LMFDB - Embedded newform 370.2.g.e.327.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.8
Root			$-1.23675 - 1.23675i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.e.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.23675	+	1.23675i	0.714039	+	0.714039i	0.967378	−	0.253339i	$-0.0815287\pi$
$3$	1.23675	+	1.23675i	0.714039	+	0.714039i	−0.253339	+	0.967378i	$0.581529\pi$
$4$	−1.00000			−0.500000
$5$	−1.84145	+	1.26849i	−0.823522	+	0.567285i
$5$	−1.84145	+	1.26849i	−0.823522	+	0.567285i
$6$	1.23675	−	1.23675i	0.504902	−	0.504902i
$7$	1.28708	+	1.28708i	0.486471	+	0.486471i	0.907191	−	0.420720i	$-0.138222\pi$
$7$	1.28708	+	1.28708i	0.486471	+	0.486471i	−0.420720	+	0.907191i	$0.638222\pi$
$8$			1.00000i			0.353553i
$9$			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
$13$			1.50964i			0.418700i	0.977841	+	0.209350i	$0.0671348\pi$
$13$			1.50964i			0.418700i	−0.977841	+	0.209350i	$0.932865\pi$
$14$	1.28708	−	1.28708i	0.343987	−	0.343987i
$15$	−3.84622	−	0.708613i	−0.993090	−	0.182963i
$16$	1.00000			0.250000
$17$	2.12121			0.514470			0.257235	−	0.966349i	$-0.417189\pi$
$17$	2.12121			0.514470			0.257235	+	0.966349i	$0.417189\pi$
$18$	0.0591090			0.0139321
$19$	0.381960	+	0.381960i	0.0876277	+	0.0876277i	0.749562	−	0.661934i	$-0.230264\pi$
$19$	0.381960	+	0.381960i	0.0876277	+	0.0876277i	−0.661934	+	0.749562i	$0.730264\pi$
$20$	1.84145	−	1.26849i	0.411761	−	0.283642i
$21$			3.18360i			0.694718i
$22$	4.27563			0.911568
$23$			8.90184i			1.85616i	0.372379	+	0.928081i	$0.378542\pi$
$23$			8.90184i			1.85616i	−0.372379	+	0.928081i	$0.621458\pi$
$24$	−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	−0.732617	−	0.680641i	$-0.761702\pi$
$29$	−0.279903	+	0.279903i	−0.0519767	+	0.0519767i	0.680641	+	0.732617i	$0.261702\pi$
$30$	−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	$0.814857\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.28790	+	5.28790i	−0.920505	+	0.920505i
$34$		−	2.12121i		−	0.363785i
$35$	−4.00274	−	0.737449i	−0.676587	−	0.124652i
$36$		−	0.0591090i		−	0.00985149i
$37$	−2.28498	−	5.63727i	−0.375649	−	0.926762i
$37$	−2.28498	−	5.63727i	−0.375649	−	0.926762i
$38$	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	$-0.00673350\pi$
$42$	3.18360			0.491240
$43$		−	0.302660i		−	0.0461552i	−0.999734	−	0.0230776i	$-0.992654\pi$
$43$		−	0.302660i		−	0.0461552i	0.999734	−	0.0230776i	$-0.00734648\pi$
$44$		−	4.27563i		−	0.644576i
$45$	−0.0749790	−	0.108846i	−0.0111772	−	0.0162258i
$46$	8.90184			1.31250
$47$	−3.17973	−	3.17973i	−0.463811	−	0.463811i	0.436091	−	0.899902i	$-0.356362\pi$
$47$	−3.17973	−	3.17973i	−0.463811	−	0.463811i	−0.899902	+	0.436091i	$0.856362\pi$
$48$	1.23675	+	1.23675i	0.178510	+	0.178510i
$49$		−	3.68685i		−	0.526692i
$50$	−4.67171	−	1.78188i	−0.660680	−	0.251996i
$51$	2.62341	+	2.62341i	0.367351	+	0.367351i
$52$		−	1.50964i		−	0.209350i
$53$	9.71066	−	9.71066i	1.33386	−	1.33386i	0.431978	−	0.901884i	$-0.357816\pi$
$53$	9.71066	−	9.71066i	1.33386	−	1.33386i	0.901884	−	0.431978i	$-0.142184\pi$
$54$	−3.63715	−	3.63715i	−0.494954	−	0.494954i
$55$	−5.42359	−	7.87337i	−0.731316	−	1.06164i
$56$	−1.28708	+	1.28708i	−0.171993	+	0.171993i
$57$			0.944780i			0.125139i
$58$	0.279903	+	0.279903i	0.0367531	+	0.0367531i
$59$	4.06655	+	4.06655i	0.529420	+	0.529420i	0.920399	−	0.390979i	$-0.127864\pi$
$59$	4.06655	+	4.06655i	0.529420	+	0.529420i	−0.390979	+	0.920399i	$0.627864\pi$
$60$	3.84622	+	0.708613i	0.496545	+	0.0914815i
$61$	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	$-0.570851\pi$
$67$	6.17649	−	6.17649i	0.754578	−	0.754578i	0.975330	+	0.220752i	$0.0708510\pi$
$68$	−2.12121			−0.257235
$69$	−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	$0.655478\pi$
$72$	−0.0591090			−0.00696606
$73$	−8.32545	−	8.32545i	−0.974420	−	0.974420i	0.0252606	−	0.999681i	$-0.491958\pi$
$73$	−8.32545	−	8.32545i	−0.974420	−	0.974420i	−0.999681	+	0.0252606i	$0.991958\pi$
$74$	−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	0.819980	−	0.572392i	$-0.193984\pi$
$79$	2.20061	+	2.20061i	0.247588	+	0.247588i	−0.572392	+	0.819980i	$0.693984\pi$
$80$	−1.84145	+	1.26849i	−0.205880	+	0.141821i
$81$	9.17383			1.01931
$82$	−0.270882			−0.0299139
$83$	10.1305	−	10.1305i	1.11197	−	1.11197i	0.119087	−	0.992884i	$-0.462003\pi$
$83$	10.1305	−	10.1305i	1.11197	−	1.11197i	0.992884	−	0.119087i	$-0.0379968\pi$
$84$		−	3.18360i		−	0.347359i
$85$	−3.90611	+	2.69073i	−0.423677	+	0.291851i
$86$	−0.302660			−0.0326367
$87$	−0.692342			−0.0742268
$88$	−4.27563			−0.455784
$89$	−5.24983	+	5.24983i	−0.556481	+	0.556481i	−0.928304	−	0.371823i	$-0.878733\pi$
$89$	−5.24983	+	5.24983i	−0.556481	+	0.556481i	0.371823	+	0.928304i	$0.378733\pi$
$90$	−0.108846	+	0.0749790i	−0.0114734	+	0.00790348i
$91$	−1.94303	+	1.94303i	−0.203685	+	0.203685i
$92$		−	8.90184i		−	0.928081i
$93$		−	3.94099i		−	0.408662i
$94$	−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
$97$	−12.2566			−1.24447			−0.622237	−	0.782829i	$-0.713776\pi$
$97$	−12.2566			−1.24447			−0.622237	+	0.782829i	$0.713776\pi$
$98$	−3.68685			−0.372428
$99$	−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
$103$	10.5846			1.04293			0.521466	−	0.853272i	$-0.325385\pi$
$103$	10.5846			1.04293			0.521466	+	0.853272i	$0.325385\pi$
$104$	−1.50964			−0.148033
$105$	−4.03835	−	5.86244i	−0.394103	−	0.572115i
$106$	−9.71066	−	9.71066i	−0.943183	−	0.943183i
$107$	2.77915	+	2.77915i	0.268670	+	0.268670i	0.828564	−	0.559894i	$-0.189158\pi$
$107$	2.77915	+	2.77915i	0.268670	+	0.268670i	−0.559894	+	0.828564i	$0.689158\pi$
$108$	−3.63715	+	3.63715i	−0.349985	+	0.349985i
$109$	−4.14598	−	4.14598i	−0.397113	−	0.397113i	0.480101	−	0.877213i	$-0.340600\pi$
$109$	−4.14598	−	4.14598i	−0.397113	−	0.397113i	−0.877213	+	0.480101i	$0.840600\pi$
$110$	−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
$113$	−2.26739			−0.213298			−0.106649	−	0.994297i	$-0.534012\pi$
$113$	−2.26739			−0.213298			−0.106649	+	0.994297i	$0.534012\pi$
$114$	0.944780			0.0884867
$115$	−11.2919	−	16.3923i	−1.05297	−	1.52859i
$116$	0.279903	−	0.279903i	0.0259884	−	0.0259884i
$117$	−0.0892335			−0.00824964
$118$	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
$125$	2.64477	+	10.8630i	0.236555	+	0.971618i
$126$	0.0760780	+	0.0760780i	0.00677757	+	0.00677757i
$127$	−7.95386	−	7.95386i	−0.705791	−	0.705791i	0.259857	−	0.965647i	$-0.416325\pi$
$127$	−7.95386	−	7.95386i	−0.705791	−	0.705791i	−0.965647	+	0.259857i	$0.916325\pi$
$128$			1.00000i			0.0883883i
$129$	0.374315	−	0.374315i	0.0329566	−	0.0329566i
$130$	−2.77993	+	1.91496i	−0.243816	+	0.167954i
$131$	−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
$133$			0.983227i			0.0852566i
$134$	−6.17649	−	6.17649i	−0.533567	−	0.533567i
$135$	−2.08395	+	11.3113i	−0.179358	+	0.973523i
$136$			2.12121i			0.181893i
$137$	−3.53660	−	3.53660i	−0.302152	−	0.302152i	0.539703	−	0.841855i	$-0.318536\pi$
$137$	−3.53660	−	3.53660i	−0.302152	−	0.302152i	−0.841855	+	0.539703i	$0.818536\pi$
$138$	11.0094	+	11.0094i	0.937179	+	0.937179i
$139$	5.70896			0.484228			0.242114	−	0.970248i	$-0.422159\pi$
$139$	5.70896			0.484228			0.242114	+	0.970248i	$0.422159\pi$
$140$	4.00274	+	0.737449i	0.338293	+	0.0623258i
$141$		−	7.86507i		−	0.662358i
$142$			7.90805i			0.663629i
$143$	−6.45468			−0.539768
$144$			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
$148$	2.28498	+	5.63727i	0.187824	+	0.463381i
$149$			7.36973i			0.603752i	0.953347	+	0.301876i	$0.0976129\pi$
$149$			7.36973i			0.603752i	−0.953347	+	0.301876i	$0.902387\pi$
$150$	−3.57401	−	7.98149i	−0.291817	−	0.651686i
$151$			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
$153$			0.125383i			0.0101366i
$154$	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	0.955644	−	0.294525i	$-0.0951615\pi$
$157$	8.28379	+	8.28379i	0.661119	+	0.661119i	−0.294525	+	0.955644i	$0.595161\pi$
$158$	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
$162$		−	9.17383i		−	0.720764i
$163$	19.2629			1.50879			0.754394	−	0.656422i	$-0.227931\pi$
$163$	19.2629			1.50879			0.754394	+	0.656422i	$0.227931\pi$
$164$			0.270882i			0.0211524i
$165$	3.02977	−	16.4450i	0.235867	−	1.28024i
$166$	−10.1305	−	10.1305i	−0.786282	−	0.786282i
$167$	22.3611			1.73036			0.865178	−	0.501466i	$-0.167206\pi$
$167$	22.3611			1.73036			0.865178	+	0.501466i	$0.167206\pi$
$168$	−3.18360			−0.245620
$169$	10.7210			0.824690
$170$	2.69073	+	3.90611i	0.206370	+	0.299585i
$171$	−0.0225773	+	0.0225773i	−0.00172653	+	0.00172653i
$172$			0.302660i			0.0230776i
$173$	6.44977	+	6.44977i	0.490367	+	0.490367i	0.908422	−	0.418055i	$-0.137288\pi$
$173$	6.44977	+	6.44977i	0.490367	+	0.490367i	−0.418055	+	0.908422i	$0.637288\pi$
$174$			0.692342i			0.0524863i
$175$	8.30629	−	3.71945i	0.627897	−	0.281164i
$176$			4.27563i			0.322288i
$177$			10.0586i			0.756053i
$178$	5.24983	+	5.24983i	0.393492	+	0.393492i
$179$	8.44973	−	8.44973i	0.631562	−	0.631562i	−0.316897	−	0.948460i	$-0.602641\pi$
$179$	8.44973	−	8.44973i	0.631562	−	0.631562i	0.948460	+	0.316897i	$0.102641\pi$
$180$	0.0749790	+	0.108846i	0.00558860	+	0.00811292i
$181$	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
$183$			11.0591i			0.817511i
$184$	−8.90184			−0.656252
$185$	11.3585	+	7.48229i	0.835093	+	0.550109i
$186$	−3.94099			−0.288967
$187$			9.06953i			0.663230i
$188$	3.17973	+	3.17973i	0.231905	+	0.231905i
$189$	9.36262			0.681030
$190$	−0.218849	+	1.18787i	−0.0158770	+	0.0861773i
$191$	−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
$193$			1.88527i			0.135705i	0.997695	+	0.0678525i	$0.0216147\pi$
$193$			1.88527i			0.135705i	−0.997695	+	0.0678525i	$0.978385\pi$
$194$			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	−0.972904	−	0.231210i	$-0.925732\pi$
$197$	−16.9005	−	16.9005i	−1.20411	−	1.20411i	−0.231210	−	0.972904i	$-0.574268\pi$
$198$			0.252728i			0.0179606i
$199$	−6.68597	+	6.68597i	−0.473956	+	0.473956i	−0.903192	−	0.429236i	$-0.858783\pi$
$199$	−6.68597	+	6.68597i	−0.473956	+	0.473956i	0.429236	+	0.903192i	$0.358783\pi$
$200$	4.67171	+	1.78188i	0.330340	+	0.125998i
$201$	15.2776			1.07760
$202$	19.3052			1.35831
$203$	−0.720516			−0.0505703
$204$	−2.62341	−	2.62341i	−0.183676	−	0.183676i
$205$	0.343611	+	0.498816i	0.0239988	+	0.0348388i
$206$		−	10.5846i		−	0.737464i
$207$	−0.526178			−0.0365719
$208$			1.50964i			0.104675i
$209$	−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
$217$		−	4.10137i		−	0.278419i
$218$	−4.14598	+	4.14598i	−0.280801	+	0.280801i
$219$		−	20.5930i		−	1.39155i
$220$	5.42359	+	7.87337i	0.365658	+	0.530822i
$221$			3.20228i			0.215408i
$222$	−9.79786	−	4.14595i	−0.657590	−	0.278258i
$223$	13.7600	−	13.7600i	0.921436	−	0.921436i	−0.0756947	−	0.997131i	$-0.524117\pi$
$223$	13.7600	−	13.7600i	0.921436	−	0.921436i	0.997131	+	0.0756947i	$0.0241175\pi$
$224$	1.28708	−	1.28708i	0.0859967	−	0.0859967i
$225$	0.276140	+	0.105325i	0.0184093	+	0.00702167i
$226$			2.26739i			0.150825i
$227$	5.23067			0.347172			0.173586	−	0.984819i	$-0.444465\pi$
$227$	5.23067			0.347172			0.173586	+	0.984819i	$0.444465\pi$
$228$		−	0.944780i		−	0.0625696i
$229$			3.12544i			0.206535i	0.994654	+	0.103267i	$0.0329298\pi$
$229$			3.12544i			0.206535i	−0.994654	+	0.103267i	$0.967070\pi$
$230$	−16.3923	+	11.2919i	−1.08088	+	0.744564i
$231$	−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	$-0.138064\pi$
$233$	7.43576	+	7.43576i	0.487133	+	0.487133i	−0.420268	+	0.907400i	$0.638064\pi$
$234$			0.0892335i			0.00583338i
$235$	9.88875	+	1.82187i	0.645071	+	0.118845i
$236$	−4.06655	−	4.06655i	−0.264710	−	0.264710i
$237$			5.44322i			0.353575i
$238$	2.73017	−	2.73017i	0.176971	−	0.176971i
$239$	−19.2129	−	19.2129i	−1.24278	−	1.24278i	−0.958842	−	0.283939i	$-0.908359\pi$
$239$	−19.2129	−	19.2129i	−1.24278	−	1.24278i	−0.283939	−	0.958842i	$-0.591641\pi$
$240$	−3.84622	−	0.708613i	−0.248272	−	0.0457407i
$241$	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	$-0.0830073\pi$
$242$			7.28104i			0.468043i
$243$	0.434298	+	0.434298i	0.0278602	+	0.0278602i
$244$	−4.47102	−	4.47102i	−0.286228	−	0.286228i
$245$	4.67672	+	6.78914i	0.298785	+	0.433743i
$246$	−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
$253$	−38.0610			−2.39287
$254$	−7.95386	+	7.95386i	−0.499069	+	0.499069i
$255$	−8.15865	−	1.50312i	−0.510915	−	0.0941289i
$256$	1.00000			0.0625000
$257$	−13.8993			−0.867015			−0.433507	−	0.901150i	$-0.642724\pi$
$257$	−13.8993			−0.867015			−0.433507	+	0.901150i	$0.642724\pi$
$258$	−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	$-0.463004\pi$
$263$	−14.2273	−	14.2273i	−0.877290	−	0.877290i	−0.993253	+	0.115964i	$0.963004\pi$
$264$	−5.28790	−	5.28790i	−0.325448	−	0.325448i
$265$	−5.56385	+	30.1996i	−0.341784	+	1.85514i
$266$	0.983227			0.0602855
$267$	−12.9855			−0.794699
$268$	−6.17649	+	6.17649i	−0.377289	+	0.377289i
$269$			21.4303i			1.30663i	0.757086	+	0.653315i	$0.226622\pi$
$269$			21.4303i			1.30663i	−0.757086	+	0.653315i	$0.773378\pi$
$270$	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	$0.678453\pi$
$272$	2.12121			0.128617
$273$	−4.80610			−0.290878
$274$	−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
$277$		−	9.92772i		−	0.596499i	−0.954488	−	0.298249i	$-0.903597\pi$
$277$		−	9.92772i		−	0.596499i	0.954488	−	0.298249i	$-0.0964027\pi$
$278$		−	5.70896i		−	0.342401i
$279$	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	$0.122290\pi$
$282$	−7.86507			−0.468358
$283$	7.32826			0.435620			0.217810	−	0.975991i	$-0.430109\pi$
$283$	7.32826			0.435620			0.217810	+	0.975991i	$0.430109\pi$
$284$	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
$288$	0.0591090			0.00348303
$289$	−12.5005			−0.735321
$290$	−0.870482	−	0.160374i	−0.0511165	−	0.00941750i
$291$	−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	−0.971933	−	0.235258i	$-0.924406\pi$
$293$	−12.6098	+	12.6098i	−0.736675	+	0.736675i	0.235258	+	0.971933i	$0.424406\pi$
$294$	−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
$298$	7.36973			0.426917
$299$	−13.4386			−0.777175
$300$	−7.98149	+	3.57401i	−0.460812	+	0.206345i
$301$	0.389548	−	0.389548i	0.0224532	−	0.0224532i
$302$	4.96769			0.285858
$303$	−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	$-0.991177\pi$
$307$	−17.0291	+	17.0291i	−0.971903	+	0.971903i	0.0277133	+	0.999616i	$0.491177\pi$
$308$	5.50309	−	5.50309i	0.313567	−	0.313567i
$309$	13.0905	+	13.0905i	0.744694	+	0.744694i
$310$	0.912892	−	4.95501i	0.0518488	−	0.281426i
$311$	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
$313$		−	14.7056i		−	0.831208i	−0.909546	−	0.415604i	$-0.863570\pi$
$313$		−	14.7056i		−	0.831208i	0.909546	−	0.415604i	$-0.136430\pi$
$314$	8.28379	−	8.28379i	0.467481	−	0.467481i
$315$	0.0435899	−	0.236598i	0.00245601	−	0.0133308i
$316$	−2.20061	−	2.20061i	−0.123794	−	0.123794i
$317$	−13.6458	+	13.6458i	−0.766423	+	0.766423i	−0.977475	−	0.211052i	$-0.932311\pi$
$317$	−13.6458	+	13.6458i	−0.766423	+	0.766423i	0.211052	+	0.977475i	$0.432311\pi$
$318$		−	24.0194i		−	1.34694i
$319$	−1.19676	−	1.19676i	−0.0670059	−	0.0670059i
$320$	1.84145	−	1.26849i	0.102940	−	0.0709106i
$321$			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
$325$	7.05262	+	2.69000i	0.391209	+	0.149214i
$326$		−	19.2629i		−	1.06687i
$327$		−	10.2551i		−	0.567108i
$328$	0.270882			0.0149570
$329$		−	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
$333$	0.333213	−	0.135063i	0.0182600	−	0.00740141i
$334$		−	22.3611i		−	1.22355i
$335$	−3.53890	+	19.2085i	−0.193351	+	1.04947i
$336$			3.18360i			0.173680i
$337$	−14.8294	+	14.8294i	−0.807811	+	0.807811i	−0.984302	−	0.176491i	$-0.943525\pi$
$337$	−14.8294	+	14.8294i	−0.807811	+	0.807811i	0.176491	+	0.984302i	$0.443525\pi$
$338$		−	10.7210i		−	0.583144i
$339$	−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
$347$		−	8.24738i		−	0.442742i	−0.975190	−	0.221371i	$-0.928947\pi$
$347$		−	8.24738i		−	0.442742i	0.975190	−	0.221371i	$-0.0710532\pi$
$348$	0.692342			0.0371134
$349$		−	16.1967i		−	0.866991i	−0.901156	−	0.433496i	$-0.857280\pi$
$349$		−	16.1967i		−	0.866991i	0.901156	−	0.433496i	$-0.142720\pi$
$350$	−3.71945	−	8.30629i	−0.198813	−	0.443990i
$351$	5.49080	+	5.49080i	0.293077	+	0.293077i
$352$	4.27563			0.227892
$353$	−20.3765			−1.08453			−0.542266	−	0.840207i	$-0.682433\pi$
$353$	−20.3765			−1.08453			−0.542266	+	0.840207i	$0.682433\pi$
$354$	10.0586			0.534610
$355$	14.5623	−	10.0313i	0.772885	−	0.532404i
$356$	5.24983	−	5.24983i	0.278241	−	0.278241i
$357$			6.75309i			0.357411i
$358$	−8.44973	−	8.44973i	−0.446582	−	0.446582i
$359$		−	30.2708i		−	1.59763i	−0.601575	−	0.798816i	$-0.705460\pi$
$359$		−	30.2708i		−	1.59763i	0.601575	−	0.798816i	$-0.294540\pi$
$360$	0.108846	−	0.0749790i	0.00573670	−	0.00395174i
$361$		−	18.7082i		−	0.984643i
$362$		−	1.63147i		−	0.0857480i
$363$	−9.00484	−	9.00484i	−0.472632	−	0.472632i
$364$	1.94303	−	1.94303i	0.101843	−	0.101843i
$365$	25.8916	+	4.77017i	1.35523	+	0.249682i
$366$	11.0591			0.578067
$367$	13.0615	+	13.0615i	0.681804	+	0.681804i	0.960406	−	0.278603i	$-0.0898713\pi$
$367$	13.0615	+	13.0615i	0.681804	+	0.681804i	−0.278603	+	0.960406i	$0.589871\pi$
$368$			8.90184i			0.464040i
$369$	0.0160116			0.000833529
$370$	7.48229	−	11.3585i	0.388986	−	0.590500i
$371$	24.9968			1.29777
$372$			3.94099i			0.204331i
$373$	16.1154	+	16.1154i	0.834423	+	0.834423i	0.988118	−	0.153695i	$-0.0491174\pi$
$373$	16.1154	+	16.1154i	0.834423	+	0.834423i	−0.153695	+	0.988118i	$0.549117\pi$
$374$	9.06953			0.468974
$375$	−10.1639	+	16.7058i	−0.524863	+	0.862683i
$376$	3.17973	−	3.17973i	0.163982	−	0.163982i
$377$	−0.422554	−	0.422554i	−0.0217627	−	0.0217627i
$378$		−	9.36262i		−	0.481561i
$379$			7.07736i			0.363539i	0.983341	+	0.181770i	$0.0581825\pi$
$379$			7.07736i			0.363539i	−0.983341	+	0.181770i	$0.941817\pi$
$380$	1.18787	+	0.218849i	0.0609366	+	0.0112267i
$381$		−	19.6739i		−	1.00792i
$382$	14.3915	+	14.3915i	0.736331	+	0.736331i
$383$			17.6507i			0.901911i	0.892546	+	0.450955i	$0.148917\pi$
$383$			17.6507i			0.901911i	−0.892546	+	0.450955i	$0.851083\pi$
$384$	−1.23675	+	1.23675i	−0.0631127	+	0.0631127i
$385$	3.15306	−	17.1143i	0.160695	−	0.872223i
$386$	1.88527			0.0959579
$387$	0.0178899			0.000909395
$388$	12.2566			0.622237
$389$	−14.9010	−	14.9010i	−0.755508	−	0.755508i	0.219993	−	0.975501i	$-0.429397\pi$
$389$	−14.9010	−	14.9010i	−0.755508	−	0.755508i	−0.975501	+	0.219993i	$0.929397\pi$
$390$	−5.80642	−	1.06975i	−0.294020	−	0.0541690i
$391$			18.8827i			0.954939i
$392$	3.68685			0.186214
$393$		−	15.6244i		−	0.788144i
$394$	−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	$-0.709021\pi$
$397$	3.61759	−	3.61759i	0.181562	−	0.181562i	0.792036	+	0.610474i	$0.209021\pi$
$398$	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	$0.901780\pi$
$402$		−	15.2776i		−	0.761976i
$403$	2.40529	−	2.40529i	0.119816	−	0.119816i
$404$		−	19.3052i		−	0.960470i
$405$	−16.8932	+	11.6369i	−0.839428	+	0.578242i
$406$			0.720516i			0.0357586i
$407$	24.1029	−	9.76975i	1.19474	−	0.484269i
$408$	−2.62341	+	2.62341i	−0.129878	+	0.129878i
$409$	−1.73592	+	1.73592i	−0.0858355	+	0.0858355i	−0.748721	−	0.662885i	$-0.769332\pi$
$409$	−1.73592	+	1.73592i	−0.0858355	+	0.0858355i	0.662885	+	0.748721i	$0.269332\pi$
$410$	0.498816	−	0.343611i	0.0246348	−	0.0169697i
$411$		−	8.74779i		−	0.431497i
$412$	−10.5846			−0.521466
$413$			10.4680i			0.515095i
$414$			0.526178i			0.0258603i
$415$	−5.80442	+	31.5053i	−0.284928	+	1.54654i
$416$	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	$0.134112\pi$
$419$			16.7428i			0.817941i	−0.912548	+	0.408970i	$0.865888\pi$
$420$	4.03835	+	5.86244i	0.197052	+	0.286058i
$421$	−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	$0.755082\pi$
$422$		−	16.4186i		−	0.799245i
$423$	0.187950	−	0.187950i	0.00913846	−	0.00913846i
$424$	9.71066	+	9.71066i	0.471592	+	0.471592i
$425$	3.77974	−	9.90970i	0.183345	−	0.480691i
$426$	−9.78029	+	9.78029i	−0.473857	+	0.473857i
$427$			11.5091i			0.556965i
$428$	−2.77915	−	2.77915i	−0.134335	−	0.134335i
$429$	−7.98284	−	7.98284i	−0.385415	−	0.385415i
$430$	0.557333	−	0.383920i	0.0268770	−	0.0185143i
$431$	−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	−0.161253	−	0.986913i	$-0.551554\pi$
$433$	17.1809	−	17.1809i	0.825660	−	0.825660i	0.986913	+	0.161253i	$0.0515536\pi$
$434$	−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
$438$	−20.5930			−0.983973
$439$	−13.3023	+	13.3023i	−0.634886	+	0.634886i	−0.949289	−	0.314404i	$-0.898195\pi$
$439$	−13.3023	+	13.3023i	−0.634886	+	0.634886i	0.314404	+	0.949289i	$0.398195\pi$
$440$	7.87337	−	5.42359i	0.375348	−	0.258559i
$441$	0.217926			0.0103774
$442$	3.20228			0.152317
$443$	−24.4725	−	24.4725i	−1.16272	−	1.16272i	−0.983877	−	0.178845i	$-0.942764\pi$
$443$	−24.4725	−	24.4725i	−1.16272	−	1.16272i	−0.178845	−	0.983877i	$-0.557236\pi$
$444$	−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	0.999482	−	0.0321863i	$-0.0102470\pi$
$449$	20.4966	+	20.4966i	0.967296	+	0.967296i	−0.0321863	+	0.999482i	$0.510247\pi$
$450$	0.105325	−	0.276140i	0.00496507	−	0.0130174i
$451$	1.15819			0.0545372
$452$	2.26739			0.106649
$453$	−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
$457$	−25.3795			−1.18720			−0.593601	−	0.804759i	$-0.702294\pi$
$457$	−25.3795			−1.18720			−0.593601	+	0.804759i	$0.702294\pi$
$458$	3.12544			0.146042
$459$	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	$0.472914\pi$
$462$			13.6119i			0.633283i
$463$			40.3494i			1.87520i	0.347720	+	0.937599i	$0.386956\pi$
$463$			40.3494i			1.87520i	−0.347720	+	0.937599i	$0.613044\pi$
$464$	−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
$467$	6.84915			0.316941			0.158471	−	0.987364i	$-0.449344\pi$
$467$	6.84915			0.316941			0.158471	+	0.987364i	$0.449344\pi$
$468$	0.0892335			0.00412482
$469$	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
$473$	1.29406			0.0595011
$474$	5.44322			0.250015
$475$	2.46501	−	1.10380i	0.113103	−	0.0506459i
$476$	−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	$0.193792\pi$
$479$	30.4703	+	30.4703i	1.39222	+	1.39222i	0.571895	+	0.820327i	$0.306208\pi$
$480$	−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
$483$	−28.3399			−1.28951
$484$	7.28104			0.330956
$485$	22.5700	−	15.5474i	1.02485	−	0.705971i
$486$	0.434298	−	0.434298i	0.0197001	−	0.0197001i
$487$	−38.9294			−1.76406			−0.882029	−	0.471194i	$-0.843823\pi$
$487$	−38.9294			−1.76406			−0.882029	+	0.471194i	$0.843823\pi$
$488$	−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
$495$	0.465387	−	0.320583i	0.0209176	−	0.0144091i
$496$	−1.59328	−	1.59328i	−0.0715405	−	0.0715405i
$497$	−10.1783	−	10.1783i	−0.456559	−	0.456559i
$498$		−	25.0579i		−	1.12287i
$499$	10.9240	−	10.9240i	0.489024	−	0.489024i	−0.418974	−	0.907998i	$-0.637610\pi$
$499$	10.9240	−	10.9240i	0.489024	−	0.489024i	0.907998	+	0.418974i	$0.137610\pi$
$500$	−2.64477	−	10.8630i	−0.118278	−	0.485809i
$501$	27.6551	+	27.6551i	1.23554	+	1.23554i
$502$	−2.56669	+	2.56669i	−0.114557	+	0.114557i
$503$		−	37.0071i		−	1.65007i	−0.565085	−	0.825033i	$-0.691157\pi$
$503$		−	37.0071i		−	1.65007i	0.565085	−	0.825033i	$-0.308843\pi$
$504$	−0.0760780	−	0.0760780i	−0.00338878	−	0.00338878i
$505$	−24.4884	−	35.5496i	−1.08972	−	1.58194i
$506$			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	$-0.509831\pi$
$509$	−1.39333			−0.0617583			−0.0308791	+	0.999523i	$0.509831\pi$
$510$	−1.50312	+	8.15865i	−0.0665592	+	0.361271i
$511$		−	21.4311i		−	0.948054i
$512$		−	1.00000i		−	0.0441942i
$513$	2.77849			0.122673
$514$			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
$518$	−10.1966	−	4.31467i	−0.448012	−	0.189576i
$519$			15.9535i			0.700282i
$520$	2.77993	−	1.91496i	0.121908	−	0.0839768i
$521$			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
$523$			6.99302i			0.305783i	0.988243	+	0.152892i	$0.0488586\pi$
$523$			6.99302i			0.305783i	−0.988243	+	0.152892i	$0.951141\pi$
$524$	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
$532$		−	0.983227i		−	0.0426283i
$533$	0.408936			0.0177130
$534$			12.9855i			0.561937i
$535$	−8.64297	−	1.59235i	−0.373668	−	0.0688432i
$536$	6.17649	+	6.17649i	0.266784	+	0.266784i
$537$	20.9004			0.901920
$538$	21.4303			0.923927
$539$	15.7636			0.678986
$540$	2.08395	−	11.3113i	0.0896790	−	0.486762i
$541$	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	$0.212581\pi$
$542$			17.5063i			0.751962i
$543$	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
$547$		−	5.76769i		−	0.246609i	−0.992369	−	0.123304i	$-0.960651\pi$
$547$		−	5.76769i		−	0.246609i	0.992369	−	0.123304i	$-0.0393491\pi$
$548$	3.53660	+	3.53660i	0.151076	+	0.151076i
$549$	−0.264277	+	0.264277i	−0.0112791	+	0.0112791i
$550$	7.61866	−	19.9745i	0.324861	−	0.851717i
$551$	−0.213824			−0.00910920
$552$	−11.0094	−	11.0094i	−0.468590	−	0.468590i
$553$			5.66473i			0.240889i
$554$	−9.92772			−0.421788
$555$	4.79391	+	23.3014i	0.203490	+	0.989088i
$556$	−5.70896			−0.242114
$557$		−	33.4435i		−	1.41705i	−0.705687	−	0.708524i	$-0.749361\pi$
$557$		−	33.4435i		−	1.41705i	0.705687	−	0.708524i	$-0.250639\pi$
$558$	−0.0941773	−	0.0941773i	−0.00398684	−	0.00398684i
$559$	0.456909			0.0193252
$560$	−4.00274	−	0.737449i	−0.169147	−	0.0311629i
$561$	−11.2168	+	11.2168i	−0.473572	+	0.473572i
$562$	−9.25821	−	9.25821i	−0.390534	−	0.390534i
$563$		−	14.9840i		−	0.631500i	−0.948842	−	0.315750i	$-0.897744\pi$
$563$		−	14.9840i		−	0.631500i	0.948842	−	0.315750i	$-0.102256\pi$
$564$			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
$568$		−	7.90805i		−	0.331814i
$569$	−8.42505	+	8.42505i	−0.353197	+	0.353197i	−0.861298	−	0.508101i	$-0.830348\pi$
$569$	−8.42505	+	8.42505i	−0.353197	+	0.353197i	0.508101	+	0.861298i	$0.330348\pi$
$570$	−1.73976	+	1.19844i	−0.0728707	+	0.0501972i
$571$	−22.3944			−0.937176			−0.468588	−	0.883417i	$-0.655237\pi$
$571$	−22.3944			−0.937176			−0.468588	+	0.883417i	$0.655237\pi$
$572$	6.45468			0.269884
$573$	−35.5973			−1.48710
$574$	−0.348647	−	0.348647i	−0.0145523	−	0.0145523i
$575$	41.5868	+	15.8620i	1.73429	+	0.661491i
$576$		−	0.0591090i		−	0.00246287i
$577$	−15.1857			−0.632189			−0.316094	−	0.948728i	$-0.602372\pi$
$577$	−15.1857			−0.632189			−0.316094	+	0.948728i	$0.602372\pi$
$578$			12.5005i			0.519950i
$579$	−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
$587$			36.1936i			1.49387i	0.664898	+	0.746934i	$0.268475\pi$
$587$			36.1936i			1.49387i	−0.664898	+	0.746934i	$0.731525\pi$
$588$	−4.55971	+	4.55971i	−0.188039	+	0.188039i
$589$		−	1.21714i		−	0.0501514i
$590$	−2.32998	+	12.6467i	−0.0959239	+	0.520657i
$591$		−	41.8036i		−	1.71957i
$592$	−2.28498	−	5.63727i	−0.0939122	−	0.231691i
$593$	28.1253	−	28.1253i	1.15497	−	1.15497i	0.169424	−	0.985543i	$-0.445809\pi$
$593$	28.1253	−	28.1253i	1.15497	−	1.15497i	0.985543	−	0.169424i	$-0.0541906\pi$
$594$	15.5511	−	15.5511i	0.638070	−	0.638070i
$595$	−8.49067	−	1.56429i	−0.348083	−	0.0641295i
$596$		−	7.36973i		−	0.301876i
$597$	−16.5378			−0.676846
$598$			13.4386i			0.549545i
$599$		−	8.68551i		−	0.354880i	−0.984132	−	0.177440i	$-0.943218\pi$
$599$		−	8.68551i		−	0.354880i	0.984132	−	0.177440i	$-0.0567816\pi$
$600$	3.57401	+	7.98149i	0.145908	+	0.325843i
$601$	−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
$605$	13.4077	−	9.23591i	0.545100	−	0.375493i
$606$	23.8758	+	23.8758i	0.969886	+	0.969886i
$607$			40.1612i			1.63009i	0.579395	+	0.815047i	$0.303289\pi$
$607$			40.1612i			1.63009i	−0.579395	+	0.815047i	$0.696711\pi$
$608$	0.381960	−	0.381960i	0.0154905	−	0.0154905i
$609$	−0.891100	−	0.891100i	−0.0361092	−	0.0361092i
$610$	−2.56173	+	13.9046i	−0.103721	+	0.562980i
$611$	4.80026	−	4.80026i	0.194198	−	0.194198i
$612$		−	0.125383i		−	0.00506830i
$613$	12.5774	+	12.5774i	0.507997	+	0.507997i	0.913911	−	0.405914i	$-0.133047\pi$
$613$	12.5774	+	12.5774i	0.507997	+	0.507997i	−0.405914	+	0.913911i	$0.633047\pi$
$614$	17.0291	+	17.0291i	0.687239	+	0.687239i
$615$	−0.191951	+	1.04187i	−0.00774019	+	0.0420124i
$616$	−5.50309	−	5.50309i	−0.221726	−	0.221726i
$617$	33.9984	−	33.9984i	1.36872	−	1.36872i	0.506459	−	0.862264i	$-0.330954\pi$
$617$	33.9984	−	33.9984i	1.36872	−	1.36872i	0.862264	−	0.506459i	$-0.169046\pi$
$618$	13.0905	−	13.0905i	0.526578	−	0.526578i
$619$	5.28421			0.212390			0.106195	−	0.994345i	$-0.466133\pi$
$619$	5.28421			0.212390			0.106195	+	0.994345i	$0.466133\pi$
$620$	−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
$623$	−13.5139			−0.541424
$624$	−1.86705	+	1.86705i	−0.0747420	+	0.0747420i
$625$	−18.6498	−	16.6489i	−0.745993	−	0.665954i
$626$	−14.7056			−0.587753
$627$	−4.03953			−0.161323
$628$	−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
$635$	24.7360	+	4.55726i	0.981618	+	0.180849i
$636$	−24.0194			−0.952430
$637$	5.56582			0.220526
$638$	−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	$0.342136\pi$
$642$	6.87423			0.271304
$643$	6.55586			0.258538			0.129269	−	0.991610i	$-0.458737\pi$
$643$	6.55586			0.258538			0.129269	+	0.991610i	$0.458737\pi$
$644$	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
$647$		−	6.75259i		−	0.265472i	−0.991151	−	0.132736i	$-0.957624\pi$
$647$		−	6.75259i		−	0.265472i	0.991151	−	0.132736i	$-0.0423762\pi$
$648$			9.17383i			0.360382i
$649$	−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
$652$	−19.2629			−0.754394
$653$	−18.5694			−0.726675			−0.363338	−	0.931658i	$-0.618363\pi$
$653$	−18.5694			−0.726675			−0.363338	+	0.931658i	$0.618363\pi$
$654$	−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
$658$	−8.18513			−0.319090
$659$	−29.5588			−1.15145			−0.575724	−	0.817644i	$-0.695280\pi$
$659$	−29.5588			−1.15145			−0.575724	+	0.817644i	$0.695280\pi$
$660$	−3.02977	+	16.4450i	−0.117934	+	0.640122i
$661$	−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
$668$	−22.3611			−0.865178
$669$	34.0353			1.31588
$670$	19.2085	+	3.53890i	0.742089	+	0.136720i
$671$	−19.1164	+	19.1164i	−0.737982	+	0.737982i
$672$	3.18360			0.122810
$673$	−1.64758	+	1.64758i	−0.0635097	+	0.0635097i	−0.738148	−	0.674639i	$-0.764300\pi$
$673$	−1.64758	+	1.64758i	−0.0635097	+	0.0635097i	0.674639	+	0.738148i	$0.264300\pi$
$674$	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	$-0.580897\pi$
$677$	18.6418	−	18.6418i	0.716461	−	0.716461i	0.967879	+	0.251417i	$0.0808967\pi$
$678$	−2.80420	+	2.80420i	−0.107695	+	0.107695i
$679$	−15.7753	−	15.7753i	−0.605400	−	0.605400i
$680$	−2.69073	−	3.90611i	−0.103185	−	0.149792i
$681$	6.46904	+	6.46904i	0.247894	+	0.247894i
$682$	−6.81229	−	6.81229i	−0.260856	−	0.260856i
$683$		−	21.7547i		−	0.832421i	−0.909268	−	0.416210i	$-0.863358\pi$
$683$		−	21.7547i		−	0.832421i	0.909268	−	0.416210i	$-0.136642\pi$
$684$	0.0225773	−	0.0225773i	0.000863263	−	0.000863263i
$685$	10.9986	+	2.02634i	0.420235	+	0.0774225i
$686$	−13.7548	−	13.7548i	−0.525162	−	0.525162i
$687$	−3.86539	+	3.86539i	−0.147474	+	0.147474i
$688$		−	0.302660i		−	0.0115388i
$689$	14.6596	+	14.6596i	0.558488	+	0.558488i
$690$	−34.2384	−	6.30795i	−1.30343	−	0.240140i
$691$		−	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
$695$	−10.5128	+	7.24175i	−0.398772	+	0.274695i
$696$		−	0.692342i		−	0.0262431i
$697$		−	0.574599i		−	0.0217645i
$698$	−16.1967			−0.613056
$699$			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
$703$	1.28044	−	3.02599i	0.0482927	−	0.114127i
$704$		−	4.27563i		−	0.161144i
$705$	9.97674	+	14.4831i	0.375746	+	0.545466i
$706$			20.3765i			0.766880i
$707$	−24.8474	+	24.8474i	−0.934481	+	0.934481i
$708$		−	10.0586i		−	0.378026i
$709$	−35.9766	−	35.9766i	−1.35113	−	1.35113i	−0.884402	−	0.466725i	$-0.845434\pi$
$709$	−35.9766	−	35.9766i	−1.35113	−	1.35113i	−0.466725	−	0.884402i	$-0.654566\pi$
$710$	−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
$717$		−	47.5233i		−	1.77479i
$718$	−30.2708			−1.12970
$719$			10.7340i			0.400310i	0.979764	+	0.200155i	$0.0641446\pi$
$719$			10.7340i			0.400310i	−0.979764	+	0.200155i	$0.935855\pi$
$720$	−0.0749790	−	0.108846i	−0.00279430	−	0.00405646i
$721$	13.6232	+	13.6232i	0.507356	+	0.507356i
$722$	−18.7082			−0.696248
$723$	47.0013			1.74800
$724$	−1.63147			−0.0606330
$725$	0.808875	+	1.80638i	0.0300408	+	0.0670873i
$726$	−9.00484	+	9.00484i	−0.334201	+	0.334201i
$727$		−	14.6699i		−	0.544078i	−0.962286	−	0.272039i	$-0.912302\pi$
$727$		−	14.6699i		−	0.544078i	0.962286	−	0.272039i	$-0.0876980\pi$
$728$	−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
$732$		−	11.0591i		−	0.408755i
$733$	22.2345	+	22.2345i	0.821249	+	0.821249i	0.986287	−	0.165039i	$-0.0527748\pi$
$733$	22.2345	+	22.2345i	0.821249	+	0.821249i	−0.165039	+	0.986287i	$0.552775\pi$
$734$	13.0615	−	13.0615i	0.482108	−	0.482108i
$735$	−2.61255	+	14.1804i	−0.0963652	+	0.523053i
$736$	8.90184			0.328126
$737$	26.4084	+	26.4084i	0.972766	+	0.972766i
$738$		−	0.0160116i		−	0.000589394i
$739$	4.21587			0.155083			0.0775416	−	0.996989i	$-0.475293\pi$
$739$	4.21587			0.155083			0.0775416	+	0.996989i	$0.475293\pi$
$740$	−11.3585	−	7.48229i	−0.417547	−	0.275054i
$741$	−1.42628			−0.0523957
$742$		−	24.9968i		−	0.917662i
$743$	−0.649329	−	0.649329i	−0.0238216	−	0.0238216i	0.695096	−	0.718917i	$-0.255362\pi$
$743$	−0.649329	−	0.649329i	−0.0238216	−	0.0238216i	−0.718917	+	0.695096i	$0.755362\pi$
$744$	3.94099			0.144484
$745$	−9.34842	−	13.5710i	−0.342499	−	0.497203i
$746$	16.1154	−	16.1154i	0.590026	−	0.590026i
$747$	0.598806	+	0.598806i	0.0219091	+	0.0219091i
$748$		−	9.06953i		−	0.331615i
$749$			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
$753$		−	6.34872i		−	0.231360i
$754$	−0.422554	+	0.422554i	−0.0153885	+	0.0153885i
$755$	−6.30145	−	9.14775i	−0.229333	−	0.332921i
$756$	−9.36262			−0.340515
$757$	15.9640			0.580222			0.290111	−	0.956993i	$-0.406308\pi$
$757$	15.9640			0.580222			0.290111	+	0.956993i	$0.406308\pi$
$758$	7.07736			0.257061
$759$	−47.0720	−	47.0720i	−1.70861	−	1.70861i
$760$	0.218849	−	1.18787i	0.00793848	−	0.0430887i
$761$			28.4393i			1.03092i	0.856912	+	0.515462i	$0.172380\pi$
$761$			28.4393i			1.03092i	−0.856912	+	0.515462i	$0.827620\pi$
$762$	−19.6739			−0.712710
$763$		−	10.6724i		−	0.386368i
$764$	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	−0.981833	−	0.189749i	$-0.939232\pi$
$769$	−21.9651	+	21.9651i	−0.792083	+	0.792083i	0.189749	+	0.981833i	$0.439232\pi$
$770$	−17.1143	−	3.15306i	−0.616755	−	0.113629i
$771$	−17.1900	−	17.1900i	−0.619082	−	0.619082i
$772$		−	1.88527i		−	0.0678525i
$773$	2.60816	−	2.60816i	0.0938089	−	0.0938089i	−0.658645	−	0.752454i	$-0.728870\pi$
$773$	2.60816	−	2.60816i	0.0938089	−	0.0938089i	0.752454	+	0.658645i	$0.228870\pi$
$774$		−	0.0178899i		−	0.000643040i
$775$	−10.2824	+	4.60433i	−0.369355	+	0.165392i
$776$		−	12.2566i		−	0.439988i
$777$	17.9468	−	7.27447i	0.643838	−	0.260970i
$778$	−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
$782$	18.8827			0.675244
$783$			2.03610i			0.0727643i
$784$		−	3.68685i		−	0.131673i
$785$	−25.7621	−	4.74630i	−0.919488	−	0.169403i
$786$	−15.6244			−0.557302
$787$	−2.48943	−	2.48943i	−0.0887387	−	0.0887387i	0.661344	−	0.750083i	$-0.269986\pi$
$787$	−2.48943	−	2.48943i	−0.0887387	−	0.0887387i	−0.750083	+	0.661344i	$0.769986\pi$
$788$	16.9005	+	16.9005i	0.602057	+	0.602057i
$789$		−	35.1912i		−	1.25284i
$790$	−1.26087	+	6.84376i	−0.0448597	+	0.243490i
$791$	−2.91832	−	2.91832i	−0.103763	−	0.103763i
$792$		−	0.252728i		−	0.00898031i
$793$	−6.74965	+	6.74965i	−0.239687	+	0.239687i
$794$	−3.61759	−	3.61759i	−0.128384	−	0.128384i
$795$	−44.2305	+	30.4683i	−1.56869	+	1.08060i
$796$	6.68597	−	6.68597i	0.236978	−	0.236978i
$797$		−	30.0363i		−	1.06394i	−0.846763	−	0.531970i	$-0.821452\pi$
$797$		−	30.0363i		−	1.06394i	0.846763	−	0.531970i	$-0.178548\pi$
$798$	1.21601	+	1.21601i	0.0430462	+	0.0430462i
$799$	−6.74488	−	6.74488i	−0.238617	−	0.238617i
$800$	−4.67171	−	1.78188i	−0.165170	−	0.0629989i
$801$	−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
$808$	−19.3052			−0.679155
$809$	−4.17505	+	4.17505i	−0.146787	+	0.146787i	−0.776681	−	0.629894i	$-0.783098\pi$
$809$	−4.17505	+	4.17505i	−0.146787	+	0.146787i	0.629894	+	0.776681i	$0.283098\pi$
$810$	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	$0.379237\pi$
$812$	0.720516			0.0252852
$813$	−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
$820$	−0.343611	−	0.498816i	−0.0119994	−	0.0174194i
$821$	−27.8919			−0.973434			−0.486717	−	0.873560i	$-0.661806\pi$
$821$	−27.8919			−0.973434			−0.486717	+	0.873560i	$0.661806\pi$
$822$	−8.74779			−0.305114
$823$	7.17157	−	7.17157i	0.249985	−	0.249985i	−0.570979	−	0.820964i	$-0.693436\pi$
$823$	7.17157	−	7.17157i	0.249985	−	0.249985i	0.820964	+	0.570979i	$0.193436\pi$
$824$			10.5846i			0.368732i
$825$	15.2811	+	34.1259i	0.532021	+	1.18811i
$826$	10.4680			0.364227
$827$	46.4436			1.61500			0.807501	−	0.589866i	$-0.200819\pi$
$827$	46.4436			1.61500			0.807501	+	0.589866i	$0.200819\pi$
$828$	0.526178			0.0182860
$829$	−2.54664	+	2.54664i	−0.0884484	+	0.0884484i	−0.749947	−	0.661498i	$-0.769921\pi$
$829$	−2.54664	+	2.54664i	−0.0884484	+	0.0884484i	0.661498	+	0.749947i	$0.269921\pi$
$830$	31.5053	+	5.80442i	1.09357	+	0.201474i
$831$	12.2781	−	12.2781i	0.425923	−	0.425923i
$832$		−	1.50964i		−	0.0523375i
$833$		−	7.82059i		−	0.270967i
$834$	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
$837$	−11.5900			−0.400610
$838$	16.7428			0.578372
$839$	−29.4346			−1.01619			−0.508097	−	0.861300i	$-0.669651\pi$
$839$	−29.4346			−1.01619			−0.508097	+	0.861300i	$0.669651\pi$
$840$	5.86244	−	4.03835i	0.202273	−	0.139336i
$841$			28.8433i			0.994597i
$842$	−0.463240	+	0.463240i	−0.0159643	+	0.0159643i
$843$	22.9002			0.788725
$844$	−16.4186			−0.565151
$845$	−19.7421	+	13.5994i	−0.679150	+	0.467834i
$846$	−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
$853$	−17.8225			−0.610230			−0.305115	−	0.952315i	$-0.598695\pi$
$853$	−17.8225			−0.610230			−0.305115	+	0.952315i	$0.598695\pi$
$854$	11.5091			0.393834
$855$	0.0129359	−	0.0702139i	0.000442400	−	0.00240126i
$856$	−2.77915	+	2.77915i	−0.0949892	+	0.0949892i
$857$	42.4300			1.44938			0.724691	−	0.689074i	$-0.241983\pi$
$857$	42.4300			1.44938			0.724691	+	0.689074i	$0.241983\pi$
$858$	−7.98284	+	7.98284i	−0.272530	+	0.272530i
$859$	7.52410	+	7.52410i	0.256719	+	0.256719i	0.823718	−	0.566999i	$-0.191896\pi$
$859$	7.52410	+	7.52410i	0.256719	+	0.256719i	−0.566999	+	0.823718i	$0.691896\pi$
$860$	−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	−0.106983	+	0.994261i	$0.534119\pi$
$863$	−32.3511	+	32.3511i	−1.10124	+	1.10124i	−0.994261	+	0.106983i	$0.965881\pi$
$864$	−3.63715	−	3.63715i	−0.123738	−	0.123738i
$865$	−20.0584	−	3.69548i	−0.682005	−	0.125650i
$866$	−17.1809	−	17.1809i	−0.583830	−	0.583830i
$867$	−15.4600	−	15.4600i	−0.525048	−	0.525048i
$868$			4.10137i			0.139209i
$869$	−9.40901	+	9.40901i	−0.319179	+	0.319179i
$870$	−0.878227	−	1.27491i	−0.0297747	−	0.0432236i
$871$	9.32430	+	9.32430i	0.315942	+	0.315942i
$872$	4.14598	−	4.14598i	0.140401	−	0.140401i
$873$		−	0.724478i		−	0.0245198i
$874$	3.40015	+	3.40015i	0.115012	+	0.115012i
$875$	−10.5776	+	17.3856i	−0.357586	+	0.587741i
$876$			20.5930i			0.695774i
$877$	33.8258	+	33.8258i	1.14222	+	1.14222i	0.988044	+	0.154171i	$0.0492707\pi$
$877$	33.8258	+	33.8258i	1.14222	+	1.14222i	0.154171	+	0.988044i	$0.450729\pi$
$878$	13.3023	+	13.3023i	0.448932	+	0.448932i
$879$	−31.1905			−1.05203
$880$	−5.42359	−	7.87337i	−0.182829	−	0.265411i
$881$			49.3397i			1.66230i	0.556050	+	0.831149i	$0.312316\pi$
$881$			49.3397i			1.66230i	−0.556050	+	0.831149i	$0.687684\pi$
$882$		−	0.217926i		−	0.00733794i
$883$	14.6163			0.491878			0.245939	−	0.969285i	$-0.420904\pi$
$883$	14.6163			0.491878			0.245939	+	0.969285i	$0.420904\pi$
$884$		−	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	0.433560	−	0.901125i	$-0.357257\pi$
$887$	39.7503	−	39.7503i	1.33468	−	1.33468i	0.901125	−	0.433560i	$-0.142743\pi$
$888$	9.79786	+	4.14595i	0.328795	+	0.139129i
$889$		−	20.4745i		−	0.686693i
$890$	−16.3267	−	3.00796i	−0.547271	−	0.100827i
$891$			39.2239i			1.31405i
$892$	−13.7600	+	13.7600i	−0.460718	+	0.460718i
$893$		−	2.42906i		−	0.0812853i
$894$	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
$902$		−	1.15819i		−	0.0385636i
$903$	0.963548			0.0320649
$904$		−	2.26739i		−	0.0754124i
$905$	−3.00427	+	2.06950i	−0.0998652	+	0.0687924i
$906$	6.14380	+	6.14380i	0.204114	+	0.204114i
$907$	9.06842			0.301112			0.150556	−	0.988601i	$-0.451894\pi$
$907$	9.06842			0.301112			0.150556	+	0.988601i	$0.451894\pi$
$908$	−5.23067			−0.173586
$909$	−1.14111			−0.0378483
$910$	−6.04271	−	1.11329i	−0.200314	−	0.0369051i
$911$	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	$0.145495\pi$
$912$			0.944780i			0.0312848i
$913$	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
$917$		−	16.2602i		−	0.536959i
$918$	−7.71517	−	7.71517i	−0.254639	−	0.254639i
$919$	20.8694	−	20.8694i	0.688418	−	0.688418i	−0.273464	−	0.961882i	$-0.588170\pi$
$919$	20.8694	−	20.8694i	0.688418	−	0.688418i	0.961882	+	0.273464i	$0.0881696\pi$
$920$	16.3923	−	11.2919i	0.540438	−	0.372282i
$921$	−42.1216			−1.38795
$922$	19.5684	+	19.5684i	0.644452	+	0.644452i
$923$		−	11.9383i		−	0.392955i
$924$	13.6119			0.447799
$925$	−30.4073	+	0.629852i	−0.999786	+	0.0207094i
$926$	40.3494			1.32596
$927$			0.625645i			0.0205489i
$928$	0.279903	+	0.279903i	0.00918828	+	0.00918828i
$929$	−26.4042			−0.866294			−0.433147	−	0.901323i	$-0.642597\pi$
$929$	−26.4042			−0.866294			−0.433147	+	0.901323i	$0.642597\pi$
$930$	7.25714	−	4.99910i	0.237971	−	0.163927i
$931$	1.40823	−	1.40823i	0.0461528	−	0.0461528i
$932$	−7.43576	−	7.43576i	−0.243566	−	0.243566i
$933$			9.26748i			0.303404i
$934$		−	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	0.743581	−	0.668646i	$-0.233126\pi$
$937$	2.29378	+	2.29378i	0.0749346	+	0.0749346i	−0.668646	+	0.743581i	$0.733126\pi$
$938$		−	15.8993i		−	0.519130i
$939$	18.1871	−	18.1871i	0.593515	−	0.593515i
$940$	−9.88875	−	1.82187i	−0.322536	−	0.0594227i
$941$	46.2380			1.50732			0.753658	−	0.657267i	$-0.228288\pi$
$941$	46.2380			1.50732			0.753658	+	0.657267i	$0.228288\pi$
$942$	20.4900			0.667600
$943$	2.41135			0.0785244
$944$	4.06655	+	4.06655i	0.132355	+	0.132355i
$945$	−17.2408	+	11.8764i	−0.560843	+	0.386338i
$946$		−	1.29406i		−	0.0420736i
$947$	−45.6330			−1.48287			−0.741436	−	0.671023i	$-0.765855\pi$
$947$	−45.6330			−1.48287			−0.741436	+	0.671023i	$0.765855\pi$
$948$		−	5.44322i		−	0.176787i
$949$	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	$-0.115874\pi$
$953$	17.8564	+	17.8564i	0.578427	+	0.578427i	−0.356043	+	0.934470i	$0.615874\pi$
$954$	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
$957$		−	2.96020i		−	0.0956897i
$958$	30.4703	−	30.4703i	0.984450	−	0.984450i
$959$		−	9.10378i		−	0.293976i
$960$	3.84622	+	0.708613i	0.124136	+	0.0228704i
$961$		−	25.9229i		−	0.836223i
$962$	−3.44951	−	8.51028i	−0.111217	−	0.274382i
$963$	−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
$967$	21.9000			0.704256			0.352128	−	0.935952i	$-0.385458\pi$
$967$	21.9000			0.704256			0.352128	+	0.935952i	$0.385458\pi$
$968$		−	7.28104i		−	0.234022i
$969$			2.00408i			0.0643803i
$970$	−15.5474	−	22.5700i	−0.499197	−	0.724679i
$971$	−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
$975$	5.39548	+	12.0492i	0.172794	+	0.385883i
$976$	4.47102	+	4.47102i	0.143114	+	0.143114i
$977$			39.9367i			1.27769i	0.769336	+	0.638844i	$0.220587\pi$
$977$			39.9367i			1.27769i	−0.769336	+	0.638844i	$0.779413\pi$
$978$	23.8234	−	23.8234i	0.761789	−	0.761789i
$979$	−22.4464	−	22.4464i	−0.717389	−	0.717389i
$980$	−4.67672	−	6.78914i	−0.149392	−	0.216871i
$981$	0.245065	−	0.245065i	0.00782431	−	0.00782431i
$982$		−	8.64964i		−	0.276021i
$983$	27.5089	+	27.5089i	0.877396	+	0.877396i	0.993265	−	0.115868i	$-0.0369651\pi$
$983$	27.5089	+	27.5089i	0.877396	+	0.877396i	−0.115868	+	0.993265i	$0.536965\pi$
$984$	0.335014	+	0.335014i	0.0106799	+	0.0106799i
$985$	52.5596	+	9.68338i	1.67469	+	0.308538i
$986$	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
$993$	−38.4438			−1.21998
$994$	−10.1783	+	10.1783i	−0.322836	+	0.322836i
$995$	3.83081	−	20.7930i	0.121445	−	0.659181i
$996$	−25.0579			−0.793990
$997$	44.3360			1.40414			0.702068	−	0.712110i	$-0.252260\pi$
$997$	44.3360			1.40414			0.702068	+	0.712110i	$0.252260\pi$
$998$	−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.g.e.327.8	yes	20
5.3	odd	4		370.2.h.e.253.3	yes	20
37.6	odd	4		370.2.h.e.117.3	yes	20
185.43	even	4	inner	370.2.g.e.43.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.8	✓	20	185.43	even	4	inner
370.2.g.e.327.8	yes	20	1.1	even	1	trivial
370.2.h.e.117.3	yes	20	37.6	odd	4
370.2.h.e.253.3	yes	20	5.3	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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