LMFDB - Embedded newform 370.2.h.c.117.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
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			117.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	370.117
Dual form			370.2.h.c.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	0.985599	−	0.169102i	$-0.0540867\pi$
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	−0.169102	+	0.985599i	$0.554087\pi$
$4$	1.00000			0.500000
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$	1.41421	+	1.41421i	0.577350	+	0.577350i
$7$	1.29289	+	1.29289i	0.488668	+	0.488668i	0.907886	−	0.419218i	$-0.137696\pi$
$7$	1.29289	+	1.29289i	0.488668	+	0.488668i	−0.419218	+	0.907886i	$0.637696\pi$
$8$	1.00000			0.353553
$9$			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
$13$	−6.24264			−1.73140			−0.865699	−	0.500566i	$-0.833125\pi$
$13$	−6.24264			−1.73140			−0.865699	+	0.500566i	$0.833125\pi$
$14$	1.29289	+	1.29289i	0.345540	+	0.345540i
$15$	4.00000	−	2.00000i	1.03280	−	0.516398i
$16$	1.00000			0.250000
$17$			3.82843i			0.928530i	0.885696	+	0.464265i	$0.153681\pi$
$17$			3.82843i			0.928530i	−0.885696	+	0.464265i	$0.846319\pi$
$18$			1.00000i			0.235702i
$19$	0.171573	−	0.171573i	0.0393615	−	0.0393615i	−0.687152	−	0.726514i	$-0.741139\pi$
$19$	0.171573	−	0.171573i	0.0393615	−	0.0393615i	0.726514	+	0.687152i	$0.241139\pi$
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$			3.65685i			0.797991i
$22$		−	1.82843i		−	0.389822i
$23$	−5.41421			−1.12894			−0.564471	−	0.825453i	$-0.690920\pi$
$23$	−5.41421			−1.12894			−0.564471	+	0.825453i	$0.690920\pi$
$24$	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	0.999856	−	0.0169901i	$-0.00540837\pi$
$29$	5.29289	+	5.29289i	0.982866	+	0.982866i	−0.0169901	+	0.999856i	$0.505408\pi$
$30$	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	$0.245095\pi$
$32$	1.00000			0.176777
$33$	2.58579	−	2.58579i	0.450128	−	0.450128i
$34$			3.82843i			0.656570i
$35$	3.65685	−	1.82843i	0.618121	−	0.309061i
$36$			1.00000i			0.166667i
$37$	−3.53553	+	4.94975i	−0.581238	+	0.813733i
$37$	−3.53553	+	4.94975i	−0.581238	+	0.813733i
$38$	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	$0.815919\pi$
$42$			3.65685i			0.564265i
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$		−	1.82843i		−	0.275646i
$45$	2.12132	+	0.707107i	0.316228	+	0.105409i
$46$	−5.41421			−0.798282
$47$	0.242641	+	0.242641i	0.0353928	+	0.0353928i	0.724582	−	0.689189i	$-0.242033\pi$
$47$	0.242641	+	0.242641i	0.0353928	+	0.0353928i	−0.689189	+	0.724582i	$0.742033\pi$
$48$	1.41421	+	1.41421i	0.204124	+	0.204124i
$49$		−	3.65685i		−	0.522408i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−5.41421	+	5.41421i	−0.758142	+	0.758142i
$52$	−6.24264			−0.865699
$53$	−2.12132	+	2.12132i	−0.291386	+	0.291386i	−0.837628	−	0.546242i	$-0.816058\pi$
$53$	−2.12132	+	2.12132i	−0.291386	+	0.291386i	0.546242	+	0.837628i	$0.316058\pi$
$54$	2.82843	−	2.82843i	0.384900	−	0.384900i
$55$	−3.87868	−	1.29289i	−0.523001	−	0.174334i
$56$	1.29289	+	1.29289i	0.172770	+	0.172770i
$57$	0.485281			0.0642771
$58$	5.29289	+	5.29289i	0.694991	+	0.694991i
$59$	6.82843	−	6.82843i	0.888985	−	0.888985i	−0.105440	−	0.994426i	$-0.533625\pi$
$59$	6.82843	−	6.82843i	0.888985	−	0.888985i	0.994426	+	0.105440i	$0.0336251\pi$
$60$	4.00000	−	2.00000i	0.516398	−	0.258199i
$61$	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	$-0.534826\pi$
$67$	7.24264	−	7.24264i	0.884829	−	0.884829i	0.994021	+	0.109191i	$0.0348261\pi$
$68$			3.82843i			0.464265i
$69$	−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	$0.743141\pi$
$72$			1.00000i			0.117851i
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	0.262646	−	0.964892i	$-0.415405\pi$
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	−0.964892	+	0.262646i	$0.915405\pi$
$74$	−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	−0.607732	−	0.794142i	$-0.707920\pi$
$79$	1.65685	−	1.65685i	0.186411	−	0.186411i	0.794142	+	0.607732i	$0.207920\pi$
$80$	0.707107	−	2.12132i	0.0790569	−	0.237171i
$81$	11.0000			1.22222
$82$			7.00000i			0.773021i
$83$	4.82843	−	4.82843i	0.529989	−	0.529989i	−0.390580	−	0.920569i	$-0.627726\pi$
$83$	4.82843	−	4.82843i	0.529989	−	0.529989i	0.920569	+	0.390580i	$0.127726\pi$
$84$			3.65685i			0.398996i
$85$	8.12132	+	2.70711i	0.880881	+	0.293627i
$86$	−7.00000			−0.754829
$87$			14.9706i			1.60501i
$88$		−	1.82843i		−	0.194911i
$89$	−4.58579	−	4.58579i	−0.486092	−	0.486092i	0.420978	−	0.907071i	$-0.361687\pi$
$89$	−4.58579	−	4.58579i	−0.486092	−	0.486092i	−0.907071	+	0.420978i	$0.861687\pi$
$90$	2.12132	+	0.707107i	0.223607	+	0.0745356i
$91$	−8.07107	−	8.07107i	−0.846078	−	0.846078i
$92$	−5.41421			−0.564471
$93$	0.343146			0.0355826
$94$	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
$97$		−	7.00000i		−	0.710742i	−0.934725	−	0.355371i	$-0.884354\pi$
$97$		−	7.00000i		−	0.710742i	0.934725	−	0.355371i	$-0.115646\pi$
$98$		−	3.65685i		−	0.369398i
$99$	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
$103$			17.5563i			1.72988i	0.501877	+	0.864939i	$0.332643\pi$
$103$			17.5563i			1.72988i	−0.501877	+	0.864939i	$0.667357\pi$
$104$	−6.24264			−0.612141
$105$	7.75736	+	2.58579i	0.757041	+	0.252347i
$106$	−2.12132	+	2.12132i	−0.206041	+	0.206041i
$107$	5.07107	+	5.07107i	0.490239	+	0.490239i	0.908381	−	0.418143i	$-0.137319\pi$
$107$	5.07107	+	5.07107i	0.490239	+	0.490239i	−0.418143	+	0.908381i	$0.637319\pi$
$108$	2.82843	−	2.82843i	0.272166	−	0.272166i
$109$	−8.94975	+	8.94975i	−0.857230	+	0.857230i	−0.991011	−	0.133781i	$-0.957288\pi$
$109$	−8.94975	+	8.94975i	−0.857230	+	0.857230i	0.133781	+	0.991011i	$0.457288\pi$
$110$	−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
$113$		−	1.82843i		−	0.172004i	−0.996295	−	0.0860020i	$-0.972591\pi$
$113$		−	1.82843i		−	0.172004i	0.996295	−	0.0860020i	$-0.0274091\pi$
$114$	0.485281			0.0454508
$115$	−3.82843	+	11.4853i	−0.357003	+	1.07101i
$116$	5.29289	+	5.29289i	0.491433	+	0.491433i
$117$		−	6.24264i		−	0.577132i
$118$	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
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	−1.29289	+	1.29289i	−0.115180	+	0.115180i
$127$	5.41421	+	5.41421i	0.480434	+	0.480434i	0.905270	−	0.424836i	$-0.139668\pi$
$127$	5.41421	+	5.41421i	0.480434	+	0.480434i	−0.424836	+	0.905270i	$0.639668\pi$
$128$	1.00000			0.0883883
$129$	−9.89949	−	9.89949i	−0.871602	−	0.871602i
$130$	−4.41421	+	13.2426i	−0.387152	+	1.16146i
$131$	−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
$133$	0.443651			0.0384694
$134$	7.24264	−	7.24264i	0.625669	−	0.625669i
$135$	−4.00000	−	8.00000i	−0.344265	−	0.688530i
$136$			3.82843i			0.328285i
$137$	5.58579	+	5.58579i	0.477226	+	0.477226i	0.904243	−	0.427017i	$-0.140436\pi$
$137$	5.58579	+	5.58579i	0.477226	+	0.477226i	−0.427017	+	0.904243i	$0.640436\pi$
$138$	−7.65685	−	7.65685i	−0.651795	−	0.651795i
$139$	11.8284			1.00327			0.501637	−	0.865078i	$-0.332731\pi$
$139$	11.8284			1.00327			0.501637	+	0.865078i	$0.332731\pi$
$140$	3.65685	−	1.82843i	0.309061	−	0.154530i
$141$			0.686292i			0.0577962i
$142$	−11.6569			−0.978221
$143$			11.4142i			0.954504i
$144$			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
$148$	−3.53553	+	4.94975i	−0.290619	+	0.406867i
$149$			0.242641i			0.0198779i	0.999951	+	0.00993895i	$0.00316372\pi$
$149$			0.242641i			0.0198779i	−0.999951	+	0.00993895i	$0.996836\pi$
$150$	−1.41421	−	9.89949i	−0.115470	−	0.808290i
$151$		−	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
$153$	−3.82843			−0.309510
$154$	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	0.984296	−	0.176527i	$-0.0564862\pi$
$157$	10.1213	+	10.1213i	0.807769	+	0.807769i	−0.176527	+	0.984296i	$0.556486\pi$
$158$	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
$162$	11.0000			0.864242
$163$			3.34315i			0.261855i	0.991392	+	0.130928i	$0.0417956\pi$
$163$			3.34315i			0.261855i	−0.991392	+	0.130928i	$0.958204\pi$
$164$			7.00000i			0.546608i
$165$	−3.65685	−	7.31371i	−0.284686	−	0.569371i
$166$	4.82843	−	4.82843i	0.374759	−	0.374759i
$167$		−	6.82843i		−	0.528400i	−0.964468	−	0.264200i	$-0.914892\pi$
$167$		−	6.82843i		−	0.528400i	0.964468	−	0.264200i	$-0.0851078\pi$
$168$			3.65685i			0.282132i
$169$	25.9706			1.99774
$170$	8.12132	+	2.70711i	0.622877	+	0.207626i
$171$	0.171573	+	0.171573i	0.0131205	+	0.0131205i
$172$	−7.00000			−0.533745
$173$	18.0208	+	18.0208i	1.37010	+	1.37010i	0.860287	+	0.509810i	$0.170284\pi$
$173$	18.0208	+	18.0208i	1.37010	+	1.37010i	0.509810	+	0.860287i	$0.329716\pi$
$174$			14.9706i			1.13492i
$175$	−1.29289	−	9.05025i	−0.0977335	−	0.684135i
$176$		−	1.82843i		−	0.137823i
$177$	19.3137			1.45171
$178$	−4.58579	−	4.58579i	−0.343719	−	0.343719i
$179$	−2.48528	−	2.48528i	−0.185759	−	0.185759i	0.608101	−	0.793860i	$-0.291932\pi$
$179$	−2.48528	−	2.48528i	−0.185759	−	0.185759i	−0.793860	+	0.608101i	$0.791932\pi$
$180$	2.12132	+	0.707107i	0.158114	+	0.0527046i
$181$	−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
$183$	30.2843			2.23868
$184$	−5.41421			−0.399141
$185$	8.00000	+	11.0000i	0.588172	+	0.808736i
$186$	0.343146			0.0251607
$187$	7.00000			0.511891
$188$	0.242641	+	0.242641i	0.0176964	+	0.0176964i
$189$	7.31371			0.531994
$190$	−0.242641	−	0.485281i	−0.0176030	−	0.0352060i
$191$	−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
$193$	−3.51472			−0.252995			−0.126497	−	0.991967i	$-0.540374\pi$
$193$	−3.51472			−0.252995			−0.126497	+	0.991967i	$0.540374\pi$
$194$		−	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	0.632261	−	0.774755i	$-0.282127\pi$
$197$	−2.00000	−	2.00000i	−0.142494	−	0.142494i	−0.774755	+	0.632261i	$0.782127\pi$
$198$	1.82843			0.129941
$199$	−15.8995	−	15.8995i	−1.12709	−	1.12709i	−0.990649	−	0.136436i	$-0.956435\pi$
$199$	−15.8995	−	15.8995i	−1.12709	−	1.12709i	−0.136436	−	0.990649i	$-0.543565\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	20.4853			1.44492
$202$			3.07107i			0.216080i
$203$			13.6863i			0.960589i
$204$	−5.41421	+	5.41421i	−0.379071	+	0.379071i
$205$	14.8492	+	4.94975i	1.03712	+	0.345705i
$206$			17.5563i			1.22321i
$207$		−	5.41421i		−	0.376314i
$208$	−6.24264			−0.432849
$209$	−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
$217$	0.313708			0.0212959
$218$	−8.94975	+	8.94975i	−0.606153	+	0.606153i
$219$		−	16.9706i		−	1.14676i
$220$	−3.87868	−	1.29289i	−0.261501	−	0.0871668i
$221$		−	23.8995i		−	1.60765i
$222$	−12.0000	+	2.00000i	−0.805387	+	0.134231i
$223$	18.1213	−	18.1213i	1.21349	−	1.21349i	0.243623	−	0.969870i	$-0.421664\pi$
$223$	18.1213	−	18.1213i	1.21349	−	1.21349i	0.969870	−	0.243623i	$-0.0783361\pi$
$224$	1.29289	+	1.29289i	0.0863851	+	0.0863851i
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$		−	1.82843i		−	0.121625i
$227$			9.48528i			0.629560i	0.949165	+	0.314780i	$0.101931\pi$
$227$			9.48528i			0.629560i	−0.949165	+	0.314780i	$0.898069\pi$
$228$	0.485281			0.0321385
$229$		−	1.41421i		−	0.0934539i	−0.998908	−	0.0467269i	$-0.985121\pi$
$229$		−	1.41421i		−	0.0934539i	0.998908	−	0.0467269i	$-0.0148791\pi$
$230$	−3.82843	+	11.4853i	−0.252439	+	0.757317i
$231$	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	$-0.0240017\pi$
$233$	14.0711	+	14.0711i	0.921826	+	0.921826i	−0.0753322	+	0.997158i	$0.524002\pi$
$234$		−	6.24264i		−	0.408094i
$235$	0.686292	−	0.343146i	0.0447687	−	0.0223844i
$236$	6.82843	−	6.82843i	0.444493	−	0.444493i
$237$	4.68629			0.304407
$238$	−4.94975	+	4.94975i	−0.320844	+	0.320844i
$239$	−16.9497	+	16.9497i	−1.09639	+	1.09639i	−0.101558	+	0.994830i	$0.532383\pi$
$239$	−16.9497	+	16.9497i	−1.09639	+	1.09639i	−0.994830	+	0.101558i	$0.967617\pi$
$240$	4.00000	−	2.00000i	0.258199	−	0.129099i
$241$	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	$0.611682\pi$
$242$	7.65685			0.492201
$243$	7.07107	+	7.07107i	0.453609	+	0.453609i
$244$	10.7071	−	10.7071i	0.685452	−	0.685452i
$245$	−7.75736	−	2.58579i	−0.495600	−	0.165200i
$246$	−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
$253$			9.89949i			0.622376i
$254$	5.41421	+	5.41421i	0.339718	+	0.339718i
$255$	7.65685	+	15.3137i	0.479491	+	0.958982i
$256$	1.00000			0.0625000
$257$			13.1716i			0.821620i	0.911721	+	0.410810i	$0.134754\pi$
$257$			13.1716i			0.821620i	−0.911721	+	0.410810i	$0.865246\pi$
$258$	−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	$-0.343011\pi$
$263$	−6.60660	−	6.60660i	−0.407381	−	0.407381i	−0.880824	+	0.473444i	$0.843011\pi$
$264$	2.58579	−	2.58579i	0.159144	−	0.159144i
$265$	3.00000	+	6.00000i	0.184289	+	0.368577i
$266$	0.443651			0.0272020
$267$		−	12.9706i		−	0.793786i
$268$	7.24264	−	7.24264i	0.442415	−	0.442415i
$269$			21.7990i			1.32911i	0.747240	+	0.664554i	$0.231378\pi$
$269$			21.7990i			1.32911i	−0.747240	+	0.664554i	$0.768622\pi$
$270$	−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	$0.390838\pi$
$272$			3.82843i			0.232132i
$273$		−	22.8284i		−	1.38164i
$274$	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
$277$	−31.7990			−1.91062			−0.955308	−	0.295612i	$-0.904476\pi$
$277$	−31.7990			−1.91062			−0.955308	+	0.295612i	$0.904476\pi$
$278$	11.8284			0.709422
$279$	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	$0.696033\pi$
$282$			0.686292i			0.0408681i
$283$		−	28.0000i		−	1.66443i	−0.554455	−	0.832214i	$-0.687073\pi$
$283$		−	28.0000i		−	1.66443i	0.554455	−	0.832214i	$-0.312927\pi$
$284$	−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
$288$			1.00000i			0.0589256i
$289$	2.34315			0.137832
$290$	14.9706	−	7.48528i	0.879102	−	0.439551i
$291$	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	−0.178932	−	0.983861i	$-0.557264\pi$
$293$	13.7782	−	13.7782i	0.804930	−	0.804930i	0.983861	+	0.178932i	$0.0572642\pi$
$294$	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
$298$			0.242641i			0.0140558i
$299$	33.7990			1.95465
$300$	−1.41421	−	9.89949i	−0.0816497	−	0.571548i
$301$	−9.05025	−	9.05025i	−0.521648	−	0.521648i
$302$		−	12.0000i		−	0.690522i
$303$	−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	−0.0218161	+	0.999762i	$0.506945\pi$
$307$	−17.8995	+	17.8995i	−1.02158	+	1.02158i	−0.999762	+	0.0218161i	$0.993055\pi$
$308$	2.36396	−	2.36396i	0.134699	−	0.134699i
$309$	−24.8284	+	24.8284i	−1.41244	+	1.41244i
$310$	−0.171573	−	0.343146i	−0.00974468	−	0.0194894i
$311$	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
$313$	−23.3137			−1.31777			−0.658884	−	0.752244i	$-0.728971\pi$
$313$	−23.3137			−1.31777			−0.658884	+	0.752244i	$0.728971\pi$
$314$	10.1213	+	10.1213i	0.571179	+	0.571179i
$315$	1.82843	+	3.65685i	0.103020	+	0.206040i
$316$	1.65685	−	1.65685i	0.0932053	−	0.0932053i
$317$	−8.46447	+	8.46447i	−0.475412	+	0.475412i	−0.903661	−	0.428249i	$-0.859131\pi$
$317$	−8.46447	+	8.46447i	−0.475412	+	0.475412i	0.428249	+	0.903661i	$0.359131\pi$
$318$	−6.00000			−0.336463
$319$	9.67767	−	9.67767i	0.541845	−	0.541845i
$320$	0.707107	−	2.12132i	0.0395285	−	0.118585i
$321$			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
$325$	24.9706	+	18.7279i	1.38512	+	1.03884i
$326$			3.34315i			0.185160i
$327$	−25.3137			−1.39985
$328$			7.00000i			0.386510i
$329$			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
$333$	−4.94975	−	3.53553i	−0.271244	−	0.193746i
$334$		−	6.82843i		−	0.373635i
$335$	−10.2426	−	20.4853i	−0.559615	−	1.11923i
$336$			3.65685i			0.199498i
$337$	5.65685	−	5.65685i	0.308148	−	0.308148i	−0.536043	−	0.844191i	$-0.680081\pi$
$337$	5.65685	−	5.65685i	0.308148	−	0.308148i	0.844191	+	0.536043i	$0.180081\pi$
$338$	25.9706			1.41261
$339$	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
$347$	5.31371			0.285255			0.142627	−	0.989776i	$-0.454445\pi$
$347$	5.31371			0.285255			0.142627	+	0.989776i	$0.454445\pi$
$348$			14.9706i			0.802506i
$349$		−	24.1421i		−	1.29230i	−0.763211	−	0.646149i	$-0.776378\pi$
$349$		−	24.1421i		−	1.29230i	0.763211	−	0.646149i	$-0.223622\pi$
$350$	−1.29289	−	9.05025i	−0.0691080	−	0.483756i
$351$	−17.6569	+	17.6569i	−0.942453	+	0.942453i
$352$		−	1.82843i		−	0.0974555i
$353$		−	18.6569i		−	0.993004i	−0.868036	−	0.496502i	$-0.834618\pi$
$353$		−	18.6569i		−	0.993004i	0.868036	−	0.496502i	$-0.165382\pi$
$354$	19.3137			1.02651
$355$	−8.24264	+	24.7279i	−0.437474	+	1.31242i
$356$	−4.58579	−	4.58579i	−0.243046	−	0.243046i
$357$	−14.0000			−0.740959
$358$	−2.48528	−	2.48528i	−0.131351	−	0.131351i
$359$			34.5269i			1.82226i	0.412118	+	0.911130i	$0.364789\pi$
$359$			34.5269i			1.82226i	−0.412118	+	0.911130i	$0.635211\pi$
$360$	2.12132	+	0.707107i	0.111803	+	0.0372678i
$361$			18.9411i			0.996901i
$362$	−3.65685			−0.192200
$363$	10.8284	+	10.8284i	0.568345	+	0.568345i
$364$	−8.07107	−	8.07107i	−0.423039	−	0.423039i
$365$	−16.9706	+	8.48528i	−0.888280	+	0.444140i
$366$	30.2843			1.58298
$367$	−25.0919	−	25.0919i	−1.30979	−	1.30979i	−0.921568	−	0.388218i	$-0.873091\pi$
$367$	−25.0919	−	25.0919i	−1.30979	−	1.30979i	−0.388218	−	0.921568i	$-0.626909\pi$
$368$	−5.41421			−0.282235
$369$	−7.00000			−0.364405
$370$	8.00000	+	11.0000i	0.415900	+	0.571863i
$371$	−5.48528			−0.284782
$372$	0.343146			0.0177913
$373$	5.17157	+	5.17157i	0.267774	+	0.267774i	0.828203	−	0.560429i	$-0.189364\pi$
$373$	5.17157	+	5.17157i	0.267774	+	0.267774i	−0.560429	+	0.828203i	$0.689364\pi$
$374$	7.00000			0.361961
$375$	−22.0000	−	4.00000i	−1.13608	−	0.206559i
$376$	0.242641	+	0.242641i	0.0125132	+	0.0125132i
$377$	−33.0416	−	33.0416i	−1.70173	−	1.70173i
$378$	7.31371			0.376177
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	−0.242641	−	0.485281i	−0.0124472	−	0.0248944i
$381$			15.3137i			0.784545i
$382$	−5.53553	−	5.53553i	−0.283223	−	0.283223i
$383$	−19.4142			−0.992020			−0.496010	−	0.868317i	$-0.665202\pi$
$383$	−19.4142			−0.992020			−0.496010	+	0.868317i	$0.665202\pi$
$384$	1.41421	+	1.41421i	0.0721688	+	0.0721688i
$385$	−3.34315	−	6.68629i	−0.170382	−	0.340765i
$386$	−3.51472			−0.178894
$387$		−	7.00000i		−	0.355830i
$388$		−	7.00000i		−	0.355371i
$389$	−11.7782	+	11.7782i	−0.597177	+	0.597177i	−0.939560	−	0.342383i	$-0.888766\pi$
$389$	−11.7782	+	11.7782i	−0.597177	+	0.597177i	0.342383	+	0.939560i	$0.388766\pi$
$390$	−24.9706	+	12.4853i	−1.26443	+	0.632217i
$391$		−	20.7279i		−	1.04826i
$392$		−	3.65685i		−	0.184699i
$393$	−6.82843			−0.344449
$394$	−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	$-0.652636\pi$
$397$	8.48528	−	8.48528i	0.425864	−	0.425864i	0.887217	+	0.461353i	$0.152636\pi$
$398$	−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	$0.169672\pi$
$402$	20.4853			1.02171
$403$	−0.757359	+	0.757359i	−0.0377268	+	0.0377268i
$404$			3.07107i			0.152791i
$405$	7.77817	−	23.3345i	0.386501	−	1.15950i
$406$			13.6863i			0.679239i
$407$	9.05025	+	6.46447i	0.448604	+	0.320432i
$408$	−5.41421	+	5.41421i	−0.268044	+	0.268044i
$409$	−19.7990	−	19.7990i	−0.978997	−	0.978997i	0.0207869	−	0.999784i	$-0.493383\pi$
$409$	−19.7990	−	19.7990i	−0.978997	−	0.978997i	−0.999784	+	0.0207869i	$0.993383\pi$
$410$	14.8492	+	4.94975i	0.733352	+	0.244451i
$411$			15.7990i			0.779307i
$412$			17.5563i			0.864939i
$413$	17.6569			0.868837
$414$		−	5.41421i		−	0.266094i
$415$	−6.82843	−	13.6569i	−0.335194	−	0.670389i
$416$	−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	$-0.945537\pi$
$419$		−	6.97056i		−	0.340534i	0.985398	−	0.170267i	$-0.0544631\pi$
$420$	7.75736	+	2.58579i	0.378520	+	0.126173i
$421$	−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	$0.279510\pi$
$422$	−9.00000			−0.438113
$423$	−0.242641	+	0.242641i	−0.0117976	+	0.0117976i
$424$	−2.12132	+	2.12132i	−0.103020	+	0.103020i
$425$	11.4853	−	15.3137i	0.557118	−	0.742824i
$426$	−16.4853	−	16.4853i	−0.798714	−	0.798714i
$427$	27.6863			1.33983
$428$	5.07107	+	5.07107i	0.245119	+	0.245119i
$429$	−16.1421	+	16.1421i	−0.779350	+	0.779350i
$430$	−4.94975	+	14.8492i	−0.238698	+	0.716094i
$431$	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	−0.119279	+	0.992861i	$0.538058\pi$
$433$	−23.1421	+	23.1421i	−1.11214	+	1.11214i	−0.992861	+	0.119279i	$0.961942\pi$
$434$	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
$438$		−	16.9706i		−	0.810885i
$439$	−17.7782	−	17.7782i	−0.848506	−	0.848506i	0.141441	−	0.989947i	$-0.454827\pi$
$439$	−17.7782	−	17.7782i	−0.848506	−	0.848506i	−0.989947	+	0.141441i	$0.954827\pi$
$440$	−3.87868	−	1.29289i	−0.184909	−	0.0616363i
$441$	3.65685			0.174136
$442$		−	23.8995i		−	1.13678i
$443$	16.6569	+	16.6569i	0.791391	+	0.791391i	0.981720	−	0.190329i	$-0.0609556\pi$
$443$	16.6569	+	16.6569i	0.791391	+	0.791391i	−0.190329	+	0.981720i	$0.560956\pi$
$444$	−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	−0.997463	−	0.0711878i	$-0.977321\pi$
$449$	−19.6274	+	19.6274i	−0.926275	+	0.926275i	0.0711878	+	0.997463i	$0.477321\pi$
$450$	3.00000	−	4.00000i	0.141421	−	0.188562i
$451$	12.7990			0.602681
$452$		−	1.82843i		−	0.0860020i
$453$	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
$457$		−	26.3137i		−	1.23090i	−0.788175	−	0.615452i	$-0.788974\pi$
$457$		−	26.3137i		−	1.23090i	0.788175	−	0.615452i	$-0.211026\pi$
$458$		−	1.41421i		−	0.0660819i
$459$	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	$0.554028\pi$
$462$	6.68629			0.311074
$463$	−37.9411			−1.76327			−0.881637	−	0.471929i	$-0.843558\pi$
$463$	−37.9411			−1.76327			−0.881637	+	0.471929i	$0.843558\pi$
$464$	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
$467$		−	20.3137i		−	0.940006i	−0.882665	−	0.470003i	$-0.844253\pi$
$467$		−	20.3137i		−	0.940006i	0.882665	−	0.470003i	$-0.155747\pi$
$468$		−	6.24264i		−	0.288566i
$469$	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
$473$			12.7990i			0.588498i
$474$	4.68629			0.215248
$475$	−1.20101	+	0.171573i	−0.0551061	+	0.00787230i
$476$	−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	−0.255912	−	0.966700i	$-0.582376\pi$
$479$	15.5563	−	15.5563i	0.710788	−	0.710788i	0.966700	+	0.255912i	$0.0823758\pi$
$480$	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
$483$		−	19.7990i		−	0.900885i
$484$	7.65685			0.348039
$485$	−14.8492	−	4.94975i	−0.674269	−	0.224756i
$486$	7.07107	+	7.07107i	0.320750	+	0.320750i
$487$		−	6.97056i		−	0.315866i	−0.987450	−	0.157933i	$-0.949517\pi$
$487$		−	6.97056i		−	0.315866i	0.987450	−	0.157933i	$-0.0504831\pi$
$488$	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
$495$	1.29289	−	3.87868i	0.0581112	−	0.174334i
$496$	0.121320	−	0.121320i	0.00544744	−	0.00544744i
$497$	−15.0711	−	15.0711i	−0.676030	−	0.676030i
$498$	13.6569			0.611978
$499$	1.75736	+	1.75736i	0.0786702	+	0.0786702i	0.745347	−	0.666677i	$-0.232284\pi$
$499$	1.75736	+	1.75736i	0.0786702	+	0.0786702i	−0.666677	+	0.745347i	$0.732284\pi$
$500$	−9.19239	+	6.36396i	−0.411096	+	0.284605i
$501$	9.65685	−	9.65685i	0.431436	−	0.431436i
$502$	1.89949	−	1.89949i	0.0847786	−	0.0847786i
$503$	−35.4142			−1.57904			−0.789521	−	0.613724i	$-0.789671\pi$
$503$	−35.4142			−1.57904			−0.789521	+	0.613724i	$0.789671\pi$
$504$	−1.29289	+	1.29289i	−0.0575900	+	0.0575900i
$505$	6.51472	+	2.17157i	0.289901	+	0.0966337i
$506$			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	$-0.701799\pi$
$509$	−26.7279			−1.18469			−0.592347	+	0.805683i	$0.701799\pi$
$510$	7.65685	+	15.3137i	0.339051	+	0.678102i
$511$		−	15.5147i		−	0.686331i
$512$	1.00000			0.0441942
$513$		−	0.970563i		−	0.0428514i
$514$			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
$518$	−10.9706	+	1.82843i	−0.482019	+	0.0803365i
$519$			50.9706i			2.23736i
$520$	−4.41421	+	13.2426i	−0.193576	+	0.580728i
$521$			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
$523$	32.3431			1.41427			0.707134	−	0.707080i	$-0.249988\pi$
$523$	32.3431			1.41427			0.707134	+	0.707080i	$0.249988\pi$
$524$	−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
$532$	0.443651			0.0192347
$533$		−	43.6985i		−	1.89279i
$534$		−	12.9706i		−	0.561291i
$535$	14.3431	−	7.17157i	0.620108	−	0.310054i
$536$	7.24264	−	7.24264i	0.312834	−	0.312834i
$537$		−	7.02944i		−	0.303343i
$538$			21.7990i			0.939821i
$539$	−6.68629			−0.287999
$540$	−4.00000	−	8.00000i	−0.172133	−	0.344265i
$541$	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	$0.633220\pi$
$542$	11.0711			0.475543
$543$	−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
$547$	−22.1716			−0.947988			−0.473994	−	0.880528i	$-0.657188\pi$
$547$	−22.1716			−0.947988			−0.473994	+	0.880528i	$0.657188\pi$
$548$	5.58579	+	5.58579i	0.238613	+	0.238613i
$549$	10.7071	+	10.7071i	0.456968	+	0.456968i
$550$	−5.48528	+	7.31371i	−0.233893	+	0.311858i
$551$	1.81623			0.0773742
$552$	−7.65685	−	7.65685i	−0.325897	−	0.325897i
$553$	4.28427			0.182186
$554$	−31.7990			−1.35101
$555$	−4.24264	+	26.8701i	−0.180090	+	1.14057i
$556$	11.8284			0.501637
$557$	−19.2132			−0.814090			−0.407045	−	0.913408i	$-0.633441\pi$
$557$	−19.2132			−0.814090			−0.407045	+	0.913408i	$0.633441\pi$
$558$	0.121320	+	0.121320i	0.00513590	+	0.00513590i
$559$	43.6985			1.84825
$560$	3.65685	−	1.82843i	0.154530	−	0.0772651i
$561$	9.89949	+	9.89949i	0.417957	+	0.417957i
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	38.1127			1.60626			0.803129	−	0.595805i	$-0.203167\pi$
$563$	38.1127			1.60626			0.803129	+	0.595805i	$0.203167\pi$
$564$			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
$568$	−11.6569			−0.489111
$569$	24.3137	+	24.3137i	1.01928	+	1.01928i	0.999810	+	0.0194733i	$0.00619894\pi$
$569$	24.3137	+	24.3137i	1.01928	+	1.01928i	0.0194733	+	0.999810i	$0.493801\pi$
$570$	0.343146	−	1.02944i	0.0143728	−	0.0431184i
$571$	7.20101			0.301353			0.150676	−	0.988583i	$-0.451855\pi$
$571$	7.20101			0.301353			0.150676	+	0.988583i	$0.451855\pi$
$572$			11.4142i			0.477252i
$573$		−	15.6569i		−	0.654074i
$574$	−9.05025	+	9.05025i	−0.377750	+	0.377750i
$575$	21.6569	+	16.2426i	0.903153	+	0.677365i
$576$			1.00000i			0.0416667i
$577$			10.3431i			0.430591i	0.976549	+	0.215295i	$0.0690714\pi$
$577$			10.3431i			0.430591i	−0.976549	+	0.215295i	$0.930929\pi$
$578$	2.34315			0.0974620
$579$	−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
$587$	46.4558			1.91744			0.958719	−	0.284355i	$-0.0917796\pi$
$587$	46.4558			1.91744			0.958719	+	0.284355i	$0.0917796\pi$
$588$	5.17157	−	5.17157i	0.213272	−	0.213272i
$589$		−	0.0416306i		−	0.00171536i
$590$	−9.65685	−	19.3137i	−0.397566	−	0.795133i
$591$		−	5.65685i		−	0.232692i
$592$	−3.53553	+	4.94975i	−0.145310	+	0.203433i
$593$	2.14214	−	2.14214i	0.0879670	−	0.0879670i	−0.661754	−	0.749721i	$-0.730188\pi$
$593$	2.14214	−	2.14214i	0.0879670	−	0.0879670i	0.749721	+	0.661754i	$0.230188\pi$
$594$	−5.17157	−	5.17157i	−0.212192	−	0.212192i
$595$	7.00000	+	14.0000i	0.286972	+	0.573944i
$596$			0.242641i			0.00993895i
$597$		−	44.9706i		−	1.84052i
$598$	33.7990			1.38214
$599$		−	42.2426i		−	1.72599i	−0.505215	−	0.862994i	$-0.668587\pi$
$599$		−	42.2426i		−	1.72599i	0.505215	−	0.862994i	$-0.331413\pi$
$600$	−1.41421	−	9.89949i	−0.0577350	−	0.404145i
$601$	−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
$605$	5.41421	−	16.2426i	0.220119	−	0.660357i
$606$	−4.34315	+	4.34315i	−0.176428	+	0.176428i
$607$	42.1838			1.71219			0.856093	−	0.516822i	$-0.172885\pi$
$607$	42.1838			1.71219			0.856093	+	0.516822i	$0.172885\pi$
$608$	0.171573	−	0.171573i	0.00695820	−	0.00695820i
$609$	−19.3553	+	19.3553i	−0.784318	+	0.784318i
$610$	−15.1421	−	30.2843i	−0.613087	−	1.22617i
$611$	−1.51472	−	1.51472i	−0.0612790	−	0.0612790i
$612$	−3.82843			−0.154755
$613$	7.87868	+	7.87868i	0.318217	+	0.318217i	0.848082	−	0.529865i	$-0.177757\pi$
$613$	7.87868	+	7.87868i	0.318217	+	0.318217i	−0.529865	+	0.848082i	$0.677757\pi$
$614$	−17.8995	+	17.8995i	−0.722365	+	0.722365i
$615$	14.0000	+	28.0000i	0.564534	+	1.12907i
$616$	2.36396	−	2.36396i	0.0952467	−	0.0952467i
$617$	2.27208	−	2.27208i	0.0914704	−	0.0914704i	−0.659891	−	0.751361i	$-0.729398\pi$
$617$	2.27208	−	2.27208i	0.0914704	−	0.0914704i	0.751361	+	0.659891i	$0.229398\pi$
$618$	−24.8284	+	24.8284i	−0.998746	+	0.998746i
$619$	32.5980			1.31022			0.655112	−	0.755532i	$-0.272622\pi$
$619$	32.5980			1.31022			0.655112	+	0.755532i	$0.272622\pi$
$620$	−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
$623$		−	11.8579i		−	0.475075i
$624$	−8.82843	−	8.82843i	−0.353420	−	0.353420i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	−23.3137			−0.931803
$627$		−	0.887302i		−	0.0354354i
$628$	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
$635$	15.3137	−	7.65685i	0.607706	−	0.303853i
$636$	−6.00000			−0.237915
$637$			22.8284i			0.904495i
$638$	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	$0.711987\pi$
$642$			14.3431i			0.566079i
$643$			41.4853i			1.63602i	0.575204	+	0.818010i	$0.304923\pi$
$643$			41.4853i			1.63602i	−0.575204	+	0.818010i	$0.695077\pi$
$644$	−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
$647$	4.68629			0.184237			0.0921186	−	0.995748i	$-0.470636\pi$
$647$	4.68629			0.184237			0.0921186	+	0.995748i	$0.470636\pi$
$648$	11.0000			0.432121
$649$	−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
$652$			3.34315i			0.130928i
$653$			8.34315i			0.326493i	0.986585	+	0.163246i	$0.0521965\pi$
$653$			8.34315i			0.326493i	−0.986585	+	0.163246i	$0.947803\pi$
$654$	−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
$658$			0.627417i			0.0244593i
$659$	−8.14214			−0.317173			−0.158586	−	0.987345i	$-0.550694\pi$
$659$	−8.14214			−0.317173			−0.158586	+	0.987345i	$0.550694\pi$
$660$	−3.65685	−	7.31371i	−0.142343	−	0.284686i
$661$	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
$668$		−	6.82843i		−	0.264200i
$669$	51.2548			1.98163
$670$	−10.2426	−	20.4853i	−0.395708	−	0.791415i
$671$	−19.5772	−	19.5772i	−0.755768	−	0.755768i
$672$			3.65685i			0.141066i
$673$	−27.4853	+	27.4853i	−1.05948	+	1.05948i	−0.0613643	+	0.998115i	$0.519545\pi$
$673$	−27.4853	+	27.4853i	−1.05948	+	1.05948i	−0.998115	+	0.0613643i	$0.980455\pi$
$674$	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	0.189827	−	0.981818i	$-0.439207\pi$
$677$	30.4853	−	30.4853i	1.17164	−	1.17164i	0.981818	−	0.189827i	$-0.0607927\pi$
$678$	2.58579	−	2.58579i	0.0993065	−	0.0993065i
$679$	9.05025	−	9.05025i	0.347317	−	0.347317i
$680$	8.12132	+	2.70711i	0.311438	+	0.103813i
$681$	−13.4142	+	13.4142i	−0.514034	+	0.514034i
$682$	−0.221825	−	0.221825i	−0.00849413	−	0.00849413i
$683$	−10.3137			−0.394643			−0.197322	−	0.980339i	$-0.563224\pi$
$683$	−10.3137			−0.394643			−0.197322	+	0.980339i	$0.563224\pi$
$684$	0.171573	+	0.171573i	0.00656025	+	0.00656025i
$685$	15.7990	−	7.89949i	0.603648	−	0.301824i
$686$	13.7782	−	13.7782i	0.526053	−	0.526053i
$687$	2.00000	−	2.00000i	0.0763048	−	0.0763048i
$688$	−7.00000			−0.266872
$689$	13.2426	−	13.2426i	0.504504	−	0.504504i
$690$	−21.6569	+	10.8284i	−0.824462	+	0.412231i
$691$		−	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
$695$	8.36396	−	25.0919i	0.317263	−	0.951789i
$696$			14.9706i			0.567458i
$697$	−26.7990			−1.01508
$698$		−	24.1421i		−	0.913793i
$699$			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
$703$	0.242641	+	1.45584i	0.00915137	+	0.0549082i
$704$		−	1.82843i		−	0.0689114i
$705$	1.45584	+	0.485281i	0.0548303	+	0.0182768i
$706$		−	18.6569i		−	0.702160i
$707$	−3.97056	+	3.97056i	−0.149328	+	0.149328i
$708$	19.3137			0.725854
$709$	−9.29289	+	9.29289i	−0.349002	+	0.349002i	−0.859738	−	0.510736i	$-0.829373\pi$
$709$	−9.29289	+	9.29289i	−0.349002	+	0.349002i	0.510736	+	0.859738i	$0.329373\pi$
$710$	−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
$717$	−47.9411			−1.79039
$718$			34.5269i			1.28853i
$719$			4.14214i			0.154476i	0.997013	+	0.0772378i	$0.0246101\pi$
$719$			4.14214i			0.154476i	−0.997013	+	0.0772378i	$0.975390\pi$
$720$	2.12132	+	0.707107i	0.0790569	+	0.0263523i
$721$	−22.6985	+	22.6985i	−0.845336	+	0.845336i
$722$			18.9411i			0.704916i
$723$			26.1421i			0.972236i
$724$	−3.65685			−0.135906
$725$	−5.29289	−	37.0503i	−0.196573	−	1.37601i
$726$	10.8284	+	10.8284i	0.401881	+	0.401881i
$727$	−42.1421			−1.56297			−0.781483	−	0.623927i	$-0.785536\pi$
$727$	−42.1421			−1.56297			−0.781483	+	0.623927i	$0.785536\pi$
$728$	−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
$732$	30.2843			1.11934
$733$	−26.7487	−	26.7487i	−0.987987	−	0.987987i	0.0119415	−	0.999929i	$-0.496199\pi$
$733$	−26.7487	−	26.7487i	−0.987987	−	0.987987i	−0.999929	+	0.0119415i	$0.996199\pi$
$734$	−25.0919	−	25.0919i	−0.926158	−	0.926158i
$735$	−7.31371	−	14.6274i	−0.269770	−	0.539540i
$736$	−5.41421			−0.199571
$737$	−13.2426	−	13.2426i	−0.487799	−	0.487799i
$738$	−7.00000			−0.257674
$739$	−28.7990			−1.05939			−0.529694	−	0.848189i	$-0.677693\pi$
$739$	−28.7990			−1.05939			−0.529694	+	0.848189i	$0.677693\pi$
$740$	8.00000	+	11.0000i	0.294086	+	0.404368i
$741$	−3.02944			−0.111289
$742$	−5.48528			−0.201371
$743$	−14.9497	−	14.9497i	−0.548453	−	0.548453i	0.377540	−	0.925993i	$-0.376770\pi$
$743$	−14.9497	−	14.9497i	−0.548453	−	0.548453i	−0.925993	+	0.377540i	$0.876770\pi$
$744$	0.343146			0.0125803
$745$	0.514719	+	0.171573i	0.0188578	+	0.00628594i
$746$	5.17157	+	5.17157i	0.189345	+	0.189345i
$747$	4.82843	+	4.82843i	0.176663	+	0.176663i
$748$	7.00000			0.255945
$749$			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
$753$	5.37258			0.195788
$754$	−33.0416	−	33.0416i	−1.20331	−	1.20331i
$755$	−25.4558	−	8.48528i	−0.926433	−	0.308811i
$756$	7.31371			0.265997
$757$			16.3431i			0.594002i	0.954877	+	0.297001i	$0.0959864\pi$
$757$			16.3431i			0.594002i	−0.954877	+	0.297001i	$0.904014\pi$
$758$		−	18.0000i		−	0.653789i
$759$	−14.0000	+	14.0000i	−0.508168	+	0.508168i
$760$	−0.242641	−	0.485281i	−0.00880150	−	0.0176030i
$761$		−	34.3137i		−	1.24387i	−0.783068	−	0.621935i	$-0.786347\pi$
$761$		−	34.3137i		−	1.24387i	0.783068	−	0.621935i	$-0.213653\pi$
$762$			15.3137i			0.554757i
$763$	−23.1421			−0.837802
$764$	−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	0.995019	−	0.0996832i	$-0.0317829\pi$
$769$	24.8284	+	24.8284i	0.895336	+	0.895336i	−0.0996832	+	0.995019i	$0.531783\pi$
$770$	−3.34315	−	6.68629i	−0.120479	−	0.240957i
$771$	−18.6274	+	18.6274i	−0.670850	+	0.670850i
$772$	−3.51472			−0.126497
$773$	5.87868	−	5.87868i	0.211441	−	0.211441i	−0.593438	−	0.804880i	$-0.702230\pi$
$773$	5.87868	−	5.87868i	0.211441	−	0.211441i	0.804880	+	0.593438i	$0.202230\pi$
$774$		−	7.00000i		−	0.251610i
$775$	−0.849242	+	0.121320i	−0.0305057	+	0.00435796i
$776$		−	7.00000i		−	0.251285i
$777$	−18.1005	−	12.9289i	−0.649352	−	0.463823i
$778$	−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
$782$		−	20.7279i		−	0.741229i
$783$	29.9411			1.07001
$784$		−	3.65685i		−	0.130602i
$785$	28.6274	−	14.3137i	1.02176	−	0.510878i
$786$	−6.82843			−0.243562
$787$	7.75736	+	7.75736i	0.276520	+	0.276520i	0.831718	−	0.555198i	$-0.187358\pi$
$787$	7.75736	+	7.75736i	0.276520	+	0.276520i	−0.555198	+	0.831718i	$0.687358\pi$
$788$	−2.00000	−	2.00000i	−0.0712470	−	0.0712470i
$789$		−	18.6863i		−	0.665250i
$790$	−2.34315	−	4.68629i	−0.0833654	−	0.166731i
$791$	2.36396	−	2.36396i	0.0840528	−	0.0840528i
$792$	1.82843			0.0649703
$793$	−66.8406	+	66.8406i	−2.37358	+	2.37358i
$794$	8.48528	−	8.48528i	0.301131	−	0.301131i
$795$	−4.24264	+	12.7279i	−0.150471	+	0.451413i
$796$	−15.8995	−	15.8995i	−0.563543	−	0.563543i
$797$	39.2548			1.39048			0.695239	−	0.718779i	$-0.255299\pi$
$797$	39.2548			1.39048			0.695239	+	0.718779i	$0.255299\pi$
$798$	0.627417	+	0.627417i	0.0222103	+	0.0222103i
$799$	−0.928932	+	0.928932i	−0.0328633	+	0.0328633i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	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
$808$			3.07107i			0.108040i
$809$	−6.02944	−	6.02944i	−0.211984	−	0.211984i	0.593126	−	0.805110i	$-0.297894\pi$
$809$	−6.02944	−	6.02944i	−0.211984	−	0.211984i	−0.805110	+	0.593126i	$0.797894\pi$
$810$	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	$0.449657\pi$
$812$			13.6863i			0.480295i
$813$	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
$820$	14.8492	+	4.94975i	0.518558	+	0.172853i
$821$	−10.4437			−0.364486			−0.182243	−	0.983254i	$-0.558336\pi$
$821$	−10.4437			−0.364486			−0.182243	+	0.983254i	$0.558336\pi$
$822$			15.7990i			0.551053i
$823$	4.97056	−	4.97056i	0.173263	−	0.173263i	−0.615148	−	0.788411i	$-0.710904\pi$
$823$	4.97056	−	4.97056i	0.173263	−	0.173263i	0.788411	+	0.615148i	$0.210904\pi$
$824$			17.5563i			0.611604i
$825$	−18.1005	+	2.58579i	−0.630179	+	0.0900255i
$826$	17.6569			0.614361
$827$		−	1.82843i		−	0.0635806i	−0.999495	−	0.0317903i	$-0.989879\pi$
$827$		−	1.82843i		−	0.0635806i	0.999495	−	0.0317903i	$-0.0101209\pi$
$828$		−	5.41421i		−	0.188157i
$829$	−24.7487	−	24.7487i	−0.859559	−	0.859559i	0.131727	−	0.991286i	$-0.457948\pi$
$829$	−24.7487	−	24.7487i	−0.859559	−	0.859559i	−0.991286	+	0.131727i	$0.957948\pi$
$830$	−6.82843	−	13.6569i	−0.237018	−	0.474036i
$831$	−44.9706	−	44.9706i	−1.56001	−	1.56001i
$832$	−6.24264			−0.216425
$833$	14.0000			0.485071
$834$	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
$837$		−	0.686292i		−	0.0237217i
$838$		−	6.97056i		−	0.240794i
$839$	45.3553			1.56584			0.782920	−	0.622122i	$-0.213729\pi$
$839$	45.3553			1.56584			0.782920	+	0.622122i	$0.213729\pi$
$840$	7.75736	+	2.58579i	0.267654	+	0.0892181i
$841$			27.0294i			0.932050i
$842$	−2.68629	+	2.68629i	−0.0925757	+	0.0925757i
$843$			11.3137i			0.389665i
$844$	−9.00000			−0.309793
$845$	18.3640	−	55.0919i	0.631739	−	1.89522i
$846$	−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
$853$			32.8284i			1.12402i	0.827129	+	0.562012i	$0.189973\pi$
$853$			32.8284i			1.12402i	−0.827129	+	0.562012i	$0.810027\pi$
$854$	27.6863			0.947405
$855$	0.485281	−	0.242641i	0.0165963	−	0.00829814i
$856$	5.07107	+	5.07107i	0.173326	+	0.173326i
$857$		−	15.1421i		−	0.517245i	−0.965978	−	0.258623i	$-0.916731\pi$
$857$		−	15.1421i		−	0.517245i	0.965978	−	0.258623i	$-0.0832686\pi$
$858$	−16.1421	+	16.1421i	−0.551083	+	0.551083i
$859$	5.44365	−	5.44365i	0.185735	−	0.185735i	−0.608114	−	0.793849i	$-0.708074\pi$
$859$	5.44365	−	5.44365i	0.185735	−	0.185735i	0.793849	+	0.608114i	$0.208074\pi$
$860$	−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	−0.297869	−	0.954607i	$-0.596276\pi$
$863$	19.2929	−	19.2929i	0.656738	−	0.656738i	0.954607	+	0.297869i	$0.0962759\pi$
$864$	2.82843	−	2.82843i	0.0962250	−	0.0962250i
$865$	50.9706	−	25.4853i	1.73305	−	0.866526i
$866$	−23.1421	+	23.1421i	−0.786402	+	0.786402i
$867$	3.31371	+	3.31371i	0.112539	+	0.112539i
$868$	0.313708			0.0106480
$869$	−3.02944	−	3.02944i	−0.102767	−	0.102767i
$870$	31.7574	+	10.5858i	1.07668	+	0.358892i
$871$	−45.2132	+	45.2132i	−1.53199	+	1.53199i
$872$	−8.94975	+	8.94975i	−0.303077	+	0.303077i
$873$	7.00000			0.236914
$874$	−0.928932	+	0.928932i	−0.0314216	+	0.0314216i
$875$	−20.1127	−	3.65685i	−0.679933	−	0.123624i
$876$		−	16.9706i		−	0.573382i
$877$	10.0208	+	10.0208i	0.338379	+	0.338379i	0.855757	−	0.517378i	$-0.173092\pi$
$877$	10.0208	+	10.0208i	0.338379	+	0.338379i	−0.517378	+	0.855757i	$0.673092\pi$
$878$	−17.7782	−	17.7782i	−0.599984	−	0.599984i
$879$	38.9706			1.31444
$880$	−3.87868	−	1.29289i	−0.130750	−	0.0435834i
$881$			7.48528i			0.252186i	0.992018	+	0.126093i	$0.0402437\pi$
$881$			7.48528i			0.252186i	−0.992018	+	0.126093i	$0.959756\pi$
$882$	3.65685			0.123133
$883$		−	53.6274i		−	1.80471i	−0.430997	−	0.902353i	$-0.641838\pi$
$883$		−	53.6274i		−	1.80471i	0.430997	−	0.902353i	$-0.358162\pi$
$884$		−	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	−0.336233	+	0.941779i	$0.609153\pi$
$887$	−38.0624	+	38.0624i	−1.27801	+	1.27801i	−0.941779	+	0.336233i	$0.890847\pi$
$888$	−12.0000	+	2.00000i	−0.402694	+	0.0671156i
$889$			14.0000i			0.469545i
$890$	−12.9706	+	6.48528i	−0.434774	+	0.217387i
$891$		−	20.1127i		−	0.673801i
$892$	18.1213	−	18.1213i	0.606747	−	0.606747i
$893$	0.0832611			0.00278623
$894$	−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
$902$	12.7990			0.426160
$903$		−	25.5980i		−	0.851847i
$904$		−	1.82843i		−	0.0608126i
$905$	−2.58579	+	7.75736i	−0.0859544	+	0.257863i
$906$	16.9706	−	16.9706i	0.563809	−	0.563809i
$907$		−	14.0000i		−	0.464862i	−0.972613	−	0.232431i	$-0.925332\pi$
$907$		−	14.0000i		−	0.464862i	0.972613	−	0.232431i	$-0.0746680\pi$
$908$			9.48528i			0.314780i
$909$	−3.07107			−0.101861
$910$	−22.8284	+	11.4142i	−0.756755	+	0.378377i
$911$	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	$0.528003\pi$
$912$	0.485281			0.0160693
$913$	−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
$917$	−6.24264			−0.206150
$918$	10.8284	+	10.8284i	0.357391	+	0.357391i
$919$	−10.6274	−	10.6274i	−0.350566	−	0.350566i	0.509754	−	0.860320i	$-0.329736\pi$
$919$	−10.6274	−	10.6274i	−0.350566	−	0.350566i	−0.860320	+	0.509754i	$0.829736\pi$
$920$	−3.82843	+	11.4853i	−0.126220	+	0.378659i
$921$	−50.6274			−1.66823
$922$	17.5355	+	17.5355i	0.577502	+	0.577502i
$923$	72.7696			2.39524
$924$	6.68629			0.219963
$925$	28.9914	−	9.19239i	0.953231	−	0.302244i
$926$	−37.9411			−1.24682
$927$	−17.5563			−0.576626
$928$	5.29289	+	5.29289i	0.173748	+	0.173748i
$929$	−20.6569			−0.677729			−0.338865	−	0.940835i	$-0.610043\pi$
$929$	−20.6569			−0.677729			−0.338865	+	0.940835i	$0.610043\pi$
$930$	0.242641	−	0.727922i	0.00795650	−	0.0238695i
$931$	−0.627417	−	0.627417i	−0.0205628	−	0.0205628i
$932$	14.0711	+	14.0711i	0.460913	+	0.460913i
$933$	10.6863			0.349853
$934$		−	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	0.817765	−	0.575553i	$-0.195213\pi$
$937$	7.41421	+	7.41421i	0.242212	+	0.242212i	−0.575553	+	0.817765i	$0.695213\pi$
$938$	18.7279			0.611488
$939$	−32.9706	−	32.9706i	−1.07595	−	1.07595i
$940$	0.686292	−	0.343146i	0.0223844	−	0.0111922i
$941$	35.0711			1.14328			0.571642	−	0.820503i	$-0.306307\pi$
$941$	35.0711			1.14328			0.571642	+	0.820503i	$0.306307\pi$
$942$			28.6274i			0.932732i
$943$		−	37.8995i		−	1.23418i
$944$	6.82843	−	6.82843i	0.222246	−	0.222246i
$945$	5.17157	−	15.5147i	0.168231	−	0.504694i
$946$			12.7990i			0.416131i
$947$			30.7990i			1.00083i	0.865785	+	0.500416i	$0.166820\pi$
$947$			30.7990i			1.00083i	−0.865785	+	0.500416i	$0.833180\pi$
$948$	4.68629			0.152204
$949$	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	−0.999667	−	0.0257989i	$-0.991787\pi$
$953$	−31.6569	−	31.6569i	−1.02547	−	1.02547i	−0.0257989	−	0.999667i	$-0.508213\pi$
$954$	−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
$957$	27.3726			0.884830
$958$	15.5563	−	15.5563i	0.502603	−	0.502603i
$959$			14.4437i			0.466410i
$960$	4.00000	−	2.00000i	0.129099	−	0.0645497i
$961$			30.9706i			0.999050i
$962$	22.0711	−	30.8995i	0.711600	−	0.996240i
$963$	−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
$967$			13.9411i			0.448316i	0.974553	+	0.224158i	$0.0719632\pi$
$967$			13.9411i			0.448316i	−0.974553	+	0.224158i	$0.928037\pi$
$968$	7.65685			0.246101
$969$			1.85786i			0.0596832i
$970$	−14.8492	−	4.94975i	−0.476780	−	0.158927i
$971$	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
$975$	8.82843	+	61.7990i	0.282736	+	1.97915i
$976$	10.7071	−	10.7071i	0.342726	−	0.342726i
$977$	49.4853			1.58317			0.791587	−	0.611056i	$-0.209255\pi$
$977$	49.4853			1.58317			0.791587	+	0.611056i	$0.209255\pi$
$978$	−4.72792	+	4.72792i	−0.151182	+	0.151182i
$979$	−8.38478	+	8.38478i	−0.267979	+	0.267979i
$980$	−7.75736	−	2.58579i	−0.247800	−	0.0825999i
$981$	−8.94975	−	8.94975i	−0.285743	−	0.285743i
$982$	−21.7990			−0.695634
$983$	−9.39340	−	9.39340i	−0.299603	−	0.299603i	0.541255	−	0.840858i	$-0.317949\pi$
$983$	−9.39340	−	9.39340i	−0.299603	−	0.299603i	−0.840858	+	0.541255i	$0.817949\pi$
$984$	−9.89949	+	9.89949i	−0.315584	+	0.315584i
$985$	−5.65685	+	2.82843i	−0.180242	+	0.0901212i
$986$	−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
$993$			15.3137i			0.485966i
$994$	−15.0711	−	15.0711i	−0.478025	−	0.478025i
$995$	−44.9706	+	22.4853i	−1.42566	+	0.712831i
$996$	13.6569			0.432734
$997$		−	13.4558i		−	0.426151i	−0.977036	−	0.213075i	$-0.931652\pi$
$997$		−	13.4558i		−	0.426151i	0.977036	−	0.213075i	$-0.0683480\pi$
$998$	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.h.c.117.2	yes	4
5.3	odd	4		370.2.g.c.43.1	✓	4
37.31	odd	4		370.2.g.c.327.1	yes	4
185.68	even	4	inner	370.2.h.c.253.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.c.43.1	✓	4	5.3	odd	4
370.2.g.c.327.1	yes	4	37.31	odd	4
370.2.h.c.117.2	yes	4	1.1	even	1	trivial
370.2.h.c.253.2	yes	4	185.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

Introduction

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