.951367
$10$	5.23607	1.65579
$11$	−1.61803	−0.487856	−0.243928	−	0.969793i	$-0.578436\pi$
$11$	−1.61803	−0.487856	−0.243928	+	0.969793i	$0.578436\pi$
$12$	0.236068	0.0681470
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	4.85410	1.29731
$15$	1.23607	0.319151
$16$	−4.85410	−1.21353
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	−4.61803	−1.08848
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	1.14590	0.250055
$22$	−2.61803	−0.558167
$23$	5.38197	1.12222	0.561109	−	0.827742i	$-0.310375\pi$
$23$	5.38197	1.12222	0.561109	+	0.827742i	$0.310375\pi$
$24$	−0.854102	−0.174343
$25$	5.47214	1.09443
$26$	−1.61803	−0.317323
$27$	−2.23607	−0.430331
$28$	1.85410	0.350392
$29$	−3.61803	−0.671852	−0.335926	−	0.941888i	$-0.609049\pi$
$29$	−3.61803	−0.671852	−0.335926	+	0.941888i	$0.609049\pi$
$30$	2.00000	0.365148
$31$	−8.85410	−1.59024	−0.795122	−	0.606450i	$-0.792593\pi$
$31$	−8.85410	−1.59024	−0.795122	+	0.606450i	$0.792593\pi$
$32$	−3.38197	−0.597853
$33$	−0.618034	−0.107586
$34$	1.23607	0.211984
$35$	9.70820	1.64099
$36$	−1.76393	−0.293989
$37$	8.85410	1.45561	0.727803	−	0.685787i	$-0.240542\pi$
$37$	8.85410	1.45561	0.727803	+	0.685787i	$0.240542\pi$
$38$	0	0
$39$	−0.381966	−0.0611635
$40$	−7.23607	−1.14412
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	1.85410	0.286094
$43$	−0.145898	−0.0222492	−0.0111246	−	0.999938i	$-0.503541\pi$
$43$	−0.145898	−0.0222492	−0.0111246	+	0.999938i	$0.503541\pi$
$44$	−1.00000	−0.150756
$45$	−9.23607	−1.37683
$46$	8.70820	1.28395
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.85410	−0.267617
$49$	2.00000	0.285714
$50$	8.85410	1.25216
$51$	0.291796	0.0408596
$52$	−0.618034	−0.0857059
$53$	−6.32624	−0.868976	−0.434488	−	0.900678i	$-0.643071\pi$
$53$	−6.32624	−0.868976	−0.434488	+	0.900678i	$0.643071\pi$
$54$	−3.61803	−0.492352
$55$	−5.23607	−0.706031
$56$	−6.70820	−0.896421
$57$	0	0
$58$	−5.85410	−0.768681
$59$	0.326238	0.0424726	0.0212363	−	0.999774i	$-0.493240\pi$
$59$	0.326238	0.0424726	0.0212363	+	0.999774i	$0.493240\pi$
$60$	0.763932	0.0986232
$61$	−10.2361	−1.31059	−0.655297	−	0.755371i	$-0.727457\pi$
$61$	−10.2361	−1.31059	−0.655297	+	0.755371i	$0.727457\pi$
$62$	−14.3262	−1.81943
$63$	−8.56231	−1.07875
$64$	4.23607	0.529508
$65$	−3.23607	−0.401385
$66$	−1.00000	−0.123091
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	0.472136	0.0572549
$69$	2.05573	0.247481
$70$	15.7082	1.87749
$71$	−7.47214	−0.886779	−0.443390	−	0.896329i	$-0.646224\pi$
$71$	−7.47214	−0.886779	−0.443390	+	0.896329i	$0.646224\pi$
$72$	6.38197	0.752122
$73$	−2.70820	−0.316971	−0.158486	−	0.987361i	$-0.550661\pi$
$73$	−2.70820	−0.316971	−0.158486	+	0.987361i	$0.550661\pi$
$74$	14.3262	1.66539
$75$	2.09017	0.241352
$76$	0	0
$77$	−4.85410	−0.553176
$78$	−0.618034	−0.0699786
$79$	13.4164	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$79$	13.4164	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$80$	−15.7082	−1.75623
$81$	7.70820	0.856467
$82$	−4.85410	−0.536046
$83$	8.47214	0.929938	0.464969	−	0.885327i	$-0.346066\pi$
$83$	8.47214	0.929938	0.464969	+	0.885327i	$0.346066\pi$
$84$	0.708204	0.0772714
$85$	2.47214	0.268141
$86$	−0.236068	−0.0254559
$87$	−1.38197	−0.148162
$88$	3.61803	0.385684
$89$	−7.76393	−0.822975	−0.411488	−	0.911415i	$-0.634991\pi$
$89$	−7.76393	−0.822975	−0.411488	+	0.911415i	$0.634991\pi$
$90$	−14.9443	−1.57526
$91$	−3.00000	−0.314485
$92$	3.32624	0.346784
$93$	−3.38197	−0.350694
$94$	4.85410	0.500662
$95$	0	0
$96$	−1.29180	−0.131843
$97$	13.8541	1.40667	0.703335	−	0.710858i	$-0.251693\pi$
$97$	13.8541	1.40667	0.703335	+	0.710858i	$0.251693\pi$
$98$	3.23607	0.326892
$99$	4.61803	0.464130
$100$	3.38197	0.338197
$101$	−9.18034	−0.913478	−0.456739	−	0.889601i	$-0.650983\pi$
$101$	−9.18034	−0.913478	−0.456739	+	0.889601i	$0.650983\pi$
$102$	0.472136	0.0467484
$103$	14.3262	1.41161	0.705803	−	0.708408i	$-0.250586\pi$
$103$	14.3262	1.41161	0.705803	+	0.708408i	$0.250586\pi$
$104$	2.23607	0.219265
$105$	3.70820	0.361884
$106$	−10.2361	−0.994215
$107$	16.4164	1.58703	0.793517	−	0.608548i	$-0.208248\pi$
$107$	16.4164	1.58703	0.793517	+	0.608548i	$0.208248\pi$
$108$	−1.38197	−0.132980
$109$	−3.29180	−0.315297	−0.157648	−	0.987495i	$-0.550391\pi$
$109$	−3.29180	−0.315297	−0.157648	+	0.987495i	$0.550391\pi$
$110$	−8.47214	−0.807786
$111$	3.38197	0.321002
$112$	−14.5623	−1.37601
$113$	6.76393	0.636297	0.318149	−	0.948041i	$-0.396939\pi$
$113$	6.76393	0.636297	0.318149	+	0.948041i	$0.396939\pi$
$114$	0	0
$115$	17.4164	1.62409
$116$	−2.23607	−0.207614
$117$	2.85410	0.263862
$118$	0.527864	0.0485938
$119$	2.29180	0.210089
$120$	−2.76393	−0.252311
$121$	−8.38197	−0.761997
$122$	−16.5623	−1.49948
$123$	−1.14590	−0.103322
$124$	−5.47214	−0.491412
$125$	1.52786	0.136656
$126$	−13.8541	−1.23422
$127$	5.76393	0.511466	0.255733	−	0.966747i	$-0.417683\pi$
$127$	5.76393	0.511466	0.255733	+	0.966747i	$0.417683\pi$
$128$	13.6180	1.20368
$129$	−0.0557281	−0.00490658
$130$	−5.23607	−0.459234
$131$	15.0902	1.31843	0.659217	−	0.751953i	$-0.270888\pi$
$131$	15.0902	1.31843	0.659217	+	0.751953i	$0.270888\pi$
$132$	−0.381966	−0.0332459
$133$	0	0
$134$	−11.3262	−0.978438
$135$	−7.23607	−0.622782
$136$	−1.70820	−0.146477
$137$	7.47214	0.638388	0.319194	−	0.947689i	$-0.396588\pi$
$137$	7.47214	0.638388	0.319194	+	0.947689i	$0.396588\pi$
$138$	3.32624	0.283148
$139$	14.7984	1.25518	0.627591	−	0.778543i	$-0.284041\pi$
$139$	14.7984	1.25518	0.627591	+	0.778543i	$0.284041\pi$
$140$	6.00000	0.507093
$141$	1.14590	0.0965020
$142$	−12.0902	−1.01458
$143$	1.61803	0.135307
$144$	13.8541	1.15451
$145$	−11.7082	−0.972313
$146$	−4.38197	−0.362654
$147$	0.763932	0.0630081
$148$	5.47214	0.449807
$149$	−1.90983	−0.156459	−0.0782297	−	0.996935i	$-0.524927\pi$
$149$	−1.90983	−0.156459	−0.0782297	+	0.996935i	$0.524927\pi$
$150$	3.38197	0.276136
$151$	−21.0902	−1.71629	−0.858147	−	0.513404i	$-0.828384\pi$
$151$	−21.0902	−1.71629	−0.858147	+	0.513404i	$0.828384\pi$
$152$	0	0
$153$	−2.18034	−0.176270
$154$	−7.85410	−0.632902
$155$	−28.6525	−2.30142
$156$	−0.236068	−0.0189006
$157$	−17.8541	−1.42491	−0.712456	−	0.701717i	$-0.752417\pi$
$157$	−17.8541	−1.42491	−0.712456	+	0.701717i	$0.752417\pi$
$158$	21.7082	1.72701
$159$	−2.41641	−0.191634
$160$	−10.9443	−0.865221
$161$	16.1459	1.27248
$162$	12.4721	0.979904
$163$	1.76393	0.138162	0.0690809	−	0.997611i	$-0.477993\pi$
$163$	1.76393	0.138162	0.0690809	+	0.997611i	$0.477993\pi$
$164$	−1.85410	−0.144781
$165$	−2.00000	−0.155700
$166$	13.7082	1.06396
$167$	20.2361	1.56591	0.782957	−	0.622076i	$-0.213710\pi$
$167$	20.2361	1.56591	0.782957	+	0.622076i	$0.213710\pi$
$168$	−2.56231	−0.197686
$169$	−12.0000	−0.923077
$170$	4.00000	0.306786
$171$	0	0
$172$	−0.0901699	−0.00687539
$173$	−0.472136	−0.0358958	−0.0179479	−	0.999839i	$-0.505713\pi$
$173$	−0.472136	−0.0358958	−0.0179479	+	0.999839i	$0.505713\pi$
$174$	−2.23607	−0.169516
$175$	16.4164	1.24096
$176$	7.85410	0.592025
$177$	0.124612	0.00936640
$178$	−12.5623	−0.941585
$179$	12.2361	0.914567	0.457283	−	0.889321i	$-0.348823\pi$
$179$	12.2361	0.914567	0.457283	+	0.889321i	$0.348823\pi$
$180$	−5.70820	−0.425464
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−4.85410	−0.359810
$183$	−3.90983	−0.289023
$184$	−12.0344	−0.887191
$185$	28.6525	2.10657
$186$	−5.47214	−0.401236
$187$	−1.23607	−0.0903902
$188$	1.85410	0.135224
$189$	−6.70820	−0.487950
$190$	0	0
$191$	14.2361	1.03009	0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361	1.03009	0.515043	+	0.857164i	$0.327776\pi$
$192$	1.61803	0.116772
$193$	5.05573	0.363919	0.181960	−	0.983306i	$-0.441756\pi$
$193$	5.05573	0.363919	0.181960	+	0.983306i	$0.441756\pi$
$194$	22.4164	1.60940
$195$	−1.23607	−0.0885167
$196$	1.23607	0.0882906
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	7.47214	0.531022
$199$	−13.4164	−0.951064	−0.475532	−	0.879698i	$-0.657744\pi$
$199$	−13.4164	−0.951064	−0.475532	+	0.879698i	$0.657744\pi$
$200$	−12.2361	−0.865221
$201$	−2.67376	−0.188593
$202$	−14.8541	−1.04513
$203$	−10.8541	−0.761809
$204$	0.180340	0.0126263
$205$	−9.70820	−0.678050
$206$	23.1803	1.61505
$207$	−15.3607	−1.06764
$208$	4.85410	0.336571
$209$	0	0
$210$	6.00000	0.414039
$211$	−3.85410	−0.265327	−0.132664	−	0.991161i	$-0.542353\pi$
$211$	−3.85410	−0.265327	−0.132664	+	0.991161i	$0.542353\pi$
$212$	−3.90983	−0.268528
$213$	−2.85410	−0.195560
$214$	26.5623	1.81576
$215$	−0.472136	−0.0321994
$216$	5.00000	0.340207
$217$	−26.5623	−1.80317
$218$	−5.32624	−0.360738
$219$	−1.03444	−0.0699011
$220$	−3.23607	−0.218176
$221$	−0.763932	−0.0513876
$222$	5.47214	0.367266
$223$	−11.6525	−0.780307	−0.390154	−	0.920750i	$-0.627578\pi$
$223$	−11.6525	−0.780307	−0.390154	+	0.920750i	$0.627578\pi$
$224$	−10.1459	−0.677901
$225$	−15.6180	−1.04120
$226$	10.9443	0.728002
$227$	16.4164	1.08960	0.544798	−	0.838568i	$-0.316606\pi$
$227$	16.4164	1.08960	0.544798	+	0.838568i	$0.316606\pi$
$228$	0	0
$229$	−13.6180	−0.899905	−0.449953	−	0.893052i	$-0.648559\pi$
$229$	−13.6180	−0.899905	−0.449953	+	0.893052i	$0.648559\pi$
$230$	28.1803	1.85816
$231$	−1.85410	−0.121991
$232$	8.09017	0.531146
$233$	4.52786	0.296630	0.148315	−	0.988940i	$-0.452615\pi$
$233$	4.52786	0.296630	0.148315	+	0.988940i	$0.452615\pi$
$234$	4.61803	0.301890
$235$	9.70820	0.633293
$236$	0.201626	0.0131247
$237$	5.12461	0.332879
$238$	3.70820	0.240367
$239$	−0.326238	−0.0211026	−0.0105513	−	0.999944i	$-0.503359\pi$
$239$	−0.326238	−0.0211026	−0.0105513	+	0.999944i	$0.503359\pi$
$240$	−6.00000	−0.387298
$241$	3.18034	0.204864	0.102432	−	0.994740i	$-0.467338\pi$
$241$	3.18034	0.204864	0.102432	+	0.994740i	$0.467338\pi$
$242$	−13.5623	−0.871818
$243$	9.65248	0.619207
$244$	−6.32624	−0.404996
$245$	6.47214	0.413490
$246$	−1.85410	−0.118213
$247$	0	0
$248$	19.7984	1.25720
$249$	3.23607	0.205077
$250$	2.47214	0.156352
$251$	−25.3607	−1.60075	−0.800376	−	0.599498i	$-0.795367\pi$
$251$	−25.3607	−1.60075	−0.800376	+	0.599498i	$0.795367\pi$
$252$	−5.29180	−0.333352
$253$	−8.70820	−0.547480
$254$	9.32624	0.585180
$255$	0.944272	0.0591326
$256$	13.5623	0.847644
$257$	20.3607	1.27006	0.635032	−	0.772486i	$-0.280987\pi$
$257$	20.3607	1.27006	0.635032	+	0.772486i	$0.280987\pi$
$258$	−0.0901699	−0.00561374
$259$	26.5623	1.65050
$260$	−2.00000	−0.124035
$261$	10.3262	0.639178
$262$	24.4164	1.50845
$263$	−14.9443	−0.921503	−0.460752	−	0.887529i	$-0.652420\pi$
$263$	−14.9443	−0.921503	−0.460752	+	0.887529i	$0.652420\pi$
$264$	1.38197	0.0850541
$265$	−20.4721	−1.25759
$266$	0	0
$267$	−2.96556	−0.181489
$268$	−4.32624	−0.264267
$269$	30.3262	1.84902	0.924512	−	0.381154i	$-0.124473\pi$
$269$	30.3262	1.84902	0.924512	+	0.381154i	$0.124473\pi$
$270$	−11.7082	−0.712539
$271$	1.14590	0.0696083	0.0348042	−	0.999394i	$-0.488919\pi$
$271$	1.14590	0.0696083	0.0348042	+	0.999394i	$0.488919\pi$
$272$	−3.70820	−0.224843
$273$	−1.14590	−0.0693529
$274$	12.0902	0.730394
$275$	−8.85410	−0.533922
$276$	1.27051	0.0764757
$277$	11.4164	0.685945	0.342973	−	0.939345i	$-0.388566\pi$
$277$	11.4164	0.685945	0.342973	+	0.939345i	$0.388566\pi$
$278$	23.9443	1.43608
$279$	25.2705	1.51291
$280$	−21.7082	−1.29731
$281$	−29.5066	−1.76021	−0.880107	−	0.474775i	$-0.842530\pi$
$281$	−29.5066	−1.76021	−0.880107	+	0.474775i	$0.842530\pi$
$282$	1.85410	0.110410
$283$	26.0344	1.54759	0.773793	−	0.633438i	$-0.218357\pi$
$283$	26.0344	1.54759	0.773793	+	0.633438i	$0.218357\pi$
$284$	−4.61803	−0.274030
$285$	0	0
$286$	2.61803	0.154808
$287$	−9.00000	−0.531253
$288$	9.65248	0.568778
$289$	−16.4164	−0.965671
$290$	−18.9443	−1.11245
$291$	5.29180	0.310211
$292$	−1.67376	−0.0979495
$293$	−10.1459	−0.592730	−0.296365	−	0.955075i	$-0.595774\pi$
$293$	−10.1459	−0.592730	−0.296365	+	0.955075i	$0.595774\pi$
$294$	1.23607	0.0720889
$295$	1.05573	0.0614669
$296$	−19.7984	−1.15076
$297$	3.61803	0.209940
$298$	−3.09017	−0.179009
$299$	−5.38197	−0.311247
$300$	1.29180	0.0745819
$301$	−0.437694	−0.0252283
$302$	−34.1246	−1.96365
$303$	−3.50658	−0.201448
$304$	0	0
$305$	−33.1246	−1.89671
$306$	−3.52786	−0.201675
$307$	−17.3262	−0.988861	−0.494430	−	0.869217i	$-0.664623\pi$
$307$	−17.3262	−0.988861	−0.494430	+	0.869217i	$0.664623\pi$
$308$	−3.00000	−0.170941
$309$	5.47214	0.311299
$310$	−46.3607	−2.63311
$311$	12.6525	0.717456	0.358728	−	0.933442i	$-0.383211\pi$
$311$	12.6525	0.717456	0.358728	+	0.933442i	$0.383211\pi$
$312$	0.854102	0.0483540
$313$	−11.3262	−0.640197	−0.320098	−	0.947384i	$-0.603716\pi$
$313$	−11.3262	−0.640197	−0.320098	+	0.947384i	$0.603716\pi$
$314$	−28.8885	−1.63027
$315$	−27.7082	−1.56118
$316$	8.29180	0.466450
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−3.90983	−0.219252
$319$	5.85410	0.327767
$320$	13.7082	0.766312
$321$	6.27051	0.349986
$322$	26.1246	1.45587
$323$	0	0
$324$	4.76393	0.264663
$325$	−5.47214	−0.303539
$326$	2.85410	0.158074
$327$	−1.25735	−0.0695318
$328$	6.70820	0.370399
$329$	9.00000	0.496186
$330$	−3.23607	−0.178140
$331$	10.9443	0.601552	0.300776	−	0.953695i	$-0.402754\pi$
$331$	10.9443	0.601552	0.300776	+	0.953695i	$0.402754\pi$
$332$	5.23607	0.287367
$333$	−25.2705	−1.38482
$334$	32.7426	1.79160
$335$	−22.6525	−1.23764
$336$	−5.56231	−0.303449
$337$	−17.1246	−0.932837	−0.466419	−	0.884564i	$-0.654456\pi$
$337$	−17.1246	−0.932837	−0.466419	+	0.884564i	$0.654456\pi$
$338$	−19.4164	−1.05611
$339$	2.58359	0.140321
$340$	1.52786	0.0828601
$341$	14.3262	0.775809
$342$	0	0
$343$	−15.0000	−0.809924
$344$	0.326238	0.0175896
$345$	6.65248	0.358157
$346$	−0.763932	−0.0410692
$347$	−25.4164	−1.36442	−0.682212	−	0.731154i	$-0.738982\pi$
$347$	−25.4164	−1.36442	−0.682212	+	0.731154i	$0.738982\pi$
$348$	−0.854102	−0.0457847
$349$	−20.9787	−1.12296	−0.561482	−	0.827489i	$-0.689769\pi$
$349$	−20.9787	−1.12296	−0.561482	+	0.827489i	$0.689769\pi$
$350$	26.5623	1.41981
$351$	2.23607	0.119352
$352$	5.47214	0.291666
$353$	24.4508	1.30139	0.650694	−	0.759340i	$-0.274478\pi$
$353$	24.4508	1.30139	0.650694	+	0.759340i	$0.274478\pi$
$354$	0.201626	0.0107163
$355$	−24.1803	−1.28336
$356$	−4.79837	−0.254313
$357$	0.875388	0.0463305
$358$	19.7984	1.04638
$359$	7.03444	0.371264	0.185632	−	0.982619i	$-0.440567\pi$
$359$	7.03444	0.371264	0.185632	+	0.982619i	$0.440567\pi$
$360$	20.6525	1.08848
$361$	0	0
$362$	19.4164	1.02050
$363$	−3.20163	−0.168042
$364$	−1.85410	−0.0971813
$365$	−8.76393	−0.458725
$366$	−6.32624	−0.330678
$367$	−15.9443	−0.832284	−0.416142	−	0.909300i	$-0.636618\pi$
$367$	−15.9443	−0.832284	−0.416142	+	0.909300i	$0.636618\pi$
$368$	−26.1246	−1.36184
$369$	8.56231	0.445736
$370$	46.3607	2.41018
$371$	−18.9787	−0.985326
$372$	−2.09017	−0.108370
$373$	−5.47214	−0.283336	−0.141668	−	0.989914i	$-0.545247\pi$
$373$	−5.47214	−0.283336	−0.141668	+	0.989914i	$0.545247\pi$
$374$	−2.00000	−0.103418
$375$	0.583592	0.0301366
$376$	−6.70820	−0.345949
$377$	3.61803	0.186338
$378$	−10.8541	−0.558275
$379$	−15.1246	−0.776899	−0.388450	−	0.921470i	$-0.626989\pi$
$379$	−15.1246	−0.776899	−0.388450	+	0.921470i	$0.626989\pi$
$380$	0	0
$381$	2.20163	0.112793
$382$	23.0344	1.17854
$383$	0.381966	0.0195176	0.00975878	−	0.999952i	$-0.496894\pi$
$383$	0.381966	0.0195176	0.00975878	+	0.999952i	$0.496894\pi$
$384$	5.20163	0.265444
$385$	−15.7082	−0.800564
$386$	8.18034	0.416368
$387$	0.416408	0.0211672
$388$	8.56231	0.434685
$389$	9.27051	0.470034	0.235017	−	0.971991i	$-0.424485\pi$
$389$	9.27051	0.470034	0.235017	+	0.971991i	$0.424485\pi$
$390$	−2.00000	−0.101274
$391$	4.11146	0.207925
$392$	−4.47214	−0.225877
$393$	5.76393	0.290752
$394$	4.85410	0.244546
$395$	43.4164	2.18452
$396$	2.85410	0.143424
$397$	−11.4721	−0.575770	−0.287885	−	0.957665i	$-0.592952\pi$
$397$	−11.4721	−0.575770	−0.287885	+	0.957665i	$0.592952\pi$
$398$	−21.7082	−1.08813
$399$	0	0
$400$	−26.5623	−1.32812
$401$	−35.8885	−1.79219	−0.896094	−	0.443864i	$-0.853607\pi$
$401$	−35.8885	−1.79219	−0.896094	+	0.443864i	$0.853607\pi$
$402$	−4.32624	−0.215773
$403$	8.85410	0.441054
$404$	−5.67376	−0.282280
$405$	24.9443	1.23949
$406$	−17.5623	−0.871603
$407$	−14.3262	−0.710125
$408$	−0.652476	−0.0323024
$409$	−8.29180	−0.410003	−0.205001	−	0.978762i	$-0.565720\pi$
$409$	−8.29180	−0.410003	−0.205001	+	0.978762i	$0.565720\pi$
$410$	−15.7082	−0.775773
$411$	2.85410	0.140782
$412$	8.85410	0.436210
$413$	0.978714	0.0481594
$414$	−24.8541	−1.22151
$415$	27.4164	1.34582
$416$	3.38197	0.165815
$417$	5.65248	0.276803
$418$	0	0
$419$	−8.94427	−0.436956	−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−8.94427	−0.436956	−0.218478	+	0.975842i	$0.570109\pi$
$420$	2.29180	0.111828
$421$	−27.4721	−1.33891	−0.669455	−	0.742853i	$-0.733472\pi$
$421$	−27.4721	−1.33891	−0.669455	+	0.742853i	$0.733472\pi$
$422$	−6.23607	−0.303567
$423$	−8.56231	−0.416314
$424$	14.1459	0.686986
$425$	4.18034	0.202776
$426$	−4.61803	−0.223744
$427$	−30.7082	−1.48607
$428$	10.1459	0.490420
$429$	0.618034	0.0298390
$430$	−0.763932	−0.0368401
$431$	27.6525	1.33197	0.665986	−	0.745964i	$-0.268011\pi$
$431$	27.6525	1.33197	0.665986	+	0.745964i	$0.268011\pi$
$432$	10.8541	0.522218
$433$	−3.43769	−0.165205	−0.0826025	−	0.996583i	$-0.526323\pi$
$433$	−3.43769	−0.165205	−0.0826025	+	0.996583i	$0.526323\pi$
$434$	−42.9787	−2.06304
$435$	−4.47214	−0.214423
$436$	−2.03444	−0.0974321
$437$	0	0
$438$	−1.67376	−0.0799754
$439$	−34.5967	−1.65121	−0.825606	−	0.564247i	$-0.809167\pi$
$439$	−34.5967	−1.65121	−0.825606	+	0.564247i	$0.809167\pi$
$440$	11.7082	0.558167
$441$	−5.70820	−0.271819
$442$	−1.23607	−0.0587938
$443$	−7.58359	−0.360307	−0.180154	−	0.983638i	$-0.557660\pi$
$443$	−7.58359	−0.360307	−0.180154	+	0.983638i	$0.557660\pi$
$444$	2.09017	0.0991951
$445$	−25.1246	−1.19102
$446$	−18.8541	−0.892768
$447$	−0.729490	−0.0345037
$448$	12.7082	0.600406
$449$	2.88854	0.136319	0.0681594	−	0.997674i	$-0.478287\pi$
$449$	2.88854	0.136319	0.0681594	+	0.997674i	$0.478287\pi$
$450$	−25.2705	−1.19126
$451$	4.85410	0.228571
$452$	4.18034	0.196627
$453$	−8.05573	−0.378491
$454$	26.5623	1.24663
$455$	−9.70820	−0.455128
$456$	0	0
$457$	19.7082	0.921911	0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082	0.921911	0.460955	+	0.887423i	$0.347507\pi$
$458$	−22.0344	−1.02960
$459$	−1.70820	−0.0797321
$460$	10.7639	0.501871
$461$	20.9443	0.975472	0.487736	−	0.872991i	$-0.337823\pi$
$461$	20.9443	0.975472	0.487736	+	0.872991i	$0.337823\pi$
$462$	−3.00000	−0.139573
$463$	28.2705	1.31384	0.656921	−	0.753959i	$-0.271858\pi$
$463$	28.2705	1.31384	0.656921	+	0.753959i	$0.271858\pi$
$464$	17.5623	0.815310
$465$	−10.9443	−0.507528
$466$	7.32624	0.339381
$467$	−15.9443	−0.737813	−0.368906	−	0.929467i	$-0.620268\pi$
$467$	−15.9443	−0.737813	−0.368906	+	0.929467i	$0.620268\pi$
$468$	1.76393	0.0815378
$469$	−21.0000	−0.969690
$470$	15.7082	0.724565
$471$	−6.81966	−0.314233
$472$	−0.729490	−0.0335775
$473$	0.236068	0.0108544
$474$	8.29180	0.380855
$475$	0	0
$476$	1.41641	0.0649209
$477$	18.0557	0.826715
$478$	−0.527864	−0.0241439
$479$	23.0902	1.05502	0.527508	−	0.849550i	$-0.323126\pi$
$479$	23.0902	1.05502	0.527508	+	0.849550i	$0.323126\pi$
$480$	−4.18034	−0.190806
$481$	−8.85410	−0.403712
$482$	5.14590	0.234389
$483$	6.16718	0.280617
$484$	−5.18034	−0.235470
$485$	44.8328	2.03575
$486$	15.6180	0.708448
$487$	4.18034	0.189429	0.0947146	−	0.995504i	$-0.469806\pi$
$487$	4.18034	0.189429	0.0947146	+	0.995504i	$0.469806\pi$
$488$	22.8885	1.03612
$489$	0.673762	0.0304686
$490$	10.4721	0.473083
$491$	−21.2148	−0.957410	−0.478705	−	0.877976i	$-0.658894\pi$
$491$	−21.2148	−0.957410	−0.478705	+	0.877976i	$0.658894\pi$
$492$	−0.708204	−0.0319283
$493$	−2.76393	−0.124481
$494$	0	0
$495$	14.9443	0.671695
$496$	42.9787	1.92980
$497$	−22.4164	−1.00551
$498$	5.23607	0.234634
$499$	25.1246	1.12473	0.562366	−	0.826888i	$-0.309891\pi$
$499$	25.1246	1.12473	0.562366	+	0.826888i	$0.309891\pi$
$500$	0.944272	0.0422291
$501$	7.72949	0.345328
$502$	−41.0344	−1.83146
$503$	35.8328	1.59771	0.798853	−	0.601526i	$-0.205440\pi$
$503$	35.8328	1.59771	0.798853	+	0.601526i	$0.205440\pi$
$504$	19.1459	0.852826
$505$	−29.7082	−1.32200
$506$	−14.0902	−0.626384
$507$	−4.58359	−0.203564
$508$	3.56231	0.158052
$509$	2.03444	0.0901750	0.0450875	−	0.998983i	$-0.485643\pi$
$509$	2.03444	0.0901750	0.0450875	+	0.998983i	$0.485643\pi$
$510$	1.52786	0.0676550
$511$	−8.12461	−0.359412
$512$	−5.29180	−0.233867
$513$	0	0
$514$	32.9443	1.45311
$515$	46.3607	2.04290
$516$	−0.0344419	−0.00151622
$517$	−4.85410	−0.213483
$518$	42.9787	1.88838
$519$	−0.180340	−0.00791604
$520$	7.23607	0.317323
$521$	6.27051	0.274716	0.137358	−	0.990521i	$-0.456139\pi$
$521$	6.27051	0.274716	0.137358	+	0.990521i	$0.456139\pi$
$522$	16.7082	0.731298
$523$	−4.41641	−0.193116	−0.0965580	−	0.995327i	$-0.530783\pi$
$523$	−4.41641	−0.193116	−0.0965580	+	0.995327i	$0.530783\pi$
$524$	9.32624	0.407419
$525$	6.27051	0.273667
$526$	−24.1803	−1.05431
$527$	−6.76393	−0.294642
$528$	3.00000	0.130558
$529$	5.96556	0.259372
$530$	−33.1246	−1.43884
$531$	−0.931116	−0.0404070
$532$	0	0
$533$	3.00000	0.129944
$534$	−4.79837	−0.207646
$535$	53.1246	2.29678
$536$	15.6525	0.676084
$537$	4.67376	0.201688
$538$	49.0689	2.11551
$539$	−3.23607	−0.139387
$540$	−4.47214	−0.192450
$541$	−29.8328	−1.28261	−0.641306	−	0.767285i	$-0.721607\pi$
$541$	−29.8328	−1.28261	−0.641306	+	0.767285i	$0.721607\pi$
$542$	1.85410	0.0796405
$543$	4.58359	0.196701
$544$	−2.58359	−0.110771
$545$	−10.6525	−0.456302
$546$	−1.85410	−0.0793482
$547$	−26.9230	−1.15114	−0.575572	−	0.817751i	$-0.695221\pi$
$547$	−26.9230	−1.15114	−0.575572	+	0.817751i	$0.695221\pi$
$548$	4.61803	0.197273
$549$	29.2148	1.24686
$550$	−14.3262	−0.610873
$551$	0	0
$552$	−4.59675	−0.195651
$553$	40.2492	1.71157
$554$	18.4721	0.784806
$555$	10.9443	0.464558
$556$	9.14590	0.387872
$557$	−0.819660	−0.0347301	−0.0173651	−	0.999849i	$-0.505528\pi$
$557$	−0.819660	−0.0347301	−0.0173651	+	0.999849i	$0.505528\pi$
$558$	40.8885	1.73095
$559$	0.145898	0.00617083
$560$	−47.1246	−1.99138
$561$	−0.472136	−0.0199336
$562$	−47.7426	−2.01390
$563$	−32.8328	−1.38374	−0.691869	−	0.722023i	$-0.743212\pi$
$563$	−32.8328	−1.38374	−0.691869	+	0.722023i	$0.743212\pi$
$564$	0.708204	0.0298208
$565$	21.8885	0.920858
$566$	42.1246	1.77063
$567$	23.1246	0.971142
$568$	16.7082	0.701061
$569$	16.9098	0.708897	0.354448	−	0.935076i	$-0.384669\pi$
$569$	16.9098	0.708897	0.354448	+	0.935076i	$0.384669\pi$
$570$	0	0
$571$	6.67376	0.279288	0.139644	−	0.990202i	$-0.455404\pi$
$571$	6.67376	0.279288	0.139644	+	0.990202i	$0.455404\pi$
$572$	1.00000	0.0418121
$573$	5.43769	0.227163
$574$	−14.5623	−0.607819
$575$	29.4508	1.22819
$576$	−12.0902	−0.503757
$577$	−12.1246	−0.504754	−0.252377	−	0.967629i	$-0.581212\pi$
$577$	−12.1246	−0.504754	−0.252377	+	0.967629i	$0.581212\pi$
$578$	−26.5623	−1.10485
$579$	1.93112	0.0802545
$580$	−7.23607	−0.300461
$581$	25.4164	1.05445
$582$	8.56231	0.354919
$583$	10.2361	0.423935
$584$	6.05573	0.250588
$585$	9.23607	0.381864
$586$	−16.4164	−0.678156
$587$	−2.12461	−0.0876921	−0.0438461	−	0.999038i	$-0.513961\pi$
$587$	−2.12461	−0.0876921	−0.0438461	+	0.999038i	$0.513961\pi$
$588$	0.472136	0.0194706
$589$	0	0
$590$	1.70820	0.0703256
$591$	1.14590	0.0471359
$592$	−42.9787	−1.76641
$593$	0.708204	0.0290824	0.0145412	−	0.999894i	$-0.495371\pi$
$593$	0.708204	0.0290824	0.0145412	+	0.999894i	$0.495371\pi$
$594$	5.85410	0.240197
$595$	7.41641	0.304043
$596$	−1.18034	−0.0483486
$597$	−5.12461	−0.209736
$598$	−8.70820	−0.356105
$599$	28.4164	1.16106	0.580531	−	0.814238i	$-0.302845\pi$
$599$	28.4164	1.16106	0.580531	+	0.814238i	$0.302845\pi$
$600$	−4.67376	−0.190806
$601$	20.2918	0.827720	0.413860	−	0.910341i	$-0.364180\pi$
$601$	20.2918	0.827720	0.413860	+	0.910341i	$0.364180\pi$
$602$	−0.708204	−0.0288642
$603$	19.9787	0.813596
$604$	−13.0344	−0.530364
$605$	−27.1246	−1.10277
$606$	−5.67376	−0.230481
$607$	−6.27051	−0.254512	−0.127256	−	0.991870i	$-0.540617\pi$
$607$	−6.27051	−0.254512	−0.127256	+	0.991870i	$0.540617\pi$
$608$	0	0
$609$	−4.14590	−0.168000
$610$	−53.5967	−2.17007
$611$	−3.00000	−0.121367
$612$	−1.34752	−0.0544704
$613$	−19.9443	−0.805542	−0.402771	−	0.915301i	$-0.631953\pi$
$613$	−19.9443	−0.805542	−0.402771	+	0.915301i	$0.631953\pi$
$614$	−28.0344	−1.13138
$615$	−3.70820	−0.149529
$616$	10.8541	0.437324
$617$	7.67376	0.308934	0.154467	−	0.987998i	$-0.450634\pi$
$617$	7.67376	0.308934	0.154467	+	0.987998i	$0.450634\pi$
$618$	8.85410	0.356164
$619$	10.1246	0.406943	0.203471	−	0.979081i	$-0.434778\pi$
$619$	10.1246	0.406943	0.203471	+	0.979081i	$0.434778\pi$
$620$	−17.7082	−0.711179
$621$	−12.0344	−0.482926
$622$	20.4721	0.820858
$623$	−23.2918	−0.933166
$624$	1.85410	0.0742235
$625$	−22.4164	−0.896656
$626$	−18.3262	−0.732464
$627$	0	0
$628$	−11.0344	−0.440322
$629$	6.76393	0.269696
$630$	−44.8328	−1.78618
$631$	29.3607	1.16883	0.584415	−	0.811455i	$-0.301324\pi$
$631$	29.3607	1.16883	0.584415	+	0.811455i	$0.301324\pi$
$632$	−30.0000	−1.19334
$633$	−1.47214	−0.0585122
$634$	29.1246	1.15669
$635$	18.6525	0.740201
$636$	−1.49342	−0.0592180
$637$	−2.00000	−0.0792429
$638$	9.47214	0.375005
$639$	21.3262	0.843653
$640$	44.0689	1.74198
$641$	−39.5066	−1.56042	−0.780208	−	0.625520i	$-0.784887\pi$
$641$	−39.5066	−1.56042	−0.780208	+	0.625520i	$0.784887\pi$
$642$	10.1459	0.400427
$643$	−24.2918	−0.957975	−0.478987	−	0.877822i	$-0.658996\pi$
$643$	−24.2918	−0.957975	−0.478987	+	0.877822i	$0.658996\pi$
$644$	9.97871	0.393216
$645$	−0.180340	−0.00710088
$646$	0	0
$647$	7.47214	0.293760	0.146880	−	0.989154i	$-0.453077\pi$
$647$	7.47214	0.293760	0.146880	+	0.989154i	$0.453077\pi$
$648$	−17.2361	−0.677097
$649$	−0.527864	−0.0207205
$650$	−8.85410	−0.347286
$651$	−10.1459	−0.397649
$652$	1.09017	0.0426944
$653$	−23.5623	−0.922064	−0.461032	−	0.887383i	$-0.652521\pi$
$653$	−23.5623	−0.922064	−0.461032	+	0.887383i	$0.652521\pi$
$654$	−2.03444	−0.0795530
$655$	48.8328	1.90806
$656$	14.5623	0.568563
$657$	7.72949	0.301556
$658$	14.5623	0.567698
$659$	−25.7771	−1.00413	−0.502066	−	0.864829i	$-0.667427\pi$
$659$	−25.7771	−1.00413	−0.502066	+	0.864829i	$0.667427\pi$
$660$	−1.23607	−0.0481139
$661$	5.41641	0.210674	0.105337	−	0.994437i	$-0.466408\pi$
$661$	5.41641	0.210674	0.105337	+	0.994437i	$0.466408\pi$
$662$	17.7082	0.688249
$663$	−0.291796	−0.0113324
$664$	−18.9443	−0.735180
$665$	0	0
$666$	−40.8885	−1.58440
$667$	−19.4721	−0.753964
$668$	12.5066	0.483894
$669$	−4.45085	−0.172080
$670$	−36.6525	−1.41601
$671$	16.5623	0.639381
$672$	−3.87539	−0.149496
$673$	34.1246	1.31541	0.657704	−	0.753277i	$-0.271528\pi$
$673$	34.1246	1.31541	0.657704	+	0.753277i	$0.271528\pi$
$674$	−27.7082	−1.06728
$675$	−12.2361	−0.470966
$676$	−7.41641	−0.285246
$677$	−30.7426	−1.18154	−0.590768	−	0.806842i	$-0.701175\pi$
$677$	−30.7426	−1.18154	−0.590768	+	0.806842i	$0.701175\pi$
$678$	4.18034	0.160545
$679$	41.5623	1.59501
$680$	−5.52786	−0.211984
$681$	6.27051	0.240286
$682$	23.1803	0.887621
$683$	9.65248	0.369342	0.184671	−	0.982800i	$-0.440878\pi$
$683$	9.65248	0.369342	0.184671	+	0.982800i	$0.440878\pi$
$684$	0	0
$685$	24.1803	0.923883
$686$	−24.2705	−0.926652
$687$	−5.20163	−0.198454
$688$	0.708204	0.0270000
$689$	6.32624	0.241010
$690$	10.7639	0.409776
$691$	−39.1803	−1.49049	−0.745245	−	0.666791i	$-0.767668\pi$
$691$	−39.1803	−1.49049	−0.745245	+	0.666791i	$0.767668\pi$
$692$	−0.291796	−0.0110924
$693$	13.8541	0.526274
$694$	−41.1246	−1.56107
$695$	47.8885	1.81652
$696$	3.09017	0.117133
$697$	−2.29180	−0.0868080
$698$	−33.9443	−1.28481
$699$	1.72949	0.0654153
$700$	10.1459	0.383479
$701$	−39.6312	−1.49685	−0.748425	−	0.663220i	$-0.769189\pi$
$701$	−39.6312	−1.49685	−0.748425	+	0.663220i	$0.769189\pi$
$702$	3.61803	0.136554
$703$	0	0
$704$	−6.85410	−0.258324
$705$	3.70820	0.139659
$706$	39.5623	1.48895
$707$	−27.5410	−1.03579
$708$	0.0770143	0.00289438
$709$	16.5836	0.622810	0.311405	−	0.950277i	$-0.399200\pi$
$709$	16.5836	0.622810	0.311405	+	0.950277i	$0.399200\pi$
$710$	−39.1246	−1.46832
$711$	−38.2918	−1.43605
$712$	17.3607	0.650619
$713$	−47.6525	−1.78460
$714$	1.41641	0.0530077
$715$	5.23607	0.195818
$716$	7.56231	0.282617
$717$	−0.124612	−0.00465371
$718$	11.3820	0.424771
$719$	47.0344	1.75409	0.877044	−	0.480409i	$-0.159512\pi$
$719$	47.0344	1.75409	0.877044	+	0.480409i	$0.159512\pi$
$720$	44.8328	1.67082
$721$	42.9787	1.60061
$722$	0	0
$723$	1.21478	0.0451782
$724$	7.41641	0.275629
$725$	−19.7984	−0.735293
$726$	−5.18034	−0.192260
$727$	−16.0689	−0.595962	−0.297981	−	0.954572i	$-0.596313\pi$
$727$	−16.0689	−0.595962	−0.297981	+	0.954572i	$0.596313\pi$
$728$	6.70820	0.248623
$729$	−19.4377	−0.719915
$730$	−14.1803	−0.524838
$731$	−0.111456	−0.00412236
$732$	−2.41641	−0.0893130
$733$	−52.9574	−1.95603	−0.978014	−	0.208541i	$-0.933129\pi$
$733$	−52.9574	−1.95603	−0.978014	+	0.208541i	$0.933129\pi$
$734$	−25.7984	−0.952235
$735$	2.47214	0.0911861
$736$	−18.2016	−0.670921
$737$	11.3262	0.417207
$738$	13.8541	0.509977
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	17.7082	0.650967
$741$	0	0
$742$	−30.7082	−1.12733
$743$	−3.36068	−0.123291	−0.0616457	−	0.998098i	$-0.519635\pi$
$743$	−3.36068	−0.123291	−0.0616457	+	0.998098i	$0.519635\pi$
$744$	7.56231	0.277248
$745$	−6.18034	−0.226430
$746$	−8.85410	−0.324172
$747$	−24.1803	−0.884712
$748$	−0.763932	−0.0279321
$749$	49.2492	1.79953
$750$	0.944272	0.0344799
$751$	−17.1459	−0.625663	−0.312831	−	0.949809i	$-0.601277\pi$
$751$	−17.1459	−0.625663	−0.312831	+	0.949809i	$0.601277\pi$
$752$	−14.5623	−0.531033
$753$	−9.68692	−0.353011
$754$	5.85410	0.213194
$755$	−68.2492	−2.48384
$756$	−4.14590	−0.150785
$757$	26.7426	0.971978	0.485989	−	0.873965i	$-0.338460\pi$
$757$	26.7426	0.971978	0.485989	+	0.873965i	$0.338460\pi$
$758$	−24.4721	−0.888868
$759$	−3.32624	−0.120735
$760$	0	0
$761$	4.88854	0.177210	0.0886048	−	0.996067i	$-0.471759\pi$
$761$	4.88854	0.177210	0.0886048	+	0.996067i	$0.471759\pi$
$762$	3.56231	0.129049
$763$	−9.87539	−0.357513
$764$	8.79837	0.318314
$765$	−7.05573	−0.255100
$766$	0.618034	0.0223305
$767$	−0.326238	−0.0117798
$768$	5.18034	0.186929
$769$	36.6312	1.32095	0.660477	−	0.750846i	$-0.270354\pi$
$769$	36.6312	1.32095	0.660477	+	0.750846i	$0.270354\pi$
$770$	−25.4164	−0.915944
$771$	7.77709	0.280085
$772$	3.12461	0.112457
$773$	−35.9230	−1.29206	−0.646030	−	0.763312i	$-0.723572\pi$
$773$	−35.9230	−1.29206	−0.646030	+	0.763312i	$0.723572\pi$
$774$	0.673762	0.0242179
$775$	−48.4508	−1.74041
$776$	−30.9787	−1.11207
$777$	10.1459	0.363982
$778$	15.0000	0.537776
$779$	0	0
$780$	−0.763932	−0.0273532
$781$	12.0902	0.432620
$782$	6.65248	0.237892
$783$	8.09017	0.289119
$784$	−9.70820	−0.346722
$785$	−57.7771	−2.06215
$786$	9.32624	0.332656
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	1.85410	0.0660496
$789$	−5.70820	−0.203217
$790$	70.2492	2.49936
$791$	20.2918	0.721493
$792$	−10.3262	−0.366927
$793$	10.2361	0.363493
$794$	−18.5623	−0.658752
$795$	−7.81966	−0.277335
$796$	−8.29180	−0.293895
$797$	−20.2918	−0.718772	−0.359386	−	0.933189i	$-0.617014\pi$
$797$	−20.2918	−0.718772	−0.359386	+	0.933189i	$0.617014\pi$
$798$	0	0
$799$	2.29180	0.0810779
$800$	−18.5066	−0.654306
$801$	22.1591	0.782952
$802$	−58.0689	−2.05048
$803$	4.38197	0.154636
$804$	−1.65248	−0.0582783
$805$	52.2492	1.84154
$806$	14.3262	0.504620
$807$	11.5836	0.407762
$808$	20.5279	0.722168
$809$	−24.7984	−0.871864	−0.435932	−	0.899980i	$-0.643581\pi$
$809$	−24.7984	−0.871864	−0.435932	+	0.899980i	$0.643581\pi$
$810$	40.3607	1.41813
$811$	22.9787	0.806892	0.403446	−	0.915004i	$-0.367812\pi$
$811$	22.9787	0.806892	0.403446	+	0.915004i	$0.367812\pi$
$812$	−6.70820	−0.235412
$813$	0.437694	0.0153506
$814$	−23.1803	−0.812470
$815$	5.70820	0.199950
$816$	−1.41641	−0.0495842
$817$	0	0
$818$	−13.4164	−0.469094
$819$	8.56231	0.299191
$820$	−6.00000	−0.209529
$821$	52.0476	1.81647	0.908237	−	0.418457i	$-0.137429\pi$
$821$	52.0476	1.81647	0.908237	+	0.418457i	$0.137429\pi$
$822$	4.61803	0.161072
$823$	−25.5967	−0.892247	−0.446123	−	0.894972i	$-0.647196\pi$
$823$	−25.5967	−0.892247	−0.446123	+	0.894972i	$0.647196\pi$
$824$	−32.0344	−1.11597
$825$	−3.38197	−0.117745
$826$	1.58359	0.0551002
$827$	32.5967	1.13350	0.566750	−	0.823890i	$-0.308201\pi$
$827$	32.5967	1.13350	0.566750	+	0.823890i	$0.308201\pi$
$828$	−9.49342	−0.329919
$829$	4.67376	0.162326	0.0811632	−	0.996701i	$-0.474136\pi$
$829$	4.67376	0.162326	0.0811632	+	0.996701i	$0.474136\pi$
$830$	44.3607	1.53978
$831$	4.36068	0.151270
$832$	−4.23607	−0.146859
$833$	1.52786	0.0529374
$834$	9.14590	0.316697
$835$	65.4853	2.26621
$836$	0	0
$837$	19.7984	0.684332
$838$	−14.4721	−0.499932
$839$	15.2016	0.524818	0.262409	−	0.964957i	$-0.415483\pi$
$839$	15.2016	0.524818	0.262409	+	0.964957i	$0.415483\pi$
$840$	−8.29180	−0.286094
$841$	−15.9098	−0.548615
$842$	−44.4508	−1.53188
$843$	−11.2705	−0.388177
$844$	−2.38197	−0.0819907
$845$	−38.8328	−1.33589
$846$	−13.8541	−0.476314
$847$	−25.1459	−0.864023
$848$	30.7082	1.05452
$849$	9.94427	0.341287
$850$	6.76393	0.232001
$851$	47.6525	1.63351
$852$	−1.76393	−0.0604313
$853$	30.7082	1.05143	0.525714	−	0.850661i	$-0.323798\pi$
$853$	30.7082	1.05143	0.525714	+	0.850661i	$0.323798\pi$
$854$	−49.6869	−1.70025
$855$	0	0
$856$	−36.7082	−1.25466
$857$	−10.6180	−0.362705	−0.181353	−	0.983418i	$-0.558048\pi$
$857$	−10.6180	−0.362705	−0.181353	+	0.983418i	$0.558048\pi$
$858$	1.00000	0.0341394
$859$	−48.5410	−1.65620	−0.828099	−	0.560582i	$-0.810578\pi$
$859$	−48.5410	−1.65620	−0.828099	+	0.560582i	$0.810578\pi$
$860$	−0.291796	−0.00995016
$861$	−3.43769	−0.117156
$862$	44.7426	1.52394
$863$	−27.0557	−0.920988	−0.460494	−	0.887663i	$-0.652328\pi$
$863$	−27.0557	−0.920988	−0.460494	+	0.887663i	$0.652328\pi$
$864$	7.56231	0.257275
$865$	−1.52786	−0.0519489
$866$	−5.56231	−0.189015
$867$	−6.27051	−0.212958
$868$	−16.4164	−0.557209
$869$	−21.7082	−0.736400
$870$	−7.23607	−0.245326
$871$	7.00000	0.237186
$872$	7.36068	0.249264
$873$	−39.5410	−1.33826
$874$	0	0
$875$	4.58359	0.154954
$876$	−0.639320	−0.0216006
$877$	11.8197	0.399122	0.199561	−	0.979885i	$-0.436048\pi$
$877$	11.8197	0.399122	0.199561	+	0.979885i	$0.436048\pi$
$878$	−55.9787	−1.88919
$879$	−3.87539	−0.130714
$880$	25.4164	0.856787
$881$	32.4508	1.09330	0.546648	−	0.837362i	$-0.315903\pi$
$881$	32.4508	1.09330	0.546648	+	0.837362i	$0.315903\pi$
$882$	−9.23607	−0.310995
$883$	−50.9230	−1.71369	−0.856847	−	0.515570i	$-0.827580\pi$
$883$	−50.9230	−1.71369	−0.856847	+	0.515570i	$0.827580\pi$
$884$	−0.472136	−0.0158797
$885$	0.403252	0.0135552
$886$	−12.2705	−0.412236
$887$	27.3475	0.918240	0.459120	−	0.888374i	$-0.348165\pi$
$887$	27.3475	0.918240	0.459120	+	0.888374i	$0.348165\pi$
$888$	−7.56231	−0.253774
$889$	17.2918	0.579948
$890$	−40.6525	−1.36267
$891$	−12.4721	−0.417832
$892$	−7.20163	−0.241128
$893$	0	0
$894$	−1.18034	−0.0394765
$895$	39.5967	1.32357
$896$	40.8541	1.36484
$897$	−2.05573	−0.0686388
$898$	4.67376	0.155965
$899$	32.0344	1.06841
$900$	−9.65248	−0.321749
$901$	−4.83282	−0.161004
$902$	7.85410	0.261513
$903$	−0.167184	−0.00556354
$904$	−15.1246	−0.503037
$905$	38.8328	1.29085
$906$	−13.0344	−0.433040
$907$	−26.4721	−0.878993	−0.439496	−	0.898244i	$-0.644843\pi$
$907$	−26.4721	−0.878993	−0.439496	+	0.898244i	$0.644843\pi$
$908$	10.1459	0.336703
$909$	26.2016	0.869053
$910$	−15.7082	−0.520722
$911$	3.38197	0.112050	0.0560248	−	0.998429i	$-0.482157\pi$
$911$	3.38197	0.112050	0.0560248	+	0.998429i	$0.482157\pi$
$912$	0	0
$913$	−13.7082	−0.453675
$914$	31.8885	1.05478
$915$	−12.6525	−0.418278
$916$	−8.41641	−0.278086
$917$	45.2705	1.49496
$918$	−2.76393	−0.0912234
$919$	23.2918	0.768325	0.384163	−	0.923265i	$-0.374490\pi$
$919$	23.2918	0.768325	0.384163	+	0.923265i	$0.374490\pi$
$920$	−38.9443	−1.28395
$921$	−6.61803	−0.218072
$922$	33.8885	1.11606
$923$	7.47214	0.245948
$924$	−1.14590	−0.0376973
$925$	48.4508	1.59305
$926$	45.7426	1.50320
$927$	−40.8885	−1.34296
$928$	12.2361	0.401669
$929$	16.3820	0.537475	0.268737	−	0.963213i	$-0.413394\pi$
$929$	16.3820	0.537475	0.268737	+	0.963213i	$0.413394\pi$
$930$	−17.7082	−0.580675
$931$	0	0
$932$	2.79837	0.0916638
$933$	4.83282	0.158219
$934$	−25.7984	−0.844149
$935$	−4.00000	−0.130814
$936$	−6.38197	−0.208601
$937$	40.5623	1.32511	0.662556	−	0.749012i	$-0.269471\pi$
$937$	40.5623	1.32511	0.662556	+	0.749012i	$0.269471\pi$
$938$	−33.9787	−1.10944
$939$	−4.32624	−0.141181
$940$	6.00000	0.195698
$941$	−10.6869	−0.348384	−0.174192	−	0.984712i	$-0.555731\pi$
$941$	−10.6869	−0.348384	−0.174192	+	0.984712i	$0.555731\pi$
$942$	−11.0344	−0.359522
$943$	−16.1459	−0.525783
$944$	−1.58359	−0.0515415
$945$	−21.7082	−0.706168
$946$	0.381966	0.0124188
$947$	−32.6525	−1.06106	−0.530531	−	0.847665i	$-0.678008\pi$
$947$	−32.6525	−1.06106	−0.530531	+	0.847665i	$0.678008\pi$
$948$	3.16718	0.102865
$949$	2.70820	0.0879120
$950$	0	0
$951$	6.87539	0.222950
$952$	−5.12461	−0.166090
$953$	17.2918	0.560136	0.280068	−	0.959980i	$-0.409643\pi$
$953$	17.2918	0.560136	0.280068	+	0.959980i	$0.409643\pi$
$954$	29.2148	0.945863
$955$	46.0689	1.49075
$956$	−0.201626	−0.00652105
$957$	2.23607	0.0722818
$958$	37.3607	1.20707
$959$	22.4164	0.723864
$960$	5.23607	0.168993
$961$	47.3951	1.52887
$962$	−14.3262	−0.461896
$963$	−46.8541	−1.50985
$964$	1.96556	0.0633064
$965$	16.3607	0.526669
$966$	9.97871	0.321060
$967$	6.54102	0.210345	0.105173	−	0.994454i	$-0.466461\pi$
$967$	6.54102	0.210345	0.105173	+	0.994454i	$0.466461\pi$
$968$	18.7426	0.602411
$969$	0	0
$970$	72.5410	2.32915
$971$	23.5066	0.754362	0.377181	−	0.926140i	$-0.376893\pi$
$971$	23.5066	0.754362	0.377181	+	0.926140i	$0.376893\pi$
$972$	5.96556	0.191345
$973$	44.3951	1.42324
$974$	6.76393	0.216730
$975$	−2.09017	−0.0669390
$976$	49.6869	1.59044
$977$	10.6393	0.340382	0.170191	−	0.985411i	$-0.445562\pi$
$977$	10.6393	0.340382	0.170191	+	0.985411i	$0.445562\pi$
$978$	1.09017	0.0348598
$979$	12.5623	0.401493
$980$	4.00000	0.127775
$981$	9.39512	0.299963
$982$	−34.3262	−1.09539
$983$	32.6180	1.04035	0.520177	−	0.854059i	$-0.325866\pi$
$983$	32.6180	1.04035	0.520177	+	0.854059i	$0.325866\pi$
$984$	2.56231	0.0816833
$985$	9.70820	0.309329
$986$	−4.47214	−0.142422
$987$	3.43769	0.109423
$988$	0	0
$989$	−0.785218	−0.0249685
$990$	24.1803	0.768502
$991$	7.45085	0.236684	0.118342	−	0.992973i	$-0.462242\pi$
$991$	7.45085	0.236684	0.118342	+	0.992973i	$0.462242\pi$
$992$	29.9443	0.950732
$993$	4.18034	0.132659
$994$	−36.2705	−1.15043
$995$	−43.4164	−1.37639
$996$	2.00000	0.0633724
$997$	39.7082	1.25757	0.628786	−	0.777579i	$-0.283552\pi$
$997$	39.7082	1.25757	0.628786	+	0.777579i	$0.283552\pi$
$998$	40.6525	1.28683
$999$	−19.7984	−0.626393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.a.f.1.2	yes	2
3.2	odd	2		3249.2.a.i.1.1		2
4.3	odd	2		5776.2.a.s.1.2		2
5.4	even	2		9025.2.a.n.1.1		2
19.2	odd	18		361.2.e.i.99.2		12
19.3	odd	18		361.2.e.i.28.1		12
19.4	even	9		361.2.e.j.54.2		12
19.5	even	9		361.2.e.j.234.2		12
19.6	even	9		361.2.e.j.245.2		12
19.7	even	3		361.2.c.d.68.1		4
19.8	odd	6		361.2.c.g.292.2		4
19.9	even	9		361.2.e.j.62.1		12
19.10	odd	18		361.2.e.i.62.2		12
19.11	even	3		361.2.c.d.292.1		4
19.12	odd	6		361.2.c.g.68.2		4
19.13	odd	18		361.2.e.i.245.1		12
19.14	odd	18		361.2.e.i.234.1		12
19.15	odd	18		361.2.e.i.54.1		12
19.16	even	9		361.2.e.j.28.2		12
19.17	even	9		361.2.e.j.99.1		12
19.18	odd	2		361.2.a.c.1.1	✓	2
57.56	even	2		3249.2.a.o.1.2		2
76.75	even	2		5776.2.a.bg.1.1		2
95.94	odd	2		9025.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.1	✓	2	19.18	odd	2
361.2.a.f.1.2	yes	2	1.1	even	1	trivial
361.2.c.d.68.1		4	19.7	even	3
361.2.c.d.292.1		4	19.11	even	3
361.2.c.g.68.2		4	19.12	odd	6
361.2.c.g.292.2		4	19.8	odd	6
361.2.e.i.28.1		12	19.3	odd	18
361.2.e.i.54.1		12	19.15	odd	18
361.2.e.i.62.2		12	19.10	odd	18
361.2.e.i.99.2		12	19.2	odd	18
361.2.e.i.234.1		12	19.14	odd	18
361.2.e.i.245.1		12	19.13	odd	18
361.2.e.j.28.2		12	19.16	even	9
361.2.e.j.54.2		12	19.4	even	9
361.2.e.j.62.1		12	19.9	even	9
361.2.e.j.99.1		12	19.17	even	9
361.2.e.j.234.2		12	19.5	even	9
361.2.e.j.245.2		12	19.6	even	9
3249.2.a.i.1.1		2	3.2	odd	2
3249.2.a.o.1.2		2	57.56	even	2
5776.2.a.s.1.2		2	4.3	odd	2
5776.2.a.bg.1.1		2	76.75	even	2
9025.2.a.n.1.1		2	5.4	even	2
9025.2.a.s.1.2		2	95.94	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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +0.381966 q^{3} +0.618034 q^{4} +3.23607 q^{5} +0.618034 q^{6} +3.00000 q^{7} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} +0.381966 q^{3} +0.618034 q^{4} +3.23607 q^{5} +0.618034 q^{6} +3.00000 q^{7} -2.23607 q^{8} -2.85410 q^{9} +5.23607 q^{10} -1.61803 q^{11} +0.236068 q^{12} -1.00000 q^{13} +4.85410 q^{14} +1.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} -4.61803 q^{18} +2.00000 q^{20} +1.14590 q^{21} -2.61803 q^{22} +5.38197 q^{23} -0.854102 q^{24} +5.47214 q^{25} -1.61803 q^{26} -2.23607 q^{27} +1.85410 q^{28} -3.61803 q^{29} +2.00000 q^{30} -8.85410 q^{31} -3.38197 q^{32} -0.618034 q^{33} +1.23607 q^{34} +9.70820 q^{35} -1.76393 q^{36} +8.85410 q^{37} -0.381966 q^{39} -7.23607 q^{40} -3.00000 q^{41} +1.85410 q^{42} -0.145898 q^{43} -1.00000 q^{44} -9.23607 q^{45} +8.70820 q^{46} +3.00000 q^{47} -1.85410 q^{48} +2.00000 q^{49} +8.85410 q^{50} +0.291796 q^{51} -0.618034 q^{52} -6.32624 q^{53} -3.61803 q^{54} -5.23607 q^{55} -6.70820 q^{56} -5.85410 q^{58} +0.326238 q^{59} +0.763932 q^{60} -10.2361 q^{61} -14.3262 q^{62} -8.56231 q^{63} +4.23607 q^{64} -3.23607 q^{65} -1.00000 q^{66} -7.00000 q^{67} +0.472136 q^{68} +2.05573 q^{69} +15.7082 q^{70} -7.47214 q^{71} +6.38197 q^{72} -2.70820 q^{73} +14.3262 q^{74} +2.09017 q^{75} -4.85410 q^{77} -0.618034 q^{78} +13.4164 q^{79} -15.7082 q^{80} +7.70820 q^{81} -4.85410 q^{82} +8.47214 q^{83} +0.708204 q^{84} +2.47214 q^{85} -0.236068 q^{86} -1.38197 q^{87} +3.61803 q^{88} -7.76393 q^{89} -14.9443 q^{90} -3.00000 q^{91} +3.32624 q^{92} -3.38197 q^{93} +4.85410 q^{94} -1.29180 q^{96} +13.8541 q^{97} +3.23607 q^{98} +4.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - q^{6} + 6 q^{7} + q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 - q^6 + 6 * q^7 + q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - q^{6} + 6 q^{7} + q^{9} + 6 q^{10} - q^{11} - 4 q^{12} - 2 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - 7 q^{18} + 4 q^{20} + 9 q^{21} - 3 q^{22} + 13 q^{23} + 5 q^{24} + 2 q^{25} - q^{26} - 3 q^{28} - 5 q^{29} + 4 q^{30} - 11 q^{31} - 9 q^{32} + q^{33} - 2 q^{34} + 6 q^{35} - 8 q^{36} + 11 q^{37} - 3 q^{39} - 10 q^{40} - 6 q^{41} - 3 q^{42} - 7 q^{43} - 2 q^{44} - 14 q^{45} + 4 q^{46} + 6 q^{47} + 3 q^{48} + 4 q^{49} + 11 q^{50} + 14 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 6 q^{55} - 5 q^{58} - 15 q^{59} + 6 q^{60} - 16 q^{61} - 13 q^{62} + 3 q^{63} + 4 q^{64} - 2 q^{65} - 2 q^{66} - 14 q^{67} - 8 q^{68} + 22 q^{69} + 18 q^{70} - 6 q^{71} + 15 q^{72} + 8 q^{73} + 13 q^{74} - 7 q^{75} - 3 q^{77} + q^{78} - 18 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 12 q^{84} - 4 q^{85} + 4 q^{86} - 5 q^{87} + 5 q^{88} - 20 q^{89} - 12 q^{90} - 6 q^{91} - 9 q^{92} - 9 q^{93} + 3 q^{94} - 16 q^{96} + 21 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 - q^6 + 6 * q^7 + q^9 + 6 * q^10 - q^11 - 4 * q^12 - 2 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - 7 * q^18 + 4 * q^20 + 9 * q^21 - 3 * q^22 + 13 * q^23 + 5 * q^24 + 2 * q^25 - q^26 - 3 * q^28 - 5 * q^29 + 4 * q^30 - 11 * q^31 - 9 * q^32 + q^33 - 2 * q^34 + 6 * q^35 - 8 * q^36 + 11 * q^37 - 3 * q^39 - 10 * q^40 - 6 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 14 * q^45 + 4 * q^46 + 6 * q^47 + 3 * q^48 + 4 * q^49 + 11 * q^50 + 14 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 6 * q^55 - 5 * q^58 - 15 * q^59 + 6 * q^60 - 16 * q^61 - 13 * q^62 + 3 * q^63 + 4 * q^64 - 2 * q^65 - 2 * q^66 - 14 * q^67 - 8 * q^68 + 22 * q^69 + 18 * q^70 - 6 * q^71 + 15 * q^72 + 8 * q^73 + 13 * q^74 - 7 * q^75 - 3 * q^77 + q^78 - 18 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 12 * q^84 - 4 * q^85 + 4 * q^86 - 5 * q^87 + 5 * q^88 - 20 * q^89 - 12 * q^90 - 6 * q^91 - 9 * q^92 - 9 * q^93 + 3 * q^94 - 16 * q^96 + 21 * q^97 + 2 * q^98 + 7 * q^99

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