LMFDB - Embedded newform 1110.2.bb.b.1009.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.b.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00000 + 1.00000i) q^{10} +(-0.866025 - 0.500000i) q^{12} +(-4.33013 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.133975 + 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.50000 + 6.06218i) q^{19} +(2.23205 + 0.133975i) q^{20} +(0.500000 - 0.866025i) q^{21} +4.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.96410 - 4.59808i) q^{25} +5.00000 q^{26} +1.00000i q^{27} +(-0.866025 - 0.500000i) q^{28} +3.00000 q^{29} +(1.23205 - 1.86603i) q^{30} +2.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.00000 + 1.73205i) q^{34} +(-0.133975 + 2.23205i) q^{35} +1.00000 q^{36} +(-6.06218 + 0.500000i) q^{37} -7.00000i q^{38} +(2.50000 - 4.33013i) q^{39} +(-1.86603 - 1.23205i) q^{40} +(-0.866025 + 0.500000i) q^{42} -2.00000i q^{43} +(-1.00000 - 2.00000i) q^{45} +(2.00000 - 3.46410i) q^{46} +4.00000i q^{47} -1.00000i q^{48} +(-3.00000 + 5.19615i) q^{49} +(-0.598076 + 4.96410i) q^{50} +2.00000 q^{51} +(-4.33013 - 2.50000i) q^{52} +(6.92820 + 4.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} +(-6.06218 - 3.50000i) q^{57} +(-2.59808 - 1.50000i) q^{58} +(-2.00000 + 1.00000i) q^{60} +(2.00000 + 3.46410i) q^{61} +(-1.73205 - 1.00000i) q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-0.669873 + 11.1603i) q^{65} +(3.46410 - 2.00000i) q^{67} -2.00000i q^{68} +(-2.00000 - 3.46410i) q^{69} +(1.23205 - 1.86603i) q^{70} +(6.50000 + 11.2583i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.00000i q^{73} +(5.50000 + 2.59808i) q^{74} +(4.00000 + 3.00000i) q^{75} +(-3.50000 + 6.06218i) q^{76} +(-4.33013 + 2.50000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{83} +1.00000 q^{84} +(-4.00000 + 2.00000i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-2.59808 + 1.50000i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-0.133975 + 2.23205i) q^{90} +(2.50000 - 4.33013i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(-1.73205 + 1.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +(15.6244 + 0.937822i) q^{95} +(-0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(5.19615 - 3.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9} - 8 q^{10} + 4 q^{14} - 4 q^{15} - 2 q^{16} + 14 q^{19} + 2 q^{20} + 2 q^{21} + 2 q^{24} + 6 q^{25} + 20 q^{26} + 12 q^{29} - 2 q^{30} + 8 q^{31} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 10 q^{39} - 4 q^{40} - 4 q^{45} + 8 q^{46} - 12 q^{49} + 8 q^{50} + 8 q^{51} + 2 q^{54} + 2 q^{56} - 8 q^{60} + 8 q^{61} - 4 q^{64} - 20 q^{65} - 8 q^{69} - 2 q^{70} + 26 q^{71} + 22 q^{74} + 16 q^{75} - 14 q^{76} - 20 q^{79} + 4 q^{80} - 2 q^{81} + 4 q^{84} - 16 q^{85} - 4 q^{86} - 24 q^{89} - 4 q^{90} + 10 q^{91} + 8 q^{94} + 14 q^{95} - 2 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9 - 8 * q^10 + 4 * q^14 - 4 * q^15 - 2 * q^16 + 14 * q^19 + 2 * q^20 + 2 * q^21 + 2 * q^24 + 6 * q^25 + 20 * q^26 + 12 * q^29 - 2 * q^30 + 8 * q^31 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 10 * q^39 - 4 * q^40 - 4 * q^45 + 8 * q^46 - 12 * q^49 + 8 * q^50 + 8 * q^51 + 2 * q^54 + 2 * q^56 - 8 * q^60 + 8 * q^61 - 4 * q^64 - 20 * q^65 - 8 * q^69 - 2 * q^70 + 26 * q^71 + 22 * q^74 + 16 * q^75 - 14 * q^76 - 20 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^84 - 16 * q^85 - 4 * q^86 - 24 * q^89 - 4 * q^90 + 10 * q^91 + 8 * q^94 + 14 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$6$	1.00000			0.408248
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−4.33013	+	2.50000i	−1.20096	+	0.693375i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$	−4.33013	+	2.50000i	−1.20096	+	0.693375i	−0.240192	+	0.970725i	$0.577210\pi$
$14$	1.00000			0.267261
$15$	−0.133975	+	2.23205i	−0.0345921	+	0.576313i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	2.23205	+	0.133975i	0.499102	+	0.0299576i
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	5.00000			0.980581
$27$			1.00000i			0.192450i
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	1.23205	−	1.86603i	0.224941	−	0.340688i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	−0.133975	+	2.23205i	−0.0226458	+	0.377285i
$36$	1.00000			0.166667
$37$	−6.06218	+	0.500000i	−0.996616	+	0.0821995i
$37$	−6.06218	+	0.500000i	−0.996616	+	0.0821995i
$38$		−	7.00000i		−	1.13555i
$39$	2.50000	−	4.33013i	0.400320	−	0.693375i
$40$	−1.86603	−	1.23205i	−0.295045	−	0.194804i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.866025	+	0.500000i	−0.133631	+	0.0771517i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$		0			0
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$	−0.598076	+	4.96410i	−0.0845807	+	0.702030i
$51$	2.00000			0.280056
$52$	−4.33013	−	2.50000i	−0.600481	−	0.346688i
$53$	6.92820	+	4.00000i	0.951662	+	0.549442i	0.893597	−	0.448871i	$-0.148174\pi$
$53$	6.92820	+	4.00000i	0.951662	+	0.549442i	0.0580651	+	0.998313i	$0.481507\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−6.06218	−	3.50000i	−0.802955	−	0.463586i
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−2.00000	+	1.00000i	−0.258199	+	0.129099i
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−1.73205	−	1.00000i	−0.219971	−	0.127000i
$63$			1.00000i			0.125988i
$64$	−1.00000			−0.125000
$65$	−0.669873	+	11.1603i	−0.0830875	+	1.38426i
$66$		0			0
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$		−	2.00000i		−	0.242536i
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$	1.23205	−	1.86603i	0.147258	−	0.223033i
$71$	6.50000	+	11.2583i	0.771408	+	1.33612i	0.936791	+	0.349889i	$0.113781\pi$
$71$	6.50000	+	11.2583i	0.771408	+	1.33612i	−0.165383	+	0.986229i	$0.552886\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	5.50000	+	2.59808i	0.639362	+	0.302020i
$75$	4.00000	+	3.00000i	0.461880	+	0.346410i
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		0			0
$78$	−4.33013	+	2.50000i	−0.490290	+	0.283069i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	7.79423	+	4.50000i	0.855528	+	0.493939i	0.862512	−	0.506036i	$-0.168890\pi$
$83$	7.79423	+	4.50000i	0.855528	+	0.493939i	−0.00698436	+	0.999976i	$0.502223\pi$
$84$	1.00000			0.109109
$85$	−4.00000	+	2.00000i	−0.433861	+	0.216930i
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	−2.59808	+	1.50000i	−0.278543	+	0.160817i
$88$		0			0
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$	−0.133975	+	2.23205i	−0.0141222	+	0.235279i
$91$	2.50000	−	4.33013i	0.262071	−	0.453921i
$92$	−3.46410	+	2.00000i	−0.361158	+	0.208514i
$93$	−1.73205	+	1.00000i	−0.179605	+	0.103695i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	15.6244	+	0.937822i	1.60303	+	0.0962185i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	5.19615	−	3.00000i	0.524891	−	0.303046i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$	−1.73205	−	1.00000i	−0.171499	−	0.0990148i
$103$			5.00000i			0.492665i	0.969185	+	0.246332i	$0.0792255\pi$
$103$			5.00000i			0.492665i	−0.969185	+	0.246332i	$0.920775\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$	−1.00000	−	2.00000i	−0.0975900	−	0.195180i
$106$	−4.00000	−	6.92820i	−0.388514	−	0.672927i
$107$	−3.46410	+	2.00000i	−0.334887	+	0.193347i	−0.658009	−	0.753010i	$-0.728601\pi$
$107$	−3.46410	+	2.00000i	−0.334887	+	0.193347i	0.323122	+	0.946357i	$0.395268\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$		0			0
$111$	5.00000	−	3.46410i	0.474579	−	0.328798i
$112$		−	1.00000i		−	0.0944911i
$113$	11.2583	+	6.50000i	1.05909	+	0.611469i	0.925182	−	0.379525i	$-0.123912\pi$
$113$	11.2583	+	6.50000i	1.05909	+	0.611469i	0.133913	+	0.990993i	$0.457246\pi$
$114$	3.50000	+	6.06218i	0.327805	+	0.567775i
$115$	7.46410	+	4.92820i	0.696031	+	0.459557i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$			5.00000i			0.462250i
$118$		0			0
$119$	2.00000			0.183340
$120$	2.23205	+	0.133975i	0.203757	+	0.0122302i
$121$	−11.0000			−1.00000
$122$		−	4.00000i		−	0.362143i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	−7.79423	−	4.50000i	−0.691626	−	0.399310i	0.112595	−	0.993641i	$-0.464084\pi$
$127$	−7.79423	−	4.50000i	−0.691626	−	0.399310i	−0.804221	+	0.594331i	$0.797417\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	6.16025	−	9.33013i	0.540290	−	0.818306i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−6.06218	−	3.50000i	−0.525657	−	0.303488i
$134$	−4.00000			−0.345547
$135$	1.86603	+	1.23205i	0.160602	+	0.106038i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$			7.00000i			0.598050i	0.954245	+	0.299025i	$0.0966615\pi$
$137$			7.00000i			0.598050i	−0.954245	+	0.299025i	$0.903339\pi$
$138$			4.00000i			0.340503i
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	−2.00000	+	1.00000i	−0.169031	+	0.0845154i
$141$	−2.00000	−	3.46410i	−0.168430	−	0.291730i
$142$		−	13.0000i		−	1.09094i
$143$		0			0
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.69615	−	5.59808i	0.306949	−	0.464895i
$146$	4.00000	−	6.92820i	0.331042	−	0.573382i
$147$		−	6.00000i		−	0.494872i
$148$	−3.46410	−	5.00000i	−0.284747	−	0.410997i
$149$	−5.00000			−0.409616			−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000			−0.409616			−0.204808	+	0.978802i	$0.565657\pi$
$150$	−1.96410	−	4.59808i	−0.160368	−	0.375431i
$151$	6.00000	+	10.3923i	0.488273	+	0.845714i	0.999909	−	0.0134886i	$-0.00429367\pi$
$151$	6.00000	+	10.3923i	0.488273	+	0.845714i	−0.511636	+	0.859202i	$0.670960\pi$
$152$	6.06218	−	3.50000i	0.491708	−	0.283887i
$153$	−1.73205	+	1.00000i	−0.140028	+	0.0808452i
$154$		0			0
$155$	2.46410	−	3.73205i	0.197921	−	0.299766i
$156$	5.00000			0.400320
$157$	−2.59808	−	1.50000i	−0.207349	−	0.119713i	0.392730	−	0.919654i	$-0.371531\pi$
$157$	−2.59808	−	1.50000i	−0.207349	−	0.119713i	−0.600079	+	0.799941i	$0.704864\pi$
$158$			10.0000i			0.795557i
$159$	−8.00000			−0.634441
$160$	0.133975	−	2.23205i	0.0105916	−	0.176459i
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$			1.00000i			0.0785674i
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.989170	−	0.146772i	$-0.0468885\pi$
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.367477	+	0.930033i	$0.380222\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	−0.0407502	−	0.999169i	$-0.512975\pi$
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	0.844931	+	0.534875i	$0.179641\pi$
$168$	−0.866025	−	0.500000i	−0.0668153	−	0.0385758i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	4.46410	+	0.267949i	0.342381	+	0.0205508i
$171$	7.00000			0.535303
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	3.46410	+	2.00000i	0.263371	+	0.152057i	0.625871	−	0.779926i	$-0.284744\pi$
$173$	3.46410	+	2.00000i	0.263371	+	0.152057i	−0.362500	+	0.931984i	$0.618077\pi$
$174$	3.00000			0.227429
$175$	4.00000	+	3.00000i	0.302372	+	0.226779i
$176$		0			0
$177$		0			0
$178$	10.3923	−	6.00000i	0.778936	−	0.449719i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.23205	−	1.86603i	0.0918316	−	0.139085i
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	0.552143	−	0.833749i	$-0.313810\pi$
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	−0.998120	+	0.0612954i	$0.980477\pi$
$182$	−4.33013	+	2.50000i	−0.320970	+	0.185312i
$183$	−3.46410	−	2.00000i	−0.256074	−	0.147844i
$184$	4.00000			0.294884
$185$	−6.53590	+	11.9282i	−0.480529	+	0.876979i
$186$	2.00000			0.146647
$187$		0			0
$188$	−3.46410	+	2.00000i	−0.252646	+	0.145865i
$189$	−0.500000	−	0.866025i	−0.0363696	−	0.0629941i
$190$	−13.0622	−	8.62436i	−0.947630	−	0.625677i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$	−5.00000	−	10.0000i	−0.358057	−	0.716115i
$196$	−6.00000			−0.428571
$197$	−22.5167	−	13.0000i	−1.60425	−	0.926212i	−0.990625	−	0.136611i	$-0.956379\pi$
$197$	−22.5167	−	13.0000i	−1.60425	−	0.926212i	−0.613621	−	0.789601i	$-0.710288\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	−4.59808	+	1.96410i	−0.325133	+	0.138883i
$201$	−2.00000	+	3.46410i	−0.141069	+	0.244339i
$202$	−1.73205	−	1.00000i	−0.121867	−	0.0703598i
$203$	−2.59808	+	1.50000i	−0.182349	+	0.105279i
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$		0			0
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	3.46410	+	2.00000i	0.240772	+	0.139010i
$208$		−	5.00000i		−	0.346688i
$209$		0			0
$210$	−0.133975	+	2.23205i	−0.00924513	+	0.154026i
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$			8.00000i			0.549442i
$213$	−11.2583	−	6.50000i	−0.771408	−	0.445373i
$214$	4.00000			0.273434
$215$	−3.73205	−	2.46410i	−0.254524	−	0.168050i
$216$	1.00000			0.0680414
$217$	−1.73205	+	1.00000i	−0.117579	+	0.0678844i
$218$	5.19615	−	3.00000i	0.351928	−	0.203186i
$219$	−4.00000	−	6.92820i	−0.270295	−	0.468165i
$220$		0			0
$221$	10.0000			0.672673
$222$	−6.06218	+	0.500000i	−0.406867	+	0.0335578i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−4.96410	−	0.598076i	−0.330940	−	0.0398717i
$226$	−6.50000	−	11.2583i	−0.432374	−	0.748893i
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	−0.411296	−	0.911502i	$-0.634924\pi$
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	0.583736	+	0.811943i	$0.301590\pi$
$228$		−	7.00000i		−	0.463586i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	−4.00000	−	8.00000i	−0.263752	−	0.527504i
$231$		0			0
$232$		−	3.00000i		−	0.196960i
$233$		−	27.0000i		−	1.76883i	−0.466702	−	0.884414i	$-0.654558\pi$
$233$		−	27.0000i		−	1.76883i	0.466702	−	0.884414i	$-0.345442\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$	7.46410	+	4.92820i	0.486904	+	0.321481i
$236$		0			0
$237$	8.66025	+	5.00000i	0.562544	+	0.324785i
$238$	−1.73205	−	1.00000i	−0.112272	−	0.0648204i
$239$	3.50000	−	6.06218i	0.226396	−	0.392130i	−0.730341	−	0.683082i	$-0.760639\pi$
$239$	3.50000	−	6.06218i	0.226396	−	0.392130i	0.956737	+	0.290953i	$0.0939723\pi$
$240$	−1.86603	−	1.23205i	−0.120451	−	0.0795285i
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.00000	+	3.46410i	−0.128037	+	0.221766i
$245$	6.00000	+	12.0000i	0.383326	+	0.766652i
$246$		0			0
$247$	−30.3109	−	17.5000i	−1.92864	−	1.11350i
$248$		−	2.00000i		−	0.127000i
$249$	−9.00000			−0.570352
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−0.866025	+	0.500000i	−0.0545545	+	0.0314970i
$253$		0			0
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$	2.46410	−	3.73205i	0.154308	−	0.233710i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.33013	−	2.50000i	−0.270106	−	0.155946i	0.358830	−	0.933403i	$-0.383176\pi$
$257$	−4.33013	−	2.50000i	−0.270106	−	0.155946i	−0.628936	+	0.777457i	$0.716509\pi$
$258$		−	2.00000i		−	0.124515i
$259$	5.00000	−	3.46410i	0.310685	−	0.215249i
$260$	−10.0000	+	5.00000i	−0.620174	+	0.310087i
$261$	1.50000	−	2.59808i	0.0928477	−	0.160817i
$262$	−10.3923	+	6.00000i	−0.642039	+	0.370681i
$263$	25.9808	−	15.0000i	1.60204	−	0.924940i	0.610964	−	0.791658i	$-0.290782\pi$
$263$	25.9808	−	15.0000i	1.60204	−	0.924940i	0.991078	−	0.133281i	$-0.0425514\pi$
$264$		0			0
$265$	16.0000	−	8.00000i	0.982872	−	0.491436i
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$		−	12.0000i		−	0.734388i
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	−0.998497	+	0.0548050i	$0.982546\pi$
$272$	1.73205	−	1.00000i	0.105021	−	0.0606339i
$273$			5.00000i			0.302614i
$274$	3.50000	−	6.06218i	0.211443	−	0.366230i
$275$		0			0
$276$	2.00000	−	3.46410i	0.120386	−	0.208514i
$277$	−21.6506	+	12.5000i	−1.30086	+	0.751052i	−0.980552	−	0.196261i	$-0.937120\pi$
$277$	−21.6506	+	12.5000i	−1.30086	+	0.751052i	−0.320309	+	0.947313i	$0.603787\pi$
$278$	10.3923	−	6.00000i	0.623289	−	0.359856i
$279$	1.00000	−	1.73205i	0.0598684	−	0.103695i
$280$	2.23205	+	0.133975i	0.133391	+	0.00800651i
$281$	8.00000	−	13.8564i	0.477240	−	0.826604i	−0.522420	−	0.852688i	$-0.674971\pi$
$281$	8.00000	−	13.8564i	0.477240	−	0.826604i	0.999660	+	0.0260845i	$0.00830391\pi$
$282$			4.00000i			0.238197i
$283$	−20.7846	+	12.0000i	−1.23552	+	0.713326i	−0.968175	−	0.250276i	$-0.919479\pi$
$283$	−20.7846	+	12.0000i	−1.23552	+	0.713326i	−0.267342	+	0.963602i	$0.586145\pi$
$284$	−6.50000	+	11.2583i	−0.385704	+	0.668059i
$285$	−14.0000	+	7.00000i	−0.829288	+	0.414644i
$286$		0			0
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−6.00000	+	3.00000i	−0.352332	+	0.176166i
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	−6.92820	+	4.00000i	−0.405442	+	0.234082i
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	−0.644042	−	0.764990i	$-0.722744\pi$
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	0.340480	+	0.940252i	$0.389411\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$		0			0
$296$	0.500000	+	6.06218i	0.0290619	+	0.352357i
$297$		0			0
$298$	4.33013	+	2.50000i	0.250838	+	0.144821i
$299$	−10.0000	−	17.3205i	−0.578315	−	1.00167i
$300$	−0.598076	+	4.96410i	−0.0345299	+	0.286603i
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$		−	12.0000i		−	0.690522i
$303$	−1.73205	+	1.00000i	−0.0995037	+	0.0574485i
$304$	−7.00000			−0.401478
$305$	8.92820	+	0.535898i	0.511227	+	0.0306855i
$306$	2.00000			0.114332
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−2.50000	−	4.33013i	−0.142220	−	0.246332i
$310$	−4.00000	+	2.00000i	−0.227185	+	0.113592i
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$	−4.33013	−	2.50000i	−0.245145	−	0.141535i
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.991006	−	0.133819i	$-0.0427240\pi$
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.379612	+	0.925146i	$0.376057\pi$
$314$	1.50000	+	2.59808i	0.0846499	+	0.146618i
$315$	1.86603	+	1.23205i	0.105139	+	0.0694182i
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	0.292655	−	0.956218i	$-0.405461\pi$
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	−0.681782	+	0.731556i	$0.738795\pi$
$318$	6.92820	+	4.00000i	0.388514	+	0.224309i
$319$		0			0
$320$	−1.23205	+	1.86603i	−0.0688737	+	0.104314i
$321$	2.00000	−	3.46410i	0.111629	−	0.193347i
$322$			4.00000i			0.222911i
$323$		−	14.0000i		−	0.778981i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	20.0000	+	15.0000i	1.10940	+	0.832050i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$	−2.00000	−	3.46410i	−0.110264	−	0.190982i
$330$		0			0
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	0.477500	+	0.878632i	$0.341543\pi$
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	−0.999667	+	0.0257885i	$0.991790\pi$
$332$			9.00000i			0.493939i
$333$	−2.59808	+	5.50000i	−0.142374	+	0.301398i
$334$	−12.0000			−0.656611
$335$	0.535898	−	8.92820i	0.0292793	−	0.487800i
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	−1.73205	+	1.00000i	−0.0943508	+	0.0544735i	−0.546433	−	0.837503i	$-0.684015\pi$
$337$	−1.73205	+	1.00000i	−0.0943508	+	0.0544735i	0.452082	+	0.891976i	$0.350681\pi$
$338$	−10.3923	+	6.00000i	−0.565267	+	0.326357i
$339$	−13.0000			−0.706063
$340$	−3.73205	−	2.46410i	−0.202399	−	0.133635i
$341$		0			0
$342$	−6.06218	−	3.50000i	−0.327805	−	0.189258i
$343$		−	13.0000i		−	0.701934i
$344$	−2.00000			−0.107833
$345$	−8.92820	−	0.535898i	−0.480678	−	0.0288518i
$346$	−2.00000	−	3.46410i	−0.107521	−	0.186231i
$347$			5.00000i			0.268414i	0.990953	+	0.134207i	$0.0428487\pi$
$347$			5.00000i			0.268414i	−0.990953	+	0.134207i	$0.957151\pi$
$348$	−2.59808	−	1.50000i	−0.139272	−	0.0804084i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	−1.96410	−	4.59808i	−0.104986	−	0.245778i
$351$	−2.50000	−	4.33013i	−0.133440	−	0.231125i
$352$		0			0
$353$	26.8468	+	15.5000i	1.42891	+	0.824982i	0.997035	−	0.0769515i	$-0.0245187\pi$
$353$	26.8468	+	15.5000i	1.42891	+	0.824982i	0.431875	+	0.901933i	$0.357852\pi$
$354$		0			0
$355$	29.0167	+	1.74167i	1.54004	+	0.0924382i
$356$	−12.0000			−0.635999
$357$	−1.73205	+	1.00000i	−0.0916698	+	0.0529256i
$358$	10.3923	+	6.00000i	0.549250	+	0.317110i
$359$	−35.0000			−1.84723			−0.923615	−	0.383322i	$-0.874780\pi$
$359$	−35.0000			−1.84723			−0.923615	+	0.383322i	$0.874780\pi$
$360$	−2.00000	+	1.00000i	−0.105409	+	0.0527046i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$			12.0000i			0.630706i
$363$	9.52628	−	5.50000i	0.500000	−	0.288675i
$364$	5.00000			0.262071
$365$	14.9282	+	9.85641i	0.781378	+	0.515908i
$366$	2.00000	+	3.46410i	0.104542	+	0.181071i
$367$	4.33013	−	2.50000i	0.226031	−	0.130499i	−0.382709	−	0.923869i	$-0.625009\pi$
$367$	4.33013	−	2.50000i	0.226031	−	0.130499i	0.608740	+	0.793370i	$0.291675\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$		0			0
$370$	11.6244	−	7.06218i	0.604321	−	0.367145i
$371$	−8.00000			−0.415339
$372$	−1.73205	−	1.00000i	−0.0898027	−	0.0518476i
$373$	−16.4545	+	9.50000i	−0.851981	+	0.491891i	−0.861319	−	0.508065i	$-0.830361\pi$
$373$	−16.4545	+	9.50000i	−0.851981	+	0.491891i	0.00933789	+	0.999956i	$0.497028\pi$
$374$		0			0
$375$	10.5263	−	3.76795i	0.543575	−	0.194576i
$376$	4.00000			0.206284
$377$	−12.9904	+	7.50000i	−0.669039	+	0.386270i
$378$			1.00000i			0.0514344i
$379$	−6.50000	+	11.2583i	−0.333883	+	0.578302i	−0.983270	−	0.182157i	$-0.941692\pi$
$379$	−6.50000	+	11.2583i	−0.333883	+	0.578302i	0.649387	+	0.760458i	$0.275026\pi$
$380$	7.00000	+	14.0000i	0.359092	+	0.718185i
$381$	9.00000			0.461084
$382$	3.46410	+	2.00000i	0.177239	+	0.102329i
$383$	19.0526	−	11.0000i	0.973540	−	0.562074i	0.0732266	−	0.997315i	$-0.476670\pi$
$383$	19.0526	−	11.0000i	0.973540	−	0.562074i	0.900314	+	0.435242i	$0.143337\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−5.00000	+	8.66025i	−0.254493	+	0.440795i
$387$	−1.73205	−	1.00000i	−0.0880451	−	0.0508329i
$388$	−6.92820	+	4.00000i	−0.351726	+	0.203069i
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$	−0.669873	+	11.1603i	−0.0339203	+	0.565121i
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$	5.19615	+	3.00000i	0.262445	+	0.151523i
$393$			12.0000i			0.605320i
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$	−22.3205	−	1.33975i	−1.12307	−	0.0674099i
$396$		0			0
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	−8.66025	−	5.00000i	−0.434099	−	0.250627i
$399$	7.00000			0.350438
$400$	4.96410	+	0.598076i	0.248205	+	0.0299038i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	3.46410	−	2.00000i	0.172774	−	0.0997509i
$403$	−8.66025	+	5.00000i	−0.431398	+	0.249068i
$404$	1.00000	+	1.73205i	0.0497519	+	0.0861727i
$405$	−2.23205	−	0.133975i	−0.110911	−	0.00665725i
$406$	3.00000			0.148888
$407$		0			0
$408$		−	2.00000i		−	0.0990148i
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	−0.00141047	−	0.999999i	$-0.500449\pi$
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	0.866730	−	0.498778i	$-0.166218\pi$
$410$		0			0
$411$	−3.50000	−	6.06218i	−0.172642	−	0.299025i
$412$	−4.33013	+	2.50000i	−0.213330	+	0.123166i
$413$		0			0
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	18.0000	−	9.00000i	0.883585	−	0.441793i
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$		−	12.0000i		−	0.587643i
$418$		0			0
$419$	20.0000	−	34.6410i	0.977064	−	1.69232i	0.304115	−	0.952635i	$-0.401639\pi$
$419$	20.0000	−	34.6410i	0.977064	−	1.69232i	0.672949	−	0.739689i	$-0.265027\pi$
$420$	1.23205	−	1.86603i	0.0601179	−	0.0910527i
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−6.06218	−	3.50000i	−0.295102	−	0.170377i
$423$	3.46410	+	2.00000i	0.168430	+	0.0972433i
$424$	4.00000	−	6.92820i	0.194257	−	0.336463i
$425$	−1.19615	+	9.92820i	−0.0580219	+	0.481589i
$426$	6.50000	+	11.2583i	0.314926	+	0.545468i
$427$	−3.46410	−	2.00000i	−0.167640	−	0.0967868i
$428$	−3.46410	−	2.00000i	−0.167444	−	0.0966736i
$429$		0			0
$430$	2.00000	+	4.00000i	0.0964486	+	0.192897i
$431$	17.5000	+	30.3109i	0.842945	+	1.46002i	0.887394	+	0.461012i	$0.152514\pi$
$431$	17.5000	+	30.3109i	0.842945	+	1.46002i	−0.0444483	+	0.999012i	$0.514153\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$	2.00000			0.0960031
$435$	−0.401924	+	6.69615i	−0.0192708	+	0.321056i
$436$	−6.00000			−0.287348
$437$	−24.2487	+	14.0000i	−1.15997	+	0.669711i
$438$			8.00000i			0.382255i
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	0.999576	+	0.0291138i	$0.00926853\pi$
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	−0.474575	+	0.880215i	$0.657398\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	−8.66025	−	5.00000i	−0.411926	−	0.237826i
$443$		−	39.0000i		−	1.85295i	−0.376361	−	0.926473i	$-0.622825\pi$
$443$		−	39.0000i		−	1.85295i	0.376361	−	0.926473i	$-0.377175\pi$
$444$	5.50000	+	2.59808i	0.261018	+	0.123299i
$445$	12.0000	+	24.0000i	0.568855	+	1.13771i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	4.33013	−	2.50000i	0.204808	−	0.118246i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	−4.00000	−	6.92820i	−0.188772	−	0.326962i	0.756069	−	0.654492i	$-0.227117\pi$
$449$	−4.00000	−	6.92820i	−0.188772	−	0.326962i	−0.944841	+	0.327529i	$0.893784\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$		0			0
$452$			13.0000i			0.611469i
$453$	−10.3923	−	6.00000i	−0.488273	−	0.281905i
$454$	−3.00000			−0.140797
$455$	−5.00000	−	10.0000i	−0.234404	−	0.468807i
$456$	−3.50000	+	6.06218i	−0.163903	+	0.283887i
$457$	22.5167	−	13.0000i	1.05328	−	0.608114i	0.129718	−	0.991551i	$-0.458593\pi$
$457$	22.5167	−	13.0000i	1.05328	−	0.608114i	0.923567	+	0.383437i	$0.125260\pi$
$458$			10.0000i			0.467269i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	−0.535898	+	8.92820i	−0.0249864	+	0.416280i
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.0916500	−	0.995791i	$-0.470786\pi$
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.816556	−	0.577267i	$-0.195881\pi$
$462$		0			0
$463$	−9.52628	+	5.50000i	−0.442724	+	0.255607i	−0.704752	−	0.709453i	$-0.748942\pi$
$463$	−9.52628	+	5.50000i	−0.442724	+	0.255607i	0.262029	+	0.965060i	$0.415609\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	−0.267949	+	4.46410i	−0.0124258	+	0.207018i
$466$	−13.5000	+	23.3827i	−0.625375	+	1.08318i
$467$		−	27.0000i		−	1.24941i	−0.780860	−	0.624705i	$-0.785219\pi$
$467$		−	27.0000i		−	1.24941i	0.780860	−	0.624705i	$-0.214781\pi$
$468$	−4.33013	+	2.50000i	−0.200160	+	0.115563i
$469$	−2.00000	+	3.46410i	−0.0923514	+	0.159957i
$470$	−4.00000	−	8.00000i	−0.184506	−	0.369012i
$471$	3.00000			0.138233
$472$		0			0
$473$		0			0
$474$	−5.00000	−	8.66025i	−0.229658	−	0.397779i
$475$	21.0000	−	28.0000i	0.963546	−	1.28473i
$476$	1.00000	+	1.73205i	0.0458349	+	0.0793884i
$477$	6.92820	−	4.00000i	0.317221	−	0.183147i
$478$	−6.06218	+	3.50000i	−0.277278	+	0.160086i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	1.00000	+	2.00000i	0.0456435	+	0.0912871i
$481$	25.0000	−	17.3205i	1.13990	−	0.789747i
$482$			14.0000i			0.637683i
$483$	3.46410	+	2.00000i	0.157622	+	0.0910032i
$484$	−5.50000	−	9.52628i	−0.250000	−	0.433013i
$485$	14.9282	+	9.85641i	0.677855	+	0.447556i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$			9.00000i			0.407829i	0.978989	+	0.203914i	$0.0653664\pi$
$487$			9.00000i			0.407829i	−0.978989	+	0.203914i	$0.934634\pi$
$488$	3.46410	−	2.00000i	0.156813	−	0.0905357i
$489$	−20.0000			−0.904431
$490$	0.803848	−	13.3923i	0.0363141	−	0.605003i
$491$	38.0000			1.71492			0.857458	−	0.514554i	$-0.172042\pi$
$491$	38.0000			1.71492			0.857458	+	0.514554i	$0.172042\pi$
$492$		0			0
$493$	−5.19615	−	3.00000i	−0.234023	−	0.135113i
$494$	17.5000	+	30.3109i	0.787362	+	1.36375i
$495$		0			0
$496$	−1.00000	+	1.73205i	−0.0449013	+	0.0777714i
$497$	−11.2583	−	6.50000i	−0.505005	−	0.291565i
$498$	7.79423	+	4.50000i	0.349268	+	0.201650i
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	0.948995	−	0.315291i	$-0.102102\pi$
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	−0.747547	+	0.664208i	$0.768769\pi$
$500$	−3.76795	−	10.5263i	−0.168508	−	0.470750i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	10.3923	+	6.00000i	0.463831	+	0.267793i
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	0.611349	−	0.791361i	$-0.290627\pi$
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	−0.379664	+	0.925124i	$0.623960\pi$
$504$	1.00000			0.0445435
$505$	2.46410	−	3.73205i	0.109651	−	0.166074i
$506$		0			0
$507$			12.0000i			0.532939i
$508$		−	9.00000i		−	0.399310i
$509$	−15.5000	+	26.8468i	−0.687025	+	1.18996i	0.285770	+	0.958298i	$0.407751\pi$
$509$	−15.5000	+	26.8468i	−0.687025	+	1.18996i	−0.972796	+	0.231665i	$0.925583\pi$
$510$	−4.00000	+	2.00000i	−0.177123	+	0.0885615i
$511$	−4.00000	−	6.92820i	−0.176950	−	0.306486i
$512$			1.00000i			0.0441942i
$513$	−6.06218	+	3.50000i	−0.267652	+	0.154529i
$514$	2.50000	+	4.33013i	0.110270	+	0.190994i
$515$	9.33013	+	6.16025i	0.411135	+	0.271453i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$		0			0
$518$	−6.06218	+	0.500000i	−0.266357	+	0.0219687i
$519$	−4.00000			−0.175581
$520$	11.1603	+	0.669873i	0.489410	+	0.0293759i
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$	−2.59808	+	1.50000i	−0.113715	+	0.0656532i
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	−0.255273	−	0.966869i	$-0.582165\pi$
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	0.709697	+	0.704507i	$0.248832\pi$
$524$	12.0000			0.524222
$525$	−4.96410	−	0.598076i	−0.216651	−	0.0261022i
$526$	−30.0000			−1.30806
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$		0			0
$529$	7.00000			0.304348
$530$	−17.8564	−	1.07180i	−0.775633	−	0.0465559i
$531$		0			0
$532$		−	7.00000i		−	0.303488i
$533$		0			0
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$	−0.535898	+	8.92820i	−0.0231689	+	0.386000i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	10.3923	−	6.00000i	0.448461	−	0.258919i
$538$	2.59808	+	1.50000i	0.112011	+	0.0646696i
$539$		0			0
$540$	−0.133975	+	2.23205i	−0.00576535	+	0.0960522i
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$	15.5885	−	9.00000i	0.669582	−	0.386583i
$543$	10.3923	+	6.00000i	0.445976	+	0.257485i
$544$	−2.00000			−0.0857493
$545$	6.00000	+	12.0000i	0.257012	+	0.514024i
$546$	2.50000	−	4.33013i	0.106990	−	0.185312i
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	−6.06218	+	3.50000i	−0.258963	+	0.149513i
$549$	4.00000			0.170716
$550$		0			0
$551$	10.5000	+	18.1865i	0.447315	+	0.774772i
$552$	−3.46410	+	2.00000i	−0.147442	+	0.0851257i
$553$	8.66025	+	5.00000i	0.368271	+	0.212622i
$554$	25.0000			1.06215
$555$	−0.303848	−	13.5981i	−0.0128976	−	0.577206i
$556$	−12.0000			−0.508913
$557$	−10.3923	−	6.00000i	−0.440336	−	0.254228i	0.263404	−	0.964686i	$-0.415155\pi$
$557$	−10.3923	−	6.00000i	−0.440336	−	0.254228i	−0.703740	+	0.710457i	$0.748488\pi$
$558$	−1.73205	+	1.00000i	−0.0733236	+	0.0423334i
$559$	5.00000	+	8.66025i	0.211477	+	0.366290i
$560$	−1.86603	−	1.23205i	−0.0788540	−	0.0520636i
$561$		0			0
$562$	−13.8564	+	8.00000i	−0.584497	+	0.337460i
$563$			21.0000i			0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$563$			21.0000i			0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$564$	2.00000	−	3.46410i	0.0842152	−	0.145865i
$565$	26.0000	−	13.0000i	1.09383	−	0.546914i
$566$	24.0000			1.00880
$567$	0.866025	+	0.500000i	0.0363696	+	0.0209980i
$568$	11.2583	−	6.50000i	0.472389	−	0.272734i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	15.6244	+	0.937822i	0.654432	+	0.0392810i
$571$	−20.5000	+	35.5070i	−0.857898	+	1.48592i	0.0160316	+	0.999871i	$0.494897\pi$
$571$	−20.5000	+	35.5070i	−0.857898	+	1.48592i	−0.873930	+	0.486052i	$0.838437\pi$
$572$		0			0
$573$	3.46410	−	2.00000i	0.144715	−	0.0835512i
$574$		0			0
$575$	18.3923	−	7.85641i	0.767012	−	0.327635i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.949786	−	0.312900i	$-0.101301\pi$
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.203913	+	0.978989i	$0.434634\pi$
$578$			13.0000i			0.540729i
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$	6.69615	+	0.401924i	0.278043	+	0.0166890i
$581$	−9.00000			−0.373383
$582$			8.00000i			0.331611i
$583$		0			0
$584$	8.00000			0.331042
$585$	9.33013	+	6.16025i	0.385753	+	0.254695i
$586$	6.00000			0.247858
$587$	−26.8468	+	15.5000i	−1.10809	+	0.639753i	−0.938333	−	0.345733i	$-0.887630\pi$
$587$	−26.8468	+	15.5000i	−1.10809	+	0.639753i	−0.169753	+	0.985487i	$0.554297\pi$
$588$	5.19615	−	3.00000i	0.214286	−	0.123718i
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$		0			0
$591$	26.0000			1.06950
$592$	2.59808	−	5.50000i	0.106780	−	0.226049i
$593$		−	26.0000i		−	1.06769i	−0.845582	−	0.533846i	$-0.820746\pi$
$593$		−	26.0000i		−	1.06769i	0.845582	−	0.533846i	$-0.179254\pi$
$594$		0			0
$595$	2.46410	−	3.73205i	0.101018	−	0.152999i
$596$	−2.50000	−	4.33013i	−0.102404	−	0.177369i
$597$	−8.66025	+	5.00000i	−0.354441	+	0.204636i
$598$			20.0000i			0.817861i
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	0.976710	+	0.214563i	$0.0688326\pi$
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	−0.302539	+	0.953137i	$0.597834\pi$
$600$	3.00000	−	4.00000i	0.122474	−	0.163299i
$601$	−9.00000	+	15.5885i	−0.367118	+	0.635866i	−0.989114	−	0.147154i	$-0.952989\pi$
$601$	−9.00000	+	15.5885i	−0.367118	+	0.635866i	0.621996	+	0.783020i	$0.286322\pi$
$602$		−	2.00000i		−	0.0815139i
$603$		−	4.00000i		−	0.162893i
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	−13.5526	+	20.5263i	−0.550990	+	0.834512i
$606$	2.00000			0.0812444
$607$	21.6506	+	12.5000i	0.878772	+	0.507359i	0.870253	−	0.492604i	$-0.163955\pi$
$607$	21.6506	+	12.5000i	0.878772	+	0.507359i	0.00851879	+	0.999964i	$0.497288\pi$
$608$	6.06218	+	3.50000i	0.245854	+	0.141944i
$609$	1.50000	−	2.59808i	0.0607831	−	0.105279i
$610$	−7.46410	−	4.92820i	−0.302213	−	0.199537i
$611$	−10.0000	−	17.3205i	−0.404557	−	0.700713i
$612$	−1.73205	−	1.00000i	−0.0700140	−	0.0404226i
$613$	−26.8468	−	15.5000i	−1.08433	−	0.626039i	−0.152270	−	0.988339i	$-0.548658\pi$
$613$	−26.8468	−	15.5000i	−1.08433	−	0.626039i	−0.932062	+	0.362300i	$0.881992\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$		0			0
$616$		0			0
$617$	−26.8468	−	15.5000i	−1.08081	−	0.624007i	−0.149696	−	0.988732i	$-0.547829\pi$
$617$	−26.8468	−	15.5000i	−1.08081	−	0.624007i	−0.931115	+	0.364726i	$0.881163\pi$
$618$			5.00000i			0.201129i
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$	4.46410	+	0.267949i	0.179283	+	0.0107611i
$621$	−4.00000			−0.160514
$622$	17.3205	−	10.0000i	0.694489	−	0.400963i
$623$		−	12.0000i		−	0.480770i
$624$	2.50000	+	4.33013i	0.100080	+	0.173344i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−14.0000	−	24.2487i	−0.559553	−	0.969173i
$627$		0			0
$628$		−	3.00000i		−	0.119713i
$629$	11.0000	+	5.19615i	0.438599	+	0.207184i
$630$	−1.00000	−	2.00000i	−0.0398410	−	0.0796819i
$631$	−24.0000	+	41.5692i	−0.955425	+	1.65484i	−0.222032	+	0.975039i	$0.571269\pi$
$631$	−24.0000	+	41.5692i	−0.955425	+	1.65484i	−0.733393	+	0.679805i	$0.762064\pi$
$632$	−8.66025	+	5.00000i	−0.344486	+	0.198889i
$633$	−6.06218	+	3.50000i	−0.240950	+	0.139113i
$634$	4.00000	+	6.92820i	0.158860	+	0.275154i
$635$	−18.0000	+	9.00000i	−0.714308	+	0.357154i
$636$	−4.00000	−	6.92820i	−0.158610	−	0.274721i
$637$		−	30.0000i		−	1.18864i
$638$		0			0
$639$	13.0000			0.514272
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$	−7.00000	+	12.1244i	−0.276483	+	0.478883i	−0.970508	−	0.241068i	$-0.922502\pi$
$641$	−7.00000	+	12.1244i	−0.276483	+	0.478883i	0.694025	+	0.719951i	$0.255836\pi$
$642$	−3.46410	+	2.00000i	−0.136717	+	0.0789337i
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$	4.46410	+	0.267949i	0.175774	+	0.0105505i
$646$	−7.00000	+	12.1244i	−0.275411	+	0.477026i
$647$	−36.3731	+	21.0000i	−1.42997	+	0.825595i	−0.997118	−	0.0758684i	$-0.975827\pi$
$647$	−36.3731	+	21.0000i	−1.42997	+	0.825595i	−0.432855	+	0.901464i	$0.642494\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$		0			0
$650$	−9.82051	−	22.9904i	−0.385192	−	0.901757i
$651$	1.00000	−	1.73205i	0.0391931	−	0.0678844i
$652$			20.0000i			0.783260i
$653$	−43.3013	+	25.0000i	−1.69451	+	0.978326i	−0.743719	+	0.668493i	$0.766940\pi$
$653$	−43.3013	+	25.0000i	−1.69451	+	0.978326i	−0.950791	+	0.309833i	$0.899727\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$	−12.0000	−	24.0000i	−0.468879	−	0.937758i
$656$		0			0
$657$	6.92820	+	4.00000i	0.270295	+	0.156055i
$658$			4.00000i			0.155936i
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	16.4545	−	9.50000i	0.639522	−	0.369228i
$663$	−8.66025	+	5.00000i	−0.336336	+	0.194184i
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$	−14.0000	+	7.00000i	−0.542897	+	0.271448i
$666$	5.00000	−	3.46410i	0.193746	−	0.134231i
$667$			12.0000i			0.464642i
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	−4.92820	+	7.46410i	−0.190393	+	0.288363i
$671$		0			0
$672$		−	1.00000i		−	0.0385758i
$673$	38.1051	−	22.0000i	1.46884	−	0.848038i	0.469454	−	0.882957i	$-0.344451\pi$
$673$	38.1051	−	22.0000i	1.46884	−	0.848038i	0.999390	+	0.0349191i	$0.0111174\pi$
$674$	2.00000			0.0770371
$675$	4.59808	−	1.96410i	0.176980	−	0.0755983i
$676$	12.0000			0.461538
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	11.2583	+	6.50000i	0.432374	+	0.249631i
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	2.00000	+	4.00000i	0.0766965	+	0.153393i
$681$	−1.50000	+	2.59808i	−0.0574801	+	0.0995585i
$682$		0			0
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$	3.50000	+	6.06218i	0.133826	+	0.231793i
$685$	13.0622	+	8.62436i	0.499080	+	0.329520i
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	8.66025	+	5.00000i	0.330409	+	0.190762i
$688$	1.73205	+	1.00000i	0.0660338	+	0.0381246i
$689$	−40.0000			−1.52388
$690$	7.46410	+	4.92820i	0.284153	+	0.187613i
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	−0.814548	−	0.580097i	$-0.803015\pi$
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	0.909652	+	0.415371i	$0.136348\pi$
$692$			4.00000i			0.152057i
$693$		0			0
$694$	2.50000	−	4.33013i	0.0948987	−	0.164369i
$695$	12.0000	+	24.0000i	0.455186	+	0.910372i
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$		0			0
$698$	−8.66025	+	5.00000i	−0.327795	+	0.189253i
$699$	13.5000	+	23.3827i	0.510617	+	0.884414i
$700$	−0.598076	+	4.96410i	−0.0226052	+	0.187625i
$701$	5.00000	−	8.66025i	0.188847	−	0.327093i	−0.756019	−	0.654550i	$-0.772858\pi$
$701$	5.00000	−	8.66025i	0.188847	−	0.327093i	0.944866	+	0.327457i	$0.106192\pi$
$702$			5.00000i			0.188713i
$703$	−24.2487	−	35.0000i	−0.914557	−	1.32005i
$704$		0			0
$705$	−8.92820	−	0.535898i	−0.336256	−	0.0201831i
$706$	−15.5000	−	26.8468i	−0.583350	−	1.01039i
$707$	−1.73205	+	1.00000i	−0.0651405	+	0.0376089i
$708$		0			0
$709$	−4.00000			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$710$	−24.2583	−	16.0167i	−0.910399	−	0.601095i
$711$	−10.0000			−0.375029
$712$	10.3923	+	6.00000i	0.389468	+	0.224860i
$713$			8.00000i			0.299602i
$714$	2.00000			0.0748481
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$			7.00000i			0.261420i
$718$	30.3109	+	17.5000i	1.13119	+	0.653094i
$719$	−12.5000	+	21.6506i	−0.466171	+	0.807432i	−0.999254	−	0.0386310i	$-0.987700\pi$
$719$	−12.5000	+	21.6506i	−0.466171	+	0.807432i	0.533082	+	0.846063i	$0.321034\pi$
$720$	2.23205	+	0.133975i	0.0831836	+	0.00499294i
$721$	−2.50000	−	4.33013i	−0.0931049	−	0.161262i
$722$	25.9808	−	15.0000i	0.966904	−	0.558242i
$723$	12.1244	+	7.00000i	0.450910	+	0.260333i
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	−5.89230	−	13.7942i	−0.218835	−	0.512305i
$726$	−11.0000			−0.408248
$727$	−11.2583	+	6.50000i	−0.417548	+	0.241072i	−0.694028	−	0.719948i	$-0.744166\pi$
$727$	−11.2583	+	6.50000i	−0.417548	+	0.241072i	0.276479	+	0.961020i	$0.410832\pi$
$728$	−4.33013	−	2.50000i	−0.160485	−	0.0926562i
$729$	−1.00000			−0.0370370
$730$	−8.00000	−	16.0000i	−0.296093	−	0.592187i
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		−	4.00000i		−	0.147844i
$733$	−43.3013	+	25.0000i	−1.59937	+	0.923396i	−0.607760	+	0.794121i	$0.707932\pi$
$733$	−43.3013	+	25.0000i	−1.59937	+	0.923396i	−0.991609	+	0.129275i	$0.958735\pi$
$734$	−5.00000			−0.184553
$735$	−11.1962	−	7.39230i	−0.412976	−	0.272669i
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$		0			0
$738$		0			0
$739$	7.00000			0.257499			0.128750	−	0.991677i	$-0.458904\pi$
$739$	7.00000			0.257499			0.128750	+	0.991677i	$0.458904\pi$
$740$	−13.5981	+	0.303848i	−0.499875	+	0.0111697i
$741$	35.0000			1.28576
$742$	6.92820	+	4.00000i	0.254342	+	0.146845i
$743$	−22.5167	+	13.0000i	−0.826056	+	0.476924i	−0.852500	−	0.522727i	$-0.824915\pi$
$743$	−22.5167	+	13.0000i	−0.826056	+	0.476924i	0.0264443	+	0.999650i	$0.491582\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$	−6.16025	+	9.33013i	−0.225694	+	0.341829i
$746$	19.0000			0.695639
$747$	7.79423	−	4.50000i	0.285176	−	0.164646i
$748$		0			0
$749$	2.00000	−	3.46410i	0.0730784	−	0.126576i
$750$	−11.0000	−	2.00000i	−0.401663	−	0.0730297i
$751$	−34.0000			−1.24068			−0.620339	−	0.784334i	$-0.713005\pi$
$751$	−34.0000			−1.24068			−0.620339	+	0.784334i	$0.713005\pi$
$752$	−3.46410	−	2.00000i	−0.126323	−	0.0729325i
$753$	10.3923	−	6.00000i	0.378717	−	0.218652i
$754$	15.0000			0.546268
$755$	26.7846	+	1.60770i	0.974792	+	0.0585100i
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	45.8993	+	26.5000i	1.66824	+	0.963159i	0.968587	+	0.248677i	$0.0799956\pi$
$757$	45.8993	+	26.5000i	1.66824	+	0.963159i	0.699654	+	0.714482i	$0.253338\pi$
$758$	11.2583	−	6.50000i	0.408921	−	0.236091i
$759$		0			0
$760$	0.937822	−	15.6244i	0.0340184	−	0.566755i
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	−7.79423	−	4.50000i	−0.282355	−	0.163018i
$763$		−	6.00000i		−	0.217215i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	−0.267949	+	4.46410i	−0.00968772	+	0.161400i
$766$	−22.0000			−0.794892
$767$		0			0
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−7.00000			−0.252426			−0.126213	−	0.992003i	$-0.540282\pi$
$769$	−7.00000			−0.252426			−0.126213	+	0.992003i	$0.540282\pi$
$770$		0			0
$771$	5.00000			0.180071
$772$	8.66025	−	5.00000i	0.311689	−	0.179954i
$773$	−15.5885	+	9.00000i	−0.560678	+	0.323708i	−0.753418	−	0.657542i	$-0.771596\pi$
$773$	−15.5885	+	9.00000i	−0.560678	+	0.323708i	0.192740	+	0.981250i	$0.438263\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	−3.92820	−	9.19615i	−0.141105	−	0.330336i
$776$	8.00000			0.287183
$777$	−2.59808	+	5.50000i	−0.0932055	+	0.197311i
$778$			19.0000i			0.681183i
$779$		0			0
$780$	6.16025	−	9.33013i	0.220572	−	0.334072i
$781$		0			0
$782$	−6.92820	+	4.00000i	−0.247752	+	0.143040i
$783$			3.00000i			0.107211i
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$	−6.00000	+	3.00000i	−0.214149	+	0.107075i
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$			18.0000i			0.641631i	0.947142	+	0.320815i	$0.103957\pi$
$787$			18.0000i			0.641631i	−0.947142	+	0.320815i	$0.896043\pi$
$788$		−	26.0000i		−	0.926212i
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$	18.6603	+	12.3205i	0.663902	+	0.438344i
$791$	−13.0000			−0.462227
$792$		0			0
$793$	−17.3205	−	10.0000i	−0.615069	−	0.355110i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	−9.85641	+	14.9282i	−0.349571	+	0.529449i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	31.1769	+	18.0000i	1.10434	+	0.637593i	0.937358	−	0.348367i	$-0.113264\pi$
$797$	31.1769	+	18.0000i	1.10434	+	0.637593i	0.166985	+	0.985959i	$0.446597\pi$
$798$	−6.06218	−	3.50000i	−0.214599	−	0.123899i
$799$	4.00000	−	6.92820i	0.141510	−	0.245102i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−5.19615	−	3.00000i	−0.183483	−	0.105934i
$803$		0			0
$804$	−4.00000			−0.141069
$805$	−8.92820	−	0.535898i	−0.314678	−	0.0188879i
$806$	10.0000			0.352235
$807$	2.59808	−	1.50000i	0.0914566	−	0.0528025i
$808$		−	2.00000i		−	0.0703598i
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$	1.86603	+	1.23205i	0.0655654	+	0.0432899i
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	0.986451	−	0.164057i	$-0.0524582\pi$
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	−0.635303	+	0.772263i	$0.719125\pi$
$812$	−2.59808	−	1.50000i	−0.0911746	−	0.0526397i
$813$		−	18.0000i		−	0.631288i
$814$		0			0
$815$	40.0000	−	20.0000i	1.40114	−	0.700569i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	12.1244	−	7.00000i	0.424178	−	0.244899i
$818$	−30.3109	+	17.5000i	−1.05980	+	0.611873i
$819$	−2.50000	−	4.33013i	−0.0873571	−	0.151307i
$820$		0			0
$821$	−10.5000	−	18.1865i	−0.366453	−	0.634714i	0.622556	−	0.782576i	$-0.286094\pi$
$821$	−10.5000	−	18.1865i	−0.366453	−	0.634714i	−0.989008	+	0.147861i	$0.952761\pi$
$822$			7.00000i			0.244153i
$823$	35.5070	+	20.5000i	1.23770	+	0.714585i	0.968623	−	0.248534i	$-0.0799489\pi$
$823$	35.5070	+	20.5000i	1.23770	+	0.714585i	0.269075	+	0.963119i	$0.413282\pi$
$824$	5.00000			0.174183
$825$		0			0
$826$		0			0
$827$	4.33013	−	2.50000i	0.150573	−	0.0869335i	−0.422820	−	0.906213i	$-0.638960\pi$
$827$	4.33013	−	2.50000i	0.150573	−	0.0869335i	0.573394	+	0.819280i	$0.305627\pi$
$828$			4.00000i			0.139010i
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	0.920383	−	0.391018i	$-0.127877\pi$
$830$	−20.0885	−	1.20577i	−0.697281	−	0.0418529i
$831$	12.5000	−	21.6506i	0.433620	−	0.751052i
$832$	4.33013	−	2.50000i	0.150120	−	0.0866719i
$833$	10.3923	−	6.00000i	0.360072	−	0.207888i
$834$	−6.00000	+	10.3923i	−0.207763	+	0.359856i
$835$	1.60770	−	26.7846i	0.0556366	−	0.926920i
$836$		0			0
$837$			2.00000i			0.0691301i
$838$	−34.6410	+	20.0000i	−1.19665	+	0.690889i
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	−0.0705865	−	0.997506i	$-0.522487\pi$
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	0.899158	−	0.437623i	$-0.144180\pi$
$840$	−2.00000	+	1.00000i	−0.0690066	+	0.0345033i
$841$	−20.0000			−0.689655
$842$	−19.0526	−	11.0000i	−0.656595	−	0.379085i
$843$			16.0000i			0.551069i
$844$	3.50000	+	6.06218i	0.120475	+	0.208669i
$845$	−12.0000	−	24.0000i	−0.412813	−	0.825625i
$846$	−2.00000	−	3.46410i	−0.0687614	−	0.119098i
$847$	9.52628	−	5.50000i	0.327327	−	0.188982i
$848$	−6.92820	+	4.00000i	−0.237915	+	0.137361i
$849$	12.0000	−	20.7846i	0.411839	−	0.713326i
$850$	6.00000	−	8.00000i	0.205798	−	0.274398i
$851$	−2.00000	−	24.2487i	−0.0685591	−	0.831235i
$852$		−	13.0000i		−	0.445373i
$853$	−29.4449	−	17.0000i	−1.00817	−	0.582069i	−0.0975167	−	0.995234i	$-0.531090\pi$
$853$	−29.4449	−	17.0000i	−1.00817	−	0.582069i	−0.910656	+	0.413165i	$0.864423\pi$
$854$	2.00000	+	3.46410i	0.0684386	+	0.118539i
$855$	8.62436	−	13.0622i	0.294947	−	0.446717i
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$		−	7.00000i		−	0.239115i	−0.992827	−	0.119558i	$-0.961852\pi$
$857$		−	7.00000i		−	0.239115i	0.992827	−	0.119558i	$-0.0381477\pi$
$858$		0			0
$859$	−41.0000			−1.39890			−0.699451	−	0.714681i	$-0.746572\pi$
$859$	−41.0000			−1.39890			−0.699451	+	0.714681i	$0.746572\pi$
$860$	0.267949	−	4.46410i	0.00913699	−	0.152225i
$861$		0			0
$862$		−	35.0000i		−	1.19210i
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.908932	−	0.416944i	$-0.136899\pi$
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.0933825	+	0.995630i	$0.470232\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	8.00000	−	4.00000i	0.272008	−	0.136004i
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	11.2583	+	6.50000i	0.382353	+	0.220752i
$868$	−1.73205	−	1.00000i	−0.0587896	−	0.0339422i
$869$		0			0
$870$	3.69615	−	5.59808i	0.125311	−	0.189793i
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$	5.19615	+	3.00000i	0.175964	+	0.101593i
$873$	6.92820	+	4.00000i	0.234484	+	0.135379i
$874$	28.0000			0.947114
$875$	10.5263	−	3.76795i	0.355853	−	0.127380i
$876$	4.00000	−	6.92820i	0.135147	−	0.234082i
$877$		−	29.0000i		−	0.979260i	−0.871930	−	0.489630i	$-0.837132\pi$
$877$		−	29.0000i		−	0.979260i	0.871930	−	0.489630i	$-0.162868\pi$
$878$		−	22.0000i		−	0.742464i
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$		0			0
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	0.747074	−	0.664741i	$-0.231458\pi$
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	−0.949219	+	0.314615i	$0.898125\pi$
$882$		−	6.00000i		−	0.202031i
$883$	10.3923	−	6.00000i	0.349729	−	0.201916i	−0.314837	−	0.949146i	$-0.601950\pi$
$883$	10.3923	−	6.00000i	0.349729	−	0.201916i	0.664566	+	0.747230i	$0.268617\pi$
$884$	5.00000	+	8.66025i	0.168168	+	0.291276i
$885$		0			0
$886$	−19.5000	+	33.7750i	−0.655115	+	1.13469i
$887$		−	24.0000i		−	0.805841i	−0.915235	−	0.402921i	$-0.867995\pi$
$887$		−	24.0000i		−	0.805841i	0.915235	−	0.402921i	$-0.132005\pi$
$888$	−3.46410	−	5.00000i	−0.116248	−	0.167789i
$889$	9.00000			0.301850
$890$	1.60770	−	26.7846i	0.0538901	−	0.897822i
$891$		0			0
$892$	6.92820	−	4.00000i	0.231973	−	0.133930i
$893$	−24.2487	+	14.0000i	−0.811452	+	0.468492i
$894$	−5.00000			−0.167225
$895$	−14.7846	+	22.3923i	−0.494195	+	0.748492i
$896$	−1.00000			−0.0334077
$897$	17.3205	+	10.0000i	0.578315	+	0.333890i
$898$			8.00000i			0.266963i
$899$	6.00000			0.200111
$900$	−1.96410	−	4.59808i	−0.0654701	−	0.153269i
$901$	−8.00000	−	13.8564i	−0.266519	−	0.461624i
$902$		0			0
$903$	−1.73205	−	1.00000i	−0.0576390	−	0.0332779i
$904$	6.50000	−	11.2583i	0.216187	−	0.374446i
$905$	−26.7846	−	1.60770i	−0.890351	−	0.0534416i
$906$	6.00000	+	10.3923i	0.199337	+	0.345261i
$907$	45.0333	−	26.0000i	1.49531	−	0.863316i	0.495321	−	0.868710i	$-0.335050\pi$
$907$	45.0333	−	26.0000i	1.49531	−	0.863316i	0.999985	+	0.00539395i	$0.00171696\pi$
$908$	2.59808	+	1.50000i	0.0862202	+	0.0497792i
$909$	1.00000	−	1.73205i	0.0331679	−	0.0574485i
$910$	−0.669873	+	11.1603i	−0.0222061	+	0.369959i
$911$	−1.00000			−0.0331315			−0.0165657	−	0.999863i	$-0.505273\pi$
$911$	−1.00000			−0.0331315			−0.0165657	+	0.999863i	$0.505273\pi$
$912$	6.06218	−	3.50000i	0.200739	−	0.115897i
$913$		0			0
$914$	−26.0000			−0.860004
$915$	−8.00000	+	4.00000i	−0.264472	+	0.132236i
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$			12.0000i			0.396275i
$918$	−1.73205	+	1.00000i	−0.0571662	+	0.0330049i
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$	4.92820	−	7.46410i	0.162478	−	0.246084i
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	−33.7750	+	19.5000i	−1.11232	+	0.642198i
$923$	−56.2917	−	32.5000i	−1.85286	−	1.06975i
$924$		0			0
$925$	14.2058	+	26.8923i	0.467083	+	0.884214i
$926$	11.0000			0.361482
$927$	4.33013	+	2.50000i	0.142220	+	0.0821108i
$928$	2.59808	−	1.50000i	0.0852860	−	0.0492399i
$929$	−2.00000	−	3.46410i	−0.0656179	−	0.113653i	0.831350	−	0.555749i	$-0.187569\pi$
$929$	−2.00000	−	3.46410i	−0.0656179	−	0.113653i	−0.896968	+	0.442096i	$0.854235\pi$
$930$	2.46410	−	3.73205i	0.0808011	−	0.122379i
$931$	−42.0000			−1.37649
$932$	23.3827	−	13.5000i	0.765925	−	0.442207i
$933$		−	20.0000i		−	0.654771i
$934$	−13.5000	+	23.3827i	−0.441733	+	0.765105i
$935$		0			0
$936$	5.00000			0.163430
$937$	20.7846	+	12.0000i	0.679004	+	0.392023i	0.799480	−	0.600693i	$-0.205109\pi$
$937$	20.7846	+	12.0000i	0.679004	+	0.392023i	−0.120476	+	0.992716i	$0.538442\pi$
$938$	3.46410	−	2.00000i	0.113107	−	0.0653023i
$939$	−28.0000			−0.913745
$940$	−0.535898	+	8.92820i	−0.0174791	+	0.291206i
$941$	−2.50000	+	4.33013i	−0.0814977	+	0.141158i	−0.903893	−	0.427758i	$-0.859304\pi$
$941$	−2.50000	+	4.33013i	−0.0814977	+	0.141158i	0.822396	+	0.568916i	$0.192637\pi$
$942$	−2.59808	−	1.50000i	−0.0846499	−	0.0488726i
$943$		0			0
$944$		0			0
$945$	−2.23205	−	0.133975i	−0.0726086	−	0.00435819i
$946$		0			0
$947$	6.06218	+	3.50000i	0.196994	+	0.113735i	0.595253	−	0.803539i	$-0.297052\pi$
$947$	6.06218	+	3.50000i	0.196994	+	0.113735i	−0.398258	+	0.917273i	$0.630385\pi$
$948$			10.0000i			0.324785i
$949$	−20.0000	−	34.6410i	−0.649227	−	1.12449i
$950$	−32.1865	+	13.7487i	−1.04427	+	0.446067i
$951$	8.00000			0.259418
$952$		−	2.00000i		−	0.0648204i
$953$	−0.866025	−	0.500000i	−0.0280533	−	0.0161966i	0.485908	−	0.874010i	$-0.338489\pi$
$953$	−0.866025	−	0.500000i	−0.0280533	−	0.0161966i	−0.513961	+	0.857814i	$0.671822\pi$
$954$	−8.00000			−0.259010
$955$	−4.92820	+	7.46410i	−0.159473	+	0.241533i
$956$	7.00000			0.226396
$957$		0			0
$958$	−20.7846	+	12.0000i	−0.671520	+	0.387702i
$959$	−3.50000	−	6.06218i	−0.113021	−	0.195758i
$960$	0.133975	−	2.23205i	0.00432401	−	0.0720391i
$961$	−27.0000			−0.870968
$962$	−30.3109	+	2.50000i	−0.977262	+	0.0806032i
$963$			4.00000i			0.128898i
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$	−18.6603	−	12.3205i	−0.600695	−	0.396611i
$966$	−2.00000	−	3.46410i	−0.0643489	−	0.111456i
$967$	−40.7032	+	23.5000i	−1.30893	+	0.755709i	−0.981917	−	0.189312i	$-0.939374\pi$
$967$	−40.7032	+	23.5000i	−1.30893	+	0.755709i	−0.327009	+	0.945021i	$0.606041\pi$
$968$			11.0000i			0.353553i
$969$	7.00000	+	12.1244i	0.224872	+	0.389490i
$970$	−8.00000	−	16.0000i	−0.256865	−	0.513729i
$971$	−5.00000	+	8.66025i	−0.160458	+	0.277921i	−0.935033	−	0.354561i	$-0.884630\pi$
$971$	−5.00000	+	8.66025i	−0.160458	+	0.277921i	0.774575	+	0.632482i	$0.217964\pi$
$972$			1.00000i			0.0320750i
$973$		−	12.0000i		−	0.384702i
$974$	4.50000	−	7.79423i	0.144189	−	0.249743i
$975$	−24.8205	−	2.99038i	−0.794892	−	0.0957688i
$976$	−4.00000			−0.128037
$977$	44.1673	+	25.5000i	1.41304	+	0.815817i	0.995673	−	0.0929223i	$-0.0296208\pi$
$977$	44.1673	+	25.5000i	1.41304	+	0.815817i	0.417364	+	0.908740i	$0.362954\pi$
$978$	17.3205	+	10.0000i	0.553849	+	0.319765i
$979$		0			0
$980$	−7.39230	+	11.1962i	−0.236139	+	0.357648i
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	−32.9090	−	19.0000i	−1.05017	−	0.606314i
$983$	−19.0526	−	11.0000i	−0.607682	−	0.350846i	0.164376	−	0.986398i	$-0.447439\pi$
$983$	−19.0526	−	11.0000i	−0.607682	−	0.350846i	−0.772058	+	0.635552i	$0.780772\pi$
$984$		0			0
$985$	−52.0000	+	26.0000i	−1.65686	+	0.828429i
$986$	3.00000	+	5.19615i	0.0955395	+	0.165479i
$987$	3.46410	+	2.00000i	0.110264	+	0.0636607i
$988$		−	35.0000i		−	1.11350i
$989$	8.00000			0.254385
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	1.73205	−	1.00000i	0.0549927	−	0.0317500i
$993$		−	19.0000i		−	0.602947i
$994$	6.50000	+	11.2583i	0.206167	+	0.357093i
$995$	12.3205	−	18.6603i	0.390586	−	0.591570i
$996$	−4.50000	−	7.79423i	−0.142588	−	0.246970i
$997$	45.8993	+	26.5000i	1.45365	+	0.839263i	0.998686	−	0.0512480i	$-0.0163199\pi$
$997$	45.8993	+	26.5000i	1.45365	+	0.839263i	0.454961	+	0.890511i	$0.349653\pi$
$998$		−	9.00000i		−	0.284890i
$999$	−0.500000	−	6.06218i	−0.0158193	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.b.1009.1	✓	4
5.4	even	2	inner	1110.2.bb.b.1009.2	yes	4
37.26	even	3	inner	1110.2.bb.b.1099.2	yes	4
185.174	even	6	inner	1110.2.bb.b.1099.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.b.1009.1	✓	4	1.1	even	1	trivial
1110.2.bb.b.1009.2	yes	4	5.4	even	2	inner
1110.2.bb.b.1099.1	yes	4	185.174	even	6	inner
1110.2.bb.b.1099.2	yes	4	37.26	even	3	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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 - 1.86603i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00000 + 1.00000i) q^{10} +(-0.866025 - 0.500000i) q^{12} +(-4.33013 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.133975 + 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.50000 + 6.06218i) q^{19} +(2.23205 + 0.133975i) q^{20} +(0.500000 - 0.866025i) q^{21} +4.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.96410 - 4.59808i) q^{25} +5.00000 q^{26} +1.00000i q^{27} +(-0.866025 - 0.500000i) q^{28} +3.00000 q^{29} +(1.23205 - 1.86603i) q^{30} +2.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.00000 + 1.73205i) q^{34} +(-0.133975 + 2.23205i) q^{35} +1.00000 q^{36} +(-6.06218 + 0.500000i) q^{37} -7.00000i q^{38} +(2.50000 - 4.33013i) q^{39} +(-1.86603 - 1.23205i) q^{40} +(-0.866025 + 0.500000i) q^{42} -2.00000i q^{43} +(-1.00000 - 2.00000i) q^{45} +(2.00000 - 3.46410i) q^{46} +4.00000i q^{47} -1.00000i q^{48} +(-3.00000 + 5.19615i) q^{49} +(-0.598076 + 4.96410i) q^{50} +2.00000 q^{51} +(-4.33013 - 2.50000i) q^{52} +(6.92820 + 4.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} +(-6.06218 - 3.50000i) q^{57} +(-2.59808 - 1.50000i) q^{58} +(-2.00000 + 1.00000i) q^{60} +(2.00000 + 3.46410i) q^{61} +(-1.73205 - 1.00000i) q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-0.669873 + 11.1603i) q^{65} +(3.46410 - 2.00000i) q^{67} -2.00000i q^{68} +(-2.00000 - 3.46410i) q^{69} +(1.23205 - 1.86603i) q^{70} +(6.50000 + 11.2583i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.00000i q^{73} +(5.50000 + 2.59808i) q^{74} +(4.00000 + 3.00000i) q^{75} +(-3.50000 + 6.06218i) q^{76} +(-4.33013 + 2.50000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{83} +1.00000 q^{84} +(-4.00000 + 2.00000i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-2.59808 + 1.50000i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-0.133975 + 2.23205i) q^{90} +(2.50000 - 4.33013i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(-1.73205 + 1.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +(15.6244 + 0.937822i) q^{95} +(-0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(5.19615 - 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9} - 8 q^{10} + 4 q^{14} - 4 q^{15} - 2 q^{16} + 14 q^{19} + 2 q^{20} + 2 q^{21} + 2 q^{24} + 6 q^{25} + 20 q^{26} + 12 q^{29} - 2 q^{30} + 8 q^{31} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 10 q^{39} - 4 q^{40} - 4 q^{45} + 8 q^{46} - 12 q^{49} + 8 q^{50} + 8 q^{51} + 2 q^{54} + 2 q^{56} - 8 q^{60} + 8 q^{61} - 4 q^{64} - 20 q^{65} - 8 q^{69} - 2 q^{70} + 26 q^{71} + 22 q^{74} + 16 q^{75} - 14 q^{76} - 20 q^{79} + 4 q^{80} - 2 q^{81} + 4 q^{84} - 16 q^{85} - 4 q^{86} - 24 q^{89} - 4 q^{90} + 10 q^{91} + 8 q^{94} + 14 q^{95} - 2 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9 - 8 * q^10 + 4 * q^14 - 4 * q^15 - 2 * q^16 + 14 * q^19 + 2 * q^20 + 2 * q^21 + 2 * q^24 + 6 * q^25 + 20 * q^26 + 12 * q^29 - 2 * q^30 + 8 * q^31 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 10 * q^39 - 4 * q^40 - 4 * q^45 + 8 * q^46 - 12 * q^49 + 8 * q^50 + 8 * q^51 + 2 * q^54 + 2 * q^56 - 8 * q^60 + 8 * q^61 - 4 * q^64 - 20 * q^65 - 8 * q^69 - 2 * q^70 + 26 * q^71 + 22 * q^74 + 16 * q^75 - 14 * q^76 - 20 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^84 - 16 * q^85 - 4 * q^86 - 24 * q^89 - 4 * q^90 + 10 * q^91 + 8 * q^94 + 14 * q^95 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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