LMFDB - Embedded newform 1110.2.u.b.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.b.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} +4.24264 q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(2.82843 + 2.82843i) q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-2.00000 - 2.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-5.65685 - 4.00000i) q^{21} +(3.00000 + 3.00000i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -1.41421i q^{26} +(1.41421 - 5.00000i) q^{27} +4.00000i q^{28} +(-1.41421 - 1.00000i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.00000 - 4.24264i) q^{33} -2.00000 q^{34} +(2.82843 - 2.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(6.00000 - 1.00000i) q^{37} -2.82843i q^{38} +(0.414214 + 2.41421i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 - 6.82843i) q^{42} +(9.00000 + 9.00000i) q^{43} +4.24264i q^{44} +(2.70711 + 1.29289i) q^{45} -6.00000 q^{46} +1.41421i q^{47} +(1.41421 + 1.00000i) q^{48} +9.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(1.00000 - 1.00000i) q^{52} +2.82843i q^{53} +(4.53553 - 2.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(0.828427 + 4.82843i) q^{57} +(-2.82843 + 2.82843i) q^{59} +(-0.292893 - 1.70711i) q^{60} +(4.00000 - 4.00000i) q^{61} +7.07107 q^{62} +(4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -1.41421 q^{65} +(-1.24264 - 7.24264i) q^{66} +2.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(10.2426 - 1.75736i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -6.00000i q^{73} +(4.94975 + 3.53553i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(2.00000 - 2.00000i) q^{76} +16.9706 q^{77} +(-1.41421 + 2.00000i) q^{78} +(-3.00000 - 3.00000i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} +2.00000i q^{85} +12.7279i q^{86} +(-3.00000 + 3.00000i) q^{88} +(-12.7279 - 12.7279i) q^{89} +(1.00000 + 2.82843i) q^{90} +(-4.00000 - 4.00000i) q^{91} +(-4.24264 - 4.24264i) q^{92} +(-12.0711 + 2.07107i) q^{93} +(-1.00000 + 1.00000i) q^{94} -2.82843 q^{95} +(0.292893 + 1.70711i) q^{96} +(-12.0000 - 12.0000i) q^{97} +(6.36396 + 6.36396i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{6} + 16 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^6 + 16 * q^7 + 4 * q^9	$ 4 q - 4 q^{6} + 16 q^{7} + 4 q^{9} + 4 q^{10} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} - 8 q^{19} + 12 q^{22} + 4 q^{24} + 20 q^{31} - 24 q^{33} - 8 q^{34} + 24 q^{37} - 4 q^{39} - 16 q^{42} + 36 q^{43} + 8 q^{45} - 24 q^{46} + 36 q^{49} + 8 q^{51} + 4 q^{52} + 4 q^{54} + 12 q^{55} - 8 q^{57} - 4 q^{60} + 16 q^{61} + 16 q^{63} + 12 q^{66} + 24 q^{69} + 16 q^{70} - 8 q^{72} - 4 q^{75} + 8 q^{76} - 12 q^{79} - 28 q^{81} + 16 q^{82} + 16 q^{84} - 12 q^{88} + 4 q^{90} - 16 q^{91} - 20 q^{93} - 4 q^{94} + 4 q^{96} - 48 q^{97}+O(q^{100}) $ 4 * q - 4 * q^6 + 16 * q^7 + 4 * q^9 + 4 * q^10 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 - 8 * q^19 + 12 * q^22 + 4 * q^24 + 20 * q^31 - 24 * q^33 - 8 * q^34 + 24 * q^37 - 4 * q^39 - 16 * q^42 + 36 * q^43 + 8 * q^45 - 24 * q^46 + 36 * q^49 + 8 * q^51 + 4 * q^52 + 4 * q^54 + 12 * q^55 - 8 * q^57 - 4 * q^60 + 16 * q^61 + 16 * q^63 + 12 * q^66 + 24 * q^69 + 16 * q^70 - 8 * q^72 - 4 * q^75 + 8 * q^76 - 12 * q^79 - 28 * q^81 + 16 * q^82 + 16 * q^84 - 12 * q^88 + 4 * q^90 - 16 * q^91 - 20 * q^93 - 4 * q^94 + 4 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$4$			1.00000i			0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.292893	−	1.70711i	−0.119573	−	0.696923i
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$	1.00000			0.316228
$11$	4.24264			1.27920			0.639602	−	0.768706i	$-0.279099\pi$
$11$	4.24264			1.27920			0.639602	+	0.768706i	$0.279099\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	0.554700	−	0.832050i	$-0.312833\pi$
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.82843	+	2.82843i	0.755929	+	0.755929i
$15$	−1.70711	+	0.292893i	−0.440773	+	0.0756247i
$16$	−1.00000			−0.250000
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	−5.65685	−	4.00000i	−1.23443	−	0.872872i
$22$	3.00000	+	3.00000i	0.639602	+	0.639602i
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	−0.994003	−	0.109351i	$-0.965123\pi$
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	0.109351	+	0.994003i	$0.465123\pi$
$24$	1.70711	−	0.292893i	0.348462	−	0.0597866i
$25$		−	1.00000i		−	0.200000i
$26$		−	1.41421i		−	0.277350i
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$			4.00000i			0.755929i
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$	−1.41421	−	1.00000i	−0.258199	−	0.182574i
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−6.00000	−	4.24264i	−1.04447	−	0.738549i
$34$	−2.00000			−0.342997
$35$	2.82843	−	2.82843i	0.478091	−	0.478091i
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$38$		−	2.82843i		−	0.458831i
$39$	0.414214	+	2.41421i	0.0663273	+	0.386584i
$40$			1.00000i			0.158114i
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$	−1.17157	−	6.82843i	−0.180778	−	1.05365i
$43$	9.00000	+	9.00000i	1.37249	+	1.37249i	0.856742	+	0.515745i	$0.172485\pi$
$43$	9.00000	+	9.00000i	1.37249	+	1.37249i	0.515745	+	0.856742i	$0.327515\pi$
$44$			4.24264i			0.639602i
$45$	2.70711	+	1.29289i	0.403552	+	0.192733i
$46$	−6.00000			−0.884652
$47$			1.41421i			0.206284i	0.994667	+	0.103142i	$0.0328896\pi$
$47$			1.41421i			0.206284i	−0.994667	+	0.103142i	$0.967110\pi$
$48$	1.41421	+	1.00000i	0.204124	+	0.144338i
$49$	9.00000			1.28571
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	3.41421	−	0.585786i	0.478086	−	0.0820265i
$52$	1.00000	−	1.00000i	0.138675	−	0.138675i
$53$			2.82843i			0.388514i	0.980951	+	0.194257i	$0.0622296\pi$
$53$			2.82843i			0.388514i	−0.980951	+	0.194257i	$0.937770\pi$
$54$	4.53553	−	2.53553i	0.617208	−	0.345042i
$55$	3.00000	−	3.00000i	0.404520	−	0.404520i
$56$	−2.82843	+	2.82843i	−0.377964	+	0.377964i
$57$	0.828427	+	4.82843i	0.109728	+	0.639541i
$58$		0			0
$59$	−2.82843	+	2.82843i	−0.368230	+	0.368230i	−0.866831	−	0.498601i	$-0.833847\pi$
$59$	−2.82843	+	2.82843i	−0.368230	+	0.368230i	0.498601	+	0.866831i	$0.333847\pi$
$60$	−0.292893	−	1.70711i	−0.0378124	−	0.220387i
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	−0.403036	−	0.915184i	$-0.632045\pi$
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	0.915184	+	0.403036i	$0.132045\pi$
$62$	7.07107			0.898027
$63$	4.00000	+	11.3137i	0.503953	+	1.42539i
$64$		−	1.00000i		−	0.125000i
$65$	−1.41421			−0.175412
$66$	−1.24264	−	7.24264i	−0.152958	−	0.891507i
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	−1.41421	−	1.41421i	−0.171499	−	0.171499i
$69$	10.2426	−	1.75736i	1.23307	−	0.211561i
$70$	4.00000			0.478091
$71$		−	2.82843i		−	0.335673i	−0.985815	−	0.167836i	$-0.946322\pi$
$71$		−	2.82843i		−	0.335673i	0.985815	−	0.167836i	$-0.0536780\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	4.94975	+	3.53553i	0.575396	+	0.410997i
$75$	−1.00000	+	1.41421i	−0.115470	+	0.163299i
$76$	2.00000	−	2.00000i	0.229416	−	0.229416i
$77$	16.9706			1.93398
$78$	−1.41421	+	2.00000i	−0.160128	+	0.226455i
$79$	−3.00000	−	3.00000i	−0.337526	−	0.337526i	0.517909	−	0.855436i	$-0.326710\pi$
$79$	−3.00000	−	3.00000i	−0.337526	−	0.337526i	−0.855436	+	0.517909i	$0.826710\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$		−	2.82843i		−	0.310460i	−0.987878	−	0.155230i	$-0.950388\pi$
$83$		−	2.82843i		−	0.310460i	0.987878	−	0.155230i	$-0.0496119\pi$
$84$	4.00000	−	5.65685i	0.436436	−	0.617213i
$85$			2.00000i			0.216930i
$86$			12.7279i			1.37249i
$87$		0			0
$88$	−3.00000	+	3.00000i	−0.319801	+	0.319801i
$89$	−12.7279	−	12.7279i	−1.34916	−	1.34916i	−0.886578	−	0.462579i	$-0.846924\pi$
$89$	−12.7279	−	12.7279i	−1.34916	−	1.34916i	−0.462579	−	0.886578i	$-0.653076\pi$
$90$	1.00000	+	2.82843i	0.105409	+	0.298142i
$91$	−4.00000	−	4.00000i	−0.419314	−	0.419314i
$92$	−4.24264	−	4.24264i	−0.442326	−	0.442326i
$93$	−12.0711	+	2.07107i	−1.25171	+	0.214760i
$94$	−1.00000	+	1.00000i	−0.103142	+	0.103142i
$95$	−2.82843			−0.290191
$96$	0.292893	+	1.70711i	0.0298933	+	0.174231i
$97$	−12.0000	−	12.0000i	−1.21842	−	1.21842i	−0.968187	−	0.250229i	$-0.919494\pi$
$97$	−12.0000	−	12.0000i	−1.21842	−	1.21842i	−0.250229	−	0.968187i	$-0.580506\pi$
$98$	6.36396	+	6.36396i	0.642857	+	0.642857i
$99$	4.24264	+	12.0000i	0.426401	+	1.20605i
$100$	1.00000			0.100000
$101$	15.5563			1.54791			0.773957	−	0.633238i	$-0.218274\pi$
$101$	15.5563			1.54791			0.773957	+	0.633238i	$0.218274\pi$
$102$	2.82843	+	2.00000i	0.280056	+	0.198030i
$103$	−10.0000	+	10.0000i	−0.985329	+	0.985329i	−0.999894	−	0.0145647i	$-0.995364\pi$
$103$	−10.0000	+	10.0000i	−0.985329	+	0.985329i	0.0145647	+	0.999894i	$0.495364\pi$
$104$	1.41421			0.138675
$105$	−6.82843	+	1.17157i	−0.666386	+	0.114334i
$106$	−2.00000	+	2.00000i	−0.194257	+	0.194257i
$107$		−	14.1421i		−	1.36717i	−0.729870	−	0.683586i	$-0.760419\pi$
$107$		−	14.1421i		−	1.36717i	0.729870	−	0.683586i	$-0.239581\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$	12.0000	+	12.0000i	1.14939	+	1.14939i	0.986672	+	0.162719i	$0.0520264\pi$
$109$	12.0000	+	12.0000i	1.14939	+	1.14939i	0.162719	+	0.986672i	$0.447974\pi$
$110$	4.24264			0.404520
$111$	−9.48528	−	4.58579i	−0.900303	−	0.435264i
$112$	−4.00000			−0.377964
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$	−2.82843	+	4.00000i	−0.264906	+	0.374634i
$115$			6.00000i			0.559503i
$116$		0			0
$117$	1.82843	−	3.82843i	0.169038	−	0.353938i
$118$	−4.00000			−0.368230
$119$	−5.65685	+	5.65685i	−0.518563	+	0.518563i
$120$	1.00000	−	1.41421i	0.0912871	−	0.129099i
$121$	7.00000			0.636364
$122$	5.65685			0.512148
$123$	−8.00000	−	5.65685i	−0.721336	−	0.510061i
$124$	5.00000	+	5.00000i	0.449013	+	0.449013i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−5.17157	+	10.8284i	−0.460720	+	0.964673i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.72792	−	21.7279i	−0.328225	−	1.91304i
$130$	−1.00000	−	1.00000i	−0.0877058	−	0.0877058i
$131$	8.48528	+	8.48528i	0.741362	+	0.741362i	0.972840	−	0.231478i	$-0.0743560\pi$
$131$	8.48528	+	8.48528i	0.741362	+	0.741362i	−0.231478	+	0.972840i	$0.574356\pi$
$132$	4.24264	−	6.00000i	0.369274	−	0.522233i
$133$	−8.00000	−	8.00000i	−0.693688	−	0.693688i
$134$	−1.41421	+	1.41421i	−0.122169	+	0.122169i
$135$	−2.53553	−	4.53553i	−0.218224	−	0.390357i
$136$		−	2.00000i		−	0.171499i
$137$			9.89949i			0.845771i	0.906183	+	0.422885i	$0.138983\pi$
$137$			9.89949i			0.845771i	−0.906183	+	0.422885i	$0.861017\pi$
$138$	8.48528	+	6.00000i	0.722315	+	0.510754i
$139$			16.0000i			1.35710i	0.734553	+	0.678551i	$0.237392\pi$
$139$			16.0000i			1.35710i	−0.734553	+	0.678551i	$0.762608\pi$
$140$	2.82843	+	2.82843i	0.239046	+	0.239046i
$141$	1.41421	−	2.00000i	0.119098	−	0.168430i
$142$	2.00000	−	2.00000i	0.167836	−	0.167836i
$143$	−4.24264	−	4.24264i	−0.354787	−	0.354787i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$		0			0
$146$	4.24264	−	4.24264i	0.351123	−	0.351123i
$147$	−12.7279	−	9.00000i	−1.04978	−	0.742307i
$148$	1.00000	+	6.00000i	0.0821995	+	0.493197i
$149$		−	9.89949i		−	0.810998i	−0.914095	−	0.405499i	$-0.867098\pi$
$149$		−	9.89949i		−	0.810998i	0.914095	−	0.405499i	$-0.132902\pi$
$150$	−1.70711	+	0.292893i	−0.139385	+	0.0239146i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	2.82843			0.229416
$153$	−5.41421	−	2.58579i	−0.437713	−	0.209048i
$154$	12.0000	+	12.0000i	0.966988	+	0.966988i
$155$		−	7.07107i		−	0.567962i
$156$	−2.41421	+	0.414214i	−0.193292	+	0.0331636i
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$		−	4.24264i		−	0.337526i
$159$	2.82843	−	4.00000i	0.224309	−	0.317221i
$160$	−1.00000			−0.0790569
$161$	−16.9706	+	16.9706i	−1.33747	+	1.33747i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	−0.875268	−	0.483638i	$-0.839315\pi$
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	0.483638	+	0.875268i	$0.339315\pi$
$164$			5.65685i			0.441726i
$165$	−7.24264	+	1.24264i	−0.563839	+	0.0967394i
$166$	2.00000	−	2.00000i	0.155230	−	0.155230i
$167$	−12.7279	+	12.7279i	−0.984916	+	0.984916i	−0.999888	−	0.0149717i	$-0.995234\pi$
$167$	−12.7279	+	12.7279i	−0.984916	+	0.984916i	0.0149717	+	0.999888i	$0.495234\pi$
$168$	6.82843	−	1.17157i	0.526825	−	0.0903888i
$169$		−	11.0000i		−	0.846154i
$170$	−1.41421	+	1.41421i	−0.108465	+	0.108465i
$171$	3.65685	−	7.65685i	0.279647	−	0.585534i
$172$	−9.00000	+	9.00000i	−0.686244	+	0.686244i
$173$	−2.82843			−0.215041			−0.107521	−	0.994203i	$-0.534291\pi$
$173$	−2.82843			−0.215041			−0.107521	+	0.994203i	$0.534291\pi$
$174$		0			0
$175$		−	4.00000i		−	0.302372i
$176$	−4.24264			−0.319801
$177$	6.82843	−	1.17157i	0.513256	−	0.0880608i
$178$		−	18.0000i		−	1.34916i
$179$	−12.7279	−	12.7279i	−0.951330	−	0.951330i	0.0475398	−	0.998869i	$-0.484862\pi$
$179$	−12.7279	−	12.7279i	−0.951330	−	0.951330i	−0.998869	+	0.0475398i	$0.984862\pi$
$180$	−1.29289	+	2.70711i	−0.0963666	+	0.201776i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		−	5.65685i		−	0.419314i
$183$	−9.65685	+	1.65685i	−0.713855	+	0.122478i
$184$		−	6.00000i		−	0.442326i
$185$	3.53553	−	4.94975i	0.259938	−	0.363913i
$186$	−10.0000	−	7.07107i	−0.733236	−	0.518476i
$187$	−6.00000	+	6.00000i	−0.438763	+	0.438763i
$188$	−1.41421			−0.103142
$189$	5.65685	−	20.0000i	0.411476	−	1.45479i
$190$	−2.00000	−	2.00000i	−0.145095	−	0.145095i
$191$	2.82843	−	2.82843i	0.204658	−	0.204658i	−0.597334	−	0.801992i	$-0.703773\pi$
$191$	2.82843	−	2.82843i	0.204658	−	0.204658i	0.801992	+	0.597334i	$0.203773\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$	18.0000	+	18.0000i	1.29567	+	1.29567i	0.931226	+	0.364442i	$0.118740\pi$
$193$	18.0000	+	18.0000i	1.29567	+	1.29567i	0.364442	+	0.931226i	$0.381260\pi$
$194$		−	16.9706i		−	1.21842i
$195$	2.00000	+	1.41421i	0.143223	+	0.101274i
$196$			9.00000i			0.642857i
$197$		−	19.7990i		−	1.41062i	−0.708899	−	0.705310i	$-0.750808\pi$
$197$		−	19.7990i		−	1.41062i	0.708899	−	0.705310i	$-0.249192\pi$
$198$	−5.48528	+	11.4853i	−0.389822	+	0.816223i
$199$	−3.00000	+	3.00000i	−0.212664	+	0.212664i	−0.805398	−	0.592734i	$-0.798049\pi$
$199$	−3.00000	+	3.00000i	−0.212664	+	0.212664i	0.592734	+	0.805398i	$0.298049\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	2.00000	−	2.82843i	0.141069	−	0.199502i
$202$	11.0000	+	11.0000i	0.773957	+	0.773957i
$203$		0			0
$204$	0.585786	+	3.41421i	0.0410133	+	0.239043i
$205$	4.00000	−	4.00000i	0.279372	−	0.279372i
$206$	−14.1421			−0.985329
$207$	−16.2426	−	7.75736i	−1.12894	−	0.539174i
$208$	1.00000	+	1.00000i	0.0693375	+	0.0693375i
$209$	−8.48528	−	8.48528i	−0.586939	−	0.586939i
$210$	−5.65685	−	4.00000i	−0.390360	−	0.276026i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	−2.82843			−0.194257
$213$	−2.82843	+	4.00000i	−0.193801	+	0.274075i
$214$	10.0000	−	10.0000i	0.683586	−	0.683586i
$215$	12.7279			0.868037
$216$	2.53553	+	4.53553i	0.172521	+	0.308604i
$217$	20.0000	−	20.0000i	1.35769	−	1.35769i
$218$			16.9706i			1.14939i
$219$	−6.00000	+	8.48528i	−0.405442	+	0.573382i
$220$	3.00000	+	3.00000i	0.202260	+	0.202260i
$221$	2.82843			0.190261
$222$	−3.46447	−	9.94975i	−0.232520	−	0.667783i
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$	−2.82843	−	2.82843i	−0.188982	−	0.188982i
$225$	2.82843	−	1.00000i	0.188562	−	0.0666667i
$226$			6.00000i			0.399114i
$227$	−19.7990	+	19.7990i	−1.31411	+	1.31411i	−0.395744	+	0.918361i	$0.629513\pi$
$227$	−19.7990	+	19.7990i	−1.31411	+	1.31411i	−0.918361	+	0.395744i	$0.870487\pi$
$228$	−4.82843	+	0.828427i	−0.319770	+	0.0548639i
$229$	26.0000			1.71813			0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000			1.71813			0.859064	+	0.511868i	$0.171046\pi$
$230$	−4.24264	+	4.24264i	−0.279751	+	0.279751i
$231$	−24.0000	−	16.9706i	−1.57908	−	1.11658i
$232$		0			0
$233$	−7.07107			−0.463241			−0.231621	−	0.972806i	$-0.574403\pi$
$233$	−7.07107			−0.463241			−0.231621	+	0.972806i	$0.574403\pi$
$234$	4.00000	−	1.41421i	0.261488	−	0.0924500i
$235$	1.00000	+	1.00000i	0.0652328	+	0.0652328i
$236$	−2.82843	−	2.82843i	−0.184115	−	0.184115i
$237$	1.24264	+	7.24264i	0.0807182	+	0.470460i
$238$	−8.00000			−0.518563
$239$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$239$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$240$	1.70711	−	0.292893i	0.110193	−	0.0189062i
$241$	3.00000	+	3.00000i	0.193247	+	0.193247i	0.797098	−	0.603851i	$-0.206368\pi$
$241$	3.00000	+	3.00000i	0.193247	+	0.193247i	−0.603851	+	0.797098i	$0.706368\pi$
$242$	4.94975	+	4.94975i	0.318182	+	0.318182i
$243$	15.5563	−	1.00000i	0.997940	−	0.0641500i
$244$	4.00000	+	4.00000i	0.256074	+	0.256074i
$245$	6.36396	−	6.36396i	0.406579	−	0.406579i
$246$	−1.65685	−	9.65685i	−0.105637	−	0.615699i
$247$			4.00000i			0.254514i
$248$			7.07107i			0.449013i
$249$	−2.82843	+	4.00000i	−0.179244	+	0.253490i
$250$		−	1.00000i		−	0.0632456i
$251$	−2.82843	−	2.82843i	−0.178529	−	0.178529i	0.612185	−	0.790714i	$-0.290291\pi$
$251$	−2.82843	−	2.82843i	−0.178529	−	0.178529i	−0.790714	+	0.612185i	$0.790291\pi$
$252$	−11.3137	+	4.00000i	−0.712697	+	0.251976i
$253$	−18.0000	+	18.0000i	−1.13165	+	1.13165i
$254$	−8.48528	−	8.48528i	−0.532414	−	0.532414i
$255$	2.00000	−	2.82843i	0.125245	−	0.177123i
$256$	1.00000			0.0625000
$257$	2.82843	−	2.82843i	0.176432	−	0.176432i	−0.613366	−	0.789799i	$-0.710185\pi$
$257$	2.82843	−	2.82843i	0.176432	−	0.176432i	0.789799	+	0.613366i	$0.210185\pi$
$258$	12.7279	−	18.0000i	0.792406	−	1.12063i
$259$	24.0000	−	4.00000i	1.49129	−	0.248548i
$260$		−	1.41421i		−	0.0877058i
$261$		0			0
$262$			12.0000i			0.741362i
$263$	−26.8701			−1.65688			−0.828439	−	0.560079i	$-0.810771\pi$
$263$	−26.8701			−1.65688			−0.828439	+	0.560079i	$0.810771\pi$
$264$	7.24264	−	1.24264i	0.445754	−	0.0764792i
$265$	2.00000	+	2.00000i	0.122859	+	0.122859i
$266$		−	11.3137i		−	0.693688i
$267$	5.27208	+	30.7279i	0.322646	+	1.88052i
$268$	−2.00000			−0.122169
$269$		−	21.2132i		−	1.29339i	−0.762748	−	0.646696i	$-0.776150\pi$
$269$		−	21.2132i		−	1.29339i	0.762748	−	0.646696i	$-0.223850\pi$
$270$	1.41421	−	5.00000i	0.0860663	−	0.304290i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	1.41421	−	1.41421i	0.0857493	−	0.0857493i
$273$	1.65685	+	9.65685i	0.100277	+	0.584459i
$274$	−7.00000	+	7.00000i	−0.422885	+	0.422885i
$275$		−	4.24264i		−	0.255841i
$276$	1.75736	+	10.2426i	0.105781	+	0.616535i
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$	−11.3137	+	11.3137i	−0.678551	+	0.678551i
$279$	19.1421	+	9.14214i	1.14601	+	0.547325i
$280$			4.00000i			0.239046i
$281$	−7.07107	+	7.07107i	−0.421825	+	0.421825i	−0.885832	−	0.464007i	$-0.846411\pi$
$281$	−7.07107	+	7.07107i	−0.421825	+	0.421825i	0.464007	+	0.885832i	$0.346411\pi$
$282$	2.41421	−	0.414214i	0.143764	−	0.0246661i
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	−0.994679	−	0.103022i	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$	2.82843			0.167836
$285$	4.00000	+	2.82843i	0.236940	+	0.167542i
$286$		−	6.00000i		−	0.354787i
$287$	22.6274			1.33565
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$			13.0000i			0.764706i
$290$		0			0
$291$	4.97056	+	28.9706i	0.291380	+	1.69828i
$292$	6.00000			0.351123
$293$		−	28.2843i		−	1.65238i	−0.563388	−	0.826192i	$-0.690502\pi$
$293$		−	28.2843i		−	1.65238i	0.563388	−	0.826192i	$-0.309498\pi$
$294$	−2.63604	−	15.3640i	−0.153737	−	0.896044i
$295$			4.00000i			0.232889i
$296$	−3.53553	+	4.94975i	−0.205499	+	0.287698i
$297$	6.00000	−	21.2132i	0.348155	−	1.23091i
$298$	7.00000	−	7.00000i	0.405499	−	0.405499i
$299$	8.48528			0.490716
$300$	−1.41421	−	1.00000i	−0.0816497	−	0.0577350i
$301$	36.0000	+	36.0000i	2.07501	+	2.07501i
$302$		0			0
$303$	−22.0000	−	15.5563i	−1.26387	−	0.893689i
$304$	2.00000	+	2.00000i	0.114708	+	0.114708i
$305$		−	5.65685i		−	0.323911i
$306$	−2.00000	−	5.65685i	−0.114332	−	0.323381i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$			16.9706i			0.966988i
$309$	24.1421	−	4.14214i	1.37340	−	0.235638i
$310$	5.00000	−	5.00000i	0.283981	−	0.283981i
$311$	−8.48528	−	8.48528i	−0.481156	−	0.481156i	0.424345	−	0.905501i	$-0.360505\pi$
$311$	−8.48528	−	8.48528i	−0.481156	−	0.481156i	−0.905501	+	0.424345i	$0.860505\pi$
$312$	−2.00000	−	1.41421i	−0.113228	−	0.0800641i
$313$	6.00000	+	6.00000i	0.339140	+	0.339140i	0.856044	−	0.516904i	$-0.172915\pi$
$313$	6.00000	+	6.00000i	0.339140	+	0.339140i	−0.516904	+	0.856044i	$0.672915\pi$
$314$	−12.7279	−	12.7279i	−0.718278	−	0.718278i
$315$	10.8284	+	5.17157i	0.610113	+	0.291385i
$316$	3.00000	−	3.00000i	0.168763	−	0.168763i
$317$	8.48528			0.476581			0.238290	−	0.971194i	$-0.423413\pi$
$317$	8.48528			0.476581			0.238290	+	0.971194i	$0.423413\pi$
$318$	4.82843	−	0.828427i	0.270765	−	0.0464559i
$319$		0			0
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	−14.1421	+	20.0000i	−0.789337	+	1.11629i
$322$	−24.0000			−1.33747
$323$	5.65685			0.314756
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−1.00000	+	1.00000i	−0.0554700	+	0.0554700i
$326$	−7.07107			−0.391630
$327$	−4.97056	−	28.9706i	−0.274873	−	1.60208i
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$			5.65685i			0.311872i
$330$	−6.00000	−	4.24264i	−0.330289	−	0.233550i
$331$	−4.00000	−	4.00000i	−0.219860	−	0.219860i	0.588579	−	0.808439i	$-0.299687\pi$
$331$	−4.00000	−	4.00000i	−0.219860	−	0.219860i	−0.808439	+	0.588579i	$0.799687\pi$
$332$	2.82843			0.155230
$333$	8.82843	+	15.9706i	0.483795	+	0.875181i
$334$	−18.0000			−0.984916
$335$	1.41421	+	1.41421i	0.0772667	+	0.0772667i
$336$	5.65685	+	4.00000i	0.308607	+	0.218218i
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$	7.77817	−	7.77817i	0.423077	−	0.423077i
$339$	−1.75736	−	10.2426i	−0.0954467	−	0.556304i
$340$	−2.00000			−0.108465
$341$	21.2132	−	21.2132i	1.14876	−	1.14876i
$342$	8.00000	−	2.82843i	0.432590	−	0.152944i
$343$	8.00000			0.431959
$344$	−12.7279			−0.686244
$345$	6.00000	−	8.48528i	0.323029	−	0.456832i
$346$	−2.00000	−	2.00000i	−0.107521	−	0.107521i
$347$	8.48528	+	8.48528i	0.455514	+	0.455514i	0.897180	−	0.441666i	$-0.145612\pi$
$347$	8.48528	+	8.48528i	0.455514	+	0.455514i	−0.441666	+	0.897180i	$0.645612\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	2.82843	−	2.82843i	0.151186	−	0.151186i
$351$	−6.41421	+	3.58579i	−0.342365	+	0.191395i
$352$	−3.00000	−	3.00000i	−0.159901	−	0.159901i
$353$	−24.0416	−	24.0416i	−1.27961	−	1.27961i	−0.940887	−	0.338719i	$-0.890006\pi$
$353$	−24.0416	−	24.0416i	−1.27961	−	1.27961i	−0.338719	−	0.940887i	$-0.609994\pi$
$354$	5.65685	+	4.00000i	0.300658	+	0.212598i
$355$	−2.00000	−	2.00000i	−0.106149	−	0.106149i
$356$	12.7279	−	12.7279i	0.674579	−	0.674579i
$357$	13.6569	−	2.34315i	0.722797	−	0.124012i
$358$		−	18.0000i		−	0.951330i
$359$			11.3137i			0.597115i	0.954392	+	0.298557i	$0.0965054\pi$
$359$			11.3137i			0.597115i	−0.954392	+	0.298557i	$0.903495\pi$
$360$	−2.82843	+	1.00000i	−0.149071	+	0.0527046i
$361$		−	11.0000i		−	0.578947i
$362$	4.24264	+	4.24264i	0.222988	+	0.222988i
$363$	−9.89949	−	7.00000i	−0.519589	−	0.367405i
$364$	4.00000	−	4.00000i	0.209657	−	0.209657i
$365$	−4.24264	−	4.24264i	−0.222070	−	0.222070i
$366$	−8.00000	−	5.65685i	−0.418167	−	0.295689i
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	4.24264	−	4.24264i	0.221163	−	0.221163i
$369$	5.65685	+	16.0000i	0.294484	+	0.832927i
$370$	6.00000	−	1.00000i	0.311925	−	0.0519875i
$371$			11.3137i			0.587378i
$372$	−2.07107	−	12.0711i	−0.107380	−	0.625856i
$373$		−	34.0000i		−	1.76045i	−0.474554	−	0.880227i	$-0.657390\pi$
$373$		−	34.0000i		−	1.76045i	0.474554	−	0.880227i	$-0.342610\pi$
$374$	−8.48528			−0.438763
$375$	0.292893	+	1.70711i	0.0151249	+	0.0881546i
$376$	−1.00000	−	1.00000i	−0.0515711	−	0.0515711i
$377$		0			0
$378$	18.1421	−	10.1421i	0.933131	−	0.521655i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		−	2.82843i		−	0.145095i
$381$	16.9706	+	12.0000i	0.869428	+	0.614779i
$382$	4.00000			0.204658
$383$	11.3137	−	11.3137i	0.578103	−	0.578103i	−0.356277	−	0.934380i	$-0.615954\pi$
$383$	11.3137	−	11.3137i	0.578103	−	0.578103i	0.934380	+	0.356277i	$0.115954\pi$
$384$	−1.70711	+	0.292893i	−0.0871154	+	0.0149466i
$385$	12.0000	−	12.0000i	0.611577	−	0.611577i
$386$			25.4558i			1.29567i
$387$	−16.4558	+	34.4558i	−0.836498	+	1.75149i
$388$	12.0000	−	12.0000i	0.609208	−	0.609208i
$389$	−8.48528	+	8.48528i	−0.430221	+	0.430221i	−0.888703	−	0.458483i	$-0.848393\pi$
$389$	−8.48528	+	8.48528i	−0.430221	+	0.430221i	0.458483	+	0.888703i	$0.348393\pi$
$390$	0.414214	+	2.41421i	0.0209745	+	0.122248i
$391$		−	12.0000i		−	0.606866i
$392$	−6.36396	+	6.36396i	−0.321429	+	0.321429i
$393$	−3.51472	−	20.4853i	−0.177294	−	1.03335i
$394$	14.0000	−	14.0000i	0.705310	−	0.705310i
$395$	−4.24264			−0.213470
$396$	−12.0000	+	4.24264i	−0.603023	+	0.213201i
$397$			18.0000i			0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$			18.0000i			0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$	−4.24264			−0.212664
$399$	3.31371	+	19.3137i	0.165893	+	0.966895i
$400$			1.00000i			0.0500000i
$401$	−15.5563	−	15.5563i	−0.776847	−	0.776847i	0.202446	−	0.979293i	$-0.435111\pi$
$401$	−15.5563	−	15.5563i	−0.776847	−	0.776847i	−0.979293	+	0.202446i	$0.935111\pi$
$402$	3.41421	−	0.585786i	0.170285	−	0.0292164i
$403$	−10.0000			−0.498135
$404$			15.5563i			0.773957i
$405$	−0.949747	+	8.94975i	−0.0471933	+	0.444717i
$406$		0			0
$407$	25.4558	−	4.24264i	1.26180	−	0.210300i
$408$	−2.00000	+	2.82843i	−0.0990148	+	0.140028i
$409$	9.00000	−	9.00000i	0.445021	−	0.445021i	−0.448674	−	0.893695i	$-0.648104\pi$
$409$	9.00000	−	9.00000i	0.445021	−	0.445021i	0.893695	+	0.448674i	$0.148104\pi$
$410$	5.65685			0.279372
$411$	9.89949	−	14.0000i	0.488306	−	0.690569i
$412$	−10.0000	−	10.0000i	−0.492665	−	0.492665i
$413$	−11.3137	+	11.3137i	−0.556711	+	0.556711i
$414$	−6.00000	−	16.9706i	−0.294884	−	0.834058i
$415$	−2.00000	−	2.00000i	−0.0981761	−	0.0981761i
$416$			1.41421i			0.0693375i
$417$	16.0000	−	22.6274i	0.783523	−	1.10807i
$418$		−	12.0000i		−	0.586939i
$419$			12.7279i			0.621800i	0.950443	+	0.310900i	$0.100630\pi$
$419$			12.7279i			0.621800i	−0.950443	+	0.310900i	$0.899370\pi$
$420$	−1.17157	−	6.82843i	−0.0571669	−	0.333193i
$421$	−14.0000	+	14.0000i	−0.682318	+	0.682318i	−0.960522	−	0.278204i	$-0.910261\pi$
$421$	−14.0000	+	14.0000i	−0.682318	+	0.682318i	0.278204	+	0.960522i	$0.410261\pi$
$422$	−11.3137	−	11.3137i	−0.550743	−	0.550743i
$423$	−4.00000	+	1.41421i	−0.194487	+	0.0687614i
$424$	−2.00000	−	2.00000i	−0.0971286	−	0.0971286i
$425$	1.41421	+	1.41421i	0.0685994	+	0.0685994i
$426$	−4.82843	+	0.828427i	−0.233938	+	0.0401374i
$427$	16.0000	−	16.0000i	0.774294	−	0.774294i
$428$	14.1421			0.683586
$429$	1.75736	+	10.2426i	0.0848461	+	0.494519i
$430$	9.00000	+	9.00000i	0.434019	+	0.434019i
$431$	8.48528	+	8.48528i	0.408722	+	0.408722i	0.881293	−	0.472571i	$-0.156674\pi$
$431$	8.48528	+	8.48528i	0.408722	+	0.408722i	−0.472571	+	0.881293i	$0.656674\pi$
$432$	−1.41421	+	5.00000i	−0.0680414	+	0.240563i
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$	28.2843			1.35769
$435$		0			0
$436$	−12.0000	+	12.0000i	−0.574696	+	0.574696i
$437$	16.9706			0.811812
$438$	−10.2426	+	1.75736i	−0.489412	+	0.0839699i
$439$	5.00000	−	5.00000i	0.238637	−	0.238637i	−0.577649	−	0.816286i	$-0.696030\pi$
$439$	5.00000	−	5.00000i	0.238637	−	0.238637i	0.816286	+	0.577649i	$0.196030\pi$
$440$			4.24264i			0.202260i
$441$	9.00000	+	25.4558i	0.428571	+	1.21218i
$442$	2.00000	+	2.00000i	0.0951303	+	0.0951303i
$443$	2.82843			0.134383			0.0671913	−	0.997740i	$-0.478596\pi$
$443$	2.82843			0.134383			0.0671913	+	0.997740i	$0.478596\pi$
$444$	4.58579	−	9.48528i	0.217632	−	0.450152i
$445$	−18.0000			−0.853282
$446$	−8.48528	−	8.48528i	−0.401790	−	0.401790i
$447$	−9.89949	+	14.0000i	−0.468230	+	0.662177i
$448$		−	4.00000i		−	0.188982i
$449$	−12.7279	+	12.7279i	−0.600668	+	0.600668i	−0.940490	−	0.339822i	$-0.889633\pi$
$449$	−12.7279	+	12.7279i	−0.600668	+	0.600668i	0.339822	+	0.940490i	$0.389633\pi$
$450$	2.70711	+	1.29289i	0.127614	+	0.0609476i
$451$	24.0000			1.13012
$452$	−4.24264	+	4.24264i	−0.199557	+	0.199557i
$453$		0			0
$454$	−28.0000			−1.31411
$455$	−5.65685			−0.265197
$456$	−4.00000	−	2.82843i	−0.187317	−	0.132453i
$457$	−12.0000	−	12.0000i	−0.561336	−	0.561336i	0.368351	−	0.929687i	$-0.379923\pi$
$457$	−12.0000	−	12.0000i	−0.561336	−	0.561336i	−0.929687	+	0.368351i	$0.879923\pi$
$458$	18.3848	+	18.3848i	0.859064	+	0.859064i
$459$	5.07107	+	9.07107i	0.236697	+	0.423401i
$460$	−6.00000			−0.279751
$461$	−24.0416	+	24.0416i	−1.11973	+	1.11973i	−0.127950	+	0.991781i	$0.540840\pi$
$461$	−24.0416	+	24.0416i	−1.11973	+	1.11973i	−0.991781	+	0.127950i	$0.959160\pi$
$462$	−4.97056	−	28.9706i	−0.231252	−	1.34783i
$463$	−22.0000	−	22.0000i	−1.02243	−	1.02243i	−0.999743	−	0.0226840i	$-0.992779\pi$
$463$	−22.0000	−	22.0000i	−1.02243	−	1.02243i	−0.0226840	−	0.999743i	$-0.507221\pi$
$464$		0			0
$465$	−7.07107	+	10.0000i	−0.327913	+	0.463739i
$466$	−5.00000	−	5.00000i	−0.231621	−	0.231621i
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	−0.482980	−	0.875632i	$-0.660445\pi$
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	0.875632	+	0.482980i	$0.160445\pi$
$468$	3.82843	+	1.82843i	0.176969	+	0.0845191i
$469$			8.00000i			0.369406i
$470$			1.41421i			0.0652328i
$471$	25.4558	+	18.0000i	1.17294	+	0.829396i
$472$		−	4.00000i		−	0.184115i
$473$	38.1838	+	38.1838i	1.75569	+	1.75569i
$474$	−4.24264	+	6.00000i	−0.194871	+	0.275589i
$475$	−2.00000	+	2.00000i	−0.0917663	+	0.0917663i
$476$	−5.65685	−	5.65685i	−0.259281	−	0.259281i
$477$	−8.00000	+	2.82843i	−0.366295	+	0.129505i
$478$		0			0
$479$	25.4558	−	25.4558i	1.16311	−	1.16311i	0.179316	−	0.983792i	$-0.442612\pi$
$479$	25.4558	−	25.4558i	1.16311	−	1.16311i	0.983792	−	0.179316i	$-0.0573883\pi$
$480$	1.41421	+	1.00000i	0.0645497	+	0.0456435i
$481$	−7.00000	−	5.00000i	−0.319173	−	0.227980i
$482$			4.24264i			0.193247i
$483$	40.9706	−	7.02944i	1.86423	−	0.319850i
$484$			7.00000i			0.318182i
$485$	−16.9706			−0.770594
$486$	11.7071	+	10.2929i	0.531045	+	0.466895i
$487$	22.0000	+	22.0000i	0.996915	+	0.996915i	0.999995	−	0.00308010i	$-0.000980427\pi$
$487$	22.0000	+	22.0000i	0.996915	+	0.996915i	−0.00308010	+	0.999995i	$0.500980\pi$
$488$			5.65685i			0.256074i
$489$	12.0711	−	2.07107i	0.545873	−	0.0936569i
$490$	9.00000			0.406579
$491$			21.2132i			0.957338i	0.877995	+	0.478669i	$0.158881\pi$
$491$			21.2132i			0.957338i	−0.877995	+	0.478669i	$0.841119\pi$
$492$	5.65685	−	8.00000i	0.255031	−	0.360668i
$493$		0			0
$494$	−2.82843	+	2.82843i	−0.127257	+	0.127257i
$495$	11.4853	+	5.48528i	0.516225	+	0.246545i
$496$	−5.00000	+	5.00000i	−0.224507	+	0.224507i
$497$		−	11.3137i		−	0.507489i
$498$	−4.82843	+	0.828427i	−0.216367	+	0.0371227i
$499$	−12.0000	+	12.0000i	−0.537194	+	0.537194i	−0.922704	−	0.385510i	$-0.874026\pi$
$499$	−12.0000	+	12.0000i	−0.537194	+	0.537194i	0.385510	+	0.922704i	$0.374026\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	30.7279	−	5.27208i	1.37282	−	0.235539i
$502$		−	4.00000i		−	0.178529i
$503$	−21.2132	+	21.2132i	−0.945850	+	0.945850i	−0.998607	−	0.0527574i	$-0.983199\pi$
$503$	−21.2132	+	21.2132i	−0.945850	+	0.945850i	0.0527574	+	0.998607i	$0.483199\pi$
$504$	−10.8284	−	5.17157i	−0.482336	−	0.230360i
$505$	11.0000	−	11.0000i	0.489494	−	0.489494i
$506$	−25.4558			−1.13165
$507$	−11.0000	+	15.5563i	−0.488527	+	0.690882i
$508$		−	12.0000i		−	0.532414i
$509$	−24.0416			−1.06563			−0.532813	−	0.846233i	$-0.678865\pi$
$509$	−24.0416			−1.06563			−0.532813	+	0.846233i	$0.678865\pi$
$510$	3.41421	−	0.585786i	0.151184	−	0.0259391i
$511$		−	24.0000i		−	1.06170i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−12.8284	+	7.17157i	−0.566389	+	0.316633i
$514$	4.00000			0.176432
$515$			14.1421i			0.623177i
$516$	21.7279	−	3.72792i	0.956518	−	0.164113i
$517$			6.00000i			0.263880i
$518$	19.7990	+	14.1421i	0.869918	+	0.621370i
$519$	4.00000	+	2.82843i	0.175581	+	0.124154i
$520$	1.00000	−	1.00000i	0.0438529	−	0.0438529i
$521$	8.48528			0.371747			0.185873	−	0.982574i	$-0.440489\pi$
$521$	8.48528			0.371747			0.185873	+	0.982574i	$0.440489\pi$
$522$		0			0
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	0.482405	−	0.875948i	$-0.339763\pi$
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	−0.875948	+	0.482405i	$0.839763\pi$
$524$	−8.48528	+	8.48528i	−0.370681	+	0.370681i
$525$	−4.00000	+	5.65685i	−0.174574	+	0.246885i
$526$	−19.0000	−	19.0000i	−0.828439	−	0.828439i
$527$			14.1421i			0.616041i
$528$	6.00000	+	4.24264i	0.261116	+	0.184637i
$529$		−	13.0000i		−	0.565217i
$530$			2.82843i			0.122859i
$531$	−10.8284	−	5.17157i	−0.469914	−	0.224427i
$532$	8.00000	−	8.00000i	0.346844	−	0.346844i
$533$	−5.65685	−	5.65685i	−0.245026	−	0.245026i
$534$	−18.0000	+	25.4558i	−0.778936	+	1.10158i
$535$	−10.0000	−	10.0000i	−0.432338	−	0.432338i
$536$	−1.41421	−	1.41421i	−0.0610847	−	0.0610847i
$537$	5.27208	+	30.7279i	0.227507	+	1.32601i
$538$	15.0000	−	15.0000i	0.646696	−	0.646696i
$539$	38.1838			1.64469
$540$	4.53553	−	2.53553i	0.195178	−	0.109112i
$541$	2.00000	+	2.00000i	0.0859867	+	0.0859867i	0.748792	−	0.662805i	$-0.230634\pi$
$541$	2.00000	+	2.00000i	0.0859867	+	0.0859867i	−0.662805	+	0.748792i	$0.730634\pi$
$542$	−5.65685	−	5.65685i	−0.242983	−	0.242983i
$543$	−8.48528	−	6.00000i	−0.364138	−	0.257485i
$544$	2.00000			0.0857493
$545$	16.9706			0.726939
$546$	−5.65685	+	8.00000i	−0.242091	+	0.342368i
$547$	−21.0000	+	21.0000i	−0.897895	+	0.897895i	−0.995250	−	0.0973546i	$-0.968962\pi$
$547$	−21.0000	+	21.0000i	−0.897895	+	0.897895i	0.0973546	+	0.995250i	$0.468962\pi$
$548$	−9.89949			−0.422885
$549$	15.3137	+	7.31371i	0.653573	+	0.312141i
$550$	3.00000	−	3.00000i	0.127920	−	0.127920i
$551$		0			0
$552$	−6.00000	+	8.48528i	−0.255377	+	0.361158i
$553$	−12.0000	−	12.0000i	−0.510292	−	0.510292i
$554$	−21.2132			−0.901263
$555$	−9.94975	+	3.46447i	−0.422343	+	0.147058i
$556$	−16.0000			−0.678551
$557$	−24.0416	−	24.0416i	−1.01868	−	1.01868i	−0.999822	−	0.0188543i	$-0.993998\pi$
$557$	−24.0416	−	24.0416i	−1.01868	−	1.01868i	−0.0188543	−	0.999822i	$-0.506002\pi$
$558$	7.07107	+	20.0000i	0.299342	+	0.846668i
$559$		−	18.0000i		−	0.761319i
$560$	−2.82843	+	2.82843i	−0.119523	+	0.119523i
$561$	14.4853	−	2.48528i	0.611569	−	0.104929i
$562$	−10.0000			−0.421825
$563$	5.65685	−	5.65685i	0.238408	−	0.238408i	−0.577783	−	0.816191i	$-0.696082\pi$
$563$	5.65685	−	5.65685i	0.238408	−	0.238408i	0.816191	+	0.577783i	$0.196082\pi$
$564$	2.00000	+	1.41421i	0.0842152	+	0.0595491i
$565$	6.00000			0.252422
$566$	−21.2132			−0.891657
$567$	−28.0000	+	22.6274i	−1.17589	+	0.950262i
$568$	2.00000	+	2.00000i	0.0839181	+	0.0839181i
$569$	18.3848	+	18.3848i	0.770730	+	0.770730i	0.978234	−	0.207504i	$-0.0665341\pi$
$569$	18.3848	+	18.3848i	0.770730	+	0.770730i	−0.207504	+	0.978234i	$0.566534\pi$
$570$	0.828427	+	4.82843i	0.0346990	+	0.202241i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	4.24264	−	4.24264i	0.177394	−	0.177394i
$573$	−6.82843	+	1.17157i	−0.285262	+	0.0489432i
$574$	16.0000	+	16.0000i	0.667827	+	0.667827i
$575$	4.24264	+	4.24264i	0.176930	+	0.176930i
$576$	2.82843	−	1.00000i	0.117851	−	0.0416667i
$577$	20.0000	+	20.0000i	0.832611	+	0.832611i	0.987873	−	0.155262i	$-0.0496223\pi$
$577$	20.0000	+	20.0000i	0.832611	+	0.832611i	−0.155262	+	0.987873i	$0.549622\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$	−7.45584	−	43.4558i	−0.309854	−	1.80596i
$580$		0			0
$581$		−	11.3137i		−	0.469372i
$582$	−16.9706	+	24.0000i	−0.703452	+	0.994832i
$583$			12.0000i			0.496989i
$584$	4.24264	+	4.24264i	0.175562	+	0.175562i
$585$	−1.41421	−	4.00000i	−0.0584705	−	0.165380i
$586$	20.0000	−	20.0000i	0.826192	−	0.826192i
$587$	16.9706	+	16.9706i	0.700450	+	0.700450i	0.964507	−	0.264057i	$-0.0850607\pi$
$587$	16.9706	+	16.9706i	0.700450	+	0.700450i	−0.264057	+	0.964507i	$0.585061\pi$
$588$	9.00000	−	12.7279i	0.371154	−	0.524891i
$589$	−20.0000			−0.824086
$590$	−2.82843	+	2.82843i	−0.116445	+	0.116445i
$591$	−19.7990	+	28.0000i	−0.814422	+	1.15177i
$592$	−6.00000	+	1.00000i	−0.246598	+	0.0410997i
$593$		−	15.5563i		−	0.638823i	−0.947616	−	0.319411i	$-0.896515\pi$
$593$		−	15.5563i		−	0.638823i	0.947616	−	0.319411i	$-0.103485\pi$
$594$	19.2426	−	10.7574i	0.789535	−	0.441380i
$595$			8.00000i			0.327968i
$596$	9.89949			0.405499
$597$	7.24264	−	1.24264i	0.296422	−	0.0508579i
$598$	6.00000	+	6.00000i	0.245358	+	0.245358i
$599$		−	16.9706i		−	0.693398i	−0.937976	−	0.346699i	$-0.887302\pi$
$599$		−	16.9706i		−	0.693398i	0.937976	−	0.346699i	$-0.112698\pi$
$600$	−0.292893	−	1.70711i	−0.0119573	−	0.0696923i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$			50.9117i			2.07501i
$603$	−5.65685	+	2.00000i	−0.230365	+	0.0814463i
$604$		0			0
$605$	4.94975	−	4.94975i	0.201236	−	0.201236i
$606$	−4.55635	−	26.5563i	−0.185089	−	1.07878i
$607$	−22.0000	+	22.0000i	−0.892952	+	0.892952i	−0.994800	−	0.101848i	$-0.967525\pi$
$607$	−22.0000	+	22.0000i	−0.892952	+	0.892952i	0.101848	+	0.994800i	$0.467525\pi$
$608$			2.82843i			0.114708i
$609$		0			0
$610$	4.00000	−	4.00000i	0.161955	−	0.161955i
$611$	1.41421	−	1.41421i	0.0572130	−	0.0572130i
$612$	2.58579	−	5.41421i	0.104524	−	0.218857i
$613$			16.0000i			0.646234i	0.946359	+	0.323117i	$0.104731\pi$
$613$			16.0000i			0.646234i	−0.946359	+	0.323117i	$0.895269\pi$
$614$	2.82843	−	2.82843i	0.114146	−	0.114146i
$615$	−9.65685	+	1.65685i	−0.389402	+	0.0668108i
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	−21.2132			−0.854011			−0.427006	−	0.904249i	$-0.640432\pi$
$617$	−21.2132			−0.854011			−0.427006	+	0.904249i	$0.640432\pi$
$618$	20.0000	+	14.1421i	0.804518	+	0.568880i
$619$		−	16.0000i		−	0.643094i	−0.946894	−	0.321547i	$-0.895797\pi$
$619$		−	16.0000i		−	0.643094i	0.946894	−	0.321547i	$-0.104203\pi$
$620$	7.07107			0.283981
$621$	15.2132	+	27.2132i	0.610485	+	1.09203i
$622$		−	12.0000i		−	0.481156i
$623$	−50.9117	−	50.9117i	−2.03973	−	2.03973i
$624$	−0.414214	−	2.41421i	−0.0165818	−	0.0966459i
$625$	−1.00000			−0.0400000
$626$			8.48528i			0.339140i
$627$	3.51472	+	20.4853i	0.140364	+	0.818103i
$628$		−	18.0000i		−	0.718278i
$629$	−7.07107	+	9.89949i	−0.281942	+	0.394719i
$630$	4.00000	+	11.3137i	0.159364	+	0.450749i
$631$	1.00000	−	1.00000i	0.0398094	−	0.0398094i	−0.686922	−	0.726731i	$-0.741039\pi$
$631$	1.00000	−	1.00000i	0.0398094	−	0.0398094i	0.726731	+	0.686922i	$0.241039\pi$
$632$	4.24264			0.168763
$633$	22.6274	+	16.0000i	0.899359	+	0.635943i
$634$	6.00000	+	6.00000i	0.238290	+	0.238290i
$635$	−8.48528	+	8.48528i	−0.336728	+	0.336728i
$636$	4.00000	+	2.82843i	0.158610	+	0.112154i
$637$	−9.00000	−	9.00000i	−0.356593	−	0.356593i
$638$		0			0
$639$	8.00000	−	2.82843i	0.316475	−	0.111891i
$640$		−	1.00000i		−	0.0395285i
$641$		−	22.6274i		−	0.893729i	−0.894602	−	0.446865i	$-0.852541\pi$
$641$		−	22.6274i		−	0.893729i	0.894602	−	0.446865i	$-0.147459\pi$
$642$	−24.1421	+	4.14214i	−0.952814	+	0.163477i
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	−0.287397	−	0.957812i	$-0.592790\pi$
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	0.957812	+	0.287397i	$0.0927899\pi$
$644$	−16.9706	−	16.9706i	−0.668734	−	0.668734i
$645$	−18.0000	−	12.7279i	−0.708749	−	0.501161i
$646$	4.00000	+	4.00000i	0.157378	+	0.157378i
$647$	22.6274	+	22.6274i	0.889576	+	0.889576i	0.994482	−	0.104907i	$-0.0334543\pi$
$647$	22.6274	+	22.6274i	0.889576	+	0.889576i	−0.104907	+	0.994482i	$0.533454\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$	−12.0000	+	12.0000i	−0.471041	+	0.471041i
$650$	−1.41421			−0.0554700
$651$	−48.2843	+	8.28427i	−1.89241	+	0.324686i
$652$	−5.00000	−	5.00000i	−0.195815	−	0.195815i
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$	16.9706	−	24.0000i	0.663602	−	0.938474i
$655$	12.0000			0.468879
$656$	−5.65685			−0.220863
$657$	16.9706	−	6.00000i	0.662085	−	0.234082i
$658$	−4.00000	+	4.00000i	−0.155936	+	0.155936i
$659$	9.89949			0.385630			0.192815	−	0.981235i	$-0.438238\pi$
$659$	9.89949			0.385630			0.192815	+	0.981235i	$0.438238\pi$
$660$	−1.24264	−	7.24264i	−0.0483697	−	0.281919i
$661$	10.0000	−	10.0000i	0.388955	−	0.388955i	−0.485360	−	0.874315i	$-0.661311\pi$
$661$	10.0000	−	10.0000i	0.388955	−	0.388955i	0.874315	+	0.485360i	$0.161311\pi$
$662$		−	5.65685i		−	0.219860i
$663$	−4.00000	−	2.82843i	−0.155347	−	0.109847i
$664$	2.00000	+	2.00000i	0.0776151	+	0.0776151i
$665$	−11.3137			−0.438727
$666$	−5.05025	+	17.5355i	−0.195693	+	0.679488i
$667$		0			0
$668$	−12.7279	−	12.7279i	−0.492458	−	0.492458i
$669$	16.9706	+	12.0000i	0.656120	+	0.463947i
$670$			2.00000i			0.0772667i
$671$	16.9706	−	16.9706i	0.655141	−	0.655141i
$672$	1.17157	+	6.82843i	0.0451944	+	0.263412i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	1.41421	−	1.41421i	0.0544735	−	0.0544735i
$675$	−5.00000	−	1.41421i	−0.192450	−	0.0544331i
$676$	11.0000			0.423077
$677$	28.2843			1.08705			0.543526	−	0.839392i	$-0.317089\pi$
$677$	28.2843			1.08705			0.543526	+	0.839392i	$0.317089\pi$
$678$	6.00000	−	8.48528i	0.230429	−	0.325875i
$679$	−48.0000	−	48.0000i	−1.84207	−	1.84207i
$680$	−1.41421	−	1.41421i	−0.0542326	−	0.0542326i
$681$	47.7990	−	8.20101i	1.83166	−	0.314263i
$682$	30.0000			1.14876
$683$	22.6274	−	22.6274i	0.865814	−	0.865814i	−0.126192	−	0.992006i	$-0.540275\pi$
$683$	22.6274	−	22.6274i	0.865814	−	0.865814i	0.992006	+	0.126192i	$0.0402755\pi$
$684$	7.65685	+	3.65685i	0.292767	+	0.139823i
$685$	7.00000	+	7.00000i	0.267456	+	0.267456i
$686$	5.65685	+	5.65685i	0.215980	+	0.215980i
$687$	−36.7696	−	26.0000i	−1.40285	−	0.991962i
$688$	−9.00000	−	9.00000i	−0.343122	−	0.343122i
$689$	2.82843	−	2.82843i	0.107754	−	0.107754i
$690$	10.2426	−	1.75736i	0.389931	−	0.0669015i
$691$		−	28.0000i		−	1.06517i	−0.846376	−	0.532585i	$-0.821221\pi$
$691$		−	28.0000i		−	1.06517i	0.846376	−	0.532585i	$-0.178779\pi$
$692$		−	2.82843i		−	0.107521i
$693$	16.9706	+	48.0000i	0.644658	+	1.82337i
$694$			12.0000i			0.455514i
$695$	11.3137	+	11.3137i	0.429153	+	0.429153i
$696$		0			0
$697$	−8.00000	+	8.00000i	−0.303022	+	0.303022i
$698$	−9.89949	−	9.89949i	−0.374701	−	0.374701i
$699$	10.0000	+	7.07107i	0.378235	+	0.267452i
$700$	4.00000			0.151186
$701$	−35.3553	+	35.3553i	−1.33535	+	1.33535i	−0.434850	+	0.900503i	$0.643198\pi$
$701$	−35.3553	+	35.3553i	−1.33535	+	1.33535i	−0.900503	+	0.434850i	$0.856802\pi$
$702$	−7.07107	−	2.00000i	−0.266880	−	0.0754851i
$703$	−14.0000	−	10.0000i	−0.528020	−	0.377157i
$704$		−	4.24264i		−	0.159901i
$705$	−0.414214	−	2.41421i	−0.0156002	−	0.0909245i
$706$		−	34.0000i		−	1.27961i
$707$	62.2254			2.34023
$708$	1.17157	+	6.82843i	0.0440304	+	0.256628i
$709$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$709$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$710$		−	2.82843i		−	0.106149i
$711$	5.48528	−	11.4853i	0.205714	−	0.430732i
$712$	18.0000			0.674579
$713$			42.4264i			1.58888i
$714$	11.3137	+	8.00000i	0.423405	+	0.299392i
$715$	−6.00000			−0.224387
$716$	12.7279	−	12.7279i	0.475665	−	0.475665i
$717$		0			0
$718$	−8.00000	+	8.00000i	−0.298557	+	0.298557i
$719$			19.7990i			0.738378i	0.929354	+	0.369189i	$0.120364\pi$
$719$			19.7990i			0.738378i	−0.929354	+	0.369189i	$0.879636\pi$
$720$	−2.70711	−	1.29289i	−0.100888	−	0.0481833i
$721$	−40.0000	+	40.0000i	−1.48968	+	1.48968i
$722$	7.77817	−	7.77817i	0.289474	−	0.289474i
$723$	−1.24264	−	7.24264i	−0.0462143	−	0.269357i
$724$			6.00000i			0.222988i
$725$		0			0
$726$	−2.05025	−	11.9497i	−0.0760920	−	0.443497i
$727$	8.00000	−	8.00000i	0.296704	−	0.296704i	−0.543018	−	0.839721i	$-0.682718\pi$
$727$	8.00000	−	8.00000i	0.296704	−	0.296704i	0.839721	+	0.543018i	$0.182718\pi$
$728$	5.65685			0.209657
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		−	6.00000i		−	0.222070i
$731$	−25.4558			−0.941518
$732$	−1.65685	−	9.65685i	−0.0612391	−	0.356928i
$733$			24.0000i			0.886460i	0.896408	+	0.443230i	$0.146168\pi$
$733$			24.0000i			0.886460i	−0.896408	+	0.443230i	$0.853832\pi$
$734$	5.65685	+	5.65685i	0.208798	+	0.208798i
$735$	−15.3640	+	2.63604i	−0.566708	+	0.0972318i
$736$	6.00000			0.221163
$737$			8.48528i			0.312559i
$738$	−7.31371	+	15.3137i	−0.269221	+	0.563705i
$739$			40.0000i			1.47142i	0.677295	+	0.735712i	$0.263152\pi$
$739$			40.0000i			1.47142i	−0.677295	+	0.735712i	$0.736848\pi$
$740$	4.94975	+	3.53553i	0.181956	+	0.129969i
$741$	4.00000	−	5.65685i	0.146944	−	0.207810i
$742$	−8.00000	+	8.00000i	−0.293689	+	0.293689i
$743$	49.4975			1.81589			0.907943	−	0.419093i	$-0.137652\pi$
$743$	49.4975			1.81589			0.907943	+	0.419093i	$0.137652\pi$
$744$	7.07107	−	10.0000i	0.259238	−	0.366618i
$745$	−7.00000	−	7.00000i	−0.256460	−	0.256460i
$746$	24.0416	−	24.0416i	0.880227	−	0.880227i
$747$	8.00000	−	2.82843i	0.292705	−	0.103487i
$748$	−6.00000	−	6.00000i	−0.219382	−	0.219382i
$749$		−	56.5685i		−	2.06697i
$750$	−1.00000	+	1.41421i	−0.0365148	+	0.0516398i
$751$		−	2.00000i		−	0.0729810i	−0.999334	−	0.0364905i	$-0.988382\pi$
$751$		−	2.00000i		−	0.0729810i	0.999334	−	0.0364905i	$-0.0116179\pi$
$752$		−	1.41421i		−	0.0515711i
$753$	1.17157	+	6.82843i	0.0426945	+	0.248842i
$754$		0			0
$755$		0			0
$756$	20.0000	+	5.65685i	0.727393	+	0.205738i
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	0.610380	−	0.792108i	$-0.291017\pi$
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	−0.792108	+	0.610380i	$0.791017\pi$
$758$		0			0
$759$	43.4558	−	7.45584i	1.57735	−	0.270630i
$760$	2.00000	−	2.00000i	0.0725476	−	0.0725476i
$761$	22.6274			0.820243			0.410122	−	0.912031i	$-0.365486\pi$
$761$	22.6274			0.820243			0.410122	+	0.912031i	$0.365486\pi$
$762$	3.51472	+	20.4853i	0.127325	+	0.742103i
$763$	48.0000	+	48.0000i	1.73772	+	1.73772i
$764$	2.82843	+	2.82843i	0.102329	+	0.102329i
$765$	−5.65685	+	2.00000i	−0.204524	+	0.0723102i
$766$	16.0000			0.578103
$767$	5.65685			0.204257
$768$	−1.41421	−	1.00000i	−0.0510310	−	0.0360844i
$769$	19.0000	−	19.0000i	0.685158	−	0.685158i	−0.276000	−	0.961158i	$-0.589009\pi$
$769$	19.0000	−	19.0000i	0.685158	−	0.685158i	0.961158	+	0.276000i	$0.0890090\pi$
$770$	16.9706			0.611577
$771$	−6.82843	+	1.17157i	−0.245920	+	0.0421932i
$772$	−18.0000	+	18.0000i	−0.647834	+	0.647834i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−36.0000	+	12.7279i	−1.29399	+	0.457496i
$775$	−5.00000	−	5.00000i	−0.179605	−	0.179605i
$776$	16.9706			0.609208
$777$	−37.9411	−	18.3431i	−1.36113	−	0.658057i
$778$	−12.0000			−0.430221
$779$	−11.3137	−	11.3137i	−0.405356	−	0.405356i
$780$	−1.41421	+	2.00000i	−0.0506370	+	0.0716115i
$781$		−	12.0000i		−	0.429394i
$782$	8.48528	−	8.48528i	0.303433	−	0.303433i
$783$		0			0
$784$	−9.00000			−0.321429
$785$	−12.7279	+	12.7279i	−0.454279	+	0.454279i
$786$	12.0000	−	16.9706i	0.428026	−	0.605320i
$787$	14.0000			0.499046			0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000			0.499046			0.249523	+	0.968369i	$0.419726\pi$
$788$	19.7990			0.705310
$789$	38.0000	+	26.8701i	1.35284	+	0.956599i
$790$	−3.00000	−	3.00000i	−0.106735	−	0.106735i
$791$	16.9706	+	16.9706i	0.603404	+	0.603404i
$792$	−11.4853	−	5.48528i	−0.408112	−	0.194911i
$793$	−8.00000			−0.284088
$794$	−12.7279	+	12.7279i	−0.451697	+	0.451697i
$795$	−0.828427	−	4.82843i	−0.0293813	−	0.171247i
$796$	−3.00000	−	3.00000i	−0.106332	−	0.106332i
$797$	18.3848	+	18.3848i	0.651222	+	0.651222i	0.953287	−	0.302065i	$-0.0976760\pi$
$797$	18.3848	+	18.3848i	0.651222	+	0.651222i	−0.302065	+	0.953287i	$0.597676\pi$
$798$	−11.3137	+	16.0000i	−0.400501	+	0.566394i
$799$	−2.00000	−	2.00000i	−0.0707549	−	0.0707549i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	23.2721	−	48.7279i	0.822278	−	1.72172i
$802$		−	22.0000i		−	0.776847i
$803$		−	25.4558i		−	0.898317i
$804$	2.82843	+	2.00000i	0.0997509	+	0.0705346i
$805$			24.0000i			0.845889i
$806$	−7.07107	−	7.07107i	−0.249068	−	0.249068i
$807$	−21.2132	+	30.0000i	−0.746740	+	1.05605i
$808$	−11.0000	+	11.0000i	−0.386979	+	0.386979i
$809$	−7.07107	−	7.07107i	−0.248606	−	0.248606i	0.571793	−	0.820398i	$-0.306248\pi$
$809$	−7.07107	−	7.07107i	−0.248606	−	0.248606i	−0.820398	+	0.571793i	$0.806248\pi$
$810$	−7.00000	+	5.65685i	−0.245955	+	0.198762i
$811$	48.0000			1.68551			0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000			1.68551			0.842754	+	0.538299i	$0.180933\pi$
$812$		0			0
$813$	11.3137	+	8.00000i	0.396789	+	0.280572i
$814$	21.0000	+	15.0000i	0.736050	+	0.525750i
$815$			7.07107i			0.247689i
$816$	−3.41421	+	0.585786i	−0.119521	+	0.0205066i
$817$		−	36.0000i		−	1.25948i
$818$	12.7279			0.445021
$819$	7.31371	−	15.3137i	0.255562	−	0.535104i
$820$	4.00000	+	4.00000i	0.139686	+	0.139686i
$821$		−	26.8701i		−	0.937771i	−0.883259	−	0.468886i	$-0.844656\pi$
$821$		−	26.8701i		−	0.937771i	0.883259	−	0.468886i	$-0.155344\pi$
$822$	16.8995	−	2.89949i	0.589438	−	0.101131i
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$		−	14.1421i		−	0.492665i
$825$	−4.24264	+	6.00000i	−0.147710	+	0.208893i
$826$	−16.0000			−0.556711
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	−0.347541	−	0.937665i	$-0.612983\pi$
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	0.937665	+	0.347541i	$0.112983\pi$
$828$	7.75736	−	16.2426i	0.269587	−	0.564471i
$829$	12.0000	−	12.0000i	0.416777	−	0.416777i	−0.467314	−	0.884091i	$-0.654778\pi$
$829$	12.0000	−	12.0000i	0.416777	−	0.416777i	0.884091	+	0.467314i	$0.154778\pi$
$830$		−	2.82843i		−	0.0981761i
$831$	36.2132	−	6.21320i	1.25622	−	0.215534i
$832$	−1.00000	+	1.00000i	−0.0346688	+	0.0346688i
$833$	−12.7279	+	12.7279i	−0.440996	+	0.440996i
$834$	27.3137	−	4.68629i	0.945796	−	0.162273i
$835$			18.0000i			0.622916i
$836$	8.48528	−	8.48528i	0.293470	−	0.293470i
$837$	−17.9289	−	32.0711i	−0.619715	−	1.10854i
$838$	−9.00000	+	9.00000i	−0.310900	+	0.310900i
$839$	19.7990			0.683537			0.341769	−	0.939784i	$-0.388974\pi$
$839$	19.7990			0.683537			0.341769	+	0.939784i	$0.388974\pi$
$840$	4.00000	−	5.65685i	0.138013	−	0.195180i
$841$		−	29.0000i		−	1.00000i
$842$	−19.7990			−0.682318
$843$	17.0711	−	2.92893i	0.587959	−	0.100878i
$844$		−	16.0000i		−	0.550743i
$845$	−7.77817	−	7.77817i	−0.267577	−	0.267577i
$846$	−3.82843	−	1.82843i	−0.131624	−	0.0628626i
$847$	28.0000			0.962091
$848$		−	2.82843i		−	0.0971286i
$849$	36.2132	−	6.21320i	1.24283	−	0.213237i
$850$			2.00000i			0.0685994i
$851$	−21.2132	+	29.6985i	−0.727179	+	1.01805i
$852$	−4.00000	−	2.82843i	−0.137038	−	0.0969003i
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.319152	−	0.947703i	$-0.396602\pi$
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.947703	−	0.319152i	$-0.103398\pi$
$854$	22.6274			0.774294
$855$	−2.82843	−	8.00000i	−0.0967302	−	0.273594i
$856$	10.0000	+	10.0000i	0.341793	+	0.341793i
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	−0.455472	−	0.890250i	$-0.650530\pi$
$857$	12.7279	−	12.7279i	0.434778	−	0.434778i	0.890250	+	0.455472i	$0.150530\pi$
$858$	−6.00000	+	8.48528i	−0.204837	+	0.289683i
$859$	−34.0000	−	34.0000i	−1.16007	−	1.16007i	−0.984461	−	0.175604i	$-0.943812\pi$
$859$	−34.0000	−	34.0000i	−1.16007	−	1.16007i	−0.175604	−	0.984461i	$-0.556188\pi$
$860$			12.7279i			0.434019i
$861$	−32.0000	−	22.6274i	−1.09056	−	0.771140i
$862$			12.0000i			0.408722i
$863$			7.07107i			0.240702i	0.992731	+	0.120351i	$0.0384020\pi$
$863$			7.07107i			0.240702i	−0.992731	+	0.120351i	$0.961598\pi$
$864$	−4.53553	+	2.53553i	−0.154302	+	0.0862606i
$865$	−2.00000	+	2.00000i	−0.0680020	+	0.0680020i
$866$	−4.24264	−	4.24264i	−0.144171	−	0.144171i
$867$	13.0000	−	18.3848i	0.441503	−	0.624380i
$868$	20.0000	+	20.0000i	0.678844	+	0.678844i
$869$	−12.7279	−	12.7279i	−0.431765	−	0.431765i
$870$		0			0
$871$	2.00000	−	2.00000i	0.0677674	−	0.0677674i
$872$	−16.9706			−0.574696
$873$	21.9411	−	45.9411i	0.742595	−	1.55487i
$874$	12.0000	+	12.0000i	0.405906	+	0.405906i
$875$	−2.82843	−	2.82843i	−0.0956183	−	0.0956183i
$876$	−8.48528	−	6.00000i	−0.286691	−	0.202721i
$877$	20.0000			0.675352			0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000			0.675352			0.337676	+	0.941262i	$0.390359\pi$
$878$	7.07107			0.238637
$879$	−28.2843	+	40.0000i	−0.954005	+	1.34917i
$880$	−3.00000	+	3.00000i	−0.101130	+	0.101130i
$881$	−11.3137			−0.381169			−0.190584	−	0.981671i	$-0.561038\pi$
$881$	−11.3137			−0.381169			−0.190584	+	0.981671i	$0.561038\pi$
$882$	−11.6360	+	24.3640i	−0.391806	+	0.820377i
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	−0.654824	−	0.755782i	$-0.727257\pi$
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	0.755782	+	0.654824i	$0.227257\pi$
$884$			2.82843i			0.0951303i
$885$	4.00000	−	5.65685i	0.134459	−	0.190153i
$886$	2.00000	+	2.00000i	0.0671913	+	0.0671913i
$887$	−26.8701			−0.902208			−0.451104	−	0.892471i	$-0.648970\pi$
$887$	−26.8701			−0.902208			−0.451104	+	0.892471i	$0.648970\pi$
$888$	9.94975	−	3.46447i	0.333892	−	0.116260i
$889$	−48.0000			−1.60987
$890$	−12.7279	−	12.7279i	−0.426641	−	0.426641i
$891$	−29.6985	+	24.0000i	−0.994937	+	0.804030i
$892$		−	12.0000i		−	0.401790i
$893$	2.82843	−	2.82843i	0.0946497	−	0.0946497i
$894$	−16.8995	+	2.89949i	−0.565204	+	0.0969736i
$895$	−18.0000			−0.601674
$896$	2.82843	−	2.82843i	0.0944911	−	0.0944911i
$897$	−12.0000	−	8.48528i	−0.400668	−	0.283315i
$898$	−18.0000			−0.600668
$899$		0			0
$900$	1.00000	+	2.82843i	0.0333333	+	0.0942809i
$901$	−4.00000	−	4.00000i	−0.133259	−	0.133259i
$902$	16.9706	+	16.9706i	0.565058	+	0.565058i
$903$	−14.9117	−	86.9117i	−0.496230	−	2.89224i
$904$	−6.00000			−0.199557
$905$	4.24264	−	4.24264i	0.141030	−	0.141030i
$906$		0			0
$907$	−19.0000	−	19.0000i	−0.630885	−	0.630885i	0.317405	−	0.948290i	$-0.397188\pi$
$907$	−19.0000	−	19.0000i	−0.630885	−	0.630885i	−0.948290	+	0.317405i	$0.897188\pi$
$908$	−19.7990	−	19.7990i	−0.657053	−	0.657053i
$909$	15.5563	+	44.0000i	0.515972	+	1.45939i
$910$	−4.00000	−	4.00000i	−0.132599	−	0.132599i
$911$	5.65685	−	5.65685i	0.187420	−	0.187420i	−0.607160	−	0.794580i	$-0.707691\pi$
$911$	5.65685	−	5.65685i	0.187420	−	0.187420i	0.794580	+	0.607160i	$0.207691\pi$
$912$	−0.828427	−	4.82843i	−0.0274320	−	0.159885i
$913$		−	12.0000i		−	0.397142i
$914$		−	16.9706i		−	0.561336i
$915$	−5.65685	+	8.00000i	−0.187010	+	0.264472i
$916$			26.0000i			0.859064i
$917$	33.9411	+	33.9411i	1.12083	+	1.12083i
$918$	−2.82843	+	10.0000i	−0.0933520	+	0.330049i
$919$	−5.00000	+	5.00000i	−0.164935	+	0.164935i	−0.784749	−	0.619814i	$-0.787208\pi$
$919$	−5.00000	+	5.00000i	−0.164935	+	0.164935i	0.619814	+	0.784749i	$0.287208\pi$
$920$	−4.24264	−	4.24264i	−0.139876	−	0.139876i
$921$	−4.00000	+	5.65685i	−0.131804	+	0.186400i
$922$	−34.0000			−1.11973
$923$	−2.82843	+	2.82843i	−0.0930988	+	0.0930988i
$924$	16.9706	−	24.0000i	0.558291	−	0.789542i
$925$	−1.00000	−	6.00000i	−0.0328798	−	0.197279i
$926$		−	31.1127i		−	1.02243i
$927$	−38.2843	−	18.2843i	−1.25742	−	0.600534i
$928$		0			0
$929$	−53.7401			−1.76316			−0.881578	−	0.472038i	$-0.843518\pi$
$929$	−53.7401			−1.76316			−0.881578	+	0.472038i	$0.843518\pi$
$930$	−12.0711	+	2.07107i	−0.395826	+	0.0679130i
$931$	−18.0000	−	18.0000i	−0.589926	−	0.589926i
$932$		−	7.07107i		−	0.231621i
$933$	3.51472	+	20.4853i	0.115067	+	0.670658i
$934$	12.0000			0.392652
$935$			8.48528i			0.277498i
$936$	1.41421	+	4.00000i	0.0462250	+	0.130744i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−5.65685	+	5.65685i	−0.184703	+	0.184703i
$939$	−2.48528	−	14.4853i	−0.0811041	−	0.472709i
$940$	−1.00000	+	1.00000i	−0.0326164	+	0.0326164i
$941$			24.0416i			0.783735i	0.920022	+	0.391867i	$0.128171\pi$
$941$			24.0416i			0.783735i	−0.920022	+	0.391867i	$0.871829\pi$
$942$	5.27208	+	30.7279i	0.171774	+	1.00117i
$943$	−24.0000	+	24.0000i	−0.781548	+	0.781548i
$944$	2.82843	−	2.82843i	0.0920575	−	0.0920575i
$945$	−10.1421	−	18.1421i	−0.329924	−	0.590164i
$946$			54.0000i			1.75569i
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	−0.751568	−	0.659656i	$-0.770702\pi$
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	0.659656	+	0.751568i	$0.270702\pi$
$948$	−7.24264	+	1.24264i	−0.235230	+	0.0403591i
$949$	−6.00000	+	6.00000i	−0.194768	+	0.194768i
$950$	−2.82843			−0.0917663
$951$	−12.0000	−	8.48528i	−0.389127	−	0.275154i
$952$		−	8.00000i		−	0.259281i
$953$	−57.9828			−1.87825			−0.939123	−	0.343582i	$-0.888360\pi$
$953$	−57.9828			−1.87825			−0.939123	+	0.343582i	$0.888360\pi$
$954$	−7.65685	−	3.65685i	−0.247900	−	0.118395i
$955$		−	4.00000i		−	0.129437i
$956$		0			0
$957$		0			0
$958$	36.0000			1.16311
$959$			39.5980i			1.27869i
$960$	0.292893	+	1.70711i	0.00945309	+	0.0550966i
$961$		−	19.0000i		−	0.612903i
$962$	−1.41421	−	8.48528i	−0.0455961	−	0.273576i
$963$	40.0000	−	14.1421i	1.28898	−	0.455724i
$964$	−3.00000	+	3.00000i	−0.0966235	+	0.0966235i
$965$	25.4558			0.819453
$966$	33.9411	+	24.0000i	1.09204	+	0.772187i
$967$	−12.0000	−	12.0000i	−0.385894	−	0.385894i	0.487326	−	0.873220i	$-0.337972\pi$
$967$	−12.0000	−	12.0000i	−0.385894	−	0.385894i	−0.873220	+	0.487326i	$0.837972\pi$
$968$	−4.94975	+	4.94975i	−0.159091	+	0.159091i
$969$	−8.00000	−	5.65685i	−0.256997	−	0.181724i
$970$	−12.0000	−	12.0000i	−0.385297	−	0.385297i
$971$		−	7.07107i		−	0.226921i	−0.993542	−	0.113461i	$-0.963806\pi$
$971$		−	7.07107i		−	0.226921i	0.993542	−	0.113461i	$-0.0361936\pi$
$972$	1.00000	+	15.5563i	0.0320750	+	0.498970i
$973$			64.0000i			2.05175i
$974$			31.1127i			0.996915i
$975$	2.41421	−	0.414214i	0.0773167	−	0.0132655i
$976$	−4.00000	+	4.00000i	−0.128037	+	0.128037i
$977$	22.6274	+	22.6274i	0.723915	+	0.723915i	0.969400	−	0.245485i	$-0.0789473\pi$
$977$	22.6274	+	22.6274i	0.723915	+	0.723915i	−0.245485	+	0.969400i	$0.578947\pi$
$978$	10.0000	+	7.07107i	0.319765	+	0.226108i
$979$	−54.0000	−	54.0000i	−1.72585	−	1.72585i
$980$	6.36396	+	6.36396i	0.203289	+	0.203289i
$981$	−21.9411	+	45.9411i	−0.700526	+	1.46679i
$982$	−15.0000	+	15.0000i	−0.478669	+	0.478669i
$983$	−1.41421			−0.0451064			−0.0225532	−	0.999746i	$-0.507180\pi$
$983$	−1.41421			−0.0451064			−0.0225532	+	0.999746i	$0.507180\pi$
$984$	9.65685	−	1.65685i	0.307849	−	0.0528186i
$985$	−14.0000	−	14.0000i	−0.446077	−	0.446077i
$986$		0			0
$987$	5.65685	−	8.00000i	0.180060	−	0.254643i
$988$	−4.00000			−0.127257
$989$	−76.3675			−2.42835
$990$	4.24264	+	12.0000i	0.134840	+	0.381385i
$991$	3.00000	−	3.00000i	0.0952981	−	0.0952981i	−0.657850	−	0.753149i	$-0.728534\pi$
$991$	3.00000	−	3.00000i	0.0952981	−	0.0952981i	0.753149	+	0.657850i	$0.228534\pi$
$992$	−7.07107			−0.224507
$993$	1.65685	+	9.65685i	0.0525787	+	0.306451i
$994$	8.00000	−	8.00000i	0.253745	−	0.253745i
$995$			4.24264i			0.134501i
$996$	−4.00000	−	2.82843i	−0.126745	−	0.0896221i
$997$	43.0000	+	43.0000i	1.36182	+	1.36182i	0.871592	+	0.490231i	$0.163088\pi$
$997$	43.0000	+	43.0000i	1.36182	+	1.36182i	0.490231	+	0.871592i	$0.336912\pi$
$998$	−16.9706			−0.537194
$999$	3.48528	−	31.4142i	0.110269	−	0.993902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.b.191.2	yes	4
3.2	odd	2	inner	1110.2.u.b.191.1	✓	4
37.31	odd	4	inner	1110.2.u.b.401.1	yes	4
111.68	even	4	inner	1110.2.u.b.401.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.b.191.1	✓	4	3.2	odd	2	inner
1110.2.u.b.191.2	yes	4	1.1	even	1	trivial
1110.2.u.b.401.1	yes	4	37.31	odd	4	inner
1110.2.u.b.401.2	yes	4	111.68	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} +4.24264 q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(2.82843 + 2.82843i) q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-2.00000 - 2.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-5.65685 - 4.00000i) q^{21} +(3.00000 + 3.00000i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -1.41421i q^{26} +(1.41421 - 5.00000i) q^{27} +4.00000i q^{28} +(-1.41421 - 1.00000i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.00000 - 4.24264i) q^{33} -2.00000 q^{34} +(2.82843 - 2.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(6.00000 - 1.00000i) q^{37} -2.82843i q^{38} +(0.414214 + 2.41421i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 - 6.82843i) q^{42} +(9.00000 + 9.00000i) q^{43} +4.24264i q^{44} +(2.70711 + 1.29289i) q^{45} -6.00000 q^{46} +1.41421i q^{47} +(1.41421 + 1.00000i) q^{48} +9.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(1.00000 - 1.00000i) q^{52} +2.82843i q^{53} +(4.53553 - 2.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(0.828427 + 4.82843i) q^{57} +(-2.82843 + 2.82843i) q^{59} +(-0.292893 - 1.70711i) q^{60} +(4.00000 - 4.00000i) q^{61} +7.07107 q^{62} +(4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -1.41421 q^{65} +(-1.24264 - 7.24264i) q^{66} +2.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(10.2426 - 1.75736i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -6.00000i q^{73} +(4.94975 + 3.53553i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(2.00000 - 2.00000i) q^{76} +16.9706 q^{77} +(-1.41421 + 2.00000i) q^{78} +(-3.00000 - 3.00000i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} +2.00000i q^{85} +12.7279i q^{86} +(-3.00000 + 3.00000i) q^{88} +(-12.7279 - 12.7279i) q^{89} +(1.00000 + 2.82843i) q^{90} +(-4.00000 - 4.00000i) q^{91} +(-4.24264 - 4.24264i) q^{92} +(-12.0711 + 2.07107i) q^{93} +(-1.00000 + 1.00000i) q^{94} -2.82843 q^{95} +(0.292893 + 1.70711i) q^{96} +(-12.0000 - 12.0000i) q^{97} +(6.36396 + 6.36396i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{6} + 16 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^6 + 16 * q^7 + 4 * q^9	\( 4 q - 4 q^{6} + 16 q^{7} + 4 q^{9} + 4 q^{10} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} - 8 q^{19} + 12 q^{22} + 4 q^{24} + 20 q^{31} - 24 q^{33} - 8 q^{34} + 24 q^{37} - 4 q^{39} - 16 q^{42} + 36 q^{43} + 8 q^{45} - 24 q^{46} + 36 q^{49} + 8 q^{51} + 4 q^{52} + 4 q^{54} + 12 q^{55} - 8 q^{57} - 4 q^{60} + 16 q^{61} + 16 q^{63} + 12 q^{66} + 24 q^{69} + 16 q^{70} - 8 q^{72} - 4 q^{75} + 8 q^{76} - 12 q^{79} - 28 q^{81} + 16 q^{82} + 16 q^{84} - 12 q^{88} + 4 q^{90} - 16 q^{91} - 20 q^{93} - 4 q^{94} + 4 q^{96} - 48 q^{97}+O(q^{100}) \) 4 * q - 4 * q^6 + 16 * q^7 + 4 * q^9 + 4 * q^10 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 - 8 * q^19 + 12 * q^22 + 4 * q^24 + 20 * q^31 - 24 * q^33 - 8 * q^34 + 24 * q^37 - 4 * q^39 - 16 * q^42 + 36 * q^43 + 8 * q^45 - 24 * q^46 + 36 * q^49 + 8 * q^51 + 4 * q^52 + 4 * q^54 + 12 * q^55 - 8 * q^57 - 4 * q^60 + 16 * q^61 + 16 * q^63 + 12 * q^66 + 24 * q^69 + 16 * q^70 - 8 * q^72 - 4 * q^75 + 8 * q^76 - 12 * q^79 - 28 * q^81 + 16 * q^82 + 16 * q^84 - 12 * q^88 + 4 * q^90 - 16 * q^91 - 20 * q^93 - 4 * q^94 + 4 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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