LMFDB - Embedded newform 525.2.n.c.106.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (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:	$4.19214610612$
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			106.3
Character	$\chi$	$=$	525.106
Dual form			525.2.n.c.421.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.262997 - 0.809422i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.03204 - 0.749819i) q^{4} +(2.19857 + 0.407800i) q^{5} +(0.688536 + 0.500250i) q^{6} +1.00000 q^{7} +(-2.25541 - 1.63865i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.262997 - 0.809422i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.03204 - 0.749819i) q^{4} +(2.19857 + 0.407800i) q^{5} +(0.688536 + 0.500250i) q^{6} +1.00000 q^{7} +(-2.25541 - 1.63865i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.248135 - 1.88682i) q^{10} +(-1.56133 - 4.80529i) q^{11} +(-0.394203 + 1.21323i) q^{12} +(-0.139126 + 0.428185i) q^{13} +(-0.262997 - 0.809422i) q^{14} +(-2.01838 + 0.962369i) q^{15} +(0.0552106 - 0.169921i) q^{16} +(2.91373 + 2.11695i) q^{17} -0.851077 q^{18} +(2.70138 + 1.96267i) q^{19} +(2.57478 - 1.22766i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-3.47888 + 2.52755i) q^{22} +(-0.551200 - 1.69642i) q^{23} +2.78785 q^{24} +(4.66740 + 1.79315i) q^{25} +0.383172 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.03204 - 0.749819i) q^{28} +(0.874434 - 0.635314i) q^{29} +(1.30979 + 1.38062i) q^{30} +(-2.36407 - 1.71760i) q^{31} -5.72775 q^{32} +(4.08762 + 2.96983i) q^{33} +(0.947204 - 2.91519i) q^{34} +(2.19857 + 0.407800i) q^{35} +(-0.394203 - 1.21323i) q^{36} +(0.176558 - 0.543391i) q^{37} +(0.878170 - 2.70273i) q^{38} +(-0.139126 - 0.428185i) q^{39} +(-4.29044 - 4.52245i) q^{40} +(3.73281 - 11.4884i) q^{41} +(0.688536 + 0.500250i) q^{42} +3.57628 q^{43} +(-5.21445 - 3.78852i) q^{44} +(1.06724 - 1.96494i) q^{45} +(-1.22816 + 0.892308i) q^{46} +(-8.02241 + 5.82862i) q^{47} +(0.0552106 + 0.169921i) q^{48} +1.00000 q^{49} +(0.223903 - 4.24949i) q^{50} -3.60157 q^{51} +(0.177478 + 0.546222i) q^{52} +(-0.654118 + 0.475245i) q^{53} +(0.688536 - 0.500250i) q^{54} +(-1.47310 - 11.2015i) q^{55} +(-2.25541 - 1.63865i) q^{56} -3.33909 q^{57} +(-0.744211 - 0.540701i) q^{58} +(2.60289 - 8.01088i) q^{59} +(-1.36144 + 2.50662i) q^{60} +(0.739007 + 2.27443i) q^{61} +(-0.768519 + 2.36526i) q^{62} +(0.309017 - 0.951057i) q^{63} +(1.39596 + 4.29633i) q^{64} +(-0.480491 + 0.884658i) q^{65} +(1.32881 - 4.08967i) q^{66} +(10.9897 + 7.98449i) q^{67} +4.59441 q^{68} +(1.44306 + 1.04845i) q^{69} +(-0.248135 - 1.88682i) q^{70} +(-4.54020 + 3.29865i) q^{71} +(-2.25541 + 1.63865i) q^{72} +(3.85698 + 11.8706i) q^{73} -0.486267 q^{74} +(-4.82999 + 1.29274i) q^{75} +4.25956 q^{76} +(-1.56133 - 4.80529i) q^{77} +(-0.309993 + 0.225223i) q^{78} +(-1.90302 + 1.38262i) q^{79} +(0.190678 - 0.351067i) q^{80} +(-0.809017 - 0.587785i) q^{81} -10.2807 q^{82} +(-4.08135 - 2.96527i) q^{83} +(-0.394203 + 1.21323i) q^{84} +(5.54275 + 5.84248i) q^{85} +(-0.940552 - 2.89472i) q^{86} +(-0.334004 + 1.02796i) q^{87} +(-4.35275 + 13.3964i) q^{88} +(4.73020 + 14.5580i) q^{89} +(-1.87115 - 0.347069i) q^{90} +(-0.139126 + 0.428185i) q^{91} +(-1.84087 - 1.33747i) q^{92} +2.92216 q^{93} +(6.82769 + 4.96061i) q^{94} +(5.13879 + 5.41667i) q^{95} +(4.63385 - 3.36669i) q^{96} +(-2.36287 + 1.71673i) q^{97} +(-0.262997 - 0.809422i) q^{98} -5.05258 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.262997	−	0.809422i	−0.185967	−	0.572348i	0.813997	−	0.580870i	$-0.197287\pi$
$2$	−0.262997	−	0.809422i	−0.185967	−	0.572348i	−0.999964	+	0.00852173i	$0.997287\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	1.03204	−	0.749819i	0.516019	−	0.374909i
$5$	2.19857	+	0.407800i	0.983229	+	0.182374i
$5$	2.19857	+	0.407800i	0.983229	+	0.182374i
$6$	0.688536	+	0.500250i	0.281094	+	0.204226i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.25541	−	1.63865i	−0.797409	−	0.579352i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.248135	−	1.88682i	−0.0784671	−	0.596665i
$11$	−1.56133	−	4.80529i	−0.470759	−	1.44885i	−0.851592	−	0.524205i	$-0.824363\pi$
$11$	−1.56133	−	4.80529i	−0.470759	−	1.44885i	0.380833	−	0.924644i	$-0.375637\pi$
$12$	−0.394203	+	1.21323i	−0.113797	+	0.350230i
$13$	−0.139126	+	0.428185i	−0.0385865	+	0.118757i	−0.968494	−	0.249036i	$-0.919886\pi$
$13$	−0.139126	+	0.428185i	−0.0385865	+	0.118757i	0.929908	+	0.367793i	$0.119886\pi$
$14$	−0.262997	−	0.809422i	−0.0702890	−	0.216327i
$15$	−2.01838	+	0.962369i	−0.521143	+	0.248482i
$16$	0.0552106	−	0.169921i	0.0138026	−	0.0424802i
$17$	2.91373	+	2.11695i	0.706684	+	0.513436i	0.882102	−	0.471058i	$-0.156128\pi$
$17$	2.91373	+	2.11695i	0.706684	+	0.513436i	−0.175418	+	0.984494i	$0.556128\pi$
$18$	−0.851077			−0.200601
$19$	2.70138	+	1.96267i	0.619738	+	0.450266i	0.852830	−	0.522188i	$-0.174884\pi$
$19$	2.70138	+	1.96267i	0.619738	+	0.450266i	−0.233092	+	0.972455i	$0.574884\pi$
$20$	2.57478	−	1.22766i	0.575738	−	0.274514i
$21$	−0.809017	+	0.587785i	−0.176542	+	0.128265i
$22$	−3.47888	+	2.52755i	−0.741700	+	0.538876i
$23$	−0.551200	−	1.69642i	−0.114933	−	0.353728i	0.877000	−	0.480491i	$-0.159541\pi$
$23$	−0.551200	−	1.69642i	−0.114933	−	0.353728i	−0.991933	+	0.126762i	$0.959541\pi$
$24$	2.78785			0.569067
$25$	4.66740	+	1.79315i	0.933480	+	0.358630i
$26$	0.383172			0.0751462
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.03204	−	0.749819i	0.195037	−	0.141702i
$29$	0.874434	−	0.635314i	0.162378	−	0.117975i	−0.503629	−	0.863920i	$-0.668002\pi$
$29$	0.874434	−	0.635314i	0.162378	−	0.117975i	0.666007	+	0.745945i	$0.268002\pi$
$30$	1.30979	+	1.38062i	0.239134	+	0.252065i
$31$	−2.36407	−	1.71760i	−0.424600	−	0.308490i	0.354886	−	0.934910i	$-0.384520\pi$
$31$	−2.36407	−	1.71760i	−0.424600	−	0.308490i	−0.779486	+	0.626419i	$0.784520\pi$
$32$	−5.72775			−1.01253
$33$	4.08762	+	2.96983i	0.711564	+	0.516981i
$34$	0.947204	−	2.91519i	0.162444	−	0.499952i
$35$	2.19857	+	0.407800i	0.371626	+	0.0689308i
$36$	−0.394203	−	1.21323i	−0.0657005	−	0.202205i
$37$	0.176558	−	0.543391i	0.0290260	−	0.0893329i	−0.935494	−	0.353342i	$-0.885045\pi$
$37$	0.176558	−	0.543391i	0.0290260	−	0.0893329i	0.964520	+	0.264010i	$0.0850450\pi$
$38$	0.878170	−	2.70273i	0.142458	−	0.438441i
$39$	−0.139126	−	0.428185i	−0.0222779	−	0.0685645i
$40$	−4.29044	−	4.52245i	−0.678378	−	0.715062i
$41$	3.73281	−	11.4884i	0.582967	−	1.79419i	−0.0243209	−	0.999704i	$-0.507742\pi$
$41$	3.73281	−	11.4884i	0.582967	−	1.79419i	0.607287	−	0.794482i	$-0.292258\pi$
$42$	0.688536	+	0.500250i	0.106243	+	0.0771903i
$43$	3.57628			0.545378			0.272689	−	0.962102i	$-0.412087\pi$
$43$	3.57628			0.545378			0.272689	+	0.962102i	$0.412087\pi$
$44$	−5.21445	−	3.78852i	−0.786108	−	0.571141i
$45$	1.06724	−	1.96494i	0.159094	−	0.292917i
$46$	−1.22816	+	0.892308i	−0.181082	+	0.131564i
$47$	−8.02241	+	5.82862i	−1.17019	+	0.850192i	−0.991031	−	0.133629i	$-0.957337\pi$
$47$	−8.02241	+	5.82862i	−1.17019	+	0.850192i	−0.179157	+	0.983820i	$0.557337\pi$
$48$	0.0552106	+	0.169921i	0.00796896	+	0.0245259i
$49$	1.00000			0.142857
$50$	0.223903	−	4.24949i	0.0316647	−	0.600969i
$51$	−3.60157			−0.504321
$52$	0.177478	+	0.546222i	0.0246118	+	0.0757473i
$53$	−0.654118	+	0.475245i	−0.0898501	+	0.0652799i	−0.631803	−	0.775129i	$-0.717685\pi$
$53$	−0.654118	+	0.475245i	−0.0898501	+	0.0652799i	0.541953	+	0.840409i	$0.317685\pi$
$54$	0.688536	−	0.500250i	0.0936978	−	0.0680755i
$55$	−1.47310	−	11.2015i	−0.198633	−	1.51040i
$56$	−2.25541	−	1.63865i	−0.301392	−	0.218974i
$57$	−3.33909			−0.442273
$58$	−0.744211	−	0.540701i	−0.0977196	−	0.0709975i
$59$	2.60289	−	8.01088i	0.338868	−	1.04293i	−0.625918	−	0.779889i	$-0.715275\pi$
$59$	2.60289	−	8.01088i	0.338868	−	1.04293i	0.964785	−	0.263038i	$-0.0847245\pi$
$60$	−1.36144	+	2.50662i	−0.175761	+	0.323603i
$61$	0.739007	+	2.27443i	0.0946201	+	0.291211i	0.987154	−	0.159769i	$-0.0510748\pi$
$61$	0.739007	+	2.27443i	0.0946201	+	0.291211i	−0.892534	+	0.450979i	$0.851075\pi$
$62$	−0.768519	+	2.36526i	−0.0976020	+	0.300388i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	1.39596	+	4.29633i	0.174495	+	0.537041i
$65$	−0.480491	+	0.884658i	−0.0595976	+	0.109728i
$66$	1.32881	−	4.08967i	0.163566	−	0.503403i
$67$	10.9897	+	7.98449i	1.34261	+	0.975460i	0.999344	+	0.0362208i	$0.0115320\pi$
$67$	10.9897	+	7.98449i	1.34261	+	0.975460i	0.343262	+	0.939240i	$0.388468\pi$
$68$	4.59441			0.557154
$69$	1.44306	+	1.04845i	0.173724	+	0.126218i
$70$	−0.248135	−	1.88682i	−0.0296578	−	0.225518i
$71$	−4.54020	+	3.29865i	−0.538823	+	0.391478i	−0.823648	−	0.567102i	$-0.808065\pi$
$71$	−4.54020	+	3.29865i	−0.538823	+	0.391478i	0.284825	+	0.958580i	$0.408065\pi$
$72$	−2.25541	+	1.63865i	−0.265803	+	0.193117i
$73$	3.85698	+	11.8706i	0.451426	+	1.38934i	0.875281	+	0.483615i	$0.160677\pi$
$73$	3.85698	+	11.8706i	0.451426	+	1.38934i	−0.423855	+	0.905730i	$0.639323\pi$
$74$	−0.486267			−0.0565274
$75$	−4.82999	+	1.29274i	−0.557719	+	0.149273i
$76$	4.25956			0.488606
$77$	−1.56133	−	4.80529i	−0.177930	−	0.547613i
$78$	−0.309993	+	0.225223i	−0.0350998	+	0.0255015i
$79$	−1.90302	+	1.38262i	−0.214106	+	0.155557i	−0.689670	−	0.724124i	$-0.742244\pi$
$79$	−1.90302	+	1.38262i	−0.214106	+	0.155557i	0.475564	+	0.879681i	$0.342244\pi$
$80$	0.190678	−	0.351067i	0.0213184	−	0.0392505i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−10.2807			−1.13531
$83$	−4.08135	−	2.96527i	−0.447986	−	0.325481i	0.340814	−	0.940131i	$-0.389297\pi$
$83$	−4.08135	−	2.96527i	−0.447986	−	0.325481i	−0.788800	+	0.614650i	$0.789297\pi$
$84$	−0.394203	+	1.21323i	−0.0430111	+	0.132375i
$85$	5.54275	+	5.84248i	0.601196	+	0.633706i
$86$	−0.940552	−	2.89472i	−0.101422	−	0.312146i
$87$	−0.334004	+	1.02796i	−0.0358090	+	0.110209i
$88$	−4.35275	+	13.3964i	−0.464005	+	1.42806i
$89$	4.73020	+	14.5580i	0.501400	+	1.54315i	0.806740	+	0.590907i	$0.201230\pi$
$89$	4.73020	+	14.5580i	0.501400	+	1.54315i	−0.305340	+	0.952243i	$0.598770\pi$
$90$	−1.87115	−	0.347069i	−0.197237	−	0.0365843i
$91$	−0.139126	+	0.428185i	−0.0145843	+	0.0448860i
$92$	−1.84087	−	1.33747i	−0.191924	−	0.139441i
$93$	2.92216			0.303014
$94$	6.82769	+	4.96061i	0.704222	+	0.511647i
$95$	5.13879	+	5.41667i	0.527228	+	0.555739i
$96$	4.63385	−	3.36669i	0.472940	−	0.343611i
$97$	−2.36287	+	1.71673i	−0.239914	+	0.174307i	−0.701245	−	0.712921i	$-0.747372\pi$
$97$	−2.36287	+	1.71673i	−0.239914	+	0.174307i	0.461331	+	0.887228i	$0.347372\pi$
$98$	−0.262997	−	0.809422i	−0.0265667	−	0.0817640i
$99$	−5.05258			−0.507803
$100$	6.16147	−	1.64911i	0.616147	−	0.164911i
$101$	−11.7326			−1.16744			−0.583721	−	0.811954i	$-0.698404\pi$
$101$	−11.7326			−1.16744			−0.583721	+	0.811954i	$0.698404\pi$
$102$	0.947204	+	2.91519i	0.0937872	+	0.288647i
$103$	3.48447	−	2.53161i	0.343335	−	0.249447i	−0.402733	−	0.915318i	$-0.631940\pi$
$103$	3.48447	−	2.53161i	0.343335	−	0.249447i	0.746067	+	0.665870i	$0.231940\pi$
$104$	1.01543	−	0.737755i	0.0995714	−	0.0723429i
$105$	−2.01838	+	0.962369i	−0.196973	+	0.0939176i
$106$	0.556705	+	0.404470i	0.0540720	+	0.0392856i
$107$	−17.3249			−1.67486			−0.837430	−	0.546545i	$-0.815943\pi$
$107$	−17.3249			−1.67486			−0.837430	+	0.546545i	$0.815943\pi$
$108$	1.03204	+	0.749819i	0.0993078	+	0.0721514i
$109$	−5.78926	+	17.8175i	−0.554510	+	1.70661i	0.142723	+	0.989763i	$0.454414\pi$
$109$	−5.78926	+	17.8175i	−0.554510	+	1.70661i	−0.697233	+	0.716844i	$0.745586\pi$
$110$	−8.67929	+	4.13831i	−0.827538	+	0.394573i
$111$	0.176558	+	0.543391i	0.0167582	+	0.0515764i
$112$	0.0552106	−	0.169921i	0.00521691	−	0.0160560i
$113$	0.0593362	−	0.182618i	0.00558188	−	0.0171793i	−0.948227	−	0.317594i	$-0.897125\pi$
$113$	0.0593362	−	0.182618i	0.00558188	−	0.0171793i	0.953809	+	0.300415i	$0.0971251\pi$
$114$	0.878170	+	2.70273i	0.0822482	+	0.253134i
$115$	−0.520051	−	3.95447i	−0.0484950	−	0.368757i
$116$	0.426078	−	1.31133i	0.0395604	−	0.121754i
$117$	0.364236	+	0.264633i	0.0336736	+	0.0244653i
$118$	−7.16873			−0.659936
$119$	2.91373	+	2.11695i	0.267102	+	0.194061i
$120$	6.12927	+	1.13688i	0.559523	+	0.103783i
$121$	−11.7538	+	8.53966i	−1.06853	+	0.776333i
$122$	1.64662	−	1.19634i	0.149078	−	0.108311i
$123$	3.73281	+	11.4884i	0.336576	+	1.03587i
$124$	−3.72770			−0.334758
$125$	9.53034	+	5.84573i	0.852420	+	0.522858i
$126$	−0.851077			−0.0758200
$127$	−4.52435	−	13.9245i	−0.401471	−	1.23560i	−0.923806	−	0.382861i	$-0.874939\pi$
$127$	−4.52435	−	13.9245i	−0.401471	−	1.23560i	0.522334	−	0.852741i	$-0.325061\pi$
$128$	−6.15728	+	4.47353i	−0.544232	+	0.395408i
$129$	−2.89327	+	2.10209i	−0.254738	+	0.185078i
$130$	0.842430	+	0.156258i	0.0738860	+	0.0137047i
$131$	11.6273	+	8.44773i	1.01588	+	0.738081i	0.965435	−	0.260646i	$-0.0839354\pi$
$131$	11.6273	+	8.44773i	1.01588	+	0.738081i	0.0504470	+	0.998727i	$0.483935\pi$
$132$	6.44541			0.561001
$133$	2.70138	+	1.96267i	0.234239	+	0.170185i
$134$	3.57256	−	10.9952i	0.308622	−	0.949841i
$135$	0.291554	+	2.21698i	0.0250930	+	0.190807i
$136$	−3.10273	−	9.54921i	−0.266057	−	0.818838i
$137$	−3.62124	+	11.1450i	−0.309383	+	0.952184i	0.668622	+	0.743603i	$0.266885\pi$
$137$	−3.62124	+	11.1450i	−0.309383	+	0.952184i	−0.978005	+	0.208581i	$0.933115\pi$
$138$	0.469114	−	1.44378i	0.0399336	−	0.122903i
$139$	−2.01458	−	6.20025i	−0.170875	−	0.525898i	0.828546	−	0.559920i	$-0.189168\pi$
$139$	−2.01458	−	6.20025i	−0.170875	−	0.525898i	−0.999421	+	0.0340222i	$0.989168\pi$
$140$	2.57478	−	1.22766i	0.217609	−	0.103756i
$141$	3.06429	−	9.43091i	0.258060	−	0.794226i
$142$	3.86406	+	2.80741i	0.324265	+	0.235592i
$143$	2.27477			0.190226
$144$	−0.144543	−	0.105017i	−0.0120453	−	0.00875140i
$145$	2.18158	−	1.04019i	0.181171	−	0.0863827i
$146$	8.59393	−	6.24385i	0.711238	−	0.516745i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−0.225230	−	0.693186i	−0.0185138	−	0.0569796i
$149$	19.8460			1.62584			0.812922	−	0.582372i	$-0.197875\pi$
$149$	19.8460			1.62584			0.812922	+	0.582372i	$0.197875\pi$
$150$	2.31665	+	3.56952i	0.189153	+	0.291450i
$151$	−15.4993			−1.26132			−0.630659	−	0.776060i	$-0.717216\pi$
$151$	−15.4993			−1.26132			−0.630659	+	0.776060i	$0.717216\pi$
$152$	−2.87659	−	8.85325i	−0.233323	−	0.718093i
$153$	2.91373	−	2.11695i	0.235561	−	0.171145i
$154$	−3.47888	+	2.52755i	−0.280336	+	0.203676i
$155$	−4.49714	−	4.74033i	−0.361219	−	0.380753i
$156$	−0.464644	−	0.337584i	−0.0372013	−	0.0270283i
$157$	4.29644			0.342894			0.171447	−	0.985193i	$-0.445156\pi$
$157$	4.29644			0.342894			0.171447	+	0.985193i	$0.445156\pi$
$158$	1.61961	+	1.17672i	0.128849	+	0.0936146i
$159$	0.249851	−	0.768962i	0.0198145	−	0.0609827i
$160$	−12.5928	−	2.33578i	−0.995552	−	0.184659i
$161$	−0.551200	−	1.69642i	−0.0434407	−	0.133697i
$162$	−0.262997	+	0.809422i	−0.0206630	+	0.0635942i
$163$	−2.03573	+	6.26532i	−0.159450	+	0.490738i	−0.998585	−	0.0531866i	$-0.983062\pi$
$163$	−2.03573	+	6.26532i	−0.159450	+	0.490738i	0.839134	+	0.543924i	$0.183062\pi$
$164$	−4.76182	−	14.6554i	−0.371836	−	1.14439i
$165$	7.77581	+	8.19630i	0.605346	+	0.638081i
$166$	−1.32677	+	4.08339i	−0.102978	+	0.316933i
$167$	0.890086	+	0.646686i	0.0688769	+	0.0500420i	0.621691	−	0.783263i	$-0.286446\pi$
$167$	0.890086	+	0.646686i	0.0688769	+	0.0500420i	−0.552814	+	0.833305i	$0.686446\pi$
$168$	2.78785			0.215087
$169$	10.3532	+	7.52207i	0.796403	+	0.578620i
$170$	3.27131	−	6.02298i	0.250898	−	0.461942i
$171$	2.70138	−	1.96267i	0.206579	−	0.150089i
$172$	3.69086	−	2.68156i	0.281425	−	0.204467i
$173$	7.46168	+	22.9647i	0.567301	+	1.74597i	0.661014	+	0.750374i	$0.270126\pi$
$173$	7.46168	+	22.9647i	0.567301	+	1.74597i	−0.0937130	+	0.995599i	$0.529874\pi$
$174$	0.919895			0.0697371
$175$	4.66740	+	1.79315i	0.352822	+	0.135549i
$176$	−0.902720			−0.0680451
$177$	2.60289	+	8.01088i	0.195645	+	0.602134i
$178$	10.5396	−	7.65745i	0.789975	−	0.573950i
$179$	1.29568	−	0.941368i	0.0968438	−	0.0703612i	−0.538310	−	0.842747i	$-0.680937\pi$
$179$	1.29568	−	0.941368i	0.0968438	−	0.0703612i	0.635153	+	0.772386i	$0.280937\pi$
$180$	−0.371926	−	2.82813i	−0.0277217	−	0.210796i
$181$	−10.4558	−	7.59657i	−0.777172	−	0.564648i	0.126957	−	0.991908i	$-0.459479\pi$
$181$	−10.4558	−	7.59657i	−0.777172	−	0.564648i	−0.904129	+	0.427260i	$0.859479\pi$
$182$	0.383172			0.0284026
$183$	−1.93474	−	1.40567i	−0.143020	−	0.103910i
$184$	−1.53666	+	4.72936i	−0.113284	+	0.348653i
$185$	0.609770	−	1.12268i	0.0448312	−	0.0825412i
$186$	−0.768519	−	2.36526i	−0.0563506	−	0.173429i
$187$	5.62325	−	17.3066i	0.411213	−	1.26558i
$188$	−3.90901	+	12.0307i	−0.285094	+	0.877430i
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	3.03289	−	5.58402i	0.220029	−	0.405107i
$191$	−5.88125	+	18.1006i	−0.425552	+	1.30971i	0.476912	+	0.878951i	$0.341756\pi$
$191$	−5.88125	+	18.1006i	−0.425552	+	1.30971i	−0.902465	+	0.430764i	$0.858244\pi$
$192$	−3.65467	−	2.65528i	−0.263753	−	0.191628i
$193$	−24.1902			−1.74125			−0.870624	−	0.491949i	$-0.836285\pi$
$193$	−24.1902			−1.74125			−0.870624	+	0.491949i	$0.836285\pi$
$194$	2.01099	+	1.46107i	0.144381	+	0.104899i
$195$	−0.131264	−	0.998129i	−0.00939998	−	0.0714775i
$196$	1.03204	−	0.749819i	0.0737169	−	0.0535585i
$197$	4.57415	−	3.32331i	0.325895	−	0.236776i	−0.412792	−	0.910825i	$-0.635446\pi$
$197$	4.57415	−	3.32331i	0.325895	−	0.236776i	0.738687	+	0.674049i	$0.235446\pi$
$198$	1.32881	+	4.08967i	0.0944347	+	0.290640i
$199$	12.5031			0.886319			0.443159	−	0.896443i	$-0.353858\pi$
$199$	12.5031			0.886319			0.443159	+	0.896443i	$0.353858\pi$
$200$	−7.58856	−	11.6926i	−0.536592	−	0.826788i
$201$	−13.5840			−0.958143
$202$	3.08565	+	9.49666i	0.217106	+	0.668183i
$203$	0.874434	−	0.635314i	0.0613732	−	0.0445903i
$204$	−3.71696	+	2.70053i	−0.260239	+	0.189075i
$205$	12.8918	−	23.7358i	0.900402	−	1.65778i
$206$	−2.96555	−	2.15460i	−0.206620	−	0.150118i
$207$	−1.78372			−0.123977
$208$	0.0650763	+	0.0472807i	0.00451223	+	0.00327832i
$209$	5.21342	−	16.0453i	0.360620	−	1.10987i
$210$	1.30979	+	1.38062i	0.0903841	+	0.0952718i
$211$	−1.92314	−	5.91883i	−0.132395	−	0.407469i	0.862781	−	0.505578i	$-0.168721\pi$
$211$	−1.92314	−	5.91883i	−0.132395	−	0.407469i	−0.995176	+	0.0981088i	$0.968721\pi$
$212$	−0.318727	+	0.980941i	−0.0218903	+	0.0673713i
$213$	1.73420	−	5.33733i	0.118826	−	0.365708i
$214$	4.55640	+	14.0231i	0.311469	+	0.958603i
$215$	7.86270	+	1.45841i	0.536232	+	0.0994626i
$216$	0.861492	−	2.65140i	0.0586171	−	0.180405i
$217$	−2.36407	−	1.71760i	−0.160484	−	0.116598i
$218$	15.9444			1.07989
$219$	−10.0977	−	7.33641i	−0.682340	−	0.495749i
$220$	−9.91936	−	10.4558i	−0.668763	−	0.704927i
$221$	−1.31182	+	0.953095i	−0.0882427	+	0.0641121i
$222$	0.393398	−	0.285821i	0.0264032	−	0.0191830i
$223$	−3.45669	−	10.6386i	−0.231477	−	0.712412i	−0.997569	−	0.0696820i	$-0.977802\pi$
$223$	−3.45669	−	10.6386i	−0.231477	−	0.712412i	0.766092	−	0.642730i	$-0.222198\pi$
$224$	−5.72775			−0.382701
$225$	3.14769	−	3.88485i	0.209846	−	0.258990i
$226$	−0.163420			−0.0108706
$227$	5.23359	+	16.1073i	0.347365	+	1.06908i	0.960305	+	0.278951i	$0.0899868\pi$
$227$	5.23359	+	16.1073i	0.347365	+	1.06908i	−0.612940	+	0.790130i	$0.710013\pi$
$228$	−3.44606	+	2.50371i	−0.228221	+	0.165812i
$229$	8.34155	−	6.06049i	0.551225	−	0.400489i	−0.277012	−	0.960867i	$-0.589344\pi$
$229$	8.34155	−	6.06049i	0.551225	−	0.400489i	0.828237	+	0.560378i	$0.189344\pi$
$230$	−3.06407	+	1.46096i	−0.202039	+	0.0963327i
$231$	4.08762	+	2.96983i	0.268946	+	0.195401i
$232$	−3.01327			−0.197831
$233$	0.299704	+	0.217748i	0.0196343	+	0.0142651i	0.597559	−	0.801825i	$-0.296137\pi$
$233$	0.299704	+	0.217748i	0.0196343	+	0.0142651i	−0.577925	+	0.816090i	$0.696137\pi$
$234$	0.118407	−	0.364418i	0.00774049	−	0.0238228i
$235$	−20.0147	+	9.54308i	−1.30562	+	0.622522i
$236$	−3.32043	−	10.2192i	−0.216141	−	0.665215i
$237$	0.726887	−	2.23713i	0.0472164	−	0.145317i
$238$	0.947204	−	2.91519i	0.0613981	−	0.188964i
$239$	−3.87697	−	11.9321i	−0.250780	−	0.771822i	−0.994632	−	0.103477i	$-0.967003\pi$
$239$	−3.87697	−	11.9321i	−0.250780	−	0.771822i	0.743852	−	0.668345i	$-0.232997\pi$
$240$	0.0520906	+	0.396097i	0.00336243	+	0.0255680i
$241$	−6.49543	+	19.9909i	−0.418407	+	1.28773i	0.490760	+	0.871295i	$0.336719\pi$
$241$	−6.49543	+	19.9909i	−0.418407	+	1.28773i	−0.909167	+	0.416431i	$0.863281\pi$
$242$	10.0034	+	7.26791i	0.643044	+	0.467199i
$243$	1.00000			0.0641500
$244$	2.46809	+	1.79317i	0.158003	+	0.114796i
$245$	2.19857	+	0.407800i	0.140461	+	0.0260534i
$246$	8.31725	−	6.04283i	0.530288	−	0.385277i
$247$	−1.21621	+	0.883632i	−0.0773859	+	0.0562241i
$248$	2.51741	+	7.74780i	0.159856	+	0.491986i
$249$	5.04482			0.319703
$250$	2.22521	−	9.25148i	0.140735	−	0.585115i
$251$	−11.3924			−0.719080			−0.359540	−	0.933130i	$-0.617066\pi$
$251$	−11.3924			−0.719080			−0.359540	+	0.933130i	$0.617066\pi$
$252$	−0.394203	−	1.21323i	−0.0248325	−	0.0764265i
$253$	−7.29118	+	5.29735i	−0.458393	+	0.333042i
$254$	−10.0809	+	7.32423i	−0.632534	+	0.459563i
$255$	−7.91830	−	1.46872i	−0.495863	−	0.0919749i
$256$	12.5497	+	9.11787i	0.784354	+	0.569867i
$257$	−16.5848			−1.03453			−0.517266	−	0.855825i	$-0.673050\pi$
$257$	−16.5848			−1.03453			−0.517266	+	0.855825i	$0.673050\pi$
$258$	2.46240	+	1.78904i	0.153302	+	0.111381i
$259$	0.176558	−	0.543391i	0.0109708	−	0.0337647i
$260$	0.167449	+	1.27328i	0.0103847	+	0.0789655i
$261$	−0.334004	−	1.02796i	−0.0206743	−	0.0636291i
$262$	3.77983	−	11.6331i	0.233519	−	0.718697i
$263$	7.61471	−	23.4357i	0.469543	−	1.44511i	−0.383634	−	0.923485i	$-0.625328\pi$
$263$	7.61471	−	23.4357i	0.469543	−	1.44511i	0.853178	−	0.521621i	$-0.174672\pi$
$264$	−4.35275	−	13.3964i	−0.267893	−	0.824491i
$265$	−1.63193	+	0.778108i	−0.100249	+	0.0477988i
$266$	0.878170	−	2.70273i	0.0538441	−	0.165715i
$267$	−12.3838	−	8.99737i	−0.757877	−	0.550630i
$268$	17.3287			1.05852
$269$	9.36160	+	6.80160i	0.570787	+	0.414701i	0.835391	−	0.549656i	$-0.185241\pi$
$269$	9.36160	+	6.80160i	0.570787	+	0.414701i	−0.264604	+	0.964357i	$0.585241\pi$
$270$	1.71779	−	0.819050i	0.104542	−	0.0498458i
$271$	−17.6822	+	12.8468i	−1.07412	+	0.780390i	−0.976647	−	0.214848i	$-0.931074\pi$
$271$	−17.6822	+	12.8468i	−1.07412	+	0.780390i	−0.0974678	+	0.995239i	$0.531074\pi$
$272$	0.520583	−	0.378226i	0.0315650	−	0.0229333i
$273$	−0.139126	−	0.428185i	−0.00842027	−	0.0259149i
$274$	9.97341			0.602516
$275$	1.32924	−	25.2279i	0.0801565	−	1.52130i
$276$	2.27544			0.136965
$277$	−6.92367	−	21.3089i	−0.416003	−	1.28032i	−0.911351	−	0.411630i	$-0.864959\pi$
$277$	−6.92367	−	21.3089i	−0.416003	−	1.28032i	0.495348	−	0.868695i	$-0.335041\pi$
$278$	−4.48879	+	3.26130i	−0.269220	+	0.195600i
$279$	−2.36407	+	1.71760i	−0.141533	+	0.102830i
$280$	−4.29044	−	4.52245i	−0.256403	−	0.270268i
$281$	18.1476	+	13.1850i	1.08260	+	0.786553i	0.978134	−	0.207976i	$-0.0666875\pi$
$281$	18.1476	+	13.1850i	1.08260	+	0.786553i	0.104463	+	0.994529i	$0.466688\pi$
$282$	−8.43949			−0.502564
$283$	−14.9492	−	10.8613i	−0.888639	−	0.645634i	0.0468835	−	0.998900i	$-0.485071\pi$
$283$	−14.9492	−	10.8613i	−0.888639	−	0.645634i	−0.935523	+	0.353266i	$0.885071\pi$
$284$	−2.21227	+	6.80866i	−0.131274	+	0.404020i
$285$	−7.34121	−	1.36168i	−0.434855	−	0.0806589i
$286$	−0.598259	−	1.84125i	−0.0353758	−	0.108875i
$287$	3.73281	−	11.4884i	0.220341	−	0.678139i
$288$	−1.76997	+	5.44741i	−0.104297	+	0.320992i
$289$	−1.24493	−	3.83149i	−0.0732310	−	0.225382i
$290$	−1.41570	−	1.49226i	−0.0831328	−	0.0876283i
$291$	0.902538	−	2.77773i	0.0529077	−	0.162833i
$292$	12.8813	+	9.35883i	0.753823	+	0.547684i
$293$	−11.6736			−0.681978			−0.340989	−	0.940067i	$-0.610762\pi$
$293$	−11.6736			−0.681978			−0.340989	+	0.940067i	$0.610762\pi$
$294$	0.688536	+	0.500250i	0.0401562	+	0.0291752i
$295$	8.98947	−	16.5510i	0.523387	−	0.963636i
$296$	−1.28864	+	0.936253i	−0.0749008	+	0.0544186i
$297$	4.08762	−	2.96983i	0.237188	−	0.172327i
$298$	−5.21943	−	16.0638i	−0.302354	−	0.930549i
$299$	0.803068			0.0464426
$300$	−4.01541	+	4.95577i	−0.231830	+	0.286122i
$301$	3.57628			0.206133
$302$	4.07629	+	12.5455i	0.234564	+	0.721913i
$303$	9.49191	−	6.89628i	0.545296	−	0.396181i
$304$	0.482642	−	0.350660i	0.0276814	−	0.0201117i
$305$	0.697244	+	5.30185i	0.0399241	+	0.303583i
$306$	−2.47981	−	1.80169i	−0.141761	−	0.102996i
$307$	0.228226			0.0130256			0.00651278	−	0.999979i	$-0.497927\pi$
$307$	0.228226			0.0130256			0.00651278	+	0.999979i	$0.497927\pi$
$308$	−5.21445	−	3.78852i	−0.297121	−	0.215871i
$309$	−1.33095	+	4.09623i	−0.0757150	+	0.233027i
$310$	−2.65419	+	4.88678i	−0.150748	+	0.277550i
$311$	−6.42356	−	19.7697i	−0.364246	−	1.12104i	−0.950452	−	0.310873i	$-0.899379\pi$
$311$	−6.42356	−	19.7697i	−0.364246	−	1.12104i	0.586205	−	0.810163i	$-0.300621\pi$
$312$	−0.387861	+	1.19371i	−0.0219583	+	0.0675807i
$313$	−3.56231	+	10.9637i	−0.201354	+	0.619703i	0.798490	+	0.602008i	$0.205633\pi$
$313$	−3.56231	+	10.9637i	−0.201354	+	0.619703i	−0.999843	+	0.0176944i	$0.994367\pi$
$314$	−1.12995	−	3.47764i	−0.0637669	−	0.196254i
$315$	1.06724	−	1.96494i	0.0601319	−	0.110712i
$316$	−0.927267	+	2.85383i	−0.0521628	+	0.160541i
$317$	−10.3472	−	7.51768i	−0.581157	−	0.422235i	0.257984	−	0.966149i	$-0.416942\pi$
$317$	−10.3472	−	7.51768i	−0.581157	−	0.422235i	−0.839141	+	0.543914i	$0.816942\pi$
$318$	−0.688125			−0.0385882
$319$	−4.41815	−	3.20997i	−0.247369	−	0.179724i
$320$	1.31707	+	10.0150i	0.0736266	+	0.559858i
$321$	14.0161	−	10.1833i	0.782304	−	0.568377i
$322$	−1.22816	+	0.892308i	−0.0684425	+	0.0497264i
$323$	3.71623	+	11.4374i	0.206776	+	0.636392i
$324$	−1.27567			−0.0708704
$325$	−1.41716	+	1.74904i	−0.0786096	+	0.0970191i
$326$	5.60668			0.310525
$327$	−5.78926	−	17.8175i	−0.320147	−	0.985310i
$328$	−27.2445	+	19.7943i	−1.50433	+	1.09296i
$329$	−8.02241	+	5.82862i	−0.442290	+	0.321342i
$330$	4.58925	−	8.44952i	0.252630	−	0.465131i
$331$	22.4485	+	16.3098i	1.23388	+	0.896466i	0.997175	−	0.0751161i	$-0.0239328\pi$
$331$	22.4485	+	16.3098i	1.23388	+	0.896466i	0.236704	+	0.971582i	$0.423933\pi$
$332$	−6.43552			−0.353195
$333$	−0.462236	−	0.335834i	−0.0253304	−	0.0184036i
$334$	0.289351	−	0.890532i	0.0158326	−	0.0487278i
$335$	20.9055	+	22.0360i	1.14219	+	1.20396i
$336$	0.0552106	+	0.169921i	0.00301198	+	0.00926993i
$337$	11.2569	−	34.6451i	0.613201	−	1.88724i	0.187895	−	0.982189i	$-0.439834\pi$
$337$	11.2569	−	34.6451i	0.613201	−	1.88724i	0.425306	−	0.905050i	$-0.360166\pi$
$338$	3.36565	−	10.3584i	0.183067	−	0.563424i
$339$	0.0593362	+	0.182618i	0.00322270	+	0.00991845i
$340$	10.1011	+	1.87360i	0.547811	+	0.101610i
$341$	−4.56246	+	14.0418i	−0.247071	+	0.760406i
$342$	−2.29908	−	1.67038i	−0.124320	−	0.0903238i
$343$	1.00000			0.0539949
$344$	−8.06600	−	5.86029i	−0.434889	−	0.315966i
$345$	2.74511	+	2.89356i	0.147792	+	0.155784i
$346$	16.6257	−	12.0793i	0.893805	−	0.649387i
$347$	−9.66738	+	7.02376i	−0.518972	+	0.377055i	−0.816216	−	0.577746i	$-0.803932\pi$
$347$	−9.66738	+	7.02376i	−0.518972	+	0.377055i	0.297245	+	0.954801i	$0.403932\pi$
$348$	0.426078	+	1.31133i	0.0228402	+	0.0702949i
$349$	27.6183			1.47837			0.739187	−	0.673500i	$-0.235210\pi$
$349$	27.6183			1.47837			0.739187	+	0.673500i	$0.235210\pi$
$350$	0.223903	−	4.24949i	0.0119681	−	0.227145i
$351$	−0.450220			−0.0240310
$352$	8.94292	+	27.5235i	0.476659	+	1.46701i
$353$	14.6352	−	10.6331i	0.778955	−	0.565944i	−0.125710	−	0.992067i	$-0.540121\pi$
$353$	14.6352	−	10.6331i	0.778955	−	0.565944i	0.904665	+	0.426123i	$0.140121\pi$
$354$	5.79963	−	4.21368i	0.308247	−	0.223954i
$355$	−11.3271	+	5.40081i	−0.601182	+	0.286645i
$356$	15.7976	+	11.4777i	0.837273	+	0.608315i
$357$	−3.60157			−0.190615
$358$	−1.10273	−	0.801177i	−0.0582808	−	0.0423435i
$359$	1.84108	−	5.66627i	0.0971687	−	0.299054i	−0.890644	−	0.454701i	$-0.849746\pi$
$359$	1.84108	−	5.66627i	0.0971687	−	0.299054i	0.987813	+	0.155647i	$0.0497461\pi$
$360$	−5.62692	+	2.68293i	−0.296565	+	0.141403i
$361$	−2.42594	−	7.46628i	−0.127681	−	0.392962i
$362$	−3.39899	+	10.4610i	−0.178647	+	0.549819i
$363$	4.48957	−	13.8175i	0.235641	−	0.725229i
$364$	0.177478	+	0.546222i	0.00930239	+	0.0286298i
$365$	3.63902	+	27.6711i	0.190475	+	1.44837i
$366$	−0.628952	+	1.93571i	−0.0328758	+	0.101181i
$367$	10.6591	+	7.74428i	0.556400	+	0.404248i	0.830140	−	0.557556i	$-0.188261\pi$
$367$	10.6591	+	7.74428i	0.556400	+	0.404248i	−0.273740	+	0.961804i	$0.588261\pi$
$368$	−0.318689			−0.0166128
$369$	−9.77262	−	7.10022i	−0.508742	−	0.369623i
$370$	−1.06909	−	0.198300i	−0.0555794	−	0.0103091i
$371$	−0.654118	+	0.475245i	−0.0339601	+	0.0246735i
$372$	3.01578	−	2.19109i	0.156361	−	0.113603i
$373$	−6.36866	−	19.6007i	−0.329757	−	1.01489i	−0.969247	−	0.246088i	$-0.920855\pi$
$373$	−6.36866	−	19.6007i	−0.329757	−	1.01489i	0.639491	−	0.768799i	$-0.279145\pi$
$374$	−15.4872			−0.800826
$375$	−11.1462	+	0.872502i	−0.575590	+	0.0450558i
$376$	27.6450			1.42568
$377$	0.150375	+	0.462808i	0.00774473	+	0.0238358i
$378$	0.688536	−	0.500250i	0.0354145	−	0.0257301i
$379$	−11.6820	+	8.48744i	−0.600062	+	0.435971i	−0.845901	−	0.533340i	$-0.820937\pi$
$379$	−11.6820	+	8.48744i	−0.600062	+	0.435971i	0.245839	+	0.969311i	$0.420937\pi$
$380$	9.36494	+	1.73705i	0.480411	+	0.0891088i
$381$	11.8449	+	8.60583i	0.606833	+	0.440890i
$382$	16.1978			0.828751
$383$	7.52627	+	5.46816i	0.384574	+	0.279410i	0.763229	−	0.646129i	$-0.223613\pi$
$383$	7.52627	+	5.46816i	0.384574	+	0.279410i	−0.378654	+	0.925538i	$0.623613\pi$
$384$	2.35187	−	7.23832i	0.120019	−	0.369379i
$385$	−1.47310	−	11.2015i	−0.0750761	−	0.570879i
$386$	6.36195	+	19.5801i	0.323815	+	0.996600i
$387$	1.10513	−	3.40125i	0.0561770	−	0.172895i
$388$	−1.15134	+	3.54346i	−0.0584504	+	0.179892i
$389$	1.55265	+	4.77857i	0.0787226	+	0.242283i	0.982671	−	0.185358i	$-0.0593446\pi$
$389$	1.55265	+	4.77857i	0.0787226	+	0.242283i	−0.903948	+	0.427642i	$0.859345\pi$
$390$	−0.773386	+	0.368753i	−0.0391619	+	0.0186725i
$391$	1.98519	−	6.10978i	0.100395	−	0.308985i
$392$	−2.25541	−	1.63865i	−0.113916	−	0.0827645i
$393$	−14.3721			−0.724978
$394$	−3.89295	−	2.82840i	−0.196124	−	0.142493i
$395$	−4.74774	+	2.26374i	−0.238885	+	0.113901i
$396$	−5.21445	+	3.78852i	−0.262036	+	0.190380i
$397$	25.9130	−	18.8269i	1.30054	−	0.944896i	0.300578	−	0.953757i	$-0.402821\pi$
$397$	25.9130	−	18.8269i	1.30054	−	0.944896i	0.999961	+	0.00886089i	$0.00282055\pi$
$398$	−3.28827	−	10.1203i	−0.164826	−	0.507283i
$399$	−3.33909			−0.167163
$400$	0.562383	−	0.694087i	0.0281192	−	0.0347043i
$401$	30.6935			1.53276			0.766380	−	0.642387i	$-0.222056\pi$
$401$	30.6935			1.53276			0.766380	+	0.642387i	$0.222056\pi$
$402$	3.57256	+	10.9952i	0.178183	+	0.548391i
$403$	1.06435	−	0.773299i	0.0530193	−	0.0385208i
$404$	−12.1085	+	8.79736i	−0.602422	+	0.437685i
$405$	−1.53898	−	1.62220i	−0.0764725	−	0.0806079i
$406$	−0.744211	−	0.540701i	−0.0369346	−	0.0268345i
$407$	−2.88682			−0.143094
$408$	8.12304	+	5.90173i	0.402150	+	0.292179i
$409$	2.93359	−	9.02867i	0.145057	−	0.446439i	−0.851961	−	0.523604i	$-0.824587\pi$
$409$	2.93359	−	9.02867i	0.145057	−	0.446439i	0.997018	+	0.0771655i	$0.0245870\pi$
$410$	−22.6028	−	4.19246i	−1.11627	−	0.207051i
$411$	−3.62124	−	11.1450i	−0.178623	−	0.549744i
$412$	1.69785	−	5.22544i	0.0836469	−	0.257439i
$413$	2.60289	−	8.01088i	0.128080	−	0.394189i
$414$	0.469114	+	1.44378i	0.0230557	+	0.0709581i
$415$	−7.76388	−	8.18372i	−0.381114	−	0.401723i
$416$	0.796877	−	2.45254i	0.0390701	−	0.120245i
$417$	5.27425	+	3.83196i	0.258281	+	0.187652i
$418$	−14.3585			−0.702298
$419$	21.9755	+	15.9661i	1.07357	+	0.779995i	0.976551	−	0.215287i	$-0.0690687\pi$
$419$	21.9755	+	15.9661i	1.07357	+	0.779995i	0.0970206	+	0.995282i	$0.469069\pi$
$420$	−1.36144	+	2.50662i	−0.0664314	+	0.122310i
$421$	0.487970	−	0.354531i	0.0237822	−	0.0172788i	−0.575831	−	0.817569i	$-0.695321\pi$
$421$	0.487970	−	0.354531i	0.0237822	−	0.0172788i	0.599613	+	0.800290i	$0.295321\pi$
$422$	−4.28505	+	3.11327i	−0.208593	+	0.151552i
$423$	3.06429	+	9.43091i	0.148991	+	0.458546i
$424$	2.25407			0.109467
$425$	9.80355	+	15.1054i	0.475542	+	0.732721i
$426$	−4.77624			−0.231410
$427$	0.739007	+	2.27443i	0.0357630	+	0.110067i
$428$	−17.8799	+	12.9905i	−0.864259	+	0.627921i
$429$	−1.84033	+	1.33708i	−0.0888520	+	0.0645547i
$430$	−0.887400	−	6.74780i	−0.0427942	−	0.325408i
$431$	9.51193	+	6.91082i	0.458174	+	0.332883i	0.792814	−	0.609463i	$-0.208615\pi$
$431$	9.51193	+	6.91082i	0.458174	+	0.332883i	−0.334641	+	0.942346i	$0.608615\pi$
$432$	0.178665			0.00859603
$433$	−24.2877	−	17.6460i	−1.16719	−	0.848013i	−0.176520	−	0.984297i	$-0.556484\pi$
$433$	−24.2877	−	17.6460i	−1.16719	−	0.848013i	−0.990670	+	0.136284i	$0.956484\pi$
$434$	−0.768519	+	2.36526i	−0.0368901	+	0.113536i
$435$	−1.15353	+	2.12383i	−0.0553076	+	0.101830i
$436$	7.38517	+	22.7292i	0.353686	+	1.08853i
$437$	1.84051	−	5.66449i	0.0880433	−	0.270969i
$438$	−3.28259	+	10.1028i	−0.156848	+	0.482729i
$439$	−4.35029	−	13.3888i	−0.207628	−	0.639013i	−0.999595	−	0.0284496i	$-0.990943\pi$
$439$	−4.35029	−	13.3888i	−0.207628	−	0.639013i	0.791967	−	0.610564i	$-0.209057\pi$
$440$	−15.0329	+	27.6778i	−0.716664	+	1.31949i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	1.11646	+	0.811157i	0.0531047	+	0.0385828i
$443$	11.0263			0.523874			0.261937	−	0.965085i	$-0.415639\pi$
$443$	11.0263			0.523874			0.261937	+	0.965085i	$0.415639\pi$
$444$	0.589660	+	0.428413i	0.0279840	+	0.0203316i
$445$	4.46289	+	33.9358i	0.211561	+	1.60871i
$446$	−7.70201	+	5.59584i	−0.364701	+	0.264971i
$447$	−16.0557	+	11.6652i	−0.759410	+	0.551743i
$448$	1.39596	+	4.29633i	0.0659530	+	0.202982i
$449$	−25.9842			−1.22627			−0.613135	−	0.789978i	$-0.710092\pi$
$449$	−25.9842			−1.22627			−0.613135	+	0.789978i	$0.710092\pi$
$450$	−3.97232	−	1.52611i	−0.187257	−	0.0719415i
$451$	−61.0332			−2.87394
$452$	−0.0756933	−	0.232960i	−0.00356031	−	0.0109575i
$453$	12.5392	−	9.11029i	0.589145	−	0.428039i
$454$	11.6612	−	8.47237i	0.547288	−	0.397628i
$455$	−0.480491	+	0.884658i	−0.0225258	+	0.0414734i
$456$	7.53102	+	5.47161i	0.352672	+	0.256231i
$457$	6.44321			0.301401			0.150700	−	0.988579i	$-0.451847\pi$
$457$	6.44321			0.301401			0.150700	+	0.988579i	$0.451847\pi$
$458$	−7.09930	−	5.15795i	−0.331729	−	0.241015i
$459$	−1.11295	+	3.42530i	−0.0519479	+	0.159879i
$460$	−3.50185	−	3.69122i	−0.163275	−	0.172104i
$461$	−8.73530	−	26.8845i	−0.406843	−	1.25213i	−0.919346	−	0.393449i	$-0.871282\pi$
$461$	−8.73530	−	26.8845i	−0.406843	−	1.25213i	0.512503	−	0.858685i	$-0.328718\pi$
$462$	1.32881	−	4.08967i	0.0618220	−	0.190269i
$463$	5.02753	−	15.4732i	0.233649	−	0.719098i	−0.763648	−	0.645632i	$-0.776594\pi$
$463$	5.02753	−	15.4732i	0.233649	−	0.719098i	0.997298	−	0.0734662i	$-0.0234061\pi$
$464$	−0.0596749	−	0.183660i	−0.00277034	−	0.00852622i
$465$	6.42456	+	1.19166i	0.297932	+	0.0552617i
$466$	0.0974286	−	0.299854i	0.00451329	−	0.0138905i
$467$	29.3532	+	21.3263i	1.35830	+	0.986865i	0.998551	+	0.0538165i	$0.0171386\pi$
$467$	29.3532	+	21.3263i	1.35830	+	0.986865i	0.359752	+	0.933048i	$0.382861\pi$
$468$	0.574332			0.0265485
$469$	10.9897	+	7.98449i	0.507457	+	0.368689i
$470$	12.9882	+	13.6906i	0.599101	+	0.631498i
$471$	−3.47590	+	2.52539i	−0.160161	+	0.116364i
$472$	−18.9977	+	13.8026i	−0.874438	+	0.635316i
$473$	−5.58377	−	17.1851i	−0.256742	−	0.790170i
$474$	−2.00195			−0.0919527
$475$	9.08905	+	14.0045i	0.417034	+	0.642571i
$476$	4.59441			0.210585
$477$	0.249851	+	0.768962i	0.0114399	+	0.0352084i
$478$	−8.63846	+	6.27621i	−0.395114	+	0.287067i
$479$	−8.23910	+	5.98606i	−0.376454	+	0.273510i	−0.759882	−	0.650061i	$-0.774743\pi$
$479$	−8.23910	+	5.98606i	−0.376454	+	0.273510i	0.383428	+	0.923571i	$0.374743\pi$
$480$	11.5608	−	5.51221i	0.527674	−	0.251597i
$481$	0.208108	+	0.151199i	0.00948891	+	0.00689409i
$482$	17.8893			0.814837
$483$	1.44306	+	1.04845i	0.0656616	+	0.0477059i
$484$	−5.72720	+	17.6265i	−0.260327	+	0.801204i
$485$	−5.89502	+	2.81076i	−0.267679	+	0.127630i
$486$	−0.262997	−	0.809422i	−0.0119298	−	0.0367161i
$487$	2.18526	−	6.72553i	0.0990234	−	0.304763i	−0.889258	−	0.457406i	$-0.848779\pi$
$487$	2.18526	−	6.72553i	0.0990234	−	0.304763i	0.988281	+	0.152643i	$0.0487786\pi$
$488$	2.06024	−	6.34076i	0.0932625	−	0.287033i
$489$	−2.03573	−	6.26532i	−0.0920587	−	0.283328i
$490$	−0.248135	−	1.88682i	−0.0112096	−	0.0852378i
$491$	−7.14069	+	21.9768i	−0.322255	+	0.991799i	0.650409	+	0.759584i	$0.274597\pi$
$491$	−7.14069	+	21.9768i	−0.322255	+	0.991799i	−0.972664	+	0.232215i	$0.925403\pi$
$492$	12.4666	+	9.05753i	0.562038	+	0.408345i
$493$	3.89280			0.175323
$494$	1.03509	+	0.752038i	0.0465710	+	0.0338358i
$495$	−11.1084	−	2.06044i	−0.499287	−	0.0926099i
$496$	−0.422378	+	0.306876i	−0.0189653	+	0.0137791i
$497$	−4.54020	+	3.29865i	−0.203656	+	0.147965i
$498$	−1.32677	−	4.08339i	−0.0594542	−	0.182981i
$499$	−3.90877			−0.174981			−0.0874903	−	0.996165i	$-0.527885\pi$
$499$	−3.90877			−0.174981			−0.0874903	+	0.996165i	$0.527885\pi$
$500$	14.2189	−	1.11302i	0.635889	−	0.0497759i
$501$	−1.10021			−0.0491536
$502$	2.99616	+	9.22124i	0.133725	+	0.411564i
$503$	−18.1625	+	13.1958i	−0.809824	+	0.588371i	−0.913780	−	0.406210i	$-0.866850\pi$
$503$	−18.1625	+	13.1958i	−0.809824	+	0.588371i	0.103956	+	0.994582i	$0.466850\pi$
$504$	−2.25541	+	1.63865i	−0.100464	+	0.0729915i
$505$	−25.7950	−	4.78457i	−1.14786	−	0.212911i
$506$	6.20536	+	4.50845i	0.275862	+	0.200425i
$507$	−12.7973			−0.568348
$508$	−15.1102	−	10.9782i	−0.670406	−	0.487078i
$509$	−5.49242	+	16.9039i	−0.243447	+	0.749254i	0.752441	+	0.658660i	$0.228877\pi$
$509$	−5.49242	+	16.9039i	−0.243447	+	0.749254i	−0.995888	+	0.0905938i	$0.971123\pi$
$510$	0.893676	+	6.79552i	0.0395726	+	0.300911i
$511$	3.85698	+	11.8706i	0.170623	+	0.525123i
$512$	−0.624070	+	1.92069i	−0.0275802	+	0.0848832i
$513$	−1.03183	+	3.17566i	−0.0455566	+	0.140209i
$514$	4.36176	+	13.4241i	0.192389	+	0.592112i
$515$	8.69322	−	4.14496i	0.383069	−	0.182649i
$516$	−1.40978	+	4.33886i	−0.0620622	+	0.191008i
$517$	40.5338	+	29.4496i	1.78268	+	1.29519i
$518$	−0.486267			−0.0213653
$519$	−19.5349	−	14.1930i	−0.857488	−	0.623002i
$520$	2.53336	−	1.20791i	0.111095	−	0.0529704i
$521$	−7.84420	+	5.69914i	−0.343661	+	0.249684i	−0.746205	−	0.665717i	$-0.768126\pi$
$521$	−7.84420	+	5.69914i	−0.343661	+	0.249684i	0.402544	+	0.915401i	$0.368126\pi$
$522$	−0.744211	+	0.540701i	−0.0325732	+	0.0236658i
$523$	1.29438	+	3.98368i	0.0565991	+	0.174194i	0.975360	−	0.220621i	$-0.0708085\pi$
$523$	1.29438	+	3.98368i	0.0565991	+	0.174194i	−0.918760	+	0.394815i	$0.870809\pi$
$524$	18.3341			0.800927
$525$	−4.82999	+	1.29274i	−0.210798	+	0.0564197i
$526$	−20.9720			−0.914423
$527$	−3.25221	−	10.0093i	−0.141668	−	0.436010i
$528$	0.730316	−	0.530605i	0.0317829	−	0.0230916i
$529$	16.0334	−	11.6489i	0.697103	−	0.506475i
$530$	1.05901	+	1.11628i	0.0460005	+	0.0484880i
$531$	−6.81446	−	4.95099i	−0.295722	−	0.214855i
$532$	4.25956			0.184676
$533$	4.39983	+	3.19666i	0.190578	+	0.138463i
$534$	−4.02576	+	12.3900i	−0.174212	+	0.536169i
$535$	−38.0899	−	7.06509i	−1.64677	−	0.305450i
$536$	−11.7025	−	36.0167i	−0.505472	−	1.55568i
$537$	−0.494906	+	1.52317i	−0.0213568	+	0.0657294i
$538$	3.04329	−	9.36629i	0.131206	−	0.403809i
$539$	−1.56133	−	4.80529i	−0.0672513	−	0.206978i
$540$	1.96323	+	2.06939i	0.0844839	+	0.0890525i
$541$	−1.81926	+	5.59909i	−0.0782159	+	0.240724i	−0.982517	−	0.186170i	$-0.940392\pi$
$541$	−1.81926	+	5.59909i	−0.0782159	+	0.240724i	0.904302	+	0.426894i	$0.140392\pi$
$542$	15.0489	+	10.9337i	0.646405	+	0.469641i
$543$	12.9241			0.554624
$544$	−16.6891	−	12.1254i	−0.715541	−	0.519871i
$545$	−19.9940	+	36.8121i	−0.856451	+	1.57686i
$546$	−0.309993	+	0.225223i	−0.0132665	+	0.00963865i
$547$	1.14720	−	0.833489i	0.0490507	−	0.0356374i	−0.562990	−	0.826464i	$-0.690349\pi$
$547$	1.14720	−	0.833489i	0.0490507	−	0.0356374i	0.612040	+	0.790826i	$0.290349\pi$
$548$	4.61950	+	14.2174i	0.197335	+	0.607335i
$549$	2.39148			0.102066
$550$	−20.7696	+	5.55895i	−0.885619	+	0.237034i
$551$	3.60908			0.153752
$552$	−1.53666	−	4.72936i	−0.0654047	−	0.201295i
$553$	−1.90302	+	1.38262i	−0.0809245	+	0.0587951i
$554$	−15.4270	+	11.2083i	−0.655429	+	0.476197i
$555$	0.166581	+	1.26668i	0.00707096	+	0.0537677i
$556$	−6.72819	−	4.88831i	−0.285339	−	0.207311i
$557$	−28.5493			−1.20967			−0.604836	−	0.796350i	$-0.706762\pi$
$557$	−28.5493			−1.20967			−0.604836	+	0.796350i	$0.706762\pi$
$558$	2.01201	+	1.46181i	0.0851752	+	0.0618834i
$559$	−0.497553	+	1.53131i	−0.0210442	+	0.0647675i
$560$	0.190678	−	0.351067i	0.00805761	−	0.0148353i
$561$	5.62325	+	17.3066i	0.237414	+	0.730685i
$562$	5.89948	−	18.1567i	0.248854	−	0.765895i
$563$	10.1341	−	31.1895i	0.427100	−	1.31448i	−0.473869	−	0.880595i	$-0.657143\pi$
$563$	10.1341	−	31.1895i	0.427100	−	1.31448i	0.900969	−	0.433884i	$-0.142857\pi$
$564$	−3.90901	−	12.0307i	−0.164599	−	0.506584i
$565$	0.204926	−	0.377301i	0.00862132	−	0.0158732i
$566$	−4.85973	+	14.9567i	−0.204270	+	0.628678i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	15.6454			0.656466
$569$	−33.3625	−	24.2393i	−1.39863	−	1.01616i	−0.994855	−	0.101305i	$-0.967698\pi$
$569$	−33.3625	−	24.2393i	−1.39863	−	1.01616i	−0.403774	−	0.914859i	$-0.632302\pi$
$570$	0.828544	+	6.30025i	0.0347039	+	0.263889i
$571$	20.5007	−	14.8946i	0.857927	−	0.623320i	−0.0693935	−	0.997589i	$-0.522106\pi$
$571$	20.5007	−	14.8946i	0.857927	−	0.623320i	0.927320	+	0.374269i	$0.122106\pi$
$572$	2.34765	−	1.70567i	0.0981602	−	0.0713175i
$573$	−5.88125	−	18.1006i	−0.245693	−	0.756164i
$574$	−10.2807			−0.429107
$575$	0.469266	−	8.90626i	0.0195698	−	0.371417i
$576$	4.51742			0.188226
$577$	2.75830	+	8.48919i	0.114830	+	0.353410i	0.991911	−	0.126932i	$-0.0405129\pi$
$577$	2.75830	+	8.48919i	0.114830	+	0.353410i	−0.877082	+	0.480341i	$0.840513\pi$
$578$	−2.77388	+	2.01534i	−0.115378	+	0.0838272i
$579$	19.5703	−	14.2186i	0.813313	−	0.590906i
$580$	1.47152	−	2.70930i	0.0611017	−	0.112498i
$581$	−4.08135	−	2.96527i	−0.169323	−	0.123020i
$582$	−2.48572			−0.103036
$583$	3.30498	+	2.40121i	0.136878	+	0.0994480i
$584$	10.7527	−	33.0933i	0.444949	−	1.36941i
$585$	0.692880	+	0.730348i	0.0286471	+	0.0301962i
$586$	3.07012	+	9.44886i	0.126825	+	0.390329i
$587$	13.9715	−	42.9999i	0.576666	−	1.77480i	−0.0537693	−	0.998553i	$-0.517124\pi$
$587$	13.9715	−	42.9999i	0.576666	−	1.77480i	0.630435	−	0.776242i	$-0.282876\pi$
$588$	−0.394203	+	1.21323i	−0.0162567	+	0.0500329i
$589$	−3.01518	−	9.27978i	−0.124238	−	0.382366i
$590$	−15.7609	−	2.92341i	−0.648868	−	0.120355i
$591$	−1.74717	+	5.37724i	−0.0718690	+	0.221190i
$592$	−0.0825855	−	0.0600019i	−0.00339424	−	0.00246606i
$593$	24.6673			1.01296			0.506482	−	0.862251i	$-0.330946\pi$
$593$	24.6673			1.01296			0.506482	+	0.862251i	$0.330946\pi$
$594$	−3.47888	−	2.52755i	−0.142740	−	0.103707i
$595$	5.54275	+	5.84248i	0.227231	+	0.239518i
$596$	20.4818	−	14.8809i	0.838966	−	0.609545i
$597$	−10.1152	+	7.34912i	−0.413987	+	0.300779i
$598$	−0.211205	−	0.650021i	−0.00863680	−	0.0265813i
$599$	−6.80763			−0.278152			−0.139076	−	0.990282i	$-0.544413\pi$
$599$	−6.80763			−0.278152			−0.139076	+	0.990282i	$0.544413\pi$
$600$	13.0120	+	4.99903i	0.531212	+	0.204084i
$601$	−6.24937			−0.254917			−0.127459	−	0.991844i	$-0.540682\pi$
$601$	−6.24937			−0.254917			−0.127459	+	0.991844i	$0.540682\pi$
$602$	−0.940552	−	2.89472i	−0.0383341	−	0.117980i
$603$	10.9897	−	7.98449i	0.447535	−	0.325153i
$604$	−15.9959	+	11.6217i	−0.650864	+	0.472880i
$605$	−29.3241	+	13.9818i	−1.19219	+	0.568441i
$606$	−8.07834	−	5.86926i	−0.328160	−	0.238422i
$607$	−30.6861			−1.24551			−0.622755	−	0.782417i	$-0.713987\pi$
$607$	−30.6861			−1.24551			−0.622755	+	0.782417i	$0.713987\pi$
$608$	−15.4728	−	11.2417i	−0.627505	−	0.455909i
$609$	−0.334004	+	1.02796i	−0.0135345	+	0.0416550i
$610$	4.10806	−	1.95874i	0.166331	−	0.0793070i
$611$	−1.37960	−	4.24599i	−0.0558128	−	0.171774i
$612$	1.41975	−	4.36955i	0.0573901	−	0.176628i
$613$	3.42230	−	10.5328i	0.138225	−	0.425414i	−0.857852	−	0.513896i	$-0.828202\pi$
$613$	3.42230	−	10.5328i	0.138225	−	0.425414i	0.996078	+	0.0884823i	$0.0282017\pi$
$614$	−0.0600229	−	0.184732i	−0.00242233	−	0.00745516i
$615$	3.52186	+	26.7803i	0.142015	+	1.07988i
$616$	−4.35275	+	13.3964i	−0.175377	+	0.539756i
$617$	−9.05517	−	6.57897i	−0.364548	−	0.264859i	0.390399	−	0.920646i	$-0.372337\pi$
$617$	−9.05517	−	6.57897i	−0.364548	−	0.264859i	−0.754946	+	0.655787i	$0.772337\pi$
$618$	3.66562			0.147453
$619$	28.4446	+	20.6662i	1.14329	+	0.830646i	0.987574	−	0.157157i	$-0.0502327\pi$
$619$	28.4446	+	20.6662i	1.14329	+	0.830646i	0.155712	+	0.987802i	$0.450233\pi$
$620$	−8.19561	−	1.52016i	−0.329143	−	0.0610510i
$621$	1.44306	−	1.04845i	0.0579081	−	0.0420727i
$622$	−14.3126	+	10.3987i	−0.573884	+	0.416951i
$623$	4.73020	+	14.5580i	0.189511	+	0.583256i
$624$	−0.0804387			−0.00322012
$625$	18.5692	+	16.7387i	0.742769	+	0.669548i
$626$	9.81111			0.392131
$627$	5.21342	+	16.0453i	0.208204	+	0.640786i
$628$	4.43409	−	3.22155i	0.176939	−	0.128554i
$629$	1.66478	−	1.20953i	0.0663790	−	0.0482272i
$630$	−1.87115	−	0.347069i	−0.0745484	−	0.0138276i
$631$	12.4642	+	9.05574i	0.496190	+	0.360503i	0.807560	−	0.589785i	$-0.200788\pi$
$631$	12.4642	+	9.05574i	0.496190	+	0.360503i	−0.311370	+	0.950289i	$0.600788\pi$
$632$	6.55773			0.260852
$633$	5.03486	+	3.65804i	0.200118	+	0.145394i
$634$	−3.36369	+	10.3524i	−0.133589	+	0.411146i
$635$	−4.26868	−	32.4591i	−0.169397	−	1.28810i
$636$	−0.318727	−	0.980941i	−0.0126383	−	0.0388968i
$637$	−0.139126	+	0.428185i	−0.00551236	+	0.0169653i
$638$	−1.43626	+	4.42036i	−0.0568621	+	0.175004i
$639$	1.73420	+	5.33733i	0.0686040	+	0.211142i
$640$	−15.3615	+	7.32442i	−0.607217	+	0.289523i
$641$	11.2021	−	34.4766i	0.442457	−	1.36174i	−0.442791	−	0.896625i	$-0.646012\pi$
$641$	11.2021	−	34.4766i	0.442457	−	1.36174i	0.885248	−	0.465119i	$-0.153988\pi$
$642$	−11.9288	−	8.66678i	−0.470792	−	0.342051i
$643$	18.8248			0.742378			0.371189	−	0.928557i	$-0.378950\pi$
$643$	18.8248			0.742378			0.371189	+	0.928557i	$0.378950\pi$
$644$	−1.84087	−	1.33747i	−0.0725403	−	0.0527036i
$645$	−7.21829	+	3.44170i	−0.284220	+	0.135517i
$646$	8.28030	−	6.01599i	0.325784	−	0.236696i
$647$	9.48453	−	6.89092i	0.372876	−	0.270910i	−0.385527	−	0.922697i	$-0.625980\pi$
$647$	9.48453	−	6.89092i	0.372876	−	0.270910i	0.758402	+	0.651787i	$0.225980\pi$
$648$	0.861492	+	2.65140i	0.0338426	+	0.104157i
$649$	−42.5585			−1.67057
$650$	1.78842	+	0.687085i	0.0701475	+	0.0269497i
$651$	2.92216			0.114528
$652$	2.59691	+	7.99247i	0.101703	+	0.313009i
$653$	6.31877	−	4.59086i	0.247273	−	0.179654i	−0.457245	−	0.889341i	$-0.651164\pi$
$653$	6.31877	−	4.59086i	0.247273	−	0.179654i	0.704517	+	0.709687i	$0.251164\pi$
$654$	−12.8993	+	9.37191i	−0.504403	+	0.366471i
$655$	22.1184	+	23.3145i	0.864238	+	0.910973i
$656$	−1.74603	−	1.26856i	−0.0681709	−	0.0495290i
$657$	12.4815			0.486948
$658$	6.82769	+	4.96061i	0.266171	+	0.193385i
$659$	−13.7474	+	42.3102i	−0.535523	+	1.64817i	0.206992	+	0.978343i	$0.433632\pi$
$659$	−13.7474	+	42.3102i	−0.535523	+	1.64817i	−0.742516	+	0.669829i	$0.766368\pi$
$660$	14.1707	+	2.62844i	0.551593	+	0.102312i
$661$	13.8172	+	42.5251i	0.537428	+	1.65403i	0.738343	+	0.674426i	$0.235609\pi$
$661$	13.8172	+	42.5251i	0.537428	+	1.65403i	−0.200914	+	0.979609i	$0.564391\pi$
$662$	7.29760	−	22.4597i	0.283629	−	0.872921i
$663$	0.501071	−	1.54214i	0.0194600	−	0.0598917i
$664$	4.34607	+	13.3758i	0.168660	+	0.519083i
$665$	5.13879	+	5.41667i	0.199274	+	0.210050i
$666$	−0.150265	+	0.462467i	−0.00582264	+	0.0179202i
$667$	−1.55975	−	1.13322i	−0.0603937	−	0.0438786i
$668$	1.40350			0.0543030
$669$	9.04972	+	6.57501i	0.349882	+	0.254204i
$670$	12.3384	−	22.7168i	0.476672	−	0.877627i
$671$	9.77545	−	7.10228i	0.377377	−	0.274180i
$672$	4.63385	−	3.36669i	0.178754	−	0.129873i
$673$	−5.86305	−	18.0446i	−0.226004	−	0.695569i	−0.998188	−	0.0601698i	$-0.980836\pi$
$673$	−5.86305	−	18.0446i	−0.226004	−	0.695569i	0.772184	−	0.635399i	$-0.219164\pi$
$674$	−31.0030			−1.19419
$675$	−0.263083	+	4.99307i	−0.0101261	+	0.192184i
$676$	16.3251			0.627889
$677$	−5.03498	−	15.4961i	−0.193510	−	0.595563i	−0.999991	−	0.00430237i	$-0.998631\pi$
$677$	−5.03498	−	15.4961i	−0.193510	−	0.595563i	0.806481	−	0.591260i	$-0.201369\pi$
$678$	0.132210	−	0.0960561i	0.00507749	−	0.00368901i
$679$	−2.36287	+	1.71673i	−0.0906788	+	0.0658820i
$680$	−2.92739	−	22.2599i	−0.112260	−	0.853627i
$681$	−13.7017	−	9.95488i	−0.525051	−	0.381472i
$682$	12.5657			0.481164
$683$	6.66033	+	4.83901i	0.254850	+	0.185160i	0.707874	−	0.706339i	$-0.249655\pi$
$683$	6.66033	+	4.83901i	0.254850	+	0.185160i	−0.453023	+	0.891499i	$0.649655\pi$
$684$	1.31628	−	4.05109i	0.0503291	−	0.154897i
$685$	−12.5065	+	23.0264i	−0.477848	+	0.879792i
$686$	−0.262997	−	0.809422i	−0.0100413	−	0.0309039i
$687$	−3.18619	+	9.80608i	−0.121561	+	0.374125i
$688$	0.197449	−	0.607684i	0.00752766	−	0.0231678i
$689$	−0.112488	−	0.346202i	−0.00428545	−	0.0131893i
$690$	1.62015	−	2.98295i	0.0616782	−	0.113559i
$691$	8.69065	−	26.7471i	0.330608	−	1.01751i	−0.638237	−	0.769840i	$-0.720336\pi$
$691$	8.69065	−	26.7471i	0.330608	−	1.01751i	0.968845	−	0.247667i	$-0.0796639\pi$
$692$	24.9201	+	18.1055i	0.947320	+	0.688268i
$693$	−5.05258			−0.191932
$694$	8.22768	+	5.97776i	0.312318	+	0.226913i
$695$	−1.90074	−	14.4532i	−0.0720990	−	0.548242i
$696$	2.43779	−	1.77116i	0.0924041	−	0.0671355i
$697$	35.1968	−	25.5720i	1.33317	−	0.968607i
$698$	−7.26354	−	22.3549i	−0.274929	−	0.846145i
$699$	−0.370455			−0.0140119
$700$	6.16147	−	1.64911i	0.232882	−	0.0623303i
$701$	24.7805			0.935947			0.467973	−	0.883743i	$-0.344984\pi$
$701$	24.7805			0.935947			0.467973	+	0.883743i	$0.344984\pi$
$702$	0.118407	+	0.364418i	0.00446897	+	0.0137541i
$703$	1.54345	−	1.12138i	0.0582121	−	0.0422936i
$704$	18.4655	−	13.4160i	0.695945	−	0.505634i
$705$	10.5830	−	19.4849i	0.398578	−	0.733843i
$706$	−12.4557	−	9.04961i	−0.468777	−	0.340586i
$707$	−11.7326			−0.441251
$708$	8.69299	+	6.31582i	0.326702	+	0.237363i
$709$	−6.06079	+	18.6532i	−0.227618	+	0.700535i	0.770398	+	0.637564i	$0.220058\pi$
$709$	−6.06079	+	18.6532i	−0.227618	+	0.700535i	−0.998015	+	0.0629714i	$0.979942\pi$
$710$	7.35054	+	7.74804i	0.275861	+	0.290779i
$711$	0.726887	+	2.23713i	0.0272604	+	0.0838989i
$712$	13.1871	−	40.5856i	0.494206	−	1.52101i
$713$	−1.61069	+	4.95721i	−0.0603210	+	0.185649i
$714$	0.947204	+	2.91519i	0.0354482	+	0.109098i
$715$	5.00124	+	0.927652i	0.187036	+	0.0346922i
$716$	0.631336	−	1.94305i	0.0235941	−	0.0726153i
$717$	10.1500	+	7.37443i	0.379060	+	0.275403i
$718$	−5.07061			−0.189233
$719$	4.23441	+	3.07648i	0.157917	+	0.114733i	0.663938	−	0.747788i	$-0.268884\pi$
$719$	4.23441	+	3.07648i	0.157917	+	0.114733i	−0.506021	+	0.862521i	$0.668884\pi$
$720$	−0.274962	−	0.289831i	−0.0102472	−	0.0108014i
$721$	3.48447	−	2.53161i	0.129768	−	0.0942822i
$722$	−5.40535	+	3.92722i	−0.201166	+	0.146156i
$723$	−6.49543	−	19.9909i	−0.241568	−	0.743469i
$724$	−16.4868			−0.612727
$725$	5.22055	−	1.39727i	0.193886	−	0.0518933i
$726$	−12.3649			−0.458905
$727$	8.11249	+	24.9677i	0.300875	+	0.925999i	0.981184	+	0.193074i	$0.0618457\pi$
$727$	8.11249	+	24.9677i	0.300875	+	0.925999i	−0.680309	+	0.732926i	$0.738154\pi$
$728$	1.01543	−	0.737755i	0.0376345	−	0.0273430i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	21.4406	−	10.2229i	0.793551	−	0.378368i
$731$	10.4203	+	7.57082i	0.385410	+	0.280017i
$732$	−3.05073			−0.112758
$733$	−12.6825	−	9.21438i	−0.468439	−	0.340341i	0.328394	−	0.944541i	$-0.393493\pi$
$733$	−12.6825	−	9.21438i	−0.468439	−	0.340341i	−0.796833	+	0.604200i	$0.793493\pi$
$734$	3.46508	−	10.6644i	0.127899	−	0.393631i
$735$	−2.01838	+	0.962369i	−0.0744490	+	0.0354975i
$736$	3.15714	+	9.71667i	0.116374	+	0.358161i
$737$	21.2092	−	65.2751i	0.781250	−	2.40444i
$738$	−3.17691	+	9.77751i	−0.116944	+	0.359915i
$739$	−8.43740	−	25.9676i	−0.310375	−	0.955235i	−0.977617	−	0.210394i	$-0.932525\pi$
$739$	−8.43740	−	25.9676i	−0.310375	−	0.955235i	0.667242	−	0.744841i	$-0.267475\pi$
$740$	−0.212502	−	1.61587i	−0.00781172	−	0.0594004i
$741$	0.464553	−	1.42975i	0.0170658	−	0.0525230i
$742$	0.556705	+	0.404470i	0.0204373	+	0.0148486i
$743$	15.7789			0.578873			0.289437	−	0.957197i	$-0.406532\pi$
$743$	15.7789			0.578873			0.289437	+	0.957197i	$0.406532\pi$
$744$	−6.59068	−	4.78841i	−0.241626	−	0.175551i
$745$	43.6327	+	8.09318i	1.59858	+	0.296511i
$746$	−14.1903	+	10.3099i	−0.519545	+	0.377471i
$747$	−4.08135	+	2.96527i	−0.149329	+	0.108494i
$748$	−7.17341	−	22.0775i	−0.262286	−	0.807232i
$749$	−17.3249			−0.633038
$750$	3.63765	+	8.79255i	0.132828	+	0.321059i
$751$	−49.0572			−1.79012			−0.895061	−	0.445943i	$-0.852868\pi$
$751$	−49.0572			−1.79012			−0.895061	+	0.445943i	$0.852868\pi$
$752$	0.547482	+	1.68498i	0.0199646	+	0.0614447i
$753$	9.21663	−	6.69627i	0.335872	−	0.244026i
$754$	0.335059	−	0.243434i	0.0122021	−	0.00886536i
$755$	−34.0764	−	6.32063i	−1.24017	−	0.230031i
$756$	1.03204	+	0.749819i	0.0375348	+	0.0272706i
$757$	−25.9671			−0.943789			−0.471895	−	0.881655i	$-0.656430\pi$
$757$	−25.9671			−0.943789			−0.471895	+	0.881655i	$0.656430\pi$
$758$	9.94225	+	7.22347i	0.361119	+	0.262368i
$759$	2.78498	−	8.57130i	0.101088	−	0.311118i
$760$	−2.71403	−	20.6375i	−0.0984484	−	0.748602i
$761$	−2.53235	−	7.79376i	−0.0917975	−	0.282524i	0.894608	−	0.446851i	$-0.147455\pi$
$761$	−2.53235	−	7.79376i	−0.0917975	−	0.282524i	−0.986406	+	0.164327i	$0.947455\pi$
$762$	3.85057	−	11.8508i	0.139492	−	0.429311i
$763$	−5.78926	+	17.8175i	−0.209585	+	0.645037i
$764$	7.50252	+	23.0904i	0.271432	+	0.835381i
$765$	7.26933	−	3.46604i	0.262823	−	0.125315i
$766$	2.44666	−	7.53004i	0.0884014	−	0.272071i
$767$	3.06801	+	2.22904i	0.110779	+	0.0804859i
$768$	−15.5122			−0.559750
$769$	−16.5357	−	12.0139i	−0.596292	−	0.433232i	0.248269	−	0.968691i	$-0.420138\pi$
$769$	−16.5357	−	12.0139i	−0.596292	−	0.433232i	−0.844561	+	0.535460i	$0.820138\pi$
$770$	−8.67929	+	4.13831i	−0.312780	+	0.149134i
$771$	13.4174	−	9.74830i	0.483215	−	0.351076i
$772$	−24.9652	+	18.1383i	−0.898516	+	0.652810i
$773$	6.95753	+	21.4131i	0.250245	+	0.770175i	0.994729	+	0.102535i	$0.0326954\pi$
$773$	6.95753	+	21.4131i	0.250245	+	0.770175i	−0.744484	+	0.667640i	$0.767305\pi$
$774$	−3.04369			−0.109403
$775$	−7.95416	−	12.2559i	−0.285722	−	0.440244i
$776$	8.14239			0.292295
$777$	0.176558	+	0.543391i	0.00633400	+	0.0194940i
$778$	3.45954	−	2.51350i	0.124031	−	0.0901135i
$779$	32.6316	−	23.7082i	1.16915	−	0.849436i
$780$	−0.883885	−	0.931682i	−0.0316481	−	0.0333596i
$781$	22.9397	+	16.6667i	0.820848	+	0.596381i
$782$	−5.46749			−0.195517
$783$	0.874434	+	0.635314i	0.0312497	+	0.0227043i
$784$	0.0552106	−	0.169921i	0.00197181	−	0.00606860i
$785$	9.44602	+	1.75209i	0.337143	+	0.0625347i
$786$	3.77983	+	11.6331i	0.134822	+	0.414940i
$787$	−11.9053	+	36.6407i	−0.424377	+	1.30610i	0.479212	+	0.877699i	$0.340922\pi$
$787$	−11.9053	+	36.6407i	−0.424377	+	1.30610i	−0.903589	+	0.428400i	$0.859078\pi$
$788$	2.22881	−	6.85957i	0.0793980	−	0.244362i
$789$	7.61471	+	23.4357i	0.271091	+	0.834332i
$790$	3.08096	+	3.24757i	0.109616	+	0.115543i
$791$	0.0593362	−	0.182618i	0.00210975	−	0.00649315i
$792$	11.3957	+	8.27943i	0.404927	+	0.294197i
$793$	−1.07669			−0.0382344
$794$	−22.0540	−	16.0232i	−0.782667	−	0.568641i
$795$	0.862897	−	1.58873i	0.0306038	−	0.0563463i
$796$	12.9036	−	9.37503i	0.457357	−	0.332289i
$797$	−12.4950	+	9.07815i	−0.442596	+	0.321565i	−0.786666	−	0.617379i	$-0.788194\pi$
$797$	−12.4950	+	9.07815i	−0.442596	+	0.321565i	0.344070	+	0.938944i	$0.388194\pi$
$798$	0.878170	+	2.70273i	0.0310869	+	0.0956756i
$799$	−35.7141			−1.26347
$800$	−26.7337	−	10.2707i	−0.945179	−	0.363125i
$801$	15.3072			0.540855
$802$	−8.07230	−	24.8440i	−0.285043	−	0.877272i
$803$	51.0195	−	37.0678i	1.80044	−	1.30809i
$804$	−14.0192	+	10.1856i	−0.494420	+	0.359217i
$805$	−0.520051	−	3.95447i	−0.0183294	−	0.139377i
$806$	−0.905847	−	0.658137i	−0.0319071	−	0.0231819i
$807$	−11.5716			−0.407339
$808$	26.4620	+	19.2257i	0.930929	+	0.676360i
$809$	13.0709	−	40.2282i	0.459549	−	1.41435i	−0.406161	−	0.913802i	$-0.633133\pi$
$809$	13.0709	−	40.2282i	0.459549	−	1.41435i	0.865710	−	0.500546i	$-0.166867\pi$
$810$	−0.908299	+	1.67232i	−0.0319144	+	0.0587593i
$811$	−6.87658	−	21.1639i	−0.241469	−	0.743166i	−0.996197	−	0.0871280i	$-0.972231\pi$
$811$	−6.87658	−	21.1639i	−0.241469	−	0.743166i	0.754728	−	0.656038i	$-0.227769\pi$
$812$	0.426078	−	1.31133i	0.0149524	−	0.0460188i
$813$	6.75399	−	20.7866i	0.236873	−	0.729019i
$814$	0.759224	+	2.33665i	0.0266108	+	0.0818996i
$815$	−7.03068	+	12.9446i	−0.246274	+	0.453428i
$816$	−0.198845	+	0.611982i	−0.00696097	+	0.0214237i
$817$	9.66089	+	7.01904i	0.337992	+	0.245565i
$818$	−8.07953			−0.282494
$819$	0.364236	+	0.264633i	0.0127274	+	0.00924702i
$820$	−4.49273	−	34.1627i	−0.156893	−	1.19301i
$821$	−16.3105	+	11.8502i	−0.569239	+	0.413576i	−0.834829	−	0.550510i	$-0.814433\pi$
$821$	−16.3105	+	11.8502i	−0.569239	+	0.413576i	0.265590	+	0.964086i	$0.414433\pi$
$822$	−8.06866	+	5.86222i	−0.281427	+	0.204469i
$823$	−10.6637	−	32.8196i	−0.371715	−	1.14402i	−0.945669	−	0.325132i	$-0.894591\pi$
$823$	−10.6637	−	32.8196i	−0.371715	−	1.14402i	0.573954	−	0.818888i	$-0.305409\pi$
$824$	−12.0074			−0.418296
$825$	13.7532	+	21.1911i	0.478825	+	0.737780i
$826$	−7.16873			−0.249432
$827$	−11.1022	−	34.1691i	−0.386062	−	1.18818i	−0.935707	−	0.352778i	$-0.885237\pi$
$827$	−11.1022	−	34.1691i	−0.386062	−	1.18818i	0.549646	−	0.835398i	$-0.314763\pi$
$828$	−1.84087	+	1.33747i	−0.0639746	+	0.0464802i
$829$	33.3069	−	24.1989i	1.15680	−	0.840461i	0.167426	−	0.985885i	$-0.446454\pi$
$829$	33.3069	−	24.1989i	1.15680	−	0.840461i	0.989370	+	0.145423i	$0.0464544\pi$
$830$	−4.58221	+	8.43655i	−0.159051	+	0.292837i
$831$	18.1264	+	13.1696i	0.628798	+	0.456848i
$832$	−2.03384			−0.0705106
$833$	2.91373	+	2.11695i	0.100955	+	0.0733480i
$834$	1.71456	−	5.27689i	0.0593705	−	0.182724i
$835$	1.69320	+	1.78476i	0.0585955	+	0.0617641i
$836$	−6.65060	−	20.4684i	−0.230016	−	0.707915i
$837$	0.902996	−	2.77914i	0.0312121	−	0.0960610i
$838$	7.14384	−	21.9865i	0.246780	−	0.759510i
$839$	−0.616457	−	1.89726i	−0.0212825	−	0.0655007i	0.939851	−	0.341584i	$-0.110963\pi$
$839$	−0.616457	−	1.89726i	−0.0212825	−	0.0655007i	−0.961134	+	0.276083i	$0.910963\pi$
$840$	6.12927	+	1.13688i	0.211480	+	0.0392262i
$841$	−8.60048	+	26.4696i	−0.296568	+	0.912743i
$842$	−0.415300	−	0.301733i	−0.0143122	−	0.0103984i
$843$	−22.4317			−0.772589
$844$	−6.42281	−	4.66644i	−0.221082	−	0.160626i
$845$	19.6948	+	20.7598i	0.677521	+	0.714159i
$846$	6.82769	−	4.96061i	0.234741	−	0.170549i
$847$	−11.7538	+	8.53966i	−0.403867	+	0.293426i
$848$	0.0446397	+	0.137387i	0.00153293	+	0.00471788i
$849$	18.4783			0.634172
$850$	9.64836	−	11.9079i	0.330936	−	0.408437i
$851$	−1.01914			−0.0349356
$852$	−2.21227	−	6.80866i	−0.0757911	−	0.233261i
$853$	−15.8381	+	11.5071i	−0.542286	+	0.393994i	−0.824933	−	0.565230i	$-0.808787\pi$
$853$	−15.8381	+	11.5071i	−0.542286	+	0.393994i	0.282647	+	0.959224i	$0.408787\pi$
$854$	1.64662	−	1.19634i	0.0563461	−	0.0409378i
$855$	6.73953	−	3.21343i	0.230487	−	0.109897i
$856$	39.0748	+	28.3895i	1.33555	+	0.970333i
$857$	−7.40712			−0.253022			−0.126511	−	0.991965i	$-0.540378\pi$
$857$	−7.40712			−0.253022			−0.126511	+	0.991965i	$0.540378\pi$
$858$	1.56626	+	1.13796i	0.0534713	+	0.0388492i
$859$	−6.74352	+	20.7544i	−0.230086	+	0.708132i	0.767649	+	0.640870i	$0.221426\pi$
$859$	−6.74352	+	20.7544i	−0.230086	+	0.708132i	−0.997735	+	0.0672616i	$0.978574\pi$
$860$	9.20814	−	4.39047i	0.313995	−	0.149714i
$861$	3.73281	+	11.4884i	0.127214	+	0.391524i
$862$	3.09216	−	9.51670i	0.105319	−	0.324140i
$863$	−4.36253	+	13.4265i	−0.148502	+	0.457043i	−0.997445	−	0.0714422i	$-0.977240\pi$
$863$	−4.36253	+	13.4265i	−0.148502	+	0.457043i	0.848942	+	0.528485i	$0.177240\pi$
$864$	−1.76997	−	5.44741i	−0.0602157	−	0.185325i
$865$	7.04001	+	53.5323i	0.239368	+	1.82015i
$866$	−7.89549	+	24.2998i	−0.268300	+	0.825742i
$867$	3.25926	+	2.36799i	0.110690	+	0.0804212i
$868$	−3.72770			−0.126526
$869$	9.61513	+	6.98580i	0.326171	+	0.236977i
$870$	2.02245	+	0.375133i	0.0685675	+	0.0127182i
$871$	−4.94779	+	3.59478i	−0.167649	+	0.121804i
$872$	42.2539	−	30.6993i	1.43090	−	1.03961i
$873$	0.902538	+	2.77773i	0.0305463	+	0.0940118i
$874$	−5.06902			−0.171462
$875$	9.53034	+	5.84573i	0.322184	+	0.197622i
$876$	−15.9222			−0.537961
$877$	−13.8075	−	42.4952i	−0.466248	−	1.43496i	−0.857407	−	0.514639i	$-0.827926\pi$
$877$	−13.8075	−	42.4952i	−0.466248	−	1.43496i	0.391159	−	0.920323i	$-0.372074\pi$
$878$	−9.69309	+	7.04244i	−0.327126	+	0.237671i
$879$	9.44413	−	6.86156i	0.318543	−	0.231435i
$880$	−1.98469	−	0.368129i	−0.0669039	−	0.0124096i
$881$	−11.5925	−	8.42248i	−0.390563	−	0.283761i	0.375123	−	0.926975i	$-0.377600\pi$
$881$	−11.5925	−	8.42248i	−0.390563	−	0.283761i	−0.765686	+	0.643214i	$0.777600\pi$
$882$	−0.851077			−0.0286573
$883$	29.8865	+	21.7138i	1.00576	+	0.730728i	0.963316	−	0.268371i	$-0.0864854\pi$
$883$	29.8865	+	21.7138i	1.00576	+	0.730728i	0.0424447	+	0.999099i	$0.486485\pi$
$884$	−0.639201	+	1.96726i	−0.0214987	+	0.0661661i
$885$	2.45580	+	18.6739i	0.0825508	+	0.627717i
$886$	−2.89988	−	8.92491i	−0.0974234	−	0.299838i
$887$	−14.5550	+	44.7956i	−0.488708	+	1.50409i	0.337829	+	0.941208i	$0.390308\pi$
$887$	−14.5550	+	44.7956i	−0.488708	+	1.50409i	−0.826537	+	0.562882i	$0.809692\pi$
$888$	0.492218	−	1.51489i	0.0165177	−	0.0508364i
$889$	−4.52435	−	13.9245i	−0.151742	−	0.467014i
$890$	26.2947	−	12.5374i	0.881400	−	0.420254i
$891$	−1.56133	+	4.80529i	−0.0523066	+	0.160983i
$892$	−11.5444	−	8.38753i	−0.386536	−	0.280835i
$893$	−33.1112			−1.10802
$894$	13.6647	+	9.92795i	0.457014	+	0.332040i
$895$	3.23253	−	1.54128i	0.108052	−	0.0515194i
$896$	−6.15728	+	4.47353i	−0.205700	+	0.149450i
$897$	−0.649696	+	0.472031i	−0.0216927	+	0.0157607i
$898$	6.83377	+	21.0322i	0.228046	+	0.701853i
$899$	−3.15844			−0.105340
$900$	0.335606	−	6.36951i	0.0111869	−	0.212317i
$901$	−2.91200			−0.0970127
$902$	16.0516	+	49.4016i	0.534459	+	1.64489i
$903$	−2.89327	+	2.10209i	−0.0962821	+	0.0699530i
$904$	−0.433076	+	0.314648i	−0.0144039	+	0.0104650i
$905$	−19.8899	−	20.9654i	−0.661161	−	0.696915i
$906$	−10.6719	−	7.75356i	−0.354549	−	0.257595i
$907$	22.3437			0.741909			0.370954	−	0.928651i	$-0.379031\pi$
$907$	22.3437			0.741909			0.370954	+	0.928651i	$0.379031\pi$
$908$	17.4788	+	12.6991i	0.580056	+	0.421435i
$909$	−3.62559	+	11.1584i	−0.120253	+	0.370101i
$910$	0.842430	+	0.156258i	0.0279263	+	0.00517989i
$911$	−10.7705	−	33.1483i	−0.356843	−	1.09825i	−0.954933	−	0.296822i	$-0.904073\pi$
$911$	−10.7705	−	33.1483i	−0.356843	−	1.09825i	0.598089	−	0.801429i	$-0.295927\pi$
$912$	−0.184353	+	0.567380i	−0.00610453	+	0.0187878i
$913$	−7.87664	+	24.2418i	−0.260679	+	0.802287i
$914$	−1.69455	−	5.21528i	−0.0560507	−	0.172506i
$915$	−3.68043	−	3.87946i	−0.121671	−	0.128251i
$916$	4.06452	−	12.5093i	0.134296	−	0.413319i
$917$	11.6273	+	8.44773i	0.383967	+	0.278968i
$918$	3.06522			0.101167
$919$	−36.8437	−	26.7685i	−1.21536	−	0.883012i	−0.219655	−	0.975578i	$-0.570493\pi$
$919$	−36.8437	−	26.7685i	−1.21536	−	0.883012i	−0.995707	+	0.0925656i	$0.970493\pi$
$920$	−5.30709	+	9.77116i	−0.174969	+	0.322146i
$921$	−0.184639	+	0.134148i	−0.00608406	+	0.00442033i
$922$	−19.4635	+	14.1411i	−0.640997	+	0.465712i
$923$	−0.780774	−	2.40297i	−0.0256995	−	0.0790949i
$924$	6.44541			0.212038
$925$	1.79845	−	2.21963i	0.0591327	−	0.0729808i
$926$	−13.8465			−0.455026
$927$	−1.33095	−	4.09623i	−0.0437140	−	0.134538i
$928$	−5.00854	+	3.63892i	−0.164413	+	0.119453i
$929$	−11.9593	+	8.68897i	−0.392373	+	0.285076i	−0.766427	−	0.642331i	$-0.777967\pi$
$929$	−11.9593	+	8.68897i	−0.392373	+	0.285076i	0.374054	+	0.927407i	$0.377967\pi$
$930$	−0.725089	−	5.51358i	−0.0237766	−	0.180798i
$931$	2.70138	+	1.96267i	0.0885341	+	0.0643238i
$932$	0.472577			0.0154798
$933$	16.8171	+	12.2183i	0.550567	+	0.400010i
$934$	9.54220	−	29.3679i	0.312230	−	0.960946i
$935$	19.4207	−	35.7566i	0.635126	−	1.16936i
$936$	−0.387861	−	1.19371i	−0.0126776	−	0.0390177i
$937$	−13.1886	+	40.5903i	−0.430852	+	1.32603i	0.466426	+	0.884560i	$0.345541\pi$
$937$	−13.1886	+	40.5903i	−0.430852	+	1.32603i	−0.897278	+	0.441466i	$0.854459\pi$
$938$	3.57256	−	10.9952i	0.116648	−	0.359006i
$939$	−3.56231	−	10.9637i	−0.116252	−	0.357786i
$940$	−13.5004	+	24.8562i	−0.440333	+	0.810721i
$941$	1.46570	−	4.51096i	0.0477804	−	0.147053i	−0.924320	−	0.381619i	$-0.875367\pi$
$941$	1.46570	−	4.51096i	0.0477804	−	0.147053i	0.972100	+	0.234566i	$0.0753668\pi$
$942$	2.95825	+	2.14930i	0.0963851	+	0.0700279i
$943$	−21.5467			−0.701657
$944$	−1.21751	−	0.884570i	−0.0396265	−	0.0287903i
$945$	0.291554	+	2.21698i	0.00948425	+	0.0721183i
$946$	−12.4415	+	9.03925i	−0.404507	+	0.293891i
$947$	−26.6047	+	19.3294i	−0.864537	+	0.628123i	−0.929115	−	0.369790i	$-0.879430\pi$
$947$	−26.6047	+	19.3294i	−0.864537	+	0.628123i	0.0645788	+	0.997913i	$0.479430\pi$
$948$	−0.927267	−	2.85383i	−0.0301162	−	0.0926882i
$949$	−5.61940			−0.182414
$950$	8.94517	−	11.0400i	0.290220	−	0.358186i
$951$	12.7898			0.414739
$952$	−3.10273	−	9.54921i	−0.100560	−	0.309492i
$953$	−8.55784	+	6.21764i	−0.277216	+	0.201409i	−0.717702	−	0.696350i	$-0.754806\pi$
$953$	−8.55784	+	6.21764i	−0.277216	+	0.201409i	0.440486	+	0.897759i	$0.354806\pi$
$954$	0.556705	−	0.404470i	0.0180240	−	0.0130952i
$955$	−20.3118	+	37.3971i	−0.657273	+	1.21014i
$956$	−12.9481	−	9.40732i	−0.418771	−	0.304255i
$957$	5.46113			0.176533
$958$	7.01211	+	5.09460i	0.226551	+	0.164599i
$959$	−3.62124	+	11.1450i	−0.116936	+	0.359892i
$960$	−6.95222	−	7.32818i	−0.224382	−	0.236516i
$961$	−6.94083	−	21.3617i	−0.223898	−	0.689086i
$962$	0.0676522	−	0.208212i	0.00218120	−	0.00671303i
$963$	−5.35368	+	16.4769i	−0.172520	+	0.530962i
$964$	8.28601	+	25.5017i	0.266874	+	0.821355i
$965$	−53.1838	−	9.86476i	−1.71205	−	0.317558i
$966$	0.469114	−	1.44378i	0.0150935	−	0.0464530i
$967$	−38.2807	−	27.8126i	−1.23103	−	0.894393i	−0.234059	−	0.972222i	$-0.575201\pi$
$967$	−38.2807	−	27.8126i	−1.23103	−	0.894393i	−0.996967	+	0.0778298i	$0.975201\pi$
$968$	40.5033			1.30183
$969$	−9.72921	−	7.06868i	−0.312547	−	0.227079i
$970$	3.82547	+	4.03234i	0.122828	+	0.129471i
$971$	−16.8136	+	12.2158i	−0.539573	+	0.392022i	−0.823926	−	0.566697i	$-0.808221\pi$
$971$	−16.8136	+	12.2158i	−0.539573	+	0.392022i	0.284354	+	0.958719i	$0.408221\pi$
$972$	1.03204	−	0.749819i	0.0331026	−	0.0240505i
$973$	−2.01458	−	6.20025i	−0.0645846	−	0.198771i
$974$	−6.01851			−0.192845
$975$	0.118445	−	2.24798i	0.00379328	−	0.0719931i
$976$	0.427274			0.0136767
$977$	12.1922	+	37.5239i	0.390065	+	1.20050i	0.932739	+	0.360552i	$0.117412\pi$
$977$	12.1922	+	37.5239i	0.390065	+	1.20050i	−0.542675	+	0.839943i	$0.682588\pi$
$978$	−4.53590	+	3.29552i	−0.145042	+	0.105379i
$979$	62.5702	−	45.4599i	1.99975	−	1.45290i
$980$	2.57478	−	1.22766i	0.0822483	−	0.0392163i
$981$	15.1565	+	11.0118i	0.483909	+	0.351580i
$982$	19.6665			0.627583
$983$	−43.9276	−	31.9153i	−1.40107	−	1.01794i	−0.994546	−	0.104301i	$-0.966739\pi$
$983$	−43.9276	−	31.9153i	−1.40107	−	1.01794i	−0.406528	−	0.913638i	$-0.633261\pi$
$984$	10.4065	−	32.0279i	0.331747	−	1.02101i
$985$	11.4118	−	5.44119i	0.363611	−	0.173371i
$986$	−1.02379	−	3.15092i	−0.0326043	−	0.100346i
$987$	3.06429	−	9.43091i	0.0975374	−	0.300189i
$988$	−0.592615	+	1.82388i	−0.0188536	+	0.0580254i
$989$	−1.97125	−	6.06688i	−0.0626821	−	0.192916i
$990$	1.25372	+	9.53330i	0.0398459	+	0.302988i
$991$	−7.41183	+	22.8113i	−0.235445	+	0.724624i	0.761618	+	0.648027i	$0.224406\pi$
$991$	−7.41183	+	22.8113i	−0.235445	+	0.724624i	−0.997062	+	0.0765970i	$0.975594\pi$
$992$	13.5408	+	9.83799i	0.429922	+	0.312356i
$993$	−27.7478			−0.880551
$994$	3.86406	+	2.80741i	0.122561	+	0.0890455i
$995$	27.4888	+	5.09875i	0.871455	+	0.161641i
$996$	5.20644	−	3.78270i	0.164972	−	0.119860i
$997$	30.7542	−	22.3443i	0.973996	−	0.707650i	0.0176375	−	0.999844i	$-0.494386\pi$
$997$	30.7542	−	22.3443i	0.973996	−	0.707650i	0.956359	+	0.292195i	$0.0943855\pi$
$998$	1.02800	+	3.16385i	0.0325406	+	0.100150i
$999$	0.571355			0.0180769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.106.3	✓	24
25.21	even	5	inner	525.2.n.c.421.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.106.3	✓	24	1.1	even	1	trivial
525.2.n.c.421.3	yes	24	25.21	even	5	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262997 - 0.809422i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.03204 - 0.749819i) q^{4} +(2.19857 + 0.407800i) q^{5} +(0.688536 + 0.500250i) q^{6} +1.00000 q^{7} +(-2.25541 - 1.63865i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.262997 - 0.809422i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.03204 - 0.749819i) q^{4} +(2.19857 + 0.407800i) q^{5} +(0.688536 + 0.500250i) q^{6} +1.00000 q^{7} +(-2.25541 - 1.63865i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.248135 - 1.88682i) q^{10} +(-1.56133 - 4.80529i) q^{11} +(-0.394203 + 1.21323i) q^{12} +(-0.139126 + 0.428185i) q^{13} +(-0.262997 - 0.809422i) q^{14} +(-2.01838 + 0.962369i) q^{15} +(0.0552106 - 0.169921i) q^{16} +(2.91373 + 2.11695i) q^{17} -0.851077 q^{18} +(2.70138 + 1.96267i) q^{19} +(2.57478 - 1.22766i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-3.47888 + 2.52755i) q^{22} +(-0.551200 - 1.69642i) q^{23} +2.78785 q^{24} +(4.66740 + 1.79315i) q^{25} +0.383172 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.03204 - 0.749819i) q^{28} +(0.874434 - 0.635314i) q^{29} +(1.30979 + 1.38062i) q^{30} +(-2.36407 - 1.71760i) q^{31} -5.72775 q^{32} +(4.08762 + 2.96983i) q^{33} +(0.947204 - 2.91519i) q^{34} +(2.19857 + 0.407800i) q^{35} +(-0.394203 - 1.21323i) q^{36} +(0.176558 - 0.543391i) q^{37} +(0.878170 - 2.70273i) q^{38} +(-0.139126 - 0.428185i) q^{39} +(-4.29044 - 4.52245i) q^{40} +(3.73281 - 11.4884i) q^{41} +(0.688536 + 0.500250i) q^{42} +3.57628 q^{43} +(-5.21445 - 3.78852i) q^{44} +(1.06724 - 1.96494i) q^{45} +(-1.22816 + 0.892308i) q^{46} +(-8.02241 + 5.82862i) q^{47} +(0.0552106 + 0.169921i) q^{48} +1.00000 q^{49} +(0.223903 - 4.24949i) q^{50} -3.60157 q^{51} +(0.177478 + 0.546222i) q^{52} +(-0.654118 + 0.475245i) q^{53} +(0.688536 - 0.500250i) q^{54} +(-1.47310 - 11.2015i) q^{55} +(-2.25541 - 1.63865i) q^{56} -3.33909 q^{57} +(-0.744211 - 0.540701i) q^{58} +(2.60289 - 8.01088i) q^{59} +(-1.36144 + 2.50662i) q^{60} +(0.739007 + 2.27443i) q^{61} +(-0.768519 + 2.36526i) q^{62} +(0.309017 - 0.951057i) q^{63} +(1.39596 + 4.29633i) q^{64} +(-0.480491 + 0.884658i) q^{65} +(1.32881 - 4.08967i) q^{66} +(10.9897 + 7.98449i) q^{67} +4.59441 q^{68} +(1.44306 + 1.04845i) q^{69} +(-0.248135 - 1.88682i) q^{70} +(-4.54020 + 3.29865i) q^{71} +(-2.25541 + 1.63865i) q^{72} +(3.85698 + 11.8706i) q^{73} -0.486267 q^{74} +(-4.82999 + 1.29274i) q^{75} +4.25956 q^{76} +(-1.56133 - 4.80529i) q^{77} +(-0.309993 + 0.225223i) q^{78} +(-1.90302 + 1.38262i) q^{79} +(0.190678 - 0.351067i) q^{80} +(-0.809017 - 0.587785i) q^{81} -10.2807 q^{82} +(-4.08135 - 2.96527i) q^{83} +(-0.394203 + 1.21323i) q^{84} +(5.54275 + 5.84248i) q^{85} +(-0.940552 - 2.89472i) q^{86} +(-0.334004 + 1.02796i) q^{87} +(-4.35275 + 13.3964i) q^{88} +(4.73020 + 14.5580i) q^{89} +(-1.87115 - 0.347069i) q^{90} +(-0.139126 + 0.428185i) q^{91} +(-1.84087 - 1.33747i) q^{92} +2.92216 q^{93} +(6.82769 + 4.96061i) q^{94} +(5.13879 + 5.41667i) q^{95} +(4.63385 - 3.36669i) q^{96} +(-2.36287 + 1.71673i) q^{97} +(-0.262997 - 0.809422i) q^{98} -5.05258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

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