LMFDB - Embedded newform 370.2.h.c.253.2

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			253.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.c.117.2

$q$-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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.41421	−	1.41421i	0.816497	−	0.816497i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	1.41421	−	1.41421i	0.816497	−	0.816497i	0.985599	+	0.169102i	$0.0540867\pi$
$4$	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	−0.419218	−	0.907886i	$-0.637696\pi$
$7$	1.29289	−	1.29289i	0.488668	−	0.488668i	0.907886	+	0.419218i	$0.137696\pi$
$8$	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	$0.0888917\pi$
$11$			1.82843i			0.551292i	−0.961259	+	0.275646i	$0.911108\pi$
$12$	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	$-0.846319\pi$
$17$		−	3.82843i		−	0.928530i	0.885696	−	0.464265i	$-0.153681\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.171573	+	0.171573i	0.0393615	+	0.0393615i	0.726514	−	0.687152i	$-0.241139\pi$
$19$	0.171573	+	0.171573i	0.0393615	+	0.0393615i	−0.687152	+	0.726514i	$0.741139\pi$
$20$	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	−0.0169901	−	0.999856i	$-0.505408\pi$
$29$	5.29289	−	5.29289i	0.982866	−	0.982866i	0.999856	+	0.0169901i	$0.00540837\pi$
$30$	4.00000	+	2.00000i	0.730297	+	0.365148i
$31$	0.121320	+	0.121320i	0.0217898	+	0.0217898i	0.717918	−	0.696128i	$-0.245095\pi$
$31$	0.121320	+	0.121320i	0.0217898	+	0.0217898i	−0.696128	+	0.717918i	$0.745095\pi$
$32$	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	$-0.815919\pi$
$41$		−	7.00000i		−	1.09322i	0.837389	−	0.546608i	$-0.184081\pi$
$42$		−	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	−0.689189	−	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
$50$	−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	0.546242	−	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
$55$	−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	0.994426	−	0.105440i	$-0.0336251\pi$
$59$	6.82843	+	6.82843i	0.888985	+	0.888985i	−0.105440	+	0.994426i	$0.533625\pi$
$60$	4.00000	+	2.00000i	0.516398	+	0.258199i
$61$	10.7071	+	10.7071i	1.37090	+	1.37090i	0.859105	+	0.511800i	$0.171021\pi$
$61$	10.7071	+	10.7071i	1.37090	+	1.37090i	0.511800	+	0.859105i	$0.328979\pi$
$62$	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	0.994021	−	0.109191i	$-0.0348261\pi$
$67$	7.24264	+	7.24264i	0.884829	+	0.884829i	−0.109191	+	0.994021i	$0.534826\pi$
$68$		−	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	−0.964892	−	0.262646i	$-0.915405\pi$
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	0.262646	+	0.964892i	$0.415405\pi$
$74$	−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	$-0.207920\pi$
$79$	1.65685	+	1.65685i	0.186411	+	0.186411i	−0.607732	+	0.794142i	$0.707920\pi$
$80$	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	0.920569	−	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
$87$		−	14.9706i		−	1.60501i
$88$			1.82843i			0.194911i
$89$	−4.58579	+	4.58579i	−0.486092	+	0.486092i	−0.907071	−	0.420978i	$-0.861687\pi$
$89$	−4.58579	+	4.58579i	−0.486092	+	0.486092i	0.420978	+	0.907071i	$0.361687\pi$
$90$	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	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$			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	$-0.951174\pi$
$101$		−	3.07107i		−	0.305583i	0.988258	−	0.152791i	$-0.0488262\pi$
$102$	−5.41421	−	5.41421i	−0.536087	−	0.536087i
$103$		−	17.5563i		−	1.72988i	−0.501877	−	0.864939i	$-0.667357\pi$
$103$		−	17.5563i		−	1.72988i	0.501877	−	0.864939i	$-0.332643\pi$
$104$	−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	−0.418143	−	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	$-0.457288\pi$
$109$	−8.94975	−	8.94975i	−0.857230	−	0.857230i	−0.991011	+	0.133781i	$0.957288\pi$
$110$	−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	$0.0274091\pi$
$113$			1.82843i			0.172004i	−0.996295	+	0.0860020i	$0.972591\pi$
$114$	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	−0.424836	−	0.905270i	$-0.639668\pi$
$127$	5.41421	−	5.41421i	0.480434	−	0.480434i	0.905270	+	0.424836i	$0.139668\pi$
$128$	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	0.593732	−	0.804663i	$-0.297654\pi$
$131$	−2.41421	−	2.41421i	−0.210931	−	0.210931i	−0.804663	+	0.593732i	$0.797654\pi$
$132$	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	−0.427017	−	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	$-0.332731\pi$
$139$	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	$-0.996836\pi$
$149$		−	0.242641i		−	0.0198779i	0.999951	−	0.00993895i	$-0.00316372\pi$
$150$	−1.41421	+	9.89949i	−0.115470	+	0.808290i
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$	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	−0.176527	−	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
$162$	11.0000			0.864242
$163$		−	3.34315i		−	0.261855i	−0.991392	−	0.130928i	$-0.958204\pi$
$163$		−	3.34315i		−	0.261855i	0.991392	−	0.130928i	$-0.0417956\pi$
$164$		−	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	$0.0851078\pi$
$167$			6.82843i			0.528400i	−0.964468	+	0.264200i	$0.914892\pi$
$168$		−	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	0.509810	−	0.860287i	$-0.329716\pi$
$173$	18.0208	−	18.0208i	1.37010	−	1.37010i	0.860287	−	0.509810i	$-0.170284\pi$
$174$		−	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	−0.793860	−	0.608101i	$-0.791932\pi$
$179$	−2.48528	+	2.48528i	−0.185759	+	0.185759i	0.608101	+	0.793860i	$0.291932\pi$
$180$	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	−0.878422	−	0.477885i	$-0.841404\pi$
$191$	−5.53553	+	5.53553i	−0.400537	+	0.400537i	0.477885	+	0.878422i	$0.341404\pi$
$192$	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	−0.774755	−	0.632261i	$-0.782127\pi$
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	0.632261	+	0.774755i	$0.282127\pi$
$198$	1.82843			0.129941
$199$	−15.8995	+	15.8995i	−1.12709	+	1.12709i	−0.136436	+	0.990649i	$0.543565\pi$
$199$	−15.8995	+	15.8995i	−1.12709	+	1.12709i	−0.990649	+	0.136436i	$0.956435\pi$
$200$	−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	0.969870	+	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
$227$		−	9.48528i		−	0.629560i	−0.949165	−	0.314780i	$-0.898069\pi$
$227$		−	9.48528i		−	0.629560i	0.949165	−	0.314780i	$-0.101931\pi$
$228$	0.485281			0.0321385
$229$			1.41421i			0.0934539i	0.998908	+	0.0467269i	$0.0148791\pi$
$229$			1.41421i			0.0934539i	−0.998908	+	0.0467269i	$0.985121\pi$
$230$	−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	−0.0753322	−	0.997158i	$-0.524002\pi$
$233$	14.0711	−	14.0711i	0.921826	−	0.921826i	0.997158	+	0.0753322i	$0.0240017\pi$
$234$			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	−0.994830	−	0.101558i	$-0.967617\pi$
$239$	−16.9497	−	16.9497i	−1.09639	−	1.09639i	−0.101558	−	0.994830i	$-0.532383\pi$
$240$	4.00000	+	2.00000i	0.258199	+	0.129099i
$241$	9.24264	−	9.24264i	0.595371	−	0.595371i	−0.343706	−	0.939077i	$-0.611682\pi$
$241$	9.24264	−	9.24264i	0.595371	−	0.595371i	0.939077	+	0.343706i	$0.111682\pi$
$242$	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	0.764509	−	0.644614i	$-0.222982\pi$
$251$	1.89949	+	1.89949i	0.119895	+	0.119895i	−0.644614	+	0.764509i	$0.722982\pi$
$252$	−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	$-0.865246\pi$
$257$		−	13.1716i		−	0.821620i	0.911721	−	0.410810i	$-0.134754\pi$
$258$	−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	−0.880824	−	0.473444i	$-0.843011\pi$
$263$	−6.60660	+	6.60660i	−0.407381	+	0.407381i	0.473444	+	0.880824i	$0.343011\pi$
$264$	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	$-0.768622\pi$
$269$		−	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	$0.390838\pi$
$272$		−	3.82843i		−	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	−0.577659	−	0.816279i	$-0.696033\pi$
$281$	4.00000	−	4.00000i	0.238620	−	0.238620i	0.816279	+	0.577659i	$0.196033\pi$
$282$		−	0.686292i		−	0.0408681i
$283$			28.0000i			1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$			28.0000i			1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$	−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	0.983861	−	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
$298$		−	0.242641i		−	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	−0.999762	−	0.0218161i	$-0.993055\pi$
$307$	−17.8995	−	17.8995i	−1.02158	−	1.02158i	−0.0218161	−	0.999762i	$-0.506945\pi$
$308$	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	0.806066	−	0.591825i	$-0.201593\pi$
$311$	3.77817	+	3.77817i	0.214241	+	0.214241i	−0.591825	+	0.806066i	$0.701593\pi$
$312$	−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	0.428249	−	0.903661i	$-0.359131\pi$
$317$	−8.46447	−	8.46447i	−0.475412	−	0.475412i	−0.903661	+	0.428249i	$0.859131\pi$
$318$	−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	−0.542478	−	0.840070i	$-0.682514\pi$
$331$	5.41421	−	5.41421i	0.297592	−	0.297592i	0.840070	+	0.542478i	$0.182514\pi$
$332$	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	0.844191	−	0.536043i	$-0.180081\pi$
$337$	5.65685	+	5.65685i	0.308148	+	0.308148i	−0.536043	+	0.844191i	$0.680081\pi$
$338$	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	$0.223622\pi$
$349$			24.1421i			1.29230i	−0.763211	+	0.646149i	$0.776378\pi$
$350$	−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	$0.165382\pi$
$353$			18.6569i			0.993004i	−0.868036	+	0.496502i	$0.834618\pi$
$354$	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	$-0.635211\pi$
$359$		−	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
$362$	−3.65685			−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	−0.388218	+	0.921568i	$0.626909\pi$
$367$	−25.0919	+	25.0919i	−1.30979	+	1.30979i	−0.921568	+	0.388218i	$0.873091\pi$
$368$	−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	−0.560429	−	0.828203i	$-0.689364\pi$
$373$	5.17157	−	5.17157i	0.267774	−	0.267774i	0.828203	+	0.560429i	$0.189364\pi$
$374$	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	$0.152975\pi$
$379$			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
$383$	−19.4142			−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	0.342383	−	0.939560i	$-0.388766\pi$
$389$	−11.7782	−	11.7782i	−0.597177	−	0.597177i	−0.939560	+	0.342383i	$0.888766\pi$
$390$	−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	0.887217	−	0.461353i	$-0.152636\pi$
$397$	8.48528	+	8.48528i	0.425864	+	0.425864i	−0.461353	+	0.887217i	$0.652636\pi$
$398$	−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	0.861266	−	0.508154i	$-0.169672\pi$
$401$	7.07107	+	7.07107i	0.353112	+	0.353112i	−0.508154	+	0.861266i	$0.669672\pi$
$402$	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	−0.999784	−	0.0207869i	$-0.993383\pi$
$409$	−19.7990	+	19.7990i	−0.978997	+	0.978997i	0.0207869	+	0.999784i	$0.493383\pi$
$410$	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	$0.0544631\pi$
$419$			6.97056i			0.340534i	−0.985398	+	0.170267i	$0.945537\pi$
$420$	7.75736	−	2.58579i	0.378520	−	0.126173i
$421$	−2.68629	−	2.68629i	−0.130922	−	0.130922i	0.638609	−	0.769531i	$-0.279510\pi$
$421$	−2.68629	−	2.68629i	−0.130922	−	0.130922i	−0.769531	+	0.638609i	$0.779510\pi$
$422$	−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	0.999926	−	0.0121819i	$-0.00387771\pi$
$431$	20.5061	+	20.5061i	0.987744	+	0.987744i	−0.0121819	+	0.999926i	$0.503878\pi$
$432$	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
$438$			16.9706i			0.810885i
$439$	−17.7782	+	17.7782i	−0.848506	+	0.848506i	−0.989947	−	0.141441i	$-0.954827\pi$
$439$	−17.7782	+	17.7782i	−0.848506	+	0.848506i	0.141441	+	0.989947i	$0.454827\pi$
$440$	−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	−0.190329	−	0.981720i	$-0.560956\pi$
$443$	16.6569	−	16.6569i	0.791391	−	0.791391i	0.981720	+	0.190329i	$0.0609556\pi$
$444$	−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	$-0.477321\pi$
$449$	−19.6274	−	19.6274i	−0.926275	−	0.926275i	−0.997463	+	0.0711878i	$0.977321\pi$
$450$	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	$0.211026\pi$
$457$			26.3137i			1.23090i	−0.788175	+	0.615452i	$0.788974\pi$
$458$			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	−0.168919	−	0.985630i	$-0.554028\pi$
$461$	17.5355	−	17.5355i	0.816711	−	0.816711i	0.985630	+	0.168919i	$0.0540275\pi$
$462$	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	$0.155747\pi$
$467$			20.3137i			0.940006i	−0.882665	+	0.470003i	$0.844253\pi$
$468$			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	0.966700	−	0.255912i	$-0.0823758\pi$
$479$	15.5563	+	15.5563i	0.710788	+	0.710788i	−0.255912	+	0.966700i	$0.582376\pi$
$480$	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	$0.0504831\pi$
$487$			6.97056i			0.315866i	−0.987450	+	0.157933i	$0.949517\pi$
$488$	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	−0.666677	−	0.745347i	$-0.732284\pi$
$499$	1.75736	−	1.75736i	0.0786702	−	0.0786702i	0.745347	+	0.666677i	$0.232284\pi$
$500$	−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	$-0.873810\pi$
$521$		−	17.6274i		−	0.772271i	0.922442	−	0.386136i	$-0.126190\pi$
$522$	−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	−0.406412	−	0.913690i	$-0.633220\pi$
$541$	11.7990	−	11.7990i	0.507278	−	0.507278i	0.913690	+	0.406412i	$0.133220\pi$
$542$	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	0.0194733	−	0.999810i	$-0.493801\pi$
$569$	24.3137	−	24.3137i	1.01928	−	1.01928i	0.999810	−	0.0194733i	$-0.00619894\pi$
$570$	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	$-0.930929\pi$
$577$		−	10.3431i		−	0.430591i	0.976549	−	0.215295i	$-0.0690714\pi$
$578$	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	0.749721	−	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
$597$			44.9706i			1.84052i
$598$	33.7990			1.38214
$599$			42.2426i			1.72599i	0.505215	+	0.862994i	$0.331413\pi$
$599$			42.2426i			1.72599i	−0.505215	+	0.862994i	$0.668587\pi$
$600$	−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	−0.529865	−	0.848082i	$-0.677757\pi$
$613$	7.87868	−	7.87868i	0.318217	−	0.318217i	0.848082	+	0.529865i	$0.177757\pi$
$614$	−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	0.751361	−	0.659891i	$-0.229398\pi$
$617$	2.27208	+	2.27208i	0.0914704	+	0.0914704i	−0.659891	+	0.751361i	$0.729398\pi$
$618$	−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	0.889275	−	0.457373i	$-0.151210\pi$
$631$	10.8492	+	10.8492i	0.431902	+	0.431902i	−0.457373	+	0.889275i	$0.651210\pi$
$632$	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	$-0.695077\pi$
$643$		−	41.4853i		−	1.63602i	0.575204	−	0.818010i	$-0.304923\pi$
$644$	−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	$-0.947803\pi$
$653$		−	8.34315i		−	0.326493i	0.986585	−	0.163246i	$-0.0521965\pi$
$654$	−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	0.904169	−	0.427176i	$-0.140491\pi$
$661$	12.2635	+	12.2635i	0.476993	+	0.476993i	−0.427176	+	0.904169i	$0.640491\pi$
$662$	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	−0.998115	−	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	$0.0607927\pi$
$677$	30.4853	+	30.4853i	1.17164	+	1.17164i	0.189827	+	0.981818i	$0.439207\pi$
$678$	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	$0.150697\pi$
$691$			23.9706i			0.911883i	−0.890010	+	0.455942i	$0.849303\pi$
$692$	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	−0.346645	−	0.937996i	$-0.612679\pi$
$701$	15.6569	−	15.6569i	0.591351	−	0.591351i	0.937996	+	0.346645i	$0.112679\pi$
$702$	−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	0.510736	−	0.859738i	$-0.329373\pi$
$709$	−9.29289	−	9.29289i	−0.349002	−	0.349002i	−0.859738	+	0.510736i	$0.829373\pi$
$710$	−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	$-0.975390\pi$
$719$		−	4.14214i		−	0.154476i	0.997013	−	0.0772378i	$-0.0246101\pi$
$720$	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	−0.999929	−	0.0119415i	$-0.996199\pi$
$733$	−26.7487	+	26.7487i	−0.987987	+	0.987987i	0.0119415	+	0.999929i	$0.496199\pi$
$734$	−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	−0.925993	−	0.377540i	$-0.876770\pi$
$743$	−14.9497	+	14.9497i	−0.548453	+	0.548453i	0.377540	+	0.925993i	$0.376770\pi$
$744$	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	$-0.801248\pi$
$751$		−	32.0416i		−	1.16922i	0.811316	−	0.584608i	$-0.198752\pi$
$752$	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	$-0.904014\pi$
$757$		−	16.3431i		−	0.594002i	0.954877	−	0.297001i	$-0.0959864\pi$
$758$			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	$0.213653\pi$
$761$			34.3137i			1.24387i	−0.783068	+	0.621935i	$0.786347\pi$
$762$		−	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	−0.0996832	−	0.995019i	$-0.531783\pi$
$769$	24.8284	−	24.8284i	0.895336	−	0.895336i	0.995019	+	0.0996832i	$0.0317829\pi$
$770$	−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	0.804880	−	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
$775$	−0.849242	−	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	−0.555198	−	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
$790$	−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	−0.805110	−	0.593126i	$-0.797894\pi$
$809$	−6.02944	+	6.02944i	−0.211984	+	0.211984i	0.593126	+	0.805110i	$0.297894\pi$
$810$	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	0.788411	−	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
$827$			1.82843i			0.0635806i	0.999495	+	0.0317903i	$0.0101209\pi$
$827$			1.82843i			0.0635806i	−0.999495	+	0.0317903i	$0.989879\pi$
$828$			5.41421i			0.188157i
$829$	−24.7487	+	24.7487i	−0.859559	+	0.859559i	−0.991286	−	0.131727i	$-0.957948\pi$
$829$	−24.7487	+	24.7487i	−0.859559	+	0.859559i	0.131727	+	0.991286i	$0.457948\pi$
$830$	−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	$-0.810027\pi$
$853$		−	32.8284i		−	1.12402i	0.827129	−	0.562012i	$-0.189973\pi$
$854$	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	$0.0832686\pi$
$857$			15.1421i			0.517245i	−0.965978	+	0.258623i	$0.916731\pi$
$858$	−16.1421	−	16.1421i	−0.551083	−	0.551083i
$859$	5.44365	+	5.44365i	0.185735	+	0.185735i	0.793849	−	0.608114i	$-0.208074\pi$
$859$	5.44365	+	5.44365i	0.185735	+	0.185735i	−0.608114	+	0.793849i	$0.708074\pi$
$860$	−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
$865$	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	−0.517378	−	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
$880$	−3.87868	+	1.29289i	−0.130750	+	0.0435834i
$881$		−	7.48528i		−	0.252186i	−0.992018	−	0.126093i	$-0.959756\pi$
$881$		−	7.48528i		−	0.252186i	0.992018	−	0.126093i	$-0.0402437\pi$
$882$	3.65685			0.123133
$883$			53.6274i			1.80471i	0.430997	+	0.902353i	$0.358162\pi$
$883$			53.6274i			1.80471i	−0.430997	+	0.902353i	$0.641838\pi$
$884$			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	$-0.890847\pi$
$887$	−38.0624	−	38.0624i	−1.27801	−	1.27801i	−0.336233	−	0.941779i	$-0.609153\pi$
$888$	−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	$0.0746680\pi$
$907$			14.0000i			0.464862i	−0.972613	+	0.232431i	$0.925332\pi$
$908$		−	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	−0.0878595	−	0.996133i	$-0.528003\pi$
$911$	27.4142	−	27.4142i	0.908273	−	0.908273i	0.996133	+	0.0878595i	$0.0280026\pi$
$912$	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	−0.860320	−	0.509754i	$-0.829736\pi$
$919$	−10.6274	+	10.6274i	−0.350566	+	0.350566i	0.509754	+	0.860320i	$0.329736\pi$
$920$	−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	−0.575553	−	0.817765i	$-0.695213\pi$
$937$	7.41421	−	7.41421i	0.242212	−	0.242212i	0.817765	+	0.575553i	$0.195213\pi$
$938$	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	$-0.833180\pi$
$947$		−	30.7990i		−	1.00083i	0.865785	−	0.500416i	$-0.166820\pi$
$948$	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	−0.0257989	+	0.999667i	$0.508213\pi$
$953$	−31.6569	+	31.6569i	−1.02547	+	1.02547i	−0.999667	+	0.0257989i	$0.991787\pi$
$954$	−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	$-0.928037\pi$
$967$		−	13.9411i		−	0.448316i	0.974553	−	0.224158i	$-0.0719632\pi$
$968$	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	−0.840858	−	0.541255i	$-0.817949\pi$
$983$	−9.39340	+	9.39340i	−0.299603	+	0.299603i	0.541255	+	0.840858i	$0.317949\pi$
$984$	−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	0.837350	−	0.546667i	$-0.184104\pi$
$991$	9.15076	+	9.15076i	0.290683	+	0.290683i	−0.546667	+	0.837350i	$0.684104\pi$
$992$	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	$0.0683480\pi$
$997$			13.4558i			0.426151i	−0.977036	+	0.213075i	$0.931652\pi$
$998$	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.253.2	yes	4
5.2	odd	4		370.2.g.c.327.1	yes	4
37.6	odd	4		370.2.g.c.43.1	✓	4
185.117	even	4	inner	370.2.h.c.117.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.c.43.1	✓	4	37.6	odd	4
370.2.g.c.327.1	yes	4	5.2	odd	4
370.2.h.c.117.2	yes	4	185.117	even	4	inner
370.2.h.c.253.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.41421 - 1.41421i) q^{3} +1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +(1.41421 - 1.41421i) q^{6} +(1.29289 - 1.29289i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(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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