LMFDB - Embedded newform 432.3.o.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(127,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.o (of order $6$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$2.33086i$ of defining polynomial
Character	$\chi$	$=$	432.127
Dual form			432.3.o.b.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.355304 - 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +O(q^{10})$	$q+(-0.355304 - 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +(-14.3822 - 8.30359i) q^{11} +(-9.17743 - 15.8958i) q^{13} +9.69321 q^{17} +8.20686i q^{19} +(-1.94815 + 1.12477i) q^{23} +(12.2475 - 21.2133i) q^{25} +(20.8217 - 36.0642i) q^{29} +(-21.6298 + 12.4879i) q^{31} -2.21940i q^{35} -40.3888 q^{37} +(-25.6944 - 44.5040i) q^{41} +(-56.6621 - 32.7139i) q^{43} +(-29.2894 - 16.9102i) q^{47} +(-19.6227 - 33.9875i) q^{49} +90.6691 q^{53} +11.8012i q^{55} +(66.2243 - 38.2346i) q^{59} +(1.35822 - 2.35250i) q^{61} +(-6.52157 + 11.2957i) q^{65} +(-34.5422 + 19.9429i) q^{67} +102.923i q^{71} +38.1741 q^{73} +(-25.9341 - 44.9192i) q^{77} +(94.4994 + 54.5593i) q^{79} +(-113.503 - 65.5311i) q^{83} +(-3.44404 - 5.96526i) q^{85} -38.0903 q^{89} -57.3266i q^{91} +(5.05055 - 2.91593i) q^{95} +(-12.1961 + 21.1243i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 8 * q - 3 * q^5 + 3 * q^7	$ 8 q - 3 q^{5} + 3 q^{7} - 18 q^{11} + 5 q^{13} - 6 q^{17} + 81 q^{23} - 23 q^{25} - 69 q^{29} + 45 q^{31} - 20 q^{37} - 54 q^{41} - 207 q^{47} + 41 q^{49} + 252 q^{53} + 306 q^{59} + 7 q^{61} - 93 q^{65} + 12 q^{67} + 74 q^{73} - 207 q^{77} + 33 q^{79} - 549 q^{83} - 30 q^{85} + 168 q^{89} + 684 q^{95} - 10 q^{97}+O(q^{100}) $ 8 * q - 3 * q^5 + 3 * q^7 - 18 * q^11 + 5 * q^13 - 6 * q^17 + 81 * q^23 - 23 * q^25 - 69 * q^29 + 45 * q^31 - 20 * q^37 - 54 * q^41 - 207 * q^47 + 41 * q^49 + 252 * q^53 + 306 * q^59 + 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 - 207 * q^77 + 33 * q^79 - 549 * q^83 - 30 * q^85 + 168 * q^89 + 684 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.355304	−	0.615405i	−0.0710609	−	0.123081i	0.828306	−	0.560277i	$-0.189305\pi$
$5$	−0.355304	−	0.615405i	−0.0710609	−	0.123081i	−0.899367	+	0.437195i	$0.855972\pi$
$6$		0			0
$7$	2.70480	+	1.56162i	0.386401	+	0.223088i	0.680599	−	0.732656i	$-0.261719\pi$
$7$	2.70480	+	1.56162i	0.386401	+	0.223088i	−0.294199	+	0.955744i	$0.595053\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−14.3822	−	8.30359i	−1.30748	−	0.754872i	−0.325802	−	0.945438i	$-0.605634\pi$
$11$	−14.3822	−	8.30359i	−1.30748	−	0.754872i	−0.981674	+	0.190566i	$0.938968\pi$
$12$		0			0
$13$	−9.17743	−	15.8958i	−0.705956	−	1.22275i	−0.966345	−	0.257248i	$-0.917184\pi$
$13$	−9.17743	−	15.8958i	−0.705956	−	1.22275i	0.260389	−	0.965504i	$-0.416149\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	9.69321			0.570189			0.285095	−	0.958499i	$-0.407975\pi$
$17$	9.69321			0.570189			0.285095	+	0.958499i	$0.407975\pi$
$18$		0			0
$19$			8.20686i			0.431940i	0.976400	+	0.215970i	$0.0692913\pi$
$19$			8.20686i			0.431940i	−0.976400	+	0.215970i	$0.930709\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.94815	+	1.12477i	−0.0847022	+	0.0489028i	−0.541753	−	0.840538i	$-0.682239\pi$
$23$	−1.94815	+	1.12477i	−0.0847022	+	0.0489028i	0.457051	+	0.889441i	$0.348906\pi$
$24$		0			0
$25$	12.2475	−	21.2133i	0.489901	−	0.848533i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	20.8217	−	36.0642i	0.717989	−	1.24359i	−0.243806	−	0.969824i	$-0.578396\pi$
$29$	20.8217	−	36.0642i	0.717989	−	1.24359i	0.961795	−	0.273770i	$-0.0882707\pi$
$30$		0			0
$31$	−21.6298	+	12.4879i	−0.697734	+	0.402837i	−0.806503	−	0.591230i	$-0.798642\pi$
$31$	−21.6298	+	12.4879i	−0.697734	+	0.402837i	0.108769	+	0.994067i	$0.465309\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	2.21940i		−	0.0634115i
$36$		0			0
$37$	−40.3888			−1.09159			−0.545794	−	0.837919i	$-0.683772\pi$
$37$	−40.3888			−1.09159			−0.545794	+	0.837919i	$0.683772\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−25.6944	−	44.5040i	−0.626692	−	1.08546i	−0.988211	−	0.153098i	$-0.951075\pi$
$41$	−25.6944	−	44.5040i	−0.626692	−	1.08546i	0.361519	−	0.932365i	$-0.382258\pi$
$42$		0			0
$43$	−56.6621	−	32.7139i	−1.31772	−	0.760787i	−0.334360	−	0.942445i	$-0.608520\pi$
$43$	−56.6621	−	32.7139i	−1.31772	−	0.760787i	−0.983362	+	0.181658i	$0.941854\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−29.2894	−	16.9102i	−0.623179	−	0.359793i	0.154927	−	0.987926i	$-0.450486\pi$
$47$	−29.2894	−	16.9102i	−0.623179	−	0.359793i	−0.778106	+	0.628133i	$0.783819\pi$
$48$		0			0
$49$	−19.6227	−	33.9875i	−0.400463	−	0.693622i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	90.6691			1.71074			0.855369	−	0.518019i	$-0.173330\pi$
$53$	90.6691			1.71074			0.855369	+	0.518019i	$0.173330\pi$
$54$		0			0
$55$			11.8012i			0.214567i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	66.2243	−	38.2346i	1.12245	−	0.648045i	0.180422	−	0.983589i	$-0.442254\pi$
$59$	66.2243	−	38.2346i	1.12245	−	0.648045i	0.942024	+	0.335545i	$0.108920\pi$
$60$		0			0
$61$	1.35822	−	2.35250i	0.0222659	−	0.0385656i	−0.854678	−	0.519159i	$-0.826245\pi$
$61$	1.35822	−	2.35250i	0.0222659	−	0.0385656i	0.876944	+	0.480593i	$0.159579\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.52157	+	11.2957i	−0.100332	+	0.173780i
$66$		0			0
$67$	−34.5422	+	19.9429i	−0.515555	+	0.297656i	−0.735114	−	0.677943i	$-0.762871\pi$
$67$	−34.5422	+	19.9429i	−0.515555	+	0.297656i	0.219559	+	0.975599i	$0.429538\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			102.923i			1.44962i	0.688950	+	0.724809i	$0.258072\pi$
$71$			102.923i			1.44962i	−0.688950	+	0.724809i	$0.741928\pi$
$72$		0			0
$73$	38.1741			0.522933			0.261466	−	0.965213i	$-0.415794\pi$
$73$	38.1741			0.522933			0.261466	+	0.965213i	$0.415794\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−25.9341	−	44.9192i	−0.336806	−	0.583366i
$78$		0			0
$79$	94.4994	+	54.5593i	1.19620	+	0.690624i	0.959705	−	0.281010i	$-0.0906694\pi$
$79$	94.4994	+	54.5593i	1.19620	+	0.690624i	0.236491	+	0.971634i	$0.424003\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−113.503	−	65.5311i	−1.36751	−	0.789531i	−0.376899	−	0.926254i	$-0.623010\pi$
$83$	−113.503	−	65.5311i	−1.36751	−	0.789531i	−0.990609	+	0.136723i	$0.956343\pi$
$84$		0			0
$85$	−3.44404	−	5.96526i	−0.0405181	−	0.0701795i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−38.0903			−0.427981			−0.213991	−	0.976836i	$-0.568646\pi$
$89$	−38.0903			−0.427981			−0.213991	+	0.976836i	$0.568646\pi$
$90$		0			0
$91$		−	57.3266i		−	0.629963i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.05055	−	2.91593i	0.0531636	−	0.0306940i
$96$		0			0
$97$	−12.1961	+	21.1243i	−0.125733	+	0.217776i	−0.922019	−	0.387144i	$-0.873462\pi$
$97$	−12.1961	+	21.1243i	−0.125733	+	0.217776i	0.796286	+	0.604920i	$0.206795\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−98.1305	+	169.967i	−0.971589	+	1.68284i	−0.280829	+	0.959758i	$0.590609\pi$
$101$	−98.1305	+	169.967i	−0.971589	+	1.68284i	−0.690760	+	0.723084i	$0.742724\pi$
$102$		0			0
$103$	104.472	−	60.3172i	1.01430	−	0.585604i	0.101849	−	0.994800i	$-0.467524\pi$
$103$	104.472	−	60.3172i	1.01430	−	0.585604i	0.912446	+	0.409196i	$0.134191\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6.52440i		−	0.0609757i	−0.999535	−	0.0304878i	$-0.990294\pi$
$107$		−	6.52440i		−	0.0609757i	0.999535	−	0.0304878i	$-0.00970609\pi$
$108$		0			0
$109$	38.0272			0.348873			0.174437	−	0.984668i	$-0.444190\pi$
$109$	38.0272			0.348873			0.174437	+	0.984668i	$0.444190\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	53.5086	+	92.6795i	0.473527	+	0.820173i	0.999541	−	0.0303032i	$-0.00964728\pi$
$113$	53.5086	+	92.6795i	0.473527	+	0.820173i	−0.526014	+	0.850476i	$0.676314\pi$
$114$		0			0
$115$	1.38437	+	0.799268i	0.0120380	+	0.00695016i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	26.2182	+	15.1371i	0.220321	+	0.127203i
$120$		0			0
$121$	77.3992	+	134.059i	0.639662	+	1.10793i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−35.1716			−0.281373
$126$		0			0
$127$			101.437i			0.798713i	0.916796	+	0.399357i	$0.130766\pi$
$127$			101.437i			0.798713i	−0.916796	+	0.399357i	$0.869234\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	162.820	−	94.0042i	1.24290	−	0.717589i	0.273217	−	0.961952i	$-0.411912\pi$
$131$	162.820	−	94.0042i	1.24290	−	0.717589i	0.969684	+	0.244363i	$0.0785790\pi$
$132$		0			0
$133$	−12.8160	+	22.1979i	−0.0963608	+	0.166902i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−31.3271	+	54.2601i	−0.228665	+	0.396059i	−0.957413	−	0.288723i	$-0.906769\pi$
$137$	−31.3271	+	54.2601i	−0.228665	+	0.396059i	0.728748	+	0.684782i	$0.240103\pi$
$138$		0			0
$139$	40.5801	−	23.4289i	0.291943	−	0.168553i	−0.346875	−	0.937911i	$-0.612757\pi$
$139$	40.5801	−	23.4289i	0.291943	−	0.168553i	0.638818	+	0.769358i	$0.279424\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			304.822i			2.13163i
$144$		0			0
$145$	−29.5922			−0.204084
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−53.9860	−	93.5064i	−0.362322	−	0.627560i	0.626021	−	0.779806i	$-0.284683\pi$
$149$	−53.9860	−	93.5064i	−0.362322	−	0.627560i	−0.988343	+	0.152247i	$0.951349\pi$
$150$		0			0
$151$	−2.75240	−	1.58910i	−0.0182278	−	0.0105238i	0.490858	−	0.871239i	$-0.336683\pi$
$151$	−2.75240	−	1.58910i	−0.0182278	−	0.0105238i	−0.509086	+	0.860716i	$0.670017\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.3703	+	8.87405i	0.0991632	+	0.0572519i
$156$		0			0
$157$	128.215	+	222.075i	0.816656	+	1.41449i	0.908133	+	0.418683i	$0.137508\pi$
$157$	128.215	+	222.075i	0.816656	+	1.41449i	−0.0914764	+	0.995807i	$0.529159\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.02582			−0.0436386
$162$		0			0
$163$		−	201.100i		−	1.23374i	−0.787065	−	0.616870i	$-0.788400\pi$
$163$		−	201.100i		−	1.23374i	0.787065	−	0.616870i	$-0.211600\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	110.689	−	63.9062i	0.662807	−	0.382672i	−0.130538	−	0.991443i	$-0.541671\pi$
$167$	110.689	−	63.9062i	0.662807	−	0.382672i	0.793346	+	0.608771i	$0.208337\pi$
$168$		0			0
$169$	−83.9505	+	145.407i	−0.496749	+	0.860394i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−100.718	+	174.448i	−0.582183	+	1.00837i	0.413037	+	0.910714i	$0.364468\pi$
$173$	−100.718	+	174.448i	−0.582183	+	1.00837i	−0.995220	+	0.0976562i	$0.968865\pi$
$174$		0			0
$175$	66.2543	−	38.2519i	0.378596	−	0.218582i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			5.83187i			0.0325803i	0.999867	+	0.0162901i	$0.00518554\pi$
$179$			5.83187i			0.0325803i	−0.999867	+	0.0162901i	$0.994814\pi$
$180$		0			0
$181$	132.737			0.733353			0.366677	−	0.930348i	$-0.380496\pi$
$181$	132.737			0.733353			0.366677	+	0.930348i	$0.380496\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.3503	+	24.8555i	0.0775693	+	0.134354i
$186$		0			0
$187$	−139.410	−	80.4885i	−0.745509	−	0.430420i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	36.0843	+	20.8333i	0.188923	+	0.109075i	0.591478	−	0.806321i	$-0.298545\pi$
$191$	36.0843	+	20.8333i	0.188923	+	0.109075i	−0.402555	+	0.915396i	$0.631878\pi$
$192$		0			0
$193$	−69.1927	−	119.845i	−0.358511	−	0.620960i	0.629201	−	0.777242i	$-0.283382\pi$
$193$	−69.1927	−	119.845i	−0.358511	−	0.620960i	−0.987712	+	0.156283i	$0.950049\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	109.421			0.555438			0.277719	−	0.960662i	$-0.410422\pi$
$197$	109.421			0.555438			0.277719	+	0.960662i	$0.410422\pi$
$198$		0			0
$199$			87.0243i			0.437308i	0.975802	+	0.218654i	$0.0701666\pi$
$199$			87.0243i			0.437308i	−0.975802	+	0.218654i	$0.929833\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	112.637	−	65.0311i	0.554863	−	0.320350i
$204$		0			0
$205$	−18.2587	+	31.6249i	−0.0890666	+	0.154268i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	68.1464	−	118.033i	0.326059	−	0.564751i
$210$		0			0
$211$	−244.383	+	141.095i	−1.15821	+	0.668695i	−0.950875	−	0.309574i	$-0.899814\pi$
$211$	−244.383	+	141.095i	−1.15821	+	0.668695i	−0.207339	+	0.978269i	$0.566480\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			46.4935i			0.216249i
$216$		0			0
$217$	−78.0057			−0.359473
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−88.9588	−	154.081i	−0.402529	−	0.697200i
$222$		0			0
$223$	255.359	+	147.432i	1.14511	+	0.661129i	0.947691	−	0.319190i	$-0.103411\pi$
$223$	255.359	+	147.432i	1.14511	+	0.661129i	0.197419	+	0.980319i	$0.436744\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−124.390	−	71.8164i	−0.547972	−	0.316372i	0.200332	−	0.979728i	$-0.435798\pi$
$227$	−124.390	−	71.8164i	−0.547972	−	0.316372i	−0.748304	+	0.663356i	$0.769131\pi$
$228$		0			0
$229$	−141.426	−	244.958i	−0.617583	−	1.06968i	−0.989925	−	0.141590i	$-0.954779\pi$
$229$	−141.426	−	244.958i	−0.617583	−	1.06968i	0.372343	−	0.928095i	$-0.378555\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.9127			0.111213			0.0556067	−	0.998453i	$-0.482291\pi$
$233$	25.9127			0.111213			0.0556067	+	0.998453i	$0.482291\pi$
$234$		0			0
$235$			24.0331i			0.102269i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−310.807	+	179.444i	−1.30045	+	0.750813i	−0.980481	−	0.196616i	$-0.937005\pi$
$239$	−310.807	+	179.444i	−1.30045	+	0.750813i	−0.319966	+	0.947429i	$0.603672\pi$
$240$		0			0
$241$	87.7048	−	151.909i	0.363920	−	0.630328i	−0.624682	−	0.780879i	$-0.714771\pi$
$241$	87.7048	−	151.909i	0.363920	−	0.630328i	0.988602	+	0.150551i	$0.0481048\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.9441	+	24.1518i	−0.0569145	+	0.0985789i
$246$		0			0
$247$	130.454	−	75.3179i	0.528156	−	0.304931i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	410.044i		−	1.63364i	−0.576891	−	0.816821i	$-0.695734\pi$
$251$		−	410.044i		−	1.63364i	0.576891	−	0.816821i	$-0.304266\pi$
$252$		0			0
$253$	37.3583			0.147661
$254$		0			0
$255$		0			0
$256$		0			0
$257$	86.4280	+	149.698i	0.336296	+	0.582481i	0.983733	−	0.179638i	$-0.0574925\pi$
$257$	86.4280	+	149.698i	0.336296	+	0.582481i	−0.647437	+	0.762119i	$0.724159\pi$
$258$		0			0
$259$	−109.244	−	63.0719i	−0.421790	−	0.243521i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−132.696	−	76.6118i	−0.504546	−	0.291300i	0.226043	−	0.974117i	$-0.427421\pi$
$263$	−132.696	−	76.6118i	−0.504546	−	0.291300i	−0.730589	+	0.682818i	$0.760754\pi$
$264$		0			0
$265$	−32.2151	−	55.7983i	−0.121567	−	0.210559i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.6752			−0.0471198			−0.0235599	−	0.999722i	$-0.507500\pi$
$269$	−12.6752			−0.0471198			−0.0235599	+	0.999722i	$0.507500\pi$
$270$		0			0
$271$			40.7101i			0.150222i	0.997175	+	0.0751108i	$0.0239311\pi$
$271$			40.7101i			0.150222i	−0.997175	+	0.0751108i	$0.976069\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−352.293	+	203.397i	−1.28107	+	0.739624i
$276$		0			0
$277$	184.143	−	318.945i	0.664776	−	1.15143i	−0.314570	−	0.949234i	$-0.601860\pi$
$277$	184.143	−	318.945i	0.664776	−	1.15143i	0.979346	−	0.202191i	$-0.0648063\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	238.310	−	412.765i	0.848078	−	1.46891i	−0.0348433	−	0.999393i	$-0.511093\pi$
$281$	238.310	−	412.765i	0.848078	−	1.46891i	0.882921	−	0.469521i	$-0.155573\pi$
$282$		0			0
$283$	150.052	−	86.6323i	0.530217	−	0.306121i	−0.210888	−	0.977510i	$-0.567635\pi$
$283$	150.052	−	86.6323i	0.530217	−	0.306121i	0.741105	+	0.671389i	$0.234302\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	160.499i		−	0.559231i
$288$		0			0
$289$	−195.042			−0.674884
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.91833	+	5.05470i	0.00996017	+	0.0172515i	0.870963	−	0.491349i	$-0.163496\pi$
$293$	2.91833	+	5.05470i	0.00996017	+	0.0172515i	−0.861002	+	0.508601i	$0.830163\pi$
$294$		0			0
$295$	−47.0596	−	27.1699i	−0.159524	−	0.0921013i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	35.7580	+	20.6449i	0.119592	+	0.0690465i
$300$		0			0
$301$	−102.173	−	176.969i	−0.339446	−	0.587937i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.93032			−0.00632893
$306$		0			0
$307$			371.717i			1.21080i	0.795920	+	0.605402i	$0.206988\pi$
$307$			371.717i			1.21080i	−0.795920	+	0.605402i	$0.793012\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	193.964	−	111.985i	0.623679	−	0.360081i	−0.154621	−	0.987974i	$-0.549416\pi$
$311$	193.964	−	111.985i	0.623679	−	0.360081i	0.778300	+	0.627892i	$0.216082\pi$
$312$		0			0
$313$	79.0960	−	136.998i	0.252703	−	0.437694i	−0.711566	−	0.702619i	$-0.752014\pi$
$313$	79.0960	−	136.998i	0.252703	−	0.437694i	0.964269	+	0.264925i	$0.0853472\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	206.428	−	357.543i	0.651191	−	1.12790i	−0.331643	−	0.943405i	$-0.607603\pi$
$317$	206.428	−	357.543i	0.651191	−	1.12790i	0.982834	−	0.184491i	$-0.0590637\pi$
$318$		0			0
$319$	−598.925	+	345.789i	−1.87751	+	1.08398i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			79.5508i			0.246287i
$324$		0			0
$325$	−449.603			−1.38339
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−52.8147	−	91.4778i	−0.160531	−	0.278048i
$330$		0			0
$331$	−126.937	−	73.2871i	−0.383495	−	0.221411i	0.295843	−	0.955237i	$-0.404400\pi$
$331$	−126.937	−	73.2871i	−0.383495	−	0.221411i	−0.679338	+	0.733826i	$0.737733\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	24.5460	+	14.1716i	0.0732716	+	0.0423034i
$336$		0			0
$337$	−47.3499	−	82.0124i	−0.140504	−	0.243360i	0.787182	−	0.616720i	$-0.211539\pi$
$337$	−47.3499	−	82.0124i	−0.140504	−	0.243360i	−0.927687	+	0.373360i	$0.878206\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	414.779			1.21636
$342$		0			0
$343$		−	275.611i		−	0.803532i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	81.3438	−	46.9639i	0.234420	−	0.135343i	−0.378189	−	0.925728i	$-0.623453\pi$
$347$	81.3438	−	46.9639i	0.234420	−	0.135343i	0.612609	+	0.790386i	$0.290120\pi$
$348$		0			0
$349$	−115.579	+	200.188i	−0.331171	+	0.573605i	−0.982742	−	0.184983i	$-0.940777\pi$
$349$	−115.579	+	200.188i	−0.331171	+	0.573605i	0.651571	+	0.758588i	$0.274110\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	48.9623	−	84.8052i	0.138703	−	0.240241i	−0.788303	−	0.615288i	$-0.789040\pi$
$353$	48.9623	−	84.8052i	0.138703	−	0.240241i	0.927006	+	0.375046i	$0.122373\pi$
$354$		0			0
$355$	63.3393	−	36.5690i	0.178421	−	0.103011i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	244.287i		−	0.680465i	−0.940341	−	0.340233i	$-0.889494\pi$
$359$		−	244.287i		−	0.680465i	0.940341	−	0.340233i	$-0.110506\pi$
$360$		0			0
$361$	293.647			0.813428
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.5634	−	23.4925i	−0.0371601	−	0.0643631i
$366$		0			0
$367$	−368.327	−	212.654i	−1.00362	−	0.579438i	−0.0942999	−	0.995544i	$-0.530061\pi$
$367$	−368.327	−	212.654i	−1.00362	−	0.579438i	−0.909316	+	0.416106i	$0.863395\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	245.242	+	141.591i	0.661030	+	0.381646i
$372$		0			0
$373$	44.8567	+	77.6941i	0.120259	+	0.208295i	0.919870	−	0.392224i	$-0.128294\pi$
$373$	44.8567	+	77.6941i	0.120259	+	0.208295i	−0.799611	+	0.600519i	$0.794961\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−764.359			−2.02748
$378$		0			0
$379$		−	406.140i		−	1.07161i	−0.844342	−	0.535805i	$-0.820008\pi$
$379$		−	406.140i		−	1.07161i	0.844342	−	0.535805i	$-0.179992\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−280.901	+	162.178i	−0.733423	+	0.423442i	−0.819673	−	0.572832i	$-0.805845\pi$
$383$	−280.901	+	162.178i	−0.733423	+	0.423442i	0.0862502	+	0.996274i	$0.472512\pi$
$384$		0			0
$385$	−18.4290	+	31.9200i	−0.0478675	+	0.0829090i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	28.6761	−	49.6685i	0.0737176	−	0.127683i	−0.826810	−	0.562481i	$-0.809847\pi$
$389$	28.6761	−	49.6685i	0.0737176	−	0.127683i	0.900528	+	0.434798i	$0.143180\pi$
$390$		0			0
$391$	−18.8838	+	10.9026i	−0.0482963	+	0.0278839i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	77.5406i		−	0.196305i
$396$		0			0
$397$	194.475			0.489861			0.244931	−	0.969541i	$-0.421235\pi$
$397$	194.475			0.489861			0.244931	+	0.969541i	$0.421235\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	163.943	+	283.958i	0.408836	+	0.708124i	0.994760	−	0.102242i	$-0.0326016\pi$
$401$	163.943	+	283.958i	0.408836	+	0.708124i	−0.585924	+	0.810366i	$0.699268\pi$
$402$		0			0
$403$	397.011	+	229.215i	0.985140	+	0.568771i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	580.881	+	335.372i	1.42723	+	0.824009i
$408$		0			0
$409$	−36.6786	−	63.5292i	−0.0896787	−	0.155328i	0.817697	−	0.575649i	$-0.195251\pi$
$409$	−36.6786	−	63.5292i	−0.0896787	−	0.155328i	−0.907375	+	0.420321i	$0.861917\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	238.832			0.578285
$414$		0			0
$415$			93.1340i			0.224419i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−557.390	+	321.809i	−1.33029	+	0.768041i	−0.985343	−	0.170582i	$-0.945435\pi$
$419$	−557.390	+	321.809i	−1.33029	+	0.768041i	−0.344943	+	0.938624i	$0.612102\pi$
$420$		0			0
$421$	−280.151	+	485.236i	−0.665441	+	1.15258i	0.313724	+	0.949514i	$0.398423\pi$
$421$	−280.151	+	485.236i	−0.665441	+	1.15258i	−0.979165	+	0.203064i	$0.934910\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	118.718	−	205.625i	0.279336	−	0.483824i
$426$		0			0
$427$	7.34742	−	4.24204i	0.0172071	−	0.00993451i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	536.437i		−	1.24463i	−0.782765	−	0.622317i	$-0.786191\pi$
$431$		−	536.437i		−	1.24463i	0.782765	−	0.622317i	$-0.213809\pi$
$432$		0			0
$433$	281.999			0.651268			0.325634	−	0.945496i	$-0.394422\pi$
$433$	281.999			0.651268			0.325634	+	0.945496i	$0.394422\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.23079	−	15.9882i	−0.0211231	−	0.0365863i
$438$		0			0
$439$	87.2604	+	50.3798i	0.198771	+	0.114760i	0.596082	−	0.802924i	$-0.296723\pi$
$439$	87.2604	+	50.3798i	0.198771	+	0.114760i	−0.397311	+	0.917684i	$0.630057\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	519.799	+	300.106i	1.17336	+	0.677440i	0.954469	−	0.298309i	$-0.0964227\pi$
$443$	519.799	+	300.106i	1.17336	+	0.677440i	0.218891	+	0.975749i	$0.429756\pi$
$444$		0			0
$445$	13.5337	+	23.4410i	0.0304127	+	0.0526764i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−639.843			−1.42504			−0.712520	−	0.701651i	$-0.752446\pi$
$449$	−639.843			−1.42504			−0.712520	+	0.701651i	$0.752446\pi$
$450$		0			0
$451$			853.422i			1.89229i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−35.2791	+	20.3684i	−0.0775365	+	0.0447657i
$456$		0			0
$457$	86.7721	−	150.294i	0.189873	−	0.328870i	−0.755334	−	0.655339i	$-0.772526\pi$
$457$	86.7721	−	150.294i	0.189873	−	0.328870i	0.945208	+	0.326469i	$0.105859\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−361.655	+	626.406i	−0.784502	+	1.35880i	0.144794	+	0.989462i	$0.453748\pi$
$461$	−361.655	+	626.406i	−0.784502	+	1.35880i	−0.929296	+	0.369336i	$0.879585\pi$
$462$		0			0
$463$	643.880	−	371.744i	1.39067	−	0.802903i	0.397280	−	0.917698i	$-0.369954\pi$
$463$	643.880	−	371.744i	1.39067	−	0.802903i	0.993389	+	0.114794i	$0.0366210\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			98.0700i			0.210000i	0.994472	+	0.105000i	$0.0334842\pi$
$467$			98.0700i			0.210000i	−0.994472	+	0.105000i	$0.966516\pi$
$468$		0			0
$469$	−124.573			−0.265614
$470$		0			0
$471$		0			0
$472$		0			0
$473$	543.285	+	940.997i	1.14859	+	1.98942i
$474$		0			0
$475$	174.095	+	100.514i	0.366515	+	0.211608i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−293.648	−	169.538i	−0.613043	−	0.353941i	0.161112	−	0.986936i	$-0.448492\pi$
$479$	−293.648	−	169.538i	−0.613043	−	0.353941i	−0.774156	+	0.632995i	$0.781825\pi$
$480$		0			0
$481$	370.665	+	642.011i	0.770614	+	1.33474i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.3334			0.0357389
$486$		0			0
$487$		−	777.718i		−	1.59696i	−0.602023	−	0.798479i	$-0.705638\pi$
$487$		−	777.718i		−	1.59696i	0.602023	−	0.798479i	$-0.294362\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	52.0054	−	30.0254i	0.105917	−	0.0611514i	−0.446106	−	0.894980i	$-0.647189\pi$
$491$	52.0054	−	30.0254i	0.105917	−	0.0611514i	0.552023	+	0.833829i	$0.313856\pi$
$492$		0			0
$493$	201.829	−	349.578i	0.409390	−	0.709084i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−160.726	+	278.386i	−0.323393	+	0.560133i
$498$		0			0
$499$	250.110	−	144.401i	0.501222	−	0.289381i	−0.227996	−	0.973662i	$-0.573217\pi$
$499$	250.110	−	144.401i	0.501222	−	0.289381i	0.729218	+	0.684281i	$0.239884\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	567.389i		−	1.12801i	−0.825772	−	0.564005i	$-0.809260\pi$
$503$		−	567.389i		−	1.12801i	0.825772	−	0.564005i	$-0.190740\pi$
$504$		0			0
$505$	139.465			0.276168
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−158.283	−	274.155i	−0.310970	−	0.538615i	0.667603	−	0.744517i	$-0.267320\pi$
$509$	−158.283	−	274.155i	−0.310970	−	0.538615i	−0.978573	+	0.205902i	$0.933987\pi$
$510$		0			0
$511$	103.253	+	59.6134i	0.202061	+	0.116660i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−74.2390	−	42.8619i	−0.144153	−	0.0832271i
$516$		0			0
$517$	280.831	+	486.414i	0.543194	+	0.940840i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−597.419			−1.14668			−0.573339	−	0.819318i	$-0.694352\pi$
$521$	−597.419			−1.14668			−0.573339	+	0.819318i	$0.694352\pi$
$522$		0			0
$523$		−	630.846i		−	1.20621i	−0.797663	−	0.603103i	$-0.793931\pi$
$523$		−	630.846i		−	1.20621i	0.797663	−	0.603103i	$-0.206069\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−209.662	+	121.048i	−0.397840	+	0.229693i
$528$		0			0
$529$	−261.970	+	453.745i	−0.495217	+	0.857741i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−471.617	+	816.865i	−0.884835	+	1.53258i
$534$		0			0
$535$	−4.01515	+	2.31815i	−0.00750495	+	0.00433299i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			651.755i			1.20919i
$540$		0			0
$541$	−144.808			−0.267667			−0.133834	−	0.991004i	$-0.542729\pi$
$541$	−144.808			−0.267667			−0.133834	+	0.991004i	$0.542729\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.5112	−	23.4022i	−0.0247913	−	0.0429397i
$546$		0			0
$547$	679.104	+	392.081i	1.24151	+	0.716784i	0.969401	−	0.245484i	$-0.0789468\pi$
$547$	679.104	+	392.081i	1.24151	+	0.716784i	0.272105	+	0.962268i	$0.412280\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	295.974	+	170.881i	0.537158	+	0.310128i
$552$		0			0
$553$	170.402	+	295.144i	0.308140	+	0.533715i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−92.1884			−0.165509			−0.0827544	−	0.996570i	$-0.526372\pi$
$557$	−92.1884			−0.165509			−0.0827544	+	0.996570i	$0.526372\pi$
$558$		0			0
$559$			1200.92i			2.14833i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−141.939	+	81.9485i	−0.252112	+	0.145557i	−0.620731	−	0.784024i	$-0.713164\pi$
$563$	−141.939	+	81.9485i	−0.252112	+	0.145557i	0.368619	+	0.929581i	$0.379831\pi$
$564$		0			0
$565$	38.0237	−	65.8589i	0.0672985	−	0.116564i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	352.219	−	610.061i	0.619014	−	1.07216i	−0.370652	−	0.928772i	$-0.620866\pi$
$569$	352.219	−	610.061i	0.619014	−	1.07216i	0.989666	−	0.143392i	$-0.0458009\pi$
$570$		0			0
$571$	413.817	−	238.917i	0.724723	−	0.418419i	−0.0917653	−	0.995781i	$-0.529251\pi$
$571$	413.817	−	238.917i	0.724723	−	0.418419i	0.816489	+	0.577361i	$0.195918\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			55.1023i			0.0958301i
$576$		0			0
$577$	−21.5525			−0.0373527			−0.0186764	−	0.999826i	$-0.505945\pi$
$577$	−21.5525			−0.0373527			−0.0186764	+	0.999826i	$0.505945\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−204.669	−	354.498i	−0.352271	−	0.610151i
$582$		0			0
$583$	−1304.02	−	752.879i	−2.23675	−	1.29139i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	686.177	+	396.164i	1.16896	+	0.674897i	0.953434	−	0.301602i	$-0.0975215\pi$
$587$	686.177	+	396.164i	1.16896	+	0.674897i	0.215522	+	0.976499i	$0.430855\pi$
$588$		0			0
$589$	−102.487	−	177.512i	−0.174001	−	0.301379i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	571.777			0.964211			0.482105	−	0.876113i	$-0.339872\pi$
$593$	571.777			0.964211			0.482105	+	0.876113i	$0.339872\pi$
$594$		0			0
$595$		−	21.5131i		−	0.0361565i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	803.662	−	463.994i	1.34167	−	0.774615i	0.354620	−	0.935011i	$-0.384610\pi$
$599$	803.662	−	463.994i	1.34167	−	0.774615i	0.987053	+	0.160396i	$0.0512770\pi$
$600$		0			0
$601$	−66.4316	+	115.063i	−0.110535	+	0.191452i	−0.915986	−	0.401210i	$-0.868590\pi$
$601$	−66.4316	+	115.063i	−0.110535	+	0.191452i	0.805451	+	0.592662i	$0.201923\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	55.0005	−	95.2637i	0.0909100	−	0.157461i
$606$		0			0
$607$	−480.102	+	277.187i	−0.790942	+	0.456651i	−0.840294	−	0.542131i	$-0.817618\pi$
$607$	−480.102	+	277.187i	−0.790942	+	0.456651i	0.0493520	+	0.998781i	$0.484284\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			620.771i			1.01599i
$612$		0			0
$613$	1096.88			1.78937			0.894684	−	0.446700i	$-0.147401\pi$
$613$	1096.88			1.78937			0.894684	+	0.446700i	$0.147401\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	311.636	+	539.770i	0.505083	+	0.874829i	0.999983	+	0.00587917i	$0.00187141\pi$
$617$	311.636	+	539.770i	0.505083	+	0.874829i	−0.494900	+	0.868950i	$0.664795\pi$
$618$		0			0
$619$	613.432	+	354.165i	0.991005	+	0.572157i	0.905575	−	0.424187i	$-0.139440\pi$
$619$	613.432	+	354.165i	0.991005	+	0.572157i	0.0854305	+	0.996344i	$0.472773\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−103.027	−	59.4826i	−0.165372	−	0.0954777i
$624$		0			0
$625$	−293.691	−	508.688i	−0.469906	−	0.813901i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−391.497			−0.622412
$630$		0			0
$631$		−	1142.86i		−	1.81119i	−0.424139	−	0.905597i	$-0.639423\pi$
$631$		−	1142.86i		−	1.81119i	0.424139	−	0.905597i	$-0.360577\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	62.4246	−	36.0409i	0.0983065	−	0.0567573i
$636$		0			0
$637$	−360.172	+	623.836i	−0.565419	+	0.979334i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	138.542	−	239.961i	0.216134	−	0.374354i	−0.737489	−	0.675359i	$-0.763989\pi$
$641$	138.542	−	239.961i	0.216134	−	0.374354i	0.953623	+	0.301005i	$0.0973220\pi$
$642$		0			0
$643$	−737.236	+	425.644i	−1.14656	+	0.661965i	−0.948046	−	0.318133i	$-0.896944\pi$
$643$	−737.236	+	425.644i	−1.14656	+	0.661965i	−0.198511	+	0.980099i	$0.563611\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	706.622i		−	1.09215i	−0.837736	−	0.546076i	$-0.816121\pi$
$647$		−	706.622i		−	1.09215i	0.837736	−	0.546076i	$-0.183879\pi$
$648$		0			0
$649$	−1269.94			−1.95676
$650$		0			0
$651$		0			0
$652$		0			0
$653$	390.342	+	676.092i	0.597767	+	1.03536i	0.993150	+	0.116846i	$0.0372784\pi$
$653$	390.342	+	676.092i	0.597767	+	1.03536i	−0.395383	+	0.918516i	$0.629388\pi$
$654$		0			0
$655$	−115.701	−	66.8002i	−0.176643	−	0.101985i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−491.322	−	283.665i	−0.745557	−	0.430447i	0.0785296	−	0.996912i	$-0.474977\pi$
$659$	−491.322	−	283.665i	−0.745557	−	0.430447i	−0.824086	+	0.566465i	$0.808311\pi$
$660$		0			0
$661$	46.9164	+	81.2615i	0.0709778	+	0.122937i	0.899330	−	0.437270i	$-0.144055\pi$
$661$	46.9164	+	81.2615i	0.0709778	+	0.122937i	−0.828352	+	0.560208i	$0.810721\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	18.2143			0.0273899
$666$		0			0
$667$			93.6780i			0.140447i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−39.0684	+	22.5562i	−0.0582241	+	0.0336157i
$672$		0			0
$673$	100.742	−	174.490i	0.149691	−	0.259272i	−0.781422	−	0.624003i	$-0.785505\pi$
$673$	100.742	−	174.490i	0.149691	−	0.259272i	0.931113	+	0.364730i	$0.118839\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	336.988	−	583.680i	0.497766	−	0.862157i	−0.502230	−	0.864734i	$-0.667487\pi$
$677$	336.988	−	583.680i	0.497766	−	0.862157i	0.999997	+	0.00257723i	$0.000820358\pi$
$678$		0			0
$679$	−65.9763	+	38.0914i	−0.0971668	+	0.0560993i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	155.633i		−	0.227867i	−0.993488	−	0.113933i	$-0.963655\pi$
$683$		−	155.633i		−	0.227867i	0.993488	−	0.113933i	$-0.0363450\pi$
$684$		0			0
$685$	44.5226			0.0649965
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−832.110	−	1441.26i	−1.20771	−	2.09181i
$690$		0			0
$691$	−693.263	−	400.255i	−1.00327	−	0.579241i	−0.0940588	−	0.995567i	$-0.529984\pi$
$691$	−693.263	−	400.255i	−1.00327	−	0.579241i	−0.909215	+	0.416326i	$0.863318\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.8366	−	16.6488i	−0.0414915	−	0.0239551i
$696$		0			0
$697$	−249.061	−	431.387i	−0.357333	−	0.618919i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	488.317			0.696601			0.348300	−	0.937383i	$-0.386759\pi$
$701$	488.317			0.696601			0.348300	+	0.937383i	$0.386759\pi$
$702$		0			0
$703$		−	331.465i		−	0.471501i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−530.848	+	306.485i	−0.750845	+	0.433501i
$708$		0			0
$709$	358.633	−	621.170i	0.505829	−	0.876121i	−0.494149	−	0.869377i	$-0.664520\pi$
$709$	358.633	−	621.170i	0.505829	−	0.876121i	0.999977	−	0.00674353i	$-0.00214655\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	28.0920	−	48.6568i	0.0393997	−	0.0682423i
$714$		0			0
$715$	187.589	−	108.305i	0.262363	−	0.151475i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			512.219i			0.712404i	0.934409	+	0.356202i	$0.115929\pi$
$719$			512.219i			0.712404i	−0.934409	+	0.356202i	$0.884071\pi$
$720$		0			0
$721$	376.770			0.522566
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−510.028	−	883.394i	−0.703487	−	1.21848i
$726$		0			0
$727$	574.499	+	331.687i	0.790232	+	0.456241i	0.840044	−	0.542518i	$-0.182529\pi$
$727$	574.499	+	331.687i	0.790232	+	0.456241i	−0.0498122	+	0.998759i	$0.515862\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−549.237	−	317.102i	−0.751351	−	0.433793i
$732$		0			0
$733$	−146.883	−	254.408i	−0.200386	−	0.347078i	0.748267	−	0.663398i	$-0.230886\pi$
$733$	−146.883	−	254.408i	−0.200386	−	0.347078i	−0.948653	+	0.316320i	$0.897553\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	662.392			0.898768
$738$		0			0
$739$			1335.27i			1.80686i	0.428736	+	0.903430i	$0.358959\pi$
$739$			1335.27i			1.80686i	−0.428736	+	0.903430i	$0.641041\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	488.188	−	281.855i	0.657050	−	0.379348i	−0.134102	−	0.990968i	$-0.542815\pi$
$743$	488.188	−	281.855i	0.657050	−	0.379348i	0.791152	+	0.611620i	$0.209482\pi$
$744$		0			0
$745$	−38.3629	+	66.4465i	−0.0514938	+	0.0891899i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.1886	−	17.6472i	0.0136030	−	0.0235610i
$750$		0			0
$751$	−591.407	+	341.449i	−0.787493	+	0.454659i	−0.839079	−	0.544009i	$-0.816906\pi$
$751$	−591.407	+	341.449i	−0.787493	+	0.454659i	0.0515861	+	0.998669i	$0.483572\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			2.25845i			0.00299133i
$756$		0			0
$757$	−534.746			−0.706401			−0.353201	−	0.935548i	$-0.614907\pi$
$757$	−534.746			−0.706401			−0.353201	+	0.935548i	$0.614907\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	416.191	+	720.863i	0.546900	+	0.947258i	0.998485	+	0.0550300i	$0.0175254\pi$
$761$	416.191	+	720.863i	0.546900	+	0.947258i	−0.451585	+	0.892228i	$0.649141\pi$
$762$		0			0
$763$	102.856	+	59.3840i	0.134805	+	0.0778296i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1215.54	−	701.791i	−1.58480	−	0.914982i
$768$		0			0
$769$	−351.020	−	607.985i	−0.456464	−	0.790618i	0.542308	−	0.840180i	$-0.317551\pi$
$769$	−351.020	−	607.985i	−0.456464	−	0.790618i	−0.998771	+	0.0495620i	$0.984217\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	472.477			0.611225			0.305612	−	0.952156i	$-0.401139\pi$
$773$	472.477			0.611225			0.305612	+	0.952156i	$0.401139\pi$
$774$		0			0
$775$			611.785i			0.789400i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	365.238	−	210.870i	0.468855	−	0.270693i
$780$		0			0
$781$	854.630	−	1480.26i	1.09428	−	1.89534i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	91.1107	−	157.808i	0.116065	−	0.201030i
$786$		0			0
$787$	556.186	−	321.114i	0.706717	−	0.408023i	−0.103127	−	0.994668i	$-0.532885\pi$
$787$	556.186	−	321.114i	0.706717	−	0.408023i	0.809844	+	0.586645i	$0.199552\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			334.240i			0.422554i
$792$		0			0
$793$	−49.8598			−0.0628749
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−42.3167	−	73.2947i	−0.0530950	−	0.0919632i	0.838256	−	0.545276i	$-0.183575\pi$
$797$	−42.3167	−	73.2947i	−0.0530950	−	0.0919632i	−0.891351	+	0.453313i	$0.850242\pi$
$798$		0			0
$799$	−283.909	−	163.915i	−0.355330	−	0.205150i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−549.029	−	316.982i	−0.683722	−	0.394747i
$804$		0			0
$805$	2.49630	+	4.32373i	0.00310100	+	0.00537109i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1071.63			1.32464			0.662319	−	0.749222i	$-0.269573\pi$
$809$	1071.63			1.32464			0.662319	+	0.749222i	$0.269573\pi$
$810$		0			0
$811$		−	745.523i		−	0.919264i	−0.888110	−	0.459632i	$-0.847981\pi$
$811$		−	745.523i		−	0.919264i	0.888110	−	0.459632i	$-0.152019\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−123.758	+	71.4516i	−0.151850	+	0.0876707i
$816$		0			0
$817$	268.478	−	465.017i	0.328614	−	0.569177i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−417.550	+	723.217i	−0.508587	+	0.880898i	0.491364	+	0.870954i	$0.336499\pi$
$821$	−417.550	+	723.217i	−0.508587	+	0.880898i	−0.999951	+	0.00994363i	$0.996835\pi$
$822$		0			0
$823$	369.777	−	213.491i	0.449304	−	0.259406i	−0.258232	−	0.966083i	$-0.583140\pi$
$823$	369.777	−	213.491i	0.449304	−	0.259406i	0.707536	+	0.706677i	$0.249807\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	235.457i		−	0.284713i	−0.989815	−	0.142356i	$-0.954532\pi$
$827$		−	235.457i		−	0.284713i	0.989815	−	0.142356i	$-0.0454679\pi$
$828$		0			0
$829$	−1336.05			−1.61164			−0.805819	−	0.592161i	$-0.798275\pi$
$829$	−1336.05			−1.61164			−0.805819	+	0.592161i	$0.798275\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−190.207	−	329.448i	−0.228340	−	0.395496i
$834$		0			0
$835$	−78.6565	−	45.4123i	−0.0941994	−	0.0543860i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1315.40	−	759.449i	−1.56782	−	0.905183i	−0.996422	−	0.0845127i	$-0.973067\pi$
$839$	−1315.40	−	759.449i	−1.56782	−	0.905183i	−0.571401	−	0.820671i	$-0.693600\pi$
$840$		0			0
$841$	−446.586	−	773.509i	−0.531017	−	0.919749i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	119.312			0.141198
$846$		0			0
$847$			483.472i			0.570805i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	78.6834	−	45.4279i	0.0924599	−	0.0533818i
$852$		0			0
$853$	−219.635	+	380.418i	−0.257485	+	0.445977i	−0.965568	−	0.260153i	$-0.916227\pi$
$853$	−219.635	+	380.418i	−0.257485	+	0.445977i	0.708083	+	0.706130i	$0.249560\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−42.9674	+	74.4218i	−0.0501370	+	0.0868399i	−0.890005	−	0.455951i	$-0.849299\pi$
$857$	−42.9674	+	74.4218i	−0.0501370	+	0.0868399i	0.839868	+	0.542791i	$0.182632\pi$
$858$		0			0
$859$	−750.391	+	433.239i	−0.873564	+	0.504352i	−0.868531	−	0.495635i	$-0.834935\pi$
$859$	−750.391	+	433.239i	−0.873564	+	0.504352i	−0.00503295	+	0.999987i	$0.501602\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			651.682i			0.755136i	0.925982	+	0.377568i	$0.123240\pi$
$863$			651.682i			0.755136i	−0.925982	+	0.377568i	$0.876760\pi$
$864$		0			0
$865$	143.142			0.165482
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−906.076	−	1569.37i	−1.04266	−	1.80595i
$870$		0			0
$871$	634.017	+	366.050i	0.727919	+	0.420264i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−95.1323	−	54.9247i	−0.108723	−	0.0627711i
$876$		0			0
$877$	−359.003	−	621.811i	−0.409353	−	0.709020i	0.585464	−	0.810698i	$-0.300912\pi$
$877$	−359.003	−	621.811i	−0.409353	−	0.709020i	−0.994817	+	0.101678i	$0.967579\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−292.378			−0.331870			−0.165935	−	0.986137i	$-0.553064\pi$
$881$	−292.378			−0.331870			−0.165935	+	0.986137i	$0.553064\pi$
$882$		0			0
$883$			507.123i			0.574318i	0.957883	+	0.287159i	$0.0927109\pi$
$883$			507.123i			0.574318i	−0.957883	+	0.287159i	$0.907289\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	222.320	−	128.356i	0.250642	−	0.144708i	−0.369416	−	0.929264i	$-0.620442\pi$
$887$	222.320	−	128.356i	0.250642	−	0.144708i	0.620058	+	0.784556i	$0.287109\pi$
$888$		0			0
$889$	−158.405	+	274.366i	−0.178184	+	0.308623i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	138.780	−	240.374i	0.155409	−	0.269176i
$894$		0			0
$895$	3.58896	−	2.07209i	0.00401001	−	0.00231518i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1040.08i			1.15693i
$900$		0			0
$901$	878.875			0.975444
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−47.1620	−	81.6870i	−0.0521127	−	0.0902619i
$906$		0			0
$907$	−1341.24	−	774.365i	−1.47877	−	0.853766i	−0.479054	−	0.877785i	$-0.659020\pi$
$907$	−1341.24	−	774.365i	−1.47877	−	0.853766i	−0.999711	+	0.0240198i	$0.992354\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	465.815	+	268.938i	0.511322	+	0.295212i	0.733377	−	0.679822i	$-0.237943\pi$
$911$	465.815	+	268.938i	0.511322	+	0.295212i	−0.222055	+	0.975034i	$0.571276\pi$
$912$		0			0
$913$	1088.29	+	1884.97i	1.19199	+	2.06459i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	587.195			0.640343
$918$		0			0
$919$		−	1099.66i		−	1.19659i	−0.801277	−	0.598294i	$-0.795845\pi$
$919$		−	1099.66i		−	1.19659i	0.801277	−	0.598294i	$-0.204155\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1636.04	−	944.568i	1.77252	−	1.02337i
$924$		0			0
$925$	−494.662	+	856.780i	−0.534770	+	0.926249i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	97.6555	−	169.144i	0.105119	−	0.182071i	−0.808668	−	0.588265i	$-0.799811\pi$
$929$	97.6555	−	169.144i	0.105119	−	0.182071i	0.913787	+	0.406194i	$0.133144\pi$
$930$		0			0
$931$	278.931	−	161.041i	0.299603	−	0.172976i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			114.392i			0.122344i
$936$		0			0
$937$	1286.97			1.37350			0.686752	−	0.726892i	$-0.259036\pi$
$937$	1286.97			1.37350			0.686752	+	0.726892i	$0.259036\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	505.685	+	875.873i	0.537391	+	0.930789i	0.999043	+	0.0437282i	$0.0139236\pi$
$941$	505.685	+	875.873i	0.537391	+	0.930789i	−0.461652	+	0.887061i	$0.652743\pi$
$942$		0			0
$943$	100.113	+	57.8003i	0.106164	+	0.0612941i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	598.516	+	345.553i	0.632013	+	0.364893i	0.781531	−	0.623866i	$-0.214439\pi$
$947$	598.516	+	345.553i	0.632013	+	0.364893i	−0.149519	+	0.988759i	$0.547772\pi$
$948$		0			0
$949$	−350.340	−	606.807i	−0.369168	−	0.639417i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−659.310			−0.691826			−0.345913	−	0.938267i	$-0.612431\pi$
$953$	−659.310			−0.691826			−0.345913	+	0.938267i	$0.612431\pi$
$954$		0			0
$955$		−	29.6086i		−	0.0310038i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−169.467	+	97.8419i	−0.176712	+	0.102025i
$960$		0			0
$961$	−168.602	+	292.028i	−0.175445	+	0.303879i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−49.1689	+	85.1631i	−0.0509522	+	0.0882519i
$966$		0			0
$967$	−980.817	+	566.275i	−1.01429	+	0.585600i	−0.912444	−	0.409201i	$-0.865808\pi$
$967$	−980.817	+	566.275i	−1.01429	+	0.585600i	−0.101844	+	0.994800i	$0.532474\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	277.255i		−	0.285536i	−0.989756	−	0.142768i	$-0.954400\pi$
$971$		−	277.255i		−	0.285536i	0.989756	−	0.142768i	$-0.0456002\pi$
$972$		0			0
$973$	146.348			0.150409
$974$		0			0
$975$		0			0
$976$		0			0
$977$	166.546	+	288.467i	0.170467	+	0.295257i	0.938583	−	0.345053i	$-0.112139\pi$
$977$	166.546	+	288.467i	0.170467	+	0.295257i	−0.768116	+	0.640310i	$0.778806\pi$
$978$		0			0
$979$	547.824	+	316.286i	0.559575	+	0.323071i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1287.12	+	743.121i	1.30938	+	0.755973i	0.981993	−	0.188916i	$-0.0604975\pi$
$983$	1287.12	+	743.121i	1.30938	+	0.755973i	0.327390	+	0.944889i	$0.393831\pi$
$984$		0			0
$985$	−38.8778	−	67.3384i	−0.0394699	−	0.0683639i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	147.182			0.148819
$990$		0			0
$991$		−	17.1782i		−	0.0173343i	−0.999962	−	0.00866713i	$-0.997241\pi$
$991$		−	17.1782i		−	0.0173343i	0.999962	−	0.00866713i	$-0.00275887\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	53.5552	−	30.9201i	0.0538243	−	0.0310755i
$996$		0			0
$997$	−737.655	+	1277.66i	−0.739874	+	1.28150i	0.212677	+	0.977123i	$0.431782\pi$
$997$	−737.655	+	1277.66i	−0.739874	+	1.28150i	−0.952552	+	0.304377i	$0.901552\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.o.b.127.2		8
3.2	odd	2		144.3.o.a.79.4	yes	8
4.3	odd	2		432.3.o.a.127.2		8
8.3	odd	2		1728.3.o.e.127.3		8
8.5	even	2		1728.3.o.f.127.3		8
9.2	odd	6		1296.3.g.j.1135.3		8
9.4	even	3		432.3.o.a.415.2		8
9.5	odd	6		144.3.o.c.31.1	yes	8
9.7	even	3		1296.3.g.k.1135.5		8
12.11	even	2		144.3.o.c.79.1	yes	8
24.5	odd	2		576.3.o.f.511.1		8
24.11	even	2		576.3.o.d.511.4		8
36.7	odd	6		1296.3.g.k.1135.6		8
36.11	even	6		1296.3.g.j.1135.4		8
36.23	even	6		144.3.o.a.31.4	✓	8
36.31	odd	6	inner	432.3.o.b.415.2		8
72.5	odd	6		576.3.o.d.319.4		8
72.13	even	6		1728.3.o.e.1279.3		8
72.59	even	6		576.3.o.f.319.1		8
72.67	odd	6		1728.3.o.f.1279.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.4	✓	8	36.23	even	6
144.3.o.a.79.4	yes	8	3.2	odd	2
144.3.o.c.31.1	yes	8	9.5	odd	6
144.3.o.c.79.1	yes	8	12.11	even	2
432.3.o.a.127.2		8	4.3	odd	2
432.3.o.a.415.2		8	9.4	even	3
432.3.o.b.127.2		8	1.1	even	1	trivial
432.3.o.b.415.2		8	36.31	odd	6	inner
576.3.o.d.319.4		8	72.5	odd	6
576.3.o.d.511.4		8	24.11	even	2
576.3.o.f.319.1		8	72.59	even	6
576.3.o.f.511.1		8	24.5	odd	2
1296.3.g.j.1135.3		8	9.2	odd	6
1296.3.g.j.1135.4		8	36.11	even	6
1296.3.g.k.1135.5		8	9.7	even	3
1296.3.g.k.1135.6		8	36.7	odd	6
1728.3.o.e.127.3		8	8.3	odd	2
1728.3.o.e.1279.3		8	72.13	even	6
1728.3.o.f.127.3		8	8.5	even	2
1728.3.o.f.1279.3		8	72.67	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.355304 - 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +O(q^{10})\)	\(q+(-0.355304 - 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +(-14.3822 - 8.30359i) q^{11} +(-9.17743 - 15.8958i) q^{13} +9.69321 q^{17} +8.20686i q^{19} +(-1.94815 + 1.12477i) q^{23} +(12.2475 - 21.2133i) q^{25} +(20.8217 - 36.0642i) q^{29} +(-21.6298 + 12.4879i) q^{31} -2.21940i q^{35} -40.3888 q^{37} +(-25.6944 - 44.5040i) q^{41} +(-56.6621 - 32.7139i) q^{43} +(-29.2894 - 16.9102i) q^{47} +(-19.6227 - 33.9875i) q^{49} +90.6691 q^{53} +11.8012i q^{55} +(66.2243 - 38.2346i) q^{59} +(1.35822 - 2.35250i) q^{61} +(-6.52157 + 11.2957i) q^{65} +(-34.5422 + 19.9429i) q^{67} +102.923i q^{71} +38.1741 q^{73} +(-25.9341 - 44.9192i) q^{77} +(94.4994 + 54.5593i) q^{79} +(-113.503 - 65.5311i) q^{83} +(-3.44404 - 5.96526i) q^{85} -38.0903 q^{89} -57.3266i q^{91} +(5.05055 - 2.91593i) q^{95} +(-12.1961 + 21.1243i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 8 * q - 3 * q^5 + 3 * q^7	\( 8 q - 3 q^{5} + 3 q^{7} - 18 q^{11} + 5 q^{13} - 6 q^{17} + 81 q^{23} - 23 q^{25} - 69 q^{29} + 45 q^{31} - 20 q^{37} - 54 q^{41} - 207 q^{47} + 41 q^{49} + 252 q^{53} + 306 q^{59} + 7 q^{61} - 93 q^{65} + 12 q^{67} + 74 q^{73} - 207 q^{77} + 33 q^{79} - 549 q^{83} - 30 q^{85} + 168 q^{89} + 684 q^{95} - 10 q^{97}+O(q^{100}) \) 8 * q - 3 * q^5 + 3 * q^7 - 18 * q^11 + 5 * q^13 - 6 * q^17 + 81 * q^23 - 23 * q^25 - 69 * q^29 + 45 * q^31 - 20 * q^37 - 54 * q^41 - 207 * q^47 + 41 * q^49 + 252 * q^53 + 306 * q^59 + 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 - 207 * q^77 + 33 * q^79 - 549 * q^83 - 30 * q^85 + 168 * q^89 + 684 * q^95 - 10 * q^97

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