LMFDB - Embedded newform 561.2.m.d.460.3

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			460.3
Character	$\chi$	$=$	561.460
Dual form			561.2.m.d.511.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.134444 + 0.413775i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.46490 + 1.06431i) q^{4} +(0.472638 + 1.45463i) q^{5} +(-0.134444 - 0.413775i) q^{6} +(-2.28531 - 1.66038i) q^{7} +(-1.34129 + 0.974502i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.134444 + 0.413775i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.46490 + 1.06431i) q^{4} +(0.472638 + 1.45463i) q^{5} +(-0.134444 - 0.413775i) q^{6} +(-2.28531 - 1.66038i) q^{7} +(-1.34129 + 0.974502i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.665433 q^{10} +(-3.30593 + 0.266128i) q^{11} -1.81072 q^{12} +(-1.42266 + 4.37849i) q^{13} +(0.994268 - 0.722378i) q^{14} +(-1.23738 - 0.899012i) q^{15} +(0.896187 + 2.75818i) q^{16} +(0.309017 + 0.951057i) q^{17} +(0.351978 + 0.255727i) q^{18} +(-0.0765408 + 0.0556102i) q^{19} +(-0.855814 + 2.63392i) q^{20} +2.82480 q^{21} +(0.334344 - 1.40369i) q^{22} -7.76492 q^{23} +(0.512326 - 1.57678i) q^{24} +(2.15252 - 1.56390i) q^{25} +(-1.62044 - 1.17732i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.58060 - 4.86457i) q^{28} +(2.45493 + 1.78361i) q^{29} +(0.538347 - 0.391132i) q^{30} +(1.44482 - 4.44669i) q^{31} -4.57760 q^{32} +(2.51813 - 2.15848i) q^{33} -0.435069 q^{34} +(1.33511 - 4.10905i) q^{35} +(1.46490 - 1.06431i) q^{36} +(6.28190 + 4.56407i) q^{37} +(-0.0127197 - 0.0391471i) q^{38} +(-1.42266 - 4.37849i) q^{39} +(-2.05149 - 1.49049i) q^{40} +(-5.74226 + 4.17199i) q^{41} +(-0.379777 + 1.16883i) q^{42} -4.25499 q^{43} +(-5.12610 - 3.12869i) q^{44} +1.52949 q^{45} +(1.04394 - 3.21293i) q^{46} +(-1.24298 + 0.903076i) q^{47} +(-2.34625 - 1.70465i) q^{48} +(0.302685 + 0.931569i) q^{49} +(0.357709 + 1.10091i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(-6.74413 + 4.89990i) q^{52} +(-4.02720 + 12.3944i) q^{53} -0.435069 q^{54} +(-1.94963 - 4.68313i) q^{55} +4.68330 q^{56} +(0.0292360 - 0.0899791i) q^{57} +(-1.06806 + 0.775992i) q^{58} +(9.84105 + 7.14994i) q^{59} +(-0.855814 - 2.63392i) q^{60} +(-4.03164 - 12.4081i) q^{61} +(1.64568 + 1.19566i) q^{62} +(-2.28531 + 1.66038i) q^{63} +(-1.17694 + 3.62226i) q^{64} -7.04149 q^{65} +(0.554578 + 1.33213i) q^{66} +9.34815 q^{67} +(-0.559542 + 1.72209i) q^{68} +(6.28196 - 4.56411i) q^{69} +(1.52072 + 1.10487i) q^{70} +(0.201831 + 0.621172i) q^{71} +(0.512326 + 1.57678i) q^{72} +(-0.732105 - 0.531905i) q^{73} +(-2.73306 + 1.98568i) q^{74} +(-0.822189 + 2.53044i) q^{75} -0.171311 q^{76} +(7.99696 + 4.88091i) q^{77} +2.00298 q^{78} +(-2.77155 + 8.52996i) q^{79} +(-3.58856 + 2.60724i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.954256 - 2.93690i) q^{82} +(-1.98165 - 6.09888i) q^{83} +(4.13805 + 3.00647i) q^{84} +(-1.23738 + 0.899012i) q^{85} +(0.572057 - 1.76061i) q^{86} -3.03445 q^{87} +(4.17486 - 3.57859i) q^{88} +7.32239 q^{89} +(-0.205630 + 0.632864i) q^{90} +(10.5212 - 7.64407i) q^{91} +(-11.3748 - 8.26430i) q^{92} +(1.44482 + 4.44669i) q^{93} +(-0.206560 - 0.635725i) q^{94} +(-0.117068 - 0.0850552i) q^{95} +(3.70335 - 2.69064i) q^{96} +(-1.96804 + 6.05701i) q^{97} -0.426154 q^{98} +(-0.768486 + 3.22636i) 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 $

$2$	−0.134444	+	0.413775i	−0.0950660	+	0.292583i	−0.987271	−	0.159048i	$-0.949158\pi$
$2$	−0.134444	+	0.413775i	−0.0950660	+	0.292583i	0.892205	+	0.451631i	$0.149158\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	1.46490	+	1.06431i	0.732450	+	0.532156i
$5$	0.472638	+	1.45463i	0.211370	+	0.650531i	0.999391	+	0.0348827i	$0.0111058\pi$
$5$	0.472638	+	1.45463i	0.211370	+	0.650531i	−0.788021	+	0.615648i	$0.788894\pi$
$6$	−0.134444	−	0.413775i	−0.0548864	−	0.168923i
$7$	−2.28531	−	1.66038i	−0.863767	−	0.627564i	0.0651400	−	0.997876i	$-0.479251\pi$
$7$	−2.28531	−	1.66038i	−0.863767	−	0.627564i	−0.928907	+	0.370313i	$0.879251\pi$
$8$	−1.34129	+	0.974502i	−0.474217	+	0.344539i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.665433			−0.210428
$11$	−3.30593	+	0.266128i	−0.996776	+	0.0802406i
$11$	−3.30593	+	0.266128i	−0.996776	+	0.0802406i
$12$	−1.81072			−0.522708
$13$	−1.42266	+	4.37849i	−0.394574	+	1.21437i	0.534718	+	0.845030i	$0.320418\pi$
$13$	−1.42266	+	4.37849i	−0.394574	+	1.21437i	−0.929293	+	0.369344i	$0.879582\pi$
$14$	0.994268	−	0.722378i	0.265729	−	0.193064i
$15$	−1.23738	−	0.899012i	−0.319491	−	0.232124i
$16$	0.896187	+	2.75818i	0.224047	+	0.689545i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	0.351978	+	0.255727i	0.0829620	+	0.0602754i
$19$	−0.0765408	+	0.0556102i	−0.0175597	+	0.0127578i	−0.596530	−	0.802590i	$-0.703455\pi$
$19$	−0.0765408	+	0.0556102i	−0.0175597	+	0.0127578i	0.578971	+	0.815348i	$0.303455\pi$
$20$	−0.855814	+	2.63392i	−0.191366	+	0.588963i
$21$	2.82480			0.616422
$22$	0.334344	−	1.40369i	0.0712824	−	0.299268i
$23$	−7.76492			−1.61910			−0.809549	−	0.587052i	$-0.800288\pi$
$23$	−7.76492			−1.61910			−0.809549	+	0.587052i	$0.800288\pi$
$24$	0.512326	−	1.57678i	0.104578	−	0.321858i
$25$	2.15252	−	1.56390i	0.430504	−	0.312779i
$26$	−1.62044	−	1.17732i	−0.317795	−	0.230891i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.58060	−	4.86457i	−0.298704	−	0.919318i
$29$	2.45493	+	1.78361i	0.455868	+	0.331208i	0.791908	−	0.610640i	$-0.209088\pi$
$29$	2.45493	+	1.78361i	0.455868	+	0.331208i	−0.336040	+	0.941848i	$0.609088\pi$
$30$	0.538347	−	0.391132i	0.0982882	−	0.0714106i
$31$	1.44482	−	4.44669i	0.259497	−	0.798649i	−0.733414	−	0.679783i	$-0.762074\pi$
$31$	1.44482	−	4.44669i	0.259497	−	0.798649i	0.992910	−	0.118866i	$-0.0379259\pi$
$32$	−4.57760			−0.809212
$33$	2.51813	−	2.15848i	0.438350	−	0.375743i
$34$	−0.435069			−0.0746136
$35$	1.33511	−	4.10905i	0.225675	−	0.694556i
$36$	1.46490	−	1.06431i	0.244150	−	0.177385i
$37$	6.28190	+	4.56407i	1.03274	+	0.750329i	0.968855	−	0.247629i	$-0.0796513\pi$
$37$	6.28190	+	4.56407i	1.03274	+	0.750329i	0.0638838	+	0.997957i	$0.479651\pi$
$38$	−0.0127197	−	0.0391471i	−0.00206340	−	0.00635050i
$39$	−1.42266	−	4.37849i	−0.227808	−	0.701120i
$40$	−2.05149	−	1.49049i	−0.324368	−	0.235667i
$41$	−5.74226	+	4.17199i	−0.896790	+	0.651556i	−0.937639	−	0.347609i	$-0.886994\pi$
$41$	−5.74226	+	4.17199i	−0.896790	+	0.651556i	0.0408495	+	0.999165i	$0.486994\pi$
$42$	−0.379777	+	1.16883i	−0.0586008	+	0.180355i
$43$	−4.25499			−0.648880			−0.324440	−	0.945906i	$-0.605176\pi$
$43$	−4.25499			−0.648880			−0.324440	+	0.945906i	$0.605176\pi$
$44$	−5.12610	−	3.12869i	−0.772788	−	0.471668i
$45$	1.52949			0.228003
$46$	1.04394	−	3.21293i	0.153921	−	0.473721i
$47$	−1.24298	+	0.903076i	−0.181307	+	0.131727i	−0.674737	−	0.738058i	$-0.735743\pi$
$47$	−1.24298	+	0.903076i	−0.181307	+	0.131727i	0.493430	+	0.869785i	$0.335743\pi$
$48$	−2.34625	−	1.70465i	−0.338652	−	0.246045i
$49$	0.302685	+	0.931569i	0.0432407	+	0.133081i
$50$	0.357709	+	1.10091i	0.0505877	+	0.155693i
$51$	−0.809017	−	0.587785i	−0.113285	−	0.0823064i
$52$	−6.74413	+	4.89990i	−0.935243	+	0.679493i
$53$	−4.02720	+	12.3944i	−0.553178	+	1.70251i	0.147528	+	0.989058i	$0.452868\pi$
$53$	−4.02720	+	12.3944i	−0.553178	+	1.70251i	−0.700707	+	0.713450i	$0.747132\pi$
$54$	−0.435069			−0.0592053
$55$	−1.94963	−	4.68313i	−0.262888	−	0.631473i
$56$	4.68330			0.625833
$57$	0.0292360	−	0.0899791i	0.00387240	−	0.0119180i
$58$	−1.06806	+	0.775992i	−0.140243	+	0.101893i
$59$	9.84105	+	7.14994i	1.28119	+	0.930843i	0.999588	−	0.0286873i	$-0.00913271\pi$
$59$	9.84105	+	7.14994i	1.28119	+	0.930843i	0.281607	+	0.959530i	$0.409133\pi$
$60$	−0.855814	−	2.63392i	−0.110485	−	0.340038i
$61$	−4.03164	−	12.4081i	−0.516199	−	1.58870i	−0.781090	−	0.624418i	$-0.785336\pi$
$61$	−4.03164	−	12.4081i	−0.516199	−	1.58870i	0.264892	−	0.964278i	$-0.414664\pi$
$62$	1.64568	+	1.19566i	0.209002	+	0.151849i
$63$	−2.28531	+	1.66038i	−0.287922	+	0.209188i
$64$	−1.17694	+	3.62226i	−0.147118	+	0.452783i
$65$	−7.04149			−0.873390
$66$	0.554578	+	1.33213i	0.0682638	+	0.163974i
$67$	9.34815			1.14206			0.571029	−	0.820930i	$-0.306544\pi$
$67$	9.34815			1.14206			0.571029	+	0.820930i	$0.306544\pi$
$68$	−0.559542	+	1.72209i	−0.0678544	+	0.208834i
$69$	6.28196	−	4.56411i	0.756259	−	0.549454i
$70$	1.52072	+	1.10487i	0.181761	+	0.132057i
$71$	0.201831	+	0.621172i	0.0239529	+	0.0737196i	0.962318	−	0.271925i	$-0.0876603\pi$
$71$	0.201831	+	0.621172i	0.0239529	+	0.0737196i	−0.938365	+	0.345645i	$0.887660\pi$
$72$	0.512326	+	1.57678i	0.0603782	+	0.185825i
$73$	−0.732105	−	0.531905i	−0.0856864	−	0.0622548i	0.544117	−	0.839009i	$-0.316865\pi$
$73$	−0.732105	−	0.531905i	−0.0856864	−	0.0622548i	−0.629804	+	0.776754i	$0.716865\pi$
$74$	−2.73306	+	1.98568i	−0.317712	+	0.230831i
$75$	−0.822189	+	2.53044i	−0.0949382	+	0.292190i
$76$	−0.171311			−0.0196507
$77$	7.99696	+	4.88091i	0.911338	+	0.556231i
$78$	2.00298			0.226792
$79$	−2.77155	+	8.52996i	−0.311824	+	0.959695i	0.665218	+	0.746649i	$0.268338\pi$
$79$	−2.77155	+	8.52996i	−0.311824	+	0.959695i	−0.977042	+	0.213046i	$0.931662\pi$
$80$	−3.58856	+	2.60724i	−0.401213	+	0.291499i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.954256	−	2.93690i	−0.105380	−	0.324326i
$83$	−1.98165	−	6.09888i	−0.217514	−	0.669439i	−0.998966	−	0.0454733i	$-0.985520\pi$
$83$	−1.98165	−	6.09888i	−0.217514	−	0.669439i	0.781452	−	0.623966i	$-0.214480\pi$
$84$	4.13805	+	3.00647i	0.451498	+	0.328033i
$85$	−1.23738	+	0.899012i	−0.134213	+	0.0975115i
$86$	0.572057	−	1.76061i	0.0616864	−	0.189851i
$87$	−3.03445			−0.325328
$88$	4.17486	−	3.57859i	0.445042	−	0.381479i
$89$	7.32239			0.776171			0.388086	−	0.921623i	$-0.373136\pi$
$89$	7.32239			0.776171			0.388086	+	0.921623i	$0.373136\pi$
$90$	−0.205630	+	0.632864i	−0.0216753	+	0.0667098i
$91$	10.5212	−	7.64407i	1.10292	−	0.801317i
$92$	−11.3748	−	8.26430i	−1.18591	−	0.861613i
$93$	1.44482	+	4.44669i	0.149820	+	0.461100i
$94$	−0.206560	−	0.635725i	−0.0213050	−	0.0655701i
$95$	−0.117068	−	0.0850552i	−0.0120110	−	0.00872648i
$96$	3.70335	−	2.69064i	0.377972	−	0.274613i
$97$	−1.96804	+	6.05701i	−0.199824	+	0.614996i	0.800062	+	0.599917i	$0.204800\pi$
$97$	−1.96804	+	6.05701i	−0.199824	+	0.614996i	−0.999886	+	0.0150786i	$0.995200\pi$
$98$	−0.426154			−0.0430480
$99$	−0.768486	+	3.22636i	−0.0772358	+	0.324262i
$100$	4.81770			0.481770
$101$	2.66291	−	8.19559i	0.264969	−	0.815492i	−0.726731	−	0.686922i	$-0.758961\pi$
$101$	2.66291	−	8.19559i	0.264969	−	0.815492i	0.991700	−	0.128570i	$-0.0410387\pi$
$102$	0.351978	−	0.255727i	0.0348510	−	0.0253207i
$103$	13.1623	+	9.56295i	1.29692	+	0.942265i	0.999920	−	0.0126135i	$-0.00401509\pi$
$103$	13.1623	+	9.56295i	1.29692	+	0.942265i	0.296996	+	0.954879i	$0.404015\pi$
$104$	−2.35866	−	7.25920i	−0.231285	−	0.711823i
$105$	1.33511	+	4.10905i	0.130293	+	0.401002i
$106$	−4.58708	−	3.33271i	−0.445536	−	0.323701i
$107$	−0.310375	+	0.225500i	−0.0300051	+	0.0217999i	−0.602687	−	0.797978i	$-0.705903\pi$
$107$	−0.310375	+	0.225500i	−0.0300051	+	0.0217999i	0.572682	+	0.819778i	$0.305903\pi$
$108$	−0.559542	+	1.72209i	−0.0538419	+	0.165708i
$109$	17.3162			1.65859			0.829297	−	0.558808i	$-0.188741\pi$
$109$	17.3162			1.65859			0.829297	+	0.558808i	$0.188741\pi$
$110$	2.19988	−	0.177090i	0.209750	−	0.0168849i
$111$	−7.76486			−0.737008
$112$	2.53155	−	7.79131i	0.239209	−	0.736210i
$113$	0.473152	−	0.343765i	0.0445104	−	0.0323387i	−0.565308	−	0.824880i	$-0.691243\pi$
$113$	0.473152	−	0.343765i	0.0445104	−	0.0323387i	0.609818	+	0.792541i	$0.291243\pi$
$114$	0.0333005	+	0.0241942i	0.00311888	+	0.00226600i
$115$	−3.67000	−	11.2951i	−0.342229	−	1.05327i
$116$	1.69790	+	5.22561i	0.157646	+	0.485186i
$117$	3.72457	+	2.70606i	0.344336	+	0.250175i
$118$	−4.28153	+	3.11071i	−0.394147	+	0.286364i
$119$	0.872912	−	2.68655i	0.0800197	−	0.246275i
$120$	2.53578			0.231484
$121$	10.8584	−	1.75960i	0.987123	−	0.159964i
$122$	5.67619			0.513898
$123$	2.19335	−	6.75043i	0.197767	−	0.608666i
$124$	6.84917	−	4.97621i	0.615074	−	0.446877i
$125$	9.47917	+	6.88702i	0.847843	+	0.615994i
$126$	−0.379777	−	1.16883i	−0.0338332	−	0.104128i
$127$	0.188878	+	0.581306i	0.0167602	+	0.0515826i	0.959087	−	0.283112i	$-0.0913668\pi$
$127$	0.188878	+	0.581306i	0.0167602	+	0.0515826i	−0.942327	+	0.334695i	$0.891367\pi$
$128$	−8.74728	−	6.35527i	−0.773157	−	0.561732i
$129$	3.44236	−	2.50102i	0.303083	−	0.220203i
$130$	0.946683	−	2.91359i	0.0830296	−	0.255539i
$131$	3.20487			0.280011			0.140006	−	0.990151i	$-0.455288\pi$
$131$	3.20487			0.280011			0.140006	+	0.990151i	$0.455288\pi$
$132$	5.98610	−	0.481882i	0.521023	−	0.0419424i
$133$	0.267254			0.0231738
$134$	−1.25680	+	3.86803i	−0.108571	+	0.334147i
$135$	−1.23738	+	0.899012i	−0.106497	+	0.0773746i
$136$	−1.34129	−	0.974502i	−0.115014	−	0.0835629i
$137$	−0.713047	−	2.19453i	−0.0609198	−	0.187492i	0.915965	−	0.401258i	$-0.131427\pi$
$137$	−0.713047	−	2.19453i	−0.0609198	−	0.187492i	−0.976885	+	0.213766i	$0.931427\pi$
$138$	1.04394	+	3.21293i	0.0888664	+	0.273503i
$139$	12.5117	+	9.09030i	1.06123	+	0.771029i	0.974316	−	0.225186i	$-0.0722991\pi$
$139$	12.5117	+	9.09030i	1.06123	+	0.771029i	0.0869150	+	0.996216i	$0.472299\pi$
$140$	6.32911	−	4.59837i	0.534907	−	0.388633i
$141$	0.474775	−	1.46121i	0.0399833	−	0.123056i
$142$	−0.284160			−0.0238462
$143$	3.53797	−	14.8536i	0.295860	−	1.24212i
$144$	2.90012			0.241677
$145$	−1.43420	+	4.41401i	−0.119104	+	0.366564i
$146$	0.318516	−	0.231415i	0.0263606	−	0.0191521i
$147$	−0.792440	−	0.575741i	−0.0653593	−	0.0474863i
$148$	4.34476	+	13.3718i	0.357137	+	1.09916i
$149$	2.32561	+	7.15748i	0.190521	+	0.586364i	1.00000		0.000785715i	$-0.000250101\pi$
$149$	2.32561	+	7.15748i	0.190521	+	0.586364i	−0.809479	+	0.587149i	$0.800250\pi$
$150$	−0.936494	−	0.680402i	−0.0764644	−	0.0555546i
$151$	−15.9162	+	11.5638i	−1.29524	+	0.941048i	−0.999897	−	0.0143430i	$-0.995434\pi$
$151$	−15.9162	+	11.5638i	−1.29524	+	0.941048i	−0.295344	+	0.955391i	$0.595434\pi$
$152$	0.0484710	−	0.149178i	0.00393152	−	0.0121000i
$153$	1.00000			0.0808452
$154$	−3.09474	+	2.65273i	−0.249381	+	0.213763i
$155$	7.15117			0.574395
$156$	2.57603	−	7.92820i	0.206247	−	0.634764i
$157$	−12.1470	+	8.82532i	−0.969437	+	0.704337i	−0.955323	−	0.295563i	$-0.904493\pi$
$157$	−12.1470	+	8.82532i	−0.969437	+	0.704337i	−0.0141141	+	0.999900i	$0.504493\pi$
$158$	−3.15686	−	2.29360i	−0.251147	−	0.182469i
$159$	−4.02720	−	12.3944i	−0.319378	−	0.982943i
$160$	−2.16355	−	6.65872i	−0.171043	−	0.526418i
$161$	17.7453	+	12.8927i	1.39852	+	1.01609i
$162$	0.351978	−	0.255727i	0.0276540	−	0.0200918i
$163$	1.58372	−	4.87418i	0.124046	−	0.381775i	−0.869680	−	0.493616i	$-0.835675\pi$
$163$	1.58372	−	4.87418i	0.124046	−	0.381775i	0.993726	+	0.111841i	$0.0356747\pi$
$164$	−12.8521			−1.00358
$165$	4.32996	+	2.64277i	0.337087	+	0.205739i
$166$	2.78998			0.216545
$167$	1.07923	−	3.32153i	0.0835133	−	0.257027i	−0.900577	−	0.434696i	$-0.856856\pi$
$167$	1.07923	−	3.32153i	0.0835133	−	0.257027i	0.984090	+	0.177669i	$0.0568557\pi$
$168$	−3.78887	+	2.75278i	−0.292318	+	0.212381i
$169$	−6.63000	−	4.81698i	−0.510000	−	0.370537i
$170$	−0.205630	−	0.632864i	−0.0157711	−	0.0485385i
$171$	0.0292360	+	0.0899791i	0.00223573	+	0.00688088i
$172$	−6.23314	−	4.52864i	−0.475272	−	0.345306i
$173$	−9.54554	+	6.93524i	−0.725734	+	0.527277i	−0.888211	−	0.459436i	$-0.848052\pi$
$173$	−9.54554	+	6.93524i	−0.725734	+	0.527277i	0.162477	+	0.986712i	$0.448052\pi$
$174$	0.407963	−	1.25558i	0.0309276	−	0.0951853i
$175$	−7.51584			−0.568144
$176$	−3.69676	−	8.87985i	−0.278654	−	0.669344i
$177$	−12.1642			−0.914317
$178$	−0.984448	+	3.02982i	−0.0737875	+	0.227095i
$179$	−4.28883	+	3.11602i	−0.320562	+	0.232902i	−0.736415	−	0.676530i	$-0.763483\pi$
$179$	−4.28883	+	3.11602i	−0.320562	+	0.232902i	0.415853	+	0.909432i	$0.363483\pi$
$180$	2.24055	+	1.62785i	0.167001	+	0.121333i
$181$	−2.97535	−	9.15719i	−0.221156	−	0.680649i	−0.998659	−	0.0517695i	$-0.983514\pi$
$181$	−2.97535	−	9.15719i	−0.221156	−	0.680649i	0.777503	−	0.628879i	$-0.216486\pi$
$182$	1.74842	+	5.38109i	0.129602	+	0.398873i
$183$	10.5550	+	7.66864i	0.780246	+	0.566882i
$184$	10.4150	−	7.56694i	0.767804	−	0.557842i
$185$	−3.66997	+	11.2950i	−0.269822	+	0.830426i
$186$	−2.03417			−0.149153
$187$	−1.27469	−	3.06189i	−0.0932147	−	0.223907i
$188$	−2.78199			−0.202898
$189$	0.872912	−	2.68655i	0.0634950	−	0.195418i
$190$	0.0509328	−	0.0370048i	0.00369505	−	0.00268461i
$191$	17.1510	+	12.4610i	1.24101	+	0.901643i	0.997665	−	0.0682980i	$-0.0217569\pi$
$191$	17.1510	+	12.4610i	1.24101	+	0.901643i	0.243340	+	0.969941i	$0.421757\pi$
$192$	−1.17694	−	3.62226i	−0.0849387	−	0.261414i
$193$	7.22140	+	22.2252i	0.519808	+	1.59980i	0.774361	+	0.632744i	$0.218072\pi$
$193$	7.22140	+	22.2252i	0.519808	+	1.59980i	−0.254553	+	0.967059i	$0.581928\pi$
$194$	−2.24165	−	1.62865i	−0.160941	−	0.116930i
$195$	5.69669	−	4.13889i	0.407948	−	0.296392i
$196$	−0.548077	+	1.68681i	−0.0391483	+	0.120486i
$197$	−0.769431			−0.0548197			−0.0274099	−	0.999624i	$-0.508726\pi$
$197$	−0.769431			−0.0548197			−0.0274099	+	0.999624i	$0.508726\pi$
$198$	−1.23167	−	0.751744i	−0.0875310	−	0.0534241i
$199$	−16.9533			−1.20179			−0.600895	−	0.799328i	$-0.705189\pi$
$199$	−16.9533			−1.20179			−0.600895	+	0.799328i	$0.705189\pi$
$200$	−1.36313	+	4.19527i	−0.0963876	+	0.296650i
$201$	−7.56281	+	5.49471i	−0.533440	+	0.387567i
$202$	3.03312	+	2.20369i	0.213410	+	0.155051i
$203$	−2.64881	−	8.15221i	−0.185910	−	0.572173i
$204$	−0.559542	−	1.72209i	−0.0391758	−	0.120571i
$205$	−8.78273	−	6.38102i	−0.613412	−	0.445670i
$206$	−5.72649	+	4.16054i	−0.398983	+	0.289878i
$207$	−2.39949	+	7.38488i	−0.166776	+	0.513285i
$208$	−13.3516			−0.925769
$209$	0.238239	−	0.204213i	0.0164794	−	0.0141257i
$210$	−1.87972			−0.129713
$211$	4.21880	−	12.9841i	0.290434	−	0.893864i	−0.694283	−	0.719702i	$-0.744278\pi$
$211$	4.21880	−	12.9841i	0.290434	−	0.893864i	0.984717	−	0.174162i	$-0.0557215\pi$
$212$	−19.0910	+	13.8704i	−1.31117	+	0.952624i
$213$	−0.528401	−	0.383905i	−0.0362054	−	0.0263048i
$214$	−0.0515785	−	0.158742i	−0.00352583	−	0.0108514i
$215$	−2.01107	−	6.18945i	−0.137154	−	0.422117i
$216$	−1.34129	−	0.974502i	−0.0912631	−	0.0663065i
$217$	−10.6850	+	7.76313i	−0.725347	+	0.526996i
$218$	−2.32806	+	7.16502i	−0.157676	+	0.485276i
$219$	0.904932			0.0611496
$220$	2.12830	−	8.93532i	0.143490	−	0.602419i
$221$	−4.60382			−0.309686
$222$	1.04394	−	3.21290i	0.0700644	−	0.215636i
$223$	19.0964	−	13.8744i	1.27879	−	0.929097i	0.279276	−	0.960211i	$-0.409906\pi$
$223$	19.0964	−	13.8744i	1.27879	−	0.929097i	0.999516	+	0.0311144i	$0.00990561\pi$
$224$	10.4612	+	7.60054i	0.698971	+	0.507832i
$225$	−0.822189	−	2.53044i	−0.0548126	−	0.168696i
$226$	0.0786290	+	0.241995i	0.00523033	+	0.0160973i
$227$	8.03720	+	5.83937i	0.533448	+	0.387573i	0.821646	−	0.569998i	$-0.193056\pi$
$227$	8.03720	+	5.83937i	0.533448	+	0.387573i	−0.288198	+	0.957571i	$0.593056\pi$
$228$	0.138594	−	0.100694i	0.00917859	−	0.00666863i
$229$	−5.90700	+	18.1799i	−0.390346	+	1.20136i	0.542182	+	0.840261i	$0.317599\pi$
$229$	−5.90700	+	18.1799i	−0.390346	+	1.20136i	−0.932527	+	0.361099i	$0.882401\pi$
$230$	5.16704			0.340704
$231$	−9.33860	+	0.751758i	−0.614435	+	0.0494621i
$232$	−5.03089			−0.330294
$233$	8.29927	−	25.5425i	0.543703	−	1.67335i	−0.180351	−	0.983602i	$-0.557723\pi$
$233$	8.29927	−	25.5425i	0.543703	−	1.67335i	0.724054	−	0.689744i	$-0.242277\pi$
$234$	−1.62044	+	1.17732i	−0.105932	+	0.0769638i
$235$	−1.90112	−	1.38125i	−0.124015	−	0.0901025i
$236$	6.80638	+	20.9479i	0.443058	+	1.36359i
$237$	−2.77155	−	8.52996i	−0.180032	−	0.554080i
$238$	0.994268	+	0.722378i	0.0644488	+	0.0468248i
$239$	11.8608	−	8.61739i	0.767213	−	0.557413i	−0.133902	−	0.990995i	$-0.542751\pi$
$239$	11.8608	−	8.61739i	0.767213	−	0.557413i	0.901114	+	0.433582i	$0.142751\pi$
$240$	1.37071	−	4.21861i	0.0884788	−	0.272310i
$241$	11.8393			0.762634			0.381317	−	0.924444i	$-0.375471\pi$
$241$	11.8393			0.762634			0.381317	+	0.924444i	$0.375471\pi$
$242$	−0.731758	+	4.72948i	−0.0470392	+	0.304022i
$243$	1.00000			0.0641500
$244$	7.30015	−	22.4676i	0.467344	−	1.43834i
$245$	−1.21203	+	0.880591i	−0.0774337	+	0.0562589i
$246$	2.49828	+	1.81510i	0.159284	+	0.115727i
$247$	−0.134597	−	0.414248i	−0.00856421	−	0.0263579i
$248$	2.39539	+	7.37226i	0.152108	+	0.468139i
$249$	5.18802	+	3.76932i	0.328777	+	0.238871i
$250$	−4.12409	+	2.99633i	−0.260830	+	0.189504i
$251$	−0.346997	+	1.06795i	−0.0219023	+	0.0674083i	−0.961410	−	0.275119i	$-0.911283\pi$
$251$	−0.346997	+	1.06795i	−0.0219023	+	0.0674083i	0.939508	+	0.342527i	$0.111283\pi$
$252$	−5.11491			−0.322209
$253$	25.6703	−	2.06646i	1.61388	−	0.129917i
$254$	−0.265923			−0.0166855
$255$	0.472638	−	1.45463i	0.0295978	−	0.0910926i
$256$	−2.35690	+	1.71239i	−0.147306	+	0.107024i
$257$	−18.4937	−	13.4365i	−1.15361	−	0.838144i	−0.164650	−	0.986352i	$-0.552650\pi$
$257$	−18.4937	−	13.4365i	−1.15361	−	0.838144i	−0.988956	+	0.148208i	$0.952650\pi$
$258$	0.572057	+	1.76061i	0.0356147	+	0.109611i
$259$	−6.77804	−	20.8607i	−0.421167	−	1.29622i
$260$	−10.3151	−	7.49434i	−0.639714	−	0.464779i
$261$	2.45493	−	1.78361i	0.151956	−	0.110403i
$262$	−0.430875	+	1.32610i	−0.0266195	+	0.0819265i
$263$	−1.35973			−0.0838445			−0.0419222	−	0.999121i	$-0.513348\pi$
$263$	−1.35973			−0.0838445			−0.0419222	+	0.999121i	$0.513348\pi$
$264$	−1.27409	+	5.34906i	−0.0784148	+	0.329212i
$265$	−19.9328			−1.22446
$266$	−0.0359305	+	0.110583i	−0.00220304	+	0.00678027i
$267$	−5.92393	+	4.30399i	−0.362539	+	0.263400i
$268$	13.6941	+	9.94935i	0.836500	+	0.607753i
$269$	−8.56569	−	26.3625i	−0.522259	−	1.60735i	−0.769672	−	0.638439i	$-0.779580\pi$
$269$	−8.56569	−	26.3625i	−0.522259	−	1.60735i	0.247413	−	0.968910i	$-0.420420\pi$
$270$	−0.205630	−	0.632864i	−0.0125143	−	0.0385149i
$271$	−24.5439	−	17.8322i	−1.49094	−	1.08323i	−0.973822	−	0.227313i	$-0.927006\pi$
$271$	−24.5439	−	17.8322i	−1.49094	−	1.08323i	−0.517115	−	0.855916i	$-0.672994\pi$
$272$	−2.34625	+	1.70465i	−0.142262	+	0.103359i
$273$	−4.01873	+	12.3684i	−0.243224	+	0.748568i
$274$	1.00391			0.0606483
$275$	−6.69988	+	5.74298i	−0.404018	+	0.346315i
$276$	14.0601			0.846317
$277$	−2.52928	+	7.78431i	−0.151969	+	0.467714i	−0.997841	−	0.0656723i	$-0.979081\pi$
$277$	−2.52928	+	7.78431i	−0.151969	+	0.467714i	0.845872	+	0.533386i	$0.179081\pi$
$278$	−5.44346	+	3.95490i	−0.326477	+	0.237199i
$279$	−3.78258	−	2.74820i	−0.226457	−	0.164531i
$280$	2.21351	+	6.81248i	0.132282	+	0.407124i
$281$	−3.52684	−	10.8545i	−0.210393	−	0.647524i	−0.999449	−	0.0332020i	$-0.989430\pi$
$281$	−3.52684	−	10.8545i	−0.210393	−	0.647524i	0.789055	−	0.614322i	$-0.210570\pi$
$282$	0.540780	+	0.392900i	0.0322030	+	0.0233969i
$283$	−17.2203	+	12.5113i	−1.02364	+	0.743720i	−0.967026	−	0.254676i	$-0.918031\pi$
$283$	−17.2203	+	12.5113i	−1.02364	+	0.743720i	−0.0566162	+	0.998396i	$0.518031\pi$
$284$	−0.365459	+	1.12477i	−0.0216860	+	0.0667426i
$285$	0.144705			0.00857156
$286$	5.67039	+	3.46089i	0.335297	+	0.204647i
$287$	20.0499			1.18351
$288$	−1.41456	+	4.35355i	−0.0833535	+	0.256536i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−1.63359	−	1.18687i	−0.0959276	−	0.0696955i
$291$	−1.96804	−	6.05701i	−0.115369	−	0.355068i
$292$	−0.506347	−	1.55838i	−0.0296317	−	0.0911971i
$293$	3.12523	+	2.27061i	0.182578	+	0.132651i	0.675320	−	0.737525i	$-0.264005\pi$
$293$	3.12523	+	2.27061i	0.182578	+	0.132651i	−0.492742	+	0.870175i	$0.664005\pi$
$294$	0.344766	−	0.250487i	0.0201071	−	0.0146087i
$295$	−5.74927	+	17.6944i	−0.334735	+	1.03021i
$296$	−12.8735			−0.748259
$297$	−1.27469	−	3.06189i	−0.0739651	−	0.177669i
$298$	−3.27425			−0.189672
$299$	11.0468	−	33.9986i	0.638855	−	1.96619i
$300$	−3.89760	+	2.83177i	−0.225028	+	0.163492i
$301$	9.72399	+	7.06489i	0.560482	+	0.407214i
$302$	−2.64498	−	8.14040i	−0.152201	−	0.468427i
$303$	2.66291	+	8.19559i	0.152980	+	0.470825i
$304$	−0.221978	−	0.161276i	−0.0127313	−	0.00924982i
$305$	16.1437	−	11.7291i	0.924387	−	0.671606i
$306$	−0.134444	+	0.413775i	−0.00768563	+	0.0236539i
$307$	−12.3198			−0.703131			−0.351565	−	0.936163i	$-0.614350\pi$
$307$	−12.3198			−0.703131			−0.351565	+	0.936163i	$0.614350\pi$
$308$	6.51994	+	15.6613i	0.371508	+	0.892385i
$309$	−16.2695			−0.925537
$310$	−0.961428	+	2.95897i	−0.0546055	+	0.168058i
$311$	−12.0170	+	8.73087i	−0.681422	+	0.495082i	−0.873829	−	0.486233i	$-0.838371\pi$
$311$	−12.0170	+	8.73087i	−0.681422	+	0.495082i	0.192407	+	0.981315i	$0.438371\pi$
$312$	6.17504	+	4.48643i	0.349593	+	0.253994i
$313$	1.76127	+	5.42062i	0.0995526	+	0.306391i	0.988413	−	0.151786i	$-0.0485024\pi$
$313$	1.76127	+	5.42062i	0.0995526	+	0.306391i	−0.888861	+	0.458177i	$0.848502\pi$
$314$	−2.01861	−	6.21264i	−0.113917	−	0.350599i
$315$	−3.49536	−	2.53953i	−0.196941	−	0.143086i
$316$	−13.1386	+	9.54573i	−0.739103	+	0.536990i
$317$	−0.0955985	+	0.294222i	−0.00536935	+	0.0165252i	−0.953705	−	0.300743i	$-0.902765\pi$
$317$	−0.0955985	+	0.294222i	−0.00536935	+	0.0165252i	0.948336	+	0.317268i	$0.102765\pi$
$318$	5.66994			0.317954
$319$	−8.59048	−	5.24316i	−0.480975	−	0.293561i
$320$	−5.82533			−0.325646
$321$	0.118553	−	0.364867i	0.00661696	−	0.0203649i
$322$	−7.72042	+	5.60921i	−0.430242	+	0.312589i
$323$	−0.0765408	−	0.0556102i	−0.00425885	−	0.00309423i
$324$	−0.559542	−	1.72209i	−0.0310857	−	0.0956718i
$325$	3.78521	+	11.6497i	0.209966	+	0.646208i
$326$	1.80389	+	1.31060i	0.0999084	+	0.0725877i
$327$	−14.0091	+	10.1782i	−0.774707	+	0.562857i
$328$	3.63640	−	11.1917i	0.200787	−	0.617958i
$329$	4.34004			0.239274
$330$	−1.67565	+	1.43632i	−0.0922412	+	0.0790670i
$331$	−7.01157			−0.385391			−0.192695	−	0.981259i	$-0.561723\pi$
$331$	−7.01157			−0.385391			−0.192695	+	0.981259i	$0.561723\pi$
$332$	3.58820	−	11.0433i	0.196928	−	0.606082i
$333$	6.28190	−	4.56407i	0.344246	−	0.250110i
$334$	1.22927	+	0.893116i	0.0672626	+	0.0488691i
$335$	4.41830	+	13.5981i	0.241397	+	0.742944i
$336$	2.53155	+	7.79131i	0.138107	+	0.425051i
$337$	−4.66760	−	3.39121i	−0.254261	−	0.184731i	0.453352	−	0.891331i	$-0.350228\pi$
$337$	−4.66760	−	3.39121i	−0.254261	−	0.184731i	−0.707613	+	0.706600i	$0.750228\pi$
$338$	2.88451	−	2.09572i	0.156896	−	0.113992i
$339$	−0.180728	+	0.556223i	−0.00981579	+	0.0302099i
$340$	−2.76947			−0.150196
$341$	−3.59307	+	15.0849i	−0.194576	+	0.816895i
$342$	−0.0411617			−0.00222577
$343$	−5.25536	+	16.1743i	−0.283763	+	0.873332i
$344$	5.70717	−	4.14650i	0.307710	−	0.223564i
$345$	9.60819	+	6.98076i	0.517287	+	0.375831i
$346$	−1.58629	−	4.88210i	−0.0852796	−	0.262463i
$347$	1.89470	+	5.83128i	0.101713	+	0.313039i	0.988945	−	0.148284i	$-0.0473749\pi$
$347$	1.89470	+	5.83128i	0.101713	+	0.313039i	−0.887232	+	0.461323i	$0.847375\pi$
$348$	−4.44517	−	3.22961i	−0.238286	−	0.173125i
$349$	17.8642	−	12.9791i	0.956248	−	0.694755i	0.00397147	−	0.999992i	$-0.498736\pi$
$349$	17.8642	−	12.9791i	0.956248	−	0.694755i	0.952276	+	0.305237i	$0.0987358\pi$
$350$	1.01046	−	3.10987i	0.0540112	−	0.166229i
$351$	−4.60382			−0.245734
$352$	15.1332	−	1.21823i	0.806603	−	0.0649316i
$353$	−21.0837			−1.12217			−0.561085	−	0.827758i	$-0.689616\pi$
$353$	−21.0837			−1.12217			−0.561085	+	0.827758i	$0.689616\pi$
$354$	1.63540	−	5.03324i	0.0869205	−	0.267514i
$355$	−0.808183	+	0.587180i	−0.0428939	+	0.0311643i
$356$	10.7266	+	7.79330i	0.568507	+	0.413044i
$357$	0.872912	+	2.68655i	0.0461994	+	0.142187i
$358$	−0.712723	−	2.19354i	−0.0376686	−	0.115932i
$359$	24.1731	+	17.5628i	1.27581	+	0.926929i	0.999418	−	0.0341171i	$-0.0108619\pi$
$359$	24.1731	+	17.5628i	1.27581	+	0.926929i	0.276390	+	0.961046i	$0.410862\pi$
$360$	−2.05149	+	1.49049i	−0.108123	+	0.0785558i
$361$	−5.86856	+	18.0616i	−0.308871	+	0.950608i
$362$	4.18903			0.220171
$363$	−7.75032	+	7.80593i	−0.406787	+	0.409705i
$364$	23.5481			1.23426
$365$	0.427705	−	1.31634i	0.0223871	−	0.0689005i
$366$	−4.59214	+	3.33638i	−0.240035	+	0.174395i
$367$	−23.5303	−	17.0957i	−1.22827	−	0.892390i	−0.231511	−	0.972832i	$-0.574367\pi$
$367$	−23.5303	−	17.0957i	−1.22827	−	0.892390i	−0.996759	+	0.0804421i	$0.974367\pi$
$368$	−6.95882	−	21.4170i	−0.362754	−	1.11644i
$369$	2.19335	+	6.75043i	0.114181	+	0.351413i
$370$	−4.18019	−	3.03708i	−0.217318	−	0.157890i
$371$	29.7829	−	21.6385i	1.54625	−	1.12342i
$372$	−2.61615	+	8.05168i	−0.135641	+	0.417460i
$373$	−25.6329			−1.32722			−0.663611	−	0.748078i	$-0.730977\pi$
$373$	−25.6329			−1.32722			−0.663611	+	0.748078i	$0.730977\pi$
$374$	1.43831	−	0.115784i	0.0743731	−	0.00598704i
$375$	−11.7169			−0.605058
$376$	0.787140	−	2.42257i	0.0405937	−	0.124934i
$377$	−11.3020	+	8.21140i	−0.582084	+	0.422909i
$378$	0.994268	+	0.722378i	0.0511396	+	0.0371551i
$379$	−1.80735	−	5.56246i	−0.0928375	−	0.285724i	0.893847	−	0.448373i	$-0.147996\pi$
$379$	−1.80735	−	5.56246i	−0.0928375	−	0.285724i	−0.986684	+	0.162648i	$0.947996\pi$
$380$	−0.0809682	−	0.249195i	−0.00415358	−	0.0127834i
$381$	−0.494489	−	0.359267i	−0.0253334	−	0.0184058i
$382$	−7.46187	+	5.42137i	−0.381783	+	0.277381i
$383$	10.8330	−	33.3404i	0.553539	−	1.70362i	−0.146233	−	0.989250i	$-0.546715\pi$
$383$	10.8330	−	33.3404i	0.553539	−	1.70362i	0.699771	−	0.714367i	$-0.253285\pi$
$384$	10.8122			0.551759
$385$	−3.32025	+	13.9395i	−0.169216	+	0.710424i
$386$	−10.1671			−0.517491
$387$	−1.31487	+	4.04674i	−0.0668384	+	0.205707i
$388$	−9.32953	+	6.77830i	−0.473635	+	0.344116i
$389$	25.2220	+	18.3249i	1.27881	+	0.929107i	0.999516	−	0.0310994i	$-0.00990085\pi$
$389$	25.2220	+	18.3249i	1.27881	+	0.929107i	0.279290	+	0.960207i	$0.409901\pi$
$390$	0.946683	+	2.91359i	0.0479372	+	0.147535i
$391$	−2.39949	−	7.38488i	−0.121348	−	0.373470i
$392$	−1.31380	−	0.954534i	−0.0663571	−	0.0482113i
$393$	−2.59280	+	1.88378i	−0.130789	+	0.0950240i
$394$	0.103445	−	0.318371i	0.00521149	−	0.0160393i
$395$	−13.7179			−0.690222
$396$	−4.55961	+	3.90839i	−0.229129	+	0.196404i
$397$	17.8178			0.894251			0.447125	−	0.894471i	$-0.352448\pi$
$397$	17.8178			0.894251			0.447125	+	0.894471i	$0.352448\pi$
$398$	2.27927	−	7.01487i	0.114249	−	0.351623i
$399$	−0.216213	+	0.157088i	−0.0108242	+	0.00786422i
$400$	6.24257	+	4.53549i	0.312128	+	0.226775i
$401$	−10.4951	−	32.3007i	−0.524102	−	1.61302i	−0.766085	−	0.642740i	$-0.777798\pi$
$401$	−10.4951	−	32.3007i	−0.524102	−	1.61302i	0.241983	−	0.970281i	$-0.422202\pi$
$402$	−1.25680	−	3.86803i	−0.0626834	−	0.192920i
$403$	17.4143	+	12.6522i	0.867468	+	0.630252i
$404$	12.6236	−	9.17156i	0.628046	−	0.456302i
$405$	0.472638	−	1.45463i	0.0234856	−	0.0722812i
$406$	3.72929			0.185082
$407$	−21.9822	−	13.4167i	−1.08962	−	0.665042i
$408$	1.65792			0.0820794
$409$	−1.45723	+	4.48488i	−0.0720551	+	0.221763i	−0.980598	−	0.196028i	$-0.937196\pi$
$409$	−1.45723	+	4.48488i	−0.0720551	+	0.221763i	0.908543	+	0.417791i	$0.137196\pi$
$410$	3.82109	−	2.77618i	0.188710	−	0.137106i
$411$	1.86678	+	1.35630i	0.0920816	+	0.0669012i
$412$	9.10344	+	28.0175i	0.448494	+	1.38032i
$413$	−10.6183	−	32.6797i	−0.522491	−	1.60806i
$414$	−2.73308	−	1.98570i	−0.134324	−	0.0975918i
$415$	7.93502	−	5.76513i	0.389515	−	0.282999i
$416$	6.51235	−	20.0430i	0.319294	−	0.982687i
$417$	−15.4653			−0.757341
$418$	0.0524684	+	0.126033i	0.00256632	+	0.00616445i
$419$	−8.91290			−0.435423			−0.217712	−	0.976013i	$-0.569859\pi$
$419$	−8.91290			−0.435423			−0.217712	+	0.976013i	$0.569859\pi$
$420$	−2.41750	+	7.44031i	−0.117962	+	0.363050i
$421$	3.76433	−	2.73495i	0.183462	−	0.133293i	−0.492263	−	0.870446i	$-0.663830\pi$
$421$	3.76433	−	2.73495i	0.183462	−	0.133293i	0.675726	+	0.737153i	$0.263830\pi$
$422$	4.80531	+	3.49126i	0.233919	+	0.169952i
$423$	0.474775	+	1.46121i	0.0230844	+	0.0710463i
$424$	−6.67678	−	20.5490i	−0.324253	−	0.997949i
$425$	2.15252	+	1.56390i	0.104413	+	0.0758601i
$426$	0.229890	−	0.167025i	0.0111382	−	0.00809240i
$427$	−11.3886	+	35.0505i	−0.551132	+	1.69621i
$428$	−0.694670			−0.0335782
$429$	5.86845	+	14.0964i	0.283331	+	0.680579i
$430$	2.83141			0.136543
$431$	−9.96982	+	30.6840i	−0.480229	+	1.47799i	0.358544	+	0.933513i	$0.383273\pi$
$431$	−9.96982	+	30.6840i	−0.480229	+	1.47799i	−0.838773	+	0.544481i	$0.816727\pi$
$432$	−2.34625	+	1.70465i	−0.112884	+	0.0820149i
$433$	−29.8162	−	21.6627i	−1.43287	−	1.04104i	−0.989473	−	0.144720i	$-0.953772\pi$
$433$	−29.8162	−	21.6627i	−1.43287	−	1.04104i	−0.443401	−	0.896323i	$-0.646228\pi$
$434$	−1.77565	−	5.46490i	−0.0852341	−	0.262324i
$435$	−1.43420	−	4.41401i	−0.0687646	−	0.211636i
$436$	25.3665	+	18.4299i	1.21484	+	0.882631i
$437$	0.594334	−	0.431809i	0.0284308	−	0.0206562i
$438$	−0.121662	+	0.374438i	−0.00581325	+	0.0178913i
$439$	−28.0363			−1.33810			−0.669049	−	0.743218i	$-0.733298\pi$
$439$	−28.0363			−1.33810			−0.669049	+	0.743218i	$0.733298\pi$
$440$	7.17873	+	4.38150i	0.342233	+	0.208880i
$441$	0.979510			0.0466433
$442$	0.618954	−	1.90494i	0.0294406	−	0.0906089i
$443$	23.4579	−	17.0432i	1.11452	−	0.809745i	0.131149	−	0.991363i	$-0.458133\pi$
$443$	23.4579	−	17.0432i	1.11452	−	0.809745i	0.983369	+	0.181617i	$0.0581333\pi$
$444$	−11.3747	−	8.26423i	−0.539821	−	0.392203i
$445$	3.46084	+	10.6514i	0.164060	+	0.504923i
$446$	3.17347	+	9.76694i	0.150268	+	0.462478i
$447$	−6.08852	−	4.42357i	−0.287977	−	0.209228i
$448$	8.70401	−	6.32383i	0.411226	−	0.298773i
$449$	0.364819	−	1.12280i	0.0172169	−	0.0529880i	−0.942079	−	0.335391i	$-0.891132\pi$
$449$	0.364819	−	1.12280i	0.0172169	−	0.0529880i	0.959296	+	0.282403i	$0.0911315\pi$
$450$	1.15757			0.0545684
$451$	17.8732	−	15.3205i	0.841617	−	0.721414i
$452$	1.05899			0.0498108
$453$	6.07944	−	18.7106i	0.285637	−	0.879101i
$454$	−3.49673	+	2.54053i	−0.164110	+	0.119233i
$455$	16.0920	+	11.6915i	0.754405	+	0.548108i
$456$	0.0484710	+	0.149178i	0.00226986	+	0.00698592i
$457$	7.98072	+	24.5621i	0.373322	+	1.14897i	0.944604	+	0.328214i	$0.106447\pi$
$457$	7.98072	+	24.5621i	0.373322	+	1.14897i	−0.571281	+	0.820754i	$0.693553\pi$
$458$	−6.72822	−	4.88834i	−0.314389	−	0.228417i
$459$	−0.809017	+	0.587785i	−0.0377617	+	0.0274355i
$460$	6.64533	−	20.4522i	0.309840	−	0.953589i
$461$	−10.4035			−0.484540			−0.242270	−	0.970209i	$-0.577892\pi$
$461$	−10.4035			−0.484540			−0.242270	+	0.970209i	$0.577892\pi$
$462$	0.944456	−	3.96515i	0.0439401	−	0.184475i
$463$	30.6319			1.42358			0.711792	−	0.702391i	$-0.247884\pi$
$463$	30.6319			1.42358			0.711792	+	0.702391i	$0.247884\pi$
$464$	−2.71944	+	8.36957i	−0.126247	+	0.388547i
$465$	−5.78541	+	4.20335i	−0.268292	+	0.194926i
$466$	9.45307	+	6.86805i	0.437905	+	0.318156i
$467$	−0.158811	−	0.488769i	−0.00734888	−	0.0226175i	0.947315	−	0.320304i	$-0.103785\pi$
$467$	−0.158811	−	0.488769i	−0.00734888	−	0.0226175i	−0.954664	+	0.297686i	$0.903785\pi$
$468$	2.57603	+	7.92820i	0.119077	+	0.366481i
$469$	−21.3635	−	15.5215i	−0.986473	−	0.716714i
$470$	0.827118	−	0.600937i	0.0381521	−	0.0277191i
$471$	4.63975	−	14.2797i	0.213788	−	0.657973i
$472$	−20.1673			−0.928275
$473$	14.0667	−	1.13237i	0.646788	−	0.0520665i
$474$	3.90210			0.179229
$475$	−0.0777871	+	0.239404i	−0.00356911	+	0.0109846i
$476$	4.13805	−	3.00647i	0.189667	−	0.137801i
$477$	10.5433	+	7.66019i	0.482746	+	0.350736i
$478$	1.97105	+	6.06626i	0.0901536	+	0.277464i
$479$	−3.12573	−	9.62000i	−0.142818	−	0.439549i	0.853906	−	0.520428i	$-0.174227\pi$
$479$	−3.12573	−	9.62000i	−0.142818	−	0.439549i	−0.996724	+	0.0808785i	$0.974227\pi$
$480$	5.66424	+	4.11531i	0.258536	+	0.187837i
$481$	−28.9207	+	21.0122i	−1.31867	+	0.958072i
$482$	−1.59171	+	4.89879i	−0.0725005	+	0.223134i
$483$	−21.9344			−0.998049
$484$	17.7792	+	8.97903i	0.808144	+	0.408138i
$485$	−9.74088			−0.442311
$486$	−0.134444	+	0.413775i	−0.00609848	+	0.0187692i
$487$	3.75897	−	2.73105i	0.170335	−	0.123756i	−0.499352	−	0.866399i	$-0.666428\pi$
$487$	3.75897	−	2.73105i	0.170335	−	0.123756i	0.669687	+	0.742644i	$0.266428\pi$
$488$	17.4993	+	12.7140i	0.792157	+	0.575536i
$489$	1.58372	+	4.87418i	0.0716182	+	0.220418i
$490$	−0.201417	−	0.619897i	−0.00909908	−	0.0280041i
$491$	−11.6249	−	8.44598i	−0.524624	−	0.381162i	0.293719	−	0.955892i	$-0.405107\pi$
$491$	−11.6249	−	8.44598i	−0.524624	−	0.381162i	−0.818343	+	0.574730i	$0.805107\pi$
$492$	10.3976	−	7.55429i	0.468760	−	0.340574i
$493$	−0.937698	+	2.88594i	−0.0422318	+	0.129976i
$494$	0.189501			0.00852605
$495$	−5.05639	+	0.407040i	−0.227268	+	0.0182951i
$496$	13.5596			0.608843
$497$	0.570133	−	1.75469i	0.0255740	−	0.0787085i
$498$	−2.25714	+	1.63991i	−0.101145	+	0.0734862i
$499$	0.391459	+	0.284412i	0.0175241	+	0.0127320i	0.596513	−	0.802604i	$-0.296552\pi$
$499$	0.391459	+	0.284412i	0.0175241	+	0.0127320i	−0.578989	+	0.815336i	$0.696552\pi$
$500$	6.55610	+	20.1776i	0.293198	+	0.902369i
$501$	1.07923	+	3.32153i	0.0482164	+	0.148395i
$502$	−0.395238	−	0.287158i	−0.0176404	−	0.0128165i
$503$	0.396654	−	0.288186i	0.0176859	−	0.0128496i	−0.578907	−	0.815393i	$-0.696521\pi$
$503$	0.396654	−	0.288186i	0.0176859	−	0.0128496i	0.596593	+	0.802544i	$0.296521\pi$
$504$	1.44722	−	4.45409i	0.0644643	−	0.198401i
$505$	13.1802			0.586510
$506$	−2.59616	+	10.8995i	−0.115413	+	0.484544i
$507$	8.19513			0.363959
$508$	−0.342004	+	1.05258i	−0.0151740	+	0.0467007i
$509$	3.27114	−	2.37662i	0.144991	−	0.105342i	−0.512925	−	0.858433i	$-0.671438\pi$
$509$	3.27114	−	2.37662i	0.144991	−	0.105342i	0.657916	+	0.753091i	$0.271438\pi$
$510$	0.538347	+	0.391132i	0.0238384	+	0.0173196i
$511$	0.789926	+	2.43114i	0.0349443	+	0.107547i
$512$	−7.07400	−	21.7715i	−0.312629	−	0.962174i
$513$	−0.0765408	−	0.0556102i	−0.00337936	−	0.00245525i
$514$	8.04604	−	5.84579i	0.354895	−	0.257847i
$515$	−7.68957	+	23.6661i	−0.338843	+	1.04285i
$516$	7.70458			0.339175
$517$	3.86886	−	3.31630i	0.170152	−	0.145851i
$518$	9.54288			0.419290
$519$	3.64607	−	11.2215i	0.160045	−	0.492567i
$520$	9.44467	−	6.86195i	0.414176	−	0.300916i
$521$	28.9354	+	21.0228i	1.26768	+	0.921026i	0.999108	−	0.0422327i	$-0.0134471\pi$
$521$	28.9354	+	21.0228i	1.26768	+	0.921026i	0.268576	+	0.963259i	$0.413447\pi$
$522$	0.407963	+	1.25558i	0.0178561	+	0.0549553i
$523$	−11.1248	−	34.2385i	−0.486452	−	1.49714i	−0.829867	−	0.557961i	$-0.811584\pi$
$523$	−11.1248	−	34.2385i	−0.486452	−	1.49714i	0.343416	−	0.939184i	$-0.388416\pi$
$524$	4.69482	+	3.41098i	0.205094	+	0.149010i
$525$	6.08044	−	4.41770i	0.265372	−	0.192804i
$526$	0.182807	−	0.562621i	0.00797075	−	0.0245315i
$527$	4.67552			0.203669
$528$	8.21018	+	5.01105i	0.357302	+	0.218078i
$529$	37.2941			1.62148
$530$	2.67983	−	8.24767i	0.116404	−	0.358256i
$531$	9.84105	−	7.14994i	0.427065	−	0.310281i
$532$	0.391500	+	0.284441i	0.0169737	+	0.0123321i
$533$	−10.0978	−	31.0777i	−0.437383	−	1.34613i
$534$	−0.984448	−	3.02982i	−0.0426012	−	0.131113i
$535$	−0.474715	−	0.344901i	−0.0205237	−	0.0149114i
$536$	−12.5386	+	9.10980i	−0.541583	+	0.393483i
$537$	1.63819	−	5.04182i	0.0706930	−	0.217571i
$538$	12.0597			0.519932
$539$	−1.24857	−	2.99915i	−0.0537798	−	0.129183i
$540$	−2.76947			−0.119179
$541$	1.79004	−	5.50916i	0.0769596	−	0.236857i	−0.905174	−	0.425041i	$-0.860260\pi$
$541$	1.79004	−	5.50916i	0.0769596	−	0.236857i	0.982134	+	0.188183i	$0.0602598\pi$
$542$	10.6783	−	7.75823i	0.458672	−	0.333245i
$543$	7.78957	+	5.65946i	0.334283	+	0.242871i
$544$	−1.41456	−	4.35355i	−0.0606485	−	0.186657i
$545$	8.18432	+	25.1887i	0.350578	+	1.07897i
$546$	−4.57743	−	3.32570i	−0.195896	−	0.142327i
$547$	16.6811	−	12.1195i	0.713232	−	0.518194i	−0.170982	−	0.985274i	$-0.554694\pi$
$547$	16.6811	−	12.1195i	0.713232	−	0.518194i	0.884215	+	0.467080i	$0.154694\pi$
$548$	1.29113	−	3.97368i	0.0551542	−	0.169747i
$549$	−13.0467			−0.556818
$550$	−1.47554	−	3.54435i	−0.0629174	−	0.151132i
$551$	−0.287089			−0.0122304
$552$	−3.97817	+	12.2436i	−0.169322	+	0.521121i
$553$	20.4968	−	14.8918i	0.871613	−	0.633264i
$554$	−2.88091	−	2.09310i	−0.122398	−	0.0889274i
$555$	−3.66997	−	11.2950i	−0.155782	−	0.479447i
$556$	8.65351	+	26.6328i	0.366990	+	1.12948i
$557$	33.5833	+	24.3997i	1.42297	+	1.03385i	0.991273	+	0.131828i	$0.0420846\pi$
$557$	33.5833	+	24.3997i	1.42297	+	1.03385i	0.431696	+	0.902019i	$0.357915\pi$
$558$	1.64568	−	1.19566i	0.0696672	−	0.0506162i
$559$	6.05340	−	18.6304i	0.256032	−	0.787984i
$560$	12.5300			0.529489
$561$	2.83098	+	1.72788i	0.119524	+	0.0729509i
$562$	4.96547			0.209456
$563$	2.55561	−	7.86535i	0.107706	−	0.331485i	−0.882650	−	0.470031i	$-0.844243\pi$
$563$	2.55561	−	7.86535i	0.107706	−	0.331485i	0.990356	+	0.138546i	$0.0442428\pi$
$564$	2.25068	−	1.63521i	0.0947706	−	0.0688549i
$565$	0.723681	+	0.525785i	0.0304455	+	0.0221199i
$566$	−2.86170	−	8.80741i	−0.120286	−	0.370203i
$567$	0.872912	+	2.68655i	0.0366589	+	0.112824i
$568$	−0.876047	−	0.636485i	−0.0367581	−	0.0267063i
$569$	5.58279	−	4.05614i	0.234043	−	0.170042i	−0.464582	−	0.885530i	$-0.653796\pi$
$569$	5.58279	−	4.05614i	0.234043	−	0.170042i	0.698625	+	0.715488i	$0.253796\pi$
$570$	−0.0194546	+	0.0598751i	−0.000814863	+	0.00250789i
$571$	5.19937			0.217587			0.108794	−	0.994064i	$-0.465301\pi$
$571$	5.19937			0.217587			0.108794	+	0.994064i	$0.465301\pi$
$572$	20.9916	−	17.9935i	0.877704	−	0.752347i
$573$	−21.1998			−0.885636
$574$	−2.69559	+	8.29616i	−0.112512	+	0.346275i
$575$	−16.7142	+	12.1435i	−0.697028	+	0.506421i
$576$	3.08128	+	2.23868i	0.128387	+	0.0932784i
$577$	7.27139	+	22.3791i	0.302712	+	0.931652i	0.980521	+	0.196414i	$0.0629297\pi$
$577$	7.27139	+	22.3791i	0.302712	+	0.931652i	−0.677809	+	0.735238i	$0.737070\pi$
$578$	−0.134444	−	0.413775i	−0.00559212	−	0.0172108i
$579$	−18.9059	−	13.7359i	−0.785701	−	0.570845i
$580$	−6.79884	+	4.93965i	−0.282307	+	0.205108i
$581$	−5.59776	+	17.2281i	−0.232234	+	0.714743i
$582$	2.77083			0.114854
$583$	10.0151	−	42.0469i	0.414784	−	1.74140i
$584$	1.50031			0.0620831
$585$	−2.17594	+	6.69686i	−0.0899641	+	0.276881i
$586$	−1.35969	+	0.987872i	−0.0561682	+	0.0408086i
$587$	−21.9230	−	15.9280i	−0.904861	−	0.657420i	0.0348493	−	0.999393i	$-0.488905\pi$
$587$	−21.9230	−	15.9280i	−0.904861	−	0.657420i	−0.939710	+	0.341973i	$0.888905\pi$
$588$	−0.548077	−	1.68681i	−0.0226023	−	0.0695627i
$589$	0.136694	+	0.420700i	0.00563236	+	0.0173346i
$590$	−6.54856	−	4.75780i	−0.269600	−	0.195876i
$591$	0.622483	−	0.452260i	0.0256055	−	0.0186035i
$592$	−6.95876	+	21.4169i	−0.286003	+	0.880228i
$593$	2.08537			0.0856358			0.0428179	−	0.999083i	$-0.486366\pi$
$593$	2.08537			0.0856358			0.0428179	+	0.999083i	$0.486366\pi$
$594$	1.43831	−	0.115784i	0.0590144	−	0.00475067i
$595$	4.32051			0.177124
$596$	−4.21101	+	12.9602i	−0.172490	+	0.530869i
$597$	13.7155	−	9.96492i	0.561340	−	0.407837i
$598$	12.5826	+	9.14180i	0.514541	+	0.373836i
$599$	6.86030	+	21.1138i	0.280304	+	0.862687i	0.987767	+	0.155937i	$0.0498397\pi$
$599$	6.86030	+	21.1138i	0.280304	+	0.862687i	−0.707463	+	0.706751i	$0.750160\pi$
$600$	−1.36313	−	4.19527i	−0.0556494	−	0.171271i
$601$	22.6324	+	16.4434i	0.923195	+	0.670741i	0.944317	−	0.329036i	$-0.106724\pi$
$601$	22.6324	+	16.4434i	0.923195	+	0.670741i	−0.0211219	+	0.999777i	$0.506724\pi$
$602$	−4.23060	+	3.07371i	−0.172427	+	0.125275i
$603$	2.88874	−	8.89062i	0.117638	−	0.362054i
$604$	−35.6231			−1.44948
$605$	7.69164	+	14.9632i	0.312710	+	0.608342i
$606$	−3.74914			−0.152298
$607$	3.09565	−	9.52744i	0.125649	−	0.386707i	−0.868370	−	0.495917i	$-0.834832\pi$
$607$	3.09565	−	9.52744i	0.125649	−	0.386707i	0.994019	+	0.109210i	$0.0348321\pi$
$608$	0.350373	−	0.254561i	0.0142095	−	0.0103238i
$609$	6.93468	+	5.03834i	0.281007	+	0.204164i
$610$	2.68279	+	8.25677i	0.108623	+	0.334307i
$611$	−2.18578	−	6.72713i	−0.0884271	−	0.272151i
$612$	1.46490	+	1.06431i	0.0592151	+	0.0430223i
$613$	−5.84687	+	4.24800i	−0.236153	+	0.171575i	−0.699568	−	0.714566i	$-0.746624\pi$
$613$	−5.84687	+	4.24800i	−0.236153	+	0.171575i	0.463415	+	0.886142i	$0.346624\pi$
$614$	1.65632	−	5.09764i	0.0668438	−	0.205724i
$615$	10.8560			0.437758
$616$	−15.4827	+	1.24636i	−0.623815	+	0.0502172i
$617$	−19.3172			−0.777679			−0.388840	−	0.921305i	$-0.627124\pi$
$617$	−19.3172			−0.777679			−0.388840	+	0.921305i	$0.627124\pi$
$618$	2.18732	−	6.73189i	0.0879871	−	0.270796i
$619$	−12.3802	+	8.99471i	−0.497600	+	0.361528i	−0.808100	−	0.589046i	$-0.799504\pi$
$619$	−12.3802	+	8.99471i	−0.497600	+	0.361528i	0.310499	+	0.950574i	$0.399504\pi$
$620$	10.4757	+	7.61107i	0.420716	+	0.305668i
$621$	−2.39949	−	7.38488i	−0.0962884	−	0.296345i
$622$	−1.99700	−	6.14615i	−0.0800726	−	0.246438i
$623$	−16.7339	−	12.1579i	−0.670431	−	0.487097i
$624$	10.8017	−	7.84789i	0.432414	−	0.314167i
$625$	−1.42691	+	4.39158i	−0.0570765	+	0.175663i
$626$	−2.47971			−0.0991090
$627$	−0.0727062	+	0.305245i	−0.00290361	+	0.0121903i
$628$	−27.1871			−1.08488
$629$	−2.39947	+	7.38482i	−0.0956733	+	0.294452i
$630$	1.52072	−	1.10487i	0.0605871	−	0.0440191i
$631$	−10.6014	−	7.70233i	−0.422033	−	0.306625i	0.356422	−	0.934325i	$-0.383996\pi$
$631$	−10.6014	−	7.70233i	−0.422033	−	0.306625i	−0.778455	+	0.627700i	$0.783996\pi$
$632$	−4.59502	−	14.1420i	−0.182780	−	0.562539i
$633$	4.21880	+	12.9841i	0.167682	+	0.516072i
$634$	−0.108889	−	0.0791125i	−0.00432454	−	0.00314196i
$635$	−0.756316	+	0.549495i	−0.0300135	+	0.0218061i
$636$	7.29211	−	22.4428i	0.289151	−	0.889915i
$637$	−4.50948			−0.178672
$638$	3.32442	−	2.84962i	0.131615	−	0.112817i
$639$	0.653139			0.0258378
$640$	5.11027	−	15.7278i	0.202001	−	0.621696i
$641$	18.2707	−	13.2744i	0.721648	−	0.524308i	−0.165262	−	0.986250i	$-0.552847\pi$
$641$	18.2707	−	13.2744i	0.721648	−	0.524308i	0.886910	+	0.461942i	$0.152847\pi$
$642$	0.135034	+	0.0981081i	0.00532938	+	0.00387202i
$643$	5.77710	+	17.7801i	0.227826	+	0.701178i	0.997992	+	0.0633341i	$0.0201734\pi$
$643$	5.77710	+	17.7801i	0.227826	+	0.701178i	−0.770166	+	0.637844i	$0.779827\pi$
$644$	12.2732	+	37.7730i	0.483632	+	1.48847i
$645$	5.26506	+	3.82529i	0.207311	+	0.150621i
$646$	0.0333005	−	0.0241942i	0.00131019	−	0.000951909i
$647$	1.74251	−	5.36290i	0.0685052	−	0.210837i	−0.910943	−	0.412531i	$-0.864645\pi$
$647$	1.74251	−	5.36290i	0.0685052	−	0.210837i	0.979449	+	0.201694i	$0.0646447\pi$
$648$	1.65792			0.0651293
$649$	−34.4366	−	21.0182i	−1.35176	−	0.825037i
$650$	−5.32924			−0.209030
$651$	4.08132	−	12.5610i	0.159960	−	0.492305i
$652$	7.50763	−	5.45461i	0.294022	−	0.213619i
$653$	−4.38331	−	3.18466i	−0.171532	−	0.124625i	0.498707	−	0.866771i	$-0.333808\pi$
$653$	−4.38331	−	3.18466i	−0.171532	−	0.124625i	−0.670239	+	0.742145i	$0.733808\pi$
$654$	−2.32806	−	7.16502i	−0.0910342	−	0.280175i
$655$	1.51475	+	4.66191i	0.0591860	+	0.182156i
$656$	−16.6532	−	12.0993i	−0.650200	−	0.472398i
$657$	−0.732105	+	0.531905i	−0.0285621	+	0.0207516i
$658$	−0.583490	+	1.79580i	−0.0227468	+	0.0700075i
$659$	33.2872			1.29669			0.648343	−	0.761349i	$-0.275462\pi$
$659$	33.2872			1.29669			0.648343	+	0.761349i	$0.275462\pi$
$660$	3.53022	+	8.47981i	0.137414	+	0.330076i
$661$	7.54735			0.293558			0.146779	−	0.989169i	$-0.453109\pi$
$661$	7.54735			0.293558			0.146779	+	0.989169i	$0.453109\pi$
$662$	0.942660	−	2.90121i	0.0366375	−	0.112759i
$663$	3.72457	−	2.70606i	0.144650	−	0.105095i
$664$	8.60133	+	6.24923i	0.333796	+	0.242517i
$665$	0.126314	+	0.388756i	0.00489826	+	0.0150753i
$666$	1.04394	+	3.21290i	0.0404517	+	0.124498i
$667$	−19.0623	−	13.8496i	−0.738096	−	0.536258i
$668$	5.11610	−	3.71707i	0.197948	−	0.143818i
$669$	−7.29419	+	22.4492i	−0.282010	+	0.867936i
$670$	−6.22057			−0.240322
$671$	16.6305	+	39.9474i	0.642012	+	1.54215i
$672$	−12.9308			−0.498817
$673$	8.21802	−	25.2925i	0.316782	−	0.974953i	−0.658233	−	0.752814i	$-0.728696\pi$
$673$	8.21802	−	25.2925i	0.316782	−	0.974953i	0.975015	−	0.222139i	$-0.0713040\pi$
$674$	2.03073	−	1.47541i	0.0782207	−	0.0568307i
$675$	2.15252	+	1.56390i	0.0828505	+	0.0601944i
$676$	−4.58552	−	14.1128i	−0.176366	−	0.542799i
$677$	−2.49887	−	7.69074i	−0.0960395	−	0.295579i	0.891484	−	0.453053i	$-0.149665\pi$
$677$	−2.49887	−	7.69074i	−0.0960395	−	0.295579i	−0.987523	+	0.157474i	$0.949665\pi$
$678$	−0.205853	−	0.149561i	−0.00790576	−	0.00574387i
$679$	14.5545	−	10.5745i	0.558551	−	0.405811i
$680$	0.783598	−	2.41167i	0.0300496	−	0.0924832i
$681$	−9.93453			−0.380692
$682$	−5.75870	−	3.51480i	−0.220512	−	0.134589i
$683$	0.691058			0.0264426			0.0132213	−	0.999913i	$-0.495791\pi$
$683$	0.691058			0.0264426			0.0132213	+	0.999913i	$0.495791\pi$
$684$	−0.0529381	+	0.162927i	−0.00202414	+	0.00622965i
$685$	2.85522	−	2.07444i	0.109093	−	0.0792604i
$686$	−5.98598	−	4.34907i	−0.228546	−	0.166048i
$687$	−5.90700	−	18.1799i	−0.225366	−	0.693606i
$688$	−3.81327	−	11.7360i	−0.145379	−	0.447432i
$689$	−48.5396	−	35.2661i	−1.84921	−	1.34353i
$690$	−4.18022	+	3.03711i	−0.159138	+	0.115621i
$691$	4.83119	−	14.8689i	0.183787	−	0.565638i	−0.816138	−	0.577857i	$-0.803889\pi$
$691$	4.83119	−	14.8689i	0.183787	−	0.565638i	0.999925	+	0.0122182i	$0.00388928\pi$
$692$	−21.3645			−0.812157
$693$	7.11321	−	6.09728i	0.270209	−	0.231616i
$694$	−2.66757			−0.101259
$695$	−7.30951	+	22.4964i	−0.277266	+	0.853336i
$696$	4.07008	−	2.95708i	0.154276	−	0.112088i
$697$	−5.74226	−	4.17199i	−0.217504	−	0.158026i
$698$	2.96869	+	9.13670i	0.112367	+	0.345829i
$699$	8.29927	+	25.5425i	0.313907	+	0.966107i
$700$	−11.0100	−	7.99920i	−0.416137	−	0.302341i
$701$	−17.8595	+	12.9757i	−0.674542	+	0.490084i	−0.871543	−	0.490320i	$-0.836880\pi$
$701$	−17.8595	+	12.9757i	−0.674542	+	0.490084i	0.197000	+	0.980403i	$0.436880\pi$
$702$	0.618954	−	1.90494i	0.0233609	−	0.0718975i
$703$	−0.734631			−0.0277071
$704$	2.92691	−	12.2882i	0.110312	−	0.463128i
$705$	2.34992			0.0885029
$706$	2.83456	−	8.72389i	0.106680	−	0.328328i
$707$	−19.6934	+	14.3081i	−0.740645	+	0.538110i
$708$	−17.8193	−	12.9465i	−0.669691	−	0.486559i
$709$	7.11850	+	21.9085i	0.267341	+	0.822790i	0.991145	+	0.132785i	$0.0423919\pi$
$709$	7.11850	+	21.9085i	0.267341	+	0.822790i	−0.723804	+	0.690005i	$0.757608\pi$
$710$	−0.134305	−	0.413348i	−0.00504038	−	0.0155127i
$711$	7.25601	+	5.27180i	0.272122	+	0.197708i
$712$	−9.82142	+	7.13568i	−0.368073	+	0.267421i
$713$	−11.2189	+	34.5282i	−0.420151	+	1.29309i
$714$	−1.22898			−0.0459935
$715$	23.2787	−	1.87394i	0.870573	−	0.0700813i
$716$	−9.59911			−0.358736
$717$	−4.53043	+	13.9432i	−0.169192	+	0.520719i
$718$	−10.5170	+	7.64102i	−0.392489	+	0.285160i
$719$	7.11294	+	5.16785i	0.265268	+	0.192728i	0.712466	−	0.701707i	$-0.247578\pi$
$719$	7.11294	+	5.16785i	0.265268	+	0.192728i	−0.447198	+	0.894435i	$0.647578\pi$
$720$	1.37071	+	4.21861i	0.0510833	+	0.157218i
$721$	−14.2018	−	43.7087i	−0.528903	−	1.62780i
$722$	−6.68443	−	4.85652i	−0.248769	−	0.180741i
$723$	−9.57816	+	6.95894i	−0.356216	+	0.258806i
$724$	5.38752	−	16.5811i	0.200225	−	0.616231i
$725$	8.07365			0.299848
$726$	−2.18791	−	4.25635i	−0.0812011	−	0.157968i
$727$	−25.0311			−0.928354			−0.464177	−	0.885743i	$-0.653650\pi$
$727$	−25.0311			−0.928354			−0.464177	+	0.885743i	$0.653650\pi$
$728$	−6.66274	+	20.5058i	−0.246938	+	0.759996i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.487167	+	0.353947i	0.0180309	+	0.0131002i
$731$	−1.31487	−	4.04674i	−0.0486321	−	0.149674i
$732$	7.30015	+	22.4676i	0.269821	+	0.830425i
$733$	10.1074	+	7.34344i	0.373325	+	0.271236i	0.758588	−	0.651570i	$-0.225889\pi$
$733$	10.1074	+	7.34344i	0.373325	+	0.271236i	−0.385264	+	0.922807i	$0.625889\pi$
$734$	10.2373	−	7.43782i	0.377865	−	0.274535i
$735$	0.462954	−	1.42483i	0.0170763	−	0.0525555i
$736$	35.5447			1.31019
$737$	−30.9043	+	2.48780i	−1.13838	+	0.0916394i
$738$	−3.08804			−0.113672
$739$	−14.6318	+	45.0321i	−0.538240	+	1.65653i	0.198303	+	0.980141i	$0.436457\pi$
$739$	−14.6318	+	45.0321i	−0.538240	+	1.65653i	−0.736543	+	0.676391i	$0.763543\pi$
$740$	−17.3976	+	12.6401i	−0.639547	+	0.464658i
$741$	0.352380	+	0.256019i	0.0129450	+	0.00940509i
$742$	4.94936	+	15.2326i	0.181697	+	0.559205i
$743$	7.68142	+	23.6410i	0.281804	+	0.867303i	0.987338	+	0.158628i	$0.0507070\pi$
$743$	7.68142	+	23.6410i	0.281804	+	0.867303i	−0.705535	+	0.708676i	$0.749293\pi$
$744$	−6.27122	−	4.55631i	−0.229914	−	0.167042i
$745$	−9.31233	+	6.76580i	−0.341177	+	0.247880i
$746$	3.44618	−	10.6062i	0.126174	−	0.388322i
$747$	−6.41274			−0.234630
$748$	1.39151	−	5.84203i	0.0508786	−	0.213606i
$749$	1.08372			0.0395982
$750$	1.57526	−	4.84816i	0.0575205	−	0.177030i
$751$	−32.6497	+	23.7214i	−1.19141	+	0.865606i	−0.993412	−	0.114597i	$-0.963442\pi$
$751$	−32.6497	+	23.7214i	−1.19141	+	0.865606i	−0.197993	+	0.980203i	$0.563442\pi$
$752$	−3.60478	−	2.61903i	−0.131453	−	0.0955062i
$753$	−0.346997	−	1.06795i	−0.0126453	−	0.0389182i
$754$	−1.87819	−	5.78047i	−0.0683995	−	0.210512i
$755$	−24.3437	−	17.6867i	−0.885956	−	0.643685i
$756$	4.13805	−	3.00647i	0.150499	−	0.109344i
$757$	7.73897	−	23.8181i	0.281278	−	0.865684i	−0.706212	−	0.708001i	$-0.749597\pi$
$757$	7.73897	−	23.8181i	0.281278	−	0.865684i	0.987490	−	0.157684i	$-0.0504026\pi$
$758$	2.54459			0.0924238
$759$	−19.5531	+	16.7604i	−0.709732	+	0.608365i
$760$	0.239909			0.00870241
$761$	9.05008	−	27.8533i	0.328065	−	1.00968i	−0.641973	−	0.766727i	$-0.721884\pi$
$761$	9.05008	−	27.8533i	0.328065	−	1.00968i	0.970038	−	0.242953i	$-0.0781161\pi$
$762$	0.215137	−	0.156306i	0.00779357	−	0.00566236i
$763$	−39.5730	−	28.7515i	−1.43264	−	1.04087i
$764$	11.8622	+	36.5081i	0.429159	+	1.32082i
$765$	0.472638	+	1.45463i	0.0170883	+	0.0525923i
$766$	12.3390	+	8.96482i	0.445827	+	0.323912i
$767$	−45.3064	+	32.9170i	−1.63592	+	1.18856i
$768$	0.900255	−	2.77070i	0.0324852	−	0.0999790i
$769$	50.4870			1.82061			0.910304	−	0.413941i	$-0.135848\pi$
$769$	50.4870			1.82061			0.910304	+	0.413941i	$0.135848\pi$
$770$	−5.32144	−	3.24792i	−0.191771	−	0.117047i
$771$	22.8595			0.823265
$772$	−13.0759	+	40.2435i	−0.470612	+	1.44839i
$773$	5.98248	−	4.34652i	0.215175	−	0.156334i	−0.474977	−	0.879998i	$-0.657544\pi$
$773$	5.98248	−	4.34652i	0.215175	−	0.156334i	0.690152	+	0.723665i	$0.257544\pi$
$774$	−1.49766	−	1.08812i	−0.0538324	−	0.0391115i
$775$	−3.84417	−	11.8311i	−0.138086	−	0.424987i
$776$	−3.26286	−	10.0420i	−0.117130	−	0.360489i
$777$	17.7451	+	12.8926i	0.636603	+	0.462519i
$778$	−10.9733	+	7.97257i	−0.393412	+	0.285831i
$779$	0.207512	−	0.638656i	0.00743488	−	0.0228822i
$780$	12.7501			0.456528
$781$	−0.832551	−	1.99984i	−0.0297910	−	0.0715599i
$782$	3.37827			0.120807
$783$	−0.937698	+	2.88594i	−0.0335106	+	0.103135i
$784$	−2.29817	+	1.66972i	−0.0820775	+	0.0596328i
$785$	−18.5787	−	13.4982i	−0.663104	−	0.481773i
$786$	−0.430875	−	1.32610i	−0.0153688	−	0.0473003i
$787$	−2.13349	−	6.56621i	−0.0760507	−	0.234060i	0.905803	−	0.423698i	$-0.139268\pi$
$787$	−2.13349	−	6.56621i	−0.0760507	−	0.234060i	−0.981854	+	0.189639i	$0.939268\pi$
$788$	−1.12714	−	0.818915i	−0.0401527	−	0.0291726i
$789$	1.10004	−	0.799228i	0.0391626	−	0.0284533i
$790$	1.84428	−	5.67611i	0.0656166	−	0.201947i
$791$	−1.65208			−0.0587412
$792$	−2.11334	−	5.07637i	−0.0750942	−	0.180381i
$793$	60.0644			2.13295
$794$	−2.39549	+	7.37256i	−0.0850128	+	0.261643i
$795$	16.1259	−	11.7162i	0.571928	−	0.415530i
$796$	−24.8349	−	18.0436i	−0.880251	−	0.639540i
$797$	6.49920	+	20.0025i	0.230213	+	0.708524i	0.997720	+	0.0674833i	$0.0214970\pi$
$797$	6.49920	+	20.0025i	0.230213	+	0.708524i	−0.767507	+	0.641041i	$0.778503\pi$
$798$	−0.0359305	−	0.110583i	−0.00127193	−	0.00391459i
$799$	−1.24298	−	0.903076i	−0.0439734	−	0.0319485i
$800$	−9.85337	+	7.15889i	−0.348369	+	0.253105i
$801$	2.26274	−	6.96400i	0.0799500	−	0.246061i
$802$	14.7762			0.521766
$803$	2.56184	+	1.56361i	0.0904055	+	0.0551786i
$804$	−16.9268			−0.596964
$805$	−10.3670	+	31.9064i	−0.365390	+	1.12455i
$806$	−7.57641	+	5.50459i	−0.266868	+	0.193891i
$807$	22.4253	+	16.2929i	0.789407	+	0.573538i
$808$	4.41490	+	13.5877i	0.155316	+	0.478012i
$809$	2.52508	+	7.77139i	0.0887770	+	0.273227i	0.985582	−	0.169199i	$-0.0541179\pi$
$809$	2.52508	+	7.77139i	0.0887770	+	0.273227i	−0.896805	+	0.442426i	$0.854118\pi$
$810$	0.538347	+	0.391132i	0.0189156	+	0.0137430i
$811$	−17.6590	+	12.8300i	−0.620091	+	0.450523i	−0.852953	−	0.521987i	$-0.825191\pi$
$811$	−17.6590	+	12.8300i	−0.620091	+	0.450523i	0.232862	+	0.972510i	$0.425191\pi$
$812$	4.79624	−	14.7613i	0.168315	−	0.518021i
$813$	30.3380			1.06400
$814$	8.50686	−	7.29188i	0.298165	−	0.255580i
$815$	7.83866			0.274576
$816$	0.896187	−	2.75818i	0.0313728	−	0.0965556i
$817$	0.325681	−	0.236621i	0.0113941	−	0.00827832i
$818$	−1.65981	−	1.20593i	−0.0580341	−	0.0421642i
$819$	−4.01873	−	12.3684i	−0.140426	−	0.432186i
$820$	−6.07441	−	18.6951i	−0.212128	−	0.652862i
$821$	43.7797	+	31.8078i	1.52792	+	1.11010i	0.957380	+	0.288832i	$0.0932670\pi$
$821$	43.7797	+	31.8078i	1.52792	+	1.11010i	0.570542	+	0.821268i	$0.306733\pi$
$822$	−0.812178	+	0.590082i	−0.0283280	+	0.0205815i
$823$	−6.11454	+	18.8186i	−0.213139	+	0.655975i	0.786141	+	0.618047i	$0.212076\pi$
$823$	−6.11454	+	18.8186i	−0.213139	+	0.655975i	−0.999280	+	0.0379284i	$0.987924\pi$
$824$	−26.9735			−0.939666
$825$	2.04468	−	8.58426i	0.0711866	−	0.298866i
$826$	14.9496			0.520163
$827$	−11.5530	+	35.5564i	−0.401736	+	1.23642i	0.521854	+	0.853035i	$0.325241\pi$
$827$	−11.5530	+	35.5564i	−0.401736	+	1.23642i	−0.923590	+	0.383382i	$0.874759\pi$
$828$	−11.3748	+	8.26430i	−0.395303	+	0.287204i
$829$	−39.4347	−	28.6510i	−1.36963	−	0.995091i	−0.997766	−	0.0668016i	$-0.978721\pi$
$829$	−39.4347	−	28.6510i	−1.36963	−	0.995091i	−0.371859	−	0.928289i	$-0.621279\pi$
$830$	1.31865	+	4.05840i	0.0457711	+	0.140869i
$831$	−2.52928	−	7.78431i	−0.0877396	−	0.270035i
$832$	−14.1857	−	10.3065i	−0.491799	−	0.357313i
$833$	−0.792440	+	0.575741i	−0.0274564	+	0.0199483i
$834$	2.07922	−	6.39917i	0.0719974	−	0.221585i
$835$	5.34168			0.184857
$836$	0.566343	−	0.0455907i	0.0195874	−	0.00157679i
$837$	4.67552			0.161610
$838$	1.19828	−	3.68793i	0.0413940	−	0.127397i
$839$	44.0258	−	31.9866i	1.51994	−	1.10430i	0.558423	−	0.829556i	$-0.311407\pi$
$839$	44.0258	−	31.9866i	1.51994	−	1.10430i	0.961517	−	0.274745i	$-0.0885934\pi$
$840$	−5.79504	−	4.21034i	−0.199948	−	0.145271i
$841$	−6.11609	−	18.8234i	−0.210900	−	0.649082i
$842$	0.625562	+	1.92528i	0.0215583	+	0.0663496i
$843$	9.23338	+	6.70844i	0.318014	+	0.231051i
$844$	19.9993	−	14.5303i	0.688403	−	0.500154i
$845$	3.87334	−	11.9209i	0.133247	−	0.410091i
$846$	−0.668441			−0.0229815
$847$	−27.7363	−	14.0077i	−0.953032	−	0.481311i
$848$	−37.7952			−1.29789
$849$	6.57758	−	20.2437i	0.225742	−	0.694763i
$850$	−0.936494	+	0.680402i	−0.0321215	+	0.0233376i
$851$	−48.7785	−	35.4397i	−1.67211	−	1.21486i
$852$	−0.365459	−	1.12477i	−0.0125204	−	0.0385338i
$853$	−3.92854	−	12.0908i	−0.134511	−	0.413981i	0.861003	−	0.508600i	$-0.169837\pi$
$853$	−3.92854	−	12.0908i	−0.134511	−	0.413981i	−0.995514	+	0.0946188i	$0.969837\pi$
$854$	−12.9719	−	9.42462i	−0.443889	−	0.322504i
$855$	−0.117068	+	0.0850552i	−0.00400366	+	0.00290883i
$856$	0.196551	−	0.604922i	0.00671797	−	0.0206758i
$857$	−9.03881			−0.308760			−0.154380	−	0.988012i	$-0.549338\pi$
$857$	−9.03881			−0.308760			−0.154380	+	0.988012i	$0.549338\pi$
$858$	−6.62170	+	0.533048i	−0.226061	+	0.0181979i
$859$	27.4207			0.935583			0.467791	−	0.883839i	$-0.345050\pi$
$859$	27.4207			0.935583			0.467791	+	0.883839i	$0.345050\pi$
$860$	3.64148	−	11.2073i	0.124173	−	0.382167i
$861$	−16.2207	+	11.7851i	−0.552801	+	0.401634i
$862$	−11.3559	−	8.25052i	−0.386782	−	0.281014i
$863$	3.56850	+	10.9827i	0.121473	+	0.373856i	0.993242	−	0.116061i	$-0.0370269\pi$
$863$	3.56850	+	10.9827i	0.121473	+	0.373856i	−0.871769	+	0.489917i	$0.837027\pi$
$864$	−1.41456	−	4.35355i	−0.0481241	−	0.148111i
$865$	−14.5998	−	10.6074i	−0.496408	−	0.360662i
$866$	12.9721	−	9.42477i	0.440809	−	0.320267i
$867$	0.309017	−	0.951057i	0.0104948	−	0.0322996i
$868$	−23.9149			−0.811724
$869$	6.89250	−	28.9370i	0.233812	−	0.981621i
$870$	2.01923			0.0684582
$871$	−13.2992	+	40.9308i	−0.450627	+	1.38689i
$872$	−23.2260	+	16.8747i	−0.786533	+	0.571450i
$873$	5.15240	+	3.74344i	0.174382	+	0.126696i
$874$	0.0987672	+	0.303974i	0.00334085	+	0.0102821i
$875$	−10.2278	−	31.4780i	−0.345764	−	1.06415i
$876$	1.32563	+	0.963129i	0.0447890	+	0.0325411i
$877$	−41.0864	+	29.8510i	−1.38739	+	1.00800i	−0.391244	+	0.920287i	$0.627955\pi$
$877$	−41.0864	+	29.8510i	−1.38739	+	1.00800i	−0.996146	+	0.0877108i	$0.972045\pi$
$878$	3.76930	−	11.6007i	0.127208	−	0.391505i
$879$	−3.86300			−0.130296
$880$	11.1697	−	9.57438i	0.376530	−	0.322752i
$881$	3.90441			0.131543			0.0657715	−	0.997835i	$-0.479049\pi$
$881$	3.90441			0.131543			0.0657715	+	0.997835i	$0.479049\pi$
$882$	−0.131689	+	0.405296i	−0.00443419	+	0.0136470i
$883$	6.00226	−	4.36090i	0.201992	−	0.146756i	−0.482191	−	0.876066i	$-0.660159\pi$
$883$	6.00226	−	4.36090i	0.201992	−	0.146756i	0.684183	+	0.729310i	$0.260159\pi$
$884$	−6.74413	−	4.89990i	−0.226830	−	0.164801i
$885$	−5.74927	−	17.6944i	−0.193260	−	0.594792i
$886$	3.89827	+	11.9976i	0.130965	+	0.403068i
$887$	31.1246	+	22.6134i	1.04506	+	0.759282i	0.971267	−	0.237991i	$-0.0764889\pi$
$887$	31.1246	+	22.6134i	1.04506	+	0.759282i	0.0737950	+	0.997273i	$0.476489\pi$
$888$	10.4149	−	7.56688i	0.349502	−	0.253928i
$889$	0.533543	−	1.64208i	0.0178944	−	0.0550735i
$890$	−4.87256			−0.163328
$891$	2.83098	+	1.72788i	0.0948414	+	0.0578860i
$892$	42.7410			1.43107
$893$	0.0449183	−	0.138244i	0.00150313	−	0.00462617i
$894$	2.64892	−	1.92455i	0.0885932	−	0.0643667i
$895$	−6.55972	−	4.76591i	−0.219267	−	0.159307i
$896$	9.43812	+	29.0476i	0.315306	+	0.970411i
$897$	11.0468	+	33.9986i	0.368843	+	1.13518i
$898$	0.415537	+	0.301906i	0.0138667	+	0.0100747i
$899$	11.4781	−	8.33930i	0.382815	−	0.278131i
$900$	1.48875	−	4.58190i	0.0496250	−	0.152730i
$901$	−13.0323			−0.434168
$902$	3.93630	+	9.45523i	0.131064	+	0.314825i
$903$	−12.0195			−0.399984
$904$	−0.299633	+	0.922175i	−0.00996564	+	0.0306711i
$905$	11.9141	−	8.65608i	0.396037	−	0.287738i
$906$	6.92463	+	5.03104i	0.230056	+	0.167145i
$907$	5.66817	+	17.4448i	0.188209	+	0.579246i	0.999989	−	0.00471652i	$-0.00150132\pi$
$907$	5.66817	+	17.4448i	0.188209	+	0.579246i	−0.811780	+	0.583963i	$0.801501\pi$
$908$	5.55879	+	17.1082i	0.184475	+	0.567755i
$909$	−6.97159	−	5.06516i	−0.231233	−	0.168001i
$910$	−7.00113	+	5.08662i	−0.232085	+	0.168620i
$911$	−14.8456	+	45.6901i	−0.491857	+	1.51378i	0.329942	+	0.944001i	$0.392971\pi$
$911$	−14.8456	+	45.6901i	−0.491857	+	1.51378i	−0.821799	+	0.569778i	$0.807029\pi$
$912$	0.274379			0.00908561
$913$	8.17427	+	19.6351i	0.270529	+	0.649827i
$914$	−11.2361			−0.371659
$915$	−6.16635	+	18.9781i	−0.203853	+	0.627396i
$916$	−28.0022	+	20.3448i	−0.925220	+	0.672212i
$917$	−7.32414	−	5.32130i	−0.241864	−	0.175725i
$918$	−0.134444	−	0.413775i	−0.00443730	−	0.0136566i
$919$	8.16492	+	25.1290i	0.269336	+	0.828931i	0.990663	+	0.136336i	$0.0435326\pi$
$919$	8.16492	+	25.1290i	0.269336	+	0.828931i	−0.721327	+	0.692595i	$0.756467\pi$
$920$	15.9296	+	11.5736i	0.525184	+	0.381569i
$921$	9.96696	−	7.24142i	0.328423	−	0.238613i
$922$	1.39869	−	4.30472i	0.0460633	−	0.141768i
$923$	−3.00693			−0.0989744
$924$	−14.4802	−	8.83793i	−0.476364	−	0.290747i
$925$	20.6597			0.679285
$926$	−4.11826	+	12.6747i	−0.135334	+	0.416516i
$927$	13.1623	−	9.56295i	0.432306	−	0.314088i
$928$	−11.2377	−	8.16464i	−0.368894	−	0.268017i
$929$	−5.39320	−	16.5986i	−0.176945	−	0.544581i	0.822772	−	0.568372i	$-0.192427\pi$
$929$	−5.39320	−	16.5986i	−0.176945	−	0.544581i	−0.999717	+	0.0237906i	$0.992427\pi$
$930$	−0.961428	−	2.95897i	−0.0315265	−	0.0970285i
$931$	−0.0749725	−	0.0544707i	−0.00245712	−	0.00178520i
$932$	39.3428	−	28.5842i	1.28872	−	0.936307i
$933$	4.59009	−	14.1268i	0.150273	−	0.462492i
$934$	0.223591			0.00731613
$935$	3.85145	−	3.30137i	0.125956	−	0.107966i
$936$	−7.63277			−0.249485
$937$	1.66476	−	5.12361i	0.0543854	−	0.167381i	−0.920174	−	0.391509i	$-0.871953\pi$
$937$	1.66476	−	5.12361i	0.0543854	−	0.167381i	0.974560	+	0.224128i	$0.0719533\pi$
$938$	9.29457	−	6.75290i	0.303478	−	0.220490i
$939$	−4.61105	−	3.35013i	−0.150476	−	0.109327i
$940$	−1.31488	−	4.04677i	−0.0428865	−	0.131991i
$941$	5.19338	+	15.9836i	0.169299	+	0.521050i	0.999327	−	0.0366720i	$-0.0116757\pi$
$941$	5.19338	+	15.9836i	0.169299	+	0.521050i	−0.830028	+	0.557722i	$0.811676\pi$
$942$	5.28478	+	3.83962i	0.172188	+	0.125102i
$943$	44.5882	−	32.3952i	1.45199	−	1.05493i
$944$	−10.9014	+	33.5510i	−0.354810	+	1.09199i
$945$	4.32051			0.140546
$946$	−1.42263	+	5.97269i	−0.0462538	+	0.194189i
$947$	−20.1426			−0.654545			−0.327273	−	0.944930i	$-0.606130\pi$
$947$	−20.1426			−0.654545			−0.327273	+	0.944930i	$0.606130\pi$
$948$	5.01849	−	15.4453i	0.162993	−	0.501641i
$949$	3.37048	−	2.44880i	0.109410	−	0.0794913i
$950$	−0.0886013	−	0.0643726i	−0.00287461	−	0.00208852i
$951$	−0.0955985	−	0.294222i	−0.00309999	−	0.00954080i
$952$	1.44722	+	4.45409i	0.0469047	+	0.144358i
$953$	−32.7543	−	23.7974i	−1.06102	−	0.770873i	−0.0867395	−	0.996231i	$-0.527645\pi$
$953$	−32.7543	−	23.7974i	−1.06102	−	0.770873i	−0.974276	+	0.225358i	$0.927645\pi$
$954$	−4.58708	+	3.33271i	−0.148512	+	0.107900i
$955$	−10.0199	+	30.8380i	−0.324235	+	0.997893i
$956$	26.5465			0.858575
$957$	10.0317	−	0.807553i	0.324279	−	0.0261045i
$958$	4.40075			0.142182
$959$	−2.01422	+	6.19913i	−0.0650425	+	0.200180i
$960$	4.71279	−	3.42404i	0.152105	−	0.110510i
$961$	7.39400	+	5.37205i	0.238516	+	0.173292i
$962$	−4.80609	−	14.7916i	−0.154955	−	0.476901i
$963$	0.118553	+	0.364867i	0.00382030	+	0.0117577i
$964$	17.3433	+	12.6007i	0.558591	+	0.405840i
$965$	−28.9163	+	21.0089i	−0.930850	+	0.676302i
$966$	2.94894	−	9.07589i	0.0948805	−	0.292012i
$967$	16.5138			0.531050			0.265525	−	0.964104i	$-0.414455\pi$
$967$	16.5138			0.531050			0.265525	+	0.964104i	$0.414455\pi$
$968$	−12.8494	+	12.9416i	−0.412997	+	0.415959i
$969$	0.0946097			0.00303930
$970$	1.30960	−	4.03053i	0.0420487	−	0.129413i
$971$	−14.4462	+	10.4958i	−0.463599	+	0.336825i	−0.794942	−	0.606686i	$-0.792499\pi$
$971$	−14.4462	+	10.4958i	−0.463599	+	0.336825i	0.331342	+	0.943511i	$0.392499\pi$
$972$	1.46490	+	1.06431i	0.0469867	+	0.0341378i
$973$	−13.4999	−	41.5484i	−0.432786	−	1.33198i
$974$	0.624670	+	1.92254i	0.0200157	+	0.0616021i
$975$	−9.90981	−	7.19990i	−0.317368	−	0.230581i
$976$	30.6107	−	22.2400i	0.979824	−	0.711884i
$977$	−8.34589	+	25.6860i	−0.267009	+	0.821769i	0.724215	+	0.689574i	$0.242202\pi$
$977$	−8.34589	+	25.6860i	−0.267009	+	0.821769i	−0.991224	+	0.132194i	$0.957798\pi$
$978$	−2.22973			−0.0712990
$979$	−24.2073	+	1.94869i	−0.773669	+	0.0622804i
$980$	−2.71272			−0.0866548
$981$	5.35101	−	16.4687i	0.170845	−	0.525806i
$982$	5.05762	−	3.67458i	0.161395	−	0.117261i
$983$	35.4607	+	25.7637i	1.13102	+	0.821735i	0.985843	−	0.167671i	$-0.0536245\pi$
$983$	35.4607	+	25.7637i	1.13102	+	0.821735i	0.145178	+	0.989406i	$0.453625\pi$
$984$	3.63640	+	11.1917i	0.115924	+	0.356778i
$985$	−0.363663	−	1.11924i	−0.0115873	−	0.0356619i
$986$	−1.06806	−	0.775992i	−0.0340140	−	0.0247126i
$987$	−3.51117	+	2.55101i	−0.111762	+	0.0811996i
$988$	0.243717	−	0.750084i	0.00775368	−	0.0238634i
$989$	33.0397			1.05060
$990$	0.511376	−	2.14693i	0.0162526	−	0.0682339i
$991$	−20.2423			−0.643018			−0.321509	−	0.946906i	$-0.604190\pi$
$991$	−20.2423			−0.643018			−0.321509	+	0.946906i	$0.604190\pi$
$992$	−6.61379	+	20.3551i	−0.209988	+	0.646276i
$993$	5.67248	−	4.12130i	0.180011	−	0.130785i
$994$	0.649395	+	0.471813i	0.0205976	+	0.0149650i
$995$	−8.01280	−	24.6609i	−0.254023	−	0.781802i
$996$	3.58820	+	11.0433i	0.113696	+	0.349922i
$997$	16.2628	+	11.8156i	0.515049	+	0.374205i	0.814736	−	0.579833i	$-0.196882\pi$
$997$	16.2628	+	11.8156i	0.515049	+	0.374205i	−0.299687	+	0.954038i	$0.596882\pi$
$998$	−0.170312	+	0.123739i	−0.00539112	+	0.00391688i
$999$	−2.39947	+	7.38482i	−0.0759160	+	0.233645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.460.3	✓	24
11.4	even	5		6171.2.a.bk.1.6		12
11.5	even	5	inner	561.2.m.d.511.3	yes	24
11.7	odd	10		6171.2.a.bl.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.460.3	✓	24	1.1	even	1	trivial
561.2.m.d.511.3	yes	24	11.5	even	5	inner
6171.2.a.bk.1.6		12	11.4	even	5
6171.2.a.bl.1.7		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)

\(f(q)\)	\(=\)	\(q+(-0.134444 + 0.413775i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.46490 + 1.06431i) q^{4} +(0.472638 + 1.45463i) q^{5} +(-0.134444 - 0.413775i) q^{6} +(-2.28531 - 1.66038i) q^{7} +(-1.34129 + 0.974502i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.134444 + 0.413775i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.46490 + 1.06431i) q^{4} +(0.472638 + 1.45463i) q^{5} +(-0.134444 - 0.413775i) q^{6} +(-2.28531 - 1.66038i) q^{7} +(-1.34129 + 0.974502i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.665433 q^{10} +(-3.30593 + 0.266128i) q^{11} -1.81072 q^{12} +(-1.42266 + 4.37849i) q^{13} +(0.994268 - 0.722378i) q^{14} +(-1.23738 - 0.899012i) q^{15} +(0.896187 + 2.75818i) q^{16} +(0.309017 + 0.951057i) q^{17} +(0.351978 + 0.255727i) q^{18} +(-0.0765408 + 0.0556102i) q^{19} +(-0.855814 + 2.63392i) q^{20} +2.82480 q^{21} +(0.334344 - 1.40369i) q^{22} -7.76492 q^{23} +(0.512326 - 1.57678i) q^{24} +(2.15252 - 1.56390i) q^{25} +(-1.62044 - 1.17732i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.58060 - 4.86457i) q^{28} +(2.45493 + 1.78361i) q^{29} +(0.538347 - 0.391132i) q^{30} +(1.44482 - 4.44669i) q^{31} -4.57760 q^{32} +(2.51813 - 2.15848i) q^{33} -0.435069 q^{34} +(1.33511 - 4.10905i) q^{35} +(1.46490 - 1.06431i) q^{36} +(6.28190 + 4.56407i) q^{37} +(-0.0127197 - 0.0391471i) q^{38} +(-1.42266 - 4.37849i) q^{39} +(-2.05149 - 1.49049i) q^{40} +(-5.74226 + 4.17199i) q^{41} +(-0.379777 + 1.16883i) q^{42} -4.25499 q^{43} +(-5.12610 - 3.12869i) q^{44} +1.52949 q^{45} +(1.04394 - 3.21293i) q^{46} +(-1.24298 + 0.903076i) q^{47} +(-2.34625 - 1.70465i) q^{48} +(0.302685 + 0.931569i) q^{49} +(0.357709 + 1.10091i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(-6.74413 + 4.89990i) q^{52} +(-4.02720 + 12.3944i) q^{53} -0.435069 q^{54} +(-1.94963 - 4.68313i) q^{55} +4.68330 q^{56} +(0.0292360 - 0.0899791i) q^{57} +(-1.06806 + 0.775992i) q^{58} +(9.84105 + 7.14994i) q^{59} +(-0.855814 - 2.63392i) q^{60} +(-4.03164 - 12.4081i) q^{61} +(1.64568 + 1.19566i) q^{62} +(-2.28531 + 1.66038i) q^{63} +(-1.17694 + 3.62226i) q^{64} -7.04149 q^{65} +(0.554578 + 1.33213i) q^{66} +9.34815 q^{67} +(-0.559542 + 1.72209i) q^{68} +(6.28196 - 4.56411i) q^{69} +(1.52072 + 1.10487i) q^{70} +(0.201831 + 0.621172i) q^{71} +(0.512326 + 1.57678i) q^{72} +(-0.732105 - 0.531905i) q^{73} +(-2.73306 + 1.98568i) q^{74} +(-0.822189 + 2.53044i) q^{75} -0.171311 q^{76} +(7.99696 + 4.88091i) q^{77} +2.00298 q^{78} +(-2.77155 + 8.52996i) q^{79} +(-3.58856 + 2.60724i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.954256 - 2.93690i) q^{82} +(-1.98165 - 6.09888i) q^{83} +(4.13805 + 3.00647i) q^{84} +(-1.23738 + 0.899012i) q^{85} +(0.572057 - 1.76061i) q^{86} -3.03445 q^{87} +(4.17486 - 3.57859i) q^{88} +7.32239 q^{89} +(-0.205630 + 0.632864i) q^{90} +(10.5212 - 7.64407i) q^{91} +(-11.3748 - 8.26430i) q^{92} +(1.44482 + 4.44669i) q^{93} +(-0.206560 - 0.635725i) q^{94} +(-0.117068 - 0.0850552i) q^{95} +(3.70335 - 2.69064i) q^{96} +(-1.96804 + 6.05701i) q^{97} -0.426154 q^{98} +(-0.768486 + 3.22636i) 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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