LMFDB - Embedded newform 370.2.g.c.43.1

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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.c.327.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.41421 + 1.41421i) q^{3} -1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 - 1.29289i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.41421 + 1.41421i) q^{3} -1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 - 1.29289i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 + 2.12132i) q^{10} -1.82843i q^{11} +(1.41421 - 1.41421i) q^{12} -6.24264i q^{13} +(-1.29289 - 1.29289i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} +3.82843 q^{17} -1.00000 q^{18} +(-0.171573 + 0.171573i) q^{19} +(2.12132 - 0.707107i) q^{20} +3.65685i q^{21} -1.82843 q^{22} -5.41421i q^{23} +(-1.41421 - 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} -6.24264 q^{26} +(-2.82843 - 2.82843i) q^{27} +(-1.29289 + 1.29289i) q^{28} +(-5.29289 - 5.29289i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(0.121320 - 0.121320i) q^{31} -1.00000i q^{32} +(2.58579 + 2.58579i) q^{33} -3.82843i q^{34} +(-1.82843 + 3.65685i) q^{35} +1.00000i q^{36} +(4.94975 + 3.53553i) q^{37} +(0.171573 + 0.171573i) q^{38} +(8.82843 + 8.82843i) q^{39} +(-0.707107 - 2.12132i) q^{40} +7.00000i q^{41} +3.65685 q^{42} -7.00000i q^{43} +1.82843i q^{44} +(0.707107 + 2.12132i) q^{45} -5.41421 q^{46} +(0.242641 - 0.242641i) q^{47} +(-1.41421 + 1.41421i) q^{48} +3.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-5.41421 + 5.41421i) q^{51} +6.24264i q^{52} +(-2.12132 - 2.12132i) q^{53} +(-2.82843 + 2.82843i) q^{54} +(1.29289 + 3.87868i) q^{55} +(1.29289 + 1.29289i) q^{56} -0.485281i q^{57} +(-5.29289 + 5.29289i) q^{58} +(-6.82843 + 6.82843i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(10.7071 - 10.7071i) q^{61} +(-0.121320 - 0.121320i) q^{62} +(-1.29289 - 1.29289i) q^{63} -1.00000 q^{64} +(4.41421 + 13.2426i) q^{65} +(2.58579 - 2.58579i) q^{66} +(-7.24264 - 7.24264i) q^{67} -3.82843 q^{68} +(7.65685 + 7.65685i) q^{69} +(3.65685 + 1.82843i) q^{70} -11.6569 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-1.41421 + 9.89949i) q^{75} +(0.171573 - 0.171573i) q^{76} +(-2.36396 - 2.36396i) q^{77} +(8.82843 - 8.82843i) q^{78} +(-1.65685 + 1.65685i) q^{79} +(-2.12132 + 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(4.82843 + 4.82843i) q^{83} -3.65685i q^{84} +(-8.12132 + 2.70711i) q^{85} -7.00000 q^{86} +14.9706 q^{87} +1.82843 q^{88} +(4.58579 + 4.58579i) q^{89} +(2.12132 - 0.707107i) q^{90} +(-8.07107 - 8.07107i) q^{91} +5.41421i q^{92} +0.343146i q^{93} +(-0.242641 - 0.242641i) q^{94} +(0.242641 - 0.485281i) q^{95} +(1.41421 + 1.41421i) q^{96} -7.00000 q^{97} +3.65685 q^{98} -1.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^7	$ 4 q - 4 q^{4} + 8 q^{7} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 4 q^{22} + 16 q^{25} - 8 q^{26} - 8 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} + 16 q^{33} + 4 q^{35} + 12 q^{38} + 24 q^{39} - 8 q^{42} - 16 q^{46} - 16 q^{47} - 12 q^{50} - 16 q^{51} + 8 q^{55} + 8 q^{56} - 24 q^{58} - 16 q^{59} - 8 q^{60} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 4 q^{64} + 12 q^{65} + 16 q^{66} - 12 q^{67} - 4 q^{68} + 8 q^{69} - 8 q^{70} - 24 q^{71} + 4 q^{72} + 24 q^{73} + 12 q^{76} + 16 q^{77} + 24 q^{78} + 16 q^{79} + 44 q^{81} + 28 q^{82} + 8 q^{83} - 24 q^{85} - 28 q^{86} - 8 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} - 28 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^7 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 4 * q^22 + 16 * q^25 - 8 * q^26 - 8 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 + 16 * q^33 + 4 * q^35 + 12 * q^38 + 24 * q^39 - 8 * q^42 - 16 * q^46 - 16 * q^47 - 12 * q^50 - 16 * q^51 + 8 * q^55 + 8 * q^56 - 24 * q^58 - 16 * q^59 - 8 * q^60 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 4 * q^64 + 12 * q^65 + 16 * q^66 - 12 * q^67 - 4 * q^68 + 8 * q^69 - 8 * q^70 - 24 * q^71 + 4 * q^72 + 24 * q^73 + 12 * q^76 + 16 * q^77 + 24 * q^78 + 16 * q^79 + 44 * q^81 + 28 * q^82 + 8 * q^83 - 24 * q^85 - 28 * q^86 - 8 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^91 + 16 * q^94 - 16 * q^95 - 28 * q^97 - 8 * q^98 + 4 * 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
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	0.169102	+	0.985599i	$0.445913\pi$
$4$	−1.00000			−0.500000
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$	1.41421	+	1.41421i	0.577350	+	0.577350i
$7$	1.29289	−	1.29289i	0.488668	−	0.488668i	−0.419218	−	0.907886i	$-0.637696\pi$
$7$	1.29289	−	1.29289i	0.488668	−	0.488668i	0.907886	+	0.419218i	$0.137696\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.707107	+	2.12132i	0.223607	+	0.670820i
$11$		−	1.82843i		−	0.551292i	−0.961259	−	0.275646i	$-0.911108\pi$
$11$		−	1.82843i		−	0.551292i	0.961259	−	0.275646i	$-0.0888917\pi$
$12$	1.41421	−	1.41421i	0.408248	−	0.408248i
$13$		−	6.24264i		−	1.73140i	−0.500566	−	0.865699i	$-0.666875\pi$
$13$		−	6.24264i		−	1.73140i	0.500566	−	0.865699i	$-0.333125\pi$
$14$	−1.29289	−	1.29289i	−0.345540	−	0.345540i
$15$	2.00000	−	4.00000i	0.516398	−	1.03280i
$16$	1.00000			0.250000
$17$	3.82843			0.928530			0.464265	−	0.885696i	$-0.346319\pi$
$17$	3.82843			0.928530			0.464265	+	0.885696i	$0.346319\pi$
$18$	−1.00000			−0.235702
$19$	−0.171573	+	0.171573i	−0.0393615	+	0.0393615i	−0.726514	−	0.687152i	$-0.758861\pi$
$19$	−0.171573	+	0.171573i	−0.0393615	+	0.0393615i	0.687152	+	0.726514i	$0.258861\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$			3.65685i			0.797991i
$22$	−1.82843			−0.389822
$23$		−	5.41421i		−	1.12894i	−0.825453	−	0.564471i	$-0.809080\pi$
$23$		−	5.41421i		−	1.12894i	0.825453	−	0.564471i	$-0.190920\pi$
$24$	−1.41421	−	1.41421i	−0.288675	−	0.288675i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$	−6.24264			−1.22428
$27$	−2.82843	−	2.82843i	−0.544331	−	0.544331i
$28$	−1.29289	+	1.29289i	−0.244334	+	0.244334i
$29$	−5.29289	−	5.29289i	−0.982866	−	0.982866i	0.0169901	−	0.999856i	$-0.494592\pi$
$29$	−5.29289	−	5.29289i	−0.982866	−	0.982866i	−0.999856	+	0.0169901i	$0.994592\pi$
$30$	−4.00000	−	2.00000i	−0.730297	−	0.365148i
$31$	0.121320	−	0.121320i	0.0217898	−	0.0217898i	−0.696128	−	0.717918i	$-0.745095\pi$
$31$	0.121320	−	0.121320i	0.0217898	−	0.0217898i	0.717918	+	0.696128i	$0.245095\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.58579	+	2.58579i	0.450128	+	0.450128i
$34$		−	3.82843i		−	0.656570i
$35$	−1.82843	+	3.65685i	−0.309061	+	0.618121i
$36$			1.00000i			0.166667i
$37$	4.94975	+	3.53553i	0.813733	+	0.581238i
$37$	4.94975	+	3.53553i	0.813733	+	0.581238i
$38$	0.171573	+	0.171573i	0.0278328	+	0.0278328i
$39$	8.82843	+	8.82843i	1.41368	+	1.41368i
$40$	−0.707107	−	2.12132i	−0.111803	−	0.335410i
$41$			7.00000i			1.09322i	0.837389	+	0.546608i	$0.184081\pi$
$41$			7.00000i			1.09322i	−0.837389	+	0.546608i	$0.815919\pi$
$42$	3.65685			0.564265
$43$		−	7.00000i		−	1.06749i	−0.845645	−	0.533745i	$-0.820784\pi$
$43$		−	7.00000i		−	1.06749i	0.845645	−	0.533745i	$-0.179216\pi$
$44$			1.82843i			0.275646i
$45$	0.707107	+	2.12132i	0.105409	+	0.316228i
$46$	−5.41421			−0.798282
$47$	0.242641	−	0.242641i	0.0353928	−	0.0353928i	−0.689189	−	0.724582i	$-0.742033\pi$
$47$	0.242641	−	0.242641i	0.0353928	−	0.0353928i	0.724582	+	0.689189i	$0.242033\pi$
$48$	−1.41421	+	1.41421i	−0.204124	+	0.204124i
$49$			3.65685i			0.522408i
$50$	−3.00000	−	4.00000i	−0.424264	−	0.565685i
$51$	−5.41421	+	5.41421i	−0.758142	+	0.758142i
$52$			6.24264i			0.865699i
$53$	−2.12132	−	2.12132i	−0.291386	−	0.291386i	0.546242	−	0.837628i	$-0.316058\pi$
$53$	−2.12132	−	2.12132i	−0.291386	−	0.291386i	−0.837628	+	0.546242i	$0.816058\pi$
$54$	−2.82843	+	2.82843i	−0.384900	+	0.384900i
$55$	1.29289	+	3.87868i	0.174334	+	0.523001i
$56$	1.29289	+	1.29289i	0.172770	+	0.172770i
$57$		−	0.485281i		−	0.0642771i
$58$	−5.29289	+	5.29289i	−0.694991	+	0.694991i
$59$	−6.82843	+	6.82843i	−0.888985	+	0.888985i	−0.994426	−	0.105440i	$-0.966375\pi$
$59$	−6.82843	+	6.82843i	−0.888985	+	0.888985i	0.105440	+	0.994426i	$0.466375\pi$
$60$	−2.00000	+	4.00000i	−0.258199	+	0.516398i
$61$	10.7071	−	10.7071i	1.37090	−	1.37090i	0.511800	−	0.859105i	$-0.328979\pi$
$61$	10.7071	−	10.7071i	1.37090	−	1.37090i	0.859105	−	0.511800i	$-0.171021\pi$
$62$	−0.121320	−	0.121320i	−0.0154077	−	0.0154077i
$63$	−1.29289	−	1.29289i	−0.162889	−	0.162889i
$64$	−1.00000			−0.125000
$65$	4.41421	+	13.2426i	0.547516	+	1.64255i
$66$	2.58579	−	2.58579i	0.318288	−	0.318288i
$67$	−7.24264	−	7.24264i	−0.884829	−	0.884829i	0.109191	−	0.994021i	$-0.465174\pi$
$67$	−7.24264	−	7.24264i	−0.884829	−	0.884829i	−0.994021	+	0.109191i	$0.965174\pi$
$68$	−3.82843			−0.464265
$69$	7.65685	+	7.65685i	0.921777	+	0.921777i
$70$	3.65685	+	1.82843i	0.437078	+	0.218539i
$71$	−11.6569			−1.38341			−0.691707	−	0.722178i	$-0.743141\pi$
$71$	−11.6569			−1.38341			−0.691707	+	0.722178i	$0.743141\pi$
$72$	1.00000			0.117851
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	−0.262646	−	0.964892i	$-0.584595\pi$
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	0.964892	+	0.262646i	$0.0845950\pi$
$74$	3.53553	−	4.94975i	0.410997	−	0.575396i
$75$	−1.41421	+	9.89949i	−0.163299	+	1.14310i
$76$	0.171573	−	0.171573i	0.0196808	−	0.0196808i
$77$	−2.36396	−	2.36396i	−0.269398	−	0.269398i
$78$	8.82843	−	8.82843i	0.999623	−	0.999623i
$79$	−1.65685	+	1.65685i	−0.186411	+	0.186411i	−0.794142	−	0.607732i	$-0.792080\pi$
$79$	−1.65685	+	1.65685i	−0.186411	+	0.186411i	0.607732	+	0.794142i	$0.292080\pi$
$80$	−2.12132	+	0.707107i	−0.237171	+	0.0790569i
$81$	11.0000			1.22222
$82$	7.00000			0.773021
$83$	4.82843	+	4.82843i	0.529989	+	0.529989i	0.920569	−	0.390580i	$-0.127726\pi$
$83$	4.82843	+	4.82843i	0.529989	+	0.529989i	−0.390580	+	0.920569i	$0.627726\pi$
$84$		−	3.65685i		−	0.398996i
$85$	−8.12132	+	2.70711i	−0.880881	+	0.293627i
$86$	−7.00000			−0.754829
$87$	14.9706			1.60501
$88$	1.82843			0.194911
$89$	4.58579	+	4.58579i	0.486092	+	0.486092i	0.907071	−	0.420978i	$-0.138313\pi$
$89$	4.58579	+	4.58579i	0.486092	+	0.486092i	−0.420978	+	0.907071i	$0.638313\pi$
$90$	2.12132	−	0.707107i	0.223607	−	0.0745356i
$91$	−8.07107	−	8.07107i	−0.846078	−	0.846078i
$92$			5.41421i			0.564471i
$93$			0.343146i			0.0355826i
$94$	−0.242641	−	0.242641i	−0.0250265	−	0.0250265i
$95$	0.242641	−	0.485281i	0.0248944	−	0.0497888i
$96$	1.41421	+	1.41421i	0.144338	+	0.144338i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	3.65685			0.369398
$99$	−1.82843			−0.183764
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$			3.07107i			0.305583i	0.988258	+	0.152791i	$0.0488262\pi$
$101$			3.07107i			0.305583i	−0.988258	+	0.152791i	$0.951174\pi$
$102$	5.41421	+	5.41421i	0.536087	+	0.536087i
$103$	−17.5563			−1.72988			−0.864939	−	0.501877i	$-0.832643\pi$
$103$	−17.5563			−1.72988			−0.864939	+	0.501877i	$0.832643\pi$
$104$	6.24264			0.612141
$105$	−2.58579	−	7.75736i	−0.252347	−	0.757041i
$106$	−2.12132	+	2.12132i	−0.206041	+	0.206041i
$107$	5.07107	−	5.07107i	0.490239	−	0.490239i	−0.418143	−	0.908381i	$-0.637319\pi$
$107$	5.07107	−	5.07107i	0.490239	−	0.490239i	0.908381	+	0.418143i	$0.137319\pi$
$108$	2.82843	+	2.82843i	0.272166	+	0.272166i
$109$	8.94975	−	8.94975i	0.857230	−	0.857230i	−0.133781	−	0.991011i	$-0.542712\pi$
$109$	8.94975	−	8.94975i	0.857230	−	0.857230i	0.991011	+	0.133781i	$0.0427118\pi$
$110$	3.87868	−	1.29289i	0.369818	−	0.123273i
$111$	−12.0000	+	2.00000i	−1.13899	+	0.189832i
$112$	1.29289	−	1.29289i	0.122167	−	0.122167i
$113$	1.82843			0.172004			0.0860020	−	0.996295i	$-0.472591\pi$
$113$	1.82843			0.172004			0.0860020	+	0.996295i	$0.472591\pi$
$114$	−0.485281			−0.0454508
$115$	3.82843	+	11.4853i	0.357003	+	1.07101i
$116$	5.29289	+	5.29289i	0.491433	+	0.491433i
$117$	−6.24264			−0.577132
$118$	6.82843	+	6.82843i	0.628608	+	0.628608i
$119$	4.94975	−	4.94975i	0.453743	−	0.453743i
$120$	4.00000	+	2.00000i	0.365148	+	0.182574i
$121$	7.65685			0.696078
$122$	−10.7071	−	10.7071i	−0.969376	−	0.969376i
$123$	−9.89949	−	9.89949i	−0.892607	−	0.892607i
$124$	−0.121320	+	0.121320i	−0.0108949	+	0.0108949i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$	−1.29289	+	1.29289i	−0.115180	+	0.115180i
$127$	5.41421	−	5.41421i	0.480434	−	0.480434i	−0.424836	−	0.905270i	$-0.639668\pi$
$127$	5.41421	−	5.41421i	0.480434	−	0.480434i	0.905270	+	0.424836i	$0.139668\pi$
$128$			1.00000i			0.0883883i
$129$	9.89949	+	9.89949i	0.871602	+	0.871602i
$130$	13.2426	−	4.41421i	1.16146	−	0.387152i
$131$	−2.41421	+	2.41421i	−0.210931	+	0.210931i	−0.804663	−	0.593732i	$-0.797654\pi$
$131$	−2.41421	+	2.41421i	−0.210931	+	0.210931i	0.593732	+	0.804663i	$0.297654\pi$
$132$	−2.58579	−	2.58579i	−0.225064	−	0.225064i
$133$			0.443651i			0.0384694i
$134$	−7.24264	+	7.24264i	−0.625669	+	0.625669i
$135$	8.00000	+	4.00000i	0.688530	+	0.344265i
$136$			3.82843i			0.328285i
$137$	5.58579	−	5.58579i	0.477226	−	0.477226i	−0.427017	−	0.904243i	$-0.640436\pi$
$137$	5.58579	−	5.58579i	0.477226	−	0.477226i	0.904243	+	0.427017i	$0.140436\pi$
$138$	7.65685	−	7.65685i	0.651795	−	0.651795i
$139$	−11.8284			−1.00327			−0.501637	−	0.865078i	$-0.667269\pi$
$139$	−11.8284			−1.00327			−0.501637	+	0.865078i	$0.667269\pi$
$140$	1.82843	−	3.65685i	0.154530	−	0.309061i
$141$			0.686292i			0.0577962i
$142$			11.6569i			0.978221i
$143$	−11.4142			−0.954504
$144$		−	1.00000i		−	0.0833333i
$145$	14.9706	+	7.48528i	1.24324	+	0.621619i
$146$	−6.00000	−	6.00000i	−0.496564	−	0.496564i
$147$	−5.17157	−	5.17157i	−0.426544	−	0.426544i
$148$	−4.94975	−	3.53553i	−0.406867	−	0.290619i
$149$		−	0.242641i		−	0.0198779i	−0.999951	−	0.00993895i	$-0.996836\pi$
$149$		−	0.242641i		−	0.0198779i	0.999951	−	0.00993895i	$-0.00316372\pi$
$150$	9.89949	+	1.41421i	0.808290	+	0.115470i
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	−0.171573	−	0.171573i	−0.0139164	−	0.0139164i
$153$		−	3.82843i		−	0.309510i
$154$	−2.36396	+	2.36396i	−0.190493	+	0.190493i
$155$	−0.171573	+	0.343146i	−0.0137811	+	0.0275621i
$156$	−8.82843	−	8.82843i	−0.706840	−	0.706840i
$157$	10.1213	−	10.1213i	0.807769	−	0.807769i	−0.176527	−	0.984296i	$-0.556486\pi$
$157$	10.1213	−	10.1213i	0.807769	−	0.807769i	0.984296	+	0.176527i	$0.0564862\pi$
$158$	1.65685	+	1.65685i	0.131812	+	0.131812i
$159$	6.00000			0.475831
$160$	0.707107	+	2.12132i	0.0559017	+	0.167705i
$161$	−7.00000	−	7.00000i	−0.551677	−	0.551677i
$162$		−	11.0000i		−	0.864242i
$163$	−3.34315			−0.261855			−0.130928	−	0.991392i	$-0.541796\pi$
$163$	−3.34315			−0.261855			−0.130928	+	0.991392i	$0.541796\pi$
$164$		−	7.00000i		−	0.546608i
$165$	−7.31371	−	3.65685i	−0.569371	−	0.284686i
$166$	4.82843	−	4.82843i	0.374759	−	0.374759i
$167$	−6.82843			−0.528400			−0.264200	−	0.964468i	$-0.585108\pi$
$167$	−6.82843			−0.528400			−0.264200	+	0.964468i	$0.585108\pi$
$168$	−3.65685			−0.282132
$169$	−25.9706			−1.99774
$170$	2.70711	+	8.12132i	0.207626	+	0.622877i
$171$	0.171573	+	0.171573i	0.0131205	+	0.0131205i
$172$			7.00000i			0.533745i
$173$	−18.0208	+	18.0208i	−1.37010	+	1.37010i	−0.509810	+	0.860287i	$0.670284\pi$
$173$	−18.0208	+	18.0208i	−1.37010	+	1.37010i	−0.860287	+	0.509810i	$0.829716\pi$
$174$		−	14.9706i		−	1.13492i
$175$	1.29289	−	9.05025i	0.0977335	−	0.684135i
$176$		−	1.82843i		−	0.137823i
$177$		−	19.3137i		−	1.45171i
$178$	4.58579	−	4.58579i	0.343719	−	0.343719i
$179$	2.48528	+	2.48528i	0.185759	+	0.185759i	0.793860	−	0.608101i	$-0.208068\pi$
$179$	2.48528	+	2.48528i	0.185759	+	0.185759i	−0.608101	+	0.793860i	$0.708068\pi$
$180$	−0.707107	−	2.12132i	−0.0527046	−	0.158114i
$181$	−3.65685			−0.271812			−0.135906	−	0.990722i	$-0.543394\pi$
$181$	−3.65685			−0.271812			−0.135906	+	0.990722i	$0.543394\pi$
$182$	−8.07107	+	8.07107i	−0.598267	+	0.598267i
$183$			30.2843i			2.23868i
$184$	5.41421			0.399141
$185$	−13.0000	−	4.00000i	−0.955779	−	0.294086i
$186$	0.343146			0.0251607
$187$		−	7.00000i		−	0.511891i
$188$	−0.242641	+	0.242641i	−0.0176964	+	0.0176964i
$189$	−7.31371			−0.531994
$190$	−0.485281	−	0.242641i	−0.0352060	−	0.0176030i
$191$	−5.53553	−	5.53553i	−0.400537	−	0.400537i	0.477885	−	0.878422i	$-0.341404\pi$
$191$	−5.53553	−	5.53553i	−0.400537	−	0.400537i	−0.878422	+	0.477885i	$0.841404\pi$
$192$	1.41421	−	1.41421i	0.102062	−	0.102062i
$193$		−	3.51472i		−	0.252995i	−0.991967	−	0.126497i	$-0.959626\pi$
$193$		−	3.51472i		−	0.252995i	0.991967	−	0.126497i	$-0.0403736\pi$
$194$			7.00000i			0.502571i
$195$	−24.9706	−	12.4853i	−1.78818	−	0.894090i
$196$		−	3.65685i		−	0.261204i
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	−0.774755	−	0.632261i	$-0.782127\pi$
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	0.632261	+	0.774755i	$0.282127\pi$
$198$			1.82843i			0.129941i
$199$	15.8995	+	15.8995i	1.12709	+	1.12709i	0.990649	+	0.136436i	$0.0435650\pi$
$199$	15.8995	+	15.8995i	1.12709	+	1.12709i	0.136436	+	0.990649i	$0.456435\pi$
$200$	3.00000	+	4.00000i	0.212132	+	0.282843i
$201$	20.4853			1.44492
$202$	3.07107			0.216080
$203$	−13.6863			−0.960589
$204$	5.41421	−	5.41421i	0.379071	−	0.379071i
$205$	−4.94975	−	14.8492i	−0.345705	−	1.03712i
$206$			17.5563i			1.22321i
$207$	−5.41421			−0.376314
$208$		−	6.24264i		−	0.432849i
$209$	0.313708	+	0.313708i	0.0216997	+	0.0216997i
$210$	−7.75736	+	2.58579i	−0.535309	+	0.178436i
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	2.12132	+	2.12132i	0.145693	+	0.145693i
$213$	16.4853	−	16.4853i	1.12955	−	1.12955i
$214$	−5.07107	−	5.07107i	−0.346651	−	0.346651i
$215$	4.94975	+	14.8492i	0.337570	+	1.01271i
$216$	2.82843	−	2.82843i	0.192450	−	0.192450i
$217$		−	0.313708i		−	0.0212959i
$218$	−8.94975	−	8.94975i	−0.606153	−	0.606153i
$219$			16.9706i			1.14676i
$220$	−1.29289	−	3.87868i	−0.0871668	−	0.261501i
$221$		−	23.8995i		−	1.60765i
$222$	2.00000	+	12.0000i	0.134231	+	0.805387i
$223$	18.1213	+	18.1213i	1.21349	+	1.21349i	0.969870	+	0.243623i	$0.0783361\pi$
$223$	18.1213	+	18.1213i	1.21349	+	1.21349i	0.243623	+	0.969870i	$0.421664\pi$
$224$	−1.29289	−	1.29289i	−0.0863851	−	0.0863851i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$		−	1.82843i		−	0.121625i
$227$	9.48528			0.629560			0.314780	−	0.949165i	$-0.398069\pi$
$227$	9.48528			0.629560			0.314780	+	0.949165i	$0.398069\pi$
$228$			0.485281i			0.0321385i
$229$			1.41421i			0.0934539i	0.998908	+	0.0467269i	$0.0148791\pi$
$229$			1.41421i			0.0934539i	−0.998908	+	0.0467269i	$0.985121\pi$
$230$	11.4853	−	3.82843i	0.757317	−	0.252439i
$231$	6.68629			0.439926
$232$	5.29289	−	5.29289i	0.347495	−	0.347495i
$233$	−14.0711	+	14.0711i	−0.921826	+	0.921826i	−0.997158	−	0.0753322i	$-0.975998\pi$
$233$	−14.0711	+	14.0711i	−0.921826	+	0.921826i	0.0753322	+	0.997158i	$0.475998\pi$
$234$			6.24264i			0.408094i
$235$	−0.343146	+	0.686292i	−0.0223844	+	0.0447687i
$236$	6.82843	−	6.82843i	0.444493	−	0.444493i
$237$		−	4.68629i		−	0.304407i
$238$	−4.94975	−	4.94975i	−0.320844	−	0.320844i
$239$	16.9497	−	16.9497i	1.09639	−	1.09639i	0.101558	−	0.994830i	$-0.467617\pi$
$239$	16.9497	−	16.9497i	1.09639	−	1.09639i	0.994830	−	0.101558i	$-0.0323829\pi$
$240$	2.00000	−	4.00000i	0.129099	−	0.258199i
$241$	9.24264	+	9.24264i	0.595371	+	0.595371i	0.939077	−	0.343706i	$-0.111682\pi$
$241$	9.24264	+	9.24264i	0.595371	+	0.595371i	−0.343706	+	0.939077i	$0.611682\pi$
$242$		−	7.65685i		−	0.492201i
$243$	−7.07107	+	7.07107i	−0.453609	+	0.453609i
$244$	−10.7071	+	10.7071i	−0.685452	+	0.685452i
$245$	−2.58579	−	7.75736i	−0.165200	−	0.495600i
$246$	−9.89949	+	9.89949i	−0.631169	+	0.631169i
$247$	1.07107	+	1.07107i	0.0681504	+	0.0681504i
$248$	0.121320	+	0.121320i	0.00770385	+	0.00770385i
$249$	−13.6569			−0.865468
$250$	9.19239	+	6.36396i	0.581378	+	0.402492i
$251$	1.89949	−	1.89949i	0.119895	−	0.119895i	−0.644614	−	0.764509i	$-0.722982\pi$
$251$	1.89949	−	1.89949i	0.119895	−	0.119895i	0.764509	+	0.644614i	$0.222982\pi$
$252$	1.29289	+	1.29289i	0.0814446	+	0.0814446i
$253$	−9.89949			−0.622376
$254$	−5.41421	−	5.41421i	−0.339718	−	0.339718i
$255$	7.65685	−	15.3137i	0.479491	−	0.958982i
$256$	1.00000			0.0625000
$257$	13.1716			0.821620			0.410810	−	0.911721i	$-0.365246\pi$
$257$	13.1716			0.821620			0.410810	+	0.911721i	$0.365246\pi$
$258$	9.89949	−	9.89949i	0.616316	−	0.616316i
$259$	10.9706	−	1.82843i	0.681678	−	0.113613i
$260$	−4.41421	−	13.2426i	−0.273758	−	0.821274i
$261$	−5.29289	+	5.29289i	−0.327622	+	0.327622i
$262$	2.41421	+	2.41421i	0.149151	+	0.149151i
$263$	6.60660	−	6.60660i	0.407381	−	0.407381i	−0.473444	−	0.880824i	$-0.656989\pi$
$263$	6.60660	−	6.60660i	0.407381	−	0.407381i	0.880824	+	0.473444i	$0.156989\pi$
$264$	−2.58579	+	2.58579i	−0.159144	+	0.159144i
$265$	6.00000	+	3.00000i	0.368577	+	0.184289i
$266$	0.443651			0.0272020
$267$	−12.9706			−0.793786
$268$	7.24264	+	7.24264i	0.442415	+	0.442415i
$269$		−	21.7990i		−	1.32911i	−0.747240	−	0.664554i	$-0.768622\pi$
$269$		−	21.7990i		−	1.32911i	0.747240	−	0.664554i	$-0.231378\pi$
$270$	4.00000	−	8.00000i	0.243432	−	0.486864i
$271$	11.0711			0.672519			0.336260	−	0.941769i	$-0.390838\pi$
$271$	11.0711			0.672519			0.336260	+	0.941769i	$0.390838\pi$
$272$	3.82843			0.232132
$273$	22.8284			1.38164
$274$	−5.58579	−	5.58579i	−0.337450	−	0.337450i
$275$	−5.48528	−	7.31371i	−0.330775	−	0.441033i
$276$	−7.65685	−	7.65685i	−0.460888	−	0.460888i
$277$			31.7990i			1.91062i	0.295612	+	0.955308i	$0.404476\pi$
$277$			31.7990i			1.91062i	−0.295612	+	0.955308i	$0.595524\pi$
$278$			11.8284i			0.709422i
$279$	−0.121320	−	0.121320i	−0.00726326	−	0.00726326i
$280$	−3.65685	−	1.82843i	−0.218539	−	0.109269i
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	0.816279	−	0.577659i	$-0.196033\pi$
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	−0.577659	+	0.816279i	$0.696033\pi$
$282$	0.686292			0.0408681
$283$	28.0000			1.66443			0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000			1.66443			0.832214	+	0.554455i	$0.187073\pi$
$284$	11.6569			0.691707
$285$	0.343146	+	1.02944i	0.0203262	+	0.0609786i
$286$			11.4142i			0.674937i
$287$	9.05025	+	9.05025i	0.534220	+	0.534220i
$288$	−1.00000			−0.0589256
$289$	−2.34315			−0.137832
$290$	7.48528	−	14.9706i	0.439551	−	0.879102i
$291$	9.89949	−	9.89949i	0.580319	−	0.580319i
$292$	−6.00000	+	6.00000i	−0.351123	+	0.351123i
$293$	13.7782	+	13.7782i	0.804930	+	0.804930i	0.983861	−	0.178932i	$-0.0572642\pi$
$293$	13.7782	+	13.7782i	0.804930	+	0.804930i	−0.178932	+	0.983861i	$0.557264\pi$
$294$	−5.17157	+	5.17157i	−0.301612	+	0.301612i
$295$	9.65685	−	19.3137i	0.562244	−	1.12449i
$296$	−3.53553	+	4.94975i	−0.205499	+	0.287698i
$297$	−5.17157	+	5.17157i	−0.300085	+	0.300085i
$298$	−0.242641			−0.0140558
$299$	−33.7990			−1.95465
$300$	1.41421	−	9.89949i	0.0816497	−	0.571548i
$301$	−9.05025	−	9.05025i	−0.521648	−	0.521648i
$302$	−12.0000			−0.690522
$303$	−4.34315	−	4.34315i	−0.249507	−	0.249507i
$304$	−0.171573	+	0.171573i	−0.00984038	+	0.00984038i
$305$	−15.1421	+	30.2843i	−0.867036	+	1.73407i
$306$	−3.82843			−0.218857
$307$	17.8995	+	17.8995i	1.02158	+	1.02158i	0.999762	+	0.0218161i	$0.00694484\pi$
$307$	17.8995	+	17.8995i	1.02158	+	1.02158i	0.0218161	+	0.999762i	$0.493055\pi$
$308$	2.36396	+	2.36396i	0.134699	+	0.134699i
$309$	24.8284	−	24.8284i	1.41244	−	1.41244i
$310$	0.343146	+	0.171573i	0.0194894	+	0.00974468i
$311$	3.77817	−	3.77817i	0.214241	−	0.214241i	−0.591825	−	0.806066i	$-0.701593\pi$
$311$	3.77817	−	3.77817i	0.214241	−	0.214241i	0.806066	+	0.591825i	$0.201593\pi$
$312$	−8.82843	+	8.82843i	−0.499811	+	0.499811i
$313$		−	23.3137i		−	1.31777i	−0.752244	−	0.658884i	$-0.771029\pi$
$313$		−	23.3137i		−	1.31777i	0.752244	−	0.658884i	$-0.228971\pi$
$314$	−10.1213	−	10.1213i	−0.571179	−	0.571179i
$315$	3.65685	+	1.82843i	0.206040	+	0.103020i
$316$	1.65685	−	1.65685i	0.0932053	−	0.0932053i
$317$	8.46447	+	8.46447i	0.475412	+	0.475412i	0.903661	−	0.428249i	$-0.140869\pi$
$317$	8.46447	+	8.46447i	0.475412	+	0.475412i	−0.428249	+	0.903661i	$0.640869\pi$
$318$		−	6.00000i		−	0.336463i
$319$	−9.67767	+	9.67767i	−0.541845	+	0.541845i
$320$	2.12132	−	0.707107i	0.118585	−	0.0395285i
$321$			14.3431i			0.800556i
$322$	−7.00000	+	7.00000i	−0.390095	+	0.390095i
$323$	−0.656854	+	0.656854i	−0.0365483	+	0.0365483i
$324$	−11.0000			−0.611111
$325$	−18.7279	−	24.9706i	−1.03884	−	1.38512i
$326$			3.34315i			0.185160i
$327$			25.3137i			1.39985i
$328$	−7.00000			−0.386510
$329$		−	0.627417i		−	0.0345906i
$330$	−3.65685	+	7.31371i	−0.201303	+	0.402606i
$331$	5.41421	+	5.41421i	0.297592	+	0.297592i	0.840070	−	0.542478i	$-0.182514\pi$
$331$	5.41421	+	5.41421i	0.297592	+	0.297592i	−0.542478	+	0.840070i	$0.682514\pi$
$332$	−4.82843	−	4.82843i	−0.264994	−	0.264994i
$333$	3.53553	−	4.94975i	0.193746	−	0.271244i
$334$			6.82843i			0.373635i
$335$	20.4853	+	10.2426i	1.11923	+	0.559615i
$336$			3.65685i			0.199498i
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	0.536043	−	0.844191i	$-0.319919\pi$
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	−0.844191	+	0.536043i	$0.819919\pi$
$338$			25.9706i			1.41261i
$339$	−2.58579	+	2.58579i	−0.140441	+	0.140441i
$340$	8.12132	−	2.70711i	0.440440	−	0.146813i
$341$	−0.221825	−	0.221825i	−0.0120125	−	0.0120125i
$342$	0.171573	−	0.171573i	0.00927760	−	0.00927760i
$343$	13.7782	+	13.7782i	0.743951	+	0.743951i
$344$	7.00000			0.377415
$345$	−21.6569	−	10.8284i	−1.16597	−	0.582983i
$346$	18.0208	+	18.0208i	0.968805	+	0.968805i
$347$		−	5.31371i		−	0.285255i	−0.989776	−	0.142627i	$-0.954445\pi$
$347$		−	5.31371i		−	0.285255i	0.989776	−	0.142627i	$-0.0455551\pi$
$348$	−14.9706			−0.802506
$349$			24.1421i			1.29230i	0.763211	+	0.646149i	$0.223622\pi$
$349$			24.1421i			1.29230i	−0.763211	+	0.646149i	$0.776378\pi$
$350$	−9.05025	−	1.29289i	−0.483756	−	0.0691080i
$351$	−17.6569	+	17.6569i	−0.942453	+	0.942453i
$352$	−1.82843			−0.0974555
$353$	18.6569			0.993004			0.496502	−	0.868036i	$-0.334618\pi$
$353$	18.6569			0.993004			0.496502	+	0.868036i	$0.334618\pi$
$354$	−19.3137			−1.02651
$355$	24.7279	−	8.24264i	1.31242	−	0.437474i
$356$	−4.58579	−	4.58579i	−0.243046	−	0.243046i
$357$			14.0000i			0.740959i
$358$	2.48528	−	2.48528i	0.131351	−	0.131351i
$359$		−	34.5269i		−	1.82226i	−0.412118	−	0.911130i	$-0.635211\pi$
$359$		−	34.5269i		−	1.82226i	0.412118	−	0.911130i	$-0.364789\pi$
$360$	−2.12132	+	0.707107i	−0.111803	+	0.0372678i
$361$			18.9411i			0.996901i
$362$			3.65685i			0.192200i
$363$	−10.8284	+	10.8284i	−0.568345	+	0.568345i
$364$	8.07107	+	8.07107i	0.423039	+	0.423039i
$365$	−8.48528	+	16.9706i	−0.444140	+	0.888280i
$366$	30.2843			1.58298
$367$	−25.0919	+	25.0919i	−1.30979	+	1.30979i	−0.388218	+	0.921568i	$0.626909\pi$
$367$	−25.0919	+	25.0919i	−1.30979	+	1.30979i	−0.921568	+	0.388218i	$0.873091\pi$
$368$		−	5.41421i		−	0.282235i
$369$	7.00000			0.364405
$370$	−4.00000	+	13.0000i	−0.207950	+	0.675838i
$371$	−5.48528			−0.284782
$372$		−	0.343146i		−	0.0177913i
$373$	−5.17157	+	5.17157i	−0.267774	+	0.267774i	−0.828203	−	0.560429i	$-0.810636\pi$
$373$	−5.17157	+	5.17157i	−0.267774	+	0.267774i	0.560429	+	0.828203i	$0.310636\pi$
$374$	−7.00000			−0.361961
$375$	−4.00000	−	22.0000i	−0.206559	−	1.13608i
$376$	0.242641	+	0.242641i	0.0125132	+	0.0125132i
$377$	−33.0416	+	33.0416i	−1.70173	+	1.70173i
$378$			7.31371i			0.376177i
$379$			18.0000i			0.924598i	0.886724	+	0.462299i	$0.152975\pi$
$379$			18.0000i			0.924598i	−0.886724	+	0.462299i	$0.847025\pi$
$380$	−0.242641	+	0.485281i	−0.0124472	+	0.0248944i
$381$			15.3137i			0.784545i
$382$	−5.53553	+	5.53553i	−0.283223	+	0.283223i
$383$		−	19.4142i		−	0.992020i	−0.868317	−	0.496010i	$-0.834798\pi$
$383$		−	19.4142i		−	0.992020i	0.868317	−	0.496010i	$-0.165202\pi$
$384$	−1.41421	−	1.41421i	−0.0721688	−	0.0721688i
$385$	6.68629	+	3.34315i	0.340765	+	0.170382i
$386$	−3.51472			−0.178894
$387$	−7.00000			−0.355830
$388$	7.00000			0.355371
$389$	11.7782	−	11.7782i	0.597177	−	0.597177i	−0.342383	−	0.939560i	$-0.611234\pi$
$389$	11.7782	−	11.7782i	0.597177	−	0.597177i	0.939560	+	0.342383i	$0.111234\pi$
$390$	−12.4853	+	24.9706i	−0.632217	+	1.26443i
$391$		−	20.7279i		−	1.04826i
$392$	−3.65685			−0.184699
$393$		−	6.82843i		−	0.344449i
$394$	2.00000	+	2.00000i	0.100759	+	0.100759i
$395$	2.34315	−	4.68629i	0.117896	−	0.235793i
$396$	1.82843			0.0918819
$397$	−8.48528	−	8.48528i	−0.425864	−	0.425864i	0.461353	−	0.887217i	$-0.347364\pi$
$397$	−8.48528	−	8.48528i	−0.425864	−	0.425864i	−0.887217	+	0.461353i	$0.847364\pi$
$398$	15.8995	−	15.8995i	0.796970	−	0.796970i
$399$	−0.627417	−	0.627417i	−0.0314101	−	0.0314101i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	7.07107	−	7.07107i	0.353112	−	0.353112i	−0.508154	−	0.861266i	$-0.669672\pi$
$401$	7.07107	−	7.07107i	0.353112	−	0.353112i	0.861266	+	0.508154i	$0.169672\pi$
$402$		−	20.4853i		−	1.02171i
$403$	−0.757359	−	0.757359i	−0.0377268	−	0.0377268i
$404$		−	3.07107i		−	0.152791i
$405$	−23.3345	+	7.77817i	−1.15950	+	0.386501i
$406$			13.6863i			0.679239i
$407$	6.46447	−	9.05025i	0.320432	−	0.448604i
$408$	−5.41421	−	5.41421i	−0.268044	−	0.268044i
$409$	19.7990	+	19.7990i	0.978997	+	0.978997i	0.999784	−	0.0207869i	$-0.00661715\pi$
$409$	19.7990	+	19.7990i	0.978997	+	0.978997i	−0.0207869	+	0.999784i	$0.506617\pi$
$410$	−14.8492	+	4.94975i	−0.733352	+	0.244451i
$411$			15.7990i			0.779307i
$412$	17.5563			0.864939
$413$			17.6569i			0.868837i
$414$			5.41421i			0.266094i
$415$	−13.6569	−	6.82843i	−0.670389	−	0.335194i
$416$	−6.24264			−0.306071
$417$	16.7279	−	16.7279i	0.819170	−	0.819170i
$418$	0.313708	−	0.313708i	0.0153440	−	0.0153440i
$419$			6.97056i			0.340534i	0.985398	+	0.170267i	$0.0544631\pi$
$419$			6.97056i			0.340534i	−0.985398	+	0.170267i	$0.945537\pi$
$420$	2.58579	+	7.75736i	0.126173	+	0.378520i
$421$	−2.68629	+	2.68629i	−0.130922	+	0.130922i	−0.769531	−	0.638609i	$-0.779510\pi$
$421$	−2.68629	+	2.68629i	−0.130922	+	0.130922i	0.638609	+	0.769531i	$0.279510\pi$
$422$			9.00000i			0.438113i
$423$	−0.242641	−	0.242641i	−0.0117976	−	0.0117976i
$424$	2.12132	−	2.12132i	0.103020	−	0.103020i
$425$	15.3137	−	11.4853i	0.742824	−	0.557118i
$426$	−16.4853	−	16.4853i	−0.798714	−	0.798714i
$427$		−	27.6863i		−	1.33983i
$428$	−5.07107	+	5.07107i	−0.245119	+	0.245119i
$429$	16.1421	−	16.1421i	0.779350	−	0.779350i
$430$	14.8492	−	4.94975i	0.716094	−	0.238698i
$431$	20.5061	−	20.5061i	0.987744	−	0.987744i	−0.0121819	−	0.999926i	$-0.503878\pi$
$431$	20.5061	−	20.5061i	0.987744	−	0.987744i	0.999926	+	0.0121819i	$0.00387771\pi$
$432$	−2.82843	−	2.82843i	−0.136083	−	0.136083i
$433$	−23.1421	−	23.1421i	−1.11214	−	1.11214i	−0.992861	−	0.119279i	$-0.961942\pi$
$433$	−23.1421	−	23.1421i	−1.11214	−	1.11214i	−0.119279	−	0.992861i	$-0.538058\pi$
$434$	−0.313708			−0.0150585
$435$	−31.7574	+	10.5858i	−1.52265	+	0.507550i
$436$	−8.94975	+	8.94975i	−0.428615	+	0.428615i
$437$	0.928932	+	0.928932i	0.0444369	+	0.0444369i
$438$	16.9706			0.810885
$439$	17.7782	+	17.7782i	0.848506	+	0.848506i	0.989947	−	0.141441i	$-0.0451735\pi$
$439$	17.7782	+	17.7782i	0.848506	+	0.848506i	−0.141441	+	0.989947i	$0.545173\pi$
$440$	−3.87868	+	1.29289i	−0.184909	+	0.0616363i
$441$	3.65685			0.174136
$442$	−23.8995			−1.13678
$443$	−16.6569	+	16.6569i	−0.791391	+	0.791391i	−0.981720	−	0.190329i	$-0.939044\pi$
$443$	−16.6569	+	16.6569i	−0.791391	+	0.791391i	0.190329	+	0.981720i	$0.439044\pi$
$444$	12.0000	−	2.00000i	0.569495	−	0.0949158i
$445$	−12.9706	−	6.48528i	−0.614864	−	0.307432i
$446$	18.1213	−	18.1213i	0.858069	−	0.858069i
$447$	0.343146	+	0.343146i	0.0162302	+	0.0162302i
$448$	−1.29289	+	1.29289i	−0.0610835	+	0.0610835i
$449$	19.6274	−	19.6274i	0.926275	−	0.926275i	−0.0711878	−	0.997463i	$-0.522679\pi$
$449$	19.6274	−	19.6274i	0.926275	−	0.926275i	0.997463	+	0.0711878i	$0.0226790\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	12.7990			0.602681
$452$	−1.82843			−0.0860020
$453$	16.9706	+	16.9706i	0.797347	+	0.797347i
$454$		−	9.48528i		−	0.445166i
$455$	22.8284	+	11.4142i	1.07021	+	0.535107i
$456$	0.485281			0.0227254
$457$	−26.3137			−1.23090			−0.615452	−	0.788175i	$-0.711026\pi$
$457$	−26.3137			−1.23090			−0.615452	+	0.788175i	$0.711026\pi$
$458$	1.41421			0.0660819
$459$	−10.8284	−	10.8284i	−0.505428	−	0.505428i
$460$	−3.82843	−	11.4853i	−0.178501	−	0.535504i
$461$	17.5355	+	17.5355i	0.816711	+	0.816711i	0.985630	−	0.168919i	$-0.0540275\pi$
$461$	17.5355	+	17.5355i	0.816711	+	0.816711i	−0.168919	+	0.985630i	$0.554028\pi$
$462$		−	6.68629i		−	0.311074i
$463$		−	37.9411i		−	1.76327i	−0.471929	−	0.881637i	$-0.656442\pi$
$463$		−	37.9411i		−	1.76327i	0.471929	−	0.881637i	$-0.343558\pi$
$464$	−5.29289	−	5.29289i	−0.245716	−	0.245716i
$465$	−0.242641	−	0.727922i	−0.0112522	−	0.0337566i
$466$	14.0711	+	14.0711i	0.651830	+	0.651830i
$467$	−20.3137			−0.940006			−0.470003	−	0.882665i	$-0.655747\pi$
$467$	−20.3137			−0.940006			−0.470003	+	0.882665i	$0.655747\pi$
$468$	6.24264			0.288566
$469$	−18.7279			−0.864775
$470$	0.686292	+	0.343146i	0.0316563	+	0.0158281i
$471$			28.6274i			1.31908i
$472$	−6.82843	−	6.82843i	−0.314304	−	0.314304i
$473$	−12.7990			−0.588498
$474$	−4.68629			−0.215248
$475$	−0.171573	+	1.20101i	−0.00787230	+	0.0551061i
$476$	−4.94975	+	4.94975i	−0.226871	+	0.226871i
$477$	−2.12132	+	2.12132i	−0.0971286	+	0.0971286i
$478$	−16.9497	−	16.9497i	−0.775263	−	0.775263i
$479$	−15.5563	+	15.5563i	−0.710788	+	0.710788i	−0.966700	−	0.255912i	$-0.917624\pi$
$479$	−15.5563	+	15.5563i	−0.710788	+	0.710788i	0.255912	+	0.966700i	$0.417624\pi$
$480$	−4.00000	−	2.00000i	−0.182574	−	0.0912871i
$481$	22.0711	−	30.8995i	1.00635	−	1.40890i
$482$	9.24264	−	9.24264i	0.420991	−	0.420991i
$483$	19.7990			0.900885
$484$	−7.65685			−0.348039
$485$	14.8492	−	4.94975i	0.674269	−	0.224756i
$486$	7.07107	+	7.07107i	0.320750	+	0.320750i
$487$	−6.97056			−0.315866			−0.157933	−	0.987450i	$-0.550483\pi$
$487$	−6.97056			−0.315866			−0.157933	+	0.987450i	$0.550483\pi$
$488$	10.7071	+	10.7071i	0.484688	+	0.484688i
$489$	4.72792	−	4.72792i	0.213804	−	0.213804i
$490$	−7.75736	+	2.58579i	−0.350442	+	0.116814i
$491$	−21.7990			−0.983775			−0.491887	−	0.870659i	$-0.663693\pi$
$491$	−21.7990			−0.983775			−0.491887	+	0.870659i	$0.663693\pi$
$492$	9.89949	+	9.89949i	0.446304	+	0.446304i
$493$	−20.2635	−	20.2635i	−0.912620	−	0.912620i
$494$	1.07107	−	1.07107i	0.0481896	−	0.0481896i
$495$	3.87868	−	1.29289i	0.174334	−	0.0581112i
$496$	0.121320	−	0.121320i	0.00544744	−	0.00544744i
$497$	−15.0711	+	15.0711i	−0.676030	+	0.676030i
$498$			13.6569i			0.611978i
$499$	−1.75736	−	1.75736i	−0.0786702	−	0.0786702i	0.666677	−	0.745347i	$-0.267716\pi$
$499$	−1.75736	−	1.75736i	−0.0786702	−	0.0786702i	−0.745347	+	0.666677i	$0.767716\pi$
$500$	6.36396	−	9.19239i	0.284605	−	0.411096i
$501$	9.65685	−	9.65685i	0.431436	−	0.431436i
$502$	−1.89949	−	1.89949i	−0.0847786	−	0.0847786i
$503$		−	35.4142i		−	1.57904i	−0.613724	−	0.789521i	$-0.710329\pi$
$503$		−	35.4142i		−	1.57904i	0.613724	−	0.789521i	$-0.289671\pi$
$504$	1.29289	−	1.29289i	0.0575900	−	0.0575900i
$505$	−2.17157	−	6.51472i	−0.0966337	−	0.289901i
$506$			9.89949i			0.440086i
$507$	36.7279	−	36.7279i	1.63114	−	1.63114i
$508$	−5.41421	+	5.41421i	−0.240217	+	0.240217i
$509$	26.7279			1.18469			0.592347	−	0.805683i	$-0.298201\pi$
$509$	26.7279			1.18469			0.592347	+	0.805683i	$0.298201\pi$
$510$	−15.3137	−	7.65685i	−0.678102	−	0.339051i
$511$		−	15.5147i		−	0.686331i
$512$		−	1.00000i		−	0.0441942i
$513$	0.970563			0.0428514
$514$		−	13.1716i		−	0.580973i
$515$	37.2426	−	12.4142i	1.64111	−	0.547036i
$516$	−9.89949	−	9.89949i	−0.435801	−	0.435801i
$517$	−0.443651	−	0.443651i	−0.0195117	−	0.0195117i
$518$	−1.82843	−	10.9706i	−0.0803365	−	0.482019i
$519$		−	50.9706i		−	2.23736i
$520$	−13.2426	+	4.41421i	−0.580728	+	0.193576i
$521$			17.6274i			0.772271i	0.922442	+	0.386136i	$0.126190\pi$
$521$			17.6274i			0.772271i	−0.922442	+	0.386136i	$0.873810\pi$
$522$	5.29289	+	5.29289i	0.231664	+	0.231664i
$523$			32.3431i			1.41427i	0.707080	+	0.707134i	$0.250012\pi$
$523$			32.3431i			1.41427i	−0.707080	+	0.707134i	$0.749988\pi$
$524$	2.41421	−	2.41421i	0.105465	−	0.105465i
$525$	10.9706	+	14.6274i	0.478795	+	0.638393i
$526$	−6.60660	−	6.60660i	−0.288062	−	0.288062i
$527$	0.464466	−	0.464466i	0.0202325	−	0.0202325i
$528$	2.58579	+	2.58579i	0.112532	+	0.112532i
$529$	−6.31371			−0.274509
$530$	3.00000	−	6.00000i	0.130312	−	0.260623i
$531$	6.82843	+	6.82843i	0.296328	+	0.296328i
$532$		−	0.443651i		−	0.0192347i
$533$	43.6985			1.89279
$534$			12.9706i			0.561291i
$535$	−7.17157	+	14.3431i	−0.310054	+	0.620108i
$536$	7.24264	−	7.24264i	0.312834	−	0.312834i
$537$	−7.02944			−0.303343
$538$	−21.7990			−0.939821
$539$	6.68629			0.287999
$540$	−8.00000	−	4.00000i	−0.344265	−	0.172133i
$541$	11.7990	+	11.7990i	0.507278	+	0.507278i	0.913690	−	0.406412i	$-0.133220\pi$
$541$	11.7990	+	11.7990i	0.507278	+	0.507278i	−0.406412	+	0.913690i	$0.633220\pi$
$542$		−	11.0711i		−	0.475543i
$543$	5.17157	−	5.17157i	0.221933	−	0.221933i
$544$		−	3.82843i		−	0.164142i
$545$	−12.6569	+	25.3137i	−0.542160	+	1.08432i
$546$		−	22.8284i		−	0.976966i
$547$			22.1716i			0.947988i	0.880528	+	0.473994i	$0.157188\pi$
$547$			22.1716i			0.947988i	−0.880528	+	0.473994i	$0.842812\pi$
$548$	−5.58579	+	5.58579i	−0.238613	+	0.238613i
$549$	−10.7071	−	10.7071i	−0.456968	−	0.456968i
$550$	−7.31371	+	5.48528i	−0.311858	+	0.233893i
$551$	1.81623			0.0773742
$552$	−7.65685	+	7.65685i	−0.325897	+	0.325897i
$553$			4.28427i			0.182186i
$554$	31.7990			1.35101
$555$	24.0416	−	12.7279i	1.02051	−	0.540270i
$556$	11.8284			0.501637
$557$			19.2132i			0.814090i	0.913408	+	0.407045i	$0.133441\pi$
$557$			19.2132i			0.814090i	−0.913408	+	0.407045i	$0.866559\pi$
$558$	−0.121320	+	0.121320i	−0.00513590	+	0.00513590i
$559$	−43.6985			−1.84825
$560$	−1.82843	+	3.65685i	−0.0772651	+	0.154530i
$561$	9.89949	+	9.89949i	0.417957	+	0.417957i
$562$	4.00000	−	4.00000i	0.168730	−	0.168730i
$563$			38.1127i			1.60626i	0.595805	+	0.803129i	$0.296833\pi$
$563$			38.1127i			1.60626i	−0.595805	+	0.803129i	$0.703167\pi$
$564$		−	0.686292i		−	0.0288981i
$565$	−3.87868	+	1.29289i	−0.163177	+	0.0543924i
$566$		−	28.0000i		−	1.17693i
$567$	14.2218	−	14.2218i	0.597261	−	0.597261i
$568$		−	11.6569i		−	0.489111i
$569$	−24.3137	−	24.3137i	−1.01928	−	1.01928i	−0.999810	−	0.0194733i	$-0.993801\pi$
$569$	−24.3137	−	24.3137i	−1.01928	−	1.01928i	−0.0194733	−	0.999810i	$-0.506199\pi$
$570$	1.02944	−	0.343146i	0.0431184	−	0.0143728i
$571$	7.20101			0.301353			0.150676	−	0.988583i	$-0.451855\pi$
$571$	7.20101			0.301353			0.150676	+	0.988583i	$0.451855\pi$
$572$	11.4142			0.477252
$573$	15.6569			0.654074
$574$	9.05025	−	9.05025i	0.377750	−	0.377750i
$575$	−16.2426	−	21.6569i	−0.677365	−	0.903153i
$576$			1.00000i			0.0416667i
$577$	10.3431			0.430591			0.215295	−	0.976549i	$-0.430929\pi$
$577$	10.3431			0.430591			0.215295	+	0.976549i	$0.430929\pi$
$578$			2.34315i			0.0974620i
$579$	4.97056	+	4.97056i	0.206570	+	0.206570i
$580$	−14.9706	−	7.48528i	−0.621619	−	0.310809i
$581$	12.4853			0.517977
$582$	−9.89949	−	9.89949i	−0.410347	−	0.410347i
$583$	−3.87868	+	3.87868i	−0.160638	+	0.160638i
$584$	6.00000	+	6.00000i	0.248282	+	0.248282i
$585$	13.2426	−	4.41421i	0.547516	−	0.182505i
$586$	13.7782	−	13.7782i	0.569171	−	0.569171i
$587$		−	46.4558i		−	1.91744i	−0.284355	−	0.958719i	$-0.591780\pi$
$587$		−	46.4558i		−	1.91744i	0.284355	−	0.958719i	$-0.408220\pi$
$588$	5.17157	+	5.17157i	0.213272	+	0.213272i
$589$			0.0416306i			0.00171536i
$590$	−19.3137	−	9.65685i	−0.795133	−	0.397566i
$591$		−	5.65685i		−	0.232692i
$592$	4.94975	+	3.53553i	0.203433	+	0.145310i
$593$	2.14214	+	2.14214i	0.0879670	+	0.0879670i	0.749721	−	0.661754i	$-0.230188\pi$
$593$	2.14214	+	2.14214i	0.0879670	+	0.0879670i	−0.661754	+	0.749721i	$0.730188\pi$
$594$	5.17157	+	5.17157i	0.212192	+	0.212192i
$595$	−7.00000	+	14.0000i	−0.286972	+	0.573944i
$596$			0.242641i			0.00993895i
$597$	−44.9706			−1.84052
$598$			33.7990i			1.38214i
$599$			42.2426i			1.72599i	0.505215	+	0.862994i	$0.331413\pi$
$599$			42.2426i			1.72599i	−0.505215	+	0.862994i	$0.668587\pi$
$600$	−9.89949	−	1.41421i	−0.404145	−	0.0577350i
$601$	−33.4853			−1.36589			−0.682947	−	0.730468i	$-0.739302\pi$
$601$	−33.4853			−1.36589			−0.682947	+	0.730468i	$0.739302\pi$
$602$	−9.05025	+	9.05025i	−0.368861	+	0.368861i
$603$	−7.24264	+	7.24264i	−0.294943	+	0.294943i
$604$			12.0000i			0.488273i
$605$	−16.2426	+	5.41421i	−0.660357	+	0.220119i
$606$	−4.34315	+	4.34315i	−0.176428	+	0.176428i
$607$		−	42.1838i		−	1.71219i	−0.516822	−	0.856093i	$-0.672885\pi$
$607$		−	42.1838i		−	1.71219i	0.516822	−	0.856093i	$-0.327115\pi$
$608$	0.171573	+	0.171573i	0.00695820	+	0.00695820i
$609$	19.3553	−	19.3553i	0.784318	−	0.784318i
$610$	30.2843	+	15.1421i	1.22617	+	0.613087i
$611$	−1.51472	−	1.51472i	−0.0612790	−	0.0612790i
$612$			3.82843i			0.154755i
$613$	−7.87868	+	7.87868i	−0.318217	+	0.318217i	−0.848082	−	0.529865i	$-0.822243\pi$
$613$	−7.87868	+	7.87868i	−0.318217	+	0.318217i	0.529865	+	0.848082i	$0.322243\pi$
$614$	17.8995	−	17.8995i	0.722365	−	0.722365i
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$	2.36396	−	2.36396i	0.0952467	−	0.0952467i
$617$	−2.27208	−	2.27208i	−0.0914704	−	0.0914704i	0.659891	−	0.751361i	$-0.270602\pi$
$617$	−2.27208	−	2.27208i	−0.0914704	−	0.0914704i	−0.751361	+	0.659891i	$0.770602\pi$
$618$	−24.8284	−	24.8284i	−0.998746	−	0.998746i
$619$	−32.5980			−1.31022			−0.655112	−	0.755532i	$-0.727378\pi$
$619$	−32.5980			−1.31022			−0.655112	+	0.755532i	$0.727378\pi$
$620$	0.171573	−	0.343146i	0.00689053	−	0.0137811i
$621$	−15.3137	+	15.3137i	−0.614518	+	0.614518i
$622$	−3.77817	−	3.77817i	−0.151491	−	0.151491i
$623$	11.8579			0.475075
$624$	8.82843	+	8.82843i	0.353420	+	0.353420i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−23.3137			−0.931803
$627$	−0.887302			−0.0354354
$628$	−10.1213	+	10.1213i	−0.403885	+	0.403885i
$629$	18.9497	+	13.5355i	0.755576	+	0.539697i
$630$	1.82843	−	3.65685i	0.0728463	−	0.145693i
$631$	10.8492	−	10.8492i	0.431902	−	0.431902i	−0.457373	−	0.889275i	$-0.651210\pi$
$631$	10.8492	−	10.8492i	0.431902	−	0.431902i	0.889275	+	0.457373i	$0.151210\pi$
$632$	−1.65685	−	1.65685i	−0.0659061	−	0.0659061i
$633$	12.7279	−	12.7279i	0.505889	−	0.505889i
$634$	8.46447	−	8.46447i	0.336167	−	0.336167i
$635$	−7.65685	+	15.3137i	−0.303853	+	0.607706i
$636$	−6.00000			−0.237915
$637$	22.8284			0.904495
$638$	9.67767	+	9.67767i	0.383143	+	0.383143i
$639$			11.6569i			0.461138i
$640$	−0.707107	−	2.12132i	−0.0279508	−	0.0838525i
$641$	−31.2843			−1.23565			−0.617827	−	0.786314i	$-0.711987\pi$
$641$	−31.2843			−1.23565			−0.617827	+	0.786314i	$0.711987\pi$
$642$	14.3431			0.566079
$643$	−41.4853			−1.63602			−0.818010	−	0.575204i	$-0.804923\pi$
$643$	−41.4853			−1.63602			−0.818010	+	0.575204i	$0.804923\pi$
$644$	7.00000	+	7.00000i	0.275839	+	0.275839i
$645$	−28.0000	−	14.0000i	−1.10250	−	0.551249i
$646$	0.656854	+	0.656854i	0.0258436	+	0.0258436i
$647$		−	4.68629i		−	0.184237i	−0.995748	−	0.0921186i	$-0.970636\pi$
$647$		−	4.68629i		−	0.184237i	0.995748	−	0.0921186i	$-0.0293639\pi$
$648$			11.0000i			0.432121i
$649$	12.4853	+	12.4853i	0.490090	+	0.490090i
$650$	−24.9706	+	18.7279i	−0.979426	+	0.734570i
$651$	0.443651	+	0.443651i	0.0173880	+	0.0173880i
$652$	3.34315			0.130928
$653$	−8.34315			−0.326493			−0.163246	−	0.986585i	$-0.552197\pi$
$653$	−8.34315			−0.326493			−0.163246	+	0.986585i	$0.552197\pi$
$654$	25.3137			0.989844
$655$	3.41421	−	6.82843i	0.133404	−	0.266809i
$656$			7.00000i			0.273304i
$657$	−6.00000	−	6.00000i	−0.234082	−	0.234082i
$658$	−0.627417			−0.0244593
$659$	8.14214			0.317173			0.158586	−	0.987345i	$-0.449306\pi$
$659$	8.14214			0.317173			0.158586	+	0.987345i	$0.449306\pi$
$660$	7.31371	+	3.65685i	0.284686	+	0.142343i
$661$	12.2635	−	12.2635i	0.476993	−	0.476993i	−0.427176	−	0.904169i	$-0.640491\pi$
$661$	12.2635	−	12.2635i	0.476993	−	0.476993i	0.904169	+	0.427176i	$0.140491\pi$
$662$	5.41421	−	5.41421i	0.210429	−	0.210429i
$663$	33.7990	+	33.7990i	1.31264	+	1.31264i
$664$	−4.82843	+	4.82843i	−0.187379	+	0.187379i
$665$	−0.313708	−	0.941125i	−0.0121651	−	0.0364953i
$666$	−4.94975	−	3.53553i	−0.191799	−	0.136999i
$667$	−28.6569	+	28.6569i	−1.10960	+	1.10960i
$668$	6.82843			0.264200
$669$	−51.2548			−1.98163
$670$	10.2426	−	20.4853i	0.395708	−	0.791415i
$671$	−19.5772	−	19.5772i	−0.755768	−	0.755768i
$672$	3.65685			0.141066
$673$	−27.4853	−	27.4853i	−1.05948	−	1.05948i	−0.998115	−	0.0613643i	$-0.980455\pi$
$673$	−27.4853	−	27.4853i	−1.05948	−	1.05948i	−0.0613643	−	0.998115i	$-0.519545\pi$
$674$	−5.65685	+	5.65685i	−0.217894	+	0.217894i
$675$	−19.7990	−	2.82843i	−0.762063	−	0.108866i
$676$	25.9706			0.998868
$677$	−30.4853	−	30.4853i	−1.17164	−	1.17164i	−0.981818	−	0.189827i	$-0.939207\pi$
$677$	−30.4853	−	30.4853i	−1.17164	−	1.17164i	−0.189827	−	0.981818i	$-0.560793\pi$
$678$	2.58579	+	2.58579i	0.0993065	+	0.0993065i
$679$	−9.05025	+	9.05025i	−0.347317	+	0.347317i
$680$	−2.70711	−	8.12132i	−0.103813	−	0.311438i
$681$	−13.4142	+	13.4142i	−0.514034	+	0.514034i
$682$	−0.221825	+	0.221825i	−0.00849413	+	0.00849413i
$683$		−	10.3137i		−	0.394643i	−0.980339	−	0.197322i	$-0.936776\pi$
$683$		−	10.3137i		−	0.394643i	0.980339	−	0.197322i	$-0.0632243\pi$
$684$	−0.171573	−	0.171573i	−0.00656025	−	0.00656025i
$685$	−7.89949	+	15.7990i	−0.301824	+	0.603648i
$686$	13.7782	−	13.7782i	0.526053	−	0.526053i
$687$	−2.00000	−	2.00000i	−0.0763048	−	0.0763048i
$688$		−	7.00000i		−	0.266872i
$689$	−13.2426	+	13.2426i	−0.504504	+	0.504504i
$690$	−10.8284	+	21.6569i	−0.412231	+	0.824462i
$691$		−	23.9706i		−	0.911883i	−0.890010	−	0.455942i	$-0.849303\pi$
$691$		−	23.9706i		−	0.911883i	0.890010	−	0.455942i	$-0.150697\pi$
$692$	18.0208	−	18.0208i	0.685049	−	0.685049i
$693$	−2.36396	+	2.36396i	−0.0897995	+	0.0897995i
$694$	−5.31371			−0.201706
$695$	25.0919	−	8.36396i	0.951789	−	0.317263i
$696$			14.9706i			0.567458i
$697$			26.7990i			1.01508i
$698$	24.1421			0.913793
$699$		−	39.7990i		−	1.50534i
$700$	−1.29289	+	9.05025i	−0.0488668	+	0.342067i
$701$	15.6569	+	15.6569i	0.591351	+	0.591351i	0.937996	−	0.346645i	$-0.112679\pi$
$701$	15.6569	+	15.6569i	0.591351	+	0.591351i	−0.346645	+	0.937996i	$0.612679\pi$
$702$	17.6569	+	17.6569i	0.666415	+	0.666415i
$703$	−1.45584	+	0.242641i	−0.0549082	+	0.00915137i
$704$			1.82843i			0.0689114i
$705$	−0.485281	−	1.45584i	−0.0182768	−	0.0548303i
$706$		−	18.6569i		−	0.702160i
$707$	3.97056	+	3.97056i	0.149328	+	0.149328i
$708$			19.3137i			0.725854i
$709$	9.29289	−	9.29289i	0.349002	−	0.349002i	−0.510736	−	0.859738i	$-0.670627\pi$
$709$	9.29289	−	9.29289i	0.349002	−	0.349002i	0.859738	+	0.510736i	$0.170627\pi$
$710$	−8.24264	−	24.7279i	−0.309341	−	0.928022i
$711$	1.65685	+	1.65685i	0.0621369	+	0.0621369i
$712$	−4.58579	+	4.58579i	−0.171860	+	0.171860i
$713$	−0.656854	−	0.656854i	−0.0245994	−	0.0245994i
$714$	14.0000			0.523937
$715$	24.2132	−	8.07107i	0.905522	−	0.301841i
$716$	−2.48528	−	2.48528i	−0.0928793	−	0.0928793i
$717$			47.9411i			1.79039i
$718$	−34.5269			−1.28853
$719$		−	4.14214i		−	0.154476i	−0.997013	−	0.0772378i	$-0.975390\pi$
$719$		−	4.14214i		−	0.154476i	0.997013	−	0.0772378i	$-0.0246101\pi$
$720$	0.707107	+	2.12132i	0.0263523	+	0.0790569i
$721$	−22.6985	+	22.6985i	−0.845336	+	0.845336i
$722$	18.9411			0.704916
$723$	−26.1421			−0.972236
$724$	3.65685			0.135906
$725$	−37.0503	−	5.29289i	−1.37601	−	0.196573i
$726$	10.8284	+	10.8284i	0.401881	+	0.401881i
$727$			42.1421i			1.56297i	0.623927	+	0.781483i	$0.285536\pi$
$727$			42.1421i			1.56297i	−0.623927	+	0.781483i	$0.714464\pi$
$728$	8.07107	−	8.07107i	0.299134	−	0.299134i
$729$			13.0000i			0.481481i
$730$	16.9706	+	8.48528i	0.628109	+	0.314054i
$731$		−	26.7990i		−	0.991196i
$732$		−	30.2843i		−	1.11934i
$733$	26.7487	−	26.7487i	0.987987	−	0.987987i	−0.0119415	−	0.999929i	$-0.503801\pi$
$733$	26.7487	−	26.7487i	0.987987	−	0.987987i	0.999929	+	0.0119415i	$0.00380120\pi$
$734$	25.0919	+	25.0919i	0.926158	+	0.926158i
$735$	14.6274	+	7.31371i	0.539540	+	0.269770i
$736$	−5.41421			−0.199571
$737$	−13.2426	+	13.2426i	−0.487799	+	0.487799i
$738$		−	7.00000i		−	0.257674i
$739$	28.7990			1.05939			0.529694	−	0.848189i	$-0.322307\pi$
$739$	28.7990			1.05939			0.529694	+	0.848189i	$0.322307\pi$
$740$	13.0000	+	4.00000i	0.477890	+	0.147043i
$741$	−3.02944			−0.111289
$742$			5.48528i			0.201371i
$743$	14.9497	−	14.9497i	0.548453	−	0.548453i	−0.377540	−	0.925993i	$-0.623230\pi$
$743$	14.9497	−	14.9497i	0.548453	−	0.548453i	0.925993	+	0.377540i	$0.123230\pi$
$744$	−0.343146			−0.0125803
$745$	0.171573	+	0.514719i	0.00628594	+	0.0188578i
$746$	5.17157	+	5.17157i	0.189345	+	0.189345i
$747$	4.82843	−	4.82843i	0.176663	−	0.176663i
$748$			7.00000i			0.255945i
$749$		−	13.1127i		−	0.479128i
$750$	−22.0000	+	4.00000i	−0.803326	+	0.146059i
$751$			32.0416i			1.16922i	0.811316	+	0.584608i	$0.198752\pi$
$751$			32.0416i			1.16922i	−0.811316	+	0.584608i	$0.801248\pi$
$752$	0.242641	−	0.242641i	0.00884820	−	0.00884820i
$753$			5.37258i			0.195788i
$754$	33.0416	+	33.0416i	1.20331	+	1.20331i
$755$	8.48528	+	25.4558i	0.308811	+	0.926433i
$756$	7.31371			0.265997
$757$	16.3431			0.594002			0.297001	−	0.954877i	$-0.404014\pi$
$757$	16.3431			0.594002			0.297001	+	0.954877i	$0.404014\pi$
$758$	18.0000			0.653789
$759$	14.0000	−	14.0000i	0.508168	−	0.508168i
$760$	0.485281	+	0.242641i	0.0176030	+	0.00880150i
$761$		−	34.3137i		−	1.24387i	−0.783068	−	0.621935i	$-0.786347\pi$
$761$		−	34.3137i		−	1.24387i	0.783068	−	0.621935i	$-0.213653\pi$
$762$	15.3137			0.554757
$763$		−	23.1421i		−	0.837802i
$764$	5.53553	+	5.53553i	0.200269	+	0.200269i
$765$	2.70711	+	8.12132i	0.0978757	+	0.293627i
$766$	−19.4142			−0.701464
$767$	42.6274	+	42.6274i	1.53919	+	1.53919i
$768$	−1.41421	+	1.41421i	−0.0510310	+	0.0510310i
$769$	−24.8284	−	24.8284i	−0.895336	−	0.895336i	0.0996832	−	0.995019i	$-0.468217\pi$
$769$	−24.8284	−	24.8284i	−0.895336	−	0.895336i	−0.995019	+	0.0996832i	$0.968217\pi$
$770$	3.34315	−	6.68629i	0.120479	−	0.240957i
$771$	−18.6274	+	18.6274i	−0.670850	+	0.670850i
$772$			3.51472i			0.126497i
$773$	5.87868	+	5.87868i	0.211441	+	0.211441i	0.804880	−	0.593438i	$-0.202230\pi$
$773$	5.87868	+	5.87868i	0.211441	+	0.211441i	−0.593438	+	0.804880i	$0.702230\pi$
$774$			7.00000i			0.251610i
$775$	0.121320	−	0.849242i	0.00435796	−	0.0305057i
$776$		−	7.00000i		−	0.251285i
$777$	−12.9289	+	18.1005i	−0.463823	+	0.649352i
$778$	−11.7782	−	11.7782i	−0.422268	−	0.422268i
$779$	−1.20101	−	1.20101i	−0.0430307	−	0.0430307i
$780$	24.9706	+	12.4853i	0.894090	+	0.447045i
$781$			21.3137i			0.762664i
$782$	−20.7279			−0.741229
$783$			29.9411i			1.07001i
$784$			3.65685i			0.130602i
$785$	−14.3137	+	28.6274i	−0.510878	+	1.02176i
$786$	−6.82843			−0.243562
$787$	7.75736	−	7.75736i	0.276520	−	0.276520i	−0.555198	−	0.831718i	$-0.687358\pi$
$787$	7.75736	−	7.75736i	0.276520	−	0.276520i	0.831718	+	0.555198i	$0.187358\pi$
$788$	2.00000	−	2.00000i	0.0712470	−	0.0712470i
$789$			18.6863i			0.665250i
$790$	−4.68629	−	2.34315i	−0.166731	−	0.0833654i
$791$	2.36396	−	2.36396i	0.0840528	−	0.0840528i
$792$		−	1.82843i		−	0.0649703i
$793$	−66.8406	−	66.8406i	−2.37358	−	2.37358i
$794$	−8.48528	+	8.48528i	−0.301131	+	0.301131i
$795$	−12.7279	+	4.24264i	−0.451413	+	0.150471i
$796$	−15.8995	−	15.8995i	−0.563543	−	0.563543i
$797$		−	39.2548i		−	1.39048i	−0.718779	−	0.695239i	$-0.755299\pi$
$797$		−	39.2548i		−	1.39048i	0.718779	−	0.695239i	$-0.244701\pi$
$798$	−0.627417	+	0.627417i	−0.0222103	+	0.0222103i
$799$	0.928932	−	0.928932i	0.0328633	−	0.0328633i
$800$	−3.00000	−	4.00000i	−0.106066	−	0.141421i
$801$	4.58579	−	4.58579i	0.162031	−	0.162031i
$802$	−7.07107	−	7.07107i	−0.249688	−	0.249688i
$803$	−10.9706	−	10.9706i	−0.387143	−	0.387143i
$804$	−20.4853			−0.722460
$805$	19.7990	+	9.89949i	0.697823	+	0.348911i
$806$	−0.757359	+	0.757359i	−0.0266768	+	0.0266768i
$807$	30.8284	+	30.8284i	1.08521	+	1.08521i
$808$	−3.07107			−0.108040
$809$	6.02944	+	6.02944i	0.211984	+	0.211984i	0.805110	−	0.593126i	$-0.202106\pi$
$809$	6.02944	+	6.02944i	0.211984	+	0.211984i	−0.593126	+	0.805110i	$0.702106\pi$
$810$	7.77817	+	23.3345i	0.273297	+	0.819892i
$811$	8.97056			0.314999			0.157500	−	0.987519i	$-0.449657\pi$
$811$	8.97056			0.314999			0.157500	+	0.987519i	$0.449657\pi$
$812$	13.6863			0.480295
$813$	−15.6569	+	15.6569i	−0.549110	+	0.549110i
$814$	−9.05025	−	6.46447i	−0.317211	−	0.226579i
$815$	7.09188	−	2.36396i	0.248418	−	0.0828059i
$816$	−5.41421	+	5.41421i	−0.189535	+	0.189535i
$817$	1.20101	+	1.20101i	0.0420180	+	0.0420180i
$818$	19.7990	−	19.7990i	0.692255	−	0.692255i
$819$	−8.07107	+	8.07107i	−0.282026	+	0.282026i
$820$	4.94975	+	14.8492i	0.172853	+	0.518558i
$821$	−10.4437			−0.364486			−0.182243	−	0.983254i	$-0.558336\pi$
$821$	−10.4437			−0.364486			−0.182243	+	0.983254i	$0.558336\pi$
$822$	15.7990			0.551053
$823$	4.97056	+	4.97056i	0.173263	+	0.173263i	0.788411	−	0.615148i	$-0.210904\pi$
$823$	4.97056	+	4.97056i	0.173263	+	0.173263i	−0.615148	+	0.788411i	$0.710904\pi$
$824$		−	17.5563i		−	0.611604i
$825$	18.1005	+	2.58579i	0.630179	+	0.0900255i
$826$	17.6569			0.614361
$827$	−1.82843			−0.0635806			−0.0317903	−	0.999495i	$-0.510121\pi$
$827$	−1.82843			−0.0635806			−0.0317903	+	0.999495i	$0.510121\pi$
$828$	5.41421			0.188157
$829$	24.7487	+	24.7487i	0.859559	+	0.859559i	0.991286	−	0.131727i	$-0.0420522\pi$
$829$	24.7487	+	24.7487i	0.859559	+	0.859559i	−0.131727	+	0.991286i	$0.542052\pi$
$830$	−6.82843	+	13.6569i	−0.237018	+	0.474036i
$831$	−44.9706	−	44.9706i	−1.56001	−	1.56001i
$832$			6.24264i			0.216425i
$833$			14.0000i			0.485071i
$834$	−16.7279	−	16.7279i	−0.579241	−	0.579241i
$835$	14.4853	−	4.82843i	0.501284	−	0.167095i
$836$	−0.313708	−	0.313708i	−0.0108498	−	0.0108498i
$837$	−0.686292			−0.0237217
$838$	6.97056			0.240794
$839$	−45.3553			−1.56584			−0.782920	−	0.622122i	$-0.786271\pi$
$839$	−45.3553			−1.56584			−0.782920	+	0.622122i	$0.786271\pi$
$840$	7.75736	−	2.58579i	0.267654	−	0.0892181i
$841$			27.0294i			0.932050i
$842$	2.68629	+	2.68629i	0.0925757	+	0.0925757i
$843$	−11.3137			−0.389665
$844$	9.00000			0.309793
$845$	55.0919	−	18.3640i	1.89522	−	0.631739i
$846$	−0.242641	+	0.242641i	−0.00834216	+	0.00834216i
$847$	9.89949	−	9.89949i	0.340151	−	0.340151i
$848$	−2.12132	−	2.12132i	−0.0728464	−	0.0728464i
$849$	−39.5980	+	39.5980i	−1.35900	+	1.35900i
$850$	−11.4853	−	15.3137i	−0.393942	−	0.525256i
$851$	19.1421	−	26.7990i	0.656184	−	0.918658i
$852$	−16.4853	+	16.4853i	−0.564776	+	0.564776i
$853$	−32.8284			−1.12402			−0.562012	−	0.827129i	$-0.689973\pi$
$853$	−32.8284			−1.12402			−0.562012	+	0.827129i	$0.689973\pi$
$854$	−27.6863			−0.947405
$855$	−0.485281	−	0.242641i	−0.0165963	−	0.00829814i
$856$	5.07107	+	5.07107i	0.173326	+	0.173326i
$857$	−15.1421			−0.517245			−0.258623	−	0.965978i	$-0.583269\pi$
$857$	−15.1421			−0.517245			−0.258623	+	0.965978i	$0.583269\pi$
$858$	−16.1421	−	16.1421i	−0.551083	−	0.551083i
$859$	−5.44365	+	5.44365i	−0.185735	+	0.185735i	−0.793849	−	0.608114i	$-0.791926\pi$
$859$	−5.44365	+	5.44365i	−0.185735	+	0.185735i	0.608114	+	0.793849i	$0.291926\pi$
$860$	−4.94975	−	14.8492i	−0.168785	−	0.506355i
$861$	−25.5980			−0.872377
$862$	−20.5061	−	20.5061i	−0.698440	−	0.698440i
$863$	19.2929	+	19.2929i	0.656738	+	0.656738i	0.954607	−	0.297869i	$-0.0962759\pi$
$863$	19.2929	+	19.2929i	0.656738	+	0.656738i	−0.297869	+	0.954607i	$0.596276\pi$
$864$	−2.82843	+	2.82843i	−0.0962250	+	0.0962250i
$865$	25.4853	−	50.9706i	0.866526	−	1.73305i
$866$	−23.1421	+	23.1421i	−0.786402	+	0.786402i
$867$	3.31371	−	3.31371i	0.112539	−	0.112539i
$868$			0.313708i			0.0106480i
$869$	3.02944	+	3.02944i	0.102767	+	0.102767i
$870$	10.5858	+	31.7574i	0.358892	+	1.07668i
$871$	−45.2132	+	45.2132i	−1.53199	+	1.53199i
$872$	8.94975	+	8.94975i	0.303077	+	0.303077i
$873$			7.00000i			0.236914i
$874$	0.928932	−	0.928932i	0.0314216	−	0.0314216i
$875$	3.65685	+	20.1127i	0.123624	+	0.679933i
$876$		−	16.9706i		−	0.573382i
$877$	10.0208	−	10.0208i	0.338379	−	0.338379i	−0.517378	−	0.855757i	$-0.673092\pi$
$877$	10.0208	−	10.0208i	0.338379	−	0.338379i	0.855757	+	0.517378i	$0.173092\pi$
$878$	17.7782	−	17.7782i	0.599984	−	0.599984i
$879$	−38.9706			−1.31444
$880$	1.29289	+	3.87868i	0.0435834	+	0.130750i
$881$			7.48528i			0.252186i	0.992018	+	0.126093i	$0.0402437\pi$
$881$			7.48528i			0.252186i	−0.992018	+	0.126093i	$0.959756\pi$
$882$		−	3.65685i		−	0.123133i
$883$	53.6274			1.80471			0.902353	−	0.430997i	$-0.141838\pi$
$883$	53.6274			1.80471			0.902353	+	0.430997i	$0.141838\pi$
$884$			23.8995i			0.803827i
$885$	13.6569	+	40.9706i	0.459070	+	1.37721i
$886$	16.6569	+	16.6569i	0.559598	+	0.559598i
$887$	38.0624	+	38.0624i	1.27801	+	1.27801i	0.941779	+	0.336233i	$0.109153\pi$
$887$	38.0624	+	38.0624i	1.27801	+	1.27801i	0.336233	+	0.941779i	$0.390847\pi$
$888$	−2.00000	−	12.0000i	−0.0671156	−	0.402694i
$889$		−	14.0000i		−	0.469545i
$890$	−6.48528	+	12.9706i	−0.217387	+	0.434774i
$891$		−	20.1127i		−	0.673801i
$892$	−18.1213	−	18.1213i	−0.606747	−	0.606747i
$893$			0.0832611i			0.00278623i
$894$	0.343146	−	0.343146i	0.0114765	−	0.0114765i
$895$	−7.02944	−	3.51472i	−0.234968	−	0.117484i
$896$	1.29289	+	1.29289i	0.0431925	+	0.0431925i
$897$	47.7990	−	47.7990i	1.59596	−	1.59596i
$898$	−19.6274	−	19.6274i	−0.654975	−	0.654975i
$899$	−1.28427			−0.0428328
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	−8.12132	−	8.12132i	−0.270560	−	0.270560i
$902$		−	12.7990i		−	0.426160i
$903$	25.5980			0.851847
$904$			1.82843i			0.0608126i
$905$	7.75736	−	2.58579i	0.257863	−	0.0859544i
$906$	16.9706	−	16.9706i	0.563809	−	0.563809i
$907$	−14.0000			−0.464862			−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000			−0.464862			−0.232431	+	0.972613i	$0.574668\pi$
$908$	−9.48528			−0.314780
$909$	3.07107			0.101861
$910$	11.4142	−	22.8284i	0.378377	−	0.756755i
$911$	27.4142	+	27.4142i	0.908273	+	0.908273i	0.996133	−	0.0878595i	$-0.0280026\pi$
$911$	27.4142	+	27.4142i	0.908273	+	0.908273i	−0.0878595	+	0.996133i	$0.528003\pi$
$912$		−	0.485281i		−	0.0160693i
$913$	8.82843	−	8.82843i	0.292178	−	0.292178i
$914$			26.3137i			0.870380i
$915$	−21.4142	−	64.2426i	−0.707932	−	2.12380i
$916$		−	1.41421i		−	0.0467269i
$917$			6.24264i			0.206150i
$918$	−10.8284	+	10.8284i	−0.357391	+	0.357391i
$919$	10.6274	+	10.6274i	0.350566	+	0.350566i	0.860320	−	0.509754i	$-0.170264\pi$
$919$	10.6274	+	10.6274i	0.350566	+	0.350566i	−0.509754	+	0.860320i	$0.670264\pi$
$920$	−11.4853	+	3.82843i	−0.378659	+	0.126220i
$921$	−50.6274			−1.66823
$922$	17.5355	−	17.5355i	0.577502	−	0.577502i
$923$			72.7696i			2.39524i
$924$	−6.68629			−0.219963
$925$	30.4056	−	0.707107i	0.999730	−	0.0232495i
$926$	−37.9411			−1.24682
$927$			17.5563i			0.576626i
$928$	−5.29289	+	5.29289i	−0.173748	+	0.173748i
$929$	20.6569			0.677729			0.338865	−	0.940835i	$-0.389957\pi$
$929$	20.6569			0.677729			0.338865	+	0.940835i	$0.389957\pi$
$930$	−0.727922	+	0.242641i	−0.0238695	+	0.00795650i
$931$	−0.627417	−	0.627417i	−0.0205628	−	0.0205628i
$932$	14.0711	−	14.0711i	0.460913	−	0.460913i
$933$			10.6863i			0.349853i
$934$			20.3137i			0.664685i
$935$	4.94975	+	14.8492i	0.161874	+	0.485622i
$936$		−	6.24264i		−	0.204047i
$937$	7.41421	−	7.41421i	0.242212	−	0.242212i	−0.575553	−	0.817765i	$-0.695213\pi$
$937$	7.41421	−	7.41421i	0.242212	−	0.242212i	0.817765	+	0.575553i	$0.195213\pi$
$938$			18.7279i			0.611488i
$939$	32.9706	+	32.9706i	1.07595	+	1.07595i
$940$	0.343146	−	0.686292i	0.0111922	−	0.0223844i
$941$	35.0711			1.14328			0.571642	−	0.820503i	$-0.306307\pi$
$941$	35.0711			1.14328			0.571642	+	0.820503i	$0.306307\pi$
$942$	28.6274			0.932732
$943$	37.8995			1.23418
$944$	−6.82843	+	6.82843i	−0.222246	+	0.222246i
$945$	15.5147	−	5.17157i	0.504694	−	0.168231i
$946$			12.7990i			0.416131i
$947$	30.7990			1.00083			0.500416	−	0.865785i	$-0.333180\pi$
$947$	30.7990			1.00083			0.500416	+	0.865785i	$0.333180\pi$
$948$			4.68629i			0.152204i
$949$	−37.4558	−	37.4558i	−1.21587	−	1.21587i
$950$	1.20101	+	0.171573i	0.0389659	+	0.00556656i
$951$	−23.9411			−0.776344
$952$	4.94975	+	4.94975i	0.160422	+	0.160422i
$953$	31.6569	−	31.6569i	1.02547	−	1.02547i	0.0257989	−	0.999667i	$-0.491787\pi$
$953$	31.6569	−	31.6569i	1.02547	−	1.02547i	0.999667	−	0.0257989i	$-0.00821297\pi$
$954$	2.12132	+	2.12132i	0.0686803	+	0.0686803i
$955$	15.6569	+	7.82843i	0.506644	+	0.253322i
$956$	−16.9497	+	16.9497i	−0.548194	+	0.548194i
$957$		−	27.3726i		−	0.884830i
$958$	15.5563	+	15.5563i	0.502603	+	0.502603i
$959$		−	14.4437i		−	0.466410i
$960$	−2.00000	+	4.00000i	−0.0645497	+	0.129099i
$961$			30.9706i			0.999050i
$962$	−30.8995	−	22.0711i	−0.996240	−	0.711600i
$963$	−5.07107	−	5.07107i	−0.163413	−	0.163413i
$964$	−9.24264	−	9.24264i	−0.297685	−	0.297685i
$965$	2.48528	+	7.45584i	0.0800040	+	0.240012i
$966$		−	19.7990i		−	0.637022i
$967$	13.9411			0.448316			0.224158	−	0.974553i	$-0.428037\pi$
$967$	13.9411			0.448316			0.224158	+	0.974553i	$0.428037\pi$
$968$			7.65685i			0.246101i
$969$		−	1.85786i		−	0.0596832i
$970$	−4.94975	−	14.8492i	−0.158927	−	0.476780i
$971$	19.7696			0.634435			0.317218	−	0.948353i	$-0.397251\pi$
$971$	19.7696			0.634435			0.317218	+	0.948353i	$0.397251\pi$
$972$	7.07107	−	7.07107i	0.226805	−	0.226805i
$973$	−15.2929	+	15.2929i	−0.490268	+	0.490268i
$974$			6.97056i			0.223351i
$975$	61.7990	+	8.82843i	1.97915	+	0.282736i
$976$	10.7071	−	10.7071i	0.342726	−	0.342726i
$977$		−	49.4853i		−	1.58317i	−0.611056	−	0.791587i	$-0.709255\pi$
$977$		−	49.4853i		−	1.58317i	0.611056	−	0.791587i	$-0.290745\pi$
$978$	−4.72792	−	4.72792i	−0.151182	−	0.151182i
$979$	8.38478	−	8.38478i	0.267979	−	0.267979i
$980$	2.58579	+	7.75736i	0.0825999	+	0.247800i
$981$	−8.94975	−	8.94975i	−0.285743	−	0.285743i
$982$			21.7990i			0.695634i
$983$	9.39340	−	9.39340i	0.299603	−	0.299603i	−0.541255	−	0.840858i	$-0.682051\pi$
$983$	9.39340	−	9.39340i	0.299603	−	0.299603i	0.840858	+	0.541255i	$0.182051\pi$
$984$	9.89949	−	9.89949i	0.315584	−	0.315584i
$985$	2.82843	−	5.65685i	0.0901212	−	0.180242i
$986$	−20.2635	+	20.2635i	−0.645320	+	0.645320i
$987$	0.887302	+	0.887302i	0.0282431	+	0.0282431i
$988$	−1.07107	−	1.07107i	−0.0340752	−	0.0340752i
$989$	−37.8995			−1.20513
$990$	−1.29289	−	3.87868i	−0.0410908	−	0.123273i
$991$	9.15076	−	9.15076i	0.290683	−	0.290683i	−0.546667	−	0.837350i	$-0.684104\pi$
$991$	9.15076	−	9.15076i	0.290683	−	0.290683i	0.837350	+	0.546667i	$0.184104\pi$
$992$	−0.121320	−	0.121320i	−0.00385192	−	0.00385192i
$993$	−15.3137			−0.485966
$994$	15.0711	+	15.0711i	0.478025	+	0.478025i
$995$	−44.9706	−	22.4853i	−1.42566	−	0.712831i
$996$	13.6569			0.432734
$997$	−13.4558			−0.426151			−0.213075	−	0.977036i	$-0.568348\pi$
$997$	−13.4558			−0.426151			−0.213075	+	0.977036i	$0.568348\pi$
$998$	−1.75736	+	1.75736i	−0.0556282	+	0.0556282i
$999$	−4.00000	−	24.0000i	−0.126554	−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.c.43.1	✓	4
5.2	odd	4		370.2.h.c.117.2	yes	4
37.31	odd	4		370.2.h.c.253.2	yes	4
185.142	even	4	inner	370.2.g.c.327.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.c.43.1	✓	4	1.1	even	1	trivial
370.2.g.c.327.1	yes	4	185.142	even	4	inner
370.2.h.c.117.2	yes	4	5.2	odd	4
370.2.h.c.253.2	yes	4	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.41421 + 1.41421i) q^{3} -1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 - 1.29289i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.41421 + 1.41421i) q^{3} -1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 - 1.29289i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 + 2.12132i) q^{10} -1.82843i q^{11} +(1.41421 - 1.41421i) q^{12} -6.24264i q^{13} +(-1.29289 - 1.29289i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} +3.82843 q^{17} -1.00000 q^{18} +(-0.171573 + 0.171573i) q^{19} +(2.12132 - 0.707107i) q^{20} +3.65685i q^{21} -1.82843 q^{22} -5.41421i q^{23} +(-1.41421 - 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} -6.24264 q^{26} +(-2.82843 - 2.82843i) q^{27} +(-1.29289 + 1.29289i) q^{28} +(-5.29289 - 5.29289i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(0.121320 - 0.121320i) q^{31} -1.00000i q^{32} +(2.58579 + 2.58579i) q^{33} -3.82843i q^{34} +(-1.82843 + 3.65685i) q^{35} +1.00000i q^{36} +(4.94975 + 3.53553i) q^{37} +(0.171573 + 0.171573i) q^{38} +(8.82843 + 8.82843i) q^{39} +(-0.707107 - 2.12132i) q^{40} +7.00000i q^{41} +3.65685 q^{42} -7.00000i q^{43} +1.82843i q^{44} +(0.707107 + 2.12132i) q^{45} -5.41421 q^{46} +(0.242641 - 0.242641i) q^{47} +(-1.41421 + 1.41421i) q^{48} +3.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-5.41421 + 5.41421i) q^{51} +6.24264i q^{52} +(-2.12132 - 2.12132i) q^{53} +(-2.82843 + 2.82843i) q^{54} +(1.29289 + 3.87868i) q^{55} +(1.29289 + 1.29289i) q^{56} -0.485281i q^{57} +(-5.29289 + 5.29289i) q^{58} +(-6.82843 + 6.82843i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(10.7071 - 10.7071i) q^{61} +(-0.121320 - 0.121320i) q^{62} +(-1.29289 - 1.29289i) q^{63} -1.00000 q^{64} +(4.41421 + 13.2426i) q^{65} +(2.58579 - 2.58579i) q^{66} +(-7.24264 - 7.24264i) q^{67} -3.82843 q^{68} +(7.65685 + 7.65685i) q^{69} +(3.65685 + 1.82843i) q^{70} -11.6569 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-1.41421 + 9.89949i) q^{75} +(0.171573 - 0.171573i) q^{76} +(-2.36396 - 2.36396i) q^{77} +(8.82843 - 8.82843i) q^{78} +(-1.65685 + 1.65685i) q^{79} +(-2.12132 + 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(4.82843 + 4.82843i) q^{83} -3.65685i q^{84} +(-8.12132 + 2.70711i) q^{85} -7.00000 q^{86} +14.9706 q^{87} +1.82843 q^{88} +(4.58579 + 4.58579i) q^{89} +(2.12132 - 0.707107i) q^{90} +(-8.07107 - 8.07107i) q^{91} +5.41421i q^{92} +0.343146i q^{93} +(-0.242641 - 0.242641i) q^{94} +(0.242641 - 0.485281i) q^{95} +(1.41421 + 1.41421i) q^{96} -7.00000 q^{97} +3.65685 q^{98} -1.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^7	\( 4 q - 4 q^{4} + 8 q^{7} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 4 q^{22} + 16 q^{25} - 8 q^{26} - 8 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} + 16 q^{33} + 4 q^{35} + 12 q^{38} + 24 q^{39} - 8 q^{42} - 16 q^{46} - 16 q^{47} - 12 q^{50} - 16 q^{51} + 8 q^{55} + 8 q^{56} - 24 q^{58} - 16 q^{59} - 8 q^{60} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 4 q^{64} + 12 q^{65} + 16 q^{66} - 12 q^{67} - 4 q^{68} + 8 q^{69} - 8 q^{70} - 24 q^{71} + 4 q^{72} + 24 q^{73} + 12 q^{76} + 16 q^{77} + 24 q^{78} + 16 q^{79} + 44 q^{81} + 28 q^{82} + 8 q^{83} - 24 q^{85} - 28 q^{86} - 8 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} - 28 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^7 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 4 * q^22 + 16 * q^25 - 8 * q^26 - 8 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 + 16 * q^33 + 4 * q^35 + 12 * q^38 + 24 * q^39 - 8 * q^42 - 16 * q^46 - 16 * q^47 - 12 * q^50 - 16 * q^51 + 8 * q^55 + 8 * q^56 - 24 * q^58 - 16 * q^59 - 8 * q^60 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 4 * q^64 + 12 * q^65 + 16 * q^66 - 12 * q^67 - 4 * q^68 + 8 * q^69 - 8 * q^70 - 24 * q^71 + 4 * q^72 + 24 * q^73 + 12 * q^76 + 16 * q^77 + 24 * q^78 + 16 * q^79 + 44 * q^81 + 28 * q^82 + 8 * q^83 - 24 * q^85 - 28 * q^86 - 8 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^91 + 16 * q^94 - 16 * q^95 - 28 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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