LMFDB - Embedded newform 561.2.m.d.460.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, 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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			460.6
Character	$\chi$	$=$	561.460
Dual form			561.2.m.d.511.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.768351 - 2.36474i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.38360 - 2.45833i) q^{4} +(-1.12021 - 3.44766i) q^{5} +(0.768351 + 2.36474i) q^{6} +(0.586739 + 0.426291i) q^{7} +(-4.38997 + 3.18950i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.768351 - 2.36474i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.38360 - 2.45833i) q^{4} +(-1.12021 - 3.44766i) q^{5} +(0.768351 + 2.36474i) q^{6} +(0.586739 + 0.426291i) q^{7} +(-4.38997 + 3.18950i) q^{8} +(0.309017 - 0.951057i) q^{9} -9.01354 q^{10} +(-1.82015 - 2.77256i) q^{11} +4.18236 q^{12} +(-1.35232 + 4.16203i) q^{13} +(1.45889 - 1.05994i) q^{14} +(2.93275 + 2.13077i) q^{15} +(1.58446 + 4.87646i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-2.01157 - 1.46149i) q^{18} +(2.28002 - 1.65653i) q^{19} +(-4.68513 + 14.4194i) q^{20} -0.725250 q^{21} +(-7.95489 + 2.17388i) q^{22} +1.17318 q^{23} +(1.67682 - 5.16071i) q^{24} +(-6.58640 + 4.78530i) q^{25} +(8.80305 + 6.39579i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.937327 - 2.88480i) q^{28} +(-6.25010 - 4.54096i) q^{29} +(7.29210 - 5.29802i) q^{30} +(-1.24187 + 3.82209i) q^{31} +1.89639 q^{32} +(3.10220 + 1.17319i) q^{33} +2.48644 q^{34} +(0.812434 - 2.50041i) q^{35} +(-3.38360 + 2.45833i) q^{36} +(5.56433 + 4.04272i) q^{37} +(-2.16541 - 6.66445i) q^{38} +(-1.35232 - 4.16203i) q^{39} +(15.9140 + 11.5622i) q^{40} +(6.03883 - 4.38746i) q^{41} +(-0.557246 + 1.71503i) q^{42} -4.72866 q^{43} +(-0.657210 + 13.8557i) q^{44} -3.62508 q^{45} +(0.901416 - 2.77427i) q^{46} +(6.13709 - 4.45886i) q^{47} +(-4.14816 - 3.01382i) q^{48} +(-2.00058 - 6.15715i) q^{49} +(6.25532 + 19.2519i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(14.8074 - 10.7582i) q^{52} +(-3.25738 + 10.0252i) q^{53} +2.48644 q^{54} +(-7.51988 + 9.38110i) q^{55} -3.93542 q^{56} +(-0.870890 + 2.68032i) q^{57} +(-15.5405 + 11.2908i) q^{58} +(-7.83628 - 5.69339i) q^{59} +(-4.68513 - 14.4194i) q^{60} +(-2.23986 - 6.89359i) q^{61} +(8.08406 + 5.87342i) q^{62} +(0.586739 - 0.426291i) q^{63} +(-1.71182 + 5.26845i) q^{64} +15.8641 q^{65} +(5.15787 - 6.43447i) q^{66} -2.28767 q^{67} +(1.29242 - 3.97766i) q^{68} +(-0.949125 + 0.689580i) q^{69} +(-5.28859 - 3.84239i) q^{70} +(-3.05132 - 9.39099i) q^{71} +(1.67682 + 5.16071i) q^{72} +(-4.68756 - 3.40571i) q^{73} +(13.8353 - 10.0520i) q^{74} +(2.51578 - 7.74277i) q^{75} -11.7870 q^{76} +(0.113965 - 2.40268i) q^{77} -10.8812 q^{78} +(5.13999 - 15.8193i) q^{79} +(15.0374 - 10.9253i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.73528 - 17.6514i) q^{82} +(-3.66246 - 11.2719i) q^{83} +(2.45395 + 1.78290i) q^{84} +(2.93275 - 2.13077i) q^{85} +(-3.63327 + 11.1821i) q^{86} +7.72554 q^{87} +(16.8334 + 6.36608i) q^{88} +12.1940 q^{89} +(-2.78534 + 8.57238i) q^{90} +(-2.56770 + 1.86554i) q^{91} +(-3.96958 - 2.88407i) q^{92} +(-1.24187 - 3.82209i) q^{93} +(-5.82860 - 17.9386i) q^{94} +(-8.26526 - 6.00506i) q^{95} +(-1.53421 + 1.11467i) q^{96} +(4.13455 - 12.7248i) q^{97} -16.0972 q^{98} +(-3.19931 + 0.874295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.768351	−	2.36474i	0.543306	−	1.67212i	−0.181678	−	0.983358i	$-0.558153\pi$
$2$	0.768351	−	2.36474i	0.543306	−	1.67212i	0.724984	−	0.688766i	$-0.241847\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−3.38360	−	2.45833i	−1.69180	−	1.22916i
$5$	−1.12021	−	3.44766i	−0.500974	−	1.54184i	−0.807435	−	0.589957i	$-0.799145\pi$
$5$	−1.12021	−	3.44766i	−0.500974	−	1.54184i	0.306461	−	0.951883i	$-0.400855\pi$
$6$	0.768351	+	2.36474i	0.313678	+	0.965401i
$7$	0.586739	+	0.426291i	0.221767	+	0.161123i	0.693122	−	0.720821i	$-0.256235\pi$
$7$	0.586739	+	0.426291i	0.221767	+	0.161123i	−0.471355	+	0.881944i	$0.656235\pi$
$8$	−4.38997	+	3.18950i	−1.55209	+	1.12766i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−9.01354			−2.85033
$11$	−1.82015	−	2.77256i	−0.548795	−	0.835957i
$11$	−1.82015	−	2.77256i	−0.548795	−	0.835957i
$12$	4.18236			1.20734
$13$	−1.35232	+	4.16203i	−0.375067	+	1.15434i	0.568366	+	0.822776i	$0.307576\pi$
$13$	−1.35232	+	4.16203i	−0.375067	+	1.15434i	−0.943433	+	0.331563i	$0.892424\pi$
$14$	1.45889	−	1.05994i	0.389905	−	0.283282i
$15$	2.93275	+	2.13077i	0.757234	+	0.550163i
$16$	1.58446	+	4.87646i	0.396114	+	1.21911i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−2.01157	−	1.46149i	−0.474131	−	0.344476i
$19$	2.28002	−	1.65653i	0.523072	−	0.380034i	−0.294688	−	0.955594i	$-0.595216\pi$
$19$	2.28002	−	1.65653i	0.523072	−	0.380034i	0.817760	+	0.575559i	$0.195216\pi$
$20$	−4.68513	+	14.4194i	−1.04763	+	3.22427i
$21$	−0.725250			−0.158262
$22$	−7.95489	+	2.17388i	−1.69599	+	0.463472i
$23$	1.17318			0.244626			0.122313	−	0.992492i	$-0.460969\pi$
$23$	1.17318			0.244626			0.122313	+	0.992492i	$0.460969\pi$
$24$	1.67682	−	5.16071i	0.342279	−	1.05343i
$25$	−6.58640	+	4.78530i	−1.31728	+	0.957059i
$26$	8.80305	+	6.39579i	1.72642	+	1.25432i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.937327	−	2.88480i	−0.177138	−	0.545175i
$29$	−6.25010	−	4.54096i	−1.16061	−	0.843235i	−0.170758	−	0.985313i	$-0.554622\pi$
$29$	−6.25010	−	4.54096i	−1.16061	−	0.843235i	−0.989856	+	0.142078i	$0.954622\pi$
$30$	7.29210	−	5.29802i	1.33135	−	0.967282i
$31$	−1.24187	+	3.82209i	−0.223047	+	0.686468i	0.775437	+	0.631425i	$0.217530\pi$
$31$	−1.24187	+	3.82209i	−0.223047	+	0.686468i	−0.998484	+	0.0550432i	$0.982470\pi$
$32$	1.89639			0.335237
$33$	3.10220	+	1.17319i	0.540023	+	0.204226i
$34$	2.48644			0.426420
$35$	0.812434	−	2.50041i	0.137326	−	0.422647i
$36$	−3.38360	+	2.45833i	−0.563933	+	0.409722i
$37$	5.56433	+	4.04272i	0.914770	+	0.664619i	0.942217	−	0.335004i	$-0.108738\pi$
$37$	5.56433	+	4.04272i	0.914770	+	0.664619i	−0.0274466	+	0.999623i	$0.508738\pi$
$38$	−2.16541	−	6.66445i	−0.351276	−	1.08112i
$39$	−1.35232	−	4.16203i	−0.216545	−	0.666458i
$40$	15.9140	+	11.5622i	2.51622	+	1.82814i
$41$	6.03883	−	4.38746i	0.943106	−	0.685207i	−0.00606021	−	0.999982i	$-0.501929\pi$
$41$	6.03883	−	4.38746i	0.943106	−	0.685207i	0.949166	+	0.314775i	$0.101929\pi$
$42$	−0.557246	+	1.71503i	−0.0859849	+	0.264634i
$43$	−4.72866			−0.721115			−0.360557	−	0.932737i	$-0.617413\pi$
$43$	−4.72866			−0.721115			−0.360557	+	0.932737i	$0.617413\pi$
$44$	−0.657210	+	13.8557i	−0.0990782	+	2.08883i
$45$	−3.62508			−0.540396
$46$	0.901416	−	2.77427i	0.132907	−	0.409044i
$47$	6.13709	−	4.45886i	0.895187	−	0.650391i	−0.0420382	−	0.999116i	$-0.513385\pi$
$47$	6.13709	−	4.45886i	0.895187	−	0.650391i	0.937225	+	0.348725i	$0.113385\pi$
$48$	−4.14816	−	3.01382i	−0.598736	−	0.435007i
$49$	−2.00058	−	6.15715i	−0.285797	−	0.879593i
$50$	6.25532	+	19.2519i	0.884636	+	2.72263i
$51$	−0.809017	−	0.587785i	−0.113285	−	0.0823064i
$52$	14.8074	−	10.7582i	2.05341	−	1.49189i
$53$	−3.25738	+	10.0252i	−0.447435	+	1.37706i	0.432356	+	0.901703i	$0.357682\pi$
$53$	−3.25738	+	10.0252i	−0.447435	+	1.37706i	−0.879791	+	0.475361i	$0.842318\pi$
$54$	2.48644			0.338361
$55$	−7.51988	+	9.38110i	−1.01398	+	1.26495i
$56$	−3.93542			−0.525892
$57$	−0.870890	+	2.68032i	−0.115352	+	0.355017i
$58$	−15.5405	+	11.2908i	−2.04056	+	1.48256i
$59$	−7.83628	−	5.69339i	−1.02020	−	0.741216i	−0.0538734	−	0.998548i	$-0.517157\pi$
$59$	−7.83628	−	5.69339i	−1.02020	−	0.741216i	−0.966323	+	0.257332i	$0.917157\pi$
$60$	−4.68513	−	14.4194i	−0.604848	−	1.86153i
$61$	−2.23986	−	6.89359i	−0.286785	−	0.882634i	−0.985858	−	0.167583i	$-0.946404\pi$
$61$	−2.23986	−	6.89359i	−0.286785	−	0.882634i	0.699073	−	0.715051i	$-0.253596\pi$
$62$	8.08406	+	5.87342i	1.02668	+	0.745925i
$63$	0.586739	−	0.426291i	0.0739222	−	0.0537076i
$64$	−1.71182	+	5.26845i	−0.213978	+	0.658557i
$65$	15.8641			1.96770
$66$	5.15787	−	6.43447i	0.634889	−	0.792028i
$67$	−2.28767			−0.279484			−0.139742	−	0.990188i	$-0.544627\pi$
$67$	−2.28767			−0.279484			−0.139742	+	0.990188i	$0.544627\pi$
$68$	1.29242	−	3.97766i	0.156729	−	0.482362i
$69$	−0.949125	+	0.689580i	−0.114261	+	0.0830157i
$70$	−5.28859	−	3.84239i	−0.632108	−	0.459253i
$71$	−3.05132	−	9.39099i	−0.362125	−	1.11451i	−0.951762	−	0.306837i	$-0.900729\pi$
$71$	−3.05132	−	9.39099i	−0.362125	−	1.11451i	0.589637	−	0.807668i	$-0.299271\pi$
$72$	1.67682	+	5.16071i	0.197615	+	0.608196i
$73$	−4.68756	−	3.40571i	−0.548638	−	0.398609i	0.278645	−	0.960394i	$-0.410115\pi$
$73$	−4.68756	−	3.40571i	−0.548638	−	0.398609i	−0.827283	+	0.561786i	$0.810115\pi$
$74$	13.8353	−	10.0520i	1.60833	−	1.16852i
$75$	2.51578	−	7.74277i	0.290497	−	0.894058i
$76$	−11.7870			−1.35206
$77$	0.113965	−	2.40268i	0.0129875	−	0.273811i
$78$	−10.8812			−1.23205
$79$	5.13999	−	15.8193i	0.578295	−	1.77981i	−0.0463816	−	0.998924i	$-0.514769\pi$
$79$	5.13999	−	15.8193i	0.578295	−	1.77981i	0.624676	−	0.780884i	$-0.285231\pi$
$80$	15.0374	−	10.9253i	1.68124	−	1.22149i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−5.73528	−	17.6514i	−0.633355	−	1.94927i
$83$	−3.66246	−	11.2719i	−0.402007	−	1.23725i	−0.923369	−	0.383914i	$-0.874576\pi$
$83$	−3.66246	−	11.2719i	−0.402007	−	1.23725i	0.521362	−	0.853335i	$-0.325424\pi$
$84$	2.45395	+	1.78290i	0.267748	+	0.194531i
$85$	2.93275	−	2.13077i	0.318102	−	0.231115i
$86$	−3.63327	+	11.1821i	−0.391786	+	1.20579i
$87$	7.72554			0.828265
$88$	16.8334	+	6.36608i	1.79445	+	0.678626i
$89$	12.1940			1.29257			0.646283	−	0.763098i	$-0.276323\pi$
$89$	12.1940			1.29257			0.646283	+	0.763098i	$0.276323\pi$
$90$	−2.78534	+	8.57238i	−0.293600	+	0.903608i
$91$	−2.56770	+	1.86554i	−0.269168	+	0.195562i
$92$	−3.96958	−	2.88407i	−0.413858	−	0.300685i
$93$	−1.24187	−	3.82209i	−0.128776	−	0.396333i
$94$	−5.82860	−	17.9386i	−0.601175	−	1.85023i
$95$	−8.26526	−	6.00506i	−0.847998	−	0.616106i
$96$	−1.53421	+	1.11467i	−0.156585	+	0.113765i
$97$	4.13455	−	12.7248i	0.419800	−	1.29201i	−0.488086	−	0.872795i	$-0.662305\pi$
$97$	4.13455	−	12.7248i	0.419800	−	1.29201i	0.907886	−	0.419217i	$-0.137695\pi$
$98$	−16.0972			−1.62606
$99$	−3.19931	+	0.874295i	−0.321543	+	0.0878699i
$100$	34.0496			3.40496
$101$	−4.19399	+	12.9078i	−0.417317	+	1.28437i	0.492845	+	0.870117i	$0.335957\pi$
$101$	−4.19399	+	12.9078i	−0.417317	+	1.28437i	−0.910162	+	0.414253i	$0.864043\pi$
$102$	−2.01157	+	1.46149i	−0.199175	+	0.144709i
$103$	0.511220	+	0.371423i	0.0503720	+	0.0365974i	0.612686	−	0.790326i	$-0.290089\pi$
$103$	0.511220	+	0.371423i	0.0503720	+	0.0365974i	−0.562314	+	0.826924i	$0.690089\pi$
$104$	−7.33811	−	22.5844i	−0.719561	−	2.21458i
$105$	0.812434	+	2.50041i	0.0792854	+	0.244015i
$106$	21.2041	+	15.4057i	2.05953	+	1.49633i
$107$	−6.07676	+	4.41502i	−0.587463	+	0.426816i	−0.841407	−	0.540402i	$-0.818272\pi$
$107$	−6.07676	+	4.41502i	−0.587463	+	0.426816i	0.253944	+	0.967219i	$0.418272\pi$
$108$	1.29242	−	3.97766i	0.124363	−	0.382751i
$109$	4.97803			0.476809			0.238404	−	0.971166i	$-0.423376\pi$
$109$	4.97803			0.476809			0.238404	+	0.971166i	$0.423376\pi$
$110$	16.4060	+	24.9905i	1.56425	+	2.38275i
$111$	−6.87789			−0.652820
$112$	−1.14913	+	3.53665i	−0.108582	+	0.334182i
$113$	7.95258	−	5.77789i	0.748116	−	0.543538i	−0.147127	−	0.989118i	$-0.547002\pi$
$113$	7.95258	−	5.77789i	0.748116	−	0.543538i	0.895242	+	0.445580i	$0.147002\pi$
$114$	5.66912	+	4.11886i	0.530962	+	0.385766i
$115$	−1.31421	−	4.04474i	−0.122551	−	0.377174i
$116$	9.98465	+	30.7296i	0.927051	+	2.85317i
$117$	3.54043	+	2.57227i	0.327313	+	0.237807i
$118$	−19.4844	+	14.1562i	−1.79368	+	1.30319i
$119$	−0.224114	+	0.689753i	−0.0205445	+	0.0632296i
$120$	−19.6708			−1.79569
$121$	−4.37414	+	10.0929i	−0.397649	+	0.917538i
$122$	−18.0226			−1.63169
$123$	−2.30663	+	7.09907i	−0.207981	+	0.640101i
$124$	13.5980	−	9.87950i	1.22113	−	0.887205i
$125$	9.21246	+	6.69325i	0.823988	+	0.598662i
$126$	−0.557246	−	1.71503i	−0.0496434	−	0.152787i
$127$	−4.37329	−	13.4596i	−0.388067	−	1.19435i	−0.934231	−	0.356669i	$-0.883912\pi$
$127$	−4.37329	−	13.4596i	−0.388067	−	1.19435i	0.546164	−	0.837678i	$-0.316088\pi$
$128$	14.2117	+	10.3254i	1.25615	+	0.912643i
$129$	3.82557	−	2.77944i	0.336823	−	0.244716i
$130$	12.1892	−	37.5146i	1.06907	−	3.29025i
$131$	−7.88245			−0.688693			−0.344347	−	0.938843i	$-0.611900\pi$
$131$	−7.88245			−0.688693			−0.344347	+	0.938843i	$0.611900\pi$
$132$	−7.61251	−	11.5958i	−0.662584	−	1.00929i
$133$	2.04394			0.177232
$134$	−1.75773	+	5.40975i	−0.151845	+	0.467331i
$135$	2.93275	−	2.13077i	0.252411	−	0.183388i
$136$	−4.38997	−	3.18950i	−0.376436	−	0.273497i
$137$	5.52529	+	17.0051i	0.472057	+	1.45284i	0.849886	+	0.526967i	$0.176671\pi$
$137$	5.52529	+	17.0051i	0.472057	+	1.45284i	−0.377829	+	0.925876i	$0.623329\pi$
$138$	0.901416	+	2.77427i	0.0767336	+	0.236162i
$139$	6.78161	+	4.92713i	0.575208	+	0.417913i	0.836993	−	0.547213i	$-0.184311\pi$
$139$	6.78161	+	4.92713i	0.575208	+	0.417913i	−0.261785	+	0.965126i	$0.584311\pi$
$140$	−8.89579	+	6.46317i	−0.751832	+	0.546238i
$141$	−2.34416	+	7.21459i	−0.197414	+	0.607578i
$142$	−24.5517			−2.06034
$143$	14.0009	−	3.82610i	1.17081	−	0.319955i
$144$	5.12741			0.427284
$145$	−8.65425	+	26.6350i	−0.718696	+	2.21192i
$146$	−11.6553	+	8.46809i	−0.964601	+	0.700824i
$147$	5.23759	+	3.80533i	0.431989	+	0.313858i
$148$	−8.88912	−	27.3579i	−0.730681	−	2.24881i
$149$	1.10702	+	3.40706i	0.0906908	+	0.279118i	0.986107	−	0.166113i	$-0.0531217\pi$
$149$	1.10702	+	3.40706i	0.0906908	+	0.279118i	−0.895416	+	0.445231i	$0.853122\pi$
$150$	−16.3766	−	11.8983i	−1.33715	−	0.971494i
$151$	−3.09866	+	2.25131i	−0.252166	+	0.183209i	−0.706686	−	0.707527i	$-0.749811\pi$
$151$	−3.09866	+	2.25131i	−0.252166	+	0.183209i	0.454520	+	0.890736i	$0.349811\pi$
$152$	−4.72571	+	14.5442i	−0.383305	+	1.17969i
$153$	1.00000			0.0808452
$154$	−5.59415	−	2.11560i	−0.450789	−	0.170480i
$155$	14.5684			1.17017
$156$	−5.65591	+	17.4071i	−0.452835	+	1.39368i
$157$	13.2785	−	9.64742i	1.05974	−	0.769948i	0.0857017	−	0.996321i	$-0.472687\pi$
$157$	13.2785	−	9.64742i	1.05974	−	0.769948i	0.974041	+	0.226373i	$0.0726868\pi$
$158$	−33.4592	−	24.3095i	−2.66187	−	1.93396i
$159$	−3.25738	−	10.0252i	−0.258327	−	0.795048i
$160$	−2.12436	−	6.53810i	−0.167945	−	0.516882i
$161$	0.688353	+	0.500118i	0.0542498	+	0.0394148i
$162$	−2.01157	+	1.46149i	−0.158044	+	0.114825i
$163$	−0.297511	+	0.915645i	−0.0233029	+	0.0717188i	−0.962032	−	0.272938i	$-0.912005\pi$
$163$	−0.297511	+	0.915645i	−0.0233029	+	0.0717188i	0.938729	+	0.344657i	$0.112005\pi$
$164$	−31.2188			−2.43778
$165$	0.569641	−	12.0095i	0.0443465	−	0.934941i
$166$	−29.4691			−2.28725
$167$	−0.375861	+	1.15678i	−0.0290850	+	0.0895143i	−0.964545	−	0.263917i	$-0.914985\pi$
$167$	−0.375861	+	1.15678i	−0.0290850	+	0.0895143i	0.935460	+	0.353432i	$0.114985\pi$
$168$	3.18382	−	2.31318i	0.245637	−	0.178466i
$169$	−4.97647	−	3.61562i	−0.382805	−	0.278124i
$170$	−2.78534	−	8.57238i	−0.213625	−	0.657472i
$171$	−0.870890	−	2.68032i	−0.0665986	−	0.204969i
$172$	15.9999	+	11.6246i	1.21998	+	0.886369i
$173$	1.96384	−	1.42681i	0.149308	−	0.108478i	−0.510624	−	0.859804i	$-0.670585\pi$
$173$	1.96384	−	1.42681i	0.149308	−	0.108478i	0.659931	+	0.751326i	$0.270585\pi$
$174$	5.93593	−	18.2689i	0.450001	−	1.38496i
$175$	−5.90443			−0.446333
$176$	10.6363	−	13.2689i	0.801742	−	1.00018i
$177$	9.68617			0.728057
$178$	9.36930	−	28.8357i	0.702259	−	2.16133i
$179$	0.193641	−	0.140689i	0.0144734	−	0.0105156i	−0.580525	−	0.814242i	$-0.697153\pi$
$179$	0.193641	−	0.140689i	0.0144734	−	0.0105156i	0.594998	+	0.803727i	$0.297153\pi$
$180$	12.2658	+	8.91165i	0.914241	+	0.664235i
$181$	−0.416198	−	1.28093i	−0.0309358	−	0.0952105i	0.934396	−	0.356235i	$-0.115940\pi$
$181$	−0.416198	−	1.28093i	−0.0309358	−	0.0952105i	−0.965332	+	0.261024i	$0.915940\pi$
$182$	2.43863	+	7.50533i	0.180763	+	0.556332i
$183$	5.86404	+	4.26047i	0.433482	+	0.314943i
$184$	−5.15023	+	3.74186i	−0.379680	+	0.275854i
$185$	7.70470	−	23.7126i	0.566461	−	1.74339i
$186$	−9.99245			−0.732682
$187$	2.07440	−	2.58783i	0.151695	−	0.189241i
$188$	−31.7268			−2.31392
$189$	−0.224114	+	0.689753i	−0.0163019	+	0.0501722i
$190$	−20.5510	+	14.9312i	−1.49093	+	1.08322i
$191$	11.6026	+	8.42978i	0.839534	+	0.609957i	0.922241	−	0.386617i	$-0.126356\pi$
$191$	11.6026	+	8.42978i	0.839534	+	0.609957i	−0.0827062	+	0.996574i	$0.526356\pi$
$192$	−1.71182	−	5.26845i	−0.123540	−	0.380218i
$193$	3.70974	+	11.4174i	0.267033	+	0.821842i	0.991218	+	0.132237i	$0.0422160\pi$
$193$	3.70974	+	11.4174i	0.267033	+	0.821842i	−0.724185	+	0.689605i	$0.757784\pi$
$194$	−26.9142	−	19.5543i	−1.93232	−	1.40392i
$195$	−12.8344	+	9.32471i	−0.919088	+	0.667756i
$196$	−8.36715	+	25.7514i	−0.597653	+	1.83939i
$197$	8.58144			0.611402			0.305701	−	0.952128i	$-0.401109\pi$
$197$	8.58144			0.611402			0.305701	+	0.952128i	$0.401109\pi$
$198$	−0.390715	+	8.23731i	−0.0277669	+	0.585400i
$199$	24.4696			1.73460			0.867301	−	0.497784i	$-0.165853\pi$
$199$	24.4696			1.73460			0.867301	+	0.497784i	$0.165853\pi$
$200$	13.6514	−	42.0146i	0.965297	−	2.97088i
$201$	1.85077	−	1.34466i	0.130543	−	0.0948450i
$202$	27.3011	+	19.8354i	1.92090	+	1.39561i
$203$	−1.73141	−	5.32872i	−0.121521	−	0.374003i
$204$	1.29242	+	3.97766i	0.0904875	+	0.278492i
$205$	−21.8912	−	15.9049i	−1.52895	−	1.11085i
$206$	1.27111	−	0.923519i	0.0885628	−	0.0643446i
$207$	0.362534	−	1.11576i	0.0251978	−	0.0775509i
$208$	−22.4387			−1.55584
$209$	−8.74279	−	3.30635i	−0.604752	−	0.228705i
$210$	6.53706			0.451100
$211$	−1.05011	+	3.23190i	−0.0722924	+	0.222493i	−0.980674	−	0.195649i	$-0.937319\pi$
$211$	−1.05011	+	3.23190i	−0.0722924	+	0.222493i	0.908382	+	0.418142i	$0.137319\pi$
$212$	35.6668	−	25.9135i	2.44961	−	1.77975i
$213$	7.98845	+	5.80395i	0.547360	+	0.397680i
$214$	5.77130	+	17.7622i	0.394518	+	1.21420i
$215$	5.29711	+	16.3028i	0.361260	+	1.11184i
$216$	−4.38997	−	3.18950i	−0.298699	−	0.217018i
$217$	−2.35798	+	1.71317i	−0.160070	+	0.116298i
$218$	3.82487	−	11.7717i	0.259053	−	0.797283i
$219$	5.79415			0.391532
$220$	48.5061	−	13.2555i	3.27028	−	0.893688i
$221$	−4.37621			−0.294376
$222$	−5.28463	+	16.2644i	−0.354681	+	1.09160i
$223$	−11.0367	+	8.01861i	−0.739070	+	0.536966i	−0.892420	−	0.451206i	$-0.850994\pi$
$223$	−11.0367	+	8.01861i	−0.739070	+	0.536966i	0.153349	+	0.988172i	$0.450994\pi$
$224$	1.11269	+	0.808413i	0.0743444	+	0.0540144i
$225$	2.51578	+	7.74277i	0.167719	+	0.516185i
$226$	−7.55283	−	23.2452i	−0.502407	−	1.54625i
$227$	−21.2695	−	15.4532i	−1.41171	−	1.02566i	−0.993072	−	0.117510i	$-0.962509\pi$
$227$	−21.2695	−	15.4532i	−1.41171	−	1.02566i	−0.418635	−	0.908155i	$-0.637491\pi$
$228$	9.53586	−	6.92821i	0.631528	−	0.458832i
$229$	−7.66374	+	23.5866i	−0.506434	+	1.55864i	0.291912	+	0.956445i	$0.405708\pi$
$229$	−7.66374	+	23.5866i	−0.506434	+	1.55864i	−0.798346	+	0.602199i	$0.794292\pi$
$230$	−10.5745			−0.697264
$231$	1.32006	+	2.01080i	0.0868536	+	0.132301i
$232$	41.9211			2.75225
$233$	−1.97924	+	6.09148i	−0.129664	+	0.399066i	−0.994722	−	0.102606i	$-0.967282\pi$
$233$	−1.97924	+	6.09148i	−0.129664	+	0.399066i	0.865058	+	0.501673i	$0.167282\pi$
$234$	8.80305	−	6.39579i	0.575474	−	0.418106i
$235$	−22.2475	−	16.1637i	−1.45127	−	1.05441i
$236$	12.5186	+	38.5283i	0.814892	+	2.50798i
$237$	5.13999	+	15.8193i	0.333879	+	1.02757i
$238$	1.45889	+	1.05994i	0.0945657	+	0.0687060i
$239$	−15.7112	+	11.4148i	−1.01627	+	0.738365i	−0.965515	−	0.260346i	$-0.916163\pi$
$239$	−15.7112	+	11.4148i	−1.01627	+	0.738365i	−0.0507568	+	0.998711i	$0.516163\pi$
$240$	−5.74379	+	17.6776i	−0.370760	+	1.14108i
$241$	22.7317			1.46428			0.732140	−	0.681154i	$-0.238522\pi$
$241$	22.7317			1.46428			0.732140	+	0.681154i	$0.238522\pi$
$242$	20.5063	+	18.0986i	1.31819	+	1.16342i
$243$	1.00000			0.0641500
$244$	−9.36792	+	28.8315i	−0.599719	+	1.84575i
$245$	−18.9867	+	13.7946i	−1.21302	+	0.881307i
$246$	15.0151	+	10.9091i	0.957331	+	0.695542i
$247$	3.81120	+	11.7297i	0.242501	+	0.746341i
$248$	−6.73877	−	20.7398i	−0.427912	−	1.31698i
$249$	9.58843	+	6.96640i	0.607642	+	0.441478i
$250$	22.9062	−	16.6423i	1.44871	−	1.05255i
$251$	1.80227	−	5.54681i	0.113758	−	0.350112i	−0.877928	−	0.478793i	$-0.841074\pi$
$251$	1.80227	−	5.54681i	0.113758	−	0.350112i	0.991686	+	0.128681i	$0.0410744\pi$
$252$	−3.03325			−0.191077
$253$	−2.13537	−	3.25272i	−0.134249	−	0.204497i
$254$	−35.1887			−2.20794
$255$	−1.12021	+	3.44766i	−0.0701504	+	0.215901i
$256$	26.3732	−	19.1612i	1.64832	−	1.19758i
$257$	2.90925	+	2.11370i	0.181474	+	0.131849i	0.674814	−	0.737988i	$-0.264224\pi$
$257$	2.90925	+	2.11370i	0.181474	+	0.131849i	−0.493339	+	0.869837i	$0.664224\pi$
$258$	−3.63327	−	11.1821i	−0.226198	−	0.696165i
$259$	1.54143	+	4.74405i	0.0957801	+	0.294781i
$260$	−53.6779	−	38.9993i	−3.32896	−	2.41863i
$261$	−6.25010	+	4.54096i	−0.386871	+	0.281078i
$262$	−6.05649	+	18.6400i	−0.374171	+	1.15158i
$263$	20.2491			1.24861			0.624307	−	0.781179i	$-0.285381\pi$
$263$	20.2491			1.24861			0.624307	+	0.781179i	$0.285381\pi$
$264$	−17.3604	+	4.74418i	−1.06846	+	0.291984i
$265$	38.2123			2.34737
$266$	1.57046	−	4.83339i	0.0962913	−	0.296354i
$267$	−9.86519	+	7.16748i	−0.603740	+	0.438643i
$268$	7.74057	+	5.62385i	0.472830	+	0.343531i
$269$	−6.34154	−	19.5172i	−0.386650	−	1.18999i	−0.935276	−	0.353919i	$-0.884849\pi$
$269$	−6.34154	−	19.5172i	−0.386650	−	1.18999i	0.548626	−	0.836068i	$-0.315151\pi$
$270$	−2.78534	−	8.57238i	−0.169510	−	0.521699i
$271$	−7.96199	−	5.78473i	−0.483657	−	0.351397i	0.319083	−	0.947727i	$-0.396625\pi$
$271$	−7.96199	−	5.78473i	−0.483657	−	0.351397i	−0.802740	+	0.596330i	$0.796625\pi$
$272$	−4.14816	+	3.01382i	−0.251519	+	0.182740i
$273$	0.980773	−	3.01851i	0.0593591	−	0.182688i
$274$	44.4580			2.68580
$275$	25.2557	+	9.55121i	1.52298	+	0.575960i
$276$	4.90667			0.295347
$277$	6.19388	−	19.0628i	0.372154	−	1.14537i	−0.573224	−	0.819398i	$-0.694308\pi$
$277$	6.19388	−	19.0628i	0.372154	−	1.14537i	0.945379	−	0.325974i	$-0.105692\pi$
$278$	16.8620	−	12.2510i	1.01132	−	0.734765i
$279$	3.25127	+	2.36218i	0.194648	+	0.141420i
$280$	4.40851	+	13.5680i	0.263459	+	0.810842i
$281$	−2.94475	−	9.06301i	−0.175669	−	0.540654i	0.823994	−	0.566598i	$-0.191741\pi$
$281$	−2.94475	−	9.06301i	−0.175669	−	0.540654i	−0.999663	+	0.0259442i	$0.991741\pi$
$282$	15.2595	+	11.0867i	0.908689	+	0.660201i
$283$	−11.9741	+	8.69972i	−0.711789	+	0.517145i	−0.883750	−	0.467959i	$-0.844990\pi$
$283$	−11.9741	+	8.69972i	−0.711789	+	0.517145i	0.171962	+	0.985104i	$0.444990\pi$
$284$	−12.7617	+	39.2765i	−0.757268	+	2.33063i
$285$	10.2164			0.605169
$286$	1.70985	−	36.0482i	0.101106	−	2.13158i
$287$	5.41355			0.319552
$288$	0.586016	−	1.80357i	0.0345313	−	0.106277i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	56.3355	+	40.9301i	3.30813	+	2.40350i
$291$	4.13455	+	12.7248i	0.242372	+	0.745944i
$292$	7.48847	+	23.0471i	0.438230	+	1.34873i
$293$	24.9473	+	18.1253i	1.45744	+	1.05889i	0.984022	+	0.178049i	$0.0569786\pi$
$293$	24.9473	+	18.1253i	1.45744	+	1.05889i	0.473414	+	0.880840i	$0.343021\pi$
$294$	13.0229	−	9.46170i	0.759512	−	0.551818i
$295$	−10.8506	+	33.3946i	−0.631745	+	1.94431i
$296$	−37.3215			−2.16927
$297$	2.07440	−	2.58783i	0.120369	−	0.150161i
$298$	8.90740			0.515992
$299$	−1.58652	+	4.88282i	−0.0917511	+	0.282381i
$300$	−27.5467	+	20.0138i	−1.59041	+	1.15550i
$301$	−2.77449	−	2.01579i	−0.159919	−	0.116188i
$302$	2.94290	+	9.05733i	0.169345	+	0.521191i
$303$	−4.19399	−	12.9078i	−0.240938	−	0.741532i
$304$	11.6906	+	8.49372i	0.670502	+	0.487148i
$305$	−21.2576	+	15.4446i	−1.21721	+	0.884354i
$306$	0.768351	−	2.36474i	0.0439237	−	0.135183i
$307$	−3.92208			−0.223845			−0.111923	−	0.993717i	$-0.535701\pi$
$307$	−3.92208			−0.223845			−0.111923	+	0.993717i	$0.535701\pi$
$308$	−6.29219	+	7.84954i	−0.358531	+	0.447269i
$309$	−0.631902			−0.0359477
$310$	11.1937	−	34.4506i	0.635758	−	1.95666i
$311$	27.8027	−	20.1998i	1.57654	−	1.14543i	0.656018	−	0.754745i	$-0.272240\pi$
$311$	27.8027	−	20.1998i	1.57654	−	1.14543i	0.920526	−	0.390681i	$-0.127760\pi$
$312$	19.2114	+	13.9579i	1.08763	+	0.790212i
$313$	−0.0655283	−	0.201675i	−0.00370388	−	0.0113994i	0.949187	−	0.314711i	$-0.101908\pi$
$313$	−0.0655283	−	0.201675i	−0.00370388	−	0.0113994i	−0.952891	+	0.303312i	$0.901908\pi$
$314$	−12.6111	−	38.8129i	−0.711684	−	2.19034i
$315$	−2.12698	−	1.54534i	−0.119842	−	0.0870701i
$316$	−56.2807	+	40.8903i	−3.16604	+	2.30026i
$317$	9.26659	−	28.5196i	0.520463	−	1.60182i	−0.252653	−	0.967557i	$-0.581303\pi$
$317$	9.26659	−	28.5196i	0.520463	−	1.60182i	0.773116	−	0.634265i	$-0.218697\pi$
$318$	−26.2097			−1.46977
$319$	−1.21398	+	25.5940i	−0.0679699	+	1.43299i
$320$	20.0814			1.12259
$321$	2.32112	−	7.14366i	0.129552	−	0.398720i
$322$	1.71154	−	1.24351i	0.0953806	−	0.0692981i
$323$	2.28002	+	1.65653i	0.126864	+	0.0921718i
$324$	1.29242	+	3.97766i	0.0718011	+	0.220981i
$325$	−11.0096	−	33.8840i	−0.610702	−	1.87955i
$326$	1.93667	+	1.40707i	0.107262	+	0.0779305i
$327$	−4.02731	+	2.92601i	−0.222711	+	0.161809i
$328$	−12.5164	+	38.5216i	−0.691105	+	2.12700i
$329$	5.50164			0.303315
$330$	−27.9618	−	10.5746i	−1.53924	−	0.582112i
$331$	−2.48112			−0.136375			−0.0681873	−	0.997673i	$-0.521722\pi$
$331$	−2.48112			−0.136375			−0.0681873	+	0.997673i	$0.521722\pi$
$332$	−15.3177	+	47.1430i	−0.840668	+	2.58731i
$333$	5.56433	−	4.04272i	0.304923	−	0.221540i
$334$	2.44669	+	1.77763i	0.133877	+	0.0972673i
$335$	2.56268	+	7.88711i	0.140014	+	0.430919i
$336$	−1.14913	−	3.53665i	−0.0626900	−	0.192940i
$337$	−5.57154	−	4.04796i	−0.303501	−	0.220506i	0.425602	−	0.904911i	$-0.360062\pi$
$337$	−5.57154	−	4.04796i	−0.303501	−	0.220506i	−0.729103	+	0.684404i	$0.760062\pi$
$338$	−12.3737	+	8.98999i	−0.673039	+	0.488991i
$339$	−3.03761	+	9.34882i	−0.164981	+	0.507758i
$340$	−15.1614			−0.822243
$341$	12.8574	−	3.51360i	0.696265	−	0.190272i
$342$	−7.00742			−0.378918
$343$	3.01972	−	9.29375i	0.163050	−	0.501815i
$344$	20.7587	−	15.0821i	1.11923	−	0.813170i
$345$	3.44066	+	2.49978i	0.185239	+	0.134584i
$346$	−1.86512	−	5.74026i	−0.100270	−	0.308598i
$347$	1.50864	+	4.64310i	0.0809878	+	0.249255i	0.983349	−	0.181725i	$-0.0581680\pi$
$347$	1.50864	+	4.64310i	0.0809878	+	0.249255i	−0.902362	+	0.430980i	$0.858168\pi$
$348$	−26.1402	−	18.9919i	−1.40126	−	1.01807i
$349$	18.6409	−	13.5434i	0.997826	−	0.724963i	0.0362053	−	0.999344i	$-0.488473\pi$
$349$	18.6409	−	13.5434i	0.997826	−	0.724963i	0.961621	+	0.274381i	$0.0884730\pi$
$350$	−4.53667	+	13.9624i	−0.242495	+	0.746323i
$351$	−4.37621			−0.233585
$352$	−3.45170	−	5.25784i	−0.183976	−	0.280244i
$353$	5.81039			0.309256			0.154628	−	0.987973i	$-0.450582\pi$
$353$	5.81039			0.309256			0.154628	+	0.987973i	$0.450582\pi$
$354$	7.44238	−	22.9053i	0.395558	−	1.21740i
$355$	−28.9588	+	21.0398i	−1.53697	+	1.11668i
$356$	−41.2598	−	29.9770i	−2.18676	−	1.58878i
$357$	−0.224114	−	0.689753i	−0.0118614	−	0.0365056i
$358$	−0.183908	−	0.566010i	−0.00971983	−	0.0299145i
$359$	−14.4569	−	10.5035i	−0.763004	−	0.554355i	0.136826	−	0.990595i	$-0.456310\pi$
$359$	−14.4569	−	10.5035i	−0.763004	−	0.554355i	−0.899830	+	0.436240i	$0.856310\pi$
$360$	15.9140	−	11.5622i	0.838741	−	0.609381i
$361$	−3.41693	+	10.5162i	−0.179838	+	0.553486i
$362$	−3.34884			−0.176011
$363$	−2.39372	−	10.7364i	−0.125637	−	0.563514i
$364$	13.2742			0.695756
$365$	−6.49067	+	19.9762i	−0.339737	+	1.04560i
$366$	14.5806	−	10.5934i	0.762138	−	0.553726i
$367$	7.63322	+	5.54586i	0.398451	+	0.289491i	0.768910	−	0.639357i	$-0.220800\pi$
$367$	7.63322	+	5.54586i	0.398451	+	0.289491i	−0.370459	+	0.928849i	$0.620800\pi$
$368$	1.85886	+	5.72098i	0.0968997	+	0.298227i
$369$	−2.30663	−	7.09907i	−0.120078	−	0.369563i
$370$	−50.1543	−	36.4392i	−2.60740	−	1.89438i
$371$	−6.18487	+	4.49357i	−0.321103	+	0.233295i
$372$	−5.19396	+	15.9854i	−0.269294	+	0.828803i
$373$	30.6348			1.58621			0.793104	−	0.609086i	$-0.208463\pi$
$373$	30.6348			1.58621			0.793104	+	0.609086i	$0.208463\pi$
$374$	−4.52567	−	6.89378i	−0.234017	−	0.356469i
$375$	−11.3872			−0.588034
$376$	−12.7201	+	39.1485i	−0.655990	+	2.01893i
$377$	27.3518	−	19.8722i	1.40869	−	1.02347i
$378$	1.45889	+	1.05994i	0.0750372	+	0.0545177i
$379$	8.10951	+	24.9585i	0.416558	+	1.28203i	0.910850	+	0.412737i	$0.135427\pi$
$379$	8.10951	+	24.9585i	0.416558	+	1.28203i	−0.494293	+	0.869295i	$0.664573\pi$
$380$	13.2039	+	40.6375i	0.677346	+	2.08466i
$381$	11.4494	+	8.31850i	0.586572	+	0.426169i
$382$	28.8491	−	20.9601i	1.47605	−	1.07241i
$383$	6.56975	−	20.2196i	0.335699	−	1.03317i	−0.630678	−	0.776045i	$-0.717223\pi$
$383$	6.56975	−	20.2196i	0.335699	−	1.03317i	0.966377	−	0.257130i	$-0.0827769\pi$
$384$	−17.5666			−0.896441
$385$	−8.41129	+	2.29860i	−0.428679	+	0.117147i
$386$	29.8496			1.51930
$387$	−1.46124	+	4.49723i	−0.0742789	+	0.228607i
$388$	−45.2715	+	32.8917i	−2.29831	+	1.66982i
$389$	−18.8965	−	13.7291i	−0.958091	−	0.696094i	−0.00538464	−	0.999986i	$-0.501714\pi$
$389$	−18.8965	−	13.7291i	−0.958091	−	0.696094i	−0.952707	+	0.303891i	$0.901714\pi$
$390$	12.1892	+	37.5146i	0.617225	+	1.89962i
$391$	0.362534	+	1.11576i	0.0183341	+	0.0564266i
$392$	28.4207	+	20.6488i	1.43546	+	1.04292i
$393$	6.37704	−	4.63319i	0.321679	−	0.233714i
$394$	6.59355	−	20.2929i	0.332178	−	1.02234i
$395$	−60.2974			−3.03389
$396$	12.9745	+	4.90670i	0.651993	+	0.246571i
$397$	−5.85334			−0.293770			−0.146885	−	0.989154i	$-0.546925\pi$
$397$	−5.85334			−0.293770			−0.146885	+	0.989154i	$0.546925\pi$
$398$	18.8012	−	57.8642i	0.942420	−	2.90047i
$399$	−1.65358	+	1.20140i	−0.0827827	+	0.0601451i
$400$	−33.7712	−	24.5362i	−1.68856	−	1.22681i
$401$	−6.48251	−	19.9511i	−0.323721	−	0.996311i	−0.972015	−	0.234920i	$-0.924517\pi$
$401$	−6.48251	−	19.9511i	−0.323721	−	0.996311i	0.648294	−	0.761390i	$-0.275483\pi$
$402$	−1.75773	−	5.40975i	−0.0876678	−	0.269814i
$403$	−14.2282	−	10.3374i	−0.708759	−	0.514944i
$404$	45.9223	−	33.3645i	2.28472	−	1.65995i
$405$	−1.12021	+	3.44766i	−0.0556638	+	0.171316i
$406$	−13.9314			−0.691402
$407$	1.08078	−	22.7858i	0.0535724	−	1.12945i
$408$	5.42630			0.268642
$409$	5.18998	−	15.9731i	0.256628	−	0.789820i	−0.736876	−	0.676027i	$-0.763700\pi$
$409$	5.18998	−	15.9731i	0.256628	−	0.789820i	0.993505	−	0.113793i	$-0.0362999\pi$
$410$	−54.4312	+	39.5466i	−2.68816	+	1.95307i
$411$	−14.4654	−	10.5097i	−0.713525	−	0.518406i
$412$	−0.816683	−	2.51349i	−0.0402351	−	0.123831i
$413$	−2.17081	−	6.68107i	−0.106819	−	0.328754i
$414$	−2.35994	−	1.71460i	−0.115985	−	0.0842678i
$415$	−34.7589	+	25.2538i	−1.70625	+	1.23966i
$416$	−2.56453	+	7.89282i	−0.125737	+	0.386977i
$417$	−8.38253			−0.410494
$418$	−14.5362	+	18.1340i	−0.710989	+	0.886963i
$419$	−10.0879			−0.492827			−0.246413	−	0.969165i	$-0.579252\pi$
$419$	−10.0879			−0.492827			−0.246413	+	0.969165i	$0.579252\pi$
$420$	3.39789	−	10.4576i	0.165800	−	0.510280i
$421$	−1.52955	+	1.11129i	−0.0745459	+	0.0541608i	−0.624434	−	0.781078i	$-0.714670\pi$
$421$	−1.52955	+	1.11129i	−0.0745459	+	0.0541608i	0.549888	+	0.835238i	$0.314670\pi$
$422$	6.83575	+	4.96646i	0.332759	+	0.241764i
$423$	−2.34416	−	7.21459i	−0.113977	−	0.350785i
$424$	−17.6755	−	54.3996i	−0.858398	−	2.64188i
$425$	−6.58640	−	4.78530i	−0.319487	−	0.232121i
$426$	19.8628	−	14.4311i	0.962355	−	0.699191i
$427$	1.62446	−	4.99958i	0.0786132	−	0.241946i
$428$	31.4149			1.51850
$429$	−9.07803	+	11.3249i	−0.438291	+	0.546771i
$430$	42.6220			2.05541
$431$	−10.1600	+	31.2692i	−0.489389	+	1.50618i	0.336133	+	0.941815i	$0.390881\pi$
$431$	−10.1600	+	31.2692i	−0.489389	+	1.50618i	−0.825522	+	0.564370i	$0.809119\pi$
$432$	−4.14816	+	3.01382i	−0.199579	+	0.145002i
$433$	−20.4478	−	14.8562i	−0.982658	−	0.713943i	−0.0243566	−	0.999703i	$-0.507754\pi$
$433$	−20.4478	−	14.8562i	−0.982658	−	0.713943i	−0.958301	+	0.285761i	$0.907754\pi$
$434$	2.23945	+	6.89233i	0.107497	+	0.330842i
$435$	−8.65425	−	26.6350i	−0.414940	−	1.27705i
$436$	−16.8437	−	12.2376i	−0.806665	−	0.586076i
$437$	2.67488	−	1.94341i	0.127957	−	0.0929661i
$438$	4.45194	−	13.7016i	0.212722	−	0.654690i
$439$	−25.2515			−1.20519			−0.602594	−	0.798048i	$-0.705866\pi$
$439$	−25.2515			−1.20519			−0.602594	+	0.798048i	$0.705866\pi$
$440$	3.09104	−	65.1673i	0.147360	−	3.10673i
$441$	−6.47401			−0.308286
$442$	−3.36247	+	10.3486i	−0.159936	+	0.492233i
$443$	29.6520	−	21.5435i	1.40881	−	1.02356i	0.415317	−	0.909677i	$-0.363671\pi$
$443$	29.6520	−	21.5435i	1.40881	−	1.02356i	0.993494	−	0.113884i	$-0.0363293\pi$
$444$	23.2720	+	16.9081i	1.10444	+	0.802424i
$445$	−13.6599	−	42.0409i	−0.647542	−	1.99293i
$446$	10.4819	+	32.2600i	0.496332	+	1.52755i
$447$	−2.89822	−	2.10568i	−0.137081	−	0.0995953i
$448$	−3.25029	+	2.36147i	−0.153562	+	0.111569i
$449$	−11.5021	+	35.3997i	−0.542816	+	1.67062i	0.183309	+	0.983055i	$0.441319\pi$
$449$	−11.5021	+	35.3997i	−0.542816	+	1.67062i	−0.726126	+	0.687562i	$0.758681\pi$
$450$	20.2426			0.954247
$451$	−23.1560	−	8.75716i	−1.09038	−	0.412359i
$452$	−41.1123			−1.93376
$453$	1.18358	−	3.64270i	0.0556096	−	0.171149i
$454$	−52.8852	+	38.4234i	−2.48203	+	1.80330i
$455$	9.30812	+	6.76274i	0.436371	+	0.317042i
$456$	−4.72571	−	14.5442i	−0.221301	−	0.681096i
$457$	6.41487	+	19.7429i	0.300075	+	0.923535i	0.981469	+	0.191619i	$0.0613738\pi$
$457$	6.41487	+	19.7429i	0.300075	+	0.923535i	−0.681395	+	0.731916i	$0.738626\pi$
$458$	49.8877	+	36.2455i	2.33110	+	1.69364i
$459$	−0.809017	+	0.587785i	−0.0377617	+	0.0274355i
$460$	−5.49652	+	16.9165i	−0.256276	+	0.788738i
$461$	11.5120			0.536169			0.268084	−	0.963395i	$-0.413609\pi$
$461$	11.5120			0.536169			0.268084	+	0.963395i	$0.413609\pi$
$462$	5.76928	−	1.57660i	0.268411	−	0.0733502i
$463$	26.6302			1.23761			0.618805	−	0.785545i	$-0.287617\pi$
$463$	26.6302			1.23761			0.618805	+	0.785545i	$0.287617\pi$
$464$	12.2408	−	37.6733i	0.568265	−	1.74894i
$465$	−11.7861	+	8.56311i	−0.546568	+	0.397105i
$466$	12.8840	+	9.36079i	0.596841	+	0.433630i
$467$	−9.29176	−	28.5971i	−0.429971	−	1.32332i	−0.898153	−	0.439684i	$-0.855091\pi$
$467$	−9.29176	−	28.5971i	−0.429971	−	1.32332i	0.468181	−	0.883632i	$-0.344909\pi$
$468$	−5.65591	−	17.4071i	−0.261444	−	0.804643i
$469$	−1.34227	−	0.975214i	−0.0619801	−	0.0450312i
$470$	−55.3169	+	40.1901i	−2.55158	+	1.85383i
$471$	−5.07195	+	15.6099i	−0.233703	+	0.719264i
$472$	52.5600			2.41927
$473$	8.60686	+	13.1105i	0.395744	+	0.602821i
$474$	41.3578			1.89963
$475$	−7.09012	+	21.8211i	−0.325317	+	1.00122i
$476$	2.45395	−	1.78290i	0.112477	−	0.0817192i
$477$	8.52792	+	6.19590i	0.390467	+	0.283691i
$478$	14.9214	+	45.9235i	0.682491	+	2.10049i
$479$	−0.858335	−	2.64168i	−0.0392183	−	0.120702i	0.929531	−	0.368745i	$-0.120212\pi$
$479$	−0.858335	−	2.64168i	−0.0392183	−	0.120702i	−0.968749	+	0.248043i	$0.920212\pi$
$480$	5.56164	+	4.04077i	0.253853	+	0.184435i
$481$	−24.3507	+	17.6918i	−1.11030	+	0.806677i
$482$	17.4660	−	53.7547i	0.795552	−	2.44846i
$483$	−0.850851			−0.0387151
$484$	39.6120	−	23.3973i	1.80055	−	1.06351i
$485$	−48.5025			−2.20239
$486$	0.768351	−	2.36474i	0.0348531	−	0.107267i
$487$	−19.8059	+	14.3898i	−0.897491	+	0.652066i	−0.937820	−	0.347121i	$-0.887159\pi$
$487$	−19.8059	+	14.3898i	−0.897491	+	0.652066i	0.0403291	+	0.999186i	$0.487159\pi$
$488$	31.8200	+	23.1186i	1.44042	+	1.04653i
$489$	−0.297511	−	0.915645i	−0.0134539	−	0.0414069i
$490$	18.0323	+	55.4977i	0.814616	+	2.50713i
$491$	3.64720	+	2.64984i	0.164596	+	0.119586i	0.667034	−	0.745027i	$-0.267564\pi$
$491$	3.64720	+	2.64984i	0.164596	+	0.119586i	−0.502438	+	0.864613i	$0.667564\pi$
$492$	25.2565	−	18.3500i	1.13865	−	0.827280i
$493$	2.38732	−	7.34743i	0.107520	−	0.330912i
$494$	30.6660			1.37973
$495$	6.59818	+	10.0507i	0.296566	+	0.451748i
$496$	−20.6060			−0.925236
$497$	2.21297	−	6.81081i	0.0992651	−	0.305507i
$498$	23.8410	−	17.3215i	1.06834	−	0.776195i
$499$	18.2838	+	13.2839i	0.818494	+	0.594671i	0.916281	−	0.400536i	$-0.131176\pi$
$499$	18.2838	+	13.2839i	0.818494	+	0.594671i	−0.0977864	+	0.995207i	$0.531176\pi$
$500$	−14.7171	−	45.2945i	−0.658168	−	2.02563i
$501$	−0.375861	−	1.15678i	−0.0167922	−	0.0516811i
$502$	−11.7320	−	8.52380i	−0.523625	−	0.380436i
$503$	19.4359	−	14.1210i	0.866602	−	0.629623i	−0.0630709	−	0.998009i	$-0.520089\pi$
$503$	19.4359	−	14.1210i	0.866602	−	0.629623i	0.929673	+	0.368386i	$0.120089\pi$
$504$	−1.21611	+	3.74281i	−0.0541699	+	0.166718i
$505$	49.1997			2.18936
$506$	−9.33254	+	2.55036i	−0.414882	+	0.113377i
$507$	6.15125			0.273187
$508$	−18.2907	+	56.2929i	−0.811518	+	2.49759i
$509$	22.6823	−	16.4796i	1.00537	−	0.730447i	0.0421404	−	0.999112i	$-0.486582\pi$
$509$	22.6823	−	16.4796i	1.00537	−	0.730447i	0.963234	+	0.268665i	$0.0865823\pi$
$510$	7.29210	+	5.29802i	0.322900	+	0.234600i
$511$	−1.29855	−	3.99653i	−0.0574445	−	0.176796i
$512$	−14.1907	−	43.6746i	−0.627147	−	1.93016i
$513$	2.28002	+	1.65653i	0.100665	+	0.0731376i
$514$	7.23367	−	5.25557i	0.319063	−	0.231813i
$515$	0.707865	−	2.17858i	0.0311923	−	0.0959999i
$516$	−19.7770			−0.870633
$517$	−23.5328	−	8.89966i	−1.03497	−	0.391407i
$518$	12.4028			0.544948
$519$	−0.750119	+	2.30863i	−0.0329266	+	0.101338i
$520$	−69.6430	+	50.5986i	−3.05405	+	2.21890i
$521$	−17.5737	−	12.7680i	−0.769916	−	0.559377i	0.132019	−	0.991247i	$-0.457854\pi$
$521$	−17.5737	−	12.7680i	−0.769916	−	0.559377i	−0.901936	+	0.431870i	$0.857854\pi$
$522$	5.93593	+	18.2689i	0.259808	+	0.799608i
$523$	−3.32054	−	10.2196i	−0.145197	−	0.446871i	0.851839	−	0.523803i	$-0.175487\pi$
$523$	−3.32054	−	10.2196i	−0.145197	−	0.446871i	−0.997036	+	0.0769327i	$0.975487\pi$
$524$	26.6711	+	19.3777i	1.16513	+	0.846517i
$525$	4.77678	−	3.47053i	0.208476	−	0.151467i
$526$	15.5584	−	47.8839i	0.678380	−	2.08784i
$527$	−4.01879			−0.175061
$528$	−0.805715	+	16.9866i	−0.0350642	+	0.739247i
$529$	−21.6236			−0.940158
$530$	29.3605	−	90.3623i	1.27534	−	3.92509i
$531$	−7.83628	+	5.69339i	−0.340066	+	0.247072i
$532$	−6.91588	−	5.02468i	−0.299841	−	0.217847i
$533$	10.0943	+	31.0670i	0.437232	+	1.34566i
$534$	9.36930	+	28.8357i	0.405449	+	1.24784i
$535$	22.0288	+	16.0048i	0.952386	+	0.691949i
$536$	10.0428	−	7.29652i	0.433783	−	0.315162i
$537$	−0.0739644	+	0.227639i	−0.00319180	+	0.00982335i
$538$	−51.0257			−2.19988
$539$	−13.4297	+	16.7536i	−0.578458	+	0.721630i
$540$	−15.1614			−0.652443
$541$	2.12504	−	6.54019i	0.0913624	−	0.281185i	−0.894926	−	0.446214i	$-0.852772\pi$
$541$	2.12504	−	6.54019i	0.0913624	−	0.281185i	0.986289	+	0.165030i	$0.0527720\pi$
$542$	−19.7970	+	14.3833i	−0.850353	+	0.617818i
$543$	1.08962	+	0.791656i	0.0467601	+	0.0339732i
$544$	0.586016	+	1.80357i	0.0251252	+	0.0773275i
$545$	−5.57645	−	17.1625i	−0.238869	−	0.735163i
$546$	−6.38441	−	4.63855i	−0.273228	−	0.198511i
$547$	−28.0934	+	20.4111i	−1.20119	+	0.872714i	−0.994401	−	0.105672i	$-0.966301\pi$
$547$	−28.0934	+	20.4111i	−1.20119	+	0.872714i	−0.206787	+	0.978386i	$0.566301\pi$
$548$	23.1087	−	71.1214i	0.987156	−	3.03816i
$549$	−7.24835			−0.309352
$550$	41.9914	−	52.3845i	1.79052	−	2.23368i
$551$	−21.7726			−0.927543
$552$	1.96721	−	6.05446i	0.0837302	−	0.257695i
$553$	9.75945	−	7.09066i	0.415014	−	0.301525i
$554$	−40.3195	−	29.2938i	−1.71301	−	1.24458i
$555$	7.70470	+	23.7126i	0.327046	+	1.00654i
$556$	−10.8337	−	33.3428i	−0.459453	−	1.41405i
$557$	22.3764	+	16.2574i	0.948117	+	0.688847i	0.950361	−	0.311150i	$-0.100714\pi$
$557$	22.3764	+	16.2574i	0.948117	+	0.688847i	−0.00224367	+	0.999997i	$0.500714\pi$
$558$	8.08406	−	5.87342i	0.342226	−	0.248642i
$559$	6.39469	−	19.6808i	0.270467	−	0.832411i
$560$	13.4804			0.569652
$561$	−0.157139	+	3.31290i	−0.00663440	+	0.139871i
$562$	−23.6943			−0.999482
$563$	2.41262	−	7.42529i	0.101680	−	0.312939i	−0.887257	−	0.461275i	$-0.847392\pi$
$563$	2.41262	−	7.42529i	0.101680	−	0.312939i	0.988937	+	0.148337i	$0.0473920\pi$
$564$	25.6675	−	18.6486i	1.08080	−	0.785246i
$565$	−28.8288	−	20.9453i	−1.21284	−	0.881176i
$566$	11.3722	+	35.0002i	0.478011	+	1.47117i
$567$	−0.224114	−	0.689753i	−0.00941192	−	0.0289669i
$568$	43.3477	+	31.4940i	1.81883	+	1.32146i
$569$	−29.3063	+	21.2923i	−1.22858	+	0.892618i	−0.996783	−	0.0801459i	$-0.974461\pi$
$569$	−29.3063	+	21.2923i	−1.22858	+	0.892618i	−0.231800	+	0.972764i	$0.574461\pi$
$570$	7.84980	−	24.1592i	0.328792	−	1.01192i
$571$	−19.8527			−0.830810			−0.415405	−	0.909636i	$-0.636360\pi$
$571$	−19.8527			−0.830810			−0.415405	+	0.909636i	$0.636360\pi$
$572$	−56.7792	−	21.4728i	−2.37406	−	0.897822i
$573$	−14.3416			−0.599129
$574$	4.15951	−	12.8016i	0.173614	−	0.534330i
$575$	−7.72705	+	5.61403i	−0.322240	+	0.234121i
$576$	4.48161	+	3.25608i	0.186734	+	0.135670i
$577$	4.33209	+	13.3328i	0.180347	+	0.555052i	0.999837	−	0.0180416i	$-0.00574314\pi$
$577$	4.33209	+	13.3328i	0.180347	+	0.555052i	−0.819490	+	0.573094i	$0.805743\pi$
$578$	0.768351	+	2.36474i	0.0319592	+	0.0983602i
$579$	−9.71222	−	7.05634i	−0.403626	−	0.293252i
$580$	94.7602	−	68.8473i	3.93470	−	2.85873i
$581$	2.65619	−	8.17492i	0.110197	−	0.339153i
$582$	33.2677			1.37899
$583$	33.7243	−	9.21602i	1.39672	−	0.381689i
$584$	31.4407			1.30103
$585$	4.90229	−	15.0877i	0.202685	−	0.623800i
$586$	62.0298	−	45.0673i	2.56243	−	1.86171i
$587$	20.9404	+	15.2141i	0.864305	+	0.627954i	0.929053	−	0.369948i	$-0.120624\pi$
$587$	20.9404	+	15.2141i	0.864305	+	0.627954i	−0.0647480	+	0.997902i	$0.520624\pi$
$588$	−8.36715	−	25.7514i	−0.345055	−	1.06197i
$589$	3.49992	+	10.7716i	0.144212	+	0.443838i
$590$	70.6326	+	51.3176i	2.90790	+	2.11271i
$591$	−6.94253	+	5.04404i	−0.285577	+	0.207484i
$592$	−10.8977	+	33.5397i	−0.447894	+	1.37848i
$593$	−37.7979			−1.55217			−0.776086	−	0.630627i	$-0.782798\pi$
$593$	−37.7979			−1.55217			−0.776086	+	0.630627i	$0.782798\pi$
$594$	−4.52567	−	6.89378i	−0.185691	−	0.282855i
$595$	2.62909			0.107782
$596$	4.62997	−	14.2496i	0.189651	−	0.583685i
$597$	−19.7963	+	14.3829i	−0.810209	+	0.588651i
$598$	10.3276	+	7.50344i	0.422327	+	0.306838i
$599$	−12.9107	−	39.7352i	−0.527518	−	1.62353i	−0.759281	−	0.650763i	$-0.774449\pi$
$599$	−12.9107	−	39.7352i	−0.527518	−	1.62353i	0.231763	−	0.972772i	$-0.425551\pi$
$600$	13.6514	+	42.0146i	0.557314	+	1.71524i
$601$	20.6823	+	15.0266i	0.843651	+	0.612948i	0.923388	−	0.383868i	$-0.125408\pi$
$601$	20.6823	+	15.0266i	0.843651	+	0.612948i	−0.0797374	+	0.996816i	$0.525408\pi$
$602$	−6.89860	+	5.01212i	−0.281166	+	0.204279i
$603$	−0.706929	+	2.17571i	−0.0287884	+	0.0886016i
$604$	16.0191			0.651808
$605$	39.6969	+	3.77433i	1.61391	+	0.153448i
$606$	−33.7460			−1.37084
$607$	10.6659	−	32.8262i	0.432915	−	1.33238i	−0.462293	−	0.886727i	$-0.652973\pi$
$607$	10.6659	−	32.8262i	0.432915	−	1.33238i	0.895208	−	0.445649i	$-0.147027\pi$
$608$	4.32380	−	3.14142i	0.175353	−	0.127402i
$609$	4.53288	+	3.29333i	0.183682	+	0.133452i
$610$	20.1891	+	62.1356i	0.817433	+	2.51580i
$611$	10.2586	+	31.5726i	0.415017	+	1.27729i
$612$	−3.38360	−	2.45833i	−0.136774	−	0.0993721i
$613$	0.279660	−	0.203185i	0.0112954	−	0.00820657i	−0.582123	−	0.813101i	$-0.697778\pi$
$613$	0.279660	−	0.203185i	0.0112954	−	0.00820657i	0.593419	+	0.804894i	$0.297778\pi$
$614$	−3.01353	+	9.27471i	−0.121616	+	0.374297i
$615$	27.0591			1.09113
$616$	7.16304	+	10.9112i	0.288607	+	0.439624i
$617$	−15.0314			−0.605140			−0.302570	−	0.953127i	$-0.597845\pi$
$617$	−15.0314			−0.605140			−0.302570	+	0.953127i	$0.597845\pi$
$618$	−0.485523	+	1.49428i	−0.0195306	+	0.0601090i
$619$	28.4334	−	20.6581i	1.14283	−	0.830317i	0.155322	−	0.987864i	$-0.450358\pi$
$619$	28.4334	−	20.6581i	1.14283	−	0.830317i	0.987512	+	0.157547i	$0.0503584\pi$
$620$	−49.2938	−	35.8140i	−1.97969	−	1.43833i
$621$	0.362534	+	1.11576i	0.0145480	+	0.0447741i
$622$	−26.4051	−	81.2666i	−1.05875	−	3.25849i
$623$	7.15472	+	5.19821i	0.286648	+	0.208262i
$624$	18.1533	−	13.1891i	0.726712	−	0.527987i
$625$	0.177221	−	0.545430i	0.00708883	−	0.0218172i
$626$	−0.527259			−0.0210735
$627$	9.01649	−	2.46399i	0.360084	−	0.0984022i
$628$	−68.6458			−2.73926
$629$	−2.12538	+	6.54126i	−0.0847446	+	0.260817i
$630$	−5.28859	+	3.84239i	−0.210703	+	0.153084i
$631$	30.0859	+	21.8587i	1.19770	+	0.870181i	0.994057	−	0.108863i	$-0.0347211\pi$
$631$	30.0859	+	21.8587i	1.19770	+	0.870181i	0.203645	+	0.979045i	$0.434721\pi$
$632$	27.8911	+	85.8401i	1.10945	+	3.41453i
$633$	−1.05011	−	3.23190i	−0.0417380	−	0.128456i
$634$	−60.3215	−	43.8262i	−2.39567	−	1.74056i
$635$	−41.5051	+	30.1552i	−1.64708	+	1.19667i
$636$	−13.6235	+	41.9289i	−0.540208	+	1.66259i
$637$	28.3317			1.12254
$638$	59.5903	+	22.5359i	2.35920	+	0.892204i
$639$	−9.87427			−0.390620
$640$	19.6783	−	60.5636i	0.777853	−	2.39399i
$641$	−1.68420	+	1.22364i	−0.0665218	+	0.0483309i	−0.620549	−	0.784168i	$-0.713090\pi$
$641$	−1.68420	+	1.22364i	−0.0665218	+	0.0483309i	0.554027	+	0.832498i	$0.313090\pi$
$642$	−15.1095	−	10.9777i	−0.596323	−	0.433254i
$643$	5.88659	+	18.1171i	0.232145	+	0.714468i	0.997487	+	0.0708448i	$0.0225695\pi$
$643$	5.88659	+	18.1171i	0.232145	+	0.714468i	−0.765343	+	0.643623i	$0.777431\pi$
$644$	−1.09966	−	3.38440i	−0.0433325	−	0.133364i
$645$	−13.8680	−	10.0757i	−0.546052	−	0.396730i
$646$	5.66912	−	4.11886i	0.223049	−	0.162054i
$647$	−2.39784	+	7.37979i	−0.0942688	+	0.290129i	−0.987062	−	0.160336i	$-0.948742\pi$
$647$	−2.39784	+	7.37979i	−0.0942688	+	0.290129i	0.892794	+	0.450466i	$0.148742\pi$
$648$	5.42630			0.213165
$649$	−1.52207	+	32.0893i	−0.0597466	+	1.25962i
$650$	−88.5862			−3.47463
$651$	0.900668	−	2.77197i	0.0353000	−	0.108642i
$652$	3.25761	−	2.36680i	0.127578	−	0.0926909i
$653$	16.8177	+	12.2188i	0.658129	+	0.478158i	0.866030	−	0.499991i	$-0.166663\pi$
$653$	16.8177	+	12.2188i	0.658129	+	0.478158i	−0.207902	+	0.978150i	$0.566663\pi$
$654$	3.82487	+	11.7717i	0.149564	+	0.460312i
$655$	8.83002	+	27.1760i	0.345018	+	1.06185i
$656$	30.9636	+	22.4963i	1.20892	+	0.878334i
$657$	−4.68756	+	3.40571i	−0.182879	+	0.132870i
$658$	4.22719	−	13.0100i	0.164793	−	0.507181i
$659$	−23.2987			−0.907588			−0.453794	−	0.891107i	$-0.649930\pi$
$659$	−23.2987			−0.907588			−0.453794	+	0.891107i	$0.649930\pi$
$660$	−31.4508	+	39.2351i	−1.22422	+	1.52722i
$661$	18.5932			0.723194			0.361597	−	0.932335i	$-0.382232\pi$
$661$	18.5932			0.723194			0.361597	+	0.932335i	$0.382232\pi$
$662$	−1.90637	+	5.86720i	−0.0740932	+	0.228035i
$663$	3.54043	−	2.57227i	0.137499	−	0.0998989i
$664$	52.0297	+	37.8018i	2.01914	+	1.46699i
$665$	−2.28965	−	7.04681i	−0.0887887	−	0.273264i
$666$	−5.28463	−	16.2644i	−0.204775	−	0.630234i
$667$	−7.33251	−	5.32738i	−0.283916	−	0.206277i
$668$	4.11551	−	2.99009i	0.159234	−	0.115690i
$669$	4.21563	−	12.9744i	0.162986	−	0.501619i
$670$	20.6200			0.796620
$671$	−15.0360	+	18.7575i	−0.580458	+	0.724125i
$672$	−1.37535			−0.0530555
$673$	−3.04108	+	9.35949i	−0.117225	+	0.360782i	−0.992405	−	0.123016i	$-0.960743\pi$
$673$	−3.04108	+	9.35949i	−0.117225	+	0.360782i	0.875179	+	0.483798i	$0.160743\pi$
$674$	−13.8533	+	10.0650i	−0.533608	+	0.387689i
$675$	−6.58640	−	4.78530i	−0.253510	−	0.184186i
$676$	7.95000	+	24.4676i	0.305769	+	0.941061i
$677$	1.40648	+	4.32869i	0.0540553	+	0.166365i	0.974439	−	0.224650i	$-0.0721240\pi$
$677$	1.40648	+	4.32869i	0.0540553	+	0.166365i	−0.920384	+	0.391015i	$0.872124\pi$
$678$	19.7736	+	14.3663i	0.759399	+	0.551736i
$679$	7.85039	−	5.70364i	0.301270	−	0.218886i
$680$	−6.07860	+	18.7080i	−0.233104	+	0.717420i
$681$	26.2906			1.00746
$682$	1.57020	−	33.1040i	0.0601261	−	1.26762i
$683$	−29.5799			−1.13184			−0.565921	−	0.824459i	$-0.691479\pi$
$683$	−29.5799			−1.13184			−0.565921	+	0.824459i	$0.691479\pi$
$684$	−3.64237	+	11.2101i	−0.139270	+	0.428628i
$685$	52.4383	−	38.0986i	2.00356	−	1.45567i
$686$	−19.6571	−	14.2817i	−0.750511	−	0.545278i
$687$	−7.66374	−	23.5866i	−0.292390	−	0.899883i
$688$	−7.49237	−	23.0591i	−0.285644	−	0.879122i
$689$	−37.3200	−	27.1146i	−1.42178	−	1.03298i
$690$	8.55497	−	6.21555i	0.325682	−	0.236622i
$691$	3.59636	−	11.0684i	0.136812	−	0.421064i	−0.859056	−	0.511882i	$-0.828948\pi$
$691$	3.59636	−	11.0684i	0.136812	−	0.421064i	0.995867	+	0.0908188i	$0.0289484\pi$
$692$	−10.1524			−0.385937
$693$	−2.24987	−	0.850856i	−0.0854654	−	0.0323213i
$694$	12.1389			0.460786
$695$	9.39021	−	28.9001i	0.356191	−	1.09624i
$696$	−33.9149	+	24.6406i	−1.28554	+	0.933999i
$697$	6.03883	+	4.38746i	0.228737	+	0.166187i
$698$	−17.7039	−	54.4871i	−0.670103	−	2.06237i
$699$	−1.97924	−	6.09148i	−0.0748618	−	0.230401i
$700$	19.9782	+	14.5150i	0.755105	+	0.548616i
$701$	−31.4097	+	22.8204i	−1.18633	+	0.861916i	−0.992871	−	0.119193i	$-0.961969\pi$
$701$	−31.4097	+	22.8204i	−1.18633	+	0.861916i	−0.193455	+	0.981109i	$0.561969\pi$
$702$	−3.36247	+	10.3486i	−0.126908	+	0.390583i
$703$	19.3837			0.731069
$704$	17.7229	−	4.84323i	0.667955	−	0.182536i
$705$	27.4994			1.03569
$706$	4.46442	−	13.7401i	0.168021	−	0.517114i
$707$	−7.96324	+	5.78563i	−0.299488	+	0.217591i
$708$	−32.7741	−	23.8118i	−1.23173	−	0.894902i
$709$	−1.70968	−	5.26186i	−0.0642084	−	0.197613i	0.913806	−	0.406151i	$-0.133129\pi$
$709$	−1.70968	−	5.26186i	−0.0642084	−	0.197613i	−0.978014	+	0.208538i	$0.933129\pi$
$710$	27.5032	+	84.6460i	1.03218	+	3.17671i
$711$	−13.4567	−	9.77685i	−0.504665	−	0.366661i
$712$	−53.5314	+	38.8929i	−2.00617	+	1.45757i
$713$	−1.45695	+	4.48402i	−0.0545630	+	0.167928i
$714$	−1.80329			−0.0674863
$715$	−28.8751	−	43.9842i	−1.07987	−	1.64492i
$716$	−1.00106			−0.0374115
$717$	6.00114	−	18.4696i	0.224117	−	0.689760i
$718$	−35.9461	+	26.1163i	−1.34150	+	0.974653i
$719$	15.7746	+	11.4609i	0.588293	+	0.427420i	0.841704	−	0.539938i	$-0.181553\pi$
$719$	15.7746	+	11.4609i	0.588293	+	0.427420i	−0.253411	+	0.967359i	$0.581553\pi$
$720$	−5.74379	−	17.6776i	−0.214058	−	0.658804i
$721$	0.141618	+	0.435857i	0.00527415	+	0.0162322i
$722$	22.2428	+	16.1603i	0.827790	+	0.601424i
$723$	−18.3904	+	13.3614i	−0.683945	+	0.496915i
$724$	−1.74069	+	5.35729i	−0.0646922	+	0.199102i
$725$	62.8954			2.33588
$726$	−27.2280	−	2.58880i	−1.01053	−	0.0960794i
$727$	−43.6235			−1.61791			−0.808953	−	0.587873i	$-0.799966\pi$
$727$	−43.6235			−1.61791			−0.808953	+	0.587873i	$0.799966\pi$
$728$	5.32196	−	16.3793i	0.197245	−	0.607058i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	42.2515	+	30.6975i	1.56380	+	1.13617i
$731$	−1.46124	−	4.49723i	−0.0540458	−	0.166336i
$732$	−9.36792	−	28.8315i	−0.346248	−	1.06564i
$733$	33.6496	+	24.4478i	1.24287	+	0.903001i	0.997786	−	0.0664993i	$-0.0211830\pi$
$733$	33.6496	+	24.4478i	1.24287	+	0.903001i	0.245088	+	0.969501i	$0.421183\pi$
$734$	18.9795	−	13.7894i	0.700546	−	0.508977i
$735$	7.25227	−	22.3202i	0.267504	−	0.823293i
$736$	2.22481			0.0820076
$737$	4.16390	+	6.34270i	0.153379	+	0.233636i
$738$	−18.5597			−0.683194
$739$	5.89789	−	18.1518i	0.216957	−	0.667726i	−0.782052	−	0.623214i	$-0.785827\pi$
$739$	5.89789	−	18.1518i	0.216957	−	0.667726i	0.999009	−	0.0445122i	$-0.0141734\pi$
$740$	−84.3630	+	61.2933i	−3.10125	+	2.25319i
$741$	−9.97785	−	7.24933i	−0.366546	−	0.266311i
$742$	5.87398	+	18.0783i	0.215641	+	0.663674i
$743$	−13.4344	−	41.3470i	−0.492862	−	1.51687i	−0.820262	−	0.571988i	$-0.806173\pi$
$743$	−13.4344	−	41.3470i	−0.492862	−	1.51687i	0.327400	−	0.944886i	$-0.393827\pi$
$744$	17.6423	+	12.8179i	0.646799	+	0.469927i
$745$	10.5063	−	7.63327i	0.384921	−	0.279661i
$746$	23.5383	−	72.4433i	0.861797	−	2.65234i
$747$	−11.8520			−0.433640
$748$	−13.3807	+	3.65661i	−0.489246	+	0.133699i
$749$	−5.44756			−0.199049
$750$	−8.74939	+	26.9278i	−0.319482	+	0.983266i
$751$	39.7229	−	28.8604i	1.44951	−	1.05313i	0.463563	−	0.886064i	$-0.346571\pi$
$751$	39.7229	−	28.8604i	1.44951	−	1.05313i	0.985946	−	0.167065i	$-0.0534291\pi$
$752$	31.4674	+	22.8624i	1.14750	+	0.833706i
$753$	1.80227	+	5.54681i	0.0656783	+	0.202137i
$754$	−25.9769	−	79.9486i	−0.946023	−	2.91156i
$755$	11.2329	+	8.16119i	0.408808	+	0.297016i
$756$	2.45395	−	1.78290i	0.0892495	−	0.0648435i
$757$	2.35711	−	7.25445i	0.0856708	−	0.263668i	−0.899040	−	0.437868i	$-0.855734\pi$
$757$	2.35711	−	7.25445i	0.0856708	−	0.263668i	0.984710	+	0.174200i	$0.0557339\pi$
$758$	65.2513			2.37004
$759$	3.63945	+	1.37637i	0.132104	+	0.0499590i
$760$	55.4373			2.01092
$761$	−2.34195	+	7.20778i	−0.0848957	+	0.261282i	−0.984489	−	0.175447i	$-0.943863\pi$
$761$	−2.34195	+	7.20778i	−0.0848957	+	0.261282i	0.899593	+	0.436729i	$0.143863\pi$
$762$	28.4683	−	20.6834i	1.03130	−	0.749280i
$763$	2.92080	+	2.12209i	0.105740	+	0.0768248i
$764$	−18.5354	−	57.0460i	−0.670586	−	2.06385i
$765$	−1.12021	−	3.44766i	−0.0405014	−	0.124650i
$766$	−42.7663	−	31.0715i	−1.54521	−	1.12266i
$767$	34.2932	−	24.9155i	1.23826	−	0.899646i
$768$	−10.0736	+	31.0035i	−0.363501	+	1.11874i
$769$	9.50751			0.342849			0.171425	−	0.985197i	$-0.445163\pi$
$769$	9.50751			0.342849			0.171425	+	0.985197i	$0.445163\pi$
$770$	−1.02723	+	21.6566i	−0.0370186	+	0.780451i
$771$	−3.59603			−0.129508
$772$	15.5155	−	47.7517i	0.558414	−	1.71862i
$773$	−38.4060	+	27.9036i	−1.38137	+	1.00362i	−0.384617	+	0.923076i	$0.625667\pi$
$773$	−38.4060	+	27.9036i	−1.38137	+	1.00362i	−0.996751	+	0.0805464i	$0.974333\pi$
$774$	9.51203	+	6.91090i	0.341903	+	0.248407i
$775$	−10.1104	−	31.1165i	−0.363176	−	1.11774i
$776$	22.4353	+	69.0488i	0.805380	+	2.47871i
$777$	−4.03553	−	2.93198i	−0.144774	−	0.105184i
$778$	−46.9850	+	34.1366i	−1.68449	+	1.22386i
$779$	6.50067	−	20.0070i	0.232911	−	0.716825i
$780$	66.3496			2.37570
$781$	−20.4832	+	25.5529i	−0.732947	+	0.914356i
$782$	2.91704			0.104313
$783$	2.38732	−	7.34743i	0.0853160	−	0.262576i
$784$	26.8553	−	19.5115i	0.959117	−	0.696839i
$785$	−48.1358	−	34.9727i	−1.71804	−	1.24823i
$786$	−6.05649	−	18.6400i	−0.216028	−	0.664865i
$787$	14.6864	+	45.2002i	0.523515	+	1.61121i	0.767234	+	0.641368i	$0.221633\pi$
$787$	14.6864	+	45.2002i	0.523515	+	1.61121i	−0.243719	+	0.969846i	$0.578367\pi$
$788$	−29.0362	−	21.0960i	−1.03437	−	0.751514i
$789$	−16.3819	+	11.9021i	−0.583211	+	0.423727i
$790$	−46.3295	+	142.588i	−1.64833	+	5.07304i
$791$	7.12915			0.253483
$792$	11.2563	−	14.0423i	0.399976	−	0.498972i
$793$	31.7203			1.12642
$794$	−4.49741	+	13.8416i	−0.159607	+	0.491221i
$795$	−30.9144	+	22.4607i	−1.09642	+	0.796597i
$796$	−82.7952	−	60.1543i	−2.93460	−	2.13211i
$797$	−5.64661	−	17.3785i	−0.200013	−	0.615577i	−0.999881	−	0.0154017i	$-0.995097\pi$
$797$	−5.64661	−	17.3785i	−0.200013	−	0.615577i	0.799868	−	0.600176i	$-0.204903\pi$
$798$	1.57046	+	4.83339i	0.0555938	+	0.171100i
$799$	6.13709	+	4.45886i	0.217115	+	0.157743i
$800$	−12.4904	+	9.07478i	−0.441601	+	0.320842i
$801$	3.76817	−	11.5972i	0.133142	−	0.409768i
$802$	−52.1600			−1.84183
$803$	−0.910484	+	19.1954i	−0.0321303	+	0.677392i
$804$	−9.56787			−0.337433
$805$	0.953134	−	2.93344i	0.0335935	−	0.103390i
$806$	−35.3776	+	25.7033i	−1.24612	+	0.905361i
$807$	16.6024	+	12.0623i	0.584431	+	0.424614i
$808$	−22.7578	−	70.0413i	−0.800617	−	2.46405i
$809$	12.6676	+	38.9870i	0.445370	+	1.37071i	0.882077	+	0.471105i	$0.156145\pi$
$809$	12.6676	+	38.9870i	0.445370	+	1.37071i	−0.436707	+	0.899604i	$0.643855\pi$
$810$	7.29210	+	5.29802i	0.256218	+	0.186154i
$811$	−19.4368	+	14.1217i	−0.682519	+	0.495879i	−0.874192	−	0.485580i	$-0.838609\pi$
$811$	−19.4368	+	14.1217i	−0.682519	+	0.495879i	0.191673	+	0.981459i	$0.438609\pi$
$812$	−7.24136	+	22.2866i	−0.254122	+	0.782107i
$813$	9.84156			0.345159
$814$	−53.0520	−	20.0632i	−1.85947	−	0.703216i
$815$	3.49011			0.122253
$816$	1.58446	−	4.87646i	0.0554671	−	0.170710i
$817$	−10.7814	+	7.83318i	−0.377195	+	0.274048i
$818$	−33.7846	−	24.5459i	−1.18125	−	0.858228i
$819$	0.980773	+	3.01851i	0.0342710	+	0.105475i
$820$	34.9717	+	107.632i	1.22126	+	3.75867i
$821$	−29.0963	−	21.1397i	−1.01547	−	0.737781i	−0.0501194	−	0.998743i	$-0.515960\pi$
$821$	−29.0963	−	21.1397i	−1.01547	−	0.737781i	−0.965349	+	0.260962i	$0.915960\pi$
$822$	−35.9673	+	26.1317i	−1.25450	+	0.911449i
$823$	0.556066	−	1.71139i	0.0193832	−	0.0596554i	−0.940897	−	0.338693i	$-0.890015\pi$
$823$	0.556066	−	1.71139i	0.0193832	−	0.0596554i	0.960280	+	0.279037i	$0.0900153\pi$
$824$	−3.42889			−0.119451
$825$	−26.0464	+	7.11784i	−0.906818	+	0.247811i
$826$	−17.4669			−0.607753
$827$	2.26102	−	6.95870i	0.0786233	−	0.241978i	−0.904018	−	0.427495i	$-0.859396\pi$
$827$	2.26102	−	6.95870i	0.0786233	−	0.241978i	0.982641	+	0.185517i	$0.0593961\pi$
$828$	−3.96958	+	2.88407i	−0.137953	+	0.100228i
$829$	31.4398	+	22.8423i	1.09195	+	0.793347i	0.979727	−	0.200336i	$-0.0642033\pi$
$829$	31.4398	+	22.8423i	1.09195	+	0.793347i	0.112222	+	0.993683i	$0.464203\pi$
$830$	33.0117	+	101.599i	1.14585	+	3.52657i
$831$	6.19388	+	19.0628i	0.214863	+	0.661281i
$832$	−19.6125	−	14.2493i	−0.679941	−	0.494006i
$833$	5.23759	−	3.80533i	0.181472	−	0.131847i
$834$	−6.44072	+	19.8225i	−0.223024	+	0.686397i
$835$	4.40923			0.152588
$836$	21.4540	+	32.6800i	0.742002	+	1.13026i
$837$	−4.01879			−0.138910
$838$	−7.75106	+	23.8553i	−0.267756	+	0.824068i
$839$	15.1036	−	10.9734i	0.521435	−	0.378845i	−0.295709	−	0.955278i	$-0.595556\pi$
$839$	15.1036	−	10.9734i	0.521435	−	0.378845i	0.817144	+	0.576433i	$0.195556\pi$
$840$	−11.5416	−	8.38547i	−0.398224	−	0.289326i
$841$	9.48189	+	29.1822i	0.326962	+	1.00628i
$842$	1.45267	+	4.47086i	0.0500623	+	0.154076i
$843$	7.70946	+	5.60125i	0.265528	+	0.192917i
$844$	11.4982	−	8.35394i	0.395785	−	0.287554i
$845$	−6.89071	+	21.2074i	−0.237048	+	0.729558i
$846$	−18.8618			−0.648481
$847$	−6.86900	+	4.05725i	−0.236022	+	0.139409i
$848$	−54.0485			−1.85603
$849$	4.57371	−	14.0764i	0.156969	−	0.483102i
$850$	−16.3766	+	11.8983i	−0.561714	+	0.408109i
$851$	6.52798	+	4.74285i	0.223776	+	0.162583i
$852$	−12.7617	−	39.2765i	−0.437209	−	1.34559i
$853$	5.50143	+	16.9317i	0.188365	+	0.579729i	0.999990	−	0.00445028i	$-0.00141657\pi$
$853$	5.50143	+	16.9317i	0.188365	+	0.579729i	−0.811625	+	0.584179i	$0.801417\pi$
$854$	−10.5745	−	7.68285i	−0.361853	−	0.262902i
$855$	−8.26526	+	6.00506i	−0.282666	+	0.205369i
$856$	12.5951	−	38.7636i	0.430490	−	1.32491i
$857$	−47.9883			−1.63925			−0.819625	−	0.572900i	$-0.805818\pi$
$857$	−47.9883			−1.63925			−0.819625	+	0.572900i	$0.805818\pi$
$858$	19.8053	+	30.1687i	0.676143	+	1.02994i
$859$	−26.5401			−0.905537			−0.452769	−	0.891628i	$-0.649564\pi$
$859$	−26.5401			−0.905537			−0.452769	+	0.891628i	$0.649564\pi$
$860$	22.1544	−	68.1843i	0.755459	−	2.32506i
$861$	−4.37966	+	3.18201i	−0.149258	+	0.108442i
$862$	66.1371	+	48.0514i	2.25264	+	1.63664i
$863$	0.333282	+	1.02574i	0.0113451	+	0.0349165i	0.956569	−	0.291507i	$-0.0941566\pi$
$863$	0.333282	+	1.02574i	0.0113451	+	0.0349165i	−0.945224	+	0.326423i	$0.894157\pi$
$864$	0.586016	+	1.80357i	0.0199367	+	0.0613588i
$865$	−7.11907	−	5.17231i	−0.242056	−	0.175864i
$866$	−50.8421	+	36.9389i	−1.72768	+	1.25524i
$867$	0.309017	−	0.951057i	0.0104948	−	0.0322996i
$868$	12.1900			0.413756
$869$	−53.2154	+	14.5425i	−1.80521	+	0.493319i
$870$	−69.6345			−2.36083
$871$	3.09367	−	9.52135i	0.104825	−	0.322619i
$872$	−21.8534	+	15.8774i	−0.740049	+	0.537677i
$873$	−10.8244	−	7.86439i	−0.366350	−	0.266169i
$874$	−2.54042	−	7.81862i	−0.0859311	−	0.264469i
$875$	2.55204	+	7.85438i	0.0862748	+	0.265526i
$876$	−19.6051	−	14.2439i	−0.662394	−	0.481257i
$877$	−15.9504	+	11.5886i	−0.538606	+	0.391320i	−0.823567	−	0.567219i	$-0.808019\pi$
$877$	−15.9504	+	11.5886i	−0.538606	+	0.391320i	0.284961	+	0.958539i	$0.408019\pi$
$878$	−19.4020	+	59.7132i	−0.654786	+	2.01522i
$879$	−30.8365			−1.04009
$880$	−57.6615	−	21.8064i	−1.94377	−	0.735095i
$881$	−2.53279			−0.0853319			−0.0426660	−	0.999089i	$-0.513585\pi$
$881$	−2.53279			−0.0853319			−0.0426660	+	0.999089i	$0.513585\pi$
$882$	−4.97431	+	15.3094i	−0.167494	+	0.515493i
$883$	33.3411	−	24.2237i	1.12202	−	0.815194i	0.137504	−	0.990501i	$-0.456092\pi$
$883$	33.3411	−	24.2237i	1.12202	−	0.815194i	0.984514	+	0.175307i	$0.0560919\pi$
$884$	14.8074	+	10.7582i	0.498025	+	0.361837i
$885$	−10.8506	−	33.3946i	−0.364738	−	1.12255i
$886$	−28.1615	−	86.6723i	−0.946106	−	2.91181i
$887$	9.92698	+	7.21237i	0.333315	+	0.242168i	0.741836	−	0.670581i	$-0.233955\pi$
$887$	9.92698	+	7.21237i	0.333315	+	0.242168i	−0.408521	+	0.912749i	$0.633955\pi$
$888$	30.1937	−	21.9370i	1.01323	−	0.736158i
$889$	3.17173	−	9.76158i	0.106376	−	0.327393i
$890$	−109.911			−3.68424
$891$	−0.157139	+	3.31290i	−0.00526434	+	0.110986i
$892$	57.0561			1.91038
$893$	6.60645	−	20.3326i	0.221076	−	0.680403i
$894$	−7.20624	+	5.23564i	−0.241013	+	0.175106i
$895$	−0.701966	−	0.510008i	−0.0234641	−	0.0170477i
$896$	3.93692	+	12.1166i	0.131523	+	0.404787i
$897$	−1.58652	−	4.88282i	−0.0529725	−	0.163033i
$898$	74.8736	+	54.3988i	2.49856	+	1.81531i
$899$	25.1178	−	18.2492i	0.837726	−	0.608643i
$900$	10.5219	−	32.3831i	0.350730	−	1.07944i
$901$	−10.5411			−0.351175
$902$	−38.5004	+	48.0294i	−1.28192	+	1.59921i
$903$	3.42946			0.114125
$904$	−16.4830	+	50.7294i	−0.548216	+	1.68724i
$905$	−3.94997	+	2.86982i	−0.131301	+	0.0953960i
$906$	−7.70462	−	5.59774i	−0.255969	−	0.185972i
$907$	4.67602	+	14.3913i	0.155265	+	0.477855i	0.998188	−	0.0601788i	$-0.0191671\pi$
$907$	4.67602	+	14.3913i	0.155265	+	0.477855i	−0.842923	+	0.538034i	$0.819167\pi$
$908$	33.9784	+	104.575i	1.12761	+	3.47044i
$909$	10.9800	+	7.97744i	0.364184	+	0.264595i
$910$	23.1440	−	16.8151i	0.767217	−	0.557416i
$911$	1.96205	−	6.03858i	0.0650057	−	0.200067i	−0.913278	−	0.407336i	$-0.866458\pi$
$911$	1.96205	−	6.03858i	0.0650057	−	0.200067i	0.978284	+	0.207269i	$0.0664577\pi$
$912$	−14.4504			−0.478500
$913$	−24.5857	+	30.6708i	−0.813668	+	1.01506i
$914$	51.6158			1.70730
$915$	8.11969	−	24.9899i	0.268429	−	0.826139i
$916$	83.9146	−	60.9675i	2.77261	−	2.01442i
$917$	−4.62495	−	3.36022i	−0.152729	−	0.110964i
$918$	0.768351	+	2.36474i	0.0253594	+	0.0780481i
$919$	−1.16370	−	3.58149i	−0.0383868	−	0.118142i	0.930027	−	0.367492i	$-0.119783\pi$
$919$	−1.16370	−	3.58149i	−0.0383868	−	0.118142i	−0.968414	+	0.249349i	$0.919783\pi$
$920$	18.6700	+	13.5646i	0.615533	+	0.447211i
$921$	3.17303	−	2.30534i	0.104555	−	0.0759636i
$922$	8.84528	−	27.2230i	0.291304	−	0.896541i
$923$	43.2119			1.42234
$924$	0.476642	−	10.0489i	0.0156804	−	0.330584i
$925$	−55.9945			−1.84109
$926$	20.4613	−	62.9735i	0.672401	−	2.06944i
$927$	0.511220	−	0.371423i	0.0167907	−	0.0121991i
$928$	−11.8526	−	8.61142i	−0.389081	−	0.282684i
$929$	−0.873784	−	2.68923i	−0.0286679	−	0.0882308i	0.935699	−	0.352800i	$-0.114770\pi$
$929$	−0.873784	−	2.68923i	−0.0286679	−	0.0882308i	−0.964367	+	0.264569i	$0.914770\pi$
$930$	11.1937	+	34.4506i	0.367055	+	1.12968i
$931$	−14.7609	−	10.7244i	−0.483768	−	0.351478i
$932$	21.6718	−	15.7455i	0.709884	−	0.515761i
$933$	−10.6197	+	32.6840i	−0.347672	+	1.07003i
$934$	−74.7641			−2.44635
$935$	−11.2457	−	4.25291i	−0.367774	−	0.139085i
$936$	−23.7466			−0.776183
$937$	−5.73601	+	17.6536i	−0.187387	+	0.576719i	−0.999981	−	0.00611124i	$-0.998055\pi$
$937$	−5.73601	+	17.6536i	−0.187387	+	0.576719i	0.812594	+	0.582830i	$0.198055\pi$
$938$	−3.33746	+	2.42481i	−0.108972	+	0.0791727i
$939$	0.171555	+	0.124642i	0.00559850	+	0.00406755i
$940$	35.5408	+	109.383i	1.15921	+	3.56769i
$941$	13.0396	+	40.1319i	0.425080	+	1.30826i	0.902917	+	0.429814i	$0.141421\pi$
$941$	13.0396	+	40.1319i	0.425080	+	1.30826i	−0.477837	+	0.878448i	$0.658579\pi$
$942$	33.0162	+	23.9877i	1.07573	+	0.781561i
$943$	7.08465	−	5.14730i	0.230708	−	0.167619i
$944$	15.3473	−	47.2342i	0.499513	−	1.53734i
$945$	2.62909			0.0855243
$946$	37.6160	−	10.2795i	1.22300	−	0.334217i
$947$	17.4051			0.565590			0.282795	−	0.959180i	$-0.408738\pi$
$947$	17.4051			0.565590			0.282795	+	0.959180i	$0.408738\pi$
$948$	21.4973	−	66.1619i	0.698200	−	2.14884i
$949$	20.5138	−	14.9041i	0.665905	−	0.483809i
$950$	46.1536	+	33.5326i	1.49742	+	1.08794i
$951$	9.26659	+	28.5196i	0.300490	+	0.924812i
$952$	−1.21611	−	3.74281i	−0.0394144	−	0.121305i
$953$	27.7316	+	20.1482i	0.898314	+	0.652663i	0.938032	−	0.346548i	$-0.112646\pi$
$953$	27.7316	+	20.1482i	0.898314	+	0.652663i	−0.0397187	+	0.999211i	$0.512646\pi$
$954$	21.2041	−	15.4057i	0.686509	−	0.498778i
$955$	16.0656	−	49.4449i	0.519872	−	1.60000i
$956$	81.2218			2.62690
$957$	−14.0616	−	21.4195i	−0.454548	−	0.692394i
$958$	−6.90640			−0.223136
$959$	−4.00721	+	12.3329i	−0.129400	+	0.398251i
$960$	−16.2462	+	11.8036i	−0.524345	+	0.380959i
$961$	12.0134	+	8.72823i	0.387528	+	0.281556i
$962$	23.1267	+	71.1766i	0.745634	+	2.29483i
$963$	2.32112	+	7.14366i	0.0747969	+	0.230201i
$964$	−76.9151	−	55.8821i	−2.47727	−	1.79984i
$965$	35.2076	−	25.5798i	1.13337	−	0.823444i
$966$	−0.653752	+	2.01204i	−0.0210341	+	0.0647364i
$967$	44.3834			1.42728			0.713638	−	0.700515i	$-0.247046\pi$
$967$	44.3834			1.42728			0.713638	+	0.700515i	$0.247046\pi$
$968$	−12.9890	−	58.2588i	−0.417482	−	1.87251i
$969$	−2.81826			−0.0905355
$970$	−37.2669	+	114.696i	−1.19657	+	3.68266i
$971$	33.3332	−	24.2180i	1.06971	−	0.777192i	0.0938527	−	0.995586i	$-0.470082\pi$
$971$	33.3332	−	24.2180i	1.06971	−	0.777192i	0.975861	+	0.218394i	$0.0700817\pi$
$972$	−3.38360	−	2.45833i	−0.108529	−	0.0788509i
$973$	1.87865	+	5.78188i	0.0602266	+	0.185358i
$974$	18.8103	+	57.8923i	0.602722	+	1.85499i
$975$	28.8235	+	20.9415i	0.923090	+	0.670664i
$976$	30.0674	−	21.8452i	0.962433	−	0.699248i
$977$	−1.25312	+	3.85670i	−0.0400907	+	0.123387i	−0.969099	−	0.246673i	$-0.920663\pi$
$977$	−1.25312	+	3.85670i	−0.0400907	+	0.123387i	0.929008	+	0.370059i	$0.120663\pi$
$978$	−2.39385			−0.0765470
$979$	−22.1949	−	33.8087i	−0.709353	−	1.08053i
$980$	98.1551			3.13545
$981$	1.53830	−	4.73439i	0.0491140	−	0.151157i
$982$	9.06852	−	6.58866i	0.289388	−	0.210253i
$983$	13.7453	+	9.98654i	0.438407	+	0.318521i	0.785002	−	0.619494i	$-0.212662\pi$
$983$	13.7453	+	9.98654i	0.438407	+	0.318521i	−0.346595	+	0.938015i	$0.612662\pi$
$984$	−12.5164	−	38.5216i	−0.399009	−	1.22802i
$985$	−9.61303	−	29.5859i	−0.306297	−	0.942684i
$986$	−15.5405	−	11.2908i	−0.494909	−	0.359572i
$987$	−4.45092	+	3.23379i	−0.141674	+	0.102933i
$988$	15.9398	−	49.0577i	0.507113	−	1.56073i
$989$	−5.54759			−0.176403
$990$	28.8371	−	7.88049i	0.916504	−	0.250458i
$991$	−8.40575			−0.267017			−0.133509	−	0.991048i	$-0.542624\pi$
$991$	−8.40575			−0.267017			−0.133509	+	0.991048i	$0.542624\pi$
$992$	−2.35507	+	7.24817i	−0.0747737	+	0.230130i
$993$	2.00727	−	1.45837i	0.0636987	−	0.0462798i
$994$	−14.4055	−	10.4662i	−0.456914	−	0.331967i
$995$	−27.4111	−	84.3628i	−0.868991	−	2.67448i
$996$	−15.3177	−	47.1430i	−0.485360	−	1.49378i
$997$	0.419801	+	0.305003i	0.0132952	+	0.00965955i	0.594413	−	0.804160i	$-0.297384\pi$
$997$	0.419801	+	0.305003i	0.0132952	+	0.00965955i	−0.581118	+	0.813819i	$0.697384\pi$
$998$	45.4614	−	33.0297i	1.43906	−	1.04554i
$999$	−2.12538	+	6.54126i	−0.0672442	+	0.206956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.460.6	✓	24
11.4	even	5		6171.2.a.bk.1.12		12
11.5	even	5	inner	561.2.m.d.511.6	yes	24
11.7	odd	10		6171.2.a.bl.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.460.6	✓	24	1.1	even	1	trivial
561.2.m.d.511.6	yes	24	11.5	even	5	inner
6171.2.a.bk.1.12		12	11.4	even	5
6171.2.a.bl.1.1		12	11.7	odd	10

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:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.768351 - 2.36474i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.38360 - 2.45833i) q^{4} +(-1.12021 - 3.44766i) q^{5} +(0.768351 + 2.36474i) q^{6} +(0.586739 + 0.426291i) q^{7} +(-4.38997 + 3.18950i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.768351 - 2.36474i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.38360 - 2.45833i) q^{4} +(-1.12021 - 3.44766i) q^{5} +(0.768351 + 2.36474i) q^{6} +(0.586739 + 0.426291i) q^{7} +(-4.38997 + 3.18950i) q^{8} +(0.309017 - 0.951057i) q^{9} -9.01354 q^{10} +(-1.82015 - 2.77256i) q^{11} +4.18236 q^{12} +(-1.35232 + 4.16203i) q^{13} +(1.45889 - 1.05994i) q^{14} +(2.93275 + 2.13077i) q^{15} +(1.58446 + 4.87646i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-2.01157 - 1.46149i) q^{18} +(2.28002 - 1.65653i) q^{19} +(-4.68513 + 14.4194i) q^{20} -0.725250 q^{21} +(-7.95489 + 2.17388i) q^{22} +1.17318 q^{23} +(1.67682 - 5.16071i) q^{24} +(-6.58640 + 4.78530i) q^{25} +(8.80305 + 6.39579i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.937327 - 2.88480i) q^{28} +(-6.25010 - 4.54096i) q^{29} +(7.29210 - 5.29802i) q^{30} +(-1.24187 + 3.82209i) q^{31} +1.89639 q^{32} +(3.10220 + 1.17319i) q^{33} +2.48644 q^{34} +(0.812434 - 2.50041i) q^{35} +(-3.38360 + 2.45833i) q^{36} +(5.56433 + 4.04272i) q^{37} +(-2.16541 - 6.66445i) q^{38} +(-1.35232 - 4.16203i) q^{39} +(15.9140 + 11.5622i) q^{40} +(6.03883 - 4.38746i) q^{41} +(-0.557246 + 1.71503i) q^{42} -4.72866 q^{43} +(-0.657210 + 13.8557i) q^{44} -3.62508 q^{45} +(0.901416 - 2.77427i) q^{46} +(6.13709 - 4.45886i) q^{47} +(-4.14816 - 3.01382i) q^{48} +(-2.00058 - 6.15715i) q^{49} +(6.25532 + 19.2519i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(14.8074 - 10.7582i) q^{52} +(-3.25738 + 10.0252i) q^{53} +2.48644 q^{54} +(-7.51988 + 9.38110i) q^{55} -3.93542 q^{56} +(-0.870890 + 2.68032i) q^{57} +(-15.5405 + 11.2908i) q^{58} +(-7.83628 - 5.69339i) q^{59} +(-4.68513 - 14.4194i) q^{60} +(-2.23986 - 6.89359i) q^{61} +(8.08406 + 5.87342i) q^{62} +(0.586739 - 0.426291i) q^{63} +(-1.71182 + 5.26845i) q^{64} +15.8641 q^{65} +(5.15787 - 6.43447i) q^{66} -2.28767 q^{67} +(1.29242 - 3.97766i) q^{68} +(-0.949125 + 0.689580i) q^{69} +(-5.28859 - 3.84239i) q^{70} +(-3.05132 - 9.39099i) q^{71} +(1.67682 + 5.16071i) q^{72} +(-4.68756 - 3.40571i) q^{73} +(13.8353 - 10.0520i) q^{74} +(2.51578 - 7.74277i) q^{75} -11.7870 q^{76} +(0.113965 - 2.40268i) q^{77} -10.8812 q^{78} +(5.13999 - 15.8193i) q^{79} +(15.0374 - 10.9253i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.73528 - 17.6514i) q^{82} +(-3.66246 - 11.2719i) q^{83} +(2.45395 + 1.78290i) q^{84} +(2.93275 - 2.13077i) q^{85} +(-3.63327 + 11.1821i) q^{86} +7.72554 q^{87} +(16.8334 + 6.36608i) q^{88} +12.1940 q^{89} +(-2.78534 + 8.57238i) q^{90} +(-2.56770 + 1.86554i) q^{91} +(-3.96958 - 2.88407i) q^{92} +(-1.24187 - 3.82209i) q^{93} +(-5.82860 - 17.9386i) q^{94} +(-8.26526 - 6.00506i) q^{95} +(-1.53421 + 1.11467i) q^{96} +(4.13455 - 12.7248i) q^{97} -16.0972 q^{98} +(-3.19931 + 0.874295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

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