LMFDB - Embedded newform 2268.2.k.g.1621.5

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			1621.5
Root			$-1.30887 - 2.01944i$ of defining polynomial
Character	$\chi$	$=$	2268.1621
Dual form			2268.2.k.g.1297.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.171869 + 0.297685i) q^{5} +(-2.41508 + 1.08045i) q^{7} +O(q^{10})$	$q+(0.171869 + 0.297685i) q^{5} +(-2.41508 + 1.08045i) q^{7} +(2.45988 - 4.26064i) q^{11} -1.94832 q^{13} +(-2.07359 + 3.59156i) q^{17} +(0.202315 + 0.350420i) q^{19} +(1.37943 + 2.38925i) q^{23} +(2.44092 - 4.22780i) q^{25} +3.27721 q^{29} +(1.64324 - 2.84617i) q^{31} +(-0.736710 - 0.533240i) q^{35} +(-3.38925 - 5.87035i) q^{37} -5.62500 q^{41} +9.92590 q^{43} +(-6.60038 - 11.4322i) q^{47} +(4.66527 - 5.21874i) q^{49} +(-1.38163 + 2.39306i) q^{53} +1.69110 q^{55} +(-4.22560 + 7.31896i) q^{59} +(-5.37804 - 9.31503i) q^{61} +(-0.334856 - 0.579987i) q^{65} +(4.21277 - 7.29673i) q^{67} +5.08888 q^{71} +(4.58416 - 7.94000i) q^{73} +(-1.33742 + 12.9476i) q^{77} +(-2.24601 - 3.89020i) q^{79} +9.25931 q^{83} -1.42554 q^{85} +(-3.54253 - 6.13584i) q^{89} +(4.70537 - 2.10506i) q^{91} +(-0.0695431 + 0.120452i) q^{95} +2.62462 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.171869	+	0.297685i	0.0768620	+	0.133129i	0.901894	−	0.431956i	$-0.142177\pi$
$5$	0.171869	+	0.297685i	0.0768620	+	0.133129i	−0.825032	+	0.565085i	$0.808843\pi$
$6$		0			0
$7$	−2.41508	+	1.08045i	−0.912816	+	0.408371i
$7$	−2.41508	+	1.08045i	−0.912816	+	0.408371i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.45988	−	4.26064i	0.741682	−	1.28463i	−0.210048	−	0.977691i	$-0.567362\pi$
$11$	2.45988	−	4.26064i	0.741682	−	1.28463i	0.951729	−	0.306939i	$-0.0993048\pi$
$12$		0			0
$13$	−1.94832			−0.540368			−0.270184	−	0.962809i	$-0.587085\pi$
$13$	−1.94832			−0.540368			−0.270184	+	0.962809i	$0.587085\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.07359	+	3.59156i	−0.502919	+	0.871082i	0.497075	+	0.867708i	$0.334407\pi$
$17$	−2.07359	+	3.59156i	−0.502919	+	0.871082i	−0.999994	+	0.00337409i	$0.998926\pi$
$18$		0			0
$19$	0.202315	+	0.350420i	0.0464142	+	0.0803918i	0.888299	−	0.459265i	$-0.151887\pi$
$19$	0.202315	+	0.350420i	0.0464142	+	0.0803918i	−0.841885	+	0.539657i	$0.818554\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.37943	+	2.38925i	0.287631	+	0.498192i	0.973244	−	0.229774i	$-0.0737988\pi$
$23$	1.37943	+	2.38925i	0.287631	+	0.498192i	−0.685612	+	0.727967i	$0.740465\pi$
$24$		0			0
$25$	2.44092	−	4.22780i	0.488184	−	0.845560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.27721			0.608563			0.304282	−	0.952582i	$-0.401584\pi$
$29$	3.27721			0.608563			0.304282	+	0.952582i	$0.401584\pi$
$30$		0			0
$31$	1.64324	−	2.84617i	0.295134	−	0.511187i	−0.679882	−	0.733322i	$-0.737969\pi$
$31$	1.64324	−	2.84617i	0.295134	−	0.511187i	0.975016	+	0.222134i	$0.0713023\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.736710	−	0.533240i	−0.124527	−	0.0901340i
$36$		0			0
$37$	−3.38925	−	5.87035i	−0.557189	−	0.965079i	−0.997730	−	0.0673466i	$-0.978547\pi$
$37$	−3.38925	−	5.87035i	−0.557189	−	0.965079i	0.440541	−	0.897733i	$-0.354787\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.62500			−0.878477			−0.439238	−	0.898371i	$-0.644752\pi$
$41$	−5.62500			−0.878477			−0.439238	+	0.898371i	$0.644752\pi$
$42$		0			0
$43$	9.92590			1.51369			0.756843	−	0.653597i	$-0.226741\pi$
$43$	9.92590			1.51369			0.756843	+	0.653597i	$0.226741\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.60038	−	11.4322i	−0.962764	−	1.66756i	−0.715507	−	0.698606i	$-0.753804\pi$
$47$	−6.60038	−	11.4322i	−0.962764	−	1.66756i	−0.247257	−	0.968950i	$-0.579529\pi$
$48$		0			0
$49$	4.66527	−	5.21874i	0.666467	−	0.745535i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.38163	+	2.39306i	−0.189782	+	0.328711i	−0.945177	−	0.326557i	$-0.894111\pi$
$53$	−1.38163	+	2.39306i	−0.189782	+	0.328711i	0.755396	+	0.655269i	$0.227445\pi$
$54$		0			0
$55$	1.69110			0.228028
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.22560	+	7.31896i	−0.550127	+	0.952847i	0.448138	+	0.893964i	$0.352087\pi$
$59$	−4.22560	+	7.31896i	−0.550127	+	0.952847i	−0.998265	+	0.0588830i	$0.981246\pi$
$60$		0			0
$61$	−5.37804	−	9.31503i	−0.688587	−	1.19267i	−0.972295	−	0.233757i	$-0.924898\pi$
$61$	−5.37804	−	9.31503i	−0.688587	−	1.19267i	0.283708	−	0.958911i	$-0.408435\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.334856	−	0.579987i	−0.0415337	−	0.0719386i
$66$		0			0
$67$	4.21277	−	7.29673i	0.514672	−	0.891438i	−0.485183	−	0.874412i	$-0.661247\pi$
$67$	4.21277	−	7.29673i	0.514672	−	0.891438i	0.999855	−	0.0170251i	$-0.00541953\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.08888			0.603939			0.301970	−	0.953318i	$-0.402356\pi$
$71$	5.08888			0.603939			0.301970	+	0.953318i	$0.402356\pi$
$72$		0			0
$73$	4.58416	−	7.94000i	0.536535	−	0.929306i	−0.462552	−	0.886592i	$-0.653066\pi$
$73$	4.58416	−	7.94000i	0.536535	−	0.929306i	0.999087	−	0.0427143i	$-0.0136005\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.33742	+	12.9476i	−0.152414	+	1.47551i
$78$		0			0
$79$	−2.24601	−	3.89020i	−0.252696	−	0.437682i	0.711571	−	0.702614i	$-0.247984\pi$
$79$	−2.24601	−	3.89020i	−0.252696	−	0.437682i	−0.964267	+	0.264932i	$0.914651\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.25931			1.01634			0.508171	−	0.861256i	$-0.330322\pi$
$83$	9.25931			1.01634			0.508171	+	0.861256i	$0.330322\pi$
$84$		0			0
$85$	−1.42554			−0.154621
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.54253	−	6.13584i	−0.375507	−	0.650397i	0.614896	−	0.788608i	$-0.289198\pi$
$89$	−3.54253	−	6.13584i	−0.375507	−	0.650397i	−0.990403	+	0.138211i	$0.955865\pi$
$90$		0			0
$91$	4.70537	−	2.10506i	0.493257	−	0.220670i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0695431	+	0.120452i	−0.00713498	+	0.0123581i
$96$		0			0
$97$	2.62462			0.266490			0.133245	−	0.991083i	$-0.457460\pi$
$97$	2.62462			0.266490			0.133245	+	0.991083i	$0.457460\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.85269	−	13.6013i	0.781372	−	1.35338i	−0.149771	−	0.988721i	$-0.547854\pi$
$101$	7.85269	−	13.6013i	0.781372	−	1.35338i	0.931143	−	0.364655i	$-0.118813\pi$
$102$		0			0
$103$	3.87139	+	6.70544i	0.381459	+	0.660707i	0.991271	−	0.131839i	$-0.0420883\pi$
$103$	3.87139	+	6.70544i	0.381459	+	0.660707i	−0.609812	+	0.792546i	$0.708755\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.12952	+	10.6166i	0.592563	+	1.02635i	0.993886	+	0.110413i	$0.0352173\pi$
$107$	6.12952	+	10.6166i	0.592563	+	1.02635i	−0.401323	+	0.915937i	$0.631449\pi$
$108$		0			0
$109$	4.89342	−	8.47565i	0.468705	−	0.811820i	−0.530656	−	0.847588i	$-0.678054\pi$
$109$	4.89342	−	8.47565i	0.468705	−	0.811820i	0.999360	+	0.0357675i	$0.0113876\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.09328			0.479136			0.239568	−	0.970880i	$-0.422994\pi$
$113$	5.09328			0.479136			0.239568	+	0.970880i	$0.422994\pi$
$114$		0			0
$115$	−0.474162	+	0.821273i	−0.0442158	+	0.0765841i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.12740	−	10.9143i	0.103348	−	1.00051i
$120$		0			0
$121$	−6.60202	−	11.4350i	−0.600183	−	1.03955i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.39676			0.303815
$126$		0			0
$127$	2.24242			0.198982			0.0994911	−	0.995038i	$-0.468279\pi$
$127$	2.24242			0.198982			0.0994911	+	0.995038i	$0.468279\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.72722	+	6.45573i	0.325648	+	0.564039i	0.981643	−	0.190726i	$-0.0610841\pi$
$131$	3.72722	+	6.45573i	0.325648	+	0.564039i	−0.655995	+	0.754765i	$0.727751\pi$
$132$		0			0
$133$	−0.867218	−	0.627702i	−0.0751973	−	0.0544287i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.22340	−	7.31515i	0.360830	−	0.624975i	−0.627268	−	0.778804i	$-0.715827\pi$
$137$	4.22340	−	7.31515i	0.360830	−	0.624975i	0.988098	+	0.153828i	$0.0491602\pi$
$138$		0			0
$139$	−3.64705			−0.309338			−0.154669	−	0.987966i	$-0.549431\pi$
$139$	−3.64705			−0.309338			−0.154669	+	0.987966i	$0.549431\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.79264	+	8.30110i	−0.400781	+	0.694173i
$144$		0			0
$145$	0.563250	+	0.975578i	0.0467754	+	0.0810173i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.147078	−	0.254746i	−0.0120491	−	0.0208696i	0.859938	−	0.510399i	$-0.170502\pi$
$149$	−0.147078	−	0.254746i	−0.0120491	−	0.0208696i	−0.871987	+	0.489529i	$0.837169\pi$
$150$		0			0
$151$	9.60202	−	16.6312i	0.781401	−	1.35343i	−0.149725	−	0.988728i	$-0.547839\pi$
$151$	9.60202	−	16.6312i	0.781401	−	1.35343i	0.931126	−	0.364699i	$-0.118828\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.12968			0.0907384
$156$		0			0
$157$	6.55832	−	11.3593i	0.523411	−	0.906575i	−0.476218	−	0.879327i	$-0.657993\pi$
$157$	6.55832	−	11.3593i	0.523411	−	0.906575i	0.999629	−	0.0272471i	$-0.00867410\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.91290	−	4.27983i	−0.466002	−	0.337298i
$162$		0			0
$163$	0.496191	+	0.859428i	0.0388647	+	0.0673156i	0.884803	−	0.465964i	$-0.154293\pi$
$163$	0.496191	+	0.859428i	0.0388647	+	0.0673156i	−0.845939	+	0.533280i	$0.820959\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.8608			−1.07258			−0.536291	−	0.844033i	$-0.680175\pi$
$167$	−13.8608			−1.07258			−0.536291	+	0.844033i	$0.680175\pi$
$168$		0			0
$169$	−9.20403			−0.708003
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.50243	+	4.33434i	0.190256	+	0.329534i	0.945335	−	0.326100i	$-0.105735\pi$
$173$	2.50243	+	4.33434i	0.190256	+	0.329534i	−0.755079	+	0.655634i	$0.772401\pi$
$174$		0			0
$175$	−1.32712	+	12.8478i	−0.100321	+	0.971201i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.8101	+	18.7236i	−0.807982	+	1.39947i	0.106277	+	0.994337i	$0.466107\pi$
$179$	−10.8101	+	18.7236i	−0.807982	+	1.39947i	−0.914259	+	0.405130i	$0.867226\pi$
$180$		0			0
$181$	−26.0342			−1.93511			−0.967553	−	0.252666i	$-0.918693\pi$
$181$	−26.0342			−1.93511			−0.967553	+	0.252666i	$0.918693\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.16501	−	2.01786i	0.0856532	−	0.148356i
$186$		0			0
$187$	10.2016	+	17.6696i	0.746012	+	1.29213i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.85252	−	15.3330i	−0.640546	−	1.10946i	−0.985311	−	0.170769i	$-0.945375\pi$
$191$	−8.85252	−	15.3330i	−0.640546	−	1.10946i	0.344766	−	0.938689i	$-0.387958\pi$
$192$		0			0
$193$	1.48214	−	2.56715i	0.106687	−	0.184787i	−0.807739	−	0.589540i	$-0.799309\pi$
$193$	1.48214	−	2.56715i	0.106687	−	0.184787i	0.914426	+	0.404753i	$0.132642\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.2357			−1.29924			−0.649618	−	0.760260i	$-0.725071\pi$
$197$	−18.2357			−1.29924			−0.649618	+	0.760260i	$0.725071\pi$
$198$		0			0
$199$	1.61323	−	2.79419i	0.114359	−	0.198075i	−0.803165	−	0.595757i	$-0.796852\pi$
$199$	1.61323	−	2.79419i	0.114359	−	0.198075i	0.917523	+	0.397682i	$0.130185\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.91475	+	3.54086i	−0.555506	+	0.248519i
$204$		0			0
$205$	−0.966760	−	1.67448i	−0.0675215	−	0.116951i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.99068			0.137698
$210$		0			0
$211$	9.45479			0.650895			0.325447	−	0.945560i	$-0.394485\pi$
$211$	9.45479			0.650895			0.325447	+	0.945560i	$0.394485\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.70595	+	2.95479i	0.116345	+	0.201515i
$216$		0			0
$217$	−0.893419	+	8.64917i	−0.0606492	+	0.587144i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.04002	−	6.99753i	0.271761	−	0.470705i
$222$		0			0
$223$	−19.2641			−1.29002			−0.645008	−	0.764176i	$-0.723146\pi$
$223$	−19.2641			−1.29002			−0.645008	+	0.764176i	$0.723146\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.08878	+	1.88583i	−0.0722652	+	0.125167i	−0.899894	−	0.436109i	$-0.856356\pi$
$227$	−1.08878	+	1.88583i	−0.0722652	+	0.125167i	0.827629	+	0.561276i	$0.189689\pi$
$228$		0			0
$229$	−3.10619	−	5.38008i	−0.205263	−	0.355525i	0.744954	−	0.667116i	$-0.232472\pi$
$229$	−3.10619	−	5.38008i	−0.205263	−	0.355525i	−0.950216	+	0.311591i	$0.899138\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.76391	−	11.7154i	−0.443118	−	0.767503i	0.554801	−	0.831983i	$-0.312794\pi$
$233$	−6.76391	−	11.7154i	−0.443118	−	0.767503i	−0.997919	+	0.0644799i	$0.979461\pi$
$234$		0			0
$235$	2.26879	−	3.92967i	0.148000	−	0.256343i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.42797			0.286422			0.143211	−	0.989692i	$-0.454257\pi$
$239$	4.42797			0.286422			0.143211	+	0.989692i	$0.454257\pi$
$240$		0			0
$241$	11.0545	−	19.1470i	0.712084	−	1.23337i	−0.251990	−	0.967730i	$-0.581085\pi$
$241$	11.0545	−	19.1470i	0.712084	−	1.23337i	0.964074	−	0.265635i	$-0.0855817\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.35536	+	0.491842i	0.150478	+	0.0314226i
$246$		0			0
$247$	−0.394175	−	0.682731i	−0.0250808	−	0.0434411i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	29.4679			1.86000			0.929998	−	0.367564i	$-0.119808\pi$
$251$	29.4679			1.86000			0.929998	+	0.367564i	$0.119808\pi$
$252$		0			0
$253$	13.5729			0.853324
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.6027	+	27.0247i	0.973270	+	1.68575i	0.685528	+	0.728046i	$0.259571\pi$
$257$	15.6027	+	27.0247i	0.973270	+	1.68575i	0.287742	+	0.957708i	$0.407095\pi$
$258$		0			0
$259$	14.5279	+	10.5155i	0.902721	+	0.653400i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.4058	+	19.7555i	−0.703314	+	1.21818i	0.263982	+	0.964528i	$0.414964\pi$
$263$	−11.4058	+	19.7555i	−0.703314	+	1.21818i	−0.967296	+	0.253648i	$0.918369\pi$
$264$		0			0
$265$	−0.949836			−0.0583480
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.7838	−	20.4101i	0.718471	−	1.24443i	−0.243135	−	0.969992i	$-0.578176\pi$
$269$	11.7838	−	20.4101i	0.718471	−	1.24443i	0.961606	−	0.274435i	$-0.0884908\pi$
$270$		0			0
$271$	0.0112106	+	0.0194174i	0.000680998	+	0.00117952i	0.866366	−	0.499410i	$-0.166450\pi$
$271$	0.0112106	+	0.0194174i	0.000680998	+	0.00117952i	−0.865685	+	0.500590i	$0.833117\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.0088	−	20.7998i	−0.724155	−	1.25427i
$276$		0			0
$277$	−5.53913	+	9.59405i	−0.332814	+	0.576451i	−0.983062	−	0.183271i	$-0.941331\pi$
$277$	−5.53913	+	9.59405i	−0.332814	+	0.576451i	0.650248	+	0.759722i	$0.274665\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.273084			−0.0162908			−0.00814541	−	0.999967i	$-0.502593\pi$
$281$	−0.273084			−0.0162908			−0.00814541	+	0.999967i	$0.502593\pi$
$282$		0			0
$283$	−5.57676	+	9.65923i	−0.331504	+	0.574181i	−0.982807	−	0.184636i	$-0.940889\pi$
$283$	−5.57676	+	9.65923i	−0.331504	+	0.574181i	0.651303	+	0.758818i	$0.274223\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.5848	−	6.07751i	0.801888	−	0.358744i
$288$		0			0
$289$	−0.0995427	−	0.172413i	−0.00585545	−	0.0101419i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−28.1195			−1.64276			−0.821379	−	0.570382i	$-0.806795\pi$
$293$	−28.1195			−1.64276			−0.821379	+	0.570382i	$0.806795\pi$
$294$		0			0
$295$	−2.90499			−0.169135
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.68758	−	4.65503i	−0.155427	−	0.269207i
$300$		0			0
$301$	−23.9719	+	10.7244i	−1.38172	+	0.618145i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.84863	−	3.20192i	0.105852	−	0.183342i
$306$		0			0
$307$	22.3340			1.27467			0.637333	−	0.770588i	$-0.280037\pi$
$307$	22.3340			1.27467			0.637333	+	0.770588i	$0.280037\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.9513	−	24.1643i	0.791105	−	1.37023i	−0.134179	−	0.990957i	$-0.542840\pi$
$311$	13.9513	−	24.1643i	0.791105	−	1.37023i	0.925283	−	0.379277i	$-0.123827\pi$
$312$		0			0
$313$	6.15786	+	10.6657i	0.348063	+	0.602863i	0.985905	−	0.167304i	$-0.0535062\pi$
$313$	6.15786	+	10.6657i	0.348063	+	0.602863i	−0.637842	+	0.770167i	$0.720173\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.7767	+	23.8619i	0.773775	+	1.34022i	0.935480	+	0.353379i	$0.114967\pi$
$317$	13.7767	+	23.8619i	0.773775	+	1.34022i	−0.161705	+	0.986839i	$0.551699\pi$
$318$		0			0
$319$	8.06155	−	13.9630i	0.451360	−	0.781779i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.67807			−0.0933704
$324$		0			0
$325$	−4.75571	+	8.23713i	−0.263799	+	0.456914i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	28.2923	+	20.4783i	1.55981	+	1.12901i
$330$		0			0
$331$	−5.05585	−	8.75699i	−0.277895	−	0.481327i	0.692967	−	0.720970i	$-0.256303\pi$
$331$	−5.05585	−	8.75699i	−0.277895	−	0.481327i	−0.970861	+	0.239642i	$0.922970\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.89617			0.158235
$336$		0			0
$337$	11.8302			0.644430			0.322215	−	0.946666i	$-0.395573\pi$
$337$	11.8302			0.644430			0.322215	+	0.946666i	$0.395573\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.08433	−	14.0025i	−0.437791	−	0.758276i
$342$		0			0
$343$	−5.62843	+	17.6443i	−0.303907	+	0.952702i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.2249	−	24.6383i	0.763634	−	1.32265i	−0.177331	−	0.984151i	$-0.556746\pi$
$347$	14.2249	−	24.6383i	0.763634	−	1.32265i	0.940966	−	0.338502i	$-0.109920\pi$
$348$		0			0
$349$	−17.5806			−0.941066			−0.470533	−	0.882382i	$-0.655938\pi$
$349$	−17.5806			−0.941066			−0.470533	+	0.882382i	$0.655938\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.7573	+	23.8283i	−0.732225	+	1.26825i	0.223705	+	0.974657i	$0.428185\pi$
$353$	−13.7573	+	23.8283i	−0.732225	+	1.26825i	−0.955930	+	0.293594i	$0.905149\pi$
$354$		0			0
$355$	0.874619	+	1.51489i	0.0464200	+	0.0804018i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.73182	+	16.8560i	0.513626	+	0.889626i	0.999875	+	0.0158059i	$0.00503137\pi$
$359$	9.73182	+	16.8560i	0.513626	+	0.889626i	−0.486249	+	0.873820i	$0.661635\pi$
$360$		0			0
$361$	9.41814	−	16.3127i	0.495691	−	0.858563i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.15149			0.164957
$366$		0			0
$367$	−3.48214	+	6.03125i	−0.181766	+	0.314829i	−0.942482	−	0.334257i	$-0.891515\pi$
$367$	−3.48214	+	6.03125i	−0.181766	+	0.314829i	0.760716	+	0.649085i	$0.224848\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.751185	−	7.27221i	0.0389996	−	0.377554i
$372$		0			0
$373$	6.90747	+	11.9641i	0.357655	+	0.619477i	0.987569	−	0.157188i	$-0.0502430\pi$
$373$	6.90747	+	11.9641i	0.357655	+	0.619477i	−0.629914	+	0.776665i	$0.716910\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.38507			−0.328848
$378$		0			0
$379$	−13.3822			−0.687398			−0.343699	−	0.939080i	$-0.611680\pi$
$379$	−13.3822			−0.687398			−0.343699	+	0.939080i	$0.611680\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.23395	+	3.86931i	0.114149	+	0.197712i	0.917439	−	0.397876i	$-0.130252\pi$
$383$	2.23395	+	3.86931i	0.114149	+	0.197712i	−0.803290	+	0.595588i	$0.796919\pi$
$384$		0			0
$385$	−4.08416	+	1.82715i	−0.208148	+	0.0931202i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.1232	+	24.4620i	−0.716072	+	1.24027i	0.246472	+	0.969150i	$0.420729\pi$
$389$	−14.1232	+	24.4620i	−0.716072	+	1.24027i	−0.962545	+	0.271124i	$0.912605\pi$
$390$		0			0
$391$	−11.4415			−0.578622
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.772037	−	1.33721i	0.0388454	−	0.0672822i
$396$		0			0
$397$	0.293513	+	0.508379i	0.0147310	+	0.0255148i	0.873297	−	0.487188i	$-0.161977\pi$
$397$	0.293513	+	0.508379i	0.0147310	+	0.0255148i	−0.858566	+	0.512703i	$0.828644\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.5150	−	25.1408i	−0.724846	−	1.25547i	−0.959037	−	0.283280i	$-0.908577\pi$
$401$	−14.5150	−	25.1408i	−0.724846	−	1.25547i	0.234191	−	0.972191i	$-0.424756\pi$
$402$		0			0
$403$	−3.20156	+	5.54526i	−0.159481	+	0.276229i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.3486			−1.65303
$408$		0			0
$409$	−11.0021	+	19.0562i	−0.544018	+	0.942267i	0.454650	+	0.890670i	$0.349764\pi$
$409$	−11.0021	+	19.0562i	−0.544018	+	0.942267i	−0.998668	+	0.0515965i	$0.983569\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.29744	−	22.2414i	0.113049	−	1.09443i
$414$		0			0
$415$	1.59138	+	2.75636i	0.0781180	+	0.135304i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−25.1231			−1.22734			−0.613671	−	0.789562i	$-0.710308\pi$
$419$	−25.1231			−1.22734			−0.613671	+	0.789562i	$0.710308\pi$
$420$		0			0
$421$	0.192252			0.00936980			0.00468490	−	0.999989i	$-0.498509\pi$
$421$	0.192252			0.00936980			0.00468490	+	0.999989i	$0.498509\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.1229	+	17.5334i	0.491035	+	0.850497i
$426$		0			0
$427$	23.0528	+	16.6859i	1.11560	+	0.807487i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.7344	+	18.5925i	−0.517057	+	0.895569i	0.482747	+	0.875760i	$0.339639\pi$
$431$	−10.7344	+	18.5925i	−0.517057	+	0.895569i	−0.999804	+	0.0198093i	$0.993694\pi$
$432$		0			0
$433$	−40.3807			−1.94057			−0.970286	−	0.241960i	$-0.922210\pi$
$433$	−40.3807			−1.94057			−0.970286	+	0.241960i	$0.922210\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.558159	+	0.966760i	−0.0267004	+	0.0462464i
$438$		0			0
$439$	16.8288	+	29.1484i	0.803196	+	1.39118i	0.917502	+	0.397731i	$0.130202\pi$
$439$	16.8288	+	29.1484i	0.803196	+	1.39118i	−0.114306	+	0.993446i	$0.536464\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.77416	+	10.0011i	0.274339	+	0.475168i	0.969968	−	0.243232i	$-0.0782078\pi$
$443$	5.77416	+	10.0011i	0.274339	+	0.475168i	−0.695629	+	0.718401i	$0.744874\pi$
$444$		0			0
$445$	1.21770	−	2.10911i	0.0577244	−	0.0999816i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−22.6025			−1.06668			−0.533338	−	0.845902i	$-0.679063\pi$
$449$	−22.6025			−1.06668			−0.533338	+	0.845902i	$0.679063\pi$
$450$		0			0
$451$	−13.8368	+	23.9661i	−0.651550	+	1.12852i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.43535	+	1.03892i	0.0672903	+	0.0487055i
$456$		0			0
$457$	−1.04064	−	1.80244i	−0.0486792	−	0.0843148i	0.840659	−	0.541565i	$-0.182168\pi$
$457$	−1.04064	−	1.80244i	−0.0486792	−	0.0843148i	−0.889338	+	0.457250i	$0.848835\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	8.43675			0.392939			0.196469	−	0.980510i	$-0.437052\pi$
$461$	8.43675			0.392939			0.196469	+	0.980510i	$0.437052\pi$
$462$		0			0
$463$	−5.84462			−0.271623			−0.135811	−	0.990735i	$-0.543364\pi$
$463$	−5.84462			−0.271623			−0.135811	+	0.990735i	$0.543364\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.04009	−	1.80149i	−0.0481298	−	0.0833632i	0.840957	−	0.541102i	$-0.181993\pi$
$467$	−1.04009	−	1.80149i	−0.0481298	−	0.0833632i	−0.889087	+	0.457739i	$0.848659\pi$
$468$		0			0
$469$	−2.29046	+	22.1739i	−0.105764	+	1.02390i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	24.4165	−	42.2907i	1.12267	−	1.94453i
$474$		0			0
$475$	1.97534			0.0906348
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.51538	+	14.7491i	−0.389077	+	0.673902i	−0.992326	−	0.123652i	$-0.960539\pi$
$479$	−8.51538	+	14.7491i	−0.389077	+	0.673902i	0.603248	+	0.797553i	$0.293873\pi$
$480$		0			0
$481$	6.60335	+	11.4373i	0.301087	+	0.521498i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.451091	+	0.781312i	0.0204830	+	0.0354775i
$486$		0			0
$487$	−11.0758	+	19.1838i	−0.501892	+	0.869302i	0.498106	+	0.867116i	$0.334029\pi$
$487$	−11.0758	+	19.1838i	−0.501892	+	0.869302i	−0.999998	+	0.00218582i	$0.999304\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.76779			0.260297			0.130148	−	0.991495i	$-0.458455\pi$
$491$	5.76779			0.260297			0.130148	+	0.991495i	$0.458455\pi$
$492$		0			0
$493$	−6.79559	+	11.7703i	−0.306058	+	0.530108i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.2901	+	5.49827i	−0.551286	+	0.246631i
$498$		0			0
$499$	5.16034	+	8.93797i	0.231008	+	0.400118i	0.958105	−	0.286417i	$-0.0924642\pi$
$499$	5.16034	+	8.93797i	0.231008	+	0.400118i	−0.727097	+	0.686535i	$0.759131\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.4644			1.31375			0.656876	−	0.753998i	$-0.271877\pi$
$503$	29.4644			1.31375			0.656876	+	0.753998i	$0.271877\pi$
$504$		0			0
$505$	5.39852			0.240231
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.87465	+	3.24698i	0.0830922	+	0.143920i	0.904577	−	0.426311i	$-0.140187\pi$
$509$	1.87465	+	3.24698i	0.0830922	+	0.143920i	−0.821484	+	0.570231i	$0.806854\pi$
$510$		0			0
$511$	−2.49238	+	24.1287i	−0.110257	+	1.06739i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.33074	+	2.30491i	−0.0586394	+	0.101566i
$516$		0			0
$517$	−64.9445			−2.85626
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.9592	+	24.1780i	−0.611562	+	1.05926i	0.379415	+	0.925226i	$0.376125\pi$
$521$	−13.9592	+	24.1780i	−0.611562	+	1.05926i	−0.990977	+	0.134030i	$0.957208\pi$
$522$		0			0
$523$	21.0680	+	36.4909i	0.921240	+	1.59563i	0.797499	+	0.603320i	$0.206156\pi$
$523$	21.0680	+	36.4909i	0.921240	+	1.59563i	0.123741	+	0.992315i	$0.460511\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.81480	+	11.8036i	0.296857	+	0.514172i
$528$		0			0
$529$	7.69433	−	13.3270i	0.334536	−	0.579434i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.9593			0.474701
$534$		0			0
$535$	−2.10694	+	3.64934i	−0.0910912	+	0.157775i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.7592	−	32.7145i	−0.463431	−	1.40911i
$540$		0			0
$541$	−14.5992	−	25.2865i	−0.627667	−	1.08715i	−0.988019	−	0.154334i	$-0.950677\pi$
$541$	−14.5992	−	25.2865i	−0.627667	−	1.08715i	0.360352	−	0.932816i	$-0.382657\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.36410			0.144102
$546$		0			0
$547$	−11.5224			−0.492664			−0.246332	−	0.969186i	$-0.579225\pi$
$547$	−11.5224			−0.492664			−0.246332	+	0.969186i	$0.579225\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.663029	+	1.14840i	0.0282460	+	0.0489235i
$552$		0			0
$553$	9.62746	+	6.96847i	0.409401	+	0.296330i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.97631	−	10.3513i	0.253224	−	0.438597i	−0.711187	−	0.703002i	$-0.751842\pi$
$557$	5.97631	−	10.3513i	0.253224	−	0.438597i	0.964412	+	0.264405i	$0.0851756\pi$
$558$		0			0
$559$	−19.3389			−0.817947
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.8099	−	20.4553i	0.497728	−	0.862090i	−0.502269	−	0.864711i	$-0.667501\pi$
$563$	11.8099	−	20.4553i	0.497728	−	0.862090i	0.999997	+	0.00262192i	$0.000834585\pi$
$564$		0			0
$565$	0.875375	+	1.51619i	0.0368273	+	0.0637868i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.9745	+	20.7405i	0.501999	+	0.869487i	0.999997	+	0.00230931i	$0.000735078\pi$
$569$	11.9745	+	20.7405i	0.501999	+	0.869487i	−0.497999	+	0.867178i	$0.665932\pi$
$570$		0			0
$571$	−5.04958	+	8.74614i	−0.211319	+	0.366014i	−0.952127	−	0.305701i	$-0.901109\pi$
$571$	−5.04958	+	8.74614i	−0.211319	+	0.366014i	0.740809	+	0.671716i	$0.234442\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.4683			0.561669
$576$		0			0
$577$	16.1744	−	28.0149i	0.673348	−	1.16627i	−0.303600	−	0.952800i	$-0.598189\pi$
$577$	16.1744	−	28.0149i	0.673348	−	1.16627i	0.976949	−	0.213474i	$-0.0684780\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−22.3620	+	10.0042i	−0.927733	+	0.415044i
$582$		0			0
$583$	6.79729	+	11.7733i	0.281515	+	0.487598i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.0549			−0.415011			−0.207505	−	0.978234i	$-0.566534\pi$
$587$	−10.0549			−0.415011			−0.207505	+	0.978234i	$0.566534\pi$
$588$		0			0
$589$	1.32981			0.0547937
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17.0673	−	29.5613i	−0.700868	−	1.21394i	−0.968162	−	0.250324i	$-0.919463\pi$
$593$	−17.0673	−	29.5613i	−0.700868	−	1.21394i	0.267294	−	0.963615i	$-0.413870\pi$
$594$		0			0
$595$	3.44280	−	1.54022i	0.141141	−	0.0631429i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.2141	−	26.3517i	0.621633	−	1.07670i	−0.367549	−	0.930004i	$-0.619803\pi$
$599$	15.2141	−	26.3517i	0.621633	−	1.07670i	0.989182	−	0.146695i	$-0.0468637\pi$
$600$		0			0
$601$	−47.3933			−1.93321			−0.966606	−	0.256268i	$-0.917507\pi$
$601$	−47.3933			−1.93321			−0.966606	+	0.256268i	$0.917507\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.26936	−	3.93064i	0.0922625	−	0.159803i
$606$		0			0
$607$	21.9060	+	37.9422i	0.889135	+	1.54003i	0.840899	+	0.541192i	$0.182027\pi$
$607$	21.9060	+	37.9422i	0.889135	+	1.54003i	0.0482359	+	0.998836i	$0.484640\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.8597	+	22.2736i	0.520247	+	0.901094i
$612$		0			0
$613$	0.997163	−	1.72714i	0.0402750	−	0.0697584i	−0.845185	−	0.534474i	$-0.820510\pi$
$613$	0.997163	−	1.72714i	0.0402750	−	0.0697584i	0.885460	+	0.464715i	$0.153843\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	42.1124			1.69538			0.847690	−	0.530492i	$-0.177993\pi$
$617$	42.1124			1.69538			0.847690	+	0.530492i	$0.177993\pi$
$618$		0			0
$619$	−5.88221	+	10.1883i	−0.236426	+	0.409502i	−0.959686	−	0.281074i	$-0.909309\pi$
$619$	−5.88221	+	10.1883i	−0.236426	+	0.409502i	0.723260	+	0.690576i	$0.242643\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.1849	+	10.9910i	0.608372	+	0.440347i
$624$		0			0
$625$	−11.6208	−	20.1278i	−0.464833	−	0.805114i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	28.1116			1.12088
$630$		0			0
$631$	37.3202			1.48570			0.742848	−	0.669460i	$-0.233475\pi$
$631$	37.3202			1.48570			0.742848	+	0.669460i	$0.233475\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.385401	+	0.667534i	0.0152942	+	0.0264903i
$636$		0			0
$637$	−9.08945	+	10.1678i	−0.360137	+	0.402863i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−20.2296	+	35.0387i	−0.799022	+	1.38395i	0.121231	+	0.992624i	$0.461316\pi$
$641$	−20.2296	+	35.0387i	−0.799022	+	1.38395i	−0.920254	+	0.391323i	$0.872018\pi$
$642$		0			0
$643$	−2.86891			−0.113139			−0.0565693	−	0.998399i	$-0.518016\pi$
$643$	−2.86891			−0.113139			−0.0565693	+	0.998399i	$0.518016\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.71712	−	2.97413i	0.0675068	−	0.116925i	−0.830296	−	0.557322i	$-0.811829\pi$
$647$	1.71712	−	2.97413i	0.0675068	−	0.116925i	0.897803	+	0.440397i	$0.145162\pi$
$648$		0			0
$649$	20.7889	+	36.0075i	0.816038	+	1.41342i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.2475	−	21.2133i	−0.479283	−	0.830142i	0.520435	−	0.853901i	$-0.325770\pi$
$653$	−12.2475	−	21.2133i	−0.479283	−	0.830142i	−0.999718	+	0.0237590i	$0.992437\pi$
$654$		0			0
$655$	−1.28118	+	2.21907i	−0.0500599	+	0.0867064i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−23.2750			−0.906664			−0.453332	−	0.891342i	$-0.649765\pi$
$659$	−23.2750			−0.906664			−0.453332	+	0.891342i	$0.649765\pi$
$660$		0			0
$661$	16.7899	−	29.0809i	0.653051	−	1.13112i	−0.329328	−	0.944216i	$-0.606822\pi$
$661$	16.7899	−	29.0809i	0.653051	−	1.13112i	0.982379	−	0.186902i	$-0.0598446\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.0378102	−	0.366040i	0.00146622	−	0.0141944i
$666$		0			0
$667$	4.52069	+	7.83007i	0.175042	+	0.303182i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−52.9173			−2.04285
$672$		0			0
$673$	46.7162			1.80078			0.900388	−	0.435088i	$-0.143283\pi$
$673$	46.7162			1.80078			0.900388	+	0.435088i	$0.143283\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.73653	−	3.00777i	−0.0667404	−	0.115598i	0.830724	−	0.556684i	$-0.187927\pi$
$677$	−1.73653	−	3.00777i	−0.0667404	−	0.115598i	−0.897465	+	0.441086i	$0.854593\pi$
$678$		0			0
$679$	−6.33869	+	2.83577i	−0.243257	+	0.108827i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.49075	+	6.04615i	−0.133570	+	0.231349i	−0.925050	−	0.379845i	$-0.875977\pi$
$683$	−3.49075	+	6.04615i	−0.133570	+	0.231349i	0.791480	+	0.611194i	$0.209311\pi$
$684$		0			0
$685$	2.90348			0.110936
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.69187	−	4.66245i	0.102552	−	0.177625i
$690$		0			0
$691$	−16.5416	−	28.6509i	−0.629272	−	1.08993i	−0.987698	−	0.156373i	$-0.950020\pi$
$691$	−16.5416	−	28.6509i	−0.629272	−	1.08993i	0.358426	−	0.933558i	$-0.383314\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.626813	−	1.08567i	−0.0237764	−	0.0411819i
$696$		0			0
$697$	11.6639	−	20.2025i	0.441803	−	0.765225i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	39.4243			1.48904			0.744518	−	0.667602i	$-0.232679\pi$
$701$	39.4243			1.48904			0.744518	+	0.667602i	$0.232679\pi$
$702$		0			0
$703$	1.37139	−	2.37532i	0.0517230	−	0.0895868i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.26947	+	41.3326i	−0.160570	+	1.55447i
$708$		0			0
$709$	−10.5771	−	18.3201i	−0.397232	−	0.688026i	0.596151	−	0.802872i	$-0.296696\pi$
$709$	−10.5771	−	18.3201i	−0.397232	−	0.688026i	−0.993383	+	0.114846i	$0.963363\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.06694			0.339559
$714$		0			0
$715$	−3.29482			−0.123219
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.7586	−	23.8305i	−0.513108	−	0.888729i	−0.999884	−	0.0152024i	$-0.995161\pi$
$719$	−13.7586	−	23.8305i	−0.513108	−	0.888729i	0.486777	−	0.873527i	$-0.338173\pi$
$720$		0			0
$721$	−16.5946	−	12.0114i	−0.618016	−	0.447327i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.99942	−	13.8554i	0.297091	−	0.514577i
$726$		0			0
$727$	21.0190			0.779550			0.389775	−	0.920910i	$-0.372553\pi$
$727$	21.0190			0.779550			0.389775	+	0.920910i	$0.372553\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.5822	+	35.6495i	−0.761262	+	1.31854i
$732$		0			0
$733$	3.21219	+	5.56368i	0.118645	+	0.205499i	0.919231	−	0.393719i	$-0.128812\pi$
$733$	3.21219	+	5.56368i	0.118645	+	0.205499i	−0.800586	+	0.599218i	$0.795478\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−20.7258	−	35.8982i	−0.763445	−	1.32233i
$738$		0			0
$739$	19.2219	−	33.2933i	0.707089	−	1.22471i	−0.258844	−	0.965919i	$-0.583342\pi$
$739$	19.2219	−	33.2933i	0.707089	−	1.22471i	0.965932	−	0.258794i	$-0.0833252\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.7146			0.723257			0.361629	−	0.932322i	$-0.382221\pi$
$743$	19.7146			0.723257			0.361629	+	0.932322i	$0.382221\pi$
$744$		0			0
$745$	0.0505562	−	0.0875658i	0.00185223	−	0.00320816i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−26.2740	−	19.0175i	−0.960033	−	0.694883i
$750$		0			0
$751$	−11.4624	−	19.8534i	−0.418268	−	0.724461i	0.577497	−	0.816392i	$-0.304029\pi$
$751$	−11.4624	−	19.8534i	−0.418268	−	0.724461i	−0.995765	+	0.0919312i	$0.970696\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.60114			0.240240
$756$		0			0
$757$	−52.3408			−1.90236			−0.951179	−	0.308639i	$-0.900127\pi$
$757$	−52.3408			−1.90236			−0.951179	+	0.308639i	$0.900127\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.939077	+	1.62653i	0.0340415	+	0.0589616i	0.882544	−	0.470229i	$-0.155829\pi$
$761$	0.939077	+	1.62653i	0.0340415	+	0.0589616i	−0.848503	+	0.529191i	$0.822495\pi$
$762$		0			0
$763$	−2.66053	+	25.7565i	−0.0963175	+	0.932448i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.23284	−	14.2597i	0.297271	−	0.514888i
$768$		0			0
$769$	26.8119			0.966862			0.483431	−	0.875382i	$-0.339390\pi$
$769$	26.8119			0.966862			0.483431	+	0.875382i	$0.339390\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.67835	+	8.10314i	−0.168268	+	0.291450i	−0.937811	−	0.347146i	$-0.887151\pi$
$773$	−4.67835	+	8.10314i	−0.168268	+	0.291450i	0.769543	+	0.638595i	$0.220484\pi$
$774$		0			0
$775$	−8.02203	−	13.8946i	−0.288160	−	0.499107i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.13802	−	1.97111i	−0.0407738	−	0.0706223i
$780$		0			0
$781$	12.5180	−	21.6819i	0.447931	−	0.775839i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.50868			0.160922
$786$		0			0
$787$	−9.43675	+	16.3449i	−0.336384	+	0.582634i	−0.983750	−	0.179546i	$-0.942537\pi$
$787$	−9.43675	+	16.3449i	−0.336384	+	0.582634i	0.647366	+	0.762179i	$0.275871\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.3007	+	5.50302i	−0.437363	+	0.195665i
$792$		0			0
$793$	10.4782	+	18.1487i	0.372090	+	0.644479i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.8047			−1.26827			−0.634134	−	0.773223i	$-0.718643\pi$
$797$	−35.8047			−1.26827			−0.634134	+	0.773223i	$0.718643\pi$
$798$		0			0
$799$	54.7459			1.93677
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22.5530	−	39.0629i	−0.795877	−	1.37850i
$804$		0			0
$805$	0.257799	−	2.49575i	0.00908623	−	0.0879637i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−18.8027	+	32.5672i	−0.661068	+	1.14500i	0.319268	+	0.947665i	$0.396563\pi$
$809$	−18.8027	+	32.5672i	−0.661068	+	1.14500i	−0.980335	+	0.197338i	$0.936770\pi$
$810$		0			0
$811$	−38.9673			−1.36833			−0.684163	−	0.729329i	$-0.739832\pi$
$811$	−38.9673			−1.36833			−0.684163	+	0.729329i	$0.739832\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.170559	+	0.295418i	−0.00597443	+	0.0103480i
$816$		0			0
$817$	2.00816	+	3.47823i	0.0702565	+	0.121688i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5874	+	21.8020i	0.439304	+	0.760897i	0.997636	−	0.0687210i	$-0.0218918\pi$
$821$	12.5874	+	21.8020i	0.439304	+	0.760897i	−0.558332	+	0.829618i	$0.688558\pi$
$822$		0			0
$823$	−3.91792	+	6.78604i	−0.136570	+	0.236546i	−0.926196	−	0.377042i	$-0.876941\pi$
$823$	−3.91792	+	6.78604i	−0.136570	+	0.236546i	0.789626	+	0.613588i	$0.210275\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.4941			−0.643103			−0.321552	−	0.946892i	$-0.604204\pi$
$827$	−18.4941			−0.643103			−0.321552	+	0.946892i	$0.604204\pi$
$828$		0			0
$829$	−6.83264	+	11.8345i	−0.237307	+	0.411029i	−0.959941	−	0.280203i	$-0.909598\pi$
$829$	−6.83264	+	11.8345i	−0.237307	+	0.411029i	0.722633	+	0.691232i	$0.242932\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.06960	+	27.5771i	0.314243	+	0.955491i
$834$		0			0
$835$	−2.38224	−	4.12616i	−0.0824407	−	0.142791i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	51.0340			1.76189			0.880945	−	0.473218i	$-0.156908\pi$
$839$	51.0340			1.76189			0.880945	+	0.473218i	$0.156908\pi$
$840$		0			0
$841$	−18.2599			−0.629651
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.58188	−	2.73990i	−0.0544185	−	0.0942556i
$846$		0			0
$847$	28.2994	+	20.4834i	0.972378	+	0.703819i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.35047	−	16.1955i	0.320530	−	0.555174i
$852$		0			0
$853$	−15.8526			−0.542782			−0.271391	−	0.962469i	$-0.587484\pi$
$853$	−15.8526			−0.542782			−0.271391	+	0.962469i	$0.587484\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.1000	−	36.5464i	0.720764	−	1.24840i	−0.239930	−	0.970790i	$-0.577125\pi$
$857$	21.1000	−	36.5464i	0.720764	−	1.24840i	0.960694	−	0.277610i	$-0.0895421\pi$
$858$		0			0
$859$	14.1628	+	24.5307i	0.483228	+	0.836976i	0.999815	−	0.0192593i	$-0.00613079\pi$
$859$	14.1628	+	24.5307i	0.483228	+	0.836976i	−0.516586	+	0.856235i	$0.672797\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17.6891	+	30.6385i	0.602145	+	1.04295i	0.992496	+	0.122279i	$0.0390203\pi$
$863$	17.6891	+	30.6385i	0.602145	+	1.04295i	−0.390351	+	0.920666i	$0.627646\pi$
$864$		0			0
$865$	−0.860179	+	1.48987i	−0.0292470	+	0.0506572i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−22.0997			−0.749679
$870$		0			0
$871$	−8.20784	+	14.2164i	−0.278112	+	0.481704i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.20346	+	3.67002i	−0.277327	+	0.124069i
$876$		0			0
$877$	−6.47664	−	11.2179i	−0.218700	−	0.378800i	0.735710	−	0.677296i	$-0.236848\pi$
$877$	−6.47664	−	11.2179i	−0.218700	−	0.378800i	−0.954411	+	0.298496i	$0.903515\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.1995			0.882683			0.441341	−	0.897339i	$-0.354503\pi$
$881$	26.1995			0.882683			0.441341	+	0.897339i	$0.354503\pi$
$882$		0			0
$883$	−6.36625			−0.214241			−0.107121	−	0.994246i	$-0.534163\pi$
$883$	−6.36625			−0.214241			−0.107121	+	0.994246i	$0.534163\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.0538	+	41.6625i	0.807649	+	1.39889i	0.914488	+	0.404612i	$0.132593\pi$
$887$	24.0538	+	41.6625i	0.807649	+	1.39889i	−0.106840	+	0.994276i	$0.534073\pi$
$888$		0			0
$889$	−5.41562	+	2.42281i	−0.181634	+	0.0812585i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.67071	−	4.62580i	0.0893718	−	0.154797i
$894$		0			0
$895$	−7.43165			−0.248412
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.38524	−	9.32751i	0.179608	−	0.311090i
$900$		0			0
$901$	−5.72987	−	9.92443i	−0.190890	−	0.330631i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.47446	−	7.74999i	−0.148736	−	0.257619i
$906$		0			0
$907$	21.7040	−	37.5925i	0.720671	−	1.24824i	−0.240061	−	0.970758i	$-0.577167\pi$
$907$	21.7040	−	37.5925i	0.720671	−	1.24824i	0.960731	−	0.277480i	$-0.0894993\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.0282			0.762957			0.381479	−	0.924378i	$-0.375415\pi$
$911$	23.0282			0.762957			0.381479	+	0.924378i	$0.375415\pi$
$912$		0			0
$913$	22.7768	−	39.4506i	0.753802	−	1.30562i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.9766	−	11.5641i	−0.527594	−	0.381879i
$918$		0			0
$919$	−17.2599	−	29.8950i	−0.569351	−	0.986145i	−0.996630	−	0.0820251i	$-0.973861\pi$
$919$	−17.2599	−	29.8950i	−0.569351	−	0.986145i	0.427279	−	0.904120i	$-0.359472\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.91480			−0.326350
$924$		0			0
$925$	−33.0916			−1.08804
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.3176	−	24.7988i	−0.469746	−	0.813623i	0.529656	−	0.848213i	$-0.322321\pi$
$929$	−14.3176	−	24.7988i	−0.469746	−	0.813623i	−0.999402	+	0.0345892i	$0.988988\pi$
$930$		0			0
$931$	2.77260	+	0.578971i	0.0908684	+	0.0189750i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.50666	+	6.07370i	−0.114680	+	0.198631i
$936$		0			0
$937$	13.9020			0.454158			0.227079	−	0.973876i	$-0.427083\pi$
$937$	13.9020			0.454158			0.227079	+	0.973876i	$0.427083\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.4340	+	31.9286i	−0.600930	+	1.04084i	0.391750	+	0.920072i	$0.371870\pi$
$941$	−18.4340	+	31.9286i	−0.600930	+	1.04084i	−0.992681	+	0.120770i	$0.961464\pi$
$942$		0			0
$943$	−7.75930	−	13.4395i	−0.252678	−	0.437650i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.8909	−	32.7200i	−0.613872	−	1.06326i	−0.990581	−	0.136925i	$-0.956278\pi$
$947$	−18.8909	−	32.7200i	−0.613872	−	1.06326i	0.376710	−	0.926331i	$-0.377055\pi$
$948$		0			0
$949$	−8.93143	+	15.4697i	−0.289926	+	0.502167i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.5184			−1.40970			−0.704850	−	0.709356i	$-0.748986\pi$
$953$	−43.5184			−1.40970			−0.704850	+	0.709356i	$0.748986\pi$
$954$		0			0
$955$	3.04294	−	5.27052i	0.0984672	−	0.170550i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.29624	+	22.2299i	−0.0741495	+	0.717840i
$960$		0			0
$961$	10.0995	+	17.4929i	0.325792	+	0.564288i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.01894			0.0328007
$966$		0			0
$967$	35.6064			1.14502			0.572512	−	0.819896i	$-0.305969\pi$
$967$	35.6064			1.14502			0.572512	+	0.819896i	$0.305969\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.2654	+	31.6366i	0.586164	+	1.01527i	0.994729	+	0.102537i	$0.0326960\pi$
$971$	18.2654	+	31.6366i	0.586164	+	1.01527i	−0.408565	+	0.912729i	$0.633971\pi$
$972$		0			0
$973$	8.80792	−	3.94044i	0.282369	−	0.126325i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.6369	−	20.1558i	0.372299	−	0.644840i	−0.617620	−	0.786477i	$-0.711903\pi$
$977$	11.6369	−	20.1558i	0.372299	−	0.644840i	0.989919	+	0.141637i	$0.0452364\pi$
$978$		0			0
$979$	−34.8568			−1.11403
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.01170	−	3.48437i	0.0641634	−	0.111134i	−0.832159	−	0.554537i	$-0.812895\pi$
$983$	2.01170	−	3.48437i	0.0641634	−	0.111134i	0.896323	+	0.443403i	$0.146229\pi$
$984$		0			0
$985$	−3.13414	−	5.42848i	−0.0998619	−	0.172966i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.6921	+	23.7154i	0.435384	+	0.754107i
$990$		0			0
$991$	21.3820	−	37.0348i	0.679223	−	1.17645i	−0.295993	−	0.955190i	$-0.595650\pi$
$991$	21.3820	−	37.0348i	0.679223	−	1.17645i	0.975215	−	0.221258i	$-0.0710163\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.10905			0.0351593
$996$		0			0
$997$	4.03324	−	6.98578i	0.127734	−	0.221242i	−0.795064	−	0.606525i	$-0.792563\pi$
$997$	4.03324	−	6.98578i	0.127734	−	0.221242i	0.922798	+	0.385283i	$0.125896\pi$
$998$		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.1621.5	yes	16
3.2	odd	2	inner	2268.2.k.g.1621.4	yes	16
7.2	even	3	inner	2268.2.k.g.1297.5	yes	16
9.2	odd	6		2268.2.l.n.109.5		16
9.4	even	3		2268.2.i.n.865.5		16
9.5	odd	6		2268.2.i.n.865.4		16
9.7	even	3		2268.2.l.n.109.4		16
21.2	odd	6	inner	2268.2.k.g.1297.4	✓	16
63.2	odd	6		2268.2.i.n.2053.4		16
63.16	even	3		2268.2.i.n.2053.5		16
63.23	odd	6		2268.2.l.n.541.5		16
63.58	even	3		2268.2.l.n.541.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.4		16	9.5	odd	6
2268.2.i.n.865.5		16	9.4	even	3
2268.2.i.n.2053.4		16	63.2	odd	6
2268.2.i.n.2053.5		16	63.16	even	3
2268.2.k.g.1297.4	✓	16	21.2	odd	6	inner
2268.2.k.g.1297.5	yes	16	7.2	even	3	inner
2268.2.k.g.1621.4	yes	16	3.2	odd	2	inner
2268.2.k.g.1621.5	yes	16	1.1	even	1	trivial
2268.2.l.n.109.4		16	9.7	even	3
2268.2.l.n.109.5		16	9.2	odd	6
2268.2.l.n.541.4		16	63.58	even	3
2268.2.l.n.541.5		16	63.23	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.171869 + 0.297685i) q^{5} +(-2.41508 + 1.08045i) q^{7} +O(q^{10})\)	\(q+(0.171869 + 0.297685i) q^{5} +(-2.41508 + 1.08045i) q^{7} +(2.45988 - 4.26064i) q^{11} -1.94832 q^{13} +(-2.07359 + 3.59156i) q^{17} +(0.202315 + 0.350420i) q^{19} +(1.37943 + 2.38925i) q^{23} +(2.44092 - 4.22780i) q^{25} +3.27721 q^{29} +(1.64324 - 2.84617i) q^{31} +(-0.736710 - 0.533240i) q^{35} +(-3.38925 - 5.87035i) q^{37} -5.62500 q^{41} +9.92590 q^{43} +(-6.60038 - 11.4322i) q^{47} +(4.66527 - 5.21874i) q^{49} +(-1.38163 + 2.39306i) q^{53} +1.69110 q^{55} +(-4.22560 + 7.31896i) q^{59} +(-5.37804 - 9.31503i) q^{61} +(-0.334856 - 0.579987i) q^{65} +(4.21277 - 7.29673i) q^{67} +5.08888 q^{71} +(4.58416 - 7.94000i) q^{73} +(-1.33742 + 12.9476i) q^{77} +(-2.24601 - 3.89020i) q^{79} +9.25931 q^{83} -1.42554 q^{85} +(-3.54253 - 6.13584i) q^{89} +(4.70537 - 2.10506i) q^{91} +(-0.0695431 + 0.120452i) q^{95} +2.62462 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{7}+O(q^{10}) \) 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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