LMFDB - Embedded newform 2268.2.i.n.865.1

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			865.1
Root			$0.817131 - 0.735533i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.n.2053.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83843 + 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +O(q^{10})$	$q+(-1.83843 + 3.18426i) q^{5} +(-1.55575 + 2.14001i) q^{7} +(-0.301572 - 0.522337i) q^{11} +(2.62851 + 4.55271i) q^{13} +(-2.12557 + 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +(-0.578891 + 1.00267i) q^{23} +(-4.25969 - 7.37799i) q^{25} +(3.98826 - 6.90786i) q^{29} +3.15085 q^{31} +(-3.95419 - 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} +(2.00937 + 3.48033i) q^{41} +(-3.66193 + 6.34264i) q^{43} -12.2173 q^{47} +(-2.15926 - 6.65865i) q^{49} +(4.64928 - 8.05279i) q^{53} +2.21768 q^{55} -6.61521 q^{59} -1.93850 q^{61} -19.3294 q^{65} +8.63088 q^{67} -1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(1.58698 + 0.167264i) q^{77} +4.14551 q^{79} +(-6.24088 + 10.8095i) q^{83} +(-7.81544 - 13.5367i) q^{85} +(4.09464 + 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} -27.0931 q^{95} +(6.77935 - 11.7422i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.473905\pi$
$5$	−1.83843	+	3.18426i	−0.822173	+	1.42405i	−0.904061	+	0.427404i	$0.859428\pi$
$6$		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	0.816974	−	0.576674i	$-0.195650\pi$
$11$	−0.301572	−	0.522337i	−0.0909273	−	0.157491i	−0.907902	+	0.419183i	$0.862316\pi$
$12$		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	$0.339070\pi$
$17$	−2.12557	+	3.68159i	−0.515526	+	0.892918i	−0.999838	+	0.0180219i	$0.994263\pi$
$18$		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	−0.920047	−	0.391809i	$-0.871850\pi$
$23$	−0.578891	+	1.00267i	−0.120707	+	0.209071i	0.799340	+	0.600880i	$0.205183\pi$
$24$		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	$-0.567874\pi$
$29$	3.98826	−	6.90786i	0.740601	−	1.28276i	0.952222	−	0.305406i	$-0.0987922\pi$
$30$		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	0.979184	−	0.202974i	$-0.0650609\pi$
$41$	2.00937	+	3.48033i	0.313811	+	0.543537i	−0.665373	+	0.746511i	$0.731728\pi$
$42$		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	$-0.850021\pi$
$47$	−12.2173			−1.78207			−0.891036	+	0.453933i	$0.850021\pi$
$48$		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	$-0.612836\pi$
$53$	4.64928	−	8.05279i	0.638628	−	1.10614i	0.985734	−	0.168310i	$-0.0538309\pi$
$54$		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	$-0.641703\pi$
$59$	−6.61521			−0.861227			−0.430613	+	0.902537i	$0.641703\pi$
$60$		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	$-0.521514\pi$
$71$	−1.13815			−0.135074			−0.0675370	+	0.997717i	$0.521514\pi$
$72$		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	$0.406876\pi$
$83$	−6.24088	+	10.8095i	−0.685026	+	1.18650i	−0.973429	+	0.228990i	$0.926458\pi$
$84$		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	0.997216	−	0.0745672i	$-0.0237575\pi$
$89$	4.09464	+	7.09212i	0.434031	+	0.751764i	−0.563185	+	0.826331i	$0.690424\pi$
$90$		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	$-0.890309\pi$
$101$	−7.66975	−	13.2844i	−0.763169	−	1.32185i	0.178041	−	0.984023i	$-0.443024\pi$
$102$		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	0.652477	−	0.757808i	$-0.273730\pi$
$107$	−3.41399	−	5.91320i	−0.330043	−	0.571651i	−0.982520	+	0.186158i	$0.940396\pi$
$108$		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	0.997412	−	0.0718940i	$-0.0229043\pi$
$113$	4.63946	+	8.03579i	0.436444	+	0.755943i	−0.560968	+	0.827837i	$0.689571\pi$
$114$		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	$-0.356061\pi$
$131$	11.4164	−	19.7737i	0.997452	−	1.72764i	0.560508	−	0.828149i	$-0.310606\pi$
$132$		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	0.896769	−	0.442499i	$-0.145908\pi$
$137$	0.762784	+	1.32118i	0.0651690	+	0.112876i	−0.831600	+	0.555375i	$0.812575\pi$
$138$		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	$0.426258\pi$
$149$	−8.88746	+	15.3935i	−0.728089	+	1.26109i	−0.957690	+	0.287802i	$0.907075\pi$
$150$		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	0.955156	−	0.296104i	$-0.0956875\pi$
$167$	2.85782	+	4.94988i	0.221144	+	0.383033i	−0.734011	+	0.679137i	$0.762354\pi$
$168$		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	$-0.522966\pi$
$173$	−1.89631			−0.144174			−0.0720871	+	0.997398i	$0.522966\pi$
$174$		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	$0.350304\pi$
$179$	−7.29747	+	12.6396i	−0.545438	+	0.944727i	−0.998579	+	0.0532881i	$0.983030\pi$
$180$		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	$-0.400823\pi$
$191$	8.47340			0.613114			0.306557	+	0.951852i	$0.400823\pi$
$192$		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	$-0.696332\pi$
$197$	−16.2371			−1.15685			−0.578424	+	0.815736i	$0.696332\pi$
$198$		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	0.726268	−	0.687411i	$-0.241253\pi$
$227$	−3.49817	−	6.05900i	−0.232182	−	0.402150i	−0.958450	+	0.285261i	$0.907920\pi$
$228$		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	$0.0945756\pi$
$233$	11.1679	+	19.3434i	0.731635	+	1.26723i	−0.224550	+	0.974463i	$0.572091\pi$
$234$		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	0.833491	−	0.552534i	$-0.186339\pi$
$239$	−0.954829	−	1.65381i	−0.0617628	−	0.106976i	−0.895253	+	0.445557i	$0.853006\pi$
$240$		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	$-0.373113\pi$
$251$	12.2990			0.776306			0.388153	+	0.921595i	$0.373113\pi$
$252$		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	−0.631030	−	0.775758i	$-0.717368\pi$
$257$	5.71210	−	9.89365i	0.356311	−	0.617149i	0.987341	+	0.158609i	$0.0507010\pi$
$258$		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	$-0.963668\pi$
$263$	−9.65544	−	16.7237i	−0.595380	−	1.03123i	0.398114	−	0.917336i	$-0.369665\pi$
$264$		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	−0.717607	−	0.696448i	$-0.754763\pi$
$269$	4.00745	−	6.94110i	0.244338	−	0.423206i	0.961945	+	0.273242i	$0.0880959\pi$
$270$		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	$-0.636049\pi$
$281$	9.73700	−	16.8650i	0.580861	−	1.00608i	0.995378	−	0.0960386i	$-0.0306172\pi$
$282$		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	$0.0640888\pi$
$293$	11.3503	+	19.6593i	0.663090	+	1.14851i	−0.316709	+	0.948523i	$0.602578\pi$
$294$		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	$-0.357194\pi$
$311$	15.2982			0.867479			0.433739	+	0.901038i	$0.357194\pi$
$312$		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	$-0.418533\pi$
$317$	9.01444			0.506301			0.253151	+	0.967427i	$0.418533\pi$
$318$		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	$-0.490663\pi$
$347$	1.09272			0.0586600			0.0293300	+	0.999570i	$0.490663\pi$
$348$		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	$0.00493933\pi$
$353$	9.64549	+	16.7065i	0.513378	+	0.889196i	−0.486502	+	0.873680i	$0.661727\pi$
$354$		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	0.933307	−	0.359079i	$-0.116909\pi$
$359$	2.94976	+	5.10914i	0.155682	+	0.269650i	−0.777625	+	0.628729i	$0.783576\pi$
$360$		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	−0.545826	−	0.837898i	$-0.683784\pi$
$383$	8.86006	−	15.3461i	0.452728	−	0.784148i	0.998554	+	0.0537502i	$0.0171175\pi$
$384$		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	0.999763	−	0.0217610i	$-0.00692730\pi$
$389$	9.48751	+	16.4329i	0.481036	+	0.833179i	−0.518727	+	0.854940i	$0.673594\pi$
$390$		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	−0.620361	−	0.784317i	$-0.713014\pi$
$401$	7.39038	−	12.8005i	0.369058	−	0.639227i	0.989419	+	0.145090i	$0.0463470\pi$
$402$		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	$0.0766661\pi$
$419$	14.1678	+	24.5393i	0.692142	+	1.19883i	−0.278993	+	0.960293i	$0.590001\pi$
$420$		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	$0.393079\pi$
$431$	−13.5528	+	23.4741i	−0.652815	+	1.13071i	−0.982437	+	0.186595i	$0.940255\pi$
$432$		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	$-0.432630\pi$
$443$	8.84301			0.420144			0.210072	+	0.977686i	$0.432630\pi$
$444$		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	$-0.0950629\pi$
$449$	40.5033			1.91147			0.955735	+	0.294229i	$0.0950629\pi$
$450$		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	$-0.562723\pi$
$461$	16.1328	−	27.9428i	0.751378	−	1.30142i	0.947155	−	0.320776i	$-0.103944\pi$
$462$		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	0.958793	−	0.284107i	$-0.0916970\pi$
$467$	5.04280	+	8.73438i	0.233353	+	0.404179i	−0.725440	+	0.688286i	$0.758364\pi$
$468$		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	0.947346	−	0.320211i	$-0.103754\pi$
$479$	4.29759	+	7.44365i	0.196362	+	0.340109i	−0.750984	+	0.660320i	$0.770421\pi$
$480$		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	$-0.884887\pi$
$491$	−17.1521	−	29.7084i	−0.774066	−	1.34072i	0.161253	−	0.986913i	$-0.448447\pi$
$492$		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	$-0.635829\pi$
$503$	−18.5650			−0.827773			−0.413887	+	0.910328i	$0.635829\pi$
$504$		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	−0.933254	−	0.359216i	$-0.883044\pi$
$509$	−3.50908	+	6.07790i	−0.155537	+	0.269398i	0.777717	+	0.628614i	$0.216377\pi$
$510$		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	$0.396285\pi$
$521$	−15.0742	+	26.1092i	−0.660411	+	1.14387i	−0.980508	+	0.196481i	$0.937049\pi$
$522$		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	$0.478423\pi$
$557$	−19.5927	+	33.9355i	−0.830169	+	1.43789i	−0.897904	+	0.440191i	$0.854911\pi$
$558$		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	$-0.800180\pi$
$563$	−38.4078			−1.61870			−0.809349	+	0.587328i	$0.800180\pi$
$564$		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	$-0.560959\pi$
$569$	−9.08064			−0.380680			−0.190340	+	0.981718i	$0.560959\pi$
$570$		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	−0.947369	−	0.320143i	$-0.896269\pi$
$587$	−4.75919	+	8.24316i	−0.196433	+	0.340232i	0.750936	+	0.660374i	$0.229602\pi$
$588$		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	0.665668	−	0.746248i	$-0.268147\pi$
$593$	−7.63267	−	13.2202i	−0.313436	−	0.542887i	−0.979104	+	0.203361i	$0.934814\pi$
$594$		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	$-0.365169\pi$
$599$	20.1195			0.822059			0.411030	+	0.911622i	$0.365169\pi$
$600$		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	$0.158611\pi$
$617$	21.1904	+	36.7029i	0.853095	+	1.47760i	−0.0253061	+	0.999680i	$0.508056\pi$
$618$		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	$-0.991257\pi$
$641$	−13.2564	−	22.9608i	−0.523597	−	0.906896i	0.476026	−	0.879431i	$-0.342077\pi$
$642$		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	−0.574551	−	0.818469i	$-0.694823\pi$
$647$	10.7224	−	18.5717i	0.421540	−	0.730128i	0.996090	+	0.0883409i	$0.0281565\pi$
$648$		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	−0.898147	−	0.439696i	$-0.855086\pi$
$653$	−1.74496	+	3.02235i	−0.0682854	+	0.118274i	0.829861	+	0.557970i	$0.188420\pi$
$654$		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	$-0.581165\pi$
$659$	18.2754	−	31.6539i	0.711908	−	1.23306i	0.964140	−	0.265394i	$-0.0855021\pi$
$660$		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	$-0.291341\pi$
$677$	31.7213			1.21915			0.609574	+	0.792729i	$0.291341\pi$
$678$		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	$0.472639\pi$
$683$	−21.4275	+	37.1136i	−0.819902	+	1.42011i	−0.905754	+	0.423804i	$0.860695\pi$
$684$		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	$-0.622214\pi$
$701$	−19.8352			−0.749167			−0.374583	+	0.927193i	$0.622214\pi$
$702$		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	$-0.959029\pi$
$719$	−16.2769	−	28.1924i	−0.607025	−	1.05140i	0.384703	−	0.923040i	$-0.374304\pi$
$720$		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	0.598024	−	0.801478i	$-0.295953\pi$
$743$	−10.7693	−	18.6530i	−0.395089	−	0.684314i	−0.993112	+	0.117165i	$0.962619\pi$
$744$		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	−0.650530	−	0.759481i	$-0.725453\pi$
$761$	9.17145	−	15.8854i	0.332465	−	0.575846i	0.982995	+	0.183635i	$0.0587864\pi$
$762$		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	$0.345100\pi$
$773$	−14.7818	+	25.6029i	−0.531666	+	0.920873i	−0.999317	+	0.0369592i	$0.988233\pi$
$774$		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	0.996203	−	0.0870647i	$-0.0277487\pi$
$797$	11.9334	+	20.6692i	0.422701	+	0.732140i	−0.573502	+	0.819204i	$0.694415\pi$
$798$		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	$0.384194\pi$
$809$	−17.9594	+	31.1066i	−0.631418	+	1.09365i	−0.987262	+	0.159103i	$0.949140\pi$
$810$		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	$-0.601421\pi$
$821$	−17.9516			−0.626517			−0.313258	+	0.949668i	$0.601421\pi$
$822$		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	$-0.295383\pi$
$827$	34.4779			1.19891			0.599457	+	0.800407i	$0.295383\pi$
$828$		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	$0.595435\pi$
$839$	−28.2433	+	48.9187i	−0.975065	+	1.68886i	−0.679719	+	0.733472i	$0.737898\pi$
$840$		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	0.949919	−	0.312497i	$-0.101165\pi$
$857$	5.98166	+	10.3605i	0.204329	+	0.353909i	−0.745589	+	0.666406i	$0.767832\pi$
$858$		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	$0.161242\pi$
$863$	25.1871	+	43.6253i	0.857379	+	1.48502i	−0.0170411	+	0.999855i	$0.505425\pi$
$864$		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	$-0.478568\pi$
$881$	3.99396			0.134560			0.0672800	+	0.997734i	$0.478568\pi$
$882$		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	$0.450460\pi$
$887$	−23.1725	+	40.1359i	−0.778055	+	1.34763i	−0.933061	+	0.359718i	$0.882873\pi$
$888$		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	−0.969851	−	0.243699i	$-0.921639\pi$
$911$	−8.26635	+	14.3177i	−0.273876	+	0.474368i	0.695975	+	0.718066i	$0.254973\pi$
$912$		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	$-0.700853\pi$
$929$	−35.9629			−1.17990			−0.589952	+	0.807438i	$0.700853\pi$
$930$		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	$-0.532896\pi$
$941$	−6.32907			−0.206322			−0.103161	+	0.994665i	$0.532896\pi$
$942$		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	$-0.645759\pi$
$947$	−27.2086			−0.884161			−0.442080	+	0.896975i	$0.645759\pi$
$948$		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	$-0.367322\pi$
$953$	24.9963			0.809711			0.404855	+	0.914381i	$0.367322\pi$
$954$		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	0.868222	−	0.496175i	$-0.165263\pi$
$971$	0.137437	+	0.238048i	0.00441057	+	0.00763933i	−0.863812	+	0.503815i	$0.831929\pi$
$972$		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	$-0.665257\pi$
$977$	−31.0169			−0.992317			−0.496159	+	0.868232i	$0.665257\pi$
$978$		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	$0.0280714\pi$
$983$	18.0069	+	31.1889i	0.574332	+	0.994772i	−0.421782	+	0.906697i	$0.638595\pi$
$984$		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.865.1		16
3.2	odd	2	inner	2268.2.i.n.865.8		16
7.2	even	3		2268.2.l.n.541.8		16
9.2	odd	6		2268.2.k.g.1621.8	yes	16
9.4	even	3		2268.2.l.n.109.8		16
9.5	odd	6		2268.2.l.n.109.1		16
9.7	even	3		2268.2.k.g.1621.1	yes	16
21.2	odd	6		2268.2.l.n.541.1		16
63.2	odd	6		2268.2.k.g.1297.8	yes	16
63.16	even	3		2268.2.k.g.1297.1	✓	16
63.23	odd	6	inner	2268.2.i.n.2053.8		16
63.58	even	3	inner	2268.2.i.n.2053.1		16

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

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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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