LMFDB - Embedded newform 216.3.m.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(17,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("216.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.m (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	216.89
Dual form			216.3.m.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.39898 - 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +O(q^{10})$	$q+(3.39898 - 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +(14.2980 + 8.25493i) q^{11} +(1.39898 + 2.42310i) q^{13} -2.54270i q^{17} +21.5959 q^{19} +(-2.60102 + 1.50170i) q^{23} +(-4.79796 + 8.31031i) q^{25} +(13.1969 + 7.61926i) q^{29} +(13.6010 + 23.5577i) q^{31} +50.2295i q^{35} -10.4041 q^{37} +(34.5000 - 19.9186i) q^{41} +(-17.0959 + 29.6110i) q^{43} +(-58.1969 - 33.6000i) q^{47} +(-57.3939 - 99.4091i) q^{49} -100.680i q^{53} +64.7980 q^{55} +(-5.29796 + 3.05878i) q^{59} +(-20.3990 + 35.3321i) q^{61} +(9.51021 + 5.49072i) q^{65} +(-54.4898 - 94.3791i) q^{67} +52.8829i q^{71} +68.7878 q^{73} +(-182.985 + 105.646i) q^{77} +(12.7929 - 22.1579i) q^{79} +(-52.0857 - 30.0717i) q^{83} +(-4.98979 - 8.64258i) q^{85} -7.62809i q^{89} -35.8082 q^{91} +(73.4041 - 42.3799i) q^{95} +(50.7020 - 87.8185i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{5} - 6 q^{7}+O(q^{10}) $ 4 * q - 6 * q^5 - 6 * q^7	$ 4 q - 6 q^{5} - 6 q^{7} + 18 q^{11} - 14 q^{13} + 8 q^{19} - 30 q^{23} + 20 q^{25} - 6 q^{29} + 74 q^{31} - 120 q^{37} + 138 q^{41} + 10 q^{43} - 174 q^{47} - 112 q^{49} + 220 q^{55} + 18 q^{59} - 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} - 438 q^{77} - 86 q^{79} + 66 q^{83} + 176 q^{85} - 300 q^{91} + 372 q^{95} + 242 q^{97}+O(q^{100}) $ 4 * q - 6 * q^5 - 6 * q^7 + 18 * q^11 - 14 * q^13 + 8 * q^19 - 30 * q^23 + 20 * q^25 - 6 * q^29 + 74 * q^31 - 120 * q^37 + 138 * q^41 + 10 * q^43 - 174 * q^47 - 112 * q^49 + 220 * q^55 + 18 * q^59 - 62 * q^61 + 234 * q^65 - 22 * q^67 + 40 * q^73 - 438 * q^77 - 86 * q^79 + 66 * q^83 + 176 * q^85 - 300 * q^91 + 372 * q^95 + 242 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	3.39898	−	1.96240i	0.679796	−	0.392480i	−0.119982	−	0.992776i	$-0.538284\pi$
$5$	3.39898	−	1.96240i	0.679796	−	0.392480i	0.799778	+	0.600296i	$0.204950\pi$
$6$		0			0
$7$	−6.39898	+	11.0834i	−0.914140	+	1.58334i	−0.105984	+	0.994368i	$0.533799\pi$
$7$	−6.39898	+	11.0834i	−0.914140	+	1.58334i	−0.808156	+	0.588969i	$0.799534\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	14.2980	+	8.25493i	1.29981	+	0.750448i	0.980372	−	0.197157i	$-0.0631710\pi$
$11$	14.2980	+	8.25493i	1.29981	+	0.750448i	0.319443	+	0.947606i	$0.396504\pi$
$12$		0			0
$13$	1.39898	+	2.42310i	0.107614	+	0.186393i	0.914803	−	0.403900i	$-0.132346\pi$
$13$	1.39898	+	2.42310i	0.107614	+	0.186393i	−0.807189	+	0.590293i	$0.799012\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	2.54270i		−	0.149570i	−0.997200	−	0.0747852i	$-0.976173\pi$
$17$		−	2.54270i		−	0.149570i	0.997200	−	0.0747852i	$-0.0238271\pi$
$18$		0			0
$19$	21.5959			1.13663			0.568314	−	0.822812i	$-0.307596\pi$
$19$	21.5959			1.13663			0.568314	+	0.822812i	$0.307596\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.60102	+	1.50170i	−0.113088	+	0.0652913i	−0.555477	−	0.831532i	$-0.687464\pi$
$23$	−2.60102	+	1.50170i	−0.113088	+	0.0652913i	0.442389	+	0.896823i	$0.354131\pi$
$24$		0			0
$25$	−4.79796	+	8.31031i	−0.191918	+	0.332412i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	13.1969	+	7.61926i	0.455067	+	0.262733i	0.709968	−	0.704234i	$-0.248710\pi$
$29$	13.1969	+	7.61926i	0.455067	+	0.262733i	−0.254901	+	0.966967i	$0.582043\pi$
$30$		0			0
$31$	13.6010	+	23.5577i	0.438743	+	0.759924i	0.997593	−	0.0693442i	$-0.0220907\pi$
$31$	13.6010	+	23.5577i	0.438743	+	0.759924i	−0.558850	+	0.829269i	$0.688757\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			50.2295i			1.43513i
$36$		0			0
$37$	−10.4041			−0.281191			−0.140596	−	0.990067i	$-0.544902\pi$
$37$	−10.4041			−0.281191			−0.140596	+	0.990067i	$0.544902\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	34.5000	−	19.9186i	0.841463	−	0.485819i	−0.0162980	−	0.999867i	$-0.505188\pi$
$41$	34.5000	−	19.9186i	0.841463	−	0.485819i	0.857761	+	0.514048i	$0.171855\pi$
$42$		0			0
$43$	−17.0959	+	29.6110i	−0.397579	+	0.688628i	−0.993427	−	0.114470i	$-0.963483\pi$
$43$	−17.0959	+	29.6110i	−0.397579	+	0.688628i	0.595847	+	0.803098i	$0.296816\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−58.1969	−	33.6000i	−1.23823	−	0.714894i	−0.269500	−	0.963000i	$-0.586858\pi$
$47$	−58.1969	−	33.6000i	−1.23823	−	0.714894i	−0.968733	+	0.248106i	$0.920192\pi$
$48$		0			0
$49$	−57.3939	−	99.4091i	−1.17130	−	2.02876i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	100.680i		−	1.89963i	−0.312810	−	0.949816i	$-0.601270\pi$
$53$		−	100.680i		−	1.89963i	0.312810	−	0.949816i	$-0.398730\pi$
$54$		0			0
$55$	64.7980			1.17814
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.29796	+	3.05878i	−0.0897959	+	0.0518437i	−0.544226	−	0.838939i	$-0.683176\pi$
$59$	−5.29796	+	3.05878i	−0.0897959	+	0.0518437i	0.454430	+	0.890783i	$0.349843\pi$
$60$		0			0
$61$	−20.3990	+	35.3321i	−0.334409	+	0.579214i	−0.983371	−	0.181607i	$-0.941870\pi$
$61$	−20.3990	+	35.3321i	−0.334409	+	0.579214i	0.648962	+	0.760821i	$0.275204\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.51021	+	5.49072i	0.146311	+	0.0844726i
$66$		0			0
$67$	−54.4898	−	94.3791i	−0.813281	−	1.40864i	−0.910556	−	0.413386i	$-0.864346\pi$
$67$	−54.4898	−	94.3791i	−0.813281	−	1.40864i	0.0972755	−	0.995257i	$-0.468987\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			52.8829i			0.744830i	0.928066	+	0.372415i	$0.121470\pi$
$71$			52.8829i			0.744830i	−0.928066	+	0.372415i	$0.878530\pi$
$72$		0			0
$73$	68.7878			0.942298			0.471149	−	0.882054i	$-0.343839\pi$
$73$	68.7878			0.942298			0.471149	+	0.882054i	$0.343839\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−182.985	+	105.646i	−2.37642	+	1.37203i
$78$		0			0
$79$	12.7929	−	22.1579i	0.161935	−	0.280479i	−0.773628	−	0.633640i	$-0.781560\pi$
$79$	12.7929	−	22.1579i	0.161935	−	0.280479i	0.935563	+	0.353161i	$0.114893\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−52.0857	−	30.0717i	−0.627539	−	0.362310i	0.152260	−	0.988341i	$-0.451345\pi$
$83$	−52.0857	−	30.0717i	−0.627539	−	0.362310i	−0.779798	+	0.626031i	$0.784678\pi$
$84$		0			0
$85$	−4.98979	−	8.64258i	−0.0587035	−	0.101677i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	7.62809i		−	0.0857089i	−0.999081	−	0.0428545i	$-0.986355\pi$
$89$		−	7.62809i		−	0.0857089i	0.999081	−	0.0428545i	$-0.0136452\pi$
$90$		0			0
$91$	−35.8082			−0.393496
$92$		0			0
$93$		0			0
$94$		0			0
$95$	73.4041	−	42.3799i	0.772675	−	0.446104i
$96$		0			0
$97$	50.7020	−	87.8185i	0.522701	−	0.905345i	−0.476950	−	0.878931i	$-0.658258\pi$
$97$	50.7020	−	87.8185i	0.522701	−	0.905345i	0.999651	−	0.0264148i	$-0.00840908\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.19694	+	0.691053i	0.0118509	+	0.00684211i	0.505914	−	0.862584i	$-0.331155\pi$
$101$	1.19694	+	0.691053i	0.0118509	+	0.00684211i	−0.494063	+	0.869426i	$0.664489\pi$
$102$		0			0
$103$	0.792856	+	1.37327i	0.00769763	+	0.0133327i	0.869849	−	0.493319i	$-0.164216\pi$
$103$	0.792856	+	1.37327i	0.00769763	+	0.0133327i	−0.862151	+	0.506652i	$0.830883\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	103.223i		−	0.964702i	−0.875978	−	0.482351i	$-0.839783\pi$
$107$		−	103.223i		−	0.964702i	0.875978	−	0.482351i	$-0.160217\pi$
$108$		0			0
$109$	14.4041			0.132148			0.0660738	−	0.997815i	$-0.478953\pi$
$109$	14.4041			0.132148			0.0660738	+	0.997815i	$0.478953\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	92.0755	−	53.1598i	0.814828	−	0.470441i	−0.0338020	−	0.999429i	$-0.510762\pi$
$113$	92.0755	−	53.1598i	0.814828	−	0.470441i	0.848630	+	0.528988i	$0.177428\pi$
$114$		0			0
$115$	−5.89388	+	10.2085i	−0.0512511	+	0.0887695i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	28.1816	+	16.2707i	0.236820	+	0.136728i
$120$		0			0
$121$	75.7878	+	131.268i	0.626345	+	1.08486i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			135.782i			1.08626i
$126$		0			0
$127$	−183.980			−1.44866			−0.724329	−	0.689454i	$-0.757850\pi$
$127$	−183.980			−1.44866			−0.724329	+	0.689454i	$0.757850\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	91.6918	−	52.9383i	0.699938	−	0.404109i	−0.107387	−	0.994217i	$-0.534248\pi$
$131$	91.6918	−	52.9383i	0.699938	−	0.404109i	0.807324	+	0.590108i	$0.200915\pi$
$132$		0			0
$133$	−138.192	+	239.355i	−1.03904	+	1.79966i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	165.288	+	95.4289i	1.20648	+	0.696562i	0.961989	−	0.273090i	$-0.0880457\pi$
$137$	165.288	+	95.4289i	1.20648	+	0.696562i	0.244491	+	0.969651i	$0.421379\pi$
$138$		0			0
$139$	47.4898	+	82.2547i	0.341653	+	0.591761i	0.984740	−	0.174033i	$-0.0556798\pi$
$139$	47.4898	+	82.2547i	0.341653	+	0.591761i	−0.643087	+	0.765793i	$0.722347\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			46.1939i			0.323034i
$144$		0			0
$145$	59.8082			0.412470
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−79.6112	+	45.9636i	−0.534304	+	0.308480i	−0.742767	−	0.669550i	$-0.766487\pi$
$149$	−79.6112	+	45.9636i	−0.534304	+	0.308480i	0.208464	+	0.978030i	$0.433154\pi$
$150$		0			0
$151$	8.20714	−	14.2152i	0.0543519	−	0.0941403i	−0.837569	−	0.546331i	$-0.816024\pi$
$151$	8.20714	−	14.2152i	0.0543519	−	0.0941403i	0.891921	+	0.452191i	$0.149357\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	92.4592	+	53.3813i	0.596511	+	0.344396i
$156$		0			0
$157$	105.985	+	183.571i	0.675062	+	1.16924i	0.976451	+	0.215740i	$0.0692164\pi$
$157$	105.985	+	183.571i	0.675062	+	1.16924i	−0.301389	+	0.953501i	$0.597450\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	38.4374i		−	0.238742i
$162$		0			0
$163$	172.788			1.06005			0.530024	−	0.847983i	$-0.322183\pi$
$163$	172.788			1.06005			0.530024	+	0.847983i	$0.322183\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	163.197	−	94.2218i	0.977227	−	0.564202i	0.0757953	−	0.997123i	$-0.475850\pi$
$167$	163.197	−	94.2218i	0.977227	−	0.564202i	0.901432	+	0.432921i	$0.142517\pi$
$168$		0			0
$169$	80.5857	−	139.579i	0.476839	−	0.825909i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−52.1969	−	30.1359i	−0.301716	−	0.174196i	0.341497	−	0.939883i	$-0.389066\pi$
$173$	−52.1969	−	30.1359i	−0.301716	−	0.174196i	−0.643214	+	0.765687i	$0.722399\pi$
$174$		0			0
$175$	−61.4041	−	106.355i	−0.350880	−	0.607743i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			72.7108i			0.406205i	0.979157	+	0.203103i	$0.0651025\pi$
$179$			72.7108i			0.406205i	−0.979157	+	0.203103i	$0.934897\pi$
$180$		0			0
$181$	−97.5959			−0.539204			−0.269602	−	0.962972i	$-0.586892\pi$
$181$	−97.5959			−0.539204			−0.269602	+	0.962972i	$0.586892\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−35.3633	+	20.4170i	−0.191153	+	0.110362i
$186$		0			0
$187$	20.9898	−	36.3554i	0.112245	−	0.194414i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−282.560	−	163.136i	−1.47937	−	0.854116i	−0.479645	−	0.877462i	$-0.659235\pi$
$191$	−282.560	−	163.136i	−1.47937	−	0.854116i	−0.999727	+	0.0233462i	$0.992568\pi$
$192$		0			0
$193$	−10.5102	−	18.2042i	−0.0544570	−	0.0943223i	0.837512	−	0.546419i	$-0.184009\pi$
$193$	−10.5102	−	18.2042i	−0.0544570	−	0.0943223i	−0.891969	+	0.452097i	$0.850676\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			32.5413i			0.165184i	0.996583	+	0.0825922i	$0.0263199\pi$
$197$			32.5413i			0.165184i	−0.996583	+	0.0825922i	$0.973680\pi$
$198$		0			0
$199$	−62.0000			−0.311558			−0.155779	−	0.987792i	$-0.549789\pi$
$199$	−62.0000			−0.311558			−0.155779	+	0.987792i	$0.549789\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−168.894	+	97.5109i	−0.831990	+	0.480349i
$204$		0			0
$205$	78.1765	−	135.406i	0.381349	−	0.660516i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	308.778	+	178.273i	1.47740	+	0.852980i
$210$		0			0
$211$	84.2980	+	146.008i	0.399516	+	0.691983i	0.993666	−	0.112372i	$-0.0358447\pi$
$211$	84.2980	+	146.008i	0.399516	+	0.691983i	−0.594150	+	0.804354i	$0.702511\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			134.196i			0.624169i
$216$		0			0
$217$	−348.131			−1.60429
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.16122	−	3.55718i	0.0278788	−	0.0160958i
$222$		0			0
$223$	78.1867	−	135.423i	0.350613	−	0.607280i	−0.635744	−	0.771900i	$-0.719307\pi$
$223$	78.1867	−	135.423i	0.350613	−	0.607280i	0.986357	+	0.164620i	$0.0526399\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−86.6510	−	50.0280i	−0.381723	−	0.220388i	0.296845	−	0.954926i	$-0.404066\pi$
$227$	−86.6510	−	50.0280i	−0.381723	−	0.220388i	−0.678567	+	0.734538i	$0.737399\pi$
$228$		0			0
$229$	104.995	+	181.856i	0.458493	+	0.794133i	0.998882	−	0.0472824i	$-0.0150561\pi$
$229$	104.995	+	181.856i	0.458493	+	0.794133i	−0.540389	+	0.841416i	$0.681723\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	307.127i		−	1.31814i	−0.752081	−	0.659070i	$-0.770950\pi$
$233$		−	307.127i		−	1.31814i	0.752081	−	0.659070i	$-0.229050\pi$
$234$		0			0
$235$	−263.747			−1.12233
$236$		0			0
$237$		0			0
$238$		0			0
$239$	70.3888	−	40.6390i	0.294514	−	0.170038i	−0.345462	−	0.938433i	$-0.612278\pi$
$239$	70.3888	−	40.6390i	0.294514	−	0.170038i	0.639976	+	0.768395i	$0.278944\pi$
$240$		0			0
$241$	180.096	−	311.935i	0.747286	−	1.29434i	−0.201833	−	0.979420i	$-0.564690\pi$
$241$	180.096	−	311.935i	0.747286	−	1.29434i	0.949119	−	0.314917i	$-0.101977\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−390.161	−	225.260i	−1.59249	−	0.919427i
$246$		0			0
$247$	30.2122	+	52.3291i	0.122317	+	0.211859i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	400.179i		−	1.59434i	−0.603755	−	0.797170i	$-0.706330\pi$
$251$		−	400.179i		−	1.59434i	0.603755	−	0.797170i	$-0.293670\pi$
$252$		0			0
$253$	−49.5857			−0.195991
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−315.035	+	181.885i	−1.22582	+	0.707725i	−0.966152	−	0.257974i	$-0.916945\pi$
$257$	−315.035	+	181.885i	−1.22582	+	0.707725i	−0.259664	+	0.965699i	$0.583612\pi$
$258$		0			0
$259$	66.5755	−	115.312i	0.257048	−	0.445221i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	326.570	+	188.546i	1.24171	+	0.716903i	0.969443	−	0.245318i	$-0.0788923\pi$
$263$	326.570	+	188.546i	1.24171	+	0.716903i	0.272270	+	0.962221i	$0.412226\pi$
$264$		0			0
$265$	−197.576	−	342.211i	−0.745568	−	1.29136i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	170.849i		−	0.635125i	−0.948237	−	0.317562i	$-0.897136\pi$
$269$		−	170.849i		−	0.635125i	0.948237	−	0.317562i	$-0.102864\pi$
$270$		0			0
$271$	−50.4041			−0.185993			−0.0929965	−	0.995666i	$-0.529645\pi$
$271$	−50.4041			−0.185993			−0.0929965	+	0.995666i	$0.529645\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−137.202	+	79.2136i	−0.498917	+	0.288050i
$276$		0			0
$277$	−12.8031	+	22.1756i	−0.0462204	+	0.0800561i	−0.888210	−	0.459438i	$-0.848051\pi$
$277$	−12.8031	+	22.1756i	−0.0462204	+	0.0800561i	0.841990	+	0.539494i	$0.181384\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−290.267	−	167.586i	−1.03298	−	0.596391i	−0.115143	−	0.993349i	$-0.536733\pi$
$281$	−290.267	−	167.586i	−1.03298	−	0.596391i	−0.917837	+	0.396958i	$0.870066\pi$
$282$		0			0
$283$	7.48979	+	12.9727i	0.0264657	+	0.0458399i	0.878955	−	0.476905i	$-0.158241\pi$
$283$	7.48979	+	12.9727i	0.0264657	+	0.0458399i	−0.852489	+	0.522745i	$0.824908\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			509.834i			1.77643i
$288$		0			0
$289$	282.535			0.977629
$290$		0			0
$291$		0			0
$292$		0			0
$293$	261.015	−	150.697i	0.890837	−	0.514325i	0.0166210	−	0.999862i	$-0.494709\pi$
$293$	261.015	−	150.697i	0.890837	−	0.514325i	0.874216	+	0.485537i	$0.161376\pi$
$294$		0			0
$295$	−12.0051	+	20.7934i	−0.0406953	+	0.0704863i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.27755	−	4.20169i	−0.0243396	−	0.0140525i
$300$		0			0
$301$	−218.793	−	378.960i	−0.726887	−	1.25900i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			160.124i			0.524997i
$306$		0			0
$307$	−44.7469			−0.145755			−0.0728777	−	0.997341i	$-0.523218\pi$
$307$	−44.7469			−0.145755			−0.0728777	+	0.997341i	$0.523218\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−281.348	+	162.436i	−0.904656	+	0.522303i	−0.878708	−	0.477360i	$-0.841594\pi$
$311$	−281.348	+	162.436i	−0.904656	+	0.522303i	−0.0259480	+	0.999663i	$0.508260\pi$
$312$		0			0
$313$	−156.894	+	271.748i	−0.501258	+	0.868205i	0.498741	+	0.866751i	$0.333796\pi$
$313$	−156.894	+	271.748i	−0.501258	+	0.868205i	−0.999999	+	0.00145368i	$0.999537\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	47.9847	+	27.7040i	0.151371	+	0.0873942i	0.573773	−	0.819015i	$-0.305479\pi$
$317$	47.9847	+	27.7040i	0.151371	+	0.0873942i	−0.422401	+	0.906409i	$0.638813\pi$
$318$		0			0
$319$	125.793	+	217.880i	0.394335	+	0.683008i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	54.9119i		−	0.170006i
$324$		0			0
$325$	−26.8490			−0.0826123
$326$		0			0
$327$		0			0
$328$		0			0
$329$	744.802	−	430.012i	2.26384	−	1.30703i
$330$		0			0
$331$	−7.70204	+	13.3403i	−0.0232690	+	0.0403031i	−0.877425	−	0.479713i	$-0.840741\pi$
$331$	−7.70204	+	13.3403i	−0.0232690	+	0.0403031i	0.854156	+	0.520016i	$0.174074\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−370.419	−	213.862i	−1.10573	−	0.638393i
$336$		0			0
$337$	−37.8837	−	65.6164i	−0.112414	−	0.194708i	0.804329	−	0.594184i	$-0.202525\pi$
$337$	−37.8837	−	65.6164i	−0.112414	−	0.194708i	−0.916743	+	0.399477i	$0.869192\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			449.102i			1.31701i
$342$		0			0
$343$	841.949			2.45466
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−578.651	+	334.084i	−1.66758	+	0.962779i	−0.698646	+	0.715467i	$0.746214\pi$
$347$	−578.651	+	334.084i	−1.66758	+	0.962779i	−0.968936	+	0.247312i	$0.920453\pi$
$348$		0			0
$349$	123.015	−	213.069i	0.352479	−	0.610512i	−0.634204	−	0.773166i	$-0.718672\pi$
$349$	123.015	−	213.069i	0.352479	−	0.610512i	0.986683	+	0.162654i	$0.0520053\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−156.510	−	90.3612i	−0.443372	−	0.255981i	0.261655	−	0.965161i	$-0.415732\pi$
$353$	−156.510	−	90.3612i	−0.443372	−	0.255981i	−0.705027	+	0.709181i	$0.749065\pi$
$354$		0			0
$355$	103.778	+	179.748i	0.292331	+	0.506332i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	256.273i		−	0.713852i	−0.934133	−	0.356926i	$-0.883825\pi$
$359$		−	256.273i		−	0.713852i	0.934133	−	0.356926i	$-0.116175\pi$
$360$		0			0
$361$	105.384			0.291922
$362$		0			0
$363$		0			0
$364$		0			0
$365$	233.808	−	134.989i	0.640570	−	0.369833i
$366$		0			0
$367$	−270.358	+	468.274i	−0.736671	+	1.27595i	0.217316	+	0.976101i	$0.430270\pi$
$367$	−270.358	+	468.274i	−0.736671	+	1.27595i	−0.953986	+	0.299850i	$0.903063\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1115.88	+	644.252i	3.00776	+	1.73653i
$372$		0			0
$373$	85.9847	+	148.930i	0.230522	+	0.399276i	0.957962	−	0.286896i	$-0.0926233\pi$
$373$	85.9847	+	148.930i	0.230522	+	0.399276i	−0.727440	+	0.686171i	$0.759290\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			42.6367i			0.113095i
$378$		0			0
$379$	−170.849			−0.450789			−0.225394	−	0.974268i	$-0.572367\pi$
$379$	−170.849			−0.450789			−0.225394	+	0.974268i	$0.572367\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	505.681	−	291.955i	1.32031	−	0.762284i	0.336536	−	0.941671i	$-0.390745\pi$
$383$	505.681	−	291.955i	1.32031	−	0.762284i	0.983779	+	0.179386i	$0.0574112\pi$
$384$		0			0
$385$	−414.641	+	718.179i	−1.07699	+	1.86540i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	384.752	+	222.137i	0.989080	+	0.571045i	0.904999	−	0.425413i	$-0.139871\pi$
$389$	384.752	+	222.137i	0.989080	+	0.571045i	0.0840807	+	0.996459i	$0.473205\pi$
$390$		0			0
$391$	3.81837	+	6.61361i	0.00976565	+	0.0169146i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	100.419i		−	0.254225i
$396$		0			0
$397$	−575.090			−1.44859			−0.724294	−	0.689491i	$-0.757834\pi$
$397$	−575.090			−1.44859			−0.724294	+	0.689491i	$0.757834\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−141.318	+	81.5902i	−0.352415	+	0.203467i	−0.665748	−	0.746176i	$-0.731888\pi$
$401$	−141.318	+	81.5902i	−0.352415	+	0.203467i	0.313333	+	0.949643i	$0.398554\pi$
$402$		0			0
$403$	−38.0551	+	65.9134i	−0.0944295	+	0.163557i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−148.757	−	85.8850i	−0.365497	−	0.211020i
$408$		0			0
$409$	300.641	+	520.725i	0.735063	+	1.27317i	0.954696	+	0.297584i	$0.0961808\pi$
$409$	300.641	+	520.725i	0.735063	+	1.27317i	−0.219633	+	0.975583i	$0.570486\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	78.2922i		−	0.189570i
$414$		0			0
$415$	−236.051			−0.568798
$416$		0			0
$417$		0			0
$418$		0			0
$419$	158.620	−	91.5795i	0.378569	−	0.218567i	−0.298626	−	0.954370i	$-0.596528\pi$
$419$	158.620	−	91.5795i	0.378569	−	0.218567i	0.677195	+	0.735803i	$0.263195\pi$
$420$		0			0
$421$	−83.7724	+	145.098i	−0.198984	+	0.344651i	−0.948199	−	0.317676i	$-0.897098\pi$
$421$	−83.7724	+	145.098i	−0.198984	+	0.344651i	0.749215	+	0.662327i	$0.230431\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	21.1306	+	12.1998i	0.0497191	+	0.0287053i
$426$		0			0
$427$	−261.065	−	452.178i	−0.611394	−	1.05897i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	644.766i		−	1.49598i	−0.663712	−	0.747988i	$-0.731020\pi$
$431$		−	644.766i		−	1.49598i	0.663712	−	0.747988i	$-0.268980\pi$
$432$		0			0
$433$	133.514			0.308347			0.154174	−	0.988044i	$-0.450729\pi$
$433$	133.514			0.308347			0.154174	+	0.988044i	$0.450729\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−56.1714	+	32.4306i	−0.128539	+	0.0742119i
$438$		0			0
$439$	46.2276	−	80.0685i	0.105302	−	0.182388i	−0.808560	−	0.588414i	$-0.799752\pi$
$439$	46.2276	−	80.0685i	0.105302	−	0.182388i	0.913862	+	0.406026i	$0.133086\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	150.157	+	86.6933i	0.338955	+	0.195696i	0.659810	−	0.751433i	$-0.270637\pi$
$443$	150.157	+	86.6933i	0.338955	+	0.195696i	−0.320855	+	0.947128i	$0.603970\pi$
$444$		0			0
$445$	−14.9694	−	25.9277i	−0.0336391	−	0.0582646i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			430.692i			0.959224i	0.877481	+	0.479612i	$0.159223\pi$
$449$			430.692i			0.959224i	−0.877481	+	0.479612i	$0.840777\pi$
$450$		0			0
$451$	657.706			1.45833
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−121.711	+	70.2700i	−0.267497	+	0.154440i
$456$		0			0
$457$	262.843	−	455.257i	0.575148	−	0.996186i	−0.420877	−	0.907118i	$-0.638278\pi$
$457$	262.843	−	455.257i	0.575148	−	0.996186i	0.996025	−	0.0890687i	$-0.0283891\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.54999	−	0.894890i	−0.00336224	−	0.00194119i	0.498318	−	0.866994i	$-0.333951\pi$
$461$	−1.54999	−	0.894890i	−0.00336224	−	0.00194119i	−0.501680	+	0.865053i	$0.667285\pi$
$462$		0			0
$463$	−263.166	−	455.817i	−0.568394	−	0.984487i	−0.996725	−	0.0808651i	$-0.974232\pi$
$463$	−263.166	−	455.817i	−0.568394	−	0.984487i	0.428331	−	0.903622i	$-0.359102\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			409.322i			0.876494i	0.898855	+	0.438247i	$0.144400\pi$
$467$			409.322i			0.876494i	−0.898855	+	0.438247i	$0.855600\pi$
$468$		0			0
$469$	1394.72			2.97381
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−488.873	+	282.251i	−1.03356	+	0.596726i
$474$		0			0
$475$	−103.616	+	179.469i	−0.218140	+	0.377829i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−525.207	−	303.228i	−1.09647	−	0.633045i	−0.161175	−	0.986926i	$-0.551528\pi$
$479$	−525.207	−	303.228i	−1.09647	−	0.633045i	−0.935290	+	0.353881i	$0.884862\pi$
$480$		0			0
$481$	−14.5551	−	25.2102i	−0.0302601	−	0.0524120i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	397.991i		−	0.820600i
$486$		0			0
$487$	−275.131			−0.564950			−0.282475	−	0.959275i	$-0.591155\pi$
$487$	−275.131			−0.564950			−0.282475	+	0.959275i	$0.591155\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	127.469	−	73.5945i	0.259612	−	0.149887i	−0.364546	−	0.931186i	$-0.618776\pi$
$491$	127.469	−	73.5945i	0.259612	−	0.149887i	0.624157	+	0.781299i	$0.285442\pi$
$492$		0			0
$493$	19.3735	−	33.5558i	0.0392971	−	0.0680646i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−586.120	−	338.397i	−1.17932	−	0.680879i
$498$		0			0
$499$	−226.308	−	391.977i	−0.453523	−	0.785526i	0.545079	−	0.838385i	$-0.316500\pi$
$499$	−226.308	−	391.977i	−0.453523	−	0.785526i	−0.998602	+	0.0528594i	$0.983166\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			571.541i			1.13627i	0.822937	+	0.568133i	$0.192334\pi$
$503$			571.541i			1.13627i	−0.822937	+	0.568133i	$0.807666\pi$
$504$		0			0
$505$	5.42449			0.0107416
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−394.136	+	227.554i	−0.774333	+	0.447062i	−0.834418	−	0.551132i	$-0.814196\pi$
$509$	−394.136	+	227.554i	−0.774333	+	0.447062i	0.0600849	+	0.998193i	$0.480863\pi$
$510$		0			0
$511$	−440.171	+	762.399i	−0.861392	+	1.49198i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.38981	+	3.11181i	0.0104656	+	0.00604234i
$516$		0			0
$517$	−554.732	−	960.823i	−1.07298	−	1.85846i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			846.127i			1.62404i	0.583627	+	0.812022i	$0.301633\pi$
$521$			846.127i			1.62404i	−0.583627	+	0.812022i	$0.698367\pi$
$522$		0			0
$523$	−487.616			−0.932345			−0.466172	−	0.884694i	$-0.654367\pi$
$523$	−487.616			−0.932345			−0.466172	+	0.884694i	$0.654367\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	59.9000	−	34.5833i	0.113662	−	0.0656229i
$528$		0			0
$529$	−259.990	+	450.316i	−0.491474	+	0.851258i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	96.5296	+	55.7314i	0.181106	+	0.104562i
$534$		0			0
$535$	−202.565	−	350.853i	−0.378627	−	0.655801i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	1895.13i		−	3.51601i
$540$		0			0
$541$	608.302			1.12440			0.562202	−	0.827000i	$-0.309955\pi$
$541$	608.302			1.12440			0.562202	+	0.827000i	$0.309955\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	48.9592	−	28.2666i	0.0898334	−	0.0518653i
$546$		0			0
$547$	431.671	−	747.677i	0.789162	−	1.36687i	−0.137319	−	0.990527i	$-0.543849\pi$
$547$	431.671	−	747.677i	0.789162	−	1.36687i	0.926481	−	0.376341i	$-0.122818\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	285.000	+	164.545i	0.517241	+	0.298629i
$552$		0			0
$553$	163.722	+	283.576i	0.296062	+	0.512795i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			331.526i			0.595200i	0.954691	+	0.297600i	$0.0961861\pi$
$557$			331.526i			0.595200i	−0.954691	+	0.297600i	$0.903814\pi$
$558$		0			0
$559$	−95.6674			−0.171140
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−514.024	+	296.772i	−0.913010	+	0.527126i	−0.881398	−	0.472374i	$-0.843397\pi$
$563$	−514.024	+	296.772i	−0.913010	+	0.527126i	−0.0316114	+	0.999500i	$0.510064\pi$
$564$		0			0
$565$	208.642	−	361.378i	0.369278	−	0.639608i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−889.155	−	513.354i	−1.56266	−	0.902204i	−0.996986	−	0.0775764i	$-0.975282\pi$
$569$	−889.155	−	513.354i	−1.56266	−	0.902204i	−0.565676	−	0.824627i	$-0.691385\pi$
$570$		0			0
$571$	−191.843	−	332.282i	−0.335977	−	0.581929i	0.647695	−	0.761900i	$-0.275733\pi$
$571$	−191.843	−	332.282i	−0.335977	−	0.581929i	−0.983672	+	0.179971i	$0.942400\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	28.8204i		−	0.0501224i
$576$		0			0
$577$	−777.433			−1.34737			−0.673685	−	0.739019i	$-0.735290\pi$
$577$	−777.433			−1.34737			−0.673685	+	0.739019i	$0.735290\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	666.591	−	384.856i	1.14732	−	0.662403i
$582$		0			0
$583$	831.110	−	1439.53i	1.42557	−	2.46917i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−581.520	−	335.741i	−0.990665	−	0.571961i	−0.0851921	−	0.996365i	$-0.527150\pi$
$587$	−581.520	−	335.741i	−0.990665	−	0.571961i	−0.905473	+	0.424404i	$0.860484\pi$
$588$		0			0
$589$	293.727	+	508.749i	0.498687	+	0.863751i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	536.457i		−	0.904650i	−0.891853	−	0.452325i	$-0.850595\pi$
$593$		−	536.457i		−	0.904650i	0.891853	−	0.452325i	$-0.149405\pi$
$594$		0			0
$595$	127.718			0.214653
$596$		0			0
$597$		0			0
$598$		0			0
$599$	735.438	−	424.605i	1.22778	−	0.708857i	0.261212	−	0.965282i	$-0.415878\pi$
$599$	735.438	−	424.605i	1.22778	−	0.708857i	0.966564	+	0.256425i	$0.0825446\pi$
$600$		0			0
$601$	−330.692	+	572.775i	−0.550236	+	0.953037i	0.448021	+	0.894023i	$0.352129\pi$
$601$	−330.692	+	572.775i	−0.550236	+	0.953037i	−0.998257	+	0.0590138i	$0.981204\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	515.202	+	297.452i	0.851574	+	0.491656i
$606$		0			0
$607$	10.9541	+	18.9730i	0.0180463	+	0.0312570i	0.874908	−	0.484290i	$-0.160922\pi$
$607$	10.9541	+	18.9730i	0.0180463	+	0.0312570i	−0.856861	+	0.515547i	$0.827589\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	188.023i		−	0.307730i
$612$		0			0
$613$	−1164.75			−1.90008			−0.950038	−	0.312133i	$-0.898956\pi$
$613$	−1164.75			−1.90008			−0.950038	+	0.312133i	$0.898956\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−558.227	+	322.292i	−0.904743	+	0.522354i	−0.878736	−	0.477308i	$-0.841613\pi$
$617$	−558.227	+	322.292i	−0.904743	+	0.522354i	−0.0260071	+	0.999662i	$0.508279\pi$
$618$		0			0
$619$	−564.469	+	977.690i	−0.911905	+	1.57947i	−0.100535	+	0.994933i	$0.532056\pi$
$619$	−564.469	+	977.690i	−0.911905	+	1.57947i	−0.811370	+	0.584533i	$0.801278\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	84.5449	+	48.8120i	0.135706	+	0.0783499i
$624$		0			0
$625$	146.510	+	253.763i	0.234416	+	0.406021i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			26.4544i			0.0420579i
$630$		0			0
$631$	143.212			0.226961			0.113480	−	0.993540i	$-0.463800\pi$
$631$	143.212			0.226961			0.113480	+	0.993540i	$0.463800\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−625.343	+	361.042i	−0.984792	+	0.568570i
$636$		0			0
$637$	160.586	−	278.143i	0.252097	−	0.436645i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	198.418	+	114.557i	0.309545	+	0.178716i	0.646723	−	0.762725i	$-0.276139\pi$
$641$	198.418	+	114.557i	0.309545	+	0.178716i	−0.337178	+	0.941441i	$0.609472\pi$
$642$		0			0
$643$	554.682	+	960.737i	0.862646	+	1.49415i	0.869365	+	0.494170i	$0.164528\pi$
$643$	554.682	+	960.737i	0.862646	+	1.49415i	−0.00671893	+	0.999977i	$0.502139\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1052.57i			1.62685i	0.581669	+	0.813426i	$0.302400\pi$
$647$			1052.57i			1.62685i	−0.581669	+	0.813426i	$0.697600\pi$
$648$		0			0
$649$	−101.000			−0.155624
$650$		0			0
$651$		0			0
$652$		0			0
$653$	795.499	−	459.282i	1.21822	−	0.703341i	0.253685	−	0.967287i	$-0.418357\pi$
$653$	795.499	−	459.282i	1.21822	−	0.703341i	0.964537	+	0.263946i	$0.0850241\pi$
$654$		0			0
$655$	207.772	−	359.872i	0.317210	−	0.549424i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	207.288	+	119.678i	0.314549	+	0.181605i	0.648960	−	0.760822i	$-0.275204\pi$
$659$	207.288	+	119.678i	0.314549	+	0.181605i	−0.334411	+	0.942427i	$0.608537\pi$
$660$		0			0
$661$	−177.793	−	307.946i	−0.268976	−	0.465879i	0.699622	−	0.714513i	$-0.253352\pi$
$661$	−177.793	−	307.946i	−0.268976	−	0.465879i	−0.968598	+	0.248634i	$0.920018\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			1084.75i			1.63121i
$666$		0			0
$667$	−45.7673			−0.0686167
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−583.328	+	336.784i	−0.869341	+	0.501914i
$672$		0			0
$673$	291.429	−	504.769i	0.433029	−	0.750028i	−0.564103	−	0.825704i	$-0.690778\pi$
$673$	291.429	−	504.769i	0.433029	−	0.750028i	0.997132	+	0.0756758i	$0.0241114\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	154.450	+	89.1718i	0.228139	+	0.131716i	0.609713	−	0.792622i	$-0.291285\pi$
$677$	154.450	+	89.1718i	0.228139	+	0.131716i	−0.381574	+	0.924338i	$0.624618\pi$
$678$		0			0
$679$	648.883	+	1123.90i	0.955645	+	1.65522i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			660.510i			0.967072i	0.875325	+	0.483536i	$0.160648\pi$
$683$			660.510i			0.967072i	−0.875325	+	0.483536i	$0.839352\pi$
$684$		0			0
$685$	749.080			1.09355
$686$		0			0
$687$		0			0
$688$		0			0
$689$	243.959	−	140.850i	0.354077	−	0.204427i
$690$		0			0
$691$	−43.2571	+	74.9236i	−0.0626008	+	0.108428i	−0.895627	−	0.444805i	$-0.853273\pi$
$691$	−43.2571	+	74.9236i	−0.0626008	+	0.108428i	0.833026	+	0.553233i	$0.186606\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	322.834	+	186.388i	0.464509	+	0.268184i
$696$		0			0
$697$	−50.6469	−	87.7231i	−0.0726642	−	0.125858i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1204.11i		−	1.71770i	−0.512227	−	0.858850i	$-0.671179\pi$
$701$		−	1204.11i		−	1.71770i	0.512227	−	0.858850i	$-0.328821\pi$
$702$		0			0
$703$	−224.686			−0.319610
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.3184	+	8.84406i	−0.0216667	+	0.0125093i
$708$		0			0
$709$	401.944	−	696.187i	0.566917	−	0.981928i	−0.429952	−	0.902852i	$-0.641470\pi$
$709$	401.944	−	696.187i	0.566917	−	0.981928i	0.996869	−	0.0790766i	$-0.0251972\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−70.7531	−	40.8493i	−0.0992329	−	0.0572921i
$714$		0			0
$715$	90.6510	+	157.012i	0.126785	+	0.219597i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	66.1101i		−	0.0919474i	−0.998943	−	0.0459737i	$-0.985361\pi$
$719$		−	66.1101i		−	0.0919474i	0.998943	−	0.0459737i	$-0.0146390\pi$
$720$		0			0
$721$	−20.2939			−0.0281469
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−126.637	+	73.1138i	−0.174671	+	0.100847i
$726$		0			0
$727$	−259.834	+	450.045i	−0.357405	+	0.619044i	−0.987527	−	0.157453i	$-0.949672\pi$
$727$	−259.834	+	450.045i	−0.357405	+	0.619044i	0.630121	+	0.776497i	$0.283005\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	75.2918	+	43.4698i	0.102998	+	0.0594662i
$732$		0			0
$733$	80.1459	+	138.817i	0.109340	+	0.189382i	0.915503	−	0.402311i	$-0.131793\pi$
$733$	80.1459	+	138.817i	0.109340	+	0.189382i	−0.806163	+	0.591693i	$0.798460\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1799.24i		−	2.44130i
$738$		0			0
$739$	−122.849			−0.166237			−0.0831184	−	0.996540i	$-0.526488\pi$
$739$	−122.849			−0.166237			−0.0831184	+	0.996540i	$0.526488\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	585.944	−	338.295i	0.788619	−	0.455309i	−0.0508572	−	0.998706i	$-0.516195\pi$
$743$	585.944	−	338.295i	0.788619	−	0.455309i	0.839476	+	0.543397i	$0.182862\pi$
$744$		0			0
$745$	−180.398	+	312.458i	−0.242145	+	0.419407i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1144.06	+	660.523i	1.52745	+	0.881873i
$750$		0			0
$751$	−171.430	−	296.925i	−0.228268	−	0.395373i	0.729027	−	0.684485i	$-0.239973\pi$
$751$	−171.430	−	296.925i	−0.228268	−	0.395373i	−0.957295	+	0.289113i	$0.906640\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	64.4229i		−	0.0853283i
$756$		0			0
$757$	−452.220			−0.597385			−0.298692	−	0.954349i	$-0.596550\pi$
$757$	−452.220			−0.597385			−0.298692	+	0.954349i	$0.596550\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−203.520	+	117.503i	−0.267438	+	0.154405i	−0.627723	−	0.778437i	$-0.716013\pi$
$761$	−203.520	+	117.503i	−0.267438	+	0.154405i	0.360285	+	0.932842i	$0.382680\pi$
$762$		0			0
$763$	−92.1714	+	159.646i	−0.120801	+	0.209234i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.8235	−	8.55834i	−0.0193266	−	0.0111582i
$768$		0			0
$769$	318.439	+	551.552i	0.414095	+	0.717233i	0.995333	−	0.0965005i	$-0.0307649\pi$
$769$	318.439	+	551.552i	0.414095	+	0.717233i	−0.581238	+	0.813733i	$0.697432\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			592.885i			0.766992i	0.923543	+	0.383496i	$0.125280\pi$
$773$			592.885i			0.766992i	−0.923543	+	0.383496i	$0.874720\pi$
$774$		0			0
$775$	−261.029			−0.336811
$776$		0			0
$777$		0			0
$778$		0			0
$779$	745.059	−	430.160i	0.956430	−	0.552195i
$780$		0			0
$781$	−436.545	+	756.118i	−0.558956	+	0.968141i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	720.480	+	415.969i	0.917808	+	0.529897i
$786$		0			0
$787$	666.904	+	1155.11i	0.847400	+	1.46774i	0.883520	+	0.468393i	$0.155167\pi$
$787$	666.904	+	1155.11i	0.847400	+	1.46774i	−0.0361199	+	0.999347i	$0.511500\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			1360.67i			1.72020i
$792$		0			0
$793$	−114.151			−0.143948
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−638.540	+	368.661i	−0.801179	+	0.462561i	−0.843883	−	0.536527i	$-0.819736\pi$
$797$	−638.540	+	368.661i	−0.801179	+	0.462561i	0.0427041	+	0.999088i	$0.486403\pi$
$798$		0			0
$799$	−85.4347	+	147.977i	−0.106927	+	0.185203i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	983.524	+	567.838i	1.22481	+	0.707146i
$804$		0			0
$805$	−75.4296	−	130.648i	−0.0937014	−	0.162296i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	71.6833i		−	0.0886073i	−0.999018	−	0.0443037i	$-0.985893\pi$
$809$		−	71.6833i		−	0.0886073i	0.999018	−	0.0443037i	$-0.0141069\pi$
$810$		0			0
$811$	1086.24			1.33938			0.669692	−	0.742639i	$-0.266426\pi$
$811$	1086.24			1.33938			0.669692	+	0.742639i	$0.266426\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	587.302	−	339.079i	0.720616	−	0.416048i
$816$		0			0
$817$	−369.202	+	639.477i	−0.451900	+	0.782713i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1232.92	−	711.829i	−1.50173	−	0.867026i	−0.999998	−	0.00200552i	$-0.999362\pi$
$821$	−1232.92	−	711.829i	−1.50173	−	0.867026i	−0.501736	−	0.865021i	$-0.667305\pi$
$822$		0			0
$823$	217.379	+	376.511i	0.264129	+	0.457486i	0.967335	−	0.253501i	$-0.0815820\pi$
$823$	217.379	+	376.511i	0.264129	+	0.457486i	−0.703206	+	0.710986i	$0.748249\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			677.821i			0.819614i	0.912172	+	0.409807i	$0.134404\pi$
$827$			677.821i			0.819614i	−0.912172	+	0.409807i	$0.865596\pi$
$828$		0			0
$829$	−995.775			−1.20118			−0.600588	−	0.799558i	$-0.705067\pi$
$829$	−995.775			−1.20118			−0.600588	+	0.799558i	$0.705067\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−252.767	+	145.935i	−0.303442	+	0.175192i
$834$		0			0
$835$	369.802	−	640.516i	0.442877	−	0.767085i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1149.53	−	663.681i	−1.37012	−	0.791038i	−0.379176	−	0.925325i	$-0.623793\pi$
$839$	−1149.53	−	663.681i	−1.37012	−	0.791038i	−0.990943	+	0.134286i	$0.957126\pi$
$840$		0			0
$841$	−304.394	−	527.226i	−0.361943	−	0.626903i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	632.566i		−	0.748599i
$846$		0			0
$847$	−1939.86			−2.29027
$848$		0			0
$849$		0			0
$850$		0			0
$851$	27.0612	−	15.6238i	0.0317993	−	0.0183594i
$852$		0			0
$853$	685.317	−	1187.00i	0.803420	−	1.39156i	−0.113932	−	0.993489i	$-0.536345\pi$
$853$	685.317	−	1187.00i	0.803420	−	1.39156i	0.917352	−	0.398076i	$-0.130322\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1038.74	+	599.717i	1.21207	+	0.699787i	0.963209	−	0.268753i	$-0.0866117\pi$
$857$	1038.74	+	599.717i	1.21207	+	0.699787i	0.248857	+	0.968540i	$0.419945\pi$
$858$		0			0
$859$	−31.1163	−	53.8951i	−0.0362239	−	0.0627416i	0.847345	−	0.531043i	$-0.178200\pi$
$859$	−31.1163	−	53.8951i	−0.0362239	−	0.0627416i	−0.883569	+	0.468301i	$0.844866\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	154.565i		−	0.179102i	−0.995982	−	0.0895509i	$-0.971457\pi$
$863$		−	154.565i		−	0.179102i	0.995982	−	0.0895509i	$-0.0285432\pi$
$864$		0			0
$865$	−236.555			−0.273474
$866$		0			0
$867$		0			0
$868$		0			0
$869$	365.823	−	211.208i	0.420971	−	0.243048i
$870$		0			0
$871$	152.460	−	264.069i	0.175040	−	0.303179i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1504.92	−	868.867i	−1.71991	−	0.992991i
$876$		0			0
$877$	548.187	+	949.487i	0.625070	+	1.08265i	0.988527	+	0.151043i	$0.0482631\pi$
$877$	548.187	+	949.487i	0.625070	+	1.08265i	−0.363457	+	0.931611i	$0.618404\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1241.22i		−	1.40888i	−0.709765	−	0.704438i	$-0.751199\pi$
$881$		−	1241.22i		−	1.40888i	0.709765	−	0.704438i	$-0.248801\pi$
$882$		0			0
$883$	553.555			0.626903			0.313451	−	0.949604i	$-0.398515\pi$
$883$	553.555			0.626903			0.313451	+	0.949604i	$0.398515\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	351.905	−	203.173i	0.396736	−	0.229056i	−0.288338	−	0.957529i	$-0.593103\pi$
$887$	351.905	−	203.173i	0.396736	−	0.229056i	0.685075	+	0.728473i	$0.259769\pi$
$888$		0			0
$889$	1177.28	−	2039.11i	1.32428	−	2.29371i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1256.82	−	725.623i	−1.40741	−	0.812568i
$894$		0			0
$895$	142.688	+	247.142i	0.159428	+	0.276137i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			414.519i			0.461089i
$900$		0			0
$901$	−256.000			−0.284129
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−331.727	+	191.522i	−0.366549	+	0.211627i
$906$		0			0
$907$	231.712	−	401.337i	0.255471	−	0.442489i	−0.709552	−	0.704653i	$-0.751103\pi$
$907$	231.712	−	401.337i	0.255471	−	0.442489i	0.965023	+	0.262164i	$0.0844361\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−997.489	−	575.900i	−1.09494	−	0.632163i	−0.160051	−	0.987109i	$-0.551166\pi$
$911$	−997.489	−	575.900i	−1.09494	−	0.632163i	−0.934887	+	0.354946i	$0.884499\pi$
$912$		0			0
$913$	−496.480	−	859.928i	−0.543789	−	0.941871i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			1355.00i			1.47765i
$918$		0			0
$919$	944.665			1.02793			0.513964	−	0.857812i	$-0.328177\pi$
$919$	944.665			1.02793			0.513964	+	0.857812i	$0.328177\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−128.141	+	73.9821i	−0.138831	+	0.0801540i
$924$		0			0
$925$	49.9184	−	86.4611i	0.0539658	−	0.0934715i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	912.702	+	526.949i	0.982456	+	0.567221i	0.903011	−	0.429618i	$-0.141352\pi$
$929$	912.702	+	526.949i	0.982456	+	0.567221i	0.0794456	+	0.996839i	$0.474685\pi$
$930$		0			0
$931$	−1239.47	−	2146.83i	−1.33134	−	2.30594i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	164.762i		−	0.176216i
$936$		0			0
$937$	561.392			0.599137			0.299569	−	0.954075i	$-0.403157\pi$
$937$	561.392			0.599137			0.299569	+	0.954075i	$0.403157\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	98.4092	−	56.8166i	0.104579	−	0.0603789i	−0.446798	−	0.894635i	$-0.647436\pi$
$941$	98.4092	−	56.8166i	0.104579	−	0.0603789i	0.551377	+	0.834256i	$0.314102\pi$
$942$		0			0
$943$	−59.8235	+	103.617i	−0.0634395	+	0.109880i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−62.6510	−	36.1716i	−0.0661574	−	0.0381960i	0.466556	−	0.884491i	$-0.345494\pi$
$947$	−62.6510	−	36.1716i	−0.0661574	−	0.0381960i	−0.532714	+	0.846295i	$0.678828\pi$
$948$		0			0
$949$	96.2327	+	166.680i	0.101404	+	0.175637i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	776.447i		−	0.814739i	−0.913263	−	0.407370i	$-0.866446\pi$
$953$		−	776.447i		−	0.814739i	0.913263	−	0.407370i	$-0.133554\pi$
$954$		0			0
$955$	−1280.56			−1.34090
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2115.35	+	1221.30i	−2.20578	+	1.27351i
$960$		0			0
$961$	110.524	−	191.434i	0.115010	−	0.199203i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−71.4479	−	41.2505i	−0.0740393	−	0.0427466i
$966$		0			0
$967$	−11.3888	−	19.7259i	−0.0117774	−	0.0203991i	0.860077	−	0.510165i	$-0.170416\pi$
$967$	−11.3888	−	19.7259i	−0.0117774	−	0.0203991i	−0.871854	+	0.489766i	$0.837082\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1016.98i			1.04735i	0.851919	+	0.523674i	$0.175439\pi$
$971$			1016.98i			1.04735i	−0.851919	+	0.523674i	$0.824561\pi$
$972$		0			0
$973$	−1215.54			−1.24928
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−975.802	+	563.380i	−0.998774	+	0.576642i	−0.907885	−	0.419219i	$-0.862304\pi$
$977$	−975.802	+	563.380i	−0.998774	+	0.576642i	−0.0908886	+	0.995861i	$0.528971\pi$
$978$		0			0
$979$	62.9694	−	109.066i	0.0643201	−	0.111406i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	280.105	+	161.719i	0.284949	+	0.164516i	0.635662	−	0.771968i	$-0.280727\pi$
$983$	280.105	+	161.719i	0.284949	+	0.164516i	−0.350713	+	0.936483i	$0.614061\pi$
$984$		0			0
$985$	63.8592	+	110.607i	0.0648317	+	0.112292i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	102.692i		−	0.103834i
$990$		0			0
$991$	1961.47			1.97929			0.989644	−	0.143547i	$-0.0458508\pi$
$991$	1961.47			1.97929			0.989644	+	0.143547i	$0.0458508\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−210.737	+	121.669i	−0.211796	+	0.122280i
$996$		0			0
$997$	−559.954	+	969.869i	−0.561639	+	0.972787i	0.435715	+	0.900085i	$0.356496\pi$
$997$	−559.954	+	969.869i	−0.561639	+	0.972787i	−0.997354	+	0.0727024i	$0.976838\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.m.a.89.2		4
3.2	odd	2		72.3.m.a.65.1	yes	4
4.3	odd	2		432.3.q.c.305.2		4
8.3	odd	2		1728.3.q.f.1601.1		4
8.5	even	2		1728.3.q.e.1601.1		4
9.2	odd	6		648.3.e.b.161.2		4
9.4	even	3		72.3.m.a.41.1	✓	4
9.5	odd	6	inner	216.3.m.a.17.2		4
9.7	even	3		648.3.e.b.161.3		4
12.11	even	2		144.3.q.d.65.1		4
24.5	odd	2		576.3.q.h.65.2		4
24.11	even	2		576.3.q.c.65.2		4
36.7	odd	6		1296.3.e.c.161.3		4
36.11	even	6		1296.3.e.c.161.2		4
36.23	even	6		432.3.q.c.17.2		4
36.31	odd	6		144.3.q.d.113.1		4
72.5	odd	6		1728.3.q.e.449.1		4
72.13	even	6		576.3.q.h.257.2		4
72.59	even	6		1728.3.q.f.449.1		4
72.67	odd	6		576.3.q.c.257.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.a.41.1	✓	4	9.4	even	3
72.3.m.a.65.1	yes	4	3.2	odd	2
144.3.q.d.65.1		4	12.11	even	2
144.3.q.d.113.1		4	36.31	odd	6
216.3.m.a.17.2		4	9.5	odd	6	inner
216.3.m.a.89.2		4	1.1	even	1	trivial
432.3.q.c.17.2		4	36.23	even	6
432.3.q.c.305.2		4	4.3	odd	2
576.3.q.c.65.2		4	24.11	even	2
576.3.q.c.257.2		4	72.67	odd	6
576.3.q.h.65.2		4	24.5	odd	2
576.3.q.h.257.2		4	72.13	even	6
648.3.e.b.161.2		4	9.2	odd	6
648.3.e.b.161.3		4	9.7	even	3
1296.3.e.c.161.2		4	36.11	even	6
1296.3.e.c.161.3		4	36.7	odd	6
1728.3.q.e.449.1		4	72.5	odd	6
1728.3.q.e.1601.1		4	8.5	even	2
1728.3.q.f.449.1		4	72.59	even	6
1728.3.q.f.1601.1		4	8.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.39898 - 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +O(q^{10})\)	\(q+(3.39898 - 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +(14.2980 + 8.25493i) q^{11} +(1.39898 + 2.42310i) q^{13} -2.54270i q^{17} +21.5959 q^{19} +(-2.60102 + 1.50170i) q^{23} +(-4.79796 + 8.31031i) q^{25} +(13.1969 + 7.61926i) q^{29} +(13.6010 + 23.5577i) q^{31} +50.2295i q^{35} -10.4041 q^{37} +(34.5000 - 19.9186i) q^{41} +(-17.0959 + 29.6110i) q^{43} +(-58.1969 - 33.6000i) q^{47} +(-57.3939 - 99.4091i) q^{49} -100.680i q^{53} +64.7980 q^{55} +(-5.29796 + 3.05878i) q^{59} +(-20.3990 + 35.3321i) q^{61} +(9.51021 + 5.49072i) q^{65} +(-54.4898 - 94.3791i) q^{67} +52.8829i q^{71} +68.7878 q^{73} +(-182.985 + 105.646i) q^{77} +(12.7929 - 22.1579i) q^{79} +(-52.0857 - 30.0717i) q^{83} +(-4.98979 - 8.64258i) q^{85} -7.62809i q^{89} -35.8082 q^{91} +(73.4041 - 42.3799i) q^{95} +(50.7020 - 87.8185i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) 4 * q - 6 * q^5 - 6 * q^7	\( 4 q - 6 q^{5} - 6 q^{7} + 18 q^{11} - 14 q^{13} + 8 q^{19} - 30 q^{23} + 20 q^{25} - 6 q^{29} + 74 q^{31} - 120 q^{37} + 138 q^{41} + 10 q^{43} - 174 q^{47} - 112 q^{49} + 220 q^{55} + 18 q^{59} - 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} - 438 q^{77} - 86 q^{79} + 66 q^{83} + 176 q^{85} - 300 q^{91} + 372 q^{95} + 242 q^{97}+O(q^{100}) \) 4 * q - 6 * q^5 - 6 * q^7 + 18 * q^11 - 14 * q^13 + 8 * q^19 - 30 * q^23 + 20 * q^25 - 6 * q^29 + 74 * q^31 - 120 * q^37 + 138 * q^41 + 10 * q^43 - 174 * q^47 - 112 * q^49 + 220 * q^55 + 18 * q^59 - 62 * q^61 + 234 * q^65 - 22 * q^67 + 40 * q^73 - 438 * q^77 - 86 * q^79 + 66 * q^83 + 176 * q^85 - 300 * q^91 + 372 * q^95 + 242 * q^97

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