LMFDB - Embedded newform 3179.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, 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("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.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:	$25.3844428026$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 10x^{6} + 8x^{5} + 28x^{4} - 18x^{3} - 20x^{2} + 6x + 4 $ x^8 - x^7 - 10x^6 + 8x^5 + 28x^4 - 18x^3 - 20x^2 + 6x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.89309$ of defining polynomial
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89309 q^{2} -1.04073 q^{3} +1.58380 q^{4} -1.83662 q^{5} +1.97021 q^{6} -1.61788 q^{7} +0.787912 q^{8} -1.91687 q^{9} +O(q^{10})$	\(q-1.89309 q^{2} -1.04073 q^{3} +1.58380 q^{4} -1.83662 q^{5} +1.97021 q^{6} -1.61788 q^{7} +0.787912 q^{8} -1.91687 q^{9} +3.47689 q^{10} -1.00000 q^{11} -1.64831 q^{12} +1.28326 q^{13} +3.06279 q^{14} +1.91143 q^{15} -4.65918 q^{16} +3.62882 q^{18} +3.44044 q^{19} -2.90883 q^{20} +1.68378 q^{21} +1.89309 q^{22} -4.87213 q^{23} -0.820007 q^{24} -1.62683 q^{25} -2.42933 q^{26} +5.11716 q^{27} -2.56239 q^{28} +5.71335 q^{29} -3.61852 q^{30} -3.11322 q^{31} +7.24444 q^{32} +1.04073 q^{33} +2.97142 q^{35} -3.03594 q^{36} -6.82692 q^{37} -6.51307 q^{38} -1.33553 q^{39} -1.44709 q^{40} +4.07841 q^{41} -3.18755 q^{42} +8.87325 q^{43} -1.58380 q^{44} +3.52056 q^{45} +9.22340 q^{46} +5.88243 q^{47} +4.84897 q^{48} -4.38248 q^{49} +3.07974 q^{50} +2.03242 q^{52} +3.22736 q^{53} -9.68725 q^{54} +1.83662 q^{55} -1.27474 q^{56} -3.58058 q^{57} -10.8159 q^{58} +2.40670 q^{59} +3.02732 q^{60} +13.3232 q^{61} +5.89361 q^{62} +3.10126 q^{63} -4.39602 q^{64} -2.35686 q^{65} -1.97021 q^{66} +5.72734 q^{67} +5.07060 q^{69} -5.62517 q^{70} -6.48669 q^{71} -1.51033 q^{72} -4.32713 q^{73} +12.9240 q^{74} +1.69310 q^{75} +5.44895 q^{76} +1.61788 q^{77} +2.52828 q^{78} -15.1696 q^{79} +8.55714 q^{80} +0.425016 q^{81} -7.72080 q^{82} +8.83664 q^{83} +2.66676 q^{84} -16.7979 q^{86} -5.94608 q^{87} -0.787912 q^{88} -0.224416 q^{89} -6.66475 q^{90} -2.07615 q^{91} -7.71647 q^{92} +3.24004 q^{93} -11.1360 q^{94} -6.31877 q^{95} -7.53953 q^{96} +3.00802 q^{97} +8.29644 q^{98} +1.91687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{5} - 4 q^{6} - 5 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 8 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^5 - 4 * q^6 - 5 * q^7 + 3 * q^8 + 10 * q^9	\( 8 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{5} - 4 q^{6} - 5 q^{7} + 3 q^{8} + 10 q^{9} + 4 q^{10} - 8 q^{11} + 10 q^{12} - 8 q^{13} - 20 q^{14} - 2 q^{15} + 3 q^{16} - 5 q^{18} - 10 q^{19} - 8 q^{20} + 6 q^{21} - q^{22} + 10 q^{23} - 26 q^{24} - 2 q^{25} + 6 q^{26} + 4 q^{27} - 16 q^{28} - 3 q^{29} + 14 q^{30} - 2 q^{31} + 17 q^{32} + 2 q^{33} + 6 q^{35} + 9 q^{36} - 16 q^{37} - 28 q^{39} + 32 q^{40} - 21 q^{41} - 4 q^{43} - 5 q^{44} - 34 q^{45} - 6 q^{46} + 7 q^{47} - 38 q^{48} + 21 q^{49} - 17 q^{50} - 22 q^{52} - 13 q^{53} - 28 q^{54} + 4 q^{55} - 16 q^{56} + 32 q^{57} - 48 q^{58} + 15 q^{59} - 36 q^{60} - 28 q^{61} - 14 q^{62} + 9 q^{63} - 5 q^{64} + 8 q^{65} + 4 q^{66} + 5 q^{67} + 2 q^{69} + 4 q^{70} - 26 q^{71} - 23 q^{72} + q^{73} + 36 q^{74} - 20 q^{75} - 18 q^{76} + 5 q^{77} + 34 q^{78} - 20 q^{79} + 30 q^{80} - 4 q^{81} - 22 q^{82} + 4 q^{83} + 46 q^{84} + 28 q^{86} - 4 q^{87} - 3 q^{88} + 5 q^{89} + 14 q^{90} + 36 q^{91} - 38 q^{92} + 10 q^{93} - 4 q^{94} + 6 q^{95} - 18 q^{96} - 26 q^{97} + 19 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^5 - 4 * q^6 - 5 * q^7 + 3 * q^8 + 10 * q^9 + 4 * q^10 - 8 * q^11 + 10 * q^12 - 8 * q^13 - 20 * q^14 - 2 * q^15 + 3 * q^16 - 5 * q^18 - 10 * q^19 - 8 * q^20 + 6 * q^21 - q^22 + 10 * q^23 - 26 * q^24 - 2 * q^25 + 6 * q^26 + 4 * q^27 - 16 * q^28 - 3 * q^29 + 14 * q^30 - 2 * q^31 + 17 * q^32 + 2 * q^33 + 6 * q^35 + 9 * q^36 - 16 * q^37 - 28 * q^39 + 32 * q^40 - 21 * q^41 - 4 * q^43 - 5 * q^44 - 34 * q^45 - 6 * q^46 + 7 * q^47 - 38 * q^48 + 21 * q^49 - 17 * q^50 - 22 * q^52 - 13 * q^53 - 28 * q^54 + 4 * q^55 - 16 * q^56 + 32 * q^57 - 48 * q^58 + 15 * q^59 - 36 * q^60 - 28 * q^61 - 14 * q^62 + 9 * q^63 - 5 * q^64 + 8 * q^65 + 4 * q^66 + 5 * q^67 + 2 * q^69 + 4 * q^70 - 26 * q^71 - 23 * q^72 + q^73 + 36 * q^74 - 20 * q^75 - 18 * q^76 + 5 * q^77 + 34 * q^78 - 20 * q^79 + 30 * q^80 - 4 * q^81 - 22 * q^82 + 4 * q^83 + 46 * q^84 + 28 * q^86 - 4 * q^87 - 3 * q^88 + 5 * q^89 + 14 * q^90 + 36 * q^91 - 38 * q^92 + 10 * q^93 - 4 * q^94 + 6 * q^95 - 18 * q^96 - 26 * q^97 + 19 * q^98 - 10 * 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 $

$2$	−1.89309	−1.33862	−0.669309	−	0.742984i	$-0.733410\pi$
$2$	−1.89309	−1.33862	−0.669309	+	0.742984i	$0.733410\pi$
$3$	−1.04073	−0.600868	−0.300434	−	0.953803i	$-0.597132\pi$
$3$	−1.04073	−0.600868	−0.300434	+	0.953803i	$0.597132\pi$
$4$	1.58380	0.791898
$5$	−1.83662	−0.821361	−0.410680	−	0.911779i	$-0.634709\pi$
$5$	−1.83662	−0.821361	−0.410680	+	0.911779i	$0.634709\pi$
$6$	1.97021	0.804333
$7$	−1.61788	−0.611499	−0.305750	−	0.952112i	$-0.598907\pi$
$7$	−1.61788	−0.611499	−0.305750	+	0.952112i	$0.598907\pi$
$8$	0.787912	0.278569
$9$	−1.91687	−0.638957
$10$	3.47689	1.09949
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.64831	−0.475826
$13$	1.28326	0.355912	0.177956	−	0.984038i	$-0.443052\pi$
$13$	1.28326	0.355912	0.177956	+	0.984038i	$0.443052\pi$
$14$	3.06279	0.818564
$15$	1.91143	0.493530
$16$	−4.65918	−1.16480
$17$	0	0
$17$	0	0
$18$	3.62882	0.855320
$19$	3.44044	0.789291	0.394645	−	0.918834i	$-0.370867\pi$
$19$	3.44044	0.789291	0.394645	+	0.918834i	$0.370867\pi$
$20$	−2.90883	−0.650434
$21$	1.68378	0.367431
$22$	1.89309	0.403609
$23$	−4.87213	−1.01591	−0.507955	−	0.861384i	$-0.669598\pi$
$23$	−4.87213	−1.01591	−0.507955	+	0.861384i	$0.669598\pi$
$24$	−0.820007	−0.167383
$25$	−1.62683	−0.325366
$26$	−2.42933	−0.476430
$27$	5.11716	0.984797
$28$	−2.56239	−0.484245
$29$	5.71335	1.06094	0.530472	−	0.847703i	$-0.322015\pi$
$29$	5.71335	1.06094	0.530472	+	0.847703i	$0.322015\pi$
$30$	−3.61852	−0.660648
$31$	−3.11322	−0.559151	−0.279576	−	0.960124i	$-0.590194\pi$
$31$	−3.11322	−0.559151	−0.279576	+	0.960124i	$0.590194\pi$
$32$	7.24444	1.28065
$33$	1.04073	0.181169
$34$	0	0
$35$	2.97142	0.502262
$36$	−3.03594	−0.505989
$37$	−6.82692	−1.12234	−0.561169	−	0.827701i	$-0.689648\pi$
$37$	−6.82692	−1.12234	−0.561169	+	0.827701i	$0.689648\pi$
$38$	−6.51307	−1.05656
$39$	−1.33553	−0.213856
$40$	−1.44709	−0.228806
$41$	4.07841	0.636940	0.318470	−	0.947933i	$-0.396831\pi$
$41$	4.07841	0.636940	0.318470	+	0.947933i	$0.396831\pi$
$42$	−3.18755	−0.491849
$43$	8.87325	1.35316	0.676579	−	0.736370i	$-0.263462\pi$
$43$	8.87325	1.35316	0.676579	+	0.736370i	$0.263462\pi$
$44$	−1.58380	−0.238766
$45$	3.52056	0.524815
$46$	9.22340	1.35992
$47$	5.88243	0.858041	0.429021	−	0.903295i	$-0.358859\pi$
$47$	5.88243	0.858041	0.429021	+	0.903295i	$0.358859\pi$
$48$	4.84897	0.699889
$49$	−4.38248	−0.626068
$50$	3.07974	0.435541
$51$	0	0
$52$	2.03242	0.281846
$53$	3.22736	0.443312	0.221656	−	0.975125i	$-0.428854\pi$
$53$	3.22736	0.443312	0.221656	+	0.975125i	$0.428854\pi$
$54$	−9.68725	−1.31827
$55$	1.83662	0.247650
$56$	−1.27474	−0.170345
$57$	−3.58058	−0.474260
$58$	−10.8159	−1.42020
$59$	2.40670	0.313326	0.156663	−	0.987652i	$-0.449926\pi$
$59$	2.40670	0.313326	0.156663	+	0.987652i	$0.449926\pi$
$60$	3.02732	0.390825
$61$	13.3232	1.70587	0.852933	−	0.522020i	$-0.174821\pi$
$61$	13.3232	1.70587	0.852933	+	0.522020i	$0.174821\pi$
$62$	5.89361	0.748490
$63$	3.10126	0.390722
$64$	−4.39602	−0.549502
$65$	−2.35686	−0.292332
$66$	−1.97021	−0.242516
$67$	5.72734	0.699706	0.349853	−	0.936805i	$-0.386232\pi$
$67$	5.72734	0.699706	0.349853	+	0.936805i	$0.386232\pi$
$68$	0	0
$69$	5.07060	0.610428
$70$	−5.62517	−0.672337
$71$	−6.48669	−0.769828	−0.384914	−	0.922952i	$-0.625769\pi$
$71$	−6.48669	−0.769828	−0.384914	+	0.922952i	$0.625769\pi$
$72$	−1.51033	−0.177994
$73$	−4.32713	−0.506453	−0.253226	−	0.967407i	$-0.581492\pi$
$73$	−4.32713	−0.506453	−0.253226	+	0.967407i	$0.581492\pi$
$74$	12.9240	1.50238
$75$	1.69310	0.195502
$76$	5.44895	0.625038
$77$	1.61788	0.184374
$78$	2.52828	0.286272
$79$	−15.1696	−1.70671	−0.853355	−	0.521330i	$-0.825436\pi$
$79$	−15.1696	−1.70671	−0.853355	+	0.521330i	$0.825436\pi$
$80$	8.55714	0.956717
$81$	0.425016	0.0472240
$82$	−7.72080	−0.852620
$83$	8.83664	0.969947	0.484974	−	0.874529i	$-0.338829\pi$
$83$	8.83664	0.969947	0.484974	+	0.874529i	$0.338829\pi$
$84$	2.66676	0.290968
$85$	0	0
$86$	−16.7979	−1.81136
$87$	−5.94608	−0.637487
$88$	−0.787912	−0.0839917
$89$	−0.224416	−0.0237881	−0.0118940	−	0.999929i	$-0.503786\pi$
$89$	−0.224416	−0.0237881	−0.0118940	+	0.999929i	$0.503786\pi$
$90$	−6.66475	−0.702526
$91$	−2.07615	−0.217640
$92$	−7.71647	−0.804498
$93$	3.24004	0.335976
$94$	−11.1360	−1.14859
$95$	−6.31877	−0.648293
$96$	−7.53953	−0.769500
$97$	3.00802	0.305418	0.152709	−	0.988271i	$-0.451200\pi$
$97$	3.00802	0.305418	0.152709	+	0.988271i	$0.451200\pi$
$98$	8.29644	0.838067
$99$	1.91687	0.192653
$100$	−2.57657	−0.257657
$101$	10.9859	1.09314	0.546570	−	0.837413i	$-0.315933\pi$
$101$	10.9859	1.09314	0.546570	+	0.837413i	$0.315933\pi$
$102$	0	0
$103$	−2.28423	−0.225071	−0.112536	−	0.993648i	$-0.535897\pi$
$103$	−2.28423	−0.225071	−0.112536	+	0.993648i	$0.535897\pi$
$104$	1.01109	0.0991459
$105$	−3.09246	−0.301793
$106$	−6.10968	−0.593425
$107$	0.820377	0.0793088	0.0396544	−	0.999213i	$-0.487374\pi$
$107$	0.820377	0.0793088	0.0396544	+	0.999213i	$0.487374\pi$
$108$	8.10454	0.779859
$109$	14.9626	1.43316	0.716581	−	0.697504i	$-0.245706\pi$
$109$	14.9626	1.43316	0.716581	+	0.697504i	$0.245706\pi$
$110$	−3.47689	−0.331508
$111$	7.10501	0.674377
$112$	7.53798	0.712272
$113$	−7.81788	−0.735444	−0.367722	−	0.929936i	$-0.619862\pi$
$113$	−7.81788	−0.735444	−0.367722	+	0.929936i	$0.619862\pi$
$114$	6.77837	0.634853
$115$	8.94825	0.834429
$116$	9.04879	0.840159
$117$	−2.45984	−0.227412
$118$	−4.55611	−0.419423
$119$	0	0
$120$	1.50604	0.137482
$121$	1.00000	0.0909091
$122$	−25.2221	−2.28350
$123$	−4.24454	−0.382717
$124$	−4.93071	−0.442791
$125$	12.1710	1.08860
$126$	−5.87097	−0.523028
$127$	−1.46313	−0.129832	−0.0649159	−	0.997891i	$-0.520678\pi$
$127$	−1.46313	−0.129832	−0.0649159	+	0.997891i	$0.520678\pi$
$128$	−6.16681	−0.545074
$129$	−9.23470	−0.813070
$130$	4.46175	0.391321
$131$	19.7300	1.72382	0.861910	−	0.507061i	$-0.169268\pi$
$131$	19.7300	1.72382	0.861910	+	0.507061i	$0.169268\pi$
$132$	1.64831	0.143467
$133$	−5.56620	−0.482651
$134$	−10.8424	−0.936639
$135$	−9.39827	−0.808874
$136$	0	0
$137$	−4.14244	−0.353913	−0.176956	−	0.984219i	$-0.556625\pi$
$137$	−4.14244	−0.353913	−0.176956	+	0.984219i	$0.556625\pi$
$138$	−9.59911	−0.817130
$139$	−12.5213	−1.06204	−0.531020	−	0.847359i	$-0.678191\pi$
$139$	−12.5213	−1.06204	−0.531020	+	0.847359i	$0.678191\pi$
$140$	4.70613	0.397740
$141$	−6.12205	−0.515570
$142$	12.2799	1.03051
$143$	−1.28326	−0.107311
$144$	8.93106	0.744255
$145$	−10.4933	−0.871417
$146$	8.19166	0.677946
$147$	4.56100	0.376185
$148$	−10.8124	−0.888778
$149$	−10.1258	−0.829538	−0.414769	−	0.909927i	$-0.636138\pi$
$149$	−10.1258	−0.829538	−0.414769	+	0.909927i	$0.636138\pi$
$150$	−3.20519	−0.261703
$151$	−12.6399	−1.02862	−0.514310	−	0.857604i	$-0.671952\pi$
$151$	−12.6399	−1.02862	−0.514310	+	0.857604i	$0.671952\pi$
$152$	2.71076	0.219872
$153$	0	0
$154$	−3.06279	−0.246806
$155$	5.71780	0.459265
$156$	−2.11521	−0.169352
$157$	19.0978	1.52417	0.762084	−	0.647478i	$-0.224176\pi$
$157$	19.0978	1.52417	0.762084	+	0.647478i	$0.224176\pi$
$158$	28.7174	2.28463
$159$	−3.35882	−0.266372
$160$	−13.3053	−1.05187
$161$	7.88251	0.621229
$162$	−0.804594	−0.0632149
$163$	−14.6835	−1.15010	−0.575049	−	0.818119i	$-0.695017\pi$
$163$	−14.6835	−1.15010	−0.575049	+	0.818119i	$0.695017\pi$
$164$	6.45937	0.504392
$165$	−1.91143	−0.148805
$166$	−16.7286	−1.29839
$167$	14.4124	1.11526	0.557631	−	0.830089i	$-0.311710\pi$
$167$	14.4124	1.11526	0.557631	+	0.830089i	$0.311710\pi$
$168$	1.32667	0.102355
$169$	−11.3532	−0.873327
$170$	0	0
$171$	−6.59488	−0.504323
$172$	14.0534	1.07156
$173$	2.54891	0.193790	0.0968949	−	0.995295i	$-0.469109\pi$
$173$	2.54891	0.193790	0.0968949	+	0.995295i	$0.469109\pi$
$174$	11.2565	0.853352
$175$	2.63201	0.198961
$176$	4.65918	0.351199
$177$	−2.50474	−0.188267
$178$	0.424840	0.0318431
$179$	22.0524	1.64828	0.824138	−	0.566389i	$-0.191660\pi$
$179$	22.0524	1.64828	0.824138	+	0.566389i	$0.191660\pi$
$180$	5.57586	0.415600
$181$	−8.84565	−0.657492	−0.328746	−	0.944418i	$-0.606626\pi$
$181$	−8.84565	−0.657492	−0.328746	+	0.944418i	$0.606626\pi$
$182$	3.93035	0.291337
$183$	−13.8660	−1.02500
$184$	−3.83881	−0.283001
$185$	12.5384	0.921845
$186$	−6.13369	−0.449744
$187$	0	0
$188$	9.31658	0.679481
$189$	−8.27892	−0.602203
$190$	11.9620	0.867816
$191$	−19.2858	−1.39547	−0.697735	−	0.716356i	$-0.745809\pi$
$191$	−19.2858	−1.39547	−0.697735	+	0.716356i	$0.745809\pi$
$192$	4.57509	0.330178
$193$	−4.08551	−0.294081	−0.147041	−	0.989130i	$-0.546975\pi$
$193$	−4.08551	−0.294081	−0.147041	+	0.989130i	$0.546975\pi$
$194$	−5.69446	−0.408838
$195$	2.45286	0.175653
$196$	−6.94095	−0.495782
$197$	−23.2199	−1.65435	−0.827175	−	0.561944i	$-0.810054\pi$
$197$	−23.2199	−1.65435	−0.827175	+	0.561944i	$0.810054\pi$
$198$	−3.62882	−0.257889
$199$	−11.8668	−0.841218	−0.420609	−	0.907242i	$-0.638184\pi$
$199$	−11.8668	−0.841218	−0.420609	+	0.907242i	$0.638184\pi$
$200$	−1.28180	−0.0906369
$201$	−5.96064	−0.420431
$202$	−20.7974	−1.46330
$203$	−9.24350	−0.648766
$204$	0	0
$205$	−7.49048	−0.523158
$206$	4.32425	0.301285
$207$	9.33926	0.649123
$208$	−5.97893	−0.414564
$209$	−3.44044	−0.237980
$210$	5.85431	0.403986
$211$	2.35501	0.162126	0.0810629	−	0.996709i	$-0.474169\pi$
$211$	2.35501	0.162126	0.0810629	+	0.996709i	$0.474169\pi$
$212$	5.11148	0.351058
$213$	6.75092	0.462565
$214$	−1.55305	−0.106164
$215$	−16.2968	−1.11143
$216$	4.03187	0.274334
$217$	5.03681	0.341921
$218$	−28.3257	−1.91846
$219$	4.50339	0.304311
$220$	2.90883	0.196113
$221$	0	0
$222$	−13.4504	−0.902734
$223$	17.4889	1.17115	0.585573	−	0.810619i	$-0.300869\pi$
$223$	17.4889	1.17115	0.585573	+	0.810619i	$0.300869\pi$
$224$	−11.7206	−0.783115
$225$	3.11843	0.207895
$226$	14.8000	0.984479
$227$	18.8429	1.25064	0.625322	−	0.780366i	$-0.284967\pi$
$227$	18.8429	1.25064	0.625322	+	0.780366i	$0.284967\pi$
$228$	−5.67091	−0.375565
$229$	−28.7799	−1.90183	−0.950913	−	0.309457i	$-0.899853\pi$
$229$	−28.7799	−1.90183	−0.950913	+	0.309457i	$0.899853\pi$
$230$	−16.9399	−1.11698
$231$	−1.68378	−0.110784
$232$	4.50162	0.295546
$233$	11.3102	0.740957	0.370479	−	0.928841i	$-0.379194\pi$
$233$	11.3102	0.740957	0.370479	+	0.928841i	$0.379194\pi$
$234$	4.65671	0.304418
$235$	−10.8038	−0.704761
$236$	3.81172	0.248122
$237$	15.7875	1.02551
$238$	0	0
$239$	12.5722	0.813226	0.406613	−	0.913601i	$-0.366710\pi$
$239$	12.5722	0.813226	0.406613	+	0.913601i	$0.366710\pi$
$240$	−8.90571	−0.574861
$241$	−8.91176	−0.574057	−0.287029	−	0.957922i	$-0.592667\pi$
$241$	−8.91176	−0.574057	−0.287029	+	0.957922i	$0.592667\pi$
$242$	−1.89309	−0.121693
$243$	−15.7938	−1.01317
$244$	21.1013	1.35087
$245$	8.04894	0.514228
$246$	8.03530	0.512312
$247$	4.41497	0.280918
$248$	−2.45294	−0.155762
$249$	−9.19660	−0.582811
$250$	−23.0407	−1.45722
$251$	−11.2312	−0.708905	−0.354453	−	0.935074i	$-0.615333\pi$
$251$	−11.2312	−0.708905	−0.354453	+	0.935074i	$0.615333\pi$
$252$	4.91176	0.309412
$253$	4.87213	0.306308
$254$	2.76984	0.173795
$255$	0	0
$256$	20.4664	1.27915
$257$	9.26127	0.577702	0.288851	−	0.957374i	$-0.406727\pi$
$257$	9.26127	0.577702	0.288851	+	0.957374i	$0.406727\pi$
$258$	17.4821	1.08839
$259$	11.0451	0.686309
$260$	−3.73278	−0.231497
$261$	−10.9518	−0.677898
$262$	−37.3507	−2.30754
$263$	−23.0851	−1.42349	−0.711743	−	0.702440i	$-0.752094\pi$
$263$	−23.0851	−1.42349	−0.711743	+	0.702440i	$0.752094\pi$
$264$	0.820007	0.0504679
$265$	−5.92743	−0.364119
$266$	10.5373	0.646085
$267$	0.233558	0.0142935
$268$	9.07094	0.554096
$269$	−11.3134	−0.689789	−0.344895	−	0.938641i	$-0.612085\pi$
$269$	−11.3134	−0.689789	−0.344895	+	0.938641i	$0.612085\pi$
$270$	17.7918	1.08277
$271$	25.3568	1.54032	0.770159	−	0.637852i	$-0.220177\pi$
$271$	25.3568	1.54032	0.770159	+	0.637852i	$0.220177\pi$
$272$	0	0
$273$	2.16072	0.130773
$274$	7.84202	0.473754
$275$	1.62683	0.0981016
$276$	8.03079	0.483397
$277$	−11.6243	−0.698434	−0.349217	−	0.937042i	$-0.613552\pi$
$277$	−11.6243	−0.698434	−0.349217	+	0.937042i	$0.613552\pi$
$278$	23.7039	1.42167
$279$	5.96765	0.357274
$280$	2.34122	0.139914
$281$	−28.2677	−1.68631	−0.843156	−	0.537669i	$-0.819305\pi$
$281$	−28.2677	−1.68631	−0.843156	+	0.537669i	$0.819305\pi$
$282$	11.5896	0.690151
$283$	−21.0144	−1.24917	−0.624587	−	0.780955i	$-0.714733\pi$
$283$	−21.0144	−1.24917	−0.624587	+	0.780955i	$0.714733\pi$
$284$	−10.2736	−0.609625
$285$	6.57616	0.389538
$286$	2.42933	0.143649
$287$	−6.59835	−0.389489
$288$	−13.8867	−0.818279
$289$	0	0
$290$	19.8647	1.16649
$291$	−3.13055	−0.183516
$292$	−6.85330	−0.401059
$293$	−8.19871	−0.478974	−0.239487	−	0.970900i	$-0.576979\pi$
$293$	−8.19871	−0.478974	−0.239487	+	0.970900i	$0.576979\pi$
$294$	−8.63438	−0.503568
$295$	−4.42019	−0.257354
$296$	−5.37901	−0.312649
$297$	−5.11716	−0.296928
$298$	19.1691	1.11043
$299$	−6.25221	−0.361574
$300$	2.68152	0.154818
$301$	−14.3558	−0.827455
$302$	23.9285	1.37693
$303$	−11.4334	−0.656834
$304$	−16.0296	−0.919362
$305$	−24.4697	−1.40113
$306$	0	0
$307$	2.90161	0.165604	0.0828020	−	0.996566i	$-0.473613\pi$
$307$	2.90161	0.165604	0.0828020	+	0.996566i	$0.473613\pi$
$308$	2.56239	0.146005
$309$	2.37727	0.135238
$310$	−10.8243	−0.614780
$311$	−14.2764	−0.809541	−0.404770	−	0.914418i	$-0.632649\pi$
$311$	−14.2764	−0.809541	−0.404770	+	0.914418i	$0.632649\pi$
$312$	−1.05228	−0.0595736
$313$	−23.8601	−1.34866	−0.674328	−	0.738432i	$-0.735566\pi$
$313$	−23.8601	−1.34866	−0.674328	+	0.738432i	$0.735566\pi$
$314$	−36.1538	−2.04028
$315$	−5.69583	−0.320924
$316$	−24.0255	−1.35154
$317$	5.67962	0.318999	0.159499	−	0.987198i	$-0.449012\pi$
$317$	5.67962	0.318999	0.159499	+	0.987198i	$0.449012\pi$
$318$	6.35856	0.356570
$319$	−5.71335	−0.319886
$320$	8.07381	0.451340
$321$	−0.853794	−0.0476541
$322$	−14.9223	−0.831588
$323$	0	0
$324$	0.673139	0.0373966
$325$	−2.08764	−0.115802
$326$	27.7971	1.53954
$327$	−15.5721	−0.861141
$328$	3.21342	0.177432
$329$	−9.51704	−0.524692
$330$	3.61852	0.199193
$331$	−12.1892	−0.669976	−0.334988	−	0.942222i	$-0.608732\pi$
$331$	−12.1892	−0.669976	−0.334988	+	0.942222i	$0.608732\pi$
$332$	13.9954	0.768100
$333$	13.0863	0.717126
$334$	−27.2839	−1.49291
$335$	−10.5189	−0.574711
$336$	−7.84503	−0.427981
$337$	−17.3002	−0.942403	−0.471201	−	0.882026i	$-0.656180\pi$
$337$	−17.3002	−0.942403	−0.471201	+	0.882026i	$0.656180\pi$
$338$	21.4927	1.16905
$339$	8.13634	0.441905
$340$	0	0
$341$	3.11322	0.168590
$342$	12.4847	0.675096
$343$	18.4154	0.994340
$344$	6.99134	0.376948
$345$	−9.31276	−0.501382
$346$	−4.82531	−0.259410
$347$	16.5351	0.887652	0.443826	−	0.896113i	$-0.353621\pi$
$347$	16.5351	0.887652	0.443826	+	0.896113i	$0.353621\pi$
$348$	−9.41739	−0.504825
$349$	−18.3064	−0.979917	−0.489958	−	0.871746i	$-0.662988\pi$
$349$	−18.3064	−0.979917	−0.489958	+	0.871746i	$0.662988\pi$
$350$	−4.98264	−0.266333
$351$	6.56663	0.350501
$352$	−7.24444	−0.386130
$353$	20.1864	1.07442	0.537208	−	0.843450i	$-0.319479\pi$
$353$	20.1864	1.07442	0.537208	+	0.843450i	$0.319479\pi$
$354$	4.74169	0.252018
$355$	11.9136	0.632307
$356$	−0.355429	−0.0188377
$357$	0	0
$358$	−41.7473	−2.20641
$359$	−2.91364	−0.153776	−0.0768880	−	0.997040i	$-0.524498\pi$
$359$	−2.91364	−0.153776	−0.0768880	+	0.997040i	$0.524498\pi$
$360$	2.77389	0.146197
$361$	−7.16338	−0.377020
$362$	16.7456	0.880131
$363$	−1.04073	−0.0546244
$364$	−3.28820	−0.172349
$365$	7.94729	0.415980
$366$	26.2495	1.37208
$367$	−4.13761	−0.215982	−0.107991	−	0.994152i	$-0.534442\pi$
$367$	−4.13761	−0.215982	−0.107991	+	0.994152i	$0.534442\pi$
$368$	22.7002	1.18333
$369$	−7.81779	−0.406978
$370$	−23.7364	−1.23400
$371$	−5.22146	−0.271085
$372$	5.13156	0.266059
$373$	−21.3727	−1.10664	−0.553319	−	0.832969i	$-0.686639\pi$
$373$	−21.3727	−1.10664	−0.553319	+	0.832969i	$0.686639\pi$
$374$	0	0
$375$	−12.6667	−0.654108
$376$	4.63484	0.239024
$377$	7.33171	0.377602
$378$	15.6728	0.806120
$379$	−23.5046	−1.20735	−0.603675	−	0.797231i	$-0.706297\pi$
$379$	−23.5046	−1.20735	−0.603675	+	0.797231i	$0.706297\pi$
$380$	−10.0077	−0.513382
$381$	1.52273	0.0780118
$382$	36.5098	1.86800
$383$	−2.05353	−0.104930	−0.0524651	−	0.998623i	$-0.516708\pi$
$383$	−2.05353	−0.104930	−0.0524651	+	0.998623i	$0.516708\pi$
$384$	6.41801	0.327518
$385$	−2.97142	−0.151438
$386$	7.73424	0.393663
$387$	−17.0089	−0.864610
$388$	4.76409	0.241860
$389$	−19.2367	−0.975338	−0.487669	−	0.873029i	$-0.662153\pi$
$389$	−19.2367	−0.975338	−0.487669	+	0.873029i	$0.662153\pi$
$390$	−4.64349	−0.235132
$391$	0	0
$392$	−3.45301	−0.174403
$393$	−20.5337	−1.03579
$394$	43.9574	2.21454
$395$	27.8607	1.40183
$396$	3.03594	0.152561
$397$	−32.8511	−1.64875	−0.824375	−	0.566044i	$-0.808473\pi$
$397$	−32.8511	−1.64875	−0.824375	+	0.566044i	$0.808473\pi$
$398$	22.4650	1.12607
$399$	5.79294	0.290010
$400$	7.57970	0.378985
$401$	−34.5217	−1.72393	−0.861966	−	0.506965i	$-0.830767\pi$
$401$	−34.5217	−1.72393	−0.861966	+	0.506965i	$0.830767\pi$
$402$	11.2840	0.562797
$403$	−3.99507	−0.199009
$404$	17.3995	0.865656
$405$	−0.780592	−0.0387879
$406$	17.4988	0.868450
$407$	6.82692	0.338398
$408$	0	0
$409$	−4.94755	−0.244641	−0.122320	−	0.992491i	$-0.539034\pi$
$409$	−4.94755	−0.244641	−0.122320	+	0.992491i	$0.539034\pi$
$410$	14.1802	0.700308
$411$	4.31118	0.212655
$412$	−3.61775	−0.178234
$413$	−3.89374	−0.191599
$414$	−17.6801	−0.868928
$415$	−16.2295	−0.796677
$416$	9.29648	0.455798
$417$	13.0313	0.638146
$418$	6.51307	0.318564
$419$	−35.9029	−1.75397	−0.876985	−	0.480517i	$-0.840449\pi$
$419$	−35.9029	−1.75397	−0.876985	+	0.480517i	$0.840449\pi$
$420$	−4.89783	−0.238989
$421$	36.4835	1.77810	0.889048	−	0.457815i	$-0.151368\pi$
$421$	36.4835	1.77810	0.889048	+	0.457815i	$0.151368\pi$
$422$	−4.45825	−0.217024
$423$	−11.2759	−0.548252
$424$	2.54287	0.123493
$425$	0	0
$426$	−12.7801	−0.619198
$427$	−21.5553	−1.04314
$428$	1.29931	0.0628045
$429$	1.33553	0.0644800
$430$	30.8513	1.48778
$431$	16.8667	0.812438	0.406219	−	0.913776i	$-0.366847\pi$
$431$	16.8667	0.812438	0.406219	+	0.913776i	$0.366847\pi$
$432$	−23.8418	−1.14709
$433$	37.6635	1.80999	0.904996	−	0.425419i	$-0.139873\pi$
$433$	37.6635	1.80999	0.904996	+	0.425419i	$0.139873\pi$
$434$	−9.53513	−0.457701
$435$	10.9207	0.523607
$436$	23.6978	1.13492
$437$	−16.7623	−0.801849
$438$	−8.52534	−0.407356
$439$	−6.36970	−0.304009	−0.152005	−	0.988380i	$-0.548573\pi$
$439$	−6.36970	−0.304009	−0.152005	+	0.988380i	$0.548573\pi$
$440$	1.44709	0.0689875
$441$	8.40065	0.400031
$442$	0	0
$443$	32.7843	1.55763	0.778814	−	0.627254i	$-0.215821\pi$
$443$	32.7843	1.55763	0.778814	+	0.627254i	$0.215821\pi$
$444$	11.2529	0.534038
$445$	0.412167	0.0195386
$446$	−33.1082	−1.56772
$447$	10.5383	0.498443
$448$	7.11221	0.336020
$449$	26.9500	1.27185	0.635925	−	0.771751i	$-0.280619\pi$
$449$	26.9500	1.27185	0.635925	+	0.771751i	$0.280619\pi$
$450$	−5.90347	−0.278292
$451$	−4.07841	−0.192045
$452$	−12.3819	−0.582397
$453$	13.1548	0.618065
$454$	−35.6713	−1.67414
$455$	3.81310	0.178761
$456$	−2.82118	−0.132114
$457$	38.4562	1.79890	0.899451	−	0.437021i	$-0.143966\pi$
$457$	38.4562	1.79890	0.899451	+	0.437021i	$0.143966\pi$
$458$	54.4829	2.54582
$459$	0	0
$460$	14.1722	0.660783
$461$	−9.17232	−0.427197	−0.213599	−	0.976921i	$-0.568518\pi$
$461$	−9.17232	−0.427197	−0.213599	+	0.976921i	$0.568518\pi$
$462$	3.18755	0.148298
$463$	17.3391	0.805816	0.402908	−	0.915241i	$-0.368000\pi$
$463$	17.3391	0.805816	0.402908	+	0.915241i	$0.368000\pi$
$464$	−26.6196	−1.23578
$465$	−5.95071	−0.275958
$466$	−21.4113	−0.991859
$467$	14.5702	0.674228	0.337114	−	0.941464i	$-0.390549\pi$
$467$	14.5702	0.674228	0.337114	+	0.941464i	$0.390549\pi$
$468$	−3.89589	−0.180088
$469$	−9.26612	−0.427870
$470$	20.4526	0.943406
$471$	−19.8757	−0.915824
$472$	1.89627	0.0872828
$473$	−8.87325	−0.407992
$474$	−29.8872	−1.37276
$475$	−5.59701	−0.256809
$476$	0	0
$477$	−6.18643	−0.283257
$478$	−23.8003	−1.08860
$479$	−17.1903	−0.785447	−0.392723	−	0.919657i	$-0.628467\pi$
$479$	−17.1903	−0.785447	−0.392723	+	0.919657i	$0.628467\pi$
$480$	13.8472	0.632037
$481$	−8.76070	−0.399453
$482$	16.8708	0.768443
$483$	−8.20359	−0.373276
$484$	1.58380	0.0719907
$485$	−5.52459	−0.250859
$486$	29.8991	1.35625
$487$	−14.8971	−0.675052	−0.337526	−	0.941316i	$-0.609590\pi$
$487$	−14.8971	−0.675052	−0.337526	+	0.941316i	$0.609590\pi$
$488$	10.4975	0.475201
$489$	15.2816	0.691057
$490$	−15.2374	−0.688355
$491$	−26.9549	−1.21646	−0.608230	−	0.793761i	$-0.708120\pi$
$491$	−26.9549	−1.21646	−0.608230	+	0.793761i	$0.708120\pi$
$492$	−6.72248	−0.303073
$493$	0	0
$494$	−8.35794	−0.376042
$495$	−3.52056	−0.158238
$496$	14.5051	0.651297
$497$	10.4947	0.470749
$498$	17.4100	0.780161
$499$	−35.3431	−1.58218	−0.791088	−	0.611703i	$-0.790485\pi$
$499$	−35.3431	−1.58218	−0.791088	+	0.611703i	$0.790485\pi$
$500$	19.2763	0.862064
$501$	−14.9994	−0.670125
$502$	21.2616	0.948953
$503$	14.1091	0.629092	0.314546	−	0.949242i	$-0.398148\pi$
$503$	14.1091	0.629092	0.314546	+	0.949242i	$0.398148\pi$
$504$	2.44352	0.108843
$505$	−20.1770	−0.897863
$506$	−9.22340	−0.410030
$507$	11.8157	0.524754
$508$	−2.31730	−0.102814
$509$	−34.9202	−1.54781	−0.773905	−	0.633302i	$-0.781699\pi$
$509$	−34.9202	−1.54781	−0.773905	+	0.633302i	$0.781699\pi$
$510$	0	0
$511$	7.00076	0.309695
$512$	−26.4111	−1.16722
$513$	17.6053	0.777291
$514$	−17.5324	−0.773322
$515$	4.19525	0.184865
$516$	−14.6259	−0.643868
$517$	−5.88243	−0.258709
$518$	−20.9094	−0.918706
$519$	−2.65273	−0.116442
$520$	−1.85699	−0.0814346
$521$	16.3331	0.715566	0.357783	−	0.933805i	$-0.383533\pi$
$521$	16.3331	0.715566	0.357783	+	0.933805i	$0.383533\pi$
$522$	20.7327	0.907446
$523$	−38.9674	−1.70393	−0.851963	−	0.523602i	$-0.824588\pi$
$523$	−38.9674	−1.70393	−0.851963	+	0.523602i	$0.824588\pi$
$524$	31.2483	1.36509
$525$	−2.73922	−0.119549
$526$	43.7022	1.90550
$527$	0	0
$528$	−4.84897	−0.211024
$529$	0.737696	0.0320738
$530$	11.2212	0.487416
$531$	−4.61334	−0.200202
$532$	−8.81573	−0.382210
$533$	5.23365	0.226695
$534$	−0.442146	−0.0191335
$535$	−1.50672	−0.0651412
$536$	4.51264	0.194916
$537$	−22.9507	−0.990396
$538$	21.4173	0.923364
$539$	4.38248	0.188767
$540$	−14.8849	−0.640546
$541$	2.74107	0.117848	0.0589240	−	0.998262i	$-0.481233\pi$
$541$	2.74107	0.117848	0.0589240	+	0.998262i	$0.481233\pi$
$542$	−48.0028	−2.06190
$543$	9.20598	0.395066
$544$	0	0
$545$	−27.4807	−1.17714
$546$	−4.09045	−0.175055
$547$	15.7423	0.673090	0.336545	−	0.941667i	$-0.390742\pi$
$547$	15.7423	0.673090	0.336545	+	0.941667i	$0.390742\pi$
$548$	−6.56079	−0.280263
$549$	−25.5390	−1.08998
$550$	−3.07974	−0.131321
$551$	19.6564	0.837393
$552$	3.99518	0.170046
$553$	24.5425	1.04365
$554$	22.0058	0.934936
$555$	−13.0492	−0.553907
$556$	−19.8311	−0.841027
$557$	−35.4962	−1.50402	−0.752011	−	0.659151i	$-0.770916\pi$
$557$	−35.4962	−1.50402	−0.752011	+	0.659151i	$0.770916\pi$
$558$	−11.2973	−0.478253
$559$	11.3867	0.481605
$560$	−13.8444	−0.585032
$561$	0	0
$562$	53.5134	2.25733
$563$	9.71344	0.409373	0.204686	−	0.978828i	$-0.434383\pi$
$563$	9.71344	0.409373	0.204686	+	0.978828i	$0.434383\pi$
$564$	−9.69608	−0.408279
$565$	14.3585	0.604065
$566$	39.7821	1.67217
$567$	−0.687623	−0.0288774
$568$	−5.11094	−0.214450
$569$	40.5109	1.69831	0.849153	−	0.528146i	$-0.177113\pi$
$569$	40.5109	1.69831	0.849153	+	0.528146i	$0.177113\pi$
$570$	−12.4493	−0.521443
$571$	11.6285	0.486639	0.243319	−	0.969946i	$-0.421764\pi$
$571$	11.6285	0.486639	0.243319	+	0.969946i	$0.421764\pi$
$572$	−2.03242	−0.0849797
$573$	20.0714	0.838494
$574$	12.4913	0.521376
$575$	7.92614	0.330543
$576$	8.42660	0.351108
$577$	−39.1972	−1.63180	−0.815901	−	0.578191i	$-0.803759\pi$
$577$	−39.1972	−1.63180	−0.815901	+	0.578191i	$0.803759\pi$
$578$	0	0
$579$	4.25193	0.176704
$580$	−16.6192	−0.690074
$581$	−14.2966	−0.593122
$582$	5.92642	0.245658
$583$	−3.22736	−0.133663
$584$	−3.40940	−0.141082
$585$	4.51779	0.186788
$586$	15.5209	0.641163
$587$	1.65131	0.0681570	0.0340785	−	0.999419i	$-0.489150\pi$
$587$	1.65131	0.0681570	0.0340785	+	0.999419i	$0.489150\pi$
$588$	7.22369	0.297900
$589$	−10.7108	−0.441333
$590$	8.36783	0.344498
$591$	24.1658	0.994047
$592$	31.8079	1.30729
$593$	16.1778	0.664344	0.332172	−	0.943219i	$-0.392219\pi$
$593$	16.1778	0.664344	0.332172	+	0.943219i	$0.392219\pi$
$594$	9.68725	0.397473
$595$	0	0
$596$	−16.0372	−0.656910
$597$	12.3502	0.505461
$598$	11.8360	0.484010
$599$	−24.6091	−1.00550	−0.502751	−	0.864431i	$-0.667679\pi$
$599$	−24.6091	−1.00550	−0.502751	+	0.864431i	$0.667679\pi$
$600$	1.33401	0.0544608
$601$	21.8034	0.889379	0.444690	−	0.895685i	$-0.353314\pi$
$601$	21.8034	0.889379	0.444690	+	0.895685i	$0.353314\pi$
$602$	27.1769	1.10765
$603$	−10.9786	−0.447082
$604$	−20.0190	−0.814562
$605$	−1.83662	−0.0746692
$606$	21.6445	0.879249
$607$	−23.6599	−0.960326	−0.480163	−	0.877179i	$-0.659422\pi$
$607$	−23.6599	−0.960326	−0.480163	+	0.877179i	$0.659422\pi$
$608$	24.9240	1.01080
$609$	9.62002	0.389823
$610$	46.3234	1.87558
$611$	7.54868	0.305387
$612$	0	0
$613$	9.35899	0.378006	0.189003	−	0.981977i	$-0.439474\pi$
$613$	9.35899	0.378006	0.189003	+	0.981977i	$0.439474\pi$
$614$	−5.49302	−0.221680
$615$	7.79560	0.314349
$616$	1.27474	0.0513609
$617$	44.6480	1.79746	0.898731	−	0.438501i	$-0.144490\pi$
$617$	44.6480	1.79746	0.898731	+	0.438501i	$0.144490\pi$
$618$	−4.50039	−0.181032
$619$	48.1191	1.93407	0.967034	−	0.254646i	$-0.0819591\pi$
$619$	48.1191	1.93407	0.967034	+	0.254646i	$0.0819591\pi$
$620$	9.05583	0.363691
$621$	−24.9315	−1.00047
$622$	27.0265	1.08367
$623$	0.363077	0.0145464
$624$	6.22248	0.249099
$625$	−14.2193	−0.568771
$626$	45.1694	1.80533
$627$	3.58058	0.142995
$628$	30.2470	1.20699
$629$	0	0
$630$	10.7827	0.429594
$631$	−0.800363	−0.0318620	−0.0159310	−	0.999873i	$-0.505071\pi$
$631$	−0.800363	−0.0318620	−0.0159310	+	0.999873i	$0.505071\pi$
$632$	−11.9523	−0.475436
$633$	−2.45094	−0.0974162
$634$	−10.7520	−0.427018
$635$	2.68721	0.106639
$636$	−5.31969	−0.210939
$637$	−5.62385	−0.222825
$638$	10.8159	0.428206
$639$	12.4342	0.491887
$640$	11.3261	0.447702
$641$	31.4348	1.24160	0.620799	−	0.783970i	$-0.286808\pi$
$641$	31.4348	1.24160	0.620799	+	0.783970i	$0.286808\pi$
$642$	1.61631	0.0637907
$643$	17.2003	0.678313	0.339156	−	0.940730i	$-0.389858\pi$
$643$	17.2003	0.678313	0.339156	+	0.940730i	$0.389858\pi$
$644$	12.4843	0.491950
$645$	16.9606	0.667824
$646$	0	0
$647$	−30.8508	−1.21287	−0.606434	−	0.795134i	$-0.707401\pi$
$647$	−30.8508	−1.21287	−0.606434	+	0.795134i	$0.707401\pi$
$648$	0.334875	0.0131551
$649$	−2.40670	−0.0944713
$650$	3.95210	0.155014
$651$	−5.24198	−0.205449
$652$	−23.2556	−0.910760
$653$	27.8033	1.08803	0.544014	−	0.839076i	$-0.316904\pi$
$653$	27.8033	1.08803	0.544014	+	0.839076i	$0.316904\pi$
$654$	29.4795	1.15274
$655$	−36.2365	−1.41588
$656$	−19.0020	−0.741905
$657$	8.29456	0.323602
$658$	18.0166	0.702362
$659$	26.7714	1.04286	0.521432	−	0.853293i	$-0.325398\pi$
$659$	26.7714	1.04286	0.521432	+	0.853293i	$0.325398\pi$
$660$	−3.02732	−0.117838
$661$	−29.0467	−1.12979	−0.564893	−	0.825164i	$-0.691083\pi$
$661$	−29.0467	−1.12979	−0.564893	+	0.825164i	$0.691083\pi$
$662$	23.0752	0.896842
$663$	0	0
$664$	6.96249	0.270197
$665$	10.2230	0.396431
$666$	−24.7736	−0.959958
$667$	−27.8362	−1.07782
$668$	22.8262	0.883174
$669$	−18.2013	−0.703705
$670$	19.9133	0.769319
$671$	−13.3232	−0.514338
$672$	12.1980	0.470549
$673$	−11.2184	−0.432436	−0.216218	−	0.976345i	$-0.569372\pi$
$673$	−11.2184	−0.432436	−0.216218	+	0.976345i	$0.569372\pi$
$674$	32.7509	1.26152
$675$	−8.32475	−0.320420
$676$	−17.9812	−0.691586
$677$	38.4702	1.47853	0.739265	−	0.673415i	$-0.235173\pi$
$677$	38.4702	1.47853	0.739265	+	0.673415i	$0.235173\pi$
$678$	−15.4028	−0.591542
$679$	−4.86660	−0.186763
$680$	0	0
$681$	−19.6104	−0.751473
$682$	−5.89361	−0.225678
$683$	−1.93556	−0.0740620	−0.0370310	−	0.999314i	$-0.511790\pi$
$683$	−1.93556	−0.0740620	−0.0370310	+	0.999314i	$0.511790\pi$
$684$	−10.4449	−0.399373
$685$	7.60809	0.290690
$686$	−34.8621	−1.33104
$687$	29.9522	1.14275
$688$	−41.3421	−1.57615
$689$	4.14153	0.157780
$690$	17.6299	0.671159
$691$	15.0187	0.571336	0.285668	−	0.958329i	$-0.407784\pi$
$691$	15.0187	0.571336	0.285668	+	0.958329i	$0.407784\pi$
$692$	4.03695	0.153462
$693$	−3.10126	−0.117807
$694$	−31.3025	−1.18823
$695$	22.9968	0.872318
$696$	−4.68499	−0.177584
$697$	0	0
$698$	34.6556	1.31173
$699$	−11.7709	−0.445218
$700$	4.16857	0.157557
$701$	12.0090	0.453573	0.226787	−	0.973944i	$-0.427178\pi$
$701$	12.0090	0.453573	0.226787	+	0.973944i	$0.427178\pi$
$702$	−12.4312	−0.469187
$703$	−23.4876	−0.885851
$704$	4.39602	0.165681
$705$	11.2439	0.423469
$706$	−38.2148	−1.43823
$707$	−17.7739	−0.668455
$708$	−3.96699	−0.149089
$709$	−5.86949	−0.220433	−0.110217	−	0.993908i	$-0.535154\pi$
$709$	−5.86949	−0.220433	−0.110217	+	0.993908i	$0.535154\pi$
$710$	−22.5535	−0.846417
$711$	29.0781	1.09052
$712$	−0.176820	−0.00662661
$713$	15.1680	0.568047
$714$	0	0
$715$	2.35686	0.0881414
$716$	34.9266	1.30527
$717$	−13.0843	−0.488641
$718$	5.51579	0.205847
$719$	16.3726	0.610596	0.305298	−	0.952257i	$-0.401244\pi$
$719$	16.3726	0.610596	0.305298	+	0.952257i	$0.401244\pi$
$720$	−16.4029	−0.611302
$721$	3.69559	0.137631
$722$	13.5609	0.504686
$723$	9.27478	0.344933
$724$	−14.0097	−0.520667
$725$	−9.29466	−0.345195
$726$	1.97021	0.0731212
$727$	2.82341	0.104714	0.0523572	−	0.998628i	$-0.483327\pi$
$727$	2.82341	0.104714	0.0523572	+	0.998628i	$0.483327\pi$
$728$	−1.63582	−0.0606277
$729$	15.1621	0.561559
$730$	−15.0450	−0.556839
$731$	0	0
$732$	−21.9608	−0.811696
$733$	12.8741	0.475515	0.237757	−	0.971325i	$-0.423588\pi$
$733$	12.8741	0.475515	0.237757	+	0.971325i	$0.423588\pi$
$734$	7.83288	0.289117
$735$	−8.37681	−0.308983
$736$	−35.2959	−1.30102
$737$	−5.72734	−0.210969
$738$	14.7998	0.544788
$739$	3.30278	0.121495	0.0607473	−	0.998153i	$-0.480652\pi$
$739$	3.30278	0.121495	0.0607473	+	0.998153i	$0.480652\pi$
$740$	19.8583	0.730007
$741$	−4.59481	−0.168795
$742$	9.88471	0.362879
$743$	32.6094	1.19632	0.598161	−	0.801376i	$-0.295898\pi$
$743$	32.6094	1.19632	0.598161	+	0.801376i	$0.295898\pi$
$744$	2.55286	0.0935925
$745$	18.5972	0.681350
$746$	40.4606	1.48137
$747$	−16.9387	−0.619755
$748$	0	0
$749$	−1.32727	−0.0484973
$750$	23.9793	0.875600
$751$	−8.35109	−0.304736	−0.152368	−	0.988324i	$-0.548690\pi$
$751$	−8.35109	−0.304736	−0.152368	+	0.988324i	$0.548690\pi$
$752$	−27.4073	−0.999442
$753$	11.6887	0.425959
$754$	−13.8796	−0.505465
$755$	23.2147	0.844868
$756$	−13.1121	−0.476883
$757$	−24.5010	−0.890504	−0.445252	−	0.895405i	$-0.646886\pi$
$757$	−24.5010	−0.890504	−0.445252	+	0.895405i	$0.646886\pi$
$758$	44.4963	1.61618
$759$	−5.07060	−0.184051
$760$	−4.97864	−0.180594
$761$	−45.1252	−1.63579	−0.817893	−	0.575370i	$-0.804858\pi$
$761$	−45.1252	−1.63579	−0.817893	+	0.575370i	$0.804858\pi$
$762$	−2.88267	−0.104428
$763$	−24.2077	−0.876377
$764$	−30.5447	−1.10507
$765$	0	0
$766$	3.88751	0.140462
$767$	3.08842	0.111516
$768$	−21.3000	−0.768599
$769$	−44.8524	−1.61742	−0.808709	−	0.588208i	$-0.799834\pi$
$769$	−44.8524	−1.61742	−0.808709	+	0.588208i	$0.799834\pi$
$770$	5.62517	0.202717
$771$	−9.63852	−0.347123
$772$	−6.47061	−0.232882
$773$	31.7881	1.14334	0.571670	−	0.820484i	$-0.306296\pi$
$773$	31.7881	1.14334	0.571670	+	0.820484i	$0.306296\pi$
$774$	32.1994	1.15738
$775$	5.06469	0.181929
$776$	2.37006	0.0850800
$777$	−11.4950	−0.412381
$778$	36.4168	1.30560
$779$	14.0315	0.502731
$780$	3.88483	0.139099
$781$	6.48669	0.232112
$782$	0	0
$783$	29.2361	1.04481
$784$	20.4188	0.729242
$785$	−35.0753	−1.25189
$786$	38.8722	1.38653
$787$	−5.53260	−0.197216	−0.0986079	−	0.995126i	$-0.531439\pi$
$787$	−5.53260	−0.197216	−0.0986079	+	0.995126i	$0.531439\pi$
$788$	−36.7756	−1.31008
$789$	24.0254	0.855328
$790$	−52.7429	−1.87651
$791$	12.6484	0.449724
$792$	1.51033	0.0536671
$793$	17.0972	0.607138
$794$	62.1902	2.20705
$795$	6.16888	0.218787
$796$	−18.7947	−0.666159
$797$	−13.0130	−0.460943	−0.230471	−	0.973079i	$-0.574027\pi$
$797$	−13.0130	−0.460943	−0.230471	+	0.973079i	$0.574027\pi$
$798$	−10.9666	−0.388212
$799$	0	0
$800$	−11.7855	−0.416679
$801$	0.430177	0.0151996
$802$	65.3528	2.30769
$803$	4.32713	0.152701
$804$	−9.44044	−0.332939
$805$	−14.4772	−0.510253
$806$	7.56303	0.266396
$807$	11.7742	0.414472
$808$	8.65594	0.304515
$809$	−53.2764	−1.87310	−0.936549	−	0.350537i	$-0.885999\pi$
$809$	−53.2764	−1.87310	−0.936549	+	0.350537i	$0.885999\pi$
$810$	1.47773	0.0519222
$811$	7.78374	0.273324	0.136662	−	0.990618i	$-0.456363\pi$
$811$	7.78374	0.273324	0.136662	+	0.990618i	$0.456363\pi$
$812$	−14.6398	−0.513757
$813$	−26.3897	−0.925528
$814$	−12.9240	−0.452985
$815$	26.9679	0.944645
$816$	0	0
$817$	30.5279	1.06803
$818$	9.36617	0.327480
$819$	3.97972	0.139063
$820$	−11.8634	−0.414288
$821$	6.90266	0.240904	0.120452	−	0.992719i	$-0.461566\pi$
$821$	6.90266	0.240904	0.120452	+	0.992719i	$0.461566\pi$
$822$	−8.16146	−0.284664
$823$	14.9280	0.520359	0.260179	−	0.965560i	$-0.416218\pi$
$823$	14.9280	0.520359	0.260179	+	0.965560i	$0.416218\pi$
$824$	−1.79977	−0.0626979
$825$	−1.69310	−0.0589461
$826$	7.37121	0.256477
$827$	37.7846	1.31390	0.656949	−	0.753935i	$-0.271847\pi$
$827$	37.7846	1.31390	0.656949	+	0.753935i	$0.271847\pi$
$828$	14.7915	0.514040
$829$	21.2552	0.738225	0.369112	−	0.929385i	$-0.379662\pi$
$829$	21.2552	0.738225	0.369112	+	0.929385i	$0.379662\pi$
$830$	30.7240	1.06645
$831$	12.0978	0.419667
$832$	−5.64123	−0.195574
$833$	0	0
$834$	−24.6695	−0.854233
$835$	−26.4700	−0.916032
$836$	−5.44895	−0.188456
$837$	−15.9308	−0.550651
$838$	67.9675	2.34790
$839$	45.0109	1.55395	0.776974	−	0.629533i	$-0.216754\pi$
$839$	45.0109	1.55395	0.776974	+	0.629533i	$0.216754\pi$
$840$	−2.43658	−0.0840702
$841$	3.64242	0.125601
$842$	−69.0666	−2.38019
$843$	29.4192	1.01325
$844$	3.72986	0.128387
$845$	20.8516	0.717317
$846$	21.3463	0.733900
$847$	−1.61788	−0.0555909
$848$	−15.0368	−0.516367
$849$	21.8704	0.750589
$850$	0	0
$851$	33.2617	1.14020
$852$	10.6921	0.366305
$853$	22.2427	0.761575	0.380787	−	0.924663i	$-0.375653\pi$
$853$	22.2427	0.761575	0.380787	+	0.924663i	$0.375653\pi$
$854$	40.8062	1.39636
$855$	12.1123	0.414231
$856$	0.646384	0.0220930
$857$	−16.2076	−0.553643	−0.276821	−	0.960921i	$-0.589281\pi$
$857$	−16.2076	−0.553643	−0.276821	+	0.960921i	$0.589281\pi$
$858$	−2.52828	−0.0863141
$859$	49.0231	1.67265	0.836324	−	0.548236i	$-0.184700\pi$
$859$	49.0231	1.67265	0.836324	+	0.548236i	$0.184700\pi$
$860$	−25.8108	−0.880140
$861$	6.86713	0.234031
$862$	−31.9301	−1.08754
$863$	38.6478	1.31559	0.657793	−	0.753199i	$-0.271490\pi$
$863$	38.6478	1.31559	0.657793	+	0.753199i	$0.271490\pi$
$864$	37.0709	1.26118
$865$	−4.68137	−0.159171
$866$	−71.3005	−2.42289
$867$	0	0
$868$	7.97727	0.270766
$869$	15.1696	0.514593
$870$	−20.6739	−0.700910
$871$	7.34966	0.249034
$872$	11.7892	0.399234
$873$	−5.76599	−0.195149
$874$	31.7325	1.07337
$875$	−19.6911	−0.665681
$876$	7.13246	0.240983
$877$	20.9561	0.707636	0.353818	−	0.935314i	$-0.384883\pi$
$877$	20.9561	0.707636	0.353818	+	0.935314i	$0.384883\pi$
$878$	12.0584	0.406952
$879$	8.53267	0.287800
$880$	−8.55714	−0.288461
$881$	12.6670	0.426763	0.213381	−	0.976969i	$-0.431552\pi$
$881$	12.6670	0.426763	0.213381	+	0.976969i	$0.431552\pi$
$882$	−15.9032	−0.535489
$883$	−18.7345	−0.630466	−0.315233	−	0.949014i	$-0.602083\pi$
$883$	−18.7345	−0.630466	−0.315233	+	0.949014i	$0.602083\pi$
$884$	0	0
$885$	4.60025	0.154636
$886$	−62.0637	−2.08507
$887$	−53.7375	−1.80433	−0.902165	−	0.431392i	$-0.858023\pi$
$887$	−53.7375	−1.80433	−0.902165	+	0.431392i	$0.858023\pi$
$888$	5.59812	0.187861
$889$	2.36716	0.0793921
$890$	−0.780270	−0.0261547
$891$	−0.425016	−0.0142386
$892$	27.6989	0.927429
$893$	20.2381	0.677244
$894$	−19.9499	−0.667225
$895$	−40.5019	−1.35383
$896$	9.97713	0.333312
$897$	6.50689	0.217259
$898$	−51.0189	−1.70252
$899$	−17.7869	−0.593228
$900$	4.93895	0.164632
$901$	0	0
$902$	7.72080	0.257074
$903$	14.9406	0.497192
$904$	−6.15980	−0.204872
$905$	16.2461	0.540039
$906$	−24.9032	−0.827353
$907$	46.0800	1.53006	0.765031	−	0.643994i	$-0.222724\pi$
$907$	46.0800	1.53006	0.765031	+	0.643994i	$0.222724\pi$
$908$	29.8433	0.990383
$909$	−21.0586	−0.698470
$910$	−7.21855	−0.239293
$911$	48.5919	1.60992	0.804960	−	0.593329i	$-0.202186\pi$
$911$	48.5919	1.60992	0.804960	+	0.593329i	$0.202186\pi$
$912$	16.6826	0.552415
$913$	−8.83664	−0.292450
$914$	−72.8010	−2.40804
$915$	25.4665	0.841896
$916$	−45.5814	−1.50605
$917$	−31.9207	−1.05411
$918$	0	0
$919$	−39.7916	−1.31260	−0.656301	−	0.754499i	$-0.727880\pi$
$919$	−39.7916	−1.31260	−0.656301	+	0.754499i	$0.727880\pi$
$920$	7.05043	0.232446
$921$	−3.01981	−0.0995061
$922$	17.3640	0.571854
$923$	−8.32409	−0.273991
$924$	−2.66676	−0.0877300
$925$	11.1062	0.365171
$926$	−32.8245	−1.07868
$927$	4.37857	0.143811
$928$	41.3900	1.35869
$929$	−25.1461	−0.825015	−0.412508	−	0.910954i	$-0.635347\pi$
$929$	−25.1461	−0.825015	−0.412508	+	0.910954i	$0.635347\pi$
$930$	11.2652	0.369402
$931$	−15.0776	−0.494150
$932$	17.9131	0.586763
$933$	14.8579	0.486427
$934$	−27.5827	−0.902534
$935$	0	0
$936$	−1.93814	−0.0633500
$937$	−17.0306	−0.556365	−0.278182	−	0.960528i	$-0.589732\pi$
$937$	−17.0306	−0.556365	−0.278182	+	0.960528i	$0.589732\pi$
$938$	17.5416	0.572754
$939$	24.8321	0.810364
$940$	−17.1110	−0.558099
$941$	−6.00656	−0.195808	−0.0979041	−	0.995196i	$-0.531214\pi$
$941$	−6.00656	−0.195808	−0.0979041	+	0.995196i	$0.531214\pi$
$942$	37.6265	1.22594
$943$	−19.8705	−0.647074
$944$	−11.2133	−0.364960
$945$	15.2052	0.494626
$946$	16.7979	0.546146
$947$	−11.9775	−0.389217	−0.194609	−	0.980881i	$-0.562344\pi$
$947$	−11.9775	−0.389217	−0.194609	+	0.980881i	$0.562344\pi$
$948$	25.0042	0.812098
$949$	−5.55283	−0.180252
$950$	10.5957	0.343768
$951$	−5.91097	−0.191676
$952$	0	0
$953$	−8.71556	−0.282325	−0.141162	−	0.989986i	$-0.545084\pi$
$953$	−8.71556	−0.282325	−0.141162	+	0.989986i	$0.545084\pi$
$954$	11.7115	0.379173
$955$	35.4206	1.14618
$956$	19.9117	0.643992
$957$	5.94608	0.192210
$958$	32.5429	1.05141
$959$	6.70196	0.216417
$960$	−8.40269	−0.271196
$961$	−21.3078	−0.687350
$962$	16.5848	0.534716
$963$	−1.57256	−0.0506749
$964$	−14.1144	−0.454595
$965$	7.50352	0.241547
$966$	15.5302	0.499675
$967$	−16.1880	−0.520571	−0.260286	−	0.965532i	$-0.583817\pi$
$967$	−16.1880	−0.520571	−0.260286	+	0.965532i	$0.583817\pi$
$968$	0.787912	0.0253244
$969$	0	0
$970$	10.4586	0.335804
$971$	−6.82159	−0.218915	−0.109458	−	0.993991i	$-0.534911\pi$
$971$	−6.82159	−0.218915	−0.109458	+	0.993991i	$0.534911\pi$
$972$	−25.0142	−0.802330
$973$	20.2578	0.649436
$974$	28.2016	0.903637
$975$	2.17268	0.0695815
$976$	−62.0754	−1.98699
$977$	−49.6393	−1.58810	−0.794050	−	0.607852i	$-0.792031\pi$
$977$	−49.6393	−1.58810	−0.794050	+	0.607852i	$0.792031\pi$
$978$	−28.9294	−0.925062
$979$	0.224416	0.00717237
$980$	12.7479	0.407216
$981$	−28.6815	−0.915729
$982$	51.0282	1.62837
$983$	39.8844	1.27212	0.636058	−	0.771641i	$-0.280564\pi$
$983$	39.8844	1.27212	0.636058	+	0.771641i	$0.280564\pi$
$984$	−3.34432	−0.106613
$985$	42.6461	1.35882
$986$	0	0
$987$	9.90471	0.315271
$988$	6.99241	0.222458
$989$	−43.2317	−1.37469
$990$	6.66475	0.211820
$991$	−51.9941	−1.65165	−0.825824	−	0.563928i	$-0.809289\pi$
$991$	−51.9941	−1.65165	−0.825824	+	0.563928i	$0.809289\pi$
$992$	−22.5535	−0.716075
$993$	12.6857	0.402568
$994$	−19.8673	−0.630154
$995$	21.7949	0.690944
$996$	−14.5655	−0.461527
$997$	37.2080	1.17839	0.589195	−	0.807991i	$-0.299445\pi$
$997$	37.2080	1.17839	0.589195	+	0.807991i	$0.299445\pi$
$998$	66.9078	2.11793
$999$	−34.9344	−1.10528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bb.1.2		8
17.4	even	4		187.2.d.a.67.14	yes	16
17.13	even	4		187.2.d.a.67.13	✓	16
17.16	even	2		3179.2.a.bc.1.2		8
51.38	odd	4		1683.2.g.b.1189.3		16
51.47	odd	4		1683.2.g.b.1189.4		16
68.47	odd	4		2992.2.b.g.1937.11		16
68.55	odd	4		2992.2.b.g.1937.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.13	✓	16	17.13	even	4
187.2.d.a.67.14	yes	16	17.4	even	4
1683.2.g.b.1189.3		16	51.38	odd	4
1683.2.g.b.1189.4		16	51.47	odd	4
2992.2.b.g.1937.6		16	68.55	odd	4
2992.2.b.g.1937.11		16	68.47	odd	4
3179.2.a.bb.1.2		8	1.1	even	1	trivial
3179.2.a.bc.1.2		8	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89309 q^{2} -1.04073 q^{3} +1.58380 q^{4} -1.83662 q^{5} +1.97021 q^{6} -1.61788 q^{7} +0.787912 q^{8} -1.91687 q^{9} +O(q^{10})\)	\(q-1.89309 q^{2} -1.04073 q^{3} +1.58380 q^{4} -1.83662 q^{5} +1.97021 q^{6} -1.61788 q^{7} +0.787912 q^{8} -1.91687 q^{9} +3.47689 q^{10} -1.00000 q^{11} -1.64831 q^{12} +1.28326 q^{13} +3.06279 q^{14} +1.91143 q^{15} -4.65918 q^{16} +3.62882 q^{18} +3.44044 q^{19} -2.90883 q^{20} +1.68378 q^{21} +1.89309 q^{22} -4.87213 q^{23} -0.820007 q^{24} -1.62683 q^{25} -2.42933 q^{26} +5.11716 q^{27} -2.56239 q^{28} +5.71335 q^{29} -3.61852 q^{30} -3.11322 q^{31} +7.24444 q^{32} +1.04073 q^{33} +2.97142 q^{35} -3.03594 q^{36} -6.82692 q^{37} -6.51307 q^{38} -1.33553 q^{39} -1.44709 q^{40} +4.07841 q^{41} -3.18755 q^{42} +8.87325 q^{43} -1.58380 q^{44} +3.52056 q^{45} +9.22340 q^{46} +5.88243 q^{47} +4.84897 q^{48} -4.38248 q^{49} +3.07974 q^{50} +2.03242 q^{52} +3.22736 q^{53} -9.68725 q^{54} +1.83662 q^{55} -1.27474 q^{56} -3.58058 q^{57} -10.8159 q^{58} +2.40670 q^{59} +3.02732 q^{60} +13.3232 q^{61} +5.89361 q^{62} +3.10126 q^{63} -4.39602 q^{64} -2.35686 q^{65} -1.97021 q^{66} +5.72734 q^{67} +5.07060 q^{69} -5.62517 q^{70} -6.48669 q^{71} -1.51033 q^{72} -4.32713 q^{73} +12.9240 q^{74} +1.69310 q^{75} +5.44895 q^{76} +1.61788 q^{77} +2.52828 q^{78} -15.1696 q^{79} +8.55714 q^{80} +0.425016 q^{81} -7.72080 q^{82} +8.83664 q^{83} +2.66676 q^{84} -16.7979 q^{86} -5.94608 q^{87} -0.787912 q^{88} -0.224416 q^{89} -6.66475 q^{90} -2.07615 q^{91} -7.71647 q^{92} +3.24004 q^{93} -11.1360 q^{94} -6.31877 q^{95} -7.53953 q^{96} +3.00802 q^{97} +8.29644 q^{98} +1.91687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{5} - 4 q^{6} - 5 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 8 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^5 - 4 * q^6 - 5 * q^7 + 3 * q^8 + 10 * q^9	\( 8 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{5} - 4 q^{6} - 5 q^{7} + 3 q^{8} + 10 q^{9} + 4 q^{10} - 8 q^{11} + 10 q^{12} - 8 q^{13} - 20 q^{14} - 2 q^{15} + 3 q^{16} - 5 q^{18} - 10 q^{19} - 8 q^{20} + 6 q^{21} - q^{22} + 10 q^{23} - 26 q^{24} - 2 q^{25} + 6 q^{26} + 4 q^{27} - 16 q^{28} - 3 q^{29} + 14 q^{30} - 2 q^{31} + 17 q^{32} + 2 q^{33} + 6 q^{35} + 9 q^{36} - 16 q^{37} - 28 q^{39} + 32 q^{40} - 21 q^{41} - 4 q^{43} - 5 q^{44} - 34 q^{45} - 6 q^{46} + 7 q^{47} - 38 q^{48} + 21 q^{49} - 17 q^{50} - 22 q^{52} - 13 q^{53} - 28 q^{54} + 4 q^{55} - 16 q^{56} + 32 q^{57} - 48 q^{58} + 15 q^{59} - 36 q^{60} - 28 q^{61} - 14 q^{62} + 9 q^{63} - 5 q^{64} + 8 q^{65} + 4 q^{66} + 5 q^{67} + 2 q^{69} + 4 q^{70} - 26 q^{71} - 23 q^{72} + q^{73} + 36 q^{74} - 20 q^{75} - 18 q^{76} + 5 q^{77} + 34 q^{78} - 20 q^{79} + 30 q^{80} - 4 q^{81} - 22 q^{82} + 4 q^{83} + 46 q^{84} + 28 q^{86} - 4 q^{87} - 3 q^{88} + 5 q^{89} + 14 q^{90} + 36 q^{91} - 38 q^{92} + 10 q^{93} - 4 q^{94} + 6 q^{95} - 18 q^{96} - 26 q^{97} + 19 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^5 - 4 * q^6 - 5 * q^7 + 3 * q^8 + 10 * q^9 + 4 * q^10 - 8 * q^11 + 10 * q^12 - 8 * q^13 - 20 * q^14 - 2 * q^15 + 3 * q^16 - 5 * q^18 - 10 * q^19 - 8 * q^20 + 6 * q^21 - q^22 + 10 * q^23 - 26 * q^24 - 2 * q^25 + 6 * q^26 + 4 * q^27 - 16 * q^28 - 3 * q^29 + 14 * q^30 - 2 * q^31 + 17 * q^32 + 2 * q^33 + 6 * q^35 + 9 * q^36 - 16 * q^37 - 28 * q^39 + 32 * q^40 - 21 * q^41 - 4 * q^43 - 5 * q^44 - 34 * q^45 - 6 * q^46 + 7 * q^47 - 38 * q^48 + 21 * q^49 - 17 * q^50 - 22 * q^52 - 13 * q^53 - 28 * q^54 + 4 * q^55 - 16 * q^56 + 32 * q^57 - 48 * q^58 + 15 * q^59 - 36 * q^60 - 28 * q^61 - 14 * q^62 + 9 * q^63 - 5 * q^64 + 8 * q^65 + 4 * q^66 + 5 * q^67 + 2 * q^69 + 4 * q^70 - 26 * q^71 - 23 * q^72 + q^73 + 36 * q^74 - 20 * q^75 - 18 * q^76 + 5 * q^77 + 34 * q^78 - 20 * q^79 + 30 * q^80 - 4 * q^81 - 22 * q^82 + 4 * q^83 + 46 * q^84 + 28 * q^86 - 4 * q^87 - 3 * q^88 + 5 * q^89 + 14 * q^90 + 36 * q^91 - 38 * q^92 + 10 * q^93 - 4 * q^94 + 6 * q^95 - 18 * q^96 - 26 * q^97 + 19 * q^98 - 10 * q^99

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