LMFDB - Embedded newform 637.2.bl.a.53.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.10
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971314 - 0.662231i) q^{2} +(1.44449 + 1.34029i) q^{3} +(-0.225781 - 0.575279i) q^{4} +(-0.154277 + 0.0475881i) q^{5} +(-0.515472 - 2.25843i) q^{6} +(2.49647 + 0.876147i) q^{7} +(-0.684849 + 3.00052i) q^{8} +(0.0659823 + 0.880472i) q^{9} +O(q^{10})$	\(q+(-0.971314 - 0.662231i) q^{2} +(1.44449 + 1.34029i) q^{3} +(-0.225781 - 0.575279i) q^{4} +(-0.154277 + 0.0475881i) q^{5} +(-0.515472 - 2.25843i) q^{6} +(2.49647 + 0.876147i) q^{7} +(-0.684849 + 3.00052i) q^{8} +(0.0659823 + 0.880472i) q^{9} +(0.181366 + 0.0559439i) q^{10} +(-0.385571 + 5.14508i) q^{11} +(0.444905 - 1.13360i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.84465 - 2.50425i) q^{14} +(-0.286634 - 0.138036i) q^{15} +(1.74619 - 1.62022i) q^{16} +(-4.86347 + 0.733050i) q^{17} +(0.518986 - 0.898910i) q^{18} +(2.26408 + 3.92150i) q^{19} +(0.0622092 + 0.0780079i) q^{20} +(2.43184 + 4.61159i) q^{21} +(3.78174 - 4.74216i) q^{22} +(1.27803 + 0.192632i) q^{23} +(-5.01083 + 3.41633i) q^{24} +(-4.10966 + 2.80192i) q^{25} +(-1.16245 - 0.175212i) q^{26} +(2.60101 - 3.26157i) q^{27} +(-0.0596254 - 1.63399i) q^{28} +(2.10701 + 2.64211i) q^{29} +(0.187000 + 0.323894i) q^{30} +(4.23372 - 7.33302i) q^{31} +(3.31755 - 0.500041i) q^{32} +(-7.45287 + 6.91525i) q^{33} +(5.20940 + 2.50872i) q^{34} +(-0.426842 - 0.0163668i) q^{35} +(0.491620 - 0.236752i) q^{36} +(2.63478 - 6.71330i) q^{37} +(0.397806 - 5.30835i) q^{38} +(1.88297 + 0.580820i) q^{39} +(-0.0371327 - 0.495501i) q^{40} +(-1.41910 + 6.21749i) q^{41} +(0.691856 - 6.08974i) q^{42} +(2.77762 + 12.1696i) q^{43} +(3.04692 - 0.939849i) q^{44} +(-0.0520796 - 0.132697i) q^{45} +(-1.11380 - 1.03346i) q^{46} +(-2.44020 - 1.66370i) q^{47} +4.69393 q^{48} +(5.46473 + 4.37455i) q^{49} +5.84728 q^{50} +(-8.00774 - 5.45958i) q^{51} +(-0.453026 - 0.420346i) q^{52} +(0.410204 + 1.04518i) q^{53} +(-4.68631 + 1.44554i) q^{54} +(-0.185360 - 0.812117i) q^{55} +(-4.33860 + 6.89068i) q^{56} +(-1.98551 + 8.69909i) q^{57} +(-0.296885 - 3.96165i) q^{58} +(0.454641 + 0.140238i) q^{59} +(-0.0146927 + 0.196060i) q^{60} +(-1.73401 + 4.41818i) q^{61} +(-8.96842 + 4.31896i) q^{62} +(-0.606700 + 2.25588i) q^{63} +(-7.84589 - 3.77838i) q^{64} +(-0.118351 + 0.109814i) q^{65} +(11.8186 - 1.78136i) q^{66} +(-0.0180687 + 0.0312959i) q^{67} +(1.51978 + 2.63234i) q^{68} +(1.58792 + 1.99119i) q^{69} +(0.403759 + 0.298565i) q^{70} +(5.16801 - 6.48048i) q^{71} +(-2.68706 - 0.405009i) q^{72} +(-1.48444 + 1.01208i) q^{73} +(-7.00495 + 4.77589i) q^{74} +(-9.69175 - 1.46080i) q^{75} +(1.74477 - 2.18787i) q^{76} +(-5.47041 + 12.5067i) q^{77} +(-1.44432 - 1.81112i) q^{78} +(-5.95234 - 10.3097i) q^{79} +(-0.192293 + 0.333061i) q^{80} +(10.7478 - 1.61998i) q^{81} +(5.49580 - 5.09936i) q^{82} +(13.4294 + 6.46727i) q^{83} +(2.10389 - 2.44019i) q^{84} +(0.715436 - 0.344536i) q^{85} +(5.36111 - 13.6599i) q^{86} +(-0.497639 + 6.64053i) q^{87} +(-15.1739 - 4.68052i) q^{88} +(-0.583394 - 7.78485i) q^{89} +(-0.0372901 + 0.163379i) q^{90} +(2.62939 - 0.293797i) q^{91} +(-0.177737 - 0.778718i) q^{92} +(15.9440 - 4.91806i) q^{93} +(1.26844 + 3.23194i) q^{94} +(-0.535912 - 0.497253i) q^{95} +(5.46238 + 3.72419i) q^{96} +5.41424 q^{97} +(-2.41101 - 7.86798i) q^{98} -4.55554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	−0.971314	−	0.662231i	−0.686823	−	0.468268i	0.168947	−	0.985625i	$-0.445963\pi$
$2$	−0.971314	−	0.662231i	−0.686823	−	0.468268i	−0.855769	+	0.517357i	$0.826916\pi$
$3$	1.44449	+	1.34029i	0.833978	+	0.773818i	0.976396	−	0.215988i	$-0.0692973\pi$
$3$	1.44449	+	1.34029i	0.833978	+	0.773818i	−0.142418	+	0.989807i	$0.545488\pi$
$4$	−0.225781	−	0.575279i	−0.112890	−	0.287640i
$5$	−0.154277	+	0.0475881i	−0.0689948	+	0.0212821i	−0.329060	−	0.944309i	$-0.606732\pi$
$5$	−0.154277	+	0.0475881i	−0.0689948	+	0.0212821i	0.260066	+	0.965591i	$0.416256\pi$
$6$	−0.515472	−	2.25843i	−0.210441	−	0.922001i
$7$	2.49647	+	0.876147i	0.943577	+	0.331152i
$7$	2.49647	+	0.876147i	0.943577	+	0.331152i
$8$	−0.684849	+	3.00052i	−0.242131	+	1.06084i
$9$	0.0659823	+	0.880472i	0.0219941	+	0.293491i
$10$	0.181366	+	0.0559439i	0.0573529	+	0.0176910i
$11$	−0.385571	+	5.14508i	−0.116254	+	1.55130i	0.568596	+	0.822617i	$0.307487\pi$
$11$	−0.385571	+	5.14508i	−0.116254	+	1.55130i	−0.684850	+	0.728684i	$0.740132\pi$
$12$	0.444905	−	1.13360i	0.128433	−	0.327242i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	−1.84465	−	2.50425i	−0.493002	−	0.669290i
$15$	−0.286634	−	0.138036i	−0.0740085	−	0.0356406i
$16$	1.74619	−	1.62022i	0.436547	−	0.405056i
$17$	−4.86347	+	0.733050i	−1.17956	+	0.177791i	−0.709411	−	0.704795i	$-0.751039\pi$
$17$	−4.86347	+	0.733050i	−1.17956	+	0.177791i	−0.470152	+	0.882585i	$0.655801\pi$
$18$	0.518986	−	0.898910i	0.122326	−	0.211875i
$19$	2.26408	+	3.92150i	0.519415	+	0.899653i	0.999745	+	0.0225653i	$0.00718337\pi$
$19$	2.26408	+	3.92150i	0.519415	+	0.899653i	−0.480331	+	0.877088i	$0.659483\pi$
$20$	0.0622092	+	0.0780079i	0.0139104	+	0.0174431i
$21$	2.43184	+	4.61159i	0.530671	+	1.00633i
$22$	3.78174	−	4.74216i	0.806270	−	1.01103i
$23$	1.27803	+	0.192632i	0.266488	+	0.0401666i	0.280927	−	0.959729i	$-0.409358\pi$
$23$	1.27803	+	0.192632i	0.266488	+	0.0401666i	−0.0144388	+	0.999896i	$0.504596\pi$
$24$	−5.01083	+	3.41633i	−1.02283	+	0.697355i
$25$	−4.10966	+	2.80192i	−0.821931	+	0.560383i
$26$	−1.16245	−	0.175212i	−0.227976	−	0.0343619i
$27$	2.60101	−	3.26157i	0.500565	−	0.627689i
$28$	−0.0596254	−	1.63399i	−0.0112681	−	0.308794i
$29$	2.10701	+	2.64211i	0.391263	+	0.490628i	0.937980	−	0.346689i	$-0.112694\pi$
$29$	2.10701	+	2.64211i	0.391263	+	0.490628i	−0.546717	+	0.837317i	$0.684123\pi$
$30$	0.187000	+	0.323894i	0.0341414	+	0.0591346i
$31$	4.23372	−	7.33302i	0.760398	−	1.31705i	−0.182247	−	0.983253i	$-0.558337\pi$
$31$	4.23372	−	7.33302i	0.760398	−	1.31705i	0.942645	−	0.333796i	$-0.108330\pi$
$32$	3.31755	−	0.500041i	0.586466	−	0.0883956i
$33$	−7.45287	+	6.91525i	−1.29738	+	1.20379i
$34$	5.20940	+	2.50872i	0.893405	+	0.430241i
$35$	−0.426842	−	0.0163668i	−0.0721495	−	0.00276650i
$36$	0.491620	−	0.236752i	0.0819366	−	0.0394586i
$37$	2.63478	−	6.71330i	0.433155	−	1.10366i	−0.533096	−	0.846055i	$-0.678971\pi$
$37$	2.63478	−	6.71330i	0.433155	−	1.10366i	0.966250	−	0.257605i	$-0.0829333\pi$
$38$	0.397806	−	5.30835i	0.0645326	−	0.861127i
$39$	1.88297	+	0.580820i	0.301517	+	0.0930057i
$40$	−0.0371327	−	0.495501i	−0.00587119	−	0.0783456i
$41$	−1.41910	+	6.21749i	−0.221626	+	0.971008i	0.734628	+	0.678471i	$0.237357\pi$
$41$	−1.41910	+	6.21749i	−0.221626	+	0.971008i	−0.956254	+	0.292538i	$0.905500\pi$
$42$	0.691856	−	6.08974i	0.106756	−	0.939667i
$43$	2.77762	+	12.1696i	0.423583	+	1.85584i	0.510871	+	0.859657i	$0.329323\pi$
$43$	2.77762	+	12.1696i	0.423583	+	1.85584i	−0.0872877	+	0.996183i	$0.527820\pi$
$44$	3.04692	−	0.939849i	0.459340	−	0.141688i
$45$	−0.0520796	−	0.132697i	−0.00776356	−	0.0197812i
$46$	−1.11380	−	1.03346i	−0.164221	−	0.152375i
$47$	−2.44020	−	1.66370i	−0.355939	−	0.242675i	0.372127	−	0.928182i	$-0.378628\pi$
$47$	−2.44020	−	1.66370i	−0.355939	−	0.242675i	−0.728066	+	0.685507i	$0.759581\pi$
$48$	4.69393			0.677510
$49$	5.46473	+	4.37455i	0.780676	+	0.624936i
$50$	5.84728			0.826931
$51$	−8.00774	−	5.45958i	−1.12131	−	0.764495i
$52$	−0.453026	−	0.420346i	−0.0628233	−	0.0582915i
$53$	0.410204	+	1.04518i	0.0563458	+	0.143567i	0.956275	−	0.292470i	$-0.0944771\pi$
$53$	0.410204	+	1.04518i	0.0563458	+	0.143567i	−0.899929	+	0.436037i	$0.856382\pi$
$54$	−4.68631	+	1.44554i	−0.637726	+	0.196713i
$55$	−0.185360	−	0.812117i	−0.0249940	−	0.109506i
$56$	−4.33860	+	6.89068i	−0.579770	+	0.920805i
$57$	−1.98551	+	8.69909i	−0.262987	+	1.15222i
$58$	−0.296885	−	3.96165i	−0.0389829	−	0.520190i
$59$	0.454641	+	0.140238i	0.0591892	+	0.0182575i	0.324208	−	0.945986i	$-0.394902\pi$
$59$	0.454641	+	0.140238i	0.0591892	+	0.0182575i	−0.265019	+	0.964243i	$0.585378\pi$
$60$	−0.0146927	+	0.196060i	−0.00189682	+	0.0253113i
$61$	−1.73401	+	4.41818i	−0.222017	+	0.565690i	−0.997871	−	0.0652228i	$-0.979224\pi$
$61$	−1.73401	+	4.41818i	−0.222017	+	0.565690i	0.775854	+	0.630913i	$0.217319\pi$
$62$	−8.96842	+	4.31896i	−1.13899	+	0.548509i
$63$	−0.606700	+	2.25588i	−0.0764370	+	0.284215i
$64$	−7.84589	−	3.77838i	−0.980736	−	0.472297i
$65$	−0.118351	+	0.109814i	−0.0146796	+	0.0136207i
$66$	11.8186	−	1.78136i	1.45477	−	0.219271i
$67$	−0.0180687	+	0.0312959i	−0.00220745	+	0.00382341i	−0.867127	−	0.498087i	$-0.834036\pi$
$67$	−0.0180687	+	0.0312959i	−0.00220745	+	0.00382341i	0.864920	+	0.501910i	$0.167369\pi$
$68$	1.51978	+	2.63234i	0.184301	+	0.319219i
$69$	1.58792	+	1.99119i	0.191164	+	0.239712i
$70$	0.403759	+	0.298565i	0.0482584	+	0.0356854i
$71$	5.16801	−	6.48048i	0.613330	−	0.769092i	−0.374059	−	0.927405i	$-0.622034\pi$
$71$	5.16801	−	6.48048i	0.613330	−	0.769092i	0.987389	+	0.158313i	$0.0506056\pi$
$72$	−2.68706	−	0.405009i	−0.316673	−	0.0477308i
$73$	−1.48444	+	1.01208i	−0.173741	+	0.118455i	−0.647068	−	0.762432i	$-0.724005\pi$
$73$	−1.48444	+	1.01208i	−0.173741	+	0.118455i	0.473327	+	0.880887i	$0.343053\pi$
$74$	−7.00495	+	4.77589i	−0.814309	+	0.555186i
$75$	−9.69175	−	1.46080i	−1.11911	−	0.168678i
$76$	1.74477	−	2.18787i	0.200139	−	0.250966i
$77$	−5.47041	+	12.5067i	−0.623412	+	1.42527i
$78$	−1.44432	−	1.81112i	−0.163537	−	0.205069i
$79$	−5.95234	−	10.3097i	−0.669690	−	1.15994i	−0.977991	−	0.208648i	$-0.933094\pi$
$79$	−5.95234	−	10.3097i	−0.669690	−	1.15994i	0.308301	−	0.951289i	$-0.400240\pi$
$80$	−0.192293	+	0.333061i	−0.0214990	+	0.0372374i
$81$	10.7478	−	1.61998i	1.19420	−	0.179997i
$82$	5.49580	−	5.09936i	0.606910	−	0.563130i
$83$	13.4294	+	6.46727i	1.47407	+	0.709875i	0.986584	−	0.163255i	$-0.0521994\pi$
$83$	13.4294	+	6.46727i	1.47407	+	0.709875i	0.487487	+	0.873130i	$0.337914\pi$
$84$	2.10389	−	2.44019i	0.229553	−	0.266247i
$85$	0.715436	−	0.344536i	0.0776000	−	0.0373702i
$86$	5.36111	−	13.6599i	0.578104	−	1.47298i
$87$	−0.497639	+	6.64053i	−0.0533525	+	0.711939i
$88$	−15.1739	−	4.68052i	−1.61754	−	0.498945i
$89$	−0.583394	−	7.78485i	−0.0618396	−	0.825192i	−0.938763	−	0.344563i	$-0.888027\pi$
$89$	−0.583394	−	7.78485i	−0.0618396	−	0.825192i	0.876924	−	0.480630i	$-0.159592\pi$
$90$	−0.0372901	+	0.163379i	−0.00393072	+	0.0172216i
$91$	2.62939	−	0.293797i	0.275635	−	0.0307983i
$92$	−0.177737	−	0.778718i	−0.0185304	−	0.0811870i
$93$	15.9440	−	4.91806i	1.65331	−	0.509979i
$94$	1.26844	+	3.23194i	0.130830	+	0.333350i
$95$	−0.535912	−	0.497253i	−0.0549834	−	0.0510171i
$96$	5.46238	+	3.72419i	0.557502	+	0.380098i
$97$	5.41424			0.549732			0.274866	−	0.961482i	$-0.411366\pi$
$97$	5.41424			0.549732			0.274866	+	0.961482i	$0.411366\pi$
$98$	−2.41101	−	7.86798i	−0.243549	−	0.794786i
$99$	−4.55554			−0.457849
$100$	2.53977	+	1.73158i	0.253977	+	0.173158i
$101$	6.08027	+	5.64167i	0.605010	+	0.561367i	0.922063	−	0.387041i	$-0.126503\pi$
$101$	6.08027	+	5.64167i	0.605010	+	0.561367i	−0.317053	+	0.948408i	$0.602693\pi$
$102$	4.16253	+	10.6059i	0.412151	+	1.05014i
$103$	0.0141296	−	0.00435841i	0.00139223	−	0.000429447i	−0.294059	−	0.955787i	$-0.595006\pi$
$103$	0.0141296	−	0.00435841i	0.00139223	−	0.000429447i	0.295451	+	0.955358i	$0.404530\pi$
$104$	0.684849	+	3.00052i	0.0671549	+	0.294225i
$105$	−0.594634	−	0.595735i	−0.0580303	−	0.0581378i
$106$	0.293715	−	1.28685i	0.0285281	−	0.124990i
$107$	−0.732279	−	9.77158i	−0.0707921	−	0.944654i	−0.913646	−	0.406512i	$-0.866745\pi$
$107$	−0.732279	−	9.77158i	−0.0707921	−	0.944654i	0.842854	−	0.538143i	$-0.180874\pi$
$108$	−2.46357	−	0.759911i	−0.237057	−	0.0731225i
$109$	0.872851	−	11.6474i	0.0836040	−	1.11562i	−0.784796	−	0.619754i	$-0.787232\pi$
$109$	0.872851	−	11.6474i	0.0836040	−	1.11562i	0.868400	−	0.495864i	$-0.165149\pi$
$110$	−0.357765	+	0.911572i	−0.0341116	+	0.0869149i
$111$	12.8037	−	6.16594i	1.21527	−	0.585245i
$112$	5.77886	−	2.51493i	0.546051	−	0.237638i
$113$	−18.4237	−	8.87238i	−1.73315	−	0.834643i	−0.985311	−	0.170768i	$-0.945375\pi$
$113$	−18.4237	−	8.87238i	−1.73315	−	0.834643i	−0.747843	−	0.663875i	$-0.768911\pi$
$114$	7.68936	−	7.13469i	0.720175	−	0.668225i
$115$	−0.206338	+	0.0311005i	−0.0192411	+	0.00290013i
$116$	1.04423	−	1.80866i	0.0969543	−	0.167930i
$117$	0.441470	+	0.764649i	0.0408140	+	0.0706918i
$118$	−0.348729	−	0.437293i	−0.0321031	−	0.0402561i
$119$	−12.7838	−	2.43107i	−1.17189	−	0.222856i
$120$	0.610479	−	0.765516i	0.0557288	−	0.0698818i
$121$	−15.4461	−	2.32812i	−1.40419	−	0.211648i
$122$	4.61012	−	3.14313i	0.417381	−	0.284565i
$123$	−10.3831	+	7.07910i	−0.936215	+	0.638301i
$124$	−5.17442	−	0.779919i	−0.464677	−	0.0700388i
$125$	1.00400	−	1.25897i	0.0898004	−	0.112606i
$126$	2.08321	−	1.78940i	0.185587	−	0.159412i
$127$	−3.13853	−	3.93559i	−0.278499	−	0.349227i	0.622833	−	0.782354i	$-0.285981\pi$
$127$	−3.13853	−	3.93559i	−0.278499	−	0.349227i	−0.901333	+	0.433127i	$0.857410\pi$
$128$	1.76363	+	3.05470i	0.155885	+	0.270000i
$129$	−12.2985	+	21.3017i	−1.08282	+	1.87551i
$130$	0.187678	−	0.0282879i	0.0164605	−	0.00248101i
$131$	−6.57819	+	6.10367i	−0.574739	+	0.533280i	−0.913100	−	0.407737i	$-0.866318\pi$
$131$	−6.57819	+	6.10367i	−0.574739	+	0.533280i	0.338361	+	0.941017i	$0.390128\pi$
$132$	5.66092	+	2.72615i	0.492720	+	0.237281i
$133$	2.21640	+	11.7736i	0.192186	+	1.02090i
$134$	0.0382755	−	0.0184325i	0.00330650	−	0.00159233i
$135$	−0.246065	+	0.626962i	−0.0211779	+	0.0539603i
$136$	1.13121	−	15.0949i	0.0970004	−	1.29438i
$137$	6.89180	+	2.12584i	0.588806	+	0.181623i	0.574821	−	0.818280i	$-0.305072\pi$
$137$	6.89180	+	2.12584i	0.588806	+	0.181623i	0.0139858	+	0.999902i	$0.495548\pi$
$138$	−0.223743	−	2.98565i	−0.0190463	−	0.254155i
$139$	3.47896	−	15.2423i	0.295081	−	1.29284i	−0.582273	−	0.812993i	$-0.697837\pi$
$139$	3.47896	−	15.2423i	0.295081	−	1.29284i	0.877354	−	0.479843i	$-0.159306\pi$
$140$	0.0869571	+	0.249249i	0.00734922	+	0.0210654i
$141$	−1.29500	−	5.67377i	−0.109059	−	0.477818i
$142$	−9.31134	+	2.87217i	−0.781390	+	0.241027i
$143$	1.88498	+	4.80285i	0.157630	+	0.401635i
$144$	1.54178	+	1.43056i	0.128482	+	0.119214i
$145$	−0.450797	−	0.307348i	−0.0374366	−	0.0255239i
$146$	2.11209			0.174798
$147$	2.03059	+	13.6433i	0.167480	+	1.12528i
$148$	−4.45690			−0.366355
$149$	−11.5139	−	7.85003i	−0.943254	−	0.643100i	−0.00909586	−	0.999959i	$-0.502895\pi$
$149$	−11.5139	−	7.85003i	−0.943254	−	0.643100i	−0.934158	+	0.356859i	$0.883848\pi$
$150$	8.44635	+	7.83707i	0.689642	+	0.639894i
$151$	−6.30598	−	16.0674i	−0.513173	−	1.30754i	−0.919239	−	0.393700i	$-0.871195\pi$
$151$	−6.30598	−	16.0674i	−0.513173	−	1.30754i	0.406066	−	0.913844i	$-0.366900\pi$
$152$	−13.3171	+	4.10777i	−1.08016	+	0.333184i
$153$	−0.966332	−	4.23378i	−0.0781233	−	0.342281i
$154$	13.5958	−	8.52529i	1.09558	−	0.686988i
$155$	−0.304201	+	1.33279i	−0.0244340	+	0.107052i
$156$	−0.0910047	−	1.21437i	−0.00728621	−	0.0972277i
$157$	8.28642	+	2.55602i	0.661328	+	0.203993i	0.607209	−	0.794542i	$-0.292289\pi$
$157$	8.28642	+	2.55602i	0.661328	+	0.203993i	0.0541186	+	0.998535i	$0.482765\pi$
$158$	−1.04584	+	13.9558i	−0.0832029	+	1.11027i
$159$	−0.808314	+	2.05955i	−0.0641034	+	0.163333i
$160$	−0.488026	+	0.235021i	−0.0385819	+	0.0185800i
$161$	3.02180	+	1.60065i	0.238151	+	0.126149i
$162$	−11.5123	−	5.54404i	−0.904494	−	0.435581i
$163$	−7.33134	+	6.80249i	−0.574235	+	0.532812i	−0.912947	−	0.408078i	$-0.866199\pi$
$163$	−7.33134	+	6.80249i	−0.574235	+	0.532812i	0.338712	+	0.940890i	$0.390009\pi$
$164$	3.89720	−	0.587408i	0.304320	−	0.0458689i
$165$	0.820722	−	1.42153i	0.0638931	−	0.110666i
$166$	−8.76136	−	15.1751i	−0.680014	−	1.17782i
$167$	6.58983	+	8.26338i	0.509936	+	0.639440i	0.968438	−	0.249254i	$-0.0801853\pi$
$167$	6.58983	+	8.26338i	0.509936	+	0.639440i	−0.458502	+	0.888693i	$0.651614\pi$
$168$	−15.5026	+	4.13854i	−1.19605	+	0.319295i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−0.923076	−	0.139131i	−0.0707967	−	0.0106709i
$171$	−3.30338	+	2.25221i	−0.252616	+	0.172230i
$172$	6.37376	−	4.34556i	0.485995	−	0.331346i
$173$	−16.4509	−	2.47957i	−1.25074	−	0.188518i	−0.509918	−	0.860223i	$-0.670324\pi$
$173$	−16.4509	−	2.47957i	−1.25074	−	0.188518i	−0.740819	+	0.671705i	$0.765562\pi$
$174$	4.88092	−	6.12048i	0.370022	−	0.463993i
$175$	−12.7145	+	3.39424i	−0.961128	+	0.256581i
$176$	7.66291	+	9.60899i	0.577614	+	0.724305i
$177$	0.468765	+	0.811925i	0.0352345	+	0.0610280i
$178$	−4.58871	+	7.94787i	−0.343938	+	0.595718i
$179$	7.56431	−	1.14014i	0.565383	−	0.0852178i	0.139870	−	0.990170i	$-0.455332\pi$
$179$	7.56431	−	1.14014i	0.565383	−	0.0852178i	0.425513	+	0.904952i	$0.360094\pi$
$180$	−0.0645790	+	0.0599206i	−0.00481344	+	0.00446622i
$181$	−17.7022	−	8.52494i	−1.31580	−	0.633654i	−0.361459	−	0.932388i	$-0.617721\pi$
$181$	−17.7022	−	8.52494i	−1.31580	−	0.633654i	−0.954336	+	0.298734i	$0.903436\pi$
$182$	−2.74852	−	1.45589i	−0.203734	−	0.107918i
$183$	−8.42641	+	4.05795i	−0.622898	+	0.299972i
$184$	−1.45326	+	3.70284i	−0.107135	+	0.272977i
$185$	−0.0870118	+	1.16109i	−0.00639723	+	0.0853652i
$186$	−18.7435	−	5.78160i	−1.37434	−	0.423927i
$187$	−1.89639	−	25.3056i	−0.138678	−	1.85053i
$188$	−0.406142	+	1.77942i	−0.0296209	+	0.129778i
$189$	9.35097	−	5.86354i	0.680183	−	0.426510i
$190$	0.191242	+	0.837886i	0.0138742	+	0.0607867i
$191$	−6.84623	+	2.11178i	−0.495376	+	0.152803i	−0.532369	−	0.846512i	$-0.678698\pi$
$191$	−6.84623	+	2.11178i	−0.495376	+	0.152803i	0.0369934	+	0.999316i	$0.488222\pi$
$192$	−6.26918	−	15.9736i	−0.452439	−	1.15280i
$193$	−10.1138	−	9.38420i	−0.728004	−	0.675489i	0.226390	−	0.974037i	$-0.427307\pi$
$193$	−10.1138	−	9.38420i	−0.728004	−	0.675489i	−0.954395	+	0.298547i	$0.903498\pi$
$194$	−5.25892	−	3.58547i	−0.377569	−	0.257422i
$195$	−0.318140			−0.0227824
$196$	1.28276	−	4.13144i	0.0916255	−	0.295103i
$197$	−2.04098			−0.145414			−0.0727068	−	0.997353i	$-0.523164\pi$
$197$	−2.04098			−0.145414			−0.0727068	+	0.997353i	$0.523164\pi$
$198$	4.42486	+	3.01682i	0.314461	+	0.214396i
$199$	−0.517927	−	0.480566i	−0.0367148	−	0.0340664i	0.661602	−	0.749855i	$-0.269877\pi$
$199$	−0.517927	−	0.480566i	−0.0367148	−	0.0340664i	−0.698317	+	0.715789i	$0.746067\pi$
$200$	−5.59271	−	14.2500i	−0.395464	−	1.00763i
$201$	−0.0680458	+	0.0209894i	−0.00479958	+	0.00148048i
$202$	−2.16977	−	9.50638i	−0.152664	−	0.668866i
$203$	2.94522	+	8.44201i	0.206714	+	0.592513i
$204$	−1.33279	+	5.83935i	−0.0933143	+	0.408837i
$205$	−0.0769441	−	1.02675i	−0.00537401	−	0.0717111i
$206$	−0.0166106	−	0.00512368i	−0.00115731	−	0.000356984i
$207$	−0.0852800	+	1.13798i	−0.00592737	+	0.0790952i
$208$	0.870271	−	2.21741i	0.0603424	−	0.153750i
$209$	−21.0494	+	10.1369i	−1.45602	+	0.701181i
$210$	0.183062	+	0.972431i	0.0126325	+	0.0671041i
$211$	24.2222	+	11.6648i	1.66753	+	0.803039i	0.998194	+	0.0600771i	$0.0191346\pi$
$211$	24.2222	+	11.6648i	1.66753	+	0.803039i	0.669334	+	0.742962i	$0.266580\pi$
$212$	0.508656	−	0.471963i	0.0349346	−	0.0324146i
$213$	16.1509	−	2.43436i	1.10664	−	0.166799i
$214$	−5.75977	+	9.97621i	−0.393730	+	0.681960i
$215$	−1.00765	−	1.74530i	−0.0687211	−	0.119029i
$216$	8.00509	+	10.0381i	0.544678	+	0.683004i
$217$	16.9942	−	14.5973i	1.15364	−	0.990929i
$218$	−8.56107	+	10.7352i	−0.579829	+	0.727083i
$219$	−3.50074	−	0.527652i	−0.236558	−	0.0356554i
$220$	−0.425343	+	0.289994i	−0.0286766	+	0.0195514i
$221$	−4.06377	+	2.77063i	−0.273359	+	0.186373i
$222$	−16.5197	−	2.48994i	−1.10873	−	0.167114i
$223$	−2.24752	+	2.81830i	−0.150505	+	0.188728i	−0.851369	−	0.524568i	$-0.824227\pi$
$223$	−2.24752	+	2.81830i	−0.150505	+	0.188728i	0.700863	+	0.713296i	$0.252798\pi$
$224$	8.72029	+	1.65833i	0.582649	+	0.110802i
$225$	−2.73817	−	3.43356i	−0.182545	−	0.228904i
$226$	12.0196	+	20.8186i	0.799533	+	1.38483i
$227$	−6.80594	+	11.7882i	−0.451726	+	0.782412i	−0.998493	−	0.0548723i	$-0.982525\pi$
$227$	−6.80594	+	11.7882i	−0.451726	+	0.782412i	0.546767	+	0.837285i	$0.315858\pi$
$228$	5.45270	−	0.821862i	0.361114	−	0.0544291i
$229$	−2.12580	+	1.97245i	−0.140477	+	0.130343i	−0.747282	−	0.664508i	$-0.768641\pi$
$229$	−2.12580	+	1.97245i	−0.140477	+	0.130343i	0.606805	+	0.794851i	$0.292451\pi$
$230$	0.221015	+	0.106435i	0.0145733	+	0.00701812i
$231$	−24.6647	+	10.7339i	−1.62282	+	0.706240i
$232$	−9.37069	+	4.51269i	−0.615216	+	0.296272i
$233$	6.77055	−	17.2511i	0.443554	−	1.13016i	−0.517961	−	0.855404i	$-0.673309\pi$
$233$	6.77055	−	17.2511i	0.443554	−	1.13016i	0.961515	−	0.274752i	$-0.0885958\pi$
$234$	0.0775678	−	1.03507i	0.00507076	−	0.0676646i
$235$	0.455638	+	0.140546i	0.0297226	+	0.00916819i
$236$	−0.0219730	−	0.293209i	−0.00143032	−	0.0190863i
$237$	5.21998	−	22.8702i	0.339074	−	1.48558i
$238$	10.8071	+	10.8271i	0.700521	+	0.701819i
$239$	0.627514	+	2.74932i	0.0405905	+	0.177839i	0.991160	−	0.132674i	$-0.0423564\pi$
$239$	0.627514	+	2.74932i	0.0405905	+	0.177839i	−0.950569	+	0.310513i	$0.899499\pi$
$240$	−0.724165	+	0.223375i	−0.0467446	+	0.0144188i
$241$	−8.46719	−	21.5740i	−0.545419	−	1.38971i	−0.892149	−	0.451741i	$-0.850803\pi$
$241$	−8.46719	−	21.5740i	−0.545419	−	1.38971i	0.346730	−	0.937965i	$-0.387292\pi$
$242$	13.4613	+	12.4902i	0.865322	+	0.802901i
$243$	7.35594	+	5.01519i	0.471884	+	0.321725i
$244$	2.93319			0.187778
$245$	−1.05126	−	0.414836i	−0.0671625	−	0.0265029i
$246$	14.7733			0.941910
$247$	3.74134	+	2.55080i	0.238056	+	0.162303i
$248$	19.1034	+	17.7254i	1.21307	+	1.12556i
$249$	10.7307	+	27.3413i	0.680028	+	1.73268i
$250$	−1.80893	+	0.557981i	−0.114407	+	0.0352898i
$251$	−5.90618	−	25.8767i	−0.372795	−	1.63332i	−0.718892	−	0.695121i	$-0.755351\pi$
$251$	−5.90618	−	25.8767i	−0.372795	−	1.63332i	0.346098	−	0.938198i	$-0.387506\pi$
$252$	1.43474	−	0.160312i	0.0903804	−	0.0100987i
$253$	−1.48388	+	6.50131i	−0.0932909	+	0.408734i
$254$	0.442228	+	5.90112i	0.0277478	+	0.370269i
$255$	1.49522	+	0.461215i	0.0936344	+	0.0288824i
$256$	−0.991665	+	13.2328i	−0.0619790	+	0.827053i
$257$	5.54513	−	14.1288i	0.345896	−	0.881329i	−0.647016	−	0.762476i	$-0.723983\pi$
$257$	5.54513	−	14.1288i	0.345896	−	0.881329i	0.992912	−	0.118852i	$-0.0379214\pi$
$258$	26.0523	−	12.5461i	1.62195	−	0.781089i
$259$	12.4595	−	14.4511i	0.774194	−	0.897948i
$260$	0.0898949	+	0.0432911i	0.00557505	+	0.00268480i
$261$	−2.18728	+	2.02950i	−0.135389	+	0.125623i
$262$	10.4315	−	1.57230i	0.644462	−	0.0971370i
$263$	−8.22733	+	14.2501i	−0.507319	+	0.878702i	0.492645	+	0.870230i	$0.336030\pi$
$263$	−8.22733	+	14.2501i	−0.507319	+	0.878702i	−0.999964	+	0.00847167i	$0.997303\pi$
$264$	−15.6453	−	27.0984i	−0.962899	−	1.66779i
$265$	−0.113023	−	0.141727i	−0.00694296	−	0.00870620i
$266$	5.64400	−	12.9036i	0.346056	−	0.791170i
$267$	9.59127	−	12.0271i	0.586976	−	0.736045i
$268$	0.0220835	+	0.00332855i	0.00134896	+	0.000203323i
$269$	−9.28014	+	6.32709i	−0.565820	+	0.385770i	−0.812178	−	0.583409i	$-0.801718\pi$
$269$	−9.28014	+	6.32709i	−0.565820	+	0.385770i	0.246358	+	0.969179i	$0.420766\pi$
$270$	0.654200	−	0.446026i	0.0398133	−	0.0271443i
$271$	27.2518	+	4.10755i	1.65543	+	0.249516i	0.909257	−	0.416234i	$-0.136650\pi$
$271$	27.2518	+	4.10755i	1.65543	+	0.249516i	0.746174	+	0.665751i	$0.231889\pi$
$272$	−7.30482	+	9.15995i	−0.442920	+	0.555404i
$273$	4.19190	+	3.09976i	0.253706	+	0.187606i
$274$	−5.28631	−	6.62882i	−0.319358	−	0.400462i
$275$	−12.8315	−	22.2249i	−0.773771	−	1.34021i
$276$	0.786970	−	1.36307i	0.0473700	−	0.0820473i
$277$	31.0984	−	4.68733i	1.86852	−	0.281634i	0.885432	−	0.464768i	$-0.153862\pi$
$277$	31.0984	−	4.68733i	1.86852	−	0.281634i	0.983088	+	0.183134i	$0.0586243\pi$
$278$	−13.4731	+	12.5012i	−0.808062	+	0.749772i
$279$	6.73586	+	3.24382i	0.403266	+	0.194203i
$280$	0.341431	−	1.26954i	0.0204044	−	0.0758694i
$281$	−12.4003	+	5.97168i	−0.739741	+	0.356241i	−0.765507	−	0.643427i	$-0.777512\pi$
$281$	−12.4003	+	5.97168i	−0.739741	+	0.356241i	0.0257660	+	0.999668i	$0.491798\pi$
$282$	−2.49949	+	6.36860i	−0.148843	+	0.379245i
$283$	−0.269339	+	3.59408i	−0.0160106	+	0.213646i	0.983460	+	0.181123i	$0.0579732\pi$
$283$	−0.269339	+	3.59408i	−0.0160106	+	0.213646i	−0.999471	+	0.0325229i	$0.989646\pi$
$284$	−4.89492	−	1.50988i	−0.290460	−	0.0895951i
$285$	−0.107655	−	1.43656i	−0.00637693	−	0.0850943i
$286$	1.34969	−	5.91337i	0.0798088	−	0.349665i
$287$	−8.99017	+	14.2784i	−0.530673	+	0.842829i
$288$	0.659172	+	2.88802i	0.0388421	+	0.170178i
$289$	6.87121	−	2.11949i	0.404189	−	0.124676i
$290$	0.234330	+	0.597063i	0.0137603	+	0.0350608i
$291$	7.82082	+	7.25666i	0.458465	+	0.425393i
$292$	0.917385	+	0.625462i	0.0536859	+	0.0366024i
$293$	27.7405			1.62062			0.810309	−	0.586003i	$-0.199299\pi$
$293$	27.7405			1.62062			0.810309	+	0.586003i	$0.199299\pi$
$294$	7.06270	−	14.5967i	0.411905	−	0.851296i
$295$	−0.0768143			−0.00447230
$296$	18.3390	+	12.5033i	1.06593	+	0.726739i
$297$	15.7782	+	14.6400i	0.915542	+	0.849499i
$298$	5.98507	+	15.2497i	0.346706	+	0.883391i
$299$	1.23505	−	0.380962i	0.0714247	−	0.0220316i
$300$	1.34784	+	5.90529i	0.0778177	+	0.340942i
$301$	−3.72806	+	32.8146i	−0.214882	+	1.89140i
$302$	−4.51522	+	19.7825i	−0.259822	+	1.13835i
$303$	1.22142	+	16.2987i	0.0701686	+	0.936335i
$304$	10.3072	+	3.17935i	0.591159	+	0.182348i
$305$	0.0572645	−	0.764142i	0.00327896	−	0.0437546i
$306$	−1.86513	+	4.75226i	−0.106622	+	0.271669i
$307$	−13.8179	+	6.65433i	−0.788627	+	0.379783i	−0.784437	−	0.620208i	$-0.787048\pi$
$307$	−13.8179	+	6.65433i	−0.788627	+	0.379783i	−0.00419020	+	0.999991i	$0.501334\pi$
$308$	8.42998	+	0.323239i	0.480343	+	0.0184183i
$309$	0.0262517	+	0.0126421i	0.00149340	+	0.000719186i
$310$	1.17809	−	1.09311i	0.0669110	−	0.0620843i
$311$	2.93288	−	0.442060i	0.166308	−	0.0250669i	−0.0653603	−	0.997862i	$-0.520820\pi$
$311$	2.93288	−	0.442060i	0.166308	−	0.0250669i	0.231668	+	0.972795i	$0.425582\pi$
$312$	−3.03231	+	5.25212i	−0.171671	+	0.297343i
$313$	13.2355	+	22.9245i	0.748113	+	1.29577i	0.948726	+	0.316099i	$0.102373\pi$
$313$	13.2355	+	22.9245i	0.748113	+	1.29577i	−0.200614	+	0.979670i	$0.564294\pi$
$314$	−6.35604	−	7.97022i	−0.358692	−	0.449785i
$315$	−0.0137535	−	0.376902i	−0.000774920	−	0.0212360i
$316$	−4.58706	+	5.75200i	−0.258043	+	0.323575i
$317$	25.5276	+	3.84767i	1.43377	+	0.216107i	0.819542	−	0.573019i	$-0.194228\pi$
$317$	25.5276	+	3.84767i	1.43377	+	0.216107i	0.614231	+	0.789126i	$0.289466\pi$
$318$	2.14902	−	1.46518i	0.120511	−	0.0821632i
$319$	−14.4063	+	9.82204i	−0.806598	+	0.549929i
$320$	1.39025	+	0.209546i	0.0777171	+	0.0117140i
$321$	12.0390	−	15.0964i	0.671952	−	0.842601i
$322$	−1.87512	−	3.55586i	−0.104496	−	0.198160i
$323$	−13.8859	−	17.4124i	−0.772633	−	0.968851i
$324$	−3.35859	−	5.81725i	−0.186588	−	0.323181i
$325$	−2.48697	+	4.30755i	−0.137952	+	0.238940i
$326$	11.6259	−	1.75232i	0.643897	−	0.0970518i
$327$	16.8717	−	15.6547i	0.933009	−	0.865706i
$328$	−17.6838	−	8.51607i	−0.976425	−	0.470222i
$329$	−4.63423	−	6.29134i	−0.255494	−	0.346853i
$330$	−1.73856	+	0.837247i	−0.0957047	+	0.0460889i
$331$	−0.188239	+	0.479626i	−0.0103466	+	0.0263626i	−0.935954	−	0.352123i	$-0.885460\pi$
$331$	−0.188239	+	0.479626i	−0.0103466	+	0.0263626i	0.925607	+	0.378486i	$0.123555\pi$
$332$	0.688385	−	9.18585i	0.0377800	−	0.504139i
$333$	6.08472	+	1.87689i	0.333441	+	0.102853i
$334$	−0.928526	−	12.3903i	−0.0508067	−	0.677968i
$335$	0.00129827	−	0.00568810i	7.09322e−5	−	0.000310774i
$336$	11.7183	+	4.11257i	0.639283	+	0.224359i
$337$	4.09205	+	17.9285i	0.222908	+	0.976625i	0.955276	+	0.295716i	$0.0955581\pi$
$337$	4.09205	+	17.9285i	0.222908	+	0.976625i	−0.732368	+	0.680909i	$0.761585\pi$
$338$	−1.12336	+	0.346510i	−0.0611026	+	0.0188477i
$339$	−14.7213	−	37.5092i	−0.799550	−	2.03722i
$340$	−0.359736	−	0.333786i	−0.0195094	−	0.0181021i
$341$	36.0966	+	24.6102i	1.95474	+	1.33272i
$342$	4.70010			0.254152
$343$	9.80980	+	15.7088i	0.529680	+	0.848198i
$344$	−38.4172			−2.07132
$345$	−0.339737	−	0.231629i	−0.0182908	−	0.0124705i
$346$	14.3369	+	13.3027i	0.770757	+	0.715158i
$347$	−10.9093	−	27.7963i	−0.585640	−	1.49219i	−0.849481	−	0.527620i	$-0.823085\pi$
$347$	−10.9093	−	27.7963i	−0.585640	−	1.49219i	0.263841	−	0.964566i	$-0.415011\pi$
$348$	3.93251	−	1.21302i	0.210805	−	0.0650247i
$349$	4.76779	+	20.8891i	0.255214	+	1.11817i	0.926300	+	0.376786i	$0.122971\pi$
$349$	4.76779	+	20.8891i	0.255214	+	1.11817i	−0.671086	+	0.741379i	$0.734172\pi$
$350$	14.5976	+	5.12308i	0.780273	+	0.273840i
$351$	0.928291	−	4.06711i	0.0495485	−	0.217086i
$352$	1.29360	+	17.2619i	0.0689491	+	0.920062i
$353$	26.8976	+	8.29681i	1.43162	+	0.441595i	0.911074	−	0.412242i	$-0.135254\pi$
$353$	26.8976	+	8.29681i	1.43162	+	0.441595i	0.520541	+	0.853837i	$0.325730\pi$
$354$	0.0823635	−	1.09907i	0.00437757	−	0.0584146i
$355$	−0.488911	+	1.24573i	−0.0259487	+	0.0661162i
$356$	−4.34674	+	2.09328i	−0.230377	+	0.110944i
$357$	−15.2077	−	20.6456i	−0.804876	−	1.09268i
$358$	−8.10236	−	3.90189i	−0.428223	−	0.206221i
$359$	−19.7849	+	18.3577i	−1.04421	+	0.968884i	−0.999546	−	0.0301186i	$-0.990412\pi$
$359$	−19.7849	+	18.3577i	−1.04421	+	0.968884i	−0.0446618	+	0.999002i	$0.514221\pi$
$360$	0.433825	−	0.0653886i	0.0228646	−	0.00344628i
$361$	−0.752087	+	1.30265i	−0.0395835	+	0.0685606i
$362$	11.5489	+	20.0034i	0.606999	+	1.05135i
$363$	−19.1914	−	24.0652i	−1.00729	−	1.26310i
$364$	−0.762680	−	1.44630i	−0.0399753	−	0.0758067i
$365$	0.180852	−	0.226782i	0.00946625	−	0.0118703i
$366$	10.8720	+	1.63869i	0.568288	+	0.0856557i
$367$	26.2285	−	17.8823i	1.36912	−	0.933449i	0.369126	−	0.929379i	$-0.379657\pi$
$367$	26.2285	−	17.8823i	1.36912	−	0.933449i	0.999992	−	0.00406983i	$-0.00129547\pi$
$368$	2.54379	−	1.73433i	0.132604	−	0.0904081i
$369$	−5.56796	−	0.839235i	−0.289856	−	0.0436888i
$370$	0.853426	−	1.07016i	0.0443675	−	0.0556351i
$371$	0.108329	+	2.96866i	0.00562416	+	0.154125i
$372$	−6.42909	−	8.06183i	−0.333333	−	0.417986i
$373$	−14.6602	−	25.3922i	−0.759075	−	1.31476i	−0.943323	−	0.331877i	$-0.892318\pi$
$373$	−14.6602	−	25.3922i	−0.759075	−	1.31476i	0.184247	−	0.982880i	$-0.441015\pi$
$374$	−14.9161	+	25.8355i	−0.771296	+	1.33592i
$375$	3.13766	−	0.472926i	0.162028	−	0.0244218i
$376$	6.66312	−	6.18247i	0.343624	−	0.318836i
$377$	3.04472	+	1.46626i	0.156811	+	0.0755163i
$378$	−12.9657	−	0.497159i	−0.666886	−	0.0255711i
$379$	11.4177	−	5.49845i	0.586486	−	0.282437i	−0.117016	−	0.993130i	$-0.537333\pi$
$379$	11.4177	−	5.49845i	0.586486	−	0.282437i	0.703502	+	0.710693i	$0.251619\pi$
$380$	−0.165061	+	0.420569i	−0.00846746	+	0.0215747i
$381$	0.741263	−	9.89147i	0.0379761	−	0.506755i
$382$	8.04832	+	2.48258i	0.411788	+	0.127020i
$383$	−0.428952	−	5.72396i	−0.0219184	−	0.292481i	−0.997382	−	0.0723182i	$-0.976960\pi$
$383$	−0.428952	−	5.72396i	−0.0219184	−	0.292481i	0.975463	−	0.220163i	$-0.0706588\pi$
$384$	−1.54664	+	6.77628i	−0.0789267	+	0.345801i
$385$	0.248787	−	2.18983i	0.0126793	−	0.111604i
$386$	3.60913	+	15.8126i	0.183700	+	0.804843i
$387$	−10.5317	+	3.24859i	−0.535356	+	0.165135i
$388$	−1.22243	−	3.11470i	−0.0620594	−	0.158125i
$389$	−6.50384	−	6.03468i	−0.329758	−	0.305970i	0.497866	−	0.867254i	$-0.334117\pi$
$389$	−6.50384	−	6.03468i	−0.329758	−	0.305970i	−0.827624	+	0.561284i	$0.810308\pi$
$390$	0.309013	+	0.210682i	0.0156475	+	0.0106683i
$391$	−6.35688			−0.321481
$392$	−16.8684	+	13.4011i	−0.851984	+	0.676859i
$393$	−17.6828			−0.891981
$394$	1.98243	+	1.35160i	0.0998734	+	0.0680925i
$395$	1.40893	+	1.30730i	0.0708910	+	0.0657772i
$396$	1.02855	+	2.62071i	0.0516867	+	0.131696i
$397$	8.98220	−	2.77064i	0.450804	−	0.139055i	−0.0610358	−	0.998136i	$-0.519440\pi$
$397$	8.98220	−	2.77064i	0.450804	−	0.139055i	0.511840	+	0.859081i	$0.328964\pi$
$398$	0.184824	+	0.809767i	0.00926439	+	0.0405900i
$399$	−12.5785	+	19.9774i	−0.629710	+	1.00012i
$400$	−2.63649	+	11.5512i	−0.131825	+	0.577562i
$401$	−0.0784244	−	1.04650i	−0.00391633	−	0.0522598i	0.994903	−	0.100834i	$-0.0321512\pi$
$401$	−0.0784244	−	1.04650i	−0.00391633	−	0.0522598i	−0.998820	+	0.0485745i	$0.984532\pi$
$402$	0.0799937	+	0.0246748i	0.00398972	+	0.00123067i
$403$	0.632772	−	8.44376i	0.0315206	−	0.420614i
$404$	1.87273	−	4.77163i	0.0931717	−	0.237398i
$405$	−1.58105	+	0.761395i	−0.0785631	+	0.0378340i
$406$	2.72982	−	10.1503i	0.135479	−	0.503749i
$407$	33.5246	+	16.1446i	1.66175	+	0.800258i
$408$	21.8657	−	20.2884i	1.08251	−	1.00442i
$409$	12.8145	−	1.93148i	0.633636	−	0.0955053i	0.175633	−	0.984456i	$-0.443803\pi$
$409$	12.8145	−	1.93148i	0.633636	−	0.0955053i	0.458003	+	0.888950i	$0.348565\pi$
$410$	−0.605207	+	1.04825i	−0.0298890	+	0.0517693i
$411$	7.10590	+	12.3078i	0.350508	+	0.607098i
$412$	−0.00569750	−	0.00714443i	−0.000280695	−	0.000351981i
$413$	1.01213	+	0.748433i	0.0498036	+	0.0368280i
$414$	0.836441	−	1.04886i	0.0411088	−	0.0515488i
$415$	−2.37962	−	0.358669i	−0.116811	−	0.0176064i
$416$	2.77205	−	1.88995i	0.135911	−	0.0926626i
$417$	25.4545	−	17.3546i	1.24651	−	0.849857i
$418$	27.1585	+	4.09349i	1.32837	+	0.200219i
$419$	1.61597	−	2.02636i	0.0789453	−	0.0989943i	−0.740790	−	0.671736i	$-0.765549\pi$
$419$	1.61597	−	2.02636i	0.0789453	−	0.0989943i	0.819736	+	0.572742i	$0.194120\pi$
$420$	−0.208457	+	0.476586i	−0.0101717	+	0.0232550i
$421$	−8.02926	−	10.0684i	−0.391322	−	0.490703i	0.546675	−	0.837345i	$-0.315893\pi$
$421$	−8.02926	−	10.0684i	−0.391322	−	0.490703i	−0.937997	+	0.346642i	$0.887322\pi$
$422$	−15.8026	−	27.3709i	−0.769259	−	1.33239i
$423$	1.30383	−	2.25830i	0.0633943	−	0.109802i
$424$	−3.41701	+	0.515032i	−0.165945	+	0.0250122i
$425$	17.9332	−	16.6396i	0.869890	−	0.807140i
$426$	−17.2997	−	8.33110i	−0.838173	−	0.403643i
$427$	−8.19987	+	9.51061i	−0.396820	+	0.460251i
$428$	−5.45605	+	2.62750i	−0.263728	+	0.127005i
$429$	−3.71439	+	9.46411i	−0.179332	+	0.456932i
$430$	−0.177047	+	2.36253i	−0.00853798	+	0.113931i
$431$	23.3867	+	7.21384i	1.12650	+	0.347479i	0.801357	−	0.598187i	$-0.204112\pi$
$431$	23.3867	+	7.21384i	1.12650	+	0.347479i	0.325141	+	0.945665i	$0.394588\pi$
$432$	−0.742617	−	9.90954i	−0.0357292	−	0.476773i
$433$	−5.35867	+	23.4779i	−0.257521	+	1.12827i	0.666371	+	0.745620i	$0.267847\pi$
$433$	−5.35867	+	23.4779i	−0.257521	+	1.12827i	−0.923892	+	0.382653i	$0.875010\pi$
$434$	−26.1734	+	2.92452i	−1.25637	+	0.140381i
$435$	−0.239236	−	1.04816i	−0.0114705	−	0.0502555i
$436$	−6.89758	+	2.12762i	−0.330334	+	0.101895i
$437$	2.13816	+	5.44793i	0.102282	+	0.260610i
$438$	3.05089	+	2.83082i	0.145777	+	0.135262i
$439$	−19.8332	−	13.5220i	−0.946587	−	0.645372i	−0.0115542	−	0.999933i	$-0.503678\pi$
$439$	−19.8332	−	13.5220i	−0.946587	−	0.645372i	−0.935033	+	0.354561i	$0.884630\pi$
$440$	2.56371			0.122220
$441$	−3.49109	+	5.10019i	−0.166243	+	0.242866i
$442$	5.78200			0.275022
$443$	−10.0265	−	6.83594i	−0.476373	−	0.324785i	0.301219	−	0.953555i	$-0.402606\pi$
$443$	−10.0265	−	6.83594i	−0.476373	−	0.324785i	−0.777592	+	0.628770i	$0.783559\pi$
$444$	−6.43796	−	5.97356i	−0.305532	−	0.283492i
$445$	0.460471	+	1.17326i	0.0218284	+	0.0556179i
$446$	4.04942	−	1.24908i	0.191745	−	0.0591456i
$447$	−6.11037	−	26.7713i	−0.289011	−	1.26624i
$448$	−16.2766	−	16.3068i	−0.768998	−	0.770422i
$449$	−6.07214	+	26.6038i	−0.286562	+	1.25551i	0.602646	+	0.798009i	$0.294113\pi$
$449$	−6.07214	+	26.6038i	−0.286562	+	1.25551i	−0.889208	+	0.457502i	$0.848744\pi$
$450$	0.385817	+	5.14837i	0.0181876	+	0.242696i
$451$	−31.4423	−	9.69868i	−1.48056	−	0.456693i
$452$	−0.944388	+	12.6020i	−0.0444203	+	0.592747i
$453$	12.4260	−	31.6610i	0.583826	−	1.48757i
$454$	14.4172	−	6.94297i	0.676634	−	0.325850i
$455$	−0.391673	+	0.170454i	−0.0183619	+	0.00799100i
$456$	−24.7420	−	11.9151i	−1.15865	−	0.557977i
$457$	−3.27133	+	3.03535i	−0.153026	+	0.141988i	−0.752971	−	0.658054i	$-0.771380\pi$
$457$	−3.27133	+	3.03535i	−0.153026	+	0.141988i	0.599944	+	0.800042i	$0.295189\pi$
$458$	3.37103	−	0.508101i	0.157518	−	0.0237420i
$459$	−10.2591	+	17.7692i	−0.478852	+	0.829395i
$460$	0.0644785	+	0.111680i	0.00300633	+	0.00520711i
$461$	10.0558	+	12.6095i	0.468344	+	0.587285i	0.958765	−	0.284201i	$-0.0917283\pi$
$461$	10.0558	+	12.6095i	0.468344	+	0.587285i	−0.490421	+	0.871486i	$0.663157\pi$
$462$	31.0655	+	5.90768i	1.44530	+	0.274850i
$463$	15.9362	−	19.9834i	0.740618	−	0.928706i	−0.258688	−	0.965961i	$-0.583290\pi$
$463$	15.9362	−	19.9834i	0.740618	−	0.928706i	0.999306	+	0.0372552i	$0.0118614\pi$
$464$	7.96006	+	1.19979i	0.369536	+	0.0556986i
$465$	−2.22574	+	1.51749i	−0.103216	+	0.0703718i
$466$	−18.0005	+	12.2726i	−0.833859	+	0.568515i
$467$	−20.6591	−	3.11387i	−0.955991	−	0.144093i	−0.347524	−	0.937671i	$-0.612977\pi$
$467$	−20.6591	−	3.11387i	−0.955991	−	0.144093i	−0.608468	+	0.793579i	$0.708215\pi$
$468$	0.340211	−	0.426612i	0.0157263	−	0.0197201i
$469$	−0.0725279	+	0.0622986i	−0.00334903	+	0.00287668i
$470$	−0.349494	−	0.438252i	−0.0161210	−	0.0202150i
$471$	8.54385	+	14.7984i	0.393680	+	0.681873i
$472$	−0.732148	+	1.26812i	−0.0336998	+	0.0583698i
$473$	−63.6844	+	9.59888i	−2.92821	+	0.441357i
$474$	−20.2156	+	18.7573i	−0.928533	+	0.861553i
$475$	−20.2923	−	9.77225i	−0.931074	−	0.448382i
$476$	1.48778	+	7.90312i	0.0681922	+	0.362239i
$477$	−0.893187	+	0.430136i	−0.0408962	+	0.0196946i
$478$	1.21117	−	3.08601i	0.0553976	−	0.141151i
$479$	0.540987	−	7.21897i	0.0247183	−	0.329843i	−0.971112	−	0.238623i	$-0.923304\pi$
$479$	0.540987	−	7.21897i	0.0247183	−	0.329843i	0.995831	−	0.0912206i	$-0.0290768\pi$
$480$	−1.01995	−	0.314612i	−0.0465540	−	0.0143600i
$481$	−0.538941	−	7.19166i	−0.0245736	−	0.327912i
$482$	−6.06269	+	26.5624i	−0.276148	+	1.20988i
$483$	2.21963	+	6.36221i	0.100997	+	0.289491i
$484$	2.14810	+	9.41146i	0.0976411	+	0.427794i
$485$	−0.835292	+	0.257653i	−0.0379286	+	0.0116994i
$486$	−3.82371	−	9.74266i	−0.173447	−	0.441936i
$487$	14.9633	+	13.8839i	0.678051	+	0.629139i	0.942085	−	0.335374i	$-0.108863\pi$
$487$	14.9633	+	13.8839i	0.678051	+	0.629139i	−0.264034	+	0.964513i	$0.585053\pi$
$488$	−12.0693	−	8.22870i	−0.546351	−	0.372496i
$489$	−19.7074			−0.891199
$490$	0.746386	+	1.09911i	0.0337183	+	0.0496528i
$491$	−25.1682			−1.13582			−0.567912	−	0.823089i	$-0.692249\pi$
$491$	−25.1682			−1.13582			−0.567912	+	0.823089i	$0.692249\pi$
$492$	6.41677	+	4.37488i	0.289290	+	0.197235i
$493$	−12.1842	−	11.3053i	−0.548748	−	0.509164i
$494$	−1.94479	−	4.95526i	−0.0875004	−	0.222947i
$495$	0.702815	−	0.216790i	0.0315892	−	0.00974398i
$496$	−4.48827	−	19.6644i	−0.201529	−	0.882957i
$497$	18.5796	−	11.6504i	0.833411	−	0.522592i
$498$	7.68339	−	33.6631i	0.344301	−	1.50848i
$499$	1.41449	+	18.8750i	0.0633212	+	0.844963i	0.934946	+	0.354789i	$0.115447\pi$
$499$	1.41449	+	18.8750i	0.0633212	+	0.844963i	−0.871625	+	0.490173i	$0.836934\pi$
$500$	−0.950945	−	0.293328i	−0.0425276	−	0.0131180i
$501$	−1.55640	+	20.7687i	−0.0695347	+	0.927876i
$502$	−11.3996	+	29.0456i	−0.508787	+	1.29637i
$503$	−32.1335	+	15.4747i	−1.43276	+	0.689982i	−0.979509	−	0.201400i	$-0.935451\pi$
$503$	−32.1335	+	15.4747i	−1.43276	+	0.689982i	−0.453253	+	0.891382i	$0.649737\pi$
$504$	−6.35332	−	3.36535i	−0.282999	−	0.149905i
$505$	−1.20652	−	0.581031i	−0.0536895	−	0.0258555i
$506$	5.74668	−	5.33214i	0.255471	−	0.237043i
$507$	1.94851	−	0.293690i	0.0865363	−	0.0130433i
$508$	−1.55544	+	2.69411i	−0.0690117	+	0.119532i
$509$	−0.0665249	−	0.115224i	−0.00294866	−	0.00510723i	0.864547	−	0.502551i	$-0.167605\pi$
$509$	−0.0665249	−	0.115224i	−0.00294866	−	0.00510723i	−0.867496	+	0.497444i	$0.834272\pi$
$510$	−1.14690	−	1.43817i	−0.0507855	−	0.0636830i
$511$	−4.59260	+	1.22603i	−0.203164	+	0.0542363i
$512$	14.1248	−	17.7120i	0.624236	−	0.782767i
$513$	18.6791	+	2.81542i	0.824703	+	0.124304i
$514$	−14.7426	+	10.0513i	−0.650267	+	0.443345i
$515$	−0.00197247	+	0.00134480i	−8.69172e−5	+	5.92592e-5i
$516$	15.0312	+	2.26558i	0.661710	+	0.0997368i
$517$	9.50073	−	11.9135i	0.417842	−	0.523957i
$518$	−21.6720	+	5.78552i	−0.952215	+	0.254201i
$519$	−20.4398	−	25.6307i	−0.897207	−	1.12506i
$520$	−0.248445	−	0.430320i	−0.0108951	−	0.0188708i
$521$	12.1963	−	21.1246i	0.534329	−	0.925485i	−0.464866	−	0.885381i	$-0.653898\pi$
$521$	12.1963	−	21.1246i	0.534329	−	0.925485i	0.999195	−	0.0401044i	$-0.0127690\pi$
$522$	3.46853	−	0.522797i	0.151814	−	0.0228822i
$523$	−18.4119	+	17.0837i	−0.805095	+	0.747019i	−0.970989	−	0.239125i	$-0.923139\pi$
$523$	−18.4119	+	17.0837i	−0.805095	+	0.747019i	0.165894	+	0.986144i	$0.446949\pi$
$524$	4.99654	+	2.40621i	0.218275	+	0.105116i
$525$	−22.9153	−	12.1382i	−1.00011	−	0.529756i
$526$	17.4282	−	8.39298i	0.759906	−	0.365951i
$527$	−15.2151	+	38.7674i	−0.662779	+	1.68873i
$528$	−1.80984	+	24.1507i	−0.0787632	+	1.05102i
$529$	−20.3819	−	6.28699i	−0.886170	−	0.273347i
$530$	0.0159253	+	0.212509i	0.000691751	+	0.00923078i
$531$	−0.0934776	+	0.409552i	−0.00405658	+	0.0177730i
$532$	6.27267	−	3.93329i	0.271955	−	0.170530i
$533$	1.41910	+	6.21749i	0.0614681	+	0.269309i
$534$	−17.2808	+	5.33043i	−0.747815	+	0.230670i
$535$	0.577985	+	1.47268i	0.0249885	+	0.0636696i
$536$	−0.0815297	−	0.0756485i	−0.00352155	−	0.00326752i
$537$	12.4547	+	8.49147i	0.537460	+	0.366434i
$538$	13.2039			0.569262
$539$	−24.6145	+	26.4298i	−1.06022	+	1.13841i
$540$	0.416235			0.0179119
$541$	−1.63855	−	1.11715i	−0.0704468	−	0.0480298i	0.527585	−	0.849503i	$-0.323098\pi$
$541$	−1.63855	−	1.11715i	−0.0704468	−	0.0480298i	−0.598031	+	0.801473i	$0.704050\pi$
$542$	−23.7500	−	22.0367i	−1.02015	−	0.946559i
$543$	−14.1448	−	36.0404i	−0.607012	−	1.54664i
$544$	−15.7683	+	4.86386i	−0.676058	+	0.208536i
$545$	0.419617	+	1.83846i	0.0179744	+	0.0787510i
$546$	−2.01890	−	5.78685i	−0.0864009	−	0.247654i
$547$	0.698358	−	3.05971i	0.0298596	−	0.130824i	−0.957801	−	0.287431i	$-0.907199\pi$
$547$	0.698358	−	3.05971i	0.0298596	−	0.130824i	0.987661	+	0.156608i	$0.0500558\pi$
$548$	−0.333083	−	4.44468i	−0.0142286	−	0.189867i
$549$	−4.00450	−	1.23522i	−0.170908	−	0.0527181i
$550$	−2.25454	+	30.0848i	−0.0961340	+	1.28282i
$551$	−5.59059	+	14.2446i	−0.238167	+	0.606840i
$552$	−7.06210	+	3.40093i	−0.300583	+	0.144753i
$553$	−5.82698	−	30.9531i	−0.247789	−	1.31626i
$554$	−33.3104	−	16.0414i	−1.41522	−	0.681535i
$555$	−1.68189	+	1.56057i	−0.0713923	+	0.0662423i
$556$	−9.55407	+	1.44004i	−0.405183	+	0.0610715i
$557$	8.07873	−	13.9928i	0.342307	−	0.592893i	−0.642554	−	0.766240i	$-0.722125\pi$
$557$	8.07873	−	13.9928i	0.342307	−	0.592893i	0.984861	+	0.173348i	$0.0554585\pi$
$558$	−4.39448	−	7.61147i	−0.186033	−	0.322219i
$559$	7.78273	+	9.75923i	0.329174	+	0.412771i
$560$	−0.771864	+	0.663001i	−0.0326172	+	0.0280169i
$561$	31.1776	−	39.0954i	1.31632	−	1.65061i
$562$	15.9992	+	2.41150i	0.674887	+	0.101723i
$563$	12.8099	−	8.73365i	0.539873	−	0.368079i	−0.262472	−	0.964940i	$-0.584538\pi$
$563$	12.8099	−	8.73365i	0.539873	−	0.368079i	0.802345	+	0.596860i	$0.203585\pi$
$564$	−2.97162	+	2.02601i	−0.125128	+	0.0853106i
$565$	3.26457	+	0.492055i	0.137341	+	0.0207009i
$566$	2.64172	−	3.31262i	0.111040	−	0.139240i
$567$	28.2510	+	5.37246i	1.18643	+	0.225622i
$568$	15.9055	+	19.9449i	0.667380	+	0.836868i
$569$	−2.72169	−	4.71411i	−0.114099	−	0.197626i	0.803320	−	0.595548i	$-0.203065\pi$
$569$	−2.72169	−	4.71411i	−0.114099	−	0.197626i	−0.917419	+	0.397922i	$0.869732\pi$
$570$	−0.846765	+	1.46664i	−0.0354671	+	0.0614308i
$571$	−3.32169	+	0.500664i	−0.139008	+	0.0209521i	−0.218178	−	0.975909i	$-0.570011\pi$
$571$	−3.32169	+	0.500664i	−0.139008	+	0.0209521i	0.0791695	+	0.996861i	$0.474773\pi$
$572$	2.33739	−	2.16878i	0.0977312	−	0.0906813i
$573$	−12.7197	−	6.12550i	−0.531374	−	0.255896i
$574$	18.1879	−	7.91528i	0.759148	−	0.330377i
$575$	−5.79202	+	2.78929i	−0.241544	+	0.116321i
$576$	2.80907	−	7.15739i	0.117045	−	0.298225i
$577$	−1.19657	+	15.9671i	−0.0498139	+	0.664720i	0.915280	+	0.402817i	$0.131969\pi$
$577$	−1.19657	+	15.9671i	−0.0498139	+	0.664720i	−0.965094	+	0.261903i	$0.915650\pi$
$578$	−8.07769	−	2.49164i	−0.335988	−	0.103638i
$579$	−2.03167	−	27.1108i	−0.0844335	−	1.12669i
$580$	−0.0750299	+	0.328727i	−0.00311545	+	0.0136497i
$581$	27.8599	+	27.9115i	1.15582	+	1.15796i
$582$	−2.79089	−	12.2277i	−0.115686	−	0.506854i
$583$	−5.53571	+	1.70754i	−0.229266	+	0.0707191i
$584$	−2.02013	−	5.14722i	−0.0835937	−	0.212993i
$585$	−0.104497	−	0.0969590i	−0.00432042	−	0.00400876i
$586$	−26.9447	−	18.3706i	−1.11308	−	0.758883i
$587$	39.0142			1.61029			0.805143	−	0.593080i	$-0.202088\pi$
$587$	39.0142			1.61029			0.805143	+	0.593080i	$0.202088\pi$
$588$	7.39027	−	4.24856i	0.304769	−	0.175208i
$589$	38.3419			1.57985
$590$	0.0746108	+	0.0508688i	0.00307168	+	0.00209424i
$591$	−2.94817	−	2.73551i	−0.121272	−	0.112524i
$592$	−6.27624	−	15.9916i	−0.257952	−	0.657251i
$593$	35.7549	−	11.0289i	1.46828	−	0.452904i	0.545459	−	0.838137i	$-0.316355\pi$
$593$	35.7549	−	11.0289i	1.46828	−	0.452904i	0.922819	+	0.385233i	$0.125879\pi$
$594$	−5.63050	−	24.6688i	−0.231022	−	1.01217i
$595$	2.08793	−	0.233297i	0.0855968	−	0.00956424i
$596$	−1.91635	+	8.39608i	−0.0784968	+	0.343917i
$597$	−0.104042	−	1.38835i	−0.00425816	−	0.0568212i
$598$	−1.45190	−	0.447853i	−0.0593728	−	0.0183141i
$599$	0.826927	−	11.0346i	0.0337873	−	0.450860i	−0.954495	−	0.298226i	$-0.903605\pi$
$599$	0.826927	−	11.0346i	0.0337873	−	0.450860i	0.988283	−	0.152635i	$-0.0487758\pi$
$600$	11.0205	−	28.0799i	0.449911	−	1.14636i
$601$	13.4343	−	6.46960i	0.547995	−	0.263901i	−0.139336	−	0.990245i	$-0.544497\pi$
$601$	13.4343	−	6.46960i	0.547995	−	0.263901i	0.687331	+	0.726345i	$0.258782\pi$
$602$	25.3519	−	29.4044i	1.03327	−	1.19843i
$603$	−0.0287474	−	0.0138440i	−0.00117069	−	0.000563772i
$604$	−7.81946	+	7.25540i	−0.318169	+	0.295218i
$605$	2.49377	−	0.375875i	0.101386	−	0.0152815i
$606$	9.60711	−	16.6400i	0.390262	−	0.675954i
$607$	−4.23189	−	7.32986i	−0.171767	−	0.297510i	0.767271	−	0.641324i	$-0.221614\pi$
$607$	−4.23189	−	7.32986i	−0.171767	−	0.297510i	−0.939038	+	0.343814i	$0.888281\pi$
$608$	9.47210	+	11.8776i	0.384145	+	0.481702i
$609$	−7.06041	+	16.1419i	−0.286102	+	0.654102i
$610$	−0.561660	+	0.704299i	−0.0227409	+	0.0285162i
$611$	−2.92039	−	0.440178i	−0.118146	−	0.0178077i
$612$	−2.21743	+	1.51182i	−0.0896341	+	0.0611115i
$613$	18.3275	−	12.4955i	0.740241	−	0.504688i	−0.133518	−	0.991046i	$-0.542627\pi$
$613$	18.3275	−	12.4955i	0.740241	−	0.504688i	0.873759	+	0.486358i	$0.161675\pi$
$614$	17.8282	+	2.68717i	0.719487	+	0.108445i
$615$	1.26500	−	1.58626i	0.0510096	−	0.0639640i
$616$	−33.7803	−	24.9793i	−1.36105	−	1.00644i
$617$	−23.5667	−	29.5517i	−0.948758	−	1.18971i	−0.981736	−	0.190249i	$-0.939070\pi$
$617$	−23.5667	−	29.5517i	−0.948758	−	1.18971i	0.0329775	−	0.999456i	$-0.489501\pi$
$618$	−0.0171266	−	0.0296641i	−0.000688933	−	0.00119327i
$619$	−17.1641	+	29.7291i	−0.689884	+	1.19491i	0.281992	+	0.959417i	$0.409005\pi$
$619$	−17.1641	+	29.7291i	−0.689884	+	1.19491i	−0.971875	+	0.235497i	$0.924328\pi$
$620$	0.835409	−	0.125918i	0.0335508	−	0.00505698i
$621$	3.95247	−	3.66735i	0.158607	−	0.147166i
$622$	−3.14149	−	1.51286i	−0.125962	−	0.0606602i
$623$	5.36424	−	19.9458i	0.214914	−	0.799111i
$624$	4.22908	−	2.03662i	0.169299	−	0.0815300i
$625$	8.99093	−	22.9085i	0.359637	−	0.916341i
$626$	2.32551	−	31.0318i	0.0929462	−	1.24028i
$627$	−43.9920	−	13.5697i	−1.75687	−	0.541923i
$628$	−0.400485	−	5.34410i	−0.0159811	−	0.213253i
$629$	−7.89296	+	34.5813i	−0.314713	+	1.37885i
$630$	−0.236237	+	0.375199i	−0.00941193	+	0.0149483i
$631$	3.03983	+	13.3184i	0.121014	+	0.530196i	0.998701	+	0.0509614i	$0.0162285\pi$
$631$	3.03983	+	13.3184i	0.121014	+	0.530196i	−0.877687	+	0.479235i	$0.840914\pi$
$632$	35.0110	−	10.7995i	1.39266	−	0.429580i
$633$	19.3546	+	49.3146i	0.769275	+	1.96008i
$634$	−22.2473	−	20.6425i	−0.883552	−	0.819817i
$635$	0.671490	+	0.457814i	0.0266473	+	0.0181678i
$636$	1.36732			0.0542177
$637$	6.82160	+	1.57027i	0.270282	+	0.0622165i
$638$	20.4975			0.811504
$639$	6.04688	+	4.12269i	0.239211	+	0.163091i
$640$	−0.417456	−	0.387342i	−0.0165014	−	0.0153110i
$641$	8.04691	+	20.5032i	0.317834	+	0.809827i	0.997112	+	0.0759462i	$0.0241977\pi$
$641$	8.04691	+	20.5032i	0.317834	+	0.809827i	−0.679278	+	0.733881i	$0.737707\pi$
$642$	−21.6910	+	6.69078i	−0.856075	+	0.264064i
$643$	6.89370	+	30.2033i	0.271861	+	1.19110i	0.907814	+	0.419373i	$0.137750\pi$
$643$	6.89370	+	30.2033i	0.271861	+	1.19110i	−0.635953	+	0.771728i	$0.719393\pi$
$644$	0.238555	−	2.09977i	0.00940040	−	0.0827426i
$645$	0.883672	−	3.87162i	0.0347945	−	0.152445i
$646$	1.95657	+	26.1086i	0.0769801	+	1.02723i
$647$	18.6328	+	5.74744i	0.732529	+	0.225955i	0.638508	−	0.769615i	$-0.279552\pi$
$647$	18.6328	+	5.74744i	0.732529	+	0.225955i	0.0940209	+	0.995570i	$0.470028\pi$
$648$	−2.49987	+	33.3585i	−0.0982044	+	1.31045i
$649$	−0.896834	+	2.28510i	−0.0352038	+	0.0896978i
$650$	5.26822	−	2.53704i	0.206637	−	0.0995109i
$651$	44.1126	+	1.69145i	1.72891	+	0.0662932i
$652$	5.56861	+	2.68170i	0.218084	+	0.105023i
$653$	28.7045	−	26.6338i	1.12329	−	1.04226i	0.124546	−	0.992214i	$-0.460253\pi$
$653$	28.7045	−	26.6338i	1.12329	−	1.04226i	0.998747	−	0.0500492i	$-0.0159378\pi$
$654$	−26.7548	+	4.03263i	−1.04619	+	0.157688i
$655$	0.724401	−	1.25470i	0.0283047	−	0.0490251i
$656$	7.59571	+	13.1562i	0.296563	+	0.513662i
$657$	−0.989051	−	1.24023i	−0.0385866	−	0.0483860i
$658$	0.334978	+	9.17980i	0.0130588	+	0.357866i
$659$	12.1312	−	15.2121i	0.472566	−	0.592578i	−0.487232	−	0.873273i	$-0.661993\pi$
$659$	12.1312	−	15.2121i	0.472566	−	0.592578i	0.959797	+	0.280694i	$0.0905647\pi$
$660$	−1.00308	−	0.151190i	−0.0390449	−	0.00588507i
$661$	19.9096	−	13.5741i	0.774393	−	0.527972i	−0.110439	−	0.993883i	$-0.535226\pi$
$661$	19.9096	−	13.5741i	0.774393	−	0.527972i	0.884832	+	0.465911i	$0.154273\pi$
$662$	0.500463	−	0.341210i	0.0194510	−	0.0132615i
$663$	−9.58355	−	1.44449i	−0.372194	−	0.0560992i
$664$	−28.6023	+	35.8661i	−1.10998	+	1.39188i
$665$	−0.902221	−	1.71092i	−0.0349866	−	0.0663465i
$666$	−4.66724	−	5.85254i	−0.180852	−	0.226781i
$667$	2.18388	+	3.78259i	0.0845600	+	0.146462i
$668$	3.26590	−	5.65670i	0.126361	−	0.218864i
$669$	−7.02388	+	1.05868i	−0.271559	+	0.0409309i
$670$	−0.00502786	+	0.00466518i	−0.000194243	+	0.000180231i
$671$	−22.0633	−	10.6251i	−0.851745	−	0.410179i
$672$	10.3737	+	14.0832i	0.400176	+	0.543270i
$673$	13.1868	−	6.35043i	0.508314	−	0.244791i	−0.162106	−	0.986773i	$-0.551829\pi$
$673$	13.1868	−	6.35043i	0.508314	−	0.244791i	0.670419	+	0.741982i	$0.266114\pi$
$674$	7.89810	−	20.1240i	0.304224	−	0.775149i
$675$	−1.55063	+	20.6918i	−0.0596839	+	0.796426i
$676$	−0.590543	−	0.182158i	−0.0227132	−	0.00700610i
$677$	1.61483	+	21.5484i	0.0620631	+	0.828174i	0.938196	+	0.346105i	$0.112496\pi$
$677$	1.61483	+	21.5484i	0.0620631	+	0.828174i	−0.876133	+	0.482070i	$0.839885\pi$
$678$	−10.5408	+	46.1821i	−0.404816	+	1.77361i
$679$	13.5165	+	4.74366i	0.518715	+	0.182045i
$680$	0.543821	+	2.38263i	0.0208546	+	0.0913698i
$681$	−25.6308	+	7.90605i	−0.982174	+	0.302961i
$682$	−18.7635	−	47.8085i	−0.718490	−	1.83068i
$683$	−1.74966	−	1.62345i	−0.0669489	−	0.0621195i	0.645989	−	0.763347i	$-0.276445\pi$
$683$	−1.74966	−	1.62345i	−0.0669489	−	0.0621195i	−0.712938	+	0.701227i	$0.752636\pi$
$684$	2.04149	+	1.39186i	0.0780582	+	0.0532191i
$685$	−1.16441			−0.0444898
$686$	0.874479	−	21.7546i	0.0333878	−	0.830594i
$687$	−5.71435			−0.218016
$688$	24.5677	+	16.7500i	0.936634	+	0.638586i
$689$	0.823068	+	0.763696i	0.0313564	+	0.0290945i
$690$	0.176600	+	0.449969i	0.00672304	+	0.0171300i
$691$	−20.4673	+	6.31333i	−0.778613	+	0.240170i	−0.658491	−	0.752589i	$-0.728805\pi$
$691$	−20.4673	+	6.31333i	−0.778613	+	0.240170i	−0.120122	+	0.992759i	$0.538329\pi$
$692$	2.28784	+	10.0237i	0.0869706	+	0.381043i
$693$	−11.3728	−	3.99132i	−0.432016	−	0.151618i
$694$	−7.81127	+	34.2234i	−0.296512	+	1.29910i
$695$	0.188630	+	2.51709i	0.00715515	+	0.0954788i
$696$	−19.5842	−	6.04093i	−0.742337	−	0.228981i
$697$	2.34402	−	31.2788i	0.0887862	−	1.18477i
$698$	9.20236	−	23.4472i	0.348314	−	0.887490i
$699$	32.9015	−	15.8445i	1.24445	−	0.599295i
$700$	4.82333	+	6.54805i	0.182305	+	0.247493i
$701$	11.1173	+	5.35383i	0.419896	+	0.202211i	0.631887	−	0.775060i	$-0.282280\pi$
$701$	11.1173	+	5.35383i	0.419896	+	0.202211i	−0.211991	+	0.977272i	$0.567995\pi$
$702$	−3.59503	+	3.33570i	−0.135686	+	0.125898i
$703$	32.2915	−	4.86716i	1.21790	−	0.183569i
$704$	22.4652	−	38.9109i	0.846690	−	1.46651i
$705$	0.469793	+	0.813706i	0.0176934	+	0.0306459i
$706$	−20.6316	−	25.8712i	−0.776481	−	0.973677i
$707$	10.2363	+	19.4115i	0.384975	+	0.730043i
$708$	0.361246	−	0.452988i	0.0135764	−	0.0170243i
$709$	−32.3616	−	4.87773i	−1.21537	−	0.183187i	−0.490107	−	0.871662i	$-0.663042\pi$
$709$	−32.3616	−	4.87773i	−1.21537	−	0.183187i	−0.725260	+	0.688476i	$0.758280\pi$
$710$	1.29984	−	0.886219i	0.0487823	−	0.0332592i
$711$	8.68470	−	5.92113i	0.325702	−	0.222060i
$712$	23.7581	+	3.58096i	0.890373	+	0.134202i
$713$	6.82341	−	8.55628i	0.255539	−	0.320435i
$714$	1.09926	+	30.1244i	0.0411389	+	1.12738i
$715$	−0.519368	−	0.651267i	−0.0194233	−	0.0243560i
$716$	−2.36377	−	4.09417i	−0.0883383	−	0.153006i
$717$	−2.77845	+	4.81242i	−0.103763	+	0.179723i
$718$	31.3744	−	4.72893i	1.17088	−	0.176482i
$719$	0.954707	−	0.885838i	0.0356045	−	0.0330362i	−0.662170	−	0.749354i	$-0.730364\pi$
$719$	0.954707	−	0.885838i	0.0356045	−	0.0330362i	0.697774	+	0.716318i	$0.254174\pi$
$720$	−0.305939	−	0.147332i	−0.0114017	−	0.00549075i
$721$	0.0390928	+	0.00149897i	0.00145589	+	5.58247e-5i
$722$	1.59317	−	0.767230i	0.0592916	−	0.0285533i
$723$	16.6847	−	42.5120i	0.620512	−	1.58104i
$724$	−0.907406	+	12.1085i	−0.0337235	+	0.450008i
$725$	−16.0621	−	4.95450i	−0.596531	−	0.184005i
$726$	2.70412	+	36.0840i	0.100359	+	1.33920i
$727$	−11.0723	+	48.5111i	−0.410651	+	1.79918i	0.170473	+	0.985362i	$0.445470\pi$
$727$	−11.0723	+	48.5111i	−0.410651	+	1.79918i	−0.581124	+	0.813815i	$0.697387\pi$
$728$	−0.919189	+	8.09073i	−0.0340674	+	0.299862i
$729$	−3.35213	−	14.6867i	−0.124153	−	0.543950i
$730$	−0.325847	+	0.100510i	−0.0120601	+	0.00372005i
$731$	−22.4298	−	57.1501i	−0.829595	−	2.11377i
$732$	4.23697	+	3.93134i	0.156603	+	0.145306i
$733$	32.4708	+	22.1382i	1.19934	+	0.817693i	0.987191	−	0.159545i	$-0.0510026\pi$
$733$	32.4708	+	22.1382i	1.19934	+	0.817693i	0.212145	+	0.977238i	$0.431955\pi$
$734$	−37.3184			−1.37745
$735$	−0.962534	−	2.00822i	−0.0355036	−	0.0740744i
$736$	4.33627			0.159837
$737$	−0.154054	−	0.105032i	−0.00567463	−	0.00386890i
$738$	4.85247	+	4.50243i	0.178622	+	0.165737i
$739$	−8.20378	−	20.9029i	−0.301781	−	0.768926i	−0.998661	−	0.0517375i	$-0.983524\pi$
$739$	−8.20378	−	20.9029i	−0.301781	−	0.768926i	0.696880	−	0.717188i	$-0.254571\pi$
$740$	0.687598	−	0.212096i	0.0252766	−	0.00779680i
$741$	1.98551	+	8.69909i	0.0729396	+	0.319569i
$742$	1.86072	−	2.95524i	0.0683092	−	0.108490i
$743$	4.08702	−	17.9064i	0.149938	−	0.656922i	−0.842962	−	0.537973i	$-0.819190\pi$
$743$	4.08702	−	17.9064i	0.149938	−	0.656922i	0.992900	−	0.118949i	$-0.0379525\pi$
$744$	3.83753	+	51.2082i	0.140691	+	1.87739i
$745$	2.14990	+	0.663155i	0.0787661	+	0.0242961i
$746$	−2.57584	+	34.3722i	−0.0943082	+	1.25846i
$747$	−4.80815	+	12.2510i	−0.175921	+	0.448239i
$748$	−14.1296	+	6.80446i	−0.516630	+	0.248796i
$749$	6.73323	−	25.0361i	0.246027	−	0.914797i
$750$	−3.36084	−	1.61850i	−0.122721	−	0.0590991i
$751$	−36.5479	+	33.9115i	−1.33365	+	1.23745i	−0.384309	+	0.923205i	$0.625560\pi$
$751$	−36.5479	+	33.9115i	−1.33365	+	1.23745i	−0.949343	+	0.314243i	$0.898249\pi$
$752$	−6.95660	+	1.04854i	−0.253681	+	0.0382363i
$753$	26.1509	−	45.2946i	0.952990	−	1.65063i
$754$	−1.98638	−	3.44051i	−0.0723397	−	0.125296i
$755$	1.73748	+	2.17873i	0.0632335	+	0.0792923i
$756$	−5.48444	−	4.05555i	−0.199467	−	0.147499i
$757$	−31.0110	+	38.8865i	−1.12711	+	1.41335i	−0.229090	+	0.973405i	$0.573575\pi$
$757$	−31.0110	+	38.8865i	−1.12711	+	1.41335i	−0.898023	+	0.439949i	$0.854997\pi$
$758$	−14.7314	−	2.22040i	−0.535068	−	0.0806485i
$759$	−10.8571	+	7.40226i	−0.394088	+	0.268685i
$760$	1.85904	−	1.26747i	0.0674343	−	0.0459759i
$761$	−15.2445	−	2.29773i	−0.552611	−	0.0832927i	−0.133200	−	0.991089i	$-0.542525\pi$
$761$	−15.2445	−	2.29773i	−0.552611	−	0.0832927i	−0.419411	+	0.907796i	$0.637763\pi$
$762$	−7.27043	+	9.11684i	−0.263380	+	0.330268i
$763$	12.3839	−	28.3126i	0.448326	−	1.02499i
$764$	2.76061	+	3.46169i	0.0998753	+	0.125240i
$765$	0.350560	+	0.607188i	0.0126745	+	0.0219529i
$766$	−3.37394	+	5.84383i	−0.121905	+	0.211146i
$767$	0.470465	−	0.0709111i	0.0169875	−	0.00256045i
$768$	−19.1683	+	17.7856i	−0.691678	+	0.641783i
$769$	−11.2022	−	5.39472i	−0.403963	−	0.194538i	0.220859	−	0.975306i	$-0.429114\pi$
$769$	−11.2022	−	5.39472i	−0.403963	−	0.194538i	−0.624822	+	0.780767i	$0.714828\pi$
$770$	−1.69182	+	1.96226i	−0.0609690	+	0.0707148i
$771$	26.9466	−	12.9768i	0.970458	−	0.467348i
$772$	−3.11505	+	7.93701i	−0.112113	+	0.285659i
$773$	3.09496	−	41.2994i	0.111318	−	1.48544i	−0.609762	−	0.792585i	$-0.708735\pi$
$773$	3.09496	−	41.2994i	0.111318	−	1.48544i	0.721080	−	0.692852i	$-0.243646\pi$
$774$	12.3809	+	3.81900i	0.445022	+	0.137271i
$775$	3.14737	+	41.9987i	0.113057	+	1.50864i
$776$	−3.70793	+	16.2455i	−0.133107	+	0.583180i
$777$	37.3663	−	4.17516i	1.34051	−	0.149783i
$778$	2.32092	+	10.1686i	0.0832090	+	0.364562i
$779$	−27.5948	+	8.51187i	−0.988686	+	0.304969i
$780$	0.0718297	+	0.183019i	0.00257192	+	0.00655314i
$781$	31.3500	+	29.0885i	1.12179	+	1.04087i
$782$	6.17453	+	4.20972i	0.220801	+	0.150539i
$783$	14.0978			0.503814
$784$	16.6302	−	1.21532i	0.593936	−	0.0434042i
$785$	−1.40004			−0.0499695
$786$	17.1756	+	11.7101i	0.612633	+	0.417686i
$787$	−31.4059	−	29.1404i	−1.11950	−	1.03874i	−0.998940	−	0.0460370i	$-0.985341\pi$
$787$	−31.4059	−	29.1404i	−1.11950	−	1.03874i	−0.120559	−	0.992706i	$-0.538469\pi$
$788$	0.460813	+	1.17413i	0.0164158	+	0.0418267i
$789$	−30.9837	+	9.55720i	−1.10305	+	0.340245i
$790$	−0.502782	−	2.20283i	−0.0178882	−	0.0783732i
$791$	−38.2207	−	38.2915i	−1.35897	−	1.36149i
$792$	3.11986	−	13.6690i	0.110859	−	0.485706i
$793$	0.354689	+	4.73300i	0.0125954	+	0.168074i
$794$	−10.5593	−	3.25713i	−0.374737	−	0.115591i
$795$	0.0266940	−	0.356207i	0.000946740	−	0.0126334i
$796$	−0.159522	+	0.406455i	−0.00565410	+	0.0144064i
$797$	−13.9243	+	6.70560i	−0.493225	+	0.237524i	−0.663926	−	0.747798i	$-0.731111\pi$
$797$	−13.9243	+	6.70560i	−0.493225	+	0.237524i	0.170701	+	0.985323i	$0.445397\pi$
$798$	25.4473	−	11.0745i	0.900825	−	0.392034i
$799$	13.0874	+	6.30255i	0.462998	+	0.222968i
$800$	−12.2329	+	11.3505i	−0.432500	+	0.401301i
$801$	6.81585	−	1.02732i	0.240826	−	0.0362987i
$802$	−0.616851	+	1.06842i	−0.0217818	+	0.0377271i
$803$	−4.63486	−	8.02781i	−0.163561	−	0.283295i
$804$	0.0274382	+	0.0344064i	0.000967670	+	0.00121342i
$805$	−0.542365	−	0.103141i	−0.0191159	−	0.00363524i
$806$	−6.20634	+	7.78250i	−0.218609	+	0.274127i
$807$	−21.8852	−	3.29867i	−0.770397	−	0.116119i
$808$	−21.0920	+	14.3803i	−0.742014	+	0.505896i
$809$	−29.6758	+	20.2326i	−1.04335	+	0.711342i	−0.958512	−	0.285053i	$-0.907989\pi$
$809$	−29.6758	+	20.2326i	−1.04335	+	0.711342i	−0.0848350	+	0.996395i	$0.527036\pi$
$810$	2.03992	+	0.307468i	0.0716754	+	0.0108033i
$811$	15.6202	−	19.5871i	0.548500	−	0.687797i	−0.427886	−	0.903833i	$-0.640741\pi$
$811$	15.6202	−	19.5871i	0.548500	−	0.687797i	0.976385	+	0.216036i	$0.0693128\pi$
$812$	4.19154	−	3.60037i	0.147094	−	0.126348i
$813$	33.8597	+	42.4588i	1.18751	+	1.48909i
$814$	−21.8715	−	37.8825i	−0.766595	−	1.32778i
$815$	0.807339	−	1.39835i	0.0282799	−	0.0489822i
$816$	−22.8288	+	3.44088i	−0.799166	+	0.120455i
$817$	−41.4341	+	38.4453i	−1.44960	+	1.34503i
$818$	−13.7260	−	6.61009i	−0.479918	−	0.231116i
$819$	0.432173	+	2.29572i	0.0151014	+	0.0802189i
$820$	−0.573294	+	0.276084i	−0.0200203	+	0.00964127i
$821$	5.51167	−	14.0435i	0.192359	−	0.490122i	−0.801858	−	0.597515i	$-0.796155\pi$
$821$	5.51167	−	14.0435i	0.192359	−	0.490122i	0.994217	+	0.107393i	$0.0342502\pi$
$822$	1.24853	−	16.6605i	0.0435475	−	0.581101i
$823$	8.56181	+	2.64097i	0.298446	+	0.0920584i	0.440362	−	0.897820i	$-0.354850\pi$
$823$	8.56181	+	2.64097i	0.298446	+	0.0920584i	−0.141916	+	0.989879i	$0.545326\pi$
$824$	0.00340084	+	0.0453810i	0.000118474	+	0.00158092i
$825$	11.2528	−	49.3017i	0.391772	−	1.71646i
$826$	−0.487460	−	1.39723i	−0.0169609	−	0.0486157i
$827$	−2.14491	−	9.39748i	−0.0745860	−	0.326782i	0.923846	−	0.382765i	$-0.125028\pi$
$827$	−2.14491	−	9.39748i	−0.0745860	−	0.326782i	−0.998432	+	0.0559824i	$0.982171\pi$
$828$	0.673912	−	0.207874i	0.0234201	−	0.00722414i
$829$	−2.39798	−	6.10995i	−0.0832853	−	0.212208i	0.883164	−	0.469064i	$-0.155409\pi$
$829$	−2.39798	−	6.10995i	−0.0832853	−	0.212208i	−0.966450	+	0.256856i	$0.917313\pi$
$830$	2.07383	+	1.92424i	0.0719838	+	0.0667912i
$831$	51.2037	+	34.9101i	1.77624	+	1.21102i
$832$	−8.70828			−0.301905
$833$	−29.7843	−	17.2696i	−1.03197	−	0.598355i
$834$	−36.2170			−1.25409
$835$	−1.40990	−	0.961252i	−0.0487915	−	0.0332655i
$836$	10.5841	+	9.82058i	0.366057	+	0.339652i
$837$	−12.9052	−	32.8818i	−0.446068	−	1.13656i
$838$	−2.91153	+	0.898089i	−0.100577	+	0.0310240i
$839$	0.925591	+	4.05528i	0.0319549	+	0.140004i	0.988389	−	0.151945i	$-0.0485536\pi$
$839$	0.925591	+	4.05528i	0.0319549	+	0.140004i	−0.956434	+	0.291948i	$0.905696\pi$
$840$	2.19475	−	1.37622i	0.0757260	−	0.0474841i
$841$	3.91186	−	17.1390i	0.134892	−	0.590999i
$842$	1.13135	+	15.0968i	0.0389888	+	0.520269i
$843$	−25.9160	−	7.99401i	−0.892593	−	0.275328i
$844$	1.24162	−	16.5682i	0.0427383	−	0.570302i
$845$	−0.0589842	+	0.150289i	−0.00202912	+	0.00517011i
$846$	−2.76194	+	1.33008i	−0.0949575	+	0.0457291i
$847$	−36.5209	−	19.3451i	−1.25487	−	0.664707i
$848$	2.40972	+	1.16046i	0.0827502	+	0.0398504i
$849$	−5.20618	+	4.83063i	−0.178676	+	0.165787i
$850$	−28.4381	+	4.28635i	−0.975418	+	0.147021i
$851$	4.66053	−	8.07227i	0.159761	−	0.276714i
$852$	−5.04699	−	8.74165i	−0.172907	−	0.299484i
$853$	0.525407	+	0.658839i	0.0179896	+	0.0225582i	0.790745	−	0.612146i	$-0.209693\pi$
$853$	0.525407	+	0.658839i	0.0179896	+	0.0225582i	−0.772755	+	0.634704i	$0.781122\pi$
$854$	14.2629	−	3.80758i	0.488065	−	0.130293i
$855$	0.402457	−	0.504665i	0.0137637	−	0.0172592i
$856$	29.8213	+	4.49484i	1.01927	+	0.153630i
$857$	20.7577	−	14.1524i	0.709069	−	0.483435i	−0.154290	−	0.988026i	$-0.549309\pi$
$857$	20.7577	−	14.1524i	0.709069	−	0.483435i	0.863359	+	0.504590i	$0.168356\pi$
$858$	9.87526	−	6.73284i	0.337136	−	0.229855i
$859$	29.4319	+	4.43615i	1.00420	+	0.151359i	0.630501	−	0.776189i	$-0.282850\pi$
$859$	29.4319	+	4.43615i	1.00420	+	0.151359i	0.373704	+	0.927548i	$0.378088\pi$
$860$	−0.776528	+	0.973735i	−0.0264794	+	0.0332041i
$861$	−32.1235	+	8.57562i	−1.09477	+	0.292256i
$862$	−17.9386	−	22.4943i	−0.610991	−	0.766159i
$863$	−25.4012	−	43.9962i	−0.864667	−	1.49765i	−0.867377	−	0.497651i	$-0.834196\pi$
$863$	−25.4012	−	43.9962i	−0.864667	−	1.49765i	0.00271035	−	0.999996i	$-0.499137\pi$
$864$	6.99809	−	12.1210i	0.238080	−	0.412366i
$865$	2.65599	−	0.400326i	0.0903063	−	0.0136115i
$866$	20.7527	−	19.2557i	0.705206	−	0.654335i
$867$	12.7661	+	6.14785i	0.433561	+	0.208792i
$868$	−12.2345	−	6.48060i	−0.415265	−	0.219966i
$869$	55.3396	−	26.6501i	1.87727	−	0.904044i
$870$	−0.461752	+	1.17652i	−0.0156548	+	0.0398879i
$871$	−0.00270055	+	0.0360364i	−9.15048e−5	+	0.00122105i
$872$	34.3504	+	10.5957i	1.16325	+	0.358816i
$873$	0.357244	+	4.76708i	0.0120909	+	0.161341i
$874$	1.53097	−	6.70761i	0.0517858	−	0.226888i
$875$	3.60950	−	2.26334i	0.122023	−	0.0765150i
$876$	0.486852	+	2.13304i	0.0164492	+	0.0720687i
$877$	−22.1397	+	6.82919i	−0.747604	+	0.230605i	−0.645069	−	0.764124i	$-0.723172\pi$
$877$	−22.1397	+	6.82919i	−0.747604	+	0.230605i	−0.102535	+	0.994729i	$0.532695\pi$
$878$	10.3096	+	26.2683i	0.347931	+	0.886513i
$879$	40.0709	+	37.1804i	1.35156	+	1.25406i
$880$	−1.63948	−	1.11778i	−0.0552670	−	0.0376804i
$881$	−38.2834			−1.28980			−0.644901	−	0.764266i	$-0.723101\pi$
$881$	−38.2834			−1.28980			−0.644901	+	0.764266i	$0.723101\pi$
$882$	6.76845	−	2.64198i	0.227906	−	0.0889599i
$883$	24.6944			0.831034			0.415517	−	0.909585i	$-0.363601\pi$
$883$	24.6944			0.831034			0.415517	+	0.909585i	$0.363601\pi$
$884$	2.51141	+	1.71225i	0.0844678	+	0.0575892i
$885$	−0.110958	−	0.102954i	−0.00372980	−	0.00346075i
$886$	5.21189	+	13.2797i	0.175097	+	0.446140i
$887$	−8.53547	+	2.63284i	−0.286593	+	0.0884023i	−0.434719	−	0.900566i	$-0.643152\pi$
$887$	−8.53547	+	2.63284i	−0.286593	+	0.0884023i	0.148126	+	0.988969i	$0.452676\pi$
$888$	9.73241	+	42.6405i	0.326598	+	1.43092i
$889$	−4.38709	−	12.5749i	−0.147138	−	0.421748i
$890$	0.329707	−	1.44454i	0.0110518	−	0.0484212i
$891$	4.19086	+	55.9231i	0.140399	+	1.87350i
$892$	2.12876	+	0.656635i	0.0712761	+	0.0219858i
$893$	0.999391	−	13.3360i	0.0334434	−	0.446271i
$894$	−11.7937	+	30.0498i	−0.394440	+	1.00502i
$895$	−1.11274	+	0.535868i	−0.0371949	+	0.0179121i
$896$	1.72649	+	9.17118i	0.0576781	+	0.306388i
$897$	2.29462	+	1.10503i	0.0766150	+	0.0368958i
$898$	23.5158	−	21.8195i	0.784733	−	0.728126i
$899$	28.2952	−	4.26481i	0.943696	−	0.142239i
$900$	−1.35703	+	2.35045i	−0.0452344	+	0.0783482i
$901$	−2.76118	−	4.78251i	−0.0919883	−	0.159328i
$902$	24.1176	+	30.2425i	0.803029	+	1.00697i
$903$	−49.3663	+	42.4037i	−1.64281	+	1.41111i
$904$	39.2392	−	49.2044i	1.30508	−	1.63651i
$905$	3.13673	+	0.472786i	0.104268	+	0.0157159i
$906$	−33.0365	+	22.5239i	−1.09756	+	0.748307i
$907$	−33.7611	+	23.0179i	−1.12102	+	0.764298i	−0.974384	−	0.224892i	$-0.927797\pi$
$907$	−33.7611	+	23.0179i	−1.12102	+	0.764298i	−0.146636	+	0.989191i	$0.546845\pi$
$908$	8.31817	+	1.25376i	0.276048	+	0.0416076i
$909$	−4.56614	+	5.72576i	−0.151449	+	0.189911i
$910$	0.493317	+	0.0938135i	0.0163533	+	0.00310989i
$911$	−26.1129	−	32.7446i	−0.865160	−	1.08488i	−0.995626	−	0.0934231i	$-0.970219\pi$
$911$	−26.1129	−	32.7446i	−0.865160	−	1.08488i	0.130467	−	0.991453i	$-0.458352\pi$
$912$	10.6274	+	18.4072i	0.351909	+	0.609524i
$913$	−38.4526	+	66.6019i	−1.27260	+	2.20420i
$914$	5.18759	−	0.781904i	0.171590	−	0.0258631i
$915$	1.10689	−	1.02705i	0.0365927	−	0.0339531i
$916$	1.61467	+	0.777586i	0.0533503	+	0.0256921i
$917$	−21.7700	+	9.47417i	−0.718907	+	0.312865i
$918$	21.7321	−	10.4656i	0.717265	−	0.345417i
$919$	−0.941590	+	2.39913i	−0.0310602	+	0.0791401i	−0.945562	−	0.325441i	$-0.894487\pi$
$919$	−0.941590	+	2.39913i	−0.0310602	+	0.0791401i	0.914502	+	0.404581i	$0.132583\pi$
$920$	0.0479928	−	0.640420i	0.00158228	−	0.0211140i
$921$	−28.8786	−	8.90785i	−0.951581	−	0.293524i
$922$	−1.41689	−	18.9071i	−0.0466628	−	0.622671i
$923$	1.84444	−	8.08103i	0.0607106	−	0.265990i
$924$	11.7438	+	11.7656i	0.386343	+	0.387058i
$925$	7.98208	+	34.9718i	0.262449	+	1.14987i
$926$	−28.7127	+	8.85668i	−0.943557	+	0.291049i
$927$	0.00476976	+	0.0121532i	0.000156660	+	0.000399162i
$928$	8.31130	+	7.71176i	0.272832	+	0.253151i
$929$	41.0474	+	27.9856i	1.34672	+	0.918179i	0.999806	−	0.0197173i	$-0.00627661\pi$
$929$	41.0474	+	27.9856i	1.34672	+	0.918179i	0.346916	+	0.937896i	$0.387229\pi$
$930$	3.16682			0.103844
$931$	−4.78220	+	31.3342i	−0.156730	+	1.02694i
$932$	−11.4529			−0.375151
$933$	4.82900	+	3.29236i	0.158094	+	0.107787i
$934$	18.0044	+	16.7057i	0.589123	+	0.546626i
$935$	1.49682	+	3.81382i	0.0489511	+	0.124725i
$936$	−2.59668	+	0.800971i	−0.0848753	+	0.0261806i
$937$	3.89694	+	17.0736i	0.127307	+	0.557770i	0.997842	+	0.0656628i	$0.0209162\pi$
$937$	3.89694	+	17.0736i	0.127307	+	0.557770i	−0.870534	+	0.492108i	$0.836227\pi$
$938$	0.111703	−	0.0124813i	0.00364724	−	0.000407528i
$939$	−11.6070	+	50.8536i	−0.378781	+	1.65955i
$940$	−0.0220211	−	0.293852i	−0.000718250	−	0.00958438i
$941$	−12.0460	−	3.71571i	−0.392689	−	0.121129i	0.0921214	−	0.995748i	$-0.470635\pi$
$941$	−12.0460	−	3.71571i	−0.392689	−	0.121129i	−0.484810	+	0.874619i	$0.661111\pi$
$942$	1.50118	−	20.0319i	0.0489111	−	0.652673i
$943$	−3.01135	+	7.67279i	−0.0980630	+	0.249860i
$944$	1.02111	−	0.491739i	0.0332342	−	0.0160047i
$945$	−1.16360	+	1.34960i	−0.0378520	+	0.0439026i
$946$	68.2142	+	32.8502i	2.21784	+	1.06805i
$947$	18.1936	−	16.8812i	0.591213	−	0.548565i	−0.326812	−	0.945090i	$-0.605974\pi$
$947$	18.1936	−	16.8812i	0.591213	−	0.548565i	0.918024	+	0.396524i	$0.129784\pi$
$948$	−14.3353	+	2.16070i	−0.465590	+	0.0701764i
$949$	−0.898313	+	1.55592i	−0.0291605	+	0.0505074i
$950$	13.2387	+	22.9301i	0.429520	+	0.743951i
$951$	31.7174	+	39.7724i	1.02851	+	1.28971i
$952$	16.0494	−	36.6930i	0.520165	−	1.18923i
$953$	19.5337	−	24.4945i	0.632759	−	0.793455i	−0.357317	−	0.933983i	$-0.616309\pi$
$953$	19.5337	−	24.4945i	0.632759	−	0.793455i	0.990077	+	0.140528i	$0.0448800\pi$
$954$	1.15241	+	0.173699i	0.0373108	+	0.00562370i
$955$	0.955719	−	0.651598i	0.0309264	−	0.0210852i
$956$	1.43995	−	0.981738i	0.0465712	−	0.0317517i
$957$	−33.9742	−	5.12078i	−1.09823	−	0.165531i
$958$	−5.30609	+	6.65363i	−0.171432	+	0.214969i
$959$	15.3426	+	11.3453i	0.495439	+	0.366360i
$960$	1.72735	+	2.16602i	0.0557498	+	0.0699081i
$961$	−20.3487	−	35.2451i	−0.656411	−	1.13694i
$962$	−4.23906	+	7.34227i	−0.136673	+	0.236724i
$963$	8.55529	−	1.28950i	0.275690	−	0.0415536i
$964$	−10.4994	+	9.74199i	−0.338162	+	0.313769i
$965$	2.00690	+	0.966471i	0.0646043	+	0.0311118i
$966$	2.05730	−	7.64961i	0.0661924	−	0.246122i
$967$	−45.5853	+	21.9527i	−1.46593	+	0.705952i	−0.985278	−	0.170961i	$-0.945313\pi$
$967$	−45.5853	+	21.9527i	−1.46593	+	0.705952i	−0.480648	+	0.876914i	$0.659598\pi$
$968$	17.5638	−	44.7519i	0.564522	−	1.43838i
$969$	3.27960	−	43.7632i	0.105356	−	1.40588i
$970$	0.981957	+	0.302894i	0.0315287	+	0.00972533i
$971$	0.799491	+	10.6685i	0.0256569	+	0.342367i	0.995229	+	0.0975629i	$0.0311047\pi$
$971$	0.799491	+	10.6685i	0.0256569	+	0.342367i	−0.969572	+	0.244804i	$0.921276\pi$
$972$	1.22431	−	5.36405i	0.0392698	−	0.172052i
$973$	22.0396	−	35.0039i	0.706558	−	1.12217i
$974$	−5.33970	−	23.3948i	−0.171095	−	0.749617i
$975$	−9.36579	+	2.88896i	−0.299945	+	0.0925208i
$976$	4.13054	+	10.5244i	0.132215	+	0.336879i
$977$	0.201367	+	0.186841i	0.00644229	+	0.00597757i	0.683387	−	0.730056i	$-0.260506\pi$
$977$	0.201367	+	0.186841i	0.00644229	+	0.00597757i	−0.676945	+	0.736034i	$0.736697\pi$
$978$	19.1421	+	13.0508i	0.612096	+	0.417320i
$979$	40.2786			1.28731
$980$	−0.00129253	+	0.698429i	−4.12884e−5	+	0.0223105i
$981$	10.3128			0.329262
$982$	24.4462	+	16.6671i	0.780110	+	0.531870i
$983$	7.16950	+	6.65232i	0.228672	+	0.212176i	0.786184	−	0.617992i	$-0.212054\pi$
$983$	7.16950	+	6.65232i	0.228672	+	0.212176i	−0.557513	+	0.830168i	$0.688244\pi$
$984$	−14.1301	−	36.0029i	−0.450451	−	1.14773i
$985$	0.314876	−	0.0971263i	0.0100328	−	0.00309470i
$986$	4.34797	+	19.0497i	0.138468	+	0.606667i
$987$	1.73812	−	15.2990i	0.0553251	−	0.486973i
$988$	0.622702	−	2.72823i	0.0198108	−	0.0867967i
$989$	1.20564	+	16.0882i	0.0383371	+	0.511574i
$990$	−0.826219	−	0.254855i	−0.0262590	−	0.00809982i
$991$	4.20783	−	56.1496i	0.133666	−	1.78365i	−0.379332	−	0.925261i	$-0.623846\pi$
$991$	4.20783	−	56.1496i	0.133666	−	1.78365i	0.512998	−	0.858390i	$-0.328535\pi$
$992$	10.3788	−	26.4447i	0.329527	−	0.839620i
$993$	−0.914749	+	0.440520i	−0.0290287	+	0.0139795i
$994$	−25.7619	−	0.987815i	−0.817119	−	0.0313316i
$995$	0.102773	+	0.0494930i	0.00325813	+	0.00156903i
$996$	13.3061	−	12.3463i	0.421620	−	0.391206i
$997$	24.2428	−	3.65401i	0.767776	−	0.115724i	0.246536	−	0.969134i	$-0.420708\pi$
$997$	24.2428	−	3.65401i	0.767776	−	0.115724i	0.521240	+	0.853410i	$0.325470\pi$
$998$	11.1257	−	19.2703i	0.352178	−	0.609991i
$999$	−15.0428	−	26.0549i	−0.475933	−	0.824340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.10	✓	324
49.37	even	21	inner	637.2.bl.a.625.10	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.10	✓	324	1.1	even	1	trivial
637.2.bl.a.625.10	yes	324	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971314 - 0.662231i) q^{2} +(1.44449 + 1.34029i) q^{3} +(-0.225781 - 0.575279i) q^{4} +(-0.154277 + 0.0475881i) q^{5} +(-0.515472 - 2.25843i) q^{6} +(2.49647 + 0.876147i) q^{7} +(-0.684849 + 3.00052i) q^{8} +(0.0659823 + 0.880472i) q^{9} +O(q^{10})\)	\(q+(-0.971314 - 0.662231i) q^{2} +(1.44449 + 1.34029i) q^{3} +(-0.225781 - 0.575279i) q^{4} +(-0.154277 + 0.0475881i) q^{5} +(-0.515472 - 2.25843i) q^{6} +(2.49647 + 0.876147i) q^{7} +(-0.684849 + 3.00052i) q^{8} +(0.0659823 + 0.880472i) q^{9} +(0.181366 + 0.0559439i) q^{10} +(-0.385571 + 5.14508i) q^{11} +(0.444905 - 1.13360i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.84465 - 2.50425i) q^{14} +(-0.286634 - 0.138036i) q^{15} +(1.74619 - 1.62022i) q^{16} +(-4.86347 + 0.733050i) q^{17} +(0.518986 - 0.898910i) q^{18} +(2.26408 + 3.92150i) q^{19} +(0.0622092 + 0.0780079i) q^{20} +(2.43184 + 4.61159i) q^{21} +(3.78174 - 4.74216i) q^{22} +(1.27803 + 0.192632i) q^{23} +(-5.01083 + 3.41633i) q^{24} +(-4.10966 + 2.80192i) q^{25} +(-1.16245 - 0.175212i) q^{26} +(2.60101 - 3.26157i) q^{27} +(-0.0596254 - 1.63399i) q^{28} +(2.10701 + 2.64211i) q^{29} +(0.187000 + 0.323894i) q^{30} +(4.23372 - 7.33302i) q^{31} +(3.31755 - 0.500041i) q^{32} +(-7.45287 + 6.91525i) q^{33} +(5.20940 + 2.50872i) q^{34} +(-0.426842 - 0.0163668i) q^{35} +(0.491620 - 0.236752i) q^{36} +(2.63478 - 6.71330i) q^{37} +(0.397806 - 5.30835i) q^{38} +(1.88297 + 0.580820i) q^{39} +(-0.0371327 - 0.495501i) q^{40} +(-1.41910 + 6.21749i) q^{41} +(0.691856 - 6.08974i) q^{42} +(2.77762 + 12.1696i) q^{43} +(3.04692 - 0.939849i) q^{44} +(-0.0520796 - 0.132697i) q^{45} +(-1.11380 - 1.03346i) q^{46} +(-2.44020 - 1.66370i) q^{47} +4.69393 q^{48} +(5.46473 + 4.37455i) q^{49} +5.84728 q^{50} +(-8.00774 - 5.45958i) q^{51} +(-0.453026 - 0.420346i) q^{52} +(0.410204 + 1.04518i) q^{53} +(-4.68631 + 1.44554i) q^{54} +(-0.185360 - 0.812117i) q^{55} +(-4.33860 + 6.89068i) q^{56} +(-1.98551 + 8.69909i) q^{57} +(-0.296885 - 3.96165i) q^{58} +(0.454641 + 0.140238i) q^{59} +(-0.0146927 + 0.196060i) q^{60} +(-1.73401 + 4.41818i) q^{61} +(-8.96842 + 4.31896i) q^{62} +(-0.606700 + 2.25588i) q^{63} +(-7.84589 - 3.77838i) q^{64} +(-0.118351 + 0.109814i) q^{65} +(11.8186 - 1.78136i) q^{66} +(-0.0180687 + 0.0312959i) q^{67} +(1.51978 + 2.63234i) q^{68} +(1.58792 + 1.99119i) q^{69} +(0.403759 + 0.298565i) q^{70} +(5.16801 - 6.48048i) q^{71} +(-2.68706 - 0.405009i) q^{72} +(-1.48444 + 1.01208i) q^{73} +(-7.00495 + 4.77589i) q^{74} +(-9.69175 - 1.46080i) q^{75} +(1.74477 - 2.18787i) q^{76} +(-5.47041 + 12.5067i) q^{77} +(-1.44432 - 1.81112i) q^{78} +(-5.95234 - 10.3097i) q^{79} +(-0.192293 + 0.333061i) q^{80} +(10.7478 - 1.61998i) q^{81} +(5.49580 - 5.09936i) q^{82} +(13.4294 + 6.46727i) q^{83} +(2.10389 - 2.44019i) q^{84} +(0.715436 - 0.344536i) q^{85} +(5.36111 - 13.6599i) q^{86} +(-0.497639 + 6.64053i) q^{87} +(-15.1739 - 4.68052i) q^{88} +(-0.583394 - 7.78485i) q^{89} +(-0.0372901 + 0.163379i) q^{90} +(2.62939 - 0.293797i) q^{91} +(-0.177737 - 0.778718i) q^{92} +(15.9440 - 4.91806i) q^{93} +(1.26844 + 3.23194i) q^{94} +(-0.535912 - 0.497253i) q^{95} +(5.46238 + 3.72419i) q^{96} +5.41424 q^{97} +(-2.41101 - 7.86798i) q^{98} -4.55554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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Database

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