LMFDB - Embedded newform 341.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [341,2,Mod(1,341)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(341, 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("341.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 341 = 11 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	341.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:	$2.72289870893$
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:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -2.85410 q^{7} -2.23607 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -2.85410 q^{7} -2.23607 q^{8} -2.00000 q^{9} -4.23607 q^{10} +1.00000 q^{11} -0.618034 q^{12} +3.47214 q^{13} -4.61803 q^{14} +2.61803 q^{15} -4.85410 q^{16} +0.236068 q^{17} -3.23607 q^{18} -2.76393 q^{19} -1.61803 q^{20} +2.85410 q^{21} +1.61803 q^{22} +1.23607 q^{23} +2.23607 q^{24} +1.85410 q^{25} +5.61803 q^{26} +5.00000 q^{27} -1.76393 q^{28} +4.23607 q^{30} +1.00000 q^{31} -3.38197 q^{32} -1.00000 q^{33} +0.381966 q^{34} +7.47214 q^{35} -1.23607 q^{36} -4.23607 q^{37} -4.47214 q^{38} -3.47214 q^{39} +5.85410 q^{40} -1.09017 q^{41} +4.61803 q^{42} -9.61803 q^{43} +0.618034 q^{44} +5.23607 q^{45} +2.00000 q^{46} -10.0902 q^{47} +4.85410 q^{48} +1.14590 q^{49} +3.00000 q^{50} -0.236068 q^{51} +2.14590 q^{52} +7.09017 q^{53} +8.09017 q^{54} -2.61803 q^{55} +6.38197 q^{56} +2.76393 q^{57} -2.23607 q^{59} +1.61803 q^{60} +0.0901699 q^{61} +1.61803 q^{62} +5.70820 q^{63} +4.23607 q^{64} -9.09017 q^{65} -1.61803 q^{66} -7.00000 q^{67} +0.145898 q^{68} -1.23607 q^{69} +12.0902 q^{70} +0.0901699 q^{71} +4.47214 q^{72} -2.70820 q^{73} -6.85410 q^{74} -1.85410 q^{75} -1.70820 q^{76} -2.85410 q^{77} -5.61803 q^{78} -5.00000 q^{79} +12.7082 q^{80} +1.00000 q^{81} -1.76393 q^{82} +12.6180 q^{83} +1.76393 q^{84} -0.618034 q^{85} -15.5623 q^{86} -2.23607 q^{88} +5.32624 q^{89} +8.47214 q^{90} -9.90983 q^{91} +0.763932 q^{92} -1.00000 q^{93} -16.3262 q^{94} +7.23607 q^{95} +3.38197 q^{96} +16.9443 q^{97} +1.85410 q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} - 4 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 3 * q^5 - q^6 + q^7 - 4 * q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} - 4 q^{9} - 4 q^{10} + 2 q^{11} + q^{12} - 2 q^{13} - 7 q^{14} + 3 q^{15} - 3 q^{16} - 4 q^{17} - 2 q^{18} - 10 q^{19} - q^{20} - q^{21} + q^{22} - 2 q^{23} - 3 q^{25} + 9 q^{26} + 10 q^{27} - 8 q^{28} + 4 q^{30} + 2 q^{31} - 9 q^{32} - 2 q^{33} + 3 q^{34} + 6 q^{35} + 2 q^{36} - 4 q^{37} + 2 q^{39} + 5 q^{40} + 9 q^{41} + 7 q^{42} - 17 q^{43} - q^{44} + 6 q^{45} + 4 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} + 6 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 5 q^{54} - 3 q^{55} + 15 q^{56} + 10 q^{57} + q^{60} - 11 q^{61} + q^{62} - 2 q^{63} + 4 q^{64} - 7 q^{65} - q^{66} - 14 q^{67} + 7 q^{68} + 2 q^{69} + 13 q^{70} - 11 q^{71} + 8 q^{73} - 7 q^{74} + 3 q^{75} + 10 q^{76} + q^{77} - 9 q^{78} - 10 q^{79} + 12 q^{80} + 2 q^{81} - 8 q^{82} + 23 q^{83} + 8 q^{84} + q^{85} - 11 q^{86} - 5 q^{89} + 8 q^{90} - 31 q^{91} + 6 q^{92} - 2 q^{93} - 17 q^{94} + 10 q^{95} + 9 q^{96} + 16 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 3 * q^5 - q^6 + q^7 - 4 * q^9 - 4 * q^10 + 2 * q^11 + q^12 - 2 * q^13 - 7 * q^14 + 3 * q^15 - 3 * q^16 - 4 * q^17 - 2 * q^18 - 10 * q^19 - q^20 - q^21 + q^22 - 2 * q^23 - 3 * q^25 + 9 * q^26 + 10 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 - 9 * q^32 - 2 * q^33 + 3 * q^34 + 6 * q^35 + 2 * q^36 - 4 * q^37 + 2 * q^39 + 5 * q^40 + 9 * q^41 + 7 * q^42 - 17 * q^43 - q^44 + 6 * q^45 + 4 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 + 6 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 5 * q^54 - 3 * q^55 + 15 * q^56 + 10 * q^57 + q^60 - 11 * q^61 + q^62 - 2 * q^63 + 4 * q^64 - 7 * q^65 - q^66 - 14 * q^67 + 7 * q^68 + 2 * q^69 + 13 * q^70 - 11 * q^71 + 8 * q^73 - 7 * q^74 + 3 * q^75 + 10 * q^76 + q^77 - 9 * q^78 - 10 * q^79 + 12 * q^80 + 2 * q^81 - 8 * q^82 + 23 * q^83 + 8 * q^84 + q^85 - 11 * q^86 - 5 * q^89 + 8 * q^90 - 31 * q^91 + 6 * q^92 - 2 * q^93 - 17 * q^94 + 10 * q^95 + 9 * q^96 + 16 * q^97 - 3 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0.618034	0.309017
$5$	−2.61803	−1.17082	−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803	−1.17082	−0.585410	+	0.810737i	$0.699067\pi$
$6$	−1.61803	−0.660560
$7$	−2.85410	−1.07875	−0.539375	−	0.842066i	$-0.681339\pi$
$7$	−2.85410	−1.07875	−0.539375	+	0.842066i	$0.681339\pi$
$8$	−2.23607	−0.790569
$9$	−2.00000	−0.666667
$10$	−4.23607	−1.33956
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.618034	−0.178411
$13$	3.47214	0.962997	0.481499	−	0.876447i	$-0.340093\pi$
$13$	3.47214	0.962997	0.481499	+	0.876447i	$0.340093\pi$
$14$	−4.61803	−1.23422
$15$	2.61803	0.675973
$16$	−4.85410	−1.21353
$17$	0.236068	0.0572549	0.0286274	−	0.999590i	$-0.490886\pi$
$17$	0.236068	0.0572549	0.0286274	+	0.999590i	$0.490886\pi$
$18$	−3.23607	−0.762749
$19$	−2.76393	−0.634089	−0.317045	−	0.948411i	$-0.602691\pi$
$19$	−2.76393	−0.634089	−0.317045	+	0.948411i	$0.602691\pi$
$20$	−1.61803	−0.361803
$21$	2.85410	0.622816
$22$	1.61803	0.344966
$23$	1.23607	0.257738	0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607	0.257738	0.128869	+	0.991662i	$0.458865\pi$
$24$	2.23607	0.456435
$25$	1.85410	0.370820
$26$	5.61803	1.10179
$27$	5.00000	0.962250
$28$	−1.76393	−0.333352
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	4.23607	0.773397
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.38197	−0.597853
$33$	−1.00000	−0.174078
$34$	0.381966	0.0655066
$35$	7.47214	1.26302
$36$	−1.23607	−0.206011
$37$	−4.23607	−0.696405	−0.348203	−	0.937419i	$-0.613208\pi$
$37$	−4.23607	−0.696405	−0.348203	+	0.937419i	$0.613208\pi$
$38$	−4.47214	−0.725476
$39$	−3.47214	−0.555987
$40$	5.85410	0.925615
$41$	−1.09017	−0.170256	−0.0851280	−	0.996370i	$-0.527130\pi$
$41$	−1.09017	−0.170256	−0.0851280	+	0.996370i	$0.527130\pi$
$42$	4.61803	0.712578
$43$	−9.61803	−1.46674	−0.733368	−	0.679832i	$-0.762053\pi$
$43$	−9.61803	−1.46674	−0.733368	+	0.679832i	$0.762053\pi$
$44$	0.618034	0.0931721
$45$	5.23607	0.780547
$46$	2.00000	0.294884
$47$	−10.0902	−1.47180	−0.735901	−	0.677089i	$-0.763241\pi$
$47$	−10.0902	−1.47180	−0.735901	+	0.677089i	$0.763241\pi$
$48$	4.85410	0.700629
$49$	1.14590	0.163700
$50$	3.00000	0.424264
$51$	−0.236068	−0.0330561
$52$	2.14590	0.297583
$53$	7.09017	0.973910	0.486955	−	0.873427i	$-0.338108\pi$
$53$	7.09017	0.973910	0.486955	+	0.873427i	$0.338108\pi$
$54$	8.09017	1.10093
$55$	−2.61803	−0.353016
$56$	6.38197	0.852826
$57$	2.76393	0.366092
$58$	0	0
$59$	−2.23607	−0.291111	−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607	−0.291111	−0.145556	+	0.989350i	$0.546497\pi$
$60$	1.61803	0.208887
$61$	0.0901699	0.0115451	0.00577254	−	0.999983i	$-0.498163\pi$
$61$	0.0901699	0.0115451	0.00577254	+	0.999983i	$0.498163\pi$
$62$	1.61803	0.205491
$63$	5.70820	0.719166
$64$	4.23607	0.529508
$65$	−9.09017	−1.12750
$66$	−1.61803	−0.199166
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	0.145898	0.0176927
$69$	−1.23607	−0.148805
$70$	12.0902	1.44505
$71$	0.0901699	0.0107012	0.00535060	−	0.999986i	$-0.498297\pi$
$71$	0.0901699	0.0107012	0.00535060	+	0.999986i	$0.498297\pi$
$72$	4.47214	0.527046
$73$	−2.70820	−0.316971	−0.158486	−	0.987361i	$-0.550661\pi$
$73$	−2.70820	−0.316971	−0.158486	+	0.987361i	$0.550661\pi$
$74$	−6.85410	−0.796773
$75$	−1.85410	−0.214093
$76$	−1.70820	−0.195944
$77$	−2.85410	−0.325255
$78$	−5.61803	−0.636117
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	12.7082	1.42082
$81$	1.00000	0.111111
$82$	−1.76393	−0.194794
$83$	12.6180	1.38501	0.692505	−	0.721413i	$-0.256507\pi$
$83$	12.6180	1.38501	0.692505	+	0.721413i	$0.256507\pi$
$84$	1.76393	0.192461
$85$	−0.618034	−0.0670352
$86$	−15.5623	−1.67813
$87$	0	0
$88$	−2.23607	−0.238366
$89$	5.32624	0.564580	0.282290	−	0.959329i	$-0.408906\pi$
$89$	5.32624	0.564580	0.282290	+	0.959329i	$0.408906\pi$
$90$	8.47214	0.893042
$91$	−9.90983	−1.03883
$92$	0.763932	0.0796454
$93$	−1.00000	−0.103695
$94$	−16.3262	−1.68392
$95$	7.23607	0.742405
$96$	3.38197	0.345170
$97$	16.9443	1.72043	0.860215	−	0.509931i	$-0.170329\pi$
$97$	16.9443	1.72043	0.860215	+	0.509931i	$0.170329\pi$
$98$	1.85410	0.187293
$99$	−2.00000	−0.201008
$100$	1.14590	0.114590
$101$	−4.18034	−0.415959	−0.207980	−	0.978133i	$-0.566689\pi$
$101$	−4.18034	−0.415959	−0.207980	+	0.978133i	$0.566689\pi$
$102$	−0.381966	−0.0378203
$103$	9.00000	0.886796	0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000	0.886796	0.443398	+	0.896325i	$0.353773\pi$
$104$	−7.76393	−0.761316
$105$	−7.47214	−0.729206
$106$	11.4721	1.11427
$107$	−7.32624	−0.708254	−0.354127	−	0.935197i	$-0.615222\pi$
$107$	−7.32624	−0.708254	−0.354127	+	0.935197i	$0.615222\pi$
$108$	3.09017	0.297352
$109$	−16.7082	−1.60036	−0.800178	−	0.599763i	$-0.795262\pi$
$109$	−16.7082	−1.60036	−0.800178	+	0.599763i	$0.795262\pi$
$110$	−4.23607	−0.403893
$111$	4.23607	0.402070
$112$	13.8541	1.30909
$113$	−4.94427	−0.465118	−0.232559	−	0.972582i	$-0.574710\pi$
$113$	−4.94427	−0.465118	−0.232559	+	0.972582i	$0.574710\pi$
$114$	4.47214	0.418854
$115$	−3.23607	−0.301765
$116$	0	0
$117$	−6.94427	−0.641998
$118$	−3.61803	−0.333067
$119$	−0.673762	−0.0617637
$120$	−5.85410	−0.534404
$121$	1.00000	0.0909091
$122$	0.145898	0.0132090
$123$	1.09017	0.0982973
$124$	0.618034	0.0555011
$125$	8.23607	0.736656
$126$	9.23607	0.822814
$127$	−18.7082	−1.66008	−0.830042	−	0.557700i	$-0.811684\pi$
$127$	−18.7082	−1.66008	−0.830042	+	0.557700i	$0.811684\pi$
$128$	13.6180	1.20368
$129$	9.61803	0.846821
$130$	−14.7082	−1.28999
$131$	−4.90983	−0.428974	−0.214487	−	0.976727i	$-0.568808\pi$
$131$	−4.90983	−0.428974	−0.214487	+	0.976727i	$0.568808\pi$
$132$	−0.618034	−0.0537930
$133$	7.88854	0.684023
$134$	−11.3262	−0.978438
$135$	−13.0902	−1.12662
$136$	−0.527864	−0.0452640
$137$	−3.70820	−0.316813	−0.158407	−	0.987374i	$-0.550636\pi$
$137$	−3.70820	−0.316813	−0.158407	+	0.987374i	$0.550636\pi$
$138$	−2.00000	−0.170251
$139$	−18.4164	−1.56206	−0.781030	−	0.624494i	$-0.785305\pi$
$139$	−18.4164	−1.56206	−0.781030	+	0.624494i	$0.785305\pi$
$140$	4.61803	0.390295
$141$	10.0902	0.849746
$142$	0.145898	0.0122435
$143$	3.47214	0.290355
$144$	9.70820	0.809017
$145$	0	0
$146$	−4.38197	−0.362654
$147$	−1.14590	−0.0945121
$148$	−2.61803	−0.215201
$149$	−2.23607	−0.183186	−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607	−0.183186	−0.0915929	+	0.995797i	$0.529196\pi$
$150$	−3.00000	−0.244949
$151$	16.2705	1.32408	0.662038	−	0.749471i	$-0.269692\pi$
$151$	16.2705	1.32408	0.662038	+	0.749471i	$0.269692\pi$
$152$	6.18034	0.501292
$153$	−0.472136	−0.0381699
$154$	−4.61803	−0.372132
$155$	−2.61803	−0.210286
$156$	−2.14590	−0.171809
$157$	10.5623	0.842964	0.421482	−	0.906837i	$-0.361510\pi$
$157$	10.5623	0.842964	0.421482	+	0.906837i	$0.361510\pi$
$158$	−8.09017	−0.643619
$159$	−7.09017	−0.562287
$160$	8.85410	0.699978
$161$	−3.52786	−0.278035
$162$	1.61803	0.127125
$163$	−11.0000	−0.861586	−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000	−0.861586	−0.430793	+	0.902451i	$0.641766\pi$
$164$	−0.673762	−0.0526120
$165$	2.61803	0.203814
$166$	20.4164	1.58462
$167$	11.6180	0.899030	0.449515	−	0.893273i	$-0.351597\pi$
$167$	11.6180	0.899030	0.449515	+	0.893273i	$0.351597\pi$
$168$	−6.38197	−0.492379
$169$	−0.944272	−0.0726363
$170$	−1.00000	−0.0766965
$171$	5.52786	0.422726
$172$	−5.94427	−0.453246
$173$	22.0902	1.67948	0.839742	−	0.542985i	$-0.182706\pi$
$173$	22.0902	1.67948	0.839742	+	0.542985i	$0.182706\pi$
$174$	0	0
$175$	−5.29180	−0.400022
$176$	−4.85410	−0.365892
$177$	2.23607	0.168073
$178$	8.61803	0.645949
$179$	−22.2361	−1.66200	−0.831001	−	0.556271i	$-0.812232\pi$
$179$	−22.2361	−1.66200	−0.831001	+	0.556271i	$0.812232\pi$
$180$	3.23607	0.241202
$181$	5.09017	0.378349	0.189175	−	0.981943i	$-0.439419\pi$
$181$	5.09017	0.378349	0.189175	+	0.981943i	$0.439419\pi$
$182$	−16.0344	−1.18855
$183$	−0.0901699	−0.00666555
$184$	−2.76393	−0.203760
$185$	11.0902	0.815366
$186$	−1.61803	−0.118640
$187$	0.236068	0.0172630
$188$	−6.23607	−0.454812
$189$	−14.2705	−1.03803
$190$	11.7082	0.849402
$191$	−14.1803	−1.02605	−0.513027	−	0.858373i	$-0.671476\pi$
$191$	−14.1803	−1.02605	−0.513027	+	0.858373i	$0.671476\pi$
$192$	−4.23607	−0.305712
$193$	25.1803	1.81252	0.906260	−	0.422720i	$-0.138925\pi$
$193$	25.1803	1.81252	0.906260	+	0.422720i	$0.138925\pi$
$194$	27.4164	1.96838
$195$	9.09017	0.650961
$196$	0.708204	0.0505860
$197$	−3.70820	−0.264199	−0.132099	−	0.991236i	$-0.542172\pi$
$197$	−3.70820	−0.264199	−0.132099	+	0.991236i	$0.542172\pi$
$198$	−3.23607	−0.229977
$199$	−12.8885	−0.913645	−0.456822	−	0.889558i	$-0.651012\pi$
$199$	−12.8885	−0.913645	−0.456822	+	0.889558i	$0.651012\pi$
$200$	−4.14590	−0.293159
$201$	7.00000	0.493742
$202$	−6.76393	−0.475909
$203$	0	0
$204$	−0.145898	−0.0102149
$205$	2.85410	0.199339
$206$	14.5623	1.01460
$207$	−2.47214	−0.171825
$208$	−16.8541	−1.16862
$209$	−2.76393	−0.191185
$210$	−12.0902	−0.834301
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	4.38197	0.300955
$213$	−0.0901699	−0.00617834
$214$	−11.8541	−0.810330
$215$	25.1803	1.71728
$216$	−11.1803	−0.760726
$217$	−2.85410	−0.193749
$218$	−27.0344	−1.83100
$219$	2.70820	0.183003
$220$	−1.61803	−0.109088
$221$	0.819660	0.0551363
$222$	6.85410	0.460017
$223$	−22.7082	−1.52065	−0.760327	−	0.649541i	$-0.774961\pi$
$223$	−22.7082	−1.52065	−0.760327	+	0.649541i	$0.774961\pi$
$224$	9.65248	0.644933
$225$	−3.70820	−0.247214
$226$	−8.00000	−0.532152
$227$	15.3607	1.01952	0.509762	−	0.860315i	$-0.329733\pi$
$227$	15.3607	1.01952	0.509762	+	0.860315i	$0.329733\pi$
$228$	1.70820	0.113129
$229$	−19.1459	−1.26520	−0.632598	−	0.774480i	$-0.718012\pi$
$229$	−19.1459	−1.26520	−0.632598	+	0.774480i	$0.718012\pi$
$230$	−5.23607	−0.345256
$231$	2.85410	0.187786
$232$	0	0
$233$	−11.5279	−0.755215	−0.377608	−	0.925966i	$-0.623253\pi$
$233$	−11.5279	−0.755215	−0.377608	+	0.925966i	$0.623253\pi$
$234$	−11.2361	−0.734525
$235$	26.4164	1.72322
$236$	−1.38197	−0.0899583
$237$	5.00000	0.324785
$238$	−1.09017	−0.0706652
$239$	16.3820	1.05966	0.529831	−	0.848103i	$-0.322255\pi$
$239$	16.3820	1.05966	0.529831	+	0.848103i	$0.322255\pi$
$240$	−12.7082	−0.820311
$241$	15.0902	0.972043	0.486022	−	0.873947i	$-0.338448\pi$
$241$	15.0902	0.972043	0.486022	+	0.873947i	$0.338448\pi$
$242$	1.61803	0.104011
$243$	−16.0000	−1.02640
$244$	0.0557281	0.00356763
$245$	−3.00000	−0.191663
$246$	1.76393	0.112464
$247$	−9.59675	−0.610626
$248$	−2.23607	−0.141990
$249$	−12.6180	−0.799635
$250$	13.3262	0.842825
$251$	3.90983	0.246786	0.123393	−	0.992358i	$-0.460622\pi$
$251$	3.90983	0.246786	0.123393	+	0.992358i	$0.460622\pi$
$252$	3.52786	0.222235
$253$	1.23607	0.0777109
$254$	−30.2705	−1.89934
$255$	0.618034	0.0387028
$256$	13.5623	0.847644
$257$	−31.0689	−1.93802	−0.969012	−	0.247014i	$-0.920551\pi$
$257$	−31.0689	−1.93802	−0.969012	+	0.247014i	$0.920551\pi$
$258$	15.5623	0.968867
$259$	12.0902	0.751247
$260$	−5.61803	−0.348416
$261$	0	0
$262$	−7.94427	−0.490799
$263$	22.6180	1.39469	0.697344	−	0.716737i	$-0.254365\pi$
$263$	22.6180	1.39469	0.697344	+	0.716737i	$0.254365\pi$
$264$	2.23607	0.137620
$265$	−18.5623	−1.14027
$266$	12.7639	0.782607
$267$	−5.32624	−0.325960
$268$	−4.32624	−0.264267
$269$	28.7426	1.75247	0.876235	−	0.481884i	$-0.160047\pi$
$269$	28.7426	1.75247	0.876235	+	0.481884i	$0.160047\pi$
$270$	−21.1803	−1.28899
$271$	11.2705	0.684635	0.342317	−	0.939584i	$-0.388788\pi$
$271$	11.2705	0.684635	0.342317	+	0.939584i	$0.388788\pi$
$272$	−1.14590	−0.0694803
$273$	9.90983	0.599770
$274$	−6.00000	−0.362473
$275$	1.85410	0.111807
$276$	−0.763932	−0.0459833
$277$	−0.291796	−0.0175323	−0.00876616	−	0.999962i	$-0.502790\pi$
$277$	−0.291796	−0.0175323	−0.00876616	+	0.999962i	$0.502790\pi$
$278$	−29.7984	−1.78719
$279$	−2.00000	−0.119737
$280$	−16.7082	−0.998506
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	16.3262	0.972213
$283$	−29.2148	−1.73664	−0.868319	−	0.496006i	$-0.834799\pi$
$283$	−29.2148	−1.73664	−0.868319	+	0.496006i	$0.834799\pi$
$284$	0.0557281	0.00330685
$285$	−7.23607	−0.428628
$286$	5.61803	0.332201
$287$	3.11146	0.183663
$288$	6.76393	0.398569
$289$	−16.9443	−0.996722
$290$	0	0
$291$	−16.9443	−0.993291
$292$	−1.67376	−0.0979495
$293$	17.9443	1.04832	0.524158	−	0.851621i	$-0.324380\pi$
$293$	17.9443	1.04832	0.524158	+	0.851621i	$0.324380\pi$
$294$	−1.85410	−0.108133
$295$	5.85410	0.340839
$296$	9.47214	0.550557
$297$	5.00000	0.290129
$298$	−3.61803	−0.209587
$299$	4.29180	0.248201
$300$	−1.14590	−0.0661585
$301$	27.4508	1.58224
$302$	26.3262	1.51490
$303$	4.18034	0.240154
$304$	13.4164	0.769484
$305$	−0.236068	−0.0135172
$306$	−0.763932	−0.0436711
$307$	−34.6869	−1.97969	−0.989843	−	0.142161i	$-0.954595\pi$
$307$	−34.6869	−1.97969	−0.989843	+	0.142161i	$0.954595\pi$
$308$	−1.76393	−0.100509
$309$	−9.00000	−0.511992
$310$	−4.23607	−0.240592
$311$	27.4508	1.55659	0.778297	−	0.627896i	$-0.216084\pi$
$311$	27.4508	1.55659	0.778297	+	0.627896i	$0.216084\pi$
$312$	7.76393	0.439546
$313$	29.1246	1.64622	0.823110	−	0.567882i	$-0.192237\pi$
$313$	29.1246	1.64622	0.823110	+	0.567882i	$0.192237\pi$
$314$	17.0902	0.964454
$315$	−14.9443	−0.842014
$316$	−3.09017	−0.173836
$317$	23.1246	1.29881	0.649404	−	0.760444i	$-0.275019\pi$
$317$	23.1246	1.29881	0.649404	+	0.760444i	$0.275019\pi$
$318$	−11.4721	−0.643325
$319$	0	0
$320$	−11.0902	−0.619959
$321$	7.32624	0.408911
$322$	−5.70820	−0.318106
$323$	−0.652476	−0.0363047
$324$	0.618034	0.0343352
$325$	6.43769	0.357099
$326$	−17.7984	−0.985761
$327$	16.7082	0.923966
$328$	2.43769	0.134599
$329$	28.7984	1.58771
$330$	4.23607	0.233188
$331$	−34.1803	−1.87872	−0.939361	−	0.342931i	$-0.888580\pi$
$331$	−34.1803	−1.87872	−0.939361	+	0.342931i	$0.888580\pi$
$332$	7.79837	0.427991
$333$	8.47214	0.464270
$334$	18.7984	1.02860
$335$	18.3262	1.00127
$336$	−13.8541	−0.755803
$337$	22.1459	1.20636	0.603182	−	0.797604i	$-0.293899\pi$
$337$	22.1459	1.20636	0.603182	+	0.797604i	$0.293899\pi$
$338$	−1.52786	−0.0831048
$339$	4.94427	0.268536
$340$	−0.381966	−0.0207150
$341$	1.00000	0.0541530
$342$	8.94427	0.483651
$343$	16.7082	0.902158
$344$	21.5066	1.15956
$345$	3.23607	0.174224
$346$	35.7426	1.92154
$347$	30.8885	1.65818	0.829092	−	0.559112i	$-0.188858\pi$
$347$	30.8885	1.65818	0.829092	+	0.559112i	$0.188858\pi$
$348$	0	0
$349$	−20.9787	−1.12296	−0.561482	−	0.827489i	$-0.689769\pi$
$349$	−20.9787	−1.12296	−0.561482	+	0.827489i	$0.689769\pi$
$350$	−8.56231	−0.457675
$351$	17.3607	0.926645
$352$	−3.38197	−0.180259
$353$	12.7426	0.678223	0.339111	−	0.940746i	$-0.389874\pi$
$353$	12.7426	0.678223	0.339111	+	0.940746i	$0.389874\pi$
$354$	3.61803	0.192296
$355$	−0.236068	−0.0125292
$356$	3.29180	0.174465
$357$	0.673762	0.0356593
$358$	−35.9787	−1.90153
$359$	20.1246	1.06214	0.531068	−	0.847329i	$-0.321791\pi$
$359$	20.1246	1.06214	0.531068	+	0.847329i	$0.321791\pi$
$360$	−11.7082	−0.617077
$361$	−11.3607	−0.597931
$362$	8.23607	0.432878
$363$	−1.00000	−0.0524864
$364$	−6.12461	−0.321017
$365$	7.09017	0.371116
$366$	−0.145898	−0.00762621
$367$	13.8541	0.723178	0.361589	−	0.932338i	$-0.382234\pi$
$367$	13.8541	0.723178	0.361589	+	0.932338i	$0.382234\pi$
$368$	−6.00000	−0.312772
$369$	2.18034	0.113504
$370$	17.9443	0.932878
$371$	−20.2361	−1.05060
$372$	−0.618034	−0.0320436
$373$	5.90983	0.305999	0.153000	−	0.988226i	$-0.451107\pi$
$373$	5.90983	0.305999	0.153000	+	0.988226i	$0.451107\pi$
$374$	0.381966	0.0197510
$375$	−8.23607	−0.425309
$376$	22.5623	1.16356
$377$	0	0
$378$	−23.0902	−1.18763
$379$	−19.2705	−0.989860	−0.494930	−	0.868933i	$-0.664806\pi$
$379$	−19.2705	−0.989860	−0.494930	+	0.868933i	$0.664806\pi$
$380$	4.47214	0.229416
$381$	18.7082	0.958450
$382$	−22.9443	−1.17393
$383$	−15.4721	−0.790589	−0.395295	−	0.918554i	$-0.629357\pi$
$383$	−15.4721	−0.790589	−0.395295	+	0.918554i	$0.629357\pi$
$384$	−13.6180	−0.694942
$385$	7.47214	0.380815
$386$	40.7426	2.07375
$387$	19.2361	0.977824
$388$	10.4721	0.531642
$389$	−27.7639	−1.40769	−0.703844	−	0.710355i	$-0.748534\pi$
$389$	−27.7639	−1.40769	−0.703844	+	0.710355i	$0.748534\pi$
$390$	14.7082	0.744779
$391$	0.291796	0.0147568
$392$	−2.56231	−0.129416
$393$	4.90983	0.247668
$394$	−6.00000	−0.302276
$395$	13.0902	0.658638
$396$	−1.23607	−0.0621148
$397$	13.0000	0.652451	0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000	0.652451	0.326226	+	0.945292i	$0.394223\pi$
$398$	−20.8541	−1.04532
$399$	−7.88854	−0.394921
$400$	−9.00000	−0.450000
$401$	−6.81966	−0.340558	−0.170279	−	0.985396i	$-0.554467\pi$
$401$	−6.81966	−0.340558	−0.170279	+	0.985396i	$0.554467\pi$
$402$	11.3262	0.564901
$403$	3.47214	0.172959
$404$	−2.58359	−0.128539
$405$	−2.61803	−0.130091
$406$	0	0
$407$	−4.23607	−0.209974
$408$	0.527864	0.0261332
$409$	−10.1246	−0.500630	−0.250315	−	0.968164i	$-0.580534\pi$
$409$	−10.1246	−0.500630	−0.250315	+	0.968164i	$0.580534\pi$
$410$	4.61803	0.228068
$411$	3.70820	0.182912
$412$	5.56231	0.274035
$413$	6.38197	0.314036
$414$	−4.00000	−0.196589
$415$	−33.0344	−1.62160
$416$	−11.7426	−0.575731
$417$	18.4164	0.901855
$418$	−4.47214	−0.218739
$419$	−5.52786	−0.270054	−0.135027	−	0.990842i	$-0.543112\pi$
$419$	−5.52786	−0.270054	−0.135027	+	0.990842i	$0.543112\pi$
$420$	−4.61803	−0.225337
$421$	−3.00000	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$422$	−29.1246	−1.41776
$423$	20.1803	0.981202
$424$	−15.8541	−0.769943
$425$	0.437694	0.0212313
$426$	−0.145898	−0.00706878
$427$	−0.257354	−0.0124542
$428$	−4.52786	−0.218863
$429$	−3.47214	−0.167636
$430$	40.7426	1.96478
$431$	−14.9098	−0.718181	−0.359091	−	0.933303i	$-0.616913\pi$
$431$	−14.9098	−0.718181	−0.359091	+	0.933303i	$0.616913\pi$
$432$	−24.2705	−1.16772
$433$	−28.5623	−1.37262	−0.686308	−	0.727311i	$-0.740770\pi$
$433$	−28.5623	−1.37262	−0.686308	+	0.727311i	$0.740770\pi$
$434$	−4.61803	−0.221673
$435$	0	0
$436$	−10.3262	−0.494537
$437$	−3.41641	−0.163429
$438$	4.38197	0.209378
$439$	−16.1803	−0.772245	−0.386123	−	0.922447i	$-0.626186\pi$
$439$	−16.1803	−0.772245	−0.386123	+	0.922447i	$0.626186\pi$
$440$	5.85410	0.279083
$441$	−2.29180	−0.109133
$442$	1.32624	0.0630827
$443$	−32.8328	−1.55993	−0.779967	−	0.625821i	$-0.784764\pi$
$443$	−32.8328	−1.55993	−0.779967	+	0.625821i	$0.784764\pi$
$444$	2.61803	0.124246
$445$	−13.9443	−0.661022
$446$	−36.7426	−1.73981
$447$	2.23607	0.105762
$448$	−12.0902	−0.571207
$449$	4.79837	0.226449	0.113225	−	0.993569i	$-0.463882\pi$
$449$	4.79837	0.226449	0.113225	+	0.993569i	$0.463882\pi$
$450$	−6.00000	−0.282843
$451$	−1.09017	−0.0513341
$452$	−3.05573	−0.143729
$453$	−16.2705	−0.764455
$454$	24.8541	1.16646
$455$	25.9443	1.21629
$456$	−6.18034	−0.289421
$457$	9.50658	0.444699	0.222349	−	0.974967i	$-0.428627\pi$
$457$	9.50658	0.444699	0.222349	+	0.974967i	$0.428627\pi$
$458$	−30.9787	−1.44754
$459$	1.18034	0.0550935
$460$	−2.00000	−0.0932505
$461$	8.18034	0.380996	0.190498	−	0.981688i	$-0.438990\pi$
$461$	8.18034	0.380996	0.190498	+	0.981688i	$0.438990\pi$
$462$	4.61803	0.214850
$463$	8.47214	0.393734	0.196867	−	0.980430i	$-0.436923\pi$
$463$	8.47214	0.393734	0.196867	+	0.980430i	$0.436923\pi$
$464$	0	0
$465$	2.61803	0.121408
$466$	−18.6525	−0.864059
$467$	−1.14590	−0.0530258	−0.0265129	−	0.999648i	$-0.508440\pi$
$467$	−1.14590	−0.0530258	−0.0265129	+	0.999648i	$0.508440\pi$
$468$	−4.29180	−0.198388
$469$	19.9787	0.922531
$470$	42.7426	1.97157
$471$	−10.5623	−0.486685
$472$	5.00000	0.230144
$473$	−9.61803	−0.442238
$474$	8.09017	0.371594
$475$	−5.12461	−0.235133
$476$	−0.416408	−0.0190860
$477$	−14.1803	−0.649273
$478$	26.5066	1.21238
$479$	8.61803	0.393768	0.196884	−	0.980427i	$-0.436918\pi$
$479$	8.61803	0.393768	0.196884	+	0.980427i	$0.436918\pi$
$480$	−8.85410	−0.404133
$481$	−14.7082	−0.670636
$482$	24.4164	1.11214
$483$	3.52786	0.160523
$484$	0.618034	0.0280925
$485$	−44.3607	−2.01431
$486$	−25.8885	−1.17433
$487$	15.0344	0.681276	0.340638	−	0.940195i	$-0.389357\pi$
$487$	15.0344	0.681276	0.340638	+	0.940195i	$0.389357\pi$
$488$	−0.201626	−0.00912719
$489$	11.0000	0.497437
$490$	−4.85410	−0.219286
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	0.673762	0.0303755
$493$	0	0
$494$	−15.5279	−0.698632
$495$	5.23607	0.235344
$496$	−4.85410	−0.217956
$497$	−0.257354	−0.0115439
$498$	−20.4164	−0.914881
$499$	34.3951	1.53974	0.769869	−	0.638202i	$-0.220322\pi$
$499$	34.3951	1.53974	0.769869	+	0.638202i	$0.220322\pi$
$500$	5.09017	0.227639
$501$	−11.6180	−0.519055
$502$	6.32624	0.282354
$503$	11.2361	0.500992	0.250496	−	0.968118i	$-0.419406\pi$
$503$	11.2361	0.500992	0.250496	+	0.968118i	$0.419406\pi$
$504$	−12.7639	−0.568551
$505$	10.9443	0.487014
$506$	2.00000	0.0889108
$507$	0.944272	0.0419366
$508$	−11.5623	−0.512994
$509$	−26.1803	−1.16042	−0.580212	−	0.814466i	$-0.697030\pi$
$509$	−26.1803	−1.16042	−0.580212	+	0.814466i	$0.697030\pi$
$510$	1.00000	0.0442807
$511$	7.72949	0.341933
$512$	−5.29180	−0.233867
$513$	−13.8197	−0.610153
$514$	−50.2705	−2.21734
$515$	−23.5623	−1.03828
$516$	5.94427	0.261682
$517$	−10.0902	−0.443765
$518$	19.5623	0.859518
$519$	−22.0902	−0.969651
$520$	20.3262	0.891364
$521$	−38.4508	−1.68456	−0.842281	−	0.539038i	$-0.818788\pi$
$521$	−38.4508	−1.68456	−0.842281	+	0.539038i	$0.818788\pi$
$522$	0	0
$523$	−15.2705	−0.667733	−0.333866	−	0.942620i	$-0.608353\pi$
$523$	−15.2705	−0.667733	−0.333866	+	0.942620i	$0.608353\pi$
$524$	−3.03444	−0.132560
$525$	5.29180	0.230953
$526$	36.5967	1.59569
$527$	0.236068	0.0102833
$528$	4.85410	0.211248
$529$	−21.4721	−0.933571
$530$	−30.0344	−1.30461
$531$	4.47214	0.194074
$532$	4.87539	0.211375
$533$	−3.78522	−0.163956
$534$	−8.61803	−0.372939
$535$	19.1803	0.829238
$536$	15.6525	0.676084
$537$	22.2361	0.959557
$538$	46.5066	2.00504
$539$	1.14590	0.0493573
$540$	−8.09017	−0.348145
$541$	−5.36068	−0.230474	−0.115237	−	0.993338i	$-0.536763\pi$
$541$	−5.36068	−0.230474	−0.115237	+	0.993338i	$0.536763\pi$
$542$	18.2361	0.783306
$543$	−5.09017	−0.218440
$544$	−0.798374	−0.0342300
$545$	43.7426	1.87373
$546$	16.0344	0.686211
$547$	6.61803	0.282967	0.141483	−	0.989941i	$-0.454813\pi$
$547$	6.61803	0.282967	0.141483	+	0.989941i	$0.454813\pi$
$548$	−2.29180	−0.0979007
$549$	−0.180340	−0.00769672
$550$	3.00000	0.127920
$551$	0	0
$552$	2.76393	0.117641
$553$	14.2705	0.606844
$554$	−0.472136	−0.0200591
$555$	−11.0902	−0.470751
$556$	−11.3820	−0.482703
$557$	−25.4164	−1.07693	−0.538464	−	0.842649i	$-0.680995\pi$
$557$	−25.4164	−1.07693	−0.538464	+	0.842649i	$0.680995\pi$
$558$	−3.23607	−0.136994
$559$	−33.3951	−1.41246
$560$	−36.2705	−1.53271
$561$	−0.236068	−0.00996680
$562$	19.4164	0.819032
$563$	−0.875388	−0.0368932	−0.0184466	−	0.999830i	$-0.505872\pi$
$563$	−0.875388	−0.0368932	−0.0184466	+	0.999830i	$0.505872\pi$
$564$	6.23607	0.262586
$565$	12.9443	0.544570
$566$	−47.2705	−1.98693
$567$	−2.85410	−0.119861
$568$	−0.201626	−0.00846004
$569$	1.58359	0.0663876	0.0331938	−	0.999449i	$-0.489432\pi$
$569$	1.58359	0.0663876	0.0331938	+	0.999449i	$0.489432\pi$
$570$	−11.7082	−0.490403
$571$	21.2705	0.890143	0.445072	−	0.895495i	$-0.353178\pi$
$571$	21.2705	0.890143	0.445072	+	0.895495i	$0.353178\pi$
$572$	2.14590	0.0897245
$573$	14.1803	0.592392
$574$	5.03444	0.210134
$575$	2.29180	0.0955745
$576$	−8.47214	−0.353006
$577$	5.03444	0.209587	0.104793	−	0.994494i	$-0.466582\pi$
$577$	5.03444	0.209587	0.104793	+	0.994494i	$0.466582\pi$
$578$	−27.4164	−1.14037
$579$	−25.1803	−1.04646
$580$	0	0
$581$	−36.0132	−1.49408
$582$	−27.4164	−1.13645
$583$	7.09017	0.293645
$584$	6.05573	0.250588
$585$	18.1803	0.751665
$586$	29.0344	1.19940
$587$	−30.0902	−1.24195	−0.620977	−	0.783829i	$-0.713264\pi$
$587$	−30.0902	−1.24195	−0.620977	+	0.783829i	$0.713264\pi$
$588$	−0.708204	−0.0292058
$589$	−2.76393	−0.113886
$590$	9.47214	0.389962
$591$	3.70820	0.152535
$592$	20.5623	0.845106
$593$	−12.5066	−0.513584	−0.256792	−	0.966467i	$-0.582665\pi$
$593$	−12.5066	−0.513584	−0.256792	+	0.966467i	$0.582665\pi$
$594$	8.09017	0.331944
$595$	1.76393	0.0723142
$596$	−1.38197	−0.0566075
$597$	12.8885	0.527493
$598$	6.94427	0.283972
$599$	15.6525	0.639543	0.319771	−	0.947495i	$-0.396394\pi$
$599$	15.6525	0.639543	0.319771	+	0.947495i	$0.396394\pi$
$600$	4.14590	0.169256
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	44.4164	1.81028
$603$	14.0000	0.570124
$604$	10.0557	0.409162
$605$	−2.61803	−0.106438
$606$	6.76393	0.274766
$607$	−7.12461	−0.289179	−0.144590	−	0.989492i	$-0.546186\pi$
$607$	−7.12461	−0.289179	−0.144590	+	0.989492i	$0.546186\pi$
$608$	9.34752	0.379092
$609$	0	0
$610$	−0.381966	−0.0154654
$611$	−35.0344	−1.41734
$612$	−0.291796	−0.0117952
$613$	−23.7639	−0.959816	−0.479908	−	0.877319i	$-0.659330\pi$
$613$	−23.7639	−0.959816	−0.479908	+	0.877319i	$0.659330\pi$
$614$	−56.1246	−2.26500
$615$	−2.85410	−0.115088
$616$	6.38197	0.257137
$617$	29.3050	1.17977	0.589886	−	0.807486i	$-0.299172\pi$
$617$	29.3050	1.17977	0.589886	+	0.807486i	$0.299172\pi$
$618$	−14.5623	−0.585782
$619$	−11.3820	−0.457480	−0.228740	−	0.973488i	$-0.573461\pi$
$619$	−11.3820	−0.457480	−0.228740	+	0.973488i	$0.573461\pi$
$620$	−1.61803	−0.0649818
$621$	6.18034	0.248008
$622$	44.4164	1.78094
$623$	−15.2016	−0.609040
$624$	16.8541	0.674704
$625$	−30.8328	−1.23331
$626$	47.1246	1.88348
$627$	2.76393	0.110381
$628$	6.52786	0.260490
$629$	−1.00000	−0.0398726
$630$	−24.1803	−0.963368
$631$	6.27051	0.249625	0.124813	−	0.992180i	$-0.460167\pi$
$631$	6.27051	0.249625	0.124813	+	0.992180i	$0.460167\pi$
$632$	11.1803	0.444730
$633$	18.0000	0.715436
$634$	37.4164	1.48600
$635$	48.9787	1.94366
$636$	−4.38197	−0.173756
$637$	3.97871	0.157642
$638$	0	0
$639$	−0.180340	−0.00713414
$640$	−35.6525	−1.40929
$641$	25.0902	0.991002	0.495501	−	0.868607i	$-0.334984\pi$
$641$	25.0902	0.991002	0.495501	+	0.868607i	$0.334984\pi$
$642$	11.8541	0.467844
$643$	−8.43769	−0.332750	−0.166375	−	0.986063i	$-0.553206\pi$
$643$	−8.43769	−0.332750	−0.166375	+	0.986063i	$0.553206\pi$
$644$	−2.18034	−0.0859174
$645$	−25.1803	−0.991475
$646$	−1.05573	−0.0415371
$647$	−3.50658	−0.137858	−0.0689289	−	0.997622i	$-0.521958\pi$
$647$	−3.50658	−0.137858	−0.0689289	+	0.997622i	$0.521958\pi$
$648$	−2.23607	−0.0878410
$649$	−2.23607	−0.0877733
$650$	10.4164	0.408565
$651$	2.85410	0.111861
$652$	−6.79837	−0.266245
$653$	−36.4508	−1.42643	−0.713216	−	0.700944i	$-0.752762\pi$
$653$	−36.4508	−1.42643	−0.713216	+	0.700944i	$0.752762\pi$
$654$	27.0344	1.05713
$655$	12.8541	0.502251
$656$	5.29180	0.206610
$657$	5.41641	0.211314
$658$	46.5967	1.81653
$659$	35.1246	1.36826	0.684130	−	0.729360i	$-0.260182\pi$
$659$	35.1246	1.36826	0.684130	+	0.729360i	$0.260182\pi$
$660$	1.61803	0.0629819
$661$	−46.5410	−1.81024	−0.905118	−	0.425161i	$-0.860218\pi$
$661$	−46.5410	−1.81024	−0.905118	+	0.425161i	$0.860218\pi$
$662$	−55.3050	−2.14949
$663$	−0.819660	−0.0318330
$664$	−28.2148	−1.09495
$665$	−20.6525	−0.800869
$666$	13.7082	0.531182
$667$	0	0
$668$	7.18034	0.277816
$669$	22.7082	0.877950
$670$	29.6525	1.14558
$671$	0.0901699	0.00348097
$672$	−9.65248	−0.372352
$673$	41.3607	1.59434	0.797169	−	0.603757i	$-0.206330\pi$
$673$	41.3607	1.59434	0.797169	+	0.603757i	$0.206330\pi$
$674$	35.8328	1.38023
$675$	9.27051	0.356822
$676$	−0.583592	−0.0224459
$677$	−40.7426	−1.56587	−0.782934	−	0.622105i	$-0.786278\pi$
$677$	−40.7426	−1.56587	−0.782934	+	0.622105i	$0.786278\pi$
$678$	8.00000	0.307238
$679$	−48.3607	−1.85591
$680$	1.38197	0.0529960
$681$	−15.3607	−0.588623
$682$	1.61803	0.0619577
$683$	−13.3607	−0.511232	−0.255616	−	0.966778i	$-0.582278\pi$
$683$	−13.3607	−0.511232	−0.255616	+	0.966778i	$0.582278\pi$
$684$	3.41641	0.130630
$685$	9.70820	0.370931
$686$	27.0344	1.03218
$687$	19.1459	0.730462
$688$	46.6869	1.77992
$689$	24.6180	0.937872
$690$	5.23607	0.199334
$691$	−11.8197	−0.449641	−0.224821	−	0.974400i	$-0.572180\pi$
$691$	−11.8197	−0.449641	−0.224821	+	0.974400i	$0.572180\pi$
$692$	13.6525	0.518989
$693$	5.70820	0.216837
$694$	49.9787	1.89717
$695$	48.2148	1.82889
$696$	0	0
$697$	−0.257354	−0.00974799
$698$	−33.9443	−1.28481
$699$	11.5279	0.436024
$700$	−3.27051	−0.123614
$701$	−19.9098	−0.751984	−0.375992	−	0.926623i	$-0.622698\pi$
$701$	−19.9098	−0.751984	−0.375992	+	0.926623i	$0.622698\pi$
$702$	28.0902	1.06020
$703$	11.7082	0.441583
$704$	4.23607	0.159653
$705$	−26.4164	−0.994899
$706$	20.6180	0.775970
$707$	11.9311	0.448716
$708$	1.38197	0.0519375
$709$	−33.5410	−1.25966	−0.629830	−	0.776733i	$-0.716875\pi$
$709$	−33.5410	−1.25966	−0.629830	+	0.776733i	$0.716875\pi$
$710$	−0.381966	−0.0143349
$711$	10.0000	0.375029
$712$	−11.9098	−0.446340
$713$	1.23607	0.0462911
$714$	1.09017	0.0407986
$715$	−9.09017	−0.339953
$716$	−13.7426	−0.513587
$717$	−16.3820	−0.611796
$718$	32.5623	1.21521
$719$	−12.8885	−0.480662	−0.240331	−	0.970691i	$-0.577256\pi$
$719$	−12.8885	−0.480662	−0.240331	+	0.970691i	$0.577256\pi$
$720$	−25.4164	−0.947214
$721$	−25.6869	−0.956631
$722$	−18.3820	−0.684106
$723$	−15.0902	−0.561209
$724$	3.14590	0.116916
$725$	0	0
$726$	−1.61803	−0.0600509
$727$	24.7082	0.916377	0.458188	−	0.888855i	$-0.348499\pi$
$727$	24.7082	0.916377	0.458188	+	0.888855i	$0.348499\pi$
$728$	22.1591	0.821269
$729$	13.0000	0.481481
$730$	11.4721	0.424603
$731$	−2.27051	−0.0839778
$732$	−0.0557281	−0.00205977
$733$	25.8328	0.954157	0.477078	−	0.878861i	$-0.341696\pi$
$733$	25.8328	0.954157	0.477078	+	0.878861i	$0.341696\pi$
$734$	22.4164	0.827405
$735$	3.00000	0.110657
$736$	−4.18034	−0.154089
$737$	−7.00000	−0.257848
$738$	3.52786	0.129862
$739$	−1.58359	−0.0582534	−0.0291267	−	0.999576i	$-0.509273\pi$
$739$	−1.58359	−0.0582534	−0.0291267	+	0.999576i	$0.509273\pi$
$740$	6.85410	0.251962
$741$	9.59675	0.352545
$742$	−32.7426	−1.20202
$743$	−1.85410	−0.0680204	−0.0340102	−	0.999421i	$-0.510828\pi$
$743$	−1.85410	−0.0680204	−0.0340102	+	0.999421i	$0.510828\pi$
$744$	2.23607	0.0819782
$745$	5.85410	0.214478
$746$	9.56231	0.350101
$747$	−25.2361	−0.923339
$748$	0.145898	0.00533456
$749$	20.9098	0.764029
$750$	−13.3262	−0.486605
$751$	−26.5410	−0.968496	−0.484248	−	0.874931i	$-0.660907\pi$
$751$	−26.5410	−0.968496	−0.484248	+	0.874931i	$0.660907\pi$
$752$	48.9787	1.78607
$753$	−3.90983	−0.142482
$754$	0	0
$755$	−42.5967	−1.55025
$756$	−8.81966	−0.320768
$757$	46.4164	1.68703	0.843517	−	0.537103i	$-0.180481\pi$
$757$	46.4164	1.68703	0.843517	+	0.537103i	$0.180481\pi$
$758$	−31.1803	−1.13252
$759$	−1.23607	−0.0448664
$760$	−16.1803	−0.586923
$761$	−31.0902	−1.12702	−0.563509	−	0.826110i	$-0.690549\pi$
$761$	−31.0902	−1.12702	−0.563509	+	0.826110i	$0.690549\pi$
$762$	30.2705	1.09658
$763$	47.6869	1.72638
$764$	−8.76393	−0.317068
$765$	1.23607	0.0446901
$766$	−25.0344	−0.904531
$767$	−7.76393	−0.280339
$768$	−13.5623	−0.489388
$769$	45.0000	1.62274	0.811371	−	0.584532i	$-0.198722\pi$
$769$	45.0000	1.62274	0.811371	+	0.584532i	$0.198722\pi$
$770$	12.0902	0.435699
$771$	31.0689	1.11892
$772$	15.5623	0.560100
$773$	47.9443	1.72444	0.862218	−	0.506538i	$-0.169075\pi$
$773$	47.9443	1.72444	0.862218	+	0.506538i	$0.169075\pi$
$774$	31.1246	1.11875
$775$	1.85410	0.0666013
$776$	−37.8885	−1.36012
$777$	−12.0902	−0.433732
$778$	−44.9230	−1.61057
$779$	3.01316	0.107958
$780$	5.61803	0.201158
$781$	0.0901699	0.00322653
$782$	0.472136	0.0168835
$783$	0	0
$784$	−5.56231	−0.198654
$785$	−27.6525	−0.986959
$786$	7.94427	0.283363
$787$	23.1246	0.824303	0.412152	−	0.911115i	$-0.364777\pi$
$787$	23.1246	0.824303	0.412152	+	0.911115i	$0.364777\pi$
$788$	−2.29180	−0.0816419
$789$	−22.6180	−0.805223
$790$	21.1803	0.753563
$791$	14.1115	0.501746
$792$	4.47214	0.158910
$793$	0.313082	0.0111179
$794$	21.0344	0.746484
$795$	18.5623	0.658337
$796$	−7.96556	−0.282332
$797$	−34.4853	−1.22153	−0.610766	−	0.791811i	$-0.709138\pi$
$797$	−34.4853	−1.22153	−0.610766	+	0.791811i	$0.709138\pi$
$798$	−12.7639	−0.451838
$799$	−2.38197	−0.0842679
$800$	−6.27051	−0.221696
$801$	−10.6525	−0.376387
$802$	−11.0344	−0.389640
$803$	−2.70820	−0.0955704
$804$	4.32624	0.152575
$805$	9.23607	0.325529
$806$	5.61803	0.197887
$807$	−28.7426	−1.01179
$808$	9.34752	0.328845
$809$	24.5967	0.864776	0.432388	−	0.901688i	$-0.357671\pi$
$809$	24.5967	0.864776	0.432388	+	0.901688i	$0.357671\pi$
$810$	−4.23607	−0.148840
$811$	39.3607	1.38214	0.691070	−	0.722788i	$-0.257140\pi$
$811$	39.3607	1.38214	0.691070	+	0.722788i	$0.257140\pi$
$812$	0	0
$813$	−11.2705	−0.395274
$814$	−6.85410	−0.240236
$815$	28.7984	1.00876
$816$	1.14590	0.0401145
$817$	26.5836	0.930042
$818$	−16.3820	−0.572782
$819$	19.8197	0.692555
$820$	1.76393	0.0615992
$821$	−21.5410	−0.751787	−0.375893	−	0.926663i	$-0.622664\pi$
$821$	−21.5410	−0.751787	−0.375893	+	0.926663i	$0.622664\pi$
$822$	6.00000	0.209274
$823$	19.4508	0.678014	0.339007	−	0.940784i	$-0.389909\pi$
$823$	19.4508	0.678014	0.339007	+	0.940784i	$0.389909\pi$
$824$	−20.1246	−0.701074
$825$	−1.85410	−0.0645515
$826$	10.3262	0.359296
$827$	−42.6525	−1.48317	−0.741586	−	0.670858i	$-0.765926\pi$
$827$	−42.6525	−1.48317	−0.741586	+	0.670858i	$0.765926\pi$
$828$	−1.52786	−0.0530969
$829$	−10.1246	−0.351642	−0.175821	−	0.984422i	$-0.556258\pi$
$829$	−10.1246	−0.351642	−0.175821	+	0.984422i	$0.556258\pi$
$830$	−53.4508	−1.85531
$831$	0.291796	0.0101223
$832$	14.7082	0.509915
$833$	0.270510	0.00937261
$834$	29.7984	1.03183
$835$	−30.4164	−1.05260
$836$	−1.70820	−0.0590795
$837$	5.00000	0.172825
$838$	−8.94427	−0.308975
$839$	−1.58359	−0.0546717	−0.0273358	−	0.999626i	$-0.508702\pi$
$839$	−1.58359	−0.0546717	−0.0273358	+	0.999626i	$0.508702\pi$
$840$	16.7082	0.576488
$841$	−29.0000	−1.00000
$842$	−4.85410	−0.167283
$843$	−12.0000	−0.413302
$844$	−11.1246	−0.382925
$845$	2.47214	0.0850441
$846$	32.6525	1.12262
$847$	−2.85410	−0.0980681
$848$	−34.4164	−1.18186
$849$	29.2148	1.00265
$850$	0.708204	0.0242912
$851$	−5.23607	−0.179490
$852$	−0.0557281	−0.00190921
$853$	12.9443	0.443203	0.221602	−	0.975137i	$-0.428872\pi$
$853$	12.9443	0.443203	0.221602	+	0.975137i	$0.428872\pi$
$854$	−0.416408	−0.0142492
$855$	−14.4721	−0.494937
$856$	16.3820	0.559924
$857$	−37.2492	−1.27241	−0.636205	−	0.771520i	$-0.719497\pi$
$857$	−37.2492	−1.27241	−0.636205	+	0.771520i	$0.719497\pi$
$858$	−5.61803	−0.191797
$859$	−16.0557	−0.547814	−0.273907	−	0.961756i	$-0.588316\pi$
$859$	−16.0557	−0.547814	−0.273907	+	0.961756i	$0.588316\pi$
$860$	15.5623	0.530670
$861$	−3.11146	−0.106038
$862$	−24.1246	−0.821688
$863$	−13.0344	−0.443698	−0.221849	−	0.975081i	$-0.571209\pi$
$863$	−13.0344	−0.443698	−0.221849	+	0.975081i	$0.571209\pi$
$864$	−16.9098	−0.575284
$865$	−57.8328	−1.96637
$866$	−46.2148	−1.57044
$867$	16.9443	0.575458
$868$	−1.76393	−0.0598718
$869$	−5.00000	−0.169613
$870$	0	0
$871$	−24.3050	−0.823542
$872$	37.3607	1.26519
$873$	−33.8885	−1.14695
$874$	−5.52786	−0.186983
$875$	−23.5066	−0.794667
$876$	1.67376	0.0565512
$877$	31.9443	1.07868	0.539341	−	0.842088i	$-0.318674\pi$
$877$	31.9443	1.07868	0.539341	+	0.842088i	$0.318674\pi$
$878$	−26.1803	−0.883544
$879$	−17.9443	−0.605245
$880$	12.7082	0.428393
$881$	−14.9098	−0.502325	−0.251162	−	0.967945i	$-0.580813\pi$
$881$	−14.9098	−0.502325	−0.251162	+	0.967945i	$0.580813\pi$
$882$	−3.70820	−0.124862
$883$	−6.00000	−0.201916	−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000	−0.201916	−0.100958	+	0.994891i	$0.532191\pi$
$884$	0.506578	0.0170381
$885$	−5.85410	−0.196783
$886$	−53.1246	−1.78476
$887$	1.09017	0.0366043	0.0183022	−	0.999833i	$-0.494174\pi$
$887$	1.09017	0.0366043	0.0183022	+	0.999833i	$0.494174\pi$
$888$	−9.47214	−0.317864
$889$	53.3951	1.79081
$890$	−22.5623	−0.756290
$891$	1.00000	0.0335013
$892$	−14.0344	−0.469908
$893$	27.8885	0.933255
$894$	3.61803	0.121005
$895$	58.2148	1.94591
$896$	−38.8673	−1.29846
$897$	−4.29180	−0.143299
$898$	7.76393	0.259086
$899$	0	0
$900$	−2.29180	−0.0763932
$901$	1.67376	0.0557611
$902$	−1.76393	−0.0587325
$903$	−27.4508	−0.913507
$904$	11.0557	0.367708
$905$	−13.3262	−0.442979
$906$	−26.3262	−0.874631
$907$	26.4164	0.877142	0.438571	−	0.898696i	$-0.355485\pi$
$907$	26.4164	0.877142	0.438571	+	0.898696i	$0.355485\pi$
$908$	9.49342	0.315050
$909$	8.36068	0.277306
$910$	41.9787	1.39158
$911$	33.1803	1.09931	0.549657	−	0.835391i	$-0.314758\pi$
$911$	33.1803	1.09931	0.549657	+	0.835391i	$0.314758\pi$
$912$	−13.4164	−0.444262
$913$	12.6180	0.417596
$914$	15.3820	0.508790
$915$	0.236068	0.00780417
$916$	−11.8328	−0.390967
$917$	14.0132	0.462755
$918$	1.90983	0.0630338
$919$	42.8115	1.41222	0.706111	−	0.708101i	$-0.250448\pi$
$919$	42.8115	1.41222	0.706111	+	0.708101i	$0.250448\pi$
$920$	7.23607	0.238566
$921$	34.6869	1.14297
$922$	13.2361	0.435907
$923$	0.313082	0.0103052
$924$	1.76393	0.0580291
$925$	−7.85410	−0.258241
$926$	13.7082	0.450480
$927$	−18.0000	−0.591198
$928$	0	0
$929$	−22.9656	−0.753476	−0.376738	−	0.926320i	$-0.622954\pi$
$929$	−22.9656	−0.753476	−0.376738	+	0.926320i	$0.622954\pi$
$930$	4.23607	0.138906
$931$	−3.16718	−0.103800
$932$	−7.12461	−0.233374
$933$	−27.4508	−0.898700
$934$	−1.85410	−0.0606681
$935$	−0.618034	−0.0202119
$936$	15.5279	0.507544
$937$	−31.1459	−1.01749	−0.508746	−	0.860917i	$-0.669891\pi$
$937$	−31.1459	−1.01749	−0.508746	+	0.860917i	$0.669891\pi$
$938$	32.3262	1.05549
$939$	−29.1246	−0.950446
$940$	16.3262	0.532503
$941$	35.0902	1.14391	0.571953	−	0.820286i	$-0.306186\pi$
$941$	35.0902	1.14391	0.571953	+	0.820286i	$0.306186\pi$
$942$	−17.0902	−0.556828
$943$	−1.34752	−0.0438814
$944$	10.8541	0.353271
$945$	37.3607	1.21534
$946$	−15.5623	−0.505974
$947$	49.4296	1.60624	0.803122	−	0.595814i	$-0.203170\pi$
$947$	49.4296	1.60624	0.803122	+	0.595814i	$0.203170\pi$
$948$	3.09017	0.100364
$949$	−9.40325	−0.305242
$950$	−8.29180	−0.269021
$951$	−23.1246	−0.749867
$952$	1.50658	0.0488285
$953$	−49.8673	−1.61536	−0.807679	−	0.589622i	$-0.799277\pi$
$953$	−49.8673	−1.61536	−0.807679	+	0.589622i	$0.799277\pi$
$954$	−22.9443	−0.742848
$955$	37.1246	1.20132
$956$	10.1246	0.327453
$957$	0	0
$958$	13.9443	0.450519
$959$	10.5836	0.341762
$960$	11.0902	0.357934
$961$	1.00000	0.0322581
$962$	−23.7984	−0.767290
$963$	14.6525	0.472169
$964$	9.32624	0.300378
$965$	−65.9230	−2.12214
$966$	5.70820	0.183658
$967$	13.0000	0.418052	0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000	0.418052	0.209026	+	0.977910i	$0.432971\pi$
$968$	−2.23607	−0.0718699
$969$	0.652476	0.0209605
$970$	−71.7771	−2.30462
$971$	−18.0000	−0.577647	−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000	−0.577647	−0.288824	+	0.957382i	$0.593264\pi$
$972$	−9.88854	−0.317175
$973$	52.5623	1.68507
$974$	24.3262	0.779463
$975$	−6.43769	−0.206171
$976$	−0.437694	−0.0140102
$977$	38.7771	1.24059	0.620294	−	0.784369i	$-0.287013\pi$
$977$	38.7771	1.24059	0.620294	+	0.784369i	$0.287013\pi$
$978$	17.7984	0.569129
$979$	5.32624	0.170227
$980$	−1.85410	−0.0592271
$981$	33.4164	1.06690
$982$	−29.1246	−0.929404
$983$	−21.3262	−0.680201	−0.340101	−	0.940389i	$-0.610461\pi$
$983$	−21.3262	−0.680201	−0.340101	+	0.940389i	$0.610461\pi$
$984$	−2.43769	−0.0777108
$985$	9.70820	0.309329
$986$	0	0
$987$	−28.7984	−0.916662
$988$	−5.93112	−0.188694
$989$	−11.8885	−0.378034
$990$	8.47214	0.269262
$991$	−49.1803	−1.56226	−0.781132	−	0.624365i	$-0.785358\pi$
$991$	−49.1803	−1.56226	−0.781132	+	0.624365i	$0.785358\pi$
$992$	−3.38197	−0.107378
$993$	34.1803	1.08468
$994$	−0.416408	−0.0132077
$995$	33.7426	1.06971
$996$	−7.79837	−0.247101
$997$	−19.2361	−0.609212	−0.304606	−	0.952478i	$-0.598525\pi$
$997$	−19.2361	−0.609212	−0.304606	+	0.952478i	$0.598525\pi$
$998$	55.6525	1.76165
$999$	−21.1803	−0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	341.2.a.a.1.2	✓	2
3.2	odd	2		3069.2.a.b.1.1		2
4.3	odd	2		5456.2.a.r.1.1		2
5.4	even	2		8525.2.a.d.1.1		2
11.10	odd	2		3751.2.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
341.2.a.a.1.2	✓	2	1.1	even	1	trivial
3069.2.a.b.1.1		2	3.2	odd	2
3751.2.a.a.1.1		2	11.10	odd	2
5456.2.a.r.1.1		2	4.3	odd	2
8525.2.a.d.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:	\( N \)	\(=\)	\( 341 = 11 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	341.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -2.85410 q^{7} -2.23607 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -2.85410 q^{7} -2.23607 q^{8} -2.00000 q^{9} -4.23607 q^{10} +1.00000 q^{11} -0.618034 q^{12} +3.47214 q^{13} -4.61803 q^{14} +2.61803 q^{15} -4.85410 q^{16} +0.236068 q^{17} -3.23607 q^{18} -2.76393 q^{19} -1.61803 q^{20} +2.85410 q^{21} +1.61803 q^{22} +1.23607 q^{23} +2.23607 q^{24} +1.85410 q^{25} +5.61803 q^{26} +5.00000 q^{27} -1.76393 q^{28} +4.23607 q^{30} +1.00000 q^{31} -3.38197 q^{32} -1.00000 q^{33} +0.381966 q^{34} +7.47214 q^{35} -1.23607 q^{36} -4.23607 q^{37} -4.47214 q^{38} -3.47214 q^{39} +5.85410 q^{40} -1.09017 q^{41} +4.61803 q^{42} -9.61803 q^{43} +0.618034 q^{44} +5.23607 q^{45} +2.00000 q^{46} -10.0902 q^{47} +4.85410 q^{48} +1.14590 q^{49} +3.00000 q^{50} -0.236068 q^{51} +2.14590 q^{52} +7.09017 q^{53} +8.09017 q^{54} -2.61803 q^{55} +6.38197 q^{56} +2.76393 q^{57} -2.23607 q^{59} +1.61803 q^{60} +0.0901699 q^{61} +1.61803 q^{62} +5.70820 q^{63} +4.23607 q^{64} -9.09017 q^{65} -1.61803 q^{66} -7.00000 q^{67} +0.145898 q^{68} -1.23607 q^{69} +12.0902 q^{70} +0.0901699 q^{71} +4.47214 q^{72} -2.70820 q^{73} -6.85410 q^{74} -1.85410 q^{75} -1.70820 q^{76} -2.85410 q^{77} -5.61803 q^{78} -5.00000 q^{79} +12.7082 q^{80} +1.00000 q^{81} -1.76393 q^{82} +12.6180 q^{83} +1.76393 q^{84} -0.618034 q^{85} -15.5623 q^{86} -2.23607 q^{88} +5.32624 q^{89} +8.47214 q^{90} -9.90983 q^{91} +0.763932 q^{92} -1.00000 q^{93} -16.3262 q^{94} +7.23607 q^{95} +3.38197 q^{96} +16.9443 q^{97} +1.85410 q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} - 4 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 3 * q^5 - q^6 + q^7 - 4 * q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} - 4 q^{9} - 4 q^{10} + 2 q^{11} + q^{12} - 2 q^{13} - 7 q^{14} + 3 q^{15} - 3 q^{16} - 4 q^{17} - 2 q^{18} - 10 q^{19} - q^{20} - q^{21} + q^{22} - 2 q^{23} - 3 q^{25} + 9 q^{26} + 10 q^{27} - 8 q^{28} + 4 q^{30} + 2 q^{31} - 9 q^{32} - 2 q^{33} + 3 q^{34} + 6 q^{35} + 2 q^{36} - 4 q^{37} + 2 q^{39} + 5 q^{40} + 9 q^{41} + 7 q^{42} - 17 q^{43} - q^{44} + 6 q^{45} + 4 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} + 6 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 5 q^{54} - 3 q^{55} + 15 q^{56} + 10 q^{57} + q^{60} - 11 q^{61} + q^{62} - 2 q^{63} + 4 q^{64} - 7 q^{65} - q^{66} - 14 q^{67} + 7 q^{68} + 2 q^{69} + 13 q^{70} - 11 q^{71} + 8 q^{73} - 7 q^{74} + 3 q^{75} + 10 q^{76} + q^{77} - 9 q^{78} - 10 q^{79} + 12 q^{80} + 2 q^{81} - 8 q^{82} + 23 q^{83} + 8 q^{84} + q^{85} - 11 q^{86} - 5 q^{89} + 8 q^{90} - 31 q^{91} + 6 q^{92} - 2 q^{93} - 17 q^{94} + 10 q^{95} + 9 q^{96} + 16 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 3 * q^5 - q^6 + q^7 - 4 * q^9 - 4 * q^10 + 2 * q^11 + q^12 - 2 * q^13 - 7 * q^14 + 3 * q^15 - 3 * q^16 - 4 * q^17 - 2 * q^18 - 10 * q^19 - q^20 - q^21 + q^22 - 2 * q^23 - 3 * q^25 + 9 * q^26 + 10 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 - 9 * q^32 - 2 * q^33 + 3 * q^34 + 6 * q^35 + 2 * q^36 - 4 * q^37 + 2 * q^39 + 5 * q^40 + 9 * q^41 + 7 * q^42 - 17 * q^43 - q^44 + 6 * q^45 + 4 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 + 6 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 5 * q^54 - 3 * q^55 + 15 * q^56 + 10 * q^57 + q^60 - 11 * q^61 + q^62 - 2 * q^63 + 4 * q^64 - 7 * q^65 - q^66 - 14 * q^67 + 7 * q^68 + 2 * q^69 + 13 * q^70 - 11 * q^71 + 8 * q^73 - 7 * q^74 + 3 * q^75 + 10 * q^76 + q^77 - 9 * q^78 - 10 * q^79 + 12 * q^80 + 2 * q^81 - 8 * q^82 + 23 * q^83 + 8 * q^84 + q^85 - 11 * q^86 - 5 * q^89 + 8 * q^90 - 31 * q^91 + 6 * q^92 - 2 * q^93 - 17 * q^94 + 10 * q^95 + 9 * q^96 + 16 * q^97 - 3 * q^98 - 4 * q^99

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