LMFDB - Embedded newform 363.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(1,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("363.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.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:	$2.89856959337$
Analytic rank:	$1$
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:	no (minimal twist has level 33)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +1.61803 q^{5} +0.381966 q^{6} -1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +1.61803 q^{5} +0.381966 q^{6} -1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} -0.618034 q^{10} +1.85410 q^{12} -4.23607 q^{13} +0.381966 q^{14} -1.61803 q^{15} +3.14590 q^{16} -7.85410 q^{17} -0.381966 q^{18} -0.854102 q^{19} -3.00000 q^{20} +1.00000 q^{21} -4.23607 q^{23} -1.47214 q^{24} -2.38197 q^{25} +1.61803 q^{26} -1.00000 q^{27} +1.85410 q^{28} -6.00000 q^{29} +0.618034 q^{30} +5.09017 q^{31} -4.14590 q^{32} +3.00000 q^{34} -1.61803 q^{35} -1.85410 q^{36} -1.76393 q^{37} +0.326238 q^{38} +4.23607 q^{39} +2.38197 q^{40} -4.23607 q^{41} -0.381966 q^{42} +6.70820 q^{43} +1.61803 q^{45} +1.61803 q^{46} +1.09017 q^{47} -3.14590 q^{48} -6.00000 q^{49} +0.909830 q^{50} +7.85410 q^{51} +7.85410 q^{52} -2.61803 q^{53} +0.381966 q^{54} -1.47214 q^{56} +0.854102 q^{57} +2.29180 q^{58} +9.61803 q^{59} +3.00000 q^{60} +8.56231 q^{61} -1.94427 q^{62} -1.00000 q^{63} -4.70820 q^{64} -6.85410 q^{65} -4.85410 q^{67} +14.5623 q^{68} +4.23607 q^{69} +0.618034 q^{70} -5.32624 q^{71} +1.47214 q^{72} +7.70820 q^{73} +0.673762 q^{74} +2.38197 q^{75} +1.58359 q^{76} -1.61803 q^{78} +11.0000 q^{79} +5.09017 q^{80} +1.00000 q^{81} +1.61803 q^{82} -7.47214 q^{83} -1.85410 q^{84} -12.7082 q^{85} -2.56231 q^{86} +6.00000 q^{87} -3.76393 q^{89} -0.618034 q^{90} +4.23607 q^{91} +7.85410 q^{92} -5.09017 q^{93} -0.416408 q^{94} -1.38197 q^{95} +4.14590 q^{96} +1.14590 q^{97} +2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + q^{5} + 3 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + q^5 + 3 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	$ 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + q^{5} + 3 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} - 3 q^{12} - 4 q^{13} + 3 q^{14} - q^{15} + 13 q^{16} - 9 q^{17} - 3 q^{18} + 5 q^{19} - 6 q^{20} + 2 q^{21} - 4 q^{23} + 6 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 3 q^{28} - 12 q^{29} - q^{30} - q^{31} - 15 q^{32} + 6 q^{34} - q^{35} + 3 q^{36} - 8 q^{37} - 15 q^{38} + 4 q^{39} + 7 q^{40} - 4 q^{41} - 3 q^{42} + q^{45} + q^{46} - 9 q^{47} - 13 q^{48} - 12 q^{49} + 13 q^{50} + 9 q^{51} + 9 q^{52} - 3 q^{53} + 3 q^{54} + 6 q^{56} - 5 q^{57} + 18 q^{58} + 17 q^{59} + 6 q^{60} - 3 q^{61} + 14 q^{62} - 2 q^{63} + 4 q^{64} - 7 q^{65} - 3 q^{67} + 9 q^{68} + 4 q^{69} - q^{70} + 5 q^{71} - 6 q^{72} + 2 q^{73} + 17 q^{74} + 7 q^{75} + 30 q^{76} - q^{78} + 22 q^{79} - q^{80} + 2 q^{81} + q^{82} - 6 q^{83} + 3 q^{84} - 12 q^{85} + 15 q^{86} + 12 q^{87} - 12 q^{89} + q^{90} + 4 q^{91} + 9 q^{92} + q^{93} + 26 q^{94} - 5 q^{95} + 15 q^{96} + 9 q^{97} + 18 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + q^5 + 3 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + q^10 - 3 * q^12 - 4 * q^13 + 3 * q^14 - q^15 + 13 * q^16 - 9 * q^17 - 3 * q^18 + 5 * q^19 - 6 * q^20 + 2 * q^21 - 4 * q^23 + 6 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 3 * q^28 - 12 * q^29 - q^30 - q^31 - 15 * q^32 + 6 * q^34 - q^35 + 3 * q^36 - 8 * q^37 - 15 * q^38 + 4 * q^39 + 7 * q^40 - 4 * q^41 - 3 * q^42 + q^45 + q^46 - 9 * q^47 - 13 * q^48 - 12 * q^49 + 13 * q^50 + 9 * q^51 + 9 * q^52 - 3 * q^53 + 3 * q^54 + 6 * q^56 - 5 * q^57 + 18 * q^58 + 17 * q^59 + 6 * q^60 - 3 * q^61 + 14 * q^62 - 2 * q^63 + 4 * q^64 - 7 * q^65 - 3 * q^67 + 9 * q^68 + 4 * q^69 - q^70 + 5 * q^71 - 6 * q^72 + 2 * q^73 + 17 * q^74 + 7 * q^75 + 30 * q^76 - q^78 + 22 * q^79 - q^80 + 2 * q^81 + q^82 - 6 * q^83 + 3 * q^84 - 12 * q^85 + 15 * q^86 + 12 * q^87 - 12 * q^89 + q^90 + 4 * q^91 + 9 * q^92 + q^93 + 26 * q^94 - 5 * q^95 + 15 * q^96 + 9 * q^97 + 18 * q^98

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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.85410	−0.927051
$5$	1.61803	0.723607	0.361803	−	0.932254i	$-0.382161\pi$
$5$	1.61803	0.723607	0.361803	+	0.932254i	$0.382161\pi$
$6$	0.381966	0.155937
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.47214	0.520479
$9$	1.00000	0.333333
$10$	−0.618034	−0.195440
$11$	0	0
$11$	0	0
$12$	1.85410	0.535233
$13$	−4.23607	−1.17487	−0.587437	−	0.809270i	$-0.699863\pi$
$13$	−4.23607	−1.17487	−0.587437	+	0.809270i	$0.699863\pi$
$14$	0.381966	0.102085
$15$	−1.61803	−0.417775
$16$	3.14590	0.786475
$17$	−7.85410	−1.90490	−0.952450	−	0.304696i	$-0.901445\pi$
$17$	−7.85410	−1.90490	−0.952450	+	0.304696i	$0.901445\pi$
$18$	−0.381966	−0.0900303
$19$	−0.854102	−0.195944	−0.0979722	−	0.995189i	$-0.531236\pi$
$19$	−0.854102	−0.195944	−0.0979722	+	0.995189i	$0.531236\pi$
$20$	−3.00000	−0.670820
$21$	1.00000	0.218218
$22$	0	0
$23$	−4.23607	−0.883281	−0.441641	−	0.897192i	$-0.645603\pi$
$23$	−4.23607	−0.883281	−0.441641	+	0.897192i	$0.645603\pi$
$24$	−1.47214	−0.300498
$25$	−2.38197	−0.476393
$26$	1.61803	0.317323
$27$	−1.00000	−0.192450
$28$	1.85410	0.350392
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0.618034	0.112837
$31$	5.09017	0.914222	0.457111	−	0.889410i	$-0.348884\pi$
$31$	5.09017	0.914222	0.457111	+	0.889410i	$0.348884\pi$
$32$	−4.14590	−0.732898
$33$	0	0
$34$	3.00000	0.514496
$35$	−1.61803	−0.273498
$36$	−1.85410	−0.309017
$37$	−1.76393	−0.289989	−0.144994	−	0.989432i	$-0.546316\pi$
$37$	−1.76393	−0.289989	−0.144994	+	0.989432i	$0.546316\pi$
$38$	0.326238	0.0529228
$39$	4.23607	0.678314
$40$	2.38197	0.376622
$41$	−4.23607	−0.661563	−0.330781	−	0.943707i	$-0.607312\pi$
$41$	−4.23607	−0.661563	−0.330781	+	0.943707i	$0.607312\pi$
$42$	−0.381966	−0.0589386
$43$	6.70820	1.02299	0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820	1.02299	0.511496	+	0.859286i	$0.329092\pi$
$44$	0	0
$45$	1.61803	0.241202
$46$	1.61803	0.238566
$47$	1.09017	0.159018	0.0795088	−	0.996834i	$-0.474665\pi$
$47$	1.09017	0.159018	0.0795088	+	0.996834i	$0.474665\pi$
$48$	−3.14590	−0.454071
$49$	−6.00000	−0.857143
$50$	0.909830	0.128669
$51$	7.85410	1.09979
$52$	7.85410	1.08917
$53$	−2.61803	−0.359615	−0.179807	−	0.983702i	$-0.557547\pi$
$53$	−2.61803	−0.359615	−0.179807	+	0.983702i	$0.557547\pi$
$54$	0.381966	0.0519790
$55$	0	0
$56$	−1.47214	−0.196722
$57$	0.854102	0.113129
$58$	2.29180	0.300928
$59$	9.61803	1.25216	0.626081	−	0.779758i	$-0.284658\pi$
$59$	9.61803	1.25216	0.626081	+	0.779758i	$0.284658\pi$
$60$	3.00000	0.387298
$61$	8.56231	1.09629	0.548145	−	0.836383i	$-0.315334\pi$
$61$	8.56231	1.09629	0.548145	+	0.836383i	$0.315334\pi$
$62$	−1.94427	−0.246923
$63$	−1.00000	−0.125988
$64$	−4.70820	−0.588525
$65$	−6.85410	−0.850147
$66$	0	0
$67$	−4.85410	−0.593023	−0.296511	−	0.955029i	$-0.595823\pi$
$67$	−4.85410	−0.593023	−0.296511	+	0.955029i	$0.595823\pi$
$68$	14.5623	1.76594
$69$	4.23607	0.509963
$70$	0.618034	0.0738692
$71$	−5.32624	−0.632108	−0.316054	−	0.948741i	$-0.602358\pi$
$71$	−5.32624	−0.632108	−0.316054	+	0.948741i	$0.602358\pi$
$72$	1.47214	0.173493
$73$	7.70820	0.902177	0.451089	−	0.892479i	$-0.351036\pi$
$73$	7.70820	0.902177	0.451089	+	0.892479i	$0.351036\pi$
$74$	0.673762	0.0783233
$75$	2.38197	0.275046
$76$	1.58359	0.181650
$77$	0	0
$78$	−1.61803	−0.183206
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	5.09017	0.569098
$81$	1.00000	0.111111
$82$	1.61803	0.178682
$83$	−7.47214	−0.820173	−0.410087	−	0.912047i	$-0.634502\pi$
$83$	−7.47214	−0.820173	−0.410087	+	0.912047i	$0.634502\pi$
$84$	−1.85410	−0.202299
$85$	−12.7082	−1.37840
$86$	−2.56231	−0.276301
$87$	6.00000	0.643268
$88$	0	0
$89$	−3.76393	−0.398976	−0.199488	−	0.979900i	$-0.563928\pi$
$89$	−3.76393	−0.398976	−0.199488	+	0.979900i	$0.563928\pi$
$90$	−0.618034	−0.0651465
$91$	4.23607	0.444061
$92$	7.85410	0.818847
$93$	−5.09017	−0.527826
$94$	−0.416408	−0.0429492
$95$	−1.38197	−0.141787
$96$	4.14590	0.423139
$97$	1.14590	0.116348	0.0581742	−	0.998306i	$-0.481472\pi$
$97$	1.14590	0.116348	0.0581742	+	0.998306i	$0.481472\pi$
$98$	2.29180	0.231506
$99$	0	0
$100$	4.41641	0.441641
$101$	−5.76393	−0.573533	−0.286766	−	0.958001i	$-0.592580\pi$
$101$	−5.76393	−0.573533	−0.286766	+	0.958001i	$0.592580\pi$
$102$	−3.00000	−0.297044
$103$	6.94427	0.684239	0.342120	−	0.939656i	$-0.388855\pi$
$103$	6.94427	0.684239	0.342120	+	0.939656i	$0.388855\pi$
$104$	−6.23607	−0.611497
$105$	1.61803	0.157904
$106$	1.00000	0.0971286
$107$	−2.52786	−0.244378	−0.122189	−	0.992507i	$-0.538991\pi$
$107$	−2.52786	−0.244378	−0.122189	+	0.992507i	$0.538991\pi$
$108$	1.85410	0.178411
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	0	0
$111$	1.76393	0.167425
$112$	−3.14590	−0.297259
$113$	4.52786	0.425946	0.212973	−	0.977058i	$-0.431685\pi$
$113$	4.52786	0.425946	0.212973	+	0.977058i	$0.431685\pi$
$114$	−0.326238	−0.0305550
$115$	−6.85410	−0.639148
$116$	11.1246	1.03289
$117$	−4.23607	−0.391625
$118$	−3.67376	−0.338197
$119$	7.85410	0.719984
$120$	−2.38197	−0.217443
$121$	0	0
$122$	−3.27051	−0.296098
$123$	4.23607	0.381953
$124$	−9.43769	−0.847530
$125$	−11.9443	−1.06833
$126$	0.381966	0.0340282
$127$	−5.70820	−0.506521	−0.253261	−	0.967398i	$-0.581503\pi$
$127$	−5.70820	−0.506521	−0.253261	+	0.967398i	$0.581503\pi$
$128$	10.0902	0.891853
$129$	−6.70820	−0.590624
$130$	2.61803	0.229617
$131$	12.7984	1.11820	0.559100	−	0.829101i	$-0.311147\pi$
$131$	12.7984	1.11820	0.559100	+	0.829101i	$0.311147\pi$
$132$	0	0
$133$	0.854102	0.0740600
$134$	1.85410	0.160170
$135$	−1.61803	−0.139258
$136$	−11.5623	−0.991460
$137$	14.2361	1.21627	0.608135	−	0.793834i	$-0.291918\pi$
$137$	14.2361	1.21627	0.608135	+	0.793834i	$0.291918\pi$
$138$	−1.61803	−0.137736
$139$	−5.56231	−0.471789	−0.235894	−	0.971779i	$-0.575802\pi$
$139$	−5.56231	−0.471789	−0.235894	+	0.971779i	$0.575802\pi$
$140$	3.00000	0.253546
$141$	−1.09017	−0.0918089
$142$	2.03444	0.170727
$143$	0	0
$144$	3.14590	0.262158
$145$	−9.70820	−0.806222
$146$	−2.94427	−0.243670
$147$	6.00000	0.494872
$148$	3.27051	0.268834
$149$	0.236068	0.0193394	0.00966972	−	0.999953i	$-0.496922\pi$
$149$	0.236068	0.0193394	0.00966972	+	0.999953i	$0.496922\pi$
$150$	−0.909830	−0.0742873
$151$	18.9443	1.54166	0.770831	−	0.637039i	$-0.219841\pi$
$151$	18.9443	1.54166	0.770831	+	0.637039i	$0.219841\pi$
$152$	−1.25735	−0.101985
$153$	−7.85410	−0.634967
$154$	0	0
$155$	8.23607	0.661537
$156$	−7.85410	−0.628831
$157$	2.29180	0.182905	0.0914526	−	0.995809i	$-0.470849\pi$
$157$	2.29180	0.182905	0.0914526	+	0.995809i	$0.470849\pi$
$158$	−4.20163	−0.334263
$159$	2.61803	0.207624
$160$	−6.70820	−0.530330
$161$	4.23607	0.333849
$162$	−0.381966	−0.0300101
$163$	−11.8541	−0.928485	−0.464242	−	0.885708i	$-0.653673\pi$
$163$	−11.8541	−0.928485	−0.464242	+	0.885708i	$0.653673\pi$
$164$	7.85410	0.613302
$165$	0	0
$166$	2.85410	0.221521
$167$	−17.0344	−1.31816	−0.659082	−	0.752071i	$-0.729055\pi$
$167$	−17.0344	−1.31816	−0.659082	+	0.752071i	$0.729055\pi$
$168$	1.47214	0.113578
$169$	4.94427	0.380329
$170$	4.85410	0.372293
$171$	−0.854102	−0.0653148
$172$	−12.4377	−0.948365
$173$	11.0344	0.838933	0.419467	−	0.907771i	$-0.362217\pi$
$173$	11.0344	0.838933	0.419467	+	0.907771i	$0.362217\pi$
$174$	−2.29180	−0.173741
$175$	2.38197	0.180060
$176$	0	0
$177$	−9.61803	−0.722936
$178$	1.43769	0.107760
$179$	−17.4721	−1.30593	−0.652964	−	0.757389i	$-0.726475\pi$
$179$	−17.4721	−1.30593	−0.652964	+	0.757389i	$0.726475\pi$
$180$	−3.00000	−0.223607
$181$	11.4721	0.852717	0.426359	−	0.904554i	$-0.359796\pi$
$181$	11.4721	0.852717	0.426359	+	0.904554i	$0.359796\pi$
$182$	−1.61803	−0.119937
$183$	−8.56231	−0.632944
$184$	−6.23607	−0.459729
$185$	−2.85410	−0.209838
$186$	1.94427	0.142561
$187$	0	0
$188$	−2.02129	−0.147417
$189$	1.00000	0.0727393
$190$	0.527864	0.0382953
$191$	−23.1803	−1.67727	−0.838635	−	0.544693i	$-0.816646\pi$
$191$	−23.1803	−1.67727	−0.838635	+	0.544693i	$0.816646\pi$
$192$	4.70820	0.339785
$193$	−9.85410	−0.709314	−0.354657	−	0.934997i	$-0.615402\pi$
$193$	−9.85410	−0.709314	−0.354657	+	0.934997i	$0.615402\pi$
$194$	−0.437694	−0.0314246
$195$	6.85410	0.490832
$196$	11.1246	0.794615
$197$	−16.0344	−1.14241	−0.571203	−	0.820809i	$-0.693523\pi$
$197$	−16.0344	−1.14241	−0.571203	+	0.820809i	$0.693523\pi$
$198$	0	0
$199$	−6.70820	−0.475532	−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820	−0.475532	−0.237766	+	0.971322i	$0.576415\pi$
$200$	−3.50658	−0.247952
$201$	4.85410	0.342382
$202$	2.20163	0.154906
$203$	6.00000	0.421117
$204$	−14.5623	−1.01957
$205$	−6.85410	−0.478711
$206$	−2.65248	−0.184807
$207$	−4.23607	−0.294427
$208$	−13.3262	−0.924008
$209$	0	0
$210$	−0.618034	−0.0426484
$211$	1.38197	0.0951385	0.0475692	−	0.998868i	$-0.484853\pi$
$211$	1.38197	0.0951385	0.0475692	+	0.998868i	$0.484853\pi$
$212$	4.85410	0.333381
$213$	5.32624	0.364948
$214$	0.965558	0.0660042
$215$	10.8541	0.740244
$216$	−1.47214	−0.100166
$217$	−5.09017	−0.345543
$218$	4.58359	0.310440
$219$	−7.70820	−0.520872
$220$	0	0
$221$	33.2705	2.23802
$222$	−0.673762	−0.0452199
$223$	−15.1803	−1.01655	−0.508275	−	0.861195i	$-0.669717\pi$
$223$	−15.1803	−1.01655	−0.508275	+	0.861195i	$0.669717\pi$
$224$	4.14590	0.277009
$225$	−2.38197	−0.158798
$226$	−1.72949	−0.115044
$227$	−9.18034	−0.609321	−0.304660	−	0.952461i	$-0.598543\pi$
$227$	−9.18034	−0.609321	−0.304660	+	0.952461i	$0.598543\pi$
$228$	−1.58359	−0.104876
$229$	−8.47214	−0.559855	−0.279927	−	0.960021i	$-0.590310\pi$
$229$	−8.47214	−0.559855	−0.279927	+	0.960021i	$0.590310\pi$
$230$	2.61803	0.172628
$231$	0	0
$232$	−8.83282	−0.579903
$233$	−10.8541	−0.711076	−0.355538	−	0.934662i	$-0.615702\pi$
$233$	−10.8541	−0.711076	−0.355538	+	0.934662i	$0.615702\pi$
$234$	1.61803	0.105774
$235$	1.76393	0.115066
$236$	−17.8328	−1.16082
$237$	−11.0000	−0.714527
$238$	−3.00000	−0.194461
$239$	2.61803	0.169347	0.0846733	−	0.996409i	$-0.473015\pi$
$239$	2.61803	0.169347	0.0846733	+	0.996409i	$0.473015\pi$
$240$	−5.09017	−0.328569
$241$	21.7082	1.39835	0.699174	−	0.714951i	$-0.253551\pi$
$241$	21.7082	1.39835	0.699174	+	0.714951i	$0.253551\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−15.8754	−1.01632
$245$	−9.70820	−0.620234
$246$	−1.61803	−0.103162
$247$	3.61803	0.230210
$248$	7.49342	0.475833
$249$	7.47214	0.473527
$250$	4.56231	0.288546
$251$	24.9787	1.57664	0.788321	−	0.615264i	$-0.210951\pi$
$251$	24.9787	1.57664	0.788321	+	0.615264i	$0.210951\pi$
$252$	1.85410	0.116797
$253$	0	0
$254$	2.18034	0.136807
$255$	12.7082	0.795819
$256$	5.56231	0.347644
$257$	−12.7426	−0.794864	−0.397432	−	0.917632i	$-0.630099\pi$
$257$	−12.7426	−0.794864	−0.397432	+	0.917632i	$0.630099\pi$
$258$	2.56231	0.159522
$259$	1.76393	0.109605
$260$	12.7082	0.788129
$261$	−6.00000	−0.371391
$262$	−4.88854	−0.302015
$263$	18.2705	1.12661	0.563304	−	0.826250i	$-0.309530\pi$
$263$	18.2705	1.12661	0.563304	+	0.826250i	$0.309530\pi$
$264$	0	0
$265$	−4.23607	−0.260220
$266$	−0.326238	−0.0200029
$267$	3.76393	0.230349
$268$	9.00000	0.549762
$269$	1.41641	0.0863599	0.0431800	−	0.999067i	$-0.486251\pi$
$269$	1.41641	0.0863599	0.0431800	+	0.999067i	$0.486251\pi$
$270$	0.618034	0.0376124
$271$	16.3820	0.995134	0.497567	−	0.867426i	$-0.334227\pi$
$271$	16.3820	0.995134	0.497567	+	0.867426i	$0.334227\pi$
$272$	−24.7082	−1.49815
$273$	−4.23607	−0.256378
$274$	−5.43769	−0.328503
$275$	0	0
$276$	−7.85410	−0.472761
$277$	22.2148	1.33476	0.667378	−	0.744719i	$-0.267416\pi$
$277$	22.2148	1.33476	0.667378	+	0.744719i	$0.267416\pi$
$278$	2.12461	0.127426
$279$	5.09017	0.304741
$280$	−2.38197	−0.142350
$281$	29.2361	1.74408	0.872039	−	0.489437i	$-0.162798\pi$
$281$	29.2361	1.74408	0.872039	+	0.489437i	$0.162798\pi$
$282$	0.416408	0.0247967
$283$	7.70820	0.458205	0.229103	−	0.973402i	$-0.426421\pi$
$283$	7.70820	0.458205	0.229103	+	0.973402i	$0.426421\pi$
$284$	9.87539	0.585996
$285$	1.38197	0.0818606
$286$	0	0
$287$	4.23607	0.250047
$288$	−4.14590	−0.244299
$289$	44.6869	2.62864
$290$	3.70820	0.217753
$291$	−1.14590	−0.0671737
$292$	−14.2918	−0.836364
$293$	9.65248	0.563904	0.281952	−	0.959429i	$-0.409018\pi$
$293$	9.65248	0.563904	0.281952	+	0.959429i	$0.409018\pi$
$294$	−2.29180	−0.133660
$295$	15.5623	0.906072
$296$	−2.59675	−0.150933
$297$	0	0
$298$	−0.0901699	−0.00522340
$299$	17.9443	1.03774
$300$	−4.41641	−0.254981
$301$	−6.70820	−0.386654
$302$	−7.23607	−0.416389
$303$	5.76393	0.331129
$304$	−2.68692	−0.154105
$305$	13.8541	0.793284
$306$	3.00000	0.171499
$307$	−18.9787	−1.08317	−0.541586	−	0.840645i	$-0.682176\pi$
$307$	−18.9787	−1.08317	−0.541586	+	0.840645i	$0.682176\pi$
$308$	0	0
$309$	−6.94427	−0.395046
$310$	−3.14590	−0.178675
$311$	−19.6525	−1.11439	−0.557195	−	0.830382i	$-0.688122\pi$
$311$	−19.6525	−1.11439	−0.557195	+	0.830382i	$0.688122\pi$
$312$	6.23607	0.353048
$313$	−11.4721	−0.648443	−0.324222	−	0.945981i	$-0.605102\pi$
$313$	−11.4721	−0.648443	−0.324222	+	0.945981i	$0.605102\pi$
$314$	−0.875388	−0.0494010
$315$	−1.61803	−0.0911659
$316$	−20.3951	−1.14732
$317$	−29.1803	−1.63893	−0.819466	−	0.573128i	$-0.805730\pi$
$317$	−29.1803	−1.63893	−0.819466	+	0.573128i	$0.805730\pi$
$318$	−1.00000	−0.0560772
$319$	0	0
$320$	−7.61803	−0.425861
$321$	2.52786	0.141092
$322$	−1.61803	−0.0901695
$323$	6.70820	0.373254
$324$	−1.85410	−0.103006
$325$	10.0902	0.559702
$326$	4.52786	0.250775
$327$	12.0000	0.663602
$328$	−6.23607	−0.344329
$329$	−1.09017	−0.0601030
$330$	0	0
$331$	3.29180	0.180933	0.0904667	−	0.995899i	$-0.471164\pi$
$331$	3.29180	0.180933	0.0904667	+	0.995899i	$0.471164\pi$
$332$	13.8541	0.760343
$333$	−1.76393	−0.0966629
$334$	6.50658	0.356024
$335$	−7.85410	−0.429115
$336$	3.14590	0.171623
$337$	4.18034	0.227718	0.113859	−	0.993497i	$-0.463679\pi$
$337$	4.18034	0.227718	0.113859	+	0.993497i	$0.463679\pi$
$338$	−1.88854	−0.102723
$339$	−4.52786	−0.245920
$340$	23.5623	1.27785
$341$	0	0
$342$	0.326238	0.0176409
$343$	13.0000	0.701934
$344$	9.87539	0.532445
$345$	6.85410	0.369012
$346$	−4.21478	−0.226588
$347$	−10.4721	−0.562174	−0.281087	−	0.959682i	$-0.590695\pi$
$347$	−10.4721	−0.562174	−0.281087	+	0.959682i	$0.590695\pi$
$348$	−11.1246	−0.596342
$349$	−0.708204	−0.0379093	−0.0189546	−	0.999820i	$-0.506034\pi$
$349$	−0.708204	−0.0379093	−0.0189546	+	0.999820i	$0.506034\pi$
$350$	−0.909830	−0.0486325
$351$	4.23607	0.226105
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	3.67376	0.195258
$355$	−8.61803	−0.457398
$356$	6.97871	0.369871
$357$	−7.85410	−0.415683
$358$	6.67376	0.352719
$359$	3.70820	0.195712	0.0978558	−	0.995201i	$-0.468802\pi$
$359$	3.70820	0.195712	0.0978558	+	0.995201i	$0.468802\pi$
$360$	2.38197	0.125541
$361$	−18.2705	−0.961606
$362$	−4.38197	−0.230311
$363$	0	0
$364$	−7.85410	−0.411667
$365$	12.4721	0.652821
$366$	3.27051	0.170952
$367$	28.8541	1.50617	0.753086	−	0.657922i	$-0.228564\pi$
$367$	28.8541	1.50617	0.753086	+	0.657922i	$0.228564\pi$
$368$	−13.3262	−0.694678
$369$	−4.23607	−0.220521
$370$	1.09017	0.0566752
$371$	2.61803	0.135922
$372$	9.43769	0.489322
$373$	−34.8885	−1.80646	−0.903230	−	0.429156i	$-0.858811\pi$
$373$	−34.8885	−1.80646	−0.903230	+	0.429156i	$0.858811\pi$
$374$	0	0
$375$	11.9443	0.616800
$376$	1.60488	0.0827653
$377$	25.4164	1.30901
$378$	−0.381966	−0.0196462
$379$	10.8885	0.559307	0.279653	−	0.960101i	$-0.409780\pi$
$379$	10.8885	0.559307	0.279653	+	0.960101i	$0.409780\pi$
$380$	2.56231	0.131444
$381$	5.70820	0.292440
$382$	8.85410	0.453015
$383$	0.708204	0.0361875	0.0180938	−	0.999836i	$-0.494240\pi$
$383$	0.708204	0.0361875	0.0180938	+	0.999836i	$0.494240\pi$
$384$	−10.0902	−0.514912
$385$	0	0
$386$	3.76393	0.191579
$387$	6.70820	0.340997
$388$	−2.12461	−0.107861
$389$	5.74265	0.291164	0.145582	−	0.989346i	$-0.453495\pi$
$389$	5.74265	0.291164	0.145582	+	0.989346i	$0.453495\pi$
$390$	−2.61803	−0.132569
$391$	33.2705	1.68256
$392$	−8.83282	−0.446125
$393$	−12.7984	−0.645593
$394$	6.12461	0.308553
$395$	17.7984	0.895533
$396$	0	0
$397$	−5.29180	−0.265588	−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180	−0.265588	−0.132794	+	0.991144i	$0.542395\pi$
$398$	2.56231	0.128437
$399$	−0.854102	−0.0427586
$400$	−7.49342	−0.374671
$401$	28.6869	1.43256	0.716278	−	0.697815i	$-0.245844\pi$
$401$	28.6869	1.43256	0.716278	+	0.697815i	$0.245844\pi$
$402$	−1.85410	−0.0924742
$403$	−21.5623	−1.07409
$404$	10.6869	0.531694
$405$	1.61803	0.0804008
$406$	−2.29180	−0.113740
$407$	0	0
$408$	11.5623	0.572419
$409$	2.47214	0.122239	0.0611196	−	0.998130i	$-0.480533\pi$
$409$	2.47214	0.122239	0.0611196	+	0.998130i	$0.480533\pi$
$410$	2.61803	0.129295
$411$	−14.2361	−0.702213
$412$	−12.8754	−0.634325
$413$	−9.61803	−0.473273
$414$	1.61803	0.0795220
$415$	−12.0902	−0.593483
$416$	17.5623	0.861063
$417$	5.56231	0.272387
$418$	0	0
$419$	−24.4508	−1.19450	−0.597251	−	0.802054i	$-0.703740\pi$
$419$	−24.4508	−1.19450	−0.597251	+	0.802054i	$0.703740\pi$
$420$	−3.00000	−0.146385
$421$	−27.5066	−1.34059	−0.670294	−	0.742095i	$-0.733832\pi$
$421$	−27.5066	−1.34059	−0.670294	+	0.742095i	$0.733832\pi$
$422$	−0.527864	−0.0256960
$423$	1.09017	0.0530059
$424$	−3.85410	−0.187172
$425$	18.7082	0.907481
$426$	−2.03444	−0.0985690
$427$	−8.56231	−0.414359
$428$	4.68692	0.226551
$429$	0	0
$430$	−4.14590	−0.199933
$431$	−17.0902	−0.823205	−0.411602	−	0.911364i	$-0.635031\pi$
$431$	−17.0902	−0.823205	−0.411602	+	0.911364i	$0.635031\pi$
$432$	−3.14590	−0.151357
$433$	−27.3050	−1.31219	−0.656096	−	0.754677i	$-0.727793\pi$
$433$	−27.3050	−1.31219	−0.656096	+	0.754677i	$0.727793\pi$
$434$	1.94427	0.0933280
$435$	9.70820	0.465473
$436$	22.2492	1.06554
$437$	3.61803	0.173074
$438$	2.94427	0.140683
$439$	36.7082	1.75199	0.875993	−	0.482323i	$-0.160207\pi$
$439$	36.7082	1.75199	0.875993	+	0.482323i	$0.160207\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−12.7082	−0.604468
$443$	17.5967	0.836047	0.418023	−	0.908436i	$-0.362723\pi$
$443$	17.5967	0.836047	0.418023	+	0.908436i	$0.362723\pi$
$444$	−3.27051	−0.155212
$445$	−6.09017	−0.288702
$446$	5.79837	0.274561
$447$	−0.236068	−0.0111656
$448$	4.70820	0.222442
$449$	−26.9443	−1.27158	−0.635789	−	0.771863i	$-0.719325\pi$
$449$	−26.9443	−1.27158	−0.635789	+	0.771863i	$0.719325\pi$
$450$	0.909830	0.0428898
$451$	0	0
$452$	−8.39512	−0.394873
$453$	−18.9443	−0.890080
$454$	3.50658	0.164572
$455$	6.85410	0.321325
$456$	1.25735	0.0588810
$457$	−22.9787	−1.07490	−0.537449	−	0.843296i	$-0.680612\pi$
$457$	−22.9787	−1.07490	−0.537449	+	0.843296i	$0.680612\pi$
$458$	3.23607	0.151212
$459$	7.85410	0.366598
$460$	12.7082	0.592523
$461$	−24.2705	−1.13039	−0.565195	−	0.824957i	$-0.691199\pi$
$461$	−24.2705	−1.13039	−0.565195	+	0.824957i	$0.691199\pi$
$462$	0	0
$463$	35.2705	1.63916	0.819580	−	0.572965i	$-0.194207\pi$
$463$	35.2705	1.63916	0.819580	+	0.572965i	$0.194207\pi$
$464$	−18.8754	−0.876268
$465$	−8.23607	−0.381939
$466$	4.14590	0.192055
$467$	−14.8885	−0.688960	−0.344480	−	0.938794i	$-0.611945\pi$
$467$	−14.8885	−0.688960	−0.344480	+	0.938794i	$0.611945\pi$
$468$	7.85410	0.363056
$469$	4.85410	0.224142
$470$	−0.673762	−0.0310783
$471$	−2.29180	−0.105600
$472$	14.1591	0.651723
$473$	0	0
$474$	4.20163	0.192987
$475$	2.03444	0.0933466
$476$	−14.5623	−0.667462
$477$	−2.61803	−0.119872
$478$	−1.00000	−0.0457389
$479$	−30.6180	−1.39897	−0.699487	−	0.714645i	$-0.746588\pi$
$479$	−30.6180	−1.39897	−0.699487	+	0.714645i	$0.746588\pi$
$480$	6.70820	0.306186
$481$	7.47214	0.340700
$482$	−8.29180	−0.377681
$483$	−4.23607	−0.192748
$484$	0	0
$485$	1.85410	0.0841904
$486$	0.381966	0.0173263
$487$	0.708204	0.0320918	0.0160459	−	0.999871i	$-0.494892\pi$
$487$	0.708204	0.0320918	0.0160459	+	0.999871i	$0.494892\pi$
$488$	12.6049	0.570596
$489$	11.8541	0.536061
$490$	3.70820	0.167520
$491$	−29.0902	−1.31282	−0.656410	−	0.754404i	$-0.727926\pi$
$491$	−29.0902	−1.31282	−0.656410	+	0.754404i	$0.727926\pi$
$492$	−7.85410	−0.354090
$493$	47.1246	2.12239
$494$	−1.38197	−0.0621776
$495$	0	0
$496$	16.0132	0.719012
$497$	5.32624	0.238914
$498$	−2.85410	−0.127895
$499$	−24.8541	−1.11262	−0.556311	−	0.830974i	$-0.687784\pi$
$499$	−24.8541	−1.11262	−0.556311	+	0.830974i	$0.687784\pi$
$500$	22.1459	0.990395
$501$	17.0344	0.761043
$502$	−9.54102	−0.425837
$503$	−22.6525	−1.01002	−0.505012	−	0.863112i	$-0.668512\pi$
$503$	−22.6525	−1.01002	−0.505012	+	0.863112i	$0.668512\pi$
$504$	−1.47214	−0.0655741
$505$	−9.32624	−0.415012
$506$	0	0
$507$	−4.94427	−0.219583
$508$	10.5836	0.469571
$509$	−3.74265	−0.165890	−0.0829449	−	0.996554i	$-0.526433\pi$
$509$	−3.74265	−0.165890	−0.0829449	+	0.996554i	$0.526433\pi$
$510$	−4.85410	−0.214943
$511$	−7.70820	−0.340991
$512$	−22.3050	−0.985749
$513$	0.854102	0.0377095
$514$	4.86726	0.214686
$515$	11.2361	0.495120
$516$	12.4377	0.547539
$517$	0	0
$518$	−0.673762	−0.0296034
$519$	−11.0344	−0.484358
$520$	−10.0902	−0.442483
$521$	−8.94427	−0.391856	−0.195928	−	0.980618i	$-0.562772\pi$
$521$	−8.94427	−0.391856	−0.195928	+	0.980618i	$0.562772\pi$
$522$	2.29180	0.100309
$523$	−15.2705	−0.667733	−0.333866	−	0.942620i	$-0.608353\pi$
$523$	−15.2705	−0.667733	−0.333866	+	0.942620i	$0.608353\pi$
$524$	−23.7295	−1.03663
$525$	−2.38197	−0.103958
$526$	−6.97871	−0.304286
$527$	−39.9787	−1.74150
$528$	0	0
$529$	−5.05573	−0.219814
$530$	1.61803	0.0702829
$531$	9.61803	0.417387
$532$	−1.58359	−0.0686574
$533$	17.9443	0.777253
$534$	−1.43769	−0.0622151
$535$	−4.09017	−0.176833
$536$	−7.14590	−0.308656
$537$	17.4721	0.753978
$538$	−0.541020	−0.0233250
$539$	0	0
$540$	3.00000	0.129099
$541$	−45.5066	−1.95648	−0.978240	−	0.207475i	$-0.933475\pi$
$541$	−45.5066	−1.95648	−0.978240	+	0.207475i	$0.933475\pi$
$542$	−6.25735	−0.268776
$543$	−11.4721	−0.492316
$544$	32.5623	1.39610
$545$	−19.4164	−0.831708
$546$	1.61803	0.0692455
$547$	11.7426	0.502079	0.251040	−	0.967977i	$-0.419228\pi$
$547$	11.7426	0.502079	0.251040	+	0.967977i	$0.419228\pi$
$548$	−26.3951	−1.12754
$549$	8.56231	0.365430
$550$	0	0
$551$	5.12461	0.218316
$552$	6.23607	0.265425
$553$	−11.0000	−0.467768
$554$	−8.48529	−0.360505
$555$	2.85410	0.121150
$556$	10.3131	0.437372
$557$	−40.6312	−1.72160	−0.860799	−	0.508944i	$-0.830036\pi$
$557$	−40.6312	−1.72160	−0.860799	+	0.508944i	$0.830036\pi$
$558$	−1.94427	−0.0823076
$559$	−28.4164	−1.20189
$560$	−5.09017	−0.215099
$561$	0	0
$562$	−11.1672	−0.471059
$563$	−8.59675	−0.362310	−0.181155	−	0.983455i	$-0.557984\pi$
$563$	−8.59675	−0.362310	−0.181155	+	0.983455i	$0.557984\pi$
$564$	2.02129	0.0851115
$565$	7.32624	0.308217
$566$	−2.94427	−0.123757
$567$	−1.00000	−0.0419961
$568$	−7.84095	−0.328999
$569$	11.8197	0.495506	0.247753	−	0.968823i	$-0.420308\pi$
$569$	11.8197	0.495506	0.247753	+	0.968823i	$0.420308\pi$
$570$	−0.527864	−0.0221098
$571$	2.09017	0.0874709	0.0437354	−	0.999043i	$-0.486074\pi$
$571$	2.09017	0.0874709	0.0437354	+	0.999043i	$0.486074\pi$
$572$	0	0
$573$	23.1803	0.968373
$574$	−1.61803	−0.0675354
$575$	10.0902	0.420789
$576$	−4.70820	−0.196175
$577$	18.2918	0.761497	0.380749	−	0.924679i	$-0.375666\pi$
$577$	18.2918	0.761497	0.380749	+	0.924679i	$0.375666\pi$
$578$	−17.0689	−0.709972
$579$	9.85410	0.409523
$580$	18.0000	0.747409
$581$	7.47214	0.309996
$582$	0.437694	0.0181430
$583$	0	0
$584$	11.3475	0.469564
$585$	−6.85410	−0.283382
$586$	−3.68692	−0.152305
$587$	38.1246	1.57357	0.786786	−	0.617226i	$-0.211744\pi$
$587$	38.1246	1.57357	0.786786	+	0.617226i	$0.211744\pi$
$588$	−11.1246	−0.458771
$589$	−4.34752	−0.179137
$590$	−5.94427	−0.244722
$591$	16.0344	0.659569
$592$	−5.54915	−0.228069
$593$	15.0344	0.617391	0.308695	−	0.951161i	$-0.400108\pi$
$593$	15.0344	0.617391	0.308695	+	0.951161i	$0.400108\pi$
$594$	0	0
$595$	12.7082	0.520986
$596$	−0.437694	−0.0179286
$597$	6.70820	0.274549
$598$	−6.85410	−0.280285
$599$	−18.6525	−0.762120	−0.381060	−	0.924550i	$-0.624441\pi$
$599$	−18.6525	−0.762120	−0.381060	+	0.924550i	$0.624441\pi$
$600$	3.50658	0.143155
$601$	28.8885	1.17839	0.589194	−	0.807992i	$-0.299445\pi$
$601$	28.8885	1.17839	0.589194	+	0.807992i	$0.299445\pi$
$602$	2.56231	0.104432
$603$	−4.85410	−0.197674
$604$	−35.1246	−1.42920
$605$	0	0
$606$	−2.20163	−0.0894349
$607$	3.56231	0.144590	0.0722948	−	0.997383i	$-0.476968\pi$
$607$	3.56231	0.144590	0.0722948	+	0.997383i	$0.476968\pi$
$608$	3.54102	0.143607
$609$	−6.00000	−0.243132
$610$	−5.29180	−0.214259
$611$	−4.61803	−0.186826
$612$	14.5623	0.588646
$613$	−27.7082	−1.11912	−0.559562	−	0.828789i	$-0.689031\pi$
$613$	−27.7082	−1.11912	−0.559562	+	0.828789i	$0.689031\pi$
$614$	7.24922	0.292555
$615$	6.85410	0.276384
$616$	0	0
$617$	−11.1803	−0.450104	−0.225052	−	0.974347i	$-0.572255\pi$
$617$	−11.1803	−0.450104	−0.225052	+	0.974347i	$0.572255\pi$
$618$	2.65248	0.106698
$619$	−16.1246	−0.648103	−0.324051	−	0.946039i	$-0.605045\pi$
$619$	−16.1246	−0.648103	−0.324051	+	0.946039i	$0.605045\pi$
$620$	−15.2705	−0.613278
$621$	4.23607	0.169988
$622$	7.50658	0.300986
$623$	3.76393	0.150799
$624$	13.3262	0.533476
$625$	−7.41641	−0.296656
$626$	4.38197	0.175139
$627$	0	0
$628$	−4.24922	−0.169562
$629$	13.8541	0.552399
$630$	0.618034	0.0246231
$631$	−32.2148	−1.28245	−0.641225	−	0.767353i	$-0.721574\pi$
$631$	−32.2148	−1.28245	−0.641225	+	0.767353i	$0.721574\pi$
$632$	16.1935	0.644143
$633$	−1.38197	−0.0549282
$634$	11.1459	0.442660
$635$	−9.23607	−0.366522
$636$	−4.85410	−0.192478
$637$	25.4164	1.00703
$638$	0	0
$639$	−5.32624	−0.210703
$640$	16.3262	0.645351
$641$	−13.9098	−0.549405	−0.274703	−	0.961529i	$-0.588579\pi$
$641$	−13.9098	−0.549405	−0.274703	+	0.961529i	$0.588579\pi$
$642$	−0.965558	−0.0381075
$643$	14.1459	0.557860	0.278930	−	0.960311i	$-0.410020\pi$
$643$	14.1459	0.557860	0.278930	+	0.960311i	$0.410020\pi$
$644$	−7.85410	−0.309495
$645$	−10.8541	−0.427380
$646$	−2.56231	−0.100813
$647$	15.9656	0.627671	0.313835	−	0.949477i	$-0.398386\pi$
$647$	15.9656	0.627671	0.313835	+	0.949477i	$0.398386\pi$
$648$	1.47214	0.0578310
$649$	0	0
$650$	−3.85410	−0.151170
$651$	5.09017	0.199499
$652$	21.9787	0.860753
$653$	−3.38197	−0.132347	−0.0661733	−	0.997808i	$-0.521079\pi$
$653$	−3.38197	−0.132347	−0.0661733	+	0.997808i	$0.521079\pi$
$654$	−4.58359	−0.179233
$655$	20.7082	0.809136
$656$	−13.3262	−0.520302
$657$	7.70820	0.300726
$658$	0.416408	0.0162333
$659$	−0.875388	−0.0341003	−0.0170501	−	0.999855i	$-0.505427\pi$
$659$	−0.875388	−0.0341003	−0.0170501	+	0.999855i	$0.505427\pi$
$660$	0	0
$661$	16.4377	0.639352	0.319676	−	0.947527i	$-0.396426\pi$
$661$	16.4377	0.639352	0.319676	+	0.947527i	$0.396426\pi$
$662$	−1.25735	−0.0488685
$663$	−33.2705	−1.29212
$664$	−11.0000	−0.426883
$665$	1.38197	0.0535903
$666$	0.673762	0.0261078
$667$	25.4164	0.984127
$668$	31.5836	1.22201
$669$	15.1803	0.586906
$670$	3.00000	0.115900
$671$	0	0
$672$	−4.14590	−0.159931
$673$	−17.8328	−0.687405	−0.343702	−	0.939079i	$-0.611681\pi$
$673$	−17.8328	−0.687405	−0.343702	+	0.939079i	$0.611681\pi$
$674$	−1.59675	−0.0615044
$675$	2.38197	0.0916819
$676$	−9.16718	−0.352584
$677$	22.4721	0.863674	0.431837	−	0.901952i	$-0.357866\pi$
$677$	22.4721	0.863674	0.431837	+	0.901952i	$0.357866\pi$
$678$	1.72949	0.0664207
$679$	−1.14590	−0.0439755
$680$	−18.7082	−0.717427
$681$	9.18034	0.351791
$682$	0	0
$683$	−49.0689	−1.87757	−0.938784	−	0.344505i	$-0.888047\pi$
$683$	−49.0689	−1.87757	−0.938784	+	0.344505i	$0.888047\pi$
$684$	1.58359	0.0605502
$685$	23.0344	0.880101
$686$	−4.96556	−0.189586
$687$	8.47214	0.323232
$688$	21.1033	0.804557
$689$	11.0902	0.422502
$690$	−2.61803	−0.0996669
$691$	32.6525	1.24216	0.621079	−	0.783748i	$-0.286694\pi$
$691$	32.6525	1.24216	0.621079	+	0.783748i	$0.286694\pi$
$692$	−20.4590	−0.777734
$693$	0	0
$694$	4.00000	0.151838
$695$	−9.00000	−0.341389
$696$	8.83282	0.334807
$697$	33.2705	1.26021
$698$	0.270510	0.0102389
$699$	10.8541	0.410540
$700$	−4.41641	−0.166925
$701$	−10.2016	−0.385310	−0.192655	−	0.981267i	$-0.561710\pi$
$701$	−10.2016	−0.385310	−0.192655	+	0.981267i	$0.561710\pi$
$702$	−1.61803	−0.0610688
$703$	1.50658	0.0568217
$704$	0	0
$705$	−1.76393	−0.0664335
$706$	4.58359	0.172506
$707$	5.76393	0.216775
$708$	17.8328	0.670198
$709$	−40.2148	−1.51030	−0.755149	−	0.655553i	$-0.772435\pi$
$709$	−40.2148	−1.51030	−0.755149	+	0.655553i	$0.772435\pi$
$710$	3.29180	0.123539
$711$	11.0000	0.412532
$712$	−5.54102	−0.207658
$713$	−21.5623	−0.807515
$714$	3.00000	0.112272
$715$	0	0
$716$	32.3951	1.21066
$717$	−2.61803	−0.0977723
$718$	−1.41641	−0.0528599
$719$	46.4853	1.73361	0.866804	−	0.498648i	$-0.166170\pi$
$719$	46.4853	1.73361	0.866804	+	0.498648i	$0.166170\pi$
$720$	5.09017	0.189699
$721$	−6.94427	−0.258618
$722$	6.97871	0.259721
$723$	−21.7082	−0.807337
$724$	−21.2705	−0.790512
$725$	14.2918	0.530784
$726$	0	0
$727$	−15.8541	−0.587996	−0.293998	−	0.955806i	$-0.594986\pi$
$727$	−15.8541	−0.587996	−0.293998	+	0.955806i	$0.594986\pi$
$728$	6.23607	0.231124
$729$	1.00000	0.0370370
$730$	−4.76393	−0.176321
$731$	−52.6869	−1.94870
$732$	15.8754	0.586771
$733$	−49.5967	−1.83190	−0.915949	−	0.401295i	$-0.868560\pi$
$733$	−49.5967	−1.83190	−0.915949	+	0.401295i	$0.868560\pi$
$734$	−11.0213	−0.406803
$735$	9.70820	0.358092
$736$	17.5623	0.647355
$737$	0	0
$738$	1.61803	0.0595607
$739$	3.00000	0.110357	0.0551784	−	0.998477i	$-0.482427\pi$
$739$	3.00000	0.110357	0.0551784	+	0.998477i	$0.482427\pi$
$740$	5.29180	0.194530
$741$	−3.61803	−0.132912
$742$	−1.00000	−0.0367112
$743$	−7.11146	−0.260894	−0.130447	−	0.991455i	$-0.541641\pi$
$743$	−7.11146	−0.260894	−0.130447	+	0.991455i	$0.541641\pi$
$744$	−7.49342	−0.274722
$745$	0.381966	0.0139942
$746$	13.3262	0.487908
$747$	−7.47214	−0.273391
$748$	0	0
$749$	2.52786	0.0923661
$750$	−4.56231	−0.166592
$751$	22.8541	0.833958	0.416979	−	0.908916i	$-0.363089\pi$
$751$	22.8541	0.833958	0.416979	+	0.908916i	$0.363089\pi$
$752$	3.42956	0.125063
$753$	−24.9787	−0.910275
$754$	−9.70820	−0.353552
$755$	30.6525	1.11556
$756$	−1.85410	−0.0674330
$757$	5.00000	0.181728	0.0908640	−	0.995863i	$-0.471037\pi$
$757$	5.00000	0.181728	0.0908640	+	0.995863i	$0.471037\pi$
$758$	−4.15905	−0.151064
$759$	0	0
$760$	−2.03444	−0.0737970
$761$	42.7082	1.54817	0.774086	−	0.633081i	$-0.218210\pi$
$761$	42.7082	1.54817	0.774086	+	0.633081i	$0.218210\pi$
$762$	−2.18034	−0.0789854
$763$	12.0000	0.434429
$764$	42.9787	1.55492
$765$	−12.7082	−0.459466
$766$	−0.270510	−0.00977392
$767$	−40.7426	−1.47113
$768$	−5.56231	−0.200712
$769$	3.50658	0.126450	0.0632252	−	0.997999i	$-0.479861\pi$
$769$	3.50658	0.126450	0.0632252	+	0.997999i	$0.479861\pi$
$770$	0	0
$771$	12.7426	0.458915
$772$	18.2705	0.657570
$773$	4.81966	0.173351	0.0866756	−	0.996237i	$-0.472376\pi$
$773$	4.81966	0.173351	0.0866756	+	0.996237i	$0.472376\pi$
$774$	−2.56231	−0.0921002
$775$	−12.1246	−0.435529
$776$	1.68692	0.0605568
$777$	−1.76393	−0.0632807
$778$	−2.19350	−0.0786406
$779$	3.61803	0.129630
$780$	−12.7082	−0.455027
$781$	0	0
$782$	−12.7082	−0.454444
$783$	6.00000	0.214423
$784$	−18.8754	−0.674121
$785$	3.70820	0.132351
$786$	4.88854	0.174369
$787$	3.70820	0.132183	0.0660916	−	0.997814i	$-0.478947\pi$
$787$	3.70820	0.132183	0.0660916	+	0.997814i	$0.478947\pi$
$788$	29.7295	1.05907
$789$	−18.2705	−0.650447
$790$	−6.79837	−0.241875
$791$	−4.52786	−0.160992
$792$	0	0
$793$	−36.2705	−1.28800
$794$	2.02129	0.0717328
$795$	4.23607	0.150238
$796$	12.4377	0.440842
$797$	−48.5410	−1.71941	−0.859706	−	0.510790i	$-0.829353\pi$
$797$	−48.5410	−1.71941	−0.859706	+	0.510790i	$0.829353\pi$
$798$	0.326238	0.0115487
$799$	−8.56231	−0.302913
$800$	9.87539	0.349148
$801$	−3.76393	−0.132992
$802$	−10.9574	−0.386920
$803$	0	0
$804$	−9.00000	−0.317406
$805$	6.85410	0.241575
$806$	8.23607	0.290103
$807$	−1.41641	−0.0498599
$808$	−8.48529	−0.298512
$809$	15.9098	0.559360	0.279680	−	0.960093i	$-0.409772\pi$
$809$	15.9098	0.559360	0.279680	+	0.960093i	$0.409772\pi$
$810$	−0.618034	−0.0217155
$811$	16.4377	0.577206	0.288603	−	0.957449i	$-0.406809\pi$
$811$	16.4377	0.577206	0.288603	+	0.957449i	$0.406809\pi$
$812$	−11.1246	−0.390397
$813$	−16.3820	−0.574541
$814$	0	0
$815$	−19.1803	−0.671858
$816$	24.7082	0.864960
$817$	−5.72949	−0.200449
$818$	−0.944272	−0.0330157
$819$	4.23607	0.148020
$820$	12.7082	0.443790
$821$	−8.59675	−0.300029	−0.150014	−	0.988684i	$-0.547932\pi$
$821$	−8.59675	−0.300029	−0.150014	+	0.988684i	$0.547932\pi$
$822$	5.43769	0.189661
$823$	25.8328	0.900475	0.450238	−	0.892909i	$-0.351339\pi$
$823$	25.8328	0.900475	0.450238	+	0.892909i	$0.351339\pi$
$824$	10.2229	0.356132
$825$	0	0
$826$	3.67376	0.127827
$827$	20.6525	0.718157	0.359078	−	0.933307i	$-0.383091\pi$
$827$	20.6525	0.718157	0.359078	+	0.933307i	$0.383091\pi$
$828$	7.85410	0.272949
$829$	42.3951	1.47244	0.736222	−	0.676740i	$-0.236608\pi$
$829$	42.3951	1.47244	0.736222	+	0.676740i	$0.236608\pi$
$830$	4.61803	0.160294
$831$	−22.2148	−0.770622
$832$	19.9443	0.691443
$833$	47.1246	1.63277
$834$	−2.12461	−0.0735693
$835$	−27.5623	−0.953833
$836$	0	0
$837$	−5.09017	−0.175942
$838$	9.33939	0.322624
$839$	35.8328	1.23709	0.618543	−	0.785751i	$-0.287723\pi$
$839$	35.8328	1.23709	0.618543	+	0.785751i	$0.287723\pi$
$840$	2.38197	0.0821856
$841$	7.00000	0.241379
$842$	10.5066	0.362081
$843$	−29.2361	−1.00694
$844$	−2.56231	−0.0881982
$845$	8.00000	0.275208
$846$	−0.416408	−0.0143164
$847$	0	0
$848$	−8.23607	−0.282828
$849$	−7.70820	−0.264545
$850$	−7.14590	−0.245102
$851$	7.47214	0.256142
$852$	−9.87539	−0.338325
$853$	−2.16718	−0.0742030	−0.0371015	−	0.999312i	$-0.511812\pi$
$853$	−2.16718	−0.0742030	−0.0371015	+	0.999312i	$0.511812\pi$
$854$	3.27051	0.111915
$855$	−1.38197	−0.0472622
$856$	−3.72136	−0.127193
$857$	32.2361	1.10116	0.550582	−	0.834781i	$-0.314406\pi$
$857$	32.2361	1.10116	0.550582	+	0.834781i	$0.314406\pi$
$858$	0	0
$859$	−7.58359	−0.258749	−0.129374	−	0.991596i	$-0.541297\pi$
$859$	−7.58359	−0.258749	−0.129374	+	0.991596i	$0.541297\pi$
$860$	−20.1246	−0.686244
$861$	−4.23607	−0.144365
$862$	6.52786	0.222340
$863$	35.8885	1.22166	0.610830	−	0.791762i	$-0.290836\pi$
$863$	35.8885	1.22166	0.610830	+	0.791762i	$0.290836\pi$
$864$	4.14590	0.141046
$865$	17.8541	0.607058
$866$	10.4296	0.354411
$867$	−44.6869	−1.51765
$868$	9.43769	0.320336
$869$	0	0
$870$	−3.70820	−0.125720
$871$	20.5623	0.696727
$872$	−17.6656	−0.598234
$873$	1.14590	0.0387828
$874$	−1.38197	−0.0467457
$875$	11.9443	0.403790
$876$	14.2918	0.482875
$877$	−40.0557	−1.35259	−0.676293	−	0.736633i	$-0.736415\pi$
$877$	−40.0557	−1.35259	−0.676293	+	0.736633i	$0.736415\pi$
$878$	−14.0213	−0.473195
$879$	−9.65248	−0.325570
$880$	0	0
$881$	30.7984	1.03762	0.518812	−	0.854888i	$-0.326375\pi$
$881$	30.7984	1.03762	0.518812	+	0.854888i	$0.326375\pi$
$882$	2.29180	0.0771688
$883$	18.9443	0.637526	0.318763	−	0.947835i	$-0.396733\pi$
$883$	18.9443	0.637526	0.318763	+	0.947835i	$0.396733\pi$
$884$	−61.6869	−2.07476
$885$	−15.5623	−0.523121
$886$	−6.72136	−0.225808
$887$	30.4853	1.02360	0.511798	−	0.859106i	$-0.328980\pi$
$887$	30.4853	1.02360	0.511798	+	0.859106i	$0.328980\pi$
$888$	2.59675	0.0871411
$889$	5.70820	0.191447
$890$	2.32624	0.0779757
$891$	0	0
$892$	28.1459	0.942394
$893$	−0.931116	−0.0311586
$894$	0.0901699	0.00301573
$895$	−28.2705	−0.944979
$896$	−10.0902	−0.337089
$897$	−17.9443	−0.599142
$898$	10.2918	0.343442
$899$	−30.5410	−1.01860
$900$	4.41641	0.147214
$901$	20.5623	0.685030
$902$	0	0
$903$	6.70820	0.223235
$904$	6.66563	0.221696
$905$	18.5623	0.617032
$906$	7.23607	0.240402
$907$	31.3951	1.04246	0.521229	−	0.853417i	$-0.325474\pi$
$907$	31.3951	1.04246	0.521229	+	0.853417i	$0.325474\pi$
$908$	17.0213	0.564871
$909$	−5.76393	−0.191178
$910$	−2.61803	−0.0867870
$911$	−10.5967	−0.351086	−0.175543	−	0.984472i	$-0.556168\pi$
$911$	−10.5967	−0.351086	−0.175543	+	0.984472i	$0.556168\pi$
$912$	2.68692	0.0889727
$913$	0	0
$914$	8.77709	0.290320
$915$	−13.8541	−0.458002
$916$	15.7082	0.519014
$917$	−12.7984	−0.422640
$918$	−3.00000	−0.0990148
$919$	−5.65248	−0.186458	−0.0932290	−	0.995645i	$-0.529719\pi$
$919$	−5.65248	−0.186458	−0.0932290	+	0.995645i	$0.529719\pi$
$920$	−10.0902	−0.332663
$921$	18.9787	0.625370
$922$	9.27051	0.305308
$923$	22.5623	0.742647
$924$	0	0
$925$	4.20163	0.138149
$926$	−13.4721	−0.442722
$927$	6.94427	0.228080
$928$	24.8754	0.816575
$929$	0.708204	0.0232354	0.0116177	−	0.999933i	$-0.496302\pi$
$929$	0.708204	0.0232354	0.0116177	+	0.999933i	$0.496302\pi$
$930$	3.14590	0.103158
$931$	5.12461	0.167952
$932$	20.1246	0.659204
$933$	19.6525	0.643393
$934$	5.68692	0.186082
$935$	0	0
$936$	−6.23607	−0.203832
$937$	10.3475	0.338039	0.169019	−	0.985613i	$-0.445940\pi$
$937$	10.3475	0.338039	0.169019	+	0.985613i	$0.445940\pi$
$938$	−1.85410	−0.0605386
$939$	11.4721	0.374379
$940$	−3.27051	−0.106672
$941$	41.4508	1.35126	0.675630	−	0.737241i	$-0.263872\pi$
$941$	41.4508	1.35126	0.675630	+	0.737241i	$0.263872\pi$
$942$	0.875388	0.0285217
$943$	17.9443	0.584346
$944$	30.2574	0.984793
$945$	1.61803	0.0526346
$946$	0	0
$947$	41.3951	1.34516	0.672580	−	0.740024i	$-0.265186\pi$
$947$	41.3951	1.34516	0.672580	+	0.740024i	$0.265186\pi$
$948$	20.3951	0.662403
$949$	−32.6525	−1.05994
$950$	−0.777088	−0.0252121
$951$	29.1803	0.946237
$952$	11.5623	0.374736
$953$	42.6525	1.38165	0.690825	−	0.723022i	$-0.257248\pi$
$953$	42.6525	1.38165	0.690825	+	0.723022i	$0.257248\pi$
$954$	1.00000	0.0323762
$955$	−37.5066	−1.21368
$956$	−4.85410	−0.156993
$957$	0	0
$958$	11.6950	0.377850
$959$	−14.2361	−0.459707
$960$	7.61803	0.245871
$961$	−5.09017	−0.164199
$962$	−2.85410	−0.0920199
$963$	−2.52786	−0.0814593
$964$	−40.2492	−1.29634
$965$	−15.9443	−0.513264
$966$	1.61803	0.0520594
$967$	−20.9230	−0.672838	−0.336419	−	0.941712i	$-0.609216\pi$
$967$	−20.9230	−0.672838	−0.336419	+	0.941712i	$0.609216\pi$
$968$	0	0
$969$	−6.70820	−0.215499
$970$	−0.708204	−0.0227391
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	1.85410	0.0594703
$973$	5.56231	0.178319
$974$	−0.270510	−0.00866769
$975$	−10.0902	−0.323144
$976$	26.9361	0.862205
$977$	48.5967	1.55475	0.777374	−	0.629039i	$-0.216551\pi$
$977$	48.5967	1.55475	0.777374	+	0.629039i	$0.216551\pi$
$978$	−4.52786	−0.144785
$979$	0	0
$980$	18.0000	0.574989
$981$	−12.0000	−0.383131
$982$	11.1115	0.354581
$983$	−43.8885	−1.39983	−0.699914	−	0.714228i	$-0.746778\pi$
$983$	−43.8885	−1.39983	−0.699914	+	0.714228i	$0.746778\pi$
$984$	6.23607	0.198799
$985$	−25.9443	−0.826653
$986$	−18.0000	−0.573237
$987$	1.09017	0.0347005
$988$	−6.70820	−0.213416
$989$	−28.4164	−0.903589
$990$	0	0
$991$	−38.7426	−1.23070	−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426	−1.23070	−0.615350	+	0.788254i	$0.710985\pi$
$992$	−21.1033	−0.670031
$993$	−3.29180	−0.104462
$994$	−2.03444	−0.0645286
$995$	−10.8541	−0.344098
$996$	−13.8541	−0.438984
$997$	−45.7984	−1.45045	−0.725225	−	0.688512i	$-0.758264\pi$
$997$	−45.7984	−1.45045	−0.725225	+	0.688512i	$0.758264\pi$
$998$	9.49342	0.300509
$999$	1.76393	0.0558083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.a.d.1.2		2
3.2	odd	2		1089.2.a.t.1.1		2
4.3	odd	2		5808.2.a.cj.1.2		2
5.4	even	2		9075.2.a.cb.1.1		2
11.2	odd	10		363.2.e.f.202.1		4
11.3	even	5		363.2.e.k.130.1		4
11.4	even	5		363.2.e.k.148.1		4
11.5	even	5		33.2.e.b.25.1	yes	4
11.6	odd	10		363.2.e.f.124.1		4
11.7	odd	10		363.2.e.b.148.1		4
11.8	odd	10		363.2.e.b.130.1		4
11.9	even	5		33.2.e.b.4.1	✓	4
11.10	odd	2		363.2.a.i.1.1		2
33.5	odd	10		99.2.f.a.91.1		4
33.20	odd	10		99.2.f.a.37.1		4
33.32	even	2		1089.2.a.l.1.2		2
44.27	odd	10		528.2.y.b.289.1		4
44.31	odd	10		528.2.y.b.433.1		4
44.43	even	2		5808.2.a.ci.1.2		2
55.9	even	10		825.2.n.c.301.1		4
55.27	odd	20		825.2.bx.d.124.2		8
55.38	odd	20		825.2.bx.d.124.1		8
55.42	odd	20		825.2.bx.d.499.1		8
55.49	even	10		825.2.n.c.751.1		4
55.53	odd	20		825.2.bx.d.499.2		8
55.54	odd	2		9075.2.a.u.1.2		2
99.5	odd	30		891.2.n.b.784.1		8
99.16	even	15		891.2.n.c.190.1		8
99.20	odd	30		891.2.n.b.433.1		8
99.31	even	15		891.2.n.c.136.1		8
99.38	odd	30		891.2.n.b.190.1		8
99.49	even	15		891.2.n.c.784.1		8
99.86	odd	30		891.2.n.b.136.1		8
99.97	even	15		891.2.n.c.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	11.9	even	5
33.2.e.b.25.1	yes	4	11.5	even	5
99.2.f.a.37.1		4	33.20	odd	10
99.2.f.a.91.1		4	33.5	odd	10
363.2.a.d.1.2		2	1.1	even	1	trivial
363.2.a.i.1.1		2	11.10	odd	2
363.2.e.b.130.1		4	11.8	odd	10
363.2.e.b.148.1		4	11.7	odd	10
363.2.e.f.124.1		4	11.6	odd	10
363.2.e.f.202.1		4	11.2	odd	10
363.2.e.k.130.1		4	11.3	even	5
363.2.e.k.148.1		4	11.4	even	5
528.2.y.b.289.1		4	44.27	odd	10
528.2.y.b.433.1		4	44.31	odd	10
825.2.n.c.301.1		4	55.9	even	10
825.2.n.c.751.1		4	55.49	even	10
825.2.bx.d.124.1		8	55.38	odd	20
825.2.bx.d.124.2		8	55.27	odd	20
825.2.bx.d.499.1		8	55.42	odd	20
825.2.bx.d.499.2		8	55.53	odd	20
891.2.n.b.136.1		8	99.86	odd	30
891.2.n.b.190.1		8	99.38	odd	30
891.2.n.b.433.1		8	99.20	odd	30
891.2.n.b.784.1		8	99.5	odd	30
891.2.n.c.136.1		8	99.31	even	15
891.2.n.c.190.1		8	99.16	even	15
891.2.n.c.433.1		8	99.97	even	15
891.2.n.c.784.1		8	99.49	even	15
1089.2.a.l.1.2		2	33.32	even	2
1089.2.a.t.1.1		2	3.2	odd	2
5808.2.a.ci.1.2		2	44.43	even	2
5808.2.a.cj.1.2		2	4.3	odd	2
9075.2.a.u.1.2		2	55.54	odd	2
9075.2.a.cb.1.1		2	5.4	even	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +1.61803 q^{5} +0.381966 q^{6} -1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +1.61803 q^{5} +0.381966 q^{6} -1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} -0.618034 q^{10} +1.85410 q^{12} -4.23607 q^{13} +0.381966 q^{14} -1.61803 q^{15} +3.14590 q^{16} -7.85410 q^{17} -0.381966 q^{18} -0.854102 q^{19} -3.00000 q^{20} +1.00000 q^{21} -4.23607 q^{23} -1.47214 q^{24} -2.38197 q^{25} +1.61803 q^{26} -1.00000 q^{27} +1.85410 q^{28} -6.00000 q^{29} +0.618034 q^{30} +5.09017 q^{31} -4.14590 q^{32} +3.00000 q^{34} -1.61803 q^{35} -1.85410 q^{36} -1.76393 q^{37} +0.326238 q^{38} +4.23607 q^{39} +2.38197 q^{40} -4.23607 q^{41} -0.381966 q^{42} +6.70820 q^{43} +1.61803 q^{45} +1.61803 q^{46} +1.09017 q^{47} -3.14590 q^{48} -6.00000 q^{49} +0.909830 q^{50} +7.85410 q^{51} +7.85410 q^{52} -2.61803 q^{53} +0.381966 q^{54} -1.47214 q^{56} +0.854102 q^{57} +2.29180 q^{58} +9.61803 q^{59} +3.00000 q^{60} +8.56231 q^{61} -1.94427 q^{62} -1.00000 q^{63} -4.70820 q^{64} -6.85410 q^{65} -4.85410 q^{67} +14.5623 q^{68} +4.23607 q^{69} +0.618034 q^{70} -5.32624 q^{71} +1.47214 q^{72} +7.70820 q^{73} +0.673762 q^{74} +2.38197 q^{75} +1.58359 q^{76} -1.61803 q^{78} +11.0000 q^{79} +5.09017 q^{80} +1.00000 q^{81} +1.61803 q^{82} -7.47214 q^{83} -1.85410 q^{84} -12.7082 q^{85} -2.56231 q^{86} +6.00000 q^{87} -3.76393 q^{89} -0.618034 q^{90} +4.23607 q^{91} +7.85410 q^{92} -5.09017 q^{93} -0.416408 q^{94} -1.38197 q^{95} +4.14590 q^{96} +1.14590 q^{97} +2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + q^{5} + 3 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + q^5 + 3 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + q^{5} + 3 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} - 3 q^{12} - 4 q^{13} + 3 q^{14} - q^{15} + 13 q^{16} - 9 q^{17} - 3 q^{18} + 5 q^{19} - 6 q^{20} + 2 q^{21} - 4 q^{23} + 6 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 3 q^{28} - 12 q^{29} - q^{30} - q^{31} - 15 q^{32} + 6 q^{34} - q^{35} + 3 q^{36} - 8 q^{37} - 15 q^{38} + 4 q^{39} + 7 q^{40} - 4 q^{41} - 3 q^{42} + q^{45} + q^{46} - 9 q^{47} - 13 q^{48} - 12 q^{49} + 13 q^{50} + 9 q^{51} + 9 q^{52} - 3 q^{53} + 3 q^{54} + 6 q^{56} - 5 q^{57} + 18 q^{58} + 17 q^{59} + 6 q^{60} - 3 q^{61} + 14 q^{62} - 2 q^{63} + 4 q^{64} - 7 q^{65} - 3 q^{67} + 9 q^{68} + 4 q^{69} - q^{70} + 5 q^{71} - 6 q^{72} + 2 q^{73} + 17 q^{74} + 7 q^{75} + 30 q^{76} - q^{78} + 22 q^{79} - q^{80} + 2 q^{81} + q^{82} - 6 q^{83} + 3 q^{84} - 12 q^{85} + 15 q^{86} + 12 q^{87} - 12 q^{89} + q^{90} + 4 q^{91} + 9 q^{92} + q^{93} + 26 q^{94} - 5 q^{95} + 15 q^{96} + 9 q^{97} + 18 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + q^5 + 3 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + q^10 - 3 * q^12 - 4 * q^13 + 3 * q^14 - q^15 + 13 * q^16 - 9 * q^17 - 3 * q^18 + 5 * q^19 - 6 * q^20 + 2 * q^21 - 4 * q^23 + 6 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 3 * q^28 - 12 * q^29 - q^30 - q^31 - 15 * q^32 + 6 * q^34 - q^35 + 3 * q^36 - 8 * q^37 - 15 * q^38 + 4 * q^39 + 7 * q^40 - 4 * q^41 - 3 * q^42 + q^45 + q^46 - 9 * q^47 - 13 * q^48 - 12 * q^49 + 13 * q^50 + 9 * q^51 + 9 * q^52 - 3 * q^53 + 3 * q^54 + 6 * q^56 - 5 * q^57 + 18 * q^58 + 17 * q^59 + 6 * q^60 - 3 * q^61 + 14 * q^62 - 2 * q^63 + 4 * q^64 - 7 * q^65 - 3 * q^67 + 9 * q^68 + 4 * q^69 - q^70 + 5 * q^71 - 6 * q^72 + 2 * q^73 + 17 * q^74 + 7 * q^75 + 30 * q^76 - q^78 + 22 * q^79 - q^80 + 2 * q^81 + q^82 - 6 * q^83 + 3 * q^84 - 12 * q^85 + 15 * q^86 + 12 * q^87 - 12 * q^89 + q^90 + 4 * q^91 + 9 * q^92 + q^93 + 26 * q^94 - 5 * q^95 + 15 * q^96 + 9 * q^97 + 18 * q^98

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