LMFDB - Embedded newform 177.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,2,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	177.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:	$1.41335211578$
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			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.00000 q^{5} -2.61803 q^{6} -2.38197 q^{7} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.00000 q^{5} -2.61803 q^{6} -2.38197 q^{7} -7.47214 q^{8} +1.00000 q^{9} +7.85410 q^{10} +3.47214 q^{11} +4.85410 q^{12} -6.70820 q^{13} +6.23607 q^{14} -3.00000 q^{15} +9.85410 q^{16} -2.61803 q^{17} -2.61803 q^{18} -5.85410 q^{19} -14.5623 q^{20} -2.38197 q^{21} -9.09017 q^{22} -1.38197 q^{23} -7.47214 q^{24} +4.00000 q^{25} +17.5623 q^{26} +1.00000 q^{27} -11.5623 q^{28} -4.38197 q^{29} +7.85410 q^{30} -2.38197 q^{31} -10.8541 q^{32} +3.47214 q^{33} +6.85410 q^{34} +7.14590 q^{35} +4.85410 q^{36} +5.09017 q^{37} +15.3262 q^{38} -6.70820 q^{39} +22.4164 q^{40} -6.09017 q^{41} +6.23607 q^{42} +12.7082 q^{43} +16.8541 q^{44} -3.00000 q^{45} +3.61803 q^{46} -4.85410 q^{47} +9.85410 q^{48} -1.32624 q^{49} -10.4721 q^{50} -2.61803 q^{51} -32.5623 q^{52} +5.47214 q^{53} -2.61803 q^{54} -10.4164 q^{55} +17.7984 q^{56} -5.85410 q^{57} +11.4721 q^{58} +1.00000 q^{59} -14.5623 q^{60} +12.0902 q^{61} +6.23607 q^{62} -2.38197 q^{63} +8.70820 q^{64} +20.1246 q^{65} -9.09017 q^{66} -4.23607 q^{67} -12.7082 q^{68} -1.38197 q^{69} -18.7082 q^{70} +4.23607 q^{71} -7.47214 q^{72} +8.09017 q^{73} -13.3262 q^{74} +4.00000 q^{75} -28.4164 q^{76} -8.27051 q^{77} +17.5623 q^{78} -3.00000 q^{79} -29.5623 q^{80} +1.00000 q^{81} +15.9443 q^{82} -1.14590 q^{83} -11.5623 q^{84} +7.85410 q^{85} -33.2705 q^{86} -4.38197 q^{87} -25.9443 q^{88} +6.09017 q^{89} +7.85410 q^{90} +15.9787 q^{91} -6.70820 q^{92} -2.38197 q^{93} +12.7082 q^{94} +17.5623 q^{95} -10.8541 q^{96} -9.47214 q^{97} +3.47214 q^{98} +3.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 6 * q^5 - 3 * q^6 - 7 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 6 q^{8} + 2 q^{9} + 9 q^{10} - 2 q^{11} + 3 q^{12} + 8 q^{14} - 6 q^{15} + 13 q^{16} - 3 q^{17} - 3 q^{18} - 5 q^{19} - 9 q^{20} - 7 q^{21} - 7 q^{22} - 5 q^{23} - 6 q^{24} + 8 q^{25} + 15 q^{26} + 2 q^{27} - 3 q^{28} - 11 q^{29} + 9 q^{30} - 7 q^{31} - 15 q^{32} - 2 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - q^{37} + 15 q^{38} + 18 q^{40} - q^{41} + 8 q^{42} + 12 q^{43} + 27 q^{44} - 6 q^{45} + 5 q^{46} - 3 q^{47} + 13 q^{48} + 13 q^{49} - 12 q^{50} - 3 q^{51} - 45 q^{52} + 2 q^{53} - 3 q^{54} + 6 q^{55} + 11 q^{56} - 5 q^{57} + 14 q^{58} + 2 q^{59} - 9 q^{60} + 13 q^{61} + 8 q^{62} - 7 q^{63} + 4 q^{64} - 7 q^{66} - 4 q^{67} - 12 q^{68} - 5 q^{69} - 24 q^{70} + 4 q^{71} - 6 q^{72} + 5 q^{73} - 11 q^{74} + 8 q^{75} - 30 q^{76} + 17 q^{77} + 15 q^{78} - 6 q^{79} - 39 q^{80} + 2 q^{81} + 14 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} - 33 q^{86} - 11 q^{87} - 34 q^{88} + q^{89} + 9 q^{90} - 15 q^{91} - 7 q^{93} + 12 q^{94} + 15 q^{95} - 15 q^{96} - 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 6 * q^5 - 3 * q^6 - 7 * q^7 - 6 * q^8 + 2 * q^9 + 9 * q^10 - 2 * q^11 + 3 * q^12 + 8 * q^14 - 6 * q^15 + 13 * q^16 - 3 * q^17 - 3 * q^18 - 5 * q^19 - 9 * q^20 - 7 * q^21 - 7 * q^22 - 5 * q^23 - 6 * q^24 + 8 * q^25 + 15 * q^26 + 2 * q^27 - 3 * q^28 - 11 * q^29 + 9 * q^30 - 7 * q^31 - 15 * q^32 - 2 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - q^37 + 15 * q^38 + 18 * q^40 - q^41 + 8 * q^42 + 12 * q^43 + 27 * q^44 - 6 * q^45 + 5 * q^46 - 3 * q^47 + 13 * q^48 + 13 * q^49 - 12 * q^50 - 3 * q^51 - 45 * q^52 + 2 * q^53 - 3 * q^54 + 6 * q^55 + 11 * q^56 - 5 * q^57 + 14 * q^58 + 2 * q^59 - 9 * q^60 + 13 * q^61 + 8 * q^62 - 7 * q^63 + 4 * q^64 - 7 * q^66 - 4 * q^67 - 12 * q^68 - 5 * q^69 - 24 * q^70 + 4 * q^71 - 6 * q^72 + 5 * q^73 - 11 * q^74 + 8 * q^75 - 30 * q^76 + 17 * q^77 + 15 * q^78 - 6 * q^79 - 39 * q^80 + 2 * q^81 + 14 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 - 33 * q^86 - 11 * q^87 - 34 * q^88 + q^89 + 9 * q^90 - 15 * q^91 - 7 * q^93 + 12 * q^94 + 15 * q^95 - 15 * q^96 - 10 * q^97 - 2 * q^98 - 2 * 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 $

$2$	−2.61803	−1.85123	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803	−1.85123	−0.925615	+	0.378467i	$0.876451\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.85410	2.42705
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−2.61803	−1.06881
$7$	−2.38197	−0.900299	−0.450149	−	0.892953i	$-0.648629\pi$
$7$	−2.38197	−0.900299	−0.450149	+	0.892953i	$0.648629\pi$
$8$	−7.47214	−2.64180
$9$	1.00000	0.333333
$10$	7.85410	2.48369
$11$	3.47214	1.04689	0.523444	−	0.852060i	$-0.324647\pi$
$11$	3.47214	1.04689	0.523444	+	0.852060i	$0.324647\pi$
$12$	4.85410	1.40126
$13$	−6.70820	−1.86052	−0.930261	−	0.366900i	$-0.880419\pi$
$13$	−6.70820	−1.86052	−0.930261	+	0.366900i	$0.880419\pi$
$14$	6.23607	1.66666
$15$	−3.00000	−0.774597
$16$	9.85410	2.46353
$17$	−2.61803	−0.634967	−0.317483	−	0.948264i	$-0.602838\pi$
$17$	−2.61803	−0.634967	−0.317483	+	0.948264i	$0.602838\pi$
$18$	−2.61803	−0.617077
$19$	−5.85410	−1.34302	−0.671512	−	0.740994i	$-0.734355\pi$
$19$	−5.85410	−1.34302	−0.671512	+	0.740994i	$0.734355\pi$
$20$	−14.5623	−3.25623
$21$	−2.38197	−0.519788
$22$	−9.09017	−1.93803
$23$	−1.38197	−0.288160	−0.144080	−	0.989566i	$-0.546022\pi$
$23$	−1.38197	−0.288160	−0.144080	+	0.989566i	$0.546022\pi$
$24$	−7.47214	−1.52524
$25$	4.00000	0.800000
$26$	17.5623	3.44425
$27$	1.00000	0.192450
$28$	−11.5623	−2.18507
$29$	−4.38197	−0.813711	−0.406855	−	0.913493i	$-0.633375\pi$
$29$	−4.38197	−0.813711	−0.406855	+	0.913493i	$0.633375\pi$
$30$	7.85410	1.43396
$31$	−2.38197	−0.427814	−0.213907	−	0.976854i	$-0.568619\pi$
$31$	−2.38197	−0.427814	−0.213907	+	0.976854i	$0.568619\pi$
$32$	−10.8541	−1.91875
$33$	3.47214	0.604421
$34$	6.85410	1.17547
$35$	7.14590	1.20788
$36$	4.85410	0.809017
$37$	5.09017	0.836819	0.418409	−	0.908259i	$-0.362588\pi$
$37$	5.09017	0.836819	0.418409	+	0.908259i	$0.362588\pi$
$38$	15.3262	2.48624
$39$	−6.70820	−1.07417
$40$	22.4164	3.54435
$41$	−6.09017	−0.951125	−0.475562	−	0.879682i	$-0.657755\pi$
$41$	−6.09017	−0.951125	−0.475562	+	0.879682i	$0.657755\pi$
$42$	6.23607	0.962246
$43$	12.7082	1.93798	0.968991	−	0.247094i	$-0.0794757\pi$
$43$	12.7082	1.93798	0.968991	+	0.247094i	$0.0794757\pi$
$44$	16.8541	2.54085
$45$	−3.00000	−0.447214
$46$	3.61803	0.533450
$47$	−4.85410	−0.708044	−0.354022	−	0.935237i	$-0.615186\pi$
$47$	−4.85410	−0.708044	−0.354022	+	0.935237i	$0.615186\pi$
$48$	9.85410	1.42232
$49$	−1.32624	−0.189463
$50$	−10.4721	−1.48098
$51$	−2.61803	−0.366598
$52$	−32.5623	−4.51558
$53$	5.47214	0.751656	0.375828	−	0.926690i	$-0.377358\pi$
$53$	5.47214	0.751656	0.375828	+	0.926690i	$0.377358\pi$
$54$	−2.61803	−0.356269
$55$	−10.4164	−1.40455
$56$	17.7984	2.37841
$57$	−5.85410	−0.775395
$58$	11.4721	1.50637
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−14.5623	−1.87999
$61$	12.0902	1.54799	0.773994	−	0.633193i	$-0.218256\pi$
$61$	12.0902	1.54799	0.773994	+	0.633193i	$0.218256\pi$
$62$	6.23607	0.791981
$63$	−2.38197	−0.300100
$64$	8.70820	1.08853
$65$	20.1246	2.49615
$66$	−9.09017	−1.11892
$67$	−4.23607	−0.517518	−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607	−0.517518	−0.258759	+	0.965942i	$0.583314\pi$
$68$	−12.7082	−1.54110
$69$	−1.38197	−0.166369
$70$	−18.7082	−2.23606
$71$	4.23607	0.502729	0.251364	−	0.967893i	$-0.419121\pi$
$71$	4.23607	0.502729	0.251364	+	0.967893i	$0.419121\pi$
$72$	−7.47214	−0.880600
$73$	8.09017	0.946883	0.473441	−	0.880825i	$-0.343012\pi$
$73$	8.09017	0.946883	0.473441	+	0.880825i	$0.343012\pi$
$74$	−13.3262	−1.54914
$75$	4.00000	0.461880
$76$	−28.4164	−3.25959
$77$	−8.27051	−0.942512
$78$	17.5623	1.98854
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	−29.5623	−3.30517
$81$	1.00000	0.111111
$82$	15.9443	1.76075
$83$	−1.14590	−0.125779	−0.0628893	−	0.998021i	$-0.520032\pi$
$83$	−1.14590	−0.125779	−0.0628893	+	0.998021i	$0.520032\pi$
$84$	−11.5623	−1.26155
$85$	7.85410	0.851897
$86$	−33.2705	−3.58765
$87$	−4.38197	−0.469796
$88$	−25.9443	−2.76567
$89$	6.09017	0.645557	0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017	0.645557	0.322778	+	0.946475i	$0.395383\pi$
$90$	7.85410	0.827895
$91$	15.9787	1.67502
$92$	−6.70820	−0.699379
$93$	−2.38197	−0.246998
$94$	12.7082	1.31075
$95$	17.5623	1.80185
$96$	−10.8541	−1.10779
$97$	−9.47214	−0.961750	−0.480875	−	0.876789i	$-0.659681\pi$
$97$	−9.47214	−0.961750	−0.480875	+	0.876789i	$0.659681\pi$
$98$	3.47214	0.350739
$99$	3.47214	0.348963
$100$	19.4164	1.94164
$101$	−6.76393	−0.673036	−0.336518	−	0.941677i	$-0.609249\pi$
$101$	−6.76393	−0.673036	−0.336518	+	0.941677i	$0.609249\pi$
$102$	6.85410	0.678657
$103$	−19.2361	−1.89539	−0.947693	−	0.319183i	$-0.896591\pi$
$103$	−19.2361	−1.89539	−0.947693	+	0.319183i	$0.896591\pi$
$104$	50.1246	4.91512
$105$	7.14590	0.697368
$106$	−14.3262	−1.39149
$107$	−10.0344	−0.970066	−0.485033	−	0.874496i	$-0.661192\pi$
$107$	−10.0344	−0.970066	−0.485033	+	0.874496i	$0.661192\pi$
$108$	4.85410	0.467086
$109$	0.145898	0.0139745	0.00698725	−	0.999976i	$-0.497776\pi$
$109$	0.145898	0.0139745	0.00698725	+	0.999976i	$0.497776\pi$
$110$	27.2705	2.60014
$111$	5.09017	0.483138
$112$	−23.4721	−2.21791
$113$	5.76393	0.542225	0.271113	−	0.962548i	$-0.412608\pi$
$113$	5.76393	0.542225	0.271113	+	0.962548i	$0.412608\pi$
$114$	15.3262	1.43543
$115$	4.14590	0.386607
$116$	−21.2705	−1.97492
$117$	−6.70820	−0.620174
$118$	−2.61803	−0.241010
$119$	6.23607	0.571659
$120$	22.4164	2.04633
$121$	1.05573	0.0959753
$122$	−31.6525	−2.86568
$123$	−6.09017	−0.549132
$124$	−11.5623	−1.03833
$125$	3.00000	0.268328
$126$	6.23607	0.555553
$127$	−2.52786	−0.224312	−0.112156	−	0.993691i	$-0.535776\pi$
$127$	−2.52786	−0.224312	−0.112156	+	0.993691i	$0.535776\pi$
$128$	−1.09017	−0.0963583
$129$	12.7082	1.11889
$130$	−52.6869	−4.62095
$131$	6.76393	0.590967	0.295484	−	0.955348i	$-0.404519\pi$
$131$	6.76393	0.590967	0.295484	+	0.955348i	$0.404519\pi$
$132$	16.8541	1.46696
$133$	13.9443	1.20912
$134$	11.0902	0.958045
$135$	−3.00000	−0.258199
$136$	19.5623	1.67745
$137$	−4.52786	−0.386842	−0.193421	−	0.981116i	$-0.561958\pi$
$137$	−4.52786	−0.386842	−0.193421	+	0.981116i	$0.561958\pi$
$138$	3.61803	0.307988
$139$	−18.7082	−1.58681	−0.793405	−	0.608695i	$-0.791693\pi$
$139$	−18.7082	−1.58681	−0.793405	+	0.608695i	$0.791693\pi$
$140$	34.6869	2.93158
$141$	−4.85410	−0.408789
$142$	−11.0902	−0.930666
$143$	−23.2918	−1.94776
$144$	9.85410	0.821175
$145$	13.1459	1.09171
$146$	−21.1803	−1.75290
$147$	−1.32624	−0.109386
$148$	24.7082	2.03100
$149$	−22.0344	−1.80513	−0.902566	−	0.430552i	$-0.858319\pi$
$149$	−22.0344	−1.80513	−0.902566	+	0.430552i	$0.858319\pi$
$150$	−10.4721	−0.855046
$151$	8.85410	0.720537	0.360268	−	0.932849i	$-0.382685\pi$
$151$	8.85410	0.720537	0.360268	+	0.932849i	$0.382685\pi$
$152$	43.7426	3.54800
$153$	−2.61803	−0.211656
$154$	21.6525	1.74481
$155$	7.14590	0.573972
$156$	−32.5623	−2.60707
$157$	7.94427	0.634022	0.317011	−	0.948422i	$-0.397321\pi$
$157$	7.94427	0.634022	0.317011	+	0.948422i	$0.397321\pi$
$158$	7.85410	0.624839
$159$	5.47214	0.433969
$160$	32.5623	2.57428
$161$	3.29180	0.259430
$162$	−2.61803	−0.205692
$163$	−9.61803	−0.753343	−0.376671	−	0.926347i	$-0.622931\pi$
$163$	−9.61803	−0.753343	−0.376671	+	0.926347i	$0.622931\pi$
$164$	−29.5623	−2.30843
$165$	−10.4164	−0.810916
$166$	3.00000	0.232845
$167$	−4.67376	−0.361667	−0.180833	−	0.983514i	$-0.557879\pi$
$167$	−4.67376	−0.361667	−0.180833	+	0.983514i	$0.557879\pi$
$168$	17.7984	1.37317
$169$	32.0000	2.46154
$170$	−20.5623	−1.57706
$171$	−5.85410	−0.447674
$172$	61.6869	4.70358
$173$	14.3820	1.09344	0.546720	−	0.837315i	$-0.315876\pi$
$173$	14.3820	1.09344	0.546720	+	0.837315i	$0.315876\pi$
$174$	11.4721	0.869700
$175$	−9.52786	−0.720239
$176$	34.2148	2.57904
$177$	1.00000	0.0751646
$178$	−15.9443	−1.19507
$179$	−13.1803	−0.985145	−0.492572	−	0.870271i	$-0.663943\pi$
$179$	−13.1803	−0.985145	−0.492572	+	0.870271i	$0.663943\pi$
$180$	−14.5623	−1.08541
$181$	−8.56231	−0.636431	−0.318216	−	0.948018i	$-0.603084\pi$
$181$	−8.56231	−0.636431	−0.318216	+	0.948018i	$0.603084\pi$
$182$	−41.8328	−3.10085
$183$	12.0902	0.893731
$184$	10.3262	0.761260
$185$	−15.2705	−1.12271
$186$	6.23607	0.457251
$187$	−9.09017	−0.664739
$188$	−23.5623	−1.71846
$189$	−2.38197	−0.173263
$190$	−45.9787	−3.33565
$191$	−18.7082	−1.35368	−0.676839	−	0.736131i	$-0.736651\pi$
$191$	−18.7082	−1.35368	−0.676839	+	0.736131i	$0.736651\pi$
$192$	8.70820	0.628460
$193$	−0.583592	−0.0420079	−0.0210039	−	0.999779i	$-0.506686\pi$
$193$	−0.583592	−0.0420079	−0.0210039	+	0.999779i	$0.506686\pi$
$194$	24.7984	1.78042
$195$	20.1246	1.44115
$196$	−6.43769	−0.459835
$197$	10.1803	0.725319	0.362660	−	0.931922i	$-0.381869\pi$
$197$	10.1803	0.725319	0.362660	+	0.931922i	$0.381869\pi$
$198$	−9.09017	−0.646010
$199$	−13.5066	−0.957456	−0.478728	−	0.877963i	$-0.658902\pi$
$199$	−13.5066	−0.957456	−0.478728	+	0.877963i	$0.658902\pi$
$200$	−29.8885	−2.11344
$201$	−4.23607	−0.298789
$202$	17.7082	1.24594
$203$	10.4377	0.732583
$204$	−12.7082	−0.889752
$205$	18.2705	1.27607
$206$	50.3607	3.50879
$207$	−1.38197	−0.0960533
$208$	−66.1033	−4.58344
$209$	−20.3262	−1.40600
$210$	−18.7082	−1.29099
$211$	4.61803	0.317919	0.158959	−	0.987285i	$-0.449186\pi$
$211$	4.61803	0.317919	0.158959	+	0.987285i	$0.449186\pi$
$212$	26.5623	1.82431
$213$	4.23607	0.290251
$214$	26.2705	1.79582
$215$	−38.1246	−2.60008
$216$	−7.47214	−0.508414
$217$	5.67376	0.385160
$218$	−0.381966	−0.0258700
$219$	8.09017	0.546683
$220$	−50.5623	−3.40891
$221$	17.5623	1.18137
$222$	−13.3262	−0.894399
$223$	−15.4164	−1.03236	−0.516180	−	0.856480i	$-0.672646\pi$
$223$	−15.4164	−1.03236	−0.516180	+	0.856480i	$0.672646\pi$
$224$	25.8541	1.72745
$225$	4.00000	0.266667
$226$	−15.0902	−1.00378
$227$	−9.38197	−0.622703	−0.311351	−	0.950295i	$-0.600782\pi$
$227$	−9.38197	−0.622703	−0.311351	+	0.950295i	$0.600782\pi$
$228$	−28.4164	−1.88192
$229$	27.9787	1.84889	0.924443	−	0.381321i	$-0.124531\pi$
$229$	27.9787	1.84889	0.924443	+	0.381321i	$0.124531\pi$
$230$	−10.8541	−0.715698
$231$	−8.27051	−0.544160
$232$	32.7426	2.14966
$233$	5.23607	0.343026	0.171513	−	0.985182i	$-0.445134\pi$
$233$	5.23607	0.343026	0.171513	+	0.985182i	$0.445134\pi$
$234$	17.5623	1.14808
$235$	14.5623	0.949940
$236$	4.85410	0.315975
$237$	−3.00000	−0.194871
$238$	−16.3262	−1.05827
$239$	−5.29180	−0.342298	−0.171149	−	0.985245i	$-0.554748\pi$
$239$	−5.29180	−0.342298	−0.171149	+	0.985245i	$0.554748\pi$
$240$	−29.5623	−1.90824
$241$	−6.47214	−0.416907	−0.208453	−	0.978032i	$-0.566843\pi$
$241$	−6.47214	−0.416907	−0.208453	+	0.978032i	$0.566843\pi$
$242$	−2.76393	−0.177672
$243$	1.00000	0.0641500
$244$	58.6869	3.75704
$245$	3.97871	0.254191
$246$	15.9443	1.01657
$247$	39.2705	2.49872
$248$	17.7984	1.13020
$249$	−1.14590	−0.0726183
$250$	−7.85410	−0.496737
$251$	−5.94427	−0.375199	−0.187600	−	0.982246i	$-0.560071\pi$
$251$	−5.94427	−0.375199	−0.187600	+	0.982246i	$0.560071\pi$
$252$	−11.5623	−0.728357
$253$	−4.79837	−0.301671
$254$	6.61803	0.415252
$255$	7.85410	0.491843
$256$	−14.5623	−0.910144
$257$	13.8885	0.866344	0.433172	−	0.901311i	$-0.357394\pi$
$257$	13.8885	0.866344	0.433172	+	0.901311i	$0.357394\pi$
$258$	−33.2705	−2.07133
$259$	−12.1246	−0.753387
$260$	97.6869	6.05829
$261$	−4.38197	−0.271237
$262$	−17.7082	−1.09402
$263$	−3.61803	−0.223098	−0.111549	−	0.993759i	$-0.535581\pi$
$263$	−3.61803	−0.223098	−0.111549	+	0.993759i	$0.535581\pi$
$264$	−25.9443	−1.59676
$265$	−16.4164	−1.00845
$266$	−36.5066	−2.23836
$267$	6.09017	0.372712
$268$	−20.5623	−1.25604
$269$	4.81966	0.293860	0.146930	−	0.989147i	$-0.453061\pi$
$269$	4.81966	0.293860	0.146930	+	0.989147i	$0.453061\pi$
$270$	7.85410	0.477985
$271$	1.18034	0.0717005	0.0358503	−	0.999357i	$-0.488586\pi$
$271$	1.18034	0.0717005	0.0358503	+	0.999357i	$0.488586\pi$
$272$	−25.7984	−1.56426
$273$	15.9787	0.967076
$274$	11.8541	0.716132
$275$	13.8885	0.837511
$276$	−6.70820	−0.403786
$277$	5.00000	0.300421	0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000	0.300421	0.150210	+	0.988654i	$0.452005\pi$
$278$	48.9787	2.93755
$279$	−2.38197	−0.142605
$280$	−53.3951	−3.19097
$281$	−17.1246	−1.02157	−0.510784	−	0.859709i	$-0.670645\pi$
$281$	−17.1246	−1.02157	−0.510784	+	0.859709i	$0.670645\pi$
$282$	12.7082	0.756763
$283$	11.8541	0.704653	0.352327	−	0.935877i	$-0.385391\pi$
$283$	11.8541	0.704653	0.352327	+	0.935877i	$0.385391\pi$
$284$	20.5623	1.22015
$285$	17.5623	1.04030
$286$	60.9787	3.60575
$287$	14.5066	0.856296
$288$	−10.8541	−0.639584
$289$	−10.1459	−0.596818
$290$	−34.4164	−2.02100
$291$	−9.47214	−0.555266
$292$	39.2705	2.29813
$293$	21.7426	1.27022	0.635109	−	0.772422i	$-0.280955\pi$
$293$	21.7426	1.27022	0.635109	+	0.772422i	$0.280955\pi$
$294$	3.47214	0.202499
$295$	−3.00000	−0.174667
$296$	−38.0344	−2.21071
$297$	3.47214	0.201474
$298$	57.6869	3.34171
$299$	9.27051	0.536127
$300$	19.4164	1.12101
$301$	−30.2705	−1.74476
$302$	−23.1803	−1.33388
$303$	−6.76393	−0.388578
$304$	−57.6869	−3.30857
$305$	−36.2705	−2.07684
$306$	6.85410	0.391823
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	−40.1459	−2.28752
$309$	−19.2361	−1.09430
$310$	−18.7082	−1.06255
$311$	30.9787	1.75664	0.878321	−	0.478072i	$-0.158664\pi$
$311$	30.9787	1.75664	0.878321	+	0.478072i	$0.158664\pi$
$312$	50.1246	2.83775
$313$	−27.5623	−1.55791	−0.778957	−	0.627078i	$-0.784251\pi$
$313$	−27.5623	−1.55791	−0.778957	+	0.627078i	$0.784251\pi$
$314$	−20.7984	−1.17372
$315$	7.14590	0.402626
$316$	−14.5623	−0.819194
$317$	3.00000	0.168497	0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000	0.168497	0.0842484	+	0.996445i	$0.473151\pi$
$318$	−14.3262	−0.803376
$319$	−15.2148	−0.851864
$320$	−26.1246	−1.46041
$321$	−10.0344	−0.560068
$322$	−8.61803	−0.480264
$323$	15.3262	0.852775
$324$	4.85410	0.269672
$325$	−26.8328	−1.48842
$326$	25.1803	1.39461
$327$	0.145898	0.00806818
$328$	45.5066	2.51268
$329$	11.5623	0.637451
$330$	27.2705	1.50119
$331$	14.7639	0.811499	0.405750	−	0.913984i	$-0.367011\pi$
$331$	14.7639	0.811499	0.405750	+	0.913984i	$0.367011\pi$
$332$	−5.56231	−0.305271
$333$	5.09017	0.278940
$334$	12.2361	0.669528
$335$	12.7082	0.694323
$336$	−23.4721	−1.28051
$337$	−35.5623	−1.93720	−0.968601	−	0.248620i	$-0.920023\pi$
$337$	−35.5623	−1.93720	−0.968601	+	0.248620i	$0.920023\pi$
$338$	−83.7771	−4.55687
$339$	5.76393	0.313054
$340$	38.1246	2.06760
$341$	−8.27051	−0.447873
$342$	15.3262	0.828748
$343$	19.8328	1.07087
$344$	−94.9574	−5.11976
$345$	4.14590	0.223208
$346$	−37.6525	−2.02421
$347$	−14.7426	−0.791427	−0.395713	−	0.918374i	$-0.629503\pi$
$347$	−14.7426	−0.791427	−0.395713	+	0.918374i	$0.629503\pi$
$348$	−21.2705	−1.14022
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	24.9443	1.33333
$351$	−6.70820	−0.358057
$352$	−37.6869	−2.00872
$353$	−15.2705	−0.812767	−0.406384	−	0.913703i	$-0.633210\pi$
$353$	−15.2705	−0.812767	−0.406384	+	0.913703i	$0.633210\pi$
$354$	−2.61803	−0.139147
$355$	−12.7082	−0.674481
$356$	29.5623	1.56680
$357$	6.23607	0.330048
$358$	34.5066	1.82373
$359$	−29.8885	−1.57746	−0.788729	−	0.614742i	$-0.789260\pi$
$359$	−29.8885	−1.57746	−0.788729	+	0.614742i	$0.789260\pi$
$360$	22.4164	1.18145
$361$	15.2705	0.803711
$362$	22.4164	1.17818
$363$	1.05573	0.0554114
$364$	77.5623	4.06537
$365$	−24.2705	−1.27038
$366$	−31.6525	−1.65450
$367$	4.41641	0.230535	0.115267	−	0.993335i	$-0.463228\pi$
$367$	4.41641	0.230535	0.115267	+	0.993335i	$0.463228\pi$
$368$	−13.6180	−0.709889
$369$	−6.09017	−0.317042
$370$	39.9787	2.07839
$371$	−13.0344	−0.676715
$372$	−11.5623	−0.599478
$373$	−15.5623	−0.805786	−0.402893	−	0.915247i	$-0.631995\pi$
$373$	−15.5623	−0.805786	−0.402893	+	0.915247i	$0.631995\pi$
$374$	23.7984	1.23058
$375$	3.00000	0.154919
$376$	36.2705	1.87051
$377$	29.3951	1.51393
$378$	6.23607	0.320749
$379$	6.41641	0.329589	0.164794	−	0.986328i	$-0.447304\pi$
$379$	6.41641	0.329589	0.164794	+	0.986328i	$0.447304\pi$
$380$	85.2492	4.37319
$381$	−2.52786	−0.129506
$382$	48.9787	2.50597
$383$	37.9443	1.93886	0.969431	−	0.245365i	$-0.0789077\pi$
$383$	37.9443	1.93886	0.969431	+	0.245365i	$0.0789077\pi$
$384$	−1.09017	−0.0556325
$385$	24.8115	1.26451
$386$	1.52786	0.0777662
$387$	12.7082	0.645994
$388$	−45.9787	−2.33422
$389$	−11.8885	−0.602773	−0.301387	−	0.953502i	$-0.597449\pi$
$389$	−11.8885	−0.602773	−0.301387	+	0.953502i	$0.597449\pi$
$390$	−52.6869	−2.66791
$391$	3.61803	0.182972
$392$	9.90983	0.500522
$393$	6.76393	0.341195
$394$	−26.6525	−1.34273
$395$	9.00000	0.452839
$396$	16.8541	0.846950
$397$	−7.58359	−0.380610	−0.190305	−	0.981725i	$-0.560948\pi$
$397$	−7.58359	−0.380610	−0.190305	+	0.981725i	$0.560948\pi$
$398$	35.3607	1.77247
$399$	13.9443	0.698087
$400$	39.4164	1.97082
$401$	−6.43769	−0.321483	−0.160742	−	0.986997i	$-0.551389\pi$
$401$	−6.43769	−0.321483	−0.160742	+	0.986997i	$0.551389\pi$
$402$	11.0902	0.553127
$403$	15.9787	0.795956
$404$	−32.8328	−1.63349
$405$	−3.00000	−0.149071
$406$	−27.3262	−1.35618
$407$	17.6738	0.876056
$408$	19.5623	0.968478
$409$	25.4164	1.25676	0.628380	−	0.777906i	$-0.283718\pi$
$409$	25.4164	1.25676	0.628380	+	0.777906i	$0.283718\pi$
$410$	−47.8328	−2.36229
$411$	−4.52786	−0.223343
$412$	−93.3738	−4.60020
$413$	−2.38197	−0.117209
$414$	3.61803	0.177817
$415$	3.43769	0.168750
$416$	72.8115	3.56988
$417$	−18.7082	−0.916145
$418$	53.2148	2.60282
$419$	14.9443	0.730075	0.365038	−	0.930993i	$-0.381056\pi$
$419$	14.9443	0.730075	0.365038	+	0.930993i	$0.381056\pi$
$420$	34.6869	1.69255
$421$	−16.4164	−0.800087	−0.400043	−	0.916496i	$-0.631005\pi$
$421$	−16.4164	−0.800087	−0.400043	+	0.916496i	$0.631005\pi$
$422$	−12.0902	−0.588540
$423$	−4.85410	−0.236015
$424$	−40.8885	−1.98572
$425$	−10.4721	−0.507973
$426$	−11.0902	−0.537320
$427$	−28.7984	−1.39365
$428$	−48.7082	−2.35440
$429$	−23.2918	−1.12454
$430$	99.8115	4.81334
$431$	−23.5066	−1.13227	−0.566136	−	0.824312i	$-0.691562\pi$
$431$	−23.5066	−1.13227	−0.566136	+	0.824312i	$0.691562\pi$
$432$	9.85410	0.474106
$433$	10.1459	0.487581	0.243790	−	0.969828i	$-0.421609\pi$
$433$	10.1459	0.487581	0.243790	+	0.969828i	$0.421609\pi$
$434$	−14.8541	−0.713020
$435$	13.1459	0.630298
$436$	0.708204	0.0339168
$437$	8.09017	0.387005
$438$	−21.1803	−1.01204
$439$	7.85410	0.374856	0.187428	−	0.982278i	$-0.439985\pi$
$439$	7.85410	0.374856	0.187428	+	0.982278i	$0.439985\pi$
$440$	77.8328	3.71053
$441$	−1.32624	−0.0631542
$442$	−45.9787	−2.18698
$443$	−0.437694	−0.0207955	−0.0103977	−	0.999946i	$-0.503310\pi$
$443$	−0.437694	−0.0207955	−0.0103977	+	0.999946i	$0.503310\pi$
$444$	24.7082	1.17260
$445$	−18.2705	−0.866105
$446$	40.3607	1.91113
$447$	−22.0344	−1.04219
$448$	−20.7426	−0.979998
$449$	−41.0689	−1.93816	−0.969080	−	0.246746i	$-0.920639\pi$
$449$	−41.0689	−1.93816	−0.969080	+	0.246746i	$0.920639\pi$
$450$	−10.4721	−0.493661
$451$	−21.1459	−0.995721
$452$	27.9787	1.31601
$453$	8.85410	0.416002
$454$	24.5623	1.15277
$455$	−47.9361	−2.24728
$456$	43.7426	2.04844
$457$	1.14590	0.0536028	0.0268014	−	0.999641i	$-0.491468\pi$
$457$	1.14590	0.0536028	0.0268014	+	0.999641i	$0.491468\pi$
$458$	−73.2492	−3.42271
$459$	−2.61803	−0.122199
$460$	20.1246	0.938315
$461$	18.3262	0.853538	0.426769	−	0.904361i	$-0.359652\pi$
$461$	18.3262	0.853538	0.426769	+	0.904361i	$0.359652\pi$
$462$	21.6525	1.00736
$463$	−18.0344	−0.838132	−0.419066	−	0.907956i	$-0.637642\pi$
$463$	−18.0344	−0.838132	−0.419066	+	0.907956i	$0.637642\pi$
$464$	−43.1803	−2.00460
$465$	7.14590	0.331383
$466$	−13.7082	−0.635020
$467$	24.9443	1.15428	0.577142	−	0.816644i	$-0.304168\pi$
$467$	24.9443	1.15428	0.577142	+	0.816644i	$0.304168\pi$
$468$	−32.5623	−1.50519
$469$	10.0902	0.465921
$470$	−38.1246	−1.75856
$471$	7.94427	0.366053
$472$	−7.47214	−0.343933
$473$	44.1246	2.02885
$474$	7.85410	0.360751
$475$	−23.4164	−1.07442
$476$	30.2705	1.38745
$477$	5.47214	0.250552
$478$	13.8541	0.633672
$479$	14.5066	0.662822	0.331411	−	0.943486i	$-0.392475\pi$
$479$	14.5066	0.662822	0.331411	+	0.943486i	$0.392475\pi$
$480$	32.5623	1.48626
$481$	−34.1459	−1.55692
$482$	16.9443	0.771790
$483$	3.29180	0.149782
$484$	5.12461	0.232937
$485$	28.4164	1.29032
$486$	−2.61803	−0.118756
$487$	11.5623	0.523938	0.261969	−	0.965076i	$-0.415628\pi$
$487$	11.5623	0.523938	0.261969	+	0.965076i	$0.415628\pi$
$488$	−90.3394	−4.08947
$489$	−9.61803	−0.434943
$490$	−10.4164	−0.470565
$491$	24.9230	1.12476	0.562379	−	0.826879i	$-0.309886\pi$
$491$	24.9230	1.12476	0.562379	+	0.826879i	$0.309886\pi$
$492$	−29.5623	−1.33277
$493$	11.4721	0.516679
$494$	−102.812	−4.62571
$495$	−10.4164	−0.468183
$496$	−23.4721	−1.05393
$497$	−10.0902	−0.452606
$498$	3.00000	0.134433
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	14.5623	0.651246
$501$	−4.67376	−0.208808
$502$	15.5623	0.694580
$503$	−36.0902	−1.60918	−0.804591	−	0.593830i	$-0.797615\pi$
$503$	−36.0902	−1.60918	−0.804591	+	0.593830i	$0.797615\pi$
$504$	17.7984	0.792803
$505$	20.2918	0.902973
$506$	12.5623	0.558463
$507$	32.0000	1.42117
$508$	−12.2705	−0.544416
$509$	−43.2148	−1.91546	−0.957731	−	0.287666i	$-0.907121\pi$
$509$	−43.2148	−1.91546	−0.957731	+	0.287666i	$0.907121\pi$
$510$	−20.5623	−0.910514
$511$	−19.2705	−0.852477
$512$	40.3050	1.78124
$513$	−5.85410	−0.258465
$514$	−36.3607	−1.60380
$515$	57.7082	2.54293
$516$	61.6869	2.71562
$517$	−16.8541	−0.741243
$518$	31.7426	1.39469
$519$	14.3820	0.631298
$520$	−150.374	−6.59433
$521$	39.2148	1.71803	0.859015	−	0.511950i	$-0.171077\pi$
$521$	39.2148	1.71803	0.859015	+	0.511950i	$0.171077\pi$
$522$	11.4721	0.502122
$523$	3.36068	0.146952	0.0734761	−	0.997297i	$-0.476591\pi$
$523$	3.36068	0.146952	0.0734761	+	0.997297i	$0.476591\pi$
$524$	32.8328	1.43431
$525$	−9.52786	−0.415830
$526$	9.47214	0.413005
$527$	6.23607	0.271647
$528$	34.2148	1.48901
$529$	−21.0902	−0.916964
$530$	42.9787	1.86688
$531$	1.00000	0.0433963
$532$	67.6869	2.93460
$533$	40.8541	1.76959
$534$	−15.9443	−0.689976
$535$	30.1033	1.30148
$536$	31.6525	1.36718
$537$	−13.1803	−0.568774
$538$	−12.6180	−0.544002
$539$	−4.60488	−0.198346
$540$	−14.5623	−0.626662
$541$	2.70820	0.116435	0.0582174	−	0.998304i	$-0.481458\pi$
$541$	2.70820	0.116435	0.0582174	+	0.998304i	$0.481458\pi$
$542$	−3.09017	−0.132734
$543$	−8.56231	−0.367444
$544$	28.4164	1.21834
$545$	−0.437694	−0.0187488
$546$	−41.8328	−1.79028
$547$	−22.9787	−0.982499	−0.491249	−	0.871019i	$-0.663460\pi$
$547$	−22.9787	−0.982499	−0.491249	+	0.871019i	$0.663460\pi$
$548$	−21.9787	−0.938884
$549$	12.0902	0.515996
$550$	−36.3607	−1.55042
$551$	25.6525	1.09283
$552$	10.3262	0.439514
$553$	7.14590	0.303874
$554$	−13.0902	−0.556148
$555$	−15.2705	−0.648197
$556$	−90.8115	−3.85127
$557$	−26.9443	−1.14167	−0.570833	−	0.821066i	$-0.693380\pi$
$557$	−26.9443	−1.14167	−0.570833	+	0.821066i	$0.693380\pi$
$558$	6.23607	0.263994
$559$	−85.2492	−3.60566
$560$	70.4164	2.97564
$561$	−9.09017	−0.383787
$562$	44.8328	1.89116
$563$	−24.5279	−1.03373	−0.516863	−	0.856068i	$-0.672900\pi$
$563$	−24.5279	−1.03373	−0.516863	+	0.856068i	$0.672900\pi$
$564$	−23.5623	−0.992152
$565$	−17.2918	−0.727471
$566$	−31.0344	−1.30447
$567$	−2.38197	−0.100033
$568$	−31.6525	−1.32811
$569$	11.2148	0.470148	0.235074	−	0.971977i	$-0.424467\pi$
$569$	11.2148	0.470148	0.235074	+	0.971977i	$0.424467\pi$
$570$	−45.9787	−1.92584
$571$	−19.8328	−0.829978	−0.414989	−	0.909827i	$-0.636214\pi$
$571$	−19.8328	−0.829978	−0.414989	+	0.909827i	$0.636214\pi$
$572$	−113.061	−4.72731
$573$	−18.7082	−0.781546
$574$	−37.9787	−1.58520
$575$	−5.52786	−0.230528
$576$	8.70820	0.362842
$577$	23.3607	0.972518	0.486259	−	0.873815i	$-0.338361\pi$
$577$	23.3607	0.972518	0.486259	+	0.873815i	$0.338361\pi$
$578$	26.5623	1.10485
$579$	−0.583592	−0.0242533
$580$	63.8115	2.64963
$581$	2.72949	0.113238
$582$	24.7984	1.02793
$583$	19.0000	0.786900
$584$	−60.4508	−2.50147
$585$	20.1246	0.832050
$586$	−56.9230	−2.35147
$587$	−15.0689	−0.621959	−0.310980	−	0.950417i	$-0.600657\pi$
$587$	−15.0689	−0.621959	−0.310980	+	0.950417i	$0.600657\pi$
$588$	−6.43769	−0.265486
$589$	13.9443	0.574564
$590$	7.85410	0.323348
$591$	10.1803	0.418763
$592$	50.1591	2.06152
$593$	33.3262	1.36854	0.684272	−	0.729227i	$-0.260120\pi$
$593$	33.3262	1.36854	0.684272	+	0.729227i	$0.260120\pi$
$594$	−9.09017	−0.372974
$595$	−18.7082	−0.766962
$596$	−106.957	−4.38115
$597$	−13.5066	−0.552787
$598$	−24.2705	−0.992495
$599$	−8.18034	−0.334240	−0.167120	−	0.985937i	$-0.553447\pi$
$599$	−8.18034	−0.334240	−0.167120	+	0.985937i	$0.553447\pi$
$600$	−29.8885	−1.22019
$601$	−3.96556	−0.161758	−0.0808792	−	0.996724i	$-0.525773\pi$
$601$	−3.96556	−0.161758	−0.0808792	+	0.996724i	$0.525773\pi$
$602$	79.2492	3.22996
$603$	−4.23607	−0.172506
$604$	42.9787	1.74878
$605$	−3.16718	−0.128764
$606$	17.7082	0.719347
$607$	−16.3475	−0.663526	−0.331763	−	0.943363i	$-0.607643\pi$
$607$	−16.3475	−0.663526	−0.331763	+	0.943363i	$0.607643\pi$
$608$	63.5410	2.57693
$609$	10.4377	0.422957
$610$	94.9574	3.84471
$611$	32.5623	1.31733
$612$	−12.7082	−0.513699
$613$	26.2918	1.06192	0.530958	−	0.847398i	$-0.321832\pi$
$613$	26.2918	1.06192	0.530958	+	0.847398i	$0.321832\pi$
$614$	31.4164	1.26786
$615$	18.2705	0.736738
$616$	61.7984	2.48993
$617$	−47.6312	−1.91756	−0.958780	−	0.284150i	$-0.908289\pi$
$617$	−47.6312	−1.91756	−0.958780	+	0.284150i	$0.908289\pi$
$618$	50.3607	2.02580
$619$	25.0689	1.00760	0.503802	−	0.863819i	$-0.331934\pi$
$619$	25.0689	1.00760	0.503802	+	0.863819i	$0.331934\pi$
$620$	34.6869	1.39306
$621$	−1.38197	−0.0554564
$622$	−81.1033	−3.25195
$623$	−14.5066	−0.581194
$624$	−66.1033	−2.64625
$625$	−29.0000	−1.16000
$626$	72.1591	2.88406
$627$	−20.3262	−0.811752
$628$	38.5623	1.53880
$629$	−13.3262	−0.531352
$630$	−18.7082	−0.745353
$631$	−4.41641	−0.175814	−0.0879072	−	0.996129i	$-0.528018\pi$
$631$	−4.41641	−0.175814	−0.0879072	+	0.996129i	$0.528018\pi$
$632$	22.4164	0.891677
$633$	4.61803	0.183550
$634$	−7.85410	−0.311926
$635$	7.58359	0.300946
$636$	26.5623	1.05326
$637$	8.89667	0.352499
$638$	39.8328	1.57700
$639$	4.23607	0.167576
$640$	3.27051	0.129278
$641$	−18.5967	−0.734527	−0.367264	−	0.930117i	$-0.619705\pi$
$641$	−18.5967	−0.734527	−0.367264	+	0.930117i	$0.619705\pi$
$642$	26.2705	1.03681
$643$	10.6180	0.418734	0.209367	−	0.977837i	$-0.432860\pi$
$643$	10.6180	0.418734	0.209367	+	0.977837i	$0.432860\pi$
$644$	15.9787	0.629650
$645$	−38.1246	−1.50116
$646$	−40.1246	−1.57868
$647$	1.52786	0.0600665	0.0300333	−	0.999549i	$-0.490439\pi$
$647$	1.52786	0.0600665	0.0300333	+	0.999549i	$0.490439\pi$
$648$	−7.47214	−0.293533
$649$	3.47214	0.136293
$650$	70.2492	2.75540
$651$	5.67376	0.222372
$652$	−46.6869	−1.82840
$653$	33.3262	1.30416	0.652078	−	0.758152i	$-0.273897\pi$
$653$	33.3262	1.30416	0.652078	+	0.758152i	$0.273897\pi$
$654$	−0.381966	−0.0149361
$655$	−20.2918	−0.792866
$656$	−60.0132	−2.34312
$657$	8.09017	0.315628
$658$	−30.2705	−1.18007
$659$	9.09017	0.354103	0.177051	−	0.984202i	$-0.443344\pi$
$659$	9.09017	0.354103	0.177051	+	0.984202i	$0.443344\pi$
$660$	−50.5623	−1.96814
$661$	9.43769	0.367084	0.183542	−	0.983012i	$-0.441244\pi$
$661$	9.43769	0.367084	0.183542	+	0.983012i	$0.441244\pi$
$662$	−38.6525	−1.50227
$663$	17.5623	0.682063
$664$	8.56231	0.332282
$665$	−41.8328	−1.62221
$666$	−13.3262	−0.516381
$667$	6.05573	0.234479
$668$	−22.6869	−0.877783
$669$	−15.4164	−0.596033
$670$	−33.2705	−1.28535
$671$	41.9787	1.62057
$672$	25.8541	0.997344
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	93.1033	3.58621
$675$	4.00000	0.153960
$676$	155.331	5.97428
$677$	−28.1803	−1.08306	−0.541529	−	0.840682i	$-0.682154\pi$
$677$	−28.1803	−1.08306	−0.541529	+	0.840682i	$0.682154\pi$
$678$	−15.0902	−0.579534
$679$	22.5623	0.865862
$680$	−58.6869	−2.25054
$681$	−9.38197	−0.359518
$682$	21.6525	0.829116
$683$	29.1803	1.11655	0.558277	−	0.829654i	$-0.311463\pi$
$683$	29.1803	1.11655	0.558277	+	0.829654i	$0.311463\pi$
$684$	−28.4164	−1.08653
$685$	13.5836	0.519002
$686$	−51.9230	−1.98243
$687$	27.9787	1.06745
$688$	125.228	4.77427
$689$	−36.7082	−1.39847
$690$	−10.8541	−0.413209
$691$	44.6525	1.69866	0.849330	−	0.527862i	$-0.177006\pi$
$691$	44.6525	1.69866	0.849330	+	0.527862i	$0.177006\pi$
$692$	69.8115	2.65384
$693$	−8.27051	−0.314171
$694$	38.5967	1.46511
$695$	56.1246	2.12893
$696$	32.7426	1.24111
$697$	15.9443	0.603932
$698$	−60.2148	−2.27916
$699$	5.23607	0.198046
$700$	−46.2492	−1.74806
$701$	33.8673	1.27915	0.639574	−	0.768729i	$-0.279111\pi$
$701$	33.8673	1.27915	0.639574	+	0.768729i	$0.279111\pi$
$702$	17.5623	0.662847
$703$	−29.7984	−1.12387
$704$	30.2361	1.13956
$705$	14.5623	0.548448
$706$	39.9787	1.50462
$707$	16.1115	0.605934
$708$	4.85410	0.182428
$709$	−15.7082	−0.589934	−0.294967	−	0.955507i	$-0.595309\pi$
$709$	−15.7082	−0.589934	−0.294967	+	0.955507i	$0.595309\pi$
$710$	33.2705	1.24862
$711$	−3.00000	−0.112509
$712$	−45.5066	−1.70543
$713$	3.29180	0.123279
$714$	−16.3262	−0.610994
$715$	69.8754	2.61319
$716$	−63.9787	−2.39100
$717$	−5.29180	−0.197626
$718$	78.2492	2.92024
$719$	6.43769	0.240085	0.120043	−	0.992769i	$-0.461697\pi$
$719$	6.43769	0.240085	0.120043	+	0.992769i	$0.461697\pi$
$720$	−29.5623	−1.10172
$721$	45.8197	1.70641
$722$	−39.9787	−1.48785
$723$	−6.47214	−0.240701
$724$	−41.5623	−1.54465
$725$	−17.5279	−0.650969
$726$	−2.76393	−0.102579
$727$	5.41641	0.200883	0.100442	−	0.994943i	$-0.467974\pi$
$727$	5.41641	0.200883	0.100442	+	0.994943i	$0.467974\pi$
$728$	−119.395	−4.42508
$729$	1.00000	0.0370370
$730$	63.5410	2.35176
$731$	−33.2705	−1.23055
$732$	58.6869	2.16913
$733$	−1.94427	−0.0718133	−0.0359067	−	0.999355i	$-0.511432\pi$
$733$	−1.94427	−0.0718133	−0.0359067	+	0.999355i	$0.511432\pi$
$734$	−11.5623	−0.426772
$735$	3.97871	0.146757
$736$	15.0000	0.552907
$737$	−14.7082	−0.541784
$738$	15.9443	0.586917
$739$	18.1459	0.667508	0.333754	−	0.942660i	$-0.391685\pi$
$739$	18.1459	0.667508	0.333754	+	0.942660i	$0.391685\pi$
$740$	−74.1246	−2.72487
$741$	39.2705	1.44264
$742$	34.1246	1.25275
$743$	20.7984	0.763018	0.381509	−	0.924365i	$-0.375404\pi$
$743$	20.7984	0.763018	0.381509	+	0.924365i	$0.375404\pi$
$744$	17.7984	0.652520
$745$	66.1033	2.42184
$746$	40.7426	1.49169
$747$	−1.14590	−0.0419262
$748$	−44.1246	−1.61336
$749$	23.9017	0.873349
$750$	−7.85410	−0.286791
$751$	−38.5410	−1.40638	−0.703191	−	0.711001i	$-0.748242\pi$
$751$	−38.5410	−1.40638	−0.703191	+	0.711001i	$0.748242\pi$
$752$	−47.8328	−1.74428
$753$	−5.94427	−0.216621
$754$	−76.9574	−2.80262
$755$	−26.5623	−0.966701
$756$	−11.5623	−0.420517
$757$	33.4508	1.21579	0.607896	−	0.794017i	$-0.292014\pi$
$757$	33.4508	1.21579	0.607896	+	0.794017i	$0.292014\pi$
$758$	−16.7984	−0.610144
$759$	−4.79837	−0.174170
$760$	−131.228	−4.76014
$761$	2.88854	0.104710	0.0523548	−	0.998629i	$-0.483327\pi$
$761$	2.88854	0.104710	0.0523548	+	0.998629i	$0.483327\pi$
$762$	6.61803	0.239746
$763$	−0.347524	−0.0125812
$764$	−90.8115	−3.28545
$765$	7.85410	0.283966
$766$	−99.3394	−3.58928
$767$	−6.70820	−0.242219
$768$	−14.5623	−0.525472
$769$	23.2705	0.839156	0.419578	−	0.907719i	$-0.362178\pi$
$769$	23.2705	0.839156	0.419578	+	0.907719i	$0.362178\pi$
$770$	−64.9574	−2.34090
$771$	13.8885	0.500184
$772$	−2.83282	−0.101955
$773$	−12.6525	−0.455078	−0.227539	−	0.973769i	$-0.573068\pi$
$773$	−12.6525	−0.455078	−0.227539	+	0.973769i	$0.573068\pi$
$774$	−33.2705	−1.19588
$775$	−9.52786	−0.342251
$776$	70.7771	2.54075
$777$	−12.1246	−0.434968
$778$	31.1246	1.11587
$779$	35.6525	1.27738
$780$	97.6869	3.49775
$781$	14.7082	0.526301
$782$	−9.47214	−0.338723
$783$	−4.38197	−0.156599
$784$	−13.0689	−0.466746
$785$	−23.8328	−0.850630
$786$	−17.7082	−0.631631
$787$	15.7082	0.559937	0.279968	−	0.960009i	$-0.409676\pi$
$787$	15.7082	0.559937	0.279968	+	0.960009i	$0.409676\pi$
$788$	49.4164	1.76039
$789$	−3.61803	−0.128805
$790$	−23.5623	−0.838309
$791$	−13.7295	−0.488164
$792$	−25.9443	−0.921890
$793$	−81.1033	−2.88006
$794$	19.8541	0.704596
$795$	−16.4164	−0.582230
$796$	−65.5623	−2.32379
$797$	−32.0689	−1.13594	−0.567969	−	0.823050i	$-0.692271\pi$
$797$	−32.0689	−1.13594	−0.567969	+	0.823050i	$0.692271\pi$
$798$	−36.5066	−1.29232
$799$	12.7082	0.449584
$800$	−43.4164	−1.53500
$801$	6.09017	0.215186
$802$	16.8541	0.595139
$803$	28.0902	0.991281
$804$	−20.5623	−0.725177
$805$	−9.87539	−0.348062
$806$	−41.8328	−1.47350
$807$	4.81966	0.169660
$808$	50.5410	1.77803
$809$	37.7426	1.32696	0.663480	−	0.748194i	$-0.269079\pi$
$809$	37.7426	1.32696	0.663480	+	0.748194i	$0.269079\pi$
$810$	7.85410	0.275965
$811$	−24.5410	−0.861752	−0.430876	−	0.902411i	$-0.641795\pi$
$811$	−24.5410	−0.861752	−0.430876	+	0.902411i	$0.641795\pi$
$812$	50.6656	1.77802
$813$	1.18034	0.0413963
$814$	−46.2705	−1.62178
$815$	28.8541	1.01072
$816$	−25.7984	−0.903124
$817$	−74.3951	−2.60276
$818$	−66.5410	−2.32655
$819$	15.9787	0.558341
$820$	88.6869	3.09708
$821$	24.6312	0.859634	0.429817	−	0.902916i	$-0.358578\pi$
$821$	24.6312	0.859634	0.429817	+	0.902916i	$0.358578\pi$
$822$	11.8541	0.413459
$823$	−31.0689	−1.08299	−0.541497	−	0.840703i	$-0.682142\pi$
$823$	−31.0689	−1.08299	−0.541497	+	0.840703i	$0.682142\pi$
$824$	143.735	5.00723
$825$	13.8885	0.483537
$826$	6.23607	0.216981
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	−6.70820	−0.233126
$829$	13.7295	0.476845	0.238422	−	0.971162i	$-0.423370\pi$
$829$	13.7295	0.476845	0.238422	+	0.971162i	$0.423370\pi$
$830$	−9.00000	−0.312395
$831$	5.00000	0.173448
$832$	−58.4164	−2.02522
$833$	3.47214	0.120302
$834$	48.9787	1.69599
$835$	14.0213	0.485227
$836$	−98.6656	−3.41242
$837$	−2.38197	−0.0823328
$838$	−39.1246	−1.35154
$839$	−15.0000	−0.517858	−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000	−0.517858	−0.258929	+	0.965896i	$0.583369\pi$
$840$	−53.3951	−1.84231
$841$	−9.79837	−0.337875
$842$	42.9787	1.48114
$843$	−17.1246	−0.589803
$844$	22.4164	0.771605
$845$	−96.0000	−3.30250
$846$	12.7082	0.436917
$847$	−2.51471	−0.0864064
$848$	53.9230	1.85172
$849$	11.8541	0.406832
$850$	27.4164	0.940375
$851$	−7.03444	−0.241138
$852$	20.5623	0.704453
$853$	40.6180	1.39073	0.695367	−	0.718654i	$-0.255242\pi$
$853$	40.6180	1.39073	0.695367	+	0.718654i	$0.255242\pi$
$854$	75.3951	2.57997
$855$	17.5623	0.600618
$856$	74.9787	2.56272
$857$	31.6525	1.08123	0.540614	−	0.841271i	$-0.318192\pi$
$857$	31.6525	1.08123	0.540614	+	0.841271i	$0.318192\pi$
$858$	60.9787	2.08178
$859$	−32.4721	−1.10793	−0.553967	−	0.832538i	$-0.686887\pi$
$859$	−32.4721	−1.10793	−0.553967	+	0.832538i	$0.686887\pi$
$860$	−185.061	−6.31052
$861$	14.5066	0.494383
$862$	61.5410	2.09610
$863$	−8.03444	−0.273496	−0.136748	−	0.990606i	$-0.543665\pi$
$863$	−8.03444	−0.273496	−0.136748	+	0.990606i	$0.543665\pi$
$864$	−10.8541	−0.369264
$865$	−43.1459	−1.46700
$866$	−26.5623	−0.902624
$867$	−10.1459	−0.344573
$868$	27.5410	0.934803
$869$	−10.4164	−0.353352
$870$	−34.4164	−1.16683
$871$	28.4164	0.962853
$872$	−1.09017	−0.0369178
$873$	−9.47214	−0.320583
$874$	−21.1803	−0.716436
$875$	−7.14590	−0.241575
$876$	39.2705	1.32683
$877$	9.41641	0.317970	0.158985	−	0.987281i	$-0.449178\pi$
$877$	9.41641	0.317970	0.158985	+	0.987281i	$0.449178\pi$
$878$	−20.5623	−0.693944
$879$	21.7426	0.733361
$880$	−102.644	−3.46014
$881$	−28.6525	−0.965326	−0.482663	−	0.875806i	$-0.660330\pi$
$881$	−28.6525	−0.965326	−0.482663	+	0.875806i	$0.660330\pi$
$882$	3.47214	0.116913
$883$	−14.1115	−0.474888	−0.237444	−	0.971401i	$-0.576310\pi$
$883$	−14.1115	−0.474888	−0.237444	+	0.971401i	$0.576310\pi$
$884$	85.2492	2.86724
$885$	−3.00000	−0.100844
$886$	1.14590	0.0384972
$887$	−50.2361	−1.68676	−0.843381	−	0.537316i	$-0.819438\pi$
$887$	−50.2361	−1.68676	−0.843381	+	0.537316i	$0.819438\pi$
$888$	−38.0344	−1.27635
$889$	6.02129	0.201947
$890$	47.8328	1.60336
$891$	3.47214	0.116321
$892$	−74.8328	−2.50559
$893$	28.4164	0.950919
$894$	57.6869	1.92934
$895$	39.5410	1.32171
$896$	2.59675	0.0867513
$897$	9.27051	0.309533
$898$	107.520	3.58798
$899$	10.4377	0.348117
$900$	19.4164	0.647214
$901$	−14.3262	−0.477276
$902$	55.3607	1.84331
$903$	−30.2705	−1.00734
$904$	−43.0689	−1.43245
$905$	25.6869	0.853862
$906$	−23.1803	−0.770115
$907$	−7.58359	−0.251809	−0.125905	−	0.992042i	$-0.540183\pi$
$907$	−7.58359	−0.251809	−0.125905	+	0.992042i	$0.540183\pi$
$908$	−45.5410	−1.51133
$909$	−6.76393	−0.224345
$910$	125.498	4.16023
$911$	14.9656	0.495831	0.247916	−	0.968782i	$-0.420254\pi$
$911$	14.9656	0.495831	0.247916	+	0.968782i	$0.420254\pi$
$912$	−57.6869	−1.91020
$913$	−3.97871	−0.131676
$914$	−3.00000	−0.0992312
$915$	−36.2705	−1.19907
$916$	135.812	4.48734
$917$	−16.1115	−0.532047
$918$	6.85410	0.226219
$919$	32.2918	1.06521	0.532604	−	0.846365i	$-0.321214\pi$
$919$	32.2918	1.06521	0.532604	+	0.846365i	$0.321214\pi$
$920$	−30.9787	−1.02134
$921$	−12.0000	−0.395413
$922$	−47.9787	−1.58009
$923$	−28.4164	−0.935337
$924$	−40.1459	−1.32070
$925$	20.3607	0.669455
$926$	47.2148	1.55157
$927$	−19.2361	−0.631795
$928$	47.5623	1.56131
$929$	3.36068	0.110260	0.0551302	−	0.998479i	$-0.482443\pi$
$929$	3.36068	0.110260	0.0551302	+	0.998479i	$0.482443\pi$
$930$	−18.7082	−0.613466
$931$	7.76393	0.254453
$932$	25.4164	0.832542
$933$	30.9787	1.01420
$934$	−65.3050	−2.13684
$935$	27.2705	0.891841
$936$	50.1246	1.63837
$937$	1.94427	0.0635166	0.0317583	−	0.999496i	$-0.489889\pi$
$937$	1.94427	0.0635166	0.0317583	+	0.999496i	$0.489889\pi$
$938$	−26.4164	−0.862526
$939$	−27.5623	−0.899462
$940$	70.6869	2.30555
$941$	−3.76393	−0.122701	−0.0613503	−	0.998116i	$-0.519541\pi$
$941$	−3.76393	−0.122701	−0.0613503	+	0.998116i	$0.519541\pi$
$942$	−20.7984	−0.677648
$943$	8.41641	0.274076
$944$	9.85410	0.320724
$945$	7.14590	0.232456
$946$	−115.520	−3.75587
$947$	−6.45085	−0.209624	−0.104812	−	0.994492i	$-0.533424\pi$
$947$	−6.45085	−0.209624	−0.104812	+	0.994492i	$0.533424\pi$
$948$	−14.5623	−0.472962
$949$	−54.2705	−1.76170
$950$	61.3050	1.98900
$951$	3.00000	0.0972817
$952$	−46.5967	−1.51021
$953$	−22.4721	−0.727944	−0.363972	−	0.931410i	$-0.618580\pi$
$953$	−22.4721	−0.727944	−0.363972	+	0.931410i	$0.618580\pi$
$954$	−14.3262	−0.463829
$955$	56.1246	1.81615
$956$	−25.6869	−0.830774
$957$	−15.2148	−0.491824
$958$	−37.9787	−1.22704
$959$	10.7852	0.348273
$960$	−26.1246	−0.843168
$961$	−25.3262	−0.816975
$962$	89.3951	2.88221
$963$	−10.0344	−0.323355
$964$	−31.4164	−1.01185
$965$	1.75078	0.0563595
$966$	−8.61803	−0.277281
$967$	42.9787	1.38210	0.691051	−	0.722806i	$-0.257148\pi$
$967$	42.9787	1.38210	0.691051	+	0.722806i	$0.257148\pi$
$968$	−7.88854	−0.253547
$969$	15.3262	0.492350
$970$	−74.3951	−2.38868
$971$	−47.9230	−1.53792	−0.768961	−	0.639296i	$-0.779226\pi$
$971$	−47.9230	−1.53792	−0.768961	+	0.639296i	$0.779226\pi$
$972$	4.85410	0.155695
$973$	44.5623	1.42860
$974$	−30.2705	−0.969930
$975$	−26.8328	−0.859338
$976$	119.138	3.81351
$977$	21.0689	0.674053	0.337027	−	0.941495i	$-0.390579\pi$
$977$	21.0689	0.674053	0.337027	+	0.941495i	$0.390579\pi$
$978$	25.1803	0.805178
$979$	21.1459	0.675826
$980$	19.3131	0.616934
$981$	0.145898	0.00465817
$982$	−65.2492	−2.08219
$983$	−53.8328	−1.71700	−0.858500	−	0.512813i	$-0.828603\pi$
$983$	−53.8328	−1.71700	−0.858500	+	0.512813i	$0.828603\pi$
$984$	45.5066	1.45070
$985$	−30.5410	−0.973118
$986$	−30.0344	−0.956491
$987$	11.5623	0.368032
$988$	190.623	6.06453
$989$	−17.5623	−0.558449
$990$	27.2705	0.866714
$991$	10.1459	0.322295	0.161148	−	0.986930i	$-0.448481\pi$
$991$	10.1459	0.322295	0.161148	+	0.986930i	$0.448481\pi$
$992$	25.8541	0.820869
$993$	14.7639	0.468519
$994$	26.4164	0.837878
$995$	40.5197	1.28456
$996$	−5.56231	−0.176248
$997$	8.27051	0.261930	0.130965	−	0.991387i	$-0.458192\pi$
$997$	8.27051	0.261930	0.130965	+	0.991387i	$0.458192\pi$
$998$	−13.0902	−0.414362
$999$	5.09017	0.161046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.a.a.1.1	✓	2
3.2	odd	2		531.2.a.c.1.2		2
4.3	odd	2		2832.2.a.h.1.1		2
5.4	even	2		4425.2.a.u.1.2		2
7.6	odd	2		8673.2.a.j.1.1		2
12.11	even	2		8496.2.a.bg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.a.1.1	✓	2	1.1	even	1	trivial
531.2.a.c.1.2		2	3.2	odd	2
2832.2.a.h.1.1		2	4.3	odd	2
4425.2.a.u.1.2		2	5.4	even	2
8496.2.a.bg.1.1		2	12.11	even	2
8673.2.a.j.1.1		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.00000 q^{5} -2.61803 q^{6} -2.38197 q^{7} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.00000 q^{5} -2.61803 q^{6} -2.38197 q^{7} -7.47214 q^{8} +1.00000 q^{9} +7.85410 q^{10} +3.47214 q^{11} +4.85410 q^{12} -6.70820 q^{13} +6.23607 q^{14} -3.00000 q^{15} +9.85410 q^{16} -2.61803 q^{17} -2.61803 q^{18} -5.85410 q^{19} -14.5623 q^{20} -2.38197 q^{21} -9.09017 q^{22} -1.38197 q^{23} -7.47214 q^{24} +4.00000 q^{25} +17.5623 q^{26} +1.00000 q^{27} -11.5623 q^{28} -4.38197 q^{29} +7.85410 q^{30} -2.38197 q^{31} -10.8541 q^{32} +3.47214 q^{33} +6.85410 q^{34} +7.14590 q^{35} +4.85410 q^{36} +5.09017 q^{37} +15.3262 q^{38} -6.70820 q^{39} +22.4164 q^{40} -6.09017 q^{41} +6.23607 q^{42} +12.7082 q^{43} +16.8541 q^{44} -3.00000 q^{45} +3.61803 q^{46} -4.85410 q^{47} +9.85410 q^{48} -1.32624 q^{49} -10.4721 q^{50} -2.61803 q^{51} -32.5623 q^{52} +5.47214 q^{53} -2.61803 q^{54} -10.4164 q^{55} +17.7984 q^{56} -5.85410 q^{57} +11.4721 q^{58} +1.00000 q^{59} -14.5623 q^{60} +12.0902 q^{61} +6.23607 q^{62} -2.38197 q^{63} +8.70820 q^{64} +20.1246 q^{65} -9.09017 q^{66} -4.23607 q^{67} -12.7082 q^{68} -1.38197 q^{69} -18.7082 q^{70} +4.23607 q^{71} -7.47214 q^{72} +8.09017 q^{73} -13.3262 q^{74} +4.00000 q^{75} -28.4164 q^{76} -8.27051 q^{77} +17.5623 q^{78} -3.00000 q^{79} -29.5623 q^{80} +1.00000 q^{81} +15.9443 q^{82} -1.14590 q^{83} -11.5623 q^{84} +7.85410 q^{85} -33.2705 q^{86} -4.38197 q^{87} -25.9443 q^{88} +6.09017 q^{89} +7.85410 q^{90} +15.9787 q^{91} -6.70820 q^{92} -2.38197 q^{93} +12.7082 q^{94} +17.5623 q^{95} -10.8541 q^{96} -9.47214 q^{97} +3.47214 q^{98} +3.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 6 * q^5 - 3 * q^6 - 7 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} - 7 q^{7} - 6 q^{8} + 2 q^{9} + 9 q^{10} - 2 q^{11} + 3 q^{12} + 8 q^{14} - 6 q^{15} + 13 q^{16} - 3 q^{17} - 3 q^{18} - 5 q^{19} - 9 q^{20} - 7 q^{21} - 7 q^{22} - 5 q^{23} - 6 q^{24} + 8 q^{25} + 15 q^{26} + 2 q^{27} - 3 q^{28} - 11 q^{29} + 9 q^{30} - 7 q^{31} - 15 q^{32} - 2 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - q^{37} + 15 q^{38} + 18 q^{40} - q^{41} + 8 q^{42} + 12 q^{43} + 27 q^{44} - 6 q^{45} + 5 q^{46} - 3 q^{47} + 13 q^{48} + 13 q^{49} - 12 q^{50} - 3 q^{51} - 45 q^{52} + 2 q^{53} - 3 q^{54} + 6 q^{55} + 11 q^{56} - 5 q^{57} + 14 q^{58} + 2 q^{59} - 9 q^{60} + 13 q^{61} + 8 q^{62} - 7 q^{63} + 4 q^{64} - 7 q^{66} - 4 q^{67} - 12 q^{68} - 5 q^{69} - 24 q^{70} + 4 q^{71} - 6 q^{72} + 5 q^{73} - 11 q^{74} + 8 q^{75} - 30 q^{76} + 17 q^{77} + 15 q^{78} - 6 q^{79} - 39 q^{80} + 2 q^{81} + 14 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} - 33 q^{86} - 11 q^{87} - 34 q^{88} + q^{89} + 9 q^{90} - 15 q^{91} - 7 q^{93} + 12 q^{94} + 15 q^{95} - 15 q^{96} - 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 6 * q^5 - 3 * q^6 - 7 * q^7 - 6 * q^8 + 2 * q^9 + 9 * q^10 - 2 * q^11 + 3 * q^12 + 8 * q^14 - 6 * q^15 + 13 * q^16 - 3 * q^17 - 3 * q^18 - 5 * q^19 - 9 * q^20 - 7 * q^21 - 7 * q^22 - 5 * q^23 - 6 * q^24 + 8 * q^25 + 15 * q^26 + 2 * q^27 - 3 * q^28 - 11 * q^29 + 9 * q^30 - 7 * q^31 - 15 * q^32 - 2 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - q^37 + 15 * q^38 + 18 * q^40 - q^41 + 8 * q^42 + 12 * q^43 + 27 * q^44 - 6 * q^45 + 5 * q^46 - 3 * q^47 + 13 * q^48 + 13 * q^49 - 12 * q^50 - 3 * q^51 - 45 * q^52 + 2 * q^53 - 3 * q^54 + 6 * q^55 + 11 * q^56 - 5 * q^57 + 14 * q^58 + 2 * q^59 - 9 * q^60 + 13 * q^61 + 8 * q^62 - 7 * q^63 + 4 * q^64 - 7 * q^66 - 4 * q^67 - 12 * q^68 - 5 * q^69 - 24 * q^70 + 4 * q^71 - 6 * q^72 + 5 * q^73 - 11 * q^74 + 8 * q^75 - 30 * q^76 + 17 * q^77 + 15 * q^78 - 6 * q^79 - 39 * q^80 + 2 * q^81 + 14 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 - 33 * q^86 - 11 * q^87 - 34 * q^88 + q^89 + 9 * q^90 - 15 * q^91 - 7 * q^93 + 12 * q^94 + 15 * q^95 - 15 * q^96 - 10 * q^97 - 2 * q^98 - 2 * q^99

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