LMFDB - Embedded newform 370.2.h.e.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.3
Root			$-1.23675 - 1.23675i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +(1.26849 - 1.84145i) q^{10} +4.27563i q^{11} +(-1.23675 + 1.23675i) q^{12} -1.50964 q^{13} +(-1.28708 + 1.28708i) q^{14} +(-0.708613 - 3.84622i) q^{15} +1.00000 q^{16} -2.12121i q^{17} +0.0591090i q^{18} +(-0.381960 - 0.381960i) q^{19} +(-1.26849 + 1.84145i) q^{20} +3.18360i q^{21} -4.27563i q^{22} -8.90184 q^{23} +(1.23675 - 1.23675i) q^{24} +(-1.78188 - 4.67171i) q^{25} +1.50964 q^{26} +(-3.63715 - 3.63715i) q^{27} +(1.28708 - 1.28708i) q^{28} +(0.279903 - 0.279903i) q^{29} +(0.708613 + 3.84622i) q^{30} +(-1.59328 - 1.59328i) q^{31} -1.00000 q^{32} +(-5.28790 - 5.28790i) q^{33} +2.12121i q^{34} +(0.737449 + 4.00274i) q^{35} -0.0591090i q^{36} +(-5.63727 + 2.28498i) q^{37} +(0.381960 + 0.381960i) q^{38} +(1.86705 - 1.86705i) q^{39} +(1.26849 - 1.84145i) q^{40} -0.270882i q^{41} -3.18360i q^{42} +0.302660 q^{43} +4.27563i q^{44} +(0.108846 + 0.0749790i) q^{45} +8.90184 q^{46} +(-3.17973 + 3.17973i) q^{47} +(-1.23675 + 1.23675i) q^{48} +3.68685i q^{49} +(1.78188 + 4.67171i) q^{50} +(2.62341 + 2.62341i) q^{51} -1.50964 q^{52} +(9.71066 + 9.71066i) q^{53} +(3.63715 + 3.63715i) q^{54} +(-7.87337 - 5.42359i) q^{55} +(-1.28708 + 1.28708i) q^{56} +0.944780 q^{57} +(-0.279903 + 0.279903i) q^{58} +(-4.06655 - 4.06655i) q^{59} +(-0.708613 - 3.84622i) q^{60} +(4.47102 + 4.47102i) q^{61} +(1.59328 + 1.59328i) q^{62} +(-0.0760780 - 0.0760780i) q^{63} +1.00000 q^{64} +(1.91496 - 2.77993i) q^{65} +(5.28790 + 5.28790i) q^{66} +(-6.17649 - 6.17649i) q^{67} -2.12121i q^{68} +(11.0094 - 11.0094i) q^{69} +(-0.737449 - 4.00274i) q^{70} -7.90805 q^{71} +0.0591090i q^{72} +(8.32545 - 8.32545i) q^{73} +(5.63727 - 2.28498i) q^{74} +(7.98149 + 3.57401i) q^{75} +(-0.381960 - 0.381960i) q^{76} +(5.50309 + 5.50309i) q^{77} +(-1.86705 + 1.86705i) q^{78} +(-2.20061 - 2.20061i) q^{79} +(-1.26849 + 1.84145i) q^{80} +9.17383 q^{81} +0.270882i q^{82} +(10.1305 + 10.1305i) q^{83} +3.18360i q^{84} +(3.90611 + 2.69073i) q^{85} -0.302660 q^{86} +0.692342i q^{87} -4.27563i q^{88} +(5.24983 - 5.24983i) q^{89} +(-0.108846 - 0.0749790i) q^{90} +(-1.94303 + 1.94303i) q^{91} -8.90184 q^{92} +3.94099 q^{93} +(3.17973 - 3.17973i) q^{94} +(1.18787 - 0.218849i) q^{95} +(1.23675 - 1.23675i) q^{96} +12.2566i q^{97} -3.68685i q^{98} +0.252728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.23675	+	1.23675i	−0.714039	+	0.714039i	−0.967378	−	0.253339i	$-0.918471\pi$
$3$	−1.23675	+	1.23675i	−0.714039	+	0.714039i	0.253339	+	0.967378i	$0.418471\pi$
$4$	1.00000			0.500000
$5$	−1.26849	+	1.84145i	−0.567285	+	0.823522i
$5$	−1.26849	+	1.84145i	−0.567285	+	0.823522i
$6$	1.23675	−	1.23675i	0.504902	−	0.504902i
$7$	1.28708	−	1.28708i	0.486471	−	0.486471i	−0.420720	−	0.907191i	$-0.638222\pi$
$7$	1.28708	−	1.28708i	0.486471	−	0.486471i	0.907191	+	0.420720i	$0.138222\pi$
$8$	−1.00000			−0.353553
$9$		−	0.0591090i		−	0.0197030i
$10$	1.26849	−	1.84145i	0.401131	−	0.582318i
$11$			4.27563i			1.28915i	0.764540	+	0.644576i	$0.222966\pi$
$11$			4.27563i			1.28915i	−0.764540	+	0.644576i	$0.777034\pi$
$12$	−1.23675	+	1.23675i	−0.357019	+	0.357019i
$13$	−1.50964			−0.418700			−0.209350	−	0.977841i	$-0.567135\pi$
$13$	−1.50964			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$14$	−1.28708	+	1.28708i	−0.343987	+	0.343987i
$15$	−0.708613	−	3.84622i	−0.182963	−	0.993090i
$16$	1.00000			0.250000
$17$		−	2.12121i		−	0.514470i	−0.966349	−	0.257235i	$-0.917189\pi$
$17$		−	2.12121i		−	0.514470i	0.966349	−	0.257235i	$-0.0828114\pi$
$18$			0.0591090i			0.0139321i
$19$	−0.381960	−	0.381960i	−0.0876277	−	0.0876277i	0.661934	−	0.749562i	$-0.269736\pi$
$19$	−0.381960	−	0.381960i	−0.0876277	−	0.0876277i	−0.749562	+	0.661934i	$0.769736\pi$
$20$	−1.26849	+	1.84145i	−0.283642	+	0.411761i
$21$			3.18360i			0.694718i
$22$		−	4.27563i		−	0.911568i
$23$	−8.90184			−1.85616			−0.928081	−	0.372379i	$-0.878542\pi$
$23$	−8.90184			−1.85616			−0.928081	+	0.372379i	$0.878542\pi$
$24$	1.23675	−	1.23675i	0.252451	−	0.252451i
$25$	−1.78188	−	4.67171i	−0.356376	−	0.934343i
$26$	1.50964			0.296066
$27$	−3.63715	−	3.63715i	−0.699970	−	0.699970i
$28$	1.28708	−	1.28708i	0.243235	−	0.243235i
$29$	0.279903	−	0.279903i	0.0519767	−	0.0519767i	−0.680641	−	0.732617i	$-0.738298\pi$
$29$	0.279903	−	0.279903i	0.0519767	−	0.0519767i	0.732617	+	0.680641i	$0.238298\pi$
$30$	0.708613	+	3.84622i	0.129374	+	0.702221i
$31$	−1.59328	−	1.59328i	−0.286162	−	0.286162i	0.549398	−	0.835561i	$-0.314857\pi$
$31$	−1.59328	−	1.59328i	−0.286162	−	0.286162i	−0.835561	+	0.549398i	$0.814857\pi$
$32$	−1.00000			−0.176777
$33$	−5.28790	−	5.28790i	−0.920505	−	0.920505i
$34$			2.12121i			0.363785i
$35$	0.737449	+	4.00274i	0.124652	+	0.676587i
$36$		−	0.0591090i		−	0.00985149i
$37$	−5.63727	+	2.28498i	−0.926762	+	0.375649i
$37$	−5.63727	+	2.28498i	−0.926762	+	0.375649i
$38$	0.381960	+	0.381960i	0.0619621	+	0.0619621i
$39$	1.86705	−	1.86705i	0.298968	−	0.298968i
$40$	1.26849	−	1.84145i	0.200565	−	0.291159i
$41$		−	0.270882i		−	0.0423047i	−0.999776	−	0.0211524i	$-0.993266\pi$
$41$		−	0.270882i		−	0.0423047i	0.999776	−	0.0211524i	$-0.00673350\pi$
$42$		−	3.18360i		−	0.491240i
$43$	0.302660			0.0461552			0.0230776	−	0.999734i	$-0.492654\pi$
$43$	0.302660			0.0461552			0.0230776	+	0.999734i	$0.492654\pi$
$44$			4.27563i			0.644576i
$45$	0.108846	+	0.0749790i	0.0162258	+	0.0111772i
$46$	8.90184			1.31250
$47$	−3.17973	+	3.17973i	−0.463811	+	0.463811i	−0.899902	−	0.436091i	$-0.856362\pi$
$47$	−3.17973	+	3.17973i	−0.463811	+	0.463811i	0.436091	+	0.899902i	$0.356362\pi$
$48$	−1.23675	+	1.23675i	−0.178510	+	0.178510i
$49$			3.68685i			0.526692i
$50$	1.78188	+	4.67171i	0.251996	+	0.660680i
$51$	2.62341	+	2.62341i	0.367351	+	0.367351i
$52$	−1.50964			−0.209350
$53$	9.71066	+	9.71066i	1.33386	+	1.33386i	0.901884	+	0.431978i	$0.142184\pi$
$53$	9.71066	+	9.71066i	1.33386	+	1.33386i	0.431978	+	0.901884i	$0.357816\pi$
$54$	3.63715	+	3.63715i	0.494954	+	0.494954i
$55$	−7.87337	−	5.42359i	−1.06164	−	0.731316i
$56$	−1.28708	+	1.28708i	−0.171993	+	0.171993i
$57$	0.944780			0.125139
$58$	−0.279903	+	0.279903i	−0.0367531	+	0.0367531i
$59$	−4.06655	−	4.06655i	−0.529420	−	0.529420i	0.390979	−	0.920399i	$-0.372136\pi$
$59$	−4.06655	−	4.06655i	−0.529420	−	0.529420i	−0.920399	+	0.390979i	$0.872136\pi$
$60$	−0.708613	−	3.84622i	−0.0914815	−	0.496545i
$61$	4.47102	+	4.47102i	0.572455	+	0.572455i	0.932814	−	0.360359i	$-0.117346\pi$
$61$	4.47102	+	4.47102i	0.572455	+	0.572455i	−0.360359	+	0.932814i	$0.617346\pi$
$62$	1.59328	+	1.59328i	0.202347	+	0.202347i
$63$	−0.0760780	−	0.0760780i	−0.00958493	−	0.00958493i
$64$	1.00000			0.125000
$65$	1.91496	−	2.77993i	0.237522	−	0.344808i
$66$	5.28790	+	5.28790i	0.650895	+	0.650895i
$67$	−6.17649	−	6.17649i	−0.754578	−	0.754578i	0.220752	−	0.975330i	$-0.429149\pi$
$67$	−6.17649	−	6.17649i	−0.754578	−	0.754578i	−0.975330	+	0.220752i	$0.929149\pi$
$68$		−	2.12121i		−	0.257235i
$69$	11.0094	−	11.0094i	1.32537	−	1.32537i
$70$	−0.737449	−	4.00274i	−0.0881420	−	0.478419i
$71$	−7.90805			−0.938513			−0.469256	−	0.883062i	$-0.655478\pi$
$71$	−7.90805			−0.938513			−0.469256	+	0.883062i	$0.655478\pi$
$72$			0.0591090i			0.00696606i
$73$	8.32545	−	8.32545i	0.974420	−	0.974420i	−0.0252606	−	0.999681i	$-0.508042\pi$
$73$	8.32545	−	8.32545i	0.974420	−	0.974420i	0.999681	+	0.0252606i	$0.00804156\pi$
$74$	5.63727	−	2.28498i	0.655320	−	0.265624i
$75$	7.98149	+	3.57401i	0.921623	+	0.412691i
$76$	−0.381960	−	0.381960i	−0.0438138	−	0.0438138i
$77$	5.50309	+	5.50309i	0.627135	+	0.627135i
$78$	−1.86705	+	1.86705i	−0.211402	+	0.211402i
$79$	−2.20061	−	2.20061i	−0.247588	−	0.247588i	0.572392	−	0.819980i	$-0.306016\pi$
$79$	−2.20061	−	2.20061i	−0.247588	−	0.247588i	−0.819980	+	0.572392i	$0.806016\pi$
$80$	−1.26849	+	1.84145i	−0.141821	+	0.205880i
$81$	9.17383			1.01931
$82$			0.270882i			0.0299139i
$83$	10.1305	+	10.1305i	1.11197	+	1.11197i	0.992884	+	0.119087i	$0.0379968\pi$
$83$	10.1305	+	10.1305i	1.11197	+	1.11197i	0.119087	+	0.992884i	$0.462003\pi$
$84$			3.18360i			0.347359i
$85$	3.90611	+	2.69073i	0.423677	+	0.291851i
$86$	−0.302660			−0.0326367
$87$			0.692342i			0.0742268i
$88$		−	4.27563i		−	0.455784i
$89$	5.24983	−	5.24983i	0.556481	−	0.556481i	−0.371823	−	0.928304i	$-0.621267\pi$
$89$	5.24983	−	5.24983i	0.556481	−	0.556481i	0.928304	+	0.371823i	$0.121267\pi$
$90$	−0.108846	−	0.0749790i	−0.0114734	−	0.00790348i
$91$	−1.94303	+	1.94303i	−0.203685	+	0.203685i
$92$	−8.90184			−0.928081
$93$	3.94099			0.408662
$94$	3.17973	−	3.17973i	0.327964	−	0.327964i
$95$	1.18787	−	0.218849i	0.121873	−	0.0224534i
$96$	1.23675	−	1.23675i	0.126225	−	0.126225i
$97$			12.2566i			1.24447i	0.782829	+	0.622237i	$0.213776\pi$
$97$			12.2566i			1.24447i	−0.782829	+	0.622237i	$0.786224\pi$
$98$		−	3.68685i		−	0.372428i
$99$	0.252728			0.0254001
$100$	−1.78188	−	4.67171i	−0.178188	−	0.467171i
$101$			19.3052i			1.92094i	0.278383	+	0.960470i	$0.410202\pi$
$101$			19.3052i			1.92094i	−0.278383	+	0.960470i	$0.589798\pi$
$102$	−2.62341	−	2.62341i	−0.259757	−	0.259757i
$103$			10.5846i			1.04293i	0.853272	+	0.521466i	$0.174615\pi$
$103$			10.5846i			1.04293i	−0.853272	+	0.521466i	$0.825385\pi$
$104$	1.50964			0.148033
$105$	−5.86244	−	4.03835i	−0.572115	−	0.394103i
$106$	−9.71066	−	9.71066i	−0.943183	−	0.943183i
$107$	2.77915	−	2.77915i	0.268670	−	0.268670i	−0.559894	−	0.828564i	$-0.689158\pi$
$107$	2.77915	−	2.77915i	0.268670	−	0.268670i	0.828564	+	0.559894i	$0.189158\pi$
$108$	−3.63715	−	3.63715i	−0.349985	−	0.349985i
$109$	4.14598	+	4.14598i	0.397113	+	0.397113i	0.877213	−	0.480101i	$-0.159400\pi$
$109$	4.14598	+	4.14598i	0.397113	+	0.397113i	−0.480101	+	0.877213i	$0.659400\pi$
$110$	7.87337	+	5.42359i	0.750696	+	0.517119i
$111$	4.14595	−	9.79786i	0.393516	−	0.929972i
$112$	1.28708	−	1.28708i	0.121618	−	0.121618i
$113$		−	2.26739i		−	0.213298i	−0.994297	−	0.106649i	$-0.965988\pi$
$113$		−	2.26739i		−	0.213298i	0.994297	−	0.106649i	$-0.0340122\pi$
$114$	−0.944780			−0.0884867
$115$	11.2919	−	16.3923i	1.05297	−	1.52859i
$116$	0.279903	−	0.279903i	0.0259884	−	0.0259884i
$117$			0.0892335i			0.00824964i
$118$	4.06655	+	4.06655i	0.374356	+	0.374356i
$119$	−2.73017	−	2.73017i	−0.250275	−	0.250275i
$120$	0.708613	+	3.84622i	0.0646872	+	0.351110i
$121$	−7.28104			−0.661913
$122$	−4.47102	−	4.47102i	−0.404787	−	0.404787i
$123$	0.335014	+	0.335014i	0.0302072	+	0.0302072i
$124$	−1.59328	−	1.59328i	−0.143081	−	0.143081i
$125$	10.8630	+	2.64477i	0.971618	+	0.236555i
$126$	0.0760780	+	0.0760780i	0.00677757	+	0.00677757i
$127$	−7.95386	+	7.95386i	−0.705791	+	0.705791i	−0.965647	−	0.259857i	$-0.916325\pi$
$127$	−7.95386	+	7.95386i	−0.705791	+	0.705791i	0.259857	+	0.965647i	$0.416325\pi$
$128$	−1.00000			−0.0883883
$129$	−0.374315	+	0.374315i	−0.0329566	+	0.0329566i
$130$	−1.91496	+	2.77993i	−0.167954	+	0.243816i
$131$	−6.31669	−	6.31669i	−0.551892	−	0.551892i	0.375095	−	0.926987i	$-0.377610\pi$
$131$	−6.31669	−	6.31669i	−0.551892	−	0.551892i	−0.926987	+	0.375095i	$0.877610\pi$
$132$	−5.28790	−	5.28790i	−0.460252	−	0.460252i
$133$	−0.983227			−0.0852566
$134$	6.17649	+	6.17649i	0.533567	+	0.533567i
$135$	11.3113	−	2.08395i	0.973523	−	0.179358i
$136$			2.12121i			0.181893i
$137$	−3.53660	+	3.53660i	−0.302152	+	0.302152i	−0.841855	−	0.539703i	$-0.818536\pi$
$137$	−3.53660	+	3.53660i	−0.302152	+	0.302152i	0.539703	+	0.841855i	$0.318536\pi$
$138$	−11.0094	+	11.0094i	−0.937179	+	0.937179i
$139$	−5.70896			−0.484228			−0.242114	−	0.970248i	$-0.577841\pi$
$139$	−5.70896			−0.484228			−0.242114	+	0.970248i	$0.577841\pi$
$140$	0.737449	+	4.00274i	0.0623258	+	0.338293i
$141$		−	7.86507i		−	0.662358i
$142$	7.90805			0.663629
$143$		−	6.45468i		−	0.539768i
$144$		−	0.0591090i		−	0.00492575i
$145$	0.160374	+	0.870482i	0.0133184	+	0.0722896i
$146$	−8.32545	+	8.32545i	−0.689019	+	0.689019i
$147$	−4.55971	−	4.55971i	−0.376079	−	0.376079i
$148$	−5.63727	+	2.28498i	−0.463381	+	0.187824i
$149$		−	7.36973i		−	0.603752i	−0.953347	−	0.301876i	$-0.902387\pi$
$149$		−	7.36973i		−	0.603752i	0.953347	−	0.301876i	$-0.0976129\pi$
$150$	−7.98149	−	3.57401i	−0.651686	−	0.291817i
$151$			4.96769i			0.404265i	0.979358	+	0.202132i	$0.0647871\pi$
$151$			4.96769i			0.404265i	−0.979358	+	0.202132i	$0.935213\pi$
$152$	0.381960	+	0.381960i	0.0309811	+	0.0309811i
$153$	−0.125383			−0.0101366
$154$	−5.50309	−	5.50309i	−0.443451	−	0.443451i
$155$	4.95501	−	0.912892i	0.397996	−	0.0733252i
$156$	1.86705	−	1.86705i	0.149484	−	0.149484i
$157$	8.28379	−	8.28379i	0.661119	−	0.661119i	−0.294525	−	0.955644i	$-0.595161\pi$
$157$	8.28379	−	8.28379i	0.661119	−	0.661119i	0.955644	+	0.294525i	$0.0951615\pi$
$158$	2.20061	+	2.20061i	0.175071	+	0.175071i
$159$	−24.0194			−1.90486
$160$	1.26849	−	1.84145i	0.100283	−	0.145579i
$161$	−11.4574	+	11.4574i	−0.902968	+	0.902968i
$162$	−9.17383			−0.720764
$163$			19.2629i			1.50879i	0.656422	+	0.754394i	$0.272069\pi$
$163$			19.2629i			1.50879i	−0.656422	+	0.754394i	$0.727931\pi$
$164$		−	0.270882i		−	0.0211524i
$165$	16.4450	−	3.02977i	1.28024	−	0.235867i
$166$	−10.1305	−	10.1305i	−0.786282	−	0.786282i
$167$		−	22.3611i		−	1.73036i	−0.501466	−	0.865178i	$-0.667206\pi$
$167$		−	22.3611i		−	1.73036i	0.501466	−	0.865178i	$-0.332794\pi$
$168$		−	3.18360i		−	0.245620i
$169$	−10.7210			−0.824690
$170$	−3.90611	−	2.69073i	−0.299585	−	0.206370i
$171$	−0.0225773	+	0.0225773i	−0.00172653	+	0.00172653i
$172$	0.302660			0.0230776
$173$	−6.44977	+	6.44977i	−0.490367	+	0.490367i	−0.908422	−	0.418055i	$-0.862712\pi$
$173$	−6.44977	+	6.44977i	−0.490367	+	0.490367i	0.418055	+	0.908422i	$0.362712\pi$
$174$		−	0.692342i		−	0.0524863i
$175$	−8.30629	−	3.71945i	−0.627897	−	0.281164i
$176$			4.27563i			0.322288i
$177$	10.0586			0.756053
$178$	−5.24983	+	5.24983i	−0.393492	+	0.393492i
$179$	−8.44973	+	8.44973i	−0.631562	+	0.631562i	−0.948460	−	0.316897i	$-0.897359\pi$
$179$	−8.44973	+	8.44973i	−0.631562	+	0.631562i	0.316897	+	0.948460i	$0.397359\pi$
$180$	0.108846	+	0.0749790i	0.00811292	+	0.00558860i
$181$	1.63147			0.121266			0.0606330	−	0.998160i	$-0.480688\pi$
$181$	1.63147			0.121266			0.0606330	+	0.998160i	$0.480688\pi$
$182$	1.94303	−	1.94303i	0.144027	−	0.144027i
$183$	−11.0591			−0.817511
$184$	8.90184			0.656252
$185$	2.94313	−	13.2792i	0.216383	−	0.976309i
$186$	−3.94099			−0.288967
$187$	9.06953			0.663230
$188$	−3.17973	+	3.17973i	−0.231905	+	0.231905i
$189$	−9.36262			−0.681030
$190$	−1.18787	+	0.218849i	−0.0861773	+	0.0158770i
$191$	−14.3915	+	14.3915i	−1.04133	+	1.04133i	−0.0422206	+	0.999108i	$0.513443\pi$
$191$	−14.3915	+	14.3915i	−1.04133	+	1.04133i	−0.999108	+	0.0422206i	$0.986557\pi$
$192$	−1.23675	+	1.23675i	−0.0892549	+	0.0892549i
$193$	−1.88527			−0.135705			−0.0678525	−	0.997695i	$-0.521615\pi$
$193$	−1.88527			−0.135705			−0.0678525	+	0.997695i	$0.521615\pi$
$194$		−	12.2566i		−	0.879976i
$195$	1.06975	+	5.80642i	0.0766066	+	0.415807i
$196$			3.68685i			0.263346i
$197$	−16.9005	+	16.9005i	−1.20411	+	1.20411i	−0.231210	+	0.972904i	$0.574268\pi$
$197$	−16.9005	+	16.9005i	−1.20411	+	1.20411i	−0.972904	+	0.231210i	$0.925732\pi$
$198$	−0.252728			−0.0179606
$199$	6.68597	−	6.68597i	0.473956	−	0.473956i	−0.429236	−	0.903192i	$-0.641217\pi$
$199$	6.68597	−	6.68597i	0.473956	−	0.473956i	0.903192	+	0.429236i	$0.141217\pi$
$200$	1.78188	+	4.67171i	0.125998	+	0.330340i
$201$	15.2776			1.07760
$202$		−	19.3052i		−	1.35831i
$203$		−	0.720516i		−	0.0505703i
$204$	2.62341	+	2.62341i	0.183676	+	0.183676i
$205$	0.498816	+	0.343611i	0.0348388	+	0.0239988i
$206$		−	10.5846i		−	0.737464i
$207$			0.526178i			0.0365719i
$208$	−1.50964			−0.104675
$209$	1.63312	−	1.63312i	0.112965	−	0.112965i
$210$	5.86244	+	4.03835i	0.404547	+	0.278673i
$211$	16.4186			1.13030			0.565151	−	0.824987i	$-0.308818\pi$
$211$	16.4186			1.13030			0.565151	+	0.824987i	$0.308818\pi$
$212$	9.71066	+	9.71066i	0.666931	+	0.666931i
$213$	9.78029	−	9.78029i	0.670135	−	0.670135i
$214$	−2.77915	+	2.77915i	−0.189978	+	0.189978i
$215$	−0.383920	+	0.557333i	−0.0261832	+	0.0380098i
$216$	3.63715	+	3.63715i	0.247477	+	0.247477i
$217$	−4.10137			−0.278419
$218$	−4.14598	−	4.14598i	−0.280801	−	0.280801i
$219$			20.5930i			1.39155i
$220$	−7.87337	−	5.42359i	−0.530822	−	0.365658i
$221$			3.20228i			0.215408i
$222$	−4.14595	+	9.79786i	−0.278258	+	0.657590i
$223$	13.7600	+	13.7600i	0.921436	+	0.921436i	0.997131	−	0.0756947i	$-0.0241175\pi$
$223$	13.7600	+	13.7600i	0.921436	+	0.921436i	−0.0756947	+	0.997131i	$0.524117\pi$
$224$	−1.28708	+	1.28708i	−0.0859967	+	0.0859967i
$225$	−0.276140	+	0.105325i	−0.0184093	+	0.00702167i
$226$			2.26739i			0.150825i
$227$		−	5.23067i		−	0.347172i	−0.984819	−	0.173586i	$-0.944465\pi$
$227$		−	5.23067i		−	0.347172i	0.984819	−	0.173586i	$-0.0555355\pi$
$228$	0.944780			0.0625696
$229$		−	3.12544i		−	0.206535i	−0.994654	−	0.103267i	$-0.967070\pi$
$229$		−	3.12544i		−	0.206535i	0.994654	−	0.103267i	$-0.0329298\pi$
$230$	−11.2919	+	16.3923i	−0.744564	+	1.08088i
$231$	−13.6119			−0.895597
$232$	−0.279903	+	0.279903i	−0.0183766	+	0.0183766i
$233$	−7.43576	+	7.43576i	−0.487133	+	0.487133i	−0.907400	−	0.420268i	$-0.861936\pi$
$233$	−7.43576	+	7.43576i	−0.487133	+	0.487133i	0.420268	+	0.907400i	$0.361936\pi$
$234$		−	0.0892335i		−	0.00583338i
$235$	−1.82187	−	9.88875i	−0.118845	−	0.645071i
$236$	−4.06655	−	4.06655i	−0.264710	−	0.264710i
$237$	5.44322			0.353575
$238$	2.73017	+	2.73017i	0.176971	+	0.176971i
$239$	19.2129	+	19.2129i	1.24278	+	1.24278i	0.958842	+	0.283939i	$0.0916414\pi$
$239$	19.2129	+	19.2129i	1.24278	+	1.24278i	0.283939	+	0.958842i	$0.408359\pi$
$240$	−0.708613	−	3.84622i	−0.0457407	−	0.248272i
$241$	19.0019	−	19.0019i	1.22402	−	1.22402i	0.257830	−	0.966190i	$-0.416993\pi$
$241$	19.0019	−	19.0019i	1.22402	−	1.22402i	0.966190	−	0.257830i	$-0.0830073\pi$
$242$	7.28104			0.468043
$243$	−0.434298	+	0.434298i	−0.0278602	+	0.0278602i
$244$	4.47102	+	4.47102i	0.286228	+	0.286228i
$245$	−6.78914	−	4.67672i	−0.433743	−	0.298785i
$246$	−0.335014	−	0.335014i	−0.0213597	−	0.0213597i
$247$	0.576624	+	0.576624i	0.0366897	+	0.0366897i
$248$	1.59328	+	1.59328i	0.101174	+	0.101174i
$249$	−25.0579			−1.58798
$250$	−10.8630	−	2.64477i	−0.687038	−	0.167270i
$251$	−2.56669	−	2.56669i	−0.162008	−	0.162008i	0.621448	−	0.783456i	$-0.286545\pi$
$251$	−2.56669	−	2.56669i	−0.162008	−	0.162008i	−0.783456	+	0.621448i	$0.786545\pi$
$252$	−0.0760780	−	0.0760780i	−0.00479246	−	0.00479246i
$253$		−	38.0610i		−	2.39287i
$254$	7.95386	−	7.95386i	0.499069	−	0.499069i
$255$	−8.15865	+	1.50312i	−0.510915	+	0.0941289i
$256$	1.00000			0.0625000
$257$			13.8993i			0.867015i	0.901150	+	0.433507i	$0.142724\pi$
$257$			13.8993i			0.867015i	−0.901150	+	0.433507i	$0.857276\pi$
$258$	0.374315	−	0.374315i	0.0233038	−	0.0233038i
$259$	−4.31467	+	10.1966i	−0.268100	+	0.633585i
$260$	1.91496	−	2.77993i	0.118761	−	0.172404i
$261$	−0.0165448	−	0.0165448i	−0.00102410	−	0.00102410i
$262$	6.31669	+	6.31669i	0.390246	+	0.390246i
$263$	14.2273	−	14.2273i	0.877290	−	0.877290i	−0.115964	−	0.993253i	$-0.536996\pi$
$263$	14.2273	−	14.2273i	0.877290	−	0.877290i	0.993253	+	0.115964i	$0.0369956\pi$
$264$	5.28790	+	5.28790i	0.325448	+	0.325448i
$265$	−30.1996	+	5.56385i	−1.85514	+	0.341784i
$266$	0.983227			0.0602855
$267$			12.9855i			0.794699i
$268$	−6.17649	−	6.17649i	−0.377289	−	0.377289i
$269$		−	21.4303i		−	1.30663i	−0.757086	−	0.653315i	$-0.773378\pi$
$269$		−	21.4303i		−	1.30663i	0.757086	−	0.653315i	$-0.226622\pi$
$270$	−11.3113	+	2.08395i	−0.688385	+	0.126825i
$271$	−17.5063			−1.06343			−0.531717	−	0.846922i	$-0.678453\pi$
$271$	−17.5063			−1.06343			−0.531717	+	0.846922i	$0.678453\pi$
$272$		−	2.12121i		−	0.128617i
$273$		−	4.80610i		−	0.290878i
$274$	3.53660	−	3.53660i	0.213654	−	0.213654i
$275$	19.9745	−	7.61866i	1.20451	−	0.459422i
$276$	11.0094	−	11.0094i	0.662686	−	0.662686i
$277$	−9.92772			−0.596499			−0.298249	−	0.954488i	$-0.596403\pi$
$277$	−9.92772			−0.596499			−0.298249	+	0.954488i	$0.596403\pi$
$278$	5.70896			0.342401
$279$	−0.0941773	+	0.0941773i	−0.00563825	+	0.00563825i
$280$	−0.737449	−	4.00274i	−0.0440710	−	0.239210i
$281$	9.25821	−	9.25821i	0.552299	−	0.552299i	−0.374805	−	0.927104i	$-0.622290\pi$
$281$	9.25821	−	9.25821i	0.552299	−	0.552299i	0.927104	+	0.374805i	$0.122290\pi$
$282$			7.86507i			0.468358i
$283$			7.32826i			0.435620i	0.975991	+	0.217810i	$0.0698912\pi$
$283$			7.32826i			0.435620i	−0.975991	+	0.217810i	$0.930109\pi$
$284$	−7.90805			−0.469256
$285$	−1.19844	+	1.73976i	−0.0709895	+	0.103055i
$286$			6.45468i			0.381673i
$287$	−0.348647	−	0.348647i	−0.0205800	−	0.0205800i
$288$			0.0591090i			0.00348303i
$289$	12.5005			0.735321
$290$	−0.160374	−	0.870482i	−0.00941750	−	0.0511165i
$291$	−15.1584	−	15.1584i	−0.888603	−	0.888603i
$292$	8.32545	−	8.32545i	0.487210	−	0.487210i
$293$	−12.6098	−	12.6098i	−0.736675	−	0.736675i	0.235258	−	0.971933i	$-0.424406\pi$
$293$	−12.6098	−	12.6098i	−0.736675	−	0.736675i	−0.971933	+	0.235258i	$0.924406\pi$
$294$	4.55971	+	4.55971i	0.265928	+	0.265928i
$295$	12.6467	−	2.32998i	0.736321	−	0.135657i
$296$	5.63727	−	2.28498i	0.327660	−	0.132812i
$297$	15.5511	−	15.5511i	0.902368	−	0.902368i
$298$			7.36973i			0.426917i
$299$	13.4386			0.777175
$300$	7.98149	+	3.57401i	0.460812	+	0.206345i
$301$	0.389548	−	0.389548i	0.0224532	−	0.0224532i
$302$		−	4.96769i		−	0.285858i
$303$	−23.8758	−	23.8758i	−1.37163	−	1.37163i
$304$	−0.381960	−	0.381960i	−0.0219069	−	0.0219069i
$305$	−13.9046	+	2.56173i	−0.796174	+	0.146684i
$306$	0.125383			0.00716765
$307$	17.0291	+	17.0291i	0.971903	+	0.971903i	0.999616	−	0.0277133i	$-0.00882256\pi$
$307$	17.0291	+	17.0291i	0.971903	+	0.971903i	−0.0277133	+	0.999616i	$0.508823\pi$
$308$	5.50309	+	5.50309i	0.313567	+	0.313567i
$309$	−13.0905	−	13.0905i	−0.744694	−	0.744694i
$310$	−4.95501	+	0.912892i	−0.281426	+	0.0518488i
$311$	3.74670	+	3.74670i	0.212456	+	0.212456i	0.805310	−	0.592854i	$-0.201999\pi$
$311$	3.74670	+	3.74670i	0.212456	+	0.212456i	−0.592854	+	0.805310i	$0.701999\pi$
$312$	−1.86705	+	1.86705i	−0.105701	+	0.105701i
$313$	14.7056			0.831208			0.415604	−	0.909546i	$-0.363570\pi$
$313$	14.7056			0.831208			0.415604	+	0.909546i	$0.363570\pi$
$314$	−8.28379	+	8.28379i	−0.467481	+	0.467481i
$315$	0.236598	−	0.0435899i	0.0133308	−	0.00245601i
$316$	−2.20061	−	2.20061i	−0.123794	−	0.123794i
$317$	13.6458	+	13.6458i	0.766423	+	0.766423i	0.977475	−	0.211052i	$-0.0676890\pi$
$317$	13.6458	+	13.6458i	0.766423	+	0.766423i	−0.211052	+	0.977475i	$0.567689\pi$
$318$	24.0194			1.34694
$319$	1.19676	+	1.19676i	0.0670059	+	0.0670059i
$320$	−1.26849	+	1.84145i	−0.0709106	+	0.102940i
$321$			6.87423i			0.383682i
$322$	11.4574	−	11.4574i	0.638495	−	0.638495i
$323$	−0.810219	+	0.810219i	−0.0450818	+	0.0450818i
$324$	9.17383			0.509657
$325$	2.69000	+	7.05262i	0.149214	+	0.391209i
$326$		−	19.2629i		−	1.06687i
$327$	−10.2551			−0.567108
$328$			0.270882i			0.0149570i
$329$			8.18513i			0.451261i
$330$	−16.4450	+	3.02977i	−0.905269	+	0.166783i
$331$	−15.5423	+	15.5423i	−0.854280	+	0.854280i	−0.990657	−	0.136377i	$-0.956454\pi$
$331$	−15.5423	+	15.5423i	−0.854280	+	0.854280i	0.136377	+	0.990657i	$0.456454\pi$
$332$	10.1305	+	10.1305i	0.555985	+	0.555985i
$333$	0.135063	+	0.333213i	0.00740141	+	0.0182600i
$334$			22.3611i			1.22355i
$335$	19.2085	−	3.53890i	1.04947	−	0.193351i
$336$			3.18360i			0.173680i
$337$	14.8294	+	14.8294i	0.807811	+	0.807811i	0.984302	−	0.176491i	$-0.0564747\pi$
$337$	14.8294	+	14.8294i	0.807811	+	0.807811i	−0.176491	+	0.984302i	$0.556475\pi$
$338$	10.7210			0.583144
$339$	2.80420	+	2.80420i	0.152303	+	0.152303i
$340$	3.90611	+	2.69073i	0.211838	+	0.145925i
$341$	6.81229	−	6.81229i	0.368906	−	0.368906i
$342$	0.0225773	−	0.0225773i	0.00122084	−	0.00122084i
$343$	13.7548	+	13.7548i	0.742691	+	0.742691i
$344$	−0.302660			−0.0163183
$345$	6.30795	+	34.2384i	0.339609	+	1.84334i
$346$	6.44977	−	6.44977i	0.346742	−	0.346742i
$347$	−8.24738			−0.442742			−0.221371	−	0.975190i	$-0.571053\pi$
$347$	−8.24738			−0.442742			−0.221371	+	0.975190i	$0.571053\pi$
$348$			0.692342i			0.0371134i
$349$			16.1967i			0.866991i	0.901156	+	0.433496i	$0.142720\pi$
$349$			16.1967i			0.866991i	−0.901156	+	0.433496i	$0.857280\pi$
$350$	8.30629	+	3.71945i	0.443990	+	0.198813i
$351$	5.49080	+	5.49080i	0.293077	+	0.293077i
$352$		−	4.27563i		−	0.227892i
$353$		−	20.3765i		−	1.08453i	−0.840207	−	0.542266i	$-0.817567\pi$
$353$		−	20.3765i		−	1.08453i	0.840207	−	0.542266i	$-0.182433\pi$
$354$	−10.0586			−0.534610
$355$	10.0313	−	14.5623i	0.532404	−	0.772885i
$356$	5.24983	−	5.24983i	0.278241	−	0.278241i
$357$	6.75309			0.357411
$358$	8.44973	−	8.44973i	0.446582	−	0.446582i
$359$			30.2708i			1.59763i	0.601575	+	0.798816i	$0.294540\pi$
$359$			30.2708i			1.59763i	−0.601575	+	0.798816i	$0.705460\pi$
$360$	−0.108846	−	0.0749790i	−0.00573670	−	0.00395174i
$361$		−	18.7082i		−	0.984643i
$362$	−1.63147			−0.0857480
$363$	9.00484	−	9.00484i	0.472632	−	0.472632i
$364$	−1.94303	+	1.94303i	−0.101843	+	0.101843i
$365$	4.77017	+	25.8916i	0.249682	+	1.35523i
$366$	11.0591			0.578067
$367$	13.0615	−	13.0615i	0.681804	−	0.681804i	−0.278603	−	0.960406i	$-0.589871\pi$
$367$	13.0615	−	13.0615i	0.681804	−	0.681804i	0.960406	+	0.278603i	$0.0898713\pi$
$368$	−8.90184			−0.464040
$369$	−0.0160116			−0.000833529
$370$	−2.94313	+	13.2792i	−0.153006	+	0.690354i
$371$	24.9968			1.29777
$372$	3.94099			0.204331
$373$	−16.1154	+	16.1154i	−0.834423	+	0.834423i	−0.988118	−	0.153695i	$-0.950883\pi$
$373$	−16.1154	+	16.1154i	−0.834423	+	0.834423i	0.153695	+	0.988118i	$0.450883\pi$
$374$	−9.06953			−0.468974
$375$	−16.7058	+	10.1639i	−0.862683	+	0.524863i
$376$	3.17973	−	3.17973i	0.163982	−	0.163982i
$377$	−0.422554	+	0.422554i	−0.0217627	+	0.0217627i
$378$	9.36262			0.481561
$379$		−	7.07736i		−	0.363539i	−0.983341	−	0.181770i	$-0.941817\pi$
$379$		−	7.07736i		−	0.363539i	0.983341	−	0.181770i	$-0.0581825\pi$
$380$	1.18787	−	0.218849i	0.0609366	−	0.0112267i
$381$		−	19.6739i		−	1.00792i
$382$	14.3915	−	14.3915i	0.736331	−	0.736331i
$383$	−17.6507			−0.901911			−0.450955	−	0.892546i	$-0.648917\pi$
$383$	−17.6507			−0.901911			−0.450955	+	0.892546i	$0.648917\pi$
$384$	1.23675	−	1.23675i	0.0631127	−	0.0631127i
$385$	−17.1143	+	3.15306i	−0.872223	+	0.160695i
$386$	1.88527			0.0959579
$387$		−	0.0178899i		−	0.000909395i
$388$			12.2566i			0.622237i
$389$	14.9010	+	14.9010i	0.755508	+	0.755508i	0.975501	−	0.219993i	$-0.0706035\pi$
$389$	14.9010	+	14.9010i	0.755508	+	0.755508i	−0.219993	+	0.975501i	$0.570603\pi$
$390$	−1.06975	−	5.80642i	−0.0541690	−	0.294020i
$391$			18.8827i			0.954939i
$392$		−	3.68685i		−	0.186214i
$393$	15.6244			0.788144
$394$	16.9005	−	16.9005i	0.851437	−	0.851437i
$395$	6.84376	−	1.26087i	0.344347	−	0.0634412i
$396$	0.252728			0.0127001
$397$	−3.61759	−	3.61759i	−0.181562	−	0.181562i	0.610474	−	0.792036i	$-0.290979\pi$
$397$	−3.61759	−	3.61759i	−0.181562	−	0.181562i	−0.792036	+	0.610474i	$0.790979\pi$
$398$	−6.68597	+	6.68597i	−0.335137	+	0.335137i
$399$	1.21601	−	1.21601i	0.0608765	−	0.0608765i
$400$	−1.78188	−	4.67171i	−0.0890939	−	0.233586i
$401$	−12.9977	−	12.9977i	−0.649075	−	0.649075i	0.303694	−	0.952770i	$-0.401780\pi$
$401$	−12.9977	−	12.9977i	−0.649075	−	0.649075i	−0.952770	+	0.303694i	$0.901780\pi$
$402$	−15.2776			−0.761976
$403$	2.40529	+	2.40529i	0.119816	+	0.119816i
$404$			19.3052i			0.960470i
$405$	−11.6369	+	16.8932i	−0.578242	+	0.839428i
$406$			0.720516i			0.0357586i
$407$	−9.76975	−	24.1029i	−0.484269	−	1.19474i
$408$	−2.62341	−	2.62341i	−0.129878	−	0.129878i
$409$	1.73592	−	1.73592i	0.0858355	−	0.0858355i	−0.662885	−	0.748721i	$-0.730668\pi$
$409$	1.73592	−	1.73592i	0.0858355	−	0.0858355i	0.748721	+	0.662885i	$0.230668\pi$
$410$	−0.498816	−	0.343611i	−0.0246348	−	0.0169697i
$411$		−	8.74779i		−	0.431497i
$412$			10.5846i			0.521466i
$413$	−10.4680			−0.515095
$414$		−	0.526178i		−	0.0258603i
$415$	−31.5053	+	5.80442i	−1.54654	+	0.284928i
$416$	1.50964			0.0740164
$417$	7.06057	−	7.06057i	0.345758	−	0.345758i
$418$	−1.63312	+	1.63312i	−0.0798786	+	0.0798786i
$419$		−	16.7428i		−	0.817941i	−0.912548	−	0.408970i	$-0.865888\pi$
$419$		−	16.7428i		−	0.817941i	0.912548	−	0.408970i	$-0.134112\pi$
$420$	−5.86244	−	4.03835i	−0.286058	−	0.197052i
$421$	−0.463240	−	0.463240i	−0.0225770	−	0.0225770i	0.695728	−	0.718305i	$-0.255082\pi$
$421$	−0.463240	−	0.463240i	−0.0225770	−	0.0225770i	−0.718305	+	0.695728i	$0.755082\pi$
$422$	−16.4186			−0.799245
$423$	0.187950	+	0.187950i	0.00913846	+	0.00913846i
$424$	−9.71066	−	9.71066i	−0.471592	−	0.471592i
$425$	−9.90970	+	3.77974i	−0.480691	+	0.183345i
$426$	−9.78029	+	9.78029i	−0.473857	+	0.473857i
$427$	11.5091			0.556965
$428$	2.77915	−	2.77915i	0.134335	−	0.134335i
$429$	7.98284	+	7.98284i	0.385415	+	0.385415i
$430$	0.383920	−	0.557333i	0.0185143	−	0.0268770i
$431$	−27.2475	−	27.2475i	−1.31247	−	1.31247i	−0.919591	−	0.392877i	$-0.871480\pi$
$431$	−27.2475	−	27.2475i	−1.31247	−	1.31247i	−0.392877	−	0.919591i	$-0.628520\pi$
$432$	−3.63715	−	3.63715i	−0.174993	−	0.174993i
$433$	17.1809	+	17.1809i	0.825660	+	0.825660i	0.986913	−	0.161253i	$-0.0515536\pi$
$433$	17.1809	+	17.1809i	0.825660	+	0.825660i	−0.161253	+	0.986913i	$0.551554\pi$
$434$	4.10137			0.196872
$435$	−1.27491	−	0.878227i	−0.0611274	−	0.0421078i
$436$	4.14598	+	4.14598i	0.198556	+	0.198556i
$437$	3.40015	+	3.40015i	0.162651	+	0.162651i
$438$		−	20.5930i		−	0.983973i
$439$	13.3023	−	13.3023i	0.634886	−	0.634886i	−0.314404	−	0.949289i	$-0.601805\pi$
$439$	13.3023	−	13.3023i	0.634886	−	0.634886i	0.949289	+	0.314404i	$0.101805\pi$
$440$	7.87337	+	5.42359i	0.375348	+	0.258559i
$441$	0.217926			0.0103774
$442$		−	3.20228i		−	0.152317i
$443$	24.4725	−	24.4725i	1.16272	−	1.16272i	0.178845	−	0.983877i	$-0.442764\pi$
$443$	24.4725	−	24.4725i	1.16272	−	1.16272i	0.983877	−	0.178845i	$-0.0572360\pi$
$444$	4.14595	−	9.79786i	0.196758	−	0.464986i
$445$	3.00796	+	16.3267i	0.142591	+	0.773958i
$446$	−13.7600	−	13.7600i	−0.651554	−	0.651554i
$447$	9.11453	+	9.11453i	0.431102	+	0.431102i
$448$	1.28708	−	1.28708i	0.0608088	−	0.0608088i
$449$	−20.4966	−	20.4966i	−0.967296	−	0.967296i	0.0321863	−	0.999482i	$-0.489753\pi$
$449$	−20.4966	−	20.4966i	−0.967296	−	0.967296i	−0.999482	+	0.0321863i	$0.989753\pi$
$450$	0.276140	−	0.105325i	0.0130174	−	0.00496507i
$451$	1.15819			0.0545372
$452$		−	2.26739i		−	0.106649i
$453$	−6.14380	−	6.14380i	−0.288661	−	0.288661i
$454$			5.23067i			0.245488i
$455$	−1.11329	−	6.04271i	−0.0521916	−	0.283287i
$456$	−0.944780			−0.0442434
$457$			25.3795i			1.18720i	0.804759	+	0.593601i	$0.202294\pi$
$457$			25.3795i			1.18720i	−0.804759	+	0.593601i	$0.797706\pi$
$458$			3.12544i			0.146042i
$459$	−7.71517	+	7.71517i	−0.360113	+	0.360113i
$460$	11.2919	−	16.3923i	0.526486	−	0.764295i
$461$	−19.5684	+	19.5684i	−0.911392	+	0.911392i	−0.996382	−	0.0849894i	$-0.972914\pi$
$461$	−19.5684	+	19.5684i	−0.911392	+	0.911392i	0.0849894	+	0.996382i	$0.472914\pi$
$462$	13.6119			0.633283
$463$	−40.3494			−1.87520			−0.937599	−	0.347720i	$-0.886956\pi$
$463$	−40.3494			−1.87520			−0.937599	+	0.347720i	$0.886956\pi$
$464$	0.279903	−	0.279903i	0.0129942	−	0.0129942i
$465$	−4.99910	+	7.25714i	−0.231828	+	0.336542i
$466$	7.43576	−	7.43576i	0.344455	−	0.344455i
$467$		−	6.84915i		−	0.316941i	−0.987364	−	0.158471i	$-0.949344\pi$
$467$		−	6.84915i		−	0.316941i	0.987364	−	0.158471i	$-0.0506563\pi$
$468$			0.0892335i			0.00412482i
$469$	−15.8993			−0.734161
$470$	1.82187	+	9.88875i	0.0840364	+	0.456134i
$471$			20.4900i			0.944129i
$472$	4.06655	+	4.06655i	0.187178	+	0.187178i
$473$			1.29406i			0.0595011i
$474$	−5.44322			−0.250015
$475$	−1.10380	+	2.46501i	−0.0506459	+	0.113103i
$476$	−2.73017	−	2.73017i	−0.125137	−	0.125137i
$477$	0.573987	−	0.573987i	0.0262811	−	0.0262811i
$478$	−19.2129	−	19.2129i	−0.878779	−	0.878779i
$479$	−30.4703	−	30.4703i	−1.39222	−	1.39222i	−0.820327	−	0.571895i	$-0.806208\pi$
$479$	−30.4703	−	30.4703i	−1.39222	−	1.39222i	−0.571895	−	0.820327i	$-0.693792\pi$
$480$	0.708613	+	3.84622i	0.0323436	+	0.175555i
$481$	8.51028	−	3.44951i	0.388035	−	0.157284i
$482$	−19.0019	+	19.0019i	−0.865513	+	0.865513i
$483$		−	28.3399i		−	1.28951i
$484$	−7.28104			−0.330956
$485$	−22.5700	−	15.5474i	−1.02485	−	0.705971i
$486$	0.434298	−	0.434298i	0.0197001	−	0.0197001i
$487$			38.9294i			1.76406i	0.471194	+	0.882029i	$0.343823\pi$
$487$			38.9294i			1.76406i	−0.471194	+	0.882029i	$0.656177\pi$
$488$	−4.47102	−	4.47102i	−0.202393	−	0.202393i
$489$	−23.8234	−	23.8234i	−1.07733	−	1.07733i
$490$	6.78914	+	4.67672i	0.306702	+	0.211273i
$491$	8.64964			0.390353			0.195176	−	0.980768i	$-0.437472\pi$
$491$	8.64964			0.390353			0.195176	+	0.980768i	$0.437472\pi$
$492$	0.335014	+	0.335014i	0.0151036	+	0.0151036i
$493$	−0.593735	−	0.593735i	−0.0267405	−	0.0267405i
$494$	−0.576624	−	0.576624i	−0.0259435	−	0.0259435i
$495$	−0.320583	+	0.465387i	−0.0144091	+	0.0209176i
$496$	−1.59328	−	1.59328i	−0.0715405	−	0.0715405i
$497$	−10.1783	+	10.1783i	−0.456559	+	0.456559i
$498$	25.0579			1.12287
$499$	−10.9240	+	10.9240i	−0.489024	+	0.489024i	−0.907998	−	0.418974i	$-0.862390\pi$
$499$	−10.9240	+	10.9240i	−0.489024	+	0.489024i	0.418974	+	0.907998i	$0.362390\pi$
$500$	10.8630	+	2.64477i	0.485809	+	0.118278i
$501$	27.6551	+	27.6551i	1.23554	+	1.23554i
$502$	2.56669	+	2.56669i	0.114557	+	0.114557i
$503$	37.0071			1.65007			0.825033	−	0.565085i	$-0.191157\pi$
$503$	37.0071			1.65007			0.825033	+	0.565085i	$0.191157\pi$
$504$	0.0760780	+	0.0760780i	0.00338878	+	0.00338878i
$505$	−35.5496	−	24.4884i	−1.58194	−	1.08972i
$506$			38.0610i			1.69202i
$507$	13.2592	−	13.2592i	0.588861	−	0.588861i
$508$	−7.95386	+	7.95386i	−0.352895	+	0.352895i
$509$	1.39333			0.0617583			0.0308791	−	0.999523i	$-0.490169\pi$
$509$	1.39333			0.0617583			0.0308791	+	0.999523i	$0.490169\pi$
$510$	8.15865	−	1.50312i	0.361271	−	0.0665592i
$511$		−	21.4311i		−	0.948054i
$512$	−1.00000			−0.0441942
$513$			2.77849i			0.122673i
$514$		−	13.8993i		−	0.613072i
$515$	−19.4910	−	13.4264i	−0.858877	−	0.591640i
$516$	−0.374315	+	0.374315i	−0.0164783	+	0.0164783i
$517$	−13.5953	−	13.5953i	−0.597923	−	0.597923i
$518$	4.31467	−	10.1966i	0.189576	−	0.448012i
$519$		−	15.9535i		−	0.700282i
$520$	−1.91496	+	2.77993i	−0.0839768	+	0.121908i
$521$			3.37437i			0.147834i	0.997264	+	0.0739169i	$0.0235500\pi$
$521$			3.37437i			0.147834i	−0.997264	+	0.0739169i	$0.976450\pi$
$522$	0.0165448	+	0.0165448i	0.000724146	+	0.000724146i
$523$	−6.99302			−0.305783			−0.152892	−	0.988243i	$-0.548859\pi$
$523$	−6.99302			−0.305783			−0.152892	+	0.988243i	$0.548859\pi$
$524$	−6.31669	−	6.31669i	−0.275946	−	0.275946i
$525$	14.8729	−	5.67279i	0.649105	−	0.247581i
$526$	−14.2273	+	14.2273i	−0.620338	+	0.620338i
$527$	−3.37969	+	3.37969i	−0.147222	+	0.147222i
$528$	−5.28790	−	5.28790i	−0.230126	−	0.230126i
$529$	56.2427			2.44534
$530$	30.1996	−	5.56385i	1.31179	−	0.241678i
$531$	−0.240370	+	0.240370i	−0.0104312	+	0.0104312i
$532$	−0.983227			−0.0426283
$533$			0.408936i			0.0177130i
$534$		−	12.9855i		−	0.561937i
$535$	1.59235	+	8.64297i	0.0688432	+	0.373668i
$536$	6.17649	+	6.17649i	0.266784	+	0.266784i
$537$		−	20.9004i		−	0.901920i
$538$			21.4303i			0.923927i
$539$	−15.7636			−0.678986
$540$	11.3113	−	2.08395i	0.486762	−	0.0896790i
$541$	3.85792	−	3.85792i	0.165865	−	0.165865i	−0.619294	−	0.785159i	$-0.712581\pi$
$541$	3.85792	−	3.85792i	0.165865	−	0.165865i	0.785159	+	0.619294i	$0.212581\pi$
$542$	17.5063			0.751962
$543$	−2.01772	+	2.01772i	−0.0865886	+	0.0865886i
$544$			2.12121i			0.0909463i
$545$	−12.8937	+	2.37549i	−0.552307	+	0.101755i
$546$			4.80610i			0.205682i
$547$	−5.76769			−0.246609			−0.123304	−	0.992369i	$-0.539349\pi$
$547$	−5.76769			−0.246609			−0.123304	+	0.992369i	$0.539349\pi$
$548$	−3.53660	+	3.53660i	−0.151076	+	0.151076i
$549$	0.264277	−	0.264277i	0.0112791	−	0.0112791i
$550$	−19.9745	+	7.61866i	−0.851717	+	0.324861i
$551$	−0.213824			−0.00910920
$552$	−11.0094	+	11.0094i	−0.468590	+	0.468590i
$553$	−5.66473			−0.240889
$554$	9.92772			0.421788
$555$	12.7832	+	20.0630i	0.542616	+	0.851628i
$556$	−5.70896			−0.242114
$557$	−33.4435			−1.41705			−0.708524	−	0.705687i	$-0.750639\pi$
$557$	−33.4435			−1.41705			−0.708524	+	0.705687i	$0.750639\pi$
$558$	0.0941773	−	0.0941773i	0.00398684	−	0.00398684i
$559$	−0.456909			−0.0193252
$560$	0.737449	+	4.00274i	0.0311629	+	0.169147i
$561$	−11.2168	+	11.2168i	−0.473572	+	0.473572i
$562$	−9.25821	+	9.25821i	−0.390534	+	0.390534i
$563$	14.9840			0.631500			0.315750	−	0.948842i	$-0.397744\pi$
$563$	14.9840			0.631500			0.315750	+	0.948842i	$0.397744\pi$
$564$		−	7.86507i		−	0.331179i
$565$	4.17529	+	2.87616i	0.175656	+	0.121001i
$566$		−	7.32826i		−	0.308030i
$567$	11.8075	−	11.8075i	0.495867	−	0.495867i
$568$	7.90805			0.331814
$569$	8.42505	−	8.42505i	0.353197	−	0.353197i	−0.508101	−	0.861298i	$-0.669652\pi$
$569$	8.42505	−	8.42505i	0.353197	−	0.353197i	0.861298	+	0.508101i	$0.169652\pi$
$570$	1.19844	−	1.73976i	0.0501972	−	0.0728707i
$571$	−22.3944			−0.937176			−0.468588	−	0.883417i	$-0.655237\pi$
$571$	−22.3944			−0.937176			−0.468588	+	0.883417i	$0.655237\pi$
$572$		−	6.45468i		−	0.269884i
$573$		−	35.5973i		−	1.48710i
$574$	0.348647	+	0.348647i	0.0145523	+	0.0145523i
$575$	15.8620	+	41.5868i	0.661491	+	1.73429i
$576$		−	0.0591090i		−	0.00246287i
$577$			15.1857i			0.632189i	0.948728	+	0.316094i	$0.102372\pi$
$577$			15.1857i			0.632189i	−0.948728	+	0.316094i	$0.897628\pi$
$578$	−12.5005			−0.519950
$579$	2.33162	−	2.33162i	0.0968986	−	0.0968986i
$580$	0.160374	+	0.870482i	0.00665918	+	0.0361448i
$581$	26.0776			1.08188
$582$	15.1584	+	15.1584i	0.628337	+	0.628337i
$583$	−41.5192	+	41.5192i	−1.71955	+	1.71955i
$584$	−8.32545	+	8.32545i	−0.344510	+	0.344510i
$585$	−0.164319	−	0.113192i	−0.00679376	−	0.00467990i
$586$	12.6098	+	12.6098i	0.520908	+	0.520908i
$587$	36.1936			1.49387			0.746934	−	0.664898i	$-0.231525\pi$
$587$	36.1936			1.49387			0.746934	+	0.664898i	$0.231525\pi$
$588$	−4.55971	−	4.55971i	−0.188039	−	0.188039i
$589$			1.21714i			0.0501514i
$590$	−12.6467	+	2.32998i	−0.520657	+	0.0959239i
$591$		−	41.8036i		−	1.71957i
$592$	−5.63727	+	2.28498i	−0.231691	+	0.0939122i
$593$	28.1253	+	28.1253i	1.15497	+	1.15497i	0.985543	+	0.169424i	$0.0541906\pi$
$593$	28.1253	+	28.1253i	1.15497	+	1.15497i	0.169424	+	0.985543i	$0.445809\pi$
$594$	−15.5511	+	15.5511i	−0.638070	+	0.638070i
$595$	8.49067	−	1.56429i	0.348083	−	0.0641295i
$596$		−	7.36973i		−	0.301876i
$597$			16.5378i			0.676846i
$598$	−13.4386			−0.549545
$599$			8.68551i			0.354880i	0.984132	+	0.177440i	$0.0567816\pi$
$599$			8.68551i			0.354880i	−0.984132	+	0.177440i	$0.943218\pi$
$600$	−7.98149	−	3.57401i	−0.325843	−	0.145908i
$601$	−17.1654			−0.700191			−0.350095	−	0.936714i	$-0.613851\pi$
$601$	−17.1654			−0.700191			−0.350095	+	0.936714i	$0.613851\pi$
$602$	−0.389548	+	0.389548i	−0.0158768	+	0.0158768i
$603$	−0.365086	+	0.365086i	−0.0148674	+	0.0148674i
$604$			4.96769i			0.202132i
$605$	9.23591	−	13.4077i	0.375493	−	0.545100i
$606$	23.8758	+	23.8758i	0.969886	+	0.969886i
$607$	40.1612			1.63009			0.815047	−	0.579395i	$-0.196711\pi$
$607$	40.1612			1.63009			0.815047	+	0.579395i	$0.196711\pi$
$608$	0.381960	+	0.381960i	0.0154905	+	0.0154905i
$609$	0.891100	+	0.891100i	0.0361092	+	0.0361092i
$610$	13.9046	−	2.56173i	0.562980	−	0.103721i
$611$	4.80026	−	4.80026i	0.194198	−	0.194198i
$612$	−0.125383			−0.00506830
$613$	−12.5774	+	12.5774i	−0.507997	+	0.507997i	−0.913911	−	0.405914i	$-0.866953\pi$
$613$	−12.5774	+	12.5774i	−0.507997	+	0.507997i	0.405914	+	0.913911i	$0.366953\pi$
$614$	−17.0291	−	17.0291i	−0.687239	−	0.687239i
$615$	−1.04187	+	0.191951i	−0.0420124	+	0.00774019i
$616$	−5.50309	−	5.50309i	−0.221726	−	0.221726i
$617$	−33.9984	−	33.9984i	−1.36872	−	1.36872i	−0.862264	−	0.506459i	$-0.830954\pi$
$617$	−33.9984	−	33.9984i	−1.36872	−	1.36872i	−0.506459	−	0.862264i	$-0.669046\pi$
$618$	13.0905	+	13.0905i	0.526578	+	0.526578i
$619$	−5.28421			−0.212390			−0.106195	−	0.994345i	$-0.533867\pi$
$619$	−5.28421			−0.212390			−0.106195	+	0.994345i	$0.533867\pi$
$620$	4.95501	−	0.912892i	0.198998	−	0.0366626i
$621$	32.3773	+	32.3773i	1.29926	+	1.29926i
$622$	−3.74670	−	3.74670i	−0.150229	−	0.150229i
$623$		−	13.5139i		−	0.541424i
$624$	1.86705	−	1.86705i	0.0747420	−	0.0747420i
$625$	−18.6498	+	16.6489i	−0.745993	+	0.665954i
$626$	−14.7056			−0.587753
$627$			4.03953i			0.161323i
$628$	8.28379	−	8.28379i	0.330559	−	0.330559i
$629$	4.84694	+	11.9579i	0.193260	+	0.476791i
$630$	−0.236598	+	0.0435899i	−0.00942628	+	0.00173666i
$631$	−5.35861	−	5.35861i	−0.213323	−	0.213323i	0.592355	−	0.805677i	$-0.298198\pi$
$631$	−5.35861	−	5.35861i	−0.213323	−	0.213323i	−0.805677	+	0.592355i	$0.798198\pi$
$632$	2.20061	+	2.20061i	0.0875356	+	0.0875356i
$633$	−20.3057	+	20.3057i	−0.807080	+	0.807080i
$634$	−13.6458	−	13.6458i	−0.541943	−	0.541943i
$635$	−4.55726	−	24.7360i	−0.180849	−	0.981618i
$636$	−24.0194			−0.952430
$637$		−	5.56582i		−	0.220526i
$638$	−1.19676	−	1.19676i	−0.0473803	−	0.0473803i
$639$			0.467437i			0.0184915i
$640$	1.26849	−	1.84145i	0.0501414	−	0.0727897i
$641$	24.0958			0.951727			0.475864	−	0.879519i	$-0.342136\pi$
$641$	24.0958			0.951727			0.475864	+	0.879519i	$0.342136\pi$
$642$		−	6.87423i		−	0.271304i
$643$			6.55586i			0.258538i	0.991610	+	0.129269i	$0.0412631\pi$
$643$			6.55586i			0.258538i	−0.991610	+	0.129269i	$0.958737\pi$
$644$	−11.4574	+	11.4574i	−0.451484	+	0.451484i
$645$	−0.214469	−	1.16410i	−0.00844469	−	0.0458363i
$646$	0.810219	−	0.810219i	0.0318776	−	0.0318776i
$647$	−6.75259			−0.265472			−0.132736	−	0.991151i	$-0.542376\pi$
$647$	−6.75259			−0.265472			−0.132736	+	0.991151i	$0.542376\pi$
$648$	−9.17383			−0.360382
$649$	17.3871	−	17.3871i	0.682503	−	0.682503i
$650$	−2.69000	−	7.05262i	−0.105511	−	0.276627i
$651$	5.07237	−	5.07237i	0.198802	−	0.198802i
$652$			19.2629i			0.754394i
$653$		−	18.5694i		−	0.726675i	−0.931658	−	0.363338i	$-0.881637\pi$
$653$		−	18.5694i		−	0.726675i	0.931658	−	0.363338i	$-0.118363\pi$
$654$	10.2551			0.401006
$655$	19.6445	−	3.61923i	0.767575	−	0.141415i
$656$		−	0.270882i		−	0.0105762i
$657$	−0.492109	−	0.492109i	−0.0191990	−	0.0191990i
$658$		−	8.18513i		−	0.319090i
$659$	29.5588			1.15145			0.575724	−	0.817644i	$-0.304720\pi$
$659$	29.5588			1.15145			0.575724	+	0.817644i	$0.304720\pi$
$660$	16.4450	−	3.02977i	0.640122	−	0.117934i
$661$	−35.1268	−	35.1268i	−1.36627	−	1.36627i	−0.865686	−	0.500587i	$-0.833118\pi$
$661$	−35.1268	−	35.1268i	−1.36627	−	1.36627i	−0.500587	−	0.865686i	$-0.666882\pi$
$662$	15.5423	−	15.5423i	0.604067	−	0.604067i
$663$	−3.96042	−	3.96042i	−0.153810	−	0.153810i
$664$	−10.1305	−	10.1305i	−0.393141	−	0.393141i
$665$	1.24721	−	1.81056i	0.0483648	−	0.0702106i
$666$	−0.135063	−	0.333213i	−0.00523358	−	0.0129118i
$667$	−2.49165	+	2.49165i	−0.0964772	+	0.0964772i
$668$		−	22.3611i		−	0.865178i
$669$	−34.0353			−1.31588
$670$	−19.2085	+	3.53890i	−0.742089	+	0.136720i
$671$	−19.1164	+	19.1164i	−0.737982	+	0.737982i
$672$		−	3.18360i		−	0.122810i
$673$	−1.64758	−	1.64758i	−0.0635097	−	0.0635097i	0.674639	−	0.738148i	$-0.264300\pi$
$673$	−1.64758	−	1.64758i	−0.0635097	−	0.0635097i	−0.738148	+	0.674639i	$0.764300\pi$
$674$	−14.8294	−	14.8294i	−0.571209	−	0.571209i
$675$	−10.5108	+	23.4727i	−0.404560	+	0.903464i
$676$	−10.7210			−0.412345
$677$	−18.6418	−	18.6418i	−0.716461	−	0.716461i	0.251417	−	0.967879i	$-0.419103\pi$
$677$	−18.6418	−	18.6418i	−0.716461	−	0.716461i	−0.967879	+	0.251417i	$0.919103\pi$
$678$	−2.80420	−	2.80420i	−0.107695	−	0.107695i
$679$	15.7753	+	15.7753i	0.605400	+	0.605400i
$680$	−3.90611	−	2.69073i	−0.149792	−	0.103185i
$681$	6.46904	+	6.46904i	0.247894	+	0.247894i
$682$	−6.81229	+	6.81229i	−0.260856	+	0.260856i
$683$	21.7547			0.832421			0.416210	−	0.909268i	$-0.363358\pi$
$683$	21.7547			0.832421			0.416210	+	0.909268i	$0.363358\pi$
$684$	−0.0225773	+	0.0225773i	−0.000863263	+	0.000863263i
$685$	−2.02634	−	10.9986i	−0.0774225	−	0.420235i
$686$	−13.7548	−	13.7548i	−0.525162	−	0.525162i
$687$	3.86539	+	3.86539i	0.147474	+	0.147474i
$688$	0.302660			0.0115388
$689$	−14.6596	−	14.6596i	−0.558488	−	0.558488i
$690$	−6.30795	−	34.2384i	−0.240140	−	1.30343i
$691$		−	10.1836i		−	0.387401i	−0.981061	−	0.193700i	$-0.937951\pi$
$691$		−	10.1836i		−	0.387401i	0.981061	−	0.193700i	$-0.0620490\pi$
$692$	−6.44977	+	6.44977i	−0.245183	+	0.245183i
$693$	0.325282	−	0.325282i	0.0123564	−	0.0123564i
$694$	8.24738			0.313066
$695$	7.24175	−	10.5128i	0.274695	−	0.398772i
$696$		−	0.692342i		−	0.0262431i
$697$	−0.574599			−0.0217645
$698$		−	16.1967i		−	0.613056i
$699$		−	18.3924i		−	0.695663i
$700$	−8.30629	−	3.71945i	−0.313948	−	0.140582i
$701$	10.1893	−	10.1893i	0.384844	−	0.384844i	−0.488000	−	0.872844i	$-0.662273\pi$
$701$	10.1893	−	10.1893i	0.384844	−	0.384844i	0.872844	+	0.488000i	$0.162273\pi$
$702$	−5.49080	−	5.49080i	−0.207237	−	0.207237i
$703$	3.02599	+	1.28044i	0.114127	+	0.0482927i
$704$			4.27563i			0.161144i
$705$	14.4831	+	9.97674i	0.545466	+	0.375746i
$706$			20.3765i			0.766880i
$707$	24.8474	+	24.8474i	0.934481	+	0.934481i
$708$	10.0586			0.378026
$709$	35.9766	+	35.9766i	1.35113	+	1.35113i	0.884402	+	0.466725i	$0.154566\pi$
$709$	35.9766	+	35.9766i	1.35113	+	1.35113i	0.466725	+	0.884402i	$0.345434\pi$
$710$	−10.0313	+	14.5623i	−0.376467	+	0.546513i
$711$	−0.130076	+	0.130076i	−0.00487822	+	0.00487822i
$712$	−5.24983	+	5.24983i	−0.196746	+	0.196746i
$713$	14.1831	+	14.1831i	0.531163	+	0.531163i
$714$	−6.75309			−0.252728
$715$	11.8860	+	8.18769i	0.444510	+	0.306202i
$716$	−8.44973	+	8.44973i	−0.315781	+	0.315781i
$717$	−47.5233			−1.77479
$718$		−	30.2708i		−	1.12970i
$719$		−	10.7340i		−	0.400310i	−0.979764	−	0.200155i	$-0.935855\pi$
$719$		−	10.7340i		−	0.400310i	0.979764	−	0.200155i	$-0.0641446\pi$
$720$	0.108846	+	0.0749790i	0.00405646	+	0.00279430i
$721$	13.6232	+	13.6232i	0.507356	+	0.507356i
$722$			18.7082i			0.696248i
$723$			47.0013i			1.74800i
$724$	1.63147			0.0606330
$725$	−1.80638	−	0.808875i	−0.0670873	−	0.0300408i
$726$	−9.00484	+	9.00484i	−0.334201	+	0.334201i
$727$	−14.6699			−0.544078			−0.272039	−	0.962286i	$-0.587698\pi$
$727$	−14.6699			−0.544078			−0.272039	+	0.962286i	$0.587698\pi$
$728$	1.94303	−	1.94303i	0.0720136	−	0.0720136i
$729$			26.4473i			0.979528i
$730$	−4.77017	−	25.8916i	−0.176552	−	0.958292i
$731$		−	0.642006i		−	0.0237455i
$732$	−11.0591			−0.408755
$733$	−22.2345	+	22.2345i	−0.821249	+	0.821249i	−0.986287	−	0.165039i	$-0.947225\pi$
$733$	−22.2345	+	22.2345i	−0.821249	+	0.821249i	0.165039	+	0.986287i	$0.447225\pi$
$734$	−13.0615	+	13.0615i	−0.482108	+	0.482108i
$735$	14.1804	−	2.61255i	0.523053	−	0.0963652i
$736$	8.90184			0.328126
$737$	26.4084	−	26.4084i	0.972766	−	0.972766i
$738$	0.0160116			0.000589394
$739$	−4.21587			−0.155083			−0.0775416	−	0.996989i	$-0.524707\pi$
$739$	−4.21587			−0.155083			−0.0775416	+	0.996989i	$0.524707\pi$
$740$	2.94313	−	13.2792i	0.108192	−	0.488154i
$741$	−1.42628			−0.0523957
$742$	−24.9968			−0.917662
$743$	0.649329	−	0.649329i	0.0238216	−	0.0238216i	−0.695096	−	0.718917i	$-0.744638\pi$
$743$	0.649329	−	0.649329i	0.0238216	−	0.0238216i	0.718917	+	0.695096i	$0.244638\pi$
$744$	−3.94099			−0.144484
$745$	13.5710	+	9.34842i	0.497203	+	0.342499i
$746$	16.1154	−	16.1154i	0.590026	−	0.590026i
$747$	0.598806	−	0.598806i	0.0219091	−	0.0219091i
$748$	9.06953			0.331615
$749$		−	7.15397i		−	0.261400i
$750$	16.7058	−	10.1639i	0.610009	−	0.371134i
$751$		−	25.7790i		−	0.940688i	−0.882483	−	0.470344i	$-0.844130\pi$
$751$		−	25.7790i		−	0.940688i	0.882483	−	0.470344i	$-0.155870\pi$
$752$	−3.17973	+	3.17973i	−0.115953	+	0.115953i
$753$	6.34872			0.231360
$754$	0.422554	−	0.422554i	0.0153885	−	0.0153885i
$755$	−9.14775	−	6.30145i	−0.332921	−	0.229333i
$756$	−9.36262			−0.340515
$757$		−	15.9640i		−	0.580222i	−0.956993	−	0.290111i	$-0.906308\pi$
$757$		−	15.9640i		−	0.580222i	0.956993	−	0.290111i	$-0.0936923\pi$
$758$			7.07736i			0.257061i
$759$	47.0720	+	47.0720i	1.70861	+	1.70861i
$760$	−1.18787	+	0.218849i	−0.0430887	+	0.00793848i
$761$			28.4393i			1.03092i	0.856912	+	0.515462i	$0.172380\pi$
$761$			28.4393i			1.03092i	−0.856912	+	0.515462i	$0.827620\pi$
$762$			19.6739i			0.712710i
$763$	10.6724			0.386368
$764$	−14.3915	+	14.3915i	−0.520664	+	0.520664i
$765$	0.159046	−	0.230886i	0.00575033	−	0.00834770i
$766$	17.6507			0.637747
$767$	6.13905	+	6.13905i	0.221668	+	0.221668i
$768$	−1.23675	+	1.23675i	−0.0446274	+	0.0446274i
$769$	21.9651	−	21.9651i	0.792083	−	0.792083i	−0.189749	−	0.981833i	$-0.560768\pi$
$769$	21.9651	−	21.9651i	0.792083	−	0.792083i	0.981833	+	0.189749i	$0.0607675\pi$
$770$	17.1143	−	3.15306i	0.616755	−	0.113629i
$771$	−17.1900	−	17.1900i	−0.619082	−	0.619082i
$772$	−1.88527			−0.0678525
$773$	2.60816	+	2.60816i	0.0938089	+	0.0938089i	0.752454	−	0.658645i	$-0.228870\pi$
$773$	2.60816	+	2.60816i	0.0938089	+	0.0938089i	−0.658645	+	0.752454i	$0.728870\pi$
$774$			0.0178899i			0.000643040i
$775$	−4.60433	+	10.2824i	−0.165392	+	0.369355i
$776$		−	12.2566i		−	0.439988i
$777$	−7.27447	−	17.9468i	−0.260970	−	0.643838i
$778$	−14.9010	−	14.9010i	−0.534225	−	0.534225i
$779$	−0.103466	+	0.103466i	−0.00370706	+	0.00370706i
$780$	1.06975	+	5.80642i	0.0383033	+	0.207903i
$781$		−	33.8119i		−	1.20989i
$782$		−	18.8827i		−	0.675244i
$783$	−2.03610			−0.0727643
$784$			3.68685i			0.131673i
$785$	4.74630	+	25.7621i	0.169403	+	0.919488i
$786$	−15.6244			−0.557302
$787$	−2.48943	+	2.48943i	−0.0887387	+	0.0887387i	−0.750083	−	0.661344i	$-0.769986\pi$
$787$	−2.48943	+	2.48943i	−0.0887387	+	0.0887387i	0.661344	+	0.750083i	$0.269986\pi$
$788$	−16.9005	+	16.9005i	−0.602057	+	0.602057i
$789$			35.1912i			1.25284i
$790$	−6.84376	+	1.26087i	−0.243490	+	0.0448597i
$791$	−2.91832	−	2.91832i	−0.103763	−	0.103763i
$792$	−0.252728			−0.00898031
$793$	−6.74965	−	6.74965i	−0.239687	−	0.239687i
$794$	3.61759	+	3.61759i	0.128384	+	0.128384i
$795$	30.4683	−	44.2305i	1.08060	−	1.56869i
$796$	6.68597	−	6.68597i	0.236978	−	0.236978i
$797$	−30.0363			−1.06394			−0.531970	−	0.846763i	$-0.678548\pi$
$797$	−30.0363			−1.06394			−0.531970	+	0.846763i	$0.678548\pi$
$798$	−1.21601	+	1.21601i	−0.0430462	+	0.0430462i
$799$	6.74488	+	6.74488i	0.238617	+	0.238617i
$800$	1.78188	+	4.67171i	0.0629989	+	0.165170i
$801$	−0.310312	−	0.310312i	−0.0109643	−	0.0109643i
$802$	12.9977	+	12.9977i	0.458965	+	0.458965i
$803$	35.5966	+	35.5966i	1.25618	+	1.25618i
$804$	15.2776			0.538798
$805$	−6.56465	−	35.6318i	−0.231374	−	1.25585i
$806$	−2.40529	−	2.40529i	−0.0847227	−	0.0847227i
$807$	26.5040	+	26.5040i	0.932984	+	0.932984i
$808$		−	19.3052i		−	0.679155i
$809$	4.17505	−	4.17505i	0.146787	−	0.146787i	−0.629894	−	0.776681i	$-0.716902\pi$
$809$	4.17505	−	4.17505i	0.146787	−	0.146787i	0.776681	+	0.629894i	$0.216902\pi$
$810$	11.6369	−	16.8932i	0.408879	−	0.593565i
$811$	21.0938			0.740702			0.370351	−	0.928892i	$-0.379237\pi$
$811$	21.0938			0.740702			0.370351	+	0.928892i	$0.379237\pi$
$812$		−	0.720516i		−	0.0252852i
$813$	21.6510	−	21.6510i	0.759334	−	0.759334i
$814$	9.76975	+	24.1029i	0.342430	+	0.844807i
$815$	−35.4717	−	24.4348i	−1.24252	−	0.855912i
$816$	2.62341	+	2.62341i	0.0918378	+	0.0918378i
$817$	−0.115604	−	0.115604i	−0.00404447	−	0.00404447i
$818$	−1.73592	+	1.73592i	−0.0606949	+	0.0606949i
$819$	0.114851	+	0.114851i	0.00401321	+	0.00401321i
$820$	0.498816	+	0.343611i	0.0174194	+	0.0119994i
$821$	−27.8919			−0.973434			−0.486717	−	0.873560i	$-0.661806\pi$
$821$	−27.8919			−0.973434			−0.486717	+	0.873560i	$0.661806\pi$
$822$			8.74779i			0.305114i
$823$	7.17157	+	7.17157i	0.249985	+	0.249985i	0.820964	−	0.570979i	$-0.193436\pi$
$823$	7.17157	+	7.17157i	0.249985	+	0.249985i	−0.570979	+	0.820964i	$0.693436\pi$
$824$		−	10.5846i		−	0.368732i
$825$	−15.2811	+	34.1259i	−0.532021	+	1.18811i
$826$	10.4680			0.364227
$827$		−	46.4436i		−	1.61500i	−0.589866	−	0.807501i	$-0.700819\pi$
$827$		−	46.4436i		−	1.61500i	0.589866	−	0.807501i	$-0.299181\pi$
$828$			0.526178i			0.0182860i
$829$	2.54664	−	2.54664i	0.0884484	−	0.0884484i	−0.661498	−	0.749947i	$-0.730079\pi$
$829$	2.54664	−	2.54664i	0.0884484	−	0.0884484i	0.749947	+	0.661498i	$0.230079\pi$
$830$	31.5053	−	5.80442i	1.09357	−	0.201474i
$831$	12.2781	−	12.2781i	0.425923	−	0.425923i
$832$	−1.50964			−0.0523375
$833$	7.82059			0.270967
$834$	−7.06057	+	7.06057i	−0.244488	+	0.244488i
$835$	41.1769	+	28.3648i	1.42498	+	0.981604i
$836$	1.63312	−	1.63312i	0.0564827	−	0.0564827i
$837$			11.5900i			0.400610i
$838$			16.7428i			0.578372i
$839$	29.4346			1.01619			0.508097	−	0.861300i	$-0.330349\pi$
$839$	29.4346			1.01619			0.508097	+	0.861300i	$0.330349\pi$
$840$	5.86244	+	4.03835i	0.202273	+	0.139336i
$841$			28.8433i			0.994597i
$842$	0.463240	+	0.463240i	0.0159643	+	0.0159643i
$843$			22.9002i			0.788725i
$844$	16.4186			0.565151
$845$	13.5994	−	19.7421i	0.467834	−	0.679150i
$846$	−0.187950	−	0.187950i	−0.00646187	−	0.00646187i
$847$	−9.37129	+	9.37129i	−0.322001	+	0.322001i
$848$	9.71066	+	9.71066i	0.333466	+	0.333466i
$849$	−9.06323	−	9.06323i	−0.311049	−	0.311049i
$850$	9.90970	−	3.77974i	0.339900	−	0.129644i
$851$	50.1821	−	20.3406i	1.72022	−	0.697265i
$852$	9.78029	−	9.78029i	0.335067	−	0.335067i
$853$		−	17.8225i		−	0.610230i	−0.952315	−	0.305115i	$-0.901305\pi$
$853$		−	17.8225i		−	0.610230i	0.952315	−	0.305115i	$-0.0986949\pi$
$854$	−11.5091			−0.393834
$855$	−0.0129359	−	0.0702139i	−0.000442400	−	0.00240126i
$856$	−2.77915	+	2.77915i	−0.0949892	+	0.0949892i
$857$		−	42.4300i		−	1.44938i	−0.689074	−	0.724691i	$-0.741983\pi$
$857$		−	42.4300i		−	1.44938i	0.689074	−	0.724691i	$-0.258017\pi$
$858$	−7.98284	−	7.98284i	−0.272530	−	0.272530i
$859$	−7.52410	−	7.52410i	−0.256719	−	0.256719i	0.566999	−	0.823718i	$-0.308104\pi$
$859$	−7.52410	−	7.52410i	−0.256719	−	0.256719i	−0.823718	+	0.566999i	$0.808104\pi$
$860$	−0.383920	+	0.557333i	−0.0130916	+	0.0190049i
$861$	0.862380			0.0293898
$862$	27.2475	+	27.2475i	0.928055	+	0.928055i
$863$	−32.3511	−	32.3511i	−1.10124	−	1.10124i	−0.994261	−	0.106983i	$-0.965881\pi$
$863$	−32.3511	−	32.3511i	−1.10124	−	1.10124i	−0.106983	−	0.994261i	$-0.534119\pi$
$864$	3.63715	+	3.63715i	0.123738	+	0.123738i
$865$	−3.69548	−	20.0584i	−0.125650	−	0.682005i
$866$	−17.1809	−	17.1809i	−0.583830	−	0.583830i
$867$	−15.4600	+	15.4600i	−0.525048	+	0.525048i
$868$	−4.10137			−0.139209
$869$	9.40901	−	9.40901i	0.319179	−	0.319179i
$870$	1.27491	+	0.878227i	0.0432236	+	0.0297747i
$871$	9.32430	+	9.32430i	0.315942	+	0.315942i
$872$	−4.14598	−	4.14598i	−0.140401	−	0.140401i
$873$	0.724478			0.0245198
$874$	−3.40015	−	3.40015i	−0.115012	−	0.115012i
$875$	17.3856	−	10.5776i	0.587741	−	0.357586i
$876$			20.5930i			0.695774i
$877$	33.8258	−	33.8258i	1.14222	−	1.14222i	0.154171	−	0.988044i	$-0.450729\pi$
$877$	33.8258	−	33.8258i	1.14222	−	1.14222i	0.988044	−	0.154171i	$-0.0492707\pi$
$878$	−13.3023	+	13.3023i	−0.448932	+	0.448932i
$879$	31.1905			1.05203
$880$	−7.87337	−	5.42359i	−0.265411	−	0.182829i
$881$			49.3397i			1.66230i	0.556050	+	0.831149i	$0.312316\pi$
$881$			49.3397i			1.66230i	−0.556050	+	0.831149i	$0.687684\pi$
$882$	−0.217926			−0.00733794
$883$			14.6163i			0.491878i	0.969285	+	0.245939i	$0.0790963\pi$
$883$			14.6163i			0.491878i	−0.969285	+	0.245939i	$0.920904\pi$
$884$			3.20228i			0.107704i
$885$	−12.7592	+	18.5225i	−0.428897	+	0.622626i
$886$	−24.4725	+	24.4725i	−0.822169	+	0.822169i
$887$	−39.7503	−	39.7503i	−1.33468	−	1.33468i	−0.901125	−	0.433560i	$-0.857257\pi$
$887$	−39.7503	−	39.7503i	−1.33468	−	1.33468i	−0.433560	−	0.901125i	$-0.642743\pi$
$888$	−4.14595	+	9.79786i	−0.139129	+	0.328795i
$889$			20.4745i			0.686693i
$890$	−3.00796	−	16.3267i	−0.100827	−	0.547271i
$891$			39.2239i			1.31405i
$892$	13.7600	+	13.7600i	0.460718	+	0.460718i
$893$	2.42906			0.0812853
$894$	−9.11453	−	9.11453i	−0.304835	−	0.304835i
$895$	−4.84138	−	26.2781i	−0.161829	−	0.878381i
$896$	−1.28708	+	1.28708i	−0.0429984	+	0.0429984i
$897$	−16.6202	+	16.6202i	−0.554933	+	0.554933i
$898$	20.4966	+	20.4966i	0.683981	+	0.683981i
$899$	−0.891930			−0.0297475
$900$	−0.276140	+	0.105325i	−0.00920467	+	0.00351083i
$901$	20.5984	−	20.5984i	0.686232	−	0.686232i
$902$	−1.15819			−0.0385636
$903$			0.963548i			0.0320649i
$904$			2.26739i			0.0754124i
$905$	−2.06950	+	3.00427i	−0.0687924	+	0.0998652i
$906$	6.14380	+	6.14380i	0.204114	+	0.204114i
$907$		−	9.06842i		−	0.301112i	−0.988601	−	0.150556i	$-0.951894\pi$
$907$		−	9.06842i		−	0.301112i	0.988601	−	0.150556i	$-0.0481064\pi$
$908$		−	5.23067i		−	0.173586i
$909$	1.14111			0.0378483
$910$	1.11329	+	6.04271i	0.0369051	+	0.200314i
$911$	13.7635	−	13.7635i	0.456006	−	0.456006i	−0.441336	−	0.897342i	$-0.645495\pi$
$911$	13.7635	−	13.7635i	0.456006	−	0.456006i	0.897342	+	0.441336i	$0.145495\pi$
$912$	0.944780			0.0312848
$913$	−43.3145	+	43.3145i	−1.43350	+	1.43350i
$914$		−	25.3795i		−	0.839479i
$915$	14.0283	−	20.3647i	0.463761	−	0.673238i
$916$		−	3.12544i		−	0.103267i
$917$	−16.2602			−0.536959
$918$	7.71517	−	7.71517i	0.254639	−	0.254639i
$919$	−20.8694	+	20.8694i	−0.688418	+	0.688418i	−0.961882	−	0.273464i	$-0.911830\pi$
$919$	−20.8694	+	20.8694i	−0.688418	+	0.688418i	0.273464	+	0.961882i	$0.411830\pi$
$920$	−11.2919	+	16.3923i	−0.372282	+	0.540438i
$921$	−42.1216			−1.38795
$922$	19.5684	−	19.5684i	0.644452	−	0.644452i
$923$	11.9383			0.392955
$924$	−13.6119			−0.447799
$925$	20.7197	+	22.2642i	0.681260	+	0.732041i
$926$	40.3494			1.32596
$927$	0.625645			0.0205489
$928$	−0.279903	+	0.279903i	−0.00918828	+	0.00918828i
$929$	26.4042			0.866294			0.433147	−	0.901323i	$-0.357403\pi$
$929$	26.4042			0.866294			0.433147	+	0.901323i	$0.357403\pi$
$930$	4.99910	−	7.25714i	0.163927	−	0.237971i
$931$	1.40823	−	1.40823i	0.0461528	−	0.0461528i
$932$	−7.43576	+	7.43576i	−0.243566	+	0.243566i
$933$	−9.26748			−0.303404
$934$			6.84915i			0.224111i
$935$	−11.5046	+	16.7011i	−0.376240	+	0.546184i
$936$		−	0.0892335i		−	0.00291669i
$937$	2.29378	−	2.29378i	0.0749346	−	0.0749346i	−0.668646	−	0.743581i	$-0.733126\pi$
$937$	2.29378	−	2.29378i	0.0749346	−	0.0749346i	0.743581	+	0.668646i	$0.233126\pi$
$938$	15.8993			0.519130
$939$	−18.1871	+	18.1871i	−0.593515	+	0.593515i
$940$	−1.82187	−	9.88875i	−0.0594227	−	0.322536i
$941$	46.2380			1.50732			0.753658	−	0.657267i	$-0.228288\pi$
$941$	46.2380			1.50732			0.753658	+	0.657267i	$0.228288\pi$
$942$		−	20.4900i		−	0.667600i
$943$			2.41135i			0.0785244i
$944$	−4.06655	−	4.06655i	−0.132355	−	0.132355i
$945$	11.8764	−	17.2408i	0.386338	−	0.560843i
$946$		−	1.29406i		−	0.0420736i
$947$			45.6330i			1.48287i	0.671023	+	0.741436i	$0.265855\pi$
$947$			45.6330i			1.48287i	−0.671023	+	0.741436i	$0.734145\pi$
$948$	5.44322			0.176787
$949$	−12.5685	+	12.5685i	−0.407990	+	0.407990i
$950$	1.10380	−	2.46501i	0.0358121	−	0.0799756i
$951$	−33.7528			−1.09451
$952$	2.73017	+	2.73017i	0.0884854	+	0.0884854i
$953$	−17.8564	+	17.8564i	−0.578427	+	0.578427i	−0.934470	−	0.356043i	$-0.884126\pi$
$953$	−17.8564	+	17.8564i	−0.578427	+	0.578427i	0.356043	+	0.934470i	$0.384126\pi$
$954$	−0.573987	+	0.573987i	−0.0185835	+	0.0185835i
$955$	−8.24577	−	44.7565i	−0.266827	−	1.44829i
$956$	19.2129	+	19.2129i	0.621391	+	0.621391i
$957$	−2.96020			−0.0956897
$958$	30.4703	+	30.4703i	0.984450	+	0.984450i
$959$			9.10378i			0.293976i
$960$	−0.708613	−	3.84622i	−0.0228704	−	0.124136i
$961$		−	25.9229i		−	0.836223i
$962$	−8.51028	+	3.44951i	−0.274382	+	0.111217i
$963$	−0.164272	−	0.164272i	−0.00529360	−	0.00529360i
$964$	19.0019	−	19.0019i	0.612010	−	0.612010i
$965$	2.39145	−	3.47164i	0.0769834	−	0.111756i
$966$			28.3399i			0.911821i
$967$		−	21.9000i		−	0.704256i	−0.935952	−	0.352128i	$-0.885458\pi$
$967$		−	21.9000i		−	0.704256i	0.935952	−	0.352128i	$-0.114542\pi$
$968$	7.28104			0.234022
$969$		−	2.00408i		−	0.0643803i
$970$	22.5700	+	15.5474i	0.724679	+	0.499197i
$971$	−56.4041			−1.81009			−0.905047	−	0.425313i	$-0.860164\pi$
$971$	−56.4041			−1.81009			−0.905047	+	0.425313i	$0.860164\pi$
$972$	−0.434298	+	0.434298i	−0.0139301	+	0.0139301i
$973$	−7.34790	+	7.34790i	−0.235563	+	0.235563i
$974$		−	38.9294i		−	1.24738i
$975$	−12.0492	−	5.39548i	−0.385883	−	0.172794i
$976$	4.47102	+	4.47102i	0.143114	+	0.143114i
$977$	39.9367			1.27769			0.638844	−	0.769336i	$-0.279413\pi$
$977$	39.9367			1.27769			0.638844	+	0.769336i	$0.279413\pi$
$978$	23.8234	+	23.8234i	0.761789	+	0.761789i
$979$	22.4464	+	22.4464i	0.717389	+	0.717389i
$980$	−6.78914	−	4.67672i	−0.216871	−	0.149392i
$981$	0.245065	−	0.245065i	0.00782431	−	0.00782431i
$982$	−8.64964			−0.276021
$983$	−27.5089	+	27.5089i	−0.877396	+	0.877396i	−0.993265	−	0.115868i	$-0.963035\pi$
$983$	−27.5089	+	27.5089i	−0.877396	+	0.877396i	0.115868	+	0.993265i	$0.463035\pi$
$984$	−0.335014	−	0.335014i	−0.0106799	−	0.0106799i
$985$	−9.68338	−	52.5596i	−0.308538	−	1.67469i
$986$	0.593735	+	0.593735i	0.0189084	+	0.0189084i
$987$	−10.1230	−	10.1230i	−0.322218	−	0.322218i
$988$	0.576624	+	0.576624i	0.0183448	+	0.0183448i
$989$	−2.69423			−0.0856715
$990$	0.320583	−	0.465387i	0.0101888	−	0.0147910i
$991$	31.0307	+	31.0307i	0.985721	+	0.985721i	0.999899	−	0.0141781i	$-0.00451317\pi$
$991$	31.0307	+	31.0307i	0.985721	+	0.985721i	−0.0141781	+	0.999899i	$0.504513\pi$
$992$	1.59328	+	1.59328i	0.0505868	+	0.0505868i
$993$		−	38.4438i		−	1.21998i
$994$	10.1783	−	10.1783i	0.322836	−	0.322836i
$995$	3.83081	+	20.7930i	0.121445	+	0.659181i
$996$	−25.0579			−0.793990
$997$		−	44.3360i		−	1.40414i	−0.712110	−	0.702068i	$-0.752260\pi$
$997$		−	44.3360i		−	1.40414i	0.712110	−	0.702068i	$-0.247740\pi$
$998$	10.9240	−	10.9240i	0.345792	−	0.345792i
$999$	28.8144	+	12.1928i	0.911649	+	0.385763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.253.3	yes	20
5.2	odd	4		370.2.g.e.327.8	yes	20
37.6	odd	4		370.2.g.e.43.8	✓	20
185.117	even	4	inner	370.2.h.e.117.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.8	✓	20	37.6	odd	4
370.2.g.e.327.8	yes	20	5.2	odd	4
370.2.h.e.117.3	yes	20	185.117	even	4	inner
370.2.h.e.253.3	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +(1.26849 - 1.84145i) q^{10} +4.27563i q^{11} +(-1.23675 + 1.23675i) q^{12} -1.50964 q^{13} +(-1.28708 + 1.28708i) q^{14} +(-0.708613 - 3.84622i) q^{15} +1.00000 q^{16} -2.12121i q^{17} +0.0591090i q^{18} +(-0.381960 - 0.381960i) q^{19} +(-1.26849 + 1.84145i) q^{20} +3.18360i q^{21} -4.27563i q^{22} -8.90184 q^{23} +(1.23675 - 1.23675i) q^{24} +(-1.78188 - 4.67171i) q^{25} +1.50964 q^{26} +(-3.63715 - 3.63715i) q^{27} +(1.28708 - 1.28708i) q^{28} +(0.279903 - 0.279903i) q^{29} +(0.708613 + 3.84622i) q^{30} +(-1.59328 - 1.59328i) q^{31} -1.00000 q^{32} +(-5.28790 - 5.28790i) q^{33} +2.12121i q^{34} +(0.737449 + 4.00274i) q^{35} -0.0591090i q^{36} +(-5.63727 + 2.28498i) q^{37} +(0.381960 + 0.381960i) q^{38} +(1.86705 - 1.86705i) q^{39} +(1.26849 - 1.84145i) q^{40} -0.270882i q^{41} -3.18360i q^{42} +0.302660 q^{43} +4.27563i q^{44} +(0.108846 + 0.0749790i) q^{45} +8.90184 q^{46} +(-3.17973 + 3.17973i) q^{47} +(-1.23675 + 1.23675i) q^{48} +3.68685i q^{49} +(1.78188 + 4.67171i) q^{50} +(2.62341 + 2.62341i) q^{51} -1.50964 q^{52} +(9.71066 + 9.71066i) q^{53} +(3.63715 + 3.63715i) q^{54} +(-7.87337 - 5.42359i) q^{55} +(-1.28708 + 1.28708i) q^{56} +0.944780 q^{57} +(-0.279903 + 0.279903i) q^{58} +(-4.06655 - 4.06655i) q^{59} +(-0.708613 - 3.84622i) q^{60} +(4.47102 + 4.47102i) q^{61} +(1.59328 + 1.59328i) q^{62} +(-0.0760780 - 0.0760780i) q^{63} +1.00000 q^{64} +(1.91496 - 2.77993i) q^{65} +(5.28790 + 5.28790i) q^{66} +(-6.17649 - 6.17649i) q^{67} -2.12121i q^{68} +(11.0094 - 11.0094i) q^{69} +(-0.737449 - 4.00274i) q^{70} -7.90805 q^{71} +0.0591090i q^{72} +(8.32545 - 8.32545i) q^{73} +(5.63727 - 2.28498i) q^{74} +(7.98149 + 3.57401i) q^{75} +(-0.381960 - 0.381960i) q^{76} +(5.50309 + 5.50309i) q^{77} +(-1.86705 + 1.86705i) q^{78} +(-2.20061 - 2.20061i) q^{79} +(-1.26849 + 1.84145i) q^{80} +9.17383 q^{81} +0.270882i q^{82} +(10.1305 + 10.1305i) q^{83} +3.18360i q^{84} +(3.90611 + 2.69073i) q^{85} -0.302660 q^{86} +0.692342i q^{87} -4.27563i q^{88} +(5.24983 - 5.24983i) q^{89} +(-0.108846 - 0.0749790i) q^{90} +(-1.94303 + 1.94303i) q^{91} -8.90184 q^{92} +3.94099 q^{93} +(3.17973 - 3.17973i) q^{94} +(1.18787 - 0.218849i) q^{95} +(1.23675 - 1.23675i) q^{96} +12.2566i q^{97} -3.68685i q^{98} +0.252728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more