LMFDB - Embedded newform 261.2.l.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(41,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("261.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.l (of order $12$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	261.41
Dual form			261.2.l.a.191.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.726652 - 0.194706i) q^{2} +(0.184317 - 1.72222i) q^{3} +(-1.24194 - 0.717034i) q^{4} +(0.993651 - 1.72105i) q^{5} +(-0.469260 + 1.21556i) q^{6} +(-0.796821 - 1.38013i) q^{7} +(1.82674 + 1.82674i) q^{8} +(-2.93205 - 0.634868i) q^{9} +O(q^{10})$	\(q+(-0.726652 - 0.194706i) q^{2} +(0.184317 - 1.72222i) q^{3} +(-1.24194 - 0.717034i) q^{4} +(0.993651 - 1.72105i) q^{5} +(-0.469260 + 1.21556i) q^{6} +(-0.796821 - 1.38013i) q^{7} +(1.82674 + 1.82674i) q^{8} +(-2.93205 - 0.634868i) q^{9} +(-1.05714 + 1.05714i) q^{10} +(-3.84963 - 1.03150i) q^{11} +(-1.46380 + 2.00672i) q^{12} +(5.20946 + 3.00768i) q^{13} +(0.310291 + 1.15802i) q^{14} +(-2.78088 - 2.02850i) q^{15} +(0.462342 + 0.800799i) q^{16} +(-0.996830 + 0.996830i) q^{17} +(2.00697 + 1.03222i) q^{18} +(-3.65492 - 3.65492i) q^{19} +(-2.46811 + 1.42496i) q^{20} +(-2.52376 + 1.11791i) q^{21} +(2.59650 + 1.49909i) q^{22} +(-3.97804 - 2.29672i) q^{23} +(3.48274 - 2.80934i) q^{24} +(0.525314 + 0.909871i) q^{25} +(-3.19985 - 3.19985i) q^{26} +(-1.63381 + 4.93261i) q^{27} +2.28539i q^{28} +(-3.13850 - 4.37605i) q^{29} +(1.62577 + 2.01547i) q^{30} +(5.02217 - 1.34569i) q^{31} +(-1.51731 - 5.66266i) q^{32} +(-2.48602 + 6.43976i) q^{33} +(0.918437 - 0.530260i) q^{34} -3.16705 q^{35} +(3.18621 + 2.89085i) q^{36} +(7.98902 - 7.98902i) q^{37} +(1.94422 + 3.36749i) q^{38} +(6.14007 - 8.41745i) q^{39} +(4.95906 - 1.32877i) q^{40} +(-2.32830 + 0.623865i) q^{41} +(2.05156 - 0.320945i) q^{42} +(-1.74915 + 6.52792i) q^{43} +(4.04138 + 4.04138i) q^{44} +(-4.00608 + 4.41539i) q^{45} +(2.44346 + 2.44346i) q^{46} +(1.36376 - 5.08962i) q^{47} +(1.46437 - 0.648651i) q^{48} +(2.23015 - 3.86274i) q^{49} +(-0.204563 - 0.763441i) q^{50} +(1.53302 + 1.90049i) q^{51} +(-4.31322 - 7.47072i) q^{52} -4.08882i q^{53} +(2.14762 - 3.26618i) q^{54} +(-5.60046 + 5.60046i) q^{55} +(1.06556 - 3.97672i) q^{56} +(-6.96823 + 5.62090i) q^{57} +(1.42856 + 3.79095i) q^{58} +(8.55999 + 4.94211i) q^{59} +(1.99918 + 4.51326i) q^{60} +(-1.48897 + 5.55692i) q^{61} -3.91138 q^{62} +(1.46012 + 4.55250i) q^{63} +2.56084i q^{64} +(10.3528 - 5.97718i) q^{65} +(3.06033 - 4.19542i) q^{66} +(-4.68028 - 2.70216i) q^{67} +(1.95276 - 0.523241i) q^{68} +(-4.68867 + 6.42772i) q^{69} +(2.30134 + 0.616642i) q^{70} +13.7144 q^{71} +(-4.19636 - 6.51583i) q^{72} +(8.70450 - 8.70450i) q^{73} +(-7.36074 + 4.24973i) q^{74} +(1.66382 - 0.737000i) q^{75} +(1.91849 + 7.15989i) q^{76} +(1.64385 + 6.13492i) q^{77} +(-6.10062 + 4.92104i) q^{78} +(2.26755 - 8.46261i) q^{79} +1.83763 q^{80} +(8.19389 + 3.72293i) q^{81} +1.81333 q^{82} +(-4.05925 + 2.34361i) q^{83} +(3.93593 + 0.421236i) q^{84} +(0.725097 + 2.70610i) q^{85} +(2.54204 - 4.40295i) q^{86} +(-8.11498 + 4.59860i) q^{87} +(-5.14797 - 8.91654i) q^{88} +(-2.43156 + 2.43156i) q^{89} +(3.77073 - 2.42844i) q^{90} -9.58634i q^{91} +(3.29365 + 5.70478i) q^{92} +(-1.39189 - 8.89730i) q^{93} +(-1.98196 + 3.43285i) q^{94} +(-9.92204 + 2.65860i) q^{95} +(-10.0320 + 1.56940i) q^{96} +(-0.513620 - 0.137624i) q^{97} +(-2.37264 + 2.37264i) q^{98} +(10.6324 + 5.46843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 112 * q - 6 * q^2 - 4 * q^3 - 4 * q^7	$ 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7} + 6 q^{11} - 18 q^{12} - 18 q^{14} - 8 q^{15} + 40 q^{16} + 22 q^{18} - 8 q^{19} - 12 q^{20} + 24 q^{21} - 12 q^{23} - 96 q^{24} - 44 q^{25} + 20 q^{27} - 42 q^{29} + 28 q^{30} - 2 q^{31} - 66 q^{32} + 12 q^{36} - 8 q^{37} - 12 q^{39} - 12 q^{40} - 18 q^{41} - 2 q^{43} - 52 q^{45} + 8 q^{46} - 36 q^{49} + 24 q^{50} - 36 q^{52} + 8 q^{54} + 36 q^{55} + 84 q^{56} + 28 q^{58} + 48 q^{59} - 36 q^{60} - 14 q^{61} + 24 q^{65} + 18 q^{66} - 102 q^{68} + 36 q^{69} - 8 q^{73} + 144 q^{74} + 18 q^{75} + 14 q^{76} - 72 q^{77} + 12 q^{78} - 2 q^{79} - 56 q^{81} + 80 q^{82} - 120 q^{83} - 14 q^{84} - 48 q^{85} - 76 q^{87} - 36 q^{88} + 160 q^{90} - 40 q^{94} + 204 q^{95} + 22 q^{97} - 54 q^{99}+O(q^{100}) $ 112 * q - 6 * q^2 - 4 * q^3 - 4 * q^7 + 6 * q^11 - 18 * q^12 - 18 * q^14 - 8 * q^15 + 40 * q^16 + 22 * q^18 - 8 * q^19 - 12 * q^20 + 24 * q^21 - 12 * q^23 - 96 * q^24 - 44 * q^25 + 20 * q^27 - 42 * q^29 + 28 * q^30 - 2 * q^31 - 66 * q^32 + 12 * q^36 - 8 * q^37 - 12 * q^39 - 12 * q^40 - 18 * q^41 - 2 * q^43 - 52 * q^45 + 8 * q^46 - 36 * q^49 + 24 * q^50 - 36 * q^52 + 8 * q^54 + 36 * q^55 + 84 * q^56 + 28 * q^58 + 48 * q^59 - 36 * q^60 - 14 * q^61 + 24 * q^65 + 18 * q^66 - 102 * q^68 + 36 * q^69 - 8 * q^73 + 144 * q^74 + 18 * q^75 + 14 * q^76 - 72 * q^77 + 12 * q^78 - 2 * q^79 - 56 * q^81 + 80 * q^82 - 120 * q^83 - 14 * q^84 - 48 * q^85 - 76 * q^87 - 36 * q^88 + 160 * q^90 - 40 * q^94 + 204 * q^95 + 22 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.726652	−	0.194706i	−0.513820	−	0.137678i	−0.00741360	−	0.999973i	$-0.502360\pi$
$2$	−0.726652	−	0.194706i	−0.513820	−	0.137678i	−0.506407	+	0.862295i	$0.669027\pi$
$3$	0.184317	−	1.72222i	0.106416	−	0.994322i
$3$	0.184317	−	1.72222i	0.106416	−	0.994322i
$4$	−1.24194	−	0.717034i	−0.620969	−	0.358517i
$5$	0.993651	−	1.72105i	0.444374	−	0.769679i	−0.553634	−	0.832760i	$-0.686759\pi$
$5$	0.993651	−	1.72105i	0.444374	−	0.769679i	0.998008	+	0.0630811i	$0.0200927\pi$
$6$	−0.469260	+	1.21556i	−0.191574	+	0.496252i
$7$	−0.796821	−	1.38013i	−0.301170	−	0.521642i	0.675231	−	0.737606i	$-0.264044\pi$
$7$	−0.796821	−	1.38013i	−0.301170	−	0.521642i	−0.976401	+	0.215964i	$0.930710\pi$
$8$	1.82674	+	1.82674i	0.645849	+	0.645849i
$9$	−2.93205	−	0.634868i	−0.977351	−	0.211623i
$10$	−1.05714	+	1.05714i	−0.334296	+	0.334296i
$11$	−3.84963	−	1.03150i	−1.16071	−	0.311010i	−0.373458	−	0.927647i	$-0.621828\pi$
$11$	−3.84963	−	1.03150i	−1.16071	−	0.311010i	−0.787248	+	0.616637i	$0.788495\pi$
$12$	−1.46380	+	2.00672i	−0.422562	+	0.579292i
$13$	5.20946	+	3.00768i	1.44484	+	0.834181i	0.998167	−	0.0605137i	$-0.0192739\pi$
$13$	5.20946	+	3.00768i	1.44484	+	0.834181i	0.446677	+	0.894695i	$0.352607\pi$
$14$	0.310291	+	1.15802i	0.0829288	+	0.309494i
$15$	−2.78088	−	2.02850i	−0.718020	−	0.523757i
$16$	0.462342	+	0.800799i	0.115585	+	0.200200i
$17$	−0.996830	+	0.996830i	−0.241767	+	0.241767i	−0.817581	−	0.575814i	$-0.804685\pi$
$17$	−0.996830	+	0.996830i	−0.241767	+	0.241767i	0.575814	+	0.817581i	$0.304685\pi$
$18$	2.00697	+	1.03222i	0.473047	+	0.243295i
$19$	−3.65492	−	3.65492i	−0.838497	−	0.838497i	0.150164	−	0.988661i	$-0.452020\pi$
$19$	−3.65492	−	3.65492i	−0.838497	−	0.838497i	−0.988661	+	0.150164i	$0.952020\pi$
$20$	−2.46811	+	1.42496i	−0.551886	+	0.318631i
$21$	−2.52376	+	1.11791i	−0.550729	+	0.243949i
$22$	2.59650	+	1.49909i	0.553575	+	0.319607i
$23$	−3.97804	−	2.29672i	−0.829479	−	0.478900i	0.0241955	−	0.999707i	$-0.492298\pi$
$23$	−3.97804	−	2.29672i	−0.829479	−	0.478900i	−0.853674	+	0.520808i	$0.825631\pi$
$24$	3.48274	−	2.80934i	0.710910	−	0.573454i
$25$	0.525314	+	0.909871i	0.105063	+	0.181974i
$26$	−3.19985	−	3.19985i	−0.627542	−	0.627542i
$27$	−1.63381	+	4.93261i	−0.314426	+	0.949282i
$28$			2.28539i			0.431898i
$29$	−3.13850	−	4.37605i	−0.582806	−	0.812612i
$29$	−3.13850	−	4.37605i	−0.582806	−	0.812612i
$30$	1.62577	+	2.01547i	0.296824	+	0.367972i
$31$	5.02217	−	1.34569i	0.902009	−	0.241693i	0.222130	−	0.975017i	$-0.428699\pi$
$31$	5.02217	−	1.34569i	0.902009	−	0.241693i	0.679879	+	0.733325i	$0.262032\pi$
$32$	−1.51731	−	5.66266i	−0.268224	−	1.00103i
$33$	−2.48602	+	6.43976i	−0.432761	+	1.12102i
$34$	0.918437	−	0.530260i	0.157511	−	0.0909388i
$35$	−3.16705			−0.535329
$36$	3.18621	+	2.89085i	0.531035	+	0.481808i
$37$	7.98902	−	7.98902i	1.31339	−	1.31339i	0.394484	−	0.918903i	$-0.370923\pi$
$37$	7.98902	−	7.98902i	1.31339	−	1.31339i	0.918903	−	0.394484i	$-0.129077\pi$
$38$	1.94422	+	3.36749i	0.315394	+	0.546279i
$39$	6.14007	−	8.41745i	0.983199	−	1.34787i
$40$	4.95906	−	1.32877i	0.784096	−	0.210098i
$41$	−2.32830	+	0.623865i	−0.363619	+	0.0974313i	−0.436002	−	0.899946i	$-0.643606\pi$
$41$	−2.32830	+	0.623865i	−0.363619	+	0.0974313i	0.0723836	+	0.997377i	$0.476939\pi$
$42$	2.05156	−	0.320945i	0.316562	−	0.0495229i
$43$	−1.74915	+	6.52792i	−0.266743	+	0.995498i	0.694432	+	0.719558i	$0.255656\pi$
$43$	−1.74915	+	6.52792i	−0.266743	+	0.995498i	−0.961175	+	0.275940i	$0.911011\pi$
$44$	4.04138	+	4.04138i	0.609260	+	0.609260i
$45$	−4.00608	+	4.41539i	−0.597191	+	0.658207i
$46$	2.44346	+	2.44346i	0.360269	+	0.360269i
$47$	1.36376	−	5.08962i	0.198925	−	0.742397i	−0.792291	−	0.610143i	$-0.791112\pi$
$47$	1.36376	−	5.08962i	0.198925	−	0.742397i	0.991216	−	0.132254i	$-0.0422214\pi$
$48$	1.46437	−	0.648651i	0.211363	−	0.0936247i
$49$	2.23015	−	3.86274i	0.318593	−	0.551820i
$50$	−0.204563	−	0.763441i	−0.0289296	−	0.107967i
$51$	1.53302	+	1.90049i	0.214666	+	0.266122i
$52$	−4.31322	−	7.47072i	−0.598136	−	1.03600i
$53$		−	4.08882i		−	0.561642i	−0.959760	−	0.280821i	$-0.909393\pi$
$53$		−	4.08882i		−	0.561642i	0.959760	−	0.280821i	$-0.0906068\pi$
$54$	2.14762	−	3.26618i	0.292254	−	0.444471i
$55$	−5.60046	+	5.60046i	−0.755166	+	0.755166i
$56$	1.06556	−	3.97672i	0.142391	−	0.531412i
$57$	−6.96823	+	5.62090i	−0.922965	+	0.744507i
$58$	1.42856	+	3.79095i	0.187579	+	0.497776i
$59$	8.55999	+	4.94211i	1.11442	+	0.643408i	0.939970	−	0.341258i	$-0.110853\pi$
$59$	8.55999	+	4.94211i	1.11442	+	0.643408i	0.174446	+	0.984667i	$0.444186\pi$
$60$	1.99918	+	4.51326i	0.258093	+	0.582659i
$61$	−1.48897	+	5.55692i	−0.190643	+	0.711490i	0.802709	+	0.596372i	$0.203391\pi$
$61$	−1.48897	+	5.55692i	−0.190643	+	0.711490i	−0.993352	+	0.115119i	$0.963275\pi$
$62$	−3.91138			−0.496746
$63$	1.46012	+	4.55250i	0.183958	+	0.573561i
$64$			2.56084i			0.320106i
$65$	10.3528	−	5.97718i	1.28410	−	0.741378i
$66$	3.06033	−	4.19542i	0.376701	−	0.516421i
$67$	−4.68028	−	2.70216i	−0.571788	−	0.330122i	0.186075	−	0.982535i	$-0.440423\pi$
$67$	−4.68028	−	2.70216i	−0.571788	−	0.330122i	−0.757863	+	0.652414i	$0.773756\pi$
$68$	1.95276	−	0.523241i	0.236807	−	0.0634523i
$69$	−4.68867	+	6.42772i	−0.564450	+	0.773806i
$70$	2.30134	+	0.616642i	0.275063	+	0.0737028i
$71$	13.7144			1.62760			0.813802	−	0.581143i	$-0.197394\pi$
$71$	13.7144			1.62760			0.813802	+	0.581143i	$0.197394\pi$
$72$	−4.19636	−	6.51583i	−0.494545	−	0.767898i
$73$	8.70450	−	8.70450i	1.01879	−	1.01879i	0.0189649	−	0.999820i	$-0.493963\pi$
$73$	8.70450	−	8.70450i	1.01879	−	1.01879i	0.999820	−	0.0189649i	$-0.00603707\pi$
$74$	−7.36074	+	4.24973i	−0.855669	+	0.494021i
$75$	1.66382	−	0.737000i	0.192121	−	0.0851014i
$76$	1.91849	+	7.15989i	0.220066	+	0.821296i
$77$	1.64385	+	6.13492i	0.187334	+	0.699139i
$78$	−6.10062	+	4.92104i	−0.690759	+	0.557199i
$79$	2.26755	−	8.46261i	0.255119	−	0.952118i	−0.712905	−	0.701261i	$-0.752621\pi$
$79$	2.26755	−	8.46261i	0.255119	−	0.952118i	0.968024	−	0.250857i	$-0.0807124\pi$
$80$	1.83763			0.205453
$81$	8.19389	+	3.72293i	0.910432	+	0.413659i
$82$	1.81333			0.200249
$83$	−4.05925	+	2.34361i	−0.445560	+	0.257244i	−0.705953	−	0.708258i	$-0.749481\pi$
$83$	−4.05925	+	2.34361i	−0.445560	+	0.257244i	0.260393	+	0.965503i	$0.416148\pi$
$84$	3.93593	+	0.421236i	0.429445	+	0.0459607i
$85$	0.725097	+	2.70610i	0.0786479	+	0.293518i
$86$	2.54204	−	4.40295i	0.274116	−	0.474782i
$87$	−8.11498	+	4.59860i	−0.870017	+	0.493022i
$88$	−5.14797	−	8.91654i	−0.548775	−	0.950507i
$89$	−2.43156	+	2.43156i	−0.257745	+	0.257745i	−0.824136	−	0.566392i	$-0.808339\pi$
$89$	−2.43156	+	2.43156i	−0.257745	+	0.257745i	0.566392	+	0.824136i	$0.308339\pi$
$90$	3.77073	−	2.42844i	0.397469	−	0.255980i
$91$		−	9.58634i		−	1.00492i
$92$	3.29365	+	5.70478i	0.343387	+	0.594764i
$93$	−1.39189	−	8.89730i	−0.144332	−	0.922607i
$94$	−1.98196	+	3.43285i	−0.204423	+	0.354071i
$95$	−9.92204	+	2.65860i	−1.01798	+	0.272767i
$96$	−10.0320	+	1.56940i	−1.02389	+	0.160176i
$97$	−0.513620	−	0.137624i	−0.0521502	−	0.0139736i	0.232650	−	0.972561i	$-0.425260\pi$
$97$	−0.513620	−	0.137624i	−0.0521502	−	0.0139736i	−0.284800	+	0.958587i	$0.591927\pi$
$98$	−2.37264	+	2.37264i	−0.239673	+	0.239673i
$99$	10.6324	+	5.46843i	1.06860	+	0.549598i
$100$		−	1.50667i		−	0.150667i
$101$	−12.9481	−	3.46944i	−1.28839	−	0.345223i	−0.451340	−	0.892352i	$-0.649054\pi$
$101$	−12.9481	−	3.46944i	−1.28839	−	0.345223i	−0.837048	+	0.547129i	$0.815721\pi$
$102$	−0.743938	−	1.67948i	−0.0736608	−	0.166294i
$103$	−3.29745	+	5.71136i	−0.324908	+	0.562757i	−0.981494	−	0.191495i	$-0.938667\pi$
$103$	−3.29745	+	5.71136i	−0.324908	+	0.562757i	0.656586	+	0.754251i	$0.272000\pi$
$104$	4.02207	+	15.0106i	0.394396	+	1.47191i
$105$	−0.583741	+	5.45434i	−0.0569673	+	0.532289i
$106$	−0.796116	+	2.97115i	−0.0773257	+	0.288583i
$107$		−	14.8570i		−	1.43628i	−0.695900	−	0.718138i	$-0.744994\pi$
$107$		−	14.8570i		−	1.43628i	0.695900	−	0.718138i	$-0.255006\pi$
$108$	5.56594	−	4.95451i	0.535583	−	0.476748i
$109$			10.9732i			1.05104i	0.850782	+	0.525519i	$0.176129\pi$
$109$			10.9732i			1.05104i	−0.850782	+	0.525519i	$0.823871\pi$
$110$	5.16002	−	2.97914i	0.491989	−	0.284050i
$111$	−12.2863	−	15.2313i	−1.16616	−	1.44569i
$112$	0.736807	−	1.27619i	0.0696217	−	0.120588i
$113$	3.82180	−	1.02405i	0.359525	−	0.0963344i	−0.0745351	−	0.997218i	$-0.523747\pi$
$113$	3.82180	−	1.02405i	0.359525	−	0.0963344i	0.434060	+	0.900884i	$0.357081\pi$
$114$	6.15790	−	2.72768i	0.576740	−	0.255471i
$115$	−7.90557	+	4.56428i	−0.737198	+	0.425621i
$116$	0.760056	+	7.68520i	0.0705694	+	0.713553i
$117$	−13.3649	−	12.1260i	−1.23559	−	1.12105i
$118$	−5.25787	−	5.25787i	−0.484026	−	0.484026i
$119$	2.17005	+	0.581464i	0.198928	+	0.0533027i
$120$	−1.37440	−	8.78548i	−0.125465	−	0.802001i
$121$	4.22934	+	2.44181i	0.384485	+	0.221983i
$122$	2.16393	−	3.74803i	0.195913	−	0.339331i
$123$	0.645285	+	4.12482i	0.0581834	+	0.371922i
$124$	−7.20213	−	1.92981i	−0.646771	−	0.173302i
$125$	12.0244			1.07550
$126$	−0.174599	−	3.59238i	−0.0155545	−	0.320034i
$127$	−10.3167	−	10.3167i	−0.915459	−	0.915459i	0.0812356	−	0.996695i	$-0.474113\pi$
$127$	−10.3167	−	10.3167i	−0.915459	−	0.915459i	−0.996695	+	0.0812356i	$0.974113\pi$
$128$	−2.53600	+	9.46448i	−0.224153	+	0.836550i
$129$	10.9201	+	4.21562i	0.961459	+	0.371165i
$130$	−8.68665	+	2.32758i	−0.761870	+	0.204142i
$131$	−7.32315	+	1.96223i	−0.639826	+	0.171441i	−0.564125	−	0.825690i	$-0.690786\pi$
$131$	−7.32315	+	1.96223i	−0.639826	+	0.171441i	−0.0757016	+	0.997131i	$0.524120\pi$
$132$	7.70502	−	6.21523i	0.670636	−	0.540966i
$133$	−2.13196	+	7.95660i	−0.184865	+	0.689925i
$134$	2.87481	+	2.87481i	0.248346	+	0.248346i
$135$	6.86586	+	7.71317i	0.590919	+	0.663844i
$136$	−3.64189			−0.312290
$137$	5.84048	+	1.56495i	0.498986	+	0.133703i	0.499529	−	0.866297i	$-0.333506\pi$
$137$	5.84048	+	1.56495i	0.498986	+	0.133703i	−0.000543628		1.00000i	$0.500173\pi$
$138$	4.65854	−	3.75780i	0.396562	−	0.319885i
$139$	0.479812	−	0.831059i	0.0406971	−	0.0704895i	−0.844959	−	0.534831i	$-0.820375\pi$
$139$	0.479812	−	0.831059i	0.0406971	−	0.0704895i	0.885656	+	0.464341i	$0.153709\pi$
$140$	3.93328	+	2.27088i	0.332423	+	0.191924i
$141$	−8.51406	−	3.28679i	−0.717013	−	0.276798i
$142$	−9.96561	−	2.67028i	−0.836296	−	0.224085i
$143$	−16.9520	−	16.9520i	−1.41760	−	1.41760i
$144$	−0.847209	−	2.64151i	−0.0706008	−	0.220126i
$145$	−10.6500	+	1.05327i	−0.884434	+	0.0874693i
$146$	−8.01996	+	4.63032i	−0.663736	+	0.383208i
$147$	−6.24142	−	4.55278i	−0.514783	−	0.375507i
$148$	−15.6503	+	4.19348i	−1.28644	+	0.344702i
$149$	2.29276	−	3.97117i	0.187830	−	0.325331i	−0.756696	−	0.653766i	$-0.773188\pi$
$149$	2.29276	−	3.97117i	0.187830	−	0.325331i	0.944527	+	0.328435i	$0.106521\pi$
$150$	−1.35251	+	0.211587i	−0.110432	+	0.0172760i
$151$	−0.898512	+	0.518756i	−0.0731199	+	0.0422158i	−0.536114	−	0.844145i	$-0.680108\pi$
$151$	−0.898512	+	0.518756i	−0.0731199	+	0.0422158i	0.462994	+	0.886361i	$0.346775\pi$
$152$		−	13.3532i		−	1.08309i
$153$	3.55562	−	2.28990i	0.287454	−	0.185128i
$154$		−	4.77802i		−	0.385024i
$155$	2.67429	−	9.98058i	0.214804	−	0.801659i
$156$	−13.6612	+	6.05132i	−1.09377	+	0.484493i
$157$	1.73417	+	6.47200i	0.138402	+	0.516522i	0.999961	+	0.00886466i	$0.00282175\pi$
$157$	1.73417	+	6.47200i	0.138402	+	0.516522i	−0.861559	+	0.507657i	$0.830512\pi$
$158$	−3.29544	+	5.70786i	−0.262171	+	0.454093i
$159$	−7.04183	−	0.753640i	−0.558453	−	0.0597675i
$160$	−11.2534	−	3.01535i	−0.889661	−	0.238384i
$161$			7.32030i			0.576921i
$162$	−5.22922	−	4.30067i	−0.410847	−	0.337893i
$163$	3.93066	−	3.93066i	0.307873	−	0.307873i	−0.536211	−	0.844084i	$-0.680145\pi$
$163$	3.93066	−	3.93066i	0.307873	−	0.307873i	0.844084	+	0.536211i	$0.180145\pi$
$164$	3.33893	+	0.894664i	0.260727	+	0.0698615i
$165$	8.61294	+	10.6775i	0.670516	+	0.831239i
$166$	3.40597	−	0.912627i	0.264355	−	0.0708336i
$167$	−2.13681	+	3.70106i	−0.165351	+	0.286396i	−0.936780	−	0.349919i	$-0.886209\pi$
$167$	−2.13681	+	3.70106i	−0.165351	+	0.286396i	0.771429	+	0.636316i	$0.219542\pi$
$168$	−6.65238	−	2.56810i	−0.513242	−	0.198133i
$169$	11.5923	+	20.0785i	0.891717	+	1.54450i
$170$		−	2.10757i		−	0.161643i
$171$	8.39604	+	13.0368i	0.642061	+	0.996951i
$172$	6.85307	−	6.85307i	0.522542	−	0.522542i
$173$	6.21727	+	10.7686i	0.472691	+	0.818724i	0.999512	−	0.0312522i	$-0.00994950\pi$
$173$	6.21727	+	10.7686i	0.472691	+	0.818724i	−0.526821	+	0.849976i	$0.676616\pi$
$174$	6.79214	−	1.76155i	0.514910	−	0.133543i
$175$	0.837162	−	1.45001i	0.0632835	−	0.109610i
$176$	−0.953815	−	3.55968i	−0.0718965	−	0.268321i
$177$	10.0891	−	13.8312i	0.758346	−	1.03962i
$178$	2.24033	−	1.29346i	0.167920	−	0.0969487i
$179$	−6.88546			−0.514644			−0.257322	−	0.966326i	$-0.582840\pi$
$179$	−6.88546			−0.514644			−0.257322	+	0.966326i	$0.582840\pi$
$180$	8.14129	−	2.61115i	0.606816	−	0.194623i
$181$	15.0091			1.11562			0.557809	−	0.829969i	$-0.311642\pi$
$181$	15.0091			1.11562			0.557809	+	0.829969i	$0.311642\pi$
$182$	−1.86651	+	6.96593i	−0.138355	+	0.516349i
$183$	9.29577	+	3.58856i	0.687163	+	0.265274i
$184$	−3.07133	−	11.4623i	−0.226421	−	0.845015i
$185$	−5.81124	−	21.6878i	−0.427251	−	1.59452i
$186$	−0.720935	+	6.73624i	−0.0528615	+	0.493925i
$187$	4.86566	−	2.80919i	0.355812	−	0.205428i
$188$	−5.34313	+	5.34313i	−0.389688	+	0.389688i
$189$	8.10952	−	1.67554i	0.589881	−	0.121877i
$190$	7.72751			0.560613
$191$	19.5960	+	5.25074i	1.41792	+	0.379930i	0.884745	−	0.466075i	$-0.154332\pi$
$191$	19.5960	+	5.25074i	1.41792	+	0.379930i	0.533174	+	0.846006i	$0.320999\pi$
$192$	4.41033	+	0.472008i	0.318288	+	0.0340642i
$193$	−13.7960	+	3.69663i	−0.993059	+	0.266089i	−0.718535	−	0.695491i	$-0.755187\pi$
$193$	−13.7960	+	3.69663i	−0.993059	+	0.266089i	−0.274524	+	0.961580i	$0.588520\pi$
$194$	0.346426	+	0.200009i	0.0248720	+	0.0143598i
$195$	−8.38580	−	18.9314i	−0.600519	−	1.35571i
$196$	−5.53943	+	3.19819i	−0.395673	+	0.228442i
$197$			22.0063i			1.56788i	0.620834	+	0.783942i	$0.286794\pi$
$197$			22.0063i			1.56788i	−0.620834	+	0.783942i	$0.713206\pi$
$198$	−6.66135	−	6.04384i	−0.473401	−	0.429517i
$199$	14.9264			1.05811			0.529054	−	0.848588i	$-0.322547\pi$
$199$	14.9264			1.05811			0.529054	+	0.848588i	$0.322547\pi$
$200$	−0.702484	+	2.62171i	−0.0496731	+	0.185383i
$201$	−5.51637	+	7.56240i	−0.389094	+	0.533411i
$202$	8.73327	+	5.04215i	0.614471	+	0.354765i
$203$	−3.53871	+	7.81848i	−0.248369	+	0.548750i
$204$	−0.541207	−	3.45952i	−0.0378920	−	0.242215i
$205$	−1.23981	+	4.62703i	−0.0865920	+	0.323166i
$206$	3.50813	−	3.50813i	0.244423	−	0.244423i
$207$	10.2057	+	9.25964i	0.709346	+	0.643590i
$208$			5.56231i			0.385677i
$209$	10.3000	+	17.8402i	0.712467	+	1.23403i
$210$	1.48617	−	3.84975i	0.102555	−	0.265658i
$211$	3.11267	+	11.6166i	0.214285	+	0.799722i	0.986417	+	0.164260i	$0.0525237\pi$
$211$	3.11267	+	11.6166i	0.214285	+	0.799722i	−0.772132	+	0.635462i	$0.780810\pi$
$212$	−2.93182	+	5.07806i	−0.201358	+	0.348763i
$213$	2.52781	−	23.6192i	0.173202	−	1.61836i
$214$	−2.89274	+	10.7958i	−0.197743	+	0.737988i
$215$	9.49685	+	9.49685i	0.647680	+	0.647680i
$216$	−11.9951	+	6.02605i	−0.816165	+	0.410021i
$217$	−5.85900	−	5.85900i	−0.397735	−	0.397735i
$218$	2.13654	−	7.97366i	0.144704	−	0.540044i
$219$	−13.3866	−	16.5954i	−0.904586	−	1.12141i
$220$	10.9711	−	2.93971i	0.739675	−	0.198195i
$221$	−8.19110	+	2.19480i	−0.550993	+	0.147638i
$222$	5.96223	+	13.4601i	0.400159	+	0.903381i
$223$	10.4520	+	18.1034i	0.699918	+	1.21229i	0.968494	+	0.249036i	$0.0801136\pi$
$223$	10.4520	+	18.1034i	0.699918	+	1.21229i	−0.268576	+	0.963258i	$0.586553\pi$
$224$	−6.60621	+	6.60621i	−0.441396	+	0.441396i
$225$	−0.962602	−	3.00130i	−0.0641735	−	0.200086i
$226$	−2.97651			−0.197994
$227$	3.25496	−	1.87925i	0.216039	−	0.124730i	−0.388076	−	0.921627i	$-0.626860\pi$
$227$	3.25496	−	1.87925i	0.216039	−	0.124730i	0.604115	+	0.796897i	$0.293527\pi$
$228$	12.6845	−	1.98436i	0.840051	−	0.131417i
$229$	0.234024	+	0.873389i	0.0154647	+	0.0577152i	0.973227	−	0.229846i	$-0.0738222\pi$
$229$	0.234024	+	0.873389i	0.0154647	+	0.0577152i	−0.957762	+	0.287561i	$0.907156\pi$
$230$	6.63329	−	1.77738i	0.437386	−	0.117197i
$231$	10.8686	−	1.70029i	0.715105	−	0.111871i
$232$	2.26067	−	13.7271i	0.148420	−	0.901229i
$233$			15.8233i			1.03662i	0.855194	+	0.518308i	$0.173438\pi$
$233$			15.8233i			1.03662i	−0.855194	+	0.518308i	$0.826562\pi$
$234$	7.35065	+	11.4136i	0.480527	+	0.746131i
$235$	−7.40441	−	7.40441i	−0.483010	−	0.483010i
$236$	−7.08732	−	12.2756i	−0.461345	−	0.799074i
$237$	−14.1565	−	5.46501i	−0.919563	−	0.354991i
$238$	−1.46366	−	0.845044i	−0.0948749	−	0.0547760i
$239$	14.3049	+	8.25896i	0.925310	+	0.534228i	0.885325	−	0.464973i	$-0.153936\pi$
$239$	14.3049	+	8.25896i	0.925310	+	0.534228i	0.0399845	+	0.999200i	$0.487269\pi$
$240$	0.338706	−	3.16479i	0.0218634	−	0.204286i
$241$	5.65990	−	3.26775i	0.364586	−	0.210494i	−0.306504	−	0.951869i	$-0.599159\pi$
$241$	5.65990	−	3.26775i	0.364586	−	0.210494i	0.671091	+	0.741375i	$0.265826\pi$
$242$	−2.59782	−	2.59782i	−0.166994	−	0.166994i
$243$	7.92197	−	13.4254i	0.508195	−	0.861242i
$244$	5.83371	−	5.83371i	0.373465	−	0.373465i
$245$	−4.43199	−	7.67643i	−0.283149	−	0.490429i
$246$	0.334228	−	3.12295i	0.0213096	−	0.199112i
$247$	−8.04733	−	30.0330i	−0.512039	−	1.91096i
$248$	11.6324	+	6.71597i	0.738659	+	0.426465i
$249$	3.28801	+	7.42287i	0.208369	+	0.470405i
$250$	−8.73757	−	2.34122i	−0.552612	−	0.148072i
$251$	4.75546	−	4.75546i	0.300162	−	0.300162i	−0.540915	−	0.841077i	$-0.681922\pi$
$251$	4.75546	−	4.75546i	0.300162	−	0.300162i	0.841077	+	0.540915i	$0.181922\pi$
$252$	1.45092	−	6.70088i	0.0913994	−	0.422116i
$253$	12.9449	+	12.9449i	0.813838	+	0.813838i
$254$	5.48793	+	9.50537i	0.344343	+	0.596420i
$255$	4.79414	−	0.749993i	0.300221	−	0.0469664i
$256$	6.24642	−	10.8191i	0.390401	−	0.676195i
$257$	−2.50692	−	1.44737i	−0.156377	−	0.0902846i	0.419769	−	0.907631i	$-0.362111\pi$
$257$	−2.50692	−	1.44737i	−0.156377	−	0.0902846i	−0.576147	+	0.817346i	$0.695444\pi$
$258$	−7.11429	−	5.18949i	−0.442916	−	0.323083i
$259$	−17.3917	−	4.66010i	−1.08067	−	0.289565i
$260$	−17.1434			−1.06319
$261$	6.42405	+	14.8233i	0.397639	+	0.917542i
$262$	5.70343			0.352359
$263$	4.83391	+	1.29524i	0.298071	+	0.0798680i	0.404755	−	0.914425i	$-0.367357\pi$
$263$	4.83391	+	1.29524i	0.298071	+	0.0798680i	−0.106684	+	0.994293i	$0.534023\pi$
$264$	−16.3051	+	7.22244i	−1.00351	+	0.444511i
$265$	−7.03708	−	4.06286i	−0.432284	−	0.249580i
$266$	3.09839	−	5.36657i	0.189975	−	0.329046i
$267$	3.73949	+	4.63585i	0.228853	+	0.283709i
$268$	3.87508	+	6.71184i	0.236708	+	0.409991i
$269$	−12.2861	−	12.2861i	−0.749095	−	0.749095i	0.225214	−	0.974309i	$-0.427692\pi$
$269$	−12.2861	−	12.2861i	−0.749095	−	0.749095i	−0.974309	+	0.225214i	$0.927692\pi$
$270$	−3.48729	−	6.94161i	−0.212230	−	0.422453i
$271$	−10.1810	+	10.1810i	−0.618450	+	0.618450i	−0.945134	−	0.326684i	$-0.894069\pi$
$271$	−10.1810	+	10.1810i	−0.618450	+	0.618450i	0.326684	+	0.945134i	$0.394069\pi$
$272$	−1.25914	−	0.337385i	−0.0763464	−	0.0204570i
$273$	−16.5097	−	1.76693i	−0.999215	−	0.106939i
$274$	−3.93929	−	2.27435i	−0.237981	−	0.137398i
$275$	−1.08373	−	4.04453i	−0.0653512	−	0.243894i
$276$	10.4319	−	4.62089i	0.627929	−	0.278145i
$277$	−11.4588	−	19.8473i	−0.688495	−	1.19251i	−0.972325	−	0.233634i	$-0.924938\pi$
$277$	−11.4588	−	19.8473i	−0.688495	−	1.19251i	0.283829	−	0.958875i	$-0.408395\pi$
$278$	−0.510468	+	0.510468i	−0.0306158	+	0.0306158i
$279$	−15.5796	+	0.757212i	−0.932727	+	0.0453331i
$280$	−5.78536	−	5.78536i	−0.345742	−	0.345742i
$281$	24.7424	−	14.2851i	1.47601	−	0.852175i	0.476376	−	0.879242i	$-0.341950\pi$
$281$	24.7424	−	14.2851i	1.47601	−	0.852175i	0.999634	+	0.0270669i	$0.00861672\pi$
$282$	5.54680	+	4.04609i	0.330307	+	0.240941i
$283$	16.6787	+	9.62943i	0.991444	+	0.572410i	0.905706	−	0.423907i	$-0.139342\pi$
$283$	16.6787	+	9.62943i	0.991444	+	0.572410i	0.0857383	+	0.996318i	$0.472675\pi$
$284$	−17.0325	−	9.83371i	−1.01069	−	0.583523i
$285$	2.74989	+	17.5779i	0.162889	+	1.04123i
$286$	9.01757	+	15.6189i	0.533220	+	0.923564i
$287$	2.71625	+	2.71625i	0.160335	+	0.160335i
$288$	0.853781	+	17.5665i	0.0503095	+	1.03512i
$289$			15.0127i			0.883098i
$290$	7.94391	+	1.30825i	0.466483	+	0.0768233i
$291$	−0.331687	+	0.859197i	−0.0194438	+	0.0503670i
$292$	−17.0519	+	4.56904i	−0.997886	+	0.267383i
$293$	−5.68051	−	21.1999i	−0.331859	−	1.23851i	−0.907235	−	0.420625i	$-0.861811\pi$
$293$	−5.68051	−	21.1999i	−0.331859	−	1.23851i	0.575376	−	0.817889i	$-0.304856\pi$
$294$	3.64888	+	4.52352i	0.212807	+	0.263817i
$295$	17.0113	−	9.82147i	0.990436	−	0.571828i
$296$	29.1877			1.69650
$297$	11.3776	−	17.3034i	0.660193	−	1.00405i
$298$	−2.43925	+	2.43925i	−0.141302	+	0.141302i
$299$	−13.8156	−	23.9294i	−0.798979	−	1.38387i
$300$	−2.59481	−	0.277706i	−0.149812	−	0.0160333i
$301$	10.4032	−	2.78752i	0.599628	−	0.160670i
$302$	0.753910	−	0.202010i	0.0433826	−	0.0116243i
$303$	−8.36170	+	21.6600i	−0.480367	+	1.24434i
$304$	1.23704	−	4.61668i	0.0709489	−	0.264785i
$305$	8.08424	+	8.08424i	0.462902	+	0.462902i
$306$	−3.02955	+	0.971664i	−0.173188	+	0.0555463i
$307$	−9.76625	−	9.76625i	−0.557389	−	0.557389i	0.371174	−	0.928563i	$-0.378955\pi$
$307$	−9.76625	−	9.76625i	−0.557389	−	0.557389i	−0.928563	+	0.371174i	$0.878955\pi$
$308$	2.35739	−	8.79789i	0.134325	−	0.501306i
$309$	9.22841	+	6.73163i	0.524986	+	0.382949i
$310$	−3.88655	+	6.73170i	−0.220741	+	0.382335i
$311$	6.59037	+	24.5956i	0.373706	+	1.39469i	0.855227	+	0.518254i	$0.173418\pi$
$311$	6.59037	+	24.5956i	0.373706	+	1.39469i	−0.481521	+	0.876435i	$0.659915\pi$
$312$	26.5928	−	4.16017i	1.50552	−	0.235523i
$313$	0.571840	+	0.990456i	0.0323223	+	0.0559839i	0.881734	−	0.471747i	$-0.156376\pi$
$313$	0.571840	+	0.990456i	0.0323223	+	0.0559839i	−0.849412	+	0.527731i	$0.823043\pi$
$314$		−	5.04054i		−	0.284454i
$315$	9.28595	+	2.01066i	0.523204	+	0.113288i
$316$	−8.88413	+	8.88413i	−0.499771	+	0.499771i
$317$	−4.27602	+	15.9583i	−0.240165	+	0.896308i	0.735587	+	0.677430i	$0.236906\pi$
$317$	−4.27602	+	15.9583i	−0.240165	+	0.896308i	−0.975752	+	0.218878i	$0.929760\pi$
$318$	4.97022	+	1.91872i	0.278716	+	0.107596i
$319$	7.56815	+	20.0835i	0.423735	+	1.12446i
$320$	4.40735	+	2.54459i	0.246378	+	0.142247i
$321$	−25.5869	−	2.73839i	−1.42812	−	0.152842i
$322$	1.42530	−	5.31931i	0.0794291	−	0.296433i
$323$	7.28667			0.405441
$324$	−7.50683	−	10.4989i	−0.417046	−	0.583275i
$325$			6.31992i			0.350566i
$326$	−3.62154	+	2.09090i	−0.200579	+	0.115804i
$327$	18.8981	+	2.02254i	1.04507	+	0.111847i
$328$	−5.39282	−	3.11355i	−0.297769	−	0.171917i
$329$	−8.11103	+	2.17334i	−0.447175	+	0.119820i
$330$	−4.17964	−	9.43578i	−0.230082	−	0.519423i
$331$	2.86957	+	0.768899i	0.157726	+	0.0422625i	0.336818	−	0.941570i	$-0.390649\pi$
$331$	2.86957	+	0.768899i	0.157726	+	0.0422625i	−0.179092	+	0.983832i	$0.557316\pi$
$332$	6.72178			0.368906
$333$	−28.4962	+	18.3523i	−1.56158	+	1.00570i
$334$	2.27333	−	2.27333i	0.124391	−	0.124391i
$335$	−9.30114	+	5.37002i	−0.508176	+	0.293395i
$336$	−2.06206	−	1.50416i	−0.112495	−	0.0820588i
$337$	6.92941	+	25.8609i	0.377469	+	1.40873i	0.849703	+	0.527261i	$0.176781\pi$
$337$	6.92941	+	25.8609i	0.377469	+	1.40873i	−0.472234	+	0.881473i	$0.656552\pi$
$338$	−4.51418	−	16.8472i	−0.245539	−	0.916365i
$339$	−1.05921	−	6.77072i	−0.0575283	−	0.367735i
$340$	1.03984	−	3.88073i	0.0563932	−	0.210462i
$341$	−20.7216			−1.12214
$342$	−3.56265	−	11.1080i	−0.192646	−	0.600651i
$343$	−18.2636			−0.986143
$344$	−15.1200	+	8.72955i	−0.815217	+	0.470666i
$345$	6.40355	+	14.4564i	0.344755	+	0.778305i
$346$	−2.42108	−	9.03558i	−0.130158	−	0.485756i
$347$	2.90592	−	5.03320i	0.155998	−	0.270196i	−0.777424	−	0.628977i	$-0.783474\pi$
$347$	2.90592	−	5.03320i	0.155998	−	0.270196i	0.933422	+	0.358781i	$0.116807\pi$
$348$	13.3757	+	0.107534i	0.717010	+	0.00576441i
$349$	9.80815	+	16.9882i	0.525018	+	0.909358i	0.999576	+	0.0291337i	$0.00927487\pi$
$349$	9.80815	+	16.9882i	0.525018	+	0.909358i	−0.474557	+	0.880225i	$0.657392\pi$
$350$	−0.890650	+	0.890650i	−0.0476073	+	0.0476073i
$351$	−23.3470	+	20.7823i	−1.24617	+	1.10928i
$352$			23.3642i			1.24532i
$353$	−5.81004	−	10.0633i	−0.309237	−	0.535614i	0.668959	−	0.743300i	$-0.266740\pi$
$353$	−5.81004	−	10.0633i	−0.309237	−	0.535614i	−0.978196	+	0.207685i	$0.933407\pi$
$354$	−10.0243	+	8.08607i	−0.532786	+	0.429770i
$355$	13.6274	−	23.6033i	0.723265	−	1.25273i
$356$	4.76336	−	1.27634i	0.252457	−	0.0676457i
$357$	1.40138	−	3.63013i	0.0741692	−	0.192127i
$358$	5.00333	+	1.34064i	0.264434	+	0.0708550i
$359$	−19.2607	+	19.2607i	−1.01654	+	1.01654i	−0.0166796	+	0.999861i	$0.505310\pi$
$359$	−19.2607	+	19.2607i	−1.01654	+	1.01654i	−0.999861	+	0.0166796i	$0.994690\pi$
$360$	−15.3838	+	0.747695i	−0.810798	+	0.0394070i
$361$			7.71692i			0.406154i
$362$	−10.9064	−	2.92236i	−0.573227	−	0.153596i
$363$	4.98486	−	6.83377i	0.261637	−	0.358680i
$364$	−6.87373	+	11.9056i	−0.360281	+	0.624025i
$365$	−6.33168	−	23.6302i	−0.331415	−	1.23686i
$366$	−6.05607	−	4.41757i	−0.316556	−	0.230910i
$367$	5.13838	−	19.1767i	0.268222	−	1.00102i	−0.692027	−	0.721871i	$-0.743282\pi$
$367$	5.13838	−	19.1767i	0.268222	−	1.00102i	0.960249	−	0.279145i	$-0.0900510\pi$
$368$		−	4.24748i		−	0.221415i
$369$	7.22276	−	0.351046i	0.376002	−	0.0182747i
$370$			16.8910i			0.878120i
$371$	−5.64312	+	3.25806i	−0.292976	+	0.169150i
$372$	−4.65102	+	12.0479i	−0.241144	+	0.624656i
$373$	17.8732	−	30.9572i	0.925438	−	1.60291i	0.134582	−	0.990902i	$-0.457031\pi$
$373$	17.8732	−	30.9572i	0.925438	−	1.60291i	0.790856	−	0.612003i	$-0.209636\pi$
$374$	−4.08260	+	1.09393i	−0.211106	+	0.0565658i
$375$	2.21631	−	20.7087i	0.114450	−	1.06939i
$376$	11.7886	−	6.80617i	0.607952	−	0.351001i
$377$	−3.18815	−	32.2365i	−0.164198	−	1.66026i
$378$	−6.21903	−	0.361439i	−0.319872	−	0.0185904i
$379$	−24.0666	−	24.0666i	−1.23622	−	1.23622i	−0.961534	−	0.274685i	$-0.911426\pi$
$379$	−24.0666	−	24.0666i	−1.23622	−	1.23622i	−0.274685	−	0.961534i	$-0.588574\pi$
$380$	14.2289	+	3.81262i	0.729926	+	0.195583i
$381$	−19.6691	+	15.8660i	−1.00768	+	0.812842i
$382$	−13.2171	−	7.63092i	−0.676248	−	0.390432i
$383$	−3.69428	+	6.39868i	−0.188769	+	0.326957i	−0.944840	−	0.327532i	$-0.893783\pi$
$383$	−3.69428	+	6.39868i	−0.188769	+	0.326957i	0.756071	+	0.654489i	$0.227116\pi$
$384$	15.8325	+	6.11201i	0.807947	+	0.311902i
$385$	12.1919	+	3.26682i	0.621359	+	0.166493i
$386$	10.7447			0.546889
$387$	9.27297	−	18.0297i	0.471371	−	0.916502i
$388$	0.539203	+	0.539203i	0.0273739	+	0.0273739i
$389$	0.362716	−	1.35368i	0.0183904	−	0.0686341i	−0.956121	−	0.292973i	$-0.905355\pi$
$389$	0.362716	−	1.35368i	0.0183904	−	0.0686341i	0.974511	+	0.224339i	$0.0720222\pi$
$390$	2.40750	+	15.3893i	0.121908	+	0.779268i
$391$	6.25487	−	1.67599i	0.316322	−	0.0847584i
$392$	11.1301	−	2.98231i	0.562156	−	0.150629i
$393$	2.02960	+	12.9737i	0.102380	+	0.654437i
$394$	4.28475	−	15.9909i	0.215863	−	0.805610i
$395$	−12.3115	−	12.3115i	−0.619457	−	0.619457i
$396$	−9.28379	−	14.4153i	−0.466528	−	0.724395i
$397$	−24.5232			−1.23078			−0.615392	−	0.788221i	$-0.711002\pi$
$397$	−24.5232			−1.23078			−0.615392	+	0.788221i	$0.711002\pi$
$398$	−10.8463	−	2.90626i	−0.543677	−	0.145678i
$399$	13.3100	+	5.13824i	0.666335	+	0.257234i
$400$	−0.485749	+	0.841343i	−0.0242875	+	0.0420671i
$401$	5.39062	+	3.11228i	0.269195	+	0.155420i	0.628522	−	0.777792i	$-0.283660\pi$
$401$	5.39062	+	3.11228i	0.269195	+	0.155420i	−0.359327	+	0.933212i	$0.616994\pi$
$402$	5.48092	−	4.42117i	0.273363	−	0.220508i
$403$	30.2102	+	8.09480i	1.50488	+	0.403231i
$404$	13.5931	+	13.5931i	0.676282	+	0.676282i
$405$	14.5492	−	10.4028i	0.722957	−	0.516921i
$406$	4.09371	−	4.99230i	0.203167	−	0.247764i
$407$	−38.9954	+	22.5140i	−1.93293	+	1.11598i
$408$	−0.671264	+	6.27213i	−0.0332325	+	0.310517i
$409$	−7.73223	+	2.07184i	−0.382334	+	0.102446i	−0.444867	−	0.895597i	$-0.646749\pi$
$409$	−7.73223	+	2.07184i	−0.382334	+	0.102446i	0.0625326	+	0.998043i	$0.480082\pi$
$410$	1.80182	−	3.12084i	0.0889854	−	0.154127i
$411$	3.77168	−	9.77011i	0.186043	−	0.481924i
$412$	8.19047	−	4.72877i	0.403515	−	0.232970i
$413$		−	15.7519i		−	0.775101i
$414$	−5.61309	−	8.71565i	−0.275868	−	0.428351i
$415$			9.31491i			0.457251i
$416$	9.12715	−	34.0630i	0.447496	−	1.67008i
$417$	−1.34283	−	0.979518i	−0.0657584	−	0.0479672i
$418$	−4.01094	−	14.9690i	−0.196182	−	0.732160i
$419$	6.15418	−	10.6594i	0.300651	−	0.520744i	−0.675632	−	0.737239i	$-0.736129\pi$
$419$	6.15418	−	10.6594i	0.300651	−	0.520744i	0.976284	+	0.216495i	$0.0694626\pi$
$420$	4.63591	−	6.35539i	0.226209	−	0.310111i
$421$	−23.6352	−	6.33304i	−1.15191	−	0.308653i	−0.368180	−	0.929755i	$-0.620019\pi$
$421$	−23.6352	−	6.33304i	−1.15191	−	0.308653i	−0.783731	+	0.621101i	$0.786686\pi$
$422$		−	9.04730i		−	0.440416i
$423$	−7.22985	+	14.0572i	−0.351527	+	0.683486i
$424$	7.46920	−	7.46920i	0.362736	−	0.362736i
$425$	−1.43064	−	0.383338i	−0.0693960	−	0.0185946i
$426$	−6.43563	+	16.6708i	−0.311807	+	0.807701i
$427$	8.85573	−	2.37289i	0.428559	−	0.114832i
$428$	−10.6529	+	18.4514i	−0.514929	+	0.891884i
$429$	−32.3196	+	26.0705i	−1.56041	+	1.25870i
$430$	−5.05181	−	8.74999i	−0.243620	−	0.421962i
$431$		−	3.47673i		−	0.167468i	−0.996488	−	0.0837341i	$-0.973315\pi$
$431$		−	3.47673i		−	0.167468i	0.996488	−	0.0837341i	$-0.0266846\pi$
$432$	−4.70541	+	0.972201i	−0.226389	+	0.0467750i
$433$	3.64035	−	3.64035i	0.174944	−	0.174944i	−0.614204	−	0.789148i	$-0.710523\pi$
$433$	3.64035	−	3.64035i	0.174944	−	0.174944i	0.789148	+	0.614204i	$0.210523\pi$
$434$	3.11667	+	5.39823i	0.149605	+	0.259123i
$435$	−0.149018	+	18.5357i	−0.00714486	+	0.888720i
$436$	7.86812	−	13.6280i	0.376815	−	0.652662i
$437$	6.14509	+	22.9338i	0.293959	+	1.09707i
$438$	6.49620	+	14.6655i	0.310401	+	0.700747i
$439$	11.4254	−	6.59645i	0.545304	−	0.314831i	−0.201922	−	0.979402i	$-0.564719\pi$
$439$	11.4254	−	6.59645i	0.545304	−	0.314831i	0.747226	+	0.664570i	$0.231385\pi$
$440$	−20.4611			−0.975447
$441$	−8.99126	+	9.90991i	−0.428155	+	0.471900i
$442$	6.37941			0.303438
$443$	7.02277	−	26.2093i	0.333662	−	1.24524i	−0.571650	−	0.820497i	$-0.693697\pi$
$443$	7.02277	−	26.2093i	0.333662	−	1.24524i	0.905312	−	0.424746i	$-0.139637\pi$
$444$	4.33746	+	27.7261i	0.205847	+	1.31582i
$445$	1.76872	+	6.60097i	0.0838455	+	0.312916i
$446$	−4.07013	−	15.1899i	−0.192726	−	0.719264i
$447$	−6.41662	−	4.68058i	−0.303496	−	0.221384i
$448$	3.53431	−	2.04053i	0.166980	−	0.0964061i
$449$	12.7670	−	12.7670i	0.602514	−	0.602514i	−0.338465	−	0.940979i	$-0.609908\pi$
$449$	12.7670	−	12.7670i	0.602514	−	0.602514i	0.940979	+	0.338465i	$0.109908\pi$
$450$	0.115107	+	2.36832i	0.00542619	+	0.111644i
$451$	9.60659			0.452357
$452$	−5.48072	−	1.46855i	−0.257791	−	0.0690750i
$453$	0.727799	+	1.64305i	0.0341950	+	0.0771971i
$454$	−2.73112	+	0.731801i	−0.128178	+	0.0343451i
$455$	−16.4986	−	9.52548i	−0.773467	−	0.446561i
$456$	−22.9970	−	2.46122i	−1.07694	−	0.115257i
$457$	−21.9898	+	12.6958i	−1.02864	+	0.593884i	−0.916594	−	0.399819i	$-0.869073\pi$
$457$	−21.9898	+	12.6958i	−1.02864	+	0.593884i	−0.112044	+	0.993703i	$0.535740\pi$
$458$		−	0.680215i		−	0.0317844i
$459$	−3.28835	−	6.54561i	−0.153487	−	0.305523i
$460$	13.0910			0.610370
$461$	−5.17555	+	19.3154i	−0.241049	+	0.899609i	0.734279	+	0.678848i	$0.237521\pi$
$461$	−5.17555	+	19.3154i	−0.241049	+	0.899609i	−0.975328	+	0.220761i	$0.929146\pi$
$462$	−8.22878	−	0.880671i	−0.382837	−	0.0409725i
$463$	−29.0783	−	16.7884i	−1.35138	−	0.780222i	−0.362941	−	0.931812i	$-0.618227\pi$
$463$	−29.0783	−	16.7884i	−1.35138	−	0.780222i	−0.988443	+	0.151590i	$0.951561\pi$
$464$	2.05327	−	4.53654i	0.0953209	−	0.210604i
$465$	−16.6958	−	6.44529i	−0.774249	−	0.298893i
$466$	3.08088	−	11.4980i	0.142719	−	0.532635i
$467$	−17.0375	+	17.0375i	−0.788402	+	0.788402i	−0.981232	−	0.192830i	$-0.938233\pi$
$467$	−17.0375	+	17.0375i	−0.788402	+	0.788402i	0.192830	+	0.981232i	$0.438233\pi$
$468$	7.90368	+	24.6429i	0.365348	+	1.13912i
$469$			8.61256i			0.397691i
$470$	3.93874	+	6.82211i	0.181681	+	0.314680i
$471$	11.4658	−	1.79371i	0.528317	−	0.0826498i
$472$	6.60891	+	24.6648i	0.304200	+	1.13529i
$473$	13.4671	−	23.3258i	0.619220	−	1.07252i
$474$	9.22277	+	6.72751i	0.423616	+	0.309005i
$475$	1.40553	−	5.24549i	0.0644899	−	0.240680i
$476$	−2.27814	−	2.27814i	−0.104419	−	0.104419i
$477$	−2.59586	+	11.9886i	−0.118856	+	0.548922i
$478$	−8.78664	−	8.78664i	−0.401892	−	0.401892i
$479$	−4.98552	+	18.6062i	−0.227794	+	0.850139i	0.753472	+	0.657480i	$0.228378\pi$
$479$	−4.98552	+	18.6062i	−0.227794	+	0.850139i	−0.981266	+	0.192659i	$0.938289\pi$
$480$	−7.26728	+	18.8250i	−0.331704	+	0.859242i
$481$	65.6469	−	17.5900i	2.99324	−	0.802037i
$482$	−4.74902	+	1.27250i	−0.216312	+	0.0579607i
$483$	12.6071	+	1.34926i	0.573645	+	0.0613933i
$484$	−3.50172	−	6.06516i	−0.159169	−	0.275689i
$485$	−0.747217	+	0.747217i	−0.0339294	+	0.0339294i
$486$	−8.37052	+	8.21316i	−0.379695	+	0.372557i
$487$	24.3442			1.10314			0.551572	−	0.834128i	$-0.314028\pi$
$487$	24.3442			1.10314			0.551572	+	0.834128i	$0.314028\pi$
$488$	−12.8710	+	7.43107i	−0.582642	+	0.336389i
$489$	−6.04496	−	7.49394i	−0.273362	−	0.338887i
$490$	1.72587	+	6.44103i	0.0779667	+	0.290976i
$491$	32.1406	−	8.61206i	1.45049	−	0.388657i	0.554294	−	0.832321i	$-0.312988\pi$
$491$	32.1406	−	8.61206i	1.45049	−	0.388657i	0.896193	+	0.443664i	$0.146322\pi$
$492$	2.15623	−	5.58546i	0.0972102	−	0.251812i
$493$	7.49073	+	1.23362i	0.337366	+	0.0555595i
$494$			23.3904i			1.05238i
$495$	19.9764	−	12.8653i	0.897873	−	0.578252i
$496$	3.39958	+	3.39958i	0.152646	+	0.152646i
$497$	−10.9279	−	18.9277i	−0.490185	−	0.849026i
$498$	−0.943962	−	6.03403i	−0.0423000	−	0.270391i
$499$	−26.3362	−	15.2052i	−1.17897	−	0.680679i	−0.223195	−	0.974774i	$-0.571649\pi$
$499$	−26.3362	−	15.2052i	−1.17897	−	0.680679i	−0.955776	+	0.294095i	$0.904982\pi$
$500$	−14.9336	−	8.62192i	−0.667851	−	0.385584i
$501$	5.98017	+	4.36221i	0.267174	+	0.194889i
$502$	−4.38148	+	2.52965i	−0.195555	+	0.112904i
$503$	6.30981	+	6.30981i	0.281341	+	0.281341i	0.833643	−	0.552303i	$-0.186251\pi$
$503$	6.30981	+	6.30981i	0.281341	+	0.281341i	−0.552303	+	0.833643i	$0.686251\pi$
$504$	−5.64898	+	10.9835i	−0.251625	+	0.489243i
$505$	−18.8370	+	18.8370i	−0.838237	+	0.838237i
$506$	−6.88598	−	11.9269i	−0.306119	−	0.530214i
$507$	36.7162	−	16.2637i	1.63062	−	0.722295i
$508$	5.41529	+	20.2101i	0.240265	+	0.896680i
$509$	8.59867	+	4.96444i	0.381129	+	0.220045i	0.678309	−	0.734776i	$-0.262713\pi$
$509$	8.59867	+	4.96444i	0.381129	+	0.220045i	−0.297180	+	0.954821i	$0.596046\pi$
$510$	−3.62970	−	0.388462i	−0.160726	−	0.0172014i
$511$	−18.9493	−	5.07745i	−0.838268	−	0.224613i
$512$	7.21145	−	7.21145i	0.318704	−	0.318704i
$513$	23.9998	−	12.0569i	1.05962	−	0.532324i
$514$	1.53985	+	1.53985i	0.0679197	+	0.0679197i
$515$	6.55304	+	11.3502i	0.288761	+	0.500149i
$516$	−10.5393	−	13.0656i	−0.463968	−	0.575181i
$517$	−10.4999	+	18.1864i	−0.461786	+	0.799837i
$518$	11.7304	+	6.77254i	0.515403	+	0.297568i
$519$	19.6919	−	8.72264i	0.864377	−	0.382882i
$520$	29.8305	+	7.99307i	1.30816	+	0.350519i
$521$	34.0191			1.49041			0.745203	−	0.666838i	$-0.232353\pi$
$521$	34.0191			1.49041			0.745203	+	0.666838i	$0.232353\pi$
$522$	−1.78186	−	12.0222i	−0.0779898	−	0.526198i
$523$	33.1794			1.45083			0.725416	−	0.688310i	$-0.241647\pi$
$523$	33.1794			1.45083			0.725416	+	0.688310i	$0.241647\pi$
$524$	10.5019	+	2.81397i	0.458777	+	0.122929i
$525$	−2.34292	−	1.70904i	−0.102254	−	0.0745884i
$526$	−3.26037	−	1.88238i	−0.142159	−	0.0820756i
$527$	−3.66483	+	6.34767i	−0.159643	+	0.276509i
$528$	−6.30635	+	0.986564i	−0.274449	+	0.0429347i
$529$	−0.950133	−	1.64568i	−0.0413102	−	0.0715513i
$530$	4.32244	+	4.32244i	0.187755	+	0.187755i
$531$	−21.9608	−	19.9250i	−0.953016	−	0.864672i
$532$	8.35292	−	8.35292i	0.362145	−	0.362145i
$533$	−14.0056	−	3.75278i	−0.606648	−	0.162551i
$534$	−1.81468	−	4.09674i	−0.0785289	−	0.177283i
$535$	−25.5696	−	14.7626i	−1.10547	−	0.638245i
$536$	−3.61351	−	13.4858i	−0.156080	−	0.582498i
$537$	−1.26911	+	11.8583i	−0.0547661	+	0.511721i
$538$	6.53552	+	11.3199i	0.281766	+	0.488034i
$539$	−12.5697	+	12.5697i	−0.541415	+	0.541415i
$540$	−2.99638	−	14.5023i	−0.128944	−	0.624081i
$541$	18.4694	+	18.4694i	0.794063	+	0.794063i	0.982152	−	0.188089i	$-0.0602294\pi$
$541$	18.4694	+	18.4694i	0.794063	+	0.794063i	−0.188089	+	0.982152i	$0.560229\pi$
$542$	9.38031	−	5.41572i	0.402919	−	0.232625i
$543$	2.76644	−	25.8489i	0.118719	−	1.10928i
$544$	7.15721	+	4.13222i	0.306863	+	0.177167i
$545$	18.8854	+	10.9035i	0.808962	+	0.467054i
$546$	11.6528	+	4.49848i	0.498694	+	0.192517i
$547$	−13.2156	−	22.8901i	−0.565059	−	0.978711i	−0.997044	−	0.0768300i	$-0.975520\pi$
$547$	−13.2156	−	22.8901i	−0.565059	−	0.978711i	0.431985	−	0.901881i	$-0.357813\pi$
$548$	−6.13139	−	6.13139i	−0.261920	−	0.261920i
$549$	7.89365	−	15.3479i	0.336893	−	0.655032i
$550$			3.14997i			0.134315i
$551$	−4.52313	+	27.4651i	−0.192692	+	1.17005i
$552$	−20.3067	+	3.17678i	−0.864312	+	0.135213i
$553$	−13.4864	+	3.61366i	−0.573498	+	0.153668i
$554$	4.46221	+	16.6532i	0.189581	+	0.707526i
$555$	−38.4222	+	6.01077i	−1.63093	+	0.255143i
$556$	−1.19179	+	0.688083i	−0.0505433	+	0.0291812i
$557$	−19.9045			−0.843381			−0.421690	−	0.906740i	$-0.638563\pi$
$557$	−19.9045			−0.843381			−0.421690	+	0.906740i	$0.638563\pi$
$558$	11.4684	+	2.48321i	0.485495	+	0.105123i
$559$	−28.7460	+	28.7460i	−1.21583	+	1.21583i
$560$	−1.46426	−	2.53617i	−0.0618762	−	0.107173i
$561$	−3.94120	−	8.89749i	−0.166398	−	0.375652i
$562$	−20.7605	+	5.56276i	−0.875729	+	0.234651i
$563$	−9.68029	+	2.59383i	−0.407976	+	0.109317i	−0.456970	−	0.889482i	$-0.651065\pi$
$563$	−9.68029	+	2.59383i	−0.407976	+	0.109317i	0.0489940	+	0.998799i	$0.484398\pi$
$564$	8.21720	+	10.1869i	0.346006	+	0.428944i
$565$	2.03509	−	7.59508i	0.0856171	−	0.319527i
$566$	−10.2447	−	10.2447i	−0.430616	−	0.430616i
$567$	−1.39091	−	14.2752i	−0.0584127	−	0.599501i
$568$	25.0527	+	25.0527i	1.05119	+	1.05119i
$569$	5.37792	−	20.0707i	0.225454	−	0.841406i	−0.756768	−	0.653683i	$-0.773223\pi$
$569$	5.37792	−	20.0707i	0.225454	−	0.841406i	0.982222	−	0.187722i	$-0.0601105\pi$
$570$	1.42431	−	13.3084i	0.0596579	−	0.557429i
$571$	−15.1686	+	26.2728i	−0.634786	+	1.09948i	0.351774	+	0.936085i	$0.385579\pi$
$571$	−15.1686	+	26.2728i	−0.634786	+	1.09948i	−0.986560	+	0.163397i	$0.947755\pi$
$572$	8.89821	+	33.2086i	0.372053	+	1.38852i
$573$	12.6548	−	32.7808i	0.528662	−	1.36944i
$574$	−1.44490	−	2.50264i	−0.0603089	−	0.104458i
$575$		−	4.82600i		−	0.201258i
$576$	1.62580	−	7.50853i	0.0677416	−	0.312856i
$577$	−7.96367	+	7.96367i	−0.331532	+	0.331532i	−0.853168	−	0.521636i	$-0.825322\pi$
$577$	−7.96367	+	7.96367i	−0.331532	+	0.331532i	0.521636	+	0.853168i	$0.325322\pi$
$578$	2.92305	−	10.9090i	0.121583	−	0.453753i
$579$	3.82356	+	24.4411i	0.158902	+	1.01574i
$580$	13.9819	+	6.32831i	0.580566	+	0.262769i
$581$	6.46898	+	3.73487i	0.268379	+	0.154948i
$582$	0.408312	−	0.559756i	0.0169251	−	0.0232026i
$583$	−4.21763	+	15.7404i	−0.174677	+	0.651902i
$584$	31.8017			1.31596
$585$	−34.1496	+	10.9528i	−1.41191	+	0.452841i
$586$			16.5110i			0.682063i
$587$	5.46064	−	3.15270i	0.225385	−	0.130126i	−0.383056	−	0.923725i	$-0.625129\pi$
$587$	5.46064	−	3.15270i	0.225385	−	0.130126i	0.608441	+	0.793599i	$0.291795\pi$
$588$	4.48696	+	10.1296i	0.185039	+	0.417737i
$589$	−23.2740	−	13.4373i	−0.958990	−	0.553673i
$590$	−14.2736	+	3.82459i	−0.587634	+	0.157456i
$591$	37.8996	+	4.05614i	1.55898	+	0.166847i
$592$	10.0913	+	2.70394i	0.414748	+	0.111131i
$593$	27.2425			1.11871			0.559357	−	0.828927i	$-0.311048\pi$
$593$	27.2425			1.11871			0.559357	+	0.828927i	$0.311048\pi$
$594$	−11.6366	+	10.3583i	−0.477455	+	0.425006i
$595$	3.15701	−	3.15701i	0.129425	−	0.129425i
$596$	−5.69493	+	3.28797i	−0.233273	+	0.134680i
$597$	2.75120	−	25.7065i	0.112599	−	1.05210i
$598$	5.37996	+	20.0783i	0.220003	+	0.821063i
$599$	4.27927	+	15.9705i	0.174846	+	0.652535i	0.996578	+	0.0826602i	$0.0263416\pi$
$599$	4.27927	+	15.9705i	0.174846	+	0.652535i	−0.821732	+	0.569875i	$0.806992\pi$
$600$	4.38567	+	1.69306i	0.179044	+	0.0691187i
$601$	−7.00352	+	26.1375i	−0.285679	+	1.06617i	0.662662	+	0.748918i	$0.269427\pi$
$601$	−7.00352	+	26.1375i	−0.285679	+	1.06617i	−0.948341	+	0.317251i	$0.897240\pi$
$602$	−8.10221			−0.330222
$603$	12.0073	+	10.8943i	0.488976	+	0.443648i
$604$	1.48786			0.0605403
$605$	8.40498	−	4.85261i	0.341711	−	0.197287i
$606$	10.2934	−	14.1112i	0.418140	−	0.573229i
$607$	−8.45916	−	31.5700i	−0.343347	−	1.28139i	−0.894532	−	0.447004i	$-0.852491\pi$
$607$	−8.45916	−	31.5700i	−0.343347	−	1.28139i	0.551185	−	0.834383i	$-0.314176\pi$
$608$	−15.1510	+	26.2422i	−0.614453	+	1.06426i
$609$	12.8129	+	7.53550i	0.519203	+	0.305354i
$610$	−4.30038	−	7.44847i	−0.174117	−	0.301580i
$611$	22.4124	−	22.4124i	0.906709	−	0.906709i
$612$	−6.05780	+	0.294425i	−0.244872	+	0.0119014i
$613$		−	20.2593i		−	0.818264i	−0.912475	−	0.409132i	$-0.865832\pi$
$613$		−	20.2593i		−	0.818264i	0.912475	−	0.409132i	$-0.134168\pi$
$614$	5.19512	+	8.99821i	0.209658	+	0.363138i
$615$	7.74022	+	2.98806i	0.312116	+	0.120490i
$616$	−8.20402	+	14.2098i	−0.330549	+	0.572528i
$617$	−39.6356	+	10.6203i	−1.59567	+	0.427558i	−0.943731	−	0.330714i	$-0.892710\pi$
$617$	−39.6356	+	10.6203i	−1.59567	+	0.427558i	−0.651938	+	0.758272i	$0.726044\pi$
$618$	−5.39515	−	6.68837i	−0.217025	−	0.269046i
$619$	39.5046	+	10.5852i	1.58782	+	0.425456i	0.941337	−	0.337469i	$-0.109571\pi$
$619$	39.5046	+	10.5852i	1.58782	+	0.425456i	0.646487	+	0.762925i	$0.276237\pi$
$620$	−10.4777	+	10.4777i	−0.420795	+	0.420795i
$621$	17.8282	−	15.8697i	0.715421	−	0.636830i
$622$		−	19.1556i		−	0.768070i
$623$	5.29339	+	1.41836i	0.212075	+	0.0568254i
$624$	9.57950	+	1.02523i	0.383487	+	0.0410420i
$625$	9.32152	−	16.1453i	0.372861	−	0.645814i
$626$	−0.222681	−	0.831057i	−0.00890012	−	0.0332157i
$627$	32.6231	−	14.4506i	1.30284	−	0.577102i
$628$	2.48691	−	9.28129i	0.0992386	−	0.370364i
$629$			15.9274i			0.635067i
$630$	−6.35617	−	3.26907i	−0.253236	−	0.130243i
$631$			10.5402i			0.419598i	0.977745	+	0.209799i	$0.0672809\pi$
$631$			10.5402i			0.419598i	−0.977745	+	0.209799i	$0.932719\pi$
$632$	19.6012	−	11.3167i	0.779693	−	0.450156i
$633$	20.5801	−	3.21954i	0.817984	−	0.127965i
$634$	6.21435	−	10.7636i	0.246803	−	0.427476i
$635$	−28.0068	+	7.50440i	−1.11142	+	0.297803i
$636$	8.20513	+	5.98520i	0.325355	+	0.237329i
$637$	23.2358	−	13.4152i	0.920636	−	0.531529i
$638$	−1.58903	−	16.0673i	−0.0629104	−	0.636110i
$639$	−40.2115	−	8.70685i	−1.59074	−	0.344438i
$640$	13.7690	+	13.7690i	0.544267	+	0.544267i
$641$	−9.44197	−	2.52997i	−0.372935	−	0.0999277i	0.0674830	−	0.997720i	$-0.478503\pi$
$641$	−9.44197	−	2.52997i	−0.372935	−	0.0999277i	−0.440418	+	0.897793i	$0.645170\pi$
$642$	18.0596	+	6.97177i	0.712755	+	0.275154i
$643$	−6.45427	−	3.72638i	−0.254532	−	0.146954i	0.367306	−	0.930100i	$-0.380280\pi$
$643$	−6.45427	−	3.72638i	−0.254532	−	0.146954i	−0.621838	+	0.783146i	$0.713614\pi$
$644$	5.24890	−	9.09137i	0.206836	−	0.358250i
$645$	18.1061	−	14.6052i	0.712926	−	0.575079i
$646$	−5.29487	−	1.41876i	−0.208324	−	0.0558202i
$647$	−4.29505			−0.168856			−0.0844280	−	0.996430i	$-0.526906\pi$
$647$	−4.29505			−0.168856			−0.0844280	+	0.996430i	$0.526906\pi$
$648$	8.16726	+	21.7689i	0.320840	+	0.855163i
$649$	−27.8549	−	27.8549i	−1.09340	−	1.09340i
$650$	1.23052	−	4.59238i	0.0482651	−	0.180128i
$651$	−11.1704	+	9.01055i	−0.437801	+	0.353151i
$652$	−7.70006	+	2.06322i	−0.301557	+	0.0808021i
$653$	7.73186	−	2.07175i	0.302571	−	0.0810737i	−0.104339	−	0.994542i	$-0.533273\pi$
$653$	7.73186	−	2.07175i	0.302571	−	0.0810737i	0.406910	+	0.913468i	$0.366606\pi$
$654$	−13.3386	−	5.14926i	−0.521579	−	0.201352i
$655$	−3.89955	+	14.5533i	−0.152368	+	0.568645i
$656$	−1.57606	−	1.57606i	−0.0615348	−	0.0615348i
$657$	−31.0483	+	19.9959i	−1.21131	+	0.780113i
$658$	6.31705			0.246264
$659$	22.7907	+	6.10676i	0.887801	+	0.237886i	0.673770	−	0.738941i	$-0.264674\pi$
$659$	22.7907	+	6.10676i	0.887801	+	0.237886i	0.214031	+	0.976827i	$0.431341\pi$
$660$	−3.04064	−	19.4365i	−0.118357	−	0.756566i
$661$	16.7323	−	28.9813i	0.650812	−	1.12724i	−0.332114	−	0.943239i	$-0.607762\pi$
$661$	16.7323	−	28.9813i	0.650812	−	1.12724i	0.982926	−	0.184001i	$-0.0589049\pi$
$662$	−1.93547	−	1.11744i	−0.0752241	−	0.0434306i
$663$	2.27016	+	14.5114i	0.0881656	+	0.563575i
$664$	−11.6963	−	3.13402i	−0.453906	−	0.121624i
$665$	11.5753	+	11.5753i	0.448871	+	0.448871i
$666$	24.2801	−	7.78733i	0.940835	−	0.301753i
$667$	2.43453	+	24.6164i	0.0942652	+	0.953149i
$668$	5.30757	−	3.06432i	0.205356	−	0.118562i
$669$	33.1045	−	14.6638i	1.27989	−	0.566937i
$670$	7.80426	−	2.09115i	0.301505	−	0.0807880i
$671$	11.4640	−	19.8562i	0.442561	−	0.766539i
$672$	10.1597	+	12.5950i	0.391918	+	0.485861i
$673$	−5.66606	+	3.27130i	−0.218410	+	0.126099i	−0.605214	−	0.796063i	$-0.706912\pi$
$673$	−5.66606	+	3.27130i	−0.218410	+	0.126099i	0.386804	+	0.922162i	$0.373579\pi$
$674$		−	20.1411i		−	0.775805i
$675$	−5.34630	+	1.10462i	−0.205779	+	0.0425168i
$676$		−	33.2484i		−	1.27878i
$677$	6.70658	−	25.0293i	0.257755	−	0.961954i	−0.708782	−	0.705427i	$-0.750755\pi$
$677$	6.70658	−	25.0293i	0.257755	−	0.961954i	0.966537	−	0.256527i	$-0.0825781\pi$
$678$	−0.548621	+	5.12619i	−0.0210697	+	0.196870i
$679$	0.219323	+	0.818525i	0.00841685	+	0.0314121i
$680$	−3.61877	+	6.26790i	−0.138774	+	0.240363i
$681$	−2.63653	−	5.95212i	−0.101032	−	0.228086i
$682$	15.0574	+	4.03461i	0.576576	+	0.154493i
$683$			47.4502i			1.81563i	0.419369	+	0.907816i	$0.362251\pi$
$683$			47.4502i			1.81563i	−0.419369	+	0.907816i	$0.637749\pi$
$684$	−1.07952	−	22.2112i	−0.0412766	−	0.849266i
$685$	8.49676	−	8.49676i	0.324645	−	0.324645i
$686$	13.2713	+	3.55603i	0.506700	+	0.135770i
$687$	1.54730	−	0.242059i	0.0590332	−	0.00923513i
$688$	−6.03625	+	1.61741i	−0.230130	+	0.0616632i
$689$	12.2979	−	21.3005i	0.468512	−	0.811486i
$690$	−1.83841	−	11.7516i	−0.0699870	−	0.447374i
$691$	2.35425	+	4.07768i	0.0895598	+	0.155122i	0.907325	−	0.420430i	$-0.138121\pi$
$691$	2.35425	+	4.07768i	0.0895598	+	0.155122i	−0.817765	+	0.575552i	$0.804787\pi$
$692$		−	17.8320i		−	0.677870i
$693$	−0.924985	−	19.0316i	−0.0351373	−	0.722949i
$694$	−3.09158	+	3.09158i	−0.117355	+	0.117355i
$695$	−0.953532	−	1.65157i	−0.0361695	−	0.0626474i
$696$	−23.2244	−	6.42350i	−0.880318	−	0.243482i
$697$	1.69903	−	2.94280i	0.0643553	−	0.111467i
$698$	−3.81941	−	14.2542i	−0.144567	−	0.539530i
$699$	27.2511	+	2.91650i	1.03073	+	0.110312i
$700$	−2.07941	+	1.20055i	−0.0785943	+	0.0453764i
$701$	−8.19483			−0.309514			−0.154757	−	0.987953i	$-0.549460\pi$
$701$	−8.19483			−0.309514			−0.154757	+	0.987953i	$0.549460\pi$
$702$	21.0116	−	10.5557i	0.793030	−	0.398399i
$703$	−58.3985			−2.20254
$704$	2.64152	−	9.85829i	0.0995561	−	0.371548i
$705$	−14.1168	+	11.3872i	−0.531668	+	0.428868i
$706$	2.26250	+	8.44375i	0.0851501	+	0.317785i
$707$	5.52905	+	20.6347i	0.207941	+	0.776048i
$708$	−22.4475	+	9.94329i	−0.843631	+	0.373692i
$709$	−21.1775	+	12.2269i	−0.795339	+	0.459189i	−0.841839	−	0.539729i	$-0.818527\pi$
$709$	−21.1775	+	12.2269i	−0.795339	+	0.459189i	0.0464999	+	0.998918i	$0.485193\pi$
$710$	−14.4980	+	14.4980i	−0.544102	+	0.544102i
$711$	−12.0212	+	23.3732i	−0.450831	+	0.876565i
$712$	−8.88364			−0.332928
$713$	−23.0691	−	6.18134i	−0.863943	−	0.231493i
$714$	−1.72512	+	2.36498i	−0.0645612	+	0.0885071i
$715$	−46.0198	+	12.3310i	−1.72104	+	0.461152i
$716$	8.55132	+	4.93711i	0.319578	+	0.184508i
$717$	16.8604	−	23.1139i	0.629662	−	0.863205i
$718$	17.7460	−	10.2456i	0.662274	−	0.382364i
$719$			33.5666i			1.25182i	0.779895	+	0.625911i	$0.215273\pi$
$719$			33.5666i			1.25182i	−0.779895	+	0.625911i	$0.784727\pi$
$720$	−5.38802	−	1.16665i	−0.200800	−	0.0434785i
$721$	10.5099			0.391410
$722$	1.50253	−	5.60751i	0.0559183	−	0.208690i
$723$	−4.58455	−	10.3499i	−0.170501	−	0.384916i
$724$	−18.6404	−	10.7620i	−0.692765	−	0.399968i
$725$	2.33294	−	5.15443i	0.0866432	−	0.191431i
$726$	−4.95283	+	3.99519i	−0.183817	+	0.148275i
$727$	−6.46422	+	24.1248i	−0.239745	+	0.894739i	0.736208	+	0.676755i	$0.236615\pi$
$727$	−6.46422	+	24.1248i	−0.239745	+	0.894739i	−0.975952	+	0.217983i	$0.930052\pi$
$728$	17.5117	−	17.5117i	0.649028	−	0.649028i
$729$	−21.6613	−	16.1179i	−0.802272	−	0.596959i
$730$			18.4037i			0.681152i
$731$	−4.76362	−	8.25083i	−0.176189	−	0.305168i
$732$	−8.97165	−	11.1222i	−0.331602	−	0.411087i
$733$	−6.10762	−	22.7939i	−0.225590	−	0.841914i	−0.982167	−	0.188009i	$-0.939797\pi$
$733$	−6.10762	−	22.7939i	−0.225590	−	0.841914i	0.756577	−	0.653904i	$-0.226870\pi$
$734$	−7.46763	+	12.9343i	−0.275635	+	0.477414i
$735$	−14.0374	+	6.21795i	−0.517776	+	0.229352i
$736$	−6.96966	+	26.0111i	−0.256905	+	0.958783i
$737$	15.2301	+	15.2301i	0.561006	+	0.561006i
$738$	−5.31678	−	1.15122i	−0.195713	−	0.0423772i
$739$	−5.47150	−	5.47150i	−0.201272	−	0.201272i	0.599273	−	0.800545i	$-0.295457\pi$
$739$	−5.47150	−	5.47150i	−0.201272	−	0.201272i	−0.800545	+	0.599273i	$0.795457\pi$
$740$	−8.33371	+	31.1018i	−0.306353	+	1.14333i
$741$	−53.2066	+	8.32363i	−1.95459	+	0.305776i
$742$	4.73494	−	1.26872i	0.173825	−	0.0465763i
$743$	−16.9879	+	4.55189i	−0.623224	+	0.166992i	−0.556593	−	0.830785i	$-0.687892\pi$
$743$	−16.9879	+	4.55189i	−0.623224	+	0.166992i	−0.0666313	+	0.997778i	$0.521225\pi$
$744$	13.7104	−	18.7956i	0.502648	−	0.689082i
$745$	−4.55640	−	7.89192i	−0.166934	−	0.289138i
$746$	−19.0151	+	19.0151i	−0.696193	+	0.696193i
$747$	13.3898	−	4.29450i	0.489908	−	0.157127i
$748$	−8.05713			−0.294598
$749$	−20.5046	+	11.8383i	−0.749222	+	0.432563i
$750$	−5.64258	+	14.6165i	−0.206038	+	0.533717i
$751$	2.02966	+	7.57481i	0.0740635	+	0.276409i	0.993019	−	0.117952i	$-0.0376328\pi$
$751$	2.02966	+	7.57481i	0.0740635	+	0.276409i	−0.918956	+	0.394360i	$0.870966\pi$
$752$	4.70629	−	1.26105i	0.171621	−	0.0459856i
$753$	−7.31342	−	9.06644i	−0.266516	−	0.330400i
$754$	−3.95996	+	24.0454i	−0.144213	+	0.875683i
$755$			2.06185i			0.0750384i
$756$	−11.2729	−	3.73388i	−0.409993	−	0.135800i
$757$	−24.7797	−	24.7797i	−0.900635	−	0.900635i	0.0948558	−	0.995491i	$-0.469761\pi$
$757$	−24.7797	−	24.7797i	−0.900635	−	0.900635i	−0.995491	+	0.0948558i	$0.969761\pi$
$758$	12.8021	+	22.1740i	0.464995	+	0.805394i
$759$	24.6799	−	19.9079i	0.895822	−	0.722612i
$760$	−22.9815	−	13.2684i	−0.833628	−	0.481295i
$761$	−3.01412	−	1.74020i	−0.109262	−	0.0630823i	0.444373	−	0.895842i	$-0.353426\pi$
$761$	−3.01412	−	1.74020i	−0.109262	−	0.0630823i	−0.553635	+	0.832759i	$0.686760\pi$
$762$	17.3818	−	7.69939i	0.629677	−	0.278920i
$763$	15.1444	−	8.74364i	0.548265	−	0.316541i
$764$	−20.5721	−	20.5721i	−0.744273	−	0.744273i
$765$	−0.408009	−	8.39478i	−0.0147516	−	0.303514i
$766$	3.93032	−	3.93032i	0.142008	−	0.142008i
$767$	29.7286	+	51.4915i	1.07344	+	1.85925i
$768$	−17.4815	−	12.7518i	−0.630811	−	0.460142i
$769$	−2.72620	−	10.1743i	−0.0983094	−	0.366896i	0.899191	−	0.437556i	$-0.144156\pi$
$769$	−2.72620	−	10.1743i	−0.0983094	−	0.366896i	−0.997500	+	0.0706606i	$0.977489\pi$
$770$	−8.22323	−	4.74768i	−0.296345	−	0.171095i
$771$	−2.95475	+	4.05068i	−0.106413	+	0.145882i
$772$	19.7844	+	5.30122i	0.712057	+	0.190795i
$773$	18.7455	−	18.7455i	0.674230	−	0.674230i	−0.284458	−	0.958688i	$-0.591814\pi$
$773$	18.7455	−	18.7455i	0.674230	−	0.674230i	0.958688	+	0.284458i	$0.0918138\pi$
$774$	−10.2487	+	11.2958i	−0.368382	+	0.406020i
$775$	3.86262	+	3.86262i	0.138749	+	0.138749i
$776$	−0.686846	−	1.18965i	−0.0246563	−	0.0427060i
$777$	−11.2313	+	29.0934i	−0.402920	+	1.04372i
$778$	−0.527137	+	0.913028i	−0.0188988	+	0.0327336i
$779$	10.7899	+	6.22956i	0.386589	+	0.223197i
$780$	−3.15981	+	29.5245i	−0.113139	+	1.05715i
$781$	−52.7954	−	14.1465i	−1.88917	−	0.506201i
$782$	−4.87144			−0.174202
$783$	26.7131	−	8.33141i	0.954647	−	0.297740i
$784$	4.12437			0.147299
$785$	12.8618	+	3.44632i	0.459058	+	0.123004i
$786$	1.05124	−	9.82254i	0.0374965	−	0.350359i
$787$	−13.1356	−	7.58383i	−0.468233	−	0.270334i	0.247267	−	0.968947i	$-0.420468\pi$
$787$	−13.1356	−	7.58383i	−0.468233	−	0.270334i	−0.715500	+	0.698613i	$0.753801\pi$
$788$	15.7793	−	27.3305i	0.562113	−	0.973608i
$789$	3.12166	−	8.08629i	0.111134	−	0.287880i
$790$	6.54903	+	11.3432i	0.233004	+	0.403575i
$791$	−4.45861	−	4.45861i	−0.158530	−	0.158530i
$792$	9.43330	+	29.4121i	0.335198	+	1.04511i
$793$	−24.4702	+	24.4702i	−0.868962	+	0.868962i
$794$	17.8198	+	4.77480i	0.632401	+	0.169451i
$795$	−8.29418	+	11.3705i	−0.294164	+	0.403271i
$796$	−18.5377	−	10.7028i	−0.657052	−	0.379349i
$797$	3.29512	+	12.2976i	0.116719	+	0.435602i	0.999410	−	0.0343527i	$-0.0109369\pi$
$797$	3.29512	+	12.2976i	0.116719	+	0.435602i	−0.882691	+	0.469955i	$0.844270\pi$
$798$	−8.67131	−	6.32525i	−0.306961	−	0.223911i
$799$	3.71405	+	6.43292i	0.131394	+	0.227580i
$800$	4.35523	−	4.35523i	0.153981	−	0.153981i
$801$	8.67318	−	5.58574i	0.306452	−	0.197363i
$802$	−3.31113	−	3.31113i	−0.116920	−	0.116920i
$803$	−42.4878	+	24.5303i	−1.49936	+	0.865657i
$804$	12.2735	−	5.43662i	0.432852	−	0.191735i
$805$	12.5986	+	7.27383i	0.444044	+	0.256369i
$806$	−20.3762	−	11.7642i	−0.717721	−	0.414376i
$807$	−23.4238	+	18.8947i	−0.824557	+	0.665126i
$808$	−17.3151	−	29.9906i	−0.609143	−	1.05507i
$809$	−34.1162	−	34.1162i	−1.19946	−	1.19946i	−0.974328	−	0.225133i	$-0.927718\pi$
$809$	−34.1162	−	34.1162i	−1.19946	−	1.19946i	−0.225133	−	0.974328i	$-0.572282\pi$
$810$	−12.5977	+	4.72641i	−0.442639	+	0.166069i
$811$		−	13.8125i		−	0.485022i	−0.970149	−	0.242511i	$-0.922029\pi$
$811$		−	13.8125i		−	0.485022i	0.970149	−	0.242511i	$-0.0779711\pi$
$812$	10.0010	−	7.17270i	0.350965	−	0.251712i
$813$	15.6573	+	19.4103i	0.549125	+	0.680751i
$814$	32.7197	−	8.76722i	1.14683	−	0.307291i
$815$	−2.85918	−	10.6706i	−0.100153	−	0.373774i
$816$	−0.813130	+	2.10632i	−0.0284652	+	0.0737359i
$817$	30.2520	−	17.4660i	1.05838	−	0.611059i
$818$	6.02204			0.210556
$819$	−6.08606	+	28.1077i	−0.212664	+	0.982161i
$820$	4.85750	−	4.85750i	0.169631	−	0.169631i
$821$	19.9932	+	34.6292i	0.697766	+	1.20857i	0.969239	+	0.246120i	$0.0791558\pi$
$821$	19.9932	+	34.6292i	0.697766	+	1.20857i	−0.271473	+	0.962446i	$0.587511\pi$
$822$	−4.64300	+	6.36510i	−0.161943	+	0.222008i
$823$	10.4216	−	2.79246i	0.363274	−	0.0973391i	−0.0725647	−	0.997364i	$-0.523118\pi$
$823$	10.4216	−	2.79246i	0.363274	−	0.0973391i	0.435839	+	0.900025i	$0.356452\pi$
$824$	−16.4567	+	4.40957i	−0.573297	+	0.153615i
$825$	−7.16530	+	1.12094i	−0.249464	+	0.0390260i
$826$	−3.06699	+	11.4461i	−0.106714	+	0.398262i
$827$	13.5031	+	13.5031i	0.469547	+	0.469547i	0.901768	−	0.432221i	$-0.142270\pi$
$827$	13.5031	+	13.5031i	0.469547	+	0.469547i	−0.432221	+	0.901768i	$0.642270\pi$
$828$	−6.03539	−	18.8177i	−0.209744	−	0.653962i
$829$	−5.73435	−	5.73435i	−0.199162	−	0.199162i	0.600479	−	0.799641i	$-0.294977\pi$
$829$	−5.73435	−	5.73435i	−0.199162	−	0.199162i	−0.799641	+	0.600479i	$0.794977\pi$
$830$	1.81367	−	6.76870i	0.0629533	−	0.234945i
$831$	−36.2934	+	16.0764i	−1.25900	+	0.557684i
$832$	−7.70221	+	13.3406i	−0.267026	+	0.462503i
$833$	1.62741	+	6.07358i	0.0563864	+	0.210437i
$834$	0.785048	+	0.973224i	0.0271840	+	0.0337000i
$835$	4.24648	+	7.35512i	0.146956	+	0.254534i
$836$		−	29.5418i		−	1.02173i
$837$	−1.56751	+	26.9710i	−0.0541810	+	0.932255i
$838$	−6.54738	+	6.54738i	−0.226176	+	0.226176i
$839$	1.19625	−	4.46445i	0.0412990	−	0.154130i	−0.942197	−	0.335059i	$-0.891244\pi$
$839$	1.19625	−	4.46445i	0.0412990	−	0.154130i	0.983496	+	0.180929i	$0.0579104\pi$
$840$	−11.0300	+	8.89730i	−0.380571	+	0.306986i
$841$	−9.29959	+	27.4685i	−0.320675	+	0.947189i
$842$	15.9415	+	9.20383i	0.549380	+	0.317185i
$843$	−20.0415	−	45.2448i	−0.690265	−	1.55831i
$844$	4.46378	−	16.6590i	0.153649	−	0.573428i
$845$	46.0749			1.58503
$846$	7.99060	−	8.80701i	0.274723	−	0.302791i
$847$		−	7.78274i		−	0.267418i
$848$	3.27432	−	1.89043i	0.112441	−	0.0649177i
$849$	19.6581	−	26.9494i	0.674665	−	0.924901i
$850$	0.964936	+	0.557106i	0.0330970	+	0.0191086i
$851$	−50.1292	+	13.4321i	−1.71841	+	0.460446i
$852$	−20.0751	+	27.5211i	−0.687763	+	0.942857i
$853$	−39.1918	−	10.5014i	−1.34190	−	0.359561i	−0.484762	−	0.874646i	$-0.661094\pi$
$853$	−39.1918	−	10.5014i	−1.34190	−	0.359561i	−0.857139	+	0.515085i	$0.827761\pi$
$854$	−6.89704			−0.236012
$855$	30.7798	−	1.49598i	1.05265	−	0.0511615i
$856$	27.1398	−	27.1398i	0.927618	−	0.927618i
$857$	29.8558	−	17.2373i	1.01986	−	0.588814i	0.105793	−	0.994388i	$-0.466262\pi$
$857$	29.8558	−	17.2373i	1.01986	−	0.588814i	0.914062	+	0.405574i	$0.132928\pi$
$858$	28.5612	−	12.6514i	0.975063	−	0.431911i
$859$	−5.89620	−	22.0049i	−0.201176	−	0.750799i	−0.990581	−	0.136926i	$-0.956278\pi$
$859$	−5.89620	−	22.0049i	−0.201176	−	0.750799i	0.789405	−	0.613872i	$-0.210389\pi$
$860$	−4.98495	−	18.6041i	−0.169985	−	0.634394i
$861$	5.17862	−	4.17732i	0.176487	−	0.142363i
$862$	−0.676939	+	2.52637i	−0.0230566	+	0.0860486i
$863$	−14.9442			−0.508706			−0.254353	−	0.967111i	$-0.581863\pi$
$863$	−14.9442			−0.508706			−0.254353	+	0.967111i	$0.581863\pi$
$864$	30.4107	+	1.76742i	1.03459	+	0.0601288i
$865$	24.7112			0.840206
$866$	−3.35406	+	1.93647i	−0.113976	+	0.0658038i
$867$	25.8550	+	2.76709i	0.878083	+	0.0939753i
$868$	3.07542	+	11.4776i	0.104386	+	0.389576i
$869$	−17.4584	+	30.2389i	−0.592237	+	1.02578i
$870$	3.71730	−	13.4400i	0.126028	−	0.455659i
$871$	−16.2545	−	28.1536i	−0.550763	−	0.953949i
$872$	−20.0451	+	20.0451i	−0.678812	+	0.678812i
$873$	1.41859	+	0.729602i	0.0480119	+	0.0246933i
$874$		−	17.8613i		−	0.604169i
$875$	−9.58131	−	16.5953i	−0.323907	−	0.561024i
$876$	4.72591	+	30.2092i	0.159674	+	1.02067i
$877$	−19.8642	+	34.4059i	−0.670768	+	1.16180i	0.306919	+	0.951736i	$0.400702\pi$
$877$	−19.8642	+	34.4059i	−0.670768	+	1.16180i	−0.977687	+	0.210068i	$0.932631\pi$
$878$	−9.58664	+	2.56873i	−0.323533	+	0.0866905i
$879$	−37.5579	+	5.87555i	−1.26680	+	0.198177i
$880$	−7.07417	−	1.89552i	−0.238470	−	0.0638979i
$881$	30.4947	−	30.4947i	1.02739	−	1.02739i	0.0277787	−	0.999614i	$-0.491157\pi$
$881$	30.4947	−	30.4947i	1.02739	−	1.02739i	0.999614	−	0.0277787i	$-0.00884339\pi$
$882$	8.46303	−	5.45040i	0.284965	−	0.183525i
$883$			10.0771i			0.339123i	0.985520	+	0.169561i	$0.0542351\pi$
$883$			10.0771i			0.339123i	−0.985520	+	0.169561i	$0.945765\pi$
$884$	11.7466	+	3.14749i	0.395080	+	0.105861i
$885$	−13.7792	−	31.1074i	−0.463184	−	1.04566i
$886$	−10.2062	+	17.6777i	−0.342885	+	0.593894i
$887$	14.3476	+	53.5460i	0.481745	+	1.79790i	0.594290	+	0.804251i	$0.297433\pi$
$887$	14.3476	+	53.5460i	0.481745	+	1.79790i	−0.112545	+	0.993647i	$0.535900\pi$
$888$	5.37979	−	50.2675i	0.180534	−	1.68687i
$889$	−6.01787	+	22.4590i	−0.201833	+	0.753250i
$890$		−	5.14098i		−	0.172326i
$891$	−27.7032	−	22.7839i	−0.928091	−	0.763290i
$892$		−	29.9778i		−	1.00373i
$893$	−23.5866	+	13.6177i	−0.789295	+	0.455700i
$894$	3.75131	+	4.65050i	0.125463	+	0.155536i
$895$	−6.84175	+	11.8503i	−0.228694	+	0.396110i
$896$	15.0830	−	4.04148i	0.503887	−	0.135016i
$897$	−43.7580	+	19.3829i	−1.46104	+	0.647176i
$898$	−11.7630	+	6.79137i	−0.392536	+	0.226631i
$899$	−21.6509	−	17.7538i	−0.722098	−	0.592123i
$900$	−0.956538	+	4.41764i	−0.0318846	+	0.147255i
$901$	4.07586	+	4.07586i	0.135787	+	0.135787i
$902$	−6.98064	−	1.87046i	−0.232430	−	0.0622794i
$903$	−2.88323	−	18.4303i	−0.0959477	−	0.613321i
$904$	8.85210	+	5.11076i	0.294416	+	0.169981i
$905$	14.9138	−	25.8315i	0.495752	−	0.858668i
$906$	−0.208946	−	1.33563i	−0.00694175	−	0.0443733i
$907$	−8.50623	−	2.27924i	−0.282445	−	0.0756808i	0.114816	−	0.993387i	$-0.463372\pi$
$907$	−8.50623	−	2.27924i	−0.282445	−	0.0756808i	−0.397260	+	0.917706i	$0.630039\pi$
$908$	−5.38994			−0.178872
$909$	35.7620	+	18.3930i	1.18615	+	0.610056i
$910$	10.1341	+	10.1341i	0.335941	+	0.335941i
$911$	14.0214	−	52.3285i	0.464549	−	1.73372i	−0.193832	−	0.981035i	$-0.562092\pi$
$911$	14.0214	−	52.3285i	0.464549	−	1.73372i	0.658381	−	0.752685i	$-0.271242\pi$
$912$	−7.72292	−	2.98138i	−0.255731	−	0.0987233i
$913$	18.0440	−	4.83488i	0.597170	−	0.160011i
$914$	18.4508	−	4.94389i	0.610300	−	0.163529i
$915$	15.4129	−	12.4327i	0.509534	−	0.411014i
$916$	0.335606	−	1.25250i	0.0110887	−	0.0413837i
$917$	8.54338	+	8.54338i	0.282127	+	0.282127i
$918$	1.11502	+	5.39664i	0.0368010	+	0.178115i
$919$	−28.4491			−0.938448			−0.469224	−	0.883079i	$-0.655466\pi$
$919$	−28.4491			−0.938448			−0.469224	+	0.883079i	$0.655466\pi$
$920$	−22.7791	−	6.10365i	−0.751006	−	0.201232i
$921$	−18.6197	+	15.0195i	−0.613539	+	0.494910i
$922$	7.52164	−	13.0279i	0.247712	−	0.429050i
$923$	71.4448	+	41.2487i	2.35163	+	1.35772i
$924$	−14.7174	−	5.68153i	−0.484166	−	0.186909i
$925$	11.4657	+	3.07223i	0.376991	+	0.101014i
$926$	17.8610	+	17.8610i	0.586950	+	0.586950i
$927$	13.2943	−	14.6526i	0.436641	−	0.481253i
$928$	−20.0180	+	24.4121i	−0.657123	+	0.801366i
$929$	33.8528	−	19.5450i	1.11068	−	0.641249i	0.171672	−	0.985154i	$-0.445083\pi$
$929$	33.8528	−	19.5450i	1.11068	−	0.641249i	0.939004	+	0.343905i	$0.111750\pi$
$930$	10.8771	+	7.93425i	0.356674	+	0.260174i
$931$	−22.2691	+	5.96698i	−0.729839	+	0.195560i
$932$	11.3458	−	19.6515i	0.371644	−	0.643707i
$933$	43.5737	−	6.81665i	1.42654	−	0.223167i
$934$	15.6976	−	9.06304i	0.513642	−	0.296552i
$935$		−	11.1654i		−	0.365148i
$936$	−2.26320	−	46.5653i	−0.0739750	−	1.52203i
$937$		−	22.2136i		−	0.725686i	−0.931850	−	0.362843i	$-0.881806\pi$
$937$		−	22.2136i		−	0.725686i	0.931850	−	0.362843i	$-0.118194\pi$
$938$	1.67691	−	6.25833i	0.0547532	−	0.204342i
$939$	1.81118	−	0.802274i	0.0591056	−	0.0261812i
$940$	3.88661	+	14.5050i	0.126767	+	0.473102i
$941$	23.6685	−	40.9951i	0.771572	−	1.33640i	−0.165129	−	0.986272i	$-0.552804\pi$
$941$	23.6685	−	40.9951i	0.771572	−	1.33640i	0.936701	−	0.350130i	$-0.113863\pi$
$942$	−8.68090	−	0.929059i	−0.282839	−	0.0302704i
$943$	10.6949	+	2.86569i	0.348274	+	0.0933197i
$944$			9.13978i			0.297474i
$945$	5.17435	−	15.6218i	0.168321	−	0.508178i
$946$	−14.3276	+	14.3276i	−0.465830	+	0.465830i
$947$	37.5981	+	10.0744i	1.22177	+	0.327373i	0.811371	−	0.584532i	$-0.198722\pi$
$947$	37.5981	+	10.0744i	1.22177	+	0.327373i	0.410402	+	0.911905i	$0.365388\pi$
$948$	13.6629	+	16.9379i	0.443750	+	0.550117i
$949$	71.5262	−	19.1654i	2.32184	−	0.622135i
$950$	−2.04265	+	3.53798i	−0.0662725	+	0.114787i
$951$	26.6955	+	10.3056i	0.865661	+	0.334182i
$952$	2.90194	+	5.02630i	0.0940523	+	0.162903i
$953$			15.8963i			0.514932i	0.966287	+	0.257466i	$0.0828876\pi$
$953$			15.8963i			0.514932i	−0.966287	+	0.257466i	$0.917112\pi$
$954$	4.22054	−	8.20613i	0.136645	−	0.265683i
$955$	28.5084	−	28.5084i	0.922511	−	0.922511i
$956$	−11.8439	−	20.5142i	−0.383059	−	0.663478i
$957$	35.9831	−	9.33225i	1.16317	−	0.301669i
$958$	7.24547	−	12.5495i	0.234090	−	0.405457i
$959$	−2.49397	−	9.30762i	−0.0805345	−	0.300559i
$960$	5.19468	−	7.12140i	0.167657	−	0.229842i
$961$	−3.43545	+	1.98346i	−0.110821	+	0.0639824i
$962$	−51.1273			−1.64841
$963$	−9.43221	+	43.5614i	−0.303949	+	1.40375i
$964$	−9.37233			−0.301863
$965$	−7.34633	+	27.4169i	−0.236487	+	0.882580i
$966$	−8.89829	−	3.43512i	−0.286298	−	0.110523i
$967$	9.77486	+	36.4803i	0.314338	+	1.17313i	0.924604	+	0.380930i	$0.124396\pi$
$967$	9.77486	+	36.4803i	0.314338	+	1.17313i	−0.610266	+	0.792197i	$0.708937\pi$
$968$	3.26535	+	12.1864i	0.104952	+	0.391687i
$969$	1.34306	−	12.5492i	0.0431453	−	0.403139i
$970$	0.688454	−	0.397479i	0.0221049	−	0.0127623i
$971$	−8.00353	+	8.00353i	−0.256846	+	0.256846i	−0.823770	−	0.566924i	$-0.808133\pi$
$971$	−8.00353	+	8.00353i	−0.256846	+	0.256846i	0.566924	+	0.823770i	$0.308133\pi$
$972$	−19.4651	+	10.9933i	−0.624343	+	0.352609i
$973$	−1.52930			−0.0490270
$974$	−17.6898	−	4.73996i	−0.566817	−	0.151878i
$975$	10.8843	+	1.16487i	0.348575	+	0.0373057i
$976$	−5.13839	+	1.37683i	−0.164476	+	0.0440712i
$977$	−7.53675	−	4.35135i	−0.241122	−	0.139212i	0.374570	−	0.927199i	$-0.377790\pi$
$977$	−7.53675	−	4.35135i	−0.241122	−	0.139212i	−0.615692	+	0.787987i	$0.711124\pi$
$978$	2.93347	+	6.62247i	0.0938019	+	0.211763i
$979$	11.8688	−	6.85243i	0.379327	−	0.219005i
$980$			12.7115i			0.406055i
$981$	6.96650	−	32.1739i	0.222423	−	1.02723i
$982$	−25.0319			−0.798799
$983$	−3.58848	+	13.3924i	−0.114455	+	0.427150i	−0.999246	−	0.0388378i	$-0.987634\pi$
$983$	−3.58848	+	13.3924i	−0.114455	+	0.427150i	0.884791	+	0.465988i	$0.154301\pi$
$984$	−6.35619	+	8.71373i	−0.202628	+	0.277783i
$985$	37.8740	+	21.8666i	1.20677	+	0.696727i
$986$	−5.20296	−	2.35490i	−0.165696	−	0.0749953i
$987$	2.24796	+	14.3695i	0.0715535	+	0.457387i
$988$	−11.5404	+	43.0694i	−0.367149	+	1.37022i
$989$	21.9510	−	21.9510i	0.698001	−	0.698001i
$990$	−17.0208	+	5.45907i	−0.540958	+	0.173501i
$991$			36.0143i			1.14403i	0.820242	+	0.572017i	$0.193839\pi$
$991$			36.0143i			1.14403i	−0.820242	+	0.572017i	$0.806161\pi$
$992$	−15.2403	−	26.3971i	−0.483881	−	0.838107i
$993$	1.85312	−	4.80030i	0.0588070	−	0.152333i
$994$	4.25546	+	15.8816i	0.134975	+	0.503734i
$995$	14.8317	−	25.6892i	0.470196	−	0.814403i
$996$	1.23894	−	11.5764i	0.0392573	−	0.366811i
$997$	3.94561	−	14.7252i	0.124959	−	0.466352i	−0.874880	−	0.484340i	$-0.839060\pi$
$997$	3.94561	−	14.7252i	0.124959	−	0.466352i	0.999838	+	0.0179887i	$0.00572629\pi$
$998$	16.1767	+	16.1767i	0.512065	+	0.512065i
$999$	26.3542	+	52.4593i	0.833811	+	1.65974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.l.a.41.12	✓	112
3.2	odd	2		783.2.m.a.476.17		112
9.2	odd	6	inner	261.2.l.a.128.12	yes	112
9.7	even	3		783.2.m.a.737.17		112
29.17	odd	4	inner	261.2.l.a.104.12	yes	112
87.17	even	4		783.2.m.a.17.17		112
261.133	odd	12		783.2.m.a.278.17		112
261.191	even	12	inner	261.2.l.a.191.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.l.a.41.12	✓	112	1.1	even	1	trivial
261.2.l.a.104.12	yes	112	29.17	odd	4	inner
261.2.l.a.128.12	yes	112	9.2	odd	6	inner
261.2.l.a.191.12	yes	112	261.191	even	12	inner
783.2.m.a.17.17		112	87.17	even	4
783.2.m.a.278.17		112	261.133	odd	12
783.2.m.a.476.17		112	3.2	odd	2
783.2.m.a.737.17		112	9.7	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.726652 - 0.194706i) q^{2} +(0.184317 - 1.72222i) q^{3} +(-1.24194 - 0.717034i) q^{4} +(0.993651 - 1.72105i) q^{5} +(-0.469260 + 1.21556i) q^{6} +(-0.796821 - 1.38013i) q^{7} +(1.82674 + 1.82674i) q^{8} +(-2.93205 - 0.634868i) q^{9} +O(q^{10})\)	\(q+(-0.726652 - 0.194706i) q^{2} +(0.184317 - 1.72222i) q^{3} +(-1.24194 - 0.717034i) q^{4} +(0.993651 - 1.72105i) q^{5} +(-0.469260 + 1.21556i) q^{6} +(-0.796821 - 1.38013i) q^{7} +(1.82674 + 1.82674i) q^{8} +(-2.93205 - 0.634868i) q^{9} +(-1.05714 + 1.05714i) q^{10} +(-3.84963 - 1.03150i) q^{11} +(-1.46380 + 2.00672i) q^{12} +(5.20946 + 3.00768i) q^{13} +(0.310291 + 1.15802i) q^{14} +(-2.78088 - 2.02850i) q^{15} +(0.462342 + 0.800799i) q^{16} +(-0.996830 + 0.996830i) q^{17} +(2.00697 + 1.03222i) q^{18} +(-3.65492 - 3.65492i) q^{19} +(-2.46811 + 1.42496i) q^{20} +(-2.52376 + 1.11791i) q^{21} +(2.59650 + 1.49909i) q^{22} +(-3.97804 - 2.29672i) q^{23} +(3.48274 - 2.80934i) q^{24} +(0.525314 + 0.909871i) q^{25} +(-3.19985 - 3.19985i) q^{26} +(-1.63381 + 4.93261i) q^{27} +2.28539i q^{28} +(-3.13850 - 4.37605i) q^{29} +(1.62577 + 2.01547i) q^{30} +(5.02217 - 1.34569i) q^{31} +(-1.51731 - 5.66266i) q^{32} +(-2.48602 + 6.43976i) q^{33} +(0.918437 - 0.530260i) q^{34} -3.16705 q^{35} +(3.18621 + 2.89085i) q^{36} +(7.98902 - 7.98902i) q^{37} +(1.94422 + 3.36749i) q^{38} +(6.14007 - 8.41745i) q^{39} +(4.95906 - 1.32877i) q^{40} +(-2.32830 + 0.623865i) q^{41} +(2.05156 - 0.320945i) q^{42} +(-1.74915 + 6.52792i) q^{43} +(4.04138 + 4.04138i) q^{44} +(-4.00608 + 4.41539i) q^{45} +(2.44346 + 2.44346i) q^{46} +(1.36376 - 5.08962i) q^{47} +(1.46437 - 0.648651i) q^{48} +(2.23015 - 3.86274i) q^{49} +(-0.204563 - 0.763441i) q^{50} +(1.53302 + 1.90049i) q^{51} +(-4.31322 - 7.47072i) q^{52} -4.08882i q^{53} +(2.14762 - 3.26618i) q^{54} +(-5.60046 + 5.60046i) q^{55} +(1.06556 - 3.97672i) q^{56} +(-6.96823 + 5.62090i) q^{57} +(1.42856 + 3.79095i) q^{58} +(8.55999 + 4.94211i) q^{59} +(1.99918 + 4.51326i) q^{60} +(-1.48897 + 5.55692i) q^{61} -3.91138 q^{62} +(1.46012 + 4.55250i) q^{63} +2.56084i q^{64} +(10.3528 - 5.97718i) q^{65} +(3.06033 - 4.19542i) q^{66} +(-4.68028 - 2.70216i) q^{67} +(1.95276 - 0.523241i) q^{68} +(-4.68867 + 6.42772i) q^{69} +(2.30134 + 0.616642i) q^{70} +13.7144 q^{71} +(-4.19636 - 6.51583i) q^{72} +(8.70450 - 8.70450i) q^{73} +(-7.36074 + 4.24973i) q^{74} +(1.66382 - 0.737000i) q^{75} +(1.91849 + 7.15989i) q^{76} +(1.64385 + 6.13492i) q^{77} +(-6.10062 + 4.92104i) q^{78} +(2.26755 - 8.46261i) q^{79} +1.83763 q^{80} +(8.19389 + 3.72293i) q^{81} +1.81333 q^{82} +(-4.05925 + 2.34361i) q^{83} +(3.93593 + 0.421236i) q^{84} +(0.725097 + 2.70610i) q^{85} +(2.54204 - 4.40295i) q^{86} +(-8.11498 + 4.59860i) q^{87} +(-5.14797 - 8.91654i) q^{88} +(-2.43156 + 2.43156i) q^{89} +(3.77073 - 2.42844i) q^{90} -9.58634i q^{91} +(3.29365 + 5.70478i) q^{92} +(-1.39189 - 8.89730i) q^{93} +(-1.98196 + 3.43285i) q^{94} +(-9.92204 + 2.65860i) q^{95} +(-10.0320 + 1.56940i) q^{96} +(-0.513620 - 0.137624i) q^{97} +(-2.37264 + 2.37264i) q^{98} +(10.6324 + 5.46843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 112 * q - 6 * q^2 - 4 * q^3 - 4 * q^7	\( 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7} + 6 q^{11} - 18 q^{12} - 18 q^{14} - 8 q^{15} + 40 q^{16} + 22 q^{18} - 8 q^{19} - 12 q^{20} + 24 q^{21} - 12 q^{23} - 96 q^{24} - 44 q^{25} + 20 q^{27} - 42 q^{29} + 28 q^{30} - 2 q^{31} - 66 q^{32} + 12 q^{36} - 8 q^{37} - 12 q^{39} - 12 q^{40} - 18 q^{41} - 2 q^{43} - 52 q^{45} + 8 q^{46} - 36 q^{49} + 24 q^{50} - 36 q^{52} + 8 q^{54} + 36 q^{55} + 84 q^{56} + 28 q^{58} + 48 q^{59} - 36 q^{60} - 14 q^{61} + 24 q^{65} + 18 q^{66} - 102 q^{68} + 36 q^{69} - 8 q^{73} + 144 q^{74} + 18 q^{75} + 14 q^{76} - 72 q^{77} + 12 q^{78} - 2 q^{79} - 56 q^{81} + 80 q^{82} - 120 q^{83} - 14 q^{84} - 48 q^{85} - 76 q^{87} - 36 q^{88} + 160 q^{90} - 40 q^{94} + 204 q^{95} + 22 q^{97} - 54 q^{99}+O(q^{100}) \) 112 * q - 6 * q^2 - 4 * q^3 - 4 * q^7 + 6 * q^11 - 18 * q^12 - 18 * q^14 - 8 * q^15 + 40 * q^16 + 22 * q^18 - 8 * q^19 - 12 * q^20 + 24 * q^21 - 12 * q^23 - 96 * q^24 - 44 * q^25 + 20 * q^27 - 42 * q^29 + 28 * q^30 - 2 * q^31 - 66 * q^32 + 12 * q^36 - 8 * q^37 - 12 * q^39 - 12 * q^40 - 18 * q^41 - 2 * q^43 - 52 * q^45 + 8 * q^46 - 36 * q^49 + 24 * q^50 - 36 * q^52 + 8 * q^54 + 36 * q^55 + 84 * q^56 + 28 * q^58 + 48 * q^59 - 36 * q^60 - 14 * q^61 + 24 * q^65 + 18 * q^66 - 102 * q^68 + 36 * q^69 - 8 * q^73 + 144 * q^74 + 18 * q^75 + 14 * q^76 - 72 * q^77 + 12 * q^78 - 2 * q^79 - 56 * q^81 + 80 * q^82 - 120 * q^83 - 14 * q^84 - 48 * q^85 - 76 * q^87 - 36 * q^88 + 160 * q^90 - 40 * q^94 + 204 * q^95 + 22 * q^97 - 54 * q^99

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