LMFDB - Embedded newform 63.2.f.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.2.f.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 - 1.16679i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} +(-0.500000 - 0.866025i) q^{7} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(-0.673648 - 1.16679i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} +(-0.500000 - 0.866025i) q^{7} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} +3.41147 q^{10} +(-0.233956 - 0.405223i) q^{11} +(0.109470 - 0.300767i) q^{12} +(-2.91147 + 5.04282i) q^{13} +(-0.673648 + 1.16679i) q^{14} +(-1.50000 + 4.12122i) q^{15} +(1.79813 + 3.11446i) q^{16} +3.87939 q^{17} +(-3.09627 - 2.59808i) q^{18} -2.18479 q^{19} +(0.233956 + 0.405223i) q^{20} +(-1.11334 - 1.32683i) q^{21} +(-0.315207 + 0.545955i) q^{22} +(0.0530334 - 0.0918566i) q^{23} +(-5.02094 + 0.885328i) q^{24} +(-0.705737 - 1.22237i) q^{25} +7.84524 q^{26} +(4.50000 - 2.59808i) q^{27} -0.184793 q^{28} +(-4.39053 - 7.60462i) q^{29} +(5.81908 - 1.02606i) q^{30} +(3.84002 - 6.65111i) q^{31} +(-0.520945 + 0.902302i) q^{32} +(-0.520945 - 0.620838i) q^{33} +(-2.61334 - 4.52644i) q^{34} +2.53209 q^{35} +(0.0962667 - 0.545955i) q^{36} -7.68004 q^{37} +(1.47178 + 2.54920i) q^{38} +(-3.44949 + 9.47740i) q^{39} +(3.72668 - 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.798133 + 2.19285i) q^{42} +(-0.613341 - 1.06234i) q^{43} -0.0864665 q^{44} +(-1.31908 + 7.48086i) q^{45} -0.142903 q^{46} +(2.66637 + 4.61830i) q^{47} +(4.00387 + 4.77163i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.950837 + 1.64690i) q^{50} +(6.61721 - 1.16679i) q^{51} +(0.538019 + 0.931876i) q^{52} -0.716881 q^{53} +(-6.06283 - 3.50038i) q^{54} +1.18479 q^{55} +(1.47178 + 2.54920i) q^{56} +(-3.72668 + 0.657115i) q^{57} +(-5.91534 + 10.2457i) q^{58} +(-0.368241 + 0.637812i) q^{59} +(0.520945 + 0.620838i) q^{60} +(-0.479055 - 0.829748i) q^{61} -10.3473 q^{62} +(-2.29813 - 1.92836i) q^{63} +8.59627 q^{64} +(-7.37211 - 12.7689i) q^{65} +(-0.373455 + 1.02606i) q^{66} +(4.81908 - 8.34689i) q^{67} +(0.358441 - 0.620838i) q^{68} +(0.0628336 - 0.172634i) q^{69} +(-1.70574 - 2.95442i) q^{70} +13.2344 q^{71} +(-8.29813 + 3.02027i) q^{72} -10.2686 q^{73} +(5.17365 + 8.96102i) q^{74} +(-1.57145 - 1.87278i) q^{75} +(-0.201867 + 0.349643i) q^{76} +(-0.233956 + 0.405223i) q^{77} +(13.3819 - 2.35959i) q^{78} +(6.31908 + 10.9450i) q^{79} -9.10607 q^{80} +(6.89440 - 5.78509i) q^{81} -3.00000 q^{82} +(1.36571 + 2.36549i) q^{83} +(-0.315207 + 0.0555796i) q^{84} +(-4.91147 + 8.50692i) q^{85} +(-0.826352 + 1.43128i) q^{86} +(-9.77631 - 11.6510i) q^{87} +(0.688663 + 1.19280i) q^{88} -8.11381 q^{89} +(9.61721 - 3.50038i) q^{90} +5.82295 q^{91} +(-0.00980018 - 0.0169744i) q^{92} +(4.54963 - 12.5000i) q^{93} +(3.59240 - 6.22221i) q^{94} +(2.76604 - 4.79093i) q^{95} +(-0.617211 + 1.69577i) q^{96} +(6.80200 + 11.7814i) q^{97} +1.34730 q^{98} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24} + 6 q^{25} - 6 q^{26} + 27 q^{27} + 6 q^{28} - 9 q^{29} + 18 q^{30} + 3 q^{31} - 9 q^{34} + 6 q^{35} - 27 q^{36} - 6 q^{37} - 6 q^{38} - 18 q^{39} + 9 q^{40} + 9 q^{42} + 3 q^{43} + 30 q^{44} + 9 q^{45} - 3 q^{47} - 3 q^{49} + 6 q^{50} + 9 q^{51} + 21 q^{52} + 12 q^{53} - 27 q^{54} - 6 q^{56} - 9 q^{57} + 9 q^{58} + 3 q^{59} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} + 36 q^{66} + 12 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 36 q^{72} - 42 q^{73} + 30 q^{74} - 9 q^{75} - 15 q^{76} - 6 q^{77} + 54 q^{78} + 21 q^{79} - 30 q^{80} - 18 q^{82} + 18 q^{83} - 9 q^{84} - 9 q^{85} - 6 q^{86} + 9 q^{87} - 27 q^{88} + 24 q^{89} + 27 q^{90} - 6 q^{91} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 27 q^{96} + 3 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.673648	−	1.16679i	−0.476341	−	0.825047i	0.523291	−	0.852154i	$-0.324704\pi$
$2$	−0.673648	−	1.16679i	−0.476341	−	0.825047i	−0.999633	+	0.0271067i	$0.991371\pi$
$3$	1.70574	−	0.300767i	0.984808	−	0.173648i
$3$	1.70574	−	0.300767i	0.984808	−	0.173648i
$4$	0.0923963	−	0.160035i	0.0461981	−	0.0800175i
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	0.430745	+	0.902473i	$0.358251\pi$
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	−0.996938	+	0.0782003i	$0.975083\pi$
$6$	−1.50000	−	1.78763i	−0.612372	−	0.729797i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−2.94356			−1.04071
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$	3.41147			1.07880
$11$	−0.233956	−	0.405223i	−0.0705403	−	0.122179i	0.828598	−	0.559844i	$-0.189139\pi$
$11$	−0.233956	−	0.405223i	−0.0705403	−	0.122179i	−0.899138	+	0.437665i	$0.855806\pi$
$12$	0.109470	−	0.300767i	0.0316014	−	0.0868241i
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	0.107094	+	0.994249i	$0.465845\pi$
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	−0.914592	+	0.404378i	$0.867488\pi$
$14$	−0.673648	+	1.16679i	−0.180040	+	0.311839i
$15$	−1.50000	+	4.12122i	−0.387298	+	1.06409i
$16$	1.79813	+	3.11446i	0.449533	+	0.778615i
$17$	3.87939			0.940889			0.470445	−	0.882430i	$-0.344094\pi$
$17$	3.87939			0.940889			0.470445	+	0.882430i	$0.344094\pi$
$18$	−3.09627	−	2.59808i	−0.729797	−	0.612372i
$19$	−2.18479			−0.501226			−0.250613	−	0.968087i	$-0.580632\pi$
$19$	−2.18479			−0.501226			−0.250613	+	0.968087i	$0.580632\pi$
$20$	0.233956	+	0.405223i	0.0523141	+	0.0906106i
$21$	−1.11334	−	1.32683i	−0.242951	−	0.289538i
$22$	−0.315207	+	0.545955i	−0.0672025	+	0.116398i
$23$	0.0530334	−	0.0918566i	0.0110582	−	0.0191534i	−0.860443	−	0.509546i	$-0.829813\pi$
$23$	0.0530334	−	0.0918566i	0.0110582	−	0.0191534i	0.871502	+	0.490393i	$0.163147\pi$
$24$	−5.02094	+	0.885328i	−1.02490	+	0.180717i
$25$	−0.705737	−	1.22237i	−0.141147	−	0.244474i
$26$	7.84524			1.53858
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$	−0.184793			−0.0349225
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	−0.909112	−	0.416552i	$-0.863238\pi$
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	0.0938108	−	0.995590i	$-0.470095\pi$
$30$	5.81908	−	1.02606i	1.06241	−	0.187332i
$31$	3.84002	−	6.65111i	0.689688	−	1.19458i	−0.282250	−	0.959341i	$-0.591081\pi$
$31$	3.84002	−	6.65111i	0.689688	−	1.19458i	0.971939	−	0.235235i	$-0.0755858\pi$
$32$	−0.520945	+	0.902302i	−0.0920909	+	0.159506i
$33$	−0.520945	−	0.620838i	−0.0906848	−	0.108074i
$34$	−2.61334	−	4.52644i	−0.448184	−	0.776278i
$35$	2.53209			0.428001
$36$	0.0962667	−	0.545955i	0.0160444	−	0.0909926i
$37$	−7.68004			−1.26259			−0.631296	−	0.775542i	$-0.717477\pi$
$37$	−7.68004			−1.26259			−0.631296	+	0.775542i	$0.717477\pi$
$38$	1.47178	+	2.54920i	0.238754	+	0.413535i
$39$	−3.44949	+	9.47740i	−0.552361	+	1.51760i
$40$	3.72668	−	6.45480i	0.589240	−	1.02059i
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	−0.765897	−	0.642964i	$-0.777705\pi$
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	0.939771	+	0.341804i	$0.111038\pi$
$42$	−0.798133	+	2.19285i	−0.123155	+	0.338365i
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	0.815462	−	0.578811i	$-0.196483\pi$
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	−0.908996	+	0.416806i	$0.863150\pi$
$44$	−0.0864665			−0.0130353
$45$	−1.31908	+	7.48086i	−0.196637	+	1.11518i
$46$	−0.142903			−0.0210700
$47$	2.66637	+	4.61830i	0.388931	+	0.673648i	0.992306	−	0.123810i	$-0.0395112\pi$
$47$	2.66637	+	4.61830i	0.388931	+	0.673648i	−0.603375	+	0.797457i	$0.706178\pi$
$48$	4.00387	+	4.77163i	0.577909	+	0.688725i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.950837	+	1.64690i	−0.134469	+	0.232907i
$51$	6.61721	−	1.16679i	0.926595	−	0.163384i
$52$	0.538019	+	0.931876i	0.0746098	+	0.129228i
$53$	−0.716881			−0.0984712			−0.0492356	−	0.998787i	$-0.515679\pi$
$53$	−0.716881			−0.0984712			−0.0492356	+	0.998787i	$0.515679\pi$
$54$	−6.06283	−	3.50038i	−0.825047	−	0.476341i
$55$	1.18479			0.159757
$56$	1.47178	+	2.54920i	0.196675	+	0.340651i
$57$	−3.72668	+	0.657115i	−0.493611	+	0.0870369i
$58$	−5.91534	+	10.2457i	−0.776723	+	1.34532i
$59$	−0.368241	+	0.637812i	−0.0479409	+	0.0830360i	−0.889000	−	0.457907i	$-0.848599\pi$
$59$	−0.368241	+	0.637812i	−0.0479409	+	0.0830360i	0.841059	+	0.540943i	$0.181933\pi$
$60$	0.520945	+	0.620838i	0.0672537	+	0.0801498i
$61$	−0.479055	−	0.829748i	−0.0613368	−	0.106238i	0.833726	−	0.552178i	$-0.186203\pi$
$61$	−0.479055	−	0.829748i	−0.0613368	−	0.106238i	−0.895063	+	0.445939i	$0.852870\pi$
$62$	−10.3473			−1.31411
$63$	−2.29813	−	1.92836i	−0.289538	−	0.242951i
$64$	8.59627			1.07453
$65$	−7.37211	−	12.7689i	−0.914398	−	1.58378i
$66$	−0.373455	+	1.02606i	−0.0459692	+	0.126299i
$67$	4.81908	−	8.34689i	0.588744	−	1.01973i	−0.405653	−	0.914027i	$-0.632956\pi$
$67$	4.81908	−	8.34689i	0.588744	−	1.01973i	0.994397	−	0.105708i	$-0.0337107\pi$
$68$	0.358441	−	0.620838i	0.0434673	−	0.0752876i
$69$	0.0628336	−	0.172634i	0.00756428	−	0.0207827i
$70$	−1.70574	−	2.95442i	−0.203875	−	0.353121i
$71$	13.2344			1.57064			0.785318	−	0.619092i	$-0.212499\pi$
$71$	13.2344			1.57064			0.785318	+	0.619092i	$0.212499\pi$
$72$	−8.29813	+	3.02027i	−0.977944	+	0.355943i
$73$	−10.2686			−1.20185			−0.600923	−	0.799307i	$-0.705200\pi$
$73$	−10.2686			−1.20185			−0.600923	+	0.799307i	$0.705200\pi$
$74$	5.17365	+	8.96102i	0.601424	+	1.04170i
$75$	−1.57145	−	1.87278i	−0.181456	−	0.216250i
$76$	−0.201867	+	0.349643i	−0.0231557	+	0.0401068i
$77$	−0.233956	+	0.405223i	−0.0266617	+	0.0461794i
$78$	13.3819	−	2.35959i	1.51520	−	0.267171i
$79$	6.31908	+	10.9450i	0.710952	+	1.23140i	0.964500	+	0.264082i	$0.0850689\pi$
$79$	6.31908	+	10.9450i	0.710952	+	1.23140i	−0.253548	+	0.967323i	$0.581598\pi$
$80$	−9.10607			−1.01809
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$	−3.00000			−0.331295
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	0.931193	−	0.364527i	$-0.118769\pi$
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	−0.781286	+	0.624173i	$0.785436\pi$
$84$	−0.315207	+	0.0555796i	−0.0343920	+	0.00606423i
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$	−0.826352	+	1.43128i	−0.0891078	+	0.154339i
$87$	−9.77631	−	11.6510i	−1.04813	−	1.24911i
$88$	0.688663	+	1.19280i	0.0734117	+	0.127153i
$89$	−8.11381			−0.860062			−0.430031	−	0.902814i	$-0.641497\pi$
$89$	−8.11381			−0.860062			−0.430031	+	0.902814i	$0.641497\pi$
$90$	9.61721	−	3.50038i	1.01374	−	0.368972i
$91$	5.82295			0.610411
$92$	−0.00980018	−	0.0169744i	−0.00102174	−	0.00176970i
$93$	4.54963	−	12.5000i	0.471775	−	1.29619i
$94$	3.59240	−	6.22221i	0.370527	−	0.641772i
$95$	2.76604	−	4.79093i	0.283790	−	0.491539i
$96$	−0.617211	+	1.69577i	−0.0629939	+	0.173074i
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	0.971629	+	0.236511i	$0.0760039\pi$
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	−0.280990	+	0.959711i	$0.590663\pi$
$98$	1.34730			0.136097
$99$	−1.07532	−	0.902302i	−0.108074	−	0.0906848i
$100$	−0.260830			−0.0260830
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	0.999632	−	0.0271271i	$-0.00863590\pi$
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	−0.523309	+	0.852143i	$0.675303\pi$
$102$	−5.81908	−	6.93491i	−0.576175	−	0.686658i
$103$	−1.52094	+	2.63435i	−0.149863	+	0.259571i	−0.931177	−	0.364568i	$-0.881217\pi$
$103$	−1.52094	+	2.63435i	−0.149863	+	0.259571i	0.781314	+	0.624139i	$0.214550\pi$
$104$	8.57011	−	14.8439i	0.840368	−	1.45556i
$105$	4.31908	−	0.761570i	0.421499	−	0.0743216i
$106$	0.482926	+	0.836452i	0.0469059	+	0.0812434i
$107$	−6.51754			−0.630074			−0.315037	−	0.949079i	$-0.602017\pi$
$107$	−6.51754			−0.630074			−0.315037	+	0.949079i	$0.602017\pi$
$108$		−	0.960210i		−	0.0923963i
$109$	10.6382			1.01895			0.509475	−	0.860485i	$-0.329840\pi$
$109$	10.6382			1.01895			0.509475	+	0.860485i	$0.329840\pi$
$110$	−0.798133	−	1.38241i	−0.0760990	−	0.131807i
$111$	−13.1001	+	2.30991i	−1.24341	+	0.219247i
$112$	1.79813	−	3.11446i	0.169908	−	0.294289i
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	−0.961711	−	0.274065i	$-0.911632\pi$
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	0.718203	+	0.695834i	$0.244965\pi$
$114$	3.27719	+	3.90560i	0.306937	+	0.365793i
$115$	0.134285	+	0.232589i	0.0125222	+	0.0216890i
$116$	−1.62267			−0.150662
$117$	−3.03343	+	17.2035i	−0.280441	+	1.59046i
$118$	0.992259			0.0913449
$119$	−1.93969	−	3.35965i	−0.177811	−	0.307978i
$120$	4.41534	−	12.1311i	0.403064	−	1.10741i
$121$	5.39053	−	9.33667i	0.490048	−	0.848788i
$122$	−0.645430	+	1.11792i	−0.0584345	+	0.101211i
$123$	1.31908	−	3.62414i	0.118937	−	0.326777i
$124$	−0.709607	−	1.22908i	−0.0637246	−	0.110374i
$125$	−9.08647			−0.812718
$126$	−0.701867	+	3.98048i	−0.0625273	+	0.354610i
$127$	−8.88207			−0.788157			−0.394078	−	0.919077i	$-0.628936\pi$
$127$	−8.88207			−0.788157			−0.394078	+	0.919077i	$0.628936\pi$
$128$	−4.74897	−	8.22546i	−0.419754	−	0.727035i
$129$	−1.36571	−	1.62760i	−0.120244	−	0.143302i
$130$	−9.93242	+	17.2035i	−0.871131	+	1.50884i
$131$	−5.68139	+	9.84045i	−0.496385	+	0.859764i	−0.999991	−	0.00416893i	$-0.998673\pi$
$131$	−5.68139	+	9.84045i	−0.496385	+	0.859764i	0.503606	+	0.863933i	$0.332006\pi$
$132$	−0.147489	+	0.0260063i	−0.0128373	+	0.00226356i
$133$	1.09240	+	1.89209i	0.0947228	+	0.164065i
$134$	−12.9855			−1.12177
$135$			13.1571i			1.13238i
$136$	−11.4192			−0.979190
$137$	2.86231	+	4.95767i	0.244544	+	0.423562i	0.962003	−	0.273038i	$-0.0880285\pi$
$137$	2.86231	+	4.95767i	0.244544	+	0.423562i	−0.717459	+	0.696600i	$0.754695\pi$
$138$	−0.243756	+	0.0429807i	−0.0207499	+	0.00365876i
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	−0.845768	−	0.533551i	$-0.820857\pi$
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	0.884953	+	0.465681i	$0.154191\pi$
$140$	0.233956	−	0.405223i	0.0197729	−	0.0342476i
$141$	5.93717	+	7.07564i	0.500000	+	0.595876i
$142$	−8.91534	−	15.4418i	−0.748159	−	1.29585i
$143$	2.72462			0.227844
$144$	8.26470	+	6.93491i	0.688725	+	0.577909i
$145$	22.2344			1.84647
$146$	6.91740	+	11.9813i	0.572488	+	0.991579i
$147$	−0.592396	+	1.62760i	−0.0488600	+	0.134242i
$148$	−0.709607	+	1.22908i	−0.0583294	+	0.101029i
$149$	−4.36231	+	7.55574i	−0.357374	+	0.618991i	−0.987521	−	0.157485i	$-0.949661\pi$
$149$	−4.36231	+	7.55574i	−0.357374	+	0.618991i	0.630147	+	0.776476i	$0.282995\pi$
$150$	−1.12654	+	3.09516i	−0.0919820	+	0.252718i
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	−0.947927	−	0.318488i	$-0.896825\pi$
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	0.198145	−	0.980173i	$-0.436508\pi$
$152$	6.43107			0.521629
$153$	10.9363	−	3.98048i	0.884147	−	0.321803i
$154$	0.630415			0.0508003
$155$	9.72328	+	16.8412i	0.780992	+	1.35272i
$156$	1.19800	+	1.42772i	0.0959165	+	0.114309i
$157$	−2.46198	+	4.26428i	−0.196488	+	0.340326i	−0.947387	−	0.320090i	$-0.896287\pi$
$157$	−2.46198	+	4.26428i	−0.196488	+	0.340326i	0.750900	+	0.660416i	$0.229620\pi$
$158$	8.51367	−	14.7461i	0.677311	−	1.17314i
$159$	−1.22281	+	0.215615i	−0.0969752	+	0.0170994i
$160$	−1.31908	−	2.28471i	−0.104282	−	0.180622i
$161$	−0.106067			−0.00835924
$162$	−11.3944	−	4.14722i	−0.895229	−	0.325837i
$163$	7.63816			0.598267			0.299133	−	0.954211i	$-0.403302\pi$
$163$	7.63816			0.598267			0.299133	+	0.954211i	$0.403302\pi$
$164$	−0.205737	−	0.356347i	−0.0160654	−	0.0278260i
$165$	2.02094	−	0.356347i	0.157330	−	0.0277416i
$166$	1.84002	−	3.18701i	0.142813	−	0.247360i
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	−0.735632	−	0.677382i	$-0.763115\pi$
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	0.954446	+	0.298385i	$0.0964480\pi$
$168$	3.27719	+	3.90560i	0.252841	+	0.301324i
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$	13.2344			1.01503
$171$	−6.15910	+	2.24173i	−0.470998	+	0.171429i
$172$	−0.226682			−0.0172843
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	−0.919003	−	0.394250i	$-0.871005\pi$
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	0.118071	−	0.993005i	$-0.462329\pi$
$174$	−7.00846	+	19.2556i	−0.531310	+	1.45976i
$175$	−0.705737	+	1.22237i	−0.0533487	+	0.0924027i
$176$	0.841367	−	1.45729i	0.0634204	−	0.109847i
$177$	−0.436289	+	1.19869i	−0.0327935	+	0.0900994i
$178$	5.46585	+	9.46713i	0.409683	+	0.709592i
$179$	−5.12061			−0.382733			−0.191366	−	0.981519i	$-0.561292\pi$
$179$	−5.12061			−0.382733			−0.191366	+	0.981519i	$0.561292\pi$
$180$	1.07532	+	0.902302i	0.0801498	+	0.0672537i
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$	−3.92262	−	6.79417i	−0.290764	−	0.503618i
$183$	−1.06670	−	1.27125i	−0.0788530	−	0.0939734i
$184$	−0.156107	+	0.270386i	−0.0115084	+	0.0199331i
$185$	9.72328	−	16.8412i	0.714870	−	1.23819i
$186$	−17.6498	+	3.11213i	−1.29414	+	0.228192i
$187$	−0.907604	−	1.57202i	−0.0663706	−	0.114957i
$188$	0.985452			0.0718715
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$	−7.45336			−0.540724
$191$	7.78359	+	13.4816i	0.563200	+	0.975492i	0.997215	+	0.0745858i	$0.0237635\pi$
$191$	7.78359	+	13.4816i	0.563200	+	0.975492i	−0.434014	+	0.900906i	$0.642903\pi$
$192$	14.6630	−	2.58548i	1.05821	−	0.186591i
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	−0.954028	−	0.299716i	$-0.903108\pi$
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	0.736576	+	0.676355i	$0.236441\pi$
$194$	9.16431	−	15.8731i	0.657959	−	1.13962i
$195$	−16.4153	−	19.5630i	−1.17553	−	1.40094i
$196$	0.0923963	+	0.160035i	0.00659973	+	0.0114311i
$197$	25.2344			1.79788			0.898939	−	0.438074i	$-0.144339\pi$
$197$	25.2344			1.79788			0.898939	+	0.438074i	$0.144339\pi$
$198$	−0.328411	+	1.86251i	−0.0233392	+	0.132363i
$199$	3.04189			0.215634			0.107817	−	0.994171i	$-0.465614\pi$
$199$	3.04189			0.215634			0.107817	+	0.994171i	$0.465614\pi$
$200$	2.07738	+	3.59813i	0.146893	+	0.254426i
$201$	5.70961	−	15.6870i	0.402725	−	1.10648i
$202$	6.44949	−	11.1708i	0.453785	−	0.785978i
$203$	−4.39053	+	7.60462i	−0.308155	+	0.533740i
$204$	0.424678	−	1.16679i	0.0297334	−	0.0816918i
$205$	2.81908	+	4.88279i	0.196893	+	0.341029i
$206$	4.09833			0.285544
$207$	0.0552549	−	0.313366i	0.00384048	−	0.0217805i
$208$	−20.9409			−1.45199
$209$	0.511144	+	0.885328i	0.0353566	+	0.0612394i
$210$	−3.79813	−	4.52644i	−0.262096	−	0.312354i
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	−0.756775	−	0.653676i	$-0.773226\pi$
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	0.944487	+	0.328548i	$0.106559\pi$
$212$	−0.0662372	+	0.114726i	−0.00454919	+	0.00787942i
$213$	22.5744	−	3.98048i	1.54678	−	0.272738i
$214$	4.39053	+	7.60462i	0.300130	+	0.519841i
$215$	3.10607			0.211832
$216$	−13.2460	+	7.64760i	−0.901278	+	0.520353i
$217$	−7.68004			−0.521355
$218$	−7.16637	−	12.4125i	−0.485368	−	0.840682i
$219$	−17.5155	+	3.08845i	−1.18359	+	0.208698i
$220$	0.109470	−	0.189608i	0.00738049	−	0.0127834i
$221$	−11.2947	+	19.5630i	−0.759766	+	1.31595i
$222$	11.5201	+	13.7291i	0.773176	+	0.921436i
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	0.524395	−	0.851475i	$-0.324291\pi$
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	−0.999597	+	0.0284023i	$0.990958\pi$
$224$	1.04189			0.0696141
$225$	−3.24376	−	2.72183i	−0.216250	−	0.181456i
$226$	6.97502			0.463972
$227$	1.44697	+	2.50622i	0.0960385	+	0.166344i	0.910042	−	0.414517i	$-0.136049\pi$
$227$	1.44697	+	2.50622i	0.0960385	+	0.166344i	−0.814003	+	0.580861i	$0.802716\pi$
$228$	−0.239170	+	0.657115i	−0.0158394	+	0.0435185i
$229$	−4.58378	+	7.93934i	−0.302905	+	0.524646i	−0.976793	−	0.214187i	$-0.931290\pi$
$229$	−4.58378	+	7.93934i	−0.302905	+	0.524646i	0.673888	+	0.738834i	$0.264623\pi$
$230$	0.180922	−	0.313366i	0.0119297	−	0.0206628i
$231$	−0.277189	+	0.761570i	−0.0182377	+	0.0501076i
$232$	12.9238	+	22.3847i	0.848489	+	1.46963i
$233$	13.2713			0.869429			0.434715	−	0.900568i	$-0.356849\pi$
$233$	13.2713			0.869429			0.434715	+	0.900568i	$0.356849\pi$
$234$	22.1163	−	8.04969i	1.44579	−	0.526225i
$235$	−13.5030			−0.880838
$236$	0.0680482	+	0.117863i	0.00442956	+	0.00767222i
$237$	14.0706	+	16.7687i	0.913982	+	1.08924i
$238$	−2.61334	+	4.52644i	−0.169398	+	0.293405i
$239$	−4.76857	+	8.25941i	−0.308453	+	0.534257i	−0.978024	−	0.208491i	$-0.933145\pi$
$239$	−4.76857	+	8.25941i	−0.308453	+	0.534257i	0.669571	+	0.742748i	$0.266478\pi$
$240$	−15.5326	+	2.73881i	−1.00262	+	0.176789i
$241$	4.47906	+	7.75795i	0.288521	+	0.499734i	0.973457	−	0.228870i	$-0.0735031\pi$
$241$	4.47906	+	7.75795i	0.288521	+	0.499734i	−0.684936	+	0.728604i	$0.740170\pi$
$242$	−14.5253			−0.933720
$243$	10.0201	−	11.9415i	0.642788	−	0.766044i
$244$	−0.177052			−0.0113346
$245$	−1.26604	−	2.19285i	−0.0808846	−	0.140096i
$246$	−5.11721	+	0.902302i	−0.326261	+	0.0575287i
$247$	6.36097	−	11.0175i	0.404739	−	0.701028i
$248$	−11.3033	+	19.5780i	−0.717763	+	1.24320i
$249$	3.04101	+	3.62414i	0.192716	+	0.229670i
$250$	6.12108	+	10.6020i	0.387131	+	0.670531i
$251$	−24.9982			−1.57788			−0.788938	−	0.614473i	$-0.789369\pi$
$251$	−24.9982			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$252$	−0.520945	+	0.189608i	−0.0328164	+	0.0119442i
$253$	−0.0496299			−0.00312020
$254$	5.98339	+	10.3635i	0.375431	+	0.650266i
$255$	−5.81908	+	15.9878i	−0.364405	+	1.00119i
$256$	2.19800	−	3.80704i	0.137375	−	0.237940i
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	−0.984144	−	0.177369i	$-0.943241\pi$
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	0.645678	+	0.763609i	$0.276575\pi$
$258$	−0.979055	+	2.68993i	−0.0609533	+	0.167468i
$259$	3.84002	+	6.65111i	0.238607	+	0.413280i
$260$	−2.72462			−0.168974
$261$	−20.1800	−	16.9331i	−1.24911	−	1.04813i
$262$	15.3090			0.945795
$263$	−13.0437	−	22.5924i	−0.804309	−	1.39310i	−0.916757	−	0.399446i	$-0.869202\pi$
$263$	−13.0437	−	22.5924i	−0.804309	−	1.39310i	0.112448	−	0.993658i	$-0.464131\pi$
$264$	1.53343	+	1.82747i	0.0943763	+	0.112473i
$265$	0.907604	−	1.57202i	0.0557537	−	0.0965682i
$266$	1.47178	−	2.54920i	0.0902407	−	0.156302i
$267$	−13.8400	+	2.44037i	−0.846996	+	0.149348i
$268$	−0.890530	−	1.54244i	−0.0543978	−	0.0942197i
$269$	−7.63310			−0.465399			−0.232699	−	0.972549i	$-0.574756\pi$
$269$	−7.63310			−0.465399			−0.232699	+	0.972549i	$0.574756\pi$
$270$	15.3516	−	8.86327i	0.934271	−	0.539401i
$271$	3.40373			0.206762			0.103381	−	0.994642i	$-0.467034\pi$
$271$	3.40373			0.206762			0.103381	+	0.994642i	$0.467034\pi$
$272$	6.97565	+	12.0822i	0.422961	+	0.732590i
$273$	9.93242	−	1.75135i	0.601137	−	0.105997i
$274$	3.85638	−	6.67945i	0.232973	−	0.403520i
$275$	−0.330222	+	0.571962i	−0.0199131	+	0.0344906i
$276$	−0.0218219	−	0.0260063i	−0.00131352	−	0.00156540i
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	0.939084	−	0.343689i	$-0.111676\pi$
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	−0.767185	+	0.641426i	$0.778343\pi$
$278$	−1.24485			−0.0746612
$279$	4.00088	−	22.6901i	0.239526	−	1.35842i
$280$	−7.45336			−0.445424
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	−0.884378	−	0.466771i	$-0.845417\pi$
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	0.0379535	−	0.999280i	$-0.487916\pi$
$282$	4.25624	−	11.6939i	0.253456	−	0.696364i
$283$	−2.28564	+	3.95885i	−0.135867	+	0.235329i	−0.925929	−	0.377699i	$-0.876715\pi$
$283$	−2.28564	+	3.95885i	−0.135867	+	0.235329i	0.790061	+	0.613028i	$0.210049\pi$
$284$	1.22281	−	2.11797i	0.0725605	−	0.125678i
$285$	3.27719	−	9.00400i	0.194124	−	0.533351i
$286$	−1.83544	−	3.17907i	−0.108532	−	0.187982i
$287$	−2.22668			−0.131437
$288$	−0.542766	+	3.07818i	−0.0319828	+	0.181384i
$289$	−1.95037			−0.114728
$290$	−14.9782	−	25.9430i	−0.879549	−	1.52342i
$291$	15.1459	+	18.0502i	0.887868	+	1.05812i
$292$	−0.948778	+	1.64333i	−0.0555230	+	0.0961687i
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	−0.922285	−	0.386512i	$-0.873680\pi$
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	0.795871	+	0.605466i	$0.207013\pi$
$294$	2.29813	−	0.405223i	0.134030	−	0.0236331i
$295$	−0.932419	−	1.61500i	−0.0542875	−	0.0940287i
$296$	22.6067			1.31399
$297$	−2.10560	−	1.21567i	−0.122179	−	0.0705403i
$298$	11.7547			0.680929
$299$	0.308811	+	0.534876i	0.0178590	+	0.0309327i
$300$	−0.444907	+	0.0784491i	−0.0256867	+	0.00452926i
$301$	−0.613341	+	1.06234i	−0.0353524	+	0.0612321i
$302$	−12.4133	+	21.5004i	−0.714304	+	1.23721i
$303$	10.6591	+	12.7030i	0.612349	+	0.729769i
$304$	−3.92855	−	6.80445i	−0.225318	−	0.390262i
$305$	2.42602			0.138914
$306$	−12.0116	−	10.0789i	−0.686658	−	0.576175i
$307$	12.3773			0.706411			0.353206	−	0.935546i	$-0.385092\pi$
$307$	12.3773			0.706411			0.353206	+	0.935546i	$0.385092\pi$
$308$	0.0432332	+	0.0748822i	0.00246344	+	0.00426681i
$309$	−1.80200	+	4.95096i	−0.102512	+	0.281651i
$310$	13.1001	−	22.6901i	0.744038	−	1.28871i
$311$	10.9927	−	19.0400i	0.623340	−	1.07966i	−0.365519	−	0.930804i	$-0.619108\pi$
$311$	10.9927	−	19.0400i	0.623340	−	1.07966i	0.988859	−	0.148853i	$-0.0475582\pi$
$312$	10.1538	−	27.8973i	0.574846	−	1.57938i
$313$	6.94491	+	12.0289i	0.392549	+	0.679915i	0.992785	−	0.119908i	$-0.0382599\pi$
$313$	6.94491	+	12.0289i	0.392549	+	0.679915i	−0.600236	+	0.799823i	$0.704927\pi$
$314$	6.63404			0.374380
$315$	7.13816	−	2.59808i	0.402190	−	0.146385i
$316$	2.33544			0.131379
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	0.939680	−	0.342056i	$-0.111123\pi$
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	−0.766069	+	0.642759i	$0.777790\pi$
$318$	1.07532	+	1.28152i	0.0603011	+	0.0718640i
$319$	−2.05438	+	3.55829i	−0.115023	+	0.199226i
$320$	−10.8833	+	18.8504i	−0.608392	+	1.05377i
$321$	−11.1172	+	1.96026i	−0.620502	+	0.109411i
$322$	0.0714517	+	0.123758i	0.00398185	+	0.00689677i
$323$	−8.47565			−0.471598
$324$	−0.288800	−	1.63787i	−0.0160444	−	0.0909926i
$325$	8.21894			0.455905
$326$	−5.14543	−	8.91215i	−0.284979	−	0.493598i
$327$	18.1459	−	3.19961i	1.00347	−	0.176939i
$328$	−3.27719	+	5.67626i	−0.180952	+	0.313419i
$329$	2.66637	−	4.61830i	0.147002	−	0.254615i
$330$	−1.77719	−	2.11797i	−0.0978310	−	0.116590i
$331$	−5.36571	−	9.29369i	−0.294926	−	0.510827i	0.680041	−	0.733174i	$-0.261962\pi$
$331$	−5.36571	−	9.29369i	−0.294926	−	0.510827i	−0.974968	+	0.222346i	$0.928628\pi$
$332$	0.504748			0.0277016
$333$	−21.6506	+	7.88019i	−1.18645	+	0.431832i
$334$	−7.61949			−0.416920
$335$	12.2023	+	21.1351i	0.666685	+	1.15473i
$336$	2.13041	−	5.85327i	0.116224	−	0.319322i
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	−0.493518	−	0.869735i	$-0.664289\pi$
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	0.999972	−	0.00746831i	$-0.00237726\pi$
$338$	−14.0838	+	24.3938i	−0.766057	+	1.32685i
$339$	−3.06687	+	8.42615i	−0.166569	+	0.457645i
$340$	0.907604	+	1.57202i	0.0492217	+	0.0852545i
$341$	−3.59358			−0.194603
$342$	6.76470	+	5.67626i	0.365793	+	0.306937i
$343$	1.00000			0.0539949
$344$	1.80541	+	3.12706i	0.0973410	+	0.168600i
$345$	0.299011	+	0.356347i	0.0160982	+	0.0191851i
$346$	−14.1932	+	24.5834i	−0.763034	+	1.32161i
$347$	10.2062	−	17.6777i	0.547898	−	0.948987i	−0.450521	−	0.892766i	$-0.648762\pi$
$347$	10.2062	−	17.6777i	0.547898	−	0.948987i	0.998418	−	0.0562207i	$-0.0179050\pi$
$348$	−2.76786	+	0.488048i	−0.148373	+	0.0261621i
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	0.909750	−	0.415157i	$-0.136274\pi$
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	−0.814412	+	0.580288i	$0.802940\pi$
$350$	1.90167			0.101649
$351$			30.2569i			1.61500i
$352$	0.487511			0.0259844
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	0.701296	−	0.712871i	$-0.252605\pi$
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	−0.968012	+	0.250904i	$0.919272\pi$
$354$	1.69253	−	0.298439i	0.0899571	−	0.0158619i
$355$	−16.7554	+	29.0211i	−0.889283	+	1.54028i
$356$	−0.749686	+	1.29849i	−0.0397333	+	0.0688200i
$357$	−4.31908	−	5.14728i	−0.228590	−	0.272423i
$358$	3.44949	+	5.97470i	0.182311	+	0.315773i
$359$	9.48070			0.500372			0.250186	−	0.968198i	$-0.419508\pi$
$359$	9.48070			0.500372			0.250186	+	0.968198i	$0.419508\pi$
$360$	3.88279	−	22.0204i	0.204641	−	1.16058i
$361$	−14.2267			−0.748773
$362$	0.215537	+	0.373321i	0.0113284	+	0.0196213i
$363$	6.38666	−	17.5472i	0.335213	−	0.920989i
$364$	0.538019	−	0.931876i	0.0281998	−	0.0488436i
$365$	13.0005	−	22.5175i	0.680476	−	1.17862i
$366$	−0.764700	+	2.10100i	−0.0399715	+	0.109821i
$367$	−8.06670	−	13.9719i	−0.421079	−	0.729329i	0.574967	−	0.818177i	$-0.305015\pi$
$367$	−8.06670	−	13.9719i	−0.421079	−	0.729329i	−0.996045	+	0.0888474i	$0.971682\pi$
$368$	0.381445			0.0198842
$369$	1.15998	−	6.57856i	0.0603860	−	0.342466i
$370$	−26.2003			−1.36209
$371$	0.358441	+	0.620838i	0.0186093	+	0.0322323i
$372$	−1.58007	−	1.88305i	−0.0819228	−	0.0976318i
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	−0.988572	−	0.150752i	$-0.951831\pi$
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	0.624841	+	0.780752i	$0.285164\pi$
$374$	−1.22281	+	2.11797i	−0.0632301	+	0.109518i
$375$	−15.4991	+	2.73291i	−0.800371	+	0.141127i
$376$	−7.84864	−	13.5942i	−0.404763	−	0.701070i
$377$	51.1317			2.63341
$378$			7.00076i			0.360080i
$379$	16.0574			0.824812			0.412406	−	0.911000i	$-0.364689\pi$
$379$	16.0574			0.824812			0.412406	+	0.911000i	$0.364689\pi$
$380$	−0.511144	−	0.885328i	−0.0262212	−	0.0454164i
$381$	−15.1505	+	2.67144i	−0.776183	+	0.136862i
$382$	10.4868	−	18.1637i	0.536551	−	0.929334i
$383$	16.0103	−	27.7306i	0.818086	−	1.41697i	−0.0890039	−	0.996031i	$-0.528368\pi$
$383$	16.0103	−	27.7306i	0.818086	−	1.41697i	0.907090	−	0.420936i	$-0.138298\pi$
$384$	−10.5744	−	12.6021i	−0.539625	−	0.643100i
$385$	−0.592396	−	1.02606i	−0.0301913	−	0.0522929i
$386$	8.14022			0.414326
$387$	−2.81908	−	2.36549i	−0.143302	−	0.120244i
$388$	2.51392			0.127625
$389$	15.0214	+	26.0178i	0.761616	+	1.31916i	0.942017	+	0.335564i	$0.108927\pi$
$389$	15.0214	+	26.0178i	0.761616	+	1.31916i	−0.180402	+	0.983593i	$0.557740\pi$
$390$	−11.7679	+	32.3319i	−0.595889	+	1.63719i
$391$	0.205737	−	0.356347i	0.0104046	−	0.0180212i
$392$	1.47178	−	2.54920i	0.0743362	−	0.128754i
$393$	−6.73127	+	18.4940i	−0.339548	+	0.932899i
$394$	−16.9991	−	29.4433i	−0.856403	−	1.48333i
$395$	−32.0009			−1.61014
$396$	−0.243756	+	0.0887198i	−0.0122492	+	0.00445834i
$397$	−12.3200			−0.618321			−0.309160	−	0.951010i	$-0.600048\pi$
$397$	−12.3200			−0.618321			−0.309160	+	0.951010i	$0.600048\pi$
$398$	−2.04916	−	3.54925i	−0.102715	−	0.177908i
$399$	2.43242	+	2.89884i	0.121773	+	0.145124i
$400$	2.53802	−	4.39598i	0.126901	−	0.219799i
$401$	−10.4880	+	18.1657i	−0.523745	+	0.907152i	0.475873	+	0.879514i	$0.342132\pi$
$401$	−10.4880	+	18.1657i	−0.523745	+	0.907152i	−0.999618	+	0.0276385i	$0.991201\pi$
$402$	−22.1498	+	3.90560i	−1.10473	+	0.194794i
$403$	22.3603	+	38.7291i	1.11384	+	1.92923i
$404$	1.76920			0.0880210
$405$	3.95723	+	22.4426i	0.196637	+	1.11518i
$406$	11.8307			0.587147
$407$	1.79679	+	3.11213i	0.0890635	+	0.154263i
$408$	−19.4782	+	3.43453i	−0.964314	+	0.170034i
$409$	−12.8307	+	22.2234i	−0.634437	+	1.09888i	0.352197	+	0.935926i	$0.385435\pi$
$409$	−12.8307	+	22.2234i	−0.634437	+	1.09888i	−0.986634	+	0.162951i	$0.947899\pi$
$410$	3.79813	−	6.57856i	0.187576	−	0.324892i
$411$	6.37346	+	7.59559i	0.314379	+	0.374663i
$412$	0.281059	+	0.486809i	0.0138468	+	0.0239833i
$413$	0.736482			0.0362399
$414$	−0.402856	+	0.146628i	−0.0197993	+	0.00720635i
$415$	−6.91622			−0.339504
$416$	−3.03343	−	5.25406i	−0.148726	−	0.257601i
$417$	0.547352	−	1.50384i	0.0268039	−	0.0736432i
$418$	0.688663	−	1.19280i	0.0336836	−	0.0583417i
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	−0.847387	−	0.530976i	$-0.821825\pi$
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	0.883532	+	0.468370i	$0.155159\pi$
$420$	0.277189	−	0.761570i	0.0135254	−	0.0371608i
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	0.660965	−	0.750417i	$-0.270147\pi$
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	−0.980363	+	0.197203i	$0.936814\pi$
$422$	−7.34730			−0.357661
$423$	12.2554	+	10.2835i	0.595876	+	0.500000i
$424$	2.11019			0.102480
$425$	−2.73783	−	4.74205i	−0.132804	−	0.230023i
$426$	−19.8516	−	23.6583i	−0.961815	−	1.14625i
$427$	−0.479055	+	0.829748i	−0.0231831	+	0.0401543i
$428$	−0.602196	+	1.04303i	−0.0291083	+	0.0504170i
$429$	4.64749	−	0.819478i	0.224383	−	0.0395648i
$430$	−2.09240	−	3.62414i	−0.100904	−	0.174771i
$431$	17.7270			0.853879			0.426939	−	0.904280i	$-0.359592\pi$
$431$	17.7270			0.853879			0.426939	+	0.904280i	$0.359592\pi$
$432$	16.1832	+	9.34337i	0.778615	+	0.449533i
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$	5.17365	+	8.96102i	0.248343	+	0.430143i
$435$	37.9261	−	6.68739i	1.81842	−	0.320636i
$436$	0.982926	−	1.70248i	0.0470736	−	0.0815339i
$437$	−0.115867	+	0.200688i	−0.00554267	+	0.00960019i
$438$	15.4029	+	18.3564i	0.735977	+	0.877103i
$439$	−14.9277	−	25.8555i	−0.712459	−	1.23401i	−0.963931	−	0.266151i	$-0.914248\pi$
$439$	−14.9277	−	25.8555i	−0.712459	−	1.23401i	0.251473	−	0.967864i	$-0.419085\pi$
$440$	−3.48751			−0.166261
$441$	−0.520945	+	2.95442i	−0.0248069	+	0.140687i
$442$	30.4347			1.44763
$443$	−5.33275	−	9.23659i	−0.253367	−	0.438844i	0.711084	−	0.703107i	$-0.248205\pi$
$443$	−5.33275	−	9.23659i	−0.253367	−	0.438844i	−0.964451	+	0.264263i	$0.914871\pi$
$444$	−0.840738	+	2.30991i	−0.0398996	+	0.109623i
$445$	10.2724	−	17.7924i	0.486960	−	0.843440i
$446$	−9.56077	+	16.5597i	−0.452716	+	0.784127i
$447$	−5.16843	+	14.2002i	−0.244459	+	0.671644i
$448$	−4.29813	−	7.44459i	−0.203068	−	0.351724i
$449$	3.55438			0.167741			0.0838707	−	0.996477i	$-0.473272\pi$
$449$	3.55438			0.167741			0.0838707	+	0.996477i	$0.473272\pi$
$450$	−0.990667	+	5.61835i	−0.0467005	+	0.264852i
$451$	−1.04189			−0.0490606
$452$	0.478340	+	0.828510i	0.0224992	+	0.0389698i
$453$	−20.5155	−	24.4494i	−0.963901	−	1.14873i
$454$	1.94949	−	3.37662i	0.0914942	−	0.158473i
$455$	−7.37211	+	12.7689i	−0.345610	+	0.598614i
$456$	10.9697	−	1.93426i	0.513704	−	0.0905799i
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	0.801283	−	0.598285i	$-0.204151\pi$
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	−0.918772	+	0.394789i	$0.870818\pi$
$458$	12.3514			0.577144
$459$	17.4572	−	10.0789i	0.814834	−	0.470445i
$460$	0.0496299			0.00231400
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	0.566955	−	0.823749i	$-0.308121\pi$
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	−0.996865	+	0.0791233i	$0.974788\pi$
$462$	1.07532	−	0.189608i	0.0500285	−	0.00882138i
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	−0.651897	−	0.758307i	$-0.726027\pi$
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	0.982662	+	0.185406i	$0.0593600\pi$
$464$	15.7895	−	27.3482i	0.733010	−	1.26961i
$465$	21.6506	+	25.8022i	1.00402	+	1.19655i
$466$	−8.94016	−	15.4848i	−0.414145	−	0.717320i
$467$	−3.36865			−0.155883			−0.0779413	−	0.996958i	$-0.524835\pi$
$467$	−3.36865			−0.155883			−0.0779413	+	0.996958i	$0.524835\pi$
$468$	2.47288	+	2.07499i	0.114309	+	0.0959165i
$469$	−9.63816			−0.445049
$470$	9.09627	+	15.7552i	0.419579	+	0.726733i
$471$	−2.91694	+	8.01422i	−0.134405	+	0.369276i
$472$	1.08394	−	1.87744i	0.0498924	−	0.0864162i
$473$	−0.286989	+	0.497079i	−0.0131958	+	0.0228557i
$474$	10.0869	−	27.7136i	0.463308	−	1.27293i
$475$	1.54189	+	2.67063i	0.0707467	+	0.122537i
$476$	−0.716881			−0.0328582
$477$	−2.02094	+	0.735564i	−0.0925327	+	0.0336791i
$478$	12.8494			0.587716
$479$	18.3833	+	31.8407i	0.839952	+	1.45484i	0.889934	+	0.456090i	$0.150751\pi$
$479$	18.3833	+	31.8407i	0.839952	+	1.45484i	−0.0499812	+	0.998750i	$0.515916\pi$
$480$	−2.93717	−	3.50038i	−0.134063	−	0.159770i
$481$	22.3603	−	38.7291i	1.01954	−	1.76589i
$482$	6.03462	−	10.4523i	0.274869	−	0.476087i
$483$	−0.180922	+	0.0319015i	−0.00823224	+	0.00145157i
$484$	−0.996130	−	1.72535i	−0.0452786	−	0.0784249i
$485$	−34.4466			−1.56414
$486$	−20.6832	−	3.64701i	−0.938209	−	0.165432i
$487$	−37.4175			−1.69555			−0.847773	−	0.530358i	$-0.822057\pi$
$487$	−37.4175			−1.69555			−0.847773	+	0.530358i	$0.822057\pi$
$488$	1.41013	+	2.44242i	0.0638336	+	0.110563i
$489$	13.0287	−	2.29731i	0.589178	−	0.103888i
$490$	−1.70574	+	2.95442i	−0.0770573	+	0.133467i
$491$	13.3353	−	23.0974i	0.601813	−	1.04237i	−0.390734	−	0.920504i	$-0.627779\pi$
$491$	13.3353	−	23.0974i	0.601813	−	1.04237i	0.992547	−	0.121866i	$-0.0388879\pi$
$492$	−0.458111	−	0.545955i	−0.0206532	−	0.0246136i
$493$	−17.0326	−	29.5013i	−0.767108	−	1.32867i
$494$	−17.1402			−0.771175
$495$	3.34002	−	1.21567i	0.150123	−	0.0546402i
$496$	27.6195			1.24015
$497$	−6.61721	−	11.4613i	−0.296822	−	0.514112i
$498$	2.18004	−	5.98962i	0.0976901	−	0.268401i
$499$	−16.8726	+	29.2242i	−0.755320	+	1.30825i	0.189895	+	0.981804i	$0.439185\pi$
$499$	−16.8726	+	29.2242i	−0.755320	+	1.30825i	−0.945215	+	0.326449i	$0.894148\pi$
$500$	−0.839556	+	1.45415i	−0.0375461	+	0.0650317i
$501$	3.35023	−	9.20469i	0.149677	−	0.411235i
$502$	16.8400	+	29.1678i	0.751607	+	1.30182i
$503$	−32.0401			−1.42860			−0.714299	−	0.699840i	$-0.753255\pi$
$503$	−32.0401			−1.42860			−0.714299	+	0.699840i	$0.753255\pi$
$504$	6.76470	+	5.67626i	0.301324	+	0.252841i
$505$	−24.2422			−1.07876
$506$	0.0334331	+	0.0579078i	0.00148628	+	0.00257431i
$507$	−23.2763	−	27.7396i	−1.03374	−	1.23196i
$508$	−0.820670	+	1.42144i	−0.0364114	+	0.0630663i
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	−0.764550	−	0.644564i	$-0.777039\pi$
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	0.940484	+	0.339838i	$0.110372\pi$
$510$	22.5744	−	3.98048i	0.999613	−	0.176259i
$511$	5.13429	+	8.89284i	0.227127	+	0.393396i
$512$	−24.9186			−1.10126
$513$	−9.83157	+	5.67626i	−0.434074	+	0.250613i
$514$	14.6209			0.644901
$515$	−3.85117	−	6.67042i	−0.169703	−	0.293934i
$516$	−0.386659	+	0.0681784i	−0.0170217	+	0.00300139i
$517$	1.24763	−	2.16095i	0.0548705	−	0.0950386i
$518$	5.17365	−	8.96102i	0.227317	−	0.393725i
$519$	−23.4572	−	27.9552i	−1.02966	−	1.22710i
$520$	21.7003	+	37.5860i	0.951620	+	1.64825i
$521$	−14.6750			−0.642923			−0.321462	−	0.946923i	$-0.604174\pi$
$521$	−14.6750			−0.642923			−0.321462	+	0.946923i	$0.604174\pi$
$522$	−6.16313	+	34.9529i	−0.269753	+	1.52985i
$523$	28.3432			1.23936			0.619680	−	0.784854i	$-0.287262\pi$
$523$	28.3432			1.23936			0.619680	+	0.784854i	$0.287262\pi$
$524$	1.04988	+	1.81844i	0.0458641	+	0.0794390i
$525$	−0.836152	+	2.29731i	−0.0364927	+	0.100263i
$526$	−17.5737	+	30.4386i	−0.766251	+	1.32719i
$527$	14.8969	−	25.8022i	0.648920	−	1.12396i
$528$	0.996845	−	2.73881i	0.0433821	−	0.119191i
$529$	11.4944	+	19.9088i	0.499755	+	0.865602i
$530$	−2.44562			−0.106231
$531$	−0.383666	+	2.17588i	−0.0166497	+	0.0944251i
$532$	0.403733			0.0175041
$533$	6.48293	+	11.2288i	0.280807	+	0.486371i
$534$	12.1707	+	14.5045i	0.526678	+	0.627671i
$535$	8.25150	−	14.2920i	0.356743	−	0.617898i
$536$	−14.1853	+	24.5696i	−0.612710	+	1.06124i
$537$	−8.73442	+	1.54011i	−0.376918	+	0.0664608i
$538$	5.14203	+	8.90625i	0.221688	+	0.383976i
$539$	0.467911			0.0201544
$540$	2.10560	+	1.21567i	0.0906106	+	0.0523141i
$541$	11.2858			0.485215			0.242607	−	0.970125i	$-0.421997\pi$
$541$	11.2858			0.485215			0.242607	+	0.970125i	$0.421997\pi$
$542$	−2.29292	−	3.97145i	−0.0984893	−	0.170588i
$543$	−0.545759	+	0.0962321i	−0.0234208	+	0.00412972i
$544$	−2.02094	+	3.50038i	−0.0866473	+	0.150077i
$545$	−13.4684	+	23.3279i	−0.576922	+	0.999258i
$546$	−8.73442	−	10.4093i	−0.373799	−	0.445476i
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	0.988519	+	0.151099i	$0.0482812\pi$
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	−0.363404	+	0.931632i	$0.618385\pi$
$548$	1.05787			0.0451899
$549$	−2.20187	−	1.84759i	−0.0939734	−	0.0788530i
$550$	0.889814			0.0379418
$551$	9.59240	+	16.6145i	0.408650	+	0.707802i
$552$	−0.184955	+	0.508159i	−0.00787219	+	0.0216287i
$553$	6.31908	−	10.9450i	0.268715	−	0.465427i
$554$	3.85457	−	6.67631i	0.163765	−	0.283649i
$555$	11.5201	−	31.6511i	0.489000	−	1.34352i
$556$	−0.0853707	−	0.147866i	−0.00362052	−	0.00627093i
$557$	−0.775682			−0.0328667			−0.0164334	−	0.999865i	$-0.505231\pi$
$557$	−0.775682			−0.0328667			−0.0164334	+	0.999865i	$0.505231\pi$
$558$	−29.1698	+	10.6170i	−1.23486	+	0.449451i
$559$	7.14290			0.302113
$560$	4.55303	+	7.88609i	0.192401	+	0.333248i
$561$	−2.02094	−	2.40847i	−0.0853243	−	0.101686i
$562$	−19.1163	+	33.1105i	−0.806374	+	1.39668i
$563$	−12.4761	+	21.6093i	−0.525806	+	0.910722i	0.473742	+	0.880663i	$0.342903\pi$
$563$	−12.4761	+	21.6093i	−0.525806	+	0.910722i	−0.999548	+	0.0300588i	$0.990431\pi$
$564$	1.68092	−	0.296392i	0.0707796	−	0.0124804i
$565$	−6.55438	−	11.3525i	−0.275745	−	0.477604i
$566$	6.15888			0.258877
$567$	−8.45723	−	3.07818i	−0.355170	−	0.129271i
$568$	−38.9564			−1.63457
$569$	12.4017	+	21.4803i	0.519905	+	0.900502i	0.999732	+	0.0231391i	$0.00736608\pi$
$569$	12.4017	+	21.4803i	0.519905	+	0.900502i	−0.479827	+	0.877363i	$0.659301\pi$
$570$	−12.7135	+	2.24173i	−0.532509	+	0.0938957i
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	−0.943260	−	0.332055i	$-0.892258\pi$
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	0.759198	+	0.650860i	$0.225591\pi$
$572$	0.251745	−	0.436035i	0.0105260	−	0.0182315i
$573$	17.3316	+	20.6550i	0.724037	+	0.862873i
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$	−0.149711			−0.00624336
$576$	24.2335	−	8.82029i	1.00973	−	0.367512i
$577$	−12.8743			−0.535965			−0.267983	−	0.963424i	$-0.586357\pi$
$577$	−12.8743			−0.535965			−0.267983	+	0.963424i	$0.586357\pi$
$578$	1.31386	+	2.27568i	0.0546495	+	0.0946557i
$579$	−3.57919	+	9.83375i	−0.148746	+	0.408677i
$580$	2.05438	−	3.55829i	0.0853034	−	0.147750i
$581$	1.36571	−	2.36549i	0.0566594	−	0.0981369i
$582$	10.8578	−	29.8316i	0.450071	−	1.23656i
$583$	0.167718	+	0.290497i	0.00694619	+	0.0120311i
$584$	30.2262			1.25077
$585$	−33.8842	−	28.4322i	−1.40094	−	1.17553i
$586$	5.83069			0.240864
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.790190	−	0.612861i	$-0.790018\pi$
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.135658	−	0.990756i	$-0.543315\pi$
$588$	0.205737	+	0.245188i	0.00848445	+	0.0101114i
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$	−1.25624	+	2.17588i	−0.0517188	+	0.0895795i
$591$	43.0433	−	7.58969i	1.77056	−	0.312198i
$592$	−13.8097	−	23.9192i	−0.567577	−	0.983072i
$593$	3.76053			0.154426			0.0772131	−	0.997015i	$-0.475398\pi$
$593$	3.76053			0.154426			0.0772131	+	0.997015i	$0.475398\pi$
$594$			3.27573i			0.134405i
$595$	9.82295			0.402702
$596$	0.806123	+	1.39625i	0.0330201	+	0.0571924i
$597$	5.18866	−	0.914901i	0.212358	−	0.0374444i
$598$	0.416060	−	0.720637i	0.0170139	−	0.0294690i
$599$	1.84524	−	3.19604i	0.0753943	−	0.130587i	−0.825863	−	0.563870i	$-0.809312\pi$
$599$	1.84524	−	3.19604i	0.0753943	−	0.130587i	0.901258	+	0.433283i	$0.142645\pi$
$600$	4.62567	+	5.51266i	0.188842	+	0.225053i
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	0.998107	−	0.0615091i	$-0.0195913\pi$
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$602$	1.65270			0.0673592
$603$	5.02094	−	28.4752i	0.204469	−	1.15960i
$604$	−3.40516			−0.138554
$605$	13.6493	+	23.6413i	0.554923	+	0.961155i
$606$	7.64131	−	20.9943i	0.310407	−	0.852836i
$607$	−12.1973	+	21.1263i	−0.495072	+	0.857490i	−0.999984	−	0.00568063i	$-0.998192\pi$
$607$	−12.1973	+	21.1263i	−0.495072	+	0.857490i	0.504911	+	0.863171i	$0.331525\pi$
$608$	1.13816	−	1.97134i	0.0461583	−	0.0799485i
$609$	−5.20187	+	14.2920i	−0.210790	+	0.579142i
$610$	−1.63429	−	2.83067i	−0.0661703	−	0.114610i
$611$	−31.0523			−1.25624
$612$	0.373455	−	2.11797i	0.0150960	−	0.0856139i
$613$	42.0215			1.69723			0.848616	−	0.529010i	$-0.177437\pi$
$613$	42.0215			1.69723			0.848616	+	0.529010i	$0.177437\pi$
$614$	−8.33796	−	14.4418i	−0.336493	−	0.582823i
$615$	6.27719	+	7.48086i	0.253121	+	0.301657i
$616$	0.688663	−	1.19280i	0.0277470	−	0.0480592i
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.158125	+	0.987419i	$0.550545\pi$
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.776068	+	0.630650i	$0.782788\pi$
$618$	6.99067	−	1.23264i	0.281206	−	0.0495842i
$619$	13.6047	+	23.5641i	0.546820	+	0.947120i	0.998490	+	0.0549349i	$0.0174951\pi$
$619$	13.6047	+	23.5641i	0.546820	+	0.947120i	−0.451670	+	0.892185i	$0.649172\pi$
$620$	3.59358			0.144322
$621$		−	0.551139i		−	0.0221165i
$622$	−29.6209			−1.18769
$623$	4.05690	+	7.02676i	0.162536	+	0.281521i
$624$	−35.7196	+	6.29833i	−1.42993	+	0.252135i
$625$	15.0326	−	26.0372i	0.601302	−	1.04149i
$626$	9.35685	−	16.2065i	0.373975	−	0.647743i
$627$	1.13816	+	1.35640i	0.0454536	+	0.0541694i
$628$	0.454956	+	0.788006i	0.0181547	+	0.0314449i
$629$	−29.7939			−1.18796
$630$	−7.84002	−	6.57856i	−0.312354	−	0.262096i
$631$	−29.6023			−1.17845			−0.589224	−	0.807970i	$-0.700566\pi$
$631$	−29.6023			−1.17845			−0.589224	+	0.807970i	$0.700566\pi$
$632$	−18.6006	−	32.2172i	−0.739892	−	1.28153i
$633$	3.23055	−	8.87587i	0.128403	−	0.352784i
$634$	4.16456	−	7.21324i	0.165396	−	0.286474i
$635$	11.2451	−	19.4771i	0.446248	−	0.772925i
$636$	−0.0784773	+	0.215615i	−0.00311183	+	0.00854968i
$637$	−2.91147	−	5.04282i	−0.115357	−	0.199804i
$638$	5.53571			0.219161
$639$	37.3089	−	13.5793i	1.47592	−	0.537189i
$640$	24.0496			0.950645
$641$	0.139500	+	0.241621i	0.00550991	+	0.00954345i	0.868767	−	0.495221i	$-0.164913\pi$
$641$	0.139500	+	0.241621i	0.00550991	+	0.00954345i	−0.863257	+	0.504764i	$0.831579\pi$
$642$	9.77631	+	11.6510i	0.385840	+	0.459826i
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	−0.628181	−	0.778067i	$-0.716200\pi$
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	0.987916	+	0.154988i	$0.0495338\pi$
$644$	−0.00980018	+	0.0169744i	−0.000386181	+	0.000668885i
$645$	5.29813	−	0.934204i	0.208614	−	0.0367842i
$646$	5.70961	+	9.88933i	0.224642	+	0.389090i
$647$	22.4570			0.882875			0.441438	−	0.897292i	$-0.354469\pi$
$647$	22.4570			0.882875			0.441438	+	0.897292i	$0.354469\pi$
$648$	−20.2941	+	17.0288i	−0.797228	+	0.668953i
$649$	0.344608			0.0135270
$650$	−5.53667	−	9.58980i	−0.217166	−	0.376143i
$651$	−13.1001	+	2.30991i	−0.513435	+	0.0905324i
$652$	0.705737	−	1.22237i	0.0276388	−	0.0478718i
$653$	25.2656	−	43.7614i	0.988721	−	1.71251i	0.364655	−	0.931143i	$-0.381187\pi$
$653$	25.2656	−	43.7614i	0.988721	−	1.71251i	0.624066	−	0.781372i	$-0.285480\pi$
$654$	−15.9572	−	19.0171i	−0.623977	−	0.743627i
$655$	−14.3858	−	24.9169i	−0.562099	−	0.973584i
$656$	8.00774			0.312650
$657$	−28.9479	+	10.5362i	−1.12937	+	0.411055i
$658$	−7.18479			−0.280092
$659$	1.33631	+	2.31456i	0.0520554	+	0.0901626i	0.890879	−	0.454241i	$-0.150089\pi$
$659$	1.33631	+	2.31456i	0.0520554	+	0.0901626i	−0.838824	+	0.544403i	$0.816756\pi$
$660$	0.129700	−	0.356347i	0.00504855	−	0.0138708i
$661$	17.3050	−	29.9731i	0.673086	−	1.16582i	−0.303938	−	0.952692i	$-0.598302\pi$
$661$	17.3050	−	29.9731i	0.673086	−	1.16582i	0.977024	−	0.213128i	$-0.0683651\pi$
$662$	−7.22921	+	12.5214i	−0.280971	+	0.486656i
$663$	−13.3819	+	36.7665i	−0.519710	+	1.42789i
$664$	−4.02007	−	6.96296i	−0.156009	−	0.270215i
$665$	−5.53209			−0.214525
$666$	23.7795	+	19.9533i	0.921436	+	0.773176i
$667$	−0.931379			−0.0360631
$668$	−0.522537	−	0.905061i	−0.0202176	−	0.0350179i
$669$	−15.8011	−	18.8310i	−0.610907	−	0.728050i
$670$	16.4402	−	28.4752i	0.635139	−	1.10009i
$671$	−0.224155	+	0.388249i	−0.00865342	+	0.0149882i
$672$	1.77719	−	0.313366i	0.0685565	−	0.0120884i
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	0.661869	−	0.749619i	$-0.269763\pi$
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	−0.980124	+	0.198386i	$0.936430\pi$
$674$	−25.0523			−0.964979
$675$	−6.35163	−	3.66712i	−0.244474	−	0.141147i
$676$	−3.86341			−0.148593
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	0.889154	+	0.457608i	$0.151294\pi$
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	−0.0482766	+	0.998834i	$0.515373\pi$
$678$	11.8976	−	2.09786i	0.456923	−	0.0805678i
$679$	6.80200	−	11.7814i	0.261037	−	0.452129i
$680$	14.4572	−	25.0407i	0.554410	−	0.960266i
$681$	3.22193	+	3.83975i	0.123465	+	0.147140i
$682$	2.42081	+	4.19296i	0.0926975	+	0.160557i
$683$	28.2412			1.08062			0.540310	−	0.841466i	$-0.318307\pi$
$683$	28.2412			1.08062			0.540310	+	0.841466i	$0.318307\pi$
$684$	−0.210323	+	1.19280i	−0.00804189	+	0.0456078i
$685$	−14.4953			−0.553835
$686$	−0.673648	−	1.16679i	−0.0257200	−	0.0445484i
$687$	−5.43083	+	14.9211i	−0.207199	+	0.569274i
$688$	2.20574	−	3.82045i	0.0840929	−	0.145653i
$689$	2.08718	−	3.61510i	0.0795153	−	0.137725i
$690$	0.214355	−	0.588936i	0.00816036	−	0.0224204i
$691$	14.5326	+	25.1711i	0.552844	+	0.957555i	0.998068	+	0.0621351i	$0.0197910\pi$
$691$	14.5326	+	25.1711i	0.552844	+	0.957555i	−0.445223	+	0.895420i	$0.646876\pi$
$692$	−3.89344			−0.148006
$693$	−0.243756	+	1.38241i	−0.00925951	+	0.0525133i
$694$	−27.5016			−1.04395
$695$	1.16978	+	2.02611i	0.0443722	+	0.0768549i
$696$	28.7772	+	34.2953i	1.09080	+	1.29996i
$697$	4.31908	−	7.48086i	0.163597	−	0.283358i
$698$	2.39961	−	4.15625i	0.0908268	−	0.157317i
$699$	22.6373	−	3.99156i	0.856221	−	0.150975i
$700$	0.130415	+	0.225885i	0.00492922	+	0.00853766i
$701$	−1.10876			−0.0418771			−0.0209386	−	0.999781i	$-0.506665\pi$
$701$	−1.10876			−0.0418771			−0.0209386	+	0.999781i	$0.506665\pi$
$702$	35.3036	−	20.3825i	1.33245	−	0.769289i
$703$	16.7793			0.632843
$704$	−2.01114	−	3.48340i	−0.0757979	−	0.131286i
$705$	−23.0326	+	4.06126i	−0.867456	+	0.152956i
$706$	−6.75150	+	11.6939i	−0.254096	+	0.440107i
$707$	4.78699	−	8.29131i	0.180033	−	0.311827i
$708$	0.151522	+	0.180576i	0.00569453	+	0.00678648i
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	0.985680	−	0.168626i	$-0.0539329\pi$
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	−0.638874	+	0.769311i	$0.720600\pi$
$710$	45.1489			1.69441
$711$	29.0442	+	24.3709i	1.08924	+	0.913982i
$712$	23.8835			0.895072
$713$	−0.407299	−	0.705463i	−0.0152535	−	0.0264198i
$714$	−3.09627	+	8.50692i	−0.115875	+	0.318364i
$715$	−3.44949	+	5.97470i	−0.129004	+	0.223441i
$716$	−0.473126	+	0.819478i	−0.0176815	+	0.0306253i
$717$	−5.64977	+	15.5226i	−0.210994	+	0.579702i
$718$	−6.38666	−	11.0620i	−0.238348	−	0.412831i
$719$	−33.7769			−1.25967			−0.629834	−	0.776730i	$-0.716877\pi$
$719$	−33.7769			−1.25967			−0.629834	+	0.776730i	$0.716877\pi$
$720$	−25.6707	+	9.34337i	−0.956691	+	0.348207i
$721$	3.04189			0.113286
$722$	9.58378	+	16.5996i	0.356671	+	0.617773i
$723$	9.97343	+	11.8859i	0.370916	+	0.442040i
$724$	−0.0295627	+	0.0512040i	−0.00109869	+	0.00190298i
$725$	−6.19712	+	10.7337i	−0.230155	+	0.398641i
$726$	−24.7763	+	4.36873i	−0.919535	+	0.162139i
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	0.667095	−	0.744973i	$-0.267538\pi$
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	−0.978713	+	0.205234i	$0.934204\pi$
$728$	−17.1402			−0.635259
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−35.0310			−1.29655
$731$	−2.37939	−	4.12122i	−0.0880047	−	0.152429i
$732$	−0.302004	+	0.0532514i	−0.0111624	+	0.00196823i
$733$	6.81820	−	11.8095i	0.251836	−	0.436193i	−0.712195	−	0.701981i	$-0.752299\pi$
$733$	6.81820	−	11.8095i	0.251836	−	0.436193i	0.964031	+	0.265789i	$0.0856323\pi$
$734$	−10.8682	+	18.8243i	−0.401154	+	0.694819i
$735$	−2.81908	−	3.35965i	−0.103983	−	0.123922i
$736$	0.0552549	+	0.0957044i	0.00203672	+	0.00352771i
$737$	−4.50980			−0.166121
$738$	−8.45723	+	3.07818i	−0.311315	+	0.113309i
$739$	−32.0419			−1.17868			−0.589340	−	0.807885i	$-0.700612\pi$
$739$	−32.0419			−1.17868			−0.589340	+	0.807885i	$0.700612\pi$
$740$	−1.79679	−	3.11213i	−0.0660513	−	0.114404i
$741$	7.53643	−	20.7062i	0.276858	−	0.760660i
$742$	0.482926	−	0.836452i	0.0177288	−	0.0307071i
$743$	−16.8764	+	29.2309i	−0.619137	+	1.07238i	0.370507	+	0.928830i	$0.379184\pi$
$743$	−16.8764	+	29.2309i	−0.619137	+	1.07238i	−0.989644	+	0.143547i	$0.954149\pi$
$744$	−13.3921	+	36.7946i	−0.490979	+	1.34895i
$745$	−11.0458	−	19.1318i	−0.404685	−	0.700936i
$746$	18.9290			0.693040
$747$	6.27719	+	5.26719i	0.229670	+	0.192716i
$748$	−0.335437			−0.0122648
$749$	3.25877	+	5.64436i	0.119073	+	0.206240i
$750$	13.6297	+	16.2432i	0.497686	+	0.593119i
$751$	−13.0582	+	22.6175i	−0.476502	+	0.825326i	−0.999637	−	0.0269236i	$-0.991429\pi$
$751$	−13.0582	+	22.6175i	−0.476502	+	0.825326i	0.523135	+	0.852250i	$0.324762\pi$
$752$	−9.58899	+	16.6086i	−0.349675	+	0.605654i
$753$	−42.6404	+	7.51866i	−1.55390	+	0.273995i
$754$	−34.4447	−	59.6600i	−1.25440	−	2.17269i
$755$	46.6587			1.69808
$756$	−0.831566	+	0.480105i	−0.0302438	+	0.0174613i
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$	−10.8170	−	18.7356i	−0.392892	−	0.680509i
$759$	−0.0846555	+	0.0149270i	−0.00307280	+	0.000541817i
$760$	−8.14203	+	14.1024i	−0.295342	+	0.511548i
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	0.214148	+	0.976801i	$0.431302\pi$
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	−0.953009	+	0.302943i	$0.902031\pi$
$762$	13.3231	+	15.8779i	0.482645	+	0.575194i
$763$	−5.31908	−	9.21291i	−0.192564	−	0.333530i
$764$	2.87670			0.104075
$765$	−5.11721	+	29.0211i	−0.185013	+	1.04926i
$766$	−43.1411			−1.55875
$767$	−2.14425	−	3.71395i	−0.0774243	−	0.134103i
$768$	2.60417	−	7.15490i	0.0939699	−	0.258180i
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	0.253639	+	0.967299i	$0.418373\pi$
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	−0.964525	+	0.263992i	$0.914961\pi$
$770$	−0.798133	+	1.38241i	−0.0287627	+	0.0498185i
$771$	−6.42871	+	17.6627i	−0.231524	+	0.636108i
$772$	0.558248	+	0.966914i	0.0200918	+	0.0348000i
$773$	24.9026			0.895685			0.447842	−	0.894113i	$-0.352193\pi$
$773$	24.9026			0.895685			0.447842	+	0.894113i	$0.352193\pi$
$774$	−0.860967	+	4.88279i	−0.0309468	+	0.175508i
$775$	−10.8402			−0.389391
$776$	−20.0221	−	34.6793i	−0.718752	−	1.24492i
$777$	8.55051	+	10.1901i	0.306748	+	0.365568i
$778$	20.2383	−	35.0538i	0.725578	−	1.25674i
$779$	−2.43242	+	4.21307i	−0.0871504	+	0.150949i
$780$	−4.64749	+	0.819478i	−0.166407	+	0.0293420i
$781$	−3.09627	−	5.36289i	−0.110793	−	0.191899i
$782$	−0.554378			−0.0198245
$783$	−39.5148	−	22.8139i	−1.41214	−	0.815301i
$784$	−3.59627			−0.128438
$785$	−6.23396	−	10.7975i	−0.222499	−	0.385380i
$786$	26.1132	−	4.60446i	0.931426	−	0.164236i
$787$	15.3525	−	26.5913i	0.547258	−	0.947879i	−0.451203	−	0.892421i	$-0.649005\pi$
$787$	15.3525	−	26.5913i	0.547258	−	0.947879i	0.998461	−	0.0554572i	$-0.0176616\pi$
$788$	2.33157	−	4.03839i	0.0830586	−	0.143862i
$789$	−29.0442	−	34.6135i	−1.03400	−	1.23227i
$790$	21.5574	+	37.3385i	0.766977	+	1.32844i
$791$	5.17705			0.184075
$792$	3.16528	+	2.65598i	0.112473	+	0.0943763i
$793$	5.57903			0.198117
$794$	8.29932	+	14.3748i	0.294532	+	0.510144i
$795$	1.07532	−	2.95442i	0.0381377	−	0.104783i
$796$	0.281059	−	0.486809i	0.00996188	−	0.0172545i
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	−0.751858	−	0.659325i	$-0.770842\pi$
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	0.946921	+	0.321466i	$0.104175\pi$
$798$	1.74376	−	4.79093i	0.0617283	−	0.169597i
$799$	10.3439	+	17.9161i	0.365941	+	0.633828i
$800$	1.47060			0.0519935
$801$	−22.8735	+	8.32526i	−0.808194	+	0.294158i
$802$	28.2608			0.997925
$803$	2.40239	+	4.16106i	0.0847785	+	0.146841i
$804$	−1.98293	−	2.36316i	−0.0699324	−	0.0833422i
$805$	0.134285	−	0.232589i	0.00473294	−	0.00819769i
$806$	30.1259	−	52.1796i	1.06114	−	1.83795i
$807$	−13.0201	+	2.29579i	−0.458328	+	0.0808156i
$808$	−14.0908	−	24.4060i	−0.495713	−	0.858600i
$809$	16.9881			0.597271			0.298636	−	0.954367i	$-0.403468\pi$
$809$	16.9881			0.597271			0.298636	+	0.954367i	$0.403468\pi$
$810$	23.5201	−	19.7357i	0.826411	−	0.693441i
$811$	37.9796			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$811$	37.9796			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$812$	0.811337	+	1.40528i	0.0284723	+	0.0493156i
$813$	5.80587	−	1.02373i	0.203621	−	0.0359039i
$814$	2.42081	−	4.19296i	0.0848493	−	0.146963i
$815$	−9.67024	+	16.7494i	−0.338734	+	0.586704i
$816$	15.5326	+	18.5110i	0.543748	+	0.648014i
$817$	1.34002	+	2.32099i	0.0468814	+	0.0812011i
$818$	34.5735			1.20883
$819$	16.4153	−	5.97470i	0.573599	−	0.208773i
$820$	1.04189			0.0363843
$821$	−4.13934	−	7.16954i	−0.144464	−	0.250219i	0.784709	−	0.619864i	$-0.212812\pi$
$821$	−4.13934	−	7.16954i	−0.144464	−	0.250219i	−0.929173	+	0.369646i	$0.879479\pi$
$822$	4.56901	−	12.5533i	0.159363	−	0.437845i
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.207077	+	0.978325i	$0.566395\pi$
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.743716	+	0.668496i	$0.766938\pi$
$824$	4.47700	−	7.75438i	0.155964	−	0.270137i
$825$	−0.391245	+	1.07494i	−0.0136214	+	0.0374245i
$826$	−0.496130	−	0.859322i	−0.0172626	−	0.0298996i
$827$	−31.8708			−1.10826			−0.554129	−	0.832431i	$-0.686948\pi$
$827$	−31.8708			−1.10826			−0.554129	+	0.832431i	$0.686948\pi$
$828$	−0.0450442	−	0.0377966i	−0.00156540	−	0.00131352i
$829$	−0.352349			−0.0122376			−0.00611879	−	0.999981i	$-0.501948\pi$
$829$	−0.352349			−0.0122376			−0.00611879	+	0.999981i	$0.501948\pi$
$830$	4.65910	+	8.06980i	0.161720	+	0.280107i
$831$	6.37046	+	7.59202i	0.220989	+	0.263364i
$832$	−25.0278	+	43.3494i	−0.867683	+	1.50287i
$833$	−1.93969	+	3.35965i	−0.0672064	+	0.116405i
$834$	−2.12339	+	0.374411i	−0.0735270	+	0.0129648i
$835$	7.15998	+	12.4014i	0.247781	+	0.429170i
$836$	0.188911			0.00653363
$837$		−	39.9067i		−	1.37938i
$838$	−1.99369			−0.0688709
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	0.565215	−	0.824944i	$-0.308793\pi$
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	−0.997030	+	0.0770182i	$0.975460\pi$
$840$	−12.7135	+	2.24173i	−0.438657	+	0.0773470i
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$	−8.82951	+	15.2932i	−0.304285	+	0.527037i
$843$	−31.5936	−	37.6518i	−1.08814	−	1.29680i
$844$	−0.503870	−	0.872729i	−0.0173439	−	0.0300406i
$845$	52.9377			1.82111
$846$	3.74288	−	21.2269i	0.128683	−	0.729796i
$847$	−10.7811			−0.370442
$848$	−1.28905	−	2.23270i	−0.0442661	−	0.0766711i
$849$	−2.70801	+	7.44021i	−0.0929388	+	0.255347i
$850$	−3.68866	+	6.38895i	−0.126520	+	0.219139i
$851$	−0.407299	+	0.705463i	−0.0139620	+	0.0241829i
$852$	1.44878	−	3.98048i	0.0496343	−	0.136369i
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	0.306706	−	0.951804i	$-0.400773\pi$
$854$	1.29086			0.0441723
$855$	2.88191	−	16.3441i	0.0985593	−	0.558958i
$856$	19.1848			0.655723
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	0.691210	−	0.722654i	$-0.257078\pi$
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	−0.971442	+	0.237278i	$0.923745\pi$
$858$	−4.08693	−	4.87062i	−0.139526	−	0.166280i
$859$	13.4162	−	23.2376i	0.457756	−	0.792856i	−0.541086	−	0.840967i	$-0.681987\pi$
$859$	13.4162	−	23.2376i	0.457756	−	0.792856i	0.998842	+	0.0481111i	$0.0153201\pi$
$860$	0.286989	−	0.497079i	0.00978624	−	0.0169503i
$861$	−3.79813	+	0.669713i	−0.129440	+	0.0228238i
$862$	−11.9418	−	20.6837i	−0.406738	−	0.704490i
$863$	14.5057			0.493779			0.246890	−	0.969044i	$-0.420592\pi$
$863$	14.5057			0.493779			0.246890	+	0.969044i	$0.420592\pi$
$864$			5.41381i			0.184182i
$865$	53.3492			1.81393
$866$	3.93305	+	6.81224i	0.133650	+	0.231489i
$867$	−3.32682	+	0.586608i	−0.112985	+	0.0199222i
$868$	−0.709607	+	1.22908i	−0.0240856	+	0.0417176i
$869$	2.95677	−	5.12127i	0.100301	−	0.173727i
$870$	−33.3516	−	39.7469i	−1.13073	−	1.34755i
$871$	28.0612	+	48.6035i	0.950819	+	1.64687i
$872$	−31.3141			−1.06043
$873$	31.2638	+	26.2335i	1.05812	+	0.887868i
$874$	0.312214			0.0105608
$875$	4.54323	+	7.86911i	0.153589	+	0.266024i
$876$	−1.12410	+	3.08845i	−0.0379800	+	0.104349i
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	−0.980352	−	0.197255i	$-0.936797\pi$
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270131\pi$
$878$	−20.1120	+	34.8350i	−0.678747	+	1.17562i
$879$	−2.56371	+	7.04374i	−0.0864718	+	0.237579i
$880$	2.13041	+	3.68999i	0.0718163	+	0.124389i
$881$	53.8976			1.81585			0.907927	−	0.419128i	$-0.137664\pi$
$881$	53.8976			1.81585			0.907927	+	0.419128i	$0.137664\pi$
$882$	3.79813	−	1.38241i	0.127890	−	0.0465481i
$883$	43.4252			1.46137			0.730687	−	0.682712i	$-0.239200\pi$
$883$	43.4252			1.46137			0.730687	+	0.682712i	$0.239200\pi$
$884$	2.08718	+	3.61510i	0.0701995	+	0.121589i
$885$	−2.07620	−	2.47432i	−0.0697907	−	0.0831733i
$886$	−7.18479	+	12.4444i	−0.241378	+	0.418079i
$887$	19.4800	−	33.7403i	0.654074	−	1.13289i	−0.328051	−	0.944660i	$-0.606392\pi$
$887$	19.4800	−	33.7403i	0.654074	−	1.13289i	0.982125	−	0.188229i	$-0.0602749\pi$
$888$	38.5611	−	6.79936i	1.29403	−	0.228172i
$889$	4.44104	+	7.69210i	0.148948	+	0.257985i
$890$	−27.6800			−0.927837
$891$	−3.95723	−	1.44032i	−0.132572	−	0.0482524i
$892$	−2.62267			−0.0878136
$893$	−5.82547	−	10.0900i	−0.194942	−	0.337650i
$894$	20.0503	−	3.53542i	0.670584	−	0.118242i
$895$	6.48293	−	11.2288i	0.216700	−	0.375336i
$896$	−4.74897	+	8.22546i	−0.158652	+	0.274793i
$897$	0.687623	+	0.819478i	0.0229591	+	0.0273616i
$898$	−2.39440	−	4.14722i	−0.0799022	−	0.138395i
$899$	−67.4389			−2.24921
$900$	−0.735300	+	0.267627i	−0.0245100	+	0.00892091i
$901$	−2.78106			−0.0926505
$902$	0.701867	+	1.21567i	0.0233696	+	0.0404773i
$903$	−0.726682	+	1.99654i	−0.0241824	+	0.0664407i
$904$	7.61949	−	13.1973i	0.253420	−	0.438937i
$905$	0.405078	−	0.701615i	0.0134652	−	0.0233225i
$906$	−14.7072	+	40.4076i	−0.488613	+	1.34245i
$907$	−17.2638	−	29.9018i	−0.573236	−	0.992874i	−0.996231	−	0.0867416i	$-0.972355\pi$
$907$	−17.2638	−	29.9018i	−0.573236	−	0.992874i	0.422995	−	0.906132i	$-0.360979\pi$
$908$	0.534777			0.0177472
$909$	22.0023	+	18.4621i	0.729769	+	0.612349i
$910$	19.8648			0.658513
$911$	−23.2631	−	40.2929i	−0.770741	−	1.33496i	−0.937157	−	0.348907i	$-0.886553\pi$
$911$	−23.2631	−	40.2929i	−0.770741	−	1.33496i	0.166416	−	0.986056i	$-0.446780\pi$
$912$	−8.74763	−	10.4250i	−0.289663	−	0.345207i
$913$	0.639033	−	1.10684i	0.0211489	−	0.0366310i
$914$	−3.38388	+	5.86106i	−0.111929	+	0.193867i
$915$	4.13816	−	0.729669i	0.136803	−	0.0241221i
$916$	0.847048	+	1.46713i	0.0279873	+	0.0484753i
$917$	11.3628			0.375232
$918$	−23.5201	−	13.5793i	−0.776278	−	0.448184i
$919$	−9.95636			−0.328430			−0.164215	−	0.986425i	$-0.552509\pi$
$919$	−9.95636			−0.328430			−0.164215	+	0.986425i	$0.552509\pi$
$920$	−0.395277	−	0.684640i	−0.0130319	−	0.0225719i
$921$	21.1125	−	3.72270i	0.695679	−	0.122667i
$922$	−12.4363	+	21.5403i	−0.409567	+	0.709391i
$923$	−38.5317	+	66.7388i	−1.26829	+	2.19674i
$924$	0.0962667	+	0.114726i	0.00316694	+	0.00377421i
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$	−19.1780			−0.630228
$927$	−1.58466	+	8.98703i	−0.0520469	+	0.295173i
$928$	9.14889			0.300327
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	0.782239	−	0.622978i	$-0.214077\pi$
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	−0.930634	+	0.365950i	$0.880744\pi$
$930$	15.5209	−	42.6434i	0.508952	−	1.39833i
$931$	1.09240	−	1.89209i	0.0358018	−	0.0620106i
$932$	1.22621	−	2.12387i	0.0401660	−	0.0695696i
$933$	13.0241	−	35.7834i	0.426390	−	1.17150i
$934$	2.26929	+	3.93052i	0.0742533	+	0.128610i
$935$	4.59627			0.150314
$936$	8.92910	−	50.6395i	0.291857	−	1.65520i
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$	6.49273	+	11.2457i	0.211995	+	0.367186i
$939$	15.4641	+	18.4294i	0.504652	+	0.601421i
$940$	−1.24763	+	2.16095i	−0.0406931	+	0.0704825i
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.276223	−	0.961094i	$-0.410917\pi$
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.694220	−	0.719763i	$-0.255749\pi$
$942$	11.3159	−	1.99530i	0.368693	−	0.0650105i
$943$	−0.118089	−	0.204535i	−0.00384549	−	0.00666059i
$944$	−2.64858			−0.0862041
$945$	11.3944	−	6.57856i	0.370660	−	0.214001i
$946$	0.773318			0.0251428
$947$	−4.32429	−	7.48989i	−0.140521	−	0.243389i	0.787172	−	0.616733i	$-0.211544\pi$
$947$	−4.32429	−	7.48989i	−0.140521	−	0.243389i	−0.927693	+	0.373344i	$0.878211\pi$
$948$	3.98364	−	0.702423i	0.129383	−	0.0228137i
$949$	29.8967	−	51.7826i	0.970487	−	1.68093i
$950$	2.07738	−	3.59813i	0.0673992	−	0.116739i
$951$	6.88279	+	8.20259i	0.223190	+	0.265987i
$952$	5.70961	+	9.88933i	0.185049	+	0.320515i
$953$	3.78249			0.122527			0.0612634	−	0.998122i	$-0.480487\pi$
$953$	3.78249			0.122527			0.0612634	+	0.998122i	$0.480487\pi$
$954$	2.21966	+	1.86251i	0.0718640	+	0.0603011i
$955$	−39.4175			−1.27552
$956$	0.881196	+	1.52628i	0.0284999	+	0.0493633i
$957$	−2.43401	+	6.68739i	−0.0786804	+	0.216173i
$958$	24.7677	−	42.8989i	0.800208	−	1.38600i
$959$	2.86231	−	4.95767i	0.0924288	−	0.160091i
$960$	−12.8944	+	35.4271i	−0.416165	+	1.14340i
$961$	−13.9915	−	24.2341i	−0.451340	−	0.781744i
$962$	−60.2518			−1.94260
$963$	−18.3735	+	6.68739i	−0.592076	+	0.215498i
$964$	1.65539			0.0533166
$965$	−7.64930	−	13.2490i	−0.246240	−	0.426500i
$966$	0.159100	+	0.189608i	0.00511897	+	0.00610055i
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	−0.469613	−	0.882872i	$-0.655607\pi$
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	0.999396	−	0.0347392i	$-0.0110601\pi$
$968$	−15.8674	+	27.4831i	−0.509996	+	0.883340i
$969$	−14.4572	+	2.54920i	−0.464433	+	0.0818921i
$970$	23.2049	+	40.1920i	0.745063	+	1.29049i
$971$	−55.4570			−1.77970			−0.889850	−	0.456254i	$-0.849191\pi$
$971$	−55.4570			−1.77970			−0.889850	+	0.456254i	$0.849191\pi$
$972$	−0.985234	−	2.70691i	−0.0316014	−	0.0868241i
$973$	−0.923963			−0.0296209
$974$	25.2062	+	43.6584i	0.807659	+	1.39891i
$975$	14.0194	−	2.47199i	0.448979	−	0.0791670i
$976$	1.72281	−	2.98400i	0.0551458	−	0.0955154i
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.0830847	+	0.996542i	$0.526477\pi$
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.821489	+	0.570225i	$0.806856\pi$
$978$	−11.4572	−	13.6542i	−0.366362	−	0.436613i
$979$	1.89827	+	3.28790i	0.0606690	+	0.105082i
$980$	−0.467911			−0.0149469
$981$	29.9898	−	10.9154i	0.957500	−	0.348502i
$982$	−35.9331			−1.14667
$983$	−14.4987	−	25.1124i	−0.462435	−	0.800961i	0.536646	−	0.843807i	$-0.319691\pi$
$983$	−14.4987	−	25.1124i	−0.462435	−	0.800961i	−0.999082	+	0.0428458i	$0.986358\pi$
$984$	−3.88279	+	10.6679i	−0.123779	+	0.340079i
$985$	−31.9479	+	55.3354i	−1.01794	+	1.76313i
$986$	−22.9479	+	39.7469i	−0.730810	+	1.26580i
$987$	3.15910	−	8.67956i	0.100555	−	0.276273i
$988$	−1.17546	−	2.03596i	−0.0373963	−	0.0647724i
$989$	−0.130110			−0.00413726
$990$	−3.66843	−	3.07818i	−0.116590	−	0.0978310i
$991$	6.80922			0.216302			0.108151	−	0.994134i	$-0.465507\pi$
$991$	6.80922			0.216302			0.108151	+	0.994134i	$0.465507\pi$
$992$	4.00088	+	6.92972i	0.127028	+	0.220019i
$993$	−11.9477	−	14.2388i	−0.379150	−	0.451853i
$994$	−8.91534	+	15.4418i	−0.282778	+	0.489785i
$995$	−3.85117	+	6.67042i	−0.122090	+	0.211466i
$996$	0.860967	−	0.151812i	0.0272808	−	0.00481034i
$997$	19.4688	+	33.7210i	0.616585	+	1.06796i	0.990104	+	0.140333i	$0.0448175\pi$
$997$	19.4688	+	33.7210i	0.616585	+	1.06796i	−0.373520	+	0.927622i	$0.621849\pi$
$998$	45.4647			1.43916
$999$	−34.5602	+	19.9533i	−1.09344	+	0.631296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.a.22.2	✓	6
3.2	odd	2		189.2.f.b.64.2		6
4.3	odd	2		1008.2.r.h.337.1		6
7.2	even	3		441.2.g.c.67.2		6
7.3	odd	6		441.2.h.e.373.2		6
7.4	even	3		441.2.h.d.373.2		6
7.5	odd	6		441.2.g.b.67.2		6
7.6	odd	2		441.2.f.c.148.2		6
9.2	odd	6		189.2.f.b.127.2		6
9.4	even	3		567.2.a.h.1.2		3
9.5	odd	6		567.2.a.c.1.2		3
9.7	even	3	inner	63.2.f.a.43.2	yes	6
12.11	even	2		3024.2.r.k.1009.3		6
21.2	odd	6		1323.2.g.d.361.2		6
21.5	even	6		1323.2.g.e.361.2		6
21.11	odd	6		1323.2.h.c.226.2		6
21.17	even	6		1323.2.h.b.226.2		6
21.20	even	2		1323.2.f.d.442.2		6
36.7	odd	6		1008.2.r.h.673.1		6
36.11	even	6		3024.2.r.k.2017.3		6
36.23	even	6		9072.2.a.bs.1.1		3
36.31	odd	6		9072.2.a.ca.1.3		3
63.2	odd	6		1323.2.h.c.802.2		6
63.11	odd	6		1323.2.g.d.667.2		6
63.13	odd	6		3969.2.a.q.1.2		3
63.16	even	3		441.2.h.d.214.2		6
63.20	even	6		1323.2.f.d.883.2		6
63.25	even	3		441.2.g.c.79.2		6
63.34	odd	6		441.2.f.c.295.2		6
63.38	even	6		1323.2.g.e.667.2		6
63.41	even	6		3969.2.a.l.1.2		3
63.47	even	6		1323.2.h.b.802.2		6
63.52	odd	6		441.2.g.b.79.2		6
63.61	odd	6		441.2.h.e.214.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	1.1	even	1	trivial
63.2.f.a.43.2	yes	6	9.7	even	3	inner
189.2.f.b.64.2		6	3.2	odd	2
189.2.f.b.127.2		6	9.2	odd	6
441.2.f.c.148.2		6	7.6	odd	2
441.2.f.c.295.2		6	63.34	odd	6
441.2.g.b.67.2		6	7.5	odd	6
441.2.g.b.79.2		6	63.52	odd	6
441.2.g.c.67.2		6	7.2	even	3
441.2.g.c.79.2		6	63.25	even	3
441.2.h.d.214.2		6	63.16	even	3
441.2.h.d.373.2		6	7.4	even	3
441.2.h.e.214.2		6	63.61	odd	6
441.2.h.e.373.2		6	7.3	odd	6
567.2.a.c.1.2		3	9.5	odd	6
567.2.a.h.1.2		3	9.4	even	3
1008.2.r.h.337.1		6	4.3	odd	2
1008.2.r.h.673.1		6	36.7	odd	6
1323.2.f.d.442.2		6	21.20	even	2
1323.2.f.d.883.2		6	63.20	even	6
1323.2.g.d.361.2		6	21.2	odd	6
1323.2.g.d.667.2		6	63.11	odd	6
1323.2.g.e.361.2		6	21.5	even	6
1323.2.g.e.667.2		6	63.38	even	6
1323.2.h.b.226.2		6	21.17	even	6
1323.2.h.b.802.2		6	63.47	even	6
1323.2.h.c.226.2		6	21.11	odd	6
1323.2.h.c.802.2		6	63.2	odd	6
3024.2.r.k.1009.3		6	12.11	even	2
3024.2.r.k.2017.3		6	36.11	even	6
3969.2.a.l.1.2		3	63.41	even	6
3969.2.a.q.1.2		3	63.13	odd	6
9072.2.a.bs.1.1		3	36.23	even	6
9072.2.a.ca.1.3		3	36.31	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 - 1.16679i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} +(-0.500000 - 0.866025i) q^{7} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(-0.673648 - 1.16679i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} +(-0.500000 - 0.866025i) q^{7} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} +3.41147 q^{10} +(-0.233956 - 0.405223i) q^{11} +(0.109470 - 0.300767i) q^{12} +(-2.91147 + 5.04282i) q^{13} +(-0.673648 + 1.16679i) q^{14} +(-1.50000 + 4.12122i) q^{15} +(1.79813 + 3.11446i) q^{16} +3.87939 q^{17} +(-3.09627 - 2.59808i) q^{18} -2.18479 q^{19} +(0.233956 + 0.405223i) q^{20} +(-1.11334 - 1.32683i) q^{21} +(-0.315207 + 0.545955i) q^{22} +(0.0530334 - 0.0918566i) q^{23} +(-5.02094 + 0.885328i) q^{24} +(-0.705737 - 1.22237i) q^{25} +7.84524 q^{26} +(4.50000 - 2.59808i) q^{27} -0.184793 q^{28} +(-4.39053 - 7.60462i) q^{29} +(5.81908 - 1.02606i) q^{30} +(3.84002 - 6.65111i) q^{31} +(-0.520945 + 0.902302i) q^{32} +(-0.520945 - 0.620838i) q^{33} +(-2.61334 - 4.52644i) q^{34} +2.53209 q^{35} +(0.0962667 - 0.545955i) q^{36} -7.68004 q^{37} +(1.47178 + 2.54920i) q^{38} +(-3.44949 + 9.47740i) q^{39} +(3.72668 - 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.798133 + 2.19285i) q^{42} +(-0.613341 - 1.06234i) q^{43} -0.0864665 q^{44} +(-1.31908 + 7.48086i) q^{45} -0.142903 q^{46} +(2.66637 + 4.61830i) q^{47} +(4.00387 + 4.77163i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.950837 + 1.64690i) q^{50} +(6.61721 - 1.16679i) q^{51} +(0.538019 + 0.931876i) q^{52} -0.716881 q^{53} +(-6.06283 - 3.50038i) q^{54} +1.18479 q^{55} +(1.47178 + 2.54920i) q^{56} +(-3.72668 + 0.657115i) q^{57} +(-5.91534 + 10.2457i) q^{58} +(-0.368241 + 0.637812i) q^{59} +(0.520945 + 0.620838i) q^{60} +(-0.479055 - 0.829748i) q^{61} -10.3473 q^{62} +(-2.29813 - 1.92836i) q^{63} +8.59627 q^{64} +(-7.37211 - 12.7689i) q^{65} +(-0.373455 + 1.02606i) q^{66} +(4.81908 - 8.34689i) q^{67} +(0.358441 - 0.620838i) q^{68} +(0.0628336 - 0.172634i) q^{69} +(-1.70574 - 2.95442i) q^{70} +13.2344 q^{71} +(-8.29813 + 3.02027i) q^{72} -10.2686 q^{73} +(5.17365 + 8.96102i) q^{74} +(-1.57145 - 1.87278i) q^{75} +(-0.201867 + 0.349643i) q^{76} +(-0.233956 + 0.405223i) q^{77} +(13.3819 - 2.35959i) q^{78} +(6.31908 + 10.9450i) q^{79} -9.10607 q^{80} +(6.89440 - 5.78509i) q^{81} -3.00000 q^{82} +(1.36571 + 2.36549i) q^{83} +(-0.315207 + 0.0555796i) q^{84} +(-4.91147 + 8.50692i) q^{85} +(-0.826352 + 1.43128i) q^{86} +(-9.77631 - 11.6510i) q^{87} +(0.688663 + 1.19280i) q^{88} -8.11381 q^{89} +(9.61721 - 3.50038i) q^{90} +5.82295 q^{91} +(-0.00980018 - 0.0169744i) q^{92} +(4.54963 - 12.5000i) q^{93} +(3.59240 - 6.22221i) q^{94} +(2.76604 - 4.79093i) q^{95} +(-0.617211 + 1.69577i) q^{96} +(6.80200 + 11.7814i) q^{97} +1.34730 q^{98} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24} + 6 q^{25} - 6 q^{26} + 27 q^{27} + 6 q^{28} - 9 q^{29} + 18 q^{30} + 3 q^{31} - 9 q^{34} + 6 q^{35} - 27 q^{36} - 6 q^{37} - 6 q^{38} - 18 q^{39} + 9 q^{40} + 9 q^{42} + 3 q^{43} + 30 q^{44} + 9 q^{45} - 3 q^{47} - 3 q^{49} + 6 q^{50} + 9 q^{51} + 21 q^{52} + 12 q^{53} - 27 q^{54} - 6 q^{56} - 9 q^{57} + 9 q^{58} + 3 q^{59} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} + 36 q^{66} + 12 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 36 q^{72} - 42 q^{73} + 30 q^{74} - 9 q^{75} - 15 q^{76} - 6 q^{77} + 54 q^{78} + 21 q^{79} - 30 q^{80} - 18 q^{82} + 18 q^{83} - 9 q^{84} - 9 q^{85} - 6 q^{86} + 9 q^{87} - 27 q^{88} + 24 q^{89} + 27 q^{90} - 6 q^{91} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 27 q^{96} + 3 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

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