LMFDB - Embedded newform 510.2.m.a.259.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(259,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("510.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.m (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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.3
Root			$0.360409i$ of defining polynomial
Character	$\chi$	$=$	510.259
Dual form			510.2.m.a.319.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.292893 - 2.21680i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.56350 + 2.56350i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.292893 - 2.21680i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.56350 + 2.56350i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(0.292893 + 2.21680i) q^{10} +(-3.41421 - 3.41421i) q^{11} +(0.707107 + 0.707107i) q^{12} -4.05894i q^{13} +(2.56350 - 2.56350i) q^{14} +(1.36041 - 1.77462i) q^{15} +1.00000 q^{16} +(1.65898 - 3.77462i) q^{17} -1.00000i q^{18} -2.82843i q^{19} +(-0.292893 - 2.21680i) q^{20} -3.62534 q^{21} +(3.41421 + 3.41421i) q^{22} +(-2.33812 + 2.33812i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.82843 + 1.29857i) q^{25} +4.05894i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.56350 + 2.56350i) q^{28} +(4.13503 - 4.13503i) q^{29} +(-1.36041 + 1.77462i) q^{30} +(-3.75234 + 3.75234i) q^{31} -1.00000 q^{32} -4.82843i q^{33} +(-1.65898 + 3.77462i) q^{34} +(6.43361 + 4.93194i) q^{35} +1.00000i q^{36} +(-0.422246 - 0.422246i) q^{37} +2.82843i q^{38} +(2.87011 - 2.87011i) q^{39} +(0.292893 + 2.21680i) q^{40} +(-4.18884 - 4.18884i) q^{41} +3.62534 q^{42} -4.93194 q^{43} +(-3.41421 - 3.41421i) q^{44} +(2.21680 - 0.292893i) q^{45} +(2.33812 - 2.33812i) q^{46} -11.8193i q^{47} +(0.707107 + 0.707107i) q^{48} -6.14306i q^{49} +(4.82843 - 1.29857i) q^{50} +(3.84214 - 1.49598i) q^{51} -4.05894i q^{52} +11.2895 q^{53} +(0.707107 - 0.707107i) q^{54} +(-6.56864 + 8.56864i) q^{55} +(2.56350 - 2.56350i) q^{56} +(2.00000 - 2.00000i) q^{57} +(-4.13503 + 4.13503i) q^{58} -1.65276i q^{59} +(1.36041 - 1.77462i) q^{60} +(3.62534 + 3.62534i) q^{61} +(3.75234 - 3.75234i) q^{62} +(-2.56350 - 2.56350i) q^{63} +1.00000 q^{64} +(-8.99787 + 1.18884i) q^{65} +4.82843i q^{66} -6.58880i q^{67} +(1.65898 - 3.77462i) q^{68} -3.30661 q^{69} +(-6.43361 - 4.93194i) q^{70} +(-10.9097 + 10.9097i) q^{71} -1.00000i q^{72} +(5.17671 + 5.17671i) q^{73} +(0.422246 + 0.422246i) q^{74} +(-4.33244 - 2.49598i) q^{75} -2.82843i q^{76} +17.5047 q^{77} +(-2.87011 + 2.87011i) q^{78} +(1.90452 + 1.90452i) q^{79} +(-0.292893 - 2.21680i) q^{80} -1.00000 q^{81} +(4.18884 + 4.18884i) q^{82} -7.42557 q^{83} -3.62534 q^{84} +(-8.85350 - 2.57207i) q^{85} +4.93194 q^{86} +5.84782 q^{87} +(3.41421 + 3.41421i) q^{88} -10.1179 q^{89} +(-2.21680 + 0.292893i) q^{90} +(10.4051 + 10.4051i) q^{91} +(-2.33812 + 2.33812i) q^{92} -5.30661 q^{93} +11.8193i q^{94} +(-6.27006 + 0.828427i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-7.36342 - 7.36342i) q^{97} +6.14306i q^{98} +(3.41421 - 3.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} + 8 q^{10} - 16 q^{11} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} - 8 q^{20} - 16 q^{21} + 16 q^{22} + 16 q^{23} - 16 q^{25} - 4 q^{28} + 8 q^{29} - 4 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 16 q^{35} + 4 q^{39} + 8 q^{40} - 4 q^{41} + 16 q^{42} - 24 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{50} + 16 q^{53} + 8 q^{55} + 4 q^{56} + 16 q^{57} - 8 q^{58} + 4 q^{60} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} - 44 q^{65} - 4 q^{68} - 24 q^{69} - 16 q^{70} - 44 q^{71} + 20 q^{73} - 16 q^{75} + 48 q^{77} - 4 q^{78} + 16 q^{79} - 8 q^{80} - 8 q^{81} + 4 q^{82} - 16 q^{83} - 16 q^{84} - 8 q^{85} + 24 q^{86} + 16 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 40 q^{93} + 20 q^{97} + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 + 8 * q^10 - 16 * q^11 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 - 8 * q^20 - 16 * q^21 + 16 * q^22 + 16 * q^23 - 16 * q^25 - 4 * q^28 + 8 * q^29 - 4 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 16 * q^35 + 4 * q^39 + 8 * q^40 - 4 * q^41 + 16 * q^42 - 24 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^50 + 16 * q^53 + 8 * q^55 + 4 * q^56 + 16 * q^57 - 8 * q^58 + 4 * q^60 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 - 44 * q^65 - 4 * q^68 - 24 * q^69 - 16 * q^70 - 44 * q^71 + 20 * q^73 - 16 * q^75 + 48 * q^77 - 4 * q^78 + 16 * q^79 - 8 * q^80 - 8 * q^81 + 4 * q^82 - 16 * q^83 - 16 * q^84 - 8 * q^85 + 24 * q^86 + 16 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 40 * q^93 + 20 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−0.292893	−	2.21680i	−0.130986	−	0.991384i
$5$	−0.292893	−	2.21680i	−0.130986	−	0.991384i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−2.56350	+	2.56350i	−0.968912	+	0.968912i	−0.999531	−	0.0306192i	$-0.990252\pi$
$7$	−2.56350	+	2.56350i	−0.968912	+	0.968912i	0.0306192	+	0.999531i	$0.490252\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	0.292893	+	2.21680i	0.0926210	+	0.701015i
$11$	−3.41421	−	3.41421i	−1.02942	−	1.02942i	−0.999554	−	0.0298703i	$-0.990491\pi$
$11$	−3.41421	−	3.41421i	−1.02942	−	1.02942i	−0.0298703	−	0.999554i	$-0.509509\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$		−	4.05894i		−	1.12575i	−0.826543	−	0.562874i	$-0.809696\pi$
$13$		−	4.05894i		−	1.12575i	0.826543	−	0.562874i	$-0.190304\pi$
$14$	2.56350	−	2.56350i	0.685124	−	0.685124i
$15$	1.36041	−	1.77462i	0.351256	−	0.458206i
$16$	1.00000			0.250000
$17$	1.65898	−	3.77462i	0.402362	−	0.915481i
$17$	1.65898	−	3.77462i	0.402362	−	0.915481i
$18$		−	1.00000i		−	0.235702i
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$	−0.292893	−	2.21680i	−0.0654929	−	0.495692i
$21$	−3.62534			−0.791113
$22$	3.41421	+	3.41421i	0.727913	+	0.727913i
$23$	−2.33812	+	2.33812i	−0.487532	+	0.487532i	−0.907527	−	0.419994i	$-0.862032\pi$
$23$	−2.33812	+	2.33812i	−0.487532	+	0.487532i	0.419994	+	0.907527i	$0.362032\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−4.82843	+	1.29857i	−0.965685	+	0.259715i
$26$			4.05894i			0.796024i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.56350	+	2.56350i	−0.484456	+	0.484456i
$29$	4.13503	−	4.13503i	0.767856	−	0.767856i	−0.209873	−	0.977729i	$-0.567305\pi$
$29$	4.13503	−	4.13503i	0.767856	−	0.767856i	0.977729	+	0.209873i	$0.0673049\pi$
$30$	−1.36041	+	1.77462i	−0.248376	+	0.324000i
$31$	−3.75234	+	3.75234i	−0.673940	+	0.673940i	−0.958622	−	0.284682i	$-0.908112\pi$
$31$	−3.75234	+	3.75234i	−0.673940	+	0.673940i	0.284682	+	0.958622i	$0.408112\pi$
$32$	−1.00000			−0.176777
$33$		−	4.82843i		−	0.840521i
$34$	−1.65898	+	3.77462i	−0.284513	+	0.647342i
$35$	6.43361	+	4.93194i	1.08748	+	0.833650i
$36$			1.00000i			0.166667i
$37$	−0.422246	−	0.422246i	−0.0694168	−	0.0694168i	0.671546	−	0.740963i	$-0.265631\pi$
$37$	−0.422246	−	0.422246i	−0.0694168	−	0.0694168i	−0.740963	+	0.671546i	$0.765631\pi$
$38$			2.82843i			0.458831i
$39$	2.87011	−	2.87011i	0.459585	−	0.459585i
$40$	0.292893	+	2.21680i	0.0463105	+	0.350507i
$41$	−4.18884	−	4.18884i	−0.654186	−	0.654186i	0.299812	−	0.953998i	$-0.403076\pi$
$41$	−4.18884	−	4.18884i	−0.654186	−	0.654186i	−0.953998	+	0.299812i	$0.903076\pi$
$42$	3.62534			0.559402
$43$	−4.93194			−0.752114			−0.376057	−	0.926597i	$-0.622720\pi$
$43$	−4.93194			−0.752114			−0.376057	+	0.926597i	$0.622720\pi$
$44$	−3.41421	−	3.41421i	−0.514712	−	0.514712i
$45$	2.21680	−	0.292893i	0.330461	−	0.0436619i
$46$	2.33812	−	2.33812i	0.344737	−	0.344737i
$47$		−	11.8193i		−	1.72402i	−0.506888	−	0.862012i	$-0.669204\pi$
$47$		−	11.8193i		−	1.72402i	0.506888	−	0.862012i	$-0.330796\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	6.14306i		−	0.877581i
$50$	4.82843	−	1.29857i	0.682843	−	0.183646i
$51$	3.84214	−	1.49598i	0.538007	−	0.209480i
$52$		−	4.05894i		−	0.562874i
$53$	11.2895			1.55073			0.775363	−	0.631516i	$-0.217567\pi$
$53$	11.2895			1.55073			0.775363	+	0.631516i	$0.217567\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−6.56864	+	8.56864i	−0.885715	+	1.15539i
$56$	2.56350	−	2.56350i	0.342562	−	0.342562i
$57$	2.00000	−	2.00000i	0.264906	−	0.264906i
$58$	−4.13503	+	4.13503i	−0.542956	+	0.542956i
$59$		−	1.65276i		−	0.215171i	−0.994196	−	0.107586i	$-0.965688\pi$
$59$		−	1.65276i		−	0.215171i	0.994196	−	0.107586i	$-0.0343119\pi$
$60$	1.36041	−	1.77462i	0.175628	−	0.229103i
$61$	3.62534	+	3.62534i	0.464177	+	0.464177i	0.900022	−	0.435845i	$-0.143550\pi$
$61$	3.62534	+	3.62534i	0.464177	+	0.464177i	−0.435845	+	0.900022i	$0.643550\pi$
$62$	3.75234	−	3.75234i	0.476547	−	0.476547i
$63$	−2.56350	−	2.56350i	−0.322971	−	0.322971i
$64$	1.00000			0.125000
$65$	−8.99787	+	1.18884i	−1.11605	+	0.147457i
$66$			4.82843i			0.594338i
$67$		−	6.58880i		−	0.804950i	−0.915431	−	0.402475i	$-0.868150\pi$
$67$		−	6.58880i		−	0.804950i	0.915431	−	0.402475i	$-0.131850\pi$
$68$	1.65898	−	3.77462i	0.201181	−	0.457740i
$69$	−3.30661			−0.398068
$70$	−6.43361	−	4.93194i	−0.768963	−	0.589480i
$71$	−10.9097	+	10.9097i	−1.29474	+	1.29474i	−0.362916	+	0.931822i	$0.618219\pi$
$71$	−10.9097	+	10.9097i	−1.29474	+	1.29474i	−0.931822	+	0.362916i	$0.881781\pi$
$72$		−	1.00000i		−	0.117851i
$73$	5.17671	+	5.17671i	0.605888	+	0.605888i	0.941869	−	0.335981i	$-0.109068\pi$
$73$	5.17671	+	5.17671i	0.605888	+	0.605888i	−0.335981	+	0.941869i	$0.609068\pi$
$74$	0.422246	+	0.422246i	0.0490851	+	0.0490851i
$75$	−4.33244	−	2.49598i	−0.500267	−	0.288211i
$76$		−	2.82843i		−	0.324443i
$77$	17.5047			1.99484
$78$	−2.87011	+	2.87011i	−0.324975	+	0.324975i
$79$	1.90452	+	1.90452i	0.214275	+	0.214275i	0.806081	−	0.591806i	$-0.201585\pi$
$79$	1.90452	+	1.90452i	0.214275	+	0.214275i	−0.591806	+	0.806081i	$0.701585\pi$
$80$	−0.292893	−	2.21680i	−0.0327465	−	0.247846i
$81$	−1.00000			−0.111111
$82$	4.18884	+	4.18884i	0.462580	+	0.462580i
$83$	−7.42557			−0.815063			−0.407531	−	0.913191i	$-0.633610\pi$
$83$	−7.42557			−0.815063			−0.407531	+	0.913191i	$0.633610\pi$
$84$	−3.62534			−0.395557
$85$	−8.85350	−	2.57207i	−0.960297	−	0.278981i
$86$	4.93194			0.531825
$87$	5.84782			0.626952
$88$	3.41421	+	3.41421i	0.363956	+	0.363956i
$89$	−10.1179			−1.07249			−0.536247	−	0.844061i	$-0.680158\pi$
$89$	−10.1179			−1.07249			−0.536247	+	0.844061i	$0.680158\pi$
$90$	−2.21680	+	0.292893i	−0.233672	+	0.0308737i
$91$	10.4051	+	10.4051i	1.09075	+	1.09075i
$92$	−2.33812	+	2.33812i	−0.243766	+	0.243766i
$93$	−5.30661			−0.550269
$94$			11.8193i			1.21907i
$95$	−6.27006	+	0.828427i	−0.643295	+	0.0849948i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−7.36342	−	7.36342i	−0.747642	−	0.747642i	0.226394	−	0.974036i	$-0.427306\pi$
$97$	−7.36342	−	7.36342i	−0.747642	−	0.747642i	−0.974036	+	0.226394i	$0.927306\pi$
$98$			6.14306i			0.620543i
$99$	3.41421	−	3.41421i	0.343141	−	0.343141i
$100$	−4.82843	+	1.29857i	−0.482843	+	0.129857i
$101$	−5.10684			−0.508150			−0.254075	−	0.967185i	$-0.581771\pi$
$101$	−5.10684			−0.508150			−0.254075	+	0.967185i	$0.581771\pi$
$102$	−3.84214	+	1.49598i	−0.380428	+	0.148124i
$103$		−	4.78811i		−	0.471787i	−0.971779	−	0.235893i	$-0.924198\pi$
$103$		−	4.78811i		−	0.471787i	0.971779	−	0.235893i	$-0.0758016\pi$
$104$			4.05894i			0.398012i
$105$	1.06184	+	8.03666i	0.103625	+	0.784297i
$106$	−11.2895			−1.09653
$107$	8.77249	+	8.77249i	0.848069	+	0.848069i	0.989892	−	0.141823i	$-0.0452964\pi$
$107$	8.77249	+	8.77249i	0.848069	+	0.848069i	−0.141823	+	0.989892i	$0.545296\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	12.1666	+	12.1666i	1.16534	+	1.16534i	0.983288	+	0.182056i	$0.0582752\pi$
$109$	12.1666	+	12.1666i	1.16534	+	1.16534i	0.182056	+	0.983288i	$0.441725\pi$
$110$	6.56864	−	8.56864i	0.626295	−	0.816988i
$111$		−	0.597146i		−	0.0566786i
$112$	−2.56350	+	2.56350i	−0.242228	+	0.242228i
$113$	4.52182	−	4.52182i	0.425377	−	0.425377i	−0.461673	−	0.887050i	$-0.652751\pi$
$113$	4.52182	−	4.52182i	0.425377	−	0.425377i	0.887050	+	0.461673i	$0.152751\pi$
$114$	−2.00000	+	2.00000i	−0.187317	+	0.187317i
$115$	5.86798	+	4.49834i	0.547192	+	0.419472i
$116$	4.13503	−	4.13503i	0.383928	−	0.383928i
$117$	4.05894			0.375249
$118$			1.65276i			0.152149i
$119$	5.42344	+	13.9290i	0.497166	+	1.27687i
$120$	−1.36041	+	1.77462i	−0.124188	+	0.162000i
$121$			12.3137i			1.11943i
$122$	−3.62534	−	3.62534i	−0.328223	−	0.328223i
$123$		−	5.92391i		−	0.534141i
$124$	−3.75234	+	3.75234i	−0.336970	+	0.336970i
$125$	4.29289	+	10.3233i	0.383968	+	0.923346i
$126$	2.56350	+	2.56350i	0.228375	+	0.228375i
$127$	20.1524			1.78824			0.894119	−	0.447830i	$-0.147803\pi$
$127$	20.1524			1.78824			0.894119	+	0.447830i	$0.147803\pi$
$128$	−1.00000			−0.0883883
$129$	−3.48741	−	3.48741i	−0.307049	−	0.307049i
$130$	8.99787	−	1.18884i	0.789166	−	0.104268i
$131$	−6.83569	+	6.83569i	−0.597237	+	0.597237i	−0.939576	−	0.342339i	$-0.888781\pi$
$131$	−6.83569	+	6.83569i	−0.597237	+	0.597237i	0.342339	+	0.939576i	$0.388781\pi$
$132$		−	4.82843i		−	0.420261i
$133$	7.25067	+	7.25067i	0.628713	+	0.628713i
$134$			6.58880i			0.569185i
$135$	1.77462	+	1.36041i	0.152735	+	0.117085i
$136$	−1.65898	+	3.77462i	−0.142257	+	0.323671i
$137$			12.1464i			1.03774i	0.854854	+	0.518868i	$0.173646\pi$
$137$			12.1464i			1.03774i	−0.854854	+	0.518868i	$0.826354\pi$
$138$	3.30661			0.281477
$139$	15.7919	−	15.7919i	1.33945	−	1.33945i	0.442859	−	0.896591i	$-0.353964\pi$
$139$	15.7919	−	15.7919i	1.33945	−	1.33945i	0.896591	−	0.442859i	$-0.146036\pi$
$140$	6.43361	+	4.93194i	0.543739	+	0.416825i
$141$	8.35751	−	8.35751i	0.703830	−	0.703830i
$142$	10.9097	−	10.9097i	0.915518	−	0.915518i
$143$	−13.8581	+	13.8581i	−1.15887	+	1.15887i
$144$			1.00000i			0.0833333i
$145$	−10.3777	−	7.95543i	−0.861819	−	0.660662i
$146$	−5.17671	−	5.17671i	−0.428428	−	0.428428i
$147$	4.34380	−	4.34380i	0.358271	−	0.358271i
$148$	−0.422246	−	0.422246i	−0.0347084	−	0.0347084i
$149$	−2.89316			−0.237017			−0.118508	−	0.992953i	$-0.537811\pi$
$149$	−2.89316			−0.237017			−0.118508	+	0.992953i	$0.537811\pi$
$150$	4.33244	+	2.49598i	0.353743	+	0.203796i
$151$		−	7.26312i		−	0.591064i	−0.955333	−	0.295532i	$-0.904503\pi$
$151$		−	7.26312i		−	0.591064i	0.955333	−	0.295532i	$-0.0954969\pi$
$152$			2.82843i			0.229416i
$153$	3.77462	+	1.65898i	0.305160	+	0.134121i
$154$	−17.5047			−1.41057
$155$	9.41722	+	7.21916i	0.756410	+	0.579856i
$156$	2.87011	−	2.87011i	0.229792	−	0.229792i
$157$			4.17081i			0.332867i	0.986053	+	0.166433i	$0.0532250\pi$
$157$			4.17081i			0.332867i	−0.986053	+	0.166433i	$0.946775\pi$
$158$	−1.90452	−	1.90452i	−0.151515	−	0.151515i
$159$	7.98285	+	7.98285i	0.633081	+	0.633081i
$160$	0.292893	+	2.21680i	0.0231552	+	0.175254i
$161$		−	11.9876i		−	0.944752i
$162$	1.00000			0.0785674
$163$	−10.5888	+	10.5888i	−0.829378	+	0.829378i	−0.987431	−	0.158052i	$-0.949479\pi$
$163$	−10.5888	+	10.5888i	−0.829378	+	0.829378i	0.158052	+	0.987431i	$0.449479\pi$
$164$	−4.18884	−	4.18884i	−0.327093	−	0.327093i
$165$	−10.7037	+	1.41421i	−0.833280	+	0.110096i
$166$	7.42557			0.576336
$167$	12.0396	+	12.0396i	0.931648	+	0.931648i	0.997809	−	0.0661606i	$-0.0210750\pi$
$167$	12.0396	+	12.0396i	0.931648	+	0.931648i	−0.0661606	+	0.997809i	$0.521075\pi$
$168$	3.62534			0.279701
$169$	−3.47501			−0.267308
$170$	8.85350	+	2.57207i	0.679032	+	0.197269i
$171$	2.82843			0.216295
$172$	−4.93194			−0.376057
$173$	−16.0703	−	16.0703i	−1.22180	−	1.22180i	−0.966991	−	0.254812i	$-0.917987\pi$
$173$	−16.0703	−	16.0703i	−1.22180	−	1.22180i	−0.254812	−	0.966991i	$-0.582013\pi$
$174$	−5.84782			−0.443322
$175$	9.04878	−	15.7066i	0.684024	−	1.18730i
$176$	−3.41421	−	3.41421i	−0.257356	−	0.257356i
$177$	1.16868	−	1.16868i	0.0878432	−	0.0878432i
$178$	10.1179			0.758367
$179$		−	14.2559i		−	1.06554i	−0.846261	−	0.532769i	$-0.821151\pi$
$179$		−	14.2559i		−	1.06554i	0.846261	−	0.532769i	$-0.178849\pi$
$180$	2.21680	−	0.292893i	0.165231	−	0.0218310i
$181$	−5.20201	−	5.20201i	−0.386662	−	0.386662i	0.486833	−	0.873495i	$-0.338152\pi$
$181$	−5.20201	−	5.20201i	−0.386662	−	0.386662i	−0.873495	+	0.486833i	$0.838152\pi$
$182$	−10.4051	−	10.4051i	−0.771277	−	0.771277i
$183$			5.12700i			0.378999i
$184$	2.33812	−	2.33812i	0.172369	−	0.172369i
$185$	−0.812363	+	1.05971i	−0.0597261	+	0.0779113i
$186$	5.30661			0.389099
$187$	−18.5515	+	7.22325i	−1.35662	+	0.528216i
$188$		−	11.8193i		−	0.862012i
$189$		−	3.62534i		−	0.263704i
$190$	6.27006	−	0.828427i	0.454878	−	0.0601004i
$191$	−4.37767			−0.316757			−0.158379	−	0.987378i	$-0.550627\pi$
$191$	−4.37767			−0.316757			−0.158379	+	0.987378i	$0.550627\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−4.49621	+	4.49621i	−0.323644	+	0.323644i	−0.850163	−	0.526519i	$-0.823497\pi$
$193$	−4.49621	+	4.49621i	−0.323644	+	0.323644i	0.526519	+	0.850163i	$0.323497\pi$
$194$	7.36342	+	7.36342i	0.528663	+	0.528663i
$195$	−7.20309	−	5.52182i	−0.515824	−	0.395426i
$196$		−	6.14306i		−	0.438790i
$197$	10.6447	−	10.6447i	0.758405	−	0.758405i	−0.217627	−	0.976032i	$-0.569832\pi$
$197$	10.6447	−	10.6447i	0.758405	−	0.758405i	0.976032	+	0.217627i	$0.0698315\pi$
$198$	−3.41421	+	3.41421i	−0.242638	+	0.242638i
$199$	−3.53712	+	3.53712i	−0.250740	+	0.250740i	−0.821274	−	0.570534i	$-0.806736\pi$
$199$	−3.53712	+	3.53712i	−0.250740	+	0.250740i	0.570534	+	0.821274i	$0.306736\pi$
$200$	4.82843	−	1.29857i	0.341421	−	0.0918230i
$201$	4.65898	−	4.65898i	0.328619	−	0.328619i
$202$	5.10684			0.359316
$203$			21.2003i			1.48797i
$204$	3.84214	−	1.49598i	0.269004	−	0.104740i
$205$	−8.05894	+	10.5127i	−0.562861	+	0.734239i
$206$			4.78811i			0.333603i
$207$	−2.33812	−	2.33812i	−0.162511	−	0.162511i
$208$		−	4.05894i		−	0.281437i
$209$	−9.65685	+	9.65685i	−0.667979	+	0.667979i
$210$	−1.06184	−	8.03666i	−0.0732737	−	0.554582i
$211$	−2.21522	−	2.21522i	−0.152502	−	0.152502i	0.626733	−	0.779234i	$-0.284392\pi$
$211$	−2.21522	−	2.21522i	−0.152502	−	0.152502i	−0.779234	+	0.626733i	$0.784392\pi$
$212$	11.2895			0.775363
$213$	−15.4286			−1.05715
$214$	−8.77249	−	8.77249i	−0.599675	−	0.599675i
$215$	1.44453	+	10.9331i	0.0985163	+	0.745634i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$		−	19.2382i		−	1.30598i
$218$	−12.1666	−	12.1666i	−0.824023	−	0.824023i
$219$			7.32097i			0.494706i
$220$	−6.56864	+	8.56864i	−0.442857	+	0.577697i
$221$	−15.3210	−	6.73371i	−1.03060	−	0.452958i
$222$			0.597146i			0.0400778i
$223$	14.6923			0.983870			0.491935	−	0.870632i	$-0.336290\pi$
$223$	14.6923			0.983870			0.491935	+	0.870632i	$0.336290\pi$
$224$	2.56350	−	2.56350i	0.171281	−	0.171281i
$225$	−1.29857	−	4.82843i	−0.0865715	−	0.321895i
$226$	−4.52182	+	4.52182i	−0.300787	+	0.300787i
$227$	6.55728	−	6.55728i	0.435222	−	0.435222i	−0.455178	−	0.890400i	$-0.650425\pi$
$227$	6.55728	−	6.55728i	0.435222	−	0.435222i	0.890400	+	0.455178i	$0.150425\pi$
$228$	2.00000	−	2.00000i	0.132453	−	0.132453i
$229$			11.2346i			0.742404i	0.928552	+	0.371202i	$0.121054\pi$
$229$			11.2346i			0.742404i	−0.928552	+	0.371202i	$0.878946\pi$
$230$	−5.86798	−	4.49834i	−0.386923	−	0.296612i
$231$	12.3777	+	12.3777i	0.814391	+	0.814391i
$232$	−4.13503	+	4.13503i	−0.271478	+	0.271478i
$233$	−7.10652	−	7.10652i	−0.465564	−	0.465564i	0.434910	−	0.900474i	$-0.356780\pi$
$233$	−7.10652	−	7.10652i	−0.465564	−	0.465564i	−0.900474	+	0.434910i	$0.856780\pi$
$234$	−4.05894			−0.265341
$235$	−26.2011	+	3.46180i	−1.70917	+	0.225823i
$236$		−	1.65276i		−	0.107586i
$237$			2.69339i			0.174955i
$238$	−5.42344	−	13.9290i	−0.351550	−	0.902886i
$239$	21.5638			1.39484			0.697422	−	0.716660i	$-0.254330\pi$
$239$	21.5638			1.39484			0.697422	+	0.716660i	$0.254330\pi$
$240$	1.36041	−	1.77462i	0.0878140	−	0.114551i
$241$	8.71170	−	8.71170i	0.561170	−	0.561170i	−0.368470	−	0.929640i	$-0.620118\pi$
$241$	8.71170	−	8.71170i	0.561170	−	0.561170i	0.929640	+	0.368470i	$0.120118\pi$
$242$		−	12.3137i		−	0.791555i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	3.62534	+	3.62534i	0.232088	+	0.232088i
$245$	−13.6180	+	1.79926i	−0.870020	+	0.114951i
$246$			5.92391i			0.377695i
$247$	−11.4804			−0.730482
$248$	3.75234	−	3.75234i	0.238274	−	0.238274i
$249$	−5.25067	−	5.25067i	−0.332748	−	0.332748i
$250$	−4.29289	−	10.3233i	−0.271506	−	0.652904i
$251$	−16.1768			−1.02107			−0.510536	−	0.859856i	$-0.670553\pi$
$251$	−16.1768			−1.02107			−0.510536	+	0.859856i	$0.670553\pi$
$252$	−2.56350	−	2.56350i	−0.161485	−	0.161485i
$253$	15.9657			1.00376
$254$	−20.1524			−1.26447
$255$	−4.44164	−	8.07910i	−0.278146	−	0.505933i
$256$	1.00000			0.0625000
$257$	−30.3895			−1.89564			−0.947822	−	0.318800i	$-0.896720\pi$
$257$	−30.3895			−1.89564			−0.947822	+	0.318800i	$0.896720\pi$
$258$	3.48741	+	3.48741i	0.217117	+	0.217117i
$259$	2.16485			0.134517
$260$	−8.99787	+	1.18884i	−0.558024	+	0.0737285i
$261$	4.13503	+	4.13503i	0.255952	+	0.255952i
$262$	6.83569	−	6.83569i	0.422310	−	0.422310i
$263$	16.8344			1.03806			0.519028	−	0.854757i	$-0.326294\pi$
$263$	16.8344			1.03806			0.519028	+	0.854757i	$0.326294\pi$
$264$			4.82843i			0.297169i
$265$	−3.30661	−	25.0265i	−0.203123	−	1.53737i
$266$	−7.25067	−	7.25067i	−0.444567	−	0.444567i
$267$	−7.15442	−	7.15442i	−0.437844	−	0.437844i
$268$		−	6.58880i		−	0.402475i
$269$	22.4092	−	22.4092i	1.36631	−	1.36631i	0.500680	−	0.865632i	$-0.333083\pi$
$269$	22.4092	−	22.4092i	1.36631	−	1.36631i	0.865632	−	0.500680i	$-0.166917\pi$
$270$	−1.77462	−	1.36041i	−0.108000	−	0.0827919i
$271$	22.4392			1.36308			0.681541	−	0.731780i	$-0.261310\pi$
$271$	22.4392			1.36308			0.681541	+	0.731780i	$0.261310\pi$
$272$	1.65898	−	3.77462i	0.100591	−	0.228870i
$273$			14.7150i			0.890594i
$274$		−	12.1464i		−	0.733790i
$275$	20.9189	+	12.0517i	1.26146	+	0.726743i
$276$	−3.30661			−0.199034
$277$	−0.538204	−	0.538204i	−0.0323376	−	0.0323376i	0.690753	−	0.723091i	$-0.257279\pi$
$277$	−0.538204	−	0.538204i	−0.0323376	−	0.0323376i	−0.723091	+	0.690753i	$0.757279\pi$
$278$	−15.7919	+	15.7919i	−0.947134	+	0.947134i
$279$	−3.75234	−	3.75234i	−0.224647	−	0.224647i
$280$	−6.43361	−	4.93194i	−0.384481	−	0.294740i
$281$		−	5.52074i		−	0.329340i	−0.986349	−	0.164670i	$-0.947344\pi$
$281$		−	5.52074i		−	0.329340i	0.986349	−	0.164670i	$-0.0526558\pi$
$282$	−8.35751	+	8.35751i	−0.497683	+	0.497683i
$283$	10.3290	−	10.3290i	0.613996	−	0.613996i	−0.329989	−	0.943985i	$-0.607045\pi$
$283$	10.3290	−	10.3290i	0.613996	−	0.613996i	0.943985	+	0.329989i	$0.107045\pi$
$284$	−10.9097	+	10.9097i	−0.647369	+	0.647369i
$285$	−5.01939	−	3.84782i	−0.297323	−	0.227925i
$286$	13.8581	−	13.8581i	0.819446	−	0.819446i
$287$	21.4762			1.26770
$288$		−	1.00000i		−	0.0589256i
$289$	−11.4956	−	12.5241i	−0.676209	−	0.736710i
$290$	10.3777	+	7.95543i	0.609398	+	0.467159i
$291$		−	10.4134i		−	0.610447i
$292$	5.17671	+	5.17671i	0.302944	+	0.302944i
$293$			1.88212i			0.109954i	0.998488	+	0.0549772i	$0.0175086\pi$
$293$			1.88212i			0.109954i	−0.998488	+	0.0549772i	$0.982491\pi$
$294$	−4.34380	+	4.34380i	−0.253336	+	0.253336i
$295$	−3.66384	+	0.484082i	−0.213317	+	0.0281844i
$296$	0.422246	+	0.422246i	0.0245425	+	0.0245425i
$297$	4.82843			0.280174
$298$	2.89316			0.167596
$299$	9.49030	+	9.49030i	0.548838	+	0.548838i
$300$	−4.33244	−	2.49598i	−0.250134	−	0.144106i
$301$	12.6430	−	12.6430i	0.728732	−	0.728732i
$302$			7.26312i			0.417945i
$303$	−3.61108	−	3.61108i	−0.207451	−	0.207451i
$304$		−	2.82843i		−	0.162221i
$305$	6.97482	−	9.09849i	0.399377	−	0.520978i
$306$	−3.77462	−	1.65898i	−0.215781	−	0.0948377i
$307$		−	20.2396i		−	1.15514i	−0.816342	−	0.577568i	$-0.804002\pi$
$307$		−	20.2396i		−	1.15514i	0.816342	−	0.577568i	$-0.195998\pi$
$308$	17.5047			0.997421
$309$	3.38571	−	3.38571i	0.192606	−	0.192606i
$310$	−9.41722	−	7.21916i	−0.534862	−	0.410020i
$311$	5.93058	−	5.93058i	0.336292	−	0.336292i	−0.518678	−	0.854970i	$-0.673575\pi$
$311$	5.93058	−	5.93058i	0.336292	−	0.336292i	0.854970	+	0.518678i	$0.173575\pi$
$312$	−2.87011	+	2.87011i	−0.162488	+	0.162488i
$313$	5.12186	−	5.12186i	0.289505	−	0.289505i	−0.547380	−	0.836884i	$-0.684375\pi$
$313$	5.12186	−	5.12186i	0.289505	−	0.289505i	0.836884	+	0.547380i	$0.184375\pi$
$314$		−	4.17081i		−	0.235372i
$315$	−4.93194	+	6.43361i	−0.277883	+	0.362493i
$316$	1.90452	+	1.90452i	0.107137	+	0.107137i
$317$	−23.2822	+	23.2822i	−1.30766	+	1.30766i	−0.384557	+	0.923101i	$0.625646\pi$
$317$	−23.2822	+	23.2822i	−1.30766	+	1.30766i	−0.923101	+	0.384557i	$0.874354\pi$
$318$	−7.98285	−	7.98285i	−0.447656	−	0.447656i
$319$	−28.2358			−1.58090
$320$	−0.292893	−	2.21680i	−0.0163732	−	0.123923i
$321$			12.4062i			0.692446i
$322$			11.9876i			0.668040i
$323$	−10.6762	−	4.69231i	−0.594042	−	0.261087i
$324$	−1.00000			−0.0555556
$325$	5.27083	+	19.5983i	0.292373	+	1.08712i
$326$	10.5888	−	10.5888i	0.586459	−	0.586459i
$327$			17.2061i			0.951500i
$328$	4.18884	+	4.18884i	0.231290	+	0.231290i
$329$	30.2988	+	30.2988i	1.67043	+	1.67043i
$330$	10.7037	−	1.41421i	0.589218	−	0.0778499i
$331$		−	33.2779i		−	1.82912i	−0.404453	−	0.914559i	$-0.632538\pi$
$331$		−	33.2779i		−	1.82912i	0.404453	−	0.914559i	$-0.367462\pi$
$332$	−7.42557			−0.407531
$333$	0.422246	−	0.422246i	0.0231389	−	0.0231389i
$334$	−12.0396	−	12.0396i	−0.658775	−	0.658775i
$335$	−14.6061	+	1.92981i	−0.798014	+	0.105437i
$336$	−3.62534			−0.197778
$337$	4.55106	+	4.55106i	0.247912	+	0.247912i	0.820113	−	0.572201i	$-0.193910\pi$
$337$	4.55106	+	4.55106i	0.247912	+	0.247912i	−0.572201	+	0.820113i	$0.693910\pi$
$338$	3.47501			0.189015
$339$	6.39482			0.347319
$340$	−8.85350	−	2.57207i	−0.480148	−	0.139490i
$341$	25.6226			1.38754
$342$	−2.82843			−0.152944
$343$	−2.19675	−	2.19675i	−0.118614	−	0.118614i
$344$	4.93194			0.265912
$345$	0.968482	+	7.33009i	0.0521413	+	0.394639i
$346$	16.0703	+	16.0703i	0.863945	+	0.863945i
$347$	−16.1798	+	16.1798i	−0.868579	+	0.868579i	−0.992315	−	0.123736i	$-0.960512\pi$
$347$	−16.1798	+	16.1798i	−0.868579	+	0.868579i	0.123736	+	0.992315i	$0.460512\pi$
$348$	5.84782			0.313476
$349$		−	17.7763i		−	0.951542i	−0.879569	−	0.475771i	$-0.842169\pi$
$349$		−	17.7763i		−	0.951542i	0.879569	−	0.475771i	$-0.157831\pi$
$350$	−9.04878	+	15.7066i	−0.483678	+	0.839551i
$351$	2.87011	+	2.87011i	0.153195	+	0.153195i
$352$	3.41421	+	3.41421i	0.181978	+	0.181978i
$353$		−	30.9911i		−	1.64949i	−0.565504	−	0.824745i	$-0.691318\pi$
$353$		−	30.9911i		−	1.64949i	0.565504	−	0.824745i	$-0.308682\pi$
$354$	−1.16868	+	1.16868i	−0.0621145	+	0.0621145i
$355$	27.3799	+	20.9892i	1.45318	+	1.11399i
$356$	−10.1179			−0.536247
$357$	−6.01437	+	13.6843i	−0.318314	+	0.724249i
$358$			14.2559i			0.753449i
$359$			8.11788i			0.428445i	0.976785	+	0.214223i	$0.0687218\pi$
$359$			8.11788i			0.428445i	−0.976785	+	0.214223i	$0.931278\pi$
$360$	−2.21680	+	0.292893i	−0.116836	+	0.0154368i
$361$	11.0000			0.578947
$362$	5.20201	+	5.20201i	0.273411	+	0.273411i
$363$	−8.70711	+	8.70711i	−0.457005	+	0.457005i
$364$	10.4051	+	10.4051i	0.545375	+	0.545375i
$365$	9.95952	−	12.9920i	0.521305	−	0.680031i
$366$		−	5.12700i		−	0.267993i
$367$	−15.8530	+	15.8530i	−0.827518	+	0.827518i	−0.987173	−	0.159655i	$-0.948962\pi$
$367$	−15.8530	+	15.8530i	−0.827518	+	0.827518i	0.159655	+	0.987173i	$0.448962\pi$
$368$	−2.33812	+	2.33812i	−0.121883	+	0.121883i
$369$	4.18884	−	4.18884i	0.218062	−	0.218062i
$370$	0.812363	−	1.05971i	0.0422327	−	0.0550916i
$371$	−28.9405	+	28.9405i	−1.50252	+	1.50252i
$372$	−5.30661			−0.275135
$373$			7.14290i			0.369845i	0.982753	+	0.184923i	$0.0592035\pi$
$373$			7.14290i			0.369845i	−0.982753	+	0.184923i	$0.940797\pi$
$374$	18.5515	−	7.22325i	0.959275	−	0.373505i
$375$	−4.26416	+	10.3352i	−0.220200	+	0.533709i
$376$			11.8193i			0.609534i
$377$	−16.7839	−	16.7839i	−0.864412	−	0.864412i
$378$			3.62534i			0.186467i
$379$	19.6155	−	19.6155i	1.00758	−	1.00758i	0.00760706	−	0.999971i	$-0.497579\pi$
$379$	19.6155	−	19.6155i	1.00758	−	1.00758i	0.999971	−	0.00760706i	$-0.00242143\pi$
$380$	−6.27006	+	0.828427i	−0.321648	+	0.0424974i
$381$	14.2499	+	14.2499i	0.730045	+	0.730045i
$382$	4.37767			0.223981
$383$	−16.2373			−0.829687			−0.414844	−	0.909893i	$-0.636164\pi$
$383$	−16.2373			−0.829687			−0.414844	+	0.909893i	$0.636164\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−5.12700	−	38.8044i	−0.261296	−	1.97766i
$386$	4.49621	−	4.49621i	0.228851	−	0.228851i
$387$		−	4.93194i		−	0.250705i
$388$	−7.36342	−	7.36342i	−0.373821	−	0.373821i
$389$		−	12.7622i		−	0.647067i	−0.946217	−	0.323534i	$-0.895129\pi$
$389$		−	12.7622i		−	0.647067i	0.946217	−	0.323534i	$-0.104871\pi$
$390$	7.20309	+	5.52182i	0.364743	+	0.279608i
$391$	4.94663	+	12.7044i	0.250162	+	0.642491i
$392$			6.14306i			0.310272i
$393$	−9.66713			−0.487642
$394$	−10.6447	+	10.6447i	−0.536274	+	0.536274i
$395$	3.66412	−	4.77976i	0.184362	−	0.240496i
$396$	3.41421	−	3.41421i	0.171571	−	0.171571i
$397$	1.22024	−	1.22024i	0.0612421	−	0.0612421i	−0.675822	−	0.737064i	$-0.736211\pi$
$397$	1.22024	−	1.22024i	0.0612421	−	0.0612421i	0.737064	+	0.675822i	$0.236211\pi$
$398$	3.53712	−	3.53712i	0.177300	−	0.177300i
$399$			10.2540i			0.513342i
$400$	−4.82843	+	1.29857i	−0.241421	+	0.0649286i
$401$	5.35462	+	5.35462i	0.267397	+	0.267397i	0.828050	−	0.560654i	$-0.189450\pi$
$401$	5.35462	+	5.35462i	0.267397	+	0.267397i	−0.560654	+	0.828050i	$0.689450\pi$
$402$	−4.65898	+	4.65898i	−0.232369	+	0.232369i
$403$	15.2305	+	15.2305i	0.758686	+	0.758686i
$404$	−5.10684			−0.254075
$405$	0.292893	+	2.21680i	0.0145540	+	0.110154i
$406$		−	21.2003i		−	1.05215i
$407$			2.88327i			0.142919i
$408$	−3.84214	+	1.49598i	−0.190214	+	0.0740622i
$409$	−27.8663			−1.37790			−0.688949	−	0.724809i	$-0.741928\pi$
$409$	−27.8663			−1.37790			−0.688949	+	0.724809i	$0.741928\pi$
$410$	8.05894	−	10.5127i	0.398003	−	0.519186i
$411$	−8.58880	+	8.58880i	−0.423654	+	0.423654i
$412$		−	4.78811i		−	0.235893i
$413$	4.23685	+	4.23685i	0.208482	+	0.208482i
$414$	2.33812	+	2.33812i	0.114912	+	0.114912i
$415$	2.17490	+	16.4610i	0.106762	+	0.808040i
$416$			4.05894i			0.199006i
$417$	22.3331			1.09366
$418$	9.65685	−	9.65685i	0.472332	−	0.472332i
$419$	−12.1738	−	12.1738i	−0.594730	−	0.594730i	0.344176	−	0.938905i	$-0.388158\pi$
$419$	−12.1738	−	12.1738i	−0.594730	−	0.594730i	−0.938905	+	0.344176i	$0.888158\pi$
$420$	1.06184	+	8.03666i	0.0518123	+	0.392149i
$421$	−22.6520			−1.10399			−0.551995	−	0.833847i	$-0.686133\pi$
$421$	−22.6520			−1.10399			−0.551995	+	0.833847i	$0.686133\pi$
$422$	2.21522	+	2.21522i	0.107835	+	0.107835i
$423$	11.8193			0.574675
$424$	−11.2895			−0.548264
$425$	−3.10865	+	20.3798i	−0.150792	+	0.988566i
$426$	15.4286			0.747517
$427$	−18.5871			−0.899493
$428$	8.77249	+	8.77249i	0.424035	+	0.424035i
$429$	−19.5983			−0.946215
$430$	−1.44453	−	10.9331i	−0.0696615	−	0.527243i
$431$	−13.7220	−	13.7220i	−0.660966	−	0.660966i	0.294642	−	0.955608i	$-0.404800\pi$
$431$	−13.7220	−	13.7220i	−0.660966	−	0.660966i	−0.955608	+	0.294642i	$0.904800\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	32.8226			1.57736			0.788678	−	0.614807i	$-0.210766\pi$
$433$	32.8226			1.57736			0.788678	+	0.614807i	$0.210766\pi$
$434$			19.2382i			0.923465i
$435$	−1.71279	−	12.9635i	−0.0821218	−	0.621550i
$436$	12.1666	+	12.1666i	0.582672	+	0.582672i
$437$	6.61321	+	6.61321i	0.316353	+	0.316353i
$438$		−	7.32097i		−	0.349810i
$439$	5.00301	−	5.00301i	0.238781	−	0.238781i	−0.577564	−	0.816345i	$-0.695997\pi$
$439$	5.00301	−	5.00301i	0.238781	−	0.238781i	0.816345	+	0.577564i	$0.195997\pi$
$440$	6.56864	−	8.56864i	0.313147	−	0.408494i
$441$	6.14306			0.292527
$442$	15.3210	+	6.73371i	0.728744	+	0.320290i
$443$			9.49648i			0.451192i	0.974221	+	0.225596i	$0.0724329\pi$
$443$			9.49648i			0.451192i	−0.974221	+	0.225596i	$0.927567\pi$
$444$		−	0.597146i		−	0.0283393i
$445$	2.96346	+	22.4293i	0.140481	+	1.06325i
$446$	−14.6923			−0.695701
$447$	−2.04577	−	2.04577i	−0.0967617	−	0.0967617i
$448$	−2.56350	+	2.56350i	−0.121114	+	0.121114i
$449$	−13.9963	−	13.9963i	−0.660528	−	0.660528i	0.294976	−	0.955505i	$-0.404688\pi$
$449$	−13.9963	−	13.9963i	−0.660528	−	0.660528i	−0.955505	+	0.294976i	$0.904688\pi$
$450$	1.29857	+	4.82843i	0.0612153	+	0.227614i
$451$			28.6032i			1.34687i
$452$	4.52182	−	4.52182i	0.212689	−	0.212689i
$453$	5.13580	−	5.13580i	0.241301	−	0.241301i
$454$	−6.55728	+	6.55728i	−0.307748	+	0.307748i
$455$	20.0185	−	26.1136i	0.938480	−	1.22423i
$456$	−2.00000	+	2.00000i	−0.0936586	+	0.0936586i
$457$	13.8823			0.649389			0.324694	−	0.945819i	$-0.394739\pi$
$457$	13.8823			0.649389			0.324694	+	0.945819i	$0.394739\pi$
$458$		−	11.2346i		−	0.524959i
$459$	1.49598	+	3.84214i	0.0698265	+	0.179336i
$460$	5.86798	+	4.49834i	0.273596	+	0.209736i
$461$			15.6082i			0.726946i	0.931605	+	0.363473i	$0.118409\pi$
$461$			15.6082i			0.726946i	−0.931605	+	0.363473i	$0.881591\pi$
$462$	−12.3777	−	12.3777i	−0.575861	−	0.575861i
$463$		−	5.08396i		−	0.236272i	−0.992997	−	0.118136i	$-0.962308\pi$
$463$		−	5.08396i		−	0.236272i	0.992997	−	0.118136i	$-0.0376918\pi$
$464$	4.13503	−	4.13503i	0.191964	−	0.191964i
$465$	1.55427	+	11.7637i	0.0720775	+	0.545528i
$466$	7.10652	+	7.10652i	0.329203	+	0.329203i
$467$	−22.0615			−1.02088			−0.510442	−	0.859912i	$-0.670518\pi$
$467$	−22.0615			−1.02088			−0.510442	+	0.859912i	$0.670518\pi$
$468$	4.05894			0.187625
$469$	16.8904	+	16.8904i	0.779925	+	0.779925i
$470$	26.2011	−	3.46180i	1.20857	−	0.159681i
$471$	−2.94921	+	2.94921i	−0.135892	+	0.135892i
$472$			1.65276i			0.0760745i
$473$	16.8387	+	16.8387i	0.774244	+	0.774244i
$474$		−	2.69339i		−	0.123712i
$475$	3.67292	+	13.6569i	0.168525	+	0.626619i
$476$	5.42344	+	13.9290i	0.248583	+	0.638437i
$477$			11.2895i			0.516909i
$478$	−21.5638			−0.986304
$479$	15.0721	−	15.0721i	0.688662	−	0.688662i	−0.273274	−	0.961936i	$-0.588107\pi$
$479$	15.0721	−	15.0721i	0.688662	−	0.688662i	0.961936	+	0.273274i	$0.0881065\pi$
$480$	−1.36041	+	1.77462i	−0.0620939	+	0.0810001i
$481$	−1.71387	+	1.71387i	−0.0781458	+	0.0781458i
$482$	−8.71170	+	8.71170i	−0.396807	+	0.396807i
$483$	8.47648	−	8.47648i	0.385693	−	0.385693i
$484$			12.3137i			0.559714i
$485$	−14.1666	+	18.4799i	−0.643270	+	0.839131i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	26.6368	−	26.6368i	1.20703	−	1.20703i	0.235044	−	0.971985i	$-0.424476\pi$
$487$	26.6368	−	26.6368i	1.20703	−	1.20703i	0.971985	−	0.235044i	$-0.0755236\pi$
$488$	−3.62534	−	3.62534i	−0.164111	−	0.164111i
$489$	−14.9748			−0.677185
$490$	13.6180	−	1.79926i	0.615197	−	0.0812824i
$491$		−	2.10930i		−	0.0951916i	−0.998867	−	0.0475958i	$-0.984844\pi$
$491$		−	2.10930i		−	0.0951916i	0.998867	−	0.0475958i	$-0.0151559\pi$
$492$		−	5.92391i		−	0.267070i
$493$	−8.74824	−	22.4681i	−0.394001	−	1.01191i
$494$	11.4804			0.516529
$495$	−8.56864	−	6.56864i	−0.385132	−	0.295238i
$496$	−3.75234	+	3.75234i	−0.168485	+	0.168485i
$497$		−	55.9338i		−	2.50897i
$498$	5.25067	+	5.25067i	0.235288	+	0.235288i
$499$	−20.0045	−	20.0045i	−0.895524	−	0.895524i	0.0995126	−	0.995036i	$-0.468272\pi$
$499$	−20.0045	−	20.0045i	−0.895524	−	0.895524i	−0.995036	+	0.0995126i	$0.968272\pi$
$500$	4.29289	+	10.3233i	0.191984	+	0.461673i
$501$			17.0265i			0.760688i
$502$	16.1768			0.722007
$503$	5.09772	−	5.09772i	0.227296	−	0.227296i	−0.584266	−	0.811562i	$-0.698617\pi$
$503$	5.09772	−	5.09772i	0.227296	−	0.227296i	0.811562	+	0.584266i	$0.198617\pi$
$504$	2.56350	+	2.56350i	0.114187	+	0.114187i
$505$	1.49576	+	11.3209i	0.0665604	+	0.503772i
$506$	−15.9657			−0.709762
$507$	−2.45720	−	2.45720i	−0.109128	−	0.109128i
$508$	20.1524			0.894119
$509$	36.8488			1.63329			0.816647	−	0.577137i	$-0.195830\pi$
$509$	36.8488			1.63329			0.816647	+	0.577137i	$0.195830\pi$
$510$	4.44164	+	8.07910i	0.196679	+	0.357749i
$511$	−26.5410			−1.17410
$512$	−1.00000			−0.0441942
$513$	2.00000	+	2.00000i	0.0883022	+	0.0883022i
$514$	30.3895			1.34042
$515$	−10.6143	+	1.40240i	−0.467722	+	0.0617973i
$516$	−3.48741	−	3.48741i	−0.153525	−	0.153525i
$517$	−40.3536	+	40.3536i	−1.77475	+	1.77475i
$518$	−2.16485			−0.0951182
$519$		−	22.7268i		−	0.997597i
$520$	8.99787	−	1.18884i	0.394583	−	0.0521339i
$521$	−21.9678	−	21.9678i	−0.962428	−	0.962428i	0.0368912	−	0.999319i	$-0.488255\pi$
$521$	−21.9678	−	21.9678i	−0.962428	−	0.962428i	−0.999319	+	0.0368912i	$0.988255\pi$
$522$	−4.13503	−	4.13503i	−0.180985	−	0.180985i
$523$			5.46605i			0.239014i	0.992833	+	0.119507i	$0.0381314\pi$
$523$			5.46605i			0.239014i	−0.992833	+	0.119507i	$0.961869\pi$
$524$	−6.83569	+	6.83569i	−0.298619	+	0.298619i
$525$	17.5047	−	4.70776i	0.763967	−	0.205464i
$526$	−16.8344			−0.734017
$527$	7.93860	+	20.3887i	0.345811	+	0.888146i
$528$		−	4.82843i		−	0.210130i
$529$			12.0664i			0.524624i
$530$	3.30661	+	25.0265i	0.143630	+	1.08708i
$531$	1.65276			0.0717237
$532$	7.25067	+	7.25067i	0.314357	+	0.314357i
$533$	−17.0022	+	17.0022i	−0.736449	+	0.736449i
$534$	7.15442	+	7.15442i	0.309602	+	0.309602i
$535$	16.8775	−	22.0163i	0.729677	−	0.951847i
$536$			6.58880i			0.284593i
$537$	10.0805	−	10.0805i	0.435004	−	0.435004i
$538$	−22.4092	+	22.4092i	−0.966129	+	0.966129i
$539$	−20.9737	+	20.9737i	−0.903403	+	0.903403i
$540$	1.77462	+	1.36041i	0.0763676	+	0.0585427i
$541$	−25.0730	+	25.0730i	−1.07797	+	1.07797i	−0.0812809	+	0.996691i	$0.525901\pi$
$541$	−25.0730	+	25.0730i	−1.07797	+	1.07797i	−0.996691	+	0.0812809i	$0.974099\pi$
$542$	−22.4392			−0.963845
$543$		−	7.35675i		−	0.315708i
$544$	−1.65898	+	3.77462i	−0.0711283	+	0.161836i
$545$	23.4073	−	30.5343i	1.00266	−	1.30795i
$546$		−	14.7150i		−	0.629745i
$547$	−4.08319	−	4.08319i	−0.174585	−	0.174585i	0.614406	−	0.788990i	$-0.289396\pi$
$547$	−4.08319	−	4.08319i	−0.174585	−	0.174585i	−0.788990	+	0.614406i	$0.789396\pi$
$548$			12.1464i			0.518868i
$549$	−3.62534	+	3.62534i	−0.154726	+	0.154726i
$550$	−20.9189	−	12.0517i	−0.891984	−	0.513885i
$551$	−11.6956	−	11.6956i	−0.498251	−	0.498251i
$552$	3.30661			0.140738
$553$	−9.76446			−0.415227
$554$	0.538204	+	0.538204i	0.0228661	+	0.0228661i
$555$	−1.32375	+	0.174900i	−0.0561902	+	0.00742409i
$556$	15.7919	−	15.7919i	0.669725	−	0.669725i
$557$		−	7.99847i		−	0.338906i	−0.985538	−	0.169453i	$-0.945800\pi$
$557$		−	7.99847i		−	0.338906i	0.985538	−	0.169453i	$-0.0542001\pi$
$558$	3.75234	+	3.75234i	0.158849	+	0.158849i
$559$			20.0185i			0.846691i
$560$	6.43361	+	4.93194i	0.271869	+	0.208413i
$561$	−18.2255	−	8.01027i	−0.769481	−	0.338194i
$562$			5.52074i			0.232878i
$563$	35.2734			1.48660			0.743298	−	0.668960i	$-0.233260\pi$
$563$	35.2734			1.48660			0.743298	+	0.668960i	$0.233260\pi$
$564$	8.35751	−	8.35751i	0.351915	−	0.351915i
$565$	−11.3484	−	8.69958i	−0.477431	−	0.365994i
$566$	−10.3290	+	10.3290i	−0.434161	+	0.434161i
$567$	2.56350	−	2.56350i	0.107657	−	0.107657i
$568$	10.9097	−	10.9097i	0.457759	−	0.457759i
$569$		−	0.465285i		−	0.0195058i	−0.999952	−	0.00975288i	$-0.996896\pi$
$569$		−	0.465285i		−	0.0195058i	0.999952	−	0.00975288i	$-0.00310449\pi$
$570$	5.01939	+	3.84782i	0.210239	+	0.161167i
$571$	−1.18872	−	1.18872i	−0.0497465	−	0.0497465i	0.681796	−	0.731542i	$-0.261199\pi$
$571$	−1.18872	−	1.18872i	−0.0497465	−	0.0497465i	−0.731542	+	0.681796i	$0.761199\pi$
$572$	−13.8581	+	13.8581i	−0.579436	+	0.579436i
$573$	−3.09548	−	3.09548i	−0.129316	−	0.129316i
$574$	−21.4762			−0.896398
$575$	8.25323	−	14.3257i	0.344184	−	0.597422i
$576$			1.00000i			0.0416667i
$577$			7.16578i			0.298315i	0.988813	+	0.149158i	$0.0476562\pi$
$577$			7.16578i			0.298315i	−0.988813	+	0.149158i	$0.952344\pi$
$578$	11.4956	+	12.5241i	0.478152	+	0.520932i
$579$	−6.35860			−0.264254
$580$	−10.3777	−	7.95543i	−0.430909	−	0.330331i
$581$	19.0355	−	19.0355i	0.789724	−	0.789724i
$582$			10.4134i			0.431651i
$583$	−38.5446	−	38.5446i	−1.59635	−	1.59635i
$584$	−5.17671	−	5.17671i	−0.214214	−	0.214214i
$585$	−1.18884	−	8.99787i	−0.0491523	−	0.372016i
$586$		−	1.88212i		−	0.0777495i
$587$	−17.0742			−0.704729			−0.352365	−	0.935863i	$-0.614622\pi$
$587$	−17.0742			−0.704729			−0.352365	+	0.935863i	$0.614622\pi$
$588$	4.34380	−	4.34380i	0.179135	−	0.179135i
$589$	10.6132	+	10.6132i	0.437310	+	0.437310i
$590$	3.66384	−	0.484082i	0.150838	−	0.0199294i
$591$	15.0539			0.619235
$592$	−0.422246	−	0.422246i	−0.0173542	−	0.0173542i
$593$	−1.83329			−0.0752841			−0.0376421	−	0.999291i	$-0.511985\pi$
$593$	−1.83329			−0.0752841			−0.0376421	+	0.999291i	$0.511985\pi$
$594$	−4.82843			−0.198113
$595$	29.2895	−	16.1024i	1.20075	−	0.660135i
$596$	−2.89316			−0.118508
$597$	−5.00224			−0.204728
$598$	−9.49030	−	9.49030i	−0.388087	−	0.388087i
$599$	12.4677			0.509416			0.254708	−	0.967018i	$-0.418021\pi$
$599$	12.4677			0.509416			0.254708	+	0.967018i	$0.418021\pi$
$600$	4.33244	+	2.49598i	0.176871	+	0.101898i
$601$	−8.30552	−	8.30552i	−0.338789	−	0.338789i	0.517122	−	0.855912i	$-0.327003\pi$
$601$	−8.30552	−	8.30552i	−0.338789	−	0.338789i	−0.855912	+	0.517122i	$0.827003\pi$
$602$	−12.6430	+	12.6430i	−0.515292	+	0.515292i
$603$	6.58880			0.268317
$604$		−	7.26312i		−	0.295532i
$605$	27.2971	−	3.60660i	1.10978	−	0.146629i
$606$	3.61108	+	3.61108i	0.146690	+	0.146690i
$607$	−17.7939	−	17.7939i	−0.722230	−	0.722230i	0.246829	−	0.969059i	$-0.420611\pi$
$607$	−17.7939	−	17.7939i	−0.722230	−	0.722230i	−0.969059	+	0.246829i	$0.920611\pi$
$608$			2.82843i			0.114708i
$609$	−14.9909	+	14.9909i	−0.607461	+	0.607461i
$610$	−6.97482	+	9.09849i	−0.282402	+	0.368387i
$611$	−47.9739			−1.94082
$612$	3.77462	+	1.65898i	0.152580	+	0.0670604i
$613$		−	3.46180i		−	0.139821i	−0.997553	−	0.0699103i	$-0.977729\pi$
$613$		−	3.46180i		−	0.139821i	0.997553	−	0.0699103i	$-0.0222713\pi$
$614$			20.2396i			0.816805i
$615$	−13.1321	+	1.73507i	−0.529539	+	0.0699649i
$616$	−17.5047			−0.705283
$617$	25.8888	+	25.8888i	1.04225	+	1.04225i	0.999067	+	0.0431782i	$0.0137483\pi$
$617$	25.8888	+	25.8888i	1.04225	+	1.04225i	0.0431782	+	0.999067i	$0.486252\pi$
$618$	−3.38571	+	3.38571i	−0.136193	+	0.136193i
$619$	24.9448	+	24.9448i	1.00262	+	1.00262i	0.999997	+	0.00261864i	$0.000833541\pi$
$619$	24.9448	+	24.9448i	1.00262	+	1.00262i	0.00261864	+	0.999997i	$0.499166\pi$
$620$	9.41722	+	7.21916i	0.378205	+	0.289928i
$621$		−	3.30661i		−	0.132689i
$622$	−5.93058	+	5.93058i	−0.237795	+	0.237795i
$623$	25.9372	−	25.9372i	1.03915	−	1.03915i
$624$	2.87011	−	2.87011i	0.114896	−	0.114896i
$625$	21.6274	−	12.5401i	0.865097	−	0.501605i
$626$	−5.12186	+	5.12186i	−0.204711	+	0.204711i
$627$	−13.6569			−0.545402
$628$			4.17081i			0.166433i
$629$	−2.29432	+	0.893320i	−0.0914804	+	0.0356190i
$630$	4.93194	−	6.43361i	0.196493	−	0.256321i
$631$		−	13.3077i		−	0.529771i	−0.964280	−	0.264885i	$-0.914666\pi$
$631$		−	13.3077i		−	0.529771i	0.964280	−	0.264885i	$-0.0853341\pi$
$632$	−1.90452	−	1.90452i	−0.0757577	−	0.0757577i
$633$		−	3.13279i		−	0.124517i
$634$	23.2822	−	23.2822i	0.924654	−	0.924654i
$635$	−5.90250	−	44.6739i	−0.234234	−	1.77283i
$636$	7.98285	+	7.98285i	0.316541	+	0.316541i
$637$	−24.9343			−0.987935
$638$	28.2358			1.11786
$639$	−10.9097	−	10.9097i	−0.431579	−	0.431579i
$640$	0.292893	+	2.21680i	0.0115776	+	0.0876268i
$641$	−28.5810	+	28.5810i	−1.12888	+	1.12888i	−0.138524	+	0.990359i	$0.544236\pi$
$641$	−28.5810	+	28.5810i	−1.12888	+	1.12888i	−0.990359	+	0.138524i	$0.955764\pi$
$642$		−	12.4062i		−	0.489633i
$643$	28.2684	+	28.2684i	1.11480	+	1.11480i	0.992493	+	0.122303i	$0.0390279\pi$
$643$	28.2684	+	28.2684i	1.11480	+	1.11480i	0.122303	+	0.992493i	$0.460972\pi$
$644$		−	11.9876i		−	0.472376i
$645$	−6.70946	+	8.75234i	−0.264185	+	0.344623i
$646$	10.6762	+	4.69231i	0.420051	+	0.184616i
$647$		−	20.6647i		−	0.812412i	−0.913782	−	0.406206i	$-0.866852\pi$
$647$		−	20.6647i		−	0.812412i	0.913782	−	0.406206i	$-0.133148\pi$
$648$	1.00000			0.0392837
$649$	−5.64288	+	5.64288i	−0.221502	+	0.221502i
$650$	−5.27083	−	19.5983i	−0.206739	−	0.768709i
$651$	13.6035	−	13.6035i	0.533163	−	0.533163i
$652$	−10.5888	+	10.5888i	−0.414689	+	0.414689i
$653$	−6.51571	+	6.51571i	−0.254980	+	0.254980i	−0.823009	−	0.568029i	$-0.807706\pi$
$653$	−6.51571	+	6.51571i	−0.254980	+	0.254980i	0.568029	+	0.823009i	$0.307706\pi$
$654$		−	17.2061i		−	0.672812i
$655$	17.1555	+	13.1513i	0.670321	+	0.513862i
$656$	−4.18884	−	4.18884i	−0.163547	−	0.163547i
$657$	−5.17671	+	5.17671i	−0.201963	+	0.201963i
$658$	−30.2988	−	30.2988i	−1.18117	−	1.18117i
$659$	−0.673686			−0.0262431			−0.0131215	−	0.999914i	$-0.504177\pi$
$659$	−0.673686			−0.0262431			−0.0131215	+	0.999914i	$0.504177\pi$
$660$	−10.7037	+	1.41421i	−0.416640	+	0.0550482i
$661$		−	32.5156i		−	1.26471i	−0.774679	−	0.632354i	$-0.782089\pi$
$661$		−	32.5156i		−	1.26471i	0.774679	−	0.632354i	$-0.217911\pi$
$662$			33.2779i			1.29338i
$663$	−6.07211	−	15.5950i	−0.235821	−	0.605660i
$664$	7.42557			0.288168
$665$	13.9496	−	18.1970i	0.540944	−	0.705649i
$666$	−0.422246	+	0.422246i	−0.0163617	+	0.0163617i
$667$			19.3364i			0.748709i
$668$	12.0396	+	12.0396i	0.465824	+	0.465824i
$669$	10.3890	+	10.3890i	0.401663	+	0.401663i
$670$	14.6061	−	1.92981i	0.564281	−	0.0745552i
$671$		−	24.7553i		−	0.955670i
$672$	3.62534			0.139850
$673$	−7.18915	+	7.18915i	−0.277122	+	0.277122i	−0.831959	−	0.554837i	$-0.812780\pi$
$673$	−7.18915	+	7.18915i	−0.277122	+	0.277122i	0.554837	+	0.831959i	$0.312780\pi$
$674$	−4.55106	−	4.55106i	−0.175300	−	0.175300i
$675$	2.49598	−	4.33244i	0.0960705	−	0.166756i
$676$	−3.47501			−0.133654
$677$	28.7298	+	28.7298i	1.10418	+	1.10418i	0.993901	+	0.110277i	$0.0351737\pi$
$677$	28.7298	+	28.7298i	1.10418	+	1.10418i	0.110277	+	0.993901i	$0.464826\pi$
$678$	−6.39482			−0.245592
$679$	37.7522			1.44880
$680$	8.85350	+	2.57207i	0.339516	+	0.0986346i
$681$	9.27339			0.355357
$682$	−25.6226			−0.981138
$683$	21.5595	+	21.5595i	0.824952	+	0.824952i	0.986814	−	0.161861i	$-0.0517497\pi$
$683$	21.5595	+	21.5595i	0.824952	+	0.824952i	−0.161861	+	0.986814i	$0.551750\pi$
$684$	2.82843			0.108148
$685$	26.9262	−	3.55760i	1.02880	−	0.135929i
$686$	2.19675	+	2.19675i	0.0838725	+	0.0838725i
$687$	−7.94407	+	7.94407i	−0.303085	+	0.303085i
$688$	−4.93194			−0.188029
$689$		−	45.8232i		−	1.74573i
$690$	−0.968482	−	7.33009i	−0.0368695	−	0.279052i
$691$	24.7714	+	24.7714i	0.942349	+	0.942349i	0.998426	−	0.0560776i	$-0.0178594\pi$
$691$	24.7714	+	24.7714i	0.942349	+	0.942349i	−0.0560776	+	0.998426i	$0.517859\pi$
$692$	−16.0703	−	16.0703i	−0.610901	−	0.610901i
$693$			17.5047i			0.664948i
$694$	16.1798	−	16.1798i	0.614178	−	0.614178i
$695$	−39.6328	−	30.3822i	−1.50336	−	1.15246i
$696$	−5.84782			−0.221661
$697$	−22.7605	+	8.86207i	−0.862115	+	0.335675i
$698$			17.7763i			0.672842i
$699$		−	10.0501i		−	0.380131i
$700$	9.04878	−	15.7066i	0.342012	−	0.593652i
$701$	42.3963			1.60129			0.800643	−	0.599142i	$-0.204491\pi$
$701$	42.3963			1.60129			0.800643	+	0.599142i	$0.204491\pi$
$702$	−2.87011	−	2.87011i	−0.108325	−	0.108325i
$703$	−1.19429	+	1.19429i	−0.0450436	+	0.0450436i
$704$	−3.41421	−	3.41421i	−0.128678	−	0.128678i
$705$	−20.9748	−	16.0791i	−0.789957	−	0.605574i
$706$			30.9911i			1.16637i
$707$	13.0914	−	13.0914i	0.492352	−	0.492352i
$708$	1.16868	−	1.16868i	0.0439216	−	0.0439216i
$709$	−20.6750	+	20.6750i	−0.776466	+	0.776466i	−0.979228	−	0.202762i	$-0.935008\pi$
$709$	−20.6750	+	20.6750i	−0.776466	+	0.776466i	0.202762	+	0.979228i	$0.435008\pi$
$710$	−27.3799	−	20.9892i	−1.02755	−	0.787710i
$711$	−1.90452	+	1.90452i	−0.0714250	+	0.0714250i
$712$	10.1179			0.379184
$713$		−	17.5468i		−	0.657135i
$714$	6.01437	−	13.6843i	0.225082	−	0.512121i
$715$	34.7796	+	26.6617i	1.30068	+	0.997092i
$716$		−	14.2559i		−	0.532769i
$717$	15.2479	+	15.2479i	0.569443	+	0.569443i
$718$		−	8.11788i		−	0.302957i
$719$	−17.2998	+	17.2998i	−0.645173	+	0.645173i	−0.951822	−	0.306650i	$-0.900792\pi$
$719$	−17.2998	+	17.2998i	−0.645173	+	0.645173i	0.306650	+	0.951822i	$0.400792\pi$
$720$	2.21680	−	0.292893i	0.0826154	−	0.0109155i
$721$	12.2743	+	12.2743i	0.457120	+	0.457120i
$722$	−11.0000			−0.409378
$723$	12.3202			0.458193
$724$	−5.20201	−	5.20201i	−0.193331	−	0.193331i
$725$	−14.5961	+	25.3353i	−0.542084	+	0.940931i
$726$	8.70711	−	8.70711i	0.323151	−	0.323151i
$727$			43.5553i			1.61538i	0.589611	+	0.807688i	$0.299281\pi$
$727$			43.5553i			1.61538i	−0.589611	+	0.807688i	$0.700719\pi$
$728$	−10.4051	−	10.4051i	−0.385639	−	0.385639i
$729$		−	1.00000i		−	0.0370370i
$730$	−9.95952	+	12.9920i	−0.368618	+	0.480854i
$731$	−8.18200	+	18.6162i	−0.302622	+	0.688546i
$732$			5.12700i			0.189499i
$733$	−40.5875			−1.49913			−0.749567	−	0.661929i	$-0.769738\pi$
$733$	−40.5875			−1.49913			−0.749567	+	0.661929i	$0.769738\pi$
$734$	15.8530	−	15.8530i	0.585143	−	0.585143i
$735$	−10.9016	−	8.35708i	−0.402112	−	0.308256i
$736$	2.33812	−	2.33812i	0.0861844	−	0.0861844i
$737$	−22.4956	+	22.4956i	−0.828634	+	0.828634i
$738$	−4.18884	+	4.18884i	−0.154193	+	0.154193i
$739$		−	51.1190i		−	1.88044i	−0.340562	−	0.940222i	$-0.610617\pi$
$739$		−	51.1190i		−	1.88044i	0.340562	−	0.940222i	$-0.389383\pi$
$740$	−0.812363	+	1.05971i	−0.0298630	+	0.0389557i
$741$	−8.11788	−	8.11788i	−0.298218	−	0.298218i
$742$	28.9405	−	28.9405i	1.06244	−	1.06244i
$743$	1.23538	+	1.23538i	0.0453215	+	0.0453215i	0.729404	−	0.684083i	$-0.239797\pi$
$743$	1.23538	+	1.23538i	0.0453215	+	0.0453215i	−0.684083	+	0.729404i	$0.739797\pi$
$744$	5.30661			0.194550
$745$	0.847387	+	6.41356i	0.0310458	+	0.234975i
$746$		−	7.14290i		−	0.261520i
$747$		−	7.42557i		−	0.271688i
$748$	−18.5515	+	7.22325i	−0.678310	+	0.264108i
$749$	−44.9766			−1.64341
$750$	4.26416	−	10.3352i	0.155705	−	0.377389i
$751$	−32.7777	+	32.7777i	−1.19608	+	1.19608i	−0.220746	+	0.975331i	$0.570849\pi$
$751$	−32.7777	+	32.7777i	−1.19608	+	1.19608i	−0.975331	+	0.220746i	$0.929151\pi$
$752$		−	11.8193i		−	0.431006i
$753$	−11.4387	−	11.4387i	−0.416851	−	0.416851i
$754$	16.7839	+	16.7839i	0.611232	+	0.611232i
$755$	−16.1009	+	2.12732i	−0.585972	+	0.0774210i
$756$		−	3.62534i		−	0.131852i
$757$	−10.0835			−0.366492			−0.183246	−	0.983067i	$-0.558660\pi$
$757$	−10.0835			−0.366492			−0.183246	+	0.983067i	$0.558660\pi$
$758$	−19.6155	+	19.6155i	−0.712465	+	0.712465i
$759$	11.2895	+	11.2895i	0.409781	+	0.409781i
$760$	6.27006	−	0.828427i	0.227439	−	0.0300502i
$761$	46.1020			1.67120			0.835599	−	0.549340i	$-0.185121\pi$
$761$	46.1020			1.67120			0.835599	+	0.549340i	$0.185121\pi$
$762$	−14.2499	−	14.2499i	−0.516220	−	0.516220i
$763$	−62.3779			−2.25823
$764$	−4.37767			−0.158379
$765$	2.57207	−	8.85350i	0.0929936	−	0.320099i
$766$	16.2373			0.586678
$767$	−6.70846			−0.242228
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−5.16130			−0.186121			−0.0930606	−	0.995660i	$-0.529665\pi$
$769$	−5.16130			−0.186121			−0.0930606	+	0.995660i	$0.529665\pi$
$770$	5.12700	+	38.8044i	0.184764	+	1.39841i
$771$	−21.4886	−	21.4886i	−0.773893	−	0.773893i
$772$	−4.49621	+	4.49621i	−0.161822	+	0.161822i
$773$	−21.3853			−0.769174			−0.384587	−	0.923089i	$-0.625656\pi$
$773$	−21.3853			−0.769174			−0.384587	+	0.923089i	$0.625656\pi$
$774$			4.93194i			0.177275i
$775$	13.2452	−	22.9906i	0.475782	−	0.825845i
$776$	7.36342	+	7.36342i	0.264331	+	0.264331i
$777$	1.53078	+	1.53078i	0.0549165	+	0.0549165i
$778$			12.7622i			0.457546i
$779$	−11.8478	+	11.8478i	−0.424492	+	0.424492i
$780$	−7.20309	−	5.52182i	−0.257912	−	0.197713i
$781$	74.4958			2.66567
$782$	−4.94663	−	12.7044i	−0.176891	−	0.454310i
$783$			5.84782i			0.208984i
$784$		−	6.14306i		−	0.219395i
$785$	9.24585	−	1.22160i	0.329999	−	0.0436008i
$786$	9.66713			0.344815
$787$	−11.4358	−	11.4358i	−0.407644	−	0.407644i	0.473272	−	0.880916i	$-0.343073\pi$
$787$	−11.4358	−	11.4358i	−0.407644	−	0.407644i	−0.880916	+	0.473272i	$0.843073\pi$
$788$	10.6447	−	10.6447i	0.379203	−	0.379203i
$789$	11.9038	+	11.9038i	0.423785	+	0.423785i
$790$	−3.66412	+	4.77976i	−0.130364	+	0.170056i
$791$			23.1834i			0.824306i
$792$	−3.41421	+	3.41421i	−0.121319	+	0.121319i
$793$	14.7150	−	14.7150i	0.522546	−	0.522546i
$794$	−1.22024	+	1.22024i	−0.0433047	+	0.0433047i
$795$	15.3583	−	20.0345i	0.544702	−	0.710551i
$796$	−3.53712	+	3.53712i	−0.125370	+	0.125370i
$797$	6.55049			0.232030			0.116015	−	0.993247i	$-0.462988\pi$
$797$	6.55049			0.232030			0.116015	+	0.993247i	$0.462988\pi$
$798$		−	10.2540i		−	0.362988i
$799$	−44.6134	−	19.6080i	−1.57831	−	0.693682i
$800$	4.82843	−	1.29857i	0.170711	−	0.0459115i
$801$		−	10.1179i		−	0.357498i
$802$	−5.35462	−	5.35462i	−0.189078	−	0.189078i
$803$		−	35.3488i		−	1.24743i
$804$	4.65898	−	4.65898i	0.164310	−	0.164310i
$805$	−26.5740	+	3.51107i	−0.936612	+	0.123749i
$806$	−15.2305	−	15.2305i	−0.536472	−	0.536472i
$807$	31.6914			1.11559
$808$	5.10684			0.179658
$809$	27.0436	+	27.0436i	0.950802	+	0.950802i	0.998845	−	0.0480428i	$-0.0152984\pi$
$809$	27.0436	+	27.0436i	0.950802	+	0.950802i	−0.0480428	+	0.998845i	$0.515298\pi$
$810$	−0.292893	−	2.21680i	−0.0102912	−	0.0778905i
$811$	−11.2335	+	11.2335i	−0.394462	+	0.394462i	−0.876275	−	0.481812i	$-0.839979\pi$
$811$	−11.2335	+	11.2335i	−0.394462	+	0.394462i	0.481812	+	0.876275i	$0.339979\pi$
$812$			21.2003i			0.743985i
$813$	15.8669	+	15.8669i	0.556476	+	0.556476i
$814$		−	2.88327i		−	0.101059i
$815$	26.5747	+	20.3719i	0.930870	+	0.713596i
$816$	3.84214	−	1.49598i	0.134502	−	0.0523699i
$817$			13.9496i			0.488036i
$818$	27.8663			0.974322
$819$	−10.4051	+	10.4051i	−0.363584	+	0.363584i
$820$	−8.05894	+	10.5127i	−0.281430	+	0.367120i
$821$	29.1729	−	29.1729i	1.01814	−	1.01814i	0.0183084	−	0.999832i	$-0.494172\pi$
$821$	29.1729	−	29.1729i	1.01814	−	1.01814i	0.999832	−	0.0183084i	$-0.00582806\pi$
$822$	8.58880	−	8.58880i	0.299569	−	0.299569i
$823$	−9.12186	+	9.12186i	−0.317968	+	0.317968i	−0.847986	−	0.530018i	$-0.822185\pi$
$823$	−9.12186	+	9.12186i	−0.317968	+	0.317968i	0.530018	+	0.847986i	$0.322185\pi$
$824$			4.78811i			0.166802i
$825$	6.27006	+	23.3137i	0.218296	+	0.811679i
$826$	−4.23685	−	4.23685i	−0.147419	−	0.147419i
$827$	10.6147	−	10.6147i	0.369111	−	0.369111i	−0.498042	−	0.867153i	$-0.665947\pi$
$827$	10.6147	−	10.6147i	0.369111	−	0.369111i	0.867153	+	0.498042i	$0.165947\pi$
$828$	−2.33812	−	2.33812i	−0.0812554	−	0.0812554i
$829$	27.7117			0.962467			0.481234	−	0.876592i	$-0.340189\pi$
$829$	27.7117			0.962467			0.481234	+	0.876592i	$0.340189\pi$
$830$	−2.17490	−	16.4610i	−0.0754919	−	0.571371i
$831$		−	0.761136i		−	0.0264035i
$832$		−	4.05894i		−	0.140718i
$833$	−23.1878	−	10.1912i	−0.803408	−	0.353105i
$834$	−22.3331			−0.773332
$835$	23.1630	−	30.2156i	0.801589	−	1.04565i
$836$	−9.65685	+	9.65685i	−0.333989	+	0.333989i
$837$		−	5.30661i		−	0.183423i
$838$	12.1738	+	12.1738i	0.420537	+	0.420537i
$839$	9.34009	+	9.34009i	0.322456	+	0.322456i	0.849708	−	0.527253i	$-0.176778\pi$
$839$	9.34009	+	9.34009i	0.322456	+	0.322456i	−0.527253	+	0.849708i	$0.676778\pi$
$840$	−1.06184	−	8.03666i	−0.0366368	−	0.277291i
$841$		−	5.19698i		−	0.179206i
$842$	22.6520			0.780639
$843$	3.90375	−	3.90375i	0.134452	−	0.134452i
$844$	−2.21522	−	2.21522i	−0.0762509	−	0.0762509i
$845$	1.01781	+	7.70340i	0.0350136	+	0.265005i
$846$	−11.8193			−0.406356
$847$	−31.5662	−	31.5662i	−1.08463	−	1.08463i
$848$	11.2895			0.387682
$849$	14.6074			0.501325
$850$	3.10865	−	20.3798i	0.106626	−	0.699021i
$851$	1.97453			0.0676859
$852$	−15.4286			−0.528575
$853$	12.9665	+	12.9665i	0.443963	+	0.443963i	0.893342	−	0.449378i	$-0.148354\pi$
$853$	12.9665	+	12.9665i	0.443963	+	0.443963i	−0.449378	+	0.893342i	$0.648354\pi$
$854$	18.5871			0.636037
$855$	−0.828427	−	6.27006i	−0.0283316	−	0.214432i
$856$	−8.77249	−	8.77249i	−0.299838	−	0.299838i
$857$	0.345388	−	0.345388i	0.0117982	−	0.0117982i	−0.701183	−	0.712981i	$-0.747344\pi$
$857$	0.345388	−	0.345388i	0.0117982	−	0.0117982i	0.712981	+	0.701183i	$0.247344\pi$
$858$	19.5983			0.669075
$859$		−	22.6274i		−	0.772038i	−0.922491	−	0.386019i	$-0.873850\pi$
$859$		−	22.6274i		−	0.772038i	0.922491	−	0.386019i	$-0.126150\pi$
$860$	1.44453	+	10.9331i	0.0492581	+	0.372817i
$861$	15.1859	+	15.1859i	0.517536	+	0.517536i
$862$	13.7220	+	13.7220i	0.467374	+	0.467374i
$863$		−	5.61228i		−	0.191044i	−0.995427	−	0.0955221i	$-0.969548\pi$
$863$		−	5.61228i		−	0.191044i	0.995427	−	0.0955221i	$-0.0304521\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−30.9178	+	40.3316i	−1.05124	+	1.37131i
$866$	−32.8226			−1.11536
$867$	0.727265	−	16.9844i	0.0246992	−	0.576822i
$868$		−	19.2382i		−	0.652988i
$869$		−	13.0049i		−	0.441160i
$870$	1.71279	+	12.9635i	0.0580689	+	0.439502i
$871$	−26.7435			−0.906170
$872$	−12.1666	−	12.1666i	−0.412011	−	0.412011i
$873$	7.36342	−	7.36342i	0.249214	−	0.249214i
$874$	−6.61321	−	6.61321i	−0.223695	−	0.223695i
$875$	−37.4687	−	15.4590i	−1.26667	−	0.522610i
$876$			7.32097i			0.247353i
$877$	−31.9781	+	31.9781i	−1.07983	+	1.07983i	−0.0833008	+	0.996524i	$0.526546\pi$
$877$	−31.9781	+	31.9781i	−1.07983	+	1.07983i	−0.996524	+	0.0833008i	$0.973454\pi$
$878$	−5.00301	+	5.00301i	−0.168843	+	0.168843i
$879$	−1.33086	+	1.33086i	−0.0448887	+	0.0448887i
$880$	−6.56864	+	8.56864i	−0.221429	+	0.288849i
$881$	20.5650	−	20.5650i	0.692852	−	0.692852i	−0.270007	−	0.962858i	$-0.587026\pi$
$881$	20.5650	−	20.5650i	0.692852	−	0.692852i	0.962858	+	0.270007i	$0.0870259\pi$
$882$	−6.14306			−0.206848
$883$		−	54.8649i		−	1.84635i	−0.384380	−	0.923175i	$-0.625585\pi$
$883$		−	54.8649i		−	1.84635i	0.384380	−	0.923175i	$-0.374415\pi$
$884$	−15.3210	−	6.73371i	−0.515300	−	0.226479i
$885$	−2.93303	−	2.24843i	−0.0985926	−	0.0755802i
$886$		−	9.49648i		−	0.319041i
$887$	0.510625	+	0.510625i	0.0171451	+	0.0171451i	0.715627	−	0.698482i	$-0.246141\pi$
$887$	0.510625	+	0.510625i	0.0171451	+	0.0171451i	−0.698482	+	0.715627i	$0.746141\pi$
$888$			0.597146i			0.0200389i
$889$	−51.6607	+	51.6607i	−1.73264	+	1.73264i
$890$	−2.96346	−	22.4293i	−0.0993354	−	0.751833i
$891$	3.41421	+	3.41421i	0.114380	+	0.114380i
$892$	14.6923			0.491935
$893$	−33.4301			−1.11869
$894$	2.04577	+	2.04577i	0.0684209	+	0.0684209i
$895$	−31.6026	+	4.17546i	−1.05636	+	0.139570i
$896$	2.56350	−	2.56350i	0.0856405	−	0.0856405i
$897$			13.4213i			0.448125i
$898$	13.9963	+	13.9963i	0.467064	+	0.467064i
$899$			31.0321i			1.03498i
$900$	−1.29857	−	4.82843i	−0.0432858	−	0.160948i
$901$	18.7290	−	42.6134i	0.623954	−	1.41966i
$902$		−	28.6032i		−	0.952381i
$903$	17.8799			0.595007
$904$	−4.52182	+	4.52182i	−0.150394	+	0.150394i
$905$	−10.0082	+	13.0555i	−0.332683	+	0.433978i
$906$	−5.13580	+	5.13580i	−0.170625	+	0.170625i
$907$	15.9554	−	15.9554i	0.529791	−	0.529791i	−0.390719	−	0.920510i	$-0.627774\pi$
$907$	15.9554	−	15.9554i	0.529791	−	0.529791i	0.920510	+	0.390719i	$0.127774\pi$
$908$	6.55728	−	6.55728i	0.217611	−	0.217611i
$909$		−	5.10684i		−	0.169383i
$910$	−20.0185	+	26.1136i	−0.663606	+	0.865658i
$911$	−19.7608	−	19.7608i	−0.654705	−	0.654705i	0.299418	−	0.954122i	$-0.403208\pi$
$911$	−19.7608	−	19.7608i	−0.654705	−	0.654705i	−0.954122	+	0.299418i	$0.903208\pi$
$912$	2.00000	−	2.00000i	0.0662266	−	0.0662266i
$913$	25.3525	+	25.3525i	0.839045	+	0.839045i
$914$	−13.8823			−0.459187
$915$	11.3655	−	1.50166i	0.375733	−	0.0496435i
$916$			11.2346i			0.371202i
$917$		−	35.0466i		−	1.15734i
$918$	−1.49598	−	3.84214i	−0.0493748	−	0.126809i
$919$	−38.4512			−1.26839			−0.634194	−	0.773174i	$-0.718668\pi$
$919$	−38.4512			−1.26839			−0.634194	+	0.773174i	$0.718668\pi$
$920$	−5.86798	−	4.49834i	−0.193461	−	0.148306i
$921$	14.3116	−	14.3116i	0.471583	−	0.471583i
$922$		−	15.6082i		−	0.514028i
$923$	44.2817	+	44.2817i	1.45755	+	1.45755i
$924$	12.3777	+	12.3777i	0.407196	+	0.407196i
$925$	2.58710	+	1.49047i	0.0850633	+	0.0490062i
$926$			5.08396i			0.167069i
$927$	4.78811			0.157262
$928$	−4.13503	+	4.13503i	−0.135739	+	0.135739i
$929$	−8.35346	−	8.35346i	−0.274068	−	0.274068i	0.556667	−	0.830736i	$-0.312080\pi$
$929$	−8.35346	−	8.35346i	−0.274068	−	0.274068i	−0.830736	+	0.556667i	$0.812080\pi$
$930$	−1.55427	−	11.7637i	−0.0509665	−	0.385747i
$931$	−17.3752			−0.569450
$932$	−7.10652	−	7.10652i	−0.232782	−	0.232782i
$933$	8.38711			0.274582
$934$	22.0615			0.721874
$935$	21.4461	+	39.0093i	0.701363	+	1.27574i
$936$	−4.05894			−0.132671
$937$	18.8139			0.614623			0.307312	−	0.951609i	$-0.400571\pi$
$937$	18.8139			0.614623			0.307312	+	0.951609i	$0.400571\pi$
$938$	−16.8904	−	16.8904i	−0.551490	−	0.551490i
$939$	7.24341			0.236380
$940$	−26.2011	+	3.46180i	−0.854585	+	0.112911i
$941$	8.74245	+	8.74245i	0.284996	+	0.284996i	0.835098	−	0.550102i	$-0.185411\pi$
$941$	8.74245	+	8.74245i	0.284996	+	0.284996i	−0.550102	+	0.835098i	$0.685411\pi$
$942$	2.94921	−	2.94921i	0.0960903	−	0.0960903i
$943$	19.5880			0.637874
$944$		−	1.65276i		−	0.0537928i
$945$	−8.03666	+	1.06184i	−0.261432	+	0.0345415i
$946$	−16.8387	−	16.8387i	−0.547473	−	0.547473i
$947$	−4.32753	−	4.32753i	−0.140626	−	0.140626i	0.633289	−	0.773915i	$-0.281704\pi$
$947$	−4.32753	−	4.32753i	−0.140626	−	0.140626i	−0.773915	+	0.633289i	$0.781704\pi$
$948$			2.69339i			0.0874774i
$949$	21.0120	−	21.0120i	0.682077	−	0.682077i
$950$	−3.67292	−	13.6569i	−0.119165	−	0.443087i
$951$	−32.9260			−1.06770
$952$	−5.42344	−	13.9290i	−0.175775	−	0.451443i
$953$		−	39.7689i		−	1.28824i	−0.764923	−	0.644121i	$-0.777223\pi$
$953$		−	39.7689i		−	1.28824i	0.764923	−	0.644121i	$-0.222777\pi$
$954$		−	11.2895i		−	0.365510i
$955$	1.28219	+	9.70444i	0.0414907	+	0.314028i
$956$	21.5638			0.697422
$957$	−19.9657	−	19.9657i	−0.645399	−	0.645399i
$958$	−15.0721	+	15.0721i	−0.486958	+	0.486958i
$959$	−31.1373	−	31.1373i	−1.00548	−	1.00548i
$960$	1.36041	−	1.77462i	0.0439070	−	0.0572757i
$961$			2.83994i			0.0916110i
$962$	1.71387	−	1.71387i	0.0552574	−	0.0552574i
$963$	−8.77249	+	8.77249i	−0.282690	+	0.282690i
$964$	8.71170	−	8.71170i	0.280585	−	0.280585i
$965$	11.2841	+	8.65030i	0.363249	+	0.278463i
$966$	−8.47648	+	8.47648i	−0.272726	+	0.272726i
$967$	−0.532576			−0.0171265			−0.00856325	−	0.999963i	$-0.502726\pi$
$967$	−0.532576			−0.0171265			−0.00856325	+	0.999963i	$0.502726\pi$
$968$		−	12.3137i		−	0.395778i
$969$	−4.23128	−	10.8672i	−0.135928	−	0.349105i
$970$	14.1666	−	18.4799i	0.454861	−	0.593355i
$971$			39.1947i			1.25782i	0.777479	+	0.628909i	$0.216498\pi$
$971$			39.1947i			1.25782i	−0.777479	+	0.628909i	$0.783502\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$			80.9650i			2.59562i
$974$	−26.6368	+	26.6368i	−0.853498	+	0.853498i
$975$	−10.1311	+	17.5851i	−0.324453	+	0.563175i
$976$	3.62534	+	3.62534i	0.116044	+	0.116044i
$977$	3.19429			0.102194			0.0510972	−	0.998694i	$-0.483728\pi$
$977$	3.19429			0.102194			0.0510972	+	0.998694i	$0.483728\pi$
$978$	14.9748			0.478842
$979$	34.5446	+	34.5446i	1.10405	+	1.10405i
$980$	−13.6180	+	1.79926i	−0.435010	+	0.0574753i
$981$	−12.1666	+	12.1666i	−0.388448	+	0.388448i
$982$			2.10930i			0.0673106i
$983$	−23.3072	−	23.3072i	−0.743383	−	0.743383i	0.229845	−	0.973227i	$-0.426178\pi$
$983$	−23.3072	−	23.3072i	−0.743383	−	0.743383i	−0.973227	+	0.229845i	$0.926178\pi$
$984$			5.92391i			0.188847i
$985$	−26.7150	−	20.4795i	−0.851212	−	0.652531i
$986$	8.74824	+	22.4681i	0.278601	+	0.715531i
$987$			42.8490i			1.36390i
$988$	−11.4804			−0.365241
$989$	11.5315	−	11.5315i	0.366680	−	0.366680i
$990$	8.56864	+	6.56864i	0.272329	+	0.208765i
$991$	−21.7305	+	21.7305i	−0.690292	+	0.690292i	−0.962296	−	0.272004i	$-0.912313\pi$
$991$	−21.7305	+	21.7305i	−0.690292	+	0.690292i	0.272004	+	0.962296i	$0.412313\pi$
$992$	3.75234	−	3.75234i	0.119137	−	0.119137i
$993$	23.5310	−	23.5310i	0.746734	−	0.746734i
$994$			55.9338i			1.77411i
$995$	8.87709	+	6.80510i	0.281423	+	0.215736i
$996$	−5.25067	−	5.25067i	−0.166374	−	0.166374i
$997$	11.4029	−	11.4029i	0.361132	−	0.361132i	−0.503098	−	0.864230i	$-0.667806\pi$
$997$	11.4029	−	11.4029i	0.361132	−	0.361132i	0.864230	+	0.503098i	$0.167806\pi$
$998$	20.0045	+	20.0045i	0.633231	+	0.633231i
$999$	0.597146			0.0188929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.m.a.259.3	✓	8
3.2	odd	2		1530.2.n.r.1279.2		8
5.4	even	2		510.2.m.b.259.2	yes	8
15.14	odd	2		1530.2.n.q.1279.1		8
17.13	even	4		510.2.m.b.319.2	yes	8
51.47	odd	4		1530.2.n.q.829.1		8
85.64	even	4	inner	510.2.m.a.319.4	yes	8
255.149	odd	4		1530.2.n.r.829.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.m.a.259.3	✓	8	1.1	even	1	trivial
510.2.m.a.319.4	yes	8	85.64	even	4	inner
510.2.m.b.259.2	yes	8	5.4	even	2
510.2.m.b.319.2	yes	8	17.13	even	4
1530.2.n.q.829.1		8	51.47	odd	4
1530.2.n.q.1279.1		8	15.14	odd	2
1530.2.n.r.829.1		8	255.149	odd	4
1530.2.n.r.1279.2		8	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.292893 - 2.21680i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.56350 + 2.56350i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.292893 - 2.21680i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.56350 + 2.56350i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(0.292893 + 2.21680i) q^{10} +(-3.41421 - 3.41421i) q^{11} +(0.707107 + 0.707107i) q^{12} -4.05894i q^{13} +(2.56350 - 2.56350i) q^{14} +(1.36041 - 1.77462i) q^{15} +1.00000 q^{16} +(1.65898 - 3.77462i) q^{17} -1.00000i q^{18} -2.82843i q^{19} +(-0.292893 - 2.21680i) q^{20} -3.62534 q^{21} +(3.41421 + 3.41421i) q^{22} +(-2.33812 + 2.33812i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.82843 + 1.29857i) q^{25} +4.05894i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.56350 + 2.56350i) q^{28} +(4.13503 - 4.13503i) q^{29} +(-1.36041 + 1.77462i) q^{30} +(-3.75234 + 3.75234i) q^{31} -1.00000 q^{32} -4.82843i q^{33} +(-1.65898 + 3.77462i) q^{34} +(6.43361 + 4.93194i) q^{35} +1.00000i q^{36} +(-0.422246 - 0.422246i) q^{37} +2.82843i q^{38} +(2.87011 - 2.87011i) q^{39} +(0.292893 + 2.21680i) q^{40} +(-4.18884 - 4.18884i) q^{41} +3.62534 q^{42} -4.93194 q^{43} +(-3.41421 - 3.41421i) q^{44} +(2.21680 - 0.292893i) q^{45} +(2.33812 - 2.33812i) q^{46} -11.8193i q^{47} +(0.707107 + 0.707107i) q^{48} -6.14306i q^{49} +(4.82843 - 1.29857i) q^{50} +(3.84214 - 1.49598i) q^{51} -4.05894i q^{52} +11.2895 q^{53} +(0.707107 - 0.707107i) q^{54} +(-6.56864 + 8.56864i) q^{55} +(2.56350 - 2.56350i) q^{56} +(2.00000 - 2.00000i) q^{57} +(-4.13503 + 4.13503i) q^{58} -1.65276i q^{59} +(1.36041 - 1.77462i) q^{60} +(3.62534 + 3.62534i) q^{61} +(3.75234 - 3.75234i) q^{62} +(-2.56350 - 2.56350i) q^{63} +1.00000 q^{64} +(-8.99787 + 1.18884i) q^{65} +4.82843i q^{66} -6.58880i q^{67} +(1.65898 - 3.77462i) q^{68} -3.30661 q^{69} +(-6.43361 - 4.93194i) q^{70} +(-10.9097 + 10.9097i) q^{71} -1.00000i q^{72} +(5.17671 + 5.17671i) q^{73} +(0.422246 + 0.422246i) q^{74} +(-4.33244 - 2.49598i) q^{75} -2.82843i q^{76} +17.5047 q^{77} +(-2.87011 + 2.87011i) q^{78} +(1.90452 + 1.90452i) q^{79} +(-0.292893 - 2.21680i) q^{80} -1.00000 q^{81} +(4.18884 + 4.18884i) q^{82} -7.42557 q^{83} -3.62534 q^{84} +(-8.85350 - 2.57207i) q^{85} +4.93194 q^{86} +5.84782 q^{87} +(3.41421 + 3.41421i) q^{88} -10.1179 q^{89} +(-2.21680 + 0.292893i) q^{90} +(10.4051 + 10.4051i) q^{91} +(-2.33812 + 2.33812i) q^{92} -5.30661 q^{93} +11.8193i q^{94} +(-6.27006 + 0.828427i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-7.36342 - 7.36342i) q^{97} +6.14306i q^{98} +(3.41421 - 3.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} + 8 q^{10} - 16 q^{11} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} - 8 q^{20} - 16 q^{21} + 16 q^{22} + 16 q^{23} - 16 q^{25} - 4 q^{28} + 8 q^{29} - 4 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 16 q^{35} + 4 q^{39} + 8 q^{40} - 4 q^{41} + 16 q^{42} - 24 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{50} + 16 q^{53} + 8 q^{55} + 4 q^{56} + 16 q^{57} - 8 q^{58} + 4 q^{60} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} - 44 q^{65} - 4 q^{68} - 24 q^{69} - 16 q^{70} - 44 q^{71} + 20 q^{73} - 16 q^{75} + 48 q^{77} - 4 q^{78} + 16 q^{79} - 8 q^{80} - 8 q^{81} + 4 q^{82} - 16 q^{83} - 16 q^{84} - 8 q^{85} + 24 q^{86} + 16 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 40 q^{93} + 20 q^{97} + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 + 8 * q^10 - 16 * q^11 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 - 8 * q^20 - 16 * q^21 + 16 * q^22 + 16 * q^23 - 16 * q^25 - 4 * q^28 + 8 * q^29 - 4 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 16 * q^35 + 4 * q^39 + 8 * q^40 - 4 * q^41 + 16 * q^42 - 24 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^50 + 16 * q^53 + 8 * q^55 + 4 * q^56 + 16 * q^57 - 8 * q^58 + 4 * q^60 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 - 44 * q^65 - 4 * q^68 - 24 * q^69 - 16 * q^70 - 44 * q^71 + 20 * q^73 - 16 * q^75 + 48 * q^77 - 4 * q^78 + 16 * q^79 - 8 * q^80 - 8 * q^81 + 4 * q^82 - 16 * q^83 - 16 * q^84 - 8 * q^85 + 24 * q^86 + 16 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 40 * q^93 + 20 * q^97 + 16 * q^99

Introduction

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