LMFDB - Embedded newform 40.2.k.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,2,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.319401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.1
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	40.27
Dual form			40.2.k.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39680 - 0.221232i) q^{2} +(0.618034 - 0.618034i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(-1.00000 + 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-2.52015 - 1.28408i) q^{8} +2.23607i q^{9} +O(q^{10})$	\(q+(-1.39680 - 0.221232i) q^{2} +(0.618034 - 0.618034i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(-1.00000 + 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-2.52015 - 1.28408i) q^{8} +2.23607i q^{9} +(-2.06285 + 2.39680i) q^{10} -3.23607 q^{11} +(1.55754 - 0.793604i) q^{12} +(0.726543 + 0.726543i) q^{13} +(3.07768 - 2.23607i) q^{14} +(-0.449028 - 1.90211i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.00000 - 1.00000i) q^{17} +(0.494689 - 3.12334i) q^{18} -2.00000i q^{19} +(3.41164 - 2.89149i) q^{20} +2.35114i q^{21} +(4.52015 + 0.715921i) q^{22} +(4.25325 + 4.25325i) q^{23} +(-2.35114 + 0.763932i) q^{24} +(-2.23607 - 4.47214i) q^{25} +(-0.854102 - 1.17557i) q^{26} +(3.23607 + 3.23607i) q^{27} +(-4.79360 + 2.44246i) q^{28} -6.15537 q^{29} +(0.206396 + 2.75621i) q^{30} -8.50651i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.00000 + 2.00000i) q^{33} +(1.17557 + 1.61803i) q^{34} +(1.38197 + 5.85410i) q^{35} +(-1.38197 + 4.25325i) q^{36} +(-0.726543 + 0.726543i) q^{37} +(-0.442463 + 2.79360i) q^{38} +0.898056 q^{39} +(-5.40507 + 3.28408i) q^{40} +5.70820 q^{41} +(0.520147 - 3.28408i) q^{42} +(4.61803 - 4.61803i) q^{43} +(-6.15537 - 2.00000i) q^{44} +(4.25325 + 2.62866i) q^{45} +(-5.00000 - 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} +(3.45309 - 0.546915i) q^{48} -0.236068i q^{49} +(2.13397 + 6.74138i) q^{50} -1.23607 q^{51} +(0.932938 + 1.83099i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(-3.80423 - 5.23607i) q^{54} +(-3.80423 + 6.15537i) q^{55} +(7.23607 - 2.35114i) q^{56} +(-1.23607 - 1.23607i) q^{57} +(8.59783 + 1.36176i) q^{58} -0.472136i q^{59} +(0.321469 - 3.89555i) q^{60} +0.898056i q^{61} +(-1.88191 + 11.8819i) q^{62} +(-4.25325 - 4.25325i) q^{63} +(4.70228 + 6.47214i) q^{64} +(2.23607 - 0.527864i) q^{65} +(3.23607 - 2.35114i) q^{66} +(-4.61803 - 4.61803i) q^{67} +(-1.28408 - 2.52015i) q^{68} +5.25731 q^{69} +(-0.635220 - 8.48276i) q^{70} +11.4127i q^{71} +(2.87129 - 5.63522i) q^{72} +(-4.70820 + 4.70820i) q^{73} +(1.17557 - 0.854102i) q^{74} +(-4.14590 - 1.38197i) q^{75} +(1.23607 - 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} +(-1.25441 - 0.198678i) q^{78} +2.90617 q^{79} +(8.27636 - 3.39144i) q^{80} -2.70820 q^{81} +(-7.97323 - 1.26284i) q^{82} +(-6.61803 + 6.61803i) q^{83} +(-1.45309 + 4.47214i) q^{84} +(-3.07768 + 0.726543i) q^{85} +(-7.47214 + 5.42882i) q^{86} +(-3.80423 + 3.80423i) q^{87} +(8.15537 + 4.15537i) q^{88} +2.47214i q^{89} +(-5.35941 - 4.61267i) q^{90} -2.76393 q^{91} +(5.46151 + 10.7188i) q^{92} +(-5.25731 - 5.25731i) q^{93} +(-5.42882 + 3.94427i) q^{94} +(-3.80423 - 2.35114i) q^{95} -4.94427 q^{96} +(4.23607 + 4.23607i) q^{97} +(-0.0522257 + 0.329740i) q^{98} -7.23607i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 + 4 * q^8	$ 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} - 10 q^{10} - 8 q^{11} + 12 q^{12} + 8 q^{16} - 8 q^{17} + 10 q^{18} + 12 q^{22} + 20 q^{26} + 8 q^{27} - 20 q^{28} + 20 q^{30} - 32 q^{32} - 16 q^{33} + 20 q^{35} - 20 q^{36} - 4 q^{38} - 20 q^{40} - 8 q^{41} - 20 q^{42} + 28 q^{43} - 40 q^{46} + 16 q^{48} - 10 q^{50} + 8 q^{51} + 20 q^{52} + 40 q^{56} + 8 q^{57} + 20 q^{58} + 20 q^{60} + 40 q^{62} + 8 q^{66} - 28 q^{67} - 4 q^{68} + 20 q^{70} - 20 q^{72} + 16 q^{73} - 60 q^{75} - 8 q^{76} - 40 q^{78} + 32 q^{81} - 28 q^{82} - 44 q^{83} - 24 q^{86} + 16 q^{88} - 10 q^{90} - 40 q^{91} + 20 q^{92} + 32 q^{96} + 16 q^{97} - 6 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 + 4 * q^8 - 10 * q^10 - 8 * q^11 + 12 * q^12 + 8 * q^16 - 8 * q^17 + 10 * q^18 + 12 * q^22 + 20 * q^26 + 8 * q^27 - 20 * q^28 + 20 * q^30 - 32 * q^32 - 16 * q^33 + 20 * q^35 - 20 * q^36 - 4 * q^38 - 20 * q^40 - 8 * q^41 - 20 * q^42 + 28 * q^43 - 40 * q^46 + 16 * q^48 - 10 * q^50 + 8 * q^51 + 20 * q^52 + 40 * q^56 + 8 * q^57 + 20 * q^58 + 20 * q^60 + 40 * q^62 + 8 * q^66 - 28 * q^67 - 4 * q^68 + 20 * q^70 - 20 * q^72 + 16 * q^73 - 60 * q^75 - 8 * q^76 - 40 * q^78 + 32 * q^81 - 28 * q^82 - 44 * q^83 - 24 * q^86 + 16 * q^88 - 10 * q^90 - 40 * q^91 + 20 * q^92 + 32 * q^96 + 16 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$3$	0.618034	−	0.618034i	0.356822	−	0.356822i	−0.505818	−	0.862640i	$-0.668809\pi$
$3$	0.618034	−	0.618034i	0.356822	−	0.356822i	0.862640	+	0.505818i	$0.168809\pi$
$4$	1.90211	+	0.618034i	0.951057	+	0.309017i
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$6$	−1.00000	+	0.726543i	−0.408248	+	0.296610i
$7$	−1.90211	+	1.90211i	−0.718931	+	0.718931i	−0.968386	−	0.249455i	$-0.919748\pi$
$7$	−1.90211	+	1.90211i	−0.718931	+	0.718931i	0.249455	+	0.968386i	$0.419748\pi$
$8$	−2.52015	−	1.28408i	−0.891007	−	0.453990i
$9$			2.23607i			0.745356i
$10$	−2.06285	+	2.39680i	−0.652330	+	0.757935i
$11$	−3.23607			−0.975711			−0.487856	−	0.872924i	$-0.662221\pi$
$11$	−3.23607			−0.975711			−0.487856	+	0.872924i	$0.662221\pi$
$12$	1.55754	−	0.793604i	0.449622	−	0.229094i
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	0.800645	−	0.599139i	$-0.204490\pi$
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	−0.599139	+	0.800645i	$0.704490\pi$
$14$	3.07768	−	2.23607i	0.822546	−	0.597614i
$15$	−0.449028	−	1.90211i	−0.115939	−	0.491123i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	0.575363	−	0.817898i	$-0.304861\pi$
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	−0.817898	+	0.575363i	$0.804861\pi$
$18$	0.494689	−	3.12334i	0.116599	−	0.736179i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$	3.41164	−	2.89149i	0.762866	−	0.646557i
$21$			2.35114i			0.513061i
$22$	4.52015	+	0.715921i	0.963699	+	0.152635i
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	0.994221	−	0.107356i	$-0.0342384\pi$
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	−0.107356	+	0.994221i	$0.534238\pi$
$24$	−2.35114	+	0.763932i	−0.479925	+	0.155937i
$25$	−2.23607	−	4.47214i	−0.447214	−	0.894427i
$26$	−0.854102	−	1.17557i	−0.167503	−	0.230548i
$27$	3.23607	+	3.23607i	0.622782	+	0.622782i
$28$	−4.79360	+	2.44246i	−0.905906	+	0.461582i
$29$	−6.15537			−1.14302			−0.571511	−	0.820594i	$-0.693643\pi$
$29$	−6.15537			−1.14302			−0.571511	+	0.820594i	$0.693643\pi$
$30$	0.206396	+	2.75621i	0.0376825	+	0.503214i
$31$		−	8.50651i		−	1.52781i	−0.645326	−	0.763907i	$-0.723279\pi$
$31$		−	8.50651i		−	1.52781i	0.645326	−	0.763907i	$-0.276721\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−2.00000	+	2.00000i	−0.348155	+	0.348155i
$34$	1.17557	+	1.61803i	0.201609	+	0.277491i
$35$	1.38197	+	5.85410i	0.233595	+	0.989524i
$36$	−1.38197	+	4.25325i	−0.230328	+	0.708876i
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	−0.764302	−	0.644859i	$-0.776916\pi$
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	0.644859	+	0.764302i	$0.276916\pi$
$38$	−0.442463	+	2.79360i	−0.0717771	+	0.453182i
$39$	0.898056			0.143804
$40$	−5.40507	+	3.28408i	−0.854617	+	0.519258i
$41$	5.70820			0.891472			0.445736	−	0.895165i	$-0.352942\pi$
$41$	5.70820			0.891472			0.445736	+	0.895165i	$0.352942\pi$
$42$	0.520147	−	3.28408i	0.0802604	−	0.506744i
$43$	4.61803	−	4.61803i	0.704244	−	0.704244i	−0.261075	−	0.965319i	$-0.584077\pi$
$43$	4.61803	−	4.61803i	0.704244	−	0.704244i	0.965319	+	0.261075i	$0.0840770\pi$
$44$	−6.15537	−	2.00000i	−0.927957	−	0.301511i
$45$	4.25325	+	2.62866i	0.634038	+	0.391857i
$46$	−5.00000	−	6.88191i	−0.737210	−	1.01468i
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	−0.418713	−	0.908119i	$-0.637519\pi$
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	0.908119	+	0.418713i	$0.137519\pi$
$48$	3.45309	−	0.546915i	0.498410	−	0.0789404i
$49$		−	0.236068i		−	0.0337240i
$50$	2.13397	+	6.74138i	0.301788	+	0.953375i
$51$	−1.23607			−0.173084
$52$	0.932938	+	1.83099i	0.129375	+	0.253913i
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	0.463398	−	0.886150i	$-0.346630\pi$
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	−0.886150	+	0.463398i	$0.846630\pi$
$54$	−3.80423	−	5.23607i	−0.517690	−	0.712539i
$55$	−3.80423	+	6.15537i	−0.512962	+	0.829990i
$56$	7.23607	−	2.35114i	0.966960	−	0.314184i
$57$	−1.23607	−	1.23607i	−0.163721	−	0.163721i
$58$	8.59783	+	1.36176i	1.12895	+	0.178808i
$59$		−	0.472136i		−	0.0614669i	−0.999528	−	0.0307334i	$-0.990216\pi$
$59$		−	0.472136i		−	0.0614669i	0.999528	−	0.0307334i	$-0.00978430\pi$
$60$	0.321469	−	3.89555i	0.0415014	−	0.502913i
$61$			0.898056i			0.114984i	0.998346	+	0.0574921i	$0.0183104\pi$
$61$			0.898056i			0.114984i	−0.998346	+	0.0574921i	$0.981690\pi$
$62$	−1.88191	+	11.8819i	−0.239003	+	1.50900i
$63$	−4.25325	−	4.25325i	−0.535860	−	0.535860i
$64$	4.70228	+	6.47214i	0.587785	+	0.809017i
$65$	2.23607	−	0.527864i	0.277350	−	0.0654735i
$66$	3.23607	−	2.35114i	0.398332	−	0.289405i
$67$	−4.61803	−	4.61803i	−0.564183	−	0.564183i	0.366310	−	0.930493i	$-0.380621\pi$
$67$	−4.61803	−	4.61803i	−0.564183	−	0.564183i	−0.930493	+	0.366310i	$0.880621\pi$
$68$	−1.28408	−	2.52015i	−0.155717	−	0.305613i
$69$	5.25731			0.632906
$70$	−0.635220	−	8.48276i	−0.0759233	−	1.01388i
$71$			11.4127i			1.35444i	0.735783	+	0.677218i	$0.236815\pi$
$71$			11.4127i			1.35444i	−0.735783	+	0.677218i	$0.763185\pi$
$72$	2.87129	−	5.63522i	0.338385	−	0.664117i
$73$	−4.70820	+	4.70820i	−0.551054	+	0.551054i	−0.926745	−	0.375691i	$-0.877405\pi$
$73$	−4.70820	+	4.70820i	−0.551054	+	0.551054i	0.375691	+	0.926745i	$0.377405\pi$
$74$	1.17557	−	0.854102i	0.136657	−	0.0992873i
$75$	−4.14590	−	1.38197i	−0.478727	−	0.159576i
$76$	1.23607	−	3.80423i	0.141787	−	0.436375i
$77$	6.15537	−	6.15537i	0.701469	−	0.701469i
$78$	−1.25441	−	0.198678i	−0.142034	−	0.0224959i
$79$	2.90617			0.326970			0.163485	−	0.986546i	$-0.447727\pi$
$79$	2.90617			0.326970			0.163485	+	0.986546i	$0.447727\pi$
$80$	8.27636	−	3.39144i	0.925325	−	0.379174i
$81$	−2.70820			−0.300912
$82$	−7.97323	−	1.26284i	−0.880496	−	0.139457i
$83$	−6.61803	+	6.61803i	−0.726424	+	0.726424i	−0.969905	−	0.243482i	$-0.921710\pi$
$83$	−6.61803	+	6.61803i	−0.726424	+	0.726424i	0.243482	+	0.969905i	$0.421710\pi$
$84$	−1.45309	+	4.47214i	−0.158545	+	0.487950i
$85$	−3.07768	+	0.726543i	−0.333822	+	0.0788046i
$86$	−7.47214	+	5.42882i	−0.805741	+	0.585405i
$87$	−3.80423	+	3.80423i	−0.407856	+	0.407856i
$88$	8.15537	+	4.15537i	0.869365	+	0.442964i
$89$			2.47214i			0.262046i	0.991379	+	0.131023i	$0.0418262\pi$
$89$			2.47214i			0.262046i	−0.991379	+	0.131023i	$0.958174\pi$
$90$	−5.35941	−	4.61267i	−0.564932	−	0.486218i
$91$	−2.76393			−0.289739
$92$	5.46151	+	10.7188i	0.569402	+	1.11751i
$93$	−5.25731	−	5.25731i	−0.545158	−	0.545158i
$94$	−5.42882	+	3.94427i	−0.559940	+	0.406821i
$95$	−3.80423	−	2.35114i	−0.390305	−	0.241222i
$96$	−4.94427			−0.504623
$97$	4.23607	+	4.23607i	0.430108	+	0.430108i	0.888665	−	0.458557i	$-0.151634\pi$
$97$	4.23607	+	4.23607i	0.430108	+	0.430108i	−0.458557	+	0.888665i	$0.651634\pi$
$98$	−0.0522257	+	0.329740i	−0.00527560	+	0.0333088i
$99$		−	7.23607i		−	0.727252i
$100$	−1.48932	−	9.88847i	−0.148932	−	0.988847i
$101$			2.90617i			0.289175i	0.989492	+	0.144587i	$0.0461855\pi$
$101$			2.90617i			0.289175i	−0.989492	+	0.144587i	$0.953815\pi$
$102$	1.72654	+	0.273457i	0.170953	+	0.0270763i
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	0.522216	−	0.852813i	$-0.325106\pi$
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	−0.852813	+	0.522216i	$0.825106\pi$
$104$	−0.898056	−	2.76393i	−0.0880616	−	0.271026i
$105$	4.47214	+	2.76393i	0.436436	+	0.269732i
$106$	3.61803	+	4.97980i	0.351415	+	0.483681i
$107$	0.909830	+	0.909830i	0.0879566	+	0.0879566i	0.749716	−	0.661760i	$-0.230190\pi$
$107$	0.909830	+	0.909830i	0.0879566	+	0.0879566i	−0.661760	+	0.749716i	$0.730190\pi$
$108$	4.15537	+	8.15537i	0.399850	+	0.784751i
$109$	14.6619			1.40435			0.702176	−	0.712003i	$-0.252212\pi$
$109$	14.6619			1.40435			0.702176	+	0.712003i	$0.252212\pi$
$110$	6.67551	−	7.75621i	0.636485	−	0.739526i
$111$			0.898056i			0.0852397i
$112$	−10.6275	+	1.68323i	−1.00420	+	0.159050i
$113$	8.70820	−	8.70820i	0.819199	−	0.819199i	−0.166793	−	0.985992i	$-0.553341\pi$
$113$	8.70820	−	8.70820i	0.819199	−	0.819199i	0.985992	+	0.166793i	$0.0533412\pi$
$114$	1.45309	+	2.00000i	0.136094	+	0.187317i
$115$	13.0902	−	3.09017i	1.22066	−	0.288160i
$116$	−11.7082	−	3.80423i	−1.08708	−	0.353214i
$117$	−1.62460	+	1.62460i	−0.150194	+	0.150194i
$118$	−0.104451	+	0.659481i	−0.00961554	+	0.0607101i
$119$	3.80423			0.348733
$120$	−1.31085	+	5.37019i	−0.119663	+	0.490229i
$121$	−0.527864			−0.0479876
$122$	0.198678	−	1.25441i	0.0179875	−	0.113569i
$123$	3.52786	−	3.52786i	0.318097	−	0.318097i
$124$	5.25731	−	16.1803i	0.472120	−	1.45304i
$125$	−11.1352	−	1.00406i	−0.995959	−	0.0898056i
$126$	5.00000	+	6.88191i	0.445435	+	0.613089i
$127$	2.80017	−	2.80017i	0.248475	−	0.248475i	−0.571870	−	0.820344i	$-0.693782\pi$
$127$	2.80017	−	2.80017i	0.248475	−	0.248475i	0.820344	+	0.571870i	$0.193782\pi$
$128$	−5.13632	−	10.0806i	−0.453990	−	0.891007i
$129$		−	5.70820i		−	0.502579i
$130$	−3.24013	+	0.242632i	−0.284178	+	0.0212803i
$131$	13.7082			1.19769			0.598846	−	0.800864i	$-0.295626\pi$
$131$	13.7082			1.19769			0.598846	+	0.800864i	$0.295626\pi$
$132$	−5.04029	+	2.56816i	−0.438701	+	0.223529i
$133$	3.80423	+	3.80423i	0.329868	+	0.329868i
$134$	5.42882	+	7.47214i	0.468979	+	0.645494i
$135$	9.95959	−	2.35114i	0.857185	−	0.202354i
$136$	1.23607	+	3.80423i	0.105992	+	0.326210i
$137$	−5.47214	−	5.47214i	−0.467516	−	0.467516i	0.433593	−	0.901109i	$-0.357246\pi$
$137$	−5.47214	−	5.47214i	−0.467516	−	0.467516i	−0.901109	+	0.433593i	$0.857246\pi$
$138$	−7.34342	−	1.16308i	−0.625114	−	0.0990083i
$139$			21.4164i			1.81652i	0.418411	+	0.908258i	$0.362587\pi$
$139$			21.4164i			1.81652i	−0.418411	+	0.908258i	$0.637413\pi$
$140$	−0.989378	+	11.9893i	−0.0836177	+	1.01328i
$141$		−	4.14725i		−	0.349262i
$142$	2.52485	−	15.9413i	0.211880	−	1.33776i
$143$	−2.35114	−	2.35114i	−0.196612	−	0.196612i
$144$	−5.25731	+	7.23607i	−0.438109	+	0.603006i
$145$	−7.23607	+	11.7082i	−0.600923	+	0.972313i
$146$	7.61803	−	5.53483i	0.630473	−	0.458065i
$147$	−0.145898	−	0.145898i	−0.0120335	−	0.0120335i
$148$	−1.83099	+	0.932938i	−0.150507	+	0.0766870i
$149$	−12.8658			−1.05400			−0.527002	−	0.849864i	$-0.676684\pi$
$149$	−12.8658			−1.05400			−0.527002	+	0.849864i	$0.676684\pi$
$150$	5.48526	+	2.84754i	0.447870	+	0.232500i
$151$		−	6.71040i		−	0.546084i	−0.962002	−	0.273042i	$-0.911970\pi$
$151$		−	6.71040i		−	0.546084i	0.962002	−	0.273042i	$-0.0880298\pi$
$152$	−2.56816	+	5.04029i	−0.208305	+	0.408822i
$153$	2.23607	−	2.23607i	0.180775	−	0.180775i
$154$	−9.95959	+	7.23607i	−0.802567	+	0.583099i
$155$	−16.1803	−	10.0000i	−1.29964	−	0.803219i
$156$	1.70820	+	0.555029i	0.136766	+	0.0444379i
$157$	−13.9353	+	13.9353i	−1.11216	+	1.11216i	−0.119303	+	0.992858i	$0.538066\pi$
$157$	−13.9353	+	13.9353i	−1.11216	+	1.11216i	−0.992858	+	0.119303i	$0.961934\pi$
$158$	−4.05934	−	0.642937i	−0.322944	−	0.0511493i
$159$	−3.80423			−0.301695
$160$	−12.3107	+	2.90617i	−0.973249	+	0.229753i
$161$	−16.1803			−1.27519
$162$	3.78283	+	0.599141i	0.297207	+	0.0470729i
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.0891157	+	0.996021i	$0.528404\pi$
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.996021	+	0.0891157i	$0.971596\pi$
$164$	10.8576	+	3.52786i	0.847840	+	0.275480i
$165$	1.45309	+	6.15537i	0.113123	+	0.479195i
$166$	10.7082	−	7.77997i	0.831118	−	0.603842i
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	−0.322920	−	0.946426i	$-0.604664\pi$
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	0.946426	+	0.322920i	$0.104664\pi$
$168$	3.01905	−	5.92522i	0.232925	−	0.457141i
$169$		−	11.9443i		−	0.918790i
$170$	4.45965	−	0.333955i	0.342040	−	0.0256132i
$171$	4.47214			0.341993
$172$	11.6381	−	5.92992i	0.887399	−	0.452152i
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.994208	+	0.107474i	$0.0342762\pi$
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.107474	+	0.994208i	$0.465724\pi$
$174$	6.15537	−	4.47214i	0.466637	−	0.339032i
$175$	12.7598	+	4.25325i	0.964547	+	0.321516i
$176$	−10.4721	−	7.60845i	−0.789367	−	0.573509i
$177$	−0.291796	−	0.291796i	−0.0219327	−	0.0219327i
$178$	0.546915	−	3.45309i	0.0409930	−	0.258820i
$179$		−	7.52786i		−	0.562659i	−0.959611	−	0.281329i	$-0.909225\pi$
$179$		−	7.52786i		−	0.562659i	0.959611	−	0.281329i	$-0.0907754\pi$
$180$	6.46557	+	7.62866i	0.481915	+	0.568606i
$181$		−	15.2169i		−	1.13106i	−0.824726	−	0.565532i	$-0.808671\pi$
$181$		−	15.2169i		−	1.13106i	0.824726	−	0.565532i	$-0.191329\pi$
$182$	3.86067	+	0.611469i	0.286172	+	0.0453251i
$183$	0.555029	+	0.555029i	0.0410289	+	0.0410289i
$184$	−5.25731	−	16.1803i	−0.387574	−	1.19283i
$185$	0.527864	+	2.23607i	0.0388093	+	0.164399i
$186$	6.18034	+	8.50651i	0.453165	+	0.623727i
$187$	3.23607	+	3.23607i	0.236645	+	0.236645i
$188$	8.45559	−	4.30834i	0.616687	−	0.314218i
$189$	−12.3107			−0.895474
$190$	4.79360	+	4.12569i	0.347765	+	0.299309i
$191$			13.2088i			0.955755i	0.878427	+	0.477877i	$0.158594\pi$
$191$			13.2088i			0.955755i	−0.878427	+	0.477877i	$0.841406\pi$
$192$	6.90617	+	1.09383i	0.498410	+	0.0789404i
$193$	1.47214	−	1.47214i	0.105967	−	0.105967i	−0.652136	−	0.758102i	$-0.726127\pi$
$193$	1.47214	−	1.47214i	0.105967	−	0.105967i	0.758102	+	0.652136i	$0.226127\pi$
$194$	−4.97980	−	6.85410i	−0.357529	−	0.492096i
$195$	1.05573	−	1.70820i	0.0756023	−	0.122327i
$196$	0.145898	−	0.449028i	0.0104213	−	0.0320734i
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	−0.297038	−	0.954866i	$-0.595999\pi$
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	0.954866	+	0.297038i	$0.0959988\pi$
$198$	−1.60085	+	10.1074i	−0.113767	+	0.718299i
$199$	−21.7153			−1.53936			−0.769678	−	0.638432i	$-0.779583\pi$
$199$	−21.7153			−1.53936			−0.769678	+	0.638432i	$0.779583\pi$
$200$	−0.107356	+	14.1417i	−0.00759122	+	0.999971i
$201$	−5.70820			−0.402626
$202$	0.642937	−	4.05934i	0.0452369	−	0.285615i
$203$	11.7082	−	11.7082i	0.821755	−	0.821755i
$204$	−2.35114	−	0.763932i	−0.164613	−	0.0534859i
$205$	6.71040	−	10.8576i	0.468674	−	0.758331i
$206$	3.94427	+	5.42882i	0.274810	+	0.378244i
$207$	−9.51057	+	9.51057i	−0.661030	+	0.661030i
$208$	0.642937	+	4.05934i	0.0445797	+	0.281465i
$209$			6.47214i			0.447687i
$210$	−5.63522	−	4.85004i	−0.388867	−	0.334685i
$211$	2.29180			0.157774			0.0788869	−	0.996884i	$-0.474863\pi$
$211$	2.29180			0.157774			0.0788869	+	0.996884i	$0.474863\pi$
$212$	−3.95199	−	7.75621i	−0.271424	−	0.532699i
$213$	7.05342	+	7.05342i	0.483293	+	0.483293i
$214$	−1.06957	−	1.47214i	−0.0731143	−	0.100633i
$215$	−3.35520	−	14.2128i	−0.228823	−	0.969308i
$216$	−4.00000	−	12.3107i	−0.272166	−	0.837639i
$217$	16.1803	+	16.1803i	1.09839	+	1.09839i
$218$	−20.4797	−	3.24367i	−1.38706	−	0.219689i
$219$			5.81966i			0.393256i
$220$	−11.0403	+	9.35706i	−0.744336	+	0.630853i
$221$		−	1.45309i		−	0.0977451i
$222$	0.198678	−	1.25441i	0.0133344	−	0.0841903i
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	0.998889	−	0.0471263i	$-0.0150063\pi$
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	−0.0471263	+	0.998889i	$0.515006\pi$
$224$	15.2169			1.01672
$225$	10.0000	−	5.00000i	0.666667	−	0.333333i
$226$	−14.0902	+	10.2371i	−0.937264	+	0.680962i
$227$	−9.38197	−	9.38197i	−0.622703	−	0.622703i	0.323519	−	0.946222i	$-0.395134\pi$
$227$	−9.38197	−	9.38197i	−0.622703	−	0.622703i	−0.946222	+	0.323519i	$0.895134\pi$
$228$	−1.58721	−	3.11507i	−0.105115	−	0.206301i
$229$	7.95148			0.525449			0.262724	−	0.964871i	$-0.415379\pi$
$229$	7.95148			0.525449			0.262724	+	0.964871i	$0.415379\pi$
$230$	−18.9680	+	1.42040i	−1.25071	+	0.0936581i
$231$		−	7.60845i		−	0.500599i
$232$	15.5124	+	7.90398i	1.01844	+	0.518922i
$233$	5.47214	−	5.47214i	0.358492	−	0.358492i	−0.504765	−	0.863257i	$-0.668421\pi$
$233$	5.47214	−	5.47214i	0.358492	−	0.358492i	0.863257	+	0.504765i	$0.168421\pi$
$234$	2.62866	−	1.90983i	0.171841	−	0.124849i
$235$	−2.43769	−	10.3262i	−0.159018	−	0.673609i
$236$	0.291796	−	0.898056i	0.0189943	−	0.0584585i
$237$	1.79611	−	1.79611i	0.116670	−	0.116670i
$238$	−5.31375	−	0.841616i	−0.344439	−	0.0545538i
$239$	−13.4208			−0.868119			−0.434059	−	0.900884i	$-0.642919\pi$
$239$	−13.4208			−0.868119			−0.434059	+	0.900884i	$0.642919\pi$
$240$	3.01905	−	7.21110i	0.194879	−	0.465474i
$241$	11.2361			0.723779			0.361889	−	0.932221i	$-0.382132\pi$
$241$	11.2361			0.723779			0.361889	+	0.932221i	$0.382132\pi$
$242$	0.737322	+	0.116780i	0.0473968	+	0.00750692i
$243$	−11.3820	+	11.3820i	−0.730153	+	0.730153i
$244$	−0.555029	+	1.70820i	−0.0355321	+	0.109357i
$245$	−0.449028	−	0.277515i	−0.0286873	−	0.0177298i
$246$	−5.70820	+	4.14725i	−0.363942	+	0.264419i
$247$	1.45309	−	1.45309i	0.0924576	−	0.0924576i
$248$	−10.9230	+	21.4377i	−0.693613	+	1.36129i
$249$			8.18034i			0.518408i
$250$	15.3315	+	3.86592i	0.969649	+	0.244502i
$251$	0.180340			0.0113830			0.00569148	−	0.999984i	$-0.498188\pi$
$251$	0.180340			0.0113830			0.00569148	+	0.999984i	$0.498188\pi$
$252$	−5.46151	−	10.7188i	−0.344043	−	0.675223i
$253$	−13.7638	−	13.7638i	−0.865324	−	0.865324i
$254$	−4.53077	+	3.29180i	−0.284286	+	0.206546i
$255$	−1.45309	+	2.35114i	−0.0909957	+	0.147234i
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	5.29180	+	5.29180i	0.330093	+	0.330093i	0.852622	−	0.522529i	$-0.175011\pi$
$257$	5.29180	+	5.29180i	0.330093	+	0.330093i	−0.522529	+	0.852622i	$0.675011\pi$
$258$	−1.26284	+	7.97323i	−0.0786207	+	0.496392i
$259$		−	2.76393i		−	0.171742i
$260$	4.57949	+	0.377909i	0.284008	+	0.0234369i
$261$		−	13.7638i		−	0.851959i
$262$	−19.1477	−	3.03269i	−1.18295	−	0.187360i
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	0.436893	−	0.899514i	$-0.356079\pi$
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	−0.899514	+	0.436893i	$0.856079\pi$
$264$	7.60845	−	2.47214i	0.468268	−	0.152149i
$265$	−9.47214	+	2.23607i	−0.581869	+	0.137361i
$266$	−4.47214	−	6.15537i	−0.274204	−	0.377410i
$267$	1.52786	+	1.52786i	0.0935038	+	0.0935038i
$268$	−5.92992	−	11.6381i	−0.362228	−	0.710912i
$269$	20.4742			1.24833			0.624167	−	0.781291i	$-0.285438\pi$
$269$	20.4742			1.24833			0.624167	+	0.781291i	$0.285438\pi$
$270$	−14.4317	+	1.08070i	−0.878287	+	0.0657694i
$271$			17.2250i			1.04635i	0.852227	+	0.523173i	$0.175252\pi$
$271$			17.2250i			1.04635i	−0.852227	+	0.523173i	$0.824748\pi$
$272$	−0.884927	−	5.58721i	−0.0536566	−	0.338774i
$273$	−1.70820	+	1.70820i	−0.103385	+	0.103385i
$274$	6.43288	+	8.85410i	0.388625	+	0.534896i
$275$	7.23607	+	14.4721i	0.436351	+	0.872703i
$276$	10.0000	+	3.24920i	0.601929	+	0.195579i
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	−0.927811	−	0.373051i	$-0.878312\pi$
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	0.373051	+	0.927811i	$0.378312\pi$
$278$	4.73799	−	29.9145i	0.284166	−	1.79415i
$279$	19.0211			1.13877
$280$	4.03437	−	16.5278i	0.241100	−	0.987722i
$281$	−9.70820			−0.579143			−0.289571	−	0.957156i	$-0.593513\pi$
$281$	−9.70820			−0.579143			−0.289571	+	0.957156i	$0.593513\pi$
$282$	−0.917504	+	5.79289i	−0.0546366	+	0.344962i
$283$	13.3820	−	13.3820i	0.795475	−	0.795475i	−0.186903	−	0.982378i	$-0.559845\pi$
$283$	13.3820	−	13.3820i	0.795475	−	0.795475i	0.982378	+	0.186903i	$0.0598450\pi$
$284$	−7.05342	+	21.7082i	−0.418544	+	1.28814i
$285$	−3.80423	+	0.898056i	−0.225343	+	0.0531962i
$286$	2.76393	+	3.80423i	0.163435	+	0.224949i
$287$	−10.8576	+	10.8576i	−0.640907	+	0.640907i
$288$	8.94427	−	8.94427i	0.527046	−	0.527046i
$289$		−	15.0000i		−	0.882353i
$290$	12.6976	−	14.7532i	0.745628	−	0.866338i
$291$	5.23607			0.306944
$292$	−11.8654	+	6.04571i	−0.694368	+	0.353798i
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	0.791269	−	0.611469i	$-0.209421\pi$
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	−0.611469	+	0.791269i	$0.709421\pi$
$294$	0.171513	+	0.236068i	0.0100029	+	0.0137678i
$295$	−0.898056	−	0.555029i	−0.0522868	−	0.0323150i
$296$	2.76393	−	0.898056i	0.160650	−	0.0521984i
$297$	−10.4721	−	10.4721i	−0.607655	−	0.607655i
$298$	17.9709	+	2.84632i	1.04103	+	0.164883i
$299$			6.18034i			0.357418i
$300$	−7.03186	−	5.19096i	−0.405985	−	0.299700i
$301$			17.5680i			1.01261i
$302$	−1.48455	+	9.37310i	−0.0854264	+	0.539361i
$303$	1.79611	+	1.79611i	0.103184	+	0.103184i
$304$	4.70228	−	6.47214i	0.269694	−	0.371202i
$305$	1.70820	+	1.05573i	0.0978115	+	0.0604508i
$306$	−3.61803	+	2.62866i	−0.206829	+	0.150270i
$307$	−13.5623	−	13.5623i	−0.774042	−	0.774042i	0.204769	−	0.978810i	$-0.434356\pi$
$307$	−13.5623	−	13.5623i	−0.774042	−	0.774042i	−0.978810	+	0.204769i	$0.934356\pi$
$308$	15.5124	−	7.90398i	0.883903	−	0.450371i
$309$	−4.14725			−0.235929
$310$	20.3884	+	17.5476i	1.15798	+	0.996638i
$311$		−	20.8172i		−	1.18044i	−0.807243	−	0.590219i	$-0.799041\pi$
$311$		−	20.8172i		−	1.18044i	0.807243	−	0.590219i	$-0.200959\pi$
$312$	−2.26323	−	1.15317i	−0.128130	−	0.0652857i
$313$	−1.76393	+	1.76393i	−0.0997033	+	0.0997033i	−0.755199	−	0.655496i	$-0.772460\pi$
$313$	−1.76393	+	1.76393i	−0.0997033	+	0.0997033i	0.655496	+	0.755199i	$0.272460\pi$
$314$	22.5478	−	16.3820i	1.27245	−	0.924488i
$315$	−13.0902	+	3.09017i	−0.737548	+	0.174111i
$316$	5.52786	+	1.79611i	0.310967	+	0.101039i
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	−0.809886	−	0.586587i	$-0.800471\pi$
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	0.586587	+	0.809886i	$0.300471\pi$
$318$	5.31375	+	0.841616i	0.297980	+	0.0471955i
$319$	19.9192			1.11526
$320$	17.8386	−	1.33582i	0.997208	−	0.0746746i
$321$	1.12461			0.0627697
$322$	22.6007	+	3.57960i	1.25949	+	0.199484i
$323$	−2.00000	+	2.00000i	−0.111283	+	0.111283i
$324$	−5.15131	−	1.67376i	−0.286184	−	0.0929868i
$325$	1.62460	−	4.87380i	0.0901165	−	0.270350i
$326$	22.4164	−	16.2865i	1.24153	−	0.902024i
$327$	9.06154	−	9.06154i	0.501104	−	0.501104i
$328$	−14.3855	−	7.32979i	−0.794307	−	0.404720i
$329$			12.7639i			0.703698i
$330$	−0.667910	−	8.91930i	−0.0367672	−	0.490991i
$331$	−30.0689			−1.65274			−0.826368	−	0.563131i	$-0.809597\pi$
$331$	−30.0689			−1.65274			−0.826368	+	0.563131i	$0.809597\pi$
$332$	−16.6784	+	8.49808i	−0.915347	+	0.466393i
$333$	−1.62460	−	1.62460i	−0.0890274	−	0.0890274i
$334$	−13.0373	+	9.47214i	−0.713368	+	0.518292i
$335$	−14.2128	+	3.35520i	−0.776531	+	0.183314i
$336$	−5.52786	+	7.60845i	−0.301570	+	0.415075i
$337$	−19.9443	−	19.9443i	−1.08643	−	1.08643i	−0.995893	−	0.0905410i	$-0.971140\pi$
$337$	−19.9443	−	19.9443i	−1.08643	−	1.08643i	−0.0905410	−	0.995893i	$-0.528860\pi$
$338$	−2.64245	+	16.6838i	−0.143730	+	0.907478i
$339$		−	10.7639i		−	0.584617i
$340$	−6.30313	−	0.520147i	−0.341835	−	0.0282089i
$341$			27.5276i			1.49071i
$342$	−6.24669	−	0.989378i	−0.337782	−	0.0534995i
$343$	−12.8658	−	12.8658i	−0.694686	−	0.694686i
$344$	−17.5680	+	5.70820i	−0.947206	+	0.307766i
$345$	6.18034	−	10.0000i	0.332738	−	0.538382i
$346$	−17.0344	−	23.4459i	−0.915777	−	1.26046i
$347$	26.0344	+	26.0344i	1.39760	+	1.39760i	0.806862	+	0.590740i	$0.201164\pi$
$347$	26.0344	+	26.0344i	1.39760	+	1.39760i	0.590740	+	0.806862i	$0.298836\pi$
$348$	−9.58721	+	4.88493i	−0.513928	+	0.261860i
$349$	−16.6700			−0.892324			−0.446162	−	0.894952i	$-0.647209\pi$
$349$	−16.6700			−0.892324			−0.446162	+	0.894952i	$0.647209\pi$
$350$	−16.8819	−	8.76382i	−0.902376	−	0.468446i
$351$			4.70228i			0.250989i
$352$	12.9443	+	12.9443i	0.689932	+	0.689932i
$353$	−22.4164	+	22.4164i	−1.19311	+	1.19311i	−0.216914	+	0.976191i	$0.569599\pi$
$353$	−22.4164	+	22.4164i	−1.19311	+	1.19311i	−0.976191	+	0.216914i	$0.930401\pi$
$354$	0.343027	+	0.472136i	0.0182317	+	0.0250937i
$355$	21.7082	+	13.4164i	1.15215	+	0.712069i
$356$	−1.52786	+	4.70228i	−0.0809766	+	0.249220i
$357$	2.35114	−	2.35114i	0.124436	−	0.124436i
$358$	−1.66540	+	10.5149i	−0.0880193	+	0.555732i
$359$	19.9192			1.05129			0.525647	−	0.850703i	$-0.323823\pi$
$359$	19.9192			1.05129			0.525647	+	0.850703i	$0.323823\pi$
$360$	−7.34342	−	12.0861i	−0.387032	−	0.636994i
$361$	15.0000			0.789474
$362$	−3.36646	+	21.2550i	−0.176937	+	1.11714i
$363$	−0.326238	+	0.326238i	−0.0171231	+	0.0171231i
$364$	−5.25731	−	1.70820i	−0.275558	−	0.0895342i
$365$	3.42071	+	14.4904i	0.179048	+	0.758460i
$366$	−0.652476	−	0.898056i	−0.0341055	−	0.0469421i
$367$	12.2047	−	12.2047i	0.637082	−	0.637082i	−0.312753	−	0.949835i	$-0.601251\pi$
$367$	12.2047	−	12.2047i	0.637082	−	0.637082i	0.949835	+	0.312753i	$0.101251\pi$
$368$	3.76382	+	23.7638i	0.196203	+	1.23877i
$369$			12.7639i			0.664464i
$370$	−0.242632	−	3.24013i	−0.0126139	−	0.168446i
$371$	11.7082			0.607860
$372$	−6.75080	−	13.2492i	−0.350013	−	0.686939i
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.984038	−	0.177956i	$-0.943052\pi$
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.177956	−	0.984038i	$-0.556948\pi$
$374$	−3.80423	−	5.23607i	−0.196712	−	0.270751i
$375$	−7.50245	+	6.26137i	−0.387425	+	0.323336i
$376$	−12.7639	+	4.14725i	−0.658250	+	0.213878i
$377$	−4.47214	−	4.47214i	−0.230327	−	0.230327i
$378$	17.1957	+	2.72353i	0.884449	+	0.140083i
$379$			0.111456i			0.00572512i	0.999996	+	0.00286256i	$0.000911182\pi$
$379$			0.111456i			0.00572512i	−0.999996	+	0.00286256i	$0.999089\pi$
$380$	−5.78298	−	6.82328i	−0.296661	−	0.350027i
$381$		−	3.46120i		−	0.177323i
$382$	2.92220	−	18.4501i	0.149513	−	0.943988i
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	0.680989	−	0.732294i	$-0.261550\pi$
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	−0.732294	+	0.680989i	$0.761550\pi$
$384$	−9.40456	−	3.05573i	−0.479925	−	0.155937i
$385$	−4.47214	−	18.9443i	−0.227921	−	0.965489i
$386$	−2.38197	+	1.73060i	−0.121239	+	0.0880852i
$387$	10.3262	+	10.3262i	0.524912	+	0.524912i
$388$	5.43945	+	10.6755i	0.276146	+	0.541967i
$389$	−4.14725			−0.210274			−0.105137	−	0.994458i	$-0.533528\pi$
$389$	−4.14725			−0.210274			−0.105137	+	0.994458i	$0.533528\pi$
$390$	−1.85255	+	2.15246i	−0.0938076	+	0.108994i
$391$		−	8.50651i		−	0.430193i
$392$	−0.303130	+	0.594926i	−0.0153104	+	0.0300483i
$393$	8.47214	−	8.47214i	0.427363	−	0.427363i
$394$	−14.9394	+	10.8541i	−0.752636	+	0.546822i
$395$	3.41641	−	5.52786i	0.171898	−	0.278137i
$396$	4.47214	−	13.7638i	0.224733	−	0.691658i
$397$	24.4500	−	24.4500i	1.22711	−	1.22711i	0.262055	−	0.965053i	$-0.415600\pi$
$397$	24.4500	−	24.4500i	1.22711	−	1.22711i	0.965053	−	0.262055i	$-0.0844002\pi$
$398$	30.3320	+	4.80411i	1.52040	+	0.240808i
$399$	4.70228			0.235409
$400$	3.27855	−	19.7294i	0.163928	−	0.986472i
$401$	31.8885			1.59244			0.796219	−	0.605009i	$-0.206830\pi$
$401$	31.8885			1.59244			0.796219	+	0.605009i	$0.206830\pi$
$402$	7.97323	+	1.26284i	0.397669	+	0.0629845i
$403$	6.18034	−	6.18034i	0.307865	−	0.307865i
$404$	−1.79611	+	5.52786i	−0.0893599	+	0.275022i
$405$	−3.18368	+	5.15131i	−0.158199	+	0.255971i
$406$	−18.9443	+	13.7638i	−0.940188	+	0.683087i
$407$	2.35114	−	2.35114i	0.116542	−	0.116542i
$408$	3.11507	+	1.58721i	0.154219	+	0.0785786i
$409$		−	21.5967i		−	1.06789i	−0.845519	−	0.533945i	$-0.820709\pi$
$409$		−	21.5967i		−	1.06789i	0.845519	−	0.533945i	$-0.179291\pi$
$410$	−11.7752	+	13.6814i	−0.581533	+	0.675678i
$411$	−6.76393			−0.333640
$412$	−4.30834	−	8.45559i	−0.212257	−	0.416577i
$413$	0.898056	+	0.898056i	0.0441904	+	0.0441904i
$414$	15.3884	−	11.1803i	0.756299	−	0.549484i
$415$	4.80828	+	20.3682i	0.236029	+	0.999836i
$416$		−	5.81234i		−	0.284973i
$417$	13.2361	+	13.2361i	0.648173	+	0.648173i
$418$	1.43184	−	9.04029i	0.0700337	−	0.442175i
$419$		−	28.8328i		−	1.40858i	−0.709915	−	0.704288i	$-0.751267\pi$
$419$		−	28.8328i		−	1.40858i	0.709915	−	0.704288i	$-0.248733\pi$
$420$	6.79830	+	8.02124i	0.331723	+	0.391397i
$421$			28.4257i			1.38538i	0.721234	+	0.692692i	$0.243575\pi$
$421$			28.4257i			1.38538i	−0.721234	+	0.692692i	$0.756425\pi$
$422$	−3.20119	−	0.507018i	−0.155831	−	0.0246813i
$423$	7.50245	+	7.50245i	0.364782	+	0.364782i
$424$	3.80423	+	11.7082i	0.184750	+	0.568601i
$425$	−2.23607	+	6.70820i	−0.108465	+	0.325396i
$426$	−8.29180	−	11.4127i	−0.401739	−	0.552946i
$427$	−1.70820	−	1.70820i	−0.0826658	−	0.0826658i
$428$	1.16829	+	2.29291i	0.0564716	+	0.110832i
$429$	−2.90617			−0.140311
$430$	1.54222	+	20.5948i	0.0743722	+	0.993170i
$431$		−	19.0211i		−	0.916216i	−0.888897	−	0.458108i	$-0.848527\pi$
$431$		−	19.0211i		−	0.916216i	0.888897	−	0.458108i	$-0.151473\pi$
$432$	2.86368	+	18.0806i	0.137779	+	0.869903i
$433$	0.819660	−	0.819660i	0.0393904	−	0.0393904i	−0.687137	−	0.726528i	$-0.741133\pi$
$433$	0.819660	−	0.819660i	0.0393904	−	0.0393904i	0.726528	+	0.687137i	$0.241133\pi$
$434$	−19.0211	−	26.1803i	−0.913043	−	1.25670i
$435$	2.76393	+	11.7082i	0.132520	+	0.561365i
$436$	27.8885	+	9.06154i	1.33562	+	0.433969i
$437$	8.50651	−	8.50651i	0.406921	−	0.406921i
$438$	1.28749	−	8.12891i	0.0615188	−	0.388415i
$439$	−35.1361			−1.67695			−0.838477	−	0.544937i	$-0.816554\pi$
$439$	−35.1361			−1.67695			−0.838477	+	0.544937i	$0.816554\pi$
$440$	17.4912	−	10.6275i	0.833860	−	0.506646i
$441$	0.527864			0.0251364
$442$	−0.321469	+	2.02967i	−0.0152907	+	0.0965417i
$443$	−1.09017	+	1.09017i	−0.0517955	+	0.0517955i	−0.732530	−	0.680735i	$-0.761661\pi$
$443$	−1.09017	+	1.09017i	−0.0517955	+	0.0517955i	0.680735	+	0.732530i	$0.261661\pi$
$444$	−0.555029	+	1.70820i	−0.0263405	+	0.0810678i
$445$	4.70228	+	2.90617i	0.222910	+	0.137766i
$446$	−16.7082	−	22.9969i	−0.791156	−	1.08893i
$447$	−7.95148	+	7.95148i	−0.376092	+	0.376092i
$448$	−21.2550	−	3.36646i	−1.00420	−	0.159050i
$449$			17.5967i			0.830442i	0.909721	+	0.415221i	$0.136296\pi$
$449$			17.5967i			0.830442i	−0.909721	+	0.415221i	$0.863704\pi$
$450$	−15.0742	+	4.77169i	−0.710604	+	0.224940i
$451$	−18.4721			−0.869819
$452$	21.9460	−	11.1820i	1.03225	−	0.525958i
$453$	−4.14725	−	4.14725i	−0.194855	−	0.194855i
$454$	11.0292	+	15.1803i	0.517624	+	0.712449i
$455$	−3.24920	+	5.25731i	−0.152325	+	0.246467i
$456$	1.52786	+	4.70228i	0.0715488	+	0.220205i
$457$	9.65248	+	9.65248i	0.451524	+	0.451524i	0.895860	−	0.444336i	$-0.146560\pi$
$457$	9.65248	+	9.65248i	0.451524	+	0.451524i	−0.444336	+	0.895860i	$0.646560\pi$
$458$	−11.1066	−	1.75912i	−0.518979	−	0.0821983i
$459$		−	6.47214i		−	0.302093i
$460$	26.8088	+	2.21232i	1.24997	+	0.103150i
$461$		−	27.5276i		−	1.28209i	−0.767503	−	0.641045i	$-0.778501\pi$
$461$		−	27.5276i		−	1.28209i	0.767503	−	0.641045i	$-0.221499\pi$
$462$	−1.68323	+	10.6275i	−0.0783110	+	0.494436i
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	0.761894	−	0.647701i	$-0.224270\pi$
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	−0.647701	+	0.761894i	$0.724270\pi$
$464$	−19.9192	−	14.4721i	−0.924725	−	0.671852i
$465$	−16.1803	+	3.81966i	−0.750345	+	0.177132i
$466$	−8.85410	+	6.43288i	−0.410158	+	0.297997i
$467$	−18.3262	−	18.3262i	−0.848037	−	0.848037i	0.141851	−	0.989888i	$-0.454695\pi$
$467$	−18.3262	−	18.3262i	−0.848037	−	0.848037i	−0.989888	+	0.141851i	$0.954695\pi$
$468$	−4.09423	+	2.08611i	−0.189256	+	0.0964306i
$469$	17.5680			0.811217
$470$	1.12048	+	14.9630i	0.0516841	+	0.690192i
$471$			17.2250i			0.793687i
$472$	−0.606260	+	1.18985i	−0.0279054	+	0.0547674i
$473$	−14.9443	+	14.9443i	−0.687138	+	0.687138i
$474$	−2.90617	+	2.11146i	−0.133485	+	0.0969824i
$475$	−8.94427	+	4.47214i	−0.410391	+	0.205196i
$476$	7.23607	+	2.35114i	0.331665	+	0.107764i
$477$	6.88191	−	6.88191i	0.315101	−	0.315101i
$478$	18.7462	+	2.96911i	0.857431	+	0.135804i
$479$	−4.70228			−0.214853			−0.107426	−	0.994213i	$-0.534261\pi$
$479$	−4.70228			−0.214853			−0.107426	+	0.994213i	$0.534261\pi$
$480$	−5.81234	+	9.40456i	−0.265296	+	0.429258i
$481$	−1.05573			−0.0481371
$482$	−15.6946	−	2.48577i	−0.714868	−	0.113224i
$483$	−10.0000	+	10.0000i	−0.455016	+	0.455016i
$484$	−1.00406	−	0.326238i	−0.0456390	−	0.0148290i
$485$	13.0373	−	3.07768i	0.591992	−	0.139750i
$486$	18.4164	−	13.3803i	0.835385	−	0.606943i
$487$	−18.9151	+	18.9151i	−0.857126	+	0.857126i	−0.990999	−	0.133872i	$-0.957259\pi$
$487$	−18.9151	+	18.9151i	−0.857126	+	0.857126i	0.133872	+	0.990999i	$0.457259\pi$
$488$	1.15317	−	2.26323i	0.0522018	−	0.102452i
$489$			17.1246i			0.774402i
$490$	0.565808	+	0.486972i	0.0255606	+	0.0219992i
$491$	−15.2361			−0.687594			−0.343797	−	0.939044i	$-0.611713\pi$
$491$	−15.2361			−0.687594			−0.343797	+	0.939044i	$0.611713\pi$
$492$	8.89074	−	4.53006i	0.400825	−	0.204231i
$493$	6.15537	+	6.15537i	0.277224	+	0.277224i
$494$	−2.35114	+	1.70820i	−0.105783	+	0.0768557i
$495$	−13.7638	−	8.50651i	−0.618638	−	0.382339i
$496$	20.0000	−	27.5276i	0.898027	−	1.23603i
$497$	−21.7082	−	21.7082i	−0.973746	−	0.973746i
$498$	1.80975	−	11.4263i	0.0810969	−	0.512026i
$499$			11.8885i			0.532204i	0.963945	+	0.266102i	$0.0857359\pi$
$499$			11.8885i			0.532204i	−0.963945	+	0.266102i	$0.914264\pi$
$500$	−20.5598	−	8.79174i	−0.919462	−	0.393179i
$501$		−	9.95959i		−	0.444962i
$502$	−0.251899	−	0.0398969i	−0.0112428	−	0.00178069i
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	0.972298	−	0.233746i	$-0.0750984\pi$
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	−0.233746	+	0.972298i	$0.575098\pi$
$504$	5.25731	+	16.1803i	0.234179	+	0.720730i
$505$	5.52786	+	3.41641i	0.245987	+	0.152028i
$506$	16.1803	+	22.2703i	0.719304	+	0.990037i
$507$	−7.38197	−	7.38197i	−0.327845	−	0.327845i
$508$	7.05684	−	3.59564i	0.313097	−	0.159531i
$509$	−10.8576			−0.481257			−0.240628	−	0.970617i	$-0.577354\pi$
$509$	−10.8576			−0.481257			−0.240628	+	0.970617i	$0.577354\pi$
$510$	2.54982	−	2.96261i	0.112908	−	0.131187i
$511$		−	17.9111i		−	0.792339i
$512$	−3.53971	−	22.3488i	−0.156434	−	0.987688i
$513$	6.47214	−	6.47214i	0.285752	−	0.285752i
$514$	−6.22088	−	8.56231i	−0.274391	−	0.377667i
$515$	−10.3262	+	2.43769i	−0.455028	+	0.107418i
$516$	3.52786	−	10.8576i	0.155306	−	0.477981i
$517$	−10.8576	+	10.8576i	−0.477519	+	0.477519i
$518$	−0.611469	+	3.86067i	−0.0268664	+	0.169628i
$519$	17.9111			0.786209
$520$	−6.31304	−	1.54099i	−0.276845	−	0.0675770i
$521$	−0.472136			−0.0206847			−0.0103423	−	0.999947i	$-0.503292\pi$
$521$	−0.472136			−0.0206847			−0.0103423	+	0.999947i	$0.503292\pi$
$522$	−3.04499	+	19.2253i	−0.133276	+	0.841470i
$523$	25.7426	−	25.7426i	1.12565	−	1.12565i	0.134770	−	0.990877i	$-0.456970\pi$
$523$	25.7426	−	25.7426i	1.12565	−	1.12565i	0.990877	−	0.134770i	$-0.0430297\pi$
$524$	26.0746	+	8.47214i	1.13907	+	0.370107i
$525$	10.5146	−	5.25731i	0.458896	−	0.229448i
$526$	8.81966	+	12.1392i	0.384555	+	0.529295i
$527$	−8.50651	+	8.50651i	−0.370549	+	0.370549i
$528$	−11.1744	+	1.76985i	−0.486304	+	0.0770230i
$529$			13.1803i			0.573058i
$530$	13.7254	−	1.02781i	0.596193	−	0.0446451i
$531$	1.05573			0.0458147
$532$	4.88493	+	9.58721i	0.211788	+	0.415658i
$533$	4.14725	+	4.14725i	0.179637	+	0.179637i
$534$	−1.79611	−	2.47214i	−0.0777254	−	0.106980i
$535$	2.80017	−	0.661030i	0.121062	−	0.0285788i
$536$	5.70820	+	17.5680i	0.246557	+	0.758824i
$537$	−4.65248	−	4.65248i	−0.200769	−	0.200769i
$538$	−28.5984	−	4.52955i	−1.23297	−	0.195283i
$539$			0.763932i			0.0329049i
$540$	20.3974	+	1.68323i	0.877762	+	0.0724347i
$541$			12.3107i			0.529280i	0.964347	+	0.264640i	$0.0852531\pi$
$541$			12.3107i			0.529280i	−0.964347	+	0.264640i	$0.914747\pi$
$542$	3.81072	−	24.0599i	0.163684	−	1.03346i
$543$	−9.40456	−	9.40456i	−0.403588	−	0.403588i
$544$			8.00000i			0.342997i
$545$	17.2361	−	27.8885i	0.738312	−	1.19461i
$546$	2.76393	−	2.00811i	0.118285	−	0.0859394i
$547$	11.5623	+	11.5623i	0.494369	+	0.494369i	0.909679	−	0.415311i	$-0.136327\pi$
$547$	11.5623	+	11.5623i	0.494369	+	0.494369i	−0.415311	+	0.909679i	$0.636327\pi$
$548$	−7.02666	−	13.7906i	−0.300164	−	0.589105i
$549$	−2.00811			−0.0857042
$550$	−6.90566	−	21.8156i	−0.294458	−	0.930219i
$551$			12.3107i			0.524455i
$552$	−13.2492	−	6.75080i	−0.563923	−	0.287333i
$553$	−5.52786	+	5.52786i	−0.235069	+	0.235069i
$554$	14.9394	−	10.8541i	0.634714	−	0.461147i
$555$	1.70820	+	1.05573i	0.0725092	+	0.0448132i
$556$	−13.2361	+	40.7364i	−0.561334	+	1.72761i
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	−0.999998	−	0.00207187i	$-0.999341\pi$
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	0.00207187	+	0.999998i	$0.499341\pi$
$558$	−26.5688	−	4.20808i	−1.12475	−	0.178142i
$559$	6.71040			0.283820
$560$	−9.29168	+	22.1935i	−0.392645	+	0.937845i
$561$	4.00000			0.168880
$562$	13.5604	+	2.14776i	0.572013	+	0.0905979i
$563$	−4.32624	+	4.32624i	−0.182329	+	0.182329i	−0.792370	−	0.610041i	$-0.791153\pi$
$563$	−4.32624	+	4.32624i	−0.182329	+	0.182329i	0.610041	+	0.792370i	$0.291153\pi$
$564$	2.56314	−	7.88854i	0.107928	−	0.332168i
$565$	−6.32688	−	26.8011i	−0.266174	−	1.12753i
$566$	−21.6525	+	15.7314i	−0.910121	+	0.661242i
$567$	5.15131	−	5.15131i	0.216335	−	0.216335i
$568$	14.6548	−	28.7616i	0.614901	−	1.20681i
$569$		−	27.1246i		−	1.13712i	−0.822641	−	0.568561i	$-0.807500\pi$
$569$		−	27.1246i		−	1.13712i	0.822641	−	0.568561i	$-0.192500\pi$
$570$	5.51243	−	0.412791i	0.230890	−	0.0172899i
$571$	22.6525			0.947977			0.473988	−	0.880531i	$-0.342814\pi$
$571$	22.6525			0.947977			0.473988	+	0.880531i	$0.342814\pi$
$572$	−3.01905	−	5.92522i	−0.126233	−	0.247746i
$573$	8.16348	+	8.16348i	0.341034	+	0.341034i
$574$	17.5680	−	12.7639i	0.733276	−	0.532756i
$575$	9.51057	−	28.5317i	0.396618	−	1.18985i
$576$	−14.4721	+	10.5146i	−0.603006	+	0.438109i
$577$	26.2361	+	26.2361i	1.09222	+	1.09222i	0.995291	+	0.0969307i	$0.0309025\pi$
$577$	26.2361	+	26.2361i	1.09222	+	1.09222i	0.0969307	+	0.995291i	$0.469097\pi$
$578$	−3.31848	+	20.9520i	−0.138030	+	0.871490i
$579$		−	1.81966i		−	0.0756225i
$580$	−20.9999	+	17.7982i	−0.871973	+	0.739030i
$581$		−	25.1765i		−	1.04450i
$582$	−7.31375	−	1.15838i	−0.303165	−	0.0480166i
$583$	9.95959	+	9.95959i	0.412484	+	0.412484i
$584$	17.9111	−	5.81966i	0.741165	−	0.240819i
$585$	1.18034	+	5.00000i	0.0488010	+	0.206725i
$586$	−3.61803	−	4.97980i	−0.149460	−	0.205714i
$587$	17.0902	+	17.0902i	0.705387	+	0.705387i	0.965562	−	0.260175i	$-0.0837802\pi$
$587$	17.0902	+	17.0902i	0.705387	+	0.705387i	−0.260175	+	0.965562i	$0.583780\pi$
$588$	−0.187345	−	0.367684i	−0.00772596	−	0.0151631i
$589$	−17.0130			−0.701009
$590$	1.13162	+	0.973944i	0.0465879	+	0.0400967i
$591$		−	11.4127i		−	0.469455i
$592$	−4.05934	+	0.642937i	−0.166838	+	0.0264246i
$593$	20.4164	−	20.4164i	0.838401	−	0.838401i	−0.150247	−	0.988648i	$-0.548007\pi$
$593$	20.4164	−	20.4164i	0.838401	−	0.838401i	0.988648	+	0.150247i	$0.0480069\pi$
$594$	12.3107	+	16.9443i	0.505116	+	0.695232i
$595$	4.47214	−	7.23607i	0.183340	−	0.296650i
$596$	−24.4721	−	7.95148i	−1.00242	−	0.325705i
$597$	−13.4208	+	13.4208i	−0.549276	+	0.549276i
$598$	1.36729	−	8.63271i	0.0559125	−	0.353018i
$599$	6.49839			0.265517			0.132759	−	0.991148i	$-0.457617\pi$
$599$	6.49839			0.265517			0.132759	+	0.991148i	$0.457617\pi$
$600$	8.67372	+	8.80642i	0.354103	+	0.359521i
$601$	−17.7082			−0.722333			−0.361166	−	0.932501i	$-0.617621\pi$
$601$	−17.7082			−0.722333			−0.361166	+	0.932501i	$0.617621\pi$
$602$	3.88661	−	24.5391i	0.158406	−	1.00014i
$603$	10.3262	−	10.3262i	0.420517	−	0.420517i
$604$	4.14725	−	12.7639i	0.168749	−	0.519357i
$605$	−0.620541	+	1.00406i	−0.0252286	+	0.0408207i
$606$	−2.11146	−	2.90617i	−0.0857720	−	0.118055i
$607$	32.6789	−	32.6789i	1.32640	−	1.32640i	0.417908	−	0.908489i	$-0.362763\pi$
$607$	32.6789	−	32.6789i	1.32640	−	1.32640i	0.908489	−	0.417908i	$-0.137237\pi$
$608$	−8.00000	+	8.00000i	−0.324443	+	0.324443i
$609$		−	14.4721i		−	0.586441i
$610$	−2.15246	−	1.85255i	−0.0871507	−	0.0750077i
$611$	4.87539			0.197237
$612$	5.63522	−	2.87129i	0.227790	−	0.116065i
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	0.981337	−	0.192298i	$-0.0615941\pi$
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	−0.192298	+	0.981337i	$0.561594\pi$
$614$	15.9434	+	21.9443i	0.643425	+	0.885599i
$615$	−2.56314	−	10.8576i	−0.103356	−	0.437823i
$616$	−23.4164	+	7.60845i	−0.943474	+	0.306553i
$617$	4.88854	+	4.88854i	0.196805	+	0.196805i	0.798629	−	0.601824i	$-0.205559\pi$
$617$	4.88854	+	4.88854i	0.196805	+	0.196805i	−0.601824	+	0.798629i	$0.705559\pi$
$618$	5.79289	+	0.917504i	0.233024	+	0.0369074i
$619$			35.3050i			1.41903i	0.704692	+	0.709513i	$0.251085\pi$
$619$			35.3050i			1.41903i	−0.704692	+	0.709513i	$0.748915\pi$
$620$	−24.5965	−	29.0211i	−0.987819	−	1.16552i
$621$			27.5276i			1.10465i
$622$	−4.60543	+	29.0776i	−0.184661	+	1.16590i
$623$	−4.70228	−	4.70228i	−0.188393	−	0.188393i
$624$	2.90617	+	2.11146i	0.116340	+	0.0845259i
$625$	−15.0000	+	20.0000i	−0.600000	+	0.800000i
$626$	2.85410	−	2.07363i	0.114073	−	0.0828788i
$627$	4.00000	+	4.00000i	0.159745	+	0.159745i
$628$	−35.1191	+	17.8941i	−1.40140	+	0.714051i
$629$	1.45309			0.0579383
$630$	18.9680	−	1.42040i	0.755704	−	0.0565899i
$631$			22.6134i			0.900223i	0.892972	+	0.450112i	$0.148616\pi$
$631$			22.6134i			0.900223i	−0.892972	+	0.450112i	$0.851384\pi$
$632$	−7.32398	−	3.73175i	−0.291332	−	0.148441i
$633$	1.41641	−	1.41641i	0.0562972	−	0.0562972i
$634$	6.43288	−	4.67376i	0.255482	−	0.185619i
$635$	−2.03444	−	8.61803i	−0.0807344	−	0.341996i
$636$	−7.23607	−	2.35114i	−0.286929	−	0.0932288i
$637$	0.171513	−	0.171513i	0.00679561	−	0.00679561i
$638$	−27.8232	−	4.40676i	−1.10153	−	0.174465i
$639$	−25.5195			−1.00954
$640$	−25.2125	−	2.08059i	−0.996612	−	0.0822425i
$641$	−38.6525			−1.52668			−0.763341	−	0.645996i	$-0.776442\pi$
$641$	−38.6525			−1.52668			−0.763341	+	0.645996i	$0.776442\pi$
$642$	−1.57086	−	0.248800i	−0.0619969	−	0.00981935i
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	−0.897331	−	0.441358i	$-0.854497\pi$
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	0.441358	+	0.897331i	$0.354497\pi$
$644$	−30.7768	−	10.0000i	−1.21278	−	0.394055i
$645$	−10.8576	−	6.71040i	−0.427520	−	0.264222i
$646$	3.23607	−	2.35114i	0.127321	−	0.0925044i
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	−0.981046	−	0.193775i	$-0.937927\pi$
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	0.193775	+	0.981046i	$0.437927\pi$
$648$	6.82507	+	3.47755i	0.268114	+	0.136611i
$649$			1.52786i			0.0599739i
$650$	−3.34748	+	6.44832i	−0.131299	+	0.252924i
$651$	20.0000			0.783862
$652$	−34.9144	+	17.7898i	−1.36735	+	0.696701i
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	0.194661	−	0.980871i	$-0.437639\pi$
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	−0.980871	+	0.194661i	$0.937639\pi$
$654$	−14.6619	+	10.6525i	−0.573325	+	0.416545i
$655$	16.1150	−	26.0746i	0.629664	−	1.01882i
$656$	18.4721	+	13.4208i	0.721216	+	0.523994i
$657$	−10.5279	−	10.5279i	−0.410731	−	0.410731i
$658$	2.82379	−	17.8287i	0.110083	−	0.695035i
$659$			18.0000i			0.701180i	0.936529	+	0.350590i	$0.114019\pi$
$659$			18.0000i			0.701180i	−0.936529	+	0.350590i	$0.885981\pi$
$660$	−1.04029	+	12.6063i	−0.0404934	+	0.490698i
$661$		−	3.80423i		−	0.147967i	−0.997259	−	0.0739836i	$-0.976429\pi$
$661$		−	3.80423i		−	0.147967i	0.997259	−	0.0739836i	$-0.0235713\pi$
$662$	42.0003	+	6.65219i	1.63239	+	0.258545i
$663$	−0.898056	−	0.898056i	−0.0348776	−	0.0348776i
$664$	25.1765	−	8.18034i	0.977038	−	0.317459i
$665$	11.7082	−	2.76393i	0.454025	−	0.107181i
$666$	1.90983	+	2.62866i	0.0740044	+	0.101858i
$667$	−26.1803	−	26.1803i	−1.01371	−	1.01371i
$668$	20.3060	−	10.3464i	0.785664	−	0.400316i
$669$	17.5680			0.679220
$670$	20.5948	−	1.54222i	0.795647	−	0.0595810i
$671$		−	2.90617i		−	0.112191i
$672$	9.40456	−	9.40456i	0.362789	−	0.362789i
$673$	−17.2918	+	17.2918i	−0.666550	+	0.666550i	−0.956916	−	0.290366i	$-0.906223\pi$
$673$	−17.2918	+	17.2918i	−0.666550	+	0.666550i	0.290366	+	0.956916i	$0.406223\pi$
$674$	23.4459	+	32.2705i	0.903102	+	1.24301i
$675$	7.23607	−	21.7082i	0.278516	−	0.835549i
$676$	7.38197	−	22.7194i	0.283922	−	0.873821i
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	−0.840625	−	0.541617i	$-0.817812\pi$
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	0.541617	+	0.840625i	$0.317812\pi$
$678$	−2.38132	+	15.0351i	−0.0914542	+	0.577419i
$679$	−16.1150			−0.618435
$680$	8.68915	+	2.12099i	0.333214	+	0.0813364i
$681$	−11.5967			−0.444388
$682$	6.08999	−	38.4507i	0.233198	−	1.47235i
$683$	−22.7984	+	22.7984i	−0.872356	+	0.872356i	−0.992729	−	0.120373i	$-0.961591\pi$
$683$	−22.7984	+	22.7984i	−0.872356	+	0.872356i	0.120373	+	0.992729i	$0.461591\pi$
$684$	8.50651	+	2.76393i	0.325254	+	0.105682i
$685$	−16.8415	+	3.97574i	−0.643481	+	0.151905i
$686$	15.1246	+	20.8172i	0.577460	+	0.794806i
$687$	4.91428	−	4.91428i	0.187492	−	0.187492i
$688$	25.8019	−	4.08662i	0.983689	−	0.155801i
$689$		−	4.47214i		−	0.170375i
$690$	−10.8450	+	12.6007i	−0.412863	+	0.479702i
$691$	9.12461			0.347117			0.173558	−	0.984824i	$-0.444473\pi$
$691$	9.12461			0.347117			0.173558	+	0.984824i	$0.444473\pi$
$692$	18.6068	+	36.5178i	0.707323	+	1.38820i
$693$	13.7638	+	13.7638i	0.522844	+	0.522844i
$694$	−30.6053	−	42.1246i	−1.16176	−	1.59903i
$695$	40.7364	+	25.1765i	1.54522	+	0.954999i
$696$	14.4721	−	4.70228i	0.548565	−	0.178240i
$697$	−5.70820	−	5.70820i	−0.216214	−	0.216214i
$698$	23.2847	+	3.68793i	0.881338	+	0.139590i
$699$		−	6.76393i		−	0.255835i
$700$	21.6419	+	15.9761i	0.817985	+	0.603841i
$701$		−	19.7072i		−	0.744330i	−0.928167	−	0.372165i	$-0.878616\pi$
$701$		−	19.7072i		−	0.744330i	0.928167	−	0.372165i	$-0.121384\pi$
$702$	1.04029	−	6.56816i	0.0392634	−	0.247899i
$703$	1.45309	+	1.45309i	0.0548041	+	0.0548041i
$704$	−15.2169	−	20.9443i	−0.573509	−	0.789367i
$705$	−7.88854	−	4.87539i	−0.297100	−	0.183618i
$706$	36.2705	−	26.3521i	1.36506	−	0.991773i
$707$	−5.52786	−	5.52786i	−0.207897	−	0.207897i
$708$	−0.374689	−	0.735369i	−0.0140817	−	0.0276369i
$709$	3.24920			0.122026			0.0610131	−	0.998137i	$-0.480567\pi$
$709$	3.24920			0.122026			0.0610131	+	0.998137i	$0.480567\pi$
$710$	−27.3539	−	23.5426i	−1.02657	−	0.883539i
$711$			6.49839i			0.243709i
$712$	3.17442	−	6.23015i	0.118966	−	0.233485i
$713$	36.1803	−	36.1803i	1.35496	−	1.35496i
$714$	−3.80423	+	2.76393i	−0.142370	+	0.103438i
$715$	−7.23607	+	1.70820i	−0.270614	+	0.0638832i
$716$	4.65248	−	14.3188i	0.173871	−	0.535120i
$717$	−8.29451	+	8.29451i	−0.309764	+	0.309764i
$718$	−27.8232	−	4.40676i	−1.03835	−	0.164459i
$719$	4.01623			0.149780			0.0748900	−	0.997192i	$-0.476139\pi$
$719$	4.01623			0.149780			0.0748900	+	0.997192i	$0.476139\pi$
$720$	7.58348	+	18.5065i	0.282620	+	0.689697i
$721$	12.7639			0.475354
$722$	−20.9520	−	3.31848i	−0.779754	−	0.123501i
$723$	6.94427	−	6.94427i	0.258260	−	0.258260i
$724$	9.40456	−	28.9443i	0.349518	−	1.07571i
$725$	13.7638	+	27.5276i	0.511175	+	1.02235i
$726$	0.527864	−	0.383516i	0.0195909	−	0.0142336i
$727$	−9.51057	+	9.51057i	−0.352727	+	0.352727i	−0.861123	−	0.508396i	$-0.830239\pi$
$727$	−9.51057	+	9.51057i	−0.352727	+	0.352727i	0.508396	+	0.861123i	$0.330239\pi$
$728$	6.96552	+	3.54911i	0.258159	+	0.131539i
$729$			5.94427i			0.220158i
$730$	−1.57233	−	20.9969i	−0.0581945	−	0.777132i
$731$	−9.23607			−0.341608
$732$	0.712701	+	1.39875i	0.0263422	+	0.0516995i
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	0.966303	−	0.257407i	$-0.0828680\pi$
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	−0.257407	+	0.966303i	$0.582868\pi$
$734$	−19.7477	+	14.3475i	−0.728900	+	0.529577i
$735$	−0.449028	+	0.106001i	−0.0165626	+	0.00390991i
$736$		−	34.0260i		−	1.25422i
$737$	14.9443	+	14.9443i	0.550479	+	0.550479i
$738$	2.82379	−	17.8287i	0.103945	−	0.656283i
$739$		−	9.41641i		−	0.346388i	−0.984888	−	0.173194i	$-0.944591\pi$
$739$		−	9.41641i		−	0.346388i	0.984888	−	0.173194i	$-0.0554088\pi$
$740$	−0.377909	+	4.57949i	−0.0138922	+	0.168345i
$741$		−	1.79611i		−	0.0659818i
$742$	−16.3540	−	2.59023i	−0.600376	−	0.0950902i
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	0.789784	−	0.613385i	$-0.210193\pi$
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	−0.613385	+	0.789784i	$0.710193\pi$
$744$	6.49839	+	20.0000i	0.238243	+	0.733236i
$745$	−15.1246	+	24.4721i	−0.554123	+	0.896590i
$746$	26.3820	+	36.3117i	0.965912	+	1.32946i
$747$	−14.7984	−	14.7984i	−0.541444	−	0.541444i
$748$	4.15537	+	8.15537i	0.151935	+	0.298190i
$749$	−3.46120			−0.126469
$750$	11.8647	−	7.08611i	0.433236	−	0.258748i
$751$		−	11.4127i		−	0.416455i	−0.978080	−	0.208227i	$-0.933231\pi$
$751$		−	11.4127i		−	0.416455i	0.978080	−	0.208227i	$-0.0667694\pi$
$752$	18.7462	−	2.96911i	0.683603	−	0.108272i
$753$	0.111456	−	0.111456i	0.00406169	−	0.00406169i
$754$	5.25731	+	7.23607i	0.191460	+	0.263522i
$755$	−12.7639	−	7.88854i	−0.464527	−	0.287094i
$756$	−23.4164	−	7.60845i	−0.851647	−	0.276717i
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.166709	−	0.986006i	$-0.446686\pi$
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.986006	−	0.166709i	$-0.0533140\pi$
$758$	0.0246576	−	0.155682i	0.000895606	−	0.00565463i
$759$	−17.0130			−0.617533
$760$	6.56816	+	10.8101i	0.238252	+	0.392125i
$761$	2.94427			0.106730			0.0533649	−	0.998575i	$-0.483005\pi$
$761$	2.94427			0.106730			0.0533649	+	0.998575i	$0.483005\pi$
$762$	−0.765727	+	4.83461i	−0.0277394	+	0.175139i
$763$	−27.8885	+	27.8885i	−1.00963	+	1.00963i
$764$	−8.16348	+	25.1246i	−0.295344	+	0.908977i
$765$	−1.62460	−	6.88191i	−0.0587375	−	0.248816i
$766$	1.18034	+	1.62460i	0.0426474	+	0.0586991i
$767$	0.343027	−	0.343027i	0.0123860	−	0.0123860i
$768$	12.4603	+	6.34884i	0.449622	+	0.229094i
$769$		−	6.47214i		−	0.233391i	−0.993168	−	0.116696i	$-0.962770\pi$
$769$		−	6.47214i		−	0.233391i	0.993168	−	0.116696i	$-0.0372302\pi$
$770$	2.05562	+	27.4508i	0.0740792	+	0.989257i
$771$	6.54102			0.235569
$772$	3.71000	−	1.89034i	0.133526	−	0.0680348i
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.989659	−	0.143439i	$-0.954184\pi$
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.143439	−	0.989659i	$-0.545816\pi$
$774$	−12.1392	−	16.7082i	−0.436335	−	0.600564i
$775$	−38.0423	+	19.0211i	−1.36652	+	0.683259i
$776$	−5.23607	−	16.1150i	−0.187964	−	0.578493i
$777$	−1.70820	−	1.70820i	−0.0612815	−	0.0612815i
$778$	5.79289	+	0.917504i	0.207685	+	0.0328941i
$779$		−	11.4164i		−	0.409035i
$780$	3.06384	−	2.59672i	0.109703	−	0.0929775i
$781$		−	36.9322i		−	1.32154i
$782$	−1.88191	+	11.8819i	−0.0672969	+	0.424896i
$783$	−19.9192	−	19.9192i	−0.711854	−	0.711854i
$784$	0.555029	−	0.763932i	0.0198225	−	0.0272833i
$785$	10.1246	+	42.8885i	0.361363	+	1.53076i
$786$	−13.7082	+	9.95959i	−0.488955	+	0.355247i
$787$	17.8541	+	17.8541i	0.636430	+	0.636430i	0.949673	−	0.313243i	$-0.101415\pi$
$787$	17.8541	+	17.8541i	0.636430	+	0.636430i	−0.313243	+	0.949673i	$0.601415\pi$
$788$	23.2686	−	11.8560i	0.828911	−	0.422351i
$789$	−9.27354			−0.330147
$790$	−5.99499	+	6.96552i	−0.213292	+	0.247822i
$791$			33.1280i			1.17790i
$792$	−9.29168	+	18.2360i	−0.330166	+	0.647986i
$793$	−0.652476	+	0.652476i	−0.0231701	+	0.0231701i
$794$	−39.5609	+	28.7426i	−1.40396	+	1.02004i
$795$	−4.47214	+	7.23607i	−0.158610	+	0.256637i
$796$	−41.3050	−	13.4208i	−1.46402	−	0.475687i
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	−0.393779	−	0.919205i	$-0.628833\pi$
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	0.919205	+	0.393779i	$0.128833\pi$
$798$	−6.56816	−	1.04029i	−0.232510	−	0.0368260i
$799$	−6.71040			−0.237397
$800$	−8.94427	+	26.8328i	−0.316228	+	0.948683i
$801$	−5.52786			−0.195317
$802$	−44.5420	−	7.05476i	−1.57283	−	0.249112i
$803$	15.2361	−	15.2361i	0.537669	−	0.537669i
$804$	−10.8576	−	3.52786i	−0.382920	−	0.124418i
$805$	−19.0211	+	30.7768i	−0.670407	+	1.08474i
$806$	−10.0000	+	7.26543i	−0.352235	+	0.255914i
$807$	12.6538	−	12.6538i	0.445433	−	0.445433i
$808$	3.73175	−	7.32398i	0.131283	−	0.257657i
$809$		−	4.94427i		−	0.173831i	−0.996216	−	0.0869157i	$-0.972299\pi$
$809$		−	4.94427i		−	0.173831i	0.996216	−	0.0869157i	$-0.0277011\pi$
$810$	5.58661	−	6.49103i	0.196294	−	0.228072i
$811$	26.0689			0.915402			0.457701	−	0.889106i	$-0.348673\pi$
$811$	26.0689			0.915402			0.457701	+	0.889106i	$0.348673\pi$
$812$	29.5064	−	15.0343i	1.03547	−	0.527599i
$813$	10.6456	+	10.6456i	0.373359	+	0.373359i
$814$	−3.80423	+	2.76393i	−0.133338	+	0.0968758i
$815$	10.0656	+	42.6385i	0.352582	+	1.49356i
$816$	−4.00000	−	2.90617i	−0.140028	−	0.101736i
$817$	−9.23607	−	9.23607i	−0.323129	−	0.323129i
$818$	−4.77789	+	30.1664i	−0.167055	+	1.05474i
$819$		−	6.18034i		−	0.215959i
$820$	19.4743	−	16.5052i	0.680073	−	0.576387i
$821$		−	17.9111i		−	0.625101i	−0.949901	−	0.312550i	$-0.898817\pi$
$821$		−	17.9111i		−	0.625101i	0.949901	−	0.312550i	$-0.101183\pi$
$822$	9.44788	+	1.49640i	0.329532	+	0.0521928i
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	0.422767	−	0.906238i	$-0.361059\pi$
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	−0.906238	+	0.422767i	$0.861059\pi$
$824$	4.14725	+	12.7639i	0.144476	+	0.444653i
$825$	13.4164	+	4.47214i	0.467099	+	0.155700i
$826$	−1.05573	−	1.45309i	−0.0367335	−	0.0505593i
$827$	8.14590	+	8.14590i	0.283261	+	0.283261i	0.834408	−	0.551147i	$-0.185810\pi$
$827$	8.14590	+	8.14590i	0.283261	+	0.283261i	−0.551147	+	0.834408i	$0.685810\pi$
$828$	−23.9680	+	12.2123i	−0.832946	+	0.424407i
$829$	54.5002			1.89287			0.946436	−	0.322892i	$-0.104655\pi$
$829$	54.5002			1.89287			0.946436	+	0.322892i	$0.104655\pi$
$830$	−2.21013	−	29.5141i	−0.0767146	−	1.02445i
$831$			11.4127i			0.395901i
$832$	−1.28587	+	8.11869i	−0.0445797	+	0.281465i
$833$	−0.236068	+	0.236068i	−0.00817927	+	0.00817927i
$834$	−15.5599	−	21.4164i	−0.538796	−	0.741590i
$835$	−5.85410	−	24.7984i	−0.202590	−	0.858183i
$836$	−4.00000	+	12.3107i	−0.138343	+	0.425776i
$837$	27.5276	−	27.5276i	0.951494	−	0.951494i
$838$	−6.37873	+	40.2737i	−0.220350	+	1.39123i
$839$	15.2169			0.525346			0.262673	−	0.964885i	$-0.415396\pi$
$839$	15.2169			0.525346			0.262673	+	0.964885i	$0.415396\pi$
$840$	−7.72133	−	12.7081i	−0.266411	−	0.438471i
$841$	8.88854			0.306502
$842$	6.28867	−	39.7051i	0.216722	−	1.36833i
$843$	−6.00000	+	6.00000i	−0.206651	+	0.206651i
$844$	4.35926	+	1.41641i	0.150052	+	0.0487548i
$845$	−22.7194	−	14.0413i	−0.781570	−	0.483037i
$846$	−8.81966	−	12.1392i	−0.303226	−	0.417355i
$847$	1.00406	−	1.00406i	0.0344998	−	0.0344998i
$848$	−2.72353	−	17.1957i	−0.0935262	−	0.590501i
$849$		−	16.5410i		−	0.567686i
$850$	4.60741	−	8.87535i	0.158033	−	0.304422i
$851$	−6.18034			−0.211859
$852$	9.05715	+	17.7757i	0.310293	+	0.608984i
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	0.951877	−	0.306479i	$-0.0991509\pi$
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	−0.306479	+	0.951877i	$0.599151\pi$
$854$	2.00811	+	2.76393i	0.0687163	+	0.0945798i
$855$	5.25731	−	8.50651i	0.179796	−	0.290916i
$856$	−1.12461	−	3.46120i	−0.0384384	−	0.118301i
$857$	35.8328	+	35.8328i	1.22403	+	1.22403i	0.966188	+	0.257837i	$0.0830099\pi$
$857$	35.8328	+	35.8328i	1.22403	+	1.22403i	0.257837	+	0.966188i	$0.416990\pi$
$858$	4.05934	+	0.642937i	0.138584	+	0.0219495i
$859$		−	16.4721i		−	0.562022i	−0.959705	−	0.281011i	$-0.909330\pi$
$859$		−	16.4721i		−	0.562022i	0.959705	−	0.281011i	$-0.0906697\pi$
$860$	2.40206	−	29.1081i	0.0819095	−	0.992577i
$861$			13.4208i			0.457379i
$862$	−4.20808	+	26.5688i	−0.143328	+	0.904935i
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.970589	−	0.240743i	$-0.922609\pi$
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.240743	−	0.970589i	$-0.577391\pi$
$864$		−	25.8885i		−	0.880746i
$865$	44.5967	−	10.5279i	1.51633	−	0.357958i
$866$	−1.32624	+	0.963568i	−0.0450674	+	0.0327434i
$867$	−9.27051	−	9.27051i	−0.314843	−	0.314843i
$868$	20.7768	+	40.7768i	0.705212	+	1.38406i
$869$	−9.40456			−0.319028
$870$	−1.27044	−	16.9655i	−0.0430720	−	0.575185i
$871$		−	6.71040i		−	0.227373i
$872$	−36.9501	−	18.8270i	−1.25129	−	0.637563i
$873$	−9.47214	+	9.47214i	−0.320583	+	0.320583i
$874$	−13.7638	+	10.0000i	−0.465568	+	0.338255i
$875$	23.0902	−	19.2705i	0.780590	−	0.651462i
$876$	−3.59675	+	11.0697i	−0.121523	+	0.374009i
$877$	−21.5438	+	21.5438i	−0.727482	+	0.727482i	−0.970118	−	0.242636i	$-0.921988\pi$
$877$	−21.5438	+	21.5438i	−0.727482	+	0.727482i	0.242636	+	0.970118i	$0.421988\pi$
$878$	49.0782	+	7.77322i	1.65631	+	0.262333i
$879$	3.80423			0.128313
$880$	−26.7829	+	10.9749i	−0.902850	+	0.369964i
$881$	6.87539			0.231638			0.115819	−	0.993270i	$-0.463051\pi$
$881$	6.87539			0.231638			0.115819	+	0.993270i	$0.463051\pi$
$882$	−0.737322	−	0.116780i	−0.0248269	−	0.00393220i
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	−0.752624	−	0.658451i	$-0.771212\pi$
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	0.658451	+	0.752624i	$0.271212\pi$
$884$	0.898056	−	2.76393i	0.0302049	−	0.0929611i
$885$	−0.898056	+	0.212002i	−0.0301878	+	0.00712638i
$886$	1.76393	−	1.28157i	0.0592605	−	0.0430552i
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	−0.486770	−	0.873530i	$-0.661825\pi$
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	0.873530	+	0.486770i	$0.161825\pi$
$888$	1.15317	−	2.26323i	0.0386980	−	0.0759491i
$889$			10.6525i			0.357273i
$890$	−5.92522	−	5.09964i	−0.198614	−	0.170940i
$891$	8.76393			0.293603
$892$	18.2504	+	35.8185i	0.611069	+	1.19929i
$893$	−6.71040	−	6.71040i	−0.224555	−	0.224555i
$894$	12.8658	−	9.34752i	0.430295	−	0.312628i
$895$	−14.3188	−	8.84953i	−0.478626	−	0.295807i
$896$	28.9443	+	9.40456i	0.966960	+	0.314184i
$897$	3.81966	+	3.81966i	0.127535	+	0.127535i
$898$	3.89296	−	24.5792i	0.129910	−	0.820218i
$899$			52.3607i			1.74633i
$900$	22.1113	−	3.33023i	0.737043	−	0.111008i
$901$			6.15537i			0.205065i
$902$	25.8019	+	4.08662i	0.859110	+	0.136070i
$903$	10.8576	+	10.8576i	0.361320	+	0.361320i
$904$	−33.1280	+	10.7639i	−1.10182	+	0.358003i
$905$	−28.9443	−	17.8885i	−0.962140	−	0.594635i
$906$	4.87539	+	6.71040i	0.161974	+	0.222938i
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	0.568133	−	0.822936i	$-0.307666\pi$
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	−0.822936	+	0.568133i	$0.807666\pi$
$908$	−12.0472	−	23.6439i	−0.399800	−	0.784651i
$909$	−6.49839			−0.215538
$910$	5.70157	−	6.62460i	0.189005	−	0.219603i
$911$			10.3026i			0.341341i	0.985328	+	0.170671i	$0.0545934\pi$
$911$			10.3026i			0.341341i	−0.985328	+	0.170671i	$0.945407\pi$
$912$	−1.09383	−	6.90617i	−0.0362203	−	0.228686i
$913$	21.4164	−	21.4164i	0.708780	−	0.708780i
$914$	−11.3472	−	15.6180i	−0.375331	−	0.516599i
$915$	1.70820	−	0.403252i	0.0564715	−	0.0133311i
$916$	15.1246	+	4.91428i	0.499731	+	0.162373i
$917$	−26.0746	+	26.0746i	−0.861058	+	0.861058i
$918$	−1.43184	+	9.04029i	−0.0472578	+	0.298374i
$919$	18.1231			0.597825			0.298913	−	0.954281i	$-0.403376\pi$
$919$	18.1231			0.597825			0.298913	+	0.954281i	$0.403376\pi$
$920$	−36.9572	−	9.02113i	−1.21844	−	0.297418i
$921$	−16.7639			−0.552390
$922$	−6.08999	+	38.4507i	−0.200563	+	1.26631i
$923$	−8.29180	+	8.29180i	−0.272928	+	0.272928i
$924$	4.70228	−	14.4721i	0.154694	−	0.476098i
$925$	4.87380	+	1.62460i	0.160249	+	0.0534165i
$926$	−2.88854	−	3.97574i	−0.0949234	−	0.130651i
$927$	7.50245	−	7.50245i	0.246413	−	0.246413i
$928$	24.6215	+	24.6215i	0.808239	+	0.808239i
$929$		−	36.6525i		−	1.20253i	−0.799050	−	0.601264i	$-0.794664\pi$
$929$		−	36.6525i		−	1.20253i	0.799050	−	0.601264i	$-0.205336\pi$
$930$	23.4458	−	1.75571i	0.768817	−	0.0575718i
$931$	−0.472136			−0.0154736
$932$	13.7906	−	7.02666i	0.451726	−	0.230166i
$933$	−12.8658	−	12.8658i	−0.421206	−	0.421206i
$934$	21.5438	+	29.6525i	0.704934	+	0.970259i
$935$	9.95959	−	2.35114i	0.325714	−	0.0768905i
$936$	6.18034	−	2.00811i	0.202011	−	0.0656373i
$937$	−42.3050	−	42.3050i	−1.38204	−	1.38204i	−0.840987	−	0.541056i	$-0.818025\pi$
$937$	−42.3050	−	42.3050i	−1.38204	−	1.38204i	−0.541056	−	0.840987i	$-0.681975\pi$
$938$	−24.5391	−	3.88661i	−0.801230	−	0.126902i
$939$			2.18034i			0.0711527i
$940$	1.74520	−	21.1482i	0.0569220	−	0.689780i
$941$			37.6183i			1.22632i	0.789959	+	0.613160i	$0.210102\pi$
$941$			37.6183i			1.22632i	−0.789959	+	0.613160i	$0.789898\pi$
$942$	3.81072	−	24.0599i	0.124160	−	0.783915i
$943$	24.2784	+	24.2784i	0.790615	+	0.790615i
$944$	1.11006	−	1.52786i	0.0361293	−	0.0497277i
$945$	−14.4721	+	23.4164i	−0.470779	+	0.761736i
$946$	24.1803	−	17.5680i	0.786171	−	0.571186i
$947$	−2.14590	−	2.14590i	−0.0697323	−	0.0697323i	0.671381	−	0.741113i	$-0.265702\pi$
$947$	−2.14590	−	2.14590i	−0.0697323	−	0.0697323i	−0.741113	+	0.671381i	$0.765702\pi$
$948$	4.52647	−	2.30635i	0.147013	−	0.0749068i
$949$	−6.84142			−0.222082
$950$	13.4828	−	4.26793i	0.437438	−	0.138470i
$951$			4.91428i			0.159357i
$952$	−9.58721	−	4.88493i	−0.310723	−	0.158321i
$953$	−29.1803	+	29.1803i	−0.945244	+	0.945244i	−0.998577	−	0.0533329i	$-0.983016\pi$
$953$	−29.1803	+	29.1803i	−0.945244	+	0.945244i	0.0533329	+	0.998577i	$0.483016\pi$
$954$	−11.1352	+	8.09017i	−0.360514	+	0.261929i
$955$	25.1246	+	15.5279i	0.813013	+	0.502470i
$956$	−25.5279	−	8.29451i	−0.825630	−	0.268263i
$957$	12.3107	−	12.3107i	0.397950	−	0.397950i
$958$	6.56816	+	1.04029i	0.212208	+	0.0336104i
$959$	20.8172			0.672224
$960$	10.1993	−	11.8504i	0.329180	−	0.382471i
$961$	−41.3607			−1.33422
$962$	1.47464	+	0.233561i	0.0475444	+	0.00753029i
$963$	−2.03444	+	2.03444i	−0.0655590	+	0.0655590i
$964$	21.3723	+	6.94427i	0.688355	+	0.223660i
$965$	−1.06957	−	4.53077i	−0.0344307	−	0.145851i
$966$	16.1803	−	11.7557i	0.520594	−	0.378234i
$967$	10.9637	−	10.9637i	0.352567	−	0.352567i	−0.508497	−	0.861064i	$-0.669799\pi$
$967$	10.9637	−	10.9637i	0.352567	−	0.352567i	0.861064	+	0.508497i	$0.169799\pi$
$968$	1.33030	+	0.677819i	0.0427573	+	0.0217859i
$969$			2.47214i			0.0794164i
$970$	−18.8914	+	1.41466i	−0.606566	+	0.0454219i
$971$	−15.5967			−0.500523			−0.250262	−	0.968178i	$-0.580517\pi$
$971$	−15.5967			−0.500523			−0.250262	+	0.968178i	$0.580517\pi$
$972$	−28.6842	+	14.6153i	−0.920047	+	0.468787i
$973$	−40.7364	−	40.7364i	−1.30595	−	1.30595i
$974$	30.6053	−	22.2361i	0.980658	−	0.712490i
$975$	−2.00811	−	4.01623i	−0.0643111	−	0.128622i
$976$	−2.11146	+	2.90617i	−0.0675861	+	0.0930242i
$977$	−23.7639	−	23.7639i	−0.760276	−	0.760276i	0.216096	−	0.976372i	$-0.430667\pi$
$977$	−23.7639	−	23.7639i	−0.760276	−	0.760276i	−0.976372	+	0.216096i	$0.930667\pi$
$978$	3.78851	−	23.9197i	0.121143	−	0.764868i
$979$		−	8.00000i		−	0.255681i
$980$	−0.682589	−	0.805379i	−0.0218045	−	0.0257269i
$981$			32.7849i			1.04674i
$982$	21.2818	+	3.37070i	0.679129	+	0.107563i
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	0.358770	−	0.933426i	$-0.383196\pi$
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	−0.933426	+	0.358770i	$0.883196\pi$
$984$	−13.4208	+	4.36068i	−0.427839	+	0.139013i
$985$	−6.70820	−	28.4164i	−0.213741	−	0.905422i
$986$	−7.23607	−	9.95959i	−0.230443	−	0.317178i
$987$	7.88854	+	7.88854i	0.251095	+	0.251095i
$988$	3.66199	−	1.86588i	0.116503	−	0.0593614i
$989$	39.2833			1.24914
$990$	17.3434	+	14.9269i	0.551210	+	0.474408i
$991$			14.3188i			0.454853i	0.973795	+	0.227427i	$0.0730312\pi$
$991$			14.3188i			0.454853i	−0.973795	+	0.227427i	$0.926969\pi$
$992$	−34.0260	+	34.0260i	−1.08033	+	1.08033i
$993$	−18.5836	+	18.5836i	−0.589732	+	0.589732i
$994$	25.5195	+	35.1246i	0.809430	+	1.11409i
$995$	−25.5279	+	41.3050i	−0.809288	+	1.30945i
$996$	−5.05573	+	15.5599i	−0.160197	+	0.493035i
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	−0.993934	−	0.109979i	$-0.964922\pi$
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	0.109979	+	0.993934i	$0.464922\pi$
$998$	2.63012	−	16.6059i	0.0832551	−	0.525652i
$999$	−4.70228			−0.148774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.2.k.a.27.1	yes	8
3.2	odd	2		360.2.w.c.307.4		8
4.3	odd	2		160.2.o.a.47.2		8
5.2	odd	4		200.2.k.h.43.2		8
5.3	odd	4	inner	40.2.k.a.3.3	yes	8
5.4	even	2		200.2.k.h.107.4		8
8.3	odd	2	inner	40.2.k.a.27.3	yes	8
8.5	even	2		160.2.o.a.47.1		8
12.11	even	2		1440.2.bi.c.847.2		8
15.8	even	4		360.2.w.c.163.2		8
16.3	odd	4		1280.2.n.q.767.1		8
16.5	even	4		1280.2.n.q.767.2		8
16.11	odd	4		1280.2.n.m.767.4		8
16.13	even	4		1280.2.n.m.767.3		8
20.3	even	4		160.2.o.a.143.1		8
20.7	even	4		800.2.o.g.143.4		8
20.19	odd	2		800.2.o.g.207.3		8
24.5	odd	2		1440.2.bi.c.847.3		8
24.11	even	2		360.2.w.c.307.2		8
40.3	even	4	inner	40.2.k.a.3.1	✓	8
40.13	odd	4		160.2.o.a.143.2		8
40.19	odd	2		200.2.k.h.107.2		8
40.27	even	4		200.2.k.h.43.4		8
40.29	even	2		800.2.o.g.207.4		8
40.37	odd	4		800.2.o.g.143.3		8
60.23	odd	4		1440.2.bi.c.1423.3		8
80.3	even	4		1280.2.n.m.1023.3		8
80.13	odd	4		1280.2.n.q.1023.1		8
80.43	even	4		1280.2.n.q.1023.2		8
80.53	odd	4		1280.2.n.m.1023.4		8
120.53	even	4		1440.2.bi.c.1423.2		8
120.83	odd	4		360.2.w.c.163.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.1	✓	8	40.3	even	4	inner
40.2.k.a.3.3	yes	8	5.3	odd	4	inner
40.2.k.a.27.1	yes	8	1.1	even	1	trivial
40.2.k.a.27.3	yes	8	8.3	odd	2	inner
160.2.o.a.47.1		8	8.5	even	2
160.2.o.a.47.2		8	4.3	odd	2
160.2.o.a.143.1		8	20.3	even	4
160.2.o.a.143.2		8	40.13	odd	4
200.2.k.h.43.2		8	5.2	odd	4
200.2.k.h.43.4		8	40.27	even	4
200.2.k.h.107.2		8	40.19	odd	2
200.2.k.h.107.4		8	5.4	even	2
360.2.w.c.163.2		8	15.8	even	4
360.2.w.c.163.4		8	120.83	odd	4
360.2.w.c.307.2		8	24.11	even	2
360.2.w.c.307.4		8	3.2	odd	2
800.2.o.g.143.3		8	40.37	odd	4
800.2.o.g.143.4		8	20.7	even	4
800.2.o.g.207.3		8	20.19	odd	2
800.2.o.g.207.4		8	40.29	even	2
1280.2.n.m.767.3		8	16.13	even	4
1280.2.n.m.767.4		8	16.11	odd	4
1280.2.n.m.1023.3		8	80.3	even	4
1280.2.n.m.1023.4		8	80.53	odd	4
1280.2.n.q.767.1		8	16.3	odd	4
1280.2.n.q.767.2		8	16.5	even	4
1280.2.n.q.1023.1		8	80.13	odd	4
1280.2.n.q.1023.2		8	80.43	even	4
1440.2.bi.c.847.2		8	12.11	even	2
1440.2.bi.c.847.3		8	24.5	odd	2
1440.2.bi.c.1423.2		8	120.53	even	4
1440.2.bi.c.1423.3		8	60.23	odd	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39680 - 0.221232i) q^{2} +(0.618034 - 0.618034i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(-1.00000 + 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-2.52015 - 1.28408i) q^{8} +2.23607i q^{9} +O(q^{10})\)	\(q+(-1.39680 - 0.221232i) q^{2} +(0.618034 - 0.618034i) q^{3} +(1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(-1.00000 + 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-2.52015 - 1.28408i) q^{8} +2.23607i q^{9} +(-2.06285 + 2.39680i) q^{10} -3.23607 q^{11} +(1.55754 - 0.793604i) q^{12} +(0.726543 + 0.726543i) q^{13} +(3.07768 - 2.23607i) q^{14} +(-0.449028 - 1.90211i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.00000 - 1.00000i) q^{17} +(0.494689 - 3.12334i) q^{18} -2.00000i q^{19} +(3.41164 - 2.89149i) q^{20} +2.35114i q^{21} +(4.52015 + 0.715921i) q^{22} +(4.25325 + 4.25325i) q^{23} +(-2.35114 + 0.763932i) q^{24} +(-2.23607 - 4.47214i) q^{25} +(-0.854102 - 1.17557i) q^{26} +(3.23607 + 3.23607i) q^{27} +(-4.79360 + 2.44246i) q^{28} -6.15537 q^{29} +(0.206396 + 2.75621i) q^{30} -8.50651i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.00000 + 2.00000i) q^{33} +(1.17557 + 1.61803i) q^{34} +(1.38197 + 5.85410i) q^{35} +(-1.38197 + 4.25325i) q^{36} +(-0.726543 + 0.726543i) q^{37} +(-0.442463 + 2.79360i) q^{38} +0.898056 q^{39} +(-5.40507 + 3.28408i) q^{40} +5.70820 q^{41} +(0.520147 - 3.28408i) q^{42} +(4.61803 - 4.61803i) q^{43} +(-6.15537 - 2.00000i) q^{44} +(4.25325 + 2.62866i) q^{45} +(-5.00000 - 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} +(3.45309 - 0.546915i) q^{48} -0.236068i q^{49} +(2.13397 + 6.74138i) q^{50} -1.23607 q^{51} +(0.932938 + 1.83099i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(-3.80423 - 5.23607i) q^{54} +(-3.80423 + 6.15537i) q^{55} +(7.23607 - 2.35114i) q^{56} +(-1.23607 - 1.23607i) q^{57} +(8.59783 + 1.36176i) q^{58} -0.472136i q^{59} +(0.321469 - 3.89555i) q^{60} +0.898056i q^{61} +(-1.88191 + 11.8819i) q^{62} +(-4.25325 - 4.25325i) q^{63} +(4.70228 + 6.47214i) q^{64} +(2.23607 - 0.527864i) q^{65} +(3.23607 - 2.35114i) q^{66} +(-4.61803 - 4.61803i) q^{67} +(-1.28408 - 2.52015i) q^{68} +5.25731 q^{69} +(-0.635220 - 8.48276i) q^{70} +11.4127i q^{71} +(2.87129 - 5.63522i) q^{72} +(-4.70820 + 4.70820i) q^{73} +(1.17557 - 0.854102i) q^{74} +(-4.14590 - 1.38197i) q^{75} +(1.23607 - 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} +(-1.25441 - 0.198678i) q^{78} +2.90617 q^{79} +(8.27636 - 3.39144i) q^{80} -2.70820 q^{81} +(-7.97323 - 1.26284i) q^{82} +(-6.61803 + 6.61803i) q^{83} +(-1.45309 + 4.47214i) q^{84} +(-3.07768 + 0.726543i) q^{85} +(-7.47214 + 5.42882i) q^{86} +(-3.80423 + 3.80423i) q^{87} +(8.15537 + 4.15537i) q^{88} +2.47214i q^{89} +(-5.35941 - 4.61267i) q^{90} -2.76393 q^{91} +(5.46151 + 10.7188i) q^{92} +(-5.25731 - 5.25731i) q^{93} +(-5.42882 + 3.94427i) q^{94} +(-3.80423 - 2.35114i) q^{95} -4.94427 q^{96} +(4.23607 + 4.23607i) q^{97} +(-0.0522257 + 0.329740i) q^{98} -7.23607i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 + 4 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} - 10 q^{10} - 8 q^{11} + 12 q^{12} + 8 q^{16} - 8 q^{17} + 10 q^{18} + 12 q^{22} + 20 q^{26} + 8 q^{27} - 20 q^{28} + 20 q^{30} - 32 q^{32} - 16 q^{33} + 20 q^{35} - 20 q^{36} - 4 q^{38} - 20 q^{40} - 8 q^{41} - 20 q^{42} + 28 q^{43} - 40 q^{46} + 16 q^{48} - 10 q^{50} + 8 q^{51} + 20 q^{52} + 40 q^{56} + 8 q^{57} + 20 q^{58} + 20 q^{60} + 40 q^{62} + 8 q^{66} - 28 q^{67} - 4 q^{68} + 20 q^{70} - 20 q^{72} + 16 q^{73} - 60 q^{75} - 8 q^{76} - 40 q^{78} + 32 q^{81} - 28 q^{82} - 44 q^{83} - 24 q^{86} + 16 q^{88} - 10 q^{90} - 40 q^{91} + 20 q^{92} + 32 q^{96} + 16 q^{97} - 6 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 + 4 * q^8 - 10 * q^10 - 8 * q^11 + 12 * q^12 + 8 * q^16 - 8 * q^17 + 10 * q^18 + 12 * q^22 + 20 * q^26 + 8 * q^27 - 20 * q^28 + 20 * q^30 - 32 * q^32 - 16 * q^33 + 20 * q^35 - 20 * q^36 - 4 * q^38 - 20 * q^40 - 8 * q^41 - 20 * q^42 + 28 * q^43 - 40 * q^46 + 16 * q^48 - 10 * q^50 + 8 * q^51 + 20 * q^52 + 40 * q^56 + 8 * q^57 + 20 * q^58 + 20 * q^60 + 40 * q^62 + 8 * q^66 - 28 * q^67 - 4 * q^68 + 20 * q^70 - 20 * q^72 + 16 * q^73 - 60 * q^75 - 8 * q^76 - 40 * q^78 + 32 * q^81 - 28 * q^82 - 44 * q^83 - 24 * q^86 + 16 * q^88 - 10 * q^90 - 40 * q^91 + 20 * q^92 + 32 * q^96 + 16 * q^97 - 6 * q^98

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