LMFDB - Embedded newform 390.2.p.e.281.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(161,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, 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("390.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.p (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:	$3.11416567883$
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			281.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.281
Dual form			390.2.p.e.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +1.00000i q^{10} +(-2.00000 - 2.00000i) q^{11} +(-1.70711 - 0.292893i) q^{12} +(3.53553 + 0.707107i) q^{13} -2.82843i q^{14} +(1.00000 + 1.41421i) q^{15} -1.00000 q^{16} -4.82843 q^{17} +(-2.70711 + 1.29289i) q^{18} +(0.707107 + 0.707107i) q^{20} +(-2.82843 - 4.00000i) q^{21} -2.82843 q^{22} +6.82843 q^{23} +(-1.41421 + 1.00000i) q^{24} -1.00000i q^{25} +(3.00000 - 2.00000i) q^{26} +(-2.53553 + 4.53553i) q^{27} +(-2.00000 - 2.00000i) q^{28} -3.65685i q^{29} +(1.70711 + 0.292893i) q^{30} +(4.41421 + 4.41421i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.00000 + 2.82843i) q^{33} +(-3.41421 + 3.41421i) q^{34} +2.82843i q^{35} +(-1.00000 + 2.82843i) q^{36} +(-4.00000 + 4.00000i) q^{37} +(2.24264 - 5.82843i) q^{39} +1.00000 q^{40} +(2.17157 - 2.17157i) q^{41} +(-4.82843 - 0.828427i) q^{42} -5.07107i q^{43} +(-2.00000 + 2.00000i) q^{44} +(2.70711 - 1.29289i) q^{45} +(4.82843 - 4.82843i) q^{46} +(2.00000 + 2.00000i) q^{47} +(-0.292893 + 1.70711i) q^{48} -1.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(-1.41421 + 8.24264i) q^{51} +(0.707107 - 3.53553i) q^{52} +9.41421i q^{53} +(1.41421 + 5.00000i) q^{54} +2.82843 q^{55} -2.82843 q^{56} +(-2.58579 - 2.58579i) q^{58} +(4.00000 + 4.00000i) q^{59} +(1.41421 - 1.00000i) q^{60} +12.8284 q^{61} +6.24264 q^{62} +(-7.65685 + 3.65685i) q^{63} +1.00000i q^{64} +(-3.00000 + 2.00000i) q^{65} +(-0.828427 + 4.82843i) q^{66} +(2.24264 + 2.24264i) q^{67} +4.82843i q^{68} +(2.00000 - 11.6569i) q^{69} +(2.00000 + 2.00000i) q^{70} +(10.4142 - 10.4142i) q^{71} +(1.29289 + 2.70711i) q^{72} +(9.89949 - 9.89949i) q^{73} +5.65685i q^{74} +(-1.70711 - 0.292893i) q^{75} -8.00000 q^{77} +(-2.53553 - 5.70711i) q^{78} -8.82843 q^{79} +(0.707107 - 0.707107i) q^{80} +(7.00000 + 5.65685i) q^{81} -3.07107i q^{82} +(-1.17157 + 1.17157i) q^{83} +(-4.00000 + 2.82843i) q^{84} +(3.41421 - 3.41421i) q^{85} +(-3.58579 - 3.58579i) q^{86} +(-6.24264 - 1.07107i) q^{87} +2.82843i q^{88} +(2.65685 + 2.65685i) q^{89} +(1.00000 - 2.82843i) q^{90} +(8.48528 - 5.65685i) q^{91} -6.82843i q^{92} +(8.82843 - 6.24264i) q^{93} +2.82843 q^{94} +(1.00000 + 1.41421i) q^{96} +(-8.58579 - 8.58579i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(3.65685 + 7.65685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^6 + 8 * q^7	$ 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7} - 8 q^{11} - 4 q^{12} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 8 q^{18} + 16 q^{23} + 12 q^{26} + 4 q^{27} - 8 q^{28} + 4 q^{30} + 12 q^{31} - 16 q^{33} - 8 q^{34} - 4 q^{36} - 16 q^{37} - 8 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} - 8 q^{44} + 8 q^{45} + 8 q^{46} + 8 q^{47} - 4 q^{48} - 16 q^{58} + 16 q^{59} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 12 q^{65} + 8 q^{66} - 8 q^{67} + 8 q^{69} + 8 q^{70} + 36 q^{71} + 8 q^{72} - 4 q^{75} - 32 q^{77} + 4 q^{78} - 24 q^{79} + 28 q^{81} - 16 q^{83} - 16 q^{84} + 8 q^{85} - 20 q^{86} - 8 q^{87} - 12 q^{89} + 4 q^{90} + 24 q^{93} + 4 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 + 8 * q^7 - 8 * q^11 - 4 * q^12 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 8 * q^18 + 16 * q^23 + 12 * q^26 + 4 * q^27 - 8 * q^28 + 4 * q^30 + 12 * q^31 - 16 * q^33 - 8 * q^34 - 4 * q^36 - 16 * q^37 - 8 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 - 8 * q^44 + 8 * q^45 + 8 * q^46 + 8 * q^47 - 4 * q^48 - 16 * q^58 + 16 * q^59 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 12 * q^65 + 8 * q^66 - 8 * q^67 + 8 * q^69 + 8 * q^70 + 36 * q^71 + 8 * q^72 - 4 * q^75 - 32 * q^77 + 4 * q^78 - 24 * q^79 + 28 * q^81 - 16 * q^83 - 16 * q^84 + 8 * q^85 - 20 * q^86 - 8 * q^87 - 12 * q^89 + 4 * q^90 + 24 * q^93 + 4 * q^96 - 40 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	−0.219650	−	0.975579i	$-0.570491\pi$
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	0.975579	+	0.219650i	$0.0704915\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$			1.00000i			0.316228i
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	−0.941113	+	0.338091i	$0.890219\pi$
$12$	−1.70711	−	0.292893i	−0.492799	−	0.0845510i
$13$	3.53553	+	0.707107i	0.980581	+	0.196116i
$13$	3.53553	+	0.707107i	0.980581	+	0.196116i
$14$		−	2.82843i		−	0.755929i
$15$	1.00000	+	1.41421i	0.258199	+	0.365148i
$16$	−1.00000			−0.250000
$17$	−4.82843			−1.17107			−0.585533	−	0.810649i	$-0.699115\pi$
$17$	−4.82843			−1.17107			−0.585533	+	0.810649i	$0.699115\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$19$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	−2.82843	−	4.00000i	−0.617213	−	0.872872i
$22$	−2.82843			−0.603023
$23$	6.82843			1.42383			0.711913	−	0.702268i	$-0.247829\pi$
$23$	6.82843			1.42383			0.711913	+	0.702268i	$0.247829\pi$
$24$	−1.41421	+	1.00000i	−0.288675	+	0.204124i
$25$		−	1.00000i		−	0.200000i
$26$	3.00000	−	2.00000i	0.588348	−	0.392232i
$27$	−2.53553	+	4.53553i	−0.487964	+	0.872864i
$28$	−2.00000	−	2.00000i	−0.377964	−	0.377964i
$29$		−	3.65685i		−	0.679061i	−0.940595	−	0.339530i	$-0.889732\pi$
$29$		−	3.65685i		−	0.679061i	0.940595	−	0.339530i	$-0.110268\pi$
$30$	1.70711	+	0.292893i	0.311674	+	0.0534747i
$31$	4.41421	+	4.41421i	0.792816	+	0.792816i	0.981951	−	0.189135i	$-0.0605684\pi$
$31$	4.41421	+	4.41421i	0.792816	+	0.792816i	−0.189135	+	0.981951i	$0.560568\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−4.00000	+	2.82843i	−0.696311	+	0.492366i
$34$	−3.41421	+	3.41421i	−0.585533	+	0.585533i
$35$			2.82843i			0.478091i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	−4.00000	+	4.00000i	−0.657596	+	0.657596i	−0.954811	−	0.297215i	$-0.903942\pi$
$37$	−4.00000	+	4.00000i	−0.657596	+	0.657596i	0.297215	+	0.954811i	$0.403942\pi$
$38$		0			0
$39$	2.24264	−	5.82843i	0.359110	−	0.933295i
$40$	1.00000			0.158114
$41$	2.17157	−	2.17157i	0.339143	−	0.339143i	−0.516902	−	0.856045i	$-0.672915\pi$
$41$	2.17157	−	2.17157i	0.339143	−	0.339143i	0.856045	+	0.516902i	$0.172915\pi$
$42$	−4.82843	−	0.828427i	−0.745042	−	0.127829i
$43$		−	5.07107i		−	0.773331i	−0.922220	−	0.386665i	$-0.873627\pi$
$43$		−	5.07107i		−	0.773331i	0.922220	−	0.386665i	$-0.126373\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$	2.70711	−	1.29289i	0.403552	−	0.192733i
$46$	4.82843	−	4.82843i	0.711913	−	0.711913i
$47$	2.00000	+	2.00000i	0.291730	+	0.291730i	0.837763	−	0.546033i	$-0.183863\pi$
$47$	2.00000	+	2.00000i	0.291730	+	0.291730i	−0.546033	+	0.837763i	$0.683863\pi$
$48$	−0.292893	+	1.70711i	−0.0422755	+	0.246400i
$49$		−	1.00000i		−	0.142857i
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	−1.41421	+	8.24264i	−0.198030	+	1.15420i
$52$	0.707107	−	3.53553i	0.0980581	−	0.490290i
$53$			9.41421i			1.29314i	0.762854	+	0.646571i	$0.223798\pi$
$53$			9.41421i			1.29314i	−0.762854	+	0.646571i	$0.776202\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	2.82843			0.381385
$56$	−2.82843			−0.377964
$57$		0			0
$58$	−2.58579	−	2.58579i	−0.339530	−	0.339530i
$59$	4.00000	+	4.00000i	0.520756	+	0.520756i	0.917800	−	0.397044i	$-0.129964\pi$
$59$	4.00000	+	4.00000i	0.520756	+	0.520756i	−0.397044	+	0.917800i	$0.629964\pi$
$60$	1.41421	−	1.00000i	0.182574	−	0.129099i
$61$	12.8284			1.64251			0.821256	−	0.570560i	$-0.193274\pi$
$61$	12.8284			1.64251			0.821256	+	0.570560i	$0.193274\pi$
$62$	6.24264			0.792816
$63$	−7.65685	+	3.65685i	−0.964673	+	0.460720i
$64$			1.00000i			0.125000i
$65$	−3.00000	+	2.00000i	−0.372104	+	0.248069i
$66$	−0.828427	+	4.82843i	−0.101972	+	0.594338i
$67$	2.24264	+	2.24264i	0.273982	+	0.273982i	0.830701	−	0.556719i	$-0.187940\pi$
$67$	2.24264	+	2.24264i	0.273982	+	0.273982i	−0.556719	+	0.830701i	$0.687940\pi$
$68$			4.82843i			0.585533i
$69$	2.00000	−	11.6569i	0.240772	−	1.40332i
$70$	2.00000	+	2.00000i	0.239046	+	0.239046i
$71$	10.4142	−	10.4142i	1.23594	−	1.23594i	0.274294	−	0.961646i	$-0.411556\pi$
$71$	10.4142	−	10.4142i	1.23594	−	1.23594i	0.961646	−	0.274294i	$-0.0884441\pi$
$72$	1.29289	+	2.70711i	0.152369	+	0.319036i
$73$	9.89949	−	9.89949i	1.15865	−	1.15865i	0.173882	−	0.984767i	$-0.444369\pi$
$73$	9.89949	−	9.89949i	1.15865	−	1.15865i	0.984767	−	0.173882i	$-0.0556310\pi$
$74$			5.65685i			0.657596i
$75$	−1.70711	−	0.292893i	−0.197120	−	0.0338204i
$76$		0			0
$77$	−8.00000			−0.911685
$78$	−2.53553	−	5.70711i	−0.287093	−	0.646203i
$79$	−8.82843			−0.993276			−0.496638	−	0.867958i	$-0.665432\pi$
$79$	−8.82843			−0.993276			−0.496638	+	0.867958i	$0.665432\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$		−	3.07107i		−	0.339143i
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	−0.768476	−	0.639879i	$-0.778984\pi$
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	0.639879	+	0.768476i	$0.278984\pi$
$84$	−4.00000	+	2.82843i	−0.436436	+	0.308607i
$85$	3.41421	−	3.41421i	0.370323	−	0.370323i
$86$	−3.58579	−	3.58579i	−0.386665	−	0.386665i
$87$	−6.24264	−	1.07107i	−0.669281	−	0.114831i
$88$			2.82843i			0.301511i
$89$	2.65685	+	2.65685i	0.281626	+	0.281626i	0.833757	−	0.552131i	$-0.186185\pi$
$89$	2.65685	+	2.65685i	0.281626	+	0.281626i	−0.552131	+	0.833757i	$0.686185\pi$
$90$	1.00000	−	2.82843i	0.105409	−	0.298142i
$91$	8.48528	−	5.65685i	0.889499	−	0.592999i
$92$		−	6.82843i		−	0.711913i
$93$	8.82843	−	6.24264i	0.915465	−	0.647332i
$94$	2.82843			0.291730
$95$		0			0
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	−8.58579	−	8.58579i	−0.871755	−	0.871755i	0.120909	−	0.992664i	$-0.461419\pi$
$97$	−8.58579	−	8.58579i	−0.871755	−	0.871755i	−0.992664	+	0.120909i	$0.961419\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	3.65685	+	7.65685i	0.367528	+	0.769543i
$100$	−1.00000			−0.100000
$101$	−7.17157			−0.713598			−0.356799	−	0.934181i	$-0.616132\pi$
$101$	−7.17157			−0.713598			−0.356799	+	0.934181i	$0.616132\pi$
$102$	4.82843	+	6.82843i	0.478086	+	0.676115i
$103$			14.8284i			1.46109i	0.682865	+	0.730544i	$0.260734\pi$
$103$			14.8284i			1.46109i	−0.682865	+	0.730544i	$0.739266\pi$
$104$	−2.00000	−	3.00000i	−0.196116	−	0.294174i
$105$	4.82843	+	0.828427i	0.471206	+	0.0808462i
$106$	6.65685	+	6.65685i	0.646571	+	0.646571i
$107$			12.5858i			1.21671i	0.793664	+	0.608357i	$0.208171\pi$
$107$			12.5858i			1.21671i	−0.793664	+	0.608357i	$0.791829\pi$
$108$	4.53553	+	2.53553i	0.436432	+	0.243982i
$109$	−8.24264	−	8.24264i	−0.789502	−	0.789502i	0.191911	−	0.981412i	$-0.438532\pi$
$109$	−8.24264	−	8.24264i	−0.789502	−	0.789502i	−0.981412	+	0.191911i	$0.938532\pi$
$110$	2.00000	−	2.00000i	0.190693	−	0.190693i
$111$	5.65685	+	8.00000i	0.536925	+	0.759326i
$112$	−2.00000	+	2.00000i	−0.188982	+	0.188982i
$113$			18.4853i			1.73895i	0.493978	+	0.869474i	$0.335542\pi$
$113$			18.4853i			1.73895i	−0.493978	+	0.869474i	$0.664458\pi$
$114$		0			0
$115$	−4.82843	+	4.82843i	−0.450253	+	0.450253i
$116$	−3.65685			−0.339530
$117$	−9.29289	−	5.53553i	−0.859128	−	0.511760i
$118$	5.65685			0.520756
$119$	−9.65685	+	9.65685i	−0.885242	+	0.885242i
$120$	0.292893	−	1.70711i	0.0267374	−	0.155837i
$121$		−	3.00000i		−	0.272727i
$122$	9.07107	−	9.07107i	0.821256	−	0.821256i
$123$	−3.07107	−	4.34315i	−0.276909	−	0.391608i
$124$	4.41421	−	4.41421i	0.396408	−	0.396408i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−2.82843	+	8.00000i	−0.251976	+	0.712697i
$127$			1.65685i			0.147022i	0.997294	+	0.0735110i	$0.0234204\pi$
$127$			1.65685i			0.147022i	−0.997294	+	0.0735110i	$0.976580\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.65685	−	1.48528i	−0.762194	−	0.130772i
$130$	−0.707107	+	3.53553i	−0.0620174	+	0.310087i
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	2.82843	+	4.00000i	0.246183	+	0.348155i
$133$		0			0
$134$	3.17157			0.273982
$135$	−1.41421	−	5.00000i	−0.121716	−	0.430331i
$136$	3.41421	+	3.41421i	0.292766	+	0.292766i
$137$	−6.58579	−	6.58579i	−0.562662	−	0.562662i	0.367401	−	0.930063i	$-0.380248\pi$
$137$	−6.58579	−	6.58579i	−0.562662	−	0.562662i	−0.930063	+	0.367401i	$0.880248\pi$
$138$	−6.82843	−	9.65685i	−0.581274	−	0.822046i
$139$	−7.31371			−0.620341			−0.310170	−	0.950681i	$-0.600386\pi$
$139$	−7.31371			−0.620341			−0.310170	+	0.950681i	$0.600386\pi$
$140$	2.82843			0.239046
$141$	4.00000	−	2.82843i	0.336861	−	0.238197i
$142$		−	14.7279i		−	1.23594i
$143$	−5.65685	−	8.48528i	−0.473050	−	0.709575i
$144$	2.82843	+	1.00000i	0.235702	+	0.0833333i
$145$	2.58579	+	2.58579i	0.214738	+	0.214738i
$146$		−	14.0000i		−	1.15865i
$147$	−1.70711	−	0.292893i	−0.140800	−	0.0241574i
$148$	4.00000	+	4.00000i	0.328798	+	0.328798i
$149$	11.8995	−	11.8995i	0.974845	−	0.974845i	−0.0248467	−	0.999691i	$-0.507910\pi$
$149$	11.8995	−	11.8995i	0.974845	−	0.974845i	0.999691	+	0.0248467i	$0.00790975\pi$
$150$	−1.41421	+	1.00000i	−0.115470	+	0.0816497i
$151$	−12.4142	+	12.4142i	−1.01025	+	1.01025i	−0.0103075	+	0.999947i	$0.503281\pi$
$151$	−12.4142	+	12.4142i	−1.01025	+	1.01025i	−0.999947	+	0.0103075i	$0.996719\pi$
$152$		0			0
$153$	13.6569	+	4.82843i	1.10409	+	0.390355i
$154$	−5.65685	+	5.65685i	−0.455842	+	0.455842i
$155$	−6.24264			−0.501421
$156$	−5.82843	−	2.24264i	−0.466648	−	0.179555i
$157$	−20.7279			−1.65427			−0.827134	−	0.562005i	$-0.810030\pi$
$157$	−20.7279			−1.65427			−0.827134	+	0.562005i	$0.810030\pi$
$158$	−6.24264	+	6.24264i	−0.496638	+	0.496638i
$159$	16.0711	+	2.75736i	1.27452	+	0.218673i
$160$		−	1.00000i		−	0.0790569i
$161$	13.6569	−	13.6569i	1.07631	−	1.07631i
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	−0.860598	−	0.509284i	$-0.829910\pi$
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	0.509284	+	0.860598i	$0.329910\pi$
$164$	−2.17157	−	2.17157i	−0.169571	−	0.169571i
$165$	0.828427	−	4.82843i	0.0644930	−	0.375893i
$166$			1.65685i			0.128597i
$167$	−9.31371	−	9.31371i	−0.720716	−	0.720716i	0.248035	−	0.968751i	$-0.420215\pi$
$167$	−9.31371	−	9.31371i	−0.720716	−	0.720716i	−0.968751	+	0.248035i	$0.920215\pi$
$168$	−0.828427	+	4.82843i	−0.0639145	+	0.372521i
$169$	12.0000	+	5.00000i	0.923077	+	0.384615i
$170$		−	4.82843i		−	0.370323i
$171$		0			0
$172$	−5.07107			−0.386665
$173$	−14.5858			−1.10894			−0.554468	−	0.832205i	$-0.687078\pi$
$173$	−14.5858			−1.10894			−0.554468	+	0.832205i	$0.687078\pi$
$174$	−5.17157	+	3.65685i	−0.392056	+	0.277225i
$175$	−2.00000	−	2.00000i	−0.151186	−	0.151186i
$176$	2.00000	+	2.00000i	0.150756	+	0.150756i
$177$	8.00000	−	5.65685i	0.601317	−	0.425195i
$178$	3.75736			0.281626
$179$	2.34315			0.175135			0.0875675	−	0.996159i	$-0.472091\pi$
$179$	2.34315			0.175135			0.0875675	+	0.996159i	$0.472091\pi$
$180$	−1.29289	−	2.70711i	−0.0963666	−	0.201776i
$181$		−	11.6569i		−	0.866447i	−0.901286	−	0.433224i	$-0.857376\pi$
$181$		−	11.6569i		−	0.866447i	0.901286	−	0.433224i	$-0.142624\pi$
$182$	2.00000	−	10.0000i	0.148250	−	0.741249i
$183$	3.75736	−	21.8995i	0.277752	−	1.61886i
$184$	−4.82843	−	4.82843i	−0.355956	−	0.355956i
$185$		−	5.65685i		−	0.415900i
$186$	1.82843	−	10.6569i	0.134067	−	0.781398i
$187$	9.65685	+	9.65685i	0.706179	+	0.706179i
$188$	2.00000	−	2.00000i	0.145865	−	0.145865i
$189$	4.00000	+	14.1421i	0.290957	+	1.02869i
$190$		0			0
$191$			12.8284i			0.928232i	0.885774	+	0.464116i	$0.153628\pi$
$191$			12.8284i			0.928232i	−0.885774	+	0.464116i	$0.846372\pi$
$192$	1.70711	+	0.292893i	0.123200	+	0.0211377i
$193$	−1.07107	+	1.07107i	−0.0770971	+	0.0770971i	−0.744604	−	0.667507i	$-0.767362\pi$
$193$	−1.07107	+	1.07107i	−0.0770971	+	0.0770971i	0.667507	+	0.744604i	$0.267362\pi$
$194$	−12.1421			−0.871755
$195$	2.53553	+	5.70711i	0.181573	+	0.408694i
$196$	−1.00000			−0.0714286
$197$	−9.17157	+	9.17157i	−0.653448	+	0.653448i	−0.953822	−	0.300374i	$-0.902889\pi$
$197$	−9.17157	+	9.17157i	−0.653448	+	0.653448i	0.300374	+	0.953822i	$0.402889\pi$
$198$	8.00000	+	2.82843i	0.568535	+	0.201008i
$199$			0.828427i			0.0587256i	0.999569	+	0.0293628i	$0.00934782\pi$
$199$			0.828427i			0.0587256i	−0.999569	+	0.0293628i	$0.990652\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	4.48528	−	3.17157i	0.316367	−	0.223706i
$202$	−5.07107	+	5.07107i	−0.356799	+	0.356799i
$203$	−7.31371	−	7.31371i	−0.513322	−	0.513322i
$204$	8.24264	+	1.41421i	0.577100	+	0.0990148i
$205$			3.07107i			0.214493i
$206$	10.4853	+	10.4853i	0.730544	+	0.730544i
$207$	−19.3137	−	6.82843i	−1.34240	−	0.474608i
$208$	−3.53553	−	0.707107i	−0.245145	−	0.0490290i
$209$		0			0
$210$	4.00000	−	2.82843i	0.276026	−	0.195180i
$211$	−16.9706			−1.16830			−0.584151	−	0.811645i	$-0.698572\pi$
$211$	−16.9706			−1.16830			−0.584151	+	0.811645i	$0.698572\pi$
$212$	9.41421			0.646571
$213$	−14.7279	−	20.8284i	−1.00914	−	1.42714i
$214$	8.89949	+	8.89949i	0.608357	+	0.608357i
$215$	3.58579	+	3.58579i	0.244549	+	0.244549i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	17.6569			1.19863
$218$	−11.6569			−0.789502
$219$	−14.0000	−	19.7990i	−0.946032	−	1.33789i
$220$		−	2.82843i		−	0.190693i
$221$	−17.0711	−	3.41421i	−1.14832	−	0.229665i
$222$	9.65685	+	1.65685i	0.648126	+	0.111201i
$223$	−13.6569	−	13.6569i	−0.914531	−	0.914531i	0.0820940	−	0.996625i	$-0.473839\pi$
$223$	−13.6569	−	13.6569i	−0.914531	−	0.914531i	−0.996625	+	0.0820940i	$0.973839\pi$
$224$			2.82843i			0.188982i
$225$	−1.00000	+	2.82843i	−0.0666667	+	0.188562i
$226$	13.0711	+	13.0711i	0.869474	+	0.869474i
$227$	11.4142	−	11.4142i	0.757588	−	0.757588i	−0.218295	−	0.975883i	$-0.570049\pi$
$227$	11.4142	−	11.4142i	0.757588	−	0.757588i	0.975883	+	0.218295i	$0.0700495\pi$
$228$		0			0
$229$	−15.8995	+	15.8995i	−1.05067	+	1.05067i	−0.0520223	+	0.998646i	$0.516567\pi$
$229$	−15.8995	+	15.8995i	−1.05067	+	1.05067i	−0.998646	+	0.0520223i	$0.983433\pi$
$230$			6.82843i			0.450253i
$231$	−2.34315	+	13.6569i	−0.154168	+	0.898555i
$232$	−2.58579	+	2.58579i	−0.169765	+	0.169765i
$233$	0.142136			0.00931161			0.00465581	−	0.999989i	$-0.498518\pi$
$233$	0.142136			0.00931161			0.00465581	+	0.999989i	$0.498518\pi$
$234$	−10.4853	+	2.65685i	−0.685444	+	0.173684i
$235$	−2.82843			−0.184506
$236$	4.00000	−	4.00000i	0.260378	−	0.260378i
$237$	−2.58579	+	15.0711i	−0.167965	+	0.978971i
$238$			13.6569i			0.885242i
$239$	12.0711	−	12.0711i	0.780812	−	0.780812i	−0.199155	−	0.979968i	$-0.563820\pi$
$239$	12.0711	−	12.0711i	0.780812	−	0.780812i	0.979968	+	0.199155i	$0.0638199\pi$
$240$	−1.00000	−	1.41421i	−0.0645497	−	0.0912871i
$241$	−2.65685	+	2.65685i	−0.171143	+	0.171143i	−0.787481	−	0.616338i	$-0.788615\pi$
$241$	−2.65685	+	2.65685i	−0.171143	+	0.171143i	0.616338	+	0.787481i	$0.288615\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	11.7071	−	10.2929i	0.751011	−	0.660289i
$244$		−	12.8284i		−	0.821256i
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$	−5.24264	−	0.899495i	−0.334259	−	0.0573497i
$247$		0			0
$248$		−	6.24264i		−	0.396408i
$249$	1.65685	+	2.34315i	0.104999	+	0.148491i
$250$	1.00000			0.0632456
$251$	−4.97056			−0.313739			−0.156870	−	0.987619i	$-0.550140\pi$
$251$	−4.97056			−0.313739			−0.156870	+	0.987619i	$0.550140\pi$
$252$	3.65685	+	7.65685i	0.230360	+	0.482336i
$253$	−13.6569	−	13.6569i	−0.858599	−	0.858599i
$254$	1.17157	+	1.17157i	0.0735110	+	0.0735110i
$255$	−4.82843	−	6.82843i	−0.302368	−	0.427613i
$256$	1.00000			0.0625000
$257$	26.4853			1.65211			0.826053	−	0.563592i	$-0.190581\pi$
$257$	26.4853			1.65211			0.826053	+	0.563592i	$0.190581\pi$
$258$	−7.17157	+	5.07107i	−0.446483	+	0.315711i
$259$			16.0000i			0.994192i
$260$	2.00000	+	3.00000i	0.124035	+	0.186052i
$261$	−3.65685	+	10.3431i	−0.226354	+	0.640225i
$262$	8.00000	+	8.00000i	0.494242	+	0.494242i
$263$			7.51472i			0.463377i	0.972790	+	0.231689i	$0.0744251\pi$
$263$			7.51472i			0.463377i	−0.972790	+	0.231689i	$0.925575\pi$
$264$	4.82843	+	0.828427i	0.297169	+	0.0509862i
$265$	−6.65685	−	6.65685i	−0.408927	−	0.408927i
$266$		0			0
$267$	5.31371	−	3.75736i	0.325194	−	0.229947i
$268$	2.24264	−	2.24264i	0.136991	−	0.136991i
$269$		−	12.8284i		−	0.782163i	−0.920356	−	0.391082i	$-0.872101\pi$
$269$		−	12.8284i		−	0.782163i	0.920356	−	0.391082i	$-0.127899\pi$
$270$	−4.53553	−	2.53553i	−0.276024	−	0.154308i
$271$	12.5563	−	12.5563i	0.762744	−	0.762744i	−0.214074	−	0.976818i	$-0.568673\pi$
$271$	12.5563	−	12.5563i	0.762744	−	0.762744i	0.976818	+	0.214074i	$0.0686733\pi$
$272$	4.82843			0.292766
$273$	−7.17157	−	16.1421i	−0.434043	−	0.976966i
$274$	−9.31371			−0.562662
$275$	−2.00000	+	2.00000i	−0.120605	+	0.120605i
$276$	−11.6569	−	2.00000i	−0.701660	−	0.120386i
$277$			8.72792i			0.524410i	0.965012	+	0.262205i	$0.0844497\pi$
$277$			8.72792i			0.524410i	−0.965012	+	0.262205i	$0.915550\pi$
$278$	−5.17157	+	5.17157i	−0.310170	+	0.310170i
$279$	−8.07107	−	16.8995i	−0.483202	−	1.01175i
$280$	2.00000	−	2.00000i	0.119523	−	0.119523i
$281$	−15.0000	−	15.0000i	−0.894825	−	0.894825i	0.100148	−	0.994973i	$-0.468068\pi$
$281$	−15.0000	−	15.0000i	−0.894825	−	0.894825i	−0.994973	+	0.100148i	$0.968068\pi$
$282$	0.828427	−	4.82843i	0.0493321	−	0.287529i
$283$		−	9.75736i		−	0.580015i	−0.957024	−	0.290007i	$-0.906342\pi$
$283$		−	9.75736i		−	0.580015i	0.957024	−	0.290007i	$-0.0936578\pi$
$284$	−10.4142	−	10.4142i	−0.617970	−	0.617970i
$285$		0			0
$286$	−10.0000	−	2.00000i	−0.591312	−	0.118262i
$287$		−	8.68629i		−	0.512736i
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$	6.31371			0.371395
$290$	3.65685			0.214738
$291$	−17.1716	+	12.1421i	−1.00662	+	0.711785i
$292$	−9.89949	−	9.89949i	−0.579324	−	0.579324i
$293$	16.4853	+	16.4853i	0.963080	+	0.963080i	0.999342	−	0.0362619i	$-0.0115451\pi$
$293$	16.4853	+	16.4853i	0.963080	+	0.963080i	−0.0362619	+	0.999342i	$0.511545\pi$
$294$	−1.41421	+	1.00000i	−0.0824786	+	0.0583212i
$295$	−5.65685			−0.329355
$296$	5.65685			0.328798
$297$	14.1421	−	4.00000i	0.820610	−	0.232104i
$298$		−	16.8284i		−	0.974845i
$299$	24.1421	+	4.82843i	1.39618	+	0.279235i
$300$	−0.292893	+	1.70711i	−0.0169102	+	0.0985599i
$301$	−10.1421	−	10.1421i	−0.584583	−	0.584583i
$302$			17.5563i			1.01025i
$303$	−2.10051	+	12.2426i	−0.120671	+	0.703321i
$304$		0			0
$305$	−9.07107	+	9.07107i	−0.519408	+	0.519408i
$306$	13.0711	−	6.24264i	0.747223	−	0.356868i
$307$	−8.58579	+	8.58579i	−0.490017	+	0.490017i	−0.908311	−	0.418295i	$-0.862628\pi$
$307$	−8.58579	+	8.58579i	−0.490017	+	0.490017i	0.418295	+	0.908311i	$0.362628\pi$
$308$			8.00000i			0.455842i
$309$	25.3137	+	4.34315i	1.44005	+	0.247073i
$310$	−4.41421	+	4.41421i	−0.250710	+	0.250710i
$311$	30.6274			1.73672			0.868361	−	0.495933i	$-0.165174\pi$
$311$	30.6274			1.73672			0.868361	+	0.495933i	$0.165174\pi$
$312$	−5.70711	+	2.53553i	−0.323101	+	0.143546i
$313$	18.9706			1.07228			0.536140	−	0.844129i	$-0.319882\pi$
$313$	18.9706			1.07228			0.536140	+	0.844129i	$0.319882\pi$
$314$	−14.6569	+	14.6569i	−0.827134	+	0.827134i
$315$	2.82843	−	8.00000i	0.159364	−	0.450749i
$316$			8.82843i			0.496638i
$317$	−16.9706	+	16.9706i	−0.953162	+	0.953162i	−0.998951	−	0.0457894i	$-0.985420\pi$
$317$	−16.9706	+	16.9706i	−0.953162	+	0.953162i	0.0457894	+	0.998951i	$0.485420\pi$
$318$	13.3137	−	9.41421i	0.746596	−	0.527923i
$319$	−7.31371	+	7.31371i	−0.409489	+	0.409489i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	21.4853	+	3.68629i	1.19919	+	0.205749i
$322$		−	19.3137i		−	1.07631i
$323$		0			0
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	0.707107	−	3.53553i	0.0392232	−	0.196116i
$326$			6.34315i			0.351314i
$327$	−16.4853	+	11.6569i	−0.911638	+	0.644626i
$328$	−3.07107			−0.169571
$329$	8.00000			0.441054
$330$	−2.82843	−	4.00000i	−0.155700	−	0.220193i
$331$	−6.00000	−	6.00000i	−0.329790	−	0.329790i	0.522717	−	0.852506i	$-0.324919\pi$
$331$	−6.00000	−	6.00000i	−0.329790	−	0.329790i	−0.852506	+	0.522717i	$0.824919\pi$
$332$	1.17157	+	1.17157i	0.0642984	+	0.0642984i
$333$	15.3137	−	7.31371i	0.839186	−	0.400789i
$334$	−13.1716			−0.720716
$335$	−3.17157			−0.173282
$336$	2.82843	+	4.00000i	0.154303	+	0.218218i
$337$			25.3137i			1.37893i	0.724321	+	0.689463i	$0.242153\pi$
$337$			25.3137i			1.37893i	−0.724321	+	0.689463i	$0.757847\pi$
$338$	12.0208	−	4.94975i	0.653846	−	0.269231i
$339$	31.5563	+	5.41421i	1.71391	+	0.294060i
$340$	−3.41421	−	3.41421i	−0.185162	−	0.185162i
$341$		−	17.6569i		−	0.956172i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−3.58579	+	3.58579i	−0.193333	+	0.193333i
$345$	6.82843	+	9.65685i	0.367630	+	0.519908i
$346$	−10.3137	+	10.3137i	−0.554468	+	0.554468i
$347$			31.6985i			1.70166i	0.525438	+	0.850832i	$0.323901\pi$
$347$			31.6985i			1.70166i	−0.525438	+	0.850832i	$0.676099\pi$
$348$	−1.07107	+	6.24264i	−0.0574153	+	0.334641i
$349$	18.3848	−	18.3848i	0.984115	−	0.984115i	−0.0157613	−	0.999876i	$-0.505017\pi$
$349$	18.3848	−	18.3848i	0.984115	−	0.984115i	0.999876	+	0.0157613i	$0.00501718\pi$
$350$	−2.82843			−0.151186
$351$	−12.1716	+	14.2426i	−0.649670	+	0.760216i
$352$	2.82843			0.150756
$353$	−3.89949	+	3.89949i	−0.207549	+	0.207549i	−0.803225	−	0.595676i	$-0.796884\pi$
$353$	−3.89949	+	3.89949i	−0.207549	+	0.207549i	0.595676	+	0.803225i	$0.296884\pi$
$354$	1.65685	−	9.65685i	0.0880608	−	0.513256i
$355$			14.7279i			0.781677i
$356$	2.65685	−	2.65685i	0.140813	−	0.140813i
$357$	13.6569	+	19.3137i	0.722797	+	1.02219i
$358$	1.65685	−	1.65685i	0.0875675	−	0.0875675i
$359$	−2.41421	−	2.41421i	−0.127417	−	0.127417i	0.640522	−	0.767940i	$-0.278718\pi$
$359$	−2.41421	−	2.41421i	−0.127417	−	0.127417i	−0.767940	+	0.640522i	$0.778718\pi$
$360$	−2.82843	−	1.00000i	−0.149071	−	0.0527046i
$361$		−	19.0000i		−	1.00000i
$362$	−8.24264	−	8.24264i	−0.433224	−	0.433224i
$363$	−5.12132	−	0.878680i	−0.268800	−	0.0461187i
$364$	−5.65685	−	8.48528i	−0.296500	−	0.444750i
$365$			14.0000i			0.732793i
$366$	−12.8284	−	18.1421i	−0.670553	−	0.948305i
$367$	37.4558			1.95518			0.977590	−	0.210520i	$-0.0675157\pi$
$367$	37.4558			1.95518			0.977590	+	0.210520i	$0.0675157\pi$
$368$	−6.82843			−0.355956
$369$	−8.31371	+	3.97056i	−0.432794	+	0.206699i
$370$	−4.00000	−	4.00000i	−0.207950	−	0.207950i
$371$	18.8284	+	18.8284i	0.977523	+	0.977523i
$372$	−6.24264	−	8.82843i	−0.323666	−	0.457733i
$373$	−28.7279			−1.48748			−0.743738	−	0.668472i	$-0.766949\pi$
$373$	−28.7279			−1.48748			−0.743738	+	0.668472i	$0.766949\pi$
$374$	13.6569			0.706179
$375$	1.41421	−	1.00000i	0.0730297	−	0.0516398i
$376$		−	2.82843i		−	0.145865i
$377$	2.58579	−	12.9289i	0.133175	−	0.665874i
$378$	12.8284	+	7.17157i	0.659823	+	0.368866i
$379$	7.51472	+	7.51472i	0.386005	+	0.386005i	0.873260	−	0.487255i	$-0.162002\pi$
$379$	7.51472	+	7.51472i	0.386005	+	0.386005i	−0.487255	+	0.873260i	$0.662002\pi$
$380$		0			0
$381$	2.82843	+	0.485281i	0.144905	+	0.0248617i
$382$	9.07107	+	9.07107i	0.464116	+	0.464116i
$383$	4.00000	−	4.00000i	0.204390	−	0.204390i	−0.597488	−	0.801878i	$-0.703834\pi$
$383$	4.00000	−	4.00000i	0.204390	−	0.204390i	0.801878	+	0.597488i	$0.203834\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	5.65685	−	5.65685i	0.288300	−	0.288300i
$386$			1.51472i			0.0770971i
$387$	−5.07107	+	14.3431i	−0.257777	+	0.729103i
$388$	−8.58579	+	8.58579i	−0.435877	+	0.435877i
$389$	−31.6569			−1.60507			−0.802533	−	0.596608i	$-0.796515\pi$
$389$	−31.6569			−1.60507			−0.802533	+	0.596608i	$0.796515\pi$
$390$	5.82843	+	2.24264i	0.295134	+	0.113561i
$391$	−32.9706			−1.66739
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	19.3137	+	3.31371i	0.974248	+	0.167154i
$394$			12.9706i			0.653448i
$395$	6.24264	−	6.24264i	0.314101	−	0.314101i
$396$	7.65685	−	3.65685i	0.384771	−	0.183764i
$397$	6.58579	−	6.58579i	0.330531	−	0.330531i	−0.522257	−	0.852788i	$-0.674910\pi$
$397$	6.58579	−	6.58579i	0.330531	−	0.330531i	0.852788	+	0.522257i	$0.174910\pi$
$398$	0.585786	+	0.585786i	0.0293628	+	0.0293628i
$399$		0			0
$400$			1.00000i			0.0500000i
$401$	−21.6274	−	21.6274i	−1.08002	−	1.08002i	−0.996507	−	0.0835152i	$-0.973385\pi$
$401$	−21.6274	−	21.6274i	−1.08002	−	1.08002i	−0.0835152	−	0.996507i	$-0.526615\pi$
$402$	0.928932	−	5.41421i	0.0463309	−	0.270036i
$403$	12.4853	+	18.7279i	0.621936	+	0.932904i
$404$			7.17157i			0.356799i
$405$	−8.94975	+	0.949747i	−0.444717	+	0.0471933i
$406$	−10.3431			−0.513322
$407$	16.0000			0.793091
$408$	6.82843	−	4.82843i	0.338058	−	0.239043i
$409$	13.4853	+	13.4853i	0.666804	+	0.666804i	0.956975	−	0.290171i	$-0.0937121\pi$
$409$	13.4853	+	13.4853i	0.666804	+	0.666804i	−0.290171	+	0.956975i	$0.593712\pi$
$410$	2.17157	+	2.17157i	0.107246	+	0.107246i
$411$	−13.1716	+	9.31371i	−0.649706	+	0.459411i
$412$	14.8284			0.730544
$413$	16.0000			0.787309
$414$	−18.4853	+	8.82843i	−0.908502	+	0.433894i
$415$		−	1.65685i		−	0.0813318i
$416$	−3.00000	+	2.00000i	−0.147087	+	0.0980581i
$417$	−2.14214	+	12.4853i	−0.104901	+	0.611407i
$418$		0			0
$419$		−	5.17157i		−	0.252648i	−0.991989	−	0.126324i	$-0.959682\pi$
$419$		−	5.17157i		−	0.252648i	0.991989	−	0.126324i	$-0.0403179\pi$
$420$	0.828427	−	4.82843i	0.0404231	−	0.235603i
$421$	−5.89949	−	5.89949i	−0.287524	−	0.287524i	0.548577	−	0.836100i	$-0.315170\pi$
$421$	−5.89949	−	5.89949i	−0.287524	−	0.287524i	−0.836100	+	0.548577i	$0.815170\pi$
$422$	−12.0000	+	12.0000i	−0.584151	+	0.584151i
$423$	−3.65685	−	7.65685i	−0.177802	−	0.372289i
$424$	6.65685	−	6.65685i	0.323285	−	0.323285i
$425$			4.82843i			0.234213i
$426$	−25.1421	−	4.31371i	−1.21814	−	0.209000i
$427$	25.6569	−	25.6569i	1.24162	−	1.24162i
$428$	12.5858			0.608357
$429$	−16.1421	+	7.17157i	−0.779350	+	0.346247i
$430$	5.07107			0.244549
$431$	15.2426	−	15.2426i	0.734212	−	0.734212i	−0.237239	−	0.971451i	$-0.576242\pi$
$431$	15.2426	−	15.2426i	0.734212	−	0.734212i	0.971451	+	0.237239i	$0.0762425\pi$
$432$	2.53553	−	4.53553i	0.121991	−	0.218216i
$433$			35.6569i			1.71356i	0.515683	+	0.856780i	$0.327538\pi$
$433$			35.6569i			1.71356i	−0.515683	+	0.856780i	$0.672462\pi$
$434$	12.4853	−	12.4853i	0.599313	−	0.599313i
$435$	5.17157	−	3.65685i	0.247958	−	0.175333i
$436$	−8.24264	+	8.24264i	−0.394751	+	0.394751i
$437$		0			0
$438$	−23.8995	−	4.10051i	−1.14196	−	0.195930i
$439$		−	24.0000i		−	1.14546i	−0.819745	−	0.572729i	$-0.805885\pi$
$439$		−	24.0000i		−	1.14546i	0.819745	−	0.572729i	$-0.194115\pi$
$440$	−2.00000	−	2.00000i	−0.0953463	−	0.0953463i
$441$	−1.00000	+	2.82843i	−0.0476190	+	0.134687i
$442$	−14.4853	+	9.65685i	−0.688995	+	0.459330i
$443$			23.8995i			1.13550i	0.823201	+	0.567750i	$0.192186\pi$
$443$			23.8995i			1.13550i	−0.823201	+	0.567750i	$0.807814\pi$
$444$	8.00000	−	5.65685i	0.379663	−	0.268462i
$445$	−3.75736			−0.178116
$446$	−19.3137			−0.914531
$447$	−16.8284	−	23.7990i	−0.795957	−	1.12565i
$448$	2.00000	+	2.00000i	0.0944911	+	0.0944911i
$449$	−7.34315	−	7.34315i	−0.346544	−	0.346544i	0.512276	−	0.858821i	$-0.328802\pi$
$449$	−7.34315	−	7.34315i	−0.346544	−	0.346544i	−0.858821	+	0.512276i	$0.828802\pi$
$450$	1.29289	+	2.70711i	0.0609476	+	0.127614i
$451$	−8.68629			−0.409021
$452$	18.4853			0.869474
$453$	17.5563	+	24.8284i	0.824869	+	1.16654i
$454$		−	16.1421i		−	0.757588i
$455$	−2.00000	+	10.0000i	−0.0937614	+	0.468807i
$456$		0			0
$457$	11.4142	+	11.4142i	0.533934	+	0.533934i	0.921741	−	0.387806i	$-0.126767\pi$
$457$	11.4142	+	11.4142i	0.533934	+	0.533934i	−0.387806	+	0.921741i	$0.626767\pi$
$458$			22.4853i			1.05067i
$459$	12.2426	−	21.8995i	0.571438	−	1.02218i
$460$	4.82843	+	4.82843i	0.225127	+	0.225127i
$461$	8.72792	−	8.72792i	0.406500	−	0.406500i	−0.474016	−	0.880516i	$-0.657196\pi$
$461$	8.72792	−	8.72792i	0.406500	−	0.406500i	0.880516	+	0.474016i	$0.157196\pi$
$462$	8.00000	+	11.3137i	0.372194	+	0.526361i
$463$	12.0000	−	12.0000i	0.557687	−	0.557687i	−0.370961	−	0.928648i	$-0.620972\pi$
$463$	12.0000	−	12.0000i	0.557687	−	0.557687i	0.928648	+	0.370961i	$0.120972\pi$
$464$			3.65685i			0.169765i
$465$	−1.82843	+	10.6569i	−0.0847913	+	0.494200i
$466$	0.100505	−	0.100505i	0.00465581	−	0.00465581i
$467$	2.24264			0.103777			0.0518885	−	0.998653i	$-0.483476\pi$
$467$	2.24264			0.103777			0.0518885	+	0.998653i	$0.483476\pi$
$468$	−5.53553	+	9.29289i	−0.255880	+	0.429564i
$469$	8.97056			0.414222
$470$	−2.00000	+	2.00000i	−0.0922531	+	0.0922531i
$471$	−6.07107	+	35.3848i	−0.279740	+	1.63044i
$472$		−	5.65685i		−	0.260378i
$473$	−10.1421	+	10.1421i	−0.466336	+	0.466336i
$474$	8.82843	+	12.4853i	0.405503	+	0.573468i
$475$		0			0
$476$	9.65685	+	9.65685i	0.442621	+	0.442621i
$477$	9.41421	−	26.6274i	0.431047	−	1.21919i
$478$		−	17.0711i		−	0.780812i
$479$	−2.41421	−	2.41421i	−0.110308	−	0.110308i	0.649798	−	0.760107i	$-0.274853\pi$
$479$	−2.41421	−	2.41421i	−0.110308	−	0.110308i	−0.760107	+	0.649798i	$0.774853\pi$
$480$	−1.70711	−	0.292893i	−0.0779184	−	0.0133687i
$481$	−16.9706	+	11.3137i	−0.773791	+	0.515861i
$482$			3.75736i			0.171143i
$483$	−19.3137	−	27.3137i	−0.878804	−	1.24282i
$484$	−3.00000			−0.136364
$485$	12.1421			0.551346
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	23.4558	+	23.4558i	1.06289	+	1.06289i	0.997885	+	0.0650005i	$0.0207049\pi$
$487$	23.4558	+	23.4558i	1.06289	+	1.06289i	0.0650005	+	0.997885i	$0.479295\pi$
$488$	−9.07107	−	9.07107i	−0.410628	−	0.410628i
$489$	6.34315	+	8.97056i	0.286847	+	0.405663i
$490$	1.00000			0.0451754
$491$	−9.85786			−0.444879			−0.222440	−	0.974946i	$-0.571402\pi$
$491$	−9.85786			−0.444879			−0.222440	+	0.974946i	$0.571402\pi$
$492$	−4.34315	+	3.07107i	−0.195804	+	0.138454i
$493$			17.6569i			0.795225i
$494$		0			0
$495$	−8.00000	−	2.82843i	−0.359573	−	0.127128i
$496$	−4.41421	−	4.41421i	−0.198204	−	0.198204i
$497$		−	41.6569i		−	1.86857i
$498$	2.82843	+	0.485281i	0.126745	+	0.0217460i
$499$	22.4853	+	22.4853i	1.00658	+	1.00658i	0.999978	+	0.00660122i	$0.00210125\pi$
$499$	22.4853	+	22.4853i	1.00658	+	1.00658i	0.00660122	+	0.999978i	$0.497899\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	−18.6274	+	13.1716i	−0.832212	+	0.588462i
$502$	−3.51472	+	3.51472i	−0.156870	+	0.156870i
$503$		−	8.68629i		−	0.387303i	−0.981070	−	0.193651i	$-0.937967\pi$
$503$		−	8.68629i		−	0.387303i	0.981070	−	0.193651i	$-0.0620330\pi$
$504$	8.00000	+	2.82843i	0.356348	+	0.125988i
$505$	5.07107	−	5.07107i	0.225660	−	0.225660i
$506$	−19.3137			−0.858599
$507$	12.0503	−	19.0208i	0.535171	−	0.844744i
$508$	1.65685			0.0735110
$509$	−18.7279	+	18.7279i	−0.830101	+	0.830101i	−0.987530	−	0.157430i	$-0.949679\pi$
$509$	−18.7279	+	18.7279i	−0.830101	+	0.830101i	0.157430	+	0.987530i	$0.449679\pi$
$510$	−8.24264	−	1.41421i	−0.364990	−	0.0626224i
$511$		−	39.5980i		−	1.75171i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	18.7279	−	18.7279i	0.826053	−	0.826053i
$515$	−10.4853	−	10.4853i	−0.462037	−	0.462037i
$516$	−1.48528	+	8.65685i	−0.0653859	+	0.381097i
$517$		−	8.00000i		−	0.351840i
$518$	11.3137	+	11.3137i	0.497096	+	0.497096i
$519$	−4.27208	+	24.8995i	−0.187523	+	1.09297i
$520$	3.53553	+	0.707107i	0.155043	+	0.0310087i
$521$		−	2.68629i		−	0.117689i	−0.998267	−	0.0588443i	$-0.981258\pi$
$521$		−	2.68629i		−	0.117689i	0.998267	−	0.0588443i	$-0.0187415\pi$
$522$	4.72792	+	9.89949i	0.206936	+	0.433289i
$523$	11.8995			0.520329			0.260164	−	0.965564i	$-0.416223\pi$
$523$	11.8995			0.520329			0.260164	+	0.965564i	$0.416223\pi$
$524$	11.3137			0.494242
$525$	−4.00000	+	2.82843i	−0.174574	+	0.123443i
$526$	5.31371	+	5.31371i	0.231689	+	0.231689i
$527$	−21.3137	−	21.3137i	−0.928440	−	0.928440i
$528$	4.00000	−	2.82843i	0.174078	−	0.123091i
$529$	23.6274			1.02728
$530$	−9.41421			−0.408927
$531$	−7.31371	−	15.3137i	−0.317388	−	0.664558i
$532$		0			0
$533$	9.21320	−	6.14214i	0.399068	−	0.266045i
$534$	1.10051	−	6.41421i	0.0476235	−	0.277570i
$535$	−8.89949	−	8.89949i	−0.384759	−	0.384759i
$536$		−	3.17157i		−	0.136991i
$537$	0.686292	−	4.00000i	0.0296157	−	0.172613i
$538$	−9.07107	−	9.07107i	−0.391082	−	0.391082i
$539$	−2.00000	+	2.00000i	−0.0861461	+	0.0861461i
$540$	−5.00000	+	1.41421i	−0.215166	+	0.0608581i
$541$	−25.0711	+	25.0711i	−1.07789	+	1.07789i	−0.0811908	+	0.996699i	$0.525872\pi$
$541$	−25.0711	+	25.0711i	−1.07789	+	1.07789i	−0.996699	+	0.0811908i	$0.974128\pi$
$542$		−	17.7574i		−	0.762744i
$543$	−19.8995	−	3.41421i	−0.853969	−	0.146518i
$544$	3.41421	−	3.41421i	0.146383	−	0.146383i
$545$	11.6569			0.499325
$546$	−16.4853	−	6.34315i	−0.705505	−	0.271462i
$547$	−35.8995			−1.53495			−0.767476	−	0.641078i	$-0.778488\pi$
$547$	−35.8995			−1.53495			−0.767476	+	0.641078i	$0.778488\pi$
$548$	−6.58579	+	6.58579i	−0.281331	+	0.281331i
$549$	−36.2843	−	12.8284i	−1.54857	−	0.547504i
$550$			2.82843i			0.120605i
$551$		0			0
$552$	−9.65685	+	6.82843i	−0.411023	+	0.290637i
$553$	−17.6569	+	17.6569i	−0.750846	+	0.750846i
$554$	6.17157	+	6.17157i	0.262205	+	0.262205i
$555$	−9.65685	−	1.65685i	−0.409911	−	0.0703295i
$556$			7.31371i			0.310170i
$557$	−15.7990	−	15.7990i	−0.669425	−	0.669425i	0.288158	−	0.957583i	$-0.406957\pi$
$557$	−15.7990	−	15.7990i	−0.669425	−	0.669425i	−0.957583	+	0.288158i	$0.906957\pi$
$558$	−17.6569	−	6.24264i	−0.747474	−	0.264272i
$559$	3.58579	−	17.9289i	0.151663	−	0.758313i
$560$		−	2.82843i		−	0.119523i
$561$	19.3137	−	13.6569i	0.815425	−	0.576593i
$562$	−21.2132			−0.894825
$563$	−15.8995			−0.670084			−0.335042	−	0.942203i	$-0.608750\pi$
$563$	−15.8995			−0.670084			−0.335042	+	0.942203i	$0.608750\pi$
$564$	−2.82843	−	4.00000i	−0.119098	−	0.168430i
$565$	−13.0711	−	13.0711i	−0.549904	−	0.549904i
$566$	−6.89949	−	6.89949i	−0.290007	−	0.290007i
$567$	25.3137	−	2.68629i	1.06308	−	0.112814i
$568$	−14.7279			−0.617970
$569$	−31.9411			−1.33904			−0.669521	−	0.742793i	$-0.733501\pi$
$569$	−31.9411			−1.33904			−0.669521	+	0.742793i	$0.733501\pi$
$570$		0			0
$571$		−	1.17157i		−	0.0490288i	−0.999699	−	0.0245144i	$-0.992196\pi$
$571$		−	1.17157i		−	0.0490288i	0.999699	−	0.0245144i	$-0.00780396\pi$
$572$	−8.48528	+	5.65685i	−0.354787	+	0.236525i
$573$	21.8995	+	3.75736i	0.914865	+	0.156966i
$574$	−6.14214	−	6.14214i	−0.256368	−	0.256368i
$575$		−	6.82843i		−	0.284765i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	−0.727922	−	0.727922i	−0.0303038	−	0.0303038i	0.691793	−	0.722096i	$-0.256821\pi$
$577$	−0.727922	−	0.727922i	−0.0303038	−	0.0303038i	−0.722096	+	0.691793i	$0.756821\pi$
$578$	4.46447	−	4.46447i	0.185697	−	0.185697i
$579$	1.51472	+	2.14214i	0.0629496	+	0.0890241i
$580$	2.58579	−	2.58579i	0.107369	−	0.107369i
$581$			4.68629i			0.194420i
$582$	−3.55635	+	20.7279i	−0.147415	+	0.859200i
$583$	18.8284	−	18.8284i	0.779794	−	0.779794i
$584$	−14.0000			−0.579324
$585$	10.4853	−	2.65685i	0.433513	−	0.109847i
$586$	23.3137			0.963080
$587$	27.7990	−	27.7990i	1.14739	−	1.14739i	0.160322	−	0.987065i	$-0.448747\pi$
$587$	27.7990	−	27.7990i	1.14739	−	1.14739i	0.987065	−	0.160322i	$-0.0512534\pi$
$588$	−0.292893	+	1.70711i	−0.0120787	+	0.0703999i
$589$		0			0
$590$	−4.00000	+	4.00000i	−0.164677	+	0.164677i
$591$	12.9706	+	18.3431i	0.533538	+	0.754536i
$592$	4.00000	−	4.00000i	0.164399	−	0.164399i
$593$	−11.8995	−	11.8995i	−0.488654	−	0.488654i	0.419228	−	0.907881i	$-0.362301\pi$
$593$	−11.8995	−	11.8995i	−0.488654	−	0.488654i	−0.907881	+	0.419228i	$0.862301\pi$
$594$	7.17157	−	12.8284i	0.294253	−	0.526357i
$595$		−	13.6569i		−	0.559876i
$596$	−11.8995	−	11.8995i	−0.487422	−	0.487422i
$597$	1.41421	+	0.242641i	0.0578799	+	0.00993062i
$598$	20.4853	−	13.6569i	0.837705	−	0.558470i
$599$		−	21.5147i		−	0.879068i	−0.898226	−	0.439534i	$-0.855144\pi$
$599$		−	21.5147i		−	0.879068i	0.898226	−	0.439534i	$-0.144856\pi$
$600$	1.00000	+	1.41421i	0.0408248	+	0.0577350i
$601$	−8.28427			−0.337922			−0.168961	−	0.985623i	$-0.554041\pi$
$601$	−8.28427			−0.337922			−0.168961	+	0.985623i	$0.554041\pi$
$602$	−14.3431			−0.584583
$603$	−4.10051	−	8.58579i	−0.166985	−	0.349640i
$604$	12.4142	+	12.4142i	0.505127	+	0.505127i
$605$	2.12132	+	2.12132i	0.0862439	+	0.0862439i
$606$	7.17157	+	10.1421i	0.291325	+	0.411996i
$607$	0.686292			0.0278557			0.0139279	−	0.999903i	$-0.495566\pi$
$607$	0.686292			0.0278557			0.0139279	+	0.999903i	$0.495566\pi$
$608$		0			0
$609$	−14.6274	+	10.3431i	−0.592733	+	0.419125i
$610$			12.8284i			0.519408i
$611$	5.65685	+	8.48528i	0.228852	+	0.343278i
$612$	4.82843	−	13.6569i	0.195178	−	0.552046i
$613$	18.6274	+	18.6274i	0.752354	+	0.752354i	0.974918	−	0.222564i	$-0.0714426\pi$
$613$	18.6274	+	18.6274i	0.752354	+	0.752354i	−0.222564	+	0.974918i	$0.571443\pi$
$614$			12.1421i			0.490017i
$615$	5.24264	+	0.899495i	0.211404	+	0.0362711i
$616$	5.65685	+	5.65685i	0.227921	+	0.227921i
$617$	2.72792	−	2.72792i	0.109822	−	0.109822i	−0.650060	−	0.759882i	$-0.725256\pi$
$617$	2.72792	−	2.72792i	0.109822	−	0.109822i	0.759882	+	0.650060i	$0.225256\pi$
$618$	20.9706	−	14.8284i	0.843560	−	0.596487i
$619$	21.3137	−	21.3137i	0.856670	−	0.856670i	−0.134274	−	0.990944i	$-0.542870\pi$
$619$	21.3137	−	21.3137i	0.856670	−	0.856670i	0.990944	+	0.134274i	$0.0428702\pi$
$620$			6.24264i			0.250710i
$621$	−17.3137	+	30.9706i	−0.694775	+	1.24281i
$622$	21.6569	−	21.6569i	0.868361	−	0.868361i
$623$	10.6274			0.425778
$624$	−2.24264	+	5.82843i	−0.0897775	+	0.233324i
$625$	−1.00000			−0.0400000
$626$	13.4142	−	13.4142i	0.536140	−	0.536140i
$627$		0			0
$628$			20.7279i			0.827134i
$629$	19.3137	−	19.3137i	0.770088	−	0.770088i
$630$	−3.65685	−	7.65685i	−0.145693	−	0.305056i
$631$	34.2132	−	34.2132i	1.36201	−	1.36201i	0.490649	−	0.871358i	$-0.336760\pi$
$631$	34.2132	−	34.2132i	1.36201	−	1.36201i	0.871358	−	0.490649i	$-0.163240\pi$
$632$	6.24264	+	6.24264i	0.248319	+	0.248319i
$633$	−4.97056	+	28.9706i	−0.197562	+	1.15148i
$634$			24.0000i			0.953162i
$635$	−1.17157	−	1.17157i	−0.0464925	−	0.0464925i
$636$	2.75736	−	16.0711i	0.109336	−	0.637259i
$637$	0.707107	−	3.53553i	0.0280166	−	0.140083i
$638$			10.3431i			0.409489i
$639$	−39.8701	+	19.0416i	−1.57724	+	0.753275i
$640$	−1.00000			−0.0395285
$641$	−16.9706			−0.670297			−0.335148	−	0.942165i	$-0.608786\pi$
$641$	−16.9706			−0.670297			−0.335148	+	0.942165i	$0.608786\pi$
$642$	17.7990	−	12.5858i	0.702470	−	0.496721i
$643$	−23.7990	−	23.7990i	−0.938541	−	0.938541i	0.0596772	−	0.998218i	$-0.480993\pi$
$643$	−23.7990	−	23.7990i	−0.938541	−	0.938541i	−0.998218	+	0.0596772i	$0.980993\pi$
$644$	−13.6569	−	13.6569i	−0.538155	−	0.538155i
$645$	7.17157	−	5.07107i	0.282380	−	0.199673i
$646$		0			0
$647$	5.65685			0.222394			0.111197	−	0.993798i	$-0.464532\pi$
$647$	5.65685			0.222394			0.111197	+	0.993798i	$0.464532\pi$
$648$	−0.949747	−	8.94975i	−0.0373096	−	0.351579i
$649$		−	16.0000i		−	0.628055i
$650$	−2.00000	−	3.00000i	−0.0784465	−	0.117670i
$651$	5.17157	−	30.1421i	0.202690	−	1.18136i
$652$	4.48528	+	4.48528i	0.175657	+	0.175657i
$653$		−	9.21320i		−	0.360541i	−0.983617	−	0.180270i	$-0.942303\pi$
$653$		−	9.21320i		−	0.360541i	0.983617	−	0.180270i	$-0.0576972\pi$
$654$	−3.41421	+	19.8995i	−0.133506	+	0.778132i
$655$	−8.00000	−	8.00000i	−0.312586	−	0.312586i
$656$	−2.17157	+	2.17157i	−0.0847857	+	0.0847857i
$657$	−37.8995	+	18.1005i	−1.47860	+	0.706168i
$658$	5.65685	−	5.65685i	0.220527	−	0.220527i
$659$			17.1716i			0.668910i	0.942412	+	0.334455i	$0.108552\pi$
$659$			17.1716i			0.668910i	−0.942412	+	0.334455i	$0.891448\pi$
$660$	−4.82843	−	0.828427i	−0.187946	−	0.0322465i
$661$	10.9289	−	10.9289i	0.425086	−	0.425086i	−0.461864	−	0.886951i	$-0.652819\pi$
$661$	10.9289	−	10.9289i	0.425086	−	0.425086i	0.886951	+	0.461864i	$0.152819\pi$
$662$	−8.48528			−0.329790
$663$	−10.8284	+	28.1421i	−0.420541	+	1.09295i
$664$	1.65685			0.0642984
$665$		0			0
$666$	5.65685	−	16.0000i	0.219199	−	0.619987i
$667$		−	24.9706i		−	0.966864i
$668$	−9.31371	+	9.31371i	−0.360358	+	0.360358i
$669$	−27.3137	+	19.3137i	−1.05601	+	0.746711i
$670$	−2.24264	+	2.24264i	−0.0866408	+	0.0866408i
$671$	−25.6569	−	25.6569i	−0.990472	−	0.990472i
$672$	4.82843	+	0.828427i	0.186261	+	0.0319573i
$673$		−	45.1127i		−	1.73897i	−0.493962	−	0.869483i	$-0.664452\pi$
$673$		−	45.1127i		−	1.73897i	0.493962	−	0.869483i	$-0.335548\pi$
$674$	17.8995	+	17.8995i	0.689463	+	0.689463i
$675$	4.53553	+	2.53553i	0.174573	+	0.0975927i
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$		−	13.8995i		−	0.534201i	−0.963669	−	0.267100i	$-0.913934\pi$
$677$		−	13.8995i		−	0.534201i	0.963669	−	0.267100i	$-0.0860656\pi$
$678$	26.1421	−	18.4853i	1.00398	−	0.709923i
$679$	−34.3431			−1.31797
$680$	−4.82843			−0.185162
$681$	−16.1421	−	22.8284i	−0.618568	−	0.874787i
$682$	−12.4853	−	12.4853i	−0.478086	−	0.478086i
$683$	−23.4142	−	23.4142i	−0.895920	−	0.895920i	0.0991523	−	0.995072i	$-0.468387\pi$
$683$	−23.4142	−	23.4142i	−0.895920	−	0.895920i	−0.995072	+	0.0991523i	$0.968387\pi$
$684$		0			0
$685$	9.31371			0.355859
$686$	16.9706			0.647939
$687$	22.4853	+	31.7990i	0.857867	+	1.21321i
$688$			5.07107i			0.193333i
$689$	−6.65685	+	33.2843i	−0.253606	+	1.26803i
$690$	11.6569	+	2.00000i	0.443769	+	0.0761387i
$691$	8.14214	+	8.14214i	0.309741	+	0.309741i	0.844809	−	0.535068i	$-0.179714\pi$
$691$	8.14214	+	8.14214i	0.309741	+	0.309741i	−0.535068	+	0.844809i	$0.679714\pi$
$692$			14.5858i			0.554468i
$693$	22.6274	+	8.00000i	0.859544	+	0.303895i
$694$	22.4142	+	22.4142i	0.850832	+	0.850832i
$695$	5.17157	−	5.17157i	0.196169	−	0.196169i
$696$	3.65685	+	5.17157i	0.138613	+	0.196028i
$697$	−10.4853	+	10.4853i	−0.397158	+	0.397158i
$698$		−	26.0000i		−	0.984115i
$699$	0.0416306	−	0.242641i	0.00157461	−	0.00917751i
$700$	−2.00000	+	2.00000i	−0.0755929	+	0.0755929i
$701$	−0.142136			−0.00536839			−0.00268419	−	0.999996i	$-0.500854\pi$
$701$	−0.142136			−0.00536839			−0.00268419	+	0.999996i	$0.500854\pi$
$702$	1.46447	+	18.6777i	0.0552727	+	0.704943i
$703$		0			0
$704$	2.00000	−	2.00000i	0.0753778	−	0.0753778i
$705$	−0.828427	+	4.82843i	−0.0312004	+	0.181849i
$706$			5.51472i			0.207549i
$707$	−14.3431	+	14.3431i	−0.539430	+	0.539430i
$708$	−5.65685	−	8.00000i	−0.212598	−	0.300658i
$709$	−8.58579	+	8.58579i	−0.322446	+	0.322446i	−0.849705	−	0.527259i	$-0.823220\pi$
$709$	−8.58579	+	8.58579i	−0.322446	+	0.322446i	0.527259	+	0.849705i	$0.323220\pi$
$710$	10.4142	+	10.4142i	0.390838	+	0.390838i
$711$	24.9706	+	8.82843i	0.936469	+	0.331092i
$712$		−	3.75736i		−	0.140813i
$713$	30.1421	+	30.1421i	1.12883	+	1.12883i
$714$	23.3137	+	4.00000i	0.872494	+	0.149696i
$715$	10.0000	+	2.00000i	0.373979	+	0.0747958i
$716$		−	2.34315i		−	0.0875675i
$717$	−17.0711	−	24.1421i	−0.637531	−	0.901605i
$718$	−3.41421			−0.127417
$719$	5.51472			0.205664			0.102832	−	0.994699i	$-0.467210\pi$
$719$	5.51472			0.205664			0.102832	+	0.994699i	$0.467210\pi$
$720$	−2.70711	+	1.29289i	−0.100888	+	0.0481833i
$721$	29.6569	+	29.6569i	1.10448	+	1.10448i
$722$	−13.4350	−	13.4350i	−0.500000	−	0.500000i
$723$	3.75736	+	5.31371i	0.139738	+	0.197619i
$724$	−11.6569			−0.433224
$725$	−3.65685			−0.135812
$726$	−4.24264	+	3.00000i	−0.157459	+	0.111340i
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$	−10.0000	−	2.00000i	−0.370625	−	0.0741249i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	9.89949	+	9.89949i	0.366397	+	0.366397i
$731$			24.4853i			0.905621i
$732$	−21.8995	−	3.75736i	−0.809429	−	0.138876i
$733$	−15.5563	−	15.5563i	−0.574587	−	0.574587i	0.358820	−	0.933407i	$-0.383179\pi$
$733$	−15.5563	−	15.5563i	−0.574587	−	0.574587i	−0.933407	+	0.358820i	$0.883179\pi$
$734$	26.4853	−	26.4853i	0.977590	−	0.977590i
$735$	1.41421	−	1.00000i	0.0521641	−	0.0368856i
$736$	−4.82843	+	4.82843i	−0.177978	+	0.177978i
$737$		−	8.97056i		−	0.330435i
$738$	−3.07107	+	8.68629i	−0.113048	+	0.319747i
$739$	−5.65685	+	5.65685i	−0.208091	+	0.208091i	−0.803456	−	0.595365i	$-0.797008\pi$
$739$	−5.65685	+	5.65685i	−0.208091	+	0.208091i	0.595365	+	0.803456i	$0.297008\pi$
$740$	−5.65685			−0.207950
$741$		0			0
$742$	26.6274			0.977523
$743$	23.3137	−	23.3137i	0.855297	−	0.855297i	−0.135483	−	0.990780i	$-0.543259\pi$
$743$	23.3137	−	23.3137i	0.855297	−	0.855297i	0.990780	+	0.135483i	$0.0432585\pi$
$744$	−10.6569	−	1.82843i	−0.390699	−	0.0670334i
$745$			16.8284i			0.616546i
$746$	−20.3137	+	20.3137i	−0.743738	+	0.743738i
$747$	4.48528	−	2.14214i	0.164108	−	0.0783766i
$748$	9.65685	−	9.65685i	0.353090	−	0.353090i
$749$	25.1716	+	25.1716i	0.919749	+	0.919749i
$750$	0.292893	−	1.70711i	0.0106949	−	0.0623347i
$751$			21.6569i			0.790270i	0.918623	+	0.395135i	$0.129302\pi$
$751$			21.6569i			0.790270i	−0.918623	+	0.395135i	$0.870698\pi$
$752$	−2.00000	−	2.00000i	−0.0729325	−	0.0729325i
$753$	−1.45584	+	8.48528i	−0.0530539	+	0.309221i
$754$	−7.31371	−	10.9706i	−0.266350	−	0.399524i
$755$		−	17.5563i		−	0.638941i
$756$	14.1421	−	4.00000i	0.514344	−	0.145479i
$757$	−35.0711			−1.27468			−0.637340	−	0.770583i	$-0.719965\pi$
$757$	−35.0711			−1.27468			−0.637340	+	0.770583i	$0.719965\pi$
$758$	10.6274			0.386005
$759$	−27.3137	+	19.3137i	−0.991425	+	0.701043i
$760$		0			0
$761$	17.9706	+	17.9706i	0.651432	+	0.651432i	0.953338	−	0.301905i	$-0.0976227\pi$
$761$	17.9706	+	17.9706i	0.651432	+	0.651432i	−0.301905	+	0.953338i	$0.597623\pi$
$762$	2.34315	−	1.65685i	0.0848832	−	0.0600215i
$763$	−32.9706			−1.19361
$764$	12.8284			0.464116
$765$	−13.0711	+	6.24264i	−0.472585	+	0.225703i
$766$		−	5.65685i		−	0.204390i
$767$	11.3137	+	16.9706i	0.408514	+	0.612772i
$768$	0.292893	−	1.70711i	0.0105689	−	0.0615999i
$769$	7.97056	+	7.97056i	0.287426	+	0.287426i	0.836062	−	0.548636i	$-0.184853\pi$
$769$	7.97056	+	7.97056i	0.287426	+	0.287426i	−0.548636	+	0.836062i	$0.684853\pi$
$770$		−	8.00000i		−	0.288300i
$771$	7.75736	−	45.2132i	0.279374	−	1.62831i
$772$	1.07107	+	1.07107i	0.0385486	+	0.0385486i
$773$	−22.6274	+	22.6274i	−0.813852	+	0.813852i	−0.985209	−	0.171357i	$-0.945185\pi$
$773$	−22.6274	+	22.6274i	−0.813852	+	0.813852i	0.171357	+	0.985209i	$0.445185\pi$
$774$	6.55635	+	13.7279i	0.235663	+	0.493440i
$775$	4.41421	−	4.41421i	0.158563	−	0.158563i
$776$			12.1421i			0.435877i
$777$	27.3137	+	4.68629i	0.979874	+	0.168120i
$778$	−22.3848	+	22.3848i	−0.802533	+	0.802533i
$779$		0			0
$780$	5.70711	−	2.53553i	0.204347	−	0.0907867i
$781$	−41.6569			−1.49060
$782$	−23.3137	+	23.3137i	−0.833697	+	0.833697i
$783$	16.5858	+	9.27208i	0.592728	+	0.331357i
$784$			1.00000i			0.0357143i
$785$	14.6569	−	14.6569i	0.523126	−	0.523126i
$786$	16.0000	−	11.3137i	0.570701	−	0.403547i
$787$	14.0416	−	14.0416i	0.500530	−	0.500530i	−0.411073	−	0.911603i	$-0.634846\pi$
$787$	14.0416	−	14.0416i	0.500530	−	0.500530i	0.911603	+	0.411073i	$0.134846\pi$
$788$	9.17157	+	9.17157i	0.326724	+	0.326724i
$789$	12.8284	+	2.20101i	0.456704	+	0.0783580i
$790$		−	8.82843i		−	0.314101i
$791$	36.9706	+	36.9706i	1.31452	+	1.31452i
$792$	2.82843	−	8.00000i	0.100504	−	0.284268i
$793$	45.3553	+	9.07107i	1.61062	+	0.322123i
$794$		−	9.31371i		−	0.330531i
$795$	−13.3137	+	9.41421i	−0.472189	+	0.333888i
$796$	0.828427			0.0293628
$797$	−12.2426			−0.433657			−0.216828	−	0.976210i	$-0.569571\pi$
$797$	−12.2426			−0.433657			−0.216828	+	0.976210i	$0.569571\pi$
$798$		0			0
$799$	−9.65685	−	9.65685i	−0.341635	−	0.341635i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	−4.85786	−	10.1716i	−0.171644	−	0.359395i
$802$	−30.5858			−1.08002
$803$	−39.5980			−1.39738
$804$	−3.17157	−	4.48528i	−0.111853	−	0.158184i
$805$			19.3137i			0.680719i
$806$	22.0711	+	4.41421i	0.777420	+	0.155484i
$807$	−21.8995	−	3.75736i	−0.770899	−	0.132265i
$808$	5.07107	+	5.07107i	0.178400	+	0.178400i
$809$		−	8.00000i		−	0.281265i	−0.990062	−	0.140633i	$-0.955086\pi$
$809$		−	8.00000i		−	0.281265i	0.990062	−	0.140633i	$-0.0449136\pi$
$810$	−5.65685	+	7.00000i	−0.198762	+	0.245955i
$811$	16.4853	+	16.4853i	0.578877	+	0.578877i	0.934594	−	0.355717i	$-0.115763\pi$
$811$	16.4853	+	16.4853i	0.578877	+	0.578877i	−0.355717	+	0.934594i	$0.615763\pi$
$812$	−7.31371	+	7.31371i	−0.256661	+	0.256661i
$813$	−17.7574	−	25.1127i	−0.622778	−	0.880741i
$814$	11.3137	−	11.3137i	0.396545	−	0.396545i
$815$		−	6.34315i		−	0.222191i
$816$	1.41421	−	8.24264i	0.0495074	−	0.288550i
$817$		0			0
$818$	19.0711			0.666804
$819$	−29.6569	+	7.51472i	−1.03629	+	0.262586i
$820$	3.07107			0.107246
$821$	−4.92893	+	4.92893i	−0.172021	+	0.172021i	−0.787867	−	0.615846i	$-0.788814\pi$
$821$	−4.92893	+	4.92893i	−0.172021	+	0.172021i	0.615846	+	0.787867i	$0.288814\pi$
$822$	−2.72792	+	15.8995i	−0.0951472	+	0.554559i
$823$			52.2843i			1.82252i	0.411837	+	0.911258i	$0.364887\pi$
$823$			52.2843i			1.82252i	−0.411837	+	0.911258i	$0.635113\pi$
$824$	10.4853	−	10.4853i	0.365272	−	0.365272i
$825$	2.82843	+	4.00000i	0.0984732	+	0.139262i
$826$	11.3137	−	11.3137i	0.393654	−	0.393654i
$827$	29.5563	+	29.5563i	1.02777	+	1.02777i	0.999603	+	0.0281719i	$0.00896857\pi$
$827$	29.5563	+	29.5563i	1.02777	+	1.02777i	0.0281719	+	0.999603i	$0.491031\pi$
$828$	−6.82843	+	19.3137i	−0.237304	+	0.671198i
$829$			9.51472i			0.330460i	0.986255	+	0.165230i	$0.0528366\pi$
$829$			9.51472i			0.330460i	−0.986255	+	0.165230i	$0.947163\pi$
$830$	−1.17157	−	1.17157i	−0.0406659	−	0.0406659i
$831$	14.8995	+	2.55635i	0.516858	+	0.0886788i
$832$	−0.707107	+	3.53553i	−0.0245145	+	0.122573i
$833$			4.82843i			0.167295i
$834$	7.31371	+	10.3431i	0.253253	+	0.358154i
$835$	13.1716			0.455821
$836$		0			0
$837$	−31.2132	+	8.82843i	−1.07889	+	0.305155i
$838$	−3.65685	−	3.65685i	−0.126324	−	0.126324i
$839$	7.92893	+	7.92893i	0.273737	+	0.273737i	0.830603	−	0.556866i	$-0.187996\pi$
$839$	7.92893	+	7.92893i	0.273737	+	0.273737i	−0.556866	+	0.830603i	$0.687996\pi$
$840$	−2.82843	−	4.00000i	−0.0975900	−	0.138013i
$841$	15.6274			0.538876
$842$	−8.34315			−0.287524
$843$	−30.0000	+	21.2132i	−1.03325	+	0.730622i
$844$			16.9706i			0.584151i
$845$	−12.0208	+	4.94975i	−0.413529	+	0.170276i
$846$	−8.00000	−	2.82843i	−0.275046	−	0.0972433i
$847$	−6.00000	−	6.00000i	−0.206162	−	0.206162i
$848$		−	9.41421i		−	0.323285i
$849$	−16.6569	−	2.85786i	−0.571662	−	0.0980817i
$850$	3.41421	+	3.41421i	0.117107	+	0.117107i
$851$	−27.3137	+	27.3137i	−0.936302	+	0.936302i
$852$	−20.8284	+	14.7279i	−0.713570	+	0.504570i
$853$	−25.6569	+	25.6569i	−0.878474	+	0.878474i	−0.993377	−	0.114903i	$-0.963344\pi$
$853$	−25.6569	+	25.6569i	−0.878474	+	0.878474i	0.114903	+	0.993377i	$0.463344\pi$
$854$		−	36.2843i		−	1.24162i
$855$		0			0
$856$	8.89949	−	8.89949i	0.304178	−	0.304178i
$857$	52.6274			1.79772			0.898859	−	0.438238i	$-0.144397\pi$
$857$	52.6274			1.79772			0.898859	+	0.438238i	$0.144397\pi$
$858$	−6.34315	+	16.4853i	−0.216551	+	0.562798i
$859$	−22.8284			−0.778896			−0.389448	−	0.921048i	$-0.627334\pi$
$859$	−22.8284			−0.778896			−0.389448	+	0.921048i	$0.627334\pi$
$860$	3.58579	−	3.58579i	0.122274	−	0.122274i
$861$	−14.8284	−	2.54416i	−0.505351	−	0.0867046i
$862$		−	21.5563i		−	0.734212i
$863$	−5.79899	+	5.79899i	−0.197400	+	0.197400i	−0.798884	−	0.601485i	$-0.794576\pi$
$863$	−5.79899	+	5.79899i	−0.197400	+	0.197400i	0.601485	+	0.798884i	$0.294576\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	10.3137	−	10.3137i	0.350677	−	0.350677i
$866$	25.2132	+	25.2132i	0.856780	+	0.856780i
$867$	1.84924	−	10.7782i	0.0628036	−	0.366046i
$868$		−	17.6569i		−	0.599313i
$869$	17.6569	+	17.6569i	0.598968	+	0.598968i
$870$	1.07107	−	6.24264i	0.0363126	−	0.211645i
$871$	6.34315	+	9.51472i	0.214929	+	0.322394i
$872$			11.6569i			0.394751i
$873$	15.6985	+	32.8701i	0.531313	+	1.11248i
$874$		0			0
$875$	2.82843			0.0956183
$876$	−19.7990	+	14.0000i	−0.668946	+	0.473016i
$877$	8.72792	+	8.72792i	0.294721	+	0.294721i	0.838942	−	0.544221i	$-0.183175\pi$
$877$	8.72792	+	8.72792i	0.294721	+	0.294721i	−0.544221	+	0.838942i	$0.683175\pi$
$878$	−16.9706	−	16.9706i	−0.572729	−	0.572729i
$879$	32.9706	−	23.3137i	1.11207	−	0.786352i
$880$	−2.82843			−0.0953463
$881$	−9.31371			−0.313787			−0.156893	−	0.987616i	$-0.550148\pi$
$881$	−9.31371			−0.313787			−0.156893	+	0.987616i	$0.550148\pi$
$882$	1.29289	+	2.70711i	0.0435340	+	0.0911530i
$883$		−	48.5858i		−	1.63504i	−0.575899	−	0.817521i	$-0.695348\pi$
$883$		−	48.5858i		−	1.63504i	0.575899	−	0.817521i	$-0.304652\pi$
$884$	−3.41421	+	17.0711i	−0.114832	+	0.574162i
$885$	−1.65685	+	9.65685i	−0.0556945	+	0.324612i
$886$	16.8995	+	16.8995i	0.567750	+	0.567750i
$887$			38.1421i			1.28069i	0.768088	+	0.640344i	$0.221208\pi$
$887$			38.1421i			1.28069i	−0.768088	+	0.640344i	$0.778792\pi$
$888$	1.65685	−	9.65685i	0.0556004	−	0.324063i
$889$	3.31371	+	3.31371i	0.111138	+	0.111138i
$890$	−2.65685	+	2.65685i	−0.0890580	+	0.0890580i
$891$	−2.68629	−	25.3137i	−0.0899942	−	0.848041i
$892$	−13.6569	+	13.6569i	−0.457265	+	0.457265i
$893$		0			0
$894$	−28.7279	−	4.92893i	−0.960805	−	0.164848i
$895$	−1.65685	+	1.65685i	−0.0553825	+	0.0553825i
$896$	2.82843			0.0944911
$897$	15.3137	−	39.7990i	0.511310	−	1.32885i
$898$	−10.3848			−0.346544
$899$	16.1421	−	16.1421i	0.538370	−	0.538370i
$900$	2.82843	+	1.00000i	0.0942809	+	0.0333333i
$901$		−	45.4558i		−	1.51435i
$902$	−6.14214	+	6.14214i	−0.204511	+	0.204511i
$903$	−20.2843	+	14.3431i	−0.675018	+	0.477310i
$904$	13.0711	−	13.0711i	0.434737	−	0.434737i
$905$	8.24264	+	8.24264i	0.273995	+	0.273995i
$906$	29.9706	+	5.14214i	0.995705	+	0.170836i
$907$		−	4.10051i		−	0.136155i	−0.997680	−	0.0680775i	$-0.978313\pi$
$907$		−	4.10051i		−	0.136155i	0.997680	−	0.0680775i	$-0.0216865\pi$
$908$	−11.4142	−	11.4142i	−0.378794	−	0.378794i
$909$	20.2843	+	7.17157i	0.672787	+	0.237866i
$910$	5.65685	+	8.48528i	0.187523	+	0.281284i
$911$			29.1127i			0.964547i	0.876021	+	0.482273i	$0.160189\pi$
$911$			29.1127i			0.964547i	−0.876021	+	0.482273i	$0.839811\pi$
$912$		0			0
$913$	4.68629			0.155094
$914$	16.1421			0.533934
$915$	12.8284	+	18.1421i	0.424095	+	0.599761i
$916$	15.8995	+	15.8995i	0.525334	+	0.525334i
$917$	22.6274	+	22.6274i	0.747223	+	0.747223i
$918$	−6.82843	−	24.1421i	−0.225372	−	0.796809i
$919$	−18.3431			−0.605085			−0.302542	−	0.953136i	$-0.597835\pi$
$919$	−18.3431			−0.605085			−0.302542	+	0.953136i	$0.597835\pi$
$920$	6.82843			0.225127
$921$	12.1421	+	17.1716i	0.400097	+	0.565823i
$922$		−	12.3431i		−	0.406500i
$923$	44.1838	−	29.4558i	1.45433	−	0.969551i
$924$	13.6569	+	2.34315i	0.449278	+	0.0770838i
$925$	4.00000	+	4.00000i	0.131519	+	0.131519i
$926$		−	16.9706i		−	0.557687i
$927$	14.8284	−	41.9411i	0.487029	−	1.37753i
$928$	2.58579	+	2.58579i	0.0848826	+	0.0848826i
$929$	−25.0000	+	25.0000i	−0.820223	+	0.820223i	−0.986140	−	0.165916i	$-0.946942\pi$
$929$	−25.0000	+	25.0000i	−0.820223	+	0.820223i	0.165916	+	0.986140i	$0.446942\pi$
$930$	6.24264	+	8.82843i	0.204704	+	0.289496i
$931$		0			0
$932$		−	0.142136i		−	0.00465581i
$933$	8.97056	−	52.2843i	0.293683	−	1.71171i
$934$	1.58579	−	1.58579i	0.0518885	−	0.0518885i
$935$	−13.6569			−0.446627
$936$	2.65685	+	10.4853i	0.0868420	+	0.342722i
$937$	−11.9411			−0.390100			−0.195050	−	0.980793i	$-0.562487\pi$
$937$	−11.9411			−0.390100			−0.195050	+	0.980793i	$0.562487\pi$
$938$	6.34315	−	6.34315i	0.207111	−	0.207111i
$939$	5.55635	−	32.3848i	0.181325	−	1.05684i
$940$			2.82843i			0.0922531i
$941$	22.7279	−	22.7279i	0.740909	−	0.740909i	−0.231844	−	0.972753i	$-0.574476\pi$
$941$	22.7279	−	22.7279i	0.740909	−	0.740909i	0.972753	+	0.231844i	$0.0744759\pi$
$942$	20.7279	+	29.3137i	0.675352	+	0.955092i
$943$	14.8284	−	14.8284i	0.482880	−	0.482880i
$944$	−4.00000	−	4.00000i	−0.130189	−	0.130189i
$945$	−12.8284	−	7.17157i	−0.417309	−	0.233291i
$946$			14.3431i			0.466336i
$947$	1.75736	+	1.75736i	0.0571065	+	0.0571065i	0.735083	−	0.677977i	$-0.237143\pi$
$947$	1.75736	+	1.75736i	0.0571065	+	0.0571065i	−0.677977	+	0.735083i	$0.737143\pi$
$948$	15.0711	+	2.58579i	0.489486	+	0.0839824i
$949$	42.0000	−	28.0000i	1.36338	−	0.908918i
$950$		0			0
$951$	24.0000	+	33.9411i	0.778253	+	1.10062i
$952$	13.6569			0.442621
$953$	2.28427			0.0739948			0.0369974	−	0.999315i	$-0.488221\pi$
$953$	2.28427			0.0739948			0.0369974	+	0.999315i	$0.488221\pi$
$954$	−12.1716	−	25.4853i	−0.394069	−	0.825116i
$955$	−9.07107	−	9.07107i	−0.293533	−	0.293533i
$956$	−12.0711	−	12.0711i	−0.390406	−	0.390406i
$957$	10.3431	+	14.6274i	0.334346	+	0.472837i
$958$	−3.41421			−0.110308
$959$	−26.3431			−0.850665
$960$	−1.41421	+	1.00000i	−0.0456435	+	0.0322749i
$961$			7.97056i			0.257115i
$962$	−4.00000	+	20.0000i	−0.128965	+	0.644826i
$963$	12.5858	−	35.5980i	0.405571	−	1.14713i
$964$	2.65685	+	2.65685i	0.0855715	+	0.0855715i
$965$		−	1.51472i		−	0.0487605i
$966$	−32.9706	−	5.65685i	−1.06081	−	0.182006i
$967$	−24.2843	−	24.2843i	−0.780930	−	0.780930i	0.199058	−	0.979988i	$-0.436212\pi$
$967$	−24.2843	−	24.2843i	−0.780930	−	0.780930i	−0.979988	+	0.199058i	$0.936212\pi$
$968$	−2.12132	+	2.12132i	−0.0681818	+	0.0681818i
$969$		0			0
$970$	8.58579	−	8.58579i	0.275673	−	0.275673i
$971$		−	39.1127i		−	1.25519i	−0.778542	−	0.627593i	$-0.784040\pi$
$971$		−	39.1127i		−	1.25519i	0.778542	−	0.627593i	$-0.215960\pi$
$972$	−10.2929	−	11.7071i	−0.330145	−	0.375506i
$973$	−14.6274	+	14.6274i	−0.468933	+	0.468933i
$974$	33.1716			1.06289
$975$	−5.82843	−	2.24264i	−0.186659	−	0.0718220i
$976$	−12.8284			−0.410628
$977$	0.242641	−	0.242641i	0.00776276	−	0.00776276i	−0.703215	−	0.710978i	$-0.748253\pi$
$977$	0.242641	−	0.242641i	0.00776276	−	0.00776276i	0.710978	+	0.703215i	$0.248253\pi$
$978$	10.8284	+	1.85786i	0.346255	+	0.0594080i
$979$		−	10.6274i		−	0.339654i
$980$	0.707107	−	0.707107i	0.0225877	−	0.0225877i
$981$	15.0711	+	31.5563i	0.481182	+	1.00752i
$982$	−6.97056	+	6.97056i	−0.222440	+	0.222440i
$983$	−19.4558	−	19.4558i	−0.620545	−	0.620545i	0.325126	−	0.945671i	$-0.394593\pi$
$983$	−19.4558	−	19.4558i	−0.620545	−	0.620545i	−0.945671	+	0.325126i	$0.894593\pi$
$984$	−0.899495	+	5.24264i	−0.0286749	+	0.167129i
$985$		−	12.9706i		−	0.413276i
$986$	12.4853	+	12.4853i	0.397612	+	0.397612i
$987$	2.34315	−	13.6569i	0.0745832	−	0.434702i
$988$		0			0
$989$		−	34.6274i		−	1.10109i
$990$	−7.65685	+	3.65685i	−0.243351	+	0.116222i
$991$	12.1421			0.385708			0.192854	−	0.981227i	$-0.438226\pi$
$991$	12.1421			0.385708			0.192854	+	0.981227i	$0.438226\pi$
$992$	−6.24264			−0.198204
$993$	−12.0000	+	8.48528i	−0.380808	+	0.269272i
$994$	−29.4558	−	29.4558i	−0.934283	−	0.934283i
$995$	−0.585786	−	0.585786i	−0.0185707	−	0.0185707i
$996$	2.34315	−	1.65685i	0.0742454	−	0.0524994i
$997$	40.0416			1.26813			0.634066	−	0.773279i	$-0.281385\pi$
$997$	40.0416			1.26813			0.634066	+	0.773279i	$0.281385\pi$
$998$	31.7990			1.00658
$999$	−8.00000	−	28.2843i	−0.253109	−	0.894875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.p.e.281.2	yes	4
3.2	odd	2		390.2.p.f.281.1	yes	4
13.5	odd	4		390.2.p.f.161.1	yes	4
39.5	even	4	inner	390.2.p.e.161.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.e.161.2	✓	4	39.5	even	4	inner
390.2.p.e.281.2	yes	4	1.1	even	1	trivial
390.2.p.f.161.1	yes	4	13.5	odd	4
390.2.p.f.281.1	yes	4	3.2	odd	2

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +1.00000i q^{10} +(-2.00000 - 2.00000i) q^{11} +(-1.70711 - 0.292893i) q^{12} +(3.53553 + 0.707107i) q^{13} -2.82843i q^{14} +(1.00000 + 1.41421i) q^{15} -1.00000 q^{16} -4.82843 q^{17} +(-2.70711 + 1.29289i) q^{18} +(0.707107 + 0.707107i) q^{20} +(-2.82843 - 4.00000i) q^{21} -2.82843 q^{22} +6.82843 q^{23} +(-1.41421 + 1.00000i) q^{24} -1.00000i q^{25} +(3.00000 - 2.00000i) q^{26} +(-2.53553 + 4.53553i) q^{27} +(-2.00000 - 2.00000i) q^{28} -3.65685i q^{29} +(1.70711 + 0.292893i) q^{30} +(4.41421 + 4.41421i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.00000 + 2.82843i) q^{33} +(-3.41421 + 3.41421i) q^{34} +2.82843i q^{35} +(-1.00000 + 2.82843i) q^{36} +(-4.00000 + 4.00000i) q^{37} +(2.24264 - 5.82843i) q^{39} +1.00000 q^{40} +(2.17157 - 2.17157i) q^{41} +(-4.82843 - 0.828427i) q^{42} -5.07107i q^{43} +(-2.00000 + 2.00000i) q^{44} +(2.70711 - 1.29289i) q^{45} +(4.82843 - 4.82843i) q^{46} +(2.00000 + 2.00000i) q^{47} +(-0.292893 + 1.70711i) q^{48} -1.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(-1.41421 + 8.24264i) q^{51} +(0.707107 - 3.53553i) q^{52} +9.41421i q^{53} +(1.41421 + 5.00000i) q^{54} +2.82843 q^{55} -2.82843 q^{56} +(-2.58579 - 2.58579i) q^{58} +(4.00000 + 4.00000i) q^{59} +(1.41421 - 1.00000i) q^{60} +12.8284 q^{61} +6.24264 q^{62} +(-7.65685 + 3.65685i) q^{63} +1.00000i q^{64} +(-3.00000 + 2.00000i) q^{65} +(-0.828427 + 4.82843i) q^{66} +(2.24264 + 2.24264i) q^{67} +4.82843i q^{68} +(2.00000 - 11.6569i) q^{69} +(2.00000 + 2.00000i) q^{70} +(10.4142 - 10.4142i) q^{71} +(1.29289 + 2.70711i) q^{72} +(9.89949 - 9.89949i) q^{73} +5.65685i q^{74} +(-1.70711 - 0.292893i) q^{75} -8.00000 q^{77} +(-2.53553 - 5.70711i) q^{78} -8.82843 q^{79} +(0.707107 - 0.707107i) q^{80} +(7.00000 + 5.65685i) q^{81} -3.07107i q^{82} +(-1.17157 + 1.17157i) q^{83} +(-4.00000 + 2.82843i) q^{84} +(3.41421 - 3.41421i) q^{85} +(-3.58579 - 3.58579i) q^{86} +(-6.24264 - 1.07107i) q^{87} +2.82843i q^{88} +(2.65685 + 2.65685i) q^{89} +(1.00000 - 2.82843i) q^{90} +(8.48528 - 5.65685i) q^{91} -6.82843i q^{92} +(8.82843 - 6.24264i) q^{93} +2.82843 q^{94} +(1.00000 + 1.41421i) q^{96} +(-8.58579 - 8.58579i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(3.65685 + 7.65685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^6 + 8 * q^7	\( 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7} - 8 q^{11} - 4 q^{12} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 8 q^{18} + 16 q^{23} + 12 q^{26} + 4 q^{27} - 8 q^{28} + 4 q^{30} + 12 q^{31} - 16 q^{33} - 8 q^{34} - 4 q^{36} - 16 q^{37} - 8 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} - 8 q^{44} + 8 q^{45} + 8 q^{46} + 8 q^{47} - 4 q^{48} - 16 q^{58} + 16 q^{59} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 12 q^{65} + 8 q^{66} - 8 q^{67} + 8 q^{69} + 8 q^{70} + 36 q^{71} + 8 q^{72} - 4 q^{75} - 32 q^{77} + 4 q^{78} - 24 q^{79} + 28 q^{81} - 16 q^{83} - 16 q^{84} + 8 q^{85} - 20 q^{86} - 8 q^{87} - 12 q^{89} + 4 q^{90} + 24 q^{93} + 4 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 + 8 * q^7 - 8 * q^11 - 4 * q^12 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 8 * q^18 + 16 * q^23 + 12 * q^26 + 4 * q^27 - 8 * q^28 + 4 * q^30 + 12 * q^31 - 16 * q^33 - 8 * q^34 - 4 * q^36 - 16 * q^37 - 8 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 - 8 * q^44 + 8 * q^45 + 8 * q^46 + 8 * q^47 - 4 * q^48 - 16 * q^58 + 16 * q^59 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 12 * q^65 + 8 * q^66 - 8 * q^67 + 8 * q^69 + 8 * q^70 + 36 * q^71 + 8 * q^72 - 4 * q^75 - 32 * q^77 + 4 * q^78 - 24 * q^79 + 28 * q^81 - 16 * q^83 - 16 * q^84 + 8 * q^85 - 20 * q^86 - 8 * q^87 - 12 * q^89 + 4 * q^90 + 24 * q^93 + 4 * q^96 - 40 * q^97 - 8 * q^99

Introduction

L-functions

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Database

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