LMFDB - Embedded newform 322.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.57118294509$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} -1.10278 q^{5} +3.10278 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} -1.10278 q^{5} +3.10278 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} -1.10278 q^{10} -5.62721 q^{11} +3.10278 q^{12} -3.62721 q^{13} -1.00000 q^{14} -3.42166 q^{15} +1.00000 q^{16} +4.52444 q^{17} +6.62721 q^{18} -0.578337 q^{19} -1.10278 q^{20} -3.10278 q^{21} -5.62721 q^{22} -1.00000 q^{23} +3.10278 q^{24} -3.78389 q^{25} -3.62721 q^{26} +11.2544 q^{27} -1.00000 q^{28} +5.83276 q^{29} -3.42166 q^{30} -2.52444 q^{31} +1.00000 q^{32} -17.4600 q^{33} +4.52444 q^{34} +1.10278 q^{35} +6.62721 q^{36} -7.04888 q^{37} -0.578337 q^{38} -11.2544 q^{39} -1.10278 q^{40} +3.15667 q^{41} -3.10278 q^{42} +7.25443 q^{43} -5.62721 q^{44} -7.30833 q^{45} -1.00000 q^{46} +2.52444 q^{47} +3.10278 q^{48} +1.00000 q^{49} -3.78389 q^{50} +14.0383 q^{51} -3.62721 q^{52} +3.04888 q^{53} +11.2544 q^{54} +6.20555 q^{55} -1.00000 q^{56} -1.79445 q^{57} +5.83276 q^{58} +9.30833 q^{59} -3.42166 q^{60} +8.35720 q^{61} -2.52444 q^{62} -6.62721 q^{63} +1.00000 q^{64} +4.00000 q^{65} -17.4600 q^{66} +5.62721 q^{67} +4.52444 q^{68} -3.10278 q^{69} +1.10278 q^{70} -13.0489 q^{71} +6.62721 q^{72} -14.3033 q^{73} -7.04888 q^{74} -11.7406 q^{75} -0.578337 q^{76} +5.62721 q^{77} -11.2544 q^{78} -16.9894 q^{79} -1.10278 q^{80} +15.0383 q^{81} +3.15667 q^{82} +13.6272 q^{83} -3.10278 q^{84} -4.98944 q^{85} +7.25443 q^{86} +18.0978 q^{87} -5.62721 q^{88} -6.72999 q^{89} -7.30833 q^{90} +3.62721 q^{91} -1.00000 q^{92} -7.83276 q^{93} +2.52444 q^{94} +0.637776 q^{95} +3.10278 q^{96} +16.9355 q^{97} +1.00000 q^{98} -37.2927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * 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
$3$	3.10278	1.79139	0.895694	−	0.444671i	$-0.146679\pi$
$3$	3.10278	1.79139	0.895694	+	0.444671i	$0.146679\pi$
$4$	1.00000	0.500000
$5$	−1.10278	−0.493176	−0.246588	−	0.969120i	$-0.579309\pi$
$5$	−1.10278	−0.493176	−0.246588	+	0.969120i	$0.579309\pi$
$6$	3.10278	1.26670
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	6.62721	2.20907
$10$	−1.10278	−0.348728
$11$	−5.62721	−1.69667	−0.848334	−	0.529461i	$-0.822394\pi$
$11$	−5.62721	−1.69667	−0.848334	+	0.529461i	$0.822394\pi$
$12$	3.10278	0.895694
$13$	−3.62721	−1.00601	−0.503004	−	0.864284i	$-0.667772\pi$
$13$	−3.62721	−1.00601	−0.503004	+	0.864284i	$0.667772\pi$
$14$	−1.00000	−0.267261
$15$	−3.42166	−0.883470
$16$	1.00000	0.250000
$17$	4.52444	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$17$	4.52444	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$18$	6.62721	1.56205
$19$	−0.578337	−0.132680	−0.0663398	−	0.997797i	$-0.521132\pi$
$19$	−0.578337	−0.132680	−0.0663398	+	0.997797i	$0.521132\pi$
$20$	−1.10278	−0.246588
$21$	−3.10278	−0.677081
$22$	−5.62721	−1.19973
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.10278	0.633351
$25$	−3.78389	−0.756777
$26$	−3.62721	−0.711355
$27$	11.2544	2.16592
$28$	−1.00000	−0.188982
$29$	5.83276	1.08312	0.541558	−	0.840663i	$-0.317834\pi$
$29$	5.83276	1.08312	0.541558	+	0.840663i	$0.317834\pi$
$30$	−3.42166	−0.624707
$31$	−2.52444	−0.453402	−0.226701	−	0.973964i	$-0.572794\pi$
$31$	−2.52444	−0.453402	−0.226701	+	0.973964i	$0.572794\pi$
$32$	1.00000	0.176777
$33$	−17.4600	−3.03939
$34$	4.52444	0.775935
$35$	1.10278	0.186403
$36$	6.62721	1.10454
$37$	−7.04888	−1.15883	−0.579414	−	0.815033i	$-0.696719\pi$
$37$	−7.04888	−1.15883	−0.579414	+	0.815033i	$0.696719\pi$
$38$	−0.578337	−0.0938187
$39$	−11.2544	−1.80215
$40$	−1.10278	−0.174364
$41$	3.15667	0.492990	0.246495	−	0.969144i	$-0.420721\pi$
$41$	3.15667	0.492990	0.246495	+	0.969144i	$0.420721\pi$
$42$	−3.10278	−0.478769
$43$	7.25443	1.10629	0.553145	−	0.833085i	$-0.313428\pi$
$43$	7.25443	1.10629	0.553145	+	0.833085i	$0.313428\pi$
$44$	−5.62721	−0.848334
$45$	−7.30833	−1.08946
$46$	−1.00000	−0.147442
$47$	2.52444	0.368227	0.184114	−	0.982905i	$-0.441059\pi$
$47$	2.52444	0.368227	0.184114	+	0.982905i	$0.441059\pi$
$48$	3.10278	0.447847
$49$	1.00000	0.142857
$50$	−3.78389	−0.535122
$51$	14.0383	1.96576
$52$	−3.62721	−0.503004
$53$	3.04888	0.418795	0.209398	−	0.977831i	$-0.432850\pi$
$53$	3.04888	0.418795	0.209398	+	0.977831i	$0.432850\pi$
$54$	11.2544	1.53153
$55$	6.20555	0.836756
$56$	−1.00000	−0.133631
$57$	−1.79445	−0.237681
$58$	5.83276	0.765879
$59$	9.30833	1.21184	0.605920	−	0.795525i	$-0.292805\pi$
$59$	9.30833	1.21184	0.605920	+	0.795525i	$0.292805\pi$
$60$	−3.42166	−0.441735
$61$	8.35720	1.07003	0.535015	−	0.844843i	$-0.320306\pi$
$61$	8.35720	1.07003	0.535015	+	0.844843i	$0.320306\pi$
$62$	−2.52444	−0.320604
$63$	−6.62721	−0.834950
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	−17.4600	−2.14917
$67$	5.62721	0.687473	0.343737	−	0.939066i	$-0.388307\pi$
$67$	5.62721	0.687473	0.343737	+	0.939066i	$0.388307\pi$
$68$	4.52444	0.548669
$69$	−3.10278	−0.373530
$70$	1.10278	0.131807
$71$	−13.0489	−1.54862	−0.774308	−	0.632809i	$-0.781902\pi$
$71$	−13.0489	−1.54862	−0.774308	+	0.632809i	$0.781902\pi$
$72$	6.62721	0.781025
$73$	−14.3033	−1.67407	−0.837037	−	0.547146i	$-0.815714\pi$
$73$	−14.3033	−1.67407	−0.837037	+	0.547146i	$0.815714\pi$
$74$	−7.04888	−0.819415
$75$	−11.7406	−1.35568
$76$	−0.578337	−0.0663398
$77$	5.62721	0.641280
$78$	−11.2544	−1.27431
$79$	−16.9894	−1.91146	−0.955731	−	0.294243i	$-0.904932\pi$
$79$	−16.9894	−1.91146	−0.955731	+	0.294243i	$0.904932\pi$
$80$	−1.10278	−0.123294
$81$	15.0383	1.67092
$82$	3.15667	0.348596
$83$	13.6272	1.49578	0.747890	−	0.663822i	$-0.231067\pi$
$83$	13.6272	1.49578	0.747890	+	0.663822i	$0.231067\pi$
$84$	−3.10278	−0.338541
$85$	−4.98944	−0.541180
$86$	7.25443	0.782265
$87$	18.0978	1.94028
$88$	−5.62721	−0.599863
$89$	−6.72999	−0.713377	−0.356689	−	0.934223i	$-0.616094\pi$
$89$	−6.72999	−0.713377	−0.356689	+	0.934223i	$0.616094\pi$
$90$	−7.30833	−0.770365
$91$	3.62721	0.380235
$92$	−1.00000	−0.104257
$93$	−7.83276	−0.812220
$94$	2.52444	0.260376
$95$	0.637776	0.0654344
$96$	3.10278	0.316676
$97$	16.9355	1.71954	0.859772	−	0.510679i	$-0.170606\pi$
$97$	16.9355	1.71954	0.859772	+	0.510679i	$0.170606\pi$
$98$	1.00000	0.101015
$99$	−37.2927	−3.74806
$100$	−3.78389	−0.378389
$101$	4.37279	0.435109	0.217554	−	0.976048i	$-0.430192\pi$
$101$	4.37279	0.435109	0.217554	+	0.976048i	$0.430192\pi$
$102$	14.0383	1.39000
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−3.62721	−0.355677
$105$	3.42166	0.333920
$106$	3.04888	0.296133
$107$	−18.5089	−1.78932	−0.894659	−	0.446749i	$-0.852582\pi$
$107$	−18.5089	−1.78932	−0.894659	+	0.446749i	$0.852582\pi$
$108$	11.2544	1.08296
$109$	−0.843326	−0.0807760	−0.0403880	−	0.999184i	$-0.512859\pi$
$109$	−0.843326	−0.0807760	−0.0403880	+	0.999184i	$0.512859\pi$
$110$	6.20555	0.591676
$111$	−21.8711	−2.07591
$112$	−1.00000	−0.0944911
$113$	3.79445	0.356952	0.178476	−	0.983944i	$-0.442883\pi$
$113$	3.79445	0.356952	0.178476	+	0.983944i	$0.442883\pi$
$114$	−1.79445	−0.168066
$115$	1.10278	0.102834
$116$	5.83276	0.541558
$117$	−24.0383	−2.22234
$118$	9.30833	0.856901
$119$	−4.52444	−0.414755
$120$	−3.42166	−0.312354
$121$	20.6655	1.87868
$122$	8.35720	0.756625
$123$	9.79445	0.883136
$124$	−2.52444	−0.226701
$125$	9.68665	0.866400
$126$	−6.62721	−0.590399
$127$	−14.2056	−1.26054	−0.630269	−	0.776377i	$-0.717056\pi$
$127$	−14.2056	−1.26054	−0.630269	+	0.776377i	$0.717056\pi$
$128$	1.00000	0.0883883
$129$	22.5089	1.98179
$130$	4.00000	0.350823
$131$	22.3572	1.95336	0.976679	−	0.214705i	$-0.0688791\pi$
$131$	22.3572	1.95336	0.976679	+	0.214705i	$0.0688791\pi$
$132$	−17.4600	−1.51970
$133$	0.578337	0.0501482
$134$	5.62721	0.486117
$135$	−12.4111	−1.06818
$136$	4.52444	0.387967
$137$	−1.89220	−0.161662	−0.0808309	−	0.996728i	$-0.525757\pi$
$137$	−1.89220	−0.161662	−0.0808309	+	0.996728i	$0.525757\pi$
$138$	−3.10278	−0.264126
$139$	−6.35720	−0.539211	−0.269605	−	0.962971i	$-0.586893\pi$
$139$	−6.35720	−0.539211	−0.269605	+	0.962971i	$0.586893\pi$
$140$	1.10278	0.0932015
$141$	7.83276	0.659638
$142$	−13.0489	−1.09504
$143$	20.4111	1.70686
$144$	6.62721	0.552268
$145$	−6.43223	−0.534167
$146$	−14.3033	−1.18375
$147$	3.10278	0.255913
$148$	−7.04888	−0.579414
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−11.7406	−0.958612
$151$	18.6167	1.51500	0.757501	−	0.652834i	$-0.226420\pi$
$151$	18.6167	1.51500	0.757501	+	0.652834i	$0.226420\pi$
$152$	−0.578337	−0.0469093
$153$	29.9844	2.42410
$154$	5.62721	0.453454
$155$	2.78389	0.223607
$156$	−11.2544	−0.901075
$157$	6.89722	0.550458	0.275229	−	0.961379i	$-0.411246\pi$
$157$	6.89722	0.550458	0.275229	+	0.961379i	$0.411246\pi$
$158$	−16.9894	−1.35161
$159$	9.45998	0.750225
$160$	−1.10278	−0.0871820
$161$	1.00000	0.0788110
$162$	15.0383	1.18152
$163$	−19.3622	−1.51657	−0.758283	−	0.651925i	$-0.773962\pi$
$163$	−19.3622	−1.51657	−0.758283	+	0.651925i	$0.773962\pi$
$164$	3.15667	0.246495
$165$	19.2544	1.49896
$166$	13.6272	1.05768
$167$	−10.5244	−0.814405	−0.407203	−	0.913338i	$-0.633496\pi$
$167$	−10.5244	−0.814405	−0.407203	+	0.913338i	$0.633496\pi$
$168$	−3.10278	−0.239384
$169$	0.156674	0.0120519
$170$	−4.98944	−0.382672
$171$	−3.83276	−0.293099
$172$	7.25443	0.553145
$173$	17.4217	1.32454	0.662272	−	0.749263i	$-0.269592\pi$
$173$	17.4217	1.32454	0.662272	+	0.749263i	$0.269592\pi$
$174$	18.0978	1.37199
$175$	3.78389	0.286035
$176$	−5.62721	−0.424167
$177$	28.8816	2.17088
$178$	−6.72999	−0.504434
$179$	−11.6655	−0.871922	−0.435961	−	0.899965i	$-0.643592\pi$
$179$	−11.6655	−0.871922	−0.435961	+	0.899965i	$0.643592\pi$
$180$	−7.30833	−0.544730
$181$	6.25945	0.465261	0.232631	−	0.972565i	$-0.425267\pi$
$181$	6.25945	0.465261	0.232631	+	0.972565i	$0.425267\pi$
$182$	3.62721	0.268867
$183$	25.9305	1.91684
$184$	−1.00000	−0.0737210
$185$	7.77332	0.571506
$186$	−7.83276	−0.574326
$187$	−25.4600	−1.86182
$188$	2.52444	0.184114
$189$	−11.2544	−0.818639
$190$	0.637776	0.0462691
$191$	−2.31335	−0.167388	−0.0836940	−	0.996492i	$-0.526672\pi$
$191$	−2.31335	−0.167388	−0.0836940	+	0.996492i	$0.526672\pi$
$192$	3.10278	0.223924
$193$	5.58890	0.402298	0.201149	−	0.979561i	$-0.435532\pi$
$193$	5.58890	0.402298	0.201149	+	0.979561i	$0.435532\pi$
$194$	16.9355	1.21590
$195$	12.4111	0.888777
$196$	1.00000	0.0714286
$197$	18.4111	1.31174	0.655868	−	0.754875i	$-0.272303\pi$
$197$	18.4111	1.31174	0.655868	+	0.754875i	$0.272303\pi$
$198$	−37.2927	−2.65028
$199$	4.41110	0.312695	0.156347	−	0.987702i	$-0.450028\pi$
$199$	4.41110	0.312695	0.156347	+	0.987702i	$0.450028\pi$
$200$	−3.78389	−0.267561
$201$	17.4600	1.23153
$202$	4.37279	0.307668
$203$	−5.83276	−0.409380
$204$	14.0383	0.982879
$205$	−3.48110	−0.243131
$206$	−8.00000	−0.557386
$207$	−6.62721	−0.460623
$208$	−3.62721	−0.251502
$209$	3.25443	0.225113
$210$	3.42166	0.236117
$211$	10.8433	0.746485	0.373243	−	0.927734i	$-0.378246\pi$
$211$	10.8433	0.746485	0.373243	+	0.927734i	$0.378246\pi$
$212$	3.04888	0.209398
$213$	−40.4877	−2.77417
$214$	−18.5089	−1.26524
$215$	−8.00000	−0.545595
$216$	11.2544	0.765767
$217$	2.52444	0.171370
$218$	−0.843326	−0.0571172
$219$	−44.3799	−2.99892
$220$	6.20555	0.418378
$221$	−16.4111	−1.10393
$222$	−21.8711	−1.46789
$223$	−19.9844	−1.33826	−0.669128	−	0.743147i	$-0.733332\pi$
$223$	−19.9844	−1.33826	−0.669128	+	0.743147i	$0.733332\pi$
$224$	−1.00000	−0.0668153
$225$	−25.0766	−1.67178
$226$	3.79445	0.252403
$227$	4.98944	0.331161	0.165580	−	0.986196i	$-0.447050\pi$
$227$	4.98944	0.331161	0.165580	+	0.986196i	$0.447050\pi$
$228$	−1.79445	−0.118840
$229$	3.94610	0.260766	0.130383	−	0.991464i	$-0.458379\pi$
$229$	3.94610	0.260766	0.130383	+	0.991464i	$0.458379\pi$
$230$	1.10278	0.0727148
$231$	17.4600	1.14878
$232$	5.83276	0.382940
$233$	−2.88164	−0.188782	−0.0943912	−	0.995535i	$-0.530090\pi$
$233$	−2.88164	−0.188782	−0.0943912	+	0.995535i	$0.530090\pi$
$234$	−24.0383	−1.57143
$235$	−2.78389	−0.181601
$236$	9.30833	0.605920
$237$	−52.7144	−3.42417
$238$	−4.52444	−0.293276
$239$	20.7144	1.33990	0.669952	−	0.742405i	$-0.266315\pi$
$239$	20.7144	1.33990	0.669952	+	0.742405i	$0.266315\pi$
$240$	−3.42166	−0.220867
$241$	11.0333	0.710717	0.355358	−	0.934730i	$-0.384359\pi$
$241$	11.0333	0.710717	0.355358	+	0.934730i	$0.384359\pi$
$242$	20.6655	1.32843
$243$	12.8972	0.827357
$244$	8.35720	0.535015
$245$	−1.10278	−0.0704537
$246$	9.79445	0.624471
$247$	2.09775	0.133477
$248$	−2.52444	−0.160302
$249$	42.2822	2.67952
$250$	9.68665	0.612638
$251$	16.2439	1.02530	0.512652	−	0.858597i	$-0.328663\pi$
$251$	16.2439	1.02530	0.512652	+	0.858597i	$0.328663\pi$
$252$	−6.62721	−0.417475
$253$	5.62721	0.353780
$254$	−14.2056	−0.891335
$255$	−15.4811	−0.969464
$256$	1.00000	0.0625000
$257$	−13.6655	−0.852432	−0.426216	−	0.904621i	$-0.640154\pi$
$257$	−13.6655	−0.852432	−0.426216	+	0.904621i	$0.640154\pi$
$258$	22.5089	1.40134
$259$	7.04888	0.437996
$260$	4.00000	0.248069
$261$	38.6550	2.39268
$262$	22.3572	1.38123
$263$	24.9894	1.54091	0.770457	−	0.637492i	$-0.220028\pi$
$263$	24.9894	1.54091	0.770457	+	0.637492i	$0.220028\pi$
$264$	−17.4600	−1.07459
$265$	−3.36222	−0.206540
$266$	0.578337	0.0354601
$267$	−20.8816	−1.27794
$268$	5.62721	0.343737
$269$	−17.4983	−1.06689	−0.533445	−	0.845835i	$-0.679103\pi$
$269$	−17.4983	−1.06689	−0.533445	+	0.845835i	$0.679103\pi$
$270$	−12.4111	−0.755316
$271$	−18.5244	−1.12528	−0.562640	−	0.826702i	$-0.690214\pi$
$271$	−18.5244	−1.12528	−0.562640	+	0.826702i	$0.690214\pi$
$272$	4.52444	0.274334
$273$	11.2544	0.681149
$274$	−1.89220	−0.114312
$275$	21.2927	1.28400
$276$	−3.10278	−0.186765
$277$	−10.9894	−0.660291	−0.330146	−	0.943930i	$-0.607098\pi$
$277$	−10.9894	−0.660291	−0.330146	+	0.943930i	$0.607098\pi$
$278$	−6.35720	−0.381280
$279$	−16.7300	−1.00160
$280$	1.10278	0.0659034
$281$	−7.45998	−0.445025	−0.222512	−	0.974930i	$-0.571426\pi$
$281$	−7.45998	−0.445025	−0.222512	+	0.974930i	$0.571426\pi$
$282$	7.83276	0.466434
$283$	1.51941	0.0903198	0.0451599	−	0.998980i	$-0.485620\pi$
$283$	1.51941	0.0903198	0.0451599	+	0.998980i	$0.485620\pi$
$284$	−13.0489	−0.774308
$285$	1.97887	0.117218
$286$	20.4111	1.20693
$287$	−3.15667	−0.186333
$288$	6.62721	0.390512
$289$	3.47054	0.204149
$290$	−6.43223	−0.377713
$291$	52.5472	3.08037
$292$	−14.3033	−0.837037
$293$	−1.10278	−0.0644248	−0.0322124	−	0.999481i	$-0.510255\pi$
$293$	−1.10278	−0.0644248	−0.0322124	+	0.999481i	$0.510255\pi$
$294$	3.10278	0.180958
$295$	−10.2650	−0.597651
$296$	−7.04888	−0.409708
$297$	−63.3311	−3.67484
$298$	−2.00000	−0.115857
$299$	3.62721	0.209767
$300$	−11.7406	−0.677841
$301$	−7.25443	−0.418138
$302$	18.6167	1.07127
$303$	13.5678	0.779448
$304$	−0.578337	−0.0331699
$305$	−9.21611	−0.527713
$306$	29.9844	1.71409
$307$	−11.1028	−0.633669	−0.316834	−	0.948481i	$-0.602620\pi$
$307$	−11.1028	−0.633669	−0.316834	+	0.948481i	$0.602620\pi$
$308$	5.62721	0.320640
$309$	−24.8222	−1.41209
$310$	2.78389	0.158114
$311$	−14.2978	−0.810752	−0.405376	−	0.914150i	$-0.632859\pi$
$311$	−14.2978	−0.810752	−0.405376	+	0.914150i	$0.632859\pi$
$312$	−11.2544	−0.637156
$313$	−19.4756	−1.10082	−0.550412	−	0.834893i	$-0.685529\pi$
$313$	−19.4756	−1.10082	−0.550412	+	0.834893i	$0.685529\pi$
$314$	6.89722	0.389233
$315$	7.30833	0.411777
$316$	−16.9894	−0.955731
$317$	28.3416	1.59182	0.795912	−	0.605413i	$-0.206992\pi$
$317$	28.3416	1.59182	0.795912	+	0.605413i	$0.206992\pi$
$318$	9.45998	0.530489
$319$	−32.8222	−1.83769
$320$	−1.10278	−0.0616470
$321$	−57.4288	−3.20536
$322$	1.00000	0.0557278
$323$	−2.61665	−0.145594
$324$	15.0383	0.835462
$325$	13.7250	0.761324
$326$	−19.3622	−1.07237
$327$	−2.61665	−0.144701
$328$	3.15667	0.174298
$329$	−2.52444	−0.139177
$330$	19.2544	1.05992
$331$	−34.8122	−1.91345	−0.956725	−	0.290995i	$-0.906014\pi$
$331$	−34.8122	−1.91345	−0.956725	+	0.290995i	$0.906014\pi$
$332$	13.6272	0.747890
$333$	−46.7144	−2.55993
$334$	−10.5244	−0.575872
$335$	−6.20555	−0.339045
$336$	−3.10278	−0.169270
$337$	−4.84333	−0.263833	−0.131916	−	0.991261i	$-0.542113\pi$
$337$	−4.84333	−0.263833	−0.131916	+	0.991261i	$0.542113\pi$
$338$	0.156674	0.00852195
$339$	11.7733	0.639439
$340$	−4.98944	−0.270590
$341$	14.2056	0.769274
$342$	−3.83276	−0.207252
$343$	−1.00000	−0.0539949
$344$	7.25443	0.391132
$345$	3.42166	0.184216
$346$	17.4217	0.936594
$347$	−23.7733	−1.27622	−0.638109	−	0.769946i	$-0.720283\pi$
$347$	−23.7733	−1.27622	−0.638109	+	0.769946i	$0.720283\pi$
$348$	18.0978	0.970141
$349$	32.7527	1.75321	0.876606	−	0.481208i	$-0.159802\pi$
$349$	32.7527	1.75321	0.876606	+	0.481208i	$0.159802\pi$
$350$	3.78389	0.202257
$351$	−40.8222	−2.17893
$352$	−5.62721	−0.299931
$353$	13.5577	0.721605	0.360803	−	0.932642i	$-0.382503\pi$
$353$	13.5577	0.721605	0.360803	+	0.932642i	$0.382503\pi$
$354$	28.8816	1.53504
$355$	14.3900	0.763741
$356$	−6.72999	−0.356689
$357$	−14.0383	−0.742986
$358$	−11.6655	−0.616542
$359$	6.67609	0.352350	0.176175	−	0.984359i	$-0.443627\pi$
$359$	6.67609	0.352350	0.176175	+	0.984359i	$0.443627\pi$
$360$	−7.30833	−0.385183
$361$	−18.6655	−0.982396
$362$	6.25945	0.328989
$363$	64.1205	3.36545
$364$	3.62721	0.190118
$365$	15.7733	0.825614
$366$	25.9305	1.35541
$367$	−24.3033	−1.26862	−0.634311	−	0.773078i	$-0.718716\pi$
$367$	−24.3033	−1.26862	−0.634311	+	0.773078i	$0.718716\pi$
$368$	−1.00000	−0.0521286
$369$	20.9200	1.08905
$370$	7.77332	0.404116
$371$	−3.04888	−0.158290
$372$	−7.83276	−0.406110
$373$	−8.50885	−0.440572	−0.220286	−	0.975435i	$-0.570699\pi$
$373$	−8.50885	−0.440572	−0.220286	+	0.975435i	$0.570699\pi$
$374$	−25.4600	−1.31650
$375$	30.0555	1.55206
$376$	2.52444	0.130188
$377$	−21.1567	−1.08962
$378$	−11.2544	−0.578865
$379$	−9.21611	−0.473400	−0.236700	−	0.971583i	$-0.576066\pi$
$379$	−9.21611	−0.473400	−0.236700	+	0.971583i	$0.576066\pi$
$380$	0.637776	0.0327172
$381$	−44.0766	−2.25811
$382$	−2.31335	−0.118361
$383$	−23.9688	−1.22475	−0.612375	−	0.790567i	$-0.709786\pi$
$383$	−23.9688	−1.22475	−0.612375	+	0.790567i	$0.709786\pi$
$384$	3.10278	0.158338
$385$	−6.20555	−0.316264
$386$	5.58890	0.284468
$387$	48.0766	2.44387
$388$	16.9355	0.859772
$389$	−2.33447	−0.118363	−0.0591813	−	0.998247i	$-0.518849\pi$
$389$	−2.33447	−0.118363	−0.0591813	+	0.998247i	$0.518849\pi$
$390$	12.4111	0.628460
$391$	−4.52444	−0.228811
$392$	1.00000	0.0505076
$393$	69.3694	3.49922
$394$	18.4111	0.927538
$395$	18.7355	0.942687
$396$	−37.2927	−1.87403
$397$	−21.9406	−1.10117	−0.550583	−	0.834781i	$-0.685594\pi$
$397$	−21.9406	−1.10117	−0.550583	+	0.834781i	$0.685594\pi$
$398$	4.41110	0.221108
$399$	1.79445	0.0898349
$400$	−3.78389	−0.189194
$401$	−27.3522	−1.36590	−0.682951	−	0.730464i	$-0.739304\pi$
$401$	−27.3522	−1.36590	−0.682951	+	0.730464i	$0.739304\pi$
$402$	17.4600	0.870824
$403$	9.15667	0.456126
$404$	4.37279	0.217554
$405$	−16.5839	−0.824059
$406$	−5.83276	−0.289475
$407$	39.6655	1.96615
$408$	14.0383	0.695000
$409$	4.95112	0.244817	0.122409	−	0.992480i	$-0.460938\pi$
$409$	4.95112	0.244817	0.122409	+	0.992480i	$0.460938\pi$
$410$	−3.48110	−0.171919
$411$	−5.87108	−0.289599
$412$	−8.00000	−0.394132
$413$	−9.30833	−0.458033
$414$	−6.62721	−0.325710
$415$	−15.0278	−0.737683
$416$	−3.62721	−0.177839
$417$	−19.7250	−0.965936
$418$	3.25443	0.159179
$419$	−26.3416	−1.28687	−0.643436	−	0.765500i	$-0.722492\pi$
$419$	−26.3416	−1.28687	−0.643436	+	0.765500i	$0.722492\pi$
$420$	3.42166	0.166960
$421$	−9.36222	−0.456287	−0.228143	−	0.973628i	$-0.573266\pi$
$421$	−9.36222	−0.456287	−0.228143	+	0.973628i	$0.573266\pi$
$422$	10.8433	0.527845
$423$	16.7300	0.813440
$424$	3.04888	0.148067
$425$	−17.1200	−0.830440
$426$	−40.4877	−1.96164
$427$	−8.35720	−0.404433
$428$	−18.5089	−0.894659
$429$	63.3311	3.05765
$430$	−8.00000	−0.385794
$431$	8.82220	0.424950	0.212475	−	0.977166i	$-0.431848\pi$
$431$	8.82220	0.424950	0.212475	+	0.977166i	$0.431848\pi$
$432$	11.2544	0.541479
$433$	14.6222	0.702698	0.351349	−	0.936245i	$-0.385723\pi$
$433$	14.6222	0.702698	0.351349	+	0.936245i	$0.385723\pi$
$434$	2.52444	0.121177
$435$	−19.9577	−0.956901
$436$	−0.843326	−0.0403880
$437$	0.578337	0.0276656
$438$	−44.3799	−2.12056
$439$	−30.2978	−1.44603	−0.723017	−	0.690831i	$-0.757245\pi$
$439$	−30.2978	−1.44603	−0.723017	+	0.690831i	$0.757245\pi$
$440$	6.20555	0.295838
$441$	6.62721	0.315582
$442$	−16.4111	−0.780596
$443$	17.5678	0.834670	0.417335	−	0.908753i	$-0.362964\pi$
$443$	17.5678	0.834670	0.417335	+	0.908753i	$0.362964\pi$
$444$	−21.8711	−1.03796
$445$	7.42166	0.351821
$446$	−19.9844	−0.946289
$447$	−6.20555	−0.293512
$448$	−1.00000	−0.0472456
$449$	11.2927	0.532937	0.266469	−	0.963844i	$-0.414143\pi$
$449$	11.2927	0.532937	0.266469	+	0.963844i	$0.414143\pi$
$450$	−25.0766	−1.18212
$451$	−17.7633	−0.836440
$452$	3.79445	0.178476
$453$	57.7633	2.71396
$454$	4.98944	0.234166
$455$	−4.00000	−0.187523
$456$	−1.79445	−0.0840328
$457$	27.4600	1.28452	0.642262	−	0.766485i	$-0.277996\pi$
$457$	27.4600	1.28452	0.642262	+	0.766485i	$0.277996\pi$
$458$	3.94610	0.184389
$459$	50.9200	2.37674
$460$	1.10278	0.0514172
$461$	29.4983	1.37387	0.686936	−	0.726718i	$-0.258955\pi$
$461$	29.4983	1.37387	0.686936	+	0.726718i	$0.258955\pi$
$462$	17.4600	0.812312
$463$	14.7244	0.684303	0.342152	−	0.939645i	$-0.388844\pi$
$463$	14.7244	0.684303	0.342152	+	0.939645i	$0.388844\pi$
$464$	5.83276	0.270779
$465$	8.63778	0.400567
$466$	−2.88164	−0.133489
$467$	8.57834	0.396958	0.198479	−	0.980105i	$-0.436400\pi$
$467$	8.57834	0.396958	0.198479	+	0.980105i	$0.436400\pi$
$468$	−24.0383	−1.11117
$469$	−5.62721	−0.259841
$470$	−2.78389	−0.128411
$471$	21.4005	0.986085
$472$	9.30833	0.428450
$473$	−40.8222	−1.87701
$474$	−52.7144	−2.42125
$475$	2.18836	0.100409
$476$	−4.52444	−0.207377
$477$	20.2056	0.925149
$478$	20.7144	0.947455
$479$	−28.0766	−1.28285	−0.641427	−	0.767184i	$-0.721657\pi$
$479$	−28.0766	−1.28285	−0.641427	+	0.767184i	$0.721657\pi$
$480$	−3.42166	−0.156177
$481$	25.5678	1.16579
$482$	11.0333	0.502553
$483$	3.10278	0.141181
$484$	20.6655	0.939342
$485$	−18.6761	−0.848038
$486$	12.8972	0.585030
$487$	22.7244	1.02974	0.514872	−	0.857267i	$-0.327840\pi$
$487$	22.7244	1.02974	0.514872	+	0.857267i	$0.327840\pi$
$488$	8.35720	0.378313
$489$	−60.0766	−2.71676
$490$	−1.10278	−0.0498183
$491$	−18.7244	−0.845023	−0.422511	−	0.906358i	$-0.638851\pi$
$491$	−18.7244	−0.845023	−0.422511	+	0.906358i	$0.638851\pi$
$492$	9.79445	0.441568
$493$	26.3900	1.18854
$494$	2.09775	0.0943823
$495$	41.1255	1.84845
$496$	−2.52444	−0.113351
$497$	13.0489	0.585322
$498$	42.2822	1.89471
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	9.68665	0.433200
$501$	−32.6550	−1.45892
$502$	16.2439	0.724999
$503$	13.5678	0.604957	0.302479	−	0.953156i	$-0.402186\pi$
$503$	13.5678	0.604957	0.302479	+	0.953156i	$0.402186\pi$
$504$	−6.62721	−0.295200
$505$	−4.82220	−0.214585
$506$	5.62721	0.250160
$507$	0.486125	0.0215896
$508$	−14.2056	−0.630269
$509$	−4.14611	−0.183773	−0.0918866	−	0.995769i	$-0.529290\pi$
$509$	−4.14611	−0.183773	−0.0918866	+	0.995769i	$0.529290\pi$
$510$	−15.4811	−0.685515
$511$	14.3033	0.632741
$512$	1.00000	0.0441942
$513$	−6.50885	−0.287373
$514$	−13.6655	−0.602761
$515$	8.82220	0.388753
$516$	22.5089	0.990897
$517$	−14.2056	−0.624759
$518$	7.04888	0.309710
$519$	54.0555	2.37277
$520$	4.00000	0.175412
$521$	−28.2978	−1.23975	−0.619874	−	0.784702i	$-0.712816\pi$
$521$	−28.2978	−1.23975	−0.619874	+	0.784702i	$0.712816\pi$
$522$	38.6550	1.69188
$523$	−4.98944	−0.218173	−0.109086	−	0.994032i	$-0.534793\pi$
$523$	−4.98944	−0.218173	−0.109086	+	0.994032i	$0.534793\pi$
$524$	22.3572	0.976679
$525$	11.7406	0.512400
$526$	24.9894	1.08959
$527$	−11.4217	−0.497535
$528$	−17.4600	−0.759848
$529$	1.00000	0.0434783
$530$	−3.36222	−0.146046
$531$	61.6883	2.67704
$532$	0.578337	0.0250741
$533$	−11.4499	−0.495952
$534$	−20.8816	−0.903637
$535$	20.4111	0.882449
$536$	5.62721	0.243059
$537$	−36.1955	−1.56195
$538$	−17.4983	−0.754405
$539$	−5.62721	−0.242381
$540$	−12.4111	−0.534089
$541$	28.3416	1.21850	0.609251	−	0.792978i	$-0.291470\pi$
$541$	28.3416	1.21850	0.609251	+	0.792978i	$0.291470\pi$
$542$	−18.5244	−0.795693
$543$	19.4217	0.833463
$544$	4.52444	0.193984
$545$	0.929999	0.0398368
$546$	11.2544	0.481645
$547$	1.26447	0.0540649	0.0270325	−	0.999635i	$-0.491394\pi$
$547$	1.26447	0.0540649	0.0270325	+	0.999635i	$0.491394\pi$
$548$	−1.89220	−0.0808309
$549$	55.3850	2.36377
$550$	21.2927	0.907925
$551$	−3.37330	−0.143708
$552$	−3.10278	−0.132063
$553$	16.9894	0.722464
$554$	−10.9894	−0.466896
$555$	24.1189	1.02379
$556$	−6.35720	−0.269605
$557$	−2.21560	−0.0938778	−0.0469389	−	0.998898i	$-0.514947\pi$
$557$	−2.21560	−0.0938778	−0.0469389	+	0.998898i	$0.514947\pi$
$558$	−16.7300	−0.708237
$559$	−26.3133	−1.11294
$560$	1.10278	0.0466008
$561$	−78.9966	−3.33524
$562$	−7.45998	−0.314680
$563$	−20.7738	−0.875513	−0.437757	−	0.899094i	$-0.644227\pi$
$563$	−20.7738	−0.875513	−0.437757	+	0.899094i	$0.644227\pi$
$564$	7.83276	0.329819
$565$	−4.18442	−0.176040
$566$	1.51941	0.0638658
$567$	−15.0383	−0.631550
$568$	−13.0489	−0.547519
$569$	−35.0177	−1.46802	−0.734009	−	0.679139i	$-0.762353\pi$
$569$	−35.0177	−1.46802	−0.734009	+	0.679139i	$0.762353\pi$
$570$	1.97887	0.0828859
$571$	35.6655	1.49256	0.746278	−	0.665634i	$-0.231839\pi$
$571$	35.6655	1.49256	0.746278	+	0.665634i	$0.231839\pi$
$572$	20.4111	0.853431
$573$	−7.17780	−0.299857
$574$	−3.15667	−0.131757
$575$	3.78389	0.157799
$576$	6.62721	0.276134
$577$	12.6167	0.525238	0.262619	−	0.964900i	$-0.415414\pi$
$577$	12.6167	0.525238	0.262619	+	0.964900i	$0.415414\pi$
$578$	3.47054	0.144355
$579$	17.3411	0.720671
$580$	−6.43223	−0.267084
$581$	−13.6272	−0.565352
$582$	52.5472	2.17815
$583$	−17.1567	−0.710557
$584$	−14.3033	−0.591875
$585$	26.5089	1.09601
$586$	−1.10278	−0.0455552
$587$	−21.0816	−0.870133	−0.435066	−	0.900398i	$-0.643275\pi$
$587$	−21.0816	−0.870133	−0.435066	+	0.900398i	$0.643275\pi$
$588$	3.10278	0.127956
$589$	1.45998	0.0601573
$590$	−10.2650	−0.422603
$591$	57.1255	2.34983
$592$	−7.04888	−0.289707
$593$	−1.25443	−0.0515131	−0.0257566	−	0.999668i	$-0.508199\pi$
$593$	−1.25443	−0.0515131	−0.0257566	+	0.999668i	$0.508199\pi$
$594$	−63.3311	−2.59850
$595$	4.98944	0.204547
$596$	−2.00000	−0.0819232
$597$	13.6867	0.560157
$598$	3.62721	0.148328
$599$	−38.3900	−1.56857	−0.784286	−	0.620400i	$-0.786970\pi$
$599$	−38.3900	−1.56857	−0.784286	+	0.620400i	$0.786970\pi$
$600$	−11.7406	−0.479306
$601$	14.7144	0.600213	0.300106	−	0.953906i	$-0.402978\pi$
$601$	14.7144	0.600213	0.300106	+	0.953906i	$0.402978\pi$
$602$	−7.25443	−0.295668
$603$	37.2927	1.51868
$604$	18.6167	0.757501
$605$	−22.7894	−0.926522
$606$	13.5678	0.551153
$607$	29.5633	1.19994	0.599968	−	0.800024i	$-0.295180\pi$
$607$	29.5633	1.19994	0.599968	+	0.800024i	$0.295180\pi$
$608$	−0.578337	−0.0234547
$609$	−18.0978	−0.733358
$610$	−9.21611	−0.373150
$611$	−9.15667	−0.370439
$612$	29.9844	1.21205
$613$	−15.3522	−0.620069	−0.310034	−	0.950725i	$-0.600341\pi$
$613$	−15.3522	−0.620069	−0.310034	+	0.950725i	$0.600341\pi$
$614$	−11.1028	−0.448072
$615$	−10.8011	−0.435541
$616$	5.62721	0.226727
$617$	41.3311	1.66393	0.831963	−	0.554831i	$-0.187217\pi$
$617$	41.3311	1.66393	0.831963	+	0.554831i	$0.187217\pi$
$618$	−24.8222	−0.998495
$619$	−5.84281	−0.234842	−0.117421	−	0.993082i	$-0.537463\pi$
$619$	−5.84281	−0.234842	−0.117421	+	0.993082i	$0.537463\pi$
$620$	2.78389	0.111804
$621$	−11.2544	−0.451625
$622$	−14.2978	−0.573288
$623$	6.72999	0.269631
$624$	−11.2544	−0.450538
$625$	8.23724	0.329490
$626$	−19.4756	−0.778400
$627$	10.0978	0.403265
$628$	6.89722	0.275229
$629$	−31.8922	−1.27163
$630$	7.30833	0.291171
$631$	6.34162	0.252456	0.126228	−	0.992001i	$-0.459713\pi$
$631$	6.34162	0.252456	0.126228	+	0.992001i	$0.459713\pi$
$632$	−16.9894	−0.675804
$633$	33.6444	1.33724
$634$	28.3416	1.12559
$635$	15.6655	0.621667
$636$	9.45998	0.375112
$637$	−3.62721	−0.143715
$638$	−32.8222	−1.29944
$639$	−86.4777	−3.42100
$640$	−1.10278	−0.0435910
$641$	−32.3133	−1.27630	−0.638150	−	0.769912i	$-0.720300\pi$
$641$	−32.3133	−1.27630	−0.638150	+	0.769912i	$0.720300\pi$
$642$	−57.4288	−2.26653
$643$	28.1672	1.11081	0.555404	−	0.831581i	$-0.312564\pi$
$643$	28.1672	1.11081	0.555404	+	0.831581i	$0.312564\pi$
$644$	1.00000	0.0394055
$645$	−24.8222	−0.977373
$646$	−2.61665	−0.102951
$647$	30.2978	1.19113	0.595564	−	0.803308i	$-0.296929\pi$
$647$	30.2978	1.19113	0.595564	+	0.803308i	$0.296929\pi$
$648$	15.0383	0.590761
$649$	−52.3799	−2.05609
$650$	13.7250	0.538337
$651$	7.83276	0.306990
$652$	−19.3622	−0.758283
$653$	−4.64782	−0.181883	−0.0909417	−	0.995856i	$-0.528988\pi$
$653$	−4.64782	−0.181883	−0.0909417	+	0.995856i	$0.528988\pi$
$654$	−2.61665	−0.102319
$655$	−24.6550	−0.963349
$656$	3.15667	0.123247
$657$	−94.7910	−3.69815
$658$	−2.52444	−0.0984128
$659$	−11.8811	−0.462823	−0.231411	−	0.972856i	$-0.574334\pi$
$659$	−11.8811	−0.462823	−0.231411	+	0.972856i	$0.574334\pi$
$660$	19.2544	0.749478
$661$	3.94610	0.153486	0.0767428	−	0.997051i	$-0.475548\pi$
$661$	3.94610	0.153486	0.0767428	+	0.997051i	$0.475548\pi$
$662$	−34.8122	−1.35301
$663$	−50.9200	−1.97757
$664$	13.6272	0.528838
$665$	−0.637776	−0.0247319
$666$	−46.7144	−1.81015
$667$	−5.83276	−0.225845
$668$	−10.5244	−0.407203
$669$	−62.0071	−2.39733
$670$	−6.20555	−0.239741
$671$	−47.0278	−1.81549
$672$	−3.10278	−0.119692
$673$	24.0383	0.926609	0.463304	−	0.886199i	$-0.346664\pi$
$673$	24.0383	0.926609	0.463304	+	0.886199i	$0.346664\pi$
$674$	−4.84333	−0.186558
$675$	−42.5855	−1.63912
$676$	0.156674	0.00602593
$677$	39.2005	1.50660	0.753299	−	0.657678i	$-0.228461\pi$
$677$	39.2005	1.50660	0.753299	+	0.657678i	$0.228461\pi$
$678$	11.7733	0.452152
$679$	−16.9355	−0.649926
$680$	−4.98944	−0.191336
$681$	15.4811	0.593237
$682$	14.2056	0.543959
$683$	−0.745574	−0.0285286	−0.0142643	−	0.999898i	$-0.504541\pi$
$683$	−0.745574	−0.0285286	−0.0142643	+	0.999898i	$0.504541\pi$
$684$	−3.83276	−0.146549
$685$	2.08667	0.0797277
$686$	−1.00000	−0.0381802
$687$	12.2439	0.467133
$688$	7.25443	0.276572
$689$	−11.0589	−0.421311
$690$	3.42166	0.130260
$691$	−11.7094	−0.445446	−0.222723	−	0.974882i	$-0.571495\pi$
$691$	−11.7094	−0.445446	−0.222723	+	0.974882i	$0.571495\pi$
$692$	17.4217	0.662272
$693$	37.2927	1.41663
$694$	−23.7733	−0.902423
$695$	7.01056	0.265926
$696$	18.0978	0.685994
$697$	14.2822	0.540976
$698$	32.7527	1.23971
$699$	−8.94108	−0.338183
$700$	3.78389	0.143017
$701$	7.45998	0.281759	0.140880	−	0.990027i	$-0.455007\pi$
$701$	7.45998	0.281759	0.140880	+	0.990027i	$0.455007\pi$
$702$	−40.8222	−1.54073
$703$	4.07663	0.153753
$704$	−5.62721	−0.212084
$705$	−8.63778	−0.325317
$706$	13.5577	0.510252
$707$	−4.37279	−0.164456
$708$	28.8816	1.08544
$709$	5.69670	0.213944	0.106972	−	0.994262i	$-0.465884\pi$
$709$	5.69670	0.213944	0.106972	+	0.994262i	$0.465884\pi$
$710$	14.3900	0.540046
$711$	−112.593	−4.22255
$712$	−6.72999	−0.252217
$713$	2.52444	0.0945409
$714$	−14.0383	−0.525371
$715$	−22.5089	−0.841783
$716$	−11.6655	−0.435961
$717$	64.2721	2.40029
$718$	6.67609	0.249149
$719$	1.67107	0.0623202	0.0311601	−	0.999514i	$-0.490080\pi$
$719$	1.67107	0.0623202	0.0311601	+	0.999514i	$0.490080\pi$
$720$	−7.30833	−0.272365
$721$	8.00000	0.297936
$722$	−18.6655	−0.694659
$723$	34.2338	1.27317
$724$	6.25945	0.232631
$725$	−22.0705	−0.819678
$726$	64.1205	2.37973
$727$	36.0766	1.33801	0.669004	−	0.743259i	$-0.266721\pi$
$727$	36.0766	1.33801	0.669004	+	0.743259i	$0.266721\pi$
$728$	3.62721	0.134433
$729$	−5.09775	−0.188806
$730$	15.7733	0.583797
$731$	32.8222	1.21397
$732$	25.9305	0.958419
$733$	−12.0227	−0.444070	−0.222035	−	0.975039i	$-0.571270\pi$
$733$	−12.0227	−0.444070	−0.222035	+	0.975039i	$0.571270\pi$
$734$	−24.3033	−0.897051
$735$	−3.42166	−0.126210
$736$	−1.00000	−0.0368605
$737$	−31.6655	−1.16641
$738$	20.9200	0.770074
$739$	−41.5366	−1.52795	−0.763974	−	0.645247i	$-0.776755\pi$
$739$	−41.5366	−1.52795	−0.763974	+	0.645247i	$0.776755\pi$
$740$	7.77332	0.285753
$741$	6.50885	0.239109
$742$	−3.04888	−0.111928
$743$	−13.1849	−0.483709	−0.241854	−	0.970313i	$-0.577756\pi$
$743$	−13.1849	−0.483709	−0.241854	+	0.970313i	$0.577756\pi$
$744$	−7.83276	−0.287163
$745$	2.20555	0.0808051
$746$	−8.50885	−0.311531
$747$	90.3104	3.30429
$748$	−25.4600	−0.930909
$749$	18.5089	0.676299
$750$	30.0555	1.09747
$751$	−7.83276	−0.285822	−0.142911	−	0.989736i	$-0.545646\pi$
$751$	−7.83276	−0.285822	−0.142911	+	0.989736i	$0.545646\pi$
$752$	2.52444	0.0920568
$753$	50.4011	1.83672
$754$	−21.1567	−0.770481
$755$	−20.5300	−0.747162
$756$	−11.2544	−0.409320
$757$	36.5089	1.32694	0.663468	−	0.748204i	$-0.269084\pi$
$757$	36.5089	1.32694	0.663468	+	0.748204i	$0.269084\pi$
$758$	−9.21611	−0.334744
$759$	17.4600	0.633757
$760$	0.637776	0.0231346
$761$	35.2444	1.27761	0.638804	−	0.769370i	$-0.279430\pi$
$761$	35.2444	1.27761	0.638804	+	0.769370i	$0.279430\pi$
$762$	−44.0766	−1.59673
$763$	0.843326	0.0305304
$764$	−2.31335	−0.0836940
$765$	−33.0661	−1.19551
$766$	−23.9688	−0.866029
$767$	−33.7633	−1.21912
$768$	3.10278	0.111962
$769$	−24.4933	−0.883250	−0.441625	−	0.897200i	$-0.645598\pi$
$769$	−24.4933	−0.883250	−0.441625	+	0.897200i	$0.645598\pi$
$770$	−6.20555	−0.223633
$771$	−42.4011	−1.52704
$772$	5.58890	0.201149
$773$	−7.94610	−0.285801	−0.142901	−	0.989737i	$-0.545643\pi$
$773$	−7.94610	−0.285801	−0.142901	+	0.989737i	$0.545643\pi$
$774$	48.0766	1.72808
$775$	9.55219	0.343125
$776$	16.9355	0.607950
$777$	21.8711	0.784620
$778$	−2.33447	−0.0836949
$779$	−1.82562	−0.0654097
$780$	12.4111	0.444389
$781$	73.4288	2.62749
$782$	−4.52444	−0.161794
$783$	65.6444	2.34594
$784$	1.00000	0.0357143
$785$	−7.60609	−0.271473
$786$	69.3694	2.47432
$787$	19.5295	0.696150	0.348075	−	0.937467i	$-0.386835\pi$
$787$	19.5295	0.696150	0.348075	+	0.937467i	$0.386835\pi$
$788$	18.4111	0.655868
$789$	77.5366	2.76038
$790$	18.7355	0.666580
$791$	−3.79445	−0.134915
$792$	−37.2927	−1.32514
$793$	−30.3133	−1.07646
$794$	−21.9406	−0.778641
$795$	−10.4322	−0.369993
$796$	4.41110	0.156347
$797$	−17.7406	−0.628403	−0.314201	−	0.949356i	$-0.601737\pi$
$797$	−17.7406	−0.628403	−0.314201	+	0.949356i	$0.601737\pi$
$798$	1.79445	0.0635228
$799$	11.4217	0.404069
$800$	−3.78389	−0.133781
$801$	−44.6011	−1.57590
$802$	−27.3522	−0.965839
$803$	80.4877	2.84035
$804$	17.4600	0.615766
$805$	−1.10278	−0.0388677
$806$	9.15667	0.322530
$807$	−54.2933	−1.91121
$808$	4.37279	0.153834
$809$	−18.4111	−0.647300	−0.323650	−	0.946177i	$-0.604910\pi$
$809$	−18.4111	−0.647300	−0.323650	+	0.946177i	$0.604910\pi$
$810$	−16.5839	−0.582698
$811$	20.2594	0.711405	0.355703	−	0.934599i	$-0.384242\pi$
$811$	20.2594	0.711405	0.355703	+	0.934599i	$0.384242\pi$
$812$	−5.83276	−0.204690
$813$	−57.4772	−2.01581
$814$	39.6655	1.39028
$815$	21.3522	0.747934
$816$	14.0383	0.491439
$817$	−4.19550	−0.146782
$818$	4.95112	0.173112
$819$	24.0383	0.839967
$820$	−3.48110	−0.121565
$821$	31.8116	1.11023	0.555117	−	0.831772i	$-0.312674\pi$
$821$	31.8116	1.11023	0.555117	+	0.831772i	$0.312674\pi$
$822$	−5.87108	−0.204777
$823$	32.9099	1.14717	0.573584	−	0.819147i	$-0.305553\pi$
$823$	32.9099	1.14717	0.573584	+	0.819147i	$0.305553\pi$
$824$	−8.00000	−0.278693
$825$	66.0666	2.30014
$826$	−9.30833	−0.323878
$827$	−37.4288	−1.30153	−0.650764	−	0.759280i	$-0.725551\pi$
$827$	−37.4288	−1.30153	−0.650764	+	0.759280i	$0.725551\pi$
$828$	−6.62721	−0.230312
$829$	28.5572	0.991833	0.495916	−	0.868370i	$-0.334832\pi$
$829$	28.5572	0.991833	0.495916	+	0.868370i	$0.334832\pi$
$830$	−15.0278	−0.521621
$831$	−34.0978	−1.18284
$832$	−3.62721	−0.125751
$833$	4.52444	0.156762
$834$	−19.7250	−0.683020
$835$	11.6061	0.401645
$836$	3.25443	0.112557
$837$	−28.4111	−0.982031
$838$	−26.3416	−0.909956
$839$	13.3833	0.462045	0.231022	−	0.972948i	$-0.425793\pi$
$839$	13.3833	0.462045	0.231022	+	0.972948i	$0.425793\pi$
$840$	3.42166	0.118059
$841$	5.02113	0.173142
$842$	−9.36222	−0.322644
$843$	−23.1466	−0.797212
$844$	10.8433	0.373243
$845$	−0.172776	−0.00594369
$846$	16.7300	0.575189
$847$	−20.6655	−0.710076
$848$	3.04888	0.104699
$849$	4.71440	0.161798
$850$	−17.1200	−0.587210
$851$	7.04888	0.241632
$852$	−40.4877	−1.38709
$853$	−31.4882	−1.07814	−0.539068	−	0.842262i	$-0.681224\pi$
$853$	−31.4882	−1.07814	−0.539068	+	0.842262i	$0.681224\pi$
$854$	−8.35720	−0.285978
$855$	4.22668	0.144549
$856$	−18.5089	−0.632620
$857$	31.2333	1.06691	0.533455	−	0.845829i	$-0.320894\pi$
$857$	31.2333	1.06691	0.533455	+	0.845829i	$0.320894\pi$
$858$	63.3311	2.16209
$859$	−53.0816	−1.81112	−0.905561	−	0.424216i	$-0.860550\pi$
$859$	−53.0816	−1.81112	−0.905561	+	0.424216i	$0.860550\pi$
$860$	−8.00000	−0.272798
$861$	−9.79445	−0.333794
$862$	8.82220	0.300485
$863$	5.04888	0.171866	0.0859329	−	0.996301i	$-0.472613\pi$
$863$	5.04888	0.171866	0.0859329	+	0.996301i	$0.472613\pi$
$864$	11.2544	0.382883
$865$	−19.2122	−0.653234
$866$	14.6222	0.496882
$867$	10.7683	0.365711
$868$	2.52444	0.0856850
$869$	95.6032	3.24312
$870$	−19.9577	−0.676631
$871$	−20.4111	−0.691604
$872$	−0.843326	−0.0285586
$873$	112.235	3.79859
$874$	0.578337	0.0195625
$875$	−9.68665	−0.327469
$876$	−44.3799	−1.49946
$877$	11.7350	0.396263	0.198132	−	0.980175i	$-0.436513\pi$
$877$	11.7350	0.396263	0.198132	+	0.980175i	$0.436513\pi$
$878$	−30.2978	−1.02250
$879$	−3.42166	−0.115410
$880$	6.20555	0.209189
$881$	38.9255	1.31143	0.655717	−	0.755007i	$-0.272367\pi$
$881$	38.9255	1.31143	0.655717	+	0.755007i	$0.272367\pi$
$882$	6.62721	0.223150
$883$	17.3522	0.583947	0.291974	−	0.956426i	$-0.405688\pi$
$883$	17.3522	0.583947	0.291974	+	0.956426i	$0.405688\pi$
$884$	−16.4111	−0.551965
$885$	−31.8500	−1.07062
$886$	17.5678	0.590201
$887$	−1.55219	−0.0521174	−0.0260587	−	0.999660i	$-0.508296\pi$
$887$	−1.55219	−0.0521174	−0.0260587	+	0.999660i	$0.508296\pi$
$888$	−21.8711	−0.733945
$889$	14.2056	0.476439
$890$	7.42166	0.248775
$891$	−84.6238	−2.83500
$892$	−19.9844	−0.669128
$893$	−1.45998	−0.0488562
$894$	−6.20555	−0.207545
$895$	12.8645	0.430011
$896$	−1.00000	−0.0334077
$897$	11.2544	0.375774
$898$	11.2927	0.376844
$899$	−14.7244	−0.491088
$900$	−25.0766	−0.835888
$901$	13.7944	0.459560
$902$	−17.7633	−0.591452
$903$	−22.5089	−0.749048
$904$	3.79445	0.126202
$905$	−6.90276	−0.229456
$906$	57.7633	1.91906
$907$	43.5466	1.44594	0.722971	−	0.690878i	$-0.242776\pi$
$907$	43.5466	1.44594	0.722971	+	0.690878i	$0.242776\pi$
$908$	4.98944	0.165580
$909$	28.9794	0.961186
$910$	−4.00000	−0.132599
$911$	−25.8116	−0.855178	−0.427589	−	0.903973i	$-0.640637\pi$
$911$	−25.8116	−0.855178	−0.427589	+	0.903973i	$0.640637\pi$
$912$	−1.79445	−0.0594202
$913$	−76.6832	−2.53784
$914$	27.4600	0.908295
$915$	−28.5955	−0.945339
$916$	3.94610	0.130383
$917$	−22.3572	−0.738300
$918$	50.9200	1.68061
$919$	−17.1083	−0.564351	−0.282176	−	0.959363i	$-0.591056\pi$
$919$	−17.1083	−0.564351	−0.282176	+	0.959363i	$0.591056\pi$
$920$	1.10278	0.0363574
$921$	−34.4494	−1.13515
$922$	29.4983	0.971474
$923$	47.3311	1.55792
$924$	17.4600	0.574391
$925$	26.6722	0.876975
$926$	14.7244	0.483875
$927$	−53.0177	−1.74133
$928$	5.83276	0.191470
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	8.63778	0.283244
$931$	−0.578337	−0.0189542
$932$	−2.88164	−0.0943912
$933$	−44.3627	−1.45237
$934$	8.57834	0.280692
$935$	28.0766	0.918204
$936$	−24.0383	−0.785717
$937$	39.1411	1.27868	0.639342	−	0.768923i	$-0.279207\pi$
$937$	39.1411	1.27868	0.639342	+	0.768923i	$0.279207\pi$
$938$	−5.62721	−0.183735
$939$	−60.4283	−1.97200
$940$	−2.78389	−0.0908004
$941$	−17.4061	−0.567422	−0.283711	−	0.958910i	$-0.591566\pi$
$941$	−17.4061	−0.567422	−0.283711	+	0.958910i	$0.591566\pi$
$942$	21.4005	0.697267
$943$	−3.15667	−0.102795
$944$	9.30833	0.302960
$945$	12.4111	0.403733
$946$	−40.8222	−1.32724
$947$	−7.89220	−0.256462	−0.128231	−	0.991744i	$-0.540930\pi$
$947$	−7.89220	−0.256462	−0.128231	+	0.991744i	$0.540930\pi$
$948$	−52.7144	−1.71208
$949$	51.8811	1.68413
$950$	2.18836	0.0709998
$951$	87.9377	2.85157
$952$	−4.52444	−0.146638
$953$	22.7456	0.736801	0.368401	−	0.929667i	$-0.379905\pi$
$953$	22.7456	0.736801	0.368401	+	0.929667i	$0.379905\pi$
$954$	20.2056	0.654179
$955$	2.55110	0.0825518
$956$	20.7144	0.669952
$957$	−101.840	−3.29202
$958$	−28.0766	−0.907115
$959$	1.89220	0.0611024
$960$	−3.42166	−0.110434
$961$	−24.6272	−0.794426
$962$	25.5678	0.824338
$963$	−122.662	−3.95273
$964$	11.0333	0.355358
$965$	−6.16330	−0.198404
$966$	3.10278	0.0998302
$967$	39.6655	1.27556	0.637779	−	0.770220i	$-0.279853\pi$
$967$	39.6655	1.27556	0.637779	+	0.770220i	$0.279853\pi$
$968$	20.6655	0.664215
$969$	−8.11888	−0.260816
$970$	−18.6761	−0.599653
$971$	32.7628	1.05141	0.525704	−	0.850668i	$-0.323802\pi$
$971$	32.7628	1.05141	0.525704	+	0.850668i	$0.323802\pi$
$972$	12.8972	0.413679
$973$	6.35720	0.203803
$974$	22.7244	0.728138
$975$	42.5855	1.36383
$976$	8.35720	0.267507
$977$	13.5577	0.433750	0.216875	−	0.976199i	$-0.430414\pi$
$977$	13.5577	0.433750	0.216875	+	0.976199i	$0.430414\pi$
$978$	−60.0766	−1.92104
$979$	37.8711	1.21036
$980$	−1.10278	−0.0352269
$981$	−5.58890	−0.178440
$982$	−18.7244	−0.597521
$983$	−47.0278	−1.49995	−0.749976	−	0.661465i	$-0.769935\pi$
$983$	−47.0278	−1.49995	−0.749976	+	0.661465i	$0.769935\pi$
$984$	9.79445	0.312236
$985$	−20.3033	−0.646917
$986$	26.3900	0.840428
$987$	−7.83276	−0.249320
$988$	2.09775	0.0667384
$989$	−7.25443	−0.230677
$990$	41.1255	1.30705
$991$	42.8888	1.36241	0.681204	−	0.732094i	$-0.261457\pi$
$991$	42.8888	1.36241	0.681204	+	0.732094i	$0.261457\pi$
$992$	−2.52444	−0.0801510
$993$	−108.014	−3.42773
$994$	13.0489	0.413885
$995$	−4.86445	−0.154213
$996$	42.2822	1.33976
$997$	7.10831	0.225123	0.112561	−	0.993645i	$-0.464095\pi$
$997$	7.10831	0.225123	0.112561	+	0.993645i	$0.464095\pi$
$998$	4.00000	0.126618
$999$	−79.3311	−2.50992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.a.g.1.3	✓	3
3.2	odd	2		2898.2.a.be.1.3		3
4.3	odd	2		2576.2.a.w.1.1		3
5.4	even	2		8050.2.a.bh.1.1		3
7.6	odd	2		2254.2.a.p.1.1		3
23.22	odd	2		7406.2.a.x.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.a.g.1.3	✓	3	1.1	even	1	trivial
2254.2.a.p.1.1		3	7.6	odd	2
2576.2.a.w.1.1		3	4.3	odd	2
2898.2.a.be.1.3		3	3.2	odd	2
7406.2.a.x.1.3		3	23.22	odd	2
8050.2.a.bh.1.1		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} -1.10278 q^{5} +3.10278 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} -1.10278 q^{5} +3.10278 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} -1.10278 q^{10} -5.62721 q^{11} +3.10278 q^{12} -3.62721 q^{13} -1.00000 q^{14} -3.42166 q^{15} +1.00000 q^{16} +4.52444 q^{17} +6.62721 q^{18} -0.578337 q^{19} -1.10278 q^{20} -3.10278 q^{21} -5.62721 q^{22} -1.00000 q^{23} +3.10278 q^{24} -3.78389 q^{25} -3.62721 q^{26} +11.2544 q^{27} -1.00000 q^{28} +5.83276 q^{29} -3.42166 q^{30} -2.52444 q^{31} +1.00000 q^{32} -17.4600 q^{33} +4.52444 q^{34} +1.10278 q^{35} +6.62721 q^{36} -7.04888 q^{37} -0.578337 q^{38} -11.2544 q^{39} -1.10278 q^{40} +3.15667 q^{41} -3.10278 q^{42} +7.25443 q^{43} -5.62721 q^{44} -7.30833 q^{45} -1.00000 q^{46} +2.52444 q^{47} +3.10278 q^{48} +1.00000 q^{49} -3.78389 q^{50} +14.0383 q^{51} -3.62721 q^{52} +3.04888 q^{53} +11.2544 q^{54} +6.20555 q^{55} -1.00000 q^{56} -1.79445 q^{57} +5.83276 q^{58} +9.30833 q^{59} -3.42166 q^{60} +8.35720 q^{61} -2.52444 q^{62} -6.62721 q^{63} +1.00000 q^{64} +4.00000 q^{65} -17.4600 q^{66} +5.62721 q^{67} +4.52444 q^{68} -3.10278 q^{69} +1.10278 q^{70} -13.0489 q^{71} +6.62721 q^{72} -14.3033 q^{73} -7.04888 q^{74} -11.7406 q^{75} -0.578337 q^{76} +5.62721 q^{77} -11.2544 q^{78} -16.9894 q^{79} -1.10278 q^{80} +15.0383 q^{81} +3.15667 q^{82} +13.6272 q^{83} -3.10278 q^{84} -4.98944 q^{85} +7.25443 q^{86} +18.0978 q^{87} -5.62721 q^{88} -6.72999 q^{89} -7.30833 q^{90} +3.62721 q^{91} -1.00000 q^{92} -7.83276 q^{93} +2.52444 q^{94} +0.637776 q^{95} +3.10278 q^{96} +16.9355 q^{97} +1.00000 q^{98} -37.2927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * q^99

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