LMFDB - Embedded newform 1728.3.o.g.1279.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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([3, 0, 4]))

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

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1279.4
Root			$-1.59523 - 1.20633i$ of defining polynomial
Character	$\chi$	$=$	1728.1279
Dual form			1728.3.o.g.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10093 - 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +O(q^{10})$	$q+(1.10093 - 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +(-4.54769 + 2.62561i) q^{11} +(7.37788 - 12.7789i) q^{13} -28.2789 q^{17} -19.1376i q^{19} +(-3.16702 - 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-12.3355 - 21.3657i) q^{29} +(-32.9674 - 19.0338i) q^{31} -18.4036i q^{35} +4.21977 q^{37} +(9.92483 - 17.1903i) q^{41} +(-20.1894 + 11.6564i) q^{43} +(-25.8538 + 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} -32.1118 q^{53} +11.5624i q^{55} +(-7.96159 - 4.59663i) q^{59} +(40.8215 + 70.7049i) q^{61} +(-16.2450 - 28.1372i) q^{65} +(-6.86179 - 3.96166i) q^{67} -62.9286i q^{71} +33.3218 q^{73} +(-21.9454 + 38.0106i) q^{77} +(53.7133 - 31.0114i) q^{79} +(-103.056 + 59.4995i) q^{83} +(-31.1329 + 53.9238i) q^{85} +107.361 q^{89} -123.332i q^{91} +(-36.4927 - 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.10093	−	1.90686i	0.220185	−	0.381372i	−0.734679	−	0.678415i	$-0.762667\pi$
$5$	1.10093	−	1.90686i	0.220185	−	0.381372i	0.954864	+	0.297043i	$0.0960005\pi$
$6$		0			0
$7$	7.23844	−	4.17912i	1.03406	−	0.597017i	0.115917	−	0.993259i	$-0.463019\pi$
$7$	7.23844	−	4.17912i	1.03406	−	0.597017i	0.918146	+	0.396242i	$0.129686\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	−0.692261	−	0.721648i	$-0.743385\pi$
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	0.278835	+	0.960339i	$0.410052\pi$
$12$		0			0
$13$	7.37788	−	12.7789i	0.567529	−	0.982990i	−0.429280	−	0.903171i	$-0.641233\pi$
$13$	7.37788	−	12.7789i	0.567529	−	0.982990i	0.996809	−	0.0798182i	$-0.0254340\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−28.2789			−1.66346			−0.831732	−	0.555178i	$-0.812650\pi$
$17$	−28.2789			−1.66346			−0.831732	+	0.555178i	$0.812650\pi$
$18$		0			0
$19$		−	19.1376i		−	1.00724i	−0.863925	−	0.503620i	$-0.832001\pi$
$19$		−	19.1376i		−	1.00724i	0.863925	−	0.503620i	$-0.167999\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.16702	−	1.82848i	−0.137696	−	0.0794990i	0.429569	−	0.903034i	$-0.358665\pi$
$23$	−3.16702	−	1.82848i	−0.137696	−	0.0794990i	−0.567266	+	0.823535i	$0.691999\pi$
$24$		0			0
$25$	10.0759	+	17.4520i	0.403037	+	0.698081i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−12.3355	−	21.3657i	−0.425362	−	0.736748i	0.571092	−	0.820886i	$-0.306520\pi$
$29$	−12.3355	−	21.3657i	−0.425362	−	0.736748i	−0.996454	+	0.0841375i	$0.973187\pi$
$30$		0			0
$31$	−32.9674	−	19.0338i	−1.06347	−	0.613992i	−0.137077	−	0.990560i	$-0.543771\pi$
$31$	−32.9674	−	19.0338i	−1.06347	−	0.613992i	−0.926389	+	0.376568i	$0.877104\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	18.4036i		−	0.525817i
$36$		0			0
$37$	4.21977			0.114048			0.0570239	−	0.998373i	$-0.481839\pi$
$37$	4.21977			0.114048			0.0570239	+	0.998373i	$0.481839\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.92483	−	17.1903i	0.242069	−	0.419276i	−0.719235	−	0.694767i	$-0.755507\pi$
$41$	9.92483	−	17.1903i	0.242069	−	0.419276i	0.961303	+	0.275492i	$0.0888406\pi$
$42$		0			0
$43$	−20.1894	+	11.6564i	−0.469521	+	0.271078i	−0.716039	−	0.698060i	$-0.754047\pi$
$43$	−20.1894	+	11.6564i	−0.469521	+	0.271078i	0.246518	+	0.969138i	$0.420714\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−25.8538	+	14.9267i	−0.550082	+	0.317590i	−0.749155	−	0.662395i	$-0.769540\pi$
$47$	−25.8538	+	14.9267i	−0.550082	+	0.317590i	0.199073	+	0.979985i	$0.436207\pi$
$48$		0			0
$49$	10.4300	−	18.0654i	0.212858	−	0.368681i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−32.1118			−0.605883			−0.302942	−	0.953009i	$-0.597969\pi$
$53$	−32.1118			−0.605883			−0.302942	+	0.953009i	$0.597969\pi$
$54$		0			0
$55$			11.5624i			0.210225i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	0.431009	−	0.902348i	$-0.358158\pi$
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	−0.565951	+	0.824439i	$0.691491\pi$
$60$		0			0
$61$	40.8215	+	70.7049i	0.669205	+	1.15910i	0.978127	+	0.208009i	$0.0666985\pi$
$61$	40.8215	+	70.7049i	0.669205	+	1.15910i	−0.308922	+	0.951087i	$0.599968\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−16.2450	−	28.1372i	−0.249923	−	0.432879i
$66$		0			0
$67$	−6.86179	−	3.96166i	−0.102415	−	0.0591292i	0.447918	−	0.894075i	$-0.352166\pi$
$67$	−6.86179	−	3.96166i	−0.102415	−	0.0591292i	−0.550333	+	0.834946i	$0.685499\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	62.9286i		−	0.886318i	−0.896443	−	0.443159i	$-0.853858\pi$
$71$		−	62.9286i		−	0.886318i	0.896443	−	0.443159i	$-0.146142\pi$
$72$		0			0
$73$	33.3218			0.456463			0.228232	−	0.973607i	$-0.426706\pi$
$73$	33.3218			0.456463			0.228232	+	0.973607i	$0.426706\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−21.9454	+	38.0106i	−0.285006	+	0.493644i
$78$		0			0
$79$	53.7133	−	31.0114i	0.679916	−	0.392549i	−0.119908	−	0.992785i	$-0.538260\pi$
$79$	53.7133	−	31.0114i	0.679916	−	0.392549i	0.799823	+	0.600236i	$0.204927\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.969428	−	0.245376i	$-0.921089\pi$
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.272212	+	0.962237i	$0.587755\pi$
$84$		0			0
$85$	−31.1329	+	53.9238i	−0.366270	+	0.634398i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	107.361			1.20630			0.603152	−	0.797626i	$-0.293911\pi$
$89$	107.361			1.20630			0.603152	+	0.797626i	$0.293911\pi$
$90$		0			0
$91$		−	123.332i		−	1.35530i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−36.4927	−	21.0690i	−0.384133	−	0.221779i
$96$		0			0
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	0.875086	−	0.483968i	$-0.160805\pi$
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	−0.856671	+	0.515863i	$0.827471\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.54688	+	13.0716i	0.0747216	+	0.129422i	0.900965	−	0.433891i	$-0.142860\pi$
$101$	7.54688	+	13.0716i	0.0747216	+	0.129422i	−0.826244	+	0.563313i	$0.809527\pi$
$102$		0			0
$103$	−112.813	−	65.1324i	−1.09527	−	0.632353i	−0.160294	−	0.987069i	$-0.551244\pi$
$103$	−112.813	−	65.1324i	−1.09527	−	0.632353i	−0.934974	+	0.354716i	$0.884578\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	51.2733i		−	0.479190i	−0.970873	−	0.239595i	$-0.922985\pi$
$107$		−	51.2733i		−	0.479190i	0.970873	−	0.239595i	$-0.0770146\pi$
$108$		0			0
$109$	25.4737			0.233704			0.116852	−	0.993149i	$-0.462720\pi$
$109$	25.4737			0.233704			0.116852	+	0.993149i	$0.462720\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−76.1529	+	131.901i	−0.673919	+	1.16726i	0.302864	+	0.953034i	$0.402057\pi$
$113$	−76.1529	+	131.901i	−0.673919	+	1.16726i	−0.976783	+	0.214229i	$0.931276\pi$
$114$		0			0
$115$	−6.97330	+	4.02603i	−0.0606374	+	0.0350090i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−204.695	+	118.181i	−1.72013	+	0.993116i
$120$		0			0
$121$	−46.7124	+	80.9082i	−0.386053	+	0.668663i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	99.4176			0.795341
$126$		0			0
$127$		−	147.428i		−	1.16085i	−0.814314	−	0.580425i	$-0.802886\pi$
$127$		−	147.428i		−	1.16085i	0.814314	−	0.580425i	$-0.197114\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	0.00284803	−	0.999996i	$-0.499093\pi$
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	−0.864598	+	0.502464i	$0.832427\pi$
$132$		0			0
$133$	−79.9782	−	138.526i	−0.601340	−	1.04155i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−49.9179	−	86.4604i	−0.364364	−	0.631098i	0.624310	−	0.781177i	$-0.285380\pi$
$137$	−49.9179	−	86.4604i	−0.364364	−	0.631098i	−0.988674	+	0.150079i	$0.952047\pi$
$138$		0			0
$139$	−82.7828	−	47.7947i	−0.595560	−	0.343847i	0.171733	−	0.985144i	$-0.445063\pi$
$139$	−82.7828	−	47.7947i	−0.595560	−	0.343847i	−0.767293	+	0.641297i	$0.778397\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			77.4857i			0.541858i
$144$		0			0
$145$	−54.3218			−0.374633
$146$		0			0
$147$		0			0
$148$		0			0
$149$	34.3382	−	59.4755i	0.230458	−	0.399164i	−0.727485	−	0.686123i	$-0.759311\pi$
$149$	34.3382	−	59.4755i	0.230458	−	0.399164i	0.957943	+	0.286959i	$0.0926443\pi$
$150$		0			0
$151$	−91.2633	+	52.6909i	−0.604393	+	0.348946i	−0.770768	−	0.637116i	$-0.780127\pi$
$151$	−91.2633	+	52.6909i	−0.604393	+	0.348946i	0.166375	+	0.986063i	$0.446794\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−72.5894	+	41.9095i	−0.468319	+	0.270384i
$156$		0			0
$157$	107.502	−	186.200i	0.684729	−	1.18598i	−0.288794	−	0.957391i	$-0.593254\pi$
$157$	107.502	−	186.200i	0.684729	−	1.18598i	0.973522	−	0.228593i	$-0.0734125\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−30.5657			−0.189849
$162$		0			0
$163$		−	33.7439i		−	0.207018i	−0.994629	−	0.103509i	$-0.966993\pi$
$163$		−	33.7439i		−	0.207018i	0.994629	−	0.103509i	$-0.0330071\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−131.565	−	75.9589i	−0.787812	−	0.454843i	0.0513797	−	0.998679i	$-0.483638\pi$
$167$	−131.565	−	75.9589i	−0.787812	−	0.454843i	−0.839192	+	0.543836i	$0.816971\pi$
$168$		0			0
$169$	−24.3663	−	42.2036i	−0.144179	−	0.249726i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−59.4003	−	102.884i	−0.343354	−	0.594707i	0.641699	−	0.766957i	$-0.278230\pi$
$173$	−59.4003	−	102.884i	−0.343354	−	0.594707i	−0.985053	+	0.172249i	$0.944896\pi$
$174$		0			0
$175$	145.868	+	84.2170i	0.833532	+	0.481240i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			218.189i			1.21894i	0.792811	+	0.609468i	$0.208617\pi$
$179$			218.189i			1.21894i	−0.792811	+	0.609468i	$0.791383\pi$
$180$		0			0
$181$	−184.078			−1.01701			−0.508503	−	0.861060i	$-0.669801\pi$
$181$	−184.078			−1.01701			−0.508503	+	0.861060i	$0.669801\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.64565	−	8.04650i	0.0251116	−	0.0434946i
$186$		0			0
$187$	128.603	−	74.2492i	0.687719	−	0.397055i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	215.775	−	124.578i	1.12971	−	0.652239i	0.185849	−	0.982578i	$-0.440497\pi$
$191$	215.775	−	124.578i	1.12971	−	0.652239i	0.943862	+	0.330339i	$0.107163\pi$
$192$		0			0
$193$	125.086	−	216.656i	0.648115	−	1.12257i	−0.335457	−	0.942055i	$-0.608891\pi$
$193$	125.086	−	216.656i	0.648115	−	1.12257i	0.983573	−	0.180513i	$-0.0577758\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	255.674			1.29784			0.648919	−	0.760858i	$-0.275221\pi$
$197$	255.674			1.29784			0.648919	+	0.760858i	$0.275221\pi$
$198$		0			0
$199$		−	309.110i		−	1.55332i	−0.629921	−	0.776659i	$-0.716913\pi$
$199$		−	309.110i		−	1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−178.580	−	103.103i	−0.879702	−	0.507896i
$204$		0			0
$205$	−21.8530	−	37.8505i	−0.106600	−	0.184636i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	50.2478	+	87.0317i	0.240420	+	0.416420i
$210$		0			0
$211$	−341.158	−	196.968i	−1.61686	−	0.933497i	−0.987725	−	0.156205i	$-0.950074\pi$
$211$	−341.158	−	196.968i	−1.61686	−	0.933497i	−0.629140	−	0.777292i	$-0.716593\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			51.3311i			0.238750i
$216$		0			0
$217$	−318.177			−1.46626
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−208.638	+	361.372i	−0.944064	+	1.63517i
$222$		0			0
$223$	−89.4002	+	51.6152i	−0.400898	+	0.231458i	−0.686871	−	0.726779i	$-0.741016\pi$
$223$	−89.4002	+	51.6152i	−0.400898	+	0.231458i	0.285974	+	0.958238i	$0.407683\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	−0.206049	−	0.978542i	$-0.566061\pi$
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	0.744418	+	0.667714i	$0.232727\pi$
$228$		0			0
$229$	−105.572	+	182.856i	−0.461012	+	0.798496i	−0.999012	−	0.0444490i	$-0.985847\pi$
$229$	−105.572	+	182.856i	−0.461012	+	0.798496i	0.538000	+	0.842945i	$0.319180\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	280.109			1.20219			0.601093	−	0.799179i	$-0.294732\pi$
$233$	280.109			1.20219			0.601093	+	0.799179i	$0.294732\pi$
$234$		0			0
$235$			65.7328i			0.279714i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−339.349	−	195.923i	−1.41987	−	0.819762i	−0.423583	−	0.905857i	$-0.639228\pi$
$239$	−339.349	−	195.923i	−1.41987	−	0.819762i	−0.996287	+	0.0860949i	$0.972561\pi$
$240$		0			0
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	0.812710	−	0.582669i	$-0.197992\pi$
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	−0.910961	+	0.412493i	$0.864658\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−22.9654	−	39.7772i	−0.0937363	−	0.162356i
$246$		0			0
$247$	−244.557	−	141.195i	−0.990107	−	0.571639i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	389.416i		−	1.55146i	−0.631065	−	0.775730i	$-0.717382\pi$
$251$		−	389.416i		−	1.55146i	0.631065	−	0.775730i	$-0.282618\pi$
$252$		0			0
$253$	19.2035			0.0759030
$254$		0			0
$255$		0			0
$256$		0			0
$257$	32.5409	−	56.3625i	0.126618	−	0.219310i	−0.795746	−	0.605631i	$-0.792921\pi$
$257$	32.5409	−	56.3625i	0.126618	−	0.219310i	0.922364	+	0.386321i	$0.126254\pi$
$258$		0			0
$259$	30.5445	−	17.6349i	0.117933	−	0.0680884i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−124.773	+	72.0378i	−0.474423	+	0.273908i	−0.718089	−	0.695951i	$-0.754983\pi$
$263$	−124.773	+	72.0378i	−0.474423	+	0.273908i	0.243667	+	0.969859i	$0.421650\pi$
$264$		0			0
$265$	−35.3527	+	61.2327i	−0.133406	+	0.231067i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−72.4113			−0.269187			−0.134593	−	0.990901i	$-0.542973\pi$
$269$	−72.4113			−0.269187			−0.134593	+	0.990901i	$0.542973\pi$
$270$		0			0
$271$			35.4695i			0.130884i	0.997856	+	0.0654419i	$0.0208457\pi$
$271$			35.4695i			0.130884i	−0.997856	+	0.0654419i	$0.979154\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−91.6443	−	52.9109i	−0.333252	−	0.192403i
$276$		0			0
$277$	166.922	+	289.118i	0.602607	+	1.04375i	0.992425	+	0.122854i	$0.0392047\pi$
$277$	166.922	+	289.118i	0.602607	+	1.04375i	−0.389818	+	0.920892i	$0.627462\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.5385	+	35.5737i	0.0730906	+	0.126597i	0.900254	−	0.435364i	$-0.143380\pi$
$281$	20.5385	+	35.5737i	0.0730906	+	0.126597i	−0.827164	+	0.561961i	$0.810047\pi$
$282$		0			0
$283$	218.583	+	126.199i	0.772378	+	0.445933i	0.833722	−	0.552184i	$-0.186205\pi$
$283$	218.583	+	126.199i	0.772378	+	0.445933i	−0.0613442	+	0.998117i	$0.519539\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	165.908i		−	0.578077i
$288$		0			0
$289$	510.695			1.76711
$290$		0			0
$291$		0			0
$292$		0			0
$293$	20.3415	−	35.2325i	0.0694248	−	0.120247i	−0.829223	−	0.558917i	$-0.811217\pi$
$293$	20.3415	−	35.2325i	0.0694248	−	0.120247i	0.898648	+	0.438670i	$0.144550\pi$
$294$		0			0
$295$	−17.5302	+	10.1211i	−0.0594245	+	0.0343088i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−46.7317	+	26.9806i	−0.156293	+	0.0902361i
$300$		0			0
$301$	−97.4266	+	168.748i	−0.323677	+	0.560624i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	179.766			0.589396
$306$		0			0
$307$		−	136.830i		−	0.445701i	−0.974853	−	0.222850i	$-0.928464\pi$
$307$		−	136.830i		−	0.445701i	0.974853	−	0.222850i	$-0.0715361\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	371.260	+	214.347i	1.19376	+	0.689219i	0.959158	−	0.282871i	$-0.0912869\pi$
$311$	371.260	+	214.347i	1.19376	+	0.689219i	0.234605	+	0.972091i	$0.424620\pi$
$312$		0			0
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	0.875431	−	0.483343i	$-0.160578\pi$
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	−0.856303	+	0.516474i	$0.827244\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−23.5266	−	40.7493i	−0.0742164	−	0.128547i	0.826529	−	0.562894i	$-0.190312\pi$
$317$	−23.5266	−	40.7493i	−0.0742164	−	0.128547i	−0.900745	+	0.434348i	$0.856979\pi$
$318$		0			0
$319$	112.196	+	64.7763i	0.351711	+	0.203061i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			541.189i			1.67551i
$324$		0			0
$325$	297.356			0.914941
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−124.761	+	216.092i	−0.379213	+	0.656816i
$330$		0			0
$331$	73.1501	−	42.2332i	0.220997	−	0.127593i	−0.385415	−	0.922743i	$-0.625942\pi$
$331$	73.1501	−	42.2332i	0.220997	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.1086	+	8.72297i	−0.0451004	+	0.0260387i
$336$		0			0
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	0.198667	+	0.980067i	$0.436339\pi$
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	−0.948096	+	0.317983i	$0.896994\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	199.901			0.586219
$342$		0			0
$343$			235.200i			0.685714i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.965782	−	0.259354i	$-0.0835097\pi$
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.258284	+	0.966069i	$0.416843\pi$
$348$		0			0
$349$	−186.972	−	323.845i	−0.535736	−	0.927923i	−0.999127	−	0.0417686i	$-0.986701\pi$
$349$	−186.972	−	323.845i	−0.535736	−	0.927923i	0.463391	−	0.886154i	$-0.346633\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−297.026	−	514.465i	−0.841434	−	1.45741i	−0.888682	−	0.458523i	$-0.848379\pi$
$353$	−297.026	−	514.465i	−0.841434	−	1.45741i	0.0472483	−	0.998883i	$-0.484955\pi$
$354$		0			0
$355$	−119.996	−	69.2796i	−0.338016	−	0.195154i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			410.893i			1.14455i	0.820062	+	0.572274i	$0.193939\pi$
$359$			410.893i			1.14455i	−0.820062	+	0.572274i	$0.806061\pi$
$360$		0			0
$361$	−5.24690			−0.0145343
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36.6848	−	63.5400i	0.100506	−	0.174082i
$366$		0			0
$367$	466.176	−	269.147i	1.27023	−	0.733370i	0.295203	−	0.955435i	$-0.404613\pi$
$367$	466.176	−	269.147i	1.27023	−	0.733370i	0.975032	+	0.222064i	$0.0712795\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−232.440	+	134.199i	−0.626522	+	0.361722i
$372$		0			0
$373$	74.9606	−	129.836i	0.200967	−	0.348085i	−0.747873	−	0.663841i	$-0.768925\pi$
$373$	74.9606	−	129.836i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−364.039			−0.965621
$378$		0			0
$379$			184.361i			0.486442i	0.969971	+	0.243221i	$0.0782040\pi$
$379$			184.361i			0.486442i	−0.969971	+	0.243221i	$0.921796\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	180.514	+	104.220i	0.471315	+	0.272114i	0.716790	−	0.697289i	$-0.245611\pi$
$383$	180.514	+	104.220i	0.471315	+	0.272114i	−0.245475	+	0.969403i	$0.578944\pi$
$384$		0			0
$385$	48.3206	+	83.6937i	0.125508	+	0.217386i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−150.914	−	261.390i	−0.387953	−	0.671954i	0.604221	−	0.796816i	$-0.293484\pi$
$389$	−150.914	−	261.390i	−0.387953	−	0.671954i	−0.992174	+	0.124863i	$0.960151\pi$
$390$		0			0
$391$	89.5597	+	51.7073i	0.229053	+	0.132244i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	136.565i		−	0.345734i
$396$		0			0
$397$	246.672			0.621341			0.310670	−	0.950518i	$-0.399447\pi$
$397$	246.672			0.621341			0.310670	+	0.950518i	$0.399447\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−377.516	+	653.877i	−0.941437	+	1.63062i	−0.178703	+	0.983903i	$0.557190\pi$
$401$	−377.516	+	653.877i	−0.941437	+	1.63062i	−0.762734	+	0.646713i	$0.776143\pi$
$402$		0			0
$403$	−486.460	+	280.858i	−1.20710	+	0.696917i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−19.1902	+	11.0794i	−0.0471503	+	0.0272222i
$408$		0			0
$409$	130.730	−	226.432i	0.319634	−	0.553622i	−0.660778	−	0.750582i	$-0.729773\pi$
$409$	130.730	−	226.432i	0.319634	−	0.553622i	0.980412	+	0.196959i	$0.0631067\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−76.8394			−0.186052
$414$		0			0
$415$			262.018i			0.631369i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	0.0356217	−	0.999365i	$-0.488659\pi$
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	−0.847665	+	0.530532i	$0.821992\pi$
$420$		0			0
$421$	−102.451	−	177.450i	−0.243351	−	0.421496i	0.718316	−	0.695717i	$-0.244913\pi$
$421$	−102.451	−	177.450i	−0.243351	−	0.421496i	−0.961667	+	0.274221i	$0.911580\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−284.936	−	493.524i	−0.670438	−	1.16123i
$426$		0			0
$427$	590.968	+	341.196i	1.38400	+	0.799053i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	462.725i		−	1.07361i	−0.843707	−	0.536803i	$-0.819632\pi$
$431$		−	462.725i		−	1.07361i	0.843707	−	0.536803i	$-0.180368\pi$
$432$		0			0
$433$	190.574			0.440126			0.220063	−	0.975486i	$-0.429374\pi$
$433$	190.574			0.440126			0.220063	+	0.975486i	$0.429374\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−34.9926	+	60.6090i	−0.0800747	+	0.138693i
$438$		0			0
$439$	−379.279	+	218.977i	−0.863962	+	0.498809i	−0.865337	−	0.501190i	$-0.832896\pi$
$439$	−379.279	+	218.977i	−0.863962	+	0.498809i	0.00137479	+	0.999999i	$0.499562\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.645623	−	0.763657i	$-0.276598\pi$
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.984157	−	0.177297i	$-0.0567354\pi$
$444$		0			0
$445$	118.196	−	204.722i	0.265610	−	0.460050i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	480.789			1.07080			0.535399	−	0.844599i	$-0.320161\pi$
$449$	480.789			1.07080			0.535399	+	0.844599i	$0.320161\pi$
$450$		0			0
$451$			104.235i			0.231119i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−235.177	−	135.779i	−0.516872	−	0.298416i
$456$		0			0
$457$	109.313	+	189.336i	0.239197	+	0.414302i	0.960484	−	0.278334i	$-0.0897824\pi$
$457$	109.313	+	189.336i	0.239197	+	0.414302i	−0.721287	+	0.692636i	$0.756449\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−358.474	−	620.894i	−0.777600	−	1.34684i	−0.933322	−	0.359042i	$-0.883104\pi$
$461$	−358.474	−	620.894i	−0.777600	−	1.34684i	0.155722	−	0.987801i	$-0.450230\pi$
$462$		0			0
$463$	26.6250	+	15.3719i	0.0575053	+	0.0332007i	0.528477	−	0.848948i	$-0.322763\pi$
$463$	26.6250	+	15.3719i	0.0575053	+	0.0332007i	−0.470972	+	0.882148i	$0.656097\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	458.639i		−	0.982096i	−0.871133	−	0.491048i	$-0.836614\pi$
$467$		−	458.639i		−	0.982096i	0.871133	−	0.491048i	$-0.163386\pi$
$468$		0			0
$469$	−66.2249			−0.141204
$470$		0			0
$471$		0			0
$472$		0			0
$473$	61.2101	−	106.019i	0.129408	−	0.224142i
$474$		0			0
$475$	333.989	−	192.829i	0.703135	−	0.405955i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	570.477	−	329.365i	1.19098	−	0.687610i	0.232448	−	0.972609i	$-0.425326\pi$
$479$	570.477	−	329.365i	1.19098	−	0.687610i	0.958528	+	0.284999i	$0.0919932\pi$
$480$		0			0
$481$	31.1329	−	53.9238i	0.0647254	−	0.112108i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.86593			0.0162184
$486$		0			0
$487$			715.589i			1.46938i	0.678402	+	0.734691i	$0.262673\pi$
$487$			715.589i			1.46938i	−0.678402	+	0.734691i	$0.737327\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.953540	−	0.301266i	$-0.0974091\pi$
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.215866	+	0.976423i	$0.430742\pi$
$492$		0			0
$493$	348.834	+	604.198i	0.707574	+	1.22555i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−262.986	−	455.505i	−0.529147	−	0.916509i
$498$		0			0
$499$	458.706	+	264.834i	0.919251	+	0.530730i	0.883396	−	0.468627i	$-0.155251\pi$
$499$	458.706	+	264.834i	0.919251	+	0.530730i	0.0358546	+	0.999357i	$0.488585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			68.3537i			0.135892i	0.997689	+	0.0679460i	$0.0216446\pi$
$503$			68.3537i			0.135892i	−0.997689	+	0.0679460i	$0.978355\pi$
$504$		0			0
$505$	33.2342			0.0658103
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−400.473	+	693.640i	−0.786784	+	1.36275i	0.141143	+	0.989989i	$0.454922\pi$
$509$	−400.473	+	693.640i	−0.786784	+	1.36275i	−0.927927	+	0.372761i	$0.878411\pi$
$510$		0			0
$511$	241.198	−	139.256i	0.472012	−	0.272516i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−248.396	+	143.412i	−0.482323	+	0.278469i
$516$		0			0
$517$	78.3834	−	135.764i	0.151612	−	0.262600i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	208.227			0.399668			0.199834	−	0.979830i	$-0.435960\pi$
$521$	208.227			0.399668			0.199834	+	0.979830i	$0.435960\pi$
$522$		0			0
$523$		−	30.5350i		−	0.0583843i	−0.999574	−	0.0291921i	$-0.990707\pi$
$523$		−	30.5350i		−	0.0583843i	0.999574	−	0.0291921i	$-0.00929347\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	932.283	+	538.254i	1.76904	+	1.02135i
$528$		0			0
$529$	−257.813	−	446.546i	−0.487360	−	0.844132i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−146.448	−	253.656i	−0.274762	−	0.475903i
$534$		0			0
$535$	−97.7710	−	56.4481i	−0.182749	−	0.105510i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			109.541i			0.203230i
$540$		0			0
$541$	−526.091			−0.972442			−0.486221	−	0.873836i	$-0.661625\pi$
$541$	−526.091			−0.972442			−0.486221	+	0.873836i	$0.661625\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	28.0446	−	48.5747i	0.0514580	−	0.0891279i
$546$		0			0
$547$	−823.276	+	475.318i	−1.50507	+	0.868955i	−0.505092	+	0.863066i	$0.668541\pi$
$547$	−823.276	+	475.318i	−1.50507	+	0.868955i	−0.999983	+	0.00588962i	$0.998125\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−408.888	+	236.071i	−0.742083	+	0.428442i
$552$		0			0
$553$	259.201	−	448.949i	0.468717	−	0.811842i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	978.257			1.75630			0.878148	−	0.478390i	$-0.158779\pi$
$557$	978.257			1.75630			0.878148	+	0.478390i	$0.158779\pi$
$558$		0			0
$559$			343.997i			0.615379i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.979680	+	0.200569i	$0.0642792\pi$
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.663538	+	0.748143i	$0.269054\pi$
$564$		0			0
$565$	167.677	+	290.426i	0.296774	+	0.514028i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	481.775	+	834.459i	0.846705	+	1.46654i	0.884132	+	0.467237i	$0.154750\pi$
$569$	481.775	+	834.459i	0.846705	+	1.46654i	−0.0374271	+	0.999299i	$0.511916\pi$
$570$		0			0
$571$	243.132	+	140.372i	0.425800	+	0.245836i	0.697556	−	0.716531i	$-0.254271\pi$
$571$	243.132	+	140.372i	0.425800	+	0.245836i	−0.271756	+	0.962366i	$0.587604\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	73.6944i		−	0.128164i
$576$		0			0
$577$	−552.228			−0.957068			−0.478534	−	0.878069i	$-0.658832\pi$
$577$	−552.228			−0.957068			−0.478534	+	0.878069i	$0.658832\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−497.311	+	861.367i	−0.855956	+	1.48256i
$582$		0			0
$583$	146.034	−	84.3130i	0.250488	−	0.144619i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	−0.374628	−	0.927175i	$-0.622230\pi$
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	0.615643	+	0.788025i	$0.288896\pi$
$588$		0			0
$589$	−364.260	+	630.917i	−0.618438	+	1.07117i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	818.460			1.38020			0.690101	−	0.723713i	$-0.257566\pi$
$593$	818.460			1.38020			0.690101	+	0.723713i	$0.257566\pi$
$594$		0			0
$595$			520.433i			0.874677i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	398.849	+	230.275i	0.665857	+	0.384433i	0.794505	−	0.607257i	$-0.207730\pi$
$599$	398.849	+	230.275i	0.665857	+	0.384433i	−0.128648	+	0.991690i	$0.541064\pi$
$600$		0			0
$601$	162.324	+	281.153i	0.270090	+	0.467809i	0.968885	−	0.247513i	$-0.0796132\pi$
$601$	162.324	+	281.153i	0.270090	+	0.467809i	−0.698795	+	0.715322i	$0.746280\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	102.854	+	178.148i	0.170006	+	0.294459i
$606$		0			0
$607$	764.054	+	441.127i	1.25874	+	0.726733i	0.972829	−	0.231524i	$-0.0743712\pi$
$607$	764.054	+	441.127i	1.25874	+	0.726733i	0.285909	+	0.958257i	$0.407705\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			440.510i			0.720966i
$612$		0			0
$613$	−19.4869			−0.0317895			−0.0158947	−	0.999874i	$-0.505060\pi$
$613$	−19.4869			−0.0317895			−0.0158947	+	0.999874i	$0.505060\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	48.3314	−	83.7124i	0.0783329	−	0.135677i	−0.824198	−	0.566302i	$-0.808374\pi$
$617$	48.3314	−	83.7124i	0.0783329	−	0.135677i	0.902531	+	0.430625i	$0.141707\pi$
$618$		0			0
$619$	363.937	−	210.119i	0.587944	−	0.339449i	−0.176340	−	0.984329i	$-0.556426\pi$
$619$	363.937	−	210.119i	0.587944	−	0.339449i	0.764284	+	0.644880i	$0.223093\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	777.127	−	448.674i	1.24739	−	0.720184i
$624$		0			0
$625$	−142.447	+	246.725i	−0.227915	+	0.394760i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−119.330			−0.189714
$630$		0			0
$631$		−	483.230i		−	0.765816i	−0.923787	−	0.382908i	$-0.874923\pi$
$631$		−	483.230i		−	0.765816i	0.923787	−	0.382908i	$-0.125077\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−281.124	−	162.307i	−0.442715	−	0.255602i
$636$		0			0
$637$	−153.903	−	266.568i	−0.241606	−	0.418475i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	45.2967	+	78.4562i	0.0706657	+	0.122397i	0.899193	−	0.437552i	$-0.144154\pi$
$641$	45.2967	+	78.4562i	0.0706657	+	0.122397i	−0.828528	+	0.559948i	$0.810821\pi$
$642$		0			0
$643$	−453.773	−	261.986i	−0.705713	−	0.407444i	0.103759	−	0.994602i	$-0.466913\pi$
$643$	−453.773	−	261.986i	−0.705713	−	0.407444i	−0.809472	+	0.587159i	$0.800246\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	31.3018i		−	0.0483799i	−0.999707	−	0.0241900i	$-0.992299\pi$
$647$		−	31.3018i		−	0.0483799i	0.999707	−	0.0241900i	$-0.00770066\pi$
$648$		0			0
$649$	48.2758			0.0743848
$650$		0			0
$651$		0			0
$652$		0			0
$653$	445.115	−	770.961i	0.681646	−	1.18065i	−0.292833	−	0.956164i	$-0.594598\pi$
$653$	445.115	−	770.961i	0.681646	−	1.18065i	0.974478	−	0.224481i	$-0.0720688\pi$
$654$		0			0
$655$	−248.565	+	143.509i	−0.379489	+	0.219098i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	−0.468432	−	0.883500i	$-0.655181\pi$
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	0.530918	+	0.847423i	$0.321847\pi$
$660$		0			0
$661$	24.8421	−	43.0278i	0.0375826	−	0.0650950i	−0.846622	−	0.532194i	$-0.821368\pi$
$661$	24.8421	−	43.0278i	0.0375826	−	0.0650950i	0.884205	+	0.467099i	$0.154701\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−352.200			−0.529624
$666$		0			0
$667$			90.2207i			0.135263i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−371.287	−	214.362i	−0.553333	−	0.319467i
$672$		0			0
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	0.853556	−	0.521002i	$-0.174441\pi$
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	−0.877978	+	0.478700i	$0.841108\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	457.417	+	792.269i	0.675653	+	1.17026i	0.976278	+	0.216522i	$0.0694714\pi$
$677$	457.417	+	792.269i	0.675653	+	1.17026i	−0.300625	+	0.953742i	$0.597195\pi$
$678$		0			0
$679$	25.8587	+	14.9296i	0.0380836	+	0.0219876i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	870.646i		−	1.27474i	−0.770559	−	0.637369i	$-0.780023\pi$
$683$		−	870.646i		−	1.27474i	0.770559	−	0.637369i	$-0.219977\pi$
$684$		0			0
$685$	−219.824			−0.320910
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−236.917	+	410.352i	−0.343856	+	0.595577i
$690$		0			0
$691$	800.188	−	461.988i	1.15801	−	0.668580i	0.207187	−	0.978301i	$-0.433569\pi$
$691$	800.188	−	461.988i	1.15801	−	0.668580i	0.950827	+	0.309722i	$0.100236\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−182.275	+	105.237i	−0.262267	+	0.151420i
$696$		0			0
$697$	−280.663	+	486.123i	−0.402673	+	0.697450i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1191.44			1.69963			0.849815	−	0.527082i	$-0.176714\pi$
$701$	1191.44			1.69963			0.849815	+	0.527082i	$0.176714\pi$
$702$		0			0
$703$		−	80.7561i		−	0.114874i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	109.255	+	63.0786i	0.154534	+	0.0892201i
$708$		0			0
$709$	−655.954	−	1136.15i	−0.925182	−	1.60246i	−0.791268	−	0.611469i	$-0.790579\pi$
$709$	−655.954	−	1136.15i	−0.925182	−	1.60246i	−0.133914	−	0.990993i	$-0.542754\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	69.6056	+	120.560i	0.0976236	+	0.169089i
$714$		0			0
$715$	147.754	+	85.3059i	0.206649	+	0.119309i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	245.763i		−	0.341813i	−0.985287	−	0.170906i	$-0.945330\pi$
$719$		−	245.763i		−	0.341813i	0.985287	−	0.170906i	$-0.0546695\pi$
$720$		0			0
$721$	−1088.78			−1.51010
$722$		0			0
$723$		0			0
$724$		0			0
$725$	248.583	−	430.559i	0.342873	−	0.593874i
$726$		0			0
$727$	−1041.96	+	601.573i	−1.43323	+	0.827473i	−0.997365	−	0.0725411i	$-0.976889\pi$
$727$	−1041.96	+	601.573i	−1.43323	+	0.827473i	−0.435860	+	0.900014i	$0.643556\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	570.934	−	329.629i	0.781032	−	0.450929i
$732$		0			0
$733$	510.693	−	884.546i	0.696716	−	1.20675i	−0.272883	−	0.962047i	$-0.587977\pi$
$733$	510.693	−	884.546i	0.696716	−	1.20675i	0.969599	−	0.244700i	$-0.0786896\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	41.6070			0.0564546
$738$		0			0
$739$			259.300i			0.350879i	0.984490	+	0.175439i	$0.0561346\pi$
$739$			259.300i			0.350879i	−0.984490	+	0.175439i	$0.943865\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	100.270	+	57.8907i	0.134953	+	0.0779149i	0.565956	−	0.824435i	$-0.308507\pi$
$743$	100.270	+	57.8907i	0.134953	+	0.0779149i	−0.431004	+	0.902350i	$0.641840\pi$
$744$		0			0
$745$	−75.6076	−	130.956i	−0.101487	−	0.175780i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−214.277	−	371.139i	−0.286084	−	0.495513i
$750$		0			0
$751$	543.581	+	313.837i	0.723809	+	0.417891i	0.816153	−	0.577836i	$-0.196103\pi$
$751$	543.581	+	313.837i	0.723809	+	0.417891i	−0.0923438	+	0.995727i	$0.529436\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			232.035i			0.307331i
$756$		0			0
$757$	−49.5546			−0.0654618			−0.0327309	−	0.999464i	$-0.510420\pi$
$757$	−49.5546			−0.0654618			−0.0327309	+	0.999464i	$0.510420\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.0738	−	22.6446i	0.0171798	−	0.0297563i	−0.857308	−	0.514804i	$-0.827865\pi$
$761$	13.0738	−	22.6446i	0.0171798	−	0.0297563i	0.874488	+	0.485048i	$0.161198\pi$
$762$		0			0
$763$	184.390	−	106.458i	0.241664	−	0.139525i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−117.479	+	67.8267i	−0.153167	+	0.0884312i
$768$		0			0
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	−0.798738	−	0.601679i	$-0.794499\pi$
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	0.920438	+	0.390888i	$0.127832\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−877.069			−1.13463			−0.567315	−	0.823501i	$-0.692018\pi$
$773$	−877.069			−1.13463			−0.567315	+	0.823501i	$0.692018\pi$
$774$		0			0
$775$		−	767.131i		−	0.989847i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−328.981	−	189.937i	−0.422312	−	0.243822i
$780$		0			0
$781$	165.226	+	286.179i	0.211557	+	0.366427i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−236.704	−	409.984i	−0.301534	−	0.522272i
$786$		0			0
$787$	−577.106	−	333.192i	−0.733298	−	0.423370i	0.0863293	−	0.996267i	$-0.472486\pi$
$787$	−577.106	−	333.192i	−0.733298	−	0.423370i	−0.819628	+	0.572897i	$0.805820\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			1273.01i			1.60936i
$792$		0			0
$793$	1204.70			1.51917
$794$		0			0
$795$		0			0
$796$		0			0
$797$	90.8816	−	157.412i	0.114030	−	0.197505i	−0.803362	−	0.595491i	$-0.796957\pi$
$797$	90.8816	−	157.412i	0.114030	−	0.197505i	0.917391	+	0.397986i	$0.130291\pi$
$798$		0			0
$799$	731.118	−	422.111i	0.915041	−	0.528299i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−151.537	+	87.4900i	−0.188714	+	0.108954i
$804$		0			0
$805$	−33.6505	+	58.2844i	−0.0418019	+	0.0724030i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−114.921			−0.142053			−0.0710266	−	0.997474i	$-0.522628\pi$
$809$	−114.921			−0.142053			−0.0710266	+	0.997474i	$0.522628\pi$
$810$		0			0
$811$			1378.48i			1.69973i	0.526997	+	0.849867i	$0.323318\pi$
$811$			1378.48i			1.69973i	−0.526997	+	0.849867i	$0.676682\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−64.3449	−	37.1496i	−0.0789508	−	0.0455823i
$816$		0			0
$817$	223.075	+	386.377i	0.273041	+	0.472921i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−160.807	−	278.526i	−0.195867	−	0.339252i	0.751317	−	0.659941i	$-0.229419\pi$
$821$	−160.807	−	278.526i	−0.195867	−	0.339252i	−0.947184	+	0.320689i	$0.896085\pi$
$822$		0			0
$823$	−56.6805	−	32.7245i	−0.0688706	−	0.0397625i	0.465169	−	0.885222i	$-0.345993\pi$
$823$	−56.6805	−	32.7245i	−0.0688706	−	0.0397625i	−0.534040	+	0.845459i	$0.679327\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			778.406i			0.941240i	0.882336	+	0.470620i	$0.155970\pi$
$827$			778.406i			0.941240i	−0.882336	+	0.470620i	$0.844030\pi$
$828$		0			0
$829$	81.3426			0.0981214			0.0490607	−	0.998796i	$-0.484377\pi$
$829$	81.3426			0.0981214			0.0490607	+	0.998796i	$0.484377\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−294.950	+	510.869i	−0.354082	+	0.613288i
$834$		0			0
$835$	−289.686	+	167.250i	−0.346929	+	0.200299i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	553.733	−	319.698i	0.659992	−	0.381046i	−0.132282	−	0.991212i	$-0.542231\pi$
$839$	553.733	−	319.698i	0.659992	−	0.381046i	0.792274	+	0.610166i	$0.208897\pi$
$840$		0			0
$841$	116.171	−	201.214i	0.138135	−	0.239256i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−107.302			−0.126984
$846$		0			0
$847$			780.866i			0.921920i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.3641	−	7.71575i	−0.0157040	−	0.00906668i
$852$		0			0
$853$	38.8069	+	67.2155i	0.0454946	+	0.0787989i	0.887876	−	0.460083i	$-0.152180\pi$
$853$	38.8069	+	67.2155i	0.0454946	+	0.0787989i	−0.842381	+	0.538882i	$0.818847\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−436.010	−	755.192i	−0.508763	−	0.881204i	−0.999948	−	0.0101489i	$-0.996769\pi$
$857$	−436.010	−	755.192i	−0.508763	−	0.881204i	0.491185	−	0.871055i	$-0.336564\pi$
$858$		0			0
$859$	136.909	+	79.0444i	0.159382	+	0.0920191i	0.577570	−	0.816342i	$-0.304001\pi$
$859$	136.909	+	79.0444i	0.159382	+	0.0920191i	−0.418188	+	0.908361i	$0.637335\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	685.963i		−	0.794859i	−0.917633	−	0.397429i	$-0.869902\pi$
$863$		−	685.963i		−	0.794859i	0.917633	−	0.397429i	$-0.130098\pi$
$864$		0			0
$865$	−261.581			−0.302406
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−162.848	+	282.060i	−0.187396	+	0.324580i
$870$		0			0
$871$	−101.251	+	58.4573i	−0.116247	+	0.0671151i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	719.629	−	415.478i	0.822433	−	0.474832i
$876$		0			0
$877$	−458.905	+	794.847i	−0.523267	+	0.906325i	0.476366	+	0.879247i	$0.341954\pi$
$877$	−458.905	+	794.847i	−0.523267	+	0.906325i	−0.999633	+	0.0270780i	$0.991380\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	657.430			0.746231			0.373116	−	0.927785i	$-0.378289\pi$
$881$	657.430			0.746231			0.373116	+	0.927785i	$0.378289\pi$
$882$		0			0
$883$		−	618.879i		−	0.700882i	−0.936585	−	0.350441i	$-0.886032\pi$
$883$		−	618.879i		−	0.700882i	0.936585	−	0.350441i	$-0.113968\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−110.844	−	63.9959i	−0.124965	−	0.0721487i	0.436214	−	0.899843i	$-0.356319\pi$
$887$	−110.844	−	63.9959i	−0.124965	−	0.0721487i	−0.561180	+	0.827694i	$0.689652\pi$
$888$		0			0
$889$	−616.119	−	1067.15i	−0.693047	−	1.20039i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	285.661	+	494.780i	0.319890	+	0.554065i
$894$		0			0
$895$	416.056	+	240.210i	0.464867	+	0.268391i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			939.164i			1.04468i
$900$		0			0
$901$	908.086			1.00786
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−202.656	+	351.011i	−0.223930	+	0.387858i
$906$		0			0
$907$	−13.7946	+	7.96431i	−0.0152090	+	0.00878094i	−0.507585	−	0.861602i	$-0.669462\pi$
$907$	−13.7946	+	7.96431i	−0.0152090	+	0.00878094i	0.492376	+	0.870382i	$0.336128\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	43.9255	−	25.3604i	0.0482168	−	0.0278380i	−0.475698	−	0.879609i	$-0.657804\pi$
$911$	43.9255	−	25.3604i	0.0482168	−	0.0278380i	0.523915	+	0.851771i	$0.324471\pi$
$912$		0			0
$913$	312.445	−	541.170i	0.342218	−	0.592738i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1089.52			−1.18814
$918$		0			0
$919$			1065.04i			1.15892i	0.815002	+	0.579458i	$0.196736\pi$
$919$			1065.04i			1.15892i	−0.815002	+	0.579458i	$0.803264\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−804.156	−	464.279i	−0.871241	−	0.503011i
$924$		0			0
$925$	42.5181	+	73.6434i	0.0459655	+	0.0796145i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−171.699	−	297.392i	−0.184822	−	0.320121i	0.758695	−	0.651446i	$-0.225837\pi$
$929$	−171.699	−	297.392i	−0.184822	−	0.320121i	−0.943516	+	0.331326i	$0.892504\pi$
$930$		0			0
$931$	−345.727	−	199.606i	−0.371351	−	0.214399i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	326.971i		−	0.349702i
$936$		0			0
$937$	−267.742			−0.285744			−0.142872	−	0.989741i	$-0.545634\pi$
$937$	−267.742			−0.285744			−0.142872	+	0.989741i	$0.545634\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−610.126	+	1056.77i	−0.648380	+	1.12303i	0.335130	+	0.942172i	$0.391220\pi$
$941$	−610.126	+	1056.77i	−0.648380	+	1.12303i	−0.983510	+	0.180855i	$0.942113\pi$
$942$		0			0
$943$	−62.8642	+	36.2946i	−0.0666640	+	0.0384885i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.999570	−	0.0293240i	$-0.990665\pi$
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.474390	+	0.880315i	$0.657331\pi$
$948$		0			0
$949$	245.845	−	425.815i	0.259056	−	0.448699i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−242.459			−0.254416			−0.127208	−	0.991876i	$-0.540602\pi$
$953$	−242.459			−0.254416			−0.127208	+	0.991876i	$0.540602\pi$
$954$		0			0
$955$		−	548.603i		−	0.574453i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−722.656	−	417.226i	−0.753552	−	0.435063i
$960$		0			0
$961$	244.068	+	422.739i	0.253973	+	0.439895i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−275.421	−	477.043i	−0.285411	−	0.494346i
$966$		0			0
$967$	−1543.81	−	891.320i	−1.59650	−	0.921737i	−0.992155	−	0.125011i	$-0.960103\pi$
$967$	−1543.81	−	891.320i	−1.59650	−	0.921737i	−0.604340	−	0.796726i	$-0.706563\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	645.136i		−	0.664404i	−0.943208	−	0.332202i	$-0.892208\pi$
$971$		−	645.136i		−	0.664404i	0.943208	−	0.332202i	$-0.107792\pi$
$972$		0			0
$973$	−798.958			−0.821129
$974$		0			0
$975$		0			0
$976$		0			0
$977$	689.779	−	1194.73i	0.706017	−	1.22286i	−0.260306	−	0.965526i	$-0.583824\pi$
$977$	689.779	−	1194.73i	0.706017	−	1.22286i	0.966323	−	0.257331i	$-0.0828431\pi$
$978$		0			0
$979$	−488.244	+	281.888i	−0.498717	+	0.287935i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−639.804	+	369.391i	−0.650869	+	0.375779i	−0.788789	−	0.614664i	$-0.789292\pi$
$983$	−639.804	+	369.391i	−0.650869	+	0.375779i	0.137920	+	0.990443i	$0.455958\pi$
$984$		0			0
$985$	281.478	−	487.534i	0.285764	−	0.494959i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	85.2536			0.0862018
$990$		0			0
$991$		−	1533.69i		−	1.54762i	−0.633416	−	0.773811i	$-0.718348\pi$
$991$		−	1533.69i		−	1.54762i	0.633416	−	0.773811i	$-0.281652\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−589.430	−	340.307i	−0.592391	−	0.342017i
$996$		0			0
$997$	871.274	+	1509.09i	0.873896	+	1.51363i	0.857934	+	0.513760i	$0.171748\pi$
$997$	871.274	+	1509.09i	0.873896	+	1.51363i	0.0159621	+	0.999873i	$0.494919\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.g.1279.4		16
3.2	odd	2		576.3.o.g.319.4		16
4.3	odd	2	inner	1728.3.o.g.1279.3		16
8.3	odd	2		108.3.f.c.91.1		16
8.5	even	2		108.3.f.c.91.7		16
9.2	odd	6		576.3.o.g.511.5		16
9.7	even	3	inner	1728.3.o.g.127.3		16
12.11	even	2		576.3.o.g.319.5		16
24.5	odd	2		36.3.f.c.31.2	yes	16
24.11	even	2		36.3.f.c.31.8	yes	16
36.7	odd	6	inner	1728.3.o.g.127.4		16
36.11	even	6		576.3.o.g.511.4		16
72.5	odd	6		324.3.d.i.163.3		8
72.11	even	6		36.3.f.c.7.2	✓	16
72.13	even	6		324.3.d.g.163.6		8
72.29	odd	6		36.3.f.c.7.8	yes	16
72.43	odd	6		108.3.f.c.19.7		16
72.59	even	6		324.3.d.i.163.4		8
72.61	even	6		108.3.f.c.19.1		16
72.67	odd	6		324.3.d.g.163.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	72.11	even	6
36.3.f.c.7.8	yes	16	72.29	odd	6
36.3.f.c.31.2	yes	16	24.5	odd	2
36.3.f.c.31.8	yes	16	24.11	even	2
108.3.f.c.19.1		16	72.61	even	6
108.3.f.c.19.7		16	72.43	odd	6
108.3.f.c.91.1		16	8.3	odd	2
108.3.f.c.91.7		16	8.5	even	2
324.3.d.g.163.5		8	72.67	odd	6
324.3.d.g.163.6		8	72.13	even	6
324.3.d.i.163.3		8	72.5	odd	6
324.3.d.i.163.4		8	72.59	even	6
576.3.o.g.319.4		16	3.2	odd	2
576.3.o.g.319.5		16	12.11	even	2
576.3.o.g.511.4		16	36.11	even	6
576.3.o.g.511.5		16	9.2	odd	6
1728.3.o.g.127.3		16	9.7	even	3	inner
1728.3.o.g.127.4		16	36.7	odd	6	inner
1728.3.o.g.1279.3		16	4.3	odd	2	inner
1728.3.o.g.1279.4		16	1.1	even	1	trivial

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10093 - 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +O(q^{10})\)	\(q+(1.10093 - 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +(-4.54769 + 2.62561i) q^{11} +(7.37788 - 12.7789i) q^{13} -28.2789 q^{17} -19.1376i q^{19} +(-3.16702 - 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-12.3355 - 21.3657i) q^{29} +(-32.9674 - 19.0338i) q^{31} -18.4036i q^{35} +4.21977 q^{37} +(9.92483 - 17.1903i) q^{41} +(-20.1894 + 11.6564i) q^{43} +(-25.8538 + 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} -32.1118 q^{53} +11.5624i q^{55} +(-7.96159 - 4.59663i) q^{59} +(40.8215 + 70.7049i) q^{61} +(-16.2450 - 28.1372i) q^{65} +(-6.86179 - 3.96166i) q^{67} -62.9286i q^{71} +33.3218 q^{73} +(-21.9454 + 38.0106i) q^{77} +(53.7133 - 31.0114i) q^{79} +(-103.056 + 59.4995i) q^{83} +(-31.1329 + 53.9238i) q^{85} +107.361 q^{89} -123.332i q^{91} +(-36.4927 - 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

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