LMFDB - Embedded newform 1449.2.h.e.1126.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1449,2,Mod(1126,1449)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1449, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1449.1126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1449 = 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1449.h (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$11.5703232529$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 $ x^12 + 17x^10 + 92x^8 + 180x^6 + 92x^4 + 17*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 483)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1126.6
Root			$-2.14584i$ of defining polynomial
Character	$\chi$	$=$	1449.1126
Dual form			1449.2.h.e.1126.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.17819 q^{2} -0.611859 q^{4} -1.67982 q^{5} +(2.04406 + 1.67982i) q^{7} +3.07728 q^{8} +1.97916 q^{10} -3.72389i q^{11} +0.821806i q^{13} +(-2.40830 - 1.97916i) q^{14} -2.40191 q^{16} -1.97916 q^{17} +3.72389 q^{19} +1.02781 q^{20} +4.38746i q^{22} +(-4.61186 + 1.31558i) q^{23} -2.17819 q^{25} -0.968247i q^{26} +(-1.25068 - 1.02781i) q^{28} +5.79005 q^{29} -0.566335i q^{31} -3.32464 q^{32} +2.33183 q^{34} +(-3.43366 - 2.82181i) q^{35} +1.25068i q^{37} -4.38746 q^{38} -5.16928 q^{40} -5.00000i q^{41} -7.01863i q^{43} +2.27849i q^{44} +(5.43366 - 1.55001i) q^{46} +5.14644i q^{47} +(1.35639 + 6.86733i) q^{49} +2.56634 q^{50} -0.502829i q^{52} +0.0649054i q^{53} +6.25547i q^{55} +(6.29015 + 5.16928i) q^{56} -6.82181 q^{58} +11.0455i q^{59} +9.36202 q^{61} +0.667253i q^{62} +8.72089 q^{64} -1.38049i q^{65} -5.03947i q^{67} +1.21096 q^{68} +(4.04552 + 3.32464i) q^{70} +6.40191 q^{71} -15.8811i q^{73} -1.47354i q^{74} -2.27849 q^{76} +(6.25547 - 7.61186i) q^{77} -17.6032i q^{79} +4.03479 q^{80} +5.89097i q^{82} +9.29712 q^{83} +3.32464 q^{85} +8.26931i q^{86} -11.4594i q^{88} +11.8352 q^{89} +(-1.38049 + 1.67982i) q^{91} +(2.82181 - 0.804951i) q^{92} -6.06351i q^{94} -6.25547 q^{95} +14.9720 q^{97} +(-1.59809 - 8.09105i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8} + 68 q^{16} - 12 q^{23} - 16 q^{25} + 16 q^{29} + 44 q^{32} - 8 q^{35} + 32 q^{46} - 4 q^{49} + 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} - 20 q^{71} + 52 q^{77}+ \cdots - 116 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 + 68 * q^16 - 12 * q^23 - 16 * q^25 + 16 * q^29 + 44 * q^32 - 8 * q^35 + 32 * q^46 - 4 * q^49 + 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 - 20 * q^71 + 52 * q^77 - 44 * q^85 + 44 * q^92 - 52 * q^95 - 116 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1449\mathbb{Z}\right)^\times$.

$n$	$442$	$829$	$1289$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.17819			−0.833109			−0.416555	−	0.909111i	$-0.636762\pi$
$2$	−1.17819			−0.833109			−0.416555	+	0.909111i	$0.636762\pi$
$3$		0			0
$3$		0			0
$4$	−0.611859			−0.305929
$5$	−1.67982			−0.751240			−0.375620	−	0.926774i	$-0.622570\pi$
$5$	−1.67982			−0.751240			−0.375620	+	0.926774i	$0.622570\pi$
$6$		0			0
$7$	2.04406	+	1.67982i	0.772583	+	0.634913i
$7$	2.04406	+	1.67982i	0.772583	+	0.634913i
$8$	3.07728			1.08798
$9$		0			0
$10$	1.97916			0.625865
$11$		−	3.72389i		−	1.12279i	−0.827547	−	0.561397i	$-0.810264\pi$
$11$		−	3.72389i		−	1.12279i	0.827547	−	0.561397i	$-0.189736\pi$
$12$		0			0
$13$			0.821806i			0.227928i	0.993485	+	0.113964i	$0.0363548\pi$
$13$			0.821806i			0.227928i	−0.993485	+	0.113964i	$0.963645\pi$
$14$	−2.40830	−	1.97916i	−0.643646	−	0.528952i
$15$		0			0
$16$	−2.40191			−0.600478
$17$	−1.97916			−0.480016			−0.240008	−	0.970771i	$-0.577150\pi$
$17$	−1.97916			−0.480016			−0.240008	+	0.970771i	$0.577150\pi$
$18$		0			0
$19$	3.72389			0.854318			0.427159	−	0.904176i	$-0.359514\pi$
$19$	3.72389			0.854318			0.427159	+	0.904176i	$0.359514\pi$
$20$	1.02781			0.229826
$21$		0			0
$22$			4.38746i			0.935410i
$23$	−4.61186	+	1.31558i	−0.961639	+	0.274318i
$23$	−4.61186	+	1.31558i	−0.961639	+	0.274318i
$24$		0			0
$25$	−2.17819			−0.435639
$26$		−	0.968247i		−	0.189889i
$27$		0			0
$28$	−1.25068	−	1.02781i	−0.236356	−	0.194239i
$29$	5.79005			1.07519			0.537593	−	0.843205i	$-0.319334\pi$
$29$	5.79005			1.07519			0.537593	+	0.843205i	$0.319334\pi$
$30$		0			0
$31$		−	0.566335i		−	0.101717i	−0.998706	−	0.0508584i	$-0.983804\pi$
$31$		−	0.566335i		−	0.101717i	0.998706	−	0.0508584i	$-0.0161957\pi$
$32$	−3.32464			−0.587718
$33$		0			0
$34$	2.33183			0.399906
$35$	−3.43366	−	2.82181i	−0.580395	−	0.476972i
$36$		0			0
$37$			1.25068i			0.205610i	0.994702	+	0.102805i	$0.0327818\pi$
$37$			1.25068i			0.205610i	−0.994702	+	0.102805i	$0.967218\pi$
$38$	−4.38746			−0.711740
$39$		0			0
$40$	−5.16928			−0.817335
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$		−	7.01863i		−	1.07033i	−0.844747	−	0.535165i	$-0.820249\pi$
$43$		−	7.01863i		−	1.07033i	0.844747	−	0.535165i	$-0.179751\pi$
$44$			2.27849i			0.343496i
$45$		0			0
$46$	5.43366	−	1.55001i	0.801150	−	0.228537i
$47$			5.14644i			0.750686i	0.926886	+	0.375343i	$0.122475\pi$
$47$			5.14644i			0.750686i	−0.926886	+	0.375343i	$0.877525\pi$
$48$		0			0
$49$	1.35639	+	6.86733i	0.193770	+	0.981047i
$50$	2.56634			0.362935
$51$		0			0
$52$		−	0.502829i		−	0.0697299i
$53$			0.0649054i			0.00891544i	0.999990	+	0.00445772i	$0.00141894\pi$
$53$			0.0649054i			0.00891544i	−0.999990	+	0.00445772i	$0.998581\pi$
$54$		0			0
$55$			6.25547i			0.843487i
$56$	6.29015	+	5.16928i	0.840556	+	0.690774i
$57$		0			0
$58$	−6.82181			−0.895747
$59$			11.0455i			1.43800i	0.695008	+	0.719002i	$0.255401\pi$
$59$			11.0455i			1.43800i	−0.695008	+	0.719002i	$0.744599\pi$
$60$		0			0
$61$	9.36202			1.19868			0.599342	−	0.800493i	$-0.295429\pi$
$61$	9.36202			1.19868			0.599342	+	0.800493i	$0.295429\pi$
$62$			0.667253i			0.0847412i
$63$		0			0
$64$	8.72089			1.09011
$65$		−	1.38049i		−	0.171229i
$66$		0			0
$67$		−	5.03947i		−	0.615669i	−0.951440	−	0.307835i	$-0.900396\pi$
$67$		−	5.03947i		−	0.615669i	0.951440	−	0.307835i	$-0.0996043\pi$
$68$	1.21096			0.146851
$69$		0			0
$70$	4.04552	+	3.32464i	0.483533	+	0.397370i
$71$	6.40191			0.759767			0.379884	−	0.925034i	$-0.375964\pi$
$71$	6.40191			0.759767			0.379884	+	0.925034i	$0.375964\pi$
$72$		0			0
$73$		−	15.8811i		−	1.85874i	−0.369147	−	0.929371i	$-0.620350\pi$
$73$		−	15.8811i		−	1.85874i	0.369147	−	0.929371i	$-0.379650\pi$
$74$		−	1.47354i		−	0.171296i
$75$		0			0
$76$	−2.27849			−0.261361
$77$	6.25547	−	7.61186i	0.712877	−	0.867452i
$78$		0			0
$79$		−	17.6032i		−	1.98051i	−0.139256	−	0.990256i	$-0.544471\pi$
$79$		−	17.6032i		−	1.98051i	0.139256	−	0.990256i	$-0.455529\pi$
$80$	4.03479			0.451103
$81$		0			0
$82$			5.89097i			0.650549i
$83$	9.29712			1.02049			0.510246	−	0.860029i	$-0.329554\pi$
$83$	9.29712			1.02049			0.510246	+	0.860029i	$0.329554\pi$
$84$		0			0
$85$	3.32464			0.360607
$86$			8.26931i			0.891702i
$87$		0			0
$88$		−	11.4594i		−	1.22158i
$89$	11.8352			1.25453			0.627266	−	0.778805i	$-0.284174\pi$
$89$	11.8352			1.25453			0.627266	+	0.778805i	$0.284174\pi$
$90$		0			0
$91$	−1.38049	+	1.67982i	−0.144715	+	0.176093i
$92$	2.82181	−	0.804951i	0.294194	−	0.0839219i
$93$		0			0
$94$		−	6.06351i		−	0.625403i
$95$	−6.25547			−0.641798
$96$		0			0
$97$	14.9720			1.52018			0.760089	−	0.649819i	$-0.225155\pi$
$97$	14.9720			1.52018			0.760089	+	0.649819i	$0.225155\pi$
$98$	−1.59809	−	8.09105i	−0.161431	−	0.817319i
$99$		0			0
$100$	1.33275			0.133275
$101$			12.2692i			1.22084i	0.792080	+	0.610418i	$0.208998\pi$
$101$			12.2692i			1.22084i	−0.792080	+	0.610418i	$0.791002\pi$
$102$		0			0
$103$	8.33421			0.821194			0.410597	−	0.911817i	$-0.365320\pi$
$103$	8.33421			0.821194			0.410597	+	0.911817i	$0.365320\pi$
$104$			2.52892i			0.247981i
$105$		0			0
$106$		−	0.0764712i		−	0.00742754i
$107$		−	15.1949i		−	1.46894i	−0.678639	−	0.734472i	$-0.737430\pi$
$107$		−	15.1949i		−	1.46894i	0.678639	−	0.734472i	$-0.262570\pi$
$108$		0			0
$109$			7.22491i			0.692021i	0.938231	+	0.346010i	$0.112464\pi$
$109$			7.22491i			0.692021i	−0.938231	+	0.346010i	$0.887536\pi$
$110$		−	7.37016i		−	0.702717i
$111$		0			0
$112$	−4.90966	−	4.03479i	−0.463919	−	0.381251i
$113$			3.00697i			0.282872i	0.989947	+	0.141436i	$0.0451720\pi$
$113$			3.00697i			0.282872i	−0.989947	+	0.141436i	$0.954828\pi$
$114$		0			0
$115$	7.74711	−	2.20995i	0.722421	−	0.206079i
$116$	−3.54269			−0.328931
$117$		0			0
$118$		−	13.0138i		−	1.19801i
$119$	−4.04552	−	3.32464i	−0.370853	−	0.304769i
$120$		0			0
$121$	−2.86733			−0.260666
$122$	−11.0303			−0.998635
$123$		0			0
$124$			0.346517i			0.0311182i
$125$	12.0581			1.07851
$126$		0			0
$127$	−2.32464			−0.206278			−0.103139	−	0.994667i	$-0.532889\pi$
$127$	−2.32464			−0.206278			−0.103139	+	0.994667i	$0.532889\pi$
$128$	−3.62563			−0.320463
$129$		0			0
$130$			1.62648i			0.142652i
$131$		−	6.13267i		−	0.535814i	−0.963445	−	0.267907i	$-0.913668\pi$
$131$		−	6.13267i		−	0.535814i	0.963445	−	0.267907i	$-0.0863320\pi$
$132$		0			0
$133$	7.61186	+	6.25547i	0.660032	+	0.542418i
$134$			5.93747i			0.512920i
$135$		0			0
$136$	−6.09042			−0.522249
$137$		−	17.7611i		−	1.51744i	−0.651419	−	0.758718i	$-0.725826\pi$
$137$		−	17.7611i		−	1.51744i	0.651419	−	0.758718i	$-0.274174\pi$
$138$		0			0
$139$			16.3465i			1.38649i	0.720700	+	0.693247i	$0.243820\pi$
$139$			16.3465i			1.38649i	−0.720700	+	0.693247i	$0.756180\pi$
$140$	2.10092	+	1.72655i	0.177560	+	0.145920i
$141$		0			0
$142$	−7.54269			−0.632969
$143$	3.06031			0.255916
$144$		0			0
$145$	−9.72626			−0.807722
$146$			18.7110i			1.54853i
$147$		0			0
$148$		−	0.765238i		−	0.0629022i
$149$		−	18.5661i		−	1.52099i	−0.649342	−	0.760497i	$-0.724955\pi$
$149$		−	18.5661i		−	1.52099i	0.649342	−	0.760497i	$-0.275045\pi$
$150$		0			0
$151$	−1.30099			−0.105873			−0.0529367	−	0.998598i	$-0.516858\pi$
$151$	−1.30099			−0.105873			−0.0529367	+	0.998598i	$0.516858\pi$
$152$	11.4594			0.929482
$153$		0			0
$154$	−7.37016	+	8.96825i	−0.593904	+	0.722682i
$155$			0.951343i			0.0764137i
$156$		0			0
$157$	7.60573			0.607003			0.303502	−	0.952831i	$-0.401844\pi$
$157$	7.60573			0.607003			0.303502	+	0.952831i	$0.401844\pi$
$158$			20.7400i			1.64998i
$159$		0			0
$160$	5.58480			0.441517
$161$	−11.6369	−	5.05797i	−0.917114	−	0.398624i
$162$		0			0
$163$	−6.68914			−0.523934			−0.261967	−	0.965077i	$-0.584371\pi$
$163$	−6.68914			−0.523934			−0.261967	+	0.965077i	$0.584371\pi$
$164$			3.05929i			0.238891i
$165$		0			0
$166$	−10.9538			−0.850181
$167$			2.79816i			0.216528i	0.994122	+	0.108264i	$0.0345293\pi$
$167$			2.79816i			0.216528i	−0.994122	+	0.108264i	$0.965471\pi$
$168$		0			0
$169$	12.3246			0.948049
$170$	−3.91707			−0.300425
$171$		0			0
$172$			4.29441i			0.327446i
$173$			5.88110i			0.447132i	0.974689	+	0.223566i	$0.0717698\pi$
$173$			5.88110i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$174$		0			0
$175$	−4.45237	−	3.65898i	−0.336567	−	0.276593i
$176$			8.94445i			0.674213i
$177$		0			0
$178$	−13.9442			−1.04516
$179$	0.100918			0.00754294			0.00377147	−	0.999993i	$-0.498800\pi$
$179$	0.100918			0.00754294			0.00377147	+	0.999993i	$0.498800\pi$
$180$		0			0
$181$	−12.6568			−0.940770			−0.470385	−	0.882461i	$-0.655885\pi$
$181$	−12.6568			−0.940770			−0.470385	+	0.882461i	$0.655885\pi$
$182$	1.62648	−	1.97916i	0.120563	−	0.146705i
$183$		0			0
$184$	−14.1920	+	4.04841i	−1.04625	+	0.298453i
$185$		−	2.10092i		−	0.154463i
$186$		0			0
$187$			7.37016i			0.538959i
$188$		−	3.14889i		−	0.229657i
$189$		0			0
$190$	7.37016			0.534687
$191$			7.16000i			0.518080i	0.965867	+	0.259040i	$0.0834061\pi$
$191$			7.16000i			0.518080i	−0.965867	+	0.259040i	$0.916594\pi$
$192$		0			0
$193$	−6.79005			−0.488759			−0.244379	−	0.969680i	$-0.578584\pi$
$193$	−6.79005			−0.488759			−0.244379	+	0.969680i	$0.578584\pi$
$194$	−17.6399			−1.26647
$195$		0			0
$196$	−0.829918	−	4.20184i	−0.0592799	−	0.300131i
$197$	14.4930			1.03258			0.516290	−	0.856414i	$-0.327313\pi$
$197$	14.4930			1.03258			0.516290	+	0.856414i	$0.327313\pi$
$198$		0			0
$199$	11.3412			0.803955			0.401978	−	0.915650i	$-0.368323\pi$
$199$	11.3412			0.803955			0.401978	+	0.915650i	$0.368323\pi$
$200$	−6.70291			−0.473967
$201$		0			0
$202$		−	14.4555i		−	1.01709i
$203$	11.8352	+	9.72626i	0.830671	+	0.682650i
$204$		0			0
$205$			8.39912i			0.586620i
$206$	−9.81932			−0.684144
$207$		0			0
$208$		−	1.97391i		−	0.136866i
$209$		−	13.8673i		−	0.959223i
$210$		0			0
$211$	10.6436			0.732736			0.366368	−	0.930470i	$-0.380601\pi$
$211$	10.6436			0.732736			0.366368	+	0.930470i	$0.380601\pi$
$212$		−	0.0397129i		−	0.00272750i
$213$		0			0
$214$			17.9025i			1.22379i
$215$			11.7901i			0.804075i
$216$		0			0
$217$	0.951343	−	1.15763i	0.0645814	−	0.0785847i
$218$		−	8.51235i		−	0.576529i
$219$		0			0
$220$		−	3.82746i		−	0.258048i
$221$		−	1.62648i		−	0.109409i
$222$		0			0
$223$		−	0.877200i		−	0.0587417i	−0.999569	−	0.0293708i	$-0.990650\pi$
$223$		−	0.877200i		−	0.0587417i	0.999569	−	0.0293708i	$-0.00935037\pi$
$224$	−6.79576	−	5.58480i	−0.454061	−	0.373150i
$225$		0			0
$226$		−	3.54280i		−	0.235663i
$227$	7.95339			0.527885			0.263942	−	0.964538i	$-0.414977\pi$
$227$	7.95339			0.527885			0.263942	+	0.964538i	$0.414977\pi$
$228$		0			0
$229$	12.3293			0.814742			0.407371	−	0.913263i	$-0.366446\pi$
$229$	12.3293			0.814742			0.407371	+	0.913263i	$0.366446\pi$
$230$	−9.12760	+	2.60375i	−0.601856	+	0.171686i
$231$		0			0
$232$	17.8176			1.16978
$233$	3.38814			0.221965			0.110982	−	0.993822i	$-0.464600\pi$
$233$	3.38814			0.221965			0.110982	+	0.993822i	$0.464600\pi$
$234$		0			0
$235$		−	8.64511i		−	0.563945i
$236$		−	6.75830i		−	0.439928i
$237$		0			0
$238$	4.76641	+	3.91707i	0.308961	+	0.253906i
$239$	13.7445			0.889060			0.444530	−	0.895764i	$-0.353371\pi$
$239$	13.7445			0.889060			0.444530	+	0.895764i	$0.353371\pi$
$240$		0			0
$241$	19.0883			1.22958			0.614792	−	0.788689i	$-0.289240\pi$
$241$	19.0883			1.22958			0.614792	+	0.788689i	$0.289240\pi$
$242$	3.37827			0.217163
$243$		0			0
$244$	−5.72824			−0.366713
$245$	−2.27849	−	11.5359i	−0.145568	−	0.737002i
$246$		0			0
$247$			3.06031i			0.194723i
$248$		−	1.74277i		−	0.110666i
$249$		0			0
$250$	−14.2068			−0.898516
$251$	−7.57758			−0.478293			−0.239146	−	0.970984i	$-0.576868\pi$
$251$	−7.57758			−0.478293			−0.239146	+	0.970984i	$0.576868\pi$
$252$		0			0
$253$	4.89908	+	17.1740i	0.308003	+	1.07972i
$254$	2.73887			0.171852
$255$		0			0
$256$	−13.1701			−0.823130
$257$		−	22.1048i		−	1.37886i	−0.724352	−	0.689430i	$-0.757861\pi$
$257$		−	22.1048i		−	1.37886i	0.724352	−	0.689430i	$-0.242139\pi$
$258$		0			0
$259$	−2.10092	+	2.55646i	−0.130545	+	0.158851i
$260$			0.844664i			0.0523838i
$261$		0			0
$262$			7.22548i			0.446391i
$263$			8.67030i			0.534634i	0.963609	+	0.267317i	$0.0861371\pi$
$263$			8.67030i			0.534634i	−0.963609	+	0.267317i	$0.913863\pi$
$264$		0			0
$265$		−	0.109030i		−	0.00669764i
$266$	−8.96825	−	7.37016i	−0.549878	−	0.451893i
$267$		0			0
$268$			3.08344i			0.188351i
$269$			19.6891i			1.20047i	0.799825	+	0.600234i	$0.204926\pi$
$269$			19.6891i			1.20047i	−0.799825	+	0.600234i	$0.795074\pi$
$270$		0			0
$271$			4.65738i			0.282916i	0.989944	+	0.141458i	$0.0451790\pi$
$271$			4.65738i			0.282916i	−0.989944	+	0.141458i	$0.954821\pi$
$272$	4.75376			0.288239
$273$		0			0
$274$			20.9261i			1.26419i
$275$			8.11135i			0.489133i
$276$		0			0
$277$	−23.5011			−1.41204			−0.706021	−	0.708191i	$-0.749512\pi$
$277$	−23.5011			−1.41204			−0.706021	+	0.708191i	$0.749512\pi$
$278$		−	19.2594i		−	1.15510i
$279$		0			0
$280$	−10.5663	−	8.68348i	−0.631459	−	0.518937i
$281$			1.90269i			0.113505i	0.998388	+	0.0567524i	$0.0180746\pi$
$281$			1.90269i			0.113505i	−0.998388	+	0.0567524i	$0.981925\pi$
$282$		0			0
$283$	−12.3574			−0.734573			−0.367287	−	0.930108i	$-0.619713\pi$
$283$	−12.3574			−0.734573			−0.367287	+	0.930108i	$0.619713\pi$
$284$	−3.91707			−0.232435
$285$		0			0
$286$	−3.60564			−0.213206
$287$	8.39912	−	10.2203i	0.495784	−	0.603286i
$288$		0			0
$289$	−13.0829			−0.769584
$290$	11.4594			0.672921
$291$		0			0
$292$			9.71699i			0.568644i
$293$	−28.4871			−1.66423			−0.832116	−	0.554601i	$-0.812871\pi$
$293$	−28.4871			−1.66423			−0.832116	+	0.554601i	$0.812871\pi$
$294$		0			0
$295$		−	18.5545i		−	1.08029i
$296$			3.84868i			0.223700i
$297$		0			0
$298$			21.8745i			1.26715i
$299$	−1.08115	−	3.79005i	−0.0625248	−	0.219184i
$300$		0			0
$301$	11.7901	−	14.3465i	0.679567	−	0.826920i
$302$	1.53282			0.0882041
$303$		0			0
$304$	−8.94445			−0.512999
$305$	−15.7265			−0.900499
$306$		0			0
$307$		−	24.0357i		−	1.37179i	−0.727702	−	0.685894i	$-0.759412\pi$
$307$		−	24.0357i		−	1.37179i	0.727702	−	0.685894i	$-0.240588\pi$
$308$	−3.82746	+	4.65738i	−0.218090	+	0.265379i
$309$		0			0
$310$		−	1.12087i		−	0.0636610i
$311$		−	11.7029i		−	0.663611i	−0.943348	−	0.331805i	$-0.892342\pi$
$311$		−	11.7029i		−	0.663611i	0.943348	−	0.331805i	$-0.107658\pi$
$312$		0			0
$313$	−18.5661			−1.04942			−0.524709	−	0.851282i	$-0.675826\pi$
$313$	−18.5661			−1.04942			−0.524709	+	0.851282i	$0.675826\pi$
$314$	−8.96103			−0.505700
$315$		0			0
$316$			10.7707i			0.605897i
$317$	19.1503			1.07559			0.537795	−	0.843076i	$-0.319257\pi$
$317$	19.1503			1.07559			0.537795	+	0.843076i	$0.319257\pi$
$318$		0			0
$319$		−	21.5615i		−	1.20721i
$320$	−14.6496			−0.818935
$321$		0			0
$322$	13.7105	+	5.95927i	0.764056	+	0.332097i
$323$	−7.37016			−0.410087
$324$		0			0
$325$		−	1.79005i		−	0.0992943i
$326$	7.88110			0.436494
$327$		0			0
$328$		−	15.3864i		−	0.849571i
$329$	−8.64511	+	10.5197i	−0.476620	+	0.579967i
$330$		0			0
$331$	16.8811			0.927869			0.463935	−	0.885869i	$-0.346437\pi$
$331$	16.8811			0.927869			0.463935	+	0.885869i	$0.346437\pi$
$332$	−5.68852			−0.312198
$333$		0			0
$334$		−	3.29678i		−	0.180392i
$335$			8.46542i			0.462515i
$336$		0			0
$337$			32.7447i			1.78372i	0.452313	+	0.891859i	$0.350599\pi$
$337$			32.7447i			1.78372i	−0.452313	+	0.891859i	$0.649401\pi$
$338$	−14.5208			−0.789828
$339$		0			0
$340$	−2.03421			−0.110320
$341$	−2.10897			−0.114207
$342$		0			0
$343$	−8.76336	+	16.3157i	−0.473177	+	0.880968i
$344$		−	21.5983i		−	1.16450i
$345$		0			0
$346$		−	6.92908i		−	0.372509i
$347$	−9.01377			−0.483885			−0.241942	−	0.970291i	$-0.577784\pi$
$347$	−9.01377			−0.483885			−0.241942	+	0.970291i	$0.577784\pi$
$348$		0			0
$349$			23.6337i			1.26509i	0.774526	+	0.632543i	$0.217989\pi$
$349$			23.6337i			1.26509i	−0.774526	+	0.632543i	$0.782011\pi$
$350$	5.24575	+	4.31099i	0.280397	+	0.230432i
$351$		0			0
$352$			12.3806i			0.659886i
$353$		−	20.0357i		−	1.06639i	−0.845992	−	0.533195i	$-0.820991\pi$
$353$		−	20.0357i		−	1.06639i	0.845992	−	0.533195i	$-0.179009\pi$
$354$		0			0
$355$	−10.7541			−0.570767
$356$	−7.24149			−0.383798
$357$		0			0
$358$	−0.118901			−0.00628409
$359$		−	1.67982i		−	0.0886577i	−0.999017	−	0.0443288i	$-0.985885\pi$
$359$		−	1.67982i		−	0.0886577i	0.999017	−	0.0443288i	$-0.0141149\pi$
$360$		0			0
$361$	−5.13267			−0.270141
$362$	14.9121			0.783764
$363$		0			0
$364$	0.844664	−	1.02781i	0.0442724	−	0.0538721i
$365$			26.6774i			1.39636i
$366$		0			0
$367$	5.53352			0.288847			0.144424	−	0.989516i	$-0.453867\pi$
$367$	5.53352			0.288847			0.144424	+	0.989516i	$0.453867\pi$
$368$	11.0773	−	3.15991i	0.577443	−	0.164722i
$369$		0			0
$370$			2.47529i			0.128684i
$371$	−0.109030	+	0.132671i	−0.00566053	+	0.00688792i
$372$		0			0
$373$		−	11.1998i		−	0.579904i	−0.957041	−	0.289952i	$-0.906361\pi$
$373$		−	11.1998i		−	0.579904i	0.957041	−	0.289952i	$-0.0936393\pi$
$374$		−	8.68348i		−	0.449012i
$375$		0			0
$376$			15.8370i			0.816732i
$377$			4.75830i			0.245065i
$378$		0			0
$379$		−	6.71929i		−	0.345147i	−0.984997	−	0.172573i	$-0.944792\pi$
$379$		−	6.71929i		−	0.345147i	0.984997	−	0.172573i	$-0.0552082\pi$
$380$	3.82746			0.196345
$381$		0			0
$382$		−	8.43587i		−	0.431617i
$383$	−25.9655			−1.32678			−0.663389	−	0.748275i	$-0.730882\pi$
$383$	−25.9655			−1.32678			−0.663389	+	0.748275i	$0.730882\pi$
$384$		0			0
$385$	−10.5081	+	12.7866i	−0.535542	+	0.651664i
$386$	8.00000			0.407189
$387$		0			0
$388$	−9.16076			−0.465067
$389$		−	9.29712i		−	0.471383i	−0.971828	−	0.235691i	$-0.924265\pi$
$389$		−	9.29712i		−	0.471383i	0.971828	−	0.235691i	$-0.0757354\pi$
$390$		0			0
$391$	9.12760	−	2.60375i	0.461602	−	0.131677i
$392$	4.17398	+	21.1327i	0.210818	+	1.06736i
$393$		0			0
$394$	−17.0755			−0.860252
$395$			29.5702i			1.48784i
$396$		0			0
$397$		−	3.02188i		−	0.151664i	−0.997121	−	0.0758320i	$-0.975839\pi$
$397$		−	3.02188i		−	0.151664i	0.997121	−	0.0758320i	$-0.0241613\pi$
$398$	−13.3621			−0.669782
$399$		0			0
$400$	5.23183			0.261591
$401$			33.8540i			1.69059i	0.534300	+	0.845295i	$0.320575\pi$
$401$			33.8540i			1.69059i	−0.534300	+	0.845295i	$0.679425\pi$
$402$		0			0
$403$	0.465418			0.0231841
$404$		−	7.50704i		−	0.373489i
$405$		0			0
$406$	−13.9442	−	11.4594i	−0.692039	−	0.568722i
$407$	4.65738			0.230858
$408$		0			0
$409$		−	18.8592i		−	0.932528i	−0.884646	−	0.466264i	$-0.845600\pi$
$409$		−	18.8592i		−	0.932528i	0.884646	−	0.466264i	$-0.154400\pi$
$410$		−	9.89579i		−	0.488718i
$411$		0			0
$412$	−5.09936			−0.251227
$413$	−18.5545	+	22.5777i	−0.913009	+	1.11098i
$414$		0			0
$415$	−15.6175			−0.766634
$416$		−	2.73220i		−	0.133957i
$417$		0			0
$418$			16.3384i			0.799138i
$419$	25.9490			1.26769			0.633845	−	0.773460i	$-0.281476\pi$
$419$	25.9490			1.26769			0.633845	+	0.773460i	$0.281476\pi$
$420$		0			0
$421$		−	1.15763i		−	0.0564192i	−0.999602	−	0.0282096i	$-0.991019\pi$
$421$		−	1.15763i		−	0.0564192i	0.999602	−	0.0282096i	$-0.00898059\pi$
$422$	−12.5402			−0.610449
$423$		0			0
$424$			0.199732i			0.00969984i
$425$	4.31099			0.209114
$426$		0			0
$427$	19.1366	+	15.7265i	0.926084	+	0.761061i
$428$			9.29712i			0.449393i
$429$		0			0
$430$		−	13.8910i		−	0.669882i
$431$			37.6962i			1.81576i	0.419230	+	0.907880i	$0.362300\pi$
$431$			37.6962i			1.81576i	−0.419230	+	0.907880i	$0.637700\pi$
$432$		0			0
$433$	−39.9213			−1.91850			−0.959248	−	0.282566i	$-0.908814\pi$
$433$	−39.9213			−1.91850			−0.959248	+	0.282566i	$0.908814\pi$
$434$	−1.12087	+	1.36391i	−0.0538033	+	0.0654696i
$435$		0			0
$436$		−	4.42062i		−	0.211709i
$437$	−17.1740	+	4.89908i	−0.821546	+	0.234355i
$438$		0			0
$439$		−	16.3483i		−	0.780261i	−0.920760	−	0.390130i	$-0.872430\pi$
$439$		−	16.3483i		−	0.780261i	0.920760	−	0.390130i	$-0.127570\pi$
$440$			19.2498i			0.917699i
$441$		0			0
$442$			1.91631i			0.0911497i
$443$	−12.1821			−0.578789			−0.289394	−	0.957210i	$-0.593454\pi$
$443$	−12.1821			−0.578789			−0.289394	+	0.957210i	$0.593454\pi$
$444$		0			0
$445$	−19.8811			−0.942455
$446$			1.03351i			0.0489382i
$447$		0			0
$448$	17.8260	+	14.6496i	0.842202	+	0.692126i
$449$	−6.70291			−0.316330			−0.158165	−	0.987413i	$-0.550558\pi$
$449$	−6.70291			−0.316330			−0.158165	+	0.987413i	$0.550558\pi$
$450$		0			0
$451$	−18.6194			−0.876755
$452$		−	1.83984i		−	0.0865389i
$453$		0			0
$454$	−9.37064			−0.439786
$455$	2.31898	−	2.82181i	0.108715	−	0.132288i
$456$		0			0
$457$		−	27.3828i		−	1.28091i	−0.767995	−	0.640456i	$-0.778745\pi$
$457$		−	27.3828i		−	1.28091i	0.767995	−	0.640456i	$-0.221255\pi$
$458$	−14.5263			−0.678769
$459$		0			0
$460$	−4.74013	+	1.35218i	−0.221010	+	0.0630455i
$461$		−	34.2357i		−	1.59452i	−0.603638	−	0.797258i	$-0.706283\pi$
$461$		−	34.2357i		−	1.59452i	0.603638	−	0.797258i	$-0.293717\pi$
$462$		0			0
$463$	22.8892			1.06375			0.531876	−	0.846822i	$-0.321487\pi$
$463$	22.8892			1.06375			0.531876	+	0.846822i	$0.321487\pi$
$464$	−13.9072			−0.645625
$465$		0			0
$466$	−3.99189			−0.184921
$467$	−6.19709			−0.286767			−0.143384	−	0.989667i	$-0.545798\pi$
$467$	−6.19709			−0.286767			−0.143384	+	0.989667i	$0.545798\pi$
$468$		0			0
$469$	8.46542	−	10.3010i	0.390897	−	0.475656i
$470$			10.1856i			0.469828i
$471$		0			0
$472$			33.9901i			1.56452i
$473$	−26.1366			−1.20176
$474$		0			0
$475$	−8.11135			−0.372174
$476$	2.47529	+	2.03421i	0.113455	+	0.0932377i
$477$		0			0
$478$	−16.1937			−0.740684
$479$	34.1418			1.55998			0.779989	−	0.625793i	$-0.215225\pi$
$479$	34.1418			1.55998			0.779989	+	0.625793i	$0.215225\pi$
$480$		0			0
$481$	−1.02781			−0.0468643
$482$	−22.4897			−1.02438
$483$		0			0
$484$	1.75440			0.0797455
$485$	−25.1503			−1.14202
$486$		0			0
$487$	27.6793			1.25427			0.627134	−	0.778912i	$-0.284228\pi$
$487$	27.6793			1.25427			0.627134	+	0.778912i	$0.284228\pi$
$488$	28.8095			1.30415
$489$		0			0
$490$	2.68451	+	13.5915i	0.121274	+	0.614003i
$491$	−5.62563			−0.253881			−0.126941	−	0.991910i	$-0.540516\pi$
$491$	−5.62563			−0.253881			−0.126941	+	0.991910i	$0.540516\pi$
$492$		0			0
$493$	−11.4594			−0.516107
$494$		−	3.60564i		−	0.162225i
$495$		0			0
$496$			1.36029i			0.0610787i
$497$	13.0859	+	10.7541i	0.586983	+	0.482386i
$498$		0			0
$499$	−16.2555			−0.727695			−0.363847	−	0.931459i	$-0.618537\pi$
$499$	−16.2555			−0.727695			−0.363847	+	0.931459i	$0.618537\pi$
$500$	−7.37785			−0.329948
$501$		0			0
$502$	8.92786			0.398470
$503$	16.5754			0.739059			0.369530	−	0.929219i	$-0.379519\pi$
$503$	16.5754			0.739059			0.369530	+	0.929219i	$0.379519\pi$
$504$		0			0
$505$		−	20.6102i		−	0.917140i
$506$	−5.77207	−	20.2343i	−0.256600	−	0.899527i
$507$		0			0
$508$	1.42235			0.0631065
$509$			24.3067i			1.07737i	0.842506	+	0.538687i	$0.181079\pi$
$509$			24.3067i			1.07737i	−0.842506	+	0.538687i	$0.818921\pi$
$510$		0			0
$511$	26.6774	−	32.4620i	1.18014	−	1.43603i
$512$	22.7682			1.00622
$513$		0			0
$514$			26.0438i			1.14874i
$515$	−14.0000			−0.616914
$516$		0			0
$517$	19.1648			0.842865
$518$	2.47529	−	3.01201i	0.108758	−	0.132340i
$519$		0			0
$520$		−	4.24815i		−	0.186293i
$521$	15.1783			0.664973			0.332487	−	0.943108i	$-0.392112\pi$
$521$	15.1783			0.664973			0.332487	+	0.943108i	$0.392112\pi$
$522$		0			0
$523$	−21.4569			−0.938244			−0.469122	−	0.883133i	$-0.655430\pi$
$523$	−21.4569			−0.938244			−0.469122	+	0.883133i	$0.655430\pi$
$524$			3.75233i			0.163921i
$525$		0			0
$526$		−	10.2153i		−	0.445408i
$527$			1.12087i			0.0488257i
$528$		0			0
$529$	19.5385	−	12.1346i	0.849499	−	0.527590i
$530$			0.128458i			0.00557986i
$531$		0			0
$532$	−4.65738	−	3.82746i	−0.201923	−	0.165942i
$533$	4.10903			0.177982
$534$		0			0
$535$			25.5247i			1.10353i
$536$		−	15.5078i		−	0.669837i
$537$		0			0
$538$		−	23.1976i		−	1.00012i
$539$	25.5732	−	5.05104i	1.10151	−	0.217563i
$540$		0			0
$541$	−35.3920			−1.52162			−0.760811	−	0.648973i	$-0.775199\pi$
$541$	−35.3920			−1.52162			−0.760811	+	0.648973i	$0.775199\pi$
$542$		−	5.48730i		−	0.235700i
$543$		0			0
$544$	6.57998			0.282114
$545$		−	12.1366i		−	0.519874i
$546$		0			0
$547$	−13.4792			−0.576328			−0.288164	−	0.957581i	$-0.593045\pi$
$547$	−13.4792			−0.576328			−0.288164	+	0.957581i	$0.593045\pi$
$548$			10.8673i			0.464228i
$549$		0			0
$550$		−	9.55674i		−	0.407501i
$551$	21.5615			0.918551
$552$		0			0
$553$	29.5702	−	35.9820i	1.25745	−	1.53011i
$554$	27.6888			1.17639
$555$		0			0
$556$		−	10.0018i		−	0.424169i
$557$		−	46.4826i		−	1.96953i	−0.173883	−	0.984766i	$-0.555631\pi$
$557$		−	46.4826i		−	1.96953i	0.173883	−	0.984766i	$-0.444369\pi$
$558$		0			0
$559$	5.76795			0.243958
$560$	8.24736	+	6.77773i	0.348515	+	0.286411i
$561$		0			0
$562$		−	2.24173i		−	0.0945618i
$563$	−4.98613			−0.210140			−0.105070	−	0.994465i	$-0.533507\pi$
$563$	−4.98613			−0.210140			−0.105070	+	0.994465i	$0.533507\pi$
$564$		0			0
$565$		−	5.05118i		−	0.212505i
$566$	14.5595			0.611979
$567$		0			0
$568$	19.7005			0.826613
$569$			7.34611i			0.307965i	0.988074	+	0.153982i	$0.0492099\pi$
$569$			7.34611i			0.307965i	−0.988074	+	0.153982i	$0.950790\pi$
$570$		0			0
$571$		−	25.2039i		−	1.05475i	−0.849633	−	0.527375i	$-0.823176\pi$
$571$		−	25.2039i		−	1.05475i	0.849633	−	0.527375i	$-0.176824\pi$
$572$	−1.87248			−0.0782923
$573$		0			0
$574$	−9.89579	+	12.0415i	−0.413042	+	0.502603i
$575$	10.0455	−	2.86560i	0.418927	−	0.119504i
$576$		0			0
$577$			5.84545i			0.243349i	0.992570	+	0.121675i	$0.0388264\pi$
$577$			5.84545i			0.243349i	−0.992570	+	0.121675i	$0.961174\pi$
$578$	15.4142			0.641148
$579$		0			0
$580$	5.95110			0.247106
$581$	19.0039	+	15.6175i	0.788415	+	0.647924i
$582$		0			0
$583$	0.241700			0.0100102
$584$		−	48.8705i		−	2.02228i
$585$		0			0
$586$	33.5633			1.38649
$587$			14.0318i			0.579152i	0.957155	+	0.289576i	$0.0935144\pi$
$587$			14.0318i			0.579152i	−0.957155	+	0.289576i	$0.906486\pi$
$588$		0			0
$589$		−	2.10897i		−	0.0868985i
$590$			21.8608i			0.899996i
$591$		0			0
$592$		−	3.00402i		−	0.123464i
$593$			1.70712i			0.0701029i	0.999386	+	0.0350515i	$0.0111595\pi$
$593$			1.70712i			0.0701029i	−0.999386	+	0.0350515i	$0.988840\pi$
$594$		0			0
$595$	6.79576	+	5.58480i	0.278599	+	0.228954i
$596$			11.3598i			0.465317i
$597$		0			0
$598$	1.27381	+	4.46542i	0.0520899	+	0.182605i
$599$	−2.97636			−0.121611			−0.0608054	−	0.998150i	$-0.519367\pi$
$599$	−2.97636			−0.121611			−0.0608054	+	0.998150i	$0.519367\pi$
$600$		0			0
$601$			10.7502i			0.438509i	0.975668	+	0.219255i	$0.0703625\pi$
$601$			10.7502i			0.438509i	−0.975668	+	0.219255i	$0.929637\pi$
$602$	−13.8910	+	16.9030i	−0.566154	+	0.688914i
$603$		0			0
$604$	0.796024			0.0323898
$605$	4.81661			0.195823
$606$		0			0
$607$		−	26.4019i		−	1.07162i	−0.844338	−	0.535810i	$-0.820006\pi$
$607$		−	26.4019i		−	1.07162i	0.844338	−	0.535810i	$-0.179994\pi$
$608$	−12.3806			−0.502098
$609$		0			0
$610$	18.5289			0.750214
$611$	−4.22938			−0.171102
$612$		0			0
$613$			36.7167i			1.48297i	0.670968	+	0.741486i	$0.265879\pi$
$613$			36.7167i			1.48297i	−0.670968	+	0.741486i	$0.734121\pi$
$614$			28.3187i			1.14285i
$615$		0			0
$616$	19.2498	−	23.4238i	0.775597	−	0.943772i
$617$			0.688767i			0.0277287i	0.999904	+	0.0138644i	$0.00441330\pi$
$617$			0.688767i			0.0277287i	−0.999904	+	0.0138644i	$0.995587\pi$
$618$		0			0
$619$	9.51998			0.382640			0.191320	−	0.981528i	$-0.438723\pi$
$619$	9.51998			0.382640			0.191320	+	0.981528i	$0.438723\pi$
$620$		−	0.582088i		−	0.0233772i
$621$		0			0
$622$			13.7883i			0.552860i
$623$	24.1920	+	19.8811i	0.969231	+	0.796519i
$624$		0			0
$625$	−9.36450			−0.374580
$626$	21.8745			0.874279
$627$		0			0
$628$	−4.65363			−0.185700
$629$		−	2.47529i		−	0.0986962i
$630$		0			0
$631$		−	23.8032i		−	0.947592i	−0.880635	−	0.473796i	$-0.842883\pi$
$631$		−	23.8032i		−	0.947592i	0.880635	−	0.473796i	$-0.157117\pi$
$632$		−	54.1699i		−	2.15476i
$633$		0			0
$634$	−22.5628			−0.896084
$635$	3.90498			0.154964
$636$		0			0
$637$	−5.64361	+	1.11469i	−0.223608	+	0.0441655i
$638$			25.4036i			1.00574i
$639$		0			0
$640$	6.09042			0.240745
$641$			14.4383i			0.570277i	0.958486	+	0.285138i	$0.0920395\pi$
$641$			14.4383i			0.570277i	−0.958486	+	0.285138i	$0.907960\pi$
$642$		0			0
$643$	−3.08846			−0.121797			−0.0608985	−	0.998144i	$-0.519397\pi$
$643$	−3.08846			−0.121797			−0.0608985	+	0.998144i	$0.519397\pi$
$644$	7.12012	+	3.09476i	0.280572	+	0.121951i
$645$		0			0
$646$	8.68348			0.341647
$647$		−	49.1503i		−	1.93230i	−0.257982	−	0.966150i	$-0.583058\pi$
$647$		−	49.1503i		−	1.93230i	0.257982	−	0.966150i	$-0.416942\pi$
$648$		0			0
$649$	41.1323			1.61458
$650$			2.10903i			0.0827229i
$651$		0			0
$652$	4.09281			0.160287
$653$	21.3684			0.836210			0.418105	−	0.908399i	$-0.362694\pi$
$653$	21.3684			0.836210			0.418105	+	0.908399i	$0.362694\pi$
$654$		0			0
$655$			10.3018i			0.402525i
$656$			12.0096i			0.468894i
$657$		0			0
$658$	10.1856	−	12.3942i	0.397077	−	0.483176i
$659$		−	19.0601i		−	0.742478i	−0.928537	−	0.371239i	$-0.878933\pi$
$659$		−	19.0601i		−	0.742478i	0.928537	−	0.371239i	$-0.121067\pi$
$660$		0			0
$661$	−26.3500			−1.02489			−0.512447	−	0.858719i	$-0.671261\pi$
$661$	−26.3500			−1.02489			−0.512447	+	0.858719i	$0.671261\pi$
$662$	−19.8892			−0.773016
$663$		0			0
$664$	28.6098			1.11028
$665$	−12.7866	−	10.5081i	−0.495842	−	0.407486i
$666$		0			0
$667$	−26.7029	+	7.61730i	−1.03394	+	0.294943i
$668$		−	1.71208i		−	0.0662424i
$669$		0			0
$670$		−	9.97391i		−	0.385326i
$671$		−	34.8631i		−	1.34588i
$672$		0			0
$673$	−31.4474			−1.21221			−0.606105	−	0.795385i	$-0.707269\pi$
$673$	−31.4474			−1.21221			−0.606105	+	0.795385i	$0.707269\pi$
$674$		−	38.5796i		−	1.48603i
$675$		0			0
$676$	−7.54094			−0.290036
$677$	−22.9586			−0.882369			−0.441185	−	0.897416i	$-0.645442\pi$
$677$	−22.9586			−0.882369			−0.441185	+	0.897416i	$0.645442\pi$
$678$		0			0
$679$	30.6037	+	25.1503i	1.17446	+	0.965181i
$680$	10.2308			0.392334
$681$		0			0
$682$	2.48477			0.0951469
$683$	26.0829			0.998036			0.499018	−	0.866592i	$-0.333694\pi$
$683$	26.0829			0.998036			0.499018	+	0.866592i	$0.333694\pi$
$684$		0			0
$685$			29.8356i			1.13996i
$686$	10.3249	−	19.2231i	0.394208	−	0.733942i
$687$		0			0
$688$			16.8581i			0.642710i
$689$	−0.0533396			−0.00203208
$690$		0			0
$691$		−	22.9404i		−	0.872694i	−0.899779	−	0.436347i	$-0.856272\pi$
$691$		−	22.9404i		−	0.872694i	0.899779	−	0.436347i	$-0.143728\pi$
$692$		−	3.59840i		−	0.136791i
$693$		0			0
$694$	10.6200			0.403129
$695$		−	27.4593i		−	1.04159i
$696$		0			0
$697$			9.89579i			0.374830i
$698$		−	27.8451i		−	1.05395i
$699$		0			0
$700$	2.72422	+	2.23878i	0.102966	+	0.0846179i
$701$		−	42.0469i		−	1.58809i	−0.607860	−	0.794044i	$-0.707972\pi$
$701$		−	42.0469i		−	1.58809i	0.607860	−	0.794044i	$-0.292028\pi$
$702$		0			0
$703$			4.65738i			0.175656i
$704$		−	32.4756i		−	1.22397i
$705$		0			0
$706$			23.6059i			0.888419i
$707$	−20.6102	+	25.0791i	−0.775125	+	0.943197i
$708$		0			0
$709$			25.1440i			0.944303i	0.881517	+	0.472152i	$0.156522\pi$
$709$			25.1440i			0.944303i	−0.881517	+	0.472152i	$0.843478\pi$
$710$	12.6704			0.475511
$711$		0			0
$712$	36.4203			1.36491
$713$	0.745061	+	2.61186i	0.0279028	+	0.0978149i
$714$		0			0
$715$	−5.14078			−0.192254
$716$	−0.0617473			−0.00230761
$717$		0			0
$718$			1.97916i			0.0738615i
$719$			40.4831i			1.50976i	0.655860	+	0.754882i	$0.272306\pi$
$719$			40.4831i			1.50976i	−0.655860	+	0.754882i	$0.727694\pi$
$720$		0			0
$721$	17.0357	+	14.0000i	0.634441	+	0.521387i
$722$	6.04728			0.225057
$723$		0			0
$724$	7.74415			0.287809
$725$	−12.6119			−0.468393
$726$		0			0
$727$	46.9536			1.74141			0.870706	−	0.491805i	$-0.163663\pi$
$727$	46.9536			1.74141			0.870706	+	0.491805i	$0.163663\pi$
$728$	−4.24815	+	5.16928i	−0.157447	+	0.191586i
$729$		0			0
$730$		−	31.4312i		−	1.16332i
$731$			13.8910i			0.513776i
$732$		0			0
$733$	30.7288			1.13499			0.567497	−	0.823375i	$-0.307912\pi$
$733$	30.7288			1.13499			0.567497	+	0.823375i	$0.307912\pi$
$734$	−6.51956			−0.240641
$735$		0			0
$736$	15.3327	−	4.37383i	0.565173	−	0.161222i
$737$	−18.7664			−0.691270
$738$		0			0
$739$	45.8338			1.68602			0.843012	−	0.537895i	$-0.180780\pi$
$739$	45.8338			1.68602			0.843012	+	0.537895i	$0.180780\pi$
$740$			1.28546i			0.0472546i
$741$		0			0
$742$	0.128458	−	0.156312i	0.00471584	−	0.00573839i
$743$		−	23.6056i		−	0.866004i	−0.901393	−	0.433002i	$-0.857454\pi$
$743$		−	23.6056i		−	0.866004i	0.901393	−	0.433002i	$-0.142546\pi$
$744$		0			0
$745$			31.1878i			1.14263i
$746$			13.1955i			0.483123i
$747$		0			0
$748$		−	4.50950i		−	0.164883i
$749$	25.5247	−	31.0593i	0.932653	−	1.13488i
$750$		0			0
$751$			1.36391i			0.0497697i	0.999690	+	0.0248848i	$0.00792191\pi$
$751$			1.36391i			0.0497697i	−0.999690	+	0.0248848i	$0.992078\pi$
$752$		−	12.3613i		−	0.450770i
$753$		0			0
$754$		−	5.60620i		−	0.204166i
$755$	2.18544			0.0795363
$756$		0			0
$757$			49.5797i			1.80201i	0.433814	+	0.901003i	$0.357168\pi$
$757$			49.5797i			1.80201i	−0.433814	+	0.901003i	$0.642832\pi$
$758$			7.91663i			0.287545i
$759$		0			0
$760$	−19.2498			−0.698264
$761$			31.9227i			1.15720i	0.815612	+	0.578599i	$0.196400\pi$
$761$			31.9227i			1.15720i	−0.815612	+	0.578599i	$0.803600\pi$
$762$		0			0
$763$	−12.1366	+	14.7682i	−0.439373	+	0.534644i
$764$		−	4.38091i		−	0.158496i
$765$		0			0
$766$	30.5924			1.10535
$767$	−9.07728			−0.327761
$768$		0			0
$769$	−18.7009			−0.674372			−0.337186	−	0.941438i	$-0.609475\pi$
$769$	−18.7009			−0.674372			−0.337186	+	0.941438i	$0.609475\pi$
$770$	12.3806	−	15.0651i	0.446165	−	0.542907i
$771$		0			0
$772$	4.15455			0.149526
$773$	6.40633			0.230420			0.115210	−	0.993341i	$-0.463246\pi$
$773$	6.40633			0.230420			0.115210	+	0.993341i	$0.463246\pi$
$774$		0			0
$775$			1.23359i			0.0443118i
$776$	46.0730			1.65393
$777$		0			0
$778$			10.9538i			0.392713i
$779$		−	18.6194i		−	0.667110i
$780$		0			0
$781$		−	23.8400i		−	0.853062i
$782$	−10.7541	+	3.06772i	−0.384565	+	0.109701i
$783$		0			0
$784$	−3.25792	−	16.4947i	−0.116354	−	0.589097i
$785$	−12.7763			−0.456005
$786$		0			0
$787$	46.2085			1.64716			0.823578	−	0.567204i	$-0.191975\pi$
$787$	46.2085			1.64716			0.823578	+	0.567204i	$0.191975\pi$
$788$	−8.86764			−0.315897
$789$		0			0
$790$		−	34.8395i		−	1.23953i
$791$	−5.05118	+	6.14644i	−0.179599	+	0.218542i
$792$		0			0
$793$			7.69377i			0.273214i
$794$			3.56036i			0.126353i
$795$		0			0
$796$	−6.93920			−0.245953
$797$	−47.2111			−1.67230			−0.836152	−	0.548498i	$-0.815200\pi$
$797$	−47.2111			−1.67230			−0.836152	+	0.548498i	$0.815200\pi$
$798$		0			0
$799$		−	10.1856i		−	0.360341i
$800$	7.24170			0.256033
$801$		0			0
$802$		−	39.8866i		−	1.40845i
$803$	−59.1394			−2.08698
$804$		0			0
$805$	19.5479	+	8.49650i	0.688973	+	0.299462i
$806$	−0.548352			−0.0193149
$807$		0			0
$808$			37.7558i			1.32825i
$809$	45.4513			1.59798			0.798992	−	0.601342i	$-0.205367\pi$
$809$	45.4513			1.59798			0.798992	+	0.601342i	$0.205367\pi$
$810$		0			0
$811$			26.2375i			0.921323i	0.887576	+	0.460661i	$0.152388\pi$
$811$			26.2375i			0.921323i	−0.887576	+	0.460661i	$0.847612\pi$
$812$	−7.24149	−	5.95110i	−0.254127	−	0.208843i
$813$		0			0
$814$	−5.48730			−0.192330
$815$	11.2366			0.393600
$816$		0			0
$817$		−	26.1366i		−	0.914403i
$818$			22.2198i			0.776898i
$819$		0			0
$820$		−	5.13907i		−	0.179464i
$821$	−31.0692			−1.08432			−0.542161	−	0.840275i	$-0.682394\pi$
$821$	−31.0692			−1.08432			−0.542161	+	0.840275i	$0.682394\pi$
$822$		0			0
$823$	−44.6694			−1.55708			−0.778539	−	0.627597i	$-0.784039\pi$
$823$	−44.6694			−1.55708			−0.778539	+	0.627597i	$0.784039\pi$
$824$	25.6467			0.893444
$825$		0			0
$826$	21.8608	−	26.6010i	0.760636	−	0.925566i
$827$			18.7327i			0.651398i	0.945473	+	0.325699i	$0.105600\pi$
$827$			18.7327i			0.651398i	−0.945473	+	0.325699i	$0.894400\pi$
$828$		0			0
$829$			35.6355i			1.23767i	0.785520	+	0.618836i	$0.212395\pi$
$829$			35.6355i			1.23767i	−0.785520	+	0.618836i	$0.787605\pi$
$830$	18.4005			0.638689
$831$		0			0
$832$			7.16688i			0.248467i
$833$	−2.68451	−	13.5915i	−0.0930126	−	0.470919i
$834$		0			0
$835$		−	4.70042i		−	0.162665i
$836$			8.48485i			0.293455i
$837$		0			0
$838$	−30.5729			−1.05612
$839$	27.3063			0.942719			0.471359	−	0.881941i	$-0.343763\pi$
$839$	27.3063			0.942719			0.471359	+	0.881941i	$0.343763\pi$
$840$		0			0
$841$	4.52471			0.156025
$842$			1.36391i			0.0470033i
$843$		0			0
$844$	−6.51239			−0.224166
$845$	−20.7032			−0.712212
$846$		0			0
$847$	−5.86100	−	4.81661i	−0.201386	−	0.165501i
$848$		−	0.155897i		−	0.00535353i
$849$		0			0
$850$	−5.07918			−0.174215
$851$	−1.64537	−	5.76795i	−0.0564026	−	0.197723i
$852$		0			0
$853$			49.8730i			1.70762i	0.520586	+	0.853809i	$0.325714\pi$
$853$			49.8730i			1.70762i	−0.520586	+	0.853809i	$0.674286\pi$
$854$	−22.5466	−	18.5289i	−0.771529	−	0.634047i
$855$		0			0
$856$		−	46.7588i		−	1.59818i
$857$			1.05539i			0.0360516i	0.999838	+	0.0180258i	$0.00573810\pi$
$857$			1.05539i			0.0360516i	−0.999838	+	0.0180258i	$0.994262\pi$
$858$		0			0
$859$		−	58.0910i		−	1.98204i	−0.133710	−	0.991020i	$-0.542689\pi$
$859$		−	58.0910i		−	1.98204i	0.133710	−	0.991020i	$-0.457311\pi$
$860$		−	7.21385i		−	0.245990i
$861$		0			0
$862$		−	44.4134i		−	1.51273i
$863$	−14.2018			−0.483436			−0.241718	−	0.970347i	$-0.577711\pi$
$863$	−14.2018			−0.483436			−0.241718	+	0.970347i	$0.577711\pi$
$864$		0			0
$865$		−	9.87921i		−	0.335903i
$866$	47.0350			1.59832
$867$		0			0
$868$	−0.582088	+	0.708303i	−0.0197573	+	0.0240414i
$869$	−65.5523			−2.22371
$870$		0			0
$871$	4.14147			0.140328
$872$			22.2330i			0.752906i
$873$		0			0
$874$	20.2343	−	5.77207i	0.684437	−	0.195243i
$875$	24.6475	+	20.2555i	0.833238	+	0.684760i
$876$		0			0
$877$	−14.8973			−0.503047			−0.251523	−	0.967851i	$-0.580932\pi$
$877$	−14.8973			−0.503047			−0.251523	+	0.967851i	$0.580932\pi$
$878$			19.2614i			0.650042i
$879$		0			0
$880$		−	15.0251i		−	0.506496i
$881$	30.5759			1.03013			0.515064	−	0.857152i	$-0.327768\pi$
$881$	30.5759			1.03013			0.515064	+	0.857152i	$0.327768\pi$
$882$		0			0
$883$	−41.6532			−1.40174			−0.700870	−	0.713289i	$-0.747205\pi$
$883$	−41.6532			−1.40174			−0.700870	+	0.713289i	$0.747205\pi$
$884$			0.995178i			0.0334715i
$885$		0			0
$886$	14.3529			0.482194
$887$			10.2911i			0.345542i	0.984962	+	0.172771i	$0.0552721\pi$
$887$			10.2911i			0.345542i	−0.984962	+	0.172771i	$0.944728\pi$
$888$		0			0
$889$	−4.75170	−	3.90498i	−0.159367	−	0.130969i
$890$	23.4238			0.785167
$891$		0			0
$892$			0.536723i			0.0179708i
$893$			19.1648i			0.641324i
$894$		0			0
$895$	−0.169524			−0.00566655
$896$	−7.41101	−	6.09042i	−0.247585	−	0.203467i
$897$		0			0
$898$	7.89732			0.263537
$899$		−	3.27911i		−	0.109364i
$900$		0			0
$901$		−	0.128458i		−	0.00427956i
$902$	21.9373			0.730432
$903$		0			0
$904$			9.25328i			0.307760i
$905$	21.2611			0.706744
$906$		0			0
$907$			48.4221i			1.60783i	0.594745	+	0.803915i	$0.297253\pi$
$907$			48.4221i			1.60783i	−0.594745	+	0.803915i	$0.702747\pi$
$908$	−4.86635			−0.161496
$909$		0			0
$910$	−2.73220	+	3.32464i	−0.0905717	+	0.110211i
$911$		−	12.0048i		−	0.397735i	−0.980026	−	0.198868i	$-0.936274\pi$
$911$		−	12.0048i		−	0.397735i	0.980026	−	0.198868i	$-0.0637264\pi$
$912$		0			0
$913$		−	34.6214i		−	1.14580i
$914$			32.2622i			1.06714i
$915$		0			0
$916$	−7.54378			−0.249254
$917$	10.3018	−	12.5356i	0.340195	−	0.413961i
$918$		0			0
$919$		−	51.3757i		−	1.69473i	−0.531012	−	0.847364i	$-0.678188\pi$
$919$		−	51.3757i		−	1.69473i	0.531012	−	0.847364i	$-0.321812\pi$
$920$	23.8400	−	6.80062i	0.785981	−	0.224210i
$921$		0			0
$922$			40.3363i			1.32841i
$923$			5.26113i			0.173172i
$924$		0			0
$925$		−	2.72422i		−	0.0895718i
$926$	−26.9679			−0.886221
$927$		0			0
$928$	−19.2498			−0.631906
$929$			33.4157i			1.09633i	0.836369	+	0.548166i	$0.184674\pi$
$929$			33.4157i			1.09633i	−0.836369	+	0.548166i	$0.815326\pi$
$930$		0			0
$931$	5.05104	+	25.5732i	0.165541	+	0.838126i
$932$	−2.07306			−0.0679055
$933$		0			0
$934$	7.30138			0.238908
$935$		−	12.3806i		−	0.404888i
$936$		0			0
$937$	−36.8746			−1.20464			−0.602321	−	0.798254i	$-0.705757\pi$
$937$	−36.8746			−1.20464			−0.602321	+	0.798254i	$0.705757\pi$
$938$	−9.97391	+	12.1366i	−0.325660	+	0.396273i
$939$		0			0
$940$			5.28959i			0.172527i
$941$	−43.8283			−1.42876			−0.714382	−	0.699756i	$-0.753292\pi$
$941$	−43.8283			−1.42876			−0.714382	+	0.699756i	$0.753292\pi$
$942$		0			0
$943$	6.57792	+	23.0593i	0.214206	+	0.750914i
$944$		−	26.5304i		−	0.863490i
$945$		0			0
$946$	30.7940			1.00120
$947$	−0.0635063			−0.00206368			−0.00103184	−	0.999999i	$-0.500328\pi$
$947$	−0.0635063			−0.00206368			−0.00103184	+	0.999999i	$0.500328\pi$
$948$		0			0
$949$	13.0512			0.423659
$950$	9.55674			0.310062
$951$		0			0
$952$	−12.4492	−	10.2308i	−0.403481	−	0.331583i
$953$		−	6.83754i		−	0.221490i	−0.993849	−	0.110745i	$-0.964676\pi$
$953$		−	6.83754i		−	0.221490i	0.993849	−	0.110745i	$-0.0353236\pi$
$954$		0			0
$955$		−	12.0275i		−	0.389202i
$956$	−8.40971			−0.271989
$957$		0			0
$958$	−40.2257			−1.29963
$959$	29.8356	−	36.3049i	0.963441	−	1.17235i
$960$		0			0
$961$	30.6793			0.989654
$962$	1.21096			0.0390431
$963$		0			0
$964$	−11.6793			−0.376166
$965$	11.4061			0.367175
$966$		0			0
$967$	19.7819			0.636144			0.318072	−	0.948067i	$-0.396965\pi$
$967$	19.7819			0.636144			0.318072	+	0.948067i	$0.396965\pi$
$968$	−8.82356			−0.283600
$969$		0			0
$970$	29.6320			0.951426
$971$	36.9395			1.18545			0.592723	−	0.805406i	$-0.298053\pi$
$971$	36.9395			1.18545			0.592723	+	0.805406i	$0.298053\pi$
$972$		0			0
$973$	−27.4593	+	33.4133i	−0.880303	+	1.07118i
$974$	−32.6115			−1.04494
$975$		0			0
$976$	−22.4868			−0.719783
$977$			30.1186i			0.963578i	0.876287	+	0.481789i	$0.160013\pi$
$977$			30.1186i			0.963578i	−0.876287	+	0.481789i	$0.839987\pi$
$978$		0			0
$979$		−	44.0731i		−	1.40858i
$980$	1.39412	+	7.05834i	0.0445334	+	0.225470i
$981$		0			0
$982$	6.62808			0.211511
$983$	−22.5727			−0.719958			−0.359979	−	0.932960i	$-0.617216\pi$
$983$	−22.5727			−0.719958			−0.359979	+	0.932960i	$0.617216\pi$
$984$		0			0
$985$	−24.3456			−0.775716
$986$	13.5014			0.429973
$987$		0			0
$988$		−	1.87248i		−	0.0595715i
$989$	9.23359	+	32.3689i	0.293611	+	1.02927i
$990$		0			0
$991$	6.45165			0.204943			0.102472	−	0.994736i	$-0.467325\pi$
$991$	6.45165			0.204943			0.102472	+	0.994736i	$0.467325\pi$
$992$			1.88286i			0.0597808i
$993$		0			0
$994$	−15.4177	−	12.6704i	−0.489021	−	0.401880i
$995$	−19.0512			−0.603963
$996$		0			0
$997$			18.9227i			0.599289i	0.954051	+	0.299644i	$0.0968680\pi$
$997$			18.9227i			0.599289i	−0.954051	+	0.299644i	$0.903132\pi$
$998$	19.1521			0.606249
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1449.2.h.e.1126.6		12
3.2	odd	2		483.2.h.c.160.8	yes	12
7.6	odd	2	inner	1449.2.h.e.1126.8		12
21.20	even	2		483.2.h.c.160.5	✓	12
23.22	odd	2	inner	1449.2.h.e.1126.7		12
69.68	even	2		483.2.h.c.160.7	yes	12
161.160	even	2	inner	1449.2.h.e.1126.5		12
483.482	odd	2		483.2.h.c.160.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.c.160.5	✓	12	21.20	even	2
483.2.h.c.160.6	yes	12	483.482	odd	2
483.2.h.c.160.7	yes	12	69.68	even	2
483.2.h.c.160.8	yes	12	3.2	odd	2
1449.2.h.e.1126.5		12	161.160	even	2	inner
1449.2.h.e.1126.6		12	1.1	even	1	trivial
1449.2.h.e.1126.7		12	23.22	odd	2	inner
1449.2.h.e.1126.8		12	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1449.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.17819 q^{2} -0.611859 q^{4} -1.67982 q^{5} +(2.04406 + 1.67982i) q^{7} +3.07728 q^{8} +1.97916 q^{10} -3.72389i q^{11} +0.821806i q^{13} +(-2.40830 - 1.97916i) q^{14} -2.40191 q^{16} -1.97916 q^{17} +3.72389 q^{19} +1.02781 q^{20} +4.38746i q^{22} +(-4.61186 + 1.31558i) q^{23} -2.17819 q^{25} -0.968247i q^{26} +(-1.25068 - 1.02781i) q^{28} +5.79005 q^{29} -0.566335i q^{31} -3.32464 q^{32} +2.33183 q^{34} +(-3.43366 - 2.82181i) q^{35} +1.25068i q^{37} -4.38746 q^{38} -5.16928 q^{40} -5.00000i q^{41} -7.01863i q^{43} +2.27849i q^{44} +(5.43366 - 1.55001i) q^{46} +5.14644i q^{47} +(1.35639 + 6.86733i) q^{49} +2.56634 q^{50} -0.502829i q^{52} +0.0649054i q^{53} +6.25547i q^{55} +(6.29015 + 5.16928i) q^{56} -6.82181 q^{58} +11.0455i q^{59} +9.36202 q^{61} +0.667253i q^{62} +8.72089 q^{64} -1.38049i q^{65} -5.03947i q^{67} +1.21096 q^{68} +(4.04552 + 3.32464i) q^{70} +6.40191 q^{71} -15.8811i q^{73} -1.47354i q^{74} -2.27849 q^{76} +(6.25547 - 7.61186i) q^{77} -17.6032i q^{79} +4.03479 q^{80} +5.89097i q^{82} +9.29712 q^{83} +3.32464 q^{85} +8.26931i q^{86} -11.4594i q^{88} +11.8352 q^{89} +(-1.38049 + 1.67982i) q^{91} +(2.82181 - 0.804951i) q^{92} -6.06351i q^{94} -6.25547 q^{95} +14.9720 q^{97} +(-1.59809 - 8.09105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8} + 68 q^{16} - 12 q^{23} - 16 q^{25} + 16 q^{29} + 44 q^{32} - 8 q^{35} + 32 q^{46} - 4 q^{49} + 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} - 20 q^{71} + 52 q^{77}+ \cdots - 116 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 + 68 * q^16 - 12 * q^23 - 16 * q^25 + 16 * q^29 + 44 * q^32 - 8 * q^35 + 32 * q^46 - 4 * q^49 + 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 - 20 * q^71 + 52 * q^77 - 44 * q^85 + 44 * q^92 - 52 * q^95 - 116 * q^98

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