LMFDB - Embedded newform 525.2.n.d.106.2

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			106.2
Character	$\chi$	$=$	525.106
Dual form			525.2.n.d.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.590098 - 1.81614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.33210 + 0.967825i) q^{4} +(1.37624 + 1.76238i) q^{5} +(1.54490 + 1.12243i) q^{6} -1.00000 q^{7} +(-0.546024 - 0.396709i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.590098 - 1.81614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.33210 + 0.967825i) q^{4} +(1.37624 + 1.76238i) q^{5} +(1.54490 + 1.12243i) q^{6} -1.00000 q^{7} +(-0.546024 - 0.396709i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.38860 - 3.53941i) q^{10} +(0.322431 + 0.992340i) q^{11} +(0.508816 - 1.56597i) q^{12} +(-1.41511 + 4.35525i) q^{13} +(0.590098 + 1.81614i) q^{14} +(-2.14930 - 0.616858i) q^{15} +(-1.41590 + 4.35770i) q^{16} +(-2.46135 - 1.78828i) q^{17} -1.90960 q^{18} +(1.80766 + 1.31334i) q^{19} +(-3.53896 - 1.01570i) q^{20} +(0.809017 - 0.587785i) q^{21} +(1.61196 - 1.17116i) q^{22} +(1.68952 + 5.19982i) q^{23} +0.674922 q^{24} +(-1.21193 + 4.85090i) q^{25} +8.74478 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.33210 - 0.967825i) q^{28} +(-1.61400 + 1.17264i) q^{29} +(0.147999 + 4.26742i) q^{30} +(6.95592 + 5.05377i) q^{31} +7.39985 q^{32} +(-0.844135 - 0.613300i) q^{33} +(-1.79531 + 5.52541i) q^{34} +(-1.37624 - 1.76238i) q^{35} +(0.508816 + 1.56597i) q^{36} +(-2.28280 + 7.02575i) q^{37} +(1.31851 - 4.05796i) q^{38} +(-1.41511 - 4.35525i) q^{39} +(-0.0523083 - 1.50827i) q^{40} +(0.632019 - 1.94515i) q^{41} +(-1.54490 - 1.12243i) q^{42} -9.20245 q^{43} +(-1.38992 - 1.00984i) q^{44} +(2.10140 - 0.764277i) q^{45} +(8.44659 - 6.13680i) q^{46} +(10.3443 - 7.51560i) q^{47} +(-1.41590 - 4.35770i) q^{48} +1.00000 q^{49} +(9.52505 - 0.661474i) q^{50} +3.04240 q^{51} +(-2.33006 - 7.17120i) q^{52} +(-0.324575 + 0.235817i) q^{53} +(1.54490 - 1.12243i) q^{54} +(-1.30513 + 1.93394i) q^{55} +(0.546024 + 0.396709i) q^{56} -2.23439 q^{57} +(3.08209 + 2.23927i) q^{58} +(2.95268 - 9.08740i) q^{59} +(3.46009 - 1.25843i) q^{60} +(2.27137 + 6.99055i) q^{61} +(5.07366 - 15.6151i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-1.53483 - 4.72373i) q^{64} +(-9.62312 + 3.49992i) q^{65} +(-0.615713 + 1.89497i) q^{66} +(-4.74997 - 3.45106i) q^{67} +5.00950 q^{68} +(-4.42323 - 3.21366i) q^{69} +(-2.38860 + 3.53941i) q^{70} +(3.03479 - 2.20490i) q^{71} +(-0.546024 + 0.396709i) q^{72} +(1.16913 + 3.59821i) q^{73} +14.1068 q^{74} +(-1.87081 - 4.63682i) q^{75} -3.67907 q^{76} +(-0.322431 - 0.992340i) q^{77} +(-7.07468 + 5.14005i) q^{78} +(-5.17872 + 3.76256i) q^{79} +(-9.62852 + 3.50189i) q^{80} +(-0.809017 - 0.587785i) q^{81} -3.90562 q^{82} +(-4.22493 - 3.06959i) q^{83} +(-0.508816 + 1.56597i) q^{84} +(-0.235794 - 6.79893i) q^{85} +(5.43035 + 16.7129i) q^{86} +(0.616494 - 1.89737i) q^{87} +(0.217616 - 0.669752i) q^{88} +(4.17202 + 12.8401i) q^{89} +(-2.62806 - 3.36543i) q^{90} +(1.41511 - 4.35525i) q^{91} +(-7.28313 - 5.29150i) q^{92} -8.59799 q^{93} +(-19.7535 - 14.3518i) q^{94} +(0.173172 + 4.99325i) q^{95} +(-5.98660 + 4.34952i) q^{96} +(-12.2789 + 8.92115i) q^{97} +(-0.590098 - 1.81614i) q^{98} +1.04341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * 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 $

$2$	−0.590098	−	1.81614i	−0.417262	−	1.28420i	−0.910212	−	0.414143i	$-0.864081\pi$
$2$	−0.590098	−	1.81614i	−0.417262	−	1.28420i	0.492949	−	0.870058i	$-0.335919\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−1.33210	+	0.967825i	−0.666049	+	0.483913i
$5$	1.37624	+	1.76238i	0.615473	+	0.788158i
$5$	1.37624	+	1.76238i	0.615473	+	0.788158i
$6$	1.54490	+	1.12243i	0.630702	+	0.458231i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.546024	−	0.396709i	−0.193049	−	0.140258i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.38860	−	3.53941i	0.755340	−	1.11926i
$11$	0.322431	+	0.992340i	0.0972165	+	0.299202i	0.987825	−	0.155569i	$-0.0497211\pi$
$11$	0.322431	+	0.992340i	0.0972165	+	0.299202i	−0.890608	+	0.454771i	$0.849721\pi$
$12$	0.508816	−	1.56597i	0.146883	−	0.452058i
$13$	−1.41511	+	4.35525i	−0.392480	+	1.20793i	0.538426	+	0.842673i	$0.319019\pi$
$13$	−1.41511	+	4.35525i	−0.392480	+	1.20793i	−0.930906	+	0.365258i	$0.880981\pi$
$14$	0.590098	+	1.81614i	0.157710	+	0.485383i
$15$	−2.14930	−	0.616858i	−0.554947	−	0.159272i
$16$	−1.41590	+	4.35770i	−0.353976	+	1.08942i
$17$	−2.46135	−	1.78828i	−0.596966	−	0.433721i	0.247835	−	0.968802i	$-0.420281\pi$
$17$	−2.46135	−	1.78828i	−0.596966	−	0.433721i	−0.844801	+	0.535081i	$0.820281\pi$
$18$	−1.90960			−0.450096
$19$	1.80766	+	1.31334i	0.414706	+	0.301301i	0.775504	−	0.631342i	$-0.217496\pi$
$19$	1.80766	+	1.31334i	0.414706	+	0.301301i	−0.360798	+	0.932644i	$0.617496\pi$
$20$	−3.53896	−	1.01570i	−0.791335	−	0.227117i
$21$	0.809017	−	0.587785i	0.176542	−	0.128265i
$22$	1.61196	−	1.17116i	0.343671	−	0.249691i
$23$	1.68952	+	5.19982i	0.352290	+	1.08424i	0.957564	+	0.288220i	$0.0930634\pi$
$23$	1.68952	+	5.19982i	0.352290	+	1.08424i	−0.605274	+	0.796017i	$0.706937\pi$
$24$	0.674922			0.137768
$25$	−1.21193	+	4.85090i	−0.242386	+	0.970180i
$26$	8.74478			1.71499
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.33210	−	0.967825i	0.251743	−	0.182902i
$29$	−1.61400	+	1.17264i	−0.299712	+	0.217754i	−0.727470	−	0.686140i	$-0.759304\pi$
$29$	−1.61400	+	1.17264i	−0.299712	+	0.217754i	0.427757	+	0.903894i	$0.359304\pi$
$30$	0.147999	+	4.26742i	0.0270208	+	0.779122i
$31$	6.95592	+	5.05377i	1.24932	+	0.907684i	0.998182	−	0.0602677i	$-0.0191954\pi$
$31$	6.95592	+	5.05377i	1.24932	+	0.907684i	0.251137	+	0.967951i	$0.419195\pi$
$32$	7.39985			1.30812
$33$	−0.844135	−	0.613300i	−0.146945	−	0.106762i
$34$	−1.79531	+	5.52541i	−0.307894	+	0.947600i
$35$	−1.37624	−	1.76238i	−0.232627	−	0.297896i
$36$	0.508816	+	1.56597i	0.0848027	+	0.260996i
$37$	−2.28280	+	7.02575i	−0.375291	+	1.15503i	0.567992	+	0.823034i	$0.307721\pi$
$37$	−2.28280	+	7.02575i	−0.375291	+	1.15503i	−0.943282	+	0.331992i	$0.892279\pi$
$38$	1.31851	−	4.05796i	0.213891	−	0.658288i
$39$	−1.41511	−	4.35525i	−0.226599	−	0.697399i
$40$	−0.0523083	−	1.50827i	−0.00827068	−	0.238478i
$41$	0.632019	−	1.94515i	0.0987048	−	0.303782i	−0.889497	−	0.456942i	$-0.848945\pi$
$41$	0.632019	−	1.94515i	0.0987048	−	0.303782i	0.988201	+	0.153160i	$0.0489448\pi$
$42$	−1.54490	−	1.12243i	−0.238383	−	0.173195i
$43$	−9.20245			−1.40336			−0.701680	−	0.712492i	$-0.747566\pi$
$43$	−9.20245			−1.40336			−0.701680	+	0.712492i	$0.747566\pi$
$44$	−1.38992	−	1.00984i	−0.209539	−	0.152239i
$45$	2.10140	−	0.764277i	0.313258	−	0.113932i
$46$	8.44659	−	6.13680i	1.24538	−	0.904823i
$47$	10.3443	−	7.51560i	1.50888	−	1.09626i	0.542205	−	0.840247i	$-0.317590\pi$
$47$	10.3443	−	7.51560i	1.50888	−	1.09626i	0.966672	−	0.256017i	$-0.0824102\pi$
$48$	−1.41590	−	4.35770i	−0.204368	−	0.628980i
$49$	1.00000			0.142857
$50$	9.52505	−	0.661474i	1.34705	−	0.0935466i
$51$	3.04240			0.426021
$52$	−2.33006	−	7.17120i	−0.323122	−	0.994467i
$53$	−0.324575	+	0.235817i	−0.0445838	+	0.0323920i	−0.609854	−	0.792514i	$-0.708772\pi$
$53$	−0.324575	+	0.235817i	−0.0445838	+	0.0323920i	0.565270	+	0.824906i	$0.308772\pi$
$54$	1.54490	−	1.12243i	0.210234	−	0.152744i
$55$	−1.30513	+	1.93394i	−0.175984	+	0.260773i
$56$	0.546024	+	0.396709i	0.0729655	+	0.0530125i
$57$	−2.23439			−0.295952
$58$	3.08209	+	2.23927i	0.404699	+	0.294031i
$59$	2.95268	−	9.08740i	0.384406	−	1.18308i	−0.552505	−	0.833510i	$-0.686328\pi$
$59$	2.95268	−	9.08740i	0.384406	−	1.18308i	0.936910	−	0.349569i	$-0.113672\pi$
$60$	3.46009	−	1.25843i	0.446695	−	0.162463i
$61$	2.27137	+	6.99055i	0.290819	+	0.895048i	0.984594	+	0.174856i	$0.0559461\pi$
$61$	2.27137	+	6.99055i	0.290819	+	0.895048i	−0.693775	+	0.720191i	$0.744054\pi$
$62$	5.07366	−	15.6151i	0.644355	−	1.98312i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−1.53483	−	4.72373i	−0.191854	−	0.590466i
$65$	−9.62312	+	3.49992i	−1.19360	+	0.434112i
$66$	−0.615713	+	1.89497i	−0.0757890	+	0.233255i
$67$	−4.74997	−	3.45106i	−0.580301	−	0.421613i	0.258531	−	0.966003i	$-0.416761\pi$
$67$	−4.74997	−	3.45106i	−0.580301	−	0.421613i	−0.838833	+	0.544389i	$0.816761\pi$
$68$	5.00950			0.607492
$69$	−4.42323	−	3.21366i	−0.532494	−	0.386880i
$70$	−2.38860	+	3.53941i	−0.285492	+	0.423040i
$71$	3.03479	−	2.20490i	0.360163	−	0.261674i	−0.392957	−	0.919557i	$-0.628548\pi$
$71$	3.03479	−	2.20490i	0.360163	−	0.261674i	0.753120	+	0.657883i	$0.228548\pi$
$72$	−0.546024	+	0.396709i	−0.0643495	+	0.0467526i
$73$	1.16913	+	3.59821i	0.136836	+	0.421139i	0.995871	−	0.0907783i	$-0.0289355\pi$
$73$	1.16913	+	3.59821i	0.136836	+	0.421139i	−0.859035	+	0.511917i	$0.828935\pi$
$74$	14.1068			1.63988
$75$	−1.87081	−	4.63682i	−0.216023	−	0.535413i
$76$	−3.67907			−0.422018
$77$	−0.322431	−	0.992340i	−0.0367444	−	0.113088i
$78$	−7.07468	+	5.14005i	−0.801050	+	0.581997i
$79$	−5.17872	+	3.76256i	−0.582651	+	0.423321i	−0.839679	−	0.543083i	$-0.817257\pi$
$79$	−5.17872	+	3.76256i	−0.582651	+	0.423321i	0.257028	+	0.966404i	$0.417257\pi$
$80$	−9.62852	+	3.50189i	−1.07650	+	0.391523i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.90562			−0.431303
$83$	−4.22493	−	3.06959i	−0.463746	−	0.336931i	0.331253	−	0.943542i	$-0.392529\pi$
$83$	−4.22493	−	3.06959i	−0.463746	−	0.336931i	−0.794999	+	0.606611i	$0.792529\pi$
$84$	−0.508816	+	1.56597i	−0.0555164	+	0.170862i
$85$	−0.235794	−	6.79893i	−0.0255755	−	0.737447i
$86$	5.43035	+	16.7129i	0.585569	+	1.80220i
$87$	0.616494	−	1.89737i	0.0660950	−	0.203420i
$88$	0.217616	−	0.669752i	0.0231979	−	0.0713958i
$89$	4.17202	+	12.8401i	0.442233	+	1.36105i	0.885490	+	0.464658i	$0.153823\pi$
$89$	4.17202	+	12.8401i	0.442233	+	1.36105i	−0.443257	+	0.896394i	$0.646177\pi$
$90$	−2.62806	−	3.36543i	−0.277022	−	0.354747i
$91$	1.41511	−	4.35525i	0.148344	−	0.456555i
$92$	−7.28313	−	5.29150i	−0.759318	−	0.551677i
$93$	−8.59799			−0.891570
$94$	−19.7535	−	14.3518i	−2.03742	−	1.48027i
$95$	0.173172	+	4.99325i	0.0177670	+	0.512297i
$96$	−5.98660	+	4.34952i	−0.611005	+	0.443921i
$97$	−12.2789	+	8.92115i	−1.24673	+	0.905806i	−0.998028	−	0.0627732i	$-0.980006\pi$
$97$	−12.2789	+	8.92115i	−1.24673	+	0.905806i	−0.248707	+	0.968579i	$0.580006\pi$
$98$	−0.590098	−	1.81614i	−0.0596089	−	0.183457i
$99$	1.04341			0.104866
$100$	−3.08041	−	7.63481i	−0.308041	−	0.763481i
$101$	−9.35347			−0.930705			−0.465352	−	0.885126i	$-0.654072\pi$
$101$	−9.35347			−0.930705			−0.465352	+	0.885126i	$0.654072\pi$
$102$	−1.79531	−	5.52541i	−0.177763	−	0.547097i
$103$	14.4529	−	10.5007i	1.42409	−	1.03466i	0.433011	−	0.901389i	$-0.357451\pi$
$103$	14.4529	−	10.5007i	1.42409	−	1.03466i	0.991079	−	0.133274i	$-0.0425489\pi$
$104$	2.50045	−	1.81669i	0.245190	−	0.178141i
$105$	2.14930	+	0.616858i	0.209750	+	0.0601992i
$106$	0.619807	+	0.450316i	0.0602010	+	0.0437386i
$107$	−3.01965			−0.291920			−0.145960	−	0.989290i	$-0.546627\pi$
$107$	−3.01965			−0.291920			−0.145960	+	0.989290i	$0.546627\pi$
$108$	−1.33210	−	0.967825i	−0.128181	−	0.0931291i
$109$	−0.743832	+	2.28928i	−0.0712461	+	0.219273i	−0.980339	−	0.197320i	$-0.936776\pi$
$109$	−0.743832	+	2.28928i	−0.0712461	+	0.219273i	0.909093	+	0.416593i	$0.136776\pi$
$110$	4.28246	+	1.22908i	0.408316	+	0.117189i
$111$	−2.28280	−	7.02575i	−0.216674	−	0.666855i
$112$	1.41590	−	4.35770i	0.133790	−	0.411764i
$113$	−2.96087	+	9.11261i	−0.278535	+	0.857242i	0.709728	+	0.704476i	$0.248818\pi$
$113$	−2.96087	+	9.11261i	−0.278535	+	0.857242i	−0.988262	+	0.152766i	$0.951182\pi$
$114$	1.31851	+	4.05796i	0.123490	+	0.380062i
$115$	−6.83884	+	10.1338i	−0.637725	+	0.944978i
$116$	1.01510	−	3.12414i	0.0942493	−	0.290069i
$117$	3.70480	+	2.69170i	0.342509	+	0.248847i
$118$	−18.2463			−1.67971
$119$	2.46135	+	1.78828i	0.225632	+	0.163931i
$120$	0.928855	+	1.18947i	0.0847924	+	0.108583i
$121$	8.01841	−	5.82572i	0.728946	−	0.529611i
$122$	11.3554	−	8.25022i	1.02807	−	0.746939i
$123$	0.632019	+	1.94515i	0.0569872	+	0.175389i
$124$	−14.1571			−1.27135
$125$	−10.2170	+	4.54012i	−0.913837	+	0.406081i
$126$	1.90960			0.170120
$127$	−0.100957	−	0.310712i	−0.00895845	−	0.0275713i	0.946477	−	0.322770i	$-0.104614\pi$
$127$	−0.100957	−	0.310712i	−0.00895845	−	0.0275713i	−0.955436	+	0.295199i	$0.904614\pi$
$128$	4.29998	−	3.12412i	0.380068	−	0.276136i
$129$	7.44494	−	5.40906i	0.655490	−	0.476241i
$130$	12.0349	+	15.4116i	1.05553	+	1.35169i
$131$	−12.8814	−	9.35888i	−1.12545	−	0.817689i	−0.140426	−	0.990091i	$-0.544847\pi$
$131$	−12.8814	−	9.35888i	−1.12545	−	0.817689i	−0.985027	+	0.172402i	$0.944847\pi$
$132$	1.71804			0.149536
$133$	−1.80766	−	1.31334i	−0.156744	−	0.113881i
$134$	−3.46463	+	10.6630i	−0.299299	+	0.921147i
$135$	−1.25084	+	1.85349i	−0.107655	+	0.159523i
$136$	0.634530	+	1.95288i	0.0544105	+	0.167458i
$137$	0.382779	−	1.17807i	0.0327030	−	0.100650i	−0.933373	−	0.358909i	$-0.883149\pi$
$137$	0.382779	−	1.17807i	0.0327030	−	0.100650i	0.966076	+	0.258259i	$0.0831489\pi$
$138$	−3.22631	+	9.92956i	−0.274642	+	0.845260i
$139$	2.46177	+	7.57654i	0.208804	+	0.642634i	0.999536	+	0.0304703i	$0.00970051\pi$
$139$	2.46177	+	7.57654i	0.208804	+	0.642634i	−0.790731	+	0.612163i	$0.790299\pi$
$140$	3.53896	+	1.01570i	0.299096	+	0.0858420i
$141$	−3.95119	+	12.1605i	−0.332750	+	1.02410i
$142$	−5.79522	−	4.21047i	−0.486324	−	0.353335i
$143$	−4.77817			−0.399570
$144$	3.70688	+	2.69321i	0.308907	+	0.224434i
$145$	−4.28788	−	1.23064i	−0.356089	−	0.102199i
$146$	5.84494	−	4.24660i	0.483731	−	0.351451i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−3.75878	−	11.5683i	−0.308970	−	0.950912i
$149$	−13.9258			−1.14085			−0.570425	−	0.821350i	$-0.693221\pi$
$149$	−13.9258			−1.14085			−0.570425	+	0.821350i	$0.693221\pi$
$150$	−7.31712	+	6.13383i	−0.597440	+	0.500825i
$151$	16.7871			1.36611			0.683055	−	0.730367i	$-0.260651\pi$
$151$	16.7871			1.36611			0.683055	+	0.730367i	$0.260651\pi$
$152$	−0.466010	−	1.43423i	−0.0377984	−	0.116332i
$153$	−2.46135	+	1.78828i	−0.198989	+	0.144574i
$154$	−1.61196	+	1.17116i	−0.129895	+	0.0943744i
$155$	0.666368	+	19.2141i	0.0535239	+	1.54332i
$156$	6.10019	+	4.43205i	0.488406	+	0.354848i
$157$	12.8276			1.02375			0.511876	−	0.859059i	$-0.328951\pi$
$157$	12.8276			1.02375			0.511876	+	0.859059i	$0.328951\pi$
$158$	9.88927	+	7.18498i	0.786748	+	0.571606i
$159$	0.123977	−	0.381561i	0.00983198	−	0.0302597i
$160$	10.1840	+	13.0413i	0.805113	+	1.03101i
$161$	−1.68952	−	5.19982i	−0.133153	−	0.409803i
$162$	−0.590098	+	1.81614i	−0.0463625	+	0.142689i
$163$	5.18625	−	15.9616i	0.406218	−	1.25021i	−0.513655	−	0.857997i	$-0.671709\pi$
$163$	5.18625	−	15.9616i	0.406218	−	1.25021i	0.919874	−	0.392215i	$-0.128291\pi$
$164$	1.04066	+	3.20282i	0.0812618	+	0.250098i
$165$	−0.0808670	−	2.33173i	−0.00629549	−	0.181525i
$166$	−3.08167	+	9.48441i	−0.239184	+	0.736133i
$167$	−0.906135	−	0.658346i	−0.0701189	−	0.0509443i	0.552174	−	0.833729i	$-0.313799\pi$
$167$	−0.906135	−	0.658346i	−0.0701189	−	0.0509443i	−0.622292	+	0.782785i	$0.713799\pi$
$168$	−0.674922			−0.0520714
$169$	−6.44849	−	4.68510i	−0.496038	−	0.360392i
$170$	−12.2086	+	4.44027i	−0.936359	+	0.340553i
$171$	1.80766	−	1.31334i	0.138235	−	0.100434i
$172$	12.2586	−	8.90636i	0.934706	−	0.679104i
$173$	−6.80844	−	20.9542i	−0.517636	−	1.59312i	−0.778434	−	0.627727i	$-0.783985\pi$
$173$	−6.80844	−	20.9542i	−0.517636	−	1.59312i	0.260797	−	0.965394i	$-0.416015\pi$
$174$	−3.80968			−0.288811
$175$	1.21193	−	4.85090i	0.0916134	−	0.366693i
$176$	−4.78085			−0.360370
$177$	2.95268	+	9.08740i	0.221937	+	0.683051i
$178$	20.8575	−	15.1539i	1.56334	−	1.13583i
$179$	−8.07041	+	5.86350i	−0.603211	+	0.438258i	−0.847017	−	0.531566i	$-0.821604\pi$
$179$	−8.07041	+	5.86350i	−0.603211	+	0.438258i	0.243806	+	0.969824i	$0.421604\pi$
$180$	−2.05958	+	3.05188i	−0.153512	+	0.227474i
$181$	−18.3571	−	13.3372i	−1.36448	−	0.991349i	−0.998146	−	0.0608640i	$-0.980614\pi$
$181$	−18.3571	−	13.3372i	−1.36448	−	0.991349i	−0.366329	−	0.930485i	$-0.619386\pi$
$182$	−8.74478			−0.648207
$183$	−5.94651	−	4.32039i	−0.439579	−	0.319373i
$184$	1.14030	−	3.50947i	0.0840638	−	0.258722i
$185$	−15.5237	+	5.64595i	−1.14132	+	0.415099i
$186$	5.07366	+	15.6151i	0.372018	+	1.14496i
$187$	0.980964	−	3.01910i	0.0717352	−	0.220778i
$188$	−6.50588	+	20.0230i	−0.474490	+	1.46033i
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	8.96623	−	3.26101i	0.650479	−	0.236579i
$191$	1.88051	−	5.78760i	0.136069	−	0.418776i	−0.859686	−	0.510823i	$-0.829341\pi$
$191$	1.88051	−	5.78760i	0.136069	−	0.418776i	0.995755	+	0.0920465i	$0.0293408\pi$
$192$	4.01824	+	2.91942i	0.289992	+	0.210691i
$193$	−6.43453			−0.463167			−0.231584	−	0.972815i	$-0.574391\pi$
$193$	−6.43453			−0.463167			−0.231584	+	0.972815i	$0.574391\pi$
$194$	23.4478	+	17.0358i	1.68345	+	1.22310i
$195$	5.72807	−	8.48782i	0.410195	−	0.607826i
$196$	−1.33210	+	0.967825i	−0.0951498	+	0.0691304i
$197$	12.6417	−	9.18470i	0.900680	−	0.654383i	−0.0379603	−	0.999279i	$-0.512086\pi$
$197$	12.6417	−	9.18470i	0.900680	−	0.654383i	0.938641	+	0.344897i	$0.112086\pi$
$198$	−0.615713	−	1.89497i	−0.0437568	−	0.134670i
$199$	6.88500			0.488064			0.244032	−	0.969767i	$-0.421530\pi$
$199$	6.88500			0.488064			0.244032	+	0.969767i	$0.421530\pi$
$200$	2.58614	−	2.16792i	0.182868	−	0.153295i
$201$	5.87129			0.414129
$202$	5.51946	+	16.9872i	0.388348	+	1.19521i
$203$	1.61400	−	1.17264i	0.113281	−	0.0823032i
$204$	−4.05277	+	2.94451i	−0.283751	+	0.206157i
$205$	4.29790	−	1.56314i	0.300178	−	0.109175i
$206$	−27.5993	−	20.0521i	−1.92293	−	1.39709i
$207$	5.46741			0.380011
$208$	−16.9752	−	12.3332i	−1.17702	−	0.855156i
$209$	−0.720437	+	2.21728i	−0.0498336	+	0.153372i
$210$	−0.147999	−	4.26742i	−0.0102129	−	0.294480i
$211$	−7.25942	−	22.3422i	−0.499759	−	1.53810i	−0.809407	−	0.587249i	$-0.800211\pi$
$211$	−7.25942	−	22.3422i	−0.499759	−	1.53810i	0.309648	−	0.950851i	$-0.399789\pi$
$212$	0.204135	−	0.628264i	0.0140201	−	0.0431493i
$213$	−1.15918	+	3.56760i	−0.0794260	+	0.244448i
$214$	1.78189	+	5.48409i	0.121807	+	0.374884i
$215$	−12.6648	−	16.2182i	−0.863730	−	1.10607i
$216$	0.208562	−	0.641889i	0.0141909	−	0.0436750i
$217$	−6.95592	−	5.05377i	−0.472198	−	0.343072i
$218$	4.59657			0.311319
$219$	−3.06082	−	2.22382i	−0.206831	−	0.150272i
$220$	−0.133153	−	3.83934i	−0.00897715	−	0.258848i
$221$	11.2715	−	8.18921i	0.758202	−	0.550866i
$222$	−11.4126	+	8.29176i	−0.765966	+	0.556507i
$223$	−2.49919	−	7.69173i	−0.167358	−	0.515076i	0.831844	−	0.555010i	$-0.187285\pi$
$223$	−2.49919	−	7.69173i	−0.167358	−	0.515076i	−0.999202	+	0.0399334i	$0.987285\pi$
$224$	−7.39985			−0.494423
$225$	4.23897	+	2.65163i	0.282598	+	0.176775i
$226$	18.2969			1.21709
$227$	5.39886	+	16.6160i	0.358335	+	1.10284i	0.954050	+	0.299646i	$0.0968686\pi$
$227$	5.39886	+	16.6160i	0.358335	+	1.10284i	−0.595715	+	0.803196i	$0.703131\pi$
$228$	2.97643	−	2.16250i	0.197119	−	0.143215i
$229$	4.88187	−	3.54689i	0.322603	−	0.234385i	−0.414682	−	0.909966i	$-0.636107\pi$
$229$	4.88187	−	3.54689i	0.322603	−	0.234385i	0.737286	+	0.675581i	$0.236107\pi$
$230$	22.4399	+	6.44034i	1.47964	+	0.424664i
$231$	0.844135	+	0.613300i	0.0555400	+	0.0403522i
$232$	1.34648			0.0884008
$233$	1.10442	+	0.802410i	0.0723531	+	0.0525676i	0.623374	−	0.781924i	$-0.285761\pi$
$233$	1.10442	+	0.802410i	0.0723531	+	0.0525676i	−0.551021	+	0.834492i	$0.685761\pi$
$234$	2.70229	−	8.31678i	0.176654	−	0.543685i
$235$	27.4816	+	7.88734i	1.79270	+	0.514513i
$236$	4.86177	+	14.9630i	0.316474	+	0.974007i
$237$	1.97809	−	6.08795i	0.128491	−	0.395455i
$238$	1.79531	−	5.52541i	0.116373	−	0.358159i
$239$	8.45235	+	26.0137i	0.546737	+	1.68268i	0.716823	+	0.697255i	$0.245595\pi$
$239$	8.45235	+	26.0137i	0.546737	+	1.68268i	−0.170086	+	0.985429i	$0.554405\pi$
$240$	5.73128	−	8.49259i	0.369953	−	0.548194i
$241$	−0.544234	+	1.67498i	−0.0350572	+	0.107895i	−0.967054	−	0.254572i	$-0.918065\pi$
$241$	−0.544234	+	1.67498i	−0.0350572	+	0.107895i	0.931997	+	0.362467i	$0.118065\pi$
$242$	−15.3119	−	11.1248i	−0.984289	−	0.715127i
$243$	1.00000			0.0641500
$244$	−9.79131	−	7.11380i	−0.626824	−	0.455415i
$245$	1.37624	+	1.76238i	0.0879247	+	0.112594i
$246$	3.15971	−	2.29566i	0.201456	−	0.146366i
$247$	−8.27797	+	6.01430i	−0.526715	+	0.382681i
$248$	−1.79322	−	5.51895i	−0.113869	−	0.350454i
$249$	5.22230			0.330950
$250$	14.2745	+	15.8764i	0.902799	+	1.00411i
$251$	12.4430			0.785392			0.392696	−	0.919668i	$-0.371542\pi$
$251$	12.4430			0.785392			0.392696	+	0.919668i	$0.371542\pi$
$252$	−0.508816	−	1.56597i	−0.0320524	−	0.0986471i
$253$	−4.61523	+	3.35316i	−0.290157	+	0.210812i
$254$	−0.504721	+	0.366702i	−0.0316690	+	0.0230089i
$255$	4.18707	+	5.36185i	0.262204	+	0.335772i
$256$	−16.2477	−	11.8047i	−1.01548	−	0.737791i
$257$	29.0932			1.81479			0.907393	−	0.420284i	$-0.138069\pi$
$257$	29.0932			1.81479			0.907393	+	0.420284i	$0.138069\pi$
$258$	−14.2168	−	10.3291i	−0.885101	−	0.643064i
$259$	2.28280	−	7.02575i	0.141847	−	0.436559i
$260$	9.43162	−	13.9757i	0.584924	−	0.866738i
$261$	0.616494	+	1.89737i	0.0381600	+	0.117444i
$262$	−9.39571	+	28.9170i	−0.580469	+	1.78650i
$263$	−1.07857	+	3.31951i	−0.0665077	+	0.204690i	−0.978788	−	0.204878i	$-0.934320\pi$
$263$	−1.07857	+	3.31951i	−0.0665077	+	0.204690i	0.912280	+	0.409567i	$0.134320\pi$
$264$	0.217616	+	0.669752i	0.0133933	+	0.0412204i
$265$	−0.862291	−	0.247481i	−0.0529701	−	0.0152027i
$266$	−1.31851	+	4.05796i	−0.0808430	+	0.248809i
$267$	−10.9225	−	7.93565i	−0.668445	−	0.485654i
$268$	9.66744			0.590533
$269$	−6.22791	−	4.52484i	−0.379722	−	0.275884i	0.381509	−	0.924365i	$-0.375405\pi$
$269$	−6.22791	−	4.52484i	−0.379722	−	0.275884i	−0.761231	+	0.648481i	$0.775405\pi$
$270$	4.10430	+	1.17795i	0.249780	+	0.0716878i
$271$	8.42328	−	6.11987i	0.511678	−	0.371756i	−0.301782	−	0.953377i	$-0.597581\pi$
$271$	8.42328	−	6.11987i	0.511678	−	0.371756i	0.813460	+	0.581621i	$0.197581\pi$
$272$	11.2778	−	8.19381i	0.683818	−	0.496823i
$273$	1.41511	+	4.35525i	0.0856462	+	0.263592i
$274$	−2.36542			−0.142900
$275$	−5.20451	+	0.361431i	−0.313843	+	0.0217951i
$276$	9.00244			0.541883
$277$	9.54645	+	29.3809i	0.573590	+	1.76533i	0.640930	+	0.767599i	$0.278549\pi$
$277$	9.54645	+	29.3809i	0.573590	+	1.76533i	−0.0673396	+	0.997730i	$0.521451\pi$
$278$	12.3073	−	8.94180i	0.738145	−	0.536294i
$279$	6.95592	−	5.05377i	0.416440	−	0.302561i
$280$	0.0523083	+	1.50827i	0.00312602	+	0.0901361i
$281$	2.86578	+	2.08211i	0.170958	+	0.124208i	0.669974	−	0.742384i	$-0.266305\pi$
$281$	2.86578	+	2.08211i	0.170958	+	0.124208i	−0.499016	+	0.866593i	$0.666305\pi$
$282$	24.4167			1.45399
$283$	16.3673	+	11.8915i	0.972934	+	0.706878i	0.956118	−	0.292981i	$-0.0946472\pi$
$283$	16.3673	+	11.8915i	0.972934	+	0.706878i	0.0168156	+	0.999859i	$0.494647\pi$
$284$	−1.90867	+	5.87429i	−0.113259	+	0.348575i
$285$	−3.07506	−	3.93784i	−0.182151	−	0.233257i
$286$	2.81959	+	8.67780i	0.166726	+	0.513129i
$287$	−0.632019	+	1.94515i	−0.0373069	+	0.114819i
$288$	2.28668	−	7.03767i	0.134744	−	0.414699i
$289$	−2.39297	−	7.36479i	−0.140763	−	0.433223i
$290$	0.295260	+	8.51358i	0.0173383	+	0.499934i
$291$	4.69013	−	14.4347i	0.274940	−	0.846179i
$292$	−5.03984	−	3.66166i	−0.294934	−	0.214282i
$293$	−6.93119			−0.404924			−0.202462	−	0.979290i	$-0.564894\pi$
$293$	−6.93119			−0.404924			−0.202462	+	0.979290i	$0.564894\pi$
$294$	1.54490	+	1.12243i	0.0901002	+	0.0654616i
$295$	20.0790	−	7.30272i	1.16904	−	0.425181i
$296$	4.03365	−	2.93062i	0.234451	−	0.170339i
$297$	−0.844135	+	0.613300i	−0.0489817	+	0.0355873i
$298$	8.21762	+	25.2912i	0.476034	+	1.46508i
$299$	−25.0374			−1.44795
$300$	6.97973	+	4.36607i	0.402975	+	0.252075i
$301$	9.20245			0.530420
$302$	−9.90601	−	30.4876i	−0.570027	−	1.75436i
$303$	7.56711	−	5.49783i	0.434719	−	0.315842i
$304$	−8.28262	+	6.01768i	−0.475041	+	0.345137i
$305$	−9.19402	+	13.6237i	−0.526448	+	0.780089i
$306$	4.70019	+	3.41489i	0.268692	+	0.195216i
$307$	18.1411			1.03537			0.517684	−	0.855572i	$-0.326794\pi$
$307$	18.1411			1.03537			0.517684	+	0.855572i	$0.326794\pi$
$308$	1.38992	+	1.00984i	0.0791981	+	0.0575408i
$309$	−5.52053	+	16.9904i	−0.314052	+	0.966553i
$310$	34.5022	−	12.5484i	1.95960	−	0.712703i
$311$	5.35276	+	16.4741i	0.303527	+	0.934161i	0.980223	+	0.197898i	$0.0634114\pi$
$311$	5.35276	+	16.4741i	0.303527	+	0.934161i	−0.676696	+	0.736263i	$0.736589\pi$
$312$	−0.955088	+	2.93946i	−0.0540712	+	0.166414i
$313$	3.17326	−	9.76628i	0.179363	−	0.552023i	−0.820443	−	0.571729i	$-0.806273\pi$
$313$	3.17326	−	9.76628i	0.179363	−	0.552023i	0.999806	+	0.0197061i	$0.00627304\pi$
$314$	−7.56953	−	23.2966i	−0.427174	−	1.31470i
$315$	−2.10140	+	0.764277i	−0.118400	+	0.0430621i
$316$	3.25706	−	10.0242i	0.183224	−	0.563905i
$317$	3.96080	+	2.87769i	0.222460	+	0.161627i	0.693434	−	0.720521i	$-0.256097\pi$
$317$	3.96080	+	2.87769i	0.222460	+	0.161627i	−0.470973	+	0.882148i	$0.656097\pi$
$318$	−0.766124			−0.0429621
$319$	−1.68406	−	1.22354i	−0.0942893	−	0.0685052i
$320$	6.21268	−	9.20593i	0.347299	−	0.514627i
$321$	2.44295	−	1.77490i	0.136352	−	0.0990655i
$322$	−8.44659	+	6.13680i	−0.470710	+	0.341991i
$323$	−2.10067	−	6.46520i	−0.116884	−	0.359733i
$324$	1.64656			0.0914757
$325$	−19.4119	−	12.1428i	−1.07678	−	0.673562i
$326$	−32.0489			−1.77502
$327$	−0.743832	−	2.28928i	−0.0411340	−	0.126597i
$328$	−1.11676	+	0.811372i	−0.0616627	+	0.0448005i
$329$	−10.3443	+	7.51560i	−0.570302	+	0.414349i
$330$	−4.18702	+	1.52281i	−0.230488	+	0.0838282i
$331$	−14.1439	−	10.2761i	−0.777417	−	0.564827i	0.126786	−	0.991930i	$-0.459534\pi$
$331$	−14.1439	−	10.2761i	−0.777417	−	0.564827i	−0.904203	+	0.427104i	$0.859534\pi$
$332$	8.59885			0.471923
$333$	5.97646	+	4.34215i	0.327508	+	0.237948i
$334$	−0.660936	+	2.03415i	−0.0361648	+	0.111304i
$335$	−0.455041	−	13.1207i	−0.0248615	−	0.716861i
$336$	1.41590	+	4.35770i	0.0772438	+	0.237732i
$337$	−10.0288	+	30.8654i	−0.546302	+	1.68134i	0.171574	+	0.985171i	$0.445115\pi$
$337$	−10.0288	+	30.8654i	−0.546302	+	1.68134i	−0.717875	+	0.696172i	$0.754885\pi$
$338$	−4.70354	+	14.4760i	−0.255839	+	0.787391i
$339$	−2.96087	−	9.11261i	−0.160812	−	0.494929i
$340$	6.89427	+	8.82862i	0.373895	+	0.478799i
$341$	−2.77226	+	8.53213i	−0.150126	+	0.462040i
$342$	−3.45190	−	2.50796i	−0.186658	−	0.135615i
$343$	−1.00000			−0.0539949
$344$	5.02475	+	3.65070i	0.270917	+	0.196832i
$345$	−0.423739	−	12.2182i	−0.0228134	−	0.657804i
$346$	−34.0381	+	24.7301i	−1.82990	+	1.32950i
$347$	−3.42168	+	2.48600i	−0.183685	+	0.133455i	−0.675828	−	0.737059i	$-0.736214\pi$
$347$	−3.42168	+	2.48600i	−0.183685	+	0.133455i	0.492143	+	0.870515i	$0.336214\pi$
$348$	1.01510	+	3.12414i	0.0544148	+	0.167472i
$349$	−2.98581			−0.159827			−0.0799133	−	0.996802i	$-0.525464\pi$
$349$	−2.98581			−0.159827			−0.0799133	+	0.996802i	$0.525464\pi$
$350$	−9.52505	+	0.661474i	−0.509135	+	0.0353573i
$351$	−4.57939			−0.244430
$352$	2.38594	+	7.34316i	0.127171	+	0.391392i
$353$	21.4333	−	15.5722i	1.14078	−	0.828826i	0.153553	−	0.988140i	$-0.450928\pi$
$353$	21.4333	−	15.5722i	1.14078	−	0.828826i	0.987228	+	0.159315i	$0.0509285\pi$
$354$	14.7616	−	10.7249i	0.784569	−	0.570023i
$355$	8.06245	+	2.31396i	0.427911	+	0.122812i
$356$	−17.9846	−	13.0665i	−0.953179	−	0.692525i
$357$	−3.04240			−0.161021
$358$	15.4112	+	11.1969i	0.814509	+	0.591776i
$359$	7.38844	−	22.7393i	0.389947	−	1.20013i	−0.542880	−	0.839810i	$-0.682666\pi$
$359$	7.38844	−	22.7393i	0.389947	−	1.20013i	0.932827	−	0.360324i	$-0.117334\pi$
$360$	−1.45061	−	0.416331i	−0.0764539	−	0.0219426i
$361$	−4.32855	−	13.3219i	−0.227819	−	0.701154i
$362$	−13.3897	+	41.2093i	−0.703748	+	2.16591i
$363$	−3.06276	+	9.42621i	−0.160753	+	0.494748i
$364$	2.33006	+	7.17120i	0.122129	+	0.375873i
$365$	−4.73240	+	7.01245i	−0.247705	+	0.367048i
$366$	−4.33740	+	13.3491i	−0.226719	+	0.697770i
$367$	20.3089	+	14.7553i	1.06012	+	0.770219i	0.974110	−	0.226075i	$-0.0725895\pi$
$367$	20.3089	+	14.7553i	1.06012	+	0.770219i	0.0860061	+	0.996295i	$0.472590\pi$
$368$	−25.0514			−1.30590
$369$	−1.65465	−	1.20217i	−0.0861375	−	0.0625825i
$370$	19.4143	+	24.8615i	1.00930	+	1.29249i
$371$	0.324575	−	0.235817i	0.0168511	−	0.0122430i
$372$	11.4534	−	8.32135i	0.593829	−	0.431442i
$373$	−0.582830	−	1.79377i	−0.0301778	−	0.0928777i	0.934833	−	0.355087i	$-0.115549\pi$
$373$	−0.582830	−	1.79377i	−0.0301778	−	0.0928777i	−0.965011	+	0.262210i	$0.915549\pi$
$374$	−6.06195			−0.313456
$375$	5.59712	−	9.67844i	0.289034	−	0.499793i
$376$	−8.62976			−0.445046
$377$	−2.82316	−	8.68880i	−0.145400	−	0.447496i
$378$	−1.54490	+	1.12243i	−0.0794609	+	0.0577317i
$379$	−26.3513	+	19.1453i	−1.35357	+	0.983428i	−0.354748	+	0.934962i	$0.615433\pi$
$379$	−26.3513	+	19.1453i	−1.35357	+	0.983428i	−0.998825	+	0.0484666i	$0.984567\pi$
$380$	−5.06328	−	6.48389i	−0.259741	−	0.332617i
$381$	0.264308	+	0.192031i	0.0135409	+	0.00983804i
$382$	−11.6208			−0.594569
$383$	23.5451	+	17.1065i	1.20310	+	0.874102i	0.994586	−	0.103917i	$-0.0331378\pi$
$383$	23.5451	+	17.1065i	1.20310	+	0.874102i	0.208513	+	0.978020i	$0.433138\pi$
$384$	−1.64245	+	5.05493i	−0.0838158	+	0.257958i
$385$	1.30513	−	1.93394i	0.0665158	−	0.0985628i
$386$	3.79700	+	11.6860i	0.193262	+	0.594800i
$387$	−2.84371	+	8.75205i	−0.144554	+	0.444892i
$388$	7.72259	−	23.7677i	0.392055	−	1.20662i
$389$	2.40337	+	7.39682i	0.121856	+	0.375034i	0.993315	−	0.115434i	$-0.0368259\pi$
$389$	2.40337	+	7.39682i	0.121856	+	0.375034i	−0.871459	+	0.490468i	$0.836826\pi$
$390$	−18.7952	−	5.39429i	−0.951730	−	0.273151i
$391$	5.14021	−	15.8199i	0.259951	−	0.800048i
$392$	−0.546024	−	0.396709i	−0.0275784	−	0.0200368i
$393$	15.9223			0.803173
$394$	−24.1405	−	17.5391i	−1.21618	−	0.883606i
$395$	−13.7582	−	3.94866i	−0.692250	−	0.198679i
$396$	−1.38992	+	1.00984i	−0.0698462	+	0.0507462i
$397$	−11.6499	+	8.46413i	−0.584690	+	0.424802i	−0.840412	−	0.541948i	$-0.817687\pi$
$397$	−11.6499	+	8.46413i	−0.584690	+	0.424802i	0.255722	+	0.966750i	$0.417687\pi$
$398$	−4.06282	−	12.5041i	−0.203651	−	0.626773i
$399$	2.23439			0.111859
$400$	−19.4228	−	12.1496i	−0.971139	−	0.607482i
$401$	25.9458			1.29567			0.647836	−	0.761780i	$-0.275674\pi$
$401$	25.9458			1.29567			0.647836	+	0.761780i	$0.275674\pi$
$402$	−3.46463	−	10.6630i	−0.172800	−	0.531825i
$403$	−31.8538	+	23.1432i	−1.58675	+	1.15284i
$404$	12.4597	−	9.05252i	0.619895	−	0.450380i
$405$	−0.0775028	−	2.23472i	−0.00385114	−	0.111044i
$406$	−3.08209	−	2.23927i	−0.152962	−	0.111133i
$407$	−7.70798			−0.382070
$408$	−1.66122	−	1.20695i	−0.0822428	−	0.0597529i
$409$	5.07928	−	15.6324i	0.251154	−	0.772974i	−0.743409	−	0.668837i	$-0.766792\pi$
$409$	5.07928	−	15.6324i	0.251154	−	0.772974i	0.994563	−	0.104136i	$-0.0332078\pi$
$410$	−5.37506	−	6.88316i	−0.265455	−	0.339935i
$411$	0.382779	+	1.17807i	0.0188811	+	0.0581101i
$412$	−9.08990	+	27.9758i	−0.447827	+	1.37827i
$413$	−2.95268	+	9.08740i	−0.145292	+	0.447162i
$414$	−3.22631	−	9.92956i	−0.158564	−	0.488011i
$415$	−0.404743	−	11.6704i	−0.0198680	−	0.572878i
$416$	−10.4716	+	32.2282i	−0.513412	+	1.58012i
$417$	−6.44499	−	4.68256i	−0.315612	−	0.229306i
$418$	4.45200			0.217754
$419$	3.93058	+	2.85573i	0.192021	+	0.139512i	0.679642	−	0.733544i	$-0.262135\pi$
$419$	3.93058	+	2.85573i	0.192021	+	0.139512i	−0.487621	+	0.873056i	$0.662135\pi$
$420$	−3.46009	+	1.25843i	−0.168835	+	0.0614051i
$421$	26.0263	−	18.9092i	1.26845	−	0.921580i	0.269306	−	0.963055i	$-0.413206\pi$
$421$	26.0263	−	18.9092i	1.26845	−	0.921580i	0.999140	+	0.0414752i	$0.0132058\pi$
$422$	−36.2927	+	26.3682i	−1.76670	+	1.28358i
$423$	−3.95119	−	12.1605i	−0.192113	−	0.591264i
$424$	0.270776			0.0131501
$425$	11.6577	−	9.77251i	0.565484	−	0.474036i
$426$	7.16328			0.347062
$427$	−2.27137	−	6.99055i	−0.109919	−	0.338296i
$428$	4.02246	−	2.92249i	0.194433	−	0.141264i
$429$	3.86562	−	2.80854i	0.186634	−	0.135597i
$430$	−21.9809	+	32.5712i	−1.06001	+	1.57072i
$431$	−23.3758	−	16.9835i	−1.12597	−	0.818068i	−0.140870	−	0.990028i	$-0.544990\pi$
$431$	−23.3758	−	16.9835i	−1.12597	−	0.818068i	−0.985104	+	0.171960i	$0.944990\pi$
$432$	−4.58196			−0.220449
$433$	17.2940	+	12.5648i	0.831096	+	0.603827i	0.919869	−	0.392225i	$-0.128295\pi$
$433$	17.2940	+	12.5648i	0.831096	+	0.603827i	−0.0887729	+	0.996052i	$0.528295\pi$
$434$	−5.07366	+	15.6151i	−0.243543	+	0.749549i
$435$	4.19232	−	1.52474i	0.201007	−	0.0731059i
$436$	−1.22477	−	3.76944i	−0.0586556	−	0.180523i
$437$	−3.77506	+	11.6184i	−0.180585	+	0.555785i
$438$	−2.23257	+	6.87114i	−0.106676	+	0.328316i
$439$	10.0737	+	31.0035i	0.480790	+	1.47972i	0.837987	+	0.545690i	$0.183732\pi$
$439$	10.0737	+	31.0035i	0.480790	+	1.47972i	−0.357198	+	0.934029i	$0.616268\pi$
$440$	1.47985	−	0.538219i	0.0705489	−	0.0256586i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	−21.5240	−	15.6381i	−1.02379	−	0.743829i
$443$	14.5867			0.693035			0.346518	−	0.938043i	$-0.387364\pi$
$443$	14.5867			0.693035			0.346518	+	0.938043i	$0.387364\pi$
$444$	9.84062	+	7.14963i	0.467015	+	0.339306i
$445$	−16.8875	+	25.0238i	−0.800542	+	1.18624i
$446$	−12.4944	+	9.07775i	−0.591629	+	0.429844i
$447$	11.2662	−	8.18541i	0.532875	−	0.387157i
$448$	1.53483	+	4.72373i	0.0725140	+	0.223175i
$449$	4.12379			0.194614			0.0973069	−	0.995254i	$-0.468977\pi$
$449$	4.12379			0.194614			0.0973069	+	0.995254i	$0.468977\pi$
$450$	2.31430	−	9.26327i	0.109097	−	0.436675i
$451$	2.13404			0.100488
$452$	−4.87525	−	15.0045i	−0.229313	−	0.705752i
$453$	−13.5810	+	9.86718i	−0.638091	+	0.463601i
$454$	26.9910	−	19.6101i	1.26675	−	0.920349i
$455$	9.62312	−	3.49992i	0.451139	−	0.164079i
$456$	1.22003	+	0.886404i	0.0571332	+	0.0415097i
$457$	23.0500			1.07823			0.539117	−	0.842231i	$-0.318758\pi$
$457$	23.0500			1.07823			0.539117	+	0.842231i	$0.318758\pi$
$458$	−9.32241	−	6.77313i	−0.435608	−	0.316488i
$459$	0.940153	−	2.89349i	0.0438826	−	0.135057i
$460$	−0.697714	−	20.1180i	−0.0325311	−	0.938005i
$461$	−2.33798	−	7.19556i	−0.108890	−	0.335130i	0.881733	−	0.471748i	$-0.156377\pi$
$461$	−2.33798	−	7.19556i	−0.108890	−	0.335130i	−0.990624	+	0.136618i	$0.956377\pi$
$462$	0.615713	−	1.89497i	0.0286456	−	0.0881620i
$463$	−3.47207	+	10.6859i	−0.161361	+	0.496618i	−0.998750	−	0.0499899i	$-0.984081\pi$
$463$	−3.47207	+	10.6859i	−0.161361	+	0.496618i	0.837389	+	0.546608i	$0.184081\pi$
$464$	−2.82475	−	8.69368i	−0.131136	−	0.403594i
$465$	−11.8329	−	15.1529i	−0.548737	−	0.702698i
$466$	0.805567	−	2.47928i	0.0373172	−	0.114850i
$467$	21.2944	+	15.4713i	0.985387	+	0.715926i	0.958906	−	0.283724i	$-0.0915699\pi$
$467$	21.2944	+	15.4713i	0.985387	+	0.715926i	0.0264809	+	0.999649i	$0.491570\pi$
$468$	−7.54025			−0.348548
$469$	4.74997	+	3.45106i	0.219333	+	0.159355i
$470$	−1.89236	−	54.5646i	−0.0872881	−	2.51688i
$471$	−10.3777	+	7.53987i	−0.478181	+	0.347419i
$472$	−5.21729	+	3.79058i	−0.240145	+	0.174476i
$473$	−2.96715	−	9.13196i	−0.136430	−	0.419888i
$474$	−12.2238			−0.561458
$475$	−8.56165	+	7.17710i	−0.392836	+	0.329308i
$476$	−5.00950			−0.229610
$477$	0.123977	+	0.381561i	0.00567650	+	0.0174705i
$478$	42.2566	−	30.7012i	1.93277	−	1.40424i
$479$	−6.63320	+	4.81930i	−0.303078	+	0.220199i	−0.728921	−	0.684598i	$-0.759978\pi$
$479$	−6.63320	+	4.81930i	−0.303078	+	0.220199i	0.425842	+	0.904797i	$0.359978\pi$
$480$	−15.9045	−	4.56466i	−0.725937	−	0.208347i
$481$	−27.3685	−	19.8844i	−1.24790	−	0.906650i
$482$	3.36314			0.153187
$483$	4.42323	+	3.21366i	0.201264	+	0.146227i
$484$	−5.04303	+	15.5208i	−0.229229	+	0.705493i
$485$	−32.6211	−	9.36241i	−1.48125	−	0.425125i
$486$	−0.590098	−	1.81614i	−0.0267674	−	0.0823816i
$487$	6.03735	−	18.5810i	0.273578	−	0.841987i	−0.716014	−	0.698086i	$-0.754035\pi$
$487$	6.03735	−	18.5810i	0.273578	−	0.841987i	0.989592	−	0.143901i	$-0.0459647\pi$
$488$	1.53300	−	4.71808i	0.0693955	−	0.213577i
$489$	5.18625	+	15.9616i	0.234530	+	0.721810i
$490$	2.38860	−	3.53941i	0.107906	−	0.159894i
$491$	1.93641	−	5.95966i	0.0873890	−	0.268956i	−0.897807	−	0.440390i	$-0.854840\pi$
$491$	1.93641	−	5.95966i	0.0873890	−	0.268956i	0.985196	+	0.171434i	$0.0548401\pi$
$492$	−2.72448	−	1.97945i	−0.122829	−	0.0892405i
$493$	6.06963			0.273363
$494$	15.8076	+	11.4849i	0.711218	+	0.516730i
$495$	1.43598	+	1.83888i	0.0645425	+	0.0826513i
$496$	−31.8717	+	23.1561i	−1.43108	+	1.03974i
$497$	−3.03479	+	2.20490i	−0.136129	+	0.0989033i
$498$	−3.08167	−	9.48441i	−0.138093	−	0.425006i
$499$	28.9374			1.29541			0.647707	−	0.761890i	$-0.275728\pi$
$499$	28.9374			1.29541			0.647707	+	0.761890i	$0.275728\pi$
$500$	9.21601	−	15.9362i	0.412153	−	0.712687i
$501$	1.12005			0.0500399
$502$	−7.34256	−	22.5981i	−0.327715	−	1.00860i
$503$	−25.9952	+	18.8866i	−1.15907	+	0.842112i	−0.989660	−	0.143434i	$-0.954186\pi$
$503$	−25.9952	+	18.8866i	−1.15907	+	0.842112i	−0.169408	+	0.985546i	$0.554186\pi$
$504$	0.546024	−	0.396709i	0.0243218	−	0.0176708i
$505$	−12.8726	−	16.4843i	−0.572823	−	0.733542i
$506$	8.81324	+	6.40319i	0.391796	+	0.284657i
$507$	7.97077			0.353994
$508$	0.435199	+	0.316191i	0.0193089	+	0.0140287i
$509$	0.162727	−	0.500823i	0.00721276	−	0.0221986i	−0.947385	−	0.320095i	$-0.896285\pi$
$509$	0.162727	−	0.500823i	0.00721276	−	0.0221986i	0.954598	+	0.297897i	$0.0962851\pi$
$510$	7.26706	−	10.7683i	0.321791	−	0.476828i
$511$	−1.16913	−	3.59821i	−0.0517193	−	0.159176i
$512$	−8.56621	+	26.3641i	−0.378577	+	1.16514i
$513$	−0.690465	+	2.12503i	−0.0304848	+	0.0938225i
$514$	−17.1679	−	52.8372i	−0.757242	−	2.33055i
$515$	38.3968	+	11.0201i	1.69197	+	0.485602i
$516$	−4.68235	+	14.4108i	−0.206129	+	0.634400i
$517$	10.7934	+	7.84184i	0.474692	+	0.344884i
$518$	−14.1068			−0.619817
$519$	17.8247	+	12.9504i	0.782419	+	0.568461i
$520$	6.64290	+	1.90654i	0.291311	+	0.0836074i
$521$	−14.6049	+	10.6111i	−0.639852	+	0.464880i	−0.859799	−	0.510632i	$-0.829412\pi$
$521$	−14.6049	+	10.6111i	−0.639852	+	0.464880i	0.219947	+	0.975512i	$0.429412\pi$
$522$	3.08209	−	2.23927i	0.134900	−	0.0980102i
$523$	2.25636	+	6.94436i	0.0986636	+	0.303655i	0.988191	−	0.153226i	$-0.0489663\pi$
$523$	2.25636	+	6.94436i	0.0986636	+	0.303655i	−0.889528	+	0.456882i	$0.848966\pi$
$524$	26.2170			1.14530
$525$	1.87081	+	4.63682i	0.0816490	+	0.202367i
$526$	6.66514			0.290614
$527$	−8.08343	−	24.8782i	−0.352120	−	1.08371i
$528$	3.86779	−	2.81011i	0.168324	−	0.122294i
$529$	−5.57622	+	4.05136i	−0.242444	+	0.176146i
$530$	0.0593767	+	1.71208i	0.00257916	+	0.0743678i
$531$	−7.73021	−	5.61632i	−0.335462	−	0.243728i
$532$	3.67907			0.159508
$533$	7.57727	+	5.50521i	0.328208	+	0.238457i
$534$	−7.96687	+	24.5195i	−0.344760	+	1.06106i
$535$	−4.15576	−	5.32175i	−0.179669	−	0.230079i
$536$	1.22453	+	3.76872i	0.0528916	+	0.162784i
$537$	3.08262	−	9.48734i	0.133025	−	0.409409i
$538$	−4.54264	+	13.9808i	−0.195847	+	0.602756i
$539$	0.322431	+	0.992340i	0.0138881	+	0.0427431i
$540$	−0.127613	−	3.67961i	−0.00549160	−	0.158345i
$541$	−7.82099	+	24.0705i	−0.336251	+	1.03487i	0.629852	+	0.776715i	$0.283116\pi$
$541$	−7.82099	+	24.0705i	−0.336251	+	1.03487i	−0.966103	+	0.258158i	$0.916884\pi$
$542$	−16.0851	−	11.6865i	−0.690913	−	0.501978i
$543$	22.6907			0.973750
$544$	−18.2136	−	13.2330i	−0.780903	−	0.567360i
$545$	−5.05826	+	1.83968i	−0.216672	+	0.0788034i
$546$	7.07468	−	5.14005i	0.302768	−	0.219974i
$547$	7.66236	−	5.56703i	0.327619	−	0.238029i	−0.411801	−	0.911274i	$-0.635100\pi$
$547$	7.66236	−	5.56703i	0.327619	−	0.238029i	0.739420	+	0.673245i	$0.235100\pi$
$548$	0.630270	+	1.93977i	0.0269238	+	0.0828629i
$549$	7.35029			0.313703
$550$	3.72758	+	9.23881i	0.158944	+	0.393944i
$551$	−4.45764			−0.189902
$552$	1.14030	+	3.50947i	0.0485343	+	0.149373i
$553$	5.17872	−	3.76256i	0.220222	−	0.160000i
$554$	47.7264	−	34.6753i	2.02770	−	1.47321i
$555$	9.24032	−	13.6923i	0.392230	−	0.581204i
$556$	−10.6121	−	7.71013i	−0.450052	−	0.326982i
$557$	−7.06816			−0.299488			−0.149744	−	0.988725i	$-0.547845\pi$
$557$	−7.06816			−0.299488			−0.149744	+	0.988725i	$0.547845\pi$
$558$	−13.2830	−	9.65067i	−0.562314	−	0.408545i
$559$	13.0225	−	40.0790i	0.550791	−	1.69516i
$560$	9.62852	−	3.50189i	0.406879	−	0.147982i
$561$	0.980964	+	3.01910i	0.0414163	+	0.127466i
$562$	2.09031	−	6.43330i	0.0881742	−	0.271372i
$563$	−6.04491	+	18.6043i	−0.254763	+	0.784079i	0.739114	+	0.673581i	$0.235245\pi$
$563$	−6.04491	+	18.6043i	−0.254763	+	0.784079i	−0.993876	+	0.110498i	$0.964755\pi$
$564$	−6.50588	−	20.0230i	−0.273947	−	0.843122i
$565$	−20.1347	+	7.32297i	−0.847073	+	0.308080i
$566$	11.9383	−	36.7424i	0.501805	−	1.54440i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	−2.53177			−0.106231
$569$	−19.9631	−	14.5040i	−0.836895	−	0.608040i	0.0846068	−	0.996414i	$-0.473037\pi$
$569$	−19.9631	−	14.5040i	−0.836895	−	0.608040i	−0.921501	+	0.388375i	$0.873037\pi$
$570$	−5.33706	+	7.90843i	−0.223545	+	0.331248i
$571$	27.2606	−	19.8060i	1.14082	−	0.828854i	0.153586	−	0.988135i	$-0.450918\pi$
$571$	27.2606	−	19.8060i	1.14082	−	0.828854i	0.987233	+	0.159281i	$0.0509176\pi$
$572$	6.36499	−	4.62443i	0.266133	−	0.193357i
$573$	1.88051	+	5.78760i	0.0785593	+	0.241781i
$574$	3.90562			0.163017
$575$	−27.2714	+	1.89388i	−1.13729	+	0.0789803i
$576$	−4.96682			−0.206951
$577$	3.74596	+	11.5289i	0.155946	+	0.479953i	0.998256	−	0.0590413i	$-0.0188044\pi$
$577$	3.74596	+	11.5289i	0.155946	+	0.479953i	−0.842309	+	0.538994i	$0.818804\pi$
$578$	−11.9634	+	8.69190i	−0.497611	+	0.361535i
$579$	5.20564	−	3.78212i	0.216339	−	0.157180i
$580$	6.90293	−	2.51059i	0.286628	−	0.104247i
$581$	4.22493	+	3.06959i	0.175280	+	0.127348i
$582$	−28.9830			−1.20139
$583$	−0.338664	−	0.246054i	−0.0140260	−	0.0101905i
$584$	0.789072	−	2.42851i	0.0326520	−	0.100493i
$585$	0.354915	+	10.2337i	0.0146739	+	0.423110i
$586$	4.09008	+	12.5880i	0.168960	+	0.520004i
$587$	0.319346	−	0.982845i	0.0131808	−	0.0405663i	−0.944250	−	0.329230i	$-0.893211\pi$
$587$	0.319346	−	0.982845i	0.0131808	−	0.0405663i	0.957431	+	0.288664i	$0.0932109\pi$
$588$	0.508816	−	1.56597i	0.0209832	−	0.0645797i
$589$	5.93661	+	18.2710i	0.244614	+	0.752843i
$590$	−25.1113	−	32.1569i	−1.03382	−	1.32388i
$591$	−4.82868	+	14.8612i	−0.198625	+	0.611306i
$592$	−27.3839	−	19.8955i	−1.12547	−	0.817702i
$593$	35.2007			1.44552			0.722760	−	0.691100i	$-0.242873\pi$
$593$	35.2007			1.44552			0.722760	+	0.691100i	$0.242873\pi$
$594$	1.61196	+	1.17116i	0.0661394	+	0.0480531i
$595$	0.235794	+	6.79893i	0.00966663	+	0.278729i
$596$	18.5506	−	13.4778i	0.759862	−	0.552072i
$597$	−5.57008	+	4.04690i	−0.227968	+	0.165629i
$598$	14.7745	+	45.4713i	0.604175	+	1.85946i
$599$	−24.7372			−1.01073			−0.505366	−	0.862905i	$-0.668643\pi$
$599$	−24.7372			−1.01073			−0.505366	+	0.862905i	$0.668643\pi$
$600$	−0.817960	+	3.27398i	−0.0333931	+	0.133660i
$601$	−2.15426			−0.0878742			−0.0439371	−	0.999034i	$-0.513990\pi$
$601$	−2.15426			−0.0878742			−0.0439371	+	0.999034i	$0.513990\pi$
$602$	−5.43035	−	16.7129i	−0.221324	−	0.681167i
$603$	−4.74997	+	3.45106i	−0.193434	+	0.140538i
$604$	−22.3620	+	16.2469i	−0.909896	+	0.661078i
$605$	21.3023	+	6.11387i	0.866064	+	0.248564i
$606$	−14.4501	−	10.4986i	−0.586997	−	0.426478i
$607$	−22.5962			−0.917152			−0.458576	−	0.888655i	$-0.651640\pi$
$607$	−22.5962			−0.917152			−0.458576	+	0.888655i	$0.651640\pi$
$608$	13.3764	+	9.71853i	0.542485	+	0.394139i
$609$	−0.616494	+	1.89737i	−0.0249816	+	0.0768854i
$610$	30.1678	+	8.65829i	1.22146	+	0.350564i
$611$	18.0940	+	55.6876i	0.732005	+	2.25288i
$612$	1.54802	−	4.76432i	0.0625751	−	0.192586i
$613$	13.5616	−	41.7382i	0.547746	−	1.68579i	−0.166624	−	0.986021i	$-0.553287\pi$
$613$	13.5616	−	41.7382i	0.547746	−	1.68579i	0.714370	−	0.699768i	$-0.246713\pi$
$614$	−10.7050	−	32.9467i	−0.432020	−	1.32962i
$615$	−2.55828	+	3.79085i	−0.103160	+	0.152862i
$616$	−0.217616	+	0.669752i	−0.00876799	+	0.0269851i
$617$	−38.9474	−	28.2969i	−1.56796	−	1.13919i	−0.929074	−	0.369894i	$-0.879394\pi$
$617$	−38.9474	−	28.2969i	−1.56796	−	1.13919i	−0.638889	−	0.769299i	$-0.720606\pi$
$618$	34.1146			1.37229
$619$	6.11828	+	4.44519i	0.245914	+	0.178667i	0.703914	−	0.710285i	$-0.251434\pi$
$619$	6.11828	+	4.44519i	0.245914	+	0.178667i	−0.458000	+	0.888952i	$0.651434\pi$
$620$	−19.4836	−	24.9502i	−0.782480	−	1.00202i
$621$	−4.42323	+	3.21366i	−0.177498	+	0.128960i
$622$	26.7605	−	19.4427i	1.07300	−	0.779580i
$623$	−4.17202	−	12.8401i	−0.167148	−	0.514429i
$624$	20.9825			0.839974
$625$	−22.0624	−	11.7579i	−0.882498	−	0.470317i
$626$	−19.6094			−0.783750
$627$	−0.720437	−	2.21728i	−0.0287715	−	0.0885495i
$628$	−17.0876	+	12.4149i	−0.681869	+	0.495407i
$629$	18.1828	−	13.2106i	0.724995	−	0.526740i
$630$	2.62806	+	3.36543i	0.104705	+	0.134082i
$631$	0.984173	+	0.715044i	0.0391793	+	0.0284654i	0.607203	−	0.794547i	$-0.292292\pi$
$631$	0.984173	+	0.715044i	0.0391793	+	0.0284654i	−0.568023	+	0.823013i	$0.692292\pi$
$632$	4.32035			0.171854
$633$	19.0054	+	13.8082i	0.755397	+	0.548828i
$634$	2.88901	−	8.89146i	0.114737	−	0.353125i
$635$	0.408651	−	0.605538i	0.0162168	−	0.0240300i
$636$	0.204135	+	0.628264i	0.00809449	+	0.0249123i
$637$	−1.41511	+	4.35525i	−0.0560686	+	0.172561i
$638$	−1.22836	+	3.78049i	−0.0486311	+	0.149671i
$639$	−1.15918	−	3.56760i	−0.0458566	−	0.141132i
$640$	11.4237	+	3.27864i	0.451560	+	0.129600i
$641$	−4.00793	+	12.3351i	−0.158304	+	0.487208i	−0.998481	−	0.0551038i	$-0.982451\pi$
$641$	−4.00793	+	12.3351i	−0.158304	+	0.487208i	0.840177	+	0.542312i	$0.182451\pi$
$642$	−4.66504	−	3.38935i	−0.184115	−	0.133767i
$643$	−9.54438			−0.376393			−0.188197	−	0.982131i	$-0.560264\pi$
$643$	−9.54438			−0.376393			−0.188197	+	0.982131i	$0.560264\pi$
$644$	7.28313	+	5.29150i	0.286995	+	0.208514i
$645$	19.7788	+	5.67661i	0.778790	+	0.223516i
$646$	−10.5021	+	7.63020i	−0.413199	+	0.300206i
$647$	39.7293	−	28.8650i	1.56192	−	1.13480i	0.627505	−	0.778613i	$-0.284076\pi$
$647$	39.7293	−	28.8650i	1.56192	−	1.13480i	0.934414	−	0.356188i	$-0.115924\pi$
$648$	0.208562	+	0.641889i	0.00819311	+	0.0252158i
$649$	9.96983			0.391350
$650$	−10.5981	+	42.4201i	−0.415691	+	1.66385i
$651$	8.59799			0.336982
$652$	8.53948	+	26.2818i	0.334432	+	1.02928i
$653$	−17.9631	+	13.0509i	−0.702949	+	0.510722i	−0.880891	−	0.473319i	$-0.843056\pi$
$653$	−17.9631	+	13.0509i	−0.702949	+	0.510722i	0.177942	+	0.984041i	$0.443056\pi$
$654$	−3.71871	+	2.70180i	−0.145413	+	0.105649i
$655$	−1.23402	−	35.5819i	−0.0482172	−	1.39030i
$656$	7.58152	+	5.50830i	0.296009	+	0.215063i
$657$	3.78338			0.147604
$658$	19.7535	+	14.3518i	0.770073	+	0.559490i
$659$	−3.16292	+	9.73446i	−0.123210	+	0.379201i	−0.993571	−	0.113214i	$-0.963886\pi$
$659$	−3.16292	+	9.73446i	−0.123210	+	0.379201i	0.870361	+	0.492414i	$0.163886\pi$
$660$	2.36443	+	3.02783i	0.0920353	+	0.117858i
$661$	6.07080	+	18.6840i	0.236127	+	0.726723i	0.996970	+	0.0777876i	$0.0247856\pi$
$661$	6.07080	+	18.6840i	0.236127	+	0.726723i	−0.760843	+	0.648936i	$0.775214\pi$
$662$	−10.3166	+	31.7511i	−0.400964	+	1.23404i
$663$	−4.30532	+	13.2504i	−0.167205	+	0.514604i
$664$	1.08918	+	3.35214i	0.0422682	+	0.130088i
$665$	−0.173172	−	4.99325i	−0.00671530	−	0.193630i
$666$	4.35924	−	13.4164i	0.168917	−	0.519873i
$667$	−8.82441	−	6.41131i	−0.341682	−	0.248247i
$668$	1.84422			0.0713552
$669$	6.54297	+	4.75375i	0.252966	+	0.183791i
$670$	−23.5605	+	8.56892i	−0.910220	+	0.331046i
$671$	−6.20464	+	4.50793i	−0.239527	+	0.174027i
$672$	5.98660	−	4.34952i	0.230938	−	0.167786i
$673$	1.75483	+	5.40081i	0.0676437	+	0.208186i	0.979165	−	0.203068i	$-0.0650911\pi$
$673$	1.75483	+	5.40081i	0.0676437	+	0.208186i	−0.911521	+	0.411254i	$0.865091\pi$
$674$	61.9736			2.38713
$675$	−4.98799	+	0.346395i	−0.191988	+	0.0133327i
$676$	13.1244			0.504784
$677$	−6.45924	−	19.8795i	−0.248249	−	0.764031i	−0.995085	−	0.0990233i	$-0.968428\pi$
$677$	−6.45924	−	19.8795i	−0.248249	−	0.764031i	0.746836	−	0.665008i	$-0.231572\pi$
$678$	−14.8025	+	10.7547i	−0.568488	+	0.413031i
$679$	12.2789	−	8.92115i	0.471221	−	0.342362i
$680$	−2.56845	+	3.80592i	−0.0984955	+	0.145950i
$681$	−14.1344	−	10.2692i	−0.541631	−	0.393518i
$682$	17.1314			0.655995
$683$	−35.9105	−	26.0905i	−1.37408	−	0.998324i	−0.997406	−	0.0719767i	$-0.977069\pi$
$683$	−35.9105	−	26.0905i	−1.37408	−	0.998324i	−0.376669	−	0.926348i	$-0.622931\pi$
$684$	−1.13689	+	3.49900i	−0.0434702	+	0.133788i
$685$	2.60300	−	0.946710i	0.0994556	−	0.0361719i
$686$	0.590098	+	1.81614i	0.0225301	+	0.0693404i
$687$	−1.86471	+	5.73899i	−0.0711431	+	0.218956i
$688$	13.0298	−	40.1015i	0.496755	−	1.52886i
$689$	−0.567736	−	1.74731i	−0.0216290	−	0.0665673i
$690$	−21.9398	+	7.97948i	−0.835233	+	0.303774i
$691$	8.75375	−	26.9413i	0.333008	−	1.02489i	−0.634687	−	0.772770i	$-0.718871\pi$
$691$	8.75375	−	26.9413i	0.333008	−	1.02489i	0.967695	−	0.252124i	$-0.0811292\pi$
$692$	29.3495	+	21.3237i	1.11570	+	0.810605i
$693$	−1.04341			−0.0396358
$694$	6.53403	+	4.74725i	0.248028	+	0.180203i
$695$	−9.96472	+	14.7657i	−0.377984	+	0.560094i
$696$	−1.08933	+	0.791441i	−0.0412908	+	0.0299995i
$697$	−5.03410	+	3.65749i	−0.190680	+	0.138537i
$698$	1.76192	+	5.42263i	0.0666896	+	0.205250i
$699$	−1.36514			−0.0516344
$700$	3.08041	+	7.63481i	0.116429	+	0.288569i
$701$	29.3475			1.10844			0.554221	−	0.832370i	$-0.313016\pi$
$701$	29.3475			1.10844			0.554221	+	0.832370i	$0.313016\pi$
$702$	2.70229	+	8.31678i	0.101991	+	0.313897i
$703$	−13.3537	+	9.70207i	−0.503646	+	0.365920i
$704$	4.19267	−	3.04615i	0.158017	−	0.114806i
$705$	−26.8691	+	9.77228i	−1.01195	+	0.368046i
$706$	−40.9290	−	29.7367i	−1.54038	−	1.11915i
$707$	9.35347			0.351773
$708$	−12.7283	−	9.24763i	−0.478358	−	0.347547i
$709$	−15.7106	+	48.3522i	−0.590024	+	1.81591i	−0.0119405	+	0.999929i	$0.503801\pi$
$709$	−15.7106	+	48.3522i	−0.590024	+	1.81591i	−0.578083	+	0.815978i	$0.696199\pi$
$710$	−0.555174	−	16.0080i	−0.0208353	−	0.600768i
$711$	1.97809	+	6.08795i	0.0741844	+	0.228316i
$712$	2.81579	−	8.66610i	0.105526	−	0.324776i
$713$	−14.5265	+	44.7080i	−0.544022	+	1.67433i
$714$	1.79531	+	5.52541i	0.0671880	+	0.206783i
$715$	−6.57590	−	8.42092i	−0.245925	−	0.314925i
$716$	5.07573	−	15.6215i	0.189689	−	0.583803i
$717$	−22.1285	−	16.0773i	−0.826406	−	0.600419i
$718$	−45.6575			−1.70392
$719$	19.8734	+	14.4389i	0.741152	+	0.538479i	0.893072	−	0.449914i	$-0.148545\pi$
$719$	19.8734	+	14.4389i	0.741152	+	0.538479i	−0.151920	+	0.988393i	$0.548545\pi$
$720$	0.355114	+	10.2394i	0.0132343	+	0.381600i
$721$	−14.4529	+	10.5007i	−0.538256	+	0.391066i
$722$	−21.6401	+	15.7225i	−0.805362	+	0.585130i
$723$	−0.544234	−	1.67498i	−0.0202403	−	0.0622932i
$724$	37.3616			1.38853
$725$	−3.73230	−	9.25052i	−0.138614	−	0.343556i
$726$	18.9266			0.702432
$727$	−12.5280	−	38.5574i	−0.464640	−	1.43001i	−0.859435	−	0.511245i	$-0.829185\pi$
$727$	−12.5280	−	38.5574i	−0.464640	−	1.43001i	0.394796	−	0.918769i	$-0.370815\pi$
$728$	−2.50045	+	1.81669i	−0.0926729	+	0.0673308i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	15.5281	+	4.45664i	0.574722	+	0.164948i
$731$	22.6505	+	16.4565i	0.837758	+	0.608667i
$732$	12.1027			0.447330
$733$	31.0668	+	22.5714i	1.14748	+	0.833692i	0.988144	−	0.153532i	$-0.0490649\pi$
$733$	31.0668	+	22.5714i	1.14748	+	0.833692i	0.159335	+	0.987225i	$0.449065\pi$
$734$	14.8133	−	45.5908i	0.546770	−	1.68279i
$735$	−2.14930	−	0.616858i	−0.0792781	−	0.0227532i
$736$	12.5022	+	38.4779i	0.460838	+	1.41831i
$737$	1.89308	−	5.82631i	0.0697326	−	0.214615i
$738$	−1.20690	+	3.71446i	−0.0444267	+	0.136731i
$739$	2.61925	+	8.06122i	0.0963507	+	0.296537i	0.987603	−	0.156970i	$-0.0501727\pi$
$739$	2.61925	+	8.06122i	0.0963507	+	0.296537i	−0.891253	+	0.453507i	$0.850173\pi$
$740$	15.2148	−	22.5452i	0.559306	−	0.828777i
$741$	3.16191	−	9.73134i	0.116155	−	0.357490i
$742$	−0.619807	−	0.450316i	−0.0227538	−	0.0165316i
$743$	0.469691			0.0172313			0.00861564	−	0.999963i	$-0.497258\pi$
$743$	0.469691			0.0172313			0.00861564	+	0.999963i	$0.497258\pi$
$744$	4.69470	+	3.41090i	0.172116	+	0.125050i
$745$	−19.1653	−	24.5426i	−0.702162	−	0.899170i
$746$	−2.91380	+	2.11700i	−0.106682	+	0.0775087i
$747$	−4.22493	+	3.06959i	−0.154582	+	0.112310i
$748$	1.61522	+	4.97113i	0.0590582	+	0.181763i
$749$	3.01965			0.110335
$750$	−20.8802	−	4.45390i	−0.762437	−	0.162633i
$751$	−28.6015			−1.04368			−0.521841	−	0.853043i	$-0.674755\pi$
$751$	−28.6015			−1.04368			−0.521841	+	0.853043i	$0.674755\pi$
$752$	18.1042	+	55.7189i	0.660191	+	2.03186i
$753$	−10.0666	+	7.31379i	−0.366846	+	0.266529i
$754$	−14.1141	+	10.2545i	−0.514005	+	0.373446i
$755$	23.1030	+	29.5851i	0.840804	+	1.07671i
$756$	1.33210	+	0.967825i	0.0484479	+	0.0351995i
$757$	11.7337			0.426467			0.213234	−	0.977001i	$-0.431600\pi$
$757$	11.7337			0.426467			0.213234	+	0.977001i	$0.431600\pi$
$758$	50.3203	+	36.5598i	1.82772	+	1.32791i
$759$	1.76286	−	5.42553i	0.0639878	−	0.196934i
$760$	1.88631	−	2.79513i	0.0684238	−	0.101390i
$761$	13.5555	+	41.7195i	0.491386	+	1.51233i	0.822514	+	0.568744i	$0.192571\pi$
$761$	13.5555	+	41.7195i	0.491386	+	1.51233i	−0.331129	+	0.943586i	$0.607429\pi$
$762$	0.192786	−	0.593336i	0.00698392	−	0.0214943i
$763$	0.743832	−	2.28928i	0.0269285	−	0.0828774i
$764$	3.09637	+	9.52965i	0.112023	+	0.344771i
$765$	−6.53903	−	1.87673i	−0.236419	−	0.0678533i
$766$	17.1738	−	52.8556i	0.620516	−	1.90975i
$767$	35.3996	+	25.7193i	1.27821	+	0.928671i
$768$	20.0833			0.724693
$769$	6.75402	+	4.90708i	0.243556	+	0.176954i	0.702866	−	0.711322i	$-0.251903\pi$
$769$	6.75402	+	4.90708i	0.243556	+	0.176954i	−0.459310	+	0.888276i	$0.651903\pi$
$770$	−4.28246	−	1.22908i	−0.154329	−	0.0442931i
$771$	−23.5369	+	17.1006i	−0.847661	+	0.615862i
$772$	8.57142	−	6.22750i	0.308492	−	0.224133i
$773$	−8.97345	−	27.6175i	−0.322753	−	0.993331i	−0.972445	−	0.233133i	$-0.925102\pi$
$773$	−8.97345	−	27.6175i	−0.322753	−	0.993331i	0.649692	−	0.760197i	$-0.274898\pi$
$774$	17.5730			0.631647
$775$	−32.9454	+	27.6176i	−1.18343	+	0.992054i
$776$	10.2437			0.367727
$777$	2.28280	+	7.02575i	0.0818951	+	0.252047i
$778$	12.0154	−	8.72970i	0.430773	−	0.312975i
$779$	3.69713	−	2.68612i	0.132463	−	0.0962403i
$780$	0.584390	+	16.8504i	0.0209245	+	0.603340i
$781$	3.16652	+	2.30061i	0.113307	+	0.0823223i
$782$	−31.7643			−1.13589
$783$	−1.61400	−	1.17264i	−0.0576797	−	0.0419067i
$784$	−1.41590	+	4.35770i	−0.0505679	+	0.155632i
$785$	17.6538	+	22.6070i	0.630092	+	0.806879i
$786$	−9.39571	−	28.9170i	−0.335134	−	1.03144i
$787$	−8.27324	+	25.4624i	−0.294909	+	0.907637i	0.688343	+	0.725386i	$0.258339\pi$
$787$	−8.27324	+	25.4624i	−0.294909	+	0.907637i	−0.983252	+	0.182252i	$0.941661\pi$
$788$	−7.95073	+	24.4698i	−0.283233	+	0.871701i
$789$	−1.07857	−	3.31951i	−0.0383983	−	0.118178i
$790$	0.947379	+	27.3168i	0.0337062	+	0.971890i
$791$	2.96087	−	9.11261i	0.105276	−	0.324007i
$792$	−0.569725	−	0.413930i	−0.0202443	−	0.0147084i
$793$	−33.6598			−1.19530
$794$	22.2466	+	16.1631i	0.789501	+	0.573606i
$795$	0.843074	−	0.306625i	0.0299008	−	0.0108749i
$796$	−9.17149	+	6.66348i	−0.325075	+	0.236181i
$797$	−9.90785	+	7.19847i	−0.350954	+	0.254983i	−0.749269	−	0.662266i	$-0.769595\pi$
$797$	−9.90785	+	7.19847i	−0.350954	+	0.254983i	0.398315	+	0.917249i	$0.369595\pi$
$798$	−1.31851	−	4.05796i	−0.0466748	−	0.143650i
$799$	−38.9011			−1.37622
$800$	−8.96811	+	35.8959i	−0.317071	+	1.26911i
$801$	13.5009			0.477032
$802$	−15.3106	−	47.1211i	−0.540635	−	1.66390i
$803$	−3.19369	+	2.32035i	−0.112703	+	0.0818833i
$804$	−7.82112	+	5.68238i	−0.275830	+	0.200402i
$805$	6.83884	−	10.1338i	0.241037	−	0.357168i
$806$	60.8280	+	44.1941i	2.14257	+	1.55667i
$807$	7.69811			0.270986
$808$	5.10721	+	3.71061i	0.179671	+	0.130539i
$809$	13.3374	−	41.0483i	0.468918	−	1.44318i	−0.385069	−	0.922888i	$-0.625822\pi$
$809$	13.3374	−	41.0483i	0.468918	−	1.44318i	0.853987	−	0.520294i	$-0.174178\pi$
$810$	−4.01283	+	1.45946i	−0.140996	+	0.0512803i
$811$	−15.8833	−	48.8839i	−0.557739	−	1.71654i	−0.688598	−	0.725144i	$-0.741773\pi$
$811$	−15.8833	−	48.8839i	−0.557739	−	1.71654i	0.130859	−	0.991401i	$-0.458227\pi$
$812$	−1.01510	+	3.12414i	−0.0356229	+	0.109636i
$813$	−3.21741	+	9.90216i	−0.112839	+	0.347284i
$814$	4.54846	+	13.9987i	0.159424	+	0.490655i
$815$	35.2679	−	12.8269i	1.23538	−	0.449307i
$816$	−4.30774	+	13.2579i	−0.150801	+	0.464118i
$817$	−16.6349	−	12.0860i	−0.581982	−	0.422834i
$818$	−31.3879			−1.09745
$819$	−3.70480	−	2.69170i	−0.129456	−	0.0940554i
$820$	−4.21237	+	6.24188i	−0.147102	+	0.217976i
$821$	−9.76423	+	7.09413i	−0.340774	+	0.247587i	−0.744988	−	0.667077i	$-0.767545\pi$
$821$	−9.76423	+	7.09413i	−0.340774	+	0.247587i	0.404214	+	0.914664i	$0.367545\pi$
$822$	1.91366	−	1.39036i	0.0667466	−	0.0484943i
$823$	5.43828	+	16.7373i	0.189567	+	0.583426i	0.999997	−	0.00240877i	$-0.000766737\pi$
$823$	5.43828	+	16.7373i	0.189567	+	0.583426i	−0.810430	+	0.585835i	$0.800767\pi$
$824$	−12.0574			−0.420038
$825$	3.99809	−	3.35154i	0.139196	−	0.116685i
$826$	18.2463			0.634871
$827$	7.70762	+	23.7216i	0.268020	+	0.824881i	0.990982	+	0.133994i	$0.0427802\pi$
$827$	7.70762	+	23.7216i	0.268020	+	0.824881i	−0.722962	+	0.690888i	$0.757220\pi$
$828$	−7.28313	+	5.29150i	−0.253106	+	0.183892i
$829$	23.7867	−	17.2821i	0.826148	−	0.600231i	−0.0923192	−	0.995729i	$-0.529428\pi$
$829$	23.7867	−	17.2821i	0.826148	−	0.600231i	0.918467	+	0.395498i	$0.129428\pi$
$830$	−20.9562	+	7.62175i	−0.727400	+	0.264555i
$831$	−24.9929	−	18.1584i	−0.866995	−	0.629909i
$832$	22.7450			0.788540
$833$	−2.46135	−	1.78828i	−0.0852808	−	0.0619602i
$834$	−4.70098	+	14.4681i	−0.162782	+	0.500991i
$835$	−0.0868066	−	2.50299i	−0.00300407	−	0.0866196i
$836$	−1.18624	−	3.65088i	−0.0410271	−	0.126268i
$837$	−2.65692	+	8.17717i	−0.0918367	+	0.282644i
$838$	2.86697	−	8.82362i	0.0990378	−	0.304807i
$839$	−9.25651	−	28.4886i	−0.319570	−	0.983536i	−0.973832	−	0.227268i	$-0.927021\pi$
$839$	−9.25651	−	28.4886i	−0.319570	−	0.983536i	0.654262	−	0.756268i	$-0.272979\pi$
$840$	−0.928855	−	1.18947i	−0.0320485	−	0.0410405i
$841$	−7.73158	+	23.7954i	−0.266606	+	0.820529i
$842$	−49.6998	−	36.1090i	−1.71277	−	1.24440i
$843$	−3.54230			−0.122003
$844$	31.2936	+	22.7361i	1.07717	+	0.782610i
$845$	−0.617757	−	17.8125i	−0.0212515	−	0.612768i
$846$	−19.7535	+	14.3518i	−0.679140	+	0.493424i
$847$	−8.01841	+	5.82572i	−0.275516	+	0.200174i
$848$	−0.568055	−	1.74829i	−0.0195071	−	0.0600367i
$849$	−20.2311			−0.694329
$850$	−24.6274	−	15.4053i	−0.844713	−	0.528398i
$851$	−40.3895			−1.38453
$852$	−1.90867	−	5.87429i	−0.0653900	−	0.201250i
$853$	6.81171	−	4.94900i	0.233229	−	0.169450i	−0.465033	−	0.885294i	$-0.653957\pi$
$853$	6.81171	−	4.94900i	0.233229	−	0.169450i	0.698261	+	0.715843i	$0.253957\pi$
$854$	−11.3554	+	8.25022i	−0.388575	+	0.282317i
$855$	4.80238	+	1.37830i	0.164238	+	0.0471370i
$856$	1.64880	+	1.19792i	0.0563548	+	0.0409441i
$857$	45.6885			1.56069			0.780345	−	0.625350i	$-0.215044\pi$
$857$	45.6885			1.56069			0.780345	+	0.625350i	$0.215044\pi$
$858$	−7.38178	−	5.36317i	−0.252010	−	0.183096i
$859$	13.2606	−	40.8120i	0.452447	−	1.39249i	−0.421660	−	0.906754i	$-0.638552\pi$
$859$	13.2606	−	40.8120i	0.452447	−	1.39249i	0.874106	−	0.485734i	$-0.161448\pi$
$860$	32.5671	+	9.34689i	1.11053	+	0.318726i
$861$	−0.632019	−	1.94515i	−0.0215391	−	0.0662907i
$862$	−17.0504	+	52.4756i	−0.580738	+	1.78733i
$863$	−14.9485	+	46.0069i	−0.508854	+	1.56609i	0.285338	+	0.958427i	$0.407894\pi$
$863$	−14.9485	+	46.0069i	−0.508854	+	1.56609i	−0.794193	+	0.607666i	$0.792106\pi$
$864$	2.28668	+	7.03767i	0.0777944	+	0.239427i
$865$	27.5592	−	40.8371i	0.937040	−	1.38850i
$866$	12.6143	−	38.8227i	0.428650	−	1.31925i
$867$	6.26487	+	4.55169i	0.212766	+	0.154584i
$868$	14.1571			0.480524
$869$	−5.40352	−	3.92589i	−0.183302	−	0.133177i
$870$	−5.24303	−	6.71408i	−0.177755	−	0.227629i
$871$	21.7519	−	15.8037i	0.737036	−	0.535488i
$872$	1.31433	−	0.954915i	0.0445088	−	0.0323375i
$873$	4.69013	+	14.4347i	0.158737	+	0.488541i
$874$	23.3283			0.789091
$875$	10.2170	−	4.54012i	0.345398	−	0.153484i
$876$	6.22958			0.210478
$877$	17.7691	+	54.6878i	0.600021	+	1.84668i	0.527948	+	0.849277i	$0.322962\pi$
$877$	17.7691	+	54.6878i	0.600021	+	1.84668i	0.0720737	+	0.997399i	$0.477038\pi$
$878$	50.3622	−	36.5903i	1.69964	−	1.23486i
$879$	5.60745	−	4.07405i	0.189135	−	0.137414i
$880$	−6.57959	−	8.42565i	−0.221798	−	0.284029i
$881$	20.7461	+	15.0729i	0.698954	+	0.507820i	0.879591	−	0.475730i	$-0.157816\pi$
$881$	20.7461	+	15.0729i	0.698954	+	0.507820i	−0.180637	+	0.983550i	$0.557816\pi$
$882$	−1.90960			−0.0642995
$883$	12.0559	+	8.75913i	0.405714	+	0.294768i	0.771864	−	0.635787i	$-0.219324\pi$
$883$	12.0559	+	8.75913i	0.405714	+	0.294768i	−0.366151	+	0.930556i	$0.619324\pi$
$884$	−7.08899	+	21.8177i	−0.238428	+	0.733807i
$885$	−11.9518	+	17.7102i	−0.401756	+	0.595321i
$886$	−8.60759	−	26.4914i	−0.289178	−	0.889997i
$887$	9.58815	−	29.5093i	0.321938	−	0.990825i	−0.650865	−	0.759193i	$-0.725594\pi$
$887$	9.58815	−	29.5093i	0.321938	−	0.990825i	0.972804	−	0.231631i	$-0.0744063\pi$
$888$	−1.54072	+	4.74183i	−0.0517030	+	0.159126i
$889$	0.100957	+	0.310712i	0.00338597	+	0.0104210i
$890$	55.4118	+	15.9034i	1.85741	+	0.533084i
$891$	0.322431	−	0.992340i	0.0108018	−	0.0332446i
$892$	10.7734	+	7.82735i	0.360721	+	0.262079i
$893$	28.5696			0.956046
$894$	−21.5140	−	15.6308i	−0.719536	−	0.522773i
$895$	−21.4405	−	6.15352i	−0.716677	−	0.205689i
$896$	−4.29998	+	3.12412i	−0.143652	+	0.104369i
$897$	20.2557	−	14.7166i	0.676317	−	0.491373i
$898$	−2.43344	−	7.48936i	−0.0812050	−	0.249923i
$899$	−17.1531			−0.572088
$900$	−8.21303	+	0.570361i	−0.273768	+	0.0190120i
$901$	1.22060			0.0406641
$902$	−1.25929	−	3.87570i	−0.0419298	−	0.129047i
$903$	−7.44494	+	5.40906i	−0.247752	+	0.180002i
$904$	5.23176	−	3.80110i	0.174006	−	0.126423i
$905$	−1.75859	−	50.7074i	−0.0584575	−	1.68557i
$906$	25.9343	+	18.8423i	0.861608	+	0.625995i
$907$	4.43244			0.147177			0.0735884	−	0.997289i	$-0.476555\pi$
$907$	4.43244			0.147177			0.0735884	+	0.997289i	$0.476555\pi$
$908$	−23.2732	−	16.9090i	−0.772348	−	0.561143i
$909$	−2.89038	+	8.89567i	−0.0958678	+	0.295051i
$910$	−12.0349	−	15.4116i	−0.398953	−	0.510889i
$911$	−6.66459	−	20.5115i	−0.220808	−	0.679576i	−0.998690	−	0.0511664i	$-0.983706\pi$
$911$	−6.66459	−	20.5115i	−0.220808	−	0.679576i	0.777882	−	0.628410i	$-0.216294\pi$
$912$	3.16368	−	9.73681i	0.104760	−	0.322418i
$913$	1.68383	−	5.18230i	0.0557267	−	0.171509i
$914$	−13.6018	−	41.8619i	−0.449906	−	1.38467i
$915$	−0.569668	−	16.4259i	−0.0188326	−	0.543023i
$916$	−3.07036	+	9.44960i	−0.101448	+	0.312224i
$917$	12.8814	+	9.35888i	0.425381	+	0.309058i
$918$	−5.80976			−0.191751
$919$	−6.60924	−	4.80189i	−0.218019	−	0.158400i	0.473416	−	0.880839i	$-0.343021\pi$
$919$	−6.60924	−	4.80189i	−0.218019	−	0.158400i	−0.691434	+	0.722439i	$0.743021\pi$
$920$	7.75433	−	2.82024i	0.255653	−	0.0929807i
$921$	−14.6765	+	10.6631i	−0.483606	+	0.351361i
$922$	−11.6885	+	8.49217i	−0.384939	+	0.279675i
$923$	5.30835	+	16.3374i	0.174727	+	0.537753i
$924$	−1.71804			−0.0565193
$925$	−31.3146	−	19.5884i	−1.02962	−	0.644062i
$926$	21.4560			0.705087
$927$	−5.52053	−	16.9904i	−0.181318	−	0.558040i
$928$	−11.9434	+	8.67736i	−0.392060	+	0.284848i
$929$	−15.4415	+	11.2189i	−0.506619	+	0.368080i	−0.811540	−	0.584297i	$-0.801370\pi$
$929$	−15.4415	+	11.2189i	−0.506619	+	0.368080i	0.304920	+	0.952378i	$0.401370\pi$
$930$	−20.5371	+	30.4318i	−0.673438	+	0.997898i
$931$	1.80766	+	1.31334i	0.0592437	+	0.0430431i
$932$	−2.24779			−0.0736288
$933$	−14.0137	−	10.1816i	−0.458788	−	0.333329i
$934$	15.5322	−	47.8031i	0.508228	−	1.56416i
$935$	6.67082	−	2.42617i	0.218159	−	0.0793443i
$936$	−0.955088	−	2.93946i	−0.0312180	−	0.0960792i
$937$	8.13920	−	25.0499i	0.265896	−	0.818344i	−0.725590	−	0.688128i	$-0.758433\pi$
$937$	8.13920	−	25.0499i	0.265896	−	0.818344i	0.991486	−	0.130216i	$-0.0415671\pi$
$938$	3.46463	−	10.6630i	0.113124	−	0.348161i
$939$	3.17326	+	9.76628i	0.103555	+	0.318710i
$940$	−44.2417	+	16.0907i	−1.44301	+	0.524820i
$941$	−1.15807	+	3.56418i	−0.0377521	+	0.116189i	−0.968157	−	0.250345i	$-0.919456\pi$
$941$	−1.15807	+	3.56418i	−0.0377521	+	0.116189i	0.930405	+	0.366534i	$0.119456\pi$
$942$	19.8173	+	14.3981i	0.645682	+	0.469116i
$943$	11.1823			0.364144
$944$	35.4195	+	25.7338i	1.15281	+	0.837562i
$945$	1.25084	−	1.85349i	0.0406897	−	0.0602939i
$946$	−14.8340	+	10.7775i	−0.482294	+	0.350407i
$947$	−10.5152	+	7.63972i	−0.341697	+	0.248258i	−0.745378	−	0.666642i	$-0.767731\pi$
$947$	−10.5152	+	7.63972i	−0.341697	+	0.248258i	0.403680	+	0.914900i	$0.367731\pi$
$948$	3.25706	+	10.0242i	0.105784	+	0.325571i
$949$	−17.3256			−0.562412
$950$	18.0868	+	11.3139i	0.586813	+	0.367072i
$951$	−4.89581			−0.158758
$952$	−0.634530	−	1.95288i	−0.0205653	−	0.0632933i
$953$	3.05168	−	2.21718i	0.0988537	−	0.0718215i	−0.537260	−	0.843416i	$-0.680541\pi$
$953$	3.05168	−	2.21718i	0.0988537	−	0.0718215i	0.636114	+	0.771595i	$0.280541\pi$
$954$	0.619807	−	0.450316i	0.0200670	−	0.0145795i
$955$	12.7880	−	4.65097i	0.413808	−	0.150502i
$956$	−36.4360	−	26.4723i	−1.17843	−	0.856176i
$957$	2.08161			0.0672890
$958$	12.6667	+	9.20292i	0.409244	+	0.297333i
$959$	−0.382779	+	1.17807i	−0.0123606	+	0.0380420i
$960$	0.384942	+	11.0995i	0.0124240	+	0.358234i
$961$	13.2647	+	40.8244i	0.427892	+	1.31692i
$962$	−19.9626	+	61.4387i	−0.643621	+	1.98086i
$963$	−0.933122	+	2.87185i	−0.0300694	+	0.0925442i
$964$	−0.896115	−	2.75796i	−0.0288619	−	0.0888279i
$965$	−8.85545	−	11.3401i	−0.285067	−	0.365049i
$966$	3.22631	−	9.92956i	0.103805	−	0.319478i
$967$	−48.0445	−	34.9064i	−1.54501	−	1.12251i	−0.947096	−	0.320949i	$-0.895998\pi$
$967$	−48.0445	−	34.9064i	−1.54501	−	1.12251i	−0.597910	−	0.801563i	$-0.704002\pi$
$968$	−6.68936			−0.215004
$969$	5.49963	+	3.99571i	0.176673	+	0.128361i
$970$	2.24627	+	64.7691i	0.0721233	+	2.07961i
$971$	27.3155	−	19.8459i	0.876597	−	0.636885i	−0.0557520	−	0.998445i	$-0.517756\pi$
$971$	27.3155	−	19.8459i	0.876597	−	0.636885i	0.932349	+	0.361560i	$0.117756\pi$
$972$	−1.33210	+	0.967825i	−0.0427270	+	0.0310430i
$973$	−2.46177	−	7.57654i	−0.0789206	−	0.242893i
$974$	−37.3083			−1.19544
$975$	22.8419	−	1.58627i	0.731527	−	0.0508014i
$976$	−33.6787			−1.07803
$977$	11.1841	+	34.4211i	0.357811	+	1.10123i	0.954362	+	0.298654i	$0.0965376\pi$
$977$	11.1841	+	34.4211i	0.357811	+	1.10123i	−0.596550	+	0.802576i	$0.703462\pi$
$978$	25.9281	−	18.8379i	0.829089	−	0.602368i
$979$	−11.3966	+	8.28012i	−0.364237	+	0.264634i
$980$	−3.53896	−	1.01570i	−0.113048	−	0.0324452i
$981$	1.94738	+	1.41485i	0.0621749	+	0.0451727i
$982$	−11.9662			−0.381858
$983$	−40.4970	−	29.4228i	−1.29165	−	0.938442i	−0.291817	−	0.956474i	$-0.594260\pi$
$983$	−40.4970	−	29.4228i	−1.29165	−	0.938442i	−0.999837	+	0.0180320i	$0.994260\pi$
$984$	0.426564	−	1.31283i	0.0135984	−	0.0418514i
$985$	33.5848	+	9.63899i	1.07010	+	0.307124i
$986$	−3.58168	−	11.0233i	−0.114064	−	0.351053i
$987$	3.95119	−	12.1605i	0.125768	−	0.387073i
$988$	5.20628	−	16.0233i	0.165634	−	0.509768i
$989$	−15.5477	−	47.8511i	−0.494390	−	1.52157i
$990$	2.49228	−	3.69305i	0.0792098	−	0.117373i
$991$	6.52398	−	20.0787i	0.207241	−	0.637822i	−0.792373	−	0.610037i	$-0.791155\pi$
$991$	6.52398	−	20.0787i	0.207241	−	0.637822i	0.999614	−	0.0277854i	$-0.00884549\pi$
$992$	51.4727	+	37.3971i	1.63426	+	1.18736i
$993$	17.4828			0.554799
$994$	5.79522	+	4.21047i	0.183813	+	0.133548i
$995$	9.47540	+	12.1339i	0.300390	+	0.384672i
$996$	−6.95662	+	5.05428i	−0.220429	+	0.160151i
$997$	20.8122	−	15.1210i	0.659130	−	0.478886i	−0.207239	−	0.978290i	$-0.566448\pi$
$997$	20.8122	−	15.1210i	0.659130	−	0.478886i	0.866369	+	0.499404i	$0.166448\pi$
$998$	−17.0759	−	52.5541i	−0.540527	−	1.66357i
$999$	−7.38731			−0.233724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.106.2	✓	32
25.21	even	5	inner	525.2.n.d.421.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.106.2	✓	32	1.1	even	1	trivial
525.2.n.d.421.2	yes	32	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)

\(f(q)\)	\(=\)	\(q+(-0.590098 - 1.81614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.33210 + 0.967825i) q^{4} +(1.37624 + 1.76238i) q^{5} +(1.54490 + 1.12243i) q^{6} -1.00000 q^{7} +(-0.546024 - 0.396709i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.590098 - 1.81614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.33210 + 0.967825i) q^{4} +(1.37624 + 1.76238i) q^{5} +(1.54490 + 1.12243i) q^{6} -1.00000 q^{7} +(-0.546024 - 0.396709i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.38860 - 3.53941i) q^{10} +(0.322431 + 0.992340i) q^{11} +(0.508816 - 1.56597i) q^{12} +(-1.41511 + 4.35525i) q^{13} +(0.590098 + 1.81614i) q^{14} +(-2.14930 - 0.616858i) q^{15} +(-1.41590 + 4.35770i) q^{16} +(-2.46135 - 1.78828i) q^{17} -1.90960 q^{18} +(1.80766 + 1.31334i) q^{19} +(-3.53896 - 1.01570i) q^{20} +(0.809017 - 0.587785i) q^{21} +(1.61196 - 1.17116i) q^{22} +(1.68952 + 5.19982i) q^{23} +0.674922 q^{24} +(-1.21193 + 4.85090i) q^{25} +8.74478 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.33210 - 0.967825i) q^{28} +(-1.61400 + 1.17264i) q^{29} +(0.147999 + 4.26742i) q^{30} +(6.95592 + 5.05377i) q^{31} +7.39985 q^{32} +(-0.844135 - 0.613300i) q^{33} +(-1.79531 + 5.52541i) q^{34} +(-1.37624 - 1.76238i) q^{35} +(0.508816 + 1.56597i) q^{36} +(-2.28280 + 7.02575i) q^{37} +(1.31851 - 4.05796i) q^{38} +(-1.41511 - 4.35525i) q^{39} +(-0.0523083 - 1.50827i) q^{40} +(0.632019 - 1.94515i) q^{41} +(-1.54490 - 1.12243i) q^{42} -9.20245 q^{43} +(-1.38992 - 1.00984i) q^{44} +(2.10140 - 0.764277i) q^{45} +(8.44659 - 6.13680i) q^{46} +(10.3443 - 7.51560i) q^{47} +(-1.41590 - 4.35770i) q^{48} +1.00000 q^{49} +(9.52505 - 0.661474i) q^{50} +3.04240 q^{51} +(-2.33006 - 7.17120i) q^{52} +(-0.324575 + 0.235817i) q^{53} +(1.54490 - 1.12243i) q^{54} +(-1.30513 + 1.93394i) q^{55} +(0.546024 + 0.396709i) q^{56} -2.23439 q^{57} +(3.08209 + 2.23927i) q^{58} +(2.95268 - 9.08740i) q^{59} +(3.46009 - 1.25843i) q^{60} +(2.27137 + 6.99055i) q^{61} +(5.07366 - 15.6151i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-1.53483 - 4.72373i) q^{64} +(-9.62312 + 3.49992i) q^{65} +(-0.615713 + 1.89497i) q^{66} +(-4.74997 - 3.45106i) q^{67} +5.00950 q^{68} +(-4.42323 - 3.21366i) q^{69} +(-2.38860 + 3.53941i) q^{70} +(3.03479 - 2.20490i) q^{71} +(-0.546024 + 0.396709i) q^{72} +(1.16913 + 3.59821i) q^{73} +14.1068 q^{74} +(-1.87081 - 4.63682i) q^{75} -3.67907 q^{76} +(-0.322431 - 0.992340i) q^{77} +(-7.07468 + 5.14005i) q^{78} +(-5.17872 + 3.76256i) q^{79} +(-9.62852 + 3.50189i) q^{80} +(-0.809017 - 0.587785i) q^{81} -3.90562 q^{82} +(-4.22493 - 3.06959i) q^{83} +(-0.508816 + 1.56597i) q^{84} +(-0.235794 - 6.79893i) q^{85} +(5.43035 + 16.7129i) q^{86} +(0.616494 - 1.89737i) q^{87} +(0.217616 - 0.669752i) q^{88} +(4.17202 + 12.8401i) q^{89} +(-2.62806 - 3.36543i) q^{90} +(1.41511 - 4.35525i) q^{91} +(-7.28313 - 5.29150i) q^{92} -8.59799 q^{93} +(-19.7535 - 14.3518i) q^{94} +(0.173172 + 4.99325i) q^{95} +(-5.98660 + 4.34952i) q^{96} +(-12.2789 + 8.92115i) q^{97} +(-0.590098 - 1.81614i) q^{98} +1.04341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

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