LMFDB - Embedded newform 1122.2.l.a.727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, degree $2$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.a.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +1.17157 q^{13} +(1.41421 + 1.41421i) q^{14} -0.585786i q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} +1.00000 q^{18} +(-0.414214 - 0.414214i) q^{20} +2.00000 q^{21} +(-0.707107 - 0.707107i) q^{22} +(1.41421 - 1.41421i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.65685i q^{25} -1.17157i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.41421 - 1.41421i) q^{28} +(-3.58579 - 3.58579i) q^{29} -0.585786 q^{30} +(-2.58579 - 2.58579i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} -1.17157 q^{35} -1.00000i q^{36} +(-3.58579 - 3.58579i) q^{37} +(-0.828427 - 0.828427i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(3.00000 - 3.00000i) q^{41} -2.00000i q^{42} -1.17157i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(-1.41421 - 1.41421i) q^{46} +1.65685 q^{47} +(-0.707107 - 0.707107i) q^{48} +3.00000i q^{49} -4.65685 q^{50} +(-3.53553 + 2.12132i) q^{51} -1.17157 q^{52} -4.48528i q^{53} +(-0.707107 - 0.707107i) q^{54} +0.585786 q^{55} +(-1.41421 - 1.41421i) q^{56} +(-3.58579 + 3.58579i) q^{58} +0.585786i q^{60} +(9.24264 - 9.24264i) q^{61} +(-2.58579 + 2.58579i) q^{62} +(-1.41421 - 1.41421i) q^{63} -1.00000 q^{64} +(0.485281 + 0.485281i) q^{65} +1.00000i q^{66} -8.48528 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{69} +1.17157i q^{70} +(3.07107 + 3.07107i) q^{71} -1.00000 q^{72} +(-6.65685 - 6.65685i) q^{73} +(-3.58579 + 3.58579i) q^{74} +(-3.29289 + 3.29289i) q^{75} +2.00000i q^{77} +(-0.828427 + 0.828427i) q^{78} +(-0.242641 + 0.242641i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} +2.82843i q^{83} -2.00000 q^{84} +(2.07107 - 1.24264i) q^{85} -1.17157 q^{86} +5.07107i q^{87} +(0.707107 + 0.707107i) q^{88} +6.34315 q^{89} +(0.414214 + 0.414214i) q^{90} +(-1.65685 + 1.65685i) q^{91} +(-1.41421 + 1.41421i) q^{92} +3.65685i q^{93} -1.65685i q^{94} +(-0.707107 + 0.707107i) q^{96} +(-9.48528 - 9.48528i) q^{97} +3.00000 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^5	$ 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} - 20 q^{29} - 8 q^{30} - 16 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{35} - 20 q^{37} + 8 q^{39} + 4 q^{40} + 12 q^{41} + 4 q^{45} - 16 q^{47} + 4 q^{50} - 16 q^{52} + 8 q^{55} - 20 q^{58} + 20 q^{61} - 16 q^{62} - 4 q^{64} - 32 q^{65} - 4 q^{68} - 8 q^{69} - 16 q^{71} - 4 q^{72} - 4 q^{73} - 20 q^{74} - 16 q^{75} + 8 q^{78} + 16 q^{79} - 4 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} - 20 q^{85} - 16 q^{86} + 48 q^{89} - 4 q^{90} + 16 q^{91} - 4 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 - 20 * q^29 - 8 * q^30 - 16 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^35 - 20 * q^37 + 8 * q^39 + 4 * q^40 + 12 * q^41 + 4 * q^45 - 16 * q^47 + 4 * q^50 - 16 * q^52 + 8 * q^55 - 20 * q^58 + 20 * q^61 - 16 * q^62 - 4 * q^64 - 32 * q^65 - 4 * q^68 - 8 * q^69 - 16 * q^71 - 4 * q^72 - 4 * q^73 - 20 * q^74 - 16 * q^75 + 8 * q^78 + 16 * q^79 - 4 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 - 20 * q^85 - 16 * q^86 + 48 * q^89 - 4 * q^90 + 16 * q^91 - 4 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	0.793635	−	0.608394i	$-0.208186\pi$
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	−0.608394	+	0.793635i	$0.708186\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.41421	+	1.41421i	−0.534522	+	0.534522i	−0.921915	−	0.387392i	$-0.873376\pi$
$7$	−1.41421	+	1.41421i	−0.534522	+	0.534522i	0.387392	+	0.921915i	$0.373376\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	0.414214	−	0.414214i	0.130986	−	0.130986i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.17157			0.324936			0.162468	−	0.986714i	$-0.448055\pi$
$13$	1.17157			0.324936			0.162468	+	0.986714i	$0.448055\pi$
$14$	1.41421	+	1.41421i	0.377964	+	0.377964i
$15$		−	0.585786i		−	0.151249i
$16$	1.00000			0.250000
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$18$	1.00000			0.235702
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.414214	−	0.414214i	−0.0926210	−	0.0926210i
$21$	2.00000			0.436436
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	1.41421	−	1.41421i	0.294884	−	0.294884i	−0.544122	−	0.839006i	$-0.683137\pi$
$23$	1.41421	−	1.41421i	0.294884	−	0.294884i	0.839006	+	0.544122i	$0.183137\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	4.65685i		−	0.931371i
$26$		−	1.17157i		−	0.229764i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.41421	−	1.41421i	0.267261	−	0.267261i
$29$	−3.58579	−	3.58579i	−0.665864	−	0.665864i	0.290892	−	0.956756i	$-0.406048\pi$
$29$	−3.58579	−	3.58579i	−0.665864	−	0.665864i	−0.956756	+	0.290892i	$0.906048\pi$
$30$	−0.585786			−0.106949
$31$	−2.58579	−	2.58579i	−0.464421	−	0.464421i	0.435680	−	0.900101i	$-0.356508\pi$
$31$	−2.58579	−	2.58579i	−0.464421	−	0.464421i	−0.900101	+	0.435680i	$0.856508\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.00000			−0.174078
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$	−1.17157			−0.198032
$36$		−	1.00000i		−	0.166667i
$37$	−3.58579	−	3.58579i	−0.589500	−	0.589500i	0.347996	−	0.937496i	$-0.386862\pi$
$37$	−3.58579	−	3.58579i	−0.589500	−	0.589500i	−0.937496	+	0.347996i	$0.886862\pi$
$38$		0			0
$39$	−0.828427	−	0.828427i	−0.132655	−	0.132655i
$40$	−0.414214	+	0.414214i	−0.0654929	+	0.0654929i
$41$	3.00000	−	3.00000i	0.468521	−	0.468521i	−0.432914	−	0.901435i	$-0.642515\pi$
$41$	3.00000	−	3.00000i	0.468521	−	0.468521i	0.901435	+	0.432914i	$0.142515\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	1.17157i		−	0.178663i	−0.996002	−	0.0893316i	$-0.971527\pi$
$43$		−	1.17157i		−	0.178663i	0.996002	−	0.0893316i	$-0.0284731\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$	−0.414214	+	0.414214i	−0.0617473	+	0.0617473i
$46$	−1.41421	−	1.41421i	−0.208514	−	0.208514i
$47$	1.65685			0.241677			0.120839	−	0.992672i	$-0.461442\pi$
$47$	1.65685			0.241677			0.120839	+	0.992672i	$0.461442\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			3.00000i			0.428571i
$50$	−4.65685			−0.658579
$51$	−3.53553	+	2.12132i	−0.495074	+	0.297044i
$52$	−1.17157			−0.162468
$53$		−	4.48528i		−	0.616101i	−0.951370	−	0.308050i	$-0.900323\pi$
$53$		−	4.48528i		−	0.616101i	0.951370	−	0.308050i	$-0.0996765\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	0.585786			0.0789874
$56$	−1.41421	−	1.41421i	−0.188982	−	0.188982i
$57$		0			0
$58$	−3.58579	+	3.58579i	−0.470837	+	0.470837i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$			0.585786i			0.0756247i
$61$	9.24264	−	9.24264i	1.18340	−	1.18340i	0.204541	−	0.978858i	$-0.434430\pi$
$61$	9.24264	−	9.24264i	1.18340	−	1.18340i	0.978858	−	0.204541i	$-0.0655701\pi$
$62$	−2.58579	+	2.58579i	−0.328395	+	0.328395i
$63$	−1.41421	−	1.41421i	−0.178174	−	0.178174i
$64$	−1.00000			−0.125000
$65$	0.485281	+	0.485281i	0.0601917	+	0.0601917i
$66$			1.00000i			0.123091i
$67$	−8.48528			−1.03664			−0.518321	−	0.855186i	$-0.673443\pi$
$67$	−8.48528			−1.03664			−0.518321	+	0.855186i	$0.673443\pi$
$68$	−1.00000	+	4.00000i	−0.121268	+	0.485071i
$69$	−2.00000			−0.240772
$70$			1.17157i			0.140030i
$71$	3.07107	+	3.07107i	0.364469	+	0.364469i	0.865455	−	0.500986i	$-0.167029\pi$
$71$	3.07107	+	3.07107i	0.364469	+	0.364469i	−0.500986	+	0.865455i	$0.667029\pi$
$72$	−1.00000			−0.117851
$73$	−6.65685	−	6.65685i	−0.779126	−	0.779126i	0.200556	−	0.979682i	$-0.435725\pi$
$73$	−6.65685	−	6.65685i	−0.779126	−	0.779126i	−0.979682	+	0.200556i	$0.935725\pi$
$74$	−3.58579	+	3.58579i	−0.416839	+	0.416839i
$75$	−3.29289	+	3.29289i	−0.380231	+	0.380231i
$76$		0			0
$77$			2.00000i			0.227921i
$78$	−0.828427	+	0.828427i	−0.0938009	+	0.0938009i
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	−0.720625	−	0.693325i	$-0.756145\pi$
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	0.693325	+	0.720625i	$0.256145\pi$
$80$	0.414214	+	0.414214i	0.0463105	+	0.0463105i
$81$	−1.00000			−0.111111
$82$	−3.00000	−	3.00000i	−0.331295	−	0.331295i
$83$			2.82843i			0.310460i	0.987878	+	0.155230i	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$	−2.00000			−0.218218
$85$	2.07107	−	1.24264i	0.224639	−	0.134783i
$86$	−1.17157			−0.126334
$87$			5.07107i			0.543676i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	6.34315			0.672372			0.336186	−	0.941796i	$-0.390863\pi$
$89$	6.34315			0.672372			0.336186	+	0.941796i	$0.390863\pi$
$90$	0.414214	+	0.414214i	0.0436619	+	0.0436619i
$91$	−1.65685	+	1.65685i	−0.173686	+	0.173686i
$92$	−1.41421	+	1.41421i	−0.147442	+	0.147442i
$93$			3.65685i			0.379198i
$94$		−	1.65685i		−	0.170891i
$95$		0			0
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	0.0362581	−	0.999342i	$-0.488456\pi$
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	−0.999342	+	0.0362581i	$0.988456\pi$
$98$	3.00000			0.303046
$99$	0.707107	+	0.707107i	0.0710669	+	0.0710669i
$100$			4.65685i			0.465685i
$101$	−4.48528			−0.446302			−0.223151	−	0.974784i	$-0.571634\pi$
$101$	−4.48528			−0.446302			−0.223151	+	0.974784i	$0.571634\pi$
$102$	2.12132	+	3.53553i	0.210042	+	0.350070i
$103$	−5.17157			−0.509570			−0.254785	−	0.966998i	$-0.582005\pi$
$103$	−5.17157			−0.509570			−0.254785	+	0.966998i	$0.582005\pi$
$104$			1.17157i			0.114882i
$105$	0.828427	+	0.828427i	0.0808462	+	0.0808462i
$106$	−4.48528			−0.435649
$107$	10.8284	+	10.8284i	1.04682	+	1.04682i	0.998849	+	0.0479750i	$0.0152768\pi$
$107$	10.8284	+	10.8284i	1.04682	+	1.04682i	0.0479750	+	0.998849i	$0.484723\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	2.41421	−	2.41421i	0.231240	−	0.231240i	−0.581970	−	0.813210i	$-0.697718\pi$
$109$	2.41421	−	2.41421i	0.231240	−	0.231240i	0.813210	+	0.581970i	$0.197718\pi$
$110$		−	0.585786i		−	0.0558525i
$111$			5.07107i			0.481324i
$112$	−1.41421	+	1.41421i	−0.133631	+	0.133631i
$113$	0.171573	−	0.171573i	0.0161402	−	0.0161402i	−0.698991	−	0.715131i	$-0.746367\pi$
$113$	0.171573	−	0.171573i	0.0161402	−	0.0161402i	0.715131	+	0.698991i	$0.246367\pi$
$114$		0			0
$115$	1.17157			0.109250
$116$	3.58579	+	3.58579i	0.332932	+	0.332932i
$117$			1.17157i			0.108312i
$118$		0			0
$119$	4.24264	+	7.07107i	0.388922	+	0.648204i
$120$	0.585786			0.0534747
$121$		−	1.00000i		−	0.0909091i
$122$	−9.24264	−	9.24264i	−0.836789	−	0.836789i
$123$	−4.24264			−0.382546
$124$	2.58579	+	2.58579i	0.232210	+	0.232210i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	−1.41421	+	1.41421i	−0.125988	+	0.125988i
$127$		−	14.8284i		−	1.31581i	−0.753101	−	0.657905i	$-0.771443\pi$
$127$		−	14.8284i		−	1.31581i	0.753101	−	0.657905i	$-0.228557\pi$
$128$			1.00000i			0.0883883i
$129$	−0.828427	+	0.828427i	−0.0729389	+	0.0729389i
$130$	0.485281	−	0.485281i	0.0425620	−	0.0425620i
$131$	−6.82843	−	6.82843i	−0.596602	−	0.596602i	0.342804	−	0.939407i	$-0.388623\pi$
$131$	−6.82843	−	6.82843i	−0.596602	−	0.596602i	−0.939407	+	0.342804i	$0.888623\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$			8.48528i			0.733017i
$135$	0.585786			0.0504165
$136$	4.00000	+	1.00000i	0.342997	+	0.0857493i
$137$	−8.00000			−0.683486			−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000			−0.683486			−0.341743	+	0.939793i	$0.611017\pi$
$138$			2.00000i			0.170251i
$139$	−9.65685	−	9.65685i	−0.819084	−	0.819084i	0.166892	−	0.985975i	$-0.446627\pi$
$139$	−9.65685	−	9.65685i	−0.819084	−	0.819084i	−0.985975	+	0.166892i	$0.946627\pi$
$140$	1.17157			0.0990160
$141$	−1.17157	−	1.17157i	−0.0986642	−	0.0986642i
$142$	3.07107	−	3.07107i	0.257718	−	0.257718i
$143$	0.828427	−	0.828427i	0.0692766	−	0.0692766i
$144$			1.00000i			0.0833333i
$145$		−	2.97056i		−	0.246692i
$146$	−6.65685	+	6.65685i	−0.550925	+	0.550925i
$147$	2.12132	−	2.12132i	0.174964	−	0.174964i
$148$	3.58579	+	3.58579i	0.294750	+	0.294750i
$149$	13.3137			1.09070			0.545351	−	0.838208i	$-0.316396\pi$
$149$	13.3137			1.09070			0.545351	+	0.838208i	$0.316396\pi$
$150$	3.29289	+	3.29289i	0.268864	+	0.268864i
$151$			6.82843i			0.555690i	0.960626	+	0.277845i	$0.0896201\pi$
$151$			6.82843i			0.555690i	−0.960626	+	0.277845i	$0.910380\pi$
$152$		0			0
$153$	4.00000	+	1.00000i	0.323381	+	0.0808452i
$154$	2.00000			0.161165
$155$		−	2.14214i		−	0.172060i
$156$	0.828427	+	0.828427i	0.0663273	+	0.0663273i
$157$	9.31371			0.743315			0.371657	−	0.928370i	$-0.378790\pi$
$157$	9.31371			0.743315			0.371657	+	0.928370i	$0.378790\pi$
$158$	0.242641	+	0.242641i	0.0193035	+	0.0193035i
$159$	−3.17157	+	3.17157i	−0.251522	+	0.251522i
$160$	0.414214	−	0.414214i	0.0327465	−	0.0327465i
$161$			4.00000i			0.315244i
$162$			1.00000i			0.0785674i
$163$	8.48528	−	8.48528i	0.664619	−	0.664619i	−0.291847	−	0.956465i	$-0.594270\pi$
$163$	8.48528	−	8.48528i	0.664619	−	0.664619i	0.956465	+	0.291847i	$0.0942697\pi$
$164$	−3.00000	+	3.00000i	−0.234261	+	0.234261i
$165$	−0.414214	−	0.414214i	−0.0322465	−	0.0322465i
$166$	2.82843			0.219529
$167$	15.0711	+	15.0711i	1.16623	+	1.16623i	0.983085	+	0.183149i	$0.0586291\pi$
$167$	15.0711	+	15.0711i	1.16623	+	1.16623i	0.183149	+	0.983085i	$0.441371\pi$
$168$			2.00000i			0.154303i
$169$	−11.6274			−0.894417
$170$	−1.24264	−	2.07107i	−0.0953062	−	0.158844i
$171$		0			0
$172$			1.17157i			0.0893316i
$173$	2.75736	+	2.75736i	0.209638	+	0.209638i	0.804114	−	0.594476i	$-0.202640\pi$
$173$	2.75736	+	2.75736i	0.209638	+	0.209638i	−0.594476	+	0.804114i	$0.702640\pi$
$174$	5.07107			0.384437
$175$	6.58579	+	6.58579i	0.497839	+	0.497839i
$176$	0.707107	−	0.707107i	0.0533002	−	0.0533002i
$177$		0			0
$178$		−	6.34315i		−	0.475439i
$179$			10.1421i			0.758059i	0.925385	+	0.379029i	$0.123742\pi$
$179$			10.1421i			0.758059i	−0.925385	+	0.379029i	$0.876258\pi$
$180$	0.414214	−	0.414214i	0.0308737	−	0.0308737i
$181$	4.41421	−	4.41421i	0.328106	−	0.328106i	−0.523760	−	0.851866i	$-0.675471\pi$
$181$	4.41421	−	4.41421i	0.328106	−	0.328106i	0.851866	+	0.523760i	$0.175471\pi$
$182$	1.65685	+	1.65685i	0.122814	+	0.122814i
$183$	−13.0711			−0.966241
$184$	1.41421	+	1.41421i	0.104257	+	0.104257i
$185$		−	2.97056i		−	0.218400i
$186$	3.65685			0.268134
$187$	−2.12132	−	3.53553i	−0.155126	−	0.258544i
$188$	−1.65685			−0.120839
$189$			2.00000i			0.145479i
$190$		0			0
$191$	14.3431			1.03783			0.518917	−	0.854825i	$-0.326335\pi$
$191$	14.3431			1.03783			0.518917	+	0.854825i	$0.326335\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	15.4853	−	15.4853i	1.11465	−	1.11465i	0.122142	−	0.992513i	$-0.461024\pi$
$193$	15.4853	−	15.4853i	1.11465	−	1.11465i	0.992513	−	0.122142i	$-0.0389764\pi$
$194$	−9.48528	+	9.48528i	−0.681004	+	0.681004i
$195$		−	0.686292i		−	0.0491464i
$196$		−	3.00000i		−	0.214286i
$197$	7.24264	−	7.24264i	0.516017	−	0.516017i	−0.400347	−	0.916364i	$-0.631110\pi$
$197$	7.24264	−	7.24264i	0.516017	−	0.516017i	0.916364	+	0.400347i	$0.131110\pi$
$198$	0.707107	−	0.707107i	0.0502519	−	0.0502519i
$199$	−9.89949	−	9.89949i	−0.701757	−	0.701757i	0.263031	−	0.964787i	$-0.415278\pi$
$199$	−9.89949	−	9.89949i	−0.701757	−	0.701757i	−0.964787	+	0.263031i	$0.915278\pi$
$200$	4.65685			0.329289
$201$	6.00000	+	6.00000i	0.423207	+	0.423207i
$202$			4.48528i			0.315583i
$203$	10.1421			0.711838
$204$	3.53553	−	2.12132i	0.247537	−	0.148522i
$205$	2.48528			0.173580
$206$			5.17157i			0.360321i
$207$	1.41421	+	1.41421i	0.0982946	+	0.0982946i
$208$	1.17157			0.0812340
$209$		0			0
$210$	0.828427	−	0.828427i	0.0571669	−	0.0571669i
$211$	−9.17157	+	9.17157i	−0.631397	+	0.631397i	−0.948418	−	0.317021i	$-0.897317\pi$
$211$	−9.17157	+	9.17157i	−0.631397	+	0.631397i	0.317021	+	0.948418i	$0.397317\pi$
$212$			4.48528i			0.308050i
$213$		−	4.34315i		−	0.297587i
$214$	10.8284	−	10.8284i	0.740216	−	0.740216i
$215$	0.485281	−	0.485281i	0.0330959	−	0.0330959i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	7.31371			0.496487
$218$	−2.41421	−	2.41421i	−0.163511	−	0.163511i
$219$			9.41421i			0.636154i
$220$	−0.585786			−0.0394937
$221$	1.17157	−	4.68629i	0.0788085	−	0.315234i
$222$	5.07107			0.340348
$223$			8.48528i			0.568216i	0.958792	+	0.284108i	$0.0916975\pi$
$223$			8.48528i			0.568216i	−0.958792	+	0.284108i	$0.908302\pi$
$224$	1.41421	+	1.41421i	0.0944911	+	0.0944911i
$225$	4.65685			0.310457
$226$	−0.171573	−	0.171573i	−0.0114129	−	0.0114129i
$227$	−10.1421	+	10.1421i	−0.673157	+	0.673157i	−0.958443	−	0.285285i	$-0.907912\pi$
$227$	−10.1421	+	10.1421i	−0.673157	+	0.673157i	0.285285	+	0.958443i	$0.407912\pi$
$228$		0			0
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$		−	1.17157i		−	0.0772512i
$231$	1.41421	−	1.41421i	0.0930484	−	0.0930484i
$232$	3.58579	−	3.58579i	0.235418	−	0.235418i
$233$	−3.48528	−	3.48528i	−0.228328	−	0.228328i	0.583666	−	0.811994i	$-0.301618\pi$
$233$	−3.48528	−	3.48528i	−0.228328	−	0.228328i	−0.811994	+	0.583666i	$0.801618\pi$
$234$	1.17157			0.0765881
$235$	0.686292	+	0.686292i	0.0447687	+	0.0447687i
$236$		0			0
$237$	0.343146			0.0222897
$238$	7.07107	−	4.24264i	0.458349	−	0.275010i
$239$	2.82843			0.182956			0.0914779	−	0.995807i	$-0.470841\pi$
$239$	2.82843			0.182956			0.0914779	+	0.995807i	$0.470841\pi$
$240$		−	0.585786i		−	0.0378124i
$241$	11.4853	+	11.4853i	0.739832	+	0.739832i	0.972545	−	0.232713i	$-0.0747604\pi$
$241$	11.4853	+	11.4853i	0.739832	+	0.739832i	−0.232713	+	0.972545i	$0.574760\pi$
$242$	−1.00000			−0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−9.24264	+	9.24264i	−0.591699	+	0.591699i
$245$	−1.24264	+	1.24264i	−0.0793894	+	0.0793894i
$246$			4.24264i			0.270501i
$247$		0			0
$248$	2.58579	−	2.58579i	0.164198	−	0.164198i
$249$	2.00000	−	2.00000i	0.126745	−	0.126745i
$250$	−4.00000	−	4.00000i	−0.252982	−	0.252982i
$251$	10.1421			0.640166			0.320083	−	0.947390i	$-0.396289\pi$
$251$	10.1421			0.640166			0.320083	+	0.947390i	$0.396289\pi$
$252$	1.41421	+	1.41421i	0.0890871	+	0.0890871i
$253$		−	2.00000i		−	0.125739i
$254$	−14.8284			−0.930418
$255$	−2.34315	−	0.585786i	−0.146733	−	0.0366834i
$256$	1.00000			0.0625000
$257$			5.31371i			0.331460i	0.986171	+	0.165730i	$0.0529980\pi$
$257$			5.31371i			0.331460i	−0.986171	+	0.165730i	$0.947002\pi$
$258$	0.828427	+	0.828427i	0.0515756	+	0.0515756i
$259$	10.1421			0.630202
$260$	−0.485281	−	0.485281i	−0.0300959	−	0.0300959i
$261$	3.58579	−	3.58579i	0.221955	−	0.221955i
$262$	−6.82843	+	6.82843i	−0.421862	+	0.421862i
$263$		−	0.485281i		−	0.0299237i	−0.999888	−	0.0149619i	$-0.995237\pi$
$263$		−	0.485281i		−	0.0299237i	0.999888	−	0.0149619i	$-0.00476269\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	1.85786	−	1.85786i	0.114128	−	0.114128i
$266$		0			0
$267$	−4.48528	−	4.48528i	−0.274495	−	0.274495i
$268$	8.48528			0.518321
$269$	14.0711	+	14.0711i	0.857928	+	0.857928i	0.991094	−	0.133166i	$-0.0425142\pi$
$269$	14.0711	+	14.0711i	0.857928	+	0.857928i	−0.133166	+	0.991094i	$0.542514\pi$
$270$		−	0.585786i		−	0.0356498i
$271$	−1.17157			−0.0711680			−0.0355840	−	0.999367i	$-0.511329\pi$
$271$	−1.17157			−0.0711680			−0.0355840	+	0.999367i	$0.511329\pi$
$272$	1.00000	−	4.00000i	0.0606339	−	0.242536i
$273$	2.34315			0.141814
$274$			8.00000i			0.483298i
$275$	−3.29289	−	3.29289i	−0.198569	−	0.198569i
$276$	2.00000			0.120386
$277$	−6.41421	−	6.41421i	−0.385393	−	0.385393i	0.487648	−	0.873040i	$-0.337855\pi$
$277$	−6.41421	−	6.41421i	−0.385393	−	0.385393i	−0.873040	+	0.487648i	$0.837855\pi$
$278$	−9.65685	+	9.65685i	−0.579180	+	0.579180i
$279$	2.58579	−	2.58579i	0.154807	−	0.154807i
$280$		−	1.17157i		−	0.0700149i
$281$		−	18.3431i		−	1.09426i	−0.837048	−	0.547130i	$-0.815720\pi$
$281$		−	18.3431i		−	1.09426i	0.837048	−	0.547130i	$-0.184280\pi$
$282$	−1.17157	+	1.17157i	−0.0697661	+	0.0697661i
$283$	1.65685	−	1.65685i	0.0984898	−	0.0984898i	−0.656145	−	0.754635i	$-0.727814\pi$
$283$	1.65685	−	1.65685i	0.0984898	−	0.0984898i	0.754635	+	0.656145i	$0.227814\pi$
$284$	−3.07107	−	3.07107i	−0.182234	−	0.182234i
$285$		0			0
$286$	−0.828427	−	0.828427i	−0.0489859	−	0.0489859i
$287$			8.48528i			0.500870i
$288$	1.00000			0.0589256
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	−2.97056			−0.174437
$291$			13.4142i			0.786355i
$292$	6.65685	+	6.65685i	0.389563	+	0.389563i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	−2.12132	−	2.12132i	−0.123718	−	0.123718i
$295$		0			0
$296$	3.58579	−	3.58579i	0.208420	−	0.208420i
$297$		−	1.00000i		−	0.0580259i
$298$		−	13.3137i		−	0.771242i
$299$	1.65685	−	1.65685i	0.0958184	−	0.0958184i
$300$	3.29289	−	3.29289i	0.190115	−	0.190115i
$301$	1.65685	+	1.65685i	0.0954995	+	0.0954995i
$302$	6.82843			0.392932
$303$	3.17157	+	3.17157i	0.182202	+	0.182202i
$304$		0			0
$305$	7.65685			0.438430
$306$	1.00000	−	4.00000i	0.0571662	−	0.228665i
$307$	6.82843			0.389719			0.194859	−	0.980831i	$-0.437575\pi$
$307$	6.82843			0.389719			0.194859	+	0.980831i	$0.437575\pi$
$308$		−	2.00000i		−	0.113961i
$309$	3.65685	+	3.65685i	0.208031	+	0.208031i
$310$	−2.14214			−0.121665
$311$	−1.89949	−	1.89949i	−0.107710	−	0.107710i	0.651198	−	0.758908i	$-0.274267\pi$
$311$	−1.89949	−	1.89949i	−0.107710	−	0.107710i	−0.758908	+	0.651198i	$0.774267\pi$
$312$	0.828427	−	0.828427i	0.0469005	−	0.0469005i
$313$	4.51472	−	4.51472i	0.255187	−	0.255187i	−0.567906	−	0.823093i	$-0.692246\pi$
$313$	4.51472	−	4.51472i	0.255187	−	0.255187i	0.823093	+	0.567906i	$0.192246\pi$
$314$		−	9.31371i		−	0.525603i
$315$		−	1.17157i		−	0.0660107i
$316$	0.242641	−	0.242641i	0.0136496	−	0.0136496i
$317$	−4.89949	+	4.89949i	−0.275183	+	0.275183i	−0.831183	−	0.556000i	$-0.812336\pi$
$317$	−4.89949	+	4.89949i	−0.275183	+	0.275183i	0.556000	+	0.831183i	$0.312336\pi$
$318$	3.17157	+	3.17157i	0.177853	+	0.177853i
$319$	−5.07107			−0.283925
$320$	−0.414214	−	0.414214i	−0.0231552	−	0.0231552i
$321$		−	15.3137i		−	0.854728i
$322$	4.00000			0.222911
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	5.45584i		−	0.302636i
$326$	−8.48528	−	8.48528i	−0.469956	−	0.469956i
$327$	−3.41421			−0.188806
$328$	3.00000	+	3.00000i	0.165647	+	0.165647i
$329$	−2.34315	+	2.34315i	−0.129182	+	0.129182i
$330$	−0.414214	+	0.414214i	−0.0228017	+	0.0228017i
$331$			28.9706i			1.59237i	0.605056	+	0.796183i	$0.293151\pi$
$331$			28.9706i			1.59237i	−0.605056	+	0.796183i	$0.706849\pi$
$332$		−	2.82843i		−	0.155230i
$333$	3.58579	−	3.58579i	0.196500	−	0.196500i
$334$	15.0711	−	15.0711i	0.824652	−	0.824652i
$335$	−3.51472	−	3.51472i	−0.192030	−	0.192030i
$336$	2.00000			0.109109
$337$	−13.9706	−	13.9706i	−0.761025	−	0.761025i	0.215483	−	0.976508i	$-0.430868\pi$
$337$	−13.9706	−	13.9706i	−0.761025	−	0.761025i	−0.976508	+	0.215483i	$0.930868\pi$
$338$			11.6274i			0.632448i
$339$	−0.242641			−0.0131784
$340$	−2.07107	+	1.24264i	−0.112319	+	0.0673917i
$341$	−3.65685			−0.198030
$342$		0			0
$343$	−14.1421	−	14.1421i	−0.763604	−	0.763604i
$344$	1.17157			0.0631670
$345$	−0.828427	−	0.828427i	−0.0446010	−	0.0446010i
$346$	2.75736	−	2.75736i	0.148237	−	0.148237i
$347$	10.1421	−	10.1421i	0.544458	−	0.544458i	−0.380374	−	0.924833i	$-0.624205\pi$
$347$	10.1421	−	10.1421i	0.544458	−	0.544458i	0.924833	+	0.380374i	$0.124205\pi$
$348$		−	5.07107i		−	0.271838i
$349$			12.4853i			0.668322i	0.942516	+	0.334161i	$0.108453\pi$
$349$			12.4853i			0.668322i	−0.942516	+	0.334161i	$0.891547\pi$
$350$	6.58579	−	6.58579i	0.352025	−	0.352025i
$351$	0.828427	−	0.828427i	0.0442182	−	0.0442182i
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	−28.6274			−1.52368			−0.761842	−	0.647763i	$-0.775705\pi$
$353$	−28.6274			−1.52368			−0.761842	+	0.647763i	$0.775705\pi$
$354$		0			0
$355$			2.54416i			0.135030i
$356$	−6.34315			−0.336186
$357$	2.00000	−	8.00000i	0.105851	−	0.423405i
$358$	10.1421			0.536029
$359$			16.0000i			0.844448i	0.906492	+	0.422224i	$0.138750\pi$
$359$			16.0000i			0.844448i	−0.906492	+	0.422224i	$0.861250\pi$
$360$	−0.414214	−	0.414214i	−0.0218310	−	0.0218310i
$361$	19.0000			1.00000
$362$	−4.41421	−	4.41421i	−0.232006	−	0.232006i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	1.65685	−	1.65685i	0.0868428	−	0.0868428i
$365$		−	5.51472i		−	0.288654i
$366$			13.0711i			0.683236i
$367$	−12.2426	+	12.2426i	−0.639061	+	0.639061i	−0.950324	−	0.311263i	$-0.899248\pi$
$367$	−12.2426	+	12.2426i	−0.639061	+	0.639061i	0.311263	+	0.950324i	$0.399248\pi$
$368$	1.41421	−	1.41421i	0.0737210	−	0.0737210i
$369$	3.00000	+	3.00000i	0.156174	+	0.156174i
$370$	−2.97056			−0.154432
$371$	6.34315	+	6.34315i	0.329320	+	0.329320i
$372$		−	3.65685i		−	0.189599i
$373$	17.1716			0.889110			0.444555	−	0.895751i	$-0.353362\pi$
$373$	17.1716			0.889110			0.444555	+	0.895751i	$0.353362\pi$
$374$	−3.53553	+	2.12132i	−0.182818	+	0.109691i
$375$	−5.65685			−0.292119
$376$			1.65685i			0.0854457i
$377$	−4.20101	−	4.20101i	−0.216363	−	0.216363i
$378$	2.00000			0.102869
$379$	2.34315	+	2.34315i	0.120359	+	0.120359i	0.764721	−	0.644362i	$-0.222877\pi$
$379$	2.34315	+	2.34315i	0.120359	+	0.120359i	−0.644362	+	0.764721i	$0.722877\pi$
$380$		0			0
$381$	−10.4853	+	10.4853i	−0.537177	+	0.537177i
$382$		−	14.3431i		−	0.733859i
$383$		−	14.3431i		−	0.732901i	−0.930438	−	0.366450i	$-0.880573\pi$
$383$		−	14.3431i		−	0.732901i	0.930438	−	0.366450i	$-0.119427\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−0.828427	+	0.828427i	−0.0422206	+	0.0422206i
$386$	−15.4853	−	15.4853i	−0.788180	−	0.788180i
$387$	1.17157			0.0595544
$388$	9.48528	+	9.48528i	0.481542	+	0.481542i
$389$			23.6569i			1.19945i	0.800206	+	0.599725i	$0.204723\pi$
$389$			23.6569i			1.19945i	−0.800206	+	0.599725i	$0.795277\pi$
$390$	−0.686292			−0.0347517
$391$	−4.24264	−	7.07107i	−0.214560	−	0.357599i
$392$	−3.00000			−0.151523
$393$			9.65685i			0.487124i
$394$	−7.24264	−	7.24264i	−0.364879	−	0.364879i
$395$	−0.201010			−0.0101139
$396$	−0.707107	−	0.707107i	−0.0355335	−	0.0355335i
$397$	−22.8995	+	22.8995i	−1.14929	+	1.14929i	−0.162601	+	0.986692i	$0.551988\pi$
$397$	−22.8995	+	22.8995i	−1.14929	+	1.14929i	−0.986692	+	0.162601i	$0.948012\pi$
$398$	−9.89949	+	9.89949i	−0.496217	+	0.496217i
$399$		0			0
$400$		−	4.65685i		−	0.232843i
$401$	4.31371	−	4.31371i	0.215416	−	0.215416i	−0.591147	−	0.806564i	$-0.701325\pi$
$401$	4.31371	−	4.31371i	0.215416	−	0.215416i	0.806564	+	0.591147i	$0.201325\pi$
$402$	6.00000	−	6.00000i	0.299253	−	0.299253i
$403$	−3.02944	−	3.02944i	−0.150907	−	0.150907i
$404$	4.48528			0.223151
$405$	−0.414214	−	0.414214i	−0.0205824	−	0.0205824i
$406$		−	10.1421i		−	0.503346i
$407$	−5.07107			−0.251363
$408$	−2.12132	−	3.53553i	−0.105021	−	0.175035i
$409$	13.3137			0.658321			0.329160	−	0.944274i	$-0.393234\pi$
$409$	13.3137			0.658321			0.329160	+	0.944274i	$0.393234\pi$
$410$		−	2.48528i		−	0.122739i
$411$	5.65685	+	5.65685i	0.279032	+	0.279032i
$412$	5.17157			0.254785
$413$		0			0
$414$	1.41421	−	1.41421i	0.0695048	−	0.0695048i
$415$	−1.17157	+	1.17157i	−0.0575103	+	0.0575103i
$416$		−	1.17157i		−	0.0574411i
$417$			13.6569i			0.668779i
$418$		0			0
$419$	−23.3137	+	23.3137i	−1.13895	+	1.13895i	−0.150310	+	0.988639i	$0.548027\pi$
$419$	−23.3137	+	23.3137i	−1.13895	+	1.13895i	−0.988639	+	0.150310i	$0.951973\pi$
$420$	−0.828427	−	0.828427i	−0.0404231	−	0.0404231i
$421$	−2.14214			−0.104401			−0.0522007	−	0.998637i	$-0.516624\pi$
$421$	−2.14214			−0.104401			−0.0522007	+	0.998637i	$0.516624\pi$
$422$	9.17157	+	9.17157i	0.446465	+	0.446465i
$423$			1.65685i			0.0805590i
$424$	4.48528			0.217825
$425$	−18.6274	−	4.65685i	−0.903562	−	0.225891i
$426$	−4.34315			−0.210426
$427$			26.1421i			1.26511i
$428$	−10.8284	−	10.8284i	−0.523412	−	0.523412i
$429$	−1.17157			−0.0565641
$430$	−0.485281	−	0.485281i	−0.0234023	−	0.0234023i
$431$	6.58579	−	6.58579i	0.317226	−	0.317226i	−0.530475	−	0.847701i	$-0.677986\pi$
$431$	6.58579	−	6.58579i	0.317226	−	0.317226i	0.847701	+	0.530475i	$0.177986\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$		−	7.31371i		−	0.351069i
$435$	−2.10051	+	2.10051i	−0.100712	+	0.100712i
$436$	−2.41421	+	2.41421i	−0.115620	+	0.115620i
$437$		0			0
$438$	9.41421			0.449829
$439$	10.3848	+	10.3848i	0.495638	+	0.495638i	0.910077	−	0.414439i	$-0.136022\pi$
$439$	10.3848	+	10.3848i	0.495638	+	0.495638i	−0.414439	+	0.910077i	$0.636022\pi$
$440$			0.585786i			0.0279263i
$441$	−3.00000			−0.142857
$442$	−4.68629	−	1.17157i	−0.222904	−	0.0557260i
$443$	−31.7990			−1.51082			−0.755408	−	0.655255i	$-0.772561\pi$
$443$	−31.7990			−1.51082			−0.755408	+	0.655255i	$0.772561\pi$
$444$		−	5.07107i		−	0.240662i
$445$	2.62742	+	2.62742i	0.124552	+	0.124552i
$446$	8.48528			0.401790
$447$	−9.41421	−	9.41421i	−0.445277	−	0.445277i
$448$	1.41421	−	1.41421i	0.0668153	−	0.0668153i
$449$	5.34315	−	5.34315i	0.252159	−	0.252159i	−0.569697	−	0.821855i	$-0.692939\pi$
$449$	5.34315	−	5.34315i	0.252159	−	0.252159i	0.821855	+	0.569697i	$0.192939\pi$
$450$		−	4.65685i		−	0.219526i
$451$		−	4.24264i		−	0.199778i
$452$	−0.171573	+	0.171573i	−0.00807011	+	0.00807011i
$453$	4.82843	−	4.82843i	0.226859	−	0.226859i
$454$	10.1421	+	10.1421i	0.475994	+	0.475994i
$455$	−1.37258			−0.0643477
$456$		0			0
$457$			25.3137i			1.18413i	0.805892	+	0.592063i	$0.201686\pi$
$457$			25.3137i			1.18413i	−0.805892	+	0.592063i	$0.798314\pi$
$458$	18.0000			0.841085
$459$	−2.12132	−	3.53553i	−0.0990148	−	0.165025i
$460$	−1.17157			−0.0546249
$461$		−	12.4853i		−	0.581498i	−0.956799	−	0.290749i	$-0.906096\pi$
$461$		−	12.4853i		−	0.581498i	0.956799	−	0.290749i	$-0.0939044\pi$
$462$	−1.41421	−	1.41421i	−0.0657952	−	0.0657952i
$463$	−2.82843			−0.131448			−0.0657241	−	0.997838i	$-0.520936\pi$
$463$	−2.82843			−0.131448			−0.0657241	+	0.997838i	$0.520936\pi$
$464$	−3.58579	−	3.58579i	−0.166466	−	0.166466i
$465$	−1.51472	+	1.51472i	−0.0702434	+	0.0702434i
$466$	−3.48528	+	3.48528i	−0.161453	+	0.161453i
$467$			25.1716i			1.16480i	0.812902	+	0.582401i	$0.197887\pi$
$467$			25.1716i			1.16480i	−0.812902	+	0.582401i	$0.802113\pi$
$468$		−	1.17157i		−	0.0541560i
$469$	12.0000	−	12.0000i	0.554109	−	0.554109i
$470$	0.686292	−	0.686292i	0.0316563	−	0.0316563i
$471$	−6.58579	−	6.58579i	−0.303457	−	0.303457i
$472$		0			0
$473$	−0.828427	−	0.828427i	−0.0380911	−	0.0380911i
$474$		−	0.343146i		−	0.0157612i
$475$		0			0
$476$	−4.24264	−	7.07107i	−0.194461	−	0.324102i
$477$	4.48528			0.205367
$478$		−	2.82843i		−	0.129369i
$479$	−8.72792	−	8.72792i	−0.398789	−	0.398789i	0.479017	−	0.877806i	$-0.340993\pi$
$479$	−8.72792	−	8.72792i	−0.398789	−	0.398789i	−0.877806	+	0.479017i	$0.840993\pi$
$480$	−0.585786			−0.0267374
$481$	−4.20101	−	4.20101i	−0.191550	−	0.191550i
$482$	11.4853	−	11.4853i	0.523140	−	0.523140i
$483$	2.82843	−	2.82843i	0.128698	−	0.128698i
$484$			1.00000i			0.0454545i
$485$		−	7.85786i		−	0.356807i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	11.7574	−	11.7574i	0.532777	−	0.532777i	−0.388621	−	0.921398i	$-0.627048\pi$
$487$	11.7574	−	11.7574i	0.532777	−	0.532777i	0.921398	+	0.388621i	$0.127048\pi$
$488$	9.24264	+	9.24264i	0.418395	+	0.418395i
$489$	−12.0000			−0.542659
$490$	1.24264	+	1.24264i	0.0561368	+	0.0561368i
$491$			14.3431i			0.647297i	0.946177	+	0.323649i	$0.104910\pi$
$491$			14.3431i			0.647297i	−0.946177	+	0.323649i	$0.895090\pi$
$492$	4.24264			0.191273
$493$	−17.9289	+	10.7574i	−0.807478	+	0.484487i
$494$		0			0
$495$			0.585786i			0.0263291i
$496$	−2.58579	−	2.58579i	−0.116105	−	0.116105i
$497$	−8.68629			−0.389633
$498$	−2.00000	−	2.00000i	−0.0896221	−	0.0896221i
$499$	−24.4853	+	24.4853i	−1.09611	+	1.09611i	−0.101251	+	0.994861i	$0.532284\pi$
$499$	−24.4853	+	24.4853i	−1.09611	+	1.09611i	−0.994861	+	0.101251i	$0.967716\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$		−	21.3137i		−	0.952226i
$502$		−	10.1421i		−	0.452666i
$503$	23.0711	−	23.0711i	1.02869	−	1.02869i	0.0291119	−	0.999576i	$-0.490732\pi$
$503$	23.0711	−	23.0711i	1.02869	−	1.02869i	0.999576	−	0.0291119i	$-0.00926792\pi$
$504$	1.41421	−	1.41421i	0.0629941	−	0.0629941i
$505$	−1.85786	−	1.85786i	−0.0826739	−	0.0826739i
$506$	−2.00000			−0.0889108
$507$	8.22183	+	8.22183i	0.365144	+	0.365144i
$508$			14.8284i			0.657905i
$509$	−19.6569			−0.871275			−0.435637	−	0.900122i	$-0.643477\pi$
$509$	−19.6569			−0.871275			−0.435637	+	0.900122i	$0.643477\pi$
$510$	−0.585786	+	2.34315i	−0.0259391	+	0.103756i
$511$	18.8284			0.832921
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	5.31371			0.234378
$515$	−2.14214	−	2.14214i	−0.0943938	−	0.0943938i
$516$	0.828427	−	0.828427i	0.0364695	−	0.0364695i
$517$	1.17157	−	1.17157i	0.0515257	−	0.0515257i
$518$		−	10.1421i		−	0.445620i
$519$		−	3.89949i		−	0.171169i
$520$	−0.485281	+	0.485281i	−0.0212810	+	0.0212810i
$521$	8.31371	−	8.31371i	0.364230	−	0.364230i	−0.501137	−	0.865368i	$-0.667085\pi$
$521$	8.31371	−	8.31371i	0.364230	−	0.364230i	0.865368	+	0.501137i	$0.167085\pi$
$522$	−3.58579	−	3.58579i	−0.156946	−	0.156946i
$523$	−11.3137			−0.494714			−0.247357	−	0.968924i	$-0.579562\pi$
$523$	−11.3137			−0.494714			−0.247357	+	0.968924i	$0.579562\pi$
$524$	6.82843	+	6.82843i	0.298301	+	0.298301i
$525$		−	9.31371i		−	0.406484i
$526$	−0.485281			−0.0211593
$527$	−12.9289	+	7.75736i	−0.563193	+	0.337916i
$528$	−1.00000			−0.0435194
$529$			19.0000i			0.826087i
$530$	−1.85786	−	1.85786i	−0.0807005	−	0.0807005i
$531$		0			0
$532$		0			0
$533$	3.51472	−	3.51472i	0.152239	−	0.152239i
$534$	−4.48528	+	4.48528i	−0.194097	+	0.194097i
$535$			8.97056i			0.387831i
$536$		−	8.48528i		−	0.366508i
$537$	7.17157	−	7.17157i	0.309476	−	0.309476i
$538$	14.0711	−	14.0711i	0.606647	−	0.606647i
$539$	2.12132	+	2.12132i	0.0913717	+	0.0913717i
$540$	−0.585786			−0.0252082
$541$	3.58579	+	3.58579i	0.154165	+	0.154165i	0.779975	−	0.625810i	$-0.215232\pi$
$541$	3.58579	+	3.58579i	0.154165	+	0.154165i	−0.625810	+	0.779975i	$0.715232\pi$
$542$			1.17157i			0.0503234i
$543$	−6.24264			−0.267897
$544$	−4.00000	−	1.00000i	−0.171499	−	0.0428746i
$545$	2.00000			0.0856706
$546$		−	2.34315i		−	0.100277i
$547$	−22.1421	−	22.1421i	−0.946729	−	0.946729i	0.0519218	−	0.998651i	$-0.483465\pi$
$547$	−22.1421	−	22.1421i	−0.946729	−	0.946729i	−0.998651	+	0.0519218i	$0.983465\pi$
$548$	8.00000			0.341743
$549$	9.24264	+	9.24264i	0.394466	+	0.394466i
$550$	−3.29289	+	3.29289i	−0.140409	+	0.140409i
$551$		0			0
$552$		−	2.00000i		−	0.0851257i
$553$		−	0.686292i		−	0.0291841i
$554$	−6.41421	+	6.41421i	−0.272514	+	0.272514i
$555$	−2.10051	+	2.10051i	−0.0891615	+	0.0891615i
$556$	9.65685	+	9.65685i	0.409542	+	0.409542i
$557$	−20.4853			−0.867989			−0.433995	−	0.900915i	$-0.642896\pi$
$557$	−20.4853			−0.867989			−0.433995	+	0.900915i	$0.642896\pi$
$558$	−2.58579	−	2.58579i	−0.109465	−	0.109465i
$559$		−	1.37258i		−	0.0580541i
$560$	−1.17157			−0.0495080
$561$	−1.00000	+	4.00000i	−0.0422200	+	0.168880i
$562$	−18.3431			−0.773759
$563$		−	9.45584i		−	0.398516i	−0.979947	−	0.199258i	$-0.936147\pi$
$563$		−	9.45584i		−	0.398516i	0.979947	−	0.199258i	$-0.0638532\pi$
$564$	1.17157	+	1.17157i	0.0493321	+	0.0493321i
$565$	0.142136			0.00597969
$566$	−1.65685	−	1.65685i	−0.0696428	−	0.0696428i
$567$	1.41421	−	1.41421i	0.0593914	−	0.0593914i
$568$	−3.07107	+	3.07107i	−0.128859	+	0.128859i
$569$			37.9411i			1.59057i	0.606233	+	0.795287i	$0.292680\pi$
$569$			37.9411i			1.59057i	−0.606233	+	0.795287i	$0.707320\pi$
$570$		0			0
$571$	−8.00000	+	8.00000i	−0.334790	+	0.334790i	−0.854402	−	0.519612i	$-0.826076\pi$
$571$	−8.00000	+	8.00000i	−0.334790	+	0.334790i	0.519612	+	0.854402i	$0.326076\pi$
$572$	−0.828427	+	0.828427i	−0.0346383	+	0.0346383i
$573$	−10.1421	−	10.1421i	−0.423694	−	0.423694i
$574$	8.48528			0.354169
$575$	−6.58579	−	6.58579i	−0.274646	−	0.274646i
$576$		−	1.00000i		−	0.0416667i
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$	−21.8995			−0.910112
$580$			2.97056i			0.123346i
$581$	−4.00000	−	4.00000i	−0.165948	−	0.165948i
$582$	13.4142			0.556037
$583$	−3.17157	−	3.17157i	−0.131353	−	0.131353i
$584$	6.65685	−	6.65685i	0.275463	−	0.275463i
$585$	−0.485281	+	0.485281i	−0.0200639	+	0.0200639i
$586$		−	14.0000i		−	0.578335i
$587$		−	21.4558i		−	0.885577i	−0.896626	−	0.442789i	$-0.853989\pi$
$587$		−	21.4558i		−	0.885577i	0.896626	−	0.442789i	$-0.146011\pi$
$588$	−2.12132	+	2.12132i	−0.0874818	+	0.0874818i
$589$		0			0
$590$		0			0
$591$	−10.2426			−0.421326
$592$	−3.58579	−	3.58579i	−0.147375	−	0.147375i
$593$		−	16.2843i		−	0.668715i	−0.942446	−	0.334357i	$-0.891481\pi$
$593$		−	16.2843i		−	0.668715i	0.942446	−	0.334357i	$-0.108519\pi$
$594$	−1.00000			−0.0410305
$595$	−1.17157	+	4.68629i	−0.0480298	+	0.192119i
$596$	−13.3137			−0.545351
$597$			14.0000i			0.572982i
$598$	−1.65685	−	1.65685i	−0.0677538	−	0.0677538i
$599$	44.4853			1.81762			0.908810	−	0.417211i	$-0.136992\pi$
$599$	44.4853			1.81762			0.908810	+	0.417211i	$0.136992\pi$
$600$	−3.29289	−	3.29289i	−0.134432	−	0.134432i
$601$	7.00000	−	7.00000i	0.285536	−	0.285536i	−0.549776	−	0.835312i	$-0.685287\pi$
$601$	7.00000	−	7.00000i	0.285536	−	0.285536i	0.835312	+	0.549776i	$0.185287\pi$
$602$	1.65685	−	1.65685i	0.0675283	−	0.0675283i
$603$		−	8.48528i		−	0.345547i
$604$		−	6.82843i		−	0.277845i
$605$	0.414214	−	0.414214i	0.0168402	−	0.0168402i
$606$	3.17157	−	3.17157i	0.128836	−	0.128836i
$607$	−20.2426	−	20.2426i	−0.821623	−	0.821623i	0.164717	−	0.986341i	$-0.447329\pi$
$607$	−20.2426	−	20.2426i	−0.821623	−	0.821623i	−0.986341	+	0.164717i	$0.947329\pi$
$608$		0			0
$609$	−7.17157	−	7.17157i	−0.290607	−	0.290607i
$610$		−	7.65685i		−	0.310017i
$611$	1.94113			0.0785295
$612$	−4.00000	−	1.00000i	−0.161690	−	0.0404226i
$613$	22.2843			0.900053			0.450027	−	0.893015i	$-0.351414\pi$
$613$	22.2843			0.900053			0.450027	+	0.893015i	$0.351414\pi$
$614$		−	6.82843i		−	0.275573i
$615$	−1.75736	−	1.75736i	−0.0708636	−	0.0708636i
$616$	−2.00000			−0.0805823
$617$	1.82843	+	1.82843i	0.0736097	+	0.0736097i	0.742953	−	0.669343i	$-0.233425\pi$
$617$	1.82843	+	1.82843i	0.0736097	+	0.0736097i	−0.669343	+	0.742953i	$0.733425\pi$
$618$	3.65685	−	3.65685i	0.147100	−	0.147100i
$619$	−33.6569	+	33.6569i	−1.35278	+	1.35278i	−0.470250	+	0.882533i	$0.655836\pi$
$619$	−33.6569	+	33.6569i	−1.35278	+	1.35278i	−0.882533	+	0.470250i	$0.844164\pi$
$620$			2.14214i			0.0860302i
$621$		−	2.00000i		−	0.0802572i
$622$	−1.89949	+	1.89949i	−0.0761628	+	0.0761628i
$623$	−8.97056	+	8.97056i	−0.359398	+	0.359398i
$624$	−0.828427	−	0.828427i	−0.0331636	−	0.0331636i
$625$	−19.9706			−0.798823
$626$	−4.51472	−	4.51472i	−0.180444	−	0.180444i
$627$		0			0
$628$	−9.31371			−0.371657
$629$	−17.9289	+	10.7574i	−0.714873	+	0.428924i
$630$	−1.17157			−0.0466766
$631$			23.1127i			0.920102i	0.887892	+	0.460051i	$0.152169\pi$
$631$			23.1127i			0.920102i	−0.887892	+	0.460051i	$0.847831\pi$
$632$	−0.242641	−	0.242641i	−0.00965173	−	0.00965173i
$633$	12.9706			0.515534
$634$	4.89949	+	4.89949i	0.194584	+	0.194584i
$635$	6.14214	−	6.14214i	0.243743	−	0.243743i
$636$	3.17157	−	3.17157i	0.125761	−	0.125761i
$637$			3.51472i			0.139258i
$638$			5.07107i			0.200765i
$639$	−3.07107	+	3.07107i	−0.121490	+	0.121490i
$640$	−0.414214	+	0.414214i	−0.0163732	+	0.0163732i
$641$	−31.6274	−	31.6274i	−1.24921	−	1.24921i	−0.956070	−	0.293138i	$-0.905301\pi$
$641$	−31.6274	−	31.6274i	−1.24921	−	1.24921i	−0.293138	−	0.956070i	$-0.594699\pi$
$642$	−15.3137			−0.604384
$643$	−5.65685	−	5.65685i	−0.223085	−	0.223085i	0.586711	−	0.809796i	$-0.300422\pi$
$643$	−5.65685	−	5.65685i	−0.223085	−	0.223085i	−0.809796	+	0.586711i	$0.800422\pi$
$644$		−	4.00000i		−	0.157622i
$645$	−0.686292			−0.0270227
$646$		0			0
$647$	−6.34315			−0.249375			−0.124687	−	0.992196i	$-0.539793\pi$
$647$	−6.34315			−0.249375			−0.124687	+	0.992196i	$0.539793\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	−5.45584			−0.213996
$651$	−5.17157	−	5.17157i	−0.202690	−	0.202690i
$652$	−8.48528	+	8.48528i	−0.332309	+	0.332309i
$653$	21.2426	−	21.2426i	0.831289	−	0.831289i	−0.156404	−	0.987693i	$-0.549990\pi$
$653$	21.2426	−	21.2426i	0.831289	−	0.831289i	0.987693	+	0.156404i	$0.0499903\pi$
$654$			3.41421i			0.133506i
$655$		−	5.65685i		−	0.221032i
$656$	3.00000	−	3.00000i	0.117130	−	0.117130i
$657$	6.65685	−	6.65685i	0.259709	−	0.259709i
$658$	2.34315	+	2.34315i	0.0913453	+	0.0913453i
$659$	−5.17157			−0.201456			−0.100728	−	0.994914i	$-0.532117\pi$
$659$	−5.17157			−0.201456			−0.100728	+	0.994914i	$0.532117\pi$
$660$	0.414214	+	0.414214i	0.0161232	+	0.0161232i
$661$			26.1421i			1.01681i	0.861118	+	0.508406i	$0.169765\pi$
$661$			26.1421i			1.01681i	−0.861118	+	0.508406i	$0.830235\pi$
$662$	28.9706			1.12597
$663$	−4.14214	+	2.48528i	−0.160867	+	0.0965203i
$664$	−2.82843			−0.109764
$665$		0			0
$666$	−3.58579	−	3.58579i	−0.138946	−	0.138946i
$667$	−10.1421			−0.392705
$668$	−15.0711	−	15.0711i	−0.583117	−	0.583117i
$669$	6.00000	−	6.00000i	0.231973	−	0.231973i
$670$	−3.51472	+	3.51472i	−0.135785	+	0.135785i
$671$		−	13.0711i		−	0.504603i
$672$		−	2.00000i		−	0.0771517i
$673$	21.4853	−	21.4853i	0.828197	−	0.828197i	−0.159070	−	0.987267i	$-0.550850\pi$
$673$	21.4853	−	21.4853i	0.828197	−	0.828197i	0.987267	+	0.159070i	$0.0508497\pi$
$674$	−13.9706	+	13.9706i	−0.538126	+	0.538126i
$675$	−3.29289	−	3.29289i	−0.126744	−	0.126744i
$676$	11.6274			0.447208
$677$	−1.72792	−	1.72792i	−0.0664094	−	0.0664094i	0.673122	−	0.739531i	$-0.264953\pi$
$677$	−1.72792	−	1.72792i	−0.0664094	−	0.0664094i	−0.739531	+	0.673122i	$0.764953\pi$
$678$			0.242641i			0.00931856i
$679$	26.8284			1.02958
$680$	1.24264	+	2.07107i	0.0476531	+	0.0794218i
$681$	14.3431			0.549631
$682$			3.65685i			0.140028i
$683$	−18.8284	−	18.8284i	−0.720450	−	0.720450i	0.248247	−	0.968697i	$-0.420146\pi$
$683$	−18.8284	−	18.8284i	−0.720450	−	0.720450i	−0.968697	+	0.248247i	$0.920146\pi$
$684$		0			0
$685$	−3.31371	−	3.31371i	−0.126610	−	0.126610i
$686$	−14.1421	+	14.1421i	−0.539949	+	0.539949i
$687$	12.7279	−	12.7279i	0.485601	−	0.485601i
$688$		−	1.17157i		−	0.0446658i
$689$		−	5.25483i		−	0.200193i
$690$	−0.828427	+	0.828427i	−0.0315377	+	0.0315377i
$691$	−4.97056	+	4.97056i	−0.189089	+	0.189089i	−0.795302	−	0.606213i	$-0.792688\pi$
$691$	−4.97056	+	4.97056i	−0.189089	+	0.189089i	0.606213	+	0.795302i	$0.292688\pi$
$692$	−2.75736	−	2.75736i	−0.104819	−	0.104819i
$693$	−2.00000			−0.0759737
$694$	−10.1421	−	10.1421i	−0.384990	−	0.384990i
$695$		−	8.00000i		−	0.303457i
$696$	−5.07107			−0.192218
$697$	−9.00000	−	15.0000i	−0.340899	−	0.568166i
$698$	12.4853			0.472575
$699$			4.92893i			0.186429i
$700$	−6.58579	−	6.58579i	−0.248919	−	0.248919i
$701$	37.4558			1.41469			0.707344	−	0.706870i	$-0.249893\pi$
$701$	37.4558			1.41469			0.707344	+	0.706870i	$0.249893\pi$
$702$	−0.828427	−	0.828427i	−0.0312670	−	0.0312670i
$703$		0			0
$704$	−0.707107	+	0.707107i	−0.0266501	+	0.0266501i
$705$		−	0.970563i		−	0.0365535i
$706$			28.6274i			1.07741i
$707$	6.34315	−	6.34315i	0.238559	−	0.238559i
$708$		0			0
$709$	1.72792	+	1.72792i	0.0648935	+	0.0648935i	0.738809	−	0.673915i	$-0.235389\pi$
$709$	1.72792	+	1.72792i	0.0648935	+	0.0648935i	−0.673915	+	0.738809i	$0.735389\pi$
$710$	2.54416			0.0954805
$711$	−0.242641	−	0.242641i	−0.00909974	−	0.00909974i
$712$			6.34315i			0.237719i
$713$	−7.31371			−0.273901
$714$	−8.00000	−	2.00000i	−0.299392	−	0.0748481i
$715$	0.686292			0.0256658
$716$		−	10.1421i		−	0.379029i
$717$	−2.00000	−	2.00000i	−0.0746914	−	0.0746914i
$718$	16.0000			0.597115
$719$	−13.4142	−	13.4142i	−0.500266	−	0.500266i	0.411255	−	0.911520i	$-0.365091\pi$
$719$	−13.4142	−	13.4142i	−0.500266	−	0.500266i	−0.911520	+	0.411255i	$0.865091\pi$
$720$	−0.414214	+	0.414214i	−0.0154368	+	0.0154368i
$721$	7.31371	−	7.31371i	0.272377	−	0.272377i
$722$		−	19.0000i		−	0.707107i
$723$		−	16.2426i		−	0.604070i
$724$	−4.41421	+	4.41421i	−0.164053	+	0.164053i
$725$	−16.6985	+	16.6985i	−0.620166	+	0.620166i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	−43.3137			−1.60642			−0.803208	−	0.595698i	$-0.796875\pi$
$727$	−43.3137			−1.60642			−0.803208	+	0.595698i	$0.796875\pi$
$728$	−1.65685	−	1.65685i	−0.0614071	−	0.0614071i
$729$		−	1.00000i		−	0.0370370i
$730$	−5.51472			−0.204109
$731$	−4.68629	−	1.17157i	−0.173329	−	0.0433322i
$732$	13.0711			0.483121
$733$		−	0.201010i		−	0.00742448i	−0.999993	−	0.00371224i	$-0.998818\pi$
$733$		−	0.201010i		−	0.00742448i	0.999993	−	0.00371224i	$-0.00118165\pi$
$734$	12.2426	+	12.2426i	0.451884	+	0.451884i
$735$	1.75736			0.0648212
$736$	−1.41421	−	1.41421i	−0.0521286	−	0.0521286i
$737$	−6.00000	+	6.00000i	−0.221013	+	0.221013i
$738$	3.00000	−	3.00000i	0.110432	−	0.110432i
$739$			28.6863i			1.05524i	0.849480	+	0.527621i	$0.176916\pi$
$739$			28.6863i			1.05524i	−0.849480	+	0.527621i	$0.823084\pi$
$740$			2.97056i			0.109200i
$741$		0			0
$742$	6.34315	−	6.34315i	0.232864	−	0.232864i
$743$	20.0416	+	20.0416i	0.735256	+	0.735256i	0.971656	−	0.236400i	$-0.0759675\pi$
$743$	20.0416	+	20.0416i	0.735256	+	0.735256i	−0.236400	+	0.971656i	$0.575967\pi$
$744$	−3.65685			−0.134067
$745$	5.51472	+	5.51472i	0.202044	+	0.202044i
$746$		−	17.1716i		−	0.628696i
$747$	−2.82843			−0.103487
$748$	2.12132	+	3.53553i	0.0775632	+	0.129272i
$749$	−30.6274			−1.11910
$750$			5.65685i			0.206559i
$751$	5.41421	+	5.41421i	0.197567	+	0.197567i	0.798956	−	0.601389i	$-0.205386\pi$
$751$	5.41421	+	5.41421i	0.197567	+	0.197567i	−0.601389	+	0.798956i	$0.705386\pi$
$752$	1.65685			0.0604193
$753$	−7.17157	−	7.17157i	−0.261347	−	0.261347i
$754$	−4.20101	+	4.20101i	−0.152992	+	0.152992i
$755$	−2.82843	+	2.82843i	−0.102937	+	0.102937i
$756$		−	2.00000i		−	0.0727393i
$757$		−	9.31371i		−	0.338512i	−0.985572	−	0.169256i	$-0.945863\pi$
$757$		−	9.31371i		−	0.338512i	0.985572	−	0.169256i	$-0.0541365\pi$
$758$	2.34315	−	2.34315i	0.0851069	−	0.0851069i
$759$	−1.41421	+	1.41421i	−0.0513327	+	0.0513327i
$760$		0			0
$761$	28.0000			1.01500			0.507500	−	0.861652i	$-0.330570\pi$
$761$	28.0000			1.01500			0.507500	+	0.861652i	$0.330570\pi$
$762$	10.4853	+	10.4853i	0.379842	+	0.379842i
$763$			6.82843i			0.247206i
$764$	−14.3431			−0.518917
$765$	1.24264	+	2.07107i	0.0449278	+	0.0748796i
$766$	−14.3431			−0.518239
$767$		0			0
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	36.9706			1.33319			0.666596	−	0.745419i	$-0.267751\pi$
$769$	36.9706			1.33319			0.666596	+	0.745419i	$0.267751\pi$
$770$	0.828427	+	0.828427i	0.0298544	+	0.0298544i
$771$	3.75736	−	3.75736i	0.135318	−	0.135318i
$772$	−15.4853	+	15.4853i	−0.557327	+	0.557327i
$773$		−	38.2843i		−	1.37699i	−0.725241	−	0.688495i	$-0.758272\pi$
$773$		−	38.2843i		−	1.37699i	0.725241	−	0.688495i	$-0.241728\pi$
$774$		−	1.17157i		−	0.0421113i
$775$	−12.0416	+	12.0416i	−0.432548	+	0.432548i
$776$	9.48528	−	9.48528i	0.340502	−	0.340502i
$777$	−7.17157	−	7.17157i	−0.257279	−	0.257279i
$778$	23.6569			0.848139
$779$		0			0
$780$			0.686292i			0.0245732i
$781$	4.34315			0.155410
$782$	−7.07107	+	4.24264i	−0.252861	+	0.151717i
$783$	−5.07107			−0.181225
$784$			3.00000i			0.107143i
$785$	3.85786	+	3.85786i	0.137693	+	0.137693i
$786$	9.65685			0.344449
$787$	3.31371	+	3.31371i	0.118121	+	0.118121i	0.763696	−	0.645576i	$-0.223382\pi$
$787$	3.31371	+	3.31371i	0.118121	+	0.118121i	−0.645576	+	0.763696i	$0.723382\pi$
$788$	−7.24264	+	7.24264i	−0.258008	+	0.258008i
$789$	−0.343146	+	0.343146i	−0.0122163	+	0.0122163i
$790$			0.201010i			0.00715162i
$791$			0.485281i			0.0172546i
$792$	−0.707107	+	0.707107i	−0.0251259	+	0.0251259i
$793$	10.8284	−	10.8284i	0.384529	−	0.384529i
$794$	22.8995	+	22.8995i	0.812673	+	0.812673i
$795$	−2.62742			−0.0931849
$796$	9.89949	+	9.89949i	0.350878	+	0.350878i
$797$			28.4853i			1.00900i	0.863412	+	0.504500i	$0.168323\pi$
$797$			28.4853i			1.00900i	−0.863412	+	0.504500i	$0.831677\pi$
$798$		0			0
$799$	1.65685	−	6.62742i	0.0586153	−	0.234461i
$800$	−4.65685			−0.164645
$801$			6.34315i			0.224124i
$802$	−4.31371	−	4.31371i	−0.152322	−	0.152322i
$803$	−9.41421			−0.332220
$804$	−6.00000	−	6.00000i	−0.211604	−	0.211604i
$805$	−1.65685	+	1.65685i	−0.0583964	+	0.0583964i
$806$	−3.02944	+	3.02944i	−0.106707	+	0.106707i
$807$		−	19.8995i		−	0.700495i
$808$		−	4.48528i		−	0.157792i
$809$	21.9706	−	21.9706i	0.772444	−	0.772444i	−0.206089	−	0.978533i	$-0.566074\pi$
$809$	21.9706	−	21.9706i	0.772444	−	0.772444i	0.978533	+	0.206089i	$0.0660737\pi$
$810$	−0.414214	+	0.414214i	−0.0145540	+	0.0145540i
$811$	−12.0000	−	12.0000i	−0.421377	−	0.421377i	0.464301	−	0.885678i	$-0.346306\pi$
$811$	−12.0000	−	12.0000i	−0.421377	−	0.421377i	−0.885678	+	0.464301i	$0.846306\pi$
$812$	−10.1421			−0.355919
$813$	0.828427	+	0.828427i	0.0290542	+	0.0290542i
$814$			5.07107i			0.177741i
$815$	7.02944			0.246230
$816$	−3.53553	+	2.12132i	−0.123768	+	0.0742611i
$817$		0			0
$818$		−	13.3137i		−	0.465503i
$819$	−1.65685	−	1.65685i	−0.0578952	−	0.0578952i
$820$	−2.48528			−0.0867898
$821$	29.5858	+	29.5858i	1.03255	+	1.03255i	0.999452	+	0.0330990i	$0.0105377\pi$
$821$	29.5858	+	29.5858i	1.03255	+	1.03255i	0.0330990	+	0.999452i	$0.489462\pi$
$822$	5.65685	−	5.65685i	0.197305	−	0.197305i
$823$	12.7279	−	12.7279i	0.443667	−	0.443667i	−0.449575	−	0.893243i	$-0.648425\pi$
$823$	12.7279	−	12.7279i	0.443667	−	0.443667i	0.893243	+	0.449575i	$0.148425\pi$
$824$		−	5.17157i		−	0.180160i
$825$			4.65685i			0.162131i
$826$		0			0
$827$	38.1421	−	38.1421i	1.32633	−	1.32633i	0.417787	−	0.908545i	$-0.362806\pi$
$827$	38.1421	−	38.1421i	1.32633	−	1.32633i	0.908545	−	0.417787i	$-0.137194\pi$
$828$	−1.41421	−	1.41421i	−0.0491473	−	0.0491473i
$829$	−21.3137			−0.740256			−0.370128	−	0.928981i	$-0.620686\pi$
$829$	−21.3137			−0.740256			−0.370128	+	0.928981i	$0.620686\pi$
$830$	1.17157	+	1.17157i	0.0406659	+	0.0406659i
$831$			9.07107i			0.314672i
$832$	−1.17157			−0.0406170
$833$	12.0000	+	3.00000i	0.415775	+	0.103944i
$834$	13.6569			0.472898
$835$			12.4853i			0.432071i
$836$		0			0
$837$	−3.65685			−0.126399
$838$	23.3137	+	23.3137i	0.805359	+	0.805359i
$839$	−4.92893	+	4.92893i	−0.170166	+	0.170166i	−0.787052	−	0.616886i	$-0.788394\pi$
$839$	−4.92893	+	4.92893i	−0.170166	+	0.170166i	0.616886	+	0.787052i	$0.288394\pi$
$840$	−0.828427	+	0.828427i	−0.0285835	+	0.0285835i
$841$		−	3.28427i		−	0.113251i
$842$			2.14214i			0.0738229i
$843$	−12.9706	+	12.9706i	−0.446730	+	0.446730i
$844$	9.17157	−	9.17157i	0.315699	−	0.315699i
$845$	−4.81623	−	4.81623i	−0.165683	−	0.165683i
$846$	1.65685			0.0569638
$847$	1.41421	+	1.41421i	0.0485930	+	0.0485930i
$848$		−	4.48528i		−	0.154025i
$849$	−2.34315			−0.0804166
$850$	−4.65685	+	18.6274i	−0.159729	+	0.638915i
$851$	−10.1421			−0.347668
$852$			4.34315i			0.148794i
$853$	−7.92893	−	7.92893i	−0.271481	−	0.271481i	0.558215	−	0.829696i	$-0.311486\pi$
$853$	−7.92893	−	7.92893i	−0.271481	−	0.271481i	−0.829696	+	0.558215i	$0.811486\pi$
$854$	26.1421			0.894565
$855$		0			0
$856$	−10.8284	+	10.8284i	−0.370108	+	0.370108i
$857$	7.00000	−	7.00000i	0.239115	−	0.239115i	−0.577368	−	0.816484i	$-0.695920\pi$
$857$	7.00000	−	7.00000i	0.239115	−	0.239115i	0.816484	+	0.577368i	$0.195920\pi$
$858$			1.17157i			0.0399968i
$859$		−	4.00000i		−	0.136478i	−0.997669	−	0.0682391i	$-0.978262\pi$
$859$		−	4.00000i		−	0.136478i	0.997669	−	0.0682391i	$-0.0217381\pi$
$860$	−0.485281	+	0.485281i	−0.0165480	+	0.0165480i
$861$	6.00000	−	6.00000i	0.204479	−	0.204479i
$862$	−6.58579	−	6.58579i	−0.224313	−	0.224313i
$863$	27.5147			0.936612			0.468306	−	0.883566i	$-0.344865\pi$
$863$	27.5147			0.936612			0.468306	+	0.883566i	$0.344865\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$			2.28427i			0.0776676i
$866$	−2.00000			−0.0679628
$867$	4.94975	+	16.2635i	0.168102	+	0.552336i
$868$	−7.31371			−0.248243
$869$			0.343146i			0.0116404i
$870$	2.10051	+	2.10051i	0.0712138	+	0.0712138i
$871$	−9.94113			−0.336842
$872$	2.41421	+	2.41421i	0.0817556	+	0.0817556i
$873$	9.48528	−	9.48528i	0.321028	−	0.321028i
$874$		0			0
$875$			11.3137i			0.382473i
$876$		−	9.41421i		−	0.318077i
$877$	−18.5563	+	18.5563i	−0.626603	+	0.626603i	−0.947212	−	0.320608i	$-0.896113\pi$
$877$	−18.5563	+	18.5563i	−0.626603	+	0.626603i	0.320608	+	0.947212i	$0.396113\pi$
$878$	10.3848	−	10.3848i	0.350469	−	0.350469i
$879$	−9.89949	−	9.89949i	−0.333902	−	0.333902i
$880$	0.585786			0.0197469
$881$	28.1127	+	28.1127i	0.947141	+	0.947141i	0.998671	−	0.0515305i	$-0.0164100\pi$
$881$	28.1127	+	28.1127i	0.947141	+	0.947141i	−0.0515305	+	0.998671i	$0.516410\pi$
$882$			3.00000i			0.101015i
$883$	2.82843			0.0951842			0.0475921	−	0.998867i	$-0.484845\pi$
$883$	2.82843			0.0951842			0.0475921	+	0.998867i	$0.484845\pi$
$884$	−1.17157	+	4.68629i	−0.0394043	+	0.157617i
$885$		0			0
$886$			31.7990i			1.06831i
$887$	−14.3848	−	14.3848i	−0.482994	−	0.482994i	0.423093	−	0.906086i	$-0.360944\pi$
$887$	−14.3848	−	14.3848i	−0.482994	−	0.482994i	−0.906086	+	0.423093i	$0.860944\pi$
$888$	−5.07107			−0.170174
$889$	20.9706	+	20.9706i	0.703330	+	0.703330i
$890$	2.62742	−	2.62742i	0.0880712	−	0.0880712i
$891$	−0.707107	+	0.707107i	−0.0236890	+	0.0236890i
$892$		−	8.48528i		−	0.284108i
$893$		0			0
$894$	−9.41421	+	9.41421i	−0.314858	+	0.314858i
$895$	−4.20101	+	4.20101i	−0.140424	+	0.140424i
$896$	−1.41421	−	1.41421i	−0.0472456	−	0.0472456i
$897$	−2.34315			−0.0782354
$898$	−5.34315	−	5.34315i	−0.178303	−	0.178303i
$899$			18.5442i			0.618482i
$900$	−4.65685			−0.155228
$901$	−17.9411	−	4.48528i	−0.597706	−	0.149426i
$902$	−4.24264			−0.141264
$903$		−	2.34315i		−	0.0779750i
$904$	0.171573	+	0.171573i	0.00570643	+	0.00570643i
$905$	3.65685			0.121558
$906$	−4.82843	−	4.82843i	−0.160414	−	0.160414i
$907$	19.5147	−	19.5147i	0.647976	−	0.647976i	−0.304528	−	0.952503i	$-0.598499\pi$
$907$	19.5147	−	19.5147i	0.647976	−	0.647976i	0.952503	+	0.304528i	$0.0984987\pi$
$908$	10.1421	−	10.1421i	0.336579	−	0.336579i
$909$		−	4.48528i		−	0.148767i
$910$			1.37258i			0.0455007i
$911$	20.0416	−	20.0416i	0.664009	−	0.664009i	−0.292314	−	0.956323i	$-0.594425\pi$
$911$	20.0416	−	20.0416i	0.664009	−	0.664009i	0.956323	+	0.292314i	$0.0944251\pi$
$912$		0			0
$913$	2.00000	+	2.00000i	0.0661903	+	0.0661903i
$914$	25.3137			0.837303
$915$	−5.41421	−	5.41421i	−0.178988	−	0.178988i
$916$		−	18.0000i		−	0.594737i
$917$	19.3137			0.637795
$918$	−3.53553	+	2.12132i	−0.116690	+	0.0700140i
$919$	60.0833			1.98196			0.990982	−	0.133995i	$-0.0427807\pi$
$919$	60.0833			1.98196			0.990982	+	0.133995i	$0.0427807\pi$
$920$			1.17157i			0.0386256i
$921$	−4.82843	−	4.82843i	−0.159102	−	0.159102i
$922$	−12.4853			−0.411181
$923$	3.59798	+	3.59798i	0.118429	+	0.118429i
$924$	−1.41421	+	1.41421i	−0.0465242	+	0.0465242i
$925$	−16.6985	+	16.6985i	−0.549043	+	0.549043i
$926$			2.82843i			0.0929479i
$927$		−	5.17157i		−	0.169857i
$928$	−3.58579	+	3.58579i	−0.117709	+	0.117709i
$929$	−19.2843	+	19.2843i	−0.632696	+	0.632696i	−0.948744	−	0.316047i	$-0.897644\pi$
$929$	−19.2843	+	19.2843i	−0.632696	+	0.632696i	0.316047	+	0.948744i	$0.397644\pi$
$930$	1.51472	+	1.51472i	0.0496696	+	0.0496696i
$931$		0			0
$932$	3.48528	+	3.48528i	0.114164	+	0.114164i
$933$			2.68629i			0.0879452i
$934$	25.1716			0.823639
$935$	0.585786	−	2.34315i	0.0191573	−	0.0766291i
$936$	−1.17157			−0.0382941
$937$		−	20.6863i		−	0.675792i	−0.941184	−	0.337896i	$-0.890285\pi$
$937$		−	20.6863i		−	0.675792i	0.941184	−	0.337896i	$-0.109715\pi$
$938$	−12.0000	−	12.0000i	−0.391814	−	0.391814i
$939$	−6.38478			−0.208359
$940$	−0.686292	−	0.686292i	−0.0223844	−	0.0223844i
$941$	−8.07107	+	8.07107i	−0.263109	+	0.263109i	−0.826316	−	0.563207i	$-0.809567\pi$
$941$	−8.07107	+	8.07107i	−0.263109	+	0.263109i	0.563207	+	0.826316i	$0.309567\pi$
$942$	−6.58579	+	6.58579i	−0.214577	+	0.214577i
$943$		−	8.48528i		−	0.276319i
$944$		0			0
$945$	−0.828427	+	0.828427i	−0.0269487	+	0.0269487i
$946$	−0.828427	+	0.828427i	−0.0269345	+	0.0269345i
$947$	0.970563	+	0.970563i	0.0315391	+	0.0315391i	0.722700	−	0.691161i	$-0.242901\pi$
$947$	0.970563	+	0.970563i	0.0315391	+	0.0315391i	−0.691161	+	0.722700i	$0.742901\pi$
$948$	−0.343146			−0.0111449
$949$	−7.79899	−	7.79899i	−0.253166	−	0.253166i
$950$		0			0
$951$	6.92893			0.224686
$952$	−7.07107	+	4.24264i	−0.229175	+	0.137505i
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		−	4.48528i		−	0.145216i
$955$	5.94113	+	5.94113i	0.192250	+	0.192250i
$956$	−2.82843			−0.0914779
$957$	3.58579	+	3.58579i	0.115912	+	0.115912i
$958$	−8.72792	+	8.72792i	−0.281986	+	0.281986i
$959$	11.3137	−	11.3137i	0.365339	−	0.365339i
$960$			0.585786i			0.0189062i
$961$		−	17.6274i		−	0.568626i
$962$	−4.20101	+	4.20101i	−0.135446	+	0.135446i
$963$	−10.8284	+	10.8284i	−0.348941	+	0.348941i
$964$	−11.4853	−	11.4853i	−0.369916	−	0.369916i
$965$	12.8284			0.412962
$966$	−2.82843	−	2.82843i	−0.0910032	−	0.0910032i
$967$		−	0.686292i		−	0.0220696i	−0.999939	−	0.0110348i	$-0.996487\pi$
$967$		−	0.686292i		−	0.0220696i	0.999939	−	0.0110348i	$-0.00351256\pi$
$968$	1.00000			0.0321412
$969$		0			0
$970$	−7.85786			−0.252301
$971$		−	24.9706i		−	0.801343i	−0.916222	−	0.400672i	$-0.868777\pi$
$971$		−	24.9706i		−	0.801343i	0.916222	−	0.400672i	$-0.131223\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	27.3137			0.875637
$974$	−11.7574	−	11.7574i	−0.376730	−	0.376730i
$975$	−3.85786	+	3.85786i	−0.123551	+	0.123551i
$976$	9.24264	−	9.24264i	0.295850	−	0.295850i
$977$			22.6274i			0.723915i	0.932195	+	0.361958i	$0.117891\pi$
$977$			22.6274i			0.723915i	−0.932195	+	0.361958i	$0.882109\pi$
$978$			12.0000i			0.383718i
$979$	4.48528	−	4.48528i	0.143350	−	0.143350i
$980$	1.24264	−	1.24264i	0.0396947	−	0.0396947i
$981$	2.41421	+	2.41421i	0.0770799	+	0.0770799i
$982$	14.3431			0.457708
$983$	23.0711	+	23.0711i	0.735853	+	0.735853i	0.971773	−	0.235920i	$-0.0758103\pi$
$983$	23.0711	+	23.0711i	0.735853	+	0.735853i	−0.235920	+	0.971773i	$0.575810\pi$
$984$		−	4.24264i		−	0.135250i
$985$	6.00000			0.191176
$986$	10.7574	+	17.9289i	0.342584	+	0.570974i
$987$	3.31371			0.105477
$988$		0			0
$989$	−1.65685	−	1.65685i	−0.0526849	−	0.0526849i
$990$	0.585786			0.0186175
$991$	34.5858	+	34.5858i	1.09865	+	1.09865i	0.994568	+	0.104085i	$0.0331915\pi$
$991$	34.5858	+	34.5858i	1.09865	+	1.09865i	0.104085	+	0.994568i	$0.466808\pi$
$992$	−2.58579	+	2.58579i	−0.0820988	+	0.0820988i
$993$	20.4853	−	20.4853i	0.650081	−	0.650081i
$994$			8.68629i			0.275512i
$995$		−	8.20101i		−	0.259989i
$996$	−2.00000	+	2.00000i	−0.0633724	+	0.0633724i
$997$	7.44365	−	7.44365i	0.235743	−	0.235743i	−0.579342	−	0.815085i	$-0.696690\pi$
$997$	7.44365	−	7.44365i	0.235743	−	0.235743i	0.815085	+	0.579342i	$0.196690\pi$
$998$	24.4853	+	24.4853i	0.775068	+	0.775068i
$999$	−5.07107			−0.160441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.a.727.1	yes	4
17.4	even	4	inner	1122.2.l.a.463.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.a.463.1	✓	4	17.4	even	4	inner
1122.2.l.a.727.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.41421 + 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +1.17157 q^{13} +(1.41421 + 1.41421i) q^{14} -0.585786i q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} +1.00000 q^{18} +(-0.414214 - 0.414214i) q^{20} +2.00000 q^{21} +(-0.707107 - 0.707107i) q^{22} +(1.41421 - 1.41421i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.65685i q^{25} -1.17157i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.41421 - 1.41421i) q^{28} +(-3.58579 - 3.58579i) q^{29} -0.585786 q^{30} +(-2.58579 - 2.58579i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} -1.17157 q^{35} -1.00000i q^{36} +(-3.58579 - 3.58579i) q^{37} +(-0.828427 - 0.828427i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(3.00000 - 3.00000i) q^{41} -2.00000i q^{42} -1.17157i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(-1.41421 - 1.41421i) q^{46} +1.65685 q^{47} +(-0.707107 - 0.707107i) q^{48} +3.00000i q^{49} -4.65685 q^{50} +(-3.53553 + 2.12132i) q^{51} -1.17157 q^{52} -4.48528i q^{53} +(-0.707107 - 0.707107i) q^{54} +0.585786 q^{55} +(-1.41421 - 1.41421i) q^{56} +(-3.58579 + 3.58579i) q^{58} +0.585786i q^{60} +(9.24264 - 9.24264i) q^{61} +(-2.58579 + 2.58579i) q^{62} +(-1.41421 - 1.41421i) q^{63} -1.00000 q^{64} +(0.485281 + 0.485281i) q^{65} +1.00000i q^{66} -8.48528 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{69} +1.17157i q^{70} +(3.07107 + 3.07107i) q^{71} -1.00000 q^{72} +(-6.65685 - 6.65685i) q^{73} +(-3.58579 + 3.58579i) q^{74} +(-3.29289 + 3.29289i) q^{75} +2.00000i q^{77} +(-0.828427 + 0.828427i) q^{78} +(-0.242641 + 0.242641i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} +2.82843i q^{83} -2.00000 q^{84} +(2.07107 - 1.24264i) q^{85} -1.17157 q^{86} +5.07107i q^{87} +(0.707107 + 0.707107i) q^{88} +6.34315 q^{89} +(0.414214 + 0.414214i) q^{90} +(-1.65685 + 1.65685i) q^{91} +(-1.41421 + 1.41421i) q^{92} +3.65685i q^{93} -1.65685i q^{94} +(-0.707107 + 0.707107i) q^{96} +(-9.48528 - 9.48528i) q^{97} +3.00000 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^5	\( 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} - 20 q^{29} - 8 q^{30} - 16 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{35} - 20 q^{37} + 8 q^{39} + 4 q^{40} + 12 q^{41} + 4 q^{45} - 16 q^{47} + 4 q^{50} - 16 q^{52} + 8 q^{55} - 20 q^{58} + 20 q^{61} - 16 q^{62} - 4 q^{64} - 32 q^{65} - 4 q^{68} - 8 q^{69} - 16 q^{71} - 4 q^{72} - 4 q^{73} - 20 q^{74} - 16 q^{75} + 8 q^{78} + 16 q^{79} - 4 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} - 20 q^{85} - 16 q^{86} + 48 q^{89} - 4 q^{90} + 16 q^{91} - 4 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 - 20 * q^29 - 8 * q^30 - 16 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^35 - 20 * q^37 + 8 * q^39 + 4 * q^40 + 12 * q^41 + 4 * q^45 - 16 * q^47 + 4 * q^50 - 16 * q^52 + 8 * q^55 - 20 * q^58 + 20 * q^61 - 16 * q^62 - 4 * q^64 - 32 * q^65 - 4 * q^68 - 8 * q^69 - 16 * q^71 - 4 * q^72 - 4 * q^73 - 20 * q^74 - 16 * q^75 + 8 * q^78 + 16 * q^79 - 4 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 - 20 * q^85 - 16 * q^86 + 48 * q^89 - 4 * q^90 + 16 * q^91 - 4 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more