LMFDB - Embedded newform 165.2.p.b.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	165.101
Dual form			165.2.p.b.116.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.140144 - 0.431318i) q^{2} +(-1.58256 - 0.703911i) q^{3} +(1.45164 + 1.05468i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.525396 + 0.583940i) q^{6} +(2.72178 - 3.74621i) q^{7} +(1.39214 - 1.01145i) q^{8} +(2.00902 + 2.22797i) q^{9} +O(q^{10})$	\(q+(0.140144 - 0.431318i) q^{2} +(-1.58256 - 0.703911i) q^{3} +(1.45164 + 1.05468i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.525396 + 0.583940i) q^{6} +(2.72178 - 3.74621i) q^{7} +(1.39214 - 1.01145i) q^{8} +(2.00902 + 2.22797i) q^{9} +0.453514i q^{10} +(2.24032 - 2.44560i) q^{11} +(-1.55491 - 2.69092i) q^{12} +(-2.34827 - 0.762999i) q^{13} +(-1.23437 - 1.69896i) q^{14} +(1.72263 + 0.180419i) q^{15} +(0.867797 + 2.67080i) q^{16} +(0.465691 + 1.43325i) q^{17} +(1.24251 - 0.554291i) q^{18} +(-1.58515 - 2.18177i) q^{19} +(-1.70650 - 0.554477i) q^{20} +(-6.94438 + 4.01272i) q^{21} +(-0.740863 - 1.30903i) q^{22} +5.63898i q^{23} +(-2.91512 + 0.620741i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-0.658190 + 0.905921i) q^{26} +(-1.61111 - 4.94007i) q^{27} +(7.90208 - 2.56754i) q^{28} +(-0.463093 - 0.336457i) q^{29} +(0.319234 - 0.717716i) q^{30} +(-2.36854 + 7.28961i) q^{31} +4.71514 q^{32} +(-5.26694 + 2.29333i) q^{33} +0.683450 q^{34} +(-1.43092 + 4.40393i) q^{35} +(0.566584 + 5.35307i) q^{36} +(0.396224 + 0.287874i) q^{37} +(-1.16318 + 0.377941i) q^{38} +(3.17920 + 2.86047i) q^{39} +(-1.01145 + 1.39214i) q^{40} +(-6.82953 + 4.96195i) q^{41} +(0.757548 + 3.55759i) q^{42} +2.51824i q^{43} +(5.83146 - 1.18731i) q^{44} +(-2.59917 - 1.49810i) q^{45} +(2.43219 + 0.790268i) q^{46} +(1.96912 + 2.71027i) q^{47} +(0.506663 - 4.83757i) q^{48} +(-4.46287 - 13.7353i) q^{49} +(-0.140144 - 0.431318i) q^{50} +(0.271894 - 2.59602i) q^{51} +(-2.60412 - 3.58426i) q^{52} +(-12.6599 - 4.11346i) q^{53} +(-2.35653 + 0.00258193i) q^{54} +(-1.37494 + 3.01820i) q^{55} -7.96819i q^{56} +(0.972828 + 4.56859i) q^{57} +(-0.210019 + 0.152588i) q^{58} +(2.21091 - 3.04306i) q^{59} +(2.31035 + 2.07872i) q^{60} +(7.73467 - 2.51315i) q^{61} +(2.81220 + 2.04319i) q^{62} +(13.8145 - 1.46217i) q^{63} +(-1.07480 + 3.30788i) q^{64} +2.46912 q^{65} +(0.251026 + 2.59312i) q^{66} -7.19080 q^{67} +(-0.835601 + 2.57172i) q^{68} +(3.96934 - 8.92405i) q^{69} +(1.69896 + 1.23437i) q^{70} +(6.97057 - 2.26487i) q^{71} +(5.05032 + 1.06962i) q^{72} +(-3.93323 + 5.41362i) q^{73} +(0.179693 - 0.130555i) q^{74} +(-1.69407 + 0.360732i) q^{75} -4.83896i q^{76} +(-3.06405 - 15.0491i) q^{77} +(1.67932 - 0.970371i) q^{78} +(3.68901 + 1.19863i) q^{79} +(-1.65065 - 2.27192i) q^{80} +(-0.927679 + 8.95206i) q^{81} +(1.18306 + 3.64109i) q^{82} +(1.83123 + 5.63595i) q^{83} +(-14.3129 - 1.49906i) q^{84} +(-0.885798 - 1.21920i) q^{85} +(1.08616 + 0.352916i) q^{86} +(0.496039 + 0.858440i) q^{87} +(0.645247 - 5.67059i) q^{88} +3.19518i q^{89} +(-1.01042 + 0.911120i) q^{90} +(-9.24982 + 6.72039i) q^{91} +(-5.94731 + 8.18577i) q^{92} +(8.87960 - 9.86904i) q^{93} +(1.44495 - 0.469491i) q^{94} +(2.18177 + 1.58515i) q^{95} +(-7.46202 - 3.31904i) q^{96} +(-0.622669 + 1.91638i) q^{97} -6.54972 q^{98} +(9.94957 + 0.0781136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	0.140144	−	0.431318i	0.0990965	−	0.304988i	−0.889203	−	0.457513i	$-0.848740\pi$
$2$	0.140144	−	0.431318i	0.0990965	−	0.304988i	0.988300	+	0.152525i	$0.0487404\pi$
$3$	−1.58256	−	0.703911i	−0.913694	−	0.406403i
$3$	−1.58256	−	0.703911i	−0.913694	−	0.406403i
$4$	1.45164	+	1.05468i	0.725820	+	0.527339i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$6$	−0.525396	+	0.583940i	−0.214492	+	0.238392i
$7$	2.72178	−	3.74621i	1.02874	−	1.41593i	0.122843	−	0.992426i	$-0.460799\pi$
$7$	2.72178	−	3.74621i	1.02874	−	1.41593i	0.905893	−	0.423507i	$-0.139201\pi$
$8$	1.39214	−	1.01145i	0.492196	−	0.357602i
$9$	2.00902	+	2.22797i	0.669673	+	0.742656i
$10$			0.453514i			0.143414i
$11$	2.24032	−	2.44560i	0.675483	−	0.737376i
$11$	2.24032	−	2.44560i	0.675483	−	0.737376i
$12$	−1.55491	−	2.69092i	−0.448865	−	0.776801i
$13$	−2.34827	−	0.762999i	−0.651293	−	0.211618i	−0.0353085	−	0.999376i	$-0.511241\pi$
$13$	−2.34827	−	0.762999i	−0.651293	−	0.211618i	−0.615984	+	0.787759i	$0.711241\pi$
$14$	−1.23437	−	1.69896i	−0.329898	−	0.454066i
$15$	1.72263	+	0.180419i	0.444781	+	0.0465841i
$16$	0.867797	+	2.67080i	0.216949	+	0.667701i
$17$	0.465691	+	1.43325i	0.112947	+	0.347614i	0.991513	−	0.130006i	$-0.0414996\pi$
$17$	0.465691	+	1.43325i	0.112947	+	0.347614i	−0.878567	+	0.477620i	$0.841500\pi$
$18$	1.24251	−	0.554291i	0.292863	−	0.130648i
$19$	−1.58515	−	2.18177i	−0.363658	−	0.500532i	0.587506	−	0.809220i	$-0.300110\pi$
$19$	−1.58515	−	2.18177i	−0.363658	−	0.500532i	−0.951163	+	0.308688i	$0.900110\pi$
$20$	−1.70650	−	0.554477i	−0.381586	−	0.123985i
$21$	−6.94438	+	4.01272i	−1.51539	+	0.875648i
$22$	−0.740863	−	1.30903i	−0.157953	−	0.279085i
$23$			5.63898i			1.17581i	0.808930	+	0.587905i	$0.200047\pi$
$23$			5.63898i			1.17581i	−0.808930	+	0.587905i	$0.799953\pi$
$24$	−2.91512	+	0.620741i	−0.595047	+	0.126708i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−0.658190	+	0.905921i	−0.129082	+	0.177666i
$27$	−1.61111	−	4.94007i	−0.310059	−	0.950717i
$28$	7.90208	−	2.56754i	1.49335	−	0.485220i
$29$	−0.463093	−	0.336457i	−0.0859942	−	0.0624784i	0.543957	−	0.839113i	$-0.316925\pi$
$29$	−0.463093	−	0.336457i	−0.0859942	−	0.0624784i	−0.629952	+	0.776634i	$0.716925\pi$
$30$	0.319234	−	0.717716i	0.0582838	−	0.131036i
$31$	−2.36854	+	7.28961i	−0.425402	+	1.30925i	0.477207	+	0.878791i	$0.341649\pi$
$31$	−2.36854	+	7.28961i	−0.425402	+	1.30925i	−0.902609	+	0.430462i	$0.858351\pi$
$32$	4.71514			0.833528
$33$	−5.26694	+	2.29333i	−0.916856	+	0.399217i
$34$	0.683450			0.117211
$35$	−1.43092	+	4.40393i	−0.241870	+	0.744400i
$36$	0.566584	+	5.35307i	0.0944307	+	0.892179i
$37$	0.396224	+	0.287874i	0.0651389	+	0.0473262i	0.619878	−	0.784698i	$-0.287182\pi$
$37$	0.396224	+	0.287874i	0.0651389	+	0.0473262i	−0.554739	+	0.832024i	$0.687182\pi$
$38$	−1.16318	+	0.377941i	−0.188693	+	0.0613102i
$39$	3.17920	+	2.86047i	0.509080	+	0.458041i
$40$	−1.01145	+	1.39214i	−0.159924	+	0.220117i
$41$	−6.82953	+	4.96195i	−1.06659	+	0.774926i	−0.975297	−	0.220898i	$-0.929101\pi$
$41$	−6.82953	+	4.96195i	−1.06659	+	0.774926i	−0.0912970	+	0.995824i	$0.529101\pi$
$42$	0.757548	+	3.55759i	0.116892	+	0.548949i
$43$			2.51824i			0.384029i	0.981392	+	0.192014i	$0.0615020\pi$
$43$			2.51824i			0.384029i	−0.981392	+	0.192014i	$0.938498\pi$
$44$	5.83146	−	1.18731i	0.879125	−	0.178993i
$45$	−2.59917	−	1.49810i	−0.387462	−	0.223324i
$46$	2.43219	+	0.790268i	0.358607	+	0.116519i
$47$	1.96912	+	2.71027i	0.287226	+	0.395333i	0.928111	−	0.372304i	$-0.121432\pi$
$47$	1.96912	+	2.71027i	0.287226	+	0.395333i	−0.640885	+	0.767637i	$0.721432\pi$
$48$	0.506663	−	4.83757i	0.0731305	−	0.698243i
$49$	−4.46287	−	13.7353i	−0.637552	−	1.96218i
$50$	−0.140144	−	0.431318i	−0.0198193	−	0.0609976i
$51$	0.271894	−	2.59602i	0.0380727	−	0.363515i
$52$	−2.60412	−	3.58426i	−0.361127	−	0.497048i
$53$	−12.6599	−	4.11346i	−1.73898	−	0.565028i	−0.744279	−	0.667869i	$-0.767207\pi$
$53$	−12.6599	−	4.11346i	−1.73898	−	0.565028i	−0.994698	+	0.102842i	$0.967207\pi$
$54$	−2.35653	+	0.00258193i	−0.320683	+	0.000351357i
$55$	−1.37494	+	3.01820i	−0.185397	+	0.406974i
$56$		−	7.96819i		−	1.06479i
$57$	0.972828	+	4.56859i	0.128854	+	0.605125i
$58$	−0.210019	+	0.152588i	−0.0275769	+	0.0200358i
$59$	2.21091	−	3.04306i	0.287837	−	0.396173i	−0.640473	−	0.767980i	$-0.721262\pi$
$59$	2.21091	−	3.04306i	0.287837	−	0.396173i	0.928310	+	0.371807i	$0.121262\pi$
$60$	2.31035	+	2.07872i	0.298265	+	0.268362i
$61$	7.73467	−	2.51315i	0.990323	−	0.321776i	0.231331	−	0.972875i	$-0.425692\pi$
$61$	7.73467	−	2.51315i	0.990323	−	0.321776i	0.758992	+	0.651099i	$0.225692\pi$
$62$	2.81220	+	2.04319i	0.357150	+	0.259485i
$63$	13.8145	−	1.46217i	1.74047	−	0.184216i
$64$	−1.07480	+	3.30788i	−0.134350	+	0.413485i
$65$	2.46912			0.306256
$66$	0.251026	+	2.59312i	0.0308991	+	0.319191i
$67$	−7.19080			−0.878496			−0.439248	−	0.898366i	$-0.644755\pi$
$67$	−7.19080			−0.878496			−0.439248	+	0.898366i	$0.644755\pi$
$68$	−0.835601	+	2.57172i	−0.101332	+	0.311866i
$69$	3.96934	−	8.92405i	0.477852	−	1.07433i
$70$	1.69896	+	1.23437i	0.203064	+	0.147535i
$71$	6.97057	−	2.26487i	0.827254	−	0.268791i	0.135366	−	0.990796i	$-0.456779\pi$
$71$	6.97057	−	2.26487i	0.827254	−	0.268791i	0.691888	+	0.722005i	$0.256779\pi$
$72$	5.05032	+	1.06962i	0.595186	+	0.126056i
$73$	−3.93323	+	5.41362i	−0.460349	+	0.633617i	−0.974581	−	0.224035i	$-0.928077\pi$
$73$	−3.93323	+	5.41362i	−0.460349	+	0.633617i	0.514232	+	0.857651i	$0.328077\pi$
$74$	0.179693	−	0.130555i	0.0208889	−	0.0151767i
$75$	−1.69407	+	0.360732i	−0.195614	+	0.0416538i
$76$		−	4.83896i		−	0.555067i
$77$	−3.06405	−	15.0491i	−0.349181	−	1.71500i
$78$	1.67932	−	0.970371i	0.190145	−	0.109873i
$79$	3.68901	+	1.19863i	0.415047	+	0.134857i	0.509094	−	0.860711i	$-0.329981\pi$
$79$	3.68901	+	1.19863i	0.415047	+	0.134857i	−0.0940474	+	0.995568i	$0.529981\pi$
$80$	−1.65065	−	2.27192i	−0.184548	−	0.254009i
$81$	−0.927679	+	8.95206i	−0.103075	+	0.994674i
$82$	1.18306	+	3.64109i	0.130647	+	0.402091i
$83$	1.83123	+	5.63595i	0.201004	+	0.618626i	0.999854	+	0.0170958i	$0.00544204\pi$
$83$	1.83123	+	5.63595i	0.201004	+	0.618626i	−0.798850	+	0.601530i	$0.794558\pi$
$84$	−14.3129	−	1.49906i	−1.56166	−	0.163561i
$85$	−0.885798	−	1.21920i	−0.0960782	−	0.132240i
$86$	1.08616	+	0.352916i	0.117124	+	0.0380559i
$87$	0.496039	+	0.858440i	0.0531809	+	0.0920344i
$88$	0.645247	−	5.67059i	0.0687836	−	0.604487i
$89$			3.19518i			0.338688i	0.985557	+	0.169344i	$0.0541650\pi$
$89$			3.19518i			0.338688i	−0.985557	+	0.169344i	$0.945835\pi$
$90$	−1.01042	+	0.911120i	−0.106507	+	0.0960404i
$91$	−9.24982	+	6.72039i	−0.969644	+	0.704488i
$92$	−5.94731	+	8.18577i	−0.620050	+	0.853425i
$93$	8.87960	−	9.86904i	0.920771	−	1.02337i
$94$	1.44495	−	0.469491i	0.149035	−	0.0484243i
$95$	2.18177	+	1.58515i	0.223845	+	0.162633i
$96$	−7.46202	−	3.31904i	−0.761589	−	0.338748i
$97$	−0.622669	+	1.91638i	−0.0632224	+	0.194579i	−0.977678	−	0.210107i	$-0.932619\pi$
$97$	−0.622669	+	1.91638i	−0.0632224	+	0.194579i	0.914456	+	0.404685i	$0.132619\pi$
$98$	−6.54972			−0.661622
$99$	9.94957	+	0.0781136i	0.999969	+	0.00785071i
$100$	1.79432			0.179432
$101$	3.85644	−	11.8689i	0.383730	−	1.18100i	−0.553667	−	0.832738i	$-0.686772\pi$
$101$	3.85644	−	11.8689i	0.383730	−	1.18100i	0.937397	−	0.348262i	$-0.113228\pi$
$102$	−1.08160	−	0.481088i	−0.107095	−	0.0476348i
$103$	1.89303	+	1.37537i	0.186526	+	0.135519i	0.677130	−	0.735864i	$-0.263224\pi$
$103$	1.89303	+	1.37537i	0.186526	+	0.135519i	−0.490604	+	0.871383i	$0.663224\pi$
$104$	−4.04086	+	1.31295i	−0.396239	+	0.128746i
$105$	5.36450	−	5.96226i	0.523522	−	0.581857i
$106$	−3.54842	+	4.88398i	−0.344653	+	0.474374i
$107$	14.6054	−	10.6114i	1.41196	−	1.02585i	0.418923	−	0.908022i	$-0.362408\pi$
$107$	14.6054	−	10.6114i	1.41196	−	1.02585i	0.993034	−	0.117826i	$-0.0375924\pi$
$108$	2.87143	−	8.87041i	0.276303	−	0.853555i
$109$			19.0666i			1.82625i	0.407679	+	0.913126i	$0.366338\pi$
$109$			19.0666i			1.82625i	−0.407679	+	0.913126i	$0.633662\pi$
$110$	1.10911	+	1.01602i	0.105750	+	0.0968736i
$111$	−0.424413	−	0.734485i	−0.0402835	−	0.0697143i
$112$	12.3673	+	4.01839i	1.16860	+	0.379702i
$113$	1.01840	+	1.40170i	0.0958027	+	0.131861i	0.854227	−	0.519900i	$-0.174031\pi$
$113$	1.01840	+	1.40170i	0.0958027	+	0.131861i	−0.758425	+	0.651761i	$0.774031\pi$
$114$	2.10685	+	0.220661i	0.197325	+	0.0206668i
$115$	−1.74254	−	5.36299i	−0.162493	−	0.500101i
$116$	−0.317390	−	0.976827i	−0.0294690	−	0.0906961i
$117$	−3.01778	−	6.76475i	−0.278994	−	0.625401i
$118$	−1.00268	−	1.38007i	−0.0923044	−	0.127046i
$119$	6.63676	+	2.15641i	0.608391	+	0.197678i
$120$	2.58063	−	1.49118i	0.235578	−	0.136126i
$121$	−0.961900	−	10.9579i	−0.0874455	−	0.996169i
$122$		−	3.68831i		−	0.333923i
$123$	14.3009	−	3.04522i	1.28947	−	0.274578i
$124$	−11.1265	+	8.08384i	−0.999185	+	0.725950i
$125$	−0.587785	+	0.809017i	−0.0525731	+	0.0723607i
$126$	1.30536	−	6.16337i	0.116291	−	0.549077i
$127$	−10.1051	+	3.28335i	−0.896683	+	0.291350i	−0.720867	−	0.693073i	$-0.756256\pi$
$127$	−10.1051	+	3.28335i	−0.896683	+	0.291350i	−0.175815	+	0.984423i	$0.556256\pi$
$128$	8.90539	+	6.47014i	0.787132	+	0.571885i
$129$	1.77262	−	3.98528i	0.156070	−	0.350885i
$130$	0.346031	−	1.06497i	0.0303489	−	0.0934044i
$131$	−3.21711			−0.281081			−0.140540	−	0.990075i	$-0.544884\pi$
$131$	−3.21711			−0.281081			−0.140540	+	0.990075i	$0.544884\pi$
$132$	−10.0644	−	2.22584i	−0.875995	−	0.193734i
$133$	−12.4878			−1.08283
$134$	−1.00775	+	3.10152i	−0.0870559	+	0.267931i
$135$	3.05883	+	4.20043i	0.263262	+	0.361515i
$136$	2.09797	+	1.52426i	0.179899	+	0.130705i
$137$	−15.1500	+	4.92255i	−1.29436	+	0.420562i	−0.873614	−	0.486619i	$-0.838230\pi$
$137$	−15.1500	+	4.92255i	−1.29436	+	0.420562i	−0.420742	+	0.907181i	$0.638230\pi$
$138$	−3.29283	−	2.96270i	−0.280304	−	0.252201i
$139$	6.56849	−	9.04075i	0.557132	−	0.766827i	−0.433826	−	0.900997i	$-0.642837\pi$
$139$	6.56849	−	9.04075i	0.557132	−	0.766827i	0.990958	+	0.134170i	$0.0428368\pi$
$140$	−6.72191	+	4.88375i	−0.568105	+	0.412753i
$141$	−1.20848	−	5.67526i	−0.101772	−	0.477943i
$142$		−	3.32394i		−	0.278939i
$143$	−7.12687	+	4.03356i	−0.595979	+	0.337303i
$144$	−4.20704	+	7.29912i	−0.350587	+	0.608260i
$145$	0.544398	+	0.176886i	0.0452098	+	0.0146896i
$146$	1.78378	+	2.45516i	0.147626	+	0.203190i
$147$	−2.60564	+	24.8784i	−0.214910	+	2.05194i
$148$	0.271561	+	0.835778i	0.0223221	+	0.0687005i
$149$	5.22728	+	16.0879i	0.428236	+	1.31797i	0.899862	+	0.436175i	$0.143667\pi$
$149$	5.22728	+	16.0879i	0.428236	+	1.31797i	−0.471626	+	0.881799i	$0.656333\pi$
$150$	−0.0818229	+	0.781237i	−0.00668081	+	0.0637877i
$151$	−11.3593	−	15.6347i	−0.924405	−	1.27233i	−0.962002	−	0.273041i	$-0.911970\pi$
$151$	−11.3593	−	15.6347i	−0.924405	−	1.27233i	0.0375975	−	0.999293i	$-0.488030\pi$
$152$	−4.41350	−	1.43403i	−0.357982	−	0.116315i
$153$	−2.25765	+	3.91697i	−0.182520	+	0.316669i
$154$	−6.92035	−	0.787455i	−0.557658	−	0.0634549i
$155$		−	7.66475i		−	0.615648i
$156$	1.59819	+	7.50540i	0.127957	+	0.600913i
$157$	4.25532	−	3.09167i	0.339611	−	0.246742i	−0.404887	−	0.914367i	$-0.632689\pi$
$157$	4.25532	−	3.09167i	0.339611	−	0.246742i	0.744498	+	0.667625i	$0.232689\pi$
$158$	1.03398	−	1.42316i	0.0822594	−	0.113220i
$159$	17.1397	+	15.4213i	1.35926	+	1.22299i
$160$	−4.48437	+	1.45706i	−0.354520	+	0.115191i
$161$	21.1248	+	15.3481i	1.66487	+	1.20960i
$162$	3.73118	+	1.65470i	0.293149	+	0.130005i
$163$	−5.41702	+	16.6719i	−0.424294	+	1.30584i	0.479375	+	0.877610i	$0.340863\pi$
$163$	−5.41702	+	16.6719i	−0.424294	+	1.30584i	−0.903669	+	0.428232i	$0.859137\pi$
$164$	−15.1473			−1.18280
$165$	4.30048	−	3.80866i	0.334792	−	0.296504i
$166$	2.68752			0.208592
$167$	−0.269161	+	0.828392i	−0.0208283	+	0.0641029i	−0.960930	−	0.276790i	$-0.910729\pi$
$167$	−0.269161	+	0.828392i	−0.0208283	+	0.0641029i	0.940102	+	0.340893i	$0.110729\pi$
$168$	−5.60889	+	12.6102i	−0.432736	+	0.972896i
$169$	−5.58502	−	4.05776i	−0.429617	−	0.312135i
$170$	−0.650000	+	0.211198i	−0.0498527	+	0.0161981i
$171$	1.67632	−	7.91487i	0.128191	−	0.605265i
$172$	−2.65594	+	3.65558i	−0.202513	+	0.278736i
$173$	−13.1394	+	9.54634i	−0.998971	+	0.725795i	−0.961867	−	0.273517i	$-0.911813\pi$
$173$	−13.1394	+	9.54634i	−0.998971	+	0.725795i	−0.0371035	+	0.999311i	$0.511813\pi$
$174$	0.439777	−	0.0936454i	0.0333394	−	0.00709924i
$175$		−	4.63057i		−	0.350038i
$176$	8.47586	+	3.86118i	0.638892	+	0.291048i
$177$	−5.64096	+	3.25956i	−0.424000	+	0.245003i
$178$	1.37814	+	0.447784i	0.103296	+	0.0335629i
$179$	−10.9962	−	15.1350i	−0.821894	−	1.13124i	−0.989378	−	0.145365i	$-0.953564\pi$
$179$	−10.9962	−	15.1350i	−0.821894	−	1.13124i	0.167484	−	0.985875i	$-0.446436\pi$
$180$	−2.19304	−	4.91599i	−0.163460	−	0.366416i
$181$	2.57484	+	7.92454i	0.191386	+	0.589027i	1.00000		0.000686228i	$0.000218433\pi$
$181$	2.57484	+	7.92454i	0.191386	+	0.589027i	−0.808613	+	0.588340i	$0.799782\pi$
$182$	1.60232	+	4.93143i	0.118772	+	0.365542i
$183$	−14.0097	−	1.46730i	−1.03562	−	0.108466i
$184$	5.70355	+	7.85026i	0.420471	+	0.578729i
$185$	−0.465790	−	0.151344i	−0.0342455	−	0.0111270i
$186$	−3.01227	−	5.21301i	−0.220871	−	0.382237i
$187$	4.54845	+	2.07205i	0.332616	+	0.151523i
$188$			6.01112i			0.438406i
$189$	−22.8916	−	7.41022i	−1.66512	−	0.539014i
$190$	0.989464	−	0.718887i	0.0717832	−	0.0521536i
$191$	11.9113	−	16.3946i	0.861874	−	1.18627i	−0.119245	−	0.992865i	$-0.538047\pi$
$191$	11.9113	−	16.3946i	0.861874	−	1.18627i	0.981119	−	0.193403i	$-0.0619526\pi$
$192$	4.02939	−	4.47838i	0.290796	−	0.323199i
$193$	7.08949	−	2.30351i	0.510312	−	0.165811i	−0.0425319	−	0.999095i	$-0.513542\pi$
$193$	7.08949	−	2.30351i	0.510312	−	0.165811i	0.552844	+	0.833285i	$0.313542\pi$
$194$	0.739305	+	0.537136i	0.0530790	+	0.0385641i
$195$	−3.90753	−	1.73804i	−0.279824	−	0.124463i
$196$	8.00783	−	24.6456i	0.571988	−	1.76040i
$197$	13.6689			0.973868			0.486934	−	0.873439i	$-0.338115\pi$
$197$	13.6689			0.973868			0.486934	+	0.873439i	$0.338115\pi$
$198$	1.42806	−	4.28048i	0.101488	−	0.304200i
$199$	11.7105			0.830133			0.415067	−	0.909791i	$-0.363758\pi$
$199$	11.7105			0.830133			0.415067	+	0.909791i	$0.363758\pi$
$200$	0.531751	−	1.63656i	0.0376004	−	0.115722i
$201$	11.3799	+	5.06168i	0.802677	+	0.357023i
$202$	−4.57881	−	3.32670i	−0.322164	−	0.234066i
$203$	−2.52087	+	0.819081i	−0.176930	+	0.0574882i
$204$	3.13265	−	3.48172i	0.219329	−	0.243769i
$205$	4.96195	−	6.82953i	0.346557	−	0.476995i
$206$	0.858518	−	0.623750i	0.0598158	−	0.0434587i
$207$	−12.5635	+	11.3288i	−0.873222	+	0.787408i
$208$		−	6.93389i		−	0.480779i
$209$	−8.88697	−	1.01123i	−0.614725	−	0.0699485i
$210$	−1.81983	−	3.14938i	−0.125580	−	0.217328i
$211$	−3.66580	−	1.19109i	−0.252364	−	0.0819982i	0.180103	−	0.983648i	$-0.442357\pi$
$211$	−3.66580	−	1.19109i	−0.252364	−	0.0819982i	−0.432467	+	0.901650i	$0.642357\pi$
$212$	−14.0393	−	19.3234i	−0.964222	−	1.32714i
$213$	−12.6256	−	1.32235i	−0.865094	−	0.0906057i
$214$	−2.53005	−	7.78670i	−0.172951	−	0.532288i
$215$	−0.778180	−	2.39499i	−0.0530715	−	0.163337i
$216$	−7.23953	−	5.24772i	−0.492588	−	0.357062i
$217$	20.8618	+	28.7137i	1.41619	+	1.94922i
$218$	8.22377	+	2.67207i	0.556984	+	0.180975i
$219$	10.0353	−	5.79877i	0.678122	−	0.391844i
$220$	−5.17915	+	2.93122i	−0.349178	+	0.197623i
$221$		−	3.72098i		−	0.250300i
$222$	−0.376275	+	0.0801235i	−0.0252540	+	0.00537753i
$223$	18.9238	−	13.7489i	1.26723	−	0.920698i	0.268143	−	0.963379i	$-0.413590\pi$
$223$	18.9238	−	13.7489i	1.26723	−	0.920698i	0.999089	+	0.0426814i	$0.0135900\pi$
$224$	12.8336	−	17.6639i	0.857479	−	1.18022i
$225$	2.93490	+	0.621591i	0.195660	+	0.0414394i
$226$	0.747302	−	0.242813i	0.0497098	−	0.0161517i
$227$	5.59908	+	4.06797i	0.371624	+	0.270001i	0.757884	−	0.652389i	$-0.226233\pi$
$227$	5.59908	+	4.06797i	0.371624	+	0.270001i	−0.386260	+	0.922390i	$0.626233\pi$
$228$	−3.40620	+	7.65797i	−0.225581	+	0.507161i
$229$	−0.201744	+	0.620905i	−0.0133316	+	0.0410306i	−0.957501	−	0.288430i	$-0.906867\pi$
$229$	−0.201744	+	0.620905i	−0.0133316	+	0.0410306i	0.944169	+	0.329460i	$0.106867\pi$
$230$	−2.55736			−0.168627
$231$	−5.74416	+	25.9730i	−0.377938	+	1.70890i
$232$	−0.984999			−0.0646684
$233$	5.70562	−	17.5601i	0.373788	−	1.15040i	−0.570505	−	0.821294i	$-0.693253\pi$
$233$	5.70562	−	17.5601i	0.373788	−	1.15040i	0.944293	−	0.329106i	$-0.106747\pi$
$234$	−3.34068	+	0.353587i	−0.218387	+	0.0231147i
$235$	−2.71027	−	1.96912i	−0.176798	−	0.128451i
$236$	6.41890	−	2.08563i	0.417835	−	0.135763i
$237$	−4.99437	−	4.49365i	−0.324419	−	0.291894i
$238$	1.86020	−	2.56035i	0.120579	−	0.165963i
$239$	0.484930	−	0.352322i	0.0313675	−	0.0227898i	−0.571991	−	0.820260i	$-0.693829\pi$
$239$	0.484930	−	0.352322i	0.0313675	−	0.0227898i	0.603359	+	0.797470i	$0.293829\pi$
$240$	1.01303	+	4.75737i	0.0653906	+	0.307087i
$241$		−	3.10234i		−	0.199839i	−0.994996	−	0.0999195i	$-0.968141\pi$
$241$		−	3.10234i		−	0.199839i	0.994996	−	0.0999195i	$-0.0318585\pi$
$242$	−4.86113	−	1.12079i	−0.312485	−	0.0720471i
$243$	7.76956	−	13.5142i	0.498418	−	0.866937i
$244$	13.8785	+	4.50940i	0.888481	+	0.288685i
$245$	8.48888	+	11.6839i	0.542334	+	0.746459i
$246$	0.690729	−	6.59502i	0.0440393	−	0.420483i
$247$	2.05767	+	6.33284i	0.130926	+	0.402949i
$248$	4.07574	+	12.5438i	0.258809	+	0.796534i
$249$	1.06916	−	10.2083i	0.0677555	−	0.646923i
$250$	0.266569	+	0.366901i	0.0168593	+	0.0232049i
$251$	−25.4210	−	8.25979i	−1.60456	−	0.521353i	−0.636331	−	0.771416i	$-0.719549\pi$
$251$	−25.4210	−	8.25979i	−1.60456	−	0.521353i	−0.968230	+	0.250063i	$0.919549\pi$
$252$	21.5958	+	12.4473i	1.36041	+	0.784108i
$253$	13.7907	+	12.6331i	0.867013	+	0.794239i
$254$			4.81865i			0.302349i
$255$	0.543627	+	2.55298i	0.0340432	+	0.159874i
$256$	−1.58898	+	1.15446i	−0.0993115	+	0.0721540i
$257$	7.94749	−	10.9388i	0.495751	−	0.682343i	−0.485685	−	0.874134i	$-0.661430\pi$
$257$	7.94749	−	10.9388i	0.495751	−	0.682343i	0.981436	+	0.191791i	$0.0614297\pi$
$258$	−1.47050	−	1.32307i	−0.0915495	−	0.0823710i
$259$	2.15687	−	0.700809i	0.134021	−	0.0435462i
$260$	3.58426	+	2.60412i	0.222287	+	0.161501i
$261$	−0.180748	−	1.70770i	−0.0111880	−	0.105704i
$262$	−0.450858	+	1.38760i	−0.0278541	+	0.0857262i
$263$	−6.67606			−0.411664			−0.205832	−	0.978587i	$-0.565990\pi$
$263$	−6.67606			−0.411664			−0.205832	+	0.978587i	$0.565990\pi$
$264$	−5.01274	+	8.51988i	−0.308513	+	0.524362i
$265$	13.3114			0.817716
$266$	−1.75008	+	5.38620i	−0.107304	+	0.330249i
$267$	2.24912	−	5.05658i	0.137644	−	0.309458i
$268$	−10.4384	−	7.58398i	−0.637630	−	0.463265i
$269$	−17.3312	+	5.63123i	−1.05670	+	0.343342i	−0.785294	−	0.619123i	$-0.787488\pi$
$269$	−17.3312	+	5.63123i	−1.05670	+	0.343342i	−0.271405	+	0.962465i	$0.587488\pi$
$270$	2.24039	−	0.730663i	0.136346	−	0.0444667i
$271$	−0.952566	+	1.31109i	−0.0578643	+	0.0796433i	−0.836968	−	0.547251i	$-0.815674\pi$
$271$	−0.952566	+	1.31109i	−0.0578643	+	0.0796433i	0.779104	+	0.626894i	$0.215674\pi$
$272$	−3.42381	+	2.48754i	−0.207599	+	0.150829i
$273$	19.3690	−	4.12440i	1.17226	−	0.249620i
$274$			7.22435i			0.436439i
$275$	0.374973	−	3.29536i	0.0226117	−	0.198718i
$276$	15.1740	−	8.76813i	0.913370	−	0.527779i
$277$	−22.7632	−	7.39621i	−1.36771	−	0.444395i	−0.469098	−	0.883146i	$-0.655421\pi$
$277$	−22.7632	−	7.39621i	−1.36771	−	0.444395i	−0.898609	+	0.438751i	$0.855421\pi$
$278$	−2.97891	−	4.10011i	−0.178663	−	0.245908i
$279$	−20.9995	+	9.36795i	−1.25720	+	0.560844i
$280$	2.46231	+	7.57820i	0.147151	+	0.452884i
$281$	−5.75748	−	17.7197i	−0.343462	−	1.05707i	−0.962402	−	0.271630i	$-0.912437\pi$
$281$	−5.75748	−	17.7197i	−0.343462	−	1.05707i	0.618939	−	0.785439i	$-0.287563\pi$
$282$	−2.61720	−	0.274112i	−0.155852	−	0.0163232i
$283$	−11.7112	−	16.1191i	−0.696158	−	0.958179i	−0.999985	−	0.00545200i	$-0.998265\pi$
$283$	−11.7112	−	16.1191i	−0.696158	−	0.958179i	0.303827	−	0.952727i	$-0.401735\pi$
$284$	12.5075	+	4.06392i	0.742181	+	0.241149i
$285$	−2.33699	−	4.04437i	−0.138431	−	0.239568i
$286$	0.740960	+	3.63922i	0.0438139	+	0.215192i
$287$			39.0902i			2.30742i
$288$	9.47282	+	10.5052i	0.558191	+	0.619024i
$289$	11.9160	−	8.65744i	0.700938	−	0.509261i
$290$	0.152588	−	0.210019i	0.00896027	−	0.0123328i
$291$	2.33437	−	2.59449i	0.136843	−	0.152092i
$292$	−11.4193	+	3.71034i	−0.668261	+	0.217131i
$293$	−16.9197	−	12.2929i	−0.988459	−	0.718158i	−0.0288762	−	0.999583i	$-0.509193\pi$
$293$	−16.9197	−	12.2929i	−0.988459	−	0.718158i	−0.959583	+	0.281425i	$0.909193\pi$
$294$	10.3654	+	4.61042i	0.604520	+	0.268885i
$295$	−1.16235	+	3.57734i	−0.0676744	+	0.208281i
$296$	0.842770			0.0489850
$297$	−15.6908	−	7.12723i	−0.910475	−	0.413564i
$298$	7.67158			0.444403
$299$	4.30254	−	13.2418i	0.248822	−	0.765796i
$300$	−2.83963	−	1.26304i	−0.163946	−	0.0729219i
$301$	9.43386	+	6.85410i	0.543759	+	0.395064i
$302$	−8.33546	+	2.70835i	−0.479652	+	0.155848i
$303$	−14.4577	+	16.0687i	−0.830574	+	0.923123i
$304$	4.45149	−	6.12695i	0.255310	−	0.351405i
$305$	−6.57951	+	4.78029i	−0.376741	+	0.273719i
$306$	1.37307	+	1.52271i	0.0784929	+	0.0870473i
$307$		−	16.5273i		−	0.943264i	−0.881795	−	0.471632i	$-0.843665\pi$
$307$		−	16.5273i		−	0.943264i	0.881795	−	0.471632i	$-0.156335\pi$
$308$	11.4240	−	25.0774i	0.650945	−	1.42892i
$309$	−2.02771	−	3.50914i	−0.115352	−	0.199628i
$310$	−3.30594	−	1.07417i	−0.187765	−	0.0610085i
$311$	0.466958	+	0.642713i	0.0264788	+	0.0364449i	0.822051	−	0.569414i	$-0.192830\pi$
$311$	0.466958	+	0.642713i	0.0264788	+	0.0364449i	−0.795572	+	0.605859i	$0.792830\pi$
$312$	7.31912	+	0.766568i	0.414363	+	0.0433984i
$313$	0.394809	+	1.21510i	0.0223159	+	0.0686814i	0.961594	−	0.274475i	$-0.0885040\pi$
$313$	0.394809	+	1.21510i	0.0223159	+	0.0686814i	−0.939278	+	0.343156i	$0.888504\pi$
$314$	−0.737136	−	2.26867i	−0.0415990	−	0.128029i
$315$	−12.6866	+	5.65953i	−0.714807	+	0.318878i
$316$	4.09095	+	5.63070i	0.230134	+	0.316752i
$317$	13.3749	+	4.34577i	0.751210	+	0.244083i	0.659502	−	0.751703i	$-0.270767\pi$
$317$	13.3749	+	4.34577i	0.751210	+	0.244083i	0.0917080	+	0.995786i	$0.470767\pi$
$318$	9.05349	−	5.23145i	0.507695	−	0.293365i
$319$	−1.86032	+	0.378767i	−0.104158	+	0.0212069i
$320$		−	3.47811i		−	0.194432i
$321$	−30.5835	+	6.51240i	−1.70700	+	0.363487i
$322$	9.58040	−	6.96057i	0.533895	−	0.387897i
$323$	2.38883	−	3.28794i	0.132918	−	0.182946i
$324$	−10.7882	+	12.0168i	−0.599344	+	0.667598i
$325$	−2.34827	+	0.762999i	−0.130259	+	0.0423236i
$326$	6.43172	+	4.67292i	0.356220	+	0.258809i
$327$	13.4212	−	30.1742i	0.742194	−	1.66863i
$328$	−4.48892	+	13.8155i	−0.247859	+	0.762831i
$329$	15.5127			0.855244
$330$	−1.04006	−	2.38863i	−0.0572533	−	0.131490i
$331$	6.38930			0.351188			0.175594	−	0.984463i	$-0.443815\pi$
$331$	6.38930			0.351188			0.175594	+	0.984463i	$0.443815\pi$
$332$	−3.28582	+	10.1127i	−0.180333	+	0.555008i
$333$	0.154649	+	1.46112i	0.00847471	+	0.0800688i
$334$	0.319579	+	0.232188i	0.0174866	+	0.0127047i
$335$	6.83886	−	2.22208i	0.373647	−	0.121405i
$336$	−16.7435	−	15.0649i	−0.913434	−	0.821856i
$337$	4.07913	−	5.61443i	0.222204	−	0.305838i	−0.683331	−	0.730108i	$-0.739470\pi$
$337$	4.07913	−	5.61443i	0.222204	−	0.305838i	0.905535	+	0.424271i	$0.139470\pi$
$338$	−2.53289	+	1.84025i	−0.137771	+	0.100096i
$339$	−0.625005	−	2.93515i	−0.0339456	−	0.159415i
$340$		−	2.70406i		−	0.146648i
$341$	12.5212	+	22.1236i	0.678059	+	1.19806i
$342$	−3.17890	−	1.83224i	−0.171895	−	0.0990765i
$343$	−32.7747	−	10.6491i	−1.76967	−	0.574999i
$344$	2.54708	+	3.50575i	0.137329	+	0.189017i
$345$	−1.01738	+	9.71387i	−0.0547740	+	0.522977i
$346$	2.27610	+	7.00512i	0.122364	+	0.376598i
$347$	0.0255237	+	0.0785538i	0.00137018	+	0.00421699i	0.951739	−	0.306908i	$-0.0992943\pi$
$347$	0.0255237	+	0.0785538i	0.00137018	+	0.00421699i	−0.950369	+	0.311125i	$0.899294\pi$
$348$	−0.185308	+	1.76931i	−0.00993356	+	0.0948448i
$349$	3.42615	+	4.71569i	0.183398	+	0.252425i	0.890810	−	0.454376i	$-0.150138\pi$
$349$	3.42615	+	4.71569i	0.183398	+	0.252425i	−0.707413	+	0.706801i	$0.750138\pi$
$350$	−1.99725	−	0.648945i	−0.106757	−	0.0346875i
$351$	0.0140571	+	12.8299i	0.000750312	+	0.684809i
$352$	10.5634	−	11.5313i	0.563034	−	0.614623i
$353$			7.24504i			0.385615i	0.981237	+	0.192807i	$0.0617593\pi$
$353$			7.24504i			0.385615i	−0.981237	+	0.192807i	$0.938241\pi$
$354$	0.615360	+	2.88985i	0.0327060	+	0.153594i
$355$	−5.92952	+	4.30805i	−0.314706	+	0.228647i
$356$	−3.36989	+	4.63825i	−0.178604	+	0.245827i
$357$	−8.98518	−	8.08435i	−0.475546	−	0.427869i
$358$	−8.06902	+	2.62178i	−0.426461	+	0.138566i
$359$	12.0084	+	8.72460i	0.633778	+	0.460467i	0.857707	−	0.514139i	$-0.171888\pi$
$359$	12.0084	+	8.72460i	0.633778	+	0.460467i	−0.223929	+	0.974605i	$0.571888\pi$
$360$	−5.13367	+	0.543362i	−0.270568	+	0.0286377i
$361$	3.62390	−	11.1532i	0.190732	−	0.587012i
$362$	3.77884			0.198612
$363$	−6.19109	+	18.0186i	−0.324948	+	0.945732i
$364$	−20.5152			−1.07529
$365$	2.06782	−	6.36410i	0.108235	−	0.333112i
$366$	−2.59624	+	5.83698i	−0.135707	+	0.305104i
$367$	0.811381	+	0.589503i	0.0423538	+	0.0307718i	0.608761	−	0.793354i	$-0.291667\pi$
$367$	0.811381	+	0.589503i	0.0423538	+	0.0307718i	−0.566407	+	0.824126i	$0.691667\pi$
$368$	−15.0606	+	4.89349i	−0.785089	+	0.255091i
$369$	−24.7757	−	5.24733i	−1.28977	−	0.273165i
$370$	−0.130555	+	0.179693i	−0.00678723	+	0.00934182i
$371$	−49.8674	+	36.2308i	−2.58899	+	1.88101i
$372$	23.2986	−	4.96117i	1.20798	−	0.257225i
$373$			13.6417i			0.706340i	0.935559	+	0.353170i	$0.114896\pi$
$373$			13.6417i			0.706340i	−0.935559	+	0.353170i	$0.885104\pi$
$374$	1.53115	−	1.67144i	0.0791739	−	0.0864283i
$375$	1.49968	−	0.866573i	0.0774433	−	0.0447496i
$376$	5.48259	+	1.78140i	0.282743	+	0.0918688i
$377$	0.830750	+	1.14343i	0.0427858	+	0.0588896i
$378$	−6.40428	+	8.83507i	−0.329400	+	0.454427i
$379$	0.307672	+	0.946918i	0.0158041	+	0.0486399i	0.958648	−	0.284596i	$-0.0918594\pi$
$379$	0.307672	+	0.946918i	0.0158041	+	0.0486399i	−0.942843	+	0.333236i	$0.891859\pi$
$380$	1.49532	+	4.60212i	0.0767083	+	0.236084i
$381$	18.3032	+	1.91698i	0.937699	+	0.0982099i
$382$	−5.40197	−	7.43517i	−0.276389	−	0.380416i
$383$	34.7798	+	11.3006i	1.77716	+	0.577435i	0.998734	−	0.0502982i	$-0.0160172\pi$
$383$	34.7798	+	11.3006i	1.77716	+	0.577435i	0.778428	+	0.627733i	$0.216017\pi$
$384$	−9.53895	−	16.5080i	−0.486782	−	0.842421i
$385$	7.56451	+	13.3657i	0.385523	+	0.681179i
$386$		−	3.38065i		−	0.172070i
$387$	−5.61057	+	5.05920i	−0.285201	+	0.257174i
$388$	−2.92505	+	2.12517i	−0.148497	+	0.107889i
$389$	−10.7749	+	14.8303i	−0.546308	+	0.751928i	−0.989505	−	0.144496i	$-0.953844\pi$
$389$	−10.7749	+	14.8303i	−0.546308	+	0.751928i	0.443198	+	0.896424i	$0.353844\pi$
$390$	−1.29726	+	1.44181i	−0.0656894	+	0.0730091i
$391$	−8.08207	+	2.62602i	−0.408728	+	0.132804i
$392$	−20.1055	−	14.6075i	−1.01548	−	0.737790i
$393$	5.09129	+	2.26456i	0.256822	+	0.114232i
$394$	1.91561	−	5.89564i	0.0965070	−	0.297018i
$395$	−3.87886			−0.195167
$396$	14.3608	+	10.6070i	0.721657	+	0.533021i
$397$	1.52698			0.0766371			0.0383185	−	0.999266i	$-0.487800\pi$
$397$	1.52698			0.0766371			0.0383185	+	0.999266i	$0.487800\pi$
$398$	1.64115	−	5.05094i	0.0822633	−	0.253181i
$399$	19.7627	+	8.79028i	0.989373	+	0.440064i
$400$	2.27192	+	1.65065i	0.113596	+	0.0825324i
$401$	−11.6056	+	3.77088i	−0.579555	+	0.188309i	−0.584101	−	0.811681i	$-0.698553\pi$
$401$	−11.6056	+	3.77088i	−0.579555	+	0.188309i	0.00454647	+	0.999990i	$0.498553\pi$
$402$	3.77802	−	4.19899i	0.188430	−	0.209427i
$403$	11.1239	−	15.3108i	0.554122	−	0.762684i
$404$	18.1160	−	13.1621i	0.901306	−	0.654837i
$405$	−1.88406	−	8.80059i	−0.0936199	−	0.437305i
$406$			1.20209i			0.0596585i
$407$	1.59169	−	0.324075i	0.0788974	−	0.0160638i
$408$	−2.24723	−	3.88903i	−0.111254	−	0.192536i
$409$	−5.27054	−	1.71250i	−0.260611	−	0.0846777i	0.175797	−	0.984426i	$-0.443750\pi$
$409$	−5.27054	−	1.71250i	−0.260611	−	0.0846777i	−0.436408	+	0.899749i	$0.643750\pi$
$410$	−2.25031	−	3.09729i	−0.111135	−	0.152964i
$411$	27.4410	+	2.87403i	1.35356	+	0.141765i
$412$	1.29743	+	3.99308i	0.0639198	+	0.196725i
$413$	−5.38232	−	16.5651i	−0.264847	−	0.815115i
$414$	3.12563	+	7.00651i	0.153617	+	0.344351i
$415$	−3.48321	−	4.79423i	−0.170984	−	0.235339i
$416$	−11.0724	−	3.59765i	−0.542870	−	0.176389i
$417$	−16.7589	+	9.68394i	−0.820689	+	0.474225i
$418$	−1.68162	+	3.69139i	−0.0822505	+	0.180552i
$419$			17.0119i			0.831087i	0.909573	+	0.415543i	$0.136409\pi$
$419$			17.0119i			0.831087i	−0.909573	+	0.415543i	$0.863591\pi$
$420$	14.0756	−	2.99723i	0.686818	−	0.146250i
$421$	−15.0983	+	10.9696i	−0.735847	+	0.534624i	−0.891408	−	0.453202i	$-0.850282\pi$
$421$	−15.0983	+	10.9696i	−0.735847	+	0.534624i	0.155561	+	0.987826i	$0.450282\pi$
$422$	−1.02748	+	1.41420i	−0.0500169	+	0.0688423i
$423$	−2.08238	+	9.83212i	−0.101249	+	0.478054i
$424$	−21.7850	+	7.07837i	−1.05797	+	0.343756i
$425$	1.21920	+	0.885798i	0.0591397	+	0.0429675i
$426$	−2.33975	+	5.26034i	−0.113361	+	0.254865i
$427$	11.6373	−	35.8159i	0.563168	−	1.73325i
$428$	32.3934			1.56580
$429$	14.1180	−	1.36668i	0.681623	−	0.0659842i
$430$	−1.14206			−0.0550750
$431$	2.01436	−	6.19956i	0.0970283	−	0.298623i	−0.890749	−	0.454496i	$-0.849819\pi$
$431$	2.01436	−	6.19956i	0.0970283	−	0.298623i	0.987777	+	0.155874i	$0.0498193\pi$
$432$	11.7958	−	8.58995i	0.567528	−	0.413284i
$433$	11.2188	+	8.15095i	0.539142	+	0.391710i	0.823766	−	0.566929i	$-0.191869\pi$
$433$	11.2188	+	8.15095i	0.539142	+	0.391710i	−0.284624	+	0.958639i	$0.591869\pi$
$434$	15.3084	−	4.97400i	0.734826	−	0.238760i
$435$	−0.737033	−	0.663141i	−0.0353380	−	0.0317952i
$436$	−20.1091	+	27.6779i	−0.963053	+	1.32553i
$437$	12.3030	−	8.93862i	0.588530	−	0.427592i
$438$	−1.09473	−	5.14106i	−0.0523082	−	0.245649i
$439$		−	18.8386i		−	0.899117i	−0.893251	−	0.449558i	$-0.851581\pi$
$439$		−	18.8386i		−	0.899117i	0.893251	−	0.449558i	$-0.148419\pi$
$440$	1.13864	+	5.59245i	0.0542827	+	0.266609i
$441$	21.6358	−	37.5376i	1.03028	−	1.78750i
$442$	−1.60492	−	0.521472i	−0.0763385	−	0.0248039i
$443$	−3.93907	−	5.42166i	−0.187151	−	0.257591i	0.705124	−	0.709084i	$-0.250891\pi$
$443$	−3.93907	−	5.42166i	−0.187151	−	0.257591i	−0.892274	+	0.451493i	$0.850891\pi$
$444$	0.158551	−	1.51383i	0.00752448	−	0.0718430i
$445$	−0.987365	−	3.03880i	−0.0468056	−	0.144053i
$446$	−3.27812	−	10.0890i	−0.155223	−	0.477728i
$447$	3.05195	−	29.1397i	0.144352	−	1.37826i
$448$	9.46665	+	13.0297i	0.447257	+	0.615597i
$449$	−22.2745	−	7.23741i	−1.05120	−	0.341555i	−0.268059	−	0.963402i	$-0.586382\pi$
$449$	−22.2745	−	7.23741i	−1.05120	−	0.341555i	−0.783138	+	0.621848i	$0.786382\pi$
$450$	0.679411	−	1.17876i	0.0320277	−	0.0555674i
$451$	−3.16544	+	27.8187i	−0.149055	+	1.30993i
$452$			3.10885i			0.146228i
$453$	6.97135	+	32.7388i	0.327543	+	1.53820i
$454$	2.53926	−	1.84488i	0.119174	−	0.0865847i
$455$	6.72039	−	9.24982i	0.315057	−	0.433638i
$456$	5.97521	+	5.37616i	0.279815	+	0.251762i
$457$	−31.5191	+	10.2412i	−1.47440	+	0.479062i	−0.932434	−	0.361339i	$-0.882320\pi$
$457$	−31.5191	+	10.2412i	−1.47440	+	0.479062i	−0.541966	+	0.840401i	$0.682320\pi$
$458$	0.239534	+	0.174032i	0.0111927	+	0.00813197i
$459$	6.33008	−	4.60968i	0.295463	−	0.215161i
$460$	3.12668	−	9.62295i	0.145782	−	0.448672i
$461$	−24.1258			−1.12365			−0.561824	−	0.827257i	$-0.689900\pi$
$461$	−24.1258			−1.12365			−0.561824	+	0.827257i	$0.689900\pi$
$462$	10.3976	+	6.11751i	0.483740	+	0.284612i
$463$	21.5425			1.00117			0.500584	−	0.865688i	$-0.333119\pi$
$463$	21.5425			1.00117			0.500584	+	0.865688i	$0.333119\pi$
$464$	0.496739	−	1.52881i	0.0230605	−	0.0709730i
$465$	−5.39530	+	12.1300i	−0.250201	+	0.562513i
$466$	−6.77438	−	4.92187i	−0.313817	−	0.228001i
$467$	−2.27085	+	0.737843i	−0.105082	+	0.0341433i	−0.361086	−	0.932532i	$-0.617594\pi$
$467$	−2.27085	+	0.737843i	−0.105082	+	0.0341433i	0.256004	+	0.966676i	$0.417594\pi$
$468$	2.75390	−	13.0028i	0.127299	−	0.601053i
$469$	−19.5718	+	26.9382i	−0.903740	+	1.24389i
$470$	−1.22914	+	0.893026i	−0.0566962	+	0.0411922i
$471$	−8.91057	+	1.89740i	−0.410577	+	0.0874276i
$472$		−	6.47260i		−	0.297926i
$473$	6.15861	+	5.64168i	0.283173	+	0.259405i
$474$	−2.63812	+	1.52441i	−0.121173	+	0.0700183i
$475$	−2.56482	−	0.833361i	−0.117682	−	0.0382372i
$476$	7.35986	+	10.1300i	0.337339	+	0.464307i
$477$	−16.2694	−	36.4700i	−0.744925	−	1.66984i
$478$	−0.0840030	−	0.258535i	−0.00384221	−	0.0118251i
$479$	−5.76419	−	17.7403i	−0.263372	−	0.810577i	−0.992064	−	0.125735i	$-0.959871\pi$
$479$	−5.76419	−	17.7403i	−0.263372	−	0.810577i	0.728691	−	0.684842i	$-0.240129\pi$
$480$	8.12244	+	0.850704i	0.370737	+	0.0388291i
$481$	−0.710794	−	0.978324i	−0.0324094	−	0.0446077i
$482$	−1.33809	−	0.434773i	−0.0609485	−	0.0198034i
$483$	−22.6277	−	39.1593i	−1.02960	−	1.78181i
$484$	10.1607	−	16.9214i	0.461849	−	0.769153i
$485$		−	2.01500i		−	0.0914964i
$486$	−4.74007	−	5.24508i	−0.215014	−	0.237922i
$487$	4.03161	−	2.92914i	0.182690	−	0.132732i	−0.492682	−	0.870210i	$-0.663983\pi$
$487$	4.03161	−	2.92914i	0.182690	−	0.132732i	0.675371	+	0.737478i	$0.263983\pi$
$488$	8.22584	−	11.3219i	0.372366	−	0.512518i
$489$	20.3083	−	22.5712i	0.918373	−	1.02071i
$490$	6.22915	−	2.02397i	0.281404	−	0.0914339i
$491$	−3.19395	−	2.32054i	−0.144141	−	0.104725i	0.513378	−	0.858163i	$-0.328394\pi$
$491$	−3.19395	−	2.32054i	−0.144141	−	0.104725i	−0.657519	+	0.753438i	$0.728394\pi$
$492$	23.9715	+	10.6623i	1.08072	+	0.480695i
$493$	0.266568	−	0.820413i	0.0120056	−	0.0369495i
$494$	3.01984			0.135869
$495$	−9.48674	+	3.00030i	−0.426397	+	0.134853i
$496$	−21.5245			−0.966480
$497$	10.4876	−	32.2777i	0.470435	−	1.44785i
$498$	−4.25318	−	1.89178i	−0.190589	−	0.0847725i
$499$	5.50314	+	3.99827i	0.246354	+	0.178987i	0.704110	−	0.710091i	$-0.251346\pi$
$499$	5.50314	+	3.99827i	0.246354	+	0.178987i	−0.457755	+	0.889078i	$0.651346\pi$
$500$	−1.70650	+	0.554477i	−0.0763172	+	0.0247970i
$501$	1.00908	−	1.12152i	0.0450823	−	0.0501057i
$502$	−7.12519	+	9.80698i	−0.318013	+	0.437707i
$503$	20.7847	−	15.1010i	0.926745	−	0.673319i	−0.0184489	−	0.999830i	$-0.505873\pi$
$503$	20.7847	−	15.1010i	0.926745	−	0.673319i	0.945194	+	0.326510i	$0.105873\pi$
$504$	17.7529	−	16.0083i	0.790776	−	0.713064i
$505$			12.4797i			0.555339i
$506$	7.38158	−	4.17771i	0.328151	−	0.185722i
$507$	5.98236	+	10.3530i	0.265686	+	0.459794i
$508$	−18.1318	−	5.89139i	−0.804470	−	0.261388i
$509$	9.25404	+	12.7371i	0.410178	+	0.564562i	0.963262	−	0.268564i	$-0.0865491\pi$
$509$	9.25404	+	12.7371i	0.410178	+	0.564562i	−0.553084	+	0.833126i	$0.686549\pi$
$510$	1.17733	+	0.123308i	0.0521331	+	0.00546016i
$511$	9.57518	+	29.4694i	0.423581	+	1.30365i
$512$	7.07837	+	21.7850i	0.312823	+	0.962769i
$513$	−8.22424	+	11.3458i	−0.363109	+	0.500930i
$514$	−3.60430	−	4.96090i	−0.158979	−	0.218816i
$515$	−2.22539	−	0.723074i	−0.0980625	−	0.0318625i
$516$	6.77639	−	3.91565i	0.298314	−	0.172377i
$517$	11.0397	+	1.25619i	0.485525	+	0.0552471i
$518$		−	1.02851i		−	0.0451901i
$519$	27.5137	−	5.85873i	1.20772	−	0.257170i
$520$	3.43736	−	2.49739i	0.150738	−	0.109518i
$521$	5.56842	−	7.66428i	0.243957	−	0.335778i	−0.669426	−	0.742878i	$-0.733460\pi$
$521$	5.56842	−	7.66428i	0.243957	−	0.335778i	0.913383	+	0.407100i	$0.133460\pi$
$522$	−0.761894	−	0.161364i	−0.0333472	−	0.00706271i
$523$	0.218761	−	0.0710796i	0.00956574	−	0.00310810i	−0.304230	−	0.952599i	$-0.598399\pi$
$523$	0.218761	−	0.0710796i	0.00956574	−	0.00310810i	0.313796	+	0.949490i	$0.398399\pi$
$524$	−4.67009	−	3.39302i	−0.204014	−	0.148225i
$525$	−3.25950	+	7.32817i	−0.142256	+	0.319827i
$526$	−0.935608	+	2.87951i	−0.0407945	+	0.125552i
$527$	−11.5508			−0.503163
$528$	−10.6957	−	12.0768i	−0.465469	−	0.525576i
$529$	−8.79812			−0.382527
$530$	1.86552	−	5.74147i	0.0810328	−	0.249393i
$531$	11.2216	−	1.18773i	0.486977	−	0.0515430i
$532$	−18.1277	−	13.1706i	−0.785937	−	0.571017i
$533$	19.8235	−	6.44106i	0.858653	−	0.278993i
$534$	−1.86579	−	1.67873i	−0.0807408	−	0.0726459i
$535$	−10.6114	+	14.6054i	−0.458773	+	0.631447i
$536$	−10.0106	+	7.27313i	−0.432393	+	0.314152i
$537$	6.74852	+	31.6924i	0.291220	+	1.36763i
$538$			8.26442i			0.356304i
$539$	−43.5893	−	19.8571i	−1.87752	−	0.855307i
$540$	0.0102154	+	9.32358i	0.000439600	+	0.401223i
$541$	38.9280	+	12.6485i	1.67365	+	0.543801i	0.983662	−	0.180024i	$-0.0576176\pi$
$541$	38.9280	+	12.6485i	1.67365	+	0.543801i	0.689984	+	0.723825i	$0.257618\pi$
$542$	0.432002	+	0.594600i	0.0185561	+	0.0255403i
$543$	1.50332	−	14.3536i	0.0645136	−	0.615970i
$544$	2.19580	+	6.75798i	0.0941442	+	0.289746i
$545$	−5.89191	−	18.1334i	−0.252382	−	0.776751i
$546$	0.935514	−	8.93220i	0.0400363	−	0.382263i
$547$	16.0943	+	22.1519i	0.688142	+	0.947147i	0.999996	−	0.00298372i	$-0.000949749\pi$
$547$	16.0943	+	22.1519i	0.688142	+	0.947147i	−0.311853	+	0.950130i	$0.600950\pi$
$548$	−27.1841	−	8.83265i	−1.16125	−	0.377312i
$549$	21.1383	+	12.1836i	0.902162	+	0.519985i
$550$	−1.36880	−	0.623557i	−0.0583657	−	0.0265885i
$551$			1.54369i			0.0657636i
$552$	−3.50035	−	16.4383i	−0.148985	−	0.699662i
$553$	14.5310	−	10.5574i	0.617921	−	0.448946i
$554$	−6.38023	+	8.78164i	−0.271070	+	0.373096i
$555$	0.630609	+	0.567386i	0.0267679	+	0.0240842i
$556$	19.0702	−	6.19627i	0.808755	−	0.262780i
$557$	11.5944	+	8.42382i	0.491270	+	0.356929i	0.805673	−	0.592361i	$-0.201804\pi$
$557$	11.5944	+	8.42382i	0.491270	+	0.356929i	−0.314402	+	0.949290i	$0.601804\pi$
$558$	1.09762	+	10.3703i	0.0464660	+	0.439010i
$559$	1.92142	−	5.91351i	0.0812673	−	0.250115i
$560$	−13.0038			−0.549510
$561$	−5.73968	−	6.48086i	−0.242330	−	0.273622i
$562$	−8.44970			−0.356429
$563$	−6.17839	+	19.0151i	−0.260388	+	0.801392i	0.732332	+	0.680948i	$0.238432\pi$
$563$	−6.17839	+	19.0151i	−0.260388	+	0.801392i	−0.992720	+	0.120444i	$0.961568\pi$
$564$	4.23129	−	9.51298i	0.178169	−	0.400569i
$565$	−1.40170	−	1.01840i	−0.0589701	−	0.0428443i
$566$	−8.59369	+	2.79226i	−0.361220	+	0.117367i
$567$	31.0113	+	27.8408i	1.30235	+	1.16920i
$568$	7.41320	−	10.2034i	0.311051	−	0.428125i
$569$	4.88308	−	3.54777i	0.204709	−	0.148730i	−0.480707	−	0.876881i	$-0.659620\pi$
$569$	4.88308	−	3.54777i	0.204709	−	0.148730i	0.685417	+	0.728151i	$0.259620\pi$
$570$	−2.07192	+	0.441192i	−0.0867833	+	0.0184795i
$571$		−	42.5140i		−	1.77916i	−0.456784	−	0.889578i	$-0.650999\pi$
$571$		−	42.5140i		−	1.77916i	0.456784	−	0.889578i	$-0.349001\pi$
$572$	−14.5997	−	1.66128i	−0.610446	−	0.0694616i
$573$	−30.3908	+	17.5609i	−1.26959	+	0.733618i
$574$	16.8603	+	5.47824i	0.703735	+	0.228657i
$575$	3.31451	+	4.56203i	0.138225	+	0.190250i
$576$	−9.52914	+	4.25099i	−0.397048	+	0.177125i
$577$	−4.53707	−	13.9637i	−0.188881	−	0.581315i	0.811113	−	0.584890i	$-0.198862\pi$
$577$	−4.53707	−	13.9637i	−0.188881	−	0.581315i	−0.999994	+	0.00357457i	$0.998862\pi$
$578$	−2.06417	−	6.35285i	−0.0858580	−	0.264244i
$579$	−12.8410	−	1.34491i	−0.533655	−	0.0558924i
$580$	0.603712	+	0.830939i	0.0250678	+	0.0345028i
$581$	26.0976	+	8.47964i	1.08271	+	0.351795i
$582$	−0.791901	−	1.37046i	−0.0328254	−	0.0568073i
$583$	−38.4222	+	21.7456i	−1.59129	+	0.900612i
$584$			11.5148i			0.476485i
$585$	4.96050	+	5.50111i	0.205092	+	0.227443i
$586$	−7.67333	+	5.57500i	−0.316982	+	0.230301i
$587$	−1.89042	+	2.60194i	−0.0780260	+	0.107394i	−0.846246	−	0.532792i	$-0.821143\pi$
$587$	−1.89042	+	2.60194i	−0.0780260	+	0.107394i	0.768220	+	0.640186i	$0.221143\pi$
$588$	−30.0212	+	33.3664i	−1.23805	+	1.37601i
$589$	19.6587	−	6.38751i	0.810024	−	0.263193i
$590$	1.38007	+	1.00268i	0.0568167	+	0.0412798i
$591$	−21.6319	−	9.62168i	−0.889817	−	0.395783i
$592$	−0.425012	+	1.30805i	−0.0174679	+	0.0537607i
$593$	29.0168			1.19158			0.595789	−	0.803141i	$-0.296839\pi$
$593$	29.0168			1.19158			0.595789	+	0.803141i	$0.296839\pi$
$594$	−5.27307	+	5.76891i	−0.216357	+	0.236701i
$595$	−6.97830			−0.286083
$596$	−9.37944	+	28.8670i	−0.384197	+	1.18244i
$597$	−18.5326	−	8.24312i	−0.758488	−	0.337369i
$598$	−5.10847	−	3.71152i	−0.208901	−	0.151775i
$599$	−38.5104	+	12.5128i	−1.57349	+	0.511258i	−0.960369	−	0.278731i	$-0.910086\pi$
$599$	−38.5104	+	12.5128i	−1.57349	+	0.511258i	−0.613121	+	0.789989i	$0.710086\pi$
$600$	−1.99352	+	2.21566i	−0.0813852	+	0.0904538i
$601$	7.61646	−	10.4832i	0.310682	−	0.427617i	−0.624912	−	0.780695i	$-0.714865\pi$
$601$	7.61646	−	10.4832i	0.310682	−	0.427617i	0.935594	+	0.353079i	$0.114865\pi$
$602$	4.27839	−	3.10843i	0.174374	−	0.126690i
$603$	−14.4465	−	16.0209i	−0.588305	−	0.652420i
$604$		−	34.6763i		−	1.41096i
$605$	4.30099	+	10.1243i	0.174860	+	0.411611i
$606$	4.90457	+	8.48780i	0.199234	+	0.344793i
$607$	20.3324	+	6.60640i	0.825266	+	0.268145i	0.691050	−	0.722807i	$-0.257148\pi$
$607$	20.3324	+	6.60640i	0.825266	+	0.268145i	0.134216	+	0.990952i	$0.457148\pi$
$608$	−7.47420	−	10.2874i	−0.303119	−	0.417207i
$609$	4.56600	+	0.478220i	0.185024	+	0.0193785i
$610$	1.13975	+	3.50779i	0.0461471	+	0.142026i
$611$	−2.55610	−	7.86687i	−0.103409	−	0.318259i
$612$	−7.40844	+	3.30494i	−0.299468	+	0.133594i
$613$	3.24415	+	4.46519i	0.131030	+	0.180347i	0.869491	−	0.493949i	$-0.164447\pi$
$613$	3.24415	+	4.46519i	0.131030	+	0.180347i	−0.738461	+	0.674296i	$0.764447\pi$
$614$	−7.12853	−	2.31620i	−0.287684	−	0.0934742i
$615$	−12.6600	+	7.31541i	−0.510500	+	0.294986i
$616$	−19.4870	−	17.8513i	−0.785153	−	0.719250i
$617$			6.89327i			0.277512i	0.990327	+	0.138756i	$0.0443105\pi$
$617$			6.89327i			0.277512i	−0.990327	+	0.138756i	$0.955690\pi$
$618$	−1.79772	+	0.382804i	−0.0723150	+	0.0153986i
$619$	−24.6829	+	17.9332i	−0.992089	+	0.720795i	−0.960378	−	0.278702i	$-0.910096\pi$
$619$	−24.6829	+	17.9332i	−0.992089	+	0.720795i	−0.0317113	+	0.999497i	$0.510096\pi$
$620$	8.08384	−	11.1265i	0.324655	−	0.446849i
$621$	27.8570	−	9.08504i	1.11786	−	0.364570i
$622$	0.342655	−	0.111335i	0.0137392	−	0.00446414i
$623$	11.9698	+	8.69657i	0.479560	+	0.348421i
$624$	−4.88084	+	10.9733i	−0.195390	+	0.439285i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	0.579423			0.0231584
$627$	13.3524	+	7.85598i	0.533243	+	0.313737i
$628$	9.43789			0.376613
$629$	−0.228077	+	0.701949i	−0.00909403	+	0.0279885i
$630$	0.663115	+	6.26509i	0.0264191	+	0.249607i
$631$	−26.1345	−	18.9879i	−1.04040	−	0.755895i	−0.0700363	−	0.997544i	$-0.522312\pi$
$631$	−26.1345	−	18.9879i	−1.04040	−	0.755895i	−0.970364	+	0.241650i	$0.922312\pi$
$632$	6.34799	−	2.06259i	0.252509	−	0.0820453i
$633$	4.96295	+	4.46538i	0.197260	+	0.177483i
$634$	3.74882	−	5.15980i	0.148885	−	0.204922i
$635$	8.59591	−	6.24529i	0.341118	−	0.247837i
$636$	8.61611	+	40.4630i	0.341651	+	1.60446i
$637$			35.6593i			1.41287i
$638$	−0.0973424	+	0.855469i	−0.00385382	+	0.0338683i
$639$	19.0501	+	10.9800i	0.753609	+	0.434363i
$640$	−10.4689	−	3.40156i	−0.413820	−	0.134458i
$641$	29.0114	+	39.9308i	1.14588	+	1.57717i	0.753608	+	0.657325i	$0.228312\pi$
$641$	29.0114	+	39.9308i	1.14588	+	1.57717i	0.392275	+	0.919848i	$0.371688\pi$
$642$	−1.47717	+	14.1039i	−0.0582993	+	0.556636i
$643$	−10.6022	−	32.6304i	−0.418112	−	1.28682i	−0.909438	−	0.415840i	$-0.863488\pi$
$643$	−10.6022	−	32.6304i	−0.418112	−	1.28682i	0.491326	−	0.870976i	$-0.336512\pi$
$644$	14.4783	+	44.5597i	0.570526	+	1.75590i
$645$	−0.454340	+	4.33800i	−0.0178896	+	0.170809i
$646$	−1.08337	−	1.49113i	−0.0426246	−	0.0586677i
$647$	28.9866	+	9.41831i	1.13958	+	0.370272i	0.817209	−	0.576341i	$-0.195520\pi$
$647$	28.9866	+	9.41831i	1.13958	+	0.370272i	0.322371	+	0.946613i	$0.395520\pi$
$648$	7.76310	+	13.4008i	0.304963	+	0.526435i
$649$	−2.48894	−	12.2245i	−0.0976996	−	0.479852i
$650$			1.11978i			0.0439214i
$651$	−12.8032	−	60.1261i	−0.501795	−	2.35653i
$652$	−25.4470	+	18.4883i	−0.996582	+	0.724059i
$653$	−2.62689	+	3.61560i	−0.102798	+	0.141489i	−0.857317	−	0.514789i	$-0.827870\pi$
$653$	−2.62689	+	3.61560i	−0.102798	+	0.141489i	0.754519	+	0.656278i	$0.227870\pi$
$654$	−11.1338	−	10.0175i	−0.435364	−	0.391716i
$655$	3.05966	−	0.994143i	0.119551	−	0.0388444i
$656$	−19.1790	−	13.9344i	−0.748816	−	0.544046i
$657$	−19.9633	+	2.11297i	−0.778843	+	0.0824349i
$658$	2.17401	−	6.69092i	0.0847518	−	0.260839i
$659$	14.0453			0.547129			0.273564	−	0.961854i	$-0.411797\pi$
$659$	14.0453			0.547129			0.273564	+	0.961854i	$0.411797\pi$
$660$	10.2597	−	0.993180i	0.399356	−	0.0386595i
$661$	45.1181			1.75489			0.877445	−	0.479678i	$-0.159246\pi$
$661$	45.1181			1.75489			0.877445	+	0.479678i	$0.159246\pi$
$662$	0.895420	−	2.75582i	0.0348015	−	0.107108i
$663$	−2.61924	+	5.88869i	−0.101723	+	0.228698i
$664$	8.24981	+	5.99384i	0.320155	+	0.232606i
$665$	11.8766	−	3.85893i	0.460554	−	0.149643i
$666$	0.651880	+	0.138064i	0.0252598	+	0.00534986i
$667$	1.89727	−	2.61137i	0.0734627	−	0.101113i
$668$	−1.26441	+	0.918648i	−0.0489215	+	0.0355436i
$669$	−39.6262	+	8.43793i	−1.53204	+	0.326229i
$670$		−	3.26113i		−	0.125989i
$671$	11.1820	−	24.5462i	0.431677	−	0.947594i
$672$	−32.7438	+	18.9206i	−1.26312	+	0.729877i
$673$	−7.97155	−	2.59011i	−0.307280	−	0.0998415i	0.151318	−	0.988485i	$-0.451648\pi$
$673$	−7.97155	−	2.59011i	−0.307280	−	0.0998415i	−0.458598	+	0.888644i	$0.651648\pi$
$674$	−1.84994	−	2.54623i	−0.0712571	−	0.0980770i
$675$	−4.20712	−	3.04961i	−0.161932	−	0.117380i
$676$	−3.82781	−	11.7808i	−0.147224	−	0.453108i
$677$	3.12592	+	9.62060i	0.120139	+	0.369750i	0.992984	−	0.118247i	$-0.0377276\pi$
$677$	3.12592	+	9.62060i	0.120139	+	0.369750i	−0.872845	+	0.487997i	$0.837728\pi$
$678$	−1.35357	−	0.141766i	−0.0519836	−	0.00544450i
$679$	5.48438	+	7.54860i	0.210471	+	0.289689i
$680$	−2.46631	−	0.801353i	−0.0945787	−	0.0307305i
$681$	−5.99742	−	10.3791i	−0.229822	−	0.397727i
$682$	11.2971	−	2.30012i	0.432587	−	0.0880763i
$683$		−	8.59190i		−	0.328760i	−0.986397	−	0.164380i	$-0.947438\pi$
$683$		−	8.59190i		−	0.328760i	0.986397	−	0.164380i	$-0.0525623\pi$
$684$	10.7810	−	9.72157i	0.412224	−	0.371713i
$685$	12.8874	−	9.36325i	0.492402	−	0.357751i
$686$	−9.18632	+	12.6439i	−0.350735	+	0.482746i
$687$	0.756335	−	0.840612i	0.0288560	−	0.0320714i
$688$	−6.72574	+	2.18532i	−0.256416	+	0.0833147i
$689$	26.5904	+	19.3190i	1.01301	+	0.735997i
$690$	4.04719	+	1.80015i	0.154074	+	0.0685306i
$691$	5.53165	−	17.0247i	0.210434	−	0.647649i	−0.789012	−	0.614377i	$-0.789407\pi$
$691$	5.53165	−	17.0247i	0.210434	−	0.647649i	0.999446	−	0.0332717i	$-0.0105927\pi$
$692$	−29.1420			−1.10781
$693$	27.3731	−	37.0605i	1.03982	−	1.40781i
$694$	0.0374587			0.00142191
$695$	−3.45326	+	10.6280i	−0.130990	+	0.403145i
$696$	1.55882	+	0.693351i	0.0590871	+	0.0262814i
$697$	−10.2922	−	7.47770i	−0.389844	−	0.283238i
$698$	2.51411	−	0.816885i	0.0951606	−	0.0309196i
$699$	−21.3903	+	23.7737i	−0.809054	+	0.899206i
$700$	4.88375	−	6.72191i	0.184589	−	0.254064i
$701$	−3.94980	+	2.86970i	−0.149182	+	0.108387i	−0.659873	−	0.751378i	$-0.729390\pi$
$701$	−3.94980	+	2.86970i	−0.149182	+	0.108387i	0.510691	+	0.859765i	$0.329390\pi$
$702$	5.53573	+	1.79197i	0.208933	+	0.0676334i
$703$		−	1.32079i		−	0.0498146i
$704$	5.68186	+	10.0392i	0.214143	+	0.378368i
$705$	2.90308	+	5.02405i	0.109336	+	0.189217i
$706$	3.12492	+	1.01535i	0.117608	+	0.0382131i
$707$	−33.9670	−	46.7515i	−1.27746	−	1.75827i
$708$	−11.6264	−	1.21769i	−0.436948	−	0.0457637i
$709$	8.05063	+	24.7773i	0.302348	+	0.930531i	0.980654	+	0.195751i	$0.0627144\pi$
$709$	8.05063	+	24.7773i	0.302348	+	0.930531i	−0.678306	+	0.734780i	$0.737286\pi$
$710$	1.02715	+	3.16125i	0.0385484	+	0.118640i
$711$	4.74079	+	10.6271i	0.177793	+	0.398547i
$712$	3.23176	+	4.44814i	0.121116	+	0.166701i
$713$	−41.1060	−	13.3561i	−1.53943	−	0.500192i
$714$	−4.74614	+	2.74250i	−0.177620	+	0.102635i
$715$	5.53162	−	6.03846i	0.206871	−	0.225826i
$716$		−	33.5679i		−	1.25449i
$717$	−1.01544	+	0.216225i	−0.0379222	+	0.00807508i
$718$	5.44598	−	3.95673i	0.203242	−	0.147664i
$719$	−19.3848	+	26.6809i	−0.722933	+	0.995032i	0.276489	+	0.961017i	$0.410829\pi$
$719$	−19.3848	+	26.6809i	−0.722933	+	0.995032i	−0.999421	+	0.0340143i	$0.989171\pi$
$720$	1.74558	−	8.24193i	0.0650541	−	0.307158i
$721$	10.3048	−	3.34824i	0.383772	−	0.124695i
$722$	−4.30272	−	3.12611i	−0.160131	−	0.116342i
$723$	−2.18377	+	4.90965i	−0.0812152	+	0.182592i
$724$	−4.62010	+	14.2192i	−0.171705	+	0.528452i
$725$	−0.572414			−0.0212589
$726$	6.90411	+	5.19552i	0.256236	+	0.192824i
$727$	6.67220			0.247458			0.123729	−	0.992316i	$-0.460515\pi$
$727$	6.67220			0.247458			0.123729	+	0.992316i	$0.460515\pi$
$728$	−6.07972	+	18.7115i	−0.225329	+	0.693493i
$729$	−21.8086	+	15.9180i	−0.807727	+	0.589557i
$730$	−2.45516	−	1.78378i	−0.0908694	−	0.0660205i
$731$	−3.60927	+	1.17272i	−0.133494	+	0.0433748i
$732$	−18.7894	−	16.9057i	−0.694477	−	0.624851i
$733$	19.9176	−	27.4142i	0.735673	−	1.01257i	−0.263183	−	0.964746i	$-0.584772\pi$
$733$	19.9176	−	27.4142i	0.735673	−	1.01257i	0.998856	−	0.0478213i	$-0.0152278\pi$
$734$	0.367973	−	0.267348i	0.0135821	−	0.00986800i
$735$	−5.20975	−	24.4660i	−0.192164	−	0.902442i
$736$			26.5886i			0.980069i
$737$	−16.1097	+	17.5858i	−0.593409	+	0.647782i
$738$	−5.73543	+	9.95083i	−0.211124	+	0.366295i
$739$	−25.7910	−	8.37999i	−0.948736	−	0.308263i	−0.206534	−	0.978439i	$-0.566218\pi$
$739$	−25.7910	−	8.37999i	−0.948736	−	0.308263i	−0.742202	+	0.670176i	$0.766218\pi$
$740$	−0.516539	−	0.710955i	−0.0189884	−	0.0261352i
$741$	1.20137	−	11.4705i	0.0441333	−	0.421381i
$742$	8.63839	+	26.5862i	0.317125	+	0.976011i
$743$	−6.03306	−	18.5678i	−0.221331	−	0.681188i	−0.998643	−	0.0520726i	$-0.983417\pi$
$743$	−6.03306	−	18.5678i	−0.221331	−	0.681188i	0.777312	−	0.629115i	$-0.216583\pi$
$744$	2.37962	−	22.7204i	0.0872410	−	0.832969i
$745$	−9.94288	−	13.6852i	−0.364279	−	0.501387i
$746$	5.88390	+	1.91180i	0.215425	+	0.0699958i
$747$	−8.87774	+	15.4027i	−0.324819	+	0.563554i
$748$	4.41737	+	7.80502i	0.161515	+	0.285380i
$749$		−	83.5969i		−	3.05456i
$750$	−0.163597	−	0.768285i	−0.00597373	−	0.0280538i
$751$	−23.0149	+	16.7213i	−0.839825	+	0.610168i	−0.922322	−	0.386423i	$-0.873711\pi$
$751$	−23.0149	+	16.7213i	−0.839825	+	0.610168i	0.0824969	+	0.996591i	$0.473711\pi$
$752$	−5.52979	+	7.61110i	−0.201651	+	0.277548i
$753$	34.4162	+	30.9658i	1.25420	+	1.12846i
$754$	0.609606	−	0.198073i	0.0222005	−	0.00721339i
$755$	15.6347	+	11.3593i	0.569005	+	0.413406i
$756$	−25.4150	−	34.9002i	−0.924334	−	1.26931i
$757$	−5.72745	+	17.6273i	−0.208168	+	0.640674i	0.791401	+	0.611298i	$0.209352\pi$
$757$	−5.72745	+	17.6273i	−0.208168	+	0.640674i	−0.999568	+	0.0293764i	$0.990648\pi$
$758$	0.451541			0.0164007
$759$	−12.9320	−	29.7002i	−0.469403	−	1.07805i
$760$	4.64063			0.168333
$761$	−5.18255	+	15.9502i	−0.187867	+	0.578196i	−0.999986	−	0.00529635i	$-0.998314\pi$
$761$	−5.18255	+	15.9502i	−0.187867	+	0.578196i	0.812119	+	0.583492i	$0.198314\pi$
$762$	3.39190	−	7.62582i	0.122876	−	0.276254i
$763$	71.4275	+	51.8951i	2.58585	+	1.87873i
$764$	34.5819	−	11.2364i	1.25113	−	0.406517i
$765$	0.936744	−	4.42292i	0.0338680	−	0.159911i
$766$	9.74833	−	13.4174i	0.352221	−	0.484791i
$767$	−7.51367	+	5.45900i	−0.271303	+	0.197113i
$768$	3.32731	−	0.708512i	0.120064	−	0.0255662i
$769$			22.0263i			0.794289i	0.917756	+	0.397145i	$0.129999\pi$
$769$			22.0263i			0.794289i	−0.917756	+	0.397145i	$0.870001\pi$
$770$	6.82498	−	1.38959i	0.245955	−	0.0500774i
$771$	−20.2773	+	11.7170i	−0.730271	+	0.421978i
$772$	12.7208	+	4.13325i	0.457833	+	0.148759i
$773$	1.75385	+	2.41397i	0.0630818	+	0.0868246i	0.839392	−	0.543526i	$-0.182911\pi$
$773$	1.75385	+	2.41397i	0.0630818	+	0.0868246i	−0.776311	+	0.630351i	$0.782911\pi$
$774$	1.39584	+	3.12895i	0.0501724	+	0.112468i
$775$	2.36854	+	7.28961i	0.0850804	+	0.261851i
$776$	1.07148	+	3.29767i	0.0384638	+	0.118379i
$777$	−3.90669	−	0.409167i	−0.140152	−	0.0146788i
$778$	4.88656	+	6.72578i	0.175192	+	0.241131i
$779$	21.6516	+	7.03504i	0.775750	+	0.252057i
$780$	−3.83926	−	6.64419i	−0.137468	−	0.237900i
$781$	10.0774	−	22.1213i	0.360596	−	0.791561i
$782$			3.85396i			0.137817i
$783$	−0.916025	+	2.82978i	−0.0327361	+	0.101128i
$784$	32.8114	−	23.8389i	1.17184	−	0.851389i
$785$	−3.09167	+	4.25532i	−0.110346	+	0.151879i
$786$	1.69026	−	1.87860i	0.0602895	−	0.0670075i
$787$	51.0596	−	16.5903i	1.82008	−	0.591380i	0.820268	−	0.571980i	$-0.193824\pi$
$787$	51.0596	−	16.5903i	1.82008	−	0.591380i	0.999812	−	0.0193999i	$-0.00617557\pi$
$788$	19.8423	+	14.4163i	0.706852	+	0.513558i
$789$	10.5653	+	4.69935i	0.376135	+	0.167301i
$790$	−0.543598	+	1.67302i	−0.0193403	+	0.0595234i
$791$	8.02292			0.285262
$792$	13.9302	−	9.95474i	0.494989	−	0.353726i
$793$	−20.0806			−0.713084
$794$	0.213997	−	0.658615i	0.00759447	−	0.0233734i
$795$	−21.0662	−	9.37007i	−0.747142	−	0.332322i
$796$	16.9994	+	12.3508i	0.602527	+	0.437761i
$797$	−7.42838	+	2.41363i	−0.263127	+	0.0854950i	−0.437609	−	0.899165i	$-0.644175\pi$
$797$	−7.42838	+	2.41363i	−0.263127	+	0.0854950i	0.174483	+	0.984660i	$0.444175\pi$
$798$	6.56102	−	7.29211i	0.232258	−	0.258138i
$799$	−2.96749	+	4.08439i	−0.104982	+	0.144495i
$800$	3.81463	−	2.77149i	0.134868	−	0.0979871i
$801$	−7.11876	+	6.41918i	−0.251529	+	0.226811i
$802$			5.53416i			0.195418i
$803$	4.42784	+	21.7474i	0.156255	+	0.767448i
$804$	11.1811	+	19.3499i	0.394326	+	0.682417i
$805$	−24.8337	−	8.06895i	−0.875272	−	0.284393i
$806$	−5.04486	−	6.94366i	−0.177698	−	0.244580i
$807$	31.3916	+	3.28779i	1.10503	+	0.115736i
$808$	−6.63609	−	20.4238i	−0.233457	−	0.718506i
$809$	−11.3173	−	34.8310i	−0.397894	−	1.22459i	−0.926684	−	0.375840i	$-0.877354\pi$
$809$	−11.3173	−	34.8310i	−0.397894	−	1.22459i	0.528790	−	0.848753i	$-0.322646\pi$
$810$	−4.05989	−	0.420716i	−0.142650	−	0.0147825i
$811$	−19.5752	−	26.9430i	−0.687380	−	0.946097i	0.312613	−	0.949881i	$-0.398796\pi$
$811$	−19.5752	−	26.9430i	−0.687380	−	0.946097i	−0.999993	+	0.00378328i	$0.998796\pi$
$812$	−4.52326	−	1.46970i	−0.158735	−	0.0515762i
$813$	2.43039	−	1.40437i	0.0852375	−	0.0492534i
$814$	0.0832866	−	0.731943i	0.00291919	−	0.0256546i
$815$		−	17.5299i		−	0.614044i
$816$	7.16940	−	1.52664i	0.250979	−	0.0534431i
$817$	5.49423	−	3.99179i	0.192219	−	0.139655i
$818$	−1.47727	+	2.03328i	−0.0516514	+	0.0710920i
$819$	−33.5559	−	7.10691i	−1.17254	−	0.248335i
$820$	14.4059	−	4.68076i	0.503076	−	0.163459i
$821$	12.1588	+	8.83389i	0.424345	+	0.308305i	0.779384	−	0.626547i	$-0.215532\pi$
$821$	12.1588	+	8.83389i	0.424345	+	0.308305i	−0.355039	+	0.934852i	$0.615532\pi$
$822$	5.08530	−	11.4330i	0.177370	−	0.398772i
$823$	−4.74885	+	14.6155i	−0.165534	+	0.509463i	−0.999075	−	0.0429952i	$-0.986310\pi$
$823$	−4.74885	+	14.6155i	−0.165534	+	0.509463i	0.833541	+	0.552458i	$0.186310\pi$
$824$	4.02648			0.140269
$825$	−2.91306	+	4.95117i	−0.101420	+	0.172378i
$826$	−7.89912			−0.274845
$827$	0.194359	−	0.598176i	0.00675853	−	0.0208006i	−0.947620	−	0.319399i	$-0.896519\pi$
$827$	0.194359	−	0.598176i	0.00675853	−	0.0208006i	0.954379	+	0.298598i	$0.0965190\pi$
$828$	−30.1859	+	3.19496i	−1.04903	+	0.111032i
$829$	3.81422	+	2.77119i	0.132473	+	0.0962474i	0.652049	−	0.758177i	$-0.273910\pi$
$829$	3.81422	+	2.77119i	0.132473	+	0.0962474i	−0.519575	+	0.854425i	$0.673910\pi$
$830$	−2.55599	+	0.830490i	−0.0887196	+	0.0288267i
$831$	30.8179	+	27.7282i	1.06906	+	0.961881i
$832$	5.04782	−	6.94773i	0.175002	−	0.240869i
$833$	17.6078	−	12.7928i	0.610074	−	0.443245i
$834$	1.82820	+	8.58558i	0.0633053	+	0.297294i
$835$		−	0.871023i		−	0.0301430i
$836$	−11.8342	−	10.8408i	−0.409293	−	0.374938i
$837$	39.8272	−	0.0436367i	1.37663	−	0.00150830i
$838$	7.33755	+	2.38411i	0.253471	+	0.0823578i
$839$	11.6844	+	16.0822i	0.403391	+	0.555220i	0.961591	−	0.274486i	$-0.0885078\pi$
$839$	11.6844	+	16.0822i	0.403391	+	0.555220i	−0.558200	+	0.829706i	$0.688508\pi$
$840$	1.43762	−	13.7262i	0.0496025	−	0.473600i
$841$	−8.86024	−	27.2690i	−0.305526	−	0.940311i
$842$	2.61544	+	8.04949i	0.0901340	+	0.277404i
$843$	−3.36150	+	32.0953i	−0.115776	+	1.10542i
$844$	−4.06521	−	5.59528i	−0.139930	−	0.192597i
$845$	6.56559	+	2.13329i	0.225863	+	0.0733874i
$846$	3.94894	+	2.27608i	0.135767	+	0.0782531i
$847$	−43.6685	−	26.2214i	−1.50047	−	0.900978i
$848$		−	37.3819i		−	1.28370i
$849$	7.18733	+	33.7531i	0.246668	+	1.15840i
$850$	0.552923	−	0.401722i	0.0189651	−	0.0137790i
$851$	−1.62332	+	2.23430i	−0.0556465	+	0.0765909i
$852$	−16.9332	−	15.2355i	−0.580123	−	0.521961i
$853$	−24.4464	+	7.94313i	−0.837030	+	0.271967i	−0.696004	−	0.718038i	$-0.745040\pi$
$853$	−24.4464	+	7.94313i	−0.837030	+	0.271967i	−0.141026	+	0.990006i	$0.545040\pi$
$854$	−13.8172	−	10.0387i	−0.472813	−	0.343519i
$855$	0.851558	+	8.04550i	0.0291227	+	0.275150i
$856$	9.59984	−	29.5453i	0.328116	−	1.00984i
$857$	7.26084			0.248026			0.124013	−	0.992281i	$-0.460424\pi$
$857$	7.26084			0.248026			0.124013	+	0.992281i	$0.460424\pi$
$858$	1.38907	−	6.28088i	0.0474221	−	0.214426i
$859$	−45.4614			−1.55112			−0.775561	−	0.631273i	$-0.782533\pi$
$859$	−45.4614			−1.55112			−0.775561	+	0.631273i	$0.782533\pi$
$860$	1.39631	−	4.29739i	0.0476137	−	0.146540i
$861$	27.5160	−	61.8627i	0.937742	−	2.10827i
$862$	−2.39168	−	1.73766i	−0.0814611	−	0.0591849i
$863$	−2.62923	+	0.854289i	−0.0895000	+	0.0290803i	−0.353425	−	0.935463i	$-0.614983\pi$
$863$	−2.62923	+	0.854289i	−0.0895000	+	0.0290803i	0.263925	+	0.964543i	$0.414983\pi$
$864$	−7.59663	−	23.2932i	−0.258443	−	0.792449i
$865$	9.54634	−	13.1394i	0.324585	−	0.446753i
$866$	5.08790	−	3.69658i	0.172894	−	0.125615i
$867$	−24.9518	+	5.31320i	−0.847408	+	0.180446i
$868$			63.6844i			2.16159i
$869$	11.1960	−	6.33652i	0.379797	−	0.214952i
$870$	−0.389315	+	0.224961i	−0.0131990	+	0.00762688i
$871$	16.8859	+	5.48657i	0.572158	+	0.185905i
$872$	19.2849	+	26.5434i	0.653070	+	0.898874i
$873$	−5.52058	+	2.46275i	−0.186843	+	0.0833516i
$874$	−2.13121	−	6.55917i	−0.0720891	−	0.221867i
$875$	1.43092	+	4.40393i	0.0483740	+	0.148880i
$876$	20.6835	+	2.16628i	0.698829	+	0.0731919i
$877$	−6.47691	−	8.91471i	−0.218710	−	0.301028i	0.685537	−	0.728037i	$-0.259567\pi$
$877$	−6.47691	−	8.91471i	−0.218710	−	0.301028i	−0.904247	+	0.427009i	$0.859567\pi$
$878$	−8.12542	−	2.64011i	−0.274220	−	0.0890994i
$879$	18.1234	+	31.3642i	0.611288	+	1.05789i
$880$	−9.25419	−	1.05302i	−0.311959	−	0.0354973i
$881$		−	10.5939i		−	0.356918i	−0.983947	−	0.178459i	$-0.942889\pi$
$881$		−	10.5939i		−	0.356918i	0.983947	−	0.178459i	$-0.0571113\pi$
$882$	−13.1585	−	14.5926i	−0.443070	−	0.491357i
$883$	20.9215	−	15.2003i	0.704064	−	0.511532i	−0.177189	−	0.984177i	$-0.556701\pi$
$883$	20.9215	−	15.2003i	0.704064	−	0.511532i	0.881253	+	0.472645i	$0.156701\pi$
$884$	3.92443	−	5.40152i	0.131993	−	0.181673i
$885$	4.35761	−	4.84318i	0.146480	−	0.162802i
$886$	−2.89049	+	0.939179i	−0.0971081	+	0.0315523i
$887$	−45.6484	−	33.1655i	−1.53272	−	1.11359i	−0.954701	−	0.297567i	$-0.903825\pi$
$887$	−45.6484	−	33.1655i	−1.53272	−	1.11359i	−0.578022	−	0.816021i	$-0.696175\pi$
$888$	−1.33374	−	0.593235i	−0.0447573	−	0.0199077i
$889$	−15.2037	+	46.7923i	−0.509917	+	1.56936i
$890$	−1.44906			−0.0485726
$891$	19.8148	+	22.3242i	0.663822	+	0.747890i
$892$	41.9712			1.40530
$893$	2.79182	−	8.59234i	0.0934247	−	0.287532i
$894$	−12.1408	−	5.40011i	−0.406048	−	0.180607i
$895$	15.1350	+	10.9962i	0.505906	+	0.367562i
$896$	48.4770	−	15.7511i	1.61950	−	0.526208i
$897$	−16.1301	+	17.9275i	−0.538569	+	0.598581i
$898$	−6.24325	+	8.59310i	−0.208340	+	0.286755i
$899$	3.54949	−	2.57886i	0.118382	−	0.0860096i
$900$	3.60483	+	3.99770i	0.120161	+	0.133257i
$901$		−	20.0605i		−	0.668311i
$902$	11.5551	+	5.26392i	0.384742	+	0.175269i
$903$	−10.1050	−	17.4877i	−0.336274	−	0.581953i
$904$	2.83550	+	0.921311i	0.0943075	+	0.0306424i
$905$	−4.89764	−	6.74102i	−0.162803	−	0.224079i
$906$	15.0978	+	1.58127i	0.501592	+	0.0525342i
$907$	−12.4636	−	38.3589i	−0.413846	−	1.27369i	−0.913279	−	0.407334i	$-0.866459\pi$
$907$	−12.4636	−	38.3589i	−0.413846	−	1.27369i	0.499434	−	0.866352i	$-0.333541\pi$
$908$	3.83745	+	11.8105i	0.127350	+	0.391944i
$909$	34.1912	−	15.2528i	1.13405	−	0.505904i
$910$	−3.04779	−	4.19493i	−0.101033	−	0.139060i
$911$	−14.8092	−	4.81180i	−0.490651	−	0.159422i	0.0532340	−	0.998582i	$-0.483047\pi$
$911$	−14.8092	−	4.81180i	−0.490651	−	0.159422i	−0.543885	+	0.839160i	$0.683047\pi$
$912$	−11.3576	+	6.56284i	−0.376088	+	0.217317i
$913$	17.8858	+	8.14790i	0.591934	+	0.269656i
$914$			15.0300i			0.497147i
$915$	13.7774	−	2.93373i	0.455466	−	0.0969863i
$916$	−0.947714	+	0.688555i	−0.0313134	+	0.0227505i
$917$	−8.75627	+	12.0520i	−0.289158	+	0.397991i
$918$	−1.10112	−	3.37629i	−0.0363422	−	0.111434i
$919$	48.0102	−	15.5995i	1.58371	−	0.514579i	0.620702	−	0.784047i	$-0.286848\pi$
$919$	48.0102	−	15.5995i	1.58371	−	0.514579i	0.963009	+	0.269467i	$0.0868477\pi$
$920$	−7.85026	−	5.70355i	−0.258815	−	0.188040i
$921$	−11.6338	+	26.1556i	−0.383345	+	0.861855i
$922$	−3.38107	+	10.4059i	−0.111350	+	0.342699i
$923$	−18.0969			−0.595665
$924$	−35.7316	+	31.6451i	−1.17548	+	1.04105i
$925$	0.489760			0.0161032
$926$	3.01905	−	9.29169i	0.0992122	−	0.305344i
$927$	0.738863	+	6.98076i	0.0242674	+	0.229278i
$928$	−2.18355	−	1.58644i	−0.0716785	−	0.0520775i
$929$	−10.6157	+	3.44924i	−0.348288	+	0.113166i	−0.477937	−	0.878394i	$-0.658615\pi$
$929$	−10.6157	+	3.44924i	−0.348288	+	0.113166i	0.129648	+	0.991560i	$0.458615\pi$
$930$	4.47575	+	4.02703i	0.146766	+	0.132051i
$931$	−22.8929	+	31.5094i	−0.750285	+	1.03268i
$932$	26.8028	−	19.4733i	0.877953	−	0.637870i
$933$	−0.286579	−	1.34583i	−0.00938218	−	0.0440606i
$934$			1.08286i			0.0354323i
$935$	−4.96614	−	0.565088i	−0.162410	−	0.0184804i
$936$	−11.0434	−	6.36515i	−0.360964	−	0.208051i
$937$	15.4065	+	5.00587i	0.503308	+	0.163535i	0.549657	−	0.835391i	$-0.314759\pi$
$937$	15.4065	+	5.00587i	0.503308	+	0.163535i	−0.0463487	+	0.998925i	$0.514759\pi$
$938$	8.87608	+	12.2169i	0.289814	+	0.398895i
$939$	0.230509	−	2.20088i	0.00752238	−	0.0718230i
$940$	−1.85754	−	5.71691i	−0.0605862	−	0.186465i
$941$	9.27963	+	28.5598i	0.302507	+	0.931022i	0.980596	+	0.196042i	$0.0628087\pi$
$941$	9.27963	+	28.5598i	0.302507	+	0.931022i	−0.678088	+	0.734981i	$0.737191\pi$
$942$	−0.430377	+	4.10920i	−0.0140224	+	0.133885i
$943$	−27.9803	−	38.5116i	−0.911165	−	1.25411i
$944$	10.0461	+	3.26416i	0.326971	+	0.106239i
$945$	24.0611	−	0.0263626i	0.782708	−	0.000857575i
$946$	3.29645	−	1.86567i	0.107177	−	0.0606583i
$947$			0.626343i			0.0203534i	0.999948	+	0.0101767i	$0.00323940\pi$
$947$			0.626343i			0.0203534i	−0.999948	+	0.0101767i	$0.996761\pi$
$948$	−2.51067	−	11.7906i	−0.0815429	−	0.382941i
$949$	13.3669	−	9.71159i	0.433907	−	0.315252i
$950$	−0.718887	+	0.989464i	−0.0233238	+	0.0321024i
$951$	−18.1076	−	16.2922i	−0.587180	−	0.528311i
$952$	11.4204	−	3.71072i	0.370138	−	0.120265i
$953$	−44.3750	−	32.2403i	−1.43745	−	1.04437i	−0.988569	−	0.150772i	$-0.951824\pi$
$953$	−44.3750	−	32.2403i	−1.43745	−	1.04437i	−0.448877	−	0.893594i	$-0.648176\pi$
$954$	−18.0102	+	1.90625i	−0.583102	+	0.0617171i
$955$	−6.26216	+	19.2730i	−0.202639	+	0.623658i
$956$	1.07553			0.0347851
$957$	3.21069	+	0.710072i	0.103787	+	0.0229534i
$958$	−8.45954			−0.273315
$959$	−22.7942	+	70.1533i	−0.736063	+	2.26537i
$960$	−2.44828	+	5.50434i	−0.0790179	+	0.177652i
$961$	−22.4489	−	16.3101i	−0.724159	−	0.526132i
$962$	−0.521582	+	0.169472i	−0.0168165	+	0.00546400i
$963$	52.9845	+	11.2218i	1.70740	+	0.361616i
$964$	3.27196	−	4.50347i	0.105383	−	0.145047i
$965$	−6.03068	+	4.38154i	−0.194134	+	0.141047i
$966$	−20.0612	+	4.27180i	−0.645459	+	0.137443i
$967$			41.1782i			1.32420i	0.749414	+	0.662102i	$0.230335\pi$
$967$			41.1782i			1.32420i	−0.749414	+	0.662102i	$0.769665\pi$
$968$	−12.4224	−	14.2820i	−0.399272	−	0.459040i
$969$	−6.09490	+	3.52186i	−0.195796	+	0.113138i
$970$	−0.869105	−	0.282389i	−0.0279053	−	0.00906697i
$971$	−15.3366	−	21.1090i	−0.492174	−	0.677420i	0.488613	−	0.872501i	$-0.337503\pi$
$971$	−15.3366	−	21.1090i	−0.492174	−	0.677420i	−0.980787	+	0.195081i	$0.937503\pi$
$972$	25.5317	−	11.4234i	0.818931	−	0.366405i
$973$	−15.9906	−	49.2139i	−0.512634	−	1.57772i
$974$	−0.698385	−	2.14941i	−0.0223777	−	0.0688714i
$975$	4.25337	+	0.445477i	0.136217	+	0.0142667i
$976$	13.4243	+	18.4769i	0.429700	+	0.591431i
$977$	−6.62796	−	2.15356i	−0.212047	−	0.0688983i	0.201067	−	0.979577i	$-0.435559\pi$
$977$	−6.62796	−	2.15356i	−0.212047	−	0.0688983i	−0.413114	+	0.910679i	$0.635559\pi$
$978$	−6.88929	−	11.9225i	−0.220295	−	0.381241i
$979$	7.81413	+	7.15824i	0.249741	+	0.228778i
$980$			25.9139i			0.827789i
$981$	−42.4798	+	38.3052i	−1.35628	+	1.22299i
$982$	−1.44850	+	1.05240i	−0.0462236	+	0.0335834i
$983$	−9.92256	+	13.6572i	−0.316481	+	0.435598i	−0.937389	−	0.348285i	$-0.886764\pi$
$983$	−9.92256	+	13.6572i	−0.316481	+	0.435598i	0.620908	+	0.783883i	$0.286764\pi$
$984$	16.8288	−	18.7041i	0.536484	−	0.596264i
$985$	−12.9999	+	4.22392i	−0.414211	+	0.134585i
$986$	−0.316501	−	0.229951i	−0.0100794	−	0.00732314i
$987$	−24.5499	−	10.9196i	−0.781432	−	0.347574i
$988$	−3.69212	+	11.3632i	−0.117462	+	0.361511i
$989$	−14.2003			−0.451544
$990$	−0.0354256	+	4.51227i	−0.00112590	+	0.143409i
$991$	−42.9031			−1.36286			−0.681432	−	0.731882i	$-0.738642\pi$
$991$	−42.9031			−1.36286			−0.681432	+	0.731882i	$0.738642\pi$
$992$	−11.1680	+	34.3716i	−0.354584	+	1.09130i
$993$	−10.1115	−	4.49750i	−0.320878	−	0.142724i
$994$	−12.4522	−	9.04702i	−0.394958	−	0.286954i
$995$	−11.1373	+	3.61873i	−0.353077	+	0.114722i
$996$	12.3185	−	13.6911i	0.390326	−	0.433820i
$997$	−29.3710	+	40.4257i	−0.930189	+	1.28030i	0.0295967	+	0.999562i	$0.490578\pi$
$997$	−29.3710	+	40.4257i	−0.930189	+	1.28030i	−0.959786	+	0.280734i	$0.909422\pi$
$998$	2.49575	−	1.81327i	0.0790017	−	0.0573981i
$999$	0.783755	−	2.42117i	0.0247969	−	0.0766025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.101.8	yes	48
3.2	odd	2	inner	165.2.p.b.101.5	✓	48
5.2	odd	4		825.2.bs.g.299.8		48
5.3	odd	4		825.2.bs.h.299.5		48
5.4	even	2		825.2.bi.e.101.5		48
11.6	odd	10	inner	165.2.p.b.116.5	yes	48
15.2	even	4		825.2.bs.h.299.6		48
15.8	even	4		825.2.bs.g.299.7		48
15.14	odd	2		825.2.bi.e.101.8		48
33.17	even	10	inner	165.2.p.b.116.8	yes	48
55.17	even	20		825.2.bs.g.149.7		48
55.28	even	20		825.2.bs.h.149.6		48
55.39	odd	10		825.2.bi.e.776.8		48
165.17	odd	20		825.2.bs.h.149.5		48
165.83	odd	20		825.2.bs.g.149.8		48
165.149	even	10		825.2.bi.e.776.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.101.5	✓	48	3.2	odd	2	inner
165.2.p.b.101.8	yes	48	1.1	even	1	trivial
165.2.p.b.116.5	yes	48	11.6	odd	10	inner
165.2.p.b.116.8	yes	48	33.17	even	10	inner
825.2.bi.e.101.5		48	5.4	even	2
825.2.bi.e.101.8		48	15.14	odd	2
825.2.bi.e.776.5		48	165.149	even	10
825.2.bi.e.776.8		48	55.39	odd	10
825.2.bs.g.149.7		48	55.17	even	20
825.2.bs.g.149.8		48	165.83	odd	20
825.2.bs.g.299.7		48	15.8	even	4
825.2.bs.g.299.8		48	5.2	odd	4
825.2.bs.h.149.5		48	165.17	odd	20
825.2.bs.h.149.6		48	55.28	even	20
825.2.bs.h.299.5		48	5.3	odd	4
825.2.bs.h.299.6		48	15.2	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140144 - 0.431318i) q^{2} +(-1.58256 - 0.703911i) q^{3} +(1.45164 + 1.05468i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.525396 + 0.583940i) q^{6} +(2.72178 - 3.74621i) q^{7} +(1.39214 - 1.01145i) q^{8} +(2.00902 + 2.22797i) q^{9} +O(q^{10})\)	\(q+(0.140144 - 0.431318i) q^{2} +(-1.58256 - 0.703911i) q^{3} +(1.45164 + 1.05468i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.525396 + 0.583940i) q^{6} +(2.72178 - 3.74621i) q^{7} +(1.39214 - 1.01145i) q^{8} +(2.00902 + 2.22797i) q^{9} +0.453514i q^{10} +(2.24032 - 2.44560i) q^{11} +(-1.55491 - 2.69092i) q^{12} +(-2.34827 - 0.762999i) q^{13} +(-1.23437 - 1.69896i) q^{14} +(1.72263 + 0.180419i) q^{15} +(0.867797 + 2.67080i) q^{16} +(0.465691 + 1.43325i) q^{17} +(1.24251 - 0.554291i) q^{18} +(-1.58515 - 2.18177i) q^{19} +(-1.70650 - 0.554477i) q^{20} +(-6.94438 + 4.01272i) q^{21} +(-0.740863 - 1.30903i) q^{22} +5.63898i q^{23} +(-2.91512 + 0.620741i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-0.658190 + 0.905921i) q^{26} +(-1.61111 - 4.94007i) q^{27} +(7.90208 - 2.56754i) q^{28} +(-0.463093 - 0.336457i) q^{29} +(0.319234 - 0.717716i) q^{30} +(-2.36854 + 7.28961i) q^{31} +4.71514 q^{32} +(-5.26694 + 2.29333i) q^{33} +0.683450 q^{34} +(-1.43092 + 4.40393i) q^{35} +(0.566584 + 5.35307i) q^{36} +(0.396224 + 0.287874i) q^{37} +(-1.16318 + 0.377941i) q^{38} +(3.17920 + 2.86047i) q^{39} +(-1.01145 + 1.39214i) q^{40} +(-6.82953 + 4.96195i) q^{41} +(0.757548 + 3.55759i) q^{42} +2.51824i q^{43} +(5.83146 - 1.18731i) q^{44} +(-2.59917 - 1.49810i) q^{45} +(2.43219 + 0.790268i) q^{46} +(1.96912 + 2.71027i) q^{47} +(0.506663 - 4.83757i) q^{48} +(-4.46287 - 13.7353i) q^{49} +(-0.140144 - 0.431318i) q^{50} +(0.271894 - 2.59602i) q^{51} +(-2.60412 - 3.58426i) q^{52} +(-12.6599 - 4.11346i) q^{53} +(-2.35653 + 0.00258193i) q^{54} +(-1.37494 + 3.01820i) q^{55} -7.96819i q^{56} +(0.972828 + 4.56859i) q^{57} +(-0.210019 + 0.152588i) q^{58} +(2.21091 - 3.04306i) q^{59} +(2.31035 + 2.07872i) q^{60} +(7.73467 - 2.51315i) q^{61} +(2.81220 + 2.04319i) q^{62} +(13.8145 - 1.46217i) q^{63} +(-1.07480 + 3.30788i) q^{64} +2.46912 q^{65} +(0.251026 + 2.59312i) q^{66} -7.19080 q^{67} +(-0.835601 + 2.57172i) q^{68} +(3.96934 - 8.92405i) q^{69} +(1.69896 + 1.23437i) q^{70} +(6.97057 - 2.26487i) q^{71} +(5.05032 + 1.06962i) q^{72} +(-3.93323 + 5.41362i) q^{73} +(0.179693 - 0.130555i) q^{74} +(-1.69407 + 0.360732i) q^{75} -4.83896i q^{76} +(-3.06405 - 15.0491i) q^{77} +(1.67932 - 0.970371i) q^{78} +(3.68901 + 1.19863i) q^{79} +(-1.65065 - 2.27192i) q^{80} +(-0.927679 + 8.95206i) q^{81} +(1.18306 + 3.64109i) q^{82} +(1.83123 + 5.63595i) q^{83} +(-14.3129 - 1.49906i) q^{84} +(-0.885798 - 1.21920i) q^{85} +(1.08616 + 0.352916i) q^{86} +(0.496039 + 0.858440i) q^{87} +(0.645247 - 5.67059i) q^{88} +3.19518i q^{89} +(-1.01042 + 0.911120i) q^{90} +(-9.24982 + 6.72039i) q^{91} +(-5.94731 + 8.18577i) q^{92} +(8.87960 - 9.86904i) q^{93} +(1.44495 - 0.469491i) q^{94} +(2.18177 + 1.58515i) q^{95} +(-7.46202 - 3.31904i) q^{96} +(-0.622669 + 1.91638i) q^{97} -6.54972 q^{98} +(9.94957 + 0.0781136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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