LMFDB - Embedded newform 361.2.a.f.1.1

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			1.1
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.23607 q^{5} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.23607 q^{5} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +0.763932 q^{10} +0.618034 q^{11} -4.23607 q^{12} -1.00000 q^{13} -1.85410 q^{14} -3.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} -2.38197 q^{18} +2.00000 q^{20} +7.85410 q^{21} -0.381966 q^{22} +7.61803 q^{23} +5.85410 q^{24} -3.47214 q^{25} +0.618034 q^{26} +2.23607 q^{27} -4.85410 q^{28} -1.38197 q^{29} +2.00000 q^{30} -2.14590 q^{31} -5.61803 q^{32} +1.61803 q^{33} -3.23607 q^{34} -3.70820 q^{35} -6.23607 q^{36} +2.14590 q^{37} -2.61803 q^{39} -2.76393 q^{40} -3.00000 q^{41} -4.85410 q^{42} -6.85410 q^{43} -1.00000 q^{44} -4.76393 q^{45} -4.70820 q^{46} +3.00000 q^{47} +4.85410 q^{48} +2.00000 q^{49} +2.14590 q^{50} +13.7082 q^{51} +1.61803 q^{52} +9.32624 q^{53} -1.38197 q^{54} -0.763932 q^{55} +6.70820 q^{56} +0.854102 q^{58} -15.3262 q^{59} +5.23607 q^{60} -5.76393 q^{61} +1.32624 q^{62} +11.5623 q^{63} -0.236068 q^{64} +1.23607 q^{65} -1.00000 q^{66} -7.00000 q^{67} -8.47214 q^{68} +19.9443 q^{69} +2.29180 q^{70} +1.47214 q^{71} +8.61803 q^{72} +10.7082 q^{73} -1.32624 q^{74} -9.09017 q^{75} +1.85410 q^{77} +1.61803 q^{78} -13.4164 q^{79} -2.29180 q^{80} -5.70820 q^{81} +1.85410 q^{82} -0.472136 q^{83} -12.7082 q^{84} -6.47214 q^{85} +4.23607 q^{86} -3.61803 q^{87} +1.38197 q^{88} -12.2361 q^{89} +2.94427 q^{90} -3.00000 q^{91} -12.3262 q^{92} -5.61803 q^{93} -1.85410 q^{94} -14.7082 q^{96} +7.14590 q^{97} -1.23607 q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	−1.61803	−0.809017
$5$	−1.23607	−0.552786	−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607	−0.552786	−0.276393	+	0.961045i	$0.589139\pi$
$6$	−1.61803	−0.660560
$7$	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
$9$	3.85410	1.28470
$10$	0.763932	0.241577
$11$	0.618034	0.186344	0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034	0.186344	0.0931721	+	0.995650i	$0.470299\pi$
$12$	−4.23607	−1.22285
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.85410	−0.495530
$15$	−3.23607	−0.835549
$16$	1.85410	0.463525
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	−2.38197	−0.561435
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	7.85410	1.71391
$22$	−0.381966	−0.0814354
$23$	7.61803	1.58847	0.794235	−	0.607611i	$-0.207872\pi$
$23$	7.61803	1.58847	0.794235	+	0.607611i	$0.207872\pi$
$24$	5.85410	1.19496
$25$	−3.47214	−0.694427
$26$	0.618034	0.121206
$27$	2.23607	0.430331
$28$	−4.85410	−0.917339
$29$	−1.38197	−0.256625	−0.128312	−	0.991734i	$-0.540956\pi$
$29$	−1.38197	−0.256625	−0.128312	+	0.991734i	$0.540956\pi$
$30$	2.00000	0.365148
$31$	−2.14590	−0.385415	−0.192707	−	0.981256i	$-0.561727\pi$
$31$	−2.14590	−0.385415	−0.192707	+	0.981256i	$0.561727\pi$
$32$	−5.61803	−0.993137
$33$	1.61803	0.281664
$34$	−3.23607	−0.554981
$35$	−3.70820	−0.626801
$36$	−6.23607	−1.03934
$37$	2.14590	0.352783	0.176392	−	0.984320i	$-0.443557\pi$
$37$	2.14590	0.352783	0.176392	+	0.984320i	$0.443557\pi$
$38$	0	0
$39$	−2.61803	−0.419221
$40$	−2.76393	−0.437016
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−4.85410	−0.749004
$43$	−6.85410	−1.04524	−0.522620	−	0.852566i	$-0.675045\pi$
$43$	−6.85410	−1.04524	−0.522620	+	0.852566i	$0.675045\pi$
$44$	−1.00000	−0.150756
$45$	−4.76393	−0.710165
$46$	−4.70820	−0.694187
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	4.85410	0.700629
$49$	2.00000	0.285714
$50$	2.14590	0.303476
$51$	13.7082	1.91953
$52$	1.61803	0.224381
$53$	9.32624	1.28106	0.640529	−	0.767934i	$-0.278715\pi$
$53$	9.32624	1.28106	0.640529	+	0.767934i	$0.278715\pi$
$54$	−1.38197	−0.188062
$55$	−0.763932	−0.103009
$56$	6.70820	0.896421
$57$	0	0
$58$	0.854102	0.112149
$59$	−15.3262	−1.99531	−0.997653	−	0.0684709i	$-0.978188\pi$
$59$	−15.3262	−1.99531	−0.997653	+	0.0684709i	$0.978188\pi$
$60$	5.23607	0.675973
$61$	−5.76393	−0.737996	−0.368998	−	0.929430i	$-0.620299\pi$
$61$	−5.76393	−0.737996	−0.368998	+	0.929430i	$0.620299\pi$
$62$	1.32624	0.168432
$63$	11.5623	1.45671
$64$	−0.236068	−0.0295085
$65$	1.23607	0.153315
$66$	−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	$0.640638\pi$
$68$	−8.47214	−1.02740
$69$	19.9443	2.40101
$70$	2.29180	0.273922
$71$	1.47214	0.174710	0.0873552	−	0.996177i	$-0.472158\pi$
$71$	1.47214	0.174710	0.0873552	+	0.996177i	$0.472158\pi$
$72$	8.61803	1.01565
$73$	10.7082	1.25330	0.626650	−	0.779301i	$-0.284425\pi$
$73$	10.7082	1.25330	0.626650	+	0.779301i	$0.284425\pi$
$74$	−1.32624	−0.154172
$75$	−9.09017	−1.04964
$76$	0	0
$77$	1.85410	0.211295
$78$	1.61803	0.183206
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	−2.29180	−0.256231
$81$	−5.70820	−0.634245
$82$	1.85410	0.204751
$83$	−0.472136	−0.0518237	−0.0259118	−	0.999664i	$-0.508249\pi$
$83$	−0.472136	−0.0518237	−0.0259118	+	0.999664i	$0.508249\pi$
$84$	−12.7082	−1.38658
$85$	−6.47214	−0.702002
$86$	4.23607	0.456787
$87$	−3.61803	−0.387894
$88$	1.38197	0.147318
$89$	−12.2361	−1.29702	−0.648510	−	0.761206i	$-0.724608\pi$
$89$	−12.2361	−1.29702	−0.648510	+	0.761206i	$0.724608\pi$
$90$	2.94427	0.310354
$91$	−3.00000	−0.314485
$92$	−12.3262	−1.28510
$93$	−5.61803	−0.582563
$94$	−1.85410	−0.191236
$95$	0	0
$96$	−14.7082	−1.50115
$97$	7.14590	0.725556	0.362778	−	0.931876i	$-0.381828\pi$
$97$	7.14590	0.725556	0.362778	+	0.931876i	$0.381828\pi$
$98$	−1.23607	−0.124862
$99$	2.38197	0.239397
$100$	5.61803	0.561803
$101$	13.1803	1.31149	0.655746	−	0.754981i	$-0.272354\pi$
$101$	13.1803	1.31149	0.655746	+	0.754981i	$0.272354\pi$
$102$	−8.47214	−0.838866
$103$	−1.32624	−0.130678	−0.0653391	−	0.997863i	$-0.520813\pi$
$103$	−1.32624	−0.130678	−0.0653391	+	0.997863i	$0.520813\pi$
$104$	−2.23607	−0.219265
$105$	−9.70820	−0.947424
$106$	−5.76393	−0.559843
$107$	−10.4164	−1.00699	−0.503496	−	0.863998i	$-0.667953\pi$
$107$	−10.4164	−1.00699	−0.503496	+	0.863998i	$0.667953\pi$
$108$	−3.61803	−0.348145
$109$	−16.7082	−1.60036	−0.800178	−	0.599763i	$-0.795262\pi$
$109$	−16.7082	−1.60036	−0.800178	+	0.599763i	$0.795262\pi$
$110$	0.472136	0.0450164
$111$	5.61803	0.533240
$112$	5.56231	0.525589
$113$	11.2361	1.05700	0.528500	−	0.848933i	$-0.322755\pi$
$113$	11.2361	1.05700	0.528500	+	0.848933i	$0.322755\pi$
$114$	0	0
$115$	−9.41641	−0.878085
$116$	2.23607	0.207614
$117$	−3.85410	−0.356312
$118$	9.47214	0.871981
$119$	15.7082	1.43997
$120$	−7.23607	−0.660560
$121$	−10.6180	−0.965276
$122$	3.56231	0.322516
$123$	−7.85410	−0.708181
$124$	3.47214	0.311807
$125$	10.4721	0.936656
$126$	−7.14590	−0.636607
$127$	10.2361	0.908304	0.454152	−	0.890924i	$-0.349942\pi$
$127$	10.2361	0.908304	0.454152	+	0.890924i	$0.349942\pi$
$128$	11.3820	1.00603
$129$	−17.9443	−1.57991
$130$	−0.763932	−0.0670013
$131$	3.90983	0.341603	0.170802	−	0.985305i	$-0.445364\pi$
$131$	3.90983	0.341603	0.170802	+	0.985305i	$0.445364\pi$
$132$	−2.61803	−0.227871
$133$	0	0
$134$	4.32624	0.373730
$135$	−2.76393	−0.237881
$136$	11.7082	1.00397
$137$	−1.47214	−0.125773	−0.0628865	−	0.998021i	$-0.520031\pi$
$137$	−1.47214	−0.125773	−0.0628865	+	0.998021i	$0.520031\pi$
$138$	−12.3262	−1.04928
$139$	−9.79837	−0.831087	−0.415544	−	0.909573i	$-0.636409\pi$
$139$	−9.79837	−0.831087	−0.415544	+	0.909573i	$0.636409\pi$
$140$	6.00000	0.507093
$141$	7.85410	0.661435
$142$	−0.909830	−0.0763512
$143$	−0.618034	−0.0516826
$144$	7.14590	0.595492
$145$	1.70820	0.141859
$146$	−6.61803	−0.547712
$147$	5.23607	0.431864
$148$	−3.47214	−0.285408
$149$	−13.0902	−1.07239	−0.536194	−	0.844095i	$-0.680139\pi$
$149$	−13.0902	−1.07239	−0.536194	+	0.844095i	$0.680139\pi$
$150$	5.61803	0.458711
$151$	−9.90983	−0.806451	−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983	−0.806451	−0.403225	+	0.915101i	$0.632111\pi$
$152$	0	0
$153$	20.1803	1.63148
$154$	−1.14590	−0.0923391
$155$	2.65248	0.213052
$156$	4.23607	0.339157
$157$	−11.1459	−0.889540	−0.444770	−	0.895645i	$-0.646714\pi$
$157$	−11.1459	−0.889540	−0.444770	+	0.895645i	$0.646714\pi$
$158$	8.29180	0.659660
$159$	24.4164	1.93635
$160$	6.94427	0.548993
$161$	22.8541	1.80116
$162$	3.52786	0.277175
$163$	6.23607	0.488447	0.244223	−	0.969719i	$-0.421467\pi$
$163$	6.23607	0.488447	0.244223	+	0.969719i	$0.421467\pi$
$164$	4.85410	0.379042
$165$	−2.00000	−0.155700
$166$	0.291796	0.0226478
$167$	15.7639	1.21985	0.609925	−	0.792459i	$-0.291200\pi$
$167$	15.7639	1.21985	0.609925	+	0.792459i	$0.291200\pi$
$168$	17.5623	1.35496
$169$	−12.0000	−0.923077
$170$	4.00000	0.306786
$171$	0	0
$172$	11.0902	0.845618
$173$	8.47214	0.644125	0.322062	−	0.946718i	$-0.395624\pi$
$173$	8.47214	0.644125	0.322062	+	0.946718i	$0.395624\pi$
$174$	2.23607	0.169516
$175$	−10.4164	−0.787406
$176$	1.14590	0.0863753
$177$	−40.1246	−3.01595
$178$	7.56231	0.566819
$179$	7.76393	0.580304	0.290152	−	0.956981i	$-0.406294\pi$
$179$	7.76393	0.580304	0.290152	+	0.956981i	$0.406294\pi$
$180$	7.70820	0.574536
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	1.85410	0.137435
$183$	−15.0902	−1.11550
$184$	17.0344	1.25580
$185$	−2.65248	−0.195014
$186$	3.47214	0.254589
$187$	3.23607	0.236645
$188$	−4.85410	−0.354022
$189$	6.70820	0.487950
$190$	0	0
$191$	9.76393	0.706493	0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393	0.706493	0.353247	+	0.935530i	$0.385078\pi$
$192$	−0.618034	−0.0446028
$193$	22.9443	1.65156	0.825782	−	0.563989i	$-0.190734\pi$
$193$	22.9443	1.65156	0.825782	+	0.563989i	$0.190734\pi$
$194$	−4.41641	−0.317080
$195$	3.23607	0.231740
$196$	−3.23607	−0.231148
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	−1.47214	−0.104620
$199$	13.4164	0.951064	0.475532	−	0.879698i	$-0.342256\pi$
$199$	13.4164	0.951064	0.475532	+	0.879698i	$0.342256\pi$
$200$	−7.76393	−0.548993
$201$	−18.3262	−1.29263
$202$	−8.14590	−0.573143
$203$	−4.14590	−0.290985
$204$	−22.1803	−1.55293
$205$	3.70820	0.258992
$206$	0.819660	0.0571084
$207$	29.3607	2.04071
$208$	−1.85410	−0.128559
$209$	0	0
$210$	6.00000	0.414039
$211$	2.85410	0.196484	0.0982422	−	0.995163i	$-0.468678\pi$
$211$	2.85410	0.196484	0.0982422	+	0.995163i	$0.468678\pi$
$212$	−15.0902	−1.03640
$213$	3.85410	0.264079
$214$	6.43769	0.440072
$215$	8.47214	0.577795
$216$	5.00000	0.340207
$217$	−6.43769	−0.437019
$218$	10.3262	0.699381
$219$	28.0344	1.89439
$220$	1.23607	0.0833357
$221$	−5.23607	−0.352216
$222$	−3.47214	−0.233035
$223$	19.6525	1.31603	0.658014	−	0.753006i	$-0.271397\pi$
$223$	19.6525	1.31603	0.658014	+	0.753006i	$0.271397\pi$
$224$	−16.8541	−1.12611
$225$	−13.3820	−0.892131
$226$	−6.94427	−0.461926
$227$	−10.4164	−0.691361	−0.345681	−	0.938352i	$-0.612352\pi$
$227$	−10.4164	−0.691361	−0.345681	+	0.938352i	$0.612352\pi$
$228$	0	0
$229$	−11.3820	−0.752141	−0.376071	−	0.926591i	$-0.622725\pi$
$229$	−11.3820	−0.752141	−0.376071	+	0.926591i	$0.622725\pi$
$230$	5.81966	0.383737
$231$	4.85410	0.319376
$232$	−3.09017	−0.202880
$233$	13.4721	0.882589	0.441294	−	0.897362i	$-0.354519\pi$
$233$	13.4721	0.882589	0.441294	+	0.897362i	$0.354519\pi$
$234$	2.38197	0.155714
$235$	−3.70820	−0.241897
$236$	24.7984	1.61424
$237$	−35.1246	−2.28159
$238$	−9.70820	−0.629289
$239$	15.3262	0.991372	0.495686	−	0.868502i	$-0.334917\pi$
$239$	15.3262	0.991372	0.495686	+	0.868502i	$0.334917\pi$
$240$	−6.00000	−0.387298
$241$	−19.1803	−1.23551	−0.617757	−	0.786369i	$-0.711959\pi$
$241$	−19.1803	−1.23551	−0.617757	+	0.786369i	$0.711959\pi$
$242$	6.56231	0.421841
$243$	−21.6525	−1.38901
$244$	9.32624	0.597051
$245$	−2.47214	−0.157939
$246$	4.85410	0.309486
$247$	0	0
$248$	−4.79837	−0.304697
$249$	−1.23607	−0.0783326
$250$	−6.47214	−0.409334
$251$	19.3607	1.22204	0.611018	−	0.791617i	$-0.290760\pi$
$251$	19.3607	1.22204	0.611018	+	0.791617i	$0.290760\pi$
$252$	−18.7082	−1.17851
$253$	4.70820	0.296002
$254$	−6.32624	−0.396943
$255$	−16.9443	−1.06109
$256$	−6.56231	−0.410144
$257$	−24.3607	−1.51958	−0.759789	−	0.650170i	$-0.774698\pi$
$257$	−24.3607	−1.51958	−0.759789	+	0.650170i	$0.774698\pi$
$258$	11.0902	0.690444
$259$	6.43769	0.400019
$260$	−2.00000	−0.124035
$261$	−5.32624	−0.329686
$262$	−2.41641	−0.149286
$263$	2.94427	0.181552	0.0907758	−	0.995871i	$-0.471065\pi$
$263$	2.94427	0.181552	0.0907758	+	0.995871i	$0.471065\pi$
$264$	3.61803	0.222675
$265$	−11.5279	−0.708151
$266$	0	0
$267$	−32.0344	−1.96048
$268$	11.3262	0.691860
$269$	14.6738	0.894675	0.447338	−	0.894365i	$-0.352372\pi$
$269$	14.6738	0.894675	0.447338	+	0.894365i	$0.352372\pi$
$270$	1.70820	0.103958
$271$	7.85410	0.477103	0.238551	−	0.971130i	$-0.423327\pi$
$271$	7.85410	0.477103	0.238551	+	0.971130i	$0.423327\pi$
$272$	9.70820	0.588646
$273$	−7.85410	−0.475352
$274$	0.909830	0.0549648
$275$	−2.14590	−0.129403
$276$	−32.2705	−1.94246
$277$	−15.4164	−0.926282	−0.463141	−	0.886285i	$-0.653278\pi$
$277$	−15.4164	−0.926282	−0.463141	+	0.886285i	$0.653278\pi$
$278$	6.05573	0.363198
$279$	−8.27051	−0.495142
$280$	−8.29180	−0.495530
$281$	8.50658	0.507460	0.253730	−	0.967275i	$-0.418343\pi$
$281$	8.50658	0.507460	0.253730	+	0.967275i	$0.418343\pi$
$282$	−4.85410	−0.289058
$283$	−3.03444	−0.180379	−0.0901894	−	0.995925i	$-0.528747\pi$
$283$	−3.03444	−0.180379	−0.0901894	+	0.995925i	$0.528747\pi$
$284$	−2.38197	−0.141344
$285$	0	0
$286$	0.381966	0.0225861
$287$	−9.00000	−0.531253
$288$	−21.6525	−1.27588
$289$	10.4164	0.612730
$290$	−1.05573	−0.0619945
$291$	18.7082	1.09669
$292$	−17.3262	−1.01394
$293$	−16.8541	−0.984627	−0.492314	−	0.870418i	$-0.663849\pi$
$293$	−16.8541	−0.984627	−0.492314	+	0.870418i	$0.663849\pi$
$294$	−3.23607	−0.188731
$295$	18.9443	1.10298
$296$	4.79837	0.278900
$297$	1.38197	0.0801898
$298$	8.09017	0.468651
$299$	−7.61803	−0.440562
$300$	14.7082	0.849179
$301$	−20.5623	−1.18519
$302$	6.12461	0.352432
$303$	34.5066	1.98235
$304$	0	0
$305$	7.12461	0.407954
$306$	−12.4721	−0.712985
$307$	−1.67376	−0.0955266	−0.0477633	−	0.998859i	$-0.515209\pi$
$307$	−1.67376	−0.0955266	−0.0477633	+	0.998859i	$0.515209\pi$
$308$	−3.00000	−0.170941
$309$	−3.47214	−0.197523
$310$	−1.63932	−0.0931071
$311$	−18.6525	−1.05768	−0.528842	−	0.848720i	$-0.677374\pi$
$311$	−18.6525	−1.05768	−0.528842	+	0.848720i	$0.677374\pi$
$312$	−5.85410	−0.331423
$313$	4.32624	0.244533	0.122267	−	0.992497i	$-0.460984\pi$
$313$	4.32624	0.244533	0.122267	+	0.992497i	$0.460984\pi$
$314$	6.88854	0.388743
$315$	−14.2918	−0.805251
$316$	21.7082	1.22118
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−15.0902	−0.846215
$319$	−0.854102	−0.0478205
$320$	0.291796	0.0163119
$321$	−27.2705	−1.52209
$322$	−14.1246	−0.787134
$323$	0	0
$324$	9.23607	0.513115
$325$	3.47214	0.192599
$326$	−3.85410	−0.213459
$327$	−43.7426	−2.41897
$328$	−6.70820	−0.370399
$329$	9.00000	0.496186
$330$	1.23607	0.0680433
$331$	−6.94427	−0.381692	−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427	−0.381692	−0.190846	+	0.981620i	$0.561123\pi$
$332$	0.763932	0.0419262
$333$	8.27051	0.453221
$334$	−9.74265	−0.533094
$335$	8.65248	0.472735
$336$	14.5623	0.794439
$337$	23.1246	1.25968	0.629839	−	0.776726i	$-0.283121\pi$
$337$	23.1246	1.25968	0.629839	+	0.776726i	$0.283121\pi$
$338$	7.41641	0.403399
$339$	29.4164	1.59768
$340$	10.4721	0.567931
$341$	−1.32624	−0.0718198
$342$	0	0
$343$	−15.0000	−0.809924
$344$	−15.3262	−0.826335
$345$	−24.6525	−1.32724
$346$	−5.23607	−0.281493
$347$	1.41641	0.0760368	0.0380184	−	0.999277i	$-0.487895\pi$
$347$	1.41641	0.0760368	0.0380184	+	0.999277i	$0.487895\pi$
$348$	5.85410	0.313813
$349$	25.9787	1.39061	0.695304	−	0.718715i	$-0.255270\pi$
$349$	25.9787	1.39061	0.695304	+	0.718715i	$0.255270\pi$
$350$	6.43769	0.344109
$351$	−2.23607	−0.119352
$352$	−3.47214	−0.185065
$353$	−31.4508	−1.67396	−0.836980	−	0.547234i	$-0.815681\pi$
$353$	−31.4508	−1.67396	−0.836980	+	0.547234i	$0.815681\pi$
$354$	24.7984	1.31802
$355$	−1.81966	−0.0965775
$356$	19.7984	1.04931
$357$	41.1246	2.17655
$358$	−4.79837	−0.253602
$359$	−22.0344	−1.16293	−0.581467	−	0.813570i	$-0.697521\pi$
$359$	−22.0344	−1.16293	−0.581467	+	0.813570i	$0.697521\pi$
$360$	−10.6525	−0.561435
$361$	0	0
$362$	−7.41641	−0.389798
$363$	−27.7984	−1.45904
$364$	4.85410	0.254424
$365$	−13.2361	−0.692807
$366$	9.32624	0.487490
$367$	1.94427	0.101490	0.0507451	−	0.998712i	$-0.483840\pi$
$367$	1.94427	0.101490	0.0507451	+	0.998712i	$0.483840\pi$
$368$	14.1246	0.736296
$369$	−11.5623	−0.601910
$370$	1.63932	0.0852242
$371$	27.9787	1.45258
$372$	9.09017	0.471303
$373$	3.47214	0.179780	0.0898902	−	0.995952i	$-0.471348\pi$
$373$	3.47214	0.179780	0.0898902	+	0.995952i	$0.471348\pi$
$374$	−2.00000	−0.103418
$375$	27.4164	1.41578
$376$	6.70820	0.345949
$377$	1.38197	0.0711749
$378$	−4.14590	−0.213242
$379$	25.1246	1.29056	0.645282	−	0.763944i	$-0.276740\pi$
$379$	25.1246	1.29056	0.645282	+	0.763944i	$0.276740\pi$
$380$	0	0
$381$	26.7984	1.37292
$382$	−6.03444	−0.308749
$383$	2.61803	0.133775	0.0668876	−	0.997761i	$-0.478693\pi$
$383$	2.61803	0.133775	0.0668876	+	0.997761i	$0.478693\pi$
$384$	29.7984	1.52064
$385$	−2.29180	−0.116801
$386$	−14.1803	−0.721760
$387$	−26.4164	−1.34282
$388$	−11.5623	−0.586987
$389$	−24.2705	−1.23056	−0.615282	−	0.788307i	$-0.710958\pi$
$389$	−24.2705	−1.23056	−0.615282	+	0.788307i	$0.710958\pi$
$390$	−2.00000	−0.101274
$391$	39.8885	2.01725
$392$	4.47214	0.225877
$393$	10.2361	0.516341
$394$	−1.85410	−0.0934083
$395$	16.5836	0.834411
$396$	−3.85410	−0.193676
$397$	−2.52786	−0.126870	−0.0634349	−	0.997986i	$-0.520206\pi$
$397$	−2.52786	−0.126870	−0.0634349	+	0.997986i	$0.520206\pi$
$398$	−8.29180	−0.415630
$399$	0	0
$400$	−6.43769	−0.321885
$401$	−0.111456	−0.00556586	−0.00278293	−	0.999996i	$-0.500886\pi$
$401$	−0.111456	−0.00556586	−0.00278293	+	0.999996i	$0.500886\pi$
$402$	11.3262	0.564901
$403$	2.14590	0.106895
$404$	−21.3262	−1.06102
$405$	7.05573	0.350602
$406$	2.56231	0.127165
$407$	1.32624	0.0657392
$408$	30.6525	1.51752
$409$	−21.7082	−1.07340	−0.536701	−	0.843773i	$-0.680330\pi$
$409$	−21.7082	−1.07340	−0.536701	+	0.843773i	$0.680330\pi$
$410$	−2.29180	−0.113184
$411$	−3.85410	−0.190109
$412$	2.14590	0.105721
$413$	−45.9787	−2.26246
$414$	−18.1459	−0.891822
$415$	0.583592	0.0286474
$416$	5.61803	0.275447
$417$	−25.6525	−1.25621
$418$	0	0
$419$	8.94427	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$420$	15.7082	0.766482
$421$	−18.5279	−0.902993	−0.451496	−	0.892273i	$-0.649110\pi$
$421$	−18.5279	−0.902993	−0.451496	+	0.892273i	$0.649110\pi$
$422$	−1.76393	−0.0858669
$423$	11.5623	0.562179
$424$	20.8541	1.01276
$425$	−18.1803	−0.881876
$426$	−2.38197	−0.115407
$427$	−17.2918	−0.836809
$428$	16.8541	0.814674
$429$	−1.61803	−0.0781194
$430$	−5.23607	−0.252506
$431$	−3.65248	−0.175934	−0.0879668	−	0.996123i	$-0.528037\pi$
$431$	−3.65248	−0.175934	−0.0879668	+	0.996123i	$0.528037\pi$
$432$	4.14590	0.199470
$433$	−23.5623	−1.13233	−0.566166	−	0.824291i	$-0.691574\pi$
$433$	−23.5623	−1.13233	−0.566166	+	0.824291i	$0.691574\pi$
$434$	3.97871	0.190984
$435$	4.47214	0.214423
$436$	27.0344	1.29471
$437$	0	0
$438$	−17.3262	−0.827880
$439$	14.5967	0.696665	0.348332	−	0.937371i	$-0.386748\pi$
$439$	14.5967	0.696665	0.348332	+	0.937371i	$0.386748\pi$
$440$	−1.70820	−0.0814354
$441$	7.70820	0.367057
$442$	3.23607	0.153924
$443$	−34.4164	−1.63517	−0.817586	−	0.575806i	$-0.804688\pi$
$443$	−34.4164	−1.63517	−0.817586	+	0.575806i	$0.804688\pi$
$444$	−9.09017	−0.431400
$445$	15.1246	0.716975
$446$	−12.1459	−0.575125
$447$	−34.2705	−1.62094
$448$	−0.708204	−0.0334595
$449$	−32.8885	−1.55211	−0.776053	−	0.630667i	$-0.782781\pi$
$449$	−32.8885	−1.55211	−0.776053	+	0.630667i	$0.782781\pi$
$450$	8.27051	0.389876
$451$	−1.85410	−0.0873063
$452$	−18.1803	−0.855131
$453$	−25.9443	−1.21897
$454$	6.43769	0.302136
$455$	3.70820	0.173843
$456$	0	0
$457$	6.29180	0.294318	0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180	0.294318	0.147159	+	0.989113i	$0.452987\pi$
$458$	7.03444	0.328698
$459$	11.7082	0.546492
$460$	15.2361	0.710385
$461$	3.05573	0.142319	0.0711597	−	0.997465i	$-0.477330\pi$
$461$	3.05573	0.142319	0.0711597	+	0.997465i	$0.477330\pi$
$462$	−3.00000	−0.139573
$463$	−5.27051	−0.244941	−0.122471	−	0.992472i	$-0.539082\pi$
$463$	−5.27051	−0.244941	−0.122471	+	0.992472i	$0.539082\pi$
$464$	−2.56231	−0.118952
$465$	6.94427	0.322033
$466$	−8.32624	−0.385706
$467$	1.94427	0.0899702	0.0449851	−	0.998988i	$-0.485676\pi$
$467$	1.94427	0.0899702	0.0449851	+	0.998988i	$0.485676\pi$
$468$	6.23607	0.288262
$469$	−21.0000	−0.969690
$470$	2.29180	0.105713
$471$	−29.1803	−1.34456
$472$	−34.2705	−1.57743
$473$	−4.23607	−0.194775
$474$	21.7082	0.997091
$475$	0	0
$476$	−25.4164	−1.16496
$477$	35.9443	1.64578
$478$	−9.47214	−0.433245
$479$	11.9098	0.544174	0.272087	−	0.962273i	$-0.412286\pi$
$479$	11.9098	0.544174	0.272087	+	0.962273i	$0.412286\pi$
$480$	18.1803	0.829815
$481$	−2.14590	−0.0978445
$482$	11.8541	0.539940
$483$	59.8328	2.72249
$484$	17.1803	0.780925
$485$	−8.83282	−0.401078
$486$	13.3820	0.607018
$487$	−18.1803	−0.823830	−0.411915	−	0.911222i	$-0.635140\pi$
$487$	−18.1803	−0.823830	−0.411915	+	0.911222i	$0.635140\pi$
$488$	−12.8885	−0.583437
$489$	16.3262	0.738298
$490$	1.52786	0.0690219
$491$	30.2148	1.36357	0.681787	−	0.731551i	$-0.261203\pi$
$491$	30.2148	1.36357	0.681787	+	0.731551i	$0.261203\pi$
$492$	12.7082	0.572930
$493$	−7.23607	−0.325896
$494$	0	0
$495$	−2.94427	−0.132335
$496$	−3.97871	−0.178650
$497$	4.41641	0.198103
$498$	0.763932	0.0342326
$499$	−15.1246	−0.677071	−0.338535	−	0.940954i	$-0.609931\pi$
$499$	−15.1246	−0.677071	−0.338535	+	0.940954i	$0.609931\pi$
$500$	−16.9443	−0.757771
$501$	41.2705	1.84383
$502$	−11.9656	−0.534049
$503$	−17.8328	−0.795126	−0.397563	−	0.917575i	$-0.630144\pi$
$503$	−17.8328	−0.795126	−0.397563	+	0.917575i	$0.630144\pi$
$504$	25.8541	1.15163
$505$	−16.2918	−0.724975
$506$	−2.90983	−0.129358
$507$	−31.4164	−1.39525
$508$	−16.5623	−0.734833
$509$	−27.0344	−1.19828	−0.599140	−	0.800644i	$-0.704491\pi$
$509$	−27.0344	−1.19828	−0.599140	+	0.800644i	$0.704491\pi$
$510$	10.4721	0.463714
$511$	32.1246	1.42111
$512$	−18.7082	−0.826794
$513$	0	0
$514$	15.0557	0.664080
$515$	1.63932	0.0722371
$516$	29.0344	1.27817
$517$	1.85410	0.0815433
$518$	−3.97871	−0.174815
$519$	22.1803	0.973609
$520$	2.76393	0.121206
$521$	−27.2705	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$521$	−27.2705	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$522$	3.29180	0.144078
$523$	22.4164	0.980201	0.490101	−	0.871666i	$-0.336960\pi$
$523$	22.4164	0.980201	0.490101	+	0.871666i	$0.336960\pi$
$524$	−6.32624	−0.276363
$525$	−27.2705	−1.19018
$526$	−1.81966	−0.0793410
$527$	−11.2361	−0.489451
$528$	3.00000	0.130558
$529$	35.0344	1.52324
$530$	7.12461	0.309473
$531$	−59.0689	−2.56337
$532$	0	0
$533$	3.00000	0.129944
$534$	19.7984	0.856759
$535$	12.8754	0.556652
$536$	−15.6525	−0.676084
$537$	20.3262	0.877142
$538$	−9.06888	−0.390987
$539$	1.23607	0.0532412
$540$	4.47214	0.192450
$541$	23.8328	1.02465	0.512326	−	0.858791i	$-0.328784\pi$
$541$	23.8328	1.02465	0.512326	+	0.858791i	$0.328784\pi$
$542$	−4.85410	−0.208502
$543$	31.4164	1.34821
$544$	−29.4164	−1.26122
$545$	20.6525	0.884655
$546$	4.85410	0.207736
$547$	37.9230	1.62147	0.810735	−	0.585413i	$-0.199068\pi$
$547$	37.9230	1.62147	0.810735	+	0.585413i	$0.199068\pi$
$548$	2.38197	0.101753
$549$	−22.2148	−0.948104
$550$	1.32624	0.0565510
$551$	0	0
$552$	44.5967	1.89816
$553$	−40.2492	−1.71157
$554$	9.52786	0.404800
$555$	−6.94427	−0.294768
$556$	15.8541	0.672364
$557$	−23.1803	−0.982183	−0.491091	−	0.871108i	$-0.663402\pi$
$557$	−23.1803	−0.982183	−0.491091	+	0.871108i	$0.663402\pi$
$558$	5.11146	0.216385
$559$	6.85410	0.289898
$560$	−6.87539	−0.290538
$561$	8.47214	0.357694
$562$	−5.25735	−0.221768
$563$	20.8328	0.877999	0.438999	−	0.898487i	$-0.355333\pi$
$563$	20.8328	0.877999	0.438999	+	0.898487i	$0.355333\pi$
$564$	−12.7082	−0.535112
$565$	−13.8885	−0.584295
$566$	1.87539	0.0788284
$567$	−17.1246	−0.719166
$568$	3.29180	0.138121
$569$	28.0902	1.17760	0.588801	−	0.808278i	$-0.299600\pi$
$569$	28.0902	1.17760	0.588801	+	0.808278i	$0.299600\pi$
$570$	0	0
$571$	22.3262	0.934324	0.467162	−	0.884172i	$-0.345276\pi$
$571$	22.3262	0.934324	0.467162	+	0.884172i	$0.345276\pi$
$572$	1.00000	0.0418121
$573$	25.5623	1.06788
$574$	5.56231	0.232166
$575$	−26.4508	−1.10308
$576$	−0.909830	−0.0379096
$577$	28.1246	1.17084	0.585421	−	0.810729i	$-0.300929\pi$
$577$	28.1246	1.17084	0.585421	+	0.810729i	$0.300929\pi$
$578$	−6.43769	−0.267773
$579$	60.0689	2.49638
$580$	−2.76393	−0.114766
$581$	−1.41641	−0.0587625
$582$	−11.5623	−0.479273
$583$	5.76393	0.238718
$584$	23.9443	0.990821
$585$	4.76393	0.196964
$586$	10.4164	0.430298
$587$	38.1246	1.57357	0.786786	−	0.617226i	$-0.211744\pi$
$587$	38.1246	1.57357	0.786786	+	0.617226i	$0.211744\pi$
$588$	−8.47214	−0.349385
$589$	0	0
$590$	−11.7082	−0.482019
$591$	7.85410	0.323075
$592$	3.97871	0.163524
$593$	−12.7082	−0.521863	−0.260932	−	0.965357i	$-0.584030\pi$
$593$	−12.7082	−0.521863	−0.260932	+	0.965357i	$0.584030\pi$
$594$	−0.854102	−0.0350442
$595$	−19.4164	−0.795995
$596$	21.1803	0.867581
$597$	35.1246	1.43755
$598$	4.70820	0.192533
$599$	1.58359	0.0647038	0.0323519	−	0.999477i	$-0.489700\pi$
$599$	1.58359	0.0647038	0.0323519	+	0.999477i	$0.489700\pi$
$600$	−20.3262	−0.829815
$601$	33.7082	1.37499	0.687493	−	0.726191i	$-0.258711\pi$
$601$	33.7082	1.37499	0.687493	+	0.726191i	$0.258711\pi$
$602$	12.7082	0.517948
$603$	−26.9787	−1.09866
$604$	16.0344	0.652432
$605$	13.1246	0.533591
$606$	−21.3262	−0.866319
$607$	27.2705	1.10688	0.553438	−	0.832890i	$-0.313316\pi$
$607$	27.2705	1.10688	0.553438	+	0.832890i	$0.313316\pi$
$608$	0	0
$609$	−10.8541	−0.439830
$610$	−4.40325	−0.178282
$611$	−3.00000	−0.121367
$612$	−32.6525	−1.31990
$613$	−2.05573	−0.0830301	−0.0415150	−	0.999138i	$-0.513218\pi$
$613$	−2.05573	−0.0830301	−0.0415150	+	0.999138i	$0.513218\pi$
$614$	1.03444	0.0417467
$615$	9.70820	0.391473
$616$	4.14590	0.167043
$617$	23.3262	0.939079	0.469539	−	0.882911i	$-0.344420\pi$
$617$	23.3262	0.939079	0.469539	+	0.882911i	$0.344420\pi$
$618$	2.14590	0.0863207
$619$	−30.1246	−1.21081	−0.605405	−	0.795917i	$-0.706989\pi$
$619$	−30.1246	−1.21081	−0.605405	+	0.795917i	$0.706989\pi$
$620$	−4.29180	−0.172363
$621$	17.0344	0.683569
$622$	11.5279	0.462225
$623$	−36.7082	−1.47068
$624$	−4.85410	−0.194320
$625$	4.41641	0.176656
$626$	−2.67376	−0.106865
$627$	0	0
$628$	18.0344	0.719653
$629$	11.2361	0.448011
$630$	8.83282	0.351908
$631$	−15.3607	−0.611499	−0.305750	−	0.952112i	$-0.598907\pi$
$631$	−15.3607	−0.611499	−0.305750	+	0.952112i	$0.598907\pi$
$632$	−30.0000	−1.19334
$633$	7.47214	0.296991
$634$	−11.1246	−0.441815
$635$	−12.6525	−0.502098
$636$	−39.5066	−1.56654
$637$	−2.00000	−0.0792429
$638$	0.527864	0.0208983
$639$	5.67376	0.224451
$640$	−14.0689	−0.556121
$641$	−1.49342	−0.0589866	−0.0294933	−	0.999565i	$-0.509389\pi$
$641$	−1.49342	−0.0589866	−0.0294933	+	0.999565i	$0.509389\pi$
$642$	16.8541	0.665178
$643$	−37.7082	−1.48707	−0.743533	−	0.668699i	$-0.766851\pi$
$643$	−37.7082	−1.48707	−0.743533	+	0.668699i	$0.766851\pi$
$644$	−36.9787	−1.45717
$645$	22.1803	0.873350
$646$	0	0
$647$	−1.47214	−0.0578756	−0.0289378	−	0.999581i	$-0.509212\pi$
$647$	−1.47214	−0.0578756	−0.0289378	+	0.999581i	$0.509212\pi$
$648$	−12.7639	−0.501415
$649$	−9.47214	−0.371814
$650$	−2.14590	−0.0841690
$651$	−16.8541	−0.660564
$652$	−10.0902	−0.395162
$653$	−3.43769	−0.134527	−0.0672637	−	0.997735i	$-0.521427\pi$
$653$	−3.43769	−0.134527	−0.0672637	+	0.997735i	$0.521427\pi$
$654$	27.0344	1.05713
$655$	−4.83282	−0.188834
$656$	−5.56231	−0.217172
$657$	41.2705	1.61012
$658$	−5.56231	−0.216841
$659$	45.7771	1.78322	0.891611	−	0.452802i	$-0.149576\pi$
$659$	45.7771	1.78322	0.891611	+	0.452802i	$0.149576\pi$
$660$	3.23607	0.125964
$661$	−21.4164	−0.833002	−0.416501	−	0.909135i	$-0.636744\pi$
$661$	−21.4164	−0.833002	−0.416501	+	0.909135i	$0.636744\pi$
$662$	4.29180	0.166805
$663$	−13.7082	−0.532383
$664$	−1.05573	−0.0409702
$665$	0	0
$666$	−5.11146	−0.198065
$667$	−10.5279	−0.407641
$668$	−25.5066	−0.986879
$669$	51.4508	1.98920
$670$	−5.34752	−0.206593
$671$	−3.56231	−0.137521
$672$	−44.1246	−1.70214
$673$	−6.12461	−0.236086	−0.118043	−	0.993008i	$-0.537662\pi$
$673$	−6.12461	−0.236086	−0.118043	+	0.993008i	$0.537662\pi$
$674$	−14.2918	−0.550499
$675$	−7.76393	−0.298834
$676$	19.4164	0.746785
$677$	11.7426	0.451307	0.225653	−	0.974208i	$-0.427548\pi$
$677$	11.7426	0.451307	0.225653	+	0.974208i	$0.427548\pi$
$678$	−18.1803	−0.698212
$679$	21.4377	0.822703
$680$	−14.4721	−0.554981
$681$	−27.2705	−1.04501
$682$	0.819660	0.0313864
$683$	−21.6525	−0.828509	−0.414254	−	0.910161i	$-0.635958\pi$
$683$	−21.6525	−0.828509	−0.414254	+	0.910161i	$0.635958\pi$
$684$	0	0
$685$	1.81966	0.0695256
$686$	9.27051	0.353950
$687$	−29.7984	−1.13688
$688$	−12.7082	−0.484496
$689$	−9.32624	−0.355301
$690$	15.2361	0.580027
$691$	−16.8197	−0.639850	−0.319925	−	0.947443i	$-0.603658\pi$
$691$	−16.8197	−0.639850	−0.319925	+	0.947443i	$0.603658\pi$
$692$	−13.7082	−0.521108
$693$	7.14590	0.271450
$694$	−0.875388	−0.0332293
$695$	12.1115	0.459414
$696$	−8.09017	−0.306657
$697$	−15.7082	−0.594991
$698$	−16.0557	−0.607718
$699$	35.2705	1.33405
$700$	16.8541	0.637025
$701$	38.6312	1.45908	0.729540	−	0.683938i	$-0.239734\pi$
$701$	38.6312	1.45908	0.729540	+	0.683938i	$0.239734\pi$
$702$	1.38197	0.0521589
$703$	0	0
$704$	−0.145898	−0.00549874
$705$	−9.70820	−0.365632
$706$	19.4377	0.731547
$707$	39.5410	1.48709
$708$	64.9230	2.43996
$709$	43.4164	1.63054	0.815269	−	0.579083i	$-0.196589\pi$
$709$	43.4164	1.63054	0.815269	+	0.579083i	$0.196589\pi$
$710$	1.12461	0.0422059
$711$	−51.7082	−1.93921
$712$	−27.3607	−1.02538
$713$	−16.3475	−0.612220
$714$	−25.4164	−0.951185
$715$	0.763932	0.0285694
$716$	−12.5623	−0.469475
$717$	40.1246	1.49848
$718$	13.6180	0.508221
$719$	17.9656	0.670002	0.335001	−	0.942218i	$-0.391263\pi$
$719$	17.9656	0.670002	0.335001	+	0.942218i	$0.391263\pi$
$720$	−8.83282	−0.329180
$721$	−3.97871	−0.148175
$722$	0	0
$723$	−50.2148	−1.86751
$724$	−19.4164	−0.721605
$725$	4.79837	0.178207
$726$	17.1803	0.637622
$727$	42.0689	1.56025	0.780124	−	0.625625i	$-0.215156\pi$
$727$	42.0689	1.56025	0.780124	+	0.625625i	$0.215156\pi$
$728$	−6.70820	−0.248623
$729$	−39.5623	−1.46527
$730$	8.18034	0.302768
$731$	−35.8885	−1.32739
$732$	24.4164	0.902456
$733$	40.9574	1.51280	0.756399	−	0.654111i	$-0.226957\pi$
$733$	40.9574	1.51280	0.756399	+	0.654111i	$0.226957\pi$
$734$	−1.20163	−0.0443528
$735$	−6.47214	−0.238728
$736$	−42.7984	−1.57757
$737$	−4.32624	−0.159359
$738$	7.14590	0.263044
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	4.29180	0.157770
$741$	0	0
$742$	−17.2918	−0.634802
$743$	41.3607	1.51738	0.758688	−	0.651454i	$-0.225841\pi$
$743$	41.3607	1.51738	0.758688	+	0.651454i	$0.225841\pi$
$744$	−12.5623	−0.460556
$745$	16.1803	0.592802
$746$	−2.14590	−0.0785669
$747$	−1.81966	−0.0665779
$748$	−5.23607	−0.191450
$749$	−31.2492	−1.14182
$750$	−16.9443	−0.618717
$751$	−23.8541	−0.870449	−0.435224	−	0.900322i	$-0.643331\pi$
$751$	−23.8541	−0.870449	−0.435224	+	0.900322i	$0.643331\pi$
$752$	5.56231	0.202836
$753$	50.6869	1.84713
$754$	−0.854102	−0.0311046
$755$	12.2492	0.445795
$756$	−10.8541	−0.394760
$757$	−15.7426	−0.572176	−0.286088	−	0.958203i	$-0.592355\pi$
$757$	−15.7426	−0.572176	−0.286088	+	0.958203i	$0.592355\pi$
$758$	−15.5279	−0.563997
$759$	12.3262	0.447414
$760$	0	0
$761$	−30.8885	−1.11971	−0.559854	−	0.828591i	$-0.689143\pi$
$761$	−30.8885	−1.11971	−0.559854	+	0.828591i	$0.689143\pi$
$762$	−16.5623	−0.599989
$763$	−50.1246	−1.81463
$764$	−15.7984	−0.571565
$765$	−24.9443	−0.901862
$766$	−1.61803	−0.0584619
$767$	15.3262	0.553398
$768$	−17.1803	−0.619942
$769$	−41.6312	−1.50126	−0.750630	−	0.660723i	$-0.770250\pi$
$769$	−41.6312	−1.50126	−0.750630	+	0.660723i	$0.770250\pi$
$770$	1.41641	0.0510438
$771$	−63.7771	−2.29688
$772$	−37.1246	−1.33614
$773$	28.9230	1.04029	0.520144	−	0.854079i	$-0.325878\pi$
$773$	28.9230	1.04029	0.520144	+	0.854079i	$0.325878\pi$
$774$	16.3262	0.586835
$775$	7.45085	0.267642
$776$	15.9787	0.573602
$777$	16.8541	0.604638
$778$	15.0000	0.537776
$779$	0	0
$780$	−5.23607	−0.187481
$781$	0.909830	0.0325563
$782$	−24.6525	−0.881571
$783$	−3.09017	−0.110434
$784$	3.70820	0.132436
$785$	13.7771	0.491725
$786$	−6.32624	−0.225649
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	−4.85410	−0.172920
$789$	7.70820	0.274419
$790$	−10.2492	−0.364651
$791$	33.7082	1.19853
$792$	5.32624	0.189260
$793$	5.76393	0.204683
$794$	1.56231	0.0554442
$795$	−30.1803	−1.07039
$796$	−21.7082	−0.769427
$797$	−33.7082	−1.19401	−0.597003	−	0.802239i	$-0.703642\pi$
$797$	−33.7082	−1.19401	−0.597003	+	0.802239i	$0.703642\pi$
$798$	0	0
$799$	15.7082	0.555716
$800$	19.5066	0.689662
$801$	−47.1591	−1.66628
$802$	0.0688837	0.00243237
$803$	6.61803	0.233545
$804$	29.6525	1.04576
$805$	−28.2492	−0.995654
$806$	−1.32624	−0.0467147
$807$	38.4164	1.35232
$808$	29.4721	1.03683
$809$	−0.201626	−0.00708880	−0.00354440	−	0.999994i	$-0.501128\pi$
$809$	−0.201626	−0.00708880	−0.00354440	+	0.999994i	$0.501128\pi$
$810$	−4.36068	−0.153219
$811$	−23.9787	−0.842007	−0.421003	−	0.907059i	$-0.638322\pi$
$811$	−23.9787	−0.842007	−0.421003	+	0.907059i	$0.638322\pi$
$812$	6.70820	0.235412
$813$	20.5623	0.721152
$814$	−0.819660	−0.0287291
$815$	−7.70820	−0.270007
$816$	25.4164	0.889752
$817$	0	0
$818$	13.4164	0.469094
$819$	−11.5623	−0.404020
$820$	−6.00000	−0.209529
$821$	−53.0476	−1.85137	−0.925687	−	0.378290i	$-0.876512\pi$
$821$	−53.0476	−1.85137	−0.925687	+	0.378290i	$0.876512\pi$
$822$	2.38197	0.0830806
$823$	23.5967	0.822531	0.411265	−	0.911516i	$-0.365087\pi$
$823$	23.5967	0.822531	0.411265	+	0.911516i	$0.365087\pi$
$824$	−2.96556	−0.103310
$825$	−5.61803	−0.195595
$826$	28.4164	0.988733
$827$	−16.5967	−0.577125	−0.288563	−	0.957461i	$-0.593177\pi$
$827$	−16.5967	−0.577125	−0.288563	+	0.957461i	$0.593177\pi$
$828$	−47.5066	−1.65097
$829$	20.3262	0.705959	0.352980	−	0.935631i	$-0.385168\pi$
$829$	20.3262	0.705959	0.352980	+	0.935631i	$0.385168\pi$
$830$	−0.360680	−0.0125194
$831$	−40.3607	−1.40010
$832$	0.236068	0.00818418
$833$	10.4721	0.362838
$834$	15.8541	0.548983
$835$	−19.4853	−0.674316
$836$	0	0
$837$	−4.79837	−0.165856
$838$	−5.52786	−0.190957
$839$	39.7984	1.37399	0.686996	−	0.726661i	$-0.258929\pi$
$839$	39.7984	1.37399	0.686996	+	0.726661i	$0.258929\pi$
$840$	−21.7082	−0.749004
$841$	−27.0902	−0.934144
$842$	11.4508	0.394622
$843$	22.2705	0.767037
$844$	−4.61803	−0.158959
$845$	14.8328	0.510264
$846$	−7.14590	−0.245681
$847$	−31.8541	−1.09452
$848$	17.2918	0.593803
$849$	−7.94427	−0.272647
$850$	11.2361	0.385394
$851$	16.3475	0.560386
$852$	−6.23607	−0.213644
$853$	17.2918	0.592060	0.296030	−	0.955179i	$-0.404337\pi$
$853$	17.2918	0.592060	0.296030	+	0.955179i	$0.404337\pi$
$854$	10.6869	0.365699
$855$	0	0
$856$	−23.2918	−0.796097
$857$	−8.38197	−0.286323	−0.143161	−	0.989699i	$-0.545727\pi$
$857$	−8.38197	−0.286323	−0.143161	+	0.989699i	$0.545727\pi$
$858$	1.00000	0.0341394
$859$	18.5410	0.632611	0.316306	−	0.948657i	$-0.397557\pi$
$859$	18.5410	0.632611	0.316306	+	0.948657i	$0.397557\pi$
$860$	−13.7082	−0.467446
$861$	−23.5623	−0.803001
$862$	2.25735	0.0768858
$863$	−44.9443	−1.52992	−0.764960	−	0.644077i	$-0.777241\pi$
$863$	−44.9443	−1.52992	−0.764960	+	0.644077i	$0.777241\pi$
$864$	−12.5623	−0.427378
$865$	−10.4721	−0.356063
$866$	14.5623	0.494847
$867$	27.2705	0.926155
$868$	10.4164	0.353556
$869$	−8.29180	−0.281280
$870$	−2.76393	−0.0937061
$871$	7.00000	0.237186
$872$	−37.3607	−1.26519
$873$	27.5410	0.932122
$874$	0	0
$875$	31.4164	1.06207
$876$	−45.3607	−1.53260
$877$	34.1803	1.15419	0.577094	−	0.816678i	$-0.304187\pi$
$877$	34.1803	1.15419	0.577094	+	0.816678i	$0.304187\pi$
$878$	−9.02129	−0.304454
$879$	−44.1246	−1.48829
$880$	−1.41641	−0.0477471
$881$	−23.4508	−0.790079	−0.395040	−	0.918664i	$-0.629269\pi$
$881$	−23.4508	−0.790079	−0.395040	+	0.918664i	$0.629269\pi$
$882$	−4.76393	−0.160410
$883$	13.9230	0.468546	0.234273	−	0.972171i	$-0.424729\pi$
$883$	13.9230	0.468546	0.234273	+	0.972171i	$0.424729\pi$
$884$	8.47214	0.284949
$885$	49.5967	1.66718
$886$	21.2705	0.714597
$887$	58.6525	1.96936	0.984679	−	0.174378i	$-0.0557916\pi$
$887$	58.6525	1.96936	0.984679	+	0.174378i	$0.0557916\pi$
$888$	12.5623	0.421563
$889$	30.7082	1.02992
$890$	−9.34752	−0.313330
$891$	−3.52786	−0.118188
$892$	−31.7984	−1.06469
$893$	0	0
$894$	21.1803	0.708377
$895$	−9.59675	−0.320784
$896$	34.1459	1.14073
$897$	−19.9443	−0.665920
$898$	20.3262	0.678295
$899$	2.96556	0.0989069
$900$	21.6525	0.721749
$901$	48.8328	1.62686
$902$	1.14590	0.0381542
$903$	−53.8328	−1.79144
$904$	25.1246	0.835632
$905$	−14.8328	−0.493059
$906$	16.0344	0.532709
$907$	−17.5279	−0.582003	−0.291002	−	0.956723i	$-0.593988\pi$
$907$	−17.5279	−0.582003	−0.291002	+	0.956723i	$0.593988\pi$
$908$	16.8541	0.559323
$909$	50.7984	1.68488
$910$	−2.29180	−0.0759723
$911$	5.61803	0.186134	0.0930669	−	0.995660i	$-0.470333\pi$
$911$	5.61803	0.186134	0.0930669	+	0.995660i	$0.470333\pi$
$912$	0	0
$913$	−0.291796	−0.00965704
$914$	−3.88854	−0.128622
$915$	18.6525	0.616632
$916$	18.4164	0.608495
$917$	11.7295	0.387342
$918$	−7.23607	−0.238826
$919$	36.7082	1.21089	0.605446	−	0.795886i	$-0.292995\pi$
$919$	36.7082	1.21089	0.605446	+	0.795886i	$0.292995\pi$
$920$	−21.0557	−0.694187
$921$	−4.38197	−0.144391
$922$	−1.88854	−0.0621959
$923$	−1.47214	−0.0484559
$924$	−7.85410	−0.258381
$925$	−7.45085	−0.244982
$926$	3.25735	0.107043
$927$	−5.11146	−0.167882
$928$	7.76393	0.254864
$929$	18.6180	0.610838	0.305419	−	0.952218i	$-0.401203\pi$
$929$	18.6180	0.610838	0.305419	+	0.952218i	$0.401203\pi$
$930$	−4.29180	−0.140734
$931$	0	0
$932$	−21.7984	−0.714029
$933$	−48.8328	−1.59871
$934$	−1.20163	−0.0393184
$935$	−4.00000	−0.130814
$936$	−8.61803	−0.281689
$937$	20.4377	0.667670	0.333835	−	0.942631i	$-0.391657\pi$
$937$	20.4377	0.667670	0.333835	+	0.942631i	$0.391657\pi$
$938$	12.9787	0.423770
$939$	11.3262	0.369618
$940$	6.00000	0.195698
$941$	49.6869	1.61975	0.809874	−	0.586604i	$-0.199536\pi$
$941$	49.6869	1.61975	0.809874	+	0.586604i	$0.199536\pi$
$942$	18.0344	0.587594
$943$	−22.8541	−0.744232
$944$	−28.4164	−0.924875
$945$	−8.29180	−0.269732
$946$	2.61803	0.0851196
$947$	−1.34752	−0.0437887	−0.0218943	−	0.999760i	$-0.506970\pi$
$947$	−1.34752	−0.0437887	−0.0218943	+	0.999760i	$0.506970\pi$
$948$	56.8328	1.84584
$949$	−10.7082	−0.347603
$950$	0	0
$951$	47.1246	1.52812
$952$	35.1246	1.13840
$953$	30.7082	0.994736	0.497368	−	0.867540i	$-0.334300\pi$
$953$	30.7082	0.994736	0.497368	+	0.867540i	$0.334300\pi$
$954$	−22.2148	−0.719230
$955$	−12.0689	−0.390540
$956$	−24.7984	−0.802037
$957$	−2.23607	−0.0722818
$958$	−7.36068	−0.237813
$959$	−4.41641	−0.142613
$960$	0.763932	0.0246558
$961$	−26.3951	−0.851456
$962$	1.32624	0.0427596
$963$	−40.1459	−1.29368
$964$	31.0344	0.999552
$965$	−28.3607	−0.912963
$966$	−36.9787	−1.18977
$967$	−60.5410	−1.94687	−0.973434	−	0.228968i	$-0.926465\pi$
$967$	−60.5410	−1.94687	−0.973434	+	0.228968i	$0.926465\pi$
$968$	−23.7426	−0.763118
$969$	0	0
$970$	5.45898	0.175277
$971$	−14.5066	−0.465538	−0.232769	−	0.972532i	$-0.574779\pi$
$971$	−14.5066	−0.465538	−0.232769	+	0.972532i	$0.574779\pi$
$972$	35.0344	1.12373
$973$	−29.3951	−0.942364
$974$	11.2361	0.360027
$975$	9.09017	0.291118
$976$	−10.6869	−0.342080
$977$	55.3607	1.77115	0.885573	−	0.464501i	$-0.153766\pi$
$977$	55.3607	1.77115	0.885573	+	0.464501i	$0.153766\pi$
$978$	−10.0902	−0.322648
$979$	−7.56231	−0.241692
$980$	4.00000	0.127775
$981$	−64.3951	−2.05598
$982$	−18.6738	−0.595904
$983$	30.3820	0.969034	0.484517	−	0.874782i	$-0.338995\pi$
$983$	30.3820	0.969034	0.484517	+	0.874782i	$0.338995\pi$
$984$	−17.5623	−0.559866
$985$	−3.70820	−0.118153
$986$	4.47214	0.142422
$987$	23.5623	0.749996
$988$	0	0
$989$	−52.2148	−1.66033
$990$	1.81966	0.0578326
$991$	−48.4508	−1.53909	−0.769546	−	0.638591i	$-0.779517\pi$
$991$	−48.4508	−1.53909	−0.769546	+	0.638591i	$0.779517\pi$
$992$	12.0557	0.382770
$993$	−18.1803	−0.576936
$994$	−2.72949	−0.0865742
$995$	−16.5836	−0.525735
$996$	2.00000	0.0633724
$997$	26.2918	0.832670	0.416335	−	0.909211i	$-0.363314\pi$
$997$	26.2918	0.832670	0.416335	+	0.909211i	$0.363314\pi$
$998$	9.34752	0.295891
$999$	4.79837	0.151814

Twists

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

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

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.23607 q^{5} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.23607 q^{5} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +0.763932 q^{10} +0.618034 q^{11} -4.23607 q^{12} -1.00000 q^{13} -1.85410 q^{14} -3.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} -2.38197 q^{18} +2.00000 q^{20} +7.85410 q^{21} -0.381966 q^{22} +7.61803 q^{23} +5.85410 q^{24} -3.47214 q^{25} +0.618034 q^{26} +2.23607 q^{27} -4.85410 q^{28} -1.38197 q^{29} +2.00000 q^{30} -2.14590 q^{31} -5.61803 q^{32} +1.61803 q^{33} -3.23607 q^{34} -3.70820 q^{35} -6.23607 q^{36} +2.14590 q^{37} -2.61803 q^{39} -2.76393 q^{40} -3.00000 q^{41} -4.85410 q^{42} -6.85410 q^{43} -1.00000 q^{44} -4.76393 q^{45} -4.70820 q^{46} +3.00000 q^{47} +4.85410 q^{48} +2.00000 q^{49} +2.14590 q^{50} +13.7082 q^{51} +1.61803 q^{52} +9.32624 q^{53} -1.38197 q^{54} -0.763932 q^{55} +6.70820 q^{56} +0.854102 q^{58} -15.3262 q^{59} +5.23607 q^{60} -5.76393 q^{61} +1.32624 q^{62} +11.5623 q^{63} -0.236068 q^{64} +1.23607 q^{65} -1.00000 q^{66} -7.00000 q^{67} -8.47214 q^{68} +19.9443 q^{69} +2.29180 q^{70} +1.47214 q^{71} +8.61803 q^{72} +10.7082 q^{73} -1.32624 q^{74} -9.09017 q^{75} +1.85410 q^{77} +1.61803 q^{78} -13.4164 q^{79} -2.29180 q^{80} -5.70820 q^{81} +1.85410 q^{82} -0.472136 q^{83} -12.7082 q^{84} -6.47214 q^{85} +4.23607 q^{86} -3.61803 q^{87} +1.38197 q^{88} -12.2361 q^{89} +2.94427 q^{90} -3.00000 q^{91} -12.3262 q^{92} -5.61803 q^{93} -1.85410 q^{94} -14.7082 q^{96} +7.14590 q^{97} -1.23607 q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - q^{6} + 6 q^{7} + q^{9}+O(q^{10}) \) 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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