LMFDB - Embedded newform 1110.2.u.b.191.1

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			191.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.b.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) q^{6} +4.00000 q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) 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} +(-0.292893 + 1.70711i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(-2.70711 + 1.29289i) 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} +(0.292893 - 1.70711i) 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} +(-2.41421 - 0.414214i) q^{39} +1.00000i q^{40} -5.65685 q^{41} +(-6.82843 - 1.17157i) q^{42} +(9.00000 + 9.00000i) q^{43} -4.24264i q^{44} +(1.29289 + 2.70711i) 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} +(0.585786 - 3.41421i) q^{51} +(1.00000 - 1.00000i) q^{52} -2.82843i q^{53} +(-2.53553 + 4.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(2.82843 - 2.82843i) q^{56} +(-4.82843 - 0.828427i) q^{57} +(2.82843 - 2.82843i) q^{59} +(-1.70711 - 0.292893i) 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} +(7.24264 + 1.24264i) q^{66} +2.00000i q^{67} +(1.41421 + 1.41421i) q^{68} +(1.75736 - 10.2426i) q^{69} +4.00000 q^{70} +2.82843i q^{71} +(-1.29289 - 2.70711i) 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} +(2.07107 - 12.0711i) q^{93} +(-1.00000 + 1.00000i) q^{94} +2.82843 q^{95} +(1.70711 + 0.292893i) 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
$6$	−1.70711	−	0.292893i	−0.696923	−	0.119573i
$7$	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	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$	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
$15$	−0.292893	+	1.70711i	−0.0756247	+	0.440773i
$16$	−1.00000			−0.250000
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	−0.514496	−	0.857493i	$-0.672021\pi$
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	0.857493	+	0.514496i	$0.172021\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$	−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	−0.109351	−	0.994003i	$-0.534877\pi$
$23$	4.24264	−	4.24264i	0.884652	−	0.884652i	0.994003	+	0.109351i	$0.0348774\pi$
$24$	0.292893	−	1.70711i	0.0597866	−	0.348462i
$25$		−	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
$39$	−2.41421	−	0.414214i	−0.386584	−	0.0663273i
$40$			1.00000i			0.158114i
$41$	−5.65685			−0.883452			−0.441726	−	0.897150i	$-0.645634\pi$
$41$	−5.65685			−0.883452			−0.441726	+	0.897150i	$0.645634\pi$
$42$	−6.82843	−	1.17157i	−1.05365	−	0.180778i
$43$	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
$45$	1.29289	+	2.70711i	0.192733	+	0.403552i
$46$	−6.00000			−0.884652
$47$		−	1.41421i		−	0.206284i	−0.994667	−	0.103142i	$-0.967110\pi$
$47$		−	1.41421i		−	0.206284i	0.994667	−	0.103142i	$-0.0328896\pi$
$48$	−1.41421	+	1.00000i	−0.204124	+	0.144338i
$49$	9.00000			1.28571
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	0.585786	−	3.41421i	0.0820265	−	0.478086i
$52$	1.00000	−	1.00000i	0.138675	−	0.138675i
$53$		−	2.82843i		−	0.388514i	−0.980951	−	0.194257i	$-0.937770\pi$
$53$		−	2.82843i		−	0.388514i	0.980951	−	0.194257i	$-0.0622296\pi$
$54$	−2.53553	+	4.53553i	−0.345042	+	0.617208i
$55$	3.00000	−	3.00000i	0.404520	−	0.404520i
$56$	2.82843	−	2.82843i	0.377964	−	0.377964i
$57$	−4.82843	−	0.828427i	−0.639541	−	0.109728i
$58$		0			0
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	−0.498601	−	0.866831i	$-0.666153\pi$
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	0.866831	+	0.498601i	$0.166153\pi$
$60$	−1.70711	−	0.292893i	−0.220387	−	0.0378124i
$61$	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
$66$	7.24264	+	1.24264i	0.891507	+	0.152958i
$67$			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
$69$	1.75736	−	10.2426i	0.211561	−	1.23307i
$70$	4.00000			0.478091
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$		−	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	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$	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	$0.153076\pi$
$89$	12.7279	+	12.7279i	1.34916	+	1.34916i	0.462579	+	0.886578i	$0.346924\pi$
$90$	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
$93$	2.07107	−	12.0711i	0.214760	−	1.25171i
$94$	−1.00000	+	1.00000i	−0.103142	+	0.103142i
$95$	2.82843			0.290191
$96$	1.70711	+	0.292893i	0.174231	+	0.0298933i
$97$	−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	$-0.781726\pi$
$101$	−15.5563			−1.54791			−0.773957	+	0.633238i	$0.781726\pi$
$102$	−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
$105$	−1.17157	+	6.82843i	−0.114334	+	0.666386i
$106$	−2.00000	+	2.00000i	−0.194257	+	0.194257i
$107$			14.1421i			1.36717i	0.729870	+	0.683586i	$0.239581\pi$
$107$			14.1421i			1.36717i	−0.729870	+	0.683586i	$0.760419\pi$
$108$	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
$111$	7.48528	−	7.41421i	0.710471	−	0.703726i
$112$	−4.00000			−0.377964
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$	2.82843	+	4.00000i	0.264906	+	0.374634i
$115$			6.00000i			0.559503i
$116$		0			0
$117$	−3.82843	+	1.82843i	−0.353938	+	0.169038i
$118$	−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
$126$	−10.8284	+	5.17157i	−0.964673	+	0.460720i
$127$	−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
$129$	21.7279	+	3.72792i	1.91304	+	0.328225i
$130$	−1.00000	−	1.00000i	−0.0877058	−	0.0877058i
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	0.231478	−	0.972840i	$-0.425644\pi$
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	−0.972840	+	0.231478i	$0.925644\pi$
$132$	−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
$135$	4.53553	+	2.53553i	0.390357	+	0.218224i
$136$		−	2.00000i		−	0.171499i
$137$		−	9.89949i		−	0.845771i	−0.906183	−	0.422885i	$-0.861017\pi$
$137$		−	9.89949i		−	0.845771i	0.906183	−	0.422885i	$-0.138983\pi$
$138$	−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	$0.132902\pi$
$149$			9.89949i			0.810998i	−0.914095	+	0.405499i	$0.867098\pi$
$150$	−0.292893	+	1.70711i	−0.0239146	+	0.139385i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−2.82843			−0.229416
$153$	−2.58579	−	5.41421i	−0.209048	−	0.437713i
$154$	12.0000	+	12.0000i	0.966988	+	0.966988i
$155$			7.07107i			0.567962i
$156$	0.414214	−	2.41421i	0.0331636	−	0.193292i
$157$	−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
$162$	0.949747	+	8.94975i	0.0746192	+	0.703159i
$163$	−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
$165$	1.24264	−	7.24264i	0.0967394	−	0.563839i
$166$	2.00000	−	2.00000i	0.155230	−	0.155230i
$167$	12.7279	−	12.7279i	0.984916	−	0.984916i	−0.0149717	−	0.999888i	$-0.504766\pi$
$167$	12.7279	−	12.7279i	0.984916	−	0.984916i	0.999888	+	0.0149717i	$0.00476583\pi$
$168$	1.17157	−	6.82843i	0.0903888	−	0.526825i
$169$		−	11.0000i		−	0.846154i
$170$	1.41421	−	1.41421i	0.108465	−	0.108465i
$171$	−7.65685	+	3.65685i	−0.585534	+	0.279647i
$172$	−9.00000	+	9.00000i	−0.686244	+	0.686244i
$173$	2.82843			0.215041			0.107521	−	0.994203i	$-0.465709\pi$
$173$	2.82843			0.215041			0.107521	+	0.994203i	$0.465709\pi$
$174$		0			0
$175$		−	4.00000i		−	0.302372i
$176$	4.24264			0.319801
$177$	1.17157	−	6.82843i	0.0880608	−	0.513256i
$178$		−	18.0000i		−	1.34916i
$179$	12.7279	+	12.7279i	0.951330	+	0.951330i	0.998869	−	0.0475398i	$-0.0151381\pi$
$179$	12.7279	+	12.7279i	0.951330	+	0.951330i	−0.0475398	+	0.998869i	$0.515138\pi$
$180$	−2.70711	+	1.29289i	−0.201776	+	0.0963666i
$181$	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
$183$	1.65685	−	9.65685i	0.122478	−	0.713855i
$184$		−	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	−0.801992	−	0.597334i	$-0.796227\pi$
$191$	−2.82843	+	2.82843i	−0.204658	+	0.204658i	0.597334	+	0.801992i	$0.296227\pi$
$192$	−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	$0.249192\pi$
$197$			19.7990i			1.41062i	−0.708899	+	0.705310i	$0.750808\pi$
$198$	11.4853	−	5.48528i	0.816223	−	0.389822i
$199$	−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
$204$	3.41421	+	0.585786i	0.239043	+	0.0410133i
$205$	4.00000	−	4.00000i	0.279372	−	0.279372i
$206$	14.1421			0.985329
$207$	−7.75736	−	16.2426i	−0.539174	−	1.12894i
$208$	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
$216$	−4.53553	−	2.53553i	−0.308604	−	0.172521i
$217$	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
$222$	−10.5355	−	0.0502525i	−0.707099	−	0.00337273i
$223$	−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	$-0.370487\pi$
$227$	19.7990	−	19.7990i	1.31411	−	1.31411i	0.918361	−	0.395744i	$-0.129513\pi$
$228$	0.828427	−	4.82843i	0.0548639	−	0.319770i
$229$	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	$-0.425597\pi$
$233$	7.07107			0.463241			0.231621	+	0.972806i	$0.425597\pi$
$234$	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
$237$	−7.24264	−	1.24264i	−0.470460	−	0.0807182i
$238$	−8.00000			−0.518563
$239$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$239$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$240$	0.292893	−	1.70711i	0.0189062	−	0.110193i
$241$	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
$246$	9.65685	+	1.65685i	0.615699	+	0.105637i
$247$			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	0.790714	−	0.612185i	$-0.209709\pi$
$251$	2.82843	+	2.82843i	0.178529	+	0.178529i	−0.612185	+	0.790714i	$0.709709\pi$
$252$	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	−0.789799	−	0.613366i	$-0.789815\pi$
$257$	−2.82843	+	2.82843i	−0.176432	+	0.176432i	0.613366	+	0.789799i	$0.289815\pi$
$258$	−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	$-0.189229\pi$
$263$	26.8701			1.65688			0.828439	+	0.560079i	$0.189229\pi$
$264$	−1.24264	+	7.24264i	−0.0764792	+	0.445754i
$265$	2.00000	+	2.00000i	0.122859	+	0.122859i
$266$			11.3137i			0.693688i
$267$	30.7279	+	5.27208i	1.88052	+	0.322646i
$268$	−2.00000			−0.122169
$269$			21.2132i			1.29339i	0.762748	+	0.646696i	$0.223850\pi$
$269$			21.2132i			1.29339i	−0.762748	+	0.646696i	$0.776150\pi$
$270$	−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
$273$	−9.65685	−	1.65685i	−0.584459	−	0.100277i
$274$	−7.00000	+	7.00000i	−0.422885	+	0.422885i
$275$			4.24264i			0.255841i
$276$	10.2426	+	1.75736i	0.616535	+	0.105781i
$277$	−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
$279$	−9.14214	−	19.1421i	−0.547325	−	1.14601i
$280$			4.00000i			0.239046i
$281$	7.07107	−	7.07107i	0.421825	−	0.421825i	−0.464007	−	0.885832i	$-0.653589\pi$
$281$	7.07107	−	7.07107i	0.421825	−	0.421825i	0.885832	+	0.464007i	$0.153589\pi$
$282$	−0.414214	+	2.41421i	−0.0246661	+	0.143764i
$283$	−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
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$			13.0000i			0.764706i
$290$		0			0
$291$	−28.9706	−	4.97056i	−1.69828	−	0.291380i
$292$	6.00000			0.351123
$293$			28.2843i			1.65238i	0.563388	+	0.826192i	$0.309498\pi$
$293$			28.2843i			1.65238i	−0.563388	+	0.826192i	$0.690502\pi$
$294$	−15.3640	−	2.63604i	−0.896044	−	0.153737i
$295$			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
$309$	−4.14214	+	24.1421i	−0.235638	+	1.37340i
$310$	5.00000	−	5.00000i	0.283981	−	0.283981i
$311$	8.48528	+	8.48528i	0.481156	+	0.481156i	0.905501	−	0.424345i	$-0.139495\pi$
$311$	8.48528	+	8.48528i	0.481156	+	0.481156i	−0.424345	+	0.905501i	$0.639495\pi$
$312$	−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
$315$	5.17157	+	10.8284i	0.291385	+	0.610113i
$316$	3.00000	−	3.00000i	0.168763	−	0.168763i
$317$	−8.48528			−0.476581			−0.238290	−	0.971194i	$-0.576587\pi$
$317$	−8.48528			−0.476581			−0.238290	+	0.971194i	$0.576587\pi$
$318$	−0.828427	+	4.82843i	−0.0464559	+	0.270765i
$319$		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
$327$	28.9706	+	4.97056i	1.60208	+	0.274873i
$328$	−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
$333$	3.17157	−	17.9706i	0.173801	−	0.984781i
$334$	−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
$339$	−10.2426	−	1.75736i	−0.556304	−	0.0954467i
$340$	−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	0.441666	−	0.897180i	$-0.354388\pi$
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	−0.897180	+	0.441666i	$0.854388\pi$
$348$		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
$351$	−3.58579	+	6.41421i	−0.191395	+	0.342365i
$352$	−3.00000	−	3.00000i	−0.159901	−	0.159901i
$353$	24.0416	+	24.0416i	1.27961	+	1.27961i	0.940887	+	0.338719i	$0.109994\pi$
$353$	24.0416	+	24.0416i	1.27961	+	1.27961i	0.338719	+	0.940887i	$0.390006\pi$
$354$	−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
$357$	2.34315	−	13.6569i	0.124012	−	0.722797i
$358$		−	18.0000i		−	0.951330i
$359$		−	11.3137i		−	0.597115i	−0.954392	−	0.298557i	$-0.903495\pi$
$359$		−	11.3137i		−	0.597115i	0.954392	−	0.298557i	$-0.0965054\pi$
$360$	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
$372$	12.0711	+	2.07107i	0.625856	+	0.107380i
$373$		−	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
$375$	1.70711	+	0.292893i	0.0881546	+	0.0151249i
$376$	−1.00000	−	1.00000i	−0.0515711	−	0.0515711i
$377$		0			0
$378$	−10.1421	+	18.1421i	−0.521655	+	0.933131i
$379$		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	−0.934380	−	0.356277i	$-0.884046\pi$
$383$	−11.3137	+	11.3137i	−0.578103	+	0.578103i	0.356277	+	0.934380i	$0.384046\pi$
$384$	−0.292893	+	1.70711i	−0.0149466	+	0.0871154i
$385$	12.0000	−	12.0000i	0.611577	−	0.611577i
$386$		−	25.4558i		−	1.29567i
$387$	34.4558	−	16.4558i	1.75149	−	0.836498i
$388$	12.0000	−	12.0000i	0.609208	−	0.609208i
$389$	8.48528	−	8.48528i	0.430221	−	0.430221i	−0.458483	−	0.888703i	$-0.651607\pi$
$389$	8.48528	−	8.48528i	0.430221	−	0.430221i	0.888703	+	0.458483i	$0.151607\pi$
$390$	−2.41421	−	0.414214i	−0.122248	−	0.0209745i
$391$		−	12.0000i		−	0.606866i
$392$	6.36396	−	6.36396i	0.321429	−	0.321429i
$393$	−20.4853	−	3.51472i	−1.03335	−	0.177294i
$394$	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
$399$	−19.3137	−	3.31371i	−0.966895	−	0.165893i
$400$			1.00000i			0.0500000i
$401$	15.5563	+	15.5563i	0.776847	+	0.776847i	0.979293	−	0.202446i	$-0.0648892\pi$
$401$	15.5563	+	15.5563i	0.776847	+	0.776847i	−0.202446	+	0.979293i	$0.564889\pi$
$402$	0.585786	−	3.41421i	0.0292164	−	0.170285i
$403$	−10.0000			−0.498135
$404$		−	15.5563i		−	0.773957i
$405$	8.94975	−	0.949747i	0.444717	−	0.0471933i
$406$		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	$-0.899370\pi$
$419$		−	12.7279i		−	0.621800i	0.950443	−	0.310900i	$-0.100630\pi$
$420$	−6.82843	−	1.17157i	−0.333193	−	0.0571669i
$421$	−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
$426$	0.828427	−	4.82843i	0.0401374	−	0.233938i
$427$	16.0000	−	16.0000i	0.774294	−	0.774294i
$428$	−14.1421			−0.683586
$429$	10.2426	+	1.75736i	0.494519	+	0.0848461i
$430$	9.00000	+	9.00000i	0.434019	+	0.434019i
$431$	−8.48528	−	8.48528i	−0.408722	−	0.408722i	0.472571	−	0.881293i	$-0.343326\pi$
$431$	−8.48528	−	8.48528i	−0.408722	−	0.408722i	−0.881293	+	0.472571i	$0.843326\pi$
$432$	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
$438$	−1.75736	+	10.2426i	−0.0839699	+	0.489412i
$439$	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	$-0.521404\pi$
$443$	−2.82843			−0.134383			−0.0671913	+	0.997740i	$0.521404\pi$
$444$	7.41421	+	7.48528i	0.351863	+	0.355236i
$445$	−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	−0.339822	−	0.940490i	$-0.610367\pi$
$449$	12.7279	−	12.7279i	0.600668	−	0.600668i	0.940490	+	0.339822i	$0.110367\pi$
$450$	1.29289	+	2.70711i	0.0609476	+	0.127614i
$451$	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
$459$	−9.07107	−	5.07107i	−0.423401	−	0.236697i
$460$	−6.00000			−0.279751
$461$	24.0416	−	24.0416i	1.11973	−	1.11973i	0.127950	−	0.991781i	$-0.459160\pi$
$461$	24.0416	−	24.0416i	1.11973	−	1.11973i	0.991781	−	0.127950i	$-0.0408396\pi$
$462$	28.9706	+	4.97056i	1.34783	+	0.231252i
$463$	−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	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$	−1.82843	−	3.82843i	−0.0845191	−	0.176969i
$469$			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	$0.557388\pi$
$479$	−25.4558	+	25.4558i	−1.16311	+	1.16311i	−0.983792	+	0.179316i	$0.942612\pi$
$480$	−1.41421	+	1.00000i	−0.0645497	+	0.0456435i
$481$	−7.00000	−	5.00000i	−0.319173	−	0.227980i
$482$		−	4.24264i		−	0.193247i
$483$	7.02944	−	40.9706i	0.319850	−	1.86423i
$484$			7.00000i			0.318182i
$485$	16.9706			0.770594
$486$	10.2929	+	11.7071i	0.466895	+	0.531045i
$487$	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
$489$	−2.07107	+	12.0711i	−0.0936569	+	0.545873i
$490$	9.00000			0.406579
$491$		−	21.2132i		−	0.957338i	−0.877995	−	0.478669i	$-0.841119\pi$
$491$		−	21.2132i		−	0.957338i	0.877995	−	0.478669i	$-0.158881\pi$
$492$	−5.65685	−	8.00000i	−0.255031	−	0.360668i
$493$		0			0
$494$	2.82843	−	2.82843i	0.127257	−	0.127257i
$495$	−5.48528	−	11.4853i	−0.246545	−	0.516225i
$496$	−5.00000	+	5.00000i	−0.224507	+	0.224507i
$497$			11.3137i			0.507489i
$498$	0.828427	−	4.82843i	0.0371227	−	0.216367i
$499$	−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
$501$	5.27208	−	30.7279i	0.235539	−	1.37282i
$502$		−	4.00000i		−	0.178529i
$503$	21.2132	−	21.2132i	0.945850	−	0.945850i	−0.0527574	−	0.998607i	$-0.516801\pi$
$503$	21.2132	−	21.2132i	0.945850	−	0.945850i	0.998607	+	0.0527574i	$0.0168010\pi$
$504$	−5.17157	−	10.8284i	−0.230360	−	0.482336i
$505$	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	$-0.321135\pi$
$509$	24.0416			1.06563			0.532813	+	0.846233i	$0.321135\pi$
$510$	0.585786	−	3.41421i	0.0259391	−	0.151184i
$511$		−	24.0000i		−	1.06170i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−7.17157	+	12.8284i	−0.316633	+	0.566389i
$514$	4.00000			0.176432
$515$		−	14.1421i		−	0.623177i
$516$	−3.72792	+	21.7279i	−0.164113	+	0.956518i
$517$			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	$-0.559511\pi$
$521$	−8.48528			−0.371747			−0.185873	+	0.982574i	$0.559511\pi$
$522$		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
$531$	−5.17157	−	10.8284i	−0.224427	−	0.469914i
$532$	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
$537$	30.7279	+	5.27208i	1.32601	+	0.227507i
$538$	15.0000	−	15.0000i	0.646696	−	0.646696i
$539$	−38.1838			−1.64469
$540$	−2.53553	+	4.53553i	−0.109112	+	0.195178i
$541$	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
$549$	−7.31371	−	15.3137i	−0.312141	−	0.653573i
$550$	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
$555$	−0.0502525	+	10.5355i	−0.00213310	+	0.447209i
$556$	−16.0000			−0.678551
$557$	24.0416	+	24.0416i	1.01868	+	1.01868i	0.999822	+	0.0188543i	$0.00600188\pi$
$557$	24.0416	+	24.0416i	1.01868	+	1.01868i	0.0188543	+	0.999822i	$0.493998\pi$
$558$	−7.07107	+	20.0000i	−0.299342	+	0.846668i
$559$		−	18.0000i		−	0.761319i
$560$	2.82843	−	2.82843i	0.119523	−	0.119523i
$561$	−2.48528	+	14.4853i	−0.104929	+	0.611569i
$562$	−10.0000			−0.421825
$563$	−5.65685	+	5.65685i	−0.238408	+	0.238408i	−0.816191	−	0.577783i	$-0.803918\pi$
$563$	−5.65685	+	5.65685i	−0.238408	+	0.238408i	0.577783	+	0.816191i	$0.303918\pi$
$564$	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	0.207504	−	0.978234i	$-0.433466\pi$
$569$	−18.3848	−	18.3848i	−0.770730	−	0.770730i	−0.978234	+	0.207504i	$0.933466\pi$
$570$	−4.82843	−	0.828427i	−0.202241	−	0.0346990i
$571$	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
$573$	−1.17157	+	6.82843i	−0.0489432	+	0.285262i
$574$	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
$579$	43.4558	+	7.45584i	1.80596	+	0.309854i
$580$		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	0.264057	−	0.964507i	$-0.414939\pi$
$587$	−16.9706	−	16.9706i	−0.700450	−	0.700450i	−0.964507	+	0.264057i	$0.914939\pi$
$588$	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	$0.103485\pi$
$593$			15.5563i			0.638823i	−0.947616	+	0.319411i	$0.896515\pi$
$594$	10.7574	−	19.2426i	0.441380	−	0.789535i
$595$			8.00000i			0.327968i
$596$	−9.89949			−0.405499
$597$	−1.24264	+	7.24264i	−0.0508579	+	0.296422i
$598$	6.00000	+	6.00000i	0.245358	+	0.245358i
$599$			16.9706i			0.693398i	0.937976	+	0.346699i	$0.112698\pi$
$599$			16.9706i			0.693398i	−0.937976	+	0.346699i	$0.887302\pi$
$600$	−1.70711	−	0.292893i	−0.0696923	−	0.0119573i
$601$	−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
$606$	26.5563	+	4.55635i	1.07878	+	0.185089i
$607$	−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
$612$	5.41421	−	2.58579i	0.218857	−	0.104524i
$613$			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
$615$	1.65685	−	9.65685i	0.0668108	−	0.389402i
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	21.2132			0.854011			0.427006	−	0.904249i	$-0.359568\pi$
$617$	21.2132			0.854011			0.427006	+	0.904249i	$0.359568\pi$
$618$	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
$621$	−27.2132	−	15.2132i	−1.09203	−	0.610485i
$622$		−	12.0000i		−	0.481156i
$623$	50.9117	+	50.9117i	2.03973	+	2.03973i
$624$	2.41421	+	0.414214i	0.0966459	+	0.0165818i
$625$	−1.00000			−0.0400000
$626$		−	8.48528i		−	0.339140i
$627$	20.4853	+	3.51472i	0.818103	+	0.140364i
$628$		−	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	$0.147459\pi$
$641$			22.6274i			0.893729i	−0.894602	+	0.446865i	$0.852541\pi$
$642$	4.14214	−	24.1421i	0.163477	−	0.952814i
$643$	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	0.104907	−	0.994482i	$-0.466546\pi$
$647$	−22.6274	−	22.6274i	−0.889576	−	0.889576i	−0.994482	+	0.104907i	$0.966546\pi$
$648$	−8.94975	+	0.949747i	−0.351579	+	0.0373096i
$649$	−12.0000	+	12.0000i	−0.471041	+	0.471041i
$650$	1.41421			0.0554700
$651$	8.28427	−	48.2843i	0.324686	−	1.89241i
$652$	−5.00000	−	5.00000i	−0.195815	−	0.195815i
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	0.785231	−	0.619203i	$-0.212544\pi$
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	−0.619203	+	0.785231i	$0.712544\pi$
$654$	−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	$-0.561762\pi$
$659$	−9.89949			−0.385630			−0.192815	+	0.981235i	$0.561762\pi$
$660$	7.24264	+	1.24264i	0.281919	+	0.0483697i
$661$	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
$666$	−14.9497	+	10.4645i	−0.579291	+	0.405490i
$667$		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
$672$	6.82843	+	1.17157i	0.263412	+	0.0451944i
$673$	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	$-0.682911\pi$
$677$	−28.2843			−1.08705			−0.543526	+	0.839392i	$0.682911\pi$
$678$	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
$681$	8.20101	−	47.7990i	0.314263	−	1.83166i
$682$	30.0000			1.14876
$683$	−22.6274	+	22.6274i	−0.865814	+	0.865814i	−0.992006	−	0.126192i	$-0.959725\pi$
$683$	−22.6274	+	22.6274i	−0.865814	+	0.865814i	0.126192	+	0.992006i	$0.459725\pi$
$684$	−3.65685	−	7.65685i	−0.139823	−	0.292767i
$685$	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
$690$	1.75736	−	10.2426i	0.0669015	−	0.389931i
$691$		−	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	$-0.356802\pi$
$701$	35.3553	−	35.3553i	1.33535	−	1.33535i	0.900503	−	0.434850i	$-0.143198\pi$
$702$	7.07107	−	2.00000i	0.266880	−	0.0754851i
$703$	−14.0000	−	10.0000i	−0.528020	−	0.377157i
$704$			4.24264i			0.159901i
$705$	2.41421	+	0.414214i	0.0909245	+	0.0156002i
$706$		−	34.0000i		−	1.27961i
$707$	−62.2254			−2.34023
$708$	6.82843	+	1.17157i	0.256628	+	0.0440304i
$709$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$709$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$710$			2.82843i			0.106149i
$711$	−11.4853	+	5.48528i	−0.430732	+	0.205714i
$712$	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	$-0.879636\pi$
$719$		−	19.7990i		−	0.738378i	0.929354	−	0.369189i	$-0.120364\pi$
$720$	−1.29289	−	2.70711i	−0.0481833	−	0.100888i
$721$	−40.0000	+	40.0000i	−1.48968	+	1.48968i
$722$	−7.77817	+	7.77817i	−0.289474	+	0.289474i
$723$	7.24264	+	1.24264i	0.269357	+	0.0462143i
$724$			6.00000i			0.222988i
$725$		0			0
$726$	−11.9497	−	2.05025i	−0.443497	−	0.0760920i
$727$	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
$732$	9.65685	+	1.65685i	0.356928	+	0.0612391i
$733$			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
$735$	−2.63604	+	15.3640i	−0.0972318	+	0.566708i
$736$	6.00000			0.221163
$737$		−	8.48528i		−	0.312559i
$738$	15.3137	−	7.31371i	0.563705	−	0.269221i
$739$			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	$-0.862348\pi$
$743$	−49.4975			−1.81589			−0.907943	+	0.419093i	$0.862348\pi$
$744$	−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
$753$	6.82843	+	1.17157i	0.248842	+	0.0426945i
$754$		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
$759$	−7.45584	+	43.4558i	−0.270630	+	1.57735i
$760$	2.00000	−	2.00000i	0.0725476	−	0.0725476i
$761$	−22.6274			−0.820243			−0.410122	−	0.912031i	$-0.634514\pi$
$761$	−22.6274			−0.820243			−0.410122	+	0.912031i	$0.634514\pi$
$762$	20.4853	+	3.51472i	0.742103	+	0.127325i
$763$	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
$771$	−1.17157	+	6.82843i	−0.0421932	+	0.245920i
$772$	−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
$777$	29.9411	−	29.6569i	1.07413	−	1.06393i
$778$	−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
$792$	5.48528	+	11.4853i	0.194911	+	0.408112i
$793$	−8.00000			−0.284088
$794$	12.7279	−	12.7279i	0.451697	−	0.451697i
$795$	4.82843	+	0.828427i	0.171247	+	0.0293813i
$796$	−3.00000	−	3.00000i	−0.106332	−	0.106332i
$797$	−18.3848	−	18.3848i	−0.651222	−	0.651222i	0.302065	−	0.953287i	$-0.402324\pi$
$797$	−18.3848	−	18.3848i	−0.651222	−	0.651222i	−0.953287	+	0.302065i	$0.902324\pi$
$798$	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
$801$	48.7279	−	23.2721i	1.72172	−	0.822278i
$802$		−	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	0.820398	−	0.571793i	$-0.193752\pi$
$809$	7.07107	+	7.07107i	0.248606	+	0.248606i	−0.571793	+	0.820398i	$0.693752\pi$
$810$	−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
$816$	−0.585786	+	3.41421i	−0.0205066	+	0.119521i
$817$		−	36.0000i		−	1.25948i
$818$	−12.7279			−0.445021
$819$	−15.3137	+	7.31371i	−0.535104	+	0.255562i
$820$	4.00000	+	4.00000i	0.139686	+	0.139686i
$821$			26.8701i			0.937771i	0.883259	+	0.468886i	$0.155344\pi$
$821$			26.8701i			0.937771i	−0.883259	+	0.468886i	$0.844656\pi$
$822$	−2.89949	+	16.8995i	−0.101131	+	0.589438i
$823$	−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	−0.937665	−	0.347541i	$-0.887017\pi$
$827$	−16.9706	+	16.9706i	−0.590124	+	0.590124i	0.347541	+	0.937665i	$0.387017\pi$
$828$	16.2426	−	7.75736i	0.564471	−	0.269587i
$829$	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
$831$	−6.21320	+	36.2132i	−0.215534	+	1.25622i
$832$	−1.00000	+	1.00000i	−0.0346688	+	0.0346688i
$833$	12.7279	−	12.7279i	0.440996	−	0.440996i
$834$	4.68629	−	27.3137i	0.162273	−	0.945796i
$835$			18.0000i			0.622916i
$836$	−8.48528	+	8.48528i	−0.293470	+	0.293470i
$837$	−32.0711	−	17.9289i	−1.10854	−	0.619715i
$838$	−9.00000	+	9.00000i	−0.310900	+	0.310900i
$839$	−19.7990			−0.683537			−0.341769	−	0.939784i	$-0.611026\pi$
$839$	−19.7990			−0.683537			−0.341769	+	0.939784i	$0.611026\pi$
$840$	4.00000	+	5.65685i	0.138013	+	0.195180i
$841$		−	29.0000i		−	1.00000i
$842$	19.7990			0.682318
$843$	2.92893	−	17.0711i	0.100878	−	0.587959i
$844$		−	16.0000i		−	0.550743i
$845$	7.77817	+	7.77817i	0.267577	+	0.267577i
$846$	1.82843	+	3.82843i	0.0628626	+	0.131624i
$847$	28.0000			0.962091
$848$			2.82843i			0.0971286i
$849$	−6.21320	+	36.2132i	−0.213237	+	1.24283i
$850$			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	−0.890250	−	0.455472i	$-0.849470\pi$
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	0.455472	+	0.890250i	$0.349470\pi$
$858$	−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	$-0.961598\pi$
$863$		−	7.07107i		−	0.240702i	0.992731	−	0.120351i	$-0.0384020\pi$
$864$	2.53553	−	4.53553i	0.0862606	−	0.154302i
$865$	−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
$873$	−45.9411	+	21.9411i	−1.55487	+	0.742595i
$874$	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	$-0.438962\pi$
$881$	11.3137			0.381169			0.190584	+	0.981671i	$0.438962\pi$
$882$	−24.3640	+	11.6360i	−0.820377	+	0.391806i
$883$	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	$-0.351030\pi$
$887$	26.8701			0.902208			0.451104	+	0.892471i	$0.351030\pi$
$888$	0.0502525	−	10.5355i	0.00168636	−	0.353549i
$889$	−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
$894$	2.89949	−	16.8995i	0.0969736	−	0.565204i
$895$	−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
$903$	86.9117	+	14.9117i	2.89224	+	0.496230i
$904$	−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	−0.794580	−	0.607160i	$-0.792309\pi$
$911$	−5.65685	+	5.65685i	−0.187420	+	0.187420i	0.607160	+	0.794580i	$0.292309\pi$
$912$	4.82843	+	0.828427i	0.159885	+	0.0274320i
$913$		−	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
$927$	18.2843	+	38.2843i	0.600534	+	1.25742i
$928$		0			0
$929$	53.7401			1.76316			0.881578	−	0.472038i	$-0.156482\pi$
$929$	53.7401			1.76316			0.881578	+	0.472038i	$0.156482\pi$
$930$	2.07107	−	12.0711i	0.0679130	−	0.395826i
$931$	−18.0000	−	18.0000i	−0.589926	−	0.589926i
$932$			7.07107i			0.231621i
$933$	20.4853	+	3.51472i	0.670658	+	0.115067i
$934$	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
$939$	14.4853	+	2.48528i	0.472709	+	0.0811041i
$940$	−1.00000	+	1.00000i	−0.0326164	+	0.0326164i
$941$		−	24.0416i		−	0.783735i	−0.920022	−	0.391867i	$-0.871829\pi$
$941$		−	24.0416i		−	0.783735i	0.920022	−	0.391867i	$-0.128171\pi$
$942$	30.7279	+	5.27208i	1.00117	+	0.171774i
$943$	−24.0000	+	24.0000i	−0.781548	+	0.781548i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$	18.1421	+	10.1421i	0.590164	+	0.329924i
$946$			54.0000i			1.75569i
$947$	2.82843	−	2.82843i	0.0919115	−	0.0919115i	−0.659656	−	0.751568i	$-0.729298\pi$
$947$	2.82843	−	2.82843i	0.0919115	−	0.0919115i	0.751568	+	0.659656i	$0.229298\pi$
$948$	1.24264	−	7.24264i	0.0403591	−	0.235230i
$949$	−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	$-0.111640\pi$
$953$	57.9828			1.87825			0.939123	+	0.343582i	$0.111640\pi$
$954$	3.65685	+	7.65685i	0.118395	+	0.247900i
$955$		−	4.00000i		−	0.129437i
$956$		0			0
$957$		0			0
$958$	36.0000			1.16311
$959$		−	39.5980i		−	1.27869i
$960$	1.70711	+	0.292893i	0.0550966	+	0.00945309i
$961$		−	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	$0.0361936\pi$
$971$			7.07107i			0.226921i	−0.993542	+	0.113461i	$0.963806\pi$
$972$	1.00000	−	15.5563i	0.0320750	−	0.498970i
$973$			64.0000i			2.05175i
$974$		−	31.1127i		−	0.996915i
$975$	−0.414214	+	2.41421i	−0.0132655	+	0.0773167i
$976$	−4.00000	+	4.00000i	−0.128037	+	0.128037i
$977$	−22.6274	−	22.6274i	−0.723915	−	0.723915i	0.245485	−	0.969400i	$-0.421053\pi$
$977$	−22.6274	−	22.6274i	−0.723915	−	0.723915i	−0.969400	+	0.245485i	$0.921053\pi$
$978$	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
$981$	45.9411	−	21.9411i	1.46679	−	0.700526i
$982$	−15.0000	+	15.0000i	−0.478669	+	0.478669i
$983$	1.41421			0.0451064			0.0225532	−	0.999746i	$-0.492820\pi$
$983$	1.41421			0.0451064			0.0225532	+	0.999746i	$0.492820\pi$
$984$	−1.65685	+	9.65685i	−0.0528186	+	0.307849i
$985$	−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
$993$	−9.65685	−	1.65685i	−0.306451	−	0.0525787i
$994$	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
$999$	−13.4853	−	28.5858i	−0.426655	−	0.904414i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) q^{6} +4.00000 q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.70711 - 0.292893i) 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} +(-0.292893 + 1.70711i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(-2.70711 + 1.29289i) 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} +(0.292893 - 1.70711i) 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} +(-2.41421 - 0.414214i) q^{39} +1.00000i q^{40} -5.65685 q^{41} +(-6.82843 - 1.17157i) q^{42} +(9.00000 + 9.00000i) q^{43} -4.24264i q^{44} +(1.29289 + 2.70711i) 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} +(0.585786 - 3.41421i) q^{51} +(1.00000 - 1.00000i) q^{52} -2.82843i q^{53} +(-2.53553 + 4.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(2.82843 - 2.82843i) q^{56} +(-4.82843 - 0.828427i) q^{57} +(2.82843 - 2.82843i) q^{59} +(-1.70711 - 0.292893i) 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} +(7.24264 + 1.24264i) q^{66} +2.00000i q^{67} +(1.41421 + 1.41421i) q^{68} +(1.75736 - 10.2426i) q^{69} +4.00000 q^{70} +2.82843i q^{71} +(-1.29289 - 2.70711i) 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} +(2.07107 - 12.0711i) q^{93} +(-1.00000 + 1.00000i) q^{94} +2.82843 q^{95} +(1.70711 + 0.292893i) 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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