LMFDB - Embedded newform 670.2.e.j.171.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 17 x^{10} - 18 x^{9} + 172 x^{8} - 170 x^{7} + 887 x^{6} - 312 x^{5} + 2516 x^{4} + \cdots + 289 $ x^12 - 2x^11 + 17x^10 - 18x^9 + 172x^8 - 170x^7 + 887x^6 - 312x^5 + 2516x^4 - 1220x^3 + 3001x^2 + 816*x + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.3
Root			$0.665228 - 1.15221i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.j.431.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -1.33046 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.665228 - 1.15221i) q^{6} +(-0.407937 + 0.706567i) q^{7} -1.00000 q^{8} -1.22989 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -1.33046 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.665228 - 1.15221i) q^{6} +(-0.407937 + 0.706567i) q^{7} -1.00000 q^{8} -1.22989 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.61494 - 2.79716i) q^{11} +(0.665228 - 1.15221i) q^{12} +(0.391960 + 0.678895i) q^{13} -0.815873 q^{14} +1.33046 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.21223 - 3.83170i) q^{17} +(-0.614943 - 1.06511i) q^{18} +(0.432062 + 0.748354i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.542742 - 0.940057i) q^{21} +3.22989 q^{22} +(-3.27206 - 5.66738i) q^{23} +1.33046 q^{24} +1.00000 q^{25} +(-0.391960 + 0.678895i) q^{26} +5.62768 q^{27} +(-0.407937 - 0.706567i) q^{28} +(1.71487 - 2.97025i) q^{29} +(0.665228 + 1.15221i) q^{30} +(1.61758 - 2.80173i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.14861 + 3.72150i) q^{33} +(2.21223 - 3.83170i) q^{34} +(0.407937 - 0.706567i) q^{35} +(0.614943 - 1.06511i) q^{36} +(-2.78971 - 4.83193i) q^{37} +(-0.432062 + 0.748354i) q^{38} +(-0.521486 - 0.903240i) q^{39} +1.00000 q^{40} +(5.36288 - 9.28878i) q^{41} +1.08548 q^{42} -6.29387 q^{43} +(1.61494 + 2.79716i) q^{44} +1.22989 q^{45} +(3.27206 - 5.66738i) q^{46} +(-3.33357 + 5.77390i) q^{47} +(0.665228 + 1.15221i) q^{48} +(3.16718 + 5.48571i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.94328 + 5.09791i) q^{51} -0.783920 q^{52} +2.36335 q^{53} +(2.81384 + 4.87371i) q^{54} +(-1.61494 + 2.79716i) q^{55} +(0.407937 - 0.706567i) q^{56} +(-0.574840 - 0.995653i) q^{57} +3.42975 q^{58} -5.82226 q^{59} +(-0.665228 + 1.15221i) q^{60} +(-6.27142 - 10.8624i) q^{61} +3.23516 q^{62} +(0.501715 - 0.868997i) q^{63} +1.00000 q^{64} +(-0.391960 - 0.678895i) q^{65} -4.29722 q^{66} +(-7.83129 + 2.38135i) q^{67} +4.42447 q^{68} +(4.35334 + 7.54020i) q^{69} +0.815873 q^{70} +(-0.725057 + 1.25583i) q^{71} +1.22989 q^{72} +(-2.55132 - 4.41902i) q^{73} +(2.78971 - 4.83193i) q^{74} -1.33046 q^{75} -0.864125 q^{76} +(1.31759 + 2.28213i) q^{77} +(0.521486 - 0.903240i) q^{78} +(-0.749748 + 1.29860i) q^{79} +(0.500000 + 0.866025i) q^{80} -3.79773 q^{81} +10.7258 q^{82} +(5.04959 + 8.74615i) q^{83} +(0.542742 + 0.940057i) q^{84} +(2.21223 + 3.83170i) q^{85} +(-3.14694 - 5.45065i) q^{86} +(-2.28156 + 3.95179i) q^{87} +(-1.61494 + 2.79716i) q^{88} +1.74447 q^{89} +(0.614943 + 1.06511i) q^{90} -0.639580 q^{91} +6.54412 q^{92} +(-2.15212 + 3.72759i) q^{93} -6.66713 q^{94} +(-0.432062 - 0.748354i) q^{95} +(-0.665228 + 1.15221i) q^{96} +(-2.72010 - 4.71135i) q^{97} +(-3.16718 + 5.48571i) q^{98} +(-1.98619 + 3.44019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.33046			−0.768139			−0.384070	−	0.923304i	$-0.625478\pi$
$3$	−1.33046			−0.768139			−0.384070	+	0.923304i	$0.625478\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.665228	−	1.15221i	−0.271578	−	0.470387i
$7$	−0.407937	+	0.706567i	−0.154186	+	0.267057i	−0.932762	−	0.360492i	$-0.882609\pi$
$7$	−0.407937	+	0.706567i	−0.154186	+	0.267057i	0.778577	+	0.627550i	$0.215942\pi$
$8$	−1.00000			−0.353553
$9$	−1.22989			−0.409962
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.61494	−	2.79716i	0.486924	−	0.843376i	−0.512963	−	0.858410i	$-0.671452\pi$
$11$	1.61494	−	2.79716i	0.486924	−	0.843376i	0.999887	+	0.0150342i	$0.00478570\pi$
$12$	0.665228	−	1.15221i	0.192035	−	0.332614i
$13$	0.391960	+	0.678895i	0.108710	+	0.188292i	0.915248	−	0.402891i	$-0.131995\pi$
$13$	0.391960	+	0.678895i	0.108710	+	0.188292i	−0.806538	+	0.591183i	$0.798661\pi$
$14$	−0.815873			−0.218051
$15$	1.33046			0.343522
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.21223	−	3.83170i	−0.536545	−	0.929324i	−0.999087	−	0.0427262i	$-0.986396\pi$
$17$	−2.21223	−	3.83170i	−0.536545	−	0.929324i	0.462541	−	0.886598i	$-0.346938\pi$
$18$	−0.614943	−	1.06511i	−0.144943	−	0.251049i
$19$	0.432062	+	0.748354i	0.0991219	+	0.171684i	0.911321	−	0.411696i	$-0.135063\pi$
$19$	0.432062	+	0.748354i	0.0991219	+	0.171684i	−0.812200	+	0.583380i	$0.801730\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	0.542742	−	0.940057i	0.118436	−	0.205137i
$22$	3.22989			0.688614
$23$	−3.27206	−	5.66738i	−0.682272	−	1.18173i	−0.974286	−	0.225316i	$-0.927659\pi$
$23$	−3.27206	−	5.66738i	−0.682272	−	1.18173i	0.292014	−	0.956414i	$-0.405675\pi$
$24$	1.33046			0.271578
$25$	1.00000			0.200000
$26$	−0.391960	+	0.678895i	−0.0768697	+	0.133142i
$27$	5.62768			1.08305
$28$	−0.407937	−	0.706567i	−0.0770928	−	0.133529i
$29$	1.71487	−	2.97025i	0.318444	−	0.551561i	−0.661720	−	0.749751i	$-0.730173\pi$
$29$	1.71487	−	2.97025i	0.318444	−	0.551561i	0.980164	+	0.198190i	$0.0635064\pi$
$30$	0.665228	+	1.15221i	0.121454	+	0.210364i
$31$	1.61758	−	2.80173i	0.290526	−	0.503206i	−0.683408	−	0.730037i	$-0.739503\pi$
$31$	1.61758	−	2.80173i	0.290526	−	0.503206i	0.973934	+	0.226830i	$0.0728363\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.14861	+	3.72150i	−0.374025	+	0.647831i
$34$	2.21223	−	3.83170i	0.379395	−	0.657131i
$35$	0.407937	−	0.706567i	0.0689539	−	0.119432i
$36$	0.614943	−	1.06511i	0.102490	−	0.177519i
$37$	−2.78971	−	4.83193i	−0.458626	−	0.794364i	0.540263	−	0.841497i	$-0.318325\pi$
$37$	−2.78971	−	4.83193i	−0.458626	−	0.794364i	−0.998889	+	0.0471328i	$0.984992\pi$
$38$	−0.432062	+	0.748354i	−0.0700898	+	0.121399i
$39$	−0.521486	−	0.903240i	−0.0835046	−	0.144634i
$40$	1.00000			0.158114
$41$	5.36288	−	9.28878i	0.837541	−	1.45066i	−0.0544038	−	0.998519i	$-0.517326\pi$
$41$	5.36288	−	9.28878i	0.837541	−	1.45066i	0.891945	−	0.452144i	$-0.149341\pi$
$42$	1.08548			0.167494
$43$	−6.29387			−0.959806			−0.479903	−	0.877321i	$-0.659328\pi$
$43$	−6.29387			−0.959806			−0.479903	+	0.877321i	$0.659328\pi$
$44$	1.61494	+	2.79716i	0.243462	+	0.421688i
$45$	1.22989			0.183340
$46$	3.27206	−	5.66738i	0.482439	−	0.835609i
$47$	−3.33357	+	5.77390i	−0.486250	+	0.842211i	−0.999875	−	0.0158045i	$-0.994969\pi$
$47$	−3.33357	+	5.77390i	−0.486250	+	0.842211i	0.513625	+	0.858015i	$0.328302\pi$
$48$	0.665228	+	1.15221i	0.0960174	+	0.166307i
$49$	3.16718	+	5.48571i	0.452454	+	0.783673i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	2.94328	+	5.09791i	0.412142	+	0.713850i
$52$	−0.783920			−0.108710
$53$	2.36335			0.324631			0.162315	−	0.986739i	$-0.448104\pi$
$53$	2.36335			0.324631			0.162315	+	0.986739i	$0.448104\pi$
$54$	2.81384	+	4.87371i	0.382915	+	0.663228i
$55$	−1.61494	+	2.79716i	−0.217759	+	0.377169i
$56$	0.407937	−	0.706567i	0.0545128	−	0.0944190i
$57$	−0.574840	−	0.995653i	−0.0761395	−	0.131877i
$58$	3.42975			0.450348
$59$	−5.82226			−0.757994			−0.378997	−	0.925398i	$-0.623731\pi$
$59$	−5.82226			−0.757994			−0.378997	+	0.925398i	$0.623731\pi$
$60$	−0.665228	+	1.15221i	−0.0858806	+	0.148750i
$61$	−6.27142	−	10.8624i	−0.802973	−	1.39079i	−0.917651	−	0.397388i	$-0.869917\pi$
$61$	−6.27142	−	10.8624i	−0.802973	−	1.39079i	0.114678	−	0.993403i	$-0.463416\pi$
$62$	3.23516			0.410866
$63$	0.501715	−	0.868997i	0.0632102	−	0.109483i
$64$	1.00000			0.125000
$65$	−0.391960	−	0.678895i	−0.0486167	−	0.0842066i
$66$	−4.29722			−0.528951
$67$	−7.83129	+	2.38135i	−0.956745	+	0.290928i
$67$	−7.83129	+	2.38135i	−0.956745	+	0.290928i
$68$	4.42447			0.536545
$69$	4.35334	+	7.54020i	0.524080	+	0.907733i
$70$	0.815873			0.0975155
$71$	−0.725057	+	1.25583i	−0.0860484	+	0.149040i	−0.905837	−	0.423625i	$-0.860757\pi$
$71$	−0.725057	+	1.25583i	−0.0860484	+	0.149040i	0.819789	+	0.572666i	$0.194091\pi$
$72$	1.22989			0.144943
$73$	−2.55132	−	4.41902i	−0.298609	−	0.517207i	0.677209	−	0.735791i	$-0.263189\pi$
$73$	−2.55132	−	4.41902i	−0.298609	−	0.517207i	−0.975818	+	0.218584i	$0.929856\pi$
$74$	2.78971	−	4.83193i	0.324298	−	0.561700i
$75$	−1.33046			−0.153628
$76$	−0.864125			−0.0991219
$77$	1.31759	+	2.28213i	0.150153	+	0.260073i
$78$	0.521486	−	0.903240i	0.0590467	−	0.102272i
$79$	−0.749748	+	1.29860i	−0.0843532	+	0.146104i	−0.905115	−	0.425166i	$-0.860216\pi$
$79$	−0.749748	+	1.29860i	−0.0843532	+	0.146104i	0.820762	+	0.571270i	$0.193549\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.79773			−0.421970
$82$	10.7258			1.18446
$83$	5.04959	+	8.74615i	0.554265	+	0.960015i	0.997960	+	0.0638372i	$0.0203338\pi$
$83$	5.04959	+	8.74615i	0.554265	+	0.960015i	−0.443696	+	0.896178i	$0.646333\pi$
$84$	0.542742	+	0.940057i	0.0592180	+	0.102569i
$85$	2.21223	+	3.83170i	0.239950	+	0.415606i
$86$	−3.14694	−	5.45065i	−0.339343	−	0.587759i
$87$	−2.28156	+	3.95179i	−0.244609	+	0.423676i
$88$	−1.61494	+	2.79716i	−0.172153	+	0.298179i
$89$	1.74447			0.184913			0.0924566	−	0.995717i	$-0.470528\pi$
$89$	1.74447			0.184913			0.0924566	+	0.995717i	$0.470528\pi$
$90$	0.614943	+	1.06511i	0.0648206	+	0.112273i
$91$	−0.639580			−0.0670462
$92$	6.54412			0.682272
$93$	−2.15212	+	3.72759i	−0.223165	+	0.386533i
$94$	−6.66713			−0.687662
$95$	−0.432062	−	0.748354i	−0.0443287	−	0.0767795i
$96$	−0.665228	+	1.15221i	−0.0678946	+	0.117597i
$97$	−2.72010	−	4.71135i	−0.276184	−	0.478365i	0.694249	−	0.719735i	$-0.255737\pi$
$97$	−2.72010	−	4.71135i	−0.276184	−	0.478365i	−0.970433	+	0.241370i	$0.922403\pi$
$98$	−3.16718	+	5.48571i	−0.319933	+	0.554140i
$99$	−1.98619	+	3.44019i	−0.199620	+	0.345752i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	5.88053	−	10.1854i	0.585135	−	1.01348i	−0.409724	−	0.912210i	$-0.634375\pi$
$101$	5.88053	−	10.1854i	0.585135	−	1.01348i	0.994859	−	0.101273i	$-0.0322917\pi$
$102$	−2.94328	+	5.09791i	−0.291428	+	0.504768i
$103$	−2.20010	+	3.81069i	−0.216783	+	0.375478i	−0.953823	−	0.300371i	$-0.902890\pi$
$103$	−2.20010	+	3.81069i	−0.216783	+	0.375478i	0.737040	+	0.675849i	$0.236223\pi$
$104$	−0.391960	−	0.678895i	−0.0384349	−	0.0665711i
$105$	−0.542742	+	0.940057i	−0.0529662	+	0.0917402i
$106$	1.18167	+	2.04672i	0.114774	+	0.198795i
$107$	−1.96669			−0.190127			−0.0950633	−	0.995471i	$-0.530305\pi$
$107$	−1.96669			−0.190127			−0.0950633	+	0.995471i	$0.530305\pi$
$108$	−2.81384	+	4.87371i	−0.270762	+	0.468973i
$109$	−6.70667			−0.642383			−0.321191	−	0.947014i	$-0.604083\pi$
$109$	−6.70667			−0.642383			−0.321191	+	0.947014i	$0.604083\pi$
$110$	−3.22989			−0.307957
$111$	3.71159	+	6.42867i	0.352289	+	0.610182i
$112$	0.815873			0.0770928
$113$	−6.15427	+	10.6595i	−0.578945	+	1.00276i	0.416656	+	0.909064i	$0.363202\pi$
$113$	−6.15427	+	10.6595i	−0.578945	+	1.00276i	−0.995601	+	0.0936975i	$0.970131\pi$
$114$	0.574840	−	0.995653i	0.0538387	−	0.0932514i
$115$	3.27206	+	5.66738i	0.305121	+	0.528486i
$116$	1.71487	+	2.97025i	0.159222	+	0.275781i
$117$	−0.482066	−	0.834963i	−0.0445670	−	0.0771924i
$118$	−2.91113	−	5.04223i	−0.267991	−	0.464174i
$119$	3.60980			0.330910
$120$	−1.33046			−0.121454
$121$	0.283920	+	0.491765i	0.0258109	+	0.0447059i
$122$	6.27142	−	10.8624i	0.567788	−	0.983437i
$123$	−7.13508	+	12.3583i	−0.643348	+	1.11431i
$124$	1.61758	+	2.80173i	0.145263	+	0.251603i
$125$	−1.00000			−0.0894427
$126$	1.00343			0.0893927
$127$	−6.61785	+	11.4625i	−0.587240	+	1.01713i	0.407353	+	0.913271i	$0.366452\pi$
$127$	−6.61785	+	11.4625i	−0.587240	+	1.01713i	−0.994592	+	0.103858i	$0.966881\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.37372			0.737265
$130$	0.391960	−	0.678895i	0.0343772	−	0.0595430i
$131$	−3.61488			−0.315834			−0.157917	−	0.987452i	$-0.550478\pi$
$131$	−3.61488			−0.315834			−0.157917	+	0.987452i	$0.550478\pi$
$132$	−2.14861	−	3.72150i	−0.187013	−	0.323915i
$133$	−0.705017			−0.0611327
$134$	−5.97796	−	5.59142i	−0.516417	−	0.483025i
$135$	−5.62768			−0.484353
$136$	2.21223	+	3.83170i	0.189697	+	0.328566i
$137$	−14.4907			−1.23802			−0.619011	−	0.785382i	$-0.712466\pi$
$137$	−14.4907			−1.23802			−0.619011	+	0.785382i	$0.712466\pi$
$138$	−4.35334	+	7.54020i	−0.370581	+	0.641864i
$139$	−14.5751			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$139$	−14.5751			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$140$	0.407937	+	0.706567i	0.0344769	+	0.0597158i
$141$	4.43516	−	7.68193i	0.373508	−	0.646935i
$142$	−1.45011			−0.121691
$143$	2.53197			0.211734
$144$	0.614943	+	1.06511i	0.0512452	+	0.0887593i
$145$	−1.71487	+	2.97025i	−0.142412	+	0.246666i
$146$	2.55132	−	4.41902i	0.211149	−	0.365720i
$147$	−4.21379	−	7.29850i	−0.347547	−	0.601970i
$148$	5.57943			0.458626
$149$	10.7961			0.884449			0.442224	−	0.896904i	$-0.354190\pi$
$149$	10.7961			0.884449			0.442224	+	0.896904i	$0.354190\pi$
$150$	−0.665228	−	1.15221i	−0.0543157	−	0.0940775i
$151$	2.87474	+	4.97919i	0.233943	+	0.405201i	0.958965	−	0.283525i	$-0.0915038\pi$
$151$	2.87474	+	4.97919i	0.233943	+	0.405201i	−0.725022	+	0.688726i	$0.758170\pi$
$152$	−0.432062	−	0.748354i	−0.0350449	−	0.0606995i
$153$	2.72079	+	4.71255i	0.219963	+	0.380987i
$154$	−1.31759	+	2.28213i	−0.106174	+	0.183899i
$155$	−1.61758	+	2.80173i	−0.129927	+	0.225041i
$156$	1.04297			0.0835046
$157$	0.160793	+	0.278502i	0.0128327	+	0.0222269i	0.872370	−	0.488845i	$-0.162582\pi$
$157$	0.160793	+	0.278502i	0.0128327	+	0.0222269i	−0.859538	+	0.511072i	$0.829248\pi$
$158$	−1.49950			−0.119294
$159$	−3.14433			−0.249362
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	5.33918			0.420786
$162$	−1.89886	−	3.28893i	−0.149189	−	0.258403i
$163$	−4.51653	+	7.82286i	−0.353762	+	0.612734i	−0.986905	−	0.161301i	$-0.948431\pi$
$163$	−4.51653	+	7.82286i	−0.353762	+	0.612734i	0.633143	+	0.774035i	$0.281764\pi$
$164$	5.36288	+	9.28878i	0.418770	+	0.725332i
$165$	2.14861	−	3.72150i	0.167269	−	0.289719i
$166$	−5.04959	+	8.74615i	−0.391924	+	0.678833i
$167$	9.48637	−	16.4309i	0.734077	−	1.27146i	−0.221050	−	0.975263i	$-0.570948\pi$
$167$	9.48637	−	16.4309i	0.734077	−	1.27146i	0.955127	−	0.296197i	$-0.0957184\pi$
$168$	−0.542742	+	0.940057i	−0.0418735	+	0.0725270i
$169$	6.19273	−	10.7261i	0.476364	−	0.825087i
$170$	−2.21223	+	3.83170i	−0.169671	+	0.293878i
$171$	−0.531387	−	0.920390i	−0.0406362	−	0.0703840i
$172$	3.14694	−	5.45065i	0.239952	−	0.415608i
$173$	−10.0725	−	17.4460i	−0.765796	−	1.32640i	−0.939825	−	0.341657i	$-0.889012\pi$
$173$	−10.0725	−	17.4460i	−0.765796	−	1.32640i	0.174029	−	0.984741i	$-0.444321\pi$
$174$	−4.56313			−0.345930
$175$	−0.407937	+	0.706567i	−0.0308371	+	0.0534115i
$176$	−3.22989			−0.243462
$177$	7.74626			0.582245
$178$	0.872234	+	1.51075i	0.0653767	+	0.113236i
$179$	5.67665			0.424293			0.212146	−	0.977238i	$-0.431955\pi$
$179$	5.67665			0.424293			0.212146	+	0.977238i	$0.431955\pi$
$180$	−0.614943	+	1.06511i	−0.0458351	+	0.0793888i
$181$	7.54266	−	13.0643i	0.560641	−	0.971059i	−0.436799	−	0.899559i	$-0.643888\pi$
$181$	7.54266	−	13.0643i	0.560641	−	0.971059i	0.997441	−	0.0715000i	$-0.0227786\pi$
$182$	−0.319790	−	0.553892i	−0.0237044	−	0.0410572i
$183$	8.34385	+	14.4520i	0.616795	+	1.06832i
$184$	3.27206	+	5.66738i	0.241220	+	0.417805i
$185$	2.78971	+	4.83193i	0.205104	+	0.355250i
$186$	−4.30425			−0.315603
$187$	−14.2905			−1.04503
$188$	−3.33357	−	5.77390i	−0.243125	−	0.421105i
$189$	−2.29574	+	3.97633i	−0.166990	+	0.289236i
$190$	0.432062	−	0.748354i	0.0313451	−	0.0542913i
$191$	1.76036	+	3.04903i	0.127375	+	0.220620i	0.922659	−	0.385617i	$-0.126011\pi$
$191$	1.76036	+	3.04903i	0.127375	+	0.220620i	−0.795284	+	0.606237i	$0.792678\pi$
$192$	−1.33046			−0.0960174
$193$	5.73456			0.412782			0.206391	−	0.978470i	$-0.433828\pi$
$193$	5.73456			0.412782			0.206391	+	0.978470i	$0.433828\pi$
$194$	2.72010	−	4.71135i	0.195292	−	0.338255i
$195$	0.521486	+	0.903240i	0.0373444	+	0.0646824i
$196$	−6.33435			−0.452454
$197$	−2.34426	+	4.06038i	−0.167022	+	0.289290i	−0.937371	−	0.348332i	$-0.886748\pi$
$197$	−2.34426	+	4.06038i	−0.167022	+	0.289290i	0.770350	+	0.637622i	$0.220082\pi$
$198$	−3.97239			−0.282305
$199$	7.16333	+	12.4072i	0.507795	+	0.879527i	0.999959	+	0.00902433i	$0.00287257\pi$
$199$	7.16333	+	12.4072i	0.507795	+	0.879527i	−0.492164	+	0.870502i	$0.663794\pi$
$200$	−1.00000			−0.0707107
$201$	10.4192	−	3.16828i	0.734913	−	0.223474i
$202$	11.7611			0.827505
$203$	1.39912	+	2.42335i	0.0981989	+	0.170086i
$204$	−5.88656			−0.412142
$205$	−5.36288	+	9.28878i	−0.374560	+	0.648756i
$206$	−4.40021			−0.306577
$207$	4.02426	+	6.97022i	0.279705	+	0.484464i
$208$	0.391960	−	0.678895i	0.0271775	−	0.0470729i
$209$	2.79102			0.193059
$210$	−1.08548			−0.0749055
$211$	−11.7643	−	20.3764i	−0.809890	−	1.40277i	−0.912940	−	0.408094i	$-0.866194\pi$
$211$	−11.7643	−	20.3764i	−0.809890	−	1.40277i	0.103050	−	0.994676i	$-0.467140\pi$
$212$	−1.18167	+	2.04672i	−0.0811577	+	0.140569i
$213$	0.964656	−	1.67083i	0.0660972	−	0.114484i
$214$	−0.983343	−	1.70320i	−0.0672199	−	0.116428i
$215$	6.29387			0.429238
$216$	−5.62768			−0.382915
$217$	1.31974	+	2.28586i	0.0895900	+	0.155174i
$218$	−3.35334	−	5.80815i	−0.227117	−	0.393377i
$219$	3.39442	+	5.87931i	0.229374	+	0.397287i
$220$	−1.61494	−	2.79716i	−0.108879	−	0.188585i
$221$	1.73421	−	3.00375i	0.116656	−	0.202054i
$222$	−3.71159	+	6.42867i	−0.249106	+	0.431464i
$223$	−3.31258			−0.221827			−0.110913	−	0.993830i	$-0.535378\pi$
$223$	−3.31258			−0.221827			−0.110913	+	0.993830i	$0.535378\pi$
$224$	0.407937	+	0.706567i	0.0272564	+	0.0472095i
$225$	−1.22989			−0.0819924
$226$	−12.3085			−0.818752
$227$	7.46828	−	12.9354i	0.495687	−	0.858555i	−0.504301	−	0.863528i	$-0.668250\pi$
$227$	7.46828	−	12.9354i	0.495687	−	0.858555i	0.999988	+	0.00497301i	$0.00158297\pi$
$228$	1.14968			0.0761395
$229$	−9.48620	−	16.4306i	−0.626866	−	1.08576i	−0.988177	−	0.153318i	$-0.951004\pi$
$229$	−9.48620	−	16.4306i	−0.626866	−	1.08576i	0.361311	−	0.932445i	$-0.382329\pi$
$230$	−3.27206	+	5.66738i	−0.215753	+	0.373696i
$231$	−1.75299	−	3.03628i	−0.115339	−	0.199772i
$232$	−1.71487	+	2.97025i	−0.112587	+	0.195006i
$233$	−9.05727	+	15.6877i	−0.593362	+	1.02773i	0.400414	+	0.916334i	$0.368866\pi$
$233$	−9.05727	+	15.6877i	−0.593362	+	1.02773i	−0.993776	+	0.111398i	$0.964467\pi$
$234$	0.482066	−	0.834963i	0.0315136	−	0.0545832i
$235$	3.33357	−	5.77390i	0.217458	−	0.376648i
$236$	2.91113	−	5.04223i	0.189498	−	0.328221i
$237$	0.997507	−	1.72773i	0.0647951	−	0.112228i
$238$	1.80490	+	3.12618i	0.116994	+	0.202640i
$239$	6.78688	−	11.7552i	0.439007	−	0.760382i	−0.558607	−	0.829433i	$-0.688664\pi$
$239$	6.78688	−	11.7552i	0.439007	−	0.760382i	0.997613	+	0.0690511i	$0.0219972\pi$
$240$	−0.665228	−	1.15221i	−0.0429403	−	0.0743748i
$241$	17.8917			1.15251			0.576254	−	0.817271i	$-0.304514\pi$
$241$	17.8917			1.15251			0.576254	+	0.817271i	$0.304514\pi$
$242$	−0.283920	+	0.491765i	−0.0182511	+	0.0316118i
$243$	−11.8303			−0.758916
$244$	12.5428			0.802973
$245$	−3.16718	−	5.48571i	−0.202343	−	0.350469i
$246$	−14.2702			−0.909832
$247$	−0.338703	+	0.586650i	−0.0215511	+	0.0373277i
$248$	−1.61758	+	2.80173i	−0.102717	+	0.177910i
$249$	−6.71826	−	11.6364i	−0.425753	−	0.737425i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	7.61934	+	13.1971i	0.480929	+	0.832993i	0.999761	−	0.0218835i	$-0.00696628\pi$
$251$	7.61934	+	13.1971i	0.480929	+	0.832993i	−0.518832	+	0.854876i	$0.673633\pi$
$252$	0.501715	+	0.868997i	0.0316051	+	0.0547416i
$253$	−21.1368			−1.32886
$254$	−13.2357			−0.830482
$255$	−2.94328	−	5.09791i	−0.184315	−	0.319244i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.19330	−	15.9233i	0.573462	−	0.993266i	−0.422745	−	0.906249i	$-0.638933\pi$
$257$	9.19330	−	15.9233i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$258$	4.18686	+	7.25186i	0.260663	+	0.451481i
$259$	4.55211			0.282854
$260$	0.783920			0.0486167
$261$	−2.10910	+	3.65306i	−0.130550	+	0.226119i
$262$	−1.80744	−	3.13058i	−0.111664	−	0.193408i
$263$	15.7571			0.971627			0.485814	−	0.874062i	$-0.338523\pi$
$263$	15.7571			0.971627			0.485814	+	0.874062i	$0.338523\pi$
$264$	2.14861	−	3.72150i	0.132238	−	0.229043i
$265$	−2.36335			−0.145179
$266$	−0.352508	−	0.610562i	−0.0216137	−	0.0374360i
$267$	−2.32094			−0.142039
$268$	1.85334	−	7.97278i	0.113211	−	0.487015i
$269$	−3.13449			−0.191113			−0.0955566	−	0.995424i	$-0.530463\pi$
$269$	−3.13449			−0.191113			−0.0955566	+	0.995424i	$0.530463\pi$
$270$	−2.81384	−	4.87371i	−0.171245	−	0.296605i
$271$	3.89932			0.236867			0.118434	−	0.992962i	$-0.462213\pi$
$271$	3.89932			0.236867			0.118434	+	0.992962i	$0.462213\pi$
$272$	−2.21223	+	3.83170i	−0.134136	+	0.232331i
$273$	0.850933			0.0515008
$274$	−7.24534	−	12.5493i	−0.437707	−	0.758130i
$275$	1.61494	−	2.79716i	0.0973847	−	0.168675i
$276$	−8.70667			−0.524080
$277$	−16.8907			−1.01486			−0.507432	−	0.861692i	$-0.669405\pi$
$277$	−16.8907			−1.01486			−0.507432	+	0.861692i	$0.669405\pi$
$278$	−7.28756	−	12.6224i	−0.437079	−	0.757042i
$279$	−1.98944	+	3.44581i	−0.119105	+	0.206295i
$280$	−0.407937	+	0.706567i	−0.0243789	+	0.0422255i
$281$	13.7735	+	23.8564i	0.821658	+	1.42315i	0.904447	+	0.426587i	$0.140284\pi$
$281$	13.7735	+	23.8564i	0.821658	+	1.42315i	−0.0827882	+	0.996567i	$0.526382\pi$
$282$	8.87033			0.528220
$283$	20.6164			1.22552			0.612759	−	0.790270i	$-0.290060\pi$
$283$	20.6164			1.22552			0.612759	+	0.790270i	$0.290060\pi$
$284$	−0.725057	−	1.25583i	−0.0430242	−	0.0745201i
$285$	0.574840	+	0.995653i	0.0340506	+	0.0589774i
$286$	1.26599	+	2.19275i	0.0748593	+	0.129660i
$287$	4.37543	+	7.57847i	0.258273	+	0.447343i
$288$	−0.614943	+	1.06511i	−0.0362358	+	0.0627623i
$289$	−1.28795	+	2.23080i	−0.0757620	+	0.131224i
$290$	−3.42975			−0.201402
$291$	3.61898	+	6.26825i	0.212148	+	0.367451i
$292$	5.10264			0.298609
$293$	29.3727			1.71597			0.857985	−	0.513674i	$-0.171716\pi$
$293$	29.3727			1.71597			0.857985	+	0.513674i	$0.171716\pi$
$294$	4.21379	−	7.29850i	0.245753	−	0.425657i
$295$	5.82226			0.338985
$296$	2.78971	+	4.83193i	0.162149	+	0.280850i
$297$	9.08838	−	15.7415i	0.527361	−	0.913416i
$298$	5.39804	+	9.34967i	0.312700	+	0.541612i
$299$	2.56504	−	4.44277i	0.148340	−	0.256932i
$300$	0.665228	−	1.15221i	0.0384070	−	0.0665228i
$301$	2.56750	−	4.44704i	0.147988	−	0.256323i
$302$	−2.87474	+	4.97919i	−0.165423	+	0.286520i
$303$	−7.82379	+	13.5512i	−0.449465	+	0.778496i
$304$	0.432062	−	0.748354i	0.0247805	−	0.0429211i
$305$	6.27142	+	10.8624i	0.359101	+	0.621980i
$306$	−2.72079	+	4.71255i	−0.155537	+	0.269399i
$307$	0.0210323	+	0.0364289i	0.00120037	+	0.00207911i	0.866625	−	0.498960i	$-0.166285\pi$
$307$	0.0210323	+	0.0364289i	0.00120037	+	0.00207911i	−0.865425	+	0.501039i	$0.832951\pi$
$308$	−2.63518			−0.150153
$309$	2.92714	−	5.06996i	0.166519	−	0.288420i
$310$	−3.23516			−0.183745
$311$	23.9249			1.35666			0.678329	−	0.734758i	$-0.262704\pi$
$311$	23.9249			1.35666			0.678329	+	0.734758i	$0.262704\pi$
$312$	0.521486	+	0.903240i	0.0295233	+	0.0511359i
$313$	20.8480			1.17840			0.589199	−	0.807988i	$-0.299444\pi$
$313$	20.8480			1.17840			0.589199	+	0.807988i	$0.299444\pi$
$314$	−0.160793	+	0.278502i	−0.00907410	+	0.0157168i
$315$	−0.501715	+	0.868997i	−0.0282685	+	0.0489624i
$316$	−0.749748	−	1.29860i	−0.0421766	−	0.0730521i
$317$	−14.4623	−	25.0494i	−0.812283	−	1.40692i	−0.911262	−	0.411826i	$-0.864891\pi$
$317$	−14.4623	−	25.0494i	−0.812283	−	1.40692i	0.0989790	−	0.995090i	$-0.468442\pi$
$318$	−1.57217	−	2.72307i	−0.0881627	−	0.152702i
$319$	−5.53884	−	9.59356i	−0.310116	−	0.537136i
$320$	−1.00000			−0.0559017
$321$	2.61659			0.146044
$322$	2.66959	+	4.62386i	0.148770	+	0.257678i
$323$	1.91165	−	3.31107i	0.106367	−	0.184233i
$324$	1.89886	−	3.28893i	0.105492	−	0.182718i
$325$	0.391960	+	0.678895i	0.0217420	+	0.0376583i
$326$	−9.03306			−0.500295
$327$	8.92294			0.493439
$328$	−5.36288	+	9.28878i	−0.296115	+	0.512887i
$329$	−2.71977	−	4.71078i	−0.149946	−	0.259713i
$330$	4.29722			0.236554
$331$	−17.4784	+	30.2734i	−0.960698	+	1.66398i	−0.239943	+	0.970787i	$0.577129\pi$
$331$	−17.4784	+	30.2734i	−0.960698	+	1.66398i	−0.720754	+	0.693191i	$0.756204\pi$
$332$	−10.0992			−0.554265
$333$	3.43103	+	5.94271i	0.188019	+	0.325659i
$334$	18.9727			1.03814
$335$	7.83129	−	2.38135i	0.427869	−	0.130107i
$336$	−1.08548			−0.0592180
$337$	14.1024	+	24.4261i	0.768209	+	1.33058i	0.938533	+	0.345189i	$0.112185\pi$
$337$	14.1024	+	24.4261i	0.768209	+	1.33058i	−0.170324	+	0.985388i	$0.554481\pi$
$338$	12.3855			0.673681
$339$	8.18799	−	14.1820i	0.444710	−	0.770261i
$340$	−4.42447			−0.239950
$341$	−5.22461	−	9.04928i	−0.282928	−	0.490046i
$342$	0.531387	−	0.920390i	0.0287341	−	0.0497690i
$343$	−10.8791			−0.587418
$344$	6.29387			0.339343
$345$	−4.35334	−	7.54020i	−0.234376	−	0.405951i
$346$	10.0725	−	17.4460i	0.541499	−	0.937905i
$347$	11.7264	−	20.3107i	0.629507	−	1.09034i	−0.358144	−	0.933666i	$-0.616590\pi$
$347$	11.7264	−	20.3107i	0.629507	−	1.09034i	0.987651	−	0.156671i	$-0.0500763\pi$
$348$	−2.28156	−	3.95179i	−0.122305	−	0.211838i
$349$	−22.7872			−1.21977			−0.609885	−	0.792490i	$-0.708784\pi$
$349$	−22.7872			−1.21977			−0.609885	+	0.792490i	$0.708784\pi$
$350$	−0.815873			−0.0436103
$351$	2.20583	+	3.82060i	0.117738	+	0.203929i
$352$	−1.61494	−	2.79716i	−0.0860767	−	0.149089i
$353$	−6.70762	−	11.6179i	−0.357011	−	0.618361i	0.630449	−	0.776231i	$-0.282871\pi$
$353$	−6.70762	−	11.6179i	−0.357011	−	0.618361i	−0.987460	+	0.157870i	$0.949537\pi$
$354$	3.87313	+	6.70846i	0.205855	+	0.356551i
$355$	0.725057	−	1.25583i	0.0384820	−	0.0666528i
$356$	−0.872234	+	1.51075i	−0.0462283	+	0.0800698i
$357$	−4.80269			−0.254185
$358$	2.83832	+	4.91612i	0.150010	+	0.259825i
$359$	−9.04232			−0.477235			−0.238618	−	0.971114i	$-0.576694\pi$
$359$	−9.04232			−0.477235			−0.238618	+	0.971114i	$0.576694\pi$
$360$	−1.22989			−0.0648206
$361$	9.12664	−	15.8078i	0.480350	−	0.831990i
$362$	15.0853			0.792866
$363$	−0.377744	−	0.654271i	−0.0198264	−	0.0343403i
$364$	0.319790	−	0.553892i	0.0167615	−	0.0290318i
$365$	2.55132	+	4.41902i	0.133542	+	0.231302i
$366$	−8.34385	+	14.4520i	−0.436140	+	0.755417i
$367$	−17.7041	+	30.6644i	−0.924147	+	1.60067i	−0.131221	+	0.991353i	$0.541890\pi$
$367$	−17.7041	+	30.6644i	−0.924147	+	1.60067i	−0.792927	+	0.609317i	$0.791444\pi$
$368$	−3.27206	+	5.66738i	−0.170568	+	0.295432i
$369$	−6.59573	+	11.4241i	−0.343360	+	0.594717i
$370$	−2.78971	+	4.83193i	−0.145030	+	0.251200i
$371$	−0.964096	+	1.66986i	−0.0500534	+	0.0866950i
$372$	−2.15212	−	3.72759i	−0.111582	−	0.193266i
$373$	7.96521	−	13.7961i	0.412423	−	0.714337i	−0.582731	−	0.812665i	$-0.698016\pi$
$373$	7.96521	−	13.7961i	0.412423	−	0.714337i	0.995154	+	0.0983275i	$0.0313493\pi$
$374$	−7.14526	−	12.3760i	−0.369473	−	0.639945i
$375$	1.33046			0.0687045
$376$	3.33357	−	5.77390i	0.171916	−	0.297766i
$377$	2.68865			0.138472
$378$	−4.59147			−0.236160
$379$	−2.19102	−	3.79496i	−0.112545	−	0.194934i	0.804251	−	0.594290i	$-0.202567\pi$
$379$	−2.19102	−	3.79496i	−0.112545	−	0.194934i	−0.916796	+	0.399356i	$0.869234\pi$
$380$	0.864125			0.0443287
$381$	8.80477	−	15.2503i	0.451082	−	0.781297i
$382$	−1.76036	+	3.04903i	−0.0900679	+	0.156002i
$383$	−11.5376	−	19.9838i	−0.589546	−	1.02112i	−0.994292	−	0.106695i	$-0.965973\pi$
$383$	−11.5376	−	19.9838i	−0.589546	−	1.02112i	0.404745	−	0.914429i	$-0.367360\pi$
$384$	−0.665228	−	1.15221i	−0.0339473	−	0.0587984i
$385$	−1.31759	−	2.28213i	−0.0671505	−	0.116308i
$386$	2.86728	+	4.96627i	0.145941	+	0.252777i
$387$	7.74074			0.393484
$388$	5.44020			0.276184
$389$	6.06060	+	10.4973i	0.307285	+	0.532233i	0.977767	−	0.209692i	$-0.0672462\pi$
$389$	6.06060	+	10.4973i	0.307285	+	0.532233i	−0.670483	+	0.741925i	$0.733913\pi$
$390$	−0.521486	+	0.903240i	−0.0264065	+	0.0457373i
$391$	−14.4771	+	25.0751i	−0.732140	+	1.26810i
$392$	−3.16718	−	5.48571i	−0.159967	−	0.277070i
$393$	4.80944			0.242604
$394$	−4.68852			−0.236204
$395$	0.749748	−	1.29860i	0.0377239	−	0.0653397i
$396$	−1.98619	−	3.44019i	−0.0998100	−	0.172876i
$397$	19.7337			0.990406			0.495203	−	0.868777i	$-0.335094\pi$
$397$	19.7337			0.990406			0.495203	+	0.868777i	$0.335094\pi$
$398$	−7.16333	+	12.4072i	−0.359065	+	0.621919i
$399$	0.937994			0.0469584
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	8.36352			0.417654			0.208827	−	0.977953i	$-0.433035\pi$
$401$	8.36352			0.417654			0.208827	+	0.977953i	$0.433035\pi$
$402$	7.95341	+	7.43915i	0.396680	+	0.371031i
$403$	2.53611			0.126333
$404$	5.88053	+	10.1854i	0.292567	+	0.506741i
$405$	3.79773			0.188711
$406$	−1.39912	+	2.42335i	−0.0694371	+	0.120269i
$407$	−18.0209			−0.893263
$408$	−2.94328	−	5.09791i	−0.145714	−	0.252384i
$409$	−6.34375	+	10.9877i	−0.313678	+	0.543307i	−0.979156	−	0.203111i	$-0.934895\pi$
$409$	−6.34375	+	10.9877i	−0.313678	+	0.543307i	0.665477	+	0.746418i	$0.268228\pi$
$410$	−10.7258			−0.529707
$411$	19.2792			0.950973
$412$	−2.20010	−	3.81069i	−0.108391	−	0.187739i
$413$	2.37511	−	4.11382i	0.116872	−	0.202428i
$414$	−4.02426	+	6.97022i	−0.197782	+	0.342568i
$415$	−5.04959	−	8.74615i	−0.247875	−	0.429332i
$416$	0.783920			0.0384349
$417$	19.3916			0.949609
$418$	1.39551	+	2.41710i	0.0682567	+	0.118224i
$419$	−3.58847	−	6.21542i	−0.175308	−	0.303643i	0.764960	−	0.644078i	$-0.222759\pi$
$419$	−3.58847	−	6.21542i	−0.175308	−	0.303643i	−0.940268	+	0.340435i	$0.889426\pi$
$420$	−0.542742	−	0.940057i	−0.0264831	−	0.0458701i
$421$	3.57329	+	6.18912i	0.174151	+	0.301639i	0.939867	−	0.341540i	$-0.110948\pi$
$421$	3.57329	+	6.18912i	0.174151	+	0.301639i	−0.765716	+	0.643179i	$0.777615\pi$
$422$	11.7643	−	20.3764i	0.572679	−	0.991908i
$423$	4.09990	−	7.10124i	0.199344	−	0.345274i
$424$	−2.36335			−0.114774
$425$	−2.21223	−	3.83170i	−0.107309	−	0.185865i
$426$	1.92931			0.0934755
$427$	10.2334			0.495228
$428$	0.983343	−	1.70320i	0.0475317	−	0.0823273i
$429$	−3.36868			−0.162641
$430$	3.14694	+	5.45065i	0.151759	+	0.262854i
$431$	6.09417	−	10.5554i	0.293546	−	0.508436i	−0.681100	−	0.732191i	$-0.738498\pi$
$431$	6.09417	−	10.5554i	0.293546	−	0.508436i	0.974646	+	0.223754i	$0.0718314\pi$
$432$	−2.81384	−	4.87371i	−0.135381	−	0.234487i
$433$	10.5265	−	18.2324i	0.505870	−	0.876192i	−0.494107	−	0.869401i	$-0.664505\pi$
$433$	10.5265	−	18.2324i	0.505870	−	0.876192i	0.999977	−	0.00679133i	$-0.00216176\pi$
$434$	−1.31974	+	2.28586i	−0.0633497	+	0.109725i
$435$	2.28156	−	3.95179i	0.109393	−	0.189474i
$436$	3.35334	−	5.80815i	0.160596	−	0.278160i
$437$	2.82747	−	4.89732i	0.135256	−	0.234271i
$438$	−3.39442	+	5.87931i	−0.162192	+	0.280924i
$439$	−4.57010	−	7.91564i	−0.218119	−	0.377793i	0.736114	−	0.676858i	$-0.236659\pi$
$439$	−4.57010	−	7.91564i	−0.218119	−	0.377793i	−0.954233	+	0.299065i	$0.903325\pi$
$440$	1.61494	−	2.79716i	0.0769894	−	0.133350i
$441$	−3.89526	−	6.74679i	−0.185489	−	0.321276i
$442$	3.46843			0.164976
$443$	1.03913	−	1.79983i	0.0493708	−	0.0855127i	−0.840284	−	0.542147i	$-0.817612\pi$
$443$	1.03913	−	1.79983i	0.0493708	−	0.0855127i	0.889655	+	0.456634i	$0.150945\pi$
$444$	−7.42319			−0.352289
$445$	−1.74447			−0.0826957
$446$	−1.65629	−	2.86878i	−0.0784277	−	0.135841i
$447$	−14.3637			−0.679380
$448$	−0.407937	+	0.706567i	−0.0192732	+	0.0333822i
$449$	−6.87880	+	11.9144i	−0.324631	+	0.562277i	−0.981438	−	0.191782i	$-0.938573\pi$
$449$	−6.87880	+	11.9144i	−0.324631	+	0.562277i	0.656807	+	0.754059i	$0.271907\pi$
$450$	−0.614943	−	1.06511i	−0.0289887	−	0.0502099i
$451$	−17.3215	−	30.0017i	−0.815637	−	1.41272i
$452$	−6.15427	−	10.6595i	−0.289472	−	0.501381i
$453$	−3.82471	−	6.62460i	−0.179701	−	0.311251i
$454$	14.9366			0.701007
$455$	0.639580			0.0299840
$456$	0.574840	+	0.995653i	0.0269194	+	0.0466257i
$457$	−11.1635	+	19.3357i	−0.522204	+	0.904485i	0.477462	+	0.878652i	$0.341557\pi$
$457$	−11.1635	+	19.3357i	−0.522204	+	0.904485i	−0.999666	+	0.0258321i	$0.991776\pi$
$458$	9.48620	−	16.4306i	0.443261	−	0.767751i
$459$	−12.4497	−	21.5636i	−0.581104	−	1.00650i
$460$	−6.54412			−0.305121
$461$	−0.984155			−0.0458367			−0.0229183	−	0.999737i	$-0.507296\pi$
$461$	−0.984155			−0.0458367			−0.0229183	+	0.999737i	$0.507296\pi$
$462$	1.75299	−	3.03628i	0.0815567	−	0.141260i
$463$	6.95956	+	12.0543i	0.323438	+	0.560211i	0.981195	−	0.193019i	$-0.0618279\pi$
$463$	6.95956	+	12.0543i	0.323438	+	0.560211i	−0.657757	+	0.753230i	$0.728495\pi$
$464$	−3.42975			−0.159222
$465$	2.15212	−	3.72759i	0.0998023	−	0.172863i
$466$	−18.1145			−0.839140
$467$	−8.75167	−	15.1583i	−0.404979	−	0.701445i	0.589340	−	0.807885i	$-0.299388\pi$
$467$	−8.75167	−	15.1583i	−0.404979	−	0.701445i	−0.994319	+	0.106441i	$0.966055\pi$
$468$	0.964132			0.0445670
$469$	1.51209	−	6.50478i	0.0698217	−	0.300363i
$470$	6.66713			0.307532
$471$	−0.213929	−	0.370535i	−0.00985732	−	0.0170734i
$472$	5.82226			0.267991
$473$	−10.1642	+	17.6050i	−0.467352	+	0.809478i
$474$	1.99501			0.0916340
$475$	0.432062	+	0.748354i	0.0198244	+	0.0343368i
$476$	−1.80490	+	3.12618i	−0.0827276	+	0.143288i
$477$	−2.90665			−0.133086
$478$	13.5738			0.620849
$479$	−15.8319	−	27.4217i	−0.723380	−	1.25293i	−0.959637	−	0.281241i	$-0.909254\pi$
$479$	−15.8319	−	27.4217i	−0.723380	−	1.25293i	0.236257	−	0.971691i	$-0.424079\pi$
$480$	0.665228	−	1.15221i	0.0303634	−	0.0525909i
$481$	2.18691	−	3.78784i	0.0997147	−	0.172711i
$482$	8.94587	+	15.4947i	0.407473	+	0.705764i
$483$	−7.10354			−0.323222
$484$	−0.567841			−0.0258109
$485$	2.72010	+	4.71135i	0.123513	+	0.213932i
$486$	−5.91516	−	10.2454i	−0.268317	−	0.464739i
$487$	4.45897	+	7.72317i	0.202055	+	0.349970i	0.949191	−	0.314702i	$-0.101905\pi$
$487$	4.45897	+	7.72317i	0.202055	+	0.349970i	−0.747135	+	0.664672i	$0.768571\pi$
$488$	6.27142	+	10.8624i	0.283894	+	0.491719i
$489$	6.00905	−	10.4080i	0.271739	−	0.470665i
$490$	3.16718	−	5.48571i	0.143078	−	0.247819i
$491$	14.3009			0.645391			0.322696	−	0.946503i	$-0.395411\pi$
$491$	14.3009			0.645391			0.322696	+	0.946503i	$0.395411\pi$
$492$	−7.13508	−	12.3583i	−0.321674	−	0.557156i
$493$	−15.1748			−0.683439
$494$	−0.677405			−0.0304779
$495$	1.98619	−	3.44019i	0.0892728	−	0.154625i
$496$	−3.23516			−0.145263
$497$	−0.591554	−	1.02460i	−0.0265348	−	0.0459597i
$498$	6.71826	−	11.6364i	0.301053	−	0.521438i
$499$	−5.70771	−	9.88604i	−0.255512	−	0.442560i	0.709522	−	0.704683i	$-0.248911\pi$
$499$	−5.70771	−	9.88604i	−0.255512	−	0.442560i	−0.965034	+	0.262123i	$0.915577\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−12.6212	+	21.8606i	−0.563874	+	0.976658i
$502$	−7.61934	+	13.1971i	−0.340068	+	0.589015i
$503$	−1.12882	+	1.95518i	−0.0503317	+	0.0871771i	−0.890094	−	0.455778i	$-0.849361\pi$
$503$	−1.12882	+	1.95518i	−0.0503317	+	0.0871771i	0.839762	+	0.542955i	$0.182695\pi$
$504$	−0.501715	+	0.868997i	−0.0223482	+	0.0387082i
$505$	−5.88053	+	10.1854i	−0.261680	+	0.453243i
$506$	−10.5684	−	18.3050i	−0.469822	−	0.813756i
$507$	−8.23916	+	14.2707i	−0.365914	+	0.633782i
$508$	−6.61785	−	11.4625i	−0.293620	−	0.508564i
$509$	−39.2212			−1.73845			−0.869225	−	0.494417i	$-0.835382\pi$
$509$	−39.2212			−1.73845			−0.869225	+	0.494417i	$0.835382\pi$
$510$	2.94328	−	5.09791i	0.130331	−	0.225739i
$511$	4.16311			0.184165
$512$	−1.00000			−0.0441942
$513$	2.43151	+	4.21150i	0.107354	+	0.185942i
$514$	18.3866			0.810998
$515$	2.20010	−	3.81069i	0.0969481	−	0.167919i
$516$	−4.18686	+	7.25186i	−0.184316	+	0.319245i
$517$	10.7670	+	18.6490i	0.473534	+	0.820184i
$518$	2.27605	+	3.94224i	0.100004	+	0.173212i
$519$	13.4010	+	23.2112i	0.588238	+	1.01886i
$520$	0.391960	+	0.678895i	0.0171886	+	0.0297715i
$521$	8.49156			0.372022			0.186011	−	0.982548i	$-0.440444\pi$
$521$	8.49156			0.372022			0.186011	+	0.982548i	$0.440444\pi$
$522$	−4.21819			−0.184625
$523$	−4.37638	−	7.58012i	−0.191366	−	0.331455i	0.754337	−	0.656487i	$-0.227958\pi$
$523$	−4.37638	−	7.58012i	−0.191366	−	0.331455i	−0.945703	+	0.325032i	$0.894625\pi$
$524$	1.80744	−	3.13058i	0.0789584	−	0.136760i
$525$	0.542742	−	0.940057i	0.0236872	−	0.0410274i
$526$	7.87857	+	13.6461i	0.343522	+	0.594998i
$527$	−14.3139			−0.623522
$528$	4.29722			0.187013
$529$	−9.91278	+	17.1694i	−0.430990	+	0.746497i
$530$	−1.18167	−	2.04672i	−0.0513286	−	0.0889038i
$531$	7.16071			0.310748
$532$	0.352508	−	0.610562i	0.0152832	−	0.0264712i
$533$	8.40814			0.364197
$534$	−1.16047	−	2.00999i	−0.0502184	−	0.0869809i
$535$	1.96669			0.0850272
$536$	7.83129	−	2.38135i	0.338260	−	0.102859i
$537$	−7.55253			−0.325916
$538$	−1.56724	−	2.71455i	−0.0675687	−	0.117032i
$539$	20.4592			0.881241
$540$	2.81384	−	4.87371i	0.121088	−	0.209731i
$541$	−32.7003			−1.40589			−0.702947	−	0.711242i	$-0.748133\pi$
$541$	−32.7003			−1.40589			−0.702947	+	0.711242i	$0.748133\pi$
$542$	1.94966	+	3.37691i	0.0837452	+	0.145051i
$543$	−10.0352	+	17.3814i	−0.430651	+	0.745909i
$544$	−4.42447			−0.189697
$545$	6.70667			0.287282
$546$	0.425467	+	0.736930i	0.0182083	+	0.0315377i
$547$	−3.94701	+	6.83643i	−0.168762	+	0.292305i	−0.937985	−	0.346676i	$-0.887310\pi$
$547$	−3.94701	+	6.83643i	−0.168762	+	0.292305i	0.769223	+	0.638981i	$0.220644\pi$
$548$	7.24534	−	12.5493i	0.309505	−	0.536079i
$549$	7.71313	+	13.3595i	0.329188	+	0.570171i
$550$	3.22989			0.137723
$551$	2.96373			0.126259
$552$	−4.35334	−	7.54020i	−0.185290	−	0.320932i
$553$	−0.611699	−	1.05949i	−0.0260121	−	0.0450543i
$554$	−8.44535	−	14.6278i	−0.358808	−	0.621474i
$555$	−3.71159	−	6.42867i	−0.157548	−	0.272882i
$556$	7.28756	−	12.6224i	0.309061	−	0.535310i
$557$	16.9680	−	29.3894i	0.718956	−	1.24527i	−0.242458	−	0.970162i	$-0.577954\pi$
$557$	16.9680	−	29.3894i	0.718956	−	1.24527i	0.961414	−	0.275106i	$-0.0887131\pi$
$558$	−3.97888			−0.168439
$559$	−2.46695	−	4.27288i	−0.104341	−	0.180723i
$560$	−0.815873			−0.0344769
$561$	19.0129			0.802726
$562$	−13.7735	+	23.8564i	−0.581000	+	1.00632i
$563$	−25.5075			−1.07501			−0.537506	−	0.843260i	$-0.680634\pi$
$563$	−25.5075			−1.07501			−0.537506	+	0.843260i	$0.680634\pi$
$564$	4.43516	+	7.68193i	0.186754	+	0.323468i
$565$	6.15427	−	10.6595i	0.258912	−	0.448449i
$566$	10.3082	+	17.8543i	0.433286	+	0.750474i
$567$	1.54923	−	2.68335i	0.0650616	−	0.112690i
$568$	0.725057	−	1.25583i	0.0304227	−	0.0526937i
$569$	−11.5764	+	20.0509i	−0.485307	+	0.840577i	−0.999857	−	0.0168833i	$-0.994626\pi$
$569$	−11.5764	+	20.0509i	−0.485307	+	0.840577i	0.514550	+	0.857460i	$0.327959\pi$
$570$	−0.574840	+	0.995653i	−0.0240774	+	0.0417033i
$571$	−9.18699	+	15.9123i	−0.384463	+	0.665910i	−0.991695	−	0.128615i	$-0.958947\pi$
$571$	−9.18699	+	15.9123i	−0.384463	+	0.665910i	0.607231	+	0.794525i	$0.292280\pi$
$572$	−1.26599	+	2.19275i	−0.0529336	+	0.0916836i
$573$	−2.34208	−	4.05661i	−0.0978419	−	0.169467i
$574$	−4.37543	+	7.57847i	−0.182627	+	0.316319i
$575$	−3.27206	−	5.66738i	−0.136454	−	0.236346i
$576$	−1.22989			−0.0512452
$577$	−8.94786	+	15.4981i	−0.372504	+	0.645196i	−0.989950	−	0.141417i	$-0.954834\pi$
$577$	−8.94786	+	15.4981i	−0.372504	+	0.645196i	0.617446	+	0.786613i	$0.288167\pi$
$578$	−2.57591			−0.107144
$579$	−7.62958			−0.317074
$580$	−1.71487	−	2.97025i	−0.0712062	−	0.123333i
$581$	−8.23966			−0.341839
$582$	−3.61898	+	6.26825i	−0.150011	+	0.259827i
$583$	3.81667	−	6.61067i	0.158070	−	0.273786i
$584$	2.55132	+	4.41902i	0.105574	+	0.182860i
$585$	0.482066	+	0.834963i	0.0199310	+	0.0345215i
$586$	14.6863	+	25.4375i	0.606687	+	1.05081i
$587$	7.82538	+	13.5540i	0.322988	+	0.559432i	0.981103	−	0.193486i	$-0.0619793\pi$
$587$	7.82538	+	13.5540i	0.322988	+	0.559432i	−0.658115	+	0.752917i	$0.728646\pi$
$588$	8.42758			0.347547
$589$	2.79559			0.115190
$590$	2.91113	+	5.04223i	0.119849	+	0.207585i
$591$	3.11894	−	5.40216i	0.128296	−	0.222215i
$592$	−2.78971	+	4.83193i	−0.114657	+	0.198591i
$593$	−5.81017	−	10.0635i	−0.238595	−	0.413259i	0.721716	−	0.692189i	$-0.243354\pi$
$593$	−5.81017	−	10.0635i	−0.238595	−	0.413259i	−0.960311	+	0.278930i	$0.910020\pi$
$594$	18.1768			0.745801
$595$	−3.60980			−0.147988
$596$	−5.39804	+	9.34967i	−0.221112	+	0.382977i
$597$	−9.53050	−	16.5073i	−0.390057	−	0.675599i
$598$	5.13007			0.209784
$599$	−14.6104	+	25.3060i	−0.596965	+	1.03397i	0.396301	+	0.918121i	$0.370294\pi$
$599$	−14.6104	+	25.3060i	−0.596965	+	1.03397i	−0.993266	+	0.115854i	$0.963040\pi$
$600$	1.33046			0.0543157
$601$	−0.226313	−	0.391986i	−0.00923151	−	0.0159894i	0.861373	−	0.507973i	$-0.169605\pi$
$601$	−0.226313	−	0.391986i	−0.00923151	−	0.0159894i	−0.870604	+	0.491984i	$0.836272\pi$
$602$	5.13500			0.209287
$603$	9.63159	−	2.92879i	0.392229	−	0.119270i
$604$	−5.74947			−0.233943
$605$	−0.283920	−	0.491765i	−0.0115430	−	0.0199931i
$606$	−15.6476			−0.635640
$607$	−12.2002	+	21.1314i	−0.495193	+	0.857699i	−0.999985	−	0.00554204i	$-0.998236\pi$
$607$	−12.2002	+	21.1314i	−0.495193	+	0.857699i	0.504792	+	0.863241i	$0.331569\pi$
$608$	0.864125			0.0350449
$609$	−1.86147	−	3.22416i	−0.0754305	−	0.130649i
$610$	−6.27142	+	10.8624i	−0.253922	+	0.439807i
$611$	−5.22650			−0.211442
$612$	−5.44159			−0.219963
$613$	−2.39527	−	4.14873i	−0.0967441	−	0.167566i	0.813591	−	0.581437i	$-0.197510\pi$
$613$	−2.39527	−	4.14873i	−0.0967441	−	0.167566i	−0.910335	+	0.413872i	$0.864176\pi$
$614$	−0.0210323	+	0.0364289i	−0.000848793	+	0.00147015i
$615$	7.13508	−	12.3583i	0.287714	−	0.498335i
$616$	−1.31759	−	2.28213i	−0.0530872	−	0.0919497i
$617$	14.1260			0.568692			0.284346	−	0.958722i	$-0.408224\pi$
$617$	14.1260			0.568692			0.284346	+	0.958722i	$0.408224\pi$
$618$	5.85428			0.235494
$619$	12.9107	+	22.3620i	0.518926	+	0.898806i	0.999758	+	0.0219932i	$0.00700120\pi$
$619$	12.9107	+	22.3620i	0.518926	+	0.898806i	−0.480832	+	0.876813i	$0.659665\pi$
$620$	−1.61758	−	2.80173i	−0.0649637	−	0.112520i
$621$	−18.4141	−	31.8942i	−0.738933	−	1.27987i
$622$	11.9625	+	20.7196i	0.479651	+	0.830780i
$623$	−0.711633	+	1.23258i	−0.0285110	+	0.0493824i
$624$	−0.521486	+	0.903240i	−0.0208761	+	0.0361585i
$625$	1.00000			0.0400000
$626$	10.4240	+	18.0549i	0.416626	+	0.721618i
$627$	−3.71334			−0.148296
$628$	−0.321587			−0.0128327
$629$	−12.3430	+	21.3787i	−0.492147	+	0.852424i
$630$	−1.00343			−0.0399776
$631$	4.05743	+	7.02767i	0.161524	+	0.279767i	0.935415	−	0.353551i	$-0.115026\pi$
$631$	4.05743	+	7.02767i	0.161524	+	0.279767i	−0.773892	+	0.633318i	$0.781693\pi$
$632$	0.749748	−	1.29860i	0.0298234	−	0.0516556i
$633$	15.6519	+	27.1099i	0.622108	+	1.07752i
$634$	14.4623	−	25.0494i	0.574371	−	0.994840i
$635$	6.61785	−	11.4625i	0.262622	−	0.454874i
$636$	1.57217	−	2.72307i	0.0623404	−	0.107977i
$637$	−2.48281	+	4.30036i	−0.0983726	+	0.170386i
$638$	5.53884	−	9.59356i	0.219285	−	0.379813i
$639$	0.891736	−	1.54453i	0.0352765	−	0.0611008i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−5.36370	+	9.29020i	−0.211853	+	0.366941i	−0.952295	−	0.305180i	$-0.901283\pi$
$641$	−5.36370	+	9.29020i	−0.211853	+	0.366941i	0.740441	+	0.672121i	$0.234617\pi$
$642$	1.30829	+	2.26603i	0.0516343	+	0.0894332i
$643$	32.9360			1.29887			0.649434	−	0.760418i	$-0.275006\pi$
$643$	32.9360			1.29887			0.649434	+	0.760418i	$0.275006\pi$
$644$	−2.66959	+	4.62386i	−0.105197	+	0.182206i
$645$	−8.37372			−0.329715
$646$	3.82329			0.150425
$647$	14.9105	+	25.8258i	0.586193	+	1.01532i	0.994726	+	0.102572i	$0.0327072\pi$
$647$	14.9105	+	25.8258i	0.586193	+	1.01532i	−0.408533	+	0.912744i	$0.633959\pi$
$648$	3.79773			0.149189
$649$	−9.40262	+	16.2858i	−0.369085	+	0.639274i
$650$	−0.391960	+	0.678895i	−0.0153739	+	0.0266285i
$651$	−1.75586	−	3.04124i	−0.0688176	−	0.119196i
$652$	−4.51653	−	7.82286i	−0.176881	−	0.306367i
$653$	4.22641	+	7.32035i	0.165392	+	0.286467i	0.936794	−	0.349880i	$-0.113778\pi$
$653$	4.22641	+	7.32035i	0.165392	+	0.286467i	−0.771402	+	0.636348i	$0.780444\pi$
$654$	4.46147	+	7.72749i	0.174457	+	0.302169i
$655$	3.61488			0.141245
$656$	−10.7258			−0.418770
$657$	3.13783	+	5.43488i	0.122418	+	0.212035i
$658$	2.71977	−	4.71078i	0.106028	−	0.183645i
$659$	−0.00210435	+	0.00364485i	−8.19740e−5	+	0.000141983i	−0.866066	−	0.499929i	$-0.833359\pi$
$659$	−0.00210435	+	0.00364485i	−8.19740e−5	+	0.000141983i	0.865984	+	0.500071i	$0.166693\pi$
$660$	2.14861	+	3.72150i	0.0836346	+	0.144859i
$661$	−2.26350			−0.0880399			−0.0440199	−	0.999031i	$-0.514017\pi$
$661$	−2.26350			−0.0880399			−0.0440199	+	0.999031i	$0.514017\pi$
$662$	−34.9567			−1.35863
$663$	−2.30730	+	3.99636i	−0.0896080	+	0.155206i
$664$	−5.04959	−	8.74615i	−0.195962	−	0.339416i
$665$	0.705017			0.0273394
$666$	−3.43103	+	5.94271i	−0.132950	+	0.230276i
$667$	−22.4447			−0.869062
$668$	9.48637	+	16.4309i	0.367039	+	0.635730i
$669$	4.40725			0.170394
$670$	5.97796	+	5.59142i	0.230949	+	0.216016i
$671$	−40.5119			−1.56395
$672$	−0.542742	−	0.940057i	−0.0209367	−	0.0362635i
$673$	8.06735			0.310973			0.155487	−	0.987838i	$-0.450305\pi$
$673$	8.06735			0.310973			0.155487	+	0.987838i	$0.450305\pi$
$674$	−14.1024	+	24.4261i	−0.543206	+	0.940860i
$675$	5.62768			0.216609
$676$	6.19273	+	10.7261i	0.238182	+	0.412543i
$677$	−11.9595	+	20.7145i	−0.459641	+	0.796122i	−0.998942	−	0.0459914i	$-0.985355\pi$
$677$	−11.9595	+	20.7145i	−0.459641	+	0.796122i	0.539301	+	0.842113i	$0.318689\pi$
$678$	16.3760			0.628915
$679$	4.43852			0.170335
$680$	−2.21223	−	3.83170i	−0.0848353	−	0.146939i
$681$	−9.93622	+	17.2100i	−0.380757	+	0.659490i
$682$	5.22461	−	9.04928i	0.200060	−	0.346515i
$683$	−8.54311	−	14.7971i	−0.326893	−	0.566196i	0.655000	−	0.755628i	$-0.272668\pi$
$683$	−8.54311	−	14.7971i	−0.326893	−	0.566196i	−0.981894	+	0.189433i	$0.939335\pi$
$684$	1.06277			0.0406362
$685$	14.4907			0.553660
$686$	−5.43957	−	9.42161i	−0.207684	−	0.359719i
$687$	12.6210	+	21.8602i	0.481520	+	0.834018i
$688$	3.14694	+	5.45065i	0.119976	+	0.207804i
$689$	0.926338	+	1.60446i	0.0352907	+	0.0611252i
$690$	4.35334	−	7.54020i	0.165729	−	0.287050i
$691$	−25.7061	+	44.5243i	−0.977908	+	1.69379i	−0.307923	+	0.951411i	$0.599634\pi$
$691$	−25.7061	+	44.5243i	−0.977908	+	1.69379i	−0.669985	+	0.742375i	$0.733699\pi$
$692$	20.1449			0.765796
$693$	−1.62048	−	2.80676i	−0.0615571	−	0.106620i
$694$	23.4528			0.890257
$695$	14.5751			0.552866
$696$	2.28156	−	3.95179i	0.0864825	−	0.149792i
$697$	−47.4558			−1.79751
$698$	−11.3936	−	19.7343i	−0.431254	−	0.746953i
$699$	12.0503	−	20.8717i	0.455785	−	0.789442i
$700$	−0.407937	−	0.706567i	−0.0154186	−	0.0267057i
$701$	−8.61092	+	14.9145i	−0.325230	+	0.563315i	−0.981559	−	0.191160i	$-0.938775\pi$
$701$	−8.61092	+	14.9145i	−0.325230	+	0.563315i	0.656329	+	0.754475i	$0.272108\pi$
$702$	−2.20583	+	3.82060i	−0.0832535	+	0.144199i
$703$	2.41066	−	4.17539i	0.0909198	−	0.157478i
$704$	1.61494	−	2.79716i	0.0608654	−	0.105422i
$705$	−4.43516	+	7.68193i	−0.167038	+	0.289318i
$706$	6.70762	−	11.6179i	0.252445	−	0.437247i
$707$	4.79777	+	8.30998i	0.180439	+	0.312529i
$708$	−3.87313	+	6.70846i	−0.145561	+	0.252119i
$709$	4.41223	+	7.64221i	0.165705	+	0.287009i	0.936905	−	0.349583i	$-0.113677\pi$
$709$	4.41223	+	7.64221i	0.165705	+	0.287009i	−0.771201	+	0.636592i	$0.780343\pi$
$710$	1.45011			0.0544218
$711$	0.922104	−	1.59713i	0.0345816	−	0.0598971i
$712$	−1.74447			−0.0653767
$713$	−21.1713			−0.792872
$714$	−2.40134	−	4.15925i	−0.0898681	−	0.155656i
$715$	−2.53197			−0.0946904
$716$	−2.83832	+	4.91612i	−0.106073	+	0.183724i
$717$	−9.02964	+	15.6398i	−0.337218	+	0.584079i
$718$	−4.52116	−	7.83088i	−0.168728	−	0.292246i
$719$	5.67851	+	9.83546i	0.211773	+	0.366801i	0.952269	−	0.305259i	$-0.0987430\pi$
$719$	5.67851	+	9.83546i	0.211773	+	0.366801i	−0.740497	+	0.672060i	$0.765410\pi$
$720$	−0.614943	−	1.06511i	−0.0229176	−	0.0396944i
$721$	−1.79501	−	3.10904i	−0.0668495	−	0.115787i
$722$	18.2533			0.679317
$723$	−23.8042			−0.885287
$724$	7.54266	+	13.0643i	0.280321	+	0.485529i
$725$	1.71487	−	2.97025i	0.0636888	−	0.110312i
$726$	0.377744	−	0.654271i	0.0140194	−	0.0242823i
$727$	0.460131	+	0.796971i	0.0170653	+	0.0295580i	0.874432	−	0.485148i	$-0.161234\pi$
$727$	0.460131	+	0.796971i	0.0170653	+	0.0295580i	−0.857367	+	0.514706i	$0.827901\pi$
$728$	0.639580			0.0237044
$729$	27.1329			1.00492
$730$	−2.55132	+	4.41902i	−0.0944286	+	0.163555i
$731$	13.9235	+	24.1162i	0.514980	+	0.891971i
$732$	−16.6877			−0.616795
$733$	21.5635	−	37.3490i	0.796465	−	1.37952i	−0.125440	−	0.992101i	$-0.540034\pi$
$733$	21.5635	−	37.3490i	0.796465	−	1.37952i	0.921905	−	0.387416i	$-0.126632\pi$
$734$	−35.4082			−1.30694
$735$	4.21379	+	7.29850i	0.155428	+	0.269209i
$736$	−6.54412			−0.241220
$737$	−5.98606	+	25.7511i	−0.220499	+	0.948556i
$738$	−13.1915			−0.485584
$739$	18.2189	+	31.5560i	0.670192	+	1.16081i	0.977849	+	0.209310i	$0.0671217\pi$
$739$	18.2189	+	31.5560i	0.670192	+	1.16081i	−0.307657	+	0.951497i	$0.599545\pi$
$740$	−5.57943			−0.205104
$741$	0.450629	−	0.780512i	0.0165543	−	0.0286728i
$742$	−1.92819			−0.0707862
$743$	−8.89353	−	15.4040i	−0.326272	−	0.565119i	0.655497	−	0.755198i	$-0.272459\pi$
$743$	−8.89353	−	15.4040i	−0.326272	−	0.565119i	−0.981769	+	0.190078i	$0.939126\pi$
$744$	2.15212	−	3.72759i	0.0789007	−	0.136660i
$745$	−10.7961			−0.395537
$746$	15.9304			0.583254
$747$	−6.21042	−	10.7568i	−0.227227	−	0.393569i
$748$	7.14526	−	12.3760i	0.261257	−	0.452510i
$749$	0.802283	−	1.38960i	0.0293148	−	0.0507747i
$750$	0.665228	+	1.15221i	0.0242907	+	0.0420727i
$751$	9.28754			0.338907			0.169454	−	0.985538i	$-0.445800\pi$
$751$	9.28754			0.338907			0.169454	+	0.985538i	$0.445800\pi$
$752$	6.66713			0.243125
$753$	−10.1372	−	17.5582i	−0.369420	−	0.639855i
$754$	1.34432	+	2.32844i	0.0489574	+	0.0847967i
$755$	−2.87474	−	4.97919i	−0.104622	−	0.181211i
$756$	−2.29574	−	3.97633i	−0.0834951	−	0.144618i
$757$	−0.356861	+	0.618102i	−0.0129703	+	0.0224653i	−0.872438	−	0.488725i	$-0.837462\pi$
$757$	−0.356861	+	0.618102i	−0.0129703	+	0.0224653i	0.859467	+	0.511191i	$0.170795\pi$
$758$	2.19102	−	3.79496i	0.0795814	−	0.137839i
$759$	28.1216			1.02075
$760$	0.432062	+	0.748354i	0.0156726	+	0.0271457i
$761$	12.1013			0.438670			0.219335	−	0.975650i	$-0.429611\pi$
$761$	12.1013			0.438670			0.219335	+	0.975650i	$0.429611\pi$
$762$	17.6095			0.637926
$763$	2.73590	−	4.73871i	0.0990461	−	0.171553i
$764$	−3.52072			−0.127375
$765$	−2.72079	−	4.71255i	−0.0983705	−	0.170383i
$766$	11.5376	−	19.9838i	0.416872	−	0.722044i
$767$	−2.28209	−	3.95270i	−0.0824016	−	0.142724i
$768$	0.665228	−	1.15221i	0.0240044	−	0.0415768i
$769$	−20.1645	+	34.9259i	−0.727151	+	1.25946i	0.230932	+	0.972970i	$0.425823\pi$
$769$	−20.1645	+	34.9259i	−0.727151	+	1.25946i	−0.958083	+	0.286492i	$0.907511\pi$
$770$	1.31759	−	2.28213i	0.0474826	−	0.0822423i
$771$	−12.2313	+	21.1852i	−0.440499	+	0.762967i
$772$	−2.86728	+	4.96627i	−0.103196	+	0.178740i
$773$	8.30543	−	14.3854i	0.298725	−	0.517408i	−0.677119	−	0.735873i	$-0.736772\pi$
$773$	8.30543	−	14.3854i	0.298725	−	0.517408i	0.975845	+	0.218466i	$0.0701052\pi$
$774$	3.87037	+	6.70368i	0.139118	+	0.240959i
$775$	1.61758	−	2.80173i	0.0581053	−	0.100641i
$776$	2.72010	+	4.71135i	0.0976459	+	0.169128i
$777$	−6.05638			−0.217271
$778$	−6.06060	+	10.4973i	−0.217283	+	0.376345i
$779$	9.26839			0.332075
$780$	−1.04297			−0.0373444
$781$	2.34185	+	4.05620i	0.0837980	+	0.145142i
$782$	−28.9543			−1.03540
$783$	9.65076	−	16.7156i	0.344890	−	0.597367i
$784$	3.16718	−	5.48571i	0.113113	−	0.195918i
$785$	−0.160793	−	0.278502i	−0.00573896	−	0.00994018i
$786$	2.40472	+	4.16510i	0.0857736	+	0.148564i
$787$	4.21876	+	7.30711i	0.150383	+	0.260470i	0.931368	−	0.364079i	$-0.118616\pi$
$787$	4.21876	+	7.30711i	0.150383	+	0.260470i	−0.780985	+	0.624549i	$0.785283\pi$
$788$	−2.34426	−	4.06038i	−0.0835109	−	0.144645i
$789$	−20.9642			−0.746345
$790$	1.49950			0.0533497
$791$	−5.02110	−	8.69681i	−0.178530	−	0.309223i
$792$	1.98619	−	3.44019i	0.0705763	−	0.122242i
$793$	4.91629	−	8.51527i	0.174583	−	0.302386i
$794$	9.86685	+	17.0899i	0.350161	+	0.606497i
$795$	3.14433			0.111518
$796$	−14.3267			−0.507795
$797$	16.6676	−	28.8691i	0.590395	−	1.02259i	−0.403784	−	0.914854i	$-0.632305\pi$
$797$	16.6676	−	28.8691i	0.590395	−	1.02259i	0.994179	−	0.107740i	$-0.0343614\pi$
$798$	0.468997	+	0.812327i	0.0166023	+	0.0287560i
$799$	29.4985			1.04358
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−2.14550			−0.0758074
$802$	4.18176	+	7.24302i	0.147663	+	0.255760i
$803$	−16.4809			−0.581600
$804$	−2.46578	+	10.6074i	−0.0869615	+	0.374095i
$805$	−5.33918			−0.188181
$806$	1.26806	+	2.19634i	0.0446654	+	0.0773627i
$807$	4.17030			0.146802
$808$	−5.88053	+	10.1854i	−0.206876	+	0.358320i
$809$	−24.4913			−0.861069			−0.430535	−	0.902574i	$-0.641675\pi$
$809$	−24.4913			−0.861069			−0.430535	+	0.902574i	$0.641675\pi$
$810$	1.89886	+	3.28893i	0.0667192	+	0.115561i
$811$	14.5457	−	25.1939i	0.510769	−	0.884679i	−0.489153	−	0.872198i	$-0.662694\pi$
$811$	14.5457	−	25.1939i	0.510769	−	0.884679i	0.999922	−	0.0124804i	$-0.00397273\pi$
$812$	−2.79824			−0.0981989
$813$	−5.18788			−0.181947
$814$	−9.01045	−	15.6066i	−0.315816	−	0.547010i
$815$	4.51653	−	7.82286i	0.158207	−	0.274023i
$816$	2.94328	−	5.09791i	0.103035	−	0.178463i
$817$	−2.71935	−	4.71004i	−0.0951379	−	0.164784i
$818$	−12.6875			−0.443608
$819$	0.786610			0.0274864
$820$	−5.36288	−	9.28878i	−0.187280	−	0.324378i
$821$	−2.62059	−	4.53899i	−0.0914592	−	0.158412i	0.816666	−	0.577110i	$-0.195820\pi$
$821$	−2.62059	−	4.53899i	−0.0914592	−	0.158412i	−0.908125	+	0.418698i	$0.862486\pi$
$822$	9.63960	+	16.6963i	0.336220	+	0.582350i
$823$	1.22276	+	2.11789i	0.0426229	+	0.0738250i	0.886550	−	0.462633i	$-0.153095\pi$
$823$	1.22276	+	2.11789i	0.0426229	+	0.0738250i	−0.843927	+	0.536458i	$0.819762\pi$
$824$	2.20010	−	3.81069i	0.0766442	−	0.132752i
$825$	−2.14861	+	3.72150i	−0.0748050	+	0.129566i
$826$	4.75023			0.165282
$827$	−12.9406	−	22.4138i	−0.449989	−	0.779404i	0.548395	−	0.836219i	$-0.315239\pi$
$827$	−12.9406	−	22.4138i	−0.449989	−	0.779404i	−0.998385	+	0.0568147i	$0.981906\pi$
$828$	−8.04852			−0.279705
$829$	47.5496			1.65147			0.825733	−	0.564061i	$-0.190762\pi$
$829$	47.5496			1.65147			0.825733	+	0.564061i	$0.190762\pi$
$830$	5.04959	−	8.74615i	0.175274	−	0.303583i
$831$	22.4723			0.779557
$832$	0.391960	+	0.678895i	0.0135888	+	0.0235364i
$833$	14.0131	−	24.2713i	0.485524	−	0.840952i
$834$	9.69578	+	16.7936i	0.335737	+	0.581514i
$835$	−9.48637	+	16.4309i	−0.328289	+	0.568614i
$836$	−1.39551	+	2.41710i	−0.0482648	+	0.0835971i
$837$	9.10323	−	15.7673i	0.314654	−	0.544996i
$838$	3.58847	−	6.21542i	0.123962	−	0.214708i
$839$	15.5949	−	27.0111i	0.538395	−	0.932527i	−0.460596	−	0.887610i	$-0.652364\pi$
$839$	15.5949	−	27.0111i	0.538395	−	0.932527i	0.998991	−	0.0449172i	$-0.0143024\pi$
$840$	0.542742	−	0.940057i	0.0187264	−	0.0324350i
$841$	8.61842	+	14.9275i	0.297187	+	0.514743i
$842$	−3.57329	+	6.18912i	−0.123144	+	0.213291i
$843$	−18.3250	−	31.7399i	−0.631148	−	1.09318i
$844$	23.5287			0.809890
$845$	−6.19273	+	10.7261i	−0.213037	+	0.368990i
$846$	8.19981			0.281915
$847$	−0.463286			−0.0159187
$848$	−1.18167	−	2.04672i	−0.0405788	−	0.0702846i
$849$	−27.4292			−0.941369
$850$	2.21223	−	3.83170i	0.0758790	−	0.131426i
$851$	−18.2562	+	31.6207i	−0.625815	+	1.08394i
$852$	0.964656	+	1.67083i	0.0330486	+	0.0572418i
$853$	−9.55568	−	16.5509i	−0.327180	−	0.566693i	0.654771	−	0.755827i	$-0.272765\pi$
$853$	−9.55568	−	16.5509i	−0.327180	−	0.566693i	−0.981951	+	0.189135i	$0.939432\pi$
$854$	5.11669	+	8.86236i	0.175089	+	0.303264i
$855$	0.531387	+	0.920390i	0.0181731	+	0.0314767i
$856$	1.96669			0.0672199
$857$	0.610439			0.0208522			0.0104261	−	0.999946i	$-0.496681\pi$
$857$	0.610439			0.0208522			0.0104261	+	0.999946i	$0.496681\pi$
$858$	−1.68434	−	2.91736i	−0.0575024	−	0.0995971i
$859$	23.7717	−	41.1738i	0.811081	−	1.40483i	−0.101027	−	0.994884i	$-0.532213\pi$
$859$	23.7717	−	41.1738i	0.811081	−	1.40483i	0.912108	−	0.409950i	$-0.134454\pi$
$860$	−3.14694	+	5.45065i	−0.107310	+	0.185866i
$861$	−5.82132	−	10.0828i	−0.198390	−	0.343622i
$862$	12.1883			0.415136
$863$	31.1687			1.06100			0.530498	−	0.847686i	$-0.322005\pi$
$863$	31.1687			1.06100			0.530498	+	0.847686i	$0.322005\pi$
$864$	2.81384	−	4.87371i	0.0957288	−	0.165807i
$865$	10.0725	+	17.4460i	0.342474	+	0.593183i
$866$	21.0529			0.715408
$867$	1.71357	−	2.96798i	0.0581958	−	0.100798i
$868$	−2.63949			−0.0895900
$869$	2.42160	+	4.19433i	0.0821472	+	0.142283i
$870$	4.56313			0.154705
$871$	−4.68624	−	4.38323i	−0.158787	−	0.148520i
$872$	6.70667			0.227117
$873$	3.34541	+	5.79442i	0.113225	+	0.196112i
$874$	5.65494			0.191281
$875$	0.407937	−	0.706567i	0.0137908	−	0.0238863i
$876$	−6.78884			−0.229374
$877$	−9.30825	−	16.1224i	−0.314317	−	0.544414i	0.664975	−	0.746866i	$-0.268442\pi$
$877$	−9.30825	−	16.1224i	−0.314317	−	0.544414i	−0.979292	+	0.202452i	$0.935109\pi$
$878$	4.57010	−	7.91564i	0.154233	−	0.267140i
$879$	−39.0791			−1.31810
$880$	3.22989			0.108879
$881$	12.4701	+	21.5989i	0.420129	+	0.727685i	0.995952	−	0.0898894i	$-0.0286514\pi$
$881$	12.4701	+	21.5989i	0.420129	+	0.727685i	−0.575822	+	0.817575i	$0.695318\pi$
$882$	3.89526	−	6.74679i	0.131160	−	0.227176i
$883$	22.2208	−	38.4876i	0.747791	−	1.29521i	−0.201089	−	0.979573i	$-0.564448\pi$
$883$	22.2208	−	38.4876i	0.747791	−	1.29521i	0.948880	−	0.315638i	$-0.102219\pi$
$884$	1.73421	+	3.00375i	0.0583280	+	0.101027i
$885$	−7.74626			−0.260388
$886$	2.07827			0.0698208
$887$	7.65626	+	13.2610i	0.257072	+	0.445262i	0.965456	−	0.260565i	$-0.0839089\pi$
$887$	7.65626	+	13.2610i	0.257072	+	0.445262i	−0.708384	+	0.705827i	$0.750576\pi$
$888$	−3.71159	−	6.42867i	−0.124553	−	0.215732i
$889$	−5.39933	−	9.35192i	−0.181088	−	0.313653i
$890$	−0.872234	−	1.51075i	−0.0292374	−	0.0506406i
$891$	−6.13311	+	10.6229i	−0.205467	+	0.355879i
$892$	1.65629	−	2.86878i	0.0554567	−	0.0960539i
$893$	−5.76123			−0.192792
$894$	−7.18185	−	12.4393i	−0.240197	−	0.416033i
$895$	−5.67665			−0.189749
$896$	−0.815873			−0.0272564
$897$	−3.41267	+	5.91092i	−0.113946	+	0.197360i
$898$	−13.7576			−0.459097
$899$	−5.54790	−	9.60924i	−0.185033	−	0.320486i
$900$	0.614943	−	1.06511i	0.0204981	−	0.0355037i
$901$	−5.22828	−	9.05564i	−0.174179	−	0.301687i
$902$	17.3215	−	30.0017i	0.576742	−	0.998947i
$903$	−3.41595	+	5.91660i	−0.113676	+	0.196892i
$904$	6.15427	−	10.6595i	0.204688	−	0.354530i
$905$	−7.54266	+	13.0643i	−0.250726	+	0.434271i
$906$	3.82471	−	6.62460i	0.127068	−	0.220088i
$907$	−2.19494	+	3.80175i	−0.0728818	+	0.126235i	−0.900163	−	0.435553i	$-0.856553\pi$
$907$	−2.19494	+	3.80175i	−0.0728818	+	0.126235i	0.827281	+	0.561788i	$0.189886\pi$
$908$	7.46828	+	12.9354i	0.247844	+	0.429278i
$909$	−7.23238	+	12.5268i	−0.239883	+	0.415489i
$910$	0.319790	+	0.553892i	0.0106009	+	0.0183614i
$911$	−46.3462			−1.53552			−0.767759	−	0.640739i	$-0.778628\pi$
$911$	−46.3462			−1.53552			−0.767759	+	0.640739i	$0.778628\pi$
$912$	−0.574840	+	0.995653i	−0.0190349	+	0.0329694i
$913$	32.6192			1.07954
$914$	−22.3269			−0.738509
$915$	−8.34385	−	14.4520i	−0.275839	−	0.477768i
$916$	18.9724			0.626866
$917$	1.47464	−	2.55416i	0.0486970	−	0.0843457i
$918$	12.4497	−	21.5636i	0.410903	−	0.711704i
$919$	−21.6376	−	37.4775i	−0.713759	−	1.23627i	−0.963436	−	0.267938i	$-0.913658\pi$
$919$	−21.6376	−	37.4775i	−0.713759	−	1.23627i	0.249677	−	0.968329i	$-0.419676\pi$
$920$	−3.27206	−	5.66738i	−0.107877	−	0.186848i
$921$	−0.0279825	−	0.0484671i	−0.000922055	−	0.00159705i
$922$	−0.492078	−	0.852304i	−0.0162057	−	0.0280691i
$923$	−1.13677			−0.0374173
$924$	3.50599			0.115339
$925$	−2.78971	−	4.83193i	−0.0917252	−	0.158873i
$926$	−6.95956	+	12.0543i	−0.228705	+	0.396129i
$927$	2.70587	−	4.68671i	0.0888726	−	0.153932i
$928$	−1.71487	−	2.97025i	−0.0562935	−	0.0975032i
$929$	51.9740			1.70521			0.852606	−	0.522554i	$-0.175021\pi$
$929$	51.9740			1.70521			0.852606	+	0.522554i	$0.175021\pi$
$930$	4.30425			0.141142
$931$	−2.73684	+	4.74034i	−0.0896962	+	0.155358i
$932$	−9.05727	−	15.6877i	−0.296681	−	0.513866i
$933$	−31.8311			−1.04210
$934$	8.75167	−	15.1583i	0.286364	−	0.495996i
$935$	14.2905			0.467350
$936$	0.482066	+	0.834963i	0.0157568	+	0.0272916i
$937$	11.3793			0.371747			0.185873	−	0.982574i	$-0.440489\pi$
$937$	11.3793			0.371747			0.185873	+	0.982574i	$0.440489\pi$
$938$	6.38934	−	1.94288i	0.208619	−	0.0634373i
$939$	−27.7373			−0.905173
$940$	3.33357	+	5.77390i	0.108729	+	0.188324i
$941$	−3.31531			−0.108076			−0.0540380	−	0.998539i	$-0.517209\pi$
$941$	−3.31531			−0.108076			−0.0540380	+	0.998539i	$0.517209\pi$
$942$	0.213929	−	0.370535i	0.00697017	−	0.0120727i
$943$	−70.1907			−2.28572
$944$	2.91113	+	5.04223i	0.0947492	+	0.164110i
$945$	2.29574	−	3.97633i	0.0746803	−	0.129350i
$946$	−20.3285			−0.660936
$947$	−43.5598			−1.41550			−0.707752	−	0.706461i	$-0.750291\pi$
$947$	−43.5598			−1.41550			−0.707752	+	0.706461i	$0.750291\pi$
$948$	0.997507	+	1.72773i	0.0323975	+	0.0561142i
$949$	2.00003	−	3.46416i	0.0649238	−	0.112451i
$950$	−0.432062	+	0.748354i	−0.0140180	+	0.0242798i
$951$	19.2415	+	33.3272i	0.623947	+	1.08071i
$952$	−3.60980			−0.116994
$953$	24.8468			0.804867			0.402433	−	0.915449i	$-0.368164\pi$
$953$	24.8468			0.804867			0.402433	+	0.915449i	$0.368164\pi$
$954$	−1.45332	−	2.51723i	−0.0470531	−	0.0814983i
$955$	−1.76036	−	3.04903i	−0.0569639	−	0.0986644i
$956$	6.78688	+	11.7552i	0.219503	+	0.380191i
$957$	7.36919	+	12.7638i	0.238212	+	0.412595i
$958$	15.8319	−	27.4217i	0.511507	−	0.885956i
$959$	5.91128	−	10.2386i	0.190885	−	0.330623i
$960$	1.33046			0.0429403
$961$	10.2669	+	17.7827i	0.331189	+	0.573636i
$962$	4.37383			0.141018
$963$	2.41880			0.0779447
$964$	−8.94587	+	15.4947i	−0.288127	+	0.499051i
$965$	−5.73456			−0.184602
$966$	−3.55177	−	6.15185i	−0.114276	−	0.197932i
$967$	24.9827	−	43.2713i	0.803390	−	1.39151i	−0.113982	−	0.993483i	$-0.536361\pi$
$967$	24.9827	−	43.2713i	0.803390	−	1.39151i	0.917372	−	0.398030i	$-0.130306\pi$
$968$	−0.283920	−	0.491765i	−0.00912555	−	0.0158059i
$969$	−2.54336	+	4.40523i	−0.0817046	+	0.141516i
$970$	−2.72010	+	4.71135i	−0.0873372	+	0.151272i
$971$	19.8564	−	34.3923i	0.637223	−	1.10370i	−0.348816	−	0.937191i	$-0.613416\pi$
$971$	19.8564	−	34.3923i	0.637223	−	1.10370i	0.986039	−	0.166512i	$-0.0532503\pi$
$972$	5.91516	−	10.2454i	0.189729	−	0.328620i
$973$	5.94572	−	10.2983i	0.190611	−	0.330148i
$974$	−4.45897	+	7.72317i	−0.142875	+	0.247466i
$975$	−0.521486	−	0.903240i	−0.0167009	−	0.0289268i
$976$	−6.27142	+	10.8624i	−0.200743	+	0.347698i
$977$	−30.0477	−	52.0442i	−0.961312	−	1.66504i	−0.719212	−	0.694791i	$-0.755497\pi$
$977$	−30.0477	−	52.0442i	−0.961312	−	1.66504i	−0.242100	−	0.970251i	$-0.577836\pi$
$978$	12.0181			0.384296
$979$	2.81722	−	4.87956i	0.0900386	−	0.155951i
$980$	6.33435			0.202343
$981$	8.24844			0.263352
$982$	7.15046	+	12.3850i	0.228180	+	0.395220i
$983$	21.6290			0.689858			0.344929	−	0.938629i	$-0.387903\pi$
$983$	21.6290			0.689858			0.344929	+	0.938629i	$0.387903\pi$
$984$	7.13508	−	12.3583i	0.227458	−	0.393969i
$985$	2.34426	−	4.06038i	0.0746944	−	0.129375i
$986$	−7.58740	−	13.1418i	−0.241632	−	0.418519i
$987$	3.61853	+	6.26748i	0.115179	+	0.199496i
$988$	−0.338703	−	0.586650i	−0.0107756	−	0.0186638i
$989$	20.5939	+	35.6697i	0.654849	+	1.13423i
$990$	3.97239			0.126251
$991$	−61.7865			−1.96271			−0.981357	−	0.192196i	$-0.938439\pi$
$991$	−61.7865			−1.96271			−0.981357	+	0.192196i	$0.938439\pi$
$992$	−1.61758	−	2.80173i	−0.0513583	−	0.0889552i
$993$	23.2542	−	40.2775i	0.737950	−	1.27817i
$994$	0.591554	−	1.02460i	0.0187630	−	0.0324984i
$995$	−7.16333	−	12.4072i	−0.227093	−	0.393336i
$996$	13.4365			0.425753
$997$	31.2525			0.989777			0.494888	−	0.868957i	$-0.335209\pi$
$997$	31.2525			0.989777			0.494888	+	0.868957i	$0.335209\pi$
$998$	5.70771	−	9.88604i	0.180674	−	0.312937i
$999$	−15.6996	−	27.1925i	−0.496714	−	0.860333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.j.171.3	✓	12
67.29	even	3	inner	670.2.e.j.431.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.j.171.3	✓	12	1.1	even	1	trivial
670.2.e.j.431.3	yes	12	67.29	even	3	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -1.33046 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.665228 - 1.15221i) q^{6} +(-0.407937 + 0.706567i) q^{7} -1.00000 q^{8} -1.22989 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -1.33046 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.665228 - 1.15221i) q^{6} +(-0.407937 + 0.706567i) q^{7} -1.00000 q^{8} -1.22989 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.61494 - 2.79716i) q^{11} +(0.665228 - 1.15221i) q^{12} +(0.391960 + 0.678895i) q^{13} -0.815873 q^{14} +1.33046 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.21223 - 3.83170i) q^{17} +(-0.614943 - 1.06511i) q^{18} +(0.432062 + 0.748354i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.542742 - 0.940057i) q^{21} +3.22989 q^{22} +(-3.27206 - 5.66738i) q^{23} +1.33046 q^{24} +1.00000 q^{25} +(-0.391960 + 0.678895i) q^{26} +5.62768 q^{27} +(-0.407937 - 0.706567i) q^{28} +(1.71487 - 2.97025i) q^{29} +(0.665228 + 1.15221i) q^{30} +(1.61758 - 2.80173i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.14861 + 3.72150i) q^{33} +(2.21223 - 3.83170i) q^{34} +(0.407937 - 0.706567i) q^{35} +(0.614943 - 1.06511i) q^{36} +(-2.78971 - 4.83193i) q^{37} +(-0.432062 + 0.748354i) q^{38} +(-0.521486 - 0.903240i) q^{39} +1.00000 q^{40} +(5.36288 - 9.28878i) q^{41} +1.08548 q^{42} -6.29387 q^{43} +(1.61494 + 2.79716i) q^{44} +1.22989 q^{45} +(3.27206 - 5.66738i) q^{46} +(-3.33357 + 5.77390i) q^{47} +(0.665228 + 1.15221i) q^{48} +(3.16718 + 5.48571i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.94328 + 5.09791i) q^{51} -0.783920 q^{52} +2.36335 q^{53} +(2.81384 + 4.87371i) q^{54} +(-1.61494 + 2.79716i) q^{55} +(0.407937 - 0.706567i) q^{56} +(-0.574840 - 0.995653i) q^{57} +3.42975 q^{58} -5.82226 q^{59} +(-0.665228 + 1.15221i) q^{60} +(-6.27142 - 10.8624i) q^{61} +3.23516 q^{62} +(0.501715 - 0.868997i) q^{63} +1.00000 q^{64} +(-0.391960 - 0.678895i) q^{65} -4.29722 q^{66} +(-7.83129 + 2.38135i) q^{67} +4.42447 q^{68} +(4.35334 + 7.54020i) q^{69} +0.815873 q^{70} +(-0.725057 + 1.25583i) q^{71} +1.22989 q^{72} +(-2.55132 - 4.41902i) q^{73} +(2.78971 - 4.83193i) q^{74} -1.33046 q^{75} -0.864125 q^{76} +(1.31759 + 2.28213i) q^{77} +(0.521486 - 0.903240i) q^{78} +(-0.749748 + 1.29860i) q^{79} +(0.500000 + 0.866025i) q^{80} -3.79773 q^{81} +10.7258 q^{82} +(5.04959 + 8.74615i) q^{83} +(0.542742 + 0.940057i) q^{84} +(2.21223 + 3.83170i) q^{85} +(-3.14694 - 5.45065i) q^{86} +(-2.28156 + 3.95179i) q^{87} +(-1.61494 + 2.79716i) q^{88} +1.74447 q^{89} +(0.614943 + 1.06511i) q^{90} -0.639580 q^{91} +6.54412 q^{92} +(-2.15212 + 3.72759i) q^{93} -6.66713 q^{94} +(-0.432062 - 0.748354i) q^{95} +(-0.665228 + 1.15221i) q^{96} +(-2.72010 - 4.71135i) q^{97} +(-3.16718 + 5.48571i) q^{98} +(-1.98619 + 3.44019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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