LMFDB - Embedded newform 1122.2.l.d.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.d.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.00000 + 2.00000i) q^{10} +(0.707107 - 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} -5.65685 q^{13} +(1.41421 + 1.41421i) q^{14} +2.82843i q^{15} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} -1.00000 q^{18} +8.24264i q^{19} +(-2.00000 - 2.00000i) q^{20} +2.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-2.58579 + 2.58579i) q^{23} +(0.707107 - 0.707107i) q^{24} +3.00000i q^{25} -5.65685i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(0.414214 + 0.414214i) q^{29} -2.82843 q^{30} +(2.24264 + 2.24264i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(-1.00000 + 4.00000i) q^{34} +5.65685 q^{35} -1.00000i q^{36} +(8.41421 + 8.41421i) q^{37} -8.24264 q^{38} +(-4.00000 - 4.00000i) q^{39} +(2.00000 - 2.00000i) q^{40} +(-0.171573 + 0.171573i) q^{41} +2.00000i q^{42} -7.07107i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(-2.58579 - 2.58579i) q^{46} -2.24264 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} -3.00000 q^{50} +(2.12132 + 3.53553i) q^{51} +5.65685 q^{52} -9.65685i q^{53} +(-0.707107 - 0.707107i) q^{54} +2.82843 q^{55} +(-1.41421 - 1.41421i) q^{56} +(-5.82843 + 5.82843i) q^{57} +(-0.414214 + 0.414214i) q^{58} -0.242641i q^{59} -2.82843i q^{60} +(6.82843 - 6.82843i) q^{61} +(-2.24264 + 2.24264i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(-11.3137 - 11.3137i) q^{65} +1.00000i q^{66} -12.4853 q^{67} +(-4.00000 - 1.00000i) q^{68} -3.65685 q^{69} +5.65685i q^{70} +(8.82843 + 8.82843i) q^{71} +1.00000 q^{72} +(-3.17157 - 3.17157i) q^{73} +(-8.41421 + 8.41421i) q^{74} +(-2.12132 + 2.12132i) q^{75} -8.24264i q^{76} -2.00000i q^{77} +(4.00000 - 4.00000i) q^{78} +(4.82843 - 4.82843i) q^{79} +(2.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(-0.171573 - 0.171573i) q^{82} -4.48528i q^{83} -2.00000 q^{84} +(6.00000 + 10.0000i) q^{85} +7.07107 q^{86} +0.585786i q^{87} +(-0.707107 - 0.707107i) q^{88} -7.65685 q^{89} +(-2.00000 - 2.00000i) q^{90} +(-8.00000 + 8.00000i) q^{91} +(2.58579 - 2.58579i) q^{92} +3.17157i q^{93} -2.24264i q^{94} +(-16.4853 + 16.4853i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(10.3137 + 10.3137i) q^{97} -3.00000 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^5	$ 4 q - 4 q^{4} + 8 q^{5} - 8 q^{10} + 4 q^{16} + 16 q^{17} - 4 q^{18} - 8 q^{20} + 8 q^{21} - 16 q^{23} - 4 q^{29} - 8 q^{31} + 4 q^{33} - 4 q^{34} + 28 q^{37} - 16 q^{38} - 16 q^{39} + 8 q^{40} - 12 q^{41} - 8 q^{45} - 16 q^{46} + 8 q^{47} - 12 q^{50} - 12 q^{57} + 4 q^{58} + 16 q^{61} + 8 q^{62} - 4 q^{64} - 16 q^{67} - 16 q^{68} + 8 q^{69} + 24 q^{71} + 4 q^{72} - 24 q^{73} - 28 q^{74} + 16 q^{78} + 8 q^{79} + 8 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} + 24 q^{85} - 8 q^{89} - 8 q^{90} - 32 q^{91} + 16 q^{92} - 32 q^{95} - 4 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^5 - 8 * q^10 + 4 * q^16 + 16 * q^17 - 4 * q^18 - 8 * q^20 + 8 * q^21 - 16 * q^23 - 4 * q^29 - 8 * q^31 + 4 * q^33 - 4 * q^34 + 28 * q^37 - 16 * q^38 - 16 * q^39 + 8 * q^40 - 12 * q^41 - 8 * q^45 - 16 * q^46 + 8 * q^47 - 12 * q^50 - 12 * q^57 + 4 * q^58 + 16 * q^61 + 8 * q^62 - 4 * q^64 - 16 * q^67 - 16 * q^68 + 8 * q^69 + 24 * q^71 + 4 * q^72 - 24 * q^73 - 28 * q^74 + 16 * q^78 + 8 * q^79 + 8 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 + 24 * q^85 - 8 * q^89 - 8 * q^90 - 32 * q^91 + 16 * q^92 - 32 * q^95 - 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
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	0.994936	−	0.100509i	$-0.0320471\pi$
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	−0.100509	+	0.994936i	$0.532047\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	−0.387392	−	0.921915i	$-0.626624\pi$
$7$	1.41421	−	1.41421i	0.534522	−	0.534522i	0.921915	+	0.387392i	$0.126624\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−2.00000	+	2.00000i	−0.632456	+	0.632456i
$11$	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
$13$	−5.65685			−1.56893			−0.784465	−	0.620174i	$-0.787062\pi$
$13$	−5.65685			−1.56893			−0.784465	+	0.620174i	$0.787062\pi$
$14$	1.41421	+	1.41421i	0.377964	+	0.377964i
$15$			2.82843i			0.730297i
$16$	1.00000			0.250000
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$18$	−1.00000			−0.235702
$19$			8.24264i			1.89099i	0.325634	+	0.945496i	$0.394422\pi$
$19$			8.24264i			1.89099i	−0.325634	+	0.945496i	$0.605578\pi$
$20$	−2.00000	−	2.00000i	−0.447214	−	0.447214i
$21$	2.00000			0.436436
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	−2.58579	+	2.58579i	−0.539174	+	0.539174i	−0.923286	−	0.384113i	$-0.874507\pi$
$23$	−2.58579	+	2.58579i	−0.539174	+	0.539174i	0.384113	+	0.923286i	$0.374507\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$			3.00000i			0.600000i
$26$		−	5.65685i		−	1.10940i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.41421	+	1.41421i	−0.267261	+	0.267261i
$29$	0.414214	+	0.414214i	0.0769175	+	0.0769175i	0.744519	−	0.667601i	$-0.232679\pi$
$29$	0.414214	+	0.414214i	0.0769175	+	0.0769175i	−0.667601	+	0.744519i	$0.732679\pi$
$30$	−2.82843			−0.516398
$31$	2.24264	+	2.24264i	0.402790	+	0.402790i	0.879215	−	0.476425i	$-0.158068\pi$
$31$	2.24264	+	2.24264i	0.402790	+	0.402790i	−0.476425	+	0.879215i	$0.658068\pi$
$32$			1.00000i			0.176777i
$33$	1.00000			0.174078
$34$	−1.00000	+	4.00000i	−0.171499	+	0.685994i
$35$	5.65685			0.956183
$36$		−	1.00000i		−	0.166667i
$37$	8.41421	+	8.41421i	1.38329	+	1.38329i	0.838710	+	0.544578i	$0.183310\pi$
$37$	8.41421	+	8.41421i	1.38329	+	1.38329i	0.544578	+	0.838710i	$0.316690\pi$
$38$	−8.24264			−1.33713
$39$	−4.00000	−	4.00000i	−0.640513	−	0.640513i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$	−0.171573	+	0.171573i	−0.0267952	+	0.0267952i	−0.720377	−	0.693582i	$-0.756031\pi$
$41$	−0.171573	+	0.171573i	−0.0267952	+	0.0267952i	0.693582	+	0.720377i	$0.256031\pi$
$42$			2.00000i			0.308607i
$43$		−	7.07107i		−	1.07833i	−0.842201	−	0.539164i	$-0.818740\pi$
$43$		−	7.07107i		−	1.07833i	0.842201	−	0.539164i	$-0.181260\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$	−2.00000	+	2.00000i	−0.298142	+	0.298142i
$46$	−2.58579	−	2.58579i	−0.381253	−	0.381253i
$47$	−2.24264			−0.327123			−0.163561	−	0.986533i	$-0.552298\pi$
$47$	−2.24264			−0.327123			−0.163561	+	0.986533i	$0.552298\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			3.00000i			0.428571i
$50$	−3.00000			−0.424264
$51$	2.12132	+	3.53553i	0.297044	+	0.495074i
$52$	5.65685			0.784465
$53$		−	9.65685i		−	1.32647i	−0.748411	−	0.663235i	$-0.769183\pi$
$53$		−	9.65685i		−	1.32647i	0.748411	−	0.663235i	$-0.230817\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	2.82843			0.381385
$56$	−1.41421	−	1.41421i	−0.188982	−	0.188982i
$57$	−5.82843	+	5.82843i	−0.771994	+	0.771994i
$58$	−0.414214	+	0.414214i	−0.0543889	+	0.0543889i
$59$		−	0.242641i		−	0.0315891i	−0.999875	−	0.0157946i	$-0.994972\pi$
$59$		−	0.242641i		−	0.0315891i	0.999875	−	0.0157946i	$-0.00502777\pi$
$60$		−	2.82843i		−	0.365148i
$61$	6.82843	−	6.82843i	0.874291	−	0.874291i	−0.118646	−	0.992937i	$-0.537855\pi$
$61$	6.82843	−	6.82843i	0.874291	−	0.874291i	0.992937	+	0.118646i	$0.0378554\pi$
$62$	−2.24264	+	2.24264i	−0.284816	+	0.284816i
$63$	1.41421	+	1.41421i	0.178174	+	0.178174i
$64$	−1.00000			−0.125000
$65$	−11.3137	−	11.3137i	−1.40329	−	1.40329i
$66$			1.00000i			0.123091i
$67$	−12.4853			−1.52532			−0.762660	−	0.646800i	$-0.776107\pi$
$67$	−12.4853			−1.52532			−0.762660	+	0.646800i	$0.776107\pi$
$68$	−4.00000	−	1.00000i	−0.485071	−	0.121268i
$69$	−3.65685			−0.440234
$70$			5.65685i			0.676123i
$71$	8.82843	+	8.82843i	1.04774	+	1.04774i	0.998802	+	0.0489398i	$0.0155843\pi$
$71$	8.82843	+	8.82843i	1.04774	+	1.04774i	0.0489398	+	0.998802i	$0.484416\pi$
$72$	1.00000			0.117851
$73$	−3.17157	−	3.17157i	−0.371205	−	0.371205i	0.496711	−	0.867916i	$-0.334541\pi$
$73$	−3.17157	−	3.17157i	−0.371205	−	0.371205i	−0.867916	+	0.496711i	$0.834541\pi$
$74$	−8.41421	+	8.41421i	−0.978132	+	0.978132i
$75$	−2.12132	+	2.12132i	−0.244949	+	0.244949i
$76$		−	8.24264i		−	0.945496i
$77$		−	2.00000i		−	0.227921i
$78$	4.00000	−	4.00000i	0.452911	−	0.452911i
$79$	4.82843	−	4.82843i	0.543240	−	0.543240i	−0.381237	−	0.924477i	$-0.624502\pi$
$79$	4.82843	−	4.82843i	0.543240	−	0.543240i	0.924477	+	0.381237i	$0.124502\pi$
$80$	2.00000	+	2.00000i	0.223607	+	0.223607i
$81$	−1.00000			−0.111111
$82$	−0.171573	−	0.171573i	−0.0189471	−	0.0189471i
$83$		−	4.48528i		−	0.492324i	−0.969229	−	0.246162i	$-0.920831\pi$
$83$		−	4.48528i		−	0.492324i	0.969229	−	0.246162i	$-0.0791695\pi$
$84$	−2.00000			−0.218218
$85$	6.00000	+	10.0000i	0.650791	+	1.08465i
$86$	7.07107			0.762493
$87$			0.585786i			0.0628029i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−7.65685			−0.811625			−0.405812	−	0.913956i	$-0.633011\pi$
$89$	−7.65685			−0.811625			−0.405812	+	0.913956i	$0.633011\pi$
$90$	−2.00000	−	2.00000i	−0.210819	−	0.210819i
$91$	−8.00000	+	8.00000i	−0.838628	+	0.838628i
$92$	2.58579	−	2.58579i	0.269587	−	0.269587i
$93$			3.17157i			0.328877i
$94$		−	2.24264i		−	0.231311i
$95$	−16.4853	+	16.4853i	−1.69135	+	1.69135i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	10.3137	+	10.3137i	1.04720	+	1.04720i	0.998830	+	0.0483689i	$0.0154023\pi$
$97$	10.3137	+	10.3137i	1.04720	+	1.04720i	0.0483689	+	0.998830i	$0.484598\pi$
$98$	−3.00000			−0.303046
$99$	0.707107	+	0.707107i	0.0710669	+	0.0710669i
$100$		−	3.00000i		−	0.300000i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	−3.53553	+	2.12132i	−0.350070	+	0.210042i
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$			5.65685i			0.554700i
$105$	4.00000	+	4.00000i	0.390360	+	0.390360i
$106$	9.65685			0.937957
$107$	−4.00000	−	4.00000i	−0.386695	−	0.386695i	0.486812	−	0.873507i	$-0.338160\pi$
$107$	−4.00000	−	4.00000i	−0.386695	−	0.386695i	−0.873507	+	0.486812i	$0.838160\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	3.65685	−	3.65685i	0.350263	−	0.350263i	−0.509944	−	0.860207i	$-0.670334\pi$
$109$	3.65685	−	3.65685i	0.350263	−	0.350263i	0.860207	+	0.509944i	$0.170334\pi$
$110$			2.82843i			0.269680i
$111$			11.8995i			1.12945i
$112$	1.41421	−	1.41421i	0.133631	−	0.133631i
$113$	10.8284	−	10.8284i	1.01865	−	1.01865i	0.0188300	−	0.999823i	$-0.494006\pi$
$113$	10.8284	−	10.8284i	1.01865	−	1.01865i	0.999823	−	0.0188300i	$-0.00599414\pi$
$114$	−5.82843	−	5.82843i	−0.545882	−	0.545882i
$115$	−10.3431			−0.964503
$116$	−0.414214	−	0.414214i	−0.0384588	−	0.0384588i
$117$		−	5.65685i		−	0.522976i
$118$	0.242641			0.0223369
$119$	7.07107	−	4.24264i	0.648204	−	0.388922i
$120$	2.82843			0.258199
$121$		−	1.00000i		−	0.0909091i
$122$	6.82843	+	6.82843i	0.618217	+	0.618217i
$123$	−0.242641			−0.0218782
$124$	−2.24264	−	2.24264i	−0.201395	−	0.201395i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	−1.41421	+	1.41421i	−0.125988	+	0.125988i
$127$		−	9.07107i		−	0.804927i	−0.915436	−	0.402464i	$-0.868154\pi$
$127$		−	9.07107i		−	0.804927i	0.915436	−	0.402464i	$-0.131846\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.00000	−	5.00000i	0.440225	−	0.440225i
$130$	11.3137	−	11.3137i	0.992278	−	0.992278i
$131$	−12.4853	−	12.4853i	−1.09084	−	1.09084i	−0.995438	−	0.0954056i	$-0.969585\pi$
$131$	−12.4853	−	12.4853i	−1.09084	−	1.09084i	−0.0954056	−	0.995438i	$-0.530415\pi$
$132$	−1.00000			−0.0870388
$133$	11.6569	+	11.6569i	1.01078	+	1.01078i
$134$		−	12.4853i		−	1.07856i
$135$	−2.82843			−0.243432
$136$	1.00000	−	4.00000i	0.0857493	−	0.342997i
$137$	−5.31371			−0.453981			−0.226990	−	0.973897i	$-0.572889\pi$
$137$	−5.31371			−0.453981			−0.226990	+	0.973897i	$0.572889\pi$
$138$		−	3.65685i		−	0.311292i
$139$	1.17157	+	1.17157i	0.0993715	+	0.0993715i	0.755045	−	0.655673i	$-0.227615\pi$
$139$	1.17157	+	1.17157i	0.0993715	+	0.0993715i	−0.655673	+	0.755045i	$0.727615\pi$
$140$	−5.65685			−0.478091
$141$	−1.58579	−	1.58579i	−0.133547	−	0.133547i
$142$	−8.82843	+	8.82843i	−0.740865	+	0.740865i
$143$	−4.00000	+	4.00000i	−0.334497	+	0.334497i
$144$			1.00000i			0.0833333i
$145$			1.65685i			0.137594i
$146$	3.17157	−	3.17157i	0.262481	−	0.262481i
$147$	−2.12132	+	2.12132i	−0.174964	+	0.174964i
$148$	−8.41421	−	8.41421i	−0.691644	−	0.691644i
$149$	13.1716			1.07906			0.539529	−	0.841967i	$-0.318602\pi$
$149$	13.1716			1.07906			0.539529	+	0.841967i	$0.318602\pi$
$150$	−2.12132	−	2.12132i	−0.173205	−	0.173205i
$151$		−	7.41421i		−	0.603360i	−0.953409	−	0.301680i	$-0.902453\pi$
$151$		−	7.41421i		−	0.603360i	0.953409	−	0.301680i	$-0.0975474\pi$
$152$	8.24264			0.668566
$153$	−1.00000	+	4.00000i	−0.0808452	+	0.323381i
$154$	2.00000			0.161165
$155$			8.97056i			0.720533i
$156$	4.00000	+	4.00000i	0.320256	+	0.320256i
$157$	0.485281			0.0387297			0.0193648	−	0.999812i	$-0.493836\pi$
$157$	0.485281			0.0387297			0.0193648	+	0.999812i	$0.493836\pi$
$158$	4.82843	+	4.82843i	0.384129	+	0.384129i
$159$	6.82843	−	6.82843i	0.541529	−	0.541529i
$160$	−2.00000	+	2.00000i	−0.158114	+	0.158114i
$161$			7.31371i			0.576401i
$162$		−	1.00000i		−	0.0785674i
$163$	9.17157	−	9.17157i	0.718373	−	0.718373i	−0.249899	−	0.968272i	$-0.580397\pi$
$163$	9.17157	−	9.17157i	0.718373	−	0.718373i	0.968272	+	0.249899i	$0.0803974\pi$
$164$	0.171573	−	0.171573i	0.0133976	−	0.0133976i
$165$	2.00000	+	2.00000i	0.155700	+	0.155700i
$166$	4.48528			0.348125
$167$	7.41421	+	7.41421i	0.573729	+	0.573729i	0.933168	−	0.359439i	$-0.117032\pi$
$167$	7.41421	+	7.41421i	0.573729	+	0.573729i	−0.359439	+	0.933168i	$0.617032\pi$
$168$		−	2.00000i		−	0.154303i
$169$	19.0000			1.46154
$170$	−10.0000	+	6.00000i	−0.766965	+	0.460179i
$171$	−8.24264			−0.630330
$172$			7.07107i			0.539164i
$173$	−6.41421	−	6.41421i	−0.487664	−	0.487664i	0.419905	−	0.907568i	$-0.362064\pi$
$173$	−6.41421	−	6.41421i	−0.487664	−	0.487664i	−0.907568	+	0.419905i	$0.862064\pi$
$174$	−0.585786			−0.0444084
$175$	4.24264	+	4.24264i	0.320713	+	0.320713i
$176$	0.707107	−	0.707107i	0.0533002	−	0.0533002i
$177$	0.171573	−	0.171573i	0.0128962	−	0.0128962i
$178$		−	7.65685i		−	0.573905i
$179$		−	21.4142i		−	1.60057i	−0.599617	−	0.800287i	$-0.704681\pi$
$179$		−	21.4142i		−	1.60057i	0.599617	−	0.800287i	$-0.295319\pi$
$180$	2.00000	−	2.00000i	0.149071	−	0.149071i
$181$	16.4142	−	16.4142i	1.22006	−	1.22006i	0.252449	−	0.967610i	$-0.418764\pi$
$181$	16.4142	−	16.4142i	1.22006	−	1.22006i	0.967610	−	0.252449i	$-0.0812359\pi$
$182$	−8.00000	−	8.00000i	−0.592999	−	0.592999i
$183$	9.65685			0.713855
$184$	2.58579	+	2.58579i	0.190627	+	0.190627i
$185$			33.6569i			2.47450i
$186$	−3.17157			−0.232551
$187$	3.53553	−	2.12132i	0.258544	−	0.155126i
$188$	2.24264			0.163561
$189$			2.00000i			0.145479i
$190$	−16.4853	−	16.4853i	−1.19597	−	1.19597i
$191$	−11.8995			−0.861017			−0.430509	−	0.902586i	$-0.641666\pi$
$191$	−11.8995			−0.861017			−0.430509	+	0.902586i	$0.641666\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−9.17157	+	9.17157i	−0.660184	+	0.660184i	−0.955423	−	0.295239i	$-0.904601\pi$
$193$	−9.17157	+	9.17157i	−0.660184	+	0.660184i	0.295239	+	0.955423i	$0.404601\pi$
$194$	−10.3137	+	10.3137i	−0.740481	+	0.740481i
$195$		−	16.0000i		−	1.14578i
$196$		−	3.00000i		−	0.214286i
$197$	−4.89949	+	4.89949i	−0.349075	+	0.349075i	−0.859765	−	0.510690i	$-0.829390\pi$
$197$	−4.89949	+	4.89949i	−0.349075	+	0.349075i	0.510690	+	0.859765i	$0.329390\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	13.0711	+	13.0711i	0.926583	+	0.926583i	0.997483	−	0.0709000i	$-0.0225871\pi$
$199$	13.0711	+	13.0711i	0.926583	+	0.926583i	−0.0709000	+	0.997483i	$0.522587\pi$
$200$	3.00000			0.212132
$201$	−8.82843	−	8.82843i	−0.622709	−	0.622709i
$202$		−	6.00000i		−	0.422159i
$203$	1.17157			0.0822283
$204$	−2.12132	−	3.53553i	−0.148522	−	0.247537i
$205$	−0.686292			−0.0479327
$206$		−	8.00000i		−	0.557386i
$207$	−2.58579	−	2.58579i	−0.179725	−	0.179725i
$208$	−5.65685			−0.392232
$209$	5.82843	+	5.82843i	0.403161	+	0.403161i
$210$	−4.00000	+	4.00000i	−0.276026	+	0.276026i
$211$	17.4142	−	17.4142i	1.19884	−	1.19884i	0.224331	−	0.974513i	$-0.427980\pi$
$211$	17.4142	−	17.4142i	1.19884	−	1.19884i	0.974513	−	0.224331i	$-0.0720196\pi$
$212$			9.65685i			0.663235i
$213$			12.4853i			0.855477i
$214$	4.00000	−	4.00000i	0.273434	−	0.273434i
$215$	14.1421	−	14.1421i	0.964486	−	0.964486i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	6.34315			0.430601
$218$	3.65685	+	3.65685i	0.247673	+	0.247673i
$219$		−	4.48528i		−	0.303087i
$220$	−2.82843			−0.190693
$221$	−22.6274	−	5.65685i	−1.52208	−	0.380521i
$222$	−11.8995			−0.798642
$223$			10.1421i			0.679168i	0.940576	+	0.339584i	$0.110286\pi$
$223$			10.1421i			0.679168i	−0.940576	+	0.339584i	$0.889714\pi$
$224$	1.41421	+	1.41421i	0.0944911	+	0.0944911i
$225$	−3.00000			−0.200000
$226$	10.8284	+	10.8284i	0.720296	+	0.720296i
$227$	12.4853	−	12.4853i	0.828677	−	0.828677i	−0.158657	−	0.987334i	$-0.550716\pi$
$227$	12.4853	−	12.4853i	0.828677	−	0.828677i	0.987334	+	0.158657i	$0.0507163\pi$
$228$	5.82843	−	5.82843i	0.385997	−	0.385997i
$229$			18.8284i			1.24422i	0.782931	+	0.622109i	$0.213724\pi$
$229$			18.8284i			1.24422i	−0.782931	+	0.622109i	$0.786276\pi$
$230$		−	10.3431i		−	0.682007i
$231$	1.41421	−	1.41421i	0.0930484	−	0.0930484i
$232$	0.414214	−	0.414214i	0.0271945	−	0.0271945i
$233$	−4.65685	−	4.65685i	−0.305081	−	0.305081i	0.537917	−	0.842998i	$-0.319211\pi$
$233$	−4.65685	−	4.65685i	−0.305081	−	0.305081i	−0.842998	+	0.537917i	$0.819211\pi$
$234$	5.65685			0.369800
$235$	−4.48528	−	4.48528i	−0.292587	−	0.292587i
$236$			0.242641i			0.0157946i
$237$	6.82843			0.443554
$238$	4.24264	+	7.07107i	0.275010	+	0.458349i
$239$	−21.6569			−1.40087			−0.700433	−	0.713718i	$-0.747010\pi$
$239$	−21.6569			−1.40087			−0.700433	+	0.713718i	$0.747010\pi$
$240$			2.82843i			0.182574i
$241$	2.82843	+	2.82843i	0.182195	+	0.182195i	0.792312	−	0.610117i	$-0.208877\pi$
$241$	2.82843	+	2.82843i	0.182195	+	0.182195i	−0.610117	+	0.792312i	$0.708877\pi$
$242$	1.00000			0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−6.82843	+	6.82843i	−0.437145	+	0.437145i
$245$	−6.00000	+	6.00000i	−0.383326	+	0.383326i
$246$		−	0.242641i		−	0.0154702i
$247$		−	46.6274i		−	2.96683i
$248$	2.24264	−	2.24264i	0.142408	−	0.142408i
$249$	3.17157	−	3.17157i	0.200990	−	0.200990i
$250$	4.00000	+	4.00000i	0.252982	+	0.252982i
$251$	−22.3848			−1.41291			−0.706457	−	0.707756i	$-0.749708\pi$
$251$	−22.3848			−1.41291			−0.706457	+	0.707756i	$0.749708\pi$
$252$	−1.41421	−	1.41421i	−0.0890871	−	0.0890871i
$253$			3.65685i			0.229904i
$254$	9.07107			0.569169
$255$	−2.82843	+	11.3137i	−0.177123	+	0.708492i
$256$	1.00000			0.0625000
$257$			10.9706i			0.684325i	0.939641	+	0.342162i	$0.111159\pi$
$257$			10.9706i			0.684325i	−0.939641	+	0.342162i	$0.888841\pi$
$258$	5.00000	+	5.00000i	0.311286	+	0.311286i
$259$	23.7990			1.47880
$260$	11.3137	+	11.3137i	0.701646	+	0.701646i
$261$	−0.414214	+	0.414214i	−0.0256392	+	0.0256392i
$262$	12.4853	−	12.4853i	0.771343	−	0.771343i
$263$		−	26.1421i		−	1.61199i	−0.591920	−	0.805997i	$-0.701630\pi$
$263$		−	26.1421i		−	1.61199i	0.591920	−	0.805997i	$-0.298370\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	19.3137	−	19.3137i	1.18643	−	1.18643i
$266$	−11.6569	+	11.6569i	−0.714728	+	0.714728i
$267$	−5.41421	−	5.41421i	−0.331344	−	0.331344i
$268$	12.4853			0.762660
$269$	3.51472	+	3.51472i	0.214296	+	0.214296i	0.806090	−	0.591793i	$-0.201580\pi$
$269$	3.51472	+	3.51472i	0.214296	+	0.214296i	−0.591793	+	0.806090i	$0.701580\pi$
$270$		−	2.82843i		−	0.172133i
$271$	4.58579			0.278567			0.139283	−	0.990253i	$-0.455520\pi$
$271$	4.58579			0.278567			0.139283	+	0.990253i	$0.455520\pi$
$272$	4.00000	+	1.00000i	0.242536	+	0.0606339i
$273$	−11.3137			−0.684737
$274$		−	5.31371i		−	0.321013i
$275$	2.12132	+	2.12132i	0.127920	+	0.127920i
$276$	3.65685			0.220117
$277$	−0.343146	−	0.343146i	−0.0206176	−	0.0206176i	0.696723	−	0.717340i	$-0.254641\pi$
$277$	−0.343146	−	0.343146i	−0.0206176	−	0.0206176i	−0.717340	+	0.696723i	$0.754641\pi$
$278$	−1.17157	+	1.17157i	−0.0702663	+	0.0702663i
$279$	−2.24264	+	2.24264i	−0.134263	+	0.134263i
$280$		−	5.65685i		−	0.338062i
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$	1.58579	−	1.58579i	0.0944322	−	0.0944322i
$283$	0.928932	−	0.928932i	0.0552193	−	0.0552193i	−0.678958	−	0.734177i	$-0.737568\pi$
$283$	0.928932	−	0.928932i	0.0552193	−	0.0552193i	0.734177	+	0.678958i	$0.237568\pi$
$284$	−8.82843	−	8.82843i	−0.523871	−	0.523871i
$285$	−23.3137			−1.38098
$286$	−4.00000	−	4.00000i	−0.236525	−	0.236525i
$287$			0.485281i			0.0286453i
$288$	−1.00000			−0.0589256
$289$	15.0000	+	8.00000i	0.882353	+	0.470588i
$290$	−1.65685			−0.0972938
$291$			14.5858i			0.855034i
$292$	3.17157	+	3.17157i	0.185602	+	0.185602i
$293$	28.6274			1.67243			0.836216	−	0.548401i	$-0.184763\pi$
$293$	28.6274			1.67243			0.836216	+	0.548401i	$0.184763\pi$
$294$	−2.12132	−	2.12132i	−0.123718	−	0.123718i
$295$	0.485281	−	0.485281i	0.0282542	−	0.0282542i
$296$	8.41421	−	8.41421i	0.489066	−	0.489066i
$297$			1.00000i			0.0580259i
$298$			13.1716i			0.763009i
$299$	14.6274	−	14.6274i	0.845925	−	0.845925i
$300$	2.12132	−	2.12132i	0.122474	−	0.122474i
$301$	−10.0000	−	10.0000i	−0.576390	−	0.576390i
$302$	7.41421			0.426640
$303$	−4.24264	−	4.24264i	−0.243733	−	0.243733i
$304$			8.24264i			0.472748i
$305$	27.3137			1.56398
$306$	−4.00000	−	1.00000i	−0.228665	−	0.0571662i
$307$	−3.55635			−0.202972			−0.101486	−	0.994837i	$-0.532360\pi$
$307$	−3.55635			−0.202972			−0.101486	+	0.994837i	$0.532360\pi$
$308$			2.00000i			0.113961i
$309$	−5.65685	−	5.65685i	−0.321807	−	0.321807i
$310$	−8.97056			−0.509494
$311$	6.00000	+	6.00000i	0.340229	+	0.340229i	0.856453	−	0.516225i	$-0.172663\pi$
$311$	6.00000	+	6.00000i	0.340229	+	0.340229i	−0.516225	+	0.856453i	$0.672663\pi$
$312$	−4.00000	+	4.00000i	−0.226455	+	0.226455i
$313$	−9.82843	+	9.82843i	−0.555536	+	0.555536i	−0.928033	−	0.372498i	$-0.878501\pi$
$313$	−9.82843	+	9.82843i	−0.555536	+	0.555536i	0.372498	+	0.928033i	$0.378501\pi$
$314$			0.485281i			0.0273860i
$315$			5.65685i			0.318728i
$316$	−4.82843	+	4.82843i	−0.271620	+	0.271620i
$317$	18.1421	−	18.1421i	1.01896	−	1.01896i	0.0191472	−	0.999817i	$-0.493905\pi$
$317$	18.1421	−	18.1421i	1.01896	−	1.01896i	0.999817	−	0.0191472i	$-0.00609511\pi$
$318$	6.82843	+	6.82843i	0.382919	+	0.382919i
$319$	0.585786			0.0327977
$320$	−2.00000	−	2.00000i	−0.111803	−	0.111803i
$321$		−	5.65685i		−	0.315735i
$322$	−7.31371			−0.407577
$323$	−8.24264	+	32.9706i	−0.458633	+	1.83453i
$324$	1.00000			0.0555556
$325$		−	16.9706i		−	0.941357i
$326$	9.17157	+	9.17157i	0.507966	+	0.507966i
$327$	5.17157			0.285989
$328$	0.171573	+	0.171573i	0.00947353	+	0.00947353i
$329$	−3.17157	+	3.17157i	−0.174854	+	0.174854i
$330$	−2.00000	+	2.00000i	−0.110096	+	0.110096i
$331$			18.6274i			1.02386i	0.859029	+	0.511928i	$0.171068\pi$
$331$			18.6274i			1.02386i	−0.859029	+	0.511928i	$0.828932\pi$
$332$			4.48528i			0.246162i
$333$	−8.41421	+	8.41421i	−0.461096	+	0.461096i
$334$	−7.41421	+	7.41421i	−0.405688	+	0.405688i
$335$	−24.9706	−	24.9706i	−1.36429	−	1.36429i
$336$	2.00000			0.109109
$337$	20.4853	+	20.4853i	1.11590	+	1.11590i	0.992336	+	0.123568i	$0.0394338\pi$
$337$	20.4853	+	20.4853i	1.11590	+	1.11590i	0.123568	+	0.992336i	$0.460566\pi$
$338$			19.0000i			1.03346i
$339$	15.3137			0.831726
$340$	−6.00000	−	10.0000i	−0.325396	−	0.542326i
$341$	3.17157			0.171750
$342$		−	8.24264i		−	0.445711i
$343$	14.1421	+	14.1421i	0.763604	+	0.763604i
$344$	−7.07107			−0.381246
$345$	−7.31371	−	7.31371i	−0.393757	−	0.393757i
$346$	6.41421	−	6.41421i	0.344830	−	0.344830i
$347$	20.9706	−	20.9706i	1.12576	−	1.12576i	0.134900	−	0.990859i	$-0.456929\pi$
$347$	20.9706	−	20.9706i	1.12576	−	1.12576i	0.990859	−	0.134900i	$-0.0430712\pi$
$348$		−	0.585786i		−	0.0314014i
$349$			8.00000i			0.428230i	0.976808	+	0.214115i	$0.0686868\pi$
$349$			8.00000i			0.428230i	−0.976808	+	0.214115i	$0.931313\pi$
$350$	−4.24264	+	4.24264i	−0.226779	+	0.226779i
$351$	4.00000	−	4.00000i	0.213504	−	0.213504i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	0.171573	+	0.171573i	0.00911900	+	0.00911900i
$355$			35.3137i			1.87426i
$356$	7.65685			0.405812
$357$	8.00000	+	2.00000i	0.423405	+	0.105851i
$358$	21.4142			1.13178
$359$			3.51472i			0.185500i	0.995689	+	0.0927499i	$0.0295657\pi$
$359$			3.51472i			0.185500i	−0.995689	+	0.0927499i	$0.970434\pi$
$360$	2.00000	+	2.00000i	0.105409	+	0.105409i
$361$	−48.9411			−2.57585
$362$	16.4142	+	16.4142i	0.862712	+	0.862712i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$	8.00000	−	8.00000i	0.419314	−	0.419314i
$365$		−	12.6863i		−	0.664031i
$366$			9.65685i			0.504772i
$367$	−17.5563	+	17.5563i	−0.916434	+	0.916434i	−0.996768	−	0.0803340i	$-0.974401\pi$
$367$	−17.5563	+	17.5563i	−0.916434	+	0.916434i	0.0803340	+	0.996768i	$0.474401\pi$
$368$	−2.58579	+	2.58579i	−0.134793	+	0.134793i
$369$	−0.171573	−	0.171573i	−0.00893173	−	0.00893173i
$370$	−33.6569			−1.74974
$371$	−13.6569	−	13.6569i	−0.709029	−	0.709029i
$372$		−	3.17157i		−	0.164438i
$373$	20.9706			1.08581			0.542907	−	0.839793i	$-0.317323\pi$
$373$	20.9706			1.08581			0.542907	+	0.839793i	$0.317323\pi$
$374$	2.12132	+	3.53553i	0.109691	+	0.182818i
$375$	5.65685			0.292119
$376$			2.24264i			0.115655i
$377$	−2.34315	−	2.34315i	−0.120678	−	0.120678i
$378$	−2.00000			−0.102869
$379$	−9.17157	−	9.17157i	−0.471112	−	0.471112i	0.431162	−	0.902274i	$-0.358104\pi$
$379$	−9.17157	−	9.17157i	−0.471112	−	0.471112i	−0.902274	+	0.431162i	$0.858104\pi$
$380$	16.4853	−	16.4853i	0.845677	−	0.845677i
$381$	6.41421	−	6.41421i	0.328610	−	0.328610i
$382$		−	11.8995i		−	0.608831i
$383$		−	29.0711i		−	1.48546i	−0.669590	−	0.742731i	$-0.733530\pi$
$383$		−	29.0711i		−	1.48546i	0.669590	−	0.742731i	$-0.266470\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	4.00000	−	4.00000i	0.203859	−	0.203859i
$386$	−9.17157	−	9.17157i	−0.466821	−	0.466821i
$387$	7.07107			0.359443
$388$	−10.3137	−	10.3137i	−0.523599	−	0.523599i
$389$			4.68629i			0.237604i	0.992918	+	0.118802i	$0.0379054\pi$
$389$			4.68629i			0.237604i	−0.992918	+	0.118802i	$0.962095\pi$
$390$	16.0000			0.810191
$391$	−12.9289	+	7.75736i	−0.653844	+	0.392307i
$392$	3.00000			0.151523
$393$		−	17.6569i		−	0.890670i
$394$	−4.89949	−	4.89949i	−0.246833	−	0.246833i
$395$	19.3137			0.971778
$396$	−0.707107	−	0.707107i	−0.0355335	−	0.0355335i
$397$	−18.5563	+	18.5563i	−0.931316	+	0.931316i	−0.997788	−	0.0664718i	$-0.978826\pi$
$397$	−18.5563	+	18.5563i	−0.931316	+	0.931316i	0.0664718	+	0.997788i	$0.478826\pi$
$398$	−13.0711	+	13.0711i	−0.655193	+	0.655193i
$399$			16.4853i			0.825296i
$400$			3.00000i			0.150000i
$401$	−7.51472	+	7.51472i	−0.375267	+	0.375267i	−0.869391	−	0.494124i	$-0.835489\pi$
$401$	−7.51472	+	7.51472i	−0.375267	+	0.375267i	0.494124	+	0.869391i	$0.335489\pi$
$402$	8.82843	−	8.82843i	0.440322	−	0.440322i
$403$	−12.6863	−	12.6863i	−0.631949	−	0.631949i
$404$	6.00000			0.298511
$405$	−2.00000	−	2.00000i	−0.0993808	−	0.0993808i
$406$			1.17157i			0.0581442i
$407$	11.8995			0.589836
$408$	3.53553	−	2.12132i	0.175035	−	0.105021i
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$		−	0.686292i		−	0.0338935i
$411$	−3.75736	−	3.75736i	−0.185337	−	0.185337i
$412$	8.00000			0.394132
$413$	−0.343146	−	0.343146i	−0.0168851	−	0.0168851i
$414$	2.58579	−	2.58579i	0.127084	−	0.127084i
$415$	8.97056	−	8.97056i	0.440348	−	0.440348i
$416$		−	5.65685i		−	0.277350i
$417$			1.65685i			0.0811365i
$418$	−5.82843	+	5.82843i	−0.285078	+	0.285078i
$419$	17.4142	−	17.4142i	0.850740	−	0.850740i	−0.139484	−	0.990224i	$-0.544544\pi$
$419$	17.4142	−	17.4142i	0.850740	−	0.850740i	0.990224	+	0.139484i	$0.0445445\pi$
$420$	−4.00000	−	4.00000i	−0.195180	−	0.195180i
$421$	24.6274			1.20027			0.600133	−	0.799900i	$-0.295114\pi$
$421$	24.6274			1.20027			0.600133	+	0.799900i	$0.295114\pi$
$422$	17.4142	+	17.4142i	0.847711	+	0.847711i
$423$		−	2.24264i		−	0.109041i
$424$	−9.65685			−0.468978
$425$	−3.00000	+	12.0000i	−0.145521	+	0.582086i
$426$	−12.4853			−0.604914
$427$		−	19.3137i		−	0.934656i
$428$	4.00000	+	4.00000i	0.193347	+	0.193347i
$429$	−5.65685			−0.273115
$430$	14.1421	+	14.1421i	0.681994	+	0.681994i
$431$	−18.2426	+	18.2426i	−0.878717	+	0.878717i	−0.993402	−	0.114685i	$-0.963414\pi$
$431$	−18.2426	+	18.2426i	−0.878717	+	0.878717i	0.114685	+	0.993402i	$0.463414\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	17.6569i		−	0.848534i	−0.905537	−	0.424267i	$-0.860532\pi$
$433$		−	17.6569i		−	0.848534i	0.905537	−	0.424267i	$-0.139468\pi$
$434$			6.34315i			0.304481i
$435$	−1.17157	+	1.17157i	−0.0561726	+	0.0561726i
$436$	−3.65685	+	3.65685i	−0.175132	+	0.175132i
$437$	−21.3137	−	21.3137i	−1.01957	−	1.01957i
$438$	4.48528			0.214315
$439$	−6.00000	−	6.00000i	−0.286364	−	0.286364i	0.549276	−	0.835641i	$-0.314903\pi$
$439$	−6.00000	−	6.00000i	−0.286364	−	0.286364i	−0.835641	+	0.549276i	$0.814903\pi$
$440$		−	2.82843i		−	0.134840i
$441$	−3.00000			−0.142857
$442$	5.65685	−	22.6274i	0.269069	−	1.07628i
$443$	15.2721			0.725598			0.362799	−	0.931867i	$-0.381821\pi$
$443$	15.2721			0.725598			0.362799	+	0.931867i	$0.381821\pi$
$444$		−	11.8995i		−	0.564725i
$445$	−15.3137	−	15.3137i	−0.725939	−	0.725939i
$446$	−10.1421			−0.480244
$447$	9.31371	+	9.31371i	0.440523	+	0.440523i
$448$	−1.41421	+	1.41421i	−0.0668153	+	0.0668153i
$449$	−13.7990	+	13.7990i	−0.651215	+	0.651215i	−0.953285	−	0.302071i	$-0.902322\pi$
$449$	−13.7990	+	13.7990i	−0.651215	+	0.651215i	0.302071	+	0.953285i	$0.402322\pi$
$450$		−	3.00000i		−	0.141421i
$451$			0.242641i			0.0114255i
$452$	−10.8284	+	10.8284i	−0.509326	+	0.509326i
$453$	5.24264	−	5.24264i	0.246321	−	0.246321i
$454$	12.4853	+	12.4853i	0.585963	+	0.585963i
$455$	−32.0000			−1.50018
$456$	5.82843	+	5.82843i	0.272941	+	0.272941i
$457$		−	14.9706i		−	0.700293i	−0.936695	−	0.350147i	$-0.886132\pi$
$457$		−	14.9706i		−	0.700293i	0.936695	−	0.350147i	$-0.113868\pi$
$458$	−18.8284			−0.879795
$459$	−3.53553	+	2.12132i	−0.165025	+	0.0990148i
$460$	10.3431			0.482252
$461$		−	14.1421i		−	0.658665i	−0.944214	−	0.329332i	$-0.893176\pi$
$461$		−	14.1421i		−	0.658665i	0.944214	−	0.329332i	$-0.106824\pi$
$462$	1.41421	+	1.41421i	0.0657952	+	0.0657952i
$463$	−8.97056			−0.416897			−0.208449	−	0.978033i	$-0.566841\pi$
$463$	−8.97056			−0.416897			−0.208449	+	0.978033i	$0.566841\pi$
$464$	0.414214	+	0.414214i	0.0192294	+	0.0192294i
$465$	−6.34315	+	6.34315i	−0.294156	+	0.294156i
$466$	4.65685	−	4.65685i	0.215725	−	0.215725i
$467$		−	20.2426i		−	0.936718i	−0.883538	−	0.468359i	$-0.844845\pi$
$467$		−	20.2426i		−	0.936718i	0.883538	−	0.468359i	$-0.155155\pi$
$468$			5.65685i			0.261488i
$469$	−17.6569	+	17.6569i	−0.815318	+	0.815318i
$470$	4.48528	−	4.48528i	0.206891	−	0.206891i
$471$	0.343146	+	0.343146i	0.0158113	+	0.0158113i
$472$	−0.242641			−0.0111684
$473$	−5.00000	−	5.00000i	−0.229900	−	0.229900i
$474$			6.82843i			0.313640i
$475$	−24.7279			−1.13459
$476$	−7.07107	+	4.24264i	−0.324102	+	0.194461i
$477$	9.65685			0.442157
$478$		−	21.6569i		−	0.990561i
$479$	−21.5563	−	21.5563i	−0.984935	−	0.984935i	0.0149535	−	0.999888i	$-0.495240\pi$
$479$	−21.5563	−	21.5563i	−0.984935	−	0.984935i	−0.999888	+	0.0149535i	$0.995240\pi$
$480$	−2.82843			−0.129099
$481$	−47.5980	−	47.5980i	−2.17028	−	2.17028i
$482$	−2.82843	+	2.82843i	−0.128831	+	0.128831i
$483$	−5.17157	+	5.17157i	−0.235315	+	0.235315i
$484$			1.00000i			0.0454545i
$485$			41.2548i			1.87329i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−22.0416	+	22.0416i	−0.998802	+	0.998802i	−0.999999	−	0.00119766i	$-0.999619\pi$
$487$	−22.0416	+	22.0416i	−0.998802	+	0.998802i	0.00119766	+	0.999999i	$0.499619\pi$
$488$	−6.82843	−	6.82843i	−0.309108	−	0.309108i
$489$	12.9706			0.586549
$490$	−6.00000	−	6.00000i	−0.271052	−	0.271052i
$491$		−	1.17157i		−	0.0528723i	−0.999651	−	0.0264362i	$-0.991584\pi$
$491$		−	1.17157i		−	0.0528723i	0.999651	−	0.0264362i	$-0.00841588\pi$
$492$	0.242641			0.0109391
$493$	1.24264	+	2.07107i	0.0559657	+	0.0932762i
$494$	46.6274			2.09787
$495$			2.82843i			0.127128i
$496$	2.24264	+	2.24264i	0.100698	+	0.100698i
$497$	24.9706			1.12008
$498$	3.17157	+	3.17157i	0.142122	+	0.142122i
$499$	−18.1421	+	18.1421i	−0.812154	+	0.812154i	−0.984956	−	0.172803i	$-0.944718\pi$
$499$	−18.1421	+	18.1421i	−0.812154	+	0.812154i	0.172803	+	0.984956i	$0.444718\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$			10.4853i			0.468448i
$502$		−	22.3848i		−	0.999081i
$503$	−22.7279	+	22.7279i	−1.01339	+	1.01339i	−0.0134788	+	0.999909i	$0.504291\pi$
$503$	−22.7279	+	22.7279i	−1.01339	+	1.01339i	−0.999909	+	0.0134788i	$0.995709\pi$
$504$	1.41421	−	1.41421i	0.0629941	−	0.0629941i
$505$	−12.0000	−	12.0000i	−0.533993	−	0.533993i
$506$	−3.65685			−0.162567
$507$	13.4350	+	13.4350i	0.596671	+	0.596671i
$508$			9.07107i			0.402464i
$509$	16.9706			0.752207			0.376103	−	0.926578i	$-0.377264\pi$
$509$	16.9706			0.752207			0.376103	+	0.926578i	$0.377264\pi$
$510$	−11.3137	−	2.82843i	−0.500979	−	0.125245i
$511$	−8.97056			−0.396834
$512$			1.00000i			0.0441942i
$513$	−5.82843	−	5.82843i	−0.257331	−	0.257331i
$514$	−10.9706			−0.483891
$515$	−16.0000	−	16.0000i	−0.705044	−	0.705044i
$516$	−5.00000	+	5.00000i	−0.220113	+	0.220113i
$517$	−1.58579	+	1.58579i	−0.0697428	+	0.0697428i
$518$			23.7990i			1.04567i
$519$		−	9.07107i		−	0.398176i
$520$	−11.3137	+	11.3137i	−0.496139	+	0.496139i
$521$	−18.8284	+	18.8284i	−0.824888	+	0.824888i	−0.986805	−	0.161916i	$-0.948233\pi$
$521$	−18.8284	+	18.8284i	−0.824888	+	0.824888i	0.161916	+	0.986805i	$0.448233\pi$
$522$	−0.414214	−	0.414214i	−0.0181296	−	0.0181296i
$523$	−9.41421			−0.411655			−0.205827	−	0.978588i	$-0.565989\pi$
$523$	−9.41421			−0.411655			−0.205827	+	0.978588i	$0.565989\pi$
$524$	12.4853	+	12.4853i	0.545422	+	0.545422i
$525$			6.00000i			0.261861i
$526$	26.1421			1.13985
$527$	6.72792	+	11.2132i	0.293073	+	0.488455i
$528$	1.00000			0.0435194
$529$			9.62742i			0.418583i
$530$	19.3137	+	19.3137i	0.838934	+	0.838934i
$531$	0.242641			0.0105297
$532$	−11.6569	−	11.6569i	−0.505389	−	0.505389i
$533$	0.970563	−	0.970563i	0.0420397	−	0.0420397i
$534$	5.41421	−	5.41421i	0.234296	−	0.234296i
$535$		−	16.0000i		−	0.691740i
$536$			12.4853i			0.539282i
$537$	15.1421	−	15.1421i	0.653431	−	0.653431i
$538$	−3.51472	+	3.51472i	−0.151530	+	0.151530i
$539$	2.12132	+	2.12132i	0.0913717	+	0.0913717i
$540$	2.82843			0.121716
$541$	6.82843	+	6.82843i	0.293577	+	0.293577i	0.838492	−	0.544915i	$-0.183438\pi$
$541$	6.82843	+	6.82843i	0.293577	+	0.293577i	−0.544915	+	0.838492i	$0.683438\pi$
$542$			4.58579i			0.196976i
$543$	23.2132			0.996174
$544$	−1.00000	+	4.00000i	−0.0428746	+	0.171499i
$545$	14.6274			0.626570
$546$		−	11.3137i		−	0.484182i
$547$	−18.3848	−	18.3848i	−0.786076	−	0.786076i	0.194772	−	0.980848i	$-0.437603\pi$
$547$	−18.3848	−	18.3848i	−0.786076	−	0.786076i	−0.980848	+	0.194772i	$0.937603\pi$
$548$	5.31371			0.226990
$549$	6.82843	+	6.82843i	0.291430	+	0.291430i
$550$	−2.12132	+	2.12132i	−0.0904534	+	0.0904534i
$551$	−3.41421	+	3.41421i	−0.145450	+	0.145450i
$552$			3.65685i			0.155646i
$553$		−	13.6569i		−	0.580749i
$554$	0.343146	−	0.343146i	0.0145789	−	0.0145789i
$555$	−23.7990	+	23.7990i	−1.01021	+	1.01021i
$556$	−1.17157	−	1.17157i	−0.0496858	−	0.0496858i
$557$	−45.3137			−1.92000			−0.960002	−	0.279994i	$-0.909667\pi$
$557$	−45.3137			−1.92000			−0.960002	+	0.279994i	$0.909667\pi$
$558$	−2.24264	−	2.24264i	−0.0949386	−	0.0949386i
$559$			40.0000i			1.69182i
$560$	5.65685			0.239046
$561$	4.00000	+	1.00000i	0.168880	+	0.0422200i
$562$	−5.65685			−0.238620
$563$		−	0.201010i		−	0.00847157i	−0.999991	−	0.00423578i	$-0.998652\pi$
$563$		−	0.201010i		−	0.00847157i	0.999991	−	0.00423578i	$-0.00134830\pi$
$564$	1.58579	+	1.58579i	0.0667737	+	0.0667737i
$565$	43.3137			1.82222
$566$	0.928932	+	0.928932i	0.0390459	+	0.0390459i
$567$	−1.41421	+	1.41421i	−0.0593914	+	0.0593914i
$568$	8.82843	−	8.82843i	0.370433	−	0.370433i
$569$			10.6863i			0.447993i	0.974590	+	0.223996i	$0.0719104\pi$
$569$			10.6863i			0.447993i	−0.974590	+	0.223996i	$0.928090\pi$
$570$		−	23.3137i		−	0.976504i
$571$	4.48528	−	4.48528i	0.187703	−	0.187703i	−0.606999	−	0.794702i	$-0.707627\pi$
$571$	4.48528	−	4.48528i	0.187703	−	0.187703i	0.794702	+	0.606999i	$0.207627\pi$
$572$	4.00000	−	4.00000i	0.167248	−	0.167248i
$573$	−8.41421	−	8.41421i	−0.351509	−	0.351509i
$574$	−0.485281			−0.0202553
$575$	−7.75736	−	7.75736i	−0.323504	−	0.323504i
$576$		−	1.00000i		−	0.0416667i
$577$	−36.2843			−1.51053			−0.755267	−	0.655417i	$-0.772493\pi$
$577$	−36.2843			−1.51053			−0.755267	+	0.655417i	$0.772493\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$	−12.9706			−0.539038
$580$		−	1.65685i		−	0.0687971i
$581$	−6.34315	−	6.34315i	−0.263158	−	0.263158i
$582$	−14.5858			−0.604600
$583$	−6.82843	−	6.82843i	−0.282805	−	0.282805i
$584$	−3.17157	+	3.17157i	−0.131241	+	0.131241i
$585$	11.3137	−	11.3137i	0.467764	−	0.467764i
$586$			28.6274i			1.18259i
$587$			12.9289i			0.533634i	0.963747	+	0.266817i	$0.0859720\pi$
$587$			12.9289i			0.533634i	−0.963747	+	0.266817i	$0.914028\pi$
$588$	2.12132	−	2.12132i	0.0874818	−	0.0874818i
$589$	−18.4853	+	18.4853i	−0.761673	+	0.761673i
$590$	0.485281	+	0.485281i	0.0199787	+	0.0199787i
$591$	−6.92893			−0.285018
$592$	8.41421	+	8.41421i	0.345822	+	0.345822i
$593$			1.65685i			0.0680388i	0.999421	+	0.0340194i	$0.0108308\pi$
$593$			1.65685i			0.0680388i	−0.999421	+	0.0340194i	$0.989169\pi$
$594$	−1.00000			−0.0410305
$595$	22.6274	+	5.65685i	0.927634	+	0.231908i
$596$	−13.1716			−0.539529
$597$			18.4853i			0.756552i
$598$	14.6274	+	14.6274i	0.598160	+	0.598160i
$599$	13.2721			0.542282			0.271141	−	0.962540i	$-0.412599\pi$
$599$	13.2721			0.542282			0.271141	+	0.962540i	$0.412599\pi$
$600$	2.12132	+	2.12132i	0.0866025	+	0.0866025i
$601$	−23.4558	+	23.4558i	−0.956784	+	0.956784i	−0.999104	−	0.0423203i	$-0.986525\pi$
$601$	−23.4558	+	23.4558i	−0.956784	+	0.956784i	0.0423203	+	0.999104i	$0.486525\pi$
$602$	10.0000	−	10.0000i	0.407570	−	0.407570i
$603$		−	12.4853i		−	0.508440i
$604$			7.41421i			0.301680i
$605$	2.00000	−	2.00000i	0.0813116	−	0.0813116i
$606$	4.24264	−	4.24264i	0.172345	−	0.172345i
$607$	24.8284	+	24.8284i	1.00775	+	1.00775i	0.999970	+	0.00778507i	$0.00247809\pi$
$607$	24.8284	+	24.8284i	1.00775	+	1.00775i	0.00778507	+	0.999970i	$0.497522\pi$
$608$	−8.24264			−0.334283
$609$	0.828427	+	0.828427i	0.0335696	+	0.0335696i
$610$			27.3137i			1.10590i
$611$	12.6863			0.513232
$612$	1.00000	−	4.00000i	0.0404226	−	0.161690i
$613$	45.2548			1.82783			0.913913	−	0.405911i	$-0.133046\pi$
$613$	45.2548			1.82783			0.913913	+	0.405911i	$0.133046\pi$
$614$		−	3.55635i		−	0.143523i
$615$	−0.485281	−	0.485281i	−0.0195684	−	0.0195684i
$616$	−2.00000			−0.0805823
$617$	12.4853	+	12.4853i	0.502639	+	0.502639i	0.912257	−	0.409618i	$-0.134338\pi$
$617$	12.4853	+	12.4853i	0.502639	+	0.502639i	−0.409618	+	0.912257i	$0.634338\pi$
$618$	5.65685	−	5.65685i	0.227552	−	0.227552i
$619$	−30.8284	+	30.8284i	−1.23910	+	1.23910i	−0.278729	+	0.960370i	$0.589913\pi$
$619$	−30.8284	+	30.8284i	−1.23910	+	1.23910i	−0.960370	+	0.278729i	$0.910087\pi$
$620$		−	8.97056i		−	0.360266i
$621$		−	3.65685i		−	0.146745i
$622$	−6.00000	+	6.00000i	−0.240578	+	0.240578i
$623$	−10.8284	+	10.8284i	−0.433832	+	0.433832i
$624$	−4.00000	−	4.00000i	−0.160128	−	0.160128i
$625$	31.0000			1.24000
$626$	−9.82843	−	9.82843i	−0.392823	−	0.392823i
$627$			8.24264i			0.329179i
$628$	−0.485281			−0.0193648
$629$	25.2426	+	42.0711i	1.00649	+	1.67748i
$630$	−5.65685			−0.225374
$631$		−	27.1127i		−	1.07934i	−0.841877	−	0.539670i	$-0.818549\pi$
$631$		−	27.1127i		−	1.07934i	0.841877	−	0.539670i	$-0.181451\pi$
$632$	−4.82843	−	4.82843i	−0.192065	−	0.192065i
$633$	24.6274			0.978852
$634$	18.1421	+	18.1421i	0.720516	+	0.720516i
$635$	18.1421	−	18.1421i	0.719949	−	0.719949i
$636$	−6.82843	+	6.82843i	−0.270765	+	0.270765i
$637$		−	16.9706i		−	0.672398i
$638$			0.585786i			0.0231915i
$639$	−8.82843	+	8.82843i	−0.349247	+	0.349247i
$640$	2.00000	−	2.00000i	0.0790569	−	0.0790569i
$641$	−1.51472	−	1.51472i	−0.0598278	−	0.0598278i	0.676560	−	0.736388i	$-0.263470\pi$
$641$	−1.51472	−	1.51472i	−0.0598278	−	0.0598278i	−0.736388	+	0.676560i	$0.763470\pi$
$642$	5.65685			0.223258
$643$	−20.0000	−	20.0000i	−0.788723	−	0.788723i	0.192562	−	0.981285i	$-0.438320\pi$
$643$	−20.0000	−	20.0000i	−0.788723	−	0.788723i	−0.981285	+	0.192562i	$0.938320\pi$
$644$		−	7.31371i		−	0.288200i
$645$	20.0000			0.787499
$646$	−32.9706	−	8.24264i	−1.29721	−	0.324302i
$647$	−39.8995			−1.56861			−0.784306	−	0.620375i	$-0.786981\pi$
$647$	−39.8995			−1.56861			−0.784306	+	0.620375i	$0.786981\pi$
$648$			1.00000i			0.0392837i
$649$	−0.171573	−	0.171573i	−0.00673482	−	0.00673482i
$650$	16.9706			0.665640
$651$	4.48528	+	4.48528i	0.175792	+	0.175792i
$652$	−9.17157	+	9.17157i	−0.359187	+	0.359187i
$653$	24.6274	−	24.6274i	0.963745	−	0.963745i	−0.0356201	−	0.999365i	$-0.511341\pi$
$653$	24.6274	−	24.6274i	0.963745	−	0.963745i	0.999365	+	0.0356201i	$0.0113406\pi$
$654$			5.17157i			0.202225i
$655$		−	49.9411i		−	1.95136i
$656$	−0.171573	+	0.171573i	−0.00669880	+	0.00669880i
$657$	3.17157	−	3.17157i	0.123735	−	0.123735i
$658$	−3.17157	−	3.17157i	−0.123641	−	0.123641i
$659$	17.6569			0.687813			0.343907	−	0.939004i	$-0.388250\pi$
$659$	17.6569			0.687813			0.343907	+	0.939004i	$0.388250\pi$
$660$	−2.00000	−	2.00000i	−0.0778499	−	0.0778499i
$661$			32.4853i			1.26353i	0.775160	+	0.631766i	$0.217669\pi$
$661$			32.4853i			1.26353i	−0.775160	+	0.631766i	$0.782331\pi$
$662$	−18.6274			−0.723975
$663$	−12.0000	−	20.0000i	−0.466041	−	0.776736i
$664$	−4.48528			−0.174063
$665$			46.6274i			1.80813i
$666$	−8.41421	−	8.41421i	−0.326044	−	0.326044i
$667$	−2.14214			−0.0829438
$668$	−7.41421	−	7.41421i	−0.286865	−	0.286865i
$669$	−7.17157	+	7.17157i	−0.277269	+	0.277269i
$670$	24.9706	−	24.9706i	0.964697	−	0.964697i
$671$		−	9.65685i		−	0.372799i
$672$			2.00000i			0.0771517i
$673$	27.1127	−	27.1127i	1.04512	−	1.04512i	0.0461848	−	0.998933i	$-0.485294\pi$
$673$	27.1127	−	27.1127i	1.04512	−	1.04512i	0.998933	−	0.0461848i	$-0.0147063\pi$
$674$	−20.4853	+	20.4853i	−0.789064	+	0.789064i
$675$	−2.12132	−	2.12132i	−0.0816497	−	0.0816497i
$676$	−19.0000			−0.730769
$677$	−16.0711	−	16.0711i	−0.617661	−	0.617661i	0.327270	−	0.944931i	$-0.393871\pi$
$677$	−16.0711	−	16.0711i	−0.617661	−	0.617661i	−0.944931	+	0.327270i	$0.893871\pi$
$678$			15.3137i			0.588119i
$679$	29.1716			1.11950
$680$	10.0000	−	6.00000i	0.383482	−	0.230089i
$681$	17.6569			0.676612
$682$			3.17157i			0.121446i
$683$	−11.7574	−	11.7574i	−0.449883	−	0.449883i	0.445433	−	0.895315i	$-0.353050\pi$
$683$	−11.7574	−	11.7574i	−0.449883	−	0.449883i	−0.895315	+	0.445433i	$0.853050\pi$
$684$	8.24264			0.315165
$685$	−10.6274	−	10.6274i	−0.406053	−	0.406053i
$686$	−14.1421	+	14.1421i	−0.539949	+	0.539949i
$687$	−13.3137	+	13.3137i	−0.507950	+	0.507950i
$688$		−	7.07107i		−	0.269582i
$689$			54.6274i			2.08114i
$690$	7.31371	−	7.31371i	0.278428	−	0.278428i
$691$	−10.8284	+	10.8284i	−0.411933	+	0.411933i	−0.882411	−	0.470479i	$-0.844081\pi$
$691$	−10.8284	+	10.8284i	−0.411933	+	0.411933i	0.470479	+	0.882411i	$0.344081\pi$
$692$	6.41421	+	6.41421i	0.243832	+	0.243832i
$693$	2.00000			0.0759737
$694$	20.9706	+	20.9706i	0.796032	+	0.796032i
$695$			4.68629i			0.177761i
$696$	0.585786			0.0222042
$697$	−0.857864	+	0.514719i	−0.0324939	+	0.0194964i
$698$	−8.00000			−0.302804
$699$		−	6.58579i		−	0.249097i
$700$	−4.24264	−	4.24264i	−0.160357	−	0.160357i
$701$	−3.79899			−0.143486			−0.0717429	−	0.997423i	$-0.522856\pi$
$701$	−3.79899			−0.143486			−0.0717429	+	0.997423i	$0.522856\pi$
$702$	4.00000	+	4.00000i	0.150970	+	0.150970i
$703$	−69.3553	+	69.3553i	−2.61579	+	2.61579i
$704$	−0.707107	+	0.707107i	−0.0266501	+	0.0266501i
$705$		−	6.34315i		−	0.238897i
$706$			18.0000i			0.677439i
$707$	−8.48528	+	8.48528i	−0.319122	+	0.319122i
$708$	−0.171573	+	0.171573i	−0.00644810	+	0.00644810i
$709$	8.41421	+	8.41421i	0.316002	+	0.316002i	0.847229	−	0.531227i	$-0.178269\pi$
$709$	8.41421	+	8.41421i	0.316002	+	0.316002i	−0.531227	+	0.847229i	$0.678269\pi$
$710$	−35.3137			−1.32530
$711$	4.82843	+	4.82843i	0.181080	+	0.181080i
$712$			7.65685i			0.286953i
$713$	−11.5980			−0.434348
$714$	−2.00000	+	8.00000i	−0.0748481	+	0.299392i
$715$	−16.0000			−0.598366
$716$			21.4142i			0.800287i
$717$	−15.3137	−	15.3137i	−0.571901	−	0.571901i
$718$	−3.51472			−0.131168
$719$	7.55635	+	7.55635i	0.281804	+	0.281804i	0.833828	−	0.552024i	$-0.186144\pi$
$719$	7.55635	+	7.55635i	0.281804	+	0.281804i	−0.552024	+	0.833828i	$0.686144\pi$
$720$	−2.00000	+	2.00000i	−0.0745356	+	0.0745356i
$721$	−11.3137	+	11.3137i	−0.421345	+	0.421345i
$722$		−	48.9411i		−	1.82140i
$723$			4.00000i			0.148762i
$724$	−16.4142	+	16.4142i	−0.610029	+	0.610029i
$725$	−1.24264	+	1.24264i	−0.0461505	+	0.0461505i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	−44.4853			−1.64987			−0.824934	−	0.565229i	$-0.808788\pi$
$727$	−44.4853			−1.64987			−0.824934	+	0.565229i	$0.808788\pi$
$728$	8.00000	+	8.00000i	0.296500	+	0.296500i
$729$		−	1.00000i		−	0.0370370i
$730$	12.6863			0.469541
$731$	7.07107	−	28.2843i	0.261533	−	1.04613i
$732$	−9.65685			−0.356928
$733$			32.2843i			1.19245i	0.802819	+	0.596223i	$0.203333\pi$
$733$			32.2843i			1.19245i	−0.802819	+	0.596223i	$0.796667\pi$
$734$	−17.5563	−	17.5563i	−0.648017	−	0.648017i
$735$	−8.48528			−0.312984
$736$	−2.58579	−	2.58579i	−0.0953134	−	0.0953134i
$737$	−8.82843	+	8.82843i	−0.325199	+	0.325199i
$738$	0.171573	−	0.171573i	0.00631568	−	0.00631568i
$739$		−	36.2426i		−	1.33321i	−0.745412	−	0.666604i	$-0.767747\pi$
$739$		−	36.2426i		−	1.33321i	0.745412	−	0.666604i	$-0.232253\pi$
$740$		−	33.6569i		−	1.23725i
$741$	32.9706	−	32.9706i	1.21120	−	1.21120i
$742$	13.6569	−	13.6569i	0.501359	−	0.501359i
$743$	0.585786	+	0.585786i	0.0214904	+	0.0214904i	0.717770	−	0.696280i	$-0.245163\pi$
$743$	0.585786	+	0.585786i	0.0214904	+	0.0214904i	−0.696280	+	0.717770i	$0.745163\pi$
$744$	3.17157			0.116276
$745$	26.3431	+	26.3431i	0.965138	+	0.965138i
$746$			20.9706i			0.767787i
$747$	4.48528			0.164108
$748$	−3.53553	+	2.12132i	−0.129272	+	0.0775632i
$749$	−11.3137			−0.413394
$750$			5.65685i			0.206559i
$751$	−14.2426	−	14.2426i	−0.519721	−	0.519721i	0.397766	−	0.917487i	$-0.369786\pi$
$751$	−14.2426	−	14.2426i	−0.519721	−	0.519721i	−0.917487	+	0.397766i	$0.869786\pi$
$752$	−2.24264			−0.0817807
$753$	−15.8284	−	15.8284i	−0.576820	−	0.576820i
$754$	2.34315	−	2.34315i	0.0853323	−	0.0853323i
$755$	14.8284	−	14.8284i	0.539662	−	0.539662i
$756$		−	2.00000i		−	0.0727393i
$757$		−	28.6274i		−	1.04048i	−0.854020	−	0.520241i	$-0.825842\pi$
$757$		−	28.6274i		−	1.04048i	0.854020	−	0.520241i	$-0.174158\pi$
$758$	9.17157	−	9.17157i	0.333127	−	0.333127i
$759$	−2.58579	+	2.58579i	−0.0938581	+	0.0938581i
$760$	16.4853	+	16.4853i	0.597984	+	0.597984i
$761$	−8.00000			−0.290000			−0.145000	−	0.989432i	$-0.546318\pi$
$761$	−8.00000			−0.290000			−0.145000	+	0.989432i	$0.546318\pi$
$762$	6.41421	+	6.41421i	0.232362	+	0.232362i
$763$		−	10.3431i		−	0.374447i
$764$	11.8995			0.430509
$765$	−10.0000	+	6.00000i	−0.361551	+	0.216930i
$766$	29.0711			1.05038
$767$			1.37258i			0.0495611i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−45.5980			−1.64431			−0.822153	−	0.569267i	$-0.807227\pi$
$769$	−45.5980			−1.64431			−0.822153	+	0.569267i	$0.807227\pi$
$770$	4.00000	+	4.00000i	0.144150	+	0.144150i
$771$	−7.75736	+	7.75736i	−0.279374	+	0.279374i
$772$	9.17157	−	9.17157i	0.330092	−	0.330092i
$773$		−	17.6569i		−	0.635073i	−0.948246	−	0.317536i	$-0.897144\pi$
$773$		−	17.6569i		−	0.635073i	0.948246	−	0.317536i	$-0.102856\pi$
$774$			7.07107i			0.254164i
$775$	−6.72792	+	6.72792i	−0.241674	+	0.241674i
$776$	10.3137	−	10.3137i	0.370241	−	0.370241i
$777$	16.8284	+	16.8284i	0.603716	+	0.603716i
$778$	−4.68629			−0.168012
$779$	−1.41421	−	1.41421i	−0.0506695	−	0.0506695i
$780$			16.0000i			0.572892i
$781$	12.4853			0.446758
$782$	−7.75736	−	12.9289i	−0.277403	−	0.462338i
$783$	−0.585786			−0.0209343
$784$			3.00000i			0.107143i
$785$	0.970563	+	0.970563i	0.0346409	+	0.0346409i
$786$	17.6569			0.629799
$787$	22.1421	+	22.1421i	0.789282	+	0.789282i	0.981376	−	0.192095i	$-0.0615280\pi$
$787$	22.1421	+	22.1421i	0.789282	+	0.789282i	−0.192095	+	0.981376i	$0.561528\pi$
$788$	4.89949	−	4.89949i	0.174537	−	0.174537i
$789$	18.4853	−	18.4853i	0.658093	−	0.658093i
$790$			19.3137i			0.687151i
$791$		−	30.6274i		−	1.08899i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	−38.6274	+	38.6274i	−1.37170	+	1.37170i
$794$	−18.5563	−	18.5563i	−0.658540	−	0.658540i
$795$	27.3137			0.968717
$796$	−13.0711	−	13.0711i	−0.463292	−	0.463292i
$797$		−	42.6274i		−	1.50994i	−0.655759	−	0.754970i	$-0.727651\pi$
$797$		−	42.6274i		−	1.50994i	0.655759	−	0.754970i	$-0.272349\pi$
$798$	−16.4853			−0.583573
$799$	−8.97056	−	2.24264i	−0.317356	−	0.0793389i
$800$	−3.00000			−0.106066
$801$		−	7.65685i		−	0.270542i
$802$	−7.51472	−	7.51472i	−0.265354	−	0.265354i
$803$	−4.48528			−0.158282
$804$	8.82843	+	8.82843i	0.311355	+	0.311355i
$805$	−14.6274	+	14.6274i	−0.515549	+	0.515549i
$806$	12.6863	−	12.6863i	0.446856	−	0.446856i
$807$			4.97056i			0.174972i
$808$			6.00000i			0.211079i
$809$	20.1716	−	20.1716i	0.709195	−	0.709195i	−0.257171	−	0.966366i	$-0.582790\pi$
$809$	20.1716	−	20.1716i	0.709195	−	0.709195i	0.966366	+	0.257171i	$0.0827904\pi$
$810$	2.00000	−	2.00000i	0.0702728	−	0.0702728i
$811$	3.79899	+	3.79899i	0.133401	+	0.133401i	0.770654	−	0.637254i	$-0.219930\pi$
$811$	3.79899	+	3.79899i	0.133401	+	0.133401i	−0.637254	+	0.770654i	$0.719930\pi$
$812$	−1.17157			−0.0411141
$813$	3.24264	+	3.24264i	0.113724	+	0.113724i
$814$			11.8995i			0.417077i
$815$	36.6863			1.28506
$816$	2.12132	+	3.53553i	0.0742611	+	0.123768i
$817$	58.2843			2.03911
$818$		−	22.0000i		−	0.769212i
$819$	−8.00000	−	8.00000i	−0.279543	−	0.279543i
$820$	0.686292			0.0239663
$821$	9.92893	+	9.92893i	0.346522	+	0.346522i	0.858812	−	0.512290i	$-0.171203\pi$
$821$	9.92893	+	9.92893i	0.346522	+	0.346522i	−0.512290	+	0.858812i	$0.671203\pi$
$822$	3.75736	−	3.75736i	0.131053	−	0.131053i
$823$	21.7574	−	21.7574i	0.758414	−	0.758414i	−0.217620	−	0.976034i	$-0.569829\pi$
$823$	21.7574	−	21.7574i	0.758414	−	0.758414i	0.976034	+	0.217620i	$0.0698293\pi$
$824$			8.00000i			0.278693i
$825$			3.00000i			0.104447i
$826$	0.343146	−	0.343146i	0.0119396	−	0.0119396i
$827$	1.65685	−	1.65685i	0.0576145	−	0.0576145i	−0.677713	−	0.735327i	$-0.737029\pi$
$827$	1.65685	−	1.65685i	0.0576145	−	0.0576145i	0.735327	+	0.677713i	$0.237029\pi$
$828$	2.58579	+	2.58579i	0.0898623	+	0.0898623i
$829$	21.1716			0.735319			0.367660	−	0.929960i	$-0.380159\pi$
$829$	21.1716			0.735319			0.367660	+	0.929960i	$0.380159\pi$
$830$	8.97056	+	8.97056i	0.311373	+	0.311373i
$831$		−	0.485281i		−	0.0168342i
$832$	5.65685			0.196116
$833$	−3.00000	+	12.0000i	−0.103944	+	0.415775i
$834$	−1.65685			−0.0573722
$835$			29.6569i			1.02632i
$836$	−5.82843	−	5.82843i	−0.201580	−	0.201580i
$837$	−3.17157			−0.109626
$838$	17.4142	+	17.4142i	0.601564	+	0.601564i
$839$	19.5563	−	19.5563i	0.675160	−	0.675160i	−0.283741	−	0.958901i	$-0.591576\pi$
$839$	19.5563	−	19.5563i	0.675160	−	0.675160i	0.958901	+	0.283741i	$0.0915755\pi$
$840$	4.00000	−	4.00000i	0.138013	−	0.138013i
$841$		−	28.6569i		−	0.988167i
$842$			24.6274i			0.848717i
$843$	−4.00000	+	4.00000i	−0.137767	+	0.137767i
$844$	−17.4142	+	17.4142i	−0.599422	+	0.599422i
$845$	38.0000	+	38.0000i	1.30724	+	1.30724i
$846$	2.24264			0.0771036
$847$	−1.41421	−	1.41421i	−0.0485930	−	0.0485930i
$848$		−	9.65685i		−	0.331618i
$849$	1.31371			0.0450864
$850$	−12.0000	−	3.00000i	−0.411597	−	0.102899i
$851$	−43.5147			−1.49167
$852$		−	12.4853i		−	0.427739i
$853$	−33.4558	−	33.4558i	−1.14551	−	1.14551i	−0.987426	−	0.158080i	$-0.949470\pi$
$853$	−33.4558	−	33.4558i	−1.14551	−	1.14551i	−0.158080	−	0.987426i	$-0.550530\pi$
$854$	19.3137			0.660901
$855$	−16.4853	−	16.4853i	−0.563785	−	0.563785i
$856$	−4.00000	+	4.00000i	−0.136717	+	0.136717i
$857$	21.8284	−	21.8284i	0.745645	−	0.745645i	−0.228013	−	0.973658i	$-0.573223\pi$
$857$	21.8284	−	21.8284i	0.745645	−	0.745645i	0.973658	+	0.228013i	$0.0732229\pi$
$858$		−	5.65685i		−	0.193122i
$859$		−	20.9706i		−	0.715506i	−0.933816	−	0.357753i	$-0.883543\pi$
$859$		−	20.9706i		−	0.715506i	0.933816	−	0.357753i	$-0.116457\pi$
$860$	−14.1421	+	14.1421i	−0.482243	+	0.482243i
$861$	−0.343146	+	0.343146i	−0.0116944	+	0.0116944i
$862$	−18.2426	−	18.2426i	−0.621347	−	0.621347i
$863$	16.5858			0.564587			0.282293	−	0.959328i	$-0.408905\pi$
$863$	16.5858			0.564587			0.282293	+	0.959328i	$0.408905\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$		−	25.6569i		−	0.872359i
$866$	17.6569			0.600004
$867$	4.94975	+	16.2635i	0.168102	+	0.552336i
$868$	−6.34315			−0.215300
$869$		−	6.82843i		−	0.231639i
$870$	−1.17157	−	1.17157i	−0.0397200	−	0.0397200i
$871$	70.6274			2.39312
$872$	−3.65685	−	3.65685i	−0.123837	−	0.123837i
$873$	−10.3137	+	10.3137i	−0.349066	+	0.349066i
$874$	21.3137	−	21.3137i	0.720947	−	0.720947i
$875$		−	11.3137i		−	0.382473i
$876$			4.48528i			0.151544i
$877$	−21.4558	+	21.4558i	−0.724512	+	0.724512i	−0.969521	−	0.245009i	$-0.921209\pi$
$877$	−21.4558	+	21.4558i	−0.724512	+	0.724512i	0.245009	+	0.969521i	$0.421209\pi$
$878$	6.00000	−	6.00000i	0.202490	−	0.202490i
$879$	20.2426	+	20.2426i	0.682767	+	0.682767i
$880$	2.82843			0.0953463
$881$	4.48528	+	4.48528i	0.151113	+	0.151113i	0.778615	−	0.627502i	$-0.215923\pi$
$881$	4.48528	+	4.48528i	0.151113	+	0.151113i	−0.627502	+	0.778615i	$0.715923\pi$
$882$		−	3.00000i		−	0.101015i
$883$	1.65685			0.0557576			0.0278788	−	0.999611i	$-0.491125\pi$
$883$	1.65685			0.0557576			0.0278788	+	0.999611i	$0.491125\pi$
$884$	22.6274	+	5.65685i	0.761042	+	0.190261i
$885$	0.686292			0.0230694
$886$			15.2721i			0.513075i
$887$	34.2426	+	34.2426i	1.14976	+	1.14976i	0.986600	+	0.163155i	$0.0521670\pi$
$887$	34.2426	+	34.2426i	1.14976	+	1.14976i	0.163155	+	0.986600i	$0.447833\pi$
$888$	11.8995			0.399321
$889$	−12.8284	−	12.8284i	−0.430252	−	0.430252i
$890$	15.3137	−	15.3137i	0.513317	−	0.513317i
$891$	−0.707107	+	0.707107i	−0.0236890	+	0.0236890i
$892$		−	10.1421i		−	0.339584i
$893$		−	18.4853i		−	0.618586i
$894$	−9.31371	+	9.31371i	−0.311497	+	0.311497i
$895$	42.8284	−	42.8284i	1.43160	−	1.43160i
$896$	−1.41421	−	1.41421i	−0.0472456	−	0.0472456i
$897$	20.6863			0.690695
$898$	−13.7990	−	13.7990i	−0.460478	−	0.460478i
$899$			1.85786i			0.0619632i
$900$	3.00000			0.100000
$901$	9.65685	−	38.6274i	0.321716	−	1.28687i
$902$	−0.242641			−0.00807905
$903$		−	14.1421i		−	0.470621i
$904$	−10.8284	−	10.8284i	−0.360148	−	0.360148i
$905$	65.6569			2.18251
$906$	5.24264	+	5.24264i	0.174175	+	0.174175i
$907$	7.31371	−	7.31371i	0.242848	−	0.242848i	−0.575180	−	0.818027i	$-0.695068\pi$
$907$	7.31371	−	7.31371i	0.242848	−	0.242848i	0.818027	+	0.575180i	$0.195068\pi$
$908$	−12.4853	+	12.4853i	−0.414339	+	0.414339i
$909$		−	6.00000i		−	0.199007i
$910$		−	32.0000i		−	1.06079i
$911$	−3.85786	+	3.85786i	−0.127817	+	0.127817i	−0.768121	−	0.640304i	$-0.778808\pi$
$911$	−3.85786	+	3.85786i	−0.127817	+	0.127817i	0.640304	+	0.768121i	$0.278808\pi$
$912$	−5.82843	+	5.82843i	−0.192999	+	0.192999i
$913$	−3.17157	−	3.17157i	−0.104964	−	0.104964i
$914$	14.9706			0.495182
$915$	19.3137	+	19.3137i	0.638492	+	0.638492i
$916$		−	18.8284i		−	0.622109i
$917$	−35.3137			−1.16616
$918$	−2.12132	−	3.53553i	−0.0700140	−	0.116690i
$919$	−19.8995			−0.656424			−0.328212	−	0.944604i	$-0.606446\pi$
$919$	−19.8995			−0.656424			−0.328212	+	0.944604i	$0.606446\pi$
$920$			10.3431i			0.341003i
$921$	−2.51472	−	2.51472i	−0.0828628	−	0.0828628i
$922$	14.1421			0.465746
$923$	−49.9411	−	49.9411i	−1.64383	−	1.64383i
$924$	−1.41421	+	1.41421i	−0.0465242	+	0.0465242i
$925$	−25.2426	+	25.2426i	−0.829973	+	0.829973i
$926$		−	8.97056i		−	0.294791i
$927$		−	8.00000i		−	0.262754i
$928$	−0.414214	+	0.414214i	−0.0135972	+	0.0135972i
$929$	16.4853	−	16.4853i	0.540865	−	0.540865i	−0.382918	−	0.923782i	$-0.625081\pi$
$929$	16.4853	−	16.4853i	0.540865	−	0.540865i	0.923782	+	0.382918i	$0.125081\pi$
$930$	−6.34315	−	6.34315i	−0.208000	−	0.208000i
$931$	−24.7279			−0.810425
$932$	4.65685	+	4.65685i	0.152540	+	0.152540i
$933$			8.48528i			0.277796i
$934$	20.2426			0.662359
$935$	11.3137	+	2.82843i	0.369998	+	0.0924995i
$936$	−5.65685			−0.184900
$937$		−	16.6274i		−	0.543194i	−0.962411	−	0.271597i	$-0.912448\pi$
$937$		−	16.6274i		−	0.543194i	0.962411	−	0.271597i	$-0.0875518\pi$
$938$	−17.6569	−	17.6569i	−0.576517	−	0.576517i
$939$	−13.8995			−0.453593
$940$	4.48528	+	4.48528i	0.146294	+	0.146294i
$941$	−12.2721	+	12.2721i	−0.400058	+	0.400058i	−0.878254	−	0.478195i	$-0.841291\pi$
$941$	−12.2721	+	12.2721i	−0.400058	+	0.400058i	0.478195	+	0.878254i	$0.341291\pi$
$942$	−0.343146	+	0.343146i	−0.0111803	+	0.0111803i
$943$		−	0.887302i		−	0.0288945i
$944$		−	0.242641i		−	0.00789728i
$945$	−4.00000	+	4.00000i	−0.130120	+	0.130120i
$946$	5.00000	−	5.00000i	0.162564	−	0.162564i
$947$	−8.92893	−	8.92893i	−0.290151	−	0.290151i	0.546989	−	0.837140i	$-0.315774\pi$
$947$	−8.92893	−	8.92893i	−0.290151	−	0.290151i	−0.837140	+	0.546989i	$0.815774\pi$
$948$	−6.82843			−0.221777
$949$	17.9411	+	17.9411i	0.582394	+	0.582394i
$950$		−	24.7279i		−	0.802280i
$951$	25.6569			0.831981
$952$	−4.24264	−	7.07107i	−0.137505	−	0.229175i
$953$	−7.37258			−0.238821			−0.119411	−	0.992845i	$-0.538101\pi$
$953$	−7.37258			−0.238821			−0.119411	+	0.992845i	$0.538101\pi$
$954$			9.65685i			0.312652i
$955$	−23.7990	−	23.7990i	−0.770117	−	0.770117i
$956$	21.6569			0.700433
$957$	0.414214	+	0.414214i	0.0133896	+	0.0133896i
$958$	21.5563	−	21.5563i	0.696454	−	0.696454i
$959$	−7.51472	+	7.51472i	−0.242663	+	0.242663i
$960$		−	2.82843i		−	0.0912871i
$961$		−	20.9411i		−	0.675520i
$962$	47.5980	−	47.5980i	1.53462	−	1.53462i
$963$	4.00000	−	4.00000i	0.128898	−	0.128898i
$964$	−2.82843	−	2.82843i	−0.0910975	−	0.0910975i
$965$	−36.6863			−1.18097
$966$	−5.17157	−	5.17157i	−0.166393	−	0.166393i
$967$			29.5563i			0.950468i	0.879859	+	0.475234i	$0.157637\pi$
$967$			29.5563i			0.950468i	−0.879859	+	0.475234i	$0.842363\pi$
$968$	−1.00000			−0.0321412
$969$	−29.1421	+	17.4853i	−0.936180	+	0.561708i
$970$	−41.2548			−1.32461
$971$			51.1543i			1.64162i	0.571201	+	0.820810i	$0.306478\pi$
$971$			51.1543i			1.64162i	−0.571201	+	0.820810i	$0.693522\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	3.31371			0.106233
$974$	−22.0416	−	22.0416i	−0.706259	−	0.706259i
$975$	12.0000	−	12.0000i	0.384308	−	0.384308i
$976$	6.82843	−	6.82843i	0.218573	−	0.218573i
$977$			20.6274i			0.659930i	0.943993	+	0.329965i	$0.107037\pi$
$977$			20.6274i			0.659930i	−0.943993	+	0.329965i	$0.892963\pi$
$978$			12.9706i			0.414753i
$979$	−5.41421	+	5.41421i	−0.173039	+	0.173039i
$980$	6.00000	−	6.00000i	0.191663	−	0.191663i
$981$	3.65685	+	3.65685i	0.116754	+	0.116754i
$982$	1.17157			0.0373864
$983$	−24.0416	−	24.0416i	−0.766809	−	0.766809i	0.210734	−	0.977543i	$-0.432414\pi$
$983$	−24.0416	−	24.0416i	−0.766809	−	0.766809i	−0.977543	+	0.210734i	$0.932414\pi$
$984$			0.242641i			0.00773510i
$985$	−19.5980			−0.624444
$986$	−2.07107	+	1.24264i	−0.0659562	+	0.0395737i
$987$	−4.48528			−0.142768
$988$			46.6274i			1.48342i
$989$	18.2843	+	18.2843i	0.581406	+	0.581406i
$990$	−2.82843			−0.0898933
$991$	15.4142	+	15.4142i	0.489649	+	0.489649i	0.908195	−	0.418547i	$-0.137460\pi$
$991$	15.4142	+	15.4142i	0.489649	+	0.489649i	−0.418547	+	0.908195i	$0.637460\pi$
$992$	−2.24264	+	2.24264i	−0.0712039	+	0.0712039i
$993$	−13.1716	+	13.1716i	−0.417987	+	0.417987i
$994$			24.9706i			0.792018i
$995$			52.2843i			1.65752i
$996$	−3.17157	+	3.17157i	−0.100495	+	0.100495i
$997$	25.1716	−	25.1716i	0.797192	−	0.797192i	−0.185460	−	0.982652i	$-0.559378\pi$
$997$	25.1716	−	25.1716i	0.797192	−	0.797192i	0.982652	+	0.185460i	$0.0593775\pi$
$998$	−18.1421	−	18.1421i	−0.574279	−	0.574279i
$999$	−11.8995			−0.376483

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.00000 + 2.00000i) q^{10} +(0.707107 - 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} -5.65685 q^{13} +(1.41421 + 1.41421i) q^{14} +2.82843i q^{15} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} -1.00000 q^{18} +8.24264i q^{19} +(-2.00000 - 2.00000i) q^{20} +2.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-2.58579 + 2.58579i) q^{23} +(0.707107 - 0.707107i) q^{24} +3.00000i q^{25} -5.65685i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(0.414214 + 0.414214i) q^{29} -2.82843 q^{30} +(2.24264 + 2.24264i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(-1.00000 + 4.00000i) q^{34} +5.65685 q^{35} -1.00000i q^{36} +(8.41421 + 8.41421i) q^{37} -8.24264 q^{38} +(-4.00000 - 4.00000i) q^{39} +(2.00000 - 2.00000i) q^{40} +(-0.171573 + 0.171573i) q^{41} +2.00000i q^{42} -7.07107i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(-2.58579 - 2.58579i) q^{46} -2.24264 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} -3.00000 q^{50} +(2.12132 + 3.53553i) q^{51} +5.65685 q^{52} -9.65685i q^{53} +(-0.707107 - 0.707107i) q^{54} +2.82843 q^{55} +(-1.41421 - 1.41421i) q^{56} +(-5.82843 + 5.82843i) q^{57} +(-0.414214 + 0.414214i) q^{58} -0.242641i q^{59} -2.82843i q^{60} +(6.82843 - 6.82843i) q^{61} +(-2.24264 + 2.24264i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(-11.3137 - 11.3137i) q^{65} +1.00000i q^{66} -12.4853 q^{67} +(-4.00000 - 1.00000i) q^{68} -3.65685 q^{69} +5.65685i q^{70} +(8.82843 + 8.82843i) q^{71} +1.00000 q^{72} +(-3.17157 - 3.17157i) q^{73} +(-8.41421 + 8.41421i) q^{74} +(-2.12132 + 2.12132i) q^{75} -8.24264i q^{76} -2.00000i q^{77} +(4.00000 - 4.00000i) q^{78} +(4.82843 - 4.82843i) q^{79} +(2.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(-0.171573 - 0.171573i) q^{82} -4.48528i q^{83} -2.00000 q^{84} +(6.00000 + 10.0000i) q^{85} +7.07107 q^{86} +0.585786i q^{87} +(-0.707107 - 0.707107i) q^{88} -7.65685 q^{89} +(-2.00000 - 2.00000i) q^{90} +(-8.00000 + 8.00000i) q^{91} +(2.58579 - 2.58579i) q^{92} +3.17157i q^{93} -2.24264i q^{94} +(-16.4853 + 16.4853i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(10.3137 + 10.3137i) q^{97} -3.00000 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^5	\( 4 q - 4 q^{4} + 8 q^{5} - 8 q^{10} + 4 q^{16} + 16 q^{17} - 4 q^{18} - 8 q^{20} + 8 q^{21} - 16 q^{23} - 4 q^{29} - 8 q^{31} + 4 q^{33} - 4 q^{34} + 28 q^{37} - 16 q^{38} - 16 q^{39} + 8 q^{40} - 12 q^{41} - 8 q^{45} - 16 q^{46} + 8 q^{47} - 12 q^{50} - 12 q^{57} + 4 q^{58} + 16 q^{61} + 8 q^{62} - 4 q^{64} - 16 q^{67} - 16 q^{68} + 8 q^{69} + 24 q^{71} + 4 q^{72} - 24 q^{73} - 28 q^{74} + 16 q^{78} + 8 q^{79} + 8 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} + 24 q^{85} - 8 q^{89} - 8 q^{90} - 32 q^{91} + 16 q^{92} - 32 q^{95} - 4 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^5 - 8 * q^10 + 4 * q^16 + 16 * q^17 - 4 * q^18 - 8 * q^20 + 8 * q^21 - 16 * q^23 - 4 * q^29 - 8 * q^31 + 4 * q^33 - 4 * q^34 + 28 * q^37 - 16 * q^38 - 16 * q^39 + 8 * q^40 - 12 * q^41 - 8 * q^45 - 16 * q^46 + 8 * q^47 - 12 * q^50 - 12 * q^57 + 4 * q^58 + 16 * q^61 + 8 * q^62 - 4 * q^64 - 16 * q^67 - 16 * q^68 + 8 * q^69 + 24 * q^71 + 4 * q^72 - 24 * q^73 - 28 * q^74 + 16 * q^78 + 8 * q^79 + 8 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 + 24 * q^85 - 8 * q^89 - 8 * q^90 - 32 * q^91 + 16 * q^92 - 32 * q^95 - 4 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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