LMFDB - Embedded newform 1474.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1474,2,Mod(1,1474)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1474, 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("1474.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1474 = 2 \cdot 11 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1474.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:	$11.7699492579$
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:	$\Z[a_1, a_2, a_3]$
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	$\chi$	$=$	1474.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.23607 q^{5} +1.61803 q^{6} +3.23607 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.23607 q^{5} +1.61803 q^{6} +3.23607 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.23607 q^{10} +1.00000 q^{11} +1.61803 q^{12} -0.854102 q^{13} +3.23607 q^{14} +2.00000 q^{15} +1.00000 q^{16} +0.763932 q^{17} -0.381966 q^{18} +1.85410 q^{19} +1.23607 q^{20} +5.23607 q^{21} +1.00000 q^{22} +2.00000 q^{23} +1.61803 q^{24} -3.47214 q^{25} -0.854102 q^{26} -5.47214 q^{27} +3.23607 q^{28} -9.23607 q^{29} +2.00000 q^{30} -3.38197 q^{31} +1.00000 q^{32} +1.61803 q^{33} +0.763932 q^{34} +4.00000 q^{35} -0.381966 q^{36} +1.14590 q^{37} +1.85410 q^{38} -1.38197 q^{39} +1.23607 q^{40} -1.09017 q^{41} +5.23607 q^{42} +4.76393 q^{43} +1.00000 q^{44} -0.472136 q^{45} +2.00000 q^{46} +8.76393 q^{47} +1.61803 q^{48} +3.47214 q^{49} -3.47214 q^{50} +1.23607 q^{51} -0.854102 q^{52} +5.23607 q^{53} -5.47214 q^{54} +1.23607 q^{55} +3.23607 q^{56} +3.00000 q^{57} -9.23607 q^{58} -1.23607 q^{59} +2.00000 q^{60} -10.7984 q^{61} -3.38197 q^{62} -1.23607 q^{63} +1.00000 q^{64} -1.05573 q^{65} +1.61803 q^{66} +1.00000 q^{67} +0.763932 q^{68} +3.23607 q^{69} +4.00000 q^{70} -1.70820 q^{71} -0.381966 q^{72} -4.47214 q^{73} +1.14590 q^{74} -5.61803 q^{75} +1.85410 q^{76} +3.23607 q^{77} -1.38197 q^{78} -8.00000 q^{79} +1.23607 q^{80} -7.70820 q^{81} -1.09017 q^{82} -4.00000 q^{83} +5.23607 q^{84} +0.944272 q^{85} +4.76393 q^{86} -14.9443 q^{87} +1.00000 q^{88} -11.3820 q^{89} -0.472136 q^{90} -2.76393 q^{91} +2.00000 q^{92} -5.47214 q^{93} +8.76393 q^{94} +2.29180 q^{95} +1.61803 q^{96} +12.9443 q^{97} +3.47214 q^{98} -0.381966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} + 2 q^{11} + q^{12} + 5 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 6 q^{17} - 3 q^{18} - 3 q^{19} - 2 q^{20} + 6 q^{21} + 2 q^{22} + 4 q^{23} + q^{24} + 2 q^{25} + 5 q^{26} - 2 q^{27} + 2 q^{28} - 14 q^{29} + 4 q^{30} - 9 q^{31} + 2 q^{32} + q^{33} + 6 q^{34} + 8 q^{35} - 3 q^{36} + 9 q^{37} - 3 q^{38} - 5 q^{39} - 2 q^{40} + 9 q^{41} + 6 q^{42} + 14 q^{43} + 2 q^{44} + 8 q^{45} + 4 q^{46} + 22 q^{47} + q^{48} - 2 q^{49} + 2 q^{50} - 2 q^{51} + 5 q^{52} + 6 q^{53} - 2 q^{54} - 2 q^{55} + 2 q^{56} + 6 q^{57} - 14 q^{58} + 2 q^{59} + 4 q^{60} + 3 q^{61} - 9 q^{62} + 2 q^{63} + 2 q^{64} - 20 q^{65} + q^{66} + 2 q^{67} + 6 q^{68} + 2 q^{69} + 8 q^{70} + 10 q^{71} - 3 q^{72} + 9 q^{74} - 9 q^{75} - 3 q^{76} + 2 q^{77} - 5 q^{78} - 16 q^{79} - 2 q^{80} - 2 q^{81} + 9 q^{82} - 8 q^{83} + 6 q^{84} - 16 q^{85} + 14 q^{86} - 12 q^{87} + 2 q^{88} - 25 q^{89} + 8 q^{90} - 10 q^{91} + 4 q^{92} - 2 q^{93} + 22 q^{94} + 18 q^{95} + q^{96} + 8 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 + 2 * q^11 + q^12 + 5 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 6 * q^17 - 3 * q^18 - 3 * q^19 - 2 * q^20 + 6 * q^21 + 2 * q^22 + 4 * q^23 + q^24 + 2 * q^25 + 5 * q^26 - 2 * q^27 + 2 * q^28 - 14 * q^29 + 4 * q^30 - 9 * q^31 + 2 * q^32 + q^33 + 6 * q^34 + 8 * q^35 - 3 * q^36 + 9 * q^37 - 3 * q^38 - 5 * q^39 - 2 * q^40 + 9 * q^41 + 6 * q^42 + 14 * q^43 + 2 * q^44 + 8 * q^45 + 4 * q^46 + 22 * q^47 + q^48 - 2 * q^49 + 2 * q^50 - 2 * q^51 + 5 * q^52 + 6 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 + 6 * q^57 - 14 * q^58 + 2 * q^59 + 4 * q^60 + 3 * q^61 - 9 * q^62 + 2 * q^63 + 2 * q^64 - 20 * q^65 + q^66 + 2 * q^67 + 6 * q^68 + 2 * q^69 + 8 * q^70 + 10 * q^71 - 3 * q^72 + 9 * q^74 - 9 * q^75 - 3 * q^76 + 2 * q^77 - 5 * q^78 - 16 * q^79 - 2 * q^80 - 2 * q^81 + 9 * q^82 - 8 * q^83 + 6 * q^84 - 16 * q^85 + 14 * q^86 - 12 * q^87 + 2 * q^88 - 25 * q^89 + 8 * q^90 - 10 * q^91 + 4 * q^92 - 2 * q^93 + 22 * q^94 + 18 * q^95 + q^96 + 8 * q^97 - 2 * q^98 - 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	1.23607	0.552786	0.276393	−	0.961045i	$-0.410861\pi$
$5$	1.23607	0.552786	0.276393	+	0.961045i	$0.410861\pi$
$6$	1.61803	0.660560
$7$	3.23607	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	1.23607	0.390879
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.61803	0.467086
$13$	−0.854102	−0.236885	−0.118443	−	0.992961i	$-0.537790\pi$
$13$	−0.854102	−0.236885	−0.118443	+	0.992961i	$0.537790\pi$
$14$	3.23607	0.864876
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	−0.381966	−0.0900303
$19$	1.85410	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$19$	1.85410	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$20$	1.23607	0.276393
$21$	5.23607	1.14260
$22$	1.00000	0.213201
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	1.61803	0.330280
$25$	−3.47214	−0.694427
$26$	−0.854102	−0.167503
$27$	−5.47214	−1.05311
$28$	3.23607	0.611559
$29$	−9.23607	−1.71509	−0.857547	−	0.514405i	$-0.828013\pi$
$29$	−9.23607	−1.71509	−0.857547	+	0.514405i	$0.828013\pi$
$30$	2.00000	0.365148
$31$	−3.38197	−0.607419	−0.303710	−	0.952765i	$-0.598225\pi$
$31$	−3.38197	−0.607419	−0.303710	+	0.952765i	$0.598225\pi$
$32$	1.00000	0.176777
$33$	1.61803	0.281664
$34$	0.763932	0.131013
$35$	4.00000	0.676123
$36$	−0.381966	−0.0636610
$37$	1.14590	0.188384	0.0941922	−	0.995554i	$-0.469973\pi$
$37$	1.14590	0.188384	0.0941922	+	0.995554i	$0.469973\pi$
$38$	1.85410	0.300775
$39$	−1.38197	−0.221292
$40$	1.23607	0.195440
$41$	−1.09017	−0.170256	−0.0851280	−	0.996370i	$-0.527130\pi$
$41$	−1.09017	−0.170256	−0.0851280	+	0.996370i	$0.527130\pi$
$42$	5.23607	0.807943
$43$	4.76393	0.726493	0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393	0.726493	0.363246	+	0.931693i	$0.381668\pi$
$44$	1.00000	0.150756
$45$	−0.472136	−0.0703819
$46$	2.00000	0.294884
$47$	8.76393	1.27835	0.639175	−	0.769061i	$-0.279276\pi$
$47$	8.76393	1.27835	0.639175	+	0.769061i	$0.279276\pi$
$48$	1.61803	0.233543
$49$	3.47214	0.496019
$50$	−3.47214	−0.491034
$51$	1.23607	0.173084
$52$	−0.854102	−0.118443
$53$	5.23607	0.719229	0.359615	−	0.933101i	$-0.382908\pi$
$53$	5.23607	0.719229	0.359615	+	0.933101i	$0.382908\pi$
$54$	−5.47214	−0.744663
$55$	1.23607	0.166671
$56$	3.23607	0.432438
$57$	3.00000	0.397360
$58$	−9.23607	−1.21276
$59$	−1.23607	−0.160922	−0.0804612	−	0.996758i	$-0.525639\pi$
$59$	−1.23607	−0.160922	−0.0804612	+	0.996758i	$0.525639\pi$
$60$	2.00000	0.258199
$61$	−10.7984	−1.38259	−0.691295	−	0.722573i	$-0.742960\pi$
$61$	−10.7984	−1.38259	−0.691295	+	0.722573i	$0.742960\pi$
$62$	−3.38197	−0.429510
$63$	−1.23607	−0.155730
$64$	1.00000	0.125000
$65$	−1.05573	−0.130947
$66$	1.61803	0.199166
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	0.763932	0.0926404
$69$	3.23607	0.389577
$70$	4.00000	0.478091
$71$	−1.70820	−0.202727	−0.101363	−	0.994849i	$-0.532320\pi$
$71$	−1.70820	−0.202727	−0.101363	+	0.994849i	$0.532320\pi$
$72$	−0.381966	−0.0450151
$73$	−4.47214	−0.523424	−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214	−0.523424	−0.261712	+	0.965146i	$0.584287\pi$
$74$	1.14590	0.133208
$75$	−5.61803	−0.648715
$76$	1.85410	0.212680
$77$	3.23607	0.368784
$78$	−1.38197	−0.156477
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.23607	0.138197
$81$	−7.70820	−0.856467
$82$	−1.09017	−0.120389
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	5.23607	0.571302
$85$	0.944272	0.102421
$86$	4.76393	0.513708
$87$	−14.9443	−1.60219
$88$	1.00000	0.106600
$89$	−11.3820	−1.20649	−0.603243	−	0.797557i	$-0.706125\pi$
$89$	−11.3820	−1.20649	−0.603243	+	0.797557i	$0.706125\pi$
$90$	−0.472136	−0.0497675
$91$	−2.76393	−0.289739
$92$	2.00000	0.208514
$93$	−5.47214	−0.567434
$94$	8.76393	0.903931
$95$	2.29180	0.235133
$96$	1.61803	0.165140
$97$	12.9443	1.31429	0.657146	−	0.753763i	$-0.271764\pi$
$97$	12.9443	1.31429	0.657146	+	0.753763i	$0.271764\pi$
$98$	3.47214	0.350739
$99$	−0.381966	−0.0383890
$100$	−3.47214	−0.347214
$101$	9.79837	0.974975	0.487487	−	0.873130i	$-0.337914\pi$
$101$	9.79837	0.974975	0.487487	+	0.873130i	$0.337914\pi$
$102$	1.23607	0.122389
$103$	14.1803	1.39723	0.698615	−	0.715498i	$-0.253800\pi$
$103$	14.1803	1.39723	0.698615	+	0.715498i	$0.253800\pi$
$104$	−0.854102	−0.0837516
$105$	6.47214	0.631616
$106$	5.23607	0.508572
$107$	19.0902	1.84552	0.922758	−	0.385379i	$-0.125929\pi$
$107$	19.0902	1.84552	0.922758	+	0.385379i	$0.125929\pi$
$108$	−5.47214	−0.526557
$109$	−0.909830	−0.0871459	−0.0435730	−	0.999050i	$-0.513874\pi$
$109$	−0.909830	−0.0871459	−0.0435730	+	0.999050i	$0.513874\pi$
$110$	1.23607	0.117854
$111$	1.85410	0.175984
$112$	3.23607	0.305780
$113$	−11.4164	−1.07397	−0.536983	−	0.843593i	$-0.680436\pi$
$113$	−11.4164	−1.07397	−0.536983	+	0.843593i	$0.680436\pi$
$114$	3.00000	0.280976
$115$	2.47214	0.230528
$116$	−9.23607	−0.857547
$117$	0.326238	0.0301607
$118$	−1.23607	−0.113789
$119$	2.47214	0.226620
$120$	2.00000	0.182574
$121$	1.00000	0.0909091
$122$	−10.7984	−0.977639
$123$	−1.76393	−0.159048
$124$	−3.38197	−0.303710
$125$	−10.4721	−0.936656
$126$	−1.23607	−0.110118
$127$	−11.1459	−0.989039	−0.494519	−	0.869167i	$-0.664656\pi$
$127$	−11.1459	−0.989039	−0.494519	+	0.869167i	$0.664656\pi$
$128$	1.00000	0.0883883
$129$	7.70820	0.678670
$130$	−1.05573	−0.0925935
$131$	5.32624	0.465356	0.232678	−	0.972554i	$-0.425251\pi$
$131$	5.32624	0.465356	0.232678	+	0.972554i	$0.425251\pi$
$132$	1.61803	0.140832
$133$	6.00000	0.520266
$134$	1.00000	0.0863868
$135$	−6.76393	−0.582147
$136$	0.763932	0.0655066
$137$	−14.1803	−1.21151	−0.605754	−	0.795652i	$-0.707128\pi$
$137$	−14.1803	−1.21151	−0.605754	+	0.795652i	$0.707128\pi$
$138$	3.23607	0.275472
$139$	−4.47214	−0.379322	−0.189661	−	0.981850i	$-0.560739\pi$
$139$	−4.47214	−0.379322	−0.189661	+	0.981850i	$0.560739\pi$
$140$	4.00000	0.338062
$141$	14.1803	1.19420
$142$	−1.70820	−0.143349
$143$	−0.854102	−0.0714236
$144$	−0.381966	−0.0318305
$145$	−11.4164	−0.948081
$146$	−4.47214	−0.370117
$147$	5.61803	0.463368
$148$	1.14590	0.0941922
$149$	16.1803	1.32555	0.662773	−	0.748821i	$-0.269380\pi$
$149$	16.1803	1.32555	0.662773	+	0.748821i	$0.269380\pi$
$150$	−5.61803	−0.458711
$151$	8.09017	0.658369	0.329184	−	0.944266i	$-0.393226\pi$
$151$	8.09017	0.658369	0.329184	+	0.944266i	$0.393226\pi$
$152$	1.85410	0.150388
$153$	−0.291796	−0.0235903
$154$	3.23607	0.260770
$155$	−4.18034	−0.335773
$156$	−1.38197	−0.110646
$157$	−15.2705	−1.21872	−0.609360	−	0.792894i	$-0.708573\pi$
$157$	−15.2705	−1.21872	−0.609360	+	0.792894i	$0.708573\pi$
$158$	−8.00000	−0.636446
$159$	8.47214	0.671884
$160$	1.23607	0.0977198
$161$	6.47214	0.510076
$162$	−7.70820	−0.605614
$163$	−7.23607	−0.566773	−0.283386	−	0.959006i	$-0.591458\pi$
$163$	−7.23607	−0.566773	−0.283386	+	0.959006i	$0.591458\pi$
$164$	−1.09017	−0.0851280
$165$	2.00000	0.155700
$166$	−4.00000	−0.310460
$167$	13.0902	1.01295	0.506474	−	0.862255i	$-0.330949\pi$
$167$	13.0902	1.01295	0.506474	+	0.862255i	$0.330949\pi$
$168$	5.23607	0.403971
$169$	−12.2705	−0.943885
$170$	0.944272	0.0724223
$171$	−0.708204	−0.0541577
$172$	4.76393	0.363246
$173$	7.52786	0.572333	0.286166	−	0.958180i	$-0.407619\pi$
$173$	7.52786	0.572333	0.286166	+	0.958180i	$0.407619\pi$
$174$	−14.9443	−1.13292
$175$	−11.2361	−0.849367
$176$	1.00000	0.0753778
$177$	−2.00000	−0.150329
$178$	−11.3820	−0.853114
$179$	−7.56231	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$179$	−7.56231	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$180$	−0.472136	−0.0351909
$181$	−5.90983	−0.439274	−0.219637	−	0.975582i	$-0.570487\pi$
$181$	−5.90983	−0.439274	−0.219637	+	0.975582i	$0.570487\pi$
$182$	−2.76393	−0.204876
$183$	−17.4721	−1.29158
$184$	2.00000	0.147442
$185$	1.41641	0.104136
$186$	−5.47214	−0.401236
$187$	0.763932	0.0558642
$188$	8.76393	0.639175
$189$	−17.7082	−1.28808
$190$	2.29180	0.166264
$191$	13.2705	0.960220	0.480110	−	0.877208i	$-0.340597\pi$
$191$	13.2705	0.960220	0.480110	+	0.877208i	$0.340597\pi$
$192$	1.61803	0.116772
$193$	19.1246	1.37662	0.688310	−	0.725417i	$-0.258353\pi$
$193$	19.1246	1.37662	0.688310	+	0.725417i	$0.258353\pi$
$194$	12.9443	0.929345
$195$	−1.70820	−0.122327
$196$	3.47214	0.248010
$197$	8.61803	0.614009	0.307005	−	0.951708i	$-0.400673\pi$
$197$	8.61803	0.614009	0.307005	+	0.951708i	$0.400673\pi$
$198$	−0.381966	−0.0271451
$199$	−0.944272	−0.0669377	−0.0334688	−	0.999440i	$-0.510655\pi$
$199$	−0.944272	−0.0669377	−0.0334688	+	0.999440i	$0.510655\pi$
$200$	−3.47214	−0.245517
$201$	1.61803	0.114127
$202$	9.79837	0.689411
$203$	−29.8885	−2.09776
$204$	1.23607	0.0865421
$205$	−1.34752	−0.0941152
$206$	14.1803	0.987991
$207$	−0.763932	−0.0530969
$208$	−0.854102	−0.0592213
$209$	1.85410	0.128251
$210$	6.47214	0.446620
$211$	−2.67376	−0.184069	−0.0920347	−	0.995756i	$-0.529337\pi$
$211$	−2.67376	−0.184069	−0.0920347	+	0.995756i	$0.529337\pi$
$212$	5.23607	0.359615
$213$	−2.76393	−0.189382
$214$	19.0902	1.30498
$215$	5.88854	0.401595
$216$	−5.47214	−0.372332
$217$	−10.9443	−0.742946
$218$	−0.909830	−0.0616215
$219$	−7.23607	−0.488968
$220$	1.23607	0.0833357
$221$	−0.652476	−0.0438903
$222$	1.85410	0.124439
$223$	−8.47214	−0.567336	−0.283668	−	0.958923i	$-0.591551\pi$
$223$	−8.47214	−0.567336	−0.283668	+	0.958923i	$0.591551\pi$
$224$	3.23607	0.216219
$225$	1.32624	0.0884159
$226$	−11.4164	−0.759408
$227$	−17.5066	−1.16195	−0.580976	−	0.813921i	$-0.697329\pi$
$227$	−17.5066	−1.16195	−0.580976	+	0.813921i	$0.697329\pi$
$228$	3.00000	0.198680
$229$	−14.9443	−0.987545	−0.493773	−	0.869591i	$-0.664382\pi$
$229$	−14.9443	−0.987545	−0.493773	+	0.869591i	$0.664382\pi$
$230$	2.47214	0.163008
$231$	5.23607	0.344508
$232$	−9.23607	−0.606378
$233$	22.2705	1.45899	0.729495	−	0.683986i	$-0.239755\pi$
$233$	22.2705	1.45899	0.729495	+	0.683986i	$0.239755\pi$
$234$	0.326238	0.0213268
$235$	10.8328	0.706655
$236$	−1.23607	−0.0804612
$237$	−12.9443	−0.840821
$238$	2.47214	0.160245
$239$	−9.70820	−0.627972	−0.313986	−	0.949428i	$-0.601664\pi$
$239$	−9.70820	−0.627972	−0.313986	+	0.949428i	$0.601664\pi$
$240$	2.00000	0.129099
$241$	9.52786	0.613744	0.306872	−	0.951751i	$-0.400718\pi$
$241$	9.52786	0.613744	0.306872	+	0.951751i	$0.400718\pi$
$242$	1.00000	0.0642824
$243$	3.94427	0.253025
$244$	−10.7984	−0.691295
$245$	4.29180	0.274193
$246$	−1.76393	−0.112464
$247$	−1.58359	−0.100762
$248$	−3.38197	−0.214755
$249$	−6.47214	−0.410155
$250$	−10.4721	−0.662316
$251$	−25.0344	−1.58016	−0.790080	−	0.613004i	$-0.789961\pi$
$251$	−25.0344	−1.58016	−0.790080	+	0.613004i	$0.789961\pi$
$252$	−1.23607	−0.0778650
$253$	2.00000	0.125739
$254$	−11.1459	−0.699356
$255$	1.52786	0.0956786
$256$	1.00000	0.0625000
$257$	8.85410	0.552304	0.276152	−	0.961114i	$-0.410941\pi$
$257$	8.85410	0.552304	0.276152	+	0.961114i	$0.410941\pi$
$258$	7.70820	0.479892
$259$	3.70820	0.230417
$260$	−1.05573	−0.0654735
$261$	3.52786	0.218369
$262$	5.32624	0.329056
$263$	−7.14590	−0.440635	−0.220317	−	0.975428i	$-0.570709\pi$
$263$	−7.14590	−0.440635	−0.220317	+	0.975428i	$0.570709\pi$
$264$	1.61803	0.0995831
$265$	6.47214	0.397580
$266$	6.00000	0.367884
$267$	−18.4164	−1.12707
$268$	1.00000	0.0610847
$269$	−7.03444	−0.428897	−0.214449	−	0.976735i	$-0.568795\pi$
$269$	−7.03444	−0.428897	−0.214449	+	0.976735i	$0.568795\pi$
$270$	−6.76393	−0.411640
$271$	−29.4164	−1.78692	−0.893460	−	0.449143i	$-0.851729\pi$
$271$	−29.4164	−1.78692	−0.893460	+	0.449143i	$0.851729\pi$
$272$	0.763932	0.0463202
$273$	−4.47214	−0.270666
$274$	−14.1803	−0.856666
$275$	−3.47214	−0.209378
$276$	3.23607	0.194788
$277$	−0.291796	−0.0175323	−0.00876616	−	0.999962i	$-0.502790\pi$
$277$	−0.291796	−0.0175323	−0.00876616	+	0.999962i	$0.502790\pi$
$278$	−4.47214	−0.268221
$279$	1.29180	0.0773378
$280$	4.00000	0.239046
$281$	0.201626	0.0120280	0.00601400	−	0.999982i	$-0.498086\pi$
$281$	0.201626	0.0120280	0.00601400	+	0.999982i	$0.498086\pi$
$282$	14.1803	0.844427
$283$	14.6738	0.872265	0.436132	−	0.899883i	$-0.356348\pi$
$283$	14.6738	0.872265	0.436132	+	0.899883i	$0.356348\pi$
$284$	−1.70820	−0.101363
$285$	3.70820	0.219655
$286$	−0.854102	−0.0505041
$287$	−3.52786	−0.208243
$288$	−0.381966	−0.0225076
$289$	−16.4164	−0.965671
$290$	−11.4164	−0.670395
$291$	20.9443	1.22777
$292$	−4.47214	−0.261712
$293$	5.05573	0.295359	0.147679	−	0.989035i	$-0.452820\pi$
$293$	5.05573	0.295359	0.147679	+	0.989035i	$0.452820\pi$
$294$	5.61803	0.327650
$295$	−1.52786	−0.0889557
$296$	1.14590	0.0666040
$297$	−5.47214	−0.317526
$298$	16.1803	0.937302
$299$	−1.70820	−0.0987880
$300$	−5.61803	−0.324357
$301$	15.4164	0.888587
$302$	8.09017	0.465537
$303$	15.8541	0.910794
$304$	1.85410	0.106340
$305$	−13.3475	−0.764277
$306$	−0.291796	−0.0166809
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	3.23607	0.184392
$309$	22.9443	1.30525
$310$	−4.18034	−0.237427
$311$	14.0902	0.798980	0.399490	−	0.916738i	$-0.369187\pi$
$311$	14.0902	0.798980	0.399490	+	0.916738i	$0.369187\pi$
$312$	−1.38197	−0.0782384
$313$	−23.7082	−1.34007	−0.670033	−	0.742331i	$-0.733720\pi$
$313$	−23.7082	−1.34007	−0.670033	+	0.742331i	$0.733720\pi$
$314$	−15.2705	−0.861765
$315$	−1.52786	−0.0860854
$316$	−8.00000	−0.450035
$317$	3.20163	0.179821	0.0899106	−	0.995950i	$-0.471342\pi$
$317$	3.20163	0.179821	0.0899106	+	0.995950i	$0.471342\pi$
$318$	8.47214	0.475094
$319$	−9.23607	−0.517121
$320$	1.23607	0.0690983
$321$	30.8885	1.72403
$322$	6.47214	0.360678
$323$	1.41641	0.0788110
$324$	−7.70820	−0.428234
$325$	2.96556	0.164500
$326$	−7.23607	−0.400769
$327$	−1.47214	−0.0814093
$328$	−1.09017	−0.0601946
$329$	28.3607	1.56357
$330$	2.00000	0.110096
$331$	22.7426	1.25005	0.625024	−	0.780605i	$-0.285089\pi$
$331$	22.7426	1.25005	0.625024	+	0.780605i	$0.285089\pi$
$332$	−4.00000	−0.219529
$333$	−0.437694	−0.0239855
$334$	13.0902	0.716262
$335$	1.23607	0.0675336
$336$	5.23607	0.285651
$337$	−11.2705	−0.613944	−0.306972	−	0.951719i	$-0.599316\pi$
$337$	−11.2705	−0.613944	−0.306972	+	0.951719i	$0.599316\pi$
$338$	−12.2705	−0.667428
$339$	−18.4721	−1.00327
$340$	0.944272	0.0512103
$341$	−3.38197	−0.183144
$342$	−0.708204	−0.0382953
$343$	−11.4164	−0.616428
$344$	4.76393	0.256854
$345$	4.00000	0.215353
$346$	7.52786	0.404700
$347$	28.6525	1.53815	0.769073	−	0.639161i	$-0.220718\pi$
$347$	28.6525	1.53815	0.769073	+	0.639161i	$0.220718\pi$
$348$	−14.9443	−0.801097
$349$	15.2361	0.815568	0.407784	−	0.913078i	$-0.366302\pi$
$349$	15.2361	0.815568	0.407784	+	0.913078i	$0.366302\pi$
$350$	−11.2361	−0.600593
$351$	4.67376	0.249467
$352$	1.00000	0.0533002
$353$	8.58359	0.456859	0.228429	−	0.973561i	$-0.426641\pi$
$353$	8.58359	0.456859	0.228429	+	0.973561i	$0.426641\pi$
$354$	−2.00000	−0.106299
$355$	−2.11146	−0.112064
$356$	−11.3820	−0.603243
$357$	4.00000	0.211702
$358$	−7.56231	−0.399680
$359$	−7.20163	−0.380087	−0.190044	−	0.981776i	$-0.560863\pi$
$359$	−7.20163	−0.380087	−0.190044	+	0.981776i	$0.560863\pi$
$360$	−0.472136	−0.0248837
$361$	−15.5623	−0.819069
$362$	−5.90983	−0.310614
$363$	1.61803	0.0849248
$364$	−2.76393	−0.144869
$365$	−5.52786	−0.289342
$366$	−17.4721	−0.913283
$367$	−3.05573	−0.159508	−0.0797539	−	0.996815i	$-0.525413\pi$
$367$	−3.05573	−0.159508	−0.0797539	+	0.996815i	$0.525413\pi$
$368$	2.00000	0.104257
$369$	0.416408	0.0216773
$370$	1.41641	0.0736355
$371$	16.9443	0.879703
$372$	−5.47214	−0.283717
$373$	27.8885	1.44401	0.722007	−	0.691886i	$-0.243220\pi$
$373$	27.8885	1.44401	0.722007	+	0.691886i	$0.243220\pi$
$374$	0.763932	0.0395020
$375$	−16.9443	−0.874998
$376$	8.76393	0.451965
$377$	7.88854	0.406281
$378$	−17.7082	−0.910812
$379$	−18.3820	−0.944218	−0.472109	−	0.881540i	$-0.656507\pi$
$379$	−18.3820	−0.944218	−0.472109	+	0.881540i	$0.656507\pi$
$380$	2.29180	0.117567
$381$	−18.0344	−0.923932
$382$	13.2705	0.678978
$383$	−20.6180	−1.05353	−0.526766	−	0.850010i	$-0.676596\pi$
$383$	−20.6180	−1.05353	−0.526766	+	0.850010i	$0.676596\pi$
$384$	1.61803	0.0825700
$385$	4.00000	0.203859
$386$	19.1246	0.973417
$387$	−1.81966	−0.0924985
$388$	12.9443	0.657146
$389$	−23.7984	−1.20663	−0.603313	−	0.797505i	$-0.706153\pi$
$389$	−23.7984	−1.20663	−0.603313	+	0.797505i	$0.706153\pi$
$390$	−1.70820	−0.0864983
$391$	1.52786	0.0772674
$392$	3.47214	0.175369
$393$	8.61803	0.434722
$394$	8.61803	0.434170
$395$	−9.88854	−0.497547
$396$	−0.381966	−0.0191945
$397$	10.6180	0.532904	0.266452	−	0.963848i	$-0.414149\pi$
$397$	10.6180	0.532904	0.266452	+	0.963848i	$0.414149\pi$
$398$	−0.944272	−0.0473321
$399$	9.70820	0.486018
$400$	−3.47214	−0.173607
$401$	−26.6525	−1.33096	−0.665481	−	0.746415i	$-0.731773\pi$
$401$	−26.6525	−1.33096	−0.665481	+	0.746415i	$0.731773\pi$
$402$	1.61803	0.0807002
$403$	2.88854	0.143889
$404$	9.79837	0.487487
$405$	−9.52786	−0.473443
$406$	−29.8885	−1.48334
$407$	1.14590	0.0568001
$408$	1.23607	0.0611945
$409$	−10.9443	−0.541159	−0.270580	−	0.962698i	$-0.587215\pi$
$409$	−10.9443	−0.541159	−0.270580	+	0.962698i	$0.587215\pi$
$410$	−1.34752	−0.0665495
$411$	−22.9443	−1.13176
$412$	14.1803	0.698615
$413$	−4.00000	−0.196827
$414$	−0.763932	−0.0375452
$415$	−4.94427	−0.242705
$416$	−0.854102	−0.0418758
$417$	−7.23607	−0.354352
$418$	1.85410	0.0906871
$419$	11.5279	0.563173	0.281587	−	0.959536i	$-0.409139\pi$
$419$	11.5279	0.563173	0.281587	+	0.959536i	$0.409139\pi$
$420$	6.47214	0.315808
$421$	−7.56231	−0.368564	−0.184282	−	0.982873i	$-0.558996\pi$
$421$	−7.56231	−0.368564	−0.184282	+	0.982873i	$0.558996\pi$
$422$	−2.67376	−0.130157
$423$	−3.34752	−0.162762
$424$	5.23607	0.254286
$425$	−2.65248	−0.128664
$426$	−2.76393	−0.133913
$427$	−34.9443	−1.69107
$428$	19.0902	0.922758
$429$	−1.38197	−0.0667219
$430$	5.88854	0.283971
$431$	−16.2705	−0.783723	−0.391861	−	0.920024i	$-0.628169\pi$
$431$	−16.2705	−0.783723	−0.391861	+	0.920024i	$0.628169\pi$
$432$	−5.47214	−0.263278
$433$	25.5279	1.22679	0.613395	−	0.789776i	$-0.289803\pi$
$433$	25.5279	1.22679	0.613395	+	0.789776i	$0.289803\pi$
$434$	−10.9443	−0.525342
$435$	−18.4721	−0.885671
$436$	−0.909830	−0.0435730
$437$	3.70820	0.177387
$438$	−7.23607	−0.345753
$439$	−5.88854	−0.281045	−0.140522	−	0.990077i	$-0.544878\pi$
$439$	−5.88854	−0.281045	−0.140522	+	0.990077i	$0.544878\pi$
$440$	1.23607	0.0589272
$441$	−1.32624	−0.0631542
$442$	−0.652476	−0.0310351
$443$	−17.0902	−0.811978	−0.405989	−	0.913878i	$-0.633073\pi$
$443$	−17.0902	−0.811978	−0.405989	+	0.913878i	$0.633073\pi$
$444$	1.85410	0.0879918
$445$	−14.0689	−0.666929
$446$	−8.47214	−0.401167
$447$	26.1803	1.23829
$448$	3.23607	0.152890
$449$	24.8541	1.17294	0.586469	−	0.809972i	$-0.300518\pi$
$449$	24.8541	1.17294	0.586469	+	0.809972i	$0.300518\pi$
$450$	1.32624	0.0625195
$451$	−1.09017	−0.0513341
$452$	−11.4164	−0.536983
$453$	13.0902	0.615030
$454$	−17.5066	−0.821624
$455$	−3.41641	−0.160164
$456$	3.00000	0.140488
$457$	31.5967	1.47803	0.739017	−	0.673687i	$-0.235290\pi$
$457$	31.5967	1.47803	0.739017	+	0.673687i	$0.235290\pi$
$458$	−14.9443	−0.698300
$459$	−4.18034	−0.195122
$460$	2.47214	0.115264
$461$	−2.94427	−0.137128	−0.0685642	−	0.997647i	$-0.521842\pi$
$461$	−2.94427	−0.137128	−0.0685642	+	0.997647i	$0.521842\pi$
$462$	5.23607	0.243604
$463$	4.94427	0.229780	0.114890	−	0.993378i	$-0.463348\pi$
$463$	4.94427	0.229780	0.114890	+	0.993378i	$0.463348\pi$
$464$	−9.23607	−0.428774
$465$	−6.76393	−0.313670
$466$	22.2705	1.03166
$467$	32.7639	1.51613	0.758067	−	0.652177i	$-0.226144\pi$
$467$	32.7639	1.51613	0.758067	+	0.652177i	$0.226144\pi$
$468$	0.326238	0.0150804
$469$	3.23607	0.149428
$470$	10.8328	0.499681
$471$	−24.7082	−1.13849
$472$	−1.23607	−0.0568946
$473$	4.76393	0.219046
$474$	−12.9443	−0.594550
$475$	−6.43769	−0.295382
$476$	2.47214	0.113310
$477$	−2.00000	−0.0915737
$478$	−9.70820	−0.444043
$479$	1.88854	0.0862898	0.0431449	−	0.999069i	$-0.486262\pi$
$479$	1.88854	0.0862898	0.0431449	+	0.999069i	$0.486262\pi$
$480$	2.00000	0.0912871
$481$	−0.978714	−0.0446255
$482$	9.52786	0.433982
$483$	10.4721	0.476499
$484$	1.00000	0.0454545
$485$	16.0000	0.726523
$486$	3.94427	0.178916
$487$	20.3262	0.921070	0.460535	−	0.887642i	$-0.347658\pi$
$487$	20.3262	0.921070	0.460535	+	0.887642i	$0.347658\pi$
$488$	−10.7984	−0.488819
$489$	−11.7082	−0.529463
$490$	4.29180	0.193884
$491$	3.79837	0.171418	0.0857091	−	0.996320i	$-0.472684\pi$
$491$	3.79837	0.171418	0.0857091	+	0.996320i	$0.472684\pi$
$492$	−1.76393	−0.0795242
$493$	−7.05573	−0.317774
$494$	−1.58359	−0.0712492
$495$	−0.472136	−0.0212209
$496$	−3.38197	−0.151855
$497$	−5.52786	−0.247959
$498$	−6.47214	−0.290023
$499$	−24.1459	−1.08092	−0.540459	−	0.841370i	$-0.681750\pi$
$499$	−24.1459	−1.08092	−0.540459	+	0.841370i	$0.681750\pi$
$500$	−10.4721	−0.468328
$501$	21.1803	0.946268
$502$	−25.0344	−1.11734
$503$	21.1246	0.941900	0.470950	−	0.882160i	$-0.343911\pi$
$503$	21.1246	0.941900	0.470950	+	0.882160i	$0.343911\pi$
$504$	−1.23607	−0.0550588
$505$	12.1115	0.538953
$506$	2.00000	0.0889108
$507$	−19.8541	−0.881752
$508$	−11.1459	−0.494519
$509$	−1.67376	−0.0741882	−0.0370941	−	0.999312i	$-0.511810\pi$
$509$	−1.67376	−0.0741882	−0.0370941	+	0.999312i	$0.511810\pi$
$510$	1.52786	0.0676550
$511$	−14.4721	−0.640210
$512$	1.00000	0.0441942
$513$	−10.1459	−0.447952
$514$	8.85410	0.390538
$515$	17.5279	0.772370
$516$	7.70820	0.339335
$517$	8.76393	0.385437
$518$	3.70820	0.162929
$519$	12.1803	0.534658
$520$	−1.05573	−0.0462967
$521$	18.9443	0.829964	0.414982	−	0.909830i	$-0.363788\pi$
$521$	18.9443	0.829964	0.414982	+	0.909830i	$0.363788\pi$
$522$	3.52786	0.154410
$523$	20.3820	0.891241	0.445621	−	0.895222i	$-0.352983\pi$
$523$	20.3820	0.891241	0.445621	+	0.895222i	$0.352983\pi$
$524$	5.32624	0.232678
$525$	−18.1803	−0.793455
$526$	−7.14590	−0.311576
$527$	−2.58359	−0.112543
$528$	1.61803	0.0704159
$529$	−19.0000	−0.826087
$530$	6.47214	0.281132
$531$	0.472136	0.0204890
$532$	6.00000	0.260133
$533$	0.931116	0.0403311
$534$	−18.4164	−0.796956
$535$	23.5967	1.02018
$536$	1.00000	0.0431934
$537$	−12.2361	−0.528025
$538$	−7.03444	−0.303276
$539$	3.47214	0.149555
$540$	−6.76393	−0.291073
$541$	−15.1459	−0.651173	−0.325587	−	0.945512i	$-0.605562\pi$
$541$	−15.1459	−0.651173	−0.325587	+	0.945512i	$0.605562\pi$
$542$	−29.4164	−1.26354
$543$	−9.56231	−0.410358
$544$	0.763932	0.0327533
$545$	−1.12461	−0.0481731
$546$	−4.47214	−0.191390
$547$	33.5967	1.43649	0.718247	−	0.695789i	$-0.244945\pi$
$547$	33.5967	1.43649	0.718247	+	0.695789i	$0.244945\pi$
$548$	−14.1803	−0.605754
$549$	4.12461	0.176034
$550$	−3.47214	−0.148052
$551$	−17.1246	−0.729533
$552$	3.23607	0.137736
$553$	−25.8885	−1.10089
$554$	−0.291796	−0.0123972
$555$	2.29180	0.0972813
$556$	−4.47214	−0.189661
$557$	−3.34752	−0.141839	−0.0709196	−	0.997482i	$-0.522593\pi$
$557$	−3.34752	−0.141839	−0.0709196	+	0.997482i	$0.522593\pi$
$558$	1.29180	0.0546861
$559$	−4.06888	−0.172095
$560$	4.00000	0.169031
$561$	1.23607	0.0521868
$562$	0.201626	0.00850508
$563$	−18.6525	−0.786108	−0.393054	−	0.919515i	$-0.628581\pi$
$563$	−18.6525	−0.786108	−0.393054	+	0.919515i	$0.628581\pi$
$564$	14.1803	0.597100
$565$	−14.1115	−0.593673
$566$	14.6738	0.616784
$567$	−24.9443	−1.04756
$568$	−1.70820	−0.0716746
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	3.70820	0.155320
$571$	19.0557	0.797457	0.398729	−	0.917069i	$-0.369452\pi$
$571$	19.0557	0.797457	0.398729	+	0.917069i	$0.369452\pi$
$572$	−0.854102	−0.0357118
$573$	21.4721	0.897011
$574$	−3.52786	−0.147250
$575$	−6.94427	−0.289596
$576$	−0.381966	−0.0159153
$577$	39.7771	1.65594	0.827971	−	0.560771i	$-0.189495\pi$
$577$	39.7771	1.65594	0.827971	+	0.560771i	$0.189495\pi$
$578$	−16.4164	−0.682833
$579$	30.9443	1.28600
$580$	−11.4164	−0.474041
$581$	−12.9443	−0.537019
$582$	20.9443	0.868168
$583$	5.23607	0.216856
$584$	−4.47214	−0.185058
$585$	0.403252	0.0166724
$586$	5.05573	0.208850
$587$	33.7984	1.39501	0.697504	−	0.716581i	$-0.254294\pi$
$587$	33.7984	1.39501	0.697504	+	0.716581i	$0.254294\pi$
$588$	5.61803	0.231684
$589$	−6.27051	−0.258372
$590$	−1.52786	−0.0629012
$591$	13.9443	0.573591
$592$	1.14590	0.0470961
$593$	40.9230	1.68051	0.840253	−	0.542195i	$-0.182407\pi$
$593$	40.9230	1.68051	0.840253	+	0.542195i	$0.182407\pi$
$594$	−5.47214	−0.224524
$595$	3.05573	0.125273
$596$	16.1803	0.662773
$597$	−1.52786	−0.0625313
$598$	−1.70820	−0.0698537
$599$	−41.8541	−1.71011	−0.855056	−	0.518535i	$-0.826477\pi$
$599$	−41.8541	−1.71011	−0.855056	+	0.518535i	$0.826477\pi$
$600$	−5.61803	−0.229355
$601$	15.7082	0.640751	0.320376	−	0.947291i	$-0.396191\pi$
$601$	15.7082	0.640751	0.320376	+	0.947291i	$0.396191\pi$
$602$	15.4164	0.628326
$603$	−0.381966	−0.0155549
$604$	8.09017	0.329184
$605$	1.23607	0.0502533
$606$	15.8541	0.644029
$607$	1.74265	0.0707318	0.0353659	−	0.999374i	$-0.488740\pi$
$607$	1.74265	0.0707318	0.0353659	+	0.999374i	$0.488740\pi$
$608$	1.85410	0.0751938
$609$	−48.3607	−1.95967
$610$	−13.3475	−0.540425
$611$	−7.48529	−0.302822
$612$	−0.291796	−0.0117952
$613$	4.58359	0.185130	0.0925648	−	0.995707i	$-0.470493\pi$
$613$	4.58359	0.185130	0.0925648	+	0.995707i	$0.470493\pi$
$614$	0	0
$615$	−2.18034	−0.0879198
$616$	3.23607	0.130385
$617$	31.1459	1.25389	0.626943	−	0.779065i	$-0.284306\pi$
$617$	31.1459	1.25389	0.626943	+	0.779065i	$0.284306\pi$
$618$	22.9443	0.922954
$619$	−1.88854	−0.0759070	−0.0379535	−	0.999280i	$-0.512084\pi$
$619$	−1.88854	−0.0759070	−0.0379535	+	0.999280i	$0.512084\pi$
$620$	−4.18034	−0.167886
$621$	−10.9443	−0.439179
$622$	14.0902	0.564964
$623$	−36.8328	−1.47568
$624$	−1.38197	−0.0553229
$625$	4.41641	0.176656
$626$	−23.7082	−0.947570
$627$	3.00000	0.119808
$628$	−15.2705	−0.609360
$629$	0.875388	0.0349040
$630$	−1.52786	−0.0608716
$631$	−38.0902	−1.51635	−0.758173	−	0.652054i	$-0.773908\pi$
$631$	−38.0902	−1.51635	−0.758173	+	0.652054i	$0.773908\pi$
$632$	−8.00000	−0.318223
$633$	−4.32624	−0.171953
$634$	3.20163	0.127153
$635$	−13.7771	−0.546727
$636$	8.47214	0.335942
$637$	−2.96556	−0.117500
$638$	−9.23607	−0.365659
$639$	0.652476	0.0258115
$640$	1.23607	0.0488599
$641$	42.5410	1.68027	0.840135	−	0.542378i	$-0.182476\pi$
$641$	42.5410	1.68027	0.840135	+	0.542378i	$0.182476\pi$
$642$	30.8885	1.21907
$643$	−13.0557	−0.514868	−0.257434	−	0.966296i	$-0.582877\pi$
$643$	−13.0557	−0.514868	−0.257434	+	0.966296i	$0.582877\pi$
$644$	6.47214	0.255038
$645$	9.52786	0.375159
$646$	1.41641	0.0557278
$647$	12.9443	0.508892	0.254446	−	0.967087i	$-0.418107\pi$
$647$	12.9443	0.508892	0.254446	+	0.967087i	$0.418107\pi$
$648$	−7.70820	−0.302807
$649$	−1.23607	−0.0485199
$650$	2.96556	0.116319
$651$	−17.7082	−0.694039
$652$	−7.23607	−0.283386
$653$	14.1803	0.554920	0.277460	−	0.960737i	$-0.410507\pi$
$653$	14.1803	0.554920	0.277460	+	0.960737i	$0.410507\pi$
$654$	−1.47214	−0.0575651
$655$	6.58359	0.257242
$656$	−1.09017	−0.0425640
$657$	1.70820	0.0666434
$658$	28.3607	1.10561
$659$	37.6312	1.46590	0.732952	−	0.680281i	$-0.238142\pi$
$659$	37.6312	1.46590	0.732952	+	0.680281i	$0.238142\pi$
$660$	2.00000	0.0778499
$661$	16.2918	0.633677	0.316839	−	0.948479i	$-0.397379\pi$
$661$	16.2918	0.633677	0.316839	+	0.948479i	$0.397379\pi$
$662$	22.7426	0.883918
$663$	−1.05573	−0.0410011
$664$	−4.00000	−0.155230
$665$	7.41641	0.287596
$666$	−0.437694	−0.0169603
$667$	−18.4721	−0.715244
$668$	13.0902	0.506474
$669$	−13.7082	−0.529990
$670$	1.23607	0.0477535
$671$	−10.7984	−0.416867
$672$	5.23607	0.201986
$673$	22.2705	0.858465	0.429233	−	0.903194i	$-0.358784\pi$
$673$	22.2705	0.858465	0.429233	+	0.903194i	$0.358784\pi$
$674$	−11.2705	−0.434124
$675$	19.0000	0.731310
$676$	−12.2705	−0.471943
$677$	0.978714	0.0376150	0.0188075	−	0.999823i	$-0.494013\pi$
$677$	0.978714	0.0376150	0.0188075	+	0.999823i	$0.494013\pi$
$678$	−18.4721	−0.709418
$679$	41.8885	1.60753
$680$	0.944272	0.0362112
$681$	−28.3262	−1.08546
$682$	−3.38197	−0.129502
$683$	−6.61803	−0.253232	−0.126616	−	0.991952i	$-0.540412\pi$
$683$	−6.61803	−0.253232	−0.126616	+	0.991952i	$0.540412\pi$
$684$	−0.708204	−0.0270789
$685$	−17.5279	−0.669705
$686$	−11.4164	−0.435880
$687$	−24.1803	−0.922538
$688$	4.76393	0.181623
$689$	−4.47214	−0.170375
$690$	4.00000	0.152277
$691$	−39.8885	−1.51743	−0.758716	−	0.651422i	$-0.774173\pi$
$691$	−39.8885	−1.51743	−0.758716	+	0.651422i	$0.774173\pi$
$692$	7.52786	0.286166
$693$	−1.23607	−0.0469543
$694$	28.6525	1.08763
$695$	−5.52786	−0.209684
$696$	−14.9443	−0.566461
$697$	−0.832816	−0.0315451
$698$	15.2361	0.576694
$699$	36.0344	1.36295
$700$	−11.2361	−0.424683
$701$	36.3262	1.37202	0.686012	−	0.727591i	$-0.259360\pi$
$701$	36.3262	1.37202	0.686012	+	0.727591i	$0.259360\pi$
$702$	4.67376	0.176400
$703$	2.12461	0.0801313
$704$	1.00000	0.0376889
$705$	17.5279	0.660138
$706$	8.58359	0.323048
$707$	31.7082	1.19251
$708$	−2.00000	−0.0751646
$709$	−1.14590	−0.0430351	−0.0215176	−	0.999768i	$-0.506850\pi$
$709$	−1.14590	−0.0430351	−0.0215176	+	0.999768i	$0.506850\pi$
$710$	−2.11146	−0.0792415
$711$	3.05573	0.114599
$712$	−11.3820	−0.426557
$713$	−6.76393	−0.253311
$714$	4.00000	0.149696
$715$	−1.05573	−0.0394820
$716$	−7.56231	−0.282617
$717$	−15.7082	−0.586634
$718$	−7.20163	−0.268762
$719$	24.8328	0.926108	0.463054	−	0.886330i	$-0.346754\pi$
$719$	24.8328	0.926108	0.463054	+	0.886330i	$0.346754\pi$
$720$	−0.472136	−0.0175955
$721$	45.8885	1.70898
$722$	−15.5623	−0.579169
$723$	15.4164	0.573342
$724$	−5.90983	−0.219637
$725$	32.0689	1.19101
$726$	1.61803	0.0600509
$727$	35.2148	1.30604	0.653022	−	0.757339i	$-0.273501\pi$
$727$	35.2148	1.30604	0.653022	+	0.757339i	$0.273501\pi$
$728$	−2.76393	−0.102438
$729$	29.5066	1.09284
$730$	−5.52786	−0.204595
$731$	3.63932	0.134605
$732$	−17.4721	−0.645789
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	−3.05573	−0.112789
$735$	6.94427	0.256143
$736$	2.00000	0.0737210
$737$	1.00000	0.0368355
$738$	0.416408	0.0153282
$739$	−1.41641	−0.0521034	−0.0260517	−	0.999661i	$-0.508293\pi$
$739$	−1.41641	−0.0521034	−0.0260517	+	0.999661i	$0.508293\pi$
$740$	1.41641	0.0520682
$741$	−2.56231	−0.0941287
$742$	16.9443	0.622044
$743$	−31.3262	−1.14925	−0.574624	−	0.818417i	$-0.694852\pi$
$743$	−31.3262	−1.14925	−0.574624	+	0.818417i	$0.694852\pi$
$744$	−5.47214	−0.200618
$745$	20.0000	0.732743
$746$	27.8885	1.02107
$747$	1.52786	0.0559016
$748$	0.763932	0.0279321
$749$	61.7771	2.25729
$750$	−16.9443	−0.618717
$751$	−22.7639	−0.830668	−0.415334	−	0.909669i	$-0.636335\pi$
$751$	−22.7639	−0.830668	−0.415334	+	0.909669i	$0.636335\pi$
$752$	8.76393	0.319588
$753$	−40.5066	−1.47614
$754$	7.88854	0.287284
$755$	10.0000	0.363937
$756$	−17.7082	−0.644041
$757$	−13.1246	−0.477022	−0.238511	−	0.971140i	$-0.576659\pi$
$757$	−13.1246	−0.477022	−0.238511	+	0.971140i	$0.576659\pi$
$758$	−18.3820	−0.667663
$759$	3.23607	0.117462
$760$	2.29180	0.0831322
$761$	−13.8885	−0.503459	−0.251730	−	0.967798i	$-0.580999\pi$
$761$	−13.8885	−0.503459	−0.251730	+	0.967798i	$0.580999\pi$
$762$	−18.0344	−0.653319
$763$	−2.94427	−0.106590
$764$	13.2705	0.480110
$765$	−0.360680	−0.0130404
$766$	−20.6180	−0.744960
$767$	1.05573	0.0381201
$768$	1.61803	0.0583858
$769$	−24.3820	−0.879236	−0.439618	−	0.898185i	$-0.644886\pi$
$769$	−24.3820	−0.879236	−0.439618	+	0.898185i	$0.644886\pi$
$770$	4.00000	0.144150
$771$	14.3262	0.515947
$772$	19.1246	0.688310
$773$	−12.1115	−0.435619	−0.217809	−	0.975991i	$-0.569891\pi$
$773$	−12.1115	−0.435619	−0.217809	+	0.975991i	$0.569891\pi$
$774$	−1.81966	−0.0654063
$775$	11.7426	0.421808
$776$	12.9443	0.464672
$777$	6.00000	0.215249
$778$	−23.7984	−0.853213
$779$	−2.02129	−0.0724201
$780$	−1.70820	−0.0611635
$781$	−1.70820	−0.0611243
$782$	1.52786	0.0546363
$783$	50.5410	1.80619
$784$	3.47214	0.124005
$785$	−18.8754	−0.673691
$786$	8.61803	0.307395
$787$	−8.06888	−0.287625	−0.143812	−	0.989605i	$-0.545936\pi$
$787$	−8.06888	−0.287625	−0.143812	+	0.989605i	$0.545936\pi$
$788$	8.61803	0.307005
$789$	−11.5623	−0.411629
$790$	−9.88854	−0.351819
$791$	−36.9443	−1.31359
$792$	−0.381966	−0.0135726
$793$	9.22291	0.327515
$794$	10.6180	0.376820
$795$	10.4721	0.371408
$796$	−0.944272	−0.0334688
$797$	43.6312	1.54550	0.772748	−	0.634713i	$-0.218882\pi$
$797$	43.6312	1.54550	0.772748	+	0.634713i	$0.218882\pi$
$798$	9.70820	0.343667
$799$	6.69505	0.236854
$800$	−3.47214	−0.122759
$801$	4.34752	0.153612
$802$	−26.6525	−0.941132
$803$	−4.47214	−0.157818
$804$	1.61803	0.0570637
$805$	8.00000	0.281963
$806$	2.88854	0.101745
$807$	−11.3820	−0.400664
$808$	9.79837	0.344706
$809$	20.3820	0.716592	0.358296	−	0.933608i	$-0.383358\pi$
$809$	20.3820	0.716592	0.358296	+	0.933608i	$0.383358\pi$
$810$	−9.52786	−0.334775
$811$	15.2361	0.535011	0.267505	−	0.963556i	$-0.413801\pi$
$811$	15.2361	0.535011	0.267505	+	0.963556i	$0.413801\pi$
$812$	−29.8885	−1.04888
$813$	−47.5967	−1.66929
$814$	1.14590	0.0401637
$815$	−8.94427	−0.313304
$816$	1.23607	0.0432710
$817$	8.83282	0.309021
$818$	−10.9443	−0.382657
$819$	1.05573	0.0368901
$820$	−1.34752	−0.0470576
$821$	25.2361	0.880745	0.440372	−	0.897815i	$-0.354846\pi$
$821$	25.2361	0.880745	0.440372	+	0.897815i	$0.354846\pi$
$822$	−22.9443	−0.800273
$823$	−43.9574	−1.53226	−0.766130	−	0.642686i	$-0.777820\pi$
$823$	−43.9574	−1.53226	−0.766130	+	0.642686i	$0.777820\pi$
$824$	14.1803	0.493996
$825$	−5.61803	−0.195595
$826$	−4.00000	−0.139178
$827$	−19.2148	−0.668163	−0.334082	−	0.942544i	$-0.608426\pi$
$827$	−19.2148	−0.668163	−0.334082	+	0.942544i	$0.608426\pi$
$828$	−0.763932	−0.0265485
$829$	−22.3262	−0.775422	−0.387711	−	0.921781i	$-0.626734\pi$
$829$	−22.3262	−0.775422	−0.387711	+	0.921781i	$0.626734\pi$
$830$	−4.94427	−0.171618
$831$	−0.472136	−0.0163782
$832$	−0.854102	−0.0296107
$833$	2.65248	0.0919028
$834$	−7.23607	−0.250565
$835$	16.1803	0.559944
$836$	1.85410	0.0641255
$837$	18.5066	0.639681
$838$	11.5279	0.398223
$839$	27.1246	0.936446	0.468223	−	0.883610i	$-0.344894\pi$
$839$	27.1246	0.936446	0.468223	+	0.883610i	$0.344894\pi$
$840$	6.47214	0.223310
$841$	56.3050	1.94155
$842$	−7.56231	−0.260614
$843$	0.326238	0.0112362
$844$	−2.67376	−0.0920347
$845$	−15.1672	−0.521767
$846$	−3.34752	−0.115090
$847$	3.23607	0.111193
$848$	5.23607	0.179807
$849$	23.7426	0.814845
$850$	−2.65248	−0.0909792
$851$	2.29180	0.0785618
$852$	−2.76393	−0.0946908
$853$	−47.3050	−1.61969	−0.809845	−	0.586643i	$-0.800449\pi$
$853$	−47.3050	−1.61969	−0.809845	+	0.586643i	$0.800449\pi$
$854$	−34.9443	−1.19577
$855$	−0.875388	−0.0299376
$856$	19.0902	0.652489
$857$	55.2148	1.88610	0.943051	−	0.332650i	$-0.107943\pi$
$857$	55.2148	1.88610	0.943051	+	0.332650i	$0.107943\pi$
$858$	−1.38197	−0.0471795
$859$	22.1803	0.756783	0.378392	−	0.925646i	$-0.376477\pi$
$859$	22.1803	0.756783	0.378392	+	0.925646i	$0.376477\pi$
$860$	5.88854	0.200798
$861$	−5.70820	−0.194535
$862$	−16.2705	−0.554176
$863$	35.0132	1.19186	0.595931	−	0.803036i	$-0.296783\pi$
$863$	35.0132	1.19186	0.595931	+	0.803036i	$0.296783\pi$
$864$	−5.47214	−0.186166
$865$	9.30495	0.316378
$866$	25.5279	0.867472
$867$	−26.5623	−0.902103
$868$	−10.9443	−0.371473
$869$	−8.00000	−0.271381
$870$	−18.4721	−0.626264
$871$	−0.854102	−0.0289401
$872$	−0.909830	−0.0308107
$873$	−4.94427	−0.167338
$874$	3.70820	0.125432
$875$	−33.8885	−1.14564
$876$	−7.23607	−0.244484
$877$	15.2361	0.514485	0.257243	−	0.966347i	$-0.417186\pi$
$877$	15.2361	0.514485	0.257243	+	0.966347i	$0.417186\pi$
$878$	−5.88854	−0.198729
$879$	8.18034	0.275916
$880$	1.23607	0.0416678
$881$	−13.4164	−0.452010	−0.226005	−	0.974126i	$-0.572567\pi$
$881$	−13.4164	−0.452010	−0.226005	+	0.974126i	$0.572567\pi$
$882$	−1.32624	−0.0446568
$883$	−28.4377	−0.957005	−0.478502	−	0.878086i	$-0.658820\pi$
$883$	−28.4377	−0.957005	−0.478502	+	0.878086i	$0.658820\pi$
$884$	−0.652476	−0.0219451
$885$	−2.47214	−0.0830999
$886$	−17.0902	−0.574155
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	1.85410	0.0622196
$889$	−36.0689	−1.20971
$890$	−14.0689	−0.471590
$891$	−7.70820	−0.258235
$892$	−8.47214	−0.283668
$893$	16.2492	0.543760
$894$	26.1803	0.875602
$895$	−9.34752	−0.312453
$896$	3.23607	0.108109
$897$	−2.76393	−0.0922850
$898$	24.8541	0.829392
$899$	31.2361	1.04178
$900$	1.32624	0.0442079
$901$	4.00000	0.133259
$902$	−1.09017	−0.0362987
$903$	24.9443	0.830093
$904$	−11.4164	−0.379704
$905$	−7.30495	−0.242825
$906$	13.0902	0.434892
$907$	−4.65248	−0.154483	−0.0772415	−	0.997012i	$-0.524611\pi$
$907$	−4.65248	−0.154483	−0.0772415	+	0.997012i	$0.524611\pi$
$908$	−17.5066	−0.580976
$909$	−3.74265	−0.124136
$910$	−3.41641	−0.113253
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	3.00000	0.0993399
$913$	−4.00000	−0.132381
$914$	31.5967	1.04513
$915$	−21.5967	−0.713966
$916$	−14.9443	−0.493773
$917$	17.2361	0.569185
$918$	−4.18034	−0.137972
$919$	17.3050	0.570838	0.285419	−	0.958403i	$-0.407867\pi$
$919$	17.3050	0.570838	0.285419	+	0.958403i	$0.407867\pi$
$920$	2.47214	0.0815039
$921$	0	0
$922$	−2.94427	−0.0969644
$923$	1.45898	0.0480229
$924$	5.23607	0.172254
$925$	−3.97871	−0.130819
$926$	4.94427	0.162479
$927$	−5.41641	−0.177898
$928$	−9.23607	−0.303189
$929$	32.7639	1.07495	0.537475	−	0.843280i	$-0.319378\pi$
$929$	32.7639	1.07495	0.537475	+	0.843280i	$0.319378\pi$
$930$	−6.76393	−0.221798
$931$	6.43769	0.210987
$932$	22.2705	0.729495
$933$	22.7984	0.746385
$934$	32.7639	1.07207
$935$	0.944272	0.0308810
$936$	0.326238	0.0106634
$937$	−27.2705	−0.890889	−0.445444	−	0.895310i	$-0.646954\pi$
$937$	−27.2705	−0.890889	−0.445444	+	0.895310i	$0.646954\pi$
$938$	3.23607	0.105661
$939$	−38.3607	−1.25185
$940$	10.8328	0.353327
$941$	17.4377	0.568453	0.284226	−	0.958757i	$-0.408263\pi$
$941$	17.4377	0.568453	0.284226	+	0.958757i	$0.408263\pi$
$942$	−24.7082	−0.805037
$943$	−2.18034	−0.0710016
$944$	−1.23607	−0.0402306
$945$	−21.8885	−0.712034
$946$	4.76393	0.154889
$947$	9.70820	0.315474	0.157737	−	0.987481i	$-0.449580\pi$
$947$	9.70820	0.315474	0.157737	+	0.987481i	$0.449580\pi$
$948$	−12.9443	−0.420410
$949$	3.81966	0.123991
$950$	−6.43769	−0.208866
$951$	5.18034	0.167984
$952$	2.47214	0.0801224
$953$	46.5410	1.50761	0.753806	−	0.657097i	$-0.228216\pi$
$953$	46.5410	1.50761	0.753806	+	0.657097i	$0.228216\pi$
$954$	−2.00000	−0.0647524
$955$	16.4033	0.530797
$956$	−9.70820	−0.313986
$957$	−14.9443	−0.483080
$958$	1.88854	0.0610161
$959$	−45.8885	−1.48182
$960$	2.00000	0.0645497
$961$	−19.5623	−0.631042
$962$	−0.978714	−0.0315550
$963$	−7.29180	−0.234975
$964$	9.52786	0.306872
$965$	23.6393	0.760977
$966$	10.4721	0.336935
$967$	−15.4164	−0.495758	−0.247879	−	0.968791i	$-0.579734\pi$
$967$	−15.4164	−0.495758	−0.247879	+	0.968791i	$0.579734\pi$
$968$	1.00000	0.0321412
$969$	2.29180	0.0736231
$970$	16.0000	0.513729
$971$	17.5967	0.564707	0.282353	−	0.959311i	$-0.408885\pi$
$971$	17.5967	0.564707	0.282353	+	0.959311i	$0.408885\pi$
$972$	3.94427	0.126513
$973$	−14.4721	−0.463955
$974$	20.3262	0.651295
$975$	4.79837	0.153671
$976$	−10.7984	−0.345648
$977$	41.3951	1.32435	0.662174	−	0.749350i	$-0.269634\pi$
$977$	41.3951	1.32435	0.662174	+	0.749350i	$0.269634\pi$
$978$	−11.7082	−0.374387
$979$	−11.3820	−0.363769
$980$	4.29180	0.137096
$981$	0.347524	0.0110956
$982$	3.79837	0.121211
$983$	−4.74265	−0.151267	−0.0756335	−	0.997136i	$-0.524098\pi$
$983$	−4.74265	−0.151267	−0.0756335	+	0.997136i	$0.524098\pi$
$984$	−1.76393	−0.0562321
$985$	10.6525	0.339416
$986$	−7.05573	−0.224700
$987$	45.8885	1.46065
$988$	−1.58359	−0.0503808
$989$	9.52786	0.302968
$990$	−0.472136	−0.0150055
$991$	25.6869	0.815972	0.407986	−	0.912988i	$-0.366231\pi$
$991$	25.6869	0.815972	0.407986	+	0.912988i	$0.366231\pi$
$992$	−3.38197	−0.107378
$993$	36.7984	1.16776
$994$	−5.52786	−0.175333
$995$	−1.16718	−0.0370022
$996$	−6.47214	−0.205077
$997$	−18.0689	−0.572247	−0.286124	−	0.958193i	$-0.592367\pi$
$997$	−18.0689	−0.572247	−0.286124	+	0.958193i	$0.592367\pi$
$998$	−24.1459	−0.764325
$999$	−6.27051	−0.198390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1474.2.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1474.2.a.b.1.2	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1474 = 2 \cdot 11 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1474.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.23607 q^{5} +1.61803 q^{6} +3.23607 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.23607 q^{5} +1.61803 q^{6} +3.23607 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.23607 q^{10} +1.00000 q^{11} +1.61803 q^{12} -0.854102 q^{13} +3.23607 q^{14} +2.00000 q^{15} +1.00000 q^{16} +0.763932 q^{17} -0.381966 q^{18} +1.85410 q^{19} +1.23607 q^{20} +5.23607 q^{21} +1.00000 q^{22} +2.00000 q^{23} +1.61803 q^{24} -3.47214 q^{25} -0.854102 q^{26} -5.47214 q^{27} +3.23607 q^{28} -9.23607 q^{29} +2.00000 q^{30} -3.38197 q^{31} +1.00000 q^{32} +1.61803 q^{33} +0.763932 q^{34} +4.00000 q^{35} -0.381966 q^{36} +1.14590 q^{37} +1.85410 q^{38} -1.38197 q^{39} +1.23607 q^{40} -1.09017 q^{41} +5.23607 q^{42} +4.76393 q^{43} +1.00000 q^{44} -0.472136 q^{45} +2.00000 q^{46} +8.76393 q^{47} +1.61803 q^{48} +3.47214 q^{49} -3.47214 q^{50} +1.23607 q^{51} -0.854102 q^{52} +5.23607 q^{53} -5.47214 q^{54} +1.23607 q^{55} +3.23607 q^{56} +3.00000 q^{57} -9.23607 q^{58} -1.23607 q^{59} +2.00000 q^{60} -10.7984 q^{61} -3.38197 q^{62} -1.23607 q^{63} +1.00000 q^{64} -1.05573 q^{65} +1.61803 q^{66} +1.00000 q^{67} +0.763932 q^{68} +3.23607 q^{69} +4.00000 q^{70} -1.70820 q^{71} -0.381966 q^{72} -4.47214 q^{73} +1.14590 q^{74} -5.61803 q^{75} +1.85410 q^{76} +3.23607 q^{77} -1.38197 q^{78} -8.00000 q^{79} +1.23607 q^{80} -7.70820 q^{81} -1.09017 q^{82} -4.00000 q^{83} +5.23607 q^{84} +0.944272 q^{85} +4.76393 q^{86} -14.9443 q^{87} +1.00000 q^{88} -11.3820 q^{89} -0.472136 q^{90} -2.76393 q^{91} +2.00000 q^{92} -5.47214 q^{93} +8.76393 q^{94} +2.29180 q^{95} +1.61803 q^{96} +12.9443 q^{97} +3.47214 q^{98} -0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} + 2 q^{11} + q^{12} + 5 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 6 q^{17} - 3 q^{18} - 3 q^{19} - 2 q^{20} + 6 q^{21} + 2 q^{22} + 4 q^{23} + q^{24} + 2 q^{25} + 5 q^{26} - 2 q^{27} + 2 q^{28} - 14 q^{29} + 4 q^{30} - 9 q^{31} + 2 q^{32} + q^{33} + 6 q^{34} + 8 q^{35} - 3 q^{36} + 9 q^{37} - 3 q^{38} - 5 q^{39} - 2 q^{40} + 9 q^{41} + 6 q^{42} + 14 q^{43} + 2 q^{44} + 8 q^{45} + 4 q^{46} + 22 q^{47} + q^{48} - 2 q^{49} + 2 q^{50} - 2 q^{51} + 5 q^{52} + 6 q^{53} - 2 q^{54} - 2 q^{55} + 2 q^{56} + 6 q^{57} - 14 q^{58} + 2 q^{59} + 4 q^{60} + 3 q^{61} - 9 q^{62} + 2 q^{63} + 2 q^{64} - 20 q^{65} + q^{66} + 2 q^{67} + 6 q^{68} + 2 q^{69} + 8 q^{70} + 10 q^{71} - 3 q^{72} + 9 q^{74} - 9 q^{75} - 3 q^{76} + 2 q^{77} - 5 q^{78} - 16 q^{79} - 2 q^{80} - 2 q^{81} + 9 q^{82} - 8 q^{83} + 6 q^{84} - 16 q^{85} + 14 q^{86} - 12 q^{87} + 2 q^{88} - 25 q^{89} + 8 q^{90} - 10 q^{91} + 4 q^{92} - 2 q^{93} + 22 q^{94} + 18 q^{95} + q^{96} + 8 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 + 2 * q^11 + q^12 + 5 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 6 * q^17 - 3 * q^18 - 3 * q^19 - 2 * q^20 + 6 * q^21 + 2 * q^22 + 4 * q^23 + q^24 + 2 * q^25 + 5 * q^26 - 2 * q^27 + 2 * q^28 - 14 * q^29 + 4 * q^30 - 9 * q^31 + 2 * q^32 + q^33 + 6 * q^34 + 8 * q^35 - 3 * q^36 + 9 * q^37 - 3 * q^38 - 5 * q^39 - 2 * q^40 + 9 * q^41 + 6 * q^42 + 14 * q^43 + 2 * q^44 + 8 * q^45 + 4 * q^46 + 22 * q^47 + q^48 - 2 * q^49 + 2 * q^50 - 2 * q^51 + 5 * q^52 + 6 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 + 6 * q^57 - 14 * q^58 + 2 * q^59 + 4 * q^60 + 3 * q^61 - 9 * q^62 + 2 * q^63 + 2 * q^64 - 20 * q^65 + q^66 + 2 * q^67 + 6 * q^68 + 2 * q^69 + 8 * q^70 + 10 * q^71 - 3 * q^72 + 9 * q^74 - 9 * q^75 - 3 * q^76 + 2 * q^77 - 5 * q^78 - 16 * q^79 - 2 * q^80 - 2 * q^81 + 9 * q^82 - 8 * q^83 + 6 * q^84 - 16 * q^85 + 14 * q^86 - 12 * q^87 + 2 * q^88 - 25 * q^89 + 8 * q^90 - 10 * q^91 + 4 * q^92 - 2 * q^93 + 22 * q^94 + 18 * q^95 + q^96 + 8 * q^97 - 2 * q^98 - 3 * q^99

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