LMFDB - Embedded newform 786.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [786,2,Mod(1,786)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(786, 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("786.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 786 = 2 \cdot 3 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	786.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:	$6.27624159887$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	786.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} -1.00000 q^{6} +3.48929 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} -1.00000 q^{6} +3.48929 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.14637 q^{10} -4.68585 q^{11} +1.00000 q^{12} +2.00000 q^{13} -3.48929 q^{14} +1.14637 q^{15} +1.00000 q^{16} +4.68585 q^{17} -1.00000 q^{18} +5.19656 q^{19} +1.14637 q^{20} +3.48929 q^{21} +4.68585 q^{22} +4.68585 q^{23} -1.00000 q^{24} -3.68585 q^{25} -2.00000 q^{26} +1.00000 q^{27} +3.48929 q^{28} -8.46787 q^{29} -1.14637 q^{30} -6.81079 q^{31} -1.00000 q^{32} -4.68585 q^{33} -4.68585 q^{34} +4.00000 q^{35} +1.00000 q^{36} +4.05019 q^{37} -5.19656 q^{38} +2.00000 q^{39} -1.14637 q^{40} -5.48929 q^{41} -3.48929 q^{42} +4.97858 q^{43} -4.68585 q^{44} +1.14637 q^{45} -4.68585 q^{46} +5.37169 q^{47} +1.00000 q^{48} +5.17513 q^{49} +3.68585 q^{50} +4.68585 q^{51} +2.00000 q^{52} +1.83221 q^{53} -1.00000 q^{54} -5.37169 q^{55} -3.48929 q^{56} +5.19656 q^{57} +8.46787 q^{58} +7.66442 q^{59} +1.14637 q^{60} +1.31415 q^{61} +6.81079 q^{62} +3.48929 q^{63} +1.00000 q^{64} +2.29273 q^{65} +4.68585 q^{66} -0.175135 q^{67} +4.68585 q^{68} +4.68585 q^{69} -4.00000 q^{70} -1.27131 q^{71} -1.00000 q^{72} +2.00000 q^{73} -4.05019 q^{74} -3.68585 q^{75} +5.19656 q^{76} -16.3503 q^{77} -2.00000 q^{78} +0.753250 q^{79} +1.14637 q^{80} +1.00000 q^{81} +5.48929 q^{82} -15.5468 q^{83} +3.48929 q^{84} +5.37169 q^{85} -4.97858 q^{86} -8.46787 q^{87} +4.68585 q^{88} +9.15371 q^{89} -1.14637 q^{90} +6.97858 q^{91} +4.68585 q^{92} -6.81079 q^{93} -5.37169 q^{94} +5.95715 q^{95} -1.00000 q^{96} +16.6430 q^{97} -5.17513 q^{98} -4.68585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} - 3 q^{18} + 11 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} + 2 q^{23} - 3 q^{24} + q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 3 q^{29} - 2 q^{30} + 8 q^{31} - 3 q^{32} - 2 q^{33} - 2 q^{34} + 12 q^{35} + 3 q^{36} + 9 q^{37} - 11 q^{38} + 6 q^{39} - 2 q^{40} - 9 q^{41} - 3 q^{42} - 2 q^{44} + 2 q^{45} - 2 q^{46} - 8 q^{47} + 3 q^{48} - 4 q^{49} - q^{50} + 2 q^{51} + 6 q^{52} - 8 q^{53} - 3 q^{54} + 8 q^{55} - 3 q^{56} + 11 q^{57} + 3 q^{58} - 4 q^{59} + 2 q^{60} + 16 q^{61} - 8 q^{62} + 3 q^{63} + 3 q^{64} + 4 q^{65} + 2 q^{66} + 19 q^{67} + 2 q^{68} + 2 q^{69} - 12 q^{70} + 14 q^{71} - 3 q^{72} + 6 q^{73} - 9 q^{74} + q^{75} + 11 q^{76} - 10 q^{77} - 6 q^{78} + 10 q^{79} + 2 q^{80} + 3 q^{81} + 9 q^{82} - 3 q^{83} + 3 q^{84} - 8 q^{85} - 3 q^{87} + 2 q^{88} - 7 q^{89} - 2 q^{90} + 6 q^{91} + 2 q^{92} + 8 q^{93} + 8 q^{94} - 12 q^{95} - 3 q^{96} + 8 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 - 3 * q^18 + 11 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 + 2 * q^23 - 3 * q^24 + q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 2 * q^30 + 8 * q^31 - 3 * q^32 - 2 * q^33 - 2 * q^34 + 12 * q^35 + 3 * q^36 + 9 * q^37 - 11 * q^38 + 6 * q^39 - 2 * q^40 - 9 * q^41 - 3 * q^42 - 2 * q^44 + 2 * q^45 - 2 * q^46 - 8 * q^47 + 3 * q^48 - 4 * q^49 - q^50 + 2 * q^51 + 6 * q^52 - 8 * q^53 - 3 * q^54 + 8 * q^55 - 3 * q^56 + 11 * q^57 + 3 * q^58 - 4 * q^59 + 2 * q^60 + 16 * q^61 - 8 * q^62 + 3 * q^63 + 3 * q^64 + 4 * q^65 + 2 * q^66 + 19 * q^67 + 2 * q^68 + 2 * q^69 - 12 * q^70 + 14 * q^71 - 3 * q^72 + 6 * q^73 - 9 * q^74 + q^75 + 11 * q^76 - 10 * q^77 - 6 * q^78 + 10 * q^79 + 2 * q^80 + 3 * q^81 + 9 * q^82 - 3 * q^83 + 3 * q^84 - 8 * q^85 - 3 * q^87 + 2 * q^88 - 7 * q^89 - 2 * q^90 + 6 * q^91 + 2 * q^92 + 8 * q^93 + 8 * q^94 - 12 * q^95 - 3 * q^96 + 8 * q^97 + 4 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.14637	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$5$	1.14637	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$6$	−1.00000	−0.408248
$7$	3.48929	1.31883	0.659414	−	0.751780i	$-0.270805\pi$
$7$	3.48929	1.31883	0.659414	+	0.751780i	$0.270805\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.14637	−0.362513
$11$	−4.68585	−1.41284	−0.706418	−	0.707795i	$-0.749690\pi$
$11$	−4.68585	−1.41284	−0.706418	+	0.707795i	$0.749690\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−3.48929	−0.932552
$15$	1.14637	0.295990
$16$	1.00000	0.250000
$17$	4.68585	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$17$	4.68585	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$18$	−1.00000	−0.235702
$19$	5.19656	1.19217	0.596086	−	0.802921i	$-0.296722\pi$
$19$	5.19656	1.19217	0.596086	+	0.802921i	$0.296722\pi$
$20$	1.14637	0.256335
$21$	3.48929	0.761425
$22$	4.68585	0.999026
$23$	4.68585	0.977066	0.488533	−	0.872545i	$-0.337532\pi$
$23$	4.68585	0.977066	0.488533	+	0.872545i	$0.337532\pi$
$24$	−1.00000	−0.204124
$25$	−3.68585	−0.737169
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	3.48929	0.659414
$29$	−8.46787	−1.57244	−0.786222	−	0.617945i	$-0.787966\pi$
$29$	−8.46787	−1.57244	−0.786222	+	0.617945i	$0.787966\pi$
$30$	−1.14637	−0.209297
$31$	−6.81079	−1.22325	−0.611627	−	0.791146i	$-0.709485\pi$
$31$	−6.81079	−1.22325	−0.611627	+	0.791146i	$0.709485\pi$
$32$	−1.00000	−0.176777
$33$	−4.68585	−0.815701
$34$	−4.68585	−0.803616
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	4.05019	0.665847	0.332924	−	0.942954i	$-0.391965\pi$
$37$	4.05019	0.665847	0.332924	+	0.942954i	$0.391965\pi$
$38$	−5.19656	−0.842993
$39$	2.00000	0.320256
$40$	−1.14637	−0.181256
$41$	−5.48929	−0.857283	−0.428641	−	0.903475i	$-0.641008\pi$
$41$	−5.48929	−0.857283	−0.428641	+	0.903475i	$0.641008\pi$
$42$	−3.48929	−0.538409
$43$	4.97858	0.759226	0.379613	−	0.925145i	$-0.376057\pi$
$43$	4.97858	0.759226	0.379613	+	0.925145i	$0.376057\pi$
$44$	−4.68585	−0.706418
$45$	1.14637	0.170890
$46$	−4.68585	−0.690890
$47$	5.37169	0.783542	0.391771	−	0.920063i	$-0.371863\pi$
$47$	5.37169	0.783542	0.391771	+	0.920063i	$0.371863\pi$
$48$	1.00000	0.144338
$49$	5.17513	0.739305
$50$	3.68585	0.521257
$51$	4.68585	0.656150
$52$	2.00000	0.277350
$53$	1.83221	0.251674	0.125837	−	0.992051i	$-0.459838\pi$
$53$	1.83221	0.251674	0.125837	+	0.992051i	$0.459838\pi$
$54$	−1.00000	−0.136083
$55$	−5.37169	−0.724319
$56$	−3.48929	−0.466276
$57$	5.19656	0.688301
$58$	8.46787	1.11189
$59$	7.66442	0.997823	0.498911	−	0.866653i	$-0.333733\pi$
$59$	7.66442	0.997823	0.498911	+	0.866653i	$0.333733\pi$
$60$	1.14637	0.147995
$61$	1.31415	0.168260	0.0841301	−	0.996455i	$-0.473189\pi$
$61$	1.31415	0.168260	0.0841301	+	0.996455i	$0.473189\pi$
$62$	6.81079	0.864971
$63$	3.48929	0.439609
$64$	1.00000	0.125000
$65$	2.29273	0.284378
$66$	4.68585	0.576788
$67$	−0.175135	−0.0213961	−0.0106981	−	0.999943i	$-0.503405\pi$
$67$	−0.175135	−0.0213961	−0.0106981	+	0.999943i	$0.503405\pi$
$68$	4.68585	0.568242
$69$	4.68585	0.564110
$70$	−4.00000	−0.478091
$71$	−1.27131	−0.150877	−0.0754383	−	0.997150i	$-0.524036\pi$
$71$	−1.27131	−0.150877	−0.0754383	+	0.997150i	$0.524036\pi$
$72$	−1.00000	−0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−4.05019	−0.470825
$75$	−3.68585	−0.425605
$76$	5.19656	0.596086
$77$	−16.3503	−1.86329
$78$	−2.00000	−0.226455
$79$	0.753250	0.0847473	0.0423736	−	0.999102i	$-0.486508\pi$
$79$	0.753250	0.0847473	0.0423736	+	0.999102i	$0.486508\pi$
$80$	1.14637	0.128168
$81$	1.00000	0.111111
$82$	5.48929	0.606191
$83$	−15.5468	−1.70649	−0.853243	−	0.521514i	$-0.825368\pi$
$83$	−15.5468	−1.70649	−0.853243	+	0.521514i	$0.825368\pi$
$84$	3.48929	0.380713
$85$	5.37169	0.582642
$86$	−4.97858	−0.536854
$87$	−8.46787	−0.907850
$88$	4.68585	0.499513
$89$	9.15371	0.970292	0.485146	−	0.874433i	$-0.338767\pi$
$89$	9.15371	0.970292	0.485146	+	0.874433i	$0.338767\pi$
$90$	−1.14637	−0.120838
$91$	6.97858	0.731554
$92$	4.68585	0.488533
$93$	−6.81079	−0.706246
$94$	−5.37169	−0.554048
$95$	5.95715	0.611191
$96$	−1.00000	−0.102062
$97$	16.6430	1.68984	0.844920	−	0.534892i	$-0.179648\pi$
$97$	16.6430	1.68984	0.844920	+	0.534892i	$0.179648\pi$
$98$	−5.17513	−0.522768
$99$	−4.68585	−0.470945
$100$	−3.68585	−0.368585
$101$	−6.51806	−0.648571	−0.324285	−	0.945959i	$-0.605124\pi$
$101$	−6.51806	−0.648571	−0.324285	+	0.945959i	$0.605124\pi$
$102$	−4.68585	−0.463968
$103$	−6.12494	−0.603509	−0.301754	−	0.953386i	$-0.597572\pi$
$103$	−6.12494	−0.603509	−0.301754	+	0.953386i	$0.597572\pi$
$104$	−2.00000	−0.196116
$105$	4.00000	0.390360
$106$	−1.83221	−0.177960
$107$	4.58546	0.443293	0.221647	−	0.975127i	$-0.428857\pi$
$107$	4.58546	0.443293	0.221647	+	0.975127i	$0.428857\pi$
$108$	1.00000	0.0962250
$109$	−0.978577	−0.0937307	−0.0468653	−	0.998901i	$-0.514923\pi$
$109$	−0.978577	−0.0937307	−0.0468653	+	0.998901i	$0.514923\pi$
$110$	5.37169	0.512171
$111$	4.05019	0.384427
$112$	3.48929	0.329707
$113$	−1.38890	−0.130657	−0.0653286	−	0.997864i	$-0.520810\pi$
$113$	−1.38890	−0.130657	−0.0653286	+	0.997864i	$0.520810\pi$
$114$	−5.19656	−0.486702
$115$	5.37169	0.500913
$116$	−8.46787	−0.786222
$117$	2.00000	0.184900
$118$	−7.66442	−0.705567
$119$	16.3503	1.49883
$120$	−1.14637	−0.104648
$121$	10.9572	0.996105
$122$	−1.31415	−0.118978
$123$	−5.48929	−0.494952
$124$	−6.81079	−0.611627
$125$	−9.95715	−0.890595
$126$	−3.48929	−0.310851
$127$	5.53948	0.491549	0.245775	−	0.969327i	$-0.420958\pi$
$127$	5.53948	0.491549	0.245775	+	0.969327i	$0.420958\pi$
$128$	−1.00000	−0.0883883
$129$	4.97858	0.438339
$130$	−2.29273	−0.201086
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−4.68585	−0.407851
$133$	18.1323	1.57227
$134$	0.175135	0.0151293
$135$	1.14637	0.0986634
$136$	−4.68585	−0.401808
$137$	−18.9357	−1.61779	−0.808894	−	0.587954i	$-0.799934\pi$
$137$	−18.9357	−1.61779	−0.808894	+	0.587954i	$0.799934\pi$
$138$	−4.68585	−0.398886
$139$	−21.0361	−1.78426	−0.892130	−	0.451779i	$-0.850790\pi$
$139$	−21.0361	−1.78426	−0.892130	+	0.451779i	$0.850790\pi$
$140$	4.00000	0.338062
$141$	5.37169	0.452378
$142$	1.27131	0.106686
$143$	−9.37169	−0.783700
$144$	1.00000	0.0833333
$145$	−9.70727	−0.806145
$146$	−2.00000	−0.165521
$147$	5.17513	0.426838
$148$	4.05019	0.332924
$149$	−4.87819	−0.399637	−0.199819	−	0.979833i	$-0.564035\pi$
$149$	−4.87819	−0.399637	−0.199819	+	0.979833i	$0.564035\pi$
$150$	3.68585	0.300948
$151$	5.88240	0.478703	0.239352	−	0.970933i	$-0.423065\pi$
$151$	5.88240	0.478703	0.239352	+	0.970933i	$0.423065\pi$
$152$	−5.19656	−0.421496
$153$	4.68585	0.378828
$154$	16.3503	1.31754
$155$	−7.80765	−0.627126
$156$	2.00000	0.160128
$157$	−19.6142	−1.56539	−0.782693	−	0.622408i	$-0.786155\pi$
$157$	−19.6142	−1.56539	−0.782693	+	0.622408i	$0.786155\pi$
$158$	−0.753250	−0.0599254
$159$	1.83221	0.145304
$160$	−1.14637	−0.0906281
$161$	16.3503	1.28858
$162$	−1.00000	−0.0785674
$163$	7.66442	0.600324	0.300162	−	0.953888i	$-0.402959\pi$
$163$	7.66442	0.600324	0.300162	+	0.953888i	$0.402959\pi$
$164$	−5.48929	−0.428641
$165$	−5.37169	−0.418186
$166$	15.5468	1.20667
$167$	4.92839	0.381370	0.190685	−	0.981651i	$-0.438929\pi$
$167$	4.92839	0.381370	0.190685	+	0.981651i	$0.438929\pi$
$168$	−3.48929	−0.269204
$169$	−9.00000	−0.692308
$170$	−5.37169	−0.411990
$171$	5.19656	0.397391
$172$	4.97858	0.379613
$173$	−12.9038	−0.981060	−0.490530	−	0.871424i	$-0.663197\pi$
$173$	−12.9038	−0.981060	−0.490530	+	0.871424i	$0.663197\pi$
$174$	8.46787	0.641947
$175$	−12.8610	−0.972199
$176$	−4.68585	−0.353209
$177$	7.66442	0.576093
$178$	−9.15371	−0.686100
$179$	9.27131	0.692970	0.346485	−	0.938055i	$-0.387375\pi$
$179$	9.27131	0.692970	0.346485	+	0.938055i	$0.387375\pi$
$180$	1.14637	0.0854450
$181$	−22.6184	−1.68122	−0.840608	−	0.541644i	$-0.817802\pi$
$181$	−22.6184	−1.68122	−0.840608	+	0.541644i	$0.817802\pi$
$182$	−6.97858	−0.517287
$183$	1.31415	0.0971450
$184$	−4.68585	−0.345445
$185$	4.64300	0.341360
$186$	6.81079	0.499391
$187$	−21.9572	−1.60567
$188$	5.37169	0.391771
$189$	3.48929	0.253808
$190$	−5.95715	−0.432177
$191$	4.44331	0.321506	0.160753	−	0.986995i	$-0.448608\pi$
$191$	4.44331	0.321506	0.160753	+	0.986995i	$0.448608\pi$
$192$	1.00000	0.0721688
$193$	−16.8610	−1.21368	−0.606840	−	0.794824i	$-0.707563\pi$
$193$	−16.8610	−1.21368	−0.606840	+	0.794824i	$0.707563\pi$
$194$	−16.6430	−1.19490
$195$	2.29273	0.164186
$196$	5.17513	0.369652
$197$	−12.5682	−0.895451	−0.447725	−	0.894171i	$-0.647766\pi$
$197$	−12.5682	−0.895451	−0.447725	+	0.894171i	$0.647766\pi$
$198$	4.68585	0.333009
$199$	−1.33871	−0.0948988	−0.0474494	−	0.998874i	$-0.515109\pi$
$199$	−1.33871	−0.0948988	−0.0474494	+	0.998874i	$0.515109\pi$
$200$	3.68585	0.260629
$201$	−0.175135	−0.0123531
$202$	6.51806	0.458609
$203$	−29.5468	−2.07378
$204$	4.68585	0.328075
$205$	−6.29273	−0.439503
$206$	6.12494	0.426745
$207$	4.68585	0.325689
$208$	2.00000	0.138675
$209$	−24.3503	−1.68434
$210$	−4.00000	−0.276026
$211$	6.58546	0.453362	0.226681	−	0.973969i	$-0.427213\pi$
$211$	6.58546	0.453362	0.226681	+	0.973969i	$0.427213\pi$
$212$	1.83221	0.125837
$213$	−1.27131	−0.0871086
$214$	−4.58546	−0.313456
$215$	5.70727	0.389233
$216$	−1.00000	−0.0680414
$217$	−23.7648	−1.61326
$218$	0.978577	0.0662776
$219$	2.00000	0.135147
$220$	−5.37169	−0.362159
$221$	9.37169	0.630408
$222$	−4.05019	−0.271831
$223$	16.7679	1.12286	0.561432	−	0.827523i	$-0.310251\pi$
$223$	16.7679	1.12286	0.561432	+	0.827523i	$0.310251\pi$
$224$	−3.48929	−0.233138
$225$	−3.68585	−0.245723
$226$	1.38890	0.0923885
$227$	18.9185	1.25567	0.627833	−	0.778348i	$-0.283942\pi$
$227$	18.9185	1.25567	0.627833	+	0.778348i	$0.283942\pi$
$228$	5.19656	0.344150
$229$	−21.2467	−1.40402	−0.702012	−	0.712165i	$-0.747715\pi$
$229$	−21.2467	−1.40402	−0.702012	+	0.712165i	$0.747715\pi$
$230$	−5.37169	−0.354199
$231$	−16.3503	−1.07577
$232$	8.46787	0.555943
$233$	20.1323	1.31891	0.659455	−	0.751744i	$-0.270787\pi$
$233$	20.1323	1.31891	0.659455	+	0.751744i	$0.270787\pi$
$234$	−2.00000	−0.130744
$235$	6.15792	0.401699
$236$	7.66442	0.498911
$237$	0.753250	0.0489289
$238$	−16.3503	−1.05983
$239$	−7.90696	−0.511459	−0.255729	−	0.966748i	$-0.582316\pi$
$239$	−7.90696	−0.511459	−0.255729	+	0.966748i	$0.582316\pi$
$240$	1.14637	0.0739976
$241$	−16.0575	−1.03436	−0.517178	−	0.855878i	$-0.673018\pi$
$241$	−16.0575	−1.03436	−0.517178	+	0.855878i	$0.673018\pi$
$242$	−10.9572	−0.704353
$243$	1.00000	0.0641500
$244$	1.31415	0.0841301
$245$	5.93260	0.379020
$246$	5.48929	0.349984
$247$	10.3931	0.661298
$248$	6.81079	0.432486
$249$	−15.5468	−0.985240
$250$	9.95715	0.629746
$251$	−27.8971	−1.76085	−0.880425	−	0.474186i	$-0.842742\pi$
$251$	−27.8971	−1.76085	−0.880425	+	0.474186i	$0.842742\pi$
$252$	3.48929	0.219805
$253$	−21.9572	−1.38043
$254$	−5.53948	−0.347578
$255$	5.37169	0.336388
$256$	1.00000	0.0625000
$257$	−28.0147	−1.74751	−0.873754	−	0.486368i	$-0.838322\pi$
$257$	−28.0147	−1.74751	−0.873754	+	0.486368i	$0.838322\pi$
$258$	−4.97858	−0.309953
$259$	14.1323	0.878138
$260$	2.29273	0.142189
$261$	−8.46787	−0.524148
$262$	1.00000	0.0617802
$263$	13.2039	0.814188	0.407094	−	0.913386i	$-0.366542\pi$
$263$	13.2039	0.814188	0.407094	+	0.913386i	$0.366542\pi$
$264$	4.68585	0.288394
$265$	2.10038	0.129026
$266$	−18.1323	−1.11176
$267$	9.15371	0.560198
$268$	−0.175135	−0.0106981
$269$	20.7104	1.26274	0.631368	−	0.775484i	$-0.282494\pi$
$269$	20.7104	1.26274	0.631368	+	0.775484i	$0.282494\pi$
$270$	−1.14637	−0.0697656
$271$	−22.9933	−1.39674	−0.698371	−	0.715736i	$-0.746091\pi$
$271$	−22.9933	−1.39674	−0.698371	+	0.715736i	$0.746091\pi$
$272$	4.68585	0.284121
$273$	6.97858	0.422363
$274$	18.9357	1.14395
$275$	17.2713	1.04150
$276$	4.68585	0.282055
$277$	2.35027	0.141214	0.0706070	−	0.997504i	$-0.477506\pi$
$277$	2.35027	0.141214	0.0706070	+	0.997504i	$0.477506\pi$
$278$	21.0361	1.26166
$279$	−6.81079	−0.407751
$280$	−4.00000	−0.239046
$281$	25.5296	1.52297	0.761485	−	0.648183i	$-0.224471\pi$
$281$	25.5296	1.52297	0.761485	+	0.648183i	$0.224471\pi$
$282$	−5.37169	−0.319880
$283$	−9.91431	−0.589344	−0.294672	−	0.955598i	$-0.595210\pi$
$283$	−9.91431	−0.589344	−0.294672	+	0.955598i	$0.595210\pi$
$284$	−1.27131	−0.0754383
$285$	5.95715	0.352871
$286$	9.37169	0.554160
$287$	−19.1537	−1.13061
$288$	−1.00000	−0.0589256
$289$	4.95715	0.291597
$290$	9.70727	0.570030
$291$	16.6430	0.975630
$292$	2.00000	0.117041
$293$	12.8782	0.752352	0.376176	−	0.926548i	$-0.377239\pi$
$293$	12.8782	0.752352	0.376176	+	0.926548i	$0.377239\pi$
$294$	−5.17513	−0.301820
$295$	8.78623	0.511554
$296$	−4.05019	−0.235413
$297$	−4.68585	−0.271900
$298$	4.87819	0.282586
$299$	9.37169	0.541979
$300$	−3.68585	−0.212802
$301$	17.3717	1.00129
$302$	−5.88240	−0.338494
$303$	−6.51806	−0.374453
$304$	5.19656	0.298043
$305$	1.50650	0.0862620
$306$	−4.68585	−0.267872
$307$	33.5296	1.91364	0.956818	−	0.290687i	$-0.0938839\pi$
$307$	33.5296	1.91364	0.956818	+	0.290687i	$0.0938839\pi$
$308$	−16.3503	−0.931643
$309$	−6.12494	−0.348436
$310$	7.80765	0.443445
$311$	22.4605	1.27362	0.636810	−	0.771021i	$-0.280254\pi$
$311$	22.4605	1.27362	0.636810	+	0.771021i	$0.280254\pi$
$312$	−2.00000	−0.113228
$313$	−30.2499	−1.70982	−0.854912	−	0.518773i	$-0.826389\pi$
$313$	−30.2499	−1.70982	−0.854912	+	0.518773i	$0.826389\pi$
$314$	19.6142	1.10690
$315$	4.00000	0.225374
$316$	0.753250	0.0423736
$317$	−26.6184	−1.49504	−0.747520	−	0.664239i	$-0.768756\pi$
$317$	−26.6184	−1.49504	−0.747520	+	0.664239i	$0.768756\pi$
$318$	−1.83221	−0.102745
$319$	39.6791	2.22160
$320$	1.14637	0.0640838
$321$	4.58546	0.255936
$322$	−16.3503	−0.911165
$323$	24.3503	1.35489
$324$	1.00000	0.0555556
$325$	−7.37169	−0.408908
$326$	−7.66442	−0.424493
$327$	−0.978577	−0.0541154
$328$	5.48929	0.303095
$329$	18.7434	1.03336
$330$	5.37169	0.295702
$331$	−22.4078	−1.23164	−0.615822	−	0.787885i	$-0.711176\pi$
$331$	−22.4078	−1.23164	−0.615822	+	0.787885i	$0.711176\pi$
$332$	−15.5468	−0.853243
$333$	4.05019	0.221949
$334$	−4.92839	−0.269669
$335$	−0.200768	−0.0109692
$336$	3.48929	0.190356
$337$	−21.3545	−1.16325	−0.581626	−	0.813456i	$-0.697583\pi$
$337$	−21.3545	−1.16325	−0.581626	+	0.813456i	$0.697583\pi$
$338$	9.00000	0.489535
$339$	−1.38890	−0.0754349
$340$	5.37169	0.291321
$341$	31.9143	1.72826
$342$	−5.19656	−0.280998
$343$	−6.36748	−0.343812
$344$	−4.97858	−0.268427
$345$	5.37169	0.289202
$346$	12.9038	0.693714
$347$	−5.78202	−0.310395	−0.155198	−	0.987883i	$-0.549601\pi$
$347$	−5.78202	−0.310395	−0.155198	+	0.987883i	$0.549601\pi$
$348$	−8.46787	−0.453925
$349$	−24.1997	−1.29538	−0.647690	−	0.761904i	$-0.724265\pi$
$349$	−24.1997	−1.29538	−0.647690	+	0.761904i	$0.724265\pi$
$350$	12.8610	0.687448
$351$	2.00000	0.106752
$352$	4.68585	0.249756
$353$	9.00421	0.479246	0.239623	−	0.970866i	$-0.422976\pi$
$353$	9.00421	0.479246	0.239623	+	0.970866i	$0.422976\pi$
$354$	−7.66442	−0.407360
$355$	−1.45738	−0.0773499
$356$	9.15371	0.485146
$357$	16.3503	0.865348
$358$	−9.27131	−0.490004
$359$	10.2927	0.543230	0.271615	−	0.962406i	$-0.412442\pi$
$359$	10.2927	0.543230	0.271615	+	0.962406i	$0.412442\pi$
$360$	−1.14637	−0.0604188
$361$	8.00421	0.421274
$362$	22.6184	1.18880
$363$	10.9572	0.575101
$364$	6.97858	0.365777
$365$	2.29273	0.120007
$366$	−1.31415	−0.0686919
$367$	2.36748	0.123582	0.0617908	−	0.998089i	$-0.480319\pi$
$367$	2.36748	0.123582	0.0617908	+	0.998089i	$0.480319\pi$
$368$	4.68585	0.244267
$369$	−5.48929	−0.285761
$370$	−4.64300	−0.241378
$371$	6.39312	0.331914
$372$	−6.81079	−0.353123
$373$	37.1611	1.92413	0.962063	−	0.272826i	$-0.0879584\pi$
$373$	37.1611	1.92413	0.962063	+	0.272826i	$0.0879584\pi$
$374$	21.9572	1.13538
$375$	−9.95715	−0.514185
$376$	−5.37169	−0.277024
$377$	−16.9357	−0.872235
$378$	−3.48929	−0.179470
$379$	−16.3074	−0.837656	−0.418828	−	0.908066i	$-0.637559\pi$
$379$	−16.3074	−0.837656	−0.418828	+	0.908066i	$0.637559\pi$
$380$	5.95715	0.305596
$381$	5.53948	0.283796
$382$	−4.44331	−0.227339
$383$	3.58233	0.183048	0.0915242	−	0.995803i	$-0.470826\pi$
$383$	3.58233	0.183048	0.0915242	+	0.995803i	$0.470826\pi$
$384$	−1.00000	−0.0510310
$385$	−18.7434	−0.955251
$386$	16.8610	0.858201
$387$	4.97858	0.253075
$388$	16.6430	0.844920
$389$	−16.9185	−0.857803	−0.428901	−	0.903351i	$-0.641099\pi$
$389$	−16.9185	−0.857803	−0.428901	+	0.903351i	$0.641099\pi$
$390$	−2.29273	−0.116097
$391$	21.9572	1.11042
$392$	−5.17513	−0.261384
$393$	−1.00000	−0.0504433
$394$	12.5682	0.633179
$395$	0.863500	0.0434474
$396$	−4.68585	−0.235473
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	1.33871	0.0671036
$399$	18.1323	0.907750
$400$	−3.68585	−0.184292
$401$	14.3503	0.716618	0.358309	−	0.933603i	$-0.383353\pi$
$401$	14.3503	0.716618	0.358309	+	0.933603i	$0.383353\pi$
$402$	0.175135	0.00873493
$403$	−13.6216	−0.678539
$404$	−6.51806	−0.324285
$405$	1.14637	0.0569634
$406$	29.5468	1.46638
$407$	−18.9786	−0.940733
$408$	−4.68585	−0.231984
$409$	24.1323	1.19326	0.596632	−	0.802515i	$-0.296505\pi$
$409$	24.1323	1.19326	0.596632	+	0.802515i	$0.296505\pi$
$410$	6.29273	0.310776
$411$	−18.9357	−0.934031
$412$	−6.12494	−0.301754
$413$	26.7434	1.31596
$414$	−4.68585	−0.230297
$415$	−17.8223	−0.874865
$416$	−2.00000	−0.0980581
$417$	−21.0361	−1.03014
$418$	24.3503	1.19101
$419$	−32.1067	−1.56851	−0.784256	−	0.620437i	$-0.786955\pi$
$419$	−32.1067	−1.56851	−0.784256	+	0.620437i	$0.786955\pi$
$420$	4.00000	0.195180
$421$	5.46365	0.266282	0.133141	−	0.991097i	$-0.457494\pi$
$421$	5.46365	0.266282	0.133141	+	0.991097i	$0.457494\pi$
$422$	−6.58546	−0.320575
$423$	5.37169	0.261181
$424$	−1.83221	−0.0889801
$425$	−17.2713	−0.837782
$426$	1.27131	0.0615951
$427$	4.58546	0.221906
$428$	4.58546	0.221647
$429$	−9.37169	−0.452470
$430$	−5.70727	−0.275229
$431$	9.28960	0.447464	0.223732	−	0.974651i	$-0.428176\pi$
$431$	9.28960	0.447464	0.223732	+	0.974651i	$0.428176\pi$
$432$	1.00000	0.0481125
$433$	23.0361	1.10705	0.553523	−	0.832834i	$-0.313283\pi$
$433$	23.0361	1.10705	0.553523	+	0.832834i	$0.313283\pi$
$434$	23.7648	1.14075
$435$	−9.70727	−0.465428
$436$	−0.978577	−0.0468653
$437$	24.3503	1.16483
$438$	−2.00000	−0.0955637
$439$	7.28852	0.347862	0.173931	−	0.984758i	$-0.444353\pi$
$439$	7.28852	0.347862	0.173931	+	0.984758i	$0.444353\pi$
$440$	5.37169	0.256085
$441$	5.17513	0.246435
$442$	−9.37169	−0.445766
$443$	−24.7262	−1.17478	−0.587388	−	0.809305i	$-0.699844\pi$
$443$	−24.7262	−1.17478	−0.587388	+	0.809305i	$0.699844\pi$
$444$	4.05019	0.192214
$445$	10.4935	0.497440
$446$	−16.7679	−0.793985
$447$	−4.87819	−0.230731
$448$	3.48929	0.164853
$449$	−0.921039	−0.0434665	−0.0217333	−	0.999764i	$-0.506918\pi$
$449$	−0.921039	−0.0434665	−0.0217333	+	0.999764i	$0.506918\pi$
$450$	3.68585	0.173752
$451$	25.7220	1.21120
$452$	−1.38890	−0.0653286
$453$	5.88240	0.276379
$454$	−18.9185	−0.887890
$455$	8.00000	0.375046
$456$	−5.19656	−0.243351
$457$	−36.4250	−1.70389	−0.851945	−	0.523631i	$-0.824577\pi$
$457$	−36.4250	−1.70389	−0.851945	+	0.523631i	$0.824577\pi$
$458$	21.2467	0.992795
$459$	4.68585	0.218717
$460$	5.37169	0.250456
$461$	33.9399	1.58074	0.790370	−	0.612629i	$-0.209888\pi$
$461$	33.9399	1.58074	0.790370	+	0.612629i	$0.209888\pi$
$462$	16.3503	0.760683
$463$	26.2744	1.22108	0.610538	−	0.791987i	$-0.290953\pi$
$463$	26.2744	1.22108	0.610538	+	0.791987i	$0.290953\pi$
$464$	−8.46787	−0.393111
$465$	−7.80765	−0.362071
$466$	−20.1323	−0.932610
$467$	−30.6430	−1.41799	−0.708994	−	0.705214i	$-0.750851\pi$
$467$	−30.6430	−1.41799	−0.708994	+	0.705214i	$0.750851\pi$
$468$	2.00000	0.0924500
$469$	−0.611096	−0.0282178
$470$	−6.15792	−0.284044
$471$	−19.6142	−0.903776
$472$	−7.66442	−0.352784
$473$	−23.3288	−1.07266
$474$	−0.753250	−0.0345979
$475$	−19.1537	−0.878833
$476$	16.3503	0.749413
$477$	1.83221	0.0838912
$478$	7.90696	0.361656
$479$	17.1218	0.782315	0.391158	−	0.920324i	$-0.372075\pi$
$479$	17.1218	0.782315	0.391158	+	0.920324i	$0.372075\pi$
$480$	−1.14637	−0.0523242
$481$	8.10038	0.369346
$482$	16.0575	0.731401
$483$	16.3503	0.743963
$484$	10.9572	0.498052
$485$	19.0790	0.866331
$486$	−1.00000	−0.0453609
$487$	7.46365	0.338210	0.169105	−	0.985598i	$-0.445912\pi$
$487$	7.46365	0.338210	0.169105	+	0.985598i	$0.445912\pi$
$488$	−1.31415	−0.0594889
$489$	7.66442	0.346597
$490$	−5.93260	−0.268007
$491$	29.4611	1.32956	0.664781	−	0.747038i	$-0.268525\pi$
$491$	29.4611	1.32956	0.664781	+	0.747038i	$0.268525\pi$
$492$	−5.48929	−0.247476
$493$	−39.6791	−1.78706
$494$	−10.3931	−0.467608
$495$	−5.37169	−0.241440
$496$	−6.81079	−0.305813
$497$	−4.43596	−0.198980
$498$	15.5468	0.696670
$499$	23.7392	1.06271	0.531356	−	0.847149i	$-0.321683\pi$
$499$	23.7392	1.06271	0.531356	+	0.847149i	$0.321683\pi$
$500$	−9.95715	−0.445297
$501$	4.92839	0.220184
$502$	27.8971	1.24511
$503$	40.4998	1.80580	0.902898	−	0.429855i	$-0.141435\pi$
$503$	40.4998	1.80580	0.902898	+	0.429855i	$0.141435\pi$
$504$	−3.48929	−0.155425
$505$	−7.47208	−0.332503
$506$	21.9572	0.976115
$507$	−9.00000	−0.399704
$508$	5.53948	0.245775
$509$	20.7178	0.918298	0.459149	−	0.888359i	$-0.348154\pi$
$509$	20.7178	0.918298	0.459149	+	0.888359i	$0.348154\pi$
$510$	−5.37169	−0.237863
$511$	6.97858	0.308714
$512$	−1.00000	−0.0441942
$513$	5.19656	0.229434
$514$	28.0147	1.23568
$515$	−7.02142	−0.309401
$516$	4.97858	0.219170
$517$	−25.1709	−1.10702
$518$	−14.1323	−0.620937
$519$	−12.9038	−0.566415
$520$	−2.29273	−0.100543
$521$	−10.7005	−0.468799	−0.234400	−	0.972140i	$-0.575312\pi$
$521$	−10.7005	−0.468799	−0.234400	+	0.972140i	$0.575312\pi$
$522$	8.46787	0.370628
$523$	−10.6283	−0.464743	−0.232372	−	0.972627i	$-0.574649\pi$
$523$	−10.6283	−0.464743	−0.232372	+	0.972627i	$0.574649\pi$
$524$	−1.00000	−0.0436852
$525$	−12.8610	−0.561299
$526$	−13.2039	−0.575718
$527$	−31.9143	−1.39021
$528$	−4.68585	−0.203925
$529$	−1.04285	−0.0453411
$530$	−2.10038	−0.0912349
$531$	7.66442	0.332608
$532$	18.1323	0.786134
$533$	−10.9786	−0.475535
$534$	−9.15371	−0.396120
$535$	5.25662	0.227263
$536$	0.175135	0.00756467
$537$	9.27131	0.400086
$538$	−20.7104	−0.892889
$539$	−24.2499	−1.04452
$540$	1.14637	0.0493317
$541$	38.4067	1.65123	0.825617	−	0.564231i	$-0.190827\pi$
$541$	38.4067	1.65123	0.825617	+	0.564231i	$0.190827\pi$
$542$	22.9933	0.987646
$543$	−22.6184	−0.970650
$544$	−4.68585	−0.200904
$545$	−1.12181	−0.0480529
$546$	−6.97858	−0.298656
$547$	−23.4036	−1.00067	−0.500333	−	0.865833i	$-0.666789\pi$
$547$	−23.4036	−1.00067	−0.500333	+	0.865833i	$0.666789\pi$
$548$	−18.9357	−0.808894
$549$	1.31415	0.0560867
$550$	−17.2713	−0.736451
$551$	−44.0038	−1.87462
$552$	−4.68585	−0.199443
$553$	2.62831	0.111767
$554$	−2.35027	−0.0998534
$555$	4.64300	0.197084
$556$	−21.0361	−0.892130
$557$	−4.12494	−0.174779	−0.0873897	−	0.996174i	$-0.527853\pi$
$557$	−4.12494	−0.174779	−0.0873897	+	0.996174i	$0.527853\pi$
$558$	6.81079	0.288324
$559$	9.95715	0.421143
$560$	4.00000	0.169031
$561$	−21.9572	−0.927032
$562$	−25.5296	−1.07690
$563$	24.1004	1.01571	0.507855	−	0.861443i	$-0.330439\pi$
$563$	24.1004	1.01571	0.507855	+	0.861443i	$0.330439\pi$
$564$	5.37169	0.226189
$565$	−1.59219	−0.0669840
$566$	9.91431	0.416729
$567$	3.48929	0.146536
$568$	1.27131	0.0533429
$569$	0.467866	0.0196140	0.00980698	−	0.999952i	$-0.496878\pi$
$569$	0.467866	0.0196140	0.00980698	+	0.999952i	$0.496878\pi$
$570$	−5.95715	−0.249518
$571$	10.2180	0.427609	0.213805	−	0.976876i	$-0.431414\pi$
$571$	10.2180	0.427609	0.213805	+	0.976876i	$0.431414\pi$
$572$	−9.37169	−0.391850
$573$	4.44331	0.185622
$574$	19.1537	0.799460
$575$	−17.2713	−0.720263
$576$	1.00000	0.0416667
$577$	1.88240	0.0783655	0.0391827	−	0.999232i	$-0.487525\pi$
$577$	1.88240	0.0783655	0.0391827	+	0.999232i	$0.487525\pi$
$578$	−4.95715	−0.206190
$579$	−16.8610	−0.700718
$580$	−9.70727	−0.403072
$581$	−54.2474	−2.25056
$582$	−16.6430	−0.689875
$583$	−8.58546	−0.355574
$584$	−2.00000	−0.0827606
$585$	2.29273	0.0947928
$586$	−12.8782	−0.531993
$587$	41.4011	1.70881	0.854403	−	0.519611i	$-0.173923\pi$
$587$	41.4011	1.70881	0.854403	+	0.519611i	$0.173923\pi$
$588$	5.17513	0.213419
$589$	−35.3927	−1.45833
$590$	−8.78623	−0.361723
$591$	−12.5682	−0.516989
$592$	4.05019	0.166462
$593$	−11.5212	−0.473119	−0.236559	−	0.971617i	$-0.576020\pi$
$593$	−11.5212	−0.473119	−0.236559	+	0.971617i	$0.576020\pi$
$594$	4.68585	0.192263
$595$	18.7434	0.768404
$596$	−4.87819	−0.199819
$597$	−1.33871	−0.0547898
$598$	−9.37169	−0.383237
$599$	43.5861	1.78088	0.890439	−	0.455102i	$-0.150397\pi$
$599$	43.5861	1.78088	0.890439	+	0.455102i	$0.150397\pi$
$600$	3.68585	0.150474
$601$	41.4120	1.68923	0.844616	−	0.535373i	$-0.179829\pi$
$601$	41.4120	1.68923	0.844616	+	0.535373i	$0.179829\pi$
$602$	−17.3717	−0.708017
$603$	−0.175135	−0.00713204
$604$	5.88240	0.239352
$605$	12.5609	0.510673
$606$	6.51806	0.264778
$607$	35.4622	1.43937	0.719683	−	0.694302i	$-0.244287\pi$
$607$	35.4622	1.43937	0.719683	+	0.694302i	$0.244287\pi$
$608$	−5.19656	−0.210748
$609$	−29.5468	−1.19730
$610$	−1.50650	−0.0609964
$611$	10.7434	0.434631
$612$	4.68585	0.189414
$613$	47.7367	1.92807	0.964033	−	0.265784i	$-0.0856307\pi$
$613$	47.7367	1.92807	0.964033	+	0.265784i	$0.0856307\pi$
$614$	−33.5296	−1.35315
$615$	−6.29273	−0.253747
$616$	16.3503	0.658771
$617$	−42.2646	−1.70151	−0.850754	−	0.525564i	$-0.823854\pi$
$617$	−42.2646	−1.70151	−0.850754	+	0.525564i	$0.823854\pi$
$618$	6.12494	0.246381
$619$	−5.53213	−0.222355	−0.111178	−	0.993801i	$-0.535462\pi$
$619$	−5.53213	−0.222355	−0.111178	+	0.993801i	$0.535462\pi$
$620$	−7.80765	−0.313563
$621$	4.68585	0.188037
$622$	−22.4605	−0.900585
$623$	31.9399	1.27965
$624$	2.00000	0.0800641
$625$	7.01469	0.280588
$626$	30.2499	1.20903
$627$	−24.3503	−0.972456
$628$	−19.6142	−0.782693
$629$	18.9786	0.756725
$630$	−4.00000	−0.159364
$631$	4.86098	0.193513	0.0967563	−	0.995308i	$-0.469153\pi$
$631$	4.86098	0.193513	0.0967563	+	0.995308i	$0.469153\pi$
$632$	−0.753250	−0.0299627
$633$	6.58546	0.261749
$634$	26.6184	1.05715
$635$	6.35027	0.252003
$636$	1.83221	0.0726519
$637$	10.3503	0.410093
$638$	−39.6791	−1.57091
$639$	−1.27131	−0.0502922
$640$	−1.14637	−0.0453141
$641$	3.68164	0.145416	0.0727079	−	0.997353i	$-0.476836\pi$
$641$	3.68164	0.145416	0.0727079	+	0.997353i	$0.476836\pi$
$642$	−4.58546	−0.180974
$643$	−31.1940	−1.23017	−0.615086	−	0.788460i	$-0.710879\pi$
$643$	−31.1940	−1.23017	−0.615086	+	0.788460i	$0.710879\pi$
$644$	16.3503	0.644291
$645$	5.70727	0.224723
$646$	−24.3503	−0.958049
$647$	−23.5714	−0.926687	−0.463343	−	0.886179i	$-0.653350\pi$
$647$	−23.5714	−0.926687	−0.463343	+	0.886179i	$0.653350\pi$
$648$	−1.00000	−0.0392837
$649$	−35.9143	−1.40976
$650$	7.37169	0.289142
$651$	−23.7648	−0.931416
$652$	7.66442	0.300162
$653$	29.4109	1.15094	0.575470	−	0.817823i	$-0.304819\pi$
$653$	29.4109	1.15094	0.575470	+	0.817823i	$0.304819\pi$
$654$	0.978577	0.0382654
$655$	−1.14637	−0.0447922
$656$	−5.48929	−0.214321
$657$	2.00000	0.0780274
$658$	−18.7434	−0.730693
$659$	−36.5510	−1.42383	−0.711913	−	0.702268i	$-0.752171\pi$
$659$	−36.5510	−1.42383	−0.711913	+	0.702268i	$0.752171\pi$
$660$	−5.37169	−0.209093
$661$	−5.33619	−0.207554	−0.103777	−	0.994601i	$-0.533093\pi$
$661$	−5.33619	−0.207554	−0.103777	+	0.994601i	$0.533093\pi$
$662$	22.4078	0.870904
$663$	9.37169	0.363966
$664$	15.5468	0.603334
$665$	20.7862	0.806055
$666$	−4.05019	−0.156942
$667$	−39.6791	−1.53638
$668$	4.92839	0.190685
$669$	16.7679	0.648286
$670$	0.200768	0.00775636
$671$	−6.15792	−0.237724
$672$	−3.48929	−0.134602
$673$	−37.4292	−1.44279	−0.721395	−	0.692523i	$-0.756499\pi$
$673$	−37.4292	−1.44279	−0.721395	+	0.692523i	$0.756499\pi$
$674$	21.3545	0.822544
$675$	−3.68585	−0.141868
$676$	−9.00000	−0.346154
$677$	−23.5321	−0.904413	−0.452207	−	0.891913i	$-0.649363\pi$
$677$	−23.5321	−0.904413	−0.452207	+	0.891913i	$0.649363\pi$
$678$	1.38890	0.0533406
$679$	58.0722	2.22861
$680$	−5.37169	−0.205995
$681$	18.9185	0.724959
$682$	−31.9143	−1.22206
$683$	24.9357	0.954139	0.477070	−	0.878866i	$-0.341699\pi$
$683$	24.9357	0.954139	0.477070	+	0.878866i	$0.341699\pi$
$684$	5.19656	0.198695
$685$	−21.7073	−0.829392
$686$	6.36748	0.243112
$687$	−21.2467	−0.810614
$688$	4.97858	0.189806
$689$	3.66442	0.139603
$690$	−5.37169	−0.204497
$691$	1.79923	0.0684460	0.0342230	−	0.999414i	$-0.489104\pi$
$691$	1.79923	0.0684460	0.0342230	+	0.999414i	$0.489104\pi$
$692$	−12.9038	−0.490530
$693$	−16.3503	−0.621095
$694$	5.78202	0.219482
$695$	−24.1151	−0.914737
$696$	8.46787	0.320974
$697$	−25.7220	−0.974289
$698$	24.1997	0.915972
$699$	20.1323	0.761473
$700$	−12.8610	−0.486099
$701$	42.8683	1.61911	0.809557	−	0.587041i	$-0.199707\pi$
$701$	42.8683	1.61911	0.809557	+	0.587041i	$0.199707\pi$
$702$	−2.00000	−0.0754851
$703$	21.0471	0.793805
$704$	−4.68585	−0.176604
$705$	6.15792	0.231921
$706$	−9.00421	−0.338878
$707$	−22.7434	−0.855353
$708$	7.66442	0.288047
$709$	−37.4109	−1.40500	−0.702499	−	0.711685i	$-0.747932\pi$
$709$	−37.4109	−1.40500	−0.702499	+	0.711685i	$0.747932\pi$
$710$	1.45738	0.0546946
$711$	0.753250	0.0282491
$712$	−9.15371	−0.343050
$713$	−31.9143	−1.19520
$714$	−16.3503	−0.611893
$715$	−10.7434	−0.401780
$716$	9.27131	0.346485
$717$	−7.90696	−0.295291
$718$	−10.2927	−0.384121
$719$	−18.1997	−0.678734	−0.339367	−	0.940654i	$-0.610213\pi$
$719$	−18.1997	−0.678734	−0.339367	+	0.940654i	$0.610213\pi$
$720$	1.14637	0.0427225
$721$	−21.3717	−0.795923
$722$	−8.00421	−0.297886
$723$	−16.0575	−0.597186
$724$	−22.6184	−0.840608
$725$	31.2113	1.15916
$726$	−10.9572	−0.406658
$727$	13.5395	0.502152	0.251076	−	0.967967i	$-0.419216\pi$
$727$	13.5395	0.502152	0.251076	+	0.967967i	$0.419216\pi$
$728$	−6.97858	−0.258643
$729$	1.00000	0.0370370
$730$	−2.29273	−0.0848578
$731$	23.3288	0.862849
$732$	1.31415	0.0485725
$733$	−16.5353	−0.610744	−0.305372	−	0.952233i	$-0.598781\pi$
$733$	−16.5353	−0.610744	−0.305372	+	0.952233i	$0.598781\pi$
$734$	−2.36748	−0.0873853
$735$	5.93260	0.218827
$736$	−4.68585	−0.172723
$737$	0.820654	0.0302292
$738$	5.48929	0.202064
$739$	−42.2646	−1.55473	−0.777364	−	0.629051i	$-0.783444\pi$
$739$	−42.2646	−1.55473	−0.777364	+	0.629051i	$0.783444\pi$
$740$	4.64300	0.170680
$741$	10.3931	0.381801
$742$	−6.39312	−0.234699
$743$	42.6577	1.56496	0.782479	−	0.622676i	$-0.213955\pi$
$743$	42.6577	1.56496	0.782479	+	0.622676i	$0.213955\pi$
$744$	6.81079	0.249696
$745$	−5.59219	−0.204882
$746$	−37.1611	−1.36056
$747$	−15.5468	−0.568829
$748$	−21.9572	−0.802833
$749$	16.0000	0.584627
$750$	9.95715	0.363584
$751$	3.63144	0.132513	0.0662566	−	0.997803i	$-0.478894\pi$
$751$	3.63144	0.132513	0.0662566	+	0.997803i	$0.478894\pi$
$752$	5.37169	0.195885
$753$	−27.8971	−1.01663
$754$	16.9357	0.616763
$755$	6.74338	0.245417
$756$	3.48929	0.126904
$757$	−16.5939	−0.603115	−0.301557	−	0.953448i	$-0.597507\pi$
$757$	−16.5939	−0.603115	−0.301557	+	0.953448i	$0.597507\pi$
$758$	16.3074	0.592312
$759$	−21.9572	−0.796994
$760$	−5.95715	−0.216089
$761$	5.15623	0.186913	0.0934566	−	0.995623i	$-0.470208\pi$
$761$	5.15623	0.186913	0.0934566	+	0.995623i	$0.470208\pi$
$762$	−5.53948	−0.200674
$763$	−3.41454	−0.123615
$764$	4.44331	0.160753
$765$	5.37169	0.194214
$766$	−3.58233	−0.129435
$767$	15.3288	0.553493
$768$	1.00000	0.0360844
$769$	23.7820	0.857602	0.428801	−	0.903399i	$-0.358936\pi$
$769$	23.7820	0.857602	0.428801	+	0.903399i	$0.358936\pi$
$770$	18.7434	0.675465
$771$	−28.0147	−1.00892
$772$	−16.8610	−0.606840
$773$	10.0601	0.361835	0.180918	−	0.983498i	$-0.442093\pi$
$773$	10.0601	0.361835	0.180918	+	0.983498i	$0.442093\pi$
$774$	−4.97858	−0.178951
$775$	25.1035	0.901745
$776$	−16.6430	−0.597449
$777$	14.1323	0.506993
$778$	16.9185	0.606558
$779$	−28.5254	−1.02203
$780$	2.29273	0.0820929
$781$	5.95715	0.213164
$782$	−21.9572	−0.785186
$783$	−8.46787	−0.302617
$784$	5.17513	0.184826
$785$	−22.4851	−0.802527
$786$	1.00000	0.0356688
$787$	4.87192	0.173665	0.0868326	−	0.996223i	$-0.472325\pi$
$787$	4.87192	0.173665	0.0868326	+	0.996223i	$0.472325\pi$
$788$	−12.5682	−0.447725
$789$	13.2039	0.470071
$790$	−0.863500	−0.0307220
$791$	−4.84629	−0.172314
$792$	4.68585	0.166504
$793$	2.62831	0.0933339
$794$	22.0000	0.780751
$795$	2.10038	0.0744930
$796$	−1.33871	−0.0474494
$797$	34.8830	1.23562	0.617810	−	0.786327i	$-0.288020\pi$
$797$	34.8830	1.23562	0.617810	+	0.786327i	$0.288020\pi$
$798$	−18.1323	−0.641876
$799$	25.1709	0.890483
$800$	3.68585	0.130314
$801$	9.15371	0.323431
$802$	−14.3503	−0.506726
$803$	−9.37169	−0.330720
$804$	−0.175135	−0.00617653
$805$	18.7434	0.660618
$806$	13.6216	0.479800
$807$	20.7104	0.729041
$808$	6.51806	0.229304
$809$	−43.9803	−1.54626	−0.773132	−	0.634245i	$-0.781311\pi$
$809$	−43.9803	−1.54626	−0.773132	+	0.634245i	$0.781311\pi$
$810$	−1.14637	−0.0402792
$811$	52.0294	1.82700	0.913499	−	0.406840i	$-0.133369\pi$
$811$	52.0294	1.82700	0.913499	+	0.406840i	$0.133369\pi$
$812$	−29.5468	−1.03689
$813$	−22.9933	−0.806409
$814$	18.9786	0.665199
$815$	8.78623	0.307768
$816$	4.68585	0.164037
$817$	25.8715	0.905128
$818$	−24.1323	−0.843766
$819$	6.97858	0.243851
$820$	−6.29273	−0.219752
$821$	38.5672	1.34600	0.673002	−	0.739641i	$-0.265005\pi$
$821$	38.5672	1.34600	0.673002	+	0.739641i	$0.265005\pi$
$822$	18.9357	0.660459
$823$	13.8751	0.483654	0.241827	−	0.970319i	$-0.422253\pi$
$823$	13.8751	0.483654	0.241827	+	0.970319i	$0.422253\pi$
$824$	6.12494	0.213372
$825$	17.2713	0.601310
$826$	−26.7434	−0.930521
$827$	−3.88492	−0.135092	−0.0675460	−	0.997716i	$-0.521517\pi$
$827$	−3.88492	−0.135092	−0.0675460	+	0.997716i	$0.521517\pi$
$828$	4.68585	0.162844
$829$	−1.57873	−0.0548316	−0.0274158	−	0.999624i	$-0.508728\pi$
$829$	−1.57873	−0.0548316	−0.0274158	+	0.999624i	$0.508728\pi$
$830$	17.8223	0.618623
$831$	2.35027	0.0815299
$832$	2.00000	0.0693375
$833$	24.2499	0.840209
$834$	21.0361	0.728421
$835$	5.64973	0.195517
$836$	−24.3503	−0.842172
$837$	−6.81079	−0.235415
$838$	32.1067	1.10911
$839$	−6.73604	−0.232554	−0.116277	−	0.993217i	$-0.537096\pi$
$839$	−6.73604	−0.232554	−0.116277	+	0.993217i	$0.537096\pi$
$840$	−4.00000	−0.138013
$841$	42.7047	1.47258
$842$	−5.46365	−0.188290
$843$	25.5296	0.879287
$844$	6.58546	0.226681
$845$	−10.3173	−0.354926
$846$	−5.37169	−0.184683
$847$	38.2327	1.31369
$848$	1.83221	0.0629184
$849$	−9.91431	−0.340258
$850$	17.2713	0.592401
$851$	18.9786	0.650577
$852$	−1.27131	−0.0435543
$853$	−41.9964	−1.43793	−0.718965	−	0.695047i	$-0.755384\pi$
$853$	−41.9964	−1.43793	−0.718965	+	0.695047i	$0.755384\pi$
$854$	−4.58546	−0.156911
$855$	5.95715	0.203730
$856$	−4.58546	−0.156728
$857$	−18.7862	−0.641725	−0.320863	−	0.947126i	$-0.603973\pi$
$857$	−18.7862	−0.641725	−0.320863	+	0.947126i	$0.603973\pi$
$858$	9.37169	0.319944
$859$	−9.09617	−0.310357	−0.155179	−	0.987886i	$-0.549595\pi$
$859$	−9.09617	−0.310357	−0.155179	+	0.987886i	$0.549595\pi$
$860$	5.70727	0.194616
$861$	−19.1537	−0.652757
$862$	−9.28960	−0.316405
$863$	−1.81500	−0.0617833	−0.0308917	−	0.999523i	$-0.509835\pi$
$863$	−1.81500	−0.0617833	−0.0308917	+	0.999523i	$0.509835\pi$
$864$	−1.00000	−0.0340207
$865$	−14.7925	−0.502960
$866$	−23.0361	−0.782799
$867$	4.95715	0.168354
$868$	−23.7648	−0.806630
$869$	−3.52962	−0.119734
$870$	9.70727	0.329107
$871$	−0.350269	−0.0118684
$872$	0.978577	0.0331388
$873$	16.6430	0.563280
$874$	−24.3503	−0.823660
$875$	−34.7434	−1.17454
$876$	2.00000	0.0675737
$877$	4.14323	0.139907	0.0699535	−	0.997550i	$-0.477715\pi$
$877$	4.14323	0.139907	0.0699535	+	0.997550i	$0.477715\pi$
$878$	−7.28852	−0.245976
$879$	12.8782	0.434371
$880$	−5.37169	−0.181080
$881$	−18.7925	−0.633135	−0.316568	−	0.948570i	$-0.602530\pi$
$881$	−18.7925	−0.633135	−0.316568	+	0.948570i	$0.602530\pi$
$882$	−5.17513	−0.174256
$883$	44.6749	1.50343	0.751715	−	0.659488i	$-0.229227\pi$
$883$	44.6749	1.50343	0.751715	+	0.659488i	$0.229227\pi$
$884$	9.37169	0.315204
$885$	8.78623	0.295346
$886$	24.7262	0.830692
$887$	−8.70413	−0.292256	−0.146128	−	0.989266i	$-0.546681\pi$
$887$	−8.70413	−0.292256	−0.146128	+	0.989266i	$0.546681\pi$
$888$	−4.05019	−0.135916
$889$	19.3288	0.648269
$890$	−10.4935	−0.351743
$891$	−4.68585	−0.156982
$892$	16.7679	0.561432
$893$	27.9143	0.934117
$894$	4.87819	0.163151
$895$	10.6283	0.355265
$896$	−3.48929	−0.116569
$897$	9.37169	0.312912
$898$	0.921039	0.0307355
$899$	57.6728	1.92350
$900$	−3.68585	−0.122862
$901$	8.58546	0.286023
$902$	−25.7220	−0.856448
$903$	17.3717	0.578094
$904$	1.38890	0.0461943
$905$	−25.9290	−0.861909
$906$	−5.88240	−0.195430
$907$	4.49977	0.149412	0.0747062	−	0.997206i	$-0.476198\pi$
$907$	4.49977	0.149412	0.0747062	+	0.997206i	$0.476198\pi$
$908$	18.9185	0.627833
$909$	−6.51806	−0.216190
$910$	−8.00000	−0.265197
$911$	−44.0073	−1.45803	−0.729014	−	0.684499i	$-0.760021\pi$
$911$	−44.0073	−1.45803	−0.729014	+	0.684499i	$0.760021\pi$
$912$	5.19656	0.172075
$913$	72.8500	2.41098
$914$	36.4250	1.20483
$915$	1.50650	0.0498034
$916$	−21.2467	−0.702012
$917$	−3.48929	−0.115226
$918$	−4.68585	−0.154656
$919$	30.2253	0.997042	0.498521	−	0.866878i	$-0.333877\pi$
$919$	30.2253	0.997042	0.498521	+	0.866878i	$0.333877\pi$
$920$	−5.37169	−0.177099
$921$	33.5296	1.10484
$922$	−33.9399	−1.11775
$923$	−2.54262	−0.0836912
$924$	−16.3503	−0.537884
$925$	−14.9284	−0.490842
$926$	−26.2744	−0.863432
$927$	−6.12494	−0.201170
$928$	8.46787	0.277971
$929$	−24.5536	−0.805576	−0.402788	−	0.915293i	$-0.631959\pi$
$929$	−24.5536	−0.805576	−0.402788	+	0.915293i	$0.631959\pi$
$930$	7.80765	0.256023
$931$	26.8929	0.881379
$932$	20.1323	0.659455
$933$	22.4605	0.735324
$934$	30.6430	1.00267
$935$	−25.1709	−0.823177
$936$	−2.00000	−0.0653720
$937$	−30.8757	−1.00866	−0.504332	−	0.863510i	$-0.668261\pi$
$937$	−30.8757	−1.00866	−0.504332	+	0.863510i	$0.668261\pi$
$938$	0.611096	0.0199530
$939$	−30.2499	−0.987168
$940$	6.15792	0.200849
$941$	−28.2474	−0.920838	−0.460419	−	0.887702i	$-0.652301\pi$
$941$	−28.2474	−0.920838	−0.460419	+	0.887702i	$0.652301\pi$
$942$	19.6142	0.639066
$943$	−25.7220	−0.837622
$944$	7.66442	0.249456
$945$	4.00000	0.130120
$946$	23.3288	0.758486
$947$	−21.5897	−0.701570	−0.350785	−	0.936456i	$-0.614085\pi$
$947$	−21.5897	−0.701570	−0.350785	+	0.936456i	$0.614085\pi$
$948$	0.753250	0.0244644
$949$	4.00000	0.129845
$950$	19.1537	0.621428
$951$	−26.6184	−0.863162
$952$	−16.3503	−0.529915
$953$	45.3692	1.46965	0.734826	−	0.678256i	$-0.237264\pi$
$953$	45.3692	1.46965	0.734826	+	0.678256i	$0.237264\pi$
$954$	−1.83221	−0.0593200
$955$	5.09365	0.164827
$956$	−7.90696	−0.255729
$957$	39.6791	1.28264
$958$	−17.1218	−0.553180
$959$	−66.0722	−2.13358
$960$	1.14637	0.0369988
$961$	15.3868	0.496350
$962$	−8.10038	−0.261167
$963$	4.58546	0.147764
$964$	−16.0575	−0.517178
$965$	−19.3288	−0.622218
$966$	−16.3503	−0.526061
$967$	37.8041	1.21570	0.607848	−	0.794053i	$-0.292033\pi$
$967$	37.8041	1.21570	0.607848	+	0.794053i	$0.292033\pi$
$968$	−10.9572	−0.352176
$969$	24.3503	0.782243
$970$	−19.0790	−0.612589
$971$	−19.5384	−0.627017	−0.313509	−	0.949585i	$-0.601504\pi$
$971$	−19.5384	−0.627017	−0.313509	+	0.949585i	$0.601504\pi$
$972$	1.00000	0.0320750
$973$	−73.4011	−2.35313
$974$	−7.46365	−0.239151
$975$	−7.37169	−0.236083
$976$	1.31415	0.0420650
$977$	−20.2671	−0.648402	−0.324201	−	0.945988i	$-0.605095\pi$
$977$	−20.2671	−0.648402	−0.324201	+	0.945988i	$0.605095\pi$
$978$	−7.66442	−0.245081
$979$	−42.8929	−1.37086
$980$	5.93260	0.189510
$981$	−0.978577	−0.0312436
$982$	−29.4611	−0.940143
$983$	51.0937	1.62963	0.814817	−	0.579718i	$-0.196837\pi$
$983$	51.0937	1.62963	0.814817	+	0.579718i	$0.196837\pi$
$984$	5.48929	0.174992
$985$	−14.4078	−0.459071
$986$	39.6791	1.26364
$987$	18.7434	0.596609
$988$	10.3931	0.330649
$989$	23.3288	0.741814
$990$	5.37169	0.170724
$991$	6.54262	0.207833	0.103917	−	0.994586i	$-0.466863\pi$
$991$	6.54262	0.207833	0.103917	+	0.994586i	$0.466863\pi$
$992$	6.81079	0.216243
$993$	−22.4078	−0.711090
$994$	4.43596	0.140700
$995$	−1.53465	−0.0486518
$996$	−15.5468	−0.492620
$997$	8.19235	0.259454	0.129727	−	0.991550i	$-0.458590\pi$
$997$	8.19235	0.259454	0.129727	+	0.991550i	$0.458590\pi$
$998$	−23.7392	−0.751450
$999$	4.05019	0.128142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	786.2.a.n.1.2	✓	3
3.2	odd	2		2358.2.a.be.1.2		3
4.3	odd	2		6288.2.a.w.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
786.2.a.n.1.2	✓	3	1.1	even	1	trivial
2358.2.a.be.1.2		3	3.2	odd	2
6288.2.a.w.1.2		3	4.3	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:	\( N \)	\(=\)	\( 786 = 2 \cdot 3 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	786.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} -1.00000 q^{6} +3.48929 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} -1.00000 q^{6} +3.48929 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.14637 q^{10} -4.68585 q^{11} +1.00000 q^{12} +2.00000 q^{13} -3.48929 q^{14} +1.14637 q^{15} +1.00000 q^{16} +4.68585 q^{17} -1.00000 q^{18} +5.19656 q^{19} +1.14637 q^{20} +3.48929 q^{21} +4.68585 q^{22} +4.68585 q^{23} -1.00000 q^{24} -3.68585 q^{25} -2.00000 q^{26} +1.00000 q^{27} +3.48929 q^{28} -8.46787 q^{29} -1.14637 q^{30} -6.81079 q^{31} -1.00000 q^{32} -4.68585 q^{33} -4.68585 q^{34} +4.00000 q^{35} +1.00000 q^{36} +4.05019 q^{37} -5.19656 q^{38} +2.00000 q^{39} -1.14637 q^{40} -5.48929 q^{41} -3.48929 q^{42} +4.97858 q^{43} -4.68585 q^{44} +1.14637 q^{45} -4.68585 q^{46} +5.37169 q^{47} +1.00000 q^{48} +5.17513 q^{49} +3.68585 q^{50} +4.68585 q^{51} +2.00000 q^{52} +1.83221 q^{53} -1.00000 q^{54} -5.37169 q^{55} -3.48929 q^{56} +5.19656 q^{57} +8.46787 q^{58} +7.66442 q^{59} +1.14637 q^{60} +1.31415 q^{61} +6.81079 q^{62} +3.48929 q^{63} +1.00000 q^{64} +2.29273 q^{65} +4.68585 q^{66} -0.175135 q^{67} +4.68585 q^{68} +4.68585 q^{69} -4.00000 q^{70} -1.27131 q^{71} -1.00000 q^{72} +2.00000 q^{73} -4.05019 q^{74} -3.68585 q^{75} +5.19656 q^{76} -16.3503 q^{77} -2.00000 q^{78} +0.753250 q^{79} +1.14637 q^{80} +1.00000 q^{81} +5.48929 q^{82} -15.5468 q^{83} +3.48929 q^{84} +5.37169 q^{85} -4.97858 q^{86} -8.46787 q^{87} +4.68585 q^{88} +9.15371 q^{89} -1.14637 q^{90} +6.97858 q^{91} +4.68585 q^{92} -6.81079 q^{93} -5.37169 q^{94} +5.95715 q^{95} -1.00000 q^{96} +16.6430 q^{97} -5.17513 q^{98} -4.68585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} - 3 q^{18} + 11 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} + 2 q^{23} - 3 q^{24} + q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 3 q^{29} - 2 q^{30} + 8 q^{31} - 3 q^{32} - 2 q^{33} - 2 q^{34} + 12 q^{35} + 3 q^{36} + 9 q^{37} - 11 q^{38} + 6 q^{39} - 2 q^{40} - 9 q^{41} - 3 q^{42} - 2 q^{44} + 2 q^{45} - 2 q^{46} - 8 q^{47} + 3 q^{48} - 4 q^{49} - q^{50} + 2 q^{51} + 6 q^{52} - 8 q^{53} - 3 q^{54} + 8 q^{55} - 3 q^{56} + 11 q^{57} + 3 q^{58} - 4 q^{59} + 2 q^{60} + 16 q^{61} - 8 q^{62} + 3 q^{63} + 3 q^{64} + 4 q^{65} + 2 q^{66} + 19 q^{67} + 2 q^{68} + 2 q^{69} - 12 q^{70} + 14 q^{71} - 3 q^{72} + 6 q^{73} - 9 q^{74} + q^{75} + 11 q^{76} - 10 q^{77} - 6 q^{78} + 10 q^{79} + 2 q^{80} + 3 q^{81} + 9 q^{82} - 3 q^{83} + 3 q^{84} - 8 q^{85} - 3 q^{87} + 2 q^{88} - 7 q^{89} - 2 q^{90} + 6 q^{91} + 2 q^{92} + 8 q^{93} + 8 q^{94} - 12 q^{95} - 3 q^{96} + 8 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 - 3 * q^18 + 11 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 + 2 * q^23 - 3 * q^24 + q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 2 * q^30 + 8 * q^31 - 3 * q^32 - 2 * q^33 - 2 * q^34 + 12 * q^35 + 3 * q^36 + 9 * q^37 - 11 * q^38 + 6 * q^39 - 2 * q^40 - 9 * q^41 - 3 * q^42 - 2 * q^44 + 2 * q^45 - 2 * q^46 - 8 * q^47 + 3 * q^48 - 4 * q^49 - q^50 + 2 * q^51 + 6 * q^52 - 8 * q^53 - 3 * q^54 + 8 * q^55 - 3 * q^56 + 11 * q^57 + 3 * q^58 - 4 * q^59 + 2 * q^60 + 16 * q^61 - 8 * q^62 + 3 * q^63 + 3 * q^64 + 4 * q^65 + 2 * q^66 + 19 * q^67 + 2 * q^68 + 2 * q^69 - 12 * q^70 + 14 * q^71 - 3 * q^72 + 6 * q^73 - 9 * q^74 + q^75 + 11 * q^76 - 10 * q^77 - 6 * q^78 + 10 * q^79 + 2 * q^80 + 3 * q^81 + 9 * q^82 - 3 * q^83 + 3 * q^84 - 8 * q^85 - 3 * q^87 + 2 * q^88 - 7 * q^89 - 2 * q^90 + 6 * q^91 + 2 * q^92 + 8 * q^93 + 8 * q^94 - 12 * q^95 - 3 * q^96 + 8 * q^97 + 4 * q^98 - 2 * q^99

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