LMFDB - Embedded newform 370.2.g.e.43.5

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			43.5
Root			$0.536506 - 0.536506i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.e.327.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +(2.23241 - 0.127776i) q^{10} +4.39414i q^{11} +(0.536506 - 0.536506i) q^{12} +6.74274i q^{13} +(0.767774 + 0.767774i) q^{14} +(1.26626 + 1.12915i) q^{15} +1.00000 q^{16} +7.34365 q^{17} -2.42432 q^{18} +(2.59760 - 2.59760i) q^{19} +(0.127776 + 2.23241i) q^{20} +0.823831i q^{21} -4.39414 q^{22} +1.20395i q^{23} +(0.536506 + 0.536506i) q^{24} +(-4.96735 + 0.570497i) q^{25} -6.74274 q^{26} +(-2.91018 - 2.91018i) q^{27} +(-0.767774 + 0.767774i) q^{28} +(1.25185 + 1.25185i) q^{29} +(-1.12915 + 1.26626i) q^{30} +(-4.14855 + 4.14855i) q^{31} +1.00000i q^{32} +(-2.35748 - 2.35748i) q^{33} +7.34365i q^{34} +(-1.81209 - 1.61589i) q^{35} -2.42432i q^{36} +(0.633071 - 6.04973i) q^{37} +(2.59760 + 2.59760i) q^{38} +(-3.61752 - 3.61752i) q^{39} +(-2.23241 + 0.127776i) q^{40} +4.07091i q^{41} -0.823831 q^{42} -8.56098i q^{43} -4.39414i q^{44} +(5.41209 - 0.309770i) q^{45} -1.20395 q^{46} +(7.68569 - 7.68569i) q^{47} +(-0.536506 + 0.536506i) q^{48} +5.82104i q^{49} +(-0.570497 - 4.96735i) q^{50} +(-3.93991 + 3.93991i) q^{51} -6.74274i q^{52} +(2.31983 + 2.31983i) q^{53} +(2.91018 - 2.91018i) q^{54} +(9.80954 - 0.561465i) q^{55} +(-0.767774 - 0.767774i) q^{56} +2.78725i q^{57} +(-1.25185 + 1.25185i) q^{58} +(-7.61323 + 7.61323i) q^{59} +(-1.26626 - 1.12915i) q^{60} +(1.14451 - 1.14451i) q^{61} +(-4.14855 - 4.14855i) q^{62} +(1.86133 + 1.86133i) q^{63} -1.00000 q^{64} +(15.0526 - 0.861559i) q^{65} +(2.35748 - 2.35748i) q^{66} +(-6.25304 - 6.25304i) q^{67} -7.34365 q^{68} +(-0.645925 - 0.645925i) q^{69} +(1.61589 - 1.81209i) q^{70} -5.46460 q^{71} +2.42432 q^{72} +(1.88159 - 1.88159i) q^{73} +(6.04973 + 0.633071i) q^{74} +(2.35893 - 2.97108i) q^{75} +(-2.59760 + 2.59760i) q^{76} +(3.37371 + 3.37371i) q^{77} +(3.61752 - 3.61752i) q^{78} +(5.13322 - 5.13322i) q^{79} +(-0.127776 - 2.23241i) q^{80} -4.15032 q^{81} -4.07091 q^{82} +(0.570350 + 0.570350i) q^{83} -0.823831i q^{84} +(-0.938340 - 16.3941i) q^{85} +8.56098 q^{86} -1.34325 q^{87} +4.39414 q^{88} +(7.54653 + 7.54653i) q^{89} +(0.309770 + 5.41209i) q^{90} +(5.17690 + 5.17690i) q^{91} -1.20395i q^{92} -4.45144i q^{93} +(7.68569 + 7.68569i) q^{94} +(-6.13083 - 5.46701i) q^{95} +(-0.536506 - 0.536506i) q^{96} -5.39443 q^{97} -5.82104 q^{98} -10.6528 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.536506	+	0.536506i	−0.309752	+	0.309752i	−0.844813	−	0.535061i	$-0.820288\pi$
$3$	−0.536506	+	0.536506i	−0.309752	+	0.309752i	0.535061	+	0.844813i	$0.320288\pi$
$4$	−1.00000			−0.500000
$5$	−0.127776	−	2.23241i	−0.0571431	−	0.998366i
$5$	−0.127776	−	2.23241i	−0.0571431	−	0.998366i
$6$	−0.536506	−	0.536506i	−0.219027	−	0.219027i
$7$	0.767774	−	0.767774i	0.290191	−	0.290191i	−0.546964	−	0.837156i	$-0.684217\pi$
$7$	0.767774	−	0.767774i	0.290191	−	0.290191i	0.837156	+	0.546964i	$0.184217\pi$
$8$		−	1.00000i		−	0.353553i
$9$			2.42432i			0.808108i
$10$	2.23241	−	0.127776i	0.705951	−	0.0404063i
$11$			4.39414i			1.32488i	0.749114	+	0.662442i	$0.230480\pi$
$11$			4.39414i			1.32488i	−0.749114	+	0.662442i	$0.769520\pi$
$12$	0.536506	−	0.536506i	0.154876	−	0.154876i
$13$			6.74274i			1.87010i	0.354516	+	0.935050i	$0.384645\pi$
$13$			6.74274i			1.87010i	−0.354516	+	0.935050i	$0.615355\pi$
$14$	0.767774	+	0.767774i	0.205196	+	0.205196i
$15$	1.26626	+	1.12915i	0.326946	+	0.291545i
$16$	1.00000			0.250000
$17$	7.34365			1.78110			0.890548	−	0.454889i	$-0.150321\pi$
$17$	7.34365			1.78110			0.890548	+	0.454889i	$0.150321\pi$
$18$	−2.42432			−0.571419
$19$	2.59760	−	2.59760i	0.595930	−	0.595930i	−0.343297	−	0.939227i	$-0.611544\pi$
$19$	2.59760	−	2.59760i	0.595930	−	0.595930i	0.939227	+	0.343297i	$0.111544\pi$
$20$	0.127776	+	2.23241i	0.0285715	+	0.499183i
$21$			0.823831i			0.179775i
$22$	−4.39414			−0.936834
$23$			1.20395i			0.251040i	0.992091	+	0.125520i	$0.0400600\pi$
$23$			1.20395i			0.251040i	−0.992091	+	0.125520i	$0.959940\pi$
$24$	0.536506	+	0.536506i	0.109514	+	0.109514i
$25$	−4.96735	+	0.570497i	−0.993469	+	0.114099i
$26$	−6.74274			−1.32236
$27$	−2.91018	−	2.91018i	−0.560064	−	0.560064i
$28$	−0.767774	+	0.767774i	−0.145096	+	0.145096i
$29$	1.25185	+	1.25185i	0.232463	+	0.232463i	0.813720	−	0.581257i	$-0.197439\pi$
$29$	1.25185	+	1.25185i	0.232463	+	0.232463i	−0.581257	+	0.813720i	$0.697439\pi$
$30$	−1.12915	+	1.26626i	−0.206154	+	0.231185i
$31$	−4.14855	+	4.14855i	−0.745101	+	0.745101i	−0.973555	−	0.228454i	$-0.926633\pi$
$31$	−4.14855	+	4.14855i	−0.745101	+	0.745101i	0.228454	+	0.973555i	$0.426633\pi$
$32$			1.00000i			0.176777i
$33$	−2.35748	−	2.35748i	−0.410385	−	0.410385i
$34$			7.34365i			1.25943i
$35$	−1.81209	−	1.61589i	−0.306300	−	0.273135i
$36$		−	2.42432i		−	0.404054i
$37$	0.633071	−	6.04973i	0.104076	−	0.994569i
$37$	0.633071	−	6.04973i	0.104076	−	0.994569i
$38$	2.59760	+	2.59760i	0.421386	+	0.421386i
$39$	−3.61752	−	3.61752i	−0.579266	−	0.579266i
$40$	−2.23241	+	0.127776i	−0.352976	+	0.0202031i
$41$			4.07091i			0.635769i	0.948129	+	0.317884i	$0.102972\pi$
$41$			4.07091i			0.635769i	−0.948129	+	0.317884i	$0.897028\pi$
$42$	−0.823831			−0.127120
$43$		−	8.56098i		−	1.30554i	−0.757557	−	0.652769i	$-0.773607\pi$
$43$		−	8.56098i		−	1.30554i	0.757557	−	0.652769i	$-0.226393\pi$
$44$		−	4.39414i		−	0.662442i
$45$	5.41209	−	0.309770i	0.806787	−	0.0461778i
$46$	−1.20395			−0.177512
$47$	7.68569	−	7.68569i	1.12107	−	1.12107i	0.129493	−	0.991580i	$-0.458665\pi$
$47$	7.68569	−	7.68569i	1.12107	−	1.12107i	0.991580	−	0.129493i	$-0.0413351\pi$
$48$	−0.536506	+	0.536506i	−0.0774379	+	0.0774379i
$49$			5.82104i			0.831578i
$50$	−0.570497	−	4.96735i	−0.0806805	−	0.702489i
$51$	−3.93991	+	3.93991i	−0.551697	+	0.551697i
$52$		−	6.74274i		−	0.935050i
$53$	2.31983	+	2.31983i	0.318653	+	0.318653i	0.848250	−	0.529596i	$-0.177657\pi$
$53$	2.31983	+	2.31983i	0.318653	+	0.318653i	−0.529596	+	0.848250i	$0.677657\pi$
$54$	2.91018	−	2.91018i	0.396025	−	0.396025i
$55$	9.80954	−	0.561465i	1.32272	−	0.0757079i
$56$	−0.767774	−	0.767774i	−0.102598	−	0.102598i
$57$			2.78725i			0.369181i
$58$	−1.25185	+	1.25185i	−0.164376	+	0.164376i
$59$	−7.61323	+	7.61323i	−0.991158	+	0.991158i	−0.999961	−	0.00880307i	$-0.997198\pi$
$59$	−7.61323	+	7.61323i	−0.991158	+	0.991158i	0.00880307	+	0.999961i	$0.497198\pi$
$60$	−1.26626	−	1.12915i	−0.163473	−	0.145773i
$61$	1.14451	−	1.14451i	0.146539	−	0.146539i	−0.630031	−	0.776570i	$-0.716958\pi$
$61$	1.14451	−	1.14451i	0.146539	−	0.146539i	0.776570	+	0.630031i	$0.216958\pi$
$62$	−4.14855	−	4.14855i	−0.526866	−	0.526866i
$63$	1.86133	+	1.86133i	0.234506	+	0.234506i
$64$	−1.00000			−0.125000
$65$	15.0526	−	0.861559i	1.86704	−	0.106863i
$66$	2.35748	−	2.35748i	0.290186	−	0.290186i
$67$	−6.25304	−	6.25304i	−0.763930	−	0.763930i	0.213100	−	0.977030i	$-0.431644\pi$
$67$	−6.25304	−	6.25304i	−0.763930	−	0.763930i	−0.977030	+	0.213100i	$0.931644\pi$
$68$	−7.34365			−0.890548
$69$	−0.645925	−	0.645925i	−0.0777602	−	0.0777602i
$70$	1.61589	−	1.81209i	0.193136	−	0.216587i
$71$	−5.46460			−0.648529			−0.324265	−	0.945966i	$-0.605117\pi$
$71$	−5.46460			−0.648529			−0.324265	+	0.945966i	$0.605117\pi$
$72$	2.42432			0.285709
$73$	1.88159	−	1.88159i	0.220224	−	0.220224i	−0.588369	−	0.808593i	$-0.700230\pi$
$73$	1.88159	−	1.88159i	0.220224	−	0.220224i	0.808593	+	0.588369i	$0.200230\pi$
$74$	6.04973	+	0.633071i	0.703267	+	0.0735930i
$75$	2.35893	−	2.97108i	0.272386	−	0.343071i
$76$	−2.59760	+	2.59760i	−0.297965	+	0.297965i
$77$	3.37371	+	3.37371i	0.384470	+	0.384470i
$78$	3.61752	−	3.61752i	0.409603	−	0.409603i
$79$	5.13322	−	5.13322i	0.577533	−	0.577533i	−0.356690	−	0.934223i	$-0.616095\pi$
$79$	5.13322	−	5.13322i	0.577533	−	0.577533i	0.934223	+	0.356690i	$0.116095\pi$
$80$	−0.127776	−	2.23241i	−0.0142858	−	0.249591i
$81$	−4.15032			−0.461146
$82$	−4.07091			−0.449557
$83$	0.570350	+	0.570350i	0.0626041	+	0.0626041i	0.737716	−	0.675112i	$-0.235905\pi$
$83$	0.570350	+	0.570350i	0.0626041	+	0.0626041i	−0.675112	+	0.737716i	$0.735905\pi$
$84$		−	0.823831i		−	0.0898873i
$85$	−0.938340	−	16.3941i	−0.101777	−	1.77819i
$86$	8.56098			0.923155
$87$	−1.34325			−0.144012
$88$	4.39414			0.468417
$89$	7.54653	+	7.54653i	0.799931	+	0.799931i	0.983084	−	0.183153i	$-0.0586305\pi$
$89$	7.54653	+	7.54653i	0.799931	+	0.799931i	−0.183153	+	0.983084i	$0.558630\pi$
$90$	0.309770	+	5.41209i	0.0326526	+	0.570485i
$91$	5.17690	+	5.17690i	0.542687	+	0.542687i
$92$		−	1.20395i		−	0.125520i
$93$		−	4.45144i		−	0.461593i
$94$	7.68569	+	7.68569i	0.792719	+	0.792719i
$95$	−6.13083	−	5.46701i	−0.629009	−	0.560903i
$96$	−0.536506	−	0.536506i	−0.0547569	−	0.0547569i
$97$	−5.39443			−0.547721			−0.273861	−	0.961769i	$-0.588301\pi$
$97$	−5.39443			−0.547721			−0.273861	+	0.961769i	$0.588301\pi$
$98$	−5.82104			−0.588014
$99$	−10.6528			−1.07065
$100$	4.96735	−	0.570497i	0.496735	−	0.0570497i
$101$		−	14.5684i		−	1.44961i	−0.688956	−	0.724803i	$-0.741931\pi$
$101$		−	14.5684i		−	1.44961i	0.688956	−	0.724803i	$-0.258069\pi$
$102$	−3.93991	−	3.93991i	−0.390109	−	0.390109i
$103$	−10.1623			−1.00132			−0.500662	−	0.865643i	$-0.666910\pi$
$103$	−10.1623			−1.00132			−0.500662	+	0.865643i	$0.666910\pi$
$104$	6.74274			0.661180
$105$	1.83913	−	0.105266i	0.179481	−	0.0102729i
$106$	−2.31983	+	2.31983i	−0.225322	+	0.225322i
$107$	−13.4161	+	13.4161i	−1.29698	+	1.29698i	−0.366601	+	0.930378i	$0.619479\pi$
$107$	−13.4161	+	13.4161i	−1.29698	+	1.29698i	−0.930378	+	0.366601i	$0.880521\pi$
$108$	2.91018	+	2.91018i	0.280032	+	0.280032i
$109$	4.78437	−	4.78437i	0.458259	−	0.458259i	−0.439824	−	0.898084i	$-0.644959\pi$
$109$	4.78437	−	4.78437i	0.458259	−	0.458259i	0.898084	+	0.439824i	$0.144959\pi$
$110$	0.561465	+	9.80954i	0.0535336	+	0.935303i
$111$	2.90607	+	3.58536i	0.275832	+	0.340307i
$112$	0.767774	−	0.767774i	0.0725479	−	0.0725479i
$113$	18.0037			1.69365			0.846825	−	0.531872i	$-0.178511\pi$
$113$	18.0037			1.69365			0.846825	+	0.531872i	$0.178511\pi$
$114$	−2.78725			−0.261050
$115$	2.68771	−	0.153835i	0.250630	−	0.0143452i
$116$	−1.25185	−	1.25185i	−0.116232	−	0.116232i
$117$	−16.3466			−1.51124
$118$	−7.61323	−	7.61323i	−0.700855	−	0.700855i
$119$	5.63827	−	5.63827i	0.516859	−	0.516859i
$120$	1.12915	−	1.26626i	0.103077	−	0.115593i
$121$	−8.30847			−0.755316
$122$	1.14451	+	1.14451i	0.103619	+	0.103619i
$123$	−2.18406	−	2.18406i	−0.196930	−	0.196930i
$124$	4.14855	−	4.14855i	0.372551	−	0.372551i
$125$	1.90829	+	11.0163i	0.170683	+	0.985326i
$126$	−1.86133	+	1.86133i	−0.165821	+	0.165821i
$127$	9.21023	−	9.21023i	0.817275	−	0.817275i	−0.168437	−	0.985712i	$-0.553872\pi$
$127$	9.21023	−	9.21023i	0.817275	−	0.817275i	0.985712	+	0.168437i	$0.0538720\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.59302	+	4.59302i	0.404393	+	0.404393i
$130$	0.861559	+	15.0526i	0.0755637	+	1.32020i
$131$	−1.53844	+	1.53844i	−0.134414	+	0.134414i	−0.771113	−	0.636698i	$-0.780300\pi$
$131$	−1.53844	+	1.53844i	−0.134414	+	0.134414i	0.636698	+	0.771113i	$0.280300\pi$
$132$	2.35748	+	2.35748i	0.205192	+	0.205192i
$133$		−	3.98874i		−	0.345868i
$134$	6.25304	−	6.25304i	0.540180	−	0.540180i
$135$	−6.12488	+	6.86858i	−0.527145	+	0.591153i
$136$		−	7.34365i		−	0.629713i
$137$	11.9150	−	11.9150i	1.01797	−	1.01797i	0.0181339	−	0.999836i	$-0.494227\pi$
$137$	11.9150	−	11.9150i	1.01797	−	1.01797i	0.999836	−	0.0181339i	$-0.00577252\pi$
$138$	0.645925	−	0.645925i	0.0549847	−	0.0549847i
$139$	−6.75745			−0.573159			−0.286580	−	0.958056i	$-0.592518\pi$
$139$	−6.75745			−0.573159			−0.286580	+	0.958056i	$0.592518\pi$
$140$	1.81209	+	1.61589i	0.153150	+	0.136567i
$141$			8.24684i			0.694509i
$142$		−	5.46460i		−	0.458579i
$143$	−29.6285			−2.47766
$144$			2.42432i			0.202027i
$145$	2.63470	−	2.95461i	0.218800	−	0.245367i
$146$	1.88159	+	1.88159i	0.155722	+	0.155722i
$147$	−3.12302	−	3.12302i	−0.257583	−	0.257583i
$148$	−0.633071	+	6.04973i	−0.0520381	+	0.497285i
$149$		−	5.18543i		−	0.424807i	−0.977182	−	0.212404i	$-0.931871\pi$
$149$		−	5.18543i		−	0.424807i	0.977182	−	0.212404i	$-0.0681291\pi$
$150$	2.97108	+	2.35893i	0.242588	+	0.192606i
$151$		−	12.5372i		−	1.02026i	−0.860097	−	0.510131i	$-0.829597\pi$
$151$		−	12.5372i		−	1.02026i	0.860097	−	0.510131i	$-0.170403\pi$
$152$	−2.59760	−	2.59760i	−0.210693	−	0.210693i
$153$			17.8034i			1.43932i
$154$	−3.37371	+	3.37371i	−0.271861	+	0.271861i
$155$	9.79136	+	8.73119i	0.786461	+	0.701306i
$156$	3.61752	+	3.61752i	0.289633	+	0.289633i
$157$	−0.530292	+	0.530292i	−0.0423219	+	0.0423219i	−0.727951	−	0.685629i	$-0.759527\pi$
$157$	−0.530292	+	0.530292i	−0.0423219	+	0.0423219i	0.685629	+	0.727951i	$0.259527\pi$
$158$	5.13322	+	5.13322i	0.408377	+	0.408377i
$159$	−2.48921			−0.197407
$160$	2.23241	−	0.127776i	0.176488	−	0.0101016i
$161$	0.924360	+	0.924360i	0.0728498	+	0.0728498i
$162$		−	4.15032i		−	0.326080i
$163$	−13.0393			−1.02132			−0.510660	−	0.859783i	$-0.670599\pi$
$163$	−13.0393			−1.02132			−0.510660	+	0.859783i	$0.670599\pi$
$164$		−	4.07091i		−	0.317884i
$165$	−4.96164	+	5.56410i	−0.386264	+	0.433165i
$166$	−0.570350	+	0.570350i	−0.0442678	+	0.0442678i
$167$	24.6405			1.90674			0.953370	−	0.301805i	$-0.0975892\pi$
$167$	24.6405			1.90674			0.953370	+	0.301805i	$0.0975892\pi$
$168$	0.823831			0.0635599
$169$	−32.4645			−2.49727
$170$	16.3941	−	0.938340i	1.25737	−	0.0719674i
$171$	6.29742	+	6.29742i	0.481576	+	0.481576i
$172$			8.56098i			0.652769i
$173$	5.32250	−	5.32250i	0.404662	−	0.404662i	−0.475210	−	0.879872i	$-0.657628\pi$
$173$	5.32250	−	5.32250i	0.404662	−	0.404662i	0.879872	+	0.475210i	$0.157628\pi$
$174$		−	1.34325i		−	0.101832i
$175$	−3.37579	+	4.25182i	−0.255186	+	0.321407i
$176$			4.39414i			0.331221i
$177$		−	8.16908i		−	0.614026i
$178$	−7.54653	+	7.54653i	−0.565637	+	0.565637i
$179$	7.93007	+	7.93007i	0.592721	+	0.592721i	0.938366	−	0.345644i	$-0.112340\pi$
$179$	7.93007	+	7.93007i	0.592721	+	0.592721i	−0.345644	+	0.938366i	$0.612340\pi$
$180$	−5.41209	+	0.309770i	−0.403394	+	0.0230889i
$181$	−4.29385			−0.319160			−0.159580	−	0.987185i	$-0.551014\pi$
$181$	−4.29385			−0.319160			−0.159580	+	0.987185i	$0.551014\pi$
$182$	−5.17690	+	5.17690i	−0.383738	+	0.383738i
$183$			1.22807i			0.0907813i
$184$	1.20395			0.0887562
$185$	−13.5864	−	0.640267i	−0.998891	−	0.0470734i
$186$	4.45144			0.326395
$187$			32.2690i			2.35974i
$188$	−7.68569	+	7.68569i	−0.560537	+	0.560537i
$189$	−4.46872			−0.325052
$190$	5.46701	−	6.13083i	0.396618	−	0.444777i
$191$	2.08620	+	2.08620i	0.150952	+	0.150952i	0.778543	−	0.627591i	$-0.215959\pi$
$191$	2.08620	+	2.08620i	0.150952	+	0.150952i	−0.627591	+	0.778543i	$0.715959\pi$
$192$	0.536506	−	0.536506i	0.0387190	−	0.0387190i
$193$		−	13.6280i		−	0.980961i	−0.871452	−	0.490481i	$-0.836821\pi$
$193$		−	13.6280i		−	0.980961i	0.871452	−	0.490481i	$-0.163179\pi$
$194$		−	5.39443i		−	0.387298i
$195$	−7.61357	+	8.53803i	−0.545219	+	0.611421i
$196$		−	5.82104i		−	0.415789i
$197$	5.05224	−	5.05224i	0.359957	−	0.359957i	−0.503840	−	0.863797i	$-0.668080\pi$
$197$	5.05224	−	5.05224i	0.359957	−	0.359957i	0.863797	+	0.503840i	$0.168080\pi$
$198$		−	10.6528i		−	0.757063i
$199$	−12.1515	−	12.1515i	−0.861395	−	0.861395i	0.130105	−	0.991500i	$-0.458469\pi$
$199$	−12.1515	−	12.1515i	−0.861395	−	0.861395i	−0.991500	+	0.130105i	$0.958469\pi$
$200$	0.570497	+	4.96735i	0.0403402	+	0.351244i
$201$	6.70958			0.473257
$202$	14.5684			1.02503
$203$	1.92228			0.134918
$204$	3.93991	−	3.93991i	0.275849	−	0.275849i
$205$	9.08795	−	0.520163i	0.634730	−	0.0363298i
$206$		−	10.1623i		−	0.708043i
$207$	−2.91876			−0.202868
$208$			6.74274i			0.467525i
$209$	11.4142	+	11.4142i	0.789538	+	0.789538i
$210$	0.105266	+	1.83913i	0.00726402	+	0.126912i
$211$	8.27973			0.570000			0.285000	−	0.958527i	$-0.408006\pi$
$211$	8.27973			0.570000			0.285000	+	0.958527i	$0.408006\pi$
$212$	−2.31983	−	2.31983i	−0.159327	−	0.159327i
$213$	2.93179	−	2.93179i	0.200883	−	0.200883i
$214$	−13.4161	−	13.4161i	−0.917103	−	0.917103i
$215$	−19.1117	+	1.09389i	−1.30340	+	0.0746024i
$216$	−2.91018	+	2.91018i	−0.198013	+	0.198013i
$217$			6.37030i			0.432444i
$218$	4.78437	+	4.78437i	0.324038	+	0.324038i
$219$			2.01897i			0.136429i
$220$	−9.80954	+	0.561465i	−0.661359	+	0.0378539i
$221$			49.5163i			3.33083i
$222$	−3.58536	+	2.90607i	−0.240634	+	0.195042i
$223$	9.35468	+	9.35468i	0.626436	+	0.626436i	0.947169	−	0.320733i	$-0.103929\pi$
$223$	9.35468	+	9.35468i	0.626436	+	0.626436i	−0.320733	+	0.947169i	$0.603929\pi$
$224$	0.767774	+	0.767774i	0.0512991	+	0.0512991i
$225$	−1.38307	−	12.0425i	−0.0922046	−	0.802830i
$226$			18.0037i			1.19759i
$227$	−20.1807			−1.33944			−0.669721	−	0.742613i	$-0.733586\pi$
$227$	−20.1807			−1.33944			−0.669721	+	0.742613i	$0.733586\pi$
$228$		−	2.78725i		−	0.184590i
$229$			3.02631i			0.199984i	0.994988	+	0.0999920i	$0.0318817\pi$
$229$			3.02631i			0.199984i	−0.994988	+	0.0999920i	$0.968118\pi$
$230$	0.153835	+	2.68771i	0.0101436	+	0.177222i
$231$	−3.62003			−0.238180
$232$	1.25185	−	1.25185i	0.0821882	−	0.0821882i
$233$	4.33931	−	4.33931i	0.284278	−	0.284278i	−0.550534	−	0.834812i	$-0.685576\pi$
$233$	4.33931	−	4.33931i	0.284278	−	0.284278i	0.834812	+	0.550534i	$0.185576\pi$
$234$		−	16.3466i		−	1.06861i
$235$	−18.1397	−	16.1756i	−1.18330	−	1.05518i
$236$	7.61323	−	7.61323i	0.495579	−	0.495579i
$237$			5.50801i			0.357783i
$238$	5.63827	+	5.63827i	0.365474	+	0.365474i
$239$	−2.92398	+	2.92398i	−0.189137	+	0.189137i	−0.795323	−	0.606186i	$-0.792699\pi$
$239$	−2.92398	+	2.92398i	−0.189137	+	0.189137i	0.606186	+	0.795323i	$0.292699\pi$
$240$	1.26626	+	1.12915i	0.0817364	+	0.0728863i
$241$	−14.9825	−	14.9825i	−0.965105	−	0.965105i	0.0343063	−	0.999411i	$-0.489078\pi$
$241$	−14.9825	−	14.9825i	−0.965105	−	0.965105i	−0.999411	+	0.0343063i	$0.989078\pi$
$242$		−	8.30847i		−	0.534089i
$243$	10.9572	−	10.9572i	0.702905	−	0.702905i
$244$	−1.14451	+	1.14451i	−0.0732694	+	0.0732694i
$245$	12.9950	−	0.743789i	0.830219	−	0.0475189i
$246$	2.18406	−	2.18406i	0.139251	−	0.139251i
$247$	17.5149	+	17.5149i	1.11445	+	1.11445i
$248$	4.14855	+	4.14855i	0.263433	+	0.263433i
$249$	−0.611992			−0.0387834
$250$	−11.0163	+	1.90829i	−0.696731	+	0.120691i
$251$	9.25271	−	9.25271i	0.584026	−	0.584026i	−0.351981	−	0.936007i	$-0.614492\pi$
$251$	9.25271	−	9.25271i	0.584026	−	0.584026i	0.936007	+	0.351981i	$0.114492\pi$
$252$	−1.86133	−	1.86133i	−0.117253	−	0.117253i
$253$	−5.29031			−0.332599
$254$	9.21023	+	9.21023i	0.577901	+	0.577901i
$255$	9.29893	+	8.29208i	0.582322	+	0.519270i
$256$	1.00000			0.0625000
$257$	−11.5476			−0.720317			−0.360158	−	0.932891i	$-0.617277\pi$
$257$	−11.5476			−0.720317			−0.360158	+	0.932891i	$0.617277\pi$
$258$	−4.59302	+	4.59302i	−0.285949	+	0.285949i
$259$	−4.15877	−	5.13088i	−0.258414	−	0.318818i
$260$	−15.0526	+	0.861559i	−0.933522	+	0.0534316i
$261$	−3.03490	+	3.03490i	−0.187855	+	0.187855i
$262$	−1.53844	−	1.53844i	−0.0950454	−	0.0950454i
$263$	6.36639	−	6.36639i	0.392569	−	0.392569i	−0.483033	−	0.875602i	$-0.660465\pi$
$263$	6.36639	−	6.36639i	0.392569	−	0.392569i	0.875602	+	0.483033i	$0.160465\pi$
$264$	−2.35748	+	2.35748i	−0.145093	+	0.145093i
$265$	4.88241	−	5.47524i	0.299924	−	0.336342i
$266$	3.98874			0.244565
$267$	−8.09751			−0.495560
$268$	6.25304	+	6.25304i	0.381965	+	0.381965i
$269$			3.72238i			0.226958i	0.993540	+	0.113479i	$0.0361994\pi$
$269$			3.72238i			0.226958i	−0.993540	+	0.113479i	$0.963801\pi$
$270$	−6.86858	−	6.12488i	−0.418008	−	0.372748i
$271$	23.2312			1.41120			0.705598	−	0.708612i	$-0.250678\pi$
$271$	23.2312			1.41120			0.705598	+	0.708612i	$0.250678\pi$
$272$	7.34365			0.445274
$273$	−5.55488			−0.336196
$274$	11.9150	+	11.9150i	0.719813	+	0.719813i
$275$	−2.50684	−	21.8272i	−0.151168	−	1.31623i
$276$	0.645925	+	0.645925i	0.0388801	+	0.0388801i
$277$			12.8392i			0.771434i	0.922617	+	0.385717i	$0.126046\pi$
$277$			12.8392i			0.771434i	−0.922617	+	0.385717i	$0.873954\pi$
$278$		−	6.75745i		−	0.405285i
$279$	−10.0574	−	10.0574i	−0.602122	−	0.602122i
$280$	−1.61589	+	1.81209i	−0.0965678	+	0.108293i
$281$	15.2770	+	15.2770i	0.911350	+	0.911350i	0.996378	−	0.0850287i	$-0.0270982\pi$
$281$	15.2770	+	15.2770i	0.911350	+	0.911350i	−0.0850287	+	0.996378i	$0.527098\pi$
$282$	−8.24684			−0.491092
$283$	−20.7901			−1.23584			−0.617920	−	0.786241i	$-0.712025\pi$
$283$	−20.7901			−1.23584			−0.617920	+	0.786241i	$0.712025\pi$
$284$	5.46460			0.324265
$285$	6.22230	−	0.356143i	0.368577	−	0.0210961i
$286$		−	29.6285i		−	1.75197i
$287$	3.12554	+	3.12554i	0.184495	+	0.184495i
$288$	−2.42432			−0.142855
$289$	36.9292			2.17230
$290$	2.95461	+	2.63470i	0.173501	+	0.154715i
$291$	2.89414	−	2.89414i	0.169658	−	0.169658i
$292$	−1.88159	+	1.88159i	−0.110112	+	0.110112i
$293$	0.449201	+	0.449201i	0.0262426	+	0.0262426i	0.720106	−	0.693864i	$-0.244093\pi$
$293$	0.449201	+	0.449201i	0.0262426	+	0.0262426i	−0.693864	+	0.720106i	$0.744093\pi$
$294$	3.12302	−	3.12302i	0.182138	−	0.182138i
$295$	17.9687	+	16.0231i	1.04618	+	0.932901i
$296$	−6.04973	−	0.633071i	−0.351633	−	0.0367965i
$297$	12.7877	−	12.7877i	0.742020	−	0.742020i
$298$	5.18543			0.300384
$299$	−8.11790			−0.469471
$300$	−2.35893	+	2.97108i	−0.136193	+	0.171536i
$301$	−6.57291	−	6.57291i	−0.378856	−	0.378856i
$302$	12.5372			0.721434
$303$	7.81601	+	7.81601i	0.449018	+	0.449018i
$304$	2.59760	−	2.59760i	0.148982	−	0.148982i
$305$	−2.70125	−	2.40877i	−0.154673	−	0.137926i
$306$	−17.8034			−1.01775
$307$	0.0144735	+	0.0144735i	0.000826048	+	0.000826048i	0.707520	−	0.706694i	$-0.249814\pi$
$307$	0.0144735	+	0.0144735i	0.000826048	+	0.000826048i	−0.706694	+	0.707520i	$0.749814\pi$
$308$	−3.37371	−	3.37371i	−0.192235	−	0.192235i
$309$	5.45215	−	5.45215i	0.310162	−	0.310162i
$310$	−8.73119	+	9.79136i	−0.495899	+	0.556112i
$311$	22.9260	−	22.9260i	1.30001	−	1.30001i	0.371635	−	0.928379i	$-0.378797\pi$
$311$	22.9260	−	22.9260i	1.30001	−	1.30001i	0.928379	−	0.371635i	$-0.121203\pi$
$312$	−3.61752	+	3.61752i	−0.204802	+	0.204802i
$313$			14.6520i			0.828177i	0.910237	+	0.414089i	$0.135900\pi$
$313$			14.6520i			0.828177i	−0.910237	+	0.414089i	$0.864100\pi$
$314$	−0.530292	−	0.530292i	−0.0299261	−	0.0299261i
$315$	3.91743	−	4.39310i	0.220722	−	0.247523i
$316$	−5.13322	+	5.13322i	−0.288766	+	0.288766i
$317$	−14.2710	−	14.2710i	−0.801537	−	0.801537i	0.181799	−	0.983336i	$-0.441808\pi$
$317$	−14.2710	−	14.2710i	−0.801537	−	0.801537i	−0.983336	+	0.181799i	$0.941808\pi$
$318$		−	2.48921i		−	0.139588i
$319$	−5.50082	+	5.50082i	−0.307987	+	0.307987i
$320$	0.127776	+	2.23241i	0.00714288	+	0.124796i
$321$		−	14.3956i		−	0.803483i
$322$	−0.924360	+	0.924360i	−0.0515126	+	0.0515126i
$323$	19.0758	−	19.0758i	1.06141	−	1.06141i
$324$	4.15032			0.230573
$325$	−3.84671	−	33.4935i	−0.213377	−	1.85789i
$326$		−	13.0393i		−	0.722183i
$327$			5.13368i			0.283893i
$328$	4.07091			0.224778
$329$		−	11.8018i		−	0.650652i
$330$	−5.56410	−	4.96164i	−0.306294	−	0.273130i
$331$	−19.0443	−	19.0443i	−1.04677	−	1.04677i	−0.998851	−	0.0479194i	$-0.984741\pi$
$331$	−19.0443	−	19.0443i	−1.04677	−	1.04677i	−0.0479194	−	0.998851i	$-0.515259\pi$
$332$	−0.570350	−	0.570350i	−0.0313020	−	0.0313020i
$333$	14.6665	+	1.53477i	0.803719	+	0.0841048i
$334$			24.6405i			1.34827i
$335$	−13.1604	+	14.7584i	−0.719029	+	0.806336i
$336$			0.823831i			0.0449436i
$337$	11.2643	+	11.2643i	0.613604	+	0.613604i	0.943883	−	0.330279i	$-0.107143\pi$
$337$	11.2643	+	11.2643i	0.613604	+	0.613604i	−0.330279	+	0.943883i	$0.607143\pi$
$338$		−	32.4645i		−	1.76584i
$339$	−9.65911	+	9.65911i	−0.524611	+	0.524611i
$340$	0.938340	+	16.3941i	0.0508886	+	0.889093i
$341$	−18.2293	−	18.2293i	−0.987172	−	0.987172i
$342$	−6.29742	+	6.29742i	−0.340525	+	0.340525i
$343$	9.84367	+	9.84367i	0.531508	+	0.531508i
$344$	−8.56098			−0.461577
$345$	−1.35944	+	1.52450i	−0.0731897	+	0.0820766i
$346$	5.32250	+	5.32250i	0.286139	+	0.286139i
$347$			2.40110i			0.128898i	0.997921	+	0.0644489i	$0.0205290\pi$
$347$			2.40110i			0.128898i	−0.997921	+	0.0644489i	$0.979471\pi$
$348$	1.34325			0.0720059
$349$			13.3892i			0.716708i	0.933586	+	0.358354i	$0.116662\pi$
$349$			13.3892i			0.716708i	−0.933586	+	0.358354i	$0.883338\pi$
$350$	−4.25182	−	3.37579i	−0.227269	−	0.180444i
$351$	19.6226	−	19.6226i	1.04738	−	1.04738i
$352$	−4.39414			−0.234208
$353$	−7.34993			−0.391198			−0.195599	−	0.980684i	$-0.562665\pi$
$353$	−7.34993			−0.391198			−0.195599	+	0.980684i	$0.562665\pi$
$354$	8.16908			0.434182
$355$	0.698244	+	12.1993i	0.0370590	+	0.647470i
$356$	−7.54653	−	7.54653i	−0.399965	−	0.399965i
$357$			6.04992i			0.320196i
$358$	−7.93007	+	7.93007i	−0.419117	+	0.419117i
$359$		−	24.0685i		−	1.27029i	−0.772394	−	0.635143i	$-0.780941\pi$
$359$		−	24.0685i		−	1.27029i	0.772394	−	0.635143i	$-0.219059\pi$
$360$	−0.309770	−	5.41209i	−0.0163263	−	0.285242i
$361$			5.50496i			0.289735i
$362$		−	4.29385i		−	0.225680i
$363$	4.45754	−	4.45754i	0.233960	−	0.233960i
$364$	−5.17690	−	5.17690i	−0.271343	−	0.271343i
$365$	−4.44092	−	3.96007i	−0.232448	−	0.207280i
$366$	−1.22807			−0.0641921
$367$	−0.833192	+	0.833192i	−0.0434923	+	0.0434923i	−0.728518	−	0.685026i	$-0.759791\pi$
$367$	−0.833192	+	0.833192i	−0.0434923	+	0.0434923i	0.685026	+	0.728518i	$0.259791\pi$
$368$			1.20395i			0.0627601i
$369$	−9.86920			−0.513770
$370$	0.640267	−	13.5864i	0.0332859	−	0.706323i
$371$	3.56222			0.184941
$372$			4.45144i			0.230796i
$373$	−2.09090	+	2.09090i	−0.108262	+	0.108262i	−0.759163	−	0.650901i	$-0.774391\pi$
$373$	−2.09090	+	2.09090i	−0.108262	+	0.108262i	0.650901	+	0.759163i	$0.274391\pi$
$374$	−32.2690			−1.66859
$375$	−6.93410	−	4.88649i	−0.358076	−	0.252337i
$376$	−7.68569	−	7.68569i	−0.396359	−	0.396359i
$377$	−8.44092	+	8.44092i	−0.434729	+	0.434729i
$378$		−	4.46872i		−	0.229846i
$379$		−	4.36102i		−	0.224010i	−0.993708	−	0.112005i	$-0.964273\pi$
$379$		−	4.36102i		−	0.224010i	0.993708	−	0.112005i	$-0.0357273\pi$
$380$	6.13083	+	5.46701i	0.314505	+	0.280451i
$381$			9.88267i			0.506305i
$382$	−2.08620	+	2.08620i	−0.106739	+	0.106739i
$383$		−	16.6051i		−	0.848480i	−0.905550	−	0.424240i	$-0.860541\pi$
$383$		−	16.6051i		−	0.848480i	0.905550	−	0.424240i	$-0.139459\pi$
$384$	0.536506	+	0.536506i	0.0273784	+	0.0273784i
$385$	7.10044	−	7.96259i	0.361872	−	0.405811i
$386$	13.6280			0.693644
$387$	20.7546			1.05502
$388$	5.39443			0.273861
$389$	−12.9306	+	12.9306i	−0.655609	+	0.655609i	−0.954338	−	0.298729i	$-0.903437\pi$
$389$	−12.9306	+	12.9306i	−0.655609	+	0.655609i	0.298729	+	0.954338i	$0.403437\pi$
$390$	−8.53803	−	7.61357i	−0.432340	−	0.385528i
$391$			8.84137i			0.447127i
$392$	5.82104			0.294007
$393$		−	1.65077i		−	0.0832702i
$394$	5.05224	+	5.05224i	0.254528	+	0.254528i
$395$	−12.1154	−	10.8036i	−0.609591	−	0.543587i
$396$	10.6528			0.535324
$397$	1.98404	+	1.98404i	0.0995762	+	0.0995762i	0.755140	−	0.655564i	$-0.227569\pi$
$397$	1.98404	+	1.98404i	0.0995762	+	0.0995762i	−0.655564	+	0.755140i	$0.727569\pi$
$398$	12.1515	−	12.1515i	0.609098	−	0.609098i
$399$	2.13998	+	2.13998i	0.107133	+	0.107133i
$400$	−4.96735	+	0.570497i	−0.248367	+	0.0285248i
$401$	−14.2034	+	14.2034i	−0.709283	+	0.709283i	−0.966384	−	0.257101i	$-0.917233\pi$
$401$	−14.2034	+	14.2034i	−0.709283	+	0.709283i	0.257101	+	0.966384i	$0.417233\pi$
$402$			6.70958i			0.334644i
$403$	−27.9726	−	27.9726i	−1.39341	−	1.39341i
$404$			14.5684i			0.724803i
$405$	0.530310	+	9.26522i	0.0263513	+	0.460393i
$406$			1.92228i			0.0954012i
$407$	26.5834	+	2.78180i	1.31769	+	0.137889i
$408$	3.93991	+	3.93991i	0.195054	+	0.195054i
$409$	−13.7291	−	13.7291i	−0.678859	−	0.678859i	0.280883	−	0.959742i	$-0.409373\pi$
$409$	−13.7291	−	13.7291i	−0.678859	−	0.678859i	−0.959742	+	0.280883i	$0.909373\pi$
$410$	0.520163	+	9.08795i	0.0256890	+	0.448822i
$411$			12.7850i			0.630635i
$412$	10.1623			0.500662
$413$			11.6905i			0.575251i
$414$		−	2.91876i		−	0.143449i
$415$	1.20038	−	1.34614i	0.0589244	−	0.0660792i
$416$	−6.74274			−0.330590
$417$	3.62541	−	3.62541i	0.177537	−	0.177537i
$418$	−11.4142	+	11.4142i	−0.558287	+	0.558287i
$419$		−	10.6476i		−	0.520169i	−0.965586	−	0.260084i	$-0.916250\pi$
$419$		−	10.6476i		−	0.520169i	0.965586	−	0.260084i	$-0.0837504\pi$
$420$	−1.83913	+	0.105266i	−0.0897404	+	0.00513644i
$421$	21.3367	−	21.3367i	1.03989	−	1.03989i	0.0407156	−	0.999171i	$-0.487036\pi$
$421$	21.3367	−	21.3367i	1.03989	−	1.03989i	0.999171	−	0.0407156i	$-0.0129638\pi$
$422$			8.27973i			0.403051i
$423$	18.6326	+	18.6326i	0.905948	+	0.905948i
$424$	2.31983	−	2.31983i	0.112661	−	0.112661i
$425$	−36.4784	+	4.18953i	−1.76946	+	0.203222i
$426$	2.93179	+	2.93179i	0.142046	+	0.142046i
$427$		−	1.75744i		−	0.0850487i
$428$	13.4161	−	13.4161i	0.648490	−	0.648490i
$429$	15.8959	−	15.8959i	0.767460	−	0.767460i
$430$	−1.09389	−	19.1117i	−0.0527519	−	0.921646i
$431$	−5.16220	+	5.16220i	−0.248655	+	0.248655i	−0.820418	−	0.571764i	$-0.806259\pi$
$431$	−5.16220	+	5.16220i	−0.248655	+	0.248655i	0.571764	+	0.820418i	$0.306259\pi$
$432$	−2.91018	−	2.91018i	−0.140016	−	0.140016i
$433$	2.75289	+	2.75289i	0.132296	+	0.132296i	0.770154	−	0.637858i	$-0.220179\pi$
$433$	2.75289	+	2.75289i	0.132296	+	0.132296i	−0.637858	+	0.770154i	$0.720179\pi$
$434$	−6.37030			−0.305784
$435$	0.171635	+	2.99870i	0.00822927	+	0.143776i
$436$	−4.78437	+	4.78437i	−0.229130	+	0.229130i
$437$	3.12737	+	3.12737i	0.149602	+	0.149602i
$438$	−2.01897			−0.0964701
$439$	28.9545	+	28.9545i	1.38192	+	1.38192i	0.841200	+	0.540725i	$0.181850\pi$
$439$	28.9545	+	28.9545i	1.38192	+	1.38192i	0.540725	+	0.841200i	$0.318150\pi$
$440$	−0.561465	−	9.80954i	−0.0267668	−	0.467652i
$441$	−14.1121			−0.672005
$442$	−49.5163			−2.35525
$443$	19.2383	−	19.2383i	0.914040	−	0.914040i	−0.0825469	−	0.996587i	$-0.526305\pi$
$443$	19.2383	−	19.2383i	0.914040	−	0.914040i	0.996587	+	0.0825469i	$0.0263054\pi$
$444$	−2.90607	−	3.58536i	−0.137916	−	0.170154i
$445$	15.8827	−	17.8113i	0.752913	−	0.844334i
$446$	−9.35468	+	9.35468i	−0.442957	+	0.442957i
$447$	2.78201	+	2.78201i	0.131585	+	0.131585i
$448$	−0.767774	+	0.767774i	−0.0362739	+	0.0362739i
$449$	−21.0464	+	21.0464i	−0.993243	+	0.993243i	−0.999977	−	0.00673470i	$-0.997856\pi$
$449$	−21.0464	+	21.0464i	−0.993243	+	0.993243i	0.00673470	+	0.999977i	$0.497856\pi$
$450$	12.0425	−	1.38307i	0.567687	−	0.0651985i
$451$	−17.8881			−0.842320
$452$	−18.0037			−0.846825
$453$	6.72627	+	6.72627i	0.316028	+	0.316028i
$454$		−	20.1807i		−	0.947129i
$455$	10.8955	−	12.2185i	0.510789	−	0.572811i
$456$	2.78725			0.130525
$457$	21.7070			1.01541			0.507705	−	0.861531i	$-0.330494\pi$
$457$	21.7070			1.01541			0.507705	+	0.861531i	$0.330494\pi$
$458$	−3.02631			−0.141410
$459$	−21.3713	−	21.3713i	−0.997528	−	0.997528i
$460$	−2.68771	+	0.153835i	−0.125315	+	0.00717261i
$461$	1.31376	+	1.31376i	0.0611879	+	0.0611879i	0.737039	−	0.675851i	$-0.236224\pi$
$461$	1.31376	+	1.31376i	0.0611879	+	0.0611879i	−0.675851	+	0.737039i	$0.736224\pi$
$462$		−	3.62003i		−	0.168419i
$463$		−	8.05167i		−	0.374193i	−0.982342	−	0.187096i	$-0.940092\pi$
$463$		−	8.05167i		−	0.374193i	0.982342	−	0.187096i	$-0.0599077\pi$
$464$	1.25185	+	1.25185i	0.0581158	+	0.0581158i
$465$	−9.93746	+	0.568786i	−0.460838	+	0.0263768i
$466$	4.33931	+	4.33931i	0.201015	+	0.201015i
$467$	−5.04806			−0.233596			−0.116798	−	0.993156i	$-0.537263\pi$
$467$	−5.04806			−0.233596			−0.116798	+	0.993156i	$0.537263\pi$
$468$	16.3466			0.755621
$469$	−9.60185			−0.443372
$470$	16.1756	−	18.1397i	0.746125	−	0.836722i
$471$		−	0.569009i		−	0.0262186i
$472$	7.61323	+	7.61323i	0.350427	+	0.350427i
$473$	37.6182			1.72969
$474$	−5.50801			−0.252991
$475$	−11.4213	+	14.3851i	−0.524043	+	0.660033i
$476$	−5.63827	+	5.63827i	−0.258429	+	0.258429i
$477$	−5.62402	+	5.62402i	−0.257506	+	0.257506i
$478$	−2.92398	−	2.92398i	−0.133740	−	0.133740i
$479$	−4.20701	+	4.20701i	−0.192223	+	0.192223i	−0.796656	−	0.604433i	$-0.793400\pi$
$479$	−4.20701	+	4.20701i	−0.192223	+	0.192223i	0.604433	+	0.796656i	$0.293400\pi$
$480$	−1.12915	+	1.26626i	−0.0515384	+	0.0577964i
$481$	40.7917	+	4.26863i	1.85994	+	0.194633i
$482$	14.9825	−	14.9825i	0.682432	−	0.682432i
$483$	−0.991849			−0.0451307
$484$	8.30847			0.377658
$485$	0.689278	+	12.0426i	0.0312985	+	0.546826i
$486$	10.9572	+	10.9572i	0.497029	+	0.497029i
$487$	−23.0440			−1.04422			−0.522111	−	0.852877i	$-0.674855\pi$
$487$	−23.0440			−1.04422			−0.522111	+	0.852877i	$0.674855\pi$
$488$	−1.14451	−	1.14451i	−0.0518093	−	0.0518093i
$489$	6.99568	−	6.99568i	0.316356	−	0.316356i
$490$	0.743789	+	12.9950i	0.0336009	+	0.587053i
$491$	17.5204			0.790684			0.395342	−	0.918534i	$-0.370626\pi$
$491$	17.5204			0.790684			0.395342	+	0.918534i	$0.370626\pi$
$492$	2.18406	+	2.18406i	0.0984652	+	0.0984652i
$493$	9.19317	+	9.19317i	0.414039	+	0.414039i
$494$	−17.5149	+	17.5149i	−0.788034	+	0.788034i
$495$	1.36117	+	23.7815i	0.0611801	+	1.06890i
$496$	−4.14855	+	4.14855i	−0.186275	+	0.186275i
$497$	−4.19558	+	4.19558i	−0.188198	+	0.188198i
$498$		−	0.611992i		−	0.0274240i
$499$	3.14878	+	3.14878i	0.140959	+	0.140959i	0.774065	−	0.633106i	$-0.218220\pi$
$499$	3.14878	+	3.14878i	0.140959	+	0.140959i	−0.633106	+	0.774065i	$0.718220\pi$
$500$	−1.90829	−	11.0163i	−0.0853414	−	0.492663i
$501$	−13.2198	+	13.2198i	−0.590616	+	0.590616i
$502$	9.25271	+	9.25271i	0.412969	+	0.412969i
$503$			38.5464i			1.71870i	0.511390	+	0.859349i	$0.329131\pi$
$503$			38.5464i			1.71870i	−0.511390	+	0.859349i	$0.670869\pi$
$504$	1.86133	−	1.86133i	0.0829104	−	0.0829104i
$505$	−32.5226	+	1.86148i	−1.44724	+	0.0828350i
$506$		−	5.29031i		−	0.235183i
$507$	17.4174	−	17.4174i	0.773534	−	0.773534i
$508$	−9.21023	+	9.21023i	−0.408638	+	0.408638i
$509$	−18.2209			−0.807627			−0.403814	−	0.914841i	$-0.632316\pi$
$509$	−18.2209			−0.807627			−0.403814	+	0.914841i	$0.632316\pi$
$510$	−8.29208	+	9.29893i	−0.367180	+	0.411764i
$511$		−	2.88928i		−	0.127814i
$512$			1.00000i			0.0441942i
$513$	−15.1190			−0.667518
$514$		−	11.5476i		−	0.509341i
$515$	1.29850	+	22.6865i	0.0572188	+	0.999688i
$516$	−4.59302	−	4.59302i	−0.202196	−	0.202196i
$517$	33.7720	+	33.7720i	1.48529	+	1.48529i
$518$	5.13088	−	4.15877i	0.225438	−	0.182726i
$519$			5.71110i			0.250689i
$520$	−0.861559	−	15.0526i	−0.0377819	−	0.660100i
$521$		−	8.10778i		−	0.355208i	−0.984102	−	0.177604i	$-0.943165\pi$
$521$		−	8.10778i		−	0.355208i	0.984102	−	0.177604i	$-0.0568347\pi$
$522$	−3.03490	−	3.03490i	−0.132834	−	0.132834i
$523$			9.18819i			0.401772i	0.979615	+	0.200886i	$0.0643820\pi$
$523$			9.18819i			0.401772i	−0.979615	+	0.200886i	$0.935618\pi$
$524$	1.53844	−	1.53844i	0.0672072	−	0.0672072i
$525$	−0.469993	−	4.09225i	−0.0205122	−	0.178601i
$526$	6.36639	+	6.36639i	0.277588	+	0.277588i
$527$	−30.4655	+	30.4655i	−1.32710	+	1.32710i
$528$	−2.35748	−	2.35748i	−0.102596	−	0.102596i
$529$	21.5505			0.936979
$530$	5.47524	+	4.88241i	0.237829	+	0.212078i
$531$	−18.4569	−	18.4569i	−0.800963	−	0.800963i
$532$			3.98874i			0.172934i
$533$	−27.4491			−1.18895
$534$		−	8.09751i		−	0.350414i
$535$	31.6644	+	28.2360i	1.36897	+	1.22075i
$536$	−6.25304	+	6.25304i	−0.270090	+	0.270090i
$537$	−8.50905			−0.367193
$538$	−3.72238			−0.160483
$539$	−25.5785			−1.10174
$540$	6.12488	−	6.86858i	0.263573	−	0.295577i
$541$	−14.3951	−	14.3951i	−0.618893	−	0.618893i	0.326355	−	0.945247i	$-0.394180\pi$
$541$	−14.3951	−	14.3951i	−0.618893	−	0.618893i	−0.945247	+	0.326355i	$0.894180\pi$
$542$			23.2312i			0.997867i
$543$	2.30368	−	2.30368i	0.0988602	−	0.0988602i
$544$			7.34365i			0.314856i
$545$	−11.2920	−	10.0694i	−0.483697	−	0.431324i
$546$		−	5.55488i		−	0.237727i
$547$		−	3.07074i		−	0.131295i	−0.997843	−	0.0656477i	$-0.979089\pi$
$547$		−	3.07074i		−	0.131295i	0.997843	−	0.0656477i	$-0.0209114\pi$
$548$	−11.9150	+	11.9150i	−0.508985	+	0.508985i
$549$	2.77465	+	2.77465i	0.118419	+	0.118419i
$550$	21.8272	−	2.50684i	0.930716	−	0.106892i
$551$	6.50362			0.277064
$552$	−0.645925	+	0.645925i	−0.0274924	+	0.0274924i
$553$		−	7.88232i		−	0.335190i
$554$	−12.8392			−0.545486
$555$	7.63268	−	6.94567i	0.323989	−	0.294827i
$556$	6.75745			0.286580
$557$		−	33.2382i		−	1.40835i	−0.710028	−	0.704173i	$-0.751318\pi$
$557$		−	33.2382i		−	1.40835i	0.710028	−	0.704173i	$-0.248682\pi$
$558$	10.0574	−	10.0574i	0.425765	−	0.425765i
$559$	57.7245			2.44149
$560$	−1.81209	−	1.61589i	−0.0765749	−	0.0682837i
$561$	−17.3125	−	17.3125i	−0.730935	−	0.730935i
$562$	−15.2770	+	15.2770i	−0.644422	+	0.644422i
$563$			34.1847i			1.44071i	0.693605	+	0.720356i	$0.256021\pi$
$563$			34.1847i			1.44071i	−0.693605	+	0.720356i	$0.743979\pi$
$564$		−	8.24684i		−	0.347254i
$565$	−2.30044	−	40.1918i	−0.0967803	−	1.69088i
$566$		−	20.7901i		−	0.873871i
$567$	−3.18651	+	3.18651i	−0.133821	+	0.133821i
$568$			5.46460i			0.229290i
$569$	29.8527	+	29.8527i	1.25149	+	1.25149i	0.955052	+	0.296438i	$0.0957989\pi$
$569$	29.8527	+	29.8527i	1.25149	+	1.25149i	0.296438	+	0.955052i	$0.404201\pi$
$570$	0.356143	+	6.22230i	0.0149172	+	0.260624i
$571$	−18.1250			−0.758508			−0.379254	−	0.925293i	$-0.623819\pi$
$571$	−18.1250			−0.758508			−0.379254	+	0.925293i	$0.623819\pi$
$572$	29.6285			1.23883
$573$	−2.23851			−0.0935152
$574$	−3.12554	+	3.12554i	−0.130457	+	0.130457i
$575$	−0.686848	−	5.98042i	−0.0286436	−	0.249401i
$576$		−	2.42432i		−	0.101013i
$577$	−14.6571			−0.610182			−0.305091	−	0.952323i	$-0.598687\pi$
$577$	−14.6571			−0.610182			−0.305091	+	0.952323i	$0.598687\pi$
$578$			36.9292i			1.53605i
$579$	7.31147	+	7.31147i	0.303854	+	0.303854i
$580$	−2.63470	+	2.95461i	−0.109400	+	0.122684i
$581$	0.875801			0.0363343
$582$	2.89414	+	2.89414i	0.119966	+	0.119966i
$583$	−10.1937	+	10.1937i	−0.422179	+	0.422179i
$584$	−1.88159	−	1.88159i	−0.0778609	−	0.0778609i
$585$	2.08870	+	36.4923i	0.0863570	+	1.50877i
$586$	−0.449201	+	0.449201i	−0.0185563	+	0.0185563i
$587$		−	2.78069i		−	0.114772i	−0.998352	−	0.0573858i	$-0.981724\pi$
$587$		−	2.78069i		−	0.114772i	0.998352	−	0.0573858i	$-0.0182765\pi$
$588$	3.12302	+	3.12302i	0.128791	+	0.128791i
$589$			21.5525i			0.888056i
$590$	−16.0231	+	17.9687i	−0.659660	+	0.739758i
$591$			5.42111i			0.222995i
$592$	0.633071	−	6.04973i	0.0260190	−	0.248642i
$593$	4.64974	+	4.64974i	0.190942	+	0.190942i	0.796103	−	0.605161i	$-0.206891\pi$
$593$	4.64974	+	4.64974i	0.190942	+	0.190942i	−0.605161	+	0.796103i	$0.706891\pi$
$594$	12.7877	+	12.7877i	0.524687	+	0.524687i
$595$	−13.3074	−	11.8665i	−0.545549	−	0.486479i
$596$			5.18543i			0.212404i
$597$	13.0387			0.533637
$598$		−	8.11790i		−	0.331966i
$599$		−	8.57057i		−	0.350184i	−0.984552	−	0.175092i	$-0.943978\pi$
$599$		−	8.57057i		−	0.350184i	0.984552	−	0.175092i	$-0.0560223\pi$
$600$	−2.97108	−	2.35893i	−0.121294	−	0.0963031i
$601$	−4.61240			−0.188144			−0.0940719	−	0.995565i	$-0.529988\pi$
$601$	−4.61240			−0.188144			−0.0940719	+	0.995565i	$0.529988\pi$
$602$	6.57291	−	6.57291i	0.267892	−	0.267892i
$603$	15.1594	−	15.1594i	0.617338	−	0.617338i
$604$			12.5372i			0.510131i
$605$	1.06162	+	18.5480i	0.0431611	+	0.754081i
$606$	−7.81601	+	7.81601i	−0.317504	+	0.317504i
$607$		−	36.4725i		−	1.48037i	−0.672403	−	0.740186i	$-0.734738\pi$
$607$		−	36.4725i		−	1.48037i	0.672403	−	0.740186i	$-0.265262\pi$
$608$	2.59760	+	2.59760i	0.105347	+	0.105347i
$609$	−1.03131	+	1.03131i	−0.0417910	+	0.0417910i
$610$	2.40877	−	2.70125i	0.0975282	−	0.109370i
$611$	51.8226	+	51.8226i	2.09652	+	2.09652i
$612$		−	17.8034i		−	0.719659i
$613$	3.07671	−	3.07671i	0.124267	−	0.124267i	−0.642238	−	0.766505i	$-0.721994\pi$
$613$	3.07671	−	3.07671i	0.124267	−	0.124267i	0.766505	+	0.642238i	$0.221994\pi$
$614$	−0.0144735	+	0.0144735i	−0.000584104	+	0.000584104i
$615$	−4.59667	+	5.15481i	−0.185355	+	0.207862i
$616$	3.37371	−	3.37371i	0.135931	−	0.135931i
$617$	−6.95912	−	6.95912i	−0.280164	−	0.280164i	0.553011	−	0.833174i	$-0.313479\pi$
$617$	−6.95912	−	6.95912i	−0.280164	−	0.280164i	−0.833174	+	0.553011i	$0.813479\pi$
$618$	5.45215	+	5.45215i	0.219318	+	0.219318i
$619$	28.9801			1.16481			0.582405	−	0.812899i	$-0.302112\pi$
$619$	28.9801			1.16481			0.582405	+	0.812899i	$0.302112\pi$
$620$	−9.79136	−	8.73119i	−0.393231	−	0.350653i
$621$	3.50370	−	3.50370i	0.140599	−	0.140599i
$622$	22.9260	+	22.9260i	0.919249	+	0.919249i
$623$	11.5881			0.464266
$624$	−3.61752	−	3.61752i	−0.144817	−	0.144817i
$625$	24.3491	−	5.66771i	0.973963	−	0.226708i
$626$	−14.6520			−0.585610
$627$	−12.2476			−0.489121
$628$	0.530292	−	0.530292i	0.0211610	−	0.0211610i
$629$	4.64905	−	44.4271i	0.185370	−	1.77142i
$630$	4.39310	+	3.91743i	0.175025	+	0.156074i
$631$	−8.58133	+	8.58133i	−0.341617	+	0.341617i	−0.856975	−	0.515358i	$-0.827659\pi$
$631$	−8.58133	+	8.58133i	−0.341617	+	0.341617i	0.515358	+	0.856975i	$0.327659\pi$
$632$	−5.13322	−	5.13322i	−0.204189	−	0.204189i
$633$	−4.44212	+	4.44212i	−0.176559	+	0.176559i
$634$	14.2710	−	14.2710i	0.566772	−	0.566772i
$635$	−21.7379	−	19.3842i	−0.862642	−	0.769238i
$636$	2.48921			0.0987034
$637$	−39.2498			−1.55513
$638$	−5.50082	−	5.50082i	−0.217779	−	0.217779i
$639$		−	13.2480i		−	0.524082i
$640$	−2.23241	+	0.127776i	−0.0882439	+	0.00505078i
$641$	−39.7584			−1.57036			−0.785181	−	0.619267i	$-0.787430\pi$
$641$	−39.7584			−1.57036			−0.785181	+	0.619267i	$0.787430\pi$
$642$	14.3956			0.568148
$643$	0.0494458			0.00194995			0.000974976	−	1.00000i	$-0.499690\pi$
$643$	0.0494458			0.00194995			0.000974976		1.00000i	$0.499690\pi$
$644$	−0.924360	−	0.924360i	−0.0364249	−	0.0364249i
$645$	9.66664	−	10.8404i	0.380623	−	0.426840i
$646$	19.0758	+	19.0758i	0.750529	+	0.750529i
$647$			20.0867i			0.789689i	0.918748	+	0.394844i	$0.129202\pi$
$647$			20.0867i			0.789689i	−0.918748	+	0.394844i	$0.870798\pi$
$648$			4.15032i			0.163040i
$649$	−33.4536	−	33.4536i	−1.31317	−	1.31317i
$650$	33.4935	−	3.84671i	1.31372	−	0.150880i
$651$	−3.41770	−	3.41770i	−0.133950	−	0.133950i
$652$	13.0393			0.510660
$653$	2.91044			0.113894			0.0569471	−	0.998377i	$-0.481863\pi$
$653$	2.91044			0.113894			0.0569471	+	0.998377i	$0.481863\pi$
$654$	−5.13368			−0.200743
$655$	3.63102	+	3.23787i	0.141876	+	0.126514i
$656$			4.07091i			0.158942i
$657$	4.56159	+	4.56159i	0.177965	+	0.177965i
$658$	11.8018			0.460080
$659$	18.9341			0.737568			0.368784	−	0.929515i	$-0.379774\pi$
$659$	18.9341			0.737568			0.368784	+	0.929515i	$0.379774\pi$
$660$	4.96164	−	5.56410i	0.193132	−	0.216582i
$661$	−14.8550	+	14.8550i	−0.577792	+	0.577792i	−0.934294	−	0.356502i	$-0.883969\pi$
$661$	−14.8550	+	14.8550i	−0.577792	+	0.577792i	0.356502	+	0.934294i	$0.383969\pi$
$662$	19.0443	−	19.0443i	0.740179	−	0.740179i
$663$	−26.5658	−	26.5658i	−1.03173	−	1.03173i
$664$	0.570350	−	0.570350i	0.0221339	−	0.0221339i
$665$	−8.90452	+	0.509664i	−0.345302	+	0.0197639i
$666$	−1.53477	+	14.6665i	−0.0594711	+	0.568315i
$667$	−1.50717	+	1.50717i	−0.0583577	+	0.0583577i
$668$	−24.6405			−0.953370
$669$	−10.0377			−0.388079
$670$	−14.7584	−	13.1604i	−0.570165	−	0.508430i
$671$	5.02912	+	5.02912i	0.194147	+	0.194147i
$672$	−0.823831			−0.0317800
$673$	−4.39502	−	4.39502i	−0.169416	−	0.169416i	0.617307	−	0.786722i	$-0.288224\pi$
$673$	−4.39502	−	4.39502i	−0.169416	−	0.169416i	−0.786722	+	0.617307i	$0.788224\pi$
$674$	−11.2643	+	11.2643i	−0.433884	+	0.433884i
$675$	16.1161	+	12.7956i	0.620310	+	0.492504i
$676$	32.4645			1.24864
$677$	−15.6334	−	15.6334i	−0.600841	−	0.600841i	0.339695	−	0.940536i	$-0.389676\pi$
$677$	−15.6334	−	15.6334i	−0.600841	−	0.600841i	−0.940536	+	0.339695i	$0.889676\pi$
$678$	−9.65911	−	9.65911i	−0.370956	−	0.370956i
$679$	−4.14171	+	4.14171i	−0.158944	+	0.158944i
$680$	−16.3941	+	0.938340i	−0.628684	+	0.0359837i
$681$	10.8271	−	10.8271i	0.414895	−	0.414895i
$682$	18.2293	−	18.2293i	0.698036	−	0.698036i
$683$		−	2.66101i		−	0.101821i	−0.998703	−	0.0509104i	$-0.983788\pi$
$683$		−	2.66101i		−	0.101821i	0.998703	−	0.0509104i	$-0.0162123\pi$
$684$	−6.29742	−	6.29742i	−0.240788	−	0.240788i
$685$	−28.1217	−	25.0768i	−1.07448	−	0.958136i
$686$	−9.84367	+	9.84367i	−0.375833	+	0.375833i
$687$	−1.62363	−	1.62363i	−0.0619454	−	0.0619454i
$688$		−	8.56098i		−	0.326384i
$689$	−15.6420	+	15.6420i	−0.595914	+	0.595914i
$690$	−1.52450	−	1.35944i	−0.0580369	−	0.0517529i
$691$		−	6.84103i		−	0.260245i	−0.991498	−	0.130123i	$-0.958463\pi$
$691$		−	6.84103i		−	0.260245i	0.991498	−	0.130123i	$-0.0415371\pi$
$692$	−5.32250	+	5.32250i	−0.202331	+	0.202331i
$693$	−8.17896	+	8.17896i	−0.310693	+	0.310693i
$694$	−2.40110			−0.0911445
$695$	0.863438	+	15.0854i	0.0327521	+	0.572223i
$696$			1.34325i			0.0509158i
$697$			29.8953i			1.13237i
$698$	−13.3892			−0.506789
$699$			4.65613i			0.176111i
$700$	3.37579	−	4.25182i	0.127593	−	0.160704i
$701$	−15.1890	−	15.1890i	−0.573682	−	0.573682i	0.359473	−	0.933155i	$-0.382956\pi$
$701$	−15.1890	−	15.1890i	−0.573682	−	0.573682i	−0.933155	+	0.359473i	$0.882956\pi$
$702$	19.6226	+	19.6226i	0.740607	+	0.740607i
$703$	−14.0703	−	17.3592i	−0.530672	−	0.654716i
$704$		−	4.39414i		−	0.165610i
$705$	18.4104	−	1.05375i	0.693374	−	0.0396864i
$706$		−	7.34993i		−	0.276618i
$707$	−11.1852	−	11.1852i	−0.420663	−	0.420663i
$708$			8.16908i			0.307013i
$709$	−13.9085	+	13.9085i	−0.522343	+	0.522343i	−0.918278	−	0.395935i	$-0.870420\pi$
$709$	−13.9085	+	13.9085i	−0.522343	+	0.522343i	0.395935	+	0.918278i	$0.370420\pi$
$710$	−12.1993	+	0.698244i	−0.457830	+	0.0262046i
$711$	12.4446	+	12.4446i	0.466709	+	0.466709i
$712$	7.54653	−	7.54653i	0.282818	−	0.282818i
$713$	−4.99463	−	4.99463i	−0.187051	−	0.187051i
$714$	−6.04992			−0.226413
$715$	3.78581	+	66.1432i	0.141581	+	2.47362i
$716$	−7.93007	−	7.93007i	−0.296361	−	0.296361i
$717$		−	3.13746i		−	0.117171i
$718$	24.0685			0.898228
$719$		−	23.7742i		−	0.886629i	−0.896366	−	0.443314i	$-0.853803\pi$
$719$		−	23.7742i		−	0.886629i	0.896366	−	0.443314i	$-0.146197\pi$
$720$	5.41209	−	0.309770i	0.201697	−	0.0115444i
$721$	−7.80238	+	7.80238i	−0.290576	+	0.290576i
$722$	−5.50496			−0.204874
$723$	16.0763			0.597886
$724$	4.29385			0.159580
$725$	−6.93257	−	5.50421i	−0.257469	−	0.204421i
$726$	4.45754	+	4.45754i	0.165435	+	0.165435i
$727$			0.783597i			0.0290620i	0.999894	+	0.0145310i	$0.00462552\pi$
$727$			0.783597i			0.0290620i	−0.999894	+	0.0145310i	$0.995374\pi$
$728$	5.17690	−	5.17690i	0.191869	−	0.191869i
$729$		−	0.693741i		−	0.0256941i
$730$	3.96007	−	4.44092i	0.146569	−	0.164366i
$731$		−	62.8689i		−	2.32529i
$732$		−	1.22807i		−	0.0453907i
$733$	−8.72850	+	8.72850i	−0.322395	+	0.322395i	−0.849685	−	0.527291i	$-0.823208\pi$
$733$	−8.72850	+	8.72850i	−0.322395	+	0.322395i	0.527291	+	0.849685i	$0.323208\pi$
$734$	−0.833192	−	0.833192i	−0.0307537	−	0.0307537i
$735$	−6.57283	+	7.37093i	−0.242443	+	0.271881i
$736$	−1.20395			−0.0443781
$737$	27.4767	−	27.4767i	1.01212	−	1.01212i
$738$		−	9.86920i		−	0.363290i
$739$	11.2844			0.415102			0.207551	−	0.978224i	$-0.433451\pi$
$739$	11.2844			0.415102			0.207551	+	0.978224i	$0.433451\pi$
$740$	13.5864	+	0.640267i	0.499446	+	0.0235367i
$741$	−18.7937			−0.690404
$742$			3.56222i			0.130773i
$743$	−11.8850	+	11.8850i	−0.436018	+	0.436018i	−0.890669	−	0.454652i	$-0.849764\pi$
$743$	−11.8850	+	11.8850i	−0.436018	+	0.436018i	0.454652	+	0.890669i	$0.349764\pi$
$744$	−4.45144			−0.163198
$745$	−11.5760	+	0.662573i	−0.424113	+	0.0242748i
$746$	−2.09090	−	2.09090i	−0.0765531	−	0.0765531i
$747$	−1.38271	+	1.38271i	−0.0505909	+	0.0505909i
$748$		−	32.2690i		−	1.17987i
$749$			20.6010i			0.752745i
$750$	4.88649	−	6.93410i	0.178429	−	0.253198i
$751$			18.7371i			0.683727i	0.939750	+	0.341864i	$0.111058\pi$
$751$			18.7371i			0.683727i	−0.939750	+	0.341864i	$0.888942\pi$
$752$	7.68569	−	7.68569i	0.280268	−	0.280268i
$753$			9.92826i			0.361806i
$754$	−8.44092	−	8.44092i	−0.307400	−	0.307400i
$755$	−27.9882	+	1.60195i	−1.01859	+	0.0583009i
$756$	4.46872			0.162526
$757$	−5.00038			−0.181742			−0.0908710	−	0.995863i	$-0.528965\pi$
$757$	−5.00038			−0.181742			−0.0908710	+	0.995863i	$0.528965\pi$
$758$	4.36102			0.158399
$759$	2.83828	−	2.83828i	0.103023	−	0.103023i
$760$	−5.46701	+	6.13083i	−0.198309	+	0.222388i
$761$		−	9.44966i		−	0.342550i	−0.985223	−	0.171275i	$-0.945211\pi$
$761$		−	9.44966i		−	0.342550i	0.985223	−	0.171275i	$-0.0547887\pi$
$762$	−9.88267			−0.358012
$763$		−	7.34663i		−	0.265966i
$764$	−2.08620	−	2.08620i	−0.0754759	−	0.0754759i
$765$	39.7445	−	2.27484i	1.43697	−	0.0822470i
$766$	16.6051			0.599966
$767$	−51.3340	−	51.3340i	−1.85356	−	1.85356i
$768$	−0.536506	+	0.536506i	−0.0193595	+	0.0193595i
$769$	−11.4556	−	11.4556i	−0.413100	−	0.413100i	0.469717	−	0.882817i	$-0.344356\pi$
$769$	−11.4556	−	11.4556i	−0.413100	−	0.413100i	−0.882817	+	0.469717i	$0.844356\pi$
$770$	7.96259	+	7.10044i	0.286952	+	0.255882i
$771$	6.19533	−	6.19533i	0.223119	−	0.223119i
$772$			13.6280i			0.490481i
$773$	7.63579	+	7.63579i	0.274640	+	0.274640i	0.830965	−	0.556325i	$-0.187789\pi$
$773$	7.63579	+	7.63579i	0.274640	+	0.274640i	−0.556325	+	0.830965i	$0.687789\pi$
$774$			20.7546i			0.746009i
$775$	18.2405	−	22.9740i	0.655220	−	0.825251i
$776$			5.39443i			0.193649i
$777$	4.98395	+	0.521543i	0.178798	+	0.0187102i
$778$	−12.9306	−	12.9306i	−0.463585	−	0.463585i
$779$	10.5746	+	10.5746i	0.378874	+	0.378874i
$780$	7.61357	−	8.53803i	0.272609	−	0.305710i
$781$		−	24.0122i		−	0.859226i
$782$	−8.84137			−0.316167
$783$		−	7.28623i		−	0.260389i
$784$			5.82104i			0.207894i
$785$	1.25159	+	1.11607i	0.0446712	+	0.0398344i
$786$	1.65077			0.0588809
$787$	−28.6364	+	28.6364i	−1.02078	+	1.02078i	−0.0209994	+	0.999779i	$0.506685\pi$
$787$	−28.6364	+	28.6364i	−1.02078	+	1.02078i	−0.999779	+	0.0209994i	$0.993315\pi$
$788$	−5.05224	+	5.05224i	−0.179979	+	0.179979i
$789$			6.83121i			0.243198i
$790$	10.8036	−	12.1154i	0.384374	−	0.431046i
$791$	13.8228	−	13.8228i	0.491483	−	0.491483i
$792$			10.6528i			0.378531i
$793$	7.71710	+	7.71710i	0.274042	+	0.274042i
$794$	−1.98404	+	1.98404i	−0.0704110	+	0.0704110i
$795$	0.318060	+	5.55694i	0.0112804	+	0.197084i
$796$	12.1515	+	12.1515i	0.430698	+	0.430698i
$797$		−	14.9042i		−	0.527935i	−0.964532	−	0.263967i	$-0.914969\pi$
$797$		−	14.9042i		−	0.527935i	0.964532	−	0.263967i	$-0.0850311\pi$
$798$	−2.13998	+	2.13998i	−0.0757545	+	0.0757545i
$799$	56.4410	−	56.4410i	1.99674	−	1.99674i
$800$	−0.570497	−	4.96735i	−0.0201701	−	0.175622i
$801$	−18.2952	+	18.2952i	−0.646431	+	0.646431i
$802$	−14.2034	−	14.2034i	−0.501539	−	0.501539i
$803$	8.26798	+	8.26798i	0.291771	+	0.291771i
$804$	−6.70958			−0.236629
$805$	1.94544	−	2.18167i	0.0685679	−	0.0768936i
$806$	27.9726	−	27.9726i	0.985292	−	0.985292i
$807$	−1.99708	−	1.99708i	−0.0703005	−	0.0703005i
$808$	−14.5684			−0.512513
$809$	−34.6791	−	34.6791i	−1.21925	−	1.21925i	−0.967894	−	0.251360i	$-0.919122\pi$
$809$	−34.6791	−	34.6791i	−1.21925	−	1.21925i	−0.251360	−	0.967894i	$-0.580878\pi$
$810$	−9.26522	+	0.530310i	−0.325547	+	0.0186332i
$811$	−32.0485			−1.12538			−0.562688	−	0.826670i	$-0.690233\pi$
$811$	−32.0485			−1.12538			−0.562688	+	0.826670i	$0.690233\pi$
$812$	−1.92228			−0.0674589
$813$	−12.4637	+	12.4637i	−0.437120	+	0.437120i
$814$	−2.78180	+	26.5834i	−0.0975021	+	0.931746i
$815$	1.66611	+	29.1092i	0.0583614	+	1.01965i
$816$	−3.93991	+	3.93991i	−0.137924	+	0.137924i
$817$	−22.2380	−	22.2380i	−0.778009	−	0.778009i
$818$	13.7291	−	13.7291i	0.480026	−	0.480026i
$819$	−12.5505	+	12.5505i	−0.438550	+	0.438550i
$820$	−9.08795	+	0.520163i	−0.317365	+	0.0181649i
$821$	−12.7001			−0.443236			−0.221618	−	0.975134i	$-0.571134\pi$
$821$	−12.7001			−0.443236			−0.221618	+	0.975134i	$0.571134\pi$
$822$	−12.7850			−0.445927
$823$	−10.7759	−	10.7759i	−0.375625	−	0.375625i	0.493896	−	0.869521i	$-0.335572\pi$
$823$	−10.7759	−	10.7759i	−0.375625	−	0.375625i	−0.869521	+	0.493896i	$0.835572\pi$
$824$			10.1623i			0.354022i
$825$	13.0554	+	10.3655i	0.454529	+	0.360880i
$826$	−11.6905			−0.406764
$827$	0.404559			0.0140679			0.00703394	−	0.999975i	$-0.497761\pi$
$827$	0.404559			0.0140679			0.00703394	+	0.999975i	$0.497761\pi$
$828$	2.91876			0.101434
$829$	14.5459	+	14.5459i	0.505200	+	0.505200i	0.913049	−	0.407849i	$-0.133721\pi$
$829$	14.5459	+	14.5459i	0.505200	+	0.505200i	−0.407849	+	0.913049i	$0.633721\pi$
$830$	1.34614	+	1.20038i	0.0467250	+	0.0416658i
$831$	−6.88831	−	6.88831i	−0.238953	−	0.238953i
$832$		−	6.74274i		−	0.233762i
$833$			42.7477i			1.48112i
$834$	3.62541	+	3.62541i	0.125538	+	0.125538i
$835$	−3.14846	−	55.0078i	−0.108957	−	1.90362i
$836$	−11.4142	−	11.4142i	−0.394769	−	0.394769i
$837$	24.1460			0.834609
$838$	10.6476			0.367815
$839$	23.8438			0.823180			0.411590	−	0.911369i	$-0.364974\pi$
$839$	23.8438			0.823180			0.411590	+	0.911369i	$0.364974\pi$
$840$	−0.105266	−	1.83913i	−0.00363201	−	0.0634561i
$841$		−	25.8657i		−	0.891922i
$842$	21.3367	+	21.3367i	0.735311	+	0.735311i
$843$	−16.3924			−0.564584
$844$	−8.27973			−0.285000
$845$	4.14818	+	72.4743i	0.142702	+	2.49319i
$846$	−18.6326	+	18.6326i	−0.640602	+	0.640602i
$847$	−6.37903	+	6.37903i	−0.219186	+	0.219186i
$848$	2.31983	+	2.31983i	0.0796633	+	0.0796633i
$849$	11.1540	−	11.1540i	0.382804	−	0.382804i
$850$	−4.18953	−	36.4784i	−0.143700	−	1.25120i
$851$	7.28356	+	0.762184i	0.249677	+	0.0261273i
$852$	−2.93179	+	2.93179i	−0.100441	+	0.100441i
$853$	−7.11096			−0.243475			−0.121737	−	0.992562i	$-0.538847\pi$
$853$	−7.11096			−0.243475			−0.121737	+	0.992562i	$0.538847\pi$
$854$	1.75744			0.0601385
$855$	13.2538	−	14.8631i	0.453270	−	0.508307i
$856$	13.4161	+	13.4161i	0.458551	+	0.458551i
$857$	−30.9080			−1.05580			−0.527898	−	0.849308i	$-0.677020\pi$
$857$	−30.9080			−1.05580			−0.527898	+	0.849308i	$0.677020\pi$
$858$	15.8959	+	15.8959i	0.542676	+	0.542676i
$859$	−10.1957	+	10.1957i	−0.347872	+	0.347872i	−0.859317	−	0.511444i	$-0.829111\pi$
$859$	−10.1957	+	10.1957i	−0.347872	+	0.347872i	0.511444	+	0.859317i	$0.329111\pi$
$860$	19.1117	−	1.09389i	0.651702	−	0.0373012i
$861$	−3.35374			−0.114295
$862$	−5.16220	−	5.16220i	−0.175825	−	0.175825i
$863$	−15.0510	−	15.0510i	−0.512343	−	0.512343i	0.402901	−	0.915244i	$-0.368002\pi$
$863$	−15.0510	−	15.0510i	−0.512343	−	0.512343i	−0.915244	+	0.402901i	$0.868002\pi$
$864$	2.91018	−	2.91018i	0.0990063	−	0.0990063i
$865$	−12.5621	−	11.2019i	−0.427124	−	0.380877i
$866$	−2.75289	+	2.75289i	−0.0935472	+	0.0935472i
$867$	−19.8127	+	19.8127i	−0.672874	+	0.672874i
$868$		−	6.37030i		−	0.216222i
$869$	22.5561	+	22.5561i	0.765163	+	0.765163i
$870$	−2.99870	+	0.171635i	−0.101665	+	0.00581897i
$871$	42.1626	−	42.1626i	1.42863	−	1.42863i
$872$	−4.78437	−	4.78437i	−0.162019	−	0.162019i
$873$		−	13.0778i		−	0.442618i
$874$	−3.12737	+	3.12737i	−0.105785	+	0.105785i
$875$	9.92316	+	6.99288i	0.335464	+	0.236403i
$876$		−	2.01897i		−	0.0682147i
$877$	33.9571	−	33.9571i	1.14665	−	1.14665i	0.159441	−	0.987207i	$-0.449031\pi$
$877$	33.9571	−	33.9571i	1.14665	−	1.14665i	0.987207	−	0.159441i	$-0.0509693\pi$
$878$	−28.9545	+	28.9545i	−0.977168	+	0.977168i
$879$	−0.481998			−0.0162574
$880$	9.80954	−	0.561465i	0.330680	−	0.0189270i
$881$			28.9969i			0.976931i	0.872583	+	0.488465i	$0.162443\pi$
$881$			28.9969i			0.976931i	−0.872583	+	0.488465i	$0.837557\pi$
$882$		−	14.1121i		−	0.475179i
$883$	19.0735			0.641875			0.320938	−	0.947100i	$-0.396002\pi$
$883$	19.0735			0.641875			0.320938	+	0.947100i	$0.396002\pi$
$884$		−	49.5163i		−	1.66541i
$885$	−18.2368	+	1.04381i	−0.613022	+	0.0350873i
$886$	19.2383	+	19.2383i	0.646324	+	0.646324i
$887$	−8.61923	−	8.61923i	−0.289405	−	0.289405i	0.547440	−	0.836845i	$-0.315603\pi$
$887$	−8.61923	−	8.61923i	−0.289405	−	0.289405i	−0.836845	+	0.547440i	$0.815603\pi$
$888$	3.58536	−	2.90607i	0.120317	−	0.0975212i
$889$		−	14.1428i		−	0.474333i
$890$	17.8113	+	15.8827i	0.597035	+	0.532390i
$891$		−	18.2371i		−	0.610965i
$892$	−9.35468	−	9.35468i	−0.313218	−	0.313218i
$893$		−	39.9287i		−	1.33616i
$894$	−2.78201	+	2.78201i	−0.0930444	+	0.0930444i
$895$	16.6899	−	18.7165i	0.557883	−	0.625623i
$896$	−0.767774	−	0.767774i	−0.0256495	−	0.0256495i
$897$	4.35530	−	4.35530i	0.145419	−	0.145419i
$898$	−21.0464	−	21.0464i	−0.702329	−	0.702329i
$899$	−10.3867			−0.346417
$900$	1.38307	+	12.0425i	0.0461023	+	0.401415i
$901$	17.0360	+	17.0360i	0.567552	+	0.567552i
$902$		−	17.8881i		−	0.595610i
$903$	7.05280			0.234703
$904$		−	18.0037i		−	0.598796i
$905$	0.548650	+	9.58566i	0.0182378	+	0.318638i
$906$	−6.72627	+	6.72627i	−0.223465	+	0.223465i
$907$	41.4022			1.37474			0.687369	−	0.726308i	$-0.258765\pi$
$907$	41.4022			1.37474			0.687369	+	0.726308i	$0.258765\pi$
$908$	20.1807			0.669721
$909$	35.3184			1.17144
$910$	12.2185	+	10.8955i	0.405039	+	0.361183i
$911$	17.6170	+	17.6170i	0.583678	+	0.583678i	0.935912	−	0.352234i	$-0.114578\pi$
$911$	17.6170	+	17.6170i	0.583678	+	0.583678i	−0.352234	+	0.935912i	$0.614578\pi$
$912$			2.78725i			0.0922951i
$913$	−2.50620	+	2.50620i	−0.0829431	+	0.0829431i
$914$			21.7070i			0.718004i
$915$	2.74155	−	0.156917i	0.0906330	−	0.00518752i
$916$		−	3.02631i		−	0.0999920i
$917$			2.36236i			0.0780118i
$918$	21.3713	−	21.3713i	0.705359	−	0.705359i
$919$	23.1287	+	23.1287i	0.762946	+	0.762946i	0.976854	−	0.213908i	$-0.0686191\pi$
$919$	23.1287	+	23.1287i	0.762946	+	0.762946i	−0.213908	+	0.976854i	$0.568619\pi$
$920$	−0.153835	−	2.68771i	−0.00507180	−	0.0886112i
$921$	−0.0155303			−0.000511739
$922$	−1.31376	+	1.31376i	−0.0432664	+	0.0432664i
$923$		−	36.8464i		−	1.21281i
$924$	3.62003			0.119090
$925$	0.306671	+	30.4123i	0.0100833	+	0.999949i
$926$	8.05167			0.264594
$927$		−	24.6368i		−	0.809178i
$928$	−1.25185	+	1.25185i	−0.0410941	+	0.0410941i
$929$	28.3619			0.930524			0.465262	−	0.885173i	$-0.345960\pi$
$929$	28.3619			0.930524			0.465262	+	0.885173i	$0.345960\pi$
$930$	−0.568786	−	9.93746i	−0.0186512	−	0.325862i
$931$	15.1207	+	15.1207i	0.495562	+	0.495562i
$932$	−4.33931	+	4.33931i	−0.142139	+	0.142139i
$933$			24.5999i			0.805363i
$934$		−	5.04806i		−	0.165178i
$935$	72.0378	−	4.12320i	2.35589	−	0.134843i
$936$			16.3466i			0.534305i
$937$	42.3748	−	42.3748i	1.38433	−	1.38433i	0.547557	−	0.836769i	$-0.315558\pi$
$937$	42.3748	−	42.3748i	1.38433	−	1.38433i	0.836769	−	0.547557i	$-0.184442\pi$
$938$		−	9.60185i		−	0.313512i
$939$	−7.86085	−	7.86085i	−0.256529	−	0.256529i
$940$	18.1397	+	16.1756i	0.591652	+	0.527590i
$941$	0.472629			0.0154073			0.00770363	−	0.999970i	$-0.497548\pi$
$941$	0.472629			0.0154073			0.00770363	+	0.999970i	$0.497548\pi$
$942$	0.569009			0.0185393
$943$	−4.90116			−0.159604
$944$	−7.61323	+	7.61323i	−0.247790	+	0.247790i
$945$	0.570995	+	9.97604i	0.0185745	+	0.324521i
$946$			37.6182i			1.22307i
$947$	13.9664			0.453848			0.226924	−	0.973912i	$-0.427133\pi$
$947$	13.9664			0.453848			0.226924	+	0.973912i	$0.427133\pi$
$948$		−	5.50801i		−	0.178892i
$949$	12.6871	+	12.6871i	0.411840	+	0.411840i
$950$	−14.3851	−	11.4213i	−0.466714	−	0.370554i
$951$	15.3129			0.496555
$952$	−5.63827	−	5.63827i	−0.182737	−	0.182737i
$953$	1.44227	−	1.44227i	0.0467195	−	0.0467195i	−0.683361	−	0.730081i	$-0.739482\pi$
$953$	1.44227	−	1.44227i	0.0467195	−	0.0467195i	0.730081	+	0.683361i	$0.239482\pi$
$954$	−5.62402	−	5.62402i	−0.182084	−	0.182084i
$955$	4.39069	−	4.92382i	0.142079	−	0.159331i
$956$	2.92398	−	2.92398i	0.0945683	−	0.0945683i
$957$		−	5.90244i		−	0.190799i
$958$	−4.20701	−	4.20701i	−0.135922	−	0.135922i
$959$		−	18.2961i		−	0.590812i
$960$	−1.26626	−	1.12915i	−0.0408682	−	0.0364432i
$961$		−	3.42091i		−	0.110352i
$962$	−4.26863	+	40.7917i	−0.137626	+	1.31518i
$963$	−32.5249	−	32.5249i	−1.04810	−	1.04810i
$964$	14.9825	+	14.9825i	0.482553	+	0.482553i
$965$	−30.4232	+	1.74132i	−0.979358	+	0.0560551i
$966$		−	0.991849i		−	0.0319122i
$967$	−24.1460			−0.776483			−0.388242	−	0.921558i	$-0.626917\pi$
$967$	−24.1460			−0.776483			−0.388242	+	0.921558i	$0.626917\pi$
$968$			8.30847i			0.267044i
$969$			20.4686i			0.657546i
$970$	−12.0426	+	0.689278i	−0.386665	+	0.0221314i
$971$	−2.14562			−0.0688562			−0.0344281	−	0.999407i	$-0.510961\pi$
$971$	−2.14562			−0.0688562			−0.0344281	+	0.999407i	$0.510961\pi$
$972$	−10.9572	+	10.9572i	−0.351453	+	0.351453i
$973$	−5.18820	+	5.18820i	−0.166326	+	0.166326i
$974$		−	23.0440i		−	0.738377i
$975$	20.0332	+	15.9057i	0.641577	+	0.509389i
$976$	1.14451	−	1.14451i	0.0366347	−	0.0366347i
$977$		−	31.0494i		−	0.993360i	−0.867934	−	0.496680i	$-0.834552\pi$
$977$		−	31.0494i		−	0.993360i	0.867934	−	0.496680i	$-0.165448\pi$
$978$	6.99568	+	6.99568i	0.223697	+	0.223697i
$979$	−33.1605	+	33.1605i	−1.05982	+	1.05982i
$980$	−12.9950	+	0.743789i	−0.415110	+	0.0237595i
$981$	11.5989	+	11.5989i	0.370323	+	0.370323i
$982$			17.5204i			0.559098i
$983$	0.777158	−	0.777158i	0.0247875	−	0.0247875i	−0.694604	−	0.719392i	$-0.744421\pi$
$983$	0.777158	−	0.777158i	0.0247875	−	0.0247875i	0.719392	+	0.694604i	$0.244421\pi$
$984$	−2.18406	+	2.18406i	−0.0696254	+	0.0696254i
$985$	−11.9242	−	10.6331i	−0.379938	−	0.338800i
$986$	−9.19317	+	9.19317i	−0.292770	+	0.292770i
$987$	6.33171	+	6.33171i	0.201541	+	0.201541i
$988$	−17.5149	−	17.5149i	−0.557224	−	0.557224i
$989$	10.3070			0.327743
$990$	−23.7815	+	1.36117i	−0.755826	+	0.0432609i
$991$	15.5460	−	15.5460i	0.493834	−	0.493834i	−0.415678	−	0.909512i	$-0.636456\pi$
$991$	15.5460	−	15.5460i	0.493834	−	0.493834i	0.909512	+	0.415678i	$0.136456\pi$
$992$	−4.14855	−	4.14855i	−0.131717	−	0.131717i
$993$	20.4348			0.648478
$994$	−4.19558	−	4.19558i	−0.133076	−	0.133076i
$995$	−25.5745	+	28.6798i	−0.810765	+	0.909211i
$996$	0.611992			0.0193917
$997$	−42.9037			−1.35877			−0.679386	−	0.733781i	$-0.737754\pi$
$997$	−42.9037			−1.35877			−0.679386	+	0.733781i	$0.737754\pi$
$998$	−3.14878	+	3.14878i	−0.0996728	+	0.0996728i
$999$	−19.4481	+	15.7634i	−0.615312	+	0.498733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.e.43.5	✓	20
5.2	odd	4		370.2.h.e.117.6	yes	20
37.31	odd	4		370.2.h.e.253.6	yes	20
185.142	even	4	inner	370.2.g.e.327.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.5	✓	20	1.1	even	1	trivial
370.2.g.e.327.5	yes	20	185.142	even	4	inner
370.2.h.e.117.6	yes	20	5.2	odd	4
370.2.h.e.253.6	yes	20	37.31	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +(2.23241 - 0.127776i) q^{10} +4.39414i q^{11} +(0.536506 - 0.536506i) q^{12} +6.74274i q^{13} +(0.767774 + 0.767774i) q^{14} +(1.26626 + 1.12915i) q^{15} +1.00000 q^{16} +7.34365 q^{17} -2.42432 q^{18} +(2.59760 - 2.59760i) q^{19} +(0.127776 + 2.23241i) q^{20} +0.823831i q^{21} -4.39414 q^{22} +1.20395i q^{23} +(0.536506 + 0.536506i) q^{24} +(-4.96735 + 0.570497i) q^{25} -6.74274 q^{26} +(-2.91018 - 2.91018i) q^{27} +(-0.767774 + 0.767774i) q^{28} +(1.25185 + 1.25185i) q^{29} +(-1.12915 + 1.26626i) q^{30} +(-4.14855 + 4.14855i) q^{31} +1.00000i q^{32} +(-2.35748 - 2.35748i) q^{33} +7.34365i q^{34} +(-1.81209 - 1.61589i) q^{35} -2.42432i q^{36} +(0.633071 - 6.04973i) q^{37} +(2.59760 + 2.59760i) q^{38} +(-3.61752 - 3.61752i) q^{39} +(-2.23241 + 0.127776i) q^{40} +4.07091i q^{41} -0.823831 q^{42} -8.56098i q^{43} -4.39414i q^{44} +(5.41209 - 0.309770i) q^{45} -1.20395 q^{46} +(7.68569 - 7.68569i) q^{47} +(-0.536506 + 0.536506i) q^{48} +5.82104i q^{49} +(-0.570497 - 4.96735i) q^{50} +(-3.93991 + 3.93991i) q^{51} -6.74274i q^{52} +(2.31983 + 2.31983i) q^{53} +(2.91018 - 2.91018i) q^{54} +(9.80954 - 0.561465i) q^{55} +(-0.767774 - 0.767774i) q^{56} +2.78725i q^{57} +(-1.25185 + 1.25185i) q^{58} +(-7.61323 + 7.61323i) q^{59} +(-1.26626 - 1.12915i) q^{60} +(1.14451 - 1.14451i) q^{61} +(-4.14855 - 4.14855i) q^{62} +(1.86133 + 1.86133i) q^{63} -1.00000 q^{64} +(15.0526 - 0.861559i) q^{65} +(2.35748 - 2.35748i) q^{66} +(-6.25304 - 6.25304i) q^{67} -7.34365 q^{68} +(-0.645925 - 0.645925i) q^{69} +(1.61589 - 1.81209i) q^{70} -5.46460 q^{71} +2.42432 q^{72} +(1.88159 - 1.88159i) q^{73} +(6.04973 + 0.633071i) q^{74} +(2.35893 - 2.97108i) q^{75} +(-2.59760 + 2.59760i) q^{76} +(3.37371 + 3.37371i) q^{77} +(3.61752 - 3.61752i) q^{78} +(5.13322 - 5.13322i) q^{79} +(-0.127776 - 2.23241i) q^{80} -4.15032 q^{81} -4.07091 q^{82} +(0.570350 + 0.570350i) q^{83} -0.823831i q^{84} +(-0.938340 - 16.3941i) q^{85} +8.56098 q^{86} -1.34325 q^{87} +4.39414 q^{88} +(7.54653 + 7.54653i) q^{89} +(0.309770 + 5.41209i) q^{90} +(5.17690 + 5.17690i) q^{91} -1.20395i q^{92} -4.45144i q^{93} +(7.68569 + 7.68569i) q^{94} +(-6.13083 - 5.46701i) q^{95} +(-0.536506 - 0.536506i) q^{96} -5.39443 q^{97} -5.82104 q^{98} -10.6528 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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