LMFDB - Embedded newform 1110.2.u.c.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.c.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} -1.00000 q^{10} -1.41421 q^{11} +(-1.00000 - 1.41421i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(-2.82843 + 2.82843i) q^{14} +(-1.70711 - 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +(-1.29289 - 2.70711i) q^{18} +(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} +(-1.70711 - 0.292893i) 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} +(-1.24264 + 7.24264i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 + 6.82843i) q^{42} +(3.00000 - 3.00000i) q^{43} +1.41421i q^{44} +(-2.70711 + 1.29289i) 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} +(-3.41421 - 0.585786i) q^{51} +(3.00000 + 3.00000i) q^{52} -2.82843i q^{53} +(-4.53553 - 2.53553i) q^{54} +(1.00000 + 1.00000i) q^{55} +(2.82843 + 2.82843i) q^{56} +(1.65685 - 9.65685i) q^{57} +4.00000i q^{58} +(8.48528 + 8.48528i) q^{59} +(-0.292893 + 1.70711i) 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} +(-0.414214 + 2.41421i) q^{66} -6.00000i q^{67} +(-1.41421 + 1.41421i) q^{68} +(-3.41421 - 0.585786i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 + 1.29289i) 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} +(-1.17157 + 6.82843i) 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} +(-7.24264 - 1.24264i) q^{93} +(1.00000 + 1.00000i) q^{94} -5.65685 q^{95} +(-0.292893 + 1.70711i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	0.292893	−	1.70711i	0.119573	−	0.696923i
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−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	$-0.568389\pi$
$11$	−1.41421			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	0.155747	+	0.987797i	$0.450222\pi$
$14$	−2.82843	+	2.82843i	−0.755929	+	0.755929i
$15$	−1.70711	−	0.292893i	−0.440773	−	0.0756247i
$16$	−1.00000			−0.250000
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$	4.00000	−	4.00000i	0.917663	−	0.917663i	−0.0791961	−	0.996859i	$-0.525235\pi$
$19$	4.00000	−	4.00000i	0.917663	−	0.917663i	0.996859	+	0.0791961i	$0.0252353\pi$
$20$	−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	$-0.316863\pi$
$23$	−1.41421	−	1.41421i	−0.294884	−	0.294884i	−0.839006	+	0.544122i	$0.816863\pi$
$24$	−1.70711	−	0.292893i	−0.348462	−	0.0597866i
$25$			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	$-0.871119\pi$
$29$	−2.82843	+	2.82843i	−0.525226	+	0.525226i	0.393919	+	0.919145i	$0.371119\pi$
$30$	−1.41421	+	1.00000i	−0.258199	+	0.182574i
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	0.384365	−	0.923181i	$-0.374420\pi$
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	−0.923181	+	0.384365i	$0.874420\pi$
$32$	−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
$39$	−1.24264	+	7.24264i	−0.198982	+	1.15975i
$40$			1.00000i			0.158114i
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$	−1.17157	+	6.82843i	−0.180778	+	1.05365i
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$			1.41421i			0.213201i
$45$	−2.70711	+	1.29289i	−0.403552	+	0.192733i
$46$	−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
$51$	−3.41421	−	0.585786i	−0.478086	−	0.0820265i
$52$	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	$-0.0622296\pi$
$54$	−4.53553	−	2.53553i	−0.617208	−	0.345042i
$55$	1.00000	+	1.00000i	0.134840	+	0.134840i
$56$	2.82843	+	2.82843i	0.377964	+	0.377964i
$57$	1.65685	−	9.65685i	0.219456	−	1.27908i
$58$			4.00000i			0.525226i
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.993837	+	0.110853i	$0.0353582\pi$
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.110853	+	0.993837i	$0.464642\pi$
$60$	−0.292893	+	1.70711i	−0.0378124	+	0.220387i
$61$	−6.00000	−	6.00000i	−0.768221	−	0.768221i	0.209572	−	0.977793i	$-0.432793\pi$
$61$	−6.00000	−	6.00000i	−0.768221	−	0.768221i	−0.977793	+	0.209572i	$0.932793\pi$
$62$	−4.24264			−0.538816
$63$	−4.00000	+	11.3137i	−0.503953	+	1.42539i
$64$			1.00000i			0.125000i
$65$	4.24264			0.526235
$66$	−0.414214	+	2.41421i	−0.0509862	+	0.297169i
$67$		−	6.00000i		−	0.733017i	−0.930415	−	0.366508i	$-0.880553\pi$
$67$		−	6.00000i		−	0.733017i	0.930415	−	0.366508i	$-0.119447\pi$
$68$	−1.41421	+	1.41421i	−0.171499	+	0.171499i
$69$	−3.41421	−	0.585786i	−0.411023	−	0.0705204i
$70$	4.00000			0.478091
$71$		−	2.82843i		−	0.335673i	−0.985815	−	0.167836i	$-0.946322\pi$
$71$		−	2.82843i		−	0.335673i	0.985815	−	0.167836i	$-0.0536780\pi$
$72$	−2.70711	+	1.29289i	−0.319036	+	0.152369i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	−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	−0.367485	−	0.930029i	$-0.619781\pi$
$79$	5.00000	−	5.00000i	0.562544	−	0.562544i	0.930029	+	0.367485i	$0.119781\pi$
$80$	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
$87$	−1.17157	+	6.82843i	−0.125606	+	0.732084i
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	1.41421	−	1.41421i	0.149906	−	0.149906i	−0.628170	−	0.778076i	$-0.716196\pi$
$89$	1.41421	−	1.41421i	0.149906	−	0.149906i	0.778076	+	0.628170i	$0.216196\pi$
$90$	−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
$93$	−7.24264	−	1.24264i	−0.751027	−	0.128856i
$94$	1.00000	+	1.00000i	0.103142	+	0.103142i
$95$	−5.65685			−0.580381
$96$	−0.292893	+	1.70711i	−0.0298933	+	0.174231i
$97$	6.00000	−	6.00000i	0.609208	−	0.609208i	−0.333531	−	0.942739i	$-0.608240\pi$
$97$	6.00000	−	6.00000i	0.609208	−	0.609208i	0.942739	+	0.333531i	$0.108240\pi$
$98$	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	$-0.522415\pi$
$101$	−1.41421			−0.140720			−0.0703598	+	0.997522i	$0.522415\pi$
$102$	−2.82843	+	2.00000i	−0.280056	+	0.198030i
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	4.24264			0.416025
$105$	6.82843	+	1.17157i	0.666386	+	0.114334i
$106$	−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	0.445848	−	0.895109i	$-0.352902\pi$
$109$	14.0000	−	14.0000i	1.34096	−	1.34096i	0.895109	−	0.445848i	$-0.147098\pi$
$110$	1.41421			0.134840
$111$	−9.48528	+	4.58579i	−0.900303	+	0.435264i
$112$	4.00000			0.377964
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$	−5.65685	−	8.00000i	−0.529813	−	0.749269i
$115$			2.00000i			0.186501i
$116$	2.82843	+	2.82843i	0.262613	+	0.262613i
$117$	5.48528	+	11.4853i	0.507114	+	1.06181i
$118$	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
$126$	5.17157	+	10.8284i	0.460720	+	0.964673i
$127$	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
$129$	1.24264	−	7.24264i	0.109408	−	0.637679i
$130$	3.00000	−	3.00000i	0.263117	−	0.263117i
$131$	2.82843	−	2.82843i	0.247121	−	0.247121i	−0.572667	−	0.819788i	$-0.694091\pi$
$131$	2.82843	−	2.82843i	0.247121	−	0.247121i	0.819788	+	0.572667i	$0.194091\pi$
$132$	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
$135$	−2.53553	+	4.53553i	−0.218224	+	0.390357i
$136$			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	$-0.271428\pi$
$150$	1.70711	+	0.292893i	0.139385	+	0.0239146i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−5.65685			−0.458831
$153$	−5.41421	+	2.58579i	−0.437713	+	0.209048i
$154$	4.00000	−	4.00000i	0.322329	−	0.322329i
$155$			4.24264i			0.340777i
$156$	7.24264	+	1.24264i	0.579875	+	0.0994909i
$157$	−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
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−15.0000	−	15.0000i	−1.17489	−	1.17489i	−0.981029	−	0.193862i	$-0.937899\pi$
$163$	−15.0000	−	15.0000i	−1.17489	−	1.17489i	−0.193862	−	0.981029i	$-0.562101\pi$
$164$		−	5.65685i		−	0.441726i
$165$	2.41421	+	0.414214i	0.187946	+	0.0322465i
$166$	2.00000	+	2.00000i	0.155230	+	0.155230i
$167$	1.41421	+	1.41421i	0.109435	+	0.109435i	0.759704	−	0.650269i	$-0.225344\pi$
$167$	1.41421	+	1.41421i	0.109435	+	0.109435i	−0.650269	+	0.759704i	$0.725344\pi$
$168$	6.82843	+	1.17157i	0.526825	+	0.0903888i
$169$		−	5.00000i		−	0.384615i
$170$	1.41421	+	1.41421i	0.108465	+	0.108465i
$171$	−7.31371	−	15.3137i	−0.559293	−	1.17107i
$172$	−3.00000	−	3.00000i	−0.228748	−	0.228748i
$173$	−19.7990			−1.50529			−0.752645	−	0.658427i	$-0.771222\pi$
$173$	−19.7990			−1.50529			−0.752645	+	0.658427i	$0.771222\pi$
$174$	4.00000	+	5.65685i	0.303239	+	0.428845i
$175$		−	4.00000i		−	0.302372i
$176$	1.41421			0.106600
$177$	20.4853	+	3.51472i	1.53977	+	0.264182i
$178$		−	2.00000i		−	0.149906i
$179$	−7.07107	+	7.07107i	−0.528516	+	0.528516i	−0.920130	−	0.391613i	$-0.871917\pi$
$179$	−7.07107	+	7.07107i	−0.528516	+	0.528516i	0.391613	+	0.920130i	$0.371917\pi$
$180$	1.29289	+	2.70711i	0.0963666	+	0.201776i
$181$	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
$183$	−14.4853	−	2.48528i	−1.07078	−	0.183717i
$184$			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	−0.964739	−	0.263208i	$-0.915220\pi$
$191$	−16.9706	−	16.9706i	−1.22795	−	1.22795i	−0.263208	−	0.964739i	$-0.584780\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$	−12.0000	+	12.0000i	−0.863779	+	0.863779i	−0.991775	−	0.127996i	$-0.959146\pi$
$193$	−12.0000	+	12.0000i	−0.863779	+	0.863779i	0.127996	+	0.991775i	$0.459146\pi$
$194$		−	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	$-0.0321270\pi$
$198$	1.82843	+	3.82843i	0.129941	+	0.272074i
$199$	1.00000	+	1.00000i	0.0708881	+	0.0708881i	0.741662	−	0.670774i	$-0.234038\pi$
$199$	1.00000	+	1.00000i	0.0708881	+	0.0708881i	−0.670774	+	0.741662i	$0.734038\pi$
$200$	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
$204$	−0.585786	+	3.41421i	−0.0410133	+	0.239043i
$205$	−4.00000	−	4.00000i	−0.279372	−	0.279372i
$206$		0			0
$207$	−5.41421	+	2.58579i	−0.376314	+	0.179725i
$208$	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
$216$	−2.53553	+	4.53553i	−0.172521	+	0.308604i
$217$	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
$222$	−3.46447	+	9.94975i	−0.232520	+	0.667783i
$223$	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	0.990762	+	0.135614i	$0.0433007\pi$
$227$	16.9706	+	16.9706i	1.12638	+	1.12638i	0.135614	+	0.990762i	$0.456699\pi$
$228$	−9.65685	−	1.65685i	−0.639541	−	0.109728i
$229$	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	$-0.363111\pi$
$233$	12.7279			0.833834			0.416917	+	0.908945i	$0.363111\pi$
$234$	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
$237$	2.07107	−	12.0711i	0.134530	−	0.784100i
$238$	8.00000			0.518563
$239$	14.1421	+	14.1421i	0.914779	+	0.914779i	0.996643	−	0.0818647i	$-0.0260876\pi$
$239$	14.1421	+	14.1421i	0.914779	+	0.914779i	−0.0818647	+	0.996643i	$0.526088\pi$
$240$	1.70711	+	0.292893i	0.110193	+	0.0189062i
$241$	−13.0000	+	13.0000i	−0.837404	+	0.837404i	−0.988517	−	0.151113i	$-0.951714\pi$
$241$	−13.0000	+	13.0000i	−0.837404	+	0.837404i	0.151113	+	0.988517i	$0.451714\pi$
$242$	−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
$246$	1.65685	−	9.65685i	0.105637	−	0.615699i
$247$			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	$-0.626365\pi$
$251$	8.48528	−	8.48528i	0.535586	−	0.535586i	0.922229	+	0.386643i	$0.126365\pi$
$252$	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	−0.998173	−	0.0604217i	$-0.980755\pi$
$257$	−16.9706	−	16.9706i	−1.05859	−	1.05859i	−0.0604217	−	0.998173i	$-0.519245\pi$
$258$	−4.24264	−	6.00000i	−0.264135	−	0.373544i
$259$	24.0000	+	4.00000i	1.49129	+	0.248548i
$260$		−	4.24264i		−	0.263117i
$261$	5.17157	+	10.8284i	0.320112	+	0.670263i
$262$		−	4.00000i		−	0.247121i
$263$	26.8701			1.65688			0.828439	−	0.560079i	$-0.189229\pi$
$263$	26.8701			1.65688			0.828439	+	0.560079i	$0.189229\pi$
$264$	2.41421	+	0.414214i	0.148585	+	0.0254931i
$265$	−2.00000	+	2.00000i	−0.122859	+	0.122859i
$266$			22.6274i			1.38738i
$267$	0.585786	−	3.41421i	0.0358495	−	0.208946i
$268$	−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
$273$	4.97056	−	28.9706i	0.300832	−	1.75338i
$274$	15.0000	+	15.0000i	0.906183	+	0.906183i
$275$		−	1.41421i		−	0.0852803i
$276$	−0.585786	+	3.41421i	−0.0352602	+	0.205512i
$277$	15.0000	+	15.0000i	0.901263	+	0.901263i	0.995545	−	0.0942828i	$-0.0300558\pi$
$277$	15.0000	+	15.0000i	0.901263	+	0.901263i	−0.0942828	+	0.995545i	$0.530056\pi$
$278$		0			0
$279$	−11.4853	+	5.48528i	−0.687606	+	0.328395i
$280$		−	4.00000i		−	0.239046i
$281$	4.24264	+	4.24264i	0.253095	+	0.253095i	0.822238	−	0.569143i	$-0.192725\pi$
$281$	4.24264	+	4.24264i	0.253095	+	0.253095i	−0.569143	+	0.822238i	$0.692725\pi$
$282$	2.41421	+	0.414214i	0.143764	+	0.0246661i
$283$	−21.0000	−	21.0000i	−1.24832	−	1.24832i	−0.956461	−	0.291859i	$-0.905726\pi$
$283$	−21.0000	−	21.0000i	−1.24832	−	1.24832i	−0.291859	−	0.956461i	$-0.594274\pi$
$284$	−2.82843			−0.167836
$285$	−8.00000	+	5.65685i	−0.473879	+	0.335083i
$286$		−	6.00000i		−	0.354787i
$287$	−22.6274			−1.33565
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$		−	13.0000i		−	0.764706i
$290$	2.82843	−	2.82843i	0.166091	−	0.166091i
$291$	2.48528	−	14.4853i	0.145690	−	0.849142i
$292$	−10.0000			−0.585206
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	2.63604	−	15.3640i	0.153737	−	0.896044i
$295$		−	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	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		−	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	$-0.558085\pi$
$311$	14.1421	−	14.1421i	0.801927	−	0.801927i	0.983397	+	0.181470i	$0.0580854\pi$
$312$	6.00000	−	4.24264i	0.339683	−	0.240192i
$313$	24.0000	−	24.0000i	1.35656	−	1.35656i	0.478440	−	0.878120i	$-0.341202\pi$
$313$	24.0000	−	24.0000i	1.35656	−	1.35656i	0.878120	−	0.478440i	$-0.158798\pi$
$314$	−9.89949	+	9.89949i	−0.558661	+	0.558661i
$315$	10.8284	−	5.17157i	0.610113	−	0.291385i
$316$	−5.00000	−	5.00000i	−0.281272	−	0.281272i
$317$	−25.4558			−1.42974			−0.714871	−	0.699256i	$-0.753515\pi$
$317$	−25.4558			−1.42974			−0.714871	+	0.699256i	$0.753515\pi$
$318$	−4.82843	−	0.828427i	−0.270765	−	0.0464559i
$319$	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
$327$	5.79899	−	33.7990i	0.320685	−	1.86909i
$328$	−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	−0.759932	−	0.650002i	$-0.774768\pi$
$331$	−2.00000	+	2.00000i	−0.109930	+	0.109930i	0.650002	+	0.759932i	$0.274768\pi$
$332$	2.82843			0.155230
$333$	−8.82843	+	15.9706i	−0.483795	+	0.875181i
$334$	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	$-0.749528\pi$
$337$		−	26.0000i		−	1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$338$	−3.53553	−	3.53553i	−0.192308	−	0.192308i
$339$	−0.585786	+	3.41421i	−0.0318156	+	0.185435i
$340$	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	0.245241	−	0.969462i	$-0.421133\pi$
$347$	22.6274	−	22.6274i	1.21470	−	1.21470i	0.969462	−	0.245241i	$-0.0788672\pi$
$348$	6.82843	+	1.17157i	0.366042	+	0.0628029i
$349$	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
$351$	19.2426	+	10.7574i	1.02710	+	0.574185i
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$	−18.3848	+	18.3848i	−0.978523	+	0.978523i	−0.999774	−	0.0212513i	$-0.993235\pi$
$353$	−18.3848	+	18.3848i	−0.978523	+	0.978523i	0.0212513	+	0.999774i	$0.493235\pi$
$354$	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
$357$	13.6569	+	2.34315i	0.722797	+	0.124012i
$358$			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
$372$	−1.24264	+	7.24264i	−0.0644279	+	0.375513i
$373$			22.0000i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$373$			22.0000i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$374$	2.82843			0.146254
$375$	0.292893	−	1.70711i	0.0151249	−	0.0881546i
$376$	1.00000	−	1.00000i	0.0515711	−	0.0515711i
$377$		−	16.9706i		−	0.874028i
$378$	18.1421	+	10.1421i	0.933131	+	0.521655i
$379$	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	$-0.0398935\pi$
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	−0.125001	+	0.992157i	$0.539894\pi$
$384$	1.70711	+	0.292893i	0.0871154	+	0.0149466i
$385$	−4.00000	−	4.00000i	−0.203859	−	0.203859i
$386$			16.9706i			0.863779i
$387$	−5.48528	−	11.4853i	−0.278833	−	0.583830i
$388$	−6.00000	−	6.00000i	−0.304604	−	0.304604i
$389$	16.9706	+	16.9706i	0.860442	+	0.860442i	0.991389	−	0.130948i	$-0.0418020\pi$
$389$	16.9706	+	16.9706i	0.860442	+	0.860442i	−0.130948	+	0.991389i	$0.541802\pi$
$390$	1.24264	−	7.24264i	0.0629236	−	0.366745i
$391$			4.00000i			0.202289i
$392$	−6.36396	−	6.36396i	−0.321429	−	0.321429i
$393$	1.17157	−	6.82843i	0.0590980	−	0.344449i
$394$	−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	$-0.813837\pi$
$397$		−	22.0000i		−	1.10415i	0.833795	−	0.552074i	$-0.186163\pi$
$398$	1.41421			0.0708881
$399$	−6.62742	+	38.6274i	−0.331786	+	1.93379i
$400$		−	1.00000i		−	0.0500000i
$401$	−4.24264	+	4.24264i	−0.211867	+	0.211867i	−0.805060	−	0.593193i	$-0.797867\pi$
$401$	−4.24264	+	4.24264i	−0.211867	+	0.211867i	0.593193	+	0.805060i	$0.297867\pi$
$402$	−10.2426	−	1.75736i	−0.510856	−	0.0876491i
$403$	18.0000			0.896644
$404$			1.41421i			0.0703598i
$405$	0.949747	+	8.94975i	0.0471933	+	0.444717i
$406$		−	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	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$	−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	$0.707722\pi$
$420$	1.17157	−	6.82843i	0.0571669	−	0.333193i
$421$	20.0000	+	20.0000i	0.974740	+	0.974740i	0.999689	−	0.0249484i	$-0.00794214\pi$
$421$	20.0000	+	20.0000i	0.974740	+	0.974740i	−0.0249484	+	0.999689i	$0.507942\pi$
$422$	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
$426$	−4.82843	−	0.828427i	−0.233938	−	0.0401374i
$427$	24.0000	+	24.0000i	1.16144	+	1.16144i
$428$	8.48528			0.410152
$429$	1.75736	−	10.2426i	0.0848461	−	0.494519i
$430$	−3.00000	+	3.00000i	−0.144673	+	0.144673i
$431$	8.48528	−	8.48528i	0.408722	−	0.408722i	−0.472571	−	0.881293i	$-0.656674\pi$
$431$	8.48528	−	8.48528i	0.408722	−	0.408722i	0.881293	+	0.472571i	$0.156674\pi$
$432$	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
$438$	−17.0711	−	2.92893i	−0.815687	−	0.139950i
$439$	9.00000	+	9.00000i	0.429547	+	0.429547i	0.888474	−	0.458927i	$-0.151766\pi$
$439$	9.00000	+	9.00000i	0.429547	+	0.429547i	−0.458927	+	0.888474i	$0.651766\pi$
$440$		−	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	$-0.609060\pi$
$443$	−14.1421			−0.671913			−0.335957	+	0.941877i	$0.609060\pi$
$444$	4.58579	+	9.48528i	0.217632	+	0.450152i
$445$	−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	$-0.423741\pi$
$449$	−15.5563	−	15.5563i	−0.734150	−	0.734150i	−0.971439	+	0.237289i	$0.923741\pi$
$450$	2.70711	−	1.29289i	0.127614	−	0.0609476i
$451$	−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	−0.614157	+	0.789184i	$0.710504\pi$
$457$	−30.0000	+	30.0000i	−1.40334	+	1.40334i	−0.789184	+	0.614157i	$0.789496\pi$
$458$	7.07107	−	7.07107i	0.330409	−	0.330409i
$459$	−5.07107	+	9.07107i	−0.236697	+	0.423401i
$460$	2.00000			0.0932505
$461$	−4.24264	−	4.24264i	−0.197599	−	0.197599i	0.601371	−	0.798970i	$-0.294622\pi$
$461$	−4.24264	−	4.24264i	−0.197599	−	0.197599i	−0.798970	+	0.601371i	$0.794622\pi$
$462$	1.65685	−	9.65685i	0.0770838	−	0.449278i
$463$	−4.00000	+	4.00000i	−0.185896	+	0.185896i	−0.793919	−	0.608023i	$-0.791963\pi$
$463$	−4.00000	+	4.00000i	−0.185896	+	0.185896i	0.608023	+	0.793919i	$0.291963\pi$
$464$	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	−0.998836	−	0.0482360i	$-0.984640\pi$
$467$	−22.6274	−	22.6274i	−1.04707	−	1.04707i	−0.0482360	−	0.998836i	$-0.515360\pi$
$468$	11.4853	−	5.48528i	0.530907	−	0.253557i
$469$			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	$-0.130888\pi$
$479$	11.3137	+	11.3137i	0.516937	+	0.516937i	−0.399707	+	0.916643i	$0.630888\pi$
$480$	1.41421	−	1.00000i	0.0645497	−	0.0456435i
$481$	21.0000	−	15.0000i	0.957518	−	0.683941i
$482$			18.3848i			0.837404i
$483$	13.6569	+	2.34315i	0.621408	+	0.106617i
$484$			9.00000i			0.409091i
$485$	−8.48528			−0.385297
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	8.00000	−	8.00000i	0.362515	−	0.362515i	−0.502223	−	0.864738i	$-0.667484\pi$
$487$	8.00000	−	8.00000i	0.362515	−	0.362515i	0.864738	+	0.502223i	$0.167484\pi$
$488$			8.48528i			0.384111i
$489$	−36.2132	−	6.21320i	−1.63762	−	0.280971i
$490$	−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
$495$	3.82843	−	1.82843i	0.172075	−	0.0821817i
$496$	3.00000	+	3.00000i	0.134704	+	0.134704i
$497$			11.3137i			0.507489i
$498$	4.82843	+	0.828427i	0.216367	+	0.0371227i
$499$	6.00000	+	6.00000i	0.268597	+	0.268597i	0.828535	−	0.559938i	$-0.189175\pi$
$499$	6.00000	+	6.00000i	0.268597	+	0.268597i	−0.559938	+	0.828535i	$0.689175\pi$
$500$	−0.707107	−	0.707107i	−0.0316228	−	0.0316228i
$501$	3.41421	+	0.585786i	0.152536	+	0.0261710i
$502$		−	12.0000i		−	0.535586i
$503$	−7.07107	−	7.07107i	−0.315283	−	0.315283i	0.531669	−	0.846952i	$-0.321565\pi$
$503$	−7.07107	−	7.07107i	−0.315283	−	0.315283i	−0.846952	+	0.531669i	$0.821565\pi$
$504$	10.8284	−	5.17157i	0.482336	−	0.230360i
$505$	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	$-0.509978\pi$
$509$	−1.41421			−0.0626839			−0.0313420	+	0.999509i	$0.509978\pi$
$510$	3.41421	+	0.585786i	0.151184	+	0.0259391i
$511$			40.0000i			1.76950i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−25.6569	−	14.3431i	−1.13278	−	0.633265i
$514$	−24.0000			−1.05859
$515$		0			0
$516$	−7.24264	−	1.24264i	−0.318839	−	0.0547042i
$517$		−	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	$-0.738688\pi$
$521$	−31.1127			−1.36307			−0.681536	+	0.731785i	$0.738688\pi$
$522$	11.3137	+	4.00000i	0.495188	+	0.175075i
$523$	21.0000	−	21.0000i	0.918266	−	0.918266i	−0.0786374	−	0.996903i	$-0.525057\pi$
$523$	21.0000	−	21.0000i	0.918266	−	0.918266i	0.996903	+	0.0786374i	$0.0250569\pi$
$524$	−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
$531$	32.4853	−	15.5147i	1.40974	−	0.673281i
$532$	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
$537$	−2.92893	+	17.0711i	−0.126393	+	0.736671i
$538$	−5.00000	−	5.00000i	−0.215565	−	0.215565i
$539$	−12.7279			−0.548230
$540$	4.53553	+	2.53553i	0.195178	+	0.109112i
$541$	−12.0000	+	12.0000i	−0.515920	+	0.515920i	−0.916334	−	0.400414i	$-0.868866\pi$
$541$	−12.0000	+	12.0000i	−0.515920	+	0.515920i	0.400414	+	0.916334i	$0.368866\pi$
$542$	−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	0.640057	−	0.768328i	$-0.278911\pi$
$547$	−3.00000	−	3.00000i	−0.128271	−	0.128271i	−0.768328	+	0.640057i	$0.778911\pi$
$548$	21.2132			0.906183
$549$	−22.9706	+	10.9706i	−0.980360	+	0.468212i
$550$	−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
$555$	9.94975	+	3.46447i	0.422343	+	0.147058i
$556$		0			0
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	−0.736433	−	0.676511i	$-0.763491\pi$
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	0.676511	+	0.736433i	$0.263491\pi$
$558$	−4.24264	+	12.0000i	−0.179605	+	0.508001i
$559$			18.0000i			0.761319i
$560$	−2.82843	−	2.82843i	−0.119523	−	0.119523i
$561$	4.82843	+	0.828427i	0.203856	+	0.0349762i
$562$	6.00000			0.253095
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$	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	0.287135	−	0.957890i	$-0.407297\pi$
$569$	29.6985	−	29.6985i	1.24503	−	1.24503i	0.957890	−	0.287135i	$-0.0927029\pi$
$570$	−1.65685	+	9.65685i	−0.0693980	+	0.404481i
$571$	−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
$573$	−40.9706	−	7.02944i	−1.71157	−	0.293659i
$574$	−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	−0.467623	−	0.883928i	$-0.654889\pi$
$577$	10.0000	−	10.0000i	0.416305	−	0.416305i	0.883928	+	0.467623i	$0.154889\pi$
$578$	−9.19239	−	9.19239i	−0.382353	−	0.382353i
$579$	−4.97056	+	28.9706i	−0.206570	+	1.20398i
$580$		−	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	−0.184604	+	0.982813i	$0.559100\pi$
$587$	−28.2843	+	28.2843i	−1.16742	+	1.16742i	−0.982813	+	0.184604i	$0.940900\pi$
$588$	−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	$0.835668\pi$
$594$	6.41421	+	3.58579i	0.263178	+	0.147127i
$595$		−	8.00000i		−	0.327968i
$596$	−18.3848			−0.753070
$597$	2.41421	+	0.414214i	0.0988072	+	0.0169526i
$598$	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	$0.847037\pi$
$600$	0.292893	−	1.70711i	0.0119573	−	0.0696923i
$601$	−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
$606$	−0.414214	+	2.41421i	−0.0168263	+	0.0980707i
$607$	−8.00000	−	8.00000i	−0.324710	−	0.324710i	0.525861	−	0.850571i	$-0.323743\pi$
$607$	−8.00000	−	8.00000i	−0.324710	−	0.324710i	−0.850571	+	0.525861i	$0.823743\pi$
$608$			5.65685i			0.229416i
$609$	4.68629	−	27.3137i	0.189898	−	1.10681i
$610$	6.00000	+	6.00000i	0.242933	+	0.242933i
$611$	−4.24264	−	4.24264i	−0.171639	−	0.171639i
$612$	2.58579	+	5.41421i	0.104524	+	0.218857i
$613$		−	16.0000i		−	0.646234i	−0.946359	−	0.323117i	$-0.895269\pi$
$613$		−	16.0000i		−	0.646234i	0.946359	−	0.323117i	$-0.104731\pi$
$614$	19.7990	+	19.7990i	0.799022	+	0.799022i
$615$	−9.65685	−	1.65685i	−0.389402	−	0.0668108i
$616$	−4.00000	−	4.00000i	−0.161165	−	0.161165i
$617$	−35.3553			−1.42335			−0.711676	−	0.702508i	$-0.752064\pi$
$617$	−35.3553			−1.42335			−0.711676	+	0.702508i	$0.752064\pi$
$618$		0			0
$619$			20.0000i			0.803868i	0.915669	+	0.401934i	$0.131662\pi$
$619$			20.0000i			0.803868i	−0.915669	+	0.401934i	$0.868338\pi$
$620$	4.24264			0.170389
$621$	−5.07107	+	9.07107i	−0.203495	+	0.364009i
$622$		−	20.0000i		−	0.801927i
$623$	−5.65685	+	5.65685i	−0.226637	+	0.226637i
$624$	1.24264	−	7.24264i	0.0497454	−	0.289938i
$625$	−1.00000			−0.0400000
$626$		−	33.9411i		−	1.35656i
$627$	−2.34315	+	13.6569i	−0.0935762	+	0.545402i
$628$			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	0.453403	−	0.891306i	$-0.350210\pi$
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	−0.891306	+	0.453403i	$0.850210\pi$
$632$	−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	$-0.0717262\pi$
$642$	14.4853	+	2.48528i	0.571688	+	0.0980862i
$643$	−25.0000	−	25.0000i	−0.985904	−	0.985904i	0.0139983	−	0.999902i	$-0.495544\pi$
$643$	−25.0000	−	25.0000i	−0.985904	−	0.985904i	−0.999902	+	0.0139983i	$0.995544\pi$
$644$	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	$-0.699735\pi$
$647$	5.65685	−	5.65685i	0.222394	−	0.222394i	0.809506	+	0.587112i	$0.199735\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$	−12.0000	−	12.0000i	−0.471041	−	0.471041i
$650$	−4.24264			−0.166410
$651$	28.9706	+	4.97056i	1.13545	+	0.194812i
$652$	−15.0000	+	15.0000i	−0.587445	+	0.587445i
$653$	12.7279	−	12.7279i	0.498082	−	0.498082i	−0.412758	−	0.910841i	$-0.635435\pi$
$653$	12.7279	−	12.7279i	0.498082	−	0.498082i	0.910841	+	0.412758i	$0.135435\pi$
$654$	−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	$-0.324680\pi$
$659$	26.8701			1.04671			0.523354	+	0.852115i	$0.324680\pi$
$660$	0.414214	−	2.41421i	0.0161232	−	0.0939731i
$661$	−28.0000	−	28.0000i	−1.08907	−	1.08907i	−0.995624	−	0.0934498i	$-0.970211\pi$
$661$	−28.0000	−	28.0000i	−1.08907	−	1.08907i	−0.0934498	−	0.995624i	$-0.529789\pi$
$662$			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
$666$	5.05025	+	17.5355i	0.195693	+	0.679488i
$667$	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
$672$	1.17157	−	6.82843i	0.0451944	−	0.263412i
$673$	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	$-0.164349\pi$
$677$	45.2548			1.73928			0.869642	+	0.493682i	$0.164349\pi$
$678$	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
$681$	40.9706	+	7.02944i	1.57000	+	0.269369i
$682$	6.00000			0.229752
$683$	33.9411	+	33.9411i	1.29872	+	1.29872i	0.929237	+	0.369484i	$0.120466\pi$
$683$	33.9411	+	33.9411i	1.29872	+	1.29872i	0.369484	+	0.929237i	$0.379534\pi$
$684$	−15.3137	+	7.31371i	−0.585534	+	0.279647i
$685$	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
$690$	3.41421	+	0.585786i	0.129977	+	0.0223005i
$691$			12.0000i			0.456502i	0.973602	+	0.228251i	$0.0733006\pi$
$691$			12.0000i			0.456502i	−0.973602	+	0.228251i	$0.926699\pi$
$692$			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	$-0.441719\pi$
$701$	−21.2132	−	21.2132i	−0.801212	−	0.801212i	−0.983285	+	0.182073i	$0.941719\pi$
$702$	21.2132	−	6.00000i	0.800641	−	0.226455i
$703$	−28.0000	+	20.0000i	−1.05604	+	0.754314i
$704$		−	1.41421i		−	0.0533002i
$705$	0.414214	−	2.41421i	0.0156002	−	0.0909245i
$706$			26.0000i			0.978523i
$707$	5.65685			0.212748
$708$	3.51472	−	20.4853i	0.132091	−	0.769884i
$709$	−14.0000	+	14.0000i	−0.525781	+	0.525781i	−0.919312	−	0.393531i	$-0.871254\pi$
$709$	−14.0000	+	14.0000i	−0.525781	+	0.525781i	0.393531	+	0.919312i	$0.371254\pi$
$710$			2.82843i			0.106149i
$711$	−9.14214	−	19.1421i	−0.342857	−	0.717886i
$712$	−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
$717$	34.1421	+	5.85786i	1.27506	+	0.218766i
$718$	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	$-0.0849450\pi$
$720$	2.70711	−	1.29289i	0.100888	−	0.0481833i
$721$		0			0
$722$	−9.19239	−	9.19239i	−0.342105	−	0.342105i
$723$	−5.38478	+	31.3848i	−0.200262	+	1.16721i
$724$		−	10.0000i		−	0.371647i
$725$	−2.82843	−	2.82843i	−0.105045	−	0.105045i
$726$	−2.63604	+	15.3640i	−0.0978326	+	0.570210i
$727$	−22.0000	−	22.0000i	−0.815935	−	0.815935i	0.169581	−	0.985516i	$-0.445758\pi$
$727$	−22.0000	−	22.0000i	−0.815935	−	0.815935i	−0.985516	+	0.169581i	$0.945758\pi$
$728$	−16.9706			−0.628971
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$			10.0000i			0.370117i
$731$	−8.48528			−0.313839
$732$	−2.48528	+	14.4853i	−0.0918586	+	0.535391i
$733$			40.0000i			1.47743i	0.674016	+	0.738717i	$0.264568\pi$
$733$			40.0000i			1.47743i	−0.674016	+	0.738717i	$0.735432\pi$
$734$	−8.48528	+	8.48528i	−0.313197	+	0.313197i
$735$	−15.3640	−	2.63604i	−0.566708	−	0.0972318i
$736$	2.00000			0.0737210
$737$			8.48528i			0.312559i
$738$	−7.31371	−	15.3137i	−0.269221	−	0.563705i
$739$			4.00000i			0.147142i	0.997290	+	0.0735712i	$0.0234396\pi$
$739$			4.00000i			0.147142i	−0.997290	+	0.0735712i	$0.976560\pi$
$740$	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	$-0.228946\pi$
$743$	41.0122			1.50459			0.752296	+	0.658826i	$0.228946\pi$
$744$	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	$0.0116179\pi$
$751$			2.00000i			0.0729810i	−0.999334	+	0.0364905i	$0.988382\pi$
$752$		−	1.41421i		−	0.0515711i
$753$	3.51472	−	20.4853i	0.128083	−	0.746525i
$754$	−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	−0.610380	−	0.792108i	$-0.708983\pi$
$757$	5.00000	−	5.00000i	0.181728	−	0.181728i	0.792108	+	0.610380i	$0.208983\pi$
$758$	19.7990	−	19.7990i	0.719132	−	0.719132i
$759$	4.82843	+	0.828427i	0.175261	+	0.0300700i
$760$	4.00000	+	4.00000i	0.145095	+	0.145095i
$761$	5.65685			0.205061			0.102530	−	0.994730i	$-0.467306\pi$
$761$	5.65685			0.205061			0.102530	+	0.994730i	$0.467306\pi$
$762$	4.68629	−	27.3137i	0.169766	−	0.989471i
$763$	−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	0.611184	−	0.791489i	$-0.290694\pi$
$769$	−5.00000	−	5.00000i	−0.180305	−	0.180305i	−0.791489	+	0.611184i	$0.790694\pi$
$770$	−5.65685			−0.203859
$771$	−40.9706	−	7.02944i	−1.47552	−	0.253159i
$772$	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
$777$	37.9411	−	18.3431i	1.36113	−	0.658057i
$778$	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
$783$	18.1421	+	10.1421i	0.648347	+	0.362450i
$784$	−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
$792$	3.82843	−	1.82843i	0.136037	−	0.0649703i
$793$	36.0000			1.27840
$794$	−15.5563	−	15.5563i	−0.552074	−	0.552074i
$795$	−0.828427	+	4.82843i	−0.0293813	+	0.171247i
$796$	1.00000	−	1.00000i	0.0354441	−	0.0354441i
$797$	29.6985	−	29.6985i	1.05197	−	1.05197i	0.0534012	−	0.998573i	$-0.482994\pi$
$797$	29.6985	−	29.6985i	1.05197	−	1.05197i	0.998573	−	0.0534012i	$-0.0170062\pi$
$798$	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
$801$	−2.58579	−	5.41421i	−0.0913643	−	0.191302i
$802$			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	$-0.693752\pi$
$809$	7.07107	−	7.07107i	0.248606	−	0.248606i	0.820398	+	0.571793i	$0.193752\pi$
$810$	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
$816$	3.41421	+	0.585786i	0.119521	+	0.0205066i
$817$		−	24.0000i		−	0.839654i
$818$	−4.24264			−0.148340
$819$	−21.9411	−	45.9411i	−0.766685	−	1.60531i
$820$	−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	$-0.0393769\pi$
$822$	36.2132	+	6.21320i	1.26308	+	0.216710i
$823$	−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	−0.941450	−	0.337153i	$-0.890536\pi$
$827$	−36.7696	−	36.7696i	−1.27860	−	1.27860i	−0.337153	−	0.941450i	$-0.609464\pi$
$828$	2.58579	+	5.41421i	0.0898623	+	0.188157i
$829$	−30.0000	−	30.0000i	−1.04194	−	1.04194i	−0.999081	−	0.0428621i	$-0.986352\pi$
$829$	−30.0000	−	30.0000i	−1.04194	−	1.04194i	−0.0428621	−	0.999081i	$-0.513648\pi$
$830$		−	2.82843i		−	0.0981761i
$831$	36.2132	+	6.21320i	1.25622	+	0.215534i
$832$	−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
$837$	−10.7574	+	19.2426i	−0.371829	+	0.665123i
$838$	23.0000	+	23.0000i	0.794522	+	0.794522i
$839$	25.4558			0.878833			0.439417	−	0.898283i	$-0.355185\pi$
$839$	25.4558			0.878833			0.439417	+	0.898283i	$0.355185\pi$
$840$	−4.00000	−	5.65685i	−0.138013	−	0.195180i
$841$			13.0000i			0.448276i
$842$	28.2843			0.974740
$843$	10.2426	+	1.75736i	0.352775	+	0.0605267i
$844$		−	8.00000i		−	0.275371i
$845$	−3.53553	+	3.53553i	−0.121626	+	0.121626i
$846$	3.82843	−	1.82843i	0.131624	−	0.0628626i
$847$	36.0000			1.23697
$848$			2.82843i			0.0971286i
$849$	−50.6985	−	8.69848i	−1.73997	−	0.298531i
$850$		−	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	0.869886	−	0.493253i	$-0.164192\pi$
$853$	11.0000	+	11.0000i	0.376633	+	0.376633i	−0.493253	+	0.869886i	$0.664192\pi$
$854$	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	$-0.372616\pi$
$857$	−15.5563	−	15.5563i	−0.531395	−	0.531395i	−0.920987	+	0.389593i	$0.872616\pi$
$858$	−6.00000	−	8.48528i	−0.204837	−	0.289683i
$859$	−16.0000	+	16.0000i	−0.545913	+	0.545913i	−0.925256	−	0.379343i	$-0.876150\pi$
$859$	−16.0000	+	16.0000i	−0.545913	+	0.545913i	0.379343	+	0.925256i	$0.376150\pi$
$860$			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	$-0.117583\pi$
$864$	4.53553	+	2.53553i	0.154302	+	0.0862606i
$865$	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
$870$	1.17157	−	6.82843i	0.0397200	−	0.231505i
$871$	18.0000	+	18.0000i	0.609907	+	0.609907i
$872$	−19.7990			−0.670478
$873$	−10.9706	−	22.9706i	−0.371297	−	0.777436i
$874$	−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	$-0.306264\pi$
$881$	33.9411			1.14351			0.571753	+	0.820426i	$0.306264\pi$
$882$	−11.6360	−	24.3640i	−0.391806	−	0.820377i
$883$	21.0000	+	21.0000i	0.706706	+	0.706706i	0.965841	−	0.259135i	$-0.0834374\pi$
$883$	21.0000	+	21.0000i	0.706706	+	0.706706i	−0.259135	+	0.965841i	$0.583437\pi$
$884$		−	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	$-0.187780\pi$
$887$	49.4975			1.66196			0.830981	+	0.556300i	$0.187780\pi$
$888$	9.94975	+	3.46447i	0.333892	+	0.116260i
$889$	−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
$894$	−31.3848	−	5.38478i	−1.04966	−	0.180094i
$895$	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
$903$	−4.97056	+	28.9706i	−0.165410	+	0.964080i
$904$	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	0.363303	−	0.931671i	$-0.381649\pi$
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.931671	−	0.363303i	$-0.118351\pi$
$908$	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	$-0.313701\pi$
$911$	−8.48528	−	8.48528i	−0.281130	−	0.281130i	−0.833560	+	0.552430i	$0.813701\pi$
$912$	−1.65685	+	9.65685i	−0.0548639	+	0.319770i
$913$		−	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	−0.995676	−	0.0928935i	$-0.970388\pi$
$919$	−33.0000	−	33.0000i	−1.08857	−	1.08857i	−0.0928935	−	0.995676i	$-0.529612\pi$
$920$	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	$-0.0722143\pi$
$929$	59.3970			1.94875			0.974376	+	0.224927i	$0.0722143\pi$
$930$	7.24264	+	1.24264i	0.237496	+	0.0407478i
$931$	36.0000	−	36.0000i	1.17985	−	1.17985i
$932$		−	12.7279i		−	0.416917i
$933$	5.85786	−	34.1421i	0.191778	−	1.11776i
$934$	−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
$939$	9.94113	−	57.9411i	0.324416	−	1.89084i
$940$	−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	$0.887619\pi$
$942$	−4.10051	+	23.8995i	−0.133602	+	0.778688i
$943$	−8.00000	−	8.00000i	−0.260516	−	0.260516i
$944$	−8.48528	−	8.48528i	−0.276172	−	0.276172i
$945$	10.1421	−	18.1421i	0.329924	−	0.590164i
$946$			6.00000i			0.195077i
$947$	−36.7696	−	36.7696i	−1.19485	−	1.19485i	−0.975689	−	0.219161i	$-0.929668\pi$
$947$	−36.7696	−	36.7696i	−1.19485	−	1.19485i	−0.219161	−	0.975689i	$-0.570332\pi$
$948$	−12.0711	−	2.07107i	−0.392050	−	0.0672652i
$949$	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	$-0.305921\pi$
$953$	35.3553			1.14527			0.572636	+	0.819810i	$0.305921\pi$
$954$	−7.65685	+	3.65685i	−0.247900	+	0.118395i
$955$			24.0000i			0.776622i
$956$	14.1421	−	14.1421i	0.457389	−	0.457389i
$957$	1.65685	−	9.65685i	0.0535585	−	0.312162i
$958$	16.0000			0.516937
$959$		−	84.8528i		−	2.74004i
$960$	0.292893	−	1.70711i	0.00945309	−	0.0550966i
$961$		−	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	−0.527794	−	0.849372i	$-0.676981\pi$
$967$	10.0000	−	10.0000i	0.321578	−	0.321578i	0.849372	+	0.527794i	$0.176981\pi$
$968$	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
$975$	−7.24264	−	1.24264i	−0.231950	−	0.0397964i
$976$	6.00000	+	6.00000i	0.192055	+	0.192055i
$977$	−42.4264	+	42.4264i	−1.35734	+	1.35734i	−0.480160	+	0.877181i	$0.659421\pi$
$977$	−42.4264	+	42.4264i	−1.35734	+	1.35734i	−0.877181	+	0.480160i	$0.840579\pi$
$978$	−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
$981$	−25.5980	−	53.5980i	−0.817281	−	1.71125i
$982$	9.00000	+	9.00000i	0.287202	+	0.287202i
$983$	−43.8406			−1.39830			−0.699149	−	0.714976i	$-0.746438\pi$
$983$	−43.8406			−1.39830			−0.699149	+	0.714976i	$0.746438\pi$
$984$	−9.65685	−	1.65685i	−0.307849	−	0.0528186i
$985$	−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	0.289954	−	0.957041i	$-0.406360\pi$
$991$	−21.0000	−	21.0000i	−0.667087	−	0.667087i	−0.957041	+	0.289954i	$0.906360\pi$
$992$	4.24264			0.134704
$993$	−0.828427	+	4.82843i	−0.0262893	+	0.153226i
$994$	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	−0.970304	−	0.241887i	$-0.922234\pi$
$997$	−23.0000	+	23.0000i	−0.728417	+	0.728417i	0.241887	+	0.970304i	$0.422234\pi$
$998$	8.48528			0.268597
$999$	3.48528	+	31.4142i	0.110269	+	0.993902i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.c.191.1	✓	4	37.6	odd	4	inner
1110.2.u.c.191.2	yes	4	111.80	even	4	inner
1110.2.u.c.401.1	yes	4	3.2	odd	2	inner
1110.2.u.c.401.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} -1.00000 q^{10} -1.41421 q^{11} +(-1.00000 - 1.41421i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(-2.82843 + 2.82843i) q^{14} +(-1.70711 - 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +(-1.29289 - 2.70711i) q^{18} +(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} +(-1.70711 - 0.292893i) 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} +(-1.24264 + 7.24264i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 + 6.82843i) q^{42} +(3.00000 - 3.00000i) q^{43} +1.41421i q^{44} +(-2.70711 + 1.29289i) 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} +(-3.41421 - 0.585786i) q^{51} +(3.00000 + 3.00000i) q^{52} -2.82843i q^{53} +(-4.53553 - 2.53553i) q^{54} +(1.00000 + 1.00000i) q^{55} +(2.82843 + 2.82843i) q^{56} +(1.65685 - 9.65685i) q^{57} +4.00000i q^{58} +(8.48528 + 8.48528i) q^{59} +(-0.292893 + 1.70711i) 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} +(-0.414214 + 2.41421i) q^{66} -6.00000i q^{67} +(-1.41421 + 1.41421i) q^{68} +(-3.41421 - 0.585786i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 + 1.29289i) 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} +(-1.17157 + 6.82843i) 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} +(-7.24264 - 1.24264i) q^{93} +(1.00000 + 1.00000i) q^{94} -5.65685 q^{95} +(-0.292893 + 1.70711i) 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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