LMFDB - Embedded newform 576.6.k.a.433.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,6,Mod(145,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("576.145");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	576.k (of order $4$, 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:	$92.3810802123$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 3867 x^{16} + 20528 x^{15} + 5993890 x^{14} - 12125584 x^{13} + \cdots + 93\!\cdots\!16 $ x^18 - 8x^17 - 3867x^16 + 20528x^15 + 5993890x^14 - 12125584x^13 - 4820441926x^12 - 8265606272x^11 + 2160047956949x^10 + 11904535942584x^9 - 516092236107743x^8 - 4797958060187376x^7 + 51973134198079192x^6 + 743014063051675680x^5 - 75719701558176624x^4 - 27807708117417695360x^3 - 50069849523887397376x^2 + 334053680451369438208*x + 937540826009984214016
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{72}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.4
Root			$4.86757 + 1.00000i$ of defining polynomial
Character	$\chi$	$=$	576.433
Dual form			576.6.k.a.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.73514 - 8.73514i) q^{5} -28.0117i q^{7} +O(q^{10})$	$q+(-8.73514 - 8.73514i) q^{5} -28.0117i q^{7} +(191.858 + 191.858i) q^{11} +(-562.527 + 562.527i) q^{13} +663.401 q^{17} +(-1793.28 + 1793.28i) q^{19} -2878.23i q^{23} -2972.39i q^{25} +(3909.86 - 3909.86i) q^{29} +4451.90 q^{31} +(-244.686 + 244.686i) q^{35} +(6043.41 + 6043.41i) q^{37} +12387.3i q^{41} +(-10658.7 - 10658.7i) q^{43} -23383.1 q^{47} +16022.3 q^{49} +(-656.507 - 656.507i) q^{53} -3351.82i q^{55} +(-5988.17 - 5988.17i) q^{59} +(6863.09 - 6863.09i) q^{61} +9827.51 q^{65} +(-13054.5 + 13054.5i) q^{67} -27879.6i q^{71} +20553.5i q^{73} +(5374.28 - 5374.28i) q^{77} -103184. q^{79} +(-8215.97 + 8215.97i) q^{83} +(-5794.90 - 5794.90i) q^{85} -134430. i q^{89} +(15757.4 + 15757.4i) q^{91} +31329.0 q^{95} -53614.2 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{5}+O(q^{10}) $ 18 * q + 2 * q^5	$ 18 q + 2 q^{5} - 606 q^{11} - 2 q^{13} + 4 q^{17} + 2362 q^{19} - 4070 q^{29} + 11536 q^{31} + 8636 q^{35} - 10650 q^{37} + 15382 q^{43} + 44176 q^{47} - 14410 q^{49} - 24726 q^{53} - 29734 q^{59} - 48082 q^{61} - 27684 q^{65} + 75210 q^{67} - 41060 q^{77} + 52864 q^{79} + 227838 q^{83} - 138652 q^{85} + 231164 q^{91} - 250380 q^{95} - 4 q^{97}+O(q^{100}) $ 18 * q + 2 * q^5 - 606 * q^11 - 2 * q^13 + 4 * q^17 + 2362 * q^19 - 4070 * q^29 + 11536 * q^31 + 8636 * q^35 - 10650 * q^37 + 15382 * q^43 + 44176 * q^47 - 14410 * q^49 - 24726 * q^53 - 29734 * q^59 - 48082 * q^61 - 27684 * q^65 + 75210 * q^67 - 41060 * q^77 + 52864 * q^79 + 227838 * q^83 - 138652 * q^85 + 231164 * q^91 - 250380 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$5$	−8.73514	−	8.73514i	−0.156259	−	0.156259i	0.624648	−	0.780907i	$-0.285243\pi$
$5$	−8.73514	−	8.73514i	−0.156259	−	0.156259i	−0.780907	+	0.624648i	$0.785243\pi$
$6$		0			0
$7$		−	28.0117i		−	0.216070i	−0.994147	−	0.108035i	$-0.965544\pi$
$7$		−	28.0117i		−	0.216070i	0.994147	−	0.108035i	$-0.0344559\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	191.858	+	191.858i	0.478078	+	0.478078i	0.904517	−	0.426439i	$-0.140232\pi$
$11$	191.858	+	191.858i	0.478078	+	0.478078i	−0.426439	+	0.904517i	$0.640232\pi$
$12$		0			0
$13$	−562.527	+	562.527i	−0.923177	+	0.923177i	−0.997253	−	0.0740753i	$-0.976399\pi$
$13$	−562.527	+	562.527i	−0.923177	+	0.923177i	0.0740753	+	0.997253i	$0.476399\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	663.401			0.556741			0.278371	−	0.960474i	$-0.410206\pi$
$17$	663.401			0.556741			0.278371	+	0.960474i	$0.410206\pi$
$18$		0			0
$19$	−1793.28	+	1793.28i	−1.13963	+	1.13963i	−0.151111	+	0.988517i	$0.548285\pi$
$19$	−1793.28	+	1793.28i	−1.13963	+	1.13963i	−0.988517	+	0.151111i	$0.951715\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	2878.23i		−	1.13450i	−0.823545	−	0.567252i	$-0.808007\pi$
$23$		−	2878.23i		−	1.13450i	0.823545	−	0.567252i	$-0.191993\pi$
$24$		0			0
$25$		−	2972.39i		−	0.951166i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3909.86	−	3909.86i	0.863309	−	0.863309i	−0.128412	−	0.991721i	$-0.540988\pi$
$29$	3909.86	−	3909.86i	0.863309	−	0.863309i	0.991721	+	0.128412i	$0.0409880\pi$
$30$		0			0
$31$	4451.90			0.832034			0.416017	−	0.909357i	$-0.363426\pi$
$31$	4451.90			0.832034			0.416017	+	0.909357i	$0.363426\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−244.686	+	244.686i	−0.0337629	+	0.0337629i
$36$		0			0
$37$	6043.41	+	6043.41i	0.725734	+	0.725734i	0.969767	−	0.244033i	$-0.0784705\pi$
$37$	6043.41	+	6043.41i	0.725734	+	0.725734i	−0.244033	+	0.969767i	$0.578471\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			12387.3i			1.15085i	0.817855	+	0.575425i	$0.195163\pi$
$41$			12387.3i			1.15085i	−0.817855	+	0.575425i	$0.804837\pi$
$42$		0			0
$43$	−10658.7	−	10658.7i	−0.879088	−	0.879088i	0.114352	−	0.993440i	$-0.463521\pi$
$43$	−10658.7	−	10658.7i	−0.879088	−	0.879088i	−0.993440	+	0.114352i	$0.963521\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−23383.1			−1.54404			−0.772019	−	0.635599i	$-0.780753\pi$
$47$	−23383.1			−1.54404			−0.772019	+	0.635599i	$0.780753\pi$
$48$		0			0
$49$	16022.3			0.953314
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−656.507	−	656.507i	−0.0321033	−	0.0321033i	0.690873	−	0.722976i	$-0.257226\pi$
$53$	−656.507	−	656.507i	−0.0321033	−	0.0321033i	−0.722976	+	0.690873i	$0.757226\pi$
$54$		0			0
$55$		−	3351.82i		−	0.149408i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5988.17	−	5988.17i	−0.223957	−	0.223957i	0.586206	−	0.810162i	$-0.300621\pi$
$59$	−5988.17	−	5988.17i	−0.223957	−	0.223957i	−0.810162	+	0.586206i	$0.800621\pi$
$60$		0			0
$61$	6863.09	−	6863.09i	0.236154	−	0.236154i	−0.579101	−	0.815255i	$-0.696596\pi$
$61$	6863.09	−	6863.09i	0.236154	−	0.236154i	0.815255	+	0.579101i	$0.196596\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9827.51			0.288509
$66$		0			0
$67$	−13054.5	+	13054.5i	−0.355281	+	0.355281i	−0.862070	−	0.506789i	$-0.830832\pi$
$67$	−13054.5	+	13054.5i	−0.355281	+	0.355281i	0.506789	+	0.862070i	$0.330832\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	27879.6i		−	0.656357i	−0.944616	−	0.328179i	$-0.893565\pi$
$71$		−	27879.6i		−	0.656357i	0.944616	−	0.328179i	$-0.106435\pi$
$72$		0			0
$73$			20553.5i			0.451419i	0.974195	+	0.225709i	$0.0724700\pi$
$73$			20553.5i			0.451419i	−0.974195	+	0.225709i	$0.927530\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5374.28	−	5374.28i	0.103298	−	0.103298i
$78$		0			0
$79$	−103184.			−1.86014			−0.930071	−	0.367380i	$-0.880255\pi$
$79$	−103184.			−1.86014			−0.930071	+	0.367380i	$0.880255\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8215.97	+	8215.97i	−0.130907	+	0.130907i	−0.769524	−	0.638617i	$-0.779507\pi$
$83$	−8215.97	+	8215.97i	−0.130907	+	0.130907i	0.638617	+	0.769524i	$0.279507\pi$
$84$		0			0
$85$	−5794.90	−	5794.90i	−0.0869958	−	0.0869958i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	134430.i		−	1.79896i	−0.436961	−	0.899480i	$-0.643945\pi$
$89$		−	134430.i		−	1.79896i	0.436961	−	0.899480i	$-0.356055\pi$
$90$		0			0
$91$	15757.4	+	15757.4i	0.199471	+	0.199471i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	31329.0			0.356154
$96$		0			0
$97$	−53614.2			−0.578563			−0.289282	−	0.957244i	$-0.593416\pi$
$97$	−53614.2			−0.578563			−0.289282	+	0.957244i	$0.593416\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6782.61	−	6782.61i	−0.0661596	−	0.0661596i	0.673253	−	0.739412i	$-0.264897\pi$
$101$	−6782.61	−	6782.61i	−0.0661596	−	0.0661596i	−0.739412	+	0.673253i	$0.764897\pi$
$102$		0			0
$103$		−	23843.1i		−	0.221447i	−0.993851	−	0.110724i	$-0.964683\pi$
$103$		−	23843.1i		−	0.221447i	0.993851	−	0.110724i	$-0.0353169\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−69846.1	−	69846.1i	−0.589770	−	0.589770i	0.347799	−	0.937569i	$-0.386929\pi$
$107$	−69846.1	−	69846.1i	−0.589770	−	0.589770i	−0.937569	+	0.347799i	$0.886929\pi$
$108$		0			0
$109$	140543.	−	140543.i	1.13304	−	1.13304i	0.143365	−	0.989670i	$-0.454208\pi$
$109$	140543.	−	140543.i	1.13304	−	1.13304i	0.989670	−	0.143365i	$-0.0457924\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−95402.3			−0.702850			−0.351425	−	0.936216i	$-0.614303\pi$
$113$	−95402.3			−0.702850			−0.351425	+	0.936216i	$0.614303\pi$
$114$		0			0
$115$	−25141.7	+	25141.7i	−0.177276	+	0.177276i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	18583.0i		−	0.120295i
$120$		0			0
$121$		−	87431.8i		−	0.542883i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−53261.6	+	53261.6i	−0.304887	+	0.304887i
$126$		0			0
$127$	115026.			0.632829			0.316415	−	0.948621i	$-0.397521\pi$
$127$	115026.			0.632829			0.316415	+	0.948621i	$0.397521\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−117580.	+	117580.i	−0.598625	+	0.598625i	−0.939946	−	0.341322i	$-0.889125\pi$
$131$	−117580.	+	117580.i	−0.598625	+	0.598625i	0.341322	+	0.939946i	$0.389125\pi$
$132$		0			0
$133$	50232.8	+	50232.8i	0.246240	+	0.246240i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			25473.5i			0.115954i	0.998318	+	0.0579772i	$0.0184651\pi$
$137$			25473.5i			0.115954i	−0.998318	+	0.0579772i	$0.981535\pi$
$138$		0			0
$139$	−191375.	−	191375.i	−0.840132	−	0.840132i	0.148744	−	0.988876i	$-0.452477\pi$
$139$	−191375.	−	191375.i	−0.840132	−	0.840132i	−0.988876	+	0.148744i	$0.952477\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−215851.			−0.882702
$144$		0			0
$145$	−68306.3			−0.269799
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−238914.	−	238914.i	−0.881610	−	0.881610i	0.112088	−	0.993698i	$-0.464246\pi$
$149$	−238914.	−	238914.i	−0.881610	−	0.881610i	−0.993698	+	0.112088i	$0.964246\pi$
$150$		0			0
$151$		−	259983.i		−	0.927902i	−0.885861	−	0.463951i	$-0.846431\pi$
$151$		−	259983.i		−	0.927902i	0.885861	−	0.463951i	$-0.153569\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−38887.9	−	38887.9i	−0.130013	−	0.130013i
$156$		0			0
$157$	−208630.	+	208630.i	−0.675505	+	0.675505i	−0.958980	−	0.283475i	$-0.908513\pi$
$157$	−208630.	+	208630.i	−0.675505	+	0.675505i	0.283475	+	0.958980i	$0.408513\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−80624.2			−0.245132
$162$		0			0
$163$	−72021.3	+	72021.3i	−0.212320	+	0.212320i	−0.805253	−	0.592932i	$-0.797970\pi$
$163$	−72021.3	+	72021.3i	−0.212320	+	0.212320i	0.592932	+	0.805253i	$0.297970\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	633922.i		−	1.75891i	−0.475979	−	0.879457i	$-0.657906\pi$
$167$		−	633922.i		−	1.75891i	0.475979	−	0.879457i	$-0.342094\pi$
$168$		0			0
$169$		−	261581.i		−	0.704513i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	317844.	−	317844.i	0.807418	−	0.807418i	−0.176824	−	0.984242i	$-0.556582\pi$
$173$	317844.	−	317844.i	0.807418	−	0.807418i	0.984242	+	0.176824i	$0.0565824\pi$
$174$		0			0
$175$	−83262.0			−0.205519
$176$		0			0
$177$		0			0
$178$		0			0
$179$	437684.	−	437684.i	1.02100	−	1.02100i	0.0212302	−	0.999775i	$-0.493242\pi$
$179$	437684.	−	437684.i	1.02100	−	1.02100i	0.999775	−	0.0212302i	$-0.00675830\pi$
$180$		0			0
$181$	−83922.0	−	83922.0i	−0.190405	−	0.190405i	0.605466	−	0.795871i	$-0.292987\pi$
$181$	−83922.0	−	83922.0i	−0.190405	−	0.190405i	−0.795871	+	0.605466i	$0.792987\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	105580.i		−	0.226805i
$186$		0			0
$187$	127279.	+	127279.i	0.266166	+	0.266166i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−477461.			−0.947010			−0.473505	−	0.880791i	$-0.657011\pi$
$191$	−477461.			−0.947010			−0.473505	+	0.880791i	$0.657011\pi$
$192$		0			0
$193$	−581329.			−1.12338			−0.561692	−	0.827346i	$-0.689849\pi$
$193$	−581329.			−1.12338			−0.561692	+	0.827346i	$0.689849\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	29515.9	+	29515.9i	0.0541864	+	0.0541864i	0.733681	−	0.679494i	$-0.237801\pi$
$197$	29515.9	+	29515.9i	0.0541864	+	0.0541864i	−0.679494	+	0.733681i	$0.737801\pi$
$198$		0			0
$199$		−	68026.0i		−	0.121771i	−0.998145	−	0.0608853i	$-0.980608\pi$
$199$		−	68026.0i		−	0.121771i	0.998145	−	0.0608853i	$-0.0193924\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−109522.	−	109522.i	−0.186535	−	0.186535i
$204$		0			0
$205$	108205.	−	108205.i	0.179830	−	0.179830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−688109.			−1.08966
$210$		0			0
$211$	−176742.	+	176742.i	−0.273296	+	0.273296i	−0.830426	−	0.557129i	$-0.811903\pi$
$211$	−176742.	+	176742.i	−0.273296	+	0.273296i	0.557129	+	0.830426i	$0.311903\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			186210.i			0.274731i
$216$		0			0
$217$		−	124705.i		−	0.179778i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−373181.	+	373181.i	−0.513971	+	0.513971i
$222$		0			0
$223$	777882.			1.04749			0.523747	−	0.851874i	$-0.324534\pi$
$223$	777882.			1.04749			0.523747	+	0.851874i	$0.324534\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−906710.	+	906710.i	−1.16789	+	1.16789i	−0.185192	+	0.982702i	$0.559291\pi$
$227$	−906710.	+	906710.i	−1.16789	+	1.16789i	−0.982702	+	0.185192i	$0.940709\pi$
$228$		0			0
$229$	156955.	+	156955.i	0.197782	+	0.197782i	0.799048	−	0.601267i	$-0.205337\pi$
$229$	156955.	+	156955.i	0.197782	+	0.197782i	−0.601267	+	0.799048i	$0.705337\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	1.03950e6i		−	1.25440i	−0.778859	−	0.627199i	$-0.784201\pi$
$233$		−	1.03950e6i		−	1.25440i	0.778859	−	0.627199i	$-0.215799\pi$
$234$		0			0
$235$	204255.	+	204255.i	0.241270	+	0.241270i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.07523e6			1.21760			0.608802	−	0.793322i	$-0.291650\pi$
$239$	1.07523e6			1.21760			0.608802	+	0.793322i	$0.291650\pi$
$240$		0			0
$241$	−1.29926e6			−1.44096			−0.720482	−	0.693474i	$-0.756079\pi$
$241$	−1.29926e6			−1.44096			−0.720482	+	0.693474i	$0.756079\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−139957.	−	139957.i	−0.148964	−	0.148964i
$246$		0			0
$247$		−	2.01753e6i		−	2.10416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−843150.	−	843150.i	−0.844735	−	0.844735i	0.144735	−	0.989470i	$-0.453767\pi$
$251$	−843150.	−	843150.i	−0.844735	−	0.844735i	−0.989470	+	0.144735i	$0.953767\pi$
$252$		0			0
$253$	552212.	−	552212.i	0.542381	−	0.542381i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−819237.			−0.773707			−0.386854	−	0.922141i	$-0.626438\pi$
$257$	−819237.			−0.773707			−0.386854	+	0.922141i	$0.626438\pi$
$258$		0			0
$259$	169286.	−	169286.i	0.156810	−	0.156810i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	1.59886e6i		−	1.42535i	−0.701496	−	0.712673i	$-0.747484\pi$
$263$		−	1.59886e6i		−	1.42535i	0.701496	−	0.712673i	$-0.252516\pi$
$264$		0			0
$265$			11469.4i			0.0100329i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−224438.	+	224438.i	−0.189110	+	0.189110i	−0.795311	−	0.606201i	$-0.792693\pi$
$269$	−224438.	+	224438.i	−0.189110	+	0.189110i	0.606201	+	0.795311i	$0.292693\pi$
$270$		0			0
$271$	−1.16216e6			−0.961266			−0.480633	−	0.876922i	$-0.659593\pi$
$271$	−1.16216e6			−0.961266			−0.480633	+	0.876922i	$0.659593\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	570278.	−	570278.i	0.454732	−	0.454732i
$276$		0			0
$277$	25062.3	+	25062.3i	0.0196256	+	0.0196256i	0.716851	−	0.697226i	$-0.245583\pi$
$277$	25062.3	+	25062.3i	0.0196256	+	0.0196256i	−0.697226	+	0.716851i	$0.745583\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	107864.i		−	0.0814910i	−0.999170	−	0.0407455i	$-0.987027\pi$
$281$		−	107864.i		−	0.0814910i	0.999170	−	0.0407455i	$-0.0129733\pi$
$282$		0			0
$283$	1.82013e6	+	1.82013e6i	1.35094	+	1.35094i	0.884609	+	0.466334i	$0.154425\pi$
$283$	1.82013e6	+	1.82013e6i	1.35094	+	1.35094i	0.466334	+	0.884609i	$0.345575\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	346991.			0.248664
$288$		0			0
$289$	−979757.			−0.690039
$290$		0			0
$291$		0			0
$292$		0			0
$293$	357804.	+	357804.i	0.243487	+	0.243487i	0.818291	−	0.574804i	$-0.194922\pi$
$293$	357804.	+	357804.i	0.243487	+	0.243487i	−0.574804	+	0.818291i	$0.694922\pi$
$294$		0			0
$295$			104615.i			0.0699904i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.61908e6	+	1.61908e6i	1.04735	+	1.04735i
$300$		0			0
$301$	−298568.	+	298568.i	−0.189945	+	0.189945i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−119900.			−0.0738023
$306$		0			0
$307$	−2.19534e6	+	2.19534e6i	−1.32940	+	1.32940i	−0.423512	+	0.905890i	$0.639203\pi$
$307$	−2.19534e6	+	2.19534e6i	−1.32940	+	1.32940i	−0.905890	+	0.423512i	$0.860797\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			1.47806e6i			0.866547i	0.901263	+	0.433273i	$0.142642\pi$
$311$			1.47806e6i			0.866547i	−0.901263	+	0.433273i	$0.857358\pi$
$312$		0			0
$313$			617807.i			0.356445i	0.983990	+	0.178222i	$0.0570346\pi$
$313$			617807.i			0.356445i	−0.983990	+	0.178222i	$0.942965\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.02184e6	−	2.02184e6i	1.13005	−	1.13005i	0.139882	−	0.990168i	$-0.455328\pi$
$317$	2.02184e6	−	2.02184e6i	1.13005	−	1.13005i	0.990168	−	0.139882i	$-0.0446723\pi$
$318$		0			0
$319$	1.50028e6			0.825458
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.18966e6	+	1.18966e6i	−0.634478	+	0.634478i
$324$		0			0
$325$	1.67205e6	+	1.67205e6i	0.878095	+	0.878095i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			655002.i			0.333621i
$330$		0			0
$331$	−1.50720e6	−	1.50720e6i	−0.756136	−	0.756136i	0.219481	−	0.975617i	$-0.429564\pi$
$331$	−1.50720e6	−	1.50720e6i	−0.756136	−	0.756136i	−0.975617	+	0.219481i	$0.929564\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	228065.			0.111032
$336$		0			0
$337$	96831.6			0.0464454			0.0232227	−	0.999730i	$-0.492607\pi$
$337$	96831.6			0.0464454			0.0232227	+	0.999730i	$0.492607\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	854133.	+	854133.i	0.397777	+	0.397777i
$342$		0			0
$343$		−	919607.i		−	0.422053i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	838484.	+	838484.i	0.373827	+	0.373827i	0.868869	−	0.495042i	$-0.164847\pi$
$347$	838484.	+	838484.i	0.373827	+	0.373827i	−0.495042	+	0.868869i	$0.664847\pi$
$348$		0			0
$349$	1.50056e6	−	1.50056e6i	0.659463	−	0.659463i	−0.295790	−	0.955253i	$-0.595583\pi$
$349$	1.50056e6	−	1.50056e6i	0.659463	−	0.659463i	0.955253	+	0.295790i	$0.0955830\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.14207e6			−0.487817			−0.243908	−	0.969798i	$-0.578430\pi$
$353$	−1.14207e6			−0.487817			−0.243908	+	0.969798i	$0.578430\pi$
$354$		0			0
$355$	−243532.	+	243532.i	−0.102562	+	0.102562i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	2.07162e6i		−	0.848349i	−0.905580	−	0.424174i	$-0.860564\pi$
$359$		−	2.07162e6i		−	0.848349i	0.905580	−	0.424174i	$-0.139436\pi$
$360$		0			0
$361$		−	3.95557e6i		−	1.59750i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	179538.	−	179538.i	0.0705382	−	0.0705382i
$366$		0			0
$367$	119073.			0.0461473			0.0230737	−	0.999734i	$-0.492655\pi$
$367$	119073.			0.0461473			0.0230737	+	0.999734i	$0.492655\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18389.9	+	18389.9i	−0.00693657	+	0.00693657i
$372$		0			0
$373$	3.03626e6	+	3.03626e6i	1.12997	+	1.12997i	0.990181	+	0.139789i	$0.0446423\pi$
$373$	3.03626e6	+	3.03626e6i	1.12997	+	1.12997i	0.139789	+	0.990181i	$0.455358\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			4.39880e6i			1.59397i
$378$		0			0
$379$	738378.	+	738378.i	0.264047	+	0.264047i	0.826696	−	0.562649i	$-0.190218\pi$
$379$	738378.	+	738378.i	0.264047	+	0.264047i	−0.562649	+	0.826696i	$0.690218\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.53961e6			−1.58133			−0.790664	−	0.612251i	$-0.790264\pi$
$383$	−4.53961e6			−1.58133			−0.790664	+	0.612251i	$0.790264\pi$
$384$		0			0
$385$	−93890.2			−0.0322826
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.17974e6	+	2.17974e6i	0.730349	+	0.730349i	0.970689	−	0.240340i	$-0.0772589\pi$
$389$	2.17974e6	+	2.17974e6i	0.730349	+	0.730349i	−0.240340	+	0.970689i	$0.577259\pi$
$390$		0			0
$391$		−	1.90942e6i		−	0.631625i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	901329.	+	901329.i	0.290664	+	0.290664i
$396$		0			0
$397$	1.54162e6	−	1.54162e6i	0.490908	−	0.490908i	−0.417684	−	0.908592i	$-0.637158\pi$
$397$	1.54162e6	−	1.54162e6i	0.490908	−	0.490908i	0.908592	+	0.417684i	$0.137158\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.06724e6			0.641992			0.320996	−	0.947081i	$-0.395982\pi$
$401$	2.06724e6			0.641992			0.320996	+	0.947081i	$0.395982\pi$
$402$		0			0
$403$	−2.50431e6	+	2.50431e6i	−0.768115	+	0.768115i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			2.31895e6i			0.693915i
$408$		0			0
$409$			1.75464e6i			0.518657i	0.965789	+	0.259329i	$0.0835012\pi$
$409$			1.75464e6i			0.518657i	−0.965789	+	0.259329i	$0.916499\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−167739.	+	167739.i	−0.0483904	+	0.0483904i
$414$		0			0
$415$	143535.			0.0409108
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.56587e6	+	1.56587e6i	−0.435734	+	0.435734i	−0.890573	−	0.454840i	$-0.849697\pi$
$419$	−1.56587e6	+	1.56587e6i	−0.435734	+	0.435734i	0.454840	+	0.890573i	$0.349697\pi$
$420$		0			0
$421$	2.86763e6	+	2.86763e6i	0.788529	+	0.788529i	0.981253	−	0.192724i	$-0.0617323\pi$
$421$	2.86763e6	+	2.86763e6i	0.788529	+	0.788529i	−0.192724	+	0.981253i	$0.561732\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	1.97189e6i		−	0.529554i
$426$		0			0
$427$	−192247.	−	192247.i	−0.0510259	−	0.0510259i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5.39462e6			1.39884			0.699419	−	0.714712i	$-0.253442\pi$
$431$	5.39462e6			1.39884			0.699419	+	0.714712i	$0.253442\pi$
$432$		0			0
$433$	477220.			0.122320			0.0611602	−	0.998128i	$-0.480520\pi$
$433$	477220.			0.122320			0.0611602	+	0.998128i	$0.480520\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.16146e6	+	5.16146e6i	1.29291	+	1.29291i
$438$		0			0
$439$		−	4.17692e6i		−	1.03442i	−0.855860	−	0.517208i	$-0.826971\pi$
$439$		−	4.17692e6i		−	1.03442i	0.855860	−	0.517208i	$-0.173029\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−244827.	−	244827.i	−0.0592720	−	0.0592720i	0.676849	−	0.736121i	$-0.263345\pi$
$443$	−244827.	−	244827.i	−0.0592720	−	0.0592720i	−0.736121	+	0.676849i	$0.763345\pi$
$444$		0			0
$445$	−1.17427e6	+	1.17427e6i	−0.281104	+	0.281104i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.93133e6			0.686198			0.343099	−	0.939299i	$-0.388523\pi$
$449$	2.93133e6			0.686198			0.343099	+	0.939299i	$0.388523\pi$
$450$		0			0
$451$	−2.37661e6	+	2.37661e6i	−0.550196	+	0.550196i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	275286.i		−	0.0623383i
$456$		0			0
$457$			4.24533e6i			0.950869i	0.879751	+	0.475434i	$0.157709\pi$
$457$			4.24533e6i			0.950869i	−0.879751	+	0.475434i	$0.842291\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.71290e6	+	1.71290e6i	−0.375388	+	0.375388i	−0.869435	−	0.494047i	$-0.835517\pi$
$461$	−1.71290e6	+	1.71290e6i	−0.375388	+	0.375388i	0.494047	+	0.869435i	$0.335517\pi$
$462$		0			0
$463$	−1.39183e6			−0.301741			−0.150871	−	0.988553i	$-0.548208\pi$
$463$	−1.39183e6			−0.301741			−0.150871	+	0.988553i	$0.548208\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.72514e6	+	1.72514e6i	−0.366043	+	0.366043i	−0.866032	−	0.499989i	$-0.833338\pi$
$467$	−1.72514e6	+	1.72514e6i	−0.366043	+	0.366043i	0.499989	+	0.866032i	$0.333338\pi$
$468$		0			0
$469$	365678.	+	365678.i	0.0767657	+	0.0767657i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	4.08991e6i		−	0.840545i
$474$		0			0
$475$	5.33032e6	+	5.33032e6i	1.08398	+	1.08398i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.45862e6			1.28618			0.643089	−	0.765792i	$-0.277653\pi$
$479$	6.45862e6			1.28618			0.643089	+	0.765792i	$0.277653\pi$
$480$		0			0
$481$	−6.79916e6			−1.33996
$482$		0			0
$483$		0			0
$484$		0			0
$485$	468328.	+	468328.i	0.0904056	+	0.0904056i
$486$		0			0
$487$			3.55379e6i			0.679000i	0.940606	+	0.339500i	$0.110258\pi$
$487$			3.55379e6i			0.679000i	−0.940606	+	0.339500i	$0.889742\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.82904e6	+	1.82904e6i	0.342388	+	0.342388i	0.857264	−	0.514876i	$-0.172162\pi$
$491$	1.82904e6	+	1.82904e6i	0.342388	+	0.342388i	−0.514876	+	0.857264i	$0.672162\pi$
$492$		0			0
$493$	2.59380e6	−	2.59380e6i	0.480640	−	0.480640i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−780955.			−0.141819
$498$		0			0
$499$	692847.	−	692847.i	0.124562	−	0.124562i	−0.642078	−	0.766640i	$-0.721927\pi$
$499$	692847.	−	692847.i	0.124562	−	0.124562i	0.766640	+	0.642078i	$0.221927\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.55001e6i		−	0.801849i	−0.916111	−	0.400924i	$-0.868689\pi$
$503$		−	4.55001e6i		−	0.801849i	0.916111	−	0.400924i	$-0.131311\pi$
$504$		0			0
$505$			118494.i			0.0206761i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.05841e6	+	1.05841e6i	−0.181075	+	0.181075i	−0.791824	−	0.610749i	$-0.790868\pi$
$509$	−1.05841e6	+	1.05841e6i	−0.181075	+	0.181075i	0.610749	+	0.791824i	$0.290868\pi$
$510$		0			0
$511$	575741.			0.0975382
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−208273.	+	208273.i	−0.0346031	+	0.0346031i
$516$		0			0
$517$	−4.48625e6	−	4.48625e6i	−0.738171	−	0.738171i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			6.15364e6i			0.993202i	0.867979	+	0.496601i	$0.165419\pi$
$521$			6.15364e6i			0.993202i	−0.867979	+	0.496601i	$0.834581\pi$
$522$		0			0
$523$	3.11937e6	+	3.11937e6i	0.498669	+	0.498669i	0.911024	−	0.412354i	$-0.135293\pi$
$523$	3.11937e6	+	3.11937e6i	0.498669	+	0.498669i	−0.412354	+	0.911024i	$0.635293\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.95339e6			0.463228
$528$		0			0
$529$	−1.84786e6			−0.287098
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.96822e6	−	6.96822e6i	−1.06244	−	1.06244i
$534$		0			0
$535$			1.22023e6i			0.184314i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.07402e6	+	3.07402e6i	0.455758	+	0.455758i
$540$		0			0
$541$	3.23194e6	−	3.23194e6i	0.474756	−	0.474756i	−0.428694	−	0.903450i	$-0.641026\pi$
$541$	3.23194e6	−	3.23194e6i	0.474756	−	0.474756i	0.903450	+	0.428694i	$0.141026\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.45533e6			−0.354094
$546$		0			0
$547$	5.66538e6	−	5.66538e6i	0.809582	−	0.809582i	−0.174988	−	0.984571i	$-0.555989\pi$
$547$	5.66538e6	−	5.66538e6i	0.809582	−	0.809582i	0.984571	+	0.174988i	$0.0559887\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			1.40229e7i			1.96770i
$552$		0			0
$553$			2.89037e6i			0.401921i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.14924e6	−	1.14924e6i	0.156955	−	0.156955i	−0.624261	−	0.781216i	$-0.714600\pi$
$557$	1.14924e6	−	1.14924e6i	0.156955	−	0.156955i	0.781216	+	0.624261i	$0.214600\pi$
$558$		0			0
$559$	1.19916e7			1.62311
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−716166.	+	716166.i	−0.0952232	+	0.0952232i	−0.753114	−	0.657890i	$-0.771449\pi$
$563$	−716166.	+	716166.i	−0.0952232	+	0.0952232i	0.657890	+	0.753114i	$0.271449\pi$
$564$		0			0
$565$	833353.	+	833353.i	0.109827	+	0.109827i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	3.49909e6i		−	0.453079i	−0.974002	−	0.226540i	$-0.927259\pi$
$569$		−	3.49909e6i		−	0.453079i	0.974002	−	0.226540i	$-0.0727413\pi$
$570$		0			0
$571$	−4.24730e6	−	4.24730e6i	−0.545159	−	0.545159i	0.379878	−	0.925037i	$-0.375966\pi$
$571$	−4.24730e6	−	4.24730e6i	−0.545159	−	0.545159i	−0.925037	+	0.379878i	$0.875966\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.55523e6			−1.07910
$576$		0			0
$577$	2.94459e6			0.368201			0.184101	−	0.982907i	$-0.441063\pi$
$577$	2.94459e6			0.368201			0.184101	+	0.982907i	$0.441063\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	230144.	+	230144.i	0.0282852	+	0.0282852i
$582$		0			0
$583$		−	251913.i		−	0.0306958i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.78400e6	+	3.78400e6i	0.453269	+	0.453269i	0.896438	−	0.443169i	$-0.146146\pi$
$587$	3.78400e6	+	3.78400e6i	0.453269	+	0.453269i	−0.443169	+	0.896438i	$0.646146\pi$
$588$		0			0
$589$	−7.98348e6	+	7.98348e6i	−0.948209	+	0.948209i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.12147e7			−1.30964			−0.654821	−	0.755784i	$-0.727256\pi$
$593$	−1.12147e7			−1.30964			−0.654821	+	0.755784i	$0.727256\pi$
$594$		0			0
$595$	−162325.	+	162325.i	−0.0187972	+	0.0187972i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	1.03597e7i		−	1.17972i	−0.807506	−	0.589860i	$-0.799183\pi$
$599$		−	1.03597e7i		−	1.17972i	0.807506	−	0.589860i	$-0.200817\pi$
$600$		0			0
$601$		−	1.26288e7i		−	1.42618i	−0.701073	−	0.713090i	$-0.747295\pi$
$601$		−	1.26288e7i		−	1.42618i	0.701073	−	0.713090i	$-0.252705\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−763729.	+	763729.i	−0.0848303	+	0.0848303i
$606$		0			0
$607$	137659.			0.0151647			0.00758235	−	0.999971i	$-0.497586\pi$
$607$	137659.			0.0151647			0.00758235	+	0.999971i	$0.497586\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.31536e7	−	1.31536e7i	1.42542	−	1.42542i
$612$		0			0
$613$	3.46214e6	+	3.46214e6i	0.372129	+	0.372129i	0.868252	−	0.496123i	$-0.165244\pi$
$613$	3.46214e6	+	3.46214e6i	0.372129	+	0.372129i	−0.496123	+	0.868252i	$0.665244\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			4.66033e6i			0.492838i	0.969163	+	0.246419i	$0.0792539\pi$
$617$			4.66033e6i			0.492838i	−0.969163	+	0.246419i	$0.920746\pi$
$618$		0			0
$619$	1.08290e6	+	1.08290e6i	0.113595	+	0.113595i	0.761620	−	0.648024i	$-0.224404\pi$
$619$	1.08290e6	+	1.08290e6i	0.113595	+	0.113595i	−0.648024	+	0.761620i	$0.724404\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.76562e6			−0.388702
$624$		0			0
$625$	−8.35824e6			−0.855884
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.00920e6	+	4.00920e6i	0.404046	+	0.404046i
$630$		0			0
$631$		−	2.10213e6i		−	0.210177i	−0.994463	−	0.105089i	$-0.966487\pi$
$631$		−	2.10213e6i		−	0.210177i	0.994463	−	0.105089i	$-0.0335126\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.00477e6	−	1.00477e6i	−0.0988852	−	0.0988852i
$636$		0			0
$637$	−9.01300e6	+	9.01300e6i	−0.880078	+	0.880078i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.01356e7			0.974322			0.487161	−	0.873312i	$-0.338032\pi$
$641$	1.01356e7			0.974322			0.487161	+	0.873312i	$0.338032\pi$
$642$		0			0
$643$	−7.82677e6	+	7.82677e6i	−0.746543	+	0.746543i	−0.973828	−	0.227285i	$-0.927015\pi$
$643$	−7.82677e6	+	7.82677e6i	−0.746543	+	0.746543i	0.227285	+	0.973828i	$0.427015\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.14962e7i		−	1.07967i	−0.841770	−	0.539837i	$-0.818486\pi$
$647$		−	1.14962e7i		−	1.07967i	0.841770	−	0.539837i	$-0.181514\pi$
$648$		0			0
$649$		−	2.29776e6i		−	0.214137i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.64617e6	−	6.64617e6i	0.609942	−	0.609942i	−0.332989	−	0.942931i	$-0.608057\pi$
$653$	6.64617e6	−	6.64617e6i	0.609942	−	0.609942i	0.942931	+	0.332989i	$0.108057\pi$
$654$		0			0
$655$	2.05415e6			0.187081
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.49421e6	+	7.49421e6i	−0.672221	+	0.672221i	−0.958228	−	0.286006i	$-0.907672\pi$
$659$	−7.49421e6	+	7.49421e6i	−0.672221	+	0.672221i	0.286006	+	0.958228i	$0.407672\pi$
$660$		0			0
$661$	2.34156e6	+	2.34156e6i	0.208450	+	0.208450i	0.803609	−	0.595158i	$-0.202911\pi$
$661$	2.34156e6	+	2.34156e6i	0.208450	+	0.208450i	−0.595158	+	0.803609i	$0.702911\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	877580.i		−	0.0769543i
$666$		0			0
$667$	−1.12535e7	−	1.12535e7i	−0.979427	−	0.979427i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.63348e6			0.225800
$672$		0			0
$673$	9.65048e6			0.821318			0.410659	−	0.911789i	$-0.365299\pi$
$673$	9.65048e6			0.821318			0.410659	+	0.911789i	$0.365299\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.31841e6	−	5.31841e6i	−0.445974	−	0.445974i	0.448039	−	0.894014i	$-0.352122\pi$
$677$	−5.31841e6	−	5.31841e6i	−0.445974	−	0.445974i	−0.894014	+	0.448039i	$0.852122\pi$
$678$		0			0
$679$			1.50183e6i			0.125010i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.26533e7	−	1.26533e7i	−1.03790	−	1.03790i	−0.999253	−	0.0386419i	$-0.987697\pi$
$683$	−1.26533e7	−	1.26533e7i	−1.03790	−	1.03790i	−0.0386419	−	0.999253i	$-0.512303\pi$
$684$		0			0
$685$	222514.	−	222514.i	0.0181189	−	0.0181189i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	738607.			0.0592741
$690$		0			0
$691$	9.67217e6	−	9.67217e6i	0.770600	−	0.770600i	−0.207611	−	0.978211i	$-0.566569\pi$
$691$	9.67217e6	−	9.67217e6i	0.770600	−	0.770600i	0.978211	+	0.207611i	$0.0665690\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			3.34337e6i			0.262556i
$696$		0			0
$697$			8.21777e6i			0.640726i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.90818e6	+	2.90818e6i	−0.223525	+	0.223525i	−0.809981	−	0.586456i	$-0.800523\pi$
$701$	−2.90818e6	+	2.90818e6i	−0.223525	+	0.223525i	0.586456	+	0.809981i	$0.300523\pi$
$702$		0			0
$703$	−2.16750e7			−1.65413
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−189993.	+	189993.i	−0.0142951	+	0.0142951i
$708$		0			0
$709$	−1.62802e7	−	1.62802e7i	−1.21631	−	1.21631i	−0.968914	−	0.247396i	$-0.920425\pi$
$709$	−1.62802e7	−	1.62802e7i	−1.21631	−	1.21631i	−0.247396	−	0.968914i	$-0.579575\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	1.28136e7i		−	0.943945i
$714$		0			0
$715$	1.88549e6	+	1.88549e6i	0.137930	+	0.137930i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.68399e7			−1.21484			−0.607419	−	0.794381i	$-0.707795\pi$
$719$	−1.68399e7			−1.21484			−0.607419	+	0.794381i	$0.707795\pi$
$720$		0			0
$721$	−667888.			−0.0478482
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.16216e7	−	1.16216e7i	−0.821150	−	0.821150i
$726$		0			0
$727$			9.93566e6i			0.697205i	0.937271	+	0.348603i	$0.113344\pi$
$727$			9.93566e6i			0.697205i	−0.937271	+	0.348603i	$0.886656\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.07098e6	−	7.07098e6i	−0.489425	−	0.489425i
$732$		0			0
$733$	1.88711e7	−	1.88711e7i	1.29729	−	1.29729i	0.367113	−	0.930176i	$-0.380346\pi$
$733$	1.88711e7	−	1.88711e7i	1.29729	−	1.29729i	0.930176	−	0.367113i	$-0.119654\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.00922e6			−0.339704
$738$		0			0
$739$	4.06846e6	−	4.06846e6i	0.274043	−	0.274043i	−0.556682	−	0.830725i	$-0.687926\pi$
$739$	4.06846e6	−	4.06846e6i	0.274043	−	0.274043i	0.830725	+	0.556682i	$0.187926\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			9.53269e6i			0.633495i	0.948510	+	0.316748i	$0.102591\pi$
$743$			9.53269e6i			0.633495i	−0.948510	+	0.316748i	$0.897409\pi$
$744$		0			0
$745$			4.17390e6i			0.275519i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.95651e6	+	1.95651e6i	−0.127432	+	0.127432i
$750$		0			0
$751$	−7.24411e6			−0.468689			−0.234345	−	0.972154i	$-0.575294\pi$
$751$	−7.24411e6			−0.468689			−0.234345	+	0.972154i	$0.575294\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.27098e6	+	2.27098e6i	−0.144993	+	0.144993i
$756$		0			0
$757$	−1.61055e7	−	1.61055e7i	−1.02149	−	1.02149i	−0.999764	−	0.0217275i	$-0.993083\pi$
$757$	−1.61055e7	−	1.61055e7i	−1.02149	−	1.02149i	−0.0217275	−	0.999764i	$-0.506917\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			2.02681e6i			0.126868i	0.997986	+	0.0634340i	$0.0202052\pi$
$761$			2.02681e6i			0.126868i	−0.997986	+	0.0634340i	$0.979795\pi$
$762$		0			0
$763$	−3.93686e6	−	3.93686e6i	−0.244815	−	0.244815i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.73701e6			0.413503
$768$		0			0
$769$	1.87247e7			1.14182			0.570910	−	0.821012i	$-0.306590\pi$
$769$	1.87247e7			1.14182			0.570910	+	0.821012i	$0.306590\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.39341e6	+	7.39341e6i	0.445037	+	0.445037i	0.893701	−	0.448664i	$-0.148100\pi$
$773$	7.39341e6	+	7.39341e6i	0.445037	+	0.445037i	−0.448664	+	0.893701i	$0.648100\pi$
$774$		0			0
$775$		−	1.32328e7i		−	0.791403i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.22139e7	−	2.22139e7i	−1.31154	−	1.31154i
$780$		0			0
$781$	5.34893e6	−	5.34893e6i	0.313790	−	0.313790i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.64483e6			0.211107
$786$		0			0
$787$	1.30646e7	−	1.30646e7i	0.751896	−	0.751896i	−0.222937	−	0.974833i	$-0.571564\pi$
$787$	1.30646e7	−	1.30646e7i	0.751896	−	0.751896i	0.974833	+	0.222937i	$0.0715643\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			2.67239e6i			0.151865i
$792$		0			0
$793$			7.72135e6i			0.436024i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.46175e7	+	1.46175e7i	−0.815131	+	0.815131i	−0.985398	−	0.170267i	$-0.945537\pi$
$797$	−1.46175e7	+	1.46175e7i	−0.815131	+	0.815131i	0.170267	+	0.985398i	$0.445537\pi$
$798$		0			0
$799$	−1.55124e7			−0.859630
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.94337e6	+	3.94337e6i	−0.215813	+	0.215813i
$804$		0			0
$805$	704264.	+	704264.i	0.0383041	+	0.0383041i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			2.86509e6i			0.153910i	0.997035	+	0.0769551i	$0.0245198\pi$
$809$			2.86509e6i			0.153910i	−0.997035	+	0.0769551i	$0.975480\pi$
$810$		0			0
$811$	2.82668e6	+	2.82668e6i	0.150912	+	0.150912i	0.778525	−	0.627613i	$-0.215968\pi$
$811$	2.82668e6	+	2.82668e6i	0.150912	+	0.150912i	−0.627613	+	0.778525i	$0.715968\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.25823e6			0.0663539
$816$		0			0
$817$	3.82279e7			2.00367
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.42183e7	−	1.42183e7i	−0.736191	−	0.736191i	0.235647	−	0.971839i	$-0.424279\pi$
$821$	−1.42183e7	−	1.42183e7i	−0.736191	−	0.736191i	−0.971839	+	0.235647i	$0.924279\pi$
$822$		0			0
$823$			3.16278e7i			1.62768i	0.581088	+	0.813841i	$0.302627\pi$
$823$			3.16278e7i			1.62768i	−0.581088	+	0.813841i	$0.697373\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.48208e6	+	7.48208e6i	0.380416	+	0.380416i	0.871252	−	0.490836i	$-0.163309\pi$
$827$	7.48208e6	+	7.48208e6i	0.380416	+	0.380416i	−0.490836	+	0.871252i	$0.663309\pi$
$828$		0			0
$829$	−2.07352e7	+	2.07352e7i	−1.04790	+	1.04790i	−0.0491107	+	0.998793i	$0.515639\pi$
$829$	−2.07352e7	+	2.07352e7i	−1.04790	+	1.04790i	−0.998793	+	0.0491107i	$0.984361\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.06292e7			0.530749
$834$		0			0
$835$	−5.53739e6	+	5.53739e6i	−0.274846	+	0.274846i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			5.53194e6i			0.271314i	0.990756	+	0.135657i	$0.0433145\pi$
$839$			5.53194e6i			0.271314i	−0.990756	+	0.135657i	$0.956685\pi$
$840$		0			0
$841$		−	1.00629e7i		−	0.490604i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.28494e6	+	2.28494e6i	−0.110086	+	0.110086i
$846$		0			0
$847$	−2.44912e6			−0.117301
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.73943e7	−	1.73943e7i	0.823348	−	0.823348i
$852$		0			0
$853$	1.05005e6	+	1.05005e6i	0.0494125	+	0.0494125i	0.731381	−	0.681969i	$-0.238876\pi$
$853$	1.05005e6	+	1.05005e6i	0.0494125	+	0.0494125i	−0.681969	+	0.731381i	$0.738876\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	3.18114e7i		−	1.47955i	−0.672852	−	0.739777i	$-0.734931\pi$
$857$		−	3.18114e7i		−	1.47955i	0.672852	−	0.739777i	$-0.265069\pi$
$858$		0			0
$859$	−1.56482e7	−	1.56482e7i	−0.723572	−	0.723572i	0.245759	−	0.969331i	$-0.420963\pi$
$859$	−1.56482e7	−	1.56482e7i	−0.723572	−	0.723572i	−0.969331	+	0.245759i	$0.920963\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.33821e6			0.289694			0.144847	−	0.989454i	$-0.453731\pi$
$863$	6.33821e6			0.289694			0.144847	+	0.989454i	$0.453731\pi$
$864$		0			0
$865$	−5.55282e6			−0.252333
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.97968e7	−	1.97968e7i	−0.889293	−	0.889293i
$870$		0			0
$871$		−	1.46870e7i		−	0.655975i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.49195e6	+	1.49195e6i	0.0658770	+	0.0658770i
$876$		0			0
$877$	−2.46152e7	+	2.46152e7i	−1.08070	+	1.08070i	−0.0842560	+	0.996444i	$0.526851\pi$
$877$	−2.46152e7	+	2.46152e7i	−1.08070	+	1.08070i	−0.996444	+	0.0842560i	$0.973149\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.93261e7			0.838891			0.419445	−	0.907781i	$-0.362225\pi$
$881$	1.93261e7			0.838891			0.419445	+	0.907781i	$0.362225\pi$
$882$		0			0
$883$	1.14580e7	−	1.14580e7i	0.494546	−	0.494546i	−0.415189	−	0.909735i	$-0.636285\pi$
$883$	1.14580e7	−	1.14580e7i	0.494546	−	0.494546i	0.909735	+	0.415189i	$0.136285\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	1.19088e7i		−	0.508228i	−0.967174	−	0.254114i	$-0.918216\pi$
$887$		−	1.19088e7i		−	0.508228i	0.967174	−	0.254114i	$-0.0817839\pi$
$888$		0			0
$889$		−	3.22208e6i		−	0.136736i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.19324e7	−	4.19324e7i	1.75963	−	1.75963i
$894$		0			0
$895$	−7.64646e6			−0.319082
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.74063e7	−	1.74063e7i	0.718302	−	0.718302i
$900$		0			0
$901$	−435527.	−	435527.i	−0.0178732	−	0.0178732i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			1.46614e6i			0.0595051i
$906$		0			0
$907$	−2.14692e7	−	2.14692e7i	−0.866558	−	0.866558i	0.125532	−	0.992090i	$-0.459936\pi$
$907$	−2.14692e7	−	2.14692e7i	−0.866558	−	0.866558i	−0.992090	+	0.125532i	$0.959936\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.33971e7			−1.33325			−0.666627	−	0.745391i	$-0.732263\pi$
$911$	−3.33971e7			−1.33325			−0.666627	+	0.745391i	$0.732263\pi$
$912$		0			0
$913$	−3.15260e6			−0.125168
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.29362e6	+	3.29362e6i	0.129345	+	0.129345i
$918$		0			0
$919$			2.78332e7i			1.08711i	0.839373	+	0.543556i	$0.182923\pi$
$919$			2.78332e7i			1.08711i	−0.839373	+	0.543556i	$0.817077\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.56830e7	+	1.56830e7i	0.605934	+	0.605934i
$924$		0			0
$925$	1.79634e7	−	1.79634e7i	0.690294	−	0.690294i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.77050e7			−1.05322			−0.526609	−	0.850108i	$-0.676537\pi$
$929$	−2.77050e7			−1.05322			−0.526609	+	0.850108i	$0.676537\pi$
$930$		0			0
$931$	−2.87325e7	+	2.87325e7i	−1.08642	+	1.08642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	2.22360e6i		−	0.0831816i
$936$		0			0
$937$		−	1.14126e7i		−	0.424653i	−0.977199	−	0.212327i	$-0.931896\pi$
$937$		−	1.14126e7i		−	0.424653i	0.977199	−	0.212327i	$-0.0681041\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.72720e7	+	1.72720e7i	−0.635869	+	0.635869i	−0.949534	−	0.313665i	$-0.898443\pi$
$941$	−1.72720e7	+	1.72720e7i	−0.635869	+	0.635869i	0.313665	+	0.949534i	$0.398443\pi$
$942$		0			0
$943$	3.56536e7			1.30564
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.99199e6	+	6.99199e6i	−0.253353	+	0.253353i	−0.822344	−	0.568991i	$-0.807334\pi$
$947$	−6.99199e6	+	6.99199e6i	−0.253353	+	0.253353i	0.568991	+	0.822344i	$0.307334\pi$
$948$		0			0
$949$	−1.15619e7	−	1.15619e7i	−0.416740	−	0.416740i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			5.13807e7i			1.83260i	0.400494	+	0.916299i	$0.368839\pi$
$953$			5.13807e7i			1.83260i	−0.400494	+	0.916299i	$0.631161\pi$
$954$		0			0
$955$	4.17069e6	+	4.17069e6i	0.147979	+	0.147979i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	713557.			0.0250543
$960$		0			0
$961$	−8.80975e6			−0.307720
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.07799e6	+	5.07799e6i	0.175539	+	0.175539i
$966$		0			0
$967$			4.37686e7i			1.50521i	0.658474	+	0.752603i	$0.271202\pi$
$967$			4.37686e7i			1.50521i	−0.658474	+	0.752603i	$0.728798\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.31145e7	−	2.31145e7i	−0.786749	−	0.786749i	0.194211	−	0.980960i	$-0.437785\pi$
$971$	−2.31145e7	−	2.31145e7i	−0.786749	−	0.786749i	−0.980960	+	0.194211i	$0.937785\pi$
$972$		0			0
$973$	−5.36074e6	+	5.36074e6i	−0.181528	+	0.181528i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.42151e7			−0.476445			−0.238223	−	0.971211i	$-0.576565\pi$
$977$	−1.42151e7			−0.476445			−0.238223	+	0.971211i	$0.576565\pi$
$978$		0			0
$979$	2.57915e7	−	2.57915e7i	0.860044	−	0.860044i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			4.12375e7i			1.36116i	0.732675	+	0.680579i	$0.238272\pi$
$983$			4.12375e7i			1.36116i	−0.732675	+	0.680579i	$0.761728\pi$
$984$		0			0
$985$		−	515651.i		−	0.0169342i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.06781e7	+	3.06781e7i	−0.997329	+	0.997329i
$990$		0			0
$991$	3.91749e7			1.26714			0.633568	−	0.773687i	$-0.281590\pi$
$991$	3.91749e7			1.26714			0.633568	+	0.773687i	$0.281590\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−594217.	+	594217.i	−0.0190277	+	0.0190277i
$996$		0			0
$997$	683406.	+	683406.i	0.0217741	+	0.0217741i	0.717910	−	0.696136i	$-0.245099\pi$
$997$	683406.	+	683406.i	0.0217741	+	0.0217741i	−0.696136	+	0.717910i	$0.745099\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.6.k.a.433.4		18
3.2	odd	2		64.6.e.a.49.4		18
4.3	odd	2		144.6.k.a.37.3		18
12.11	even	2		16.6.e.a.5.7	✓	18
16.3	odd	4		144.6.k.a.109.3		18
16.13	even	4	inner	576.6.k.a.145.4		18
24.5	odd	2		128.6.e.a.97.6		18
24.11	even	2		128.6.e.b.97.4		18
48.5	odd	4		128.6.e.a.33.6		18
48.11	even	4		128.6.e.b.33.4		18
48.29	odd	4		64.6.e.a.17.4		18
48.35	even	4		16.6.e.a.13.7	yes	18
96.29	odd	8		1024.6.a.l.1.8		18
96.35	even	8		1024.6.a.k.1.11		18
96.77	odd	8		1024.6.a.l.1.11		18
96.83	even	8		1024.6.a.k.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.7	✓	18	12.11	even	2
16.6.e.a.13.7	yes	18	48.35	even	4
64.6.e.a.17.4		18	48.29	odd	4
64.6.e.a.49.4		18	3.2	odd	2
128.6.e.a.33.6		18	48.5	odd	4
128.6.e.a.97.6		18	24.5	odd	2
128.6.e.b.33.4		18	48.11	even	4
128.6.e.b.97.4		18	24.11	even	2
144.6.k.a.37.3		18	4.3	odd	2
144.6.k.a.109.3		18	16.3	odd	4
576.6.k.a.145.4		18	16.13	even	4	inner
576.6.k.a.433.4		18	1.1	even	1	trivial
1024.6.a.k.1.8		18	96.83	even	8
1024.6.a.k.1.11		18	96.35	even	8
1024.6.a.l.1.8		18	96.29	odd	8
1024.6.a.l.1.11		18	96.77	odd	8

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	576.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.73514 - 8.73514i) q^{5} -28.0117i q^{7} +O(q^{10})\)	\(q+(-8.73514 - 8.73514i) q^{5} -28.0117i q^{7} +(191.858 + 191.858i) q^{11} +(-562.527 + 562.527i) q^{13} +663.401 q^{17} +(-1793.28 + 1793.28i) q^{19} -2878.23i q^{23} -2972.39i q^{25} +(3909.86 - 3909.86i) q^{29} +4451.90 q^{31} +(-244.686 + 244.686i) q^{35} +(6043.41 + 6043.41i) q^{37} +12387.3i q^{41} +(-10658.7 - 10658.7i) q^{43} -23383.1 q^{47} +16022.3 q^{49} +(-656.507 - 656.507i) q^{53} -3351.82i q^{55} +(-5988.17 - 5988.17i) q^{59} +(6863.09 - 6863.09i) q^{61} +9827.51 q^{65} +(-13054.5 + 13054.5i) q^{67} -27879.6i q^{71} +20553.5i q^{73} +(5374.28 - 5374.28i) q^{77} -103184. q^{79} +(-8215.97 + 8215.97i) q^{83} +(-5794.90 - 5794.90i) q^{85} -134430. i q^{89} +(15757.4 + 15757.4i) q^{91} +31329.0 q^{95} -53614.2 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{5}+O(q^{10}) \) 18 * q + 2 * q^5	\( 18 q + 2 q^{5} - 606 q^{11} - 2 q^{13} + 4 q^{17} + 2362 q^{19} - 4070 q^{29} + 11536 q^{31} + 8636 q^{35} - 10650 q^{37} + 15382 q^{43} + 44176 q^{47} - 14410 q^{49} - 24726 q^{53} - 29734 q^{59} - 48082 q^{61} - 27684 q^{65} + 75210 q^{67} - 41060 q^{77} + 52864 q^{79} + 227838 q^{83} - 138652 q^{85} + 231164 q^{91} - 250380 q^{95} - 4 q^{97}+O(q^{100}) \) 18 * q + 2 * q^5 - 606 * q^11 - 2 * q^13 + 4 * q^17 + 2362 * q^19 - 4070 * q^29 + 11536 * q^31 + 8636 * q^35 - 10650 * q^37 + 15382 * q^43 + 44176 * q^47 - 14410 * q^49 - 24726 * q^53 - 29734 * q^59 - 48082 * q^61 - 27684 * q^65 + 75210 * q^67 - 41060 * q^77 + 52864 * q^79 + 227838 * q^83 - 138652 * q^85 + 231164 * q^91 - 250380 * q^95 - 4 * q^97

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