LMFDB - Embedded newform 2268.2.k.g.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1297,2268)]

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, 0, 2]))

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

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

chi := DirichletCharacter("2268.1297");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, 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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.1
Root			$0.817131 + 0.735533i$ of defining polynomial
Character	$\chi$	$=$	2268.1621
Dual form			2268.2.k.g.1297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83843 - 3.18426i) q^{5} +(2.63118 + 0.277320i) q^{7} +O(q^{10})$	$q+(-1.83843 - 3.18426i) q^{5} +(2.63118 + 0.277320i) q^{7} +(-0.301572 + 0.522337i) q^{11} -5.25702 q^{13} +(-2.12557 + 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +(-0.578891 - 1.00267i) q^{23} +(-4.25969 + 7.37799i) q^{25} -7.97651 q^{29} +(-1.57542 + 2.72871i) q^{31} +(-3.95419 - 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} -4.01874 q^{41} +7.32385 q^{43} +(6.10863 + 10.5805i) q^{47} +(6.84619 + 1.45935i) q^{49} +(4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +(3.30760 - 5.72894i) q^{59} +(0.969252 + 1.67879i) q^{61} +(9.66468 + 16.7397i) q^{65} +(-4.31544 + 7.47456i) q^{67} -1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(-0.938343 + 1.29073i) q^{77} +(-2.07275 - 3.59011i) q^{79} +12.4818 q^{83} +15.6309 q^{85} +(4.09464 + 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} +(13.5466 - 23.4633i) q^{95} -13.5587 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{7}+O(q^{10}) $ 16 * q + 6 * q^7	$ 16 q + 6 q^{7} - 20 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} + 20 q^{43} + 10 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} + 76 q^{85} - 2 q^{91} - 84 q^{97}+O(q^{100}) $ 16 * q + 6 * q^7 - 20 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 + 20 * q^43 + 10 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 + 76 * q^85 - 2 * q^91 - 84 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.83843	−	3.18426i	−0.822173	−	1.42405i	−0.904061	−	0.427404i	$-0.859428\pi$
$5$	−1.83843	−	3.18426i	−0.822173	−	1.42405i	0.0818877	−	0.996642i	$-0.473905\pi$
$6$		0			0
$7$	2.63118	+	0.277320i	0.994492	+	0.104817i
$7$	2.63118	+	0.277320i	0.994492	+	0.104817i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.301572	+	0.522337i	−0.0909273	+	0.157491i	−0.907902	−	0.419183i	$-0.862316\pi$
$11$	−0.301572	+	0.522337i	−0.0909273	+	0.157491i	0.816974	+	0.576674i	$0.195650\pi$
$12$		0			0
$13$	−5.25702			−1.45803			−0.729017	−	0.684496i	$-0.760022\pi$
$13$	−5.25702			−1.45803			−0.729017	+	0.684496i	$0.760022\pi$
$14$		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	0.799340	−	0.600880i	$-0.205183\pi$
$23$	−0.578891	−	1.00267i	−0.120707	−	0.209071i	−0.920047	+	0.391809i	$0.871850\pi$
$24$		0			0
$25$	−4.25969	+	7.37799i	−0.851937	+	1.47560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.97651			−1.48120			−0.740601	−	0.671946i	$-0.765459\pi$
$29$	−7.97651			−1.48120			−0.740601	+	0.671946i	$0.765459\pi$
$30$		0			0
$31$	−1.57542	+	2.72871i	−0.282954	+	0.490091i	−0.972111	−	0.234521i	$-0.924648\pi$
$31$	−1.57542	+	2.72871i	−0.282954	+	0.490091i	0.689157	+	0.724612i	$0.257981\pi$
$32$		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
$41$	−4.01874			−0.627622			−0.313811	−	0.949485i	$-0.601606\pi$
$41$	−4.01874			−0.627622			−0.313811	+	0.949485i	$0.601606\pi$
$42$		0			0
$43$	7.32385			1.11688			0.558438	−	0.829546i	$-0.311401\pi$
$43$	7.32385			1.11688			0.558438	+	0.829546i	$0.311401\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.10863	+	10.5805i	0.891036	+	1.54332i	0.838635	+	0.544693i	$0.183354\pi$
$47$	6.10863	+	10.5805i	0.891036	+	1.54332i	0.0524003	+	0.998626i	$0.483313\pi$
$48$		0			0
$49$	6.84619	+	1.45935i	0.978027	+	0.208479i
$50$		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
$59$	3.30760	−	5.72894i	0.430613	−	0.745844i	−0.566313	−	0.824190i	$-0.691631\pi$
$59$	3.30760	−	5.72894i	0.430613	−	0.745844i	0.996926	+	0.0783462i	$0.0249640\pi$
$60$		0			0
$61$	0.969252	+	1.67879i	0.124100	+	0.214948i	0.921381	−	0.388661i	$-0.127062\pi$
$61$	0.969252	+	1.67879i	0.124100	+	0.214948i	−0.797281	+	0.603609i	$0.793729\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.66468	+	16.7397i	1.19876	+	2.07631i
$66$		0			0
$67$	−4.31544	+	7.47456i	−0.527215	+	0.913163i	0.472282	+	0.881447i	$0.343430\pi$
$67$	−4.31544	+	7.47456i	−0.527215	+	0.913163i	−0.999497	+	0.0317155i	$0.989903\pi$
$68$		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
$77$	−0.938343	+	1.29073i	−0.106934	+	0.147092i
$78$		0			0
$79$	−2.07275	−	3.59011i	−0.233203	−	0.403919i	0.725546	−	0.688174i	$-0.241587\pi$
$79$	−2.07275	−	3.59011i	−0.233203	−	0.403919i	−0.958749	+	0.284254i	$0.908254\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	12.4818			1.37005			0.685026	−	0.728519i	$-0.259791\pi$
$83$	12.4818			1.37005			0.685026	+	0.728519i	$0.259791\pi$
$84$		0			0
$85$	15.6309			1.69541
$86$		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
$95$	13.5466	−	23.4633i	1.38985	−	2.40729i
$96$		0			0
$97$	−13.5587			−1.37668			−0.688339	−	0.725389i	$-0.741660\pi$
$97$	−13.5587			−1.37668			−0.688339	+	0.725389i	$0.741660\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.66975	+	13.2844i	−0.763169	+	1.32185i	0.178041	+	0.984023i	$0.443024\pi$
$101$	−7.66975	+	13.2844i	−0.763169	+	1.32185i	−0.941209	+	0.337824i	$0.890309\pi$
$102$		0			0
$103$	2.48033	+	4.29606i	0.244394	+	0.423303i	0.961961	−	0.273186i	$-0.0880775\pi$
$103$	2.48033	+	4.29606i	0.244394	+	0.423303i	−0.717567	+	0.696490i	$0.754744\pi$
$104$		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
$113$	−9.27893			−0.872888			−0.436444	−	0.899731i	$-0.643762\pi$
$113$	−9.27893			−0.872888			−0.436444	+	0.899731i	$0.643762\pi$
$114$		0			0
$115$	−2.12851	+	3.68668i	−0.198484	+	0.343785i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.61373	+	9.09746i	−0.606279	+	0.833963i
$120$		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	0.560508	+	0.828149i	$0.310606\pi$
$131$	11.4164	+	19.7737i	0.997452	+	1.72764i	0.436944	+	0.899489i	$0.356061\pi$
$132$		0			0
$133$	7.92428	+	17.8121i	0.687122	+	1.54451i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.762784	−	1.32118i	0.0651690	−	0.112876i	−0.831600	−	0.555375i	$-0.812575\pi$
$137$	0.762784	−	1.32118i	0.0651690	−	0.112876i	0.896769	+	0.442499i	$0.145908\pi$
$138$		0			0
$139$	6.62554			0.561971			0.280986	−	0.959712i	$-0.409339\pi$
$139$	6.62554			0.561971			0.280986	+	0.959712i	$0.409339\pi$
$140$		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	−0.957690	−	0.287802i	$-0.907075\pi$
$149$	−8.88746	−	15.3935i	−0.728089	−	1.26109i	0.229601	−	0.973285i	$-0.426258\pi$
$150$		0			0
$151$	−2.31811	+	4.01508i	−0.188645	+	0.326743i	−0.944799	−	0.327651i	$-0.893743\pi$
$151$	−2.31811	+	4.01508i	−0.188645	+	0.326743i	0.756154	+	0.654394i	$0.227076\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.5852			0.930550
$156$		0			0
$157$	−1.70660	+	2.95592i	−0.136202	+	0.235908i	−0.926056	−	0.377387i	$-0.876823\pi$
$157$	−1.70660	+	2.95592i	−0.136202	+	0.235908i	0.789854	+	0.613295i	$0.210156\pi$
$158$		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
$167$	−5.71563			−0.442289			−0.221144	−	0.975241i	$-0.570979\pi$
$167$	−5.71563			−0.442289			−0.221144	+	0.975241i	$0.570979\pi$
$168$		0			0
$169$	14.6362			1.12586
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.948157	+	1.64226i	0.0720871	+	0.124858i	0.899816	−	0.436270i	$-0.143701\pi$
$173$	0.948157	+	1.64226i	0.0720871	+	0.124858i	−0.827729	+	0.561128i	$0.810367\pi$
$174$		0			0
$175$	−13.2540	+	18.2315i	−1.00191	+	1.37817i
$176$		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
$185$	0.00981439	−	0.0169990i	0.000721569	−	0.00124979i
$186$		0			0
$187$	−1.28202	−	2.22053i	−0.0937508	−	0.162381i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.23670	−	7.33818i	−0.306557	−	0.530972i	0.671050	−	0.741412i	$-0.265844\pi$
$191$	−4.23670	−	7.33818i	−0.306557	−	0.530972i	−0.977607	+	0.210440i	$0.932510\pi$
$192$		0			0
$193$	3.48300	−	6.03273i	0.250712	−	0.434246i	−0.713010	−	0.701154i	$-0.752669\pi$
$193$	3.48300	−	6.03273i	0.250712	−	0.434246i	0.963722	+	0.266908i	$0.0860020\pi$
$194$		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
$203$	−20.9876	−	2.21204i	−1.47304	−	0.155255i
$204$		0			0
$205$	7.38819	+	12.7967i	0.516014	+	0.893762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.44428			−0.307417
$210$		0			0
$211$	−16.8211			−1.15801			−0.579005	−	0.815324i	$-0.696559\pi$
$211$	−16.8211			−1.15801			−0.579005	+	0.815324i	$0.696559\pi$
$212$		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
$221$	11.1741	−	19.3542i	0.751655	−	1.30190i
$222$		0			0
$223$	−6.91599			−0.463129			−0.231564	−	0.972820i	$-0.574384\pi$
$223$	−6.91599			−0.463129			−0.231564	+	0.972820i	$0.574384\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.49817	+	6.05900i	−0.232182	+	0.402150i	−0.958450	−	0.285261i	$-0.907920\pi$
$227$	−3.49817	+	6.05900i	−0.232182	+	0.402150i	0.726268	+	0.687411i	$0.241253\pi$
$228$		0			0
$229$	1.41350	+	2.44825i	0.0934066	+	0.161785i	0.908942	−	0.416922i	$-0.136891\pi$
$229$	1.41350	+	2.44825i	0.0934066	+	0.161785i	−0.815536	+	0.578706i	$0.803558\pi$
$230$		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
$239$	1.90966			0.123526			0.0617628	−	0.998091i	$-0.480328\pi$
$239$	1.90966			0.123526			0.0617628	+	0.998091i	$0.480328\pi$
$240$		0			0
$241$	9.84352	−	17.0495i	0.634077	−	1.09825i	−0.352633	−	0.935762i	$-0.614714\pi$
$241$	9.84352	−	17.0495i	0.634077	−	1.09825i	0.986710	−	0.162492i	$-0.0519530\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.93930	−	24.4830i	−0.507223	−	1.56416i
$246$		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	0.987341	−	0.158609i	$-0.0507010\pi$
$257$	5.71210	+	9.89365i	0.356311	+	0.617149i	−0.631030	+	0.775758i	$0.717368\pi$
$258$		0			0
$259$	0.00574109	+	0.0129048i	0.000356734	+	0.000801864i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.65544	+	16.7237i	−0.595380	+	1.03123i	0.398114	+	0.917336i	$0.369665\pi$
$263$	−9.65544	+	16.7237i	−0.595380	+	1.03123i	−0.993493	+	0.113892i	$0.963668\pi$
$264$		0			0
$265$	−34.1896			−2.10025
$266$		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	−0.626149	−	0.779703i	$-0.715370\pi$
$277$	6.02768	−	10.4402i	0.362168	−	0.627293i	0.988317	+	0.152410i	$0.0487034\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.4740			−1.16172			−0.580861	−	0.814003i	$-0.697284\pi$
$281$	−19.4740			−1.16172			−0.580861	+	0.814003i	$0.697284\pi$
$282$		0			0
$283$	14.3518	−	24.8581i	0.853127	−	1.47766i	−0.0252457	−	0.999681i	$-0.508037\pi$
$283$	14.3518	−	24.8581i	0.853127	−	1.47766i	0.878372	−	0.477977i	$-0.158630\pi$
$284$		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
$293$	−22.7006			−1.32618			−0.663090	−	0.748539i	$-0.730755\pi$
$293$	−22.7006			−1.32618			−0.663090	+	0.748539i	$0.730755\pi$
$294$		0			0
$295$	−24.3233			−1.41615
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.04324	+	5.27105i	0.175995	+	0.304833i
$300$		0			0
$301$	19.2703	+	2.03105i	1.11072	+	0.117068i
$302$		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
$311$	−7.64908	+	13.2486i	−0.433739	+	0.751259i	−0.997192	−	0.0748898i	$-0.976139\pi$
$311$	−7.64908	+	13.2486i	−0.433739	+	0.751259i	0.563452	+	0.826149i	$0.309473\pi$
$312$		0			0
$313$	−1.67051	−	2.89341i	−0.0944230	−	0.163545i	0.814945	−	0.579539i	$-0.196767\pi$
$313$	−1.67051	−	2.89341i	−0.0944230	−	0.163545i	−0.909368	+	0.415993i	$0.863434\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.50722	−	7.80673i	−0.253151	−	0.438470i	0.711241	−	0.702948i	$-0.248133\pi$
$317$	−4.50722	−	7.80673i	−0.253151	−	0.438470i	−0.964392	+	0.264479i	$0.914800\pi$
$318$		0			0
$319$	2.40549	−	4.16643i	0.134682	−	0.233275i
$320$		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
$329$	13.1387	+	29.5331i	0.724361	+	1.62821i
$330$		0			0
$331$	−9.14760	−	15.8441i	−0.502797	−	0.870870i	−0.999995	−	0.00323307i	$-0.998971\pi$
$331$	−9.14760	−	15.8441i	−0.502797	−	0.870870i	0.497197	−	0.867637i	$-0.334362\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	31.7346			1.73385
$336$		0			0
$337$	1.73765			0.0946556			0.0473278	−	0.998879i	$-0.484929\pi$
$337$	1.73765			0.0946556			0.0473278	+	0.998879i	$0.484929\pi$
$338$		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
$347$	−0.546358	+	0.946319i	−0.0293300	+	0.0508011i	−0.880318	−	0.474384i	$-0.842671\pi$
$347$	−0.546358	+	0.946319i	−0.0293300	+	0.0508011i	0.850988	+	0.525185i	$0.176004\pi$
$348$		0			0
$349$	9.40193			0.503274			0.251637	−	0.967822i	$-0.419031\pi$
$349$	9.40193			0.503274			0.251637	+	0.967822i	$0.419031\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.64549	−	16.7065i	0.513378	−	0.889196i	−0.486502	−	0.873680i	$-0.661727\pi$
$353$	9.64549	−	16.7065i	0.513378	−	0.889196i	0.999880	−	0.0155167i	$-0.00493933\pi$
$354$		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
$365$	39.2330			2.05355
$366$		0			0
$367$	−5.48300	+	9.49684i	−0.286210	+	0.495731i	−0.972902	−	0.231218i	$-0.925729\pi$
$367$	−5.48300	+	9.49684i	−0.286210	+	0.495731i	0.686692	+	0.726949i	$0.259062\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.4663	−	19.8990i	0.751052	−	1.03310i
$372$		0			0
$373$	15.9691	+	27.6592i	0.826847	+	1.43214i	0.900500	+	0.434856i	$0.143201\pi$
$373$	15.9691	+	27.6592i	0.826847	+	1.43214i	−0.0736533	+	0.997284i	$0.523466\pi$
$374$		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	$-0.0171175\pi$
$383$	8.86006	+	15.3461i	0.452728	+	0.784148i	−0.545826	+	0.837898i	$0.683784\pi$
$384$		0			0
$385$	5.83511	+	0.615006i	0.297385	+	0.0313436i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.48751	−	16.4329i	0.481036	−	0.833179i	−0.518727	−	0.854940i	$-0.673594\pi$
$389$	9.48751	−	16.4329i	0.481036	−	0.833179i	0.999763	+	0.0217610i	$0.00692730\pi$
$390$		0			0
$391$	4.92189			0.248911
$392$		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	$-0.0463470\pi$
$401$	7.39038	+	12.8005i	0.369058	+	0.639227i	−0.620361	+	0.784317i	$0.713014\pi$
$402$		0			0
$403$	8.28202	−	14.3449i	0.412557	−	0.714570i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.00321985			−0.000159602
$408$		0			0
$409$	1.86575	−	3.23158i	0.0922554	−	0.159791i	−0.816204	−	0.577763i	$-0.803926\pi$
$409$	1.86575	−	3.23158i	0.0922554	−	0.159791i	0.908460	+	0.417972i	$0.137259\pi$
$410$		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
$419$	−28.3356			−1.38428			−0.692142	−	0.721761i	$-0.743333\pi$
$419$	−28.3356			−1.38428			−0.692142	+	0.721761i	$0.743333\pi$
$420$		0			0
$421$	16.1955			0.789321			0.394661	−	0.918827i	$-0.370862\pi$
$421$	16.1955			0.789321			0.394661	+	0.918827i	$0.370862\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.1085	−	31.3649i	−0.878392	−	1.52142i
$426$		0			0
$427$	2.08471	+	4.68600i	0.100886	+	0.226771i
$428$		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
$437$	4.26558	−	7.38819i	0.204050	−	0.353425i
$438$		0			0
$439$	1.43357	+	2.48301i	0.0684205	+	0.118508i	0.898206	−	0.439574i	$-0.144871\pi$
$439$	1.43357	+	2.48301i	0.0684205	+	0.118508i	−0.829786	+	0.558082i	$0.811537\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.42151	−	7.65827i	−0.210072	−	0.363855i	0.741665	−	0.670771i	$-0.234037\pi$
$443$	−4.42151	−	7.65827i	−0.210072	−	0.363855i	−0.951737	+	0.306915i	$0.900703\pi$
$444$		0			0
$445$	15.0555	−	26.0768i	0.713697	−	1.23616i
$446$		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
$455$	20.7872	+	46.7254i	0.974521	+	2.19052i
$456$		0			0
$457$	−19.4049	−	33.6103i	−0.907723	−	1.57222i	−0.817220	−	0.576326i	$-0.804486\pi$
$457$	−19.4049	−	33.6103i	−0.907723	−	1.57222i	−0.0905025	−	0.995896i	$-0.528847\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−32.2655			−1.50276			−0.751378	−	0.659872i	$-0.770610\pi$
$461$	−32.2655			−1.50276			−0.751378	+	0.659872i	$0.770610\pi$
$462$		0			0
$463$	33.4859			1.55622			0.778112	−	0.628126i	$-0.216178\pi$
$463$	33.4859			1.55622			0.778112	+	0.628126i	$0.216178\pi$
$464$		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
$473$	−2.20867	+	3.82552i	−0.101555	+	0.175898i
$474$		0			0
$475$	−62.7752			−2.88032
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.29759	−	7.44365i	0.196362	−	0.340109i	−0.750984	−	0.660320i	$-0.770421\pi$
$479$	4.29759	−	7.44365i	0.196362	−	0.340109i	0.947346	+	0.320211i	$0.103754\pi$
$480$		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
$491$	34.3043			1.54813			0.774066	−	0.633105i	$-0.218220\pi$
$491$	34.3043			1.54813			0.774066	+	0.633105i	$0.218220\pi$
$492$		0			0
$493$	16.9546	−	29.3663i	0.763598	−	1.32259i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.99468	−	0.315632i	−0.134330	−	0.0141581i
$498$		0			0
$499$	−15.0247	−	26.0236i	−0.672598	−	1.16497i	−0.977165	−	0.212483i	$-0.931845\pi$
$499$	−15.0247	−	26.0236i	−0.672598	−	1.16497i	0.304566	−	0.952491i	$-0.401488\pi$
$500$		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	0.777717	−	0.628614i	$-0.216377\pi$
$509$	−3.50908	−	6.07790i	−0.155537	−	0.269398i	−0.933254	+	0.359216i	$0.883044\pi$
$510$		0			0
$511$	−16.6002	+	22.8343i	−0.734351	+	1.01013i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.11986	−	15.7961i	0.401869	−	0.696057i
$516$		0			0
$517$	−7.36876			−0.324078
$518$		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
$533$	21.1266			0.915094
$534$		0			0
$535$	−12.5528	+	21.7421i	−0.542704	+	0.939991i
$536$		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
$545$	−65.4626			−2.80411
$546$		0			0
$547$	17.3691			0.742649			0.371324	−	0.928503i	$-0.378904\pi$
$547$	17.3691			0.742649			0.371324	+	0.928503i	$0.378904\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−29.3876	−	50.9008i	−1.25195	−	2.16844i
$552$		0			0
$553$	−4.45817	−	10.0210i	−0.189581	−	0.426138i
$554$		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
$563$	19.2039	−	33.2622i	0.809349	−	1.40183i	−0.103967	−	0.994581i	$-0.533154\pi$
$563$	19.2039	−	33.2622i	0.809349	−	1.40183i	0.913316	−	0.407252i	$-0.133513\pi$
$564$		0			0
$565$	17.0587	+	29.5465i	0.717665	+	1.24303i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.54032	+	7.86407i	0.190340	+	0.329679i	0.945363	−	0.326020i	$-0.105708\pi$
$569$	4.54032	+	7.86407i	0.190340	+	0.329679i	−0.755023	+	0.655698i	$0.772374\pi$
$570$		0			0
$571$	18.5274	−	32.0904i	0.775347	−	1.34294i	−0.159253	−	0.987238i	$-0.550908\pi$
$571$	18.5274	−	32.0904i	0.775347	−	1.34294i	0.934599	−	0.355702i	$-0.115758\pi$
$572$		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
$581$	32.8417	+	3.46144i	1.36250	+	0.143605i
$582$		0			0
$583$	2.80418	+	4.85699i	0.116137	+	0.201156i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.51838			0.392866			0.196433	−	0.980517i	$-0.437064\pi$
$587$	9.51838			0.392866			0.196433	+	0.980517i	$0.437064\pi$
$588$		0			0
$589$	−23.2171			−0.956643
$590$		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
$599$	−10.0597	+	17.4240i	−0.411030	+	0.711924i	−0.995003	−	0.0998490i	$-0.968164\pi$
$599$	−10.0597	+	17.4240i	−0.411030	+	0.711924i	0.583973	+	0.811773i	$0.301497\pi$
$600$		0			0
$601$	20.3058			0.828292			0.414146	−	0.910210i	$-0.364080\pi$
$601$	20.3058			0.828292			0.414146	+	0.910210i	$0.364080\pi$
$602$		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	0.886294	−	0.463124i	$-0.153271\pi$
$607$	1.03649	+	1.79525i	0.0420698	+	0.0728670i	−0.844224	+	0.535991i	$0.819938\pi$
$608$		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
$617$	−42.3809			−1.70619			−0.853095	−	0.521756i	$-0.825277\pi$
$617$	−42.3809			−1.70619			−0.853095	+	0.521756i	$0.825277\pi$
$618$		0			0
$619$	−6.93536	+	12.0124i	−0.278756	+	0.482819i	−0.971076	−	0.238772i	$-0.923255\pi$
$619$	−6.93536	+	12.0124i	−0.278756	+	0.482819i	0.692320	+	0.721590i	$0.256589\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.80694	+	19.7962i	0.352843	+	0.793116i
$624$		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
$637$	−35.9905	−	7.67185i	−1.42600	−	0.303970i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.2564	+	22.9608i	−0.523597	+	0.906896i	0.476026	+	0.879431i	$0.342077\pi$
$641$	−13.2564	+	22.9608i	−0.523597	+	0.906896i	−0.999623	+	0.0274647i	$0.991257\pi$
$642$		0			0
$643$	−48.6368			−1.91805			−0.959024	−	0.283326i	$-0.908562\pi$
$643$	−48.6368			−1.91805			−0.959024	+	0.283326i	$0.908562\pi$
$644$		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	0.829861	−	0.557970i	$-0.188420\pi$
$653$	−1.74496	−	3.02235i	−0.0682854	−	0.118274i	−0.898147	+	0.439696i	$0.855086\pi$
$654$		0			0
$655$	41.9765	−	72.7054i	1.64016	−	2.84083i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−36.5508			−1.42382			−0.711908	−	0.702273i	$-0.752169\pi$
$659$	−36.5508			−1.42382			−0.711908	+	0.702273i	$0.752169\pi$
$660$		0			0
$661$	2.78748	−	4.82806i	0.108420	−	0.187790i	−0.806710	−	0.590947i	$-0.798754\pi$
$661$	2.78748	−	4.82806i	0.108420	−	0.187790i	0.915131	+	0.403158i	$0.132087\pi$
$662$		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
$671$	−1.16920			−0.0451363
$672$		0			0
$673$	−2.51323			−0.0968778			−0.0484389	−	0.998826i	$-0.515425\pi$
$673$	−2.51323			−0.0968778			−0.0484389	+	0.998826i	$0.515425\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.8606	−	27.4714i	−0.609574	−	1.05581i	−0.991311	−	0.131542i	$-0.958007\pi$
$677$	−15.8606	−	27.4714i	−0.609574	−	1.05581i	0.381737	−	0.924271i	$-0.375326\pi$
$678$		0			0
$679$	−35.6754	−	3.76010i	−1.36909	−	0.144299i
$680$		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
$689$	−24.4413	+	42.3336i	−0.931141	+	1.61278i
$690$		0			0
$691$	7.38187	+	12.7858i	0.280820	+	0.486394i	0.971587	−	0.236683i	$-0.0760604\pi$
$691$	7.38187	+	12.7858i	0.280820	+	0.486394i	−0.690767	+	0.723077i	$0.742727\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.1806	−	21.0975i	−0.462037	−	0.800272i
$696$		0			0
$697$	8.54211	−	14.7954i	0.323556	−	0.560415i
$698$		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
$707$	−23.8645	+	32.8266i	−0.897517	+	1.23457i
$708$		0			0
$709$	−5.10292	−	8.83852i	−0.191644	−	0.331937i	0.754151	−	0.656701i	$-0.228049\pi$
$709$	−5.10292	−	8.83852i	−0.191644	−	0.331937i	−0.945795	+	0.324763i	$0.894715\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.64799			0.136618
$714$		0			0
$715$	−11.6584			−0.435999
$716$		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
$725$	33.9774	−	58.8506i	1.26189	−	2.18566i
$726$		0			0
$727$	15.3019			0.567516			0.283758	−	0.958896i	$-0.408419\pi$
$727$	15.3019			0.567516			0.283758	+	0.958896i	$0.408419\pi$
$728$		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	0.935067	−	0.354472i	$-0.115339\pi$
$733$	4.34677	+	7.52882i	0.160552	+	0.278083i	−0.774515	+	0.632555i	$0.782006\pi$
$734$		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
$743$	21.5387			0.790177			0.395089	−	0.918643i	$-0.370714\pi$
$743$	21.5387			0.790177			0.395089	+	0.918643i	$0.370714\pi$
$744$		0			0
$745$	−32.6780	+	56.6000i	−1.19723	+	2.07366i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.34296	−	16.5054i	−0.268306	−	0.603096i
$750$		0			0
$751$	−19.8241	−	34.3364i	−0.723393	−	1.25295i	−0.959632	−	0.281258i	$-0.909248\pi$
$751$	−19.8241	−	34.3364i	−0.723393	−	1.25295i	0.236239	−	0.971695i	$-0.424085\pi$
$752$		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	$-0.0587864\pi$
$761$	9.17145	+	15.8854i	0.332465	+	0.575846i	−0.650530	+	0.759481i	$0.725453\pi$
$762$		0			0
$763$	27.6985	−	38.1004i	1.00275	−	1.37933i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.3881	+	30.1171i	−0.627849	+	1.08747i
$768$		0			0
$769$	−14.9270			−0.538282			−0.269141	−	0.963101i	$-0.586740\pi$
$769$	−14.9270			−0.538282			−0.269141	+	0.963101i	$0.586740\pi$
$770$		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
$785$	12.5499			0.447925
$786$		0			0
$787$	4.66430	−	8.07880i	0.166264	−	0.287978i	−0.770839	−	0.637030i	$-0.780163\pi$
$787$	4.66430	−	8.07880i	0.166264	−	0.287978i	0.937104	+	0.349052i	$0.113496\pi$
$788$		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
$797$	−23.8667			−0.845402			−0.422701	−	0.906269i	$-0.638918\pi$
$797$	−23.8667			−0.845402			−0.422701	+	0.906269i	$0.638918\pi$
$798$		0			0
$799$	−51.9373			−1.83741
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.21784	−	5.57345i	−0.113555	−	0.196683i
$804$		0			0
$805$	−6.62287	+	9.11004i	−0.233426	+	0.321087i
$806$		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
$815$	27.7608	−	48.0831i	0.972418	−	1.68428i
$816$		0			0
$817$	26.9830	+	46.7359i	0.944015	+	1.63508i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.97582	+	15.5466i	0.313258	+	0.542580i	0.979066	−	0.203544i	$-0.0652461\pi$
$821$	8.97582	+	15.5466i	0.313258	+	0.542580i	−0.665807	+	0.746124i	$0.731913\pi$
$822$		0			0
$823$	−0.969357	+	1.67898i	−0.0337897	+	0.0585254i	−0.882426	−	0.470452i	$-0.844091\pi$
$823$	−0.969357	+	1.67898i	−0.0337897	+	0.0585254i	0.848636	+	0.528977i	$0.177424\pi$
$824$		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
$833$	−19.9248	+	22.1029i	−0.690353	+	0.765821i
$834$		0			0
$835$	10.5078	+	18.2001i	0.363638	+	0.629839i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	56.4865			1.95013			0.975065	−	0.221918i	$-0.0712317\pi$
$839$	56.4865			1.95013			0.975065	+	0.221918i	$0.0712317\pi$
$840$		0			0
$841$	34.6247			1.19396
$842$		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
$851$	0.00309038	−	0.00535270i	0.000105937	−	0.000183488i
$852$		0			0
$853$	−11.6708			−0.399601			−0.199800	−	0.979837i	$-0.564029\pi$
$853$	−11.6708			−0.399601			−0.199800	+	0.979837i	$0.564029\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.98166	−	10.3605i	0.204329	−	0.353909i	−0.745589	−	0.666406i	$-0.767832\pi$
$857$	5.98166	−	10.3605i	0.204329	−	0.353909i	0.949919	+	0.312497i	$0.101165\pi$
$858$		0			0
$859$	28.7004	+	49.7105i	0.979244	+	1.69610i	0.665151	+	0.746709i	$0.268367\pi$
$859$	28.7004	+	49.7105i	0.979244	+	1.69610i	0.314094	+	0.949392i	$0.398299\pi$
$860$		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
$869$	2.50034			0.0848181
$870$		0			0
$871$	22.6863	−	39.2939i	0.768697	−	1.33142i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	34.0481	+	3.58859i	1.15104	+	0.121317i
$876$		0			0
$877$	4.22569	+	7.31911i	0.142691	+	0.247149i	0.928509	−	0.371309i	$-0.121091\pi$
$877$	4.22569	+	7.31911i	0.142691	+	0.247149i	−0.785818	+	0.618458i	$0.787758\pi$
$878$		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	−0.933061	−	0.359718i	$-0.882873\pi$
$887$	−23.1725	−	40.1359i	−0.778055	−	1.34763i	0.155006	−	0.987914i	$-0.450460\pi$
$888$		0			0
$889$	−39.4520	−	4.15815i	−1.32318	−	0.139460i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−45.0116	+	77.9624i	−1.50626	+	2.60891i
$894$		0			0
$895$	53.6637			1.79378
$896$		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	−0.899310	−	0.437312i	$-0.855931\pi$
$907$	−2.13622	+	3.70004i	−0.0709320	+	0.122858i	0.828378	+	0.560169i	$0.189264\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.5327			0.547753			0.273876	−	0.961765i	$-0.411694\pi$
$911$	16.5327			0.547753			0.273876	+	0.961765i	$0.411694\pi$
$912$		0			0
$913$	−3.76415	+	6.51969i	−0.124575	+	0.215770i
$914$		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
$923$	5.98329			0.196943
$924$		0			0
$925$	−0.0454802			−0.00149538
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.9815	+	31.1448i	0.589952	+	1.02183i	0.994238	+	0.107195i	$0.0341868\pi$
$929$	17.9815	+	31.1448i	0.589952	+	1.02183i	−0.404286	+	0.914633i	$0.632480\pi$
$930$		0			0
$931$	15.9105	+	49.0644i	0.521447	+	1.60802i
$932$		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
$941$	3.16454	−	5.48114i	0.103161	−	0.178680i	−0.809824	−	0.586672i	$-0.800438\pi$
$941$	3.16454	−	5.48114i	0.103161	−	0.178680i	0.912985	+	0.407992i	$0.133771\pi$
$942$		0			0
$943$	2.32641	+	4.02947i	0.0757585	+	0.131218i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.6043	+	23.5633i	0.442080	+	0.765706i	0.997844	−	0.0656348i	$-0.0209072\pi$
$947$	13.6043	+	23.5633i	0.442080	+	0.765706i	−0.555763	+	0.831341i	$0.687574\pi$
$948$		0			0
$949$	28.0467	−	48.5784i	0.910436	−	1.57692i
$950$		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
$959$	2.37341	−	3.26473i	0.0766414	−	0.105424i
$960$		0			0
$961$	10.5361	+	18.2490i	0.339874	+	0.588679i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−25.6131			−0.824514
$966$		0			0
$967$	−12.2234			−0.393077			−0.196539	−	0.980496i	$-0.562970\pi$
$967$	−12.2234			−0.393077			−0.196539	+	0.980496i	$0.562970\pi$
$968$		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
$977$	15.5084	−	26.8614i	0.496159	−	0.859372i	−0.503832	−	0.863802i	$-0.668077\pi$
$977$	15.5084	−	26.8614i	0.496159	−	0.859372i	0.999990	+	0.00443011i	$0.00141015\pi$
$978$		0			0
$979$	−4.93931			−0.157861
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.0069	−	31.1889i	0.574332	−	0.994772i	−0.421782	−	0.906697i	$-0.638595\pi$
$983$	18.0069	−	31.1889i	0.574332	−	0.994772i	0.996114	−	0.0880747i	$-0.0280714\pi$
$984$		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
$995$	54.0612			1.71386
$996$		0			0
$997$	12.3882	−	21.4570i	0.392338	−	0.679549i	−0.600419	−	0.799685i	$-0.705000\pi$
$997$	12.3882	−	21.4570i	0.392338	−	0.679549i	0.992757	+	0.120136i	$0.0383330\pi$
$998$		0			0
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83843 - 3.18426i) q^{5} +(2.63118 + 0.277320i) q^{7} +O(q^{10})\)	\(q+(-1.83843 - 3.18426i) q^{5} +(2.63118 + 0.277320i) q^{7} +(-0.301572 + 0.522337i) q^{11} -5.25702 q^{13} +(-2.12557 + 3.68159i) q^{17} +(3.68426 + 6.38133i) q^{19} +(-0.578891 - 1.00267i) q^{23} +(-4.25969 + 7.37799i) q^{25} -7.97651 q^{29} +(-1.57542 + 2.72871i) q^{31} +(-3.95419 - 8.88819i) q^{35} +(0.00266923 + 0.00462323i) q^{37} -4.01874 q^{41} +7.32385 q^{43} +(6.10863 + 10.5805i) q^{47} +(6.84619 + 1.45935i) q^{49} +(4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +(3.30760 - 5.72894i) q^{59} +(0.969252 + 1.67879i) q^{61} +(9.66468 + 16.7397i) q^{65} +(-4.31544 + 7.47456i) q^{67} -1.13815 q^{71} +(-5.33511 + 9.24068i) q^{73} +(-0.938343 + 1.29073i) q^{77} +(-2.07275 - 3.59011i) q^{79} +12.4818 q^{83} +15.6309 q^{85} +(4.09464 + 7.09212i) q^{89} +(-13.8321 - 1.45787i) q^{91} +(13.5466 - 23.4633i) q^{95} -13.5587 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{7}+O(q^{10}) \) 16 * q + 6 * q^7	\( 16 q + 6 q^{7} - 20 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} + 20 q^{43} + 10 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} + 76 q^{85} - 2 q^{91} - 84 q^{97}+O(q^{100}) \) 16 * q + 6 * q^7 - 20 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 + 20 * q^43 + 10 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 + 76 * q^85 - 2 * q^91 - 84 * q^97

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