LMFDB - Embedded newform 450.2.p.b.407.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.407
Dual form			450.2.p.b.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-1.50000 - 0.866025i) q^{11} +(1.67303 - 0.448288i) q^{12} +(-6.69213 - 1.79315i) q^{13} +(0.500000 - 0.866025i) q^{16} +(-2.12132 + 2.12132i) q^{17} +(-0.776457 + 2.89778i) q^{18} -4.00000i q^{19} +(0.448288 - 1.67303i) q^{22} +(1.55291 - 5.79555i) q^{23} +(0.866025 + 1.50000i) q^{24} -6.92820i q^{26} +(-3.67423 - 3.67423i) q^{27} +(1.73205 - 3.00000i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.12132 + 2.12132i) q^{33} +(-2.59808 - 1.50000i) q^{34} -3.00000 q^{36} +(-4.89898 - 4.89898i) q^{37} +(3.86370 - 1.03528i) q^{38} +(10.3923 + 6.00000i) q^{39} +(-6.00000 + 3.46410i) q^{41} +(-2.24144 - 8.36516i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(3.10583 + 11.5911i) q^{47} +(-1.22474 + 1.22474i) q^{48} +(-6.06218 + 3.50000i) q^{49} +(4.50000 - 2.59808i) q^{51} +(6.69213 - 1.79315i) q^{52} +(8.48528 + 8.48528i) q^{53} +(2.59808 - 4.50000i) q^{54} +(-1.79315 + 6.69213i) q^{57} +(3.34607 + 0.896575i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-1.50000 + 2.59808i) q^{66} +(-0.896575 + 3.34607i) q^{67} +(0.776457 - 2.89778i) q^{68} +(-5.19615 + 9.00000i) q^{69} +3.46410i q^{71} +(-0.776457 - 2.89778i) q^{72} +(-4.89898 + 4.89898i) q^{73} +(3.46410 - 6.00000i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-3.10583 + 11.5911i) q^{78} +(-3.46410 - 2.00000i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-4.89898 - 4.89898i) q^{82} +(8.69333 - 2.32937i) q^{83} +(7.50000 - 4.33013i) q^{86} +(-4.24264 + 4.24264i) q^{87} +(0.448288 + 1.67303i) q^{88} -1.73205 q^{89} +(1.55291 + 5.79555i) q^{92} +(1.79315 + 6.69213i) q^{93} +(-10.3923 + 6.00000i) q^{94} +(-1.50000 - 0.866025i) q^{96} +(15.0573 - 4.03459i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(-2.59808 - 4.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 12 q^{11} + 4 q^{16} - 16 q^{31} - 24 q^{36} - 48 q^{41} + 48 q^{46} + 36 q^{51} - 32 q^{61} - 12 q^{66} + 16 q^{76} + 36 q^{81} + 60 q^{86} - 12 q^{96}+O(q^{100}) $ 8 * q - 12 * q^11 + 4 * q^16 - 16 * q^31 - 24 * q^36 - 48 * q^41 + 48 * q^46 + 36 * q^51 - 32 * q^61 - 12 * q^66 + 16 * q^76 + 36 * q^81 + 60 * q^86 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$7$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$		0			0
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	0.256520	−	0.966539i	$-0.417424\pi$
$11$	−1.50000	−	0.866025i	−0.452267	−	0.261116i	−0.708787	+	0.705422i	$0.750757\pi$
$12$	1.67303	−	0.448288i	0.482963	−	0.129410i
$13$	−6.69213	−	1.79315i	−1.85606	−	0.497331i	−0.856248	−	0.516565i	$-0.827210\pi$
$13$	−6.69213	−	1.79315i	−1.85606	−	0.497331i	−0.999815	+	0.0192343i	$0.993877\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.12132	+	2.12132i	−0.514496	+	0.514496i	−0.915901	−	0.401405i	$-0.868522\pi$
$17$	−2.12132	+	2.12132i	−0.514496	+	0.514496i	0.401405	+	0.915901i	$0.368522\pi$
$18$	−0.776457	+	2.89778i	−0.183013	+	0.683013i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		0			0
$22$	0.448288	−	1.67303i	0.0955753	−	0.356692i
$23$	1.55291	−	5.79555i	0.323805	−	1.20846i	−0.591703	−	0.806156i	$-0.701544\pi$
$23$	1.55291	−	5.79555i	0.323805	−	1.20846i	0.915508	−	0.402300i	$-0.131789\pi$
$24$	0.866025	+	1.50000i	0.176777	+	0.306186i
$25$		0			0
$26$		−	6.92820i		−	1.35873i
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$		0			0
$29$	1.73205	−	3.00000i	0.321634	−	0.557086i	−0.659192	−	0.751975i	$-0.729101\pi$
$29$	1.73205	−	3.00000i	0.321634	−	0.557086i	0.980825	+	0.194889i	$0.0624347\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	2.12132	+	2.12132i	0.369274	+	0.369274i
$34$	−2.59808	−	1.50000i	−0.445566	−	0.257248i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	0.178545	−	0.983932i	$-0.442861\pi$
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	−0.983932	+	0.178545i	$0.942861\pi$
$38$	3.86370	−	1.03528i	0.626775	−	0.167944i
$39$	10.3923	+	6.00000i	1.66410	+	0.960769i
$40$		0			0
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.889032	−	0.457845i	$-0.848621\pi$
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.0480106	+	0.998847i	$0.515288\pi$
$42$		0			0
$43$	−2.24144	−	8.36516i	−0.341816	−	1.27568i	−0.896288	−	0.443473i	$-0.853746\pi$
$43$	−2.24144	−	8.36516i	−0.341816	−	1.27568i	0.554472	−	0.832203i	$-0.312920\pi$
$44$	1.73205			0.261116
$45$		0			0
$46$	6.00000			0.884652
$47$	3.10583	+	11.5911i	0.453032	+	1.69074i	0.693811	+	0.720157i	$0.255930\pi$
$47$	3.10583	+	11.5911i	0.453032	+	1.69074i	−0.240779	+	0.970580i	$0.577403\pi$
$48$	−1.22474	+	1.22474i	−0.176777	+	0.176777i
$49$	−6.06218	+	3.50000i	−0.866025	+	0.500000i
$50$		0			0
$51$	4.50000	−	2.59808i	0.630126	−	0.363803i
$52$	6.69213	−	1.79315i	0.928032	−	0.248665i
$53$	8.48528	+	8.48528i	1.16554	+	1.16554i	0.983243	+	0.182300i	$0.0583542\pi$
$53$	8.48528	+	8.48528i	1.16554	+	1.16554i	0.182300	+	0.983243i	$0.441646\pi$
$54$	2.59808	−	4.50000i	0.353553	−	0.612372i
$55$		0			0
$56$		0			0
$57$	−1.79315	+	6.69213i	−0.237509	+	0.886394i
$58$	3.34607	+	0.896575i	0.439360	+	0.117726i
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	−0.997166	−	0.0752304i	$-0.976031\pi$
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	0.433432	−	0.901186i	$-0.357303\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.50000	+	2.59808i	−0.184637	+	0.319801i
$67$	−0.896575	+	3.34607i	−0.109534	+	0.408787i	−0.998820	−	0.0485648i	$-0.984535\pi$
$67$	−0.896575	+	3.34607i	−0.109534	+	0.408787i	0.889286	+	0.457352i	$0.151202\pi$
$68$	0.776457	−	2.89778i	0.0941593	−	0.351407i
$69$	−5.19615	+	9.00000i	−0.625543	+	1.08347i
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$	−0.776457	−	2.89778i	−0.0915064	−	0.341506i
$73$	−4.89898	+	4.89898i	−0.573382	+	0.573382i	−0.933072	−	0.359690i	$-0.882883\pi$
$73$	−4.89898	+	4.89898i	−0.573382	+	0.573382i	0.359690	+	0.933072i	$0.382883\pi$
$74$	3.46410	−	6.00000i	0.402694	−	0.697486i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$		0			0
$78$	−3.10583	+	11.5911i	−0.351666	+	1.31243i
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	0.292306	−	0.956325i	$-0.405577\pi$
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	−0.682048	+	0.731307i	$0.738911\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−4.89898	−	4.89898i	−0.541002	−	0.541002i
$83$	8.69333	−	2.32937i	0.954217	−	0.255682i	0.252066	−	0.967710i	$-0.418890\pi$
$83$	8.69333	−	2.32937i	0.954217	−	0.255682i	0.702151	+	0.712028i	$0.252223\pi$
$84$		0			0
$85$		0			0
$86$	7.50000	−	4.33013i	0.808746	−	0.466930i
$87$	−4.24264	+	4.24264i	−0.454859	+	0.454859i
$88$	0.448288	+	1.67303i	0.0477876	+	0.178346i
$89$	−1.73205			−0.183597			−0.0917985	−	0.995778i	$-0.529262\pi$
$89$	−1.73205			−0.183597			−0.0917985	+	0.995778i	$0.529262\pi$
$90$		0			0
$91$		0			0
$92$	1.55291	+	5.79555i	0.161903	+	0.604228i
$93$	1.79315	+	6.69213i	0.185941	+	0.693942i
$94$	−10.3923	+	6.00000i	−1.07188	+	0.618853i
$95$		0			0
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	15.0573	−	4.03459i	1.52884	−	0.409651i	0.606197	−	0.795314i	$-0.292694\pi$
$97$	15.0573	−	4.03459i	1.52884	−	0.409651i	0.922639	+	0.385664i	$0.126028\pi$
$98$	−4.94975	−	4.94975i	−0.500000	−	0.500000i
$99$	−2.59808	−	4.50000i	−0.261116	−	0.452267i
$100$		0			0
$101$	12.0000	+	6.92820i	1.19404	+	0.689382i	0.959221	−	0.282656i	$-0.0912155\pi$
$101$	12.0000	+	6.92820i	1.19404	+	0.689382i	0.234823	+	0.972038i	$0.424549\pi$
$102$	3.67423	+	3.67423i	0.363803	+	0.363803i
$103$	−6.69213	−	1.79315i	−0.659395	−	0.176684i	−0.0864221	−	0.996259i	$-0.527543\pi$
$103$	−6.69213	−	1.79315i	−0.659395	−	0.176684i	−0.572973	+	0.819574i	$0.694210\pi$
$104$	3.46410	+	6.00000i	0.339683	+	0.588348i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	−0.165848	−	0.986151i	$-0.553036\pi$
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	0.986151	+	0.165848i	$0.0530362\pi$
$108$	5.01910	+	1.34486i	0.482963	+	0.129410i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$	6.00000	+	10.3923i	0.569495	+	0.986394i
$112$		0			0
$113$	−0.776457	+	2.89778i	−0.0730429	+	0.272600i	−0.992782	−	0.119929i	$-0.961733\pi$
$113$	−0.776457	+	2.89778i	−0.0730429	+	0.272600i	0.919739	+	0.392529i	$0.128400\pi$
$114$	−6.92820			−0.648886
$115$		0			0
$116$			3.46410i			0.321634i
$117$	−14.6969	−	14.6969i	−1.35873	−	1.35873i
$118$	6.12372	−	6.12372i	0.563735	−	0.563735i
$119$		0			0
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$	−7.72741	−	2.07055i	−0.699607	−	0.187459i
$123$	11.5911	−	3.10583i	1.04514	−	0.280043i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$			15.0000i			1.32068i
$130$		0			0
$131$	−15.0000	+	8.66025i	−1.31056	+	0.756650i	−0.982188	−	0.187900i	$-0.939832\pi$
$131$	−15.0000	+	8.66025i	−1.31056	+	0.756650i	−0.328368	+	0.944550i	$0.606499\pi$
$132$	−2.89778	−	0.776457i	−0.252219	−	0.0675819i
$133$		0			0
$134$	−3.46410			−0.299253
$135$		0			0
$136$	3.00000			0.257248
$137$	−4.65874	−	17.3867i	−0.398023	−	1.48544i	−0.816569	−	0.577247i	$-0.804127\pi$
$137$	−4.65874	−	17.3867i	−0.398023	−	1.48544i	0.418546	−	0.908196i	$-0.362540\pi$
$138$	−10.0382	−	2.68973i	−0.854508	−	0.228965i
$139$	−11.2583	+	6.50000i	−0.954919	+	0.551323i	−0.894606	−	0.446857i	$-0.852543\pi$
$139$	−11.2583	+	6.50000i	−0.954919	+	0.551323i	−0.0603135	+	0.998179i	$0.519210\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$	−3.34607	+	0.896575i	−0.280796	+	0.0752389i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$		0			0
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	11.7112	−	3.13801i	0.965926	−	0.258819i
$148$	6.69213	+	1.79315i	0.550090	+	0.147396i
$149$	−5.19615	−	9.00000i	−0.425685	−	0.737309i	0.570799	−	0.821090i	$-0.306634\pi$
$149$	−5.19615	−	9.00000i	−0.425685	−	0.737309i	−0.996484	+	0.0837813i	$0.973300\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−2.82843	+	2.82843i	−0.229416	+	0.229416i
$153$	−8.69333	+	2.32937i	−0.702814	+	0.188319i
$154$		0			0
$155$		0			0
$156$	−12.0000			−0.960769
$157$	−1.79315	+	6.69213i	−0.143109	+	0.534090i	0.856723	+	0.515776i	$0.172496\pi$
$157$	−1.79315	+	6.69213i	−0.143109	+	0.534090i	−0.999832	+	0.0183138i	$0.994170\pi$
$158$	1.03528	−	3.86370i	0.0823622	−	0.307380i
$159$	−10.3923	−	18.0000i	−0.824163	−	1.42749i
$160$		0			0
$161$		0			0
$162$	−6.36396	+	6.36396i	−0.500000	+	0.500000i
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	−0.753443	−	0.657513i	$-0.771608\pi$
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	0.657513	+	0.753443i	$0.271608\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$		0			0
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	5.79555	+	1.55291i	0.448474	+	0.120168i	0.475985	−	0.879453i	$-0.342092\pi$
$167$	5.79555	+	1.55291i	0.448474	+	0.120168i	−0.0275115	+	0.999621i	$0.508758\pi$
$168$		0			0
$169$	30.3109	+	17.5000i	2.33161	+	1.34615i
$170$		0			0
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$	6.12372	+	6.12372i	0.466930	+	0.466930i
$173$	−17.3867	+	4.65874i	−1.32188	+	0.354198i	−0.849683	−	0.527294i	$-0.823207\pi$
$173$	−17.3867	+	4.65874i	−1.32188	+	0.354198i	−0.472200	+	0.881491i	$0.656540\pi$
$174$	−5.19615	−	3.00000i	−0.393919	−	0.227429i
$175$		0			0
$176$	−1.50000	+	0.866025i	−0.113067	+	0.0652791i
$177$	3.88229	+	14.4889i	0.291810	+	1.08905i
$178$	−0.448288	−	1.67303i	−0.0336006	−	0.125399i
$179$	12.1244			0.906217			0.453108	−	0.891455i	$-0.350315\pi$
$179$	12.1244			0.906217			0.453108	+	0.891455i	$0.350315\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	9.79796	−	9.79796i	0.724286	−	0.724286i
$184$	−5.19615	+	3.00000i	−0.383065	+	0.221163i
$185$		0			0
$186$	−6.00000	+	3.46410i	−0.439941	+	0.254000i
$187$	5.01910	−	1.34486i	0.367033	−	0.0983461i
$188$	−8.48528	−	8.48528i	−0.618853	−	0.618853i
$189$		0			0
$190$		0			0
$191$	3.00000	+	1.73205i	0.217072	+	0.125327i	0.604594	−	0.796534i	$-0.293335\pi$
$191$	3.00000	+	1.73205i	0.217072	+	0.125327i	−0.387522	+	0.921861i	$0.626669\pi$
$192$	0.448288	−	1.67303i	0.0323524	−	0.120741i
$193$	5.01910	+	1.34486i	0.361283	+	0.0968054i	0.434894	−	0.900482i	$-0.356786\pi$
$193$	5.01910	+	1.34486i	0.361283	+	0.0968054i	−0.0736115	+	0.997287i	$0.523452\pi$
$194$	7.79423	+	13.5000i	0.559593	+	0.969244i
$195$		0			0
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	−0.841904	−	0.539628i	$-0.818565\pi$
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	0.539628	+	0.841904i	$0.318565\pi$
$198$	3.67423	−	3.67423i	0.261116	−	0.261116i
$199$		−	26.0000i		−	1.84309i	−0.388270	−	0.921546i	$-0.626927\pi$
$199$		−	26.0000i		−	1.84309i	0.388270	−	0.921546i	$-0.373073\pi$
$200$		0			0
$201$	3.00000	−	5.19615i	0.211604	−	0.366508i
$202$	−3.58630	+	13.3843i	−0.252331	+	0.941713i
$203$		0			0
$204$	−2.59808	+	4.50000i	−0.181902	+	0.315063i
$205$		0			0
$206$		−	6.92820i		−	0.482711i
$207$	12.7279	−	12.7279i	0.884652	−	0.884652i
$208$	−4.89898	+	4.89898i	−0.339683	+	0.339683i
$209$	−3.46410	+	6.00000i	−0.239617	+	0.415029i
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	−11.5911	−	3.10583i	−0.796081	−	0.213309i
$213$	1.55291	−	5.79555i	0.106404	−	0.397105i
$214$	10.3923	+	6.00000i	0.710403	+	0.410152i
$215$		0			0
$216$			5.19615i			0.353553i
$217$		0			0
$218$	1.93185	−	0.517638i	0.130842	−	0.0350589i
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$		0			0
$221$	18.0000	−	10.3923i	1.21081	−	0.699062i
$222$	−8.48528	+	8.48528i	−0.569495	+	0.569495i
$223$	0.896575	+	3.34607i	0.0600391	+	0.224069i	0.989426	−	0.145038i	$-0.0463303\pi$
$223$	0.896575	+	3.34607i	0.0600391	+	0.224069i	−0.929387	+	0.369107i	$0.879664\pi$
$224$		0			0
$225$		0			0
$226$	−3.00000			−0.199557
$227$	0.776457	+	2.89778i	0.0515353	+	0.192332i	0.986894	−	0.161367i	$-0.0515903\pi$
$227$	0.776457	+	2.89778i	0.0515353	+	0.192332i	−0.935359	+	0.353699i	$0.884924\pi$
$228$	−1.79315	−	6.69213i	−0.118754	−	0.443197i
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.197013	−	0.980401i	$-0.436876\pi$
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.947559	+	0.319582i	$0.103543\pi$
$230$		0			0
$231$		0			0
$232$	−3.34607	+	0.896575i	−0.219680	+	0.0588631i
$233$	−6.36396	−	6.36396i	−0.416917	−	0.416917i	0.467223	−	0.884140i	$-0.345255\pi$
$233$	−6.36396	−	6.36396i	−0.416917	−	0.416917i	−0.884140	+	0.467223i	$0.845255\pi$
$234$	10.3923	−	18.0000i	0.679366	−	1.17670i
$235$		0			0
$236$	7.50000	+	4.33013i	0.488208	+	0.281867i
$237$	4.89898	+	4.89898i	0.318223	+	0.318223i
$238$		0			0
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	0.983698	−	0.179830i	$-0.0575549\pi$
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	−0.647586	+	0.761992i	$0.724222\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	5.65685	−	5.65685i	0.363636	−	0.363636i
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$		−	8.00000i		−	0.512148i
$245$		0			0
$246$	6.00000	+	10.3923i	0.382546	+	0.662589i
$247$	−7.17260	+	26.7685i	−0.456382	+	1.70324i
$248$	−1.03528	+	3.86370i	−0.0657401	+	0.245345i
$249$	−15.5885			−0.987878
$250$		0			0
$251$		−	10.3923i		−	0.655956i	−0.944685	−	0.327978i	$-0.893633\pi$
$251$		−	10.3923i		−	0.655956i	0.944685	−	0.327978i	$-0.106367\pi$
$252$		0			0
$253$	−7.34847	+	7.34847i	−0.461994	+	0.461994i
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.89778	−	0.776457i	−0.180758	−	0.0484341i	0.167304	−	0.985905i	$-0.446494\pi$
$257$	−2.89778	−	0.776457i	−0.180758	−	0.0484341i	−0.348063	+	0.937471i	$0.613160\pi$
$258$	−14.4889	+	3.88229i	−0.902039	+	0.241701i
$259$		0			0
$260$		0			0
$261$	9.00000	−	5.19615i	0.557086	−	0.321634i
$262$	−12.2474	−	12.2474i	−0.756650	−	0.756650i
$263$	−23.1822	+	6.21166i	−1.42948	+	0.383027i	−0.888836	−	0.458226i	$-0.848485\pi$
$263$	−23.1822	+	6.21166i	−1.42948	+	0.383027i	−0.540641	+	0.841253i	$0.681818\pi$
$264$		−	3.00000i		−	0.184637i
$265$		0			0
$266$		0			0
$267$	2.89778	+	0.776457i	0.177341	+	0.0475184i
$268$	−0.896575	−	3.34607i	−0.0547671	−	0.204393i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	0.776457	+	2.89778i	0.0470796	+	0.175704i
$273$		0			0
$274$	15.5885	−	9.00000i	0.941733	−	0.543710i
$275$		0			0
$276$		−	10.3923i		−	0.625543i
$277$	3.34607	−	0.896575i	0.201046	−	0.0538700i	−0.156891	−	0.987616i	$-0.550147\pi$
$277$	3.34607	−	0.896575i	0.201046	−	0.0538700i	0.357936	+	0.933746i	$0.383480\pi$
$278$	−9.19239	−	9.19239i	−0.551323	−	0.551323i
$279$		−	12.0000i		−	0.718421i
$280$		0			0
$281$	−18.0000	−	10.3923i	−1.07379	−	0.619953i	−0.144575	−	0.989494i	$-0.546182\pi$
$281$	−18.0000	−	10.3923i	−1.07379	−	0.619953i	−0.929214	+	0.369541i	$0.879515\pi$
$282$	20.0764	−	5.37945i	1.19553	−	0.320342i
$283$	31.7876	+	8.51747i	1.88958	+	0.506311i	0.998637	+	0.0521913i	$0.0166205\pi$
$283$	31.7876	+	8.51747i	1.88958	+	0.506311i	0.890941	+	0.454120i	$0.150046\pi$
$284$	−1.73205	−	3.00000i	−0.102778	−	0.178017i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$	2.12132	+	2.12132i	0.125000	+	0.125000i
$289$			8.00000i			0.470588i
$290$		0			0
$291$	−27.0000			−1.58277
$292$	1.79315	−	6.69213i	0.104936	−	0.391627i
$293$	−3.10583	+	11.5911i	−0.181444	+	0.677160i	0.813919	+	0.580978i	$0.197330\pi$
$293$	−3.10583	+	11.5911i	−0.181444	+	0.677160i	−0.995364	+	0.0961820i	$0.969337\pi$
$294$	6.06218	+	10.5000i	0.353553	+	0.612372i
$295$		0			0
$296$			6.92820i			0.402694i
$297$	2.32937	+	8.69333i	0.135164	+	0.504438i
$298$	7.34847	−	7.34847i	0.425685	−	0.425685i
$299$	−20.7846	+	36.0000i	−1.20201	+	2.08193i
$300$		0			0
$301$		0			0
$302$	1.93185	+	0.517638i	0.111166	+	0.0297867i
$303$	−16.9706	−	16.9706i	−0.974933	−	0.974933i
$304$	−3.46410	−	2.00000i	−0.198680	−	0.114708i
$305$		0			0
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	−15.9217	−	15.9217i	−0.908698	−	0.908698i	0.0874688	−	0.996167i	$-0.472122\pi$
$307$	−15.9217	−	15.9217i	−0.908698	−	0.908698i	−0.996167	+	0.0874688i	$0.972122\pi$
$308$		0			0
$309$	10.3923	+	6.00000i	0.591198	+	0.341328i
$310$		0			0
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	−0.582640	−	0.812731i	$-0.697980\pi$
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	0.412525	+	0.910946i	$0.364647\pi$
$312$	−3.10583	−	11.5911i	−0.175833	−	0.656217i
$313$	−0.448288	−	1.67303i	−0.0253387	−	0.0945654i	0.952099	−	0.305791i	$-0.0989210\pi$
$313$	−0.448288	−	1.67303i	−0.0253387	−	0.0945654i	−0.977437	+	0.211226i	$0.932254\pi$
$314$	−6.92820			−0.390981
$315$		0			0
$316$	4.00000			0.225018
$317$	−7.76457	−	28.9778i	−0.436102	−	1.62755i	−0.738416	−	0.674346i	$-0.764426\pi$
$317$	−7.76457	−	28.9778i	−0.436102	−	1.62755i	0.302314	−	0.953208i	$-0.402241\pi$
$318$	14.6969	−	14.6969i	0.824163	−	0.824163i
$319$	−5.19615	+	3.00000i	−0.290929	+	0.167968i
$320$		0			0
$321$	−18.0000	+	10.3923i	−1.00466	+	0.580042i
$322$		0			0
$323$	8.48528	+	8.48528i	0.472134	+	0.472134i
$324$	−7.79423	−	4.50000i	−0.433013	−	0.250000i
$325$		0			0
$326$	−1.50000	−	0.866025i	−0.0830773	−	0.0479647i
$327$	−0.896575	+	3.34607i	−0.0495807	+	0.185038i
$328$	6.69213	+	1.79315i	0.369511	+	0.0990102i
$329$		0			0
$330$		0			0
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$	−6.36396	+	6.36396i	−0.349268	+	0.349268i
$333$	−5.37945	−	20.0764i	−0.294792	−	1.10018i
$334$			6.00000i			0.328305i
$335$		0			0
$336$		0			0
$337$	2.24144	−	8.36516i	0.122099	−	0.455679i	−0.877621	−	0.479356i	$-0.840870\pi$
$337$	2.24144	−	8.36516i	0.122099	−	0.455679i	0.999720	+	0.0236762i	$0.00753707\pi$
$338$	−9.05867	+	33.8074i	−0.492727	+	1.83888i
$339$	2.59808	−	4.50000i	0.141108	−	0.244406i
$340$		0			0
$341$			6.92820i			0.375183i
$342$	11.5911	+	3.10583i	0.626775	+	0.167944i
$343$		0			0
$344$	−4.33013	+	7.50000i	−0.233465	+	0.404373i
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	20.2844	+	5.43520i	1.08893	+	0.291777i	0.758248	−	0.651967i	$-0.226056\pi$
$347$	20.2844	+	5.43520i	1.08893	+	0.291777i	0.330678	+	0.943744i	$0.392722\pi$
$348$	1.55291	−	5.79555i	0.0832449	−	0.310674i
$349$	8.66025	+	5.00000i	0.463573	+	0.267644i	0.713545	−	0.700609i	$-0.247088\pi$
$349$	8.66025	+	5.00000i	0.463573	+	0.267644i	−0.249973	+	0.968253i	$0.580422\pi$
$350$		0			0
$351$	18.0000	+	31.1769i	0.960769	+	1.66410i
$352$	−1.22474	−	1.22474i	−0.0652791	−	0.0652791i
$353$	−8.69333	+	2.32937i	−0.462699	+	0.123980i	−0.482635	−	0.875821i	$-0.660320\pi$
$353$	−8.69333	+	2.32937i	−0.462699	+	0.123980i	0.0199361	+	0.999801i	$0.493654\pi$
$354$	−12.9904	+	7.50000i	−0.690431	+	0.398621i
$355$		0			0
$356$	1.50000	−	0.866025i	0.0794998	−	0.0458993i
$357$		0			0
$358$	3.13801	+	11.7112i	0.165849	+	0.618958i
$359$	−13.8564			−0.731313			−0.365657	−	0.930750i	$-0.619156\pi$
$359$	−13.8564			−0.731313			−0.365657	+	0.930750i	$0.619156\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−0.517638	−	1.93185i	−0.0272065	−	0.101536i
$363$	3.58630	+	13.3843i	0.188232	+	0.702492i
$364$		0			0
$365$		0			0
$366$	12.0000	+	6.92820i	0.627250	+	0.362143i
$367$	−23.4225	+	6.27603i	−1.22264	+	0.327606i	−0.811710	−	0.584060i	$-0.801463\pi$
$367$	−23.4225	+	6.27603i	−1.22264	+	0.327606i	−0.410932	+	0.911666i	$0.634797\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$	−20.7846			−1.08200
$370$		0			0
$371$		0			0
$372$	−4.89898	−	4.89898i	−0.254000	−	0.254000i
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$	2.59808	+	4.50000i	0.134343	+	0.232689i
$375$		0			0
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	−16.9706	+	16.9706i	−0.874028	+	0.874028i
$378$		0			0
$379$		−	19.0000i		−	0.975964i	−0.872854	−	0.487982i	$-0.837733\pi$
$379$		−	19.0000i		−	0.975964i	0.872854	−	0.487982i	$-0.162267\pi$
$380$		0			0
$381$		0			0
$382$	−0.896575	+	3.34607i	−0.0458728	+	0.171200i
$383$	7.76457	−	28.9778i	0.396751	−	1.48070i	−0.422026	−	0.906584i	$-0.638681\pi$
$383$	7.76457	−	28.9778i	0.396751	−	1.48070i	0.818777	−	0.574111i	$-0.194652\pi$
$384$	1.73205			0.0883883
$385$		0			0
$386$			5.19615i			0.264477i
$387$	6.72432	−	25.0955i	0.341816	−	1.27568i
$388$	−11.0227	+	11.0227i	−0.559593	+	0.559593i
$389$	−5.19615	+	9.00000i	−0.263455	+	0.456318i	−0.967158	−	0.254177i	$-0.918196\pi$
$389$	−5.19615	+	9.00000i	−0.263455	+	0.456318i	0.703702	+	0.710495i	$0.251529\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	6.76148	+	1.81173i	0.341506	+	0.0915064i
$393$	28.9778	−	7.76457i	1.46174	−	0.391671i
$394$	−5.19615	−	3.00000i	−0.261778	−	0.151138i
$395$		0			0
$396$	4.50000	+	2.59808i	0.226134	+	0.130558i
$397$	−2.44949	−	2.44949i	−0.122936	−	0.122936i	0.642962	−	0.765898i	$-0.277705\pi$
$397$	−2.44949	−	2.44949i	−0.122936	−	0.122936i	−0.765898	+	0.642962i	$0.777705\pi$
$398$	25.1141	−	6.72930i	1.25885	−	0.337309i
$399$		0			0
$400$		0			0
$401$	22.5000	−	12.9904i	1.12360	−	0.648709i	0.181280	−	0.983432i	$-0.441976\pi$
$401$	22.5000	−	12.9904i	1.12360	−	0.648709i	0.942317	+	0.334723i	$0.108643\pi$
$402$	5.79555	+	1.55291i	0.289056	+	0.0774523i
$403$	7.17260	+	26.7685i	0.357293	+	1.33344i
$404$	−13.8564			−0.689382
$405$		0			0
$406$		0			0
$407$	3.10583	+	11.5911i	0.153950	+	0.574550i
$408$	−5.01910	−	1.34486i	−0.248482	−	0.0665807i
$409$	1.73205	−	1.00000i	0.0856444	−	0.0494468i	−0.456566	−	0.889689i	$-0.650921\pi$
$409$	1.73205	−	1.00000i	0.0856444	−	0.0494468i	0.542211	+	0.840243i	$0.317588\pi$
$410$		0			0
$411$			31.1769i			1.53784i
$412$	6.69213	−	1.79315i	0.329698	−	0.0883422i
$413$		0			0
$414$	15.5885	+	9.00000i	0.766131	+	0.442326i
$415$		0			0
$416$	−6.00000	−	3.46410i	−0.294174	−	0.169842i
$417$	21.7494	−	5.82774i	1.06507	−	0.285386i
$418$	−6.69213	−	1.79315i	−0.327323	−	0.0877059i
$419$	2.59808	+	4.50000i	0.126924	+	0.219839i	0.922484	−	0.386037i	$-0.126156\pi$
$419$	2.59808	+	4.50000i	0.126924	+	0.219839i	−0.795559	+	0.605876i	$0.792823\pi$
$420$		0			0
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	0.291953	+	0.956433i	$0.405695\pi$
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	−0.974272	+	0.225377i	$0.927639\pi$
$422$	16.2635	−	16.2635i	0.791693	−	0.791693i
$423$	−9.31749	+	34.7733i	−0.453032	+	1.69074i
$424$		−	12.0000i		−	0.582772i
$425$		0			0
$426$	6.00000			0.290701
$427$		0			0
$428$	−3.10583	+	11.5911i	−0.150126	+	0.560277i
$429$	−10.3923	−	18.0000i	−0.501745	−	0.869048i
$430$		0			0
$431$			24.2487i			1.16802i	0.811747	+	0.584010i	$0.198517\pi$
$431$			24.2487i			1.16802i	−0.811747	+	0.584010i	$0.801483\pi$
$432$	−5.01910	+	1.34486i	−0.241481	+	0.0647048i
$433$	20.8207	−	20.8207i	1.00058	−	1.00058i	0.000577367	−	1.00000i	$-0.499816\pi$
$433$	20.8207	−	20.8207i	1.00058	−	1.00058i	1.00000		0.000577367i	$-0.000183782\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−23.1822	−	6.21166i	−1.10896	−	0.297144i
$438$	8.48528	+	8.48528i	0.405442	+	0.405442i
$439$	−8.66025	−	5.00000i	−0.413331	−	0.238637i	0.278889	−	0.960323i	$-0.410034\pi$
$439$	−8.66025	−	5.00000i	−0.413331	−	0.238637i	−0.692220	+	0.721686i	$0.743367\pi$
$440$		0			0
$441$	−21.0000			−1.00000
$442$	14.6969	+	14.6969i	0.699062	+	0.699062i
$443$	−8.69333	+	2.32937i	−0.413033	+	0.110672i	−0.459351	−	0.888255i	$-0.651918\pi$
$443$	−8.69333	+	2.32937i	−0.413033	+	0.110672i	0.0463181	+	0.998927i	$0.485251\pi$
$444$	−10.3923	−	6.00000i	−0.493197	−	0.284747i
$445$		0			0
$446$	−3.00000	+	1.73205i	−0.142054	+	0.0820150i
$447$	4.65874	+	17.3867i	0.220351	+	0.822361i
$448$		0			0
$449$	34.6410			1.63481			0.817405	−	0.576063i	$-0.195412\pi$
$449$	34.6410			1.63481			0.817405	+	0.576063i	$0.195412\pi$
$450$		0			0
$451$	12.0000			0.565058
$452$	−0.776457	−	2.89778i	−0.0365215	−	0.136300i
$453$	−2.44949	+	2.44949i	−0.115087	+	0.115087i
$454$	−2.59808	+	1.50000i	−0.121934	+	0.0703985i
$455$		0			0
$456$	6.00000	−	3.46410i	0.280976	−	0.162221i
$457$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$457$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$458$	14.1421	+	14.1421i	0.660819	+	0.660819i
$459$	15.5885			0.727607
$460$		0			0
$461$	15.0000	+	8.66025i	0.698620	+	0.403348i	0.806833	−	0.590779i	$-0.201180\pi$
$461$	15.0000	+	8.66025i	0.698620	+	0.403348i	−0.108213	+	0.994128i	$0.534513\pi$
$462$		0			0
$463$	−3.34607	−	0.896575i	−0.155505	−	0.0416674i	0.180227	−	0.983625i	$-0.442317\pi$
$463$	−3.34607	−	0.896575i	−0.155505	−	0.0416674i	−0.335732	+	0.941958i	$0.608984\pi$
$464$	−1.73205	−	3.00000i	−0.0804084	−	0.139272i
$465$		0			0
$466$	4.50000	−	7.79423i	0.208458	−	0.361061i
$467$	−10.6066	+	10.6066i	−0.490815	+	0.490815i	−0.908563	−	0.417748i	$-0.862820\pi$
$467$	−10.6066	+	10.6066i	−0.490815	+	0.490815i	0.417748	+	0.908563i	$0.362820\pi$
$468$	20.0764	+	5.37945i	0.928032	+	0.248665i
$469$		0			0
$470$		0			0
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$	−2.24144	+	8.36516i	−0.103171	+	0.385038i
$473$	−3.88229	+	14.4889i	−0.178508	+	0.666200i
$474$	−3.46410	+	6.00000i	−0.159111	+	0.275589i
$475$		0			0
$476$		0			0
$477$	9.31749	+	34.7733i	0.426618	+	1.59216i
$478$	−7.34847	+	7.34847i	−0.336111	+	0.336111i
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	−0.775969	−	0.630771i	$-0.782739\pi$
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	0.934248	+	0.356624i	$0.116072\pi$
$480$		0			0
$481$	24.0000	+	41.5692i	1.09431	+	1.89539i
$482$	9.65926	+	2.58819i	0.439967	+	0.117889i
$483$		0			0
$484$	6.92820	+	4.00000i	0.314918	+	0.181818i
$485$		0			0
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	12.2474	+	12.2474i	0.554985	+	0.554985i	0.927875	−	0.372890i	$-0.121633\pi$
$487$	12.2474	+	12.2474i	0.554985	+	0.554985i	−0.372890	+	0.927875i	$0.621633\pi$
$488$	7.72741	−	2.07055i	0.349803	−	0.0937295i
$489$	2.59808	−	1.50000i	0.117489	−	0.0678323i
$490$		0			0
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.870666	−	0.491875i	$-0.836312\pi$
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.00935679	+	0.999956i	$0.502978\pi$
$492$	−8.48528	+	8.48528i	−0.382546	+	0.382546i
$493$	2.68973	+	10.0382i	0.121139	+	0.452098i
$494$	−27.7128			−1.24686
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$	−4.03459	−	15.0573i	−0.180794	−	0.674733i
$499$	−4.33013	+	2.50000i	−0.193843	+	0.111915i	−0.593780	−	0.804627i	$-0.702365\pi$
$499$	−4.33013	+	2.50000i	−0.193843	+	0.111915i	0.399937	+	0.916542i	$0.369032\pi$
$500$		0			0
$501$	−9.00000	−	5.19615i	−0.402090	−	0.232147i
$502$	10.0382	−	2.68973i	0.448027	−	0.120048i
$503$	−16.9706	−	16.9706i	−0.756680	−	0.756680i	0.219037	−	0.975717i	$-0.429709\pi$
$503$	−16.9706	−	16.9706i	−0.756680	−	0.756680i	−0.975717	+	0.219037i	$0.929709\pi$
$504$		0			0
$505$		0			0
$506$	−9.00000	−	5.19615i	−0.400099	−	0.230997i
$507$	−42.8661	−	42.8661i	−1.90375	−	1.90375i
$508$		0			0
$509$	−15.5885	−	27.0000i	−0.690946	−	1.19675i	−0.971528	−	0.236924i	$-0.923861\pi$
$509$	−15.5885	−	27.0000i	−0.690946	−	1.19675i	0.280582	−	0.959830i	$-0.409473\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−14.6969	+	14.6969i	−0.648886	+	0.648886i
$514$		−	3.00000i		−	0.132324i
$515$		0			0
$516$	−7.50000	−	12.9904i	−0.330169	−	0.571870i
$517$	5.37945	−	20.0764i	0.236588	−	0.882959i
$518$		0			0
$519$	31.1769			1.36851
$520$		0			0
$521$			5.19615i			0.227648i	0.993501	+	0.113824i	$0.0363099\pi$
$521$			5.19615i			0.227648i	−0.993501	+	0.113824i	$0.963690\pi$
$522$	7.34847	+	7.34847i	0.321634	+	0.321634i
$523$	18.3712	−	18.3712i	0.803315	−	0.803315i	−0.180297	−	0.983612i	$-0.557706\pi$
$523$	18.3712	−	18.3712i	0.803315	−	0.803315i	0.983612	+	0.180297i	$0.0577059\pi$
$524$	8.66025	−	15.0000i	0.378325	−	0.655278i
$525$		0			0
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$	11.5911	+	3.10583i	0.504917	+	0.135292i
$528$	2.89778	−	0.776457i	0.126110	−	0.0337910i
$529$	−11.2583	−	6.50000i	−0.489493	−	0.282609i
$530$		0			0
$531$		−	25.9808i		−	1.12747i
$532$		0			0
$533$	46.3644	−	12.4233i	2.00827	−	0.538113i
$534$			3.00000i			0.129823i
$535$		0			0
$536$	3.00000	−	1.73205i	0.129580	−	0.0748132i
$537$	−20.2844	−	5.43520i	−0.875338	−	0.234546i
$538$	−1.79315	−	6.69213i	−0.0773082	−	0.288518i
$539$	12.1244			0.522233
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	2.07055	+	7.72741i	0.0889378	+	0.331921i
$543$	3.34607	+	0.896575i	0.143593	+	0.0384757i
$544$	−2.59808	+	1.50000i	−0.111392	+	0.0643120i
$545$		0			0
$546$		0			0
$547$	−16.7303	+	4.48288i	−0.715337	+	0.191674i	−0.598090	−	0.801429i	$-0.704074\pi$
$547$	−16.7303	+	4.48288i	−0.715337	+	0.191674i	−0.117247	+	0.993103i	$0.537407\pi$
$548$	12.7279	+	12.7279i	0.543710	+	0.543710i
$549$	−20.7846	+	12.0000i	−0.887066	+	0.512148i
$550$		0			0
$551$	−12.0000	−	6.92820i	−0.511217	−	0.295151i
$552$	10.0382	−	2.68973i	0.427254	−	0.114482i
$553$		0			0
$554$	1.73205	+	3.00000i	0.0735878	+	0.127458i
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	−4.24264	+	4.24264i	−0.179766	+	0.179766i	−0.791254	−	0.611488i	$-0.790571\pi$
$557$	−4.24264	+	4.24264i	−0.179766	+	0.179766i	0.611488	+	0.791254i	$0.290571\pi$
$558$	11.5911	−	3.10583i	0.490691	−	0.131480i
$559$			60.0000i			2.53773i
$560$		0			0
$561$	−9.00000			−0.379980
$562$	5.37945	−	20.0764i	0.226919	−	0.846871i
$563$	5.43520	−	20.2844i	0.229066	−	0.854887i	−0.751668	−	0.659542i	$-0.770750\pi$
$563$	5.43520	−	20.2844i	0.229066	−	0.854887i	0.980734	−	0.195346i	$-0.0625829\pi$
$564$	10.3923	+	18.0000i	0.437595	+	0.757937i
$565$		0			0
$566$			32.9090i			1.38327i
$567$		0			0
$568$	2.44949	−	2.44949i	0.102778	−	0.102778i
$569$	16.4545	−	28.5000i	0.689808	−	1.19478i	−0.282092	−	0.959387i	$-0.591028\pi$
$569$	16.4545	−	28.5000i	0.689808	−	1.19478i	0.971900	−	0.235395i	$-0.0756383\pi$
$570$		0			0
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	0.631526	−	0.775355i	$-0.282429\pi$
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	−0.987240	+	0.159240i	$0.949096\pi$
$572$	−11.5911	−	3.10583i	−0.484649	−	0.129861i
$573$	−4.24264	−	4.24264i	−0.177239	−	0.177239i
$574$		0			0
$575$		0			0
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	14.6969	+	14.6969i	0.611842	+	0.611842i	0.943426	−	0.331584i	$-0.107583\pi$
$577$	14.6969	+	14.6969i	0.611842	+	0.611842i	−0.331584	+	0.943426i	$0.607583\pi$
$578$	−7.72741	+	2.07055i	−0.321418	+	0.0861236i
$579$	−7.79423	−	4.50000i	−0.323917	−	0.187014i
$580$		0			0
$581$		0			0
$582$	−6.98811	−	26.0800i	−0.289667	−	1.08105i
$583$	−5.37945	−	20.0764i	−0.222794	−	0.831479i
$584$	6.92820			0.286691
$585$		0			0
$586$	−12.0000			−0.495715
$587$	−6.98811	−	26.0800i	−0.288430	−	1.07644i	−0.946296	−	0.323301i	$-0.895207\pi$
$587$	−6.98811	−	26.0800i	−0.288430	−	1.07644i	0.657866	−	0.753135i	$-0.271459\pi$
$588$	−8.57321	+	8.57321i	−0.353553	+	0.353553i
$589$	−13.8564	+	8.00000i	−0.570943	+	0.329634i
$590$		0			0
$591$	9.00000	−	5.19615i	0.370211	−	0.213741i
$592$	−6.69213	+	1.79315i	−0.275045	+	0.0736980i
$593$	−14.8492	−	14.8492i	−0.609785	−	0.609785i	0.333105	−	0.942890i	$-0.391904\pi$
$593$	−14.8492	−	14.8492i	−0.609785	−	0.609785i	−0.942890	+	0.333105i	$0.891904\pi$
$594$	−7.79423	+	4.50000i	−0.319801	+	0.184637i
$595$		0			0
$596$	9.00000	+	5.19615i	0.368654	+	0.212843i
$597$	−11.6555	+	43.4988i	−0.477027	+	1.78029i
$598$	−40.1528	−	10.7589i	−1.64197	−	0.439964i
$599$	22.5167	+	39.0000i	0.920006	+	1.59350i	0.799402	+	0.600796i	$0.205150\pi$
$599$	22.5167	+	39.0000i	0.920006	+	1.59350i	0.120603	+	0.992701i	$0.461517\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		0			0
$603$	−7.34847	+	7.34847i	−0.299253	+	0.299253i
$604$			2.00000i			0.0813788i
$605$		0			0
$606$	12.0000	−	20.7846i	0.487467	−	0.844317i
$607$	−1.79315	+	6.69213i	−0.0727818	+	0.271625i	−0.992721	−	0.120435i	$-0.961571\pi$
$607$	−1.79315	+	6.69213i	−0.0727818	+	0.271625i	0.919939	+	0.392061i	$0.128238\pi$
$608$	1.03528	−	3.86370i	0.0419860	−	0.156694i
$609$		0			0
$610$		0			0
$611$		−	83.1384i		−	3.36342i
$612$	6.36396	−	6.36396i	0.257248	−	0.257248i
$613$	−17.1464	+	17.1464i	−0.692538	+	0.692538i	−0.962790	−	0.270252i	$-0.912893\pi$
$613$	−17.1464	+	17.1464i	−0.692538	+	0.692538i	0.270252	+	0.962790i	$0.412893\pi$
$614$	11.2583	−	19.5000i	0.454349	−	0.786956i
$615$		0			0
$616$		0			0
$617$	26.0800	+	6.98811i	1.04994	+	0.281331i	0.742227	−	0.670148i	$-0.233769\pi$
$617$	26.0800	+	6.98811i	1.04994	+	0.281331i	0.307714	+	0.951479i	$0.400436\pi$
$618$	−3.10583	+	11.5911i	−0.124935	+	0.466263i
$619$	−32.0429	−	18.5000i	−1.28791	−	0.743578i	−0.309633	−	0.950856i	$-0.600206\pi$
$619$	−32.0429	−	18.5000i	−1.28791	−	0.743578i	−0.978282	+	0.207279i	$0.933539\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$	−2.44949	−	2.44949i	−0.0982156	−	0.0982156i
$623$		0			0
$624$	10.3923	−	6.00000i	0.416025	−	0.240192i
$625$		0			0
$626$	1.50000	−	0.866025i	0.0599521	−	0.0346133i
$627$	8.48528	−	8.48528i	0.338869	−	0.338869i
$628$	−1.79315	−	6.69213i	−0.0715545	−	0.267045i
$629$	20.7846			0.828737
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	1.03528	+	3.86370i	0.0411811	+	0.153690i
$633$	10.3106	+	38.4797i	0.409810	+	1.52943i
$634$	25.9808	−	15.0000i	1.03183	−	0.595726i
$635$		0			0
$636$	18.0000	+	10.3923i	0.713746	+	0.412082i
$637$	46.8449	−	12.5521i	1.85606	−	0.497331i
$638$	−4.24264	−	4.24264i	−0.167968	−	0.167968i
$639$	−5.19615	+	9.00000i	−0.205557	+	0.356034i
$640$		0			0
$641$	−16.5000	−	9.52628i	−0.651711	−	0.376265i	0.137401	−	0.990516i	$-0.456125\pi$
$641$	−16.5000	−	9.52628i	−0.651711	−	0.376265i	−0.789111	+	0.614250i	$0.789459\pi$
$642$	−14.6969	−	14.6969i	−0.580042	−	0.580042i
$643$	−45.1719	−	12.1038i	−1.78141	−	0.477326i	−0.790566	−	0.612376i	$-0.790214\pi$
$643$	−45.1719	−	12.1038i	−1.78141	−	0.477326i	−0.990839	+	0.135050i	$0.956880\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	−0.853948	−	0.520358i	$-0.825799\pi$
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	0.520358	+	0.853948i	$0.325799\pi$
$648$	2.32937	−	8.69333i	0.0915064	−	0.341506i
$649$			15.0000i			0.588802i
$650$		0			0
$651$		0			0
$652$	0.448288	−	1.67303i	0.0175563	−	0.0655210i
$653$	12.4233	−	46.3644i	0.486162	−	1.81438i	−0.0886092	−	0.996066i	$-0.528242\pi$
$653$	12.4233	−	46.3644i	0.486162	−	1.81438i	0.574771	−	0.818314i	$-0.305091\pi$
$654$	−3.46410			−0.135457
$655$		0			0
$656$			6.92820i			0.270501i
$657$	−20.0764	+	5.37945i	−0.783255	+	0.209872i
$658$		0			0
$659$	7.79423	−	13.5000i	0.303620	−	0.525885i	−0.673333	−	0.739339i	$-0.735138\pi$
$659$	7.79423	−	13.5000i	0.303620	−	0.525885i	0.976953	+	0.213454i	$0.0684713\pi$
$660$		0			0
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	0.965926	+	0.258819i	0.0375418	+	0.0100593i
$663$	−34.7733	+	9.31749i	−1.35048	+	0.361861i
$664$	−7.79423	−	4.50000i	−0.302475	−	0.174634i
$665$		0			0
$666$	18.0000	−	10.3923i	0.697486	−	0.402694i
$667$	−14.6969	−	14.6969i	−0.569068	−	0.569068i
$668$	−5.79555	+	1.55291i	−0.224237	+	0.0600841i
$669$		−	6.00000i		−	0.231973i
$670$		0			0
$671$	12.0000	−	6.92820i	0.463255	−	0.267460i
$672$		0			0
$673$	−12.5521	−	46.8449i	−0.483846	−	1.80574i	−0.585201	−	0.810888i	$-0.698984\pi$
$673$	−12.5521	−	46.8449i	−0.483846	−	1.80574i	0.101355	−	0.994850i	$-0.467682\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	−35.0000			−1.34615
$677$	−1.55291	−	5.79555i	−0.0596833	−	0.222741i	0.929642	−	0.368464i	$-0.120116\pi$
$677$	−1.55291	−	5.79555i	−0.0596833	−	0.222741i	−0.989326	+	0.145722i	$0.953449\pi$
$678$	5.01910	+	1.34486i	0.192757	+	0.0516492i
$679$		0			0
$680$		0			0
$681$		−	5.19615i		−	0.199117i
$682$	−6.69213	+	1.79315i	−0.256255	+	0.0686633i
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	0.850559	−	0.525879i	$-0.176264\pi$
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	−0.525879	+	0.850559i	$0.676264\pi$
$684$			12.0000i			0.458831i
$685$		0			0
$686$		0			0
$687$	−33.4607	+	8.96575i	−1.27660	+	0.342065i
$688$	−8.36516	−	2.24144i	−0.318919	−	0.0854540i
$689$	−41.5692	−	72.0000i	−1.58366	−	2.74298i
$690$		0			0
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	0.979086	−	0.203445i	$-0.0652137\pi$
$692$	12.7279	−	12.7279i	0.483843	−	0.483843i
$693$		0			0
$694$			21.0000i			0.797149i
$695$		0			0
$696$	6.00000			0.227429
$697$	5.37945	−	20.0764i	0.203761	−	0.760448i
$698$	−2.58819	+	9.65926i	−0.0979645	+	0.365608i
$699$	7.79423	+	13.5000i	0.294805	+	0.510617i
$700$		0			0
$701$			27.7128i			1.04670i	0.852118	+	0.523349i	$0.175318\pi$
$701$			27.7128i			1.04670i	−0.852118	+	0.523349i	$0.824682\pi$
$702$	−25.4558	+	25.4558i	−0.960769	+	0.960769i
$703$	−19.5959	+	19.5959i	−0.739074	+	0.739074i
$704$	0.866025	−	1.50000i	0.0326396	−	0.0565334i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$		0			0
$708$	−10.6066	−	10.6066i	−0.398621	−	0.398621i
$709$	−6.92820	−	4.00000i	−0.260194	−	0.150223i	0.364229	−	0.931309i	$-0.381333\pi$
$709$	−6.92820	−	4.00000i	−0.260194	−	0.150223i	−0.624423	+	0.781086i	$0.714666\pi$
$710$		0			0
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$	1.22474	+	1.22474i	0.0458993	+	0.0458993i
$713$	−23.1822	+	6.21166i	−0.868181	+	0.232628i
$714$		0			0
$715$		0			0
$716$	−10.5000	+	6.06218i	−0.392403	+	0.226554i
$717$	−4.65874	−	17.3867i	−0.173984	−	0.649317i
$718$	−3.58630	−	13.3843i	−0.133840	−	0.499496i
$719$	34.6410			1.29189			0.645946	−	0.763383i	$-0.276463\pi$
$719$	34.6410			1.29189			0.645946	+	0.763383i	$0.276463\pi$
$720$		0			0
$721$		0			0
$722$	0.776457	+	2.89778i	0.0288967	+	0.107844i
$723$	−12.2474	+	12.2474i	−0.455488	+	0.455488i
$724$	1.73205	−	1.00000i	0.0643712	−	0.0371647i
$725$		0			0
$726$	−12.0000	+	6.92820i	−0.445362	+	0.257130i
$727$	−3.34607	+	0.896575i	−0.124099	+	0.0332521i	−0.320334	−	0.947305i	$-0.603795\pi$
$727$	−3.34607	+	0.896575i	−0.124099	+	0.0332521i	0.196235	+	0.980557i	$0.437128\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	22.5000	+	12.9904i	0.832193	+	0.480467i
$732$	−3.58630	+	13.3843i	−0.132554	+	0.494697i
$733$	20.0764	+	5.37945i	0.741538	+	0.198695i	0.609762	−	0.792585i	$-0.291265\pi$
$733$	20.0764	+	5.37945i	0.741538	+	0.198695i	0.131777	+	0.991279i	$0.457932\pi$
$734$	−12.1244	−	21.0000i	−0.447518	−	0.775124i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	4.24264	−	4.24264i	0.156280	−	0.156280i
$738$	−5.37945	−	20.0764i	−0.198020	−	0.739022i
$739$			41.0000i			1.50821i	0.656754	+	0.754105i	$0.271929\pi$
$739$			41.0000i			1.50821i	−0.656754	+	0.754105i	$0.728071\pi$
$740$		0			0
$741$	24.0000	−	41.5692i	0.881662	−	1.52708i
$742$		0			0
$743$	−6.21166	+	23.1822i	−0.227884	+	0.850473i	0.753345	+	0.657625i	$0.228439\pi$
$743$	−6.21166	+	23.1822i	−0.227884	+	0.850473i	−0.981229	+	0.192848i	$0.938228\pi$
$744$	3.46410	−	6.00000i	0.127000	−	0.219971i
$745$		0			0
$746$		0			0
$747$	26.0800	+	6.98811i	0.954217	+	0.255682i
$748$	−3.67423	+	3.67423i	−0.134343	+	0.134343i
$749$		0			0
$750$		0			0
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	11.5911	+	3.10583i	0.422684	+	0.113258i
$753$	−4.65874	+	17.3867i	−0.169774	+	0.633605i
$754$	−20.7846	−	12.0000i	−0.756931	−	0.437014i
$755$		0			0
$756$		0			0
$757$	29.3939	+	29.3939i	1.06834	+	1.06834i	0.997487	+	0.0708518i	$0.0225717\pi$
$757$	29.3939	+	29.3939i	1.06834	+	1.06834i	0.0708518	+	0.997487i	$0.477428\pi$
$758$	18.3526	−	4.91756i	0.666596	−	0.178614i
$759$	15.5885	−	9.00000i	0.565825	−	0.326679i
$760$		0			0
$761$	46.5000	−	26.8468i	1.68562	−	0.973195i	0.727822	−	0.685766i	$-0.240533\pi$
$761$	46.5000	−	26.8468i	1.68562	−	0.973195i	0.957802	−	0.287429i	$-0.0928005\pi$
$762$		0			0
$763$		0			0
$764$	−3.46410			−0.125327
$765$		0			0
$766$	30.0000			1.08394
$767$	15.5291	+	57.9555i	0.560725	+	2.09265i
$768$	0.448288	+	1.67303i	0.0161762	+	0.0603704i
$769$	11.2583	−	6.50000i	0.405986	−	0.234396i	−0.283078	−	0.959097i	$-0.591355\pi$
$769$	11.2583	−	6.50000i	0.405986	−	0.234396i	0.689063	+	0.724701i	$0.258022\pi$
$770$		0			0
$771$	4.50000	+	2.59808i	0.162064	+	0.0935674i
$772$	−5.01910	+	1.34486i	−0.180641	+	0.0484027i
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	0.626680	−	0.779277i	$-0.284413\pi$
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	−0.779277	+	0.626680i	$0.784413\pi$
$774$	25.9808			0.933859
$775$		0			0
$776$	−13.5000	−	7.79423i	−0.484622	−	0.279797i
$777$		0			0
$778$	−10.0382	−	2.68973i	−0.359887	−	0.0964314i
$779$	13.8564	+	24.0000i	0.496457	+	0.859889i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$	−12.7279	+	12.7279i	−0.455150	+	0.455150i
$783$	−17.3867	+	4.65874i	−0.621349	+	0.166490i
$784$			7.00000i			0.250000i
$785$		0			0
$786$	15.0000	+	25.9808i	0.535032	+	0.926703i
$787$	13.4486	−	50.1910i	0.479392	−	1.78912i	−0.124693	−	0.992195i	$-0.539795\pi$
$787$	13.4486	−	50.1910i	0.479392	−	1.78912i	0.604085	−	0.796920i	$-0.293539\pi$
$788$	1.55291	−	5.79555i	0.0553203	−	0.206458i
$789$	41.5692			1.47990
$790$		0			0
$791$		0			0
$792$	−1.34486	+	5.01910i	−0.0477876	+	0.178346i
$793$	39.1918	−	39.1918i	1.39174	−	1.39174i
$794$	1.73205	−	3.00000i	0.0614682	−	0.106466i
$795$		0			0
$796$	13.0000	+	22.5167i	0.460773	+	0.798082i
$797$	23.1822	+	6.21166i	0.821156	+	0.220028i	0.644852	−	0.764308i	$-0.276919\pi$
$797$	23.1822	+	6.21166i	0.821156	+	0.220028i	0.176304	+	0.984336i	$0.443586\pi$
$798$		0			0
$799$	−31.1769	−	18.0000i	−1.10296	−	0.636794i
$800$		0			0
$801$	−4.50000	−	2.59808i	−0.159000	−	0.0917985i
$802$	18.3712	+	18.3712i	0.648709	+	0.648709i
$803$	11.5911	−	3.10583i	0.409041	−	0.109602i
$804$			6.00000i			0.211604i
$805$		0			0
$806$	−24.0000	+	13.8564i	−0.845364	+	0.488071i
$807$	11.5911	+	3.10583i	0.408026	+	0.109330i
$808$	−3.58630	−	13.3843i	−0.126166	−	0.470857i
$809$	−8.66025			−0.304478			−0.152239	−	0.988344i	$-0.548648\pi$
$809$	−8.66025			−0.304478			−0.152239	+	0.988344i	$0.548648\pi$
$810$		0			0
$811$	−29.0000			−1.01833			−0.509164	−	0.860670i	$-0.670045\pi$
$811$	−29.0000			−1.01833			−0.509164	+	0.860670i	$0.670045\pi$
$812$		0			0
$813$	−13.3843	−	3.58630i	−0.469407	−	0.125777i
$814$	−10.3923	+	6.00000i	−0.364250	+	0.210300i
$815$		0			0
$816$		−	5.19615i		−	0.181902i
$817$	−33.4607	+	8.96575i	−1.17064	+	0.313672i
$818$	1.41421	+	1.41421i	0.0494468	+	0.0494468i
$819$		0			0
$820$		0			0
$821$	−30.0000	−	17.3205i	−1.04701	−	0.604490i	−0.125197	−	0.992132i	$-0.539956\pi$
$821$	−30.0000	−	17.3205i	−1.04701	−	0.604490i	−0.921810	+	0.387642i	$0.873290\pi$
$822$	−30.1146	+	8.06918i	−1.05037	+	0.281445i
$823$	6.69213	+	1.79315i	0.233273	+	0.0625053i	0.373562	−	0.927605i	$-0.378136\pi$
$823$	6.69213	+	1.79315i	0.233273	+	0.0625053i	−0.140289	+	0.990111i	$0.544803\pi$
$824$	3.46410	+	6.00000i	0.120678	+	0.209020i
$825$		0			0
$826$		0			0
$827$	23.3345	−	23.3345i	0.811421	−	0.811421i	−0.173426	−	0.984847i	$-0.555484\pi$
$827$	23.3345	−	23.3345i	0.811421	−	0.811421i	0.984847	+	0.173426i	$0.0554837\pi$
$828$	−4.65874	+	17.3867i	−0.161903	+	0.604228i
$829$		−	16.0000i		−	0.555703i	−0.960624	−	0.277851i	$-0.910378\pi$
$829$		−	16.0000i		−	0.555703i	0.960624	−	0.277851i	$-0.0896223\pi$
$830$		0			0
$831$	−6.00000			−0.208138
$832$	1.79315	−	6.69213i	0.0621663	−	0.232008i
$833$	5.43520	−	20.2844i	0.188319	−	0.702814i
$834$	11.2583	+	19.5000i	0.389844	+	0.675230i
$835$		0			0
$836$		−	6.92820i		−	0.239617i
$837$	−5.37945	+	20.0764i	−0.185941	+	0.693942i
$838$	−3.67423	+	3.67423i	−0.126924	+	0.126924i
$839$	3.46410	−	6.00000i	0.119594	−	0.207143i	−0.800013	−	0.599983i	$-0.795174\pi$
$839$	3.46410	−	6.00000i	0.119594	−	0.207143i	0.919607	+	0.392840i	$0.128507\pi$
$840$		0			0
$841$	8.50000	+	14.7224i	0.293103	+	0.507670i
$842$	−27.0459	−	7.24693i	−0.932064	−	0.249746i
$843$	25.4558	+	25.4558i	0.876746	+	0.876746i
$844$	19.9186	+	11.5000i	0.685626	+	0.395846i
$845$		0			0
$846$	−36.0000			−1.23771
$847$		0			0
$848$	11.5911	−	3.10583i	0.398040	−	0.106655i
$849$	−49.3634	−	28.5000i	−1.69415	−	0.978117i
$850$		0			0
$851$	−36.0000	+	20.7846i	−1.23406	+	0.712487i
$852$	1.55291	+	5.79555i	0.0532020	+	0.198552i
$853$	4.48288	+	16.7303i	0.153491	+	0.572835i	0.999230	+	0.0392388i	$0.0124933\pi$
$853$	4.48288	+	16.7303i	0.153491	+	0.572835i	−0.845739	+	0.533597i	$0.820840\pi$
$854$		0			0
$855$		0			0
$856$	−12.0000			−0.410152
$857$	0.776457	+	2.89778i	0.0265233	+	0.0989862i	0.977919	−	0.208986i	$-0.0670163\pi$
$857$	0.776457	+	2.89778i	0.0265233	+	0.0989862i	−0.951395	+	0.307972i	$0.900350\pi$
$858$	14.6969	−	14.6969i	0.501745	−	0.501745i
$859$	−27.7128	+	16.0000i	−0.945549	+	0.545913i	−0.891695	−	0.452636i	$-0.850484\pi$
$859$	−27.7128	+	16.0000i	−0.945549	+	0.545913i	−0.0538535	+	0.998549i	$0.517150\pi$
$860$		0			0
$861$		0			0
$862$	−23.4225	+	6.27603i	−0.797772	+	0.213762i
$863$	33.9411	+	33.9411i	1.15537	+	1.15537i	0.985460	+	0.169910i	$0.0543476\pi$
$863$	33.9411	+	33.9411i	1.15537	+	1.15537i	0.169910	+	0.985460i	$0.445652\pi$
$864$	−2.59808	−	4.50000i	−0.0883883	−	0.153093i
$865$		0			0
$866$	25.5000	+	14.7224i	0.866525	+	0.500289i
$867$	3.58630	−	13.3843i	0.121797	−	0.454553i
$868$		0			0
$869$	3.46410	+	6.00000i	0.117512	+	0.203536i
$870$		0			0
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	−1.41421	+	1.41421i	−0.0478913	+	0.0478913i
$873$	45.1719	+	12.1038i	1.52884	+	0.409651i
$874$		−	24.0000i		−	0.811812i
$875$		0			0
$876$	−6.00000	+	10.3923i	−0.202721	+	0.351123i
$877$	5.37945	−	20.0764i	0.181651	−	0.677932i	−0.813671	−	0.581325i	$-0.802534\pi$
$877$	5.37945	−	20.0764i	0.181651	−	0.677932i	0.995323	−	0.0966065i	$-0.0307988\pi$
$878$	2.58819	−	9.65926i	0.0873472	−	0.325984i
$879$	10.3923	−	18.0000i	0.350524	−	0.607125i
$880$		0			0
$881$		−	34.6410i		−	1.16709i	−0.812082	−	0.583543i	$-0.801666\pi$
$881$		−	34.6410i		−	1.16709i	0.812082	−	0.583543i	$-0.198334\pi$
$882$	−5.43520	−	20.2844i	−0.183013	−	0.683013i
$883$	−18.3712	+	18.3712i	−0.618239	+	0.618239i	−0.945080	−	0.326840i	$-0.894016\pi$
$883$	−18.3712	+	18.3712i	−0.618239	+	0.618239i	0.326840	+	0.945080i	$0.394016\pi$
$884$	−10.3923	+	18.0000i	−0.349531	+	0.605406i
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−40.5689	−	10.8704i	−1.36217	−	0.364992i	−0.497557	−	0.867431i	$-0.665770\pi$
$887$	−40.5689	−	10.8704i	−1.36217	−	0.364992i	−0.864613	+	0.502439i	$0.832436\pi$
$888$	3.10583	−	11.5911i	0.104225	−	0.388972i
$889$		0			0
$890$		0			0
$891$		−	15.5885i		−	0.522233i
$892$	−2.44949	−	2.44949i	−0.0820150	−	0.0820150i
$893$	46.3644	−	12.4233i	1.55153	−	0.415730i
$894$	−15.5885	+	9.00000i	−0.521356	+	0.301005i
$895$		0			0
$896$		0			0
$897$	50.9117	−	50.9117i	1.69989	−	1.69989i
$898$	8.96575	+	33.4607i	0.299191	+	1.11660i
$899$	−13.8564			−0.462137
$900$		0			0
$901$	−36.0000			−1.19933
$902$	3.10583	+	11.5911i	0.103413	+	0.385942i
$903$		0			0
$904$	2.59808	−	1.50000i	0.0864107	−	0.0498893i
$905$		0			0
$906$	−3.00000	−	1.73205i	−0.0996683	−	0.0575435i
$907$	−8.36516	+	2.24144i	−0.277761	+	0.0744257i	−0.395010	−	0.918677i	$-0.629259\pi$
$907$	−8.36516	+	2.24144i	−0.277761	+	0.0744257i	0.117250	+	0.993102i	$0.462592\pi$
$908$	−2.12132	−	2.12132i	−0.0703985	−	0.0703985i
$909$	20.7846	+	36.0000i	0.689382	+	1.19404i
$910$		0			0
$911$	33.0000	+	19.0526i	1.09334	+	0.631239i	0.934463	−	0.356059i	$-0.115880\pi$
$911$	33.0000	+	19.0526i	1.09334	+	0.631239i	0.158875	+	0.987299i	$0.449213\pi$
$912$	4.89898	+	4.89898i	0.162221	+	0.162221i
$913$	−15.0573	−	4.03459i	−0.498324	−	0.133525i
$914$		0			0
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$		0			0
$918$	4.03459	+	15.0573i	0.133161	+	0.496965i
$919$		−	34.0000i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$919$		−	34.0000i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$920$		0			0
$921$	19.5000	+	33.7750i	0.642547	+	1.11292i
$922$	−4.48288	+	16.7303i	−0.147636	+	0.550984i
$923$	6.21166	−	23.1822i	0.204459	−	0.763052i
$924$		0			0
$925$		0			0
$926$		−	3.46410i		−	0.113837i
$927$	−14.6969	−	14.6969i	−0.482711	−	0.482711i
$928$	2.44949	−	2.44949i	0.0804084	−	0.0804084i
$929$	17.3205	−	30.0000i	0.568267	−	0.984268i	−0.428470	−	0.903556i	$-0.640947\pi$
$929$	17.3205	−	30.0000i	0.568267	−	0.984268i	0.996737	−	0.0807121i	$-0.0257194\pi$
$930$		0			0
$931$	14.0000	+	24.2487i	0.458831	+	0.794719i
$932$	8.69333	+	2.32937i	0.284760	+	0.0763011i
$933$	5.79555	−	1.55291i	0.189738	−	0.0508401i
$934$	−12.9904	−	7.50000i	−0.425058	−	0.245407i
$935$		0			0
$936$			20.7846i			0.679366i
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	0.644539	−	0.764571i	$-0.277049\pi$
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	−0.764571	+	0.644539i	$0.777049\pi$
$938$		0			0
$939$			3.00000i			0.0979013i
$940$		0			0
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	−0.763825	−	0.645424i	$-0.776681\pi$
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	0.177041	+	0.984203i	$0.443347\pi$
$942$	11.5911	+	3.10583i	0.377659	+	0.101193i
$943$	10.7589	+	40.1528i	0.350358	+	1.30755i
$944$	−8.66025			−0.281867
$945$		0			0
$946$	−15.0000			−0.487692
$947$	3.88229	+	14.4889i	0.126157	+	0.470826i	0.999878	−	0.0156019i	$-0.00496644\pi$
$947$	3.88229	+	14.4889i	0.126157	+	0.470826i	−0.873721	+	0.486427i	$0.838300\pi$
$948$	−6.69213	−	1.79315i	−0.217350	−	0.0582388i
$949$	41.5692	−	24.0000i	1.34939	−	0.779073i
$950$		0			0
$951$			51.9615i			1.68497i
$952$		0			0
$953$	14.8492	+	14.8492i	0.481014	+	0.481014i	0.905455	−	0.424441i	$-0.139529\pi$
$953$	14.8492	+	14.8492i	0.481014	+	0.481014i	−0.424441	+	0.905455i	$0.639529\pi$
$954$	−31.1769	+	18.0000i	−1.00939	+	0.582772i
$955$		0			0
$956$	−9.00000	−	5.19615i	−0.291081	−	0.168056i
$957$	10.0382	−	2.68973i	0.324489	−	0.0869465i
$958$	6.69213	+	1.79315i	0.216213	+	0.0579341i
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−33.9411	+	33.9411i	−1.09431	+	1.09431i
$963$	34.7733	−	9.31749i	1.12055	−	0.300252i
$964$			10.0000i			0.322078i
$965$		0			0
$966$		0			0
$967$	3.58630	−	13.3843i	0.115328	−	0.430409i	−0.883984	−	0.467518i	$-0.845148\pi$
$967$	3.58630	−	13.3843i	0.115328	−	0.430409i	0.999311	+	0.0371092i	$0.0118150\pi$
$968$	−2.07055	+	7.72741i	−0.0665501	+	0.248368i
$969$	−10.3923	−	18.0000i	−0.333849	−	0.578243i
$970$		0			0
$971$			12.1244i			0.389089i	0.980894	+	0.194545i	$0.0623229\pi$
$971$			12.1244i			0.389089i	−0.980894	+	0.194545i	$0.937677\pi$
$972$	11.0227	+	11.0227i	0.353553	+	0.353553i
$973$		0			0
$974$	−8.66025	+	15.0000i	−0.277492	+	0.480631i
$975$		0			0
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	−5.79555	−	1.55291i	−0.185416	−	0.0496821i	0.164916	−	0.986308i	$-0.447265\pi$
$977$	−5.79555	−	1.55291i	−0.185416	−	0.0496821i	−0.350332	+	0.936625i	$0.613931\pi$
$978$	2.12132	+	2.12132i	0.0678323	+	0.0678323i
$979$	2.59808	+	1.50000i	0.0830349	+	0.0479402i
$980$		0			0
$981$	3.00000	−	5.19615i	0.0957826	−	0.165900i
$982$	−15.9217	−	15.9217i	−0.508081	−	0.508081i
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.839158	−	0.543888i	$-0.816952\pi$
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.454788	+	0.890600i	$0.650285\pi$
$984$	−10.3923	−	6.00000i	−0.331295	−	0.191273i
$985$		0			0
$986$	−9.00000	+	5.19615i	−0.286618	+	0.165479i
$987$		0			0
$988$	−7.17260	−	26.7685i	−0.228191	−	0.851620i
$989$	−51.9615			−1.65228
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	−1.03528	−	3.86370i	−0.0328701	−	0.122673i
$993$	−1.22474	+	1.22474i	−0.0388661	+	0.0388661i
$994$		0			0
$995$		0			0
$996$	13.5000	−	7.79423i	0.427764	−	0.246970i
$997$	10.0382	−	2.68973i	0.317913	−	0.0851845i	−0.0963340	−	0.995349i	$-0.530712\pi$
$997$	10.0382	−	2.68973i	0.317913	−	0.0851845i	0.414247	+	0.910165i	$0.364045\pi$
$998$	−3.53553	−	3.53553i	−0.111915	−	0.111915i
$999$			36.0000i			1.13899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.b.407.2	yes	8
3.2	odd	2		1350.2.q.e.1007.1		8
5.2	odd	4	inner	450.2.p.b.443.1	yes	8
5.3	odd	4	inner	450.2.p.b.443.2	yes	8
5.4	even	2	inner	450.2.p.b.407.1	yes	8
9.4	even	3		1350.2.q.e.557.1		8
9.5	odd	6	inner	450.2.p.b.257.2	yes	8
15.2	even	4		1350.2.q.e.143.2		8
15.8	even	4		1350.2.q.e.143.1		8
15.14	odd	2		1350.2.q.e.1007.2		8
45.4	even	6		1350.2.q.e.557.2		8
45.13	odd	12		1350.2.q.e.1043.1		8
45.14	odd	6	inner	450.2.p.b.257.1	✓	8
45.22	odd	12		1350.2.q.e.1043.2		8
45.23	even	12	inner	450.2.p.b.293.2	yes	8
45.32	even	12	inner	450.2.p.b.293.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.b.257.1	✓	8	45.14	odd	6	inner
450.2.p.b.257.2	yes	8	9.5	odd	6	inner
450.2.p.b.293.1	yes	8	45.32	even	12	inner
450.2.p.b.293.2	yes	8	45.23	even	12	inner
450.2.p.b.407.1	yes	8	5.4	even	2	inner
450.2.p.b.407.2	yes	8	1.1	even	1	trivial
450.2.p.b.443.1	yes	8	5.2	odd	4	inner
450.2.p.b.443.2	yes	8	5.3	odd	4	inner
1350.2.q.e.143.1		8	15.8	even	4
1350.2.q.e.143.2		8	15.2	even	4
1350.2.q.e.557.1		8	9.4	even	3
1350.2.q.e.557.2		8	45.4	even	6
1350.2.q.e.1007.1		8	3.2	odd	2
1350.2.q.e.1007.2		8	15.14	odd	2
1350.2.q.e.1043.1		8	45.13	odd	12
1350.2.q.e.1043.2		8	45.22	odd	12

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-1.50000 - 0.866025i) q^{11} +(1.67303 - 0.448288i) q^{12} +(-6.69213 - 1.79315i) q^{13} +(0.500000 - 0.866025i) q^{16} +(-2.12132 + 2.12132i) q^{17} +(-0.776457 + 2.89778i) q^{18} -4.00000i q^{19} +(0.448288 - 1.67303i) q^{22} +(1.55291 - 5.79555i) q^{23} +(0.866025 + 1.50000i) q^{24} -6.92820i q^{26} +(-3.67423 - 3.67423i) q^{27} +(1.73205 - 3.00000i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.12132 + 2.12132i) q^{33} +(-2.59808 - 1.50000i) q^{34} -3.00000 q^{36} +(-4.89898 - 4.89898i) q^{37} +(3.86370 - 1.03528i) q^{38} +(10.3923 + 6.00000i) q^{39} +(-6.00000 + 3.46410i) q^{41} +(-2.24144 - 8.36516i) q^{43} +1.73205 q^{44} +6.00000 q^{46} +(3.10583 + 11.5911i) q^{47} +(-1.22474 + 1.22474i) q^{48} +(-6.06218 + 3.50000i) q^{49} +(4.50000 - 2.59808i) q^{51} +(6.69213 - 1.79315i) q^{52} +(8.48528 + 8.48528i) q^{53} +(2.59808 - 4.50000i) q^{54} +(-1.79315 + 6.69213i) q^{57} +(3.34607 + 0.896575i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-1.50000 + 2.59808i) q^{66} +(-0.896575 + 3.34607i) q^{67} +(0.776457 - 2.89778i) q^{68} +(-5.19615 + 9.00000i) q^{69} +3.46410i q^{71} +(-0.776457 - 2.89778i) q^{72} +(-4.89898 + 4.89898i) q^{73} +(3.46410 - 6.00000i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-3.10583 + 11.5911i) q^{78} +(-3.46410 - 2.00000i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-4.89898 - 4.89898i) q^{82} +(8.69333 - 2.32937i) q^{83} +(7.50000 - 4.33013i) q^{86} +(-4.24264 + 4.24264i) q^{87} +(0.448288 + 1.67303i) q^{88} -1.73205 q^{89} +(1.55291 + 5.79555i) q^{92} +(1.79315 + 6.69213i) q^{93} +(-10.3923 + 6.00000i) q^{94} +(-1.50000 - 0.866025i) q^{96} +(15.0573 - 4.03459i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(-2.59808 - 4.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 12 q^{11} + 4 q^{16} - 16 q^{31} - 24 q^{36} - 48 q^{41} + 48 q^{46} + 36 q^{51} - 32 q^{61} - 12 q^{66} + 16 q^{76} + 36 q^{81} + 60 q^{86} - 12 q^{96}+O(q^{100}) \) 8 * q - 12 * q^11 + 4 * q^16 - 16 * q^31 - 24 * q^36 - 48 * q^41 + 48 * q^46 + 36 * q^51 - 32 * q^61 - 12 * q^66 + 16 * q^76 + 36 * q^81 + 60 * q^86 - 12 * q^96

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