LMFDB - Embedded newform 750.2.g.d.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.2
Root			$1.31557 - 1.28500i$ of defining polynomial
Character	$\chi$	$=$	750.151
Dual form			750.2.g.d.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} +4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} +4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.51061 - 4.64918i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(1.43361 - 4.41219i) q^{13} +(1.31557 + 4.04892i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.815575 - 0.592550i) q^{17} +1.00000 q^{18} +(1.00000 + 0.726543i) q^{19} +(3.44422 - 2.50237i) q^{21} +(3.95483 - 2.87335i) q^{22} +(1.38197 + 4.25325i) q^{23} -1.00000 q^{24} +4.63925 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.44422 + 2.50237i) q^{28} +(-3.42049 + 2.48513i) q^{29} +(-0.826185 - 0.600258i) q^{31} +1.00000 q^{32} +(-3.95483 - 2.87335i) q^{33} +(0.311522 - 0.958765i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-3.31152 + 10.1918i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.43361 - 4.41219i) q^{39} +(1.42049 - 4.37183i) q^{41} +(3.44422 + 2.50237i) q^{42} +10.4984 q^{43} +(3.95483 + 2.87335i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-1.63925 + 1.19099i) q^{47} +(-0.309017 - 0.951057i) q^{48} +11.1245 q^{49} -1.00811 q^{51} +(1.43361 + 4.41219i) q^{52} +(8.94413 - 6.49829i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-3.44422 - 2.50237i) q^{56} +1.23607 q^{57} +(-3.42049 - 2.48513i) q^{58} +(-0.656508 + 2.02052i) q^{59} +(1.19754 + 3.68565i) q^{61} +(0.315575 - 0.971238i) q^{62} +(1.31557 - 4.04892i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.51061 - 4.64918i) q^{66} +(3.03434 + 2.20457i) q^{67} +1.00811 q^{68} +(3.61803 + 2.62866i) q^{69} +(-10.1457 + 7.37130i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-1.05975 - 3.26157i) q^{73} -10.7163 q^{74} -1.23607 q^{76} +(-6.43110 - 19.7929i) q^{77} +(3.75324 - 2.72689i) q^{78} +(-5.16968 + 3.75599i) q^{79} +(-0.809017 - 0.587785i) q^{81} +4.59681 q^{82} +(5.70151 + 4.14239i) q^{83} +(-1.31557 + 4.04892i) q^{84} +(3.24417 + 9.98454i) q^{86} +(-1.30651 + 4.02103i) q^{87} +(-1.51061 + 4.64918i) q^{88} +(0.693488 + 2.13434i) q^{89} +(6.10328 - 18.7840i) q^{91} +(-3.61803 - 2.62866i) q^{92} -1.02122 q^{93} +(-1.63925 - 1.19099i) q^{94} +(0.809017 - 0.587785i) q^{96} +(-6.49586 + 4.71952i) q^{97} +(3.43766 + 10.5800i) q^{98} -4.88844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 5 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{18} + 8 q^{19} + 3 q^{21} + 20 q^{23} - 8 q^{24} + 14 q^{26} + 2 q^{27} - 3 q^{28} - 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} - 2 q^{36} - 21 q^{37} - 12 q^{38} + 6 q^{39} + 2 q^{41} + 3 q^{42} + 32 q^{43} - 20 q^{46} + 10 q^{47} + 2 q^{48} + 22 q^{49} - 2 q^{51} - 6 q^{52} - 7 q^{53} + 2 q^{54} - 3 q^{56} - 8 q^{57} - 18 q^{58} - 25 q^{59} + 10 q^{61} - 6 q^{62} + 2 q^{63} - 2 q^{64} + 5 q^{66} + 2 q^{67} + 2 q^{68} + 20 q^{69} - 2 q^{72} + 24 q^{73} - 26 q^{74} + 8 q^{76} - 35 q^{77} + q^{78} - 6 q^{79} - 2 q^{81} + 42 q^{82} - 11 q^{83} - 2 q^{84} + 2 q^{86} - 7 q^{87} - 5 q^{88} + 9 q^{89} - 4 q^{91} - 20 q^{92} + 6 q^{93} + 10 q^{94} + 2 q^{96} - q^{97} + 7 q^{98} + 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 5 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^18 + 8 * q^19 + 3 * q^21 + 20 * q^23 - 8 * q^24 + 14 * q^26 + 2 * q^27 - 3 * q^28 - 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 - 2 * q^36 - 21 * q^37 - 12 * q^38 + 6 * q^39 + 2 * q^41 + 3 * q^42 + 32 * q^43 - 20 * q^46 + 10 * q^47 + 2 * q^48 + 22 * q^49 - 2 * q^51 - 6 * q^52 - 7 * q^53 + 2 * q^54 - 3 * q^56 - 8 * q^57 - 18 * q^58 - 25 * q^59 + 10 * q^61 - 6 * q^62 + 2 * q^63 - 2 * q^64 + 5 * q^66 + 2 * q^67 + 2 * q^68 + 20 * q^69 - 2 * q^72 + 24 * q^73 - 26 * q^74 + 8 * q^76 - 35 * q^77 + q^78 - 6 * q^79 - 2 * q^81 + 42 * q^82 - 11 * q^83 - 2 * q^84 + 2 * q^86 - 7 * q^87 - 5 * q^88 + 9 * q^89 - 4 * q^91 - 20 * q^92 + 6 * q^93 + 10 * q^94 + 2 * q^96 - q^97 + 7 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	4.25729			1.60910			0.804552	−	0.593882i	$-0.202406\pi$
$7$	4.25729			1.60910			0.804552	+	0.593882i	$0.202406\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−1.51061	−	4.64918i	−0.455466	−	1.40178i	−0.870587	−	0.492014i	$-0.836261\pi$
$11$	−1.51061	−	4.64918i	−0.455466	−	1.40178i	0.415121	−	0.909766i	$-0.363739\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	1.43361	−	4.41219i	0.397611	−	1.22372i	−0.529298	−	0.848436i	$-0.677544\pi$
$13$	1.43361	−	4.41219i	0.397611	−	1.22372i	0.926909	−	0.375286i	$-0.122456\pi$
$14$	1.31557	+	4.04892i	0.351602	+	1.08212i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.815575	−	0.592550i	−0.197806	−	0.143714i	0.484473	−	0.874806i	$-0.339011\pi$
$17$	−0.815575	−	0.592550i	−0.197806	−	0.143714i	−0.682279	+	0.731092i	$0.739011\pi$
$18$	1.00000			0.235702
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	0.696555	−	0.717504i	$-0.254715\pi$
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	−0.467139	+	0.884184i	$0.654715\pi$
$20$		0			0
$21$	3.44422	−	2.50237i	0.751590	−	0.546062i
$22$	3.95483	−	2.87335i	0.843172	−	0.612601i
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	0.985434	+	0.170060i	$0.0543961\pi$
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	−0.697274	+	0.716805i	$0.745604\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	4.63925			0.909833
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−3.44422	+	2.50237i	−0.650896	+	0.472904i
$29$	−3.42049	+	2.48513i	−0.635170	+	0.461478i	−0.858187	−	0.513337i	$-0.828409\pi$
$29$	−3.42049	+	2.48513i	−0.635170	+	0.461478i	0.223018	+	0.974814i	$0.428409\pi$
$30$		0			0
$31$	−0.826185	−	0.600258i	−0.148387	−	0.107810i	0.511115	−	0.859513i	$-0.329233\pi$
$31$	−0.826185	−	0.600258i	−0.148387	−	0.107810i	−0.659502	+	0.751703i	$0.729233\pi$
$32$	1.00000			0.176777
$33$	−3.95483	−	2.87335i	−0.688447	−	0.500186i
$34$	0.311522	−	0.958765i	0.0534255	−	0.164427i
$35$		0			0
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−3.31152	+	10.1918i	−0.544411	+	1.67552i	0.177976	+	0.984035i	$0.443045\pi$
$37$	−3.31152	+	10.1918i	−0.544411	+	1.67552i	−0.722387	+	0.691489i	$0.756955\pi$
$38$	−0.381966	+	1.17557i	−0.0619631	+	0.190703i
$39$	−1.43361	−	4.41219i	−0.229561	−	0.706516i
$40$		0			0
$41$	1.42049	−	4.37183i	0.221844	−	0.682765i	−0.776753	−	0.629806i	$-0.783135\pi$
$41$	1.42049	−	4.37183i	0.221844	−	0.682765i	0.998597	−	0.0529595i	$-0.0168654\pi$
$42$	3.44422	+	2.50237i	0.531454	+	0.386124i
$43$	10.4984			1.60099			0.800493	−	0.599342i	$-0.204571\pi$
$43$	10.4984			1.60099			0.800493	+	0.599342i	$0.204571\pi$
$44$	3.95483	+	2.87335i	0.596213	+	0.433174i
$45$		0			0
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	−1.63925	+	1.19099i	−0.239110	+	0.173723i	−0.700887	−	0.713273i	$-0.747212\pi$
$47$	−1.63925	+	1.19099i	−0.239110	+	0.173723i	0.461777	+	0.886996i	$0.347212\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	11.1245			1.58922
$50$		0			0
$51$	−1.00811			−0.141163
$52$	1.43361	+	4.41219i	0.198806	+	0.611861i
$53$	8.94413	−	6.49829i	1.22857	−	0.892609i	0.231789	−	0.972766i	$-0.425542\pi$
$53$	8.94413	−	6.49829i	1.22857	−	0.892609i	0.996782	+	0.0801570i	$0.0255422\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$		0			0
$56$	−3.44422	−	2.50237i	−0.460253	−	0.334393i
$57$	1.23607			0.163721
$58$	−3.42049	−	2.48513i	−0.449133	−	0.326314i
$59$	−0.656508	+	2.02052i	−0.0854701	+	0.263050i	−0.984653	−	0.174523i	$-0.944162\pi$
$59$	−0.656508	+	2.02052i	−0.0854701	+	0.263050i	0.899183	+	0.437573i	$0.144162\pi$
$60$		0			0
$61$	1.19754	+	3.68565i	0.153329	+	0.471899i	0.997988	−	0.0634064i	$-0.0201964\pi$
$61$	1.19754	+	3.68565i	0.153329	+	0.471899i	−0.844658	+	0.535306i	$0.820196\pi$
$62$	0.315575	−	0.971238i	0.0400780	−	0.123347i
$63$	1.31557	−	4.04892i	0.165747	−	0.510116i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$		0			0
$66$	1.51061	−	4.64918i	0.185943	−	0.572275i
$67$	3.03434	+	2.20457i	0.370703	+	0.269332i	0.757502	−	0.652832i	$-0.226419\pi$
$67$	3.03434	+	2.20457i	0.370703	+	0.269332i	−0.386799	+	0.922164i	$0.626419\pi$
$68$	1.00811			0.122251
$69$	3.61803	+	2.62866i	0.435560	+	0.316453i
$70$		0			0
$71$	−10.1457	+	7.37130i	−1.20408	+	0.874813i	−0.994679	−	0.103018i	$-0.967150\pi$
$71$	−10.1457	+	7.37130i	−1.20408	+	0.874813i	−0.209397	+	0.977831i	$0.567150\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	−1.05975	−	3.26157i	−0.124034	−	0.381738i	0.869690	−	0.493599i	$-0.164319\pi$
$73$	−1.05975	−	3.26157i	−0.124034	−	0.381738i	−0.993724	+	0.111861i	$0.964319\pi$
$74$	−10.7163			−1.24575
$75$		0			0
$76$	−1.23607			−0.141787
$77$	−6.43110	−	19.7929i	−0.732892	−	2.25561i
$78$	3.75324	−	2.72689i	0.424970	−	0.308759i
$79$	−5.16968	+	3.75599i	−0.581634	+	0.422582i	−0.839313	−	0.543649i	$-0.817042\pi$
$79$	−5.16968	+	3.75599i	−0.581634	+	0.422582i	0.257679	+	0.966231i	$0.417042\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	4.59681			0.507633
$83$	5.70151	+	4.14239i	0.625822	+	0.454686i	0.854950	−	0.518710i	$-0.173588\pi$
$83$	5.70151	+	4.14239i	0.625822	+	0.454686i	−0.229128	+	0.973396i	$0.573588\pi$
$84$	−1.31557	+	4.04892i	−0.143541	+	0.441774i
$85$		0			0
$86$	3.24417	+	9.98454i	0.349828	+	1.07666i
$87$	−1.30651	+	4.02103i	−0.140073	+	0.431100i
$88$	−1.51061	+	4.64918i	−0.161032	+	0.495604i
$89$	0.693488	+	2.13434i	0.0735096	+	0.226239i	0.981060	−	0.193704i	$-0.0620501\pi$
$89$	0.693488	+	2.13434i	0.0735096	+	0.226239i	−0.907551	+	0.419943i	$0.862050\pi$
$90$		0			0
$91$	6.10328	−	18.7840i	0.639798	−	1.96910i
$92$	−3.61803	−	2.62866i	−0.377206	−	0.274056i
$93$	−1.02122			−0.105896
$94$	−1.63925	−	1.19099i	−0.169076	−	0.122841i
$95$		0			0
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−6.49586	+	4.71952i	−0.659555	+	0.479195i	−0.866513	−	0.499155i	$-0.833644\pi$
$97$	−6.49586	+	4.71952i	−0.659555	+	0.479195i	0.206958	+	0.978350i	$0.433644\pi$
$98$	3.43766	+	10.5800i	0.347256	+	1.06874i
$99$	−4.88844			−0.491306
$100$		0			0
$101$	−17.6310			−1.75435			−0.877174	−	0.480173i	$-0.840574\pi$
$101$	−17.6310			−1.75435			−0.877174	+	0.480173i	$0.840574\pi$
$102$	−0.311522	−	0.958765i	−0.0308452	−	0.0949319i
$103$	−15.9376	+	11.5793i	−1.57038	+	1.14094i	−0.643580	+	0.765378i	$0.722552\pi$
$103$	−15.9376	+	11.5793i	−1.57038	+	1.14094i	−0.926795	+	0.375566i	$0.877448\pi$
$104$	−3.75324	+	2.72689i	−0.368035	+	0.267393i
$105$		0			0
$106$	8.94413	+	6.49829i	0.868731	+	0.631170i
$107$	−6.16695			−0.596181			−0.298091	−	0.954538i	$-0.596350\pi$
$107$	−6.16695			−0.596181			−0.298091	+	0.954538i	$0.596350\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	2.44982	−	7.53977i	0.234650	−	0.722179i	−0.762517	−	0.646968i	$-0.776037\pi$
$109$	2.44982	−	7.53977i	0.234650	−	0.722179i	0.997168	−	0.0752113i	$-0.0239631\pi$
$110$		0			0
$111$	3.31152	+	10.1918i	0.314316	+	0.967364i
$112$	1.31557	−	4.04892i	0.124310	−	0.382587i
$113$	−2.08857	+	6.42795i	−0.196476	+	0.604691i	0.803480	+	0.595332i	$0.202979\pi$
$113$	−2.08857	+	6.42795i	−0.196476	+	0.604691i	−0.999956	+	0.00935951i	$0.997021\pi$
$114$	0.381966	+	1.17557i	0.0357744	+	0.110102i
$115$		0			0
$116$	1.30651	−	4.02103i	0.121307	−	0.373343i
$117$	−3.75324	−	2.72689i	−0.346987	−	0.252101i
$118$	−2.12451			−0.195577
$119$	−3.47214	−	2.52265i	−0.318290	−	0.231251i
$120$		0			0
$121$	−10.4337	+	7.58056i	−0.948523	+	0.689142i
$122$	−3.13520	+	2.27786i	−0.283848	+	0.206228i
$123$	−1.42049	−	4.37183i	−0.128082	−	0.394195i
$124$	1.02122			0.0917083
$125$		0			0
$126$	4.25729			0.379269
$127$	−3.12054	−	9.60403i	−0.276903	−	0.852220i	−0.988710	−	0.149844i	$-0.952123\pi$
$127$	−3.12054	−	9.60403i	−0.276903	−	0.852220i	0.711807	−	0.702376i	$-0.247877\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	8.49336	−	6.17078i	0.747798	−	0.543307i
$130$		0			0
$131$	−5.43780	−	3.95079i	−0.475103	−	0.345182i	0.324324	−	0.945946i	$-0.394863\pi$
$131$	−5.43780	−	3.95079i	−0.475103	−	0.345182i	−0.799427	+	0.600764i	$0.794863\pi$
$132$	4.88844			0.425484
$133$	4.25729	+	3.09310i	0.369154	+	0.268206i
$134$	−1.15901	+	3.56708i	−0.100123	+	0.308148i
$135$		0			0
$136$	0.311522	+	0.958765i	0.0267128	+	0.0822134i
$137$	−5.44672	+	16.7633i	−0.465345	+	1.43218i	0.393203	+	0.919452i	$0.371367\pi$
$137$	−5.44672	+	16.7633i	−0.465345	+	1.43218i	−0.858548	+	0.512733i	$0.828633\pi$
$138$	−1.38197	+	4.25325i	−0.117641	+	0.362061i
$139$	−2.51976	−	7.75502i	−0.213723	−	0.657772i	−0.999242	−	0.0389342i	$-0.987604\pi$
$139$	−2.51976	−	7.75502i	−0.213723	−	0.657772i	0.785519	−	0.618838i	$-0.212396\pi$
$140$		0			0
$141$	−0.626140	+	1.92706i	−0.0527305	+	0.162288i
$142$	−10.1457	−	7.37130i	−0.851410	−	0.618586i
$143$	−22.6787			−1.89649
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$		0			0
$146$	2.77446	−	2.01576i	0.229616	−	0.166826i
$147$	8.99991	−	6.53882i	0.742300	−	0.539313i
$148$	−3.31152	−	10.1918i	−0.272205	−	0.837762i
$149$	10.2230			0.837497			0.418748	−	0.908102i	$-0.362469\pi$
$149$	10.2230			0.837497			0.418748	+	0.908102i	$0.362469\pi$
$150$		0			0
$151$	17.2016			1.39984			0.699922	−	0.714220i	$-0.253218\pi$
$151$	17.2016			1.39984			0.699922	+	0.714220i	$0.253218\pi$
$152$	−0.381966	−	1.17557i	−0.0309815	−	0.0953514i
$153$	−0.815575	+	0.592550i	−0.0659353	+	0.0479048i
$154$	16.8368	−	12.2327i	1.35675	−	0.985738i
$155$		0			0
$156$	3.75324	+	2.72689i	0.300499	+	0.218326i
$157$	18.7425			1.49582			0.747909	−	0.663802i	$-0.231058\pi$
$157$	18.7425			1.49582			0.747909	+	0.663802i	$0.231058\pi$
$158$	−5.16968	−	3.75599i	−0.411277	−	0.298811i
$159$	3.41635	−	10.5145i	0.270935	−	0.833851i
$160$		0			0
$161$	5.88343	+	18.1073i	0.463679	+	1.42706i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	4.32624	−	13.3148i	0.338857	−	1.04289i	−0.625934	−	0.779876i	$-0.715282\pi$
$163$	4.32624	−	13.3148i	0.338857	−	1.04289i	0.964791	−	0.263019i	$-0.0847181\pi$
$164$	1.42049	+	4.37183i	0.110922	+	0.341383i
$165$		0			0
$166$	−2.17778	+	6.70252i	−0.169029	+	0.520217i
$167$	−10.9309	−	7.94175i	−0.845857	−	0.614551i	0.0781438	−	0.996942i	$-0.475101\pi$
$167$	−10.9309	−	7.94175i	−0.845857	−	0.614551i	−0.924001	+	0.382391i	$0.875101\pi$
$168$	−4.25729			−0.328457
$169$	−6.89500	−	5.00951i	−0.530384	−	0.385347i
$170$		0			0
$171$	1.00000	−	0.726543i	0.0764719	−	0.0555601i
$172$	−8.49336	+	6.17078i	−0.647612	+	0.470518i
$173$	2.77609	+	8.54393i	0.211062	+	0.649583i	0.999410	+	0.0343526i	$0.0109369\pi$
$173$	2.77609	+	8.54393i	0.211062	+	0.649583i	−0.788348	+	0.615230i	$0.789063\pi$
$174$	−4.22796			−0.320521
$175$		0			0
$176$	−4.88844			−0.368480
$177$	0.656508	+	2.02052i	0.0493462	+	0.151872i
$178$	−1.81557	+	1.31909i	−0.136083	+	0.0988701i
$179$	−5.68029	+	4.12697i	−0.424565	+	0.308464i	−0.779472	−	0.626437i	$-0.784512\pi$
$179$	−5.68029	+	4.12697i	−0.424565	+	0.308464i	0.354907	+	0.934902i	$0.384512\pi$
$180$		0			0
$181$	9.66968	+	7.02543i	0.718741	+	0.522196i	0.885982	−	0.463720i	$-0.153486\pi$
$181$	9.66968	+	7.02543i	0.718741	+	0.522196i	−0.167240	+	0.985916i	$0.553486\pi$
$182$	19.7506			1.46402
$183$	3.13520	+	2.27786i	0.231761	+	0.168384i
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$		0			0
$186$	−0.315575	−	0.971238i	−0.0231390	−	0.0712147i
$187$	−1.52285	+	4.68686i	−0.111362	+	0.342737i
$188$	0.626140	−	1.92706i	0.0456659	−	0.140545i
$189$	−1.31557	−	4.04892i	−0.0956940	−	0.294516i
$190$		0			0
$191$	1.00000	−	3.07768i	0.0723575	−	0.222693i	−0.908337	−	0.418239i	$-0.862648\pi$
$191$	1.00000	−	3.07768i	0.0723575	−	0.222693i	0.980695	+	0.195545i	$0.0626476\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	7.60802			0.547637			0.273818	−	0.961781i	$-0.411713\pi$
$193$	7.60802			0.547637			0.273818	+	0.961781i	$0.411713\pi$
$194$	−6.49586	−	4.71952i	−0.466376	−	0.338842i
$195$		0			0
$196$	−8.99991	+	6.53882i	−0.642851	+	0.467059i
$197$	3.81549	−	2.77211i	0.271842	−	0.197505i	−0.443509	−	0.896270i	$-0.646267\pi$
$197$	3.81549	−	2.77211i	0.271842	−	0.197505i	0.715351	+	0.698765i	$0.246267\pi$
$198$	−1.51061	−	4.64918i	−0.107354	−	0.330403i
$199$	−15.9276			−1.12908			−0.564539	−	0.825406i	$-0.690946\pi$
$199$	−15.9276			−1.12908			−0.564539	+	0.825406i	$0.690946\pi$
$200$		0			0
$201$	3.75065			0.264550
$202$	−5.44827	−	16.7681i	−0.383339	−	1.17980i
$203$	−14.5620	+	10.5799i	−1.02205	+	0.742566i
$204$	0.815575	−	0.592550i	0.0571016	−	0.0414868i
$205$		0			0
$206$	−15.9376	−	11.5793i	−1.11042	−	0.806770i
$207$	4.47214			0.310835
$208$	−3.75324	−	2.72689i	−0.260240	−	0.189075i
$209$	1.86722	−	5.74670i	0.129158	−	0.397508i
$210$		0			0
$211$	−3.73443	−	11.4934i	−0.257089	−	0.791239i	−0.993411	−	0.114607i	$-0.963439\pi$
$211$	−3.73443	−	11.4934i	−0.257089	−	0.791239i	0.736322	−	0.676631i	$-0.236561\pi$
$212$	−3.41635	+	10.5145i	−0.234636	+	0.722136i
$213$	−3.87532	+	11.9270i	−0.265533	+	0.817226i
$214$	−1.90569	−	5.86511i	−0.130270	−	0.400931i
$215$		0			0
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−3.51731	−	2.55547i	−0.238770	−	0.173477i
$218$	7.92778			0.536937
$219$	−2.77446	−	2.01576i	−0.187480	−	0.136212i
$220$		0			0
$221$	−3.78366	+	2.74899i	−0.254516	+	0.184917i
$222$	−8.66968	+	6.29889i	−0.581871	+	0.422754i
$223$	2.89258	+	8.90243i	0.193701	+	0.596151i	0.999989	+	0.00462801i	$0.00147315\pi$
$223$	2.89258	+	8.90243i	0.193701	+	0.596151i	−0.806288	+	0.591523i	$0.798527\pi$
$224$	4.25729			0.284452
$225$		0			0
$226$	−6.75875			−0.449585
$227$	−3.12864	−	9.62898i	−0.207655	−	0.639098i	−0.999594	−	0.0284967i	$-0.990928\pi$
$227$	−3.12864	−	9.62898i	−0.207655	−	0.639098i	0.791938	−	0.610601i	$-0.209072\pi$
$228$	−1.00000	+	0.726543i	−0.0662266	+	0.0481165i
$229$	−5.99741	+	4.35737i	−0.396320	+	0.287943i	−0.768040	−	0.640401i	$-0.778768\pi$
$229$	−5.99741	+	4.35737i	−0.396320	+	0.287943i	0.371720	+	0.928345i	$0.378768\pi$
$230$		0			0
$231$	−16.8368	−	12.2327i	−1.10778	−	0.804852i
$232$	4.22796			0.277579
$233$	−4.79568	−	3.48426i	−0.314175	−	0.228262i	0.419511	−	0.907750i	$-0.362202\pi$
$233$	−4.79568	−	3.48426i	−0.314175	−	0.228262i	−0.733686	+	0.679489i	$0.762202\pi$
$234$	1.43361	−	4.41219i	0.0937179	−	0.288434i
$235$		0			0
$236$	−0.656508	−	2.02052i	−0.0427351	−	0.131525i
$237$	−1.97464	+	6.07732i	−0.128267	+	0.394764i
$238$	1.32624	−	4.08174i	0.0859672	−	0.264580i
$239$	−5.10328	−	15.7063i	−0.330104	−	1.01596i	−0.969084	−	0.246732i	$-0.920643\pi$
$239$	−5.10328	−	15.7063i	−0.330104	−	1.01596i	0.638980	−	0.769224i	$-0.279357\pi$
$240$		0			0
$241$	−2.48120	+	7.63634i	−0.159828	+	0.491900i	−0.998618	−	0.0525550i	$-0.983264\pi$
$241$	−2.48120	+	7.63634i	−0.159828	+	0.491900i	0.838790	+	0.544455i	$0.183264\pi$
$242$	−10.4337	−	7.58056i	−0.670707	−	0.487297i
$243$	−1.00000			−0.0641500
$244$	−3.13520	−	2.27786i	−0.200711	−	0.145825i
$245$		0			0
$246$	3.71890	−	2.70194i	0.237108	−	0.172269i
$247$	4.63925	−	3.37062i	0.295189	−	0.214467i
$248$	0.315575	+	0.971238i	0.0200390	+	0.0616737i
$249$	7.04745			0.446614
$250$		0			0
$251$	14.4639			0.912951			0.456475	−	0.889736i	$-0.349112\pi$
$251$	14.4639			0.912951			0.456475	+	0.889736i	$0.349112\pi$
$252$	1.31557	+	4.04892i	0.0828734	+	0.255058i
$253$	17.6865	−	12.8500i	1.11194	−	0.807874i
$254$	8.16968	−	5.93562i	0.512611	−	0.372434i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.36075			0.0848810			0.0424405	−	0.999099i	$-0.486487\pi$
$257$	1.36075			0.0848810			0.0424405	+	0.999099i	$0.486487\pi$
$258$	8.49336	+	6.17078i	0.528773	+	0.384176i
$259$	−14.0981	+	43.3895i	−0.876014	+	2.69609i
$260$		0			0
$261$	1.30651	+	4.02103i	0.0808711	+	0.248896i
$262$	2.07705	−	6.39252i	0.128321	−	0.394931i
$263$	2.09518	−	6.44830i	0.129194	−	0.397619i	−0.865448	−	0.500999i	$-0.832966\pi$
$263$	2.09518	−	6.44830i	0.129194	−	0.397619i	0.994642	+	0.103380i	$0.0329659\pi$
$264$	1.51061	+	4.64918i	0.0929716	+	0.286137i
$265$		0			0
$266$	−1.62614	+	5.00474i	−0.0997050	+	0.306860i
$267$	1.81557	+	1.31909i	0.111111	+	0.0807271i
$268$	−3.75065			−0.229107
$269$	3.19745	+	2.32309i	0.194952	+	0.141641i	0.680979	−	0.732303i	$-0.261554\pi$
$269$	3.19745	+	2.32309i	0.194952	+	0.141641i	−0.486027	+	0.873944i	$0.661554\pi$
$270$		0			0
$271$	−8.28521	+	6.01955i	−0.503290	+	0.365662i	−0.810272	−	0.586053i	$-0.800681\pi$
$271$	−8.28521	+	6.01955i	−0.503290	+	0.365662i	0.306982	+	0.951715i	$0.400681\pi$
$272$	−0.815575	+	0.592550i	−0.0494515	+	0.0359286i
$273$	−6.10328	−	18.7840i	−0.369388	−	1.13686i
$274$	−17.6260			−1.06482
$275$		0			0
$276$	−4.47214			−0.269191
$277$	3.18684	+	9.80810i	0.191479	+	0.589311i	1.00000		0.000843804i	$0.000268591\pi$
$277$	3.18684	+	9.80810i	0.191479	+	0.589311i	−0.808521	+	0.588468i	$0.799731\pi$
$278$	6.59681	−	4.79287i	0.395651	−	0.287457i
$279$	−0.826185	+	0.600258i	−0.0494624	+	0.0359365i
$280$		0			0
$281$	2.88602	+	2.09682i	0.172165	+	0.125086i	0.670531	−	0.741881i	$-0.266066\pi$
$281$	2.88602	+	2.09682i	0.172165	+	0.125086i	−0.498366	+	0.866967i	$0.666066\pi$
$282$	−2.02623			−0.120660
$283$	−23.2571	−	16.8973i	−1.38249	−	1.00444i	−0.996642	−	0.0818776i	$-0.973908\pi$
$283$	−23.2571	−	16.8973i	−1.38249	−	1.00444i	−0.385850	−	0.922562i	$-0.626092\pi$
$284$	3.87532	−	11.9270i	0.229958	−	0.707738i
$285$		0			0
$286$	−7.00811	−	21.5687i	−0.414398	−	1.27539i
$287$	6.04745	−	18.6121i	0.356970	−	1.09864i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−4.93924	−	15.2014i	−0.290544	−	0.894201i
$290$		0			0
$291$	−2.48120	+	7.63634i	−0.145450	+	0.447650i
$292$	2.77446	+	2.01576i	0.162363	+	0.117963i
$293$	−1.78543			−0.104306			−0.0521530	−	0.998639i	$-0.516608\pi$
$293$	−1.78543			−0.104306			−0.0521530	+	0.998639i	$0.516608\pi$
$294$	8.99991	+	6.53882i	0.524886	+	0.381352i
$295$		0			0
$296$	8.66968	−	6.29889i	0.503915	−	0.366115i
$297$	−3.95483	+	2.87335i	−0.229482	+	0.166729i
$298$	3.15907	+	9.72261i	0.183000	+	0.563215i
$299$	20.7474			1.19985
$300$		0			0
$301$	44.6946			2.57615
$302$	5.31557	+	16.3597i	0.305877	+	0.941392i
$303$	−14.2638	+	10.3632i	−0.819432	+	0.595352i
$304$	1.00000	−	0.726543i	0.0573539	−	0.0416701i
$305$		0			0
$306$	−0.815575	−	0.592550i	−0.0466233	−	0.0338738i
$307$	−16.2752			−0.928877			−0.464439	−	0.885605i	$-0.653744\pi$
$307$	−16.2752			−0.928877			−0.464439	+	0.885605i	$0.653744\pi$
$308$	16.8368	+	12.2327i	0.959368	+	0.697022i
$309$	−6.08761	+	18.7357i	−0.346312	+	1.06584i
$310$		0			0
$311$	4.00501	+	12.3262i	0.227103	+	0.698952i	0.998071	+	0.0620781i	$0.0197728\pi$
$311$	4.00501	+	12.3262i	0.227103	+	0.698952i	−0.770968	+	0.636874i	$0.780227\pi$
$312$	−1.43361	+	4.41219i	−0.0811621	+	0.249791i
$313$	1.29075	−	3.97253i	0.0729577	−	0.224541i	−0.907928	−	0.419127i	$-0.862336\pi$
$313$	1.29075	−	3.97253i	0.0729577	−	0.224541i	0.980885	+	0.194586i	$0.0623363\pi$
$314$	5.79176	+	17.8252i	0.326848	+	1.00594i
$315$		0			0
$316$	1.97464	−	6.07732i	0.111082	−	0.341876i
$317$	24.4480	+	17.7625i	1.37314	+	0.997643i	0.997485	+	0.0708820i	$0.0225814\pi$
$317$	24.4480	+	17.7625i	1.37314	+	0.997643i	0.375653	+	0.926761i	$0.377419\pi$
$318$	11.0556			0.619965
$319$	16.7209	+	12.1484i	0.936189	+	0.680181i
$320$		0			0
$321$	−4.98916	+	3.62484i	−0.278468	+	0.202319i
$322$	−15.4030	+	11.1909i	−0.858376	+	0.623647i
$323$	−0.385062	−	1.18510i	−0.0214254	−	0.0659407i
$324$	1.00000			0.0555556
$325$		0			0
$326$	14.0000			0.775388
$327$	−2.44982	−	7.53977i	−0.135475	−	0.416950i
$328$	−3.71890	+	2.70194i	−0.205342	+	0.149190i
$329$	−6.97878	+	5.07038i	−0.384753	+	0.279539i
$330$		0			0
$331$	−11.3949	−	8.27889i	−0.626321	−	0.455049i	0.228803	−	0.973473i	$-0.426519\pi$
$331$	−11.3949	−	8.27889i	−0.626321	−	0.455049i	−0.855124	+	0.518424i	$0.826519\pi$
$332$	−7.04745			−0.386779
$333$	8.66968	+	6.29889i	0.475095	+	0.345177i
$334$	4.17522	−	12.8500i	0.228458	−	0.703122i
$335$		0			0
$336$	−1.31557	−	4.04892i	−0.0717705	−	0.220887i
$337$	−4.15155	+	12.7772i	−0.226149	+	0.696016i	0.772023	+	0.635594i	$0.219245\pi$
$337$	−4.15155	+	12.7772i	−0.226149	+	0.696016i	−0.998173	+	0.0604224i	$0.980755\pi$
$338$	2.63365	−	8.10555i	0.143252	−	0.440884i
$339$	2.08857	+	6.42795i	0.113435	+	0.349119i
$340$		0			0
$341$	−1.54267	+	4.74784i	−0.0835401	+	0.257110i
$342$	1.00000	+	0.726543i	0.0540738	+	0.0392869i
$343$	17.5592			0.948108
$344$	−8.49336	−	6.17078i	−0.457931	−	0.332706i
$345$		0			0
$346$	−7.26790	+	5.28044i	−0.390725	+	0.283878i
$347$	4.55975	−	3.31285i	0.244780	−	0.177843i	−0.458630	−	0.888627i	$-0.651660\pi$
$347$	4.55975	−	3.31285i	0.244780	−	0.177843i	0.703410	+	0.710784i	$0.251660\pi$
$348$	−1.30651	−	4.02103i	−0.0700364	−	0.215550i
$349$	24.1159			1.29090			0.645449	−	0.763804i	$-0.276670\pi$
$349$	24.1159			1.29090			0.645449	+	0.763804i	$0.276670\pi$
$350$		0			0
$351$	−4.63925			−0.247625
$352$	−1.51061	−	4.64918i	−0.0805158	−	0.247802i
$353$	19.1672	−	13.9258i	1.02017	−	0.741196i	0.0538510	−	0.998549i	$-0.482850\pi$
$353$	19.1672	−	13.9258i	1.02017	−	0.741196i	0.966317	+	0.257353i	$0.0828504\pi$
$354$	−1.71876	+	1.24875i	−0.0913511	+	0.0663705i
$355$		0			0
$356$	−1.81557	−	1.31909i	−0.0962253	−	0.0699117i
$357$	−4.29180			−0.227146
$358$	−5.68029	−	4.12697i	−0.300212	−	0.218117i
$359$	−0.849092	+	2.61324i	−0.0448134	+	0.137921i	−0.970960	−	0.239243i	$-0.923101\pi$
$359$	−0.849092	+	2.61324i	−0.0448134	+	0.137921i	0.926146	+	0.377164i	$0.123101\pi$
$360$		0			0
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	−3.69349	+	11.3674i	−0.194125	+	0.597457i
$363$	−3.98534	+	12.2656i	−0.209176	+	0.643777i
$364$	6.10328	+	18.7840i	0.319899	+	0.984548i
$365$		0			0
$366$	−1.19754	+	3.68565i	−0.0625964	+	0.192652i
$367$	−4.33266	−	3.14786i	−0.226163	−	0.164317i	0.468934	−	0.883233i	$-0.344638\pi$
$367$	−4.33266	−	3.14786i	−0.226163	−	0.164317i	−0.695096	+	0.718917i	$0.744638\pi$
$368$	4.47214			0.233126
$369$	−3.71890	−	2.70194i	−0.193598	−	0.140657i
$370$		0			0
$371$	38.0778	−	27.6651i	1.97690	−	1.43630i
$372$	0.826185	−	0.600258i	0.0428357	−	0.0311219i
$373$	8.66048	+	26.6542i	0.448422	+	1.38010i	0.878687	+	0.477399i	$0.158420\pi$
$373$	8.66048	+	26.6542i	0.448422	+	1.38010i	−0.430264	+	0.902703i	$0.641580\pi$
$374$	−4.92806			−0.254824
$375$		0			0
$376$	2.02623			0.104495
$377$	6.06124	+	18.6546i	0.312170	+	0.960760i
$378$	3.44422	−	2.50237i	0.177151	−	0.128708i
$379$	2.20145	−	1.59945i	0.113081	−	0.0821582i	−0.529807	−	0.848118i	$-0.677736\pi$
$379$	2.20145	−	1.59945i	0.113081	−	0.0821582i	0.642889	+	0.765960i	$0.277736\pi$
$380$		0			0
$381$	−8.16968	−	5.93562i	−0.418545	−	0.304091i
$382$	3.23607			0.165572
$383$	13.6522	+	9.91890i	0.697595	+	0.506832i	0.879148	−	0.476549i	$-0.158112\pi$
$383$	13.6522	+	9.91890i	0.697595	+	0.506832i	−0.181553	+	0.983381i	$0.558112\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$		0			0
$386$	2.35101	+	7.23565i	0.119663	+	0.368285i
$387$	3.24417	−	9.98454i	0.164911	−	0.507543i
$388$	2.48120	−	7.63634i	0.125964	−	0.387677i
$389$	11.9654	+	36.8258i	0.606672	+	1.86714i	0.484862	+	0.874590i	$0.338870\pi$
$389$	11.9654	+	36.8258i	0.606672	+	1.86714i	0.121810	+	0.992553i	$0.461130\pi$
$390$		0			0
$391$	1.39317	−	4.28773i	0.0704555	−	0.216840i
$392$	−8.99991	−	6.53882i	−0.454564	−	0.330260i
$393$	−6.72149			−0.339054
$394$	3.81549	+	2.77211i	0.192222	+	0.139657i
$395$		0			0
$396$	3.95483	−	2.87335i	0.198738	−	0.144391i
$397$	20.0261	−	14.5498i	1.00508	−	0.730233i	0.0419078	−	0.999121i	$-0.486656\pi$
$397$	20.0261	−	14.5498i	1.00508	−	0.730233i	0.963171	+	0.268889i	$0.0866564\pi$
$398$	−4.92190	−	15.1481i	−0.246713	−	0.759304i
$399$	5.26230			0.263444
$400$		0			0
$401$	−3.31830			−0.165708			−0.0828541	−	0.996562i	$-0.526404\pi$
$401$	−3.31830			−0.165708			−0.0828541	+	0.996562i	$0.526404\pi$
$402$	1.15901	+	3.56708i	0.0578063	+	0.177910i
$403$	−3.83288	+	2.78475i	−0.190929	+	0.138718i
$404$	14.2638	−	10.3632i	0.709649	−	0.515590i
$405$		0			0
$406$	−14.5620	−	10.5799i	−0.722701	−	0.525073i
$407$	52.3860			2.59668
$408$	0.815575	+	0.592550i	0.0403770	+	0.0293356i
$409$	−8.76950	+	26.9897i	−0.433624	+	1.33456i	0.460866	+	0.887470i	$0.347539\pi$
$409$	−8.76950	+	26.9897i	−0.433624	+	1.33456i	−0.894490	+	0.447087i	$0.852461\pi$
$410$		0			0
$411$	5.44672	+	16.7633i	0.268667	+	0.826872i
$412$	6.08761	−	18.7357i	0.299915	−	0.923044i
$413$	−2.79495	+	8.60196i	−0.137530	+	0.423275i
$414$	1.38197	+	4.25325i	0.0679199	+	0.209036i
$415$		0			0
$416$	1.43361	−	4.41219i	0.0702884	−	0.216326i
$417$	−6.59681	−	4.79287i	−0.323047	−	0.234708i
$418$	6.04244			0.295545
$419$	−11.9931	−	8.71352i	−0.585903	−	0.425683i	0.254945	−	0.966956i	$-0.417943\pi$
$419$	−11.9931	−	8.71352i	−0.585903	−	0.425683i	−0.840847	+	0.541272i	$0.817943\pi$
$420$		0			0
$421$	−14.7255	+	10.6987i	−0.717677	+	0.521423i	−0.885641	−	0.464370i	$-0.846281\pi$
$421$	−14.7255	+	10.6987i	−0.717677	+	0.521423i	0.167964	+	0.985793i	$0.446281\pi$
$422$	9.77688	−	7.10332i	0.475931	−	0.345784i
$423$	0.626140	+	1.92706i	0.0304439	+	0.0936968i
$424$	−11.0556			−0.536905
$425$		0			0
$426$	−12.5408			−0.607604
$427$	5.09828	+	15.6909i	0.246723	+	0.759335i
$428$	4.98916	−	3.62484i	0.241160	−	0.175213i
$429$	−18.3475	+	13.3302i	−0.885824	+	0.643589i
$430$		0			0
$431$	−14.3606	−	10.4336i	−0.691724	−	0.502567i	0.185502	−	0.982644i	$-0.440609\pi$
$431$	−14.3606	−	10.4336i	−0.691724	−	0.502567i	−0.877227	+	0.480077i	$0.840609\pi$
$432$	−1.00000			−0.0481125
$433$	17.5703	+	12.7656i	0.844373	+	0.613473i	0.923589	−	0.383384i	$-0.125242\pi$
$433$	17.5703	+	12.7656i	0.844373	+	0.613473i	−0.0792155	+	0.996858i	$0.525242\pi$
$434$	1.34349	−	4.13484i	0.0644897	−	0.198479i
$435$		0			0
$436$	2.44982	+	7.53977i	0.117325	+	0.361089i
$437$	−1.70820	+	5.25731i	−0.0817145	+	0.251491i
$438$	1.05975	−	3.26157i	0.0506367	−	0.155844i
$439$	3.31399	+	10.1994i	0.158168	+	0.486792i	0.998468	−	0.0553300i	$-0.0176211\pi$
$439$	3.31399	+	10.1994i	0.158168	+	0.486792i	−0.840300	+	0.542122i	$0.817621\pi$
$440$		0			0
$441$	3.43766	−	10.5800i	0.163698	−	0.503811i
$442$	−3.78366	−	2.74899i	−0.179970	−	0.130756i
$443$	−25.5092			−1.21198			−0.605990	−	0.795472i	$-0.707223\pi$
$443$	−25.5092			−1.21198			−0.605990	+	0.795472i	$0.707223\pi$
$444$	−8.66968	−	6.29889i	−0.411445	−	0.298932i
$445$		0			0
$446$	−7.57286	+	5.50201i	−0.358585	+	0.260528i
$447$	8.27054	−	6.00890i	0.391183	−	0.284211i
$448$	1.31557	+	4.04892i	0.0621551	+	0.191294i
$449$	−12.5619			−0.592831			−0.296415	−	0.955059i	$-0.595791\pi$
$449$	−12.5619			−0.592831			−0.296415	+	0.955059i	$0.595791\pi$
$450$		0			0
$451$	−22.4712			−1.05813
$452$	−2.08857	−	6.42795i	−0.0982380	−	0.302346i
$453$	13.9164	−	10.1108i	0.653847	−	0.475048i
$454$	8.19090	−	5.95104i	0.384418	−	0.279296i
$455$		0			0
$456$	−1.00000	−	0.726543i	−0.0468293	−	0.0340235i
$457$	−3.04289			−0.142340			−0.0711702	−	0.997464i	$-0.522673\pi$
$457$	−3.04289			−0.142340			−0.0711702	+	0.997464i	$0.522673\pi$
$458$	−5.99741	−	4.35737i	−0.280241	−	0.203607i
$459$	−0.311522	+	0.958765i	−0.0145406	+	0.0447513i
$460$		0			0
$461$	−8.52674	−	26.2426i	−0.397130	−	1.22224i	−0.927291	−	0.374342i	$-0.877868\pi$
$461$	−8.52674	−	26.2426i	−0.397130	−	1.22224i	0.530161	−	0.847897i	$-0.322132\pi$
$462$	6.43110	−	19.7929i	0.299202	−	0.920849i
$463$	−9.33417	+	28.7276i	−0.433796	+	1.33509i	0.460520	+	0.887649i	$0.347663\pi$
$463$	−9.33417	+	28.7276i	−0.433796	+	1.33509i	−0.894316	+	0.447437i	$0.852337\pi$
$464$	1.30651	+	4.02103i	0.0606533	+	0.186672i
$465$		0			0
$466$	1.83179	−	5.63766i	0.0848558	−	0.261159i
$467$	24.1271	+	17.5293i	1.11647	+	0.811161i	0.983670	−	0.179982i	$-0.0576040\pi$
$467$	24.1271	+	17.5293i	1.11647	+	0.811161i	0.132797	+	0.991143i	$0.457604\pi$
$468$	4.63925			0.214450
$469$	12.9180	+	9.38551i	0.596500	+	0.433382i
$470$		0			0
$471$	15.1630	−	11.0166i	0.698676	−	0.507618i
$472$	1.71876	−	1.24875i	0.0791124	−	0.0574785i
$473$	−15.8589	−	48.8088i	−0.729195	−	2.24423i
$474$	−6.39007			−0.293506
$475$		0			0
$476$	4.29180			0.196714
$477$	−3.41635	−	10.5145i	−0.156424	−	0.481424i
$478$	13.3606	−	9.70702i	0.611098	−	0.443989i
$479$	−5.27040	+	3.82917i	−0.240811	+	0.174959i	−0.701644	−	0.712527i	$-0.747550\pi$
$479$	−5.27040	+	3.82917i	−0.240811	+	0.174959i	0.460834	+	0.887487i	$0.347550\pi$
$480$		0			0
$481$	40.2208	+	29.2221i	1.83391	+	1.33242i
$482$	−8.02933			−0.365726
$483$	15.4030	+	11.1909i	0.700861	+	0.509206i
$484$	3.98534	−	12.2656i	0.181152	−	0.557528i
$485$		0			0
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−12.4222	+	38.2315i	−0.562903	+	1.73244i	0.111199	+	0.993798i	$0.464531\pi$
$487$	−12.4222	+	38.2315i	−0.562903	+	1.73244i	−0.674102	+	0.738638i	$0.735469\pi$
$488$	1.19754	−	3.68565i	0.0542101	−	0.166842i
$489$	−4.32624	−	13.3148i	−0.195639	−	0.602116i
$490$		0			0
$491$	−11.3187	+	34.8353i	−0.510804	+	1.57209i	0.279984	+	0.960005i	$0.409671\pi$
$491$	−11.3187	+	34.8353i	−0.510804	+	1.57209i	−0.790788	+	0.612090i	$0.790329\pi$
$492$	3.71890	+	2.70194i	0.167661	+	0.121813i
$493$	4.26223			0.191961
$494$	4.63925	+	3.37062i	0.208730	+	0.151651i
$495$		0			0
$496$	−0.826185	+	0.600258i	−0.0370968	+	0.0269524i
$497$	−43.1933	+	31.3818i	−1.93748	+	1.40766i
$498$	2.17778	+	6.70252i	0.0975887	+	0.300347i
$499$	−24.9343			−1.11621			−0.558105	−	0.829770i	$-0.688471\pi$
$499$	−24.9343			−1.11621			−0.558105	+	0.829770i	$0.688471\pi$
$500$		0			0
$501$	−13.5113			−0.603641
$502$	4.46958	+	13.7559i	0.199487	+	0.613958i
$503$	34.9784	−	25.4133i	1.55961	−	1.13312i	0.623284	−	0.781996i	$-0.285798\pi$
$503$	34.9784	−	25.4133i	1.55961	−	1.13312i	0.936327	−	0.351128i	$-0.114202\pi$
$504$	−3.44422	+	2.50237i	−0.153418	+	0.111464i
$505$		0			0
$506$	17.6865	+	12.8500i	0.786262	+	0.571253i
$507$	−8.52268			−0.378506
$508$	8.16968	+	5.93562i	0.362471	+	0.263350i
$509$	9.55465	−	29.4062i	0.423503	−	1.30341i	−0.480918	−	0.876765i	$-0.659697\pi$
$509$	9.55465	−	29.4062i	0.423503	−	1.30341i	0.904421	−	0.426641i	$-0.140303\pi$
$510$		0			0
$511$	−4.51165	−	13.8854i	−0.199584	−	0.614256i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	0.381966	−	1.17557i	0.0168642	−	0.0519027i
$514$	0.420493	+	1.29415i	0.0185472	+	0.0570823i
$515$		0			0
$516$	−3.24417	+	9.98454i	−0.142817	+	0.439545i
$517$	8.01339	+	5.82207i	0.352429	+	0.256054i
$518$	−45.6224			−2.00453
$519$	7.26790	+	5.28044i	0.319025	+	0.231785i
$520$		0			0
$521$	23.9548	−	17.4042i	1.04948	−	0.762491i	0.0773654	−	0.997003i	$-0.475349\pi$
$521$	23.9548	−	17.4042i	1.04948	−	0.762491i	0.972113	+	0.234512i	$0.0753492\pi$
$522$	−3.42049	+	2.48513i	−0.149711	+	0.108771i
$523$	−3.64736	−	11.2254i	−0.159488	−	0.490853i	0.839100	−	0.543977i	$-0.183082\pi$
$523$	−3.64736	−	11.2254i	−0.159488	−	0.490853i	−0.998588	+	0.0531238i	$0.983082\pi$
$524$	6.72149			0.293630
$525$		0			0
$526$	6.78014			0.295628
$527$	0.318132	+	0.979111i	0.0138581	+	0.0426507i
$528$	−3.95483	+	2.87335i	−0.172112	+	0.125047i
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$		0			0
$531$	1.71876	+	1.24875i	0.0745879	+	0.0541913i
$532$	−5.26230			−0.228150
$533$	−17.2529	−	12.5350i	−0.747307	−	0.542950i
$534$	−0.693488	+	2.13434i	−0.0300101	+	0.0923617i
$535$		0			0
$536$	−1.15901	−	3.56708i	−0.0500617	−	0.154074i
$537$	−2.16968	+	6.67758i	−0.0936285	+	0.288159i
$538$	−1.22132	+	3.75883i	−0.0526548	+	0.162055i
$539$	−16.8048	−	51.7198i	−0.723834	−	2.22773i
$540$		0			0
$541$	4.69039	−	14.4355i	0.201656	−	0.620632i	−0.798178	−	0.602421i	$-0.794203\pi$
$541$	4.69039	−	14.4355i	0.201656	−	0.620632i	0.999834	−	0.0182113i	$-0.00579717\pi$
$542$	−8.28521	−	6.01955i	−0.355880	−	0.258562i
$543$	11.9524			0.512926
$544$	−0.815575	−	0.592550i	−0.0349675	−	0.0254054i
$545$		0			0
$546$	15.9786	−	11.6091i	0.683821	−	0.496825i
$547$	28.2147	−	20.4992i	1.20637	−	0.876481i	0.211476	−	0.977383i	$-0.432173\pi$
$547$	28.2147	−	20.4992i	1.20637	−	0.876481i	0.994896	+	0.100902i	$0.0321730\pi$
$548$	−5.44672	−	16.7633i	−0.232672	−	0.716092i
$549$	3.87532			0.165395
$550$		0			0
$551$	−5.22605			−0.222637
$552$	−1.38197	−	4.25325i	−0.0588204	−	0.181031i
$553$	−22.0088	+	15.9903i	−0.935910	+	0.679978i
$554$	−8.34327	+	6.06174i	−0.354471	+	0.257539i
$555$		0			0
$556$	6.59681	+	4.79287i	0.279767	+	0.203263i
$557$	−31.4820			−1.33393			−0.666967	−	0.745087i	$-0.732408\pi$
$557$	−31.4820			−1.33393			−0.666967	+	0.745087i	$0.732408\pi$
$558$	−0.826185	−	0.600258i	−0.0349752	−	0.0254110i
$559$	15.0505	−	46.3208i	0.636570	−	1.95916i
$560$		0			0
$561$	1.52285	+	4.68686i	0.0642950	+	0.197880i
$562$	−1.10236	+	3.39272i	−0.0465003	+	0.143113i
$563$	−0.272961	+	0.840089i	−0.0115040	+	0.0354055i	−0.956644	−	0.291261i	$-0.905925\pi$
$563$	−0.272961	+	0.840089i	−0.0115040	+	0.0354055i	0.945140	+	0.326666i	$0.105925\pi$
$564$	−0.626140	−	1.92706i	−0.0263652	−	0.0811438i
$565$		0			0
$566$	8.88343	−	27.3404i	0.373398	−	1.14920i
$567$	−3.44422	−	2.50237i	−0.144644	−	0.105090i
$568$	12.5408			0.526201
$569$	4.94008	+	3.58918i	0.207099	+	0.150466i	0.686500	−	0.727130i	$-0.259146\pi$
$569$	4.94008	+	3.58918i	0.207099	+	0.150466i	−0.479401	+	0.877596i	$0.659146\pi$
$570$		0			0
$571$	0.0293261	−	0.0213066i	0.00122726	−	0.000891655i	−0.587171	−	0.809463i	$-0.699759\pi$
$571$	0.0293261	−	0.0213066i	0.00122726	−	0.000891655i	0.588399	+	0.808571i	$0.299759\pi$
$572$	18.3475	−	13.3302i	0.767146	−	0.557364i
$573$	−1.00000	−	3.07768i	−0.0417756	−	0.128572i
$574$	19.5700			0.816834
$575$		0			0
$576$	1.00000			0.0416667
$577$	−12.3368	−	37.9688i	−0.513587	−	1.58066i	−0.785837	−	0.618433i	$-0.787768\pi$
$577$	−12.3368	−	37.9688i	−0.513587	−	1.58066i	0.272250	−	0.962227i	$-0.412232\pi$
$578$	12.9311	−	9.39500i	0.537863	−	0.390780i
$579$	6.15501	−	4.47188i	0.255794	−	0.185845i
$580$		0			0
$581$	24.2730	+	17.6353i	1.00701	+	0.731637i
$582$	−8.02933			−0.332826
$583$	−43.7228	−	31.7665i	−1.81081	−	1.31563i
$584$	−1.05975	+	3.26157i	−0.0438527	+	0.134965i
$585$		0			0
$586$	−0.551728	−	1.69805i	−0.0227917	−	0.0701456i
$587$	5.39111	−	16.5921i	0.222515	−	0.684831i	−0.776019	−	0.630709i	$-0.782764\pi$
$587$	5.39111	−	16.5921i	0.222515	−	0.684831i	0.998534	−	0.0541218i	$-0.0172359\pi$
$588$	−3.43766	+	10.5800i	−0.141767	+	0.436313i
$589$	−0.390072	−	1.20052i	−0.0160726	−	0.0494664i
$590$		0			0
$591$	1.45739	−	4.48538i	0.0599489	−	0.184504i
$592$	8.66968	+	6.29889i	0.356322	+	0.258883i
$593$	5.43780			0.223304			0.111652	−	0.993747i	$-0.464386\pi$
$593$	5.43780			0.223304			0.111652	+	0.993747i	$0.464386\pi$
$594$	−3.95483	−	2.87335i	−0.162269	−	0.117895i
$595$		0			0
$596$	−8.27054	+	6.00890i	−0.338775	+	0.246134i
$597$	−12.8857	+	9.36201i	−0.527377	+	0.383162i
$598$	6.41129	+	19.7319i	0.262177	+	0.806899i
$599$	28.7804			1.17593			0.587967	−	0.808885i	$-0.299929\pi$
$599$	28.7804			1.17593			0.587967	+	0.808885i	$0.299929\pi$
$600$		0			0
$601$	−41.4162			−1.68940			−0.844702	−	0.535237i	$-0.820222\pi$
$601$	−41.4162			−1.68940			−0.844702	+	0.535237i	$0.820222\pi$
$602$	13.8114	+	42.5071i	0.562910	+	1.73246i
$603$	3.03434	−	2.20457i	0.123568	−	0.0897772i
$604$	−13.9164	+	10.1108i	−0.566248	+	0.411404i
$605$		0			0
$606$	−14.2638	−	10.3632i	−0.579426	−	0.420977i
$607$	−23.9868			−0.973595			−0.486797	−	0.873515i	$-0.661835\pi$
$607$	−23.9868			−0.973595			−0.486797	+	0.873515i	$0.661835\pi$
$608$	1.00000	+	0.726543i	0.0405554	+	0.0294652i
$609$	−5.56220	+	17.1187i	−0.225392	+	0.693684i
$610$		0			0
$611$	2.90482	+	8.94012i	0.117516	+	0.361678i
$612$	0.311522	−	0.958765i	0.0125925	−	0.0387558i
$613$	−0.131288	+	0.404063i	−0.00530268	+	0.0163200i	−0.953673	−	0.300846i	$-0.902731\pi$
$613$	−0.131288	+	0.404063i	−0.00530268	+	0.0163200i	0.948370	+	0.317166i	$0.102731\pi$
$614$	−5.02933	−	15.4787i	−0.202967	−	0.624668i
$615$		0			0
$616$	−6.43110	+	19.7929i	−0.259117	+	0.797479i
$617$	26.5991	+	19.3253i	1.07084	+	0.778009i	0.976063	−	0.217489i	$-0.0697868\pi$
$617$	26.5991	+	19.3253i	1.07084	+	0.778009i	0.0947752	+	0.995499i	$0.469787\pi$
$618$	−19.6999			−0.792447
$619$	−9.53580	−	6.92816i	−0.383276	−	0.278466i	0.379419	−	0.925225i	$-0.376124\pi$
$619$	−9.53580	−	6.92816i	−0.383276	−	0.278466i	−0.762695	+	0.646759i	$0.776124\pi$
$620$		0			0
$621$	3.61803	−	2.62866i	0.145187	−	0.105484i
$622$	−10.4853	+	7.61798i	−0.420420	+	0.305453i
$623$	2.95238	+	9.08648i	0.118285	+	0.364042i
$624$	−4.63925			−0.185719
$625$		0			0
$626$	4.17697			0.166945
$627$	−1.86722	−	5.74670i	−0.0745695	−	0.229501i
$628$	−15.1630	+	11.0166i	−0.605071	+	0.439610i
$629$	8.73995	−	6.34994i	0.348485	−	0.253189i
$630$		0			0
$631$	−27.0900	−	19.6820i	−1.07844	−	0.783529i	−0.101026	−	0.994884i	$-0.532213\pi$
$631$	−27.0900	−	19.6820i	−1.07844	−	0.783529i	−0.977410	+	0.211354i	$0.932213\pi$
$632$	6.39007			0.254183
$633$	−9.77688	−	7.10332i	−0.388596	−	0.282331i
$634$	−9.33831	+	28.7404i	−0.370872	+	1.14143i
$635$		0			0
$636$	3.41635	+	10.5145i	0.135467	+	0.416925i
$637$	15.9482	−	49.0835i	0.631890	−	1.94476i
$638$	−6.38680	+	19.6566i	−0.252856	+	0.778211i
$639$	3.87532	+	11.9270i	0.153305	+	0.471825i
$640$		0			0
$641$	−5.17714	+	15.9336i	−0.204485	+	0.629339i	0.795250	+	0.606282i	$0.207340\pi$
$641$	−5.17714	+	15.9336i	−0.204485	+	0.629339i	−0.999734	+	0.0230567i	$0.992660\pi$
$642$	−4.98916	−	3.62484i	−0.196907	−	0.143061i
$643$	−14.5246			−0.572794			−0.286397	−	0.958111i	$-0.592458\pi$
$643$	−14.5246			−0.572794			−0.286397	+	0.958111i	$0.592458\pi$
$644$	−15.4030	−	11.1909i	−0.606964	−	0.440985i
$645$		0			0
$646$	1.00811	−	0.732432i	0.0396634	−	0.0288171i
$647$	12.8965	−	9.36989i	0.507015	−	0.368368i	−0.304675	−	0.952456i	$-0.598548\pi$
$647$	12.8965	−	9.36989i	0.507015	−	0.368368i	0.811690	+	0.584088i	$0.198548\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	10.3855			0.407667
$650$		0			0
$651$	−4.34763			−0.170397
$652$	4.32624	+	13.3148i	0.169429	+	0.521447i
$653$	−20.3233	+	14.7657i	−0.795312	+	0.577828i	−0.909535	−	0.415627i	$-0.863562\pi$
$653$	−20.3233	+	14.7657i	−0.795312	+	0.577828i	0.114223	+	0.993455i	$0.463562\pi$
$654$	6.41371	−	4.65983i	0.250796	−	0.182214i
$655$		0			0
$656$	−3.71890	−	2.70194i	−0.145199	−	0.105493i
$657$	−3.42942			−0.133794
$658$	−6.97878	−	5.07038i	−0.272061	−	0.197664i
$659$	−3.40766	+	10.4877i	−0.132744	+	0.408543i	−0.995232	−	0.0975338i	$-0.968905\pi$
$659$	−3.40766	+	10.4877i	−0.132744	+	0.408543i	0.862489	+	0.506076i	$0.168905\pi$
$660$		0			0
$661$	−4.20173	−	12.9316i	−0.163428	−	0.502981i	0.835489	−	0.549508i	$-0.185185\pi$
$661$	−4.20173	−	12.9316i	−0.163428	−	0.502981i	−0.998917	+	0.0465267i	$0.985185\pi$
$662$	4.35247	−	13.3955i	0.169163	−	0.520632i
$663$	−1.44523	+	4.44796i	−0.0561280	+	0.172744i
$664$	−2.17778	−	6.70252i	−0.0845143	−	0.260108i
$665$		0			0
$666$	−3.31152	+	10.1918i	−0.128319	+	0.394925i
$667$	−15.2969	−	11.1139i	−0.592299	−	0.430330i
$668$	13.5113			0.522768
$669$	7.57286	+	5.50201i	0.292784	+	0.212720i
$670$		0			0
$671$	15.3262	−	11.1352i	0.591663	−	0.429868i
$672$	3.44422	−	2.50237i	0.132864	−	0.0965311i
$673$	6.81053	+	20.9607i	0.262527	+	0.807974i	0.992253	+	0.124235i	$0.0396476\pi$
$673$	6.81053	+	20.9607i	0.262527	+	0.807974i	−0.729726	+	0.683740i	$0.760352\pi$
$674$	−13.4347			−0.517485
$675$		0			0
$676$	8.52268			0.327795
$677$	−10.3185	−	31.7571i	−0.396572	−	1.22052i	−0.927730	−	0.373251i	$-0.878243\pi$
$677$	−10.3185	−	31.7571i	−0.396572	−	1.22052i	0.531158	−	0.847273i	$-0.321757\pi$
$678$	−5.46794	+	3.97269i	−0.209995	+	0.152570i
$679$	−27.6548	+	20.0924i	−1.06129	+	0.771074i
$680$		0			0
$681$	−8.19090	−	5.95104i	−0.313876	−	0.228044i
$682$	−4.99217			−0.191160
$683$	2.88616	+	2.09692i	0.110436	+	0.0802363i	0.641632	−	0.767012i	$-0.278257\pi$
$683$	2.88616	+	2.09692i	0.110436	+	0.0802363i	−0.531197	+	0.847249i	$0.678257\pi$
$684$	−0.381966	+	1.17557i	−0.0146048	+	0.0449491i
$685$		0			0
$686$	5.42609	+	16.6998i	0.207169	+	0.637601i
$687$	−2.29081	+	7.05038i	−0.0873997	+	0.268989i
$688$	3.24417	−	9.98454i	0.123683	−	0.380657i
$689$	−15.8493	−	48.7792i	−0.603812	−	1.85834i
$690$		0			0
$691$	−11.6129	+	35.7407i	−0.441774	+	1.35964i	0.444210	+	0.895923i	$0.353485\pi$
$691$	−11.6129	+	35.7407i	−0.441774	+	1.35964i	−0.885983	+	0.463717i	$0.846515\pi$
$692$	−7.26790	−	5.28044i	−0.276284	−	0.200732i
$693$	−20.8115			−0.790563
$694$	4.55975	+	3.31285i	0.173086	+	0.125754i
$695$		0			0
$696$	3.42049	−	2.48513i	0.129653	−	0.0941988i
$697$	−3.74904	+	2.72384i	−0.142005	+	0.103173i
$698$	7.45224	+	22.9356i	0.282071	+	0.868126i
$699$	−5.92778			−0.224209
$700$		0			0
$701$	26.4948			1.00070			0.500348	−	0.865825i	$-0.333205\pi$
$701$	26.4948			1.00070			0.500348	+	0.865825i	$0.333205\pi$
$702$	−1.43361	−	4.41219i	−0.0541081	−	0.166528i
$703$	−10.7163	+	7.78585i	−0.404173	+	0.293649i
$704$	3.95483	−	2.87335i	0.149053	−	0.108294i
$705$		0			0
$706$	19.1672	+	13.9258i	0.721368	+	0.524105i
$707$	−75.0602			−2.82293
$708$	−1.71876	−	1.24875i	−0.0645950	−	0.0469310i
$709$	11.5055	−	35.4104i	0.432100	−	1.32987i	−0.463930	−	0.885872i	$-0.653561\pi$
$709$	11.5055	−	35.4104i	0.432100	−	1.32987i	0.896029	−	0.443995i	$-0.146439\pi$
$710$		0			0
$711$	1.97464	+	6.07732i	0.0740548	+	0.227917i
$712$	0.693488	−	2.13434i	0.0259896	−	0.0799876i
$713$	1.41129	−	4.34351i	0.0528533	−	0.162666i
$714$	−1.32624	−	4.08174i	−0.0496332	−	0.152755i
$715$		0			0
$716$	2.16968	−	6.67758i	0.0810846	−	0.249553i
$717$	−13.3606	−	9.70702i	−0.498960	−	0.362515i
$718$	−2.74772			−0.102544
$719$	0.501912	+	0.364661i	0.0187182	+	0.0135995i	0.597105	−	0.802163i	$-0.296318\pi$
$719$	0.501912	+	0.364661i	0.0187182	+	0.0135995i	−0.578387	+	0.815763i	$0.696318\pi$
$720$		0			0
$721$	−67.8509	+	49.2965i	−2.52690	+	1.83590i
$722$	14.1353	−	10.2699i	0.526060	−	0.382205i
$723$	2.48120	+	7.63634i	0.0922768	+	0.283999i
$724$	−11.9524			−0.444207
$725$		0			0
$726$	−12.8968			−0.478646
$727$	0.0770549	+	0.237151i	0.00285781	+	0.00879543i	0.952475	−	0.304616i	$-0.0985281\pi$
$727$	0.0770549	+	0.237151i	0.00285781	+	0.00879543i	−0.949617	+	0.313411i	$0.898528\pi$
$728$	−15.9786	+	11.6091i	−0.592207	+	0.430263i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−8.56220	−	6.22080i	−0.316684	−	0.230085i
$732$	−3.87532			−0.143236
$733$	34.4927	+	25.0604i	1.27402	+	0.925628i	0.999355	−	0.0359121i	$-0.0114336\pi$
$733$	34.4927	+	25.0604i	1.27402	+	0.925628i	0.274663	+	0.961540i	$0.411434\pi$
$734$	1.65493	−	5.09334i	0.0610845	−	0.187999i
$735$		0			0
$736$	1.38197	+	4.25325i	0.0509399	+	0.156777i
$737$	5.66576	−	17.4374i	0.208701	−	0.642316i
$738$	1.42049	−	4.37183i	0.0522891	−	0.160929i
$739$	4.86029	+	14.9584i	0.178789	+	0.550255i	0.999786	−	0.0206765i	$-0.00658202\pi$
$739$	4.86029	+	14.9584i	0.178789	+	0.550255i	−0.820997	+	0.570932i	$0.806582\pi$
$740$		0			0
$741$	1.77204	−	5.45377i	0.0650974	−	0.200349i
$742$	38.0778	+	27.6651i	1.39788	+	1.01562i
$743$	45.9731			1.68659			0.843294	−	0.537452i	$-0.180613\pi$
$743$	45.9731			1.68659			0.843294	+	0.537452i	$0.180613\pi$
$744$	0.826185	+	0.600258i	0.0302894	+	0.0220065i
$745$		0			0
$746$	−22.6734	+	16.4732i	−0.830133	+	0.603127i
$747$	5.70151	−	4.14239i	0.208607	−	0.151562i
$748$	−1.52285	−	4.68686i	−0.0556811	−	0.171369i
$749$	−26.2545			−0.959317
$750$		0			0
$751$	7.09608			0.258940			0.129470	−	0.991583i	$-0.458672\pi$
$751$	7.09608			0.258940			0.129470	+	0.991583i	$0.458672\pi$
$752$	0.626140	+	1.92706i	0.0228330	+	0.0702726i
$753$	11.7015	−	8.50164i	0.426427	−	0.309817i
$754$	−15.8685	+	11.5292i	−0.577898	+	0.419868i
$755$		0			0
$756$	3.44422	+	2.50237i	0.125265	+	0.0910104i
$757$	−23.7795			−0.864281			−0.432141	−	0.901806i	$-0.642242\pi$
$757$	−23.7795			−0.864281			−0.432141	+	0.901806i	$0.642242\pi$
$758$	2.20145	+	1.59945i	0.0799604	+	0.0580946i
$759$	6.75565	−	20.7918i	0.245215	−	0.754693i
$760$		0			0
$761$	1.62195	+	4.99184i	0.0587956	+	0.180954i	0.976141	−	0.217138i	$-0.0696723\pi$
$761$	1.62195	+	4.99184i	0.0587956	+	0.180954i	−0.917345	+	0.398093i	$0.869672\pi$
$762$	3.12054	−	9.60403i	0.113045	−	0.347917i
$763$	10.4296	−	32.0990i	0.377576	−	1.16206i
$764$	1.00000	+	3.07768i	0.0361787	+	0.111347i
$765$		0			0
$766$	−5.21468	+	16.0491i	−0.188414	+	0.579878i
$767$	7.97377	+	5.79328i	0.287916	+	0.209183i
$768$	−1.00000			−0.0360844
$769$	4.43639	+	3.22323i	0.159980	+	0.116233i	0.664895	−	0.746937i	$-0.268476\pi$
$769$	4.43639	+	3.22323i	0.159980	+	0.116233i	−0.504915	+	0.863169i	$0.668476\pi$
$770$		0			0
$771$	1.10087	−	0.799826i	0.0396467	−	0.0288050i
$772$	−6.15501	+	4.47188i	−0.221524	+	0.160946i
$773$	3.60661	+	11.1000i	0.129721	+	0.399239i	0.994732	−	0.102514i	$-0.0326886\pi$
$773$	3.60661	+	11.1000i	0.129721	+	0.399239i	−0.865011	+	0.501753i	$0.832689\pi$
$774$	10.4984			0.377356
$775$		0			0
$776$	8.02933			0.288236
$777$	14.0981	+	43.3895i	0.505767	+	1.55659i
$778$	−31.3259	+	22.7596i	−1.12309	+	0.815972i
$779$	4.59681	−	3.33978i	0.164698	−	0.119660i
$780$		0			0
$781$	49.5967	+	36.0341i	1.77471	+	1.28940i
$782$	4.50838			0.161220
$783$	3.42049	+	2.48513i	0.122238	+	0.0888114i
$784$	3.43766	−	10.5800i	0.122774	−	0.377858i
$785$		0			0
$786$	−2.07705	−	6.39252i	−0.0740861	−	0.228014i
$787$	7.63108	−	23.4861i	0.272019	−	0.837188i	−0.717974	−	0.696070i	$-0.754930\pi$
$787$	7.63108	−	23.4861i	0.272019	−	0.837188i	0.989993	−	0.141118i	$-0.0450696\pi$
$788$	−1.45739	+	4.48538i	−0.0519173	+	0.159785i
$789$	−2.09518	−	6.44830i	−0.0745904	−	0.229566i
$790$		0			0
$791$	−8.89164	+	27.3657i	−0.316150	+	0.973011i
$792$	3.95483	+	2.87335i	0.140529	+	0.102100i
$793$	17.9786			0.638439
$794$	20.0261	+	14.5498i	0.710698	+	0.516352i
$795$		0			0
$796$	12.8857	−	9.36201i	0.456722	−	0.331828i
$797$	16.7427	−	12.1643i	0.593056	−	0.430880i	−0.250351	−	0.968155i	$-0.580546\pi$
$797$	16.7427	−	12.1643i	0.593056	−	0.430880i	0.843407	+	0.537275i	$0.180546\pi$
$798$	1.62614	+	5.00474i	0.0575647	+	0.177166i
$799$	2.04265			0.0722639
$800$		0			0
$801$	2.24417			0.0792940
$802$	−1.02541	−	3.15590i	−0.0362086	−	0.111439i
$803$	−13.5628	+	9.85392i	−0.478619	+	0.347737i
$804$	−3.03434	+	2.20457i	−0.107013	+	0.0777493i
$805$		0			0
$806$	−3.83288	−	2.78475i	−0.135007	−	0.0980887i
$807$	3.95227			0.139127
$808$	14.2638	+	10.3632i	0.501797	+	0.364577i
$809$	−0.948863	+	2.92030i	−0.0333602	+	0.102672i	−0.966350	−	0.257230i	$-0.917190\pi$
$809$	−0.948863	+	2.92030i	−0.0333602	+	0.102672i	0.932990	+	0.359903i	$0.117190\pi$
$810$		0			0
$811$	−14.3668	−	44.2164i	−0.504485	−	1.55265i	−0.801634	−	0.597815i	$-0.796036\pi$
$811$	−14.3668	−	44.2164i	−0.504485	−	1.55265i	0.297149	−	0.954831i	$-0.403964\pi$
$812$	5.56220	−	17.1187i	0.195195	−	0.600748i
$813$	−3.16467	+	9.73984i	−0.110990	+	0.341591i
$814$	16.1882	+	49.8221i	0.567395	+	1.74626i
$815$		0			0
$816$	−0.311522	+	0.958765i	−0.0109054	+	0.0335635i
$817$	10.4984	+	7.62751i	0.367291	+	0.266853i
$818$	−28.3787			−0.992238
$819$	−15.9786	−	11.6091i	−0.558338	−	0.405656i
$820$		0			0
$821$	14.3885	−	10.4539i	0.502162	−	0.364842i	−0.307680	−	0.951490i	$-0.599553\pi$
$821$	14.3885	−	10.4539i	0.502162	−	0.364842i	0.809842	+	0.586648i	$0.199553\pi$
$822$	−14.2597	+	10.3603i	−0.497364	+	0.361356i
$823$	−1.89759	−	5.84017i	−0.0661457	−	0.203575i	0.912521	−	0.409030i	$-0.134133\pi$
$823$	−1.89759	−	5.84017i	−0.0661457	−	0.203575i	−0.978667	+	0.205454i	$0.934133\pi$
$824$	19.6999			0.686279
$825$		0			0
$826$	−9.04463			−0.314703
$827$	9.06121	+	27.8875i	0.315089	+	0.969745i	0.975718	+	0.219032i	$0.0702898\pi$
$827$	9.06121	+	27.8875i	0.315089	+	0.969745i	−0.660629	+	0.750713i	$0.729710\pi$
$828$	−3.61803	+	2.62866i	−0.125735	+	0.0913521i
$829$	40.1826	−	29.1944i	1.39560	−	1.01396i	0.400374	−	0.916352i	$-0.368880\pi$
$829$	40.1826	−	29.1944i	1.39560	−	1.01396i	0.995225	−	0.0976102i	$-0.0311199\pi$
$830$		0			0
$831$	8.34327	+	6.06174i	0.289425	+	0.210279i
$832$	4.63925			0.160837
$833$	−9.07286	−	6.59182i	−0.314356	−	0.228393i
$834$	2.51976	−	7.75502i	0.0872521	−	0.268534i
$835$		0			0
$836$	1.86722	+	5.74670i	0.0645790	+	0.198754i
$837$	−0.315575	+	0.971238i	−0.0109079	+	0.0335709i
$838$	4.58097	−	14.0988i	0.158247	−	0.487034i
$839$	8.60481	+	26.4829i	0.297071	+	0.914291i	0.982518	+	0.186168i	$0.0596069\pi$
$839$	8.60481	+	26.4829i	0.297071	+	0.914291i	−0.685447	+	0.728123i	$0.740393\pi$
$840$		0			0
$841$	−3.43761	+	10.5799i	−0.118538	+	0.364823i
$842$	−14.7255	−	10.6987i	−0.507475	−	0.368702i
$843$	3.56732			0.122865
$844$	9.77688	+	7.10332i	0.336534	+	0.244506i
$845$		0			0
$846$	−1.63925	+	1.19099i	−0.0563587	+	0.0409470i
$847$	−44.4195	+	32.2726i	−1.52627	+	1.10890i
$848$	−3.41635	−	10.5145i	−0.117318	−	0.361068i
$849$	−28.7474			−0.986607
$850$		0			0
$851$	−47.9248			−1.64284
$852$	−3.87532	−	11.9270i	−0.132766	−	0.408613i
$853$	−25.8857	+	18.8070i	−0.886309	+	0.643941i	−0.934913	−	0.354877i	$-0.884523\pi$
$853$	−25.8857	+	18.8070i	−0.886309	+	0.643941i	0.0486043	+	0.998818i	$0.484523\pi$
$854$	−13.3475	+	9.69750i	−0.456741	+	0.331841i
$855$		0			0
$856$	4.98916	+	3.62484i	0.170526	+	0.123894i
$857$	−31.7769			−1.08548			−0.542739	−	0.839902i	$-0.682613\pi$
$857$	−31.7769			−1.08548			−0.542739	+	0.839902i	$0.682613\pi$
$858$	−18.3475	−	13.3302i	−0.626372	−	0.455086i
$859$	2.55910	−	7.87611i	0.0873155	−	0.268729i	−0.897859	−	0.440282i	$-0.854878\pi$
$859$	2.55910	−	7.87611i	0.0873155	−	0.268729i	0.985175	+	0.171553i	$0.0548784\pi$
$860$		0			0
$861$	−6.04745	−	18.6121i	−0.206097	−	0.634300i
$862$	5.48525	−	16.8819i	0.186828	−	0.574999i
$863$	5.98671	−	18.4252i	0.203790	−	0.627201i	−0.795971	−	0.605335i	$-0.793039\pi$
$863$	5.98671	−	18.4252i	0.203790	−	0.627201i	0.999761	−	0.0218664i	$-0.00696084\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$		0			0
$866$	−6.71125	+	20.6551i	−0.228057	+	0.701889i
$867$	−12.9311	−	9.39500i	−0.439163	−	0.319071i
$868$	4.34763			0.147568
$869$	25.2716	+	18.3609i	0.857282	+	0.622852i
$870$		0			0
$871$	14.0771	−	10.2276i	0.476983	−	0.346548i
$872$	−6.41371	+	4.65983i	−0.217196	+	0.157802i
$873$	2.48120	+	7.63634i	0.0839758	+	0.258451i
$874$	−5.52786			−0.186983
$875$		0			0
$876$	3.42942			0.115869
$877$	9.18634	+	28.2726i	0.310201	+	0.954699i	0.977685	+	0.210076i	$0.0673710\pi$
$877$	9.18634	+	28.2726i	0.310201	+	0.954699i	−0.667485	+	0.744624i	$0.732629\pi$
$878$	−8.67615	+	6.30359i	−0.292806	+	0.212736i
$879$	−1.44444	+	1.04945i	−0.0487199	+	0.0353971i
$880$		0			0
$881$	−13.8537	−	10.0653i	−0.466741	−	0.339107i	0.329429	−	0.944180i	$-0.393144\pi$
$881$	−13.8537	−	10.0653i	−0.466741	−	0.339107i	−0.796170	+	0.605073i	$0.793144\pi$
$882$	11.1245			0.374582
$883$	−2.34718	−	1.70533i	−0.0789889	−	0.0573888i	0.547590	−	0.836747i	$-0.315545\pi$
$883$	−2.34718	−	1.70533i	−0.0789889	−	0.0573888i	−0.626579	+	0.779358i	$0.715545\pi$
$884$	1.44523	−	4.44796i	0.0486083	−	0.149601i
$885$		0			0
$886$	−7.88278	−	24.2607i	−0.264827	−	0.815055i
$887$	8.80338	−	27.0940i	0.295589	−	0.909728i	−0.687434	−	0.726246i	$-0.741263\pi$
$887$	8.80338	−	27.0940i	0.295589	−	0.909728i	0.983023	−	0.183482i	$-0.0587369\pi$
$888$	3.31152	−	10.1918i	0.111127	−	0.342015i
$889$	−13.2850	−	40.8871i	−0.445566	−	1.37131i
$890$		0			0
$891$	−1.51061	+	4.64918i	−0.0506073	+	0.155753i
$892$	−7.57286	−	5.50201i	−0.253558	−	0.184221i
$893$	−2.50456			−0.0838118
$894$	8.27054	+	6.00890i	0.276608	+	0.200968i
$895$		0			0
$896$	−3.44422	+	2.50237i	−0.115063	+	0.0835984i
$897$	16.7850	−	12.1950i	0.560434	−	0.407179i
$898$	−3.88183	−	11.9470i	−0.129538	−	0.398678i
$899$	4.31768			0.144003
$900$		0			0
$901$	−11.1452			−0.371299
$902$	−6.94399	−	21.3714i	−0.231210	−	0.711590i
$903$	36.1587	−	26.2708i	1.20329	−	0.874238i
$904$	5.46794	−	3.97269i	0.181861	−	0.132130i
$905$		0			0
$906$	13.9164	+	10.1108i	0.462340	+	0.335910i
$907$	−55.7343			−1.85063			−0.925314	−	0.379203i	$-0.876198\pi$
$907$	−55.7343			−1.85063			−0.925314	+	0.379203i	$0.876198\pi$
$908$	8.19090	+	5.95104i	0.271824	+	0.197492i
$909$	−5.44827	+	16.7681i	−0.180708	+	0.556161i
$910$		0			0
$911$	0.506472	+	1.55876i	0.0167801	+	0.0516440i	0.959096	−	0.283081i	$-0.0913566\pi$
$911$	0.506472	+	1.55876i	0.0167801	+	0.0516440i	−0.942316	+	0.334725i	$0.891357\pi$
$912$	0.381966	−	1.17557i	0.0126482	−	0.0389270i
$913$	10.6460	−	32.7649i	0.352330	−	1.08436i
$914$	−0.940305	−	2.89396i	−0.0311025	−	0.0957237i
$915$		0			0
$916$	2.29081	−	7.05038i	0.0756904	−	0.232951i
$917$	−23.1503	−	16.8197i	−0.764490	−	0.555434i
$918$	−1.00811			−0.0332724
$919$	−28.5965	−	20.7766i	−0.943310	−	0.685355i	0.00590477	−	0.999983i	$-0.498120\pi$
$919$	−28.5965	−	20.7766i	−0.943310	−	0.685355i	−0.949215	+	0.314627i	$0.898120\pi$
$920$		0			0
$921$	−13.1669	+	9.56635i	−0.433866	+	0.315222i
$922$	22.3233	−	16.2188i	0.735178	−	0.534138i
$923$	17.9786	+	55.3325i	0.591773	+	1.82129i
$924$	20.8115			0.684648
$925$		0			0
$926$	−30.2060			−0.992631
$927$	6.08761	+	18.7357i	0.199943	+	0.615363i
$928$	−3.42049	+	2.48513i	−0.112283	+	0.0815785i
$929$	7.50256	−	5.45093i	0.246151	−	0.178839i	−0.457868	−	0.889020i	$-0.651387\pi$
$929$	7.50256	−	5.45093i	0.246151	−	0.178839i	0.704019	+	0.710181i	$0.251387\pi$
$930$		0			0
$931$	11.1245	+	8.08243i	0.364591	+	0.264891i
$932$	5.92778			0.194171
$933$	10.4853	+	7.61798i	0.343272	+	0.249401i
$934$	−9.21572	+	28.3631i	−0.301548	+	0.928068i
$935$		0			0
$936$	1.43361	+	4.41219i	0.0468590	+	0.144217i
$937$	3.03856	−	9.35173i	0.0992654	−	0.305508i	−0.889076	−	0.457759i	$-0.848652\pi$
$937$	3.03856	−	9.35173i	0.0992654	−	0.305508i	0.988342	+	0.152251i	$0.0486523\pi$
$938$	−4.93425	+	15.1861i	−0.161109	+	0.495843i
$939$	−1.29075	−	3.97253i	−0.0421221	−	0.129639i
$940$		0			0
$941$	18.0203	−	55.4607i	0.587444	−	1.80797i	−0.00178292	−	0.999998i	$-0.500568\pi$
$941$	18.0203	−	55.4607i	0.587444	−	1.80797i	0.589227	−	0.807968i	$-0.299432\pi$
$942$	15.1630	+	11.0166i	0.494038	+	0.358940i
$943$	20.5576			0.669447
$944$	1.71876	+	1.24875i	0.0559409	+	0.0406434i
$945$		0			0
$946$	41.5192	−	30.1655i	1.34991	−	0.980765i
$947$	−35.0917	+	25.4956i	−1.14033	+	0.828496i	−0.987165	−	0.159705i	$-0.948946\pi$
$947$	−35.0917	+	25.4956i	−1.14033	+	0.828496i	−0.153162	+	0.988201i	$0.548946\pi$
$948$	−1.97464	−	6.07732i	−0.0641333	−	0.197382i
$949$	−15.9099			−0.516458
$950$		0			0
$951$	30.2194			0.979931
$952$	1.32624	+	4.08174i	0.0429836	+	0.132290i
$953$	−8.14992	+	5.92126i	−0.264002	+	0.191808i	−0.711909	−	0.702271i	$-0.752169\pi$
$953$	−8.14992	+	5.92126i	−0.264002	+	0.191808i	0.447908	+	0.894080i	$0.352169\pi$
$954$	8.94413	−	6.49829i	0.289577	−	0.210390i
$955$		0			0
$956$	13.3606	+	9.70702i	0.432112	+	0.313948i
$957$	20.6681			0.668106
$958$	−5.27040	−	3.82917i	−0.170279	−	0.123715i
$959$	−23.1883	+	71.3662i	−0.748788	+	2.30453i
$960$		0			0
$961$	−9.25726	−	28.4909i	−0.298621	−	0.919061i
$962$	−15.3630	+	47.2824i	−0.495323	+	1.52445i
$963$	−1.90569	+	5.86511i	−0.0614100	+	0.189001i
$964$	−2.48120	−	7.63634i	−0.0799140	−	0.245950i
$965$		0			0
$966$	−5.88343	+	18.1073i	−0.189296	+	0.582594i
$967$	−11.3754	−	8.26469i	−0.365807	−	0.265775i	0.389663	−	0.920958i	$-0.372592\pi$
$967$	−11.3754	−	8.26469i	−0.365807	−	0.265775i	−0.755470	+	0.655183i	$0.772592\pi$
$968$	12.8968			0.414520
$969$	−1.00811	−	0.732432i	−0.0323850	−	0.0235291i
$970$		0			0
$971$	24.3406	−	17.6845i	0.781127	−	0.567522i	−0.124190	−	0.992258i	$-0.539633\pi$
$971$	24.3406	−	17.6845i	0.781127	−	0.567522i	0.905317	+	0.424737i	$0.139633\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−10.7273	−	33.0154i	−0.343903	−	1.05842i
$974$	−40.1990			−1.28806
$975$		0			0
$976$	3.87532			0.124046
$977$	3.66766	+	11.2879i	0.117339	+	0.361131i	0.992428	−	0.122831i	$-0.0391972\pi$
$977$	3.66766	+	11.2879i	0.117339	+	0.361131i	−0.875089	+	0.483962i	$0.839197\pi$
$978$	11.3262	−	8.22899i	0.362173	−	0.263134i
$979$	8.87532	−	6.44830i	0.283657	−	0.206089i
$980$		0			0
$981$	−6.41371	−	4.65983i	−0.204774	−	0.148777i
$982$	−36.6280			−1.16885
$983$	−27.7898	−	20.1905i	−0.886358	−	0.643976i	0.0485682	−	0.998820i	$-0.484534\pi$
$983$	−27.7898	−	20.1905i	−0.886358	−	0.643976i	−0.934926	+	0.354843i	$0.884534\pi$
$984$	−1.42049	+	4.37183i	−0.0452837	+	0.139369i
$985$		0			0
$986$	1.31710	+	4.05362i	0.0419451	+	0.129094i
$987$	−2.66566	+	8.20405i	−0.0848488	+	0.261138i
$988$	−1.77204	+	5.45377i	−0.0563760	+	0.173508i
$989$	14.5084	+	44.6522i	0.461340	+	1.41986i
$990$		0			0
$991$	8.76632	−	26.9800i	0.278471	−	0.857046i	−0.709809	−	0.704394i	$-0.751219\pi$
$991$	8.76632	−	26.9800i	0.278471	−	0.857046i	0.988280	−	0.152652i	$-0.0487814\pi$
$992$	−0.826185	−	0.600258i	−0.0262314	−	0.0190582i
$993$	−14.0849			−0.446970
$994$	−43.1933	−	31.3818i	−1.37001	−	0.995369i
$995$		0			0
$996$	−5.70151	+	4.14239i	−0.180659	+	0.131257i
$997$	37.0128	−	26.8914i	1.17221	−	0.851658i	0.180935	−	0.983495i	$-0.442088\pi$
$997$	37.0128	−	26.8914i	1.17221	−	0.851658i	0.991271	+	0.131837i	$0.0420877\pi$
$998$	−7.70511	−	23.7139i	−0.243901	−	0.750650i
$999$	10.7163			0.339049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.d.151.2		8
5.2	odd	4		750.2.h.e.349.2		16
5.3	odd	4		750.2.h.e.349.3		16
5.4	even	2		150.2.g.c.31.1	✓	8
15.14	odd	2		450.2.h.d.181.2		8
25.2	odd	20		3750.2.c.h.1249.8		8
25.3	odd	20		750.2.h.e.649.1		16
25.4	even	10		150.2.g.c.121.1	yes	8
25.11	even	5		3750.2.a.q.1.4		4
25.14	even	10		3750.2.a.l.1.1		4
25.21	even	5	inner	750.2.g.d.601.2		8
25.22	odd	20		750.2.h.e.649.4		16
25.23	odd	20		3750.2.c.h.1249.1		8
75.29	odd	10		450.2.h.d.271.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.31.1	✓	8	5.4	even	2
150.2.g.c.121.1	yes	8	25.4	even	10
450.2.h.d.181.2		8	15.14	odd	2
450.2.h.d.271.2		8	75.29	odd	10
750.2.g.d.151.2		8	1.1	even	1	trivial
750.2.g.d.601.2		8	25.21	even	5	inner
750.2.h.e.349.2		16	5.2	odd	4
750.2.h.e.349.3		16	5.3	odd	4
750.2.h.e.649.1		16	25.3	odd	20
750.2.h.e.649.4		16	25.22	odd	20
3750.2.a.l.1.1		4	25.14	even	10
3750.2.a.q.1.4		4	25.11	even	5
3750.2.c.h.1249.1		8	25.23	odd	20
3750.2.c.h.1249.8		8	25.2	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} +4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{6} +4.25729 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.51061 - 4.64918i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(1.43361 - 4.41219i) q^{13} +(1.31557 + 4.04892i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.815575 - 0.592550i) q^{17} +1.00000 q^{18} +(1.00000 + 0.726543i) q^{19} +(3.44422 - 2.50237i) q^{21} +(3.95483 - 2.87335i) q^{22} +(1.38197 + 4.25325i) q^{23} -1.00000 q^{24} +4.63925 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.44422 + 2.50237i) q^{28} +(-3.42049 + 2.48513i) q^{29} +(-0.826185 - 0.600258i) q^{31} +1.00000 q^{32} +(-3.95483 - 2.87335i) q^{33} +(0.311522 - 0.958765i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-3.31152 + 10.1918i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.43361 - 4.41219i) q^{39} +(1.42049 - 4.37183i) q^{41} +(3.44422 + 2.50237i) q^{42} +10.4984 q^{43} +(3.95483 + 2.87335i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-1.63925 + 1.19099i) q^{47} +(-0.309017 - 0.951057i) q^{48} +11.1245 q^{49} -1.00811 q^{51} +(1.43361 + 4.41219i) q^{52} +(8.94413 - 6.49829i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-3.44422 - 2.50237i) q^{56} +1.23607 q^{57} +(-3.42049 - 2.48513i) q^{58} +(-0.656508 + 2.02052i) q^{59} +(1.19754 + 3.68565i) q^{61} +(0.315575 - 0.971238i) q^{62} +(1.31557 - 4.04892i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.51061 - 4.64918i) q^{66} +(3.03434 + 2.20457i) q^{67} +1.00811 q^{68} +(3.61803 + 2.62866i) q^{69} +(-10.1457 + 7.37130i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-1.05975 - 3.26157i) q^{73} -10.7163 q^{74} -1.23607 q^{76} +(-6.43110 - 19.7929i) q^{77} +(3.75324 - 2.72689i) q^{78} +(-5.16968 + 3.75599i) q^{79} +(-0.809017 - 0.587785i) q^{81} +4.59681 q^{82} +(5.70151 + 4.14239i) q^{83} +(-1.31557 + 4.04892i) q^{84} +(3.24417 + 9.98454i) q^{86} +(-1.30651 + 4.02103i) q^{87} +(-1.51061 + 4.64918i) q^{88} +(0.693488 + 2.13434i) q^{89} +(6.10328 - 18.7840i) q^{91} +(-3.61803 - 2.62866i) q^{92} -1.02122 q^{93} +(-1.63925 - 1.19099i) q^{94} +(0.809017 - 0.587785i) q^{96} +(-6.49586 + 4.71952i) q^{97} +(3.43766 + 10.5800i) q^{98} -4.88844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 5 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{18} + 8 q^{19} + 3 q^{21} + 20 q^{23} - 8 q^{24} + 14 q^{26} + 2 q^{27} - 3 q^{28} - 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} - 2 q^{36} - 21 q^{37} - 12 q^{38} + 6 q^{39} + 2 q^{41} + 3 q^{42} + 32 q^{43} - 20 q^{46} + 10 q^{47} + 2 q^{48} + 22 q^{49} - 2 q^{51} - 6 q^{52} - 7 q^{53} + 2 q^{54} - 3 q^{56} - 8 q^{57} - 18 q^{58} - 25 q^{59} + 10 q^{61} - 6 q^{62} + 2 q^{63} - 2 q^{64} + 5 q^{66} + 2 q^{67} + 2 q^{68} + 20 q^{69} - 2 q^{72} + 24 q^{73} - 26 q^{74} + 8 q^{76} - 35 q^{77} + q^{78} - 6 q^{79} - 2 q^{81} + 42 q^{82} - 11 q^{83} - 2 q^{84} + 2 q^{86} - 7 q^{87} - 5 q^{88} + 9 q^{89} - 4 q^{91} - 20 q^{92} + 6 q^{93} + 10 q^{94} + 2 q^{96} - q^{97} + 7 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 5 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^18 + 8 * q^19 + 3 * q^21 + 20 * q^23 - 8 * q^24 + 14 * q^26 + 2 * q^27 - 3 * q^28 - 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 - 2 * q^36 - 21 * q^37 - 12 * q^38 + 6 * q^39 + 2 * q^41 + 3 * q^42 + 32 * q^43 - 20 * q^46 + 10 * q^47 + 2 * q^48 + 22 * q^49 - 2 * q^51 - 6 * q^52 - 7 * q^53 + 2 * q^54 - 3 * q^56 - 8 * q^57 - 18 * q^58 - 25 * q^59 + 10 * q^61 - 6 * q^62 + 2 * q^63 - 2 * q^64 + 5 * q^66 + 2 * q^67 + 2 * q^68 + 20 * q^69 - 2 * q^72 + 24 * q^73 - 26 * q^74 + 8 * q^76 - 35 * q^77 + q^78 - 6 * q^79 - 2 * q^81 + 42 * q^82 - 11 * q^83 - 2 * q^84 + 2 * q^86 - 7 * q^87 - 5 * q^88 + 9 * q^89 - 4 * q^91 - 20 * q^92 + 6 * q^93 + 10 * q^94 + 2 * q^96 - q^97 + 7 * q^98 + 10 * q^99

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