LMFDB - Embedded newform 273.2.cg.a.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.4
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.a.262.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.273028 + 1.01896i) q^{2} +1.00000i q^{3} +(0.768324 + 0.443592i) q^{4} +(1.01943 + 3.80456i) q^{5} +(-1.01896 - 0.273028i) q^{6} +(1.44977 - 2.21318i) q^{7} +(-2.15363 + 2.15363i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.273028 + 1.01896i) q^{2} +1.00000i q^{3} +(0.768324 + 0.443592i) q^{4} +(1.01943 + 3.80456i) q^{5} +(-1.01896 - 0.273028i) q^{6} +(1.44977 - 2.21318i) q^{7} +(-2.15363 + 2.15363i) q^{8} -1.00000 q^{9} -4.15502 q^{10} +(0.669085 - 0.669085i) q^{11} +(-0.443592 + 0.768324i) q^{12} +(0.783899 - 3.51930i) q^{13} +(1.85931 + 2.08151i) q^{14} +(-3.80456 + 1.01943i) q^{15} +(-0.719268 - 1.24581i) q^{16} +(3.98087 - 6.89506i) q^{17} +(0.273028 - 1.01896i) q^{18} +(-1.23405 + 1.23405i) q^{19} +(-0.904422 + 3.37535i) q^{20} +(2.21318 + 1.44977i) q^{21} +(0.499089 + 0.864448i) q^{22} +(-6.00569 + 3.46739i) q^{23} +(-2.15363 - 2.15363i) q^{24} +(-9.10535 + 5.25697i) q^{25} +(3.37199 + 1.75963i) q^{26} -1.00000i q^{27} +(2.09564 - 1.05734i) q^{28} +(1.71573 - 2.97173i) q^{29} -4.15502i q^{30} +(-4.37613 - 1.17258i) q^{31} +(-4.41802 + 1.18381i) q^{32} +(0.669085 + 0.669085i) q^{33} +(5.93888 + 5.93888i) q^{34} +(9.89813 + 3.25954i) q^{35} +(-0.768324 - 0.443592i) q^{36} +(9.40483 + 2.52002i) q^{37} +(-0.920514 - 1.59438i) q^{38} +(3.51930 + 0.783899i) q^{39} +(-10.3891 - 5.99815i) q^{40} +(0.117207 + 0.437421i) q^{41} +(-2.08151 + 1.85931i) q^{42} +(0.0936549 - 0.0540717i) q^{43} +(0.810875 - 0.217273i) q^{44} +(-1.01943 - 3.80456i) q^{45} +(-1.89339 - 7.06623i) q^{46} +(4.45738 - 1.19435i) q^{47} +(1.24581 - 0.719268i) q^{48} +(-2.79636 - 6.41720i) q^{49} +(-2.87061 - 10.7132i) q^{50} +(6.89506 + 3.98087i) q^{51} +(2.16342 - 2.35623i) q^{52} +(0.747827 + 1.29527i) q^{53} +(1.01896 + 0.273028i) q^{54} +(3.22766 + 1.86349i) q^{55} +(1.64412 + 7.88864i) q^{56} +(-1.23405 - 1.23405i) q^{57} +(2.55962 + 2.55962i) q^{58} +(-4.68445 + 1.25519i) q^{59} +(-3.37535 - 0.904422i) q^{60} -6.61892i q^{61} +(2.38961 - 4.13893i) q^{62} +(-1.44977 + 2.21318i) q^{63} -7.70205i q^{64} +(14.1885 - 0.605291i) q^{65} +(-0.864448 + 0.499089i) q^{66} +(3.19896 + 3.19896i) q^{67} +(6.11719 - 3.53176i) q^{68} +(-3.46739 - 6.00569i) q^{69} +(-6.02380 + 9.19581i) q^{70} +(-2.68009 + 10.0022i) q^{71} +(2.15363 - 2.15363i) q^{72} +(1.05974 - 3.95501i) q^{73} +(-5.13557 + 8.89507i) q^{74} +(-5.25697 - 9.10535i) q^{75} +(-1.49557 + 0.400736i) q^{76} +(-0.510791 - 2.45082i) q^{77} +(-1.75963 + 3.37199i) q^{78} +(0.473848 - 0.820728i) q^{79} +(4.00652 - 4.00652i) q^{80} +1.00000 q^{81} -0.477714 q^{82} +(8.26062 - 8.26062i) q^{83} +(1.05734 + 2.09564i) q^{84} +(30.2909 + 8.11643i) q^{85} +(0.0295262 + 0.110193i) q^{86} +(2.97173 + 1.71573i) q^{87} +2.88192i q^{88} +(-1.38773 + 5.17908i) q^{89} +4.15502 q^{90} +(-6.65239 - 6.83708i) q^{91} -6.15242 q^{92} +(1.17258 - 4.37613i) q^{93} +4.86796i q^{94} +(-5.95306 - 3.43700i) q^{95} +(-1.18381 - 4.41802i) q^{96} +(11.5503 + 3.09490i) q^{97} +(7.30232 - 1.09729i) q^{98} +(-0.669085 + 0.669085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.273028	+	1.01896i	−0.193060	+	0.720511i	0.799700	+	0.600400i	$0.204992\pi$
$2$	−0.273028	+	1.01896i	−0.193060	+	0.720511i	−0.992760	+	0.120111i	$0.961675\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.768324	+	0.443592i	0.384162	+	0.221796i
$5$	1.01943	+	3.80456i	0.455903	+	1.70145i	0.685420	+	0.728148i	$0.259619\pi$
$5$	1.01943	+	3.80456i	0.455903	+	1.70145i	−0.229517	+	0.973305i	$0.573715\pi$
$6$	−1.01896	−	0.273028i	−0.415987	−	0.111463i
$7$	1.44977	−	2.21318i	0.547960	−	0.836504i
$7$	1.44977	−	2.21318i	0.547960	−	0.836504i
$8$	−2.15363	+	2.15363i	−0.761423	+	0.761423i
$9$	−1.00000			−0.333333
$10$	−4.15502			−1.31393
$11$	0.669085	−	0.669085i	0.201737	−	0.201737i	−0.599007	−	0.800744i	$-0.704438\pi$
$11$	0.669085	−	0.669085i	0.201737	−	0.201737i	0.800744	+	0.599007i	$0.204438\pi$
$12$	−0.443592	+	0.768324i	−0.128054	+	0.221796i
$13$	0.783899	−	3.51930i	0.217414	−	0.976079i
$13$	0.783899	−	3.51930i	0.217414	−	0.976079i
$14$	1.85931	+	2.08151i	0.496921	+	0.556307i
$15$	−3.80456	+	1.01943i	−0.982334	+	0.263216i
$16$	−0.719268	−	1.24581i	−0.179817	−	0.311452i
$17$	3.98087	−	6.89506i	0.965502	−	1.67230i	0.257242	−	0.966347i	$-0.417186\pi$
$17$	3.98087	−	6.89506i	0.965502	−	1.67230i	0.708260	−	0.705952i	$-0.249481\pi$
$18$	0.273028	−	1.01896i	0.0643534	−	0.240170i
$19$	−1.23405	+	1.23405i	−0.283111	+	0.283111i	−0.834348	−	0.551237i	$-0.814156\pi$
$19$	−1.23405	+	1.23405i	−0.283111	+	0.283111i	0.551237	+	0.834348i	$0.314156\pi$
$20$	−0.904422	+	3.37535i	−0.202235	+	0.754751i
$21$	2.21318	+	1.44977i	0.482956	+	0.316365i
$22$	0.499089	+	0.864448i	0.106406	+	0.184301i
$23$	−6.00569	+	3.46739i	−1.25227	+	0.723000i	−0.971560	−	0.236792i	$-0.923904\pi$
$23$	−6.00569	+	3.46739i	−1.25227	+	0.723000i	−0.280712	+	0.959792i	$0.590571\pi$
$24$	−2.15363	−	2.15363i	−0.439608	−	0.439608i
$25$	−9.10535	+	5.25697i	−1.82107	+	1.05139i
$26$	3.37199	+	1.75963i	0.661302	+	0.345092i
$27$		−	1.00000i		−	0.192450i
$28$	2.09564	−	1.05734i	0.396039	−	0.199818i
$29$	1.71573	−	2.97173i	0.318603	−	0.551836i	−0.661594	−	0.749862i	$-0.730120\pi$
$29$	1.71573	−	2.97173i	0.318603	−	0.551836i	0.980197	+	0.198026i	$0.0634531\pi$
$30$		−	4.15502i		−	0.758599i
$31$	−4.37613	−	1.17258i	−0.785976	−	0.210602i	−0.156558	−	0.987669i	$-0.550040\pi$
$31$	−4.37613	−	1.17258i	−0.785976	−	0.210602i	−0.629418	+	0.777067i	$0.716707\pi$
$32$	−4.41802	+	1.18381i	−0.781003	+	0.209269i
$33$	0.669085	+	0.669085i	0.116473	+	0.116473i
$34$	5.93888	+	5.93888i	1.01851	+	1.01851i
$35$	9.89813	+	3.25954i	1.67309	+	0.550964i
$36$	−0.768324	−	0.443592i	−0.128054	−	0.0739320i
$37$	9.40483	+	2.52002i	1.54614	+	0.414288i	0.928245	−	0.371969i	$-0.121317\pi$
$37$	9.40483	+	2.52002i	1.54614	+	0.414288i	0.617899	+	0.786257i	$0.287984\pi$
$38$	−0.920514	−	1.59438i	−0.149327	−	0.258642i
$39$	3.51930	+	0.783899i	0.563540	+	0.125524i
$40$	−10.3891	−	5.99815i	−1.64266	−	0.948391i
$41$	0.117207	+	0.437421i	0.0183046	+	0.0683137i	0.974474	−	0.224500i	$-0.0720750\pi$
$41$	0.117207	+	0.437421i	0.0183046	+	0.0683137i	−0.956169	+	0.292814i	$0.905408\pi$
$42$	−2.08151	+	1.85931i	−0.321184	+	0.286898i
$43$	0.0936549	−	0.0540717i	0.0142822	−	0.00824585i	−0.492842	−	0.870119i	$-0.664042\pi$
$43$	0.0936549	−	0.0540717i	0.0142822	−	0.00824585i	0.507124	+	0.861873i	$0.330709\pi$
$44$	0.810875	−	0.217273i	0.122244	−	0.0327552i
$45$	−1.01943	−	3.80456i	−0.151968	−	0.567151i
$46$	−1.89339	−	7.06623i	−0.279165	−	1.04186i
$47$	4.45738	−	1.19435i	0.650175	−	0.174214i	0.0813671	−	0.996684i	$-0.474071\pi$
$47$	4.45738	−	1.19435i	0.650175	−	0.174214i	0.568808	+	0.822470i	$0.307405\pi$
$48$	1.24581	−	0.719268i	0.179817	−	0.103817i
$49$	−2.79636	−	6.41720i	−0.399479	−	0.916742i
$50$	−2.87061	−	10.7132i	−0.405965	−	1.51508i
$51$	6.89506	+	3.98087i	0.965502	+	0.557433i
$52$	2.16342	−	2.35623i	0.300013	−	0.326751i
$53$	0.747827	+	1.29527i	0.102722	+	0.177920i	0.912805	−	0.408395i	$-0.133911\pi$
$53$	0.747827	+	1.29527i	0.102722	+	0.177920i	−0.810083	+	0.586315i	$0.800578\pi$
$54$	1.01896	+	0.273028i	0.138662	+	0.0371545i
$55$	3.22766	+	1.86349i	0.435218	+	0.251273i
$56$	1.64412	+	7.88864i	0.219704	+	1.05416i
$57$	−1.23405	−	1.23405i	−0.163454	−	0.163454i
$58$	2.55962	+	2.55962i	0.336094	+	0.336094i
$59$	−4.68445	+	1.25519i	−0.609863	+	0.163412i	−0.550515	−	0.834825i	$-0.685569\pi$
$59$	−4.68445	+	1.25519i	−0.609863	+	0.163412i	−0.0593479	+	0.998237i	$0.518902\pi$
$60$	−3.37535	−	0.904422i	−0.435756	−	0.116760i
$61$		−	6.61892i		−	0.847465i	−0.905787	−	0.423733i	$-0.860720\pi$
$61$		−	6.61892i		−	0.847465i	0.905787	−	0.423733i	$-0.139280\pi$
$62$	2.38961	−	4.13893i	0.303481	−	0.525645i
$63$	−1.44977	+	2.21318i	−0.182653	+	0.278835i
$64$		−	7.70205i		−	0.962757i
$65$	14.1885	−	0.605291i	1.75987	−	0.0750771i
$66$	−0.864448	+	0.499089i	−0.106406	+	0.0614336i
$67$	3.19896	+	3.19896i	0.390815	+	0.390815i	0.874978	−	0.484163i	$-0.160876\pi$
$67$	3.19896	+	3.19896i	0.390815	+	0.390815i	−0.484163	+	0.874978i	$0.660876\pi$
$68$	6.11719	−	3.53176i	0.741819	−	0.428289i
$69$	−3.46739	−	6.00569i	−0.417424	−	0.723000i
$70$	−6.02380	+	9.19581i	−0.719982	+	1.09911i
$71$	−2.68009	+	10.0022i	−0.318068	+	1.18705i	0.603030	+	0.797718i	$0.293960\pi$
$71$	−2.68009	+	10.0022i	−0.318068	+	1.18705i	−0.921099	+	0.389329i	$0.872707\pi$
$72$	2.15363	−	2.15363i	0.253808	−	0.253808i
$73$	1.05974	−	3.95501i	0.124033	−	0.462899i	−0.875770	−	0.482729i	$-0.839646\pi$
$73$	1.05974	−	3.95501i	0.124033	−	0.462899i	0.999803	+	0.0198296i	$0.00631239\pi$
$74$	−5.13557	+	8.89507i	−0.596998	+	1.03403i
$75$	−5.25697	−	9.10535i	−0.607023	−	1.05139i
$76$	−1.49557	+	0.400736i	−0.171553	+	0.0459676i
$77$	−0.510791	−	2.45082i	−0.0582100	−	0.279297i
$78$	−1.75963	+	3.37199i	−0.199239	+	0.381803i
$79$	0.473848	−	0.820728i	0.0533120	−	0.0923391i	−0.838138	−	0.545459i	$-0.816356\pi$
$79$	0.473848	−	0.820728i	0.0533120	−	0.0923391i	0.891450	+	0.453119i	$0.149689\pi$
$80$	4.00652	−	4.00652i	0.447942	−	0.447942i
$81$	1.00000			0.111111
$82$	−0.477714			−0.0527546
$83$	8.26062	−	8.26062i	0.906721	−	0.906721i	−0.0892850	−	0.996006i	$-0.528458\pi$
$83$	8.26062	−	8.26062i	0.906721	−	0.906721i	0.996006	+	0.0892850i	$0.0284582\pi$
$84$	1.05734	+	2.09564i	0.115365	+	0.228653i
$85$	30.2909	+	8.11643i	3.28551	+	0.880351i
$86$	0.0295262	+	0.110193i	0.00318389	+	0.0118824i
$87$	2.97173	+	1.71573i	0.318603	+	0.183945i
$88$			2.88192i			0.307214i
$89$	−1.38773	+	5.17908i	−0.147099	+	0.548982i	0.852554	+	0.522639i	$0.175053\pi$
$89$	−1.38773	+	5.17908i	−0.147099	+	0.548982i	−0.999653	+	0.0263421i	$0.991614\pi$
$90$	4.15502			0.437977
$91$	−6.65239	−	6.83708i	−0.697360	−	0.716721i
$92$	−6.15242			−0.641434
$93$	1.17258	−	4.37613i	0.121591	−	0.453783i
$94$			4.86796i			0.502092i
$95$	−5.95306	−	3.43700i	−0.610771	−	0.352629i
$96$	−1.18381	−	4.41802i	−0.120822	−	0.450913i
$97$	11.5503	+	3.09490i	1.17276	+	0.314240i	0.792050	−	0.610456i	$-0.209014\pi$
$97$	11.5503	+	3.09490i	1.17276	+	0.314240i	0.380708	+	0.924695i	$0.375680\pi$
$98$	7.30232	−	1.09729i	0.737646	−	0.110843i
$99$	−0.669085	+	0.669085i	−0.0672456	+	0.0672456i
$100$	−9.32781			−0.932781
$101$	−18.7168			−1.86239			−0.931194	−	0.364525i	$-0.881232\pi$
$101$	−18.7168			−1.86239			−0.931194	+	0.364525i	$0.881232\pi$
$102$	−5.93888	+	5.93888i	−0.588036	+	0.588036i
$103$	−3.28825	+	5.69542i	−0.324001	+	0.561186i	−0.981310	−	0.192435i	$-0.938361\pi$
$103$	−3.28825	+	5.69542i	−0.324001	+	0.561186i	0.657309	+	0.753621i	$0.271695\pi$
$104$	5.89105	+	9.26751i	0.577665	+	0.908754i
$105$	−3.25954	+	9.89813i	−0.318099	+	0.965959i
$106$	−1.52400	+	0.408356i	−0.148024	+	0.0396630i
$107$	−2.59676	−	4.49772i	−0.251038	−	0.434811i	0.712774	−	0.701394i	$-0.247439\pi$
$107$	−2.59676	−	4.49772i	−0.251038	−	0.434811i	−0.963812	+	0.266583i	$0.914105\pi$
$108$	0.443592	−	0.768324i	0.0426847	−	0.0739320i
$109$	−2.95407	+	11.0247i	−0.282949	+	1.05598i	0.667377	+	0.744720i	$0.267417\pi$
$109$	−2.95407	+	11.0247i	−0.282949	+	1.05598i	−0.950325	+	0.311259i	$0.899249\pi$
$110$	−2.78006	+	2.78006i	−0.265068	+	0.265068i
$111$	−2.52002	+	9.40483i	−0.239189	+	0.892667i
$112$	−3.79997	−	0.214260i	−0.359064	−	0.0202456i
$113$	−1.34429	−	2.32838i	−0.126460	−	0.219036i	0.795842	−	0.605504i	$-0.207028\pi$
$113$	−1.34429	−	2.32838i	−0.126460	−	0.219036i	−0.922303	+	0.386468i	$0.873695\pi$
$114$	1.59438	−	0.920514i	0.149327	−	0.0862140i
$115$	−19.3143	−	19.3143i	−1.80107	−	1.80107i
$116$	2.63647	−	1.52217i	0.244790	−	0.141330i
$117$	−0.783899	+	3.51930i	−0.0724715	+	0.325360i
$118$		−	5.11595i		−	0.470961i
$119$	−9.48871	−	18.8066i	−0.869829	−	1.72400i
$120$	5.99815	−	10.3891i	0.547554	−	0.948391i
$121$			10.1046i			0.918605i
$122$	6.74438	+	1.80715i	0.610608	+	0.163612i
$123$	−0.437421	+	0.117207i	−0.0394409	+	0.0105682i
$124$	−2.84214	−	2.84214i	−0.255231	−	0.255231i
$125$	−15.3571	−	15.3571i	−1.37358	−	1.37358i
$126$	−1.85931	−	2.08151i	−0.165640	−	0.185436i
$127$	−7.89995	−	4.56104i	−0.701007	−	0.404727i	0.106715	−	0.994290i	$-0.465967\pi$
$127$	−7.89995	−	4.56104i	−0.701007	−	0.404727i	−0.807722	+	0.589563i	$0.799300\pi$
$128$	−0.987991	−	0.264731i	−0.0873269	−	0.0233992i
$129$	0.0540717	+	0.0936549i	0.00476074	+	0.00824585i
$130$	−3.25711	+	14.6228i	−0.285668	+	1.28250i
$131$	−6.79059	−	3.92055i	−0.593297	−	0.342540i	0.173103	−	0.984904i	$-0.444621\pi$
$131$	−6.79059	−	3.92055i	−0.593297	−	0.342540i	−0.766400	+	0.642364i	$0.777954\pi$
$132$	0.217273	+	0.810875i	0.0189112	+	0.0705776i
$133$	0.942096	+	4.52027i	0.0816901	+	0.391957i
$134$	−4.13300	+	2.38619i	−0.357037	+	0.206135i
$135$	3.80456	−	1.01943i	0.327445	−	0.0877386i
$136$	6.27610	+	23.4227i	0.538171	+	2.00848i
$137$	1.96981	+	7.35143i	0.168292	+	0.628075i	0.997597	+	0.0692792i	$0.0220699\pi$
$137$	1.96981	+	7.35143i	0.168292	+	0.628075i	−0.829305	+	0.558796i	$0.811263\pi$
$138$	7.06623	−	1.89339i	0.601517	−	0.161176i
$139$	−3.86004	+	2.22859i	−0.327404	+	0.189027i	−0.654688	−	0.755899i	$-0.727200\pi$
$139$	−3.86004	+	2.22859i	−0.327404	+	0.189027i	0.327284	+	0.944926i	$0.393867\pi$
$140$	6.15906	+	6.89512i	0.520536	+	0.582744i
$141$	1.19435	+	4.45738i	0.100582	+	0.375379i
$142$	−9.46010	−	5.46179i	−0.793874	−	0.458343i
$143$	−1.83022	−	2.87921i	−0.153051	−	0.240772i
$144$	0.719268	+	1.24581i	0.0599390	+	0.103817i
$145$	13.0552	+	3.49813i	1.08417	+	0.290504i
$146$	3.74064	+	2.15966i	0.309578	+	0.178735i
$147$	6.41720	−	2.79636i	0.529281	−	0.230640i
$148$	6.10810	+	6.10810i	0.502082	+	0.502082i
$149$	0.532092	+	0.532092i	0.0435907	+	0.0435907i	0.728566	−	0.684975i	$-0.240187\pi$
$149$	0.532092	+	0.532092i	0.0435907	+	0.0435907i	−0.684975	+	0.728566i	$0.740187\pi$
$150$	10.7132	−	2.87061i	0.874733	−	0.234384i
$151$	0.0631804	+	0.0169291i	0.00514154	+	0.00137767i	0.261389	−	0.965234i	$-0.415819\pi$
$151$	0.0631804	+	0.0169291i	0.00514154	+	0.00137767i	−0.256247	+	0.966611i	$0.582486\pi$
$152$		−	5.31538i		−	0.431135i
$153$	−3.98087	+	6.89506i	−0.321834	+	0.557433i
$154$	2.63674	+	0.148672i	0.212475	+	0.0119803i
$155$		−	17.8446i		−	1.43331i
$156$	2.35623	+	2.16342i	0.188650	+	0.173213i
$157$	6.41355	−	3.70286i	0.511857	−	0.295521i	−0.221740	−	0.975106i	$-0.571174\pi$
$157$	6.41355	−	3.70286i	0.511857	−	0.295521i	0.733597	+	0.679585i	$0.237840\pi$
$158$	0.706912	+	0.706912i	0.0562389	+	0.0562389i
$159$	−1.29527	+	0.747827i	−0.102722	+	0.0593065i
$160$	−9.00773	−	15.6018i	−0.712124	−	1.23343i
$161$	−1.03289	+	18.3186i	−0.0814028	+	1.44371i
$162$	−0.273028	+	1.01896i	−0.0214511	+	0.0800567i
$163$	−3.27600	+	3.27600i	−0.256596	+	0.256596i	−0.823668	−	0.567072i	$-0.808076\pi$
$163$	−3.27600	+	3.27600i	−0.256596	+	0.256596i	0.567072	+	0.823668i	$0.308076\pi$
$164$	−0.103984	+	0.388073i	−0.00811978	+	0.0303034i
$165$	−1.86349	+	3.22766i	−0.145073	+	0.251273i
$166$	6.16183	+	10.6726i	0.478250	+	0.828354i
$167$	−12.2105	+	3.27179i	−0.944874	+	0.253178i	−0.698186	−	0.715916i	$-0.746009\pi$
$167$	−12.2105	+	3.27179i	−0.944874	+	0.253178i	−0.246688	+	0.969095i	$0.579342\pi$
$168$	−7.88864	+	1.64412i	−0.608622	+	0.126846i
$169$	−11.7710	−	5.51756i	−0.905462	−	0.424427i
$170$	−16.5406	+	28.6491i	−1.26860	+	2.19729i
$171$	1.23405	−	1.23405i	0.0943703	−	0.0943703i
$172$	0.0959431			0.00731559
$173$	18.3187			1.39275			0.696374	−	0.717679i	$-0.254795\pi$
$173$	18.3187			1.39275			0.696374	+	0.717679i	$0.254795\pi$
$174$	−2.55962	+	2.55962i	−0.194044	+	0.194044i
$175$	−1.56598	+	27.7732i	−0.118377	+	2.09945i
$176$	−1.31480	−	0.352301i	−0.0991070	−	0.0265557i
$177$	−1.25519	−	4.68445i	−0.0943462	−	0.352105i
$178$	−4.89837	−	2.82807i	−0.367148	−	0.211973i
$179$		−	17.9406i		−	1.34095i	−0.741934	−	0.670473i	$-0.766091\pi$
$179$		−	17.9406i		−	1.34095i	0.741934	−	0.670473i	$-0.233909\pi$
$180$	0.904422	−	3.37535i	0.0674116	−	0.251584i
$181$	11.3348			0.842512			0.421256	−	0.906942i	$-0.361589\pi$
$181$	11.3348			0.842512			0.421256	+	0.906942i	$0.361589\pi$
$182$	8.78298	−	4.91178i	0.651037	−	0.364085i
$183$	6.61892			0.489284
$184$	5.46657	−	20.4015i	0.403001	−	1.50402i
$185$			38.3503i			2.81957i
$186$	4.13893	+	2.38961i	0.303481	+	0.175215i
$187$	−1.94985	−	7.27693i	−0.142587	−	0.532141i
$188$	3.95451	+	1.05961i	0.288413	+	0.0772799i
$189$	−2.21318	−	1.44977i	−0.160985	−	0.105455i
$190$	5.12751	−	5.12751i	0.371989	−	0.371989i
$191$	−14.6688			−1.06139			−0.530697	−	0.847562i	$-0.678070\pi$
$191$	−14.6688			−1.06139			−0.530697	+	0.847562i	$0.678070\pi$
$192$	7.70205			0.555848
$193$	8.28684	−	8.28684i	0.596500	−	0.596500i	−0.342880	−	0.939379i	$-0.611402\pi$
$193$	8.28684	−	8.28684i	0.596500	−	0.596500i	0.939379	+	0.342880i	$0.111402\pi$
$194$	−6.30714	+	10.9243i	−0.452826	+	0.784318i
$195$	0.605291	+	14.1885i	0.0433458	+	1.01606i
$196$	0.698110	−	6.17093i	0.0498650	−	0.440781i
$197$	−10.2849	+	2.75584i	−0.732772	+	0.196346i	−0.605863	−	0.795569i	$-0.707172\pi$
$197$	−10.2849	+	2.75584i	−0.732772	+	0.196346i	−0.126909	+	0.991914i	$0.540505\pi$
$198$	−0.499089	−	0.864448i	−0.0354687	−	0.0614336i
$199$	10.6276	−	18.4076i	0.753372	−	1.30488i	−0.192807	−	0.981237i	$-0.561759\pi$
$199$	10.6276	−	18.4076i	0.753372	−	1.30488i	0.946179	−	0.323643i	$-0.104908\pi$
$200$	8.28797	−	30.9311i	0.586048	−	2.18716i
$201$	−3.19896	+	3.19896i	−0.225637	+	0.225637i
$202$	5.11021	−	19.0716i	0.359553	−	1.34187i
$203$	−4.08957	−	8.10553i	−0.287032	−	0.568897i
$204$	3.53176	+	6.11719i	0.247273	+	0.428289i
$205$	−1.54471	+	0.891841i	−0.107887	+	0.0622888i
$206$	−4.90559	−	4.90559i	−0.341789	−	0.341789i
$207$	6.00569	−	3.46739i	0.417424	−	0.241000i
$208$	−4.94821	+	1.55473i	−0.343097	+	0.107801i
$209$			1.65137i			0.114228i
$210$	−9.19581	−	6.02380i	−0.634571	−	0.415682i
$211$	−11.7558	+	20.3617i	−0.809305	+	1.40176i	0.104041	+	0.994573i	$0.466823\pi$
$211$	−11.7558	+	20.3617i	−0.809305	+	1.40176i	−0.913346	+	0.407184i	$0.866511\pi$
$212$			1.32692i			0.0911332i
$213$	−10.0022	−	2.68009i	−0.685342	−	0.183637i
$214$	5.29197	−	1.41798i	0.361752	−	0.0969310i
$215$	0.301194	+	0.301194i	0.0205412	+	0.0205412i
$216$	2.15363	+	2.15363i	0.146536	+	0.146536i
$217$	−8.93950	+	7.98521i	−0.606853	+	0.542071i
$218$	−10.4272	−	6.02014i	−0.706218	−	0.407735i
$219$	3.95501	+	1.05974i	0.267255	+	0.0716107i
$220$	1.65326	+	2.86353i	0.111463	+	0.193059i
$221$	−21.1452	−	19.4149i	−1.42238	−	1.30599i
$222$	−8.89507	−	5.13557i	−0.596998	−	0.344677i
$223$	1.56806	+	5.85209i	0.105005	+	0.391885i	0.998346	−	0.0574955i	$-0.0183115\pi$
$223$	1.56806	+	5.85209i	0.105005	+	0.391885i	−0.893341	+	0.449380i	$0.851645\pi$
$224$	−3.78512	+	11.4941i	−0.252904	+	0.767984i
$225$	9.10535	−	5.25697i	0.607023	−	0.350465i
$226$	2.73955	−	0.734061i	0.182232	−	0.0488290i
$227$	−5.40197	−	20.1604i	−0.358541	−	1.33809i	−0.875969	−	0.482368i	$-0.839777\pi$
$227$	−5.40197	−	20.1604i	−0.358541	−	1.33809i	0.517427	−	0.855727i	$-0.326890\pi$
$228$	−0.400736	−	1.49557i	−0.0265394	−	0.0990464i
$229$	21.1882	−	5.67737i	1.40016	−	0.375171i	0.521756	−	0.853094i	$-0.325277\pi$
$229$	21.1882	−	5.67737i	1.40016	−	0.375171i	0.878402	+	0.477923i	$0.158610\pi$
$230$	24.9537	−	14.4070i	1.64540	−	0.949973i
$231$	2.45082	−	0.510791i	0.161252	−	0.0336076i
$232$	2.70496	+	10.0950i	0.177589	+	0.662772i
$233$	−9.92317	−	5.72914i	−0.650088	−	0.375329i	0.138402	−	0.990376i	$-0.455803\pi$
$233$	−9.92317	−	5.72914i	−0.650088	−	0.375329i	−0.788490	+	0.615048i	$0.789137\pi$
$234$	−3.37199	−	1.75963i	−0.220434	−	0.115031i
$235$	9.08797	+	15.7408i	0.592833	+	1.02682i
$236$	−4.15597	−	1.11359i	−0.270531	−	0.0724884i
$237$	0.820728	+	0.473848i	0.0533120	+	0.0307797i
$238$	21.7538	−	4.53384i	1.41009	−	0.293885i
$239$	4.89413	+	4.89413i	0.316575	+	0.316575i	0.847450	−	0.530875i	$-0.178137\pi$
$239$	4.89413	+	4.89413i	0.316575	+	0.316575i	−0.530875	+	0.847450i	$0.678137\pi$
$240$	4.00652	+	4.00652i	0.258619	+	0.258619i
$241$	−8.01914	+	2.14872i	−0.516559	+	0.138411i	−0.507674	−	0.861549i	$-0.669495\pi$
$241$	−8.01914	+	2.14872i	−0.516559	+	0.138411i	−0.00888426	+	0.999961i	$0.502828\pi$
$242$	−10.2962	−	2.75886i	−0.661864	−	0.177346i
$243$			1.00000i			0.0641500i
$244$	2.93610	−	5.08547i	0.187964	−	0.325564i
$245$	21.5639	−	17.1808i	1.37767	−	1.09764i
$246$		−	0.477714i		−	0.0304579i
$247$	3.37563	+	5.31038i	0.214786	+	0.337891i
$248$	11.9499	−	6.89926i	0.758817	−	0.438103i
$249$	8.26062	+	8.26062i	0.523496	+	0.523496i
$250$	19.8411	−	11.4553i	1.25486	−	0.724495i
$251$	7.81291	+	13.5324i	0.493146	+	0.854155i	0.999969	−	0.00789592i	$-0.00251338\pi$
$251$	7.81291	+	13.5324i	0.493146	+	0.854155i	−0.506822	+	0.862050i	$0.669180\pi$
$252$	−2.09564	+	1.05734i	−0.132013	+	0.0666060i
$253$	−1.69834	+	6.33829i	−0.106774	+	0.398485i
$254$	6.80441	−	6.80441i	0.426946	−	0.426946i
$255$	−8.11643	+	30.2909i	−0.508271	+	1.89689i
$256$	8.24155	−	14.2748i	0.515097	−	0.892174i
$257$	0.281936	+	0.488328i	0.0175867	+	0.0304611i	0.874685	−	0.484692i	$-0.161068\pi$
$257$	0.281936	+	0.488328i	0.0175867	+	0.0304611i	−0.857098	+	0.515153i	$0.827735\pi$
$258$	−0.110193	+	0.0295262i	−0.00686033	+	0.00183822i
$259$	19.2121	−	17.1612i	1.19378	−	1.06634i
$260$	11.1699	+	5.82887i	0.692728	+	0.361491i
$261$	−1.71573	+	2.97173i	−0.106201	+	0.183945i
$262$	5.84889	−	5.84889i	0.361346	−	0.361346i
$263$	1.80864			0.111526			0.0557628	−	0.998444i	$-0.482241\pi$
$263$	1.80864			0.111526			0.0557628	+	0.998444i	$0.482241\pi$
$264$	−2.88192			−0.177370
$265$	−4.16560	+	4.16560i	−0.255891	+	0.255891i
$266$	−4.86318	−	0.274208i	−0.298180	−	0.0168128i
$267$	−5.17908	−	1.38773i	−0.316955	−	0.0849277i
$268$	1.03880	+	3.87687i	0.0634550	+	0.236817i
$269$	3.98883	+	2.30295i	0.243203	+	0.140413i	0.616648	−	0.787239i	$-0.288490\pi$
$269$	3.98883	+	2.30295i	0.243203	+	0.140413i	−0.373445	+	0.927652i	$0.621824\pi$
$270$			4.15502i			0.252866i
$271$	−1.05005	+	3.91882i	−0.0637857	+	0.238052i	−0.990457	−	0.137821i	$-0.955990\pi$
$271$	−1.05005	+	3.91882i	−0.0637857	+	0.238052i	0.926671	+	0.375872i	$0.122657\pi$
$272$	−11.4532			−0.694455
$273$	6.83708	−	6.65239i	0.413799	−	0.402621i
$274$	−8.02860			−0.485026
$275$	−2.57489	+	9.60962i	−0.155272	+	0.579482i
$276$		−	6.15242i		−	0.370332i
$277$	−10.5733	−	6.10452i	−0.635291	−	0.366785i	0.147507	−	0.989061i	$-0.452875\pi$
$277$	−10.5733	−	6.10452i	−0.635291	−	0.366785i	−0.782798	+	0.622276i	$0.786208\pi$
$278$	−1.21694	−	4.54168i	−0.0729871	−	0.272392i
$279$	4.37613	+	1.17258i	0.261992	+	0.0702005i
$280$	−28.3368	+	14.2971i	−1.69345	+	0.854413i
$281$	0.757979	−	0.757979i	0.0452172	−	0.0452172i	−0.684137	−	0.729354i	$-0.739821\pi$
$281$	0.757979	−	0.757979i	0.0452172	−	0.0452172i	0.729354	+	0.684137i	$0.239821\pi$
$282$	−4.86796			−0.289883
$283$	20.6773			1.22914			0.614568	−	0.788864i	$-0.289331\pi$
$283$	20.6773			1.22914			0.614568	+	0.788864i	$0.289331\pi$
$284$	−6.49609	+	6.49609i	−0.385472	+	0.385472i
$285$	3.43700	−	5.95306i	0.203590	−	0.352629i
$286$	3.43349	−	1.07881i	0.203026	−	0.0637912i
$287$	1.13802	+	0.374759i	0.0671749	+	0.0221213i
$288$	4.41802	−	1.18381i	0.260334	−	0.0697564i
$289$	−23.1946	−	40.1742i	−1.36439	−	2.36319i
$290$	−7.12888	+	12.3476i	−0.418622	+	0.725075i
$291$	−3.09490	+	11.5503i	−0.181426	+	0.677092i
$292$	2.56864	−	2.56864i	0.150318	−	0.150318i
$293$	0.652210	−	2.43408i	0.0381025	−	0.142201i	−0.944254	−	0.329217i	$-0.893215\pi$
$293$	0.652210	−	2.43408i	0.0381025	−	0.142201i	0.982357	+	0.187017i	$0.0598818\pi$
$294$	1.09729	+	7.30232i	0.0639951	+	0.425880i
$295$	−9.55094	−	16.5427i	−0.556077	−	0.963154i
$296$	−25.6817	+	14.8273i	−1.49272	+	0.861822i
$297$	−0.669085	−	0.669085i	−0.0388243	−	0.0388243i
$298$	−0.687454	+	0.396902i	−0.0398232	+	0.0229919i
$299$	7.49493	+	23.8539i	0.433443	+	1.37951i
$300$		−	9.32781i		−	0.538541i
$301$	0.0161072	−	0.285667i	0.000928403	−	0.0164655i
$302$	−0.0345001	+	0.0597559i	−0.00198526	+	0.00343856i
$303$		−	18.7168i		−	1.07525i
$304$	2.42501	+	0.649779i	0.139084	+	0.0372674i
$305$	25.1821	−	6.74752i	1.44192	−	0.386362i
$306$	−5.93888	−	5.93888i	−0.339503	−	0.339503i
$307$	−14.0560	−	14.0560i	−0.802217	−	0.802217i	0.181225	−	0.983442i	$-0.441994\pi$
$307$	−14.0560	−	14.0560i	−0.802217	−	0.802217i	−0.983442	+	0.181225i	$0.941994\pi$
$308$	0.694714	−	2.10961i	0.0395850	−	0.120206i
$309$	−5.69542	−	3.28825i	−0.324001	−	0.187062i
$310$	18.1829	+	4.87209i	1.03272	+	0.276716i
$311$	−5.07374	−	8.78798i	−0.287706	−	0.498321i	0.685556	−	0.728020i	$-0.259559\pi$
$311$	−5.07374	−	8.78798i	−0.287706	−	0.498321i	−0.973262	+	0.229699i	$0.926226\pi$
$312$	−9.26751	+	5.89105i	−0.524669	+	0.333515i
$313$	−23.2110	−	13.4009i	−1.31196	−	0.757461i	−0.329540	−	0.944141i	$-0.606894\pi$
$313$	−23.2110	−	13.4009i	−1.31196	−	0.757461i	−0.982421	+	0.186680i	$0.940227\pi$
$314$	2.02197	+	7.54611i	0.114107	+	0.425852i
$315$	−9.89813	−	3.25954i	−0.557697	−	0.183655i
$316$	0.728137	−	0.420390i	0.0409609	−	0.0236488i
$317$	12.3700	−	3.31452i	0.694767	−	0.186162i	0.105881	−	0.994379i	$-0.466234\pi$
$317$	12.3700	−	3.31452i	0.694767	−	0.186162i	0.588885	+	0.808217i	$0.299567\pi$
$318$	−0.408356	−	1.52400i	−0.0228995	−	0.0854620i
$319$	−0.840371	−	3.13631i	−0.0470517	−	0.175599i
$320$	29.3030	−	7.85171i	1.63809	−	0.438924i
$321$	4.49772	−	2.59676i	0.251038	−	0.144937i
$322$	−18.3838	−	6.05396i	−1.02449	−	0.337374i
$323$	3.59627	+	13.4215i	0.200102	+	0.746791i
$324$	0.768324	+	0.443592i	0.0426847	+	0.0246440i
$325$	11.3632	+	36.1654i	0.630318	+	2.00610i
$326$	−2.44366	−	4.23254i	−0.135342	−	0.234419i
$327$	−11.0247	−	2.95407i	−0.609670	−	0.163361i
$328$	−1.19446	−	0.689624i	−0.0659532	−	0.0380781i
$329$	3.81884	−	11.5965i	0.210539	−	0.639337i
$330$	−2.78006	−	2.78006i	−0.153037	−	0.153037i
$331$	−0.534490	−	0.534490i	−0.0293782	−	0.0293782i	0.692265	−	0.721643i	$-0.256613\pi$
$331$	−0.534490	−	0.534490i	−0.0293782	−	0.0293782i	−0.721643	+	0.692265i	$0.756613\pi$
$332$	10.0112	−	2.68249i	0.549435	−	0.147221i
$333$	−9.40483	−	2.52002i	−0.515381	−	0.138096i
$334$		−	13.3352i		−	0.729671i
$335$	−8.90953	+	15.4318i	−0.486779	+	0.843127i
$336$	0.214260	−	3.79997i	0.0116888	−	0.207305i
$337$			12.9685i			0.706440i	0.935540	+	0.353220i	$0.114913\pi$
$337$			12.9685i			0.706440i	−0.935540	+	0.353220i	$0.885087\pi$
$338$	8.83597	−	10.4877i	0.480613	−	0.570455i
$339$	2.32838	−	1.34429i	0.126460	−	0.0730120i
$340$	19.6729	+	19.6729i	1.06691	+	1.06691i
$341$	−3.71256	+	2.14345i	−0.201046	+	0.116074i
$342$	0.920514	+	1.59438i	0.0497757	+	0.0862140i
$343$	−18.2565	−	3.11459i	−0.985758	−	0.168172i
$344$	−0.0852476	+	0.318148i	−0.00459624	+	0.0171534i
$345$	19.3143	−	19.3143i	1.03985	−	1.03985i
$346$	−5.00154	+	18.6660i	−0.268884	+	1.00349i
$347$	7.19316	−	12.4589i	0.386149	−	0.668830i	−0.605779	−	0.795633i	$-0.707138\pi$
$347$	7.19316	−	12.4589i	0.386149	−	0.668830i	0.991928	+	0.126803i	$0.0404718\pi$
$348$	1.52217	+	2.63647i	0.0815967	+	0.141330i
$349$	−32.9693	+	8.83410i	−1.76481	+	0.472879i	−0.987683	−	0.156468i	$-0.949989\pi$
$349$	−32.9693	+	8.83410i	−1.76481	+	0.472879i	−0.777125	+	0.629347i	$0.783323\pi$
$350$	−27.8721	−	9.17853i	−1.48983	−	0.490613i
$351$	−3.51930	−	0.783899i	−0.187847	−	0.0418414i
$352$	−2.16397	+	3.74810i	−0.115340	+	0.199774i
$353$	−3.92198	+	3.92198i	−0.208746	+	0.208746i	−0.803734	−	0.594988i	$-0.797157\pi$
$353$	−3.92198	+	3.92198i	−0.208746	+	0.208746i	0.594988	+	0.803734i	$0.297157\pi$
$354$	5.11595			0.271910
$355$	−40.7863			−2.16471
$356$	−3.36363	+	3.36363i	−0.178272	+	0.178272i
$357$	18.8066	−	9.48871i	0.995352	−	0.502196i
$358$	18.2807	+	4.89831i	0.966166	+	0.258883i
$359$	1.72057	+	6.42126i	0.0908083	+	0.338901i	0.996351	−	0.0853548i	$-0.0272024\pi$
$359$	1.72057	+	6.42126i	0.0908083	+	0.338901i	−0.905542	+	0.424256i	$0.860536\pi$
$360$	10.3891	+	5.99815i	0.547554	+	0.316130i
$361$			15.9542i			0.839696i
$362$	−3.09473	+	11.5497i	−0.162656	+	0.607039i
$363$	−10.1046			−0.530357
$364$	−2.07832	−	8.20404i	−0.108934	−	0.430009i
$365$	16.1274			0.844148
$366$	−1.80715	+	6.74438i	−0.0944614	+	0.352535i
$367$			7.15046i			0.373251i	0.982431	+	0.186626i	$0.0597551\pi$
$367$			7.15046i			0.373251i	−0.982431	+	0.186626i	$0.940245\pi$
$368$	8.63940	+	4.98796i	0.450360	+	0.260015i
$369$	−0.117207	−	0.437421i	−0.00610153	−	0.0227712i
$370$	−39.0772	−	10.4707i	−2.03153	−	0.544346i
$371$	3.95085	+	0.222767i	0.205118	+	0.0115655i
$372$	2.84214	−	2.84214i	0.147358	−	0.147358i
$373$	15.3396			0.794254			0.397127	−	0.917764i	$-0.370007\pi$
$373$	15.3396			0.794254			0.397127	+	0.917764i	$0.370007\pi$
$374$	7.94723			0.410941
$375$	15.3571	−	15.3571i	0.793037	−	0.793037i
$376$	−7.02735	+	12.1717i	−0.362408	+	0.627709i
$377$	−9.11346	−	8.36770i	−0.469367	−	0.430958i
$378$	2.08151	−	1.85931i	0.107061	−	0.0956325i
$379$	−22.8646	+	6.12656i	−1.17448	+	0.314700i	−0.792734	−	0.609568i	$-0.791343\pi$
$379$	−22.8646	+	6.12656i	−1.17448	+	0.314700i	−0.381743	+	0.924268i	$0.624676\pi$
$380$	−3.04925	−	5.28146i	−0.156423	−	0.270933i
$381$	4.56104	−	7.89995i	0.233669	−	0.404727i
$382$	4.00499	−	14.9468i	0.204913	−	0.764746i
$383$	−0.437956	+	0.437956i	−0.0223785	+	0.0223785i	−0.718207	−	0.695829i	$-0.755037\pi$
$383$	−0.437956	+	0.437956i	−0.0223785	+	0.0223785i	0.695829	+	0.718207i	$0.255037\pi$
$384$	0.264731	−	0.987991i	0.0135095	−	0.0504182i
$385$	8.80361	−	4.44178i	0.448673	−	0.226374i
$386$	6.18138	+	10.7065i	0.314624	+	0.544945i
$387$	−0.0936549	+	0.0540717i	−0.00476074	+	0.00274862i
$388$	7.50152	+	7.50152i	0.380832	+	0.380832i
$389$	8.18610	−	4.72624i	0.415052	−	0.239630i	−0.277906	−	0.960608i	$-0.589640\pi$
$389$	8.18610	−	4.72624i	0.415052	−	0.239630i	0.692958	+	0.720978i	$0.256307\pi$
$390$	−14.6228	−	3.25711i	−0.740453	−	0.164930i
$391$			55.2128i			2.79223i
$392$	19.8426	+	7.79795i	1.00220	+	0.393856i
$393$	3.92055	−	6.79059i	0.197766	−	0.342540i
$394$		−	11.2323i		−	0.565876i
$395$	3.60557	+	0.966109i	0.181416	+	0.0486102i
$396$	−0.810875	+	0.217273i	−0.0407480	+	0.0109184i
$397$	6.32238	+	6.32238i	0.317311	+	0.317311i	0.847734	−	0.530422i	$-0.177967\pi$
$397$	6.32238	+	6.32238i	0.317311	+	0.317311i	−0.530422	+	0.847734i	$0.677967\pi$
$398$	15.8549	+	15.8549i	0.794733	+	0.794733i
$399$	−4.52027	+	0.942096i	−0.226297	+	0.0471638i
$400$	13.0984	+	7.56234i	0.654918	+	0.378117i
$401$	6.40587	+	1.71645i	0.319894	+	0.0857153i	0.415193	−	0.909733i	$-0.363714\pi$
$401$	6.40587	+	1.71645i	0.319894	+	0.0857153i	−0.0952991	+	0.995449i	$0.530381\pi$
$402$	−2.38619	−	4.13300i	−0.119012	−	0.206135i
$403$	−7.55711	+	14.4817i	−0.376446	+	0.721387i
$404$	−14.3805	−	8.30261i	−0.715459	−	0.413070i
$405$	1.01943	+	3.80456i	0.0506559	+	0.189050i
$406$	9.37575	−	1.95405i	0.465310	−	0.0969781i
$407$	7.97874	−	4.60653i	0.395491	−	0.228337i
$408$	−23.4227	+	6.27610i	−1.15960	+	0.310713i
$409$	−4.23667	−	15.8115i	−0.209490	−	0.781826i	−0.988034	−	0.154236i	$-0.950708\pi$
$409$	−4.23667	−	15.8115i	−0.209490	−	0.781826i	0.778544	−	0.627590i	$-0.215958\pi$
$410$	−0.486996	−	1.81749i	−0.0240510	−	0.0897596i
$411$	−7.35143	+	1.96981i	−0.362619	+	0.0971636i
$412$	−5.05288	+	2.91728i	−0.248938	+	0.143724i
$413$	−4.01338	+	12.1873i	−0.197486	+	0.599697i
$414$	1.89339	+	7.06623i	0.0930550	+	0.347286i
$415$	39.8492	+	23.0069i	1.95612	+	1.12937i
$416$	0.702890	+	16.4763i	0.0344620	+	0.807820i
$417$	−2.22859	−	3.86004i	−0.109135	−	0.189027i
$418$	−1.68268	−	0.450872i	−0.0823024	−	0.0220529i
$419$	−19.8994	−	11.4889i	−0.972150	−	0.561271i	−0.0722588	−	0.997386i	$-0.523021\pi$
$419$	−19.8994	−	11.4889i	−0.972150	−	0.561271i	−0.899891	+	0.436115i	$0.856354\pi$
$420$	−6.89512	+	6.15906i	−0.336447	+	0.300532i
$421$	−3.33707	−	3.33707i	−0.162639	−	0.162639i	0.621096	−	0.783735i	$-0.286688\pi$
$421$	−3.33707	−	3.33707i	−0.162639	−	0.162639i	−0.783735	+	0.621096i	$0.786688\pi$
$422$	−17.5380	−	17.5380i	−0.853736	−	0.853736i
$423$	−4.45738	+	1.19435i	−0.216725	+	0.0580713i
$424$	−4.40008	−	1.17900i	−0.213687	−	0.0572572i
$425$			83.7093i			4.06050i
$426$	5.46179	−	9.46010i	0.264625	−	0.458343i
$427$	−14.6489	−	9.59588i	−0.708909	−	0.464377i
$428$		−	4.60761i		−	0.222717i
$429$	2.87921	−	1.83022i	0.139010	−	0.0883638i
$430$	−0.389138	+	0.224669i	−0.0187659	+	0.0108345i
$431$	19.9189	+	19.9189i	0.959459	+	0.959459i	0.999210	−	0.0397503i	$-0.0126562\pi$
$431$	19.9189	+	19.9189i	0.959459	+	0.959459i	−0.0397503	+	0.999210i	$0.512656\pi$
$432$	−1.24581	+	0.719268i	−0.0599390	+	0.0346058i
$433$	9.88975	+	17.1295i	0.475271	+	0.823193i	0.999599	−	0.0283231i	$-0.00901674\pi$
$433$	9.88975	+	17.1295i	0.475271	+	0.823193i	−0.524328	+	0.851516i	$0.675683\pi$
$434$	−5.69584	−	11.2891i	−0.273409	−	0.541896i
$435$	−3.49813	+	13.0552i	−0.167722	+	0.625948i
$436$	−7.16017	+	7.16017i	−0.342910	+	0.342910i
$437$	3.13240	−	11.6903i	0.149843	−	0.559221i
$438$	−2.15966	+	3.74064i	−0.103193	+	0.178735i
$439$	10.9538	+	18.9726i	0.522797	+	0.905511i	0.999648	+	0.0265271i	$0.00844483\pi$
$439$	10.9538	+	18.9726i	0.522797	+	0.905511i	−0.476851	+	0.878984i	$0.658222\pi$
$440$	−10.9645	+	2.93792i	−0.522710	+	0.140060i
$441$	2.79636	+	6.41720i	0.133160	+	0.305581i
$442$	25.5562	−	16.2452i	1.21558	−	0.772707i
$443$	9.87688	−	17.1073i	0.469265	−	0.812791i	−0.530118	−	0.847924i	$-0.677852\pi$
$443$	9.87688	−	17.1073i	0.469265	−	0.812791i	0.999383	+	0.0351334i	$0.0111856\pi$
$444$	−6.10810	+	6.10810i	−0.289877	+	0.289877i
$445$	−21.1188			−1.00113
$446$	−6.39114			−0.302629
$447$	−0.532092	+	0.532092i	−0.0251671	+	0.0251671i
$448$	−17.0461	−	11.1662i	−0.805350	−	0.527552i
$449$	−31.7673	−	8.51202i	−1.49919	−	0.401707i	−0.586362	−	0.810049i	$-0.699440\pi$
$449$	−31.7673	−	8.51202i	−1.49919	−	0.401707i	−0.912829	+	0.408342i	$0.866107\pi$
$450$	2.87061	+	10.7132i	0.135322	+	0.505027i
$451$	0.371093	+	0.214251i	0.0174741	+	0.0100887i
$452$		−	2.38527i		−	0.112194i
$453$	−0.0169291	+	0.0631804i	−0.000795400	+	0.00296847i
$454$	22.0175			1.03333
$455$	19.2305	−	32.2794i	0.901538	−	1.51328i
$456$	5.31538			0.248916
$457$	4.06045	−	15.1538i	0.189940	−	0.708866i	−0.803579	−	0.595198i	$-0.797073\pi$
$457$	4.06045	−	15.1538i	0.189940	−	0.708866i	0.993519	−	0.113668i	$-0.0362599\pi$
$458$			23.1400i			1.08126i
$459$	−6.89506	−	3.98087i	−0.321834	−	0.185811i
$460$	−6.27196	−	23.4073i	−0.292432	−	1.09137i
$461$	1.60974	+	0.431329i	0.0749731	+	0.0200890i	0.296111	−	0.955154i	$-0.404310\pi$
$461$	1.60974	+	0.431329i	0.0749731	+	0.0200890i	−0.221138	+	0.975243i	$0.570977\pi$
$462$	−0.148672	+	2.63674i	−0.00691683	+	0.122672i
$463$	−18.8646	+	18.8646i	−0.876713	+	0.876713i	−0.993193	−	0.116480i	$-0.962839\pi$
$463$	−18.8646	+	18.8646i	−0.876713	+	0.876713i	0.116480	+	0.993193i	$0.462839\pi$
$464$	−4.93627			−0.229161
$465$	17.8446			0.827525
$466$	8.54705	−	8.54705i	0.395934	−	0.395934i
$467$	11.4518	−	19.8351i	0.529926	−	0.917859i	−0.469465	−	0.882951i	$-0.655553\pi$
$467$	11.4518	−	19.8351i	0.529926	−	0.917859i	0.999391	−	0.0349075i	$-0.0111136\pi$
$468$	−2.16342	+	2.35623i	−0.100004	+	0.108917i
$469$	11.7176	−	2.44214i	0.541069	−	0.112767i
$470$	−18.5205	+	4.96255i	−0.854286	+	0.228905i
$471$	3.70286	+	6.41355i	0.170619	+	0.295521i
$472$	7.38535	−	12.7918i	0.339938	−	0.588790i
$473$	0.0264845	−	0.0988416i	0.00121776	−	0.00454474i
$474$	−0.706912	+	0.706912i	−0.0324695	+	0.0324695i
$475$	4.74909	−	17.7239i	0.217903	−	0.813226i
$476$	1.05206	−	18.6587i	0.0482212	−	0.855220i
$477$	−0.747827	−	1.29527i	−0.0342406	−	0.0593065i
$478$	−6.32315	+	3.65067i	−0.289214	+	0.166978i
$479$	−0.542389	−	0.542389i	−0.0247824	−	0.0247824i	0.694607	−	0.719389i	$-0.255578\pi$
$479$	−0.542389	−	0.542389i	−0.0247824	−	0.0247824i	−0.719389	+	0.694607i	$0.755578\pi$
$480$	15.6018	−	9.00773i	0.712124	−	0.411145i
$481$	16.2411	−	31.1230i	0.740532	−	1.41909i
$482$		−	8.75782i		−	0.398908i
$483$	−18.3186	−	1.03289i	−0.833524	−	0.0469979i
$484$	−4.48234	+	7.76365i	−0.203743	+	0.352893i
$485$			47.0990i			2.13866i
$486$	−1.01896	−	0.273028i	−0.0462208	−	0.0123848i
$487$	7.13339	−	1.91138i	0.323245	−	0.0866131i	−0.0935479	−	0.995615i	$-0.529821\pi$
$487$	7.13339	−	1.91138i	0.323245	−	0.0866131i	0.416792	+	0.909002i	$0.363154\pi$
$488$	14.2547	+	14.2547i	0.645280	+	0.645280i
$489$	−3.27600	−	3.27600i	−0.148146	−	0.148146i
$490$	11.6189	+	26.6636i	0.524889	+	1.20454i
$491$	6.17910	+	3.56750i	0.278859	+	0.160999i	0.632907	−	0.774228i	$-0.281862\pi$
$491$	6.17910	+	3.56750i	0.278859	+	0.160999i	−0.354048	+	0.935227i	$0.615195\pi$
$492$	−0.388073	−	0.103984i	−0.0174957	−	0.00468796i
$493$	−13.6602	−	23.6601i	−0.615223	−	1.06560i
$494$	−6.33269	+	1.98974i	−0.284921	+	0.0895226i
$495$	−3.22766	−	1.86349i	−0.145073	−	0.0837577i
$496$	1.68680	+	6.29522i	0.0757395	+	0.282664i
$497$	18.2513	+	20.4324i	0.818682	+	0.916520i
$498$	−10.6726	+	6.16183i	−0.478250	+	0.276118i
$499$	20.6974	−	5.54585i	0.926542	−	0.248266i	0.236163	−	0.971714i	$-0.424110\pi$
$499$	20.6974	−	5.54585i	0.926542	−	0.248266i	0.690380	+	0.723447i	$0.257444\pi$
$500$	−4.98694	−	18.6115i	−0.223023	−	0.832332i
$501$	−3.27179	−	12.2105i	−0.146173	−	0.545523i
$502$	−15.9220	+	4.26629i	−0.710634	+	0.190414i
$503$	20.5890	−	11.8871i	0.918020	−	0.530019i	0.0350174	−	0.999387i	$-0.488851\pi$
$503$	20.5890	−	11.8871i	0.918020	−	0.530019i	0.883003	+	0.469367i	$0.155518\pi$
$504$	−1.64412	−	7.88864i	−0.0732348	−	0.351388i
$505$	−19.0804	−	71.2091i	−0.849068	−	3.16876i
$506$	−5.99475	−	3.46107i	−0.266499	−	0.153863i
$507$	5.51756	−	11.7710i	0.245043	−	0.522769i
$508$	−4.04648	−	7.00871i	−0.179534	−	0.310961i
$509$	29.9347	+	8.02098i	1.32683	+	0.355524i	0.851533	−	0.524301i	$-0.175673\pi$
$509$	29.9347	+	8.02098i	1.32683	+	0.355524i	0.475299	+	0.879824i	$0.342340\pi$
$510$	−28.6491	−	16.5406i	−1.26860	−	0.732429i
$511$	−7.21678	−	8.07924i	−0.319252	−	0.357405i
$512$	10.8487	+	10.8487i	0.479449	+	0.479449i
$513$	1.23405	+	1.23405i	0.0544847	+	0.0544847i
$514$	−0.574561	+	0.153953i	−0.0253428	+	0.00679059i
$515$	−25.0207	−	6.70428i	−1.10254	−	0.295426i
$516$			0.0959431i			0.00422366i
$517$	2.18324	−	3.78149i	0.0960189	−	0.166310i
$518$	12.2410	+	24.2617i	0.537840	+	1.06600i
$519$			18.3187i			0.804104i
$520$	−29.2533	+	31.8605i	−1.28284	+	1.39717i
$521$	23.5185	−	13.5784i	1.03036	−	0.594881i	0.113275	−	0.993564i	$-0.463866\pi$
$521$	23.5185	−	13.5784i	1.03036	−	0.594881i	0.917089	+	0.398683i	$0.130533\pi$
$522$	−2.55962	−	2.55962i	−0.112031	−	0.112031i
$523$	−36.5550	+	21.1050i	−1.59844	+	0.922859i	−0.606651	+	0.794968i	$0.707487\pi$
$523$	−36.5550	+	21.1050i	−1.59844	+	0.922859i	−0.991788	+	0.127891i	$0.959179\pi$
$524$	−3.47825	−	6.02451i	−0.151948	−	0.263182i
$525$	−27.7732	−	1.56598i	−1.21212	−	0.0683449i
$526$	−0.493811	+	1.84293i	−0.0215312	+	0.0803554i
$527$	−25.5058	+	25.5058i	−1.11105	+	1.11105i
$528$	0.352301	−	1.31480i	0.0153319	−	0.0572195i
$529$	12.5455	−	21.7295i	0.545458	−	0.944761i
$530$	−3.10723	−	5.38188i	−0.134970	−	0.233774i
$531$	4.68445	−	1.25519i	0.203288	−	0.0544708i
$532$	−1.28132	+	3.89094i	−0.0555523	+	0.168694i
$533$	1.63130	−	0.0695920i	0.0706593	−	0.00301436i
$534$	2.82807	−	4.89837i	0.122383	−	0.211973i
$535$	14.4647	−	14.4647i	0.625361	−	0.625361i
$536$	−13.7787			−0.595151
$537$	17.9406			0.774196
$538$	−3.43567	+	3.43567i	−0.148122	+	0.148122i
$539$	−6.16465	−	2.42265i	−0.265530	−	0.104351i
$540$	3.37535	+	0.904422i	0.145252	+	0.0389201i
$541$	−1.79457	−	6.69743i	−0.0771547	−	0.287945i	0.916559	−	0.399900i	$-0.130955\pi$
$541$	−1.79457	−	6.69743i	−0.0771547	−	0.287945i	−0.993713	+	0.111955i	$0.964289\pi$
$542$	−3.70642	−	2.13990i	−0.159204	−	0.0919166i
$543$			11.3348i			0.486425i
$544$	−9.42515	+	35.1751i	−0.404100	+	1.50812i
$545$	−44.9558			−1.92570
$546$	4.91178	+	8.78298i	0.210205	+	0.375877i
$547$	32.4507			1.38749			0.693747	−	0.720219i	$-0.255959\pi$
$547$	32.4507			1.38749			0.693747	+	0.720219i	$0.255959\pi$
$548$	−1.74759	+	6.52208i	−0.0746531	+	0.278609i
$549$			6.61892i			0.282488i
$550$	−9.08876	−	5.24740i	−0.387546	−	0.223750i
$551$	1.54997	+	5.78456i	0.0660309	+	0.246431i
$552$	20.4015	+	5.46657i	0.868345	+	0.232672i
$553$	−1.12945	−	2.23858i	−0.0480292	−	0.0951939i
$554$	9.10707	−	9.10707i	0.386922	−	0.386922i
$555$	−38.3503			−1.62788
$556$	−3.95434			−0.167702
$557$	−4.06289	+	4.06289i	−0.172150	+	0.172150i	−0.787923	−	0.615773i	$-0.788844\pi$
$557$	−4.06289	+	4.06289i	−0.172150	+	0.172150i	0.615773	+	0.787923i	$0.288844\pi$
$558$	−2.38961	+	4.13893i	−0.101160	+	0.175215i
$559$	−0.116879	−	0.371987i	−0.00494344	−	0.0157334i
$560$	−3.05864	−	14.6757i	−0.129251	−	0.620160i
$561$	7.27693	−	1.94985i	0.307232	−	0.0823226i
$562$	0.565397	+	0.979297i	0.0238498	+	0.0413091i
$563$	−21.8237	+	37.7998i	−0.919760	+	1.59307i	−0.119981	+	0.992776i	$0.538283\pi$
$563$	−21.8237	+	37.7998i	−0.919760	+	1.59307i	−0.799779	+	0.600294i	$0.795050\pi$
$564$	−1.05961	+	3.95451i	−0.0446176	+	0.166515i
$565$	7.48808	−	7.48808i	0.315026	−	0.315026i
$566$	−5.64548	+	21.0692i	−0.237297	+	0.885605i
$567$	1.44977	−	2.21318i	0.0608845	−	0.0929449i
$568$	−15.7692	−	27.3130i	−0.661661	−	1.14603i
$569$	−2.73813	+	1.58086i	−0.114788	+	0.0662730i	−0.556295	−	0.830985i	$-0.687778\pi$
$569$	−2.73813	+	1.58086i	−0.114788	+	0.0662730i	0.441507	+	0.897258i	$0.354444\pi$
$570$	5.12751	+	5.12751i	0.214768	+	0.214768i
$571$	31.3887	−	18.1222i	1.31357	−	0.758393i	0.330888	−	0.943670i	$-0.392652\pi$
$571$	31.3887	−	18.1222i	1.31357	−	0.758393i	0.982686	+	0.185277i	$0.0593184\pi$
$572$	−0.129007	−	3.02404i	−0.00539406	−	0.126441i
$573$		−	14.6688i		−	0.612796i
$574$	−0.692573	+	1.05727i	−0.0289074	+	0.0441295i
$575$	36.4559	−	63.1435i	1.52032	−	2.63327i
$576$			7.70205i			0.320919i
$577$	5.03959	+	1.35035i	0.209801	+	0.0562160i	0.362189	−	0.932105i	$-0.382030\pi$
$577$	5.03959	+	1.35035i	0.209801	+	0.0562160i	−0.152388	+	0.988321i	$0.548696\pi$
$578$	47.2686	−	12.6656i	1.96611	−	0.526819i
$579$	8.28684	+	8.28684i	0.344389	+	0.344389i
$580$	8.47888	+	8.47888i	0.352066	+	0.352066i
$581$	−6.30630	−	30.2582i	−0.261629	−	1.25532i
$582$	−10.9243	−	6.30714i	−0.452826	−	0.261439i
$583$	1.36701	+	0.366289i	0.0566157	+	0.0151701i
$584$	6.23534	+	10.7999i	0.258020	+	0.446904i
$585$	−14.1885	+	0.605291i	−0.586624	+	0.0250257i
$586$	2.30215	+	1.32915i	0.0951010	+	0.0549066i
$587$	−9.40982	−	35.1179i	−0.388385	−	1.44947i	−0.832762	−	0.553632i	$-0.813242\pi$
$587$	−9.40982	−	35.1179i	−0.388385	−	1.44947i	0.444377	−	0.895840i	$-0.353425\pi$
$588$	6.17093	+	0.698110i	0.254485	+	0.0287896i
$589$	6.84740	−	3.95335i	0.282142	−	0.162895i
$590$	19.4640	−	5.21535i	0.801319	−	0.214713i
$591$	−2.75584	−	10.2849i	−0.113360	−	0.423066i
$592$	−3.62513	−	13.5292i	−0.148992	−	0.556046i
$593$	−40.8740	+	10.9522i	−1.67849	+	0.449751i	−0.967381	−	0.253327i	$-0.918475\pi$
$593$	−40.8740	+	10.9522i	−1.67849	+	0.449751i	−0.711113	+	0.703078i	$0.751809\pi$
$594$	0.864448	−	0.499089i	0.0354687	−	0.0204779i
$595$	61.8779	−	55.2724i	2.53675	−	2.26595i
$596$	0.172787	+	0.644851i	0.00707764	+	0.0264141i
$597$	18.4076	+	10.6276i	0.753372	+	0.434960i
$598$	−26.3524	+	1.12421i	−1.07763	+	0.0459723i
$599$	16.9264	+	29.3174i	0.691594	+	1.19788i	0.971315	+	0.237795i	$0.0764246\pi$
$599$	16.9264	+	29.3174i	0.691594	+	1.19788i	−0.279721	+	0.960081i	$0.590242\pi$
$600$	30.9311	+	8.28797i	1.26276	+	0.338355i
$601$	21.1918	+	12.2351i	0.864431	+	0.499080i	0.865494	−	0.500920i	$-0.167005\pi$
$601$	21.1918	+	12.2351i	0.864431	+	0.499080i	−0.00106241	+	0.999999i	$0.500338\pi$
$602$	0.286684	+	0.0944076i	0.0116844	+	0.00384777i
$603$	−3.19896	−	3.19896i	−0.130272	−	0.130272i
$604$	0.0410334	+	0.0410334i	0.00166962	+	0.00166962i
$605$	−38.4438	+	10.3010i	−1.56296	+	0.418795i
$606$	19.0716	+	5.11021i	0.774729	+	0.207588i
$607$			22.9026i			0.929589i	0.885419	+	0.464795i	$0.153872\pi$
$607$			22.9026i			0.929589i	−0.885419	+	0.464795i	$0.846128\pi$
$608$	3.99119	−	6.91295i	0.161864	−	0.280357i
$609$	8.10553	−	4.08957i	0.328453	−	0.165718i
$610$			27.5017i			1.11351i
$611$	−0.709151	−	16.6231i	−0.0286892	−	0.672499i
$612$	−6.11719	+	3.53176i	−0.247273	+	0.142763i
$613$	−24.6071	−	24.6071i	−0.993870	−	0.993870i	0.00611091	−	0.999981i	$-0.498055\pi$
$613$	−24.6071	−	24.6071i	−0.993870	−	0.993870i	−0.999981	+	0.00611091i	$0.998055\pi$
$614$	18.1601	−	10.4847i	0.732882	−	0.423130i
$615$	−0.891841	−	1.54471i	−0.0359625	−	0.0622888i
$616$	6.37822	+	4.17812i	0.256986	+	0.168341i
$617$	−8.38788	+	31.3040i	−0.337684	+	1.26025i	0.563247	+	0.826289i	$0.309552\pi$
$617$	−8.38788	+	31.3040i	−0.337684	+	1.26025i	−0.900930	+	0.433963i	$0.857115\pi$
$618$	4.90559	−	4.90559i	0.197332	−	0.197332i
$619$	−10.1821	+	38.0001i	−0.409253	+	1.52735i	0.386820	+	0.922155i	$0.373573\pi$
$619$	−10.1821	+	38.0001i	−0.409253	+	1.52735i	−0.796074	+	0.605200i	$0.793093\pi$
$620$	7.91574	−	13.7105i	0.317904	−	0.550625i
$621$	3.46739	+	6.00569i	0.139141	+	0.241000i
$622$	10.3398	−	2.77055i	0.414590	−	0.111089i
$623$	9.45037	+	10.5798i	0.378621	+	0.423869i
$624$	−1.55473	−	4.94821i	−0.0622392	−	0.198087i
$625$	16.4867	−	28.5558i	0.659467	−	1.14223i
$626$	19.9921	−	19.9921i	0.799046	−	0.799046i
$627$	−1.65137			−0.0659495
$628$	6.57024			0.262181
$629$	54.8150	−	54.8150i	2.18562	−	2.18562i
$630$	6.02380	−	9.19581i	0.239994	−	0.366370i
$631$	15.0028	+	4.01998i	0.597251	+	0.160033i	0.544765	−	0.838589i	$-0.316619\pi$
$631$	15.0028	+	4.01998i	0.597251	+	0.160033i	0.0524858	+	0.998622i	$0.483286\pi$
$632$	0.747052	+	2.78804i	0.0297161	+	0.110902i
$633$	−20.3617	−	11.7558i	−0.809305	−	0.467252i
$634$			13.5094i			0.536527i
$635$	9.29932	−	34.7055i	0.369032	−	1.37725i
$636$	−1.32692			−0.0526158
$637$	−24.7761	+	4.81080i	−0.981666	+	0.190611i
$638$	3.42520			0.135605
$639$	2.68009	−	10.0022i	0.106023	−	0.395682i
$640$		−	4.02875i		−	0.159250i
$641$	11.6981	+	6.75390i	0.462047	+	0.266763i	0.712905	−	0.701261i	$-0.247379\pi$
$641$	11.6981	+	6.75390i	0.462047	+	0.266763i	−0.250857	+	0.968024i	$0.580713\pi$
$642$	1.41798	+	5.29197i	0.0559632	+	0.208857i
$643$	−25.1020	−	6.72606i	−0.989926	−	0.265250i	−0.272706	−	0.962097i	$-0.587919\pi$
$643$	−25.1020	−	6.72606i	−0.989926	−	0.265250i	−0.717219	+	0.696848i	$0.754585\pi$
$644$	−8.91957	+	13.6164i	−0.351480	+	0.536563i
$645$	−0.301194	+	0.301194i	−0.0118595	+	0.0118595i
$646$	−14.6578			−0.576702
$647$	23.1112			0.908596			0.454298	−	0.890850i	$-0.349890\pi$
$647$	23.1112			0.908596			0.454298	+	0.890850i	$0.349890\pi$
$648$	−2.15363	+	2.15363i	−0.0846026	+	0.0846026i
$649$	−2.29446	+	3.97413i	−0.0900656	+	0.155998i
$650$	−39.9535	+	1.70444i	−1.56710	+	0.0668535i
$651$	−7.98521	−	8.93950i	−0.312965	−	0.350367i
$652$	−3.97023	+	1.06382i	−0.155486	+	0.0416624i
$653$	16.7511	+	29.0138i	0.655522	+	1.13540i	0.981763	+	0.190110i	$0.0608846\pi$
$653$	16.7511	+	29.0138i	0.655522	+	1.13540i	−0.326241	+	0.945287i	$0.605782\pi$
$654$	6.02014	−	10.4272i	0.235406	−	0.407735i
$655$	7.99345	−	29.8320i	0.312330	−	1.16563i
$656$	0.460640	−	0.460640i	0.0179850	−	0.0179850i
$657$	−1.05974	+	3.95501i	−0.0413445	+	0.154300i
$658$	10.7737	+	7.05741i	0.420002	+	0.275126i
$659$	0.940246	+	1.62855i	0.0366268	+	0.0634395i	0.883758	−	0.467945i	$-0.155005\pi$
$659$	0.940246	+	1.62855i	0.0366268	+	0.0634395i	−0.847131	+	0.531384i	$0.821672\pi$
$660$	−2.86353	+	1.65326i	−0.111463	+	0.0643531i
$661$	34.5943	+	34.5943i	1.34556	+	1.34556i	0.890416	+	0.455148i	$0.150414\pi$
$661$	34.5943	+	34.5943i	1.34556	+	1.34556i	0.455148	+	0.890416i	$0.349586\pi$
$662$	0.690553	−	0.398691i	0.0268391	−	0.0154956i
$663$	19.4149	−	21.1452i	0.754013	−	0.821213i
$664$			35.5807i			1.38080i
$665$	−16.2373	+	8.19236i	−0.629654	+	0.317686i
$666$	5.13557	−	8.89507i	0.198999	−	0.344677i
$667$			23.7964i			0.921399i
$668$	−10.8329	−	2.90268i	−0.419139	−	0.112308i
$669$	−5.85209	+	1.56806i	−0.226255	+	0.0606248i
$670$	−13.2917	−	13.2917i	−0.513504	−	0.513504i
$671$	−4.42862	−	4.42862i	−0.170965	−	0.170965i
$672$	−11.4941	−	3.78512i	−0.443396	−	0.146014i
$673$	−16.4185	−	9.47923i	−0.632887	−	0.365397i	0.148982	−	0.988840i	$-0.452400\pi$
$673$	−16.4185	−	9.47923i	−0.632887	−	0.365397i	−0.781869	+	0.623442i	$0.785734\pi$
$674$	−13.2143	−	3.54077i	−0.508998	−	0.136386i
$675$	5.25697	+	9.10535i	0.202341	+	0.350465i
$676$	−6.59640	−	9.46080i	−0.253708	−	0.363877i
$677$	−7.78358	−	4.49385i	−0.299147	−	0.172713i	0.342913	−	0.939367i	$-0.388587\pi$
$677$	−7.78358	−	4.49385i	−0.299147	−	0.172713i	−0.642060	+	0.766655i	$0.721920\pi$
$678$	0.734061	+	2.73955i	0.0281914	+	0.105212i
$679$	23.5949	−	21.0761i	0.905488	−	0.808827i
$680$	−82.7153	+	47.7557i	−3.17199	+	1.83135i
$681$	20.1604	−	5.40197i	0.772549	−	0.207004i
$682$	−1.17044	−	4.36816i	−0.0448186	−	0.167265i
$683$	−7.52839	−	28.0963i	−0.288066	−	1.07508i	−0.946570	−	0.322499i	$-0.895477\pi$
$683$	−7.52839	−	28.0963i	−0.288066	−	1.07508i	0.658504	−	0.752577i	$-0.271190\pi$
$684$	1.49557	−	0.400736i	0.0571845	−	0.0153225i
$685$	−25.9609	+	14.9885i	−0.991916	+	0.572683i
$686$	8.15817	−	17.7522i	0.311480	−	0.677782i
$687$	5.67737	+	21.1882i	0.216605	+	0.808382i
$688$	−0.134726	−	0.0777840i	−0.00513638	−	0.00296549i
$689$	5.14468	−	1.61647i	0.195997	−	0.0615825i
$690$	14.4070	+	24.9537i	0.548467	+	0.949973i
$691$	−19.4172	−	5.20283i	−0.738666	−	0.197925i	−0.130181	−	0.991490i	$-0.541556\pi$
$691$	−19.4172	−	5.20283i	−0.738666	−	0.197925i	−0.608485	+	0.793565i	$0.708222\pi$
$692$	14.0747	+	8.12605i	0.535041	+	0.308906i
$693$	0.510791	+	2.45082i	0.0194033	+	0.0930991i
$694$	10.7311	+	10.7311i	0.407349	+	0.407349i
$695$	−12.4139	−	12.4139i	−0.470885	−	0.470885i
$696$	−10.0950	+	2.70496i	−0.382652	+	0.102531i
$697$	3.48263	+	0.933168i	0.131914	+	0.0353463i
$698$		−	36.0063i		−	1.36286i
$699$	5.72914	−	9.92317i	0.216696	−	0.375329i
$700$	−13.5231	+	20.6441i	−0.511127	+	0.780275i
$701$			26.4403i			0.998636i	0.866419	+	0.499318i	$0.166416\pi$
$701$			26.4403i			0.998636i	−0.866419	+	0.499318i	$0.833584\pi$
$702$	1.75963	−	3.37199i	0.0664129	−	0.127268i
$703$	−14.7159	+	8.49622i	−0.555020	+	0.320441i
$704$	−5.15333	−	5.15333i	−0.194223	−	0.194223i
$705$	−15.7408	+	9.08797i	−0.592833	+	0.342273i
$706$	−2.92551	−	5.06714i	−0.110103	−	0.190704i
$707$	−27.1349	+	41.4236i	−1.02051	+	1.55790i
$708$	1.11359	−	4.15597i	0.0418512	−	0.156191i
$709$	0.719284	−	0.719284i	0.0270133	−	0.0270133i	−0.693471	−	0.720484i	$-0.743920\pi$
$709$	0.719284	−	0.719284i	0.0270133	−	0.0270133i	0.720484	+	0.693471i	$0.243920\pi$
$710$	11.1358	−	41.5595i	0.417920	−	1.55970i
$711$	−0.473848	+	0.820728i	−0.0177707	+	0.0307797i
$712$	−8.16517	−	14.1425i	−0.306003	−	0.530012i
$713$	30.3475	−	8.13158i	1.13652	−	0.304530i
$714$	4.53384	+	21.7538i	0.169675	+	0.814116i
$715$	9.08836	−	9.89834i	0.339885	−	0.370177i
$716$	7.95833	−	13.7842i	0.297417	−	0.515141i
$717$	−4.89413	+	4.89413i	−0.182775	+	0.182775i
$718$	−7.01275			−0.261713
$719$	32.2667			1.20334			0.601672	−	0.798743i	$-0.294502\pi$
$719$	32.2667			1.20334			0.601672	+	0.798743i	$0.294502\pi$
$720$	−4.00652	+	4.00652i	−0.149314	+	0.149314i
$721$	7.83781	+	15.5345i	0.291895	+	0.578536i
$722$	−16.2567	−	4.35596i	−0.605010	−	0.162112i
$723$	−2.14872	−	8.01914i	−0.0799119	−	0.298235i
$724$	8.70883	+	5.02805i	0.323661	+	0.186866i
$725$			36.0781i			1.33991i
$726$	2.75886	−	10.2962i	0.102391	−	0.382128i
$727$	14.6393			0.542941			0.271471	−	0.962447i	$-0.412490\pi$
$727$	14.6393			0.542941			0.271471	+	0.962447i	$0.412490\pi$
$728$	29.0513	+	0.397744i	1.07671	+	0.0147414i
$729$	−1.00000			−0.0370370
$730$	−4.40325	+	16.4331i	−0.162971	+	0.608218i
$731$		−	0.861008i		−	0.0318455i
$732$	5.08547	+	2.93610i	0.187964	+	0.108521i
$733$	13.0234	+	48.6040i	0.481031	+	1.79523i	0.597305	+	0.802014i	$0.296238\pi$
$733$	13.0234	+	48.6040i	0.481031	+	1.79523i	−0.116275	+	0.993217i	$0.537095\pi$
$734$	−7.28601	−	1.95228i	−0.268931	−	0.0720599i
$735$	17.1808	+	21.5639i	0.633723	+	0.795398i
$736$	22.4286	−	22.4286i	0.826728	−	0.826728i
$737$	4.28075			0.157683
$738$	0.477714			0.0175849
$739$	−14.7764	+	14.7764i	−0.543558	+	0.543558i	−0.924570	−	0.381012i	$-0.875576\pi$
$739$	−14.7764	+	14.7764i	−0.543558	+	0.543558i	0.381012	+	0.924570i	$0.375576\pi$
$740$	−17.0119	+	29.4654i	−0.625369	+	1.08317i
$741$	−5.31038	+	3.37563i	−0.195082	+	0.124007i
$742$	−1.30568	+	3.96492i	−0.0479332	+	0.145557i
$743$	25.4705	−	6.82479i	0.934421	−	0.250377i	0.240682	−	0.970604i	$-0.422629\pi$
$743$	25.4705	−	6.82479i	0.934421	−	0.250377i	0.693739	+	0.720227i	$0.255962\pi$
$744$	6.89926	+	11.9499i	0.252939	+	0.438103i
$745$	−1.48195	+	2.56681i	−0.0542943	+	0.0940406i
$746$	−4.18815	+	15.6304i	−0.153339	+	0.572269i
$747$	−8.26062	+	8.26062i	−0.302240	+	0.302240i
$748$	1.72987	−	6.45597i	0.0632504	−	0.236054i
$749$	−13.7190	−	0.773538i	−0.501280	−	0.0282645i
$750$	11.4553	+	19.8411i	0.418287	+	0.724495i
$751$	13.2528	−	7.65152i	0.483602	−	0.279208i	−0.238314	−	0.971188i	$-0.576595\pi$
$751$	13.2528	−	7.65152i	0.483602	−	0.279208i	0.721916	+	0.691980i	$0.243261\pi$
$752$	−4.69398	−	4.69398i	−0.171172	−	0.171172i
$753$	−13.5324	+	7.81291i	−0.493146	+	0.284718i
$754$	11.0145	−	7.00159i	0.401126	−	0.254983i
$755$			0.257632i			0.00937618i
$756$	−1.05734	−	2.09564i	−0.0384550	−	0.0762177i
$757$	9.00227	−	15.5924i	0.327193	−	0.566715i	−0.654761	−	0.755836i	$-0.727231\pi$
$757$	9.00227	−	15.5924i	0.327193	−	0.566715i	0.981954	+	0.189121i	$0.0605640\pi$
$758$		−	24.9708i		−	0.906979i
$759$	−6.33829	−	1.69834i	−0.230065	−	0.0616459i
$760$	20.2227	−	5.41866i	0.733555	−	0.196556i
$761$	−29.9052	−	29.9052i	−1.08406	−	1.08406i	−0.996126	−	0.0879379i	$-0.971972\pi$
$761$	−29.9052	−	29.9052i	−1.08406	−	1.08406i	−0.0879379	−	0.996126i	$-0.528028\pi$
$762$	6.80441	+	6.80441i	0.246498	+	0.246498i
$763$	20.1171	+	22.5212i	0.728287	+	0.815322i
$764$	−11.2704	−	6.50694i	−0.407747	−	0.235413i
$765$	−30.2909	−	8.11643i	−1.09517	−	0.293450i
$766$	−0.326683	−	0.565832i	−0.0118035	−	0.0204443i
$767$	0.745278	+	17.4699i	0.0269104	+	0.630803i
$768$	14.2748	+	8.24155i	0.515097	+	0.297391i
$769$	−2.44052	−	9.10816i	−0.0880075	−	0.328449i	0.907859	−	0.419275i	$-0.137716\pi$
$769$	−2.44052	−	9.10816i	−0.0880075	−	0.328449i	−0.995867	+	0.0908266i	$0.971049\pi$
$770$	2.12234	+	10.1832i	0.0764840	+	0.366978i
$771$	−0.488328	+	0.281936i	−0.0175867	+	0.0101537i
$772$	10.0430	−	2.69100i	0.361454	−	0.0968513i
$773$	6.30495	+	23.5304i	0.226773	+	0.846329i	0.981686	+	0.190504i	$0.0610124\pi$
$773$	6.30495	+	23.5304i	0.226773	+	0.846329i	−0.754913	+	0.655825i	$0.772321\pi$
$774$	−0.0295262	−	0.110193i	−0.00106130	−	0.00396082i
$775$	46.0104	−	12.3284i	1.65274	−	0.442851i
$776$	−31.5404	+	18.2099i	−1.13223	+	0.653696i
$777$	17.1612	+	19.2121i	0.615653	+	0.689229i
$778$	2.58080	+	9.63167i	0.0925261	+	0.345312i
$779$	−0.684440	−	0.395162i	−0.0245226	−	0.0141581i
$780$	−5.82887	+	11.1699i	−0.208707	+	0.399947i
$781$	4.89914	+	8.48556i	0.175305	+	0.303637i
$782$	−56.2594	−	15.0747i	−2.01183	−	0.539069i
$783$	−2.97173	−	1.71573i	−0.106201	−	0.0613151i
$784$	−5.98327	+	8.09941i	−0.213688	+	0.289264i
$785$	20.6259	+	20.6259i	0.736171	+	0.736171i
$786$	5.84889	+	5.84889i	0.208623	+	0.208623i
$787$	−16.1021	+	4.31455i	−0.573979	+	0.153797i	−0.534121	−	0.845408i	$-0.679357\pi$
$787$	−16.1021	+	4.31455i	−0.573979	+	0.153797i	−0.0398580	+	0.999205i	$0.512691\pi$
$788$	−9.12464	−	2.44494i	−0.325052	−	0.0870974i
$789$			1.80864i			0.0643894i
$790$	−1.96884	+	3.41014i	−0.0700484	+	0.121327i
$791$	−7.10205	−	0.400446i	−0.252520	−	0.0142382i
$792$		−	2.88192i		−	0.102405i
$793$	−23.2940	−	5.18856i	−0.827193	−	0.184251i
$794$	−8.16842	+	4.71604i	−0.289886	+	0.167366i
$795$	−4.16560	−	4.16560i	−0.147738	−	0.147738i
$796$	16.3309	−	9.42866i	0.578834	−	0.334190i
$797$	7.91214	+	13.7042i	0.280263	+	0.485429i	0.971449	−	0.237247i	$-0.0762451\pi$
$797$	7.91214	+	13.7042i	0.280263	+	0.485429i	−0.691187	+	0.722676i	$0.742912\pi$
$798$	0.274208	−	4.86318i	0.00970686	−	0.172155i
$799$	9.50910	−	35.4884i	0.336408	−	1.25549i
$800$	34.0044	−	34.0044i	1.20224	−	1.20224i
$801$	1.38773	−	5.17908i	0.0490331	−	0.182994i
$802$	−3.49797	+	6.05866i	−0.123518	+	0.213939i
$803$	−1.93718	−	3.35530i	−0.0683617	−	0.118406i
$804$	−3.87687	+	1.03880i	−0.136727	+	0.0366358i
$805$	−70.7472	+	14.7448i	−2.49351	+	0.519687i
$806$	−12.6930	−	11.6543i	−0.447090	−	0.410505i
$807$	−2.30295	+	3.98883i	−0.0810677	+	0.140413i
$808$	40.3090	−	40.3090i	1.41807	−	1.41807i
$809$	−36.4976			−1.28319			−0.641594	−	0.767044i	$-0.721727\pi$
$809$	−36.4976			−1.28319			−0.641594	+	0.767044i	$0.721727\pi$
$810$	−4.15502			−0.145992
$811$	−33.0051	+	33.0051i	−1.15897	+	1.15897i	−0.174269	+	0.984698i	$0.555756\pi$
$811$	−33.0051	+	33.0051i	−1.15897	+	1.15897i	−0.984698	+	0.174269i	$0.944244\pi$
$812$	0.453432	−	8.04177i	0.0159123	−	0.282211i
$813$	−3.91882	−	1.05005i	−0.137439	−	0.0368267i
$814$	2.51542	+	9.38769i	0.0881656	+	0.329038i
$815$	−15.8034	−	9.12409i	−0.553569	−	0.319603i
$816$		−	11.4532i		−	0.400944i
$817$	−0.0488477	+	0.182302i	−0.00170897	+	0.00637795i
$818$	17.2679			0.603758
$819$	6.65239	+	6.83708i	0.232453	+	0.238907i
$820$	−1.58245			−0.0552617
$821$	−9.07253	+	33.8592i	−0.316634	+	1.18169i	0.605825	+	0.795598i	$0.292843\pi$
$821$	−9.07253	+	33.8592i	−0.316634	+	1.18169i	−0.922459	+	0.386095i	$0.873824\pi$
$822$		−	8.02860i		−	0.280030i
$823$	11.1912	+	6.46124i	0.390100	+	0.225225i	0.682204	−	0.731162i	$-0.261022\pi$
$823$	11.1912	+	6.46124i	0.390100	+	0.225225i	−0.292103	+	0.956387i	$0.594355\pi$
$824$	−5.18415	−	19.3475i	−0.180598	−	0.674002i
$825$	−9.60962	−	2.57489i	−0.334564	−	0.0896461i
$826$	−11.3225	−	7.41693i	−0.393961	−	0.258068i
$827$	16.1945	−	16.1945i	0.563138	−	0.563138i	−0.367059	−	0.930198i	$-0.619635\pi$
$827$	16.1945	−	16.1945i	0.563138	−	0.563138i	0.930198	+	0.367059i	$0.119635\pi$
$828$	6.15242			0.213811
$829$	18.0216			0.625918			0.312959	−	0.949767i	$-0.398680\pi$
$829$	18.0216			0.625918			0.312959	+	0.949767i	$0.398680\pi$
$830$	−34.3230	+	34.3230i	−1.19137	+	1.19137i
$831$	6.10452	−	10.5733i	0.211764	−	0.366785i
$832$	−27.1059	−	6.03763i	−0.939727	−	0.209317i
$833$	−55.3789	−	6.26495i	−1.91877	−	0.217068i
$834$	4.54168	−	1.21694i	0.157265	−	0.0421391i
$835$	−24.8954	−	43.1202i	−0.861542	−	1.49223i
$836$	−0.732536	+	1.26879i	−0.0253353	+	0.0438820i
$837$	−1.17258	+	4.37613i	−0.0405303	+	0.151261i
$838$	17.1398	−	17.1398i	0.592085	−	0.592085i
$839$	−9.35633	+	34.9183i	−0.323016	+	1.20551i	0.593275	+	0.805000i	$0.297835\pi$
$839$	−9.35633	+	34.9183i	−0.323016	+	1.20551i	−0.916291	+	0.400513i	$0.868832\pi$
$840$	−14.2971	−	28.3368i	−0.493296	−	0.977711i
$841$	8.61256	+	14.9174i	0.296985	+	0.514393i
$842$	4.31145	−	2.48921i	0.148582	−	0.0857840i
$843$	0.757979	+	0.757979i	0.0261062	+	0.0261062i
$844$	−18.0646	+	10.4296i	−0.621808	+	0.359001i
$845$	8.99218	−	50.4083i	0.309340	−	1.73410i
$846$		−	4.86796i		−	0.167364i
$847$	22.3634	+	14.6494i	0.768417	+	0.503359i
$848$	1.07578	−	1.86330i	0.0369423	−	0.0639859i
$849$			20.6773i			0.709641i
$850$	−85.2961	−	22.8550i	−2.92563	−	0.783920i
$851$	−65.2203	+	17.4757i	−2.23572	+	0.599060i
$852$	−6.49609	−	6.49609i	−0.222552	−	0.222552i
$853$	−9.67121	−	9.67121i	−0.331136	−	0.331136i	0.521882	−	0.853018i	$-0.325230\pi$
$853$	−9.67121	−	9.67121i	−0.331136	−	0.331136i	−0.853018	+	0.521882i	$0.825230\pi$
$854$	13.7773	−	12.3066i	0.471451	−	0.421123i
$855$	5.95306	+	3.43700i	0.203590	+	0.117543i
$856$	15.2789	+	4.09397i	0.522222	+	0.139929i
$857$	−15.8586	−	27.4680i	−0.541720	−	0.938287i	−0.998805	−	0.0488643i	$-0.984440\pi$
$857$	−15.8586	−	27.4680i	−0.541720	−	0.938287i	0.457085	−	0.889423i	$-0.348894\pi$
$858$	1.07881	+	3.43349i	0.0368299	+	0.117217i
$859$	3.30317	+	1.90709i	0.112703	+	0.0650690i	0.555292	−	0.831656i	$-0.312607\pi$
$859$	3.30317	+	1.90709i	0.112703	+	0.0650690i	−0.442589	+	0.896725i	$0.645940\pi$
$860$	0.0978072	+	0.365022i	0.00333520	+	0.0124471i
$861$	−0.374759	+	1.13802i	−0.0127717	+	0.0387835i
$862$	−25.7349	+	14.8581i	−0.876534	+	0.506067i
$863$	25.7366	−	6.89611i	0.876086	−	0.234746i	0.207368	−	0.978263i	$-0.433510\pi$
$863$	25.7366	−	6.89611i	0.876086	−	0.234746i	0.668718	+	0.743517i	$0.266844\pi$
$864$	1.18381	+	4.41802i	0.0402739	+	0.150304i
$865$	18.6747	+	69.6948i	0.634958	+	2.36970i
$866$	−20.1544	+	5.40036i	−0.684875	+	0.183512i
$867$	40.1742	−	23.1946i	1.36439	−	0.787730i
$868$	−10.4106	+	2.16974i	−0.353359	+	0.0736456i
$869$	−0.232093	−	0.866181i	−0.00787320	−	0.0293832i
$870$	−12.3476	−	7.12888i	−0.418622	−	0.241692i
$871$	13.7658	−	8.75045i	0.466435	−	0.296498i
$872$	−17.3812	−	30.1052i	−0.588603	−	1.01949i
$873$	−11.5503	−	3.09490i	−0.390919	−	0.104747i
$874$	11.0566	+	6.38355i	0.373996	+	0.215927i
$875$	−56.2522	+	11.7239i	−1.90167	+	0.396339i
$876$	2.56864	+	2.56864i	0.0867862	+	0.0867862i
$877$	−0.217046	−	0.217046i	−0.00732914	−	0.00732914i	0.703433	−	0.710762i	$-0.251650\pi$
$877$	−0.217046	−	0.217046i	−0.00732914	−	0.00732914i	−0.710762	+	0.703433i	$0.751650\pi$
$878$	−22.3229	+	5.98141i	−0.753362	+	0.201863i
$879$	2.43408	+	0.652210i	0.0820996	+	0.0219985i
$880$		−	5.36140i		−	0.180733i
$881$	4.00050	−	6.92907i	0.134780	−	0.233446i	−0.790733	−	0.612161i	$-0.790300\pi$
$881$	4.00050	−	6.92907i	0.134780	−	0.233446i	0.925513	+	0.378715i	$0.123634\pi$
$882$	−7.30232	+	1.09729i	−0.245882	+	0.0369476i
$883$			49.8829i			1.67869i	0.543597	+	0.839346i	$0.317062\pi$
$883$			49.8829i			1.67869i	−0.543597	+	0.839346i	$0.682938\pi$
$884$	−7.63409	−	24.2968i	−0.256762	−	0.817190i
$885$	16.5427	−	9.55094i	0.556077	−	0.321051i
$886$	14.7349	+	14.7349i	0.495028	+	0.495028i
$887$	8.54675	−	4.93447i	0.286972	−	0.165683i	−0.349604	−	0.936898i	$-0.613684\pi$
$887$	8.54675	−	4.93447i	0.286972	−	0.165683i	0.636575	+	0.771215i	$0.280350\pi$
$888$	−14.8273	−	25.6817i	−0.497573	−	0.861822i
$889$	−21.5475	+	10.8716i	−0.722680	+	0.364621i
$890$	5.76604	−	21.5192i	0.193278	−	0.721324i
$891$	0.669085	−	0.669085i	0.0224152	−	0.0224152i
$892$	−1.39116	+	5.19188i	−0.0465795	+	0.173837i
$893$	−4.02674	+	6.97453i	−0.134750	+	0.233394i
$894$	−0.396902	−	0.687454i	−0.0132744	−	0.0229919i
$895$	68.2563	−	18.2892i	2.28156	−	0.611341i
$896$	−2.01825	+	1.80281i	−0.0674252	+	0.0602275i
$897$	−23.8539	+	7.49493i	−0.796459	+	0.250249i
$898$	17.3467	−	30.0454i	0.578868	−	1.00263i
$899$	−10.9928	+	10.9928i	−0.366631	+	0.366631i
$900$	9.32781			0.310927
$901$	11.9080			0.396713
$902$	−0.319631	+	0.319631i	−0.0106426	+	0.0106426i
$903$	0.285667	+	0.0161072i	0.00950639	+	0.000536014i
$904$	7.90959	+	2.11937i	0.263069	+	0.0704891i
$905$	11.5551	+	43.1241i	0.384104	+	1.43349i
$906$	−0.0597559	−	0.0345001i	−0.00198526	−	0.00114619i
$907$			20.7745i			0.689806i	0.938638	+	0.344903i	$0.112088\pi$
$907$			20.7745i			0.689806i	−0.938638	+	0.344903i	$0.887912\pi$
$908$	4.79254	−	17.8860i	0.159046	−	0.593568i
$909$	18.7168			0.620796
$910$	27.6408	+	28.4082i	0.916284	+	0.941722i
$911$	15.1029			0.500380			0.250190	−	0.968197i	$-0.419507\pi$
$911$	15.1029			0.500380			0.250190	+	0.968197i	$0.419507\pi$
$912$	−0.649779	+	2.42501i	−0.0215163	+	0.0803000i
$913$		−	11.0541i		−	0.365838i
$914$	14.3325	+	8.27485i	0.474076	+	0.273708i
$915$	6.74752	+	25.1821i	0.223066	+	0.832494i
$916$	18.7979	+	5.03687i	0.621099	+	0.166423i
$917$	−18.5217	+	9.34494i	−0.611639	+	0.308597i
$918$	5.93888	−	5.93888i	0.196012	−	0.196012i
$919$	−8.72439			−0.287791			−0.143896	−	0.989593i	$-0.545963\pi$
$919$	−8.72439			−0.287791			−0.143896	+	0.989593i	$0.545963\pi$
$920$	83.1916			2.74275
$921$	14.0560	−	14.0560i	0.463160	−	0.463160i
$922$	−0.879010	+	1.52249i	−0.0289486	+	0.0501405i
$923$	33.1000	+	17.2728i	1.08950	+	0.568541i
$924$	2.10961	+	0.694714i	0.0694011	+	0.0228544i
$925$	−98.8819	+	26.4953i	−3.25122	+	0.871161i
$926$	−14.0716	−	24.3728i	−0.462422	−	0.800939i
$927$	3.28825	−	5.69542i	0.108000	−	0.187062i
$928$	−4.06218	+	15.1602i	−0.133347	+	0.497659i
$929$	13.2612	−	13.2612i	0.435087	−	0.435087i	−0.455268	−	0.890355i	$-0.650457\pi$
$929$	13.2612	−	13.2612i	0.435087	−	0.435087i	0.890355	+	0.455268i	$0.150457\pi$
$930$	−4.87209	+	18.1829i	−0.159762	+	0.596240i
$931$	11.3700	+	4.46831i	0.372637	+	0.146443i
$932$	−5.08280	−	8.80368i	−0.166493	−	0.288374i
$933$	8.78798	−	5.07374i	0.287706	−	0.166107i
$934$	17.0844	+	17.0844i	0.559019	+	0.559019i
$935$	25.6978	−	14.8366i	0.840408	−	0.485210i
$936$	−5.89105	−	9.26751i	−0.192555	−	0.302918i
$937$		−	21.0904i		−	0.688992i	−0.938788	−	0.344496i	$-0.888050\pi$
$937$		−	21.0904i		−	0.688992i	0.938788	−	0.344496i	$-0.111950\pi$
$938$	−0.710813	+	12.6065i	−0.0232089	+	0.411617i
$939$	13.4009	−	23.2110i	0.437320	−	0.757461i
$940$			16.1254i			0.525953i
$941$	−4.47139	−	1.19811i	−0.145763	−	0.0390572i	0.185200	−	0.982701i	$-0.440707\pi$
$941$	−4.47139	−	1.19811i	−0.145763	−	0.0390572i	−0.330963	+	0.943644i	$0.607374\pi$
$942$	−7.54611	+	2.02197i	−0.245866	+	0.0658795i
$943$	−2.22061	−	2.22061i	−0.0723132	−	0.0723132i
$944$	4.93311	+	4.93311i	0.160559	+	0.160559i
$945$	3.25954	−	9.89813i	0.106033	−	0.321986i
$946$	0.0934842	+	0.0539732i	0.00303943	+	0.00175482i
$947$	−31.7665	−	8.51180i	−1.03227	−	0.276596i	−0.297364	−	0.954764i	$-0.596108\pi$
$947$	−31.7665	−	8.51180i	−1.03227	−	0.276596i	−0.734907	+	0.678168i	$0.762774\pi$
$948$	0.420390	+	0.728137i	0.0136536	+	0.0236488i
$949$	−13.0882	−	6.82988i	−0.424860	−	0.221707i
$950$	16.7632	+	9.67823i	0.543870	+	0.314003i
$951$	3.31452	+	12.3700i	0.107481	+	0.401124i
$952$	60.9377	+	20.0673i	1.97500	+	0.650386i
$953$	−2.61428	+	1.50935i	−0.0846848	+	0.0488928i	−0.541744	−	0.840543i	$-0.682236\pi$
$953$	−2.61428	+	1.50935i	−0.0846848	+	0.0488928i	0.457060	+	0.889436i	$0.348903\pi$
$954$	1.52400	−	0.408356i	0.0493415	−	0.0132210i
$955$	−14.9538	−	55.8082i	−0.483893	−	1.80591i
$956$	1.58928	+	5.93128i	0.0514011	+	0.191831i
$957$	3.13631	−	0.840371i	0.101382	−	0.0271653i
$958$	0.700759	−	0.404583i	0.0226405	−	0.0130715i
$959$	19.1258	+	6.29831i	0.617605	+	0.203383i
$960$	7.85171	+	29.3030i	0.253413	+	0.945749i
$961$	−9.07123	−	5.23728i	−0.292620	−	0.168944i
$962$	27.2787	+	25.0465i	0.879500	+	0.807531i
$963$	2.59676	+	4.49772i	0.0836794	+	0.144937i
$964$	−7.11446	−	1.90631i	−0.229141	−	0.0613982i
$965$	39.9757	+	23.0800i	1.28686	+	0.742970i
$966$	6.05396	−	18.3838i	0.194783	−	0.591490i
$967$	−13.5833	−	13.5833i	−0.436809	−	0.436809i	0.454128	−	0.890936i	$-0.349951\pi$
$967$	−13.5833	−	13.5833i	−0.436809	−	0.436809i	−0.890936	+	0.454128i	$0.849951\pi$
$968$	−21.7617	−	21.7617i	−0.699447	−	0.699447i
$969$	−13.4215	+	3.59627i	−0.431160	+	0.115529i
$970$	−47.9918	−	12.8594i	−1.54092	−	0.412889i
$971$			30.1296i			0.966904i	0.875371	+	0.483452i	$0.160617\pi$
$971$			30.1296i			0.966904i	−0.875371	+	0.483452i	$0.839383\pi$
$972$	−0.443592	+	0.768324i	−0.0142282	+	0.0246440i
$973$	−0.663866	+	11.7739i	−0.0212826	+	0.377454i
$974$			7.79047i			0.249623i
$975$	−36.1654	+	11.3632i	−1.15822	+	0.363914i
$976$	−8.24590	+	4.76077i	−0.263945	+	0.152389i
$977$	14.7964	+	14.7964i	0.473379	+	0.473379i	0.903006	−	0.429628i	$-0.141355\pi$
$977$	14.7964	+	14.7964i	0.473379	+	0.473379i	−0.429628	+	0.903006i	$0.641355\pi$
$978$	4.23254	−	2.44366i	0.135342	−	0.0781395i
$979$	2.53674	+	4.39376i	0.0810745	+	0.140425i
$980$	24.1894	−	3.63483i	0.772701	−	0.116110i
$981$	2.95407	−	11.0247i	0.0943162	−	0.351993i
$982$	−5.32220	+	5.32220i	−0.169838	+	0.169838i
$983$	1.47016	−	5.48673i	0.0468910	−	0.174999i	−0.938509	−	0.345255i	$-0.887793\pi$
$983$	1.47016	−	5.48673i	0.0468910	−	0.174999i	0.985400	+	0.170255i	$0.0544592\pi$
$984$	0.689624	−	1.19446i	0.0219844	−	0.0380781i
$985$	−20.9696	−	36.3203i	−0.668146	−	1.15726i
$986$	27.8382	−	7.45923i	0.886549	−	0.237550i
$987$	11.5965	+	3.81884i	0.369121	+	0.121555i
$988$	0.237939	+	5.57750i	0.00756985	+	0.177444i
$989$	−0.374975	+	0.649475i	−0.0119235	+	0.0206521i
$990$	2.78006	−	2.78006i	0.0883561	−	0.0883561i
$991$	−52.6658			−1.67298			−0.836492	−	0.547979i	$-0.815397\pi$
$991$	−52.6658			−1.67298			−0.836492	+	0.547979i	$0.815397\pi$
$992$	20.7219			0.657922
$993$	0.534490	−	0.534490i	0.0169615	−	0.0169615i
$994$	−25.8029	+	13.0186i	−0.818417	+	0.412925i
$995$	80.8670	+	21.6682i	2.56366	+	0.686929i
$996$	2.68249	+	10.0112i	0.0849979	+	0.317216i
$997$	22.9450	+	13.2473i	0.726675	+	0.419546i	0.817205	−	0.576348i	$-0.195523\pi$
$997$	22.9450	+	13.2473i	0.726675	+	0.419546i	−0.0905295	+	0.995894i	$0.528856\pi$
$998$			22.6039i			0.715514i
$999$	2.52002	−	9.40483i	0.0797298	−	0.297556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.124.4	yes	36
3.2	odd	2		819.2.gh.c.397.6		36
7.3	odd	6		273.2.bt.a.241.4	yes	36
13.2	odd	12		273.2.bt.a.145.4	✓	36
21.17	even	6		819.2.et.c.514.6		36
39.2	even	12		819.2.et.c.145.6		36
91.80	even	12	inner	273.2.cg.a.262.4	yes	36
273.80	odd	12		819.2.gh.c.262.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.4	✓	36	13.2	odd	12
273.2.bt.a.241.4	yes	36	7.3	odd	6
273.2.cg.a.124.4	yes	36	1.1	even	1	trivial
273.2.cg.a.262.4	yes	36	91.80	even	12	inner
819.2.et.c.145.6		36	39.2	even	12
819.2.et.c.514.6		36	21.17	even	6
819.2.gh.c.262.6		36	273.80	odd	12
819.2.gh.c.397.6		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.273028 + 1.01896i) q^{2} +1.00000i q^{3} +(0.768324 + 0.443592i) q^{4} +(1.01943 + 3.80456i) q^{5} +(-1.01896 - 0.273028i) q^{6} +(1.44977 - 2.21318i) q^{7} +(-2.15363 + 2.15363i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.273028 + 1.01896i) q^{2} +1.00000i q^{3} +(0.768324 + 0.443592i) q^{4} +(1.01943 + 3.80456i) q^{5} +(-1.01896 - 0.273028i) q^{6} +(1.44977 - 2.21318i) q^{7} +(-2.15363 + 2.15363i) q^{8} -1.00000 q^{9} -4.15502 q^{10} +(0.669085 - 0.669085i) q^{11} +(-0.443592 + 0.768324i) q^{12} +(0.783899 - 3.51930i) q^{13} +(1.85931 + 2.08151i) q^{14} +(-3.80456 + 1.01943i) q^{15} +(-0.719268 - 1.24581i) q^{16} +(3.98087 - 6.89506i) q^{17} +(0.273028 - 1.01896i) q^{18} +(-1.23405 + 1.23405i) q^{19} +(-0.904422 + 3.37535i) q^{20} +(2.21318 + 1.44977i) q^{21} +(0.499089 + 0.864448i) q^{22} +(-6.00569 + 3.46739i) q^{23} +(-2.15363 - 2.15363i) q^{24} +(-9.10535 + 5.25697i) q^{25} +(3.37199 + 1.75963i) q^{26} -1.00000i q^{27} +(2.09564 - 1.05734i) q^{28} +(1.71573 - 2.97173i) q^{29} -4.15502i q^{30} +(-4.37613 - 1.17258i) q^{31} +(-4.41802 + 1.18381i) q^{32} +(0.669085 + 0.669085i) q^{33} +(5.93888 + 5.93888i) q^{34} +(9.89813 + 3.25954i) q^{35} +(-0.768324 - 0.443592i) q^{36} +(9.40483 + 2.52002i) q^{37} +(-0.920514 - 1.59438i) q^{38} +(3.51930 + 0.783899i) q^{39} +(-10.3891 - 5.99815i) q^{40} +(0.117207 + 0.437421i) q^{41} +(-2.08151 + 1.85931i) q^{42} +(0.0936549 - 0.0540717i) q^{43} +(0.810875 - 0.217273i) q^{44} +(-1.01943 - 3.80456i) q^{45} +(-1.89339 - 7.06623i) q^{46} +(4.45738 - 1.19435i) q^{47} +(1.24581 - 0.719268i) q^{48} +(-2.79636 - 6.41720i) q^{49} +(-2.87061 - 10.7132i) q^{50} +(6.89506 + 3.98087i) q^{51} +(2.16342 - 2.35623i) q^{52} +(0.747827 + 1.29527i) q^{53} +(1.01896 + 0.273028i) q^{54} +(3.22766 + 1.86349i) q^{55} +(1.64412 + 7.88864i) q^{56} +(-1.23405 - 1.23405i) q^{57} +(2.55962 + 2.55962i) q^{58} +(-4.68445 + 1.25519i) q^{59} +(-3.37535 - 0.904422i) q^{60} -6.61892i q^{61} +(2.38961 - 4.13893i) q^{62} +(-1.44977 + 2.21318i) q^{63} -7.70205i q^{64} +(14.1885 - 0.605291i) q^{65} +(-0.864448 + 0.499089i) q^{66} +(3.19896 + 3.19896i) q^{67} +(6.11719 - 3.53176i) q^{68} +(-3.46739 - 6.00569i) q^{69} +(-6.02380 + 9.19581i) q^{70} +(-2.68009 + 10.0022i) q^{71} +(2.15363 - 2.15363i) q^{72} +(1.05974 - 3.95501i) q^{73} +(-5.13557 + 8.89507i) q^{74} +(-5.25697 - 9.10535i) q^{75} +(-1.49557 + 0.400736i) q^{76} +(-0.510791 - 2.45082i) q^{77} +(-1.75963 + 3.37199i) q^{78} +(0.473848 - 0.820728i) q^{79} +(4.00652 - 4.00652i) q^{80} +1.00000 q^{81} -0.477714 q^{82} +(8.26062 - 8.26062i) q^{83} +(1.05734 + 2.09564i) q^{84} +(30.2909 + 8.11643i) q^{85} +(0.0295262 + 0.110193i) q^{86} +(2.97173 + 1.71573i) q^{87} +2.88192i q^{88} +(-1.38773 + 5.17908i) q^{89} +4.15502 q^{90} +(-6.65239 - 6.83708i) q^{91} -6.15242 q^{92} +(1.17258 - 4.37613i) q^{93} +4.86796i q^{94} +(-5.95306 - 3.43700i) q^{95} +(-1.18381 - 4.41802i) q^{96} +(11.5503 + 3.09490i) q^{97} +(7.30232 - 1.09729i) q^{98} +(-0.669085 + 0.669085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more