LMFDB - Embedded newform 1110.2.o.a.253.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.16
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.914315 + 2.04060i) q^{10} +1.09838i q^{11} +(0.707107 - 0.707107i) q^{12} -4.92901 q^{13} +(-0.867388 + 0.867388i) q^{14} +(-0.796400 - 2.08944i) q^{15} +1.00000 q^{16} -2.47393i q^{17} +1.00000i q^{18} +(-5.01453 - 5.01453i) q^{19} +(0.914315 - 2.04060i) q^{20} -1.22667i q^{21} -1.09838i q^{22} -0.254201 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.32806 - 3.73149i) q^{25} +4.92901 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.867388 - 0.867388i) q^{28} +(4.52766 - 4.52766i) q^{29} +(0.796400 + 2.08944i) q^{30} +(3.38961 + 3.38961i) q^{31} -1.00000 q^{32} +(0.776669 + 0.776669i) q^{33} +2.47393i q^{34} +(-0.976922 - 2.56305i) q^{35} -1.00000i q^{36} +(0.134999 + 6.08126i) q^{37} +(5.01453 + 5.01453i) q^{38} +(-3.48534 + 3.48534i) q^{39} +(-0.914315 + 2.04060i) q^{40} -5.96538i q^{41} +1.22667i q^{42} -11.5248 q^{43} +1.09838i q^{44} +(-2.04060 - 0.914315i) q^{45} +0.254201 q^{46} +(2.51562 - 2.51562i) q^{47} +(0.707107 - 0.707107i) q^{48} +5.49528i q^{49} +(3.32806 + 3.73149i) q^{50} +(-1.74934 - 1.74934i) q^{51} -4.92901 q^{52} +(-1.28565 - 1.28565i) q^{53} +(0.707107 + 0.707107i) q^{54} +(2.24134 + 1.00426i) q^{55} +(-0.867388 + 0.867388i) q^{56} -7.09162 q^{57} +(-4.52766 + 4.52766i) q^{58} +(3.61042 + 3.61042i) q^{59} +(-0.796400 - 2.08944i) q^{60} +(0.890776 + 0.890776i) q^{61} +(-3.38961 - 3.38961i) q^{62} +(-0.867388 - 0.867388i) q^{63} +1.00000 q^{64} +(-4.50667 + 10.0581i) q^{65} +(-0.776669 - 0.776669i) q^{66} +(-8.08465 - 8.08465i) q^{67} -2.47393i q^{68} +(-0.179747 + 0.179747i) q^{69} +(0.976922 + 2.56305i) q^{70} +12.9448 q^{71} +1.00000i q^{72} +(9.56625 - 9.56625i) q^{73} +(-0.134999 - 6.08126i) q^{74} +(-4.99186 - 0.285272i) q^{75} +(-5.01453 - 5.01453i) q^{76} +(0.952718 + 0.952718i) q^{77} +(3.48534 - 3.48534i) q^{78} +(-1.43534 - 1.43534i) q^{79} +(0.914315 - 2.04060i) q^{80} -1.00000 q^{81} +5.96538i q^{82} +(7.34416 + 7.34416i) q^{83} -1.22667i q^{84} +(-5.04830 - 2.26195i) q^{85} +11.5248 q^{86} -6.40308i q^{87} -1.09838i q^{88} +(-9.93692 + 9.93692i) q^{89} +(2.04060 + 0.914315i) q^{90} +(-4.27537 + 4.27537i) q^{91} -0.254201 q^{92} +4.79363 q^{93} +(-2.51562 + 2.51562i) q^{94} +(-14.8175 + 5.64777i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.50451i q^{97} -5.49528i q^{98} +1.09838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	0.914315	−	2.04060i	0.408894	−	0.912582i
$5$	0.914315	−	2.04060i	0.408894	−	0.912582i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	0.867388	−	0.867388i	0.327842	−	0.327842i	−0.523924	−	0.851765i	$-0.675532\pi$
$7$	0.867388	−	0.867388i	0.327842	−	0.327842i	0.851765	+	0.523924i	$0.175532\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−0.914315	+	2.04060i	−0.289132	+	0.645293i
$11$			1.09838i			0.331173i	0.986195	+	0.165586i	$0.0529517\pi$
$11$			1.09838i			0.331173i	−0.986195	+	0.165586i	$0.947048\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−4.92901			−1.36706			−0.683531	−	0.729921i	$-0.739557\pi$
$13$	−4.92901			−1.36706			−0.683531	+	0.729921i	$0.739557\pi$
$14$	−0.867388	+	0.867388i	−0.231819	+	0.231819i
$15$	−0.796400	−	2.08944i	−0.205630	−	0.539490i
$16$	1.00000			0.250000
$17$		−	2.47393i		−	0.600017i	−0.953937	−	0.300009i	$-0.903010\pi$
$17$		−	2.47393i		−	0.600017i	0.953937	−	0.300009i	$-0.0969895\pi$
$18$			1.00000i			0.235702i
$19$	−5.01453	−	5.01453i	−1.15041	−	1.15041i	−0.986470	−	0.163943i	$-0.947579\pi$
$19$	−5.01453	−	5.01453i	−1.15041	−	1.15041i	−0.163943	−	0.986470i	$-0.552421\pi$
$20$	0.914315	−	2.04060i	0.204447	−	0.456291i
$21$		−	1.22667i		−	0.267682i
$22$		−	1.09838i		−	0.234175i
$23$	−0.254201			−0.0530046			−0.0265023	−	0.999649i	$-0.508437\pi$
$23$	−0.254201			−0.0530046			−0.0265023	+	0.999649i	$0.508437\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−3.32806	−	3.73149i	−0.665611	−	0.746299i
$26$	4.92901			0.966659
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.867388	−	0.867388i	0.163921	−	0.163921i
$29$	4.52766	−	4.52766i	0.840765	−	0.840765i	−0.148193	−	0.988958i	$-0.547346\pi$
$29$	4.52766	−	4.52766i	0.840765	−	0.840765i	0.988958	+	0.148193i	$0.0473458\pi$
$30$	0.796400	+	2.08944i	0.145402	+	0.381477i
$31$	3.38961	+	3.38961i	0.608792	+	0.608792i	0.942630	−	0.333838i	$-0.108344\pi$
$31$	3.38961	+	3.38961i	0.608792	+	0.608792i	−0.333838	+	0.942630i	$0.608344\pi$
$32$	−1.00000			−0.176777
$33$	0.776669	+	0.776669i	0.135201	+	0.135201i
$34$			2.47393i			0.424276i
$35$	−0.976922	−	2.56305i	−0.165130	−	0.433235i
$36$		−	1.00000i		−	0.166667i
$37$	0.134999	+	6.08126i	0.0221937	+	0.999754i
$37$	0.134999	+	6.08126i	0.0221937	+	0.999754i
$38$	5.01453	+	5.01453i	0.813465	+	0.813465i
$39$	−3.48534	+	3.48534i	−0.558101	+	0.558101i
$40$	−0.914315	+	2.04060i	−0.144566	+	0.322646i
$41$		−	5.96538i		−	0.931635i	−0.884881	−	0.465818i	$-0.845760\pi$
$41$		−	5.96538i		−	0.931635i	0.884881	−	0.465818i	$-0.154240\pi$
$42$			1.22667i			0.189280i
$43$	−11.5248			−1.75752			−0.878760	−	0.477264i	$-0.841629\pi$
$43$	−11.5248			−1.75752			−0.878760	+	0.477264i	$0.841629\pi$
$44$			1.09838i			0.165586i
$45$	−2.04060	−	0.914315i	−0.304194	−	0.136298i
$46$	0.254201			0.0374799
$47$	2.51562	−	2.51562i	0.366941	−	0.366941i	−0.499419	−	0.866360i	$-0.666453\pi$
$47$	2.51562	−	2.51562i	0.366941	−	0.366941i	0.866360	+	0.499419i	$0.166453\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			5.49528i			0.785040i
$50$	3.32806	+	3.73149i	0.470658	+	0.527713i
$51$	−1.74934	−	1.74934i	−0.244956	−	0.244956i
$52$	−4.92901			−0.683531
$53$	−1.28565	−	1.28565i	−0.176598	−	0.176598i	0.613273	−	0.789871i	$-0.289853\pi$
$53$	−1.28565	−	1.28565i	−0.176598	−	0.176598i	−0.789871	+	0.613273i	$0.789853\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	2.24134	+	1.00426i	0.302222	+	0.135415i
$56$	−0.867388	+	0.867388i	−0.115910	+	0.115910i
$57$	−7.09162			−0.939308
$58$	−4.52766	+	4.52766i	−0.594511	+	0.594511i
$59$	3.61042	+	3.61042i	0.470037	+	0.470037i	0.901926	−	0.431890i	$-0.142153\pi$
$59$	3.61042	+	3.61042i	0.470037	+	0.470037i	−0.431890	+	0.901926i	$0.642153\pi$
$60$	−0.796400	−	2.08944i	−0.102815	−	0.269745i
$61$	0.890776	+	0.890776i	0.114052	+	0.114052i	0.761830	−	0.647777i	$-0.224301\pi$
$61$	0.890776	+	0.890776i	0.114052	+	0.114052i	−0.647777	+	0.761830i	$0.724301\pi$
$62$	−3.38961	−	3.38961i	−0.430481	−	0.430481i
$63$	−0.867388	−	0.867388i	−0.109281	−	0.109281i
$64$	1.00000			0.125000
$65$	−4.50667	+	10.0581i	−0.558984	+	1.24756i
$66$	−0.776669	−	0.776669i	−0.0956014	−	0.0956014i
$67$	−8.08465	−	8.08465i	−0.987697	−	0.987697i	0.0122281	−	0.999925i	$-0.496108\pi$
$67$	−8.08465	−	8.08465i	−0.987697	−	0.987697i	−0.999925	+	0.0122281i	$0.996108\pi$
$68$		−	2.47393i		−	0.300009i
$69$	−0.179747	+	0.179747i	−0.0216390	+	0.0216390i
$70$	0.976922	+	2.56305i	0.116764	+	0.306343i
$71$	12.9448			1.53626			0.768130	−	0.640294i	$-0.221187\pi$
$71$	12.9448			1.53626			0.768130	+	0.640294i	$0.221187\pi$
$72$			1.00000i			0.117851i
$73$	9.56625	−	9.56625i	1.11964	−	1.11964i	0.127851	−	0.991793i	$-0.459192\pi$
$73$	9.56625	−	9.56625i	1.11964	−	1.11964i	0.991793	−	0.127851i	$-0.0408081\pi$
$74$	−0.134999	−	6.08126i	−0.0156933	−	0.706933i
$75$	−4.99186	−	0.285272i	−0.576410	−	0.0329404i
$76$	−5.01453	−	5.01453i	−0.575206	−	0.575206i
$77$	0.952718	+	0.952718i	0.108572	+	0.108572i
$78$	3.48534	−	3.48534i	0.394637	−	0.394637i
$79$	−1.43534	−	1.43534i	−0.161488	−	0.161488i	0.621737	−	0.783226i	$-0.286427\pi$
$79$	−1.43534	−	1.43534i	−0.161488	−	0.161488i	−0.783226	+	0.621737i	$0.786427\pi$
$80$	0.914315	−	2.04060i	0.102223	−	0.228145i
$81$	−1.00000			−0.111111
$82$			5.96538i			0.658766i
$83$	7.34416	+	7.34416i	0.806127	+	0.806127i	0.984045	−	0.177919i	$-0.0569364\pi$
$83$	7.34416	+	7.34416i	0.806127	+	0.806127i	−0.177919	+	0.984045i	$0.556936\pi$
$84$		−	1.22667i		−	0.133841i
$85$	−5.04830	−	2.26195i	−0.547565	−	0.245343i
$86$	11.5248			1.24275
$87$		−	6.40308i		−	0.686482i
$88$		−	1.09838i		−	0.117087i
$89$	−9.93692	+	9.93692i	−1.05331	+	1.05331i	−0.0548149	+	0.998497i	$0.517457\pi$
$89$	−9.93692	+	9.93692i	−1.05331	+	1.05331i	−0.998497	+	0.0548149i	$0.982543\pi$
$90$	2.04060	+	0.914315i	0.215098	+	0.0963772i
$91$	−4.27537	+	4.27537i	−0.448180	+	0.448180i
$92$	−0.254201			−0.0265023
$93$	4.79363			0.497077
$94$	−2.51562	+	2.51562i	−0.259467	+	0.259467i
$95$	−14.8175	+	5.64777i	−1.52024	+	0.579449i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			5.50451i			0.558899i	0.960160	+	0.279449i	$0.0901519\pi$
$97$			5.50451i			0.558899i	−0.960160	+	0.279449i	$0.909848\pi$
$98$		−	5.49528i		−	0.555107i
$99$	1.09838			0.110391
$100$	−3.32806	−	3.73149i	−0.332806	−	0.373149i
$101$		−	18.0390i		−	1.79495i	−0.441068	−	0.897473i	$-0.645400\pi$
$101$		−	18.0390i		−	1.79495i	0.441068	−	0.897473i	$-0.354600\pi$
$102$	1.74934	+	1.74934i	0.173210	+	0.173210i
$103$		−	16.4190i		−	1.61781i	−0.587941	−	0.808904i	$-0.700061\pi$
$103$		−	16.4190i		−	1.61781i	0.587941	−	0.808904i	$-0.299939\pi$
$104$	4.92901			0.483330
$105$	−2.50314	−	1.12156i	−0.244281	−	0.109453i
$106$	1.28565	+	1.28565i	0.124874	+	0.124874i
$107$	−3.46603	+	3.46603i	−0.335073	+	0.335073i	−0.854509	−	0.519436i	$-0.826142\pi$
$107$	−3.46603	+	3.46603i	−0.335073	+	0.335073i	0.519436	+	0.854509i	$0.326142\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−9.52466	−	9.52466i	−0.912297	−	0.912297i	0.0841554	−	0.996453i	$-0.473181\pi$
$109$	−9.52466	−	9.52466i	−0.912297	−	0.912297i	−0.996453	+	0.0841554i	$0.973181\pi$
$110$	−2.24134	−	1.00426i	−0.213703	−	0.0957526i
$111$	4.39556	+	4.20464i	0.417208	+	0.399087i
$112$	0.867388	−	0.867388i	0.0819604	−	0.0819604i
$113$		−	12.6239i		−	1.18755i	−0.804629	−	0.593777i	$-0.797636\pi$
$113$		−	12.6239i		−	1.18755i	0.804629	−	0.593777i	$-0.202364\pi$
$114$	7.09162			0.664191
$115$	−0.232420	+	0.518722i	−0.0216733	+	0.0483711i
$116$	4.52766	−	4.52766i	0.420383	−	0.420383i
$117$			4.92901i			0.455687i
$118$	−3.61042	−	3.61042i	−0.332366	−	0.332366i
$119$	−2.14586	−	2.14586i	−0.196711	−	0.196711i
$120$	0.796400	+	2.08944i	0.0727011	+	0.190739i
$121$	9.79357			0.890325
$122$	−0.890776	−	0.890776i	−0.0806471	−	0.0806471i
$123$	−4.21816	−	4.21816i	−0.380339	−	0.380339i
$124$	3.38961	+	3.38961i	0.304396	+	0.304396i
$125$	−10.6574	+	3.37946i	−0.953223	+	0.302268i
$126$	0.867388	+	0.867388i	0.0772730	+	0.0772730i
$127$	−9.16645	+	9.16645i	−0.813391	+	0.813391i	−0.985141	−	0.171750i	$-0.945058\pi$
$127$	−9.16645	+	9.16645i	−0.813391	+	0.813391i	0.171750	+	0.985141i	$0.445058\pi$
$128$	−1.00000			−0.0883883
$129$	−8.14929	+	8.14929i	−0.717505	+	0.717505i
$130$	4.50667	−	10.0581i	0.395261	−	0.882156i
$131$	12.3216	+	12.3216i	1.07655	+	1.07655i	0.996816	+	0.0797308i	$0.0254061\pi$
$131$	12.3216	+	12.3216i	1.07655	+	1.07655i	0.0797308	+	0.996816i	$0.474594\pi$
$132$	0.776669	+	0.776669i	0.0676004	+	0.0676004i
$133$	−8.69909			−0.754307
$134$	8.08465	+	8.08465i	0.698407	+	0.698407i
$135$	−2.08944	+	0.796400i	−0.179830	+	0.0685432i
$136$			2.47393i			0.212138i
$137$	6.64965	−	6.64965i	0.568118	−	0.568118i	−0.363483	−	0.931601i	$-0.618412\pi$
$137$	6.64965	−	6.64965i	0.568118	−	0.568118i	0.931601	+	0.363483i	$0.118412\pi$
$138$	0.179747	−	0.179747i	0.0153011	−	0.0153011i
$139$	11.9768			1.01586			0.507928	−	0.861399i	$-0.330411\pi$
$139$	11.9768			1.01586			0.507928	+	0.861399i	$0.330411\pi$
$140$	−0.976922	−	2.56305i	−0.0825650	−	0.216617i
$141$		−	3.55763i		−	0.299606i
$142$	−12.9448			−1.08630
$143$		−	5.41391i		−	0.452734i
$144$		−	1.00000i		−	0.0833333i
$145$	−5.09941	−	13.3788i	−0.423483	−	1.11105i
$146$	−9.56625	+	9.56625i	−0.791708	+	0.791708i
$147$	3.88575	+	3.88575i	0.320491	+	0.320491i
$148$	0.134999	+	6.08126i	0.0110968	+	0.499877i
$149$		−	15.0455i		−	1.23258i	−0.787520	−	0.616289i	$-0.788635\pi$
$149$		−	15.0455i		−	1.23258i	0.787520	−	0.616289i	$-0.211365\pi$
$150$	4.99186	+	0.285272i	0.407583	+	0.0232924i
$151$			14.4920i			1.17934i	0.807644	+	0.589671i	$0.200743\pi$
$151$			14.4920i			1.17934i	−0.807644	+	0.589671i	$0.799257\pi$
$152$	5.01453	+	5.01453i	0.406732	+	0.406732i
$153$	−2.47393			−0.200006
$154$	−0.952718	−	0.952718i	−0.0767722	−	0.0767722i
$155$	10.0160	−	3.81765i	0.804504	−	0.306641i
$156$	−3.48534	+	3.48534i	−0.279050	+	0.279050i
$157$	−9.44787	+	9.44787i	−0.754022	+	0.754022i	−0.975227	−	0.221205i	$-0.929001\pi$
$157$	−9.44787	+	9.44787i	−0.754022	+	0.754022i	0.221205	+	0.975227i	$0.429001\pi$
$158$	1.43534	+	1.43534i	0.114190	+	0.114190i
$159$	−1.81819			−0.144192
$160$	−0.914315	+	2.04060i	−0.0722829	+	0.161323i
$161$	−0.220491	+	0.220491i	−0.0173771	+	0.0173771i
$162$	1.00000			0.0785674
$163$		−	9.52839i		−	0.746321i	−0.927767	−	0.373161i	$-0.878274\pi$
$163$		−	9.52839i		−	0.746321i	0.927767	−	0.373161i	$-0.121726\pi$
$164$		−	5.96538i		−	0.465818i
$165$	2.29499	−	0.874747i	0.178665	−	0.0680990i
$166$	−7.34416	−	7.34416i	−0.570018	−	0.570018i
$167$		−	5.43514i		−	0.420584i	−0.977639	−	0.210292i	$-0.932559\pi$
$167$		−	5.43514i		−	0.420584i	0.977639	−	0.210292i	$-0.0674415\pi$
$168$			1.22667i			0.0946398i
$169$	11.2952			0.868860
$170$	5.04830	+	2.26195i	0.387187	+	0.173484i
$171$	−5.01453	+	5.01453i	−0.383471	+	0.383471i
$172$	−11.5248			−0.878760
$173$	−5.41742	+	5.41742i	−0.411879	+	0.411879i	−0.882393	−	0.470514i	$-0.844069\pi$
$173$	−5.41742	+	5.41742i	−0.411879	+	0.411879i	0.470514	+	0.882393i	$0.344069\pi$
$174$			6.40308i			0.485416i
$175$	−6.12337	−	0.349935i	−0.462883	−	0.0264526i
$176$			1.09838i			0.0827932i
$177$	5.10591			0.383783
$178$	9.93692	−	9.93692i	0.744804	−	0.744804i
$179$	1.11655	−	1.11655i	0.0834548	−	0.0834548i	−0.664147	−	0.747602i	$-0.731205\pi$
$179$	1.11655	−	1.11655i	0.0834548	−	0.0834548i	0.747602	+	0.664147i	$0.231205\pi$
$180$	−2.04060	−	0.914315i	−0.152097	−	0.0681490i
$181$	−3.70989			−0.275754			−0.137877	−	0.990449i	$-0.544028\pi$
$181$	−3.70989			−0.275754			−0.137877	+	0.990449i	$0.544028\pi$
$182$	4.27537	−	4.27537i	0.316911	−	0.316911i
$183$	1.25975			0.0931232
$184$	0.254201			0.0187400
$185$	12.5328	+	5.28471i	0.921432	+	0.388540i
$186$	−4.79363			−0.351486
$187$	2.71731			0.198709
$188$	2.51562	−	2.51562i	0.183471	−	0.183471i
$189$	−1.22667			−0.0892272
$190$	14.8175	−	5.64777i	1.07497	−	0.409732i
$191$	−4.79894	+	4.79894i	−0.347239	+	0.347239i	−0.859080	−	0.511841i	$-0.828964\pi$
$191$	−4.79894	+	4.79894i	−0.347239	+	0.347239i	0.511841	+	0.859080i	$0.328964\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−2.16290			−0.155689			−0.0778444	−	0.996966i	$-0.524804\pi$
$193$	−2.16290			−0.155689			−0.0778444	+	0.996966i	$0.524804\pi$
$194$		−	5.50451i		−	0.395201i
$195$	3.92547	+	10.2989i	0.281109	+	0.737517i
$196$			5.49528i			0.392520i
$197$	3.85768	−	3.85768i	0.274848	−	0.274848i	−0.556200	−	0.831048i	$-0.687741\pi$
$197$	3.85768	−	3.85768i	0.274848	−	0.274848i	0.831048	+	0.556200i	$0.187741\pi$
$198$	−1.09838			−0.0780582
$199$	11.9163	−	11.9163i	0.844724	−	0.844724i	−0.144745	−	0.989469i	$-0.546236\pi$
$199$	11.9163	−	11.9163i	0.844724	−	0.844724i	0.989469	+	0.144745i	$0.0462362\pi$
$200$	3.32806	+	3.73149i	0.235329	+	0.263856i
$201$	−11.4334			−0.806451
$202$			18.0390i			1.26922i
$203$		−	7.85447i		−	0.551276i
$204$	−1.74934	−	1.74934i	−0.122478	−	0.122478i
$205$	−12.1729	−	5.45423i	−0.850194	−	0.380940i
$206$			16.4190i			1.14396i
$207$			0.254201i			0.0176682i
$208$	−4.92901			−0.341766
$209$	5.50784	−	5.50784i	0.380986	−	0.380986i
$210$	2.50314	+	1.12156i	0.172733	+	0.0773953i
$211$	25.4750			1.75377			0.876885	−	0.480700i	$-0.159617\pi$
$211$	25.4750			1.75377			0.876885	+	0.480700i	$0.159617\pi$
$212$	−1.28565	−	1.28565i	−0.0882989	−	0.0882989i
$213$	9.15333	−	9.15333i	0.627176	−	0.627176i
$214$	3.46603	−	3.46603i	0.236933	−	0.236933i
$215$	−10.5373	+	23.5175i	−0.718639	+	1.60388i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	5.88021			0.399175
$218$	9.52466	+	9.52466i	0.645092	+	0.645092i
$219$		−	13.5287i		−	0.914186i
$220$	2.24134	+	1.00426i	0.151111	+	0.0677073i
$221$			12.1941i			0.820261i
$222$	−4.39556	−	4.20464i	−0.295011	−	0.282197i
$223$	−3.60544	−	3.60544i	−0.241438	−	0.241438i	0.576007	−	0.817445i	$-0.304610\pi$
$223$	−3.60544	−	3.60544i	−0.241438	−	0.241438i	−0.817445	+	0.576007i	$0.804610\pi$
$224$	−0.867388	+	0.867388i	−0.0579548	+	0.0579548i
$225$	−3.73149	+	3.32806i	−0.248766	+	0.221870i
$226$			12.6239i			0.839728i
$227$		−	11.2463i		−	0.746442i	−0.927742	−	0.373221i	$-0.878253\pi$
$227$		−	11.2463i		−	0.746442i	0.927742	−	0.373221i	$-0.121747\pi$
$228$	−7.09162			−0.469654
$229$			18.6659i			1.23348i	0.787168	+	0.616739i	$0.211546\pi$
$229$			18.6659i			1.23348i	−0.787168	+	0.616739i	$0.788454\pi$
$230$	0.232420	−	0.518722i	0.0153253	−	0.0342035i
$231$	1.34735			0.0886489
$232$	−4.52766	+	4.52766i	−0.297255	+	0.297255i
$233$	−1.86289	+	1.86289i	−0.122042	+	0.122042i	−0.765490	−	0.643448i	$-0.777503\pi$
$233$	−1.86289	+	1.86289i	−0.122042	+	0.122042i	0.643448	+	0.765490i	$0.277503\pi$
$234$		−	4.92901i		−	0.322220i
$235$	−2.83330	−	7.43344i	−0.184824	−	0.484904i
$236$	3.61042	+	3.61042i	0.235018	+	0.235018i
$237$	−2.02988			−0.131855
$238$	2.14586	+	2.14586i	0.139095	+	0.139095i
$239$	12.7842	+	12.7842i	0.826943	+	0.826943i	0.987093	−	0.160149i	$-0.0511976\pi$
$239$	12.7842	+	12.7842i	0.826943	+	0.826943i	−0.160149	+	0.987093i	$0.551198\pi$
$240$	−0.796400	−	2.08944i	−0.0514074	−	0.134873i
$241$	−1.85063	+	1.85063i	−0.119210	+	0.119210i	−0.764195	−	0.644985i	$-0.776863\pi$
$241$	−1.85063	+	1.85063i	−0.119210	+	0.119210i	0.644985	+	0.764195i	$0.276863\pi$
$242$	−9.79357			−0.629555
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	0.890776	+	0.890776i	0.0570261	+	0.0570261i
$245$	11.2136	+	5.02441i	0.716413	+	0.320998i
$246$	4.21816	+	4.21816i	0.268940	+	0.268940i
$247$	24.7167	+	24.7167i	1.57269	+	1.57269i
$248$	−3.38961	−	3.38961i	−0.215241	−	0.215241i
$249$	10.3862			0.658200
$250$	10.6574	−	3.37946i	0.674030	−	0.213736i
$251$	14.6527	+	14.6527i	0.924870	+	0.924870i	0.997369	−	0.0724987i	$-0.0230973\pi$
$251$	14.6527	+	14.6527i	0.924870	+	0.924870i	−0.0724987	+	0.997369i	$0.523097\pi$
$252$	−0.867388	−	0.867388i	−0.0546403	−	0.0546403i
$253$		−	0.279209i		−	0.0175537i
$254$	9.16645	−	9.16645i	0.575154	−	0.575154i
$255$	−5.16913	+	1.97024i	−0.323703	+	0.123381i
$256$	1.00000			0.0625000
$257$			7.08582i			0.442001i	0.975274	+	0.221001i	$0.0709323\pi$
$257$			7.08582i			0.442001i	−0.975274	+	0.221001i	$0.929068\pi$
$258$	8.14929	−	8.14929i	0.507352	−	0.507352i
$259$	5.39191	+	5.15772i	0.335037	+	0.320485i
$260$	−4.50667	+	10.0581i	−0.279492	+	0.623778i
$261$	−4.52766	−	4.52766i	−0.280255	−	0.280255i
$262$	−12.3216	−	12.3216i	−0.761234	−	0.761234i
$263$	17.6568	−	17.6568i	1.08876	−	1.08876i	0.0931078	−	0.995656i	$-0.470320\pi$
$263$	17.6568	−	17.6568i	1.08876	−	1.08876i	0.995656	−	0.0931078i	$-0.0296801\pi$
$264$	−0.776669	−	0.776669i	−0.0478007	−	0.0478007i
$265$	−3.79899	+	1.44800i	−0.233370	+	0.0889502i
$266$	8.69909			0.533375
$267$			14.0529i			0.860025i
$268$	−8.08465	−	8.08465i	−0.493849	−	0.493849i
$269$			22.9016i			1.39633i	0.715935	+	0.698167i	$0.246001\pi$
$269$			22.9016i			1.39633i	−0.715935	+	0.698167i	$0.753999\pi$
$270$	2.08944	−	0.796400i	0.127159	−	0.0484674i
$271$	10.0289			0.609213			0.304607	−	0.952478i	$-0.401475\pi$
$271$	10.0289			0.609213			0.304607	+	0.952478i	$0.401475\pi$
$272$		−	2.47393i		−	0.150004i
$273$			6.04628i			0.365938i
$274$	−6.64965	+	6.64965i	−0.401720	+	0.401720i
$275$	4.09858	−	3.65546i	0.247154	−	0.220432i
$276$	−0.179747	+	0.179747i	−0.0108195	+	0.0108195i
$277$	−2.84725			−0.171074			−0.0855372	−	0.996335i	$-0.527261\pi$
$277$	−2.84725			−0.171074			−0.0855372	+	0.996335i	$0.527261\pi$
$278$	−11.9768			−0.718319
$279$	3.38961	−	3.38961i	0.202931	−	0.202931i
$280$	0.976922	+	2.56305i	0.0583822	+	0.153172i
$281$	13.1664	−	13.1664i	0.785440	−	0.785440i	−0.195303	−	0.980743i	$-0.562569\pi$
$281$	13.1664	−	13.1664i	0.785440	−	0.785440i	0.980743	+	0.195303i	$0.0625691\pi$
$282$			3.55763i			0.211854i
$283$			17.3118i			1.02908i	0.857467	+	0.514539i	$0.172037\pi$
$283$			17.3118i			1.02908i	−0.857467	+	0.514539i	$0.827963\pi$
$284$	12.9448			0.768130
$285$	−6.48397	+	14.4711i	−0.384077	+	0.857196i
$286$			5.41391i			0.320131i
$287$	−5.17429	−	5.17429i	−0.305429	−	0.305429i
$288$			1.00000i			0.0589256i
$289$	10.8797			0.639979
$290$	5.09941	+	13.3788i	0.299448	+	0.785631i
$291$	3.89228	+	3.89228i	0.228169	+	0.228169i
$292$	9.56625	−	9.56625i	0.559822	−	0.559822i
$293$	−6.15715	−	6.15715i	−0.359705	−	0.359705i	0.503999	−	0.863704i	$-0.331861\pi$
$293$	−6.15715	−	6.15715i	−0.359705	−	0.359705i	−0.863704	+	0.503999i	$0.831861\pi$
$294$	−3.88575	−	3.88575i	−0.226621	−	0.226621i
$295$	10.6685	−	4.06635i	0.621142	−	0.236752i
$296$	−0.134999	−	6.08126i	−0.00784665	−	0.353466i
$297$	0.776669	−	0.776669i	0.0450669	−	0.0450669i
$298$			15.0455i			0.871564i
$299$	1.25296			0.0724606
$300$	−4.99186	−	0.285272i	−0.288205	−	0.0164702i
$301$	−9.99650	+	9.99650i	−0.576188	+	0.576188i
$302$		−	14.4920i		−	0.833921i
$303$	−12.7555	−	12.7555i	−0.732784	−	0.732784i
$304$	−5.01453	−	5.01453i	−0.287603	−	0.287603i
$305$	2.63216	−	1.00326i	0.150717	−	0.0574467i
$306$	2.47393			0.141425
$307$	10.3124	+	10.3124i	0.588562	+	0.588562i	0.937242	−	0.348680i	$-0.113370\pi$
$307$	10.3124	+	10.3124i	0.588562	+	0.588562i	−0.348680	+	0.937242i	$0.613370\pi$
$308$	0.952718	+	0.952718i	0.0542861	+	0.0542861i
$309$	−11.6100	−	11.6100i	−0.660467	−	0.660467i
$310$	−10.0160	+	3.81765i	−0.568870	+	0.216828i
$311$	10.4943	+	10.4943i	0.595076	+	0.595076i	0.938998	−	0.343922i	$-0.111756\pi$
$311$	10.4943	+	10.4943i	0.595076	+	0.595076i	−0.343922	+	0.938998i	$0.611756\pi$
$312$	3.48534	−	3.48534i	0.197318	−	0.197318i
$313$	1.40586			0.0794637			0.0397319	−	0.999210i	$-0.487350\pi$
$313$	1.40586			0.0794637			0.0397319	+	0.999210i	$0.487350\pi$
$314$	9.44787	−	9.44787i	0.533174	−	0.533174i
$315$	−2.56305	+	0.976922i	−0.144412	+	0.0550433i
$316$	−1.43534	−	1.43534i	−0.0807442	−	0.0807442i
$317$	−8.94726	−	8.94726i	−0.502528	−	0.502528i	0.409694	−	0.912223i	$-0.365635\pi$
$317$	−8.94726	−	8.94726i	−0.502528	−	0.502528i	−0.912223	+	0.409694i	$0.865635\pi$
$318$	1.81819			0.101959
$319$	4.97307	+	4.97307i	0.278439	+	0.278439i
$320$	0.914315	−	2.04060i	0.0511117	−	0.114073i
$321$			4.90170i			0.273586i
$322$	0.220491	−	0.220491i	0.0122875	−	0.0122875i
$323$	−12.4056	+	12.4056i	−0.690267	+	0.690267i
$324$	−1.00000			−0.0555556
$325$	16.4040	+	18.3926i	0.909932	+	1.02024i
$326$			9.52839i			0.527729i
$327$	−13.4699			−0.744888
$328$			5.96538i			0.329383i
$329$		−	4.36404i		−	0.240597i
$330$	−2.29499	+	0.874747i	−0.126335	+	0.0481533i
$331$	10.3088	−	10.3088i	0.566624	−	0.566624i	−0.364557	−	0.931181i	$-0.618780\pi$
$331$	10.3088	−	10.3088i	0.566624	−	0.566624i	0.931181	+	0.364557i	$0.118780\pi$
$332$	7.34416	+	7.34416i	0.403063	+	0.403063i
$333$	6.08126	−	0.134999i	0.333251	−	0.00739790i
$334$			5.43514i			0.297398i
$335$	−23.8894	+	9.10558i	−1.30522	+	0.497491i
$336$		−	1.22667i		−	0.0669204i
$337$	−2.99336	−	2.99336i	−0.163059	−	0.163059i	0.620861	−	0.783920i	$-0.286783\pi$
$337$	−2.99336	−	2.99336i	−0.163059	−	0.163059i	−0.783920	+	0.620861i	$0.786783\pi$
$338$	−11.2952			−0.614376
$339$	−8.92643	−	8.92643i	−0.484817	−	0.484817i
$340$	−5.04830	−	2.26195i	−0.273782	−	0.122672i
$341$	−3.72307	+	3.72307i	−0.201615	+	0.201615i
$342$	5.01453	−	5.01453i	0.271155	−	0.271155i
$343$	10.8383	+	10.8383i	0.585211	+	0.585211i
$344$	11.5248			0.621377
$345$	0.202446	+	0.531137i	0.0108993	+	0.0285955i
$346$	5.41742	−	5.41742i	0.291242	−	0.291242i
$347$	20.2118			1.08503			0.542513	−	0.840048i	$-0.317473\pi$
$347$	20.2118			1.08503			0.542513	+	0.840048i	$0.317473\pi$
$348$		−	6.40308i		−	0.343241i
$349$		−	15.7463i		−	0.842880i	−0.906856	−	0.421440i	$-0.861525\pi$
$349$		−	15.7463i		−	0.842880i	0.906856	−	0.421440i	$-0.138475\pi$
$350$	6.12337	+	0.349935i	0.327308	+	0.0187048i
$351$	3.48534	+	3.48534i	0.186034	+	0.186034i
$352$		−	1.09838i		−	0.0585436i
$353$			3.15443i			0.167893i	0.996470	+	0.0839467i	$0.0267526\pi$
$353$			3.15443i			0.167893i	−0.996470	+	0.0839467i	$0.973247\pi$
$354$	−5.10591			−0.271376
$355$	11.8356	−	26.4150i	0.628167	−	1.40196i
$356$	−9.93692	+	9.93692i	−0.526656	+	0.526656i
$357$	−3.03470			−0.160614
$358$	−1.11655	+	1.11655i	−0.0590114	+	0.0590114i
$359$		−	6.13746i		−	0.323922i	−0.986797	−	0.161961i	$-0.948218\pi$
$359$		−	6.13746i		−	0.323922i	0.986797	−	0.161961i	$-0.0517820\pi$
$360$	2.04060	+	0.914315i	0.107549	+	0.0481886i
$361$			31.2911i			1.64690i
$362$	3.70989			0.194988
$363$	6.92510	−	6.92510i	0.363473	−	0.363473i
$364$	−4.27537	+	4.27537i	−0.224090	+	0.224090i
$365$	−10.7743	−	28.2674i	−0.563951	−	1.47958i
$366$	−1.25975			−0.0658480
$367$	10.0667	−	10.0667i	0.525478	−	0.525478i	−0.393743	−	0.919221i	$-0.628820\pi$
$367$	10.0667	−	10.0667i	0.525478	−	0.525478i	0.919221	+	0.393743i	$0.128820\pi$
$368$	−0.254201			−0.0132512
$369$	−5.96538			−0.310545
$370$	−12.5328	−	5.28471i	−0.651551	−	0.274739i
$371$	−2.23032			−0.115792
$372$	4.79363			0.248538
$373$	15.0617	−	15.0617i	0.779867	−	0.779867i	−0.199941	−	0.979808i	$-0.564075\pi$
$373$	15.0617	−	15.0617i	0.779867	−	0.779867i	0.979808	+	0.199941i	$0.0640751\pi$
$374$	−2.71731			−0.140509
$375$	−5.14625	+	9.92553i	−0.265751	+	0.512552i
$376$	−2.51562	+	2.51562i	−0.129733	+	0.129733i
$377$	−22.3169	+	22.3169i	−1.14938	+	1.14938i
$378$	1.22667			0.0630932
$379$			28.1933i			1.44819i	0.689699	+	0.724097i	$0.257743\pi$
$379$			28.1933i			1.44819i	−0.689699	+	0.724097i	$0.742257\pi$
$380$	−14.8175	+	5.64777i	−0.760121	+	0.289725i
$381$			12.9633i			0.664131i
$382$	4.79894	−	4.79894i	0.245535	−	0.245535i
$383$	28.9731			1.48045			0.740227	−	0.672357i	$-0.234718\pi$
$383$	28.9731			1.48045			0.740227	+	0.672357i	$0.234718\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	2.81520	−	1.07303i	0.143476	−	0.0546865i
$386$	2.16290			0.110089
$387$			11.5248i			0.585840i
$388$			5.50451i			0.279449i
$389$	−15.5001	−	15.5001i	−0.785886	−	0.785886i	0.194931	−	0.980817i	$-0.437552\pi$
$389$	−15.5001	−	15.5001i	−0.785886	−	0.785886i	−0.980817	+	0.194931i	$0.937552\pi$
$390$	−3.92547	−	10.2989i	−0.198774	−	0.521503i
$391$			0.628877i			0.0318037i
$392$		−	5.49528i		−	0.277553i
$393$	17.4254			0.878997
$394$	−3.85768	+	3.85768i	−0.194347	+	0.194347i
$395$	−4.24130	+	1.61660i	−0.213403	+	0.0813397i
$396$	1.09838			0.0551955
$397$	11.9173	+	11.9173i	0.598111	+	0.598111i	0.939810	−	0.341699i	$-0.111002\pi$
$397$	11.9173	+	11.9173i	0.598111	+	0.598111i	−0.341699	+	0.939810i	$0.611002\pi$
$398$	−11.9163	+	11.9163i	−0.597310	+	0.597310i
$399$	−6.15119	+	6.15119i	−0.307944	+	0.307944i
$400$	−3.32806	−	3.73149i	−0.166403	−	0.186575i
$401$	−24.2655	−	24.2655i	−1.21176	−	1.21176i	−0.970448	−	0.241312i	$-0.922422\pi$
$401$	−24.2655	−	24.2655i	−1.21176	−	1.21176i	−0.241312	−	0.970448i	$-0.577578\pi$
$402$	11.4334			0.570247
$403$	−16.7074	−	16.7074i	−0.832257	−	0.832257i
$404$		−	18.0390i		−	0.897473i
$405$	−0.914315	+	2.04060i	−0.0454327	+	0.101398i
$406$			7.85447i			0.389811i
$407$	−6.67952	+	0.148280i	−0.331091	+	0.00734995i
$408$	1.74934	+	1.74934i	0.0866050	+	0.0866050i
$409$	24.8350	−	24.8350i	1.22801	−	1.22801i	0.263299	−	0.964714i	$-0.415189\pi$
$409$	24.8350	−	24.8350i	1.22801	−	1.22801i	0.964714	−	0.263299i	$-0.0848106\pi$
$410$	12.1729	+	5.45423i	0.601178	+	0.269365i
$411$		−	9.40403i		−	0.463866i
$412$		−	16.4190i		−	0.808904i
$413$	6.26327			0.308195
$414$		−	0.254201i		−	0.0124933i
$415$	21.7013	−	8.27159i	1.06528	−	0.406036i
$416$	4.92901			0.241665
$417$	8.46886	−	8.46886i	0.414722	−	0.414722i
$418$	−5.50784	+	5.50784i	−0.269397	+	0.269397i
$419$			14.9938i			0.732494i	0.930518	+	0.366247i	$0.119358\pi$
$419$			14.9938i			0.732494i	−0.930518	+	0.366247i	$0.880642\pi$
$420$	−2.50314	−	1.12156i	−0.122141	−	0.0547267i
$421$	−14.6084	−	14.6084i	−0.711970	−	0.711970i	0.254977	−	0.966947i	$-0.417932\pi$
$421$	−14.6084	−	14.6084i	−0.711970	−	0.711970i	−0.966947	+	0.254977i	$0.917932\pi$
$422$	−25.4750			−1.24010
$423$	−2.51562	−	2.51562i	−0.122314	−	0.122314i
$424$	1.28565	+	1.28565i	0.0624368	+	0.0624368i
$425$	−9.23147	+	8.23339i	−0.447792	+	0.399378i
$426$	−9.15333	+	9.15333i	−0.443480	+	0.443480i
$427$	1.54530			0.0747821
$428$	−3.46603	+	3.46603i	−0.167537	+	0.167537i
$429$	−3.82821	−	3.82821i	−0.184828	−	0.184828i
$430$	10.5373	−	23.5175i	0.508155	−	1.13412i
$431$	−28.1159	−	28.1159i	−1.35430	−	1.35430i	−0.880790	−	0.473507i	$-0.842988\pi$
$431$	−28.1159	−	28.1159i	−1.35430	−	1.35430i	−0.473507	−	0.880790i	$-0.657012\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	3.11871	+	3.11871i	0.149876	+	0.149876i	0.778062	−	0.628187i	$-0.216203\pi$
$433$	3.11871	+	3.11871i	0.149876	+	0.149876i	−0.628187	+	0.778062i	$0.716203\pi$
$434$	−5.88021			−0.282259
$435$	−13.0661	−	5.85443i	−0.626471	−	0.280698i
$436$	−9.52466	−	9.52466i	−0.456149	−	0.456149i
$437$	1.27470	+	1.27470i	0.0609772	+	0.0609772i
$438$			13.5287i			0.646427i
$439$	−0.948240	+	0.948240i	−0.0452570	+	0.0452570i	−0.729373	−	0.684116i	$-0.760188\pi$
$439$	−0.948240	+	0.948240i	−0.0452570	+	0.0452570i	0.684116	+	0.729373i	$0.260188\pi$
$440$	−2.24134	−	1.00426i	−0.106852	−	0.0478763i
$441$	5.49528			0.261680
$442$		−	12.1941i		−	0.580012i
$443$	8.59429	−	8.59429i	0.408327	−	0.408327i	−0.472828	−	0.881155i	$-0.656767\pi$
$443$	8.59429	−	8.59429i	0.408327	−	0.408327i	0.881155	+	0.472828i	$0.156767\pi$
$444$	4.39556	+	4.20464i	0.208604	+	0.199544i
$445$	11.1918	+	29.3627i	0.530540	+	1.39193i
$446$	3.60544	+	3.60544i	0.170723	+	0.170723i
$447$	−10.6388	−	10.6388i	−0.503198	−	0.503198i
$448$	0.867388	−	0.867388i	0.0409802	−	0.0409802i
$449$	19.1095	+	19.1095i	0.901831	+	0.901831i	0.995595	−	0.0937631i	$-0.0298896\pi$
$449$	19.1095	+	19.1095i	0.901831	+	0.901831i	−0.0937631	+	0.995595i	$0.529890\pi$
$450$	3.73149	−	3.32806i	0.175904	−	0.156886i
$451$	6.55223			0.308532
$452$		−	12.6239i		−	0.593777i
$453$	10.2474	+	10.2474i	0.481464	+	0.481464i
$454$			11.2463i			0.527814i
$455$	4.81526	+	12.6333i	0.225743	+	0.592259i
$456$	7.09162			0.332096
$457$			15.6387i			0.731546i	0.930704	+	0.365773i	$0.119195\pi$
$457$			15.6387i			0.731546i	−0.930704	+	0.365773i	$0.880805\pi$
$458$		−	18.6659i		−	0.872200i
$459$	−1.74934	+	1.74934i	−0.0816520	+	0.0816520i
$460$	−0.232420	+	0.518722i	−0.0108366	+	0.0241855i
$461$	−0.984005	+	0.984005i	−0.0458297	+	0.0458297i	−0.729650	−	0.683821i	$-0.760317\pi$
$461$	−0.984005	+	0.984005i	−0.0458297	+	0.0458297i	0.683821	+	0.729650i	$0.260317\pi$
$462$	−1.34735			−0.0626842
$463$	7.27134			0.337928			0.168964	−	0.985622i	$-0.445958\pi$
$463$	7.27134			0.337928			0.168964	+	0.985622i	$0.445958\pi$
$464$	4.52766	−	4.52766i	0.210191	−	0.210191i
$465$	4.38289	−	9.78187i	0.203252	−	0.453623i
$466$	1.86289	−	1.86289i	0.0862969	−	0.0862969i
$467$			21.2081i			0.981395i	0.871330	+	0.490697i	$0.163258\pi$
$467$			21.2081i			0.981395i	−0.871330	+	0.490697i	$0.836742\pi$
$468$			4.92901i			0.227844i
$469$	−14.0251			−0.647617
$470$	2.83330	+	7.43344i	0.130690	+	0.342879i
$471$			13.3613i			0.615657i
$472$	−3.61042	−	3.61042i	−0.166183	−	0.166183i
$473$		−	12.6586i		−	0.582043i
$474$	2.02988			0.0932353
$475$	−2.02304	+	35.4003i	−0.0928235	+	1.62428i
$476$	−2.14586	−	2.14586i	−0.0983553	−	0.0983553i
$477$	−1.28565	+	1.28565i	−0.0588660	+	0.0588660i
$478$	−12.7842	−	12.7842i	−0.584737	−	0.584737i
$479$	−29.4758	−	29.4758i	−1.34678	−	1.34678i	−0.889133	−	0.457649i	$-0.848691\pi$
$479$	−29.4758	−	29.4758i	−1.34678	−	1.34678i	−0.457649	−	0.889133i	$-0.651309\pi$
$480$	0.796400	+	2.08944i	0.0363505	+	0.0953693i
$481$	−0.665412	−	29.9746i	−0.0303402	−	1.36673i
$482$	1.85063	−	1.85063i	0.0842940	−	0.0842940i
$483$			0.311821i			0.0141884i
$484$	9.79357			0.445162
$485$	11.2325	+	5.03286i	0.510041	+	0.228530i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			0.739280i			0.0335000i	0.999860	+	0.0167500i	$0.00533194\pi$
$487$			0.739280i			0.0335000i	−0.999860	+	0.0167500i	$0.994668\pi$
$488$	−0.890776	−	0.890776i	−0.0403235	−	0.0403235i
$489$	−6.73759	−	6.73759i	−0.304684	−	0.304684i
$490$	−11.2136	−	5.02441i	−0.506580	−	0.226980i
$491$	−21.9916			−0.992467			−0.496233	−	0.868189i	$-0.665284\pi$
$491$	−21.9916			−0.992467			−0.496233	+	0.868189i	$0.665284\pi$
$492$	−4.21816	−	4.21816i	−0.190169	−	0.190169i
$493$	−11.2011	−	11.2011i	−0.504473	−	0.504473i
$494$	−24.7167	−	24.7167i	−1.11206	−	1.11206i
$495$	1.00426	−	2.24134i	0.0451382	−	0.100741i
$496$	3.38961	+	3.38961i	0.152198	+	0.152198i
$497$	11.2281	−	11.2281i	0.503650	−	0.503650i
$498$	−10.3862			−0.465417
$499$	−23.3699	+	23.3699i	−1.04618	+	1.04618i	−0.0473000	+	0.998881i	$0.515062\pi$
$499$	−23.3699	+	23.3699i	−1.04618	+	1.04618i	−0.998881	+	0.0473000i	$0.984938\pi$
$500$	−10.6574	+	3.37946i	−0.476612	+	0.151134i
$501$	−3.84323	−	3.84323i	−0.171703	−	0.171703i
$502$	−14.6527	−	14.6527i	−0.653982	−	0.653982i
$503$	−2.74856			−0.122552			−0.0612762	−	0.998121i	$-0.519517\pi$
$503$	−2.74856			−0.122552			−0.0612762	+	0.998121i	$0.519517\pi$
$504$	0.867388	+	0.867388i	0.0386365	+	0.0386365i
$505$	−36.8103	−	16.4933i	−1.63804	−	0.733943i
$506$			0.279209i			0.0124123i
$507$	7.98689	−	7.98689i	0.354710	−	0.354710i
$508$	−9.16645	+	9.16645i	−0.406695	+	0.406695i
$509$	−15.4259			−0.683740			−0.341870	−	0.939747i	$-0.611060\pi$
$509$	−15.4259			−0.683740			−0.341870	+	0.939747i	$0.611060\pi$
$510$	5.16913	−	1.97024i	0.228893	−	0.0872438i
$511$		−	16.5953i		−	0.734133i
$512$	−1.00000			−0.0441942
$513$			7.09162i			0.313103i
$514$		−	7.08582i		−	0.312542i
$515$	−33.5045	−	15.0121i	−1.47638	−	0.661512i
$516$	−8.14929	+	8.14929i	−0.358752	+	0.358752i
$517$	2.76310	+	2.76310i	0.121521	+	0.121521i
$518$	−5.39191	−	5.15772i	−0.236907	−	0.226617i
$519$			7.66138i			0.336297i
$520$	4.50667	−	10.0581i	0.197631	−	0.441078i
$521$		−	2.41859i		−	0.105960i	−0.998596	−	0.0529802i	$-0.983128\pi$
$521$		−	2.41859i		−	0.105960i	0.998596	−	0.0529802i	$-0.0168720\pi$
$522$	4.52766	+	4.52766i	0.198170	+	0.198170i
$523$	−25.0092			−1.09358			−0.546789	−	0.837270i	$-0.684150\pi$
$523$	−25.0092			−1.09358			−0.546789	+	0.837270i	$0.684150\pi$
$524$	12.3216	+	12.3216i	0.538274	+	0.538274i
$525$	−4.57732	+	4.08243i	−0.199770	+	0.178172i
$526$	−17.6568	+	17.6568i	−0.769872	+	0.769872i
$527$	8.38567	−	8.38567i	0.365286	−	0.365286i
$528$	0.776669	+	0.776669i	0.0338002	+	0.0338002i
$529$	−22.9354			−0.997191
$530$	3.79899	−	1.44800i	0.165017	−	0.0628973i
$531$	3.61042	−	3.61042i	0.156679	−	0.156679i
$532$	−8.69909			−0.377153
$533$			29.4034i			1.27360i
$534$		−	14.0529i		−	0.608130i
$535$	3.90372	+	10.2418i	0.168772	+	0.442791i
$536$	8.08465	+	8.08465i	0.349204	+	0.349204i
$537$		−	1.57904i		−	0.0681405i
$538$		−	22.9016i		−	0.987357i
$539$	−6.03588			−0.259984
$540$	−2.08944	+	0.796400i	−0.0899150	+	0.0342716i
$541$	17.7792	−	17.7792i	0.764388	−	0.764388i	−0.212724	−	0.977112i	$-0.568234\pi$
$541$	17.7792	−	17.7792i	0.764388	−	0.764388i	0.977112	+	0.212724i	$0.0682337\pi$
$542$	−10.0289			−0.430779
$543$	−2.62329	+	2.62329i	−0.112576	+	0.112576i
$544$			2.47393i			0.106069i
$545$	−28.1445	+	10.7274i	−1.20558	+	0.459513i
$546$		−	6.04628i		−	0.258757i
$547$	24.0509			1.02834			0.514172	−	0.857687i	$-0.328099\pi$
$547$	24.0509			1.02834			0.514172	+	0.857687i	$0.328099\pi$
$548$	6.64965	−	6.64965i	0.284059	−	0.284059i
$549$	0.890776	−	0.890776i	0.0380174	−	0.0380174i
$550$	−4.09858	+	3.65546i	−0.174764	+	0.155869i
$551$	−45.4082			−1.93445
$552$	0.179747	−	0.179747i	0.00765056	−	0.00765056i
$553$	−2.48999			−0.105885
$554$	2.84725			0.120968
$555$	12.5989	−	5.12519i	0.534794	−	0.217552i
$556$	11.9768			0.507928
$557$	−32.7565			−1.38794			−0.693968	−	0.720006i	$-0.744139\pi$
$557$	−32.7565			−1.38794			−0.693968	+	0.720006i	$0.744139\pi$
$558$	−3.38961	+	3.38961i	−0.143494	+	0.143494i
$559$	56.8060			2.40264
$560$	−0.976922	−	2.56305i	−0.0412825	−	0.108309i
$561$	1.92143	−	1.92143i	0.0811228	−	0.0811228i
$562$	−13.1664	+	13.1664i	−0.555390	+	0.555390i
$563$	30.9683			1.30516			0.652580	−	0.757720i	$-0.273687\pi$
$563$	30.9683			1.30516			0.652580	+	0.757720i	$0.273687\pi$
$564$		−	3.55763i		−	0.149803i
$565$	−25.7602	−	11.5422i	−1.08374	−	0.485584i
$566$		−	17.3118i		−	0.727667i
$567$	−0.867388	+	0.867388i	−0.0364269	+	0.0364269i
$568$	−12.9448			−0.543150
$569$	32.3758	−	32.3758i	1.35726	−	1.35726i	0.479987	−	0.877275i	$-0.340641\pi$
$569$	32.3758	−	32.3758i	1.35726	−	1.35726i	0.877275	−	0.479987i	$-0.159359\pi$
$570$	6.48397	−	14.4711i	0.271584	−	0.606129i
$571$	40.5248			1.69591			0.847955	−	0.530068i	$-0.177833\pi$
$571$	40.5248			1.69591			0.847955	+	0.530068i	$0.177833\pi$
$572$		−	5.41391i		−	0.226367i
$573$			6.78673i			0.283520i
$574$	5.17429	+	5.17429i	0.215971	+	0.215971i
$575$	0.845996	+	0.948550i	0.0352805	+	0.0395573i
$576$		−	1.00000i		−	0.0416667i
$577$		−	16.8563i		−	0.701738i	−0.936425	−	0.350869i	$-0.885886\pi$
$577$		−	16.8563i		−	0.701738i	0.936425	−	0.350869i	$-0.114114\pi$
$578$	−10.8797			−0.452534
$579$	−1.52940	+	1.52940i	−0.0635597	+	0.0635597i
$580$	−5.09941	−	13.3788i	−0.211742	−	0.555525i
$581$	12.7405			0.528564
$582$	−3.89228	−	3.89228i	−0.161340	−	0.161340i
$583$	1.41213	−	1.41213i	0.0584844	−	0.0584844i
$584$	−9.56625	+	9.56625i	−0.395854	+	0.395854i
$585$	10.0581	+	4.50667i	0.415852	+	0.186328i
$586$	6.15715	+	6.15715i	0.254350	+	0.254350i
$587$	21.5366			0.888910			0.444455	−	0.895801i	$-0.353397\pi$
$587$	21.5366			0.888910			0.444455	+	0.895801i	$0.353397\pi$
$588$	3.88575	+	3.88575i	0.160246	+	0.160246i
$589$		−	33.9946i		−	1.40072i
$590$	−10.6685	+	4.06635i	−0.439214	+	0.167409i
$591$		−	5.45559i		−	0.224413i
$592$	0.134999	+	6.08126i	0.00554842	+	0.249938i
$593$	19.1371	+	19.1371i	0.785866	+	0.785866i	0.980814	−	0.194948i	$-0.0624538\pi$
$593$	19.1371	+	19.1371i	0.785866	+	0.785866i	−0.194948	+	0.980814i	$0.562454\pi$
$594$	−0.776669	+	0.776669i	−0.0318671	+	0.0318671i
$595$	−6.34082	+	2.41684i	−0.259948	+	0.0990808i
$596$		−	15.0455i		−	0.616289i
$597$		−	16.8522i		−	0.689714i
$598$	−1.25296			−0.0512374
$599$			28.8022i			1.17683i	0.808560	+	0.588414i	$0.200247\pi$
$599$			28.8022i			1.17683i	−0.808560	+	0.588414i	$0.799753\pi$
$600$	4.99186	+	0.285272i	0.203792	+	0.0116462i
$601$	29.7406			1.21314			0.606572	−	0.795028i	$-0.292544\pi$
$601$	29.7406			1.21314			0.606572	+	0.795028i	$0.292544\pi$
$602$	9.99650	−	9.99650i	0.407427	−	0.407427i
$603$	−8.08465	+	8.08465i	−0.329232	+	0.329232i
$604$			14.4920i			0.589671i
$605$	8.95441	−	19.9847i	0.364048	−	0.812494i
$606$	12.7555	+	12.7555i	0.518157	+	0.518157i
$607$	−34.8254			−1.41352			−0.706760	−	0.707454i	$-0.749844\pi$
$607$	−34.8254			−1.41352			−0.706760	+	0.707454i	$0.749844\pi$
$608$	5.01453	+	5.01453i	0.203366	+	0.203366i
$609$	−5.55395	−	5.55395i	−0.225057	−	0.225057i
$610$	−2.63216	+	1.00326i	−0.106573	+	0.0406209i
$611$	−12.3995	+	12.3995i	−0.501632	+	0.501632i
$612$	−2.47393			−0.100003
$613$	−20.5948	+	20.5948i	−0.831815	+	0.831815i	−0.987765	−	0.155950i	$-0.950156\pi$
$613$	−20.5948	+	20.5948i	−0.831815	+	0.831815i	0.155950	+	0.987765i	$0.450156\pi$
$614$	−10.3124	−	10.3124i	−0.416176	−	0.416176i
$615$	−12.4643	+	4.75083i	−0.502608	+	0.191572i
$616$	−0.952718	−	0.952718i	−0.0383861	−	0.0383861i
$617$	−27.4236	−	27.4236i	−1.10403	−	1.10403i	−0.993919	−	0.110115i	$-0.964878\pi$
$617$	−27.4236	−	27.4236i	−1.10403	−	1.10403i	−0.110115	−	0.993919i	$-0.535122\pi$
$618$	11.6100	+	11.6100i	0.467021	+	0.467021i
$619$	−4.08288			−0.164105			−0.0820525	−	0.996628i	$-0.526148\pi$
$619$	−4.08288			−0.164105			−0.0820525	+	0.996628i	$0.526148\pi$
$620$	10.0160	−	3.81765i	0.402252	−	0.153321i
$621$	0.179747	+	0.179747i	0.00721301	+	0.00721301i
$622$	−10.4943	−	10.4943i	−0.420782	−	0.420782i
$623$			17.2383i			0.690639i
$624$	−3.48534	+	3.48534i	−0.139525	+	0.139525i
$625$	−2.84807	+	24.8372i	−0.113923	+	0.993490i
$626$	−1.40586			−0.0561893
$627$		−	7.78927i		−	0.311073i
$628$	−9.44787	+	9.44787i	−0.377011	+	0.377011i
$629$	15.0446	−	0.333978i	0.599869	−	0.0133166i
$630$	2.56305	−	0.976922i	0.102114	−	0.0389215i
$631$	3.77897	+	3.77897i	0.150439	+	0.150439i	0.778314	−	0.627875i	$-0.216075\pi$
$631$	3.77897	+	3.77897i	0.150439	+	0.150439i	−0.627875	+	0.778314i	$0.716075\pi$
$632$	1.43534	+	1.43534i	0.0570948	+	0.0570948i
$633$	18.0135	−	18.0135i	0.715974	−	0.715974i
$634$	8.94726	+	8.94726i	0.355341	+	0.355341i
$635$	10.3240	+	27.0860i	0.409695	+	1.07488i
$636$	−1.81819			−0.0720958
$637$		−	27.0863i		−	1.07320i
$638$	−4.97307	−	4.97307i	−0.196886	−	0.196886i
$639$		−	12.9448i		−	0.512087i
$640$	−0.914315	+	2.04060i	−0.0361415	+	0.0806616i
$641$	−24.9603			−0.985873			−0.492937	−	0.870065i	$-0.664077\pi$
$641$	−24.9603			−0.985873			−0.492937	+	0.870065i	$0.664077\pi$
$642$		−	4.90170i		−	0.193455i
$643$		−	2.83684i		−	0.111874i	−0.998434	−	0.0559370i	$-0.982185\pi$
$643$		−	2.83684i		−	0.111874i	0.998434	−	0.0559370i	$-0.0178146\pi$
$644$	−0.220491	+	0.220491i	−0.00868856	+	0.00868856i
$645$	9.17838	+	24.0804i	0.361398	+	0.948165i
$646$	12.4056	−	12.4056i	0.488093	−	0.488093i
$647$	13.4627			0.529272			0.264636	−	0.964348i	$-0.414748\pi$
$647$	13.4627			0.529272			0.264636	+	0.964348i	$0.414748\pi$
$648$	1.00000			0.0392837
$649$	−3.96560	+	3.96560i	−0.155663	+	0.155663i
$650$	−16.4040	−	18.3926i	−0.643419	−	0.721416i
$651$	4.15794	−	4.15794i	0.162963	−	0.162963i
$652$		−	9.52839i		−	0.373161i
$653$			10.3817i			0.406266i	0.979151	+	0.203133i	$0.0651124\pi$
$653$			10.3817i			0.406266i	−0.979151	+	0.203133i	$0.934888\pi$
$654$	13.4699			0.526715
$655$	36.4094	−	13.8776i	1.42263	−	0.542244i
$656$		−	5.96538i		−	0.232909i
$657$	−9.56625	−	9.56625i	−0.373215	−	0.373215i
$658$			4.36404i			0.170128i
$659$	8.07050			0.314382			0.157191	−	0.987568i	$-0.449756\pi$
$659$	8.07050			0.314382			0.157191	+	0.987568i	$0.449756\pi$
$660$	2.29499	−	0.874747i	0.0893323	−	0.0340495i
$661$	−19.6260	−	19.6260i	−0.763361	−	0.763361i	0.213567	−	0.976928i	$-0.431492\pi$
$661$	−19.6260	−	19.6260i	−0.763361	−	0.763361i	−0.976928	+	0.213567i	$0.931492\pi$
$662$	−10.3088	+	10.3088i	−0.400663	+	0.400663i
$663$	8.62250	+	8.62250i	0.334870	+	0.334870i
$664$	−7.34416	−	7.34416i	−0.285009	−	0.285009i
$665$	−7.95371	+	17.7513i	−0.308432	+	0.688367i
$666$	−6.08126	+	0.134999i	−0.235644	+	0.00523110i
$667$	−1.15094	+	1.15094i	−0.0445644	+	0.0445644i
$668$		−	5.43514i		−	0.210292i
$669$	−5.09887			−0.197134
$670$	23.8894	−	9.10558i	0.922928	−	0.351779i
$671$	−0.978407	+	0.978407i	−0.0377710	+	0.0377710i
$672$			1.22667i			0.0473199i
$673$	−16.3159	−	16.3159i	−0.628931	−	0.628931i	0.318868	−	0.947799i	$-0.396697\pi$
$673$	−16.3159	−	16.3159i	−0.628931	−	0.628931i	−0.947799	+	0.318868i	$0.896697\pi$
$674$	2.99336	+	2.99336i	0.115300	+	0.115300i
$675$	−0.285272	+	4.99186i	−0.0109801	+	0.192137i
$676$	11.2952			0.434430
$677$	−0.868664	−	0.868664i	−0.0333855	−	0.0333855i	0.690217	−	0.723602i	$-0.257515\pi$
$677$	−0.868664	−	0.868664i	−0.0333855	−	0.0333855i	−0.723602	+	0.690217i	$0.757515\pi$
$678$	8.92643	+	8.92643i	0.342817	+	0.342817i
$679$	4.77455	+	4.77455i	0.183230	+	0.183230i
$680$	5.04830	+	2.26195i	0.193593	+	0.0867420i
$681$	−7.95232	−	7.95232i	−0.304734	−	0.304734i
$682$	3.72307	−	3.72307i	0.142564	−	0.142564i
$683$	−0.517143			−0.0197879			−0.00989397	−	0.999951i	$-0.503149\pi$
$683$	−0.517143			−0.0197879			−0.00989397	+	0.999951i	$0.503149\pi$
$684$	−5.01453	+	5.01453i	−0.191735	+	0.191735i
$685$	−7.48937	−	19.6491i	−0.286154	−	0.750754i
$686$	−10.8383	−	10.8383i	−0.413806	−	0.413806i
$687$	13.1988	+	13.1988i	0.503565	+	0.503565i
$688$	−11.5248			−0.439380
$689$	6.33700	+	6.33700i	0.241420	+	0.241420i
$690$	−0.202446	−	0.531137i	−0.00770699	−	0.0202201i
$691$		−	19.4361i		−	0.739384i	−0.929154	−	0.369692i	$-0.879463\pi$
$691$		−	19.4361i		−	0.739384i	0.929154	−	0.369692i	$-0.120537\pi$
$692$	−5.41742	+	5.41742i	−0.205939	+	0.205939i
$693$	0.952718	−	0.952718i	0.0361908	−	0.0361908i
$694$	−20.2118			−0.767229
$695$	10.9505	−	24.4397i	0.415378	−	0.927052i
$696$			6.40308i			0.242708i
$697$	−14.7579			−0.558997
$698$			15.7463i			0.596006i
$699$			2.63453i			0.0996471i
$700$	−6.12337	−	0.349935i	−0.231442	−	0.0132263i
$701$	0.871318	−	0.871318i	0.0329092	−	0.0329092i	−0.690461	−	0.723370i	$-0.742592\pi$
$701$	0.871318	−	0.871318i	0.0329092	−	0.0329092i	0.723370	+	0.690461i	$0.242592\pi$
$702$	−3.48534	−	3.48534i	−0.131546	−	0.131546i
$703$	29.8177	−	31.1717i	1.12460	−	1.17566i
$704$			1.09838i			0.0413966i
$705$	−7.25968	−	3.25279i	−0.273415	−	0.122507i
$706$		−	3.15443i		−	0.118719i
$707$	−15.6468	−	15.6468i	−0.588459	−	0.588459i
$708$	5.10591			0.191892
$709$	−19.1416	−	19.1416i	−0.718880	−	0.718880i	0.249496	−	0.968376i	$-0.419735\pi$
$709$	−19.1416	−	19.1416i	−0.718880	−	0.718880i	−0.968376	+	0.249496i	$0.919735\pi$
$710$	−11.8356	+	26.4150i	−0.444181	+	0.991338i
$711$	−1.43534	+	1.43534i	−0.0538295	+	0.0538295i
$712$	9.93692	−	9.93692i	0.372402	−	0.372402i
$713$	−0.861643	−	0.861643i	−0.0322688	−	0.0322688i
$714$	3.03470			0.113571
$715$	−11.0476	−	4.95002i	−0.413157	−	0.185120i
$716$	1.11655	−	1.11655i	0.0417274	−	0.0417274i
$717$	18.0796			0.675196
$718$			6.13746i			0.229048i
$719$		−	12.8203i		−	0.478117i	−0.971005	−	0.239058i	$-0.923161\pi$
$719$		−	12.8203i		−	0.478117i	0.971005	−	0.239058i	$-0.0768388\pi$
$720$	−2.04060	−	0.914315i	−0.0760485	−	0.0340745i
$721$	−14.2416	−	14.2416i	−0.530385	−	0.530385i
$722$		−	31.2911i		−	1.16453i
$723$			2.61719i			0.0973343i
$724$	−3.70989			−0.137877
$725$	−31.9632	−	1.82662i	−1.18708	−	0.0678389i
$726$	−6.92510	+	6.92510i	−0.257015	+	0.257015i
$727$	37.5040			1.39095			0.695474	−	0.718551i	$-0.255195\pi$
$727$	37.5040			1.39095			0.695474	+	0.718551i	$0.255195\pi$
$728$	4.27537	−	4.27537i	0.158456	−	0.158456i
$729$			1.00000i			0.0370370i
$730$	10.7743	+	28.2674i	0.398774	+	1.04622i
$731$			28.5117i			1.05454i
$732$	1.25975			0.0465616
$733$	−18.9861	+	18.9861i	−0.701269	+	0.701269i	−0.964683	−	0.263414i	$-0.915152\pi$
$733$	−18.9861	+	18.9861i	−0.701269	+	0.701269i	0.263414	+	0.964683i	$0.415152\pi$
$734$	−10.0667	+	10.0667i	−0.371569	+	0.371569i
$735$	11.4820	−	4.37644i	0.423521	−	0.161427i
$736$	0.254201			0.00936998
$737$	8.87999	−	8.87999i	0.327098	−	0.327098i
$738$	5.96538			0.219589
$739$	−5.07356			−0.186634			−0.0933169	−	0.995636i	$-0.529747\pi$
$739$	−5.07356			−0.186634			−0.0933169	+	0.995636i	$0.529747\pi$
$740$	12.5328	+	5.28471i	0.460716	+	0.194270i
$741$	34.9547			1.28409
$742$	2.23032			0.0818775
$743$	−1.23779	+	1.23779i	−0.0454102	+	0.0454102i	−0.729447	−	0.684037i	$-0.760223\pi$
$743$	−1.23779	+	1.23779i	−0.0454102	+	0.0454102i	0.684037	+	0.729447i	$0.260223\pi$
$744$	−4.79363			−0.175743
$745$	−30.7018	−	13.7564i	−1.12483	−	0.503994i
$746$	−15.0617	+	15.0617i	−0.551449	+	0.551449i
$747$	7.34416	−	7.34416i	0.268709	−	0.268709i
$748$	2.71731			0.0993547
$749$			6.01278i			0.219702i
$750$	5.14625	−	9.92553i	0.187915	−	0.362429i
$751$			9.88564i			0.360732i	0.983600	+	0.180366i	$0.0577282\pi$
$751$			9.88564i			0.360732i	−0.983600	+	0.180366i	$0.942272\pi$
$752$	2.51562	−	2.51562i	0.0917353	−	0.0917353i
$753$	20.7220			0.755153
$754$	22.3169	−	22.3169i	0.812733	−	0.812733i
$755$	29.5723	+	13.2502i	1.07625	+	0.482226i
$756$	−1.22667			−0.0446136
$757$			36.7008i			1.33391i	0.745097	+	0.666956i	$0.232403\pi$
$757$			36.7008i			1.33391i	−0.745097	+	0.666956i	$0.767597\pi$
$758$		−	28.1933i		−	1.02403i
$759$	−0.197430	−	0.197430i	−0.00716626	−	0.00716626i
$760$	14.8175	−	5.64777i	0.537487	−	0.204866i
$761$		−	37.6951i		−	1.36645i	−0.730209	−	0.683224i	$-0.760577\pi$
$761$		−	37.6951i		−	1.36645i	0.730209	−	0.683224i	$-0.239423\pi$
$762$		−	12.9633i		−	0.469611i
$763$	−16.5232			−0.598178
$764$	−4.79894	+	4.79894i	−0.173620	+	0.173620i
$765$	−2.26195	+	5.04830i	−0.0817811	+	0.182522i
$766$	−28.9731			−1.04684
$767$	−17.7958	−	17.7958i	−0.642570	−	0.642570i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−34.1561	+	34.1561i	−1.23170	+	1.23170i	−0.268392	+	0.963310i	$0.586492\pi$
$769$	−34.1561	+	34.1561i	−1.23170	+	1.23170i	−0.963310	+	0.268392i	$0.913508\pi$
$770$	−2.81520	+	1.07303i	−0.101453	+	0.0386692i
$771$	5.01043	+	5.01043i	0.180446	+	0.180446i
$772$	−2.16290			−0.0778444
$773$	28.6997	+	28.6997i	1.03226	+	1.03226i	0.999462	+	0.0327935i	$0.0104404\pi$
$773$	28.6997	+	28.6997i	1.03226	+	1.03226i	0.0327935	+	0.999462i	$0.489560\pi$
$774$		−	11.5248i		−	0.414251i
$775$	1.36749	−	23.9291i	0.0491217	−	0.859560i
$776$		−	5.50451i		−	0.197601i
$777$	7.45971	−	0.165599i	0.267616	−	0.00594084i
$778$	15.5001	+	15.5001i	0.555706	+	0.555706i
$779$	−29.9136	+	29.9136i	−1.07177	+	1.07177i
$780$	3.92547	+	10.2989i	0.140554	+	0.368758i
$781$			14.2182i			0.508768i
$782$		−	0.628877i		−	0.0224886i
$783$	−6.40308			−0.228827
$784$			5.49528i			0.196260i
$785$	10.6410	+	27.9176i	0.379792	+	0.996422i
$786$	−17.4254			−0.621545
$787$	−29.7297	+	29.7297i	−1.05975	+	1.05975i	−0.0616500	+	0.998098i	$0.519636\pi$
$787$	−29.7297	+	29.7297i	−1.05975	+	1.05975i	−0.998098	+	0.0616500i	$0.980364\pi$
$788$	3.85768	−	3.85768i	0.137424	−	0.137424i
$789$		−	24.9705i		−	0.888972i
$790$	4.24130	−	1.61660i	0.150899	−	0.0575159i
$791$	−10.9498	−	10.9498i	−0.389330	−	0.389330i
$792$	−1.09838			−0.0390291
$793$	−4.39065	−	4.39065i	−0.155916	−	0.155916i
$794$	−11.9173	−	11.9173i	−0.422928	−	0.422928i
$795$	−1.66239	+	3.71018i	−0.0589591	+	0.131587i
$796$	11.9163	−	11.9163i	0.422362	−	0.422362i
$797$	−29.1682			−1.03319			−0.516596	−	0.856229i	$-0.672801\pi$
$797$	−29.1682			−1.03319			−0.516596	+	0.856229i	$0.672801\pi$
$798$	6.15119	−	6.15119i	0.217750	−	0.217750i
$799$	−6.22348	−	6.22348i	−0.220171	−	0.220171i
$800$	3.32806	+	3.73149i	0.117665	+	0.131928i
$801$	9.93692	+	9.93692i	0.351104	+	0.351104i
$802$	24.2655	+	24.2655i	0.856843	+	0.856843i
$803$	10.5073	+	10.5073i	0.370796	+	0.370796i
$804$	−11.4334			−0.403226
$805$	0.248335	+	0.651531i	0.00875265	+	0.0229635i
$806$	16.7074	+	16.7074i	0.588494	+	0.588494i
$807$	16.1939	+	16.1939i	0.570051	+	0.570051i
$808$			18.0390i			0.634610i
$809$	−2.57630	+	2.57630i	−0.0905779	+	0.0905779i	−0.750944	−	0.660366i	$-0.770401\pi$
$809$	−2.57630	+	2.57630i	−0.0905779	+	0.0905779i	0.660366	+	0.750944i	$0.270401\pi$
$810$	0.914315	−	2.04060i	0.0321257	−	0.0716992i
$811$	−4.32704			−0.151943			−0.0759714	−	0.997110i	$-0.524206\pi$
$811$	−4.32704			−0.151943			−0.0759714	+	0.997110i	$0.524206\pi$
$812$		−	7.85447i		−	0.275638i
$813$	7.09151	−	7.09151i	0.248710	−	0.248710i
$814$	6.67952	−	0.148280i	0.234117	−	0.00519720i
$815$	−19.4436	−	8.71195i	−0.681079	−	0.305166i
$816$	−1.74934	−	1.74934i	−0.0612390	−	0.0612390i
$817$	57.7916	+	57.7916i	2.02187	+	2.02187i
$818$	−24.8350	+	24.8350i	−0.868337	+	0.868337i
$819$	4.27537	+	4.27537i	0.149393	+	0.149393i
$820$	−12.1729	−	5.45423i	−0.425097	−	0.190470i
$821$	4.90449			0.171168			0.0855840	−	0.996331i	$-0.472724\pi$
$821$	4.90449			0.171168			0.0855840	+	0.996331i	$0.472724\pi$
$822$			9.40403i			0.328003i
$823$	−3.10219	−	3.10219i	−0.108135	−	0.108135i	0.650969	−	0.759104i	$-0.274363\pi$
$823$	−3.10219	−	3.10219i	−0.108135	−	0.108135i	−0.759104	+	0.650969i	$0.774363\pi$
$824$			16.4190i			0.571982i
$825$	0.313336	−	5.48293i	0.0109090	−	0.190891i
$826$	−6.26327			−0.217927
$827$			45.2102i			1.57211i	0.618155	+	0.786056i	$0.287880\pi$
$827$			45.2102i			1.57211i	−0.618155	+	0.786056i	$0.712120\pi$
$828$			0.254201i			0.00883410i
$829$	30.2853	−	30.2853i	1.05185	−	1.05185i	0.0532704	−	0.998580i	$-0.483035\pi$
$829$	30.2853	−	30.2853i	1.05185	−	1.05185i	0.998580	−	0.0532704i	$-0.0169645\pi$
$830$	−21.7013	+	8.27159i	−0.753264	+	0.287111i
$831$	−2.01331	+	2.01331i	−0.0698408	+	0.0698408i
$832$	−4.92901			−0.170883
$833$	13.5950			0.471037
$834$	−8.46886	+	8.46886i	−0.293253	+	0.293253i
$835$	−11.0909	−	4.96943i	−0.383817	−	0.171974i
$836$	5.50784	−	5.50784i	0.190493	−	0.190493i
$837$		−	4.79363i		−	0.165692i
$838$		−	14.9938i		−	0.517952i
$839$	−44.0363			−1.52030			−0.760150	−	0.649747i	$-0.774875\pi$
$839$	−44.0363			−1.52030			−0.760150	+	0.649747i	$0.774875\pi$
$840$	2.50314	+	1.12156i	0.0863665	+	0.0386976i
$841$		−	11.9994i		−	0.413772i
$842$	14.6084	+	14.6084i	0.503439	+	0.503439i
$843$		−	18.6201i		−	0.641309i
$844$	25.4750			0.876885
$845$	10.3273	−	23.0489i	0.355271	−	0.792906i
$846$	2.51562	+	2.51562i	0.0864889	+	0.0864889i
$847$	8.49482	−	8.49482i	0.291886	−	0.291886i
$848$	−1.28565	−	1.28565i	−0.0441495	−	0.0441495i
$849$	12.2413	+	12.2413i	0.420119	+	0.420119i
$850$	9.23147	−	8.23339i	0.316637	−	0.282403i
$851$	−0.0343169	−	1.54586i	−0.00117637	−	0.0529916i
$852$	9.15333	−	9.15333i	0.313588	−	0.313588i
$853$			6.92076i			0.236962i	0.992956	+	0.118481i	$0.0378025\pi$
$853$			6.92076i			0.236962i	−0.992956	+	0.118481i	$0.962197\pi$
$854$	−1.54530			−0.0528789
$855$	5.64777	+	14.8175i	0.193150	+	0.506748i
$856$	3.46603	−	3.46603i	0.118466	−	0.118466i
$857$			21.7102i			0.741606i	0.928712	+	0.370803i	$0.120917\pi$
$857$			21.7102i			0.741606i	−0.928712	+	0.370803i	$0.879083\pi$
$858$	3.82821	+	3.82821i	0.130693	+	0.130693i
$859$	33.3488	+	33.3488i	1.13785	+	1.13785i	0.988835	+	0.149012i	$0.0476092\pi$
$859$	33.3488	+	33.3488i	1.13785	+	1.13785i	0.149012	+	0.988835i	$0.452391\pi$
$860$	−10.5373	+	23.5175i	−0.359320	+	0.801940i
$861$	−7.31756			−0.249382
$862$	28.1159	+	28.1159i	0.957633	+	0.957633i
$863$	8.81980	+	8.81980i	0.300229	+	0.300229i	0.841104	−	0.540874i	$-0.181906\pi$
$863$	8.81980	+	8.81980i	0.300229	+	0.300229i	−0.540874	+	0.841104i	$0.681906\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	6.10153	+	16.0080i	0.207458	+	0.544288i
$866$	−3.11871	−	3.11871i	−0.105978	−	0.105978i
$867$	7.69307	−	7.69307i	0.261271	−	0.261271i
$868$	5.88021			0.199587
$869$	1.57654	−	1.57654i	0.0534806	−	0.0534806i
$870$	13.0661	+	5.85443i	0.442982	+	0.198484i
$871$	39.8493	+	39.8493i	1.35024	+	1.35024i
$872$	9.52466	+	9.52466i	0.322546	+	0.322546i
$873$	5.50451			0.186300
$874$	−1.27470	−	1.27470i	−0.0431174	−	0.0431174i
$875$	−6.31276	+	12.1754i	−0.213410	+	0.411602i
$876$		−	13.5287i		−	0.457093i
$877$	−9.99753	+	9.99753i	−0.337593	+	0.337593i	−0.855461	−	0.517868i	$-0.826726\pi$
$877$	−9.99753	+	9.99753i	−0.337593	+	0.337593i	0.517868	+	0.855461i	$0.326726\pi$
$878$	0.948240	−	0.948240i	0.0320016	−	0.0320016i
$879$	−8.70753			−0.293698
$880$	2.24134	+	1.00426i	0.0755556	+	0.0338536i
$881$		−	5.89777i		−	0.198701i	−0.995052	−	0.0993505i	$-0.968323\pi$
$881$		−	5.89777i		−	0.198701i	0.995052	−	0.0993505i	$-0.0316765\pi$
$882$	−5.49528			−0.185036
$883$			23.6714i			0.796607i	0.917254	+	0.398304i	$0.130401\pi$
$883$			23.6714i			0.796607i	−0.917254	+	0.398304i	$0.869599\pi$
$884$			12.1941i			0.410130i
$885$	4.66841	−	10.4191i	0.156927	−	0.350234i
$886$	−8.59429	+	8.59429i	−0.288731	+	0.288731i
$887$	27.3155	+	27.3155i	0.917165	+	0.917165i	0.996822	−	0.0796570i	$-0.0253825\pi$
$887$	27.3155	+	27.3155i	0.917165	+	0.917165i	−0.0796570	+	0.996822i	$0.525383\pi$
$888$	−4.39556	−	4.20464i	−0.147505	−	0.141099i
$889$			15.9017i			0.533327i
$890$	−11.1918	−	29.3627i	−0.375149	−	0.984240i
$891$		−	1.09838i		−	0.0367970i
$892$	−3.60544	−	3.60544i	−0.120719	−	0.120719i
$893$	−25.2294			−0.844268
$894$	10.6388	+	10.6388i	0.355815	+	0.355815i
$895$	−1.25755	−	3.29930i	−0.0420352	−	0.110283i
$896$	−0.867388	+	0.867388i	−0.0289774	+	0.0289774i
$897$	0.885977	−	0.885977i	0.0295819	−	0.0295819i
$898$	−19.1095	−	19.1095i	−0.637691	−	0.637691i
$899$	30.6940			1.02370
$900$	−3.73149	+	3.32806i	−0.124383	+	0.110935i
$901$	−3.18062	+	3.18062i	−0.105962	+	0.105962i
$902$	−6.55223			−0.218165
$903$			14.1372i			0.470456i
$904$			12.6239i			0.419864i
$905$	−3.39201	+	7.57039i	−0.112754	+	0.251648i
$906$	−10.2474	−	10.2474i	−0.340447	−	0.340447i
$907$		−	15.6714i		−	0.520361i	−0.965560	−	0.260180i	$-0.916218\pi$
$907$		−	15.6714i		−	0.520361i	0.965560	−	0.260180i	$-0.0837821\pi$
$908$		−	11.2463i		−	0.373221i
$909$	−18.0390			−0.598316
$910$	−4.81526	−	12.6333i	−0.159624	−	0.418791i
$911$	−3.65431	+	3.65431i	−0.121073	+	0.121073i	−0.765047	−	0.643974i	$-0.777284\pi$
$911$	−3.65431	+	3.65431i	−0.121073	+	0.121073i	0.643974	+	0.765047i	$0.277284\pi$
$912$	−7.09162			−0.234827
$913$	−8.06665	+	8.06665i	−0.266967	+	0.266967i
$914$		−	15.6387i		−	0.517281i
$915$	1.15181	−	2.57063i	0.0380775	−	0.0849825i
$916$			18.6659i			0.616739i
$917$	21.3753			0.705874
$918$	1.74934	−	1.74934i	0.0577367	−	0.0577367i
$919$	0.866154	−	0.866154i	0.0285718	−	0.0285718i	−0.692677	−	0.721248i	$-0.743569\pi$
$919$	0.866154	−	0.866154i	0.0285718	−	0.0285718i	0.721248	+	0.692677i	$0.243569\pi$
$920$	0.232420	−	0.518722i	0.00766266	−	0.0171017i
$921$	14.5840			0.480559
$922$	0.984005	−	0.984005i	0.0324065	−	0.0324065i
$923$	−63.8049			−2.10016
$924$	1.34735			0.0443245
$925$	22.2429	−	20.7425i	0.731342	−	0.682011i
$926$	−7.27134			−0.238951
$927$	−16.4190			−0.539269
$928$	−4.52766	+	4.52766i	−0.148628	+	0.148628i
$929$	25.0933			0.823284			0.411642	−	0.911346i	$-0.364955\pi$
$929$	25.0933			0.823284			0.411642	+	0.911346i	$0.364955\pi$
$930$	−4.38289	+	9.78187i	−0.143721	+	0.320760i
$931$	27.5562	−	27.5562i	0.903120	−	0.903120i
$932$	−1.86289	+	1.86289i	−0.0610211	+	0.0610211i
$933$	14.8411			0.485877
$934$		−	21.2081i		−	0.693951i
$935$	2.48448	−	5.54493i	0.0812511	−	0.181339i
$936$		−	4.92901i		−	0.161110i
$937$	11.1505	−	11.1505i	0.364272	−	0.364272i	−0.501111	−	0.865383i	$-0.667075\pi$
$937$	11.1505	−	11.1505i	0.364272	−	0.364272i	0.865383	+	0.501111i	$0.167075\pi$
$938$	14.0251			0.457934
$939$	0.994091	−	0.994091i	0.0324409	−	0.0324409i
$940$	−2.83330	−	7.43344i	−0.0924119	−	0.242452i
$941$	−25.2689			−0.823744			−0.411872	−	0.911242i	$-0.635125\pi$
$941$	−25.2689			−0.823744			−0.411872	+	0.911242i	$0.635125\pi$
$942$		−	13.3613i		−	0.435335i
$943$			1.51641i			0.0493810i
$944$	3.61042	+	3.61042i	0.117509	+	0.117509i
$945$	−1.12156	+	2.50314i	−0.0364845	+	0.0814272i
$946$			12.6586i			0.411566i
$947$		−	20.4774i		−	0.665427i	−0.943028	−	0.332714i	$-0.892036\pi$
$947$		−	20.4774i		−	0.665427i	0.943028	−	0.332714i	$-0.107964\pi$
$948$	−2.02988			−0.0659273
$949$	−47.1522	+	47.1522i	−1.53062	+	1.53062i
$950$	2.02304	−	35.4003i	0.0656361	−	1.14854i
$951$	−12.6533			−0.410313
$952$	2.14586	+	2.14586i	0.0695477	+	0.0695477i
$953$	15.9702	−	15.9702i	0.517327	−	0.517327i	−0.399435	−	0.916762i	$-0.630794\pi$
$953$	15.9702	−	15.9702i	0.517327	−	0.517327i	0.916762	+	0.399435i	$0.130794\pi$
$954$	1.28565	−	1.28565i	0.0416245	−	0.0416245i
$955$	5.40495	+	14.1804i	0.174900	+	0.458868i
$956$	12.7842	+	12.7842i	0.413472	+	0.413472i
$957$	7.03299			0.227344
$958$	29.4758	+	29.4758i	0.952319	+	0.952319i
$959$		−	11.5357i		−	0.372506i
$960$	−0.796400	−	2.08944i	−0.0257037	−	0.0674363i
$961$		−	8.02107i		−	0.258744i
$962$	0.665412	+	29.9746i	0.0214537	+	0.966421i
$963$	3.46603	+	3.46603i	0.111691	+	0.111691i
$964$	−1.85063	+	1.85063i	−0.0596049	+	0.0596049i
$965$	−1.97757	+	4.41360i	−0.0636602	+	0.142079i
$966$		−	0.311821i		−	0.0100327i
$967$			54.4250i			1.75019i	0.483950	+	0.875095i	$0.339202\pi$
$967$			54.4250i			1.75019i	−0.483950	+	0.875095i	$0.660798\pi$
$968$	−9.79357			−0.314777
$969$			17.5442i			0.563601i
$970$	−11.2325	−	5.03286i	−0.360653	−	0.161595i
$971$	−22.8759			−0.734121			−0.367061	−	0.930197i	$-0.619636\pi$
$971$	−22.8759			−0.734121			−0.367061	+	0.930197i	$0.619636\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	10.3885	−	10.3885i	0.333040	−	0.333040i
$974$		−	0.739280i		−	0.0236881i
$975$	24.6049	+	1.40611i	0.787988	+	0.0450316i
$976$	0.890776	+	0.890776i	0.0285130	+	0.0285130i
$977$	38.0996			1.21891			0.609457	−	0.792819i	$-0.291388\pi$
$977$	38.0996			1.21891			0.609457	+	0.792819i	$0.291388\pi$
$978$	6.73759	+	6.73759i	0.215444	+	0.215444i
$979$	−10.9145	−	10.9145i	−0.348828	−	0.348828i
$980$	11.2136	+	5.02441i	0.358206	+	0.160499i
$981$	−9.52466	+	9.52466i	−0.304099	+	0.304099i
$982$	21.9916			0.701780
$983$	−11.4270	+	11.4270i	−0.364464	+	0.364464i	−0.865453	−	0.500989i	$-0.832970\pi$
$983$	−11.4270	+	11.4270i	−0.364464	+	0.364464i	0.500989	+	0.865453i	$0.332970\pi$
$984$	4.21816	+	4.21816i	0.134470	+	0.134470i
$985$	−4.34483	−	11.3991i	−0.138438	−	0.363206i
$986$	11.2011	+	11.2011i	0.356717	+	0.356717i
$987$	−3.08584	−	3.08584i	−0.0982235	−	0.0982235i
$988$	24.7167	+	24.7167i	0.786343	+	0.786343i
$989$	2.92963			0.0931567
$990$	−1.00426	+	2.24134i	−0.0319175	+	0.0712345i
$991$	3.54576	+	3.54576i	0.112635	+	0.112635i	0.761178	−	0.648543i	$-0.224621\pi$
$991$	3.54576	+	3.54576i	0.112635	+	0.112635i	−0.648543	+	0.761178i	$0.724621\pi$
$992$	−3.38961	−	3.38961i	−0.107620	−	0.107620i
$993$		−	14.5789i		−	0.462646i
$994$	−11.2281	+	11.2281i	−0.356134	+	0.356134i
$995$	−13.4211	−	35.2116i	−0.425477	−	1.11628i
$996$	10.3862			0.329100
$997$		−	42.6305i		−	1.35012i	−0.737762	−	0.675060i	$-0.764118\pi$
$997$		−	42.6305i		−	1.35012i	0.737762	−	0.675060i	$-0.235882\pi$
$998$	23.3699	−	23.3699i	0.739761	−	0.739761i
$999$	4.20464	−	4.39556i	0.133029	−	0.139069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.16	yes	36
5.2	odd	4		1110.2.l.a.697.3	yes	36
37.6	odd	4		1110.2.l.a.43.3	✓	36
185.117	even	4	inner	1110.2.o.a.487.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.3	✓	36	37.6	odd	4
1110.2.l.a.697.3	yes	36	5.2	odd	4
1110.2.o.a.253.16	yes	36	1.1	even	1	trivial
1110.2.o.a.487.16	yes	36	185.117	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.914315 + 2.04060i) q^{10} +1.09838i q^{11} +(0.707107 - 0.707107i) q^{12} -4.92901 q^{13} +(-0.867388 + 0.867388i) q^{14} +(-0.796400 - 2.08944i) q^{15} +1.00000 q^{16} -2.47393i q^{17} +1.00000i q^{18} +(-5.01453 - 5.01453i) q^{19} +(0.914315 - 2.04060i) q^{20} -1.22667i q^{21} -1.09838i q^{22} -0.254201 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.32806 - 3.73149i) q^{25} +4.92901 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.867388 - 0.867388i) q^{28} +(4.52766 - 4.52766i) q^{29} +(0.796400 + 2.08944i) q^{30} +(3.38961 + 3.38961i) q^{31} -1.00000 q^{32} +(0.776669 + 0.776669i) q^{33} +2.47393i q^{34} +(-0.976922 - 2.56305i) q^{35} -1.00000i q^{36} +(0.134999 + 6.08126i) q^{37} +(5.01453 + 5.01453i) q^{38} +(-3.48534 + 3.48534i) q^{39} +(-0.914315 + 2.04060i) q^{40} -5.96538i q^{41} +1.22667i q^{42} -11.5248 q^{43} +1.09838i q^{44} +(-2.04060 - 0.914315i) q^{45} +0.254201 q^{46} +(2.51562 - 2.51562i) q^{47} +(0.707107 - 0.707107i) q^{48} +5.49528i q^{49} +(3.32806 + 3.73149i) q^{50} +(-1.74934 - 1.74934i) q^{51} -4.92901 q^{52} +(-1.28565 - 1.28565i) q^{53} +(0.707107 + 0.707107i) q^{54} +(2.24134 + 1.00426i) q^{55} +(-0.867388 + 0.867388i) q^{56} -7.09162 q^{57} +(-4.52766 + 4.52766i) q^{58} +(3.61042 + 3.61042i) q^{59} +(-0.796400 - 2.08944i) q^{60} +(0.890776 + 0.890776i) q^{61} +(-3.38961 - 3.38961i) q^{62} +(-0.867388 - 0.867388i) q^{63} +1.00000 q^{64} +(-4.50667 + 10.0581i) q^{65} +(-0.776669 - 0.776669i) q^{66} +(-8.08465 - 8.08465i) q^{67} -2.47393i q^{68} +(-0.179747 + 0.179747i) q^{69} +(0.976922 + 2.56305i) q^{70} +12.9448 q^{71} +1.00000i q^{72} +(9.56625 - 9.56625i) q^{73} +(-0.134999 - 6.08126i) q^{74} +(-4.99186 - 0.285272i) q^{75} +(-5.01453 - 5.01453i) q^{76} +(0.952718 + 0.952718i) q^{77} +(3.48534 - 3.48534i) q^{78} +(-1.43534 - 1.43534i) q^{79} +(0.914315 - 2.04060i) q^{80} -1.00000 q^{81} +5.96538i q^{82} +(7.34416 + 7.34416i) q^{83} -1.22667i q^{84} +(-5.04830 - 2.26195i) q^{85} +11.5248 q^{86} -6.40308i q^{87} -1.09838i q^{88} +(-9.93692 + 9.93692i) q^{89} +(2.04060 + 0.914315i) q^{90} +(-4.27537 + 4.27537i) q^{91} -0.254201 q^{92} +4.79363 q^{93} +(-2.51562 + 2.51562i) q^{94} +(-14.8175 + 5.64777i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.50451i q^{97} -5.49528i q^{98} +1.09838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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