LMFDB - Embedded newform 1110.2.u.c.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.c.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} +1.41421 q^{11} +(-1.00000 - 1.41421i) q^{12} +(-3.00000 - 3.00000i) 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} +(4.00000 + 4.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(5.65685 - 4.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.41421 - 1.41421i) q^{23} +(-0.292893 + 1.70711i) q^{24} -1.00000i q^{25} +4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} -4.00000i q^{28} +(2.82843 + 2.82843i) q^{29} +(1.41421 - 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.00000 + 1.41421i) q^{33} -2.00000 q^{34} +(-2.82843 + 2.82843i) q^{35} +(2.82843 + 1.00000i) q^{36} +(-6.00000 + 1.00000i) q^{37} -5.65685i q^{38} +(7.24264 + 1.24264i) q^{39} -1.00000i q^{40} -5.65685 q^{41} +(-6.82843 - 1.17157i) q^{42} +(3.00000 + 3.00000i) q^{43} +1.41421i q^{44} +(-1.29289 - 2.70711i) q^{45} -2.00000 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} +(3.00000 - 3.00000i) q^{52} -2.82843i q^{53} +(2.53553 - 4.53553i) q^{54} +(1.00000 - 1.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(-9.65685 - 1.65685i) q^{57} -4.00000i q^{58} +(-8.48528 + 8.48528i) q^{59} +(-1.70711 - 0.292893i) q^{60} +(-6.00000 + 6.00000i) q^{61} +4.24264 q^{62} +(-4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -4.24264 q^{65} +(2.41421 + 0.414214i) q^{66} +6.00000i q^{67} +(1.41421 + 1.41421i) q^{68} +(-0.585786 + 3.41421i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-1.29289 - 2.70711i) q^{72} +10.0000i q^{73} +(4.94975 + 3.53553i) q^{74} +(1.00000 + 1.41421i) q^{75} +(-4.00000 + 4.00000i) q^{76} -5.65685 q^{77} +(-4.24264 - 6.00000i) q^{78} +(5.00000 + 5.00000i) 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} -4.24264i q^{86} +(-6.82843 - 1.17157i) q^{87} +(1.00000 - 1.00000i) q^{88} +(-1.41421 - 1.41421i) q^{89} +(-1.00000 + 2.82843i) q^{90} +(12.0000 + 12.0000i) q^{91} +(1.41421 + 1.41421i) q^{92} +(1.24264 - 7.24264i) q^{93} +(1.00000 - 1.00000i) q^{94} +5.65685 q^{95} +(-1.70711 - 0.292893i) q^{96} +(6.00000 + 6.00000i) q^{97} +(-6.36396 - 6.36396i) q^{98} +(1.41421 - 4.00000i) 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} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 16 q^{19} - 4 q^{22} - 4 q^{24} - 12 q^{31} - 8 q^{33} - 8 q^{34} - 24 q^{37} + 12 q^{39} - 16 q^{42} + 12 q^{43} - 8 q^{45} - 8 q^{46} + 36 q^{49} - 8 q^{51} + 12 q^{52} - 4 q^{54} + 4 q^{55} - 16 q^{57} - 4 q^{60} - 24 q^{61} - 16 q^{63} + 4 q^{66} - 8 q^{69} + 16 q^{70} - 8 q^{72} + 4 q^{75} - 16 q^{76} + 20 q^{79} - 28 q^{81} + 16 q^{82} + 16 q^{84} - 16 q^{87} + 4 q^{88} - 4 q^{90} + 48 q^{91} - 12 q^{93} + 4 q^{94} - 4 q^{96} + 24 q^{97}+O(q^{100}) $ 4 * q + 4 * q^6 - 16 * q^7 + 4 * q^9 - 4 * q^10 - 4 * q^12 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 16 * q^19 - 4 * q^22 - 4 * q^24 - 12 * q^31 - 8 * q^33 - 8 * q^34 - 24 * q^37 + 12 * q^39 - 16 * q^42 + 12 * q^43 - 8 * q^45 - 8 * q^46 + 36 * q^49 - 8 * q^51 + 12 * q^52 - 4 * q^54 + 4 * q^55 - 16 * q^57 - 4 * q^60 - 24 * q^61 - 16 * q^63 + 4 * q^66 - 8 * q^69 + 16 * q^70 - 8 * q^72 + 4 * q^75 - 16 * q^76 + 20 * q^79 - 28 * q^81 + 16 * q^82 + 16 * q^84 - 16 * q^87 + 4 * q^88 - 4 * q^90 + 48 * q^91 - 12 * q^93 + 4 * q^94 - 4 * q^96 + 24 * 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	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$	−1.00000			−0.316228
$11$	1.41421			0.426401			0.213201	−	0.977008i	$-0.431611\pi$
$11$	1.41421			0.426401			0.213201	+	0.977008i	$0.431611\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$	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
$19$	4.00000	+	4.00000i	0.917663	+	0.917663i	0.996859	−	0.0791961i	$-0.0252353\pi$
$19$	4.00000	+	4.00000i	0.917663	+	0.917663i	−0.0791961	+	0.996859i	$0.525235\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	5.65685	−	4.00000i	1.23443	−	0.872872i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	1.41421	−	1.41421i	0.294884	−	0.294884i	−0.544122	−	0.839006i	$-0.683137\pi$
$23$	1.41421	−	1.41421i	0.294884	−	0.294884i	0.839006	+	0.544122i	$0.183137\pi$
$24$	−0.292893	+	1.70711i	−0.0597866	+	0.348462i
$25$		−	1.00000i		−	0.200000i
$26$			4.24264i			0.832050i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$		−	4.00000i		−	0.755929i
$29$	2.82843	+	2.82843i	0.525226	+	0.525226i	0.919145	−	0.393919i	$-0.128881\pi$
$29$	2.82843	+	2.82843i	0.525226	+	0.525226i	−0.393919	+	0.919145i	$0.628881\pi$
$30$	1.41421	−	1.00000i	0.258199	−	0.182574i
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	−0.923181	−	0.384365i	$-0.874420\pi$
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	0.384365	+	0.923181i	$0.374420\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.00000	+	1.41421i	−0.348155	+	0.246183i
$34$	−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
$38$		−	5.65685i		−	0.917663i
$39$	7.24264	+	1.24264i	1.15975	+	0.198982i
$40$		−	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
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	0.897833	−	0.440337i	$-0.145141\pi$
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$44$			1.41421i			0.213201i
$45$	−1.29289	−	2.70711i	−0.192733	−	0.403552i
$46$	−2.00000			−0.294884
$47$			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
$51$	−0.585786	+	3.41421i	−0.0820265	+	0.478086i
$52$	3.00000	−	3.00000i	0.416025	−	0.416025i
$53$		−	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
$55$	1.00000	−	1.00000i	0.134840	−	0.134840i
$56$	−2.82843	+	2.82843i	−0.377964	+	0.377964i
$57$	−9.65685	−	1.65685i	−1.27908	−	0.219456i
$58$		−	4.00000i		−	0.525226i
$59$	−8.48528	+	8.48528i	−1.10469	+	1.10469i	−0.110853	+	0.993837i	$0.535358\pi$
$59$	−8.48528	+	8.48528i	−1.10469	+	1.10469i	−0.993837	+	0.110853i	$0.964642\pi$
$60$	−1.70711	−	0.292893i	−0.220387	−	0.0378124i
$61$	−6.00000	+	6.00000i	−0.768221	+	0.768221i	−0.977793	−	0.209572i	$-0.932793\pi$
$61$	−6.00000	+	6.00000i	−0.768221	+	0.768221i	0.209572	+	0.977793i	$0.432793\pi$
$62$	4.24264			0.538816
$63$	−4.00000	+	11.3137i	−0.503953	+	1.42539i
$64$		−	1.00000i		−	0.125000i
$65$	−4.24264			−0.526235
$66$	2.41421	+	0.414214i	0.297169	+	0.0509862i
$67$			6.00000i			0.733017i	0.930415	+	0.366508i	$0.119447\pi$
$67$			6.00000i			0.733017i	−0.930415	+	0.366508i	$0.880553\pi$
$68$	1.41421	+	1.41421i	0.171499	+	0.171499i
$69$	−0.585786	+	3.41421i	−0.0705204	+	0.411023i
$70$	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	$-0.0536780\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	4.94975	+	3.53553i	0.575396	+	0.410997i
$75$	1.00000	+	1.41421i	0.115470	+	0.163299i
$76$	−4.00000	+	4.00000i	−0.458831	+	0.458831i
$77$	−5.65685			−0.644658
$78$	−4.24264	−	6.00000i	−0.480384	−	0.679366i
$79$	5.00000	+	5.00000i	0.562544	+	0.562544i	0.930029	−	0.367485i	$-0.119781\pi$
$79$	5.00000	+	5.00000i	0.562544	+	0.562544i	−0.367485	+	0.930029i	$0.619781\pi$
$80$	−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
$86$		−	4.24264i		−	0.457496i
$87$	−6.82843	−	1.17157i	−0.732084	−	0.125606i
$88$	1.00000	−	1.00000i	0.106600	−	0.106600i
$89$	−1.41421	−	1.41421i	−0.149906	−	0.149906i	0.628170	−	0.778076i	$-0.283804\pi$
$89$	−1.41421	−	1.41421i	−0.149906	−	0.149906i	−0.778076	+	0.628170i	$0.783804\pi$
$90$	−1.00000	+	2.82843i	−0.105409	+	0.298142i
$91$	12.0000	+	12.0000i	1.25794	+	1.25794i
$92$	1.41421	+	1.41421i	0.147442	+	0.147442i
$93$	1.24264	−	7.24264i	0.128856	−	0.751027i
$94$	1.00000	−	1.00000i	0.103142	−	0.103142i
$95$	5.65685			0.580381
$96$	−1.70711	−	0.292893i	−0.174231	−	0.0298933i
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	0.942739	−	0.333531i	$-0.108240\pi$
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	−0.333531	+	0.942739i	$0.608240\pi$
$98$	−6.36396	−	6.36396i	−0.642857	−	0.642857i
$99$	1.41421	−	4.00000i	0.142134	−	0.402015i
$100$	1.00000			0.100000
$101$	1.41421			0.140720			0.0703598	−	0.997522i	$-0.477585\pi$
$101$	1.41421			0.140720			0.0703598	+	0.997522i	$0.477585\pi$
$102$	2.82843	−	2.00000i	0.280056	−	0.198030i
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$	−4.24264			−0.416025
$105$	1.17157	−	6.82843i	0.114334	−	0.666386i
$106$	−2.00000	+	2.00000i	−0.194257	+	0.194257i
$107$			8.48528i			0.820303i	0.912017	+	0.410152i	$0.134524\pi$
$107$			8.48528i			0.820303i	−0.912017	+	0.410152i	$0.865476\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$	14.0000	+	14.0000i	1.34096	+	1.34096i	0.895109	+	0.445848i	$0.147098\pi$
$109$	14.0000	+	14.0000i	1.34096	+	1.34096i	0.445848	+	0.895109i	$0.352902\pi$
$110$	−1.41421			−0.134840
$111$	7.48528	−	7.41421i	0.710471	−	0.703726i
$112$	4.00000			0.377964
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$	5.65685	+	8.00000i	0.529813	+	0.749269i
$115$		−	2.00000i		−	0.186501i
$116$	−2.82843	+	2.82843i	−0.262613	+	0.262613i
$117$	−11.4853	+	5.48528i	−1.06181	+	0.507114i
$118$	12.0000			1.10469
$119$	−5.65685	+	5.65685i	−0.518563	+	0.518563i
$120$	1.00000	+	1.41421i	0.0912871	+	0.129099i
$121$	−9.00000			−0.818182
$122$	8.48528			0.768221
$123$	8.00000	−	5.65685i	0.721336	−	0.510061i
$124$	−3.00000	−	3.00000i	−0.269408	−	0.269408i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	10.8284	−	5.17157i	0.964673	−	0.460720i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−7.24264	−	1.24264i	−0.637679	−	0.109408i
$130$	3.00000	+	3.00000i	0.263117	+	0.263117i
$131$	−2.82843	−	2.82843i	−0.247121	−	0.247121i	0.572667	−	0.819788i	$-0.305909\pi$
$131$	−2.82843	−	2.82843i	−0.247121	−	0.247121i	−0.819788	+	0.572667i	$0.805909\pi$
$132$	−1.41421	−	2.00000i	−0.123091	−	0.174078i
$133$	−16.0000	−	16.0000i	−1.38738	−	1.38738i
$134$	4.24264	−	4.24264i	0.366508	−	0.366508i
$135$	4.53553	+	2.53553i	0.390357	+	0.218224i
$136$		−	2.00000i		−	0.171499i
$137$			21.2132i			1.81237i	0.422885	+	0.906183i	$0.361017\pi$
$137$			21.2132i			1.81237i	−0.422885	+	0.906183i	$0.638983\pi$
$138$	2.82843	−	2.00000i	0.240772	−	0.170251i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−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
$145$	4.00000			0.332182
$146$	7.07107	−	7.07107i	0.585206	−	0.585206i
$147$	−12.7279	+	9.00000i	−1.04978	+	0.742307i
$148$	−1.00000	−	6.00000i	−0.0821995	−	0.493197i
$149$		−	18.3848i		−	1.50614i	−0.657941	−	0.753070i	$-0.728572\pi$
$149$		−	18.3848i		−	1.50614i	0.657941	−	0.753070i	$-0.271428\pi$
$150$	0.292893	−	1.70711i	0.0239146	−	0.139385i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	5.65685			0.458831
$153$	−2.58579	−	5.41421i	−0.209048	−	0.437713i
$154$	4.00000	+	4.00000i	0.322329	+	0.322329i
$155$			4.24264i			0.340777i
$156$	−1.24264	+	7.24264i	−0.0994909	+	0.579875i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$		−	7.07107i		−	0.562544i
$159$	2.82843	+	4.00000i	0.224309	+	0.317221i
$160$	1.00000			0.0790569
$161$	−5.65685	+	5.65685i	−0.445823	+	0.445823i
$162$	0.949747	+	8.94975i	0.0746192	+	0.703159i
$163$	−15.0000	+	15.0000i	−1.17489	+	1.17489i	−0.193862	+	0.981029i	$0.562101\pi$
$163$	−15.0000	+	15.0000i	−1.17489	+	1.17489i	−0.981029	+	0.193862i	$0.937899\pi$
$164$		−	5.65685i		−	0.441726i
$165$	−0.414214	+	2.41421i	−0.0322465	+	0.187946i
$166$	2.00000	−	2.00000i	0.155230	−	0.155230i
$167$	−1.41421	+	1.41421i	−0.109435	+	0.109435i	−0.759704	−	0.650269i	$-0.774656\pi$
$167$	−1.41421	+	1.41421i	−0.109435	+	0.109435i	0.650269	+	0.759704i	$0.274656\pi$
$168$	1.17157	−	6.82843i	0.0903888	−	0.526825i
$169$			5.00000i			0.384615i
$170$	−1.41421	+	1.41421i	−0.108465	+	0.108465i
$171$	15.3137	−	7.31371i	1.17107	−	0.559293i
$172$	−3.00000	+	3.00000i	−0.228748	+	0.228748i
$173$	19.7990			1.50529			0.752645	−	0.658427i	$-0.228778\pi$
$173$	19.7990			1.50529			0.752645	+	0.658427i	$0.228778\pi$
$174$	4.00000	+	5.65685i	0.303239	+	0.428845i
$175$			4.00000i			0.302372i
$176$	−1.41421			−0.106600
$177$	3.51472	−	20.4853i	0.264182	−	1.53977i
$178$			2.00000i			0.149906i
$179$	7.07107	+	7.07107i	0.528516	+	0.528516i	0.920130	−	0.391613i	$-0.128083\pi$
$179$	7.07107	+	7.07107i	0.528516	+	0.528516i	−0.391613	+	0.920130i	$0.628083\pi$
$180$	2.70711	−	1.29289i	0.201776	−	0.0963666i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		−	16.9706i		−	1.25794i
$183$	2.48528	−	14.4853i	0.183717	−	1.07078i
$184$		−	2.00000i		−	0.147442i
$185$	−3.53553	+	4.94975i	−0.259938	+	0.363913i
$186$	−6.00000	+	4.24264i	−0.439941	+	0.311086i
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	−1.41421			−0.103142
$189$	−5.65685	−	20.0000i	−0.411476	−	1.45479i
$190$	−4.00000	−	4.00000i	−0.290191	−	0.290191i
$191$	16.9706	−	16.9706i	1.22795	−	1.22795i	0.263208	−	0.964739i	$-0.415220\pi$
$191$	16.9706	−	16.9706i	1.22795	−	1.22795i	0.964739	−	0.263208i	$-0.0847804\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$	−12.0000	−	12.0000i	−0.863779	−	0.863779i	0.127996	−	0.991775i	$-0.459146\pi$
$193$	−12.0000	−	12.0000i	−0.863779	−	0.863779i	−0.991775	+	0.127996i	$0.959146\pi$
$194$		−	8.48528i		−	0.609208i
$195$	6.00000	−	4.24264i	0.429669	−	0.303822i
$196$			9.00000i			0.642857i
$197$		−	2.82843i		−	0.201517i	−0.994911	−	0.100759i	$-0.967873\pi$
$197$		−	2.82843i		−	0.201517i	0.994911	−	0.100759i	$-0.0321270\pi$
$198$	−3.82843	+	1.82843i	−0.272074	+	0.129941i
$199$	1.00000	−	1.00000i	0.0708881	−	0.0708881i	−0.670774	−	0.741662i	$-0.734038\pi$
$199$	1.00000	−	1.00000i	0.0708881	−	0.0708881i	0.741662	+	0.670774i	$0.234038\pi$
$200$	−0.707107	−	0.707107i	−0.0500000	−	0.0500000i
$201$	−6.00000	−	8.48528i	−0.423207	−	0.598506i
$202$	−1.00000	−	1.00000i	−0.0703598	−	0.0703598i
$203$	−11.3137	−	11.3137i	−0.794067	−	0.794067i
$204$	−3.41421	−	0.585786i	−0.239043	−	0.0410133i
$205$	−4.00000	+	4.00000i	−0.279372	+	0.279372i
$206$		0			0
$207$	−2.58579	−	5.41421i	−0.179725	−	0.376314i
$208$	3.00000	+	3.00000i	0.208013	+	0.208013i
$209$	5.65685	+	5.65685i	0.391293	+	0.391293i
$210$	−5.65685	+	4.00000i	−0.390360	+	0.276026i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	2.82843			0.194257
$213$	2.82843	+	4.00000i	0.193801	+	0.274075i
$214$	6.00000	−	6.00000i	0.410152	−	0.410152i
$215$	4.24264			0.289346
$216$	4.53553	+	2.53553i	0.308604	+	0.172521i
$217$	12.0000	−	12.0000i	0.814613	−	0.814613i
$218$		−	19.7990i		−	1.34096i
$219$	−10.0000	−	14.1421i	−0.675737	−	0.955637i
$220$	1.00000	+	1.00000i	0.0674200	+	0.0674200i
$221$	−8.48528			−0.570782
$222$	−10.5355	−	0.0502525i	−0.707099	−	0.00337273i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	−2.82843	−	2.82843i	−0.188982	−	0.188982i
$225$	−2.82843	−	1.00000i	−0.188562	−	0.0666667i
$226$		−	2.00000i		−	0.133038i
$227$	−16.9706	+	16.9706i	−1.12638	+	1.12638i	−0.135614	+	0.990762i	$0.543301\pi$
$227$	−16.9706	+	16.9706i	−1.12638	+	1.12638i	−0.990762	+	0.135614i	$0.956699\pi$
$228$	1.65685	−	9.65685i	0.109728	−	0.639541i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−1.41421	+	1.41421i	−0.0932505	+	0.0932505i
$231$	8.00000	−	5.65685i	0.526361	−	0.372194i
$232$	4.00000			0.262613
$233$	−12.7279			−0.833834			−0.416917	−	0.908945i	$-0.636889\pi$
$233$	−12.7279			−0.833834			−0.416917	+	0.908945i	$0.636889\pi$
$234$	12.0000	+	4.24264i	0.784465	+	0.277350i
$235$	1.00000	+	1.00000i	0.0652328	+	0.0652328i
$236$	−8.48528	−	8.48528i	−0.552345	−	0.552345i
$237$	−12.0711	−	2.07107i	−0.784100	−	0.134530i
$238$	8.00000			0.518563
$239$	−14.1421	+	14.1421i	−0.914779	+	0.914779i	−0.996643	−	0.0818647i	$-0.973912\pi$
$239$	−14.1421	+	14.1421i	−0.914779	+	0.914779i	0.0818647	+	0.996643i	$0.473912\pi$
$240$	0.292893	−	1.70711i	0.0189062	−	0.110193i
$241$	−13.0000	−	13.0000i	−0.837404	−	0.837404i	0.151113	−	0.988517i	$-0.451714\pi$
$241$	−13.0000	−	13.0000i	−0.837404	−	0.837404i	−0.988517	+	0.151113i	$0.951714\pi$
$242$	6.36396	+	6.36396i	0.409091	+	0.409091i
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$	−6.00000	−	6.00000i	−0.384111	−	0.384111i
$245$	6.36396	−	6.36396i	0.406579	−	0.406579i
$246$	−9.65685	−	1.65685i	−0.615699	−	0.105637i
$247$		−	24.0000i		−	1.52708i
$248$			4.24264i			0.269408i
$249$	−2.82843	−	4.00000i	−0.179244	−	0.253490i
$250$			1.00000i			0.0632456i
$251$	−8.48528	−	8.48528i	−0.535586	−	0.535586i	0.386643	−	0.922229i	$-0.373635\pi$
$251$	−8.48528	−	8.48528i	−0.535586	−	0.535586i	−0.922229	+	0.386643i	$0.873635\pi$
$252$	−11.3137	−	4.00000i	−0.712697	−	0.251976i
$253$	2.00000	−	2.00000i	0.125739	−	0.125739i
$254$	−11.3137	−	11.3137i	−0.709885	−	0.709885i
$255$	2.00000	+	2.82843i	0.125245	+	0.177123i
$256$	1.00000			0.0625000
$257$	16.9706	−	16.9706i	1.05859	−	1.05859i	0.0604217	−	0.998173i	$-0.480755\pi$
$257$	16.9706	−	16.9706i	1.05859	−	1.05859i	0.998173	−	0.0604217i	$-0.0192445\pi$
$258$	4.24264	+	6.00000i	0.264135	+	0.373544i
$259$	24.0000	−	4.00000i	1.49129	−	0.248548i
$260$		−	4.24264i		−	0.263117i
$261$	10.8284	−	5.17157i	0.670263	−	0.320112i
$262$			4.00000i			0.247121i
$263$	−26.8701			−1.65688			−0.828439	−	0.560079i	$-0.810771\pi$
$263$	−26.8701			−1.65688			−0.828439	+	0.560079i	$0.810771\pi$
$264$	−0.414214	+	2.41421i	−0.0254931	+	0.148585i
$265$	−2.00000	−	2.00000i	−0.122859	−	0.122859i
$266$			22.6274i			1.38738i
$267$	3.41421	+	0.585786i	0.208946	+	0.0358495i
$268$	−6.00000			−0.366508
$269$		−	7.07107i		−	0.431131i	−0.976489	−	0.215565i	$-0.930841\pi$
$269$		−	7.07107i		−	0.431131i	0.976489	−	0.215565i	$-0.0691594\pi$
$270$	−1.41421	−	5.00000i	−0.0860663	−	0.304290i
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	−1.41421	+	1.41421i	−0.0857493	+	0.0857493i
$273$	−28.9706	−	4.97056i	−1.75338	−	0.300832i
$274$	15.0000	−	15.0000i	0.906183	−	0.906183i
$275$		−	1.41421i		−	0.0852803i
$276$	−3.41421	−	0.585786i	−0.205512	−	0.0352602i
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	−0.0942828	−	0.995545i	$-0.530056\pi$
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	0.995545	+	0.0942828i	$0.0300558\pi$
$278$		0			0
$279$	5.48528	+	11.4853i	0.328395	+	0.687606i
$280$			4.00000i			0.239046i
$281$	−4.24264	+	4.24264i	−0.253095	+	0.253095i	−0.822238	−	0.569143i	$-0.807275\pi$
$281$	−4.24264	+	4.24264i	−0.253095	+	0.253095i	0.569143	+	0.822238i	$0.307275\pi$
$282$	−0.414214	+	2.41421i	−0.0246661	+	0.143764i
$283$	−21.0000	+	21.0000i	−1.24832	+	1.24832i	−0.291859	+	0.956461i	$0.594274\pi$
$283$	−21.0000	+	21.0000i	−1.24832	+	1.24832i	−0.956461	+	0.291859i	$0.905726\pi$
$284$	2.82843			0.167836
$285$	−8.00000	+	5.65685i	−0.473879	+	0.335083i
$286$			6.00000i			0.354787i
$287$	22.6274			1.33565
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$			13.0000i			0.764706i
$290$	−2.82843	−	2.82843i	−0.166091	−	0.166091i
$291$	−14.4853	−	2.48528i	−0.849142	−	0.145690i
$292$	−10.0000			−0.585206
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	15.3640	+	2.63604i	0.896044	+	0.153737i
$295$			12.0000i			0.698667i
$296$	−3.53553	+	4.94975i	−0.205499	+	0.287698i
$297$	2.00000	+	7.07107i	0.116052	+	0.410305i
$298$	−13.0000	+	13.0000i	−0.753070	+	0.753070i
$299$	−8.48528			−0.490716
$300$	−1.41421	+	1.00000i	−0.0816497	+	0.0577350i
$301$	−12.0000	−	12.0000i	−0.691669	−	0.691669i
$302$		0			0
$303$	−2.00000	+	1.41421i	−0.114897	+	0.0812444i
$304$	−4.00000	−	4.00000i	−0.229416	−	0.229416i
$305$			8.48528i			0.485866i
$306$	−2.00000	+	5.65685i	−0.114332	+	0.323381i
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$		−	5.65685i		−	0.322329i
$309$		0			0
$310$	3.00000	−	3.00000i	0.170389	−	0.170389i
$311$	−14.1421	−	14.1421i	−0.801927	−	0.801927i	0.181470	−	0.983397i	$-0.441915\pi$
$311$	−14.1421	−	14.1421i	−0.801927	−	0.801927i	−0.983397	+	0.181470i	$0.941915\pi$
$312$	6.00000	−	4.24264i	0.339683	−	0.240192i
$313$	24.0000	+	24.0000i	1.35656	+	1.35656i	0.878120	+	0.478440i	$0.158798\pi$
$313$	24.0000	+	24.0000i	1.35656	+	1.35656i	0.478440	+	0.878120i	$0.341202\pi$
$314$	9.89949	+	9.89949i	0.558661	+	0.558661i
$315$	5.17157	+	10.8284i	0.291385	+	0.610113i
$316$	−5.00000	+	5.00000i	−0.281272	+	0.281272i
$317$	25.4558			1.42974			0.714871	−	0.699256i	$-0.246485\pi$
$317$	25.4558			1.42974			0.714871	+	0.699256i	$0.246485\pi$
$318$	0.828427	−	4.82843i	0.0464559	−	0.270765i
$319$	4.00000	+	4.00000i	0.223957	+	0.223957i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	−8.48528	−	12.0000i	−0.473602	−	0.669775i
$322$	8.00000			0.445823
$323$	11.3137			0.629512
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	−3.00000	+	3.00000i	−0.166410	+	0.166410i
$326$	21.2132			1.17489
$327$	−33.7990	−	5.79899i	−1.86909	−	0.320685i
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$		−	5.65685i		−	0.311872i
$330$	2.00000	−	1.41421i	0.110096	−	0.0778499i
$331$	−2.00000	−	2.00000i	−0.109930	−	0.109930i	0.650002	−	0.759932i	$-0.274768\pi$
$331$	−2.00000	−	2.00000i	−0.109930	−	0.109930i	−0.759932	+	0.650002i	$0.774768\pi$
$332$	−2.82843			−0.155230
$333$	−3.17157	+	17.9706i	−0.173801	+	0.984781i
$334$	2.00000			0.109435
$335$	4.24264	+	4.24264i	0.231800	+	0.231800i
$336$	−5.65685	+	4.00000i	−0.308607	+	0.218218i
$337$			26.0000i			1.41631i	0.706057	+	0.708155i	$0.250472\pi$
$337$			26.0000i			1.41631i	−0.706057	+	0.708155i	$0.749528\pi$
$338$	3.53553	−	3.53553i	0.192308	−	0.192308i
$339$	−3.41421	−	0.585786i	−0.185435	−	0.0318156i
$340$	2.00000			0.108465
$341$	−4.24264	+	4.24264i	−0.229752	+	0.229752i
$342$	−16.0000	−	5.65685i	−0.865181	−	0.305888i
$343$	−8.00000			−0.431959
$344$	4.24264			0.228748
$345$	2.00000	+	2.82843i	0.107676	+	0.152277i
$346$	−14.0000	−	14.0000i	−0.752645	−	0.752645i
$347$	−22.6274	−	22.6274i	−1.21470	−	1.21470i	−0.969462	−	0.245241i	$-0.921133\pi$
$347$	−22.6274	−	22.6274i	−1.21470	−	1.21470i	−0.245241	−	0.969462i	$-0.578867\pi$
$348$	1.17157	−	6.82843i	0.0628029	−	0.366042i
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$	2.82843	−	2.82843i	0.151186	−	0.151186i
$351$	10.7574	−	19.2426i	0.574185	−	1.02710i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	18.3848	+	18.3848i	0.978523	+	0.978523i	0.999774	−	0.0212513i	$-0.00676499\pi$
$353$	18.3848	+	18.3848i	0.978523	+	0.978523i	−0.0212513	+	0.999774i	$0.506765\pi$
$354$	−16.9706	+	12.0000i	−0.901975	+	0.637793i
$355$	−2.00000	−	2.00000i	−0.106149	−	0.106149i
$356$	1.41421	−	1.41421i	0.0749532	−	0.0749532i
$357$	2.34315	−	13.6569i	0.124012	−	0.722797i
$358$		−	10.0000i		−	0.528516i
$359$			22.6274i			1.19423i	0.802156	+	0.597115i	$0.203686\pi$
$359$			22.6274i			1.19423i	−0.802156	+	0.597115i	$0.796314\pi$
$360$	−2.82843	−	1.00000i	−0.149071	−	0.0527046i
$361$			13.0000i			0.684211i
$362$	−7.07107	−	7.07107i	−0.371647	−	0.371647i
$363$	12.7279	−	9.00000i	0.668043	−	0.472377i
$364$	−12.0000	+	12.0000i	−0.628971	+	0.628971i
$365$	7.07107	+	7.07107i	0.370117	+	0.370117i
$366$	−12.0000	+	8.48528i	−0.627250	+	0.443533i
$367$	−12.0000			−0.626395			−0.313197	−	0.949688i	$-0.601400\pi$
$367$	−12.0000			−0.626395			−0.313197	+	0.949688i	$0.601400\pi$
$368$	−1.41421	+	1.41421i	−0.0737210	+	0.0737210i
$369$	−5.65685	+	16.0000i	−0.294484	+	0.832927i
$370$	6.00000	−	1.00000i	0.311925	−	0.0519875i
$371$			11.3137i			0.587378i
$372$	7.24264	+	1.24264i	0.375513	+	0.0644279i
$373$		−	22.0000i		−	1.13912i	−0.821951	−	0.569558i	$-0.807114\pi$
$373$		−	22.0000i		−	1.13912i	0.821951	−	0.569558i	$-0.192886\pi$
$374$	−2.82843			−0.146254
$375$	1.70711	+	0.292893i	0.0881546	+	0.0151249i
$376$	1.00000	+	1.00000i	0.0515711	+	0.0515711i
$377$		−	16.9706i		−	0.874028i
$378$	−10.1421	+	18.1421i	−0.521655	+	0.933131i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$			5.65685i			0.290191i
$381$	−22.6274	+	16.0000i	−1.15924	+	0.819705i
$382$	−24.0000			−1.22795
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$	0.292893	−	1.70711i	0.0149466	−	0.0871154i
$385$	−4.00000	+	4.00000i	−0.203859	+	0.203859i
$386$			16.9706i			0.863779i
$387$	11.4853	−	5.48528i	0.583830	−	0.278833i
$388$	−6.00000	+	6.00000i	−0.304604	+	0.304604i
$389$	−16.9706	+	16.9706i	−0.860442	+	0.860442i	−0.991389	−	0.130948i	$-0.958198\pi$
$389$	−16.9706	+	16.9706i	−0.860442	+	0.860442i	0.130948	+	0.991389i	$0.458198\pi$
$390$	−7.24264	−	1.24264i	−0.366745	−	0.0629236i
$391$		−	4.00000i		−	0.202289i
$392$	6.36396	−	6.36396i	0.321429	−	0.321429i
$393$	6.82843	+	1.17157i	0.344449	+	0.0590980i
$394$	−2.00000	+	2.00000i	−0.100759	+	0.100759i
$395$	7.07107			0.355784
$396$	4.00000	+	1.41421i	0.201008	+	0.0710669i
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$	−1.41421			−0.0708881
$399$	38.6274	+	6.62742i	1.93379	+	0.331786i
$400$			1.00000i			0.0500000i
$401$	4.24264	+	4.24264i	0.211867	+	0.211867i	0.805060	−	0.593193i	$-0.202133\pi$
$401$	4.24264	+	4.24264i	0.211867	+	0.211867i	−0.593193	+	0.805060i	$0.702133\pi$
$402$	−1.75736	+	10.2426i	−0.0876491	+	0.510856i
$403$	18.0000			0.896644
$404$			1.41421i			0.0703598i
$405$	−8.94975	+	0.949747i	−0.444717	+	0.0471933i
$406$			16.0000i			0.794067i
$407$	−8.48528	+	1.41421i	−0.420600	+	0.0701000i
$408$	2.00000	+	2.82843i	0.0990148	+	0.140028i
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	−0.777376	−	0.629036i	$-0.783450\pi$
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	0.629036	+	0.777376i	$0.283450\pi$
$410$	5.65685			0.279372
$411$	−21.2132	−	30.0000i	−1.04637	−	1.47979i
$412$		0			0
$413$	33.9411	−	33.9411i	1.67013	−	1.67013i
$414$	−2.00000	+	5.65685i	−0.0982946	+	0.278019i
$415$	2.00000	+	2.00000i	0.0981761	+	0.0981761i
$416$		−	4.24264i		−	0.208013i
$417$		0			0
$418$		−	8.00000i		−	0.391293i
$419$			32.5269i			1.58904i	0.607236	+	0.794522i	$0.292278\pi$
$419$			32.5269i			1.58904i	−0.607236	+	0.794522i	$0.707722\pi$
$420$	6.82843	+	1.17157i	0.333193	+	0.0571669i
$421$	20.0000	−	20.0000i	0.974740	−	0.974740i	−0.0249484	−	0.999689i	$-0.507942\pi$
$421$	20.0000	−	20.0000i	0.974740	−	0.974740i	0.999689	+	0.0249484i	$0.00794214\pi$
$422$	−5.65685	−	5.65685i	−0.275371	−	0.275371i
$423$	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
$427$	24.0000	−	24.0000i	1.16144	−	1.16144i
$428$	−8.48528			−0.410152
$429$	10.2426	+	1.75736i	0.494519	+	0.0848461i
$430$	−3.00000	−	3.00000i	−0.144673	−	0.144673i
$431$	−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
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	−16.9706			−0.814613
$435$	−5.65685	+	4.00000i	−0.271225	+	0.191785i
$436$	−14.0000	+	14.0000i	−0.670478	+	0.670478i
$437$	11.3137			0.541208
$438$	−2.92893	+	17.0711i	−0.139950	+	0.815687i
$439$	9.00000	−	9.00000i	0.429547	−	0.429547i	−0.458927	−	0.888474i	$-0.651766\pi$
$439$	9.00000	−	9.00000i	0.429547	−	0.429547i	0.888474	+	0.458927i	$0.151766\pi$
$440$		−	1.41421i		−	0.0674200i
$441$	9.00000	−	25.4558i	0.428571	−	1.21218i
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	14.1421			0.671913			0.335957	−	0.941877i	$-0.390940\pi$
$443$	14.1421			0.671913			0.335957	+	0.941877i	$0.390940\pi$
$444$	7.41421	+	7.48528i	0.351863	+	0.355236i
$445$	−2.00000			−0.0948091
$446$	−5.65685	−	5.65685i	−0.267860	−	0.267860i
$447$	18.3848	+	26.0000i	0.869570	+	1.22976i
$448$			4.00000i			0.188982i
$449$	15.5563	−	15.5563i	0.734150	−	0.734150i	−0.237289	−	0.971439i	$-0.576259\pi$
$449$	15.5563	−	15.5563i	0.734150	−	0.734150i	0.971439	+	0.237289i	$0.0762590\pi$
$450$	1.29289	+	2.70711i	0.0609476	+	0.127614i
$451$	−8.00000			−0.376705
$452$	−1.41421	+	1.41421i	−0.0665190	+	0.0665190i
$453$		0			0
$454$	24.0000			1.12638
$455$	16.9706			0.795592
$456$	−8.00000	+	5.65685i	−0.374634	+	0.264906i
$457$	−30.0000	−	30.0000i	−1.40334	−	1.40334i	−0.789184	−	0.614157i	$-0.789496\pi$
$457$	−30.0000	−	30.0000i	−1.40334	−	1.40334i	−0.614157	−	0.789184i	$-0.710504\pi$
$458$	−7.07107	−	7.07107i	−0.330409	−	0.330409i
$459$	9.07107	+	5.07107i	0.423401	+	0.236697i
$460$	2.00000			0.0932505
$461$	4.24264	−	4.24264i	0.197599	−	0.197599i	−0.601371	−	0.798970i	$-0.705378\pi$
$461$	4.24264	−	4.24264i	0.197599	−	0.197599i	0.798970	+	0.601371i	$0.205378\pi$
$462$	−9.65685	−	1.65685i	−0.449278	−	0.0770838i
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	0.608023	−	0.793919i	$-0.291963\pi$
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	−0.793919	+	0.608023i	$0.791963\pi$
$464$	−2.82843	−	2.82843i	−0.131306	−	0.131306i
$465$	−4.24264	−	6.00000i	−0.196748	−	0.278243i
$466$	9.00000	+	9.00000i	0.416917	+	0.416917i
$467$	22.6274	−	22.6274i	1.04707	−	1.04707i	0.0482360	−	0.998836i	$-0.484640\pi$
$467$	22.6274	−	22.6274i	1.04707	−	1.04707i	0.998836	−	0.0482360i	$-0.0153600\pi$
$468$	−5.48528	−	11.4853i	−0.253557	−	0.530907i
$469$		−	24.0000i		−	1.10822i
$470$		−	1.41421i		−	0.0652328i
$471$	19.7990	−	14.0000i	0.912289	−	0.645086i
$472$			12.0000i			0.552345i
$473$	4.24264	+	4.24264i	0.195077	+	0.195077i
$474$	7.07107	+	10.0000i	0.324785	+	0.459315i
$475$	4.00000	−	4.00000i	0.183533	−	0.183533i
$476$	−5.65685	−	5.65685i	−0.259281	−	0.259281i
$477$	−8.00000	−	2.82843i	−0.366295	−	0.129505i
$478$	20.0000			0.914779
$479$	−11.3137	+	11.3137i	−0.516937	+	0.516937i	−0.916643	−	0.399707i	$-0.869112\pi$
$479$	−11.3137	+	11.3137i	−0.516937	+	0.516937i	0.399707	+	0.916643i	$0.369112\pi$
$480$	−1.41421	+	1.00000i	−0.0645497	+	0.0456435i
$481$	21.0000	+	15.0000i	0.957518	+	0.683941i
$482$			18.3848i			0.837404i
$483$	2.34315	−	13.6569i	0.106617	−	0.621408i
$484$		−	9.00000i		−	0.409091i
$485$	8.48528			0.385297
$486$	−10.2929	−	11.7071i	−0.466895	−	0.531045i
$487$	8.00000	+	8.00000i	0.362515	+	0.362515i	0.864738	−	0.502223i	$-0.167484\pi$
$487$	8.00000	+	8.00000i	0.362515	+	0.362515i	−0.502223	+	0.864738i	$0.667484\pi$
$488$			8.48528i			0.384111i
$489$	6.21320	−	36.2132i	0.280971	−	1.63762i
$490$	−9.00000			−0.406579
$491$			12.7279i			0.574403i	0.957870	+	0.287202i	$0.0927249\pi$
$491$			12.7279i			0.574403i	−0.957870	+	0.287202i	$0.907275\pi$
$492$	5.65685	+	8.00000i	0.255031	+	0.360668i
$493$	8.00000			0.360302
$494$	−16.9706	+	16.9706i	−0.763542	+	0.763542i
$495$	−1.82843	−	3.82843i	−0.0821817	−	0.172075i
$496$	3.00000	−	3.00000i	0.134704	−	0.134704i
$497$			11.3137i			0.507489i
$498$	−0.828427	+	4.82843i	−0.0371227	+	0.216367i
$499$	6.00000	−	6.00000i	0.268597	−	0.268597i	−0.559938	−	0.828535i	$-0.689175\pi$
$499$	6.00000	−	6.00000i	0.268597	−	0.268597i	0.828535	+	0.559938i	$0.189175\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	0.585786	−	3.41421i	0.0261710	−	0.152536i
$502$			12.0000i			0.535586i
$503$	7.07107	−	7.07107i	0.315283	−	0.315283i	−0.531669	−	0.846952i	$-0.678435\pi$
$503$	7.07107	−	7.07107i	0.315283	−	0.315283i	0.846952	+	0.531669i	$0.178435\pi$
$504$	5.17157	+	10.8284i	0.230360	+	0.482336i
$505$	1.00000	−	1.00000i	0.0444994	−	0.0444994i
$506$	−2.82843			−0.125739
$507$	−5.00000	−	7.07107i	−0.222058	−	0.314037i
$508$			16.0000i			0.709885i
$509$	1.41421			0.0626839			0.0313420	−	0.999509i	$-0.490022\pi$
$509$	1.41421			0.0626839			0.0313420	+	0.999509i	$0.490022\pi$
$510$	0.585786	−	3.41421i	0.0259391	−	0.151184i
$511$		−	40.0000i		−	1.76950i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−14.3431	+	25.6569i	−0.633265	+	1.13278i
$514$	−24.0000			−1.05859
$515$		0			0
$516$	1.24264	−	7.24264i	0.0547042	−	0.318839i
$517$			2.00000i			0.0879599i
$518$	−19.7990	−	14.1421i	−0.869918	−	0.621370i
$519$	−28.0000	+	19.7990i	−1.22906	+	0.869079i
$520$	−3.00000	+	3.00000i	−0.131559	+	0.131559i
$521$	31.1127			1.36307			0.681536	−	0.731785i	$-0.261312\pi$
$521$	31.1127			1.36307			0.681536	+	0.731785i	$0.261312\pi$
$522$	−11.3137	−	4.00000i	−0.495188	−	0.175075i
$523$	21.0000	+	21.0000i	0.918266	+	0.918266i	0.996903	−	0.0786374i	$-0.0250569\pi$
$523$	21.0000	+	21.0000i	0.918266	+	0.918266i	−0.0786374	+	0.996903i	$0.525057\pi$
$524$	2.82843	−	2.82843i	0.123560	−	0.123560i
$525$	−4.00000	−	5.65685i	−0.174574	−	0.246885i
$526$	19.0000	+	19.0000i	0.828439	+	0.828439i
$527$			8.48528i			0.369625i
$528$	2.00000	−	1.41421i	0.0870388	−	0.0615457i
$529$			19.0000i			0.826087i
$530$			2.82843i			0.122859i
$531$	15.5147	+	32.4853i	0.673281	+	1.40974i
$532$	16.0000	−	16.0000i	0.693688	−	0.693688i
$533$	16.9706	+	16.9706i	0.735077	+	0.735077i
$534$	−2.00000	−	2.82843i	−0.0865485	−	0.122398i
$535$	6.00000	+	6.00000i	0.259403	+	0.259403i
$536$	4.24264	+	4.24264i	0.183254	+	0.183254i
$537$	−17.0711	−	2.92893i	−0.736671	−	0.126393i
$538$	−5.00000	+	5.00000i	−0.215565	+	0.215565i
$539$	12.7279			0.548230
$540$	−2.53553	+	4.53553i	−0.109112	+	0.195178i
$541$	−12.0000	−	12.0000i	−0.515920	−	0.515920i	0.400414	−	0.916334i	$-0.368866\pi$
$541$	−12.0000	−	12.0000i	−0.515920	−	0.515920i	−0.916334	+	0.400414i	$0.868866\pi$
$542$	11.3137	+	11.3137i	0.485965	+	0.485965i
$543$	−14.1421	+	10.0000i	−0.606897	+	0.429141i
$544$	2.00000			0.0857493
$545$	19.7990			0.848096
$546$	16.9706	+	24.0000i	0.726273	+	1.02711i
$547$	−3.00000	+	3.00000i	−0.128271	+	0.128271i	−0.768328	−	0.640057i	$-0.778911\pi$
$547$	−3.00000	+	3.00000i	−0.128271	+	0.128271i	0.640057	+	0.768328i	$0.278911\pi$
$548$	−21.2132			−0.906183
$549$	10.9706	+	22.9706i	0.468212	+	0.980360i
$550$	−1.00000	+	1.00000i	−0.0426401	+	0.0426401i
$551$			22.6274i			0.963960i
$552$	2.00000	+	2.82843i	0.0851257	+	0.120386i
$553$	−20.0000	−	20.0000i	−0.850487	−	0.850487i
$554$	−21.2132			−0.901263
$555$	0.0502525	−	10.5355i	0.00213310	−	0.447209i
$556$		0			0
$557$	1.41421	+	1.41421i	0.0599222	+	0.0599222i	0.736433	−	0.676511i	$-0.236509\pi$
$557$	1.41421	+	1.41421i	0.0599222	+	0.0599222i	−0.676511	+	0.736433i	$0.736509\pi$
$558$	4.24264	−	12.0000i	0.179605	−	0.508001i
$559$		−	18.0000i		−	0.761319i
$560$	2.82843	−	2.82843i	0.119523	−	0.119523i
$561$	−0.828427	+	4.82843i	−0.0349762	+	0.203856i
$562$	6.00000			0.253095
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	2.00000	−	1.41421i	0.0842152	−	0.0595491i
$565$	2.00000			0.0841406
$566$	29.6985			1.24832
$567$	28.0000	+	22.6274i	1.17589	+	0.950262i
$568$	−2.00000	−	2.00000i	−0.0839181	−	0.0839181i
$569$	−29.6985	−	29.6985i	−1.24503	−	1.24503i	−0.957890	−	0.287135i	$-0.907297\pi$
$569$	−29.6985	−	29.6985i	−1.24503	−	1.24503i	−0.287135	−	0.957890i	$-0.592703\pi$
$570$	9.65685	+	1.65685i	0.404481	+	0.0693980i
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	4.24264	−	4.24264i	0.177394	−	0.177394i
$573$	−7.02944	+	40.9706i	−0.293659	+	1.71157i
$574$	−16.0000	−	16.0000i	−0.667827	−	0.667827i
$575$	−1.41421	−	1.41421i	−0.0589768	−	0.0589768i
$576$	−2.82843	−	1.00000i	−0.117851	−	0.0416667i
$577$	10.0000	+	10.0000i	0.416305	+	0.416305i	0.883928	−	0.467623i	$-0.154889\pi$
$577$	10.0000	+	10.0000i	0.416305	+	0.416305i	−0.467623	+	0.883928i	$0.654889\pi$
$578$	9.19239	−	9.19239i	0.382353	−	0.382353i
$579$	28.9706	+	4.97056i	1.20398	+	0.206570i
$580$			4.00000i			0.166091i
$581$		−	11.3137i		−	0.469372i
$582$	8.48528	+	12.0000i	0.351726	+	0.497416i
$583$		−	4.00000i		−	0.165663i
$584$	7.07107	+	7.07107i	0.292603	+	0.292603i
$585$	−4.24264	+	12.0000i	−0.175412	+	0.496139i
$586$		0			0
$587$	28.2843	+	28.2843i	1.16742	+	1.16742i	0.982813	+	0.184604i	$0.0591002\pi$
$587$	28.2843	+	28.2843i	1.16742	+	1.16742i	0.184604	+	0.982813i	$0.440900\pi$
$588$	−9.00000	−	12.7279i	−0.371154	−	0.524891i
$589$	−24.0000			−0.988903
$590$	8.48528	−	8.48528i	0.349334	−	0.349334i
$591$	2.82843	+	4.00000i	0.116346	+	0.164538i
$592$	6.00000	−	1.00000i	0.246598	−	0.0410997i
$593$			24.0416i			0.987271i	0.869669	+	0.493636i	$0.164332\pi$
$593$			24.0416i			0.987271i	−0.869669	+	0.493636i	$0.835668\pi$
$594$	3.58579	−	6.41421i	0.147127	−	0.263178i
$595$			8.00000i			0.327968i
$596$	18.3848			0.753070
$597$	−0.414214	+	2.41421i	−0.0169526	+	0.0988072i
$598$	6.00000	+	6.00000i	0.245358	+	0.245358i
$599$			22.6274i			0.924531i	0.886742	+	0.462266i	$0.152963\pi$
$599$			22.6274i			0.924531i	−0.886742	+	0.462266i	$0.847037\pi$
$600$	1.70711	+	0.292893i	0.0696923	+	0.0119573i
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$			16.9706i			0.691669i
$603$	16.9706	+	6.00000i	0.691095	+	0.244339i
$604$		0			0
$605$	−6.36396	+	6.36396i	−0.258732	+	0.258732i
$606$	2.41421	+	0.414214i	0.0980707	+	0.0168263i
$607$	−8.00000	+	8.00000i	−0.324710	+	0.324710i	−0.850571	−	0.525861i	$-0.823743\pi$
$607$	−8.00000	+	8.00000i	−0.324710	+	0.324710i	0.525861	+	0.850571i	$0.323743\pi$
$608$			5.65685i			0.229416i
$609$	27.3137	+	4.68629i	1.10681	+	0.189898i
$610$	6.00000	−	6.00000i	0.242933	−	0.242933i
$611$	4.24264	−	4.24264i	0.171639	−	0.171639i
$612$	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	$0.895269\pi$
$614$	−19.7990	+	19.7990i	−0.799022	+	0.799022i
$615$	1.65685	−	9.65685i	0.0668108	−	0.389402i
$616$	−4.00000	+	4.00000i	−0.161165	+	0.161165i
$617$	35.3553			1.42335			0.711676	−	0.702508i	$-0.247936\pi$
$617$	35.3553			1.42335			0.711676	+	0.702508i	$0.247936\pi$
$618$		0			0
$619$		−	20.0000i		−	0.803868i	−0.915669	−	0.401934i	$-0.868338\pi$
$619$		−	20.0000i		−	0.803868i	0.915669	−	0.401934i	$-0.131662\pi$
$620$	−4.24264			−0.170389
$621$	9.07107	+	5.07107i	0.364009	+	0.203495i
$622$			20.0000i			0.801927i
$623$	5.65685	+	5.65685i	0.226637	+	0.226637i
$624$	−7.24264	−	1.24264i	−0.289938	−	0.0497454i
$625$	−1.00000			−0.0400000
$626$		−	33.9411i		−	1.35656i
$627$	−13.6569	−	2.34315i	−0.545402	−	0.0935762i
$628$		−	14.0000i		−	0.558661i
$629$	−7.07107	+	9.89949i	−0.281942	+	0.394719i
$630$	4.00000	−	11.3137i	0.159364	−	0.450749i
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	−0.891306	−	0.453403i	$-0.850210\pi$
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	0.453403	+	0.891306i	$0.350210\pi$
$632$	7.07107			0.281272
$633$	−11.3137	+	8.00000i	−0.449680	+	0.317971i
$634$	−18.0000	−	18.0000i	−0.714871	−	0.714871i
$635$	11.3137	−	11.3137i	0.448971	−	0.448971i
$636$	−4.00000	+	2.82843i	−0.158610	+	0.112154i
$637$	−27.0000	−	27.0000i	−1.06978	−	1.06978i
$638$		−	5.65685i		−	0.223957i
$639$	−8.00000	−	2.82843i	−0.316475	−	0.111891i
$640$			1.00000i			0.0395285i
$641$		−	11.3137i		−	0.446865i	−0.974719	−	0.223432i	$-0.928274\pi$
$641$		−	11.3137i		−	0.446865i	0.974719	−	0.223432i	$-0.0717262\pi$
$642$	−2.48528	+	14.4853i	−0.0980862	+	0.571688i
$643$	−25.0000	+	25.0000i	−0.985904	+	0.985904i	−0.999902	−	0.0139983i	$-0.995544\pi$
$643$	−25.0000	+	25.0000i	−0.985904	+	0.985904i	0.0139983	+	0.999902i	$0.495544\pi$
$644$	−5.65685	−	5.65685i	−0.222911	−	0.222911i
$645$	−6.00000	+	4.24264i	−0.236250	+	0.167054i
$646$	−8.00000	−	8.00000i	−0.314756	−	0.314756i
$647$	−5.65685	−	5.65685i	−0.222394	−	0.222394i	0.587112	−	0.809506i	$-0.300265\pi$
$647$	−5.65685	−	5.65685i	−0.222394	−	0.222394i	−0.809506	+	0.587112i	$0.800265\pi$
$648$	−8.94975	+	0.949747i	−0.351579	+	0.0373096i
$649$	−12.0000	+	12.0000i	−0.471041	+	0.471041i
$650$	4.24264			0.166410
$651$	−4.97056	+	28.9706i	−0.194812	+	1.13545i
$652$	−15.0000	−	15.0000i	−0.587445	−	0.587445i
$653$	−12.7279	−	12.7279i	−0.498082	−	0.498082i	0.412758	−	0.910841i	$-0.364565\pi$
$653$	−12.7279	−	12.7279i	−0.498082	−	0.498082i	−0.910841	+	0.412758i	$0.864565\pi$
$654$	19.7990	+	28.0000i	0.774202	+	1.09489i
$655$	−4.00000			−0.156293
$656$	5.65685			0.220863
$657$	28.2843	+	10.0000i	1.10347	+	0.390137i
$658$	−4.00000	+	4.00000i	−0.155936	+	0.155936i
$659$	−26.8701			−1.04671			−0.523354	−	0.852115i	$-0.675320\pi$
$659$	−26.8701			−1.04671			−0.523354	+	0.852115i	$0.675320\pi$
$660$	−2.41421	−	0.414214i	−0.0939731	−	0.0161232i
$661$	−28.0000	+	28.0000i	−1.08907	+	1.08907i	−0.0934498	+	0.995624i	$0.529789\pi$
$661$	−28.0000	+	28.0000i	−1.08907	+	1.08907i	−0.995624	+	0.0934498i	$0.970211\pi$
$662$			2.82843i			0.109930i
$663$	12.0000	−	8.48528i	0.466041	−	0.329541i
$664$	2.00000	+	2.00000i	0.0776151	+	0.0776151i
$665$	−22.6274			−0.877454
$666$	14.9497	−	10.4645i	0.579291	−	0.405490i
$667$	8.00000			0.309761
$668$	−1.41421	−	1.41421i	−0.0547176	−	0.0547176i
$669$	−11.3137	+	8.00000i	−0.437413	+	0.309298i
$670$		−	6.00000i		−	0.231800i
$671$	−8.48528	+	8.48528i	−0.327571	+	0.327571i
$672$	6.82843	+	1.17157i	0.263412	+	0.0451944i
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	18.3848	−	18.3848i	0.708155	−	0.708155i
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$	−5.00000			−0.192308
$677$	−45.2548			−1.73928			−0.869642	−	0.493682i	$-0.835651\pi$
$677$	−45.2548			−1.73928			−0.869642	+	0.493682i	$0.835651\pi$
$678$	2.00000	+	2.82843i	0.0768095	+	0.108625i
$679$	−24.0000	−	24.0000i	−0.921035	−	0.921035i
$680$	−1.41421	−	1.41421i	−0.0542326	−	0.0542326i
$681$	7.02944	−	40.9706i	0.269369	−	1.57000i
$682$	6.00000			0.229752
$683$	−33.9411	+	33.9411i	−1.29872	+	1.29872i	−0.369484	+	0.929237i	$0.620466\pi$
$683$	−33.9411	+	33.9411i	−1.29872	+	1.29872i	−0.929237	+	0.369484i	$0.879534\pi$
$684$	7.31371	+	15.3137i	0.279647	+	0.585534i
$685$	15.0000	+	15.0000i	0.573121	+	0.573121i
$686$	5.65685	+	5.65685i	0.215980	+	0.215980i
$687$	−14.1421	+	10.0000i	−0.539556	+	0.381524i
$688$	−3.00000	−	3.00000i	−0.114374	−	0.114374i
$689$	−8.48528	+	8.48528i	−0.323263	+	0.323263i
$690$	0.585786	−	3.41421i	0.0223005	−	0.129977i
$691$		−	12.0000i		−	0.456502i	−0.973602	−	0.228251i	$-0.926699\pi$
$691$		−	12.0000i		−	0.456502i	0.973602	−	0.228251i	$-0.0733006\pi$
$692$			19.7990i			0.752645i
$693$	−5.65685	+	16.0000i	−0.214886	+	0.607790i
$694$			32.0000i			1.21470i
$695$		0			0
$696$	−5.65685	+	4.00000i	−0.214423	+	0.151620i
$697$	−8.00000	+	8.00000i	−0.303022	+	0.303022i
$698$	−4.24264	−	4.24264i	−0.160586	−	0.160586i
$699$	18.0000	−	12.7279i	0.680823	−	0.481414i
$700$	−4.00000			−0.151186
$701$	21.2132	−	21.2132i	0.801212	−	0.801212i	−0.182073	−	0.983285i	$-0.558281\pi$
$701$	21.2132	−	21.2132i	0.801212	−	0.801212i	0.983285	+	0.182073i	$0.0582808\pi$
$702$	−21.2132	+	6.00000i	−0.800641	+	0.226455i
$703$	−28.0000	−	20.0000i	−1.05604	−	0.754314i
$704$		−	1.41421i		−	0.0533002i
$705$	−2.41421	−	0.414214i	−0.0909245	−	0.0156002i
$706$		−	26.0000i		−	0.978523i
$707$	−5.65685			−0.212748
$708$	20.4853	+	3.51472i	0.769884	+	0.132091i
$709$	−14.0000	−	14.0000i	−0.525781	−	0.525781i	0.393531	−	0.919312i	$-0.371254\pi$
$709$	−14.0000	−	14.0000i	−0.525781	−	0.525781i	−0.919312	+	0.393531i	$0.871254\pi$
$710$			2.82843i			0.106149i
$711$	19.1421	−	9.14214i	0.717886	−	0.342857i
$712$	−2.00000			−0.0749532
$713$			8.48528i			0.317776i
$714$	−11.3137	+	8.00000i	−0.423405	+	0.299392i
$715$	−6.00000			−0.224387
$716$	−7.07107	+	7.07107i	−0.264258	+	0.264258i
$717$	5.85786	−	34.1421i	0.218766	−	1.27506i
$718$	16.0000	−	16.0000i	0.597115	−	0.597115i
$719$		−	14.1421i		−	0.527413i	−0.964603	−	0.263706i	$-0.915055\pi$
$719$		−	14.1421i		−	0.527413i	0.964603	−	0.263706i	$-0.0849450\pi$
$720$	1.29289	+	2.70711i	0.0481833	+	0.100888i
$721$		0			0
$722$	9.19239	−	9.19239i	0.342105	−	0.342105i
$723$	31.3848	+	5.38478i	1.16721	+	0.200262i
$724$			10.0000i			0.371647i
$725$	2.82843	−	2.82843i	0.105045	−	0.105045i
$726$	−15.3640	−	2.63604i	−0.570210	−	0.0978326i
$727$	−22.0000	+	22.0000i	−0.815935	+	0.815935i	−0.985516	−	0.169581i	$-0.945758\pi$
$727$	−22.0000	+	22.0000i	−0.815935	+	0.815935i	0.169581	+	0.985516i	$0.445758\pi$
$728$	16.9706			0.628971
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		−	10.0000i		−	0.370117i
$731$	8.48528			0.313839
$732$	14.4853	+	2.48528i	0.535391	+	0.0918586i
$733$		−	40.0000i		−	1.47743i	−0.674016	−	0.738717i	$-0.735432\pi$
$733$		−	40.0000i		−	1.47743i	0.674016	−	0.738717i	$-0.264568\pi$
$734$	8.48528	+	8.48528i	0.313197	+	0.313197i
$735$	−2.63604	+	15.3640i	−0.0972318	+	0.566708i
$736$	2.00000			0.0737210
$737$			8.48528i			0.312559i
$738$	15.3137	−	7.31371i	0.563705	−	0.269221i
$739$		−	4.00000i		−	0.147142i	−0.997290	−	0.0735712i	$-0.976560\pi$
$739$		−	4.00000i		−	0.147142i	0.997290	−	0.0735712i	$-0.0234396\pi$
$740$	−4.94975	−	3.53553i	−0.181956	−	0.129969i
$741$	24.0000	+	33.9411i	0.881662	+	1.24686i
$742$	8.00000	−	8.00000i	0.293689	−	0.293689i
$743$	−41.0122			−1.50459			−0.752296	−	0.658826i	$-0.771054\pi$
$743$	−41.0122			−1.50459			−0.752296	+	0.658826i	$0.771054\pi$
$744$	−4.24264	−	6.00000i	−0.155543	−	0.219971i
$745$	−13.0000	−	13.0000i	−0.476283	−	0.476283i
$746$	−15.5563	+	15.5563i	−0.569558	+	0.569558i
$747$	8.00000	+	2.82843i	0.292705	+	0.103487i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$		−	33.9411i		−	1.24018i
$750$	−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
$753$	20.4853	+	3.51472i	0.746525	+	0.128083i
$754$	−12.0000	+	12.0000i	−0.437014	+	0.437014i
$755$		0			0
$756$	20.0000	−	5.65685i	0.727393	−	0.205738i
$757$	5.00000	+	5.00000i	0.181728	+	0.181728i	0.792108	−	0.610380i	$-0.208983\pi$
$757$	5.00000	+	5.00000i	0.181728	+	0.181728i	−0.610380	+	0.792108i	$0.708983\pi$
$758$	−19.7990	−	19.7990i	−0.719132	−	0.719132i
$759$	−0.828427	+	4.82843i	−0.0300700	+	0.175261i
$760$	4.00000	−	4.00000i	0.145095	−	0.145095i
$761$	−5.65685			−0.205061			−0.102530	−	0.994730i	$-0.532694\pi$
$761$	−5.65685			−0.205061			−0.102530	+	0.994730i	$0.532694\pi$
$762$	27.3137	+	4.68629i	0.989471	+	0.169766i
$763$	−56.0000	−	56.0000i	−2.02734	−	2.02734i
$764$	16.9706	+	16.9706i	0.613973	+	0.613973i
$765$	−5.65685	−	2.00000i	−0.204524	−	0.0723102i
$766$	24.0000			0.867155
$767$	50.9117			1.83831
$768$	−1.41421	+	1.00000i	−0.0510310	+	0.0360844i
$769$	−5.00000	+	5.00000i	−0.180305	+	0.180305i	−0.791489	−	0.611184i	$-0.790694\pi$
$769$	−5.00000	+	5.00000i	−0.180305	+	0.180305i	0.611184	+	0.791489i	$0.290694\pi$
$770$	5.65685			0.203859
$771$	−7.02944	+	40.9706i	−0.253159	+	1.47552i
$772$	12.0000	−	12.0000i	0.431889	−	0.431889i
$773$			28.2843i			1.01731i	0.860969	+	0.508657i	$0.169858\pi$
$773$			28.2843i			1.01731i	−0.860969	+	0.508657i	$0.830142\pi$
$774$	−12.0000	−	4.24264i	−0.431331	−	0.152499i
$775$	3.00000	+	3.00000i	0.107763	+	0.107763i
$776$	8.48528			0.304604
$777$	−29.9411	+	29.6569i	−1.07413	+	1.06393i
$778$	24.0000			0.860442
$779$	−22.6274	−	22.6274i	−0.810711	−	0.810711i
$780$	4.24264	+	6.00000i	0.151911	+	0.214834i
$781$		−	4.00000i		−	0.143131i
$782$	−2.82843	+	2.82843i	−0.101144	+	0.101144i
$783$	−10.1421	+	18.1421i	−0.362450	+	0.648347i
$784$	−9.00000			−0.321429
$785$	−9.89949	+	9.89949i	−0.353328	+	0.353328i
$786$	−4.00000	−	5.65685i	−0.142675	−	0.201773i
$787$	50.0000			1.78231			0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000			1.78231			0.891154	+	0.453701i	$0.149897\pi$
$788$	2.82843			0.100759
$789$	38.0000	−	26.8701i	1.35284	−	0.956599i
$790$	−5.00000	−	5.00000i	−0.177892	−	0.177892i
$791$	−5.65685	−	5.65685i	−0.201135	−	0.201135i
$792$	−1.82843	−	3.82843i	−0.0649703	−	0.136037i
$793$	36.0000			1.27840
$794$	15.5563	−	15.5563i	0.552074	−	0.552074i
$795$	4.82843	+	0.828427i	0.171247	+	0.0293813i
$796$	1.00000	+	1.00000i	0.0354441	+	0.0354441i
$797$	−29.6985	−	29.6985i	−1.05197	−	1.05197i	−0.998573	−	0.0534012i	$-0.982994\pi$
$797$	−29.6985	−	29.6985i	−1.05197	−	1.05197i	−0.0534012	−	0.998573i	$-0.517006\pi$
$798$	−22.6274	−	32.0000i	−0.801002	−	1.13279i
$799$	2.00000	+	2.00000i	0.0707549	+	0.0707549i
$800$	0.707107	−	0.707107i	0.0250000	−	0.0250000i
$801$	−5.41421	+	2.58579i	−0.191302	+	0.0913643i
$802$		−	6.00000i		−	0.211867i
$803$			14.1421i			0.499065i
$804$	8.48528	−	6.00000i	0.299253	−	0.211604i
$805$			8.00000i			0.281963i
$806$	−12.7279	−	12.7279i	−0.448322	−	0.448322i
$807$	7.07107	+	10.0000i	0.248913	+	0.352017i
$808$	1.00000	−	1.00000i	0.0351799	−	0.0351799i
$809$	−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
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	11.3137	−	11.3137i	0.397033	−	0.397033i
$813$	22.6274	−	16.0000i	0.793578	−	0.561144i
$814$	7.00000	+	5.00000i	0.245350	+	0.175250i
$815$			21.2132i			0.743066i
$816$	0.585786	−	3.41421i	0.0205066	−	0.119521i
$817$			24.0000i			0.839654i
$818$	4.24264			0.148340
$819$	45.9411	−	21.9411i	1.60531	−	0.766685i
$820$	−4.00000	−	4.00000i	−0.139686	−	0.139686i
$821$		−	7.07107i		−	0.246782i	−0.992358	−	0.123391i	$-0.960623\pi$
$821$		−	7.07107i		−	0.246782i	0.992358	−	0.123391i	$-0.0393769\pi$
$822$	−6.21320	+	36.2132i	−0.216710	+	1.26308i
$823$	−24.0000			−0.836587			−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000			−0.836587			−0.418294	+	0.908312i	$0.637372\pi$
$824$		0			0
$825$	1.41421	+	2.00000i	0.0492366	+	0.0696311i
$826$	−48.0000			−1.67013
$827$	36.7696	−	36.7696i	1.27860	−	1.27860i	0.337153	−	0.941450i	$-0.390536\pi$
$827$	36.7696	−	36.7696i	1.27860	−	1.27860i	0.941450	−	0.337153i	$-0.109464\pi$
$828$	5.41421	−	2.58579i	0.188157	−	0.0898623i
$829$	−30.0000	+	30.0000i	−1.04194	+	1.04194i	−0.0428621	+	0.999081i	$0.513648\pi$
$829$	−30.0000	+	30.0000i	−1.04194	+	1.04194i	−0.999081	+	0.0428621i	$0.986352\pi$
$830$		−	2.82843i		−	0.0981761i
$831$	−6.21320	+	36.2132i	−0.215534	+	1.25622i
$832$	−3.00000	+	3.00000i	−0.104006	+	0.104006i
$833$	12.7279	−	12.7279i	0.440996	−	0.440996i
$834$		0			0
$835$			2.00000i			0.0692129i
$836$	−5.65685	+	5.65685i	−0.195646	+	0.195646i
$837$	−19.2426	−	10.7574i	−0.665123	−	0.371829i
$838$	23.0000	−	23.0000i	0.794522	−	0.794522i
$839$	−25.4558			−0.878833			−0.439417	−	0.898283i	$-0.644815\pi$
$839$	−25.4558			−0.878833			−0.439417	+	0.898283i	$0.644815\pi$
$840$	−4.00000	−	5.65685i	−0.138013	−	0.195180i
$841$		−	13.0000i		−	0.448276i
$842$	−28.2843			−0.974740
$843$	1.75736	−	10.2426i	0.0605267	−	0.352775i
$844$			8.00000i			0.275371i
$845$	3.53553	+	3.53553i	0.121626	+	0.121626i
$846$	−1.82843	−	3.82843i	−0.0628626	−	0.131624i
$847$	36.0000			1.23697
$848$			2.82843i			0.0971286i
$849$	8.69848	−	50.6985i	0.298531	−	1.73997i
$850$			2.00000i			0.0685994i
$851$	−7.07107	+	9.89949i	−0.242393	+	0.339350i
$852$	−4.00000	+	2.82843i	−0.137038	+	0.0969003i
$853$	11.0000	−	11.0000i	0.376633	−	0.376633i	−0.493253	−	0.869886i	$-0.664192\pi$
$853$	11.0000	−	11.0000i	0.376633	−	0.376633i	0.869886	+	0.493253i	$0.164192\pi$
$854$	−33.9411			−1.16144
$855$	5.65685	−	16.0000i	0.193460	−	0.547188i
$856$	6.00000	+	6.00000i	0.205076	+	0.205076i
$857$	15.5563	−	15.5563i	0.531395	−	0.531395i	−0.389593	−	0.920987i	$-0.627384\pi$
$857$	15.5563	−	15.5563i	0.531395	−	0.531395i	0.920987	+	0.389593i	$0.127384\pi$
$858$	−6.00000	−	8.48528i	−0.204837	−	0.289683i
$859$	−16.0000	−	16.0000i	−0.545913	−	0.545913i	0.379343	−	0.925256i	$-0.376150\pi$
$859$	−16.0000	−	16.0000i	−0.545913	−	0.545913i	−0.925256	+	0.379343i	$0.876150\pi$
$860$			4.24264i			0.144673i
$861$	−32.0000	+	22.6274i	−1.09056	+	0.771140i
$862$			12.0000i			0.408722i
$863$		−	21.2132i		−	0.722106i	−0.932545	−	0.361053i	$-0.882417\pi$
$863$		−	21.2132i		−	0.722106i	0.932545	−	0.361053i	$-0.117583\pi$
$864$	−2.53553	+	4.53553i	−0.0862606	+	0.154302i
$865$	14.0000	−	14.0000i	0.476014	−	0.476014i
$866$	24.0416	+	24.0416i	0.816968	+	0.816968i
$867$	−13.0000	−	18.3848i	−0.441503	−	0.624380i
$868$	12.0000	+	12.0000i	0.407307	+	0.407307i
$869$	7.07107	+	7.07107i	0.239870	+	0.239870i
$870$	6.82843	+	1.17157i	0.231505	+	0.0397200i
$871$	18.0000	−	18.0000i	0.609907	−	0.609907i
$872$	19.7990			0.670478
$873$	22.9706	−	10.9706i	0.777436	−	0.371297i
$874$	−8.00000	−	8.00000i	−0.270604	−	0.270604i
$875$	2.82843	+	2.82843i	0.0956183	+	0.0956183i
$876$	14.1421	−	10.0000i	0.477818	−	0.337869i
$877$	−36.0000			−1.21563			−0.607817	−	0.794077i	$-0.707955\pi$
$877$	−36.0000			−1.21563			−0.607817	+	0.794077i	$0.707955\pi$
$878$	−12.7279			−0.429547
$879$		0			0
$880$	−1.00000	+	1.00000i	−0.0337100	+	0.0337100i
$881$	−33.9411			−1.14351			−0.571753	−	0.820426i	$-0.693736\pi$
$881$	−33.9411			−1.14351			−0.571753	+	0.820426i	$0.693736\pi$
$882$	−24.3640	+	11.6360i	−0.820377	+	0.391806i
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	−0.259135	−	0.965841i	$-0.583437\pi$
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	0.965841	+	0.259135i	$0.0834374\pi$
$884$		−	8.48528i		−	0.285391i
$885$	−12.0000	−	16.9706i	−0.403376	−	0.570459i
$886$	−10.0000	−	10.0000i	−0.335957	−	0.335957i
$887$	−49.4975			−1.66196			−0.830981	−	0.556300i	$-0.812220\pi$
$887$	−49.4975			−1.66196			−0.830981	+	0.556300i	$0.812220\pi$
$888$	0.0502525	−	10.5355i	0.00168636	−	0.353549i
$889$	−64.0000			−2.14649
$890$	1.41421	+	1.41421i	0.0474045	+	0.0474045i
$891$	−9.89949	−	8.00000i	−0.331646	−	0.268010i
$892$			8.00000i			0.267860i
$893$	−5.65685	+	5.65685i	−0.189299	+	0.189299i
$894$	5.38478	−	31.3848i	0.180094	−	1.04966i
$895$	10.0000			0.334263
$896$	2.82843	−	2.82843i	0.0944911	−	0.0944911i
$897$	12.0000	−	8.48528i	0.400668	−	0.283315i
$898$	−22.0000			−0.734150
$899$	−16.9706			−0.566000
$900$	1.00000	−	2.82843i	0.0333333	−	0.0942809i
$901$	−4.00000	−	4.00000i	−0.133259	−	0.133259i
$902$	5.65685	+	5.65685i	0.188353	+	0.188353i
$903$	28.9706	+	4.97056i	0.964080	+	0.165410i
$904$	2.00000			0.0665190
$905$	7.07107	−	7.07107i	0.235050	−	0.235050i
$906$		0			0
$907$	39.0000	+	39.0000i	1.29497	+	1.29497i	0.931671	+	0.363303i	$0.118351\pi$
$907$	39.0000	+	39.0000i	1.29497	+	1.29497i	0.363303	+	0.931671i	$0.381649\pi$
$908$	−16.9706	−	16.9706i	−0.563188	−	0.563188i
$909$	1.41421	−	4.00000i	0.0469065	−	0.132672i
$910$	−12.0000	−	12.0000i	−0.397796	−	0.397796i
$911$	8.48528	−	8.48528i	0.281130	−	0.281130i	−0.552430	−	0.833560i	$-0.686299\pi$
$911$	8.48528	−	8.48528i	0.281130	−	0.281130i	0.833560	+	0.552430i	$0.186299\pi$
$912$	9.65685	+	1.65685i	0.319770	+	0.0548639i
$913$			4.00000i			0.132381i
$914$			42.4264i			1.40334i
$915$	−8.48528	−	12.0000i	−0.280515	−	0.396708i
$916$			10.0000i			0.330409i
$917$	11.3137	+	11.3137i	0.373612	+	0.373612i
$918$	−2.82843	−	10.0000i	−0.0933520	−	0.330049i
$919$	−33.0000	+	33.0000i	−1.08857	+	1.08857i	−0.0928935	+	0.995676i	$0.529612\pi$
$919$	−33.0000	+	33.0000i	−1.08857	+	1.08857i	−0.995676	+	0.0928935i	$0.970388\pi$
$920$	−1.41421	−	1.41421i	−0.0466252	−	0.0466252i
$921$	28.0000	+	39.5980i	0.922631	+	1.30480i
$922$	−6.00000			−0.197599
$923$	−8.48528	+	8.48528i	−0.279296	+	0.279296i
$924$	5.65685	+	8.00000i	0.186097	+	0.263181i
$925$	1.00000	+	6.00000i	0.0328798	+	0.197279i
$926$			5.65685i			0.185896i
$927$		0			0
$928$			4.00000i			0.131306i
$929$	−59.3970			−1.94875			−0.974376	−	0.224927i	$-0.927786\pi$
$929$	−59.3970			−1.94875			−0.974376	+	0.224927i	$0.927786\pi$
$930$	−1.24264	+	7.24264i	−0.0407478	+	0.237496i
$931$	36.0000	+	36.0000i	1.17985	+	1.17985i
$932$		−	12.7279i		−	0.416917i
$933$	34.1421	+	5.85786i	1.11776	+	0.191778i
$934$	−32.0000			−1.04707
$935$		−	2.82843i		−	0.0924995i
$936$	−4.24264	+	12.0000i	−0.138675	+	0.392232i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−16.9706	+	16.9706i	−0.554109	+	0.554109i
$939$	−57.9411	−	9.94113i	−1.89084	−	0.324416i
$940$	−1.00000	+	1.00000i	−0.0326164	+	0.0326164i
$941$			21.2132i			0.691531i	0.938321	+	0.345765i	$0.112381\pi$
$941$			21.2132i			0.691531i	−0.938321	+	0.345765i	$0.887619\pi$
$942$	−23.8995	−	4.10051i	−0.778688	−	0.133602i
$943$	−8.00000	+	8.00000i	−0.260516	+	0.260516i
$944$	8.48528	−	8.48528i	0.276172	−	0.276172i
$945$	−18.1421	−	10.1421i	−0.590164	−	0.329924i
$946$		−	6.00000i		−	0.195077i
$947$	36.7696	−	36.7696i	1.19485	−	1.19485i	0.219161	−	0.975689i	$-0.429668\pi$
$947$	36.7696	−	36.7696i	1.19485	−	1.19485i	0.975689	−	0.219161i	$-0.0703321\pi$
$948$	2.07107	−	12.0711i	0.0672652	−	0.392050i
$949$	30.0000	−	30.0000i	0.973841	−	0.973841i
$950$	−5.65685			−0.183533
$951$	−36.0000	+	25.4558i	−1.16738	+	0.825462i
$952$			8.00000i			0.259281i
$953$	−35.3553			−1.14527			−0.572636	−	0.819810i	$-0.694079\pi$
$953$	−35.3553			−1.14527			−0.572636	+	0.819810i	$0.694079\pi$
$954$	3.65685	+	7.65685i	0.118395	+	0.247900i
$955$		−	24.0000i		−	0.776622i
$956$	−14.1421	−	14.1421i	−0.457389	−	0.457389i
$957$	−9.65685	−	1.65685i	−0.312162	−	0.0535585i
$958$	16.0000			0.516937
$959$		−	84.8528i		−	2.74004i
$960$	1.70711	+	0.292893i	0.0550966	+	0.00945309i
$961$			13.0000i			0.419355i
$962$	−4.24264	−	25.4558i	−0.136788	−	0.820729i
$963$	24.0000	+	8.48528i	0.773389	+	0.273434i
$964$	13.0000	−	13.0000i	0.418702	−	0.418702i
$965$	−16.9706			−0.546302
$966$	−11.3137	+	8.00000i	−0.364013	+	0.257396i
$967$	10.0000	+	10.0000i	0.321578	+	0.321578i	0.849372	−	0.527794i	$-0.176981\pi$
$967$	10.0000	+	10.0000i	0.321578	+	0.321578i	−0.527794	+	0.849372i	$0.676981\pi$
$968$	−6.36396	+	6.36396i	−0.204545	+	0.204545i
$969$	−16.0000	+	11.3137i	−0.513994	+	0.363449i
$970$	−6.00000	−	6.00000i	−0.192648	−	0.192648i
$971$			29.6985i			0.953070i	0.879156	+	0.476535i	$0.158107\pi$
$971$			29.6985i			0.953070i	−0.879156	+	0.476535i	$0.841893\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$		0			0
$974$		−	11.3137i		−	0.362515i
$975$	1.24264	−	7.24264i	0.0397964	−	0.231950i
$976$	6.00000	−	6.00000i	0.192055	−	0.192055i
$977$	42.4264	+	42.4264i	1.35734	+	1.35734i	0.877181	+	0.480160i	$0.159421\pi$
$977$	42.4264	+	42.4264i	1.35734	+	1.35734i	0.480160	+	0.877181i	$0.340579\pi$
$978$	−30.0000	+	21.2132i	−0.959294	+	0.678323i
$979$	−2.00000	−	2.00000i	−0.0639203	−	0.0639203i
$980$	6.36396	+	6.36396i	0.203289	+	0.203289i
$981$	53.5980	−	25.5980i	1.71125	−	0.817281i
$982$	9.00000	−	9.00000i	0.287202	−	0.287202i
$983$	43.8406			1.39830			0.699149	−	0.714976i	$-0.253562\pi$
$983$	43.8406			1.39830			0.699149	+	0.714976i	$0.253562\pi$
$984$	1.65685	−	9.65685i	0.0528186	−	0.307849i
$985$	−2.00000	−	2.00000i	−0.0637253	−	0.0637253i
$986$	−5.65685	−	5.65685i	−0.180151	−	0.180151i
$987$	5.65685	+	8.00000i	0.180060	+	0.254643i
$988$	24.0000			0.763542
$989$	8.48528			0.269816
$990$	−1.41421	+	4.00000i	−0.0449467	+	0.127128i
$991$	−21.0000	+	21.0000i	−0.667087	+	0.667087i	−0.957041	−	0.289954i	$-0.906360\pi$
$991$	−21.0000	+	21.0000i	−0.667087	+	0.667087i	0.289954	+	0.957041i	$0.406360\pi$
$992$	−4.24264			−0.134704
$993$	4.82843	+	0.828427i	0.153226	+	0.0262893i
$994$	8.00000	−	8.00000i	0.253745	−	0.253745i
$995$		−	1.41421i		−	0.0448336i
$996$	4.00000	−	2.82843i	0.126745	−	0.0896221i
$997$	−23.0000	−	23.0000i	−0.728417	−	0.728417i	0.241887	−	0.970304i	$-0.422234\pi$
$997$	−23.0000	−	23.0000i	−0.728417	−	0.728417i	−0.970304	+	0.241887i	$0.922234\pi$
$998$	−8.48528			−0.268597
$999$	−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.c.191.1	✓	4
3.2	odd	2	inner	1110.2.u.c.191.2	yes	4
37.31	odd	4	inner	1110.2.u.c.401.2	yes	4
111.68	even	4	inner	1110.2.u.c.401.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.c.191.1	✓	4	1.1	even	1	trivial
1110.2.u.c.191.2	yes	4	3.2	odd	2	inner
1110.2.u.c.401.1	yes	4	111.68	even	4	inner
1110.2.u.c.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} +1.41421 q^{11} +(-1.00000 - 1.41421i) q^{12} +(-3.00000 - 3.00000i) 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} +(4.00000 + 4.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(5.65685 - 4.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.41421 - 1.41421i) q^{23} +(-0.292893 + 1.70711i) q^{24} -1.00000i q^{25} +4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} -4.00000i q^{28} +(2.82843 + 2.82843i) q^{29} +(1.41421 - 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.00000 + 1.41421i) q^{33} -2.00000 q^{34} +(-2.82843 + 2.82843i) q^{35} +(2.82843 + 1.00000i) q^{36} +(-6.00000 + 1.00000i) q^{37} -5.65685i q^{38} +(7.24264 + 1.24264i) q^{39} -1.00000i q^{40} -5.65685 q^{41} +(-6.82843 - 1.17157i) q^{42} +(3.00000 + 3.00000i) q^{43} +1.41421i q^{44} +(-1.29289 - 2.70711i) q^{45} -2.00000 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} +(3.00000 - 3.00000i) q^{52} -2.82843i q^{53} +(2.53553 - 4.53553i) q^{54} +(1.00000 - 1.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(-9.65685 - 1.65685i) q^{57} -4.00000i q^{58} +(-8.48528 + 8.48528i) q^{59} +(-1.70711 - 0.292893i) q^{60} +(-6.00000 + 6.00000i) q^{61} +4.24264 q^{62} +(-4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -4.24264 q^{65} +(2.41421 + 0.414214i) q^{66} +6.00000i q^{67} +(1.41421 + 1.41421i) q^{68} +(-0.585786 + 3.41421i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-1.29289 - 2.70711i) q^{72} +10.0000i q^{73} +(4.94975 + 3.53553i) q^{74} +(1.00000 + 1.41421i) q^{75} +(-4.00000 + 4.00000i) q^{76} -5.65685 q^{77} +(-4.24264 - 6.00000i) q^{78} +(5.00000 + 5.00000i) 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} -4.24264i q^{86} +(-6.82843 - 1.17157i) q^{87} +(1.00000 - 1.00000i) q^{88} +(-1.41421 - 1.41421i) q^{89} +(-1.00000 + 2.82843i) q^{90} +(12.0000 + 12.0000i) q^{91} +(1.41421 + 1.41421i) q^{92} +(1.24264 - 7.24264i) q^{93} +(1.00000 - 1.00000i) q^{94} +5.65685 q^{95} +(-1.70711 - 0.292893i) q^{96} +(6.00000 + 6.00000i) q^{97} +(-6.36396 - 6.36396i) q^{98} +(1.41421 - 4.00000i) 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	\( 4 q + 4 q^{6} - 16 q^{7} + 4 q^{9} - 4 q^{10} - 4 q^{12} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 16 q^{19} - 4 q^{22} - 4 q^{24} - 12 q^{31} - 8 q^{33} - 8 q^{34} - 24 q^{37} + 12 q^{39} - 16 q^{42} + 12 q^{43} - 8 q^{45} - 8 q^{46} + 36 q^{49} - 8 q^{51} + 12 q^{52} - 4 q^{54} + 4 q^{55} - 16 q^{57} - 4 q^{60} - 24 q^{61} - 16 q^{63} + 4 q^{66} - 8 q^{69} + 16 q^{70} - 8 q^{72} + 4 q^{75} - 16 q^{76} + 20 q^{79} - 28 q^{81} + 16 q^{82} + 16 q^{84} - 16 q^{87} + 4 q^{88} - 4 q^{90} + 48 q^{91} - 12 q^{93} + 4 q^{94} - 4 q^{96} + 24 q^{97}+O(q^{100}) \) 4 * q + 4 * q^6 - 16 * q^7 + 4 * q^9 - 4 * q^10 - 4 * q^12 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 16 * q^19 - 4 * q^22 - 4 * q^24 - 12 * q^31 - 8 * q^33 - 8 * q^34 - 24 * q^37 + 12 * q^39 - 16 * q^42 + 12 * q^43 - 8 * q^45 - 8 * q^46 + 36 * q^49 - 8 * q^51 + 12 * q^52 - 4 * q^54 + 4 * q^55 - 16 * q^57 - 4 * q^60 - 24 * q^61 - 16 * q^63 + 4 * q^66 - 8 * q^69 + 16 * q^70 - 8 * q^72 + 4 * q^75 - 16 * q^76 + 20 * q^79 - 28 * q^81 + 16 * q^82 + 16 * q^84 - 16 * q^87 + 4 * q^88 - 4 * q^90 + 48 * q^91 - 12 * q^93 + 4 * q^94 - 4 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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