LMFDB - Embedded newform 363.2.a.i.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:	$0$
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:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q+2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} -0.618034 q^{5} -2.61803 q^{6} +1.00000 q^{7} +7.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} -0.618034 q^{5} -2.61803 q^{6} +1.00000 q^{7} +7.47214 q^{8} +1.00000 q^{9} -1.61803 q^{10} -4.85410 q^{12} -0.236068 q^{13} +2.61803 q^{14} +0.618034 q^{15} +9.85410 q^{16} +1.14590 q^{17} +2.61803 q^{18} -5.85410 q^{19} -3.00000 q^{20} -1.00000 q^{21} +0.236068 q^{23} -7.47214 q^{24} -4.61803 q^{25} -0.618034 q^{26} -1.00000 q^{27} +4.85410 q^{28} +6.00000 q^{29} +1.61803 q^{30} -6.09017 q^{31} +10.8541 q^{32} +3.00000 q^{34} -0.618034 q^{35} +4.85410 q^{36} -6.23607 q^{37} -15.3262 q^{38} +0.236068 q^{39} -4.61803 q^{40} -0.236068 q^{41} -2.61803 q^{42} +6.70820 q^{43} -0.618034 q^{45} +0.618034 q^{46} -10.0902 q^{47} -9.85410 q^{48} -6.00000 q^{49} -12.0902 q^{50} -1.14590 q^{51} -1.14590 q^{52} -0.381966 q^{53} -2.61803 q^{54} +7.47214 q^{56} +5.85410 q^{57} +15.7082 q^{58} +7.38197 q^{59} +3.00000 q^{60} +11.5623 q^{61} -15.9443 q^{62} +1.00000 q^{63} +8.70820 q^{64} +0.145898 q^{65} +1.85410 q^{67} +5.56231 q^{68} -0.236068 q^{69} -1.61803 q^{70} +10.3262 q^{71} +7.47214 q^{72} +5.70820 q^{73} -16.3262 q^{74} +4.61803 q^{75} -28.4164 q^{76} +0.618034 q^{78} -11.0000 q^{79} -6.09017 q^{80} +1.00000 q^{81} -0.618034 q^{82} -1.47214 q^{83} -4.85410 q^{84} -0.708204 q^{85} +17.5623 q^{86} -6.00000 q^{87} -8.23607 q^{89} -1.61803 q^{90} -0.236068 q^{91} +1.14590 q^{92} +6.09017 q^{93} -26.4164 q^{94} +3.61803 q^{95} -10.8541 q^{96} +7.85410 q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.61803	1.85123	0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803	1.85123	0.925615	+	0.378467i	$0.123549\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.85410	2.42705
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	−2.61803	−1.06881
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	7.47214	2.64180
$9$	1.00000	0.333333
$10$	−1.61803	−0.511667
$11$	0	0
$11$	0	0
$12$	−4.85410	−1.40126
$13$	−0.236068	−0.0654735	−0.0327367	−	0.999464i	$-0.510422\pi$
$13$	−0.236068	−0.0654735	−0.0327367	+	0.999464i	$0.510422\pi$
$14$	2.61803	0.699699
$15$	0.618034	0.159576
$16$	9.85410	2.46353
$17$	1.14590	0.277921	0.138961	−	0.990298i	$-0.455624\pi$
$17$	1.14590	0.277921	0.138961	+	0.990298i	$0.455624\pi$
$18$	2.61803	0.617077
$19$	−5.85410	−1.34302	−0.671512	−	0.740994i	$-0.734355\pi$
$19$	−5.85410	−1.34302	−0.671512	+	0.740994i	$0.734355\pi$
$20$	−3.00000	−0.670820
$21$	−1.00000	−0.218218
$22$	0	0
$23$	0.236068	0.0492236	0.0246118	−	0.999697i	$-0.492165\pi$
$23$	0.236068	0.0492236	0.0246118	+	0.999697i	$0.492165\pi$
$24$	−7.47214	−1.52524
$25$	−4.61803	−0.923607
$26$	−0.618034	−0.121206
$27$	−1.00000	−0.192450
$28$	4.85410	0.917339
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.61803	0.295411
$31$	−6.09017	−1.09383	−0.546913	−	0.837189i	$-0.684197\pi$
$31$	−6.09017	−1.09383	−0.546913	+	0.837189i	$0.684197\pi$
$32$	10.8541	1.91875
$33$	0	0
$34$	3.00000	0.514496
$35$	−0.618034	−0.104467
$36$	4.85410	0.809017
$37$	−6.23607	−1.02520	−0.512602	−	0.858627i	$-0.671318\pi$
$37$	−6.23607	−1.02520	−0.512602	+	0.858627i	$0.671318\pi$
$38$	−15.3262	−2.48624
$39$	0.236068	0.0378011
$40$	−4.61803	−0.730175
$41$	−0.236068	−0.0368676	−0.0184338	−	0.999830i	$-0.505868\pi$
$41$	−0.236068	−0.0368676	−0.0184338	+	0.999830i	$0.505868\pi$
$42$	−2.61803	−0.403971
$43$	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
$45$	−0.618034	−0.0921311
$46$	0.618034	0.0911241
$47$	−10.0902	−1.47180	−0.735901	−	0.677089i	$-0.763241\pi$
$47$	−10.0902	−1.47180	−0.735901	+	0.677089i	$0.763241\pi$
$48$	−9.85410	−1.42232
$49$	−6.00000	−0.857143
$50$	−12.0902	−1.70981
$51$	−1.14590	−0.160458
$52$	−1.14590	−0.158907
$53$	−0.381966	−0.0524671	−0.0262335	−	0.999656i	$-0.508351\pi$
$53$	−0.381966	−0.0524671	−0.0262335	+	0.999656i	$0.508351\pi$
$54$	−2.61803	−0.356269
$55$	0	0
$56$	7.47214	0.998506
$57$	5.85410	0.775395
$58$	15.7082	2.06259
$59$	7.38197	0.961050	0.480525	−	0.876981i	$-0.340446\pi$
$59$	7.38197	0.961050	0.480525	+	0.876981i	$0.340446\pi$
$60$	3.00000	0.387298
$61$	11.5623	1.48040	0.740201	−	0.672386i	$-0.234730\pi$
$61$	11.5623	1.48040	0.740201	+	0.672386i	$0.234730\pi$
$62$	−15.9443	−2.02492
$63$	1.00000	0.125988
$64$	8.70820	1.08853
$65$	0.145898	0.0180964
$66$	0	0
$67$	1.85410	0.226515	0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410	0.226515	0.113257	+	0.993566i	$0.463872\pi$
$68$	5.56231	0.674529
$69$	−0.236068	−0.0284192
$70$	−1.61803	−0.193392
$71$	10.3262	1.22550	0.612749	−	0.790277i	$-0.290063\pi$
$71$	10.3262	1.22550	0.612749	+	0.790277i	$0.290063\pi$
$72$	7.47214	0.880600
$73$	5.70820	0.668095	0.334047	−	0.942556i	$-0.391585\pi$
$73$	5.70820	0.668095	0.334047	+	0.942556i	$0.391585\pi$
$74$	−16.3262	−1.89789
$75$	4.61803	0.533245
$76$	−28.4164	−3.25959
$77$	0	0
$78$	0.618034	0.0699786
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	−6.09017	−0.680902
$81$	1.00000	0.111111
$82$	−0.618034	−0.0682504
$83$	−1.47214	−0.161588	−0.0807940	−	0.996731i	$-0.525746\pi$
$83$	−1.47214	−0.161588	−0.0807940	+	0.996731i	$0.525746\pi$
$84$	−4.85410	−0.529626
$85$	−0.708204	−0.0768155
$86$	17.5623	1.89379
$87$	−6.00000	−0.643268
$88$	0	0
$89$	−8.23607	−0.873021	−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607	−0.873021	−0.436511	+	0.899699i	$0.643786\pi$
$90$	−1.61803	−0.170556
$91$	−0.236068	−0.0247466
$92$	1.14590	0.119468
$93$	6.09017	0.631521
$94$	−26.4164	−2.72464
$95$	3.61803	0.371202
$96$	−10.8541	−1.10779
$97$	7.85410	0.797463	0.398732	−	0.917068i	$-0.369451\pi$
$97$	7.85410	0.797463	0.398732	+	0.917068i	$0.369451\pi$
$98$	−15.7082	−1.58677
$99$	0	0
$100$	−22.4164	−2.24164
$101$	10.2361	1.01853	0.509263	−	0.860611i	$-0.329918\pi$
$101$	10.2361	1.01853	0.509263	+	0.860611i	$0.329918\pi$
$102$	−3.00000	−0.297044
$103$	−10.9443	−1.07837	−0.539186	−	0.842187i	$-0.681268\pi$
$103$	−10.9443	−1.07837	−0.539186	+	0.842187i	$0.681268\pi$
$104$	−1.76393	−0.172968
$105$	0.618034	0.0603139
$106$	−1.00000	−0.0971286
$107$	11.4721	1.10905	0.554527	−	0.832166i	$-0.312899\pi$
$107$	11.4721	1.10905	0.554527	+	0.832166i	$0.312899\pi$
$108$	−4.85410	−0.467086
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	6.23607	0.591901
$112$	9.85410	0.931125
$113$	13.4721	1.26735	0.633676	−	0.773599i	$-0.281545\pi$
$113$	13.4721	1.26735	0.633676	+	0.773599i	$0.281545\pi$
$114$	15.3262	1.43543
$115$	−0.145898	−0.0136051
$116$	29.1246	2.70415
$117$	−0.236068	−0.0218245
$118$	19.3262	1.77912
$119$	1.14590	0.105044
$120$	4.61803	0.421567
$121$	0	0
$122$	30.2705	2.74056
$123$	0.236068	0.0212855
$124$	−29.5623	−2.65477
$125$	5.94427	0.531672
$126$	2.61803	0.233233
$127$	−7.70820	−0.683992	−0.341996	−	0.939701i	$-0.611103\pi$
$127$	−7.70820	−0.683992	−0.341996	+	0.939701i	$0.611103\pi$
$128$	1.09017	0.0963583
$129$	−6.70820	−0.590624
$130$	0.381966	0.0335006
$131$	11.7984	1.03083	0.515414	−	0.856941i	$-0.327638\pi$
$131$	11.7984	1.03083	0.515414	+	0.856941i	$0.327638\pi$
$132$	0	0
$133$	−5.85410	−0.507615
$134$	4.85410	0.419331
$135$	0.618034	0.0531919
$136$	8.56231	0.734212
$137$	9.76393	0.834189	0.417095	−	0.908863i	$-0.363048\pi$
$137$	9.76393	0.834189	0.417095	+	0.908863i	$0.363048\pi$
$138$	−0.618034	−0.0526105
$139$	−14.5623	−1.23516	−0.617579	−	0.786509i	$-0.711887\pi$
$139$	−14.5623	−1.23516	−0.617579	+	0.786509i	$0.711887\pi$
$140$	−3.00000	−0.253546
$141$	10.0902	0.849746
$142$	27.0344	2.26868
$143$	0	0
$144$	9.85410	0.821175
$145$	−3.70820	−0.307950
$146$	14.9443	1.23680
$147$	6.00000	0.494872
$148$	−30.2705	−2.48822
$149$	4.23607	0.347032	0.173516	−	0.984831i	$-0.444487\pi$
$149$	4.23607	0.347032	0.173516	+	0.984831i	$0.444487\pi$
$150$	12.0902	0.987158
$151$	−1.05573	−0.0859139	−0.0429570	−	0.999077i	$-0.513678\pi$
$151$	−1.05573	−0.0859139	−0.0429570	+	0.999077i	$0.513678\pi$
$152$	−43.7426	−3.54800
$153$	1.14590	0.0926404
$154$	0	0
$155$	3.76393	0.302326
$156$	1.14590	0.0917453
$157$	15.7082	1.25365	0.626826	−	0.779160i	$-0.284354\pi$
$157$	15.7082	1.25365	0.626826	+	0.779160i	$0.284354\pi$
$158$	−28.7984	−2.29108
$159$	0.381966	0.0302919
$160$	−6.70820	−0.530330
$161$	0.236068	0.0186048
$162$	2.61803	0.205692
$163$	−5.14590	−0.403058	−0.201529	−	0.979483i	$-0.564591\pi$
$163$	−5.14590	−0.403058	−0.201529	+	0.979483i	$0.564591\pi$
$164$	−1.14590	−0.0894796
$165$	0	0
$166$	−3.85410	−0.299136
$167$	−12.0344	−0.931253	−0.465627	−	0.884981i	$-0.654171\pi$
$167$	−12.0344	−0.931253	−0.465627	+	0.884981i	$0.654171\pi$
$168$	−7.47214	−0.576488
$169$	−12.9443	−0.995713
$170$	−1.85410	−0.142203
$171$	−5.85410	−0.447674
$172$	32.5623	2.48285
$173$	18.0344	1.37113	0.685567	−	0.728010i	$-0.259555\pi$
$173$	18.0344	1.37113	0.685567	+	0.728010i	$0.259555\pi$
$174$	−15.7082	−1.19084
$175$	−4.61803	−0.349091
$176$	0	0
$177$	−7.38197	−0.554863
$178$	−21.5623	−1.61616
$179$	−8.52786	−0.637402	−0.318701	−	0.947855i	$-0.603247\pi$
$179$	−8.52786	−0.637402	−0.318701	+	0.947855i	$0.603247\pi$
$180$	−3.00000	−0.223607
$181$	2.52786	0.187895	0.0939473	−	0.995577i	$-0.470051\pi$
$181$	2.52786	0.187895	0.0939473	+	0.995577i	$0.470051\pi$
$182$	−0.618034	−0.0458117
$183$	−11.5623	−0.854710
$184$	1.76393	0.130039
$185$	3.85410	0.283359
$186$	15.9443	1.16909
$187$	0	0
$188$	−48.9787	−3.57214
$189$	−1.00000	−0.0727393
$190$	9.47214	0.687181
$191$	−0.819660	−0.0593085	−0.0296543	−	0.999560i	$-0.509441\pi$
$191$	−0.819660	−0.0593085	−0.0296543	+	0.999560i	$0.509441\pi$
$192$	−8.70820	−0.628460
$193$	3.14590	0.226447	0.113223	−	0.993570i	$-0.463882\pi$
$193$	3.14590	0.226447	0.113223	+	0.993570i	$0.463882\pi$
$194$	20.5623	1.47629
$195$	−0.145898	−0.0104480
$196$	−29.1246	−2.08033
$197$	−13.0344	−0.928666	−0.464333	−	0.885661i	$-0.653706\pi$
$197$	−13.0344	−0.928666	−0.464333	+	0.885661i	$0.653706\pi$
$198$	0	0
$199$	6.70820	0.475532	0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820	0.475532	0.237766	+	0.971322i	$0.423585\pi$
$200$	−34.5066	−2.43998
$201$	−1.85410	−0.130778
$202$	26.7984	1.88553
$203$	6.00000	0.421117
$204$	−5.56231	−0.389439
$205$	0.145898	0.0101900
$206$	−28.6525	−1.99631
$207$	0.236068	0.0164079
$208$	−2.32624	−0.161296
$209$	0	0
$210$	1.61803	0.111655
$211$	−3.61803	−0.249076	−0.124538	−	0.992215i	$-0.539745\pi$
$211$	−3.61803	−0.249076	−0.124538	+	0.992215i	$0.539745\pi$
$212$	−1.85410	−0.127340
$213$	−10.3262	−0.707542
$214$	30.0344	2.05311
$215$	−4.14590	−0.282748
$216$	−7.47214	−0.508414
$217$	−6.09017	−0.413428
$218$	31.4164	2.12779
$219$	−5.70820	−0.385725
$220$	0	0
$221$	−0.270510	−0.0181965
$222$	16.3262	1.09575
$223$	7.18034	0.480831	0.240416	−	0.970670i	$-0.422716\pi$
$223$	7.18034	0.480831	0.240416	+	0.970670i	$0.422716\pi$
$224$	10.8541	0.725220
$225$	−4.61803	−0.307869
$226$	35.2705	2.34616
$227$	−13.1803	−0.874810	−0.437405	−	0.899265i	$-0.644102\pi$
$227$	−13.1803	−0.874810	−0.437405	+	0.899265i	$0.644102\pi$
$228$	28.4164	1.88192
$229$	0.472136	0.0311996	0.0155998	−	0.999878i	$-0.495034\pi$
$229$	0.472136	0.0311996	0.0155998	+	0.999878i	$0.495034\pi$
$230$	−0.381966	−0.0251861
$231$	0	0
$232$	44.8328	2.94342
$233$	4.14590	0.271607	0.135803	−	0.990736i	$-0.456638\pi$
$233$	4.14590	0.271607	0.135803	+	0.990736i	$0.456638\pi$
$234$	−0.618034	−0.0404021
$235$	6.23607	0.406796
$236$	35.8328	2.33252
$237$	11.0000	0.714527
$238$	3.00000	0.194461
$239$	−0.381966	−0.0247073	−0.0123537	−	0.999924i	$-0.503932\pi$
$239$	−0.381966	−0.0247073	−0.0123537	+	0.999924i	$0.503932\pi$
$240$	6.09017	0.393119
$241$	−8.29180	−0.534122	−0.267061	−	0.963680i	$-0.586052\pi$
$241$	−8.29180	−0.534122	−0.267061	+	0.963680i	$0.586052\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	56.1246	3.59301
$245$	3.70820	0.236908
$246$	0.618034	0.0394044
$247$	1.38197	0.0879324
$248$	−45.5066	−2.88967
$249$	1.47214	0.0932928
$250$	15.5623	0.984247
$251$	−21.9787	−1.38728	−0.693642	−	0.720320i	$-0.743995\pi$
$251$	−21.9787	−1.38728	−0.693642	+	0.720320i	$0.743995\pi$
$252$	4.85410	0.305780
$253$	0	0
$254$	−20.1803	−1.26623
$255$	0.708204	0.0443495
$256$	−14.5623	−0.910144
$257$	29.7426	1.85530	0.927648	−	0.373457i	$-0.121828\pi$
$257$	29.7426	1.85530	0.927648	+	0.373457i	$0.121828\pi$
$258$	−17.5623	−1.09338
$259$	−6.23607	−0.387490
$260$	0.708204	0.0439209
$261$	6.00000	0.371391
$262$	30.8885	1.90830
$263$	15.2705	0.941620	0.470810	−	0.882235i	$-0.343962\pi$
$263$	15.2705	0.941620	0.470810	+	0.882235i	$0.343962\pi$
$264$	0	0
$265$	0.236068	0.0145015
$266$	−15.3262	−0.939712
$267$	8.23607	0.504039
$268$	9.00000	0.549762
$269$	−25.4164	−1.54967	−0.774833	−	0.632166i	$-0.782166\pi$
$269$	−25.4164	−1.54967	−0.774833	+	0.632166i	$0.782166\pi$
$270$	1.61803	0.0984704
$271$	−18.6180	−1.13097	−0.565483	−	0.824760i	$-0.691310\pi$
$271$	−18.6180	−1.13097	−0.565483	+	0.824760i	$0.691310\pi$
$272$	11.2918	0.684666
$273$	0.236068	0.0142875
$274$	25.5623	1.54428
$275$	0	0
$276$	−1.14590	−0.0689750
$277$	29.2148	1.75535	0.877673	−	0.479260i	$-0.159095\pi$
$277$	29.2148	1.75535	0.877673	+	0.479260i	$0.159095\pi$
$278$	−38.1246	−2.28656
$279$	−6.09017	−0.364609
$280$	−4.61803	−0.275980
$281$	−24.7639	−1.47729	−0.738646	−	0.674093i	$-0.764535\pi$
$281$	−24.7639	−1.47729	−0.738646	+	0.674093i	$0.764535\pi$
$282$	26.4164	1.57307
$283$	5.70820	0.339318	0.169659	−	0.985503i	$-0.445733\pi$
$283$	5.70820	0.339318	0.169659	+	0.985503i	$0.445733\pi$
$284$	50.1246	2.97435
$285$	−3.61803	−0.214314
$286$	0	0
$287$	−0.236068	−0.0139347
$288$	10.8541	0.639584
$289$	−15.6869	−0.922760
$290$	−9.70820	−0.570085
$291$	−7.85410	−0.460416
$292$	27.7082	1.62150
$293$	21.6525	1.26495	0.632476	−	0.774580i	$-0.282039\pi$
$293$	21.6525	1.26495	0.632476	+	0.774580i	$0.282039\pi$
$294$	15.7082	0.916121
$295$	−4.56231	−0.265628
$296$	−46.5967	−2.70838
$297$	0	0
$298$	11.0902	0.642436
$299$	−0.0557281	−0.00322284
$300$	22.4164	1.29421
$301$	6.70820	0.386654
$302$	−2.76393	−0.159046
$303$	−10.2361	−0.588047
$304$	−57.6869	−3.30857
$305$	−7.14590	−0.409173
$306$	3.00000	0.171499
$307$	−27.9787	−1.59683	−0.798415	−	0.602108i	$-0.794328\pi$
$307$	−27.9787	−1.59683	−0.798415	+	0.602108i	$0.794328\pi$
$308$	0	0
$309$	10.9443	0.622598
$310$	9.85410	0.559675
$311$	11.6525	0.660751	0.330376	−	0.943850i	$-0.392825\pi$
$311$	11.6525	0.660751	0.330376	+	0.943850i	$0.392825\pi$
$312$	1.76393	0.0998630
$313$	−2.52786	−0.142883	−0.0714417	−	0.997445i	$-0.522760\pi$
$313$	−2.52786	−0.142883	−0.0714417	+	0.997445i	$0.522760\pi$
$314$	41.1246	2.32080
$315$	−0.618034	−0.0348223
$316$	−53.3951	−3.00371
$317$	−6.81966	−0.383030	−0.191515	−	0.981490i	$-0.561340\pi$
$317$	−6.81966	−0.383030	−0.191515	+	0.981490i	$0.561340\pi$
$318$	1.00000	0.0560772
$319$	0	0
$320$	−5.38197	−0.300861
$321$	−11.4721	−0.640312
$322$	0.618034	0.0344417
$323$	−6.70820	−0.373254
$324$	4.85410	0.269672
$325$	1.09017	0.0604717
$326$	−13.4721	−0.746153
$327$	−12.0000	−0.663602
$328$	−1.76393	−0.0973969
$329$	−10.0902	−0.556289
$330$	0	0
$331$	16.7082	0.918366	0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082	0.918366	0.459183	+	0.888342i	$0.348142\pi$
$332$	−7.14590	−0.392182
$333$	−6.23607	−0.341734
$334$	−31.5066	−1.72396
$335$	−1.14590	−0.0626071
$336$	−9.85410	−0.537585
$337$	18.1803	0.990346	0.495173	−	0.868794i	$-0.335105\pi$
$337$	18.1803	0.990346	0.495173	+	0.868794i	$0.335105\pi$
$338$	−33.8885	−1.84329
$339$	−13.4721	−0.731706
$340$	−3.43769	−0.186435
$341$	0	0
$342$	−15.3262	−0.828748
$343$	−13.0000	−0.701934
$344$	50.1246	2.70254
$345$	0.145898	0.00785489
$346$	47.2148	2.53828
$347$	1.52786	0.0820200	0.0410100	−	0.999159i	$-0.486942\pi$
$347$	1.52786	0.0820200	0.0410100	+	0.999159i	$0.486942\pi$
$348$	−29.1246	−1.56124
$349$	−12.7082	−0.680255	−0.340127	−	0.940379i	$-0.610470\pi$
$349$	−12.7082	−0.680255	−0.340127	+	0.940379i	$0.610470\pi$
$350$	−12.0902	−0.646247
$351$	0.236068	0.0126004
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	−19.3262	−1.02718
$355$	−6.38197	−0.338720
$356$	−39.9787	−2.11887
$357$	−1.14590	−0.0606474
$358$	−22.3262	−1.17998
$359$	9.70820	0.512379	0.256190	−	0.966627i	$-0.417533\pi$
$359$	9.70820	0.512379	0.256190	+	0.966627i	$0.417533\pi$
$360$	−4.61803	−0.243392
$361$	15.2705	0.803711
$362$	6.61803	0.347836
$363$	0	0
$364$	−1.14590	−0.0600614
$365$	−3.52786	−0.184657
$366$	−30.2705	−1.58226
$367$	22.1459	1.15601	0.578003	−	0.816034i	$-0.303832\pi$
$367$	22.1459	1.15601	0.578003	+	0.816034i	$0.303832\pi$
$368$	2.32624	0.121264
$369$	−0.236068	−0.0122892
$370$	10.0902	0.524563
$371$	−0.381966	−0.0198307
$372$	29.5623	1.53273
$373$	−0.888544	−0.0460071	−0.0230035	−	0.999735i	$-0.507323\pi$
$373$	−0.888544	−0.0460071	−0.0230035	+	0.999735i	$0.507323\pi$
$374$	0	0
$375$	−5.94427	−0.306961
$376$	−75.3951	−3.88821
$377$	−1.41641	−0.0729487
$378$	−2.61803	−0.134657
$379$	−24.8885	−1.27844	−0.639219	−	0.769024i	$-0.720742\pi$
$379$	−24.8885	−1.27844	−0.639219	+	0.769024i	$0.720742\pi$
$380$	17.5623	0.900927
$381$	7.70820	0.394903
$382$	−2.14590	−0.109794
$383$	−12.7082	−0.649359	−0.324679	−	0.945824i	$-0.605256\pi$
$383$	−12.7082	−0.649359	−0.324679	+	0.945824i	$0.605256\pi$
$384$	−1.09017	−0.0556325
$385$	0	0
$386$	8.23607	0.419205
$387$	6.70820	0.340997
$388$	38.1246	1.93548
$389$	−36.7426	−1.86293	−0.931463	−	0.363836i	$-0.881467\pi$
$389$	−36.7426	−1.86293	−0.931463	+	0.363836i	$0.881467\pi$
$390$	−0.381966	−0.0193416
$391$	0.270510	0.0136803
$392$	−44.8328	−2.26440
$393$	−11.7984	−0.595149
$394$	−34.1246	−1.71917
$395$	6.79837	0.342063
$396$	0	0
$397$	−18.7082	−0.938938	−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082	−0.938938	−0.469469	+	0.882949i	$0.655555\pi$
$398$	17.5623	0.880319
$399$	5.85410	0.293072
$400$	−45.5066	−2.27533
$401$	−31.6869	−1.58237	−0.791185	−	0.611577i	$-0.790535\pi$
$401$	−31.6869	−1.58237	−0.791185	+	0.611577i	$0.790535\pi$
$402$	−4.85410	−0.242101
$403$	1.43769	0.0716166
$404$	49.6869	2.47202
$405$	−0.618034	−0.0307104
$406$	15.7082	0.779585
$407$	0	0
$408$	−8.56231	−0.423897
$409$	6.47214	0.320027	0.160013	−	0.987115i	$-0.448846\pi$
$409$	6.47214	0.320027	0.160013	+	0.987115i	$0.448846\pi$
$410$	0.381966	0.0188640
$411$	−9.76393	−0.481619
$412$	−53.1246	−2.61726
$413$	7.38197	0.363243
$414$	0.618034	0.0303747
$415$	0.909830	0.0446618
$416$	−2.56231	−0.125627
$417$	14.5623	0.713119
$418$	0	0
$419$	31.4508	1.53647	0.768237	−	0.640165i	$-0.221134\pi$
$419$	31.4508	1.53647	0.768237	+	0.640165i	$0.221134\pi$
$420$	3.00000	0.146385
$421$	10.5066	0.512059	0.256030	−	0.966669i	$-0.417586\pi$
$421$	10.5066	0.512059	0.256030	+	0.966669i	$0.417586\pi$
$422$	−9.47214	−0.461096
$423$	−10.0902	−0.490601
$424$	−2.85410	−0.138607
$425$	−5.29180	−0.256690
$426$	−27.0344	−1.30982
$427$	11.5623	0.559539
$428$	55.6869	2.69173
$429$	0	0
$430$	−10.8541	−0.523431
$431$	5.90983	0.284666	0.142333	−	0.989819i	$-0.454540\pi$
$431$	5.90983	0.284666	0.142333	+	0.989819i	$0.454540\pi$
$432$	−9.85410	−0.474106
$433$	35.3050	1.69665	0.848324	−	0.529478i	$-0.177612\pi$
$433$	35.3050	1.69665	0.848324	+	0.529478i	$0.177612\pi$
$434$	−15.9443	−0.765350
$435$	3.70820	0.177795
$436$	58.2492	2.78963
$437$	−1.38197	−0.0661084
$438$	−14.9443	−0.714065
$439$	−23.2918	−1.11166	−0.555828	−	0.831297i	$-0.687599\pi$
$439$	−23.2918	−1.11166	−0.555828	+	0.831297i	$0.687599\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−0.708204	−0.0336858
$443$	−31.5967	−1.50121	−0.750603	−	0.660753i	$-0.770237\pi$
$443$	−31.5967	−1.50121	−0.750603	+	0.660753i	$0.770237\pi$
$444$	30.2705	1.43657
$445$	5.09017	0.241297
$446$	18.7984	0.890129
$447$	−4.23607	−0.200359
$448$	8.70820	0.411424
$449$	−9.05573	−0.427366	−0.213683	−	0.976903i	$-0.568546\pi$
$449$	−9.05573	−0.427366	−0.213683	+	0.976903i	$0.568546\pi$
$450$	−12.0902	−0.569936
$451$	0	0
$452$	65.3951	3.07593
$453$	1.05573	0.0496024
$454$	−34.5066	−1.61947
$455$	0.145898	0.00683981
$456$	43.7426	2.04844
$457$	−23.9787	−1.12168	−0.560838	−	0.827925i	$-0.689521\pi$
$457$	−23.9787	−1.12168	−0.560838	+	0.827925i	$0.689521\pi$
$458$	1.23607	0.0577577
$459$	−1.14590	−0.0534859
$460$	−0.708204	−0.0330202
$461$	−9.27051	−0.431771	−0.215885	−	0.976419i	$-0.569264\pi$
$461$	−9.27051	−0.431771	−0.215885	+	0.976419i	$0.569264\pi$
$462$	0	0
$463$	1.72949	0.0803762	0.0401881	−	0.999192i	$-0.487204\pi$
$463$	1.72949	0.0803762	0.0401881	+	0.999192i	$0.487204\pi$
$464$	59.1246	2.74479
$465$	−3.76393	−0.174548
$466$	10.8541	0.502807
$467$	20.8885	0.966607	0.483303	−	0.875453i	$-0.339437\pi$
$467$	20.8885	0.966607	0.483303	+	0.875453i	$0.339437\pi$
$468$	−1.14590	−0.0529692
$469$	1.85410	0.0856145
$470$	16.3262	0.753073
$471$	−15.7082	−0.723796
$472$	55.1591	2.53890
$473$	0	0
$474$	28.7984	1.32275
$475$	27.0344	1.24043
$476$	5.56231	0.254948
$477$	−0.381966	−0.0174890
$478$	−1.00000	−0.0457389
$479$	28.3820	1.29681	0.648403	−	0.761298i	$-0.275437\pi$
$479$	28.3820	1.29681	0.648403	+	0.761298i	$0.275437\pi$
$480$	6.70820	0.306186
$481$	1.47214	0.0671236
$482$	−21.7082	−0.988782
$483$	−0.236068	−0.0107415
$484$	0	0
$485$	−4.85410	−0.220413
$486$	−2.61803	−0.118756
$487$	−12.7082	−0.575864	−0.287932	−	0.957651i	$-0.592968\pi$
$487$	−12.7082	−0.575864	−0.287932	+	0.957651i	$0.592968\pi$
$488$	86.3951	3.91092
$489$	5.14590	0.232706
$490$	9.70820	0.438572
$491$	17.9098	0.808259	0.404130	−	0.914702i	$-0.367574\pi$
$491$	17.9098	0.808259	0.404130	+	0.914702i	$0.367574\pi$
$492$	1.14590	0.0516611
$493$	6.87539	0.309652
$494$	3.61803	0.162783
$495$	0	0
$496$	−60.0132	−2.69467
$497$	10.3262	0.463195
$498$	3.85410	0.172706
$499$	−18.1459	−0.812322	−0.406161	−	0.913802i	$-0.633133\pi$
$499$	−18.1459	−0.812322	−0.406161	+	0.913802i	$0.633133\pi$
$500$	28.8541	1.29039
$501$	12.0344	0.537659
$502$	−57.5410	−2.56818
$503$	−8.65248	−0.385795	−0.192897	−	0.981219i	$-0.561788\pi$
$503$	−8.65248	−0.385795	−0.192897	+	0.981219i	$0.561788\pi$
$504$	7.47214	0.332835
$505$	−6.32624	−0.281514
$506$	0	0
$507$	12.9443	0.574875
$508$	−37.4164	−1.66008
$509$	38.7426	1.71724	0.858619	−	0.512615i	$-0.171323\pi$
$509$	38.7426	1.71724	0.858619	+	0.512615i	$0.171323\pi$
$510$	1.85410	0.0821010
$511$	5.70820	0.252516
$512$	−40.3050	−1.78124
$513$	5.85410	0.258465
$514$	77.8673	3.43458
$515$	6.76393	0.298054
$516$	−32.5623	−1.43348
$517$	0	0
$518$	−16.3262	−0.717334
$519$	−18.0344	−0.791624
$520$	1.09017	0.0478071
$521$	8.94427	0.391856	0.195928	−	0.980618i	$-0.437228\pi$
$521$	8.94427	0.391856	0.195928	+	0.980618i	$0.437228\pi$
$522$	15.7082	0.687529
$523$	−18.2705	−0.798914	−0.399457	−	0.916752i	$-0.630801\pi$
$523$	−18.2705	−0.798914	−0.399457	+	0.916752i	$0.630801\pi$
$524$	57.2705	2.50187
$525$	4.61803	0.201548
$526$	39.9787	1.74315
$527$	−6.97871	−0.303998
$528$	0	0
$529$	−22.9443	−0.997577
$530$	0.618034	0.0268457
$531$	7.38197	0.320350
$532$	−28.4164	−1.23201
$533$	0.0557281	0.00241385
$534$	21.5623	0.933092
$535$	−7.09017	−0.306535
$536$	13.8541	0.598406
$537$	8.52786	0.368004
$538$	−66.5410	−2.86879
$539$	0	0
$540$	3.00000	0.129099
$541$	7.49342	0.322167	0.161084	−	0.986941i	$-0.448501\pi$
$541$	7.49342	0.322167	0.161084	+	0.986941i	$0.448501\pi$
$542$	−48.7426	−2.09368
$543$	−2.52786	−0.108481
$544$	12.4377	0.533262
$545$	−7.41641	−0.317684
$546$	0.618034	0.0264494
$547$	30.7426	1.31446	0.657230	−	0.753690i	$-0.271728\pi$
$547$	30.7426	1.31446	0.657230	+	0.753690i	$0.271728\pi$
$548$	47.3951	2.02462
$549$	11.5623	0.493467
$550$	0	0
$551$	−35.1246	−1.49636
$552$	−1.76393	−0.0750779
$553$	−11.0000	−0.467768
$554$	76.4853	3.24955
$555$	−3.85410	−0.163598
$556$	−70.6869	−2.99779
$557$	−37.6312	−1.59448	−0.797242	−	0.603659i	$-0.793709\pi$
$557$	−37.6312	−1.59448	−0.797242	+	0.603659i	$0.793709\pi$
$558$	−15.9443	−0.674975
$559$	−1.58359	−0.0669788
$560$	−6.09017	−0.257357
$561$	0	0
$562$	−64.8328	−2.73481
$563$	−40.5967	−1.71095	−0.855474	−	0.517845i	$-0.826734\pi$
$563$	−40.5967	−1.71095	−0.855474	+	0.517845i	$0.826734\pi$
$564$	48.9787	2.06238
$565$	−8.32624	−0.350287
$566$	14.9443	0.628155
$567$	1.00000	0.0419961
$568$	77.1591	3.23752
$569$	−34.1803	−1.43291	−0.716457	−	0.697631i	$-0.754237\pi$
$569$	−34.1803	−1.43291	−0.716457	+	0.697631i	$0.754237\pi$
$570$	−9.47214	−0.396744
$571$	9.09017	0.380412	0.190206	−	0.981744i	$-0.439084\pi$
$571$	9.09017	0.380412	0.190206	+	0.981744i	$0.439084\pi$
$572$	0	0
$573$	0.819660	0.0342418
$574$	−0.618034	−0.0257962
$575$	−1.09017	−0.0454632
$576$	8.70820	0.362842
$577$	31.7082	1.32003	0.660015	−	0.751253i	$-0.270550\pi$
$577$	31.7082	1.32003	0.660015	+	0.751253i	$0.270550\pi$
$578$	−41.0689	−1.70824
$579$	−3.14590	−0.130739
$580$	−18.0000	−0.747409
$581$	−1.47214	−0.0610745
$582$	−20.5623	−0.852335
$583$	0	0
$584$	42.6525	1.76497
$585$	0.145898	0.00603214
$586$	56.6869	2.34171
$587$	−2.12461	−0.0876921	−0.0438461	−	0.999038i	$-0.513961\pi$
$587$	−2.12461	−0.0876921	−0.0438461	+	0.999038i	$0.513961\pi$
$588$	29.1246	1.20108
$589$	35.6525	1.46903
$590$	−11.9443	−0.491738
$591$	13.0344	0.536165
$592$	−61.4508	−2.52561
$593$	14.0344	0.576325	0.288163	−	0.957581i	$-0.406956\pi$
$593$	14.0344	0.576325	0.288163	+	0.957581i	$0.406956\pi$
$594$	0	0
$595$	−0.708204	−0.0290335
$596$	20.5623	0.842265
$597$	−6.70820	−0.274549
$598$	−0.145898	−0.00596621
$599$	12.6525	0.516966	0.258483	−	0.966016i	$-0.416777\pi$
$599$	12.6525	0.516966	0.258483	+	0.966016i	$0.416777\pi$
$600$	34.5066	1.40873
$601$	6.88854	0.280990	0.140495	−	0.990081i	$-0.455131\pi$
$601$	6.88854	0.280990	0.140495	+	0.990081i	$0.455131\pi$
$602$	17.5623	0.715786
$603$	1.85410	0.0755049
$604$	−5.12461	−0.208517
$605$	0	0
$606$	−26.7984	−1.08861
$607$	16.5623	0.672243	0.336122	−	0.941819i	$-0.390885\pi$
$607$	16.5623	0.672243	0.336122	+	0.941819i	$0.390885\pi$
$608$	−63.5410	−2.57693
$609$	−6.00000	−0.243132
$610$	−18.7082	−0.757473
$611$	2.38197	0.0963640
$612$	5.56231	0.224843
$613$	14.2918	0.577240	0.288620	−	0.957444i	$-0.406804\pi$
$613$	14.2918	0.577240	0.288620	+	0.957444i	$0.406804\pi$
$614$	−73.2492	−2.95610
$615$	−0.145898	−0.00588318
$616$	0	0
$617$	11.1803	0.450104	0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803	0.450104	0.225052	+	0.974347i	$0.427745\pi$
$618$	28.6525	1.15257
$619$	24.1246	0.969650	0.484825	−	0.874611i	$-0.338883\pi$
$619$	24.1246	0.969650	0.484825	+	0.874611i	$0.338883\pi$
$620$	18.2705	0.733761
$621$	−0.236068	−0.00947308
$622$	30.5066	1.22320
$623$	−8.23607	−0.329971
$624$	2.32624	0.0931240
$625$	19.4164	0.776656
$626$	−6.61803	−0.264510
$627$	0	0
$628$	76.2492	3.04268
$629$	−7.14590	−0.284926
$630$	−1.61803	−0.0644640
$631$	19.2148	0.764928	0.382464	−	0.923970i	$-0.375076\pi$
$631$	19.2148	0.764928	0.382464	+	0.923970i	$0.375076\pi$
$632$	−82.1935	−3.26948
$633$	3.61803	0.143804
$634$	−17.8541	−0.709077
$635$	4.76393	0.189051
$636$	1.85410	0.0735199
$637$	1.41641	0.0561201
$638$	0	0
$639$	10.3262	0.408500
$640$	−0.673762	−0.0266328
$641$	−25.0902	−0.991002	−0.495501	−	0.868607i	$-0.665016\pi$
$641$	−25.0902	−0.991002	−0.495501	+	0.868607i	$0.665016\pi$
$642$	−30.0344	−1.18536
$643$	20.8541	0.822406	0.411203	−	0.911544i	$-0.365109\pi$
$643$	20.8541	0.822406	0.411203	+	0.911544i	$0.365109\pi$
$644$	1.14590	0.0451547
$645$	4.14590	0.163245
$646$	−17.5623	−0.690980
$647$	45.0344	1.77049	0.885243	−	0.465128i	$-0.153992\pi$
$647$	45.0344	1.77049	0.885243	+	0.465128i	$0.153992\pi$
$648$	7.47214	0.293533
$649$	0	0
$650$	2.85410	0.111947
$651$	6.09017	0.238693
$652$	−24.9787	−0.978242
$653$	−5.61803	−0.219851	−0.109925	−	0.993940i	$-0.535061\pi$
$653$	−5.61803	−0.219851	−0.109925	+	0.993940i	$0.535061\pi$
$654$	−31.4164	−1.22848
$655$	−7.29180	−0.284914
$656$	−2.32624	−0.0908243
$657$	5.70820	0.222698
$658$	−26.4164	−1.02982
$659$	41.1246	1.60199	0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246	1.60199	0.800994	+	0.598673i	$0.204305\pi$
$660$	0	0
$661$	36.5623	1.42211	0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623	1.42211	0.711054	+	0.703137i	$0.248218\pi$
$662$	43.7426	1.70011
$663$	0.270510	0.0105057
$664$	−11.0000	−0.426883
$665$	3.61803	0.140301
$666$	−16.3262	−0.632629
$667$	1.41641	0.0548435
$668$	−58.4164	−2.26020
$669$	−7.18034	−0.277608
$670$	−3.00000	−0.115900
$671$	0	0
$672$	−10.8541	−0.418706
$673$	−35.8328	−1.38125	−0.690627	−	0.723211i	$-0.742665\pi$
$673$	−35.8328	−1.38125	−0.690627	+	0.723211i	$0.742665\pi$
$674$	47.5967	1.83336
$675$	4.61803	0.177748
$676$	−62.8328	−2.41665
$677$	−13.5279	−0.519918	−0.259959	−	0.965620i	$-0.583709\pi$
$677$	−13.5279	−0.519918	−0.259959	+	0.965620i	$0.583709\pi$
$678$	−35.2705	−1.35456
$679$	7.85410	0.301413
$680$	−5.29180	−0.202931
$681$	13.1803	0.505072
$682$	0	0
$683$	9.06888	0.347011	0.173506	−	0.984833i	$-0.444491\pi$
$683$	9.06888	0.347011	0.173506	+	0.984833i	$0.444491\pi$
$684$	−28.4164	−1.08653
$685$	−6.03444	−0.230564
$686$	−34.0344	−1.29944
$687$	−0.472136	−0.0180131
$688$	66.1033	2.52017
$689$	0.0901699	0.00343520
$690$	0.381966	0.0145412
$691$	1.34752	0.0512622	0.0256311	−	0.999671i	$-0.491840\pi$
$691$	1.34752	0.0512622	0.0256311	+	0.999671i	$0.491840\pi$
$692$	87.5410	3.32781
$693$	0	0
$694$	4.00000	0.151838
$695$	9.00000	0.341389
$696$	−44.8328	−1.69938
$697$	−0.270510	−0.0102463
$698$	−33.2705	−1.25931
$699$	−4.14590	−0.156812
$700$	−22.4164	−0.847261
$701$	34.7984	1.31432	0.657158	−	0.753753i	$-0.271758\pi$
$701$	34.7984	1.31432	0.657158	+	0.753753i	$0.271758\pi$
$702$	0.618034	0.0233262
$703$	36.5066	1.37687
$704$	0	0
$705$	−6.23607	−0.234864
$706$	−31.4164	−1.18237
$707$	10.2361	0.384967
$708$	−35.8328	−1.34668
$709$	11.2148	0.421180	0.210590	−	0.977574i	$-0.432462\pi$
$709$	11.2148	0.421180	0.210590	+	0.977574i	$0.432462\pi$
$710$	−16.7082	−0.627048
$711$	−11.0000	−0.412532
$712$	−61.5410	−2.30635
$713$	−1.43769	−0.0538421
$714$	−3.00000	−0.112272
$715$	0	0
$716$	−41.3951	−1.54701
$717$	0.381966	0.0142648
$718$	25.4164	0.948532
$719$	−38.4853	−1.43526	−0.717630	−	0.696425i	$-0.754773\pi$
$719$	−38.4853	−1.43526	−0.717630	+	0.696425i	$0.754773\pi$
$720$	−6.09017	−0.226967
$721$	−10.9443	−0.407586
$722$	39.9787	1.48785
$723$	8.29180	0.308375
$724$	12.2705	0.456030
$725$	−27.7082	−1.02906
$726$	0	0
$727$	−9.14590	−0.339203	−0.169601	−	0.985513i	$-0.554248\pi$
$727$	−9.14590	−0.339203	−0.169601	+	0.985513i	$0.554248\pi$
$728$	−1.76393	−0.0653757
$729$	1.00000	0.0370370
$730$	−9.23607	−0.341842
$731$	7.68692	0.284311
$732$	−56.1246	−2.07443
$733$	0.403252	0.0148945	0.00744723	−	0.999972i	$-0.497629\pi$
$733$	0.403252	0.0148945	0.00744723	+	0.999972i	$0.497629\pi$
$734$	57.9787	2.14003
$735$	−3.70820	−0.136779
$736$	2.56231	0.0944478
$737$	0	0
$738$	−0.618034	−0.0227501
$739$	−3.00000	−0.110357	−0.0551784	−	0.998477i	$-0.517573\pi$
$739$	−3.00000	−0.110357	−0.0551784	+	0.998477i	$0.517573\pi$
$740$	18.7082	0.687727
$741$	−1.38197	−0.0507678
$742$	−1.00000	−0.0367112
$743$	42.8885	1.57343	0.786714	−	0.617318i	$-0.211781\pi$
$743$	42.8885	1.57343	0.786714	+	0.617318i	$0.211781\pi$
$744$	45.5066	1.66835
$745$	−2.61803	−0.0959173
$746$	−2.32624	−0.0851696
$747$	−1.47214	−0.0538626
$748$	0	0
$749$	11.4721	0.419183
$750$	−15.5623	−0.568255
$751$	16.1459	0.589172	0.294586	−	0.955625i	$-0.404818\pi$
$751$	16.1459	0.589172	0.294586	+	0.955625i	$0.404818\pi$
$752$	−99.4296	−3.62582
$753$	21.9787	0.800949
$754$	−3.70820	−0.135045
$755$	0.652476	0.0237460
$756$	−4.85410	−0.176542
$757$	5.00000	0.181728	0.0908640	−	0.995863i	$-0.471037\pi$
$757$	5.00000	0.181728	0.0908640	+	0.995863i	$0.471037\pi$
$758$	−65.1591	−2.36668
$759$	0	0
$760$	27.0344	0.980642
$761$	−29.2918	−1.06183	−0.530913	−	0.847426i	$-0.678151\pi$
$761$	−29.2918	−1.06183	−0.530913	+	0.847426i	$0.678151\pi$
$762$	20.1803	0.731057
$763$	12.0000	0.434429
$764$	−3.97871	−0.143945
$765$	−0.708204	−0.0256052
$766$	−33.2705	−1.20211
$767$	−1.74265	−0.0629233
$768$	14.5623	0.525472
$769$	34.5066	1.24434	0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066	1.24434	0.622170	+	0.782883i	$0.286251\pi$
$770$	0	0
$771$	−29.7426	−1.07116
$772$	15.2705	0.549598
$773$	27.1803	0.977609	0.488804	−	0.872393i	$-0.337433\pi$
$773$	27.1803	0.977609	0.488804	+	0.872393i	$0.337433\pi$
$774$	17.5623	0.631264
$775$	28.1246	1.01027
$776$	58.6869	2.10674
$777$	6.23607	0.223718
$778$	−96.1935	−3.44870
$779$	1.38197	0.0495141
$780$	−0.708204	−0.0253578
$781$	0	0
$782$	0.708204	0.0253253
$783$	−6.00000	−0.214423
$784$	−59.1246	−2.11159
$785$	−9.70820	−0.346501
$786$	−30.8885	−1.10176
$787$	9.70820	0.346060	0.173030	−	0.984917i	$-0.444644\pi$
$787$	9.70820	0.346060	0.173030	+	0.984917i	$0.444644\pi$
$788$	−63.2705	−2.25392
$789$	−15.2705	−0.543645
$790$	17.7984	0.633238
$791$	13.4721	0.479014
$792$	0	0
$793$	−2.72949	−0.0969270
$794$	−48.9787	−1.73819
$795$	−0.236068	−0.00837247
$796$	32.5623	1.15414
$797$	18.5410	0.656757	0.328378	−	0.944546i	$-0.393498\pi$
$797$	18.5410	0.656757	0.328378	+	0.944546i	$0.393498\pi$
$798$	15.3262	0.542543
$799$	−11.5623	−0.409045
$800$	−50.1246	−1.77217
$801$	−8.23607	−0.291007
$802$	−82.9574	−2.92933
$803$	0	0
$804$	−9.00000	−0.317406
$805$	−0.145898	−0.00514223
$806$	3.76393	0.132579
$807$	25.4164	0.894700
$808$	76.4853	2.69074
$809$	−27.0902	−0.952440	−0.476220	−	0.879326i	$-0.657993\pi$
$809$	−27.0902	−0.952440	−0.476220	+	0.879326i	$0.657993\pi$
$810$	−1.61803	−0.0568519
$811$	−36.5623	−1.28388	−0.641938	−	0.766756i	$-0.721869\pi$
$811$	−36.5623	−1.28388	−0.641938	+	0.766756i	$0.721869\pi$
$812$	29.1246	1.02207
$813$	18.6180	0.652963
$814$	0	0
$815$	3.18034	0.111402
$816$	−11.2918	−0.395292
$817$	−39.2705	−1.37390
$818$	16.9443	0.592443
$819$	−0.236068	−0.00824888
$820$	0.708204	0.0247316
$821$	−40.5967	−1.41684	−0.708418	−	0.705793i	$-0.750591\pi$
$821$	−40.5967	−1.41684	−0.708418	+	0.705793i	$0.750591\pi$
$822$	−25.5623	−0.891588
$823$	−27.8328	−0.970191	−0.485095	−	0.874461i	$-0.661215\pi$
$823$	−27.8328	−0.970191	−0.485095	+	0.874461i	$0.661215\pi$
$824$	−81.7771	−2.84884
$825$	0	0
$826$	19.3262	0.672446
$827$	10.6525	0.370423	0.185211	−	0.982699i	$-0.440703\pi$
$827$	10.6525	0.370423	0.185211	+	0.982699i	$0.440703\pi$
$828$	1.14590	0.0398227
$829$	−31.3951	−1.09040	−0.545199	−	0.838307i	$-0.683546\pi$
$829$	−31.3951	−1.09040	−0.545199	+	0.838307i	$0.683546\pi$
$830$	2.38197	0.0826792
$831$	−29.2148	−1.01345
$832$	−2.05573	−0.0712695
$833$	−6.87539	−0.238218
$834$	38.1246	1.32015
$835$	7.43769	0.257392
$836$	0	0
$837$	6.09017	0.210507
$838$	82.3394	2.84437
$839$	−17.8328	−0.615657	−0.307829	−	0.951442i	$-0.599602\pi$
$839$	−17.8328	−0.615657	−0.307829	+	0.951442i	$0.599602\pi$
$840$	4.61803	0.159337
$841$	7.00000	0.241379
$842$	27.5066	0.947939
$843$	24.7639	0.852915
$844$	−17.5623	−0.604519
$845$	8.00000	0.275208
$846$	−26.4164	−0.908215
$847$	0	0
$848$	−3.76393	−0.129254
$849$	−5.70820	−0.195905
$850$	−13.8541	−0.475192
$851$	−1.47214	−0.0504642
$852$	−50.1246	−1.71724
$853$	55.8328	1.91168	0.955840	−	0.293889i	$-0.0949496\pi$
$853$	55.8328	1.91168	0.955840	+	0.293889i	$0.0949496\pi$
$854$	30.2705	1.03584
$855$	3.61803	0.123734
$856$	85.7214	2.92990
$857$	−27.7639	−0.948398	−0.474199	−	0.880418i	$-0.657262\pi$
$857$	−27.7639	−0.948398	−0.474199	+	0.880418i	$0.657262\pi$
$858$	0	0
$859$	−34.4164	−1.17427	−0.587136	−	0.809488i	$-0.699745\pi$
$859$	−34.4164	−1.17427	−0.587136	+	0.809488i	$0.699745\pi$
$860$	−20.1246	−0.686244
$861$	0.236068	0.00804518
$862$	15.4721	0.526983
$863$	0.111456	0.00379401	0.00189701	−	0.999998i	$-0.499396\pi$
$863$	0.111456	0.00379401	0.00189701	+	0.999998i	$0.499396\pi$
$864$	−10.8541	−0.369264
$865$	−11.1459	−0.378972
$866$	92.4296	3.14088
$867$	15.6869	0.532756
$868$	−29.5623	−1.00341
$869$	0	0
$870$	9.70820	0.329139
$871$	−0.437694	−0.0148307
$872$	89.6656	3.03646
$873$	7.85410	0.265821
$874$	−3.61803	−0.122382
$875$	5.94427	0.200953
$876$	−27.7082	−0.936173
$877$	57.9443	1.95664	0.978320	−	0.207101i	$-0.0664030\pi$
$877$	57.9443	1.95664	0.978320	+	0.207101i	$0.0664030\pi$
$878$	−60.9787	−2.05793
$879$	−21.6525	−0.730320
$880$	0	0
$881$	6.20163	0.208938	0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163	0.208938	0.104469	+	0.994528i	$0.466686\pi$
$882$	−15.7082	−0.528923
$883$	1.05573	0.0355281	0.0177640	−	0.999842i	$-0.494345\pi$
$883$	1.05573	0.0355281	0.0177640	+	0.999842i	$0.494345\pi$
$884$	−1.31308	−0.0441637
$885$	4.56231	0.153360
$886$	−82.7214	−2.77908
$887$	54.4853	1.82944	0.914719	−	0.404092i	$-0.132412\pi$
$887$	54.4853	1.82944	0.914719	+	0.404092i	$0.132412\pi$
$888$	46.5967	1.56368
$889$	−7.70820	−0.258525
$890$	13.3262	0.446697
$891$	0	0
$892$	34.8541	1.16700
$893$	59.0689	1.97666
$894$	−11.0902	−0.370911
$895$	5.27051	0.176174
$896$	1.09017	0.0364200
$897$	0.0557281	0.00186071
$898$	−23.7082	−0.791153
$899$	−36.5410	−1.21871
$900$	−22.4164	−0.747214
$901$	−0.437694	−0.0145817
$902$	0	0
$903$	−6.70820	−0.223235
$904$	100.666	3.34809
$905$	−1.56231	−0.0519328
$906$	2.76393	0.0918255
$907$	−42.3951	−1.40771	−0.703853	−	0.710345i	$-0.748539\pi$
$907$	−42.3951	−1.40771	−0.703853	+	0.710345i	$0.748539\pi$
$908$	−63.9787	−2.12321
$909$	10.2361	0.339509
$910$	0.381966	0.0126620
$911$	38.5967	1.27877	0.639384	−	0.768888i	$-0.279190\pi$
$911$	38.5967	1.27877	0.639384	+	0.768888i	$0.279190\pi$
$912$	57.6869	1.91020
$913$	0	0
$914$	−62.7771	−2.07648
$915$	7.14590	0.236236
$916$	2.29180	0.0757231
$917$	11.7984	0.389617
$918$	−3.00000	−0.0990148
$919$	−25.6525	−0.846197	−0.423099	−	0.906084i	$-0.639058\pi$
$919$	−25.6525	−0.846197	−0.423099	+	0.906084i	$0.639058\pi$
$920$	−1.09017	−0.0359418
$921$	27.9787	0.921930
$922$	−24.2705	−0.799307
$923$	−2.43769	−0.0802377
$924$	0	0
$925$	28.7984	0.946885
$926$	4.52786	0.148795
$927$	−10.9443	−0.359457
$928$	65.1246	2.13782
$929$	−12.7082	−0.416943	−0.208471	−	0.978028i	$-0.566849\pi$
$929$	−12.7082	−0.416943	−0.208471	+	0.978028i	$0.566849\pi$
$930$	−9.85410	−0.323129
$931$	35.1246	1.15116
$932$	20.1246	0.659204
$933$	−11.6525	−0.381485
$934$	54.6869	1.78941
$935$	0	0
$936$	−1.76393	−0.0576559
$937$	−41.6525	−1.36073	−0.680364	−	0.732875i	$-0.738178\pi$
$937$	−41.6525	−1.36073	−0.680364	+	0.732875i	$0.738178\pi$
$938$	4.85410	0.158492
$939$	2.52786	0.0824937
$940$	30.2705	0.987315
$941$	14.4508	0.471084	0.235542	−	0.971864i	$-0.424313\pi$
$941$	14.4508	0.471084	0.235542	+	0.971864i	$0.424313\pi$
$942$	−41.1246	−1.33991
$943$	−0.0557281	−0.00181476
$944$	72.7426	2.36757
$945$	0.618034	0.0201046
$946$	0	0
$947$	−32.3951	−1.05270	−0.526350	−	0.850268i	$-0.676440\pi$
$947$	−32.3951	−1.05270	−0.526350	+	0.850268i	$0.676440\pi$
$948$	53.3951	1.73419
$949$	−1.34752	−0.0437425
$950$	70.7771	2.29631
$951$	6.81966	0.221143
$952$	8.56231	0.277506
$953$	−11.3475	−0.367582	−0.183791	−	0.982965i	$-0.558837\pi$
$953$	−11.3475	−0.367582	−0.183791	+	0.982965i	$0.558837\pi$
$954$	−1.00000	−0.0323762
$955$	0.506578	0.0163925
$956$	−1.85410	−0.0599659
$957$	0	0
$958$	74.3050	2.40068
$959$	9.76393	0.315294
$960$	5.38197	0.173702
$961$	6.09017	0.196457
$962$	3.85410	0.124261
$963$	11.4721	0.369684
$964$	−40.2492	−1.29634
$965$	−1.94427	−0.0625883
$966$	−0.618034	−0.0198849
$967$	−43.9230	−1.41247	−0.706234	−	0.707978i	$-0.749607\pi$
$967$	−43.9230	−1.41247	−0.706234	+	0.707978i	$0.749607\pi$
$968$	0	0
$969$	6.70820	0.215499
$970$	−12.7082	−0.408036
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	−4.85410	−0.155695
$973$	−14.5623	−0.466846
$974$	−33.2705	−1.06606
$975$	−1.09017	−0.0349134
$976$	113.936	3.64701
$977$	−0.596748	−0.0190917	−0.00954583	−	0.999954i	$-0.503039\pi$
$977$	−0.596748	−0.0190917	−0.00954583	+	0.999954i	$0.503039\pi$
$978$	13.4721	0.430791
$979$	0	0
$980$	18.0000	0.574989
$981$	12.0000	0.383131
$982$	46.8885	1.49627
$983$	−8.11146	−0.258715	−0.129358	−	0.991598i	$-0.541292\pi$
$983$	−8.11146	−0.258715	−0.129358	+	0.991598i	$0.541292\pi$
$984$	1.76393	0.0562321
$985$	8.05573	0.256677
$986$	18.0000	0.573237
$987$	10.0902	0.321174
$988$	6.70820	0.213416
$989$	1.58359	0.0503553
$990$	0	0
$991$	3.74265	0.118889	0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265	0.118889	0.0594445	+	0.998232i	$0.481067\pi$
$992$	−66.1033	−2.09878
$993$	−16.7082	−0.530219
$994$	27.0344	0.857480
$995$	−4.14590	−0.131434
$996$	7.14590	0.226426
$997$	21.2016	0.671462	0.335731	−	0.941958i	$-0.391017\pi$
$997$	21.2016	0.671462	0.335731	+	0.941958i	$0.391017\pi$
$998$	−47.5066	−1.50379
$999$	6.23607	0.197300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.a.i.1.2		2
3.2	odd	2		1089.2.a.l.1.1		2
4.3	odd	2		5808.2.a.ci.1.1		2
5.4	even	2		9075.2.a.u.1.1		2
11.2	odd	10		363.2.e.k.202.1		4
11.3	even	5		363.2.e.f.130.1		4
11.4	even	5		363.2.e.f.148.1		4
11.5	even	5		363.2.e.b.124.1		4
11.6	odd	10		363.2.e.k.124.1		4
11.7	odd	10		33.2.e.b.16.1	✓	4
11.8	odd	10		33.2.e.b.31.1	yes	4
11.9	even	5		363.2.e.b.202.1		4
11.10	odd	2		363.2.a.d.1.1		2
33.8	even	10		99.2.f.a.64.1		4
33.29	even	10		99.2.f.a.82.1		4
33.32	even	2		1089.2.a.t.1.2		2
44.7	even	10		528.2.y.b.49.1		4
44.19	even	10		528.2.y.b.97.1		4
44.43	even	2		5808.2.a.cj.1.1		2
55.7	even	20		825.2.bx.d.49.2		8
55.8	even	20		825.2.bx.d.724.2		8
55.18	even	20		825.2.bx.d.49.1		8
55.19	odd	10		825.2.n.c.526.1		4
55.29	odd	10		825.2.n.c.676.1		4
55.52	even	20		825.2.bx.d.724.1		8
55.54	odd	2		9075.2.a.cb.1.2		2
99.7	odd	30		891.2.n.c.676.1		8
99.29	even	30		891.2.n.b.676.1		8
99.40	odd	30		891.2.n.c.379.1		8
99.41	even	30		891.2.n.b.460.1		8
99.52	odd	30		891.2.n.c.757.1		8
99.74	even	30		891.2.n.b.757.1		8
99.85	odd	30		891.2.n.c.460.1		8
99.95	even	30		891.2.n.b.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	11.7	odd	10
33.2.e.b.31.1	yes	4	11.8	odd	10
99.2.f.a.64.1		4	33.8	even	10
99.2.f.a.82.1		4	33.29	even	10
363.2.a.d.1.1		2	11.10	odd	2
363.2.a.i.1.2		2	1.1	even	1	trivial
363.2.e.b.124.1		4	11.5	even	5
363.2.e.b.202.1		4	11.9	even	5
363.2.e.f.130.1		4	11.3	even	5
363.2.e.f.148.1		4	11.4	even	5
363.2.e.k.124.1		4	11.6	odd	10
363.2.e.k.202.1		4	11.2	odd	10
528.2.y.b.49.1		4	44.7	even	10
528.2.y.b.97.1		4	44.19	even	10
825.2.n.c.526.1		4	55.19	odd	10
825.2.n.c.676.1		4	55.29	odd	10
825.2.bx.d.49.1		8	55.18	even	20
825.2.bx.d.49.2		8	55.7	even	20
825.2.bx.d.724.1		8	55.52	even	20
825.2.bx.d.724.2		8	55.8	even	20
891.2.n.b.379.1		8	99.95	even	30
891.2.n.b.460.1		8	99.41	even	30
891.2.n.b.676.1		8	99.29	even	30
891.2.n.b.757.1		8	99.74	even	30
891.2.n.c.379.1		8	99.40	odd	30
891.2.n.c.460.1		8	99.85	odd	30
891.2.n.c.676.1		8	99.7	odd	30
891.2.n.c.757.1		8	99.52	odd	30
1089.2.a.l.1.1		2	3.2	odd	2
1089.2.a.t.1.2		2	33.32	even	2
5808.2.a.ci.1.1		2	4.3	odd	2
5808.2.a.cj.1.1		2	44.43	even	2
9075.2.a.u.1.1		2	5.4	even	2
9075.2.a.cb.1.2		2	55.54	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} -0.618034 q^{5} -2.61803 q^{6} +1.00000 q^{7} +7.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.61803 q^{2} -1.00000 q^{3} +4.85410 q^{4} -0.618034 q^{5} -2.61803 q^{6} +1.00000 q^{7} +7.47214 q^{8} +1.00000 q^{9} -1.61803 q^{10} -4.85410 q^{12} -0.236068 q^{13} +2.61803 q^{14} +0.618034 q^{15} +9.85410 q^{16} +1.14590 q^{17} +2.61803 q^{18} -5.85410 q^{19} -3.00000 q^{20} -1.00000 q^{21} +0.236068 q^{23} -7.47214 q^{24} -4.61803 q^{25} -0.618034 q^{26} -1.00000 q^{27} +4.85410 q^{28} +6.00000 q^{29} +1.61803 q^{30} -6.09017 q^{31} +10.8541 q^{32} +3.00000 q^{34} -0.618034 q^{35} +4.85410 q^{36} -6.23607 q^{37} -15.3262 q^{38} +0.236068 q^{39} -4.61803 q^{40} -0.236068 q^{41} -2.61803 q^{42} +6.70820 q^{43} -0.618034 q^{45} +0.618034 q^{46} -10.0902 q^{47} -9.85410 q^{48} -6.00000 q^{49} -12.0902 q^{50} -1.14590 q^{51} -1.14590 q^{52} -0.381966 q^{53} -2.61803 q^{54} +7.47214 q^{56} +5.85410 q^{57} +15.7082 q^{58} +7.38197 q^{59} +3.00000 q^{60} +11.5623 q^{61} -15.9443 q^{62} +1.00000 q^{63} +8.70820 q^{64} +0.145898 q^{65} +1.85410 q^{67} +5.56231 q^{68} -0.236068 q^{69} -1.61803 q^{70} +10.3262 q^{71} +7.47214 q^{72} +5.70820 q^{73} -16.3262 q^{74} +4.61803 q^{75} -28.4164 q^{76} +0.618034 q^{78} -11.0000 q^{79} -6.09017 q^{80} +1.00000 q^{81} -0.618034 q^{82} -1.47214 q^{83} -4.85410 q^{84} -0.708204 q^{85} +17.5623 q^{86} -6.00000 q^{87} -8.23607 q^{89} -1.61803 q^{90} -0.236068 q^{91} +1.14590 q^{92} +6.09017 q^{93} -26.4164 q^{94} +3.61803 q^{95} -10.8541 q^{96} +7.85410 q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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