LMFDB - Embedded newform 430.2.j.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (of order $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-2.75803 - 1.59235i) q^{3} -1.00000 q^{4} +(1.06925 + 1.96385i) q^{5} +(-1.59235 + 2.75803i) q^{6} +(3.76835 - 2.17566i) q^{7} +1.00000i q^{8} +(3.57116 + 6.18543i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-2.75803 - 1.59235i) q^{3} -1.00000 q^{4} +(1.06925 + 1.96385i) q^{5} +(-1.59235 + 2.75803i) q^{6} +(3.76835 - 2.17566i) q^{7} +1.00000i q^{8} +(3.57116 + 6.18543i) q^{9} +(1.96385 - 1.06925i) q^{10} +3.05490 q^{11} +(2.75803 + 1.59235i) q^{12} +(-2.18113 + 1.25928i) q^{13} +(-2.17566 - 3.76835i) q^{14} +(0.178113 - 7.11898i) q^{15} +1.00000 q^{16} +(4.35366 - 2.51359i) q^{17} +(6.18543 - 3.57116i) q^{18} +(-0.128404 + 0.222402i) q^{19} +(-1.06925 - 1.96385i) q^{20} -13.8576 q^{21} -3.05490i q^{22} +(-1.01417 - 0.585531i) q^{23} +(1.59235 - 2.75803i) q^{24} +(-2.71341 + 4.19969i) q^{25} +(1.25928 + 2.18113i) q^{26} -13.1920i q^{27} +(-3.76835 + 2.17566i) q^{28} +(-1.86535 - 3.23088i) q^{29} +(-7.11898 - 0.178113i) q^{30} +(0.725506 - 1.25661i) q^{31} -1.00000i q^{32} +(-8.42551 - 4.86447i) q^{33} +(-2.51359 - 4.35366i) q^{34} +(8.30196 + 5.07415i) q^{35} +(-3.57116 - 6.18543i) q^{36} +(-3.24030 - 1.87079i) q^{37} +(0.222402 + 0.128404i) q^{38} +8.02085 q^{39} +(-1.96385 + 1.06925i) q^{40} +12.5411 q^{41} +13.8576i q^{42} +(4.82556 - 4.44004i) q^{43} -3.05490 q^{44} +(-8.32879 + 13.6270i) q^{45} +(-0.585531 + 1.01417i) q^{46} +3.16187i q^{47} +(-2.75803 - 1.59235i) q^{48} +(5.96695 - 10.3351i) q^{49} +(4.19969 + 2.71341i) q^{50} -16.0100 q^{51} +(2.18113 - 1.25928i) q^{52} +(-6.49107 - 3.74762i) q^{53} -13.1920 q^{54} +(3.26645 + 5.99937i) q^{55} +(2.17566 + 3.76835i) q^{56} +(0.708284 - 0.408928i) q^{57} +(-3.23088 + 1.86535i) q^{58} +4.97573 q^{59} +(-0.178113 + 7.11898i) q^{60} +(5.56132 + 9.63249i) q^{61} +(-1.25661 - 0.725506i) q^{62} +(26.9147 + 15.5392i) q^{63} -1.00000 q^{64} +(-4.80521 - 2.93694i) q^{65} +(-4.86447 + 8.42551i) q^{66} +(-8.17813 - 4.72164i) q^{67} +(-4.35366 + 2.51359i) q^{68} +(1.86474 + 3.22983i) q^{69} +(5.07415 - 8.30196i) q^{70} +(-7.80824 - 13.5243i) q^{71} +(-6.18543 + 3.57116i) q^{72} +(-2.16077 + 1.24752i) q^{73} +(-1.87079 + 3.24030i) q^{74} +(14.1711 - 7.26217i) q^{75} +(0.128404 - 0.222402i) q^{76} +(11.5119 - 6.64641i) q^{77} -8.02085i q^{78} +(3.92279 + 6.79447i) q^{79} +(1.06925 + 1.96385i) q^{80} +(-10.2929 + 17.8278i) q^{81} -12.5411i q^{82} +(12.5145 + 7.22524i) q^{83} +13.8576 q^{84} +(9.59145 + 5.86228i) q^{85} +(-4.44004 - 4.82556i) q^{86} +11.8811i q^{87} +3.05490i q^{88} +(3.69213 - 6.39495i) q^{89} +(13.6270 + 8.32879i) q^{90} +(-5.47951 + 9.49080i) q^{91} +(1.01417 + 0.585531i) q^{92} +(-4.00194 + 2.31052i) q^{93} +3.16187 q^{94} +(-0.574060 - 0.0143627i) q^{95} +(-1.59235 + 2.75803i) q^{96} +18.7299i q^{97} +(-10.3351 - 5.96695i) q^{98} +(10.9095 + 18.8959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−2.75803	−	1.59235i	−1.59235	−	0.919344i	−0.992903	−	0.118930i	$-0.962054\pi$
$3$	−2.75803	−	1.59235i	−1.59235	−	0.919344i	−0.599447	−	0.800414i	$-0.704613\pi$
$4$	−1.00000			−0.500000
$5$	1.06925	+	1.96385i	0.478183	+	0.878260i
$5$	1.06925	+	1.96385i	0.478183	+	0.878260i
$6$	−1.59235	+	2.75803i	−0.650074	+	1.12596i
$7$	3.76835	−	2.17566i	1.42430	−	0.822320i	0.427638	−	0.903950i	$-0.359346\pi$
$7$	3.76835	−	2.17566i	1.42430	−	0.822320i	0.996663	+	0.0816298i	$0.0260125\pi$
$8$			1.00000i			0.353553i
$9$	3.57116	+	6.18543i	1.19039	+	2.06181i
$10$	1.96385	−	1.06925i	0.621024	−	0.338126i
$11$	3.05490			0.921087			0.460544	−	0.887637i	$-0.347655\pi$
$11$	3.05490			0.921087			0.460544	+	0.887637i	$0.347655\pi$
$12$	2.75803	+	1.59235i	0.796175	+	0.459672i
$13$	−2.18113	+	1.25928i	−0.604938	+	0.349261i	−0.770982	−	0.636857i	$-0.780234\pi$
$13$	−2.18113	+	1.25928i	−0.604938	+	0.349261i	0.166044	+	0.986118i	$0.446901\pi$
$14$	−2.17566	−	3.76835i	−0.581468	−	1.00713i
$15$	0.178113	−	7.11898i	0.0459887	−	1.83811i
$16$	1.00000			0.250000
$17$	4.35366	−	2.51359i	1.05592	−	0.609634i	0.131617	−	0.991301i	$-0.457983\pi$
$17$	4.35366	−	2.51359i	1.05592	−	0.609634i	0.924300	+	0.381666i	$0.124650\pi$
$18$	6.18543	−	3.57116i	1.45792	−	0.841730i
$19$	−0.128404	+	0.222402i	−0.0294579	+	0.0510226i	−0.880379	−	0.474272i	$-0.842711\pi$
$19$	−0.128404	+	0.222402i	−0.0294579	+	0.0510226i	0.850921	+	0.525294i	$0.176045\pi$
$20$	−1.06925	−	1.96385i	−0.239091	−	0.439130i
$21$	−13.8576			−3.02398
$22$		−	3.05490i		−	0.651307i
$23$	−1.01417	−	0.585531i	−0.211469	−	0.122092i	0.390525	−	0.920592i	$-0.372294\pi$
$23$	−1.01417	−	0.585531i	−0.211469	−	0.122092i	−0.601994	+	0.798501i	$0.705627\pi$
$24$	1.59235	−	2.75803i	0.325037	−	0.562981i
$25$	−2.71341	+	4.19969i	−0.542682	+	0.839938i
$26$	1.25928	+	2.18113i	0.246965	+	0.427756i
$27$		−	13.1920i		−	2.53881i
$28$	−3.76835	+	2.17566i	−0.712150	+	0.411160i
$29$	−1.86535	−	3.23088i	−0.346386	−	0.599959i	0.639218	−	0.769025i	$-0.279258\pi$
$29$	−1.86535	−	3.23088i	−0.346386	−	0.599959i	−0.985605	+	0.169067i	$0.945925\pi$
$30$	−7.11898	−	0.178113i	−1.29974	−	0.0325189i
$31$	0.725506	−	1.25661i	0.130305	−	0.225695i	−0.793489	−	0.608584i	$-0.791738\pi$
$31$	0.725506	−	1.25661i	0.130305	−	0.225695i	0.923794	+	0.382890i	$0.125071\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−8.42551	−	4.86447i	−1.46669	−	0.846796i
$34$	−2.51359	−	4.35366i	−0.431076	−	0.746646i
$35$	8.30196	+	5.07415i	1.40329	+	0.857687i
$36$	−3.57116	−	6.18543i	−0.595193	−	1.03090i
$37$	−3.24030	−	1.87079i	−0.532702	−	0.307555i	0.209414	−	0.977827i	$-0.432844\pi$
$37$	−3.24030	−	1.87079i	−0.532702	−	0.307555i	−0.742116	+	0.670272i	$0.766178\pi$
$38$	0.222402	+	0.128404i	0.0360784	+	0.0208299i
$39$	8.02085			1.28436
$40$	−1.96385	+	1.06925i	−0.310512	+	0.169063i
$41$	12.5411			1.95859			0.979297	−	0.202430i	$-0.0648839\pi$
$41$	12.5411			1.95859			0.979297	+	0.202430i	$0.0648839\pi$
$42$			13.8576i			2.13828i
$43$	4.82556	−	4.44004i	0.735891	−	0.677100i
$43$	4.82556	−	4.44004i	0.735891	−	0.677100i
$44$	−3.05490			−0.460544
$45$	−8.32879	+	13.6270i	−1.24158	+	2.03139i
$46$	−0.585531	+	1.01417i	−0.0863319	+	0.149531i
$47$			3.16187i			0.461207i	0.973048	+	0.230603i	$0.0740700\pi$
$47$			3.16187i			0.461207i	−0.973048	+	0.230603i	$0.925930\pi$
$48$	−2.75803	−	1.59235i	−0.398088	−	0.229836i
$49$	5.96695	−	10.3351i	0.852422	−	1.47644i
$50$	4.19969	+	2.71341i	0.593926	+	0.383734i
$51$	−16.0100			−2.24185
$52$	2.18113	−	1.25928i	0.302469	−	0.174631i
$53$	−6.49107	−	3.74762i	−0.891617	−	0.514775i	−0.0171461	−	0.999853i	$-0.505458\pi$
$53$	−6.49107	−	3.74762i	−0.891617	−	0.514775i	−0.874471	+	0.485077i	$0.838791\pi$
$54$	−13.1920			−1.79521
$55$	3.26645	+	5.99937i	0.440448	+	0.808954i
$56$	2.17566	+	3.76835i	0.290734	+	0.503566i
$57$	0.708284	−	0.408928i	0.0938145	−	0.0541638i
$58$	−3.23088	+	1.86535i	−0.424235	+	0.244932i
$59$	4.97573			0.647785			0.323892	−	0.946094i	$-0.395008\pi$
$59$	4.97573			0.647785			0.323892	+	0.946094i	$0.395008\pi$
$60$	−0.178113	+	7.11898i	−0.0229943	+	0.919056i
$61$	5.56132	+	9.63249i	0.712054	+	1.23331i	0.964085	+	0.265594i	$0.0855682\pi$
$61$	5.56132	+	9.63249i	0.712054	+	1.23331i	−0.252031	+	0.967719i	$0.581098\pi$
$62$	−1.25661	−	0.725506i	−0.159590	−	0.0921394i
$63$	26.9147	+	15.5392i	3.39093	+	1.95776i
$64$	−1.00000			−0.125000
$65$	−4.80521	−	2.93694i	−0.596013	−	0.364282i
$66$	−4.86447	+	8.42551i	−0.598775	+	1.03711i
$67$	−8.17813	−	4.72164i	−0.999117	−	0.576841i	−0.0911302	−	0.995839i	$-0.529048\pi$
$67$	−8.17813	−	4.72164i	−0.999117	−	0.576841i	−0.907987	+	0.418998i	$0.862381\pi$
$68$	−4.35366	+	2.51359i	−0.527959	+	0.304817i
$69$	1.86474	+	3.22983i	0.224489	+	0.388826i
$70$	5.07415	−	8.30196i	0.606476	−	0.992274i
$71$	−7.80824	−	13.5243i	−0.926668	−	1.60504i	−0.788856	−	0.614578i	$-0.789326\pi$
$71$	−7.80824	−	13.5243i	−0.926668	−	1.60504i	−0.137812	−	0.990458i	$-0.544007\pi$
$72$	−6.18543	+	3.57116i	−0.728959	+	0.420865i
$73$	−2.16077	+	1.24752i	−0.252899	+	0.146011i	−0.621091	−	0.783739i	$-0.713310\pi$
$73$	−2.16077	+	1.24752i	−0.252899	+	0.146011i	0.368192	+	0.929750i	$0.379977\pi$
$74$	−1.87079	+	3.24030i	−0.217475	+	0.376677i
$75$	14.1711	−	7.26217i	1.63633	−	0.838564i
$76$	0.128404	−	0.222402i	0.0147289	−	0.0255113i
$77$	11.5119	−	6.64641i	1.31190	−	0.757429i
$78$		−	8.02085i		−	0.908183i
$79$	3.92279	+	6.79447i	0.441349	+	0.764438i	0.997790	−	0.0664488i	$-0.0211669\pi$
$79$	3.92279	+	6.79447i	0.441349	+	0.764438i	−0.556441	+	0.830887i	$0.687834\pi$
$80$	1.06925	+	1.96385i	0.119546	+	0.219565i
$81$	−10.2929	+	17.8278i	−1.14365	+	1.98086i
$82$		−	12.5411i		−	1.38493i
$83$	12.5145	+	7.22524i	1.37364	+	0.793073i	0.991385	−	0.130982i	$-0.0418131\pi$
$83$	12.5145	+	7.22524i	1.37364	+	0.793073i	0.382258	+	0.924056i	$0.375146\pi$
$84$	13.8576			1.51199
$85$	9.59145	+	5.86228i	1.04034	+	0.635854i
$86$	−4.44004	−	4.82556i	−0.478782	−	0.520353i
$87$			11.8811i			1.27379i
$88$			3.05490i			0.325653i
$89$	3.69213	−	6.39495i	0.391364	−	0.677863i	−0.601265	−	0.799049i	$-0.705337\pi$
$89$	3.69213	−	6.39495i	0.391364	−	0.677863i	0.992630	+	0.121186i	$0.0386698\pi$
$90$	13.6270	+	8.32879i	1.43641	+	0.877932i
$91$	−5.47951	+	9.49080i	−0.574409	+	0.994906i
$92$	1.01417	+	0.585531i	0.105735	+	0.0610459i
$93$	−4.00194	+	2.31052i	−0.414982	+	0.239590i
$94$	3.16187			0.326122
$95$	−0.574060	−	0.0143627i	−0.0588973	−	0.00147358i
$96$	−1.59235	+	2.75803i	−0.162519	+	0.281490i
$97$			18.7299i			1.90173i	0.309603	+	0.950866i	$0.399804\pi$
$97$			18.7299i			1.90173i	−0.309603	+	0.950866i	$0.600196\pi$
$98$	−10.3351	−	5.96695i	−1.04400	−	0.602753i
$99$	10.9095	+	18.8959i	1.09645	+	1.89911i
$100$	2.71341	−	4.19969i	0.271341	−	0.419969i
$101$	−7.33300	−	12.7011i	−0.729660	−	1.26381i	−0.957027	−	0.290000i	$-0.906345\pi$
$101$	−7.33300	−	12.7011i	−0.729660	−	1.26381i	0.227366	−	0.973809i	$-0.426989\pi$
$102$			16.0100i			1.58523i
$103$	2.98373	−	1.72266i	0.293996	−	0.169739i	−0.345746	−	0.938328i	$-0.612374\pi$
$103$	2.98373	−	1.72266i	0.293996	−	0.169739i	0.639743	+	0.768589i	$0.279041\pi$
$104$	−1.25928	−	2.18113i	−0.123482	−	0.213878i
$105$	−14.8172	−	27.2143i	−1.44602	−	2.65584i
$106$	−3.74762	+	6.49107i	−0.364001	+	0.630469i
$107$			4.89160i			0.472889i	0.971645	+	0.236444i	$0.0759821\pi$
$107$			4.89160i			0.472889i	−0.971645	+	0.236444i	$0.924018\pi$
$108$			13.1920i			1.26940i
$109$	−3.17995	+	5.50784i	−0.304584	+	0.527555i	−0.977169	−	0.212465i	$-0.931851\pi$
$109$	−3.17995	+	5.50784i	−0.304584	+	0.527555i	0.672585	+	0.740020i	$0.265184\pi$
$110$	5.99937	−	3.26645i	0.572017	−	0.311444i
$111$	5.95789	+	10.3194i	0.565498	+	0.979472i
$112$	3.76835	−	2.17566i	0.356075	−	0.205580i
$113$		−	10.3238i		−	0.971184i	−0.874186	−	0.485592i	$-0.838604\pi$
$113$		−	10.3238i		−	0.971184i	0.874186	−	0.485592i	$-0.161396\pi$
$114$	−0.408928	−	0.708284i	−0.0382996	−	0.0663369i
$115$	0.0654950	−	2.61776i	0.00610744	−	0.244107i
$116$	1.86535	+	3.23088i	0.173193	+	0.299979i
$117$	−15.5784	−	8.99417i	−1.44022	−	0.831511i
$118$		−	4.97573i		−	0.458053i
$119$	10.9374	−	18.9441i	1.00263	−	1.73660i
$120$	7.11898	+	0.178113i	0.649871	+	0.0162595i
$121$	−1.66758			−0.151599
$122$	9.63249	−	5.56132i	0.872084	−	0.503498i
$123$	−34.5888	−	19.9698i	−3.11877	−	1.80062i
$124$	−0.725506	+	1.25661i	−0.0651524	+	0.112847i
$125$	−11.1489	−	0.838218i	−0.997186	−	0.0749725i
$126$	15.5392	−	26.9147i	1.38434	−	2.39775i
$127$		−	9.56306i		−	0.848585i	−0.905525	−	0.424292i	$-0.860523\pi$
$127$		−	9.56306i		−	0.848585i	0.905525	−	0.424292i	$-0.139477\pi$
$128$			1.00000i			0.0883883i
$129$	−20.3791	+	4.56180i	−1.79428	+	0.401644i
$130$	−2.93694	+	4.80521i	−0.257587	+	0.421445i
$131$	−12.3045			−1.07505			−0.537523	−	0.843249i	$-0.680640\pi$
$131$	−12.3045			−1.07505			−0.537523	+	0.843249i	$0.680640\pi$
$132$	8.42551	+	4.86447i	0.733347	+	0.423398i
$133$			1.11745i			0.0968953i
$134$	−4.72164	+	8.17813i	−0.407888	+	0.706483i
$135$	25.9072	−	14.1056i	2.22973	−	1.21401i
$136$	2.51359	+	4.35366i	0.215538	+	0.373323i
$137$			14.7096i			1.25673i	0.777920	+	0.628363i	$0.216275\pi$
$137$			14.7096i			1.25673i	−0.777920	+	0.628363i	$0.783725\pi$
$138$	3.22983	−	1.86474i	0.274941	−	0.158737i
$139$	−6.41680	+	11.1142i	−0.544266	+	0.942697i	0.454387	+	0.890805i	$0.349859\pi$
$139$	−6.41680	+	11.1142i	−0.544266	+	0.942697i	−0.998653	+	0.0518921i	$0.983475\pi$
$140$	−8.30196	−	5.07415i	−0.701644	−	0.428844i
$141$	5.03481	−	8.72055i	0.424007	−	0.734402i
$142$	−13.5243	+	7.80824i	−1.13493	+	0.655253i
$143$	−6.66315	+	3.84697i	−0.557201	+	0.321700i
$144$	3.57116	+	6.18543i	0.297596	+	0.515452i
$145$	4.35043	−	7.11787i	0.361284	−	0.591107i
$146$	1.24752	+	2.16077i	0.103245	+	0.178826i
$147$	−32.9141	+	19.0029i	−2.71471	+	1.56734i
$148$	3.24030	+	1.87079i	0.266351	+	0.153778i
$149$	2.90443	−	5.03061i	0.237940	−	0.412124i	−0.722183	−	0.691702i	$-0.756861\pi$
$149$	2.90443	−	5.03061i	0.237940	−	0.412124i	0.960123	+	0.279578i	$0.0901946\pi$
$150$	−7.26217	−	14.1711i	−0.592954	−	1.15706i
$151$	13.4018			1.09063			0.545313	−	0.838233i	$-0.316411\pi$
$151$	13.4018			1.09063			0.545313	+	0.838233i	$0.316411\pi$
$152$	−0.222402	−	0.128404i	−0.0180392	−	0.0104149i
$153$	31.0952	+	17.9528i	2.51390	+	1.45140i
$154$	−6.64641	−	11.5119i	−0.535583	−	0.927657i
$155$	3.24355	+	0.0811520i	0.260528	+	0.00651829i
$156$	−8.02085			−0.642182
$157$	−4.95324	+	2.85976i	−0.395312	+	0.228233i	−0.684459	−	0.729051i	$-0.739962\pi$
$157$	−4.95324	+	2.85976i	−0.395312	+	0.228233i	0.289147	+	0.957285i	$0.406628\pi$
$158$	6.79447	−	3.92279i	0.540539	−	0.312081i
$159$	11.9351	+	20.6721i	0.946511	+	1.63941i
$160$	1.96385	−	1.06925i	0.155256	−	0.0845316i
$161$	−5.09566			−0.401594
$162$	17.8278	+	10.2929i	1.40068	+	0.808683i
$163$	−5.19865	+	3.00144i	−0.407189	+	0.235091i	−0.689581	−	0.724208i	$-0.742205\pi$
$163$	−5.19865	+	3.00144i	−0.407189	+	0.235091i	0.282392	+	0.959299i	$0.408872\pi$
$164$	−12.5411			−0.979297
$165$	0.544119	−	21.7478i	0.0423596	−	1.69306i
$166$	7.22524	−	12.5145i	0.560787	−	0.971312i
$167$	−14.0983	−	8.13964i	−1.09096	−	0.629864i	−0.157126	−	0.987579i	$-0.550223\pi$
$167$	−14.0983	−	8.13964i	−1.09096	−	0.629864i	−0.933831	+	0.357714i	$0.883556\pi$
$168$		−	13.8576i		−	1.06914i
$169$	−3.32843	+	5.76502i	−0.256033	+	0.443463i
$170$	5.86228	−	9.59145i	0.449617	−	0.735631i
$171$	−1.83420			−0.140265
$172$	−4.82556	+	4.44004i	−0.367945	+	0.338550i
$173$			23.6499i			1.79807i	0.437877	+	0.899035i	$0.355730\pi$
$173$			23.6499i			1.79807i	−0.437877	+	0.899035i	$0.644270\pi$
$174$	11.8811			0.900707
$175$	−1.08800	+	21.7293i	−0.0822448	+	1.64258i
$176$	3.05490			0.230272
$177$	−13.7232	−	7.92310i	−1.03150	−	0.595537i
$178$	−6.39495	−	3.69213i	−0.479322	−	0.276736i
$179$	−1.57485	−	2.72772i	−0.117710	−	0.203880i	0.801150	−	0.598464i	$-0.204222\pi$
$179$	−1.57485	−	2.72772i	−0.117710	−	0.203880i	−0.918860	+	0.394584i	$0.870889\pi$
$180$	8.32879	−	13.6270i	0.620791	−	1.01570i
$181$	2.19593	+	3.80346i	0.163222	+	0.282709i	0.936023	−	0.351940i	$-0.114478\pi$
$181$	2.19593	+	3.80346i	0.163222	+	0.282709i	−0.772800	+	0.634649i	$0.781145\pi$
$182$	9.49080	+	5.47951i	0.703505	+	0.406169i
$183$		−	35.4223i		−	2.61849i
$184$	0.585531	−	1.01417i	0.0431659	−	0.0747656i
$185$	0.209258	−	8.36379i	0.0153850	−	0.614918i
$186$	2.31052	+	4.00194i	0.169416	+	0.293436i
$187$	13.3000	−	7.67876i	0.972592	−	0.561526i
$188$		−	3.16187i		−	0.230603i
$189$	−28.7013	−	49.7121i	−2.08771	−	3.61603i
$190$	−0.0143627	+	0.574060i	−0.00104198	+	0.0416467i
$191$	0.773041	−	1.33895i	0.0559353	−	0.0968827i	−0.836702	−	0.547659i	$-0.815519\pi$
$191$	0.773041	−	1.33895i	0.0559353	−	0.0968827i	0.892637	+	0.450776i	$0.148853\pi$
$192$	2.75803	+	1.59235i	0.199044	+	0.114918i
$193$			9.54512i			0.687073i	0.939139	+	0.343536i	$0.111625\pi$
$193$			9.54512i			0.687073i	−0.939139	+	0.343536i	$0.888375\pi$
$194$	18.7299			1.34473
$195$	8.57629	+	15.7517i	0.614161	+	1.12801i
$196$	−5.96695	+	10.3351i	−0.426211	+	0.738219i
$197$	17.3617	−	10.0238i	1.23697	−	0.714165i	0.268496	−	0.963281i	$-0.413473\pi$
$197$	17.3617	−	10.0238i	1.23697	−	0.714165i	0.968474	+	0.249116i	$0.0801401\pi$
$198$	18.8959	−	10.9095i	1.34287	−	0.775307i
$199$	−14.5458			−1.03112			−0.515561	−	0.856853i	$-0.672416\pi$
$199$	−14.5458			−1.03112			−0.515561	+	0.856853i	$0.672416\pi$
$200$	−4.19969	−	2.71341i	−0.296963	−	0.191867i
$201$	15.0370	+	26.0449i	1.06063	+	1.83706i
$202$	−12.7011	+	7.33300i	−0.893648	+	0.515948i
$203$	−14.0585	−	8.11670i	−0.986716	−	0.569681i
$204$	16.0100			1.12093
$205$	13.4096	+	24.6289i	0.936566	+	1.72015i
$206$	−1.72266	−	2.98373i	−0.120023	−	0.207887i
$207$		−	8.36410i		−	0.581345i
$208$	−2.18113	+	1.25928i	−0.151234	+	0.0873153i
$209$	−0.392261	+	0.679416i	−0.0271333	+	0.0469962i
$210$	−27.2143	+	14.8172i	−1.87796	+	1.02249i
$211$	−7.08060			−0.487448			−0.243724	−	0.969845i	$-0.578369\pi$
$211$	−7.08060			−0.487448			−0.243724	+	0.969845i	$0.578369\pi$
$212$	6.49107	+	3.74762i	0.445809	+	0.257388i
$213$			49.7338i			3.40771i
$214$	4.89160			0.334383
$215$	13.8793	+	4.72916i	0.946561	+	0.322526i
$216$	13.1920			0.897604
$217$		−	6.31381i		−	0.428609i
$218$	5.50784	+	3.17995i	0.373038	+	0.215373i
$219$	7.94595			0.536938
$220$	−3.26645	−	5.99937i	−0.220224	−	0.404477i
$221$	−6.33061	+	10.9649i	−0.425843	+	0.737582i
$222$	10.3194	−	5.95789i	0.692591	−	0.399868i
$223$		−	8.56936i		−	0.573847i	−0.957954	−	0.286923i	$-0.907368\pi$
$223$		−	8.56936i		−	0.573847i	0.957954	−	0.286923i	$-0.0926325\pi$
$224$	−2.17566	−	3.76835i	−0.145367	−	0.251783i
$225$	−35.6669	−	1.78585i	−2.37779	−	0.119057i
$226$	−10.3238			−0.686731
$227$	14.2695	+	8.23851i	0.947101	+	0.546809i	0.892179	−	0.451682i	$-0.149176\pi$
$227$	14.2695	+	8.23851i	0.947101	+	0.546809i	0.0549219	+	0.998491i	$0.482509\pi$
$228$	−0.708284	+	0.408928i	−0.0469073	+	0.0270819i
$229$	−3.35873	−	5.81749i	−0.221951	−	0.384431i	0.733449	−	0.679744i	$-0.237909\pi$
$229$	−3.35873	−	5.81749i	−0.221951	−	0.384431i	−0.955400	+	0.295313i	$0.904576\pi$
$230$	−2.61776	−	0.0654950i	−0.172610	−	0.00431861i
$231$	−42.3336			−2.78535
$232$	3.23088	−	1.86535i	0.212117	−	0.122466i
$233$	18.3546	−	10.5970i	1.20245	−	0.694235i	0.241351	−	0.970438i	$-0.422409\pi$
$233$	18.3546	−	10.5970i	1.20245	−	0.694235i	0.961099	+	0.276202i	$0.0890760\pi$
$234$	−8.99417	+	15.5784i	−0.587967	+	1.01839i
$235$	−6.20944	+	3.38083i	−0.405059	+	0.220541i
$236$	−4.97573			−0.323892
$237$		−	24.9858i		−	1.62300i
$238$	−18.9441	−	10.9374i	−1.22797	−	0.708966i
$239$	1.90547	−	3.30036i	0.123254	−	0.213483i	−0.797795	−	0.602929i	$-0.794000\pi$
$239$	1.90547	−	3.30036i	0.123254	−	0.213483i	0.921049	+	0.389446i	$0.127334\pi$
$240$	0.178113	−	7.11898i	0.0114972	−	0.459528i
$241$	3.48986	+	6.04462i	0.224802	+	0.389368i	0.956260	−	0.292518i	$-0.0944932\pi$
$241$	3.48986	+	6.04462i	0.224802	+	0.389368i	−0.731458	+	0.681886i	$0.761160\pi$
$242$			1.66758i			0.107196i
$243$	22.5021	−	12.9916i	1.44351	−	0.833413i
$244$	−5.56132	−	9.63249i	−0.356027	−	0.616657i
$245$	26.6767	+	0.667437i	1.70431	+	0.0426410i
$246$	−19.9698	+	34.5888i	−1.27323	+	2.20530i
$247$		−	0.646785i		−	0.0411540i
$248$	1.25661	+	0.725506i	0.0797951	+	0.0460697i
$249$	−23.0102	−	39.8549i	−1.45821	−	2.52570i
$250$	−0.838218	+	11.1489i	−0.0530136	+	0.705117i
$251$	5.79032	+	10.0291i	0.365482	+	0.633033i	0.988853	−	0.148893i	$-0.0475710\pi$
$251$	5.79032	+	10.0291i	0.365482	+	0.633033i	−0.623372	+	0.781926i	$0.714238\pi$
$252$	−26.9147	−	15.5392i	−1.69547	−	0.978878i
$253$	−3.09819	−	1.78874i	−0.194781	−	0.112457i
$254$	−9.56306			−0.600040
$255$	−17.1187	−	31.4413i	−1.07202	−	1.96893i
$256$	1.00000			0.0625000
$257$			16.9182i			1.05533i	0.849452	+	0.527665i	$0.176932\pi$
$257$			16.9182i			1.05533i	−0.849452	+	0.527665i	$0.823068\pi$
$258$	4.56180	+	20.3791i	0.284005	+	1.26875i
$259$	−16.2807			−1.01164
$260$	4.80521	+	2.93694i	0.298007	+	0.182141i
$261$	13.3229	−	23.0759i	0.824666	−	1.42836i
$262$			12.3045i			0.760172i
$263$	−9.18964	−	5.30564i	−0.566657	−	0.327160i	0.189156	−	0.981947i	$-0.439425\pi$
$263$	−9.18964	−	5.30564i	−0.566657	−	0.327160i	−0.755813	+	0.654787i	$0.772758\pi$
$264$	4.86447	−	8.42551i	0.299387	−	0.518554i
$265$	0.419193	−	16.7546i	0.0257508	−	1.02923i
$266$	1.11745			0.0685153
$267$	−20.3660	+	11.7583i	−1.24638	+	0.719597i
$268$	8.17813	+	4.72164i	0.499559	+	0.288420i
$269$	16.0530			0.978769			0.489384	−	0.872068i	$-0.337221\pi$
$269$	16.0530			0.978769			0.489384	+	0.872068i	$0.337221\pi$
$270$	−14.1056	−	25.9072i	−0.858438	−	1.57666i
$271$	−3.44554	−	5.96786i	−0.209302	−	0.362522i	0.742193	−	0.670186i	$-0.233786\pi$
$271$	−3.44554	−	5.96786i	−0.209302	−	0.362522i	−0.951495	+	0.307665i	$0.900452\pi$
$272$	4.35366	−	2.51359i	0.263979	−	0.152409i
$273$	30.2253	−	17.4506i	1.82932	−	1.05616i
$274$	14.7096			0.888640
$275$	−8.28920	+	12.8296i	−0.499858	+	0.773656i
$276$	−1.86474	−	3.22983i	−0.112244	−	0.194413i
$277$	7.07032	+	4.08205i	0.424814	+	0.245267i	0.697135	−	0.716940i	$-0.254458\pi$
$277$	7.07032	+	4.08205i	0.424814	+	0.245267i	−0.272321	+	0.962207i	$0.587791\pi$
$278$	11.1142	+	6.41680i	0.666587	+	0.384854i
$279$	10.3636			0.620452
$280$	−5.07415	+	8.30196i	−0.303238	+	0.496137i
$281$	−1.72022	+	2.97951i	−0.102620	+	0.177743i	−0.912763	−	0.408489i	$-0.866056\pi$
$281$	−1.72022	+	2.97951i	−0.102620	+	0.177743i	0.810143	+	0.586232i	$0.199389\pi$
$282$	−8.72055	−	5.03481i	−0.519301	−	0.299819i
$283$	−24.8416	+	14.3423i	−1.47668	+	0.852561i	−0.999653	−	0.0263277i	$-0.991619\pi$
$283$	−24.8416	+	14.3423i	−1.47668	+	0.852561i	−0.477026	+	0.878889i	$0.658285\pi$
$284$	7.80824	+	13.5243i	0.463334	+	0.802518i
$285$	1.56041	+	0.953718i	0.0924304	+	0.0564934i
$286$	3.84697	+	6.66315i	0.227476	+	0.394000i
$287$	47.2593	−	27.2851i	2.78963	−	1.61059i
$288$	6.18543	−	3.57116i	0.364480	−	0.210432i
$289$	4.13623	−	7.16416i	0.243308	−	0.421421i
$290$	−7.11787	−	4.35043i	−0.417976	−	0.255466i
$291$	29.8245	−	51.6576i	1.74835	−	3.02822i
$292$	2.16077	−	1.24752i	0.126449	−	0.0730056i
$293$			10.6880i			0.624398i	0.950017	+	0.312199i	$0.101066\pi$
$293$			10.6880i			0.624398i	−0.950017	+	0.312199i	$0.898934\pi$
$294$	19.0029	+	32.9141i	1.10827	+	1.91959i
$295$	5.32029	+	9.77158i	0.309759	+	0.568924i
$296$	1.87079	−	3.24030i	0.108737	−	0.188338i
$297$		−	40.3003i		−	2.33846i
$298$	−5.03061	−	2.90443i	−0.291416	−	0.168249i
$299$	2.94939			0.170568
$300$	−14.1711	+	7.26217i	−0.818166	+	0.419282i
$301$	8.52436	−	27.2304i	0.491336	−	1.56953i
$302$		−	13.4018i		−	0.771189i
$303$			46.7068i			2.68324i
$304$	−0.128404	+	0.222402i	−0.00736447	+	0.0127556i
$305$	−12.9703	+	21.2211i	−0.742678	+	1.21512i
$306$	17.9528	−	31.0952i	1.02629	−	1.77759i
$307$	−10.1274	−	5.84708i	−0.578003	−	0.333710i	0.182336	−	0.983236i	$-0.441634\pi$
$307$	−10.1274	−	5.84708i	−0.578003	−	0.333710i	−0.760339	+	0.649526i	$0.774967\pi$
$308$	−11.5119	+	6.64641i	−0.655952	+	0.378714i
$309$	−10.9723			−0.624193
$310$	0.0811520	−	3.24355i	0.00460912	−	0.184221i
$311$	6.51232	−	11.2797i	0.369280	−	0.639612i	−0.620173	−	0.784465i	$-0.712938\pi$
$311$	6.51232	−	11.2797i	0.369280	−	0.639612i	0.989453	+	0.144853i	$0.0462710\pi$
$312$			8.02085i			0.454091i
$313$	14.7455	+	8.51334i	0.833467	+	0.481202i	0.855038	−	0.518565i	$-0.173534\pi$
$313$	14.7455	+	8.51334i	0.833467	+	0.481202i	−0.0215714	+	0.999767i	$0.506867\pi$
$314$	2.85976	+	4.95324i	0.161385	+	0.279528i
$315$	−1.73815	+	69.4717i	−0.0979336	+	3.91429i
$316$	−3.92279	−	6.79447i	−0.220674	−	0.382219i
$317$		−	1.19709i		−	0.0672351i	−0.999435	−	0.0336175i	$-0.989297\pi$
$317$		−	1.19709i		−	0.0672351i	0.999435	−	0.0336175i	$-0.0107028\pi$
$318$	20.6721	−	11.9351i	1.15923	−	0.669285i
$319$	−5.69845	−	9.87000i	−0.319052	−	0.552614i
$320$	−1.06925	−	1.96385i	−0.0597729	−	0.109783i
$321$	7.78914	−	13.4912i	0.434747	−	0.753004i
$322$			5.09566i			0.283970i
$323$			1.29102i			0.0718341i
$324$	10.2929	−	17.8278i	0.571825	−	0.990431i
$325$	0.629737	−	12.5770i	0.0349315	−	0.697648i
$326$	3.00144	+	5.19865i	0.166234	+	0.287926i
$327$	17.5408	−	10.1272i	0.970009	−	0.560035i
$328$			12.5411i			0.692467i
$329$	6.87915	+	11.9150i	0.379260	+	0.656897i
$330$	−21.7478	−	0.544119i	−1.19718	−	0.0299527i
$331$	2.83926	+	4.91774i	0.156060	+	0.270303i	0.933444	−	0.358722i	$-0.116787\pi$
$331$	2.83926	+	4.91774i	0.156060	+	0.270303i	−0.777385	+	0.629025i	$0.783454\pi$
$332$	−12.5145	−	7.22524i	−0.686822	−	0.396537i
$333$		−	26.7235i		−	1.46444i
$334$	−8.13964	+	14.0983i	−0.445381	+	0.771423i
$335$	0.528143	−	21.1092i	0.0288555	−	1.15332i
$336$	−13.8576			−0.755995
$337$	−3.50713	+	2.02484i	−0.191046	+	0.110300i	−0.592472	−	0.805591i	$-0.701848\pi$
$337$	−3.50713	+	2.02484i	−0.191046	+	0.110300i	0.401426	+	0.915891i	$0.368515\pi$
$338$	5.76502	+	3.32843i	0.313576	+	0.181043i
$339$	−16.4392	+	28.4734i	−0.892852	+	1.54647i
$340$	−9.59145	−	5.86228i	−0.520170	−	0.317927i
$341$	2.21635	−	3.83883i	0.120022	−	0.207884i
$342$			1.83420i			0.0991823i
$343$		−	21.4689i		−	1.15921i
$344$	4.44004	+	4.82556i	0.239391	+	0.260177i
$345$	−4.34902	+	7.11556i	−0.234143	+	0.383089i
$346$	23.6499			1.27143
$347$	−14.2794	−	8.24420i	−0.766557	−	0.442572i	0.0650883	−	0.997880i	$-0.479267\pi$
$347$	−14.2794	−	8.24420i	−0.766557	−	0.442572i	−0.831645	+	0.555308i	$0.812600\pi$
$348$		−	11.8811i		−	0.636896i
$349$	0.694131	−	1.20227i	0.0371560	−	0.0643561i	−0.846849	−	0.531833i	$-0.821503\pi$
$349$	0.694131	−	1.20227i	0.0371560	−	0.0643561i	0.884005	+	0.467477i	$0.154837\pi$
$350$	21.7293	+	1.08800i	1.16148	+	0.0581558i
$351$	16.6124	+	28.7736i	0.886707	+	1.53582i
$352$		−	3.05490i		−	0.162827i
$353$	−27.3087	+	15.7667i	−1.45349	+	0.839175i	−0.998678	−	0.0514101i	$-0.983628\pi$
$353$	−27.3087	+	15.7667i	−1.45349	+	0.839175i	−0.454816	+	0.890585i	$0.650295\pi$
$354$	−7.92310	+	13.7232i	−0.421108	+	0.729381i
$355$	18.2107	−	29.7950i	0.966523	−	1.58136i
$356$	−3.69213	+	6.39495i	−0.195682	+	0.338932i
$357$	−60.3313	+	34.8323i	−3.19307	+	1.84352i
$358$	−2.72772	+	1.57485i	−0.144165	+	0.0832335i
$359$	9.26592	+	16.0491i	0.489037	+	0.847037i	0.999920	−	0.0126133i	$-0.00401505\pi$
$359$	9.26592	+	16.0491i	0.489037	+	0.847037i	−0.510884	+	0.859650i	$0.670682\pi$
$360$	−13.6270	−	8.32879i	−0.718205	−	0.438966i
$361$	9.46702	+	16.3974i	0.498264	+	0.863019i
$362$	3.80346	−	2.19593i	0.199906	−	0.115416i
$363$	4.59925	+	2.65538i	0.241398	+	0.139371i
$364$	5.47951	−	9.49080i	0.287205	−	0.497453i
$365$	−4.76034	−	2.90951i	−0.249168	−	0.152291i
$366$	−35.4223			−1.85155
$367$	−14.5905	−	8.42385i	−0.761620	−	0.439721i	0.0682573	−	0.997668i	$-0.478256\pi$
$367$	−14.5905	−	8.42385i	−0.761620	−	0.439721i	−0.829877	+	0.557946i	$0.811589\pi$
$368$	−1.01417	−	0.585531i	−0.0528673	−	0.0305229i
$369$	44.7863	+	77.5722i	2.33148	+	4.03824i
$370$	−8.36379	−	0.209258i	−0.434813	−	0.0108788i
$371$	−32.6141			−1.69324
$372$	4.00194	−	2.31052i	0.207491	−	0.119795i
$373$	−23.6436	+	13.6506i	−1.22422	+	0.706803i	−0.965815	−	0.259234i	$-0.916530\pi$
$373$	−23.6436	+	13.6506i	−1.22422	+	0.706803i	−0.258404	+	0.966037i	$0.583197\pi$
$374$	−7.67876	−	13.3000i	−0.397059	−	0.687726i
$375$	29.4142	+	20.0647i	1.51894	+	1.03614i
$376$	−3.16187			−0.163061
$377$	8.13715	+	4.69798i	0.419084	+	0.241958i
$378$	−49.7121	+	28.7013i	−2.55692	+	1.47624i
$379$	−23.3161			−1.19767			−0.598833	−	0.800874i	$-0.704369\pi$
$379$	−23.3161			−1.19767			−0.598833	+	0.800874i	$0.704369\pi$
$380$	0.574060	+	0.0143627i	0.0294487	+	0.000736792i
$381$	−15.2277	+	26.3752i	−0.780141	+	1.35124i
$382$	−1.33895	−	0.773041i	−0.0685064	−	0.0395522i
$383$		−	16.4633i		−	0.841235i	−0.907238	−	0.420617i	$-0.861814\pi$
$383$		−	16.4633i		−	0.841235i	0.907238	−	0.420617i	$-0.138186\pi$
$384$	1.59235	−	2.75803i	0.0812593	−	0.140745i
$385$	25.3617	+	15.5010i	1.29255	+	0.790005i
$386$	9.54512			0.485834
$387$	44.6964	+	13.9920i	2.27205	+	0.711255i
$388$		−	18.7299i		−	0.950866i
$389$	−5.92084			−0.300199			−0.150099	−	0.988671i	$-0.547959\pi$
$389$	−5.92084			−0.300199			−0.150099	+	0.988671i	$0.547959\pi$
$390$	15.7517	−	8.57629i	0.797621	−	0.434277i
$391$	−5.88713			−0.297725
$392$	10.3351	+	5.96695i	0.521999	+	0.301377i
$393$	33.9361	+	19.5930i	1.71185	+	0.988336i
$394$	−10.0238	−	17.3617i	−0.504991	−	0.874669i
$395$	−9.14888	+	14.9688i	−0.460330	+	0.753160i
$396$	−10.9095	−	18.8959i	−0.548224	−	0.949553i
$397$	−7.72397	−	4.45944i	−0.387655	−	0.223813i	0.293488	−	0.955963i	$-0.405184\pi$
$397$	−7.72397	−	4.45944i	−0.387655	−	0.223813i	−0.681144	+	0.732150i	$0.738517\pi$
$398$			14.5458i			0.729114i
$399$	1.77937	−	3.08196i	0.0890801	−	0.154291i
$400$	−2.71341	+	4.19969i	−0.135671	+	0.209984i
$401$	−9.15605	−	15.8587i	−0.457231	−	0.791948i	0.541582	−	0.840648i	$-0.317825\pi$
$401$	−9.15605	−	15.8587i	−0.457231	−	0.791948i	−0.998813	+	0.0487001i	$0.984492\pi$
$402$	26.0449	−	15.0370i	1.29900	−	0.749978i
$403$			3.65446i			0.182042i
$404$	7.33300	+	12.7011i	0.364830	+	0.631904i
$405$	−46.0167	−	1.15131i	−2.28659	−	0.0572093i
$406$	−8.11670	+	14.0585i	−0.402825	+	0.697714i
$407$	−9.89878	−	5.71507i	−0.490665	−	0.283285i
$408$		−	16.0100i		−	0.792615i
$409$	−19.2010			−0.949428			−0.474714	−	0.880140i	$-0.657449\pi$
$409$	−19.2010			−0.949428			−0.474714	+	0.880140i	$0.657449\pi$
$410$	24.6289	−	13.4096i	1.21633	−	0.662252i
$411$	23.4228	−	40.5696i	1.15536	−	2.00115i
$412$	−2.98373	+	1.72266i	−0.146998	+	0.0848694i
$413$	18.7503	−	10.8255i	0.922640	−	0.532686i
$414$	−8.36410			−0.411073
$415$	−0.808184	+	32.3021i	−0.0396722	+	1.58565i
$416$	1.25928	+	2.18113i	0.0617412	+	0.106939i
$417$	35.3955	−	20.4356i	1.73332	−	1.00074i
$418$	0.679416	+	0.392261i	0.0332313	+	0.0191861i
$419$	14.4024			0.703605			0.351802	−	0.936074i	$-0.385569\pi$
$419$	14.4024			0.703605			0.351802	+	0.936074i	$0.385569\pi$
$420$	14.8172	+	27.2143i	0.723008	+	1.32792i
$421$	10.8826	+	18.8492i	0.530384	+	0.918651i	0.999372	+	0.0354468i	$0.0112854\pi$
$421$	10.8826	+	18.8492i	0.530384	+	0.918651i	−0.468988	+	0.883205i	$0.655381\pi$
$422$			7.08060i			0.344678i
$423$	−19.5575	+	11.2915i	−0.950920	+	0.549014i
$424$	3.74762	−	6.49107i	0.182001	−	0.315234i
$425$	−1.25699	+	25.1044i	−0.0609728	+	1.21774i
$426$	49.7338			2.40961
$427$	41.9139	+	24.1990i	2.02836	+	1.17107i
$428$		−	4.89160i		−	0.236444i
$429$	24.5029			1.18301
$430$	4.72916	−	13.8793i	0.228060	−	0.669319i
$431$	−27.8665			−1.34228			−0.671141	−	0.741330i	$-0.734195\pi$
$431$	−27.8665			−1.34228			−0.671141	+	0.741330i	$0.734195\pi$
$432$		−	13.1920i		−	0.634702i
$433$	−12.8512	−	7.41963i	−0.617589	−	0.356565i	0.158341	−	0.987384i	$-0.449385\pi$
$433$	−12.8512	−	7.41963i	−0.617589	−	0.356565i	−0.775930	+	0.630820i	$0.782719\pi$
$434$	−6.31381			−0.303072
$435$	−23.3328	+	12.7039i	−1.11872	+	0.609105i
$436$	3.17995	−	5.50784i	0.152292	−	0.263777i
$437$	0.260447	−	0.150369i	0.0124589	−	0.00719313i
$438$		−	7.94595i		−	0.379672i
$439$	5.45277	+	9.44447i	0.260247	+	0.450760i	0.966307	−	0.257391i	$-0.0828628\pi$
$439$	5.45277	+	9.44447i	0.260247	+	0.450760i	−0.706061	+	0.708151i	$0.749530\pi$
$440$	−5.99937	+	3.26645i	−0.286009	+	0.155722i
$441$	85.2357			4.05884
$442$	10.9649	+	6.33061i	0.521549	+	0.301117i
$443$	−21.1144	+	12.1904i	−1.00318	+	0.579185i	−0.909187	−	0.416388i	$-0.863296\pi$
$443$	−21.1144	+	12.1904i	−1.00318	+	0.579185i	−0.0939905	+	0.995573i	$0.529962\pi$
$444$	−5.95789	−	10.3194i	−0.282749	−	0.489736i
$445$	16.5065	+	0.412985i	0.782484	+	0.0195774i
$446$	−8.56936			−0.405771
$447$	−16.0210	+	9.24972i	−0.757767	+	0.437497i
$448$	−3.76835	+	2.17566i	−0.178038	+	0.102790i
$449$	−8.73429	+	15.1282i	−0.412197	+	0.713946i	−0.995130	−	0.0985745i	$-0.968572\pi$
$449$	−8.73429	+	15.1282i	−0.412197	+	0.713946i	0.582933	+	0.812520i	$0.301905\pi$
$450$	−1.78585	+	35.6669i	−0.0841860	+	1.68135i
$451$	38.3119			1.80404
$452$			10.3238i			0.485592i
$453$	−36.9627	−	21.3404i	−1.73666	−	1.00266i
$454$	8.23851	−	14.2695i	0.386652	−	0.669702i
$455$	−24.4975	−	0.612915i	−1.14846	−	0.0287339i
$456$	0.408928	+	0.708284i	0.0191498	+	0.0331684i
$457$			4.76744i			0.223012i	0.993764	+	0.111506i	$0.0355674\pi$
$457$			4.76744i			0.223012i	−0.993764	+	0.111506i	$0.964433\pi$
$458$	−5.81749	+	3.35873i	−0.271834	+	0.156943i
$459$	−33.1593	−	57.4336i	−1.54774	−	2.68077i
$460$	−0.0654950	+	2.61776i	−0.00305372	+	0.122054i
$461$	5.80738	−	10.0587i	0.270476	−	0.468479i	−0.698507	−	0.715603i	$-0.746152\pi$
$461$	5.80738	−	10.0587i	0.270476	−	0.468479i	0.968984	+	0.247124i	$0.0794854\pi$
$462$			42.3336i			1.96954i
$463$	3.95596	+	2.28398i	0.183849	+	0.106145i	0.589100	−	0.808060i	$-0.299482\pi$
$463$	3.95596	+	2.28398i	0.183849	+	0.106145i	−0.405251	+	0.914206i	$0.632816\pi$
$464$	−1.86535	−	3.23088i	−0.0865966	−	0.149990i
$465$	−8.81658	−	5.38868i	−0.408859	−	0.249894i
$466$	−10.5970	−	18.3546i	−0.490899	−	0.850261i
$467$	−6.38134	−	3.68427i	−0.295293	−	0.170488i	0.345033	−	0.938590i	$-0.387868\pi$
$467$	−6.38134	−	3.68427i	−0.295293	−	0.170488i	−0.640327	+	0.768103i	$0.721201\pi$
$468$	15.5784	+	8.99417i	0.720110	+	0.415755i
$469$	−41.0907			−1.89739
$470$	3.38083	+	6.20944i	0.155946	+	0.286420i
$471$	18.2149			0.839300
$472$			4.97573i			0.229026i
$473$	14.7416	−	13.5639i	0.677819	−	0.623668i
$474$	−24.9858			−1.14764
$475$	−0.585607	−	1.14273i	−0.0268695	−	0.0524318i
$476$	−10.9374	+	18.9441i	−0.501315	+	0.868302i
$477$		−	53.5334i		−	2.45113i
$478$	−3.30036	−	1.90547i	−0.150955	−	0.0871539i
$479$	−19.1486	+	33.1663i	−0.874921	+	1.51541i	−0.0180740	+	0.999837i	$0.505753\pi$
$479$	−19.1486	+	33.1663i	−0.874921	+	1.51541i	−0.856847	+	0.515571i	$0.827580\pi$
$480$	−7.11898	−	0.178113i	−0.324935	−	0.00812973i
$481$	9.42337			0.429669
$482$	6.04462	−	3.48986i	0.275325	−	0.158959i
$483$	14.0540	+	8.11407i	0.639478	+	0.369203i
$484$	1.66758			0.0757993
$485$	−36.7827	+	20.0269i	−1.67022	+	0.909375i
$486$	−12.9916	−	22.5021i	−0.589312	−	1.02072i
$487$	1.74966	−	1.01017i	0.0792848	−	0.0457751i	−0.459834	−	0.888005i	$-0.652091\pi$
$487$	1.74966	−	1.01017i	0.0792848	−	0.0457751i	0.539118	+	0.842230i	$0.318758\pi$
$488$	−9.63249	+	5.56132i	−0.436042	+	0.251749i
$489$	19.1174			0.864517
$490$	0.667437	−	26.6767i	0.0301517	−	1.20513i
$491$	−0.726063	−	1.25758i	−0.0327668	−	0.0567537i	0.849177	−	0.528108i	$-0.177099\pi$
$491$	−0.726063	−	1.25758i	−0.0327668	−	0.0567537i	−0.881944	+	0.471355i	$0.843765\pi$
$492$	34.5888	+	19.9698i	1.55938	+	0.900310i
$493$	−16.2422	−	9.37742i	−0.731510	−	0.422338i
$494$	−0.646785			−0.0291003
$495$	−25.4436	+	41.6291i	−1.14361	+	1.87109i
$496$	0.725506	−	1.25661i	0.0325762	−	0.0564236i
$497$	−58.8483	−	33.9761i	−2.63971	−	1.52404i
$498$	−39.8549	+	23.0102i	−1.78594	+	1.03111i
$499$	−15.5503	−	26.9339i	−0.696128	−	1.20573i	−0.969799	−	0.243905i	$-0.921571\pi$
$499$	−15.5503	−	26.9339i	−0.696128	−	1.20573i	0.273671	−	0.961823i	$-0.411762\pi$
$500$	11.1489	+	0.838218i	0.498593	+	0.0374862i
$501$	25.9223	+	44.8988i	1.15812	+	2.00593i
$502$	10.0291	−	5.79032i	0.447622	−	0.258435i
$503$	10.8277	−	6.25139i	0.482784	−	0.278736i	−0.238792	−	0.971071i	$-0.576751\pi$
$503$	10.8277	−	6.25139i	0.482784	−	0.278736i	0.721576	+	0.692335i	$0.243418\pi$
$504$	−15.5392	+	26.9147i	−0.692172	+	1.19888i
$505$	17.1023	−	27.9816i	0.761042	−	1.24516i
$506$	−1.78874	+	3.09819i	−0.0795192	+	0.137731i
$507$	18.3598	−	10.6001i	0.815389	−	0.470765i
$508$			9.56306i			0.424292i
$509$	−5.15851	−	8.93480i	−0.228647	−	0.396028i	0.728760	−	0.684769i	$-0.240097\pi$
$509$	−5.15851	−	8.93480i	−0.228647	−	0.396028i	−0.957407	+	0.288741i	$0.906763\pi$
$510$	−31.4413	+	17.1187i	−1.39224	+	0.758030i
$511$	−5.42834	+	9.40217i	−0.240136	+	0.415927i
$512$		−	1.00000i		−	0.0441942i
$513$	2.93394	+	1.69391i	0.129536	+	0.0747879i
$514$	16.9182			0.746231
$515$	6.57340	+	4.01765i	0.289659	+	0.177039i
$516$	20.3791	−	4.56180i	0.897142	−	0.200822i
$517$			9.65921i			0.424811i
$518$			16.2807i			0.715335i
$519$	37.6589	−	65.2272i	1.65304	−	2.86316i
$520$	2.93694	−	4.80521i	0.128793	−	0.210722i
$521$	7.76860	−	13.4556i	0.340349	−	0.589501i	−0.644149	−	0.764900i	$-0.722788\pi$
$521$	7.76860	−	13.4556i	0.340349	−	0.589501i	0.984497	+	0.175399i	$0.0561216\pi$
$522$	−23.0759	−	13.3229i	−1.01001	−	0.583127i
$523$	10.0848	−	5.82247i	0.440978	−	0.254599i	−0.263034	−	0.964786i	$-0.584723\pi$
$523$	10.0848	−	5.82247i	0.440978	−	0.254599i	0.704012	+	0.710188i	$0.251390\pi$
$524$	12.3045			0.537523
$525$	37.6014	−	58.1977i	1.64106	−	2.53996i
$526$	−5.30564	+	9.18964i	−0.231337	+	0.400687i
$527$		−	7.29449i		−	0.317753i
$528$	−8.42551	−	4.86447i	−0.366673	−	0.211699i
$529$	−10.8143	−	18.7309i	−0.470187	−	0.814388i
$530$	−16.7546	−	0.419193i	−0.727775	−	0.0182086i
$531$	17.7691	+	30.7770i	0.771114	+	1.33561i
$532$		−	1.11745i		−	0.0484476i
$533$	−27.3539	+	15.7928i	−1.18483	+	0.684061i
$534$	11.7583	+	20.3660i	0.508832	+	0.881323i
$535$	−9.60637	+	5.23034i	−0.415319	+	0.226127i
$536$	4.72164	−	8.17813i	0.203944	−	0.353241i
$537$			10.0309i			0.432864i
$538$		−	16.0530i		−	0.692094i
$539$	18.2284	−	31.5726i	0.785154	−	1.35993i
$540$	−25.9072	+	14.1056i	−1.11487	+	0.607007i
$541$	−11.9801	−	20.7501i	−0.515065	−	0.892118i	−0.999847	−	0.0174836i	$-0.994435\pi$
$541$	−11.9801	−	20.7501i	−0.515065	−	0.892118i	0.484782	−	0.874635i	$-0.338899\pi$
$542$	−5.96786	+	3.44554i	−0.256341	+	0.147999i
$543$		−	13.9868i		−	0.600230i
$544$	−2.51359	−	4.35366i	−0.107769	−	0.186662i
$545$	−14.2167	−	0.355696i	−0.608977	−	0.0152363i
$546$	−17.4506	−	30.2253i	−0.746817	−	1.29352i
$547$	−2.75480	−	1.59049i	−0.117787	−	0.0680043i	0.439949	−	0.898023i	$-0.354996\pi$
$547$	−2.75480	−	1.59049i	−0.117787	−	0.0680043i	−0.557736	+	0.830018i	$0.688330\pi$
$548$		−	14.7096i		−	0.628363i
$549$	−39.7207	+	68.7982i	−1.69524	+	2.93624i
$550$	12.8296	+	8.28920i	0.547057	+	0.353453i
$551$	0.958072			0.0408152
$552$	−3.22983	+	1.86474i	−0.137471	+	0.0793687i
$553$	29.5649	+	17.0693i	1.25723	+	0.725860i
$554$	4.08205	−	7.07032i	0.173430	−	0.300389i
$555$	−13.8952	+	22.7344i	−0.589820	+	0.965021i
$556$	6.41680	−	11.1142i	0.272133	−	0.471348i
$557$			30.7790i			1.30415i	0.758155	+	0.652074i	$0.226101\pi$
$557$			30.7790i			1.30415i	−0.758155	+	0.652074i	$0.773899\pi$
$558$		−	10.3636i		−	0.438726i
$559$	−4.93394	+	15.7611i	−0.208683	+	0.666622i
$560$	8.30196	+	5.07415i	0.350822	+	0.214422i
$561$	−48.9091			−2.06494
$562$	2.97951	+	1.72022i	0.125683	+	0.0725632i
$563$			22.0945i			0.931174i	0.885002	+	0.465587i	$0.154157\pi$
$563$			22.0945i			0.931174i	−0.885002	+	0.465587i	$0.845843\pi$
$564$	−5.03481	+	8.72055i	−0.212004	+	0.367201i
$565$	20.2745	−	11.0387i	0.852953	−	0.464404i
$566$	14.3423	+	24.8416i	0.602852	+	1.04417i
$567$			89.5748i			3.76179i
$568$	13.5243	−	7.80824i	0.567466	−	0.327627i
$569$	0.965849	−	1.67290i	0.0404905	−	0.0701316i	−0.845070	−	0.534656i	$-0.820441\pi$
$569$	0.965849	−	1.67290i	0.0404905	−	0.0701316i	0.885560	+	0.464524i	$0.153775\pi$
$570$	0.953718	−	1.56041i	0.0399468	−	0.0653582i
$571$	14.8973	−	25.8029i	0.623433	−	1.07982i	−0.365409	−	0.930847i	$-0.619071\pi$
$571$	14.8973	−	25.8029i	0.623433	−	1.07982i	0.988842	−	0.148970i	$-0.0475957\pi$
$572$	6.66315	−	3.84697i	0.278600	−	0.160850i
$573$	−4.26414	+	2.46190i	−0.178137	+	0.102847i
$574$	−27.2851	−	47.2593i	−1.13886	−	1.97256i
$575$	5.21091	−	2.67041i	0.217310	−	0.111364i
$576$	−3.57116	−	6.18543i	−0.148798	−	0.257726i
$577$	−26.9249	+	15.5451i	−1.12090	+	0.647150i	−0.941630	−	0.336651i	$-0.890706\pi$
$577$	−26.9249	+	15.5451i	−1.12090	+	0.647150i	−0.179267	+	0.983800i	$0.557373\pi$
$578$	−7.16416	−	4.13623i	−0.297990	−	0.172045i
$579$	15.1992	−	26.3257i	0.631656	−	1.09406i
$580$	−4.35043	+	7.11787i	−0.180642	+	0.295554i
$581$	62.8785			2.60864
$582$	−51.6576	−	29.8245i	−2.14128	−	1.23627i
$583$	−19.8296	−	11.4486i	−0.821257	−	0.474153i
$584$	−1.24752	−	2.16077i	−0.0516227	−	0.0894132i
$585$	1.00605	−	40.2105i	0.0415950	−	1.66250i
$586$	10.6880			0.441516
$587$	35.6867	−	20.6037i	1.47295	−	0.850407i	0.473411	−	0.880842i	$-0.343023\pi$
$587$	35.6867	−	20.6037i	1.47295	−	0.850407i	0.999537	+	0.0304352i	$0.00968931\pi$
$588$	32.9141	−	19.0029i	1.35735	−	0.783668i
$589$	0.186316	+	0.322708i	0.00767701	+	0.0132970i
$590$	9.77158	−	5.32029i	0.402290	−	0.219033i
$591$	−63.8455			−2.62625
$592$	−3.24030	−	1.87079i	−0.133175	−	0.0768888i
$593$	16.3986	−	9.46776i	0.673411	−	0.388794i	−0.123957	−	0.992288i	$-0.539558\pi$
$593$	16.3986	−	9.46776i	0.673411	−	0.388794i	0.797368	+	0.603493i	$0.206225\pi$
$594$	−40.3003			−1.65354
$595$	48.8982	+	1.22341i	2.00463	+	0.0501549i
$596$	−2.90443	+	5.03061i	−0.118970	+	0.206062i
$597$	40.1177	+	23.1620i	1.64191	+	0.947956i
$598$		−	2.94939i		−	0.120609i
$599$	−7.77696	+	13.4701i	−0.317758	+	0.550373i	−0.980020	−	0.198899i	$-0.936263\pi$
$599$	−7.77696	+	13.4701i	−0.317758	+	0.550373i	0.662262	+	0.749273i	$0.269597\pi$
$600$	7.26217	+	14.1711i	0.296477	+	0.578531i
$601$	−0.634564			−0.0258844			−0.0129422	−	0.999916i	$-0.504120\pi$
$601$	−0.634564			−0.0258844			−0.0129422	+	0.999916i	$0.504120\pi$
$602$	−27.2304	−	8.52436i	−1.10983	−	0.347427i
$603$		−	67.4469i		−	2.74665i
$604$	−13.4018			−0.545313
$605$	−1.78306	−	3.27489i	−0.0724918	−	0.133143i
$606$	46.7068			1.89733
$607$	22.7010	+	13.1065i	0.921407	+	0.531974i	0.884084	−	0.467329i	$-0.154784\pi$
$607$	22.7010	+	13.1065i	0.921407	+	0.531974i	0.0373232	+	0.999303i	$0.488117\pi$
$608$	0.222402	+	0.128404i	0.00901960	+	0.00520747i
$609$	25.8493	+	44.7722i	1.04747	+	1.81426i
$610$	21.2211	+	12.9703i	0.859218	+	0.525153i
$611$	−3.98168	−	6.89647i	−0.161082	−	0.279001i
$612$	−31.0952	−	17.9528i	−1.25695	−	0.725700i
$613$		−	32.7540i		−	1.32292i	−0.749980	−	0.661460i	$-0.769937\pi$
$613$		−	32.7540i		−	1.32292i	0.749980	−	0.661460i	$-0.230063\pi$
$614$	−5.84708	+	10.1274i	−0.235969	+	0.408710i
$615$	2.23374	−	89.2799i	0.0900731	−	3.60011i
$616$	6.64641	+	11.5119i	0.267791	+	0.463828i
$617$	−26.6599	+	15.3921i	−1.07329	+	0.619663i	−0.929078	−	0.369884i	$-0.879398\pi$
$617$	−26.6599	+	15.3921i	−1.07329	+	0.619663i	−0.144211	+	0.989547i	$0.546064\pi$
$618$			10.9723i			0.441371i
$619$	6.03425	+	10.4516i	0.242537	+	0.420086i	0.961436	−	0.275028i	$-0.0886871\pi$
$619$	6.03425	+	10.4516i	0.242537	+	0.420086i	−0.718899	+	0.695114i	$0.755354\pi$
$620$	−3.24355	−	0.0811520i	−0.130264	−	0.00325914i
$621$	−7.72435	+	13.3790i	−0.309967	+	0.536879i
$622$	−11.2797	−	6.51232i	−0.452274	−	0.261120i
$623$		−	32.1312i		−	1.28731i
$624$	8.02085			0.321091
$625$	−10.2748	−	22.7910i	−0.410992	−	0.911639i
$626$	8.51334	−	14.7455i	0.340261	−	0.589350i
$627$	2.16374	−	1.24923i	0.0864114	−	0.0498896i
$628$	4.95324	−	2.85976i	0.197656	−	0.114117i
$629$	−18.8095			−0.749985
$630$	69.4717	+	1.73815i	2.76782	+	0.0692495i
$631$	−4.76224	−	8.24845i	−0.189582	−	0.328365i	0.755529	−	0.655115i	$-0.227380\pi$
$631$	−4.76224	−	8.24845i	−0.189582	−	0.328365i	−0.945111	+	0.326750i	$0.894047\pi$
$632$	−6.79447	+	3.92279i	−0.270270	+	0.156040i
$633$	19.5285	+	11.2748i	0.776189	+	0.448133i
$634$	−1.19709			−0.0475424
$635$	18.7804	−	10.2253i	0.745278	−	0.405779i
$636$	−11.9351	−	20.6721i	−0.473256	−	0.819703i
$637$			30.0562i			1.19087i
$638$	−9.87000	+	5.69845i	−0.390757	+	0.225604i
$639$	55.7689	−	96.5946i	2.20619	−	3.82122i
$640$	−1.96385	+	1.06925i	−0.0776280	+	0.0422658i
$641$	−5.51783			−0.217941			−0.108971	−	0.994045i	$-0.534755\pi$
$641$	−5.51783			−0.217941			−0.108971	+	0.994045i	$0.534755\pi$
$642$	−13.4912	−	7.78914i	−0.532455	−	0.307413i
$643$		−	25.8641i		−	1.01998i	−0.860180	−	0.509991i	$-0.829649\pi$
$643$		−	25.8641i		−	1.01998i	0.860180	−	0.509991i	$-0.170351\pi$
$644$	5.09566			0.200797
$645$	−30.7491	−	35.1439i	−1.21074	−	1.38379i
$646$	1.29102			0.0507944
$647$		−	36.8105i		−	1.44717i	−0.690234	−	0.723586i	$-0.742493\pi$
$647$		−	36.8105i		−	1.44717i	0.690234	−	0.723586i	$-0.257507\pi$
$648$	−17.8278	−	10.2929i	−0.700340	−	0.404342i
$649$	15.2004			0.596666
$650$	−12.5770	−	0.629737i	−0.493312	−	0.0247003i
$651$	−10.0538	+	17.4137i	−0.394039	+	0.682496i
$652$	5.19865	−	3.00144i	0.203595	−	0.117545i
$653$		−	13.5415i		−	0.529921i	−0.964259	−	0.264960i	$-0.914641\pi$
$653$		−	13.5415i		−	0.529921i	0.964259	−	0.264960i	$-0.0853589\pi$
$654$	−10.1272	−	17.5408i	−0.396004	−	0.685900i
$655$	−13.1565	−	24.1641i	−0.514068	−	0.944170i
$656$	12.5411			0.489648
$657$	−15.4329	−	8.91018i	−0.602094	−	0.347619i
$658$	11.9150	−	6.87915i	0.464496	−	0.268177i
$659$	15.8022	+	27.3702i	0.615566	+	1.06619i	0.990285	+	0.139053i	$0.0444058\pi$
$659$	15.8022	+	27.3702i	0.615566	+	1.06619i	−0.374719	+	0.927138i	$0.622261\pi$
$660$	−0.544119	+	21.7478i	−0.0211798	+	0.846531i
$661$	−29.4556			−1.14569			−0.572846	−	0.819663i	$-0.694161\pi$
$661$	−29.4556			−1.14569			−0.572846	+	0.819663i	$0.694161\pi$
$662$	4.91774	−	2.83926i	0.191133	−	0.110351i
$663$	34.9201	−	20.1611i	1.35618	−	0.782992i
$664$	−7.22524	+	12.5145i	−0.280394	+	0.485656i
$665$	−2.19451	+	1.19483i	−0.0850993	+	0.0463337i
$666$	−26.7235			−1.03551
$667$			4.36888i			0.169164i
$668$	14.0983	+	8.13964i	0.545478	+	0.314932i
$669$	−13.6454	+	23.6346i	−0.527562	+	0.913765i
$670$	−21.1092	−	0.528143i	−0.815521	−	0.0204039i
$671$	16.9893	+	29.4263i	0.655864	+	1.13599i
$672$			13.8576i			0.534569i
$673$	−18.0348	+	10.4124i	−0.695189	+	0.401367i	−0.805553	−	0.592524i	$-0.798132\pi$
$673$	−18.0348	+	10.4124i	−0.695189	+	0.401367i	0.110364	+	0.993891i	$0.464798\pi$
$674$	2.02484	+	3.50713i	0.0779941	+	0.135090i
$675$	55.4024	+	35.7954i	2.13244	+	1.37777i
$676$	3.32843	−	5.76502i	0.128017	−	0.221731i
$677$		−	8.89277i		−	0.341777i	−0.985290	−	0.170889i	$-0.945336\pi$
$677$		−	8.89277i		−	0.341777i	0.985290	−	0.170889i	$-0.0546638\pi$
$678$	28.4734	+	16.4392i	1.09352	+	0.631342i
$679$	40.7498	+	70.5807i	1.56383	+	2.70864i
$680$	−5.86228	+	9.59145i	−0.224808	+	0.367815i
$681$	−26.2372	−	45.4441i	−1.00541	−	1.74142i
$682$	−3.83883	−	2.21635i	−0.146996	−	0.0848684i
$683$	−21.2864	−	12.2897i	−0.814503	−	0.470254i	0.0340140	−	0.999421i	$-0.489171\pi$
$683$	−21.2864	−	12.2897i	−0.814503	−	0.470254i	−0.848517	+	0.529168i	$0.822504\pi$
$684$	1.83420			0.0701325
$685$	−28.8875	+	15.7282i	−1.10373	+	0.600945i
$686$	−21.4689			−0.819688
$687$			21.3931i			0.816198i
$688$	4.82556	−	4.44004i	0.183973	−	0.169275i
$689$	18.8772			0.719164
$690$	7.11556	+	4.34902i	0.270885	+	0.165564i
$691$	9.95102	−	17.2357i	0.378555	−	0.655676i	−0.612298	−	0.790627i	$-0.709755\pi$
$691$	9.95102	−	17.2357i	0.378555	−	0.655676i	0.990852	+	0.134952i	$0.0430879\pi$
$692$		−	23.6499i		−	0.899035i
$693$	82.2217	+	47.4707i	3.12335	+	1.80326i
$694$	−8.24420	+	14.2794i	−0.312945	+	0.542037i
$695$	−28.6878	−	0.717756i	−1.08819	−	0.0272260i
$696$	−11.8811			−0.450353
$697$	54.5997	−	31.5232i	2.06811	−	1.19403i
$698$	−1.20227	−	0.694131i	−0.0455066	−	0.0262733i
$699$	−67.4968			−2.55296
$700$	1.08800	−	21.7293i	0.0411224	−	0.821292i
$701$	−1.42965	−	2.47623i	−0.0539973	−	0.0935260i	0.837763	−	0.546034i	$-0.183863\pi$
$701$	−1.42965	−	2.47623i	−0.0539973	−	0.0935260i	−0.891761	+	0.452508i	$0.850530\pi$
$702$	28.7736	−	16.6124i	1.08599	−	0.626996i
$703$	0.832134	−	0.480433i	0.0313845	−	0.0181199i
$704$	−3.05490			−0.115136
$705$	22.5093	+	0.563172i	0.847750	+	0.0212103i
$706$	15.7667	+	27.3087i	0.593386	+	1.02778i
$707$	−55.2665	−	31.9081i	−2.07851	−	1.20003i
$708$	13.7232	+	7.92310i	0.515750	+	0.297768i
$709$	15.0201			0.564093			0.282046	−	0.959401i	$-0.408987\pi$
$709$	15.0201			0.564093			0.282046	+	0.959401i	$0.408987\pi$
$710$	−29.7950	−	18.2107i	−1.11819	−	0.683435i
$711$	−28.0178	+	48.5283i	−1.05075	+	1.81995i
$712$	6.39495	+	3.69213i	0.239661	+	0.138368i
$713$	−1.47157	+	0.849613i	−0.0551109	+	0.0318183i
$714$	34.8323	+	60.3313i	1.30357	+	2.25784i
$715$	−14.6794	−	8.97205i	−0.548980	−	0.335536i
$716$	1.57485	+	2.72772i	0.0588550	+	0.101940i
$717$	−10.5107	+	6.06833i	−0.392528	+	0.226626i
$718$	16.0491	−	9.26592i	0.598945	−	0.345801i
$719$	−4.18292	+	7.24503i	−0.155997	+	0.270194i	−0.933421	−	0.358782i	$-0.883192\pi$
$719$	−4.18292	+	7.24503i	−0.155997	+	0.270194i	0.777425	+	0.628976i	$0.216526\pi$
$720$	−8.32879	+	13.6270i	−0.310396	+	0.507848i
$721$	7.49583	−	12.9832i	0.279159	−	0.483518i
$722$	16.3974	−	9.46702i	0.610247	−	0.352326i
$723$		−	22.2283i		−	0.826681i
$724$	−2.19593	−	3.80346i	−0.0816111	−	0.141355i
$725$	18.6301	+	0.932818i	0.691906	+	0.0346440i
$726$	2.65538	−	4.59925i	0.0985503	−	0.170694i
$727$			32.5740i			1.20810i	0.796946	+	0.604051i	$0.206448\pi$
$727$			32.5740i			1.20810i	−0.796946	+	0.604051i	$0.793552\pi$
$728$	−9.49080	−	5.47951i	−0.351752	−	0.203084i
$729$	−20.9917			−0.777470
$730$	−2.90951	+	4.76034i	−0.107686	+	0.176188i
$731$	9.84840	−	31.4599i	0.364256	−	1.16359i
$732$			35.4223i			1.30924i
$733$			29.1991i			1.07849i	0.842148	+	0.539246i	$0.181291\pi$
$733$			29.1991i			1.07849i	−0.842148	+	0.539246i	$0.818709\pi$
$734$	−8.42385	+	14.5905i	−0.310930	+	0.538546i
$735$	−72.5123	−	44.3194i	−2.67466	−	1.63475i
$736$	−0.585531	+	1.01417i	−0.0215830	+	0.0373828i
$737$	−24.9834	−	14.4241i	−0.920274	−	0.531320i
$738$	77.5722	−	44.7863i	2.85547	−	1.64861i
$739$	−48.4514			−1.78231			−0.891157	−	0.453696i	$-0.850105\pi$
$739$	−48.4514			−1.78231			−0.891157	+	0.453696i	$0.850105\pi$
$740$	−0.209258	+	8.36379i	−0.00769248	+	0.307459i
$741$	−1.02991	+	1.78385i	−0.0378346	+	0.0655315i
$742$			32.6141i			1.19730i
$743$	−20.2335	−	11.6818i	−0.742296	−	0.428565i	0.0806076	−	0.996746i	$-0.474314\pi$
$743$	−20.2335	−	11.6818i	−0.742296	−	0.428565i	−0.822903	+	0.568181i	$0.807647\pi$
$744$	−2.31052	−	4.00194i	−0.0847078	−	0.146718i
$745$	12.9849	+	0.324877i	0.475731	+	0.0119026i
$746$	13.6506	+	23.6436i	0.499785	+	0.865653i
$747$			103.210i			3.77625i
$748$	−13.3000	+	7.67876i	−0.486296	+	0.280763i
$749$	10.6424	+	18.4332i	0.388866	+	0.673536i
$750$	20.0647	−	29.4142i	0.732661	−	1.07405i
$751$	−21.2670	+	36.8356i	−0.776045	+	1.34415i	0.158161	+	0.987413i	$0.449444\pi$
$751$	−21.2670	+	36.8356i	−0.776045	+	1.34415i	−0.934205	+	0.356735i	$0.883890\pi$
$752$			3.16187i			0.115302i
$753$		−	36.8809i		−	1.34401i
$754$	4.69798	−	8.13715i	0.171090	−	0.296337i
$755$	14.3299	+	26.3192i	0.521518	+	0.957853i
$756$	28.7013	+	49.7121i	1.04386	+	1.80801i
$757$	21.7194	−	12.5397i	0.789405	−	0.455763i	−0.0503482	−	0.998732i	$-0.516033\pi$
$757$	21.7194	−	12.5397i	0.789405	−	0.455763i	0.839753	+	0.542969i	$0.182700\pi$
$758$			23.3161i			0.846877i
$759$	5.69660	+	9.86680i	0.206773	+	0.358142i
$760$	0.0143627	−	0.574060i	0.000520990	−	0.0208234i
$761$	−5.84806	−	10.1291i	−0.211992	−	0.367181i	0.740346	−	0.672226i	$-0.234662\pi$
$761$	−5.84806	−	10.1291i	−0.211992	−	0.367181i	−0.952338	+	0.305045i	$0.901328\pi$
$762$	26.3752	+	15.2277i	0.955474	+	0.551643i
$763$			27.6739i			1.00186i
$764$	−0.773041	+	1.33895i	−0.0279676	+	0.0484414i
$765$	−2.00813	+	80.2624i	−0.0726039	+	2.90189i
$766$	−16.4633			−0.594843
$767$	−10.8527	+	6.26583i	−0.391870	+	0.226246i
$768$	−2.75803	−	1.59235i	−0.0995219	−	0.0574590i
$769$	9.41425	−	16.3060i	0.339487	−	0.588008i	−0.644850	−	0.764310i	$-0.723080\pi$
$769$	9.41425	−	16.3060i	0.339487	−	0.588008i	0.984336	+	0.176301i	$0.0564133\pi$
$770$	15.5010	−	25.3617i	0.558618	−	0.913971i
$771$	26.9398	−	46.6610i	0.970211	−	1.68046i
$772$		−	9.54512i		−	0.343536i
$773$			17.5709i			0.631981i	0.948762	+	0.315991i	$0.102337\pi$
$773$			17.5709i			0.631981i	−0.948762	+	0.315991i	$0.897663\pi$
$774$	13.9920	−	44.6964i	0.502933	−	1.60658i
$775$	3.30879	+	6.45661i	0.118855	+	0.231928i
$776$	−18.7299			−0.672364
$777$	44.9028	+	25.9246i	1.61088	+	0.930041i
$778$			5.92084i			0.212272i
$779$	−1.61033	+	2.78917i	−0.0576960	+	0.0999324i
$780$	−8.57629	−	15.7517i	−0.307080	−	0.564003i
$781$	−23.8534	−	41.3153i	−0.853542	−	1.47838i
$782$			5.88713i			0.210523i
$783$	−42.6218	+	24.6077i	−1.52318	+	0.879408i
$784$	5.96695	−	10.3351i	0.213105	−	0.369109i
$785$	−10.9124	−	6.66963i	−0.389480	−	0.238049i
$786$	19.5930	−	33.9361i	0.698859	−	1.21046i
$787$	−15.9297	+	9.19701i	−0.567832	+	0.327838i	−0.756283	−	0.654245i	$-0.772987\pi$
$787$	−15.9297	+	9.19701i	−0.567832	+	0.327838i	0.188451	+	0.982083i	$0.439653\pi$
$788$	−17.3617	+	10.0238i	−0.618485	+	0.357082i
$789$	16.8969	+	29.2662i	0.601544	+	1.04191i
$790$	14.9688	+	9.14888i	0.532565	+	0.325503i
$791$	−22.4611	−	38.9038i	−0.798625	−	1.38326i
$792$	−18.8959	+	10.9095i	−0.671435	+	0.387653i
$793$	−24.2600	−	14.0065i	−0.861497	−	0.497385i
$794$	−4.45944	+	7.72397i	−0.158260	+	0.274114i
$795$	−27.8354	+	45.5423i	−0.987219	+	1.61522i
$796$	14.5458			0.515561
$797$	21.3232	+	12.3109i	0.755305	+	0.436076i	0.827608	−	0.561307i	$-0.189701\pi$
$797$	21.3232	+	12.3109i	0.755305	+	0.436076i	−0.0723025	+	0.997383i	$0.523035\pi$
$798$	−3.08196	−	1.77937i	−0.109100	−	0.0629891i
$799$	7.94764	+	13.7657i	0.281167	+	0.486996i
$800$	4.19969	+	2.71341i	0.148481	+	0.0959336i
$801$	52.7406			1.86350
$802$	−15.8587	+	9.15605i	−0.559992	+	0.323311i
$803$	−6.60093	+	3.81105i	−0.232942	+	0.134489i
$804$	−15.0370	−	26.0449i	−0.530315	−	0.918532i
$805$	−5.44853	−	10.0071i	−0.192035	−	0.352704i
$806$	3.65446			0.128723
$807$	−44.2747	−	25.5620i	−1.55854	−	0.899825i
$808$	12.7011	−	7.33300i	0.446824	−	0.257974i
$809$	52.4313			1.84339			0.921694	−	0.387918i	$-0.126806\pi$
$809$	52.4313			1.84339			0.921694	+	0.387918i	$0.126806\pi$
$810$	−1.15131	+	46.0167i	−0.0404531	+	1.61686i
$811$	−8.18334	+	14.1740i	−0.287356	+	0.497715i	−0.973178	−	0.230055i	$-0.926110\pi$
$811$	−8.18334	+	14.1740i	−0.287356	+	0.497715i	0.685822	+	0.727769i	$0.259443\pi$
$812$	14.0585	+	8.11670i	0.493358	+	0.284840i
$813$			21.9460i			0.769682i
$814$	−5.71507	+	9.89878i	−0.200313	+	0.346952i
$815$	−11.4530	−	7.00007i	−0.401182	−	0.245202i
$816$	−16.0100			−0.560463
$817$	0.367855	+	1.64333i	0.0128696	+	0.0574930i
$818$			19.2010i			0.671347i
$819$	−78.2728			−2.73507
$820$	−13.4096	−	24.6289i	−0.468283	−	0.860077i
$821$	37.7870			1.31878			0.659388	−	0.751803i	$-0.270816\pi$
$821$	37.7870			1.31878			0.659388	+	0.751803i	$0.270816\pi$
$822$	−40.5696	−	23.4228i	−1.41503	−	0.816966i
$823$	−13.6685	−	7.89149i	−0.476453	−	0.275080i	0.242484	−	0.970155i	$-0.422038\pi$
$823$	−13.6685	−	7.89149i	−0.476453	−	0.275080i	−0.718937	+	0.695075i	$0.755371\pi$
$824$	1.72266	+	2.98373i	0.0600117	+	0.103943i
$825$	43.2911	−	22.1852i	1.50720	−	0.772390i
$826$	−10.8255	−	18.7503i	−0.376666	−	0.652405i
$827$	34.2600	+	19.7800i	1.19134	+	0.687819i	0.958610	−	0.284723i	$-0.0919016\pi$
$827$	34.2600	+	19.7800i	1.19134	+	0.687819i	0.232728	+	0.972542i	$0.425235\pi$
$828$			8.36410i			0.290673i
$829$	22.5047	−	38.9793i	0.781621	−	1.35381i	−0.149375	−	0.988781i	$-0.547726\pi$
$829$	22.5047	−	38.9793i	0.781621	−	1.35381i	0.930997	−	0.365027i	$-0.118940\pi$
$830$	32.3021	+	0.808184i	1.12122	+	0.0280525i
$831$	−13.0001	−	22.5168i	−0.450969	−	0.781100i
$832$	2.18113	−	1.25928i	0.0756172	−	0.0436576i
$833$		−	59.9938i		−	2.07866i
$834$	−20.4356	−	35.3955i	−0.707627	−	1.22565i
$835$	0.910465	−	36.3902i	0.0315079	−	1.25933i
$836$	0.392261	−	0.679416i	0.0135666	−	0.0234981i
$837$	−16.5773	−	9.57090i	−0.572995	−	0.330819i
$838$		−	14.4024i		−	0.497524i
$839$	−10.5486			−0.364177			−0.182089	−	0.983282i	$-0.558286\pi$
$839$	−10.5486			−0.364177			−0.182089	+	0.983282i	$0.558286\pi$
$840$	27.2143	−	14.8172i	0.938982	−	0.511244i
$841$	7.54096	−	13.0613i	0.260033	−	0.450391i
$842$	18.8492	−	10.8826i	0.649585	−	0.375038i
$843$	9.48886	−	5.47839i	0.326814	−	0.188686i
$844$	7.08060			0.243724
$845$	−14.8806	−	0.372304i	−0.511907	−	0.0128077i
$846$	11.2915	+	19.5575i	0.388211	+	0.672402i
$847$	−6.28403	+	3.62809i	−0.215922	+	0.124663i
$848$	−6.49107	−	3.74762i	−0.222904	−	0.128694i
$849$	91.3519			3.13519
$850$	25.1044	+	1.25699i	0.861074	+	0.0431143i
$851$	2.19081	+	3.79459i	0.0750999	+	0.130077i
$852$		−	49.7338i		−	1.70385i
$853$	−2.65991	+	1.53570i	−0.0910737	+	0.0525814i	−0.544845	−	0.838537i	$-0.683412\pi$
$853$	−2.65991	+	1.53570i	−0.0910737	+	0.0525814i	0.453771	+	0.891118i	$0.350078\pi$
$854$	24.1990	−	41.9139i	0.828074	−	1.43427i
$855$	−1.96122	−	3.60210i	−0.0670723	−	0.123189i
$856$	−4.89160			−0.167191
$857$	6.38188	+	3.68458i	0.218001	+	0.125863i	0.605024	−	0.796207i	$-0.293163\pi$
$857$	6.38188	+	3.68458i	0.218001	+	0.125863i	−0.387023	+	0.922070i	$0.626497\pi$
$858$		−	24.5029i		−	0.836515i
$859$	−12.9942			−0.443357			−0.221678	−	0.975120i	$-0.571153\pi$
$859$	−12.9942			−0.443357			−0.221678	+	0.975120i	$0.571153\pi$
$860$	−13.8793	−	4.72916i	−0.473280	−	0.161263i
$861$	−173.790			−5.92275
$862$			27.8665i			0.949136i
$863$	−30.2295	−	17.4530i	−1.02902	−	0.594107i	−0.112319	−	0.993672i	$-0.535828\pi$
$863$	−30.2295	−	17.4530i	−1.02902	−	0.594107i	−0.916705	+	0.399565i	$0.869161\pi$
$864$	−13.1920			−0.448802
$865$	−46.4449	+	25.2877i	−1.57917	+	0.859806i
$866$	−7.41963	+	12.8512i	−0.252129	+	0.436701i
$867$	−22.8157	+	13.1727i	−0.774862	+	0.447367i
$868$			6.31381i			0.214305i
$869$	11.9837	+	20.7564i	0.406520	+	0.704114i
$870$	12.7039	+	23.3328i	0.430703	+	0.791055i
$871$	23.7835			0.805872
$872$	−5.50784	−	3.17995i	−0.186519	−	0.107687i
$873$	−115.852	+	66.8874i	−3.92101	+	2.26379i
$874$	−0.150369	−	0.260447i	−0.00508631	−	0.00880975i
$875$	−43.8365	+	21.0974i	−1.48194	+	0.713223i
$876$	−7.94595			−0.268469
$877$	6.10626	−	3.52545i	0.206194	−	0.119046i	−0.393348	−	0.919390i	$-0.628683\pi$
$877$	6.10626	−	3.52545i	0.206194	−	0.119046i	0.599541	+	0.800344i	$0.295350\pi$
$878$	9.44447	−	5.45277i	0.318736	−	0.184022i
$879$	17.0190	−	29.4778i	0.574036	−	0.994260i
$880$	3.26645	+	5.99937i	0.110112	+	0.202239i
$881$	0.836780			0.0281918			0.0140959	−	0.999901i	$-0.495513\pi$
$881$	0.836780			0.0281918			0.0140959	+	0.999901i	$0.495513\pi$
$882$		−	85.2357i		−	2.87003i
$883$	43.1731	+	24.9260i	1.45289	+	0.838828i	0.998645	−	0.0520481i	$-0.0165749\pi$
$883$	43.1731	+	24.9260i	1.45289	+	0.838828i	0.454247	+	0.890876i	$0.349908\pi$
$884$	6.33061	−	10.9649i	0.212922	−	0.368791i
$885$	0.886244	−	35.4221i	0.0297908	−	1.19070i
$886$	12.1904	+	21.1144i	0.409545	+	0.709353i
$887$		−	7.90645i		−	0.265473i	−0.991151	−	0.132736i	$-0.957624\pi$
$887$		−	7.90645i		−	0.265473i	0.991151	−	0.132736i	$-0.0423763\pi$
$888$	−10.3194	+	5.95789i	−0.346296	+	0.199934i
$889$	−20.8059	−	36.0369i	−0.697808	−	1.20864i
$890$	0.412985	−	16.5065i	0.0138433	−	0.553300i
$891$	−31.4437	+	54.4620i	−1.05340	+	1.82455i
$892$			8.56936i			0.286923i
$893$	−0.703207	−	0.405997i	−0.0235319	−	0.0135862i
$894$	9.24972	+	16.0210i	0.309357	+	0.535822i
$895$	3.67293	−	6.00939i	0.122772	−	0.200872i
$896$	2.17566	+	3.76835i	0.0726835	+	0.125892i
$897$	−8.13451	−	4.69646i	−0.271603	−	0.156810i
$898$	15.1282	+	8.73429i	0.504836	+	0.291467i
$899$	−5.41328			−0.180543
$900$	35.6669	+	1.78585i	1.18890	+	0.0595285i
$901$	−37.6799			−1.25530
$902$		−	38.3119i		−	1.27565i
$903$	−66.8707	+	61.5284i	−2.22532	+	2.04754i
$904$	10.3238			0.343365
$905$	−5.12144	+	8.37933i	−0.170242	+	0.278538i
$906$	−21.3404	+	36.9627i	−0.708988	+	1.22800i
$907$			1.12848i			0.0374707i	0.999824	+	0.0187353i	$0.00596399\pi$
$907$			1.12848i			0.0374707i	−0.999824	+	0.0187353i	$0.994036\pi$
$908$	−14.2695	−	8.23851i	−0.473551	−	0.273405i
$909$	52.3746	−	90.7154i	1.73715	−	3.00884i
$910$	−0.612915	+	24.4975i	−0.0203179	+	0.812083i
$911$	−2.50709			−0.0830636			−0.0415318	−	0.999137i	$-0.513224\pi$
$911$	−2.50709			−0.0830636			−0.0415318	+	0.999137i	$0.513224\pi$
$912$	0.708284	−	0.408928i	0.0234536	−	0.0135410i
$913$	38.2305	+	22.0724i	1.26524	+	0.730489i
$914$	4.76744			0.157693
$915$	69.5640	−	37.8752i	2.29972	−	1.25212i
$916$	3.35873	+	5.81749i	0.110976	+	0.192215i
$917$	−46.3675	+	26.7703i	−1.53119	+	0.884032i
$918$	−57.4336	+	33.1593i	−1.89559	+	1.09442i
$919$	−13.8706			−0.457550			−0.228775	−	0.973479i	$-0.573472\pi$
$919$	−13.8706			−0.457550			−0.228775	+	0.973479i	$0.573472\pi$
$920$	2.61776	+	0.0654950i	0.0863049	+	0.00215931i
$921$	18.6212	+	32.2528i	0.613589	+	1.06277i
$922$	−10.0587	−	5.80738i	−0.331265	−	0.191256i
$923$	34.0617	+	19.6655i	1.12115	+	0.647298i
$924$	42.3336			1.39267
$925$	16.6490	−	8.53203i	0.547415	−	0.280531i
$926$	2.28398	−	3.95596i	0.0750561	−	0.130001i
$927$	21.3108	+	12.3038i	0.699938	+	0.404109i
$928$	−3.23088	+	1.86535i	−0.106059	+	0.0612330i
$929$	−3.55012	−	6.14899i	−0.116476	−	0.201742i	0.801893	−	0.597468i	$-0.203826\pi$
$929$	−3.55012	−	6.14899i	−0.116476	−	0.201742i	−0.918369	+	0.395726i	$0.870493\pi$
$930$	−5.38868	+	8.81658i	−0.176702	+	0.289107i
$931$	1.53236	+	2.65413i	0.0502211	+	0.0869854i
$932$	−18.3546	+	10.5970i	−0.601225	+	0.347118i
$933$	−35.9224	+	20.7398i	−1.17605	+	0.678990i
$934$	−3.68427	+	6.38134i	−0.120553	+	0.208804i
$935$	29.3009	+	17.9087i	0.958243	+	0.585677i
$936$	8.99417	−	15.5784i	0.293984	−	0.509194i
$937$	10.8318	−	6.25375i	0.353860	−	0.204301i	−0.312524	−	0.949910i	$-0.601175\pi$
$937$	10.8318	−	6.25375i	0.353860	−	0.204301i	0.666384	+	0.745609i	$0.267841\pi$
$938$			41.0907i			1.34166i
$939$	−27.1124	−	46.9601i	−0.884781	−	1.53248i
$940$	6.20944	−	3.38083i	0.202530	−	0.110271i
$941$	9.31282	−	16.1303i	0.303589	−	0.525832i	−0.673357	−	0.739317i	$-0.735148\pi$
$941$	9.31282	−	16.1303i	0.303589	−	0.525832i	0.976946	+	0.213486i	$0.0684816\pi$
$942$		−	18.2149i		−	0.593475i
$943$	−12.7188	−	7.34322i	−0.414182	−	0.239128i
$944$	4.97573			0.161946
$945$	66.9383	−	109.520i	2.17750	−	3.56268i
$946$	−13.5639	−	14.7416i	−0.441000	−	0.479291i
$947$		−	11.1789i		−	0.363266i	−0.983366	−	0.181633i	$-0.941862\pi$
$947$		−	11.1789i		−	0.363266i	0.983366	−	0.181633i	$-0.0581383\pi$
$948$			24.9858i			0.811502i
$949$	3.14195	−	5.44202i	0.101992	−	0.176655i
$950$	−1.14273	+	0.585607i	−0.0370749	+	0.0189996i
$951$	−1.90618	+	3.30160i	−0.0618121	+	0.107062i
$952$	18.9441	+	10.9374i	0.613983	+	0.354483i
$953$	46.6907	−	26.9569i	1.51246	−	0.873220i	0.512567	−	0.858647i	$-0.328694\pi$
$953$	46.6907	−	26.9569i	1.51246	−	0.873220i	0.999894	−	0.0145728i	$-0.00463884\pi$
$954$	−53.5334			−1.73321
$955$	3.45606	+	0.0864690i	0.111836	+	0.00279807i
$956$	−1.90547	+	3.30036i	−0.0616271	+	0.106741i
$957$			36.2957i			1.17327i
$958$	33.1663	+	19.1486i	1.07155	+	0.618663i
$959$	32.0030	+	55.4309i	1.03343	+	1.78996i
$960$	−0.178113	+	7.11898i	−0.00574859	+	0.229764i
$961$	14.4473	+	25.0234i	0.466041	+	0.807207i
$962$		−	9.42337i		−	0.303822i
$963$	−30.2566	+	17.4687i	−0.975006	+	0.562920i
$964$	−3.48986	−	6.04462i	−0.112401	−	0.194684i
$965$	−18.7452	+	10.2061i	−0.603429	+	0.328546i
$966$	8.11407	−	14.0540i	0.261066	−	0.452179i
$967$			44.8265i			1.44152i	0.693183	+	0.720762i	$0.256208\pi$
$967$			44.8265i			1.44152i	−0.693183	+	0.720762i	$0.743792\pi$
$968$		−	1.66758i		−	0.0535982i
$969$	2.05575	−	3.56067i	0.0660403	−	0.114385i
$970$	20.0269	+	36.7827i	0.643026	+	1.18102i
$971$	−0.169927	−	0.294323i	−0.00545323	−	0.00944527i	0.863286	−	0.504715i	$-0.168402\pi$
$971$	−0.169927	−	0.294323i	−0.00545323	−	0.00944527i	−0.868739	+	0.495270i	$0.835069\pi$
$972$	−22.5021	+	12.9916i	−0.721757	+	0.416706i
$973$			55.8430i			1.79024i
$974$	−1.01017	−	1.74966i	−0.0323679	−	0.0560628i
$975$	−21.7639	+	33.6851i	−0.697002	+	1.07879i
$976$	5.56132	+	9.63249i	0.178013	+	0.308328i
$977$	9.45368	+	5.45809i	0.302450	+	0.174620i	0.643543	−	0.765410i	$-0.277464\pi$
$977$	9.45368	+	5.45809i	0.302450	+	0.174620i	−0.341093	+	0.940030i	$0.610797\pi$
$978$		−	19.1174i		−	0.611306i
$979$	11.2791	−	19.5359i	0.360481	−	0.624371i
$980$	−26.6767	−	0.667437i	−0.852155	−	0.0213205i
$981$	−45.4244			−1.45029
$982$	−1.25758	+	0.726063i	−0.0401309	+	0.0231696i
$983$	21.0946	+	12.1790i	0.672812	+	0.388448i	0.797141	−	0.603793i	$-0.206345\pi$
$983$	21.0946	+	12.1790i	0.672812	+	0.388448i	−0.124329	+	0.992241i	$0.539678\pi$
$984$	19.9698	−	34.5888i	0.636616	−	1.10265i
$985$	38.2492	+	23.3778i	1.21872	+	0.744880i
$986$	−9.37742	+	16.2422i	−0.298638	+	0.517256i
$987$		−	43.8160i		−	1.39468i
$988$			0.646785i			0.0205770i
$989$	−7.49372	+	1.67744i	−0.238286	+	0.0533396i
$990$	41.6291	+	25.4436i	1.32306	+	0.808651i
$991$	26.2061			0.832463			0.416232	−	0.909259i	$-0.363351\pi$
$991$	26.2061			0.832463			0.416232	+	0.909259i	$0.363351\pi$
$992$	−1.25661	−	0.725506i	−0.0398975	−	0.0230348i
$993$		−	18.0844i		−	0.573890i
$994$	−33.9761	+	58.8483i	−1.07766	+	1.86656i
$995$	−15.5531	−	28.5657i	−0.493065	−	0.905594i
$996$	23.0102	+	39.8549i	0.729107	+	1.26285i
$997$		−	55.3465i		−	1.75284i	−0.481546	−	0.876421i	$-0.659924\pi$
$997$		−	55.3465i		−	1.75284i	0.481546	−	0.876421i	$-0.340076\pi$
$998$	−26.9339	+	15.5503i	−0.852579	+	0.492237i
$999$	−24.6795	+	42.7461i	−0.780824	+	1.35243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.1	✓	44
5.4	even	2	inner	430.2.j.a.49.22	yes	44
43.36	even	3	inner	430.2.j.a.79.11	yes	44
215.79	even	6	inner	430.2.j.a.79.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.1	✓	44	1.1	even	1	trivial
430.2.j.a.49.22	yes	44	5.4	even	2	inner
430.2.j.a.79.11	yes	44	43.36	even	3	inner
430.2.j.a.79.12	yes	44	215.79	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-2.75803 - 1.59235i) q^{3} -1.00000 q^{4} +(1.06925 + 1.96385i) q^{5} +(-1.59235 + 2.75803i) q^{6} +(3.76835 - 2.17566i) q^{7} +1.00000i q^{8} +(3.57116 + 6.18543i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-2.75803 - 1.59235i) q^{3} -1.00000 q^{4} +(1.06925 + 1.96385i) q^{5} +(-1.59235 + 2.75803i) q^{6} +(3.76835 - 2.17566i) q^{7} +1.00000i q^{8} +(3.57116 + 6.18543i) q^{9} +(1.96385 - 1.06925i) q^{10} +3.05490 q^{11} +(2.75803 + 1.59235i) q^{12} +(-2.18113 + 1.25928i) q^{13} +(-2.17566 - 3.76835i) q^{14} +(0.178113 - 7.11898i) q^{15} +1.00000 q^{16} +(4.35366 - 2.51359i) q^{17} +(6.18543 - 3.57116i) q^{18} +(-0.128404 + 0.222402i) q^{19} +(-1.06925 - 1.96385i) q^{20} -13.8576 q^{21} -3.05490i q^{22} +(-1.01417 - 0.585531i) q^{23} +(1.59235 - 2.75803i) q^{24} +(-2.71341 + 4.19969i) q^{25} +(1.25928 + 2.18113i) q^{26} -13.1920i q^{27} +(-3.76835 + 2.17566i) q^{28} +(-1.86535 - 3.23088i) q^{29} +(-7.11898 - 0.178113i) q^{30} +(0.725506 - 1.25661i) q^{31} -1.00000i q^{32} +(-8.42551 - 4.86447i) q^{33} +(-2.51359 - 4.35366i) q^{34} +(8.30196 + 5.07415i) q^{35} +(-3.57116 - 6.18543i) q^{36} +(-3.24030 - 1.87079i) q^{37} +(0.222402 + 0.128404i) q^{38} +8.02085 q^{39} +(-1.96385 + 1.06925i) q^{40} +12.5411 q^{41} +13.8576i q^{42} +(4.82556 - 4.44004i) q^{43} -3.05490 q^{44} +(-8.32879 + 13.6270i) q^{45} +(-0.585531 + 1.01417i) q^{46} +3.16187i q^{47} +(-2.75803 - 1.59235i) q^{48} +(5.96695 - 10.3351i) q^{49} +(4.19969 + 2.71341i) q^{50} -16.0100 q^{51} +(2.18113 - 1.25928i) q^{52} +(-6.49107 - 3.74762i) q^{53} -13.1920 q^{54} +(3.26645 + 5.99937i) q^{55} +(2.17566 + 3.76835i) q^{56} +(0.708284 - 0.408928i) q^{57} +(-3.23088 + 1.86535i) q^{58} +4.97573 q^{59} +(-0.178113 + 7.11898i) q^{60} +(5.56132 + 9.63249i) q^{61} +(-1.25661 - 0.725506i) q^{62} +(26.9147 + 15.5392i) q^{63} -1.00000 q^{64} +(-4.80521 - 2.93694i) q^{65} +(-4.86447 + 8.42551i) q^{66} +(-8.17813 - 4.72164i) q^{67} +(-4.35366 + 2.51359i) q^{68} +(1.86474 + 3.22983i) q^{69} +(5.07415 - 8.30196i) q^{70} +(-7.80824 - 13.5243i) q^{71} +(-6.18543 + 3.57116i) q^{72} +(-2.16077 + 1.24752i) q^{73} +(-1.87079 + 3.24030i) q^{74} +(14.1711 - 7.26217i) q^{75} +(0.128404 - 0.222402i) q^{76} +(11.5119 - 6.64641i) q^{77} -8.02085i q^{78} +(3.92279 + 6.79447i) q^{79} +(1.06925 + 1.96385i) q^{80} +(-10.2929 + 17.8278i) q^{81} -12.5411i q^{82} +(12.5145 + 7.22524i) q^{83} +13.8576 q^{84} +(9.59145 + 5.86228i) q^{85} +(-4.44004 - 4.82556i) q^{86} +11.8811i q^{87} +3.05490i q^{88} +(3.69213 - 6.39495i) q^{89} +(13.6270 + 8.32879i) q^{90} +(-5.47951 + 9.49080i) q^{91} +(1.01417 + 0.585531i) q^{92} +(-4.00194 + 2.31052i) q^{93} +3.16187 q^{94} +(-0.574060 - 0.0143627i) q^{95} +(-1.59235 + 2.75803i) q^{96} +18.7299i q^{97} +(-10.3351 - 5.96695i) q^{98} +(10.9095 + 18.8959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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