LMFDB - Embedded newform 1728.3.q.e.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(449,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, 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("1728.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.q (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:	$47.0845896815$
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			1601.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1728.1601
Dual form			1728.3.q.e.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.39898 + 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +O(q^{10})$	$q+(-3.39898 + 1.96240i) q^{5} +(-6.39898 + 11.0834i) q^{7} +(-14.2980 - 8.25493i) q^{11} +(-1.39898 - 2.42310i) q^{13} -2.54270i q^{17} -21.5959 q^{19} +(-2.60102 + 1.50170i) q^{23} +(-4.79796 + 8.31031i) q^{25} +(-13.1969 - 7.61926i) q^{29} +(13.6010 + 23.5577i) q^{31} -50.2295i q^{35} +10.4041 q^{37} +(34.5000 - 19.9186i) q^{41} +(17.0959 - 29.6110i) q^{43} +(-58.1969 - 33.6000i) q^{47} +(-57.3939 - 99.4091i) q^{49} +100.680i q^{53} +64.7980 q^{55} +(5.29796 - 3.05878i) q^{59} +(20.3990 - 35.3321i) q^{61} +(9.51021 + 5.49072i) q^{65} +(54.4898 + 94.3791i) q^{67} +52.8829i q^{71} +68.7878 q^{73} +(182.985 - 105.646i) q^{77} +(12.7929 - 22.1579i) q^{79} +(52.0857 + 30.0717i) q^{83} +(4.98979 + 8.64258i) q^{85} -7.62809i q^{89} +35.8082 q^{91} +(73.4041 - 42.3799i) q^{95} +(50.7020 - 87.8185i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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	−0.799778	−	0.600296i	$-0.795050\pi$
$5$	−3.39898	+	1.96240i	−0.679796	+	0.392480i	0.119982	+	0.992776i	$0.461716\pi$
$6$		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	−0.319443	−	0.947606i	$-0.603496\pi$
$11$	−14.2980	−	8.25493i	−1.29981	−	0.750448i	−0.980372	+	0.197157i	$0.936829\pi$
$12$		0			0
$13$	−1.39898	−	2.42310i	−0.107614	−	0.186393i	0.807189	−	0.590293i	$-0.200988\pi$
$13$	−1.39898	−	2.42310i	−0.107614	−	0.186393i	−0.914803	+	0.403900i	$0.867654\pi$
$14$		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	$-0.692404\pi$
$19$	−21.5959			−1.13663			−0.568314	+	0.822812i	$0.692404\pi$
$20$		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	0.254901	−	0.966967i	$-0.417957\pi$
$29$	−13.1969	−	7.61926i	−0.455067	−	0.262733i	−0.709968	+	0.704234i	$0.751290\pi$
$30$		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	$-0.455098\pi$
$37$	10.4041			0.281191			0.140596	+	0.990067i	$0.455098\pi$
$38$		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	−0.595847	−	0.803098i	$-0.703184\pi$
$43$	17.0959	−	29.6110i	0.397579	−	0.688628i	0.993427	+	0.114470i	$0.0365170\pi$
$44$		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	$0.398730\pi$
$53$			100.680i			1.89963i	−0.312810	+	0.949816i	$0.601270\pi$
$54$		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	−0.454430	−	0.890783i	$-0.650157\pi$
$59$	5.29796	−	3.05878i	0.0897959	−	0.0518437i	0.544226	+	0.838939i	$0.316824\pi$
$60$		0			0
$61$	20.3990	−	35.3321i	0.334409	−	0.579214i	−0.648962	−	0.760821i	$-0.724796\pi$
$61$	20.3990	−	35.3321i	0.334409	−	0.579214i	0.983371	+	0.181607i	$0.0581298\pi$
$62$		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	$0.135654\pi$
$67$	54.4898	+	94.3791i	0.813281	+	1.40864i	−0.0972755	+	0.995257i	$0.531013\pi$
$68$		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	0.779798	−	0.626031i	$-0.215322\pi$
$83$	52.0857	+	30.0717i	0.627539	+	0.362310i	−0.152260	+	0.988341i	$0.548655\pi$
$84$		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	0.494063	−	0.869426i	$-0.335511\pi$
$101$	−1.19694	−	0.691053i	−0.0118509	−	0.00684211i	−0.505914	+	0.862584i	$0.668845\pi$
$102$		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	$0.160217\pi$
$107$			103.223i			0.964702i	−0.875978	+	0.482351i	$0.839783\pi$
$108$		0			0
$109$	−14.4041			−0.132148			−0.0660738	−	0.997815i	$-0.521047\pi$
$109$	−14.4041			−0.132148			−0.0660738	+	0.997815i	$0.521047\pi$
$110$		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	−0.807324	−	0.590108i	$-0.799085\pi$
$131$	−91.6918	+	52.9383i	−0.699938	+	0.404109i	0.107387	+	0.994217i	$0.465752\pi$
$132$		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	0.643087	−	0.765793i	$-0.277653\pi$
$139$	−47.4898	−	82.2547i	−0.341653	−	0.591761i	−0.984740	+	0.174033i	$0.944320\pi$
$140$		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	−0.208464	−	0.978030i	$-0.566846\pi$
$149$	79.6112	−	45.9636i	0.534304	−	0.308480i	0.742767	+	0.669550i	$0.233513\pi$
$150$		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	$-0.930784\pi$
$157$	−105.985	−	183.571i	−0.675062	−	1.16924i	0.301389	−	0.953501i	$-0.402550\pi$
$158$		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	$-0.677817\pi$
$163$	−172.788			−1.06005			−0.530024	+	0.847983i	$0.677817\pi$
$164$		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	0.643214	−	0.765687i	$-0.277601\pi$
$173$	52.1969	+	30.1359i	0.301716	+	0.174196i	−0.341497	+	0.939883i	$0.610934\pi$
$174$		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	$-0.934897\pi$
$179$		−	72.7108i		−	0.406205i	0.979157	−	0.203103i	$-0.0651025\pi$
$180$		0			0
$181$	97.5959			0.539204			0.269602	−	0.962972i	$-0.413108\pi$
$181$	97.5959			0.539204			0.269602	+	0.962972i	$0.413108\pi$
$182$		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	$-0.973680\pi$
$197$		−	32.5413i		−	0.165184i	0.996583	−	0.0825922i	$-0.0263199\pi$
$198$		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	0.594150	−	0.804354i	$-0.297489\pi$
$211$	−84.2980	−	146.008i	−0.399516	−	0.691983i	−0.993666	+	0.112372i	$0.964155\pi$
$212$		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	0.678567	−	0.734538i	$-0.262601\pi$
$227$	86.6510	+	50.0280i	0.381723	+	0.220388i	−0.296845	+	0.954926i	$0.595934\pi$
$228$		0			0
$229$	−104.995	−	181.856i	−0.458493	−	0.794133i	0.540389	−	0.841416i	$-0.318277\pi$
$229$	−104.995	−	181.856i	−0.458493	−	0.794133i	−0.998882	+	0.0472824i	$0.984944\pi$
$230$		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	$0.293670\pi$
$251$			400.179i			1.59434i	−0.603755	+	0.797170i	$0.706330\pi$
$252$		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	$0.102864\pi$
$269$			170.849i			0.635125i	−0.948237	+	0.317562i	$0.897136\pi$
$270$		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	−0.841990	−	0.539494i	$-0.818616\pi$
$277$	12.8031	−	22.1756i	0.0462204	−	0.0800561i	0.888210	+	0.459438i	$0.151949\pi$
$278$		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	0.852489	−	0.522745i	$-0.175092\pi$
$283$	−7.48979	−	12.9727i	−0.0264657	−	0.0458399i	−0.878955	+	0.476905i	$0.841759\pi$
$284$		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	−0.874216	−	0.485537i	$-0.838624\pi$
$293$	−261.015	+	150.697i	−0.890837	+	0.514325i	−0.0166210	+	0.999862i	$0.505291\pi$
$294$		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	$-0.476782\pi$
$307$	44.7469			0.145755			0.0728777	+	0.997341i	$0.476782\pi$
$308$		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	0.422401	−	0.906409i	$-0.361187\pi$
$317$	−47.9847	−	27.7040i	−0.151371	−	0.0873942i	−0.573773	+	0.819015i	$0.694521\pi$
$318$		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	−0.854156	−	0.520016i	$-0.825926\pi$
$331$	7.70204	−	13.3403i	0.0232690	−	0.0403031i	0.877425	+	0.479713i	$0.159259\pi$
$332$		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	$-0.253786\pi$
$347$	578.651	−	334.084i	1.66758	−	0.962779i	0.968936	−	0.247312i	$-0.0795472\pi$
$348$		0			0
$349$	−123.015	+	213.069i	−0.352479	+	0.610512i	−0.986683	−	0.162654i	$-0.947995\pi$
$349$	−123.015	+	213.069i	−0.352479	+	0.610512i	0.634204	+	0.773166i	$0.281328\pi$
$350$		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	0.727440	−	0.686171i	$-0.240710\pi$
$373$	−85.9847	−	148.930i	−0.230522	−	0.399276i	−0.957962	+	0.286896i	$0.907377\pi$
$374$		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	$-0.427633\pi$
$379$	170.849			0.450789			0.225394	+	0.974268i	$0.427633\pi$
$380$		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	−0.0840807	−	0.996459i	$-0.526795\pi$
$389$	−384.752	−	222.137i	−0.989080	−	0.571045i	−0.904999	+	0.425413i	$0.860129\pi$
$390$		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	$-0.242166\pi$
$397$	575.090			1.44859			0.724294	+	0.689491i	$0.242166\pi$
$398$		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	−0.677195	−	0.735803i	$-0.736805\pi$
$419$	−158.620	+	91.5795i	−0.378569	+	0.218567i	0.298626	+	0.954370i	$0.403472\pi$
$420$		0			0
$421$	83.7724	−	145.098i	0.198984	−	0.344651i	−0.749215	−	0.662327i	$-0.769569\pi$
$421$	83.7724	−	145.098i	0.198984	−	0.344651i	0.948199	+	0.317676i	$0.102902\pi$
$422$		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	0.320855	−	0.947128i	$-0.396030\pi$
$443$	−150.157	−	86.6933i	−0.338955	−	0.195696i	−0.659810	+	0.751433i	$0.729363\pi$
$444$		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	0.501680	−	0.865053i	$-0.332715\pi$
$461$	1.54999	+	0.894890i	0.00336224	+	0.00194119i	−0.498318	+	0.866994i	$0.666049\pi$
$462$		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	$-0.855600\pi$
$467$		−	409.322i		−	0.876494i	0.898855	−	0.438247i	$-0.144400\pi$
$468$		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	−0.624157	−	0.781299i	$-0.714558\pi$
$491$	−127.469	+	73.5945i	−0.259612	+	0.149887i	0.364546	+	0.931186i	$0.381224\pi$
$492$		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	0.998602	−	0.0528594i	$-0.0168335\pi$
$499$	226.308	+	391.977i	0.453523	+	0.785526i	−0.545079	+	0.838385i	$0.683500\pi$
$500$		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	−0.0600849	−	0.998193i	$-0.519137\pi$
$509$	394.136	−	227.554i	0.774333	−	0.447062i	0.834418	+	0.551132i	$0.185804\pi$
$510$		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	$-0.345633\pi$
$523$	487.616			0.932345			0.466172	+	0.884694i	$0.345633\pi$
$524$		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	$-0.690045\pi$
$541$	−608.302			−1.12440			−0.562202	+	0.827000i	$0.690045\pi$
$542$		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	$0.456151\pi$
$547$	−431.671	+	747.677i	−0.789162	+	1.36687i	−0.926481	+	0.376341i	$0.877182\pi$
$548$		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	$-0.903814\pi$
$557$		−	331.526i		−	0.595200i	0.954691	−	0.297600i	$-0.0961861\pi$
$558$		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	0.0316114	−	0.999500i	$-0.489936\pi$
$563$	514.024	−	296.772i	0.913010	−	0.527126i	0.881398	+	0.472374i	$0.156603\pi$
$564$		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	0.983672	−	0.179971i	$-0.0576002\pi$
$571$	191.843	+	332.282i	0.335977	+	0.581929i	−0.647695	+	0.761900i	$0.724267\pi$
$572$		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	0.905473	−	0.424404i	$-0.139516\pi$
$587$	581.520	+	335.741i	0.990665	+	0.571961i	0.0851921	+	0.996365i	$0.472850\pi$
$588$		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	$-0.101044\pi$
$613$	1164.75			1.90008			0.950038	+	0.312133i	$0.101044\pi$
$614$		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	$-0.467944\pi$
$619$	564.469	−	977.690i	0.911905	−	1.57947i	0.811370	−	0.584533i	$-0.198722\pi$
$620$		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	$-0.835472\pi$
$643$	−554.682	−	960.737i	−0.862646	−	1.49415i	0.00671893	−	0.999977i	$-0.497861\pi$
$644$		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	−0.964537	−	0.263946i	$-0.914976\pi$
$653$	−795.499	+	459.282i	−1.21822	+	0.703341i	−0.253685	+	0.967287i	$0.581643\pi$
$654$		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	0.334411	−	0.942427i	$-0.391463\pi$
$659$	−207.288	−	119.678i	−0.314549	−	0.181605i	−0.648960	+	0.760822i	$0.724796\pi$
$660$		0			0
$661$	177.793	+	307.946i	0.268976	+	0.465879i	0.968598	−	0.248634i	$-0.0799816\pi$
$661$	177.793	+	307.946i	0.268976	+	0.465879i	−0.699622	+	0.714513i	$0.746648\pi$
$662$		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	0.381574	−	0.924338i	$-0.375382\pi$
$677$	−154.450	−	89.1718i	−0.228139	−	0.131716i	−0.609713	+	0.792622i	$0.708715\pi$
$678$		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	$-0.839352\pi$
$683$		−	660.510i		−	0.967072i	0.875325	−	0.483536i	$-0.160648\pi$
$684$		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	−0.833026	−	0.553233i	$-0.813394\pi$
$691$	43.2571	−	74.9236i	0.0626008	−	0.108428i	0.895627	+	0.444805i	$0.146727\pi$
$692$		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	$0.328821\pi$
$701$			1204.11i			1.71770i	−0.512227	+	0.858850i	$0.671179\pi$
$702$		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	$0.358530\pi$
$709$	−401.944	+	696.187i	−0.566917	+	0.981928i	−0.996869	+	0.0790766i	$0.974803\pi$
$710$		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	0.806163	−	0.591693i	$-0.201540\pi$
$733$	−80.1459	−	138.817i	−0.109340	−	0.189382i	−0.915503	+	0.402311i	$0.868207\pi$
$734$		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	$-0.473512\pi$
$739$	122.849			0.166237			0.0831184	+	0.996540i	$0.473512\pi$
$740$		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	$-0.403450\pi$
$757$	452.220			0.597385			0.298692	+	0.954349i	$0.403450\pi$
$758$		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	$-0.874720\pi$
$773$		−	592.885i		−	0.766992i	0.923543	−	0.383496i	$-0.125280\pi$
$774$		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	$-0.844833\pi$
$787$	−666.904	−	1155.11i	−0.847400	−	1.46774i	0.0361199	−	0.999347i	$-0.488500\pi$
$788$		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	−0.0427041	−	0.999088i	$-0.513597\pi$
$797$	638.540	−	368.661i	0.801179	−	0.462561i	0.843883	+	0.536527i	$0.180264\pi$
$798$		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	$-0.733574\pi$
$811$	−1086.24			−1.33938			−0.669692	+	0.742639i	$0.733574\pi$
$812$		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	$0.000638377\pi$
$821$	1232.92	+	711.829i	1.50173	+	0.867026i	0.501736	+	0.865021i	$0.332695\pi$
$822$		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	$-0.865596\pi$
$827$		−	677.821i		−	0.819614i	0.912172	−	0.409807i	$-0.134404\pi$
$828$		0			0
$829$	995.775			1.20118			0.600588	−	0.799558i	$-0.294933\pi$
$829$	995.775			1.20118			0.600588	+	0.799558i	$0.294933\pi$
$830$		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	$0.463655\pi$
$853$	−685.317	+	1187.00i	−0.803420	+	1.39156i	−0.917352	+	0.398076i	$0.869678\pi$
$854$		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	0.883569	−	0.468301i	$-0.155134\pi$
$859$	31.1163	+	53.8951i	0.0362239	+	0.0627416i	−0.847345	+	0.531043i	$0.821800\pi$
$860$		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	$-0.951737\pi$
$877$	−548.187	−	949.487i	−0.625070	−	1.08265i	0.363457	−	0.931611i	$-0.381596\pi$
$878$		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	$-0.601485\pi$
$883$	−553.555			−0.626903			−0.313451	+	0.949604i	$0.601485\pi$
$884$		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	−0.965023	−	0.262164i	$-0.915564\pi$
$907$	−231.712	+	401.337i	−0.255471	+	0.442489i	0.709552	+	0.704653i	$0.248897\pi$
$908$		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	−0.551377	−	0.834256i	$-0.685898\pi$
$941$	−98.4092	+	56.8166i	−0.104579	+	0.0603789i	0.446798	+	0.894635i	$0.352564\pi$
$942$		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	0.532714	−	0.846295i	$-0.321172\pi$
$947$	62.6510	+	36.1716i	0.0661574	+	0.0381960i	−0.466556	+	0.884491i	$0.654506\pi$
$948$		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	$-0.824561\pi$
$971$		−	1016.98i		−	1.04735i	0.851919	−	0.523674i	$-0.175439\pi$
$972$		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	$-0.643504\pi$
$997$	559.954	−	969.869i	0.561639	−	0.972787i	0.997354	−	0.0727024i	$-0.0231623\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.a.41.1	✓	4	72.13	even	6
72.3.m.a.65.1	yes	4	24.5	odd	2
144.3.q.d.65.1		4	24.11	even	2
144.3.q.d.113.1		4	72.67	odd	6
216.3.m.a.17.2		4	72.5	odd	6
216.3.m.a.89.2		4	8.5	even	2
432.3.q.c.17.2		4	72.59	even	6
432.3.q.c.305.2		4	8.3	odd	2
576.3.q.c.65.2		4	12.11	even	2
576.3.q.c.257.2		4	36.31	odd	6
576.3.q.h.65.2		4	3.2	odd	2
576.3.q.h.257.2		4	9.4	even	3
648.3.e.b.161.2		4	72.29	odd	6
648.3.e.b.161.3		4	72.61	even	6
1296.3.e.c.161.2		4	72.11	even	6
1296.3.e.c.161.3		4	72.43	odd	6
1728.3.q.e.449.1		4	9.5	odd	6	inner
1728.3.q.e.1601.1		4	1.1	even	1	trivial
1728.3.q.f.449.1		4	36.23	even	6
1728.3.q.f.1601.1		4	4.3	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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.q (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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