LMFDB - Embedded newform 2268.2.i.n.2053.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 $ x^16 - 9x^14 + 31x^12 - 282x^10 + 1695x^8 - 3318x^6 + 4606x^4 - 4116*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2053.4
Root			$1.30887 + 2.01944i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.n.865.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +O(q^{10})$	$q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +(-2.45988 + 4.26064i) q^{11} +(0.974162 - 1.68730i) q^{13} +(2.07359 + 3.59156i) q^{17} +(0.202315 - 0.350420i) q^{19} +(-1.37943 - 2.38925i) q^{23} +(2.44092 - 4.22780i) q^{25} +(1.63861 + 2.83815i) q^{29} -3.28647 q^{31} +(0.736710 - 0.533240i) q^{35} +(-3.38925 + 5.87035i) q^{37} +(-2.81250 + 4.87139i) q^{41} +(-4.96295 - 8.59608i) q^{43} -13.2008 q^{47} +(-6.85220 + 1.43087i) q^{49} +(1.38163 + 2.39306i) q^{53} +1.69110 q^{55} -8.45121 q^{59} +10.7561 q^{61} -0.669711 q^{65} -8.42554 q^{67} -5.08888 q^{71} +(4.58416 + 7.94000i) q^{73} +(-11.8816 - 5.31554i) q^{77} +4.49202 q^{79} +(4.62966 + 8.01880i) q^{83} +(0.712770 - 1.23455i) q^{85} +(3.54253 - 6.13584i) q^{89} +(4.70537 + 2.10506i) q^{91} -0.139086 q^{95} +(-1.31231 - 2.27299i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) $ 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.171869	−	0.297685i	−0.0768620	−	0.133129i	0.825032	−	0.565085i	$-0.191157\pi$
$5$	−0.171869	−	0.297685i	−0.0768620	−	0.133129i	−0.901894	+	0.431956i	$0.857823\pi$
$6$		0			0
$7$	0.271847	+	2.63175i	0.102749	+	0.994707i
$7$	0.271847	+	2.63175i	0.102749	+	0.994707i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.45988	+	4.26064i	−0.741682	+	1.28463i	0.210048	+	0.977691i	$0.432638\pi$
$11$	−2.45988	+	4.26064i	−0.741682	+	1.28463i	−0.951729	+	0.306939i	$0.900695\pi$
$12$		0			0
$13$	0.974162	−	1.68730i	0.270184	−	0.467972i	−0.698725	−	0.715391i	$-0.746249\pi$
$13$	0.974162	−	1.68730i	0.270184	−	0.467972i	0.968909	+	0.247418i	$0.0795821\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.07359	+	3.59156i	0.502919	+	0.871082i	0.999994	+	0.00337409i	$0.00107401\pi$
$17$	2.07359	+	3.59156i	0.502919	+	0.871082i	−0.497075	+	0.867708i	$0.665593\pi$
$18$		0			0
$19$	0.202315	−	0.350420i	0.0464142	−	0.0803918i	−0.841885	−	0.539657i	$-0.818554\pi$
$19$	0.202315	−	0.350420i	0.0464142	−	0.0803918i	0.888299	+	0.459265i	$0.151887\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.37943	−	2.38925i	−0.287631	−	0.498192i	0.685612	−	0.727967i	$-0.259535\pi$
$23$	−1.37943	−	2.38925i	−0.287631	−	0.498192i	−0.973244	+	0.229774i	$0.926201\pi$
$24$		0			0
$25$	2.44092	−	4.22780i	0.488184	−	0.845560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.63861	+	2.83815i	0.304282	+	0.527031i	0.977101	−	0.212775i	$-0.0682503\pi$
$29$	1.63861	+	2.83815i	0.304282	+	0.527031i	−0.672819	+	0.739807i	$0.734917\pi$
$30$		0			0
$31$	−3.28647			−0.590268			−0.295134	−	0.955456i	$-0.595364\pi$
$31$	−3.28647			−0.590268			−0.295134	+	0.955456i	$0.595364\pi$
$32$		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	0.440541	+	0.897733i	$0.354787\pi$
$37$	−3.38925	+	5.87035i	−0.557189	+	0.965079i	−0.997730	+	0.0673466i	$0.978547\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.81250	+	4.87139i	−0.439238	+	0.760783i	−0.997631	−	0.0687936i	$-0.978085\pi$
$41$	−2.81250	+	4.87139i	−0.439238	+	0.760783i	0.558392	+	0.829577i	$0.311418\pi$
$42$		0			0
$43$	−4.96295	−	8.59608i	−0.756843	−	1.31089i	−0.944453	−	0.328647i	$-0.893407\pi$
$43$	−4.96295	−	8.59608i	−0.756843	−	1.31089i	0.187610	−	0.982244i	$-0.439926\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−13.2008			−1.92553			−0.962764	−	0.270344i	$-0.912862\pi$
$47$	−13.2008			−1.92553			−0.962764	+	0.270344i	$0.912862\pi$
$48$		0			0
$49$	−6.85220	+	1.43087i	−0.978885	+	0.204410i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.38163	+	2.39306i	0.189782	+	0.328711i	0.945177	−	0.326557i	$-0.105889\pi$
$53$	1.38163	+	2.39306i	0.189782	+	0.328711i	−0.755396	+	0.655269i	$0.772555\pi$
$54$		0			0
$55$	1.69110			0.228028
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.45121			−1.10025			−0.550127	−	0.835081i	$-0.685421\pi$
$59$	−8.45121			−1.10025			−0.550127	+	0.835081i	$0.685421\pi$
$60$		0			0
$61$	10.7561			1.37717			0.688587	−	0.725154i	$-0.258231\pi$
$61$	10.7561			1.37717			0.688587	+	0.725154i	$0.258231\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.669711			−0.0830675
$66$		0			0
$67$	−8.42554			−1.02934			−0.514672	−	0.857387i	$-0.672086\pi$
$67$	−8.42554			−1.02934			−0.514672	+	0.857387i	$0.672086\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.08888			−0.603939			−0.301970	−	0.953318i	$-0.597644\pi$
$71$	−5.08888			−0.603939			−0.301970	+	0.953318i	$0.597644\pi$
$72$		0			0
$73$	4.58416	+	7.94000i	0.536535	+	0.929306i	0.999087	+	0.0427143i	$0.0136005\pi$
$73$	4.58416	+	7.94000i	0.536535	+	0.929306i	−0.462552	+	0.886592i	$0.653066\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.8816	−	5.31554i	−1.35404	−	0.605762i
$78$		0			0
$79$	4.49202			0.505392			0.252696	−	0.967546i	$-0.418683\pi$
$79$	4.49202			0.505392			0.252696	+	0.967546i	$0.418683\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.62966	+	8.01880i	0.508171	+	0.880178i	0.999955	+	0.00946064i	$0.00301146\pi$
$83$	4.62966	+	8.01880i	0.508171	+	0.880178i	−0.491784	+	0.870717i	$0.663655\pi$
$84$		0			0
$85$	0.712770	−	1.23455i	0.0773107	−	0.133906i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.54253	−	6.13584i	0.375507	−	0.650397i	−0.614896	−	0.788608i	$-0.710802\pi$
$89$	3.54253	−	6.13584i	0.375507	−	0.650397i	0.990403	+	0.138211i	$0.0441353\pi$
$90$		0			0
$91$	4.70537	+	2.10506i	0.493257	+	0.220670i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.139086			−0.0142700
$96$		0			0
$97$	−1.31231	−	2.27299i	−0.133245	−	0.230787i	0.791681	−	0.610935i	$-0.209206\pi$
$97$	−1.31231	−	2.27299i	−0.133245	−	0.230787i	−0.924926	+	0.380148i	$0.875873\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.85269	+	13.6013i	−0.781372	+	1.35338i	0.149771	+	0.988721i	$0.452146\pi$
$101$	−7.85269	+	13.6013i	−0.781372	+	1.35338i	−0.931143	+	0.364655i	$0.881187\pi$
$102$		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	0.401323	+	0.915937i	$0.368551\pi$
$107$	−6.12952	+	10.6166i	−0.592563	+	1.02635i	−0.993886	+	0.110413i	$0.964783\pi$
$108$		0			0
$109$	4.89342	+	8.47565i	0.468705	+	0.811820i	0.999360	−	0.0357675i	$-0.0113876\pi$
$109$	4.89342	+	8.47565i	0.468705	+	0.811820i	−0.530656	+	0.847588i	$0.678054\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.54664	−	4.41091i	0.239568	−	0.414944i	−0.721022	−	0.692912i	$-0.756328\pi$
$113$	2.54664	−	4.41091i	0.239568	−	0.414944i	0.960590	+	0.277968i	$0.0896609\pi$
$114$		0			0
$115$	−0.474162	+	0.821273i	−0.0442158	+	0.0765841i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.88839	+	6.43352i	−0.814797	+	0.589760i
$120$		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	0.655995	−	0.754765i	$-0.272249\pi$
$131$	−3.72722	−	6.45573i	−0.325648	−	0.564039i	−0.981643	+	0.190726i	$0.938916\pi$
$132$		0			0
$133$	0.977215	+	0.437181i	0.0847353	+	0.0379084i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.22340	+	7.31515i	−0.360830	+	0.624975i	−0.988098	−	0.153828i	$-0.950840\pi$
$137$	−4.22340	+	7.31515i	−0.360830	+	0.624975i	0.627268	+	0.778804i	$0.284173\pi$
$138$		0			0
$139$	1.82352	−	3.15843i	0.154669	−	0.267895i	−0.778269	−	0.627931i	$-0.783902\pi$
$139$	1.82352	−	3.15843i	0.154669	−	0.267895i	0.932939	+	0.360036i	$0.117235\pi$
$140$		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	0.871987	−	0.489529i	$-0.162831\pi$
$149$	0.147078	+	0.254746i	0.0120491	+	0.0208696i	−0.859938	+	0.510399i	$0.829498\pi$
$150$		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
$155$	0.564842	+	0.978335i	0.0453692	+	0.0785817i
$156$		0			0
$157$	−13.1166			−1.04682			−0.523411	−	0.852080i	$-0.675341\pi$
$157$	−13.1166			−1.04682			−0.523411	+	0.852080i	$0.675341\pi$
$158$		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	−0.845939	−	0.533280i	$-0.820959\pi$
$163$	0.496191	−	0.859428i	0.0388647	−	0.0673156i	0.884803	+	0.465964i	$0.154293\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.93040	+	12.0038i	−0.536291	+	0.928883i	0.462809	+	0.886458i	$0.346842\pi$
$167$	−6.93040	+	12.0038i	−0.536291	+	0.928883i	−0.999100	+	0.0424246i	$0.986492\pi$
$168$		0			0
$169$	4.60202	+	7.97093i	0.354001	+	0.613148i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.00487			0.380513			0.190256	−	0.981734i	$-0.439068\pi$
$173$	5.00487			0.380513			0.190256	+	0.981734i	$0.439068\pi$
$174$		0			0
$175$	11.7901	+	5.27458i	0.891245	+	0.398721i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.8101	+	18.7236i	0.807982	+	1.39947i	0.914259	+	0.405130i	$0.132774\pi$
$179$	10.8101	+	18.7236i	0.807982	+	1.39947i	−0.106277	+	0.994337i	$0.533893\pi$
$180$		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
$185$	2.33002			0.171306
$186$		0			0
$187$	−20.4031			−1.49202
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.7050			−1.28109			−0.640546	−	0.767920i	$-0.721292\pi$
$191$	−17.7050			−1.28109			−0.640546	+	0.767920i	$0.721292\pi$
$192$		0			0
$193$	−2.96429			−0.213374			−0.106687	−	0.994293i	$-0.534024\pi$
$193$	−2.96429			−0.213374			−0.106687	+	0.994293i	$0.534024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.2357			1.29924			0.649618	−	0.760260i	$-0.274929\pi$
$197$	18.2357			1.29924			0.649618	+	0.760260i	$0.274929\pi$
$198$		0			0
$199$	1.61323	+	2.79419i	0.114359	+	0.198075i	0.917523	−	0.397682i	$-0.130185\pi$
$199$	1.61323	+	2.79419i	0.114359	+	0.198075i	−0.803165	+	0.595757i	$0.796852\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.02385	+	5.08394i	−0.492977	+	0.356823i
$204$		0			0
$205$	1.93352			0.135043
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.995340	+	1.72398i	0.0688491	+	0.119250i
$210$		0			0
$211$	−4.72740	+	8.18809i	−0.325447	+	0.563691i	−0.981603	−	0.190934i	$-0.938848\pi$
$211$	−4.72740	+	8.18809i	−0.325447	+	0.563691i	0.656155	+	0.754626i	$0.272182\pi$
$212$		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
$221$	8.08005			0.543523
$222$		0			0
$223$	9.63203	+	16.6832i	0.645008	+	1.11719i	0.984300	+	0.176506i	$0.0564794\pi$
$223$	9.63203	+	16.6832i	0.645008	+	1.11719i	−0.339291	+	0.940681i	$0.610187\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.08878	−	1.88583i	0.0722652	−	0.125167i	−0.827629	−	0.561276i	$-0.810311\pi$
$227$	1.08878	−	1.88583i	0.0722652	−	0.125167i	0.899894	+	0.436109i	$0.143644\pi$
$228$		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	$-0.687206\pi$
$233$	6.76391	−	11.7154i	0.443118	−	0.767503i	0.997919	+	0.0644799i	$0.0205388\pi$
$234$		0			0
$235$	2.26879	+	3.92967i	0.148000	+	0.256343i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.21398	−	3.83473i	0.143211	−	0.248048i	−0.785493	−	0.618870i	$-0.787591\pi$
$239$	2.21398	−	3.83473i	0.143211	−	0.248048i	0.928704	+	0.370822i	$0.120924\pi$
$240$		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
$245$	1.60363	+	1.79388i	0.102452	+	0.114607i
$246$		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	$-0.880192\pi$
$251$	−29.4679			−1.86000			−0.929998	+	0.367564i	$0.880192\pi$
$252$		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	$-0.740429\pi$
$257$	−15.6027	−	27.0247i	−0.973270	−	1.68575i	−0.287742	−	0.957708i	$-0.592905\pi$
$258$		0			0
$259$	−16.3706	−	7.32381i	−1.01722	−	0.455079i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.4058	−	19.7555i	0.703314	−	1.21818i	−0.263982	−	0.964528i	$-0.585036\pi$
$263$	11.4058	−	19.7555i	0.703314	−	1.21818i	0.967296	−	0.253648i	$-0.0816306\pi$
$264$		0			0
$265$	0.474918	−	0.822582i	0.0291740	−	0.0505308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.7838	−	20.4101i	−0.718471	−	1.24443i	−0.961606	−	0.274435i	$-0.911509\pi$
$269$	−11.7838	−	20.4101i	−0.718471	−	1.24443i	0.243135	−	0.969992i	$-0.421824\pi$
$270$		0			0
$271$	0.0112106	−	0.0194174i	0.000680998	−	0.00117952i	−0.865685	−	0.500590i	$-0.833117\pi$
$271$	0.0112106	−	0.0194174i	0.000680998	−	0.00117952i	0.866366	+	0.499410i	$0.166450\pi$
$272$		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
$281$	−0.136542	−	0.236498i	−0.00814541	−	0.0141083i	0.861924	−	0.507038i	$-0.169259\pi$
$281$	−0.136542	−	0.236498i	−0.00814541	−	0.0141083i	−0.870069	+	0.492929i	$0.835926\pi$
$282$		0			0
$283$	11.1535			0.663008			0.331504	−	0.943454i	$-0.392444\pi$
$283$	11.1535			0.663008			0.331504	+	0.943454i	$0.392444\pi$
$284$		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
$293$	−14.0597	+	24.3522i	−0.821379	+	1.42267i	0.0832760	+	0.996527i	$0.473462\pi$
$293$	−14.0597	+	24.3522i	−0.821379	+	1.42267i	−0.904655	+	0.426144i	$0.859872\pi$
$294$		0			0
$295$	1.45250	+	2.51580i	0.0845676	+	0.146475i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.37516			−0.310854
$300$		0			0
$301$	21.2736	−	15.3981i	1.22619	−	0.887529i
$302$		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
$311$	27.9026			1.58221			0.791105	−	0.611681i	$-0.209506\pi$
$311$	27.9026			1.58221			0.791105	+	0.611681i	$0.209506\pi$
$312$		0			0
$313$	−12.3157			−0.696126			−0.348063	−	0.937471i	$-0.613161\pi$
$313$	−12.3157			−0.696126			−0.348063	+	0.937471i	$0.613161\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.5533			1.54755			0.773775	−	0.633461i	$-0.218366\pi$
$317$	27.5533			1.54755			0.773775	+	0.633461i	$0.218366\pi$
$318$		0			0
$319$	−16.1231			−0.902720
$320$		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
$329$	−3.58859	−	34.7411i	−0.197845	−	1.91534i
$330$		0			0
$331$	10.1117			0.555789			0.277895	−	0.960612i	$-0.410363\pi$
$331$	10.1117			0.555789			0.277895	+	0.960612i	$0.410363\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.44809	+	2.50816i	0.0791174	+	0.137035i
$336$		0			0
$337$	−5.91508	+	10.2452i	−0.322215	+	0.558093i	−0.980945	−	0.194287i	$-0.937761\pi$
$337$	−5.91508	+	10.2452i	−0.322215	+	0.558093i	0.658730	+	0.752380i	$0.271094\pi$
$338$		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
$347$	28.4499			1.52727			0.763634	−	0.645649i	$-0.223413\pi$
$347$	28.4499			1.52727			0.763634	+	0.645649i	$0.223413\pi$
$348$		0			0
$349$	8.79028	+	15.2252i	0.470533	+	0.814987i	0.999432	−	0.0336976i	$-0.0107283\pi$
$349$	8.79028	+	15.2252i	0.470533	+	0.814987i	−0.528899	+	0.848685i	$0.677395\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.7573	−	23.8283i	0.732225	−	1.26825i	−0.223705	−	0.974657i	$-0.571815\pi$
$353$	13.7573	−	23.8283i	0.732225	−	1.26825i	0.955930	−	0.293594i	$-0.0948513\pi$
$354$		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	0.486249	+	0.873820i	$0.338365\pi$
$359$	−9.73182	+	16.8560i	−0.513626	+	0.889626i	−0.999875	+	0.0158059i	$0.994969\pi$
$360$		0			0
$361$	9.41814	+	16.3127i	0.495691	+	0.858563i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.57575	−	2.72927i	0.0824783	−	0.142857i
$366$		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
$371$	−5.92233	+	4.28665i	−0.307472	+	0.222552i
$372$		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	0.803290	−	0.595588i	$-0.203081\pi$
$383$	−2.23395	−	3.86931i	−0.114149	−	0.197712i	−0.917439	+	0.397876i	$0.869748\pi$
$384$		0			0
$385$	0.459722	+	4.45056i	0.0234296	+	0.226822i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.1232	−	24.4620i	0.716072	−	1.24027i	−0.246472	−	0.969150i	$-0.579271\pi$
$389$	14.1232	−	24.4620i	0.716072	−	1.24027i	0.962545	−	0.271124i	$-0.0873953\pi$
$390$		0			0
$391$	5.72075	−	9.90863i	0.289311	−	0.501101i
$392$		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	−0.858566	−	0.512703i	$-0.828644\pi$
$397$	0.293513	−	0.508379i	0.0147310	−	0.0255148i	0.873297	+	0.487188i	$0.161977\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.5150	+	25.1408i	0.724846	+	1.25547i	0.959037	+	0.283280i	$0.0914226\pi$
$401$	14.5150	+	25.1408i	0.724846	+	1.25547i	−0.234191	+	0.972191i	$0.575244\pi$
$402$		0			0
$403$	−3.20156	+	5.54526i	−0.159481	+	0.276229i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.6743	−	28.8807i	−0.826513	−	1.43156i
$408$		0			0
$409$	22.0042			1.08804			0.544018	−	0.839074i	$-0.316902\pi$
$409$	22.0042			1.08804			0.544018	+	0.839074i	$0.316902\pi$
$410$		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
$419$	−12.5615	+	21.7572i	−0.613671	+	1.06291i	0.376945	+	0.926236i	$0.376975\pi$
$419$	−12.5615	+	21.7572i	−0.613671	+	1.06291i	−0.990616	+	0.136674i	$0.956359\pi$
$420$		0			0
$421$	−0.0961261	−	0.166495i	−0.00468490	−	0.00811449i	0.863673	−	0.504052i	$-0.168158\pi$
$421$	−0.0961261	−	0.166495i	−0.00468490	−	0.00811449i	−0.868358	+	0.495937i	$0.834825\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	20.2459			0.982069
$426$		0			0
$427$	2.92401	+	28.3073i	0.141503	+	1.36989i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.7344	+	18.5925i	0.517057	+	0.895569i	0.999804	+	0.0198093i	$0.00630591\pi$
$431$	10.7344	+	18.5925i	0.517057	+	0.895569i	−0.482747	+	0.875760i	$0.660361\pi$
$432$		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
$437$	−1.11632			−0.0534008
$438$		0			0
$439$	−33.6577			−1.60639			−0.803196	−	0.595714i	$-0.796869\pi$
$439$	−33.6577			−1.60639			−0.803196	+	0.595714i	$0.796869\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.5483			0.548677			0.274339	−	0.961633i	$-0.411541\pi$
$443$	11.5483			0.548677			0.274339	+	0.961633i	$0.411541\pi$
$444$		0			0
$445$	−2.43540			−0.115449
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.6025			1.06668			0.533338	−	0.845902i	$-0.320937\pi$
$449$	22.6025			1.06668			0.533338	+	0.845902i	$0.320937\pi$
$450$		0			0
$451$	−13.8368	−	23.9661i	−0.651550	−	1.12852i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.182059	−	1.76251i	−0.00853507	−	0.0826278i
$456$		0			0
$457$	2.08128			0.0973583			0.0486792	−	0.998814i	$-0.484499\pi$
$457$	2.08128			0.0973583			0.0486792	+	0.998814i	$0.484499\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.21838	+	7.30644i	0.196469	+	0.340295i	0.947381	−	0.320108i	$-0.103719\pi$
$461$	4.21838	+	7.30644i	0.196469	+	0.340295i	−0.750912	+	0.660402i	$0.770386\pi$
$462$		0			0
$463$	2.92231	−	5.06159i	0.135811	−	0.235232i	−0.790096	−	0.612983i	$-0.789969\pi$
$463$	2.92231	−	5.06159i	0.135811	−	0.235232i	0.925907	+	0.377751i	$0.123303\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.04009	−	1.80149i	0.0481298	−	0.0833632i	−0.840957	−	0.541102i	$-0.818007\pi$
$467$	1.04009	−	1.80149i	0.0481298	−	0.0833632i	0.889087	+	0.457739i	$0.151341\pi$
$468$		0			0
$469$	−2.29046	−	22.1739i	−0.105764	−	1.02390i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	48.8331			2.24535
$474$		0			0
$475$	−0.987670	−	1.71069i	−0.0453174	−	0.0784920i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.51538	−	14.7491i	0.389077	−	0.673902i	−0.603248	−	0.797553i	$-0.706127\pi$
$479$	8.51538	−	14.7491i	0.389077	−	0.673902i	0.992326	+	0.123652i	$0.0394605\pi$
$480$		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	−0.999998	−	0.00218582i	$-0.999304\pi$
$487$	−11.0758	−	19.1838i	−0.501892	−	0.869302i	0.498106	−	0.867116i	$-0.334029\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.88390	−	4.99505i	0.130148	−	0.225424i	−0.793585	−	0.608459i	$-0.791788\pi$
$491$	2.88390	−	4.99505i	0.130148	−	0.225424i	0.923734	+	0.383035i	$0.125121\pi$
$492$		0			0
$493$	−6.79559	+	11.7703i	−0.306058	+	0.530108i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.38340	−	13.3927i	−0.0620539	−	0.600743i
$498$		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	$-0.728123\pi$
$503$	−29.4644			−1.31375			−0.656876	+	0.753998i	$0.728123\pi$
$504$		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	0.821484	−	0.570231i	$-0.193146\pi$
$509$	−1.87465	−	3.24698i	−0.0830922	−	0.143920i	−0.904577	+	0.426311i	$0.859813\pi$
$510$		0			0
$511$	−19.6499	+	14.2228i	−0.869260	+	0.629181i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.33074	−	2.30491i	0.0586394	−	0.101566i
$516$		0			0
$517$	32.4723	−	56.2436i	1.42813	−	2.47359i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.9592	+	24.1780i	0.611562	+	1.05926i	0.990977	+	0.134030i	$0.0427919\pi$
$521$	13.9592	+	24.1780i	0.611562	+	1.05926i	−0.379415	+	0.925226i	$0.623875\pi$
$522$		0			0
$523$	21.0680	−	36.4909i	0.921240	−	1.59563i	0.123741	−	0.992315i	$-0.460511\pi$
$523$	21.0680	−	36.4909i	0.921240	−	1.59563i	0.797499	−	0.603320i	$-0.206156\pi$
$524$		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
$533$	5.47966	+	9.49105i	0.237350	+	0.411103i
$534$		0			0
$535$	4.21389			0.182182
$536$		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	0.360352	+	0.932816i	$0.382657\pi$
$541$	−14.5992	+	25.2865i	−0.627667	+	1.08715i	−0.988019	+	0.154334i	$0.950677\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.68205	−	2.91340i	0.0720511	−	0.124796i
$546$		0			0
$547$	5.76122	+	9.97872i	0.246332	+	0.426659i	0.962505	−	0.271263i	$-0.0874414\pi$
$547$	5.76122	+	9.97872i	0.246332	+	0.426659i	−0.716173	+	0.697922i	$0.754108\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.32606			0.0564920
$552$		0			0
$553$	1.22114	+	11.8219i	0.0519283	+	0.502717i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.97631	−	10.3513i	−0.253224	−	0.438597i	0.711187	−	0.703002i	$-0.248158\pi$
$557$	−5.97631	−	10.3513i	−0.253224	−	0.438597i	−0.964412	+	0.264405i	$0.914824\pi$
$558$		0			0
$559$	−19.3389			−0.817947
$560$		0			0
$561$		0			0
$562$		0			0
$563$	23.6198			0.995455			0.497728	−	0.867333i	$-0.334168\pi$
$563$	23.6198			0.995455			0.497728	+	0.867333i	$0.334168\pi$
$564$		0			0
$565$	−1.75075			−0.0736546
$566$		0			0
$567$		0			0
$568$		0			0
$569$	23.9491			1.00400			0.501999	−	0.864868i	$-0.332598\pi$
$569$	23.9491			1.00400			0.501999	+	0.864868i	$0.332598\pi$
$570$		0			0
$571$	10.0992			0.422637			0.211319	−	0.977417i	$-0.432224\pi$
$571$	10.0992			0.422637			0.211319	+	0.977417i	$0.432224\pi$
$572$		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	0.976949	+	0.213474i	$0.0684780\pi$
$577$	16.1744	+	28.0149i	0.673348	+	1.16627i	−0.303600	+	0.952800i	$0.598189\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.8449	+	14.3640i	−0.823305	+	0.595918i
$582$		0			0
$583$	−13.5946			−0.563030
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.02746	−	8.70781i	−0.207505	−	0.359410i	0.743423	−	0.668822i	$-0.233201\pi$
$587$	−5.02746	−	8.70781i	−0.207505	−	0.359410i	−0.950928	+	0.309412i	$0.899868\pi$
$588$		0			0
$589$	−0.664903	+	1.15165i	−0.0273968	+	0.0474527i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.0673	−	29.5613i	0.700868	−	1.21394i	−0.267294	−	0.963615i	$-0.586130\pi$
$593$	17.0673	−	29.5613i	0.700868	−	1.21394i	0.968162	−	0.250324i	$-0.0805371\pi$
$594$		0			0
$595$	3.44280	+	1.54022i	0.141141	+	0.0631429i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	30.4283			1.24327			0.621633	−	0.783309i	$-0.286470\pi$
$599$	30.4283			1.24327			0.621633	+	0.783309i	$0.286470\pi$
$600$		0			0
$601$	23.6966	+	41.0438i	0.966606	+	1.67421i	0.705238	+	0.708971i	$0.250840\pi$
$601$	23.6966	+	41.0438i	0.966606	+	1.67421i	0.261368	+	0.965239i	$0.415826\pi$
$602$		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	0.885460	−	0.464715i	$-0.153843\pi$
$613$	0.997163	+	1.72714i	0.0402750	+	0.0697584i	−0.845185	+	0.534474i	$0.820510\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.0562	−	36.4704i	0.847690	−	1.46824i	−0.0355743	−	0.999367i	$-0.511326\pi$
$617$	21.0562	−	36.4704i	0.847690	−	1.46824i	0.883264	−	0.468875i	$-0.155341\pi$
$618$		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
$623$	17.1110	+	7.65503i	0.685538	+	0.306692i
$624$		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
$637$	−4.26085	+	12.9556i	−0.168821	+	0.513320i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.2296	−	35.0387i	0.799022	−	1.38395i	−0.121231	−	0.992624i	$-0.538684\pi$
$641$	20.2296	−	35.0387i	0.799022	−	1.38395i	0.920254	−	0.391323i	$-0.127982\pi$
$642$		0			0
$643$	1.43445	−	2.48455i	0.0565693	−	0.0979809i	−0.836354	−	0.548190i	$-0.815317\pi$
$643$	1.43445	−	2.48455i	0.0565693	−	0.0979809i	0.892923	+	0.450209i	$0.148650\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.71712	−	2.97413i	−0.0675068	−	0.116925i	0.830296	−	0.557322i	$-0.188171\pi$
$647$	−1.71712	−	2.97413i	−0.0675068	−	0.116925i	−0.897803	+	0.440397i	$0.854838\pi$
$648$		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	0.999718	−	0.0237590i	$-0.00756342\pi$
$653$	12.2475	+	21.2133i	0.479283	+	0.830142i	−0.520435	+	0.853901i	$0.674230\pi$
$654$		0			0
$655$	−1.28118	+	2.21907i	−0.0500599	+	0.0867064i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11.6375	−	20.1567i	−0.453332	−	0.785194i	0.545259	−	0.838268i	$-0.316431\pi$
$659$	−11.6375	−	20.1567i	−0.453332	−	0.785194i	−0.998591	+	0.0530740i	$0.983098\pi$
$660$		0			0
$661$	−33.5798			−1.30610			−0.653051	−	0.757314i	$-0.726511\pi$
$661$	−33.5798			−1.30610			−0.653051	+	0.757314i	$0.726511\pi$
$662$		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
$671$	−26.4586	+	45.8277i	−1.02142	+	1.76916i
$672$		0			0
$673$	−23.3581	−	40.4574i	−0.900388	−	1.55952i	−0.826991	−	0.562215i	$-0.809949\pi$
$673$	−23.3581	−	40.4574i	−0.900388	−	1.55952i	−0.0733972	−	0.997303i	$-0.523384\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.47307			−0.133481			−0.0667404	−	0.997770i	$-0.521260\pi$
$677$	−3.47307			−0.133481			−0.0667404	+	0.997770i	$0.521260\pi$
$678$		0			0
$679$	5.62519	−	4.07158i	0.215875	−	0.156253i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.49075	+	6.04615i	0.133570	+	0.231349i	0.925050	−	0.379845i	$-0.124023\pi$
$683$	3.49075	+	6.04615i	0.133570	+	0.231349i	−0.791480	+	0.611194i	$0.790689\pi$
$684$		0			0
$685$	2.90348			0.110936
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.38373			0.205104
$690$		0			0
$691$	33.0832			1.25854			0.629272	−	0.777185i	$-0.283353\pi$
$691$	33.0832			1.25854			0.629272	+	0.777185i	$0.283353\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.25363			−0.0475527
$696$		0			0
$697$	−23.3279			−0.883606
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−39.4243			−1.48904			−0.744518	−	0.667602i	$-0.767321\pi$
$701$	−39.4243			−1.48904			−0.744518	+	0.667602i	$0.767321\pi$
$702$		0			0
$703$	1.37139	+	2.37532i	0.0517230	+	0.0895868i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−37.9298	−	16.9688i	−1.42650	−	0.638179i
$708$		0			0
$709$	21.1542			0.794464			0.397232	−	0.917718i	$-0.369971\pi$
$709$	21.1542			0.794464			0.397232	+	0.917718i	$0.369971\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.53347	+	7.85220i	0.169780	+	0.294067i
$714$		0			0
$715$	1.64741	−	2.85340i	0.0616096	−	0.106711i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.7586	−	23.8305i	0.513108	−	0.888729i	−0.486777	−	0.873527i	$-0.661827\pi$
$719$	13.7586	−	23.8305i	0.513108	−	0.888729i	0.999884	−	0.0152024i	$-0.00483926\pi$
$720$		0			0
$721$	−16.5946	+	12.0114i	−0.618016	+	0.447327i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	15.9988			0.594182
$726$		0			0
$727$	−10.5095	−	18.2030i	−0.389775	−	0.675110i	0.602644	−	0.798010i	$-0.294114\pi$
$727$	−10.5095	−	18.2030i	−0.389775	−	0.675110i	−0.992419	+	0.122900i	$0.960781\pi$
$728$		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	0.965932	+	0.258794i	$0.0833252\pi$
$739$	19.2219	+	33.2933i	0.707089	+	1.22471i	−0.258844	+	0.965919i	$0.583342\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.85728	−	17.0733i	0.361629	−	0.626359i	−0.626600	−	0.779341i	$-0.715554\pi$
$743$	9.85728	−	17.0733i	0.361629	−	0.626359i	0.988229	+	0.152982i	$0.0488875\pi$
$744$		0			0
$745$	0.0505562	−	0.0875658i	0.00185223	−	0.00320816i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−29.6066	−	13.2453i	−1.08180	−	0.483971i
$750$		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	0.848503	−	0.529191i	$-0.177505\pi$
$761$	−0.939077	−	1.62653i	−0.0340415	−	0.0589616i	−0.882544	+	0.470229i	$0.844171\pi$
$762$		0			0
$763$	−20.9755	+	15.1823i	−0.759365	+	0.549637i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.23284	+	14.2597i	−0.297271	+	0.514888i
$768$		0			0
$769$	−13.4060	+	23.2198i	−0.483431	+	0.837327i	−0.999819	−	0.0190276i	$-0.993943\pi$
$769$	−13.4060	+	23.2198i	−0.483431	+	0.837327i	0.516388	+	0.856355i	$0.327276\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.67835	+	8.10314i	0.168268	+	0.291450i	0.937811	−	0.347146i	$-0.112849\pi$
$773$	4.67835	+	8.10314i	0.168268	+	0.291450i	−0.769543	+	0.638595i	$0.779516\pi$
$774$		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
$785$	2.25434	+	3.90463i	0.0804608	+	0.139362i
$786$		0			0
$787$	18.8735			0.672768			0.336384	−	0.941725i	$-0.390796\pi$
$787$	18.8735			0.672768			0.336384	+	0.941725i	$0.390796\pi$
$788$		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
$797$	−17.9023	+	31.0078i	−0.634134	+	1.09835i	0.352564	+	0.935788i	$0.385310\pi$
$797$	−17.9023	+	31.0078i	−0.634134	+	1.09835i	−0.986698	+	0.162564i	$0.948024\pi$
$798$		0			0
$799$	−27.3729	−	47.4113i	−0.968385	−	1.67729i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−45.1059			−1.59175
$804$		0			0
$805$	−2.29028	−	1.02461i	−0.0807219	−	0.0361129i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.8027	+	32.5672i	0.661068	+	1.14500i	0.980335	+	0.197338i	$0.0632297\pi$
$809$	18.8027	+	32.5672i	0.661068	+	1.14500i	−0.319268	+	0.947665i	$0.603437\pi$
$810$		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
$815$	−0.341119			−0.0119489
$816$		0			0
$817$	−4.01632			−0.140513
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.1748			0.878608			0.439304	−	0.898339i	$-0.355225\pi$
$821$	25.1748			0.878608			0.439304	+	0.898339i	$0.355225\pi$
$822$		0			0
$823$	7.83584			0.273140			0.136570	−	0.990630i	$-0.456392\pi$
$823$	7.83584			0.273140			0.136570	+	0.990630i	$0.456392\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.4941			0.643103			0.321552	−	0.946892i	$-0.395796\pi$
$827$	18.4941			0.643103			0.321552	+	0.946892i	$0.395796\pi$
$828$		0			0
$829$	−6.83264	−	11.8345i	−0.237307	−	0.411029i	0.722633	−	0.691232i	$-0.242932\pi$
$829$	−6.83264	−	11.8345i	−0.237307	−	0.411029i	−0.959941	+	0.280203i	$0.909598\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.3477	−	21.6431i	−0.670358	−	0.749888i
$834$		0			0
$835$	4.76447			0.164881
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.5170	+	44.1968i	0.880945	+	1.52584i	0.850291	+	0.526312i	$0.176426\pi$
$839$	25.5170	+	44.1968i	0.880945	+	1.52584i	0.0306540	+	0.999530i	$0.490241\pi$
$840$		0			0
$841$	9.12994	−	15.8135i	0.314825	−	0.545294i
$842$		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
$851$	18.7009			0.641060
$852$		0			0
$853$	7.92630	+	13.7287i	0.271391	+	0.470063i	0.969218	−	0.246203i	$-0.0791830\pi$
$853$	7.92630	+	13.7287i	0.271391	+	0.470063i	−0.697827	+	0.716266i	$0.745850\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.1000	+	36.5464i	−0.720764	+	1.24840i	0.239930	+	0.970790i	$0.422875\pi$
$857$	−21.1000	+	36.5464i	−0.720764	+	1.24840i	−0.960694	+	0.277610i	$0.910458\pi$
$858$		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	0.390351	+	0.920666i	$0.372354\pi$
$863$	−17.6891	+	30.6385i	−0.602145	+	1.04295i	−0.992496	+	0.122279i	$0.960980\pi$
$864$		0			0
$865$	−0.860179	−	1.48987i	−0.0292470	−	0.0506572i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.0498	+	19.1389i	−0.374840	+	0.649241i
$870$		0			0
$871$	−8.20784	+	14.2164i	−0.278112	+	0.481704i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.923399	−	8.93941i	−0.0312166	−	0.302207i
$876$		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	$-0.645497\pi$
$881$	−26.1995			−0.882683			−0.441341	+	0.897339i	$0.645497\pi$
$882$		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	$-0.867407\pi$
$887$	−24.0538	−	41.6625i	−0.807649	−	1.39889i	0.106840	−	0.994276i	$-0.465927\pi$
$888$		0			0
$889$	0.609595	+	5.90148i	0.0204452	+	0.197929i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.67071	+	4.62580i	−0.0893718	+	0.154797i
$894$		0			0
$895$	3.71582	−	6.43599i	0.124206	−	0.215132i
$896$		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
$911$	11.5141	+	19.9430i	0.381479	+	0.660740i	0.991274	−	0.131819i	$-0.0420817\pi$
$911$	11.5141	+	19.9430i	0.381479	+	0.660740i	−0.609795	+	0.792559i	$0.708748\pi$
$912$		0			0
$913$	−45.5536			−1.50760
$914$		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	0.427279	+	0.904120i	$0.359472\pi$
$919$	−17.2599	+	29.8950i	−0.569351	+	0.986145i	−0.996630	+	0.0820251i	$0.973861\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.95740	+	8.58647i	−0.163175	+	0.282627i
$924$		0			0
$925$	16.5458	+	28.6581i	0.544022	+	0.942273i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.6352			−0.939491			−0.469746	−	0.882802i	$-0.655654\pi$
$929$	−28.6352			−0.939491			−0.469746	+	0.882802i	$0.655654\pi$
$930$		0			0
$931$	−0.884898	+	2.69063i	−0.0290013	+	0.0881819i
$932$		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
$941$	−36.8679			−1.20186			−0.600930	−	0.799301i	$-0.705203\pi$
$941$	−36.8679			−1.20186			−0.600930	+	0.799301i	$0.705203\pi$
$942$		0			0
$943$	15.5186			0.505355
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.7818			−1.22774			−0.613872	−	0.789406i	$-0.710389\pi$
$947$	−37.7818			−1.22774			−0.613872	+	0.789406i	$0.710389\pi$
$948$		0			0
$949$	17.8629			0.579853
$950$		0			0
$951$		0			0
$952$		0			0
$953$	43.5184			1.40970			0.704850	−	0.709356i	$-0.251014\pi$
$953$	43.5184			1.40970			0.704850	+	0.709356i	$0.251014\pi$
$954$		0			0
$955$	3.04294	+	5.27052i	0.0984672	+	0.170550i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−20.3998	−	9.12633i	−0.658742	−	0.294705i
$960$		0			0
$961$	−20.1991			−0.651583
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.509468	+	0.882424i	0.0164003	+	0.0284062i
$966$		0			0
$967$	−17.8032	+	30.8360i	−0.572512	+	0.991619i	0.423795	+	0.905758i	$0.360698\pi$
$967$	−17.8032	+	30.8360i	−0.572512	+	0.991619i	−0.996307	+	0.0858615i	$0.972636\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.2654	+	31.6366i	−0.586164	+	1.01527i	0.408565	+	0.912729i	$0.366029\pi$
$971$	−18.2654	+	31.6366i	−0.586164	+	1.01527i	−0.994729	+	0.102537i	$0.967304\pi$
$972$		0			0
$973$	8.80792	+	3.94044i	0.282369	+	0.126325i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.2739			0.744597			0.372299	−	0.928113i	$-0.378570\pi$
$977$	23.2739			0.744597			0.372299	+	0.928113i	$0.378570\pi$
$978$		0			0
$979$	17.4284	+	30.1868i	0.557013	+	0.964775i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.01170	+	3.48437i	−0.0641634	+	0.111134i	−0.896323	−	0.443403i	$-0.853771\pi$
$983$	−2.01170	+	3.48437i	−0.0641634	+	0.111134i	0.832159	+	0.554537i	$0.187105\pi$
$984$		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	0.975215	+	0.221258i	$0.0710163\pi$
$991$	21.3820	+	37.0348i	0.679223	+	1.17645i	−0.295993	+	0.955190i	$0.595650\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.554526	−	0.960467i	0.0175797	−	0.0304489i
$996$		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.i.n.2053.4		16
3.2	odd	2	inner	2268.2.i.n.2053.5		16
7.4	even	3		2268.2.l.n.109.5		16
9.2	odd	6		2268.2.l.n.541.4		16
9.4	even	3		2268.2.k.g.1297.4	✓	16
9.5	odd	6		2268.2.k.g.1297.5	yes	16
9.7	even	3		2268.2.l.n.541.5		16
21.11	odd	6		2268.2.l.n.109.4		16
63.4	even	3		2268.2.k.g.1621.4	yes	16
63.11	odd	6	inner	2268.2.i.n.865.5		16
63.25	even	3	inner	2268.2.i.n.865.4		16
63.32	odd	6		2268.2.k.g.1621.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.4		16	63.25	even	3	inner
2268.2.i.n.865.5		16	63.11	odd	6	inner
2268.2.i.n.2053.4		16	1.1	even	1	trivial
2268.2.i.n.2053.5		16	3.2	odd	2	inner
2268.2.k.g.1297.4	✓	16	9.4	even	3
2268.2.k.g.1297.5	yes	16	9.5	odd	6
2268.2.k.g.1621.4	yes	16	63.4	even	3
2268.2.k.g.1621.5	yes	16	63.32	odd	6
2268.2.l.n.109.4		16	21.11	odd	6
2268.2.l.n.109.5		16	7.4	even	3
2268.2.l.n.541.4		16	9.2	odd	6
2268.2.l.n.541.5		16	9.7	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +O(q^{10})\)	\(q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +(-2.45988 + 4.26064i) q^{11} +(0.974162 - 1.68730i) q^{13} +(2.07359 + 3.59156i) q^{17} +(0.202315 - 0.350420i) q^{19} +(-1.37943 - 2.38925i) q^{23} +(2.44092 - 4.22780i) q^{25} +(1.63861 + 2.83815i) q^{29} -3.28647 q^{31} +(0.736710 - 0.533240i) q^{35} +(-3.38925 + 5.87035i) q^{37} +(-2.81250 + 4.87139i) q^{41} +(-4.96295 - 8.59608i) q^{43} -13.2008 q^{47} +(-6.85220 + 1.43087i) q^{49} +(1.38163 + 2.39306i) q^{53} +1.69110 q^{55} -8.45121 q^{59} +10.7561 q^{61} -0.669711 q^{65} -8.42554 q^{67} -5.08888 q^{71} +(4.58416 + 7.94000i) q^{73} +(-11.8816 - 5.31554i) q^{77} +4.49202 q^{79} +(4.62966 + 8.01880i) q^{83} +(0.712770 - 1.23455i) q^{85} +(3.54253 - 6.13584i) q^{89} +(4.70537 + 2.10506i) q^{91} -0.139086 q^{95} +(-1.31231 - 2.27299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

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