LMFDB - Embedded newform 285.2.i.f.106.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.1
Root			$-1.12375 - 1.94639i$ of defining polynomial
Character	$\chi$	$=$	285.106
Dual form			285.2.i.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12375 + 1.94639i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.52562 - 2.64245i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.12375 + 1.94639i) q^{6} +3.16638 q^{7} +2.36264 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.12375 - 1.94639i) q^{10} +4.81770 q^{11} -3.05123 q^{12} +(-0.583191 - 1.01012i) q^{13} +(-3.55821 + 6.16301i) q^{14} +(0.500000 + 0.866025i) q^{15} +(0.396220 - 0.686273i) q^{16} +(-2.92184 + 5.06077i) q^{17} +2.24750 q^{18} +(3.21554 + 2.94284i) q^{19} +3.05123 q^{20} +(1.58319 - 2.74217i) q^{21} +(-5.41388 + 9.37711i) q^{22} +(4.29873 + 7.44562i) q^{23} +(1.18132 - 2.04611i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.62144 q^{26} -1.00000 q^{27} +(-4.83069 - 8.36699i) q^{28} +(-3.65634 - 6.33297i) q^{29} -2.24750 q^{30} -5.10247 q^{31} +(3.25314 + 5.63461i) q^{32} +(2.40885 - 4.17225i) q^{33} +(-6.56681 - 11.3741i) q^{34} +(-1.58319 + 2.74217i) q^{35} +(-1.52562 + 2.64245i) q^{36} +7.26885 q^{37} +(-9.34136 + 2.95167i) q^{38} -1.16638 q^{39} +(-1.18132 + 2.04611i) q^{40} +(1.24750 - 2.16072i) q^{41} +(3.55821 + 6.16301i) q^{42} +(-0.583191 + 1.01012i) q^{43} +(-7.34996 - 12.7305i) q^{44} +1.00000 q^{45} -19.3227 q^{46} +(-4.68830 - 8.12038i) q^{47} +(-0.396220 - 0.686273i) q^{48} +3.02597 q^{49} +2.24750 q^{50} +(2.92184 + 5.06077i) q^{51} +(-1.77945 + 3.08210i) q^{52} +(1.37689 + 2.38485i) q^{53} +(1.12375 - 1.94639i) q^{54} +(-2.40885 + 4.17225i) q^{55} +7.48103 q^{56} +(4.15634 - 1.31332i) q^{57} +16.4352 q^{58} +(5.05626 - 8.75770i) q^{59} +(1.52562 - 2.64245i) q^{60} +(2.55418 + 4.42398i) q^{61} +(5.73389 - 9.93138i) q^{62} +(-1.58319 - 2.74217i) q^{63} -13.0380 q^{64} +1.16638 q^{65} +(5.41388 + 9.37711i) q^{66} +(-0.519277 - 0.899414i) q^{67} +17.8304 q^{68} +8.59746 q^{69} +(-3.55821 - 6.16301i) q^{70} +(2.16135 - 3.74358i) q^{71} +(-1.18132 - 2.04611i) q^{72} +(-1.81673 + 3.14666i) q^{73} +(-8.16835 + 14.1480i) q^{74} -1.00000 q^{75} +(2.87062 - 12.9865i) q^{76} +15.2547 q^{77} +(1.31072 - 2.27023i) q^{78} +(7.53826 - 13.0567i) q^{79} +(0.396220 + 0.686273i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.80374 + 4.85622i) q^{82} -8.98408 q^{83} -9.66137 q^{84} +(-2.92184 - 5.06077i) q^{85} +(-1.31072 - 2.27023i) q^{86} -7.31269 q^{87} +11.3825 q^{88} +(-2.08614 - 3.61330i) q^{89} +(-1.12375 + 1.94639i) q^{90} +(-1.84661 - 3.19841i) q^{91} +(13.1164 - 22.7183i) q^{92} +(-2.55123 + 4.41887i) q^{93} +21.0739 q^{94} +(-4.15634 + 1.31332i) q^{95} +6.50629 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-3.40043 + 5.88972i) q^{98} +(-2.40885 - 4.17225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.12375	+	1.94639i	−0.794609	+	1.37630i	0.128477	+	0.991712i	$0.458991\pi$
$2$	−1.12375	+	1.94639i	−0.794609	+	1.37630i	−0.923087	+	0.384592i	$0.874342\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.52562	−	2.64245i	−0.762808	−	1.32122i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.12375	+	1.94639i	0.458768	+	0.794609i
$7$	3.16638			1.19678			0.598390	−	0.801205i	$-0.295807\pi$
$7$	3.16638			1.19678			0.598390	+	0.801205i	$0.295807\pi$
$8$	2.36264			0.835320
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.12375	−	1.94639i	−0.355360	−	0.615502i
$11$	4.81770			1.45259			0.726295	−	0.687383i	$-0.241240\pi$
$11$	4.81770			1.45259			0.726295	+	0.687383i	$0.241240\pi$
$12$	−3.05123			−0.880815
$13$	−0.583191	−	1.01012i	−0.161748	−	0.280156i	0.773748	−	0.633494i	$-0.218380\pi$
$13$	−0.583191	−	1.01012i	−0.161748	−	0.280156i	−0.935496	+	0.353338i	$0.885047\pi$
$14$	−3.55821	+	6.16301i	−0.950973	+	1.64713i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	0.396220	−	0.686273i	0.0990549	−	0.171568i
$17$	−2.92184	+	5.06077i	−0.708649	+	1.22742i	0.256709	+	0.966489i	$0.417362\pi$
$17$	−2.92184	+	5.06077i	−0.708649	+	1.22742i	−0.965358	+	0.260928i	$0.915971\pi$
$18$	2.24750			0.529740
$19$	3.21554	+	2.94284i	0.737695	+	0.675134i
$19$	3.21554	+	2.94284i	0.737695	+	0.675134i
$20$	3.05123			0.682277
$21$	1.58319	−	2.74217i	0.345481	−	0.598390i
$22$	−5.41388	+	9.37711i	−1.15424	+	1.99921i
$23$	4.29873	+	7.44562i	0.896347	+	1.55252i	0.832129	+	0.554583i	$0.187122\pi$
$23$	4.29873	+	7.44562i	0.896347	+	1.55252i	0.0642183	+	0.997936i	$0.479545\pi$
$24$	1.18132	−	2.04611i	0.241136	−	0.417660i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.62144			0.514106
$27$	−1.00000			−0.192450
$28$	−4.83069	−	8.36699i	−0.912914	−	1.58121i
$29$	−3.65634	−	6.33297i	−0.678966	−	1.17600i	−0.975293	−	0.220917i	$-0.929095\pi$
$29$	−3.65634	−	6.33297i	−0.678966	−	1.17600i	0.296326	−	0.955087i	$-0.404238\pi$
$30$	−2.24750			−0.410335
$31$	−5.10247			−0.916430			−0.458215	−	0.888841i	$-0.651511\pi$
$31$	−5.10247			−0.916430			−0.458215	+	0.888841i	$0.651511\pi$
$32$	3.25314	+	5.63461i	0.575080	+	0.996068i
$33$	2.40885	−	4.17225i	0.419327	−	0.726295i
$34$	−6.56681	−	11.3741i	−1.12620	−	1.95063i
$35$	−1.58319	+	2.74217i	−0.267608	+	0.463511i
$36$	−1.52562	+	2.64245i	−0.254269	+	0.440408i
$37$	7.26885			1.19499			0.597496	−	0.801872i	$-0.296162\pi$
$37$	7.26885			1.19499			0.597496	+	0.801872i	$0.296162\pi$
$38$	−9.34136	+	2.95167i	−1.51537	+	0.478825i
$39$	−1.16638			−0.186771
$40$	−1.18132	+	2.04611i	−0.186783	+	0.323518i
$41$	1.24750	−	2.16072i	0.194826	−	0.337449i	−0.752017	−	0.659143i	$-0.770919\pi$
$41$	1.24750	−	2.16072i	0.194826	−	0.337449i	0.946843	+	0.321695i	$0.104252\pi$
$42$	3.55821	+	6.16301i	0.549044	+	0.950973i
$43$	−0.583191	+	1.01012i	−0.0889358	+	0.154041i	−0.907062	−	0.420998i	$-0.861680\pi$
$43$	−0.583191	+	1.01012i	−0.0889358	+	0.154041i	0.818126	+	0.575039i	$0.195013\pi$
$44$	−7.34996	−	12.7305i	−1.10805	−	1.91920i
$45$	1.00000			0.149071
$46$	−19.3227			−2.84898
$47$	−4.68830	−	8.12038i	−0.683859	−	1.18448i	−0.973794	−	0.227432i	$-0.926967\pi$
$47$	−4.68830	−	8.12038i	−0.683859	−	1.18448i	0.289935	−	0.957046i	$-0.406366\pi$
$48$	−0.396220	−	0.686273i	−0.0571894	−	0.0990549i
$49$	3.02597			0.432282
$50$	2.24750			0.317844
$51$	2.92184	+	5.06077i	0.409139	+	0.708649i
$52$	−1.77945	+	3.08210i	−0.246766	+	0.427411i
$53$	1.37689	+	2.38485i	0.189131	+	0.327584i	0.944961	−	0.327184i	$-0.106100\pi$
$53$	1.37689	+	2.38485i	0.189131	+	0.327584i	−0.755830	+	0.654768i	$0.772766\pi$
$54$	1.12375	−	1.94639i	0.152923	−	0.264870i
$55$	−2.40885	+	4.17225i	−0.324809	+	0.562586i
$56$	7.48103			0.999695
$57$	4.15634	−	1.31332i	0.550521	−	0.173953i
$58$	16.4352			2.15805
$59$	5.05626	−	8.75770i	0.658269	−	1.14016i	−0.322794	−	0.946469i	$-0.604622\pi$
$59$	5.05626	−	8.75770i	0.658269	−	1.14016i	0.981063	−	0.193687i	$-0.0620445\pi$
$60$	1.52562	−	2.64245i	0.196956	−	0.341138i
$61$	2.55418	+	4.42398i	0.327030	+	0.566432i	0.981921	−	0.189291i	$-0.0606189\pi$
$61$	2.55418	+	4.42398i	0.327030	+	0.566432i	−0.654891	+	0.755723i	$0.727286\pi$
$62$	5.73389	−	9.93138i	0.728204	−	1.26129i
$63$	−1.58319	−	2.74217i	−0.199463	−	0.345481i
$64$	−13.0380			−1.62975
$65$	1.16638			0.144672
$66$	5.41388	+	9.37711i	0.666402	+	1.15424i
$67$	−0.519277	−	0.899414i	−0.0634398	−	0.109881i	0.832561	−	0.553933i	$-0.186874\pi$
$67$	−0.519277	−	0.899414i	−0.0634398	−	0.109881i	−0.896001	+	0.444052i	$0.853540\pi$
$68$	17.8304			2.16226
$69$	8.59746			1.03501
$70$	−3.55821	−	6.16301i	−0.425288	−	0.736620i
$71$	2.16135	−	3.74358i	0.256506	−	0.444281i	−0.708798	−	0.705412i	$-0.750762\pi$
$71$	2.16135	−	3.74358i	0.256506	−	0.444281i	0.965303	+	0.261131i	$0.0840955\pi$
$72$	−1.18132	−	2.04611i	−0.139220	−	0.241136i
$73$	−1.81673	+	3.14666i	−0.212632	+	0.368289i	−0.952537	−	0.304422i	$-0.901537\pi$
$73$	−1.81673	+	3.14666i	−0.212632	+	0.368289i	0.739906	+	0.672711i	$0.234870\pi$
$74$	−8.16835	+	14.1480i	−0.949552	+	1.64467i
$75$	−1.00000			−0.115470
$76$	2.87062	−	12.9865i	0.329283	−	1.48966i
$77$	15.2547			1.73843
$78$	1.31072	−	2.27023i	0.148410	−	0.257053i
$79$	7.53826	−	13.0567i	0.848121	−	1.46899i	−0.0347620	−	0.999396i	$-0.511067\pi$
$79$	7.53826	−	13.0567i	0.848121	−	1.46899i	0.882883	−	0.469593i	$-0.155599\pi$
$80$	0.396220	+	0.686273i	0.0442987	+	0.0767276i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.80374	+	4.85622i	0.309621	+	0.536280i
$83$	−8.98408			−0.986131			−0.493065	−	0.869992i	$-0.664124\pi$
$83$	−8.98408			−0.986131			−0.493065	+	0.869992i	$0.664124\pi$
$84$	−9.66137			−1.05414
$85$	−2.92184	−	5.06077i	−0.316918	−	0.548918i
$86$	−1.31072	−	2.27023i	−0.141338	−	0.244805i
$87$	−7.31269			−0.784003
$88$	11.3825			1.21338
$89$	−2.08614	−	3.61330i	−0.221130	−	0.383009i	0.734021	−	0.679127i	$-0.237641\pi$
$89$	−2.08614	−	3.61330i	−0.221130	−	0.383009i	−0.955152	+	0.296118i	$0.904308\pi$
$90$	−1.12375	+	1.94639i	−0.118453	+	0.205167i
$91$	−1.84661	−	3.19841i	−0.193577	−	0.335285i
$92$	13.1164	−	22.7183i	1.36748	−	2.36855i
$93$	−2.55123	+	4.41887i	−0.264551	+	0.458215i
$94$	21.0739			2.17360
$95$	−4.15634	+	1.31332i	−0.426432	+	0.134743i
$96$	6.50629			0.664045
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−3.40043	+	5.88972i	−0.343495	+	0.594952i
$99$	−2.40885	−	4.17225i	−0.242098	−	0.419327i
$100$	−1.52562	+	2.64245i	−0.152562	+	0.264245i
$101$	−5.46008	−	9.45714i	−0.543299	−	0.941021i	−0.998712	−	0.0507406i	$-0.983842\pi$
$101$	−5.46008	−	9.45714i	−0.543299	−	0.941021i	0.455413	−	0.890280i	$-0.349492\pi$
$102$	−13.1336			−1.30042
$103$	−5.72113			−0.563720			−0.281860	−	0.959456i	$-0.590951\pi$
$103$	−5.72113			−0.563720			−0.281860	+	0.959456i	$0.590951\pi$
$104$	−1.37787	−	2.38654i	−0.135111	−	0.234020i
$105$	1.58319	+	2.74217i	0.154504	+	0.267608i
$106$	−6.18912			−0.601140
$107$	−2.98408			−0.288482			−0.144241	−	0.989543i	$-0.546074\pi$
$107$	−2.98408			−0.288482			−0.144241	+	0.989543i	$0.546074\pi$
$108$	1.52562	+	2.64245i	0.146803	+	0.254269i
$109$	−6.43315	+	11.1425i	−0.616184	+	1.06726i	0.373991	+	0.927432i	$0.377989\pi$
$109$	−6.43315	+	11.1425i	−0.616184	+	1.06726i	−0.990175	+	0.139830i	$0.955344\pi$
$110$	−5.41388	−	9.37711i	−0.516193	−	0.894072i
$111$	3.63442	−	6.29501i	0.344964	−	0.597496i
$112$	1.25458	−	2.17300i	0.118547	−	0.205329i
$113$	−16.7739			−1.57796			−0.788978	−	0.614422i	$-0.789389\pi$
$113$	−16.7739			−1.57796			−0.788978	+	0.614422i	$0.789389\pi$
$114$	−2.11446	+	9.56569i	−0.198037	+	0.895909i
$115$	−8.59746			−0.801717
$116$	−11.1564	+	19.3234i	−1.03584	+	1.79413i
$117$	−0.583191	+	1.01012i	−0.0539160	+	0.0933853i
$118$	11.3639	+	19.6829i	1.04613	+	1.81196i
$119$	−9.25165	+	16.0243i	−0.848097	+	1.46895i
$120$	1.18132	+	2.04611i	0.107839	+	0.186783i
$121$	12.2102			1.11002
$122$	−11.4810			−1.03944
$123$	−1.24750	−	2.16072i	−0.112483	−	0.194826i
$124$	7.78441	+	13.4830i	0.699061	+	1.21081i
$125$	1.00000			0.0894427
$126$	7.11643			0.633982
$127$	−0.0512339	−	0.0887398i	−0.00454628	−	0.00787438i	0.863743	−	0.503932i	$-0.168114\pi$
$127$	−0.0512339	−	0.0887398i	−0.00454628	−	0.00787438i	−0.868290	+	0.496058i	$0.834780\pi$
$128$	8.14510	−	14.1077i	0.719932	−	1.24696i
$129$	0.583191	+	1.01012i	0.0513471	+	0.0889358i
$130$	−1.31072	+	2.27023i	−0.114958	+	0.199112i
$131$	−6.78366	+	11.7497i	−0.592691	+	1.02657i	0.401177	+	0.916001i	$0.368601\pi$
$131$	−6.78366	+	11.7497i	−0.592691	+	1.02657i	−0.993868	+	0.110571i	$0.964732\pi$
$132$	−14.6999			−1.27946
$133$	10.1816	+	9.31816i	0.882859	+	0.807987i
$134$	2.33414			0.201639
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−6.90326	+	11.9568i	−0.591949	+	1.02529i
$137$	−7.92184	−	13.7210i	−0.676808	−	1.17227i	−0.975937	−	0.218053i	$-0.930029\pi$
$137$	−7.92184	−	13.7210i	−0.676808	−	1.17227i	0.299129	−	0.954213i	$-0.403304\pi$
$138$	−9.66137	+	16.7340i	−0.822431	+	1.42449i
$139$	2.15634	+	3.73490i	0.182899	+	0.316790i	0.942866	−	0.333171i	$-0.108119\pi$
$139$	2.15634	+	3.73490i	0.182899	+	0.316790i	−0.759968	+	0.649961i	$0.774785\pi$
$140$	9.66137			0.816535
$141$	−9.37660			−0.789652
$142$	4.85763	+	8.41367i	0.407644	+	0.706059i
$143$	−2.80964	−	4.86644i	−0.234954	−	0.406952i
$144$	−0.792439			−0.0660366
$145$	7.31269			0.607286
$146$	−4.08308	−	7.07211i	−0.337918	−	0.585292i
$147$	1.51299	−	2.62057i	0.124789	−	0.216141i
$148$	−11.0895	−	19.2075i	−0.911550	−	1.57885i
$149$	−4.78869	+	8.29426i	−0.392305	+	0.679492i	−0.992753	−	0.120172i	$-0.961656\pi$
$149$	−4.78869	+	8.29426i	−0.392305	+	0.679492i	0.600448	+	0.799664i	$0.294989\pi$
$150$	1.12375	−	1.94639i	0.0917536	−	0.158922i
$151$	1.90169			0.154757			0.0773786	−	0.997002i	$-0.475345\pi$
$151$	1.90169			0.154757			0.0773786	+	0.997002i	$0.475345\pi$
$152$	7.59717	+	6.95288i	0.616212	+	0.563953i
$153$	5.84367			0.472433
$154$	−17.1424	+	29.6915i	−1.38137	+	2.39261i
$155$	2.55123	−	4.41887i	0.204920	−	0.354932i
$156$	1.77945	+	3.08210i	0.142470	+	0.246766i
$157$	9.19333	−	15.9233i	0.733708	−	1.27082i	−0.221581	−	0.975142i	$-0.571122\pi$
$157$	9.19333	−	15.9233i	0.733708	−	1.27082i	0.955288	−	0.295677i	$-0.0955451\pi$
$158$	16.9422	+	29.3448i	1.34785	+	2.33454i
$159$	2.75378			0.218389
$160$	−6.50629			−0.514367
$161$	13.6114	+	23.5757i	1.07273	+	1.85802i
$162$	−1.12375	−	1.94639i	−0.0882899	−	0.152923i
$163$	−10.6234			−0.832091			−0.416046	−	0.909344i	$-0.636584\pi$
$163$	−10.6234			−0.832091			−0.416046	+	0.909344i	$0.636584\pi$
$164$	−7.61280			−0.594460
$165$	2.40885	+	4.17225i	0.187529	+	0.324809i
$166$	10.0958	−	17.4865i	0.783589	−	1.35722i
$167$	−7.30974	−	12.6608i	−0.565645	−	0.979725i	−0.996989	−	0.0775380i	$-0.975294\pi$
$167$	−7.30974	−	12.6608i	−0.565645	−	0.979725i	0.431345	−	0.902187i	$-0.358039\pi$
$168$	3.74052	−	6.47876i	0.288587	−	0.499847i
$169$	5.81978	−	10.0801i	0.447675	−	0.775396i
$170$	13.1336			1.00730
$171$	0.940806	−	4.25616i	0.0719453	−	0.325477i
$172$	3.55890			0.271364
$173$	0.328608	−	0.569166i	0.0249836	−	0.0432729i	−0.853263	−	0.521480i	$-0.825380\pi$
$173$	0.328608	−	0.569166i	0.0249836	−	0.0432729i	0.878247	+	0.478207i	$0.158713\pi$
$174$	8.21762	−	14.2333i	0.622976	−	1.07903i
$175$	−1.58319	−	2.74217i	−0.119678	−	0.207288i
$176$	1.90887	−	3.30625i	0.143886	−	0.249218i
$177$	−5.05626	−	8.75770i	−0.380052	−	0.658269i
$178$	9.37718			0.702849
$179$	−23.2647			−1.73889			−0.869444	−	0.494032i	$-0.835523\pi$
$179$	−23.2647			−1.73889			−0.869444	+	0.494032i	$0.835523\pi$
$180$	−1.52562	−	2.64245i	−0.113713	−	0.196956i
$181$	−0.725576	−	1.25673i	−0.0539316	−	0.0934123i	0.837799	−	0.545978i	$-0.183842\pi$
$181$	−0.725576	−	1.25673i	−0.0539316	−	0.0934123i	−0.891731	+	0.452566i	$0.850509\pi$
$182$	8.30047			0.615272
$183$	5.10837			0.377621
$184$	10.1564	+	17.5913i	0.748737	+	1.29685i
$185$	−3.63442	+	6.29501i	−0.267208	+	0.462818i
$186$	−5.73389	−	9.93138i	−0.420429	−	0.728204i
$187$	−14.0765	+	24.3813i	−1.02938	+	1.78293i
$188$	−14.3051	+	24.7772i	−1.04331	+	1.80706i
$189$	−3.16638			−0.230320
$190$	2.11446	−	9.56569i	0.153399	−	0.693968i
$191$	19.0598			1.37912			0.689559	−	0.724229i	$-0.257804\pi$
$191$	19.0598			1.37912			0.689559	+	0.724229i	$0.257804\pi$
$192$	−6.51899	+	11.2912i	−0.470467	+	0.814873i
$193$	−7.84789	+	13.5929i	−0.564903	+	0.978441i	0.432156	+	0.901799i	$0.357753\pi$
$193$	−7.84789	+	13.5929i	−0.564903	+	0.978441i	−0.997059	+	0.0766418i	$0.975580\pi$
$194$	−2.24750	−	3.89278i	−0.161361	−	0.279485i
$195$	0.583191	−	1.01012i	0.0417632	−	0.0723359i
$196$	−4.61648	−	7.99597i	−0.329748	−	0.571141i
$197$	8.23620			0.586805			0.293402	−	0.955989i	$-0.405212\pi$
$197$	8.23620			0.586805			0.293402	+	0.955989i	$0.405212\pi$
$198$	10.8278			0.769495
$199$	−8.69459	−	15.0595i	−0.616343	−	1.06754i	−0.990147	−	0.140030i	$-0.955280\pi$
$199$	−8.69459	−	15.0595i	−0.616343	−	1.06754i	0.373804	−	0.927508i	$-0.378053\pi$
$200$	−1.18132	−	2.04611i	−0.0835320	−	0.144682i
$201$	−1.03855			−0.0732539
$202$	24.5430			1.72684
$203$	−11.5774	−	20.0526i	−0.812573	−	1.40742i
$204$	8.91521	−	15.4416i	0.624189	−	1.08113i
$205$	1.24750	+	2.16072i	0.0871288	+	0.150912i
$206$	6.42911	−	11.1355i	0.447937	−	0.775850i
$207$	4.29873	−	7.44562i	0.298782	−	0.517506i
$208$	−0.924287			−0.0640878
$209$	15.4915	+	14.1777i	1.07157	+	0.980694i
$210$	−7.11643			−0.491080
$211$	−10.5412	+	18.2579i	−0.725687	+	1.25693i	0.233003	+	0.972476i	$0.425145\pi$
$211$	−10.5412	+	18.2579i	−0.725687	+	1.25693i	−0.958691	+	0.284451i	$0.908189\pi$
$212$	4.20122	−	7.27673i	0.288541	−	0.499768i
$213$	−2.16135	−	3.74358i	−0.148094	−	0.256506i
$214$	3.35335	−	5.80818i	0.229231	−	0.397039i
$215$	−0.583191	−	1.01012i	−0.0397733	−	0.0688894i
$216$	−2.36264			−0.160757
$217$	−16.1564			−1.09677
$218$	−14.4585	−	25.0428i	−0.979252	−	1.69611i
$219$	1.81673	+	3.14666i	0.122763	+	0.212632i
$220$	14.6999			0.991069
$221$	6.81595			0.458491
$222$	8.16835	+	14.1480i	0.548224	+	0.949552i
$223$	−0.464804	+	0.805064i	−0.0311256	+	0.0539111i	−0.881169	−	0.472802i	$-0.843243\pi$
$223$	−0.464804	+	0.805064i	−0.0311256	+	0.0539111i	0.850043	+	0.526713i	$0.176576\pi$
$224$	10.3007	+	17.8413i	0.688244	+	1.19207i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	18.8496	−	32.6485i	1.25386	−	2.17175i
$227$	2.53770			0.168433			0.0842165	−	0.996447i	$-0.473161\pi$
$227$	2.53770			0.168433			0.0842165	+	0.996447i	$0.473161\pi$
$228$	−9.81136	−	8.97930i	−0.649773	−	0.594669i
$229$	−0.912322			−0.0602879			−0.0301440	−	0.999546i	$-0.509597\pi$
$229$	−0.912322			−0.0602879			−0.0301440	+	0.999546i	$0.509597\pi$
$230$	9.66137	−	16.7340i	0.637052	−	1.10341i
$231$	7.62734	−	13.2109i	0.501842	−	0.869216i
$232$	−8.63864	−	14.9626i	−0.567154	−	0.982340i
$233$	11.4894	−	19.9003i	0.752697	−	1.30371i	−0.193815	−	0.981038i	$-0.562086\pi$
$233$	11.4894	−	19.9003i	0.752697	−	1.30371i	0.946511	−	0.322671i	$-0.104581\pi$
$234$	−1.31072	−	2.27023i	−0.0856844	−	0.148410i
$235$	9.37660			0.611662
$236$	−30.8557			−2.00853
$237$	−7.53826	−	13.0567i	−0.489663	−	0.848121i
$238$	−20.7930	−	36.0146i	−1.34781	−	2.33448i
$239$	21.1849			1.37033			0.685167	−	0.728386i	$-0.259729\pi$
$239$	21.1849			1.37033			0.685167	+	0.728386i	$0.259729\pi$
$240$	0.792439			0.0511517
$241$	2.15132	+	3.72619i	0.138578	+	0.240025i	0.926959	−	0.375163i	$-0.122413\pi$
$241$	2.15132	+	3.72619i	0.138578	+	0.240025i	−0.788380	+	0.615188i	$0.789080\pi$
$242$	−13.7212	+	23.7658i	−0.882032	+	1.52773i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	7.79341	−	13.4986i	0.498922	−	0.864158i
$245$	−1.51299	+	2.62057i	−0.0966612	+	0.167422i
$246$	5.60748			0.357520
$247$	1.09734	−	4.96431i	0.0698220	−	0.315871i
$248$	−12.0553			−0.765513
$249$	−4.49204	+	7.78044i	−0.284671	+	0.493065i
$250$	−1.12375	+	1.94639i	−0.0710720	+	0.123100i
$251$	6.77149	+	11.7286i	0.427413	+	0.740301i	0.996642	−	0.0818779i	$-0.0260918\pi$
$251$	6.77149	+	11.7286i	0.427413	+	0.740301i	−0.569230	+	0.822179i	$0.692758\pi$
$252$	−4.83069	+	8.36699i	−0.304305	+	0.527071i
$253$	20.7100	+	35.8707i	1.30203	+	2.25517i
$254$	0.230296			0.0144501
$255$	−5.84367			−0.365945
$256$	5.26810	+	9.12462i	0.329256	+	0.570289i
$257$	10.9601	+	18.9835i	0.683672	+	1.18416i	0.973852	+	0.227183i	$0.0729516\pi$
$257$	10.9601	+	18.9835i	0.683672	+	1.18416i	−0.290180	+	0.956972i	$0.593715\pi$
$258$	−2.62144			−0.163204
$259$	23.0160			1.43014
$260$	−1.77945	−	3.08210i	−0.110357	−	0.191144i
$261$	−3.65634	+	6.33297i	−0.226322	+	0.392001i
$262$	−15.2463	−	26.4073i	−0.941917	−	1.63145i
$263$	9.58645	−	16.6042i	0.591126	−	1.02386i	−0.402955	−	0.915220i	$-0.632017\pi$
$263$	9.58645	−	16.6042i	0.591126	−	1.02386i	0.994081	−	0.108640i	$-0.0346496\pi$
$264$	5.69125	−	9.85754i	0.350272	−	0.606689i
$265$	−2.75378			−0.169164
$266$	−29.5783	+	9.34612i	−1.81356	+	0.573048i
$267$	−4.17228			−0.255339
$268$	−1.58444	+	2.74432i	−0.0967848	+	0.167636i
$269$	−10.2026	+	17.6714i	−0.622062	+	1.07744i	0.367040	+	0.930205i	$0.380371\pi$
$269$	−10.2026	+	17.6714i	−0.622062	+	1.07744i	−0.989101	+	0.147237i	$0.952962\pi$
$270$	1.12375	+	1.94639i	0.0683891	+	0.118453i
$271$	−8.16106	+	14.1354i	−0.495749	+	0.858663i	−0.999988	−	0.00490125i	$-0.998440\pi$
$271$	−8.16106	+	14.1354i	−0.495749	+	0.858663i	0.504239	+	0.863564i	$0.331773\pi$
$272$	2.31538	+	4.01035i	0.140390	+	0.243163i
$273$	−3.69321			−0.223523
$274$	35.6086			2.15119
$275$	−2.40885	−	4.17225i	−0.145259	−	0.251596i
$276$	−13.1164	−	22.7183i	−0.789516	−	1.36748i
$277$	7.08065			0.425435			0.212717	−	0.977114i	$-0.431769\pi$
$277$	7.08065			0.425435			0.212717	+	0.977114i	$0.431769\pi$
$278$	−9.69275			−0.581332
$279$	2.55123	+	4.41887i	0.152738	+	0.264551i
$280$	−3.74052	+	6.47876i	−0.223539	+	0.387180i
$281$	5.06129	+	8.76641i	0.301931	+	0.522960i	0.976573	−	0.215185i	$-0.0690354\pi$
$281$	5.06129	+	8.76641i	0.301931	+	0.522960i	−0.674642	+	0.738145i	$0.735702\pi$
$282$	10.5369	−	18.2505i	0.627465	−	1.08680i
$283$	−7.25556	+	12.5670i	−0.431298	+	0.747030i	−0.996985	−	0.0775897i	$-0.975278\pi$
$283$	−7.25556	+	12.5670i	−0.431298	+	0.747030i	0.565687	+	0.824620i	$0.308611\pi$
$284$	−13.1896			−0.782658
$285$	−0.940806	+	4.25616i	−0.0557286	+	0.252113i
$286$	12.6293			0.746786
$287$	3.95005	−	6.84168i	0.233164	−	0.403852i
$288$	3.25314	−	5.63461i	0.191693	−	0.332023i
$289$	−8.57426	−	14.8511i	−0.504368	−	0.873591i
$290$	−8.21762	+	14.2333i	−0.482555	+	0.835810i
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	11.0865			0.648789
$293$	6.10837			0.356855			0.178427	−	0.983953i	$-0.442899\pi$
$293$	6.10837			0.356855			0.178427	+	0.983953i	$0.442899\pi$
$294$	3.40043	+	5.88972i	0.198317	+	0.343495i
$295$	5.05626	+	8.75770i	0.294387	+	0.509893i
$296$	17.1737			0.998201
$297$	−4.81770			−0.279551
$298$	−10.7626	−	18.6413i	−0.623458	−	1.07986i
$299$	5.01396	−	8.68443i	0.289965	−	0.502234i
$300$	1.52562	+	2.64245i	0.0880815	+	0.152562i
$301$	−1.84661	+	3.19841i	−0.106437	+	0.184354i
$302$	−2.13702	+	3.70142i	−0.122972	+	0.212993i
$303$	−10.9202			−0.627347
$304$	3.29365	−	1.04072i	0.188904	−	0.0596896i
$305$	−5.10837			−0.292504
$306$	−6.56681	+	11.3741i	−0.375400	+	0.650211i
$307$	−6.27147	+	10.8625i	−0.357932	+	0.619956i	−0.987615	−	0.156896i	$-0.949851\pi$
$307$	−6.27147	+	10.8625i	−0.357932	+	0.619956i	0.629683	+	0.776852i	$0.283185\pi$
$308$	−23.2728	−	40.3097i	−1.32609	−	2.29686i
$309$	−2.86057	+	4.95464i	−0.162732	+	0.281860i
$310$	5.73389	+	9.93138i	0.325663	+	0.564065i
$311$	−17.9682			−1.01888			−0.509440	−	0.860506i	$-0.670148\pi$
$311$	−17.9682			−1.01888			−0.509440	+	0.860506i	$0.670148\pi$
$312$	−2.75574			−0.156013
$313$	−3.77236	−	6.53393i	−0.213227	−	0.369319i	0.739496	−	0.673161i	$-0.235064\pi$
$313$	−3.77236	−	6.53393i	−0.213227	−	0.369319i	−0.952723	+	0.303842i	$0.901731\pi$
$314$	20.6620	+	35.7876i	1.16602	+	2.01961i
$315$	3.16638			0.178405
$316$	−46.0020			−2.58782
$317$	−2.25851	−	3.91185i	−0.126850	−	0.219711i	0.795604	−	0.605817i	$-0.207153\pi$
$317$	−2.25851	−	3.91185i	−0.126850	−	0.219711i	−0.922455	+	0.386105i	$0.873820\pi$
$318$	−3.09456	+	5.35993i	−0.173534	+	0.300570i
$319$	−17.6152	−	30.5104i	−0.986260	−	1.70825i
$320$	6.51899	−	11.2912i	0.364422	−	0.631198i
$321$	−1.49204	+	2.58429i	−0.0832776	+	0.144241i
$322$	−61.1832			−3.40961
$323$	−24.2883	+	7.67459i	−1.35144	+	0.427026i
$324$	3.05123			0.169513
$325$	−0.583191	+	1.01012i	−0.0323496	+	0.0560312i
$326$	11.9381	−	20.6773i	0.661188	−	1.14521i
$327$	6.43315	+	11.1425i	0.355754	+	0.616184i
$328$	2.94739	−	5.10502i	0.162742	−	0.281878i
$329$	−14.8450	−	25.7122i	−0.818429	−	1.41756i
$330$	−10.8278			−0.596048
$331$	16.7674			0.921619			0.460809	−	0.887499i	$-0.347559\pi$
$331$	16.7674			0.921619			0.460809	+	0.887499i	$0.347559\pi$
$332$	13.7063	+	23.7399i	0.752229	+	1.30290i
$333$	−3.63442	−	6.29501i	−0.199165	−	0.344964i
$334$	32.8572			1.79787
$335$	1.03855			0.0567423
$336$	−1.25458	−	2.17300i	−0.0684431	−	0.118547i
$337$	8.71682	−	15.0980i	0.474835	−	0.822439i	−0.524749	−	0.851257i	$-0.675841\pi$
$337$	8.71682	−	15.0980i	0.474835	−	0.822439i	0.999585	+	0.0288179i	$0.00917429\pi$
$338$	13.0799	+	22.6551i	0.711454	+	1.23227i
$339$	−8.38695	+	14.5266i	−0.455516	+	0.788978i
$340$	−8.91521	+	15.4416i	−0.483495	+	0.837438i
$341$	−24.5822			−1.33120
$342$	7.22691	+	6.61402i	0.390786	+	0.357645i
$343$	−12.5833			−0.679433
$344$	−1.37787	+	2.38654i	−0.0742899	+	0.128674i
$345$	−4.29873	+	7.44562i	−0.231436	+	0.400859i
$346$	0.738545	+	1.27920i	0.0397044	+	0.0687701i
$347$	15.5446	−	26.9240i	0.834475	−	1.44535i	−0.0599815	−	0.998199i	$-0.519104\pi$
$347$	15.5446	−	26.9240i	0.834475	−	1.44535i	0.894457	−	0.447154i	$-0.147563\pi$
$348$	11.1564	+	19.3234i	0.598044	+	1.03584i
$349$	0.887477			0.0475055			0.0237528	−	0.999718i	$-0.492439\pi$
$349$	0.887477			0.0475055			0.0237528	+	0.999718i	$0.492439\pi$
$350$	7.11643			0.380389
$351$	0.583191	+	1.01012i	0.0311284	+	0.0539160i
$352$	15.6727	+	27.1459i	0.835356	+	1.44688i
$353$	−5.27079			−0.280536			−0.140268	−	0.990114i	$-0.544796\pi$
$353$	−5.27079			−0.280536			−0.140268	+	0.990114i	$0.544796\pi$
$354$	22.7278			1.20797
$355$	2.16135	+	3.74358i	0.114713	+	0.198688i
$356$	−6.36530	+	11.0250i	−0.337360	+	0.584325i
$357$	9.25165	+	16.0243i	0.489649	+	0.848097i
$358$	26.1437	−	45.2822i	1.38174	−	2.39324i
$359$	13.6315	−	23.6104i	0.719443	−	1.24611i	−0.241778	−	0.970332i	$-0.577731\pi$
$359$	13.6315	−	23.6104i	0.719443	−	1.24611i	0.961221	−	0.275780i	$-0.0889360\pi$
$360$	2.36264			0.124522
$361$	1.67937	+	18.9256i	0.0883879	+	0.996086i
$362$	3.26145			0.171418
$363$	6.10511	−	10.5744i	0.320435	−	0.555010i
$364$	−5.63442	+	9.75911i	−0.295324	+	0.511516i
$365$	−1.81673	−	3.14666i	−0.0950918	−	0.164704i
$366$	−5.74052	+	9.94286i	−0.300062	+	0.519722i
$367$	−0.685659	−	1.18760i	−0.0357911	−	0.0619920i	0.847575	−	0.530676i	$-0.178062\pi$
$367$	−0.685659	−	1.18760i	−0.0357911	−	0.0619920i	−0.883366	+	0.468684i	$0.844728\pi$
$368$	6.81296			0.355150
$369$	−2.49499			−0.129884
$370$	−8.16835	−	14.1480i	−0.424652	−	0.735520i
$371$	4.35977	+	7.55134i	0.226348	+	0.392046i
$372$	15.5688			0.807206
$373$	33.1801			1.71800			0.859001	−	0.511974i	$-0.171086\pi$
$373$	33.1801			1.71800			0.859001	+	0.511974i	$0.171086\pi$
$374$	−31.6369	−	54.7968i	−1.63591	−	2.83347i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−11.0768	−	19.1856i	−0.571241	−	0.989419i
$377$	−4.26469	+	7.38667i	−0.219643	+	0.380433i
$378$	3.55821	−	6.16301i	0.183015	−	0.316991i
$379$	−31.1642			−1.60080			−0.800399	−	0.599468i	$-0.795379\pi$
$379$	−31.1642			−1.60080			−0.800399	+	0.599468i	$0.795379\pi$
$380$	9.81136	+	8.97930i	0.503312	+	0.460628i
$381$	−0.102468			−0.00524959
$382$	−21.4184	+	37.0977i	−1.09586	+	1.89809i
$383$	−14.8307	+	25.6875i	−0.757814	+	1.31257i	0.186150	+	0.982521i	$0.440399\pi$
$383$	−14.8307	+	25.6875i	−0.757814	+	1.31257i	−0.943963	+	0.330050i	$0.892934\pi$
$384$	−8.14510	−	14.1077i	−0.415653	−	0.719932i
$385$	−7.62734	+	13.2109i	−0.388725	+	0.673292i
$386$	−17.6381	−	30.5501i	−0.897755	−	1.55496i
$387$	1.16638			0.0592905
$388$	6.10247			0.309806
$389$	10.0190	+	17.3534i	0.507983	+	0.879852i	0.999957	+	0.00924244i	$0.00294200\pi$
$389$	10.0190	+	17.3534i	0.507983	+	0.879852i	−0.491974	+	0.870610i	$0.663725\pi$
$390$	1.31072	+	2.27023i	0.0663708	+	0.114958i
$391$	−50.2407			−2.54078
$392$	7.14930			0.361094
$393$	6.78366	+	11.7497i	0.342191	+	0.592691i
$394$	−9.25540	+	16.0308i	−0.466281	+	0.807622i
$395$	7.53826	+	13.0567i	0.379291	+	0.656952i
$396$	−7.34996	+	12.7305i	−0.369350	+	0.639732i
$397$	9.73540	−	16.8622i	0.488606	−	0.846290i	−0.511309	−	0.859397i	$-0.670839\pi$
$397$	9.73540	−	16.8622i	0.488606	−	0.846290i	0.999914	+	0.0131075i	$0.00417238\pi$
$398$	39.0821			1.95901
$399$	13.1606	−	4.15846i	0.658853	−	0.208184i
$400$	−0.792439			−0.0396220
$401$	18.3816	−	31.8379i	0.917935	−	1.58991i	0.115388	−	0.993320i	$-0.463189\pi$
$401$	18.3816	−	31.8379i	0.917935	−	1.58991i	0.802547	−	0.596589i	$-0.203478\pi$
$402$	1.16707	−	2.02143i	0.0582083	−	0.100820i
$403$	2.97571	+	5.15409i	0.148231	+	0.256743i
$404$	−16.6600	+	28.8560i	−0.828866	+	1.43564i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	52.0402			2.58271
$407$	35.0191			1.73583
$408$	6.90326	+	11.9568i	0.341762	+	0.591949i
$409$	6.28240	+	10.8814i	0.310645	+	0.538053i	0.978502	−	0.206237i	$-0.0661217\pi$
$409$	6.28240	+	10.8814i	0.310645	+	0.538053i	−0.667857	+	0.744289i	$0.732788\pi$
$410$	−5.60748			−0.276934
$411$	−15.8437			−0.781511
$412$	8.72825	+	15.1178i	0.430010	+	0.744799i
$413$	16.0101	−	27.7302i	0.787803	−	1.36452i
$414$	9.66137	+	16.7340i	0.474831	+	0.822431i
$415$	4.49204	−	7.78044i	0.220506	−	0.381927i
$416$	3.79441	−	6.57211i	0.186036	−	0.322224i
$417$	4.31269			0.211193
$418$	−45.0039	+	14.2203i	−2.20121	+	0.695536i
$419$	23.8674			1.16600			0.583000	−	0.812472i	$-0.301879\pi$
$419$	23.8674			1.16600			0.583000	+	0.812472i	$0.301879\pi$
$420$	4.83069	−	8.36699i	0.235713	−	0.408267i
$421$	3.30504	−	5.72449i	0.161078	−	0.278995i	−0.774178	−	0.632968i	$-0.781836\pi$
$421$	3.30504	−	5.72449i	0.161078	−	0.278995i	0.935255	+	0.353974i	$0.115170\pi$
$422$	−23.6913	−	41.0346i	−1.15328	−	1.99753i
$423$	−4.68830	+	8.12038i	−0.227953	+	0.394826i
$424$	3.25311	+	5.63454i	0.157985	+	0.273638i
$425$	5.84367			0.283460
$426$	9.71527			0.470706
$427$	8.08752	+	14.0080i	0.391383	+	0.677895i
$428$	4.55256	+	7.88527i	0.220056	+	0.381149i
$429$	−5.61928			−0.271301
$430$	2.62144			0.126417
$431$	3.73156	+	6.46325i	0.179743	+	0.311324i	0.941792	−	0.336195i	$-0.109140\pi$
$431$	3.73156	+	6.46325i	0.179743	+	0.311324i	−0.762050	+	0.647519i	$0.775807\pi$
$432$	−0.396220	+	0.686273i	−0.0190631	+	0.0330183i
$433$	−10.7976	−	18.7019i	−0.518898	−	0.898758i	−0.999759	−	0.0219608i	$-0.993009\pi$
$433$	−10.7976	−	18.7019i	−0.518898	−	0.898758i	0.480861	−	0.876797i	$-0.340324\pi$
$434$	18.1557	−	31.4465i	0.871500	−	1.50948i
$435$	3.65634	−	6.33297i	0.175308	−	0.303643i
$436$	39.2581			1.88012
$437$	−8.08854	+	36.5921i	−0.386928	+	1.75044i
$438$	−8.16617			−0.390195
$439$	16.8740	−	29.2266i	0.805351	−	1.39491i	−0.110703	−	0.993854i	$-0.535310\pi$
$439$	16.8740	−	29.2266i	0.805351	−	1.39491i	0.916054	−	0.401055i	$-0.131356\pi$
$440$	−5.69125	+	9.85754i	−0.271320	+	0.469940i
$441$	−1.51299	−	2.62057i	−0.0720470	−	0.124789i
$442$	−7.65941	+	13.2665i	−0.364321	+	0.631023i
$443$	3.85053	+	6.66931i	0.182944	+	0.316868i	0.942882	−	0.333127i	$-0.108104\pi$
$443$	3.85053	+	6.66931i	0.182944	+	0.316868i	−0.759938	+	0.649996i	$0.774771\pi$
$444$	−22.1790			−1.05257
$445$	4.17228			0.197785
$446$	−1.04464	−	1.80938i	−0.0494653	−	0.0856765i
$447$	4.78869	+	8.29426i	0.226497	+	0.392305i
$448$	−41.2832			−1.95045
$449$	4.84306			0.228558			0.114279	−	0.993449i	$-0.463544\pi$
$449$	4.84306			0.228558			0.114279	+	0.993449i	$0.463544\pi$
$450$	−1.12375	−	1.94639i	−0.0529740	−	0.0917536i
$451$	6.01006	−	10.4097i	0.283002	−	0.490175i
$452$	25.5905	+	44.3241i	1.20368	+	2.08483i
$453$	0.950844	−	1.64691i	0.0446745	−	0.0773786i
$454$	−2.85173	+	4.93935i	−0.133838	+	0.231815i
$455$	3.69321			0.173140
$456$	9.81996	−	3.10290i	0.459862	−	0.145307i
$457$	−18.2322			−0.852868			−0.426434	−	0.904519i	$-0.640230\pi$
$457$	−18.2322			−0.852868			−0.426434	+	0.904519i	$0.640230\pi$
$458$	1.02522	−	1.77573i	0.0479054	−	0.0829745i
$459$	2.92184	−	5.06077i	0.136380	−	0.236216i
$460$	13.1164	+	22.7183i	0.611557	+	1.05925i
$461$	16.2778	−	28.1940i	0.758134	−	1.31313i	−0.185668	−	0.982613i	$-0.559445\pi$
$461$	16.2778	−	28.1940i	0.758134	−	1.31313i	0.943801	−	0.330513i	$-0.107222\pi$
$462$	17.1424	+	29.6915i	0.797537	+	1.38137i
$463$	−30.9666			−1.43914			−0.719569	−	0.694421i	$-0.755661\pi$
$463$	−30.9666			−1.43914			−0.719569	+	0.694421i	$0.755661\pi$
$464$	−5.79486			−0.269020
$465$	−2.55123	−	4.41887i	−0.118311	−	0.204920i
$466$	25.8224	+	44.7257i	1.19620	+	2.07188i
$467$	−26.4956			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$467$	−26.4956			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$468$	3.55890			0.164510
$469$	−1.64423	−	2.84789i	−0.0759234	−	0.131503i
$470$	−10.5369	+	18.2505i	−0.486033	+	0.841833i
$471$	−9.19333	−	15.9233i	−0.423606	−	0.733708i
$472$	11.9461	−	20.6913i	0.549866	−	0.952395i
$473$	−2.80964	+	4.86644i	−0.129187	+	0.223759i
$474$	33.8844			1.55636
$475$	0.940806	−	4.25616i	0.0431672	−	0.195286i
$476$	56.4579			2.58774
$477$	1.37689	−	2.38485i	0.0630436	−	0.109195i
$478$	−23.8064	+	41.2340i	−1.08888	+	1.88600i
$479$	11.5726	+	20.0443i	0.528766	+	0.915849i	0.999437	+	0.0335408i	$0.0106784\pi$
$479$	11.5726	+	20.0443i	0.528766	+	0.915849i	−0.470671	+	0.882309i	$0.655988\pi$
$480$	−3.25314	+	5.63461i	−0.148485	+	0.257184i
$481$	−4.23913	−	7.34238i	−0.193288	−	0.334784i
$482$	−9.67015			−0.440463
$483$	27.2228			1.23868
$484$	−18.6281	−	32.2649i	−0.846733	−	1.46658i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$	−2.24750			−0.101948
$487$	−38.3075			−1.73588			−0.867939	−	0.496671i	$-0.834555\pi$
$487$	−38.3075			−1.73588			−0.867939	+	0.496671i	$0.834555\pi$
$488$	6.03462	+	10.4523i	0.273175	+	0.473152i
$489$	−5.31172	+	9.20016i	−0.240204	+	0.416046i
$490$	−3.40043	−	5.88972i	−0.153616	−	0.266070i
$491$	−11.8873	+	20.5893i	−0.536464	+	0.929183i	0.462627	+	0.886553i	$0.346907\pi$
$491$	−11.8873	+	20.5893i	−0.536464	+	0.929183i	−0.999091	+	0.0426302i	$0.986426\pi$
$492$	−3.80640	+	6.59288i	−0.171606	+	0.297230i
$493$	42.7330			1.92460
$494$	8.42933	+	7.71448i	0.379254	+	0.347091i
$495$	4.81770			0.216539
$496$	−2.02170	+	3.50168i	−0.0907769	+	0.157230i
$497$	6.84367	−	11.8536i	0.306981	−	0.531706i
$498$	−10.0958	−	17.4865i	−0.452405	−	0.783589i
$499$	−0.210818	+	0.365147i	−0.00943749	+	0.0163462i	−0.870706	−	0.491805i	$-0.836337\pi$
$499$	−0.210818	+	0.365147i	−0.00943749	+	0.0163462i	0.861268	+	0.508151i	$0.169671\pi$
$500$	−1.52562	−	2.64245i	−0.0682277	−	0.118174i
$501$	−14.6195			−0.653150
$502$	−30.4378			−1.35851
$503$	−13.7328	−	23.7858i	−0.612313	−	1.06056i	−0.990850	−	0.134971i	$-0.956906\pi$
$503$	−13.7328	−	23.7858i	−0.612313	−	1.06056i	0.378536	−	0.925586i	$-0.376428\pi$
$504$	−3.74052	−	6.47876i	−0.166616	−	0.288587i
$505$	10.9202			0.485941
$506$	−93.0912			−4.13841
$507$	−5.81978	−	10.0801i	−0.258465	−	0.447675i
$508$	−0.156327	+	0.270766i	−0.00693588	+	0.0120133i
$509$	−3.91889	−	6.78771i	−0.173702	−	0.300860i	0.766010	−	0.642829i	$-0.222239\pi$
$509$	−3.91889	−	6.78771i	−0.173702	−	0.300860i	−0.939711	+	0.341969i	$0.888906\pi$
$510$	6.56681	−	11.3741i	0.290783	−	0.503652i
$511$	−5.75245	+	9.96353i	−0.254473	+	0.440761i
$512$	8.90034			0.393343
$513$	−3.21554	−	2.94284i	−0.141969	−	0.129930i
$514$	−49.2655			−2.17301
$515$	2.86057	−	4.95464i	0.126052	−	0.218328i
$516$	1.77945	−	3.08210i	0.0783360	−	0.135682i
$517$	−22.5868	−	39.1215i	−0.993367	−	1.72056i
$518$	−25.8641	+	44.7980i	−1.13640	+	1.96831i
$519$	−0.328608	−	0.569166i	−0.0144243	−	0.0249836i
$520$	2.75574			0.120847
$521$	−4.93772			−0.216325			−0.108163	−	0.994133i	$-0.534497\pi$
$521$	−4.93772			−0.216325			−0.108163	+	0.994133i	$0.534497\pi$
$522$	−8.21762	−	14.2333i	−0.359675	−	0.622976i
$523$	8.55988	+	14.8261i	0.374297	+	0.648302i	0.990222	−	0.139503i	$-0.0445506\pi$
$523$	8.55988	+	14.8261i	0.374297	+	0.648302i	−0.615924	+	0.787805i	$0.711217\pi$
$524$	41.3971			1.80844
$525$	−3.16638			−0.138192
$526$	21.5455	+	37.3179i	0.939428	+	1.62714i
$527$	14.9086	−	25.8224i	0.649428	−	1.12484i
$528$	−1.90887	−	3.30625i	−0.0830728	−	0.143886i
$529$	−25.4581	+	44.0948i	−1.10688	+	1.91716i
$530$	3.09456	−	5.35993i	0.134419	−	0.232821i
$531$	−10.1125			−0.438846
$532$	9.08948	−	41.1203i	0.394079	−	1.78279i
$533$	−2.91011			−0.126051
$534$	4.68859	−	8.12088i	0.202895	−	0.351425i
$535$	1.49204	−	2.58429i	0.0645065	−	0.111729i
$536$	−1.22687	−	2.12499i	−0.0529925	−	0.0917858i
$537$	−11.6324	+	20.1478i	−0.501974	+	0.869444i
$538$	−22.9302	−	39.7163i	−0.988592	−	1.71229i
$539$	14.5782			0.627929
$540$	−3.05123			−0.131304
$541$	3.04946	+	5.28183i	0.131107	+	0.227083i	0.924103	−	0.382142i	$-0.124814\pi$
$541$	3.04946	+	5.28183i	0.131107	+	0.227083i	−0.792997	+	0.609226i	$0.791480\pi$
$542$	−18.3420	−	31.7692i	−0.787854	−	1.36460i
$543$	−1.45115			−0.0622749
$544$	−38.0206			−1.63012
$545$	−6.43315	−	11.1425i	−0.275566	−	0.477294i
$546$	4.15024	−	7.18842i	0.177614	−	0.307636i
$547$	11.4882	+	19.8981i	0.491198	+	0.850780i	0.999949	−	0.0101341i	$-0.00322583\pi$
$547$	11.4882	+	19.8981i	0.491198	+	0.850780i	−0.508751	+	0.860914i	$0.669892\pi$
$548$	−24.1714	+	41.8661i	−1.03255	+	1.78843i
$549$	2.55418	−	4.42398i	0.109010	−	0.188811i
$550$	10.8278			0.461697
$551$	6.87982	−	31.1240i	0.293090	−	1.32593i
$552$	20.3127			0.864567
$553$	23.8690	−	41.3424i	1.01501	−	1.75806i
$554$	−7.95686	+	13.7817i	−0.338055	+	0.585528i
$555$	3.63442	+	6.29501i	0.154273	+	0.267208i
$556$	6.57951	−	11.3960i	0.279033	−	0.483300i
$557$	3.49499	+	6.05350i	0.148087	+	0.256495i	0.930521	−	0.366240i	$-0.119355\pi$
$557$	3.49499	+	6.05350i	0.148087	+	0.256495i	−0.782433	+	0.622735i	$0.786022\pi$
$558$	−11.4678			−0.485469
$559$	1.36045			0.0575408
$560$	1.25458	+	2.17300i	0.0530158	+	0.0918261i
$561$	14.0765	+	24.3813i	0.594312	+	1.02938i
$562$	−22.7504			−0.959670
$563$	−12.7111			−0.535708			−0.267854	−	0.963460i	$-0.586314\pi$
$563$	−12.7111			−0.535708			−0.267854	+	0.963460i	$0.586314\pi$
$564$	14.3051	+	24.7772i	0.602354	+	1.04331i
$565$	8.38695	−	14.5266i	0.352842	−	0.611139i
$566$	−16.3068	−	28.2442i	−0.685427	−	1.18719i
$567$	−1.58319	+	2.74217i	−0.0664878	+	0.115160i
$568$	5.10651	−	8.84473i	0.214264	−	0.371117i
$569$	−28.0036			−1.17397			−0.586986	−	0.809597i	$-0.699685\pi$
$569$	−28.0036			−1.17397			−0.586986	+	0.809597i	$0.699685\pi$
$570$	−7.22691	−	6.61402i	−0.302702	−	0.277031i
$571$	39.0506			1.63422			0.817108	−	0.576484i	$-0.195576\pi$
$571$	39.0506			1.63422			0.817108	+	0.576484i	$0.195576\pi$
$572$	−8.57286	+	14.8486i	−0.358449	+	0.620853i
$573$	9.52990	−	16.5063i	0.398117	−	0.689559i
$574$	8.87771	+	15.3766i	0.370548	+	0.641809i
$575$	4.29873	−	7.44562i	0.179269	−	0.310504i
$576$	6.51899	+	11.2912i	0.271624	+	0.470467i
$577$	18.5294			0.771389			0.385694	−	0.922627i	$-0.373962\pi$
$577$	18.5294			0.771389			0.385694	+	0.922627i	$0.373962\pi$
$578$	38.5412			1.60310
$579$	7.84789	+	13.5929i	0.326147	+	0.564903i
$580$	−11.1564	−	19.3234i	−0.463243	−	0.802360i
$581$	−28.4470			−1.18018
$582$	−4.49499			−0.186323
$583$	6.63345	+	11.4895i	0.274730	+	0.475845i
$584$	−4.29228	+	7.43444i	−0.177616	+	0.307639i
$585$	−0.583191	−	1.01012i	−0.0241120	−	0.0417632i
$586$	−6.86426	+	11.8893i	−0.283560	+	0.491140i
$587$	−9.61458	+	16.6529i	−0.396836	+	0.687341i	−0.993334	−	0.115274i	$-0.963225\pi$
$587$	−9.61458	+	16.6529i	−0.396836	+	0.687341i	0.596497	+	0.802615i	$0.296559\pi$
$588$	−9.23296			−0.380761
$589$	−16.4072	−	15.0158i	−0.676046	−	0.618713i
$590$	−22.7278			−0.935691
$591$	4.11810	−	7.13275i	0.169396	−	0.293402i
$592$	2.88006	−	4.98841i	0.118370	−	0.205022i
$593$	15.5293	+	26.8976i	0.637714	+	1.10455i	0.985933	+	0.167140i	$0.0534531\pi$
$593$	15.5293	+	26.8976i	0.637714	+	1.10455i	−0.348219	+	0.937413i	$0.613214\pi$
$594$	5.41388	−	9.37711i	0.222134	−	0.384747i
$595$	−9.25165	−	16.0243i	−0.379281	−	0.656933i
$596$	29.2228			1.19701
$597$	−17.3892			−0.711692
$598$	11.2688	+	19.5182i	0.460818	+	0.798159i
$599$	4.84691	+	8.39510i	0.198039	+	0.343014i	0.947893	−	0.318590i	$-0.103209\pi$
$599$	4.84691	+	8.39510i	0.198039	+	0.343014i	−0.749853	+	0.661604i	$0.769876\pi$
$600$	−2.36264			−0.0964545
$601$	9.02069			0.367962			0.183981	−	0.982930i	$-0.441102\pi$
$601$	9.02069			0.367962			0.183981	+	0.982930i	$0.441102\pi$
$602$	−4.15024	−	7.18842i	−0.169151	−	0.292978i
$603$	−0.519277	+	0.899414i	−0.0211466	+	0.0366270i
$604$	−2.90125	−	5.02511i	−0.118050	−	0.204469i
$605$	−6.10511	+	10.5744i	−0.248208	+	0.429909i
$606$	12.2715	−	21.2549i	0.498496	−	0.863420i
$607$	−38.5916			−1.56638			−0.783192	−	0.621780i	$-0.786410\pi$
$607$	−38.5916			−1.56638			−0.783192	+	0.621780i	$0.786410\pi$
$608$	−6.12116	+	27.6918i	−0.248246	+	1.12305i
$609$	−23.1548			−0.938278
$610$	5.74052	−	9.94286i	0.232427	−	0.402575i
$611$	−5.46835	+	9.47146i	−0.221226	+	0.383174i
$612$	−8.91521	−	15.4416i	−0.360376	−	0.624189i
$613$	10.3707	−	17.9626i	0.418869	−	0.725502i	−0.576957	−	0.816774i	$-0.695760\pi$
$613$	10.3707	−	17.9626i	0.418869	−	0.725502i	0.995826	+	0.0912724i	$0.0290934\pi$
$614$	−14.0951	−	24.4134i	−0.568832	−	0.985246i
$615$	2.49499			0.100608
$616$	36.0413			1.45215
$617$	15.2005	+	26.3280i	0.611949	+	1.05993i	0.990912	+	0.134514i	$0.0429474\pi$
$617$	15.2005	+	26.3280i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$618$	−6.42911	−	11.1355i	−0.258617	−	0.447937i
$619$	−9.69562			−0.389700			−0.194850	−	0.980833i	$-0.562422\pi$
$619$	−9.69562			−0.389700			−0.194850	+	0.980833i	$0.562422\pi$
$620$	−15.5688			−0.625259
$621$	−4.29873	−	7.44562i	−0.172502	−	0.298782i
$622$	20.1917	−	34.9730i	0.809612	−	1.40229i
$623$	−6.60552	−	11.4411i	−0.264645	−	0.458378i
$624$	−0.462143	+	0.800456i	−0.0185005	+	0.0320439i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	16.9567			0.677728
$627$	20.0240	−	6.32717i	0.799682	−	0.252683i
$628$	−56.1020			−2.23871
$629$	−21.2384	+	36.7860i	−0.846830	+	1.46675i
$630$	−3.55821	+	6.16301i	−0.141763	+	0.245540i
$631$	1.85131	+	3.20656i	0.0736994	+	0.127651i	0.900520	−	0.434815i	$-0.143186\pi$
$631$	1.85131	+	3.20656i	0.0736994	+	0.127651i	−0.826821	+	0.562466i	$0.809853\pi$
$632$	17.8102	−	30.8482i	0.708453	−	1.22708i
$633$	10.5412	+	18.2579i	0.418976	+	0.725687i
$634$	10.1520			0.403186
$635$	0.102468			0.00406631
$636$	−4.20122	−	7.27673i	−0.166589	−	0.288541i
$637$	−1.76472	−	3.05659i	−0.0699208	−	0.121106i
$638$	79.1800			3.13477
$639$	−4.32271			−0.171004
$640$	8.14510	+	14.1077i	0.321963	+	0.557657i
$641$	−9.89794	+	17.1437i	−0.390945	+	0.677137i	−0.992574	−	0.121639i	$-0.961185\pi$
$641$	−9.89794	+	17.1437i	−0.390945	+	0.677137i	0.601629	+	0.798775i	$0.294518\pi$
$642$	−3.35335	−	5.80818i	−0.132346	−	0.229231i
$643$	2.63442	−	4.56296i	0.103892	−	0.179945i	−0.809393	−	0.587267i	$-0.800204\pi$
$643$	2.63442	−	4.56296i	0.103892	−	0.179945i	0.913285	+	0.407322i	$0.133537\pi$
$644$	41.5316	−	71.9349i	1.63658	−	2.83463i
$645$	−1.16638			−0.0459262
$646$	12.3562	−	55.8988i	0.486148	−	2.19931i
$647$	25.3370			0.996098			0.498049	−	0.867149i	$-0.334050\pi$
$647$	25.3370			0.996098			0.498049	+	0.867149i	$0.334050\pi$
$648$	−1.18132	+	2.04611i	−0.0464067	+	0.0803787i
$649$	24.3595	−	42.1920i	0.956196	−	1.65618i
$650$	−1.31072	−	2.27023i	−0.0514106	−	0.0890458i
$651$	−8.07818	+	13.9918i	−0.316609	+	0.548383i
$652$	16.2073	+	28.0718i	0.634726	+	1.09938i
$653$	12.3697			0.484065			0.242032	−	0.970268i	$-0.422186\pi$
$653$	12.3697			0.484065			0.242032	+	0.970268i	$0.422186\pi$
$654$	−28.9170			−1.13074
$655$	−6.78366	−	11.7497i	−0.265060	−	0.459097i
$656$	−0.988564	−	1.71224i	−0.0385969	−	0.0668519i
$657$	3.63345			0.141754
$658$	66.7279			2.60133
$659$	11.4551	+	19.8407i	0.446226	+	0.772885i	0.998137	−	0.0610175i	$-0.0194346\pi$
$659$	11.4551	+	19.8407i	0.446226	+	0.772885i	−0.551911	+	0.833903i	$0.686101\pi$
$660$	7.34996	−	12.7305i	0.286097	−	0.495534i
$661$	−1.64082	−	2.84198i	−0.0638203	−	0.110540i	0.832350	−	0.554251i	$-0.186995\pi$
$661$	−1.64082	−	2.84198i	−0.0638203	−	0.110540i	−0.896170	+	0.443711i	$0.853662\pi$
$662$	−18.8423	+	32.6358i	−0.732327	+	1.26843i
$663$	3.40798	−	5.90279i	0.132355	−	0.229245i
$664$	−21.2262			−0.823735
$665$	−13.1606	+	4.15846i	−0.510345	+	0.161258i
$666$	16.3367			0.633034
$667$	31.4353	−	54.4475i	1.21718	−	2.10821i
$668$	−22.3037	+	38.6312i	−0.862957	+	1.49469i
$669$	0.464804	+	0.805064i	0.0179704	+	0.0311256i
$670$	−1.16707	+	2.02143i	−0.0450879	+	0.0780946i
$671$	12.3053	+	21.3134i	0.475040	+	0.822794i
$672$	20.6014			0.794716
$673$	29.2183			1.12628			0.563142	−	0.826360i	$-0.309592\pi$
$673$	29.2183			1.12628			0.563142	+	0.826360i	$0.309592\pi$
$674$	19.5910	+	33.9326i	0.754617	+	1.30704i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−35.5150			−1.36596
$677$	−36.0085			−1.38392			−0.691960	−	0.721936i	$-0.743253\pi$
$677$	−36.0085			−1.38392			−0.691960	+	0.721936i	$0.743253\pi$
$678$	−18.8496	−	32.6485i	−0.723915	−	1.25386i
$679$	−3.16638	+	5.48433i	−0.121515	+	0.210469i
$680$	−6.90326	−	11.9568i	−0.264728	−	0.458522i
$681$	1.26885	−	2.19771i	0.0486224	−	0.0842165i
$682$	27.6241	−	47.8464i	1.05778	−	1.83213i
$683$	32.7395			1.25274			0.626371	−	0.779525i	$-0.284540\pi$
$683$	32.7395			1.25274			0.626371	+	0.779525i	$0.284540\pi$
$684$	−12.6820	+	4.00724i	−0.484908	+	0.153221i
$685$	15.8437			0.605356
$686$	14.1404	−	24.4919i	0.539884	−	0.935107i
$687$	−0.456161	+	0.790094i	−0.0174036	+	0.0301440i
$688$	0.462143	+	0.800456i	0.0176191	+	0.0305171i
$689$	1.60598	−	2.78164i	0.0611831	−	0.105972i
$690$	−9.66137	−	16.7340i	−0.367802	−	0.637052i
$691$	−17.3452			−0.659842			−0.329921	−	0.944009i	$-0.607022\pi$
$691$	−17.3452			−0.659842			−0.329921	+	0.944009i	$0.607022\pi$
$692$	−2.00532			−0.0762308
$693$	−7.62734	−	13.2109i	−0.289739	−	0.501842i
$694$	34.9363	+	60.5115i	1.32616	+	2.29698i
$695$	−4.31269			−0.163590
$696$	−17.2773			−0.654893
$697$	7.28995	+	12.6266i	0.276127	+	0.478265i
$698$	−0.997300	+	1.72737i	−0.0377484	+	0.0653821i
$699$	−11.4894	−	19.9003i	−0.434570	−	0.752697i
$700$	−4.83069	+	8.36699i	−0.182583	+	0.316243i
$701$	−1.21218	+	2.09956i	−0.0457834	+	0.0792992i	−0.888009	−	0.459826i	$-0.847912\pi$
$701$	−1.21218	+	2.09956i	−0.0457834	+	0.0792992i	0.842226	+	0.539125i	$0.181245\pi$
$702$	−2.62144			−0.0989398
$703$	23.3733	+	21.3911i	0.881539	+	0.806780i
$704$	−62.8130			−2.36736
$705$	4.68830	−	8.12038i	0.176572	−	0.305831i
$706$	5.92304	−	10.2590i	0.222917	−	0.386103i
$707$	−17.2887	−	29.9449i	−0.650209	−	1.12619i
$708$	−15.4278	+	26.7218i	−0.579814	+	1.00427i
$709$	−5.25378	−	9.09982i	−0.197310	−	0.341751i	0.750345	−	0.661046i	$-0.229887\pi$
$709$	−5.25378	−	9.09982i	−0.197310	−	0.341751i	−0.947655	+	0.319295i	$0.896554\pi$
$710$	−9.71527			−0.364607
$711$	−15.0765			−0.565414
$712$	−4.92881	−	8.53694i	−0.184715	−	0.319935i
$713$	−21.9341	−	37.9910i	−0.821439	−	1.42277i
$714$	−41.5861			−1.55632
$715$	5.61928			0.210149
$716$	35.4931	+	61.4758i	1.32644	+	2.29746i
$717$	10.5924	−	18.3466i	0.395582	−	0.685167i
$718$	30.6367	+	53.0643i	1.14335	+	1.98034i
$719$	7.74161	−	13.4089i	0.288713	−	0.500066i	−0.684789	−	0.728741i	$-0.740106\pi$
$719$	7.74161	−	13.4089i	0.288713	−	0.500066i	0.973503	+	0.228675i	$0.0734392\pi$
$720$	0.396220	−	0.686273i	0.0147662	−	0.0255759i
$721$	−18.1153			−0.674648
$722$	−38.7238	−	17.9989i	−1.44115	−	0.669851i
$723$	4.30263			0.160017
$724$	−2.21390	+	3.83459i	−0.0822790	+	0.142511i
$725$	−3.65634	+	6.33297i	−0.135793	+	0.235201i
$726$	13.7212	+	23.7658i	0.509242	+	0.882032i
$727$	−9.03690	+	15.6524i	−0.335160	+	0.580514i	−0.983516	−	0.180823i	$-0.942124\pi$
$727$	−9.03690	+	15.6524i	−0.335160	+	0.580514i	0.648355	+	0.761338i	$0.275457\pi$
$728$	−4.36287	−	7.55671i	−0.161699	−	0.280070i
$729$	1.00000			0.0370370
$730$	8.16617			0.302243
$731$	−3.40798	−	5.90279i	−0.126049	−	0.218323i
$732$	−7.79341	−	13.4986i	−0.288053	−	0.498922i
$733$	−32.5312			−1.20157			−0.600784	−	0.799411i	$-0.705145\pi$
$733$	−32.5312			−1.20157			−0.600784	+	0.799411i	$0.705145\pi$
$734$	3.08203			0.113760
$735$	1.51299	+	2.62057i	0.0558074	+	0.0966612i
$736$	−27.9688	+	48.4433i	−1.03094	+	1.78565i
$737$	−2.50172	−	4.33311i	−0.0921520	−	0.159612i
$738$	2.80374	−	4.85622i	0.103207	−	0.178760i
$739$	−23.9823	+	41.5386i	−0.882205	+	1.52802i	−0.0333206	+	0.999445i	$0.510608\pi$
$739$	−23.9823	+	41.5386i	−0.882205	+	1.52802i	−0.848884	+	0.528579i	$0.822725\pi$
$740$	22.1790			0.815315
$741$	−3.75055	−	3.43248i	−0.137780	−	0.126095i
$742$	−19.5971			−0.719433
$743$	12.8553	−	22.2660i	0.471615	−	0.816861i	−0.527858	−	0.849333i	$-0.677005\pi$
$743$	12.8553	−	22.2660i	0.471615	−	0.816861i	0.999473	+	0.0324716i	$0.0103378\pi$
$744$	−6.02766	+	10.4402i	−0.220985	+	0.382756i
$745$	−4.78869	−	8.29426i	−0.175444	−	0.303878i
$746$	−37.2861	+	64.5814i	−1.36514	+	2.36449i
$747$	4.49204	+	7.78044i	0.164355	+	0.284671i
$748$	85.9016			3.14087
$749$	−9.44874			−0.345249
$750$	1.12375	+	1.94639i	0.0410335	+	0.0710720i
$751$	4.55713	+	7.89319i	0.166292	+	0.288026i	0.937113	−	0.349025i	$-0.113487\pi$
$751$	4.55713	+	7.89319i	0.166292	+	0.288026i	−0.770821	+	0.637051i	$0.780154\pi$
$752$	−7.43039			−0.270958
$753$	13.5430			0.493534
$754$	−9.58488	−	16.6015i	−0.349061	−	0.604591i
$755$	−0.950844	+	1.64691i	−0.0346048	+	0.0599372i
$756$	4.83069	+	8.36699i	0.175690	+	0.304305i
$757$	19.5958	−	33.9409i	0.712222	−	1.23360i	−0.251800	−	0.967779i	$-0.581022\pi$
$757$	19.5958	−	33.9409i	0.712222	−	1.23360i	0.964021	−	0.265825i	$-0.0856442\pi$
$758$	35.0207	−	60.6576i	1.27201	−	2.20318i
$759$	41.4200			1.50345
$760$	−9.81996	+	3.10290i	−0.356207	+	0.112554i
$761$	52.4574			1.90158			0.950790	−	0.309837i	$-0.100275\pi$
$761$	52.4574			1.90158			0.950790	+	0.309837i	$0.100275\pi$
$762$	0.115148	−	0.199442i	0.00417137	−	0.00722503i
$763$	−20.3698	+	35.2816i	−0.737437	+	1.27728i
$764$	−29.0779	−	50.3645i	−1.05200	−	1.82212i
$765$	−2.92184	+	5.06077i	−0.105639	+	0.182973i
$766$	−33.3319	−	57.7326i	−1.20433	−	2.08596i
$767$	−11.7951			−0.425895
$768$	10.5362			0.380193
$769$	−11.8286	−	20.4878i	−0.426551	−	0.738807i	0.570013	−	0.821635i	$-0.306938\pi$
$769$	−11.8286	−	20.4878i	−0.426551	−	0.738807i	−0.996564	+	0.0828283i	$0.973605\pi$
$770$	−17.1424	−	29.6915i	−0.617769	−	1.07001i
$771$	21.9202			0.789437
$772$	47.8915			1.72365
$773$	2.67555	+	4.63418i	0.0962328	+	0.166680i	0.910122	−	0.414339i	$-0.135987\pi$
$773$	2.67555	+	4.63418i	0.0962328	+	0.166680i	−0.813890	+	0.581019i	$0.802654\pi$
$774$	−1.31072	+	2.27023i	−0.0471128	+	0.0816018i
$775$	2.55123	+	4.41887i	0.0916430	+	0.158730i
$776$	−2.36264	+	4.09222i	−0.0848139	+	0.146902i
$777$	11.5080	−	19.9324i	0.412846	−	0.715071i
$778$	−45.0352			−1.61459
$779$	10.3700	−	3.27671i	0.371545	−	0.117400i
$780$	−3.55890			−0.127429
$781$	10.4128	−	18.0354i	0.372598	−	0.645358i
$782$	56.4579	−	97.7880i	2.01893	−	3.49689i
$783$	3.65634	+	6.33297i	0.130667	+	0.226322i
$784$	1.19895	−	2.07664i	0.0428197	−	0.0741658i
$785$	9.19333	+	15.9233i	0.328124	+	0.568327i
$786$	−30.4925			−1.08763
$787$	26.2322			0.935078			0.467539	−	0.883972i	$-0.345141\pi$
$787$	26.2322			0.935078			0.467539	+	0.883972i	$0.345141\pi$
$788$	−12.5653	−	21.7637i	−0.447620	−	0.775300i
$789$	−9.58645	−	16.6042i	−0.341287	−	0.591126i
$790$	−33.8844			−1.20555
$791$	−53.1126			−1.88847
$792$	−5.69125	−	9.85754i	−0.202230	−	0.350272i
$793$	2.97915	−	5.16005i	0.105793	−	0.183239i
$794$	21.8803	+	37.8977i	0.776501	+	1.34494i
$795$	−1.37689	+	2.38485i	−0.0488333	+	0.0845818i
$796$	−26.5292	+	45.9500i	−0.940304	+	1.62865i
$797$	4.25354			0.150668			0.0753341	−	0.997158i	$-0.475998\pi$
$797$	4.25354			0.150668			0.0753341	+	0.997158i	$0.475998\pi$
$798$	−6.69518	+	30.2886i	−0.237007	+	1.07221i
$799$	54.7938			1.93847
$800$	3.25314	−	5.63461i	0.115016	−	0.199214i
$801$	−2.08614	+	3.61330i	−0.0737102	+	0.127670i
$802$	41.3126	+	71.5556i	1.45880	+	2.52671i
$803$	−8.75244	+	15.1597i	−0.308867	+	0.534973i
$804$	1.58444	+	2.74432i	0.0558787	+	0.0967848i
$805$	−27.2228			−0.959479
$806$	−13.3758			−0.471143
$807$	10.2026	+	17.6714i	0.359147	+	0.622062i
$808$	−12.9002	−	22.3438i	−0.453828	−	0.786054i
$809$	−12.2708			−0.431419			−0.215710	−	0.976458i	$-0.569206\pi$
$809$	−12.2708			−0.431419			−0.215710	+	0.976458i	$0.569206\pi$
$810$	2.24750			0.0789689
$811$	5.22559	+	9.05099i	0.183495	+	0.317823i	0.943068	−	0.332599i	$-0.107925\pi$
$811$	5.22559	+	9.05099i	0.183495	+	0.317823i	−0.759573	+	0.650422i	$0.774592\pi$
$812$	−35.3253	+	61.1852i	−1.23968	+	2.14718i
$813$	8.16106	+	14.1354i	0.286221	+	0.495749i
$814$	−39.3527	+	68.1608i	−1.37931	+	2.38903i
$815$	5.31172	−	9.20016i	0.186061	−	0.322268i
$816$	4.63076			0.162109
$817$	−4.84789	+	1.53183i	−0.169606	+	0.0535919i
$818$	−28.2393			−0.987365
$819$	−1.84661	+	3.19841i	−0.0645256	+	0.111762i
$820$	3.80640	−	6.59288i	0.132925	−	0.230233i
$821$	−5.03353	−	8.71832i	−0.175671	−	0.304272i	0.764722	−	0.644360i	$-0.222876\pi$
$821$	−5.03353	−	8.71832i	−0.175671	−	0.304272i	−0.940393	+	0.340089i	$0.889543\pi$
$822$	17.8043	−	30.8379i	0.620996	−	1.07560i
$823$	−21.6974	−	37.5810i	−0.756324	−	1.30999i	−0.944713	−	0.327897i	$-0.893660\pi$
$823$	−21.6974	−	37.5810i	−0.756324	−	1.30999i	0.188390	−	0.982094i	$-0.439673\pi$
$824$	−13.5170			−0.470887
$825$	−4.81770			−0.167731
$826$	35.9825	+	62.3236i	1.25199	+	2.16851i
$827$	7.36950	+	12.7643i	0.256263	+	0.443860i	0.965238	−	0.261374i	$-0.0841755\pi$
$827$	7.36950	+	12.7643i	0.256263	+	0.443860i	−0.708975	+	0.705233i	$0.750842\pi$
$828$	−26.2329			−0.911655
$829$	54.5313			1.89395			0.946974	−	0.321309i	$-0.104123\pi$
$829$	54.5313			1.89395			0.946974	+	0.321309i	$0.104123\pi$
$830$	10.0958	+	17.4865i	0.350432	+	0.606965i
$831$	3.54032	−	6.13202i	0.122812	−	0.212717i
$832$	7.60363	+	13.1699i	0.263608	+	0.456583i
$833$	−8.84140	+	15.3138i	−0.306336	+	0.530590i
$834$	−4.84637	+	8.39416i	−0.167816	+	0.290666i
$835$	14.6195			0.505928
$836$	13.8298	−	62.5652i	0.478313	−	2.16386i
$837$	5.10247			0.176367
$838$	−26.8210	+	46.4553i	−0.926515	+	1.60477i
$839$	−18.7632	+	32.4988i	−0.647777	+	1.12198i	0.335876	+	0.941906i	$0.390968\pi$
$839$	−18.7632	+	32.4988i	−0.647777	+	1.12198i	−0.983653	+	0.180076i	$0.942366\pi$
$840$	3.74052	+	6.47876i	0.129060	+	0.223539i
$841$	−12.2377	+	21.1963i	−0.421990	+	0.730908i
$842$	7.42805	+	12.8658i	0.255988	+	0.443384i
$843$	10.1226			0.348640
$844$	64.3274			2.21424
$845$	5.81978	+	10.0801i	0.200206	+	0.346768i
$846$	−10.5369	−	18.2505i	−0.362267	−	0.627465i
$847$	38.6622			1.32845
$848$	2.18221			0.0749373
$849$	7.25556	+	12.5670i	0.249010	+	0.431298i
$850$	−6.56681	+	11.3741i	−0.225240	+	0.390127i
$851$	31.2468	+	54.1211i	1.07113	+	1.85525i
$852$	−6.59480	+	11.4225i	−0.225934	+	0.391329i
$853$	−0.876485	+	1.51812i	−0.0300103	+	0.0519793i	−0.880640	−	0.473785i	$-0.842887\pi$
$853$	−0.876485	+	1.51812i	−0.0300103	+	0.0519793i	0.850630	+	0.525764i	$0.176221\pi$
$854$	−36.3533			−1.24399
$855$	3.21554	+	2.94284i	0.109969	+	0.100643i
$856$	−7.05032			−0.240975
$857$	−15.2630	+	26.4363i	−0.521375	+	0.903048i	0.478316	+	0.878188i	$0.341247\pi$
$857$	−15.2630	+	26.4363i	−0.521375	+	0.903048i	−0.999691	+	0.0248601i	$0.992086\pi$
$858$	6.31465	−	10.9373i	0.215579	−	0.373393i
$859$	−3.63363	−	6.29363i	−0.123978	−	0.214736i	0.797355	−	0.603510i	$-0.206232\pi$
$859$	−3.63363	−	6.29363i	−0.123978	−	0.214736i	−0.921333	+	0.388775i	$0.872898\pi$
$860$	−1.77945	+	3.08210i	−0.0606788	+	0.105099i
$861$	−3.95005	−	6.84168i	−0.134617	−	0.233164i
$862$	−16.7733			−0.571301
$863$	−30.4383			−1.03613			−0.518066	−	0.855341i	$-0.673348\pi$
$863$	−30.4383			−1.03613			−0.518066	+	0.855341i	$0.673348\pi$
$864$	−3.25314	−	5.63461i	−0.110674	−	0.191693i
$865$	0.328608	+	0.569166i	0.0111730	+	0.0193522i
$866$	48.5350			1.64929
$867$	−17.1485			−0.582394
$868$	24.6484	+	42.6923i	0.836622	+	1.44907i
$869$	36.3171	−	62.9030i	1.23197	−	2.13384i
$870$	8.21762	+	14.2333i	0.278603	+	0.482555i
$871$	−0.605675	+	1.04906i	−0.0205225	+	0.0355460i
$872$	−15.1992	+	26.3259i	−0.514711	+	0.891506i
$873$	2.00000			0.0676897
$874$	−62.1330	−	56.8638i	−2.10168	−	1.92345i
$875$	3.16638			0.107043
$876$	5.54326	−	9.60120i	0.187289	−	0.324395i
$877$	−23.3318	+	40.4119i	−0.787860	+	1.36461i	0.139416	+	0.990234i	$0.455478\pi$
$877$	−23.3318	+	40.4119i	−0.787860	+	1.36461i	−0.927276	+	0.374379i	$0.877856\pi$
$878$	37.9242	+	65.6866i	1.27988	+	2.21682i
$879$	3.05418	−	5.29000i	0.103015	−	0.178427i
$880$	1.90887	+	3.30625i	0.0643479	+	0.111454i
$881$	−31.2809			−1.05388			−0.526939	−	0.849903i	$-0.676660\pi$
$881$	−31.2809			−1.05388			−0.526939	+	0.849903i	$0.676660\pi$
$882$	6.80086			0.228997
$883$	−3.87059	−	6.70405i	−0.130256	−	0.225609i	0.793519	−	0.608545i	$-0.208246\pi$
$883$	−3.87059	−	6.70405i	−0.130256	−	0.225609i	−0.923775	+	0.382936i	$0.874913\pi$
$884$	−10.3985	−	18.0108i	−0.349741	−	0.605769i
$885$	10.1125			0.339929
$886$	−17.3081			−0.581476
$887$	2.49594	+	4.32310i	0.0838056	+	0.145156i	0.904882	−	0.425663i	$-0.139959\pi$
$887$	2.49594	+	4.32310i	0.0838056	+	0.145156i	−0.821076	+	0.570819i	$0.806626\pi$
$888$	8.58685	−	14.8729i	0.288156	−	0.499100i
$889$	−0.162226	−	0.280984i	−0.00544089	−	0.00942390i
$890$	−4.68859	+	8.12088i	−0.157162	+	0.272212i
$891$	−2.40885	+	4.17225i	−0.0806995	+	0.139776i
$892$	2.83645			0.0949714
$893$	8.82157	−	39.9083i	0.295203	−	1.33548i
$894$	−21.5251			−0.719908
$895$	11.6324	−	20.1478i	0.388827	−	0.673468i
$896$	25.7905	−	44.6705i	0.861600	−	1.49234i
$897$	−5.01396	−	8.68443i	−0.167411	−	0.289965i
$898$	−5.44238	+	9.42647i	−0.181614	+	0.314565i
$899$	18.6564	+	32.3138i	0.622225	+	1.07773i
$900$	3.05123			0.101708
$901$	−16.0922			−0.536110
$902$	13.5076	+	23.3958i	0.449753	+	0.778995i
$903$	1.84661	+	3.19841i	0.0614512	+	0.106437i
$904$	−39.6307			−1.31810
$905$	1.45115			0.0482379
$906$	2.13702	+	3.70142i	0.0709976	+	0.122972i
$907$	−26.6993	+	46.2446i	−0.886537	+	1.53553i	−0.0425957	+	0.999092i	$0.513563\pi$
$907$	−26.6993	+	46.2446i	−0.886537	+	1.53553i	−0.843942	+	0.536435i	$0.819771\pi$
$908$	−3.87156	−	6.70573i	−0.128482	−	0.222538i
$909$	−5.46008	+	9.45714i	−0.181100	+	0.313674i
$910$	−4.15024	+	7.18842i	−0.137579	+	0.238294i
$911$	22.8765			0.757933			0.378967	−	0.925410i	$-0.376280\pi$
$911$	22.8765			0.757933			0.378967	+	0.925410i	$0.376280\pi$
$912$	0.745532	−	3.37275i	0.0246870	−	0.111683i
$913$	−43.2826			−1.43244
$914$	20.4884	−	35.4870i	0.677697	−	1.17381i
$915$	−2.55418	+	4.42398i	−0.0844387	+	0.146252i
$916$	1.39185	+	2.41076i	0.0459881	+	0.0796538i
$917$	−21.4797	+	37.2039i	−0.709321	+	1.22858i
$918$	6.56681	+	11.3741i	0.216737	+	0.375400i
$919$	−3.88045			−0.128004			−0.0640021	−	0.997950i	$-0.520386\pi$
$919$	−3.88045			−0.128004			−0.0640021	+	0.997950i	$0.520386\pi$
$920$	−20.3127			−0.669691
$921$	6.27147	+	10.8625i	0.206652	+	0.357932i
$922$	36.5843	+	63.3659i	1.20484	+	2.08684i
$923$	−5.04193			−0.165957
$924$	−46.5456			−1.53124
$925$	−3.63442	−	6.29501i	−0.119499	−	0.206979i
$926$	34.7986	−	60.2729i	1.14355	−	1.98069i
$927$	2.86057	+	4.95464i	0.0939533	+	0.162732i
$928$	23.7892	−	41.2042i	0.780920	−	1.35259i
$929$	−25.8821	+	44.8290i	−0.849163	+	1.47079i	0.0327938	+	0.999462i	$0.489560\pi$
$929$	−25.8821	+	44.8290i	−0.849163	+	1.47079i	−0.881956	+	0.471331i	$0.843774\pi$
$930$	11.4678			0.376043
$931$	9.73014	+	8.90496i	0.318892	+	0.291848i
$932$	−70.1138			−2.29665
$933$	−8.98408	+	15.5609i	−0.294126	+	0.509440i
$934$	29.7744	−	51.5708i	0.974248	−	1.68745i
$935$	−14.0765	−	24.3813i	−0.460352	−	0.797353i
$936$	−1.37787	+	2.38654i	−0.0450372	+	0.0780066i
$937$	2.11094	+	3.65625i	0.0689613	+	0.119444i	0.898444	−	0.439087i	$-0.144698\pi$
$937$	2.11094	+	3.65625i	0.0689613	+	0.119444i	−0.829483	+	0.558532i	$0.811365\pi$
$938$	7.39079			0.241318
$939$	−7.54473			−0.246213
$940$	−14.3051	−	24.7772i	−0.466581	−	0.808142i
$941$	8.88263	+	15.3852i	0.289566	+	0.501542i	0.973706	−	0.227808i	$-0.0731558\pi$
$941$	8.88263	+	15.3852i	0.289566	+	0.501542i	−0.684140	+	0.729350i	$0.739822\pi$
$942$	41.3239			1.34641
$943$	21.4506			0.698527
$944$	−4.00678	−	6.93995i	−0.130410	−	0.225876i
$945$	1.58319	−	2.74217i	0.0515012	−	0.0892027i
$946$	−6.31465	−	10.9373i	−0.205307	−	0.355602i
$947$	−6.73396	+	11.6636i	−0.218824	+	0.379015i	−0.954449	−	0.298375i	$-0.903555\pi$
$947$	−6.73396	+	11.6636i	−0.218824	+	0.379015i	0.735624	+	0.677390i	$0.236889\pi$
$948$	−23.0010	+	39.8389i	−0.747038	+	1.29391i
$949$	4.23799			0.137571
$950$	7.22691	+	6.61402i	0.234472	+	0.214587i
$951$	−4.51701			−0.146474
$952$	−21.8583	+	37.8598i	−0.708433	+	1.22704i
$953$	13.3390	−	23.1037i	0.432091	−	0.748404i	−0.564962	−	0.825117i	$-0.691109\pi$
$953$	13.3390	−	23.1037i	0.432091	−	0.748404i	0.997053	+	0.0767132i	$0.0244426\pi$
$954$	3.09456	+	5.35993i	0.100190	+	0.173534i
$955$	−9.52990	+	16.5063i	−0.308380	+	0.534130i
$956$	−32.3200	−	55.9799i	−1.04530	−	1.81052i
$957$	−35.2303			−1.13883
$958$	−52.0188			−1.68065
$959$	−25.0836	−	43.4460i	−0.809990	−	1.40294i
$960$	−6.51899	−	11.2912i	−0.210399	−	0.364422i
$961$	−4.96482			−0.160156
$962$	19.0548			0.614353
$963$	1.49204	+	2.58429i	0.0480803	+	0.0832776i
$964$	6.56417	−	11.3695i	0.211418	−	0.366186i
$965$	−7.84789	−	13.5929i	−0.252632	−	0.437572i
$966$	−30.5916	+	52.9862i	−0.984268	+	1.70480i
$967$	7.10344	−	12.3035i	0.228431	−	0.395655i	−0.728912	−	0.684607i	$-0.759974\pi$
$967$	7.10344	−	12.3035i	0.228431	−	0.395655i	0.957343	+	0.288953i	$0.0933071\pi$
$968$	28.8484			0.927222
$969$	−5.49777	+	24.8716i	−0.176614	+	0.798991i
$970$	4.49499			0.144325
$971$	−9.20622	+	15.9456i	−0.295442	+	0.511720i	−0.975088	−	0.221821i	$-0.928800\pi$
$971$	−9.20622	+	15.9456i	−0.295442	+	0.511720i	0.679646	+	0.733540i	$0.262133\pi$
$972$	1.52562	−	2.64245i	0.0489342	−	0.0847565i
$973$	6.82781	+	11.8261i	0.218890	+	0.379128i
$974$	43.0479	−	74.5612i	1.37934	−	2.38909i
$975$	0.583191	+	1.01012i	0.0186771	+	0.0323496i
$976$	4.04807			0.129576
$977$	−3.75672			−0.120188			−0.0600941	−	0.998193i	$-0.519140\pi$
$977$	−3.75672			−0.120188			−0.0600941	+	0.998193i	$0.519140\pi$
$978$	−11.9381	−	20.6773i	−0.381737	−	0.661188i
$979$	−10.0504	−	17.4078i	−0.321212	−	0.556356i
$980$	9.23296			0.294936
$981$	12.8663			0.410790
$982$	−26.7165	−	46.2744i	−0.852559	−	1.47668i
$983$	5.73076	−	9.92597i	0.182783	−	0.316589i	−0.760044	−	0.649871i	$-0.774823\pi$
$983$	5.73076	−	9.92597i	0.182783	−	0.316589i	0.942827	+	0.333282i	$0.108156\pi$
$984$	−2.94739	−	5.10502i	−0.0939592	−	0.162742i
$985$	−4.11810	+	7.13275i	−0.131214	+	0.227268i
$986$	−48.0211	+	83.1749i	−1.52930	+	2.64883i
$987$	−29.6899			−0.945040
$988$	−14.7920	+	4.67397i	−0.470597	+	0.148699i
$989$	−10.0279			−0.318869
$990$	−5.41388	+	9.37711i	−0.172064	+	0.298024i
$991$	4.54948	−	7.87993i	0.144519	−	0.250314i	−0.784674	−	0.619908i	$-0.787170\pi$
$991$	4.54948	−	7.87993i	0.144519	−	0.250314i	0.929193	+	0.369594i	$0.120503\pi$
$992$	−16.5991	−	28.7504i	−0.527021	−	0.912827i
$993$	8.38369	−	14.5210i	0.266048	−	0.460809i
$994$	15.3811	+	26.6409i	0.487860	+	0.844998i
$995$	17.3892			0.551274
$996$	27.4125			0.868599
$997$	−12.3463	−	21.3844i	−0.391012	−	0.677252i	0.601572	−	0.798819i	$-0.294541\pi$
$997$	−12.3463	−	21.3844i	−0.391012	−	0.677252i	−0.992583	+	0.121567i	$0.961208\pi$
$998$	−0.473811	−	0.820665i	−0.0149982	−	0.0259777i
$999$	−7.26885			−0.229976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.f.106.1	✓	10
3.2	odd	2		855.2.k.i.676.5		10
19.7	even	3	inner	285.2.i.f.121.1	yes	10
19.8	odd	6		5415.2.a.z.1.1		5
19.11	even	3		5415.2.a.y.1.5		5
57.26	odd	6		855.2.k.i.406.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.1	✓	10	1.1	even	1	trivial
285.2.i.f.121.1	yes	10	19.7	even	3	inner
855.2.k.i.406.5		10	57.26	odd	6
855.2.k.i.676.5		10	3.2	odd	2
5415.2.a.y.1.5		5	19.11	even	3
5415.2.a.z.1.1		5	19.8	odd	6

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12375 + 1.94639i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.52562 - 2.64245i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.12375 + 1.94639i) q^{6} +3.16638 q^{7} +2.36264 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.12375 - 1.94639i) q^{10} +4.81770 q^{11} -3.05123 q^{12} +(-0.583191 - 1.01012i) q^{13} +(-3.55821 + 6.16301i) q^{14} +(0.500000 + 0.866025i) q^{15} +(0.396220 - 0.686273i) q^{16} +(-2.92184 + 5.06077i) q^{17} +2.24750 q^{18} +(3.21554 + 2.94284i) q^{19} +3.05123 q^{20} +(1.58319 - 2.74217i) q^{21} +(-5.41388 + 9.37711i) q^{22} +(4.29873 + 7.44562i) q^{23} +(1.18132 - 2.04611i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.62144 q^{26} -1.00000 q^{27} +(-4.83069 - 8.36699i) q^{28} +(-3.65634 - 6.33297i) q^{29} -2.24750 q^{30} -5.10247 q^{31} +(3.25314 + 5.63461i) q^{32} +(2.40885 - 4.17225i) q^{33} +(-6.56681 - 11.3741i) q^{34} +(-1.58319 + 2.74217i) q^{35} +(-1.52562 + 2.64245i) q^{36} +7.26885 q^{37} +(-9.34136 + 2.95167i) q^{38} -1.16638 q^{39} +(-1.18132 + 2.04611i) q^{40} +(1.24750 - 2.16072i) q^{41} +(3.55821 + 6.16301i) q^{42} +(-0.583191 + 1.01012i) q^{43} +(-7.34996 - 12.7305i) q^{44} +1.00000 q^{45} -19.3227 q^{46} +(-4.68830 - 8.12038i) q^{47} +(-0.396220 - 0.686273i) q^{48} +3.02597 q^{49} +2.24750 q^{50} +(2.92184 + 5.06077i) q^{51} +(-1.77945 + 3.08210i) q^{52} +(1.37689 + 2.38485i) q^{53} +(1.12375 - 1.94639i) q^{54} +(-2.40885 + 4.17225i) q^{55} +7.48103 q^{56} +(4.15634 - 1.31332i) q^{57} +16.4352 q^{58} +(5.05626 - 8.75770i) q^{59} +(1.52562 - 2.64245i) q^{60} +(2.55418 + 4.42398i) q^{61} +(5.73389 - 9.93138i) q^{62} +(-1.58319 - 2.74217i) q^{63} -13.0380 q^{64} +1.16638 q^{65} +(5.41388 + 9.37711i) q^{66} +(-0.519277 - 0.899414i) q^{67} +17.8304 q^{68} +8.59746 q^{69} +(-3.55821 - 6.16301i) q^{70} +(2.16135 - 3.74358i) q^{71} +(-1.18132 - 2.04611i) q^{72} +(-1.81673 + 3.14666i) q^{73} +(-8.16835 + 14.1480i) q^{74} -1.00000 q^{75} +(2.87062 - 12.9865i) q^{76} +15.2547 q^{77} +(1.31072 - 2.27023i) q^{78} +(7.53826 - 13.0567i) q^{79} +(0.396220 + 0.686273i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.80374 + 4.85622i) q^{82} -8.98408 q^{83} -9.66137 q^{84} +(-2.92184 - 5.06077i) q^{85} +(-1.31072 - 2.27023i) q^{86} -7.31269 q^{87} +11.3825 q^{88} +(-2.08614 - 3.61330i) q^{89} +(-1.12375 + 1.94639i) q^{90} +(-1.84661 - 3.19841i) q^{91} +(13.1164 - 22.7183i) q^{92} +(-2.55123 + 4.41887i) q^{93} +21.0739 q^{94} +(-4.15634 + 1.31332i) q^{95} +6.50629 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-3.40043 + 5.88972i) q^{98} +(-2.40885 - 4.17225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more