LMFDB - Embedded newform 1134.2.d.b.1133.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(1133,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1134.1133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.d (of order $2$, degree $1$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
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} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + \cdots + 457 $ x^16 - 8x^15 + 56x^14 - 252x^13 + 962x^12 - 2860x^11 + 7240x^10 - 15036x^9 + 26533x^8 - 38796x^7 + 47500x^6 - 47396x^5 + 38144x^4 - 23676x^3 + 10748x^2 - 3160*x + 457
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1133.16
Root			$0.500000 - 3.18553i$ of defining polynomial
Character	$\chi$	$=$	1134.1133
Dual form			1134.2.d.b.1133.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +3.79792 q^{5} +(2.59077 + 0.536572i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +3.79792 q^{5} +(2.59077 + 0.536572i) q^{7} -1.00000i q^{8} +3.79792i q^{10} +1.61401i q^{11} +5.11225i q^{13} +(-0.536572 + 2.59077i) q^{14} +1.00000 q^{16} -2.33198 q^{17} -4.24621i q^{19} -3.79792 q^{20} -1.61401 q^{22} +2.62863i q^{23} +9.42418 q^{25} -5.11225 q^{26} +(-2.59077 - 0.536572i) q^{28} +4.01461i q^{29} -7.98863i q^{31} +1.00000i q^{32} -2.33198i q^{34} +(9.83953 + 2.03786i) q^{35} -5.74907 q^{37} +4.24621 q^{38} -3.79792i q^{40} -8.51737 q^{41} +9.25725 q^{43} -1.61401i q^{44} -2.62863 q^{46} +9.69576 q^{47} +(6.42418 + 2.78027i) q^{49} +9.42418i q^{50} -5.11225i q^{52} -2.19615i q^{53} +6.12989i q^{55} +(0.536572 - 2.59077i) q^{56} -4.01461 q^{58} +1.46594 q^{59} -14.4152i q^{61} +7.98863 q^{62} -1.00000 q^{64} +19.4159i q^{65} -5.78094 q^{67} +2.33198 q^{68} +(-2.03786 + 9.83953i) q^{70} +15.6668i q^{71} -7.65133i q^{73} -5.74907i q^{74} +4.24621i q^{76} +(-0.866035 + 4.18154i) q^{77} -1.64324 q^{79} +3.79792 q^{80} -8.51737i q^{82} -3.02145 q^{83} -8.85666 q^{85} +9.25725i q^{86} +1.61401 q^{88} -17.5236 q^{89} +(-2.74309 + 13.2447i) q^{91} -2.62863i q^{92} +9.69576i q^{94} -16.1268i q^{95} +10.3761i q^{97} +(-2.78027 + 6.42418i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 8 * q^7	$ 16 q - 16 q^{4} + 8 q^{7} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{37} + 64 q^{43} - 32 q^{49} - 48 q^{58} - 16 q^{64} - 16 q^{67} - 24 q^{70} + 32 q^{79} - 48 q^{85} + 24 q^{91}+O(q^{100}) $ 16 * q - 16 * q^4 + 8 * q^7 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^37 + 64 * q^43 - 32 * q^49 - 48 * q^58 - 16 * q^64 - 16 * q^67 - 24 * q^70 + 32 * q^79 - 48 * q^85 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	3.79792			1.69848			0.849240	−	0.528007i	$-0.177060\pi$
$5$	3.79792			1.69848			0.849240	+	0.528007i	$0.177060\pi$
$6$		0			0
$7$	2.59077	+	0.536572i	0.979219	+	0.202805i
$7$	2.59077	+	0.536572i	0.979219	+	0.202805i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			3.79792i			1.20101i
$11$			1.61401i			0.486644i	0.969946	+	0.243322i	$0.0782371\pi$
$11$			1.61401i			0.486644i	−0.969946	+	0.243322i	$0.921763\pi$
$12$		0			0
$13$			5.11225i			1.41788i	0.705268	+	0.708941i	$0.250827\pi$
$13$			5.11225i			1.41788i	−0.705268	+	0.708941i	$0.749173\pi$
$14$	−0.536572	+	2.59077i	−0.143405	+	0.692412i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.33198			−0.565587			−0.282794	−	0.959181i	$-0.591261\pi$
$17$	−2.33198			−0.565587			−0.282794	+	0.959181i	$0.591261\pi$
$18$		0			0
$19$		−	4.24621i		−	0.974148i	−0.873361	−	0.487074i	$-0.838064\pi$
$19$		−	4.24621i		−	0.974148i	0.873361	−	0.487074i	$-0.161936\pi$
$20$	−3.79792			−0.849240
$21$		0			0
$22$	−1.61401			−0.344109
$23$			2.62863i			0.548106i	0.961715	+	0.274053i	$0.0883645\pi$
$23$			2.62863i			0.548106i	−0.961715	+	0.274053i	$0.911636\pi$
$24$		0			0
$25$	9.42418			1.88484
$26$	−5.11225			−1.00259
$27$		0			0
$28$	−2.59077	−	0.536572i	−0.489610	−	0.101403i
$29$			4.01461i			0.745495i	0.927933	+	0.372747i	$0.121584\pi$
$29$			4.01461i			0.745495i	−0.927933	+	0.372747i	$0.878416\pi$
$30$		0			0
$31$		−	7.98863i		−	1.43480i	−0.696661	−	0.717401i	$-0.745332\pi$
$31$		−	7.98863i		−	1.43480i	0.696661	−	0.717401i	$-0.254668\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		−	2.33198i		−	0.399931i
$35$	9.83953	+	2.03786i	1.66318	+	0.344461i
$36$		0			0
$37$	−5.74907			−0.945141			−0.472570	−	0.881293i	$-0.656674\pi$
$37$	−5.74907			−0.945141			−0.472570	+	0.881293i	$0.656674\pi$
$38$	4.24621			0.688826
$39$		0			0
$40$		−	3.79792i		−	0.600504i
$41$	−8.51737			−1.33019			−0.665095	−	0.746759i	$-0.731609\pi$
$41$	−8.51737			−1.33019			−0.665095	+	0.746759i	$0.731609\pi$
$42$		0			0
$43$	9.25725			1.41172			0.705859	−	0.708352i	$-0.250561\pi$
$43$	9.25725			1.41172			0.705859	+	0.708352i	$0.250561\pi$
$44$		−	1.61401i		−	0.243322i
$45$		0			0
$46$	−2.62863			−0.387570
$47$	9.69576			1.41427			0.707136	−	0.707078i	$-0.249987\pi$
$47$	9.69576			1.41427			0.707136	+	0.707078i	$0.249987\pi$
$48$		0			0
$49$	6.42418	+	2.78027i	0.917740	+	0.397181i
$50$			9.42418i			1.33278i
$51$		0			0
$52$		−	5.11225i		−	0.708941i
$53$		−	2.19615i		−	0.301665i	−0.988559	−	0.150832i	$-0.951805\pi$
$53$		−	2.19615i		−	0.301665i	0.988559	−	0.150832i	$-0.0481954\pi$
$54$		0			0
$55$			6.12989i			0.826555i
$56$	0.536572	−	2.59077i	0.0717024	−	0.346206i
$57$		0			0
$58$	−4.01461			−0.527144
$59$	1.46594			0.190849			0.0954247	−	0.995437i	$-0.469579\pi$
$59$	1.46594			0.190849			0.0954247	+	0.995437i	$0.469579\pi$
$60$		0			0
$61$		−	14.4152i		−	1.84568i	−0.385186	−	0.922839i	$-0.625863\pi$
$61$		−	14.4152i		−	1.84568i	0.385186	−	0.922839i	$-0.374137\pi$
$62$	7.98863			1.01456
$63$		0			0
$64$	−1.00000			−0.125000
$65$			19.4159i			2.40824i
$66$		0			0
$67$	−5.78094			−0.706255			−0.353127	−	0.935575i	$-0.614882\pi$
$67$	−5.78094			−0.706255			−0.353127	+	0.935575i	$0.614882\pi$
$68$	2.33198			0.282794
$69$		0			0
$70$	−2.03786	+	9.83953i	−0.243570	+	1.17605i
$71$			15.6668i			1.85931i	0.368432	+	0.929655i	$0.379895\pi$
$71$			15.6668i			1.85931i	−0.368432	+	0.929655i	$0.620105\pi$
$72$		0			0
$73$		−	7.65133i		−	0.895521i	−0.894154	−	0.447760i	$-0.852222\pi$
$73$		−	7.65133i		−	0.895521i	0.894154	−	0.447760i	$-0.147778\pi$
$74$		−	5.74907i		−	0.668315i
$75$		0			0
$76$			4.24621i			0.487074i
$77$	−0.866035	+	4.18154i	−0.0986938	+	0.476531i
$78$		0			0
$79$	−1.64324			−0.184879			−0.0924394	−	0.995718i	$-0.529466\pi$
$79$	−1.64324			−0.184879			−0.0924394	+	0.995718i	$0.529466\pi$
$80$	3.79792			0.424620
$81$		0			0
$82$		−	8.51737i		−	0.940586i
$83$	−3.02145			−0.331647			−0.165824	−	0.986155i	$-0.553028\pi$
$83$	−3.02145			−0.331647			−0.165824	+	0.986155i	$0.553028\pi$
$84$		0			0
$85$	−8.85666			−0.960639
$86$			9.25725i			0.998235i
$87$		0			0
$88$	1.61401			0.172055
$89$	−17.5236			−1.85750			−0.928752	−	0.370703i	$-0.879117\pi$
$89$	−17.5236			−1.85750			−0.928752	+	0.370703i	$0.879117\pi$
$90$		0			0
$91$	−2.74309	+	13.2447i	−0.287554	+	1.38842i
$92$		−	2.62863i		−	0.274053i
$93$		0			0
$94$			9.69576i			1.00004i
$95$		−	16.1268i		−	1.65457i
$96$		0			0
$97$			10.3761i			1.05353i	0.850010	+	0.526767i	$0.176596\pi$
$97$			10.3761i			1.05353i	−0.850010	+	0.526767i	$0.823404\pi$
$98$	−2.78027	+	6.42418i	−0.280850	+	0.648940i
$99$		0			0
$100$	−9.42418			−0.942418
$101$	−7.70683			−0.766858			−0.383429	−	0.923570i	$-0.625257\pi$
$101$	−7.70683			−0.766858			−0.383429	+	0.923570i	$0.625257\pi$
$102$		0			0
$103$		−	2.93188i		−	0.288887i	−0.989513	−	0.144444i	$-0.953861\pi$
$103$		−	2.93188i		−	0.288887i	0.989513	−	0.144444i	$-0.0461392\pi$
$104$	5.11225			0.501297
$105$		0			0
$106$	2.19615			0.213309
$107$			12.3166i			1.19069i	0.803470	+	0.595345i	$0.202985\pi$
$107$			12.3166i			1.19069i	−0.803470	+	0.595345i	$0.797015\pi$
$108$		0			0
$109$	1.47720			0.141490			0.0707452	−	0.997494i	$-0.477462\pi$
$109$	1.47720			0.141490			0.0707452	+	0.997494i	$0.477462\pi$
$110$	−6.12989			−0.584462
$111$		0			0
$112$	2.59077	+	0.536572i	0.244805	+	0.0507013i
$113$		−	6.93237i		−	0.652142i	−0.945345	−	0.326071i	$-0.894275\pi$
$113$		−	6.93237i		−	0.652142i	0.945345	−	0.326071i	$-0.105725\pi$
$114$		0			0
$115$			9.98331i			0.930948i
$116$		−	4.01461i		−	0.372747i
$117$		0			0
$118$			1.46594i			0.134951i
$119$	−6.04162	−	1.25127i	−0.553834	−	0.114704i
$120$		0			0
$121$	8.39496			0.763178
$122$	14.4152			1.30509
$123$		0			0
$124$			7.98863i			0.717401i
$125$	16.8027			1.50288
$126$		0			0
$127$	14.7727			1.31086			0.655430	−	0.755256i	$-0.272487\pi$
$127$	14.7727			1.31086			0.655430	+	0.755256i	$0.272487\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−19.4159			−1.70289
$131$	7.70683			0.673348			0.336674	−	0.941621i	$-0.390698\pi$
$131$	7.70683			0.673348			0.336674	+	0.941621i	$0.390698\pi$
$132$		0			0
$133$	2.27840	−	11.0010i	0.197562	−	0.953904i
$134$		−	5.78094i		−	0.499397i
$135$		0			0
$136$			2.33198i			0.199965i
$137$		−	0.476309i		−	0.0406939i	−0.999793	−	0.0203469i	$-0.993523\pi$
$137$		−	0.476309i		−	0.0406939i	0.999793	−	0.0203469i	$-0.00647708\pi$
$138$		0			0
$139$		−	7.83702i		−	0.664727i	−0.943151	−	0.332364i	$-0.892154\pi$
$139$		−	7.83702i		−	0.664727i	0.943151	−	0.332364i	$-0.107846\pi$
$140$	−9.83953	−	2.03786i	−0.831592	−	0.172230i
$141$		0			0
$142$	−15.6668			−1.31473
$143$	−8.25124			−0.690003
$144$		0			0
$145$			15.2472i			1.26621i
$146$	7.65133			0.633229
$147$		0			0
$148$	5.74907			0.472570
$149$		−	19.7434i		−	1.61744i	−0.588191	−	0.808722i	$-0.700160\pi$
$149$		−	19.7434i		−	1.61744i	0.588191	−	0.808722i	$-0.299840\pi$
$150$		0			0
$151$	12.1750			0.990788			0.495394	−	0.868668i	$-0.335024\pi$
$151$	12.1750			0.990788			0.495394	+	0.868668i	$0.335024\pi$
$152$	−4.24621			−0.344413
$153$		0			0
$154$	−4.18154	−	0.866035i	−0.336958	−	0.0697871i
$155$		−	30.3402i		−	2.43698i
$156$		0			0
$157$			10.0794i			0.804426i	0.915546	+	0.402213i	$0.131759\pi$
$157$			10.0794i			0.804426i	−0.915546	+	0.402213i	$0.868241\pi$
$158$		−	1.64324i		−	0.130729i
$159$		0			0
$160$			3.79792i			0.300252i
$161$	−1.41045	+	6.81017i	−0.111159	+	0.536716i
$162$		0			0
$163$	−5.05934			−0.396278			−0.198139	−	0.980174i	$-0.563490\pi$
$163$	−5.05934			−0.396278			−0.198139	+	0.980174i	$0.563490\pi$
$164$	8.51737			0.665095
$165$		0			0
$166$		−	3.02145i		−	0.234510i
$167$	2.38747			0.184748			0.0923740	−	0.995724i	$-0.470554\pi$
$167$	2.38747			0.184748			0.0923740	+	0.995724i	$0.470554\pi$
$168$		0			0
$169$	−13.1351			−1.01039
$170$		−	8.85666i		−	0.679274i
$171$		0			0
$172$	−9.25725			−0.705859
$173$	0.232053			0.0176427			0.00882134	−	0.999961i	$-0.497192\pi$
$173$	0.232053			0.0176427			0.00882134	+	0.999961i	$0.497192\pi$
$174$		0			0
$175$	24.4159	+	5.05675i	1.84567	+	0.382254i
$176$			1.61401i			0.121661i
$177$		0			0
$178$		−	17.5236i		−	1.31345i
$179$		−	24.4451i		−	1.82711i	−0.406711	−	0.913557i	$-0.633325\pi$
$179$		−	24.4451i		−	1.82711i	0.406711	−	0.913557i	$-0.366675\pi$
$180$		0			0
$181$		−	10.5527i		−	0.784373i	−0.919886	−	0.392187i	$-0.871719\pi$
$181$		−	10.5527i		−	0.784373i	0.919886	−	0.392187i	$-0.128281\pi$
$182$	−13.2447	−	2.74309i	−0.981759	−	0.203331i
$183$		0			0
$184$	2.62863			0.193785
$185$	−21.8345			−1.60530
$186$		0			0
$187$		−	3.76384i		−	0.275239i
$188$	−9.69576			−0.707136
$189$		0			0
$190$	16.1268			1.16996
$191$			12.1732i			0.880825i	0.897795	+	0.440413i	$0.145168\pi$
$191$			12.1732i			0.880825i	−0.897795	+	0.440413i	$0.854832\pi$
$192$		0			0
$193$	−24.3784			−1.75479			−0.877397	−	0.479765i	$-0.840722\pi$
$193$	−24.3784			−1.75479			−0.877397	+	0.479765i	$0.840722\pi$
$194$	−10.3761			−0.744961
$195$		0			0
$196$	−6.42418	−	2.78027i	−0.458870	−	0.198591i
$197$			2.10759i			0.150159i	0.997178	+	0.0750797i	$0.0239211\pi$
$197$			2.10759i			0.150159i	−0.997178	+	0.0750797i	$0.976079\pi$
$198$		0			0
$199$		−	19.1753i		−	1.35930i	−0.733537	−	0.679650i	$-0.762132\pi$
$199$		−	19.1753i		−	1.35930i	0.733537	−	0.679650i	$-0.237868\pi$
$200$		−	9.42418i		−	0.666390i
$201$		0			0
$202$		−	7.70683i		−	0.542250i
$203$	−2.15413	+	10.4009i	−0.151190	+	0.730003i
$204$		0			0
$205$	−32.3483			−2.25930
$206$	2.93188			0.204274
$207$		0			0
$208$			5.11225i			0.354470i
$209$	6.85345			0.474063
$210$		0			0
$211$	8.67511			0.597220			0.298610	−	0.954375i	$-0.403477\pi$
$211$	8.67511			0.597220			0.298610	+	0.954375i	$0.403477\pi$
$212$			2.19615i			0.150832i
$213$		0			0
$214$	−12.3166			−0.841945
$215$	35.1583			2.39778
$216$		0			0
$217$	4.28648	−	20.6967i	0.290985	−	1.40498i
$218$			1.47720i			0.100049i
$219$		0			0
$220$		−	6.12989i		−	0.413277i
$221$		−	11.9216i		−	0.801936i
$222$		0			0
$223$		−	3.71748i		−	0.248941i	−0.992223	−	0.124470i	$-0.960277\pi$
$223$		−	3.71748i		−	0.248941i	0.992223	−	0.124470i	$-0.0397232\pi$
$224$	−0.536572	+	2.59077i	−0.0358512	+	0.173103i
$225$		0			0
$226$	6.93237			0.461134
$227$	3.21943			0.213681			0.106841	−	0.994276i	$-0.465927\pi$
$227$	3.21943			0.213681			0.106841	+	0.994276i	$0.465927\pi$
$228$		0			0
$229$		−	8.99060i		−	0.594116i	−0.954859	−	0.297058i	$-0.903995\pi$
$229$		−	8.99060i		−	0.594116i	0.954859	−	0.297058i	$-0.0960054\pi$
$230$	−9.98331			−0.658280
$231$		0			0
$232$	4.01461			0.263572
$233$		−	10.1604i		−	0.665630i	−0.942992	−	0.332815i	$-0.892002\pi$
$233$		−	10.1604i		−	0.665630i	0.942992	−	0.332815i	$-0.107998\pi$
$234$		0			0
$235$	36.8237			2.40211
$236$	−1.46594			−0.0954247
$237$		0			0
$238$	1.25127	−	6.04162i	0.0811080	−	0.391620i
$239$		−	3.59851i		−	0.232768i	−0.993204	−	0.116384i	$-0.962870\pi$
$239$		−	3.59851i		−	0.232768i	0.993204	−	0.116384i	$-0.0371304\pi$
$240$		0			0
$241$			23.2144i			1.49537i	0.664054	+	0.747685i	$0.268835\pi$
$241$			23.2144i			1.49537i	−0.664054	+	0.747685i	$0.731165\pi$
$242$			8.39496i			0.539648i
$243$		0			0
$244$			14.4152i			0.922839i
$245$	24.3985	+	10.5592i	1.55876	+	0.674605i
$246$		0			0
$247$	21.7077			1.38123
$248$	−7.98863			−0.507279
$249$		0			0
$250$			16.8027i			1.06269i
$251$	−25.9199			−1.63605			−0.818026	−	0.575181i	$-0.804932\pi$
$251$	−25.9199			−1.63605			−0.818026	+	0.575181i	$0.804932\pi$
$252$		0			0
$253$	−4.24264			−0.266733
$254$			14.7727i			0.926919i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.29638			−0.392757			−0.196379	−	0.980528i	$-0.562918\pi$
$257$	−6.29638			−0.392757			−0.196379	+	0.980528i	$0.562918\pi$
$258$		0			0
$259$	−14.8945	−	3.08479i	−0.925500	−	0.191679i
$260$		−	19.4159i		−	1.20412i
$261$		0			0
$262$			7.70683i			0.476129i
$263$		−	26.6413i		−	1.64277i	−0.570374	−	0.821385i	$-0.693202\pi$
$263$		−	26.6413i		−	1.64277i	0.570374	−	0.821385i	$-0.306798\pi$
$264$		0			0
$265$		−	8.34081i		−	0.512372i
$266$	11.0010	+	2.27840i	0.674512	+	0.139697i
$267$		0			0
$268$	5.78094			0.353127
$269$	3.27493			0.199676			0.0998379	−	0.995004i	$-0.468168\pi$
$269$	3.27493			0.199676			0.0998379	+	0.995004i	$0.468168\pi$
$270$		0			0
$271$		−	16.5466i		−	1.00514i	−0.864538	−	0.502568i	$-0.832389\pi$
$271$		−	16.5466i		−	1.00514i	0.864538	−	0.502568i	$-0.167611\pi$
$272$	−2.33198			−0.141397
$273$		0			0
$274$	0.476309			0.0287749
$275$			15.2108i			0.917244i
$276$		0			0
$277$	−6.98363			−0.419606			−0.209803	−	0.977744i	$-0.567282\pi$
$277$	−6.98363			−0.419606			−0.209803	+	0.977744i	$0.567282\pi$
$278$	7.83702			0.470033
$279$		0			0
$280$	2.03786	−	9.83953i	0.121785	−	0.588025i
$281$		−	2.15864i		−	0.128773i	−0.997925	−	0.0643867i	$-0.979491\pi$
$281$		−	2.15864i		−	0.128773i	0.997925	−	0.0643867i	$-0.0205091\pi$
$282$		0			0
$283$		−	6.34613i		−	0.377238i	−0.982050	−	0.188619i	$-0.939599\pi$
$283$		−	6.34613i		−	0.377238i	0.982050	−	0.188619i	$-0.0604012\pi$
$284$		−	15.6668i		−	0.929655i
$285$		0			0
$286$		−	8.25124i		−	0.487906i
$287$	−22.0665	−	4.57018i	−1.30255	−	0.269769i
$288$		0			0
$289$	−11.5619			−0.680111
$290$	−15.2472			−0.895344
$291$		0			0
$292$			7.65133i			0.447760i
$293$	27.7945			1.62377			0.811886	−	0.583816i	$-0.198441\pi$
$293$	27.7945			1.62377			0.811886	+	0.583816i	$0.198441\pi$
$294$		0			0
$295$	5.56753			0.324154
$296$			5.74907i			0.334158i
$297$		0			0
$298$	19.7434			1.14371
$299$	−13.4382			−0.777150
$300$		0			0
$301$	23.9834	+	4.96718i	1.38238	+	0.286304i
$302$			12.1750i			0.700593i
$303$		0			0
$304$		−	4.24621i		−	0.243537i
$305$		−	54.7478i		−	3.13485i
$306$		0			0
$307$		−	7.30829i		−	0.417106i	−0.978011	−	0.208553i	$-0.933125\pi$
$307$		−	7.30829i		−	0.417106i	0.978011	−	0.208553i	$-0.0668754\pi$
$308$	0.866035	−	4.18154i	0.0493469	−	0.238265i
$309$		0			0
$310$	30.3402			1.72321
$311$	3.65543			0.207281			0.103640	−	0.994615i	$-0.466951\pi$
$311$	3.65543			0.207281			0.103640	+	0.994615i	$0.466951\pi$
$312$		0			0
$313$			20.1737i			1.14029i	0.821545	+	0.570143i	$0.193112\pi$
$313$			20.1737i			1.14029i	−0.821545	+	0.570143i	$0.806888\pi$
$314$	−10.0794			−0.568815
$315$		0			0
$316$	1.64324			0.0924394
$317$			12.3330i			0.692688i	0.938108	+	0.346344i	$0.112577\pi$
$317$			12.3330i			0.692688i	−0.938108	+	0.346344i	$0.887423\pi$
$318$		0			0
$319$	−6.47964			−0.362790
$320$	−3.79792			−0.212310
$321$		0			0
$322$	−6.81017	−	1.41045i	−0.379516	−	0.0786011i
$323$			9.90206i			0.550966i
$324$		0			0
$325$			48.1787i			2.67247i
$326$		−	5.05934i		−	0.280211i
$327$		0			0
$328$			8.51737i			0.470293i
$329$	25.1195	+	5.20247i	1.38488	+	0.286822i
$330$		0			0
$331$	−22.5152			−1.23755			−0.618773	−	0.785570i	$-0.712370\pi$
$331$	−22.5152			−1.23755			−0.618773	+	0.785570i	$0.712370\pi$
$332$	3.02145			0.165824
$333$		0			0
$334$			2.38747i			0.130637i
$335$	−21.9555			−1.19956
$336$		0			0
$337$	−9.78726			−0.533146			−0.266573	−	0.963815i	$-0.585891\pi$
$337$	−9.78726			−0.533146			−0.266573	+	0.963815i	$0.585891\pi$
$338$		−	13.1351i		−	0.714453i
$339$		0			0
$340$	8.85666			0.480320
$341$	12.8938			0.698237
$342$		0			0
$343$	15.1518	+	10.6501i	0.818118	+	0.575050i
$344$		−	9.25725i		−	0.499118i
$345$		0			0
$346$			0.232053i			0.0124753i
$347$			10.8185i			0.580765i	0.956911	+	0.290383i	$0.0937826\pi$
$347$			10.8185i			0.580765i	−0.956911	+	0.290383i	$0.906217\pi$
$348$		0			0
$349$		−	9.87806i		−	0.528760i	−0.964419	−	0.264380i	$-0.914833\pi$
$349$		−	9.87806i		−	0.528760i	0.964419	−	0.264380i	$-0.0851674\pi$
$350$	−5.05675	+	24.4159i	−0.270295	+	1.30508i
$351$		0			0
$352$	−1.61401			−0.0860273
$353$	−10.4167			−0.554427			−0.277213	−	0.960808i	$-0.589411\pi$
$353$	−10.4167			−0.554427			−0.277213	+	0.960808i	$0.589411\pi$
$354$		0			0
$355$			59.5013i			3.15800i
$356$	17.5236			0.928752
$357$		0			0
$358$	24.4451			1.29196
$359$		−	9.97078i		−	0.526237i	−0.964763	−	0.263119i	$-0.915249\pi$
$359$		−	9.97078i		−	0.526237i	0.964763	−	0.263119i	$-0.0847511\pi$
$360$		0			0
$361$	0.969696			0.0510366
$362$	10.5527			0.554636
$363$		0			0
$364$	2.74309	−	13.2447i	0.143777	−	0.694208i
$365$		−	29.0591i		−	1.52102i
$366$		0			0
$367$		−	24.2534i		−	1.26602i	−0.774144	−	0.633010i	$-0.781819\pi$
$367$		−	24.2534i		−	1.26602i	0.774144	−	0.633010i	$-0.218181\pi$
$368$			2.62863i			0.137027i
$369$		0			0
$370$		−	21.8345i		−	1.13512i
$371$	1.17839	−	5.68973i	0.0611791	−	0.295396i
$372$		0			0
$373$	−2.65153			−0.137291			−0.0686455	−	0.997641i	$-0.521868\pi$
$373$	−2.65153			−0.137291			−0.0686455	+	0.997641i	$0.521868\pi$
$374$	3.76384			0.194624
$375$		0			0
$376$		−	9.69576i		−	0.500021i
$377$	−20.5237			−1.05702
$378$		0			0
$379$	−19.4305			−0.998078			−0.499039	−	0.866580i	$-0.666314\pi$
$379$	−19.4305			−0.998078			−0.499039	+	0.866580i	$0.666314\pi$
$380$			16.1268i			0.827285i
$381$		0			0
$382$	−12.1732			−0.622838
$383$	−21.2320			−1.08490			−0.542452	−	0.840087i	$-0.682504\pi$
$383$	−21.2320			−1.08490			−0.542452	+	0.840087i	$0.682504\pi$
$384$		0			0
$385$	−3.28913	+	15.8811i	−0.167630	+	0.809378i
$386$		−	24.3784i		−	1.24083i
$387$		0			0
$388$		−	10.3761i		−	0.526767i
$389$			4.47156i			0.226717i	0.993554	+	0.113359i	$0.0361609\pi$
$389$			4.47156i			0.226717i	−0.993554	+	0.113359i	$0.963839\pi$
$390$		0			0
$391$		−	6.12989i		−	0.310002i
$392$	2.78027	−	6.42418i	0.140425	−	0.324470i
$393$		0			0
$394$	−2.10759			−0.106179
$395$	−6.24088			−0.314013
$396$		0			0
$397$			35.0315i			1.75818i	0.476656	+	0.879090i	$0.341849\pi$
$397$			35.0315i			1.75818i	−0.476656	+	0.879090i	$0.658151\pi$
$398$	19.1753			0.961170
$399$		0			0
$400$	9.42418			0.471209
$401$			21.3229i			1.06482i	0.846488	+	0.532408i	$0.178713\pi$
$401$			21.3229i			1.06482i	−0.846488	+	0.532408i	$0.821287\pi$
$402$		0			0
$403$	40.8399			2.03438
$404$	7.70683			0.383429
$405$		0			0
$406$	−10.4009	−	2.15413i	−0.516190	−	0.106908i
$407$		−	9.27908i		−	0.459947i
$408$		0			0
$409$		−	24.0927i		−	1.19131i	−0.803241	−	0.595654i	$-0.796893\pi$
$409$		−	24.0927i		−	1.19131i	0.803241	−	0.595654i	$-0.203107\pi$
$410$		−	32.3483i		−	1.59757i
$411$		0			0
$412$			2.93188i			0.144444i
$413$	3.79792	+	0.786583i	0.186883	+	0.0387052i
$414$		0			0
$415$	−11.4752			−0.563297
$416$	−5.11225			−0.250648
$417$		0			0
$418$			6.85345i			0.335213i
$419$	−25.8304			−1.26190			−0.630948	−	0.775825i	$-0.717334\pi$
$419$	−25.8304			−1.26190			−0.630948	+	0.775825i	$0.717334\pi$
$420$		0			0
$421$	−17.0648			−0.831686			−0.415843	−	0.909436i	$-0.636513\pi$
$421$	−17.0648			−0.831686			−0.415843	+	0.909436i	$0.636513\pi$
$422$			8.67511i			0.422298i
$423$		0			0
$424$	−2.19615			−0.106655
$425$	−21.9770			−1.06604
$426$		0			0
$427$	7.73479	−	37.3465i	0.374313	−	1.80732i
$428$		−	12.3166i		−	0.595345i
$429$		0			0
$430$			35.1583i			1.69548i
$431$			27.4224i			1.32089i	0.750874	+	0.660446i	$0.229633\pi$
$431$			27.4224i			1.32089i	−0.750874	+	0.660446i	$0.770367\pi$
$432$		0			0
$433$		−	21.1385i		−	1.01585i	−0.861401	−	0.507925i	$-0.830413\pi$
$433$		−	21.1385i		−	1.01585i	0.861401	−	0.507925i	$-0.169587\pi$
$434$	20.6967	+	4.28648i	0.993474	+	0.205757i
$435$		0			0
$436$	−1.47720			−0.0707452
$437$	11.1617			0.533937
$438$		0			0
$439$			25.5428i			1.21909i	0.792750	+	0.609546i	$0.208648\pi$
$439$			25.5428i			1.21909i	−0.792750	+	0.609546i	$0.791352\pi$
$440$	6.12989			0.292231
$441$		0			0
$442$	11.9216			0.567054
$443$		−	30.9184i		−	1.46898i	−0.678620	−	0.734490i	$-0.737422\pi$
$443$		−	30.9184i		−	1.46898i	0.678620	−	0.734490i	$-0.262578\pi$
$444$		0			0
$445$	−66.5534			−3.15493
$446$	3.71748			0.176028
$447$		0			0
$448$	−2.59077	−	0.536572i	−0.122402	−	0.0253506i
$449$		−	1.16428i		−	0.0549456i	−0.999623	−	0.0274728i	$-0.991254\pi$
$449$		−	1.16428i		−	0.0549456i	0.999623	−	0.0274728i	$-0.00874596\pi$
$450$		0			0
$451$		−	13.7472i		−	0.647328i
$452$			6.93237i			0.326071i
$453$		0			0
$454$			3.21943i			0.151095i
$455$	−10.4180	+	50.3021i	−0.488404	+	2.35820i
$456$		0			0
$457$	7.21166			0.337347			0.168674	−	0.985672i	$-0.446052\pi$
$457$	7.21166			0.337347			0.168674	+	0.985672i	$0.446052\pi$
$458$	8.99060			0.420103
$459$		0			0
$460$		−	9.98331i		−	0.465474i
$461$	28.6513			1.33442			0.667211	−	0.744868i	$-0.267488\pi$
$461$	28.6513			1.33442			0.667211	+	0.744868i	$0.267488\pi$
$462$		0			0
$463$	−28.3402			−1.31708			−0.658540	−	0.752546i	$-0.728826\pi$
$463$	−28.3402			−1.31708			−0.658540	+	0.752546i	$0.728826\pi$
$464$			4.01461i			0.186374i
$465$		0			0
$466$	10.1604			0.470671
$467$	10.2188			0.472867			0.236434	−	0.971648i	$-0.424021\pi$
$467$	10.2188			0.472867			0.236434	+	0.971648i	$0.424021\pi$
$468$		0			0
$469$	−14.9771	−	3.10189i	−0.691578	−	0.143232i
$470$			36.8237i			1.69855i
$471$		0			0
$472$		−	1.46594i		−	0.0674754i
$473$			14.9413i			0.687003i
$474$		0			0
$475$		−	40.0171i		−	1.83611i
$476$	6.04162	+	1.25127i	0.276917	+	0.0573520i
$477$		0			0
$478$	3.59851			0.164592
$479$	12.6276			0.576972			0.288486	−	0.957484i	$-0.406848\pi$
$479$	12.6276			0.576972			0.288486	+	0.957484i	$0.406848\pi$
$480$		0			0
$481$		−	29.3906i		−	1.34010i
$482$	−23.2144			−1.05739
$483$		0			0
$484$	−8.39496			−0.381589
$485$			39.4076i			1.78941i
$486$		0			0
$487$	21.8841			0.991664			0.495832	−	0.868418i	$-0.334863\pi$
$487$	21.8841			0.991664			0.495832	+	0.868418i	$0.334863\pi$
$488$	−14.4152			−0.652546
$489$		0			0
$490$	−10.5592	+	24.3985i	−0.477018	+	1.10221i
$491$			7.60770i			0.343330i	0.985155	+	0.171665i	$0.0549147\pi$
$491$			7.60770i			0.343330i	−0.985155	+	0.171665i	$0.945085\pi$
$492$		0			0
$493$		−	9.36198i		−	0.421642i
$494$			21.7077i			0.976674i
$495$		0			0
$496$		−	7.98863i		−	0.358700i
$497$	−8.40638	+	40.5891i	−0.377078	+	1.82067i
$498$		0			0
$499$	3.85666			0.172648			0.0863238	−	0.996267i	$-0.472488\pi$
$499$	3.85666			0.172648			0.0863238	+	0.996267i	$0.472488\pi$
$500$	−16.8027			−0.751439
$501$		0			0
$502$		−	25.9199i		−	1.15686i
$503$	2.16549			0.0965545			0.0482773	−	0.998834i	$-0.484627\pi$
$503$	2.16549			0.0965545			0.0482773	+	0.998834i	$0.484627\pi$
$504$		0			0
$505$	−29.2699			−1.30249
$506$		−	4.24264i		−	0.188608i
$507$		0			0
$508$	−14.7727			−0.655430
$509$	−25.8985			−1.14793			−0.573966	−	0.818879i	$-0.694596\pi$
$509$	−25.8985			−1.14793			−0.573966	+	0.818879i	$0.694596\pi$
$510$		0			0
$511$	4.10549	−	19.8228i	0.181616	−	0.876911i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	6.29638i		−	0.277721i
$515$		−	11.1351i		−	0.490669i
$516$		0			0
$517$			15.6491i			0.688246i
$518$	3.08479	−	14.8945i	0.135538	−	0.654427i
$519$		0			0
$520$	19.4159			0.851443
$521$	29.9192			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$521$	29.9192			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$522$		0			0
$523$		−	13.7497i		−	0.601234i	−0.953745	−	0.300617i	$-0.902807\pi$
$523$		−	13.7497i		−	0.601234i	0.953745	−	0.300617i	$-0.0971925\pi$
$524$	−7.70683			−0.336674
$525$		0			0
$526$	26.6413			1.16161
$527$			18.6293i			0.811505i
$528$		0			0
$529$	16.0903			0.699579
$530$	8.34081			0.362301
$531$		0			0
$532$	−2.27840	+	11.0010i	−0.0987810	+	0.476952i
$533$		−	43.5429i		−	1.88605i
$534$		0			0
$535$			46.7774i			2.02236i
$536$			5.78094i			0.249699i
$537$		0			0
$538$			3.27493i			0.141192i
$539$	−4.48739	+	10.3687i	−0.193286	+	0.446612i
$540$		0			0
$541$	−37.3402			−1.60538			−0.802690	−	0.596397i	$-0.796599\pi$
$541$	−37.3402			−1.60538			−0.802690	+	0.596397i	$0.796599\pi$
$542$	16.5466			0.710738
$543$		0			0
$544$		−	2.33198i		−	0.0999827i
$545$	5.61029			0.240319
$546$		0			0
$547$	−1.35411			−0.0578975			−0.0289488	−	0.999581i	$-0.509216\pi$
$547$	−1.35411			−0.0578975			−0.0289488	+	0.999581i	$0.509216\pi$
$548$			0.476309i			0.0203469i
$549$		0			0
$550$	−15.2108			−0.648589
$551$	17.0469			0.726222
$552$		0			0
$553$	−4.25725	−	0.881715i	−0.181037	−	0.0374944i
$554$		−	6.98363i		−	0.296706i
$555$		0			0
$556$			7.83702i			0.332364i
$557$		−	21.1944i		−	0.898035i	−0.893523	−	0.449018i	$-0.851774\pi$
$557$		−	21.1944i		−	0.898035i	0.893523	−	0.449018i	$-0.148226\pi$
$558$		0			0
$559$			47.3253i			2.00165i
$560$	9.83953	+	2.03786i	0.415796	+	0.0861151i
$561$		0			0
$562$	2.15864			0.0910566
$563$	32.1608			1.35542			0.677709	−	0.735330i	$-0.262973\pi$
$563$	32.1608			1.35542			0.677709	+	0.735330i	$0.262973\pi$
$564$		0			0
$565$		−	26.3286i		−	1.10765i
$566$	6.34613			0.266748
$567$		0			0
$568$	15.6668			0.657365
$569$			28.3101i			1.18682i	0.804901	+	0.593410i	$0.202219\pi$
$569$			28.3101i			1.18682i	−0.804901	+	0.593410i	$0.797781\pi$
$570$		0			0
$571$	13.6999			0.573324			0.286662	−	0.958032i	$-0.407454\pi$
$571$	13.6999			0.573324			0.286662	+	0.958032i	$0.407454\pi$
$572$	8.25124			0.345002
$573$		0			0
$574$	4.57018	−	22.0665i	0.190756	−	0.921039i
$575$			24.7727i			1.03309i
$576$		0			0
$577$		−	18.1791i		−	0.756804i	−0.925641	−	0.378402i	$-0.876474\pi$
$577$		−	18.1791i		−	0.756804i	0.925641	−	0.378402i	$-0.123526\pi$
$578$		−	11.5619i		−	0.480911i
$579$		0			0
$580$		−	15.2472i		−	0.633104i
$581$	−7.82789	−	1.62123i	−0.324756	−	0.0672598i
$582$		0			0
$583$	3.54462			0.146803
$584$	−7.65133			−0.316614
$585$		0			0
$586$			27.7945i			1.14818i
$587$	−11.0814			−0.457378			−0.228689	−	0.973500i	$-0.573444\pi$
$587$	−11.0814			−0.457378			−0.228689	+	0.973500i	$0.573444\pi$
$588$		0			0
$589$	−33.9214			−1.39771
$590$			5.56753i			0.229211i
$591$		0			0
$592$	−5.74907			−0.236285
$593$	−32.4304			−1.33175			−0.665877	−	0.746061i	$-0.731943\pi$
$593$	−32.4304			−1.33175			−0.665877	+	0.746061i	$0.731943\pi$
$594$		0			0
$595$	−22.9456	−	4.75223i	−0.940676	−	0.194823i
$596$			19.7434i			0.808722i
$597$		0			0
$598$		−	13.4382i		−	0.549528i
$599$		−	12.7938i		−	0.522740i	−0.965239	−	0.261370i	$-0.915826\pi$
$599$		−	12.7938i		−	0.522740i	0.965239	−	0.261370i	$-0.0841743\pi$
$600$		0			0
$601$			31.2244i			1.27367i	0.771000	+	0.636836i	$0.219757\pi$
$601$			31.2244i			1.27367i	−0.771000	+	0.636836i	$0.780243\pi$
$602$	−4.96718	+	23.9834i	−0.202447	+	0.977491i
$603$		0			0
$604$	−12.1750			−0.495394
$605$	31.8834			1.29624
$606$		0			0
$607$		−	24.1607i		−	0.980653i	−0.871539	−	0.490327i	$-0.836877\pi$
$607$		−	24.1607i		−	0.980653i	0.871539	−	0.490327i	$-0.163123\pi$
$608$	4.24621			0.172207
$609$		0			0
$610$	54.7478			2.21667
$611$			49.5671i			2.00527i
$612$		0			0
$613$	−4.99979			−0.201939			−0.100970	−	0.994889i	$-0.532195\pi$
$613$	−4.99979			−0.201939			−0.100970	+	0.994889i	$0.532195\pi$
$614$	7.30829			0.294939
$615$		0			0
$616$	4.18154	+	0.866035i	0.168479	+	0.0348935i
$617$			18.0949i			0.728473i	0.931307	+	0.364236i	$0.118670\pi$
$617$			18.0949i			0.728473i	−0.931307	+	0.364236i	$0.881330\pi$
$618$		0			0
$619$			8.97221i			0.360624i	0.983610	+	0.180312i	$0.0577107\pi$
$619$			8.97221i			0.360624i	−0.983610	+	0.180312i	$0.942289\pi$
$620$			30.3402i			1.21849i
$621$		0			0
$622$			3.65543i			0.146570i
$623$	−45.3997	−	9.40270i	−1.81890	−	0.376711i
$624$		0			0
$625$	16.6943			0.667771
$626$	−20.1737			−0.806304
$627$		0			0
$628$		−	10.0794i		−	0.402213i
$629$	13.4067			0.534560
$630$		0			0
$631$	−35.6267			−1.41827			−0.709137	−	0.705070i	$-0.750915\pi$
$631$	−35.6267			−1.41827			−0.709137	+	0.705070i	$0.750915\pi$
$632$			1.64324i			0.0653645i
$633$		0			0
$634$	−12.3330			−0.489805
$635$	56.1053			2.22647
$636$		0			0
$637$	−14.2134	+	32.8420i	−0.563156	+	1.30125i
$638$		−	6.47964i		−	0.256531i
$639$		0			0
$640$		−	3.79792i		−	0.150126i
$641$			16.7338i			0.660944i	0.943816	+	0.330472i	$0.107208\pi$
$641$			16.7338i			0.660944i	−0.943816	+	0.330472i	$0.892792\pi$
$642$		0			0
$643$			17.4707i			0.688978i	0.938790	+	0.344489i	$0.111948\pi$
$643$			17.4707i			0.688978i	−0.938790	+	0.344489i	$0.888052\pi$
$644$	1.41045	−	6.81017i	0.0555794	−	0.268358i
$645$		0			0
$646$	−9.90206			−0.389591
$647$	21.0554			0.827775			0.413887	−	0.910328i	$-0.364171\pi$
$647$	21.0554			0.827775			0.413887	+	0.910328i	$0.364171\pi$
$648$		0			0
$649$			2.36605i			0.0928756i
$650$	−48.1787			−1.88973
$651$		0			0
$652$	5.05934			0.198139
$653$			1.19637i			0.0468174i	0.999726	+	0.0234087i	$0.00745190\pi$
$653$			1.19637i			0.0468174i	−0.999726	+	0.0234087i	$0.992548\pi$
$654$		0			0
$655$	29.2699			1.14367
$656$	−8.51737			−0.332547
$657$		0			0
$658$	−5.20247	+	25.1195i	−0.202813	+	0.979259i
$659$			32.1986i			1.25428i	0.778907	+	0.627140i	$0.215774\pi$
$659$			32.1986i			1.25428i	−0.778907	+	0.627140i	$0.784226\pi$
$660$		0			0
$661$			23.2109i			0.902798i	0.892322	+	0.451399i	$0.149075\pi$
$661$			23.2109i			0.902798i	−0.892322	+	0.451399i	$0.850925\pi$
$662$		−	22.5152i		−	0.875077i
$663$		0			0
$664$			3.02145i			0.117255i
$665$	8.65317	−	41.7807i	0.335555	−	1.62019i
$666$		0			0
$667$	−10.5529			−0.408610
$668$	−2.38747			−0.0923740
$669$		0			0
$670$		−	21.9555i		−	0.848217i
$671$	23.2664			0.898188
$672$		0			0
$673$	24.0153			0.925721			0.462861	−	0.886431i	$-0.346823\pi$
$673$	24.0153			0.925721			0.462861	+	0.886431i	$0.346823\pi$
$674$		−	9.78726i		−	0.376991i
$675$		0			0
$676$	13.1351			0.505194
$677$	3.45488			0.132782			0.0663908	−	0.997794i	$-0.478852\pi$
$677$	3.45488			0.132782			0.0663908	+	0.997794i	$0.478852\pi$
$678$		0			0
$679$	−5.56753	+	26.8821i	−0.213662	+	1.03164i
$680$			8.85666i			0.339637i
$681$		0			0
$682$			12.8938i			0.493728i
$683$		−	20.4853i		−	0.783848i	−0.919998	−	0.391924i	$-0.871810\pi$
$683$		−	20.4853i		−	0.783848i	0.919998	−	0.391924i	$-0.128190\pi$
$684$		0			0
$685$		−	1.80898i		−	0.0691177i
$686$	−10.6501	+	15.1518i	−0.406622	+	0.578497i
$687$		0			0
$688$	9.25725			0.352929
$689$	11.2273			0.427725
$690$		0			0
$691$			40.4968i			1.54057i	0.637698	+	0.770286i	$0.279887\pi$
$691$			40.4968i			1.54057i	−0.637698	+	0.770286i	$0.720113\pi$
$692$	−0.232053			−0.00882134
$693$		0			0
$694$	−10.8185			−0.410663
$695$		−	29.7644i		−	1.12903i
$696$		0			0
$697$	19.8623			0.752338
$698$	9.87806			0.373890
$699$		0			0
$700$	−24.4159	−	5.05675i	−0.922834	−	0.191127i
$701$			17.2261i			0.650619i	0.945608	+	0.325310i	$0.105469\pi$
$701$			17.2261i			0.650619i	−0.945608	+	0.325310i	$0.894531\pi$
$702$		0			0
$703$			24.4117i			0.920707i
$704$		−	1.61401i		−	0.0608305i
$705$		0			0
$706$		−	10.4167i		−	0.392039i
$707$	−19.9666	−	4.13527i	−0.750922	−	0.155523i
$708$		0			0
$709$	27.2472			1.02329			0.511645	−	0.859197i	$-0.329036\pi$
$709$	27.2472			1.02329			0.511645	+	0.859197i	$0.329036\pi$
$710$	−59.5013			−2.23304
$711$		0			0
$712$			17.5236i			0.656726i
$713$	20.9991			0.786424
$714$		0			0
$715$	−31.3375			−1.17196
$716$			24.4451i			0.913557i
$717$		0			0
$718$	9.97078			0.372106
$719$	−33.6709			−1.25571			−0.627857	−	0.778329i	$-0.716068\pi$
$719$	−33.6709			−1.25571			−0.627857	+	0.778329i	$0.716068\pi$
$720$		0			0
$721$	1.57317	−	7.59584i	0.0585878	−	0.282884i
$722$			0.969696i			0.0360883i
$723$		0			0
$724$			10.5527i			0.392187i
$725$			37.8344i			1.40514i
$726$		0			0
$727$			44.4862i			1.64990i	0.565205	+	0.824951i	$0.308797\pi$
$727$			44.4862i			1.64990i	−0.565205	+	0.824951i	$0.691203\pi$
$728$	13.2447	+	2.74309i	0.490880	+	0.101666i
$729$		0			0
$730$	29.0591			1.07553
$731$	−21.5877			−0.798450
$732$		0			0
$733$		−	15.7418i		−	0.581438i	−0.956809	−	0.290719i	$-0.906106\pi$
$733$		−	15.7418i		−	0.581438i	0.956809	−	0.290719i	$-0.0938944\pi$
$734$	24.2534			0.895211
$735$		0			0
$736$	−2.62863			−0.0968925
$737$		−	9.33053i		−	0.343694i
$738$		0			0
$739$	2.27818			0.0838043			0.0419022	−	0.999122i	$-0.486658\pi$
$739$	2.27818			0.0838043			0.0419022	+	0.999122i	$0.486658\pi$
$740$	21.8345			0.802652
$741$		0			0
$742$	5.68973	+	1.17839i	0.208876	+	0.0432602i
$743$		−	34.8955i		−	1.28019i	−0.768295	−	0.640096i	$-0.778894\pi$
$743$		−	34.8955i		−	1.28019i	0.768295	−	0.640096i	$-0.221106\pi$
$744$		0			0
$745$		−	74.9839i		−	2.74720i
$746$		−	2.65153i		−	0.0970794i
$747$		0			0
$748$			3.76384i			0.137620i
$749$	−6.60874	+	31.9095i	−0.241478	+	1.16595i
$750$		0			0
$751$	12.2409			0.446676			0.223338	−	0.974741i	$-0.428305\pi$
$751$	12.2409			0.446676			0.223338	+	0.974741i	$0.428305\pi$
$752$	9.69576			0.353568
$753$		0			0
$754$		−	20.5237i		−	0.747428i
$755$	46.2397			1.68283
$756$		0			0
$757$	−15.4361			−0.561036			−0.280518	−	0.959849i	$-0.590506\pi$
$757$	−15.4361			−0.561036			−0.280518	+	0.959849i	$0.590506\pi$
$758$		−	19.4305i		−	0.705748i
$759$		0			0
$760$	−16.1268			−0.584979
$761$	−10.4962			−0.380488			−0.190244	−	0.981737i	$-0.560928\pi$
$761$	−10.4962			−0.380488			−0.190244	+	0.981737i	$0.560928\pi$
$762$		0			0
$763$	3.82709	+	0.792625i	0.138550	+	0.0286950i
$764$		−	12.1732i		−	0.440413i
$765$		0			0
$766$		−	21.2320i		−	0.767143i
$767$			7.49425i			0.270602i
$768$		0			0
$769$			42.4382i			1.53036i	0.643815	+	0.765181i	$0.277351\pi$
$769$			42.4382i			1.53036i	−0.643815	+	0.765181i	$0.722649\pi$
$770$	−15.8811	−	3.28913i	−0.572317	−	0.118532i
$771$		0			0
$772$	24.3784			0.877397
$773$	−27.7852			−0.999366			−0.499683	−	0.866208i	$-0.666550\pi$
$773$	−27.7852			−0.999366			−0.499683	+	0.866208i	$0.666550\pi$
$774$		0			0
$775$		−	75.2863i		−	2.70436i
$776$	10.3761			0.372480
$777$		0			0
$778$	−4.47156			−0.160313
$779$			36.1665i			1.29580i
$780$		0			0
$781$	−25.2865			−0.904821
$782$	6.12989			0.219205
$783$		0			0
$784$	6.42418	+	2.78027i	0.229435	+	0.0992953i
$785$			38.2808i			1.36630i
$786$		0			0
$787$		−	33.1387i		−	1.18127i	−0.806940	−	0.590633i	$-0.798878\pi$
$787$		−	33.1387i		−	1.18127i	0.806940	−	0.590633i	$-0.201122\pi$
$788$		−	2.10759i		−	0.0750797i
$789$		0			0
$790$		−	6.24088i		−	0.222041i
$791$	3.71971	−	17.9602i	0.132258	−	0.638590i
$792$		0			0
$793$	73.6941			2.61695
$794$	−35.0315			−1.24322
$795$		0			0
$796$			19.1753i			0.679650i
$797$	−0.232053			−0.00821975			−0.00410987	−	0.999992i	$-0.501308\pi$
$797$	−0.232053			−0.00821975			−0.00410987	+	0.999992i	$0.501308\pi$
$798$		0			0
$799$	−22.6103			−0.799894
$800$			9.42418i			0.333195i
$801$		0			0
$802$	−21.3229			−0.752938
$803$	12.3494			0.435799
$804$		0			0
$805$	−5.35676	+	25.8645i	−0.188801	+	0.911602i
$806$			40.8399i			1.43852i
$807$		0			0
$808$			7.70683i			0.271125i
$809$		−	31.8244i		−	1.11889i	−0.828869	−	0.559443i	$-0.811015\pi$
$809$		−	31.8244i		−	1.11889i	0.828869	−	0.559443i	$-0.188985\pi$
$810$		0			0
$811$			28.9878i			1.01790i	0.860797	+	0.508949i	$0.169966\pi$
$811$			28.9878i			1.01790i	−0.860797	+	0.508949i	$0.830034\pi$
$812$	2.15413	−	10.4009i	0.0755951	−	0.365001i
$813$		0			0
$814$	9.27908			0.325231
$815$	−19.2150			−0.673071
$816$		0			0
$817$		−	39.3082i		−	1.37522i
$818$	24.0927			0.842382
$819$		0			0
$820$	32.3483			1.12965
$821$		−	11.9562i		−	0.417273i	−0.977993	−	0.208637i	$-0.933097\pi$
$821$		−	11.9562i		−	0.417273i	0.977993	−	0.208637i	$-0.0669026\pi$
$822$		0			0
$823$	−15.7729			−0.549807			−0.274904	−	0.961472i	$-0.588646\pi$
$823$	−15.7729			−0.549807			−0.274904	+	0.961472i	$0.588646\pi$
$824$	−2.93188			−0.102137
$825$		0			0
$826$	−0.786583	+	3.79792i	−0.0273687	+	0.132146i
$827$			13.4682i			0.468336i	0.972196	+	0.234168i	$0.0752366\pi$
$827$			13.4682i			0.468336i	−0.972196	+	0.234168i	$0.924763\pi$
$828$		0			0
$829$		−	14.7775i		−	0.513242i	−0.966512	−	0.256621i	$-0.917391\pi$
$829$		−	14.7775i		−	0.513242i	0.966512	−	0.256621i	$-0.0826092\pi$
$830$		−	11.4752i		−	0.398311i
$831$		0			0
$832$		−	5.11225i		−	0.177235i
$833$	−14.9810	−	6.48352i	−0.519062	−	0.224641i
$834$		0			0
$835$	9.06742			0.313791
$836$	−6.85345			−0.237031
$837$		0			0
$838$		−	25.8304i		−	0.892296i
$839$	41.3777			1.42852			0.714259	−	0.699881i	$-0.246764\pi$
$839$	41.3777			1.42852			0.714259	+	0.699881i	$0.246764\pi$
$840$		0			0
$841$	12.8829			0.444238
$842$		−	17.0648i		−	0.588091i
$843$		0			0
$844$	−8.67511			−0.298610
$845$	−49.8859			−1.71613
$846$		0			0
$847$	21.7494	+	4.50450i	0.747318	+	0.154776i
$848$		−	2.19615i		−	0.0754162i
$849$		0			0
$850$		−	21.9770i		−	0.753804i
$851$		−	15.1121i		−	0.518038i
$852$		0			0
$853$			9.08578i			0.311091i	0.987829	+	0.155546i	$0.0497135\pi$
$853$			9.08578i			0.311091i	−0.987829	+	0.155546i	$0.950286\pi$
$854$	37.3465	+	7.73479i	1.27797	+	0.264679i
$855$		0			0
$856$	12.3166			0.420972
$857$	−0.0314947			−0.00107584			−0.000537919	−	1.00000i	$-0.500171\pi$
$857$	−0.0314947			−0.00107584			−0.000537919		1.00000i	$0.500171\pi$
$858$		0			0
$859$		−	24.8682i		−	0.848493i	−0.905547	−	0.424246i	$-0.860539\pi$
$859$		−	24.8682i		−	0.848493i	0.905547	−	0.424246i	$-0.139461\pi$
$860$	−35.1583			−1.19889
$861$		0			0
$862$	−27.4224			−0.934011
$863$		−	13.7637i		−	0.468521i	−0.972174	−	0.234261i	$-0.924733\pi$
$863$		−	13.7637i		−	0.468521i	0.972174	−	0.234261i	$-0.0752669\pi$
$864$		0			0
$865$	0.881319			0.0299658
$866$	21.1385			0.718314
$867$		0			0
$868$	−4.28648	+	20.6967i	−0.145492	+	0.702492i
$869$		−	2.65221i		−	0.0899701i
$870$		0			0
$871$		−	29.5536i		−	1.00139i
$872$		−	1.47720i		−	0.0500244i
$873$		0			0
$874$			11.1617i			0.377550i
$875$	43.5319	+	9.01584i	1.47165	+	0.304791i
$876$		0			0
$877$	14.5812			0.492374			0.246187	−	0.969222i	$-0.420822\pi$
$877$	14.5812			0.492374			0.246187	+	0.969222i	$0.420822\pi$
$878$	−25.5428			−0.862029
$879$		0			0
$880$			6.12989i			0.206639i
$881$	24.9089			0.839201			0.419600	−	0.907709i	$-0.362170\pi$
$881$	24.9089			0.839201			0.419600	+	0.907709i	$0.362170\pi$
$882$		0			0
$883$	53.0681			1.78588			0.892942	−	0.450172i	$-0.148637\pi$
$883$	53.0681			1.78588			0.892942	+	0.450172i	$0.148637\pi$
$884$			11.9216i			0.400968i
$885$		0			0
$886$	30.9184			1.03873
$887$	39.1668			1.31509			0.657547	−	0.753414i	$-0.271594\pi$
$887$	39.1668			1.31509			0.657547	+	0.753414i	$0.271594\pi$
$888$		0			0
$889$	38.2725	+	7.92659i	1.28362	+	0.265849i
$890$		−	66.5534i		−	2.23087i
$891$		0			0
$892$			3.71748i			0.124470i
$893$		−	41.1702i		−	1.37771i
$894$		0			0
$895$		−	92.8405i		−	3.10332i
$896$	0.536572	−	2.59077i	0.0179256	−	0.0865516i
$897$		0			0
$898$	1.16428			0.0388524
$899$	32.0713			1.06964
$900$		0			0
$901$			5.12138i			0.170618i
$902$	13.7472			0.457730
$903$		0			0
$904$	−6.93237			−0.230567
$905$		−	40.0782i		−	1.33224i
$906$		0			0
$907$	27.8605			0.925094			0.462547	−	0.886595i	$-0.346936\pi$
$907$	27.8605			0.925094			0.462547	+	0.886595i	$0.346936\pi$
$908$	−3.21943			−0.106841
$909$		0			0
$910$	−50.3021	−	10.4180i	−1.66750	−	0.345354i
$911$		−	37.5327i		−	1.24351i	−0.783211	−	0.621756i	$-0.786419\pi$
$911$		−	37.5327i		−	1.24351i	0.783211	−	0.621756i	$-0.213581\pi$
$912$		0			0
$913$		−	4.87667i		−	0.161394i
$914$			7.21166i			0.238540i
$915$		0			0
$916$			8.99060i			0.297058i
$917$	19.9666	+	4.13527i	0.659356	+	0.136559i
$918$		0			0
$919$	−14.4325			−0.476083			−0.238042	−	0.971255i	$-0.576505\pi$
$919$	−14.4325			−0.476083			−0.238042	+	0.971255i	$0.576505\pi$
$920$	9.98331			0.329140
$921$		0			0
$922$			28.6513i			0.943579i
$923$	−80.0926			−2.63628
$924$		0			0
$925$	−54.1802			−1.78144
$926$		−	28.3402i		−	0.931316i
$927$		0			0
$928$	−4.01461			−0.131786
$929$	−6.00625			−0.197059			−0.0985293	−	0.995134i	$-0.531414\pi$
$929$	−6.00625			−0.197059			−0.0985293	+	0.995134i	$0.531414\pi$
$930$		0			0
$931$	11.8056	−	27.2784i	0.386913	−	0.894014i
$932$			10.1604i			0.332815i
$933$		0			0
$934$			10.2188i			0.334368i
$935$		−	14.2948i		−	0.467489i
$936$		0			0
$937$		−	7.11686i		−	0.232498i	−0.993220	−	0.116249i	$-0.962913\pi$
$937$		−	7.11686i		−	0.232498i	0.993220	−	0.116249i	$-0.0370870\pi$
$938$	3.10189	−	14.9771i	0.101280	−	0.489020i
$939$		0			0
$940$	−36.8237			−1.20106
$941$	−1.74214			−0.0567923			−0.0283961	−	0.999597i	$-0.509040\pi$
$941$	−1.74214			−0.0567923			−0.0283961	+	0.999597i	$0.509040\pi$
$942$		0			0
$943$		−	22.3890i		−	0.729085i
$944$	1.46594			0.0477123
$945$		0			0
$946$	−14.9413			−0.485785
$947$		−	40.4694i		−	1.31508i	−0.753421	−	0.657539i	$-0.771597\pi$
$947$		−	40.4694i		−	1.31508i	0.753421	−	0.657539i	$-0.228403\pi$
$948$		0			0
$949$	39.1155			1.26974
$950$	40.0171			1.29832
$951$		0			0
$952$	−1.25127	+	6.04162i	−0.0405540	+	0.195810i
$953$		−	14.0692i		−	0.455745i	−0.973691	−	0.227873i	$-0.926823\pi$
$953$		−	14.0692i		−	0.455745i	0.973691	−	0.227873i	$-0.0731770\pi$
$954$		0			0
$955$			46.2330i			1.49606i
$956$			3.59851i			0.116384i
$957$		0			0
$958$			12.6276i			0.407981i
$959$	0.255574	−	1.23401i	0.00825292	−	0.0398482i
$960$		0			0
$961$	−32.8183			−1.05865
$962$	29.3906			0.947592
$963$		0			0
$964$		−	23.2144i		−	0.747685i
$965$	−92.5871			−2.98048
$966$		0			0
$967$	32.6269			1.04921			0.524605	−	0.851346i	$-0.324213\pi$
$967$	32.6269			1.04921			0.524605	+	0.851346i	$0.324213\pi$
$968$		−	8.39496i		−	0.269824i
$969$		0			0
$970$	−39.4076			−1.26530
$971$	−35.0687			−1.12541			−0.562704	−	0.826658i	$-0.690239\pi$
$971$	−35.0687			−1.12541			−0.562704	+	0.826658i	$0.690239\pi$
$972$		0			0
$973$	4.20512	−	20.3039i	0.134810	−	0.650914i
$974$			21.8841i			0.701212i
$975$		0			0
$976$		−	14.4152i		−	0.461420i
$977$			26.7096i			0.854515i	0.904130	+	0.427258i	$0.140520\pi$
$977$			26.7096i			0.854515i	−0.904130	+	0.427258i	$0.859480\pi$
$978$		0			0
$979$		−	28.2834i		−	0.903942i
$980$	−24.3985	−	10.5592i	−0.779382	−	0.337302i
$981$		0			0
$982$	−7.60770			−0.242771
$983$	−17.9470			−0.572420			−0.286210	−	0.958167i	$-0.592396\pi$
$983$	−17.9470			−0.572420			−0.286210	+	0.958167i	$0.592396\pi$
$984$		0			0
$985$			8.00445i			0.255043i
$986$	9.36198			0.298146
$987$		0			0
$988$	−21.7077			−0.690613
$989$			24.3339i			0.773772i
$990$		0			0
$991$	25.9725			0.825043			0.412521	−	0.910948i	$-0.364648\pi$
$991$	25.9725			0.825043			0.412521	+	0.910948i	$0.364648\pi$
$992$	7.98863			0.253639
$993$		0			0
$994$	−40.5891	−	8.40638i	−1.28741	−	0.266634i
$995$		−	72.8261i		−	2.30874i
$996$		0			0
$997$			22.7106i			0.719252i	0.933097	+	0.359626i	$0.117096\pi$
$997$			22.7106i			0.719252i	−0.933097	+	0.359626i	$0.882904\pi$
$998$			3.85666i			0.122080i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.d.b.1133.16	yes	16
3.2	odd	2	inner	1134.2.d.b.1133.1	✓	16
7.6	odd	2	inner	1134.2.d.b.1133.9	yes	16
9.2	odd	6		1134.2.m.i.377.4		16
9.4	even	3		1134.2.m.i.755.1		16
9.5	odd	6		1134.2.m.h.755.8		16
9.7	even	3		1134.2.m.h.377.5		16
21.20	even	2	inner	1134.2.d.b.1133.8	yes	16
63.13	odd	6		1134.2.m.i.755.4		16
63.20	even	6		1134.2.m.i.377.1		16
63.34	odd	6		1134.2.m.h.377.8		16
63.41	even	6		1134.2.m.h.755.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.d.b.1133.1	✓	16	3.2	odd	2	inner
1134.2.d.b.1133.8	yes	16	21.20	even	2	inner
1134.2.d.b.1133.9	yes	16	7.6	odd	2	inner
1134.2.d.b.1133.16	yes	16	1.1	even	1	trivial
1134.2.m.h.377.5		16	9.7	even	3
1134.2.m.h.377.8		16	63.34	odd	6
1134.2.m.h.755.5		16	63.41	even	6
1134.2.m.h.755.8		16	9.5	odd	6
1134.2.m.i.377.1		16	63.20	even	6
1134.2.m.i.377.4		16	9.2	odd	6
1134.2.m.i.755.1		16	9.4	even	3
1134.2.m.i.755.4		16	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +3.79792 q^{5} +(2.59077 + 0.536572i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +3.79792 q^{5} +(2.59077 + 0.536572i) q^{7} -1.00000i q^{8} +3.79792i q^{10} +1.61401i q^{11} +5.11225i q^{13} +(-0.536572 + 2.59077i) q^{14} +1.00000 q^{16} -2.33198 q^{17} -4.24621i q^{19} -3.79792 q^{20} -1.61401 q^{22} +2.62863i q^{23} +9.42418 q^{25} -5.11225 q^{26} +(-2.59077 - 0.536572i) q^{28} +4.01461i q^{29} -7.98863i q^{31} +1.00000i q^{32} -2.33198i q^{34} +(9.83953 + 2.03786i) q^{35} -5.74907 q^{37} +4.24621 q^{38} -3.79792i q^{40} -8.51737 q^{41} +9.25725 q^{43} -1.61401i q^{44} -2.62863 q^{46} +9.69576 q^{47} +(6.42418 + 2.78027i) q^{49} +9.42418i q^{50} -5.11225i q^{52} -2.19615i q^{53} +6.12989i q^{55} +(0.536572 - 2.59077i) q^{56} -4.01461 q^{58} +1.46594 q^{59} -14.4152i q^{61} +7.98863 q^{62} -1.00000 q^{64} +19.4159i q^{65} -5.78094 q^{67} +2.33198 q^{68} +(-2.03786 + 9.83953i) q^{70} +15.6668i q^{71} -7.65133i q^{73} -5.74907i q^{74} +4.24621i q^{76} +(-0.866035 + 4.18154i) q^{77} -1.64324 q^{79} +3.79792 q^{80} -8.51737i q^{82} -3.02145 q^{83} -8.85666 q^{85} +9.25725i q^{86} +1.61401 q^{88} -17.5236 q^{89} +(-2.74309 + 13.2447i) q^{91} -2.62863i q^{92} +9.69576i q^{94} -16.1268i q^{95} +10.3761i q^{97} +(-2.78027 + 6.42418i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 8 * q^7	\( 16 q - 16 q^{4} + 8 q^{7} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{37} + 64 q^{43} - 32 q^{49} - 48 q^{58} - 16 q^{64} - 16 q^{67} - 24 q^{70} + 32 q^{79} - 48 q^{85} + 24 q^{91}+O(q^{100}) \) 16 * q - 16 * q^4 + 8 * q^7 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^37 + 64 * q^43 - 32 * q^49 - 48 * q^58 - 16 * q^64 - 16 * q^67 - 24 * q^70 + 32 * q^79 - 48 * q^85 + 24 * q^91

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