LMFDB - Embedded newform 450.2.p.c.293.2

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			293.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.c.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(1.67303 - 0.448288i) q^{12} +(1.22474 - 0.328169i) q^{13} +(-0.633975 + 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.89778 - 0.776457i) q^{18} -7.19615i q^{19} +(1.90192 - 1.09808i) q^{21} +(-0.896575 - 3.34607i) q^{22} +(-2.12132 - 7.91688i) q^{23} -1.73205i q^{24} -1.26795i q^{26} +(3.67423 + 3.67423i) q^{27} +(0.896575 + 0.896575i) q^{28} +(3.63397 + 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(-1.55291 + 1.55291i) q^{37} +(-6.95095 - 1.86250i) q^{38} +(-1.09808 + 1.90192i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(-0.568406 - 2.12132i) q^{42} +(1.67303 - 6.24384i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(-1.55291 + 5.79555i) q^{47} +(-1.67303 - 0.448288i) q^{48} +(-4.66987 - 2.69615i) q^{49} +(-1.22474 - 0.328169i) q^{52} +(1.55291 - 1.55291i) q^{53} +(4.50000 - 2.59808i) q^{54} +(1.09808 - 0.633975i) q^{56} +(8.81345 + 8.81345i) q^{57} +(7.02030 - 1.88108i) q^{58} +(-6.23205 + 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-7.20977 - 7.20977i) q^{62} +(-0.984508 + 3.67423i) q^{63} -1.00000i q^{64} +(5.19615 + 3.00000i) q^{66} +(-3.22595 - 12.0394i) q^{67} +(12.2942 + 7.09808i) q^{69} +10.7321i q^{71} +(2.12132 + 2.12132i) q^{72} +(3.67423 + 3.67423i) q^{73} +(1.09808 + 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(-4.24264 + 1.13681i) q^{77} +(1.55291 + 1.55291i) q^{78} +(-8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 + 1.22474i) q^{82} +(6.57201 + 1.76097i) q^{83} -2.19615 q^{84} +(-5.59808 - 3.23205i) q^{86} +(-12.1595 - 3.25813i) q^{87} +(-0.896575 + 3.34607i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(-2.12132 + 7.91688i) q^{92} +(4.57081 + 17.0585i) q^{93} +(5.19615 + 3.00000i) q^{94} +(-0.866025 + 1.50000i) q^{96} +(14.1607 + 3.79435i) q^{97} +(-3.81294 + 3.81294i) q^{98} +(-5.19615 - 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 24 q^{11} - 12 q^{14} + 4 q^{16} + 36 q^{21} + 36 q^{29} + 20 q^{31} - 12 q^{36} + 12 q^{39} - 12 q^{41} - 24 q^{46} - 72 q^{49} + 36 q^{54} - 12 q^{56} - 36 q^{59} + 16 q^{61} + 36 q^{69} - 12 q^{74} - 8 q^{76} - 72 q^{81} + 24 q^{84} - 24 q^{86} - 96 q^{91}+O(q^{100}) $ 8 * q + 24 * q^11 - 12 * q^14 + 4 * q^16 + 36 * q^21 + 36 * q^29 + 20 * q^31 - 12 * q^36 + 12 * q^39 - 12 * q^41 - 24 * q^46 - 72 * q^49 + 36 * q^54 - 12 * q^56 - 36 * q^59 + 16 * q^61 + 36 * q^69 - 12 * q^74 - 8 * q^76 - 72 * q^81 + 24 * q^84 - 24 * q^86 - 96 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	0.866025	+	1.50000i	0.353553	+	0.612372i
$7$	−1.22474	−	0.328169i	−0.462910	−	0.124036i	0.0198238	−	0.999803i	$-0.493689\pi$
$7$	−1.22474	−	0.328169i	−0.462910	−	0.124036i	−0.482734	+	0.875767i	$0.660356\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	1.00000i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$	1.67303	−	0.448288i	0.482963	−	0.129410i
$13$	1.22474	−	0.328169i	0.339683	−	0.0910178i	−0.0849451	−	0.996386i	$-0.527071\pi$
$13$	1.22474	−	0.328169i	0.339683	−	0.0910178i	0.424628	+	0.905368i	$0.360405\pi$
$14$	−0.633975	+	1.09808i	−0.169437	+	0.293473i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−2.89778	−	0.776457i	−0.683013	−	0.183013i
$19$		−	7.19615i		−	1.65091i	−0.564467	−	0.825455i	$-0.690918\pi$
$19$		−	7.19615i		−	1.65091i	0.564467	−	0.825455i	$-0.309082\pi$
$20$		0			0
$21$	1.90192	−	1.09808i	0.415034	−	0.239620i
$22$	−0.896575	−	3.34607i	−0.191151	−	0.713384i
$23$	−2.12132	−	7.91688i	−0.442326	−	1.65078i	−0.722902	−	0.690951i	$-0.757192\pi$
$23$	−2.12132	−	7.91688i	−0.442326	−	1.65078i	0.280576	−	0.959832i	$-0.409475\pi$
$24$		−	1.73205i		−	0.353553i
$25$		0			0
$26$		−	1.26795i		−	0.248665i
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$	0.896575	+	0.896575i	0.169437	+	0.169437i
$29$	3.63397	+	6.29423i	0.674812	+	1.16881i	0.976524	+	0.215410i	$0.0691087\pi$
$29$	3.63397	+	6.29423i	0.674812	+	1.16881i	−0.301712	+	0.953399i	$0.597558\pi$
$30$		0			0
$31$	5.09808	−	8.83013i	0.915642	−	1.58594i	0.109682	−	0.993967i	$-0.465017\pi$
$31$	5.09808	−	8.83013i	0.915642	−	1.58594i	0.805959	−	0.591971i	$-0.201650\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.55291	+	5.79555i	−0.270328	+	1.00888i
$34$		0			0
$35$		0			0
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	−1.55291	+	1.55291i	−0.255298	+	0.255298i	−0.823138	−	0.567841i	$-0.807779\pi$
$37$	−1.55291	+	1.55291i	−0.255298	+	0.255298i	0.567841	+	0.823138i	$0.307779\pi$
$38$	−6.95095	−	1.86250i	−1.12759	−	0.302138i
$39$	−1.09808	+	1.90192i	−0.175833	+	0.304552i
$40$		0			0
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$	−0.568406	−	2.12132i	−0.0877070	−	0.327327i
$43$	1.67303	−	6.24384i	0.255135	−	0.952177i	−0.712880	−	0.701286i	$-0.752610\pi$
$43$	1.67303	−	6.24384i	0.255135	−	0.952177i	0.968015	−	0.250891i	$-0.0807237\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	−8.19615			−1.20846
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	0.755276	+	0.655407i	$0.227503\pi$
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	−0.981792	+	0.189961i	$0.939164\pi$
$48$	−1.67303	−	0.448288i	−0.241481	−	0.0647048i
$49$	−4.66987	−	2.69615i	−0.667125	−	0.385165i
$50$		0			0
$51$		0			0
$52$	−1.22474	−	0.328169i	−0.169842	−	0.0455089i
$53$	1.55291	−	1.55291i	0.213309	−	0.213309i	−0.592362	−	0.805672i	$-0.701805\pi$
$53$	1.55291	−	1.55291i	0.213309	−	0.213309i	0.805672	+	0.592362i	$0.201805\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$		0			0
$56$	1.09808	−	0.633975i	0.146737	−	0.0847184i
$57$	8.81345	+	8.81345i	1.16737	+	1.16737i
$58$	7.02030	−	1.88108i	0.921811	−	0.246998i
$59$	−6.23205	+	10.7942i	−0.811344	+	1.40529i	0.100580	+	0.994929i	$0.467930\pi$
$59$	−6.23205	+	10.7942i	−0.811344	+	1.40529i	−0.911924	+	0.410360i	$0.865403\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−7.20977	−	7.20977i	−0.915642	−	0.915642i
$63$	−0.984508	+	3.67423i	−0.124036	+	0.462910i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	5.19615	+	3.00000i	0.639602	+	0.369274i
$67$	−3.22595	−	12.0394i	−0.394112	−	1.47085i	−0.823287	−	0.567625i	$-0.807862\pi$
$67$	−3.22595	−	12.0394i	−0.394112	−	1.47085i	0.429175	−	0.903221i	$-0.358804\pi$
$68$		0			0
$69$	12.2942	+	7.09808i	1.48005	+	0.854508i
$70$		0			0
$71$			10.7321i			1.27366i	0.771004	+	0.636830i	$0.219755\pi$
$71$			10.7321i			1.27366i	−0.771004	+	0.636830i	$0.780245\pi$
$72$	2.12132	+	2.12132i	0.250000	+	0.250000i
$73$	3.67423	+	3.67423i	0.430037	+	0.430037i	0.888641	−	0.458604i	$-0.151650\pi$
$73$	3.67423	+	3.67423i	0.430037	+	0.430037i	−0.458604	+	0.888641i	$0.651650\pi$
$74$	1.09808	+	1.90192i	0.127649	+	0.221094i
$75$		0			0
$76$	−3.59808	+	6.23205i	−0.412728	+	0.714865i
$77$	−4.24264	+	1.13681i	−0.483494	+	0.129552i
$78$	1.55291	+	1.55291i	0.175833	+	0.175833i
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.0737937	+	0.997274i	$0.523511\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−1.22474	+	1.22474i	−0.135250	+	0.135250i
$83$	6.57201	+	1.76097i	0.721372	+	0.193291i	0.600784	−	0.799412i	$-0.294855\pi$
$83$	6.57201	+	1.76097i	0.721372	+	0.193291i	0.120588	+	0.992703i	$0.461522\pi$
$84$	−2.19615			−0.239620
$85$		0			0
$86$	−5.59808	−	3.23205i	−0.603656	−	0.348521i
$87$	−12.1595	−	3.25813i	−1.30364	−	0.349308i
$88$	−0.896575	+	3.34607i	−0.0955753	+	0.356692i
$89$	8.66025			0.917985			0.458993	−	0.888440i	$-0.348210\pi$
$89$	8.66025			0.917985			0.458993	+	0.888440i	$0.348210\pi$
$90$		0			0
$91$	−1.60770			−0.168532
$92$	−2.12132	+	7.91688i	−0.221163	+	0.825391i
$93$	4.57081	+	17.0585i	0.473971	+	1.76888i
$94$	5.19615	+	3.00000i	0.535942	+	0.309426i
$95$		0			0
$96$	−0.866025	+	1.50000i	−0.0883883	+	0.153093i
$97$	14.1607	+	3.79435i	1.43780	+	0.385258i	0.891764	−	0.452501i	$-0.149468\pi$
$97$	14.1607	+	3.79435i	1.43780	+	0.385258i	0.546039	+	0.837760i	$0.316135\pi$
$98$	−3.81294	+	3.81294i	−0.385165	+	0.385165i
$99$	−5.19615	−	9.00000i	−0.522233	−	0.904534i
$100$		0			0
$101$	−9.29423	+	5.36603i	−0.924810	+	0.533939i	−0.885167	−	0.465274i	$-0.845956\pi$
$101$	−9.29423	+	5.36603i	−0.924810	+	0.533939i	−0.0396438	+	0.999214i	$0.512622\pi$
$102$		0			0
$103$	10.0382	−	2.68973i	0.989093	−	0.265027i	0.272223	−	0.962234i	$-0.412241\pi$
$103$	10.0382	−	2.68973i	0.989093	−	0.265027i	0.716869	+	0.697207i	$0.245574\pi$
$104$	−0.633975	+	1.09808i	−0.0621663	+	0.107675i
$105$		0			0
$106$	−1.09808	−	1.90192i	−0.106655	−	0.184731i
$107$	−0.568406	−	0.568406i	−0.0549499	−	0.0549499i	0.679098	−	0.734048i	$-0.262371\pi$
$107$	−0.568406	−	0.568406i	−0.0549499	−	0.0549499i	−0.734048	+	0.679098i	$0.762371\pi$
$108$	−1.34486	−	5.01910i	−0.129410	−	0.482963i
$109$		−	12.1962i		−	1.16818i	−0.811689	−	0.584090i	$-0.801452\pi$
$109$		−	12.1962i		−	1.16818i	0.811689	−	0.584090i	$-0.198548\pi$
$110$		0			0
$111$		−	3.80385i		−	0.361045i
$112$	−0.328169	−	1.22474i	−0.0310091	−	0.115728i
$113$	−1.91327	−	7.14042i	−0.179985	−	0.671714i	−0.995649	−	0.0931872i	$-0.970294\pi$
$113$	−1.91327	−	7.14042i	−0.179985	−	0.671714i	0.815663	−	0.578527i	$-0.196372\pi$
$114$	10.7942	−	6.23205i	1.01097	−	0.583685i
$115$		0			0
$116$		−	7.26795i		−	0.674812i
$117$	−0.984508	−	3.67423i	−0.0910178	−	0.339683i
$118$	8.81345	+	8.81345i	0.811344	+	0.811344i
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	3.86370	−	1.03528i	0.349803	−	0.0937295i
$123$	2.89778	−	0.776457i	0.261284	−	0.0700108i
$124$	−8.83013	+	5.09808i	−0.792969	+	0.457821i
$125$		0			0
$126$	3.29423	+	1.90192i	0.293473	+	0.169437i
$127$	−1.55291	+	1.55291i	−0.137799	+	0.137799i	−0.772641	−	0.634843i	$-0.781065\pi$
$127$	−1.55291	+	1.55291i	−0.137799	+	0.137799i	0.634843	+	0.772641i	$0.281065\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	5.59808	+	9.69615i	0.492883	+	0.853699i
$130$		0			0
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	0.214438	−	0.976738i	$-0.431208\pi$
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	−0.738661	+	0.674078i	$0.764541\pi$
$132$	4.24264	−	4.24264i	0.369274	−	0.369274i
$133$	−2.36156	+	8.81345i	−0.204773	+	0.764223i
$134$	−12.4641			−1.07673
$135$		0			0
$136$		0			0
$137$	−1.91327	+	7.14042i	−0.163462	+	0.610047i	0.834770	+	0.550599i	$0.185601\pi$
$137$	−1.91327	+	7.14042i	−0.163462	+	0.610047i	−0.998231	+	0.0594480i	$0.981066\pi$
$138$	10.0382	−	10.0382i	0.854508	−	0.854508i
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	0.764165	−	0.645021i	$-0.223151\pi$
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	−0.176522	+	0.984297i	$0.556485\pi$
$140$		0			0
$141$	−5.19615	−	9.00000i	−0.437595	−	0.757937i
$142$	10.3664	+	2.77766i	0.869926	+	0.233096i
$143$	3.10583	−	3.10583i	0.259722	−	0.259722i
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$		0			0
$146$	4.50000	−	2.59808i	0.372423	−	0.215018i
$147$	9.02150	−	2.41730i	0.744081	−	0.199376i
$148$	2.12132	−	0.568406i	0.174371	−	0.0467227i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	5.08845	+	5.08845i	0.412728	+	0.412728i
$153$		0			0
$154$			4.39230i			0.353942i
$155$		0			0
$156$	1.90192	−	1.09808i	0.152276	−	0.0879165i
$157$	−2.03339	−	7.58871i	−0.162282	−	0.605645i	−0.998371	−	0.0570512i	$-0.981830\pi$
$157$	−2.03339	−	7.58871i	−0.162282	−	0.605645i	0.836089	−	0.548593i	$-0.184837\pi$
$158$	2.58819	+	9.65926i	0.205905	+	0.768449i
$159$			3.80385i			0.301665i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	−2.32937	+	8.69333i	−0.183013	+	0.683013i
$163$	−14.3688	−	14.3688i	−1.12545	−	1.12545i	−0.990908	−	0.134541i	$-0.957044\pi$
$163$	−14.3688	−	14.3688i	−1.12545	−	1.12545i	−0.134541	−	0.990908i	$-0.542956\pi$
$164$	0.866025	+	1.50000i	0.0676252	+	0.117130i
$165$		0			0
$166$	3.40192	−	5.89230i	0.264040	−	0.457332i
$167$	4.24264	−	1.13681i	0.328305	−	0.0879692i	−0.0909015	−	0.995860i	$-0.528975\pi$
$167$	4.24264	−	1.13681i	0.328305	−	0.0879692i	0.419207	+	0.907891i	$0.362308\pi$
$168$	−0.568406	+	2.12132i	−0.0438535	+	0.163663i
$169$	−9.86603	+	5.69615i	−0.758925	+	0.438166i
$170$		0			0
$171$	−21.5885			−1.65091
$172$	−4.57081	+	4.57081i	−0.348521	+	0.348521i
$173$	4.24264	+	1.13681i	0.322562	+	0.0864302i	0.416467	−	0.909151i	$-0.363268\pi$
$173$	4.24264	+	1.13681i	0.322562	+	0.0864302i	−0.0939047	+	0.995581i	$0.529935\pi$
$174$	−6.29423	+	10.9019i	−0.477164	+	0.826473i
$175$		0			0
$176$	3.00000	+	1.73205i	0.226134	+	0.130558i
$177$	−5.58750	−	20.8528i	−0.419983	−	1.56740i
$178$	2.24144	−	8.36516i	0.168003	−	0.626995i
$179$	−4.85641			−0.362985			−0.181492	−	0.983392i	$-0.558093\pi$
$179$	−4.85641			−0.362985			−0.181492	+	0.983392i	$0.558093\pi$
$180$		0			0
$181$	8.39230			0.623795			0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230			0.623795			0.311898	+	0.950116i	$0.399035\pi$
$182$	−0.416102	+	1.55291i	−0.0308435	+	0.115110i
$183$	−6.69213	−	1.79315i	−0.494697	−	0.132554i
$184$	7.09808	+	4.09808i	0.523277	+	0.302114i
$185$		0			0
$186$	17.6603			1.29491
$187$		0			0
$188$	4.24264	−	4.24264i	0.309426	−	0.309426i
$189$	−3.29423	−	5.70577i	−0.239620	−	0.415034i
$190$		0			0
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	−0.387522	−	0.921861i	$-0.626669\pi$
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	0.604594	+	0.796534i	$0.293335\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$	−24.0788	+	6.45189i	−1.73323	+	0.464417i	−0.980923	−	0.194396i	$-0.937725\pi$
$193$	−24.0788	+	6.45189i	−1.73323	+	0.464417i	−0.752306	+	0.658813i	$0.771059\pi$
$194$	7.33013	−	12.6962i	0.526272	−	0.911531i
$195$		0			0
$196$	2.69615	+	4.66987i	0.192582	+	0.333562i
$197$	2.68973	+	2.68973i	0.191635	+	0.191635i	0.796402	−	0.604767i	$-0.206734\pi$
$197$	2.68973	+	2.68973i	0.191635	+	0.191635i	−0.604767	+	0.796402i	$0.706734\pi$
$198$	−10.0382	+	2.68973i	−0.713384	+	0.191151i
$199$			0.392305i			0.0278098i	0.999903	+	0.0139049i	$0.00442620\pi$
$199$			0.392305i			0.0278098i	−0.999903	+	0.0139049i	$0.995574\pi$
$200$		0			0
$201$	18.6962	+	10.7942i	1.31872	+	0.761366i
$202$	2.77766	+	10.3664i	0.195435	+	0.729375i
$203$	−2.38512	−	8.90138i	−0.167403	−	0.624755i
$204$		0			0
$205$		0			0
$206$		−	10.3923i		−	0.724066i
$207$	−23.7506	+	6.36396i	−1.65078	+	0.442326i
$208$	0.896575	+	0.896575i	0.0621663	+	0.0621663i
$209$	−12.4641	−	21.5885i	−0.862160	−	1.49330i
$210$		0			0
$211$	4.59808	−	7.96410i	0.316545	−	0.548271i	−0.663220	−	0.748424i	$-0.730811\pi$
$211$	4.59808	−	7.96410i	0.316545	−	0.548271i	0.979765	+	0.200153i	$0.0641440\pi$
$212$	−2.12132	+	0.568406i	−0.145693	+	0.0390383i
$213$	−13.1440	−	13.1440i	−0.900614	−	0.900614i
$214$	−0.696152	+	0.401924i	−0.0475880	+	0.0274749i
$215$		0			0
$216$	−5.19615			−0.353553
$217$	−9.14162	+	9.14162i	−0.620574	+	0.620574i
$218$	−11.7806	−	3.15660i	−0.797881	−	0.213792i
$219$	−9.00000			−0.608164
$220$		0			0
$221$		0			0
$222$	−3.67423	−	0.984508i	−0.246598	−	0.0660759i
$223$	−2.44949	+	9.14162i	−0.164030	+	0.612168i	0.834132	+	0.551565i	$0.185969\pi$
$223$	−2.44949	+	9.14162i	−0.164030	+	0.612168i	−0.998162	+	0.0606032i	$0.980698\pi$
$224$	−1.26795			−0.0847184
$225$		0			0
$226$	−7.39230			−0.491729
$227$	6.00361	−	22.4058i	0.398473	−	1.48712i	−0.417310	−	0.908764i	$-0.637027\pi$
$227$	6.00361	−	22.4058i	0.398473	−	1.48712i	0.815783	−	0.578358i	$-0.196306\pi$
$228$	−3.22595	−	12.0394i	−0.213644	−	0.797329i
$229$	14.0263	+	8.09808i	0.926883	+	0.535136i	0.885824	−	0.464021i	$-0.153594\pi$
$229$	14.0263	+	8.09808i	0.926883	+	0.535136i	0.0410583	+	0.999157i	$0.486927\pi$
$230$		0			0
$231$	3.80385	−	6.58846i	0.250275	−	0.433489i
$232$	−7.02030	−	1.88108i	−0.460905	−	0.123499i
$233$	−17.9551	+	17.9551i	−1.17628	+	1.17628i	−0.195590	+	0.980686i	$0.562662\pi$
$233$	−17.9551	+	17.9551i	−1.17628	+	1.17628i	−0.980686	+	0.195590i	$0.937338\pi$
$234$	−3.80385			−0.248665
$235$		0			0
$236$	10.7942	−	6.23205i	0.702644	−	0.405672i
$237$	4.48288	−	16.7303i	0.291194	−	1.08675i
$238$		0			0
$239$	−7.09808	+	12.2942i	−0.459136	+	0.795248i	−0.998916	−	0.0465591i	$-0.985174\pi$
$239$	−7.09808	+	12.2942i	−0.459136	+	0.795248i	0.539779	+	0.841807i	$0.318508\pi$
$240$		0			0
$241$	5.69615	+	9.86603i	0.366921	+	0.635527i	0.989083	−	0.147363i	$-0.0470785\pi$
$241$	5.69615	+	9.86603i	0.366921	+	0.635527i	−0.622161	+	0.782889i	$0.713745\pi$
$242$	−0.707107	−	0.707107i	−0.0454545	−	0.0454545i
$243$	11.0227	−	11.0227i	0.707107	−	0.707107i
$244$		−	4.00000i		−	0.256074i
$245$		0			0
$246$		−	3.00000i		−	0.191273i
$247$	−2.36156	−	8.81345i	−0.150262	−	0.560786i
$248$	2.63896	+	9.84873i	0.167574	+	0.625395i
$249$	−10.2058	+	5.89230i	−0.646764	+	0.373410i
$250$		0			0
$251$			9.00000i			0.568075i	0.958813	+	0.284037i	$0.0916740\pi$
$251$			9.00000i			0.568075i	−0.958813	+	0.284037i	$0.908326\pi$
$252$	2.68973	−	2.68973i	0.169437	−	0.169437i
$253$	−20.0764	−	20.0764i	−1.26219	−	1.26219i
$254$	1.09808	+	1.90192i	0.0688994	+	0.119337i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.45069	+	1.19256i	−0.277627	+	0.0743898i	−0.394946	−	0.918704i	$-0.629237\pi$
$257$	−4.45069	+	1.19256i	−0.277627	+	0.0743898i	0.117319	+	0.993094i	$0.462570\pi$
$258$	10.8147	−	2.89778i	0.673291	−	0.180408i
$259$	2.41154	−	1.39230i	0.149846	−	0.0865136i
$260$		0			0
$261$	18.8827	−	10.9019i	1.16881	−	0.674812i
$262$	−4.89898	+	4.89898i	−0.302660	+	0.302660i
$263$	17.9551	+	4.81105i	1.10716	+	0.296662i	0.765676	−	0.643227i	$-0.222405\pi$
$263$	17.9551	+	4.81105i	1.10716	+	0.296662i	0.341481	+	0.939889i	$0.389071\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$	7.90192	+	4.56218i	0.484498	+	0.279725i
$267$	−10.6066	+	10.6066i	−0.649113	+	0.649113i
$268$	−3.22595	+	12.0394i	−0.197056	+	0.735423i
$269$	28.0526			1.71039			0.855197	−	0.518303i	$-0.173436\pi$
$269$	28.0526			1.71039			0.855197	+	0.518303i	$0.173436\pi$
$270$		0			0
$271$	−4.58846			−0.278729			−0.139364	−	0.990241i	$-0.544506\pi$
$271$	−4.58846			−0.278729			−0.139364	+	0.990241i	$0.544506\pi$
$272$		0			0
$273$	1.96902	−	1.96902i	0.119170	−	0.119170i
$274$	6.40192	+	3.69615i	0.386754	+	0.223293i
$275$		0			0
$276$	−7.09808	−	12.2942i	−0.427254	−	0.740026i
$277$	24.6472	+	6.60420i	1.48091	+	0.396808i	0.906656	−	0.421871i	$-0.138627\pi$
$277$	24.6472	+	6.60420i	1.48091	+	0.396808i	0.574251	+	0.818679i	$0.305293\pi$
$278$	5.65685	−	5.65685i	0.339276	−	0.339276i
$279$	−26.4904	−	15.2942i	−1.58594	−	0.915642i
$280$		0			0
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	−0.206925	−	0.978357i	$-0.566345\pi$
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	0.743820	+	0.668380i	$0.233012\pi$
$282$	−10.0382	+	2.68973i	−0.597766	+	0.160171i
$283$	−9.58991	+	2.56961i	−0.570061	+	0.152747i	−0.532325	−	0.846540i	$-0.678681\pi$
$283$	−9.58991	+	2.56961i	−0.570061	+	0.152747i	−0.0377364	+	0.999288i	$0.512015\pi$
$284$	5.36603	−	9.29423i	0.318415	−	0.551511i
$285$		0			0
$286$	−2.19615	−	3.80385i	−0.129861	−	0.224926i
$287$	1.55291	+	1.55291i	0.0916656	+	0.0916656i
$288$	−0.776457	−	2.89778i	−0.0457532	−	0.170753i
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$	−21.9904	+	12.6962i	−1.28910	+	0.744262i
$292$	−1.34486	−	5.01910i	−0.0787022	−	0.293720i
$293$	3.67423	+	13.7124i	0.214651	+	0.801089i	0.986289	+	0.165027i	$0.0527711\pi$
$293$	3.67423	+	13.7124i	0.214651	+	0.801089i	−0.771638	+	0.636062i	$0.780562\pi$
$294$		−	9.33975i		−	0.544705i
$295$		0			0
$296$		−	2.19615i		−	0.127649i
$297$	17.3867	+	4.65874i	1.00888	+	0.270328i
$298$	−12.7279	−	12.7279i	−0.737309	−	0.737309i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	−4.09808	+	7.09808i	−0.236209	+	0.409126i
$302$	7.72741	−	2.07055i	0.444662	−	0.119147i
$303$	4.81105	−	17.9551i	0.276387	−	1.03149i
$304$	6.23205	−	3.59808i	0.357433	−	0.206364i
$305$		0			0
$306$		0			0
$307$	−2.44949	+	2.44949i	−0.139800	+	0.139800i	−0.773543	−	0.633743i	$-0.781517\pi$
$307$	−2.44949	+	2.44949i	−0.139800	+	0.139800i	0.633743	+	0.773543i	$0.281517\pi$
$308$	4.24264	+	1.13681i	0.241747	+	0.0647759i
$309$	−9.00000	+	15.5885i	−0.511992	+	0.886796i
$310$		0			0
$311$	21.5885	+	12.4641i	1.22417	+	0.706774i	0.965804	−	0.259273i	$-0.0834829\pi$
$311$	21.5885	+	12.4641i	1.22417	+	0.706774i	0.258365	+	0.966047i	$0.416816\pi$
$312$	−0.568406	−	2.12132i	−0.0321797	−	0.120096i
$313$	−0.864390	+	3.22595i	−0.0488582	+	0.182341i	−0.986043	−	0.166493i	$-0.946756\pi$
$313$	−0.864390	+	3.22595i	−0.0488582	+	0.182341i	0.937184	+	0.348834i	$0.113422\pi$
$314$	−7.85641			−0.443363
$315$		0			0
$316$	10.0000			0.562544
$317$	6.36396	−	23.7506i	0.357436	−	1.33397i	−0.519956	−	0.854193i	$-0.674052\pi$
$317$	6.36396	−	23.7506i	0.357436	−	1.33397i	0.877392	−	0.479775i	$-0.159282\pi$
$318$	3.67423	+	0.984508i	0.206041	+	0.0552085i
$319$	21.8038	+	12.5885i	1.22078	+	0.704818i
$320$		0			0
$321$	1.39230			0.0777109
$322$	10.0382	+	2.68973i	0.559407	+	0.149893i
$323$		0			0
$324$	7.79423	+	4.50000i	0.433013	+	0.250000i
$325$		0			0
$326$	−17.5981	+	10.1603i	−0.974667	+	0.562724i
$327$	14.9372	+	14.9372i	0.826028	+	0.826028i
$328$	1.67303	−	0.448288i	0.0923778	−	0.0247525i
$329$	3.80385	−	6.58846i	0.209713	−	0.363233i
$330$		0			0
$331$	−8.79423	−	15.2321i	−0.483375	−	0.837229i	0.516443	−	0.856321i	$-0.327256\pi$
$331$	−8.79423	−	15.2321i	−0.483375	−	0.837229i	−0.999818	+	0.0190922i	$0.993922\pi$
$332$	−4.81105	−	4.81105i	−0.264040	−	0.264040i
$333$	4.65874	+	4.65874i	0.255298	+	0.255298i
$334$		−	4.39230i		−	0.240336i
$335$		0			0
$336$	1.90192	+	1.09808i	0.103758	+	0.0599050i
$337$	7.10823	+	26.5283i	0.387210	+	1.44509i	0.834653	+	0.550775i	$0.185668\pi$
$337$	7.10823	+	26.5283i	0.387210	+	1.44509i	−0.447443	+	0.894312i	$0.647665\pi$
$338$	2.94855	+	11.0041i	0.160380	+	0.598545i
$339$	11.0885	+	6.40192i	0.602242	+	0.347705i
$340$		0			0
$341$		−	35.3205i		−	1.91271i
$342$	−5.58750	+	20.8528i	−0.302138	+	1.12759i
$343$	11.1106	+	11.1106i	0.599918	+	0.599918i
$344$	3.23205	+	5.59808i	0.174261	+	0.301828i
$345$		0			0
$346$	2.19615	−	3.80385i	0.118066	−	0.204496i
$347$	31.6675	−	8.48528i	1.70000	−	0.455514i	0.727061	−	0.686573i	$-0.240886\pi$
$347$	31.6675	−	8.48528i	1.70000	−	0.455514i	0.972940	+	0.231059i	$0.0742191\pi$
$348$	8.90138	+	8.90138i	0.477164	+	0.477164i
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$		0			0
$351$	5.70577	+	3.29423i	0.304552	+	0.175833i
$352$	2.44949	−	2.44949i	0.130558	−	0.130558i
$353$	14.4889	+	3.88229i	0.771166	+	0.206633i	0.622886	−	0.782312i	$-0.285960\pi$
$353$	14.4889	+	3.88229i	0.771166	+	0.206633i	0.148279	+	0.988946i	$0.452627\pi$
$354$	−21.5885			−1.14741
$355$		0			0
$356$	−7.50000	−	4.33013i	−0.397499	−	0.229496i
$357$		0			0
$358$	−1.25693	+	4.69093i	−0.0664308	+	0.247923i
$359$	−0.679492			−0.0358622			−0.0179311	−	0.999839i	$-0.505708\pi$
$359$	−0.679492			−0.0358622			−0.0179311	+	0.999839i	$0.505708\pi$
$360$		0			0
$361$	−32.7846			−1.72551
$362$	2.17209	−	8.10634i	0.114162	−	0.426060i
$363$	0.448288	+	1.67303i	0.0235290	+	0.0878114i
$364$	1.39230	+	0.803848i	0.0729766	+	0.0421331i
$365$		0			0
$366$	−3.46410	+	6.00000i	−0.181071	+	0.313625i
$367$	−30.7709	−	8.24504i	−1.60623	−	0.430388i	−0.659313	−	0.751868i	$-0.729153\pi$
$367$	−30.7709	−	8.24504i	−1.60623	−	0.430388i	−0.946916	+	0.321481i	$0.895819\pi$
$368$	5.79555	−	5.79555i	0.302114	−	0.302114i
$369$	−2.59808	+	4.50000i	−0.135250	+	0.234261i
$370$		0			0
$371$	−2.41154	+	1.39230i	−0.125201	+	0.0722849i
$372$	4.57081	−	17.0585i	0.236985	−	0.884442i
$373$	10.9348	−	2.92996i	0.566181	−	0.151708i	0.0356365	−	0.999365i	$-0.488654\pi$
$373$	10.9348	−	2.92996i	0.566181	−	0.151708i	0.530545	+	0.847657i	$0.321987\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	6.51626	+	6.51626i	0.335605	+	0.335605i
$378$	−6.36396	+	1.70522i	−0.327327	+	0.0877070i
$379$			20.3923i			1.04748i	0.851877	+	0.523741i	$0.175464\pi$
$379$			20.3923i			1.04748i	−0.851877	+	0.523741i	$0.824536\pi$
$380$		0			0
$381$		−	3.80385i		−	0.194877i
$382$	−0.896575	−	3.34607i	−0.0458728	−	0.171200i
$383$	9.46979	+	35.3417i	0.483884	+	1.80588i	0.585036	+	0.811007i	$0.301080\pi$
$383$	9.46979	+	35.3417i	0.483884	+	1.80588i	−0.101152	+	0.994871i	$0.532253\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$			24.9282i			1.26881i
$387$	−18.7315	−	5.01910i	−0.952177	−	0.255135i
$388$	−10.3664	−	10.3664i	−0.526272	−	0.526272i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$		0			0
$392$	5.20857	−	1.39563i	0.263072	−	0.0704900i
$393$	11.5911	−	3.10583i	0.584694	−	0.156668i
$394$	3.29423	−	1.90192i	0.165961	−	0.0958175i
$395$		0			0
$396$			10.3923i			0.522233i
$397$	−6.03579	+	6.03579i	−0.302928	+	0.302928i	−0.842158	−	0.539231i	$-0.818715\pi$
$397$	−6.03579	+	6.03579i	−0.302928	+	0.302928i	0.539231	+	0.842158i	$0.318715\pi$
$398$	0.378937	+	0.101536i	0.0189944	+	0.00508954i
$399$	−7.90192	−	13.6865i	−0.395591	−	0.685184i
$400$		0			0
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	0.707593	−	0.706620i	$-0.249781\pi$
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	−0.258154	+	0.966104i	$0.583114\pi$
$402$	15.2653	−	15.2653i	0.761366	−	0.761366i
$403$	3.34607	−	12.4877i	0.166679	−	0.622056i
$404$	10.7321			0.533939
$405$		0			0
$406$	−9.21539			−0.457352
$407$	−1.96902	+	7.34847i	−0.0976005	+	0.364250i
$408$		0			0
$409$	0.526279	+	0.303848i	0.0260228	+	0.0150243i	0.512955	−	0.858416i	$-0.328551\pi$
$409$	0.526279	+	0.303848i	0.0260228	+	0.0150243i	−0.486932	+	0.873440i	$0.661884\pi$
$410$		0			0
$411$	−6.40192	−	11.0885i	−0.315784	−	0.546953i
$412$	−10.0382	−	2.68973i	−0.494546	−	0.132513i
$413$	11.1750	−	11.1750i	0.549886	−	0.549886i
$414$			24.5885i			1.20846i
$415$		0			0
$416$	1.09808	−	0.633975i	0.0538376	−	0.0310832i
$417$	−13.3843	+	3.58630i	−0.655430	+	0.175622i
$418$	−24.0788	+	6.45189i	−1.17773	+	0.315572i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	4.29423	+	7.43782i	0.209288	+	0.362497i	0.951490	−	0.307678i	$-0.0995521\pi$
$421$	4.29423	+	7.43782i	0.209288	+	0.362497i	−0.742203	+	0.670176i	$0.766219\pi$
$422$	−6.50266	−	6.50266i	−0.316545	−	0.316545i
$423$	17.3867	+	4.65874i	0.845369	+	0.226516i
$424$			2.19615i			0.106655i
$425$		0			0
$426$	−16.0981	+	9.29423i	−0.779954	+	0.450307i
$427$	−1.31268	−	4.89898i	−0.0635249	−	0.237078i
$428$	0.208051	+	0.776457i	0.0100565	+	0.0375315i
$429$			7.60770i			0.367303i
$430$		0			0
$431$			3.12436i			0.150495i	0.997165	+	0.0752475i	$0.0239747\pi$
$431$			3.12436i			0.150495i	−0.997165	+	0.0752475i	$0.976025\pi$
$432$	−1.34486	+	5.01910i	−0.0647048	+	0.241481i
$433$	21.8695	+	21.8695i	1.05098	+	1.05098i	0.998629	+	0.0523546i	$0.0166726\pi$
$433$	21.8695	+	21.8695i	1.05098	+	1.05098i	0.0523546	+	0.998629i	$0.483327\pi$
$434$	6.46410	+	11.1962i	0.310287	+	0.537433i
$435$		0			0
$436$	−6.09808	+	10.5622i	−0.292045	+	0.505837i
$437$	−56.9710	+	15.2653i	−2.72529	+	0.730240i
$438$	−2.32937	+	8.69333i	−0.111302	+	0.415383i
$439$	28.2224	−	16.2942i	1.34698	−	0.777681i	0.359162	−	0.933275i	$-0.383063\pi$
$439$	28.2224	−	16.2942i	1.34698	−	0.777681i	0.987821	+	0.155594i	$0.0497292\pi$
$440$		0			0
$441$	−8.08846	+	14.0096i	−0.385165	+	0.667125i
$442$		0			0
$443$	−10.0382	−	2.68973i	−0.476929	−	0.127793i	0.0123433	−	0.999924i	$-0.496071\pi$
$443$	−10.0382	−	2.68973i	−0.476929	−	0.127793i	−0.489272	+	0.872131i	$0.662738\pi$
$444$	−1.90192	+	3.29423i	−0.0902613	+	0.156337i
$445$		0			0
$446$	8.19615	+	4.73205i	0.388099	+	0.224069i
$447$	8.06918	+	30.1146i	0.381659	+	1.42437i
$448$	−0.328169	+	1.22474i	−0.0155045	+	0.0578638i
$449$	5.87564			0.277289			0.138644	−	0.990342i	$-0.455725\pi$
$449$	5.87564			0.277289			0.138644	+	0.990342i	$0.455725\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	−1.91327	+	7.14042i	−0.0899926	+	0.335857i
$453$	−13.3843	−	3.58630i	−0.628847	−	0.168499i
$454$	−20.0885	−	11.5981i	−0.942798	−	0.544325i
$455$		0			0
$456$	−12.4641			−0.583685
$457$	−3.46618	−	0.928761i	−0.162141	−	0.0434456i	0.176835	−	0.984240i	$-0.443414\pi$
$457$	−3.46618	−	0.928761i	−0.162141	−	0.0434456i	−0.338976	+	0.940795i	$0.610081\pi$
$458$	11.4524	−	11.4524i	0.535136	−	0.535136i
$459$		0			0
$460$		0			0
$461$	−24.2942	+	14.0263i	−1.13150	+	0.653269i	−0.944310	−	0.329056i	$-0.893270\pi$
$461$	−24.2942	+	14.0263i	−1.13150	+	0.653269i	−0.187185	+	0.982325i	$0.559936\pi$
$462$	−5.37945	−	5.37945i	−0.250275	−	0.250275i
$463$	7.91688	−	2.12132i	0.367928	−	0.0985861i	−0.0701175	−	0.997539i	$-0.522337\pi$
$463$	7.91688	−	2.12132i	0.367928	−	0.0985861i	0.438046	+	0.898953i	$0.355671\pi$
$464$	−3.63397	+	6.29423i	−0.168703	+	0.292202i
$465$		0			0
$466$	12.6962	+	21.9904i	0.588138	+	1.01868i
$467$	15.2653	+	15.2653i	0.706396	+	0.706396i	0.965775	−	0.259380i	$-0.0835181\pi$
$467$	15.2653	+	15.2653i	0.706396	+	0.706396i	−0.259380	+	0.965775i	$0.583518\pi$
$468$	−0.984508	+	3.67423i	−0.0455089	+	0.169842i
$469$			15.8038i			0.729754i
$470$		0			0
$471$	11.7846	+	6.80385i	0.543006	+	0.313505i
$472$	−3.22595	−	12.0394i	−0.148486	−	0.554158i
$473$	−5.79555	−	21.6293i	−0.266480	−	0.994517i
$474$	−15.0000	−	8.66025i	−0.688973	−	0.397779i
$475$		0			0
$476$		0			0
$477$	−4.65874	−	4.65874i	−0.213309	−	0.213309i
$478$	10.0382	+	10.0382i	0.459136	+	0.459136i
$479$	10.5622	+	18.2942i	0.482598	+	0.835885i	0.999800	−	0.0199786i	$-0.00635981\pi$
$479$	10.5622	+	18.2942i	0.482598	+	0.835885i	−0.517202	+	0.855863i	$0.673026\pi$
$480$		0			0
$481$	−1.39230	+	2.41154i	−0.0634836	+	0.109957i
$482$	11.0041	−	2.94855i	0.501224	−	0.134303i
$483$	−12.7279	−	12.7279i	−0.579141	−	0.579141i
$484$	−0.866025	+	0.500000i	−0.0393648	+	0.0227273i
$485$		0			0
$486$	−7.79423	−	13.5000i	−0.353553	−	0.612372i
$487$	−15.5935	+	15.5935i	−0.706610	+	0.706610i	−0.965821	−	0.259211i	$-0.916537\pi$
$487$	−15.5935	+	15.5935i	−0.706610	+	0.706610i	0.259211	+	0.965821i	$0.416537\pi$
$488$	−3.86370	−	1.03528i	−0.174902	−	0.0468648i
$489$	35.1962			1.59163
$490$		0			0
$491$	−31.7942	−	18.3564i	−1.43485	−	0.828413i	−0.437368	−	0.899283i	$-0.644089\pi$
$491$	−31.7942	−	18.3564i	−1.43485	−	0.828413i	−0.997486	+	0.0708697i	$0.977423\pi$
$492$	−2.89778	−	0.776457i	−0.130642	−	0.0350054i
$493$		0			0
$494$	−9.12436			−0.410524
$495$		0			0
$496$	10.1962			0.457821
$497$	3.52193	−	13.1440i	0.157980	−	0.589590i
$498$	3.05008	+	11.3831i	0.136677	+	0.510087i
$499$	16.9641	+	9.79423i	0.759417	+	0.438450i	0.829087	−	0.559120i	$-0.188861\pi$
$499$	16.9641	+	9.79423i	0.759417	+	0.438450i	−0.0696691	+	0.997570i	$0.522194\pi$
$500$		0			0
$501$	−3.80385	+	6.58846i	−0.169943	+	0.294351i
$502$	8.69333	+	2.32937i	0.388002	+	0.103965i
$503$	−25.8719	+	25.8719i	−1.15357	+	1.15357i	−0.167742	+	0.985831i	$0.553648\pi$
$503$	−25.8719	+	25.8719i	−1.15357	+	1.15357i	−0.985831	+	0.167742i	$0.946352\pi$
$504$	−1.90192	−	3.29423i	−0.0847184	−	0.146737i
$505$		0			0
$506$	−24.5885	+	14.1962i	−1.09309	+	0.631096i
$507$	5.10703	−	19.0597i	0.226811	−	0.846471i
$508$	2.12132	−	0.568406i	0.0941184	−	0.0252189i
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	−0.998992	−	0.0448779i	$-0.985710\pi$
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	0.538362	+	0.842714i	$0.319043\pi$
$510$		0			0
$511$	−3.29423	−	5.70577i	−0.145728	−	0.252408i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	26.4404	−	26.4404i	1.16737	−	1.16737i
$514$			4.60770i			0.203237i
$515$		0			0
$516$		−	11.1962i		−	0.492883i
$517$	5.37945	+	20.0764i	0.236588	+	0.882959i
$518$	−0.720710	−	2.68973i	−0.0316662	−	0.118180i
$519$	−6.58846	+	3.80385i	−0.289201	+	0.166970i
$520$		0			0
$521$		−	38.7846i		−	1.69918i	−0.527440	−	0.849592i	$-0.676848\pi$
$521$		−	38.7846i		−	1.69918i	0.527440	−	0.849592i	$-0.323152\pi$
$522$	−5.64325	−	21.0609i	−0.246998	−	0.921811i
$523$	14.1929	+	14.1929i	0.620612	+	0.620612i	0.945688	−	0.325076i	$-0.105390\pi$
$523$	14.1929	+	14.1929i	0.620612	+	0.620612i	−0.325076	+	0.945688i	$0.605390\pi$
$524$	3.46410	+	6.00000i	0.151330	+	0.262111i
$525$		0			0
$526$	9.29423	−	16.0981i	0.405248	−	0.701909i
$527$		0			0
$528$	−5.79555	+	1.55291i	−0.252219	+	0.0675819i
$529$	−38.2583	+	22.0885i	−1.66341	+	0.960368i
$530$		0			0
$531$	32.3827	+	18.6962i	1.40529	+	0.811344i
$532$	6.45189	−	6.45189i	0.279725	−	0.279725i
$533$	−2.12132	−	0.568406i	−0.0918846	−	0.0246204i
$534$	7.50000	+	12.9904i	0.324557	+	0.562149i
$535$		0			0
$536$	10.7942	+	6.23205i	0.466240	+	0.269184i
$537$	5.94786	−	5.94786i	0.256669	−	0.256669i
$538$	7.26054	−	27.0967i	0.313024	−	1.16822i
$539$	−18.6795			−0.804583
$540$		0			0
$541$	12.3923			0.532787			0.266393	−	0.963864i	$-0.414168\pi$
$541$	12.3923			0.532787			0.266393	+	0.963864i	$0.414168\pi$
$542$	−1.18758	+	4.43211i	−0.0510109	+	0.190375i
$543$	−10.2784	+	10.2784i	−0.441090	+	0.441090i
$544$		0			0
$545$		0			0
$546$	−1.39230	−	2.41154i	−0.0595851	−	0.103205i
$547$	21.4213	+	5.73981i	0.915907	+	0.245416i	0.685835	−	0.727757i	$-0.259437\pi$
$547$	21.4213	+	5.73981i	0.915907	+	0.245416i	0.230072	+	0.973174i	$0.426104\pi$
$548$	5.22715	−	5.22715i	0.223293	−	0.223293i
$549$	10.3923	−	6.00000i	0.443533	−	0.256074i
$550$		0			0
$551$	45.2942	−	26.1506i	1.92960	−	1.11405i
$552$	−13.7124	+	3.67423i	−0.583640	+	0.156386i
$553$	12.2474	−	3.28169i	0.520814	−	0.139552i
$554$	12.7583	−	22.0981i	0.542050	−	0.938857i
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	11.5911	+	11.5911i	0.491131	+	0.491131i	0.908662	−	0.417531i	$-0.137105\pi$
$557$	11.5911	+	11.5911i	0.491131	+	0.491131i	−0.417531	+	0.908662i	$0.637105\pi$
$558$	−21.6293	+	21.6293i	−0.915642	+	0.915642i
$559$		−	8.19615i		−	0.346660i
$560$		0			0
$561$		0			0
$562$	−2.68973	−	10.0382i	−0.113459	−	0.423436i
$563$	−8.69333	−	32.4440i	−0.366380	−	1.36735i	−0.865540	−	0.500840i	$-0.833025\pi$
$563$	−8.69333	−	32.4440i	−0.366380	−	1.36735i	0.499160	−	0.866510i	$-0.333642\pi$
$564$			10.3923i			0.437595i
$565$		0			0
$566$			9.92820i			0.417314i
$567$	11.0227	+	2.95352i	0.462910	+	0.124036i
$568$	−7.58871	−	7.58871i	−0.318415	−	0.318415i
$569$	−5.53590	−	9.58846i	−0.232077	−	0.401969i	0.726342	−	0.687333i	$-0.241219\pi$
$569$	−5.53590	−	9.58846i	−0.232077	−	0.401969i	−0.958419	+	0.285364i	$0.907885\pi$
$570$		0			0
$571$	−4.40192	+	7.62436i	−0.184215	+	0.319069i	−0.943312	−	0.331908i	$-0.892308\pi$
$571$	−4.40192	+	7.62436i	−0.184215	+	0.319069i	0.759097	+	0.650978i	$0.225641\pi$
$572$	−4.24264	+	1.13681i	−0.177394	+	0.0475325i
$573$	−1.55291	+	5.79555i	−0.0648739	+	0.242113i
$574$	1.90192	−	1.09808i	0.0793848	−	0.0458328i
$575$		0			0
$576$	−3.00000			−0.125000
$577$	15.9217	−	15.9217i	0.662828	−	0.662828i	−0.293217	−	0.956046i	$-0.594726\pi$
$577$	15.9217	−	15.9217i	0.662828	−	0.662828i	0.956046	+	0.293217i	$0.0947260\pi$
$578$	−16.4207	−	4.39992i	−0.683013	−	0.183013i
$579$	21.5885	−	37.3923i	0.897186	−	1.55397i
$580$		0			0
$581$	−7.47114	−	4.31347i	−0.309955	−	0.178953i
$582$	6.57201	+	24.5271i	0.272419	+	1.01668i
$583$	1.96902	−	7.34847i	0.0815483	−	0.304342i
$584$	−5.19615			−0.215018
$585$		0			0
$586$	14.1962			0.586438
$587$	−4.24264	+	15.8338i	−0.175113	+	0.653529i	0.821420	+	0.570324i	$0.193182\pi$
$587$	−4.24264	+	15.8338i	−0.175113	+	0.653529i	−0.996532	+	0.0832050i	$0.973484\pi$
$588$	−9.02150	−	2.41730i	−0.372040	−	0.0996879i
$589$	−63.5429	−	36.6865i	−2.61824	−	1.51164i
$590$		0			0
$591$	−6.58846			−0.271013
$592$	−2.12132	−	0.568406i	−0.0871857	−	0.0233613i
$593$	14.8492	−	14.8492i	0.609785	−	0.609785i	−0.333105	−	0.942890i	$-0.608096\pi$
$593$	14.8492	−	14.8492i	0.609785	−	0.609785i	0.942890	+	0.333105i	$0.108096\pi$
$594$	9.00000	−	15.5885i	0.369274	−	0.639602i
$595$		0			0
$596$	−15.5885	+	9.00000i	−0.638528	+	0.368654i
$597$	−0.480473	−	0.480473i	−0.0196645	−	0.0196645i
$598$	−10.0382	+	2.68973i	−0.410492	+	0.109991i
$599$	−5.36603	+	9.29423i	−0.219250	+	0.379752i	−0.954579	−	0.297958i	$-0.903694\pi$
$599$	−5.36603	+	9.29423i	−0.219250	+	0.379752i	0.735329	+	0.677710i	$0.237028\pi$
$600$		0			0
$601$	−6.39230	−	11.0718i	−0.260748	−	0.451628i	0.705693	−	0.708518i	$-0.250636\pi$
$601$	−6.39230	−	11.0718i	−0.260748	−	0.451628i	−0.966441	+	0.256890i	$0.917302\pi$
$602$	5.79555	+	5.79555i	0.236209	+	0.236209i
$603$	−36.1182	+	9.67784i	−1.47085	+	0.394112i
$604$		−	8.00000i		−	0.325515i
$605$		0			0
$606$	−16.0981	−	9.29423i	−0.653940	−	0.377552i
$607$	−4.50644	−	16.8183i	−0.182911	−	0.682632i	−0.995068	−	0.0991937i	$-0.968374\pi$
$607$	−4.50644	−	16.8183i	−0.182911	−	0.682632i	0.812157	−	0.583438i	$-0.198293\pi$
$608$	−1.86250	−	6.95095i	−0.0755344	−	0.281898i
$609$	13.8231	+	7.98076i	0.560140	+	0.323397i
$610$		0			0
$611$			7.60770i			0.307774i
$612$		0			0
$613$	2.68973	+	2.68973i	0.108637	+	0.108637i	0.759336	−	0.650699i	$-0.225524\pi$
$613$	2.68973	+	2.68973i	0.108637	+	0.108637i	−0.650699	+	0.759336i	$0.725524\pi$
$614$	1.73205	+	3.00000i	0.0698999	+	0.121070i
$615$		0			0
$616$	2.19615	−	3.80385i	0.0884855	−	0.153261i
$617$	−28.7697	+	7.70882i	−1.15823	+	0.310346i	−0.786257	−	0.617900i	$-0.787984\pi$
$617$	−28.7697	+	7.70882i	−1.15823	+	0.310346i	−0.371969	+	0.928245i	$0.621317\pi$
$618$	12.7279	+	12.7279i	0.511992	+	0.511992i
$619$	14.2128	−	8.20577i	0.571261	−	0.329818i	−0.186392	−	0.982476i	$-0.559679\pi$
$619$	14.2128	−	8.20577i	0.571261	−	0.329818i	0.757653	+	0.652658i	$0.226346\pi$
$620$		0			0
$621$	21.2942	−	36.8827i	0.854508	−	1.48005i
$622$	17.6269	−	17.6269i	0.706774	−	0.706774i
$623$	−10.6066	−	2.84203i	−0.424945	−	0.113864i
$624$	−2.19615			−0.0879165
$625$		0			0
$626$	2.89230	+	1.66987i	0.115600	+	0.0667415i
$627$	41.7057	+	11.1750i	1.66557	+	0.446287i
$628$	−2.03339	+	7.58871i	−0.0811410	+	0.302822i
$629$		0			0
$630$		0			0
$631$	40.7846			1.62361			0.811805	−	0.583929i	$-0.198485\pi$
$631$	40.7846			1.62361			0.811805	+	0.583929i	$0.198485\pi$
$632$	2.58819	−	9.65926i	0.102953	−	0.384225i
$633$	4.12252	+	15.3855i	0.163856	+	0.611517i
$634$	−21.2942	−	12.2942i	−0.845702	−	0.488266i
$635$		0			0
$636$	1.90192	−	3.29423i	0.0754162	−	0.130625i
$637$	−6.60420	−	1.76959i	−0.261668	−	0.0701137i
$638$	17.8028	−	17.8028i	0.704818	−	0.704818i
$639$	32.1962			1.27366
$640$		0			0
$641$	−0.911543	+	0.526279i	−0.0360038	+	0.0207868i	−0.517894	−	0.855445i	$-0.673284\pi$
$641$	−0.911543	+	0.526279i	−0.0360038	+	0.0207868i	0.481890	+	0.876232i	$0.339950\pi$
$642$	0.360355	−	1.34486i	0.0142221	−	0.0530775i
$643$	16.0418	−	4.29839i	0.632627	−	0.169512i	0.0717654	−	0.997422i	$-0.477137\pi$
$643$	16.0418	−	4.29839i	0.632627	−	0.169512i	0.560861	+	0.827910i	$0.310470\pi$
$644$	5.19615	−	9.00000i	0.204757	−	0.354650i
$645$		0			0
$646$		0			0
$647$	−2.68973	−	2.68973i	−0.105744	−	0.105744i	0.652255	−	0.757999i	$-0.273823\pi$
$647$	−2.68973	−	2.68973i	−0.105744	−	0.105744i	−0.757999	+	0.652255i	$0.773823\pi$
$648$	6.36396	−	6.36396i	0.250000	−	0.250000i
$649$			43.1769i			1.69484i
$650$		0			0
$651$		−	22.3923i		−	0.877624i
$652$	5.25933	+	19.6281i	0.205971	+	0.768696i
$653$	0.568406	+	2.12132i	0.0222434	+	0.0830137i	0.976155	−	0.217073i	$-0.0696510\pi$
$653$	0.568406	+	2.12132i	0.0222434	+	0.0830137i	−0.953912	+	0.300087i	$0.902984\pi$
$654$	18.2942	−	10.5622i	0.715361	−	0.413014i
$655$		0			0
$656$		−	1.73205i		−	0.0676252i
$657$	11.0227	−	11.0227i	0.430037	−	0.430037i
$658$	−5.37945	−	5.37945i	−0.209713	−	0.209713i
$659$	−11.0885	−	19.2058i	−0.431945	−	0.748151i	0.565096	−	0.825025i	$-0.308839\pi$
$659$	−11.0885	−	19.2058i	−0.431945	−	0.748151i	−0.997041	+	0.0768747i	$0.975506\pi$
$660$		0			0
$661$	−11.5885	+	20.0718i	−0.450739	+	0.780702i	−0.998432	−	0.0559768i	$-0.982173\pi$
$661$	−11.5885	+	20.0718i	−0.450739	+	0.780702i	0.547693	+	0.836679i	$0.315506\pi$
$662$	−16.9891	+	4.55223i	−0.660302	+	0.176927i
$663$		0			0
$664$	−5.89230	+	3.40192i	−0.228666	+	0.132020i
$665$		0			0
$666$	5.70577	−	3.29423i	0.221094	−	0.127649i
$667$	42.1218	−	42.1218i	1.63096	−	1.63096i
$668$	−4.24264	−	1.13681i	−0.164153	−	0.0439846i
$669$	−8.19615	−	14.1962i	−0.316882	−	0.548855i
$670$		0			0
$671$	12.0000	+	6.92820i	0.463255	+	0.267460i
$672$	1.55291	−	1.55291i	0.0599050	−	0.0599050i
$673$	−0.416102	+	1.55291i	−0.0160396	+	0.0598604i	−0.973482	−	0.228765i	$-0.926531\pi$
$673$	−0.416102	+	1.55291i	−0.0160396	+	0.0598604i	0.957442	+	0.288625i	$0.0931981\pi$
$674$	27.4641			1.05788
$675$		0			0
$676$	11.3923			0.438166
$677$	−1.70522	+	6.36396i	−0.0655369	+	0.244587i	−0.990921	−	0.134443i	$-0.957076\pi$
$677$	−1.70522	+	6.36396i	−0.0655369	+	0.244587i	0.925384	+	0.379030i	$0.123742\pi$
$678$	9.05369	−	9.05369i	0.347705	−	0.347705i
$679$	−16.0981	−	9.29423i	−0.617787	−	0.356680i
$680$		0			0
$681$	20.0885	+	34.7942i	0.769791	+	1.33332i
$682$	−34.1170	−	9.14162i	−1.30641	−	0.350051i
$683$	−27.9933	+	27.9933i	−1.07113	+	1.07113i	−0.0738643	+	0.997268i	$0.523533\pi$
$683$	−27.9933	+	27.9933i	−1.07113	+	1.07113i	−0.997268	+	0.0738643i	$0.976467\pi$
$684$	18.6962	+	10.7942i	0.714865	+	0.412728i
$685$		0			0
$686$	13.6077	−	7.85641i	0.519544	−	0.299959i
$687$	−27.0967	+	7.26054i	−1.03380	+	0.277007i
$688$	6.24384	−	1.67303i	0.238044	−	0.0637838i
$689$	1.39230	−	2.41154i	0.0530426	−	0.0918725i
$690$		0			0
$691$	−6.20577	−	10.7487i	−0.236079	−	0.408900i	0.723507	−	0.690317i	$-0.242529\pi$
$691$	−6.20577	−	10.7487i	−0.236079	−	0.408900i	−0.959586	+	0.281417i	$0.909196\pi$
$692$	−3.10583	−	3.10583i	−0.118066	−	0.118066i
$693$	3.41044	+	12.7279i	0.129552	+	0.483494i
$694$		−	32.7846i		−	1.24449i
$695$		0			0
$696$	10.9019	−	6.29423i	0.413236	−	0.238582i
$697$		0			0
$698$	0.517638	+	1.93185i	0.0195929	+	0.0731217i
$699$		−	43.9808i		−	1.66351i
$700$		0			0
$701$			21.4641i			0.810688i	0.914164	+	0.405344i	$0.132848\pi$
$701$			21.4641i			0.810688i	−0.914164	+	0.405344i	$0.867152\pi$
$702$	4.65874	−	4.65874i	0.175833	−	0.175833i
$703$	11.1750	+	11.1750i	0.421473	+	0.421473i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	7.50000	−	12.9904i	0.282266	−	0.488899i
$707$	13.1440	−	3.52193i	0.494332	−	0.132456i
$708$	−5.58750	+	20.8528i	−0.209991	+	0.783698i
$709$	22.3468	−	12.9019i	0.839251	−	0.484542i	−0.0177584	−	0.999842i	$-0.505653\pi$
$709$	22.3468	−	12.9019i	0.839251	−	0.484542i	0.857010	+	0.515300i	$0.172320\pi$
$710$		0			0
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$	−6.12372	+	6.12372i	−0.229496	+	0.229496i
$713$	−80.7217	−	21.6293i	−3.02305	−	0.810024i
$714$		0			0
$715$		0			0
$716$	4.20577	+	2.42820i	0.157177	+	0.0907462i
$717$	−6.36396	−	23.7506i	−0.237666	−	0.886983i
$718$	−0.175865	+	0.656339i	−0.00656324	+	0.0244943i
$719$	−39.1244			−1.45909			−0.729546	−	0.683932i	$-0.760269\pi$
$719$	−39.1244			−1.45909			−0.729546	+	0.683932i	$0.760269\pi$
$720$		0			0
$721$	−13.1769			−0.490734
$722$	−8.48528	+	31.6675i	−0.315789	+	1.17854i
$723$	−19.0597	−	5.10703i	−0.708838	−	0.189933i
$724$	−7.26795	−	4.19615i	−0.270111	−	0.155949i
$725$		0			0
$726$	1.73205			0.0642824
$727$	−6.69213	−	1.79315i	−0.248197	−	0.0665043i	0.132575	−	0.991173i	$-0.457675\pi$
$727$	−6.69213	−	1.79315i	−0.248197	−	0.0665043i	−0.380773	+	0.924669i	$0.624342\pi$
$728$	1.13681	−	1.13681i	0.0421331	−	0.0421331i
$729$			27.0000i			1.00000i
$730$		0			0
$731$		0			0
$732$	4.89898	+	4.89898i	0.181071	+	0.181071i
$733$	33.2204	−	8.90138i	1.22702	−	0.328780i	0.413604	−	0.910457i	$-0.364270\pi$
$733$	33.2204	−	8.90138i	1.22702	−	0.328780i	0.813420	+	0.581677i	$0.197603\pi$
$734$	−15.9282	+	27.5885i	−0.587921	+	1.01831i
$735$		0			0
$736$	−4.09808	−	7.09808i	−0.151057	−	0.261639i
$737$	−30.5307	−	30.5307i	−1.12461	−	1.12461i
$738$	3.67423	+	3.67423i	0.135250	+	0.135250i
$739$		−	11.5885i		−	0.426288i	−0.977021	−	0.213144i	$-0.931630\pi$
$739$		−	11.5885i		−	0.426288i	0.977021	−	0.213144i	$-0.0683704\pi$
$740$		0			0
$741$	13.6865	+	7.90192i	0.502787	+	0.290284i
$742$	0.720710	+	2.68973i	0.0264581	+	0.0987430i
$743$	−10.1905	−	38.0315i	−0.373853	−	1.39524i	−0.855013	−	0.518606i	$-0.826451\pi$
$743$	−10.1905	−	38.0315i	−0.373853	−	1.39524i	0.481160	−	0.876633i	$-0.340216\pi$
$744$	−15.2942	−	8.83013i	−0.560714	−	0.323728i
$745$		0			0
$746$		−	11.3205i		−	0.414473i
$747$	5.28290	−	19.7160i	0.193291	−	0.721372i
$748$		0			0
$749$	0.509619	+	0.882686i	0.0186211	+	0.0322526i
$750$		0			0
$751$	10.2942	−	17.8301i	0.375642	−	0.650631i	−0.614781	−	0.788698i	$-0.710756\pi$
$751$	10.2942	−	17.8301i	0.375642	−	0.650631i	0.990423	+	0.138067i	$0.0440890\pi$
$752$	−5.79555	+	1.55291i	−0.211342	+	0.0566290i
$753$	−11.0227	−	11.0227i	−0.401690	−	0.401690i
$754$	7.98076	−	4.60770i	0.290642	−	0.167802i
$755$		0			0
$756$			6.58846i			0.239620i
$757$	10.5187	−	10.5187i	0.382308	−	0.382308i	−0.489625	−	0.871933i	$-0.662866\pi$
$757$	10.5187	−	10.5187i	0.382308	−	0.382308i	0.871933	+	0.489625i	$0.162866\pi$
$758$	19.6975	+	5.27792i	0.715444	+	0.191703i
$759$	49.1769			1.78501
$760$		0			0
$761$	−9.91154	−	5.72243i	−0.359293	−	0.207438i	0.309478	−	0.950907i	$-0.399846\pi$
$761$	−9.91154	−	5.72243i	−0.359293	−	0.207438i	−0.668771	+	0.743469i	$0.733179\pi$
$762$	−3.67423	−	0.984508i	−0.133103	−	0.0356650i
$763$	−4.00240	+	14.9372i	−0.144897	+	0.540762i
$764$	−3.46410			−0.125327
$765$		0			0
$766$	36.5885			1.32199
$767$	−4.09034	+	15.2653i	−0.147693	+	0.551200i
$768$	−0.448288	−	1.67303i	−0.0161762	−	0.0603704i
$769$	−28.9186	−	16.6962i	−1.04283	−	0.602079i	−0.122197	−	0.992506i	$-0.538994\pi$
$769$	−28.9186	−	16.6962i	−1.04283	−	0.602079i	−0.920634	+	0.390427i	$0.872327\pi$
$770$		0			0
$771$	3.99038	−	6.91154i	0.143710	−	0.248913i
$772$	24.0788	+	6.45189i	0.866615	+	0.232209i
$773$	−6.51626	+	6.51626i	−0.234374	+	0.234374i	−0.814516	−	0.580142i	$-0.802997\pi$
$773$	−6.51626	+	6.51626i	−0.234374	+	0.234374i	0.580142	+	0.814516i	$0.302997\pi$
$774$	−9.69615	+	16.7942i	−0.348521	+	0.603656i
$775$		0			0
$776$	−12.6962	+	7.33013i	−0.455765	+	0.263136i
$777$	−1.24831	+	4.65874i	−0.0447827	+	0.167131i
$778$	−10.0382	+	2.68973i	−0.359887	+	0.0964314i
$779$	−6.23205	+	10.7942i	−0.223286	+	0.386743i
$780$		0			0
$781$	18.5885	+	32.1962i	0.665147	+	1.15207i
$782$		0			0
$783$	−9.77440	+	36.4785i	−0.349308	+	1.30364i
$784$		−	5.39230i		−	0.192582i
$785$		0			0
$786$		−	12.0000i		−	0.428026i
$787$	−4.48288	−	16.7303i	−0.159797	−	0.596372i	−0.998647	−	0.0520081i	$-0.983438\pi$
$787$	−4.48288	−	16.7303i	−0.159797	−	0.596372i	0.838849	−	0.544364i	$-0.183229\pi$
$788$	−0.984508	−	3.67423i	−0.0350717	−	0.130889i
$789$	−27.8827	+	16.0981i	−0.992650	+	0.573107i
$790$		0			0
$791$			9.37307i			0.333268i
$792$	10.0382	+	2.68973i	0.356692	+	0.0955753i
$793$	3.58630	+	3.58630i	0.127353	+	0.127353i
$794$	4.26795	+	7.39230i	0.151464	+	0.262343i
$795$		0			0
$796$	0.196152	−	0.339746i	0.00695244	−	0.0120420i
$797$	−10.6066	+	2.84203i	−0.375705	+	0.100670i	−0.441730	−	0.897148i	$-0.645635\pi$
$797$	−10.6066	+	2.84203i	−0.375705	+	0.100670i	0.0660248	+	0.997818i	$0.478968\pi$
$798$	−15.2653	+	4.09034i	−0.540387	+	0.144796i
$799$		0			0
$800$		0			0
$801$		−	25.9808i		−	0.917985i
$802$	7.34847	−	7.34847i	0.259483	−	0.259483i
$803$	17.3867	+	4.65874i	0.613562	+	0.164403i
$804$	−10.7942	−	18.6962i	−0.380683	−	0.659362i
$805$		0			0
$806$	−11.1962	−	6.46410i	−0.394368	−	0.227688i
$807$	−34.3572	+	34.3572i	−1.20943	+	1.20943i
$808$	2.77766	−	10.3664i	0.0977177	−	0.364687i
$809$	1.73205			0.0608957			0.0304478	−	0.999536i	$-0.490307\pi$
$809$	1.73205			0.0608957			0.0304478	+	0.999536i	$0.490307\pi$
$810$		0			0
$811$	−38.3731			−1.34746			−0.673730	−	0.738977i	$-0.735309\pi$
$811$	−38.3731			−1.34746			−0.673730	+	0.738977i	$0.735309\pi$
$812$	−2.38512	+	8.90138i	−0.0837013	+	0.312377i
$813$	5.61969	−	5.61969i	0.197091	−	0.197091i
$814$	6.58846	+	3.80385i	0.230925	+	0.133325i
$815$		0			0
$816$		0			0
$817$	−44.9316	−	12.0394i	−1.57196	−	0.421205i
$818$	0.429705	−	0.429705i	0.0150243	−	0.0150243i
$819$			4.82309i			0.168532i
$820$		0			0
$821$	−18.5885	+	10.7321i	−0.648742	+	0.374551i	−0.787974	−	0.615709i	$-0.788870\pi$
$821$	−18.5885	+	10.7321i	−0.648742	+	0.374551i	0.139232	+	0.990260i	$0.455537\pi$
$822$	−12.3676	+	3.31388i	−0.431368	+	0.115585i
$823$	−27.6651	+	7.41284i	−0.964345	+	0.258395i	−0.706438	−	0.707775i	$-0.749699\pi$
$823$	−27.6651	+	7.41284i	−0.964345	+	0.258395i	−0.257906	+	0.966170i	$0.583033\pi$
$824$	−5.19615	+	9.00000i	−0.181017	+	0.313530i
$825$		0			0
$826$	−7.90192	−	13.6865i	−0.274943	−	0.476215i
$827$	−7.91688	−	7.91688i	−0.275297	−	0.275297i	0.555931	−	0.831228i	$-0.312362\pi$
$827$	−7.91688	−	7.91688i	−0.275297	−	0.275297i	−0.831228	+	0.555931i	$0.812362\pi$
$828$	23.7506	+	6.36396i	0.825391	+	0.221163i
$829$		−	2.58846i		−	0.0899008i	−0.998989	−	0.0449504i	$-0.985687\pi$
$829$		−	2.58846i		−	0.0899008i	0.998989	−	0.0449504i	$-0.0143130\pi$
$830$		0			0
$831$	−38.2750	+	22.0981i	−1.32774	+	0.766574i
$832$	−0.328169	−	1.22474i	−0.0113772	−	0.0424604i
$833$		0			0
$834$			13.8564i			0.479808i
$835$		0			0
$836$			24.9282i			0.862160i
$837$	51.1755	−	13.7124i	1.76888	−	0.473971i
$838$	6.36396	+	6.36396i	0.219839	+	0.219839i
$839$	15.7583	+	27.2942i	0.544038	+	0.942301i	0.998667	+	0.0516204i	$0.0164386\pi$
$839$	15.7583	+	27.2942i	0.544038	+	0.942301i	−0.454629	+	0.890681i	$0.650228\pi$
$840$		0			0
$841$	−11.9115	+	20.6314i	−0.410743	+	0.711427i
$842$	8.29581	−	2.22286i	0.285893	−	0.0766047i
$843$	−4.65874	+	17.3867i	−0.160456	+	0.598829i
$844$	−7.96410	+	4.59808i	−0.274136	+	0.158272i
$845$		0			0
$846$	9.00000	−	15.5885i	0.309426	−	0.535942i
$847$	−0.896575	+	0.896575i	−0.0308067	+	0.0308067i
$848$	2.12132	+	0.568406i	0.0728464	+	0.0195191i
$849$	8.59808	−	14.8923i	0.295085	−	0.511103i
$850$		0			0
$851$	15.5885	+	9.00000i	0.534365	+	0.308516i
$852$	4.81105	+	17.9551i	0.164824	+	0.615131i
$853$	13.8004	−	51.5037i	0.472515	−	1.76345i	−0.158169	−	0.987412i	$-0.550559\pi$
$853$	13.8004	−	51.5037i	0.472515	−	1.76345i	0.630684	−	0.776040i	$-0.282774\pi$
$854$	−5.07180			−0.173553
$855$		0			0
$856$	0.803848			0.0274749
$857$	0.0557471	−	0.208051i	0.00190429	−	0.00710689i	−0.964967	−	0.262371i	$-0.915496\pi$
$857$	0.0557471	−	0.208051i	0.00190429	−	0.00710689i	0.966871	+	0.255264i	$0.0821623\pi$
$858$	7.34847	+	1.96902i	0.250873	+	0.0672211i
$859$	−9.01666	−	5.20577i	−0.307644	−	0.177619i	0.338227	−	0.941064i	$-0.390173\pi$
$859$	−9.01666	−	5.20577i	−0.307644	−	0.177619i	−0.645872	+	0.763446i	$0.723506\pi$
$860$		0			0
$861$	−3.80385			−0.129635
$862$	3.01790	+	0.808643i	0.102790	+	0.0275425i
$863$	−3.52193	+	3.52193i	−0.119888	+	0.119888i	−0.764505	−	0.644617i	$-0.777017\pi$
$863$	−3.52193	+	3.52193i	−0.119888	+	0.119888i	0.644617	+	0.764505i	$0.277017\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$	26.7846	−	15.4641i	0.910178	−	0.525492i
$867$	20.8207	+	20.8207i	0.707107	+	0.707107i
$868$	12.4877	−	3.34607i	0.423860	−	0.113573i
$869$	−17.3205	+	30.0000i	−0.587558	+	1.01768i
$870$		0			0
$871$	−7.90192	−	13.6865i	−0.267746	−	0.463750i
$872$	8.62398	+	8.62398i	0.292045	+	0.292045i
$873$	11.3831	−	42.4822i	0.385258	−	1.43780i
$874$			58.9808i			1.99505i
$875$		0			0
$876$	7.79423	+	4.50000i	0.263343	+	0.152041i
$877$	5.97142	+	22.2856i	0.201641	+	0.752533i	0.990447	+	0.137892i	$0.0440325\pi$
$877$	5.97142	+	22.2856i	0.201641	+	0.752533i	−0.788807	+	0.614641i	$0.789301\pi$
$878$	−8.43451	−	31.4780i	−0.284651	−	1.06233i
$879$	−21.2942	−	12.2942i	−0.718237	−	0.414674i
$880$		0			0
$881$		−	53.3205i		−	1.79641i	−0.439573	−	0.898207i	$-0.644870\pi$
$881$		−	53.3205i		−	1.79641i	0.439573	−	0.898207i	$-0.355130\pi$
$882$	11.4388	+	11.4388i	0.385165	+	0.385165i
$883$	1.31268	+	1.31268i	0.0441751	+	0.0441751i	0.728849	−	0.684674i	$-0.240055\pi$
$883$	1.31268	+	1.31268i	0.0441751	+	0.0441751i	−0.684674	+	0.728849i	$0.740055\pi$
$884$		0			0
$885$		0			0
$886$	−5.19615	+	9.00000i	−0.174568	+	0.302361i
$887$	10.0382	−	2.68973i	0.337050	−	0.0903122i	−0.0863246	−	0.996267i	$-0.527512\pi$
$887$	10.0382	−	2.68973i	0.337050	−	0.0903122i	0.423374	+	0.905955i	$0.360846\pi$
$888$	2.68973	+	2.68973i	0.0902613	+	0.0902613i
$889$	2.41154	−	1.39230i	0.0808805	−	0.0466964i
$890$		0			0
$891$	−27.0000	+	15.5885i	−0.904534	+	0.522233i
$892$	6.69213	−	6.69213i	0.224069	−	0.224069i
$893$	41.7057	+	11.1750i	1.39563	+	0.373957i
$894$	31.1769			1.04271
$895$		0			0
$896$	1.09808	+	0.633975i	0.0366842	+	0.0211796i
$897$	17.3867	+	4.65874i	0.580524	+	0.155551i
$898$	1.52073	−	5.67544i	0.0507474	−	0.189392i
$899$	74.1051			2.47154
$900$		0			0
$901$		0			0
$902$	−1.55291	+	5.79555i	−0.0517064	+	0.192971i
$903$	−3.67423	−	13.7124i	−0.122271	−	0.456321i
$904$	6.40192	+	3.69615i	0.212925	+	0.122932i
$905$		0			0
$906$	−6.92820	+	12.0000i	−0.230174	+	0.398673i
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.312687	−	0.949856i	$-0.601229\pi$
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.745723	+	0.666256i	$0.767896\pi$
$908$	−16.4022	+	16.4022i	−0.544325	+	0.544325i
$909$	16.0981	+	27.8827i	0.533939	+	0.924810i
$910$		0			0
$911$	−12.8827	+	7.43782i	−0.426822	+	0.246426i	−0.697992	−	0.716106i	$-0.745923\pi$
$911$	−12.8827	+	7.43782i	−0.426822	+	0.246426i	0.271170	+	0.962532i	$0.412590\pi$
$912$	−3.22595	+	12.0394i	−0.106822	+	0.398664i
$913$	22.7661	−	6.10016i	0.753449	−	0.201886i
$914$	−1.79423	+	3.10770i	−0.0593478	+	0.102793i
$915$		0			0
$916$	−8.09808	−	14.0263i	−0.267568	−	0.463441i
$917$	6.21166	+	6.21166i	0.205127	+	0.205127i
$918$		0			0
$919$			27.4115i			0.904223i	0.891961	+	0.452112i	$0.149329\pi$
$919$			27.4115i			0.904223i	−0.891961	+	0.452112i	$0.850671\pi$
$920$		0			0
$921$		−	6.00000i		−	0.197707i
$922$	7.26054	+	27.0967i	0.239113	+	0.892382i
$923$	3.52193	+	13.1440i	0.115926	+	0.432641i
$924$	−6.58846	+	3.80385i	−0.216744	+	0.125137i
$925$		0			0
$926$		−	8.19615i		−	0.269342i
$927$	−8.06918	−	30.1146i	−0.265027	−	0.989093i
$928$	5.13922	+	5.13922i	0.168703	+	0.168703i
$929$	−2.07180	−	3.58846i	−0.0679734	−	0.117733i	0.830036	−	0.557710i	$-0.188320\pi$
$929$	−2.07180	−	3.58846i	−0.0679734	−	0.117733i	−0.898009	+	0.439977i	$0.854987\pi$
$930$		0			0
$931$	−19.4019	+	33.6051i	−0.635872	+	1.10136i
$932$	24.5271	−	6.57201i	0.803411	−	0.215273i
$933$	−41.7057	+	11.1750i	−1.36538	+	0.365853i
$934$	18.6962	−	10.7942i	0.611757	−	0.353198i
$935$		0			0
$936$	3.29423	+	1.90192i	0.107675	+	0.0621663i
$937$	9.22955	−	9.22955i	0.301516	−	0.301516i	−0.540091	−	0.841607i	$-0.681610\pi$
$937$	9.22955	−	9.22955i	0.301516	−	0.301516i	0.841607	+	0.540091i	$0.181610\pi$
$938$	15.2653	+	4.09034i	0.498431	+	0.133554i
$939$	−2.89230	−	5.00962i	−0.0943868	−	0.163483i
$940$		0			0
$941$	−36.8827	−	21.2942i	−1.20234	−	0.694172i	−0.241266	−	0.970459i	$-0.577563\pi$
$941$	−36.8827	−	21.2942i	−1.20234	−	0.694172i	−0.961075	+	0.276287i	$0.910896\pi$
$942$	9.62209	−	9.62209i	0.313505	−	0.313505i
$943$	−3.67423	+	13.7124i	−0.119650	+	0.446538i
$944$	−12.4641			−0.405672
$945$		0			0
$946$	−22.3923			−0.728037
$947$	7.86113	−	29.3381i	0.255452	−	0.953361i	−0.712386	−	0.701788i	$-0.752385\pi$
$947$	7.86113	−	29.3381i	0.255452	−	0.953361i	0.967838	−	0.251573i	$-0.0809479\pi$
$948$	−12.2474	+	12.2474i	−0.397779	+	0.397779i
$949$	5.70577	+	3.29423i	0.185217	+	0.106935i
$950$		0			0
$951$	21.2942	+	36.8827i	0.690513	+	1.19600i
$952$		0			0
$953$	28.5617	−	28.5617i	0.925203	−	0.925203i	−0.0721877	−	0.997391i	$-0.522998\pi$
$953$	28.5617	−	28.5617i	0.925203	−	0.925203i	0.997391	+	0.0721877i	$0.0229981\pi$
$954$	−5.70577	+	3.29423i	−0.184731	+	0.106655i
$955$		0			0
$956$	12.2942	−	7.09808i	0.397624	−	0.229568i
$957$	−42.1218	+	11.2865i	−1.36160	+	0.364841i
$958$	20.4046	−	5.46739i	0.659241	−	0.176643i
$959$	4.68653	−	8.11731i	0.151336	−	0.262122i
$960$		0			0
$961$	−36.4808	−	63.1865i	−1.17680	−	2.03828i
$962$	1.96902	+	1.96902i	0.0634836	+	0.0634836i
$963$	−1.70522	+	1.70522i	−0.0549499	+	0.0549499i
$964$		−	11.3923i		−	0.366921i
$965$		0			0
$966$	−15.5885	+	9.00000i	−0.501550	+	0.289570i
$967$	10.7589	+	40.1528i	0.345983	+	1.29123i	0.891460	+	0.453100i	$0.149682\pi$
$967$	10.7589	+	40.1528i	0.345983	+	1.29123i	−0.545476	+	0.838126i	$0.683651\pi$
$968$	0.258819	+	0.965926i	0.00831876	+	0.0310460i
$969$		0			0
$970$		0			0
$971$			36.0333i			1.15636i	0.815908	+	0.578182i	$0.196238\pi$
$971$			36.0333i			1.15636i	−0.815908	+	0.578182i	$0.803762\pi$
$972$	−15.0573	+	4.03459i	−0.482963	+	0.129410i
$973$	−7.17260	−	7.17260i	−0.229943	−	0.229943i
$974$	11.0263	+	19.0981i	0.353305	+	0.611942i
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	15.6257	−	4.18689i	0.499910	−	0.133951i	−4.80066e−5	−	1.00000i	$-0.500015\pi$
$977$	15.6257	−	4.18689i	0.499910	−	0.133951i	0.499958	+	0.866049i	$0.333349\pi$
$978$	9.10943	−	33.9969i	0.291288	−	1.08710i
$979$	25.9808	−	15.0000i	0.830349	−	0.479402i
$980$		0			0
$981$	−36.5885			−1.16818
$982$	−25.9599	+	25.9599i	−0.828413	+	0.828413i
$983$	18.5235	+	4.96335i	0.590807	+	0.158306i	0.541822	−	0.840493i	$-0.317735\pi$
$983$	18.5235	+	4.96335i	0.590807	+	0.158306i	0.0489851	+	0.998800i	$0.484401\pi$
$984$	−1.50000	+	2.59808i	−0.0478183	+	0.0828236i
$985$		0			0
$986$		0			0
$987$	3.41044	+	12.7279i	0.108555	+	0.405134i
$988$	−2.36156	+	8.81345i	−0.0751311	+	0.280393i
$989$	−52.9808			−1.68469
$990$		0			0
$991$	33.1769			1.05390			0.526950	−	0.849896i	$-0.323336\pi$
$991$	33.1769			1.05390			0.526950	+	0.849896i	$0.323336\pi$
$992$	2.63896	−	9.84873i	0.0837870	−	0.312697i
$993$	29.4261	+	7.88469i	0.933808	+	0.250213i
$994$	−11.7846	−	6.80385i	−0.373785	−	0.215805i
$995$		0			0
$996$	11.7846			0.373410
$997$	−31.0991	−	8.33298i	−0.984918	−	0.263908i	−0.269804	−	0.962915i	$-0.586959\pi$
$997$	−31.0991	−	8.33298i	−0.984918	−	0.263908i	−0.715115	+	0.699007i	$0.753625\pi$
$998$	13.8511	−	13.8511i	0.438450	−	0.438450i
$999$	−11.4115			−0.361045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.c.293.2	yes	8
3.2	odd	2		1350.2.q.d.1043.1		8
5.2	odd	4		450.2.p.e.257.2	yes	8
5.3	odd	4		450.2.p.e.257.1	yes	8
5.4	even	2	inner	450.2.p.c.293.1	✓	8
9.2	odd	6		450.2.p.e.443.2	yes	8
9.7	even	3		1350.2.q.a.143.1		8
15.2	even	4		1350.2.q.a.557.1		8
15.8	even	4		1350.2.q.a.557.2		8
15.14	odd	2		1350.2.q.d.1043.2		8
45.2	even	12	inner	450.2.p.c.407.2	yes	8
45.7	odd	12		1350.2.q.d.1007.1		8
45.29	odd	6		450.2.p.e.443.1	yes	8
45.34	even	6		1350.2.q.a.143.2		8
45.38	even	12	inner	450.2.p.c.407.1	yes	8
45.43	odd	12		1350.2.q.d.1007.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.c.293.1	✓	8	5.4	even	2	inner
450.2.p.c.293.2	yes	8	1.1	even	1	trivial
450.2.p.c.407.1	yes	8	45.38	even	12	inner
450.2.p.c.407.2	yes	8	45.2	even	12	inner
450.2.p.e.257.1	yes	8	5.3	odd	4
450.2.p.e.257.2	yes	8	5.2	odd	4
450.2.p.e.443.1	yes	8	45.29	odd	6
450.2.p.e.443.2	yes	8	9.2	odd	6
1350.2.q.a.143.1		8	9.7	even	3
1350.2.q.a.143.2		8	45.34	even	6
1350.2.q.a.557.1		8	15.2	even	4
1350.2.q.a.557.2		8	15.8	even	4
1350.2.q.d.1007.1		8	45.7	odd	12
1350.2.q.d.1007.2		8	45.43	odd	12
1350.2.q.d.1043.1		8	3.2	odd	2
1350.2.q.d.1043.2		8	15.14	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(1.67303 - 0.448288i) q^{12} +(1.22474 - 0.328169i) q^{13} +(-0.633975 + 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.89778 - 0.776457i) q^{18} -7.19615i q^{19} +(1.90192 - 1.09808i) q^{21} +(-0.896575 - 3.34607i) q^{22} +(-2.12132 - 7.91688i) q^{23} -1.73205i q^{24} -1.26795i q^{26} +(3.67423 + 3.67423i) q^{27} +(0.896575 + 0.896575i) q^{28} +(3.63397 + 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(-1.55291 + 1.55291i) q^{37} +(-6.95095 - 1.86250i) q^{38} +(-1.09808 + 1.90192i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(-0.568406 - 2.12132i) q^{42} +(1.67303 - 6.24384i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(-1.55291 + 5.79555i) q^{47} +(-1.67303 - 0.448288i) q^{48} +(-4.66987 - 2.69615i) q^{49} +(-1.22474 - 0.328169i) q^{52} +(1.55291 - 1.55291i) q^{53} +(4.50000 - 2.59808i) q^{54} +(1.09808 - 0.633975i) q^{56} +(8.81345 + 8.81345i) q^{57} +(7.02030 - 1.88108i) q^{58} +(-6.23205 + 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-7.20977 - 7.20977i) q^{62} +(-0.984508 + 3.67423i) q^{63} -1.00000i q^{64} +(5.19615 + 3.00000i) q^{66} +(-3.22595 - 12.0394i) q^{67} +(12.2942 + 7.09808i) q^{69} +10.7321i q^{71} +(2.12132 + 2.12132i) q^{72} +(3.67423 + 3.67423i) q^{73} +(1.09808 + 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(-4.24264 + 1.13681i) q^{77} +(1.55291 + 1.55291i) q^{78} +(-8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 + 1.22474i) q^{82} +(6.57201 + 1.76097i) q^{83} -2.19615 q^{84} +(-5.59808 - 3.23205i) q^{86} +(-12.1595 - 3.25813i) q^{87} +(-0.896575 + 3.34607i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(-2.12132 + 7.91688i) q^{92} +(4.57081 + 17.0585i) q^{93} +(5.19615 + 3.00000i) q^{94} +(-0.866025 + 1.50000i) q^{96} +(14.1607 + 3.79435i) q^{97} +(-3.81294 + 3.81294i) q^{98} +(-5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 24 q^{11} - 12 q^{14} + 4 q^{16} + 36 q^{21} + 36 q^{29} + 20 q^{31} - 12 q^{36} + 12 q^{39} - 12 q^{41} - 24 q^{46} - 72 q^{49} + 36 q^{54} - 12 q^{56} - 36 q^{59} + 16 q^{61} + 36 q^{69} - 12 q^{74} - 8 q^{76} - 72 q^{81} + 24 q^{84} - 24 q^{86} - 96 q^{91}+O(q^{100}) \) 8 * q + 24 * q^11 - 12 * q^14 + 4 * q^16 + 36 * q^21 + 36 * q^29 + 20 * q^31 - 12 * q^36 + 12 * q^39 - 12 * q^41 - 24 * q^46 - 72 * q^49 + 36 * q^54 - 12 * q^56 - 36 * q^59 + 16 * q^61 + 36 * q^69 - 12 * q^74 - 8 * q^76 - 72 * q^81 + 24 * q^84 - 24 * q^86 - 96 * q^91

Introduction

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