LMFDB - Embedded newform 234.2.e.d.157.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(79,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			157.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	234.157
Dual form			234.2.e.d.79.3

$q$-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} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64400 + 2.84748i) q^{5} +(1.29418 + 1.15113i) q^{6} +(1.40545 + 2.43430i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} -3.28799 q^{10} +(-2.58836 - 4.48318i) q^{11} +(-0.349814 + 1.69636i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.40545 + 2.43430i) q^{14} +(-1.15019 + 5.57761i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.699628 q^{17} +(2.75526 + 1.18682i) q^{18} +7.17673 q^{19} +(-1.64400 - 2.84748i) q^{20} +(3.63781 + 3.23569i) q^{21} +(2.58836 - 4.48318i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-1.64400 + 0.545231i) q^{24} +(-2.90545 - 5.03238i) q^{25} -1.00000 q^{26} +(2.97710 - 4.25874i) q^{27} -2.81089 q^{28} +(1.11126 + 1.92477i) q^{29} +(-5.40545 + 1.79272i) q^{30} +(-1.38874 + 2.40536i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.69963 - 5.95907i) q^{33} +(-0.349814 - 0.605896i) q^{34} -9.24219 q^{35} +(0.349814 + 2.97954i) q^{36} -0.712008 q^{37} +(3.58836 + 6.21523i) q^{38} +(-0.349814 + 1.69636i) q^{39} +(1.64400 - 2.84748i) q^{40} +(0.411636 - 0.712974i) q^{41} +(-0.983290 + 4.76828i) q^{42} +(-5.74907 - 9.95768i) q^{43} +5.17673 q^{44} +(1.15019 + 9.79669i) q^{45} +6.00000 q^{46} +(-0.761450 - 1.31887i) q^{47} +(-1.29418 - 1.15113i) q^{48} +(-0.450558 + 0.780389i) q^{49} +(2.90545 - 5.03238i) q^{50} +(-1.15019 + 0.381459i) q^{51} +(-0.500000 - 0.866025i) q^{52} -11.0210 q^{53} +(5.17673 + 0.448873i) q^{54} +17.0210 q^{55} +(-1.40545 - 2.43430i) q^{56} +(11.7985 - 3.91298i) q^{57} +(-1.11126 + 1.92477i) q^{58} +(-7.39926 + 12.8159i) q^{59} +(-4.25526 - 3.78490i) q^{60} +(-4.69963 - 8.13999i) q^{61} -2.77747 q^{62} +(7.74474 + 3.33602i) q^{63} +1.00000 q^{64} +(-1.64400 - 2.84748i) q^{65} +(1.81089 - 8.78158i) q^{66} +(-0.222528 + 0.385430i) q^{67} +(0.349814 - 0.605896i) q^{68} +(2.09888 - 10.1781i) q^{69} +(-4.62110 - 8.00397i) q^{70} -1.18911 q^{71} +(-2.40545 + 1.79272i) q^{72} -0.222528 q^{73} +(-0.356004 - 0.616617i) q^{74} +(-7.52035 - 6.68907i) q^{75} +(-3.58836 + 6.21523i) q^{76} +(7.27561 - 12.6017i) q^{77} +(-1.64400 + 0.545231i) q^{78} +(7.87636 + 13.6422i) q^{79} +3.28799 q^{80} +(2.57234 - 8.62456i) q^{81} +0.823272 q^{82} +(3.98762 + 6.90676i) q^{83} +(-4.62110 + 1.53259i) q^{84} +(1.15019 - 1.99218i) q^{85} +(5.74907 - 9.95768i) q^{86} +(2.87636 + 2.55841i) q^{87} +(2.58836 + 4.48318i) q^{88} +7.39926 q^{89} +(-7.90909 + 5.89443i) q^{90} -2.81089 q^{91} +(3.00000 + 5.19615i) q^{92} +(-0.971599 + 4.71159i) q^{93} +(0.761450 - 1.31887i) q^{94} +(-11.7985 + 20.4356i) q^{95} +(0.349814 - 1.69636i) q^{96} +(-2.47710 - 4.29046i) q^{97} -0.901116 q^{98} +(-14.2632 - 6.14384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 2 q^{14} - 13 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 20 q^{19} + 2 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 2 * q^14 - 13 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 + 20 * q^19 + 2 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^23 + 2 * q^24 - 11 * q^25 - 6 * q^26 + 7 * q^27 - 4 * q^28 + 6 * q^29 - 26 * q^30 - 9 * q^31 + 3 * q^32 - 28 * q^33 + 4 * q^34 - 10 * q^35 - 4 * q^36 - 28 * q^37 + 10 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 13 * q^42 - 4 * q^43 + 8 * q^44 + 13 * q^45 + 36 * q^46 - 10 * q^47 - 2 * q^48 - 21 * q^49 + 11 * q^50 - 13 * q^51 - 3 * q^52 - 16 * q^53 + 8 * q^54 + 52 * q^55 - 2 * q^56 + 22 * q^57 - 6 * q^58 - 20 * q^59 - 13 * q^60 - 16 * q^61 - 18 * q^62 + 59 * q^63 + 6 * q^64 + 2 * q^65 - 2 * q^66 - 4 * q^68 - 24 * q^69 - 5 * q^70 - 20 * q^71 - 8 * q^72 - 14 * q^74 + 2 * q^75 - 10 * q^76 - 16 * q^77 + 2 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 + 28 * q^82 - 12 * q^83 - 5 * q^84 + 13 * q^85 + 4 * q^86 - 18 * q^87 + 4 * q^88 + 20 * q^89 - q^90 - 4 * q^91 + 18 * q^92 + 26 * q^93 + 10 * q^94 - 22 * q^95 - 4 * q^96 - 4 * q^97 - 42 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.64400	−	0.545231i	0.949162	−	0.314789i
$3$	1.64400	−	0.545231i	0.949162	−	0.314789i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.64400	+	2.84748i	−0.735217	+	1.27343i	0.219411	+	0.975633i	$0.429587\pi$
$5$	−1.64400	+	2.84748i	−0.735217	+	1.27343i	−0.954628	+	0.297801i	$0.903747\pi$
$6$	1.29418	+	1.15113i	0.528348	+	0.469946i
$7$	1.40545	+	2.43430i	0.531209	+	0.920080i	0.999337	+	0.0364197i	$0.0115953\pi$
$7$	1.40545	+	2.43430i	0.531209	+	0.920080i	−0.468128	+	0.883661i	$0.655071\pi$
$8$	−1.00000			−0.353553
$9$	2.40545	−	1.79272i	0.801815	−	0.597572i
$10$	−3.28799			−1.03975
$11$	−2.58836	−	4.48318i	−0.780421	−	1.35173i	−0.931697	−	0.363237i	$-0.881671\pi$
$11$	−2.58836	−	4.48318i	−0.780421	−	1.35173i	0.151276	−	0.988492i	$-0.451662\pi$
$12$	−0.349814	+	1.69636i	−0.100983	+	0.489696i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−1.40545	+	2.43430i	−0.375621	+	0.650595i
$15$	−1.15019	+	5.57761i	−0.296977	+	1.44013i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.699628			−0.169685			−0.0848424	−	0.996394i	$-0.527039\pi$
$17$	−0.699628			−0.169685			−0.0848424	+	0.996394i	$0.527039\pi$
$18$	2.75526	+	1.18682i	0.649421	+	0.279736i
$19$	7.17673			1.64645			0.823227	−	0.567712i	$-0.192171\pi$
$19$	7.17673			1.64645			0.823227	+	0.567712i	$0.192171\pi$
$20$	−1.64400	−	2.84748i	−0.367609	−	0.636717i
$21$	3.63781	+	3.23569i	0.793834	+	0.706086i
$22$	2.58836	−	4.48318i	0.551841	−	0.955817i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−1.64400	+	0.545231i	−0.335579	+	0.111295i
$25$	−2.90545	−	5.03238i	−0.581089	−	1.00648i
$26$	−1.00000			−0.196116
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$	−2.81089			−0.531209
$29$	1.11126	+	1.92477i	0.206357	+	0.357420i	0.950564	−	0.310528i	$-0.100506\pi$
$29$	1.11126	+	1.92477i	0.206357	+	0.357420i	−0.744208	+	0.667948i	$0.767173\pi$
$30$	−5.40545	+	1.79272i	−0.986895	+	0.327304i
$31$	−1.38874	+	2.40536i	−0.249424	+	0.432016i	−0.963366	−	0.268189i	$-0.913575\pi$
$31$	−1.38874	+	2.40536i	−0.249424	+	0.432016i	0.713942	+	0.700205i	$0.246908\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.69963	−	5.95907i	−1.16626	−	1.03734i
$34$	−0.349814	−	0.605896i	−0.0599926	−	0.103910i
$35$	−9.24219			−1.56222
$36$	0.349814	+	2.97954i	0.0583023	+	0.496589i
$37$	−0.712008			−0.117053			−0.0585267	−	0.998286i	$-0.518640\pi$
$37$	−0.712008			−0.117053			−0.0585267	+	0.998286i	$0.518640\pi$
$38$	3.58836	+	6.21523i	0.582110	+	1.00824i
$39$	−0.349814	+	1.69636i	−0.0560151	+	0.271635i
$40$	1.64400	−	2.84748i	0.259939	−	0.450227i
$41$	0.411636	−	0.712974i	0.0642867	−	0.111348i	−0.832091	−	0.554640i	$-0.812856\pi$
$41$	0.411636	−	0.712974i	0.0642867	−	0.111348i	0.896377	+	0.443292i	$0.146189\pi$
$42$	−0.983290	+	4.76828i	−0.151725	+	0.735761i
$43$	−5.74907	−	9.95768i	−0.876725	−	1.51853i	−0.854914	−	0.518770i	$-0.826390\pi$
$43$	−5.74907	−	9.95768i	−0.876725	−	1.51853i	−0.0218113	−	0.999762i	$-0.506943\pi$
$44$	5.17673			0.780421
$45$	1.15019	+	9.79669i	0.171460	+	1.46040i
$46$	6.00000			0.884652
$47$	−0.761450	−	1.31887i	−0.111069	−	0.192377i	0.805133	−	0.593095i	$-0.202094\pi$
$47$	−0.761450	−	1.31887i	−0.111069	−	0.192377i	−0.916202	+	0.400718i	$0.868761\pi$
$48$	−1.29418	−	1.15113i	−0.186799	−	0.166151i
$49$	−0.450558	+	0.780389i	−0.0643654	+	0.111484i
$50$	2.90545	−	5.03238i	0.410892	−	0.711686i
$51$	−1.15019	+	0.381459i	−0.161058	+	0.0534149i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−11.0210			−1.51386			−0.756928	−	0.653498i	$-0.773301\pi$
$53$	−11.0210			−1.51386			−0.756928	+	0.653498i	$0.773301\pi$
$54$	5.17673	+	0.448873i	0.704463	+	0.0610839i
$55$	17.0210			2.29512
$56$	−1.40545	−	2.43430i	−0.187811	−	0.325298i
$57$	11.7985	−	3.91298i	1.56275	−	0.518286i
$58$	−1.11126	+	1.92477i	−0.145916	+	0.252734i
$59$	−7.39926	+	12.8159i	−0.963301	+	1.66849i	−0.249189	+	0.968455i	$0.580164\pi$
$59$	−7.39926	+	12.8159i	−0.963301	+	1.66849i	−0.714112	+	0.700032i	$0.753169\pi$
$60$	−4.25526	−	3.78490i	−0.549352	−	0.488628i
$61$	−4.69963	−	8.13999i	−0.601726	−	1.04222i	−0.992560	−	0.121758i	$-0.961147\pi$
$61$	−4.69963	−	8.13999i	−0.601726	−	1.04222i	0.390834	−	0.920461i	$-0.372187\pi$
$62$	−2.77747			−0.352739
$63$	7.74474	+	3.33602i	0.975745	+	0.420299i
$64$	1.00000			0.125000
$65$	−1.64400	−	2.84748i	−0.203913	−	0.353187i
$66$	1.81089	−	8.78158i	0.222905	−	1.08094i
$67$	−0.222528	+	0.385430i	−0.0271862	+	0.0470878i	−0.879298	−	0.476271i	$-0.841988\pi$
$67$	−0.222528	+	0.385430i	−0.0271862	+	0.0470878i	0.852112	+	0.523359i	$0.175321\pi$
$68$	0.349814	−	0.605896i	0.0424212	−	0.0734757i
$69$	2.09888	−	10.1781i	0.252676	−	1.22530i
$70$	−4.62110	−	8.00397i	−0.552327	−	0.956658i
$71$	−1.18911			−0.141121			−0.0705606	−	0.997507i	$-0.522479\pi$
$71$	−1.18911			−0.141121			−0.0705606	+	0.997507i	$0.522479\pi$
$72$	−2.40545	+	1.79272i	−0.283485	+	0.211274i
$73$	−0.222528			−0.0260450			−0.0130225	−	0.999915i	$-0.504145\pi$
$73$	−0.222528			−0.0260450			−0.0130225	+	0.999915i	$0.504145\pi$
$74$	−0.356004	−	0.616617i	−0.0413846	−	0.0716803i
$75$	−7.52035	−	6.68907i	−0.868375	−	0.772388i
$76$	−3.58836	+	6.21523i	−0.411614	+	0.712936i
$77$	7.27561	−	12.6017i	0.829133	−	1.43610i
$78$	−1.64400	+	0.545231i	−0.186146	+	0.0617353i
$79$	7.87636	+	13.6422i	0.886159	+	1.53487i	0.844379	+	0.535746i	$0.179970\pi$
$79$	7.87636	+	13.6422i	0.886159	+	1.53487i	0.0417802	+	0.999127i	$0.486697\pi$
$80$	3.28799			0.367609
$81$	2.57234	−	8.62456i	0.285816	−	0.958285i
$82$	0.823272			0.0909152
$83$	3.98762	+	6.90676i	0.437698	+	0.758116i	0.997512	−	0.0705032i	$-0.0224605\pi$
$83$	3.98762	+	6.90676i	0.437698	+	0.758116i	−0.559813	+	0.828619i	$0.689127\pi$
$84$	−4.62110	+	1.53259i	−0.504203	+	0.167219i
$85$	1.15019	−	1.99218i	0.124755	−	0.216082i
$86$	5.74907	−	9.95768i	0.619938	−	1.07376i
$87$	2.87636	+	2.55841i	0.308378	+	0.274291i
$88$	2.58836	+	4.48318i	0.275921	+	0.477908i
$89$	7.39926			0.784320			0.392160	−	0.919897i	$-0.371728\pi$
$89$	7.39926			0.784320			0.392160	+	0.919897i	$0.371728\pi$
$90$	−7.90909	+	5.89443i	−0.833691	+	0.621328i
$91$	−2.81089			−0.294662
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	−0.971599	+	4.71159i	−0.100750	+	0.488569i
$94$	0.761450	−	1.31887i	0.0785376	−	0.136031i
$95$	−11.7985	+	20.4356i	−1.21050	+	2.09665i
$96$	0.349814	−	1.69636i	0.0357027	−	0.173134i
$97$	−2.47710	−	4.29046i	−0.251511	−	0.435630i	0.712431	−	0.701742i	$-0.247594\pi$
$97$	−2.47710	−	4.29046i	−0.251511	−	0.435630i	−0.963942	+	0.266112i	$0.914261\pi$
$98$	−0.901116			−0.0910264
$99$	−14.2632	−	6.14384i	−1.43351	−	0.617479i
$100$	5.81089			0.581089
$101$	1.47710	+	2.55841i	0.146977	+	0.254572i	0.930109	−	0.367284i	$-0.119712\pi$
$101$	1.47710	+	2.55841i	0.146977	+	0.254572i	−0.783132	+	0.621856i	$0.786379\pi$
$102$	−0.905446	−	0.805361i	−0.0896525	−	0.0797426i
$103$	−4.69963	+	8.13999i	−0.463068	+	0.802058i	−0.999112	−	0.0421326i	$-0.986585\pi$
$103$	−4.69963	+	8.13999i	−0.463068	+	0.802058i	0.536044	+	0.844190i	$0.319918\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$	−15.1941	+	5.03913i	−1.48279	+	0.491769i
$106$	−5.51052	−	9.54450i	−0.535229	−	0.927044i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	2.19963	+	4.70761i	0.211659	+	0.452990i
$109$	−6.67487			−0.639336			−0.319668	−	0.947530i	$-0.603571\pi$
$109$	−6.67487			−0.639336			−0.319668	+	0.947530i	$0.603571\pi$
$110$	8.51052	+	14.7407i	0.811446	+	1.40547i
$111$	−1.17054	+	0.388209i	−0.111103	+	0.0368471i
$112$	1.40545	−	2.43430i	0.132802	−	0.230020i
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$	9.28799	+	8.26132i	0.869900	+	0.773744i
$115$	9.86398	+	17.0849i	0.919821	+	1.59318i
$116$	−2.22253			−0.206357
$117$	0.349814	+	2.97954i	0.0323403	+	0.275458i
$118$	−14.7985			−1.36231
$119$	−0.983290	−	1.70311i	−0.0901380	−	0.156124i
$120$	1.15019	−	5.57761i	0.104997	−	0.509164i
$121$	−7.89926	+	13.6819i	−0.718114	+	1.24381i
$122$	4.69963	−	8.13999i	0.425484	−	0.736960i
$123$	0.287992	−	1.39656i	0.0259674	−	0.125924i
$124$	−1.38874	−	2.40536i	−0.124712	−	0.216008i
$125$	2.66621			0.238473
$126$	0.983290	+	8.37515i	0.0875984	+	0.746118i
$127$	−3.42402			−0.303832			−0.151916	−	0.988393i	$-0.548544\pi$
$127$	−3.42402			−0.303832			−0.151916	+	0.988393i	$0.548544\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−14.8807	−	13.2358i	−1.31017	−	1.16535i
$130$	1.64400	−	2.84748i	0.144188	−	0.249741i
$131$	−4.12729	+	7.14867i	−0.360603	+	0.624582i	−0.988060	−	0.154069i	$-0.950762\pi$
$131$	−4.12729	+	7.14867i	−0.360603	+	0.624582i	0.627458	+	0.778651i	$0.284096\pi$
$132$	8.51052	−	2.82251i	0.740746	−	0.245668i
$133$	10.0865	+	17.4703i	0.874611	+	1.51487i
$134$	−0.445057			−0.0384470
$135$	7.23236	+	15.4786i	0.622462	+	1.33219i
$136$	0.699628			0.0599926
$137$	2.30037	+	3.98436i	0.196534	+	0.340407i	0.947402	−	0.320045i	$-0.103698\pi$
$137$	2.30037	+	3.98436i	0.196534	+	0.340407i	−0.750868	+	0.660452i	$0.770365\pi$
$138$	9.86398	−	3.27139i	0.839677	−	0.278479i
$139$	−5.29418	+	9.16979i	−0.449047	+	0.777772i	−0.998324	−	0.0578683i	$-0.981570\pi$
$139$	−5.29418	+	9.16979i	−0.449047	+	0.777772i	0.549278	+	0.835640i	$0.314903\pi$
$140$	4.62110	−	8.00397i	0.390554	−	0.676459i
$141$	−1.97091	−	1.75305i	−0.165981	−	0.147634i
$142$	−0.594554	−	1.02980i	−0.0498939	−	0.0864187i
$143$	5.17673			0.432900
$144$	−2.75526	−	1.18682i	−0.229605	−	0.0989016i
$145$	−7.30766			−0.606868
$146$	−0.111264	−	0.192715i	−0.00920829	−	0.0159492i
$147$	−0.315223	+	1.52861i	−0.0259991	+	0.126078i
$148$	0.356004	−	0.616617i	0.0292633	−	0.0506856i
$149$	8.48762	−	14.7010i	0.695333	−	1.20435i	−0.274735	−	0.961520i	$-0.588590\pi$
$149$	8.48762	−	14.7010i	0.695333	−	1.20435i	0.970068	−	0.242832i	$-0.0780764\pi$
$150$	2.03273	−	9.85735i	0.165972	−	0.804850i
$151$	−11.1087	−	19.2409i	−0.904015	−	1.56580i	−0.822235	−	0.569149i	$-0.807273\pi$
$151$	−11.1087	−	19.2409i	−0.904015	−	1.56580i	−0.0817798	−	0.996650i	$-0.526060\pi$
$152$	−7.17673			−0.582110
$153$	−1.68292	+	1.25423i	−0.136056	+	0.101399i
$154$	14.5512			1.17257
$155$	−4.56615	−	7.90881i	−0.366762	−	0.635251i
$156$	−1.29418	−	1.15113i	−0.103617	−	0.0921639i
$157$	2.33379	−	4.04225i	0.186257	−	0.322606i	−0.757742	−	0.652554i	$-0.773698\pi$
$157$	2.33379	−	4.04225i	0.186257	−	0.322606i	0.943999	+	0.329947i	$0.107031\pi$
$158$	−7.87636	+	13.6422i	−0.626609	+	1.08532i
$159$	−18.1185	+	6.00901i	−1.43689	+	0.476546i
$160$	1.64400	+	2.84748i	0.129969	+	0.225113i
$161$	16.8654			1.32918
$162$	8.75526	−	2.08457i	0.687878	−	0.163779i
$163$	−11.9752			−0.937973			−0.468987	−	0.883205i	$-0.655381\pi$
$163$	−11.9752			−0.937973			−0.468987	+	0.883205i	$0.655381\pi$
$164$	0.411636	+	0.712974i	0.0321434	+	0.0556740i
$165$	27.9825	−	9.28040i	2.17844	−	0.722478i
$166$	−3.98762	+	6.90676i	−0.309499	+	0.536069i
$167$	3.38874	−	5.86946i	0.262228	−	0.454193i	−0.704605	−	0.709599i	$-0.748876\pi$
$167$	3.38874	−	5.86946i	0.262228	−	0.454193i	0.966834	+	0.255407i	$0.0822093\pi$
$168$	−3.63781	−	3.23569i	−0.280663	−	0.249639i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.30037			0.176430
$171$	17.2632	−	12.8658i	1.32015	−	0.983875i
$172$	11.4981			0.876725
$173$	−9.57598	−	16.5861i	−0.728049	−	1.26102i	−0.957707	−	0.287746i	$-0.907094\pi$
$173$	−9.57598	−	16.5861i	−0.728049	−	1.26102i	0.229658	−	0.973271i	$-0.426239\pi$
$174$	−0.777472	+	3.77020i	−0.0589400	+	0.285818i
$175$	8.16690	−	14.1455i	0.617359	−	1.06930i
$176$	−2.58836	+	4.48318i	−0.195105	+	0.337932i
$177$	−5.17673	+	25.1036i	−0.389107	+	1.88690i
$178$	3.69963	+	6.40794i	0.277299	+	0.480296i
$179$	−0.210149			−0.0157072			−0.00785362	−	0.999969i	$-0.502500\pi$
$179$	−0.210149			−0.0157072			−0.00785362	+	0.999969i	$0.502500\pi$
$180$	−9.05927	−	3.90225i	−0.675238	−	0.290857i
$181$	6.44506			0.479057			0.239529	−	0.970889i	$-0.423007\pi$
$181$	6.44506			0.479057			0.239529	+	0.970889i	$0.423007\pi$
$182$	−1.40545	−	2.43430i	−0.104179	−	0.180443i
$183$	−12.1643	−	10.8197i	−0.899214	−	0.799818i
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	1.17054	−	2.02743i	0.0860597	−	0.149060i
$186$	−4.56615	+	1.51436i	−0.334807	+	0.111039i
$187$	1.81089	+	3.13656i	0.132426	+	0.229368i
$188$	1.52290			0.111069
$189$	14.5512	+	1.26174i	1.05845	+	0.0917777i
$190$	−23.5970			−1.71191
$191$	11.6749	+	20.2215i	0.844764	+	1.46317i	0.885826	+	0.464017i	$0.153592\pi$
$191$	11.6749	+	20.2215i	0.844764	+	1.46317i	−0.0410623	+	0.999157i	$0.513074\pi$
$192$	1.64400	−	0.545231i	0.118645	−	0.0393487i
$193$	−12.4647	+	21.5895i	−0.897230	+	1.55405i	−0.0662102	+	0.997806i	$0.521091\pi$
$193$	−12.4647	+	21.5895i	−0.897230	+	1.55405i	−0.831020	+	0.556243i	$0.812243\pi$
$194$	2.47710	−	4.29046i	0.177845	−	0.308037i
$195$	−4.25526	−	3.78490i	−0.304726	−	0.271042i
$196$	−0.450558	−	0.780389i	−0.0321827	−	0.0557421i
$197$	−10.2349			−0.729207			−0.364604	−	0.931163i	$-0.618795\pi$
$197$	−10.2349			−0.729207			−0.364604	+	0.931163i	$0.618795\pi$
$198$	−1.81089	−	15.4242i	−0.128695	−	1.09615i
$199$	26.9047			1.90722			0.953611	−	0.301041i	$-0.0973342\pi$
$199$	26.9047			1.90722			0.953611	+	0.301041i	$0.0973342\pi$
$200$	2.90545	+	5.03238i	0.205446	+	0.355843i
$201$	−0.155687	+	0.754975i	−0.0109813	+	0.0532519i
$202$	−1.47710	+	2.55841i	−0.103928	+	0.180009i
$203$	−3.12364	+	5.41031i	−0.219237	+	0.379729i
$204$	0.244740	−	1.18682i	0.0171352	−	0.0830940i
$205$	1.35346	+	2.34425i	0.0945295	+	0.163730i
$206$	−9.39926			−0.654877
$207$	−2.09888	−	17.8772i	−0.145883	−	1.24255i
$208$	1.00000			0.0693375
$209$	−18.5760	−	32.1745i	−1.28493	−	2.22556i
$210$	−11.9611	−	10.6389i	−0.825393	−	0.734156i
$211$	−2.35600	+	4.08072i	−0.162194	+	0.280928i	−0.935655	−	0.352915i	$-0.885190\pi$
$211$	−2.35600	+	4.08072i	−0.162194	+	0.280928i	0.773461	+	0.633844i	$0.218524\pi$
$212$	5.51052	−	9.54450i	0.378464	−	0.655519i
$213$	−1.95489	+	0.648338i	−0.133947	+	0.0444234i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	37.8058			2.57833
$216$	−2.97710	+	4.25874i	−0.202566	+	0.289771i
$217$	−7.80717			−0.529985
$218$	−3.33743	−	5.78061i	−0.226040	−	0.391512i
$219$	−0.365836	+	0.121329i	−0.0247209	+	0.00819868i
$220$	−8.51052	+	14.7407i	−0.573779	+	0.993815i
$221$	0.349814	−	0.605896i	0.0235310	−	0.0407570i
$222$	−0.921468	−	0.819611i	−0.0618449	−	0.0550087i
$223$	−3.81453	−	6.60697i	−0.255440	−	0.442435i	0.709575	−	0.704630i	$-0.248887\pi$
$223$	−3.81453	−	6.60697i	−0.255440	−	0.442435i	−0.965015	+	0.262195i	$0.915554\pi$
$224$	2.81089			0.187811
$225$	−16.0105	−	6.89648i	−1.06737	−	0.459765i
$226$	3.00000			0.199557
$227$	−11.0210	−	19.0890i	−0.731492	−	1.26698i	−0.956245	−	0.292566i	$-0.905491\pi$
$227$	−11.0210	−	19.0890i	−0.731492	−	1.26698i	0.224753	−	0.974416i	$-0.427842\pi$
$228$	−2.51052	+	12.1743i	−0.166263	+	0.806263i
$229$	2.24474	−	3.88800i	0.148337	−	0.256926i	−0.782276	−	0.622932i	$-0.785941\pi$
$229$	2.24474	−	3.88800i	0.148337	−	0.256926i	0.930613	+	0.366005i	$0.119275\pi$
$230$	−9.86398	+	17.0849i	−0.650411	+	1.12655i
$231$	5.09022	−	24.6841i	0.334912	−	1.62409i
$232$	−1.11126	−	1.92477i	−0.0729581	−	0.126367i
$233$	5.54256			0.363105			0.181553	−	0.983381i	$-0.441888\pi$
$233$	5.54256			0.363105			0.181553	+	0.983381i	$0.441888\pi$
$234$	−2.40545	+	1.79272i	−0.157249	+	0.117193i
$235$	5.00728			0.326639
$236$	−7.39926	−	12.8159i	−0.481651	−	0.834243i
$237$	20.3869	+	18.1334i	1.32427	+	1.17789i
$238$	0.983290	−	1.70311i	0.0637372	−	0.110396i
$239$	−3.71565	+	6.43569i	−0.240345	+	0.416290i	−0.960813	−	0.277198i	$-0.910594\pi$
$239$	−3.71565	+	6.43569i	−0.240345	+	0.416290i	0.720467	+	0.693489i	$0.243927\pi$
$240$	5.40545	−	1.79272i	0.348920	−	0.115719i
$241$	−4.69963	−	8.13999i	−0.302730	−	0.524343i	0.674024	−	0.738710i	$-0.264565\pi$
$241$	−4.69963	−	8.13999i	−0.302730	−	0.524343i	−0.976753	+	0.214367i	$0.931231\pi$
$242$	−15.7985			−1.01557
$243$	−0.473458	−	15.5813i	−0.0303723	−	0.999539i
$244$	9.39926			0.601726
$245$	−1.48143	−	2.56591i	−0.0946451	−	0.163930i
$246$	1.35346	−	0.448873i	0.0862932	−	0.0286191i
$247$	−3.58836	+	6.21523i	−0.228322	+	0.395466i
$248$	1.38874	−	2.40536i	0.0881848	−	0.152741i
$249$	10.3214	+	9.18051i	0.654093	+	0.581791i
$250$	1.33310	+	2.30900i	0.0843129	+	0.146034i
$251$	15.9963			1.00968			0.504838	−	0.863214i	$-0.331552\pi$
$251$	15.9963			1.00968			0.504838	+	0.863214i	$0.331552\pi$
$252$	−6.76145	+	5.03913i	−0.425931	+	0.317435i
$253$	−31.0604			−1.95275
$254$	−1.71201	−	2.96528i	−0.107421	−	0.186059i
$255$	0.804702	−	3.90225i	0.0503924	−	0.244369i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.0432524	−	0.0749153i	0.00269801	−	0.00467309i	−0.864673	−	0.502335i	$-0.832475\pi$
$257$	0.0432524	−	0.0749153i	0.00269801	−	0.00467309i	0.867371	+	0.497662i	$0.165808\pi$
$258$	4.02221	−	19.5050i	0.250412	−	1.21433i
$259$	−1.00069	−	1.73324i	−0.0621798	−	0.107699i
$260$	3.28799			0.203913
$261$	6.12364	+	2.63774i	0.379044	+	0.163272i
$262$	−8.25457			−0.509969
$263$	−0.489480	−	0.847803i	−0.0301826	−	0.0522778i	0.850540	−	0.525911i	$-0.176276\pi$
$263$	−0.489480	−	0.847803i	−0.0301826	−	0.0522778i	−0.880722	+	0.473633i	$0.842942\pi$
$264$	6.69963	+	5.95907i	0.412334	+	0.366755i
$265$	18.1185	−	31.3822i	1.11301	−	1.92780i
$266$	−10.0865	+	17.4703i	−0.618443	+	1.07118i
$267$	12.1643	−	4.03430i	0.744446	−	0.246895i
$268$	−0.222528	−	0.385430i	−0.0135931	−	0.0235439i
$269$	−25.5723			−1.55917			−0.779584	−	0.626297i	$-0.784570\pi$
$269$	−25.5723			−1.55917			−0.779584	+	0.626297i	$0.784570\pi$
$270$	−9.78868	+	14.0027i	−0.595720	+	0.852178i
$271$	16.9766			1.03126			0.515628	−	0.856813i	$-0.327559\pi$
$271$	16.9766			1.03126			0.515628	+	0.856813i	$0.327559\pi$
$272$	0.349814	+	0.605896i	0.0212106	+	0.0367378i
$273$	−4.62110	+	1.53259i	−0.279681	+	0.0927563i
$274$	−2.30037	+	3.98436i	−0.138971	+	0.240704i
$275$	−15.0407	+	26.0513i	−0.906989	+	1.57095i
$276$	7.76509	+	6.90676i	0.467404	+	0.415738i
$277$	−1.69963	−	2.94384i	−0.102121	−	0.176878i	0.810437	−	0.585825i	$-0.199229\pi$
$277$	−1.69963	−	2.94384i	−0.102121	−	0.176878i	−0.912558	+	0.408947i	$0.865896\pi$
$278$	−10.5884			−0.635048
$279$	0.971599	+	8.27557i	0.0581681	+	0.495446i
$280$	9.24219			0.552327
$281$	14.3411	+	24.8395i	0.855517	+	1.48180i	0.876165	+	0.482012i	$0.160094\pi$
$281$	14.3411	+	24.8395i	0.855517	+	1.48180i	−0.0206478	+	0.999787i	$0.506573\pi$
$282$	0.532732	−	2.58338i	0.0317237	−	0.153838i
$283$	5.59888	−	9.69755i	0.332819	−	0.576460i	−0.650244	−	0.759725i	$-0.725333\pi$
$283$	5.59888	−	9.69755i	0.332819	−	0.576460i	0.983063	+	0.183266i	$0.0586668\pi$
$284$	0.594554	−	1.02980i	0.0352803	−	0.0611072i
$285$	−8.25457	+	40.0290i	−0.488959	+	2.37111i
$286$	2.58836	+	4.48318i	0.153053	+	0.265096i
$287$	2.31413			0.136599
$288$	−0.349814	−	2.97954i	−0.0206130	−	0.175571i
$289$	−16.5105			−0.971207
$290$	−3.65383	−	6.32862i	−0.214560	−	0.371629i
$291$	−6.41164	−	5.70291i	−0.375857	−	0.334311i
$292$	0.111264	−	0.192715i	0.00651124	−	0.0112778i
$293$	−3.47091	+	6.01179i	−0.202773	+	0.351213i	−0.949421	−	0.314007i	$-0.898329\pi$
$293$	−3.47091	+	6.01179i	−0.202773	+	0.351213i	0.746648	+	0.665219i	$0.231662\pi$
$294$	−1.48143	+	0.491316i	−0.0863988	+	0.0286541i
$295$	−24.3287	−	42.1385i	−1.41647	−	2.45340i
$296$	0.712008			0.0413846
$297$	−26.7985	−	2.32370i	−1.55501	−	0.134835i
$298$	16.9752			0.983349
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$	9.55308	−	3.16828i	0.551548	−	0.182921i
$301$	16.1600	−	27.9900i	0.931448	−	1.61332i
$302$	11.1087	−	19.2409i	0.639235	−	1.10719i
$303$	3.82327	+	3.40066i	0.219641	+	0.195363i
$304$	−3.58836	−	6.21523i	−0.205807	−	0.356468i
$305$	30.9047			1.76960
$306$	−1.92766	−	0.830332i	−0.110197	−	0.0474669i
$307$	−15.0210			−0.857296			−0.428648	−	0.903472i	$-0.641010\pi$
$307$	−15.0210			−0.857296			−0.428648	+	0.903472i	$0.641010\pi$
$308$	7.27561	+	12.6017i	0.414566	+	0.718050i
$309$	−3.28799	+	15.9445i	−0.187047	+	0.907051i
$310$	4.56615	−	7.90881i	0.259340	−	0.449190i
$311$	3.98762	−	6.90676i	0.226117	−	0.391646i	−0.730537	−	0.682873i	$-0.760730\pi$
$311$	3.98762	−	6.90676i	0.226117	−	0.391646i	0.956654	+	0.291227i	$0.0940634\pi$
$312$	0.349814	−	1.69636i	0.0198043	−	0.0960374i
$313$	−6.99745	−	12.1199i	−0.395519	−	0.685060i	0.597648	−	0.801759i	$-0.296102\pi$
$313$	−6.99745	−	12.1199i	−0.395519	−	0.685060i	−0.993167	+	0.116699i	$0.962769\pi$
$314$	4.66758			0.263407
$315$	−22.2316	+	16.5686i	−1.25261	+	0.933536i
$316$	−15.7527			−0.886159
$317$	4.71015	+	8.15822i	0.264548	+	0.458211i	0.967445	−	0.253081i	$-0.0814438\pi$
$317$	4.71015	+	8.15822i	0.264548	+	0.458211i	−0.702897	+	0.711292i	$0.748110\pi$
$318$	−14.2632	−	12.6866i	−0.799842	−	0.711430i
$319$	5.75271	−	9.96399i	0.322090	−	0.557876i
$320$	−1.64400	+	2.84748i	−0.0919022	+	0.159179i
$321$	19.7280	−	6.54277i	1.10111	−	0.365182i
$322$	8.43268	+	14.6058i	0.469935	+	0.813951i
$323$	−5.02104			−0.279378
$324$	6.18292	+	6.53999i	0.343495	+	0.363333i
$325$	5.81089			0.322330
$326$	−5.98762	−	10.3709i	−0.331624	−	0.574389i
$327$	−10.9735	+	3.63935i	−0.606834	+	0.201256i
$328$	−0.411636	+	0.712974i	−0.0227288	+	0.0393674i
$329$	2.14035	−	3.70720i	0.118002	−	0.204385i
$330$	22.0283	+	19.5934i	1.21262	+	1.07858i
$331$	5.77747	+	10.0069i	0.317559	+	0.550028i	0.979978	−	0.199106i	$-0.0638037\pi$
$331$	5.77747	+	10.0069i	0.317559	+	0.550028i	−0.662419	+	0.749133i	$0.730470\pi$
$332$	−7.97524			−0.437698
$333$	−1.71270	+	1.27643i	−0.0938552	+	0.0699478i
$334$	6.77747			0.370847
$335$	−0.731671	−	1.26729i	−0.0399755	−	0.0692396i
$336$	0.983290	−	4.76828i	0.0536429	−	0.260131i
$337$	−0.405446	+	0.702253i	−0.0220861	+	0.0382542i	−0.876857	−	0.480751i	$-0.840364\pi$
$337$	−0.405446	+	0.702253i	−0.0220861	+	0.0382542i	0.854771	+	0.519005i	$0.173697\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	1.04944	−	5.08907i	0.0569979	−	0.276401i
$340$	1.15019	+	1.99218i	0.0623776	+	0.108041i
$341$	14.3782			0.778624
$342$	19.7738	+	8.51748i	1.06924	+	0.460573i
$343$	17.1433			0.925652
$344$	5.74907	+	9.95768i	0.309969	+	0.536882i
$345$	25.5316	+	22.7094i	1.37457	+	1.22263i
$346$	9.57598	−	16.5861i	0.514808	−	0.891674i
$347$	−7.15452	+	12.3920i	−0.384075	+	0.665237i	−0.991640	−	0.129033i	$-0.958813\pi$
$347$	−7.15452	+	12.3920i	−0.384075	+	0.665237i	0.607566	+	0.794269i	$0.292146\pi$
$348$	−3.65383	+	1.21179i	−0.195866	+	0.0649588i
$349$	7.75526	+	13.4325i	0.415130	+	0.719025i	0.995442	−	0.0953684i	$-0.0304029\pi$
$349$	7.75526	+	13.4325i	0.415130	+	0.719025i	−0.580312	+	0.814394i	$0.697070\pi$
$350$	16.3338			0.873078
$351$	2.19963	+	4.70761i	0.117407	+	0.251274i
$352$	−5.17673			−0.275921
$353$	17.3869	+	30.1150i	0.925410	+	1.60286i	0.790900	+	0.611945i	$0.209613\pi$
$353$	17.3869	+	30.1150i	0.925410	+	1.60286i	0.134510	+	0.990912i	$0.457054\pi$
$354$	−24.3287	+	8.06861i	−1.29306	+	0.428842i
$355$	1.95489	−	3.38597i	0.103755	−	0.179708i
$356$	−3.69963	+	6.40794i	−0.196080	+	0.339620i
$357$	−2.54511	−	2.26378i	−0.134702	−	0.119812i
$358$	−0.105074	−	0.181994i	−0.00555335	−	0.00961868i
$359$	−24.2829			−1.28160			−0.640801	−	0.767707i	$-0.721398\pi$
$359$	−24.2829			−1.28160			−0.640801	+	0.767707i	$0.721398\pi$
$360$	−1.15019	−	9.79669i	−0.0606201	−	0.516331i
$361$	32.5054			1.71081
$362$	3.22253	+	5.58158i	0.169372	+	0.293361i
$363$	−5.52654	+	26.7999i	−0.290068	+	1.40663i
$364$	1.40545	−	2.43430i	0.0736654	−	0.127592i
$365$	0.365836	−	0.633646i	0.0191487	−	0.0331665i
$366$	3.28799	−	15.9445i	0.171866	−	0.833433i
$367$	7.95420	+	13.7771i	0.415206	+	0.719158i	0.995450	−	0.0952849i	$-0.0303762\pi$
$367$	7.95420	+	13.7771i	0.415206	+	0.719158i	−0.580244	+	0.814443i	$0.697043\pi$
$368$	−6.00000			−0.312772
$369$	−0.287992	−	2.45297i	−0.0149923	−	0.127696i
$370$	2.34108			0.121707
$371$	−15.4895	−	26.8286i	−0.804174	−	1.39287i
$372$	−3.59455	−	3.19722i	−0.186369	−	0.165768i
$373$	−5.73305	+	9.92993i	−0.296846	+	0.514152i	−0.975413	−	0.220386i	$-0.929268\pi$
$373$	−5.73305	+	9.92993i	−0.296846	+	0.514152i	0.678567	+	0.734539i	$0.262601\pi$
$374$	−1.81089	+	3.13656i	−0.0936390	+	0.162188i
$375$	4.38323	−	1.45370i	0.226349	−	0.0750687i
$376$	0.761450	+	1.31887i	0.0392688	+	0.0680155i
$377$	−2.22253			−0.114466
$378$	6.18292	+	13.2326i	0.318015	+	0.680611i
$379$	3.71063			0.190602			0.0953011	−	0.995448i	$-0.469619\pi$
$379$	3.71063			0.190602			0.0953011	+	0.995448i	$0.469619\pi$
$380$	−11.7985	−	20.4356i	−0.605251	−	1.04833i
$381$	−5.62907	+	1.86688i	−0.288386	+	0.0956431i
$382$	−11.6749	+	20.2215i	−0.597338	+	1.03462i
$383$	−1.78366	+	3.08939i	−0.0911408	+	0.157861i	−0.907991	−	0.418989i	$-0.862385\pi$
$383$	−1.78366	+	3.08939i	−0.0911408	+	0.157861i	0.816851	+	0.576849i	$0.195718\pi$
$384$	1.29418	+	1.15113i	0.0660434	+	0.0587432i
$385$	23.9222	+	41.4344i	1.21919	+	2.11169i
$386$	−24.9294			−1.26888
$387$	−31.6804	−	13.6462i	−1.61040	−	0.693676i
$388$	4.95420			0.251511
$389$	2.71201	+	4.69734i	0.137504	+	0.238164i	0.926551	−	0.376168i	$-0.122759\pi$
$389$	2.71201	+	4.69734i	0.137504	+	0.238164i	−0.789047	+	0.614333i	$0.789425\pi$
$390$	1.15019	−	5.57761i	0.0582419	−	0.282433i
$391$	−2.09888	+	3.63537i	−0.106145	+	0.183849i
$392$	0.450558	−	0.780389i	0.0227566	−	0.0394156i
$393$	−2.88757	+	14.0027i	−0.145658	+	0.706343i
$394$	−5.11745	−	8.86369i	−0.257814	−	0.446546i
$395$	−51.7948			−2.60608
$396$	12.4523	−	9.28040i	0.625754	−	0.466358i
$397$	−28.1272			−1.41166			−0.705832	−	0.708379i	$-0.749427\pi$
$397$	−28.1272			−1.41166			−0.705832	+	0.708379i	$0.749427\pi$
$398$	13.4523	+	23.3001i	0.674305	+	1.16793i
$399$	26.1075	+	23.2217i	1.30701	+	1.16254i
$400$	−2.90545	+	5.03238i	−0.145272	+	0.251619i
$401$	7.43130	−	12.8714i	0.371101	−	0.642766i	−0.618634	−	0.785679i	$-0.712314\pi$
$401$	7.43130	−	12.8714i	0.371101	−	0.642766i	0.989735	+	0.142913i	$0.0456469\pi$
$402$	−0.731671	+	0.242659i	−0.0364925	+	0.0121027i
$403$	−1.38874	−	2.40536i	−0.0691779	−	0.119820i
$404$	−2.95420			−0.146977
$405$	20.3294	+	21.5035i	1.01018	+	1.06852i
$406$	−6.24729			−0.310048
$407$	1.84294	+	3.19206i	0.0913509	+	0.158224i
$408$	1.15019	−	0.381459i	0.0569427	−	0.0188850i
$409$	8.98762	−	15.5670i	0.444409	−	0.769739i	−0.553602	−	0.832782i	$-0.686747\pi$
$409$	8.98762	−	15.5670i	0.444409	−	0.769739i	0.998011	+	0.0630423i	$0.0200803\pi$
$410$	−1.35346	+	2.34425i	−0.0668424	+	0.115774i
$411$	5.95420	+	5.29604i	0.293699	+	0.261234i
$412$	−4.69963	−	8.13999i	−0.231534	−	0.401029i
$413$	−41.5970			−2.04686
$414$	14.4327	−	10.7563i	0.709327	−	0.528643i
$415$	−26.2225			−1.28721
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−3.70396	+	17.9617i	−0.181384	+	0.879586i
$418$	18.5760	−	32.1745i	0.908581	−	1.57371i
$419$	13.7305	−	23.7819i	0.670779	−	1.16182i	−0.306905	−	0.951740i	$-0.599293\pi$
$419$	13.7305	−	23.7819i	0.670779	−	1.16182i	0.977684	−	0.210083i	$-0.0673734\pi$
$420$	3.23305	−	15.6781i	0.157757	−	0.765011i
$421$	−1.47091	−	2.54769i	−0.0716878	−	0.124167i	0.827953	−	0.560797i	$-0.189505\pi$
$421$	−1.47091	−	2.54769i	−0.0716878	−	0.124167i	−0.899641	+	0.436630i	$0.856172\pi$
$422$	−4.71201			−0.229377
$423$	−4.19599	−	1.80741i	−0.204016	−	0.0878792i
$424$	11.0210			0.535229
$425$	2.03273	+	3.52079i	0.0986020	+	0.170784i
$426$	−1.53892	−	1.36881i	−0.0745610	−	0.0663192i
$427$	13.2101	−	22.8806i	0.639284	−	1.10727i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$	8.51052	−	2.82251i	0.410892	−	0.136272i
$430$	18.9029	+	32.7408i	0.911579	+	1.57890i
$431$	3.37959			0.162789			0.0813946	−	0.996682i	$-0.474063\pi$
$431$	3.37959			0.162789			0.0813946	+	0.996682i	$0.474063\pi$
$432$	−5.17673	−	0.448873i	−0.249065	−	0.0215964i
$433$	8.36584			0.402036			0.201018	−	0.979588i	$-0.435575\pi$
$433$	8.36584			0.402036			0.201018	+	0.979588i	$0.435575\pi$
$434$	−3.90359	−	6.76121i	−0.187378	−	0.324549i
$435$	−12.0138	+	3.98436i	−0.576016	+	0.191035i
$436$	3.33743	−	5.78061i	0.159834	−	0.276841i
$437$	21.5302	−	37.2914i	1.02993	−	1.78389i
$438$	−0.287992	−	0.256158i	−0.0137608	−	0.0122397i
$439$	14.2880	+	24.7475i	0.681929	+	1.18114i	0.974391	+	0.224858i	$0.0721919\pi$
$439$	14.2880	+	24.7475i	0.681929	+	1.18114i	−0.292463	+	0.956277i	$0.594475\pi$
$440$	−17.0210			−0.811446
$441$	0.315223	+	2.68491i	0.0150106	+	0.127853i
$442$	0.699628			0.0332779
$443$	9.26942	+	16.0551i	0.440404	+	0.762801i	0.997719	−	0.0674993i	$-0.0215020\pi$
$443$	9.26942	+	16.0551i	0.440404	+	0.762801i	−0.557316	+	0.830301i	$0.688169\pi$
$444$	0.249070	−	1.20782i	0.0118204	−	0.0573206i
$445$	−12.1643	+	21.0693i	−0.576645	+	0.998779i
$446$	3.81453	−	6.60697i	0.180623	−	0.312849i
$447$	5.93818	−	28.7961i	0.280866	−	1.36201i
$448$	1.40545	+	2.43430i	0.0664011	+	0.115010i
$449$	−14.8626			−0.701409			−0.350705	−	0.936486i	$-0.614058\pi$
$449$	−14.8626			−0.701409			−0.350705	+	0.936486i	$0.614058\pi$
$450$	−2.03273	−	17.3138i	−0.0958239	−	0.816178i
$451$	−4.26186			−0.200683
$452$	1.50000	+	2.59808i	0.0705541	+	0.122203i
$453$	−28.7534	−	25.5751i	−1.35095	−	1.20162i
$454$	11.0210	−	19.0890i	0.517243	−	0.895891i
$455$	4.62110	−	8.00397i	0.216640	−	0.375232i
$456$	−11.7985	+	3.91298i	−0.552516	+	0.183242i
$457$	−11.1520	−	19.3158i	−0.521667	−	0.903554i	−0.999682	−	0.0252024i	$-0.991977\pi$
$457$	−11.1520	−	19.3158i	−0.521667	−	0.903554i	0.478015	−	0.878352i	$-0.341356\pi$
$458$	4.48948			0.209780
$459$	−2.08286	+	2.97954i	−0.0972197	+	0.139073i
$460$	−19.7280			−0.919821
$461$	−4.87017	−	8.43538i	−0.226826	−	0.392875i	0.730040	−	0.683405i	$-0.239502\pi$
$461$	−4.87017	−	8.43538i	−0.226826	−	0.392875i	−0.956866	+	0.290530i	$0.906168\pi$
$462$	23.9222	−	7.93378i	1.11296	−	0.369113i
$463$	1.81275	−	3.13978i	0.0842457	−	0.145918i	−0.820824	−	0.571181i	$-0.806485\pi$
$463$	1.81275	−	3.13978i	0.0842457	−	0.145918i	0.905070	+	0.425264i	$0.139819\pi$
$464$	1.11126	−	1.92477i	0.0515891	−	0.0893550i
$465$	−11.8189	−	10.5124i	−0.548087	−	0.487503i
$466$	2.77128	+	4.80000i	0.128377	+	0.222356i
$467$	−0.0458003			−0.00211939			−0.00105969	−	0.999999i	$-0.500337\pi$
$467$	−0.0458003			−0.00211939			−0.00105969	+	0.999999i	$0.500337\pi$
$468$	−2.75526	−	1.18682i	−0.127362	−	0.0548608i
$469$	−1.25101			−0.0577661
$470$	2.50364	+	4.33643i	0.115484	+	0.200025i
$471$	1.63279	−	7.91789i	0.0752348	−	0.364837i
$472$	7.39926	−	12.8159i	0.340578	−	0.589899i
$473$	−29.7614	+	51.5482i	−1.36843	+	2.37019i
$474$	−5.51052	+	26.7222i	−0.253107	+	1.22739i
$475$	−20.8516	−	36.1160i	−0.956737	−	1.65712i
$476$	1.96658			0.0901380
$477$	−26.5105	+	19.7576i	−1.21383	+	0.904638i
$478$	−7.43130			−0.339900
$479$	−8.84176	−	15.3144i	−0.403991	−	0.699732i	0.590213	−	0.807248i	$-0.299044\pi$
$479$	−8.84176	−	15.3144i	−0.403991	−	0.699732i	−0.994203	+	0.107515i	$0.965710\pi$
$480$	4.25526	+	3.78490i	0.194225	+	0.172756i
$481$	0.356004	−	0.616617i	0.0162324	−	0.0281153i
$482$	4.69963	−	8.13999i	0.214062	−	0.370767i
$483$	27.7266	−	9.19551i	1.26160	−	0.418410i
$484$	−7.89926	−	13.6819i	−0.359057	−	0.621905i
$485$	16.2894			0.739662
$486$	13.2570	−	8.20066i	0.601352	−	0.371989i
$487$	−23.2436			−1.05327			−0.526633	−	0.850093i	$-0.676546\pi$
$487$	−23.2436			−1.05327			−0.526633	+	0.850093i	$0.676546\pi$
$488$	4.69963	+	8.13999i	0.212742	+	0.368480i
$489$	−19.6872	+	6.52927i	−0.890288	+	0.295264i
$490$	1.48143	−	2.56591i	0.0669242	−	0.115916i
$491$	9.27197	−	16.0595i	0.418438	−	0.724756i	−0.577344	−	0.816501i	$-0.695911\pi$
$491$	9.27197	−	16.0595i	0.418438	−	0.724756i	0.995783	+	0.0917446i	$0.0292443\pi$
$492$	1.06546	+	0.947691i	0.0480348	+	0.0427252i
$493$	−0.777472	−	1.34662i	−0.0350156	−	0.0606487i
$494$	−7.17673			−0.322896
$495$	40.9432	−	30.5139i	1.84026	−	1.37150i
$496$	2.77747			0.124712
$497$	−1.67123	−	2.89465i	−0.0749648	−	0.129843i
$498$	−2.78985	+	13.5289i	−0.125016	+	0.606243i
$499$	15.7738	−	27.3209i	0.706130	−	1.22305i	−0.260152	−	0.965568i	$-0.583773\pi$
$499$	15.7738	−	27.3209i	0.706130	−	1.22305i	0.966282	−	0.257486i	$-0.0828940\pi$
$500$	−1.33310	+	2.30900i	−0.0596182	+	0.103262i
$501$	2.37085	−	11.4970i	0.105922	−	0.513649i
$502$	7.99814	+	13.8532i	0.356974	+	0.618298i
$503$	21.2188			0.946100			0.473050	−	0.881036i	$-0.343153\pi$
$503$	21.2188			0.946100			0.473050	+	0.881036i	$0.343153\pi$
$504$	−7.74474	−	3.33602i	−0.344978	−	0.148598i
$505$	−9.71339			−0.432240
$506$	−15.5302	−	26.8991i	−0.690401	−	1.19581i
$507$	−1.29418	−	1.15113i	−0.0574766	−	0.0511233i
$508$	1.71201	−	2.96528i	0.0759581	−	0.131563i
$509$	−1.71015	+	2.96206i	−0.0758010	+	0.131291i	−0.901434	−	0.432916i	$-0.857485\pi$
$509$	−1.71015	+	2.96206i	−0.0758010	+	0.131291i	0.825633	+	0.564207i	$0.190818\pi$
$510$	3.78180	−	1.25423i	0.167461	−	0.0555384i
$511$	−0.312752	−	0.541702i	−0.0138353	−	0.0239635i
$512$	−1.00000			−0.0441942
$513$	21.3658	−	30.5638i	0.943325	−	1.34943i
$514$	0.0865047			0.00381556
$515$	−15.4523	−	26.7642i	−0.680911	−	1.17937i
$516$	18.9029	−	6.26914i	0.832154	−	0.275984i
$517$	−3.94182	+	6.82743i	−0.173361	+	0.300270i
$518$	1.00069	−	1.73324i	0.0439677	−	0.0761544i
$519$	−24.7861	−	22.0463i	−1.08799	−	0.967727i
$520$	1.64400	+	2.84748i	0.0720940	+	0.124870i
$521$	25.5498			1.11936			0.559680	−	0.828709i	$-0.310924\pi$
$521$	25.5498			1.11936			0.559680	+	0.828709i	$0.310924\pi$
$522$	0.777472	+	6.62210i	0.0340290	+	0.289842i
$523$	−16.0458			−0.701634			−0.350817	−	0.936444i	$-0.614096\pi$
$523$	−16.0458			−0.701634			−0.350817	+	0.936444i	$0.614096\pi$
$524$	−4.12729	−	7.14867i	−0.180301	−	0.312291i
$525$	5.71379	−	27.7080i	0.249370	−	1.20927i
$526$	0.489480	−	0.847803i	0.0213423	−	0.0369660i
$527$	0.971599	−	1.68286i	0.0423235	−	0.0733065i
$528$	−1.81089	+	8.78158i	−0.0788090	+	0.382169i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	36.2371			1.57404
$531$	5.17673	+	44.0927i	0.224651	+	1.91346i
$532$	−20.1730			−0.874611
$533$	0.411636	+	0.712974i	0.0178299	+	0.0308824i
$534$	9.57598	+	8.51748i	0.414393	+	0.368588i
$535$	−19.7280	+	34.1698i	−0.852914	+	1.47729i
$536$	0.222528	−	0.385430i	0.00961176	−	0.0166481i
$537$	−0.345483	+	0.114580i	−0.0149087	+	0.00494447i
$538$	−12.7861	−	22.1462i	−0.551249	−	0.954792i
$539$	4.66483			0.200928
$540$	−17.0210	−	1.47589i	−0.732469	−	0.0635123i
$541$	−0.899738			−0.0386828			−0.0193414	−	0.999813i	$-0.506157\pi$
$541$	−0.899738			−0.0386828			−0.0193414	+	0.999813i	$0.506157\pi$
$542$	8.48831	+	14.7022i	0.364604	+	0.631513i
$543$	10.5956	−	3.51405i	0.454703	−	0.150802i
$544$	−0.349814	+	0.605896i	−0.0149982	+	0.0259776i
$545$	10.9735	−	19.0066i	0.470051	−	0.814153i
$546$	−3.63781	−	3.23569i	−0.155684	−	0.138475i
$547$	16.7095	+	28.9416i	0.714445	+	1.23745i	0.963173	+	0.268882i	$0.0866540\pi$
$547$	16.7095	+	28.9416i	0.714445	+	1.23745i	−0.248728	+	0.968573i	$0.580013\pi$
$548$	−4.60074			−0.196534
$549$	−25.8974	−	11.1552i	−1.10527	−	0.476093i
$550$	−30.0814			−1.28268
$551$	7.97524	+	13.8135i	0.339757	+	0.588476i
$552$	−2.09888	+	10.1781i	−0.0893345	+	0.433211i
$553$	−22.1396	+	38.3469i	−0.941471	+	1.63068i
$554$	1.69963	−	2.94384i	0.0722103	−	0.125072i
$555$	0.818941	−	3.97130i	0.0347621	−	0.168572i
$556$	−5.29418	−	9.16979i	−0.224523	−	0.388886i
$557$	−0.123644			−0.00523896			−0.00261948	−	0.999997i	$-0.500834\pi$
$557$	−0.123644			−0.00523896			−0.00261948	+	0.999997i	$0.500834\pi$
$558$	−6.68106	+	4.97922i	−0.282832	+	0.210787i
$559$	11.4981			0.486320
$560$	4.62110	+	8.00397i	0.195277	+	0.338230i
$561$	4.68725	+	4.16913i	0.197896	+	0.176021i
$562$	−14.3411	+	24.8395i	−0.604942	+	1.04779i
$563$	−1.29418	+	2.24159i	−0.0545433	+	0.0944717i	−0.892008	−	0.452020i	$-0.850704\pi$
$563$	−1.29418	+	2.24159i	−0.0545433	+	0.0944717i	0.837465	+	0.546492i	$0.184037\pi$
$564$	2.50364	−	0.830332i	0.105422	−	0.0349633i
$565$	4.93199	+	8.54245i	0.207490	+	0.359384i
$566$	11.1978			0.470677
$567$	24.6101	−	5.85949i	1.03353	−	0.246076i
$568$	1.18911			0.0498939
$569$	3.73422	+	6.46786i	0.156547	+	0.271147i	0.933621	−	0.358262i	$-0.116631\pi$
$569$	3.73422	+	6.46786i	0.156547	+	0.271147i	−0.777074	+	0.629409i	$0.783297\pi$
$570$	−38.7934	+	12.8658i	−1.62488	+	0.538890i
$571$	16.3251	−	28.2758i	0.683182	−	1.18331i	−0.290822	−	0.956777i	$-0.593929\pi$
$571$	16.3251	−	28.2758i	0.683182	−	1.18331i	0.974004	−	0.226529i	$-0.0727379\pi$
$572$	−2.58836	+	4.48318i	−0.108225	+	0.187451i
$573$	30.2188	+	26.8785i	1.26241	+	1.12287i
$574$	1.15706	+	2.00409i	0.0482949	+	0.0836493i
$575$	−34.8654			−1.45399
$576$	2.40545	−	1.79272i	0.100227	−	0.0746965i
$577$	−18.9542			−0.789074			−0.394537	−	0.918880i	$-0.629095\pi$
$577$	−18.9542			−0.789074			−0.394537	+	0.918880i	$0.629095\pi$
$578$	−8.25526	−	14.2985i	−0.343374	−	0.594740i
$579$	−8.72067	+	42.2893i	−0.362419	+	1.75748i
$580$	3.65383	−	6.32862i	0.151717	−	0.262781i
$581$	−11.2088	+	19.4142i	−0.465018	+	0.805435i
$582$	1.73305	−	8.40410i	0.0718372	−	0.348361i
$583$	28.5265	+	49.4093i	1.18145	+	2.04632i
$584$	0.222528			0.00920829
$585$	−9.05927	−	3.90225i	−0.374555	−	0.161338i
$586$	−6.94182			−0.286764
$587$	15.5760	+	26.9784i	0.642890	+	1.11352i	0.984785	+	0.173779i	$0.0555980\pi$
$587$	15.5760	+	26.9784i	0.642890	+	1.11352i	−0.341895	+	0.939738i	$0.611069\pi$
$588$	−1.16621	−	1.03730i	−0.0480936	−	0.0427775i
$589$	−9.96658	+	17.2626i	−0.410666	+	0.711294i
$590$	24.3287	−	42.1385i	1.00160	−	1.73482i
$591$	−16.8261	+	5.58039i	−0.692135	+	0.229547i
$592$	0.356004	+	0.616617i	0.0146317	+	0.0253428i
$593$	39.0631			1.60413			0.802065	−	0.597237i	$-0.203735\pi$
$593$	39.0631			1.60413			0.802065	+	0.597237i	$0.203735\pi$
$594$	−11.3869	−	24.3700i	−0.467209	−	0.999915i
$595$	6.46610			0.265084
$596$	8.48762	+	14.7010i	0.347666	+	0.602176i
$597$	44.2312	−	14.6693i	1.81026	−	0.600373i
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−9.86398	+	17.0849i	−0.403031	+	0.698070i	−0.994090	−	0.108558i	$-0.965377\pi$
$599$	−9.86398	+	17.0849i	−0.403031	+	0.698070i	0.591059	+	0.806628i	$0.298710\pi$
$600$	7.52035	+	6.68907i	0.307017	+	0.273080i
$601$	0.703270	+	1.21810i	0.0286870	+	0.0496873i	0.880012	−	0.474951i	$-0.157534\pi$
$601$	0.703270	+	1.21810i	0.0286870	+	0.0496873i	−0.851325	+	0.524638i	$0.824201\pi$
$602$	32.3200			1.31727
$603$	0.155687	+	1.32606i	0.00634007	+	0.0540014i
$604$	22.2174			0.904015
$605$	−25.9727	−	44.9860i	−1.05594	−	1.82894i
$606$	−1.03342	+	5.01138i	−0.0419798	+	0.203573i
$607$	5.12364	−	8.87441i	0.207962	−	0.360201i	−0.743110	−	0.669169i	$-0.766650\pi$
$607$	5.12364	−	8.87441i	0.207962	−	0.360201i	0.951073	+	0.308968i	$0.0999835\pi$
$608$	3.58836	−	6.21523i	0.145527	−	0.252061i
$609$	−2.18539	+	10.5976i	−0.0885564	+	0.429438i
$610$	15.4523	+	26.7642i	0.625647	+	1.08365i
$611$	1.52290			0.0616099
$612$	−0.244740	−	2.08457i	−0.00989302	−	0.0842636i
$613$	−43.3287			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$613$	−43.3287			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$614$	−7.51052	−	13.0086i	−0.303100	−	0.524984i
$615$	3.50324	+	3.11600i	0.141264	+	0.125649i
$616$	−7.27561	+	12.6017i	−0.293143	+	0.507738i
$617$	−1.44506	+	2.50291i	−0.0581758	+	0.100763i	−0.893647	−	0.448771i	$-0.851862\pi$
$617$	−1.44506	+	2.50291i	−0.0581758	+	0.100763i	0.835471	+	0.549535i	$0.185195\pi$
$618$	−15.4523	+	5.12477i	−0.621584	+	0.206148i
$619$	−0.346172	−	0.599588i	−0.0139138	−	0.0240995i	0.858985	−	0.512001i	$-0.171096\pi$
$619$	−0.346172	−	0.599588i	−0.0139138	−	0.0240995i	−0.872898	+	0.487902i	$0.837762\pi$
$620$	9.13231			0.366762
$621$	−13.1978	−	28.2457i	−0.529608	−	1.13346i
$622$	7.97524			0.319778
$623$	10.3993	+	18.0120i	0.416637	+	0.721637i
$624$	1.64400	−	0.545231i	0.0658125	−	0.0218267i
$625$	10.1440	−	17.5699i	0.405760	−	0.702797i
$626$	6.99745	−	12.1199i	0.279674	−	0.484410i
$627$	−48.0814	−	42.7666i	−1.92019	−	1.70793i
$628$	2.33379	+	4.04225i	0.0931285	+	0.161303i
$629$	0.498141			0.0198622
$630$	−25.4646	−	10.9688i	−1.01454	−	0.437008i
$631$	30.4771			1.21327			0.606637	−	0.794979i	$-0.292518\pi$
$631$	30.4771			1.21327			0.606637	+	0.794979i	$0.292518\pi$
$632$	−7.87636	−	13.6422i	−0.313305	−	0.542660i
$633$	−1.64833	+	7.99325i	−0.0655151	+	0.317703i
$634$	−4.71015	+	8.15822i	−0.187064	+	0.324004i
$635$	5.62907	−	9.74983i	0.223383	−	0.386910i
$636$	3.85532	−	18.6956i	0.152873	−	0.741330i
$637$	−0.450558	−	0.780389i	−0.0178517	−	0.0309201i
$638$	11.5054			0.455504
$639$	−2.86033	+	2.13173i	−0.113153	+	0.0843300i
$640$	−3.28799			−0.129969
$641$	19.0970	+	33.0770i	0.754287	+	1.30646i	0.945728	+	0.324959i	$0.105351\pi$
$641$	19.0970	+	33.0770i	0.754287	+	1.30646i	−0.191441	+	0.981504i	$0.561316\pi$
$642$	15.5302	+	13.8135i	0.612927	+	0.545176i
$643$	−6.30903	+	10.9276i	−0.248804	+	0.430941i	−0.963194	−	0.268806i	$-0.913371\pi$
$643$	−6.30903	+	10.9276i	−0.248804	+	0.430941i	0.714390	+	0.699747i	$0.246704\pi$
$644$	−8.43268	+	14.6058i	−0.332294	+	0.575550i
$645$	62.1526	−	20.6129i	2.44726	−	0.811632i
$646$	−2.51052	−	4.34835i	−0.0987751	−	0.171084i
$647$	35.9257			1.41239			0.706193	−	0.708019i	$-0.250411\pi$
$647$	35.9257			1.41239			0.706193	+	0.708019i	$0.250411\pi$
$648$	−2.57234	+	8.62456i	−0.101051	+	0.338805i
$649$	76.6079			3.00712
$650$	2.90545	+	5.03238i	0.113961	+	0.197386i
$651$	−12.8350	+	4.25671i	−0.503042	+	0.166834i
$652$	5.98762	−	10.3709i	0.234493	−	0.406154i
$653$	10.7193	−	18.5664i	0.419478	−	0.726558i	−0.576409	−	0.817162i	$-0.695546\pi$
$653$	10.7193	−	18.5664i	0.419478	−	0.726558i	0.995887	+	0.0906038i	$0.0288797\pi$
$654$	−8.63849	−	7.68362i	−0.337792	−	0.300453i
$655$	−13.5705	−	23.5048i	−0.530243	−	0.918407i
$656$	−0.823272			−0.0321434
$657$	−0.535280	+	0.398930i	−0.0208833	+	0.0155637i
$658$	4.28071			0.166879
$659$	−16.3764	−	28.3647i	−0.637932	−	1.10493i	−0.985886	−	0.167419i	$-0.946457\pi$
$659$	−16.3764	−	28.3647i	−0.637932	−	1.10493i	0.347954	−	0.937512i	$-0.386877\pi$
$660$	−5.95420	+	28.8738i	−0.231767	+	1.12391i
$661$	−0.268329	+	0.464759i	−0.0104368	+	0.0180770i	−0.871197	−	0.490934i	$-0.836656\pi$
$661$	−0.268329	+	0.464759i	−0.0104368	+	0.0180770i	0.860760	+	0.509011i	$0.169989\pi$
$662$	−5.77747	+	10.0069i	−0.224548	+	0.388928i
$663$	0.244740	−	1.18682i	0.00950491	−	0.0460923i
$664$	−3.98762	−	6.90676i	−0.154750	−	0.268034i
$665$	−66.3287			−2.57212
$666$	−1.96177	−	0.845025i	−0.0760169	−	0.0327441i
$667$	13.3352			0.516340
$668$	3.38874	+	5.86946i	0.131114	+	0.227096i
$669$	−9.87340	−	8.78203i	−0.381728	−	0.339533i
$670$	0.731671	−	1.26729i	0.0282669	−	0.0489598i
$671$	−24.3287	+	42.1385i	−0.939199	+	1.62674i
$672$	4.62110	−	1.53259i	0.178263	−	0.0591208i
$673$	−16.9530	−	29.3635i	−0.653491	−	1.13188i	−0.982270	−	0.187473i	$-0.939970\pi$
$673$	−16.9530	−	29.3635i	−0.653491	−	1.13188i	0.328779	−	0.944407i	$-0.393363\pi$
$674$	−0.810892			−0.0312344
$675$	−30.0814	−	2.60836i	−1.15783	−	0.100396i
$676$	1.00000			0.0384615
$677$	13.3993	+	23.2082i	0.514975	+	0.891963i	0.999849	+	0.0173791i	$0.00553223\pi$
$677$	13.3993	+	23.2082i	0.514975	+	0.891963i	−0.484874	+	0.874584i	$0.661134\pi$
$678$	4.93199	−	1.63569i	0.189412	−	0.0628184i
$679$	6.96286	−	12.0600i	0.267210	−	0.462821i
$680$	−1.15019	+	1.99218i	−0.0441076	+	0.0763966i
$681$	−28.5265	−	25.3732i	−1.09314	−	0.972304i
$682$	7.18911	+	12.4519i	0.275285	+	0.476808i
$683$	0.978959			0.0374588			0.0187294	−	0.999825i	$-0.494038\pi$
$683$	0.978959			0.0374588			0.0187294	+	0.999825i	$0.494038\pi$
$684$	2.51052	+	21.3833i	0.0959921	+	0.817611i
$685$	−15.1272			−0.577981
$686$	8.57165	+	14.8465i	0.327267	+	0.566844i
$687$	1.57048	−	7.61576i	0.0599177	−	0.290560i
$688$	−5.74907	+	9.95768i	−0.219181	+	0.379633i
$689$	5.51052	−	9.54450i	0.209934	−	0.363617i
$690$	−6.90112	+	33.4657i	−0.262721	+	1.27402i
$691$	25.2632	+	43.7572i	0.961059	+	1.66460i	0.719851	+	0.694129i	$0.244210\pi$
$691$	25.2632	+	43.7572i	0.961059	+	1.66460i	0.241208	+	0.970473i	$0.422456\pi$
$692$	19.1520			0.728049
$693$	−5.09022	−	43.3559i	−0.193362	−	1.64695i
$694$	−14.3090			−0.543163
$695$	−17.4072	−	30.1502i	−0.660294	−	1.14366i
$696$	−2.87636	−	2.55841i	−0.109028	−	0.0969764i
$697$	−0.287992	+	0.498817i	−0.0109085	+	0.0188940i
$698$	−7.75526	+	13.4325i	−0.293541	+	0.508428i
$699$	9.11195	−	3.02198i	0.344646	−	0.114302i
$700$	8.16690	+	14.1455i	0.308680	+	0.534649i
$701$	−9.37450			−0.354070			−0.177035	−	0.984205i	$-0.556651\pi$
$701$	−9.37450			−0.354070			−0.177035	+	0.984205i	$0.556651\pi$
$702$	−2.97710	+	4.25874i	−0.112363	+	0.160736i
$703$	−5.10989			−0.192723
$704$	−2.58836	−	4.48318i	−0.0975526	−	0.168966i
$705$	8.23195	−	2.73013i	0.310033	−	0.102823i
$706$	−17.3869	+	30.1150i	−0.654364	+	1.13339i
$707$	−4.15197	+	7.19142i	−0.156151	+	0.270461i
$708$	−19.1520	−	17.0350i	−0.719775	−	0.640213i
$709$	7.28613	+	12.6200i	0.273636	+	0.473952i	0.969790	−	0.243940i	$-0.0784402\pi$
$709$	7.28613	+	12.6200i	0.273636	+	0.473952i	−0.696154	+	0.717893i	$0.745107\pi$
$710$	3.90978			0.146731
$711$	43.4028	+	18.6956i	1.62773	+	0.701141i
$712$	−7.39926			−0.277299
$713$	8.33242	+	14.4322i	0.312051	+	0.540489i
$714$	0.687937	−	3.33602i	0.0257454	−	0.124848i
$715$	−8.51052	+	14.7407i	−0.318275	+	0.551269i
$716$	0.105074	−	0.181994i	0.00392681	−	0.00680144i
$717$	−2.59957	+	12.6061i	−0.0970828	+	0.470785i
$718$	−12.1414	−	21.0296i	−0.453115	−	0.784818i
$719$	−33.3104			−1.24227			−0.621134	−	0.783704i	$-0.713328\pi$
$719$	−33.3104			−1.24227			−0.621134	+	0.783704i	$0.713328\pi$
$720$	7.90909	−	5.89443i	0.294754	−	0.219673i
$721$	−26.4203			−0.983943
$722$	16.2527	+	28.1505i	0.604863	+	1.04765i
$723$	−12.1643	−	10.8197i	−0.452397	−	0.402390i
$724$	−3.22253	+	5.58158i	−0.119764	+	0.207438i
$725$	6.45744	−	11.1846i	0.239823	−	0.415386i
$726$	−25.9727	+	8.61384i	−0.963937	+	0.319690i
$727$	16.6428	+	28.8262i	0.617248	+	1.06911i	0.989986	+	0.141168i	$0.0450859\pi$
$727$	16.6428	+	28.8262i	0.617248	+	1.06911i	−0.372737	+	0.927937i	$0.621581\pi$
$728$	2.81089			0.104179
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	0.731671			0.0270804
$731$	4.02221	+	6.96667i	0.148767	+	0.257672i
$732$	15.4523	−	5.12477i	0.571135	−	0.189417i
$733$	−23.4585	+	40.6314i	−0.866461	+	1.50075i	−0.000871020		1.00000i	$0.500277\pi$
$733$	−23.4585	+	40.6314i	−0.866461	+	1.50075i	−0.865590	+	0.500754i	$0.833056\pi$
$734$	−7.95420	+	13.7771i	−0.293595	+	0.508521i
$735$	−3.83448	−	3.41063i	−0.141437	−	0.125803i
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	2.30394			0.0848666
$738$	1.98034	−	1.47589i	0.0728972	−	0.0543284i
$739$	−43.6116			−1.60428			−0.802139	−	0.597137i	$-0.796305\pi$
$739$	−43.6116			−1.60428			−0.802139	+	0.597137i	$0.796305\pi$
$740$	1.17054	+	2.02743i	0.0430298	+	0.0745299i
$741$	−2.51052	+	12.1743i	−0.0922263	+	0.447234i
$742$	15.4895	−	26.8286i	0.568637	−	0.984908i
$743$	20.0371	−	34.7052i	0.735089	−	1.27321i	−0.219596	−	0.975591i	$-0.570474\pi$
$743$	20.0371	−	34.7052i	0.735089	−	1.27321i	0.954684	−	0.297620i	$-0.0961928\pi$
$744$	0.971599	−	4.71159i	0.0356205	−	0.172735i
$745$	27.9072	+	48.3367i	1.02244	+	1.77092i
$746$	−11.4661			−0.419804
$747$	21.9739	+	9.46517i	0.803982	+	0.346313i
$748$	−3.62178			−0.132426
$749$	16.8654	+	29.2116i	0.616247	+	1.06737i
$750$	3.45056	+	3.06914i	0.125997	+	0.112069i
$751$	−22.6538	+	39.2376i	−0.826650	+	1.43180i	0.0740019	+	0.997258i	$0.476423\pi$
$751$	−22.6538	+	39.2376i	−0.826650	+	1.43180i	−0.900652	+	0.434542i	$0.856910\pi$
$752$	−0.761450	+	1.31887i	−0.0277672	+	0.0480942i
$753$	26.2978	−	8.72167i	0.958346	−	0.317835i
$754$	−1.11126	−	1.92477i	−0.0404699	−	0.0700958i
$755$	73.0507			2.65859
$756$	−8.36831	+	11.9709i	−0.304352	+	0.435376i
$757$	38.3287			1.39308			0.696540	−	0.717518i	$-0.254722\pi$
$757$	38.3287			1.39308			0.696540	+	0.717518i	$0.254722\pi$
$758$	1.85532	+	3.21350i	0.0673881	+	0.116720i
$759$	−51.0631	+	16.9351i	−1.85347	+	0.614704i
$760$	11.7985	−	20.4356i	0.427977	−	0.741278i
$761$	5.34108	−	9.25102i	0.193614	−	0.335349i	−0.752831	−	0.658213i	$-0.771312\pi$
$761$	5.34108	−	9.25102i	0.193614	−	0.335349i	0.946445	+	0.322864i	$0.104646\pi$
$762$	−4.43130	−	3.94148i	−0.160529	−	0.142785i
$763$	−9.38117	−	16.2487i	−0.339621	−	0.588241i
$764$	−23.3497			−0.844764
$765$	−0.804702	−	6.85404i	−0.0290941	−	0.247808i
$766$	−3.56732			−0.128893
$767$	−7.39926	−	12.8159i	−0.267172	−	0.462755i
$768$	−0.349814	+	1.69636i	−0.0126228	+	0.0612120i
$769$	24.2843	−	42.0616i	0.875713	−	1.51678i	0.0197124	−	0.999806i	$-0.493725\pi$
$769$	24.2843	−	42.0616i	0.875713	−	1.51678i	0.856001	−	0.516974i	$-0.172942\pi$
$770$	−23.9222	+	41.4344i	−0.862095	+	1.49319i
$771$	0.0302606	−	0.146743i	0.00108981	−	0.00528482i
$772$	−12.4647	−	21.5895i	−0.448615	−	0.777024i
$773$	1.45881			0.0524699			0.0262349	−	0.999656i	$-0.491648\pi$
$773$	1.45881			0.0524699			0.0262349	+	0.999656i	$0.491648\pi$
$774$	−4.02221	−	34.2591i	−0.144575	−	1.23142i
$775$	16.1396			0.579751
$776$	2.47710	+	4.29046i	0.0889227	+	0.154019i
$777$	−2.59015	−	2.30384i	−0.0929210	−	0.0826498i
$778$	−2.71201	+	4.69734i	−0.0972302	+	0.168408i
$779$	2.95420	−	5.11682i	0.105845	−	0.183329i
$780$	5.40545	−	1.79272i	0.193546	−	0.0641895i
$781$	3.07784	+	5.33098i	0.110134	+	0.190758i
$782$	−4.19777			−0.150112
$783$	11.5054	+	0.997634i	0.411170	+	0.0356525i
$784$	0.901116			0.0321827
$785$	7.67349	+	13.2909i	0.273879	+	0.474372i
$786$	−13.5705	+	4.50065i	−0.484043	+	0.160533i
$787$	7.05308	−	12.2163i	0.251415	−	0.435464i	−0.712500	−	0.701672i	$-0.752437\pi$
$787$	7.05308	−	12.2163i	0.251415	−	0.435464i	0.963916	+	0.266208i	$0.0857707\pi$
$788$	5.11745	−	8.86369i	0.182302	−	0.315756i
$789$	−1.26695	−	1.12691i	−0.0451047	−	0.0401189i
$790$	−25.8974	−	44.8556i	−0.921388	−	1.59589i
$791$	8.43268			0.299831
$792$	14.2632	+	6.14384i	0.506822	+	0.218312i
$793$	9.39926			0.333777
$794$	−14.0636	−	24.3589i	−0.499099	−	0.864464i
$795$	12.6762	−	61.4711i	0.449580	−	2.18015i
$796$	−13.4523	+	23.3001i	−0.476806	+	0.825851i
$797$	−14.5970	+	25.2828i	−0.517053	+	0.895562i	0.482751	+	0.875758i	$0.339638\pi$
$797$	−14.5970	+	25.2828i	−0.517053	+	0.895562i	−0.999804	+	0.0198045i	$0.993696\pi$
$798$	−7.05680	+	34.2206i	−0.249808	+	1.21140i
$799$	0.532732	+	0.922719i	0.0188467	+	0.0326434i
$800$	−5.81089			−0.205446
$801$	17.7985	−	13.2648i	0.628880	−	0.468687i
$802$	14.8626			0.524817
$803$	0.575984	+	0.997634i	0.0203260	+	0.0352057i
$804$	−0.575984	−	0.512317i	−0.0203134	−	0.0180680i
$805$	−27.7266	+	48.0238i	−0.977233	+	1.69262i
$806$	1.38874	−	2.40536i	0.0489161	−	0.0847252i
$807$	−42.0407	+	13.9428i	−1.47990	+	0.490810i
$808$	−1.47710	−	2.55841i	−0.0519642	−	0.0900046i
$809$	−24.4523			−0.859699			−0.429849	−	0.902901i	$-0.641433\pi$
$809$	−24.4523			−0.859699			−0.429849	+	0.902901i	$0.641433\pi$
$810$	−8.45784	+	28.3575i	−0.297178	+	0.996381i
$811$	−21.5970			−0.758374			−0.379187	−	0.925320i	$-0.623796\pi$
$811$	−21.5970			−0.758374			−0.379187	+	0.925320i	$0.623796\pi$
$812$	−3.12364	−	5.41031i	−0.109618	−	0.189865i
$813$	27.9095	−	9.25618i	0.978829	−	0.324628i
$814$	−1.84294	+	3.19206i	−0.0645949	+	0.111882i
$815$	19.6872	−	34.0993i	0.689614	−	1.19445i
$816$	0.905446	+	0.805361i	0.0316970	+	0.0281933i
$817$	−41.2595	−	71.4636i	−1.44349	−	2.50019i
$818$	17.9752			0.628490
$819$	−6.76145	+	5.03913i	−0.236264	+	0.176081i
$820$	−2.70691			−0.0945295
$821$	2.16071	+	3.74245i	0.0754092	+	0.130613i	0.901264	−	0.433270i	$-0.142640\pi$
$821$	2.16071	+	3.74245i	0.0754092	+	0.130613i	−0.825855	+	0.563883i	$0.809307\pi$
$822$	−1.60940	+	7.80451i	−0.0561344	+	0.272213i
$823$	13.8764	−	24.0346i	0.483699	−	0.837792i	−0.516125	−	0.856513i	$-0.672626\pi$
$823$	13.8764	−	24.0346i	0.483699	−	0.837792i	0.999825	+	0.0187212i	$0.00595948\pi$
$824$	4.69963	−	8.13999i	0.163719	−	0.283570i
$825$	−10.5229	+	51.0288i	−0.366360	+	1.77660i
$826$	−20.7985	−	36.0241i	−0.723673	−	1.25344i
$827$	8.55122			0.297355			0.148678	−	0.988886i	$-0.452498\pi$
$827$	8.55122			0.297355			0.148678	+	0.988886i	$0.452498\pi$
$828$	16.5316	+	7.12092i	0.574511	+	0.247469i
$829$	38.2371			1.32803			0.664015	−	0.747720i	$-0.268851\pi$
$829$	38.2371			1.32803			0.664015	+	0.747720i	$0.268851\pi$
$830$	−13.1113	−	22.7094i	−0.455099	−	0.788254i
$831$	−4.39926	−	3.91298i	−0.152609	−	0.135740i
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	0.315223	−	0.545982i	0.0109218	−	0.0189172i
$834$	−17.4072	+	5.77311i	−0.602763	+	0.199906i
$835$	11.1421	+	19.2987i	0.385590	+	0.667861i
$836$	37.1520			1.28493
$837$	6.10940	+	13.0753i	0.211172	+	0.451947i
$838$	27.4610			0.948625
$839$	22.5407	+	39.0416i	0.778192	+	1.34787i	0.932983	+	0.359920i	$0.117196\pi$
$839$	22.5407	+	39.0416i	0.778192	+	1.34787i	−0.154792	+	0.987947i	$0.549471\pi$
$840$	15.1941	−	5.03913i	0.524247	−	0.173867i
$841$	12.0302	−	20.8369i	0.414834	−	0.718513i
$842$	1.47091	−	2.54769i	0.0506909	−	0.0877992i
$843$	37.1199	+	33.0168i	1.27848	+	1.13716i
$844$	−2.35600	−	4.08072i	−0.0810970	−	0.140464i
$845$	3.28799			0.113110
$846$	−0.532732	−	4.53753i	−0.0183157	−	0.156004i
$847$	−44.4079			−1.52587
$848$	5.51052	+	9.54450i	0.189232	+	0.327760i
$849$	3.91714	−	18.9954i	0.134436	−	0.651921i
$850$	−2.03273	+	3.52079i	−0.0697221	+	0.120762i
$851$	−2.13602	+	3.69970i	−0.0732219	+	0.126824i
$852$	0.415967	−	2.01715i	0.0142508	−	0.0691065i
$853$	−12.9840	−	22.4889i	−0.444563	−	0.770006i	0.553459	−	0.832877i	$-0.313308\pi$
$853$	−12.9840	−	22.4889i	−0.444563	−	0.770006i	−0.998022	+	0.0628710i	$0.979974\pi$
$854$	26.4203			0.904084
$855$	8.25457	+	70.3082i	0.282300	+	2.40449i
$856$	−12.0000			−0.410152
$857$	−9.05494	−	15.6836i	−0.309311	−	0.535742i	0.668901	−	0.743352i	$-0.266765\pi$
$857$	−9.05494	−	15.6836i	−0.309311	−	0.535742i	−0.978212	+	0.207609i	$0.933432\pi$
$858$	6.69963	+	5.95907i	0.228722	+	0.203439i
$859$	16.1080	−	27.8999i	0.549599	−	0.951933i	−0.448703	−	0.893681i	$-0.648114\pi$
$859$	16.1080	−	27.8999i	0.549599	−	0.951933i	0.998302	−	0.0582522i	$-0.0185527\pi$
$860$	−18.9029	+	32.7408i	−0.644583	+	1.11645i
$861$	3.80442	−	1.26174i	0.129654	−	0.0429998i
$862$	1.68980	+	2.92681i	0.0575547	+	0.0996877i
$863$	−5.01594			−0.170745			−0.0853724	−	0.996349i	$-0.527208\pi$
$863$	−5.01594			−0.170745			−0.0853724	+	0.996349i	$0.527208\pi$
$864$	−2.19963	−	4.70761i	−0.0748329	−	0.160156i
$865$	62.9715			2.14110
$866$	4.18292	+	7.24503i	0.142141	+	0.246196i
$867$	−27.1432	+	9.00205i	−0.921832	+	0.305726i
$868$	3.90359	−	6.76121i	0.132496	−	0.229490i
$869$	40.7738	−	70.6222i	1.38315	−	2.39569i
$870$	−9.45744	−	8.41204i	−0.320637	−	0.285195i
$871$	−0.222528	−	0.385430i	−0.00754008	−	0.0130598i
$872$	6.67487			0.226040
$873$	−13.6501	−	5.87974i	−0.461986	−	0.198999i
$874$	43.0604			1.45654
$875$	3.74721	+	6.49036i	0.126679	+	0.219414i
$876$	0.0778435	−	0.377488i	0.00263009	−	0.0127541i
$877$	−9.75526	+	16.8966i	−0.329412	+	0.570558i	−0.982395	−	0.186814i	$-0.940184\pi$
$877$	−9.75526	+	16.8966i	−0.329412	+	0.570558i	0.652984	+	0.757372i	$0.273517\pi$
$878$	−14.2880	+	24.7475i	−0.482196	+	0.835189i
$879$	−2.42835	+	11.7758i	−0.0819061	+	0.397188i
$880$	−8.51052	−	14.7407i	−0.286890	−	0.496907i
$881$	−30.4895			−1.02722			−0.513608	−	0.858025i	$-0.671692\pi$
$881$	−30.4895			−1.02722			−0.513608	+	0.858025i	$0.671692\pi$
$882$	−2.16758	+	1.61544i	−0.0729864	+	0.0543948i
$883$	−0.217432			−0.00731718			−0.00365859	−	0.999993i	$-0.501165\pi$
$883$	−0.217432			−0.00731718			−0.00365859	+	0.999993i	$0.501165\pi$
$884$	0.349814	+	0.605896i	0.0117655	+	0.0203785i
$885$	−62.9715	−	56.0108i	−2.11676	−	1.88278i
$886$	−9.26942	+	16.0551i	−0.311412	+	0.539382i
$887$	2.22253	−	3.84953i	0.0746252	−	0.129255i	−0.826298	−	0.563233i	$-0.809557\pi$
$887$	2.22253	−	3.84953i	0.0746252	−	0.129255i	0.900923	+	0.433979i	$0.142891\pi$
$888$	1.17054	−	0.388209i	0.0392807	−	0.0130274i
$889$	−4.81227	−	8.33510i	−0.161398	−	0.279550i
$890$	−24.3287			−0.815500
$891$	−45.3236	+	10.7912i	−1.51840	+	0.361520i
$892$	7.62907			0.255440
$893$	−5.46472	−	9.46517i	−0.182870	−	0.316740i
$894$	27.9072	−	9.25543i	0.933357	−	0.309548i
$895$	0.345483	−	0.598395i	0.0115482	−	0.0200021i
$896$	−1.40545	+	2.43430i	−0.0469527	+	0.0813244i
$897$	7.76509	+	6.90676i	0.259269	+	0.230610i
$898$	−7.43130	−	12.8714i	−0.247986	−	0.429524i
$899$	−6.17301			−0.205881
$900$	13.9778	−	10.4173i	0.465926	−	0.347243i
$901$	7.71063			0.256878
$902$	−2.13093	−	3.69087i	−0.0709521	−	0.122893i
$903$	11.3060	−	54.8263i	0.376240	−	1.82451i
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	−10.5956	+	18.3522i	−0.352211	+	0.610048i
$906$	7.77197	−	37.6887i	0.258206	−	1.25212i
$907$	9.25704	+	16.0337i	0.307375	+	0.532389i	0.977787	−	0.209600i	$-0.0672161\pi$
$907$	9.25704	+	16.0337i	0.307375	+	0.532389i	−0.670412	+	0.741989i	$0.733883\pi$
$908$	22.0421			0.731492
$909$	8.13959	+	3.50610i	0.269973	+	0.116290i
$910$	9.24219			0.306376
$911$	2.14468	+	3.71470i	0.0710566	+	0.123074i	0.899365	−	0.437199i	$-0.144030\pi$
$911$	2.14468	+	3.71470i	0.0710566	+	0.123074i	−0.828308	+	0.560273i	$0.810696\pi$
$912$	−9.28799	−	8.26132i	−0.307556	−	0.273560i
$913$	20.6428	−	35.7544i	0.683178	−	1.18330i
$914$	11.1520	−	19.3158i	0.368874	−	0.638909i
$915$	50.8072	−	16.8502i	1.67963	−	0.557050i
$916$	2.24474	+	3.88800i	0.0741683	+	0.128463i
$917$	−23.2027			−0.766221
$918$	−3.62178	−	0.314045i	−0.119537	−	0.0103650i
$919$	53.5302			1.76580			0.882899	−	0.469563i	$-0.155589\pi$
$919$	53.5302			1.76580			0.882899	+	0.469563i	$0.155589\pi$
$920$	−9.86398	−	17.0849i	−0.325206	−	0.563273i
$921$	−24.6945	+	8.18994i	−0.813713	+	0.269868i
$922$	4.87017	−	8.43538i	0.160390	−	0.277804i
$923$	0.594554	−	1.02980i	0.0195700	−	0.0338962i
$924$	18.8319	+	16.7503i	0.619525	+	0.551045i
$925$	2.06870	+	3.58309i	0.0680185	+	0.117811i
$926$	3.62550			0.119141
$927$	3.28799	+	28.0054i	0.107992	+	0.919819i
$928$	2.22253			0.0729581
$929$	22.8974	+	39.6595i	0.751239	+	1.30118i	0.947222	+	0.320577i	$0.103877\pi$
$929$	22.8974	+	39.6595i	0.751239	+	1.30118i	−0.195983	+	0.980607i	$0.562790\pi$
$930$	3.19461	−	15.4917i	0.104755	−	0.507991i
$931$	−3.23353	+	5.60064i	−0.105975	+	0.183554i
$932$	−2.77128	+	4.80000i	−0.0907764	+	0.157229i
$933$	2.78985	−	13.5289i	0.0913356	−	0.442915i
$934$	−0.0229002	−	0.0396643i	−0.000749316	−	0.00129785i
$935$	−11.9084			−0.389446
$936$	−0.349814	−	2.97954i	−0.0114340	−	0.0973892i
$937$	−32.0604			−1.04737			−0.523683	−	0.851913i	$-0.675442\pi$
$937$	−32.0604			−1.04737			−0.523683	+	0.851913i	$0.675442\pi$
$938$	−0.625503	−	1.08340i	−0.0204234	−	0.0353744i
$939$	−18.1120	−	16.1099i	−0.591061	−	0.525727i
$940$	−2.50364	+	4.33643i	−0.0816598	+	0.141439i
$941$	7.18430	−	12.4436i	0.234201	−	0.405649i	−0.724839	−	0.688918i	$-0.758086\pi$
$941$	7.18430	−	12.4436i	0.234201	−	0.405649i	0.959040	+	0.283270i	$0.0914192\pi$
$942$	7.67349	−	2.54491i	0.250016	−	0.0829177i
$943$	−2.46982	−	4.27785i	−0.0804283	−	0.139306i
$944$	14.7985			0.481651
$945$	−27.5149	+	39.3601i	−0.895061	+	1.28038i
$946$	−59.5227			−1.93525
$947$	1.07922	+	1.86927i	0.0350700	+	0.0607430i	0.883028	−	0.469321i	$-0.155501\pi$
$947$	1.07922	+	1.86927i	0.0350700	+	0.0607430i	−0.847958	+	0.530064i	$0.822168\pi$
$948$	−25.8974	+	8.58887i	−0.841108	+	0.278953i
$949$	0.111264	−	0.192715i	0.00361179	−	0.00625580i
$950$	20.8516	−	36.1160i	0.676515	−	1.17176i
$951$	12.1916	+	10.8440i	0.395339	+	0.351639i
$952$	0.983290	+	1.70311i	0.0318686	+	0.0551980i
$953$	−53.0480			−1.71839			−0.859196	−	0.511646i	$-0.829036\pi$
$953$	−53.0480			−1.71839			−0.859196	+	0.511646i	$0.829036\pi$
$954$	−30.3658	−	13.0800i	−0.983130	−	0.423480i
$955$	−76.7738			−2.48434
$956$	−3.71565	−	6.43569i	−0.120173	−	0.208145i
$957$	4.02476	−	19.5173i	0.130102	−	0.630905i
$958$	8.84176	−	15.3144i	0.285664	−	0.494785i
$959$	−6.46610	+	11.1996i	−0.208801	+	0.361654i
$960$	−1.15019	+	5.57761i	−0.0371221	+	0.180017i
$961$	11.6428	+	20.1660i	0.375575	+	0.650515i
$962$	0.712008			0.0229561
$963$	28.8654	−	21.5126i	0.930173	−	0.693233i
$964$	9.39926			0.302730
$965$	−40.9839	−	70.9862i	−1.31932	−	2.28513i
$966$	21.8268	+	19.4142i	0.702267	+	0.624640i
$967$	−13.5279	+	23.4310i	−0.435029	+	0.753492i	−0.997298	−	0.0734625i	$-0.976595\pi$
$967$	−13.5279	+	23.4310i	−0.435029	+	0.753492i	0.562269	+	0.826954i	$0.309928\pi$
$968$	7.89926	−	13.6819i	0.253892	−	0.439753i
$969$	−8.25457	+	2.73763i	−0.265175	+	0.0879453i
$970$	8.14468	+	14.1070i	0.261510	+	0.452949i
$971$	30.3979			0.975514			0.487757	−	0.872979i	$-0.337815\pi$
$971$	30.3979			0.975514			0.487757	+	0.872979i	$0.337815\pi$
$972$	13.7305	+	7.38061i	0.440406	+	0.236733i
$973$	−29.7628			−0.954150
$974$	−11.6218	−	20.1295i	−0.372386	−	0.644991i
$975$	9.55308	−	3.16828i	0.305944	−	0.101466i
$976$	−4.69963	+	8.13999i	−0.150431	+	0.260555i
$977$	8.55632	−	14.8200i	0.273741	−	0.474133i	−0.696076	−	0.717968i	$-0.745072\pi$
$977$	8.55632	−	14.8200i	0.273741	−	0.474133i	0.969817	+	0.243835i	$0.0784056\pi$
$978$	−15.4981	−	13.7850i	−0.495576	−	0.440796i
$979$	−19.1520	−	33.1722i	−0.612100	−	1.06019i
$980$	2.96286			0.0946451
$981$	−16.0560	+	11.9661i	−0.512630	+	0.382049i
$982$	18.5439			0.591761
$983$	−20.6861	−	35.8293i	−0.659783	−	1.14278i	−0.980672	−	0.195661i	$-0.937315\pi$
$983$	−20.6861	−	35.8293i	−0.659783	−	1.14278i	0.320888	−	0.947117i	$-0.396019\pi$
$984$	−0.287992	+	1.39656i	−0.00918085	+	0.0445208i
$985$	16.8261	−	29.1437i	0.536126	−	0.928597i
$986$	0.777472	−	1.34662i	0.0247597	−	0.0428851i
$987$	1.49745	−	7.26161i	0.0476644	−	0.231140i
$988$	−3.58836	−	6.21523i	−0.114161	−	0.197733i
$989$	−68.9888			−2.19372
$990$	46.8974	+	20.2009i	1.49050	+	0.642027i
$991$	−38.8552			−1.23427			−0.617137	−	0.786855i	$-0.711708\pi$
$991$	−38.8552			−1.23427			−0.617137	+	0.786855i	$0.711708\pi$
$992$	1.38874	+	2.40536i	0.0440924	+	0.0763703i
$993$	14.9542	+	13.3012i	0.474557	+	0.422101i
$994$	1.67123	−	2.89465i	0.0530081	−	0.0918127i
$995$	−44.2312	+	76.6107i	−1.40222	+	2.42872i
$996$	−13.1113	+	4.34835i	−0.415446	+	0.137783i
$997$	2.73167	+	4.73139i	0.0865129	+	0.149845i	0.906035	−	0.423203i	$-0.139094\pi$
$997$	2.73167	+	4.73139i	0.0865129	+	0.149845i	−0.819522	+	0.573048i	$0.805761\pi$
$998$	31.5475			0.998619
$999$	−2.11972	+	3.03226i	−0.0670649	+	0.0959364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.e.d.157.3	yes	6
3.2	odd	2		702.2.e.d.469.3		6
9.2	odd	6		702.2.e.d.235.3		6
9.4	even	3		2106.2.a.q.1.3		3
9.5	odd	6		2106.2.a.r.1.1		3
9.7	even	3	inner	234.2.e.d.79.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.e.d.79.3	✓	6	9.7	even	3	inner
234.2.e.d.157.3	yes	6	1.1	even	1	trivial
702.2.e.d.235.3		6	9.2	odd	6
702.2.e.d.469.3		6	3.2	odd	2
2106.2.a.q.1.3		3	9.4	even	3
2106.2.a.r.1.1		3	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64400 + 2.84748i) q^{5} +(1.29418 + 1.15113i) q^{6} +(1.40545 + 2.43430i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} -3.28799 q^{10} +(-2.58836 - 4.48318i) q^{11} +(-0.349814 + 1.69636i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.40545 + 2.43430i) q^{14} +(-1.15019 + 5.57761i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.699628 q^{17} +(2.75526 + 1.18682i) q^{18} +7.17673 q^{19} +(-1.64400 - 2.84748i) q^{20} +(3.63781 + 3.23569i) q^{21} +(2.58836 - 4.48318i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-1.64400 + 0.545231i) q^{24} +(-2.90545 - 5.03238i) q^{25} -1.00000 q^{26} +(2.97710 - 4.25874i) q^{27} -2.81089 q^{28} +(1.11126 + 1.92477i) q^{29} +(-5.40545 + 1.79272i) q^{30} +(-1.38874 + 2.40536i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.69963 - 5.95907i) q^{33} +(-0.349814 - 0.605896i) q^{34} -9.24219 q^{35} +(0.349814 + 2.97954i) q^{36} -0.712008 q^{37} +(3.58836 + 6.21523i) q^{38} +(-0.349814 + 1.69636i) q^{39} +(1.64400 - 2.84748i) q^{40} +(0.411636 - 0.712974i) q^{41} +(-0.983290 + 4.76828i) q^{42} +(-5.74907 - 9.95768i) q^{43} +5.17673 q^{44} +(1.15019 + 9.79669i) q^{45} +6.00000 q^{46} +(-0.761450 - 1.31887i) q^{47} +(-1.29418 - 1.15113i) q^{48} +(-0.450558 + 0.780389i) q^{49} +(2.90545 - 5.03238i) q^{50} +(-1.15019 + 0.381459i) q^{51} +(-0.500000 - 0.866025i) q^{52} -11.0210 q^{53} +(5.17673 + 0.448873i) q^{54} +17.0210 q^{55} +(-1.40545 - 2.43430i) q^{56} +(11.7985 - 3.91298i) q^{57} +(-1.11126 + 1.92477i) q^{58} +(-7.39926 + 12.8159i) q^{59} +(-4.25526 - 3.78490i) q^{60} +(-4.69963 - 8.13999i) q^{61} -2.77747 q^{62} +(7.74474 + 3.33602i) q^{63} +1.00000 q^{64} +(-1.64400 - 2.84748i) q^{65} +(1.81089 - 8.78158i) q^{66} +(-0.222528 + 0.385430i) q^{67} +(0.349814 - 0.605896i) q^{68} +(2.09888 - 10.1781i) q^{69} +(-4.62110 - 8.00397i) q^{70} -1.18911 q^{71} +(-2.40545 + 1.79272i) q^{72} -0.222528 q^{73} +(-0.356004 - 0.616617i) q^{74} +(-7.52035 - 6.68907i) q^{75} +(-3.58836 + 6.21523i) q^{76} +(7.27561 - 12.6017i) q^{77} +(-1.64400 + 0.545231i) q^{78} +(7.87636 + 13.6422i) q^{79} +3.28799 q^{80} +(2.57234 - 8.62456i) q^{81} +0.823272 q^{82} +(3.98762 + 6.90676i) q^{83} +(-4.62110 + 1.53259i) q^{84} +(1.15019 - 1.99218i) q^{85} +(5.74907 - 9.95768i) q^{86} +(2.87636 + 2.55841i) q^{87} +(2.58836 + 4.48318i) q^{88} +7.39926 q^{89} +(-7.90909 + 5.89443i) q^{90} -2.81089 q^{91} +(3.00000 + 5.19615i) q^{92} +(-0.971599 + 4.71159i) q^{93} +(0.761450 - 1.31887i) q^{94} +(-11.7985 + 20.4356i) q^{95} +(0.349814 - 1.69636i) q^{96} +(-2.47710 - 4.29046i) q^{97} -0.901116 q^{98} +(-14.2632 - 6.14384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 2 q^{14} - 13 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 20 q^{19} + 2 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 2 * q^14 - 13 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 + 20 * q^19 + 2 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^23 + 2 * q^24 - 11 * q^25 - 6 * q^26 + 7 * q^27 - 4 * q^28 + 6 * q^29 - 26 * q^30 - 9 * q^31 + 3 * q^32 - 28 * q^33 + 4 * q^34 - 10 * q^35 - 4 * q^36 - 28 * q^37 + 10 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 13 * q^42 - 4 * q^43 + 8 * q^44 + 13 * q^45 + 36 * q^46 - 10 * q^47 - 2 * q^48 - 21 * q^49 + 11 * q^50 - 13 * q^51 - 3 * q^52 - 16 * q^53 + 8 * q^54 + 52 * q^55 - 2 * q^56 + 22 * q^57 - 6 * q^58 - 20 * q^59 - 13 * q^60 - 16 * q^61 - 18 * q^62 + 59 * q^63 + 6 * q^64 + 2 * q^65 - 2 * q^66 - 4 * q^68 - 24 * q^69 - 5 * q^70 - 20 * q^71 - 8 * q^72 - 14 * q^74 + 2 * q^75 - 10 * q^76 - 16 * q^77 + 2 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 + 28 * q^82 - 12 * q^83 - 5 * q^84 + 13 * q^85 + 4 * q^86 - 18 * q^87 + 4 * q^88 + 20 * q^89 - q^90 - 4 * q^91 + 18 * q^92 + 26 * q^93 + 10 * q^94 - 22 * q^95 - 4 * q^96 - 4 * q^97 - 42 * q^98 + 10 * q^99

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