LMFDB - Embedded newform 2268.2.i.n.865.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (of order $3$, degree $2$, not 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 $ x^16 - 9x^14 + 31x^12 - 282x^10 + 1695x^8 - 3318x^6 + 4606x^4 - 4116*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.8
Root			$-0.817131 + 0.735533i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.n.2053.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83843 - 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +O(q^{10})$	$q+(1.83843 - 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +(0.301572 + 0.522337i) q^{11} +(2.62851 + 4.55271i) q^{13} +(2.12557 - 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +(0.578891 - 1.00267i) q^{23} +(-4.25969 - 7.37799i) q^{25} +(-3.98826 + 6.90786i) q^{29} +3.15085 q^{31} +(3.95419 + 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} +(-2.00937 - 3.48033i) q^{41} +(-3.66193 + 6.34264i) q^{43} +12.2173 q^{47} +(-2.15926 - 6.65865i) q^{49} +(-4.64928 + 8.05279i) q^{53} +2.21768 q^{55} +6.61521 q^{59} -1.93850 q^{61} +19.3294 q^{65} +8.63088 q^{67} +1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(-1.58698 - 0.167264i) q^{77} +4.14551 q^{79} +(6.24088 - 10.8095i) q^{83} +(-7.81544 - 13.5367i) q^{85} +(-4.09464 - 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} +27.0931 q^{95} +(6.77935 - 11.7422i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) $ 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.83843	−	3.18426i	0.822173	−	1.42405i	−0.0818877	−	0.996642i	$-0.526095\pi$
$5$	1.83843	−	3.18426i	0.822173	−	1.42405i	0.904061	−	0.427404i	$-0.140572\pi$
$6$		0			0
$7$	−1.55575	+	2.14001i	−0.588020	+	0.808846i
$7$	−1.55575	+	2.14001i	−0.588020	+	0.808846i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.301572	+	0.522337i	0.0909273	+	0.157491i	0.907902	−	0.419183i	$-0.137684\pi$
$11$	0.301572	+	0.522337i	0.0909273	+	0.157491i	−0.816974	+	0.576674i	$0.804350\pi$
$12$		0			0
$13$	2.62851	+	4.55271i	0.729017	+	1.26269i	0.957299	+	0.289099i	$0.0933558\pi$
$13$	2.62851	+	4.55271i	0.729017	+	1.26269i	−0.228282	+	0.973595i	$0.573311\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.12557	−	3.68159i	0.515526	−	0.892918i	−0.484311	−	0.874896i	$-0.660930\pi$
$17$	2.12557	−	3.68159i	0.515526	−	0.892918i	0.999838	−	0.0180219i	$-0.00573685\pi$
$18$		0			0
$19$	3.68426	+	6.38133i	0.845228	+	1.46398i	0.885423	+	0.464786i	$0.153869\pi$
$19$	3.68426	+	6.38133i	0.845228	+	1.46398i	−0.0401954	+	0.999192i	$0.512798\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.578891	−	1.00267i	0.120707	−	0.209071i	−0.799340	−	0.600880i	$-0.794817\pi$
$23$	0.578891	−	1.00267i	0.120707	−	0.209071i	0.920047	+	0.391809i	$0.128150\pi$
$24$		0			0
$25$	−4.25969	−	7.37799i	−0.851937	−	1.47560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.98826	+	6.90786i	−0.740601	+	1.28276i	0.211622	+	0.977352i	$0.432126\pi$
$29$	−3.98826	+	6.90786i	−0.740601	+	1.28276i	−0.952222	+	0.305406i	$0.901208\pi$
$30$		0			0
$31$	3.15085			0.565909			0.282954	−	0.959133i	$-0.408686\pi$
$31$	3.15085			0.565909			0.282954	+	0.959133i	$0.408686\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.95419	+	8.88819i	0.668380	+	1.50238i
$36$		0			0
$37$	0.00266923	+	0.00462323i	0.000438818	+	0.000760055i	0.866245	−	0.499620i	$-0.166527\pi$
$37$	0.00266923	+	0.00462323i	0.000438818	+	0.000760055i	−0.865806	+	0.500380i	$0.833194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.00937	−	3.48033i	−0.313811	−	0.543537i	0.665373	−	0.746511i	$-0.268272\pi$
$41$	−2.00937	−	3.48033i	−0.313811	−	0.543537i	−0.979184	+	0.202974i	$0.934939\pi$
$42$		0			0
$43$	−3.66193	+	6.34264i	−0.558438	+	0.967244i	0.439189	+	0.898395i	$0.355266\pi$
$43$	−3.66193	+	6.34264i	−0.558438	+	0.967244i	−0.997627	+	0.0688488i	$0.978067\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.2173			1.78207			0.891036	−	0.453933i	$-0.149979\pi$
$47$	12.2173			1.78207			0.891036	+	0.453933i	$0.149979\pi$
$48$		0			0
$49$	−2.15926	−	6.65865i	−0.308465	−	0.951236i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.64928	+	8.05279i	−0.638628	+	1.10614i	0.347107	+	0.937826i	$0.387164\pi$
$53$	−4.64928	+	8.05279i	−0.638628	+	1.10614i	−0.985734	+	0.168310i	$0.946169\pi$
$54$		0			0
$55$	2.21768			0.299032
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.61521			0.861227			0.430613	−	0.902537i	$-0.358297\pi$
$59$	6.61521			0.861227			0.430613	+	0.902537i	$0.358297\pi$
$60$		0			0
$61$	−1.93850			−0.248200			−0.124100	−	0.992270i	$-0.539604\pi$
$61$	−1.93850			−0.248200			−0.124100	+	0.992270i	$0.539604\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	19.3294			2.39751
$66$		0			0
$67$	8.63088			1.05443			0.527215	−	0.849732i	$-0.323236\pi$
$67$	8.63088			1.05443			0.527215	+	0.849732i	$0.323236\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.13815			0.135074			0.0675370	−	0.997717i	$-0.478486\pi$
$71$	1.13815			0.135074			0.0675370	+	0.997717i	$0.478486\pi$
$72$		0			0
$73$	−5.33511	+	9.24068i	−0.624427	+	1.08154i	0.364224	+	0.931311i	$0.381334\pi$
$73$	−5.33511	+	9.24068i	−0.624427	+	1.08154i	−0.988651	+	0.150228i	$0.951999\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.58698	−	0.167264i	−0.180853	−	0.0190614i
$78$		0			0
$79$	4.14551			0.466406			0.233203	−	0.972428i	$-0.425079\pi$
$79$	4.14551			0.466406			0.233203	+	0.972428i	$0.425079\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.24088	−	10.8095i	0.685026	−	1.18650i	−0.288403	−	0.957509i	$-0.593124\pi$
$83$	6.24088	−	10.8095i	0.685026	−	1.18650i	0.973429	−	0.228990i	$-0.0735423\pi$
$84$		0			0
$85$	−7.81544	−	13.5367i	−0.847703	−	1.46827i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.09464	−	7.09212i	−0.434031	−	0.751764i	0.563185	−	0.826331i	$-0.309576\pi$
$89$	−4.09464	−	7.09212i	−0.434031	−	0.751764i	−0.997216	+	0.0745672i	$0.976242\pi$
$90$		0			0
$91$	−13.8321	−	1.45787i	−1.45000	−	0.152827i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	27.0931			2.77969
$96$		0			0
$97$	6.77935	−	11.7422i	0.688339	−	1.19224i	−0.284036	−	0.958814i	$-0.591673\pi$
$97$	6.77935	−	11.7422i	0.688339	−	1.19224i	0.972375	−	0.233425i	$-0.0749932\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.66975	+	13.2844i	0.763169	+	1.32185i	0.941209	+	0.337824i	$0.109691\pi$
$101$	7.66975	+	13.2844i	0.763169	+	1.32185i	−0.178041	+	0.984023i	$0.556976\pi$
$102$		0			0
$103$	2.48033	−	4.29606i	0.244394	−	0.423303i	−0.717567	−	0.696490i	$-0.754744\pi$
$103$	2.48033	−	4.29606i	0.244394	−	0.423303i	0.961961	+	0.273186i	$0.0880775\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.41399	+	5.91320i	0.330043	+	0.571651i	0.982520	−	0.186158i	$-0.0596035\pi$
$107$	3.41399	+	5.91320i	0.330043	+	0.571651i	−0.652477	+	0.757808i	$0.726270\pi$
$108$		0			0
$109$	8.90194	−	15.4186i	0.852651	−	1.47684i	−0.0261554	−	0.999658i	$-0.508326\pi$
$109$	8.90194	−	15.4186i	0.852651	−	1.47684i	0.878807	−	0.477178i	$-0.158340\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.63946	−	8.03579i	−0.436444	−	0.755943i	0.560968	−	0.827837i	$-0.310429\pi$
$113$	−4.63946	−	8.03579i	−0.436444	−	0.755943i	−0.997412	+	0.0718940i	$0.977096\pi$
$114$		0			0
$115$	−2.12851	−	3.68668i	−0.198484	−	0.343785i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.57177	+	10.2764i	0.419093	+	0.942035i
$120$		0			0
$121$	5.31811	−	9.21124i	0.483464	−	0.837385i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.9403			−1.15741
$126$		0			0
$127$	−14.9941			−1.33051			−0.665254	−	0.746617i	$-0.731677\pi$
$127$	−14.9941			−1.33051			−0.665254	+	0.746617i	$0.731677\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.4164	+	19.7737i	−0.997452	+	1.72764i	−0.436944	+	0.899489i	$0.643939\pi$
$131$	−11.4164	+	19.7737i	−0.997452	+	1.72764i	−0.560508	+	0.828149i	$0.689394\pi$
$132$		0			0
$133$	−19.3879	−	2.04344i	−1.68114	−	0.177188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.762784	−	1.32118i	−0.0651690	−	0.112876i	0.831600	−	0.555375i	$-0.187425\pi$
$137$	−0.762784	−	1.32118i	−0.0651690	−	0.112876i	−0.896769	+	0.442499i	$0.854092\pi$
$138$		0			0
$139$	−3.31277	−	5.73789i	−0.280986	−	0.486681i	0.690642	−	0.723197i	$-0.257328\pi$
$139$	−3.31277	−	5.73789i	−0.280986	−	0.486681i	−0.971628	+	0.236515i	$0.923995\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.58537	+	2.74594i	−0.132575	+	0.229627i
$144$		0			0
$145$	14.6643	+	25.3993i	1.21780	+	2.10930i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.88746	−	15.3935i	0.728089	−	1.26109i	−0.229601	−	0.973285i	$-0.573742\pi$
$149$	8.88746	−	15.3935i	0.728089	−	1.26109i	0.957690	−	0.287802i	$-0.0929246\pi$
$150$		0			0
$151$	−2.31811	−	4.01508i	−0.188645	−	0.326743i	0.756154	−	0.654394i	$-0.227076\pi$
$151$	−2.31811	−	4.01508i	−0.188645	−	0.326743i	−0.944799	+	0.327651i	$0.893743\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.79262	−	10.0331i	0.465275	−	0.805880i
$156$		0			0
$157$	3.41320			0.272403			0.136202	−	0.990681i	$-0.456511\pi$
$157$	3.41320			0.272403			0.136202	+	0.990681i	$0.456511\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.24511	+	2.79874i	0.0981281	+	0.220571i
$162$		0			0
$163$	7.55012	+	13.0772i	0.591371	+	1.02428i	0.994048	+	0.108942i	$0.0347464\pi$
$163$	7.55012	+	13.0772i	0.591371	+	1.02428i	−0.402677	+	0.915342i	$0.631920\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.85782	−	4.94988i	−0.221144	−	0.383033i	0.734011	−	0.679137i	$-0.237646\pi$
$167$	−2.85782	−	4.94988i	−0.221144	−	0.383033i	−0.955156	+	0.296104i	$0.904313\pi$
$168$		0			0
$169$	−7.31811	+	12.6753i	−0.562931	+	0.975026i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.89631			0.144174			0.0720871	−	0.997398i	$-0.477034\pi$
$173$	1.89631			0.144174			0.0720871	+	0.997398i	$0.477034\pi$
$174$		0			0
$175$	22.4160	+	2.36259i	1.69449	+	0.178595i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.29747	−	12.6396i	0.545438	−	0.944727i	−0.453141	−	0.891439i	$-0.649696\pi$
$179$	7.29747	−	12.6396i	0.545438	−	0.944727i	0.998579	−	0.0532881i	$-0.0169702\pi$
$180$		0			0
$181$	7.89857			0.587096			0.293548	−	0.955944i	$-0.405164\pi$
$181$	7.89857			0.587096			0.293548	+	0.955944i	$0.405164\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0196288			0.00144314
$186$		0			0
$187$	2.56405			0.187502
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.47340			−0.613114			−0.306557	−	0.951852i	$-0.599177\pi$
$191$	−8.47340			−0.613114			−0.306557	+	0.951852i	$0.599177\pi$
$192$		0			0
$193$	−6.96600			−0.501424			−0.250712	−	0.968062i	$-0.580665\pi$
$193$	−6.96600			−0.501424			−0.250712	+	0.968062i	$0.580665\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.2371			1.15685			0.578424	−	0.815736i	$-0.303668\pi$
$197$	16.2371			1.15685			0.578424	+	0.815736i	$0.303668\pi$
$198$		0			0
$199$	−7.35153	+	12.7332i	−0.521136	+	0.902634i	0.478562	+	0.878054i	$0.341158\pi$
$199$	−7.35153	+	12.7332i	−0.521136	+	0.902634i	−0.999698	+	0.0245800i	$0.992175\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.57812	−	19.2818i	−0.602066	−	1.35332i
$204$		0			0
$205$	−14.7764			−1.03203
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.22214	+	3.84886i	−0.153709	+	0.266231i
$210$		0			0
$211$	8.41053	+	14.5675i	0.579005	+	1.00287i	0.995594	+	0.0937708i	$0.0298921\pi$
$211$	8.41053	+	14.5675i	0.579005	+	1.00287i	−0.416589	+	0.909095i	$0.636775\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.4644	+	23.3211i	0.918266	+	1.59048i
$216$		0			0
$217$	−4.90194	+	6.74283i	−0.332766	+	0.457733i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	22.3483			1.50331
$222$		0			0
$223$	3.45799	−	5.98942i	0.231564	−	0.401081i	−0.726704	−	0.686950i	$-0.758949\pi$
$223$	3.45799	−	5.98942i	0.231564	−	0.401081i	0.958269	+	0.285869i	$0.0922823\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.49817	+	6.05900i	0.232182	+	0.402150i	0.958450	−	0.285261i	$-0.0920803\pi$
$227$	3.49817	+	6.05900i	0.232182	+	0.402150i	−0.726268	+	0.687411i	$0.758747\pi$
$228$		0			0
$229$	1.41350	−	2.44825i	0.0934066	−	0.161785i	−0.815536	−	0.578706i	$-0.803558\pi$
$229$	1.41350	−	2.44825i	0.0934066	−	0.161785i	0.908942	+	0.416922i	$0.136891\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.1679	−	19.3434i	−0.731635	−	1.26723i	−0.956184	−	0.292766i	$-0.905424\pi$
$233$	−11.1679	−	19.3434i	−0.731635	−	1.26723i	0.224550	−	0.974463i	$-0.427909\pi$
$234$		0			0
$235$	22.4606	−	38.9030i	1.46517	−	2.53775i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.954829	+	1.65381i	0.0617628	+	0.106976i	0.895253	−	0.445557i	$-0.146994\pi$
$239$	0.954829	+	1.65381i	0.0617628	+	0.106976i	−0.833491	+	0.552534i	$0.813661\pi$
$240$		0			0
$241$	9.84352	+	17.0495i	0.634077	+	1.09825i	0.986710	+	0.162492i	$0.0519530\pi$
$241$	9.84352	+	17.0495i	0.634077	+	1.09825i	−0.352633	+	0.935762i	$0.614714\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−25.1725	−	5.36586i	−1.60821	−	0.342812i
$246$		0			0
$247$	−19.3682	+	33.5468i	−1.23237	+	2.13453i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.2990			−0.776306			−0.388153	−	0.921595i	$-0.626887\pi$
$251$	−12.2990			−0.776306			−0.388153	+	0.921595i	$0.626887\pi$
$252$		0			0
$253$	0.698309			0.0439023
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.71210	+	9.89365i	−0.356311	+	0.617149i	−0.987341	−	0.158609i	$-0.949299\pi$
$257$	−5.71210	+	9.89365i	−0.356311	+	0.617149i	0.631030	+	0.775758i	$0.282632\pi$
$258$		0			0
$259$	−0.0140464	−	0.00148046i	−0.000872802	−	9.19912e-5i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.65544	+	16.7237i	0.595380	+	1.03123i	0.993493	+	0.113892i	$0.0363317\pi$
$263$	9.65544	+	16.7237i	0.595380	+	1.03123i	−0.398114	+	0.917336i	$0.630335\pi$
$264$		0			0
$265$	17.0948	+	29.6091i	1.05012	+	1.81887i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.00745	+	6.94110i	−0.244338	+	0.423206i	−0.961945	−	0.273242i	$-0.911904\pi$
$269$	−4.00745	+	6.94110i	−0.244338	+	0.423206i	0.717607	+	0.696448i	$0.245237\pi$
$270$		0			0
$271$	2.96658	+	5.13827i	0.180207	+	0.312128i	0.941951	−	0.335750i	$-0.108990\pi$
$271$	2.96658	+	5.13827i	0.180207	+	0.312128i	−0.761744	+	0.647878i	$0.775657\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.56920	−	4.44999i	0.154929	−	0.268344i
$276$		0			0
$277$	6.02768	+	10.4402i	0.362168	+	0.627293i	0.988317	−	0.152410i	$-0.0487034\pi$
$277$	6.02768	+	10.4402i	0.362168	+	0.627293i	−0.626149	+	0.779703i	$0.715370\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.73700	+	16.8650i	−0.580861	+	1.00608i	0.414517	+	0.910042i	$0.363951\pi$
$281$	−9.73700	+	16.8650i	−0.580861	+	1.00608i	−0.995378	+	0.0960386i	$0.969383\pi$
$282$		0			0
$283$	−28.7036			−1.70625			−0.853127	−	0.521704i	$-0.825297\pi$
$283$	−28.7036			−1.70625			−0.853127	+	0.521704i	$0.825297\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.5740	+	1.11448i	0.624165	+	0.0657854i
$288$		0			0
$289$	−0.536086	−	0.928529i	−0.0315345	−	0.0546193i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.3503	−	19.6593i	−0.663090	−	1.14851i	−0.979799	−	0.199983i	$-0.935911\pi$
$293$	−11.3503	−	19.6593i	−0.663090	−	1.14851i	0.316709	−	0.948523i	$-0.397422\pi$
$294$		0			0
$295$	12.1616	−	21.0646i	0.708077	−	1.22643i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.08648			0.351990
$300$		0			0
$301$	−7.87624	−	17.7041i	−0.453979	−	1.02045i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.56381	+	6.17271i	−0.204063	+	0.353448i
$306$		0			0
$307$	−27.9486			−1.59511			−0.797555	−	0.603246i	$-0.793874\pi$
$307$	−27.9486			−1.59511			−0.797555	+	0.603246i	$0.793874\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.2982			−0.867479			−0.433739	−	0.901038i	$-0.642806\pi$
$311$	−15.2982			−0.867479			−0.433739	+	0.901038i	$0.642806\pi$
$312$		0			0
$313$	3.34103			0.188846			0.0944230	−	0.995532i	$-0.469899\pi$
$313$	3.34103			0.188846			0.0944230	+	0.995532i	$0.469899\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.01444			−0.506301			−0.253151	−	0.967427i	$-0.581467\pi$
$317$	−9.01444			−0.506301			−0.253151	+	0.967427i	$0.581467\pi$
$318$		0			0
$319$	−4.81098			−0.269363
$320$		0			0
$321$		0			0
$322$		0			0
$323$	31.3246			1.74295
$324$		0			0
$325$	22.3932	−	38.7862i	1.24215	−	2.15147i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−19.0071	+	26.1450i	−1.04789	+	1.44142i
$330$		0			0
$331$	18.2952			1.00559			0.502797	−	0.864404i	$-0.332304\pi$
$331$	18.2952			1.00559			0.502797	+	0.864404i	$0.332304\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	15.8673	−	27.4830i	0.866924	−	1.50156i
$336$		0			0
$337$	−0.868823	−	1.50485i	−0.0473278	−	0.0819741i	0.841391	−	0.540427i	$-0.181737\pi$
$337$	−0.868823	−	1.50485i	−0.0473278	−	0.0819741i	−0.888719	+	0.458453i	$0.848404\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.950206	+	1.64580i	0.0514565	+	0.0891253i
$342$		0			0
$343$	17.6088	+	5.73840i	0.950787	+	0.309845i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.09272			−0.0586600			−0.0293300	−	0.999570i	$-0.509337\pi$
$347$	−1.09272			−0.0586600			−0.0293300	+	0.999570i	$0.509337\pi$
$348$		0			0
$349$	−4.70096	+	8.14231i	−0.251637	+	0.435848i	−0.963977	−	0.265987i	$-0.914302\pi$
$349$	−4.70096	+	8.14231i	−0.251637	+	0.435848i	0.712340	+	0.701835i	$0.247636\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.64549	−	16.7065i	−0.513378	−	0.889196i	−0.999880	−	0.0155167i	$-0.995061\pi$
$353$	−9.64549	−	16.7065i	−0.513378	−	0.889196i	0.486502	−	0.873680i	$-0.338273\pi$
$354$		0			0
$355$	2.09242	−	3.62418i	0.111054	−	0.192352i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.94976	−	5.10914i	−0.155682	−	0.269650i	0.777625	−	0.628729i	$-0.216424\pi$
$359$	−2.94976	−	5.10914i	−0.155682	−	0.269650i	−0.933307	+	0.359079i	$0.883091\pi$
$360$		0			0
$361$	−17.6476	+	30.5665i	−0.928820	+	1.60876i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	19.6165	+	33.9768i	1.02677	+	1.77843i
$366$		0			0
$367$	−5.48300	−	9.49684i	−0.286210	−	0.495731i	0.686692	−	0.726949i	$-0.259062\pi$
$367$	−5.48300	−	9.49684i	−0.286210	−	0.495731i	−0.972902	+	0.231218i	$0.925729\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.99988	−	22.4776i	−0.519168	−	1.16698i
$372$		0			0
$373$	15.9691	−	27.6592i	0.826847	−	1.43214i	−0.0736533	−	0.997284i	$-0.523466\pi$
$373$	15.9691	−	27.6592i	0.826847	−	1.43214i	0.900500	−	0.434856i	$-0.143201\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−41.9326			−2.15964
$378$		0			0
$379$	−14.4354			−0.741495			−0.370747	−	0.928734i	$-0.620898\pi$
$379$	−14.4354			−0.741495			−0.370747	+	0.928734i	$0.620898\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.86006	+	15.3461i	−0.452728	+	0.784148i	−0.998554	−	0.0537502i	$-0.982883\pi$
$383$	−8.86006	+	15.3461i	−0.452728	+	0.784148i	0.545826	+	0.837898i	$0.316216\pi$
$384$		0			0
$385$	−3.45016	+	4.74585i	−0.175837	+	0.241871i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.48751	−	16.4329i	−0.481036	−	0.833179i	0.518727	−	0.854940i	$-0.326406\pi$
$389$	−9.48751	−	16.4329i	−0.481036	−	0.833179i	−0.999763	+	0.0217610i	$0.993073\pi$
$390$		0			0
$391$	−2.46095	−	4.26249i	−0.124455	−	0.215563i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.62124	−	13.2004i	0.383466	−	0.664183i
$396$		0			0
$397$	−10.5889	−	18.3405i	−0.531440	−	0.920482i	−0.999327	−	0.0366930i	$-0.988318\pi$
$397$	−10.5889	−	18.3405i	−0.531440	−	0.920482i	0.467886	−	0.883789i	$-0.345016\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.39038	+	12.8005i	−0.369058	+	0.639227i	−0.989419	−	0.145090i	$-0.953653\pi$
$401$	−7.39038	+	12.8005i	−0.369058	+	0.639227i	0.620361	+	0.784317i	$0.286986\pi$
$402$		0			0
$403$	8.28202	+	14.3449i	0.412557	+	0.714570i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.00160993	+	0.00278847i	−7.98011e−5	+	0.000138219i
$408$		0			0
$409$	−3.73150			−0.184511			−0.0922554	−	0.995735i	$-0.529408\pi$
$409$	−3.73150			−0.184511			−0.0922554	+	0.995735i	$0.529408\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.2916	+	14.1566i	−0.506418	+	0.696600i
$414$		0			0
$415$	−22.9469	−	39.7452i	−1.12642	−	1.95102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.1678	−	24.5393i	−0.692142	−	1.19883i	−0.971135	−	0.238532i	$-0.923334\pi$
$419$	−14.1678	−	24.5393i	−0.692142	−	1.19883i	0.278993	−	0.960293i	$-0.409999\pi$
$420$		0			0
$421$	−8.09776	+	14.0257i	−0.394661	+	0.683572i	−0.993058	−	0.117627i	$-0.962471\pi$
$421$	−8.09776	+	14.0257i	−0.394661	+	0.683572i	0.598397	+	0.801200i	$0.295805\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−36.2170			−1.75678
$426$		0			0
$427$	3.01584	−	4.14841i	0.145947	−	0.200756i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.5528	−	23.4741i	0.652815	−	1.13071i	−0.329622	−	0.944113i	$-0.606921\pi$
$431$	13.5528	−	23.4741i	0.652815	−	1.13071i	0.982437	−	0.186595i	$-0.0597453\pi$
$432$		0			0
$433$	−11.5028			−0.552789			−0.276394	−	0.961044i	$-0.589140\pi$
$433$	−11.5028			−0.552789			−0.276394	+	0.961044i	$0.589140\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.53115			0.408100
$438$		0			0
$439$	−2.86714			−0.136841			−0.0684205	−	0.997657i	$-0.521796\pi$
$439$	−2.86714			−0.136841			−0.0684205	+	0.997657i	$0.521796\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.84301			−0.420144			−0.210072	−	0.977686i	$-0.567370\pi$
$443$	−8.84301			−0.420144			−0.210072	+	0.977686i	$0.567370\pi$
$444$		0			0
$445$	−30.1109			−1.42739
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−40.5033			−1.91147			−0.955735	−	0.294229i	$-0.904937\pi$
$449$	−40.5033			−1.91147			−0.955735	+	0.294229i	$0.904937\pi$
$450$		0			0
$451$	1.21194	−	2.09914i	0.0570680	−	0.0988446i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−30.0717	+	41.3650i	−1.40979	+	1.93922i
$456$		0			0
$457$	38.8098			1.81545			0.907723	−	0.419571i	$-0.137819\pi$
$457$	38.8098			1.81545			0.907723	+	0.419571i	$0.137819\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.1328	+	27.9428i	−0.751378	+	1.30142i	0.195777	+	0.980648i	$0.437277\pi$
$461$	−16.1328	+	27.9428i	−0.751378	+	1.30142i	−0.947155	+	0.320776i	$0.896056\pi$
$462$		0			0
$463$	−16.7430	−	28.9997i	−0.778112	−	1.34773i	−0.933029	−	0.359802i	$-0.882844\pi$
$463$	−16.7430	−	28.9997i	−0.778112	−	1.34773i	0.154917	−	0.987927i	$-0.450489\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.04280	−	8.73438i	−0.233353	−	0.404179i	0.725440	−	0.688286i	$-0.241636\pi$
$467$	−5.04280	−	8.73438i	−0.233353	−	0.404179i	−0.958793	+	0.284107i	$0.908303\pi$
$468$		0			0
$469$	−13.4275	+	18.4701i	−0.620026	+	0.852872i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.41733			−0.203109
$474$		0			0
$475$	31.3876	−	54.3649i	1.44016	−	2.49443i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.29759	−	7.44365i	−0.196362	−	0.340109i	0.750984	−	0.660320i	$-0.229579\pi$
$479$	−4.29759	−	7.44365i	−0.196362	−	0.340109i	−0.947346	+	0.320211i	$0.896246\pi$
$480$		0			0
$481$	−0.0140322	+	0.0243044i	−0.000639812	+	0.00110819i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.9268	−	43.1745i	−1.13187	−	1.96045i
$486$		0			0
$487$	−0.298843	+	0.517612i	−0.0135419	+	0.0234552i	−0.872717	−	0.488227i	$-0.837644\pi$
$487$	−0.298843	+	0.517612i	−0.0135419	+	0.0234552i	0.859175	+	0.511682i	$0.170977\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.1521	+	29.7084i	0.774066	+	1.34072i	0.935318	+	0.353808i	$0.115113\pi$
$491$	17.1521	+	29.7084i	0.774066	+	1.34072i	−0.161253	+	0.986913i	$0.551553\pi$
$492$		0			0
$493$	16.9546	+	29.3663i	0.763598	+	1.32259i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.77069	+	2.43566i	−0.0794262	+	0.109254i
$498$		0			0
$499$	−15.0247	+	26.0236i	−0.672598	+	1.16497i	0.304566	+	0.952491i	$0.401488\pi$
$499$	−15.0247	+	26.0236i	−0.672598	+	1.16497i	−0.977165	+	0.212483i	$0.931845\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.5650			0.827773			0.413887	−	0.910328i	$-0.364171\pi$
$503$	18.5650			0.827773			0.413887	+	0.910328i	$0.364171\pi$
$504$		0			0
$505$	56.4013			2.50983
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.50908	−	6.07790i	0.155537	−	0.269398i	−0.777717	−	0.628614i	$-0.783623\pi$
$509$	3.50908	−	6.07790i	0.155537	−	0.269398i	0.933254	+	0.359216i	$0.116956\pi$
$510$		0			0
$511$	−11.4750	−	25.7934i	−0.507624	−	1.14103i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.11986	−	15.7961i	−0.401869	−	0.696057i
$516$		0			0
$517$	3.68438	+	6.38154i	0.162039	+	0.280660i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.0742	−	26.1092i	0.660411	−	1.14387i	−0.320096	−	0.947385i	$-0.603715\pi$
$521$	15.0742	−	26.1092i	0.660411	−	1.14387i	0.980508	−	0.196481i	$-0.0629514\pi$
$522$		0			0
$523$	−14.1726	−	24.5476i	−0.619724	−	1.07339i	−0.989536	−	0.144287i	$-0.953911\pi$
$523$	−14.1726	−	24.5476i	−0.619724	−	1.07339i	0.369812	−	0.929107i	$-0.379422\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.69734	−	11.6001i	0.291741	−	0.505310i
$528$		0			0
$529$	10.8298	+	18.7577i	0.470860	+	0.815553i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.5633	−	18.2962i	0.457547	−	0.792495i
$534$		0			0
$535$	25.1056			1.08541
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.82689	−	3.13592i	0.121763	−	0.135074i
$540$		0			0
$541$	−14.5245	−	25.1572i	−0.624458	−	1.08159i	−0.988645	−	0.150268i	$-0.951986\pi$
$541$	−14.5245	−	25.1572i	−0.624458	−	1.08159i	0.364187	−	0.931326i	$-0.381347\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−32.7313	−	56.6922i	−1.40205	−	2.42843i
$546$		0			0
$547$	−8.68455	+	15.0421i	−0.371324	+	0.643153i	−0.989770	−	0.142675i	$-0.954430\pi$
$547$	−8.68455	+	15.0421i	−0.371324	+	0.643153i	0.618445	+	0.785828i	$0.287763\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−58.7751			−2.50390
$552$		0			0
$553$	−6.44939	+	8.87141i	−0.274256	+	0.377251i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.5927	−	33.9355i	0.830169	−	1.43789i	−0.0677355	−	0.997703i	$-0.521577\pi$
$557$	19.5927	−	33.9355i	0.830169	−	1.43789i	0.897904	−	0.440191i	$-0.145089\pi$
$558$		0			0
$559$	−38.5016			−1.62844
$560$		0			0
$561$		0			0
$562$		0			0
$563$	38.4078			1.61870			0.809349	−	0.587328i	$-0.199820\pi$
$563$	38.4078			1.61870			0.809349	+	0.587328i	$0.199820\pi$
$564$		0			0
$565$	−34.1174			−1.43533
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.08064			0.380680			0.190340	−	0.981718i	$-0.439041\pi$
$569$	9.08064			0.380680			0.190340	+	0.981718i	$0.439041\pi$
$570$		0			0
$571$	−37.0548			−1.55069			−0.775347	−	0.631536i	$-0.782425\pi$
$571$	−37.0548			−1.55069			−0.775347	+	0.631536i	$0.782425\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.86358			−0.411340
$576$		0			0
$577$	1.04241	−	1.80550i	0.0433960	−	0.0751641i	−0.843512	−	0.537111i	$-0.819516\pi$
$577$	1.04241	−	1.80550i	0.0433960	−	0.0751641i	0.886908	+	0.461947i	$0.152849\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	13.4232	+	30.1725i	0.556887	+	1.25177i
$582$		0			0
$583$	−5.60836			−0.232275
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.75919	−	8.24316i	0.196433	−	0.340232i	−0.750936	−	0.660374i	$-0.770398\pi$
$587$	4.75919	−	8.24316i	0.196433	−	0.340232i	0.947369	+	0.320143i	$0.103731\pi$
$588$		0			0
$589$	11.6085	+	20.1066i	0.478322	+	0.828477i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.63267	+	13.2202i	0.313436	+	0.542887i	0.979104	−	0.203361i	$-0.0651865\pi$
$593$	7.63267	+	13.2202i	0.313436	+	0.542887i	−0.665668	+	0.746248i	$0.731853\pi$
$594$		0			0
$595$	41.1276	+	4.33475i	1.68607	+	0.177707i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.1195			−0.822059			−0.411030	−	0.911622i	$-0.634831\pi$
$599$	−20.1195			−0.822059			−0.411030	+	0.911622i	$0.634831\pi$
$600$		0			0
$601$	−10.1529	+	17.5854i	−0.414146	+	0.717322i	−0.995338	−	0.0964440i	$-0.969253\pi$
$601$	−10.1529	+	17.5854i	−0.414146	+	0.717322i	0.581192	+	0.813766i	$0.302586\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.5540	−	33.8685i	−0.794983	−	1.37695i
$606$		0			0
$607$	1.03649	−	1.79525i	0.0420698	−	0.0728670i	−0.844224	−	0.535991i	$-0.819938\pi$
$607$	1.03649	−	1.79525i	0.0420698	−	0.0728670i	0.886294	+	0.463124i	$0.153271\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	32.1132	+	55.6217i	1.29916	+	2.25021i
$612$		0			0
$613$	−1.10053	+	1.90618i	−0.0444502	+	0.0769900i	−0.887395	−	0.461011i	$-0.847487\pi$
$613$	−1.10053	+	1.90618i	−0.0444502	+	0.0769900i	0.842944	+	0.538001i	$0.180820\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.1904	−	36.7029i	−0.853095	−	1.47760i	−0.878401	−	0.477924i	$-0.841389\pi$
$617$	−21.1904	−	36.7029i	−0.853095	−	1.47760i	0.0253061	−	0.999680i	$-0.491944\pi$
$618$		0			0
$619$	−6.93536	−	12.0124i	−0.278756	−	0.482819i	0.692320	−	0.721590i	$-0.256589\pi$
$619$	−6.93536	−	12.0124i	−0.278756	−	0.482819i	−0.971076	+	0.238772i	$0.923255\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	21.5474	+	2.27105i	0.863280	+	0.0909876i
$624$		0			0
$625$	−2.49141	+	4.31525i	−0.0996565	+	0.172610i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.0226945			0.000904889
$630$		0			0
$631$	45.1845			1.79876			0.899382	−	0.437163i	$-0.144017\pi$
$631$	45.1845			1.79876			0.899382	+	0.437163i	$0.144017\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−27.5656	+	47.7450i	−1.09391	+	1.89470i
$636$		0			0
$637$	24.6393	−	27.3328i	0.976244	−	1.08296i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.2564	+	22.9608i	0.523597	+	0.906896i	0.999623	+	0.0274647i	$0.00874340\pi$
$641$	13.2564	+	22.9608i	0.523597	+	0.906896i	−0.476026	+	0.879431i	$0.657923\pi$
$642$		0			0
$643$	24.3184	+	42.1207i	0.959024	+	1.66108i	0.724879	+	0.688876i	$0.241896\pi$
$643$	24.3184	+	42.1207i	0.959024	+	1.66108i	0.234145	+	0.972202i	$0.424771\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.7224	+	18.5717i	−0.421540	+	0.730128i	−0.996090	−	0.0883409i	$-0.971844\pi$
$647$	−10.7224	+	18.5717i	−0.421540	+	0.730128i	0.574551	+	0.818469i	$0.305177\pi$
$648$		0			0
$649$	1.99496	+	3.45537i	0.0783090	+	0.135635i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.74496	−	3.02235i	0.0682854	−	0.118274i	−0.829861	−	0.557970i	$-0.811580\pi$
$653$	1.74496	−	3.02235i	0.0682854	−	0.118274i	0.898147	+	0.439696i	$0.144914\pi$
$654$		0			0
$655$	41.9765	+	72.7054i	1.64016	+	2.84083i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.2754	+	31.6539i	−0.711908	+	1.23306i	0.252232	+	0.967667i	$0.418835\pi$
$659$	−18.2754	+	31.6539i	−0.711908	+	1.23306i	−0.964140	+	0.265394i	$0.914498\pi$
$660$		0			0
$661$	−5.57496			−0.216841			−0.108420	−	0.994105i	$-0.534579\pi$
$661$	−5.57496			−0.216841			−0.108420	+	0.994105i	$0.534579\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−42.1502	+	57.9794i	−1.63452	+	2.24835i
$666$		0			0
$667$	4.61753	+	7.99780i	0.178792	+	0.309676i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.584598	−	1.01255i	−0.0225682	−	0.0390892i
$672$		0			0
$673$	1.25661	−	2.17652i	0.0484389	−	0.0838986i	−0.840789	−	0.541362i	$-0.817909\pi$
$673$	1.25661	−	2.17652i	0.0484389	−	0.0838986i	0.889228	+	0.457464i	$0.151242\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−31.7213			−1.21915			−0.609574	−	0.792729i	$-0.708659\pi$
$677$	−31.7213			−1.21915			−0.609574	+	0.792729i	$0.708659\pi$
$678$		0			0
$679$	14.5813	+	32.7758i	0.559581	+	1.25782i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.4275	−	37.1136i	0.819902	−	1.42011i	−0.0858521	−	0.996308i	$-0.527361\pi$
$683$	21.4275	−	37.1136i	0.819902	−	1.42011i	0.905754	−	0.423804i	$-0.139305\pi$
$684$		0			0
$685$	−5.60932			−0.214321
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−48.8827			−1.86228
$690$		0			0
$691$	−14.7637			−0.561639			−0.280820	−	0.959761i	$-0.590606\pi$
$691$	−14.7637			−0.561639			−0.280820	+	0.959761i	$0.590606\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.3613			−0.924075
$696$		0			0
$697$	−17.0842			−0.647111
$698$		0			0
$699$		0			0
$700$		0			0
$701$	19.8352			0.749167			0.374583	−	0.927193i	$-0.377786\pi$
$701$	19.8352			0.749167			0.374583	+	0.927193i	$0.377786\pi$
$702$		0			0
$703$	−0.0196683	+	0.0340664i	−0.000741802	+	0.00128484i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−40.3609	−	4.25394i	−1.51793	−	0.159986i
$708$		0			0
$709$	10.2058			0.383288			0.191644	−	0.981464i	$-0.438618\pi$
$709$	10.2058			0.383288			0.191644	+	0.981464i	$0.438618\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.82400	−	3.15926i	0.0683092	−	0.118315i
$714$		0			0
$715$	5.82919	+	10.0965i	0.217999	+	0.377586i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.2769	+	28.1924i	0.607025	+	1.05140i	0.991728	+	0.128358i	$0.0409706\pi$
$719$	16.2769	+	28.1924i	0.607025	+	1.05140i	−0.384703	+	0.923040i	$0.625696\pi$
$720$		0			0
$721$	5.33481	+	11.9915i	0.198679	+	0.446588i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	67.9549			2.52378
$726$		0			0
$727$	−7.65095	+	13.2518i	−0.283758	+	0.491483i	−0.972307	−	0.233706i	$-0.924915\pi$
$727$	−7.65095	+	13.2518i	−0.283758	+	0.491483i	0.688549	+	0.725190i	$0.258248\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.5673	+	26.9634i	0.575779	+	0.997279i
$732$		0			0
$733$	4.34677	−	7.52882i	0.160552	−	0.278083i	−0.774515	−	0.632555i	$-0.782006\pi$
$733$	4.34677	−	7.52882i	0.160552	−	0.278083i	0.935067	+	0.354472i	$0.115339\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.60283	+	4.50823i	0.0958764	+	0.166063i
$738$		0			0
$739$	−6.61922	+	11.4648i	−0.243492	+	0.421740i	−0.961707	−	0.274081i	$-0.911626\pi$
$739$	−6.61922	+	11.4648i	−0.243492	+	0.421740i	0.718215	+	0.695822i	$0.244960\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.7693	+	18.6530i	0.395089	+	0.684314i	0.993112	−	0.117165i	$-0.0373805\pi$
$743$	10.7693	+	18.6530i	0.395089	+	0.684314i	−0.598024	+	0.801478i	$0.704047\pi$
$744$		0			0
$745$	−32.6780	−	56.6000i	−1.19723	−	2.07366i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−17.9656	−	1.89353i	−0.656449	−	0.0691881i
$750$		0			0
$751$	−19.8241	+	34.3364i	−0.723393	+	1.25295i	0.236239	+	0.971695i	$0.424085\pi$
$751$	−19.8241	+	34.3364i	−0.723393	+	1.25295i	−0.959632	+	0.281258i	$0.909248\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.0468			−0.620395
$756$		0			0
$757$	13.0719			0.475108			0.237554	−	0.971374i	$-0.423654\pi$
$757$	13.0719			0.475108			0.237554	+	0.971374i	$0.423654\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.17145	+	15.8854i	−0.332465	+	0.575846i	−0.982995	−	0.183635i	$-0.941214\pi$
$761$	−9.17145	+	15.8854i	−0.332465	+	0.575846i	0.650530	+	0.759481i	$0.274547\pi$
$762$		0			0
$763$	19.1467	+	43.0378i	0.693157	+	1.55807i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17.3881	+	30.1171i	0.627849	+	1.08747i
$768$		0			0
$769$	7.46351	+	12.9272i	0.269141	+	0.466166i	0.968640	−	0.248467i	$-0.0799269\pi$
$769$	7.46351	+	12.9272i	0.269141	+	0.466166i	−0.699499	+	0.714633i	$0.746594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	14.7818	−	25.6029i	0.531666	−	0.920873i	−0.467651	−	0.883913i	$-0.654900\pi$
$773$	14.7818	−	25.6029i	0.531666	−	0.920873i	0.999317	−	0.0369592i	$-0.0117672\pi$
$774$		0			0
$775$	−13.4216	−	23.2469i	−0.482118	−	0.835054i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.8061	−	25.6449i	0.530483	−	0.918824i
$780$		0			0
$781$	0.343235	+	0.594500i	0.0122819	+	0.0212729i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.27495	−	10.8685i	0.223962	−	0.387914i
$786$		0			0
$787$	−9.32859			−0.332528			−0.166264	−	0.986081i	$-0.553170\pi$
$787$	−9.32859			−0.332528			−0.166264	+	0.986081i	$0.553170\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.4145	+	2.57323i	0.868080	+	0.0914935i
$792$		0			0
$793$	−5.09537	−	8.82545i	−0.180942	−	0.313401i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.9334	−	20.6692i	−0.422701	−	0.732140i	0.573502	−	0.819204i	$-0.305585\pi$
$797$	−11.9334	−	20.6692i	−0.422701	−	0.732140i	−0.996203	+	0.0870647i	$0.972251\pi$
$798$		0			0
$799$	25.9686	−	44.9790i	0.918705	−	1.59124i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.43567			−0.227110
$804$		0			0
$805$	11.2010	+	1.18055i	0.394782	+	0.0416091i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17.9594	−	31.1066i	0.631418	−	1.09365i	−0.355844	−	0.934545i	$-0.615806\pi$
$809$	17.9594	−	31.1066i	0.631418	−	1.09365i	0.987262	−	0.159103i	$-0.0508602\pi$
$810$		0			0
$811$	−36.5589			−1.28376			−0.641879	−	0.766806i	$-0.721845\pi$
$811$	−36.5589			−1.28376			−0.641879	+	0.766806i	$0.721845\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	55.5216			1.94484
$816$		0			0
$817$	−53.9660			−1.88803
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.9516			0.626517			0.313258	−	0.949668i	$-0.398579\pi$
$821$	17.9516			0.626517			0.313258	+	0.949668i	$0.398579\pi$
$822$		0			0
$823$	1.93871			0.0675793			0.0337897	−	0.999429i	$-0.489242\pi$
$823$	1.93871			0.0675793			0.0337897	+	0.999429i	$0.489242\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.4779			−1.19891			−0.599457	−	0.800407i	$-0.704617\pi$
$827$	−34.4779			−1.19891			−0.599457	+	0.800407i	$0.704617\pi$
$828$		0			0
$829$	15.6165	−	27.0487i	0.542385	−	0.939439i	−0.456381	−	0.889784i	$-0.650855\pi$
$829$	15.6165	−	27.0487i	0.542385	−	0.939439i	0.998766	−	0.0496544i	$-0.0158120\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−29.1041	−	6.20392i	−1.00840	−	0.214953i
$834$		0			0
$835$	−21.0156			−0.727276
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.2433	−	48.9187i	0.975065	−	1.68886i	0.295346	−	0.955390i	$-0.404565\pi$
$839$	28.2433	−	48.9187i	0.975065	−	1.68886i	0.679719	−	0.733472i	$-0.262102\pi$
$840$		0			0
$841$	−17.3124	−	29.9859i	−0.596978	−	1.03400i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.9077	+	46.6056i	0.925654	+	1.60328i
$846$		0			0
$847$	11.4384	+	25.7112i	0.393029	+	0.883448i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.00618077			0.000211874
$852$		0			0
$853$	5.83541	−	10.1072i	0.199800	−	0.346065i	−0.748663	−	0.662951i	$-0.769304\pi$
$853$	5.83541	−	10.1072i	0.199800	−	0.346065i	0.948464	+	0.316886i	$0.102637\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.98166	−	10.3605i	−0.204329	−	0.353909i	0.745589	−	0.666406i	$-0.232168\pi$
$857$	−5.98166	−	10.3605i	−0.204329	−	0.353909i	−0.949919	+	0.312497i	$0.898835\pi$
$858$		0			0
$859$	28.7004	−	49.7105i	0.979244	−	1.69610i	0.314094	−	0.949392i	$-0.398299\pi$
$859$	28.7004	−	49.7105i	0.979244	−	1.69610i	0.665151	−	0.746709i	$-0.268367\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.1871	−	43.6253i	−0.857379	−	1.48502i	−0.874420	−	0.485169i	$-0.838758\pi$
$863$	−25.1871	−	43.6253i	−0.857379	−	1.48502i	0.0170411	−	0.999855i	$-0.494575\pi$
$864$		0			0
$865$	3.48625	−	6.03836i	0.118536	−	0.205311i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.25017	+	2.16535i	0.0424090	+	0.0734546i
$870$		0			0
$871$	22.6863	+	39.2939i	0.768697	+	1.33142i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.1319	−	27.6923i	0.680582	−	0.936169i
$876$		0			0
$877$	4.22569	−	7.31911i	0.142691	−	0.247149i	−0.785818	−	0.618458i	$-0.787758\pi$
$877$	4.22569	−	7.31911i	0.142691	−	0.247149i	0.928509	+	0.371309i	$0.121091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.99396			−0.134560			−0.0672800	−	0.997734i	$-0.521432\pi$
$881$	−3.99396			−0.134560			−0.0672800	+	0.997734i	$0.521432\pi$
$882$		0			0
$883$	−6.72637			−0.226360			−0.113180	−	0.993574i	$-0.536104\pi$
$883$	−6.72637			−0.226360			−0.113180	+	0.993574i	$0.536104\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.1725	−	40.1359i	0.778055	−	1.34763i	−0.155006	−	0.987914i	$-0.549540\pi$
$887$	23.1725	−	40.1359i	0.778055	−	1.34763i	0.933061	−	0.359718i	$-0.117127\pi$
$888$		0			0
$889$	23.3271	−	32.0874i	0.782365	−	1.07618i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	45.0116	+	77.9624i	1.50626	+	2.60891i
$894$		0			0
$895$	−26.8318	−	46.4741i	−0.896890	−	1.55346i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.5664	+	21.7656i	−0.419112	+	0.725924i
$900$		0			0
$901$	19.7647	+	34.2335i	0.658458	+	1.14048i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.5210	−	25.1511i	0.482695	−	0.836052i
$906$		0			0
$907$	−2.13622	−	3.70004i	−0.0709320	−	0.122858i	0.828378	−	0.560169i	$-0.189264\pi$
$907$	−2.13622	−	3.70004i	−0.0709320	−	0.122858i	−0.899310	+	0.437312i	$0.855931\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.26635	−	14.3177i	0.273876	−	0.474368i	−0.695975	−	0.718066i	$-0.745027\pi$
$911$	8.26635	−	14.3177i	0.273876	−	0.474368i	0.969851	+	0.243699i	$0.0783607\pi$
$912$		0			0
$913$	7.52829			0.249150
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.5548	−	55.1941i	−0.810872	−	1.82267i
$918$		0			0
$919$	2.48862	+	4.31042i	0.0820921	+	0.142188i	0.904148	−	0.427219i	$-0.140507\pi$
$919$	2.48862	+	4.31042i	0.0820921	+	0.142188i	−0.822056	+	0.569406i	$0.807173\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.99165	+	5.18168i	0.0984713	+	0.170557i
$924$		0			0
$925$	0.0227401	−	0.0393870i	0.000747691	−	0.00129504i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	35.9629			1.17990			0.589952	−	0.807438i	$-0.299147\pi$
$929$	35.9629			1.17990			0.589952	+	0.807438i	$0.299147\pi$
$930$		0			0
$931$	34.5358	−	38.3111i	1.13186	−	1.25560i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.71383	−	8.16459i	0.154159	−	0.267011i
$936$		0			0
$937$	−24.5419			−0.801748			−0.400874	−	0.916133i	$-0.631294\pi$
$937$	−24.5419			−0.801748			−0.400874	+	0.916133i	$0.631294\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.32907			0.206322			0.103161	−	0.994665i	$-0.467104\pi$
$941$	6.32907			0.206322			0.103161	+	0.994665i	$0.467104\pi$
$942$		0			0
$943$	−4.65283			−0.151517
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.2086			0.884161			0.442080	−	0.896975i	$-0.354241\pi$
$947$	27.2086			0.884161			0.442080	+	0.896975i	$0.354241\pi$
$948$		0			0
$949$	−56.0935			−1.82087
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.9963			−0.809711			−0.404855	−	0.914381i	$-0.632678\pi$
$953$	−24.9963			−0.809711			−0.404855	+	0.914381i	$0.632678\pi$
$954$		0			0
$955$	−15.5778	+	26.9815i	−0.504086	+	0.873102i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.01404	+	0.423070i	0.129620	+	0.0136616i
$960$		0			0
$961$	−21.0722			−0.679747
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.8065	+	22.1816i	−0.412257	+	0.714050i
$966$		0			0
$967$	6.11169	+	10.5858i	0.196539	+	0.340415i	0.947404	−	0.320041i	$-0.103697\pi$
$967$	6.11169	+	10.5858i	0.196539	+	0.340415i	−0.750865	+	0.660455i	$0.770363\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.137437	−	0.238048i	−0.00441057	−	0.00763933i	0.863812	−	0.503815i	$-0.168071\pi$
$971$	−0.137437	−	0.238048i	−0.00441057	−	0.00763933i	−0.868222	+	0.496175i	$0.834737\pi$
$972$		0			0
$973$	17.4330	+	1.83739i	0.558875	+	0.0589041i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.0169			0.992317			0.496159	−	0.868232i	$-0.334743\pi$
$977$	31.0169			0.992317			0.496159	+	0.868232i	$0.334743\pi$
$978$		0			0
$979$	2.46965	−	4.27757i	0.0789305	−	0.136712i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.0069	−	31.1889i	−0.574332	−	0.994772i	−0.996114	−	0.0880747i	$-0.971929\pi$
$983$	−18.0069	−	31.1889i	−0.574332	−	0.994772i	0.421782	−	0.906697i	$-0.361405\pi$
$984$		0			0
$985$	29.8509	−	51.7033i	0.951130	−	1.64741i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.23971	+	7.34340i	0.134815	+	0.233507i
$990$		0			0
$991$	−2.19313	+	3.79862i	−0.0696672	+	0.120667i	−0.898755	−	0.438452i	$-0.855527\pi$
$991$	−2.19313	+	3.79862i	−0.0696672	+	0.120667i	0.829088	+	0.559119i	$0.188860\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	27.0306	+	46.8184i	0.856928	+	1.48424i
$996$		0			0
$997$	12.3882	+	21.4570i	0.392338	+	0.679549i	0.992757	−	0.120136i	$-0.0383330\pi$
$997$	12.3882	+	21.4570i	0.392338	+	0.679549i	−0.600419	+	0.799685i	$0.705000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.n.865.8		16
3.2	odd	2	inner	2268.2.i.n.865.1		16
7.2	even	3		2268.2.l.n.541.1		16
9.2	odd	6		2268.2.k.g.1621.1	yes	16
9.4	even	3		2268.2.l.n.109.1		16
9.5	odd	6		2268.2.l.n.109.8		16
9.7	even	3		2268.2.k.g.1621.8	yes	16
21.2	odd	6		2268.2.l.n.541.8		16
63.2	odd	6		2268.2.k.g.1297.1	✓	16
63.16	even	3		2268.2.k.g.1297.8	yes	16
63.23	odd	6	inner	2268.2.i.n.2053.1		16
63.58	even	3	inner	2268.2.i.n.2053.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.1		16	3.2	odd	2	inner
2268.2.i.n.865.8		16	1.1	even	1	trivial
2268.2.i.n.2053.1		16	63.23	odd	6	inner
2268.2.i.n.2053.8		16	63.58	even	3	inner
2268.2.k.g.1297.1	✓	16	63.2	odd	6
2268.2.k.g.1297.8	yes	16	63.16	even	3
2268.2.k.g.1621.1	yes	16	9.2	odd	6
2268.2.k.g.1621.8	yes	16	9.7	even	3
2268.2.l.n.109.1		16	9.4	even	3
2268.2.l.n.109.8		16	9.5	odd	6
2268.2.l.n.541.1		16	7.2	even	3
2268.2.l.n.541.8		16	21.2	odd	6

Overview	Random
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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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.83843 - 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +O(q^{10})\)	\(q+(1.83843 - 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +(0.301572 + 0.522337i) q^{11} +(2.62851 + 4.55271i) q^{13} +(2.12557 - 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +(0.578891 - 1.00267i) q^{23} +(-4.25969 - 7.37799i) q^{25} +(-3.98826 + 6.90786i) q^{29} +3.15085 q^{31} +(3.95419 + 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} +(-2.00937 - 3.48033i) q^{41} +(-3.66193 + 6.34264i) q^{43} +12.2173 q^{47} +(-2.15926 - 6.65865i) q^{49} +(-4.64928 + 8.05279i) q^{53} +2.21768 q^{55} +6.61521 q^{59} -1.93850 q^{61} +19.3294 q^{65} +8.63088 q^{67} +1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(-1.58698 - 0.167264i) q^{77} +4.14551 q^{79} +(6.24088 - 10.8095i) q^{83} +(-7.81544 - 13.5367i) q^{85} +(-4.09464 - 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} +27.0931 q^{95} +(6.77935 - 11.7422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

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