LMFDB - Embedded newform 966.2.l.d.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (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:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.72705 + 0.131543i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22807 - 2.12708i) q^{5} +(1.56144 + 0.749605i) q^{6} +(-0.955407 - 2.46722i) q^{7} -1.00000i q^{8} +(2.96539 - 0.454363i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72705 + 0.131543i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22807 - 2.12708i) q^{5} +(1.56144 + 0.749605i) q^{6} +(-0.955407 - 2.46722i) q^{7} -1.00000i q^{8} +(2.96539 - 0.454363i) q^{9} +(-2.12708 + 1.22807i) q^{10} +(3.22465 - 1.86175i) q^{11} +(-0.977444 - 1.42990i) q^{12} -6.32796i q^{13} +(-0.406206 + 2.61438i) q^{14} +(-1.84114 + 3.83512i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.33399 + 5.77463i) q^{17} +(-2.79529 - 1.08921i) q^{18} +(1.90728 + 1.10117i) q^{19} +2.45614 q^{20} +(1.97458 + 4.13534i) q^{21} -3.72351 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.131543 + 1.72705i) q^{24} +(-0.516322 - 0.894296i) q^{25} +(-3.16398 + 5.48017i) q^{26} +(-5.06161 + 1.17478i) q^{27} +(1.65898 - 2.06102i) q^{28} -5.16739i q^{29} +(3.51203 - 2.40074i) q^{30} +(-4.98193 + 2.87632i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.32423 + 3.63952i) q^{33} -6.66797i q^{34} +(-6.42130 - 0.997701i) q^{35} +(1.87619 + 2.34092i) q^{36} +(2.95839 - 5.12408i) q^{37} +(-1.10117 - 1.90728i) q^{38} +(0.832399 + 10.9287i) q^{39} +(-2.12708 - 1.22807i) q^{40} +6.65921 q^{41} +(0.357633 - 4.56860i) q^{42} +5.27855 q^{43} +(3.22465 + 1.86175i) q^{44} +(2.67525 - 6.86563i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-0.476032 + 0.824512i) q^{47} +(0.749605 - 1.56144i) q^{48} +(-5.17440 + 4.71441i) q^{49} +1.03264i q^{50} +(-6.51757 - 9.53451i) q^{51} +(5.48017 - 3.16398i) q^{52} +(7.33252 - 4.23343i) q^{53} +(4.97087 + 1.51341i) q^{54} -9.14547i q^{55} +(-2.46722 + 0.955407i) q^{56} +(-3.43882 - 1.65088i) q^{57} +(-2.58370 + 4.47509i) q^{58} +(4.16466 + 7.21340i) q^{59} +(-4.24188 + 0.323089i) q^{60} +(-11.0545 - 6.38231i) q^{61} +5.75264 q^{62} +(-3.95417 - 6.88219i) q^{63} -1.00000 q^{64} +(-13.4601 - 7.77119i) q^{65} +(6.43068 - 0.489802i) q^{66} +(-7.38097 - 12.7842i) q^{67} +(-3.33399 + 5.77463i) q^{68} +(1.56144 + 0.749605i) q^{69} +(5.06216 + 4.07468i) q^{70} +0.745937i q^{71} +(-0.454363 - 2.96539i) q^{72} +(-8.54298 + 4.93229i) q^{73} +(-5.12408 + 2.95839i) q^{74} +(1.00935 + 1.47657i) q^{75} +2.20234i q^{76} +(-7.67422 - 6.17721i) q^{77} +(4.74347 - 9.88072i) q^{78} +(0.560876 - 0.971465i) q^{79} +(1.22807 + 2.12708i) q^{80} +(8.58711 - 2.69473i) q^{81} +(-5.76705 - 3.32961i) q^{82} -13.9447 q^{83} +(-2.59402 + 3.77771i) q^{84} +16.3775 q^{85} +(-4.57136 - 2.63928i) q^{86} +(0.679735 + 8.92434i) q^{87} +(-1.86175 - 3.22465i) q^{88} +(-1.15386 + 1.99854i) q^{89} +(-5.74965 + 4.60818i) q^{90} +(-15.6125 + 6.04577i) q^{91} -1.00000i q^{92} +(8.22568 - 5.62288i) q^{93} +(0.824512 - 0.476032i) q^{94} +(4.68456 - 2.70463i) q^{95} +(-1.42990 + 0.977444i) q^{96} -15.2172i q^{97} +(6.83836 - 1.49560i) q^{98} +(8.71645 - 6.98599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.72705	+	0.131543i	−0.997112	+	0.0759464i
$3$	−1.72705	+	0.131543i	−0.997112	+	0.0759464i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.22807	−	2.12708i	0.549211	−	0.951261i	−0.449118	−	0.893472i	$-0.648262\pi$
$5$	1.22807	−	2.12708i	0.549211	−	0.951261i	0.998329	−	0.0577883i	$-0.0184048\pi$
$6$	1.56144	+	0.749605i	0.637455	+	0.306025i
$7$	−0.955407	−	2.46722i	−0.361110	−	0.932523i
$7$	−0.955407	−	2.46722i	−0.361110	−	0.932523i
$8$		−	1.00000i		−	0.353553i
$9$	2.96539	−	0.454363i	0.988464	−	0.151454i
$10$	−2.12708	+	1.22807i	−0.672643	+	0.388351i
$11$	3.22465	−	1.86175i	0.972269	−	0.561340i	0.0723419	−	0.997380i	$-0.476953\pi$
$11$	3.22465	−	1.86175i	0.972269	−	0.561340i	0.899927	+	0.436040i	$0.143619\pi$
$12$	−0.977444	−	1.42990i	−0.282164	−	0.412776i
$13$		−	6.32796i		−	1.75506i	−0.479522	−	0.877530i	$-0.659190\pi$
$13$		−	6.32796i		−	1.75506i	0.479522	−	0.877530i	$-0.340810\pi$
$14$	−0.406206	+	2.61438i	−0.108563	+	0.698723i
$15$	−1.84114	+	3.83512i	−0.475380	+	0.990224i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.33399	+	5.77463i	0.808611	+	1.40055i	0.913826	+	0.406105i	$0.133113\pi$
$17$	3.33399	+	5.77463i	0.808611	+	1.40055i	−0.105216	+	0.994449i	$0.533553\pi$
$18$	−2.79529	−	1.08921i	−0.658855	−	0.256729i
$19$	1.90728	+	1.10117i	0.437560	+	0.252626i	0.702562	−	0.711622i	$-0.252039\pi$
$19$	1.90728	+	1.10117i	0.437560	+	0.252626i	−0.265002	+	0.964248i	$0.585373\pi$
$20$	2.45614			0.549211
$21$	1.97458	+	4.13534i	0.430889	+	0.902405i
$22$	−3.72351			−0.793854
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	0.131543	+	1.72705i	0.0268511	+	0.352532i
$25$	−0.516322	−	0.894296i	−0.103264	−	0.178859i
$26$	−3.16398	+	5.48017i	−0.620507	+	1.07475i
$27$	−5.06161	+	1.17478i	−0.974107	+	0.226087i
$28$	1.65898	−	2.06102i	0.313517	−	0.389496i
$29$		−	5.16739i		−	0.959561i	−0.877389	−	0.479780i	$-0.840716\pi$
$29$		−	5.16739i		−	0.959561i	0.877389	−	0.479780i	$-0.159284\pi$
$30$	3.51203	−	2.40074i	0.641206	−	0.438314i
$31$	−4.98193	+	2.87632i	−0.894781	+	0.516602i	−0.875503	−	0.483212i	$-0.839470\pi$
$31$	−4.98193	+	2.87632i	−0.894781	+	0.516602i	−0.0192779	+	0.999814i	$0.506137\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.32423	+	3.63952i	−0.926829	+	0.633559i
$34$		−	6.66797i		−	1.14355i
$35$	−6.42130	−	0.997701i	−1.08540	−	0.168642i
$36$	1.87619	+	2.34092i	0.312698	+	0.390154i
$37$	2.95839	−	5.12408i	0.486356	−	0.842393i	−0.513521	−	0.858077i	$-0.671659\pi$
$37$	2.95839	−	5.12408i	0.486356	−	0.842393i	0.999877	+	0.0156839i	$0.00499253\pi$
$38$	−1.10117	−	1.90728i	−0.178633	−	0.309402i
$39$	0.832399	+	10.9287i	0.133291	+	1.74999i
$40$	−2.12708	−	1.22807i	−0.336321	−	0.194175i
$41$	6.65921			1.03999			0.519997	−	0.854168i	$-0.325933\pi$
$41$	6.65921			1.03999			0.519997	+	0.854168i	$0.325933\pi$
$42$	0.357633	−	4.56860i	0.0551840	−	0.704950i
$43$	5.27855			0.804972			0.402486	−	0.915426i	$-0.368146\pi$
$43$	5.27855			0.804972			0.402486	+	0.915426i	$0.368146\pi$
$44$	3.22465	+	1.86175i	0.486135	+	0.280670i
$45$	2.67525	−	6.86563i	0.398803	−	1.02347i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−0.476032	+	0.824512i	−0.0694364	+	0.120267i	−0.898653	−	0.438659i	$-0.855453\pi$
$47$	−0.476032	+	0.824512i	−0.0694364	+	0.120267i	0.829217	+	0.558927i	$0.188787\pi$
$48$	0.749605	−	1.56144i	0.108196	−	0.225374i
$49$	−5.17440	+	4.71441i	−0.739199	+	0.673487i
$50$			1.03264i			0.146038i
$51$	−6.51757	−	9.53451i	−0.912642	−	1.33510i
$52$	5.48017	−	3.16398i	0.759963	−	0.438765i
$53$	7.33252	−	4.23343i	1.00720	−	0.581507i	0.0968287	−	0.995301i	$-0.469130\pi$
$53$	7.33252	−	4.23343i	1.00720	−	0.581507i	0.910370	+	0.413794i	$0.135797\pi$
$54$	4.97087	+	1.51341i	0.676450	+	0.205949i
$55$		−	9.14547i		−	1.23318i
$56$	−2.46722	+	0.955407i	−0.329697	+	0.127672i
$57$	−3.43882	−	1.65088i	−0.455483	−	0.218665i
$58$	−2.58370	+	4.47509i	−0.339256	+	0.587609i
$59$	4.16466	+	7.21340i	0.542193	+	0.939105i	0.998778	+	0.0494256i	$0.0157391\pi$
$59$	4.16466	+	7.21340i	0.542193	+	0.939105i	−0.456585	+	0.889680i	$0.650928\pi$
$60$	−4.24188	+	0.323089i	−0.547624	+	0.0417106i
$61$	−11.0545	−	6.38231i	−1.41538	−	0.817171i	−0.419493	−	0.907759i	$-0.637792\pi$
$61$	−11.0545	−	6.38231i	−1.41538	−	0.817171i	−0.995888	+	0.0905881i	$0.971125\pi$
$62$	5.75264			0.730586
$63$	−3.95417	−	6.88219i	−0.498179	−	0.867074i
$64$	−1.00000			−0.125000
$65$	−13.4601	−	7.77119i	−1.66952	−	0.963897i
$66$	6.43068	−	0.489802i	0.791562	−	0.0602904i
$67$	−7.38097	−	12.7842i	−0.901728	−	1.56184i	−0.825250	−	0.564768i	$-0.808966\pi$
$67$	−7.38097	−	12.7842i	−0.901728	−	1.56184i	−0.0764789	−	0.997071i	$-0.524368\pi$
$68$	−3.33399	+	5.77463i	−0.404305	+	0.700277i
$69$	1.56144	+	0.749605i	0.187975	+	0.0902418i
$70$	5.06216	+	4.07468i	0.605044	+	0.487018i
$71$			0.745937i			0.0885265i	0.999020	+	0.0442632i	$0.0140940\pi$
$71$			0.745937i			0.0885265i	−0.999020	+	0.0442632i	$0.985906\pi$
$72$	−0.454363	−	2.96539i	−0.0535471	−	0.349475i
$73$	−8.54298	+	4.93229i	−0.999880	+	0.577281i	−0.908213	−	0.418509i	$-0.862553\pi$
$73$	−8.54298	+	4.93229i	−0.999880	+	0.577281i	−0.0916673	+	0.995790i	$0.529220\pi$
$74$	−5.12408	+	2.95839i	−0.595662	+	0.343906i
$75$	1.00935	+	1.47657i	0.116550	+	0.170500i
$76$			2.20234i			0.252626i
$77$	−7.67422	−	6.17721i	−0.874558	−	0.703958i
$78$	4.74347	−	9.88072i	0.537092	−	1.11877i
$79$	0.560876	−	0.971465i	0.0631034	−	0.109298i	−0.832748	−	0.553653i	$-0.813234\pi$
$79$	0.560876	−	0.971465i	0.0631034	−	0.109298i	0.895851	+	0.444354i	$0.146567\pi$
$80$	1.22807	+	2.12708i	0.137303	+	0.237815i
$81$	8.58711	−	2.69473i	0.954123	−	0.299414i
$82$	−5.76705	−	3.32961i	−0.636864	−	0.367694i
$83$	−13.9447			−1.53063			−0.765317	−	0.643653i	$-0.777418\pi$
$83$	−13.9447			−1.53063			−0.765317	+	0.643653i	$0.777418\pi$
$84$	−2.59402	+	3.77771i	−0.283031	+	0.412182i
$85$	16.3775			1.77639
$86$	−4.57136	−	2.63928i	−0.492943	−	0.284601i
$87$	0.679735	+	8.92434i	0.0728752	+	0.956790i
$88$	−1.86175	−	3.22465i	−0.198464	−	0.343749i
$89$	−1.15386	+	1.99854i	−0.122309	+	0.211845i	−0.920678	−	0.390323i	$-0.872363\pi$
$89$	−1.15386	+	1.99854i	−0.122309	+	0.211845i	0.798369	+	0.602169i	$0.205697\pi$
$90$	−5.74965	+	4.60818i	−0.606066	+	0.485745i
$91$	−15.6125	+	6.04577i	−1.63663	+	0.633769i
$92$		−	1.00000i		−	0.104257i
$93$	8.22568	−	5.62288i	0.852963	−	0.583066i
$94$	0.824512	−	0.476032i	0.0850419	−	0.0490990i
$95$	4.68456	−	2.70463i	0.480626	−	0.277489i
$96$	−1.42990	+	0.977444i	−0.145938	+	0.0997600i
$97$		−	15.2172i		−	1.54507i	−0.634974	−	0.772534i	$-0.718989\pi$
$97$		−	15.2172i		−	1.54507i	0.634974	−	0.772534i	$-0.281011\pi$
$98$	6.83836	−	1.49560i	0.690779	−	0.151078i
$99$	8.71645	−	6.98599i	0.876036	−	0.702119i
$100$	0.516322	−	0.894296i	0.0516322	−	0.0894296i
$101$	0.415726	+	0.720059i	0.0413663	+	0.0716485i	0.885967	−	0.463748i	$-0.153496\pi$
$101$	0.415726	+	0.720059i	0.0413663	+	0.0716485i	−0.844601	+	0.535396i	$0.820162\pi$
$102$	0.877126	+	11.5159i	0.0868484	+	1.14025i
$103$	−5.60780	−	3.23766i	−0.552553	−	0.319016i	0.197598	−	0.980283i	$-0.436686\pi$
$103$	−5.60780	−	3.23766i	−0.552553	−	0.319016i	−0.750151	+	0.661267i	$0.770019\pi$
$104$	−6.32796			−0.620507
$105$	11.2211	+	0.878399i	1.09507	+	0.0857230i
$106$	−8.46686			−0.822375
$107$	−4.43340	−	2.55963i	−0.428593	−	0.247448i	0.270154	−	0.962817i	$-0.412925\pi$
$107$	−4.43340	−	2.55963i	−0.428593	−	0.247448i	−0.698747	+	0.715369i	$0.746259\pi$
$108$	−3.54820	−	3.79609i	−0.341425	−	0.365279i
$109$	5.73238	+	9.92878i	0.549063	+	0.951004i	0.998339	+	0.0576116i	$0.0183485\pi$
$109$	5.73238	+	9.92878i	0.549063	+	0.951004i	−0.449276	+	0.893393i	$0.648318\pi$
$110$	−4.57274	+	7.92021i	−0.435993	+	0.755162i
$111$	−4.43524	+	9.23868i	−0.420974	+	0.876897i
$112$	2.61438	+	0.406206i	0.247036	+	0.0383829i
$113$			3.22150i			0.303054i	0.988453	+	0.151527i	$0.0484190\pi$
$113$			3.22150i			0.303054i	−0.988453	+	0.151527i	$0.951581\pi$
$114$	2.15266	+	3.14912i	0.201615	+	0.294942i
$115$	−2.12708	+	1.22807i	−0.198352	+	0.114518i
$116$	4.47509	−	2.58370i	0.415502	−	0.239890i
$117$	−2.87519	−	18.7649i	−0.265811	−	1.73481i
$118$		−	8.32932i		−	0.766776i
$119$	11.0620	−	13.7428i	1.01405	−	1.25980i
$120$	3.83512	+	1.84114i	0.350097	+	0.168072i
$121$	1.43225	−	2.48074i	0.130205	−	0.225521i
$122$	6.38231	+	11.0545i	0.577827	+	1.00083i
$123$	−11.5008	+	0.875973i	−1.03699	+	0.0789839i
$124$	−4.98193	−	2.87632i	−0.447391	−	0.258301i
$125$	9.74440			0.871565
$126$	−0.0166827	+	7.93724i	−0.00148621	+	0.707105i
$127$	−7.78993			−0.691244			−0.345622	−	0.938374i	$-0.612332\pi$
$127$	−7.78993			−0.691244			−0.345622	+	0.938374i	$0.612332\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−9.11632	+	0.694357i	−0.802647	+	0.0611348i
$130$	7.77119	+	13.4601i	0.681578	+	1.18053i
$131$	−2.54502	+	4.40810i	−0.222359	+	0.385137i	−0.955524	−	0.294914i	$-0.904709\pi$
$131$	−2.54502	+	4.40810i	−0.222359	+	0.385137i	0.733165	+	0.680051i	$0.238042\pi$
$132$	−5.81403	−	2.79116i	−0.506046	−	0.242939i
$133$	0.894604	−	5.75776i	0.0775720	−	0.499261i
$134$			14.7619i			1.27524i
$135$	−3.71716	+	12.2092i	−0.319922	+	1.05080i
$136$	5.77463	−	3.33399i	0.495171	−	0.285887i
$137$	12.9825	−	7.49542i	1.10917	−	0.640377i	0.170553	−	0.985349i	$-0.445445\pi$
$137$	12.9825	−	7.49542i	1.10917	−	0.640377i	0.938613	+	0.344971i	$0.112111\pi$
$138$	−0.977444	−	1.42990i	−0.0832056	−	0.121721i
$139$			8.76557i			0.743486i	0.928336	+	0.371743i	$0.121240\pi$
$139$			8.76557i			0.743486i	−0.928336	+	0.371743i	$0.878760\pi$
$140$	−2.34662	−	6.05986i	−0.198325	−	0.512152i
$141$	0.713672	−	1.48659i	0.0601020	−	0.125193i
$142$	0.372969	−	0.646001i	0.0312988	−	0.0542112i
$143$	−11.7811	−	20.4055i	−0.985185	−	1.70639i
$144$	−1.08921	+	2.79529i	−0.0907672	+	0.232941i
$145$	−10.9915	−	6.34593i	−0.912792	−	0.527001i
$146$	9.86458			0.816399
$147$	8.31629	−	8.82266i	0.685916	−	0.727681i
$148$	5.91677			0.486356
$149$	7.66328	+	4.42440i	0.627801	+	0.362461i	0.779900	−	0.625904i	$-0.215270\pi$
$149$	7.66328	+	4.42440i	0.627801	+	0.362461i	−0.152099	+	0.988365i	$0.548603\pi$
$150$	−0.135837	−	1.78343i	−0.0110911	−	0.145616i
$151$	3.35914	+	5.81821i	0.273363	+	0.473479i	0.969721	−	0.244216i	$-0.0785306\pi$
$151$	3.35914	+	5.81821i	0.273363	+	0.473479i	−0.696358	+	0.717695i	$0.745197\pi$
$152$	1.10117	−	1.90728i	0.0893167	−	0.154701i
$153$	12.5104	+	15.6092i	1.01140	+	1.26193i
$154$	3.55746	+	9.18673i	0.286669	+	0.740288i
$155$			14.1293i			1.13489i
$156$	−9.04832	+	6.18522i	−0.724446	+	0.495214i
$157$	3.39765	−	1.96163i	0.271162	−	0.156555i	−0.358254	−	0.933624i	$-0.616628\pi$
$157$	3.39765	−	1.96163i	0.271162	−	0.156555i	0.629416	+	0.777069i	$0.283294\pi$
$158$	−0.971465	+	0.560876i	−0.0772856	+	0.0446209i
$159$	−12.1067	+	8.27589i	−0.960127	+	0.656320i
$160$		−	2.45614i		−	0.194175i
$161$	−0.406206	+	2.61438i	−0.0320135	+	0.206042i
$162$	−8.78402	−	1.95985i	−0.690138	−	0.153981i
$163$	−5.11496	+	8.85937i	−0.400634	+	0.693919i	−0.993803	−	0.111159i	$-0.964544\pi$
$163$	−5.11496	+	8.85937i	−0.400634	+	0.693919i	0.593168	+	0.805079i	$0.297877\pi$
$164$	3.32961	+	5.76705i	0.259999	+	0.450331i
$165$	1.20302	+	15.7947i	0.0936553	+	1.22961i
$166$	12.0765	+	6.97237i	0.937318	+	0.541161i
$167$	9.37075			0.725131			0.362565	−	0.931958i	$-0.381901\pi$
$167$	9.37075			0.725131			0.362565	+	0.931958i	$0.381901\pi$
$168$	4.13534	−	1.97458i	0.319048	−	0.152342i
$169$	−27.0430			−2.08023
$170$	−14.1833	−	8.18875i	−1.08781	−	0.628049i
$171$	6.15617	+	2.39880i	0.470774	+	0.183441i
$172$	2.63928	+	4.57136i	0.201243	+	0.348563i
$173$	4.38197	−	7.58979i	0.333155	−	0.577041i	−0.649974	−	0.759957i	$-0.725220\pi$
$173$	4.38197	−	7.58979i	0.333155	−	0.577041i	0.983129	+	0.182915i	$0.0585534\pi$
$174$	3.87350	−	8.06857i	0.293649	−	0.611677i
$175$	−1.71313	+	2.12830i	−0.129501	+	0.160884i
$176$			3.72351i			0.280670i
$177$	−8.14145	−	11.9101i	−0.611948	−	0.895215i
$178$	1.99854	−	1.15386i	0.149797	−	0.0864854i
$179$	−13.7465	+	7.93657i	−1.02746	+	0.593207i	−0.916257	−	0.400590i	$-0.868805\pi$
$179$	−13.7465	+	7.93657i	−1.02746	+	0.593207i	−0.111207	+	0.993797i	$0.535472\pi$
$180$	7.28343	−	1.11598i	0.542875	−	0.0831802i
$181$			6.55965i			0.487575i	0.969829	+	0.243787i	$0.0783899\pi$
$181$			6.55965i			0.487575i	−0.969829	+	0.243787i	$0.921610\pi$
$182$	16.5437	+	2.57045i	1.22630	+	0.190535i
$183$	19.9312	+	9.56841i	1.47335	+	0.707317i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−7.26623	−	12.5855i	−0.534224	−	0.925302i
$186$	−9.93509	+	0.756720i	−0.728476	+	0.0554854i
$187$	21.5019	+	12.4141i	1.57237	+	0.907811i
$188$	−0.952064			−0.0694364
$189$	7.73435	+	11.3657i	0.562591	+	0.826735i
$190$	−5.40926			−0.392429
$191$	3.47679	+	2.00733i	0.251572	+	0.145245i	0.620484	−	0.784219i	$-0.286936\pi$
$191$	3.47679	+	2.00733i	0.251572	+	0.145245i	−0.368912	+	0.929464i	$0.620270\pi$
$192$	1.72705	−	0.131543i	0.124639	−	0.00949331i
$193$	5.44791	+	9.43605i	0.392149	+	0.679222i	0.992733	−	0.120340i	$-0.0383985\pi$
$193$	5.44791	+	9.43605i	0.392149	+	0.679222i	−0.600584	+	0.799562i	$0.705065\pi$
$194$	−7.60858	+	13.1784i	−0.546264	+	0.946157i
$195$	24.2685	+	11.6506i	1.73790	+	0.834319i
$196$	−6.66999	−	2.12396i	−0.476428	−	0.151711i
$197$			22.2345i			1.58414i	0.610428	+	0.792072i	$0.290998\pi$
$197$			22.2345i			1.58414i	−0.610428	+	0.792072i	$0.709002\pi$
$198$	−11.0417	+	1.69182i	−0.784697	+	0.120233i
$199$	−1.28109	+	0.739640i	−0.0908143	+	0.0524317i	−0.544719	−	0.838618i	$-0.683364\pi$
$199$	−1.28109	+	0.739640i	−0.0908143	+	0.0524317i	0.453905	+	0.891050i	$0.350031\pi$
$200$	−0.894296	+	0.516322i	−0.0632363	+	0.0365095i
$201$	14.4290	+	21.1080i	1.01774	+	1.48885i
$202$		−	0.831452i		−	0.0585008i
$203$	−12.7491	+	4.93696i	−0.894813	+	0.346507i
$204$	4.99834	−	10.4116i	0.349954	−	0.728960i
$205$	8.17799	−	14.1647i	0.571176	−	0.989306i
$206$	3.23766	+	5.60780i	0.225579	+	0.390714i
$207$	−2.79529	−	1.08921i	−0.194286	−	0.0757051i
$208$	5.48017	+	3.16398i	0.379982	+	0.219382i
$209$	8.20043			0.567235
$210$	−9.27859	−	6.37129i	−0.640284	−	0.439660i
$211$	28.1433			1.93746			0.968732	−	0.248111i	$-0.0798097\pi$
$211$	28.1433			1.93746			0.968732	+	0.248111i	$0.0798097\pi$
$212$	7.33252	+	4.23343i	0.503600	+	0.290753i
$213$	−0.0981229	−	1.28827i	−0.00672327	−	0.0882708i
$214$	2.55963	+	4.43340i	0.174972	+	0.303061i
$215$	6.48245	−	11.2279i	0.442099	−	0.765738i
$216$	1.17478	+	5.06161i	0.0799339	+	0.344399i
$217$	11.8563	+	9.54349i	0.804858	+	0.647854i
$218$		−	11.4648i		−	0.776492i
$219$	14.1053	−	9.64208i	0.953150	−	0.651551i
$220$	7.92021	−	4.57274i	0.533980	−	0.308294i
$221$	36.5416	−	21.0973i	2.45806	−	1.41916i
$222$	8.46037	−	5.78332i	0.567823	−	0.388151i
$223$			23.8880i			1.59966i	0.600227	+	0.799830i	$0.295077\pi$
$223$			23.8880i			1.59966i	−0.600227	+	0.799830i	$0.704923\pi$
$224$	−2.06102	−	1.65898i	−0.137708	−	0.110845i
$225$	−1.93743	−	2.41734i	−0.129162	−	0.161156i
$226$	1.61075	−	2.78990i	0.107146	−	0.185582i
$227$	−8.77102	−	15.1918i	−0.582153	−	1.00832i	−0.995224	−	0.0976194i	$-0.968877\pi$
$227$	−8.77102	−	15.1918i	−0.582153	−	1.00832i	0.413071	−	0.910699i	$-0.364456\pi$
$228$	−0.289703	−	3.80355i	−0.0191860	−	0.251896i
$229$	−23.5057	−	13.5710i	−1.55330	−	0.896799i	−0.997870	−	0.0652377i	$-0.979219\pi$
$229$	−23.5057	−	13.5710i	−1.55330	−	0.896799i	−0.555432	−	0.831562i	$-0.687447\pi$
$230$	2.45614			0.161953
$231$	14.0663	+	9.65885i	0.925496	+	0.635506i
$232$	−5.16739			−0.339256
$233$	−18.5749	−	10.7242i	−1.21688	−	0.702568i	−0.252634	−	0.967562i	$-0.581297\pi$
$233$	−18.5749	−	10.7242i	−1.21688	−	0.702568i	−0.964250	+	0.264994i	$0.914630\pi$
$234$	−6.89245	+	17.6885i	−0.450574	+	1.15633i
$235$	1.16920	+	2.02512i	0.0762704	+	0.132104i
$236$	−4.16466	+	7.21340i	−0.271096	+	0.469553i
$237$	−0.840870	+	1.75155i	−0.0546204	+	0.113775i
$238$	−16.4514	+	6.37063i	−1.06639	+	0.412946i
$239$		−	15.4123i		−	0.996941i	−0.866907	−	0.498471i	$-0.833895\pi$
$239$		−	15.4123i		−	0.996941i	0.866907	−	0.498471i	$-0.166105\pi$
$240$	−2.40074	−	3.51203i	−0.154967	−	0.226701i
$241$	16.3943	−	9.46523i	1.05605	−	0.609709i	0.131711	−	0.991288i	$-0.457953\pi$
$241$	16.3943	−	9.46523i	1.05605	−	0.609709i	0.924336	+	0.381579i	$0.124620\pi$
$242$	−2.48074	+	1.43225i	−0.159468	+	0.0920687i
$243$	−14.4759	+	5.78350i	−0.928628	+	0.371012i
$244$		−	12.7646i		−	0.817171i
$245$	3.67340	+	16.7960i	0.234685	+	1.07306i
$246$	10.3980	+	4.99178i	0.662950	+	0.318264i
$247$	6.96815	−	12.0692i	0.443373	−	0.767945i
$248$	2.87632	+	4.98193i	0.182646	+	0.316353i
$249$	24.0832	−	1.83433i	1.52621	−	0.116246i
$250$	−8.43890	−	4.87220i	−0.533723	−	0.308145i
$251$	1.20028			0.0757610			0.0378805	−	0.999282i	$-0.487939\pi$
$251$	1.20028			0.0757610			0.0378805	+	0.999282i	$0.487939\pi$
$252$	3.98307	−	6.86551i	0.250910	−	0.432486i
$253$	−3.72351			−0.234095
$254$	6.74628	+	3.89496i	0.423299	+	0.244392i
$255$	−28.2847	+	2.15435i	−1.77126	+	0.134910i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.06593	−	5.31035i	0.191248	−	0.331251i	−0.754416	−	0.656396i	$-0.772080\pi$
$257$	3.06593	−	5.31035i	0.191248	−	0.331251i	0.945664	+	0.325146i	$0.105413\pi$
$258$	8.24214	+	3.95683i	0.513133	+	0.246341i
$259$	−15.4687	−	2.40343i	−0.961179	−	0.149342i
$260$		−	15.5424i		−	0.963897i
$261$	−2.34787	−	15.3234i	−0.145330	−	0.948492i
$262$	4.40810	−	2.54502i	0.272333	−	0.157232i
$263$	6.44235	−	3.71949i	0.397253	−	0.229354i	−0.288045	−	0.957617i	$-0.593005\pi$
$263$	6.44235	−	3.71949i	0.397253	−	0.229354i	0.685298	+	0.728263i	$0.259672\pi$
$264$	3.63952	+	5.32423i	0.223997	+	0.327684i
$265$		−	20.7958i		−	1.27748i
$266$	−3.65363	+	4.53906i	−0.224018	+	0.278308i
$267$	1.72988	−	3.60336i	0.105867	−	0.220522i
$268$	7.38097	−	12.7842i	0.450864	−	0.780920i
$269$	3.35273	+	5.80709i	0.204419	+	0.354065i	0.949948	−	0.312409i	$-0.101136\pi$
$269$	3.35273	+	5.80709i	0.204419	+	0.354065i	−0.745528	+	0.666474i	$0.767803\pi$
$270$	9.32375	−	8.71488i	0.567425	−	0.530371i
$271$	6.84766	+	3.95350i	0.415966	+	0.240158i	0.693350	−	0.720601i	$-0.256134\pi$
$271$	6.84766	+	3.95350i	0.415966	+	0.240158i	−0.277384	+	0.960759i	$0.589467\pi$
$272$	−6.66797			−0.404305
$273$	26.1683	−	12.4951i	1.58377	−	0.756235i
$274$	−14.9908			−0.905630
$275$	−3.32992	−	1.92253i	−0.200802	−	0.115933i
$276$	0.131543	+	1.72705i	0.00791796	+	0.103956i
$277$	5.82324	+	10.0861i	0.349885	+	0.606018i	0.986229	−	0.165387i	$-0.0528875\pi$
$277$	5.82324	+	10.0861i	0.349885	+	0.606018i	−0.636344	+	0.771405i	$0.719554\pi$
$278$	4.38278	−	7.59121i	0.262862	−	0.455290i
$279$	−13.4665	+	10.7930i	−0.806218	+	0.646161i
$280$	−0.997701	+	6.42130i	−0.0596240	+	0.383746i
$281$			27.9371i			1.66659i	0.552830	+	0.833294i	$0.313548\pi$
$281$			27.9371i			1.66659i	−0.552830	+	0.833294i	$0.686452\pi$
$282$	−1.36135	+	0.930589i	−0.0810674	+	0.0554158i
$283$	−20.2968	+	11.7184i	−1.20652	+	0.696584i	−0.961997	−	0.273060i	$-0.911964\pi$
$283$	−20.2968	+	11.7184i	−1.20652	+	0.696584i	−0.244522	+	0.969644i	$0.578631\pi$
$284$	−0.646001	+	0.372969i	−0.0383331	+	0.0221316i
$285$	−7.73469	+	5.28725i	−0.458163	+	0.313190i
$286$			23.5622i			1.39326i
$287$	−6.36226	−	16.4298i	−0.375552	−	0.969819i
$288$	2.34092	−	1.87619i	0.137940	−	0.110555i
$289$	−13.7309	+	23.7827i	−0.807702	+	1.39898i
$290$	6.34593	+	10.9915i	0.372646	+	0.645442i
$291$	2.00171	+	26.2808i	0.117342	+	1.54061i
$292$	−8.54298	−	4.93229i	−0.499940	−	0.288641i
$293$	4.40479			0.257330			0.128665	−	0.991688i	$-0.458931\pi$
$293$	4.40479			0.257330			0.128665	+	0.991688i	$0.458931\pi$
$294$	−11.6134	+	3.48251i	−0.677310	+	0.203104i
$295$	20.4580			1.19111
$296$	−5.12408	−	2.95839i	−0.297831	−	0.171953i
$297$	−14.1348	+	13.2117i	−0.820183	+	0.766623i
$298$	−4.42440	−	7.66328i	−0.256298	−	0.443922i
$299$	−3.16398	+	5.48017i	−0.182978	+	0.316927i
$300$	−0.774075	+	1.61241i	−0.0446912	+	0.0930926i
$301$	−5.04317	−	13.0234i	−0.290683	−	0.750655i
$302$		−	6.71828i		−	0.386594i
$303$	−0.812698	−	1.18889i	−0.0466883	−	0.0683000i
$304$	−1.90728	+	1.10117i	−0.109390	+	0.0631564i
$305$	−27.1514	+	15.6759i	−1.55468	+	0.897597i
$306$	−3.02968	−	19.7732i	−0.173195	−	1.13036i
$307$			10.9974i			0.627653i	0.949480	+	0.313826i	$0.101611\pi$
$307$			10.9974i			0.627653i	−0.949480	+	0.313826i	$0.898389\pi$
$308$	1.51251	−	9.73467i	0.0861833	−	0.554684i
$309$	10.1108	+	4.85393i	0.575185	+	0.276131i
$310$	7.06466	−	12.2363i	0.401245	−	0.694978i
$311$	−14.5415	−	25.1866i	−0.824572	−	1.42820i	−0.902246	−	0.431222i	$-0.858083\pi$
$311$	−14.5415	−	25.1866i	−0.824572	−	1.42820i	0.0776737	−	0.996979i	$-0.475251\pi$
$312$	10.9287	−	0.832399i	0.618715	−	0.0471253i
$313$	5.12605	+	2.95953i	0.289741	+	0.167282i	0.637825	−	0.770181i	$-0.279834\pi$
$313$	5.12605	+	2.95953i	0.289741	+	0.167282i	−0.348084	+	0.937463i	$0.613168\pi$
$314$	−3.92327			−0.221403
$315$	−19.4950	−	0.0409751i	−1.09842	−	0.00230868i
$316$	1.12175			0.0631034
$317$	−5.78820	−	3.34182i	−0.325098	−	0.187695i	0.328565	−	0.944481i	$-0.393435\pi$
$317$	−5.78820	−	3.34182i	−0.325098	−	0.187695i	−0.653662	+	0.756786i	$0.726768\pi$
$318$	14.6227	−	1.11376i	0.820000	−	0.0624564i
$319$	−9.62041	−	16.6630i	−0.538640	−	0.932951i
$320$	−1.22807	+	2.12708i	−0.0686513	+	0.118908i
$321$	7.99340	+	3.83741i	0.446148	+	0.214184i
$322$	1.65898	−	2.06102i	0.0924511	−	0.114856i
$323$			14.6851i			0.817103i
$324$	6.62726	+	6.08929i	0.368181	+	0.338294i
$325$	−5.65907	+	3.26727i	−0.313909	+	0.181235i
$326$	8.85937	−	5.11496i	0.490675	−	0.283291i
$327$	−11.2062	−	16.3934i	−0.619702	−	0.906559i
$328$		−	6.65921i		−	0.367694i
$329$	2.48906	+	0.386734i	0.137226	+	0.0213213i
$330$	6.85549	−	14.2801i	0.377382	−	0.786094i
$331$	13.3392	−	23.1042i	0.733189	−	1.26992i	−0.222325	−	0.974973i	$-0.571365\pi$
$331$	13.3392	−	23.1042i	0.733189	−	1.26992i	0.955513	−	0.294947i	$-0.0953022\pi$
$332$	−6.97237	−	12.0765i	−0.382659	−	0.662784i
$333$	6.44459	−	16.5391i	0.353161	−	0.906336i
$334$	−8.11531	−	4.68538i	−0.444050	−	0.256372i
$335$	−36.2574			−1.98096
$336$	−4.56860	−	0.357633i	−0.249238	−	0.0195105i
$337$	−17.4792			−0.952155			−0.476077	−	0.879403i	$-0.657942\pi$
$337$	−17.4792			−0.952155			−0.476077	+	0.879403i	$0.657942\pi$
$338$	23.4200	+	13.5215i	1.27388	+	0.735474i
$339$	−0.423767	−	5.56369i	−0.0230158	−	0.302178i
$340$	8.18875	+	14.1833i	0.444097	+	0.769199i
$341$	−10.7100	+	18.5503i	−0.579979	+	1.00455i
$342$	−4.13200	−	5.15551i	−0.223433	−	0.278778i
$343$	16.5752	+	8.26223i	0.894974	+	0.446118i
$344$		−	5.27855i		−	0.284601i
$345$	3.51203	−	2.40074i	0.189081	−	0.129252i
$346$	−7.58979	+	4.38197i	−0.408030	+	0.235576i
$347$	30.4637	−	17.5882i	1.63538	−	0.944186i	0.652984	−	0.757372i	$-0.273517\pi$
$347$	30.4637	−	17.5882i	1.63538	−	0.944186i	0.982395	−	0.186814i	$-0.0598163\pi$
$348$	−7.38884	+	5.05084i	−0.396083	+	0.270753i
$349$		−	9.41797i		−	0.504132i	−0.967710	−	0.252066i	$-0.918890\pi$
$349$		−	9.41797i		−	0.504132i	0.967710	−	0.252066i	$-0.0811100\pi$
$350$	2.54777	−	0.986595i	0.136184	−	0.0527357i
$351$	7.43398	+	32.0296i	0.396796	+	1.70962i
$352$	1.86175	−	3.22465i	0.0992318	−	0.171875i
$353$	1.25484	+	2.17345i	0.0667886	+	0.115681i	0.897486	−	0.441043i	$-0.145391\pi$
$353$	1.25484	+	2.17345i	0.0667886	+	0.115681i	−0.830697	+	0.556724i	$0.812058\pi$
$354$	1.09566	+	14.3851i	0.0582339	+	0.764562i
$355$	1.58667	+	0.916065i	0.0842117	+	0.0486197i
$356$	−2.30772			−0.122309
$357$	−17.2969	+	25.1896i	−0.915447	+	1.33318i
$358$	15.8731			0.838921
$359$	14.3293	+	8.27302i	0.756271	+	0.436633i	0.827955	−	0.560794i	$-0.189504\pi$
$359$	14.3293	+	8.27302i	0.756271	+	0.436633i	−0.0716842	+	0.997427i	$0.522837\pi$
$360$	−6.86563	−	2.67525i	−0.361850	−	0.140998i
$361$	−7.07485	−	12.2540i	−0.372361	−	0.644947i
$362$	3.27982	−	5.68082i	0.172384	−	0.298577i
$363$	−2.14725	+	4.47275i	−0.112701	+	0.234759i
$364$	−13.0420	−	10.4979i	−0.683589	−	0.550241i
$365$			24.2288i			1.26820i
$366$	−12.4767	−	18.2521i	−0.652167	−	0.954051i
$367$	18.0483	−	10.4202i	0.942114	−	0.543930i	0.0514919	−	0.998673i	$-0.483602\pi$
$367$	18.0483	−	10.4202i	0.942114	−	0.543930i	0.890622	+	0.454743i	$0.150269\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	19.7472	−	3.02570i	1.02800	−	0.157512i
$370$			14.5325i			0.755506i
$371$	−17.4504	−	14.0463i	−0.905978	−	0.729249i
$372$	8.98240	+	4.31220i	0.465716	+	0.223577i
$373$	14.1419	−	24.4944i	0.732238	−	1.26827i	−0.223687	−	0.974661i	$-0.571809\pi$
$373$	14.1419	−	24.4944i	0.732238	−	1.26827i	0.955925	−	0.293612i	$-0.0948575\pi$
$374$	−12.4141	−	21.5019i	−0.641919	−	1.11184i
$375$	−16.8290	+	1.28181i	−0.869048	+	0.0661923i
$376$	0.824512	+	0.476032i	0.0425209	+	0.0245495i
$377$	−32.6990			−1.68409
$378$	−1.01528	−	13.7102i	−0.0522202	−	0.705176i
$379$	10.8302			0.556308			0.278154	−	0.960537i	$-0.410278\pi$
$379$	10.8302			0.556308			0.278154	+	0.960537i	$0.410278\pi$
$380$	4.68456	+	2.70463i	0.240313	+	0.138745i
$381$	13.4536	−	1.02471i	0.689248	−	0.0524975i
$382$	−2.00733	−	3.47679i	−0.102704	−	0.177888i
$383$	−11.1219	+	19.2637i	−0.568302	+	0.984329i	0.428432	+	0.903574i	$0.359066\pi$
$383$	−11.1219	+	19.2637i	−0.568302	+	0.984329i	−0.996734	+	0.0807544i	$0.974267\pi$
$384$	−1.56144	−	0.749605i	−0.0796819	−	0.0382531i
$385$	−22.5639	+	8.73764i	−1.14996	+	0.445312i
$386$		−	10.8958i		−	0.554582i
$387$	15.6530	−	2.39838i	0.795686	−	0.121916i
$388$	13.1784	−	7.60858i	0.669034	−	0.386267i
$389$	−7.21221	+	4.16397i	−0.365674	+	0.211122i	−0.671567	−	0.740944i	$-0.734378\pi$
$389$	−7.21221	+	4.16397i	−0.365674	+	0.211122i	0.305893	+	0.952066i	$0.401045\pi$
$390$	−15.1918	−	22.2240i	−0.769267	−	1.12536i
$391$		−	6.66797i		−	0.337214i
$392$	4.71441	+	5.17440i	0.238113	+	0.261346i
$393$	3.81551	−	7.94778i	0.192467	−	0.400913i
$394$	11.1173	−	19.2557i	0.560079	−	0.970086i
$395$	−1.37759	−	2.38606i	−0.0693142	−	0.120056i
$396$	10.4083	+	4.05567i	0.523035	+	0.203805i
$397$	11.0618	+	6.38655i	0.555177	+	0.320532i	0.751207	−	0.660066i	$-0.229472\pi$
$397$	11.0618	+	6.38655i	0.555177	+	0.320532i	−0.196030	+	0.980598i	$0.562805\pi$
$398$	1.47928			0.0741496
$399$	−0.787630	+	10.0616i	−0.0394308	+	0.503710i
$400$	1.03264			0.0516322
$401$	24.8620	+	14.3541i	1.24155	+	0.716807i	0.969409	−	0.245451i	$-0.0789360\pi$
$401$	24.8620	+	14.3541i	1.24155	+	0.716807i	0.272138	+	0.962258i	$0.412269\pi$
$402$	−1.94183	−	25.4946i	−0.0968497	−	1.27155i
$403$	18.2012	+	31.5254i	0.906668	+	1.57039i
$404$	−0.415726	+	0.720059i	−0.0206831	+	0.0358243i
$405$	4.81368	−	21.5748i	0.239194	−	1.07206i
$406$	13.5095	+	2.09903i	0.670467	+	0.104173i
$407$		−	22.0312i		−	1.09204i
$408$	−9.53451	+	6.51757i	−0.472029	+	0.322668i
$409$	5.71982	−	3.30234i	0.282827	−	0.163290i	−0.351876	−	0.936047i	$-0.614456\pi$
$409$	5.71982	−	3.30234i	0.282827	−	0.163290i	0.634703	+	0.772757i	$0.281123\pi$
$410$	−14.1647	+	8.17799i	−0.699545	+	0.403882i
$411$	−21.4354	+	14.6527i	−1.05733	+	0.722765i
$412$		−	6.47533i		−	0.319016i
$413$	13.8181	−	17.1669i	0.679947	−	0.844727i
$414$	1.87619	+	2.34092i	0.0922095	+	0.115050i
$415$	−17.1251	+	29.6616i	−0.840640	+	1.45603i
$416$	−3.16398	−	5.48017i	−0.155127	−	0.268688i
$417$	−1.15305	−	15.1386i	−0.0564651	−	0.741339i
$418$	−7.10178	−	4.10021i	−0.347359	−	0.200548i
$419$	15.9416			0.778797			0.389398	−	0.921069i	$-0.372683\pi$
$419$	15.9416			0.778797			0.389398	+	0.921069i	$0.372683\pi$
$420$	4.84985	+	10.1570i	0.236649	+	0.495610i
$421$	−18.2412			−0.889020			−0.444510	−	0.895774i	$-0.646622\pi$
$421$	−18.2412			−0.889020			−0.444510	+	0.895774i	$0.646622\pi$
$422$	−24.3728	−	14.0716i	−1.18645	−	0.684997i
$423$	−1.03699	+	2.66129i	−0.0504204	+	0.129396i
$424$	−4.23343	−	7.33252i	−0.205594	−	0.356099i
$425$	3.44282	−	5.96314i	0.167001	−	0.289255i
$426$	−0.559158	+	1.16474i	−0.0270913	+	0.0564316i
$427$	−5.18506	+	33.3716i	−0.250923	+	1.61496i
$428$		−	5.11925i		−	0.247448i
$429$	23.0307	+	33.6915i	1.11193	+	1.62664i
$430$	−11.2279	+	6.48245i	−0.541459	+	0.312611i
$431$	8.87858	−	5.12605i	0.427666	−	0.246913i	−0.270686	−	0.962668i	$-0.587250\pi$
$431$	8.87858	−	5.12605i	0.427666	−	0.246913i	0.698352	+	0.715755i	$0.253917\pi$
$432$	1.51341	−	4.97087i	0.0728141	−	0.239161i
$433$			35.9112i			1.72578i	0.505390	+	0.862891i	$0.331349\pi$
$433$			35.9112i			1.72578i	−0.505390	+	0.862891i	$0.668651\pi$
$434$	−5.49611	−	14.1931i	−0.263822	−	0.681288i
$435$	19.8176	+	9.51388i	0.950180	+	0.456156i
$436$	−5.73238	+	9.92878i	−0.274531	+	0.475502i
$437$	−1.10117	−	1.90728i	−0.0526761	−	0.0912377i
$438$	−17.0366	+	1.29762i	−0.814041	+	0.0620026i
$439$	−22.5828	−	13.0382i	−1.07782	−	0.622277i	−0.147510	−	0.989061i	$-0.547126\pi$
$439$	−22.5828	−	13.0382i	−1.07782	−	0.622277i	−0.930306	+	0.366783i	$0.880459\pi$
$440$	−9.14547			−0.435993
$441$	−13.2021	+	16.3311i	−0.628670	+	0.777672i
$442$	−42.1947			−2.00700
$443$	−3.36497	−	1.94277i	−0.159875	−	0.0923036i	0.417928	−	0.908480i	$-0.362756\pi$
$443$	−3.36497	−	1.94277i	−0.159875	−	0.0923036i	−0.577803	+	0.816176i	$0.696090\pi$
$444$	−10.2186	+	0.778311i	−0.484951	+	0.0369370i
$445$	2.83405	+	4.90871i	0.134347	+	0.232695i
$446$	11.9440	−	20.6876i	0.565565	−	0.979587i
$447$	−13.8169	−	6.63310i	−0.653515	−	0.313735i
$448$	0.955407	+	2.46722i	0.0451387	+	0.116565i
$449$		−	9.51870i		−	0.449215i	−0.974449	−	0.224608i	$-0.927890\pi$
$449$		−	9.51870i		−	0.449215i	0.974449	−	0.224608i	$-0.0721100\pi$
$450$	0.469195	+	3.06220i	0.0221181	+	0.144353i
$451$	21.4736	−	12.3978i	1.01115	−	0.583790i
$452$	−2.78990	+	1.61075i	−0.131226	+	0.0757634i
$453$	−6.56675	−	9.60645i	−0.308533	−	0.451350i
$454$			17.5420i			0.823288i
$455$	−6.31341	+	40.6337i	−0.295977	+	1.90494i
$456$	−1.65088	+	3.43882i	−0.0773097	+	0.161037i
$457$	−4.44242	+	7.69450i	−0.207808	+	0.359933i	−0.951024	−	0.309118i	$-0.899966\pi$
$457$	−4.44242	+	7.69450i	−0.207808	+	0.359933i	0.743216	+	0.669052i	$0.233299\pi$
$458$	13.5710	+	23.5057i	0.634133	+	1.09835i
$459$	−23.6593	−	25.3122i	−1.10432	−	1.18147i
$460$	−2.12708	−	1.22807i	−0.0991758	−	0.0572592i
$461$	−28.0831			−1.30796			−0.653980	−	0.756512i	$-0.726902\pi$
$461$	−28.0831			−1.30796			−0.653980	+	0.756512i	$0.726902\pi$
$462$	−7.35236	−	15.3980i	−0.342063	−	0.716378i
$463$	−4.54894			−0.211407			−0.105704	−	0.994398i	$-0.533709\pi$
$463$	−4.54894			−0.211407			−0.105704	+	0.994398i	$0.533709\pi$
$464$	4.47509	+	2.58370i	0.207751	+	0.119945i
$465$	−1.85861	−	24.4020i	−0.0861911	−	1.13162i
$466$	10.7242	+	18.5749i	0.496791	+	0.860467i
$467$	0.840217	−	1.45530i	0.0388806	−	0.0673432i	−0.845930	−	0.533294i	$-0.820954\pi$
$467$	0.840217	−	1.45530i	0.0388806	−	0.0673432i	0.884811	+	0.465950i	$0.154287\pi$
$468$	14.8133	−	11.8724i	0.684744	−	0.548803i
$469$	−24.4897	+	30.4246i	−1.13083	+	1.40488i
$470$		−	2.33841i		−	0.107863i
$471$	−5.60987	+	3.83478i	−0.258489	+	0.176697i
$472$	7.21340	−	4.16466i	0.332024	−	0.191694i
$473$	17.0215	−	9.82737i	0.782649	−	0.451863i
$474$	1.60399	−	1.09645i	0.0736736	−	0.0503616i
$475$		−	2.27423i		−	0.104349i
$476$	17.4326	+	2.70857i	0.799024	+	0.124147i
$477$	19.8203	−	15.8854i	0.907509	−	0.727343i
$478$	−7.70617	+	13.3475i	−0.352472	+	0.610499i
$479$	19.2533	+	33.3477i	0.879707	+	1.52370i	0.851663	+	0.524090i	$0.175594\pi$
$479$	19.2533	+	33.3477i	0.879707	+	1.52370i	0.0280437	+	0.999607i	$0.491072\pi$
$480$	0.323089	+	4.24188i	0.0147469	+	0.193614i
$481$	−32.4249	−	18.7205i	−1.47845	−	0.853584i
$482$	−18.9305			−0.862259
$483$	0.357633	−	4.56860i	0.0162729	−	0.207878i
$484$	2.86451			0.130205
$485$	−32.3682	−	18.6878i	−1.46976	−	0.848568i
$486$	15.4282	+	2.22928i	0.699839	+	0.101122i
$487$	−10.2775	−	17.8012i	−0.465719	−	0.806649i	0.533514	−	0.845791i	$-0.320871\pi$
$487$	−10.2775	−	17.8012i	−0.465719	−	0.806649i	−0.999234	+	0.0391415i	$0.987538\pi$
$488$	−6.38231	+	11.0545i	−0.288913	+	0.500413i
$489$	7.66839	−	15.9734i	0.346777	−	0.722342i
$490$	5.21674	−	16.3825i	0.235668	−	0.740084i
$491$		−	3.29864i		−	0.148866i	−0.997226	−	0.0744328i	$-0.976285\pi$
$491$		−	3.29864i		−	0.148866i	0.997226	−	0.0744328i	$-0.0237146\pi$
$492$	−6.50901	−	9.52198i	−0.293449	−	0.429284i
$493$	29.8398	−	17.2280i	1.34392	−	0.775911i
$494$	−12.0692	+	6.96815i	−0.543019	+	0.313512i
$495$	−4.15536	−	27.1199i	−0.186770	−	1.21895i
$496$		−	5.75264i		−	0.258301i
$497$	1.84039	−	0.712673i	0.0825530	−	0.0319678i
$498$	−21.7739	−	10.4530i	−0.975710	−	0.468412i
$499$	−5.23934	+	9.07480i	−0.234545	+	0.406244i	−0.959140	−	0.282931i	$-0.908693\pi$
$499$	−5.23934	+	9.07480i	−0.234545	+	0.406244i	0.724595	+	0.689174i	$0.242027\pi$
$500$	4.87220	+	8.43890i	0.217891	+	0.377399i
$501$	−16.1837	+	1.23266i	−0.723037	+	0.0550711i
$502$	−1.03947	−	0.600140i	−0.0463939	−	0.0267856i
$503$	−6.00823			−0.267894			−0.133947	−	0.990989i	$-0.542765\pi$
$503$	−6.00823			−0.267894			−0.133947	+	0.990989i	$0.542765\pi$
$504$	−6.88219	+	3.95417i	−0.306557	+	0.176133i
$505$	2.04217			0.0908752
$506$	3.22465	+	1.86175i	0.143353	+	0.0827650i
$507$	46.7047	−	3.55733i	2.07423	−	0.157986i
$508$	−3.89496	−	6.74628i	−0.172811	−	0.299318i
$509$	−9.35979	+	16.2116i	−0.414865	+	0.718568i	−0.995414	−	0.0956576i	$-0.969505\pi$
$509$	−9.35979	+	16.2116i	−0.414865	+	0.718568i	0.580549	+	0.814225i	$0.302838\pi$
$510$	25.5725	+	12.2767i	1.13237	+	0.543619i
$511$	20.3311	+	16.3651i	0.899395	+	0.723950i
$512$			1.00000i			0.0441942i
$513$	−10.9476	−	3.33305i	−0.483346	−	0.147158i
$514$	−5.31035	+	3.06593i	−0.234230	+	0.135233i
$515$	−13.7736	+	7.95217i	−0.606935	+	0.350414i
$516$	−5.15949	−	7.54779i	−0.227134	−	0.332273i
$517$			3.54502i			0.155910i
$518$	12.1946	+	9.81579i	0.535799	+	0.431281i
$519$	−6.56949	+	13.6844i	−0.288369	+	0.600677i
$520$	−7.77119	+	13.4601i	−0.340789	+	0.590264i
$521$	−11.0534	−	19.1450i	−0.484258	−	0.838759i	0.515579	−	0.856842i	$-0.327577\pi$
$521$	−11.0534	−	19.1450i	−0.484258	−	0.838759i	−0.999836	+	0.0180832i	$0.994244\pi$
$522$	−5.62836	+	14.4443i	−0.246347	+	0.632212i
$523$	3.80741	+	2.19821i	0.166486	+	0.0961209i	0.580928	−	0.813955i	$-0.302690\pi$
$523$	3.80741	+	2.19821i	0.166486	+	0.0961209i	−0.414442	+	0.910076i	$0.636023\pi$
$524$	−5.09003			−0.222359
$525$	2.67870	−	3.90103i	0.116908	−	0.170255i
$526$	−7.43899			−0.324355
$527$	−33.2194	−	19.1792i	−1.44706	−	0.835460i
$528$	−0.489802	−	6.43068i	−0.0213159	−	0.279859i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−10.3979	+	18.0097i	−0.451657	+	0.782293i
$531$	15.6274	+	19.4983i	0.678170	+	0.846155i
$532$	5.43367	−	2.10413i	0.235579	−	0.0912256i
$533$		−	42.1392i		−	1.82525i
$534$	−3.29980	+	2.25567i	−0.142796	+	0.0976122i
$535$	−10.8891	+	6.28681i	−0.470776	+	0.271802i
$536$	−12.7842	+	7.38097i	−0.552194	+	0.318809i
$537$	22.6969	−	15.5151i	0.979445	−	0.669526i
$538$		−	6.70545i		−	0.289093i
$539$	−7.90857	+	24.8358i	−0.340646	+	1.06975i
$540$	−12.4320	+	2.88544i	−0.534990	+	0.124169i
$541$	8.44144	−	14.6210i	0.362926	−	0.628606i	−0.625515	−	0.780212i	$-0.715111\pi$
$541$	8.44144	−	14.6210i	0.362926	−	0.628606i	0.988441	+	0.151606i	$0.0484445\pi$
$542$	−3.95350	−	6.84766i	−0.169817	−	0.294132i
$543$	−0.862876	−	11.3288i	−0.0370296	−	0.486167i
$544$	5.77463	+	3.33399i	0.247585	+	0.142944i
$545$	28.1591			1.20620
$546$	−28.9099	−	2.26309i	−1.23723	−	0.0968513i
$547$	37.4651			1.60189			0.800946	−	0.598737i	$-0.204330\pi$
$547$	37.4651			1.60189			0.800946	+	0.598737i	$0.204330\pi$
$548$	12.9825	+	7.49542i	0.554583	+	0.320189i
$549$	−35.6808	−	13.9033i	−1.52282	−	0.593379i
$550$	1.92253	+	3.32992i	0.0819769	+	0.141988i
$551$	5.69018	−	9.85568i	0.242410	−	0.419866i
$552$	0.749605	−	1.56144i	0.0319053	−	0.0664593i
$553$	−2.93269	−	0.455662i	−0.124711	−	0.0193767i
$554$		−	11.6465i		−	0.494812i
$555$	14.2047	+	20.7799i	0.602954	+	0.882058i
$556$	−7.59121	+	4.38278i	−0.321939	+	0.185871i
$557$	−30.8403	+	17.8057i	−1.30675	+	0.754451i	−0.981552	−	0.191196i	$-0.938763\pi$
$557$	−30.8403	+	17.8057i	−1.30675	+	0.754451i	−0.325195	+	0.945647i	$0.605430\pi$
$558$	17.0588	−	2.61378i	0.722158	−	0.110650i
$559$		−	33.4025i		−	1.41277i
$560$	4.07468	−	5.06216i	0.172187	−	0.213915i
$561$	−38.7678	−	18.6114i	−1.63678	−	0.785773i
$562$	13.9686	−	24.1942i	0.589228	−	1.02057i
$563$	9.13284	+	15.8185i	0.384903	+	0.666672i	0.991756	−	0.128142i	$-0.0409015\pi$
$563$	9.13284	+	15.8185i	0.384903	+	0.666672i	−0.606853	+	0.794814i	$0.707568\pi$
$564$	1.64426	−	0.125237i	0.0692359	−	0.00527345i
$565$	6.85241	+	3.95624i	0.288283	+	0.166440i
$566$	23.4367			0.985119
$567$	−14.8527	−	18.6118i	−0.623754	−	0.781621i
$568$	0.745937			0.0312988
$569$	11.3184	+	6.53466i	0.474491	+	0.273947i	0.718118	−	0.695922i	$-0.245004\pi$
$569$	11.3184	+	6.53466i	0.474491	+	0.273947i	−0.243627	+	0.969869i	$0.578337\pi$
$570$	9.34206	−	0.711551i	0.391296	−	0.0298036i
$571$	11.3721	+	19.6970i	0.475907	+	0.824296i	0.999619	−	0.0275999i	$-0.00878644\pi$
$571$	11.3721	+	19.6970i	0.475907	+	0.824296i	−0.523712	+	0.851896i	$0.675453\pi$
$572$	11.7811	−	20.4055i	0.492592	−	0.853195i
$573$	−6.26863	−	3.00940i	−0.261876	−	0.125720i
$574$	−2.70501	+	17.4097i	−0.112905	+	0.726668i
$575$			1.03264i			0.0430643i
$576$	−2.96539	+	0.454363i	−0.123558	+	0.0189318i
$577$	32.6624	−	18.8576i	1.35975	−	0.785053i	0.370162	−	0.928967i	$-0.379302\pi$
$577$	32.6624	−	18.8576i	1.35975	−	0.785053i	0.989590	+	0.143914i	$0.0459689\pi$
$578$	23.7827	−	13.7309i	0.989229	−	0.571132i
$579$	−10.6500	−	15.5799i	−0.442601	−	0.647478i
$580$		−	12.6919i		−	0.527001i
$581$	13.3229	+	34.4048i	0.552727	+	1.42735i
$582$	11.4068	−	23.7607i	0.472829	−	0.984911i
$583$	15.7632	−	27.3027i	0.652846	−	1.13076i
$584$	4.93229	+	8.54298i	0.204100	+	0.353511i
$585$	−43.4454	−	16.9289i	−1.79625	−	0.699922i
$586$	−3.81466	−	2.20239i	−0.157582	−	0.0909800i
$587$	22.4986			0.928616			0.464308	−	0.885674i	$-0.346303\pi$
$587$	22.4986			0.928616			0.464308	+	0.885674i	$0.346303\pi$
$588$	11.7988	+	2.79078i	0.486574	+	0.115090i
$589$	−12.6693			−0.522028
$590$	−17.7172	−	10.2290i	−0.729404	−	0.421122i
$591$	−2.92480	−	38.4001i	−0.120310	−	1.57957i
$592$	2.95839	+	5.12408i	0.121589	+	0.210598i
$593$	−12.0502	+	20.8715i	−0.494841	+	0.857089i	−0.999982	−	0.00594710i	$-0.998107\pi$
$593$	−12.0502	+	20.8715i	−0.494841	+	0.857089i	0.505142	+	0.863037i	$0.331440\pi$
$594$	18.8469	−	4.37431i	0.773299	−	0.179480i
$595$	−15.6472	−	40.4070i	−0.641472	−	1.65653i
$596$			8.84880i			0.362461i
$597$	2.11522	−	1.44591i	0.0865700	−	0.0591773i
$598$	5.48017	−	3.16398i	0.224101	−	0.129385i
$599$	17.2060	−	9.93387i	0.703017	−	0.405887i	−0.105453	−	0.994424i	$-0.533629\pi$
$599$	17.2060	−	9.93387i	0.703017	−	0.405887i	0.808470	+	0.588537i	$0.200296\pi$
$600$	1.47657	−	1.00935i	0.0602809	−	0.0412066i
$601$		−	42.9999i		−	1.75400i	−0.480487	−	0.877002i	$-0.659540\pi$
$601$		−	42.9999i		−	1.75400i	0.480487	−	0.877002i	$-0.340460\pi$
$602$	−2.14418	+	13.8002i	−0.0873903	+	0.562453i
$603$	−27.6961	−	34.5566i	−1.12787	−	1.40725i
$604$	−3.35914	+	5.81821i	−0.136682	+	0.236739i
$605$	−3.51782	−	6.09304i	−0.143020	−	0.247717i
$606$	0.109372	+	1.43596i	0.00444293	+	0.0583318i
$607$	−21.9347	−	12.6640i	−0.890303	−	0.514016i	−0.0162611	−	0.999868i	$-0.505176\pi$
$607$	−21.9347	−	12.6640i	−0.890303	−	0.514016i	−0.874041	+	0.485851i	$0.838510\pi$
$608$	2.20234			0.0893167
$609$	21.3689	−	10.2034i	0.865913	−	0.413464i
$610$	31.3517			1.26939
$611$	5.21747	+	3.01231i	0.211076	+	0.121865i
$612$	−7.26280	+	18.6389i	−0.293581	+	0.753433i
$613$	−0.300248	−	0.520045i	−0.0121269	−	0.0210044i	0.859898	−	0.510465i	$-0.170527\pi$
$613$	−0.300248	−	0.520045i	−0.0121269	−	0.0210044i	−0.872025	+	0.489461i	$0.837194\pi$
$614$	5.49868	−	9.52400i	0.221909	−	0.384357i
$615$	−12.2605	+	25.5389i	−0.494392	+	1.02983i
$616$	−6.17721	+	7.67422i	−0.248887	+	0.309203i
$617$			5.30741i			0.213668i	0.994277	+	0.106834i	$0.0340714\pi$
$617$			5.30741i			0.213668i	−0.994277	+	0.106834i	$0.965929\pi$
$618$	−6.32927	−	9.25904i	−0.254600	−	0.372453i
$619$	21.1309	−	12.1999i	0.849321	−	0.490356i	−0.0111004	−	0.999938i	$-0.503533\pi$
$619$	21.1309	−	12.1999i	0.849321	−	0.490356i	0.860422	+	0.509582i	$0.170200\pi$
$620$	−12.2363	+	7.06466i	−0.491423	+	0.283723i
$621$	4.97087	+	1.51341i	0.199474	+	0.0607311i
$622$			29.0830i			1.16612i
$623$	6.03326	+	0.937409i	0.241717	+	0.0375565i
$624$	−9.88072	−	4.74347i	−0.395545	−	0.189891i
$625$	14.5484	−	25.1986i	0.581937	−	1.00795i
$626$	−2.95953	−	5.12605i	−0.118286	−	0.204878i
$627$	−14.1625	+	1.07871i	−0.565597	+	0.0430795i
$628$	3.39765	+	1.96163i	0.135581	+	0.0782777i
$629$	39.4529			1.57309
$630$	16.8627	+	9.78298i	0.671825	+	0.389763i
$631$	5.09746			0.202927			0.101463	−	0.994839i	$-0.467648\pi$
$631$	5.09746			0.202927			0.101463	+	0.994839i	$0.467648\pi$
$632$	−0.971465	−	0.560876i	−0.0386428	−	0.0223104i
$633$	−48.6048	+	3.70205i	−1.93187	+	0.147143i
$634$	3.34182	+	5.78820i	0.132721	+	0.229879i
$635$	−9.56659	+	16.5698i	−0.379639	+	0.657553i
$636$	−13.2205	−	6.34680i	−0.524227	−	0.251667i
$637$	29.8326	+	32.7434i	1.18201	+	1.29734i
$638$			19.2408i			0.761752i
$639$	0.338926	+	2.21200i	0.0134077	+	0.0875052i
$640$	2.12708	−	1.22807i	0.0840803	−	0.0485438i
$641$	26.5699	−	15.3401i	1.04945	−	0.605898i	0.126952	−	0.991909i	$-0.459480\pi$
$641$	26.5699	−	15.3401i	1.04945	−	0.605898i	0.922494	+	0.386010i	$0.126147\pi$
$642$	−5.00378	−	7.32000i	−0.197483	−	0.288897i
$643$		−	5.85046i		−	0.230720i	−0.993324	−	0.115360i	$-0.963198\pi$
$643$		−	5.85046i		−	0.230720i	0.993324	−	0.115360i	$-0.0368021\pi$
$644$	−2.46722	+	0.955407i	−0.0972223	+	0.0376483i
$645$	−9.71854	+	20.2439i	−0.382667	+	0.797103i
$646$	7.34257	−	12.7177i	0.288890	−	0.500371i
$647$	20.4855	+	35.4820i	0.805370	+	1.39494i	0.916041	+	0.401084i	$0.131366\pi$
$647$	20.4855	+	35.4820i	0.805370	+	1.39494i	−0.110672	+	0.993857i	$0.535300\pi$
$648$	−2.69473	−	8.58711i	−0.105859	−	0.337334i
$649$	26.8592	+	15.5071i	1.05431	+	0.608709i
$650$	6.53453			0.256305
$651$	−21.7318	−	14.9225i	−0.851736	−	0.584857i
$652$	−10.2299			−0.400634
$653$	23.9896	+	13.8504i	0.938784	+	0.542007i	0.889579	−	0.456781i	$-0.150998\pi$
$653$	23.9896	+	13.8504i	0.938784	+	0.542007i	0.0492052	+	0.998789i	$0.484331\pi$
$654$	1.50811	+	19.8002i	0.0589718	+	0.774249i
$655$	6.25093	+	10.8269i	0.244244	+	0.423043i
$656$	−3.32961	+	5.76705i	−0.129999	+	0.225165i
$657$	−23.0922	+	18.5078i	−0.900914	+	0.722058i
$658$	−1.96222	−	1.57945i	−0.0764954	−	0.0615734i
$659$		−	4.53069i		−	0.176491i	−0.996099	−	0.0882454i	$-0.971874\pi$
$659$		−	4.53069i		−	0.176491i	0.996099	−	0.0882454i	$-0.0281260\pi$
$660$	−13.0771	+	8.93918i	−0.509024	+	0.347957i
$661$	−7.70388	+	4.44784i	−0.299646	+	0.173001i	−0.642284	−	0.766467i	$-0.722013\pi$
$661$	−7.70388	+	4.44784i	−0.299646	+	0.173001i	0.342638	+	0.939468i	$0.388680\pi$
$662$	−23.1042	+	13.3392i	−0.897969	+	0.518443i
$663$	−60.3340	+	41.2429i	−2.34318	+	1.60174i
$664$			13.9447i			0.541161i
$665$	−11.1486	−	8.97384i	−0.432324	−	0.347991i
$666$	−13.8507	+	11.1010i	−0.536705	+	0.430154i
$667$	−2.58370	+	4.47509i	−0.100041	+	0.173276i
$668$	4.68538	+	8.11531i	0.181283	+	0.313991i
$669$	−3.14230	−	41.2558i	−0.121488	−	1.59504i
$670$	31.3999	+	18.1287i	1.21308	+	0.700373i
$671$	−47.5291			−1.83484
$672$	3.77771	+	2.59402i	0.145728	+	0.100066i
$673$	9.36655			0.361054			0.180527	−	0.983570i	$-0.442220\pi$
$673$	9.36655			0.361054			0.180527	+	0.983570i	$0.442220\pi$
$674$	15.1375	+	8.73962i	0.583073	+	0.336638i
$675$	3.66403	+	3.92001i	0.141028	+	0.150881i
$676$	−13.5215	−	23.4200i	−0.520059	−	0.900768i
$677$	5.75743	−	9.97216i	0.221276	−	0.383261i	−0.733920	−	0.679236i	$-0.762311\pi$
$677$	5.75743	−	9.97216i	0.221276	−	0.383261i	0.955196	+	0.295975i	$0.0956445\pi$
$678$	−2.41485	+	5.03018i	−0.0927419	+	0.193183i
$679$	−37.5441	+	14.5386i	−1.44081	+	0.557939i
$680$		−	16.3775i		−	0.628049i
$681$	17.1464	+	25.0833i	0.657050	+	0.961194i
$682$	18.5503	−	10.7100i	0.710326	−	0.410107i
$683$	3.89871	−	2.25092i	0.149180	−	0.0861290i	−0.423552	−	0.905872i	$-0.639217\pi$
$683$	3.89871	−	2.25092i	0.149180	−	0.0861290i	0.572732	+	0.819743i	$0.305884\pi$
$684$	1.00066	+	6.53080i	0.0382612	+	0.249711i
$685$		−	36.8197i		−	1.40681i
$686$	−10.2234	−	15.4429i	−0.390331	−	0.589612i
$687$	42.3807	+	20.3458i	1.61692	+	0.776242i
$688$	−2.63928	+	4.57136i	−0.100622	+	0.174282i
$689$	−26.7890	−	46.3999i	−1.02058	−	1.76769i
$690$	−4.24188	+	0.323089i	−0.161486	+	0.0122998i
$691$	44.9506	+	25.9522i	1.71000	+	0.987270i	0.934527	+	0.355891i	$0.115823\pi$
$691$	44.9506	+	25.9522i	1.71000	+	0.987270i	0.775474	+	0.631379i	$0.217511\pi$
$692$	8.76394			0.333155
$693$	−25.5638	−	14.8310i	−0.971087	−	0.563382i
$694$	−35.1765			−1.33528
$695$	18.6451	+	10.7648i	0.707249	+	0.408330i
$696$	8.92434	−	0.679735i	0.338276	−	0.0257653i
$697$	22.2017	+	38.4545i	0.840950	+	1.45657i
$698$	−4.70898	+	8.15620i	−0.178238	+	0.308717i
$699$	33.4905	+	16.0779i	1.26673	+	0.608121i
$700$	−2.69973	−	0.419466i	−0.102040	−	0.0158543i
$701$		−	7.74217i		−	0.292418i	−0.989254	−	0.146209i	$-0.953293\pi$
$701$		−	7.74217i		−	0.292418i	0.989254	−	0.146209i	$-0.0467071\pi$
$702$	9.57681	−	31.4555i	0.361453	−	1.18721i
$703$	11.2850	−	6.51537i	0.425620	−	0.245732i
$704$	−3.22465	+	1.86175i	−0.121534	+	0.0701675i
$705$	−2.28566	−	3.34368i	−0.0860830	−	0.125930i
$706$		−	2.50969i		−	0.0944533i
$707$	1.37936	−	1.71364i	0.0518761	−	0.0644480i
$708$	6.24370	−	13.0057i	0.234653	−	0.488785i
$709$	−4.30667	+	7.45936i	−0.161740	+	0.280142i	−0.935493	−	0.353346i	$-0.885044\pi$
$709$	−4.30667	+	7.45936i	−0.161740	+	0.280142i	0.773753	+	0.633488i	$0.218377\pi$
$710$	−0.916065	−	1.58667i	−0.0343793	−	0.0595467i
$711$	1.22182	−	3.13562i	0.0458218	−	0.117595i
$712$	1.99854	+	1.15386i	0.0748986	+	0.0432427i
$713$	5.75264			0.215438
$714$	27.5743	−	13.1664i	1.03194	−	0.492742i
$715$	−57.8722			−2.16430
$716$	−13.7465	−	7.93657i	−0.513732	−	0.296603i
$717$	2.02739	+	26.6179i	0.0757142	+	0.994062i
$718$	−8.27302	−	14.3293i	−0.308746	−	0.534764i
$719$	16.7519	−	29.0152i	0.624741	−	1.08208i	−0.363850	−	0.931458i	$-0.618538\pi$
$719$	16.7519	−	29.0152i	0.624741	−	1.08208i	0.988591	−	0.150626i	$-0.0481288\pi$
$720$	4.60818	+	5.74965i	0.171737	+	0.214277i
$721$	−2.63032	+	16.9290i	−0.0979581	+	0.630468i
$722$			14.1497i			0.526597i
$723$	−27.0686	+	18.5035i	−1.00669	+	0.688151i
$724$	−5.68082	+	3.27982i	−0.211126	+	0.121894i
$725$	−4.62118	+	2.66804i	−0.171626	+	0.0990885i
$726$	4.09595	−	2.79989i	0.152015	−	0.103914i
$727$		−	41.7463i		−	1.54829i	−0.633011	−	0.774143i	$-0.718181\pi$
$727$		−	41.7463i		−	1.54829i	0.633011	−	0.774143i	$-0.281819\pi$
$728$	6.04577	+	15.6125i	0.224071	+	0.578638i
$729$	24.2398	−	11.8926i	0.897769	−	0.440466i
$730$	12.1144	−	20.9828i	0.448375	−	0.776608i
$731$	17.5986	+	30.4817i	0.650909	+	1.12741i
$732$	1.67910	+	22.0451i	0.0620612	+	0.814811i
$733$	15.6464	+	9.03346i	0.577913	+	0.333658i	0.760304	−	0.649568i	$-0.225050\pi$
$733$	15.6464	+	9.03346i	0.577913	+	0.333658i	−0.182390	+	0.983226i	$0.558383\pi$
$734$	−20.8404			−0.769233
$735$	−8.55354	−	28.5243i	−0.315502	−	1.05213i
$736$	−1.00000			−0.0368605
$737$	−47.6021	−	27.4831i	−1.75345	−	1.01235i
$738$	−18.6144	−	7.25326i	−0.685206	−	0.266996i
$739$	−1.60099	−	2.77300i	−0.0588934	−	0.102006i	0.835076	−	0.550135i	$-0.185424\pi$
$739$	−1.60099	−	2.77300i	−0.0588934	−	0.102006i	−0.893969	+	0.448129i	$0.852091\pi$
$740$	7.26623	−	12.5855i	0.267112	−	0.462651i
$741$	−10.4467	+	21.7607i	−0.383770	+	0.799399i
$742$	8.08930	+	20.8897i	0.296967	+	0.766884i
$743$			8.68537i			0.318635i	0.987227	+	0.159318i	$0.0509294\pi$
$743$			8.68537i			0.318635i	−0.987227	+	0.159318i	$0.949071\pi$
$744$	−5.62288	−	8.22568i	−0.206145	−	0.301568i
$745$	18.8221	−	10.8670i	0.689589	−	0.398135i
$746$	−24.4944	+	14.1419i	−0.896805	+	0.517770i
$747$	−41.3516	+	6.33597i	−1.51298	+	0.231821i
$748$			24.8282i			0.907811i
$749$	−2.07947	+	13.3837i	−0.0759822	+	0.489029i
$750$	15.2153	+	7.30444i	0.555584	+	0.266721i
$751$	19.5186	−	33.8072i	0.712243	−	1.23364i	−0.251770	−	0.967787i	$-0.581013\pi$
$751$	19.5186	−	33.8072i	0.712243	−	1.23364i	0.964013	−	0.265854i	$-0.0856540\pi$
$752$	−0.476032	−	0.824512i	−0.0173591	−	0.0300668i
$753$	−2.07294	+	0.157888i	−0.0755422	+	0.00575378i
$754$	28.3182	+	16.3495i	1.03129	+	0.595415i
$755$	16.5011			0.600536
$756$	−5.97584	+	12.3810i	−0.217339	+	0.450293i
$757$	37.4636			1.36164			0.680818	−	0.732453i	$-0.261624\pi$
$757$	37.4636			1.36164			0.680818	+	0.732453i	$0.261624\pi$
$758$	−9.37919	−	5.41508i	−0.340667	−	0.196684i
$759$	6.43068	−	0.489802i	0.233419	−	0.0177787i
$760$	−2.70463	−	4.68456i	−0.0981073	−	0.169927i
$761$	7.33028	−	12.6964i	0.265722	−	0.460244i	−0.702030	−	0.712147i	$-0.747723\pi$
$761$	7.33028	−	12.6964i	0.265722	−	0.460244i	0.967753	+	0.251903i	$0.0810563\pi$
$762$	−12.1635	−	5.83937i	−0.440637	−	0.211538i
$763$	19.0198	−	23.6291i	0.688562	−	0.855431i
$764$			4.01465i			0.145245i
$765$	48.5657	−	7.44133i	1.75590	−	0.269042i
$766$	19.2637	−	11.1219i	0.696025	−	0.401850i
$767$	45.6461	−	26.3538i	1.64819	−	0.951581i
$768$	0.977444	+	1.42990i	0.0352705	+	0.0515969i
$769$			43.8994i			1.58305i	0.611135	+	0.791527i	$0.290713\pi$
$769$			43.8994i			1.58305i	−0.611135	+	0.791527i	$0.709287\pi$
$770$	23.9098	+	3.71495i	0.861648	+	0.133877i
$771$	−4.59648	+	9.57454i	−0.165538	+	0.344819i
$772$	−5.44791	+	9.43605i	−0.196074	+	0.339611i
$773$	−13.5365	−	23.4459i	−0.486874	−	0.843291i	0.513012	−	0.858382i	$-0.328530\pi$
$773$	−13.5365	−	23.4459i	−0.486874	−	0.843291i	−0.999886	+	0.0150905i	$0.995196\pi$
$774$	−14.7551	−	5.74944i	−0.530360	−	0.206659i
$775$	5.14456	+	2.97022i	0.184798	+	0.106693i
$776$	−15.2172			−0.546264
$777$	27.0314	+	2.11604i	0.969745	+	0.0759124i
$778$	8.32795			0.298571
$779$	12.7010	+	7.33292i	0.455060	+	0.262729i
$780$	2.04449	+	26.8424i	0.0732046	+	0.961113i
$781$	1.38875	+	2.40539i	0.0496934	+	0.0860715i
$782$	−3.33399	+	5.77463i	−0.119223	+	0.206501i
$783$	6.07057	+	26.1553i	0.216944	+	0.934715i
$784$	−1.49560	−	6.83836i	−0.0534142	−	0.244227i
$785$		−	9.63611i		−	0.343928i
$786$	−7.27822	+	4.97522i	−0.259606	+	0.177460i
$787$	−17.8215	+	10.2892i	−0.635266	+	0.366771i	−0.782789	−	0.622288i	$-0.786203\pi$
$787$	−17.8215	+	10.2892i	−0.635266	+	0.366771i	0.147523	+	0.989059i	$0.452870\pi$
$788$	−19.2557	+	11.1173i	−0.685954	+	0.396036i
$789$	−10.6370	+	7.27119i	−0.378687	+	0.258861i
$790$			2.75518i			0.0980250i
$791$	7.94818	−	3.07785i	0.282605	−	0.109436i
$792$	−6.98599	−	8.71645i	−0.248236	−	0.309726i
$793$	−40.3870	+	69.9523i	−1.43418	+	2.48408i
$794$	−6.38655	−	11.0618i	−0.226650	−	0.392570i
$795$	2.73555	+	35.9154i	0.0970199	+	1.27379i
$796$	−1.28109	−	0.739640i	−0.0454072	−	0.0262158i
$797$	49.5237			1.75422			0.877109	−	0.480291i	$-0.159469\pi$
$797$	49.5237			1.75422			0.877109	+	0.480291i	$0.159469\pi$
$798$	5.71291	−	8.31979i	0.202235	−	0.294517i
$799$	−6.34834			−0.224588
$800$	−0.894296	−	0.516322i	−0.0316181	−	0.0182547i
$801$	−2.51358	+	6.45074i	−0.0888131	+	0.227926i
$802$	−14.3541	−	24.8620i	−0.506859	−	0.877906i
$803$	−18.3654	+	31.8098i	−0.648102	+	1.12255i
$804$	−11.0656	+	23.0499i	−0.390254	+	0.812906i
$805$	5.06216	+	4.07468i	0.178418	+	0.143614i
$806$		−	36.4025i		−	1.28222i
$807$	−6.55420	−	9.58810i	−0.230719	−	0.337517i
$808$	0.720059	−	0.415726i	0.0253316	−	0.0146252i
$809$	−5.79875	+	3.34791i	−0.203873	+	0.117706i	−0.598461	−	0.801152i	$-0.704221\pi$
$809$	−5.79875	+	3.34791i	−0.203873	+	0.117706i	0.394588	+	0.918858i	$0.370887\pi$
$810$	−14.9562	+	16.2775i	−0.525507	+	0.571933i
$811$		−	21.2201i		−	0.745139i	−0.928004	−	0.372570i	$-0.878477\pi$
$811$		−	21.2201i		−	0.745139i	0.928004	−	0.372570i	$-0.121523\pi$
$812$	−10.6501	−	8.57258i	−0.373745	−	0.300839i
$813$	−12.3463	−	5.92713i	−0.433004	−	0.207873i
$814$	−11.0156	+	19.0795i	−0.386096	+	0.668737i
$815$	12.5631	+	21.7599i	0.440065	+	0.762215i
$816$	11.5159	−	0.877126i	0.403138	−	0.0307056i
$817$	10.0677	+	5.81258i	0.352224	+	0.203357i
$818$	−6.60468			−0.230927
$819$	−43.5502	+	25.0218i	−1.52177	+	0.874333i
$820$	16.3560			0.571176
$821$	2.12965	+	1.22956i	0.0743255	+	0.0429118i	0.536702	−	0.843772i	$-0.319670\pi$
$821$	2.12965	+	1.22956i	0.0743255	+	0.0429118i	−0.462377	+	0.886684i	$0.653003\pi$
$822$	25.8899	−	1.97194i	0.903014	−	0.0687794i
$823$	−12.7588	−	22.0988i	−0.444742	−	0.770316i	0.553292	−	0.832987i	$-0.313371\pi$
$823$	−12.7588	−	22.0988i	−0.444742	−	0.770316i	−0.998034	+	0.0626714i	$0.980038\pi$
$824$	−3.23766	+	5.60780i	−0.112789	+	0.195357i
$825$	6.00383	+	2.88227i	0.209026	+	0.100348i
$826$	−20.5503	+	7.95789i	−0.715037	+	0.276890i
$827$		−	32.4958i		−	1.12999i	−0.825094	−	0.564996i	$-0.808878\pi$
$827$		−	32.4958i		−	1.12999i	0.825094	−	0.564996i	$-0.191122\pi$
$828$	−0.454363	−	2.96539i	−0.0157902	−	0.103055i
$829$	−28.0309	+	16.1836i	−0.973552	+	0.562081i	−0.900317	−	0.435234i	$-0.856666\pi$
$829$	−28.0309	+	16.1836i	−0.973552	+	0.562081i	−0.0732349	+	0.997315i	$0.523332\pi$
$830$	29.6616	−	17.1251i	1.02957	−	0.594423i
$831$	−11.3838	−	16.6533i	−0.394899	−	0.577695i
$832$			6.32796i			0.219382i
$833$	−44.4753	−	14.1625i	−1.54098	−	0.490701i
$834$	−6.57071	+	13.6869i	−0.227525	+	0.473939i
$835$	11.5080	−	19.9324i	0.398249	−	0.689788i
$836$	4.10021	+	7.10178i	0.141809	+	0.245620i
$837$	21.8375	−	20.4115i	0.754816	−	0.705524i
$838$	−13.8058	−	7.97078i	−0.476914	−	0.275346i
$839$	−27.9522			−0.965019			−0.482509	−	0.875891i	$-0.660275\pi$
$839$	−27.9522			−0.965019			−0.482509	+	0.875891i	$0.660275\pi$
$840$	0.878399	−	11.2211i	0.0303077	−	0.387166i
$841$	2.29804			0.0792428
$842$	15.7973	+	9.12058i	0.544411	+	0.314316i
$843$	−3.67493	−	48.2487i	−0.126571	−	1.66177i
$844$	14.0716	+	24.3728i	0.484366	+	0.838946i
$845$	−33.2108	+	57.5228i	−1.14249	+	1.97884i
$846$	2.22871	−	1.78625i	0.0766246	−	0.0614125i
$847$	−7.48892	−	1.16358i	−0.257322	−	0.0399811i
$848$			8.46686i			0.290753i
$849$	33.5121	−	22.9081i	1.15013	−	0.786203i
$850$	−5.96314	+	3.44282i	−0.204534	+	0.118088i
$851$	−5.12408	+	2.95839i	−0.175651	+	0.101412i
$852$	1.06661	−	0.729112i	0.0365416	−	0.0249790i
$853$			32.9185i			1.12711i	0.826079	+	0.563554i	$0.190566\pi$
$853$			32.9185i			1.12711i	−0.826079	+	0.563554i	$0.809434\pi$
$854$	21.1762	−	26.3081i	0.724634	−	0.900245i
$855$	12.6627	−	10.1488i	0.433054	−	0.347081i
$856$	−2.55963	+	4.43340i	−0.0874862	+	0.151531i
$857$	27.0284	+	46.8145i	0.923271	+	1.59915i	0.794318	+	0.607502i	$0.207828\pi$
$857$	27.0284	+	46.8145i	0.923271	+	1.59915i	0.128953	+	0.991651i	$0.458838\pi$
$858$	−3.09944	−	40.6931i	−0.105813	−	1.38924i
$859$	40.2808	+	23.2561i	1.37436	+	0.793488i	0.991474	−	0.130306i	$-0.0415961\pi$
$859$	40.2808	+	23.2561i	1.37436	+	0.793488i	0.382888	+	0.923795i	$0.374929\pi$
$860$	12.9649			0.442099
$861$	13.1491	+	27.5381i	0.448122	+	0.938496i
$862$	−10.2521			−0.349188
$863$	−12.1596	−	7.02037i	−0.413919	−	0.238976i	0.278553	−	0.960421i	$-0.410145\pi$
$863$	−12.1596	−	7.02037i	−0.413919	−	0.238976i	−0.692472	+	0.721445i	$0.743478\pi$
$864$	−3.79609	+	3.54820i	−0.129146	+	0.120712i
$865$	−10.7627	−	18.6416i	−0.365944	−	0.633834i
$866$	17.9556	−	31.1000i	0.610156	−	1.05682i
$867$	20.5855	−	42.8801i	0.699122	−	1.45628i
$868$	−2.33676	+	15.0396i	−0.0793147	+	0.510477i
$869$		−	4.17685i		−	0.141690i
$870$	−12.4056	−	18.1481i	−0.420589	−	0.615277i
$871$	−80.8979	+	46.7064i	−2.74112	+	1.58259i
$872$	9.92878	−	5.73238i	0.336231	−	0.194123i
$873$	−6.91411	−	45.1248i	−0.234007	−	1.52724i
$874$			2.20234i			0.0744952i
$875$	−9.30986	−	24.0416i	−0.314731	−	0.812755i
$876$	15.4029	+	7.39454i	0.520417	+	0.249838i
$877$	−9.64796	+	16.7108i	−0.325788	+	0.564282i	−0.981672	−	0.190580i	$-0.938963\pi$
$877$	−9.64796	+	16.7108i	−0.325788	+	0.564282i	0.655883	+	0.754862i	$0.272296\pi$
$878$	13.0382	+	22.5828i	0.440017	+	0.762131i
$879$	−7.60728	+	0.579419i	−0.256587	+	0.0195433i
$880$	7.92021	+	4.57274i	0.266990	+	0.154147i
$881$	13.1947			0.444540			0.222270	−	0.974985i	$-0.428653\pi$
$881$	13.1947			0.444540			0.222270	+	0.974985i	$0.428653\pi$
$882$	19.5989	−	7.54213i	0.659929	−	0.253957i
$883$	−24.7471			−0.832808			−0.416404	−	0.909180i	$-0.636710\pi$
$883$	−24.7471			−0.832808			−0.416404	+	0.909180i	$0.636710\pi$
$884$	36.5416	+	21.0973i	1.22903	+	0.709580i
$885$	−35.3320	+	2.69111i	−1.18767	+	0.0904607i
$886$	1.94277	+	3.36497i	0.0652685	+	0.113048i
$887$	10.5397	−	18.2553i	0.353888	−	0.612952i	−0.633039	−	0.774120i	$-0.718193\pi$
$887$	10.5397	−	18.2553i	0.353888	−	0.612952i	0.986927	+	0.161168i	$0.0515261\pi$
$888$	9.23868	+	4.43524i	0.310030	+	0.148837i
$889$	7.44255	+	19.2195i	0.249615	+	0.644601i
$890$		−	5.66809i		−	0.189995i
$891$	22.6735	−	24.6766i	0.759591	−	0.826699i
$892$	−20.6876	+	11.9440i	−0.692673	+	0.399915i
$893$	−1.81585	+	1.04838i	−0.0607653	+	0.0350828i
$894$	8.64920	+	12.6529i	0.289273	+	0.423175i
$895$			38.9867i			1.30318i
$896$	0.406206	−	2.61438i	0.0135704	−	0.0873404i
$897$	4.74347	−	9.88072i	0.158380	−	0.329908i
$898$	−4.75935	+	8.24343i	−0.158822	+	0.275087i
$899$	14.8631	+	25.7436i	0.495711	+	0.858597i
$900$	1.12476	−	2.88654i	0.0374921	−	0.0962179i
$901$	48.8931	+	28.2284i	1.62886	+	0.940425i
$902$	−24.7956			−0.825604
$903$	10.4229	+	21.8286i	0.346853	+	0.726411i
$904$	3.22150			0.107146
$905$	13.9529	+	8.05572i	0.463811	+	0.267781i
$906$	0.883744	+	11.6028i	0.0293604	+	0.385477i
$907$	−8.83237	−	15.2981i	−0.293274	−	0.507966i	0.681308	−	0.731997i	$-0.261411\pi$
$907$	−8.83237	−	15.2981i	−0.293274	−	0.507966i	−0.974582	+	0.224031i	$0.928078\pi$
$908$	8.77102	−	15.1918i	0.291076	−	0.504159i
$909$	1.55996	+	1.94637i	0.0517406	+	0.0645569i
$910$	25.7844	−	32.0331i	0.854746	−	1.06189i
$911$		−	22.2702i		−	0.737844i	−0.929460	−	0.368922i	$-0.879727\pi$
$911$		−	22.2702i		−	0.737844i	0.929460	−	0.368922i	$-0.120273\pi$
$912$	3.14912	−	2.15266i	0.104278	−	0.0712818i
$913$	−44.9669	+	25.9617i	−1.48819	+	0.859206i
$914$	7.69450	−	4.44242i	0.254511	−	0.146942i
$915$	44.8297	−	30.6446i	1.48203	−	1.01308i
$916$		−	27.1421i		−	0.896799i
$917$	13.3073	+	2.06760i	0.439446	+	0.0682783i
$918$	7.83342	+	33.7507i	0.258542	+	1.11394i
$919$	−7.32473	+	12.6868i	−0.241621	+	0.418499i	−0.961176	−	0.275936i	$-0.911012\pi$
$919$	−7.32473	+	12.6868i	−0.241621	+	0.418499i	0.719555	+	0.694435i	$0.244346\pi$
$920$	1.22807	+	2.12708i	0.0404883	+	0.0701279i
$921$	−1.44663	−	18.9930i	−0.0476680	−	0.625840i
$922$	24.3207	+	14.0415i	0.800959	+	0.462434i
$923$	4.72026			0.155369
$924$	−1.33165	+	17.0112i	−0.0438081	+	0.559628i
$925$	−6.10992			−0.200893
$926$	3.93949	+	2.27447i	0.129460	+	0.0747437i
$927$	−18.1004	−	7.05297i	−0.594495	−	0.231650i
$928$	−2.58370	−	4.47509i	−0.0848140	−	0.146902i
$929$	14.5222	−	25.1532i	0.476458	−	0.825249i	−0.523179	−	0.852223i	$-0.675254\pi$
$929$	14.5222	−	25.1532i	0.476458	−	0.825249i	0.999636	+	0.0269745i	$0.00858728\pi$
$930$	−10.5914	+	22.0621i	−0.347306	+	0.723444i
$931$	−15.0604	+	3.29381i	−0.493584	+	0.107950i
$932$		−	21.4485i		−	0.702568i
$933$	28.4270	+	41.5856i	0.930658	+	1.36145i
$934$	−1.45530	+	0.840217i	−0.0476188	+	0.0274927i
$935$	52.8118	−	30.4909i	1.72713	−	0.997158i
$936$	−18.7649	+	2.87519i	−0.613349	+	0.0939784i
$937$		−	29.8379i		−	0.974761i	−0.873190	−	0.487381i	$-0.837952\pi$
$937$		−	29.8379i		−	0.974761i	0.873190	−	0.487381i	$-0.162048\pi$
$938$	36.4210	−	14.1036i	1.18919	−	0.460500i
$939$	−9.24224	−	4.43695i	−0.301609	−	0.144794i
$940$	−1.16920	+	2.02512i	−0.0381352	+	0.0660521i
$941$	−3.40216	−	5.89271i	−0.110907	−	0.192097i	0.805229	−	0.592964i	$-0.202042\pi$
$941$	−3.40216	−	5.89271i	−0.110907	−	0.192097i	−0.916136	+	0.400867i	$0.868709\pi$
$942$	6.77568	−	0.516079i	0.220763	−	0.0168148i
$943$	−5.76705	−	3.32961i	−0.187801	−	0.108427i
$944$	−8.32932			−0.271096
$945$	33.6742	−	2.49367i	1.09542	−	0.0811190i
$946$	−19.6547			−0.639031
$947$	−28.5124	−	16.4617i	−0.926529	−	0.534932i	−0.0408170	−	0.999167i	$-0.512996\pi$
$947$	−28.5124	−	16.4617i	−0.926529	−	0.534932i	−0.885712	+	0.464235i	$0.846329\pi$
$948$	−1.93732	+	0.147559i	−0.0629212	+	0.00479248i
$949$	31.2113	+	54.0596i	1.01316	+	1.75485i
$950$	−1.13712	+	1.96954i	−0.0368929	+	0.0639004i
$951$	10.4361	+	5.01008i	0.338413	+	0.162463i
$952$	−13.7428	−	11.0620i	−0.445407	−	0.358522i
$953$			46.5037i			1.50640i	0.657790	+	0.753202i	$0.271492\pi$
$953$			46.5037i			1.50640i	−0.657790	+	0.753202i	$0.728508\pi$
$954$	−25.1076	+	3.84703i	−0.812888	+	0.124552i
$955$	8.53950	−	4.93028i	0.276332	−	0.159540i
$956$	13.3475	−	7.70617i	0.431688	−	0.249235i
$957$	18.8068	+	27.5124i	0.607938	+	0.889349i
$958$		−	38.5066i		−	1.24409i
$959$	−30.8964	−	24.8695i	−0.997697	−	0.803076i
$960$	1.84114	−	3.83512i	0.0594224	−	0.123778i
$961$	1.04643	−	1.81246i	0.0337557	−	0.0584665i
$962$	18.7205	+	32.4249i	0.603575	+	1.04542i
$963$	−14.3098	−	5.57592i	−0.461126	−	0.179682i
$964$	16.3943	+	9.46523i	0.528024	+	0.304855i
$965$	26.7617			0.861489
$966$	−2.59402	+	3.77771i	−0.0834612	+	0.121546i
$967$	−0.902430			−0.0290202			−0.0145101	−	0.999895i	$-0.504619\pi$
$967$	−0.902430			−0.0290202			−0.0145101	+	0.999895i	$0.504619\pi$
$968$	−2.48074	−	1.43225i	−0.0797338	−	0.0460344i
$969$	−1.93173	−	25.3620i	−0.0620561	−	0.814743i
$970$	18.6878	+	32.3682i	0.600028	+	1.03928i
$971$	26.3957	−	45.7187i	0.847078	−	1.46718i	−0.0367254	−	0.999325i	$-0.511693\pi$
$971$	26.3957	−	45.7187i	0.847078	−	1.46718i	0.883804	−	0.467858i	$-0.154974\pi$
$972$	−12.2466	−	9.64473i	−0.392810	−	0.309355i
$973$	21.6266	−	8.37468i	0.693318	−	0.268480i
$974$			20.5551i			0.658627i
$975$	9.34370	−	6.38714i	0.299238	−	0.204552i
$976$	11.0545	−	6.38231i	0.353845	−	0.204293i
$977$	−7.43215	+	4.29096i	−0.237776	+	0.137280i	−0.614154	−	0.789186i	$-0.710503\pi$
$977$	−7.43215	+	4.29096i	−0.237776	+	0.137280i	0.376378	+	0.926466i	$0.377169\pi$
$978$	−14.6277	+	9.99917i	−0.467743	+	0.319738i
$979$			8.59281i			0.274627i
$980$	−12.7091	+	11.5793i	−0.405976	+	0.369886i
$981$	21.5100	+	26.8381i	0.686762	+	0.856876i
$982$	−1.64932	+	2.85671i	−0.0526319	+	0.0911611i
$983$	16.6823	+	28.8946i	0.532083	+	0.921594i	0.999298	+	0.0374507i	$0.0119237\pi$
$983$	16.6823	+	28.8946i	0.532083	+	0.921594i	−0.467216	+	0.884143i	$0.654743\pi$
$984$	0.875973	+	11.5008i	0.0279250	+	0.366632i
$985$	47.2947	+	27.3056i	1.50693	+	0.870029i
$986$	−34.4560			−1.09730
$987$	−4.34960	−	0.340490i	−0.138449	−	0.0108379i
$988$	13.9363			0.443373
$989$	−4.57136	−	2.63928i	−0.145361	−	0.0839241i
$990$	−9.96131	+	25.5642i	−0.316591	+	0.812484i
$991$	9.55847	+	16.5558i	0.303635	+	0.525911i	0.976956	−	0.213439i	$-0.0684664\pi$
$991$	9.55847	+	16.5558i	0.303635	+	0.525911i	−0.673322	+	0.739350i	$0.735133\pi$
$992$	−2.87632	+	4.98193i	−0.0913232	+	0.158176i
$993$	−19.9983	+	41.6567i	−0.634625	+	1.32194i
$994$	−1.95017	−	0.303004i	−0.0618555	−	0.00961071i
$995$			3.63332i			0.115184i
$996$	13.6302	+	19.9395i	0.431889	+	0.631808i
$997$	−2.37320	+	1.37017i	−0.0751599	+	0.0433936i	−0.537109	−	0.843513i	$-0.680484\pi$
$997$	−2.37320	+	1.37017i	−0.0751599	+	0.0433936i	0.461949	+	0.886906i	$0.347150\pi$
$998$	9.07480	−	5.23934i	0.287258	−	0.165848i
$999$	−8.95452	+	29.4115i	−0.283308	+	0.930540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.1	✓	56
3.2	odd	2	inner	966.2.l.d.47.19	yes	56
7.3	odd	6	inner	966.2.l.d.185.19	yes	56
21.17	even	6	inner	966.2.l.d.185.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.1	✓	56	1.1	even	1	trivial
966.2.l.d.47.19	yes	56	3.2	odd	2	inner
966.2.l.d.185.1	yes	56	21.17	even	6	inner
966.2.l.d.185.19	yes	56	7.3	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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72705 + 0.131543i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22807 - 2.12708i) q^{5} +(1.56144 + 0.749605i) q^{6} +(-0.955407 - 2.46722i) q^{7} -1.00000i q^{8} +(2.96539 - 0.454363i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72705 + 0.131543i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.22807 - 2.12708i) q^{5} +(1.56144 + 0.749605i) q^{6} +(-0.955407 - 2.46722i) q^{7} -1.00000i q^{8} +(2.96539 - 0.454363i) q^{9} +(-2.12708 + 1.22807i) q^{10} +(3.22465 - 1.86175i) q^{11} +(-0.977444 - 1.42990i) q^{12} -6.32796i q^{13} +(-0.406206 + 2.61438i) q^{14} +(-1.84114 + 3.83512i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.33399 + 5.77463i) q^{17} +(-2.79529 - 1.08921i) q^{18} +(1.90728 + 1.10117i) q^{19} +2.45614 q^{20} +(1.97458 + 4.13534i) q^{21} -3.72351 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.131543 + 1.72705i) q^{24} +(-0.516322 - 0.894296i) q^{25} +(-3.16398 + 5.48017i) q^{26} +(-5.06161 + 1.17478i) q^{27} +(1.65898 - 2.06102i) q^{28} -5.16739i q^{29} +(3.51203 - 2.40074i) q^{30} +(-4.98193 + 2.87632i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.32423 + 3.63952i) q^{33} -6.66797i q^{34} +(-6.42130 - 0.997701i) q^{35} +(1.87619 + 2.34092i) q^{36} +(2.95839 - 5.12408i) q^{37} +(-1.10117 - 1.90728i) q^{38} +(0.832399 + 10.9287i) q^{39} +(-2.12708 - 1.22807i) q^{40} +6.65921 q^{41} +(0.357633 - 4.56860i) q^{42} +5.27855 q^{43} +(3.22465 + 1.86175i) q^{44} +(2.67525 - 6.86563i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-0.476032 + 0.824512i) q^{47} +(0.749605 - 1.56144i) q^{48} +(-5.17440 + 4.71441i) q^{49} +1.03264i q^{50} +(-6.51757 - 9.53451i) q^{51} +(5.48017 - 3.16398i) q^{52} +(7.33252 - 4.23343i) q^{53} +(4.97087 + 1.51341i) q^{54} -9.14547i q^{55} +(-2.46722 + 0.955407i) q^{56} +(-3.43882 - 1.65088i) q^{57} +(-2.58370 + 4.47509i) q^{58} +(4.16466 + 7.21340i) q^{59} +(-4.24188 + 0.323089i) q^{60} +(-11.0545 - 6.38231i) q^{61} +5.75264 q^{62} +(-3.95417 - 6.88219i) q^{63} -1.00000 q^{64} +(-13.4601 - 7.77119i) q^{65} +(6.43068 - 0.489802i) q^{66} +(-7.38097 - 12.7842i) q^{67} +(-3.33399 + 5.77463i) q^{68} +(1.56144 + 0.749605i) q^{69} +(5.06216 + 4.07468i) q^{70} +0.745937i q^{71} +(-0.454363 - 2.96539i) q^{72} +(-8.54298 + 4.93229i) q^{73} +(-5.12408 + 2.95839i) q^{74} +(1.00935 + 1.47657i) q^{75} +2.20234i q^{76} +(-7.67422 - 6.17721i) q^{77} +(4.74347 - 9.88072i) q^{78} +(0.560876 - 0.971465i) q^{79} +(1.22807 + 2.12708i) q^{80} +(8.58711 - 2.69473i) q^{81} +(-5.76705 - 3.32961i) q^{82} -13.9447 q^{83} +(-2.59402 + 3.77771i) q^{84} +16.3775 q^{85} +(-4.57136 - 2.63928i) q^{86} +(0.679735 + 8.92434i) q^{87} +(-1.86175 - 3.22465i) q^{88} +(-1.15386 + 1.99854i) q^{89} +(-5.74965 + 4.60818i) q^{90} +(-15.6125 + 6.04577i) q^{91} -1.00000i q^{92} +(8.22568 - 5.62288i) q^{93} +(0.824512 - 0.476032i) q^{94} +(4.68456 - 2.70463i) q^{95} +(-1.42990 + 0.977444i) q^{96} -15.2172i q^{97} +(6.83836 - 1.49560i) q^{98} +(8.71645 - 6.98599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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