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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.41421 - 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.41421 - 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} +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} +6.82843 q^{13} +(-1.41421 - 1.41421i) q^{14} -3.41421i q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} +1.00000 q^{18} +(2.41421 + 2.41421i) q^{20} +2.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-1.41421 + 1.41421i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.65685i q^{25} -6.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(-6.41421 - 6.41421i) q^{29} -3.41421 q^{30} +(-5.41421 - 5.41421i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} -6.82843 q^{35} -1.00000i q^{36} +(-6.41421 - 6.41421i) q^{37} +(4.82843 + 4.82843i) q^{39} +(2.41421 - 2.41421i) q^{40} +(3.00000 - 3.00000i) q^{41} -2.00000i q^{42} -6.82843i q^{43} +(0.707107 - 0.707107i) q^{44} +(2.41421 - 2.41421i) q^{45} +(1.41421 + 1.41421i) q^{46} -9.65685 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} +6.65685 q^{50} +(3.53553 - 2.12132i) q^{51} -6.82843 q^{52} +12.4853i q^{53} +(0.707107 + 0.707107i) q^{54} +3.41421 q^{55} +(1.41421 + 1.41421i) q^{56} +(-6.41421 + 6.41421i) q^{58} +3.41421i q^{60} +(0.757359 - 0.757359i) q^{61} +(-5.41421 + 5.41421i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(-16.4853 - 16.4853i) q^{65} +1.00000i q^{66} +8.48528 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{69} +6.82843i q^{70} +(-11.0711 - 11.0711i) q^{71} -1.00000 q^{72} +(4.65685 + 4.65685i) q^{73} +(-6.41421 + 6.41421i) q^{74} +(-4.70711 + 4.70711i) q^{75} +2.00000i q^{77} +(4.82843 - 4.82843i) q^{78} +(8.24264 - 8.24264i) q^{79} +(-2.41421 - 2.41421i) q^{80} -1.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} -2.82843i q^{83} -2.00000 q^{84} +(-12.0711 + 7.24264i) q^{85} -6.82843 q^{86} -9.07107i q^{87} +(-0.707107 - 0.707107i) q^{88} +17.6569 q^{89} +(-2.41421 - 2.41421i) q^{90} +(9.65685 - 9.65685i) q^{91} +(1.41421 - 1.41421i) q^{92} -7.65685i q^{93} +9.65685i q^{94} +(0.707107 - 0.707107i) q^{96} +(7.48528 + 7.48528i) q^{97} +3.00000 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^5	$ 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} - 20 q^{29} - 8 q^{30} - 16 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{35} - 20 q^{37} + 8 q^{39} + 4 q^{40} + 12 q^{41} + 4 q^{45} - 16 q^{47} + 4 q^{50} - 16 q^{52} + 8 q^{55} - 20 q^{58} + 20 q^{61} - 16 q^{62} - 4 q^{64} - 32 q^{65} - 4 q^{68} - 8 q^{69} - 16 q^{71} - 4 q^{72} - 4 q^{73} - 20 q^{74} - 16 q^{75} + 8 q^{78} + 16 q^{79} - 4 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} - 20 q^{85} - 16 q^{86} + 48 q^{89} - 4 q^{90} + 16 q^{91} - 4 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 - 20 * q^29 - 8 * q^30 - 16 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^35 - 20 * q^37 + 8 * q^39 + 4 * q^40 + 12 * q^41 + 4 * q^45 - 16 * q^47 + 4 * q^50 - 16 * q^52 + 8 * q^55 - 20 * q^58 + 20 * q^61 - 16 * q^62 - 4 * q^64 - 32 * q^65 - 4 * q^68 - 8 * q^69 - 16 * q^71 - 4 * q^72 - 4 * q^73 - 20 * q^74 - 16 * q^75 + 8 * q^78 + 16 * q^79 - 4 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 - 20 * q^85 - 16 * q^86 + 48 * q^89 - 4 * q^90 + 16 * q^91 - 4 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.41421	−	2.41421i	−1.07967	−	1.07967i	−0.996539	−	0.0831305i	$-0.973508\pi$
$5$	−2.41421	−	2.41421i	−1.07967	−	1.07967i	−0.0831305	−	0.996539i	$-0.526492\pi$
$6$	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
$10$	−2.41421	+	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
$13$	6.82843			1.89386			0.946932	−	0.321433i	$-0.104164\pi$
$13$	6.82843			1.89386			0.946932	+	0.321433i	$0.104164\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		−	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			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	2.41421	+	2.41421i	0.539835	+	0.539835i
$21$	2.00000			0.436436
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	−1.41421	+	1.41421i	−0.294884	+	0.294884i	−0.839006	−	0.544122i	$-0.816863\pi$
$23$	−1.41421	+	1.41421i	−0.294884	+	0.294884i	0.544122	+	0.839006i	$0.316863\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			6.65685i			1.33137i
$26$		−	6.82843i		−	1.33916i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.41421	+	1.41421i	−0.267261	+	0.267261i
$29$	−6.41421	−	6.41421i	−1.19109	−	1.19109i	−0.976762	−	0.214328i	$-0.931244\pi$
$29$	−6.41421	−	6.41421i	−1.19109	−	1.19109i	−0.214328	−	0.976762i	$-0.568756\pi$
$30$	−3.41421			−0.623347
$31$	−5.41421	−	5.41421i	−0.972421	−	0.972421i	0.0272083	−	0.999630i	$-0.491338\pi$
$31$	−5.41421	−	5.41421i	−0.972421	−	0.972421i	−0.999630	+	0.0272083i	$0.991338\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.00000			−0.174078
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$	−6.82843			−1.15421
$36$		−	1.00000i		−	0.166667i
$37$	−6.41421	−	6.41421i	−1.05449	−	1.05449i	−0.998427	−	0.0560630i	$-0.982145\pi$
$37$	−6.41421	−	6.41421i	−1.05449	−	1.05449i	−0.0560630	−	0.998427i	$-0.517855\pi$
$38$		0			0
$39$	4.82843	+	4.82843i	0.773167	+	0.773167i
$40$	2.41421	−	2.41421i	0.381721	−	0.381721i
$41$	3.00000	−	3.00000i	0.468521	−	0.468521i	−0.432914	−	0.901435i	$-0.642515\pi$
$41$	3.00000	−	3.00000i	0.468521	−	0.468521i	0.901435	+	0.432914i	$0.142515\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	6.82843i		−	1.04133i	−0.853762	−	0.520663i	$-0.825685\pi$
$43$		−	6.82843i		−	1.04133i	0.853762	−	0.520663i	$-0.174315\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	2.41421	−	2.41421i	0.359890	−	0.359890i
$46$	1.41421	+	1.41421i	0.208514	+	0.208514i
$47$	−9.65685			−1.40860			−0.704298	−	0.709904i	$-0.748738\pi$
$47$	−9.65685			−1.40860			−0.704298	+	0.709904i	$0.748738\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			3.00000i			0.428571i
$50$	6.65685			0.941421
$51$	3.53553	−	2.12132i	0.495074	−	0.297044i
$52$	−6.82843			−0.946932
$53$			12.4853i			1.71499i	0.514496	+	0.857493i	$0.327979\pi$
$53$			12.4853i			1.71499i	−0.514496	+	0.857493i	$0.672021\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	3.41421			0.460372
$56$	1.41421	+	1.41421i	0.188982	+	0.188982i
$57$		0			0
$58$	−6.41421	+	6.41421i	−0.842228	+	0.842228i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$			3.41421i			0.440773i
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	−0.656958	−	0.753928i	$-0.728157\pi$
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	0.753928	+	0.656958i	$0.228157\pi$
$62$	−5.41421	+	5.41421i	−0.687606	+	0.687606i
$63$	1.41421	+	1.41421i	0.178174	+	0.178174i
$64$	−1.00000			−0.125000
$65$	−16.4853	−	16.4853i	−2.04475	−	2.04475i
$66$			1.00000i			0.123091i
$67$	8.48528			1.03664			0.518321	−	0.855186i	$-0.326557\pi$
$67$	8.48528			1.03664			0.518321	+	0.855186i	$0.326557\pi$
$68$	−1.00000	+	4.00000i	−0.121268	+	0.485071i
$69$	−2.00000			−0.240772
$70$			6.82843i			0.816153i
$71$	−11.0711	−	11.0711i	−1.31389	−	1.31389i	−0.918520	−	0.395374i	$-0.870615\pi$
$71$	−11.0711	−	11.0711i	−1.31389	−	1.31389i	−0.395374	−	0.918520i	$-0.629385\pi$
$72$	−1.00000			−0.117851
$73$	4.65685	+	4.65685i	0.545044	+	0.545044i	0.925003	−	0.379960i	$-0.124062\pi$
$73$	4.65685	+	4.65685i	0.545044	+	0.545044i	−0.379960	+	0.925003i	$0.624062\pi$
$74$	−6.41421	+	6.41421i	−0.745637	+	0.745637i
$75$	−4.70711	+	4.70711i	−0.543530	+	0.543530i
$76$		0			0
$77$			2.00000i			0.227921i
$78$	4.82843	−	4.82843i	0.546712	−	0.546712i
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	−0.0701658	−	0.997535i	$-0.522353\pi$
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	0.997535	+	0.0701658i	$0.0223528\pi$
$80$	−2.41421	−	2.41421i	−0.269917	−	0.269917i
$81$	−1.00000			−0.111111
$82$	−3.00000	−	3.00000i	−0.331295	−	0.331295i
$83$		−	2.82843i		−	0.310460i	−0.987878	−	0.155230i	$-0.950388\pi$
$83$		−	2.82843i		−	0.310460i	0.987878	−	0.155230i	$-0.0496119\pi$
$84$	−2.00000			−0.218218
$85$	−12.0711	+	7.24264i	−1.30929	+	0.785575i
$86$	−6.82843			−0.736328
$87$		−	9.07107i		−	0.972521i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	17.6569			1.87162			0.935811	−	0.352501i	$-0.114669\pi$
$89$	17.6569			1.87162			0.935811	+	0.352501i	$0.114669\pi$
$90$	−2.41421	−	2.41421i	−0.254480	−	0.254480i
$91$	9.65685	−	9.65685i	1.01231	−	1.01231i
$92$	1.41421	−	1.41421i	0.147442	−	0.147442i
$93$		−	7.65685i		−	0.793979i
$94$			9.65685i			0.996028i
$95$		0			0
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	7.48528	+	7.48528i	0.760015	+	0.760015i	0.976325	−	0.216310i	$-0.0694021\pi$
$97$	7.48528	+	7.48528i	0.760015	+	0.760015i	−0.216310	+	0.976325i	$0.569402\pi$
$98$	3.00000			0.303046
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$		−	6.65685i		−	0.665685i
$101$	12.4853			1.24233			0.621166	−	0.783679i	$-0.286659\pi$
$101$	12.4853			1.24233			0.621166	+	0.783679i	$0.286659\pi$
$102$	−2.12132	−	3.53553i	−0.210042	−	0.350070i
$103$	−10.8284			−1.06696			−0.533478	−	0.845814i	$-0.679115\pi$
$103$	−10.8284			−1.06696			−0.533478	+	0.845814i	$0.679115\pi$
$104$			6.82843i			0.669582i
$105$	−4.82843	−	4.82843i	−0.471206	−	0.471206i
$106$	12.4853			1.21268
$107$	5.17157	+	5.17157i	0.499955	+	0.499955i	0.911424	−	0.411469i	$-0.134984\pi$
$107$	5.17157	+	5.17157i	0.499955	+	0.499955i	−0.411469	+	0.911424i	$0.634984\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−0.414214	+	0.414214i	−0.0396745	+	0.0396745i	−0.726666	−	0.686991i	$-0.758931\pi$
$109$	−0.414214	+	0.414214i	−0.0396745	+	0.0396745i	0.686991	+	0.726666i	$0.258931\pi$
$110$		−	3.41421i		−	0.325532i
$111$		−	9.07107i		−	0.860988i
$112$	1.41421	−	1.41421i	0.133631	−	0.133631i
$113$	5.82843	−	5.82843i	0.548292	−	0.548292i	−0.377654	−	0.925947i	$-0.623269\pi$
$113$	5.82843	−	5.82843i	0.548292	−	0.548292i	0.925947	+	0.377654i	$0.123269\pi$
$114$		0			0
$115$	6.82843			0.636754
$116$	6.41421	+	6.41421i	0.595545	+	0.595545i
$117$			6.82843i			0.631288i
$118$		0			0
$119$	−4.24264	−	7.07107i	−0.388922	−	0.648204i
$120$	3.41421			0.311674
$121$		−	1.00000i		−	0.0909091i
$122$	−0.757359	−	0.757359i	−0.0685681	−	0.0685681i
$123$	4.24264			0.382546
$124$	5.41421	+	5.41421i	0.486211	+	0.486211i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	1.41421	−	1.41421i	0.125988	−	0.125988i
$127$		−	9.17157i		−	0.813845i	−0.913463	−	0.406923i	$-0.866602\pi$
$127$		−	9.17157i		−	0.813845i	0.913463	−	0.406923i	$-0.133398\pi$
$128$			1.00000i			0.0883883i
$129$	4.82843	−	4.82843i	0.425119	−	0.425119i
$130$	−16.4853	+	16.4853i	−1.44585	+	1.44585i
$131$	−1.17157	−	1.17157i	−0.102361	−	0.102361i	0.654072	−	0.756433i	$-0.273059\pi$
$131$	−1.17157	−	1.17157i	−0.102361	−	0.102361i	−0.756433	+	0.654072i	$0.773059\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$		−	8.48528i		−	0.733017i
$135$	3.41421			0.293849
$136$	4.00000	+	1.00000i	0.342997	+	0.0857493i
$137$	−8.00000			−0.683486			−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000			−0.683486			−0.341743	+	0.939793i	$0.611017\pi$
$138$			2.00000i			0.170251i
$139$	1.65685	+	1.65685i	0.140533	+	0.140533i	0.773873	−	0.633341i	$-0.218317\pi$
$139$	1.65685	+	1.65685i	0.140533	+	0.140533i	−0.633341	+	0.773873i	$0.718317\pi$
$140$	6.82843			0.577107
$141$	−6.82843	−	6.82843i	−0.575057	−	0.575057i
$142$	−11.0711	+	11.0711i	−0.929063	+	0.929063i
$143$	−4.82843	+	4.82843i	−0.403773	+	0.403773i
$144$			1.00000i			0.0833333i
$145$			30.9706i			2.57197i
$146$	4.65685	−	4.65685i	0.385404	−	0.385404i
$147$	−2.12132	+	2.12132i	−0.174964	+	0.174964i
$148$	6.41421	+	6.41421i	0.527245	+	0.527245i
$149$	−9.31371			−0.763009			−0.381504	−	0.924367i	$-0.624594\pi$
$149$	−9.31371			−0.763009			−0.381504	+	0.924367i	$0.624594\pi$
$150$	4.70711	+	4.70711i	0.384334	+	0.384334i
$151$			1.17157i			0.0953412i	0.998863	+	0.0476706i	$0.0151798\pi$
$151$			1.17157i			0.0953412i	−0.998863	+	0.0476706i	$0.984820\pi$
$152$		0			0
$153$	4.00000	+	1.00000i	0.323381	+	0.0808452i
$154$	2.00000			0.161165
$155$			26.1421i			2.09979i
$156$	−4.82843	−	4.82843i	−0.386584	−	0.386584i
$157$	−13.3137			−1.06255			−0.531275	−	0.847200i	$-0.678287\pi$
$157$	−13.3137			−1.06255			−0.531275	+	0.847200i	$0.678287\pi$
$158$	−8.24264	−	8.24264i	−0.655749	−	0.655749i
$159$	−8.82843	+	8.82843i	−0.700140	+	0.700140i
$160$	−2.41421	+	2.41421i	−0.190860	+	0.190860i
$161$			4.00000i			0.315244i
$162$			1.00000i			0.0785674i
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	−0.956465	−	0.291847i	$-0.905730\pi$
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	0.291847	+	0.956465i	$0.405730\pi$
$164$	−3.00000	+	3.00000i	−0.234261	+	0.234261i
$165$	2.41421	+	2.41421i	0.187946	+	0.187946i
$166$	−2.82843			−0.219529
$167$	0.928932	+	0.928932i	0.0718829	+	0.0718829i	0.742134	−	0.670251i	$-0.233814\pi$
$167$	0.928932	+	0.928932i	0.0718829	+	0.0718829i	−0.670251	+	0.742134i	$0.733814\pi$
$168$			2.00000i			0.154303i
$169$	33.6274			2.58672
$170$	7.24264	+	12.0711i	0.555485	+	0.925809i
$171$		0			0
$172$			6.82843i			0.520663i
$173$	11.2426	+	11.2426i	0.854762	+	0.854762i	0.990715	−	0.135953i	$-0.0434097\pi$
$173$	11.2426	+	11.2426i	0.854762	+	0.854762i	−0.135953	+	0.990715i	$0.543410\pi$
$174$	−9.07107			−0.687676
$175$	9.41421	+	9.41421i	0.711648	+	0.711648i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$		0			0
$178$		−	17.6569i		−	1.32344i
$179$		−	18.1421i		−	1.35601i	−0.735059	−	0.678003i	$-0.762845\pi$
$179$		−	18.1421i		−	1.35601i	0.735059	−	0.678003i	$-0.237155\pi$
$180$	−2.41421	+	2.41421i	−0.179945	+	0.179945i
$181$	1.58579	−	1.58579i	0.117871	−	0.117871i	−0.645711	−	0.763582i	$-0.723439\pi$
$181$	1.58579	−	1.58579i	0.117871	−	0.117871i	0.763582	+	0.645711i	$0.223439\pi$
$182$	−9.65685	−	9.65685i	−0.715814	−	0.715814i
$183$	1.07107			0.0791756
$184$	−1.41421	−	1.41421i	−0.104257	−	0.104257i
$185$			30.9706i			2.27700i
$186$	−7.65685			−0.561428
$187$	2.12132	+	3.53553i	0.155126	+	0.258544i
$188$	9.65685			0.704298
$189$			2.00000i			0.145479i
$190$		0			0
$191$	25.6569			1.85646			0.928232	−	0.372001i	$-0.121328\pi$
$191$	25.6569			1.85646			0.928232	+	0.372001i	$0.121328\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−1.48528	+	1.48528i	−0.106913	+	0.106913i	−0.758540	−	0.651627i	$-0.774087\pi$
$193$	−1.48528	+	1.48528i	−0.106913	+	0.106913i	0.651627	+	0.758540i	$0.274087\pi$
$194$	7.48528	−	7.48528i	0.537412	−	0.537412i
$195$		−	23.3137i		−	1.66953i
$196$		−	3.00000i		−	0.214286i
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	−0.749987	−	0.661453i	$-0.769940\pi$
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	0.661453	+	0.749987i	$0.269940\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	9.89949	+	9.89949i	0.701757	+	0.701757i	0.964787	−	0.263031i	$-0.0847221\pi$
$199$	9.89949	+	9.89949i	0.701757	+	0.701757i	−0.263031	+	0.964787i	$0.584722\pi$
$200$	−6.65685			−0.470711
$201$	6.00000	+	6.00000i	0.423207	+	0.423207i
$202$		−	12.4853i		−	0.878461i
$203$	−18.1421			−1.27333
$204$	−3.53553	+	2.12132i	−0.247537	+	0.148522i
$205$	−14.4853			−1.01170
$206$			10.8284i			0.754452i
$207$	−1.41421	−	1.41421i	−0.0982946	−	0.0982946i
$208$	6.82843			0.473466
$209$		0			0
$210$	−4.82843	+	4.82843i	−0.333193	+	0.333193i
$211$	−14.8284	+	14.8284i	−1.02083	+	1.02083i	−0.0210527	+	0.999778i	$0.506702\pi$
$211$	−14.8284	+	14.8284i	−1.02083	+	1.02083i	−0.999778	+	0.0210527i	$0.993298\pi$
$212$		−	12.4853i		−	0.857493i
$213$		−	15.6569i		−	1.07279i
$214$	5.17157	−	5.17157i	0.353521	−	0.353521i
$215$	−16.4853	+	16.4853i	−1.12429	+	1.12429i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−15.3137			−1.03956
$218$	0.414214	+	0.414214i	0.0280541	+	0.0280541i
$219$			6.58579i			0.445026i
$220$	−3.41421			−0.230186
$221$	6.82843	−	27.3137i	0.459330	−	1.83732i
$222$	−9.07107			−0.608810
$223$		−	8.48528i		−	0.568216i	−0.958792	−	0.284108i	$-0.908302\pi$
$223$		−	8.48528i		−	0.568216i	0.958792	−	0.284108i	$-0.0916975\pi$
$224$	−1.41421	−	1.41421i	−0.0944911	−	0.0944911i
$225$	−6.65685			−0.443790
$226$	−5.82843	−	5.82843i	−0.387701	−	0.387701i
$227$	18.1421	−	18.1421i	1.20414	−	1.20414i	0.231239	−	0.972897i	$-0.425722\pi$
$227$	18.1421	−	18.1421i	1.20414	−	1.20414i	0.972897	−	0.231239i	$-0.0742779\pi$
$228$		0			0
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$		−	6.82843i		−	0.450253i
$231$	−1.41421	+	1.41421i	−0.0930484	+	0.0930484i
$232$	6.41421	−	6.41421i	0.421114	−	0.421114i
$233$	13.4853	+	13.4853i	0.883450	+	0.883450i	0.993884	−	0.110433i	$-0.0352239\pi$
$233$	13.4853	+	13.4853i	0.883450	+	0.883450i	−0.110433	+	0.993884i	$0.535224\pi$
$234$	6.82843			0.446388
$235$	23.3137	+	23.3137i	1.52082	+	1.52082i
$236$		0			0
$237$	11.6569			0.757194
$238$	−7.07107	+	4.24264i	−0.458349	+	0.275010i
$239$	−2.82843			−0.182956			−0.0914779	−	0.995807i	$-0.529159\pi$
$239$	−2.82843			−0.182956			−0.0914779	+	0.995807i	$0.529159\pi$
$240$		−	3.41421i		−	0.220387i
$241$	−5.48528	−	5.48528i	−0.353338	−	0.353338i	0.508012	−	0.861350i	$-0.330381\pi$
$241$	−5.48528	−	5.48528i	−0.353338	−	0.353338i	−0.861350	+	0.508012i	$0.830381\pi$
$242$	−1.00000			−0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−0.757359	+	0.757359i	−0.0484850	+	0.0484850i
$245$	7.24264	−	7.24264i	0.462715	−	0.462715i
$246$		−	4.24264i		−	0.270501i
$247$		0			0
$248$	5.41421	−	5.41421i	0.343803	−	0.343803i
$249$	2.00000	−	2.00000i	0.126745	−	0.126745i
$250$	−4.00000	−	4.00000i	−0.252982	−	0.252982i
$251$	−18.1421			−1.14512			−0.572561	−	0.819862i	$-0.694050\pi$
$251$	−18.1421			−1.14512			−0.572561	+	0.819862i	$0.694050\pi$
$252$	−1.41421	−	1.41421i	−0.0890871	−	0.0890871i
$253$		−	2.00000i		−	0.125739i
$254$	−9.17157			−0.575476
$255$	−13.6569	−	3.41421i	−0.855225	−	0.213806i
$256$	1.00000			0.0625000
$257$		−	17.3137i		−	1.08000i	−0.841665	−	0.540000i	$-0.818424\pi$
$257$		−	17.3137i		−	1.08000i	0.841665	−	0.540000i	$-0.181576\pi$
$258$	−4.82843	−	4.82843i	−0.300605	−	0.300605i
$259$	−18.1421			−1.12730
$260$	16.4853	+	16.4853i	1.02237	+	1.02237i
$261$	6.41421	−	6.41421i	0.397030	−	0.397030i
$262$	−1.17157	+	1.17157i	−0.0723800	+	0.0723800i
$263$			16.4853i			1.01653i	0.861202	+	0.508263i	$0.169712\pi$
$263$			16.4853i			1.01653i	−0.861202	+	0.508263i	$0.830288\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	30.1421	−	30.1421i	1.85162	−	1.85162i
$266$		0			0
$267$	12.4853	+	12.4853i	0.764087	+	0.764087i
$268$	−8.48528			−0.518321
$269$	−0.0710678	−	0.0710678i	−0.00433308	−	0.00433308i	0.704937	−	0.709270i	$-0.250975\pi$
$269$	−0.0710678	−	0.0710678i	−0.00433308	−	0.00433308i	−0.709270	+	0.704937i	$0.750975\pi$
$270$		−	3.41421i		−	0.207782i
$271$	−6.82843			−0.414797			−0.207399	−	0.978256i	$-0.566500\pi$
$271$	−6.82843			−0.414797			−0.207399	+	0.978256i	$0.566500\pi$
$272$	1.00000	−	4.00000i	0.0606339	−	0.242536i
$273$	13.6569			0.826550
$274$			8.00000i			0.483298i
$275$	−4.70711	−	4.70711i	−0.283849	−	0.283849i
$276$	2.00000			0.120386
$277$	−3.58579	−	3.58579i	−0.215449	−	0.215449i	0.591128	−	0.806577i	$-0.298683\pi$
$277$	−3.58579	−	3.58579i	−0.215449	−	0.215449i	−0.806577	+	0.591128i	$0.798683\pi$
$278$	1.65685	−	1.65685i	0.0993715	−	0.0993715i
$279$	5.41421	−	5.41421i	0.324140	−	0.324140i
$280$		−	6.82843i		−	0.408077i
$281$		−	29.6569i		−	1.76918i	−0.466370	−	0.884590i	$-0.654438\pi$
$281$		−	29.6569i		−	1.76918i	0.466370	−	0.884590i	$-0.345562\pi$
$282$	−6.82843	+	6.82843i	−0.406627	+	0.406627i
$283$	−9.65685	+	9.65685i	−0.574040	+	0.574040i	−0.933255	−	0.359215i	$-0.883045\pi$
$283$	−9.65685	+	9.65685i	−0.574040	+	0.574040i	0.359215	+	0.933255i	$0.383045\pi$
$284$	11.0711	+	11.0711i	0.656947	+	0.656947i
$285$		0			0
$286$	4.82843	+	4.82843i	0.285511	+	0.285511i
$287$		−	8.48528i		−	0.500870i
$288$	1.00000			0.0589256
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	30.9706			1.81865
$291$			10.5858i			0.620550i
$292$	−4.65685	−	4.65685i	−0.272522	−	0.272522i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	2.12132	+	2.12132i	0.123718	+	0.123718i
$295$		0			0
$296$	6.41421	−	6.41421i	0.372819	−	0.372819i
$297$		−	1.00000i		−	0.0580259i
$298$			9.31371i			0.539529i
$299$	−9.65685	+	9.65685i	−0.558470	+	0.558470i
$300$	4.70711	−	4.70711i	0.271765	−	0.271765i
$301$	−9.65685	−	9.65685i	−0.556612	−	0.556612i
$302$	1.17157			0.0674164
$303$	8.82843	+	8.82843i	0.507180	+	0.507180i
$304$		0			0
$305$	−3.65685			−0.209391
$306$	1.00000	−	4.00000i	0.0571662	−	0.228665i
$307$	1.17157			0.0668652			0.0334326	−	0.999441i	$-0.489356\pi$
$307$	1.17157			0.0668652			0.0334326	+	0.999441i	$0.489356\pi$
$308$		−	2.00000i		−	0.113961i
$309$	−7.65685	−	7.65685i	−0.435583	−	0.435583i
$310$	26.1421			1.48477
$311$	17.8995	+	17.8995i	1.01499	+	1.01499i	0.999886	+	0.0151013i	$0.00480707\pi$
$311$	17.8995	+	17.8995i	1.01499	+	1.01499i	0.0151013	+	0.999886i	$0.495193\pi$
$312$	−4.82843	+	4.82843i	−0.273356	+	0.273356i
$313$	21.4853	−	21.4853i	1.21442	−	1.21442i	0.244862	−	0.969558i	$-0.421257\pi$
$313$	21.4853	−	21.4853i	1.21442	−	1.21442i	0.969558	−	0.244862i	$-0.0787426\pi$
$314$			13.3137i			0.751336i
$315$		−	6.82843i		−	0.384738i
$316$	−8.24264	+	8.24264i	−0.463685	+	0.463685i
$317$	14.8995	−	14.8995i	0.836839	−	0.836839i	−0.151603	−	0.988442i	$-0.548443\pi$
$317$	14.8995	−	14.8995i	0.836839	−	0.836839i	0.988442	+	0.151603i	$0.0484434\pi$
$318$	8.82843	+	8.82843i	0.495074	+	0.495074i
$319$	9.07107			0.507882
$320$	2.41421	+	2.41421i	0.134959	+	0.134959i
$321$			7.31371i			0.408211i
$322$	4.00000			0.222911
$323$		0			0
$324$	1.00000			0.0555556
$325$			45.4558i			2.52144i
$326$	8.48528	+	8.48528i	0.469956	+	0.469956i
$327$	−0.585786			−0.0323941
$328$	3.00000	+	3.00000i	0.165647	+	0.165647i
$329$	−13.6569	+	13.6569i	−0.752927	+	0.752927i
$330$	2.41421	−	2.41421i	0.132898	−	0.132898i
$331$		−	4.97056i		−	0.273207i	−0.990626	−	0.136603i	$-0.956381\pi$
$331$		−	4.97056i		−	0.273207i	0.990626	−	0.136603i	$-0.0436186\pi$
$332$			2.82843i			0.155230i
$333$	6.41421	−	6.41421i	0.351497	−	0.351497i
$334$	0.928932	−	0.928932i	0.0508289	−	0.0508289i
$335$	−20.4853	−	20.4853i	−1.11923	−	1.11923i
$336$	2.00000			0.109109
$337$	19.9706	+	19.9706i	1.08787	+	1.08787i	0.995748	+	0.0921178i	$0.0293636\pi$
$337$	19.9706	+	19.9706i	1.08787	+	1.08787i	0.0921178	+	0.995748i	$0.470636\pi$
$338$		−	33.6274i		−	1.82909i
$339$	8.24264			0.447679
$340$	12.0711	−	7.24264i	0.654646	−	0.392787i
$341$	7.65685			0.414642
$342$		0			0
$343$	14.1421	+	14.1421i	0.763604	+	0.763604i
$344$	6.82843			0.368164
$345$	4.82843	+	4.82843i	0.259954	+	0.259954i
$346$	11.2426	−	11.2426i	0.604408	−	0.604408i
$347$	−18.1421	+	18.1421i	−0.973921	+	0.973921i	−0.999668	−	0.0257476i	$-0.991803\pi$
$347$	−18.1421	+	18.1421i	−0.973921	+	0.973921i	0.0257476	+	0.999668i	$0.491803\pi$
$348$			9.07107i			0.486260i
$349$		−	4.48528i		−	0.240092i	−0.992768	−	0.120046i	$-0.961696\pi$
$349$		−	4.48528i		−	0.240092i	0.992768	−	0.120046i	$-0.0383041\pi$
$350$	9.41421	−	9.41421i	0.503211	−	0.503211i
$351$	−4.82843	+	4.82843i	−0.257722	+	0.257722i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	16.6274			0.884988			0.442494	−	0.896771i	$-0.354094\pi$
$353$	16.6274			0.884988			0.442494	+	0.896771i	$0.354094\pi$
$354$		0			0
$355$			53.4558i			2.83714i
$356$	−17.6569			−0.935811
$357$	2.00000	−	8.00000i	0.105851	−	0.423405i
$358$	−18.1421			−0.958842
$359$			16.0000i			0.844448i	0.906492	+	0.422224i	$0.138750\pi$
$359$			16.0000i			0.844448i	−0.906492	+	0.422224i	$0.861250\pi$
$360$	2.41421	+	2.41421i	0.127240	+	0.127240i
$361$	19.0000			1.00000
$362$	−1.58579	−	1.58579i	−0.0833471	−	0.0833471i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$	−9.65685	+	9.65685i	−0.506157	+	0.506157i
$365$		−	22.4853i		−	1.17693i
$366$		−	1.07107i		−	0.0559856i
$367$	−3.75736	+	3.75736i	−0.196133	+	0.196133i	−0.798340	−	0.602207i	$-0.794288\pi$
$367$	−3.75736	+	3.75736i	−0.196133	+	0.196133i	0.602207	+	0.798340i	$0.294288\pi$
$368$	−1.41421	+	1.41421i	−0.0737210	+	0.0737210i
$369$	3.00000	+	3.00000i	0.156174	+	0.156174i
$370$	30.9706			1.61008
$371$	17.6569	+	17.6569i	0.916698	+	0.916698i
$372$			7.65685i			0.396989i
$373$	22.8284			1.18201			0.591006	−	0.806667i	$-0.298731\pi$
$373$	22.8284			1.18201			0.591006	+	0.806667i	$0.298731\pi$
$374$	3.53553	−	2.12132i	0.182818	−	0.109691i
$375$	5.65685			0.292119
$376$		−	9.65685i		−	0.498014i
$377$	−43.7990	−	43.7990i	−2.25576	−	2.25576i
$378$	2.00000			0.102869
$379$	13.6569	+	13.6569i	0.701505	+	0.701505i	0.964734	−	0.263228i	$-0.0847872\pi$
$379$	13.6569	+	13.6569i	0.701505	+	0.701505i	−0.263228	+	0.964734i	$0.584787\pi$
$380$		0			0
$381$	6.48528	−	6.48528i	0.332251	−	0.332251i
$382$		−	25.6569i		−	1.31272i
$383$		−	25.6569i		−	1.31100i	−0.755193	−	0.655502i	$-0.772457\pi$
$383$		−	25.6569i		−	1.31100i	0.755193	−	0.655502i	$-0.227543\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	4.82843	−	4.82843i	0.246079	−	0.246079i
$386$	1.48528	+	1.48528i	0.0755988	+	0.0755988i
$387$	6.82843			0.347108
$388$	−7.48528	−	7.48528i	−0.380008	−	0.380008i
$389$			12.3431i			0.625822i	0.949782	+	0.312911i	$0.101304\pi$
$389$			12.3431i			0.625822i	−0.949782	+	0.312911i	$0.898696\pi$
$390$	−23.3137			−1.18054
$391$	4.24264	+	7.07107i	0.214560	+	0.357599i
$392$	−3.00000			−0.151523
$393$		−	1.65685i		−	0.0835772i
$394$	1.24264	+	1.24264i	0.0626033	+	0.0626033i
$395$	−39.7990			−2.00250
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−3.10051	+	3.10051i	−0.155610	+	0.155610i	−0.780618	−	0.625008i	$-0.785096\pi$
$397$	−3.10051	+	3.10051i	−0.155610	+	0.155610i	0.625008	+	0.780618i	$0.285096\pi$
$398$	9.89949	−	9.89949i	0.496217	−	0.496217i
$399$		0			0
$400$			6.65685i			0.332843i
$401$	−18.3137	+	18.3137i	−0.914543	+	0.914543i	−0.996626	−	0.0820826i	$-0.973843\pi$
$401$	−18.3137	+	18.3137i	−0.914543	+	0.914543i	0.0820826	+	0.996626i	$0.473843\pi$
$402$	6.00000	−	6.00000i	0.299253	−	0.299253i
$403$	−36.9706	−	36.9706i	−1.84163	−	1.84163i
$404$	−12.4853			−0.621166
$405$	2.41421	+	2.41421i	0.119963	+	0.119963i
$406$			18.1421i			0.900379i
$407$	9.07107			0.449636
$408$	2.12132	+	3.53553i	0.105021	+	0.175035i
$409$	−9.31371			−0.460533			−0.230267	−	0.973128i	$-0.573960\pi$
$409$	−9.31371			−0.460533			−0.230267	+	0.973128i	$0.573960\pi$
$410$			14.4853i			0.715377i
$411$	−5.65685	−	5.65685i	−0.279032	−	0.279032i
$412$	10.8284			0.533478
$413$		0			0
$414$	−1.41421	+	1.41421i	−0.0695048	+	0.0695048i
$415$	−6.82843	+	6.82843i	−0.335194	+	0.335194i
$416$		−	6.82843i		−	0.334791i
$417$			2.34315i			0.114744i
$418$		0			0
$419$	−0.686292	+	0.686292i	−0.0335275	+	0.0335275i	−0.723672	−	0.690144i	$-0.757547\pi$
$419$	−0.686292	+	0.686292i	−0.0335275	+	0.0335275i	0.690144	+	0.723672i	$0.257547\pi$
$420$	4.82843	+	4.82843i	0.235603	+	0.235603i
$421$	26.1421			1.27409			0.637045	−	0.770827i	$-0.280157\pi$
$421$	26.1421			1.27409			0.637045	+	0.770827i	$0.280157\pi$
$422$	14.8284	+	14.8284i	0.721837	+	0.721837i
$423$		−	9.65685i		−	0.469532i
$424$	−12.4853			−0.606339
$425$	26.6274	+	6.65685i	1.29162	+	0.322905i
$426$	−15.6569			−0.758577
$427$		−	2.14214i		−	0.103665i
$428$	−5.17157	−	5.17157i	−0.249977	−	0.249977i
$429$	−6.82843			−0.329680
$430$	16.4853	+	16.4853i	0.794991	+	0.794991i
$431$	9.41421	−	9.41421i	0.453467	−	0.453467i	−0.443037	−	0.896503i	$-0.646099\pi$
$431$	9.41421	−	9.41421i	0.453467	−	0.453467i	0.896503	+	0.443037i	$0.146099\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$			15.3137i			0.735082i
$435$	−21.8995	+	21.8995i	−1.05000	+	1.05000i
$436$	0.414214	−	0.414214i	0.0198372	−	0.0198372i
$437$		0			0
$438$	6.58579			0.314681
$439$	−26.3848	−	26.3848i	−1.25928	−	1.25928i	−0.951439	−	0.307838i	$-0.900395\pi$
$439$	−26.3848	−	26.3848i	−1.25928	−	1.25928i	−0.307838	−	0.951439i	$-0.599605\pi$
$440$			3.41421i			0.162766i
$441$	−3.00000			−0.142857
$442$	−27.3137	−	6.82843i	−1.29918	−	0.324795i
$443$	7.79899			0.370541			0.185271	−	0.982688i	$-0.440684\pi$
$443$	7.79899			0.370541			0.185271	+	0.982688i	$0.440684\pi$
$444$			9.07107i			0.430494i
$445$	−42.6274	−	42.6274i	−2.02073	−	2.02073i
$446$	−8.48528			−0.401790
$447$	−6.58579	−	6.58579i	−0.311497	−	0.311497i
$448$	−1.41421	+	1.41421i	−0.0668153	+	0.0668153i
$449$	16.6569	−	16.6569i	0.786086	−	0.786086i	−0.194764	−	0.980850i	$-0.562394\pi$
$449$	16.6569	−	16.6569i	0.786086	−	0.786086i	0.980850	+	0.194764i	$0.0623943\pi$
$450$			6.65685i			0.313807i
$451$			4.24264i			0.199778i
$452$	−5.82843	+	5.82843i	−0.274146	+	0.274146i
$453$	−0.828427	+	0.828427i	−0.0389229	+	0.0389229i
$454$	−18.1421	−	18.1421i	−0.851453	−	0.851453i
$455$	−46.6274			−2.18593
$456$		0			0
$457$			2.68629i			0.125659i	0.998024	+	0.0628297i	$0.0200125\pi$
$457$			2.68629i			0.125659i	−0.998024	+	0.0628297i	$0.979988\pi$
$458$	18.0000			0.841085
$459$	2.12132	+	3.53553i	0.0990148	+	0.165025i
$460$	−6.82843			−0.318377
$461$			4.48528i			0.208900i	0.994530	+	0.104450i	$0.0333083\pi$
$461$			4.48528i			0.208900i	−0.994530	+	0.104450i	$0.966692\pi$
$462$	1.41421	+	1.41421i	0.0657952	+	0.0657952i
$463$	2.82843			0.131448			0.0657241	−	0.997838i	$-0.479064\pi$
$463$	2.82843			0.131448			0.0657241	+	0.997838i	$0.479064\pi$
$464$	−6.41421	−	6.41421i	−0.297772	−	0.297772i
$465$	−18.4853	+	18.4853i	−0.857234	+	0.857234i
$466$	13.4853	−	13.4853i	0.624694	−	0.624694i
$467$			30.8284i			1.42657i	0.700874	+	0.713285i	$0.252793\pi$
$467$			30.8284i			1.42657i	−0.700874	+	0.713285i	$0.747207\pi$
$468$		−	6.82843i		−	0.315644i
$469$	12.0000	−	12.0000i	0.554109	−	0.554109i
$470$	23.3137	−	23.3137i	1.07538	−	1.07538i
$471$	−9.41421	−	9.41421i	−0.433784	−	0.433784i
$472$		0			0
$473$	4.82843	+	4.82843i	0.222011	+	0.222011i
$474$		−	11.6569i		−	0.535417i
$475$		0			0
$476$	4.24264	+	7.07107i	0.194461	+	0.324102i
$477$	−12.4853			−0.571662
$478$			2.82843i			0.129369i
$479$	16.7279	+	16.7279i	0.764318	+	0.764318i	0.977100	−	0.212782i	$-0.0682523\pi$
$479$	16.7279	+	16.7279i	0.764318	+	0.764318i	−0.212782	+	0.977100i	$0.568252\pi$
$480$	−3.41421			−0.155837
$481$	−43.7990	−	43.7990i	−1.99706	−	1.99706i
$482$	−5.48528	+	5.48528i	−0.249848	+	0.249848i
$483$	−2.82843	+	2.82843i	−0.128698	+	0.128698i
$484$			1.00000i			0.0454545i
$485$		−	36.1421i		−	1.64113i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	20.2426	−	20.2426i	0.917282	−	0.917282i	−0.0795493	−	0.996831i	$-0.525348\pi$
$487$	20.2426	−	20.2426i	0.917282	−	0.917282i	0.996831	+	0.0795493i	$0.0253481\pi$
$488$	0.757359	+	0.757359i	0.0342840	+	0.0342840i
$489$	−12.0000			−0.542659
$490$	−7.24264	−	7.24264i	−0.327189	−	0.327189i
$491$			25.6569i			1.15788i	0.815371	+	0.578939i	$0.196533\pi$
$491$			25.6569i			1.15788i	−0.815371	+	0.578939i	$0.803467\pi$
$492$	−4.24264			−0.191273
$493$	−32.0711	+	19.2426i	−1.44441	+	0.866645i
$494$		0			0
$495$			3.41421i			0.153457i
$496$	−5.41421	−	5.41421i	−0.243105	−	0.243105i
$497$	−31.3137			−1.40461
$498$	−2.00000	−	2.00000i	−0.0896221	−	0.0896221i
$499$	−7.51472	+	7.51472i	−0.336405	+	0.336405i	−0.855012	−	0.518607i	$-0.826451\pi$
$499$	−7.51472	+	7.51472i	−0.336405	+	0.336405i	0.518607	+	0.855012i	$0.326451\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$			1.31371i			0.0586922i
$502$			18.1421i			0.809723i
$503$	8.92893	−	8.92893i	0.398121	−	0.398121i	−0.479449	−	0.877570i	$-0.659163\pi$
$503$	8.92893	−	8.92893i	0.398121	−	0.398121i	0.877570	+	0.479449i	$0.159163\pi$
$504$	−1.41421	+	1.41421i	−0.0629941	+	0.0629941i
$505$	−30.1421	−	30.1421i	−1.34131	−	1.34131i
$506$	−2.00000			−0.0889108
$507$	23.7782	+	23.7782i	1.05603	+	1.05603i
$508$			9.17157i			0.406923i
$509$	−8.34315			−0.369803			−0.184902	−	0.982757i	$-0.559197\pi$
$509$	−8.34315			−0.369803			−0.184902	+	0.982757i	$0.559197\pi$
$510$	−3.41421	+	13.6569i	−0.151184	+	0.604736i
$511$	13.1716			0.582676
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−17.3137			−0.763675
$515$	26.1421	+	26.1421i	1.15196	+	1.15196i
$516$	−4.82843	+	4.82843i	−0.212560	+	0.212560i
$517$	6.82843	−	6.82843i	0.300314	−	0.300314i
$518$			18.1421i			0.797120i
$519$			15.8995i			0.697910i
$520$	16.4853	−	16.4853i	0.722927	−	0.722927i
$521$	−14.3137	+	14.3137i	−0.627095	+	0.627095i	−0.947336	−	0.320241i	$-0.896236\pi$
$521$	−14.3137	+	14.3137i	−0.627095	+	0.627095i	0.320241	+	0.947336i	$0.396236\pi$
$522$	−6.41421	−	6.41421i	−0.280743	−	0.280743i
$523$	11.3137			0.494714			0.247357	−	0.968924i	$-0.420438\pi$
$523$	11.3137			0.494714			0.247357	+	0.968924i	$0.420438\pi$
$524$	1.17157	+	1.17157i	0.0511804	+	0.0511804i
$525$			13.3137i			0.581058i
$526$	16.4853			0.718792
$527$	−27.0711	+	16.2426i	−1.17923	+	0.707541i
$528$	−1.00000			−0.0435194
$529$			19.0000i			0.826087i
$530$	−30.1421	−	30.1421i	−1.30929	−	1.30929i
$531$		0			0
$532$		0			0
$533$	20.4853	−	20.4853i	0.887316	−	0.887316i
$534$	12.4853	−	12.4853i	0.540291	−	0.540291i
$535$		−	24.9706i		−	1.07957i
$536$			8.48528i			0.366508i
$537$	12.8284	−	12.8284i	0.553587	−	0.553587i
$538$	−0.0710678	+	0.0710678i	−0.00306395	+	0.00306395i
$539$	−2.12132	−	2.12132i	−0.0913717	−	0.0913717i
$540$	−3.41421			−0.146924
$541$	6.41421	+	6.41421i	0.275769	+	0.275769i	0.831417	−	0.555649i	$-0.187530\pi$
$541$	6.41421	+	6.41421i	0.275769	+	0.275769i	−0.555649	+	0.831417i	$0.687530\pi$
$542$			6.82843i			0.293306i
$543$	2.24264			0.0962409
$544$	−4.00000	−	1.00000i	−0.171499	−	0.0428746i
$545$	2.00000			0.0856706
$546$		−	13.6569i		−	0.584459i
$547$	6.14214	+	6.14214i	0.262619	+	0.262619i	0.826117	−	0.563498i	$-0.190545\pi$
$547$	6.14214	+	6.14214i	0.262619	+	0.262619i	−0.563498	+	0.826117i	$0.690545\pi$
$548$	8.00000			0.341743
$549$	0.757359	+	0.757359i	0.0323233	+	0.0323233i
$550$	−4.70711	+	4.70711i	−0.200712	+	0.200712i
$551$		0			0
$552$		−	2.00000i		−	0.0851257i
$553$		−	23.3137i		−	0.991400i
$554$	−3.58579	+	3.58579i	−0.152345	+	0.152345i
$555$	−21.8995	+	21.8995i	−0.929582	+	0.929582i
$556$	−1.65685	−	1.65685i	−0.0702663	−	0.0702663i
$557$	−3.51472			−0.148923			−0.0744617	−	0.997224i	$-0.523724\pi$
$557$	−3.51472			−0.148923			−0.0744617	+	0.997224i	$0.523724\pi$
$558$	−5.41421	−	5.41421i	−0.229202	−	0.229202i
$559$		−	46.6274i		−	1.97213i
$560$	−6.82843			−0.288554
$561$	−1.00000	+	4.00000i	−0.0422200	+	0.168880i
$562$	−29.6569			−1.25100
$563$			41.4558i			1.74716i	0.486685	+	0.873578i	$0.338206\pi$
$563$			41.4558i			1.74716i	−0.486685	+	0.873578i	$0.661794\pi$
$564$	6.82843	+	6.82843i	0.287529	+	0.287529i
$565$	−28.1421			−1.18395
$566$	9.65685	+	9.65685i	0.405908	+	0.405908i
$567$	−1.41421	+	1.41421i	−0.0593914	+	0.0593914i
$568$	11.0711	−	11.0711i	0.464532	−	0.464532i
$569$		−	29.9411i		−	1.25520i	−0.778537	−	0.627599i	$-0.784038\pi$
$569$		−	29.9411i		−	1.25520i	0.778537	−	0.627599i	$-0.215962\pi$
$570$		0			0
$571$	−8.00000	+	8.00000i	−0.334790	+	0.334790i	−0.854402	−	0.519612i	$-0.826076\pi$
$571$	−8.00000	+	8.00000i	−0.334790	+	0.334790i	0.519612	+	0.854402i	$0.326076\pi$
$572$	4.82843	−	4.82843i	0.201887	−	0.201887i
$573$	18.1421	+	18.1421i	0.757899	+	0.757899i
$574$	−8.48528			−0.354169
$575$	−9.41421	−	9.41421i	−0.392600	−	0.392600i
$576$		−	1.00000i		−	0.0416667i
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$	−2.10051			−0.0872940
$580$		−	30.9706i		−	1.28598i
$581$	−4.00000	−	4.00000i	−0.165948	−	0.165948i
$582$	10.5858			0.438795
$583$	−8.82843	−	8.82843i	−0.365636	−	0.365636i
$584$	−4.65685	+	4.65685i	−0.192702	+	0.192702i
$585$	16.4853	−	16.4853i	0.681582	−	0.681582i
$586$		−	14.0000i		−	0.578335i
$587$			29.4558i			1.21577i	0.794024	+	0.607886i	$0.207982\pi$
$587$			29.4558i			1.21577i	−0.794024	+	0.607886i	$0.792018\pi$
$588$	2.12132	−	2.12132i	0.0874818	−	0.0874818i
$589$		0			0
$590$		0			0
$591$	−1.75736			−0.0722881
$592$	−6.41421	−	6.41421i	−0.263623	−	0.263623i
$593$			40.2843i			1.65428i	0.561998	+	0.827138i	$0.310033\pi$
$593$			40.2843i			1.65428i	−0.561998	+	0.827138i	$0.689967\pi$
$594$	−1.00000			−0.0410305
$595$	−6.82843	+	27.3137i	−0.279938	+	1.11975i
$596$	9.31371			0.381504
$597$			14.0000i			0.572982i
$598$	9.65685	+	9.65685i	0.394898	+	0.394898i
$599$	27.5147			1.12422			0.562110	−	0.827062i	$-0.309990\pi$
$599$	27.5147			1.12422			0.562110	+	0.827062i	$0.309990\pi$
$600$	−4.70711	−	4.70711i	−0.192167	−	0.192167i
$601$	7.00000	−	7.00000i	0.285536	−	0.285536i	−0.549776	−	0.835312i	$-0.685287\pi$
$601$	7.00000	−	7.00000i	0.285536	−	0.285536i	0.835312	+	0.549776i	$0.185287\pi$
$602$	−9.65685	+	9.65685i	−0.393584	+	0.393584i
$603$			8.48528i			0.345547i
$604$		−	1.17157i		−	0.0476706i
$605$	−2.41421	+	2.41421i	−0.0981517	+	0.0981517i
$606$	8.82843	−	8.82843i	0.358630	−	0.358630i
$607$	−11.7574	−	11.7574i	−0.477216	−	0.477216i	0.427024	−	0.904240i	$-0.359562\pi$
$607$	−11.7574	−	11.7574i	−0.477216	−	0.477216i	−0.904240	+	0.427024i	$0.859562\pi$
$608$		0			0
$609$	−12.8284	−	12.8284i	−0.519834	−	0.519834i
$610$			3.65685i			0.148062i
$611$	−65.9411			−2.66769
$612$	−4.00000	−	1.00000i	−0.161690	−	0.0404226i
$613$	−34.2843			−1.38473			−0.692364	−	0.721548i	$-0.743431\pi$
$613$	−34.2843			−1.38473			−0.692364	+	0.721548i	$0.743431\pi$
$614$		−	1.17157i		−	0.0472808i
$615$	−10.2426	−	10.2426i	−0.413023	−	0.413023i
$616$	−2.00000			−0.0805823
$617$	−3.82843	−	3.82843i	−0.154127	−	0.154127i	0.625832	−	0.779958i	$-0.284760\pi$
$617$	−3.82843	−	3.82843i	−0.154127	−	0.154127i	−0.779958	+	0.625832i	$0.784760\pi$
$618$	−7.65685	+	7.65685i	−0.308004	+	0.308004i
$619$	−22.3431	+	22.3431i	−0.898047	+	0.898047i	−0.995263	−	0.0972164i	$-0.969006\pi$
$619$	−22.3431	+	22.3431i	−0.898047	+	0.898047i	0.0972164	+	0.995263i	$0.469006\pi$
$620$		−	26.1421i		−	1.04989i
$621$		−	2.00000i		−	0.0802572i
$622$	17.8995	−	17.8995i	0.717704	−	0.717704i
$623$	24.9706	−	24.9706i	1.00042	−	1.00042i
$624$	4.82843	+	4.82843i	0.193292	+	0.193292i
$625$	13.9706			0.558823
$626$	−21.4853	−	21.4853i	−0.858725	−	0.858725i
$627$		0			0
$628$	13.3137			0.531275
$629$	−32.0711	+	19.2426i	−1.27876	+	0.767254i
$630$	−6.82843			−0.272051
$631$		−	39.1127i		−	1.55705i	−0.627612	−	0.778526i	$-0.715968\pi$
$631$		−	39.1127i		−	1.55705i	0.627612	−	0.778526i	$-0.284032\pi$
$632$	8.24264	+	8.24264i	0.327875	+	0.327875i
$633$	−20.9706			−0.833505
$634$	−14.8995	−	14.8995i	−0.591735	−	0.591735i
$635$	−22.1421	+	22.1421i	−0.878684	+	0.878684i
$636$	8.82843	−	8.82843i	0.350070	−	0.350070i
$637$			20.4853i			0.811656i
$638$		−	9.07107i		−	0.359127i
$639$	11.0711	−	11.0711i	0.437965	−	0.437965i
$640$	2.41421	−	2.41421i	0.0954302	−	0.0954302i
$641$	13.6274	+	13.6274i	0.538251	+	0.538251i	0.923015	−	0.384764i	$-0.125717\pi$
$641$	13.6274	+	13.6274i	0.538251	+	0.538251i	−0.384764	+	0.923015i	$0.625717\pi$
$642$	7.31371			0.288649
$643$	5.65685	+	5.65685i	0.223085	+	0.223085i	0.809796	−	0.586711i	$-0.199578\pi$
$643$	5.65685	+	5.65685i	0.223085	+	0.223085i	−0.586711	+	0.809796i	$0.699578\pi$
$644$		−	4.00000i		−	0.157622i
$645$	−23.3137			−0.917976
$646$		0			0
$647$	−17.6569			−0.694163			−0.347081	−	0.937835i	$-0.612827\pi$
$647$	−17.6569			−0.694163			−0.347081	+	0.937835i	$0.612827\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	45.4558			1.78292
$651$	−10.8284	−	10.8284i	−0.424400	−	0.424400i
$652$	8.48528	−	8.48528i	0.332309	−	0.332309i
$653$	12.7574	−	12.7574i	0.499234	−	0.499234i	−0.411965	−	0.911199i	$-0.635158\pi$
$653$	12.7574	−	12.7574i	0.499234	−	0.499234i	0.911199	+	0.411965i	$0.135158\pi$
$654$			0.585786i			0.0229061i
$655$			5.65685i			0.221032i
$656$	3.00000	−	3.00000i	0.117130	−	0.117130i
$657$	−4.65685	+	4.65685i	−0.181681	+	0.181681i
$658$	13.6569	+	13.6569i	0.532400	+	0.532400i
$659$	−10.8284			−0.421816			−0.210908	−	0.977506i	$-0.567642\pi$
$659$	−10.8284			−0.421816			−0.210908	+	0.977506i	$0.567642\pi$
$660$	−2.41421	−	2.41421i	−0.0939731	−	0.0939731i
$661$		−	2.14214i		−	0.0833194i	−0.999132	−	0.0416597i	$-0.986735\pi$
$661$		−	2.14214i		−	0.0833194i	0.999132	−	0.0416597i	$-0.0132645\pi$
$662$	−4.97056			−0.193186
$663$	24.1421	−	14.4853i	0.937603	−	0.562562i
$664$	2.82843			0.109764
$665$		0			0
$666$	−6.41421	−	6.41421i	−0.248546	−	0.248546i
$667$	18.1421			0.702466
$668$	−0.928932	−	0.928932i	−0.0359415	−	0.0359415i
$669$	6.00000	−	6.00000i	0.231973	−	0.231973i
$670$	−20.4853	+	20.4853i	−0.791415	+	0.791415i
$671$			1.07107i			0.0413481i
$672$		−	2.00000i		−	0.0771517i
$673$	4.51472	−	4.51472i	0.174030	−	0.174030i	−0.614718	−	0.788747i	$-0.710730\pi$
$673$	4.51472	−	4.51472i	0.174030	−	0.174030i	0.788747	+	0.614718i	$0.210730\pi$
$674$	19.9706	−	19.9706i	0.769237	−	0.769237i
$675$	−4.70711	−	4.70711i	−0.181177	−	0.181177i
$676$	−33.6274			−1.29336
$677$	23.7279	+	23.7279i	0.911938	+	0.911938i	0.996425	−	0.0844865i	$-0.0269250\pi$
$677$	23.7279	+	23.7279i	0.911938	+	0.911938i	−0.0844865	+	0.996425i	$0.526925\pi$
$678$		−	8.24264i		−	0.316557i
$679$	21.1716			0.812490
$680$	−7.24264	−	12.0711i	−0.277743	−	0.462904i
$681$	25.6569			0.983173
$682$		−	7.65685i		−	0.293196i
$683$	−13.1716	−	13.1716i	−0.503996	−	0.503996i	0.408681	−	0.912677i	$-0.365989\pi$
$683$	−13.1716	−	13.1716i	−0.503996	−	0.503996i	−0.912677	+	0.408681i	$0.865989\pi$
$684$		0			0
$685$	19.3137	+	19.3137i	0.737939	+	0.737939i
$686$	14.1421	−	14.1421i	0.539949	−	0.539949i
$687$	−12.7279	+	12.7279i	−0.485601	+	0.485601i
$688$		−	6.82843i		−	0.260331i
$689$			85.2548i			3.24795i
$690$	4.82843	−	4.82843i	0.183815	−	0.183815i
$691$	28.9706	−	28.9706i	1.10209	−	1.10209i	0.107934	−	0.994158i	$-0.465576\pi$
$691$	28.9706	−	28.9706i	1.10209	−	1.10209i	0.994158	−	0.107934i	$-0.0344235\pi$
$692$	−11.2426	−	11.2426i	−0.427381	−	0.427381i
$693$	−2.00000			−0.0759737
$694$	18.1421	+	18.1421i	0.688666	+	0.688666i
$695$		−	8.00000i		−	0.303457i
$696$	9.07107			0.343838
$697$	−9.00000	−	15.0000i	−0.340899	−	0.568166i
$698$	−4.48528			−0.169770
$699$			19.0711i			0.721334i
$700$	−9.41421	−	9.41421i	−0.355824	−	0.355824i
$701$	−13.4558			−0.508220			−0.254110	−	0.967175i	$-0.581783\pi$
$701$	−13.4558			−0.508220			−0.254110	+	0.967175i	$0.581783\pi$
$702$	4.82843	+	4.82843i	0.182237	+	0.182237i
$703$		0			0
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$			32.9706i			1.24174i
$706$		−	16.6274i		−	0.625781i
$707$	17.6569	−	17.6569i	0.664054	−	0.664054i
$708$		0			0
$709$	−23.7279	−	23.7279i	−0.891121	−	0.891121i	0.103508	−	0.994629i	$-0.466993\pi$
$709$	−23.7279	−	23.7279i	−0.891121	−	0.891121i	−0.994629	+	0.103508i	$0.966993\pi$
$710$	53.4558			2.00616
$711$	8.24264	+	8.24264i	0.309123	+	0.309123i
$712$			17.6569i			0.661719i
$713$	15.3137			0.573503
$714$	−8.00000	−	2.00000i	−0.299392	−	0.0748481i
$715$	23.3137			0.871883
$716$			18.1421i			0.678003i
$717$	−2.00000	−	2.00000i	−0.0746914	−	0.0746914i
$718$	16.0000			0.597115
$719$	−10.5858	−	10.5858i	−0.394783	−	0.394783i	0.481605	−	0.876388i	$-0.340054\pi$
$719$	−10.5858	−	10.5858i	−0.394783	−	0.394783i	−0.876388	+	0.481605i	$0.840054\pi$
$720$	2.41421	−	2.41421i	0.0899724	−	0.0899724i
$721$	−15.3137	+	15.3137i	−0.570312	+	0.570312i
$722$		−	19.0000i		−	0.707107i
$723$		−	7.75736i		−	0.288499i
$724$	−1.58579	+	1.58579i	−0.0589353	+	0.0589353i
$725$	42.6985	−	42.6985i	1.58578	−	1.58578i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−20.6863			−0.767212			−0.383606	−	0.923497i	$-0.625318\pi$
$727$	−20.6863			−0.767212			−0.383606	+	0.923497i	$0.625318\pi$
$728$	9.65685	+	9.65685i	0.357907	+	0.357907i
$729$		−	1.00000i		−	0.0370370i
$730$	−22.4853			−0.832218
$731$	−27.3137	−	6.82843i	−1.01023	−	0.252559i
$732$	−1.07107			−0.0395878
$733$		−	39.7990i		−	1.47001i	−0.678062	−	0.735005i	$-0.737180\pi$
$733$		−	39.7990i		−	1.47001i	0.678062	−	0.735005i	$-0.262820\pi$
$734$	3.75736	+	3.75736i	0.138687	+	0.138687i
$735$	10.2426			0.377805
$736$	1.41421	+	1.41421i	0.0521286	+	0.0521286i
$737$	−6.00000	+	6.00000i	−0.221013	+	0.221013i
$738$	3.00000	−	3.00000i	0.110432	−	0.110432i
$739$			51.3137i			1.88761i	0.330510	+	0.943803i	$0.392779\pi$
$739$			51.3137i			1.88761i	−0.330510	+	0.943803i	$0.607221\pi$
$740$		−	30.9706i		−	1.13850i
$741$		0			0
$742$	17.6569	−	17.6569i	0.648204	−	0.648204i
$743$	−28.0416	−	28.0416i	−1.02875	−	1.02875i	−0.999574	−	0.0291733i	$-0.990713\pi$
$743$	−28.0416	−	28.0416i	−1.02875	−	1.02875i	−0.0291733	−	0.999574i	$-0.509287\pi$
$744$	7.65685			0.280714
$745$	22.4853	+	22.4853i	0.823797	+	0.823797i
$746$		−	22.8284i		−	0.835808i
$747$	2.82843			0.103487
$748$	−2.12132	−	3.53553i	−0.0775632	−	0.129272i
$749$	14.6274			0.534474
$750$		−	5.65685i		−	0.206559i
$751$	2.58579	+	2.58579i	0.0943567	+	0.0943567i	0.752709	−	0.658353i	$-0.228746\pi$
$751$	2.58579	+	2.58579i	0.0943567	+	0.0943567i	−0.658353	+	0.752709i	$0.728746\pi$
$752$	−9.65685			−0.352149
$753$	−12.8284	−	12.8284i	−0.467494	−	0.467494i
$754$	−43.7990	+	43.7990i	−1.59507	+	1.59507i
$755$	2.82843	−	2.82843i	0.102937	−	0.102937i
$756$		−	2.00000i		−	0.0727393i
$757$			13.3137i			0.483895i	0.970289	+	0.241947i	$0.0777862\pi$
$757$			13.3137i			0.483895i	−0.970289	+	0.241947i	$0.922214\pi$
$758$	13.6569	−	13.6569i	0.496039	−	0.496039i
$759$	1.41421	−	1.41421i	0.0513327	−	0.0513327i
$760$		0			0
$761$	28.0000			1.01500			0.507500	−	0.861652i	$-0.330570\pi$
$761$	28.0000			1.01500			0.507500	+	0.861652i	$0.330570\pi$
$762$	−6.48528	−	6.48528i	−0.234937	−	0.234937i
$763$			1.17157i			0.0424138i
$764$	−25.6569			−0.928232
$765$	−7.24264	−	12.0711i	−0.261858	−	0.436430i
$766$	−25.6569			−0.927020
$767$		0			0
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	3.02944			0.109244			0.0546222	−	0.998507i	$-0.482605\pi$
$769$	3.02944			0.109244			0.0546222	+	0.998507i	$0.482605\pi$
$770$	−4.82843	−	4.82843i	−0.174004	−	0.174004i
$771$	12.2426	−	12.2426i	0.440908	−	0.440908i
$772$	1.48528	−	1.48528i	0.0534564	−	0.0534564i
$773$			18.2843i			0.657640i	0.944393	+	0.328820i	$0.106651\pi$
$773$			18.2843i			0.657640i	−0.944393	+	0.328820i	$0.893349\pi$
$774$		−	6.82843i		−	0.245443i
$775$	36.0416	−	36.0416i	1.29465	−	1.29465i
$776$	−7.48528	+	7.48528i	−0.268706	+	0.268706i
$777$	−12.8284	−	12.8284i	−0.460217	−	0.460217i
$778$	12.3431			0.442523
$779$		0			0
$780$			23.3137i			0.834765i
$781$	15.6569			0.560246
$782$	7.07107	−	4.24264i	0.252861	−	0.151717i
$783$	9.07107			0.324174
$784$			3.00000i			0.107143i
$785$	32.1421	+	32.1421i	1.14720	+	1.14720i
$786$	−1.65685			−0.0590980
$787$	−19.3137	−	19.3137i	−0.688459	−	0.688459i	0.273432	−	0.961891i	$-0.411841\pi$
$787$	−19.3137	−	19.3137i	−0.688459	−	0.688459i	−0.961891	+	0.273432i	$0.911841\pi$
$788$	1.24264	−	1.24264i	0.0442672	−	0.0442672i
$789$	−11.6569	+	11.6569i	−0.414995	+	0.414995i
$790$			39.7990i			1.41598i
$791$		−	16.4853i		−	0.586149i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	5.17157	−	5.17157i	0.183648	−	0.183648i
$794$	3.10051	+	3.10051i	0.110033	+	0.110033i
$795$	42.6274			1.51184
$796$	−9.89949	−	9.89949i	−0.350878	−	0.350878i
$797$			11.5147i			0.407872i	0.978984	+	0.203936i	$0.0653735\pi$
$797$			11.5147i			0.407872i	−0.978984	+	0.203936i	$0.934627\pi$
$798$		0			0
$799$	−9.65685	+	38.6274i	−0.341635	+	1.36654i
$800$	6.65685			0.235355
$801$			17.6569i			0.623874i
$802$	18.3137	+	18.3137i	0.646680	+	0.646680i
$803$	−6.58579			−0.232407
$804$	−6.00000	−	6.00000i	−0.211604	−	0.211604i
$805$	9.65685	−	9.65685i	0.340359	−	0.340359i
$806$	−36.9706	+	36.9706i	−1.30223	+	1.30223i
$807$		−	0.100505i		−	0.00353795i
$808$			12.4853i			0.439231i
$809$	−11.9706	+	11.9706i	−0.420863	+	0.420863i	−0.885501	−	0.464638i	$-0.846184\pi$
$809$	−11.9706	+	11.9706i	−0.420863	+	0.420863i	0.464638	+	0.885501i	$0.346184\pi$
$810$	2.41421	−	2.41421i	0.0848268	−	0.0848268i
$811$	−12.0000	−	12.0000i	−0.421377	−	0.421377i	0.464301	−	0.885678i	$-0.346306\pi$
$811$	−12.0000	−	12.0000i	−0.421377	−	0.421377i	−0.885678	+	0.464301i	$0.846306\pi$
$812$	18.1421			0.636664
$813$	−4.82843	−	4.82843i	−0.169340	−	0.169340i
$814$		−	9.07107i		−	0.317941i
$815$	40.9706			1.43514
$816$	3.53553	−	2.12132i	0.123768	−	0.0742611i
$817$		0			0
$818$			9.31371i			0.325646i
$819$	9.65685	+	9.65685i	0.337438	+	0.337438i
$820$	14.4853			0.505848
$821$	32.4142	+	32.4142i	1.13126	+	1.13126i	0.989967	+	0.141297i	$0.0451271\pi$
$821$	32.4142	+	32.4142i	1.13126	+	1.13126i	0.141297	+	0.989967i	$0.454873\pi$
$822$	−5.65685	+	5.65685i	−0.197305	+	0.197305i
$823$	−12.7279	+	12.7279i	−0.443667	+	0.443667i	−0.893243	−	0.449575i	$-0.851575\pi$
$823$	−12.7279	+	12.7279i	−0.443667	+	0.443667i	0.449575	+	0.893243i	$0.351575\pi$
$824$		−	10.8284i		−	0.377226i
$825$		−	6.65685i		−	0.231762i
$826$		0			0
$827$	9.85786	−	9.85786i	0.342792	−	0.342792i	−0.514624	−	0.857416i	$-0.672069\pi$
$827$	9.85786	−	9.85786i	0.342792	−	0.342792i	0.857416	+	0.514624i	$0.172069\pi$
$828$	1.41421	+	1.41421i	0.0491473	+	0.0491473i
$829$	1.31371			0.0456270			0.0228135	−	0.999740i	$-0.492738\pi$
$829$	1.31371			0.0456270			0.0228135	+	0.999740i	$0.492738\pi$
$830$	6.82843	+	6.82843i	0.237018	+	0.237018i
$831$		−	5.07107i		−	0.175913i
$832$	−6.82843			−0.236733
$833$	12.0000	+	3.00000i	0.415775	+	0.103944i
$834$	2.34315			0.0811365
$835$		−	4.48528i		−	0.155220i
$836$		0			0
$837$	7.65685			0.264660
$838$	0.686292	+	0.686292i	0.0237075	+	0.0237075i
$839$	−19.0711	+	19.0711i	−0.658406	+	0.658406i	−0.955003	−	0.296597i	$-0.904148\pi$
$839$	−19.0711	+	19.0711i	−0.658406	+	0.658406i	0.296597	+	0.955003i	$0.404148\pi$
$840$	4.82843	−	4.82843i	0.166597	−	0.166597i
$841$			53.2843i			1.83739i
$842$		−	26.1421i		−	0.900917i
$843$	20.9706	−	20.9706i	0.722265	−	0.722265i
$844$	14.8284	−	14.8284i	0.510416	−	0.510416i
$845$	−81.1838	−	81.1838i	−2.79281	−	2.79281i
$846$	−9.65685			−0.332009
$847$	−1.41421	−	1.41421i	−0.0485930	−	0.0485930i
$848$			12.4853i			0.428746i
$849$	−13.6569			−0.468702
$850$	6.65685	−	26.6274i	0.228328	−	0.913313i
$851$	18.1421			0.621904
$852$			15.6569i			0.536395i
$853$	−22.0711	−	22.0711i	−0.755699	−	0.755699i	0.219838	−	0.975536i	$-0.429447\pi$
$853$	−22.0711	−	22.0711i	−0.755699	−	0.755699i	−0.975536	+	0.219838i	$0.929447\pi$
$854$	−2.14214			−0.0733024
$855$		0			0
$856$	−5.17157	+	5.17157i	−0.176761	+	0.176761i
$857$	7.00000	−	7.00000i	0.239115	−	0.239115i	−0.577368	−	0.816484i	$-0.695920\pi$
$857$	7.00000	−	7.00000i	0.239115	−	0.239115i	0.816484	+	0.577368i	$0.195920\pi$
$858$			6.82843i			0.233119i
$859$		−	4.00000i		−	0.136478i	−0.997669	−	0.0682391i	$-0.978262\pi$
$859$		−	4.00000i		−	0.136478i	0.997669	−	0.0682391i	$-0.0217381\pi$
$860$	16.4853	−	16.4853i	0.562143	−	0.562143i
$861$	6.00000	−	6.00000i	0.204479	−	0.204479i
$862$	−9.41421	−	9.41421i	−0.320649	−	0.320649i
$863$	44.4853			1.51430			0.757148	−	0.653243i	$-0.226592\pi$
$863$	44.4853			1.51430			0.757148	+	0.653243i	$0.226592\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$		−	54.2843i		−	1.84572i
$866$	−2.00000			−0.0679628
$867$	−4.94975	−	16.2635i	−0.168102	−	0.552336i
$868$	15.3137			0.519781
$869$			11.6569i			0.395432i
$870$	21.8995	+	21.8995i	0.742462	+	0.742462i
$871$	57.9411			1.96326
$872$	−0.414214	−	0.414214i	−0.0140270	−	0.0140270i
$873$	−7.48528	+	7.48528i	−0.253338	+	0.253338i
$874$		0			0
$875$		−	11.3137i		−	0.382473i
$876$		−	6.58579i		−	0.222513i
$877$	12.5563	−	12.5563i	0.423998	−	0.423998i	−0.462580	−	0.886578i	$-0.653076\pi$
$877$	12.5563	−	12.5563i	0.423998	−	0.423998i	0.886578	+	0.462580i	$0.153076\pi$
$878$	−26.3848	+	26.3848i	−0.890443	+	0.890443i
$879$	9.89949	+	9.89949i	0.333902	+	0.333902i
$880$	3.41421			0.115093
$881$	−34.1127	−	34.1127i	−1.14929	−	1.14929i	−0.986693	−	0.162593i	$-0.948014\pi$
$881$	−34.1127	−	34.1127i	−1.14929	−	1.14929i	−0.162593	−	0.986693i	$-0.551986\pi$
$882$			3.00000i			0.101015i
$883$	−2.82843			−0.0951842			−0.0475921	−	0.998867i	$-0.515155\pi$
$883$	−2.82843			−0.0951842			−0.0475921	+	0.998867i	$0.515155\pi$
$884$	−6.82843	+	27.3137i	−0.229665	+	0.918659i
$885$		0			0
$886$		−	7.79899i		−	0.262012i
$887$	22.3848	+	22.3848i	0.751607	+	0.751607i	0.974779	−	0.223172i	$-0.0716411\pi$
$887$	22.3848	+	22.3848i	0.751607	+	0.751607i	−0.223172	+	0.974779i	$0.571641\pi$
$888$	9.07107			0.304405
$889$	−12.9706	−	12.9706i	−0.435019	−	0.435019i
$890$	−42.6274	+	42.6274i	−1.42887	+	1.42887i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$			8.48528i			0.284108i
$893$		0			0
$894$	−6.58579	+	6.58579i	−0.220262	+	0.220262i
$895$	−43.7990	+	43.7990i	−1.46404	+	1.46404i
$896$	1.41421	+	1.41421i	0.0472456	+	0.0472456i
$897$	−13.6569			−0.455989
$898$	−16.6569	−	16.6569i	−0.555846	−	0.555846i
$899$			69.4558i			2.31648i
$900$	6.65685			0.221895
$901$	49.9411	+	12.4853i	1.66378	+	0.415945i
$902$	4.24264			0.141264
$903$		−	13.6569i		−	0.454472i
$904$	5.82843	+	5.82843i	0.193851	+	0.193851i
$905$	−7.65685			−0.254522
$906$	0.828427	+	0.828427i	0.0275226	+	0.0275226i
$907$	36.4853	−	36.4853i	1.21147	−	1.21147i	0.240932	−	0.970542i	$-0.422547\pi$
$907$	36.4853	−	36.4853i	1.21147	−	1.21147i	0.970542	−	0.240932i	$-0.0774530\pi$
$908$	−18.1421	+	18.1421i	−0.602068	+	0.602068i
$909$			12.4853i			0.414111i
$910$			46.6274i			1.54568i
$911$	−28.0416	+	28.0416i	−0.929061	+	0.929061i	−0.997645	−	0.0685846i	$-0.978152\pi$
$911$	−28.0416	+	28.0416i	−0.929061	+	0.929061i	0.0685846	+	0.997645i	$0.478152\pi$
$912$		0			0
$913$	2.00000	+	2.00000i	0.0661903	+	0.0661903i
$914$	2.68629			0.0888546
$915$	−2.58579	−	2.58579i	−0.0854835	−	0.0854835i
$916$		−	18.0000i		−	0.594737i
$917$	−3.31371			−0.109428
$918$	3.53553	−	2.12132i	0.116690	−	0.0700140i
$919$	−36.0833			−1.19028			−0.595138	−	0.803623i	$-0.702903\pi$
$919$	−36.0833			−1.19028			−0.595138	+	0.803623i	$0.702903\pi$
$920$			6.82843i			0.225127i
$921$	0.828427	+	0.828427i	0.0272976	+	0.0272976i
$922$	4.48528			0.147715
$923$	−75.5980	−	75.5980i	−2.48834	−	2.48834i
$924$	1.41421	−	1.41421i	0.0465242	−	0.0465242i
$925$	42.6985	−	42.6985i	1.40392	−	1.40392i
$926$		−	2.82843i		−	0.0929479i
$927$		−	10.8284i		−	0.355652i
$928$	−6.41421	+	6.41421i	−0.210557	+	0.210557i
$929$	37.2843	−	37.2843i	1.22326	−	1.22326i	0.256790	−	0.966467i	$-0.417335\pi$
$929$	37.2843	−	37.2843i	1.22326	−	1.22326i	0.966467	−	0.256790i	$-0.0826649\pi$
$930$	18.4853	+	18.4853i	0.606156	+	0.606156i
$931$		0			0
$932$	−13.4853	−	13.4853i	−0.441725	−	0.441725i
$933$			25.3137i			0.828734i
$934$	30.8284			1.00874
$935$	3.41421	−	13.6569i	0.111657	−	0.446627i
$936$	−6.82843			−0.223194
$937$		−	43.3137i		−	1.41500i	−0.706715	−	0.707499i	$-0.749824\pi$
$937$		−	43.3137i		−	1.41500i	0.706715	−	0.707499i	$-0.250176\pi$
$938$	−12.0000	−	12.0000i	−0.391814	−	0.391814i
$939$	30.3848			0.991570
$940$	−23.3137	−	23.3137i	−0.760409	−	0.760409i
$941$	6.07107	−	6.07107i	0.197911	−	0.197911i	−0.601193	−	0.799104i	$-0.705308\pi$
$941$	6.07107	−	6.07107i	0.197911	−	0.197911i	0.799104	+	0.601193i	$0.205308\pi$
$942$	−9.41421	+	9.41421i	−0.306732	+	0.306732i
$943$			8.48528i			0.276319i
$944$		0			0
$945$	4.82843	−	4.82843i	0.157069	−	0.157069i
$946$	4.82843	−	4.82843i	0.156986	−	0.156986i
$947$	−32.9706	−	32.9706i	−1.07140	−	1.07140i	−0.997247	−	0.0741524i	$-0.976375\pi$
$947$	−32.9706	−	32.9706i	−1.07140	−	1.07140i	−0.0741524	−	0.997247i	$-0.523625\pi$
$948$	−11.6569			−0.378597
$949$	31.7990	+	31.7990i	1.03224	+	1.03224i
$950$		0			0
$951$	21.0711			0.683276
$952$	7.07107	−	4.24264i	0.229175	−	0.137505i
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$			12.4853i			0.404226i
$955$	−61.9411	−	61.9411i	−2.00437	−	2.00437i
$956$	2.82843			0.0914779
$957$	6.41421	+	6.41421i	0.207342	+	0.207342i
$958$	16.7279	−	16.7279i	0.540455	−	0.540455i
$959$	−11.3137	+	11.3137i	−0.365339	+	0.365339i
$960$			3.41421i			0.110193i
$961$			27.6274i			0.891207i
$962$	−43.7990	+	43.7990i	−1.41214	+	1.41214i
$963$	−5.17157	+	5.17157i	−0.166652	+	0.166652i
$964$	5.48528	+	5.48528i	0.176669	+	0.176669i
$965$	7.17157			0.230861
$966$	2.82843	+	2.82843i	0.0910032	+	0.0910032i
$967$		−	23.3137i		−	0.749718i	−0.927082	−	0.374859i	$-0.877691\pi$
$967$		−	23.3137i		−	0.749718i	0.927082	−	0.374859i	$-0.122309\pi$
$968$	1.00000			0.0321412
$969$		0			0
$970$	−36.1421			−1.16045
$971$			8.97056i			0.287879i	0.989586	+	0.143940i	$0.0459771\pi$
$971$			8.97056i			0.287879i	−0.989586	+	0.143940i	$0.954023\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	4.68629			0.150236
$974$	−20.2426	−	20.2426i	−0.648616	−	0.648616i
$975$	−32.1421	+	32.1421i	−1.02937	+	1.02937i
$976$	0.757359	−	0.757359i	0.0242425	−	0.0242425i
$977$		−	22.6274i		−	0.723915i	−0.932195	−	0.361958i	$-0.882109\pi$
$977$		−	22.6274i		−	0.723915i	0.932195	−	0.361958i	$-0.117891\pi$
$978$			12.0000i			0.383718i
$979$	−12.4853	+	12.4853i	−0.399031	+	0.399031i
$980$	−7.24264	+	7.24264i	−0.231358	+	0.231358i
$981$	−0.414214	−	0.414214i	−0.0132248	−	0.0132248i
$982$	25.6569			0.818743
$983$	8.92893	+	8.92893i	0.284789	+	0.284789i	0.835015	−	0.550227i	$-0.185459\pi$
$983$	8.92893	+	8.92893i	0.284789	+	0.284789i	−0.550227	+	0.835015i	$0.685459\pi$
$984$			4.24264i			0.135250i
$985$	6.00000			0.191176
$986$	19.2426	+	32.0711i	0.612811	+	1.02135i
$987$	−19.3137			−0.614762
$988$		0			0
$989$	9.65685	+	9.65685i	0.307070	+	0.307070i
$990$	3.41421			0.108511
$991$	37.4142	+	37.4142i	1.18850	+	1.18850i	0.977482	+	0.211020i	$0.0676785\pi$
$991$	37.4142	+	37.4142i	1.18850	+	1.18850i	0.211020	+	0.977482i	$0.432322\pi$
$992$	−5.41421	+	5.41421i	−0.171901	+	0.171901i
$993$	3.51472	−	3.51472i	0.111536	−	0.111536i
$994$			31.3137i			0.993211i
$995$		−	47.7990i		−	1.51533i
$996$	−2.00000	+	2.00000i	−0.0633724	+	0.0633724i
$997$	38.5563	−	38.5563i	1.22109	−	1.22109i	0.253848	−	0.967244i	$-0.418304\pi$
$997$	38.5563	−	38.5563i	1.22109	−	1.22109i	0.967244	−	0.253848i	$-0.0816962\pi$
$998$	7.51472	+	7.51472i	0.237874	+	0.237874i
$999$	9.07107			0.286996

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.41421 - 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.41421 - 2.41421i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.41421 - 1.41421i) q^{7} +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} +6.82843 q^{13} +(-1.41421 - 1.41421i) q^{14} -3.41421i q^{15} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} +1.00000 q^{18} +(2.41421 + 2.41421i) q^{20} +2.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-1.41421 + 1.41421i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.65685i q^{25} -6.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(-6.41421 - 6.41421i) q^{29} -3.41421 q^{30} +(-5.41421 - 5.41421i) q^{31} -1.00000i q^{32} -1.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} -6.82843 q^{35} -1.00000i q^{36} +(-6.41421 - 6.41421i) q^{37} +(4.82843 + 4.82843i) q^{39} +(2.41421 - 2.41421i) q^{40} +(3.00000 - 3.00000i) q^{41} -2.00000i q^{42} -6.82843i q^{43} +(0.707107 - 0.707107i) q^{44} +(2.41421 - 2.41421i) q^{45} +(1.41421 + 1.41421i) q^{46} -9.65685 q^{47} +(0.707107 + 0.707107i) q^{48} +3.00000i q^{49} +6.65685 q^{50} +(3.53553 - 2.12132i) q^{51} -6.82843 q^{52} +12.4853i q^{53} +(0.707107 + 0.707107i) q^{54} +3.41421 q^{55} +(1.41421 + 1.41421i) q^{56} +(-6.41421 + 6.41421i) q^{58} +3.41421i q^{60} +(0.757359 - 0.757359i) q^{61} +(-5.41421 + 5.41421i) q^{62} +(1.41421 + 1.41421i) q^{63} -1.00000 q^{64} +(-16.4853 - 16.4853i) q^{65} +1.00000i q^{66} +8.48528 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{69} +6.82843i q^{70} +(-11.0711 - 11.0711i) q^{71} -1.00000 q^{72} +(4.65685 + 4.65685i) q^{73} +(-6.41421 + 6.41421i) q^{74} +(-4.70711 + 4.70711i) q^{75} +2.00000i q^{77} +(4.82843 - 4.82843i) q^{78} +(8.24264 - 8.24264i) q^{79} +(-2.41421 - 2.41421i) q^{80} -1.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} -2.82843i q^{83} -2.00000 q^{84} +(-12.0711 + 7.24264i) q^{85} -6.82843 q^{86} -9.07107i q^{87} +(-0.707107 - 0.707107i) q^{88} +17.6569 q^{89} +(-2.41421 - 2.41421i) q^{90} +(9.65685 - 9.65685i) q^{91} +(1.41421 - 1.41421i) q^{92} -7.65685i q^{93} +9.65685i q^{94} +(0.707107 - 0.707107i) q^{96} +(7.48528 + 7.48528i) q^{97} +3.00000 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^5	\( 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} - 20 q^{29} - 8 q^{30} - 16 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{35} - 20 q^{37} + 8 q^{39} + 4 q^{40} + 12 q^{41} + 4 q^{45} - 16 q^{47} + 4 q^{50} - 16 q^{52} + 8 q^{55} - 20 q^{58} + 20 q^{61} - 16 q^{62} - 4 q^{64} - 32 q^{65} - 4 q^{68} - 8 q^{69} - 16 q^{71} - 4 q^{72} - 4 q^{73} - 20 q^{74} - 16 q^{75} + 8 q^{78} + 16 q^{79} - 4 q^{80} - 4 q^{81} - 12 q^{82} - 8 q^{84} - 20 q^{85} - 16 q^{86} + 48 q^{89} - 4 q^{90} + 16 q^{91} - 4 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^20 + 8 * q^21 - 20 * q^29 - 8 * q^30 - 16 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^35 - 20 * q^37 + 8 * q^39 + 4 * q^40 + 12 * q^41 + 4 * q^45 - 16 * q^47 + 4 * q^50 - 16 * q^52 + 8 * q^55 - 20 * q^58 + 20 * q^61 - 16 * q^62 - 4 * q^64 - 32 * q^65 - 4 * q^68 - 8 * q^69 - 16 * q^71 - 4 * q^72 - 4 * q^73 - 20 * q^74 - 16 * q^75 + 8 * q^78 + 16 * q^79 - 4 * q^80 - 4 * q^81 - 12 * q^82 - 8 * q^84 - 20 * q^85 - 16 * q^86 + 48 * q^89 - 4 * q^90 + 16 * q^91 - 4 * q^97 + 12 * q^98

Introduction

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