LMFDB - Embedded newform 966.2.j.a.137.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.7
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.34224 - 1.09471i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.485598 - 0.841080i) q^{5} +(1.70977 + 0.276923i) q^{6} +(-0.839629 + 2.50899i) q^{7} +1.00000i q^{8} +(0.603233 + 2.93873i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.34224 - 1.09471i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.485598 - 0.841080i) q^{5} +(1.70977 + 0.276923i) q^{6} +(-0.839629 + 2.50899i) q^{7} +1.00000i q^{8} +(0.603233 + 2.93873i) q^{9} +(0.841080 + 0.485598i) q^{10} +(1.72804 - 2.99305i) q^{11} +(-1.61917 + 0.615063i) q^{12} -1.15868 q^{13} +(-0.527354 - 2.59266i) q^{14} +(-0.268946 + 1.66052i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.479563 + 0.830628i) q^{17} +(-1.99178 - 2.24340i) q^{18} +(4.07822 - 2.35456i) q^{19} -0.971195 q^{20} +(3.87359 - 2.44852i) q^{21} +3.45607i q^{22} +(-4.69509 - 0.977816i) q^{23} +(1.09471 - 1.34224i) q^{24} +(2.02839 - 3.51327i) q^{25} +(1.00345 - 0.579342i) q^{26} +(2.40736 - 4.60485i) q^{27} +(1.75303 + 1.98163i) q^{28} -6.13987i q^{29} +(-0.597346 - 1.57253i) q^{30} +(-3.55774 + 6.16219i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.59595 + 2.12570i) q^{33} -0.959127i q^{34} +(2.51798 - 0.512164i) q^{35} +(2.84663 + 0.946948i) q^{36} +(-5.20449 + 3.00482i) q^{37} +(-2.35456 + 4.07822i) q^{38} +(1.55523 + 1.26842i) q^{39} +(0.841080 - 0.485598i) q^{40} +10.3757i q^{41} +(-2.13037 + 4.05728i) q^{42} -12.0393i q^{43} +(-1.72804 - 2.99305i) q^{44} +(2.17877 - 1.93441i) q^{45} +(4.55498 - 1.50073i) q^{46} +(-5.20449 + 3.00481i) q^{47} +(-0.276923 + 1.70977i) q^{48} +(-5.59005 - 4.21324i) q^{49} +4.05678i q^{50} +(1.55299 - 0.589923i) q^{51} +(-0.579342 + 1.00345i) q^{52} +(-2.39368 + 4.14598i) q^{53} +(0.217589 + 5.19159i) q^{54} -3.35652 q^{55} +(-2.50899 - 0.839629i) q^{56} +(-8.05153 - 1.30406i) q^{57} +(3.06993 + 5.31728i) q^{58} +(-7.32586 - 4.22959i) q^{59} +(1.30358 + 1.06317i) q^{60} +(-4.84009 + 2.79443i) q^{61} -7.11549i q^{62} +(-7.87972 - 0.953936i) q^{63} -1.00000 q^{64} +(0.562654 + 0.974545i) q^{65} +(3.78339 - 4.63889i) q^{66} +(-13.3141 - 7.68689i) q^{67} +(0.479563 + 0.830628i) q^{68} +(5.23153 + 6.45222i) q^{69} +(-1.92455 + 1.70254i) q^{70} +10.7783i q^{71} +(-2.93873 + 0.603233i) q^{72} +(-6.57210 + 11.3832i) q^{73} +(3.00482 - 5.20449i) q^{74} +(-6.56860 + 2.49517i) q^{75} -4.70913i q^{76} +(6.05861 + 6.84867i) q^{77} +(-1.98108 - 0.320866i) q^{78} +(13.1877 - 7.61390i) q^{79} +(-0.485598 + 0.841080i) q^{80} +(-8.27222 + 3.54547i) q^{81} +(-5.18786 - 8.98564i) q^{82} -6.91498 q^{83} +(-0.183687 - 4.57889i) q^{84} +0.931500 q^{85} +(6.01963 + 10.4263i) q^{86} +(-6.72136 + 8.24119i) q^{87} +(2.99305 + 1.72804i) q^{88} +(-0.611926 - 1.05989i) q^{89} +(-0.919672 + 2.76463i) q^{90} +(0.972864 - 2.90712i) q^{91} +(-3.19436 + 3.57716i) q^{92} +(11.5212 - 4.37647i) q^{93} +(3.00481 - 5.20449i) q^{94} +(-3.96075 - 2.28674i) q^{95} +(-0.615063 - 1.61917i) q^{96} -15.3818i q^{97} +(6.94774 + 0.853749i) q^{98} +(9.83815 + 3.27272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.34224	−	1.09471i	−0.774944	−	0.632029i
$3$	−1.34224	−	1.09471i	−0.774944	−	0.632029i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.485598	−	0.841080i	−0.217166	−	0.376142i	0.736775	−	0.676139i	$-0.236348\pi$
$5$	−0.485598	−	0.841080i	−0.217166	−	0.376142i	−0.953940	+	0.299996i	$0.903015\pi$
$6$	1.70977	+	0.276923i	0.698011	+	0.113053i
$7$	−0.839629	+	2.50899i	−0.317350	+	0.948309i
$7$	−0.839629	+	2.50899i	−0.317350	+	0.948309i
$8$			1.00000i			0.353553i
$9$	0.603233	+	2.93873i	0.201078	+	0.979575i
$10$	0.841080	+	0.485598i	0.265973	+	0.153559i
$11$	1.72804	−	2.99305i	0.521022	−	0.902437i	−0.478679	−	0.877990i	$-0.658884\pi$
$11$	1.72804	−	2.99305i	0.521022	−	0.902437i	0.999701	−	0.0244471i	$-0.00778254\pi$
$12$	−1.61917	+	0.615063i	−0.467413	+	0.177553i
$13$	−1.15868			−0.321361			−0.160680	−	0.987006i	$-0.551369\pi$
$13$	−1.15868			−0.321361			−0.160680	+	0.987006i	$0.551369\pi$
$14$	−0.527354	−	2.59266i	−0.140941	−	0.692918i
$15$	−0.268946	+	1.66052i	−0.0694416	+	0.428745i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.479563	+	0.830628i	−0.116311	+	0.201457i	−0.918303	−	0.395878i	$-0.870440\pi$
$17$	−0.479563	+	0.830628i	−0.116311	+	0.201457i	0.801992	+	0.597335i	$0.203774\pi$
$18$	−1.99178	−	2.24340i	−0.469466	−	0.528773i
$19$	4.07822	−	2.35456i	0.935609	−	0.540174i	0.0470277	−	0.998894i	$-0.485025\pi$
$19$	4.07822	−	2.35456i	0.935609	−	0.540174i	0.888581	+	0.458720i	$0.151692\pi$
$20$	−0.971195			−0.217166
$21$	3.87359	−	2.44852i	0.845287	−	0.534312i
$22$			3.45607i			0.736837i
$23$	−4.69509	−	0.977816i	−0.978994	−	0.203889i
$23$	−4.69509	−	0.977816i	−0.978994	−	0.203889i
$24$	1.09471	−	1.34224i	0.223456	−	0.273984i
$25$	2.02839	−	3.51327i	0.405678	−	0.702655i
$26$	1.00345	−	0.579342i	0.196793	−	0.113618i
$27$	2.40736	−	4.60485i	0.463297	−	0.886203i
$28$	1.75303	+	1.98163i	0.331292	+	0.374494i
$29$		−	6.13987i		−	1.14014i	−0.821594	−	0.570072i	$-0.806915\pi$
$29$		−	6.13987i		−	1.14014i	0.821594	−	0.570072i	$-0.193085\pi$
$30$	−0.597346	−	1.57253i	−0.109060	−	0.287103i
$31$	−3.55774	+	6.16219i	−0.638990	+	1.10676i	0.346665	+	0.937989i	$0.387314\pi$
$31$	−3.55774	+	6.16219i	−0.638990	+	1.10676i	−0.985655	+	0.168773i	$0.946019\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.59595	+	2.12570i	−0.974130	+	0.370037i
$34$		−	0.959127i		−	0.164489i
$35$	2.51798	−	0.512164i	0.425617	−	0.0865715i
$36$	2.84663	+	0.946948i	0.474438	+	0.157825i
$37$	−5.20449	+	3.00482i	−0.855613	+	0.493989i	−0.862541	−	0.505987i	$-0.831128\pi$
$37$	−5.20449	+	3.00482i	−0.855613	+	0.493989i	0.00692752	+	0.999976i	$0.497795\pi$
$38$	−2.35456	+	4.07822i	−0.381961	+	0.661575i
$39$	1.55523	+	1.26842i	0.249037	+	0.203110i
$40$	0.841080	−	0.485598i	0.132986	−	0.0767797i
$41$			10.3757i			1.62042i	0.586142	+	0.810208i	$0.300646\pi$
$41$			10.3757i			1.62042i	−0.586142	+	0.810208i	$0.699354\pi$
$42$	−2.13037	+	4.05728i	−0.328723	+	0.626052i
$43$		−	12.0393i		−	1.83597i	−0.396615	−	0.917985i	$-0.629815\pi$
$43$		−	12.0393i		−	1.83597i	0.396615	−	0.917985i	$-0.370185\pi$
$44$	−1.72804	−	2.99305i	−0.260511	−	0.451219i
$45$	2.17877	−	1.93441i	0.324793	−	0.288364i
$46$	4.55498	−	1.50073i	0.671595	−	0.221271i
$47$	−5.20449	+	3.00481i	−0.759153	+	0.438297i	−0.828991	−	0.559261i	$-0.811085\pi$
$47$	−5.20449	+	3.00481i	−0.759153	+	0.438297i	0.0698389	+	0.997558i	$0.477751\pi$
$48$	−0.276923	+	1.70977i	−0.0399703	+	0.246784i
$49$	−5.59005	−	4.21324i	−0.798578	−	0.601891i
$50$			4.05678i			0.573715i
$51$	1.55299	−	0.589923i	0.217461	−	0.0826058i
$52$	−0.579342	+	1.00345i	−0.0803402	+	0.139153i
$53$	−2.39368	+	4.14598i	−0.328798	+	0.569494i	−0.982274	−	0.187453i	$-0.939977\pi$
$53$	−2.39368	+	4.14598i	−0.328798	+	0.569494i	0.653476	+	0.756947i	$0.273310\pi$
$54$	0.217589	+	5.19159i	0.0296101	+	0.706487i
$55$	−3.35652			−0.452593
$56$	−2.50899	−	0.839629i	−0.335278	−	0.112200i
$57$	−8.05153	−	1.30406i	−1.06645	−	0.172728i
$58$	3.06993	+	5.31728i	0.403102	+	0.698193i
$59$	−7.32586	−	4.22959i	−0.953746	−	0.550645i	−0.0595033	−	0.998228i	$-0.518952\pi$
$59$	−7.32586	−	4.22959i	−0.953746	−	0.550645i	−0.894243	+	0.447583i	$0.852285\pi$
$60$	1.30358	+	1.06317i	0.168291	+	0.137255i
$61$	−4.84009	+	2.79443i	−0.619711	+	0.357790i	−0.776756	−	0.629801i	$-0.783136\pi$
$61$	−4.84009	+	2.79443i	−0.619711	+	0.357790i	0.157046	+	0.987591i	$0.449803\pi$
$62$		−	7.11549i		−	0.903668i
$63$	−7.87972	−	0.953936i	−0.992752	−	0.120185i
$64$	−1.00000			−0.125000
$65$	0.562654	+	0.974545i	0.0697886	+	0.120877i
$66$	3.78339	−	4.63889i	0.465703	−	0.571008i
$67$	−13.3141	−	7.68689i	−1.62657	−	0.939103i	−0.985105	−	0.171954i	$-0.944992\pi$
$67$	−13.3141	−	7.68689i	−1.62657	−	0.939103i	−0.641469	−	0.767149i	$-0.721675\pi$
$68$	0.479563	+	0.830628i	0.0581556	+	0.100728i
$69$	5.23153	+	6.45222i	0.629802	+	0.776756i
$70$	−1.92455	+	1.70254i	−0.230028	+	0.203492i
$71$			10.7783i			1.27915i	0.768729	+	0.639575i	$0.220890\pi$
$71$			10.7783i			1.27915i	−0.768729	+	0.639575i	$0.779110\pi$
$72$	−2.93873	+	0.603233i	−0.346332	+	0.0710916i
$73$	−6.57210	+	11.3832i	−0.769206	+	1.33230i	0.168788	+	0.985652i	$0.446015\pi$
$73$	−6.57210	+	11.3832i	−0.769206	+	1.33230i	−0.937994	+	0.346651i	$0.887319\pi$
$74$	3.00482	−	5.20449i	0.349303	−	0.605010i
$75$	−6.56860	+	2.49517i	−0.758476	+	0.288118i
$76$		−	4.70913i		−	0.540174i
$77$	6.05861	+	6.84867i	0.690443	+	0.780478i
$78$	−1.98108	−	0.320866i	−0.224313	−	0.0363309i
$79$	13.1877	−	7.61390i	1.48373	−	0.856631i	0.483900	−	0.875124i	$-0.339220\pi$
$79$	13.1877	−	7.61390i	1.48373	−	0.856631i	0.999829	+	0.0184924i	$0.00588665\pi$
$80$	−0.485598	+	0.841080i	−0.0542915	+	0.0940356i
$81$	−8.27222	+	3.54547i	−0.919136	+	0.393941i
$82$	−5.18786	−	8.98564i	−0.572904	−	0.992298i
$83$	−6.91498			−0.759017			−0.379509	−	0.925188i	$-0.623907\pi$
$83$	−6.91498			−0.759017			−0.379509	+	0.925188i	$0.623907\pi$
$84$	−0.183687	−	4.57889i	−0.0200419	−	0.499598i
$85$	0.931500			0.101035
$86$	6.01963	+	10.4263i	0.649113	+	1.12430i
$87$	−6.72136	+	8.24119i	−0.720605	+	0.883549i
$88$	2.99305	+	1.72804i	0.319060	+	0.184209i
$89$	−0.611926	−	1.05989i	−0.0648641	−	0.112348i	0.831770	−	0.555121i	$-0.187328\pi$
$89$	−0.611926	−	1.05989i	−0.0648641	−	0.112348i	−0.896634	+	0.442773i	$0.853995\pi$
$90$	−0.919672	+	2.76463i	−0.0969419	+	0.291418i
$91$	0.972864	−	2.90712i	0.101984	−	0.304749i
$92$	−3.19436	+	3.57716i	−0.333035	+	0.372945i
$93$	11.5212	−	4.37647i	1.19469	−	0.453819i
$94$	3.00481	−	5.20449i	0.309923	−	0.536802i
$95$	−3.96075	−	2.28674i	−0.406365	−	0.234615i
$96$	−0.615063	−	1.61917i	−0.0627746	−	0.165255i
$97$		−	15.3818i		−	1.56179i	−0.624665	−	0.780893i	$-0.714765\pi$
$97$		−	15.3818i		−	1.56179i	0.624665	−	0.780893i	$-0.285235\pi$
$98$	6.94774	+	0.853749i	0.701828	+	0.0862416i
$99$	9.83815	+	3.27272i	0.988771	+	0.328921i
$100$	−2.02839	−	3.51327i	−0.202839	−	0.351327i
$101$	−5.99227	−	3.45964i	−0.596253	−	0.344247i	0.171313	−	0.985217i	$-0.445199\pi$
$101$	−5.99227	−	3.45964i	−0.596253	−	0.344247i	−0.767566	+	0.640970i	$0.778532\pi$
$102$	−1.04996	+	1.28738i	−0.103962	+	0.127470i
$103$	1.03966	−	0.600249i	0.102441	−	0.0591443i	−0.447904	−	0.894082i	$-0.647829\pi$
$103$	1.03966	−	0.600249i	0.102441	−	0.0591443i	0.550345	+	0.834937i	$0.314496\pi$
$104$		−	1.15868i		−	0.113618i
$105$	−3.94041	−	2.06900i	−0.384545	−	0.201914i
$106$		−	4.78736i		−	0.464990i
$107$	−6.91670	−	11.9801i	−0.668662	−	1.15816i	−0.978278	−	0.207295i	$-0.933534\pi$
$107$	−6.91670	−	11.9801i	−0.668662	−	1.15816i	0.309616	−	0.950862i	$-0.399799\pi$
$108$	−2.78423	−	4.38726i	−0.267913	−	0.422164i
$109$	−12.8817	−	7.43727i	−1.23385	−	0.712362i	−0.266017	−	0.963968i	$-0.585708\pi$
$109$	−12.8817	−	7.43727i	−1.23385	−	0.712362i	−0.967830	+	0.251607i	$0.919041\pi$
$110$	2.90683	−	1.67826i	0.277156	−	0.160016i
$111$	10.2751	+	1.66420i	0.975268	+	0.157959i
$112$	2.59266	−	0.527354i	0.244984	−	0.0498303i
$113$	6.99345			0.657889			0.328944	−	0.944349i	$-0.393307\pi$
$113$	6.99345			0.657889			0.328944	+	0.944349i	$0.393307\pi$
$114$	7.62486	−	2.89641i	0.714133	−	0.271274i
$115$	1.45750	+	4.42377i	0.135913	+	0.412519i
$116$	−5.31728	−	3.06993i	−0.493697	−	0.285036i
$117$	−0.698955	−	3.40505i	−0.0646184	−	0.314797i
$118$	8.45918			0.778730
$119$	−1.68138	−	1.90064i	−0.154132	−	0.174231i
$120$	−1.66052	−	0.268946i	−0.151584	−	0.0245513i
$121$	−0.472216	−	0.817901i	−0.0429287	−	0.0743547i
$122$	2.79443	−	4.84009i	0.252996	−	0.438202i
$123$	11.3584	−	13.9267i	1.02415	−	1.25573i
$124$	3.55774	+	6.16219i	0.319495	+	0.553381i
$125$	−8.79590			−0.786729
$126$	7.30101	−	3.11373i	0.650425	−	0.277393i
$127$	−9.47591			−0.840851			−0.420426	−	0.907327i	$-0.638119\pi$
$127$	−9.47591			−0.840851			−0.420426	+	0.907327i	$0.638119\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−13.1795	+	16.1596i	−1.16039	+	1.42277i
$130$	−0.974545	−	0.562654i	−0.0854732	−	0.0493480i
$131$	17.3696	−	10.0283i	1.51759	−	0.876178i	0.517799	−	0.855502i	$-0.326752\pi$
$131$	17.3696	−	10.0283i	1.51759	−	0.876178i	0.999786	−	0.0206760i	$-0.00658183\pi$
$132$	−0.957065	+	5.90909i	−0.0833018	+	0.514320i
$133$	2.48338	+	12.2092i	0.215336	+	1.05867i
$134$	15.3738			1.32809
$135$	−5.04205	+	0.211321i	−0.433951	+	0.0181876i
$136$	−0.830628	−	0.479563i	−0.0712258	−	0.0411222i
$137$	−4.81538	+	8.34049i	−0.411406	+	0.712576i	−0.995044	−	0.0994383i	$-0.968295\pi$
$137$	−4.81538	+	8.34049i	−0.411406	+	0.712576i	0.583638	+	0.812014i	$0.301629\pi$
$138$	−7.75675	−	2.97202i	−0.660298	−	0.252995i
$139$	−5.96790			−0.506190			−0.253095	−	0.967441i	$-0.581449\pi$
$139$	−5.96790			−0.506190			−0.253095	+	0.967441i	$0.581449\pi$
$140$	0.815444	−	2.43672i	0.0689176	−	0.205940i
$141$	10.2751	+	1.66420i	0.865318	+	0.140151i
$142$	−5.38916	−	9.33429i	−0.452248	−	0.783316i
$143$	−2.00225	+	3.46799i	−0.167436	+	0.290008i
$144$	2.24340	−	1.99178i	0.186950	−	0.165981i
$145$	−5.16412	+	2.98151i	−0.428857	+	0.247601i
$146$		−	13.1442i		−	1.08782i
$147$	2.89094	+	11.7747i	0.238441	+	0.971157i
$148$			6.00963i			0.493989i
$149$	0.190203	+	0.329442i	0.0155821	+	0.0269889i	0.873711	−	0.486445i	$-0.161707\pi$
$149$	0.190203	+	0.329442i	0.0155821	+	0.0269889i	−0.858129	+	0.513434i	$0.828373\pi$
$150$	4.44099	−	5.44518i	0.362605	−	0.444597i
$151$	6.87258	−	11.9037i	0.559283	−	0.968706i	−0.438274	−	0.898841i	$-0.644410\pi$
$151$	6.87258	−	11.9037i	0.559283	−	0.968706i	0.997556	−	0.0698645i	$-0.0222567\pi$
$152$	2.35456	+	4.07822i	0.190980	+	0.330788i
$153$	−2.73028	−	0.908244i	−0.220730	−	0.0734271i
$154$	−8.67124	−	2.90182i	−0.698749	−	0.233835i
$155$	6.91053			0.555067
$156$	1.87610	−	0.712663i	0.150208	−	0.0570587i
$157$	18.7347	+	10.8165i	1.49519	+	0.863249i	0.999985	−	0.00552644i	$-0.00175913\pi$
$157$	18.7347	+	10.8165i	1.49519	+	0.863249i	0.495206	+	0.868775i	$0.335092\pi$
$158$	−7.61390	+	13.1877i	−0.605730	+	1.04915i
$159$	7.75154	−	2.94453i	0.614737	−	0.233516i
$160$		−	0.971195i		−	0.0767797i
$161$	6.39546	−	10.9589i	0.504033	−	0.863684i
$162$	5.39122	−	7.20658i	0.423574	−	0.566202i
$163$	−4.98381	−	8.63221i	−0.390362	−	0.676127i	0.602135	−	0.798394i	$-0.294317\pi$
$163$	−4.98381	−	8.63221i	−0.390362	−	0.676127i	−0.992497	+	0.122267i	$0.960984\pi$
$164$	8.98564	+	5.18786i	0.701661	+	0.405104i
$165$	4.50527	+	3.67441i	0.350734	+	0.286052i
$166$	5.98854	−	3.45749i	0.464801	−	0.268353i
$167$		−	7.64006i		−	0.591206i	−0.955311	−	0.295603i	$-0.904480\pi$
$167$		−	7.64006i		−	0.591206i	0.955311	−	0.295603i	$-0.0955205\pi$
$168$	2.44852	+	3.87359i	0.188908	+	0.298854i
$169$	−11.6575			−0.896727
$170$	−0.806702	+	0.465750i	−0.0618712	+	0.0357214i
$171$	9.37954	+	10.5644i	0.717271	+	0.807882i
$172$	−10.4263	−	6.01963i	−0.794998	−	0.458992i
$173$	−8.79998	+	5.08067i	−0.669050	+	0.386276i	−0.795717	−	0.605669i	$-0.792906\pi$
$173$	−8.79998	+	5.08067i	−0.669050	+	0.386276i	0.126667	+	0.991945i	$0.459572\pi$
$174$	1.70027	−	10.4978i	0.128897	−	0.795833i
$175$	7.11167	+	8.03905i	0.537592	+	0.607695i
$176$	−3.45607			−0.260511
$177$	5.20293	+	13.6968i	0.391076	+	1.02952i
$178$	1.05989	+	0.611926i	0.0794419	+	0.0458658i
$179$	−0.805467	−	0.465036i	−0.0602034	−	0.0347584i	0.469596	−	0.882881i	$-0.344400\pi$
$179$	−0.805467	−	0.465036i	−0.0602034	−	0.0347584i	−0.529800	+	0.848123i	$0.677733\pi$
$180$	−0.585857	−	2.85408i	−0.0436672	−	0.212730i
$181$			10.1681i			0.755788i	0.925849	+	0.377894i	$0.123352\pi$
$181$			10.1681i			0.755788i	−0.925849	+	0.377894i	$0.876648\pi$
$182$	0.611036	+	3.00407i	0.0452930	+	0.222677i
$183$	9.55566	+	1.54768i	0.706375	+	0.114408i
$184$	0.977816	−	4.69509i	0.0720856	−	0.346127i
$185$	5.05458	+	2.91826i	0.371620	+	0.214555i
$186$	−7.78937	+	9.55071i	−0.571145	+	0.700292i
$187$	1.65741	+	2.87071i	0.121202	+	0.209927i
$188$			6.00962i			0.438297i
$189$	9.53222	+	9.90640i	0.693367	+	0.720585i
$190$	4.57348			0.331795
$191$	−2.90960	−	5.03958i	−0.210532	−	0.364651i	0.741349	−	0.671119i	$-0.234186\pi$
$191$	−2.90960	−	5.03958i	−0.210532	−	0.364651i	−0.951881	+	0.306468i	$0.900853\pi$
$192$	1.34224	+	1.09471i	0.0968680	+	0.0790037i
$193$	−2.48154	+	4.29816i	−0.178625	+	0.309388i	−0.941410	−	0.337264i	$-0.890498\pi$
$193$	−2.48154	+	4.29816i	−0.178625	+	0.309388i	0.762784	+	0.646653i	$0.223832\pi$
$194$	7.69090	+	13.3210i	0.552174	+	0.956394i
$195$	0.311623	−	1.92402i	0.0223158	−	0.137782i
$196$	−6.44380	+	2.73450i	−0.460271	+	0.195322i
$197$			22.8482i			1.62786i	0.580960	+	0.813932i	$0.302677\pi$
$197$			22.8482i			1.62786i	−0.580960	+	0.813932i	$0.697323\pi$
$198$	−10.1564	+	2.08481i	−0.721787	+	0.148161i
$199$	−5.19182	−	2.99750i	−0.368038	−	0.212487i	0.304563	−	0.952492i	$-0.401490\pi$
$199$	−5.19182	−	2.99750i	−0.368038	−	0.212487i	−0.672601	+	0.740005i	$0.734823\pi$
$200$	3.51327	+	2.02839i	0.248426	+	0.143429i
$201$	9.45584	+	24.8927i	0.666964	+	1.75580i
$202$	6.91927			0.486838
$203$	15.4049	+	5.15521i	1.08121	+	0.361825i
$204$	0.265604	−	1.63989i	0.0185960	−	0.114815i
$205$	8.72681	−	5.03843i	0.609507	−	0.351899i
$206$	−0.600249	+	1.03966i	−0.0418214	+	0.0724367i
$207$	0.0413031	−	14.3874i	0.00287076	−	0.999996i
$208$	0.579342	+	1.00345i	0.0401701	+	0.0695767i
$209$		−	16.2751i		−	1.12577i
$210$	4.44700	−	0.178396i	0.306872	−	0.0123105i
$211$	8.06409			0.555155			0.277578	−	0.960703i	$-0.410468\pi$
$211$	8.06409			0.555155			0.277578	+	0.960703i	$0.410468\pi$
$212$	2.39368	+	4.14598i	0.164399	+	0.284747i
$213$	11.7991	−	14.4671i	0.808461	−	0.991270i
$214$	11.9801	+	6.91670i	0.818941	+	0.472816i
$215$	−10.1260	+	5.84624i	−0.690586	+	0.398710i
$216$	4.60485	+	2.40736i	0.313320	+	0.163800i
$217$	−12.4737	−	14.1003i	−0.846769	−	0.957190i
$218$	14.8745			1.00743
$219$	21.2826	−	8.08451i	1.43815	−	0.546300i
$220$	−1.67826	+	2.90683i	−0.113148	+	0.195979i
$221$	0.555662	−	0.962435i	0.0373779	−	0.0647404i
$222$	−9.73059	+	3.69630i	−0.653074	+	0.248079i
$223$	−0.549178			−0.0367757			−0.0183879	−	0.999831i	$-0.505853\pi$
$223$	−0.549178			−0.0367757			−0.0183879	+	0.999831i	$0.505853\pi$
$224$	−1.98163	+	1.75303i	−0.132404	+	0.117129i
$225$	11.5481	+	3.84156i	0.769876	+	0.256104i
$226$	−6.05651	+	3.49673i	−0.402873	+	0.232599i
$227$	−12.6467	+	21.9047i	−0.839392	+	1.45387i	0.0510125	+	0.998698i	$0.483755\pi$
$227$	−12.6467	+	21.9047i	−0.839392	+	1.45387i	−0.890404	+	0.455171i	$0.849578\pi$
$228$	−5.15512	+	6.32079i	−0.341406	+	0.418605i
$229$	1.18719	−	0.685423i	0.0784516	−	0.0452940i	−0.460261	−	0.887784i	$-0.652244\pi$
$229$	1.18719	−	0.685423i	0.0784516	−	0.0452940i	0.538713	+	0.842490i	$0.318911\pi$
$230$	−3.47412	−	3.10235i	−0.229077	−	0.204563i
$231$	−0.634837	−	15.8250i	−0.0417692	−	1.04121i
$232$	6.13987			0.403102
$233$	17.9878	−	10.3853i	1.17842	−	0.680361i	0.222771	−	0.974871i	$-0.428490\pi$
$233$	17.9878	−	10.3853i	1.17842	−	0.680361i	0.955648	+	0.294510i	$0.0951564\pi$
$234$	2.30784	+	2.59938i	0.150868	+	0.169927i
$235$	5.05457	+	2.91826i	0.329724	+	0.190366i
$236$	−7.32586	+	4.22959i	−0.476873	+	0.275323i
$237$	−26.0361	−	4.21693i	−1.69122	−	0.273919i
$238$	2.40644	+	0.805311i	0.155986	+	0.0522005i
$239$			0.628601i			0.0406608i	0.999793	+	0.0203304i	$0.00647181\pi$
$239$			0.628601i			0.0406608i	−0.999793	+	0.0203304i	$0.993528\pi$
$240$	1.57253	−	0.597346i	0.101506	−	0.0385585i
$241$	−9.62592	−	5.55753i	−0.620060	−	0.357992i	0.156832	−	0.987625i	$-0.449872\pi$
$241$	−9.62592	−	5.55753i	−0.620060	−	0.357992i	−0.776892	+	0.629633i	$0.783205\pi$
$242$	0.817901	+	0.472216i	0.0525767	+	0.0303552i
$243$	14.9846	+	4.29678i	0.961261	+	0.275638i
$244$			5.58886i			0.357790i
$245$	−0.829157	+	6.74761i	−0.0529729	+	0.431089i
$246$	−2.87327	+	17.7401i	−0.183193	+	1.13107i
$247$	−4.72537	+	2.72819i	−0.300668	+	0.173591i
$248$	−6.16219	−	3.55774i	−0.391300	−	0.225917i
$249$	9.28158	+	7.56987i	0.588196	+	0.479721i
$250$	7.61747	−	4.39795i	0.481771	−	0.278151i
$251$	11.5623			0.729803			0.364901	−	0.931046i	$-0.381103\pi$
$251$	11.5623			0.729803			0.364901	+	0.931046i	$0.381103\pi$
$252$	−4.76599	+	6.34707i	−0.300229	+	0.399828i
$253$	−11.0399	+	12.3629i	−0.694075	+	0.777250i
$254$	8.20638	−	4.73796i	0.514914	−	0.297286i
$255$	−1.25030	−	1.01972i	−0.0782967	−	0.0638573i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.47366	−	1.42817i	0.154303	−	0.0890866i	−0.420861	−	0.907125i	$-0.638272\pi$
$257$	2.47366	−	1.42817i	0.154303	−	0.0890866i	0.575163	+	0.818039i	$0.304939\pi$
$258$	3.33394	−	20.5844i	0.207562	−	1.28153i
$259$	−3.16920	−	15.5809i	−0.196925	−	0.968153i
$260$	1.12531			0.0697886
$261$	18.0434	−	3.70377i	1.11686	−	0.229257i
$262$	−10.0283	+	17.3696i	−0.619552	+	1.07309i
$263$	5.74212	−	9.94564i	0.354074	−	0.613275i	−0.632885	−	0.774246i	$-0.718129\pi$
$263$	5.74212	−	9.94564i	0.354074	−	0.613275i	0.986959	+	0.160971i	$0.0514626\pi$
$264$	−2.12570	−	5.59595i	−0.130828	−	0.344407i
$265$	4.64947			0.285614
$266$	−8.25526	−	9.33177i	−0.506162	−	0.572167i
$267$	−0.338913	+	2.09251i	−0.0207411	+	0.128059i
$268$	−13.3141	+	7.68689i	−0.813287	+	0.469552i
$269$	−18.2365	−	10.5288i	−1.11190	−	0.641954i	−0.172577	−	0.984996i	$-0.555210\pi$
$269$	−18.2365	−	10.5288i	−1.11190	−	0.641954i	−0.939320	+	0.343042i	$0.888543\pi$
$270$	4.26088	−	2.70404i	0.259309	−	0.164562i
$271$	−9.34228	−	16.1813i	−0.567503	−	0.982944i	−0.996812	−	0.0797861i	$-0.974576\pi$
$271$	−9.34228	−	16.1813i	−0.567503	−	0.982944i	0.429309	−	0.903158i	$-0.358757\pi$
$272$	0.959127			0.0581556
$273$	−4.48827	+	2.83706i	−0.271642	+	0.171707i
$274$		−	9.63076i		−	0.581816i
$275$	−7.01026	−	12.1421i	−0.422735	−	0.732198i
$276$	8.20355	−	1.30453i	0.493796	−	0.0785235i
$277$	4.00218	−	6.93198i	0.240468	−	0.416503i	−0.720380	−	0.693580i	$-0.756032\pi$
$277$	4.00218	−	6.93198i	0.240468	−	0.416503i	0.960848	+	0.277077i	$0.0893658\pi$
$278$	5.16835	−	2.98395i	0.309977	−	0.178965i
$279$	−20.2551	−	6.73800i	−1.21264	−	0.403393i
$280$	0.512164	+	2.51798i	0.0306076	+	0.150478i
$281$	17.9082			1.06831			0.534155	−	0.845386i	$-0.320630\pi$
$281$	17.9082			1.06831			0.534155	+	0.845386i	$0.320630\pi$
$282$	−9.73058	+	3.69630i	−0.579447	+	0.220111i
$283$	2.94230	+	1.69874i	0.174902	+	0.100980i	0.584895	−	0.811109i	$-0.301136\pi$
$283$	2.94230	+	1.69874i	0.174902	+	0.100980i	−0.409993	+	0.912089i	$0.634469\pi$
$284$	9.33429	+	5.38916i	0.553888	+	0.319788i
$285$	2.81298	+	7.40523i	0.166627	+	0.438648i
$286$		−	4.00449i		−	0.236791i
$287$	−26.0326	−	8.71176i	−1.53665	−	0.514239i
$288$	−0.946948	+	2.84663i	−0.0557995	+	0.167739i
$289$	8.04004	+	13.9258i	0.472943	+	0.819162i
$290$	2.98151	−	5.16412i	0.175080	−	0.303247i
$291$	−16.8386	+	20.6461i	−0.987094	+	1.21030i
$292$	6.57210	+	11.3832i	0.384603	+	0.666152i
$293$	25.3284			1.47970			0.739849	−	0.672773i	$-0.234897\pi$
$293$	25.3284			1.47970			0.739849	+	0.672773i	$0.234897\pi$
$294$	−8.39095	−	8.75168i	−0.489370	−	0.510408i
$295$			8.21551i			0.478326i
$296$	−3.00482	−	5.20449i	−0.174651	−	0.302505i
$297$	−9.62252	−	15.1627i	−0.558355	−	0.879828i
$298$	−0.329442	−	0.190203i	−0.0190840	−	0.0110182i
$299$	5.44012	+	1.13298i	0.314610	+	0.0655219i
$300$	−1.12341	+	6.93616i	−0.0648604	+	0.400459i
$301$	30.2064	+	10.1085i	1.74107	+	0.582645i
$302$			13.7452i			0.790945i
$303$	4.25579	+	11.2035i	0.244489	+	0.643621i
$304$	−4.07822	−	2.35456i	−0.233902	−	0.135043i
$305$	4.70068	+	2.71394i	0.269160	+	0.155400i
$306$	2.81861	−	0.578577i	0.161129	−	0.0330750i
$307$	7.08193			0.404187			0.202093	−	0.979366i	$-0.435226\pi$
$307$	7.08193			0.404187			0.202093	+	0.979366i	$0.435226\pi$
$308$	8.96043	−	1.82257i	0.510568	−	0.103851i
$309$	−2.05258	−	0.332445i	−0.116767	−	0.0189122i
$310$	−5.98469	+	3.45526i	−0.339908	+	0.196246i
$311$	−15.1192	−	8.72905i	−0.857329	−	0.494979i	0.00578822	−	0.999983i	$-0.498158\pi$
$311$	−15.1192	−	8.72905i	−0.857329	−	0.494979i	−0.863117	+	0.505004i	$0.831491\pi$
$312$	−1.26842	+	1.55523i	−0.0718101	+	0.0880478i
$313$	8.93020	−	5.15586i	0.504765	−	0.291426i	−0.225914	−	0.974147i	$-0.572537\pi$
$313$	8.93020	−	5.15586i	0.504765	−	0.291426i	0.730679	+	0.682721i	$0.239204\pi$
$314$	−21.6330			−1.22082
$315$	3.02404	+	7.09070i	0.170385	+	0.399516i
$316$		−	15.2278i		−	0.856631i
$317$	15.6087	−	9.01169i	0.876673	−	0.506147i	0.00711276	−	0.999975i	$-0.497736\pi$
$317$	15.6087	−	9.01169i	0.876673	−	0.506147i	0.869560	+	0.493828i	$0.164403\pi$
$318$	−5.24076	+	6.42581i	−0.293887	+	0.360341i
$319$	−18.3769	−	10.6099i	−1.02891	−	0.594041i
$320$	0.485598	+	0.841080i	0.0271457	+	0.0470178i
$321$	−3.83078	+	23.6519i	−0.213813	+	1.32012i
$322$	−0.0591717	+	12.6884i	−0.00329751	+	0.707099i
$323$			4.51665i			0.251313i
$324$	−1.06564	+	8.93669i	−0.0592024	+	0.496483i
$325$	−2.35026	+	4.07077i	−0.130369	+	0.225806i
$326$	8.63221	+	4.98381i	0.478094	+	0.276028i
$327$	9.14878	+	24.0844i	0.505929	+	1.33187i
$328$	−10.3757			−0.572904
$329$	−3.16920	−	15.5809i	−0.174724	−	0.859004i
$330$	−5.73888	−	0.929497i	−0.315915	−	0.0511671i
$331$	−7.05294	−	12.2161i	−0.387665	−	0.671455i	0.604470	−	0.796628i	$-0.293385\pi$
$331$	−7.05294	−	12.2161i	−0.387665	−	0.671455i	−0.992135	+	0.125173i	$0.960052\pi$
$332$	−3.45749	+	5.98854i	−0.189754	+	0.328664i
$333$	−11.9698	−	13.4820i	−0.655944	−	0.738808i
$334$	3.82003	+	6.61649i	0.209023	+	0.362038i
$335$			14.9309i			0.815765i
$336$	−4.05728	−	2.13037i	−0.221343	−	0.116221i
$337$			0.680735i			0.0370820i	0.999828	+	0.0185410i	$0.00590212\pi$
$337$			0.680735i			0.0370820i	−0.999828	+	0.0185410i	$0.994098\pi$
$338$	10.0957	−	5.82873i	0.549131	−	0.317041i
$339$	−9.38692	−	7.65579i	−0.509827	−	0.415805i
$340$	0.465750	−	0.806702i	0.0252588	−	0.0437496i
$341$	12.2958	+	21.2970i	0.665856	+	1.15330i
$342$	−13.4051	−	4.45930i	−0.724867	−	0.241131i
$343$	15.2645	−	10.4878i	0.824207	−	0.566288i
$344$	12.0393			0.649113
$345$	2.88641	−	7.53331i	0.155399	−	0.405580i
$346$	5.08067	−	8.79998i	0.273139	−	0.473090i
$347$	−0.0351614	−	0.0203005i	−0.00188757	−	0.00108979i	0.499056	−	0.866570i	$-0.333680\pi$
$347$	−0.0351614	−	0.0203005i	−0.00188757	−	0.00108979i	−0.500943	+	0.865480i	$0.667014\pi$
$348$	3.77641	+	9.94146i	0.202437	+	0.532918i
$349$	−17.5571			−0.939810			−0.469905	−	0.882717i	$-0.655712\pi$
$349$	−17.5571			−0.939810			−0.469905	+	0.882717i	$0.655712\pi$
$350$	−10.1784	−	3.40619i	−0.544059	−	0.182069i
$351$	−2.78937	+	5.33556i	−0.148885	+	0.284791i
$352$	2.99305	−	1.72804i	0.159530	−	0.0921046i
$353$	−13.5168	−	7.80390i	−0.719424	−	0.415360i	0.0951165	−	0.995466i	$-0.469678\pi$
$353$	−13.5168	−	7.80390i	−0.719424	−	0.415360i	−0.814541	+	0.580106i	$0.803011\pi$
$354$	−11.3543	−	9.26032i	−0.603473	−	0.492180i
$355$	9.06542	−	5.23392i	0.481143	−	0.277788i
$356$	−1.22385			−0.0648641
$357$	0.176180	+	4.39174i	0.00932441	+	0.232435i
$358$	0.930073			0.0491559
$359$	4.75944	+	8.24359i	0.251194	+	0.435080i	0.963855	−	0.266428i	$-0.0858436\pi$
$359$	4.75944	+	8.24359i	0.251194	+	0.435080i	−0.712661	+	0.701509i	$0.752510\pi$
$360$	1.93441	+	2.17877i	0.101952	+	0.114832i
$361$	1.58794	−	2.75040i	0.0835759	−	0.144758i
$362$	−5.08404	−	8.80582i	−0.267211	−	0.462824i
$363$	−0.261534	+	1.61476i	−0.0137270	+	0.0847529i
$364$	−2.03121	−	2.29609i	−0.106464	−	0.120348i
$365$	12.7656			0.668181
$366$	−9.04929	+	3.43750i	−0.473014	+	0.179681i
$367$	30.9464	+	17.8669i	1.61539	+	0.932644i	0.988092	+	0.153863i	$0.0491714\pi$
$367$	30.9464	+	17.8669i	1.61539	+	0.932644i	0.627295	+	0.778781i	$0.284162\pi$
$368$	1.50073	+	4.55498i	0.0782310	+	0.237445i
$369$	−30.4914	+	6.25898i	−1.58732	+	0.325829i
$370$	−5.83652			−0.303426
$371$	−8.39241	−	9.48681i	−0.435712	−	0.492530i
$372$	1.97044	−	12.1658i	0.102163	−	0.630770i
$373$	−24.1533	+	13.9449i	−1.25061	+	0.722041i	−0.971231	−	0.238139i	$-0.923463\pi$
$373$	−24.1533	+	13.9449i	−1.25061	+	0.722041i	−0.279381	+	0.960180i	$0.590129\pi$
$374$	−2.87071	−	1.65741i	−0.148441	−	0.0857024i
$375$	11.8062	+	9.62894i	0.609671	+	0.497236i
$376$	−3.00481	−	5.20449i	−0.154961	−	0.268401i
$377$			7.11416i			0.366398i
$378$	−13.2083	−	3.81309i	−0.679364	−	0.196124i
$379$		−	5.09112i		−	0.261513i	−0.991414	−	0.130757i	$-0.958259\pi$
$379$		−	5.09112i		−	0.261513i	0.991414	−	0.130757i	$-0.0417407\pi$
$380$	−3.96075	+	2.28674i	−0.203182	+	0.117307i
$381$	12.7190	+	10.3733i	0.651613	+	0.531443i
$382$	5.03958	+	2.90960i	0.257848	+	0.148868i
$383$	−17.4399	−	30.2068i	−0.891138	−	1.54350i	−0.838513	−	0.544882i	$-0.816574\pi$
$383$	−17.4399	−	30.2068i	−0.891138	−	1.54350i	−0.0526253	−	0.998614i	$-0.516759\pi$
$384$	−1.70977	−	0.276923i	−0.0872513	−	0.0141317i
$385$	2.81823	−	8.42147i	0.143630	−	0.429198i
$386$		−	4.96309i		−	0.252615i
$387$	35.3801	−	7.26247i	1.79847	−	0.369172i
$388$	−13.3210	−	7.69090i	−0.676273	−	0.390446i
$389$	19.0251	−	32.9524i	0.964610	−	1.67075i	0.253950	−	0.967217i	$-0.418270\pi$
$389$	19.0251	−	32.9524i	0.964610	−	1.67075i	0.710660	−	0.703536i	$-0.248396\pi$
$390$	0.692135	+	1.82206i	0.0350476	+	0.0922636i
$391$	3.06380	−	3.43095i	0.154943	−	0.173511i
$392$	4.21324	−	5.59005i	0.212801	−	0.282340i
$393$	−34.2922	−	5.55414i	−1.72981	−	0.280169i
$394$	−11.4241	−	19.7871i	−0.575537	−	0.996859i
$395$	−12.8078	−	7.39459i	−0.644430	−	0.372062i
$396$	7.75333	−	6.88373i	0.389620	−	0.345920i
$397$	14.6080	+	25.3019i	0.733156	+	1.26986i	0.955527	+	0.294902i	$0.0952870\pi$
$397$	14.6080	+	25.3019i	0.733156	+	1.26986i	−0.222371	+	0.974962i	$0.571380\pi$
$398$	5.99500			0.300502
$399$	10.0322	−	19.1063i	0.502237	−	0.956509i
$400$	−4.05678			−0.202839
$401$	−10.8202	−	18.7411i	−0.540335	−	0.935888i	−0.998885	−	0.0472189i	$-0.984964\pi$
$401$	−10.8202	−	18.7411i	−0.540335	−	0.935888i	0.458549	−	0.888669i	$-0.348369\pi$
$402$	−20.6353	−	16.8298i	−1.02920	−	0.839394i
$403$	4.12230	−	7.14003i	0.205346	−	0.355670i
$404$	−5.99227	+	3.45964i	−0.298126	+	0.172123i
$405$	6.99899	+	5.23593i	0.347783	+	0.260175i
$406$	−15.9186	+	3.23789i	−0.790027	+	0.160694i
$407$			20.7697i			1.02952i
$408$	0.589923	+	1.55299i	0.0292056	+	0.0768842i
$409$	0.990902	−	1.71629i	0.0489969	−	0.0848652i	−0.840487	−	0.541832i	$-0.817731\pi$
$409$	0.990902	−	1.71629i	0.0489969	−	0.0848652i	0.889484	+	0.456967i	$0.151064\pi$
$410$	−5.03843	+	8.72681i	−0.248830	+	0.430987i
$411$	15.5938	−	5.92353i	0.769185	−	0.292186i
$412$		−	1.20050i		−	0.0591443i
$413$	16.7630	−	14.8292i	0.824853	−	0.729698i
$414$	7.15795	+	12.4805i	0.351794	+	0.613385i
$415$	3.35790	+	5.81605i	0.164833	+	0.285498i
$416$	−1.00345	−	0.579342i	−0.0491981	−	0.0284046i
$417$	8.01037	+	6.53310i	0.392269	+	0.319927i
$418$	8.13754	+	14.0946i	0.398020	+	0.689391i
$419$	9.95926			0.486542			0.243271	−	0.969958i	$-0.421780\pi$
$419$	9.95926			0.486542			0.243271	+	0.969958i	$0.421780\pi$
$420$	−3.76202	+	2.37800i	−0.183568	+	0.116034i
$421$			21.3991i			1.04293i	0.853274	+	0.521463i	$0.174614\pi$
$421$			21.3991i			1.04293i	−0.853274	+	0.521463i	$0.825386\pi$
$422$	−6.98371	+	4.03205i	−0.339962	+	0.196277i
$423$	−11.9698	−	13.4820i	−0.581993	−	0.655515i
$424$	−4.14598	−	2.39368i	−0.201347	−	0.116247i
$425$	1.94548	+	3.36968i	0.0943698	+	0.163453i
$426$	−2.98476	+	18.4284i	−0.144612	+	0.892861i
$427$	−2.94731	−	14.4900i	−0.142630	−	0.701221i
$428$	−13.8334			−0.668662
$429$	6.48394	−	2.46301i	0.313047	−	0.118915i
$430$	5.84624	−	10.1260i	0.281931	−	0.488318i
$431$	−12.1999	+	21.1308i	−0.587648	+	1.01784i	0.406892	+	0.913476i	$0.366613\pi$
$431$	−12.1999	+	21.1308i	−0.587648	+	1.01784i	−0.994540	+	0.104360i	$0.966721\pi$
$432$	−5.19159	+	0.217589i	−0.249781	+	0.0104688i
$433$			8.03682i			0.386225i	0.981177	+	0.193112i	$0.0618582\pi$
$433$			8.03682i			0.386225i	−0.981177	+	0.193112i	$0.938142\pi$
$434$	17.8527	+	5.97437i	0.856956	+	0.286779i
$435$	10.1954	+	1.65129i	0.488831	+	0.0791734i
$436$	−12.8817	+	7.43727i	−0.616923	+	0.356181i
$437$	−21.4500	+	7.06714i	−1.02609	+	0.338067i
$438$	−14.3890	+	17.6427i	−0.687535	+	0.843001i
$439$	−3.13462	−	5.42932i	−0.149607	−	0.259127i	0.781475	−	0.623936i	$-0.214468\pi$
$439$	−3.13462	−	5.42932i	−0.149607	−	0.259127i	−0.931082	+	0.364809i	$0.881134\pi$
$440$		−	3.35652i		−	0.160016i
$441$	9.00946	−	18.9692i	0.429022	−	0.903294i
$442$			1.11132i			0.0528603i
$443$	−18.7237	+	10.8102i	−0.889591	+	0.513606i	−0.873809	−	0.486270i	$-0.838357\pi$
$443$	−18.7237	+	10.8102i	−0.889591	+	0.513606i	−0.0157826	+	0.999875i	$0.505024\pi$
$444$	6.57879	−	8.06638i	0.312215	−	0.382814i
$445$	−0.594300	+	1.02936i	−0.0281725	+	0.0487962i
$446$	0.475602	−	0.274589i	0.0225204	−	0.0130022i
$447$	0.105343	−	0.650407i	0.00498256	−	0.0307632i
$448$	0.839629	−	2.50899i	0.0396687	−	0.118539i
$449$			9.92297i			0.468294i	0.972201	+	0.234147i	$0.0752297\pi$
$449$			9.92297i			0.468294i	−0.972201	+	0.234147i	$0.924770\pi$
$450$	−11.9218	+	2.44718i	−0.561997	+	0.115361i
$451$	31.0550	+	17.9296i	1.46232	+	0.844273i
$452$	3.49673	−	6.05651i	0.164472	−	0.284874i
$453$	−22.2557	+	8.45414i	−1.04566	+	0.397210i
$454$		−	25.2934i		−	1.18708i
$455$	−2.91754	+	0.593436i	−0.136776	+	0.0278207i
$456$	1.30406	−	8.05153i	0.0610684	−	0.377047i
$457$	−5.99306	+	3.46010i	−0.280344	+	0.161856i	−0.633579	−	0.773678i	$-0.718415\pi$
$457$	−5.99306	+	3.46010i	−0.280344	+	0.161856i	0.353235	+	0.935534i	$0.385081\pi$
$458$	−0.685423	+	1.18719i	−0.0320277	+	0.0554736i
$459$	2.67043	+	4.20794i	0.124645	+	0.196410i
$460$	4.55985	+	0.949651i	0.212604	+	0.0442777i
$461$		−	11.6895i		−	0.544435i	−0.962236	−	0.272218i	$-0.912243\pi$
$461$		−	11.6895i		−	0.544435i	0.962236	−	0.272218i	$-0.0877570\pi$
$462$	8.46228	+	13.3874i	0.393701	+	0.622839i
$463$	9.26385			0.430528			0.215264	−	0.976556i	$-0.430939\pi$
$463$	9.26385			0.430528			0.215264	+	0.976556i	$0.430939\pi$
$464$	−5.31728	+	3.06993i	−0.246849	+	0.142518i
$465$	−9.27561	−	7.56500i	−0.430146	−	0.350819i
$466$	−10.3853	+	17.9878i	−0.481088	+	0.833268i
$467$	−17.9250	−	31.0470i	−0.829470	−	1.43668i	−0.898455	−	0.439066i	$-0.855309\pi$
$467$	−17.9250	−	31.0470i	−0.829470	−	1.43668i	0.0689846	−	0.997618i	$-0.478024\pi$
$468$	−3.29834	−	1.09721i	−0.152466	−	0.0507187i
$469$	30.4652	−	26.9507i	1.40675	−	1.24447i
$470$	−5.83652			−0.269219
$471$	−13.3056	−	35.0273i	−0.613091	−	1.61397i
$472$	4.22959	−	7.32586i	0.194683	−	0.337200i
$473$	−36.0341	−	20.8043i	−1.65685	−	0.956581i
$474$	24.6563	−	9.36606i	1.13250	−	0.430197i
$475$		−	19.1039i		−	0.876547i
$476$	−2.48669	+	0.505800i	−0.113977	+	0.0231833i
$477$	−13.6278	−	4.53339i	−0.623976	−	0.207570i
$478$	−0.314300	−	0.544384i	−0.0143758	−	0.0248995i
$479$	1.03130	−	1.78627i	0.0471215	−	0.0816168i	−0.841503	−	0.540253i	$-0.818329\pi$
$479$	1.03130	−	1.78627i	0.0471215	−	0.0816168i	0.888624	+	0.458636i	$0.151662\pi$
$480$	−1.06317	+	1.30358i	−0.0485271	+	0.0595000i
$481$	6.03036	−	3.48163i	0.274961	−	0.158749i
$482$	11.1151			0.506277
$483$	−20.5811	+	7.70838i	−0.936472	+	0.350743i
$484$	−0.944431			−0.0429287
$485$	−12.9373	+	7.46937i	−0.587453	+	0.339166i
$486$	−15.1254	+	3.77117i	−0.686103	+	0.171064i
$487$	6.20073	−	10.7400i	0.280982	−	0.486675i	−0.690645	−	0.723194i	$-0.742673\pi$
$487$	6.20073	−	10.7400i	0.280982	−	0.486675i	0.971627	+	0.236519i	$0.0760066\pi$
$488$	−2.79443	−	4.84009i	−0.126498	−	0.219101i
$489$	−2.76026	+	17.0423i	−0.124823	+	0.770681i
$490$	−2.65574	−	6.25818i	−0.119974	−	0.282716i
$491$			23.3681i			1.05459i	0.849683	+	0.527293i	$0.176793\pi$
$491$			23.3681i			1.05459i	−0.849683	+	0.527293i	$0.823207\pi$
$492$	−6.38173	−	16.8000i	−0.287710	−	0.757403i
$493$	5.09995	+	2.94446i	0.229690	+	0.132612i
$494$	2.72819	−	4.72537i	0.122747	−	0.212604i
$495$	−2.02476	−	9.86389i	−0.0910063	−	0.443349i
$496$	7.11549			0.319495
$497$	−27.0427	−	9.04978i	−1.21303	−	0.405938i
$498$	−11.8230	−	1.91491i	−0.529802	−	0.0858093i
$499$	−13.9102	−	24.0931i	−0.622705	−	1.07856i	−0.988980	−	0.148050i	$-0.952700\pi$
$499$	−13.9102	−	24.0931i	−0.622705	−	1.07856i	0.366275	−	0.930507i	$-0.380633\pi$
$500$	−4.39795	+	7.61747i	−0.196682	+	0.340664i
$501$	−8.36363	+	10.2548i	−0.373659	+	0.458151i
$502$	−10.0132	+	5.78113i	−0.446911	+	0.258024i
$503$	−8.62483			−0.384562			−0.192281	−	0.981340i	$-0.561589\pi$
$503$	−8.62483			−0.384562			−0.192281	+	0.981340i	$0.561589\pi$
$504$	0.953936	−	7.87972i	0.0424917	−	0.350991i
$505$			6.71997i			0.299035i
$506$	3.37940	−	16.2266i	0.150233	−	0.721359i
$507$	15.6471	+	12.7615i	0.694914	+	0.566758i
$508$	−4.73796	+	8.20638i	−0.210213	+	0.364099i
$509$	−10.3583	+	5.98036i	−0.459123	+	0.265075i	−0.711675	−	0.702508i	$-0.752063\pi$
$509$	−10.3583	+	5.98036i	−0.459123	+	0.265075i	0.252552	+	0.967583i	$0.418730\pi$
$510$	1.59265	+	0.257953i	0.0705237	+	0.0114224i
$511$	−23.0422	−	26.0470i	−1.01933	−	1.15225i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.02465	−	24.4479i	−0.0452396	−	1.07940i
$514$	−1.42817	+	2.47366i	−0.0629937	+	0.109108i
$515$	−1.00972	−	0.582959i	−0.0444934	−	0.0256883i
$516$	7.40490	+	19.4936i	0.325983	+	0.858156i
$517$			20.7697i			0.913450i
$518$	10.5351	+	11.9089i	0.462885	+	0.523247i
$519$	17.3736	+	2.81391i	0.762615	+	0.123517i
$520$	−0.974545	+	0.562654i	−0.0427366	+	0.0246740i
$521$	2.27298	−	3.93692i	0.0995811	−	0.172480i	−0.811930	−	0.583754i	$-0.801583\pi$
$521$	2.27298	−	3.93692i	0.0995811	−	0.172480i	0.911511	+	0.411275i	$0.134916\pi$
$522$	−13.7741	+	12.2293i	−0.602878	+	0.535260i
$523$	−4.95748	+	2.86220i	−0.216775	+	0.125155i	−0.604456	−	0.796638i	$-0.706610\pi$
$523$	−4.95748	+	2.86220i	−0.216775	+	0.125155i	0.387681	+	0.921794i	$0.373276\pi$
$524$		−	20.0566i		−	0.876178i
$525$	−0.745179	−	18.5756i	−0.0325223	−	0.810704i
$526$			11.4842i			0.500737i
$527$	−3.41233	−	5.91032i	−0.148643	−	0.257458i
$528$	4.63889	+	3.78339i	0.201882	+	0.164651i
$529$	21.0878	+	9.18187i	0.916859	+	0.399212i
$530$	−4.02656	+	2.32473i	−0.174902	+	0.100980i
$531$	8.01040	−	24.0801i	0.347622	−	1.04499i
$532$	11.8151	+	3.95392i	0.512252	+	0.171424i
$533$		−	12.0222i		−	0.520738i
$534$	−0.752746	−	1.98162i	−0.0325745	−	0.0857531i
$535$	−6.71746	+	11.6350i	−0.290421	+	0.503024i
$536$	7.68689	−	13.3141i	0.332023	−	0.575081i
$537$	0.572053	+	1.50594i	0.0246859	+	0.0649862i
$538$	21.0577			0.907861
$539$	−22.2702	+	9.45064i	−0.959246	+	0.407068i
$540$	−2.33802	+	4.47221i	−0.100612	+	0.192453i
$541$	2.53911	+	4.39787i	0.109165	+	0.189079i	0.915432	−	0.402472i	$-0.131849\pi$
$541$	2.53911	+	4.39787i	0.109165	+	0.189079i	−0.806267	+	0.591551i	$0.798516\pi$
$542$	16.1813	+	9.34228i	0.695046	+	0.401285i
$543$	11.1311	−	13.6480i	0.477680	−	0.585694i
$544$	−0.830628	+	0.479563i	−0.0356129	+	0.0205611i
$545$			14.4461i			0.618803i
$546$	2.46842	−	4.70110i	0.105639	−	0.201189i
$547$	−0.453107			−0.0193734			−0.00968672	−	0.999953i	$-0.503083\pi$
$547$	−0.453107			−0.0193734			−0.00968672	+	0.999953i	$0.503083\pi$
$548$	4.81538	+	8.34049i	0.205703	+	0.356288i
$549$	−11.1318	−	12.5380i	−0.475092	−	0.535110i
$550$	12.1421	+	7.01026i	0.517742	+	0.298919i
$551$	−14.4567	−	25.0398i	−0.615877	−	1.06673i
$552$	−6.45222	+	5.23153i	−0.274625	+	0.222669i
$553$	8.03045	+	39.4806i	0.341489	+	1.67888i
$554$			8.00437i			0.340073i
$555$	−3.58983	−	9.45030i	−0.152380	−	0.401143i
$556$	−2.98395	+	5.16835i	−0.126548	+	0.219187i
$557$	−4.33575	+	7.50974i	−0.183712	+	0.318198i	−0.943142	−	0.332391i	$-0.892145\pi$
$557$	−4.33575	+	7.50974i	−0.183712	+	0.318198i	0.759430	+	0.650589i	$0.225478\pi$
$558$	20.9105	−	4.29229i	0.885211	−	0.181707i
$559$			13.9497i			0.590009i
$560$	−1.70254	−	1.92455i	−0.0719453	−	0.0813272i
$561$	0.917947	−	5.66757i	0.0387557	−	0.239285i
$562$	−15.5089	+	8.95408i	−0.654204	+	0.377705i
$563$	−9.41118	+	16.3006i	−0.396634	+	0.686990i	−0.993308	−	0.115494i	$-0.963155\pi$
$563$	−9.41118	+	16.3006i	−0.396634	+	0.686990i	0.596674	+	0.802483i	$0.296488\pi$
$564$	6.57878	−	8.06638i	0.277017	−	0.339656i
$565$	−3.39601	−	5.88205i	−0.142871	−	0.247460i
$566$	−3.39748			−0.142807
$567$	−1.94995	−	23.7318i	−0.0818901	−	0.996641i
$568$	−10.7783			−0.452248
$569$	2.56149	+	4.43664i	0.107383	+	0.185993i	0.914709	−	0.404112i	$-0.132419\pi$
$569$	2.56149	+	4.43664i	0.107383	+	0.185993i	−0.807326	+	0.590106i	$0.799086\pi$
$570$	−6.13872	−	5.00662i	−0.257123	−	0.209704i
$571$	32.9046	+	18.9975i	1.37701	+	0.795019i	0.991799	−	0.127808i	$-0.0407941\pi$
$571$	32.9046	+	18.9975i	1.37701	+	0.795019i	0.385215	+	0.922827i	$0.374127\pi$
$572$	2.00225	+	3.46799i	0.0837181	+	0.145004i
$573$	−1.61147	+	9.94951i	−0.0673202	+	0.415647i
$574$	26.9008	−	5.47168i	1.12282	−	0.228384i
$575$	−12.9588	+	14.5117i	−0.540420	+	0.605182i
$576$	−0.603233	−	2.93873i	−0.0251347	−	0.122447i
$577$	3.06656	−	5.31143i	0.127662	−	0.221118i	−0.795108	−	0.606468i	$-0.792586\pi$
$577$	3.06656	−	5.31143i	0.127662	−	0.221118i	0.922770	+	0.385350i	$0.125919\pi$
$578$	−13.9258	−	8.04004i	−0.579235	−	0.334421i
$579$	8.03606	−	3.05261i	0.333967	−	0.126862i
$580$			5.96301i			0.247601i
$581$	5.80601	−	17.3496i	0.240874	−	0.719783i
$582$	4.25957	−	26.2993i	0.176565	−	1.09014i
$583$	8.27274	+	14.3288i	0.342622	+	0.593438i
$584$	−11.3832	−	6.57210i	−0.471040	−	0.271955i
$585$	−2.52451	+	2.24136i	−0.104376	+	0.0926689i
$586$	−21.9350	+	12.6642i	−0.906127	+	0.523152i
$587$			35.8674i			1.48040i	0.672384	+	0.740202i	$0.265270\pi$
$587$			35.8674i			1.48040i	−0.672384	+	0.740202i	$0.734730\pi$
$588$	11.6426	+	3.38370i	0.480133	+	0.139541i
$589$			33.5077i			1.38066i
$590$	−4.10776	−	7.11484i	−0.169114	−	0.292913i
$591$	25.0120	−	30.6678i	1.02886	−	1.26150i
$592$	5.20449	+	3.00482i	0.213903	+	0.123497i
$593$	10.6540	−	6.15111i	0.437509	−	0.252596i	−0.265032	−	0.964240i	$-0.585382\pi$
$593$	10.6540	−	6.15111i	0.437509	−	0.252596i	0.702540	+	0.711644i	$0.252049\pi$
$594$	15.9147	+	8.32001i	0.652987	+	0.341374i
$595$	−0.782114	+	2.33712i	−0.0320635	+	0.0958126i
$596$	0.380406			0.0155821
$597$	3.68730	+	9.70689i	0.150911	+	0.397277i
$598$	−5.27777	+	1.73887i	−0.215824	+	0.0711078i
$599$	23.6139	+	13.6335i	0.964837	+	0.557049i	0.897658	−	0.440692i	$-0.145267\pi$
$599$	23.6139	+	13.6335i	0.964837	+	0.557049i	0.0671787	+	0.997741i	$0.478600\pi$
$600$	−2.49517	−	6.56860i	−0.101865	−	0.268162i
$601$	16.4666			0.671685			0.335842	−	0.941918i	$-0.390979\pi$
$601$	16.4666			0.671685			0.335842	+	0.941918i	$0.390979\pi$
$602$	−31.2137	+	6.34895i	−1.27218	+	0.258764i
$603$	14.5582	−	43.7634i	0.592855	−	1.78218i
$604$	−6.87258	−	11.9037i	−0.279641	−	0.484353i
$605$	−0.458614	+	0.794342i	−0.0186453	+	0.0322946i
$606$	−9.28735	−	7.57458i	−0.377273	−	0.307696i
$607$	−1.23808	−	2.14442i	−0.0502521	−	0.0870392i	0.839805	−	0.542888i	$-0.182669\pi$
$607$	−1.23808	−	2.14442i	−0.0502521	−	0.0870392i	−0.890057	+	0.455849i	$0.849336\pi$
$608$	4.70913			0.190980
$609$	−15.0336	−	23.7834i	−0.609193	−	0.963750i
$610$	−5.42787			−0.219768
$611$	6.03035	−	3.48163i	0.243962	−	0.140851i
$612$	−2.15170	+	1.91037i	−0.0869773	+	0.0772220i
$613$	−18.3289	−	10.5822i	−0.740295	−	0.427410i	0.0818813	−	0.996642i	$-0.473907\pi$
$613$	−18.3289	−	10.5822i	−0.740295	−	0.427410i	−0.822177	+	0.569232i	$0.807240\pi$
$614$	−6.13313	+	3.54096i	−0.247513	+	0.142902i
$615$	−17.2291	−	2.79051i	−0.694745	−	0.112524i
$616$	−6.84867	+	6.05861i	−0.275941	+	0.244108i
$617$	35.0851			1.41247			0.706237	−	0.707976i	$-0.250391\pi$
$617$	35.0851			1.41247			0.706237	+	0.707976i	$0.250391\pi$
$618$	1.94381	−	0.738382i	0.0781914	−	0.0297021i
$619$	14.7571	+	8.52000i	0.593137	+	0.342448i	0.766337	−	0.642439i	$-0.222077\pi$
$619$	14.7571	+	8.52000i	0.593137	+	0.342448i	−0.173200	+	0.984887i	$0.555411\pi$
$620$	3.45526	−	5.98469i	0.138767	−	0.240351i
$621$	−15.8055	+	19.2662i	−0.634252	+	0.773127i
$622$	17.4581			0.700006
$623$	3.17304	−	0.645404i	0.127125	−	0.0258576i
$624$	0.320866	−	1.98108i	0.0128449	−	0.0793067i
$625$	−5.87068	−	10.1683i	−0.234827	−	0.406733i
$626$	−5.15586	+	8.93020i	−0.206069	+	0.356923i
$627$	−17.8164	+	21.8451i	−0.711520	+	0.872410i
$628$	18.7347	−	10.8165i	0.747596	−	0.431624i
$629$		−	5.76400i		−	0.229826i
$630$	−6.16425	−	4.62871i	−0.245589	−	0.184412i
$631$		−	7.26081i		−	0.289048i	−0.989501	−	0.144524i	$-0.953835\pi$
$631$		−	7.26081i		−	0.289048i	0.989501	−	0.144524i	$-0.0461651\pi$
$632$	7.61390	+	13.1877i	0.302865	+	0.524577i
$633$	−10.8240	−	8.82782i	−0.430214	−	0.350874i
$634$	−9.01169	+	15.6087i	−0.357900	+	0.619901i
$635$	4.60148	+	7.97000i	0.182604	+	0.316280i
$636$	1.32573	−	8.18529i	0.0525686	−	0.324568i
$637$	6.47709	+	4.88181i	0.256632	+	0.193424i
$638$	21.2198			0.840101
$639$	−31.6745	+	6.50183i	−1.25302	+	0.257208i
$640$	−0.841080	−	0.485598i	−0.0332466	−	0.0191949i
$641$	−21.6796	+	37.5502i	−0.856294	+	1.48314i	0.0191455	+	0.999817i	$0.493905\pi$
$641$	−21.6796	+	37.5502i	−0.856294	+	1.48314i	−0.875439	+	0.483328i	$0.839428\pi$
$642$	−8.50841	−	22.3986i	−0.335800	−	0.884000i
$643$			31.7437i			1.25185i	0.779883	+	0.625925i	$0.215278\pi$
$643$			31.7437i			1.25185i	−0.779883	+	0.625925i	$0.784722\pi$
$644$	−6.29298	−	11.0181i	−0.247978	−	0.434174i
$645$	19.9914	+	3.23791i	0.787162	+	0.127493i
$646$	−2.25833	−	3.91153i	−0.0888526	−	0.153897i
$647$	8.09385	+	4.67298i	0.318202	+	0.183714i	0.650591	−	0.759428i	$-0.274521\pi$
$647$	8.09385	+	4.67298i	0.318202	+	0.183714i	−0.332389	+	0.943142i	$0.607855\pi$
$648$	−3.54547	−	8.27222i	−0.139279	−	0.324964i
$649$	−25.3187	+	14.6178i	−0.993846	+	0.573797i
$650$		−	4.70052i		−	0.184370i
$651$	1.30703	+	32.5810i	0.0512264	+	1.27695i
$652$	−9.96762			−0.390362
$653$	15.4867	−	8.94125i	0.606041	−	0.349898i	−0.165373	−	0.986231i	$-0.552883\pi$
$653$	15.4867	−	8.94125i	0.606041	−	0.349898i	0.771414	+	0.636333i	$0.219550\pi$
$654$	−19.9653	−	16.2833i	−0.780703	−	0.636726i
$655$	−16.8692	−	9.73946i	−0.659135	−	0.380552i
$656$	8.98564	−	5.18786i	0.350830	−	0.202552i
$657$	−37.4166	−	12.4469i	−1.45976	−	0.485599i
$658$	10.5351	+	11.9089i	0.410700	+	0.464256i
$659$	27.5938			1.07490			0.537450	−	0.843296i	$-0.319388\pi$
$659$	27.5938			1.07490			0.537450	+	0.843296i	$0.319388\pi$
$660$	5.43476	−	2.06447i	0.211548	−	0.0803594i
$661$	−43.8640	−	25.3249i	−1.70611	−	0.985024i	−0.939264	−	0.343197i	$-0.888490\pi$
$661$	−43.8640	−	25.3249i	−1.70611	−	0.985024i	−0.766849	−	0.641828i	$-0.778176\pi$
$662$	12.2161	+	7.05294i	0.474790	+	0.274120i
$663$	−1.79942	+	0.683534i	−0.0698836	+	0.0265463i
$664$		−	6.91498i		−	0.268353i
$665$	9.06297	−	8.01747i	0.351447	−	0.310904i
$666$	17.1072	+	5.69081i	0.662890	+	0.220514i
$667$	−6.00366	+	28.8272i	−0.232463	+	1.11619i
$668$	−6.61649	−	3.82003i	−0.255999	−	0.147801i
$669$	0.737131	+	0.601189i	0.0284991	+	0.0232433i
$670$	−7.46547	−	12.9306i	−0.288416	−	0.499552i
$671$			19.3155i			0.745667i
$672$	4.57889	−	0.183687i	0.176635	−	0.00708590i
$673$	4.32861			0.166855			0.0834277	−	0.996514i	$-0.473413\pi$
$673$	4.32861			0.166855			0.0834277	+	0.996514i	$0.473413\pi$
$674$	−0.340368	−	0.589534i	−0.0131105	−	0.0227080i
$675$	−11.2950	−	17.7981i	−0.434746	−	0.685051i
$676$	−5.82873	+	10.0957i	−0.224182	+	0.388294i
$677$	−2.88237	−	4.99242i	−0.110779	−	0.191874i	0.805306	−	0.592860i	$-0.202001\pi$
$677$	−2.88237	−	4.99242i	−0.110779	−	0.191874i	−0.916084	+	0.400985i	$0.868668\pi$
$678$	11.9572	+	1.93665i	0.459214	+	0.0743765i
$679$	38.5928	+	12.9150i	1.48105	+	0.495632i
$680$			0.931500i			0.0357214i
$681$	40.9542	−	15.5570i	1.56937	−	0.596147i
$682$	−21.2970	−	12.2958i	−0.815503	−	0.470831i
$683$	−1.46102	−	0.843522i	−0.0559045	−	0.0322765i	0.471787	−	0.881712i	$-0.343609\pi$
$683$	−1.46102	−	0.843522i	−0.0559045	−	0.0322765i	−0.527692	+	0.849436i	$0.676942\pi$
$684$	13.8388	−	2.84070i	0.529141	−	0.108617i
$685$	9.35335			0.357373
$686$	−7.97557	+	16.7150i	−0.304509	+	0.638181i
$687$	−2.34383	−	0.379618i	−0.0894228	−	0.0144833i
$688$	−10.4263	+	6.01963i	−0.397499	+	0.229496i
$689$	2.77352	−	4.80388i	0.105663	−	0.183013i
$690$	1.26695	+	7.96725i	0.0482321	+	0.303308i
$691$	−3.97394	−	6.88306i	−0.151176	−	0.261844i	0.780484	−	0.625175i	$-0.214973\pi$
$691$	−3.97394	−	6.88306i	−0.151176	−	0.261844i	−0.931660	+	0.363331i	$0.881639\pi$
$692$			10.1613i			0.386276i
$693$	−16.4716	+	21.9359i	−0.625705	+	0.833277i
$694$	0.0406009			0.00154119
$695$	2.89800	+	5.01948i	0.109927	+	0.190400i
$696$	−8.24119	−	6.72136i	−0.312382	−	0.254772i
$697$	−8.61837	−	4.97582i	−0.326444	−	0.188473i
$698$	15.2049	−	8.77855i	0.575514	−	0.332273i
$699$	−35.5128	−	5.75183i	−1.34322	−	0.217554i
$700$	10.5179	−	2.13936i	0.397538	−	0.0808602i
$701$	−40.1359			−1.51591			−0.757955	−	0.652306i	$-0.773802\pi$
$701$	−40.1359			−1.51591			−0.757955	+	0.652306i	$0.773802\pi$
$702$	−0.252117	−	6.01541i	−0.00951553	−	0.227037i
$703$	−14.1501	+	24.5086i	−0.533680	+	0.924360i
$704$	−1.72804	+	2.99305i	−0.0651278	+	0.112805i
$705$	−3.58983	−	9.45029i	−0.135201	−	0.355919i
$706$	15.6078			0.587407
$707$	13.7115	−	12.1297i	0.515673	−	0.456185i
$708$	14.4632	+	2.34254i	0.543562	+	0.0880380i
$709$	23.7472	−	13.7105i	0.891845	−	0.514907i	0.0172993	−	0.999850i	$-0.494493\pi$
$709$	23.7472	−	13.7105i	0.891845	−	0.514907i	0.874545	+	0.484944i	$0.161160\pi$
$710$	−5.23392	+	9.06542i	−0.196426	+	0.340219i
$711$	30.3304	+	34.1620i	1.13748	+	1.28117i
$712$	1.05989	−	0.611926i	0.0397210	−	0.0229329i
$713$	22.7294	−	25.4532i	0.851223	−	0.953231i
$714$	−2.34845	−	3.71527i	−0.0878884	−	0.139040i
$715$	3.88914			0.145446
$716$	−0.805467	+	0.465036i	−0.0301017	+	0.0173792i
$717$	0.688134	−	0.843735i	0.0256988	−	0.0315099i
$718$	−8.24359	−	4.75944i	−0.307648	−	0.177621i
$719$	24.7984	−	14.3174i	0.924824	−	0.533947i	0.0396532	−	0.999214i	$-0.487375\pi$
$719$	24.7984	−	14.3174i	0.924824	−	0.533947i	0.885171	+	0.465266i	$0.154041\pi$
$720$	−2.76463	−	0.919672i	−0.103032	−	0.0342741i
$721$	0.633088	+	3.11249i	0.0235774	+	0.115915i
$722$			3.17588i			0.118194i
$723$	6.83646	+	17.9971i	0.254251	+	0.669320i
$724$	8.80582	+	5.08404i	0.327266	+	0.188947i
$725$	−21.5710	−	12.4540i	−0.801128	−	0.462532i
$726$	−0.580885	−	1.52919i	−0.0215587	−	0.0567536i
$727$			27.4997i			1.01991i	0.860201	+	0.509954i	$0.170338\pi$
$727$			27.4997i			1.01991i	−0.860201	+	0.509954i	$0.829662\pi$
$728$	2.90712	+	0.972864i	0.107745	+	0.0360567i
$729$	−15.4092	−	22.1710i	−0.570713	−	0.821150i
$730$	−11.0553	+	6.38279i	−0.409176	+	0.236238i
$731$	10.0001	+	5.77359i	0.369869	+	0.213544i
$732$	6.11816	−	7.50161i	0.226134	−	0.277267i
$733$	−39.4363	+	22.7685i	−1.45661	+	0.840976i	−0.998843	−	0.0480953i	$-0.984685\pi$
$733$	−39.4363	+	22.7685i	−1.45661	+	0.840976i	−0.457770	+	0.889071i	$0.651352\pi$
$734$	−35.7338			−1.31896
$735$	8.49959	−	8.14925i	0.313512	−	0.300590i
$736$	−3.57716	−	3.19436i	−0.131856	−	0.117746i
$737$	−46.0144	+	26.5664i	−1.69496	+	0.978588i
$738$	23.2769	−	20.6661i	0.856833	−	0.760731i
$739$	−15.8372	+	27.4309i	−0.582582	+	1.00906i	0.412590	+	0.910917i	$0.364624\pi$
$739$	−15.8372	+	27.4309i	−0.582582	+	1.00906i	−0.995172	+	0.0981451i	$0.968709\pi$
$740$	5.05458	−	2.91826i	0.185810	−	0.107277i
$741$	9.32917	+	1.51100i	0.342715	+	0.0555079i
$742$	12.0114	+	4.01961i	0.440954	+	0.147565i
$743$	−0.882887			−0.0323900			−0.0161950	−	0.999869i	$-0.505155\pi$
$743$	−0.882887			−0.0323900			−0.0161950	+	0.999869i	$0.505155\pi$
$744$	4.37647	+	11.5212i	0.160449	+	0.422386i
$745$	0.184724	−	0.319952i	0.00676778	−	0.0117221i
$746$	13.9449	−	24.1533i	0.510560	−	0.884316i
$747$	−4.17134	−	20.3212i	−0.152621	−	0.743515i
$748$	3.31481			0.121202
$749$	35.8653	−	7.29510i	1.31049	−	0.266557i
$750$	−15.0390	−	2.43578i	−0.549146	−	0.0889423i
$751$	−11.0665	+	6.38925i	−0.403823	+	0.233147i	−0.688132	−	0.725585i	$-0.741569\pi$
$751$	−11.0665	+	6.38925i	−0.403823	+	0.233147i	0.284309	+	0.958733i	$0.408236\pi$
$752$	5.20449	+	3.00481i	0.189788	+	0.109574i
$753$	−15.5193	−	12.6573i	−0.565557	−	0.461257i
$754$	−3.55708	−	6.16104i	−0.129541	−	0.224372i
$755$	−13.3492			−0.485828
$756$	13.3453	−	3.30194i	0.485364	−	0.120091i
$757$		−	11.9782i		−	0.435355i	−0.976021	−	0.217677i	$-0.930152\pi$
$757$		−	11.9782i		−	0.435355i	0.976021	−	0.217677i	$-0.0698481\pi$
$758$	2.54556	+	4.40904i	0.0924589	+	0.160144i
$759$	28.3521	−	4.50855i	1.02911	−	0.163650i
$760$	2.28674	−	3.96075i	0.0829488	−	0.143672i
$761$	−7.34058	+	4.23808i	−0.266096	+	0.153630i	−0.627112	−	0.778929i	$-0.715763\pi$
$761$	−7.34058	+	4.23808i	−0.266096	+	0.153630i	0.361016	+	0.932559i	$0.382430\pi$
$762$	−16.2016	−	2.62410i	−0.586923	−	0.0950609i
$763$	29.4759	−	26.0756i	1.06710	−	0.943999i
$764$	−5.81921			−0.210532
$765$	0.561911	+	2.73742i	0.0203159	+	0.0989717i
$766$	30.2068	+	17.4399i	1.09142	+	0.630130i
$767$	8.48835	+	4.90075i	0.306497	+	0.176956i
$768$	1.61917	−	0.615063i	0.0584266	−	0.0221942i
$769$		−	17.0407i		−	0.614502i	−0.951629	−	0.307251i	$-0.900591\pi$
$769$		−	17.0407i		−	0.614502i	0.951629	−	0.307251i	$-0.0994091\pi$
$770$	1.77008	+	8.70232i	0.0637891	+	0.313610i
$771$	−4.88367	−	0.790984i	−0.175881	−	0.0284866i
$772$	2.48154	+	4.29816i	0.0893127	+	0.154694i
$773$	7.86561	−	13.6236i	0.282906	−	0.490008i	−0.689193	−	0.724578i	$-0.742035\pi$
$773$	7.86561	−	13.6236i	0.282906	−	0.490008i	0.972099	+	0.234570i	$0.0753682\pi$
$774$	−27.0088	+	23.9795i	−0.970812	+	0.861926i
$775$	14.4330	+	24.9987i	0.518448	+	0.897978i
$776$	15.3818			0.552174
$777$	−12.8027	+	24.3828i	−0.459295	+	0.874727i
$778$			38.0502i			1.36416i
$779$	24.4303	+	42.3145i	0.875307	+	1.51608i
$780$	−1.51044	−	1.23188i	−0.0540823	−	0.0441085i
$781$	32.2600	+	18.6253i	1.15435	+	0.666466i
$782$	−0.937850	+	4.50319i	−0.0335374	+	0.161034i
$783$	−28.2732	−	14.7809i	−1.01040	−	0.528225i
$784$	−0.853749	+	6.94774i	−0.0304910	+	0.248134i
$785$		−	21.0098i		−	0.749873i
$786$	32.4750	−	12.3361i	1.15835	−	0.440014i
$787$	−9.37119	−	5.41046i	−0.334047	−	0.192862i	0.323589	−	0.946198i	$-0.395110\pi$
$787$	−9.37119	−	5.41046i	−0.334047	−	0.192862i	−0.657636	+	0.753335i	$0.728444\pi$
$788$	19.7871	+	11.4241i	0.704886	+	0.406966i
$789$	−18.5949	+	7.06353i	−0.661996	+	0.251468i
$790$	14.7892			0.526175
$791$	−5.87191	+	17.5465i	−0.208781	+	0.623882i
$792$	−3.27272	+	9.83815i	−0.116291	+	0.349583i
$793$	5.60814	−	3.23786i	0.199151	−	0.114980i
$794$	−25.3019	−	14.6080i	−0.897930	−	0.518420i
$795$	−6.24071	−	5.08980i	−0.221335	−	0.180517i
$796$	−5.19182	+	2.99750i	−0.184019	+	0.106244i
$797$	−30.7760			−1.09014			−0.545071	−	0.838390i	$-0.683497\pi$
$797$	−30.7760			−1.09014			−0.545071	+	0.838390i	$0.683497\pi$
$798$	0.865007	+	21.5626i	0.0306209	+	0.763307i
$799$		−	5.76399i		−	0.203915i
$800$	3.51327	−	2.02839i	0.124213	−	0.0717144i
$801$	2.74558	−	2.43764i	0.0970105	−	0.0861299i
$802$	18.7411	+	10.8202i	0.661773	+	0.382075i
$803$	22.7136	+	39.3412i	0.801547	+	1.38832i
$804$	26.2856	+	4.25735i	0.927023	+	0.150145i
$805$	−12.3230	−	0.0574673i	−0.434327	−	0.00202546i
$806$			8.24459i			0.290403i
$807$	12.9518	+	34.0959i	0.455925	+	1.20023i
$808$	3.45964	−	5.99227i	0.121710	−	0.210807i
$809$	2.00556	+	1.15791i	0.0705118	+	0.0407100i	0.534841	−	0.844952i	$-0.320371\pi$
$809$	2.00556	+	1.15791i	0.0705118	+	0.0407100i	−0.464330	+	0.885662i	$0.653705\pi$
$810$	−8.67927	−	1.03495i	−0.304958	−	0.0363644i
$811$	6.01786			0.211316			0.105658	−	0.994403i	$-0.466305\pi$
$811$	6.01786			0.211316			0.105658	+	0.994403i	$0.466305\pi$
$812$	12.1670	−	10.7634i	0.426977	−	0.377721i
$813$	−5.17418	+	31.9463i	−0.181466	+	1.12041i
$814$	−10.3849	−	17.9871i	−0.363989	−	0.630448i
$815$	−4.84025	+	8.38356i	−0.169547	+	0.293663i
$816$	−1.28738	−	1.04996i	−0.0450674	−	0.0367561i
$817$	−28.3472	−	49.0988i	−0.991743	−	1.71775i
$818$			1.98180i			0.0692921i
$819$	9.13010	+	1.10531i	0.319031	+	0.0386226i
$820$		−	10.0769i		−	0.351899i
$821$	26.5477	−	15.3273i	0.926522	−	0.534928i	0.0408119	−	0.999167i	$-0.487006\pi$
$821$	26.5477	−	15.3273i	0.926522	−	0.534928i	0.885710	+	0.464239i	$0.153672\pi$
$822$	−10.5429	+	12.9268i	−0.367725	+	0.450875i
$823$	17.5343	−	30.3703i	0.611208	−	1.05864i	−0.379829	−	0.925057i	$-0.624017\pi$
$823$	17.5343	−	30.3703i	0.611208	−	1.05864i	0.991037	−	0.133587i	$-0.0426494\pi$
$824$	0.600249	+	1.03966i	0.0209107	+	0.0362184i
$825$	−3.88260	+	23.9719i	−0.135175	+	0.834593i
$826$	−7.10257	+	21.2240i	−0.247130	+	0.738476i
$827$	−44.7104			−1.55473			−0.777367	−	0.629048i	$-0.783445\pi$
$827$	−44.7104			−1.55473			−0.777367	+	0.629048i	$0.783445\pi$
$828$	−12.4392	−	7.22949i	−0.432293	−	0.251242i
$829$	−14.1257	+	24.4665i	−0.490606	+	0.849755i	−0.999942	−	0.0108130i	$-0.996558\pi$
$829$	−14.1257	+	24.4665i	−0.490606	+	0.849755i	0.509335	+	0.860568i	$0.329891\pi$
$830$	−5.81605	−	3.35790i	−0.201878	−	0.116554i
$831$	−12.9604	+	4.92319i	−0.449591	+	0.170784i
$832$	1.15868			0.0401701
$833$	6.18042	−	2.62274i	0.214139	−	0.0908724i
$834$	−10.2037	−	1.65265i	−0.353326	−	0.0572265i
$835$	−6.42590	+	3.70999i	−0.222377	+	0.128390i
$836$	−14.0946	−	8.13754i	−0.487473	−	0.281443i
$837$	19.8112	+	31.2175i	0.684775	+	1.07903i
$838$	−8.62497	+	4.97963i	−0.297945	+	0.172018i
$839$	10.6959			0.369262			0.184631	−	0.982808i	$-0.440891\pi$
$839$	10.6959			0.369262			0.184631	+	0.982808i	$0.440891\pi$
$840$	2.06900	−	3.94041i	0.0713874	−	0.135957i
$841$	−8.69798			−0.299930
$842$	−10.6995	−	18.5321i	−0.368730	−	0.638659i
$843$	−24.0371	−	19.6042i	−0.827882	−	0.675204i
$844$	4.03205	−	6.98371i	0.138789	−	0.240389i
$845$	5.66083	+	9.80485i	0.194739	+	0.337297i
$846$	17.1072	+	5.69080i	0.588156	+	0.195654i
$847$	2.44859	−	0.498050i	0.0841346	−	0.0171132i
$848$	4.78736			0.164399
$849$	−2.08966	−	5.50108i	−0.0717171	−	0.188797i
$850$	−3.36968	−	1.94548i	−0.115579	−	0.0667295i
$851$	27.3737	−	9.01884i	0.938359	−	0.309162i
$852$	−6.62934	−	17.4519i	−0.227117	−	0.597891i
$853$	−26.2680			−0.899400			−0.449700	−	0.893180i	$-0.648469\pi$
$853$	−26.2680			−0.899400			−0.449700	+	0.893180i	$0.648469\pi$
$854$	9.79746	+	11.0751i	0.335262	+	0.378981i
$855$	4.33085	−	13.0190i	0.148112	−	0.445240i
$856$	11.9801	−	6.91670i	0.409470	−	0.236408i
$857$	45.1433	+	26.0635i	1.54207	+	0.890312i	0.998708	+	0.0508105i	$0.0161804\pi$
$857$	45.1433	+	26.0635i	1.54207	+	0.890312i	0.543357	+	0.839502i	$0.317153\pi$
$858$	−4.38375	+	5.37500i	−0.149659	+	0.183500i
$859$	−2.56647	−	4.44525i	−0.0875667	−	0.151670i	0.818915	−	0.573914i	$-0.194576\pi$
$859$	−2.56647	−	4.44525i	−0.0875667	−	0.151670i	−0.906482	+	0.422244i	$0.861242\pi$
$860$			11.6925i			0.398710i
$861$	25.4052	+	40.1914i	0.865808	+	1.36972i
$862$		−	24.3998i		−	0.831060i
$863$	41.3423	−	23.8690i	1.40731	−	0.812509i	0.412179	−	0.911103i	$-0.364768\pi$
$863$	41.3423	−	23.8690i	1.40731	−	0.812509i	0.995128	+	0.0985939i	$0.0314345\pi$
$864$	4.38726	−	2.78423i	0.149258	−	0.0947216i
$865$	8.54650	+	4.93432i	0.290590	+	0.167772i
$866$	−4.01841	−	6.96009i	−0.136551	−	0.236513i
$867$	4.45294	−	27.4932i	0.151230	−	0.933719i
$868$	−18.4481	+	3.75238i	−0.626168	+	0.127364i
$869$		−	52.6284i		−	1.78530i
$870$	−9.65510	+	3.66763i	−0.327339	+	0.124344i
$871$	15.4268	+	8.90667i	0.522717	+	0.301791i
$872$	7.43727	−	12.8817i	0.251858	−	0.436231i
$873$	45.2029	−	9.27880i	1.52989	−	0.314040i
$874$	15.0426	−	16.8453i	0.508825	−	0.569801i
$875$	7.38529	−	22.0688i	0.249669	−	0.746062i
$876$	3.63993	−	22.4736i	0.122982	−	0.759311i
$877$	12.8586	+	22.2718i	0.434205	+	0.752065i	0.997230	−	0.0743744i	$-0.0236960\pi$
$877$	12.8586	+	22.2718i	0.434205	+	0.752065i	−0.563025	+	0.826440i	$0.690363\pi$
$878$	5.42932	+	3.13462i	0.183231	+	0.105788i
$879$	−33.9968	−	27.7271i	−1.14668	−	0.935213i
$880$	1.67826	+	2.90683i	0.0565741	+	0.0979893i
$881$	−6.94502			−0.233984			−0.116992	−	0.993133i	$-0.537325\pi$
$881$	−6.94502			−0.233984			−0.116992	+	0.993133i	$0.537325\pi$
$882$	1.68217	+	20.9325i	0.0566416	+	0.704835i
$883$	44.2921			1.49055			0.745273	−	0.666759i	$-0.232319\pi$
$883$	44.2921			1.49055			0.745273	+	0.666759i	$0.232319\pi$
$884$	−0.555662	−	0.962435i	−0.0186889	−	0.0323702i
$885$	8.99358	−	11.0272i	0.302316	−	0.370676i
$886$	10.8102	−	18.7237i	0.363174	−	0.629036i
$887$	−9.95534	+	5.74772i	−0.334268	+	0.192989i	−0.657734	−	0.753250i	$-0.728485\pi$
$887$	−9.95534	+	5.74772i	−0.334268	+	0.192989i	0.323467	+	0.946240i	$0.395152\pi$
$888$	−1.66420	+	10.2751i	−0.0558470	+	0.344809i
$889$	7.95625	−	23.7750i	0.266844	−	0.797386i
$890$		−	1.18860i		−	0.0398420i
$891$	−3.68294	+	30.8858i	−0.123383	+	1.03471i
$892$	−0.274589	+	0.475602i	−0.00919393	+	0.0159243i
$893$	−14.1500	+	24.5086i	−0.473513	+	0.820149i
$894$	0.233974	+	0.615941i	0.00782526	+	0.0206001i
$895$			0.903282i			0.0301934i
$896$	0.527354	+	2.59266i	0.0176177	+	0.0866148i
$897$	−6.06169	−	7.47607i	−0.202394	−	0.249619i
$898$	−4.96148	−	8.59354i	−0.165567	−	0.286770i
$899$	37.8350	+	21.8441i	1.26187	+	0.728541i
$900$	9.10096	−	8.08020i	0.303365	−	0.269340i
$901$	−2.29585	−	3.97652i	−0.0764857	−	0.132477i
$902$	−35.8593			−1.19398
$903$	−29.4784	−	46.6352i	−0.980980	−	1.55192i
$904$			6.99345i			0.232599i
$905$	8.55217	−	4.93760i	0.284284	−	0.164131i
$906$	15.0469	−	18.4493i	0.499901	−	0.612938i
$907$	−6.15568	−	3.55399i	−0.204396	−	0.118008i	0.394308	−	0.918978i	$-0.370984\pi$
$907$	−6.15568	−	3.55399i	−0.204396	−	0.118008i	−0.598704	+	0.800970i	$0.704318\pi$
$908$	12.6467	+	21.9047i	0.419696	+	0.726934i
$909$	6.55219	−	19.6966i	0.217323	−	0.653295i
$910$	2.22995	−	1.97270i	0.0739221	−	0.0653944i
$911$	33.2335			1.10108			0.550538	−	0.834810i	$-0.314423\pi$
$911$	33.2335			1.10108			0.550538	+	0.834810i	$0.314423\pi$
$912$	2.89641	+	7.62486i	0.0959097	+	0.252484i
$913$	−11.9493	+	20.6968i	−0.395465	+	0.684965i
$914$	3.46010	−	5.99306i	0.114450	−	0.198233i
$915$	−3.33848	−	8.78863i	−0.110367	−	0.290543i
$916$		−	1.37085i		−	0.0452940i
$917$	10.5770	+	52.0001i	0.349282	+	1.71719i
$918$	−4.41663	−	2.30896i	−0.145771	−	0.0762072i
$919$	17.4945	−	10.1004i	0.577090	−	0.333183i	−0.182886	−	0.983134i	$-0.558544\pi$
$919$	17.4945	−	10.1004i	0.577090	−	0.333183i	0.759976	+	0.649951i	$0.225211\pi$
$920$	−4.42377	+	1.45750i	−0.145847	+	0.0480525i
$921$	−9.50567	−	7.75264i	−0.313222	−	0.255458i
$922$	5.84476	+	10.1234i	0.192487	+	0.333397i
$923$		−	12.4886i		−	0.411069i
$924$	−14.0223	−	7.36271i	−0.461298	−	0.242215i
$925$			24.3797i			0.801601i
$926$	−8.02273	+	4.63193i	−0.263643	+	0.152215i
$927$	2.39113	+	2.69319i	0.0785349	+	0.0884561i
$928$	3.06993	−	5.31728i	0.100776	−	0.174548i
$929$	31.0105	−	17.9039i	1.01742	−	0.587409i	0.104066	−	0.994570i	$-0.466815\pi$
$929$	31.0105	−	17.9039i	1.01742	−	0.587409i	0.913356	+	0.407162i	$0.133481\pi$
$930$	11.8154	+	1.91368i	0.387443	+	0.0627521i
$931$	−32.7178	−	4.02041i	−1.07228	−	0.131764i
$932$		−	20.7705i		−	0.680361i
$933$	10.7378	+	28.2675i	0.351541	+	0.925438i
$934$	31.0470	+	17.9250i	1.01589	+	0.586524i
$935$	1.60966	−	2.78802i	0.0526417	−	0.0911780i
$936$	3.40505	−	0.698955i	0.111298	−	0.0228461i
$937$		−	54.0687i		−	1.76635i	−0.469045	−	0.883174i	$-0.655402\pi$
$937$		−	54.0687i		−	1.76635i	0.469045	−	0.883174i	$-0.344598\pi$
$938$	−12.9083	+	38.5726i	−0.421470	+	1.25944i
$939$	−17.6307	−	2.85555i	−0.575355	−	0.0931873i
$940$	5.05457	−	2.91826i	0.164862	−	0.0951831i
$941$	8.99568	−	15.5810i	0.293251	−	0.507925i	−0.681326	−	0.731980i	$-0.738596\pi$
$941$	8.99568	−	15.5810i	0.293251	−	0.507925i	0.974576	+	0.224055i	$0.0719296\pi$
$942$	29.0367	+	23.6818i	0.946066	+	0.771593i
$943$	10.1456	−	48.7150i	0.330385	−	1.58638i
$944$			8.45918i			0.275323i
$945$	3.70325	−	12.8279i	0.120467	−	0.417291i
$946$	41.6085			1.35281
$947$	−19.0534	+	11.0005i	−0.619153	+	0.357468i	−0.776539	−	0.630069i	$-0.783027\pi$
$947$	−19.0534	+	11.0005i	−0.619153	+	0.357468i	0.157386	+	0.987537i	$0.449693\pi$
$948$	−16.6700	+	20.4394i	−0.541416	+	0.663841i
$949$	7.61498	−	13.1895i	0.247193	−	0.428150i
$950$	9.55195	+	16.5445i	0.309906	+	0.536773i
$951$	−30.8159	−	4.99109i	−0.999272	−	0.161847i
$952$	1.90064	−	1.68138i	0.0616001	−	0.0544939i
$953$	−7.86567			−0.254794			−0.127397	−	0.991852i	$-0.540662\pi$
$953$	−7.86567			−0.254794			−0.127397	+	0.991852i	$0.540662\pi$
$954$	14.0688	−	2.88789i	0.455493	−	0.0934990i
$955$	−2.82579	+	4.89442i	−0.0914406	+	0.158380i
$956$	0.544384	+	0.314300i	0.0176066	+	0.0101652i
$957$	13.0515	+	34.3584i	0.421896	+	1.11065i
$958$			2.06261i			0.0666398i
$959$	−16.8830	−	19.0846i	−0.545182	−	0.616275i
$960$	0.268946	−	1.66052i	0.00868020	−	0.0535931i
$961$	−9.81507	−	17.0002i	−0.316615	−	0.548394i
$962$	−3.48163	+	6.03036i	−0.112252	+	0.194427i
$963$	31.0338	−	27.5530i	1.00005	−	0.887884i
$964$	−9.62592	+	5.55753i	−0.310030	+	0.178996i
$965$	4.82013			0.155165
$966$	13.9695	−	16.9662i	0.449463	−	0.545878i
$967$	14.3289			0.460786			0.230393	−	0.973098i	$-0.425999\pi$
$967$	14.3289			0.460786			0.230393	+	0.973098i	$0.425999\pi$
$968$	0.817901	−	0.472216i	0.0262883	−	0.0151776i
$969$	4.94441	−	6.06244i	0.158837	−	0.194754i
$970$	7.46937	−	12.9373i	0.239827	−	0.415392i
$971$	0.241017	+	0.417454i	0.00773461	+	0.0133967i	0.869867	−	0.493287i	$-0.164205\pi$
$971$	0.241017	+	0.417454i	0.00773461	+	0.0133967i	−0.862132	+	0.506683i	$0.830871\pi$
$972$	11.2134	−	10.8286i	0.359670	−	0.347329i
$973$	5.01082	−	14.9734i	0.160639	−	0.480025i
$974$			12.4015i			0.397368i
$975$	7.61092	−	2.89112i	0.243745	−	0.0925898i
$976$	4.84009	+	2.79443i	0.154928	+	0.0894475i
$977$	2.02133	−	3.50104i	0.0646680	−	0.112008i	−0.831879	−	0.554958i	$-0.812735\pi$
$977$	2.02133	−	3.50104i	0.0646680	−	0.112008i	0.896547	+	0.442949i	$0.146068\pi$
$978$	−6.13071	−	16.1392i	−0.196039	−	0.516076i
$979$	−4.22972			−0.135183
$980$	5.42903	+	4.09188i	0.173424	+	0.130710i
$981$	14.0854	−	42.3423i	0.449713	−	1.35189i
$982$	−11.6840	−	20.2374i	−0.372853	−	0.645800i
$983$	−19.8922	+	34.4543i	−0.634462	+	1.09892i	0.352167	+	0.935937i	$0.385445\pi$
$983$	−19.8922	+	34.4543i	−0.634462	+	1.09892i	−0.986629	+	0.162983i	$0.947888\pi$
$984$	13.9267	+	11.3584i	0.443968	+	0.362092i
$985$	19.2171	−	11.0950i	0.612308	−	0.353516i
$986$	−5.88891			−0.187541
$987$	−12.8027	+	24.3827i	−0.407515	+	0.776111i
$988$			5.45639i			0.173591i
$989$	−11.7722	+	56.5254i	−0.374334	+	1.79740i
$990$	6.68544	+	7.53000i	0.212477	+	0.239319i
$991$	−16.8937	+	29.2608i	−0.536647	+	0.929499i	0.462435	+	0.886653i	$0.346976\pi$
$991$	−16.8937	+	29.2608i	−0.536647	+	0.929499i	−0.999082	+	0.0428460i	$0.986358\pi$
$992$	−6.16219	+	3.55774i	−0.195650	+	0.112958i
$993$	−3.90624	+	24.1178i	−0.123961	+	0.765356i
$994$	27.9445	−	5.68399i	0.886346	−	0.180285i
$995$			5.82231i			0.184580i
$996$	11.1965	−	4.25315i	0.354774	−	0.134766i
$997$	12.3456	−	21.3832i	0.390989	−	0.677213i	−0.601591	−	0.798804i	$-0.705466\pi$
$997$	12.3456	−	21.3832i	0.390989	−	0.677213i	0.992580	+	0.121591i	$0.0387997\pi$
$998$	24.0931	+	13.9102i	0.762655	+	0.440319i
$999$	1.30763	+	31.1996i	0.0413716	+	0.987111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.7	✓	128
3.2	odd	2	inner	966.2.j.a.137.60	yes	128
7.2	even	3	inner	966.2.j.a.275.59	yes	128
21.2	odd	6	inner	966.2.j.a.275.8	yes	128
23.22	odd	2	inner	966.2.j.a.137.8	yes	128
69.68	even	2	inner	966.2.j.a.137.59	yes	128
161.114	odd	6	inner	966.2.j.a.275.60	yes	128
483.275	even	6	inner	966.2.j.a.275.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.7	✓	128	1.1	even	1	trivial
966.2.j.a.137.8	yes	128	23.22	odd	2	inner
966.2.j.a.137.59	yes	128	69.68	even	2	inner
966.2.j.a.137.60	yes	128	3.2	odd	2	inner
966.2.j.a.275.7	yes	128	483.275	even	6	inner
966.2.j.a.275.8	yes	128	21.2	odd	6	inner
966.2.j.a.275.59	yes	128	7.2	even	3	inner
966.2.j.a.275.60	yes	128	161.114	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.34224 - 1.09471i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.485598 - 0.841080i) q^{5} +(1.70977 + 0.276923i) q^{6} +(-0.839629 + 2.50899i) q^{7} +1.00000i q^{8} +(0.603233 + 2.93873i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.34224 - 1.09471i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.485598 - 0.841080i) q^{5} +(1.70977 + 0.276923i) q^{6} +(-0.839629 + 2.50899i) q^{7} +1.00000i q^{8} +(0.603233 + 2.93873i) q^{9} +(0.841080 + 0.485598i) q^{10} +(1.72804 - 2.99305i) q^{11} +(-1.61917 + 0.615063i) q^{12} -1.15868 q^{13} +(-0.527354 - 2.59266i) q^{14} +(-0.268946 + 1.66052i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.479563 + 0.830628i) q^{17} +(-1.99178 - 2.24340i) q^{18} +(4.07822 - 2.35456i) q^{19} -0.971195 q^{20} +(3.87359 - 2.44852i) q^{21} +3.45607i q^{22} +(-4.69509 - 0.977816i) q^{23} +(1.09471 - 1.34224i) q^{24} +(2.02839 - 3.51327i) q^{25} +(1.00345 - 0.579342i) q^{26} +(2.40736 - 4.60485i) q^{27} +(1.75303 + 1.98163i) q^{28} -6.13987i q^{29} +(-0.597346 - 1.57253i) q^{30} +(-3.55774 + 6.16219i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.59595 + 2.12570i) q^{33} -0.959127i q^{34} +(2.51798 - 0.512164i) q^{35} +(2.84663 + 0.946948i) q^{36} +(-5.20449 + 3.00482i) q^{37} +(-2.35456 + 4.07822i) q^{38} +(1.55523 + 1.26842i) q^{39} +(0.841080 - 0.485598i) q^{40} +10.3757i q^{41} +(-2.13037 + 4.05728i) q^{42} -12.0393i q^{43} +(-1.72804 - 2.99305i) q^{44} +(2.17877 - 1.93441i) q^{45} +(4.55498 - 1.50073i) q^{46} +(-5.20449 + 3.00481i) q^{47} +(-0.276923 + 1.70977i) q^{48} +(-5.59005 - 4.21324i) q^{49} +4.05678i q^{50} +(1.55299 - 0.589923i) q^{51} +(-0.579342 + 1.00345i) q^{52} +(-2.39368 + 4.14598i) q^{53} +(0.217589 + 5.19159i) q^{54} -3.35652 q^{55} +(-2.50899 - 0.839629i) q^{56} +(-8.05153 - 1.30406i) q^{57} +(3.06993 + 5.31728i) q^{58} +(-7.32586 - 4.22959i) q^{59} +(1.30358 + 1.06317i) q^{60} +(-4.84009 + 2.79443i) q^{61} -7.11549i q^{62} +(-7.87972 - 0.953936i) q^{63} -1.00000 q^{64} +(0.562654 + 0.974545i) q^{65} +(3.78339 - 4.63889i) q^{66} +(-13.3141 - 7.68689i) q^{67} +(0.479563 + 0.830628i) q^{68} +(5.23153 + 6.45222i) q^{69} +(-1.92455 + 1.70254i) q^{70} +10.7783i q^{71} +(-2.93873 + 0.603233i) q^{72} +(-6.57210 + 11.3832i) q^{73} +(3.00482 - 5.20449i) q^{74} +(-6.56860 + 2.49517i) q^{75} -4.70913i q^{76} +(6.05861 + 6.84867i) q^{77} +(-1.98108 - 0.320866i) q^{78} +(13.1877 - 7.61390i) q^{79} +(-0.485598 + 0.841080i) q^{80} +(-8.27222 + 3.54547i) q^{81} +(-5.18786 - 8.98564i) q^{82} -6.91498 q^{83} +(-0.183687 - 4.57889i) q^{84} +0.931500 q^{85} +(6.01963 + 10.4263i) q^{86} +(-6.72136 + 8.24119i) q^{87} +(2.99305 + 1.72804i) q^{88} +(-0.611926 - 1.05989i) q^{89} +(-0.919672 + 2.76463i) q^{90} +(0.972864 - 2.90712i) q^{91} +(-3.19436 + 3.57716i) q^{92} +(11.5212 - 4.37647i) q^{93} +(3.00481 - 5.20449i) q^{94} +(-3.96075 - 2.28674i) q^{95} +(-0.615063 - 1.61917i) q^{96} -15.3818i q^{97} +(6.94774 + 0.853749i) q^{98} +(9.83815 + 3.27272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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