LMFDB - Embedded newform 450.3.i.c.101.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,3,Mod(101,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.101"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.101
Dual form			450.3.i.c.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.00000 + 1.73205i) q^{4} +4.24264i q^{6} +(5.94949 - 10.3048i) q^{7} +2.82843i q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.57321 + 3.21770i) q^{11} +(-3.00000 + 5.19615i) q^{12} +(5.57321 + 9.65309i) q^{13} +(14.5732 - 8.41385i) q^{14} +(-2.00000 + 3.46410i) q^{16} +20.5775i q^{17} +(-11.0227 + 6.36396i) q^{18} +20.4495 q^{19} +35.6969 q^{21} +(4.55051 + 7.88171i) q^{22} +(-8.05051 + 4.64796i) q^{23} +(-7.34847 + 4.24264i) q^{24} +15.7634i q^{26} -27.0000 q^{27} +23.7980 q^{28} +(11.8485 + 6.84072i) q^{29} +(-26.9217 - 46.6297i) q^{31} +(-4.89898 + 2.82843i) q^{32} +19.3062i q^{33} +(-14.5505 + 25.2022i) q^{34} -18.0000 q^{36} +18.6515 q^{37} +(25.0454 + 14.4600i) q^{38} +(-16.7196 + 28.9593i) q^{39} +(-0.398979 + 0.230351i) q^{41} +(43.7196 + 25.2415i) q^{42} +(-17.5959 + 30.4770i) q^{43} +12.8708i q^{44} -13.1464 q^{46} +(-55.7474 - 32.1858i) q^{47} -12.0000 q^{48} +(-46.2929 - 80.1816i) q^{49} +(-53.4620 + 30.8663i) q^{51} +(-11.1464 + 19.3062i) q^{52} -2.25697i q^{53} +(-33.0681 - 19.0919i) q^{54} +(29.1464 + 16.8277i) q^{56} +(30.6742 + 53.1293i) q^{57} +(9.67423 + 16.7563i) q^{58} +(39.6867 - 22.9131i) q^{59} +(-4.94949 + 8.57277i) q^{61} -76.1460i q^{62} +(53.5454 + 92.7434i) q^{63} -8.00000 q^{64} +(-13.6515 + 23.6451i) q^{66} +(20.9949 + 36.3642i) q^{67} +(-35.6413 + 20.5775i) q^{68} +(-24.1515 - 13.9439i) q^{69} -121.672i q^{71} +(-22.0454 - 12.7279i) q^{72} -11.1010 q^{73} +(22.8434 + 13.1886i) q^{74} +(20.4495 + 35.4196i) q^{76} +(66.3156 - 38.2873i) q^{77} +(-40.9546 + 23.6451i) q^{78} +(72.7423 - 125.993i) q^{79} +(-40.5000 - 70.1481i) q^{81} -0.651531 q^{82} +(18.3990 + 10.6227i) q^{83} +(35.6969 + 61.8289i) q^{84} +(-43.1010 + 24.8844i) q^{86} +41.0443i q^{87} +(-9.10102 + 15.7634i) q^{88} +73.2999i q^{89} +132.631 q^{91} +(-16.1010 - 9.29593i) q^{92} +(80.7650 - 139.889i) q^{93} +(-45.5176 - 78.8388i) q^{94} +(-14.6969 - 8.48528i) q^{96} +(39.3939 - 68.2322i) q^{97} -130.936i q^{98} +(-50.1589 + 28.9593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 4 q^{4} + 14 q^{7} - 18 q^{9} - 12 q^{11} - 12 q^{12} - 12 q^{13} + 24 q^{14} - 8 q^{16} + 72 q^{19} + 84 q^{21} + 28 q^{22} - 42 q^{23} - 108 q^{27} + 56 q^{28} + 18 q^{29} - 44 q^{31}+ \cdots + 108 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 4 * q^4 + 14 * q^7 - 18 * q^9 - 12 * q^11 - 12 * q^12 - 12 * q^13 + 24 * q^14 - 8 * q^16 + 72 * q^19 + 84 * q^21 + 28 * q^22 - 42 * q^23 - 108 * q^27 + 56 * q^28 + 18 * q^29 - 44 * q^31 - 68 * q^34 - 72 * q^36 + 104 * q^37 + 12 * q^38 + 36 * q^39 + 18 * q^41 + 72 * q^42 + 8 * q^43 + 16 * q^46 - 174 * q^47 - 48 * q^48 - 48 * q^49 + 36 * q^51 + 24 * q^52 + 48 * q^56 + 108 * q^57 + 24 * q^58 - 96 * q^59 - 10 * q^61 + 126 * q^63 - 32 * q^64 - 84 * q^66 - 14 * q^67 + 24 * q^68 - 126 * q^69 - 64 * q^73 - 36 * q^74 + 72 * q^76 + 84 * q^77 - 252 * q^78 + 144 * q^79 - 162 * q^81 - 32 * q^82 + 54 * q^83 + 84 * q^84 - 192 * q^86 - 56 * q^88 + 168 * q^91 - 84 * q^92 + 132 * q^93 - 40 * q^94 + 40 * q^97 + 108 * q^99

Character values

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

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

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	1.50000	+	2.59808i	0.500000	+	0.866025i
$3$	1.50000	+	2.59808i	0.500000	+	0.866025i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			4.24264i			0.707107i
$7$	5.94949	−	10.3048i	0.849927	−	1.47212i	−0.0313455	−	0.999509i	$-0.509979\pi$
$7$	5.94949	−	10.3048i	0.849927	−	1.47212i	0.881273	−	0.472608i	$-0.156687\pi$
$8$			2.82843i			0.353553i
$9$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$10$		0			0
$11$	5.57321	+	3.21770i	0.506656	+	0.292518i	0.731458	−	0.681887i	$-0.238840\pi$
$11$	5.57321	+	3.21770i	0.506656	+	0.292518i	−0.224802	+	0.974404i	$0.572174\pi$
$12$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$13$	5.57321	+	9.65309i	0.428709	+	0.742545i	0.996759	−	0.0804487i	$-0.0256353\pi$
$13$	5.57321	+	9.65309i	0.428709	+	0.742545i	−0.568050	+	0.822994i	$0.692302\pi$
$14$	14.5732	−	8.41385i	1.04094	−	0.600989i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			20.5775i			1.21044i	0.796057	+	0.605221i	$0.206915\pi$
$17$			20.5775i			1.21044i	−0.796057	+	0.605221i	$0.793085\pi$
$18$	−11.0227	+	6.36396i	−0.612372	+	0.353553i
$19$	20.4495			1.07629			0.538144	−	0.842853i	$-0.319125\pi$
$19$	20.4495			1.07629			0.538144	+	0.842853i	$0.319125\pi$
$20$		0			0
$21$	35.6969			1.69985
$22$	4.55051	+	7.88171i	0.206841	+	0.358260i
$23$	−8.05051	+	4.64796i	−0.350022	+	0.202085i	−0.664695	−	0.747115i	$-0.731439\pi$
$23$	−8.05051	+	4.64796i	−0.350022	+	0.202085i	0.314673	+	0.949200i	$0.398105\pi$
$24$	−7.34847	+	4.24264i	−0.306186	+	0.176777i
$25$		0			0
$26$			15.7634i			0.606286i
$27$	−27.0000			−1.00000
$28$	23.7980			0.849927
$29$	11.8485	+	6.84072i	0.408568	+	0.235887i	0.690174	−	0.723643i	$-0.257534\pi$
$29$	11.8485	+	6.84072i	0.408568	+	0.235887i	−0.281606	+	0.959530i	$0.590867\pi$
$30$		0			0
$31$	−26.9217	−	46.6297i	−0.868441	−	1.50418i	−0.863589	−	0.504196i	$-0.831789\pi$
$31$	−26.9217	−	46.6297i	−0.868441	−	1.50418i	−0.00485238	−	0.999988i	$-0.501545\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$			19.3062i			0.585036i
$34$	−14.5505	+	25.2022i	−0.427956	+	0.741242i
$35$		0			0
$36$	−18.0000			−0.500000
$37$	18.6515			0.504095			0.252048	−	0.967715i	$-0.418896\pi$
$37$	18.6515			0.504095			0.252048	+	0.967715i	$0.418896\pi$
$38$	25.0454	+	14.4600i	0.659090	+	0.380526i
$39$	−16.7196	+	28.9593i	−0.428709	+	0.742545i
$40$		0			0
$41$	−0.398979	+	0.230351i	−0.00973121	+	0.00561831i	−0.504858	−	0.863203i	$-0.668455\pi$
$41$	−0.398979	+	0.230351i	−0.00973121	+	0.00561831i	0.495127	+	0.868821i	$0.335122\pi$
$42$	43.7196	+	25.2415i	1.04094	+	0.600989i
$43$	−17.5959	+	30.4770i	−0.409207	+	0.708768i	−0.994801	−	0.101837i	$-0.967528\pi$
$43$	−17.5959	+	30.4770i	−0.409207	+	0.708768i	0.585594	+	0.810605i	$0.300861\pi$
$44$			12.8708i			0.292518i
$45$		0			0
$46$	−13.1464			−0.285792
$47$	−55.7474	−	32.1858i	−1.18612	−	0.684804i	−0.228694	−	0.973498i	$-0.573446\pi$
$47$	−55.7474	−	32.1858i	−1.18612	−	0.684804i	−0.957421	+	0.288694i	$0.906779\pi$
$48$	−12.0000			−0.250000
$49$	−46.2929	−	80.1816i	−0.944752	−	1.63636i
$50$		0			0
$51$	−53.4620	+	30.8663i	−1.04827	+	0.605221i
$52$	−11.1464	+	19.3062i	−0.214354	+	0.371273i
$53$		−	2.25697i		−	0.0425843i	−0.999773	−	0.0212922i	$-0.993222\pi$
$53$		−	2.25697i		−	0.0425843i	0.999773	−	0.0212922i	$-0.00677802\pi$
$54$	−33.0681	−	19.0919i	−0.612372	−	0.353553i
$55$		0			0
$56$	29.1464	+	16.8277i	0.520472	+	0.300495i
$57$	30.6742	+	53.1293i	0.538144	+	0.932094i
$58$	9.67423	+	16.7563i	0.166797	+	0.288901i
$59$	39.6867	−	22.9131i	0.672656	−	0.388358i	−0.124426	−	0.992229i	$-0.539709\pi$
$59$	39.6867	−	22.9131i	0.672656	−	0.388358i	0.797082	+	0.603870i	$0.206376\pi$
$60$		0			0
$61$	−4.94949	+	8.57277i	−0.0811392	+	0.140537i	−0.903740	−	0.428083i	$-0.859189\pi$
$61$	−4.94949	+	8.57277i	−0.0811392	+	0.140537i	0.822600	+	0.568620i	$0.192522\pi$
$62$		−	76.1460i		−	1.22816i
$63$	53.5454	+	92.7434i	0.849927	+	1.47212i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−13.6515	+	23.6451i	−0.206841	+	0.358260i
$67$	20.9949	+	36.3642i	0.313357	+	0.542750i	0.979087	−	0.203443i	$-0.0652131\pi$
$67$	20.9949	+	36.3642i	0.313357	+	0.542750i	−0.665730	+	0.746193i	$0.731880\pi$
$68$	−35.6413	+	20.5775i	−0.524137	+	0.302611i
$69$	−24.1515	−	13.9439i	−0.350022	−	0.202085i
$70$		0			0
$71$		−	121.672i		−	1.71369i	−0.515572	−	0.856846i	$-0.672421\pi$
$71$		−	121.672i		−	1.71369i	0.515572	−	0.856846i	$-0.327579\pi$
$72$	−22.0454	−	12.7279i	−0.306186	−	0.176777i
$73$	−11.1010			−0.152069			−0.0760344	−	0.997105i	$-0.524226\pi$
$73$	−11.1010			−0.152069			−0.0760344	+	0.997105i	$0.524226\pi$
$74$	22.8434	+	13.1886i	0.308694	+	0.178225i
$75$		0			0
$76$	20.4495	+	35.4196i	0.269072	+	0.466047i
$77$	66.3156	−	38.2873i	0.861241	−	0.497238i
$78$	−40.9546	+	23.6451i	−0.525059	+	0.303143i
$79$	72.7423	−	125.993i	0.920789	−	1.59485i	0.122592	−	0.992457i	$-0.460879\pi$
$79$	72.7423	−	125.993i	0.920789	−	1.59485i	0.798197	−	0.602397i	$-0.205787\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.500000	−	0.866025i
$82$	−0.651531			−0.00794550
$83$	18.3990	+	10.6227i	0.221674	+	0.127984i	0.606725	−	0.794912i	$-0.292483\pi$
$83$	18.3990	+	10.6227i	0.221674	+	0.127984i	−0.385051	+	0.922895i	$0.625816\pi$
$84$	35.6969	+	61.8289i	0.424964	+	0.736058i
$85$		0			0
$86$	−43.1010	+	24.8844i	−0.501175	+	0.289353i
$87$			41.0443i			0.471774i
$88$	−9.10102	+	15.7634i	−0.103421	+	0.179130i
$89$			73.2999i			0.823595i	0.911275	+	0.411797i	$0.135099\pi$
$89$			73.2999i			0.823595i	−0.911275	+	0.411797i	$0.864901\pi$
$90$		0			0
$91$	132.631			1.45748
$92$	−16.1010	−	9.29593i	−0.175011	−	0.101043i
$93$	80.7650	−	139.889i	0.868441	−	1.50418i
$94$	−45.5176	−	78.8388i	−0.484230	−	0.838711i
$95$		0			0
$96$	−14.6969	−	8.48528i	−0.153093	−	0.0883883i
$97$	39.3939	−	68.2322i	0.406122	−	0.703425i	−0.588329	−	0.808622i	$-0.700214\pi$
$97$	39.3939	−	68.2322i	0.406122	−	0.703425i	0.994451	+	0.105197i	$0.0335473\pi$
$98$		−	130.936i		−	1.33608i
$99$	−50.1589	+	28.9593i	−0.506656	+	0.292518i
$100$		0			0
$101$	124.980	+	72.1570i	1.23742	+	0.714426i	0.968566	−	0.248755i	$-0.0800214\pi$
$101$	124.980	+	72.1570i	1.23742	+	0.714426i	0.268855	+	0.963181i	$0.413355\pi$
$102$	−87.3031			−0.855912
$103$	−49.8888	−	86.4099i	−0.484357	−	0.838931i	0.515481	−	0.856901i	$-0.327613\pi$
$103$	−49.8888	−	86.4099i	−0.484357	−	0.838931i	−0.999839	+	0.0179697i	$0.994280\pi$
$104$	−27.3031	+	15.7634i	−0.262529	+	0.151571i
$105$		0			0
$106$	1.59592	−	2.76421i	0.0150558	−	0.0260775i
$107$			119.512i			1.11693i	0.829528	+	0.558465i	$0.188609\pi$
$107$			119.512i			1.11693i	−0.829528	+	0.558465i	$0.811391\pi$
$108$	−27.0000	−	46.7654i	−0.250000	−	0.433013i
$109$	−151.091			−1.38615			−0.693077	−	0.720863i	$-0.743745\pi$
$109$	−151.091			−1.38615			−0.693077	+	0.720863i	$0.743745\pi$
$110$		0			0
$111$	27.9773	+	48.4581i	0.252048	+	0.436559i
$112$	23.7980	+	41.2193i	0.212482	+	0.368029i
$113$	−98.6969	+	56.9827i	−0.873424	+	0.504272i	−0.868485	−	0.495716i	$-0.834906\pi$
$113$	−98.6969	+	56.9827i	−0.873424	+	0.504272i	−0.00493960	+	0.999988i	$0.501572\pi$
$114$			86.7598i			0.761051i
$115$		0			0
$116$			27.3629i			0.235887i
$117$	−100.318			−0.857418
$118$	64.8082			0.549222
$119$	212.048	+	122.426i	1.78191	+	1.02879i
$120$		0			0
$121$	−39.7929	−	68.9232i	−0.328867	−	0.569614i
$122$	−12.1237	+	6.99964i	−0.0993748	+	0.0573741i
$123$	−1.19694	−	0.691053i	−0.00973121	−	0.00561831i
$124$	53.8434	−	93.2594i	0.434221	−	0.752092i
$125$		0			0
$126$			151.449i			1.20198i
$127$	−4.68673			−0.0369034			−0.0184517	−	0.999830i	$-0.505874\pi$
$127$	−4.68673			−0.0369034			−0.0184517	+	0.999830i	$0.505874\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	−105.576			−0.818415
$130$		0			0
$131$	4.65153	−	2.68556i	0.0355079	−	0.0205005i	−0.482141	−	0.876094i	$-0.660141\pi$
$131$	4.65153	−	2.68556i	0.0355079	−	0.0205005i	0.517649	+	0.855593i	$0.326807\pi$
$132$	−33.4393	+	19.3062i	−0.253328	+	0.146259i
$133$	121.664	−	210.728i	0.914767	−	1.58442i
$134$			59.3825i			0.443153i
$135$		0			0
$136$	−58.2020			−0.427956
$137$	−72.7423	−	41.9978i	−0.530966	−	0.306553i	0.210444	−	0.977606i	$-0.432509\pi$
$137$	−72.7423	−	41.9978i	−0.530966	−	0.306553i	−0.741410	+	0.671053i	$0.765842\pi$
$138$	−19.7196	−	34.1554i	−0.142896	−	0.247503i
$139$	34.3587	+	59.5110i	0.247185	+	0.428136i	0.962744	−	0.270416i	$-0.0871612\pi$
$139$	34.3587	+	59.5110i	0.247185	+	0.428136i	−0.715559	+	0.698552i	$0.753828\pi$
$140$		0			0
$141$		−	193.115i		−	1.36961i
$142$	86.0352	−	149.017i	0.605882	−	1.04942i
$143$			71.7316i			0.501620i
$144$	−18.0000	−	31.1769i	−0.125000	−	0.216506i
$145$		0			0
$146$	−13.5959	−	7.84961i	−0.0931227	−	0.0537644i
$147$	138.879	−	240.545i	0.944752	−	1.63636i
$148$	18.6515	+	32.3054i	0.126024	+	0.218280i
$149$	116.626	−	67.3341i	0.782725	−	0.451906i	−0.0546702	−	0.998504i	$-0.517411\pi$
$149$	116.626	−	67.3341i	0.782725	−	0.451906i	0.837395	+	0.546598i	$0.184077\pi$
$150$		0			0
$151$	41.7753	−	72.3569i	0.276657	−	0.479185i	−0.693895	−	0.720077i	$-0.744107\pi$
$151$	41.7753	−	72.3569i	0.276657	−	0.479185i	0.970552	+	0.240892i	$0.0774400\pi$
$152$			57.8399i			0.380526i
$153$	−160.386	−	92.5989i	−1.04827	−	0.605221i
$154$	108.293			0.703200
$155$		0			0
$156$	−66.8786			−0.428709
$157$	−66.6515	−	115.444i	−0.424532	−	0.735311i	0.571845	−	0.820362i	$-0.306228\pi$
$157$	−66.6515	−	115.444i	−0.424532	−	0.735311i	−0.996377	+	0.0850509i	$0.972895\pi$
$158$	178.182	−	102.873i	1.12773	−	0.651096i
$159$	5.86378	−	3.38545i	0.0368791	−	0.0212922i
$160$		0			0
$161$			110.612i			0.687031i
$162$		−	114.551i		−	0.707107i
$163$	−196.808			−1.20741			−0.603706	−	0.797207i	$-0.706310\pi$
$163$	−196.808			−1.20741			−0.603706	+	0.797207i	$0.706310\pi$
$164$	−0.797959	−	0.460702i	−0.00486560	−	0.00280916i
$165$		0			0
$166$	15.0227	+	26.0201i	0.0904982	+	0.156748i
$167$	−13.6362	+	7.87288i	−0.0816540	+	0.0471430i	−0.540271	−	0.841491i	$-0.681678\pi$
$167$	−13.6362	+	7.87288i	−0.0816540	+	0.0471430i	0.458617	+	0.888634i	$0.348345\pi$
$168$			100.966i			0.600989i
$169$	22.3786	−	38.7608i	0.132418	−	0.229354i
$170$		0			0
$171$	−92.0227	+	159.388i	−0.538144	+	0.932094i
$172$	−70.3837			−0.409207
$173$	−32.3383	−	18.6705i	−0.186926	−	0.107922i	0.403616	−	0.914928i	$-0.367753\pi$
$173$	−32.3383	−	18.6705i	−0.186926	−	0.107922i	−0.590543	+	0.807006i	$0.701086\pi$
$174$	−29.0227	+	50.2688i	−0.166797	+	0.288901i
$175$		0			0
$176$	−22.2929	+	12.8708i	−0.126664	+	0.0731295i
$177$	119.060	+	68.7394i	0.672656	+	0.388358i
$178$	−51.8309	+	89.7737i	−0.291185	+	0.504347i
$179$		−	236.209i		−	1.31960i	−0.751440	−	0.659802i	$-0.770640\pi$
$179$		−	236.209i		−	1.31960i	0.751440	−	0.659802i	$-0.229360\pi$
$180$		0			0
$181$	−265.050			−1.46436			−0.732182	−	0.681109i	$-0.761498\pi$
$181$	−265.050			−1.46436			−0.732182	+	0.681109i	$0.761498\pi$
$182$	162.439	+	93.7844i	0.892524	+	0.515299i
$183$	−29.6969			−0.162278
$184$	−13.1464	−	22.7703i	−0.0714480	−	0.123752i
$185$		0			0
$186$	197.833	−	114.219i	1.06362	−	0.614081i
$187$	−66.2122	+	114.683i	−0.354076	+	0.613278i
$188$		−	128.743i		−	0.684804i
$189$	−160.636	+	278.230i	−0.849927	+	1.47212i
$190$		0			0
$191$	81.8411	+	47.2510i	0.428487	+	0.247387i	0.698702	−	0.715413i	$-0.253761\pi$
$191$	81.8411	+	47.2510i	0.428487	+	0.247387i	−0.270215	+	0.962800i	$0.587095\pi$
$192$	−12.0000	−	20.7846i	−0.0625000	−	0.108253i
$193$	−21.1895	−	36.7014i	−0.109790	−	0.190163i	0.805895	−	0.592059i	$-0.201685\pi$
$193$	−21.1895	−	36.7014i	−0.109790	−	0.190163i	−0.915685	+	0.401896i	$0.868351\pi$
$194$	96.4949	−	55.7114i	0.497396	−	0.287172i
$195$		0			0
$196$	92.5857	−	160.363i	0.472376	−	0.818179i
$197$		−	120.765i		−	0.613021i	−0.951867	−	0.306511i	$-0.900839\pi$
$197$		−	120.765i		−	0.613021i	0.951867	−	0.306511i	$-0.0991615\pi$
$198$	−81.9092			−0.413683
$199$	29.4801			0.148141			0.0740706	−	0.997253i	$-0.476401\pi$
$199$	29.4801			0.148141			0.0740706	+	0.997253i	$0.476401\pi$
$200$		0			0
$201$	−62.9847	+	109.093i	−0.313357	+	0.542750i
$202$	102.045	+	176.748i	0.505175	+	0.874989i
$203$	140.985	−	81.3976i	0.694506	−	0.400973i
$204$	−106.924	−	61.7326i	−0.524137	−	0.302611i
$205$		0			0
$206$		−	141.107i		−	0.684984i
$207$		−	83.6634i		−	0.404171i
$208$	−44.5857			−0.214354
$209$	113.969	+	65.8003i	0.545308	+	0.314834i
$210$		0			0
$211$	−15.1237	−	26.1951i	−0.0716764	−	0.124147i	0.827960	−	0.560788i	$-0.189502\pi$
$211$	−15.1237	−	26.1951i	−0.0716764	−	0.124147i	−0.899636	+	0.436640i	$0.856168\pi$
$212$	3.90918	−	2.25697i	0.0184396	−	0.0106461i
$213$	316.114	−	182.508i	1.48410	−	0.856846i
$214$	−84.5074	+	146.371i	−0.394894	+	0.683977i
$215$		0			0
$216$		−	76.3675i		−	0.353553i
$217$	−640.681			−2.95245
$218$	−185.048	−	106.837i	−0.848843	−	0.490080i
$219$	−16.6515	−	28.8413i	−0.0760344	−	0.131695i
$220$		0			0
$221$	−198.637	+	114.683i	−0.898809	+	0.518927i
$222$			79.1317i			0.356449i
$223$	7.05051	−	12.2118i	0.0316166	−	0.0547616i	−0.849784	−	0.527131i	$-0.823268\pi$
$223$	7.05051	−	12.2118i	0.0316166	−	0.0547616i	0.881401	+	0.472369i	$0.156601\pi$
$224$			67.3108i			0.300495i
$225$		0			0
$226$	−161.171			−0.713148
$227$	223.596	+	129.093i	0.985004	+	0.568692i	0.903777	−	0.428003i	$-0.140783\pi$
$227$	223.596	+	129.093i	0.985004	+	0.568692i	0.0812269	+	0.996696i	$0.474116\pi$
$228$	−61.3485	+	106.259i	−0.269072	+	0.466047i
$229$	−46.2628	−	80.1294i	−0.202021	−	0.349910i	0.747159	−	0.664646i	$-0.231418\pi$
$229$	−46.2628	−	80.1294i	−0.202021	−	0.349910i	−0.949179	+	0.314735i	$0.898084\pi$
$230$		0			0
$231$	198.947	+	114.862i	0.861241	+	0.497238i
$232$	−19.3485	+	33.5125i	−0.0833986	+	0.144451i
$233$			320.619i			1.37605i	0.725689	+	0.688023i	$0.241521\pi$
$233$			320.619i			1.37605i	−0.725689	+	0.688023i	$0.758479\pi$
$234$	−122.864	−	70.9354i	−0.525059	−	0.303143i
$235$		0			0
$236$	79.3735	+	45.8263i	0.336328	+	0.194179i
$237$	436.454			1.84158
$238$	173.136	+	299.881i	0.727463	+	1.26000i
$239$	−281.914	+	162.763i	−1.17956	+	0.681017i	−0.955912	−	0.293654i	$-0.905129\pi$
$239$	−281.914	+	162.763i	−1.17956	+	0.681017i	−0.223644	+	0.974671i	$0.571795\pi$
$240$		0			0
$241$	42.3786	−	73.4018i	0.175845	−	0.304572i	−0.764609	−	0.644495i	$-0.777068\pi$
$241$	42.3786	−	73.4018i	0.175845	−	0.304572i	0.940453	+	0.339923i	$0.110401\pi$
$242$		−	112.551i		−	0.465088i
$243$	121.500	−	210.444i	0.500000	−	0.866025i
$244$	−19.7980			−0.0811392
$245$		0			0
$246$	−0.977296	−	1.69273i	−0.00397275	−	0.00688100i
$247$	113.969	+	197.401i	0.461415	+	0.799193i
$248$	131.889	−	76.1460i	0.531810	−	0.307040i
$249$			63.7359i			0.255968i
$250$		0			0
$251$		−	77.5314i		−	0.308890i	−0.988001	−	0.154445i	$-0.950641\pi$
$251$		−	77.5314i		−	0.308890i	0.988001	−	0.154445i	$-0.0493589\pi$
$252$	−107.091	+	185.487i	−0.424964	+	0.736058i
$253$	−59.8230			−0.236454
$254$	−5.74005	−	3.31402i	−0.0225986	−	0.0130473i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−237.167	+	136.928i	−0.922828	+	0.532795i	−0.884536	−	0.466472i	$-0.845525\pi$
$257$	−237.167	+	136.928i	−0.922828	+	0.532795i	−0.0382919	+	0.999267i	$0.512192\pi$
$258$	−129.303	−	74.6532i	−0.501175	−	0.289353i
$259$	110.967	−	192.201i	0.428444	−	0.742087i
$260$		0			0
$261$	−106.636	+	61.5665i	−0.408568	+	0.235887i
$262$	7.59592			0.0289921
$263$	32.7775	+	18.9241i	0.124629	+	0.0719549i	0.561019	−	0.827803i	$-0.310410\pi$
$263$	32.7775	+	18.9241i	0.124629	+	0.0719549i	−0.436389	+	0.899758i	$0.643743\pi$
$264$	−54.6061			−0.206841
$265$		0			0
$266$	298.015	−	172.059i	1.12036	−	0.646838i
$267$	−190.439	+	109.950i	−0.713254	+	0.411797i
$268$	−41.9898	+	72.7285i	−0.156678	+	0.271375i
$269$		−	135.240i		−	0.502749i	−0.967890	−	0.251375i	$-0.919117\pi$
$269$		−	135.240i		−	0.502749i	0.967890	−	0.251375i	$-0.0808826\pi$
$270$		0			0
$271$	147.914			0.545807			0.272904	−	0.962041i	$-0.412016\pi$
$271$	147.914			0.545807			0.272904	+	0.962041i	$0.412016\pi$
$272$	−71.2827	−	41.1551i	−0.262069	−	0.151305i
$273$	198.947	+	344.586i	0.728742	+	1.26222i
$274$	−59.3939	−	102.873i	−0.216766	−	0.375450i
$275$		0			0
$276$		−	55.7756i		−	0.202085i
$277$	232.406	−	402.540i	0.839012	−	1.45321i	−0.0517093	−	0.998662i	$-0.516467\pi$
$277$	232.406	−	402.540i	0.839012	−	1.45321i	0.890721	−	0.454550i	$-0.150200\pi$
$278$			97.1810i			0.349572i
$279$	484.590			1.73688
$280$		0			0
$281$	−7.46938	−	4.31245i	−0.0265814	−	0.0153468i	0.486650	−	0.873597i	$-0.338219\pi$
$281$	−7.46938	−	4.31245i	−0.0265814	−	0.0153468i	−0.513232	+	0.858250i	$0.671552\pi$
$282$	136.553	−	236.516i	0.484230	−	0.838711i
$283$	−40.7122	−	70.5157i	−0.143860	−	0.249172i	0.785087	−	0.619385i	$-0.212618\pi$
$283$	−40.7122	−	70.5157i	−0.143860	−	0.249172i	−0.928947	+	0.370213i	$0.879285\pi$
$284$	210.742	−	121.672i	0.742051	−	0.428423i
$285$		0			0
$286$	−50.7219	+	87.8530i	−0.177349	+	0.307178i
$287$			5.48188i			0.0191006i
$288$		−	50.9117i		−	0.176777i
$289$	−134.435			−0.465172
$290$		0			0
$291$	236.363			0.812245
$292$	−11.1010	−	19.2275i	−0.0380172	−	0.0658477i
$293$	−448.386	+	258.876i	−1.53033	+	0.883535i	−0.530981	+	0.847384i	$0.678177\pi$
$293$	−448.386	+	258.876i	−1.53033	+	0.883535i	−0.999346	+	0.0361514i	$0.988490\pi$
$294$	340.182	−	196.404i	1.15708	−	0.668041i
$295$		0			0
$296$			52.7545i			0.178225i
$297$	−150.477	−	86.8778i	−0.506656	−	0.292518i
$298$	190.449			0.639092
$299$	−89.7344	−	51.8082i	−0.300115	−	0.173272i
$300$		0			0
$301$	209.373	+	362.645i	0.695593	+	1.20480i
$302$	102.328	−	59.0791i	0.338835	−	0.195626i
$303$			432.942i			1.42885i
$304$	−40.8990	+	70.8391i	−0.134536	+	0.233023i
$305$		0			0
$306$	−130.955	−	226.820i	−0.427956	−	0.741242i
$307$	−4.59592			−0.0149704			−0.00748521	−	0.999972i	$-0.502383\pi$
$307$	−4.59592			−0.0149704			−0.00748521	+	0.999972i	$0.502383\pi$
$308$	132.631	+	76.5746i	0.430621	+	0.248619i
$309$	149.666	−	259.230i	0.484357	−	0.838931i
$310$		0			0
$311$	29.3258	−	16.9312i	0.0942951	−	0.0544413i	−0.452111	−	0.891962i	$-0.649329\pi$
$311$	29.3258	−	16.9312i	0.0942951	−	0.0544413i	0.546406	+	0.837520i	$0.315996\pi$
$312$	−81.9092	−	47.2903i	−0.262529	−	0.151571i
$313$	−58.5380	+	101.391i	−0.187022	+	0.323932i	−0.944256	−	0.329212i	$-0.893217\pi$
$313$	−58.5380	+	101.391i	−0.187022	+	0.323932i	0.757234	+	0.653144i	$0.226550\pi$
$314$		−	188.519i		−	0.600379i
$315$		0			0
$316$	290.969			0.920789
$317$	386.543	+	223.170i	1.21938	+	0.704008i	0.964785	−	0.263041i	$-0.0847253\pi$
$317$	386.543	+	223.170i	1.21938	+	0.704008i	0.254593	+	0.967048i	$0.418059\pi$
$318$	9.57551			0.0301117
$319$	44.0227	+	76.2496i	0.138002	+	0.239027i
$320$		0			0
$321$	−310.500	+	179.267i	−0.967290	+	0.558465i
$322$	−78.2145	+	135.472i	−0.242902	+	0.420719i
$323$			420.800i			1.30279i
$324$	81.0000	−	140.296i	0.250000	−	0.433013i
$325$		0			0
$326$	−241.040	−	139.164i	−0.739386	−	0.426885i
$327$	−226.636	−	392.545i	−0.693077	−	1.20044i
$328$	−0.651531	−	1.12848i	−0.00198637	−	0.00344050i
$329$	−663.338	+	382.978i	−2.01622	+	1.16407i
$330$		0			0
$331$	−259.666	+	449.755i	−0.784490	+	1.35878i	0.144813	+	0.989459i	$0.453742\pi$
$331$	−259.666	+	449.755i	−0.784490	+	1.35878i	−0.929303	+	0.369318i	$0.879591\pi$
$332$			42.4906i			0.127984i
$333$	−83.9319	+	145.374i	−0.252048	+	0.436559i
$334$	−22.2679			−0.0666702
$335$		0			0
$336$	−71.3939	+	123.658i	−0.212482	+	0.368029i
$337$	290.297	+	502.810i	0.861417	+	1.49202i	0.870562	+	0.492059i	$0.163756\pi$
$337$	290.297	+	502.810i	0.861417	+	1.49202i	−0.00914489	+	0.999958i	$0.502911\pi$
$338$	54.8161	−	31.6481i	0.162178	−	0.0936334i
$339$	−296.091	−	170.948i	−0.873424	−	0.504272i
$340$		0			0
$341$		−	346.503i		−	1.01614i
$342$	−225.409	+	130.140i	−0.659090	+	0.380526i
$343$	−518.626			−1.51203
$344$	−86.2020	−	49.7688i	−0.250587	−	0.144677i
$345$		0			0
$346$	−26.4041	−	45.7332i	−0.0763124	−	0.132177i
$347$	−225.545	+	130.218i	−0.649985	+	0.375269i	−0.788451	−	0.615098i	$-0.789116\pi$
$347$	−225.545	+	130.218i	−0.649985	+	0.375269i	0.138465	+	0.990367i	$0.455783\pi$
$348$	−71.0908	+	41.0443i	−0.204284	+	0.117943i
$349$	−320.585	+	555.270i	−0.918582	+	1.59103i	−0.117012	+	0.993131i	$0.537332\pi$
$349$	−320.585	+	555.270i	−0.918582	+	1.59103i	−0.801570	+	0.597901i	$0.796002\pi$
$350$		0			0
$351$	−150.477	−	260.633i	−0.428709	−	0.742545i
$352$	−36.4041			−0.103421
$353$	306.767	+	177.112i	0.869029	+	0.501734i	0.867026	−	0.498264i	$-0.166029\pi$
$353$	306.767	+	177.112i	0.869029	+	0.501734i	0.00200376	+	0.999998i	$0.499362\pi$
$354$	97.2122	+	168.377i	0.274611	+	0.475640i
$355$		0			0
$356$	−126.959	+	73.2999i	−0.356627	+	0.205899i
$357$			734.555i			2.05758i
$358$	167.025	−	289.296i	0.466550	−	0.808089i
$359$			388.215i			1.08138i	0.841222	+	0.540690i	$0.181837\pi$
$359$			388.215i			1.08138i	−0.841222	+	0.540690i	$0.818163\pi$
$360$		0			0
$361$	57.1816			0.158398
$362$	−324.619	−	187.419i	−0.896737	−	0.517731i
$363$	119.379	−	206.770i	0.328867	−	0.569614i
$364$	132.631	+	229.724i	0.364371	+	0.631109i
$365$		0			0
$366$	−36.3712	−	20.9989i	−0.0993748	−	0.0573741i
$367$	237.646	−	411.615i	0.647537	−	1.12157i	−0.336173	−	0.941800i	$-0.609133\pi$
$367$	237.646	−	411.615i	0.647537	−	1.12157i	0.983709	−	0.179766i	$-0.0575340\pi$
$368$		−	37.1837i		−	0.101043i
$369$		−	4.14632i		−	0.0112366i
$370$		0			0
$371$	−23.2577	−	13.4278i	−0.0626891	−	0.0361936i
$372$	323.060			0.868441
$373$	186.656	+	323.298i	0.500419	+	0.866750i	1.00000		0.000483363i	$0.000153859\pi$
$373$	186.656	+	323.298i	0.500419	+	0.866750i	−0.499581	+	0.866267i	$0.666513\pi$
$374$	−162.186	+	93.6383i	−0.433653	+	0.250370i
$375$		0			0
$376$	91.0352	−	157.678i	0.242115	−	0.419355i
$377$			152.499i			0.404507i
$378$	−393.477	+	227.174i	−1.04094	+	0.600989i
$379$	348.899			0.920578			0.460289	−	0.887769i	$-0.347746\pi$
$379$	348.899			0.920578			0.460289	+	0.887769i	$0.347746\pi$
$380$		0			0
$381$	−7.03010	−	12.1765i	−0.0184517	−	0.0319593i
$382$	66.8230	+	115.741i	0.174929	+	0.302986i
$383$	298.868	−	172.552i	0.780335	−	0.450527i	−0.0562139	−	0.998419i	$-0.517903\pi$
$383$	298.868	−	172.552i	0.780335	−	0.450527i	0.836549	+	0.547892i	$0.184570\pi$
$384$		−	33.9411i		−	0.0883883i
$385$		0			0
$386$		−	59.9331i		−	0.155267i
$387$	−158.363	−	274.293i	−0.409207	−	0.708768i
$388$	157.576			0.406122
$389$	−277.464	−	160.194i	−0.713274	−	0.411809i	0.0989978	−	0.995088i	$-0.468436\pi$
$389$	−277.464	−	160.194i	−0.713274	−	0.411809i	−0.812272	+	0.583278i	$0.801770\pi$
$390$		0			0
$391$	−95.6436	−	165.660i	−0.244613	−	0.423682i
$392$	226.788	−	130.936i	0.578540	−	0.334020i
$393$	13.9546	+	8.05669i	0.0355079	+	0.0205005i
$394$	85.3939	−	147.907i	0.216736	−	0.375397i
$395$		0			0
$396$	−100.318	−	57.9185i	−0.253328	−	0.146259i
$397$	205.344			0.517239			0.258619	−	0.965979i	$-0.416732\pi$
$397$	205.344			0.517239			0.258619	+	0.965979i	$0.416732\pi$
$398$	36.1056	+	20.8456i	0.0907176	+	0.0523758i
$399$	729.984			1.82953
$400$		0			0
$401$	−356.221	+	205.665i	−0.888333	+	0.512879i	−0.873397	−	0.487009i	$-0.838088\pi$
$401$	−356.221	+	205.665i	−0.888333	+	0.512879i	−0.0149359	+	0.999888i	$0.504754\pi$
$402$	−154.280	+	89.0738i	−0.383782	+	0.221577i
$403$	300.081	−	519.755i	0.744617	−	1.28971i
$404$			288.628i			0.714426i
$405$		0			0
$406$	230.227			0.567062
$407$	103.949	+	60.0150i	0.255403	+	0.147457i
$408$	−87.3031	−	151.213i	−0.213978	−	0.370621i
$409$	165.980	+	287.485i	0.405818	+	0.702898i	0.994416	−	0.105528i	$-0.0336533\pi$
$409$	165.980	+	287.485i	0.405818	+	0.702898i	−0.588598	+	0.808426i	$0.700320\pi$
$410$		0			0
$411$		−	251.987i		−	0.613107i
$412$	99.7775	−	172.820i	0.242179	−	0.419465i
$413$		−	545.286i		−	1.32031i
$414$	59.1589	−	102.466i	0.142896	−	0.247503i
$415$		0			0
$416$	−54.6061	−	31.5269i	−0.131265	−	0.0757857i
$417$	−103.076	+	178.533i	−0.247185	+	0.428136i
$418$	93.0556	+	161.177i	0.222621	+	0.385591i
$419$	630.229	−	363.863i	1.50413	−	0.868408i	0.504139	−	0.863623i	$-0.331810\pi$
$419$	630.229	−	363.863i	1.50413	−	0.868408i	0.999989	−	0.00478561i	$-0.00152331\pi$
$420$		0			0
$421$	−70.5857	+	122.258i	−0.167662	+	0.290399i	−0.937597	−	0.347723i	$-0.886955\pi$
$421$	−70.5857	+	122.258i	−0.167662	+	0.290399i	0.769935	+	0.638122i	$0.220288\pi$
$422$		−	42.7764i		−	0.101366i
$423$	501.727	−	289.672i	1.18612	−	0.684804i
$424$	6.38367			0.0150558
$425$		0			0
$426$	516.211			1.21176
$427$	58.8939	+	102.007i	0.137925	+	0.238893i
$428$	−207.000	+	119.512i	−0.483645	+	0.279232i
$429$	−186.364	+	107.597i	−0.434416	+	0.250810i
$430$		0			0
$431$			650.423i			1.50910i	0.656242	+	0.754551i	$0.272145\pi$
$431$			650.423i			1.50910i	−0.656242	+	0.754551i	$0.727855\pi$
$432$	54.0000	−	93.5307i	0.125000	−	0.216506i
$433$	−68.3179			−0.157778			−0.0788890	−	0.996883i	$-0.525137\pi$
$433$	−68.3179			−0.157778			−0.0788890	+	0.996883i	$0.525137\pi$
$434$	−784.671	−	453.030i	−1.80800	−	1.04385i
$435$		0			0
$436$	−151.091	−	261.697i	−0.346539	−	0.600222i
$437$	−164.629	+	95.0485i	−0.376725	+	0.217502i
$438$		−	47.0976i		−	0.107529i
$439$	−220.454	+	381.838i	−0.502173	+	0.869790i	0.497824	+	0.867278i	$0.334133\pi$
$439$	−220.454	+	381.838i	−0.502173	+	0.869790i	−0.999997	+	0.00251133i	$0.999201\pi$
$440$		0			0
$441$	833.271			1.88950
$442$	−324.372			−0.733874
$443$	−649.378	−	374.918i	−1.46586	−	0.846317i	−0.466592	−	0.884473i	$-0.654518\pi$
$443$	−649.378	−	374.918i	−1.46586	−	0.846317i	−0.999272	+	0.0381561i	$0.987852\pi$
$444$	−55.9546	+	96.9162i	−0.126024	+	0.218280i
$445$		0			0
$446$	17.2702	−	9.97093i	0.0387223	−	0.0223563i
$447$	349.878	+	202.002i	0.782725	+	0.451906i
$448$	−47.5959	+	82.4385i	−0.106241	+	0.184015i
$449$		−	802.901i		−	1.78820i	−0.447869	−	0.894099i	$-0.647817\pi$
$449$		−	802.901i		−	1.78820i	0.447869	−	0.894099i	$-0.352183\pi$
$450$		0			0
$451$	−2.96480			−0.00657383
$452$	−197.394	−	113.965i	−0.436712	−	0.252136i
$453$	250.652			0.553315
$454$	182.565	+	316.212i	0.402126	+	0.696503i
$455$		0			0
$456$	−150.272	+	86.7598i	−0.329545	+	0.190263i
$457$	227.012	−	393.197i	0.496745	−	0.860388i	−0.503248	−	0.864142i	$-0.667862\pi$
$457$	227.012	−	393.197i	0.496745	−	0.860388i	0.999993	+	0.00375440i	$0.00119506\pi$
$458$		−	130.851i		−	0.285701i
$459$		−	555.593i		−	1.21044i
$460$		0			0
$461$	−438.424	−	253.124i	−0.951028	−	0.549076i	−0.0576280	−	0.998338i	$-0.518354\pi$
$461$	−438.424	−	253.124i	−0.951028	−	0.549076i	−0.893400	+	0.449262i	$0.851687\pi$
$462$	162.439	+	281.353i	0.351600	+	0.608989i
$463$	247.182	+	428.131i	0.533870	+	0.924689i	0.999217	+	0.0395612i	$0.0125960\pi$
$463$	247.182	+	428.131i	0.533870	+	0.924689i	−0.465348	+	0.885128i	$0.654071\pi$
$464$	−47.3939	+	27.3629i	−0.102142	+	0.0589717i
$465$		0			0
$466$	−226.712	+	392.676i	−0.486506	+	0.842653i
$467$		−	390.044i		−	0.835211i	−0.908628	−	0.417606i	$-0.862869\pi$
$467$		−	390.044i		−	0.835211i	0.908628	−	0.417606i	$-0.137131\pi$
$468$	−100.318	−	173.756i	−0.214354	−	0.371273i
$469$	499.636			1.06532
$470$		0			0
$471$	199.955	−	346.332i	0.424532	−	0.735311i
$472$	64.8082	+	112.251i	0.137305	+	0.237820i
$473$	−196.132	+	113.237i	−0.414655	+	0.239401i
$474$	534.545	+	308.620i	1.12773	+	0.651096i
$475$		0			0
$476$			489.703i			1.02879i
$477$	17.5913	+	10.1564i	0.0368791	+	0.0212922i
$478$	−460.363			−0.963103
$479$	160.960	+	92.9304i	0.336034	+	0.194009i	0.658517	−	0.752566i	$-0.271184\pi$
$479$	160.960	+	92.9304i	0.336034	+	0.194009i	−0.322483	+	0.946575i	$0.604517\pi$
$480$		0			0
$481$	103.949	+	180.045i	0.216110	+	0.374314i
$482$	103.806	−	59.9323i	0.215365	−	0.124341i
$483$	−287.379	+	165.918i	−0.594987	+	0.343516i
$484$	79.5857	−	137.846i	0.164433	−	0.284807i
$485$		0			0
$486$	297.613	−	171.827i	0.612372	−	0.353553i
$487$	−828.261			−1.70074			−0.850371	−	0.526184i	$-0.823622\pi$
$487$	−828.261			−1.70074			−0.850371	+	0.526184i	$0.823622\pi$
$488$	−24.2474	−	13.9993i	−0.0496874	−	0.0286870i
$489$	−295.212	−	511.323i	−0.603706	−	1.04565i
$490$		0			0
$491$	219.167	−	126.536i	0.446368	−	0.257711i	−0.259927	−	0.965628i	$-0.583698\pi$
$491$	219.167	−	126.536i	0.446368	−	0.257711i	0.706295	+	0.707917i	$0.250365\pi$
$492$		−	2.76421i		−	0.00561831i
$493$	−140.765	+	243.812i	−0.285527	+	0.494548i
$494$			322.354i			0.652539i
$495$		0			0
$496$	215.373			0.434221
$497$	−1253.81	−	723.887i	−2.52276	−	1.45651i
$498$	−45.0681	+	78.0603i	−0.0904982	+	0.156748i
$499$	487.807	+	844.907i	0.977569	+	1.69320i	0.671181	+	0.741293i	$0.265787\pi$
$499$	487.807	+	844.907i	0.977569	+	1.69320i	0.306388	+	0.951907i	$0.400879\pi$
$500$		0			0
$501$	−40.9087	−	23.6186i	−0.0816540	−	0.0471430i
$502$	54.8230	−	94.9561i	0.109209	−	0.189156i
$503$		−	440.360i		−	0.875467i	−0.899105	−	0.437733i	$-0.855781\pi$
$503$		−	440.360i		−	0.875467i	0.899105	−	0.437733i	$-0.144219\pi$
$504$	−262.318	+	151.449i	−0.520472	+	0.300495i
$505$		0			0
$506$	−73.2679	−	42.3012i	−0.144798	−	0.0835992i
$507$	134.271			0.264835
$508$	−4.68673	−	8.11766i	−0.00922585	−	0.0159796i
$509$	−618.696	+	357.205i	−1.21551	+	0.701777i	−0.963955	−	0.266065i	$-0.914276\pi$
$509$	−618.696	+	357.205i	−1.21551	+	0.701777i	−0.251559	+	0.967842i	$0.580943\pi$
$510$		0			0
$511$	−66.0454	+	114.394i	−0.129247	+	0.223863i
$512$		−	22.6274i		−	0.0441942i
$513$	−552.136			−1.07629
$514$	−387.292			−0.753486
$515$		0			0
$516$	−105.576	−	182.862i	−0.204604	−	0.354384i
$517$	−207.128	−	358.757i	−0.400635	−	0.693920i
$518$	271.813	−	156.931i	0.524735	−	0.302956i
$519$		−	112.023i		−	0.215844i
$520$		0			0
$521$		−	328.944i		−	0.631370i	−0.948864	−	0.315685i	$-0.897766\pi$
$521$		−	328.944i		−	0.631370i	0.948864	−	0.315685i	$-0.102234\pi$
$522$	−174.136			−0.333594
$523$	416.535			0.796433			0.398217	−	0.917291i	$-0.369629\pi$
$523$	416.535			0.796433			0.398217	+	0.917291i	$0.369629\pi$
$524$	9.30306	+	5.37113i	0.0177539	+	0.0102502i
$525$		0			0
$526$	26.7628	+	46.3545i	0.0508798	+	0.0881263i
$527$	959.524	−	553.982i	1.82073	−	1.05120i
$528$	−66.8786	−	38.6124i	−0.126664	−	0.0731295i
$529$	−221.293	+	383.290i	−0.418323	+	0.724557i
$530$		0			0
$531$			412.437i			0.776717i
$532$	486.656			0.914767
$533$	−4.44720	−	2.56759i	−0.00834371	−	0.00481724i
$534$	−310.985			−0.582369
$535$		0			0
$536$	−102.854	+	59.3825i	−0.191891	+	0.110788i
$537$	613.689	−	354.314i	1.14281	−	0.659802i
$538$	95.6288	−	165.634i	0.177749	−	0.307870i
$539$		−	595.825i		−	1.10543i
$540$		0			0
$541$	161.070			0.297727			0.148864	−	0.988858i	$-0.452438\pi$
$541$	161.070			0.297727			0.148864	+	0.988858i	$0.452438\pi$
$542$	181.157	+	104.591i	0.334237	+	0.192972i
$543$	−397.575	−	688.620i	−0.732182	−	1.26818i
$544$	−58.2020	−	100.809i	−0.106989	−	0.185310i
$545$		0			0
$546$			562.706i			1.03060i
$547$	−237.187	+	410.819i	−0.433614	+	0.751041i	−0.997181	−	0.0750289i	$-0.976095\pi$
$547$	−237.187	+	410.819i	−0.433614	+	0.751041i	0.563568	+	0.826070i	$0.309428\pi$
$548$		−	167.991i		−	0.306553i
$549$	−44.5454	−	77.1549i	−0.0811392	−	0.140537i
$550$		0			0
$551$	242.295	+	139.889i	0.439737	+	0.253882i
$552$	39.4393	−	68.3108i	0.0714480	−	0.123752i
$553$	−865.560	−	1499.19i	−1.56521	−	2.71102i
$554$	569.277	−	328.672i	1.02758	−	0.593271i
$555$		0			0
$556$	−68.7173	+	119.022i	−0.123592	+	0.214068i
$557$			4.98583i			0.00895122i	0.999990	+	0.00447561i	$0.00142464\pi$
$557$			4.98583i			0.00895122i	−0.999990	+	0.00447561i	$0.998575\pi$
$558$	593.499	+	342.657i	1.06362	+	0.614081i
$559$	−392.263			−0.701723
$560$		0			0
$561$	−397.273			−0.708152
$562$	−6.09873	−	10.5633i	−0.0108518	−	0.0187959i
$563$	244.005	−	140.876i	0.433402	−	0.250225i	−0.267393	−	0.963588i	$-0.586162\pi$
$563$	244.005	−	140.876i	0.433402	−	0.250225i	0.700795	+	0.713363i	$0.252829\pi$
$564$	334.485	−	193.115i	0.593058	−	0.342402i
$565$		0			0
$566$		−	115.152i		−	0.203448i
$567$	−963.817			−1.69985
$568$	344.141			0.605882
$569$	−408.464	−	235.827i	−0.717863	−	0.414459i	0.0961024	−	0.995371i	$-0.469362\pi$
$569$	−408.464	−	235.827i	−0.717863	−	0.414459i	−0.813966	+	0.580913i	$0.802696\pi$
$570$		0			0
$571$	−232.202	−	402.186i	−0.406659	−	0.704353i	0.587854	−	0.808967i	$-0.299973\pi$
$571$	−232.202	−	402.186i	−0.406659	−	0.704353i	−0.994513	+	0.104613i	$0.966639\pi$
$572$	−124.243	+	71.7316i	−0.217208	+	0.125405i
$573$			283.506i			0.494775i
$574$	−3.87628	+	6.71391i	−0.00675309	+	0.0116967i
$575$		0			0
$576$	36.0000	−	62.3538i	0.0625000	−	0.108253i
$577$	393.090			0.681265			0.340632	−	0.940197i	$-0.389359\pi$
$577$	393.090			0.681265			0.340632	+	0.940197i	$0.389359\pi$
$578$	−164.648	−	95.0597i	−0.284858	−	0.164463i
$579$	63.5686	−	110.104i	0.109790	−	0.190163i
$580$		0			0
$581$	218.929	−	126.399i	0.376814	−	0.217554i
$582$	289.485	+	167.134i	0.497396	+	0.287172i
$583$	7.26224	−	12.5786i	0.0124567	−	0.0215756i
$584$		−	31.3984i		−	0.0537644i
$585$		0			0
$586$	−732.211			−1.24951
$587$	−41.9541	−	24.2222i	−0.0714720	−	0.0412644i	0.463838	−	0.885920i	$-0.346472\pi$
$587$	−41.9541	−	24.2222i	−0.0714720	−	0.0412644i	−0.535310	+	0.844656i	$0.679805\pi$
$588$	555.514			0.944752
$589$	−550.535	−	953.554i	−0.934694	−	1.61894i
$590$		0			0
$591$	313.757	−	181.148i	0.530892	−	0.306511i
$592$	−37.3031	+	64.6108i	−0.0630119	+	0.109140i
$593$		−	474.853i		−	0.800764i	−0.916348	−	0.400382i	$-0.868877\pi$
$593$		−	474.853i		−	0.800764i	0.916348	−	0.400382i	$-0.131123\pi$
$594$	−122.864	−	212.806i	−0.206841	−	0.358260i
$595$		0			0
$596$	233.252	+	134.668i	0.391362	+	0.225953i
$597$	44.2202	+	76.5916i	0.0740706	+	0.128294i
$598$	−73.2679	−	126.904i	−0.122522	−	0.212213i
$599$	−237.576	+	137.164i	−0.396620	+	0.228989i	−0.685025	−	0.728520i	$-0.740209\pi$
$599$	−237.576	+	137.164i	−0.396620	+	0.228989i	0.288404	+	0.957509i	$0.406875\pi$
$600$		0			0
$601$	582.565	−	1009.03i	0.969327	−	1.67892i	0.271815	−	0.962350i	$-0.412376\pi$
$601$	582.565	−	1009.03i	0.969327	−	1.67892i	0.697512	−	0.716573i	$-0.254291\pi$
$602$			592.198i			0.983717i
$603$	−377.908			−0.626713
$604$	167.101			0.276657
$605$		0			0
$606$	−306.136	+	530.243i	−0.505175	+	0.874989i
$607$	421.808	+	730.592i	0.694906	+	1.20361i	0.970213	+	0.242255i	$0.0778872\pi$
$607$	421.808	+	730.592i	0.694906	+	1.20361i	−0.275307	+	0.961356i	$0.588780\pi$
$608$	−100.182	+	57.8399i	−0.164772	+	0.0951314i
$609$	422.954	+	244.193i	0.694506	+	0.400973i
$610$		0			0
$611$		−	717.514i		−	1.17433i
$612$		−	370.396i		−	0.605221i
$613$	443.551			0.723573			0.361787	−	0.932261i	$-0.382167\pi$
$613$	443.551			0.723573			0.361787	+	0.932261i	$0.382167\pi$
$614$	−5.62883	−	3.24980i	−0.00916747	−	0.00529284i
$615$		0			0
$616$	108.293	+	187.569i	0.175800	+	0.304495i
$617$	−716.141	+	413.464i	−1.16068	+	0.670120i	−0.951467	−	0.307750i	$-0.900424\pi$
$617$	−716.141	+	413.464i	−1.16068	+	0.670120i	−0.209215	+	0.977870i	$0.567091\pi$
$618$	366.606	−	211.660i	0.593214	−	0.342492i
$619$	106.876	−	185.115i	0.172660	−	0.299055i	−0.766689	−	0.642018i	$-0.778097\pi$
$619$	106.876	−	185.115i	0.172660	−	0.299055i	0.939349	+	0.342963i	$0.111431\pi$
$620$		0			0
$621$	217.364	−	125.495i	0.350022	−	0.202085i
$622$	47.8888			0.0769916
$623$	755.342	+	436.097i	1.21243	+	0.699995i
$624$	−66.8786	−	115.837i	−0.107177	−	0.185636i
$625$		0			0
$626$	−143.388	+	82.7852i	−0.229055	+	0.132245i
$627$			394.802i			0.629668i
$628$	133.303	−	230.888i	0.212266	−	0.367656i
$629$			383.802i			0.610179i
$630$		0			0
$631$	−292.150			−0.462995			−0.231498	−	0.972835i	$-0.574363\pi$
$631$	−292.150			−0.462995			−0.231498	+	0.972835i	$0.574363\pi$
$632$	356.363	+	205.746i	0.563866	+	0.325548i
$633$	45.3712	−	78.5852i	0.0716764	−	0.124147i
$634$	315.611	+	546.654i	0.497809	+	0.862230i
$635$		0			0
$636$	11.7276	+	6.77091i	0.0184396	+	0.0106461i
$637$	516.000	−	893.738i	0.810047	−	1.40304i
$638$			124.515i			0.195165i
$639$	948.341	+	547.525i	1.48410	+	0.856846i
$640$		0			0
$641$	140.520	+	81.1295i	0.219221	+	0.126567i	0.605589	−	0.795777i	$-0.292937\pi$
$641$	140.520	+	81.1295i	0.219221	+	0.126567i	−0.386369	+	0.922344i	$0.626271\pi$
$642$	−507.044			−0.789789
$643$	366.510	+	634.814i	0.570000	+	0.987270i	0.996565	+	0.0828125i	$0.0263903\pi$
$643$	366.510	+	634.814i	0.570000	+	0.987270i	−0.426565	+	0.904457i	$0.640276\pi$
$644$	−191.586	+	110.612i	−0.297493	+	0.171758i
$645$		0			0
$646$	−297.551	+	515.373i	−0.460605	+	0.797790i
$647$			196.964i			0.304427i	0.988348	+	0.152213i	$0.0486401\pi$
$647$			196.964i			0.304427i	−0.988348	+	0.152213i	$0.951360\pi$
$648$	198.409	−	114.551i	0.306186	−	0.176777i
$649$	294.910			0.454407
$650$		0			0
$651$	−961.022	−	1664.54i	−1.47622	−	2.55689i
$652$	−196.808	−	340.882i	−0.301853	−	0.522825i
$653$	−384.588	+	222.042i	−0.588956	+	0.340034i	−0.764684	−	0.644405i	$-0.777105\pi$
$653$	−384.588	+	222.042i	−0.588956	+	0.340034i	0.175729	+	0.984439i	$0.443772\pi$
$654$		−	641.024i		−	0.980159i
$655$		0			0
$656$		−	1.84281i		−	0.00280916i
$657$	49.9546	−	86.5239i	0.0760344	−	0.131695i
$658$	−1083.23			−1.64624
$659$	−289.126	−	166.927i	−0.438734	−	0.253303i	0.264326	−	0.964433i	$-0.414850\pi$
$659$	−289.126	−	166.927i	−0.438734	−	0.253303i	−0.703061	+	0.711130i	$0.748184\pi$
$660$		0			0
$661$	246.020	+	426.120i	0.372194	+	0.644659i	0.989903	−	0.141748i	$-0.0452722\pi$
$661$	246.020	+	426.120i	0.372194	+	0.644659i	−0.617709	+	0.786407i	$0.711939\pi$
$662$	−636.050	+	367.224i	−0.960801	+	0.554718i
$663$	−595.910	−	344.049i	−0.898809	−	0.518927i
$664$	−30.0454	+	52.0402i	−0.0452491	+	0.0783738i
$665$		0			0
$666$	−205.590	+	118.698i	−0.308694	+	0.178225i
$667$	−127.182			−0.190677
$668$	−27.2724	−	15.7458i	−0.0408270	−	0.0235715i
$669$	42.3031			0.0632333
$670$		0			0
$671$	−55.1691	+	31.8519i	−0.0822193	+	0.0474693i
$672$	−174.879	+	100.966i	−0.260236	+	0.150247i
$673$	378.724	−	655.970i	0.562740	−	0.974695i	−0.434516	−	0.900664i	$-0.643080\pi$
$673$	378.724	−	655.970i	0.562740	−	0.974695i	0.997256	−	0.0740305i	$-0.0235862\pi$
$674$			821.085i			1.21823i
$675$		0			0
$676$	89.5143			0.132418
$677$	508.239	+	293.432i	0.750722	+	0.433429i	0.825955	−	0.563737i	$-0.190637\pi$
$677$	508.239	+	293.432i	0.750722	+	0.433429i	−0.0752330	+	0.997166i	$0.523970\pi$
$678$	−241.757	−	418.736i	−0.356574	−	0.617604i
$679$	−468.747	−	811.894i	−0.690349	−	1.19572i
$680$		0			0
$681$			774.559i			1.13738i
$682$	245.015	−	424.378i	0.359259	−	0.622255i
$683$			759.768i			1.11240i	0.831049	+	0.556199i	$0.187741\pi$
$683$			759.768i			1.11240i	−0.831049	+	0.556199i	$0.812259\pi$
$684$	−368.091			−0.538144
$685$		0			0
$686$	−635.184	−	366.724i	−0.925924	−	0.534583i
$687$	138.788	−	240.388i	0.202021	−	0.349910i
$688$	−70.3837	−	121.908i	−0.102302	−	0.177192i
$689$	21.7867	−	12.5786i	0.0316208	−	0.0182563i
$690$		0			0
$691$	228.919	−	396.500i	0.331287	−	0.573806i	−0.651477	−	0.758668i	$-0.725850\pi$
$691$	228.919	−	396.500i	0.331287	−	0.573806i	0.982764	+	0.184862i	$0.0591838\pi$
$692$		−	74.6820i		−	0.107922i
$693$			689.172i			0.994475i
$694$	−368.313			−0.530711
$695$		0			0
$696$	−116.091			−0.166797
$697$	−4.74005	−	8.21001i	−0.00680065	−	0.0117791i
$698$	−785.270	+	453.376i	−1.12503	+	0.649536i
$699$	−832.992	+	480.928i	−1.19169	+	0.688023i
$700$		0			0
$701$		−	196.778i		−	0.280711i	−0.990101	−	0.140355i	$-0.955176\pi$
$701$		−	196.778i		−	0.280711i	0.990101	−	0.140355i	$-0.0448245\pi$
$702$		−	425.613i		−	0.606286i
$703$	381.414			0.542552
$704$	−44.5857	−	25.7416i	−0.0633320	−	0.0365647i
$705$		0			0
$706$	250.474	+	433.835i	0.354780	+	0.614497i
$707$	1487.13	−	858.595i	2.10344	−	1.21442i
$708$			274.958i			0.388358i
$709$	240.424	−	416.427i	0.339103	−	0.587344i	−0.645161	−	0.764046i	$-0.723210\pi$
$709$	240.424	−	416.427i	0.339103	−	0.587344i	0.984264	+	0.176703i	$0.0565432\pi$
$710$		0			0
$711$	654.681	+	1133.94i	0.920789	+	1.59485i
$712$	−207.323			−0.291185
$713$	433.467	+	250.262i	0.607948	+	0.350999i
$714$	−519.409	+	899.642i	−0.727463	+	1.26000i
$715$		0			0
$716$	409.126	−	236.209i	0.571405	−	0.329901i
$717$	−845.741	−	488.289i	−1.17956	−	0.681017i
$718$	−274.510	+	475.465i	−0.382325	+	0.662207i
$719$			156.106i			0.217116i	0.994090	+	0.108558i	$0.0346232\pi$
$719$			156.106i			0.217116i	−0.994090	+	0.108558i	$0.965377\pi$
$720$		0			0
$721$	−1187.25			−1.64667
$722$	70.0329	+	40.4335i	0.0969985	+	0.0560021i
$723$	254.271			0.351689
$724$	−265.050	−	459.080i	−0.366091	−	0.634088i
$725$		0			0
$726$	292.417	−	168.827i	0.402778	−	0.232544i
$727$	−698.242	+	1209.39i	−0.960443	+	1.66354i	−0.239055	+	0.971006i	$0.576838\pi$
$727$	−698.242	+	1209.39i	−0.960443	+	1.66354i	−0.721388	+	0.692531i	$0.756496\pi$
$728$			375.137i			0.515299i
$729$	729.000			1.00000
$730$		0			0
$731$	−627.142	−	362.081i	−0.857923	−	0.495322i
$732$	−29.6969	−	51.4366i	−0.0405696	−	0.0702686i
$733$	534.005	+	924.923i	0.728519	+	1.26183i	0.957509	+	0.288403i	$0.0931244\pi$
$733$	534.005	+	924.923i	0.728519	+	1.26183i	−0.228990	+	0.973429i	$0.573542\pi$
$734$	582.111	−	336.082i	0.793067	−	0.457877i
$735$		0			0
$736$	26.2929	−	45.5406i	0.0357240	−	0.0618758i
$737$			270.221i			0.366650i
$738$	2.93189	−	5.07818i	0.00397275	−	0.00688100i
$739$	−719.464			−0.973565			−0.486782	−	0.873523i	$-0.661830\pi$
$739$	−719.464			−0.973565			−0.486782	+	0.873523i	$0.661830\pi$
$740$		0			0
$741$	−341.908	+	592.202i	−0.461415	+	0.799193i
$742$	−18.9898	−	32.8913i	−0.0255927	−	0.0443279i
$743$	−540.877	+	312.275i	−0.727964	+	0.420290i	−0.817677	−	0.575678i	$-0.804738\pi$
$743$	−540.877	+	312.275i	−0.727964	+	0.420290i	0.0897131	+	0.995968i	$0.471405\pi$
$744$	395.666	+	228.438i	0.531810	+	0.307040i
$745$		0			0
$746$			527.943i			0.707699i
$747$	−165.591	+	95.6039i	−0.221674	+	0.127984i
$748$	−264.849			−0.354076
$749$	1231.54	+	711.032i	1.64425	+	0.949309i
$750$		0			0
$751$	674.254	+	1167.84i	0.897809	+	1.55505i	0.830290	+	0.557332i	$0.188175\pi$
$751$	674.254	+	1167.84i	0.897809	+	1.55505i	0.0675192	+	0.997718i	$0.478492\pi$
$752$	222.990	−	128.743i	0.296529	−	0.171201i
$753$	201.432	−	116.297i	0.267507	−	0.154445i
$754$	−107.833	+	186.773i	−0.143015	+	0.247709i
$755$		0			0
$756$	−642.545			−0.849927
$757$	19.4689			0.0257185			0.0128592	−	0.999917i	$-0.495907\pi$
$757$	19.4689			0.0257185			0.0128592	+	0.999917i	$0.495907\pi$
$758$	427.312	+	246.709i	0.563736	+	0.325473i
$759$	−89.7344	−	155.425i	−0.118227	−	0.204775i
$760$		0			0
$761$	744.863	−	430.047i	0.978795	−	0.565108i	0.0768891	−	0.997040i	$-0.475501\pi$
$761$	744.863	−	430.047i	0.978795	−	0.565108i	0.901906	+	0.431932i	$0.142168\pi$
$762$		−	19.8841i		−	0.0260947i
$763$	−898.913	+	1556.96i	−1.17813	+	2.04058i
$764$			189.004i			0.247387i
$765$		0			0
$766$	488.050			0.637141
$767$	442.365	+	255.400i	0.576747	+	0.332985i
$768$	24.0000	−	41.5692i	0.0312500	−	0.0541266i
$769$	196.642	+	340.594i	0.255711	+	0.442905i	0.965088	−	0.261924i	$-0.0843571\pi$
$769$	196.642	+	340.594i	0.255711	+	0.442905i	−0.709377	+	0.704829i	$0.751024\pi$
$770$		0			0
$771$	−711.501	−	410.785i	−0.922828	−	0.532795i
$772$	42.3791	−	73.4027i	0.0548952	−	0.0950813i
$773$		−	626.967i		−	0.811083i	−0.914077	−	0.405541i	$-0.867083\pi$
$773$		−	626.967i		−	0.811083i	0.914077	−	0.405541i	$-0.132917\pi$
$774$		−	447.919i		−	0.578707i
$775$		0			0
$776$	192.990	+	111.423i	0.248698	+	0.143586i
$777$	665.803			0.856889
$778$	−226.548	−	392.393i	−0.291193	−	0.504361i
$779$	−8.15893	+	4.71056i	−0.0104736	+	0.00604693i
$780$		0			0
$781$	391.504	−	678.105i	0.501286	−	0.868252i
$782$		−	270.521i		−	0.345935i
$783$	−319.909	−	184.699i	−0.408568	−	0.235887i
$784$	370.343			0.472376
$785$		0			0
$786$	11.3939	+	19.7348i	0.0144960	+	0.0251079i
$787$	−34.8786	−	60.4115i	−0.0443184	−	0.0767617i	0.843015	−	0.537890i	$-0.180778\pi$
$787$	−34.8786	−	60.4115i	−0.0443184	−	0.0767617i	−0.887334	+	0.461128i	$0.847445\pi$
$788$	209.171	−	120.765i	0.265446	−	0.153255i
$789$			113.545i			0.143910i
$790$		0			0
$791$			1356.07i			1.71438i
$792$	−81.9092	−	141.871i	−0.103421	−	0.179130i
$793$	−110.338			−0.139140
$794$	251.494	+	145.200i	0.316743	+	0.182872i
$795$		0			0
$796$	29.4801	+	51.0610i	0.0370353	+	0.0641470i
$797$	−972.935	+	561.725i	−1.22075	+	0.704799i	−0.965077	−	0.261965i	$-0.915629\pi$
$797$	−972.935	+	561.725i	−1.22075	+	0.704799i	−0.255670	+	0.966764i	$0.582296\pi$
$798$	894.044	+	516.177i	1.12036	+	0.646838i
$799$	662.304	−	1147.14i	0.828917	−	1.43573i
$800$		0			0
$801$	−571.316	−	329.850i	−0.713254	−	0.411797i
$802$	−581.707			−0.725321
$803$	−61.8684	−	35.7197i	−0.0770465	−	0.0444828i
$804$	−251.939			−0.313357
$805$		0			0
$806$	735.044	−	424.378i	0.911966	−	0.526524i
$807$	351.363	−	202.859i	0.435394	−	0.251375i
$808$	−204.091	+	353.496i	−0.252588	+	0.437495i
$809$			182.198i			0.225213i	0.993640	+	0.112607i	$0.0359200\pi$
$809$			182.198i			0.225213i	−0.993640	+	0.112607i	$0.964080\pi$
$810$		0			0
$811$	831.160			1.02486			0.512429	−	0.858729i	$-0.328746\pi$
$811$	831.160			1.02486			0.512429	+	0.858729i	$0.328746\pi$
$812$	281.969	+	162.795i	0.347253	+	0.200487i
$813$	221.871	+	384.291i	0.272904	+	0.472683i
$814$	84.8740	+	147.006i	0.104268	+	0.180597i
$815$		0			0
$816$		−	246.930i		−	0.302611i
$817$	−359.828	+	623.240i	−0.440425	+	0.762839i
$818$			469.461i			0.573913i
$819$	−596.840	+	1033.76i	−0.728742	+	1.26222i
$820$		0			0
$821$	664.767	+	383.803i	0.809704	+	0.467483i	0.846853	−	0.531827i	$-0.178494\pi$
$821$	664.767	+	383.803i	0.809704	+	0.467483i	−0.0371492	+	0.999310i	$0.511828\pi$
$822$	178.182	−	308.620i	0.216766	−	0.375450i
$823$	210.474	+	364.552i	0.255740	+	0.442955i	0.965096	−	0.261896i	$-0.0843476\pi$
$823$	210.474	+	364.552i	0.255740	+	0.442955i	−0.709356	+	0.704850i	$0.751014\pi$
$824$	244.404	−	141.107i	0.296607	−	0.171246i
$825$		0			0
$826$	385.576	−	667.836i	0.466798	−	0.808519i
$827$			214.208i			0.259018i	0.991578	+	0.129509i	$0.0413400\pi$
$827$			214.208i			0.259018i	−0.991578	+	0.129509i	$0.958660\pi$
$828$	144.909	−	83.6634i	0.175011	−	0.101043i
$829$	669.311			0.807372			0.403686	−	0.914898i	$-0.367729\pi$
$829$	669.311			0.807372			0.403686	+	0.914898i	$0.367729\pi$
$830$		0			0
$831$	1394.44			1.67802
$832$	−44.5857	−	77.2247i	−0.0535886	−	0.0928182i
$833$	1649.94	−	952.593i	1.98072	−	1.14357i
$834$	−252.484	+	145.772i	−0.302738	+	0.174786i
$835$		0			0
$836$			263.201i			0.314834i
$837$	726.885	+	1259.00i	0.868441	+	1.50418i
$838$	1029.16			1.22811
$839$	893.031	+	515.592i	1.06440	+	0.614531i	0.926646	−	0.375935i	$-0.122679\pi$
$839$	893.031	+	515.592i	1.06440	+	0.614531i	0.137753	+	0.990467i	$0.456012\pi$
$840$		0			0
$841$	−326.909	−	566.223i	−0.388715	−	0.673274i
$842$	−172.899	+	99.8233i	−0.205343	+	0.118555i
$843$		−	25.8747i		−	0.0306936i
$844$	30.2474	−	52.3901i	0.0358382	−	0.0620736i
$845$		0			0
$846$	819.317			0.968460
$847$	−946.989			−1.11805
$848$	7.81837	+	4.51394i	0.00921978	+	0.00532304i
$849$	122.137	−	211.547i	0.143860	−	0.249172i
$850$		0			0
$851$	−150.154	+	86.6916i	−0.176445	+	0.101870i
$852$	632.227	+	365.016i	0.742051	+	0.428423i
$853$	−255.517	+	442.568i	−0.299550	+	0.518837i	−0.976033	−	0.217622i	$-0.930170\pi$
$853$	−255.517	+	442.568i	−0.299550	+	0.518837i	0.676483	+	0.736459i	$0.263503\pi$
$854$			166.577i			0.195055i
$855$		0			0
$856$	−338.030			−0.394894
$857$	−173.448	−	100.140i	−0.202390	−	0.116850i	0.395380	−	0.918518i	$-0.370613\pi$
$857$	−173.448	−	100.140i	−0.202390	−	0.116850i	−0.597770	+	0.801668i	$0.703946\pi$
$858$	−304.332			−0.354699
$859$	97.4620	+	168.809i	0.113460	+	0.196518i	0.917163	−	0.398512i	$-0.130473\pi$
$859$	97.4620	+	168.809i	0.113460	+	0.196518i	−0.803703	+	0.595030i	$0.797140\pi$
$860$		0			0
$861$	−14.2423	+	8.22282i	−0.0165416	+	0.00955032i
$862$	−459.918	+	796.602i	−0.533548	+	0.924132i
$863$			400.540i			0.464125i	0.972701	+	0.232063i	$0.0745475\pi$
$863$			400.540i			0.464125i	−0.972701	+	0.232063i	$0.925453\pi$
$864$	132.272	−	76.3675i	0.153093	−	0.0883883i
$865$		0			0
$866$	−83.6719	−	48.3080i	−0.0966189	−	0.0557829i
$867$	−201.652	−	349.272i	−0.232586	−	0.402851i
$868$	−640.681	−	1109.69i	−0.738112	−	1.27845i
$869$	810.817	−	468.126i	0.933046	−	0.538695i
$870$		0			0
$871$	−234.018	+	405.331i	−0.268678	+	0.465363i
$872$		−	427.349i		−	0.490080i
$873$	354.545	+	614.090i	0.406122	+	0.703425i
$874$	−268.838			−0.307595
$875$		0			0
$876$	33.3031	−	57.6826i	0.0380172	−	0.0658477i
$877$	73.0125	+	126.461i	0.0832526	+	0.144198i	0.904645	−	0.426165i	$-0.140136\pi$
$877$	73.0125	+	126.461i	0.0832526	+	0.144198i	−0.821393	+	0.570363i	$0.806803\pi$
$878$	−540.000	+	311.769i	−0.615034	+	0.355090i
$879$	−1345.16	−	776.627i	−1.53033	−	0.883535i
$880$		0			0
$881$			350.906i			0.398305i	0.979969	+	0.199152i	$0.0638189\pi$
$881$			350.906i			0.398305i	−0.979969	+	0.199152i	$0.936181\pi$
$882$	1020.54	+	589.212i	1.15708	+	0.668041i
$883$	−215.102			−0.243604			−0.121802	−	0.992554i	$-0.538867\pi$
$883$	−215.102			−0.243604			−0.121802	+	0.992554i	$0.538867\pi$
$884$	−397.273	−	229.366i	−0.449404	−	0.259464i
$885$		0			0
$886$	−530.215	−	918.359i	−0.598436	−	1.03652i
$887$	119.152	−	68.7925i	0.134332	−	0.0775563i	−0.431328	−	0.902195i	$-0.641955\pi$
$887$	119.152	−	68.7925i	0.134332	−	0.0775563i	0.565660	+	0.824639i	$0.308622\pi$
$888$	−137.060	+	79.1317i	−0.154347	+	0.0891123i
$889$	−27.8837	+	48.2959i	−0.0313652	+	0.0543261i
$890$		0			0
$891$		−	521.267i		−	0.585036i
$892$	28.2020			0.0316166
$893$	−1140.01	−	658.183i	−1.27660	−	0.737047i
$894$	285.674	+	494.802i	0.319546	+	0.553470i
$895$		0			0
$896$	−116.586	+	67.3108i	−0.130118	+	0.0751237i
$897$		−	310.849i		−	0.346543i
$898$	567.737	−	983.349i	0.632224	−	1.09504i
$899$		−	736.654i		−	0.819415i
$900$		0			0
$901$	46.4428			0.0515459
$902$	−3.63112	−	2.09643i	−0.00402563	−	0.00232420i
$903$	−628.120	+	1087.94i	−0.695593	+	1.20480i
$904$	−161.171	−	279.157i	−0.178287	−	0.308802i
$905$		0			0
$906$	306.984	+	177.237i	0.338835	+	0.195626i
$907$	−322.500	+	558.586i	−0.355568	+	0.615862i	−0.987215	−	0.159394i	$-0.949046\pi$
$907$	−322.500	+	558.586i	−0.355568	+	0.615862i	0.631647	+	0.775256i	$0.282379\pi$
$908$			516.373i			0.568692i
$909$	−1124.82	+	649.413i	−1.23742	+	0.714426i
$910$		0			0
$911$	−28.2566	−	16.3140i	−0.0310171	−	0.0179078i	0.484411	−	0.874840i	$-0.339034\pi$
$911$	−28.2566	−	16.3140i	−0.0310171	−	0.0179078i	−0.515428	+	0.856933i	$0.672367\pi$
$912$	−245.394			−0.269072
$913$	68.3610	+	118.405i	0.0748751	+	0.129687i
$914$	556.065	−	321.044i	0.608386	−	0.351252i
$915$		0			0
$916$	92.5255	−	160.259i	0.101010	−	0.174955i
$917$		−	63.9109i		−	0.0696956i
$918$	392.864	−	680.460i	0.427956	−	0.741242i
$919$	−551.978			−0.600628			−0.300314	−	0.953840i	$-0.597092\pi$
$919$	−551.978			−0.600628			−0.300314	+	0.953840i	$0.597092\pi$
$920$		0			0
$921$	−6.89388	−	11.9405i	−0.00748521	−	0.0129648i
$922$	−357.972	−	620.025i	−0.388256	−	0.672478i
$923$	1174.51	−	678.105i	1.27249	−	0.734675i
$924$			459.448i			0.497238i
$925$		0			0
$926$			699.135i			0.755006i
$927$	897.998			0.968714
$928$	−77.3939			−0.0833986
$929$	653.574	+	377.341i	0.703525	+	0.406180i	0.808659	−	0.588278i	$-0.200194\pi$
$929$	653.574	+	377.341i	0.703525	+	0.406180i	−0.105134	+	0.994458i	$0.533527\pi$
$930$		0			0
$931$	−946.665	−	1639.67i	−1.01683	−	1.76119i
$932$	−555.328	+	320.619i	−0.595846	+	0.344012i
$933$	87.9773	+	50.7937i	0.0942951	+	0.0544413i
$934$	275.803	−	477.704i	0.295292	−	0.511460i
$935$		0			0
$936$		−	283.742i		−	0.303143i
$937$	1241.31			1.32477			0.662386	−	0.749162i	$-0.269544\pi$
$937$	1241.31			1.32477			0.662386	+	0.749162i	$0.269544\pi$
$938$	611.926	+	353.296i	0.652373	+	0.376648i
$939$	−351.228			−0.374045
$940$		0			0
$941$	−1271.56	+	734.138i	−1.35129	+	0.780168i	−0.988430	−	0.151675i	$-0.951533\pi$
$941$	−1271.56	+	734.138i	−1.35129	+	0.780168i	−0.362861	+	0.931843i	$0.618200\pi$
$942$	489.787	−	282.778i	0.519943	−	0.300189i
$943$	2.14133	−	3.70888i	0.00227076	−	0.00393307i
$944$			183.305i			0.194179i
$945$		0			0
$946$	−320.282			−0.338564
$947$	224.348	+	129.527i	0.236904	+	0.136777i	0.613753	−	0.789498i	$-0.289659\pi$
$947$	224.348	+	129.527i	0.236904	+	0.136777i	−0.376849	+	0.926275i	$0.622992\pi$
$948$	436.454	+	755.961i	0.460395	+	0.797427i
$949$	−61.8684	−	107.159i	−0.0651932	−	0.112918i
$950$		0			0
$951$			1339.02i			1.40802i
$952$	−346.272	+	599.761i	−0.363732	+	0.630002i
$953$			766.123i			0.803907i	0.915660	+	0.401954i	$0.131669\pi$
$953$			766.123i			0.803907i	−0.915660	+	0.401954i	$0.868331\pi$
$954$	14.3633	+	24.8779i	0.0150558	+	0.0260775i
$955$		0			0
$956$	−563.828	−	325.526i	−0.589778	−	0.340508i
$957$	−132.068	+	228.749i	−0.138002	+	0.239027i
$958$	131.423	+	227.632i	0.137185	+	0.237612i
$959$	−865.560	+	499.731i	−0.902565	+	0.521096i
$960$		0			0
$961$	−969.054	+	1678.45i	−1.00838	+	1.74657i
$962$			294.012i			0.305626i
$963$	−931.500	−	537.802i	−0.967290	−	0.558465i
$964$	169.514			0.175845
$965$		0			0
$966$	−469.287			−0.485805
$967$	−338.363	−	586.061i	−0.349910	−	0.606061i	0.636323	−	0.771422i	$-0.280454\pi$
$967$	−338.363	−	586.061i	−0.349910	−	0.606061i	−0.986233	+	0.165361i	$0.947121\pi$
$968$	194.944	−	112.551i	0.201389	−	0.116272i
$969$	−1093.27	+	631.200i	−1.12825	+	0.651393i
$970$		0			0
$971$		−	332.231i		−	0.342154i	−0.985258	−	0.171077i	$-0.945275\pi$
$971$		−	332.231i		−	0.342154i	0.985258	−	0.171077i	$-0.0547246\pi$
$972$	486.000			0.500000
$973$	817.666			0.840356
$974$	−1014.41	−	585.669i	−1.04149	−	0.601303i
$975$		0			0
$976$	−19.7980	−	34.2911i	−0.0202848	−	0.0351343i
$977$	−73.9615	+	42.7017i	−0.0757026	+	0.0437069i	−0.537374	−	0.843344i	$-0.680583\pi$
$977$	−73.9615	+	42.7017i	−0.0757026	+	0.0437069i	0.461671	+	0.887051i	$0.347250\pi$
$978$		−	834.986i		−	0.853769i
$979$	−235.857	+	408.516i	−0.240916	+	0.417279i
$980$		0			0
$981$	679.909	−	1177.64i	0.693077	−	1.20044i
$982$	357.898			0.364458
$983$	−1426.02	−	823.312i	−1.45068	−	0.837551i	−0.452160	−	0.891937i	$-0.649347\pi$
$983$	−1426.02	−	823.312i	−1.45068	−	0.837551i	−0.998520	+	0.0543859i	$0.982680\pi$
$984$	1.95459	−	3.38545i	0.00198637	−	0.00344050i
$985$		0			0
$986$	−344.803	+	199.072i	−0.349698	+	0.201898i
$987$	−1990.01	−	1148.93i	−2.01622	−	1.16407i
$988$	−227.939	+	394.802i	−0.230707	+	0.399597i
$989$		−	327.141i		−	0.330779i
$990$		0			0
$991$	821.757			0.829220			0.414610	−	0.909999i	$-0.363918\pi$
$991$	821.757			0.829220			0.414610	+	0.909999i	$0.363918\pi$
$992$	263.778	+	152.292i	0.265905	+	0.153520i
$993$	−1558.00			−1.56898
$994$	−1023.73	−	1773.15i	−1.02991	−	1.78386i
$995$		0			0
$996$	−110.394	+	63.7359i	−0.110837	+	0.0639919i
$997$	937.176	−	1623.24i	0.939996	−	1.62812i	0.174523	−	0.984653i	$-0.444162\pi$
$997$	937.176	−	1623.24i	0.939996	−	1.62812i	0.765473	−	0.643468i	$-0.222505\pi$
$998$			1379.73i			1.38249i
$999$	−503.591			−0.504095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.i.c.101.2		4
3.2	odd	2		1350.3.i.c.251.1		4
5.2	odd	4		90.3.j.a.29.2	✓	8
5.3	odd	4		90.3.j.a.29.3	yes	8
5.4	even	2		450.3.i.a.101.1		4
9.4	even	3		1350.3.i.c.1151.1		4
9.5	odd	6	inner	450.3.i.c.401.2		4
15.2	even	4		270.3.j.a.89.4		8
15.8	even	4		270.3.j.a.89.2		8
15.14	odd	2		1350.3.i.a.251.2		4
45.2	even	12		810.3.b.a.809.4		8
45.4	even	6		1350.3.i.a.1151.2		4
45.7	odd	12		810.3.b.a.809.5		8
45.13	odd	12		270.3.j.a.179.4		8
45.14	odd	6		450.3.i.a.401.1		4
45.22	odd	12		270.3.j.a.179.2		8
45.23	even	12		90.3.j.a.59.2	yes	8
45.32	even	12		90.3.j.a.59.3	yes	8
45.38	even	12		810.3.b.a.809.6		8
45.43	odd	12		810.3.b.a.809.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.j.a.29.2	✓	8	5.2	odd	4
90.3.j.a.29.3	yes	8	5.3	odd	4
90.3.j.a.59.2	yes	8	45.23	even	12
90.3.j.a.59.3	yes	8	45.32	even	12
270.3.j.a.89.2		8	15.8	even	4
270.3.j.a.89.4		8	15.2	even	4
270.3.j.a.179.2		8	45.22	odd	12
270.3.j.a.179.4		8	45.13	odd	12
450.3.i.a.101.1		4	5.4	even	2
450.3.i.a.401.1		4	45.14	odd	6
450.3.i.c.101.2		4	1.1	even	1	trivial
450.3.i.c.401.2		4	9.5	odd	6	inner
810.3.b.a.809.3		8	45.43	odd	12
810.3.b.a.809.4		8	45.2	even	12
810.3.b.a.809.5		8	45.7	odd	12
810.3.b.a.809.6		8	45.38	even	12
1350.3.i.a.251.2		4	15.14	odd	2
1350.3.i.a.1151.2		4	45.4	even	6
1350.3.i.c.251.1		4	3.2	odd	2
1350.3.i.c.1151.1		4	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.00000 + 1.73205i) q^{4} +4.24264i q^{6} +(5.94949 - 10.3048i) q^{7} +2.82843i q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.57321 + 3.21770i) q^{11} +(-3.00000 + 5.19615i) q^{12} +(5.57321 + 9.65309i) q^{13} +(14.5732 - 8.41385i) q^{14} +(-2.00000 + 3.46410i) q^{16} +20.5775i q^{17} +(-11.0227 + 6.36396i) q^{18} +20.4495 q^{19} +35.6969 q^{21} +(4.55051 + 7.88171i) q^{22} +(-8.05051 + 4.64796i) q^{23} +(-7.34847 + 4.24264i) q^{24} +15.7634i q^{26} -27.0000 q^{27} +23.7980 q^{28} +(11.8485 + 6.84072i) q^{29} +(-26.9217 - 46.6297i) q^{31} +(-4.89898 + 2.82843i) q^{32} +19.3062i q^{33} +(-14.5505 + 25.2022i) q^{34} -18.0000 q^{36} +18.6515 q^{37} +(25.0454 + 14.4600i) q^{38} +(-16.7196 + 28.9593i) q^{39} +(-0.398979 + 0.230351i) q^{41} +(43.7196 + 25.2415i) q^{42} +(-17.5959 + 30.4770i) q^{43} +12.8708i q^{44} -13.1464 q^{46} +(-55.7474 - 32.1858i) q^{47} -12.0000 q^{48} +(-46.2929 - 80.1816i) q^{49} +(-53.4620 + 30.8663i) q^{51} +(-11.1464 + 19.3062i) q^{52} -2.25697i q^{53} +(-33.0681 - 19.0919i) q^{54} +(29.1464 + 16.8277i) q^{56} +(30.6742 + 53.1293i) q^{57} +(9.67423 + 16.7563i) q^{58} +(39.6867 - 22.9131i) q^{59} +(-4.94949 + 8.57277i) q^{61} -76.1460i q^{62} +(53.5454 + 92.7434i) q^{63} -8.00000 q^{64} +(-13.6515 + 23.6451i) q^{66} +(20.9949 + 36.3642i) q^{67} +(-35.6413 + 20.5775i) q^{68} +(-24.1515 - 13.9439i) q^{69} -121.672i q^{71} +(-22.0454 - 12.7279i) q^{72} -11.1010 q^{73} +(22.8434 + 13.1886i) q^{74} +(20.4495 + 35.4196i) q^{76} +(66.3156 - 38.2873i) q^{77} +(-40.9546 + 23.6451i) q^{78} +(72.7423 - 125.993i) q^{79} +(-40.5000 - 70.1481i) q^{81} -0.651531 q^{82} +(18.3990 + 10.6227i) q^{83} +(35.6969 + 61.8289i) q^{84} +(-43.1010 + 24.8844i) q^{86} +41.0443i q^{87} +(-9.10102 + 15.7634i) q^{88} +73.2999i q^{89} +132.631 q^{91} +(-16.1010 - 9.29593i) q^{92} +(80.7650 - 139.889i) q^{93} +(-45.5176 - 78.8388i) q^{94} +(-14.6969 - 8.48528i) q^{96} +(39.3939 - 68.2322i) q^{97} -130.936i q^{98} +(-50.1589 + 28.9593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} + 14 q^{7} - 18 q^{9} - 12 q^{11} - 12 q^{12} - 12 q^{13} + 24 q^{14} - 8 q^{16} + 72 q^{19} + 84 q^{21} + 28 q^{22} - 42 q^{23} - 108 q^{27} + 56 q^{28} + 18 q^{29} - 44 q^{31}+ \cdots + 108 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 4 * q^4 + 14 * q^7 - 18 * q^9 - 12 * q^11 - 12 * q^12 - 12 * q^13 + 24 * q^14 - 8 * q^16 + 72 * q^19 + 84 * q^21 + 28 * q^22 - 42 * q^23 - 108 * q^27 + 56 * q^28 + 18 * q^29 - 44 * q^31 - 68 * q^34 - 72 * q^36 + 104 * q^37 + 12 * q^38 + 36 * q^39 + 18 * q^41 + 72 * q^42 + 8 * q^43 + 16 * q^46 - 174 * q^47 - 48 * q^48 - 48 * q^49 + 36 * q^51 + 24 * q^52 + 48 * q^56 + 108 * q^57 + 24 * q^58 - 96 * q^59 - 10 * q^61 + 126 * q^63 - 32 * q^64 - 84 * q^66 - 14 * q^67 + 24 * q^68 - 126 * q^69 - 64 * q^73 - 36 * q^74 + 72 * q^76 + 84 * q^77 - 252 * q^78 + 144 * q^79 - 162 * q^81 - 32 * q^82 + 54 * q^83 + 84 * q^84 - 192 * q^86 - 56 * q^88 + 168 * q^91 - 84 * q^92 + 132 * q^93 - 40 * q^94 + 40 * q^97 + 108 * q^99

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