LMFDB - Embedded newform 1122.2.l.c.727.2

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			727.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.c.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.41421 + 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.41421 + 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +(2.41421 - 2.41421i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} +2.82843 q^{13} +3.41421i q^{15} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +1.00000 q^{18} -0.828427i q^{19} +(-2.41421 - 2.41421i) q^{20} +(0.707107 + 0.707107i) q^{22} +(0.828427 - 0.828427i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.65685i q^{25} -2.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.00000 - 3.00000i) q^{29} +3.41421 q^{30} +(2.00000 + 2.00000i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(4.00000 + 1.00000i) q^{34} -1.00000i q^{36} +(0.171573 + 0.171573i) q^{37} -0.828427 q^{38} +(2.00000 + 2.00000i) q^{39} +(-2.41421 + 2.41421i) q^{40} +(-5.82843 + 5.82843i) q^{41} -4.82843i q^{43} +(0.707107 - 0.707107i) q^{44} +(-2.41421 + 2.41421i) q^{45} +(-0.828427 - 0.828427i) q^{46} +8.82843 q^{47} +(0.707107 + 0.707107i) q^{48} +7.00000i q^{49} +6.65685 q^{50} +(-3.53553 + 2.12132i) q^{51} -2.82843 q^{52} +5.17157i q^{53} +(0.707107 + 0.707107i) q^{54} -3.41421 q^{55} +(0.585786 - 0.585786i) q^{57} +(-3.00000 + 3.00000i) q^{58} +0.828427i q^{59} -3.41421i q^{60} +(-1.58579 + 1.58579i) q^{61} +(2.00000 - 2.00000i) q^{62} -1.00000 q^{64} +(6.82843 + 6.82843i) q^{65} +1.00000i q^{66} -5.65685 q^{67} +(1.00000 - 4.00000i) q^{68} +1.17157 q^{69} +(5.65685 + 5.65685i) q^{71} -1.00000 q^{72} +(-4.07107 - 4.07107i) q^{73} +(0.171573 - 0.171573i) q^{74} +(-4.70711 + 4.70711i) q^{75} +0.828427i q^{76} +(2.00000 - 2.00000i) q^{78} +(8.82843 - 8.82843i) q^{79} +(2.41421 + 2.41421i) q^{80} -1.00000 q^{81} +(5.82843 + 5.82843i) q^{82} -9.65685i q^{83} +(-12.0711 + 7.24264i) q^{85} -4.82843 q^{86} -4.24264i q^{87} +(-0.707107 - 0.707107i) q^{88} +9.17157 q^{89} +(2.41421 + 2.41421i) q^{90} +(-0.828427 + 0.828427i) q^{92} +2.82843i q^{93} -8.82843i q^{94} +(2.00000 - 2.00000i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.00000 - 1.00000i) q^{97} +7.00000 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} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{20} - 8 q^{23} - 12 q^{29} + 8 q^{30} + 8 q^{31} - 4 q^{33} + 16 q^{34} + 12 q^{37} + 8 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 4 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{50} - 8 q^{55} + 8 q^{57} - 12 q^{58} - 12 q^{61} + 8 q^{62} - 4 q^{64} + 16 q^{65} + 4 q^{68} + 16 q^{69} - 4 q^{72} + 12 q^{73} + 12 q^{74} - 16 q^{75} + 8 q^{78} + 24 q^{79} + 4 q^{80} - 4 q^{81} + 12 q^{82} - 20 q^{85} - 8 q^{86} + 48 q^{89} + 4 q^{90} + 8 q^{92} + 8 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^10 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 4 * q^20 - 8 * q^23 - 12 * q^29 + 8 * q^30 + 8 * q^31 - 4 * q^33 + 16 * q^34 + 12 * q^37 + 8 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 4 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^50 - 8 * q^55 + 8 * q^57 - 12 * q^58 - 12 * q^61 + 8 * q^62 - 4 * q^64 + 16 * q^65 + 4 * q^68 + 16 * q^69 - 4 * q^72 + 12 * q^73 + 12 * q^74 - 16 * q^75 + 8 * q^78 + 24 * q^79 + 4 * q^80 - 4 * q^81 + 12 * q^82 - 20 * q^85 - 8 * q^86 + 48 * q^89 + 4 * q^90 + 8 * q^92 + 8 * q^95 - 4 * q^97 + 28 * 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
$5$	2.41421	+	2.41421i	1.07967	+	1.07967i	0.996539	+	0.0831305i	$0.0264918\pi$
$5$	2.41421	+	2.41421i	1.07967	+	1.07967i	0.0831305	+	0.996539i	$0.473508\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	2.41421	−	2.41421i	0.763441	−	0.763441i
$11$	−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
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$			3.41421i			0.881546i
$16$	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
$19$		−	0.828427i		−	0.190054i	−0.995475	−	0.0950271i	$-0.969706\pi$
$19$		−	0.828427i		−	0.190054i	0.995475	−	0.0950271i	$-0.0302938\pi$
$20$	−2.41421	−	2.41421i	−0.539835	−	0.539835i
$21$		0			0
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	0.828427	−	0.828427i	0.172739	−	0.172739i	−0.615443	−	0.788182i	$-0.711023\pi$
$23$	0.828427	−	0.828427i	0.172739	−	0.172739i	0.788182	+	0.615443i	$0.211023\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			6.65685i			1.33137i
$26$		−	2.82843i		−	0.554700i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	3.41421			0.623347
$31$	2.00000	+	2.00000i	0.359211	+	0.359211i	0.863522	−	0.504311i	$-0.168254\pi$
$31$	2.00000	+	2.00000i	0.359211	+	0.359211i	−0.504311	+	0.863522i	$0.668254\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.00000			−0.174078
$34$	4.00000	+	1.00000i	0.685994	+	0.171499i
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$	0.171573	+	0.171573i	0.0282064	+	0.0282064i	0.721069	−	0.692863i	$-0.243651\pi$
$37$	0.171573	+	0.171573i	0.0282064	+	0.0282064i	−0.692863	+	0.721069i	$0.743651\pi$
$38$	−0.828427			−0.134389
$39$	2.00000	+	2.00000i	0.320256	+	0.320256i
$40$	−2.41421	+	2.41421i	−0.381721	+	0.381721i
$41$	−5.82843	+	5.82843i	−0.910247	+	0.910247i	−0.996291	−	0.0860440i	$-0.972577\pi$
$41$	−5.82843	+	5.82843i	−0.910247	+	0.910247i	0.0860440	+	0.996291i	$0.472577\pi$
$42$		0			0
$43$		−	4.82843i		−	0.736328i	−0.929761	−	0.368164i	$-0.879986\pi$
$43$		−	4.82843i		−	0.736328i	0.929761	−	0.368164i	$-0.120014\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	−2.41421	+	2.41421i	−0.359890	+	0.359890i
$46$	−0.828427	−	0.828427i	−0.122145	−	0.122145i
$47$	8.82843			1.28776			0.643879	−	0.765127i	$-0.277324\pi$
$47$	8.82843			1.28776			0.643879	+	0.765127i	$0.277324\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			7.00000i			1.00000i
$50$	6.65685			0.941421
$51$	−3.53553	+	2.12132i	−0.495074	+	0.297044i
$52$	−2.82843			−0.392232
$53$			5.17157i			0.710370i	0.934796	+	0.355185i	$0.115582\pi$
$53$			5.17157i			0.710370i	−0.934796	+	0.355185i	$0.884418\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−3.41421			−0.460372
$56$		0			0
$57$	0.585786	−	0.585786i	0.0775893	−	0.0775893i
$58$	−3.00000	+	3.00000i	−0.393919	+	0.393919i
$59$			0.828427i			0.107852i	0.998545	+	0.0539260i	$0.0171735\pi$
$59$			0.828427i			0.107852i	−0.998545	+	0.0539260i	$0.982826\pi$
$60$		−	3.41421i		−	0.440773i
$61$	−1.58579	+	1.58579i	−0.203039	+	0.203039i	−0.801301	−	0.598262i	$-0.795858\pi$
$61$	−1.58579	+	1.58579i	−0.203039	+	0.203039i	0.598262	+	0.801301i	$0.295858\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.82843	+	6.82843i	0.846962	+	0.846962i
$66$			1.00000i			0.123091i
$67$	−5.65685			−0.691095			−0.345547	−	0.938401i	$-0.612307\pi$
$67$	−5.65685			−0.691095			−0.345547	+	0.938401i	$0.612307\pi$
$68$	1.00000	−	4.00000i	0.121268	−	0.485071i
$69$	1.17157			0.141041
$70$		0			0
$71$	5.65685	+	5.65685i	0.671345	+	0.671345i	0.958026	−	0.286681i	$-0.0925520\pi$
$71$	5.65685	+	5.65685i	0.671345	+	0.671345i	−0.286681	+	0.958026i	$0.592552\pi$
$72$	−1.00000			−0.117851
$73$	−4.07107	−	4.07107i	−0.476482	−	0.476482i	0.427522	−	0.904005i	$-0.359387\pi$
$73$	−4.07107	−	4.07107i	−0.476482	−	0.476482i	−0.904005	+	0.427522i	$0.859387\pi$
$74$	0.171573	−	0.171573i	0.0199449	−	0.0199449i
$75$	−4.70711	+	4.70711i	−0.543530	+	0.543530i
$76$			0.828427i			0.0950271i
$77$		0			0
$78$	2.00000	−	2.00000i	0.226455	−	0.226455i
$79$	8.82843	−	8.82843i	0.993276	−	0.993276i	−0.00670189	−	0.999978i	$-0.502133\pi$
$79$	8.82843	−	8.82843i	0.993276	−	0.993276i	0.999978	+	0.00670189i	$0.00213329\pi$
$80$	2.41421	+	2.41421i	0.269917	+	0.269917i
$81$	−1.00000			−0.111111
$82$	5.82843	+	5.82843i	0.643642	+	0.643642i
$83$		−	9.65685i		−	1.05998i	−0.848005	−	0.529989i	$-0.822196\pi$
$83$		−	9.65685i		−	1.05998i	0.848005	−	0.529989i	$-0.177804\pi$
$84$		0			0
$85$	−12.0711	+	7.24264i	−1.30929	+	0.785575i
$86$	−4.82843			−0.520663
$87$		−	4.24264i		−	0.454859i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	9.17157			0.972185			0.486092	−	0.873907i	$-0.338422\pi$
$89$	9.17157			0.972185			0.486092	+	0.873907i	$0.338422\pi$
$90$	2.41421	+	2.41421i	0.254480	+	0.254480i
$91$		0			0
$92$	−0.828427	+	0.828427i	−0.0863695	+	0.0863695i
$93$			2.82843i			0.293294i
$94$		−	8.82843i		−	0.910583i
$95$	2.00000	−	2.00000i	0.205196	−	0.205196i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−1.00000	−	1.00000i	−0.101535	−	0.101535i	0.654515	−	0.756049i	$-0.272873\pi$
$97$	−1.00000	−	1.00000i	−0.101535	−	0.101535i	−0.756049	+	0.654515i	$0.772873\pi$
$98$	7.00000			0.707107
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$		−	6.65685i		−	0.665685i
$101$	−4.00000			−0.398015			−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000			−0.398015			−0.199007	+	0.979998i	$0.563772\pi$
$102$	2.12132	+	3.53553i	0.210042	+	0.350070i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$			2.82843i			0.277350i
$105$		0			0
$106$	5.17157			0.502308
$107$	6.48528	+	6.48528i	0.626956	+	0.626956i	0.947301	−	0.320345i	$-0.103799\pi$
$107$	6.48528	+	6.48528i	0.626956	+	0.626956i	−0.320345	+	0.947301i	$0.603799\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	12.0711	−	12.0711i	1.15620	−	1.15620i	0.170912	−	0.985286i	$-0.445328\pi$
$109$	12.0711	−	12.0711i	1.15620	−	1.15620i	0.985286	−	0.170912i	$-0.0546715\pi$
$110$			3.41421i			0.325532i
$111$			0.242641i			0.0230304i
$112$		0			0
$113$	6.89949	−	6.89949i	0.649050	−	0.649050i	−0.303714	−	0.952763i	$-0.598227\pi$
$113$	6.89949	−	6.89949i	0.649050	−	0.649050i	0.952763	+	0.303714i	$0.0982266\pi$
$114$	−0.585786	−	0.585786i	−0.0548639	−	0.0548639i
$115$	4.00000			0.373002
$116$	3.00000	+	3.00000i	0.278543	+	0.278543i
$117$			2.82843i			0.261488i
$118$	0.828427			0.0762629
$119$		0			0
$120$	−3.41421			−0.311674
$121$		−	1.00000i		−	0.0909091i
$122$	1.58579	+	1.58579i	0.143570	+	0.143570i
$123$	−8.24264			−0.743214
$124$	−2.00000	−	2.00000i	−0.179605	−	0.179605i
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$		0			0
$127$		−	20.1421i		−	1.78733i	−0.448739	−	0.893663i	$-0.648127\pi$
$127$		−	20.1421i		−	1.78733i	0.448739	−	0.893663i	$-0.351873\pi$
$128$			1.00000i			0.0883883i
$129$	3.41421	−	3.41421i	0.300605	−	0.300605i
$130$	6.82843	−	6.82843i	0.598893	−	0.598893i
$131$	6.48528	+	6.48528i	0.566622	+	0.566622i	0.931180	−	0.364559i	$-0.118780\pi$
$131$	6.48528	+	6.48528i	0.566622	+	0.566622i	−0.364559	+	0.931180i	$0.618780\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$			5.65685i			0.488678i
$135$	−3.41421			−0.293849
$136$	−4.00000	−	1.00000i	−0.342997	−	0.0857493i
$137$	−9.17157			−0.783580			−0.391790	−	0.920055i	$-0.628144\pi$
$137$	−9.17157			−0.783580			−0.391790	+	0.920055i	$0.628144\pi$
$138$		−	1.17157i		−	0.0997309i
$139$	−7.65685	−	7.65685i	−0.649446	−	0.649446i	0.303413	−	0.952859i	$-0.401874\pi$
$139$	−7.65685	−	7.65685i	−0.649446	−	0.649446i	−0.952859	+	0.303413i	$0.901874\pi$
$140$		0			0
$141$	6.24264	+	6.24264i	0.525725	+	0.525725i
$142$	5.65685	−	5.65685i	0.474713	−	0.474713i
$143$	−2.00000	+	2.00000i	−0.167248	+	0.167248i
$144$			1.00000i			0.0833333i
$145$		−	14.4853i		−	1.20294i
$146$	−4.07107	+	4.07107i	−0.336924	+	0.336924i
$147$	−4.94975	+	4.94975i	−0.408248	+	0.408248i
$148$	−0.171573	−	0.171573i	−0.0141032	−	0.0141032i
$149$	9.31371			0.763009			0.381504	−	0.924367i	$-0.375406\pi$
$149$	9.31371			0.763009			0.381504	+	0.924367i	$0.375406\pi$
$150$	4.70711	+	4.70711i	0.384334	+	0.384334i
$151$		−	2.48528i		−	0.202249i	−0.994874	−	0.101125i	$-0.967756\pi$
$151$		−	2.48528i		−	0.202249i	0.994874	−	0.101125i	$-0.0322441\pi$
$152$	0.828427			0.0671943
$153$	−4.00000	−	1.00000i	−0.323381	−	0.0808452i
$154$		0			0
$155$			9.65685i			0.775657i
$156$	−2.00000	−	2.00000i	−0.160128	−	0.160128i
$157$	−17.3137			−1.38178			−0.690892	−	0.722958i	$-0.742782\pi$
$157$	−17.3137			−1.38178			−0.690892	+	0.722958i	$0.742782\pi$
$158$	−8.82843	−	8.82843i	−0.702352	−	0.702352i
$159$	−3.65685	+	3.65685i	−0.290007	+	0.290007i
$160$	2.41421	−	2.41421i	0.190860	−	0.190860i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	7.17157	−	7.17157i	0.561721	−	0.561721i	−0.368075	−	0.929796i	$-0.619983\pi$
$163$	7.17157	−	7.17157i	0.561721	−	0.561721i	0.929796	+	0.368075i	$0.119983\pi$
$164$	5.82843	−	5.82843i	0.455124	−	0.455124i
$165$	−2.41421	−	2.41421i	−0.187946	−	0.187946i
$166$	−9.65685			−0.749517
$167$	4.34315	+	4.34315i	0.336083	+	0.336083i	0.854891	−	0.518808i	$-0.173624\pi$
$167$	4.34315	+	4.34315i	0.336083	+	0.336083i	−0.518808	+	0.854891i	$0.673624\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	7.24264	+	12.0711i	0.555485	+	0.925809i
$171$	0.828427			0.0633514
$172$			4.82843i			0.368164i
$173$	2.65685	+	2.65685i	0.201997	+	0.201997i	0.800855	−	0.598858i	$-0.204379\pi$
$173$	2.65685	+	2.65685i	0.201997	+	0.201997i	−0.598858	+	0.800855i	$0.704379\pi$
$174$	−4.24264			−0.321634
$175$		0			0
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	−0.585786	+	0.585786i	−0.0440304	+	0.0440304i
$178$		−	9.17157i		−	0.687438i
$179$		−	3.17157i		−	0.237054i	−0.992951	−	0.118527i	$-0.962183\pi$
$179$		−	3.17157i		−	0.237054i	0.992951	−	0.118527i	$-0.0378173\pi$
$180$	2.41421	−	2.41421i	0.179945	−	0.179945i
$181$	−3.34315	+	3.34315i	−0.248494	+	0.248494i	−0.820352	−	0.571858i	$-0.806223\pi$
$181$	−3.34315	+	3.34315i	−0.248494	+	0.248494i	0.571858	+	0.820352i	$0.306223\pi$
$182$		0			0
$183$	−2.24264			−0.165781
$184$	0.828427	+	0.828427i	0.0610725	+	0.0610725i
$185$			0.828427i			0.0609072i
$186$	2.82843			0.207390
$187$	−2.12132	−	3.53553i	−0.155126	−	0.258544i
$188$	−8.82843			−0.643879
$189$		0			0
$190$	−2.00000	−	2.00000i	−0.145095	−	0.145095i
$191$	−10.4853			−0.758688			−0.379344	−	0.925256i	$-0.623850\pi$
$191$	−10.4853			−0.758688			−0.379344	+	0.925256i	$0.623850\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−4.75736	+	4.75736i	−0.342442	+	0.342442i	−0.857285	−	0.514843i	$-0.827850\pi$
$193$	−4.75736	+	4.75736i	−0.342442	+	0.342442i	0.514843	+	0.857285i	$0.327850\pi$
$194$	−1.00000	+	1.00000i	−0.0717958	+	0.0717958i
$195$			9.65685i			0.691542i
$196$		−	7.00000i		−	0.500000i
$197$	14.6569	−	14.6569i	1.04426	−	1.04426i	0.0452834	−	0.998974i	$-0.485581\pi$
$197$	14.6569	−	14.6569i	1.04426	−	1.04426i	0.998974	−	0.0452834i	$-0.0144191\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	−17.6569	−	17.6569i	−1.25166	−	1.25166i	−0.954975	−	0.296686i	$-0.904118\pi$
$199$	−17.6569	−	17.6569i	−1.25166	−	1.25166i	−0.296686	−	0.954975i	$-0.595882\pi$
$200$	−6.65685			−0.470711
$201$	−4.00000	−	4.00000i	−0.282138	−	0.282138i
$202$			4.00000i			0.281439i
$203$		0			0
$204$	3.53553	−	2.12132i	0.247537	−	0.148522i
$205$	−28.1421			−1.96553
$206$		0			0
$207$	0.828427	+	0.828427i	0.0575797	+	0.0575797i
$208$	2.82843			0.196116
$209$	0.585786	+	0.585786i	0.0405197	+	0.0405197i
$210$		0			0
$211$	12.4853	−	12.4853i	0.859522	−	0.859522i	−0.131759	−	0.991282i	$-0.542063\pi$
$211$	12.4853	−	12.4853i	0.859522	−	0.859522i	0.991282	+	0.131759i	$0.0420627\pi$
$212$		−	5.17157i		−	0.355185i
$213$			8.00000i			0.548151i
$214$	6.48528	−	6.48528i	0.443325	−	0.443325i
$215$	11.6569	−	11.6569i	0.794991	−	0.794991i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$		0			0
$218$	−12.0711	−	12.0711i	−0.817556	−	0.817556i
$219$		−	5.75736i		−	0.389046i
$220$	3.41421			0.230186
$221$	−2.82843	+	11.3137i	−0.190261	+	0.761042i
$222$	0.242641			0.0162850
$223$		−	5.65685i		−	0.378811i	−0.981899	−	0.189405i	$-0.939344\pi$
$223$		−	5.65685i		−	0.378811i	0.981899	−	0.189405i	$-0.0606561\pi$
$224$		0			0
$225$	−6.65685			−0.443790
$226$	−6.89949	−	6.89949i	−0.458948	−	0.458948i
$227$	−4.48528	+	4.48528i	−0.297699	+	0.297699i	−0.840112	−	0.542413i	$-0.817511\pi$
$227$	−4.48528	+	4.48528i	−0.297699	+	0.297699i	0.542413	+	0.840112i	$0.317511\pi$
$228$	−0.585786	+	0.585786i	−0.0387947	+	0.0387947i
$229$			2.68629i			0.177515i	0.996053	+	0.0887576i	$0.0282896\pi$
$229$			2.68629i			0.177515i	−0.996053	+	0.0887576i	$0.971710\pi$
$230$		−	4.00000i		−	0.263752i
$231$		0			0
$232$	3.00000	−	3.00000i	0.196960	−	0.196960i
$233$	−11.8284	−	11.8284i	−0.774906	−	0.774906i	0.204054	−	0.978960i	$-0.434588\pi$
$233$	−11.8284	−	11.8284i	−0.774906	−	0.774906i	−0.978960	+	0.204054i	$0.934588\pi$
$234$	2.82843			0.184900
$235$	21.3137	+	21.3137i	1.39035	+	1.39035i
$236$		−	0.828427i		−	0.0539260i
$237$	12.4853			0.811006
$238$		0			0
$239$	4.97056			0.321519			0.160759	−	0.986994i	$-0.448606\pi$
$239$	4.97056			0.321519			0.160759	+	0.986994i	$0.448606\pi$
$240$			3.41421i			0.220387i
$241$	0.899495	+	0.899495i	0.0579416	+	0.0579416i	0.735484	−	0.677542i	$-0.236955\pi$
$241$	0.899495	+	0.899495i	0.0579416	+	0.0579416i	−0.677542	+	0.735484i	$0.736955\pi$
$242$	−1.00000			−0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	1.58579	−	1.58579i	0.101520	−	0.101520i
$245$	−16.8995	+	16.8995i	−1.07967	+	1.07967i
$246$			8.24264i			0.525532i
$247$		−	2.34315i		−	0.149091i
$248$	−2.00000	+	2.00000i	−0.127000	+	0.127000i
$249$	6.82843	−	6.82843i	0.432734	−	0.432734i
$250$	4.00000	+	4.00000i	0.252982	+	0.252982i
$251$	2.48528			0.156870			0.0784348	−	0.996919i	$-0.475008\pi$
$251$	2.48528			0.156870			0.0784348	+	0.996919i	$0.475008\pi$
$252$		0			0
$253$			1.17157i			0.0736562i
$254$	−20.1421			−1.26383
$255$	−13.6569	−	3.41421i	−0.855225	−	0.213806i
$256$	1.00000			0.0625000
$257$			29.3137i			1.82854i	0.405107	+	0.914269i	$0.367234\pi$
$257$			29.3137i			1.82854i	−0.405107	+	0.914269i	$0.632766\pi$
$258$	−3.41421	−	3.41421i	−0.212560	−	0.212560i
$259$		0			0
$260$	−6.82843	−	6.82843i	−0.423481	−	0.423481i
$261$	3.00000	−	3.00000i	0.185695	−	0.185695i
$262$	6.48528	−	6.48528i	0.400662	−	0.400662i
$263$			16.0000i			0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$			16.0000i			0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	−12.4853	+	12.4853i	−0.766965	+	0.766965i
$266$		0			0
$267$	6.48528	+	6.48528i	0.396893	+	0.396893i
$268$	5.65685			0.345547
$269$	−13.5858	−	13.5858i	−0.828340	−	0.828340i	0.158947	−	0.987287i	$-0.449190\pi$
$269$	−13.5858	−	13.5858i	−0.828340	−	0.828340i	−0.987287	+	0.158947i	$0.949190\pi$
$270$			3.41421i			0.207782i
$271$	−32.1421			−1.95250			−0.976248	−	0.216657i	$-0.930485\pi$
$271$	−32.1421			−1.95250			−0.976248	+	0.216657i	$0.930485\pi$
$272$	−1.00000	+	4.00000i	−0.0606339	+	0.242536i
$273$		0			0
$274$			9.17157i			0.554075i
$275$	−4.70711	−	4.70711i	−0.283849	−	0.283849i
$276$	−1.17157			−0.0705204
$277$	14.0711	+	14.0711i	0.845449	+	0.845449i	0.989561	−	0.144113i	$-0.0460328\pi$
$277$	14.0711	+	14.0711i	0.845449	+	0.845449i	−0.144113	+	0.989561i	$0.546033\pi$
$278$	−7.65685	+	7.65685i	−0.459228	+	0.459228i
$279$	−2.00000	+	2.00000i	−0.119737	+	0.119737i
$280$		0			0
$281$		−	12.9706i		−	0.773759i	−0.922130	−	0.386879i	$-0.873553\pi$
$281$		−	12.9706i		−	0.773759i	0.922130	−	0.386879i	$-0.126447\pi$
$282$	6.24264	−	6.24264i	0.371744	−	0.371744i
$283$	−4.48528	+	4.48528i	−0.266622	+	0.266622i	−0.827738	−	0.561115i	$-0.810372\pi$
$283$	−4.48528	+	4.48528i	−0.266622	+	0.266622i	0.561115	+	0.827738i	$0.310372\pi$
$284$	−5.65685	−	5.65685i	−0.335673	−	0.335673i
$285$	2.82843			0.167542
$286$	2.00000	+	2.00000i	0.118262	+	0.118262i
$287$		0			0
$288$	1.00000			0.0589256
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	−14.4853			−0.850605
$291$		−	1.41421i		−	0.0829027i
$292$	4.07107	+	4.07107i	0.238241	+	0.238241i
$293$	−5.31371			−0.310430			−0.155215	−	0.987881i	$-0.549607\pi$
$293$	−5.31371			−0.310430			−0.155215	+	0.987881i	$0.549607\pi$
$294$	4.94975	+	4.94975i	0.288675	+	0.288675i
$295$	−2.00000	+	2.00000i	−0.116445	+	0.116445i
$296$	−0.171573	+	0.171573i	−0.00997247	+	0.00997247i
$297$		−	1.00000i		−	0.0580259i
$298$		−	9.31371i		−	0.539529i
$299$	2.34315	−	2.34315i	0.135508	−	0.135508i
$300$	4.70711	−	4.70711i	0.271765	−	0.271765i
$301$		0			0
$302$	−2.48528			−0.143012
$303$	−2.82843	−	2.82843i	−0.162489	−	0.162489i
$304$		−	0.828427i		−	0.0475136i
$305$	−7.65685			−0.438430
$306$	−1.00000	+	4.00000i	−0.0571662	+	0.228665i
$307$	−13.7990			−0.787550			−0.393775	−	0.919207i	$-0.628831\pi$
$307$	−13.7990			−0.787550			−0.393775	+	0.919207i	$0.628831\pi$
$308$		0			0
$309$		0			0
$310$	9.65685			0.548472
$311$	9.65685	+	9.65685i	0.547590	+	0.547590i	0.925743	−	0.378153i	$-0.123441\pi$
$311$	9.65685	+	9.65685i	0.547590	+	0.547590i	−0.378153	+	0.925743i	$0.623441\pi$
$312$	−2.00000	+	2.00000i	−0.113228	+	0.113228i
$313$	16.3137	−	16.3137i	0.922105	−	0.922105i	−0.0750727	−	0.997178i	$-0.523919\pi$
$313$	16.3137	−	16.3137i	0.922105	−	0.922105i	0.997178	+	0.0750727i	$0.0239189\pi$
$314$			17.3137i			0.977069i
$315$		0			0
$316$	−8.82843	+	8.82843i	−0.496638	+	0.496638i
$317$	15.2426	−	15.2426i	0.856112	−	0.856112i	−0.134766	−	0.990878i	$-0.543028\pi$
$317$	15.2426	−	15.2426i	0.856112	−	0.856112i	0.990878	+	0.134766i	$0.0430281\pi$
$318$	3.65685	+	3.65685i	0.205066	+	0.205066i
$319$	4.24264			0.237542
$320$	−2.41421	−	2.41421i	−0.134959	−	0.134959i
$321$			9.17157i			0.511907i
$322$		0			0
$323$	3.31371	+	0.828427i	0.184380	+	0.0460949i
$324$	1.00000			0.0555556
$325$			18.8284i			1.04441i
$326$	−7.17157	−	7.17157i	−0.397197	−	0.397197i
$327$	17.0711			0.944032
$328$	−5.82843	−	5.82843i	−0.321821	−	0.321821i
$329$		0			0
$330$	−2.41421	+	2.41421i	−0.132898	+	0.132898i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$			9.65685i			0.529989i
$333$	−0.171573	+	0.171573i	−0.00940214	+	0.00940214i
$334$	4.34315	−	4.34315i	0.237646	−	0.237646i
$335$	−13.6569	−	13.6569i	−0.746154	−	0.746154i
$336$		0			0
$337$	13.5858	+	13.5858i	0.740065	+	0.740065i	0.972590	−	0.232525i	$-0.0746989\pi$
$337$	13.5858	+	13.5858i	0.740065	+	0.740065i	−0.232525	+	0.972590i	$0.574699\pi$
$338$			5.00000i			0.271964i
$339$	9.75736			0.529947
$340$	12.0711	−	7.24264i	0.654646	−	0.392787i
$341$	−2.82843			−0.153168
$342$		−	0.828427i		−	0.0447962i
$343$		0			0
$344$	4.82843			0.260331
$345$	2.82843	+	2.82843i	0.152277	+	0.152277i
$346$	2.65685	−	2.65685i	0.142833	−	0.142833i
$347$	16.1421	−	16.1421i	0.866555	−	0.866555i	−0.125534	−	0.992089i	$-0.540064\pi$
$347$	16.1421	−	16.1421i	0.866555	−	0.866555i	0.992089	+	0.125534i	$0.0400644\pi$
$348$			4.24264i			0.227429i
$349$		−	13.1716i		−	0.705058i	−0.935801	−	0.352529i	$-0.885322\pi$
$349$		−	13.1716i		−	0.705058i	0.935801	−	0.352529i	$-0.114678\pi$
$350$		0			0
$351$	−2.00000	+	2.00000i	−0.106752	+	0.106752i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−32.6274			−1.73658			−0.868291	−	0.496055i	$-0.834781\pi$
$353$	−32.6274			−1.73658			−0.868291	+	0.496055i	$0.834781\pi$
$354$	0.585786	+	0.585786i	0.0311342	+	0.0311342i
$355$			27.3137i			1.44966i
$356$	−9.17157			−0.486092
$357$		0			0
$358$	−3.17157			−0.167623
$359$		−	29.6569i		−	1.56523i	−0.622507	−	0.782614i	$-0.713886\pi$
$359$		−	29.6569i		−	1.56523i	0.622507	−	0.782614i	$-0.286114\pi$
$360$	−2.41421	−	2.41421i	−0.127240	−	0.127240i
$361$	18.3137			0.963879
$362$	3.34315	+	3.34315i	0.175712	+	0.175712i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$		0			0
$365$		−	19.6569i		−	1.02889i
$366$			2.24264i			0.117225i
$367$	14.0000	−	14.0000i	0.730794	−	0.730794i	−0.239983	−	0.970777i	$-0.577142\pi$
$367$	14.0000	−	14.0000i	0.730794	−	0.730794i	0.970777	+	0.239983i	$0.0771419\pi$
$368$	0.828427	−	0.828427i	0.0431847	−	0.0431847i
$369$	−5.82843	−	5.82843i	−0.303416	−	0.303416i
$370$	0.828427			0.0430679
$371$		0			0
$372$		−	2.82843i		−	0.146647i
$373$	−29.1716			−1.51045			−0.755223	−	0.655467i	$-0.772472\pi$
$373$	−29.1716			−1.51045			−0.755223	+	0.655467i	$0.772472\pi$
$374$	−3.53553	+	2.12132i	−0.182818	+	0.109691i
$375$	−5.65685			−0.292119
$376$			8.82843i			0.455291i
$377$	−8.48528	−	8.48528i	−0.437014	−	0.437014i
$378$		0			0
$379$	14.1421	+	14.1421i	0.726433	+	0.726433i	0.969907	−	0.243475i	$-0.0782872\pi$
$379$	14.1421	+	14.1421i	0.726433	+	0.726433i	−0.243475	+	0.969907i	$0.578287\pi$
$380$	−2.00000	+	2.00000i	−0.102598	+	0.102598i
$381$	14.2426	−	14.2426i	0.729673	−	0.729673i
$382$			10.4853i			0.536474i
$383$		−	4.82843i		−	0.246721i	−0.992362	−	0.123361i	$-0.960633\pi$
$383$		−	4.82843i		−	0.246721i	0.992362	−	0.123361i	$-0.0393672\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$		0			0
$386$	4.75736	+	4.75736i	0.242143	+	0.242143i
$387$	4.82843			0.245443
$388$	1.00000	+	1.00000i	0.0507673	+	0.0507673i
$389$		−	9.31371i		−	0.472224i	−0.971726	−	0.236112i	$-0.924127\pi$
$389$		−	9.31371i		−	0.472224i	0.971726	−	0.236112i	$-0.0758732\pi$
$390$	9.65685			0.488994
$391$	2.48528	+	4.14214i	0.125686	+	0.209477i
$392$	−7.00000			−0.353553
$393$			9.17157i			0.462645i
$394$	−14.6569	−	14.6569i	−0.738402	−	0.738402i
$395$	42.6274			2.14482
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−16.3137	+	16.3137i	−0.818762	+	0.818762i	−0.985929	−	0.167167i	$-0.946538\pi$
$397$	−16.3137	+	16.3137i	−0.818762	+	0.818762i	0.167167	+	0.985929i	$0.446538\pi$
$398$	−17.6569	+	17.6569i	−0.885058	+	0.885058i
$399$		0			0
$400$			6.65685i			0.332843i
$401$	23.2426	−	23.2426i	1.16068	−	1.16068i	0.176356	−	0.984327i	$-0.443569\pi$
$401$	23.2426	−	23.2426i	1.16068	−	1.16068i	0.984327	−	0.176356i	$-0.0564308\pi$
$402$	−4.00000	+	4.00000i	−0.199502	+	0.199502i
$403$	5.65685	+	5.65685i	0.281788	+	0.281788i
$404$	4.00000			0.199007
$405$	−2.41421	−	2.41421i	−0.119963	−	0.119963i
$406$		0			0
$407$	−0.242641			−0.0120273
$408$	−2.12132	−	3.53553i	−0.105021	−	0.175035i
$409$	−13.3137			−0.658321			−0.329160	−	0.944274i	$-0.606766\pi$
$409$	−13.3137			−0.658321			−0.329160	+	0.944274i	$0.606766\pi$
$410$			28.1421i			1.38984i
$411$	−6.48528	−	6.48528i	−0.319895	−	0.319895i
$412$		0			0
$413$		0			0
$414$	0.828427	−	0.828427i	0.0407150	−	0.0407150i
$415$	23.3137	−	23.3137i	1.14442	−	1.14442i
$416$		−	2.82843i		−	0.138675i
$417$		−	10.8284i		−	0.530270i
$418$	0.585786	−	0.585786i	0.0286518	−	0.0286518i
$419$	−17.3137	+	17.3137i	−0.845830	+	0.845830i	−0.989610	−	0.143780i	$-0.954074\pi$
$419$	−17.3137	+	17.3137i	−0.845830	+	0.845830i	0.143780	+	0.989610i	$0.454074\pi$
$420$		0			0
$421$	−20.2843			−0.988595			−0.494297	−	0.869293i	$-0.664575\pi$
$421$	−20.2843			−0.988595			−0.494297	+	0.869293i	$0.664575\pi$
$422$	−12.4853	−	12.4853i	−0.607774	−	0.607774i
$423$			8.82843i			0.429253i
$424$	−5.17157			−0.251154
$425$	−26.6274	−	6.65685i	−1.29162	−	0.322905i
$426$	8.00000			0.387601
$427$		0			0
$428$	−6.48528	−	6.48528i	−0.313478	−	0.313478i
$429$	−2.82843			−0.136558
$430$	−11.6569	−	11.6569i	−0.562143	−	0.562143i
$431$	−2.68629	+	2.68629i	−0.129394	+	0.129394i	−0.768838	−	0.639444i	$-0.779165\pi$
$431$	−2.68629	+	2.68629i	−0.129394	+	0.129394i	0.639444	+	0.768838i	$0.279165\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	21.3137i		−	1.02427i	−0.858905	−	0.512136i	$-0.828854\pi$
$433$		−	21.3137i		−	1.02427i	0.858905	−	0.512136i	$-0.171146\pi$
$434$		0			0
$435$	10.2426	−	10.2426i	0.491097	−	0.491097i
$436$	−12.0711	+	12.0711i	−0.578099	+	0.578099i
$437$	−0.686292	−	0.686292i	−0.0328298	−	0.0328298i
$438$	−5.75736			−0.275097
$439$	12.1421	+	12.1421i	0.579513	+	0.579513i	0.934769	−	0.355256i	$-0.115606\pi$
$439$	12.1421	+	12.1421i	0.579513	+	0.579513i	−0.355256	+	0.934769i	$0.615606\pi$
$440$		−	3.41421i		−	0.162766i
$441$	−7.00000			−0.333333
$442$	11.3137	+	2.82843i	0.538138	+	0.134535i
$443$	23.1716			1.10091			0.550457	−	0.834863i	$-0.314453\pi$
$443$	23.1716			1.10091			0.550457	+	0.834863i	$0.314453\pi$
$444$		−	0.242641i		−	0.0115152i
$445$	22.1421	+	22.1421i	1.04964	+	1.04964i
$446$	−5.65685			−0.267860
$447$	6.58579	+	6.58579i	0.311497	+	0.311497i
$448$		0			0
$449$	−10.0711	+	10.0711i	−0.475283	+	0.475283i	−0.903619	−	0.428336i	$-0.859100\pi$
$449$	−10.0711	+	10.0711i	−0.475283	+	0.475283i	0.428336	+	0.903619i	$0.359100\pi$
$450$			6.65685i			0.313807i
$451$		−	8.24264i		−	0.388131i
$452$	−6.89949	+	6.89949i	−0.324525	+	0.324525i
$453$	1.75736	−	1.75736i	0.0825679	−	0.0825679i
$454$	4.48528	+	4.48528i	0.210505	+	0.210505i
$455$		0			0
$456$	0.585786	+	0.585786i	0.0274320	+	0.0274320i
$457$		−	12.6274i		−	0.590686i	−0.955391	−	0.295343i	$-0.904566\pi$
$457$		−	12.6274i		−	0.590686i	0.955391	−	0.295343i	$-0.0954339\pi$
$458$	2.68629			0.125522
$459$	−2.12132	−	3.53553i	−0.0990148	−	0.165025i
$460$	−4.00000			−0.186501
$461$			40.9706i			1.90819i	0.299505	+	0.954095i	$0.403178\pi$
$461$			40.9706i			1.90819i	−0.299505	+	0.954095i	$0.596822\pi$
$462$		0			0
$463$	3.02944			0.140790			0.0703949	−	0.997519i	$-0.477574\pi$
$463$	3.02944			0.140790			0.0703949	+	0.997519i	$0.477574\pi$
$464$	−3.00000	−	3.00000i	−0.139272	−	0.139272i
$465$	−6.82843	+	6.82843i	−0.316661	+	0.316661i
$466$	−11.8284	+	11.8284i	−0.547941	+	0.547941i
$467$		−	14.4853i		−	0.670299i	−0.942165	−	0.335149i	$-0.891213\pi$
$467$		−	14.4853i		−	0.670299i	0.942165	−	0.335149i	$-0.108787\pi$
$468$		−	2.82843i		−	0.130744i
$469$		0			0
$470$	21.3137	−	21.3137i	0.983128	−	0.983128i
$471$	−12.2426	−	12.2426i	−0.564111	−	0.564111i
$472$	−0.828427			−0.0381314
$473$	3.41421	+	3.41421i	0.156986	+	0.156986i
$474$		−	12.4853i		−	0.573468i
$475$	5.51472			0.253033
$476$		0			0
$477$	−5.17157			−0.236790
$478$		−	4.97056i		−	0.227348i
$479$	−16.0000	−	16.0000i	−0.731059	−	0.731059i	0.239771	−	0.970830i	$-0.422928\pi$
$479$	−16.0000	−	16.0000i	−0.731059	−	0.731059i	−0.970830	+	0.239771i	$0.922928\pi$
$480$	3.41421			0.155837
$481$	0.485281	+	0.485281i	0.0221269	+	0.0221269i
$482$	0.899495	−	0.899495i	0.0409709	−	0.0409709i
$483$		0			0
$484$			1.00000i			0.0454545i
$485$		−	4.82843i		−	0.219248i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	0.686292	−	0.686292i	0.0310988	−	0.0310988i	−0.691386	−	0.722485i	$-0.743000\pi$
$487$	0.686292	−	0.686292i	0.0310988	−	0.0310988i	0.722485	+	0.691386i	$0.243000\pi$
$488$	−1.58579	−	1.58579i	−0.0717852	−	0.0717852i
$489$	10.1421			0.458643
$490$	16.8995	+	16.8995i	0.763441	+	0.763441i
$491$		−	18.6274i		−	0.840644i	−0.907375	−	0.420322i	$-0.861917\pi$
$491$		−	18.6274i		−	0.840644i	0.907375	−	0.420322i	$-0.138083\pi$
$492$	8.24264			0.371607
$493$	15.0000	−	9.00000i	0.675566	−	0.405340i
$494$	−2.34315			−0.105423
$495$		−	3.41421i		−	0.153457i
$496$	2.00000	+	2.00000i	0.0898027	+	0.0898027i
$497$		0			0
$498$	−6.82843	−	6.82843i	−0.305989	−	0.305989i
$499$	23.1716	−	23.1716i	1.03730	−	1.03730i	0.0380253	−	0.999277i	$-0.487893\pi$
$499$	23.1716	−	23.1716i	1.03730	−	1.03730i	0.999277	−	0.0380253i	$-0.0121067\pi$
$500$	4.00000	−	4.00000i	0.178885	−	0.178885i
$501$			6.14214i			0.274410i
$502$		−	2.48528i		−	0.110924i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	−9.65685	−	9.65685i	−0.429724	−	0.429724i
$506$	1.17157			0.0520828
$507$	−3.53553	−	3.53553i	−0.157019	−	0.157019i
$508$			20.1421i			0.893663i
$509$	34.0000			1.50702			0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000			1.50702			0.753512	+	0.657434i	$0.228358\pi$
$510$	−3.41421	+	13.6569i	−0.151184	+	0.604736i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	0.585786	+	0.585786i	0.0258631	+	0.0258631i
$514$	29.3137			1.29297
$515$		0			0
$516$	−3.41421	+	3.41421i	−0.150302	+	0.150302i
$517$	−6.24264	+	6.24264i	−0.274551	+	0.274551i
$518$		0			0
$519$			3.75736i			0.164930i
$520$	−6.82843	+	6.82843i	−0.299446	+	0.299446i
$521$	−0.757359	+	0.757359i	−0.0331805	+	0.0331805i	−0.723502	−	0.690322i	$-0.757469\pi$
$521$	−0.757359	+	0.757359i	−0.0331805	+	0.0331805i	0.690322	+	0.723502i	$0.257469\pi$
$522$	−3.00000	−	3.00000i	−0.131306	−	0.131306i
$523$	−9.51472			−0.416050			−0.208025	−	0.978124i	$-0.566703\pi$
$523$	−9.51472			−0.416050			−0.208025	+	0.978124i	$0.566703\pi$
$524$	−6.48528	−	6.48528i	−0.283311	−	0.283311i
$525$		0			0
$526$	16.0000			0.697633
$527$	−10.0000	+	6.00000i	−0.435607	+	0.261364i
$528$	−1.00000			−0.0435194
$529$			21.6274i			0.940322i
$530$	12.4853	+	12.4853i	0.542326	+	0.542326i
$531$	−0.828427			−0.0359507
$532$		0			0
$533$	−16.4853	+	16.4853i	−0.714057	+	0.714057i
$534$	6.48528	−	6.48528i	0.280646	−	0.280646i
$535$			31.3137i			1.35381i
$536$		−	5.65685i		−	0.244339i
$537$	2.24264	−	2.24264i	0.0967771	−	0.0967771i
$538$	−13.5858	+	13.5858i	−0.585725	+	0.585725i
$539$	−4.94975	−	4.94975i	−0.213201	−	0.213201i
$540$	3.41421			0.146924
$541$	15.5858	+	15.5858i	0.670085	+	0.670085i	0.957736	−	0.287650i	$-0.0928741\pi$
$541$	15.5858	+	15.5858i	0.670085	+	0.670085i	−0.287650	+	0.957736i	$0.592874\pi$
$542$			32.1421i			1.38062i
$543$	−4.72792			−0.202895
$544$	4.00000	+	1.00000i	0.171499	+	0.0428746i
$545$	58.2843			2.49662
$546$		0			0
$547$	−12.4853	−	12.4853i	−0.533832	−	0.533832i	0.387878	−	0.921711i	$-0.373208\pi$
$547$	−12.4853	−	12.4853i	−0.533832	−	0.533832i	−0.921711	+	0.387878i	$0.873208\pi$
$548$	9.17157			0.391790
$549$	−1.58579	−	1.58579i	−0.0676797	−	0.0676797i
$550$	−4.70711	+	4.70711i	−0.200712	+	0.200712i
$551$	−2.48528	+	2.48528i	−0.105877	+	0.105877i
$552$			1.17157i			0.0498655i
$553$		0			0
$554$	14.0711	−	14.0711i	0.597822	−	0.597822i
$555$	−0.585786	+	0.585786i	−0.0248652	+	0.0248652i
$556$	7.65685	+	7.65685i	0.324723	+	0.324723i
$557$	−14.3431			−0.607739			−0.303869	−	0.952714i	$-0.598279\pi$
$557$	−14.3431			−0.607739			−0.303869	+	0.952714i	$0.598279\pi$
$558$	2.00000	+	2.00000i	0.0846668	+	0.0846668i
$559$		−	13.6569i		−	0.577623i
$560$		0			0
$561$	1.00000	−	4.00000i	0.0422200	−	0.168880i
$562$	−12.9706			−0.547130
$563$			19.3137i			0.813976i	0.913434	+	0.406988i	$0.133421\pi$
$563$			19.3137i			0.813976i	−0.913434	+	0.406988i	$0.866579\pi$
$564$	−6.24264	−	6.24264i	−0.262863	−	0.262863i
$565$	33.3137			1.40152
$566$	4.48528	+	4.48528i	0.188530	+	0.188530i
$567$		0			0
$568$	−5.65685	+	5.65685i	−0.237356	+	0.237356i
$569$		−	22.6274i		−	0.948591i	−0.880366	−	0.474295i	$-0.842703\pi$
$569$		−	22.6274i		−	0.948591i	0.880366	−	0.474295i	$-0.157297\pi$
$570$		−	2.82843i		−	0.118470i
$571$	6.00000	−	6.00000i	0.251092	−	0.251092i	−0.570326	−	0.821418i	$-0.693183\pi$
$571$	6.00000	−	6.00000i	0.251092	−	0.251092i	0.821418	+	0.570326i	$0.193183\pi$
$572$	2.00000	−	2.00000i	0.0836242	−	0.0836242i
$573$	−7.41421	−	7.41421i	−0.309733	−	0.309733i
$574$		0			0
$575$	5.51472	+	5.51472i	0.229980	+	0.229980i
$576$		−	1.00000i		−	0.0416667i
$577$	32.9706			1.37258			0.686291	−	0.727327i	$-0.259238\pi$
$577$	32.9706			1.37258			0.686291	+	0.727327i	$0.259238\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$	−6.72792			−0.279603
$580$			14.4853i			0.601469i
$581$		0			0
$582$	−1.41421			−0.0586210
$583$	−3.65685	−	3.65685i	−0.151451	−	0.151451i
$584$	4.07107	−	4.07107i	0.168462	−	0.168462i
$585$	−6.82843	+	6.82843i	−0.282321	+	0.282321i
$586$			5.31371i			0.219507i
$587$			29.1127i			1.20161i	0.799396	+	0.600805i	$0.205153\pi$
$587$			29.1127i			1.20161i	−0.799396	+	0.600805i	$0.794847\pi$
$588$	4.94975	−	4.94975i	0.204124	−	0.204124i
$589$	1.65685	−	1.65685i	0.0682695	−	0.0682695i
$590$	2.00000	+	2.00000i	0.0823387	+	0.0823387i
$591$	20.7279			0.852633
$592$	0.171573	+	0.171573i	0.00705160	+	0.00705160i
$593$			36.9706i			1.51820i	0.650975	+	0.759100i	$0.274360\pi$
$593$			36.9706i			1.51820i	−0.650975	+	0.759100i	$0.725640\pi$
$594$	−1.00000			−0.0410305
$595$		0			0
$596$	−9.31371			−0.381504
$597$		−	24.9706i		−	1.02198i
$598$	−2.34315	−	2.34315i	−0.0958184	−	0.0958184i
$599$	12.8284			0.524155			0.262078	−	0.965047i	$-0.415592\pi$
$599$	12.8284			0.524155			0.262078	+	0.965047i	$0.415592\pi$
$600$	−4.70711	−	4.70711i	−0.192167	−	0.192167i
$601$	−8.07107	+	8.07107i	−0.329226	+	0.329226i	−0.852292	−	0.523066i	$-0.824788\pi$
$601$	−8.07107	+	8.07107i	−0.329226	+	0.329226i	0.523066	+	0.852292i	$0.324788\pi$
$602$		0			0
$603$		−	5.65685i		−	0.230365i
$604$			2.48528i			0.101125i
$605$	2.41421	−	2.41421i	0.0981517	−	0.0981517i
$606$	−2.82843	+	2.82843i	−0.114897	+	0.114897i
$607$	−7.17157	−	7.17157i	−0.291085	−	0.291085i	0.546424	−	0.837509i	$-0.315989\pi$
$607$	−7.17157	−	7.17157i	−0.291085	−	0.291085i	−0.837509	+	0.546424i	$0.815989\pi$
$608$	−0.828427			−0.0335972
$609$		0			0
$610$			7.65685i			0.310017i
$611$	24.9706			1.01020
$612$	4.00000	+	1.00000i	0.161690	+	0.0404226i
$613$	28.6274			1.15625			0.578125	−	0.815948i	$-0.303785\pi$
$613$	28.6274			1.15625			0.578125	+	0.815948i	$0.303785\pi$
$614$			13.7990i			0.556882i
$615$	−19.8995	−	19.8995i	−0.802425	−	0.802425i
$616$		0			0
$617$	20.7574	+	20.7574i	0.835660	+	0.835660i	0.988284	−	0.152624i	$-0.0487725\pi$
$617$	20.7574	+	20.7574i	0.835660	+	0.835660i	−0.152624	+	0.988284i	$0.548772\pi$
$618$		0			0
$619$	28.4853	−	28.4853i	1.14492	−	1.14492i	0.157382	−	0.987538i	$-0.449694\pi$
$619$	28.4853	−	28.4853i	1.14492	−	1.14492i	0.987538	−	0.157382i	$-0.0503055\pi$
$620$		−	9.65685i		−	0.387829i
$621$			1.17157i			0.0470136i
$622$	9.65685	−	9.65685i	0.387205	−	0.387205i
$623$		0			0
$624$	2.00000	+	2.00000i	0.0800641	+	0.0800641i
$625$	13.9706			0.558823
$626$	−16.3137	−	16.3137i	−0.652027	−	0.652027i
$627$			0.828427i			0.0330842i
$628$	17.3137			0.690892
$629$	−0.857864	+	0.514719i	−0.0342053	+	0.0205232i
$630$		0			0
$631$			37.6569i			1.49910i	0.661950	+	0.749548i	$0.269729\pi$
$631$			37.6569i			1.49910i	−0.661950	+	0.749548i	$0.730271\pi$
$632$	8.82843	+	8.82843i	0.351176	+	0.351176i
$633$	17.6569			0.701797
$634$	−15.2426	−	15.2426i	−0.605363	−	0.605363i
$635$	48.6274	−	48.6274i	1.92972	−	1.92972i
$636$	3.65685	−	3.65685i	0.145004	−	0.145004i
$637$			19.7990i			0.784465i
$638$		−	4.24264i		−	0.167968i
$639$	−5.65685	+	5.65685i	−0.223782	+	0.223782i
$640$	−2.41421	+	2.41421i	−0.0954302	+	0.0954302i
$641$	−6.55635	−	6.55635i	−0.258960	−	0.258960i	0.565671	−	0.824631i	$-0.308617\pi$
$641$	−6.55635	−	6.55635i	−0.258960	−	0.258960i	−0.824631	+	0.565671i	$0.808617\pi$
$642$	9.17157			0.361973
$643$	18.4853	+	18.4853i	0.728988	+	0.728988i	0.970418	−	0.241430i	$-0.0776164\pi$
$643$	18.4853	+	18.4853i	0.728988	+	0.728988i	−0.241430	+	0.970418i	$0.577616\pi$
$644$		0			0
$645$	16.4853			0.649107
$646$	0.828427	−	3.31371i	0.0325940	−	0.130376i
$647$	47.4558			1.86568			0.932841	−	0.360289i	$-0.117322\pi$
$647$	47.4558			1.86568			0.932841	+	0.360289i	$0.117322\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−0.585786	−	0.585786i	−0.0229941	−	0.0229941i
$650$	18.8284			0.738512
$651$		0			0
$652$	−7.17157	+	7.17157i	−0.280860	+	0.280860i
$653$	−12.5563	+	12.5563i	−0.491368	+	0.491368i	−0.908737	−	0.417369i	$-0.862952\pi$
$653$	−12.5563	+	12.5563i	−0.491368	+	0.491368i	0.417369	+	0.908737i	$0.362952\pi$
$654$		−	17.0711i		−	0.667532i
$655$			31.3137i			1.22353i
$656$	−5.82843	+	5.82843i	−0.227562	+	0.227562i
$657$	4.07107	−	4.07107i	0.158827	−	0.158827i
$658$		0			0
$659$	16.6863			0.650006			0.325003	−	0.945713i	$-0.394635\pi$
$659$	16.6863			0.650006			0.325003	+	0.945713i	$0.394635\pi$
$660$	2.41421	+	2.41421i	0.0939731	+	0.0939731i
$661$			18.6274i			0.724523i	0.932077	+	0.362261i	$0.117995\pi$
$661$			18.6274i			0.724523i	−0.932077	+	0.362261i	$0.882005\pi$
$662$		0			0
$663$	−10.0000	+	6.00000i	−0.388368	+	0.233021i
$664$	9.65685			0.374759
$665$		0			0
$666$	0.171573	+	0.171573i	0.00664831	+	0.00664831i
$667$	−4.97056			−0.192461
$668$	−4.34315	−	4.34315i	−0.168041	−	0.168041i
$669$	4.00000	−	4.00000i	0.154649	−	0.154649i
$670$	−13.6569	+	13.6569i	−0.527610	+	0.527610i
$671$		−	2.24264i		−	0.0865762i
$672$		0			0
$673$	4.07107	−	4.07107i	0.156928	−	0.156928i	−0.624276	−	0.781204i	$-0.714606\pi$
$673$	4.07107	−	4.07107i	0.156928	−	0.156928i	0.781204	+	0.624276i	$0.214606\pi$
$674$	13.5858	−	13.5858i	0.523305	−	0.523305i
$675$	−4.70711	−	4.70711i	−0.181177	−	0.181177i
$676$	5.00000			0.192308
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	0.999261	−	0.0384331i	$-0.0122367\pi$
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	−0.0384331	+	0.999261i	$0.512237\pi$
$678$		−	9.75736i		−	0.374729i
$679$		0			0
$680$	−7.24264	−	12.0711i	−0.277743	−	0.462904i
$681$	−6.34315			−0.243070
$682$			2.82843i			0.108306i
$683$	−23.6569	−	23.6569i	−0.905204	−	0.905204i	0.0906761	−	0.995880i	$-0.471097\pi$
$683$	−23.6569	−	23.6569i	−0.905204	−	0.905204i	−0.995880	+	0.0906761i	$0.971097\pi$
$684$	−0.828427			−0.0316757
$685$	−22.1421	−	22.1421i	−0.846008	−	0.846008i
$686$		0			0
$687$	−1.89949	+	1.89949i	−0.0724703	+	0.0724703i
$688$		−	4.82843i		−	0.184082i
$689$			14.6274i			0.557260i
$690$	2.82843	−	2.82843i	0.107676	−	0.107676i
$691$	−8.14214	+	8.14214i	−0.309741	+	0.309741i	−0.844809	−	0.535068i	$-0.820286\pi$
$691$	−8.14214	+	8.14214i	−0.309741	+	0.309741i	0.535068	+	0.844809i	$0.320286\pi$
$692$	−2.65685	−	2.65685i	−0.100998	−	0.100998i
$693$		0			0
$694$	−16.1421	−	16.1421i	−0.612747	−	0.612747i
$695$		−	36.9706i		−	1.40237i
$696$	4.24264			0.160817
$697$	−17.4853	−	29.1421i	−0.662302	−	1.10384i
$698$	−13.1716			−0.498551
$699$		−	16.7279i		−	0.632708i
$700$		0			0
$701$	−2.34315			−0.0884994			−0.0442497	−	0.999021i	$-0.514090\pi$
$701$	−2.34315			−0.0884994			−0.0442497	+	0.999021i	$0.514090\pi$
$702$	2.00000	+	2.00000i	0.0754851	+	0.0754851i
$703$	0.142136	−	0.142136i	0.00536075	−	0.00536075i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$			30.1421i			1.13522i
$706$			32.6274i			1.22795i
$707$		0			0
$708$	0.585786	−	0.585786i	0.0220152	−	0.0220152i
$709$	19.6274	+	19.6274i	0.737123	+	0.737123i	0.972020	−	0.234897i	$-0.0754753\pi$
$709$	19.6274	+	19.6274i	0.737123	+	0.737123i	−0.234897	+	0.972020i	$0.575475\pi$
$710$	27.3137			1.02507
$711$	8.82843	+	8.82843i	0.331092	+	0.331092i
$712$			9.17157i			0.343719i
$713$	3.31371			0.124099
$714$		0			0
$715$	−9.65685			−0.361146
$716$			3.17157i			0.118527i
$717$	3.51472	+	3.51472i	0.131260	+	0.131260i
$718$	−29.6569			−1.10678
$719$	28.1421	+	28.1421i	1.04952	+	1.04952i	0.998708	+	0.0508166i	$0.0161824\pi$
$719$	28.1421	+	28.1421i	1.04952	+	1.04952i	0.0508166	+	0.998708i	$0.483818\pi$
$720$	−2.41421	+	2.41421i	−0.0899724	+	0.0899724i
$721$		0			0
$722$		−	18.3137i		−	0.681566i
$723$			1.27208i			0.0473091i
$724$	3.34315	−	3.34315i	0.124247	−	0.124247i
$725$	19.9706	−	19.9706i	0.741688	−	0.741688i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−28.9706			−1.07446			−0.537229	−	0.843436i	$-0.680529\pi$
$727$	−28.9706			−1.07446			−0.537229	+	0.843436i	$0.680529\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−19.6569			−0.727533
$731$	19.3137	+	4.82843i	0.714343	+	0.178586i
$732$	2.24264			0.0828904
$733$			23.5147i			0.868536i	0.900784	+	0.434268i	$0.142993\pi$
$733$			23.5147i			0.868536i	−0.900784	+	0.434268i	$0.857007\pi$
$734$	−14.0000	−	14.0000i	−0.516749	−	0.516749i
$735$	−23.8995			−0.881546
$736$	−0.828427	−	0.828427i	−0.0305362	−	0.0305362i
$737$	4.00000	−	4.00000i	0.147342	−	0.147342i
$738$	−5.82843	+	5.82843i	−0.214547	+	0.214547i
$739$		−	50.7696i		−	1.86759i	−0.357811	−	0.933794i	$-0.616477\pi$
$739$		−	50.7696i		−	1.86759i	0.357811	−	0.933794i	$-0.383523\pi$
$740$		−	0.828427i		−	0.0304536i
$741$	1.65685	−	1.65685i	0.0608661	−	0.0608661i
$742$		0			0
$743$	−28.9706	−	28.9706i	−1.06283	−	1.06283i	−0.997889	−	0.0649375i	$-0.979315\pi$
$743$	−28.9706	−	28.9706i	−1.06283	−	1.06283i	−0.0649375	−	0.997889i	$-0.520685\pi$
$744$	−2.82843			−0.103695
$745$	22.4853	+	22.4853i	0.823797	+	0.823797i
$746$			29.1716i			1.06805i
$747$	9.65685			0.353326
$748$	2.12132	+	3.53553i	0.0775632	+	0.129272i
$749$		0			0
$750$			5.65685i			0.206559i
$751$	−31.3137	−	31.3137i	−1.14265	−	1.14265i	−0.987963	−	0.154690i	$-0.950562\pi$
$751$	−31.3137	−	31.3137i	−1.14265	−	1.14265i	−0.154690	−	0.987963i	$-0.549438\pi$
$752$	8.82843			0.321940
$753$	1.75736	+	1.75736i	0.0640417	+	0.0640417i
$754$	−8.48528	+	8.48528i	−0.309016	+	0.309016i
$755$	6.00000	−	6.00000i	0.218362	−	0.218362i
$756$		0			0
$757$			19.9411i			0.724773i	0.932028	+	0.362386i	$0.118038\pi$
$757$			19.9411i			0.724773i	−0.932028	+	0.362386i	$0.881962\pi$
$758$	14.1421	−	14.1421i	0.513665	−	0.513665i
$759$	−0.828427	+	0.828427i	−0.0300700	+	0.0300700i
$760$	2.00000	+	2.00000i	0.0725476	+	0.0725476i
$761$	−42.6274			−1.54524			−0.772621	−	0.634867i	$-0.781055\pi$
$761$	−42.6274			−1.54524			−0.772621	+	0.634867i	$0.781055\pi$
$762$	−14.2426	−	14.2426i	−0.515956	−	0.515956i
$763$		0			0
$764$	10.4853			0.379344
$765$	−7.24264	−	12.0711i	−0.261858	−	0.436430i
$766$	−4.82843			−0.174458
$767$			2.34315i			0.0846061i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	22.8284			0.823214			0.411607	−	0.911361i	$-0.364968\pi$
$769$	22.8284			0.823214			0.411607	+	0.911361i	$0.364968\pi$
$770$		0			0
$771$	−20.7279	+	20.7279i	−0.746498	+	0.746498i
$772$	4.75736	−	4.75736i	0.171221	−	0.171221i
$773$		−	0.627417i		−	0.0225666i	−0.999936	−	0.0112833i	$-0.996408\pi$
$773$		−	0.627417i		−	0.0225666i	0.999936	−	0.0112833i	$-0.00359167\pi$
$774$		−	4.82843i		−	0.173554i
$775$	−13.3137	+	13.3137i	−0.478243	+	0.478243i
$776$	1.00000	−	1.00000i	0.0358979	−	0.0358979i
$777$		0			0
$778$	−9.31371			−0.333913
$779$	4.82843	+	4.82843i	0.172996	+	0.172996i
$780$		−	9.65685i		−	0.345771i
$781$	−8.00000			−0.286263
$782$	4.14214	−	2.48528i	0.148122	−	0.0888735i
$783$	4.24264			0.151620
$784$			7.00000i			0.250000i
$785$	−41.7990	−	41.7990i	−1.49187	−	1.49187i
$786$	9.17157			0.327139
$787$	−21.3137	−	21.3137i	−0.759752	−	0.759752i	0.216525	−	0.976277i	$-0.430528\pi$
$787$	−21.3137	−	21.3137i	−0.759752	−	0.759752i	−0.976277	+	0.216525i	$0.930528\pi$
$788$	−14.6569	+	14.6569i	−0.522129	+	0.522129i
$789$	−11.3137	+	11.3137i	−0.402779	+	0.402779i
$790$		−	42.6274i		−	1.51662i
$791$		0			0
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	−4.48528	+	4.48528i	−0.159277	+	0.159277i
$794$	16.3137	+	16.3137i	0.578952	+	0.578952i
$795$	−17.6569			−0.626224
$796$	17.6569	+	17.6569i	0.625831	+	0.625831i
$797$			31.5147i			1.11631i	0.829737	+	0.558154i	$0.188490\pi$
$797$			31.5147i			1.11631i	−0.829737	+	0.558154i	$0.811510\pi$
$798$		0			0
$799$	−8.82843	+	35.3137i	−0.312327	+	1.24931i
$800$	6.65685			0.235355
$801$			9.17157i			0.324062i
$802$	−23.2426	−	23.2426i	−0.820726	−	0.820726i
$803$	5.75736			0.203173
$804$	4.00000	+	4.00000i	0.141069	+	0.141069i
$805$		0			0
$806$	5.65685	−	5.65685i	0.199254	−	0.199254i
$807$		−	19.2132i		−	0.676337i
$808$		−	4.00000i		−	0.140720i
$809$	−25.2843	+	25.2843i	−0.888948	+	0.888948i	−0.994422	−	0.105474i	$-0.966364\pi$
$809$	−25.2843	+	25.2843i	−0.888948	+	0.888948i	0.105474	+	0.994422i	$0.466364\pi$
$810$	−2.41421	+	2.41421i	−0.0848268	+	0.0848268i
$811$	6.00000	+	6.00000i	0.210688	+	0.210688i	0.804560	−	0.593871i	$-0.202401\pi$
$811$	6.00000	+	6.00000i	0.210688	+	0.210688i	−0.593871	+	0.804560i	$0.702401\pi$
$812$		0			0
$813$	−22.7279	−	22.7279i	−0.797103	−	0.797103i
$814$			0.242641i			0.00850455i
$815$	34.6274			1.21295
$816$	−3.53553	+	2.12132i	−0.123768	+	0.0742611i
$817$	−4.00000			−0.139942
$818$			13.3137i			0.465503i
$819$		0			0
$820$	28.1421			0.982766
$821$	5.97056	+	5.97056i	0.208374	+	0.208374i	0.803576	−	0.595202i	$-0.202928\pi$
$821$	5.97056	+	5.97056i	0.208374	+	0.208374i	−0.595202	+	0.803576i	$0.702928\pi$
$822$	−6.48528	+	6.48528i	−0.226200	+	0.226200i
$823$	−8.00000	+	8.00000i	−0.278862	+	0.278862i	−0.832655	−	0.553792i	$-0.813180\pi$
$823$	−8.00000	+	8.00000i	−0.278862	+	0.278862i	0.553792	+	0.832655i	$0.313180\pi$
$824$		0			0
$825$		−	6.65685i		−	0.231762i
$826$		0			0
$827$	−3.51472	+	3.51472i	−0.122219	+	0.122219i	−0.765571	−	0.643352i	$-0.777543\pi$
$827$	−3.51472	+	3.51472i	−0.122219	+	0.122219i	0.643352	+	0.765571i	$0.277543\pi$
$828$	−0.828427	−	0.828427i	−0.0287898	−	0.0287898i
$829$	−47.9411			−1.66506			−0.832532	−	0.553977i	$-0.813110\pi$
$829$	−47.9411			−1.66506			−0.832532	+	0.553977i	$0.813110\pi$
$830$	−23.3137	−	23.3137i	−0.809231	−	0.809231i
$831$			19.8995i			0.690306i
$832$	−2.82843			−0.0980581
$833$	−28.0000	−	7.00000i	−0.970143	−	0.242536i
$834$	−10.8284			−0.374958
$835$			20.9706i			0.725716i
$836$	−0.585786	−	0.585786i	−0.0202598	−	0.0202598i
$837$	−2.82843			−0.0977647
$838$	17.3137	+	17.3137i	0.598092	+	0.598092i
$839$	−28.8284	+	28.8284i	−0.995268	+	0.995268i	−0.999989	−	0.00472102i	$-0.998497\pi$
$839$	−28.8284	+	28.8284i	−0.995268	+	0.995268i	0.00472102	+	0.999989i	$0.498497\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$			20.2843i			0.699042i
$843$	9.17157	−	9.17157i	0.315886	−	0.315886i
$844$	−12.4853	+	12.4853i	−0.429761	+	0.429761i
$845$	−12.0711	−	12.0711i	−0.415257	−	0.415257i
$846$	8.82843			0.303528
$847$		0			0
$848$			5.17157i			0.177593i
$849$	−6.34315			−0.217696
$850$	−6.65685	+	26.6274i	−0.228328	+	0.913313i
$851$	0.284271			0.00974469
$852$		−	8.00000i		−	0.274075i
$853$	18.8995	+	18.8995i	0.647106	+	0.647106i	0.952293	−	0.305186i	$-0.0987187\pi$
$853$	18.8995	+	18.8995i	0.647106	+	0.647106i	−0.305186	+	0.952293i	$0.598719\pi$
$854$		0			0
$855$	2.00000	+	2.00000i	0.0683986	+	0.0683986i
$856$	−6.48528	+	6.48528i	−0.221662	+	0.221662i
$857$	−36.9411	+	36.9411i	−1.26188	+	1.26188i	−0.311706	+	0.950178i	$0.600901\pi$
$857$	−36.9411	+	36.9411i	−1.26188	+	1.26188i	−0.950178	+	0.311706i	$0.899099\pi$
$858$			2.82843i			0.0965609i
$859$		−	20.6863i		−	0.705807i	−0.935660	−	0.352904i	$-0.885194\pi$
$859$		−	20.6863i		−	0.705807i	0.935660	−	0.352904i	$-0.114806\pi$
$860$	−11.6569	+	11.6569i	−0.397495	+	0.397495i
$861$		0			0
$862$	2.68629	+	2.68629i	0.0914955	+	0.0914955i
$863$	11.4558			0.389961			0.194981	−	0.980807i	$-0.437536\pi$
$863$	11.4558			0.389961			0.194981	+	0.980807i	$0.437536\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$			12.8284i			0.436180i
$866$	−21.3137			−0.724269
$867$	−4.94975	−	16.2635i	−0.168102	−	0.552336i
$868$		0			0
$869$			12.4853i			0.423534i
$870$	−10.2426	−	10.2426i	−0.347258	−	0.347258i
$871$	−16.0000			−0.542139
$872$	12.0711	+	12.0711i	0.408778	+	0.408778i
$873$	1.00000	−	1.00000i	0.0338449	−	0.0338449i
$874$	−0.686292	+	0.686292i	−0.0232142	+	0.0232142i
$875$		0			0
$876$			5.75736i			0.194523i
$877$	−16.8995	+	16.8995i	−0.570655	+	0.570655i	−0.932312	−	0.361656i	$-0.882211\pi$
$877$	−16.8995	+	16.8995i	−0.570655	+	0.570655i	0.361656	+	0.932312i	$0.382211\pi$
$878$	12.1421	−	12.1421i	0.409777	−	0.409777i
$879$	−3.75736	−	3.75736i	−0.126733	−	0.126733i
$880$	−3.41421			−0.115093
$881$	−27.3848	−	27.3848i	−0.922617	−	0.922617i	0.0745972	−	0.997214i	$-0.476233\pi$
$881$	−27.3848	−	27.3848i	−0.922617	−	0.922617i	−0.997214	+	0.0745972i	$0.976233\pi$
$882$			7.00000i			0.235702i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	2.82843	−	11.3137i	0.0951303	−	0.380521i
$885$	−2.82843			−0.0950765
$886$		−	23.1716i		−	0.778464i
$887$	−18.6863	−	18.6863i	−0.627424	−	0.627424i	0.319995	−	0.947419i	$-0.396319\pi$
$887$	−18.6863	−	18.6863i	−0.627424	−	0.627424i	−0.947419	+	0.319995i	$0.896319\pi$
$888$	−0.242641			−0.00814249
$889$		0			0
$890$	22.1421	−	22.1421i	0.742206	−	0.742206i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$			5.65685i			0.189405i
$893$		−	7.31371i		−	0.244744i
$894$	6.58579	−	6.58579i	0.220262	−	0.220262i
$895$	7.65685	−	7.65685i	0.255940	−	0.255940i
$896$		0			0
$897$	3.31371			0.110642
$898$	10.0711	+	10.0711i	0.336076	+	0.336076i
$899$		−	12.0000i		−	0.400222i
$900$	6.65685			0.221895
$901$	−20.6863	−	5.17157i	−0.689160	−	0.172290i
$902$	−8.24264			−0.274450
$903$		0			0
$904$	6.89949	+	6.89949i	0.229474	+	0.229474i
$905$	−16.1421			−0.536583
$906$	−1.75736	−	1.75736i	−0.0583844	−	0.0583844i
$907$	−20.8284	+	20.8284i	−0.691597	+	0.691597i	−0.962583	−	0.270987i	$-0.912650\pi$
$907$	−20.8284	+	20.8284i	−0.691597	+	0.691597i	0.270987	+	0.962583i	$0.412650\pi$
$908$	4.48528	−	4.48528i	0.148849	−	0.148849i
$909$		−	4.00000i		−	0.132672i
$910$		0			0
$911$	−31.3137	+	31.3137i	−1.03747	+	1.03747i	−0.0381993	+	0.999270i	$0.512162\pi$
$911$	−31.3137	+	31.3137i	−1.03747	+	1.03747i	−0.999270	+	0.0381993i	$0.987838\pi$
$912$	0.585786	−	0.585786i	0.0193973	−	0.0193973i
$913$	6.82843	+	6.82843i	0.225988	+	0.225988i
$914$	−12.6274			−0.417678
$915$	−5.41421	−	5.41421i	−0.178988	−	0.178988i
$916$		−	2.68629i		−	0.0887576i
$917$		0			0
$918$	−3.53553	+	2.12132i	−0.116690	+	0.0700140i
$919$	−3.45584			−0.113998			−0.0569989	−	0.998374i	$-0.518153\pi$
$919$	−3.45584			−0.113998			−0.0569989	+	0.998374i	$0.518153\pi$
$920$			4.00000i			0.131876i
$921$	−9.75736	−	9.75736i	−0.321516	−	0.321516i
$922$	40.9706			1.34929
$923$	16.0000	+	16.0000i	0.526646	+	0.526646i
$924$		0			0
$925$	−1.14214	+	1.14214i	−0.0375532	+	0.0375532i
$926$		−	3.02944i		−	0.0995535i
$927$		0			0
$928$	−3.00000	+	3.00000i	−0.0984798	+	0.0984798i
$929$	9.10051	−	9.10051i	0.298578	−	0.298578i	−0.541879	−	0.840457i	$-0.682287\pi$
$929$	9.10051	−	9.10051i	0.298578	−	0.298578i	0.840457	+	0.541879i	$0.182287\pi$
$930$	6.82843	+	6.82843i	0.223913	+	0.223913i
$931$	5.79899			0.190054
$932$	11.8284	+	11.8284i	0.387453	+	0.387453i
$933$			13.6569i			0.447105i
$934$	−14.4853			−0.473973
$935$	3.41421	−	13.6569i	0.111657	−	0.446627i
$936$	−2.82843			−0.0924500
$937$		−	10.1421i		−	0.331329i	−0.986182	−	0.165665i	$-0.947023\pi$
$937$		−	10.1421i		−	0.331329i	0.986182	−	0.165665i	$-0.0529769\pi$
$938$		0			0
$939$	23.0711			0.752896
$940$	−21.3137	−	21.3137i	−0.695177	−	0.695177i
$941$	17.9706	−	17.9706i	0.585824	−	0.585824i	−0.350674	−	0.936498i	$-0.614047\pi$
$941$	17.9706	−	17.9706i	0.585824	−	0.585824i	0.936498	+	0.350674i	$0.114047\pi$
$942$	−12.2426	+	12.2426i	−0.398887	+	0.398887i
$943$			9.65685i			0.314470i
$944$			0.828427i			0.0269630i
$945$		0			0
$946$	3.41421	−	3.41421i	0.111006	−	0.111006i
$947$	−29.3137	−	29.3137i	−0.952568	−	0.952568i	0.0463574	−	0.998925i	$-0.485239\pi$
$947$	−29.3137	−	29.3137i	−0.952568	−	0.952568i	−0.998925	+	0.0463574i	$0.985239\pi$
$948$	−12.4853			−0.405503
$949$	−11.5147	−	11.5147i	−0.373784	−	0.373784i
$950$		−	5.51472i		−	0.178921i
$951$	21.5563			0.699013
$952$		0			0
$953$	14.6274			0.473829			0.236914	−	0.971531i	$-0.423864\pi$
$953$	14.6274			0.473829			0.236914	+	0.971531i	$0.423864\pi$
$954$			5.17157i			0.167436i
$955$	−25.3137	−	25.3137i	−0.819132	−	0.819132i
$956$	−4.97056			−0.160759
$957$	3.00000	+	3.00000i	0.0969762	+	0.0969762i
$958$	−16.0000	+	16.0000i	−0.516937	+	0.516937i
$959$		0			0
$960$		−	3.41421i		−	0.110193i
$961$		−	23.0000i		−	0.741935i
$962$	0.485281	−	0.485281i	0.0156461	−	0.0156461i
$963$	−6.48528	+	6.48528i	−0.208985	+	0.208985i
$964$	−0.899495	−	0.899495i	−0.0289708	−	0.0289708i
$965$	−22.9706			−0.739449
$966$		0			0
$967$			36.8284i			1.18432i	0.805820	+	0.592161i	$0.201725\pi$
$967$			36.8284i			1.18432i	−0.805820	+	0.592161i	$0.798275\pi$
$968$	1.00000			0.0321412
$969$	1.75736	+	2.92893i	0.0564545	+	0.0940909i
$970$	−4.82843			−0.155031
$971$		−	33.1127i		−	1.06264i	−0.847172	−	0.531319i	$-0.821697\pi$
$971$		−	33.1127i		−	1.06264i	0.847172	−	0.531319i	$-0.178303\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$		0			0
$974$	−0.686292	−	0.686292i	−0.0219902	−	0.0219902i
$975$	−13.3137	+	13.3137i	−0.426380	+	0.426380i
$976$	−1.58579	+	1.58579i	−0.0507598	+	0.0507598i
$977$			36.4853i			1.16727i	0.812017	+	0.583634i	$0.198370\pi$
$977$			36.4853i			1.16727i	−0.812017	+	0.583634i	$0.801630\pi$
$978$		−	10.1421i		−	0.324310i
$979$	−6.48528	+	6.48528i	−0.207270	+	0.207270i
$980$	16.8995	−	16.8995i	0.539835	−	0.539835i
$981$	12.0711	+	12.0711i	0.385400	+	0.385400i
$982$	−18.6274			−0.594425
$983$	−4.14214	−	4.14214i	−0.132114	−	0.132114i	0.637958	−	0.770071i	$-0.279779\pi$
$983$	−4.14214	−	4.14214i	−0.132114	−	0.132114i	−0.770071	+	0.637958i	$0.779779\pi$
$984$		−	8.24264i		−	0.262766i
$985$	70.7696			2.25491
$986$	−9.00000	−	15.0000i	−0.286618	−	0.477697i
$987$		0			0
$988$			2.34315i			0.0745454i
$989$	−4.00000	−	4.00000i	−0.127193	−	0.127193i
$990$	−3.41421			−0.108511
$991$	6.34315	+	6.34315i	0.201497	+	0.201497i	0.800641	−	0.599144i	$-0.204492\pi$
$991$	6.34315	+	6.34315i	0.201497	+	0.201497i	−0.599144	+	0.800641i	$0.704492\pi$
$992$	2.00000	−	2.00000i	0.0635001	−	0.0635001i
$993$		0			0
$994$		0			0
$995$		−	85.2548i		−	2.70276i
$996$	−6.82843	+	6.82843i	−0.216367	+	0.216367i
$997$	−16.5563	+	16.5563i	−0.524345	+	0.524345i	−0.918881	−	0.394536i	$-0.870905\pi$
$997$	−16.5563	+	16.5563i	−0.524345	+	0.524345i	0.394536	+	0.918881i	$0.370905\pi$
$998$	−23.1716	−	23.1716i	−0.733483	−	0.733483i
$999$	−0.242641			−0.00767681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.c.727.2	yes	4
17.4	even	4	inner	1122.2.l.c.463.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.c.463.2	✓	4	17.4	even	4	inner
1122.2.l.c.727.2	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.41421 + 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.41421 + 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +(2.41421 - 2.41421i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} +2.82843 q^{13} +3.41421i q^{15} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +1.00000 q^{18} -0.828427i q^{19} +(-2.41421 - 2.41421i) q^{20} +(0.707107 + 0.707107i) q^{22} +(0.828427 - 0.828427i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.65685i q^{25} -2.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.00000 - 3.00000i) q^{29} +3.41421 q^{30} +(2.00000 + 2.00000i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(4.00000 + 1.00000i) q^{34} -1.00000i q^{36} +(0.171573 + 0.171573i) q^{37} -0.828427 q^{38} +(2.00000 + 2.00000i) q^{39} +(-2.41421 + 2.41421i) q^{40} +(-5.82843 + 5.82843i) q^{41} -4.82843i q^{43} +(0.707107 - 0.707107i) q^{44} +(-2.41421 + 2.41421i) q^{45} +(-0.828427 - 0.828427i) q^{46} +8.82843 q^{47} +(0.707107 + 0.707107i) q^{48} +7.00000i q^{49} +6.65685 q^{50} +(-3.53553 + 2.12132i) q^{51} -2.82843 q^{52} +5.17157i q^{53} +(0.707107 + 0.707107i) q^{54} -3.41421 q^{55} +(0.585786 - 0.585786i) q^{57} +(-3.00000 + 3.00000i) q^{58} +0.828427i q^{59} -3.41421i q^{60} +(-1.58579 + 1.58579i) q^{61} +(2.00000 - 2.00000i) q^{62} -1.00000 q^{64} +(6.82843 + 6.82843i) q^{65} +1.00000i q^{66} -5.65685 q^{67} +(1.00000 - 4.00000i) q^{68} +1.17157 q^{69} +(5.65685 + 5.65685i) q^{71} -1.00000 q^{72} +(-4.07107 - 4.07107i) q^{73} +(0.171573 - 0.171573i) q^{74} +(-4.70711 + 4.70711i) q^{75} +0.828427i q^{76} +(2.00000 - 2.00000i) q^{78} +(8.82843 - 8.82843i) q^{79} +(2.41421 + 2.41421i) q^{80} -1.00000 q^{81} +(5.82843 + 5.82843i) q^{82} -9.65685i q^{83} +(-12.0711 + 7.24264i) q^{85} -4.82843 q^{86} -4.24264i q^{87} +(-0.707107 - 0.707107i) q^{88} +9.17157 q^{89} +(2.41421 + 2.41421i) q^{90} +(-0.828427 + 0.828427i) q^{92} +2.82843i q^{93} -8.82843i q^{94} +(2.00000 - 2.00000i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.00000 - 1.00000i) q^{97} +7.00000 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	\( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{10} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{20} - 8 q^{23} - 12 q^{29} + 8 q^{30} + 8 q^{31} - 4 q^{33} + 16 q^{34} + 12 q^{37} + 8 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 4 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{50} - 8 q^{55} + 8 q^{57} - 12 q^{58} - 12 q^{61} + 8 q^{62} - 4 q^{64} + 16 q^{65} + 4 q^{68} + 16 q^{69} - 4 q^{72} + 12 q^{73} + 12 q^{74} - 16 q^{75} + 8 q^{78} + 24 q^{79} + 4 q^{80} - 4 q^{81} + 12 q^{82} - 20 q^{85} - 8 q^{86} + 48 q^{89} + 4 q^{90} + 8 q^{92} + 8 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^10 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 4 * q^20 - 8 * q^23 - 12 * q^29 + 8 * q^30 + 8 * q^31 - 4 * q^33 + 16 * q^34 + 12 * q^37 + 8 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 4 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^50 - 8 * q^55 + 8 * q^57 - 12 * q^58 - 12 * q^61 + 8 * q^62 - 4 * q^64 + 16 * q^65 + 4 * q^68 + 16 * q^69 - 4 * q^72 + 12 * q^73 + 12 * q^74 - 16 * q^75 + 8 * q^78 + 24 * q^79 + 4 * q^80 - 4 * q^81 + 12 * q^82 - 20 * q^85 - 8 * q^86 + 48 * q^89 + 4 * q^90 + 8 * q^92 + 8 * q^95 - 4 * q^97 + 28 * q^98

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