LMFDB - Embedded newform 140.2.o.a.131.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(31,140)] 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("140.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.13
Character	$\chi$	$=$	140.131
Dual form			140.2.o.a.31.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05472 - 0.942109i) q^{2} +(0.450639 + 0.780530i) q^{3} +(0.224860 - 1.98732i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.21064 + 0.398687i) q^{6} +(2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 - 1.89460i) q^{9} +(-1.38447 + 0.288532i) q^{10} +(-3.24107 + 1.87123i) q^{11} +(1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +(3.65805 - 0.786573i) q^{14} -0.901278i q^{15} +(-3.89888 - 0.893735i) q^{16} +(-0.505515 + 0.291859i) q^{17} +(-0.631220 - 3.02880i) q^{18} +(-3.07977 + 5.33433i) q^{19} +(-1.18839 + 1.60864i) q^{20} +(0.0151060 + 2.38451i) q^{21} +(-1.65551 + 5.02706i) q^{22} +(-3.73439 - 2.15605i) q^{23} +(1.06454 - 2.31628i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.27981 + 2.55232i) q^{26} +4.67556 q^{27} +(3.11717 - 4.27589i) q^{28} -0.435463 q^{29} +(-0.849103 - 0.950594i) q^{30} +(-1.26933 - 2.19854i) q^{31} +(-4.95421 + 2.73053i) q^{32} +(-2.92110 - 1.68650i) q^{33} +(-0.258212 + 0.784080i) q^{34} +(-1.33736 - 2.28286i) q^{35} +(-3.51922 - 2.59985i) q^{36} +(5.65039 - 9.78676i) q^{37} +(1.77723 + 8.52769i) q^{38} +(-1.88881 + 1.09050i) q^{39} +(0.262094 + 2.81626i) q^{40} +7.35068i q^{41} +(2.26240 + 2.50075i) q^{42} +5.80096i q^{43} +(2.98995 + 6.86180i) q^{44} +(-1.89460 + 1.09385i) q^{45} +(-5.96996 + 1.24418i) q^{46} +(5.78826 - 10.0256i) q^{47} +(-1.05940 - 3.44594i) q^{48} +(3.57652 + 6.01735i) q^{49} +(1.34325 + 0.442358i) q^{50} +(-0.455610 - 0.263046i) q^{51} +(4.80912 + 0.544138i) q^{52} +(1.55746 + 2.69759i) q^{53} +(4.93139 - 4.40489i) q^{54} +3.74246 q^{55} +(-0.740624 - 7.44657i) q^{56} -5.55147 q^{57} +(-0.459290 + 0.410254i) q^{58} +(-1.73534 - 3.00569i) q^{59} +(-1.79113 - 0.202661i) q^{60} +(-8.99597 - 5.19383i) q^{61} +(-3.41004 - 1.12299i) q^{62} +(4.99421 - 2.92575i) q^{63} +(-2.65284 + 7.54735i) q^{64} +(1.20995 - 2.09570i) q^{65} +(-4.66981 + 0.973217i) q^{66} +(8.52602 - 4.92250i) q^{67} +(0.466348 + 1.07025i) q^{68} -3.88640i q^{69} +(-3.56125 - 1.14783i) q^{70} -9.96771i q^{71} +(-6.16112 + 0.573383i) q^{72} +(8.48612 - 4.89946i) q^{73} +(-3.26063 - 15.6456i) q^{74} +(-0.450639 + 0.780530i) q^{75} +(9.90849 + 7.31997i) q^{76} +(-9.90142 + 0.0627260i) q^{77} +(-0.964785 + 2.92964i) q^{78} +(-0.397549 - 0.229525i) q^{79} +(2.92966 + 2.72344i) q^{80} +(-1.17456 - 2.03439i) q^{81} +(6.92515 + 7.75290i) q^{82} -2.59747 q^{83} +(4.74218 + 0.506159i) q^{84} +0.583719 q^{85} +(5.46514 + 6.11837i) q^{86} +(-0.196236 - 0.339892i) q^{87} +(9.61812 + 4.42040i) q^{88} +(-8.55647 - 4.94008i) q^{89} +(-0.967745 + 2.93862i) q^{90} +(-3.16604 + 5.56486i) q^{91} +(-5.12447 + 6.93662i) q^{92} +(1.14402 - 1.98149i) q^{93} +(-3.34020 - 16.0273i) q^{94} +(5.33433 - 3.07977i) q^{95} +(-4.36382 - 2.63643i) q^{96} +4.54044i q^{97} +(9.44122 + 2.97713i) q^{98} +8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.05472	−	0.942109i	0.745798	−	0.666172i
$2$	1.05472	−	0.942109i	0.745798	−	0.666172i
$3$	0.450639	+	0.780530i	0.260177	+	0.450639i	0.966289	−	0.257461i	$-0.0828859\pi$
$3$	0.450639	+	0.780530i	0.260177	+	0.450639i	−0.706112	+	0.708100i	$0.749553\pi$
$4$	0.224860	−	1.98732i	0.112430	−	0.993660i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.21064	+	0.398687i	0.494242	+	0.162763i
$7$	2.29962	+	1.30833i	0.869175	+	0.494504i
$7$	2.29962	+	1.30833i	0.869175	+	0.494504i
$8$	−1.63511	−	2.30790i	−0.578098	−	0.815967i
$9$	1.09385	−	1.89460i	0.364616	−	0.631534i
$10$	−1.38447	+	0.288532i	−0.437807	+	0.0912418i
$11$	−3.24107	+	1.87123i	−0.977218	+	0.564197i	−0.901429	−	0.432927i	$-0.857481\pi$
$11$	−3.24107	+	1.87123i	−0.977218	+	0.564197i	−0.0757892	+	0.997124i	$0.524148\pi$
$12$	1.65249	−	0.720054i	0.477033	−	0.207862i
$13$			2.41990i			0.671161i	0.942012	+	0.335580i	$0.108932\pi$
$13$			2.41990i			0.671161i	−0.942012	+	0.335580i	$0.891068\pi$
$14$	3.65805	−	0.786573i	0.977654	−	0.210220i
$15$		−	0.901278i		−	0.232709i
$16$	−3.89888	−	0.893735i	−0.974719	−	0.223434i
$17$	−0.505515	+	0.291859i	−0.122605	+	0.0707863i	−0.560048	−	0.828460i	$-0.689218\pi$
$17$	−0.505515	+	0.291859i	−0.122605	+	0.0707863i	0.437443	+	0.899246i	$0.355884\pi$
$18$	−0.631220	−	3.02880i	−0.148780	−	0.713894i
$19$	−3.07977	+	5.33433i	−0.706549	+	1.22378i	0.259581	+	0.965721i	$0.416416\pi$
$19$	−3.07977	+	5.33433i	−0.706549	+	1.22378i	−0.966130	+	0.258057i	$0.916918\pi$
$20$	−1.18839	+	1.60864i	−0.265733	+	0.359703i
$21$	0.0151060	+	2.38451i	0.00329639	+	0.520343i
$22$	−1.65551	+	5.02706i	−0.352955	+	1.07177i
$23$	−3.73439	−	2.15605i	−0.778674	−	0.449568i	0.0572861	−	0.998358i	$-0.481755\pi$
$23$	−3.73439	−	2.15605i	−0.778674	−	0.449568i	−0.835960	+	0.548790i	$0.815089\pi$
$24$	1.06454	−	2.31628i	0.217299	−	0.472809i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.27981	+	2.55232i	0.447108	+	0.500550i
$27$	4.67556			0.899812
$28$	3.11717	−	4.27589i	0.589090	−	0.808068i
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$	−0.849103	−	0.950594i	−0.155024	−	0.173554i
$31$	−1.26933	−	2.19854i	−0.227978	−	0.394869i	0.729231	−	0.684268i	$-0.239878\pi$
$31$	−1.26933	−	2.19854i	−0.227978	−	0.394869i	−0.957209	+	0.289399i	$0.906545\pi$
$32$	−4.95421	+	2.73053i	−0.875789	+	0.482694i
$33$	−2.92110	−	1.68650i	−0.508499	−	0.293582i
$34$	−0.258212	+	0.784080i	−0.0442831	+	0.134469i
$35$	−1.33736	−	2.28286i	−0.226056	−	0.385874i
$36$	−3.51922	−	2.59985i	−0.586536	−	0.433308i
$37$	5.65039	−	9.78676i	0.928918	−	1.60893i	0.143782	−	0.989609i	$-0.454073\pi$
$37$	5.65039	−	9.78676i	0.928918	−	1.60893i	0.785136	−	0.619324i	$-0.212593\pi$
$38$	1.77723	+	8.52769i	0.288304	+	1.38337i
$39$	−1.88881	+	1.09050i	−0.302451	+	0.174620i
$40$	0.262094	+	2.81626i	0.0414407	+	0.445289i
$41$			7.35068i			1.14798i	0.818861	+	0.573992i	$0.194606\pi$
$41$			7.35068i			1.14798i	−0.818861	+	0.573992i	$0.805394\pi$
$42$	2.26240	+	2.50075i	0.349096	+	0.385875i
$43$			5.80096i			0.884637i	0.896858	+	0.442319i	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	2.98995	+	6.86180i	0.450752	+	1.03446i
$45$	−1.89460	+	1.09385i	−0.282431	+	0.163061i
$46$	−5.96996	+	1.24418i	−0.880223	+	0.183444i
$47$	5.78826	−	10.0256i	0.844305	−	1.46238i	−0.0419181	−	0.999121i	$-0.513347\pi$
$47$	5.78826	−	10.0256i	0.844305	−	1.46238i	0.886223	−	0.463258i	$-0.153320\pi$
$48$	−1.05940	−	3.44594i	−0.152911	−	0.497379i
$49$	3.57652	+	6.01735i	0.510932	+	0.859621i
$50$	1.34325	+	0.442358i	0.189964	+	0.0625588i
$51$	−0.455610	−	0.263046i	−0.0637981	−	0.0368339i
$52$	4.80912	+	0.544138i	0.666905	+	0.0754584i
$53$	1.55746	+	2.69759i	0.213933	+	0.370543i	0.952942	−	0.303153i	$-0.0980393\pi$
$53$	1.55746	+	2.69759i	0.213933	+	0.370543i	−0.739009	+	0.673696i	$0.764706\pi$
$54$	4.93139	−	4.40489i	0.671078	−	0.599429i
$55$	3.74246			0.504633
$56$	−0.740624	−	7.44657i	−0.0989701	−	0.995090i
$57$	−5.55147			−0.735310
$58$	−0.459290	+	0.410254i	−0.0603078	+	0.0538689i
$59$	−1.73534	−	3.00569i	−0.225922	−	0.391308i	0.730674	−	0.682727i	$-0.239206\pi$
$59$	−1.73534	−	3.00569i	−0.225922	−	0.391308i	−0.956596	+	0.291419i	$0.905873\pi$
$60$	−1.79113	−	0.202661i	−0.231234	−	0.0261634i
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.202487	−	0.979285i	$-0.564902\pi$
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.949329	+	0.314284i	$0.898236\pi$
$62$	−3.41004	−	1.12299i	−0.433076	−	0.142620i
$63$	4.99421	−	2.92575i	0.629211	−	0.368610i
$64$	−2.65284	+	7.54735i	−0.331605	+	0.943418i
$65$	1.20995	−	2.09570i	0.150076	−	0.259939i
$66$	−4.66981	+	0.973217i	−0.574813	+	0.119795i
$67$	8.52602	−	4.92250i	1.04162	−	0.601379i	0.121327	−	0.992613i	$-0.461285\pi$
$67$	8.52602	−	4.92250i	1.04162	−	0.601379i	0.920291	+	0.391234i	$0.127952\pi$
$68$	0.466348	+	1.07025i	0.0565530	+	0.129787i
$69$		−	3.88640i		−	0.467868i
$70$	−3.56125	−	1.14783i	−0.425650	−	0.137192i
$71$		−	9.96771i		−	1.18295i	−0.806324	−	0.591475i	$-0.798546\pi$
$71$		−	9.96771i		−	1.18295i	0.806324	−	0.591475i	$-0.201454\pi$
$72$	−6.16112	+	0.573383i	−0.726095	+	0.0675738i
$73$	8.48612	−	4.89946i	0.993225	−	0.573439i	0.0869881	−	0.996209i	$-0.472276\pi$
$73$	8.48612	−	4.89946i	0.993225	−	0.573439i	0.906237	+	0.422771i	$0.138942\pi$
$74$	−3.26063	−	15.6456i	−0.379041	−	1.81876i
$75$	−0.450639	+	0.780530i	−0.0520353	+	0.0901278i
$76$	9.90849	+	7.31997i	1.13658	+	0.839658i
$77$	−9.90142	+	0.0627260i	−1.12837	+	0.00714829i
$78$	−0.964785	+	2.92964i	−0.109240	+	0.331716i
$79$	−0.397549	−	0.229525i	−0.0447278	−	0.0258236i	0.477469	−	0.878648i	$-0.341554\pi$
$79$	−0.397549	−	0.229525i	−0.0447278	−	0.0258236i	−0.522197	+	0.852825i	$0.674887\pi$
$80$	2.92966	+	2.72344i	0.327546	+	0.304489i
$81$	−1.17456	−	2.03439i	−0.130506	−	0.226044i
$82$	6.92515	+	7.75290i	0.764755	+	0.856164i
$83$	−2.59747			−0.285109			−0.142554	−	0.989787i	$-0.545532\pi$
$83$	−2.59747			−0.285109			−0.142554	+	0.989787i	$0.545532\pi$
$84$	4.74218	+	0.506159i	0.517414	+	0.0552265i
$85$	0.583719			0.0633132
$86$	5.46514	+	6.11837i	0.589321	+	0.659761i
$87$	−0.196236	−	0.339892i	−0.0210388	−	0.0364402i
$88$	9.61812	+	4.42040i	1.02529	+	0.471217i
$89$	−8.55647	−	4.94008i	−0.906984	−	0.523648i	−0.0275247	−	0.999621i	$-0.508763\pi$
$89$	−8.55647	−	4.94008i	−0.906984	−	0.523648i	−0.879460	+	0.475973i	$0.842096\pi$
$90$	−0.967745	+	2.93862i	−0.102009	+	0.309758i
$91$	−3.16604	+	5.56486i	−0.331891	+	0.583356i
$92$	−5.12447	+	6.93662i	−0.534263	+	0.723192i
$93$	1.14402	−	1.98149i	0.118629	−	0.205471i
$94$	−3.34020	−	16.0273i	−0.344515	−	1.65309i
$95$	5.33433	−	3.07977i	0.547290	−	0.315978i
$96$	−4.36382	−	2.63643i	−0.445381	−	0.269079i
$97$			4.54044i			0.461011i	0.973071	+	0.230506i	$0.0740380\pi$
$97$			4.54044i			0.461011i	−0.973071	+	0.230506i	$0.925962\pi$
$98$	9.44122	+	2.97713i	0.953708	+	0.300735i
$99$			8.18738i			0.822862i
$100$	1.83350	−	0.798926i	0.183350	−	0.0798926i
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	−0.0512584	−	0.998685i	$-0.516323\pi$
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	0.839258	+	0.543734i	$0.182990\pi$
$102$	−0.728358	+	0.151795i	−0.0721182	+	0.0150299i
$103$	−5.11597	+	8.86113i	−0.504092	+	0.873113i	0.495897	+	0.868381i	$0.334839\pi$
$103$	−5.11597	+	8.86113i	−0.504092	+	0.873113i	−0.999989	+	0.00473128i	$0.998494\pi$
$104$	5.58490	−	3.95681i	0.547645	−	0.387997i
$105$	1.17917	−	2.07260i	0.115075	−	0.202265i
$106$	4.18410	+	1.37790i	0.406396	+	0.133834i
$107$	−5.48368	−	3.16601i	−0.530128	−	0.306069i	0.210941	−	0.977499i	$-0.432347\pi$
$107$	−5.48368	−	3.16601i	−0.530128	−	0.306069i	−0.741068	+	0.671430i	$0.765681\pi$
$108$	1.05134	−	9.29183i	0.101166	−	0.894107i
$109$	9.38027	+	16.2471i	0.898467	+	1.55619i	0.829454	+	0.558575i	$0.188652\pi$
$109$	9.38027	+	16.2471i	0.898467	+	1.55619i	0.0690134	+	0.997616i	$0.478015\pi$
$110$	3.94724	−	3.52581i	0.376355	−	0.336173i
$111$	10.1851			0.966731
$112$	−7.79664	−	7.15629i	−0.736713	−	0.676205i
$113$	4.17847			0.393077			0.196539	−	0.980496i	$-0.437030\pi$
$113$	4.17847			0.393077			0.196539	+	0.980496i	$0.437030\pi$
$114$	−5.85523	+	5.23009i	−0.548393	+	0.489843i
$115$	2.15605	+	3.73439i	0.201053	+	0.348234i
$116$	−0.0979179	+	0.865403i	−0.00909145	+	0.0803507i
$117$	4.58475	+	2.64701i	0.423861	+	0.244716i
$118$	−4.66198	−	1.53528i	−0.429170	−	0.141334i
$119$	−1.54434	+	0.00978348i	−0.141570	+	0.000896851i
$120$	−2.08006	+	1.47369i	−0.189883	+	0.134529i
$121$	1.50301	−	2.60329i	0.136637	−	0.236663i
$122$	−14.3814	+	2.99717i	−1.30203	+	0.271351i
$123$	−5.73743	+	3.31250i	−0.517326	+	0.298678i
$124$	−4.65461	+	2.02819i	−0.417997	+	0.182137i
$125$		−	1.00000i		−	0.0894427i
$126$	2.51111	−	7.79093i	0.223707	−	0.694072i
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	4.31243	+	10.4596i	0.381169	+	0.924505i
$129$	−4.52782	+	2.61414i	−0.398652	+	0.230162i
$130$	−0.698219	−	3.35028i	−0.0612379	−	0.293839i
$131$	−7.93723	+	13.7477i	−0.693479	+	1.20114i	0.277212	+	0.960809i	$0.410590\pi$
$131$	−7.93723	+	13.7477i	−0.693479	+	1.20114i	−0.970691	+	0.240332i	$0.922744\pi$
$132$	−4.00845	+	5.42594i	−0.348891	+	0.472267i
$133$	−14.0614	+	8.23756i	−1.21928	+	0.714287i
$134$	4.35501	−	13.2243i	0.376216	−	1.14240i
$135$	−4.04915	−	2.33778i	−0.348496	−	0.201204i
$136$	1.50016	+	0.689459i	0.128637	+	0.0591206i
$137$	3.92110	+	6.79155i	0.335002	+	0.580241i	0.983485	−	0.180988i	$-0.0579295\pi$
$137$	3.92110	+	6.79155i	0.335002	+	0.580241i	−0.648483	+	0.761229i	$0.724596\pi$
$138$	−3.66142	−	4.09906i	−0.311680	−	0.348935i
$139$	−17.4044			−1.47623			−0.738113	−	0.674677i	$-0.764283\pi$
$139$	−17.4044			−1.47623			−0.738113	+	0.674677i	$0.764283\pi$
$140$	−4.83749	+	2.14445i	−0.408843	+	0.181239i
$141$	10.4337			0.878674
$142$	−9.39067	−	10.5131i	−0.788048	−	0.882242i
$143$	−4.52820	−	7.84307i	−0.378667	−	0.655871i
$144$	−5.95805	+	6.40921i	−0.496505	+	0.534101i
$145$	0.377122	+	0.217731i	0.0313183	+	0.0180816i
$146$	4.33463	−	13.1624i	0.358736	−	1.08933i
$147$	−3.08500	+	5.50324i	−0.254446	+	0.453899i
$148$	−18.1789	−	13.4298i	−1.49429	−	1.10392i
$149$	−0.825776	+	1.43029i	−0.0676502	+	0.117174i	−0.897867	−	0.440268i	$-0.854884\pi$
$149$	−0.825776	+	1.43029i	−0.0676502	+	0.117174i	0.830216	+	0.557441i	$0.188217\pi$
$150$	0.260047	+	1.24779i	0.0212328	+	0.101882i
$151$	6.37060	−	3.67807i	0.518432	−	0.299317i	−0.217861	−	0.975980i	$-0.569908\pi$
$151$	6.37060	−	3.67807i	0.518432	−	0.299317i	0.736293	+	0.676663i	$0.236575\pi$
$152$	17.3469	−	1.61438i	1.40702	−	0.130944i
$153$			1.27700i			0.103239i
$154$	−10.3841	+	9.39438i	−0.836776	+	0.757021i
$155$			2.53865i			0.203909i
$156$	1.74246	+	3.99887i	0.139509	+	0.320166i
$157$	−2.66953	+	1.54125i	−0.213052	+	0.123005i	−0.602729	−	0.797946i	$-0.705920\pi$
$157$	−2.66953	+	1.54125i	−0.213052	+	0.123005i	0.389677	+	0.920952i	$0.372587\pi$
$158$	−0.635540	+	0.132451i	−0.0505609	+	0.0105372i
$159$	−1.40370	+	2.43128i	−0.111321	+	0.192813i
$160$	5.65574	+	0.112397i	0.447125	+	0.00888579i
$161$	−5.76685	−	9.84393i	−0.454491	−	0.775810i
$162$	−3.15545	−	1.03915i	−0.247915	−	0.0816433i
$163$	3.91284	+	2.25908i	0.306477	+	0.176945i	0.645349	−	0.763888i	$-0.276712\pi$
$163$	3.91284	+	2.25908i	0.306477	+	0.176945i	−0.338872	+	0.940833i	$0.610045\pi$
$164$	14.6082	+	1.65287i	1.14071	+	0.129068i
$165$	1.68650	+	2.92110i	0.131294	+	0.227408i
$166$	−2.73959	+	2.44710i	−0.212634	+	0.189932i
$167$	−16.9358			−1.31053			−0.655266	−	0.755398i	$-0.727444\pi$
$167$	−16.9358			−1.31053			−0.655266	+	0.755398i	$0.727444\pi$
$168$	5.47852	−	3.93380i	0.422677	−	0.303499i
$169$	7.14406			0.549543
$170$	0.615659	−	0.549927i	0.0472189	−	0.0421775i
$171$	6.73762	+	11.6699i	0.515238	+	0.892419i
$172$	11.5284	+	1.30440i	0.879029	+	0.0994596i
$173$	0.114919	+	0.0663486i	0.00873715	+	0.00504439i	0.504362	−	0.863492i	$-0.331728\pi$
$173$	0.114919	+	0.0663486i	0.00873715	+	0.00504439i	−0.495625	+	0.868537i	$0.665061\pi$
$174$	−0.527189	−	0.173613i	−0.0399661	−	0.0131616i
$175$	0.0167606	+	2.64570i	0.00126698	+	0.199996i
$176$	14.3089	−	4.39904i	1.07857	−	0.331590i
$177$	1.56402	−	2.70897i	0.117559	−	0.203618i
$178$	−13.6788	+	2.85074i	−1.02527	+	0.213672i
$179$	13.9422	−	8.04953i	1.04209	−	0.601650i	0.121664	−	0.992571i	$-0.461177\pi$
$179$	13.9422	−	8.04953i	1.04209	−	0.601650i	0.920424	+	0.390921i	$0.127843\pi$
$180$	1.74781	+	4.01114i	0.130274	+	0.298973i
$181$			3.99317i			0.296810i	0.988927	+	0.148405i	$0.0474139\pi$
$181$			3.99317i			0.296810i	−0.988927	+	0.148405i	$0.952586\pi$
$182$	1.90343	+	8.85212i	0.141092	+	0.656163i
$183$		−	9.36216i		−	0.692071i
$184$	1.13018	+	12.1440i	0.0833177	+	0.895267i
$185$	−9.78676	+	5.65039i	−0.719537	+	0.415425i
$186$	−0.660170	−	3.16770i	−0.0484060	−	0.232267i
$187$	1.09227	−	1.89187i	0.0798749	−	0.138347i
$188$	−18.6225	−	13.7575i	−1.35818	−	1.00337i
$189$	10.7520	+	6.11719i	0.782094	+	0.444960i
$190$	2.72472	−	8.27381i	0.197672	−	0.600245i
$191$	17.3638	+	10.0250i	1.25640	+	0.725385i	0.972373	−	0.233431i	$-0.0749953\pi$
$191$	17.3638	+	10.0250i	1.25640	+	0.725385i	0.284030	+	0.958815i	$0.408329\pi$
$192$	−7.08640	+	1.33051i	−0.511417	+	0.0960214i
$193$	−9.66959	−	16.7482i	−0.696032	−	1.20556i	−0.969832	−	0.243776i	$-0.921614\pi$
$193$	−9.66959	−	16.7482i	−0.696032	−	1.20556i	0.273799	−	0.961787i	$-0.411720\pi$
$194$	4.27759	+	4.78888i	0.307113	+	0.343821i
$195$	2.18101			0.156185
$196$	12.7626	−	5.75464i	0.911615	−	0.411046i
$197$	−1.63738			−0.116659			−0.0583293	−	0.998297i	$-0.518577\pi$
$197$	−1.63738			−0.116659			−0.0583293	+	0.998297i	$0.518577\pi$
$198$	7.71340	+	8.63537i	0.548168	+	0.613689i
$199$	0.391632	+	0.678326i	0.0277621	+	0.0480853i	0.879573	−	0.475765i	$-0.157829\pi$
$199$	0.391632	+	0.678326i	0.0277621	+	0.0480853i	−0.851811	+	0.523850i	$0.824495\pi$
$200$	1.18115	−	2.57000i	0.0835198	−	0.181726i
$201$	7.68431	+	4.43654i	0.542009	+	0.312929i
$202$	4.04510	−	12.2832i	0.284612	−	0.864245i
$203$	−1.00140	−	0.569731i	−0.0702845	−	0.0399873i
$204$	−0.625205	+	0.846294i	−0.0437731	+	0.0592524i
$205$	3.67534	−	6.36588i	0.256697	−	0.444612i
$206$	2.95224	+	14.1658i	0.205692	+	0.986978i
$207$	−8.16972	+	4.71679i	−0.567835	+	0.327839i
$208$	2.16275	−	9.43491i	0.149960	−	0.654193i
$209$		−	23.0519i		−	1.59453i
$210$	−0.708921	−	3.29692i	−0.0489202	−	0.227509i
$211$		−	9.22534i		−	0.635099i	−0.948242	−	0.317549i	$-0.897140\pi$
$211$		−	9.22534i		−	0.635099i	0.948242	−	0.317549i	$-0.102860\pi$
$212$	5.71118	−	2.48858i	0.392246	−	0.170916i
$213$	7.78009	−	4.49184i	0.533083	−	0.307776i
$214$	−8.76646	+	1.82699i	−0.599263	+	0.124890i
$215$	2.90048	−	5.02378i	0.197811	−	0.342619i
$216$	−7.64505	−	10.7907i	−0.520180	−	0.734217i
$217$	−0.0425494	−	6.71651i	−0.00288844	−	0.455946i
$218$	25.2001	+	8.29887i	1.70677	+	0.562071i
$219$	7.64835	+	4.41578i	0.516828	+	0.298391i
$220$	0.841528	−	7.43747i	0.0567358	−	0.501434i
$221$	−0.706272	−	1.22330i	−0.0475090	−	0.0822880i
$222$	10.7425	−	9.59552i	0.720986	−	0.644009i
$223$	24.2380			1.62310			0.811550	−	0.584284i	$-0.198624\pi$
$223$	24.2380			1.62310			0.811550	+	0.584284i	$0.198624\pi$
$224$	−14.9653	−	0.202576i	−0.999908	−	0.0135352i
$225$	2.18770			0.145847
$226$	4.40710	−	3.93657i	0.293156	−	0.261857i
$227$	5.31623	+	9.20798i	0.352851	+	0.611155i	0.986748	−	0.162262i	$-0.0518791\pi$
$227$	5.31623	+	9.20798i	0.352851	+	0.611155i	−0.633897	+	0.773417i	$0.718546\pi$
$228$	−1.24830	+	11.0325i	−0.0826707	+	0.730648i
$229$	−25.5589	−	14.7564i	−1.68898	−	0.975132i	−0.955302	−	0.295633i	$-0.904470\pi$
$229$	−25.5589	−	14.7564i	−1.68898	−	0.975132i	−0.733676	−	0.679499i	$-0.762197\pi$
$230$	5.79223	+	1.90749i	0.381928	+	0.125776i
$231$	−4.51093	−	7.70009i	−0.296797	−	0.506629i
$232$	0.712029	+	1.00501i	0.0467470	+	0.0659819i
$233$	−14.0351	+	24.3096i	−0.919472	+	1.59257i	−0.119254	+	0.992864i	$0.538050\pi$
$233$	−14.0351	+	24.3096i	−0.919472	+	1.59257i	−0.800218	+	0.599709i	$0.795283\pi$
$234$	7.32940	−	1.52749i	0.479138	−	0.0998553i
$235$	−10.0256	+	5.78826i	−0.653996	+	0.377585i
$236$	−6.36348	+	2.77281i	−0.414227	+	0.180495i
$237$		−	0.413732i		−	0.0268748i
$238$	−1.61963	+	1.46526i	−0.104985	+	0.0949787i
$239$		−	13.6279i		−	0.881512i	−0.897627	−	0.440756i	$-0.854710\pi$
$239$		−	13.6279i		−	0.881512i	0.897627	−	0.440756i	$-0.145290\pi$
$240$	−0.805504	+	3.51397i	−0.0519951	+	0.226826i
$241$	−3.64372	+	2.10370i	−0.234713	+	0.135512i	−0.612744	−	0.790281i	$-0.709934\pi$
$241$	−3.64372	+	2.10370i	−0.234713	+	0.135512i	0.378031	+	0.925793i	$0.376601\pi$
$242$	−0.867332	−	4.16174i	−0.0557542	−	0.267527i
$243$	8.07194	−	13.9810i	0.517815	−	0.896882i
$244$	−12.3446	+	16.7100i	−0.790283	+	1.06975i
$245$	−0.0886870	−	6.99944i	−0.00566601	−	0.447178i
$246$	−2.93062	+	8.89904i	−0.186850	+	0.567382i
$247$	−12.9086	−	7.45276i	−0.821352	−	0.474208i
$248$	−2.99852	+	6.52433i	−0.190406	+	0.414295i
$249$	−1.17052	−	2.02740i	−0.0741787	−	0.128481i
$250$	−0.942109	−	1.05472i	−0.0595842	−	0.0667062i
$251$	−18.8826			−1.19186			−0.595928	−	0.803038i	$-0.703216\pi$
$251$	−18.8826			−1.19186			−0.595928	+	0.803038i	$0.703216\pi$
$252$	−4.69140	−	10.5830i	−0.295531	−	0.666665i
$253$	16.1379			1.01458
$254$	4.62610	+	5.17905i	0.290267	+	0.324962i
$255$	0.263046	+	0.455610i	0.0164726	+	0.0285314i
$256$	14.4025	+	6.96913i	0.900155	+	0.435570i
$257$	22.3734	+	12.9173i	1.39561	+	0.805757i	0.993929	−	0.110022i	$-0.0350923\pi$
$257$	22.3734	+	12.9173i	1.39561	+	0.805757i	0.401682	+	0.915779i	$0.368426\pi$
$258$	−2.31277	+	7.02288i	−0.143987	+	0.437225i
$259$	25.7981	−	15.1133i	1.60302	−	0.939092i
$260$	−3.89275	−	2.87580i	−0.241418	−	0.178349i
$261$	−0.476330	+	0.825028i	−0.0294841	+	0.0510680i
$262$	4.58029	+	21.9777i	0.282971	+	1.35779i
$263$	−9.26400	+	5.34857i	−0.571243	+	0.329807i	−0.757645	−	0.652666i	$-0.773650\pi$
$263$	−9.26400	+	5.34857i	−0.571243	+	0.329807i	0.186403	+	0.982473i	$0.440317\pi$
$264$	0.884043	+	9.49923i	0.0544091	+	0.584637i
$265$		−	3.11491i		−	0.191347i
$266$	−7.07012	+	21.9357i	−0.433497	+	1.34496i
$267$		−	8.90478i		−	0.544963i
$268$	−7.86542	−	18.0508i	−0.480457	−	1.10263i
$269$	−7.24441	+	4.18256i	−0.441699	+	0.255015i	−0.704318	−	0.709884i	$-0.748747\pi$
$269$	−7.24441	+	4.18256i	−0.441699	+	0.255015i	0.262619	+	0.964900i	$0.415414\pi$
$270$	−6.47316	+	1.34905i	−0.393944	+	0.0821004i
$271$	13.5557	−	23.4791i	0.823448	−	1.42625i	−0.0796525	−	0.996823i	$-0.525381\pi$
$271$	13.5557	−	23.4791i	0.823448	−	1.42625i	0.903100	−	0.429430i	$-0.141286\pi$
$272$	2.23179	−	0.686127i	0.135322	−	0.0416025i
$273$	−5.77028	+	0.0365550i	−0.349234	+	0.00221241i
$274$	10.5340	+	3.46906i	0.636385	+	0.209574i
$275$	−3.24107	−	1.87123i	−0.195444	−	0.112839i
$276$	−7.72352	−	0.873895i	−0.464901	−	0.0526023i
$277$	−1.67991	−	2.90970i	−0.100936	−	0.174827i	0.811134	−	0.584860i	$-0.198850\pi$
$277$	−1.67991	−	2.90970i	−0.100936	−	0.174827i	−0.912071	+	0.410033i	$0.865517\pi$
$278$	−18.3568	+	16.3969i	−1.10097	+	0.983420i
$279$	−5.55380			−0.332497
$280$	−3.08189	+	6.81924i	−0.184178	+	0.407527i
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	11.0046	−	9.82966i	0.655313	−	0.585348i
$283$	−3.60282	−	6.24027i	−0.214165	−	0.370945i	0.738849	−	0.673871i	$-0.235370\pi$
$283$	−3.60282	−	6.24027i	−0.214165	−	0.370945i	−0.953014	+	0.302926i	$0.902036\pi$
$284$	−19.8090	−	2.24133i	−1.17545	−	0.132999i
$285$	4.80771	+	2.77573i	0.284784	+	0.164420i
$286$	−12.1650	−	4.00617i	−0.719332	−	0.236890i
$287$	−9.61715	+	16.9038i	−0.567682	+	0.997799i
$288$	−0.245892	+	12.3730i	−0.0144893	+	0.729089i
$289$	−8.32964	+	14.4274i	−0.489979	+	0.848668i
$290$	0.602884	−	0.125645i	0.0354026	−	0.00737812i
$291$	−3.54395	+	2.04610i	−0.207750	+	0.119944i
$292$	−7.82861	−	17.9663i	−0.458135	−	1.05140i
$293$			8.47879i			0.495336i	0.968845	+	0.247668i	$0.0796642\pi$
$293$			8.47879i			0.495336i	−0.968845	+	0.247668i	$0.920336\pi$
$294$	1.93085	+	8.71077i	0.112609	+	0.508022i
$295$			3.47068i			0.202071i
$296$	−31.8259	+	2.96187i	−1.84984	+	0.172155i
$297$	−15.1538	+	8.74905i	−0.879312	+	0.507671i
$298$	0.476525	+	2.28652i	0.0276044	+	0.132455i
$299$	5.21744	−	9.03686i	0.301732	−	0.522615i
$300$	1.44983	+	1.07107i	0.0837060	+	0.0618384i
$301$	−7.58959	+	13.3400i	−0.437457	+	0.768905i
$302$	3.25404	−	9.88112i	0.187249	−	0.568595i
$303$	7.13749	+	4.12083i	0.410038	+	0.236736i
$304$	16.7751	−	18.0454i	0.962120	−	1.03497i
$305$	5.19383	+	8.99597i	0.297398	+	0.515108i
$306$	1.20307	+	1.34687i	0.0687752	+	0.0769957i
$307$	10.4271			0.595104			0.297552	−	0.954706i	$-0.403830\pi$
$307$	10.4271			0.595104			0.297552	+	0.954706i	$0.403830\pi$
$308$	−2.10177	+	19.6914i	−0.119760	+	1.12202i
$309$	−9.22183			−0.524612
$310$	2.39169	+	2.67756i	0.135839	+	0.152075i
$311$	−3.96296	−	6.86404i	−0.224719	−	0.389224i	0.731516	−	0.681824i	$-0.238813\pi$
$311$	−3.96296	−	6.86404i	−0.224719	−	0.389224i	−0.956235	+	0.292600i	$0.905480\pi$
$312$	5.60518	+	2.57609i	0.317331	+	0.145843i
$313$	12.5285	+	7.23333i	0.708152	+	0.408852i	0.810376	−	0.585910i	$-0.199263\pi$
$313$	12.5285	+	7.23333i	0.708152	+	0.408852i	−0.102224	+	0.994761i	$0.532596\pi$
$314$	−1.36357	+	4.14058i	−0.0769507	+	0.233666i
$315$	−5.78799	+	0.0366672i	−0.326116	+	0.00206596i
$316$	−0.545533	+	0.738447i	−0.0306886	+	0.0415409i
$317$	−1.76853	+	3.06318i	−0.0993305	+	0.172046i	−0.911408	−	0.411504i	$-0.865003\pi$
$317$	−1.76853	+	3.06318i	−0.0993305	+	0.172046i	0.812077	+	0.583550i	$0.198337\pi$
$318$	0.810024	+	3.88675i	0.0454239	+	0.217958i
$319$	1.41136	−	0.814851i	0.0790212	−	0.0456229i
$320$	6.07110	−	5.20978i	0.339385	−	0.291235i
$321$		−	5.70690i		−	0.318528i
$322$	−15.3565	−	4.94957i	−0.855782	−	0.275829i
$323$		−	3.59544i		−	0.200056i
$324$	−4.30710	+	1.87677i	−0.239283	+	0.104265i
$325$	−2.09570	+	1.20995i	−0.116248	+	0.0671161i
$326$	6.25524	−	1.30363i	0.346446	−	0.0722015i
$327$	−8.45423	+	14.6432i	−0.467520	+	0.809769i
$328$	16.9647	−	12.0192i	0.936717	−	0.663648i
$329$	26.4276	−	15.4820i	1.45700	−	0.853552i
$330$	4.53078	+	1.49207i	0.249411	+	0.0821359i
$331$	−20.3773	−	11.7649i	−1.12004	−	0.646655i	−0.178629	−	0.983917i	$-0.557166\pi$
$331$	−20.3773	−	11.7649i	−1.12004	−	0.646655i	−0.941411	+	0.337261i	$0.890499\pi$
$332$	−0.584065	+	5.16199i	−0.0320547	+	0.283301i
$333$	−12.3613	−	21.4105i	−0.677397	−	1.17329i
$334$	−17.8625	+	15.9554i	−0.977393	+	0.873040i
$335$	−9.84499			−0.537890
$336$	2.07222	−	9.31041i	0.113049	−	0.507924i
$337$	5.10057			0.277846			0.138923	−	0.990303i	$-0.455636\pi$
$337$	5.10057			0.277846			0.138923	+	0.990303i	$0.455636\pi$
$338$	7.53497	−	6.73049i	0.409848	−	0.366090i
$339$	1.88298	+	3.26142i	0.102269	+	0.177136i
$340$	0.131255	−	1.16004i	0.00711829	−	0.0629118i
$341$	8.22794	+	4.75040i	0.445568	+	0.257249i
$342$	18.1006	+	5.96087i	0.978768	+	0.322327i
$343$	0.351954	+	18.5169i	0.0190037	+	0.999819i
$344$	13.3880	−	9.48520i	0.721835	−	0.511407i
$345$	−1.94320	+	3.36572i	−0.104618	+	0.181204i
$346$	0.183715	−	0.0382874i	0.00987658	−	0.00205834i
$347$	−1.44316	+	0.833209i	−0.0774729	+	0.0447290i	−0.538236	−	0.842794i	$-0.680909\pi$
$347$	−1.44316	+	0.833209i	−0.0774729	+	0.0447290i	0.460763	+	0.887523i	$0.347576\pi$
$348$	−0.719599	+	0.313557i	−0.0385745	+	0.0168084i
$349$		−	27.6081i		−	1.47783i	−0.673801	−	0.738913i	$-0.735339\pi$
$349$		−	27.6081i		−	1.47783i	0.673801	−	0.738913i	$-0.264661\pi$
$350$	2.51022	+	2.77467i	0.134177	+	0.148313i
$351$			11.3144i			0.603918i
$352$	10.9475	−	18.1203i	0.583503	−	0.965815i
$353$	23.5193	−	13.5789i	1.25180	−	0.722730i	0.280337	−	0.959902i	$-0.409554\pi$
$353$	23.5193	−	13.5789i	1.25180	−	0.722730i	0.971468	+	0.237172i	$0.0762205\pi$
$354$	−0.902540	−	4.33067i	−0.0479695	−	0.230173i
$355$	−4.98385	+	8.63229i	−0.264516	+	0.458154i
$356$	−11.7415	+	15.8936i	−0.622300	+	0.842360i
$357$	−0.703578	−	1.20100i	−0.0372373	−	0.0635635i
$358$	7.12154	−	21.6251i	0.376385	−	1.14292i
$359$	14.5102	+	8.37747i	0.765819	+	0.442146i	0.831381	−	0.555703i	$-0.187551\pi$
$359$	14.5102	+	8.37747i	0.765819	+	0.442146i	−0.0655619	+	0.997849i	$0.520884\pi$
$360$	5.62238	+	2.58400i	0.296325	+	0.136189i
$361$	−9.47002	−	16.4026i	−0.498422	−	0.863293i
$362$	3.76200	+	4.21166i	0.197726	+	0.221360i
$363$	2.70926			0.142199
$364$	10.3472	+	7.54325i	0.542343	+	0.395374i
$365$	−9.79892			−0.512899
$366$	−8.82018	−	9.87444i	−0.461038	−	0.516145i
$367$	4.22213	+	7.31294i	0.220393	+	0.381732i	0.954927	−	0.296839i	$-0.0959326\pi$
$367$	4.22213	+	7.31294i	0.220393	+	0.381732i	−0.734534	+	0.678572i	$0.762599\pi$
$368$	12.6330	+	11.7437i	0.658540	+	0.612184i
$369$	13.9266	+	8.04054i	0.724991	+	0.418574i
$370$	−4.99899	+	15.1798i	−0.259885	+	0.789158i
$371$	0.0522078	+	8.24111i	0.00271049	+	0.427857i
$372$	−3.68062	−	2.71908i	−0.190831	−	0.140978i
$373$	5.18861	−	8.98694i	0.268656	−	0.465326i	−0.699859	−	0.714281i	$-0.746754\pi$
$373$	5.18861	−	8.98694i	0.268656	−	0.465326i	0.968515	+	0.248955i	$0.0800871\pi$
$374$	−0.630311	−	3.02443i	−0.0325926	−	0.156390i
$375$	0.780530	−	0.450639i	0.0403064	−	0.0232709i
$376$	−32.6025	+	3.03414i	−1.68134	+	0.156474i
$377$		−	1.05378i		−	0.0542723i
$378$	17.1034	−	3.67767i	0.879704	−	0.189159i
$379$		−	11.7976i		−	0.606002i	−0.952990	−	0.303001i	$-0.902011\pi$
$379$		−	11.7976i		−	0.606002i	0.952990	−	0.303001i	$-0.0979886\pi$
$380$	−4.92102	−	11.2935i	−0.252443	−	0.579346i
$381$	−3.83268	+	2.21280i	−0.196354	+	0.113365i
$382$	27.7586	−	5.78507i	1.42025	−	0.295990i
$383$	−0.478522	+	0.828825i	−0.0244514	+	0.0423510i	−0.877992	−	0.478675i	$-0.841117\pi$
$383$	−0.478522	+	0.828825i	−0.0244514	+	0.0423510i	0.853541	+	0.521026i	$0.174451\pi$
$384$	−6.22067	+	8.07948i	−0.317447	+	0.412304i
$385$	8.60625	+	4.89639i	0.438615	+	0.249543i
$386$	−25.9773	−	8.55483i	−1.32221	−	0.435430i
$387$	10.9905	+	6.34537i	0.558679	+	0.322553i
$388$	9.02330	+	1.02096i	0.458088	+	0.0518314i
$389$	15.0820	+	26.1228i	0.764689	+	1.32448i	0.940411	+	0.340041i	$0.110441\pi$
$389$	15.0820	+	26.1228i	0.764689	+	1.32448i	−0.175722	+	0.984440i	$0.556226\pi$
$390$	2.30035	−	2.05475i	0.116483	−	0.104046i
$391$	2.51705			0.127293
$392$	8.03945	−	18.0933i	0.406054	−	0.913849i
$393$	−14.3073			−0.721708
$394$	−1.72697	+	1.54259i	−0.0870037	+	0.0777147i
$395$	0.229525	+	0.397549i	0.0115487	+	0.0200029i
$396$	16.2709	+	1.84101i	0.817645	+	0.0925142i
$397$	−5.37540	−	3.10349i	−0.269783	−	0.155760i	0.359006	−	0.933335i	$-0.383116\pi$
$397$	−5.37540	−	3.10349i	−0.269783	−	0.155760i	−0.628789	+	0.777576i	$0.716449\pi$
$398$	1.05212	+	0.346483i	0.0527380	+	0.0173676i
$399$	−12.7663	−	7.26317i	−0.639113	−	0.363613i
$400$	−1.17544	−	3.82339i	−0.0587720	−	0.191170i
$401$	−13.1565	+	22.7877i	−0.657004	+	1.13796i	0.324384	+	0.945926i	$0.394843\pi$
$401$	−13.1565	+	22.7877i	−0.657004	+	1.13796i	−0.981387	+	0.192038i	$0.938490\pi$
$402$	12.2845	−	2.56017i	0.612694	−	0.127689i
$403$	5.32025	−	3.07165i	0.265020	−	0.153010i
$404$	−7.30571	−	16.7663i	−0.363473	−	0.834153i
$405$			2.34912i			0.116728i
$406$	−1.59294	+	0.342523i	−0.0790564	+	0.0169991i
$407$			42.2927i			2.09637i
$408$	0.137886	+	1.48161i	0.00682637	+	0.0733508i
$409$	−15.9374	+	9.20148i	−0.788055	+	0.454984i	−0.839277	−	0.543703i	$-0.817022\pi$
$409$	−15.9374	+	9.20148i	−0.788055	+	0.454984i	0.0512223	+	0.998687i	$0.483688\pi$
$410$	−2.12091	−	10.1768i	−0.104744	−	0.502595i
$411$	−3.53400	+	6.12107i	−0.174320	+	0.301930i
$412$	16.4595	+	12.1596i	0.810902	+	0.599060i
$413$	−0.0581707	−	9.18236i	−0.00286239	−	0.451834i
$414$	−4.17302	+	12.6716i	−0.205093	+	0.622777i
$415$	2.24947	+	1.29873i	0.110422	+	0.0637523i
$416$	−6.60762	−	11.9887i	−0.323965	−	0.587795i
$417$	−7.84312	−	13.5847i	−0.384079	−	0.665245i
$418$	−21.7174	−	24.3132i	−1.06223	−	1.18920i
$419$	35.2426			1.72171			0.860856	−	0.508848i	$-0.169928\pi$
$419$	35.2426			1.72171			0.860856	+	0.508848i	$0.169928\pi$
$420$	−3.85377	−	2.80944i	−0.188045	−	0.137086i
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−8.69128	−	9.73014i	−0.423085	−	0.473656i
$423$	−12.6630	−	21.9329i	−0.615695	−	1.06641i
$424$	3.67917	−	8.00531i	0.178676	−	0.388772i
$425$	−0.505515	−	0.291859i	−0.0245211	−	0.0141573i
$426$	3.97400	−	12.0673i	0.192541	−	0.584664i
$427$	−13.8921	−	23.7136i	−0.672285	−	1.14758i
$428$	−7.52492	+	10.1859i	−0.363731	+	0.492355i
$429$	4.08117	−	7.06879i	0.197041	−	0.341284i
$430$	−1.67376	−	8.03123i	−0.0807159	−	0.387300i
$431$	−1.73673	+	1.00270i	−0.0836555	+	0.0482985i	−0.541244	−	0.840865i	$-0.682047\pi$
$431$	−1.73673	+	1.00270i	−0.0836555	+	0.0482985i	0.457589	+	0.889164i	$0.348713\pi$
$432$	−18.2294	−	4.17871i	−0.877064	−	0.201048i
$433$			13.5978i			0.653469i	0.945116	+	0.326734i	$0.105948\pi$
$433$			13.5978i			0.653469i	−0.945116	+	0.326734i	$0.894052\pi$
$434$	−6.37256	−	7.04393i	−0.305893	−	0.338120i
$435$			0.392473i			0.0188176i
$436$	34.3974	−	14.9883i	1.64734	−	0.717809i
$437$	23.0022	−	13.2803i	1.10034	−	0.635283i
$438$	12.2270	−	2.54818i	0.584228	−	0.121757i
$439$	−14.5247	+	25.1574i	−0.693224	+	1.20070i	0.277552	+	0.960711i	$0.410477\pi$
$439$	−14.5247	+	25.1574i	−0.693224	+	1.20070i	−0.970776	+	0.239989i	$0.922856\pi$
$440$	−6.11933	−	8.63724i	−0.291728	−	0.411764i
$441$	15.3127	−	0.194020i	0.729174	−	0.00923907i
$442$	−1.89740	−	0.624849i	−0.0902500	−	0.0297211i
$443$	12.6757	+	7.31831i	0.602240	+	0.347703i	0.769922	−	0.638138i	$-0.220295\pi$
$443$	12.6757	+	7.31831i	0.602240	+	0.347703i	−0.167683	+	0.985841i	$0.553628\pi$
$444$	2.29023	−	20.2411i	0.108689	−	0.960601i
$445$	4.94008	+	8.55647i	0.234182	+	0.405616i
$446$	25.5643	−	22.8349i	1.21050	−	1.08126i
$447$	−1.48851			−0.0704040
$448$	−15.9750	+	13.8853i	−0.754747	+	0.656016i
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$	2.30740	−	2.06105i	0.108772	−	0.0971589i
$451$	−13.7548	−	23.8241i	−0.647689	−	1.12183i
$452$	0.939568	−	8.30395i	0.0441936	−	0.390585i
$453$	5.74168	+	3.31496i	0.269768	+	0.155750i
$454$	14.2820	+	4.70335i	0.670290	+	0.220739i
$455$	5.52431	−	3.23629i	0.258983	−	0.151720i
$456$	9.07725	+	12.8122i	0.425081	+	0.599989i
$457$	3.80306	−	6.58709i	0.177900	−	0.308131i	−0.763261	−	0.646090i	$-0.776403\pi$
$457$	3.80306	−	6.58709i	0.177900	−	0.308131i	0.941161	+	0.337959i	$0.109736\pi$
$458$	−40.8596	+	8.51539i	−1.90924	+	0.397898i
$459$	−2.36357	+	1.36461i	−0.110322	+	0.0636943i
$460$	7.90623	−	3.44505i	0.368630	−	0.160626i
$461$			12.7953i			0.595936i	0.954576	+	0.297968i	$0.0963089\pi$
$461$			12.7953i			0.595936i	−0.954576	+	0.297968i	$0.903691\pi$
$462$	−12.0121	−	3.87163i	−0.558853	−	0.180125i
$463$			27.9178i			1.29745i	0.761024	+	0.648724i	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	1.69782	+	0.389188i	0.0788191	+	0.0180676i
$465$	−1.98149	+	1.14402i	−0.0918895	+	0.0530524i
$466$	8.09917	+	38.8624i	0.375187	+	1.80026i
$467$	11.3054	−	19.5815i	0.523152	−	0.906126i	−0.476485	−	0.879183i	$-0.658089\pi$
$467$	11.3054	−	19.5815i	0.523152	−	0.906126i	0.999637	−	0.0269432i	$-0.00857731\pi$
$468$	6.29138	−	8.51617i	0.290819	−	0.393660i
$469$	26.0469	−	0.165008i	1.20273	−	0.00761937i
$470$	−5.12097	+	15.5502i	−0.236213	+	0.717276i
$471$	−2.40599	−	1.38910i	−0.110862	−	0.0640062i
$472$	−4.09938	+	8.91963i	−0.188689	+	0.410559i
$473$	−10.8549	−	18.8013i	−0.499110	−	0.864484i
$474$	−0.389781	−	0.436371i	−0.0179032	−	0.0200432i
$475$	−6.15955			−0.282620
$476$	−0.327817	+	3.07130i	−0.0150255	+	0.140773i
$477$	6.81448			0.312014
$478$	−12.8389	−	14.3735i	−0.587239	−	0.657430i
$479$	10.9907	+	19.0365i	0.502180	+	0.869801i	0.999997	+	0.00251901i	$0.000801826\pi$
$479$	10.9907	+	19.0365i	0.502180	+	0.869801i	−0.497817	+	0.867282i	$0.665865\pi$
$480$	2.46097	+	4.46512i	0.112327	+	0.203804i
$481$	23.6830	+	13.6734i	1.07985	+	0.623453i
$482$	−1.86118	+	5.65160i	−0.0847744	+	0.257423i
$483$	5.08471	−	8.93726i	0.231362	−	0.406659i
$484$	−4.83560	−	3.57234i	−0.219800	−	0.162379i
$485$	2.27022	−	3.93213i	0.103085	−	0.178549i
$486$	−4.65802	−	22.3507i	−0.211292	−	1.01385i
$487$	−21.9822	+	12.6914i	−0.996108	+	0.575103i	−0.907095	−	0.420927i	$-0.861705\pi$
$487$	−21.9822	+	12.6914i	−0.996108	+	0.575103i	−0.0890138	+	0.996030i	$0.528372\pi$
$488$	2.72254	+	29.2543i	0.123244	+	1.32428i
$489$			4.07212i			0.184147i
$490$	−6.68778	−	7.29888i	−0.302123	−	0.329730i
$491$			36.4635i			1.64557i	0.568350	+	0.822787i	$0.307582\pi$
$491$			36.4635i			1.64557i	−0.568350	+	0.822787i	$0.692418\pi$
$492$	5.29289	+	12.1469i	0.238622	+	0.547627i
$493$	0.220133	−	0.127094i	0.00991429	−	0.00572402i
$494$	−20.6362	+	4.30072i	−0.928467	+	0.193498i
$495$	4.09369	−	7.09048i	0.183998	−	0.318693i
$496$	2.98403	+	9.70626i	0.133987	+	0.435824i
$497$	13.0411	−	22.9220i	0.584973	−	1.02819i
$498$	−3.14460	−	1.03558i	−0.140913	−	0.0464053i
$499$	−10.2874	−	5.93945i	−0.460528	−	0.265886i	0.251738	−	0.967795i	$-0.418998\pi$
$499$	−10.2874	−	5.93945i	−0.460528	−	0.265886i	−0.712266	+	0.701909i	$0.752331\pi$
$500$	−1.98732	−	0.224860i	−0.0888756	−	0.0100560i
$501$	−7.63194	−	13.2189i	−0.340970	−	0.590577i
$502$	−19.9158	+	17.7894i	−0.888884	+	0.793981i
$503$	−17.3055			−0.771614			−0.385807	−	0.922580i	$-0.626077\pi$
$503$	−17.3055			−0.771614			−0.385807	+	0.922580i	$0.626077\pi$
$504$	−14.9184	−	6.74224i	−0.664520	−	0.300323i
$505$	−9.14442			−0.406921
$506$	17.0209	−	15.2036i	0.756672	−	0.675884i
$507$	3.21939	+	5.57615i	0.142978	+	0.247646i
$508$	9.75846	+	1.10414i	0.432962	+	0.0489884i
$509$	−11.8717	−	6.85414i	−0.526205	−	0.303805i	0.213265	−	0.976994i	$-0.431590\pi$
$509$	−11.8717	−	6.85414i	−0.526205	−	0.303805i	−0.739470	+	0.673190i	$0.764924\pi$
$510$	0.706674	+	0.232721i	0.0312921	+	0.0103051i
$511$	25.9250	−	0.164236i	1.14685	−	0.00726537i
$512$	21.7562	−	6.21824i	0.961498	−	0.274810i
$513$	−14.3997	+	24.9410i	−0.635761	+	1.10117i
$514$	35.7671	−	7.45408i	1.57762	−	0.328785i
$515$	8.86113	−	5.11597i	0.390468	−	0.225437i
$516$	4.17700	+	9.58603i	0.183882	+	0.422002i
$517$			43.3247i			1.90542i
$518$	12.9714	−	40.2449i	0.569930	−	1.76826i
$519$			0.119597i			0.00524973i
$520$	−6.81507	+	0.634243i	−0.298861	+	0.0278134i
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.387171	−	0.922008i	$-0.373452\pi$
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.992068	+	0.125704i	$0.0401190\pi$
$522$	0.274873	+	1.31893i	0.0120309	+	0.0577279i
$523$	2.13211	−	3.69292i	0.0932306	−	0.161480i	−0.815638	−	0.578562i	$-0.803614\pi$
$523$	2.13211	−	3.69292i	0.0932306	−	0.161480i	0.908869	+	0.417082i	$0.136947\pi$
$524$	25.5363	+	18.8651i	1.11556	+	0.824126i
$525$	−2.05749	+	1.20534i	−0.0897964	+	0.0526052i
$526$	−4.73196	+	14.3689i	−0.206323	+	0.626515i
$527$	1.28333	+	0.740929i	0.0559026	+	0.0322754i
$528$	9.88173	+	9.18614i	0.430047	+	0.399776i
$529$	−2.20289	−	3.81552i	−0.0957778	−	0.165892i
$530$	−2.93459	−	3.28535i	−0.127470	−	0.142707i
$531$	−7.59279			−0.329499
$532$	13.2088	+	29.7968i	0.572675	+	1.29185i
$533$	−17.7879			−0.770482
$534$	−8.38927	−	9.39203i	−0.363039	−	0.406433i
$535$	3.16601	+	5.48368i	0.136878	+	0.237080i
$536$	−25.3016	−	11.6284i	−1.09286	−	0.502270i
$537$	12.5658	+	7.25487i	0.542254	+	0.313071i
$538$	−3.70038	+	11.2364i	−0.159535	+	0.484438i
$539$	−22.8516	−	12.8101i	−0.984288	−	0.551771i
$540$	−5.55640	+	7.52129i	−0.239110	+	0.323665i
$541$	3.34133	−	5.78736i	0.143655	−	0.248818i	−0.785215	−	0.619223i	$-0.787448\pi$
$541$	3.34133	−	5.78736i	0.143655	−	0.248818i	0.928870	+	0.370405i	$0.120781\pi$
$542$	−7.82248	−	37.5347i	−0.336004	−	1.61225i
$543$	−3.11679	+	1.79948i	−0.133754	+	0.0772229i
$544$	1.70750	−	2.82626i	0.0732084	−	0.121175i
$545$		−	18.7605i		−	0.803614i
$546$	−6.05158	+	5.47479i	−0.258984	+	0.234300i
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	14.3787	−	6.26534i	0.614226	−	0.267642i
$549$	−19.6805	+	11.3625i	−0.839942	+	0.484941i
$550$	−5.18132	+	1.07982i	−0.220932	+	0.0460436i
$551$	1.34113	−	2.32290i	0.0571339	−	0.0989589i
$552$	−8.96944	+	6.35469i	−0.381765	+	0.270474i
$553$	−0.613918	−	1.04795i	−0.0261064	−	0.0445633i
$554$	−4.51309	−	1.48625i	−0.191743	−	0.0631445i
$555$	−8.82059	−	5.09257i	−0.374413	−	0.216168i
$556$	−3.91355	+	34.5882i	−0.165972	+	1.46687i
$557$	−2.44203	−	4.22972i	−0.103472	−	0.179219i	0.809641	−	0.586926i	$-0.199662\pi$
$557$	−2.44203	−	4.22972i	−0.103472	−	0.179219i	−0.913113	+	0.407707i	$0.866329\pi$
$558$	−5.85769	+	5.23229i	−0.247976	+	0.221500i
$559$	−14.0378			−0.593734
$560$	3.17394	+	10.0958i	0.134124	+	0.426627i
$561$	1.96888			0.0831263
$562$	−7.74107	+	6.91459i	−0.326538	+	0.291674i
$563$	1.36792	+	2.36931i	0.0576509	+	0.0998543i	0.893410	−	0.449241i	$-0.148306\pi$
$563$	1.36792	+	2.36931i	0.0576509	+	0.0998543i	−0.835760	+	0.549096i	$0.814972\pi$
$564$	2.34611	−	20.7350i	0.0987891	−	0.873103i
$565$	−3.61866	−	2.08923i	−0.152238	−	0.0878947i
$566$	−9.67897	−	3.18747i	−0.406838	−	0.133979i
$567$	−0.0393726	−	6.21505i	−0.00165349	−	0.261008i
$568$	−23.0045	+	16.2983i	−0.965248	+	0.683861i
$569$	−2.29674	+	3.97807i	−0.0962843	+	0.166769i	−0.910144	−	0.414292i	$-0.864029\pi$
$569$	−2.29674	+	3.97807i	−0.0962843	+	0.166769i	0.813860	+	0.581062i	$0.197362\pi$
$570$	7.68582	−	1.60177i	0.321924	−	0.0670910i
$571$	−4.86573	+	2.80923i	−0.203625	+	0.117563i	−0.598345	−	0.801239i	$-0.704175\pi$
$571$	−4.86573	+	2.80923i	−0.203625	+	0.117563i	0.394720	+	0.918801i	$0.370841\pi$
$572$	−16.6049	+	7.23539i	−0.694286	+	0.302527i
$573$			18.0707i			0.754912i
$574$	5.78185	+	26.8891i	0.241330	+	1.12233i
$575$		−	4.31210i		−	0.179827i
$576$	11.3974	+	13.2817i	0.474892	+	0.553405i
$577$	−29.7446	+	17.1731i	−1.23828	+	0.714924i	−0.968743	−	0.248065i	$-0.920205\pi$
$577$	−29.7446	+	17.1731i	−1.23828	+	0.714924i	−0.269541	+	0.962989i	$0.586872\pi$
$578$	4.80673	+	23.0642i	0.199934	+	0.959345i
$579$	8.71499	−	15.0948i	0.362182	−	0.627318i
$580$	0.517501	−	0.700502i	0.0214881	−	0.0290868i
$581$	−5.97319	−	3.39835i	−0.247810	−	0.140987i
$582$	−1.81021	+	5.49684i	−0.0750358	+	0.227851i
$583$	−10.0956	−	5.82872i	−0.418118	−	0.241401i
$584$	−25.1832	−	11.5740i	−1.04209	−	0.478935i
$585$	−2.64701	−	4.58475i	−0.109440	−	0.189556i
$586$	7.98795	+	8.94273i	0.329979	+	0.369421i
$587$	40.1422			1.65685			0.828423	−	0.560103i	$-0.189238\pi$
$587$	40.1422			1.65685			0.828423	+	0.560103i	$0.189238\pi$
$588$	10.2430	+	7.36833i	0.422414	+	0.303865i
$589$	15.6369			0.644309
$590$	3.26976	+	3.66058i	0.134614	+	0.150704i
$591$	−0.737868	−	1.27802i	−0.0303518	−	0.0525709i
$592$	−30.7769	+	33.1074i	−1.26492	+	1.36071i
$593$	9.46884	+	5.46684i	0.388839	+	0.224496i	0.681657	−	0.731672i	$-0.261260\pi$
$593$	9.46884	+	5.46684i	0.388839	+	0.224496i	−0.292818	+	0.956168i	$0.594593\pi$
$594$	−7.74042	+	23.5043i	−0.317593	+	0.964394i
$595$	1.34233	+	0.763699i	0.0550303	+	0.0313086i
$596$	2.65675	+	1.96269i	0.108825	+	0.0803951i
$597$	−0.352969	+	0.611361i	−0.0144461	+	0.0250213i
$598$	−3.01079	−	14.4467i	−0.123120	−	0.590771i
$599$	−4.51466	+	2.60654i	−0.184464	+	0.106500i	−0.589388	−	0.807850i	$-0.700631\pi$
$599$	−4.51466	+	2.60654i	−0.184464	+	0.106500i	0.404924	+	0.914350i	$0.367298\pi$
$600$	2.53823	−	0.236220i	0.103623	−	0.00964363i
$601$		−	16.1103i		−	0.657154i	−0.944477	−	0.328577i	$-0.893431\pi$
$601$		−	16.1103i		−	0.657154i	0.944477	−	0.328577i	$-0.106569\pi$
$602$	4.56287	+	21.2202i	0.185969	+	0.864869i
$603$		−	21.5379i		−	0.877090i
$604$	−5.87700	−	13.4875i	−0.239132	−	0.548797i
$605$	−2.60329	+	1.50301i	−0.105839	+	0.0611060i
$606$	11.4103	−	2.37798i	0.463512	−	0.0965989i
$607$	−4.82810	+	8.36252i	−0.195967	+	0.339424i	−0.947217	−	0.320593i	$-0.896118\pi$
$607$	−4.82810	+	8.36252i	−0.195967	+	0.339424i	0.751250	+	0.660017i	$0.229451\pi$
$608$	0.692317	−	34.8368i	0.0280772	−	1.41282i
$609$	−0.00657809	−	1.03837i	−0.000266558	−	0.0420767i
$610$	13.9532	+	4.59506i	0.564949	+	0.186048i
$611$	24.2609	+	14.0070i	0.981491	+	0.566664i
$612$	2.53781	+	0.287146i	0.102585	+	0.0116072i
$613$	−3.92388	−	6.79635i	−0.158484	−	0.274502i	0.775838	−	0.630932i	$-0.217327\pi$
$613$	−3.92388	−	6.79635i	−0.158484	−	0.274502i	−0.934322	+	0.356430i	$0.883994\pi$
$614$	10.9976	−	9.82343i	0.443827	−	0.396441i
$615$	6.62501			0.267146
$616$	16.3347	+	22.7490i	0.658143	+	0.916582i
$617$	−28.8434			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$617$	−28.8434			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$618$	−9.72643	+	8.68797i	−0.391254	+	0.349481i
$619$	−1.24278	−	2.15256i	−0.0499517	−	0.0865189i	0.839968	−	0.542635i	$-0.182573\pi$
$619$	−1.24278	−	2.15256i	−0.0499517	−	0.0865189i	−0.889920	+	0.456116i	$0.849240\pi$
$620$	5.04511	+	0.570840i	0.202617	+	0.0229255i
$621$	−17.4604	−	10.0807i	−0.700660	−	0.404526i
$622$	−10.6465	−	3.50609i	−0.426885	−	0.140581i
$623$	−13.2134	−	22.5550i	−0.529383	−	0.903649i
$624$	8.33885	−	2.56364i	0.333821	−	0.102628i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	20.0286	−	4.17409i	0.800504	−	0.166830i
$627$	17.9927	−	10.3881i	0.718558	−	0.414860i
$628$	2.46269	+	5.65177i	0.0982722	+	0.225530i
$629$			6.59647i			0.263019i
$630$	−6.07015	+	5.49159i	−0.241841	+	0.218790i
$631$		−	8.90728i		−	0.354593i	−0.984157	−	0.177297i	$-0.943265\pi$
$631$		−	8.90728i		−	0.354593i	0.984157	−	0.177297i	$-0.0567352\pi$
$632$	0.120314	+	1.29280i	0.00478585	+	0.0514250i
$633$	7.20066	−	4.15730i	0.286200	−	0.165238i
$634$	1.02055	+	4.89694i	0.0405314	+	0.194482i
$635$	2.45518	−	4.25250i	0.0974309	−	0.168755i
$636$	4.51609	+	3.33630i	0.179075	+	0.132293i
$637$	−14.5614	+	8.65485i	−0.576944	+	0.342917i
$638$	0.720911	−	2.18910i	0.0285412	−	0.0866672i
$639$	−18.8848	−	10.9032i	−0.747073	−	0.431323i
$640$	1.49512	−	11.2145i	0.0590996	−	0.443291i
$641$	−7.31652	−	12.6726i	−0.288985	−	0.500537i	0.684583	−	0.728935i	$-0.259984\pi$
$641$	−7.31652	−	12.6726i	−0.288985	−	0.500537i	−0.973568	+	0.228398i	$0.926651\pi$
$642$	−5.37653	−	6.01917i	−0.212195	−	0.237558i
$643$	−24.2513			−0.956380			−0.478190	−	0.878256i	$-0.658707\pi$
$643$	−24.2513			−0.956380			−0.478190	+	0.878256i	$0.658707\pi$
$644$	−20.8598	+	9.24707i	−0.821990	+	0.364386i
$645$	5.22827			0.205863
$646$	−3.38730	−	3.79218i	−0.133272	−	0.149201i
$647$	−14.9578	−	25.9077i	−0.588053	−	1.01854i	−0.994487	−	0.104857i	$-0.966561\pi$
$647$	−14.9578	−	25.9077i	−0.588053	−	1.01854i	0.406435	−	0.913680i	$-0.366772\pi$
$648$	−2.77465	+	6.03722i	−0.108999	+	0.237164i
$649$	11.2487	+	6.49444i	0.441550	+	0.254929i
$650$	−1.07046	+	3.25054i	−0.0419870	+	0.127496i
$651$	5.22326	−	3.05993i	0.204716	−	0.119928i
$652$	5.36935	−	7.26808i	0.210280	−	0.284640i
$653$	7.78155	−	13.4780i	0.304516	−	0.527436i	−0.672638	−	0.739972i	$-0.734839\pi$
$653$	7.78155	−	13.4780i	0.304516	−	0.527436i	0.977153	+	0.212535i	$0.0681721\pi$
$654$	4.87863	+	23.4092i	0.190770	+	0.915373i
$655$	13.7477	−	7.93723i	0.537167	−	0.310133i
$656$	6.56957	−	28.6594i	0.256498	−	1.11896i
$657$		−	21.4371i		−	0.836340i
$658$	13.2879	−	41.2269i	0.518016	−	1.60719i
$659$			30.2702i			1.17916i	0.807710	+	0.589580i	$0.200707\pi$
$659$			30.2702i			1.17916i	−0.807710	+	0.589580i	$0.799293\pi$
$660$	6.18439	−	2.69478i	0.240727	−	0.104894i
$661$	15.5209	−	8.96099i	0.603693	−	0.348542i	−0.166800	−	0.985991i	$-0.553344\pi$
$661$	15.5209	−	8.96099i	0.603693	−	0.348542i	0.770493	+	0.637449i	$0.220010\pi$
$662$	−32.5761	+	6.78907i	−1.26611	+	0.263865i
$663$	0.636547	−	1.10253i	0.0247214	−	0.0428188i
$664$	4.24714	+	5.99470i	0.164821	+	0.232640i
$665$	16.2963	−	0.103238i	0.631944	−	0.00400339i
$666$	−33.2087	−	10.9363i	−1.28681	−	0.423772i
$667$	1.62619	+	0.938880i	0.0629662	+	0.0363536i
$668$	−3.80818	+	33.6569i	−0.147343	+	1.30222i
$669$	10.9226	+	18.9185i	0.422292	+	0.731432i
$670$	−10.3837	+	9.27506i	−0.401157	+	0.358327i
$671$	38.8754			1.50077
$672$	−6.58581	−	11.7721i	−0.254053	−	0.454119i
$673$	21.1876			0.816723			0.408362	−	0.912820i	$-0.366100\pi$
$673$	21.1876			0.816723			0.408362	+	0.912820i	$0.366100\pi$
$674$	5.37966	−	4.80529i	0.207217	−	0.185093i
$675$	2.33778	+	4.04915i	0.0899812	+	0.155852i
$676$	1.60641	−	14.1975i	0.0617850	−	0.546059i
$677$	−21.8732	−	12.6285i	−0.840657	−	0.485353i	0.0168308	−	0.999858i	$-0.494642\pi$
$677$	−21.8732	−	12.6285i	−0.840657	−	0.485353i	−0.857487	+	0.514505i	$0.827976\pi$
$678$	5.05863	+	1.66590i	0.194275	+	0.0639786i
$679$	−5.94041	+	10.4413i	−0.227972	+	0.400700i
$680$	−0.954444	−	1.34717i	−0.0366012	−	0.0516615i
$681$	−4.79140	+	8.29895i	−0.183607	+	0.318016i
$682$	13.1536	−	2.74128i	0.503676	−	0.104969i
$683$	19.1391	−	11.0499i	0.732336	−	0.422814i	−0.0869404	−	0.996214i	$-0.527709\pi$
$683$	19.1391	−	11.0499i	0.732336	−	0.422814i	0.819276	+	0.573399i	$0.194376\pi$
$684$	24.7068	−	10.7657i	0.944689	−	0.411637i
$685$		−	7.84221i		−	0.299635i
$686$	17.8162	+	19.1985i	0.680225	+	0.733004i
$687$		−	26.5993i		−	1.01483i
$688$	5.18452	−	22.6172i	0.197658	−	0.862273i
$689$	−6.52791	+	3.76889i	−0.248694	+	0.143583i
$690$	1.12135	+	5.38060i	0.0426891	+	0.204836i
$691$	9.05508	−	15.6839i	0.344471	−	0.596642i	−0.640786	−	0.767719i	$-0.721391\pi$
$691$	9.05508	−	15.6839i	0.344471	−	0.596642i	0.985258	+	0.171077i	$0.0547248\pi$
$692$	0.157697	−	0.213462i	0.00599473	−	0.00811461i
$693$	−10.7118	+	18.8279i	−0.406908	+	0.715212i
$694$	−0.737153	+	2.23841i	−0.0279819	+	0.0849691i
$695$	15.0727	+	8.70222i	0.571740	+	0.330094i
$696$	−0.463569	+	1.00865i	−0.0175715	+	0.0382330i
$697$	−2.14537	−	3.71588i	−0.0812615	−	0.140749i
$698$	−26.0098	−	29.1187i	−0.984486	−	1.10216i
$699$	−25.2991			−0.956901
$700$	5.26162	+	0.561602i	0.198870	+	0.0212265i
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	10.6594	+	11.9335i	0.402313	+	0.450401i
$703$	34.8038	+	60.2820i	1.31265	+	2.27358i
$704$	−5.52481	−	29.4255i	−0.208224	−	1.10902i
$705$	−9.03582	−	5.21684i	−0.340309	−	0.196477i
$706$	12.0134	−	36.4796i	0.452131	−	1.37293i
$707$	24.1934	−	0.153266i	0.909885	−	0.00576416i
$708$	−5.03189	−	3.71735i	−0.189110	−	0.139706i
$709$	18.5131	−	32.0657i	0.695275	−	1.20425i	−0.274814	−	0.961498i	$-0.588616\pi$
$709$	18.5131	−	32.0657i	0.695275	−	1.20425i	0.970088	−	0.242753i	$-0.0780505\pi$
$710$	2.87600	+	13.8000i	0.107934	+	0.517904i
$711$	−0.869718	+	0.502132i	−0.0326170	+	0.0188314i
$712$	2.58953	+	27.8251i	0.0970469	+	1.04279i
$713$			10.9469i			0.409965i
$714$	−1.87355	−	0.603866i	−0.0701157	−	0.0225991i
$715$			9.05640i			0.338690i
$716$	−12.8620	−	29.5176i	−0.480674	−	1.10312i
$717$	10.6369	−	6.14124i	0.397244	−	0.229349i
$718$	23.1967	−	4.83433i	0.865692	−	0.180416i
$719$	−10.0975	+	17.4894i	−0.376573	+	0.652243i	−0.990561	−	0.137072i	$-0.956231\pi$
$719$	−10.0975	+	17.4894i	−0.376573	+	0.652243i	0.613988	+	0.789315i	$0.289564\pi$
$720$	8.36443	−	2.57151i	0.311724	−	0.0958345i
$721$	−23.3581	+	13.6838i	−0.869902	+	0.509613i
$722$	−25.4412	−	8.37828i	−0.946824	−	0.311807i
$723$	−3.28401	−	1.89602i	−0.122134	−	0.0705138i
$724$	7.93570	+	0.897902i	0.294928	+	0.0333703i
$725$	−0.217731	−	0.377122i	−0.00808634	−	0.0140060i
$726$	2.85750	−	2.55242i	0.106052	−	0.0947292i
$727$	10.7925			0.400272			0.200136	−	0.979768i	$-0.435862\pi$
$727$	10.7925			0.400272			0.200136	+	0.979768i	$0.435862\pi$
$728$	18.0200	−	1.79224i	0.667865	−	0.0664248i
$729$	7.50278			0.277881
$730$	−10.3351	+	9.23166i	−0.382519	+	0.341679i
$731$	−1.69306	−	2.93247i	−0.0626202	−	0.108461i
$732$	−18.6056	−	2.10517i	−0.687683	−	0.0778094i
$733$	6.26329	+	3.61611i	0.231340	+	0.133564i	0.611190	−	0.791484i	$-0.290691\pi$
$733$	6.26329	+	3.61611i	0.231340	+	0.133564i	−0.379850	+	0.925048i	$0.624024\pi$
$734$	11.3427	+	3.73538i	0.418668	+	0.137875i
$735$	5.42330	−	3.22344i	0.200042	−	0.118898i
$736$	24.3881	+	0.484669i	0.898958	+	0.0178651i
$737$	−18.4223	+	31.9083i	−0.678593	+	1.17536i
$738$	22.2637	−	4.63990i	0.819539	−	0.170797i
$739$	1.71927	−	0.992622i	0.0632444	−	0.0365142i	−0.468044	−	0.883705i	$-0.655041\pi$
$739$	1.71927	−	0.992622i	0.0632444	−	0.0365142i	0.531289	+	0.847191i	$0.321708\pi$
$740$	9.02848	+	20.7200i	0.331893	+	0.761681i
$741$		−	13.4340i		−	0.493511i
$742$	7.81909	+	8.64286i	0.287048	+	0.317289i
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	−6.44368	+	0.599680i	−0.236237	+	0.0219853i
$745$	1.43029	−	0.825776i	0.0524016	−	0.0302541i
$746$	−2.99416	−	14.3669i	−0.109624	−	0.526011i
$747$	−2.84124	+	4.92116i	−0.103955	+	0.180056i
$748$	−3.51414	−	2.59610i	−0.128490	−	0.0949228i
$749$	−8.46821	−	14.4551i	−0.309421	−	0.528178i
$750$	0.398687	−	1.21064i	0.0145580	−	0.0442064i
$751$	−20.8718	−	12.0504i	−0.761624	−	0.439724i	0.0682545	−	0.997668i	$-0.478257\pi$
$751$	−20.8718	−	12.0504i	−0.761624	−	0.439724i	−0.829879	+	0.557944i	$0.811590\pi$
$752$	−31.5279	+	33.9153i	−1.14971	+	1.23676i
$753$	−8.50921	−	14.7384i	−0.310093	−	0.537097i
$754$	−0.992774	−	1.11144i	−0.0361547	−	0.0404762i
$755$	−7.35613			−0.267717
$756$	14.5745	−	19.9922i	0.530070	−	0.727109i
$757$	34.8711			1.26741			0.633706	−	0.773574i	$-0.281533\pi$
$757$	34.8711			1.26741			0.633706	+	0.773574i	$0.281533\pi$
$758$	−11.1146	−	12.4431i	−0.403702	−	0.451955i
$759$	7.27236	+	12.5961i	0.263970	+	0.457209i
$760$	−15.8300	−	7.27534i	−0.574215	−	0.263904i
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	0.634113	−	0.773240i	$-0.281365\pi$
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	−0.352589	+	0.935778i	$0.614699\pi$
$762$	−1.95770	+	5.94469i	−0.0709200	+	0.215353i
$763$	0.314438	+	49.6347i	0.0113834	+	1.79690i
$764$	23.8273	−	32.2533i	0.862043	−	1.16688i
$765$	0.638500	−	1.10591i	0.0230850	−	0.0399844i
$766$	0.276138	+	1.32500i	0.00997727	+	0.0478741i
$767$	7.27349	−	4.19935i	0.262631	−	0.151630i
$768$	1.05071	+	14.3821i	0.0379141	+	0.518970i
$769$		−	0.573577i		−	0.0206837i	−0.999947	−	0.0103419i	$-0.996708\pi$
$769$		−	0.573577i		−	0.0206837i	0.999947	−	0.0103419i	$-0.00329197\pi$
$770$	13.6901	−	2.94372i	0.493357	−	0.106084i
$771$			23.2841i			0.838556i
$772$	−35.4584	+	15.4506i	−1.27617	+	0.556078i
$773$	−3.76591	+	2.17425i	−0.135450	+	0.0782023i	−0.566194	−	0.824272i	$-0.691585\pi$
$773$	−3.76591	+	2.17425i	−0.135450	+	0.0782023i	0.430744	+	0.902474i	$0.358251\pi$
$774$	17.5699	−	3.66168i	0.631537	−	0.131616i
$775$	1.26933	−	2.19854i	0.0455955	−	0.0789738i
$776$	10.4789	−	7.42411i	0.376170	−	0.266510i
$777$	23.4220	+	13.3256i	0.840259	+	0.478052i
$778$	40.5179	+	13.3433i	1.45264	+	0.478381i
$779$	−39.2109	−	22.6384i	−1.40488	−	0.811107i
$780$	0.490420	−	4.33436i	0.0175599	−	0.155195i
$781$	18.6519	+	32.3060i	0.667417	+	1.15600i
$782$	2.65478	−	2.37134i	0.0949348	−	0.0847990i
$783$	−2.03603			−0.0727618
$784$	−8.56651	−	26.6574i	−0.305947	−	0.952049i
$785$	3.08251			0.110019
$786$	−15.0902	+	13.4790i	−0.538249	+	0.480782i
$787$	−10.5248	−	18.2295i	−0.375168	−	0.649811i	0.615184	−	0.788384i	$-0.289082\pi$
$787$	−10.5248	−	18.2295i	−0.375168	−	0.649811i	−0.990352	+	0.138573i	$0.955748\pi$
$788$	−0.368181	+	3.25400i	−0.0131159	+	0.115919i
$789$	−8.34944	−	4.82055i	−0.297248	−	0.171616i
$790$	0.616619	+	0.203065i	0.0219383	+	0.00722471i
$791$	9.60890	+	5.46683i	0.341653	+	0.194378i
$792$	18.8957	−	13.3873i	0.671428	−	0.475695i
$793$	12.5686	−	21.7694i	0.446323	−	0.773054i
$794$	−8.59335	+	1.79091i	−0.304967	+	0.0635570i
$795$	2.43128	−	1.40370i	0.0862286	−	0.0497841i
$796$	1.43611	−	0.625770i	0.0509017	−	0.0221798i
$797$		−	14.7349i		−	0.521938i	−0.965347	−	0.260969i	$-0.915958\pi$
$797$		−	14.7349i		−	0.521938i	0.965347	−	0.260969i	$-0.0840420\pi$
$798$	−20.3075	+	4.36663i	−0.718879	+	0.154577i
$799$			6.75744i			0.239061i
$800$	−4.84181	−	2.92521i	−0.171184	−	0.103422i
$801$	−18.7190	+	10.8074i	−0.661403	+	0.381861i
$802$	7.59213	+	36.4295i	0.268087	+	1.28637i
$803$	−18.3360	+	31.7590i	−0.647065	+	1.12075i
$804$	10.5447	−	14.2736i	0.371883	−	0.503390i
$805$	0.0722735	+	11.4085i	0.00254731	+	0.402097i
$806$	2.71753	−	8.25198i	0.0957210	−	0.290663i
$807$	−6.52923	−	3.76965i	−0.229840	−	0.132698i
$808$	−23.5011	−	10.8009i	−0.826767	−	0.379975i
$809$	7.23808	+	12.5367i	0.254477	+	0.440768i	0.964753	−	0.263156i	$-0.0847632\pi$
$809$	7.23808	+	12.5367i	0.254477	+	0.440768i	−0.710276	+	0.703923i	$0.751430\pi$
$810$	2.21312	+	2.47765i	0.0777613	+	0.0870559i
$811$	−18.5825			−0.652521			−0.326260	−	0.945280i	$-0.605789\pi$
$811$	−18.5825			−0.652521			−0.326260	+	0.945280i	$0.605789\pi$
$812$	−1.35741	+	1.86199i	−0.0476358	+	0.0653431i
$813$	24.4348			0.856967
$814$	39.8444	+	44.6069i	1.39654	+	1.56347i
$815$	−2.25908	−	3.91284i	−0.0791321	−	0.137061i
$816$	1.54127	+	1.43278i	0.0539553	+	0.0501573i
$817$	−30.9442	−	17.8656i	−1.08260	−	0.625040i
$818$	−8.14069	+	24.7198i	−0.284633	+	0.864306i
$819$	7.08003	+	12.0855i	0.247396	+	0.422302i
$820$	−11.8246	−	8.73551i	−0.412933	−	0.305057i
$821$	8.20275	−	14.2076i	0.286278	−	0.495848i	−0.686640	−	0.726997i	$-0.740915\pi$
$821$	8.20275	−	14.2076i	0.286278	−	0.495848i	0.972918	+	0.231149i	$0.0742486\pi$
$822$	2.03934	+	9.78542i	0.0711303	+	0.341306i
$823$	−38.0161	+	21.9486i	−1.32516	+	0.765081i	−0.984547	−	0.175123i	$-0.943968\pi$
$823$	−38.0161	+	21.9486i	−1.32516	+	0.765081i	−0.340612	+	0.940204i	$0.610634\pi$
$824$	28.8158	−	2.68173i	1.00385	−	0.0934226i
$825$		−	3.37300i		−	0.117433i
$826$	−8.71214	−	9.63000i	−0.303134	−	0.335070i
$827$			8.10796i			0.281941i	0.990014	+	0.140971i	$0.0450224\pi$
$827$			8.10796i			0.281941i	−0.990014	+	0.140971i	$0.954978\pi$
$828$	7.53673	+	17.2964i	0.261919	+	0.601093i
$829$	−36.5657	+	21.1112i	−1.26998	+	0.733223i	−0.974984	−	0.222276i	$-0.928651\pi$
$829$	−36.5657	+	21.1112i	−1.26998	+	0.733223i	−0.294995	+	0.955499i	$0.595318\pi$
$830$	3.59611	−	0.749452i	0.124823	−	0.0260138i
$831$	1.51407	−	2.62245i	0.0525225	−	0.0909716i
$832$	−18.2639	−	6.41961i	−0.633185	−	0.222560i
$833$	−3.56421	−	1.99802i	−0.123492	−	0.0692273i
$834$	−21.0705	−	6.93893i	−0.729613	−	0.240275i
$835$	14.6668	+	8.46791i	0.507567	+	0.293044i
$836$	−45.8114	−	5.18343i	−1.58442	−	0.179273i
$837$	−5.93481	−	10.2794i	−0.205137	−	0.355308i
$838$	37.1710	−	33.2024i	1.28405	−	1.14696i
$839$	−31.8404			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$839$	−31.8404			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$840$	−6.71143	+	0.667509i	−0.231566	+	0.0230312i
$841$	−28.8104			−0.993461
$842$	−16.5242	+	14.7599i	−0.569460	+	0.508661i
$843$	−3.30745	−	5.72868i	−0.113915	−	0.197306i
$844$	−18.3337	−	2.07441i	−0.631072	−	0.0714040i
$845$	−6.18694	−	3.57203i	−0.212837	−	0.122882i
$846$	−34.0191	−	11.2031i	−1.16960	−	0.385171i
$847$	6.86233	−	4.02014i	0.235792	−	0.138134i
$848$	−3.66139	−	11.9095i	−0.125733	−	0.408975i
$849$	3.24714	−	5.62422i	0.111442	−	0.193023i
$850$	−0.808139	+	0.168421i	−0.0277190	+	0.00577681i
$851$	−42.2015	+	24.3650i	−1.44665	+	0.835223i
$852$	−7.17729	−	16.4716i	−0.245890	−	0.564306i
$853$			16.2023i			0.554755i	0.960761	+	0.277378i	$0.0894653\pi$
$853$			16.2023i			0.554755i	−0.960761	+	0.277378i	$0.910535\pi$
$854$	−36.9930	−	11.9233i	−1.26587	−	0.408006i
$855$		−	13.4752i		−	0.460843i
$856$	1.65958	+	17.8326i	0.0567234	+	0.609505i
$857$	35.4659	−	20.4762i	1.21149	−	0.699455i	0.248407	−	0.968656i	$-0.420093\pi$
$857$	35.4659	−	20.4762i	1.21149	−	0.699455i	0.963084	+	0.269201i	$0.0867596\pi$
$858$	−2.35509	−	11.3005i	−0.0804015	−	0.385792i
$859$	−6.02640	+	10.4380i	−0.205618	+	0.356141i	−0.950329	−	0.311246i	$-0.899254\pi$
$859$	−6.02640	+	10.4380i	−0.205618	+	0.356141i	0.744711	+	0.667387i	$0.232587\pi$
$860$	−9.33165	−	6.89382i	−0.318206	−	0.235077i
$861$	−17.5278	+	0.111039i	−0.597345	+	0.00378421i
$862$	−0.887107	+	2.69376i	−0.0302150	+	0.0917499i
$863$	−0.494372	−	0.285426i	−0.0168286	−	0.00971602i	0.491562	−	0.870843i	$-0.336426\pi$
$863$	−0.494372	−	0.285426i	−0.0168286	−	0.00971602i	−0.508391	+	0.861127i	$0.669759\pi$
$864$	−23.1637	+	12.7668i	−0.788045	+	0.434334i
$865$	−0.0663486	−	0.114919i	−0.00225592	−	0.00390737i
$866$	12.8106	+	14.3418i	0.435323	+	0.487356i
$867$	−15.0146			−0.509924
$868$	−13.3574	−	1.42571i	−0.453380	−	0.0483918i
$869$	1.71798			0.0582784
$870$	0.369753	+	0.413948i	0.0125358	+	0.0140342i
$871$	11.9120	+	20.6321i	0.403622	+	0.699093i
$872$	22.1590	−	48.2146i	0.750398	−	1.63275i
$873$	8.60232	+	4.96655i	0.291144	+	0.168092i
$874$	11.7493	−	35.6775i	0.397426	−	1.20681i
$875$	1.30833	−	2.29962i	0.0442298	−	0.0777414i
$876$	10.4954	−	14.2068i	0.354605	−	0.480003i
$877$	−9.47193	+	16.4059i	−0.319844	+	0.553987i	−0.980455	−	0.196742i	$-0.936964\pi$
$877$	−9.47193	+	16.4059i	−0.319844	+	0.553987i	0.660611	+	0.750728i	$0.270297\pi$
$878$	8.38165	+	40.2178i	0.282867	+	1.35729i
$879$	−6.61794	+	3.82087i	−0.223218	+	0.128875i
$880$	−14.5914	−	3.34477i	−0.491876	−	0.112752i
$881$			35.7695i			1.20511i	0.798079	+	0.602553i	$0.205850\pi$
$881$			35.7695i			1.20511i	−0.798079	+	0.602553i	$0.794150\pi$
$882$	15.9677	−	14.6308i	0.537662	−	0.492646i
$883$		−	25.4594i		−	0.856776i	−0.903595	−	0.428388i	$-0.859082\pi$
$883$		−	25.4594i		−	0.856776i	0.903595	−	0.428388i	$-0.140918\pi$
$884$	−2.58990	+	1.12852i	−0.0871076	+	0.0379561i
$885$	−2.70897	+	1.56402i	−0.0910609	+	0.0525740i
$886$	20.2639	−	4.22313i	0.680779	−	0.141879i
$887$	−5.30243	+	9.18408i	−0.178038	+	0.308371i	−0.941209	−	0.337826i	$-0.890308\pi$
$887$	−5.30243	+	9.18408i	−0.178038	+	0.308371i	0.763170	+	0.646197i	$0.223642\pi$
$888$	−16.6538	−	23.5063i	−0.558865	−	0.788821i
$889$	−6.42439	+	11.2920i	−0.215467	+	0.378721i
$890$	13.2715	+	4.37057i	0.444863	+	0.146502i
$891$	7.61364	+	4.39574i	0.255067	+	0.147263i
$892$	5.45015	−	48.1687i	0.182485	−	1.61281i
$893$	35.6531	+	61.7530i	1.19309	+	2.06648i
$894$	−1.56996	+	1.40234i	−0.0525072	+	0.0469012i
$895$	−16.0991			−0.538132
$896$	−3.76766	+	29.6952i	−0.125869	+	0.992047i
$897$	9.40472			0.314014
$898$	−28.5511	+	25.5028i	−0.952763	+	0.851040i
$899$	0.552744	+	0.957381i	0.0184350	+	0.0319304i
$900$	0.491925	−	4.34765i	0.0163975	−	0.144922i
$901$	−1.57463	−	0.909116i	−0.0524587	−	0.0302870i
$902$	−36.9523	−	12.1691i	−1.23038	−	0.405187i
$903$	−13.8324	+	0.0876291i	−0.460315	+	0.00291611i
$904$	−6.83225	−	9.64350i	−0.227237	−	0.320738i
$905$	1.99658	−	3.45818i	0.0663687	−	0.114954i
$906$	9.17891	−	1.91294i	0.304949	−	0.0635533i
$907$	13.3054	−	7.68190i	0.441800	−	0.255073i	−0.262561	−	0.964915i	$-0.584567\pi$
$907$	13.3054	−	7.68190i	0.441800	−	0.255073i	0.704361	+	0.709842i	$0.251234\pi$
$908$	19.4946	−	8.49454i	0.646951	−	0.281901i
$909$		−	20.0052i		−	0.663531i
$910$	2.77764	−	8.61788i	0.0920779	−	0.285680i
$911$		−	22.0734i		−	0.731324i	−0.930748	−	0.365662i	$-0.880843\pi$
$911$		−	22.0734i		−	0.731324i	0.930748	−	0.365662i	$-0.119157\pi$
$912$	21.6445	+	4.96154i	0.716720	+	0.164293i
$913$	8.41856	−	4.86046i	0.278614	−	0.160858i
$914$	−2.19461	−	10.5304i	−0.0725911	−	0.348315i
$915$	−4.68108	+	8.10787i	−0.154752	+	0.268038i
$916$	−35.0729	+	47.4755i	−1.15884	+	1.56864i
$917$	−36.2392	+	21.2299i	−1.19672	+	0.701074i
$918$	−1.20729	+	3.66601i	−0.0398464	+	0.120996i
$919$	45.1598	+	26.0730i	1.48968	+	0.860069i	0.999930	−	0.0117923i	$-0.00375369\pi$
$919$	45.1598	+	26.0730i	1.48968	+	0.860069i	0.489753	+	0.871861i	$0.337087\pi$
$920$	5.09323	−	11.0821i	0.167919	−	0.365366i
$921$	4.69884	+	8.13863i	0.154832	+	0.268177i
$922$	12.0546	+	13.4954i	0.396996	+	0.444448i
$923$	24.1209			0.793949
$924$	−16.3169	+	7.23322i	−0.536785	+	0.237955i
$925$	11.3008			0.371567
$926$	26.3016	+	29.4454i	0.864323	+	0.967634i
$927$	11.1922	+	19.3855i	0.367600	+	0.636702i
$928$	2.15737	−	1.18904i	0.0708193	−	0.0390323i
$929$	24.8707	+	14.3591i	0.815982	+	0.471107i	0.849029	−	0.528346i	$-0.177188\pi$
$929$	24.8707	+	14.3591i	0.815982	+	0.471107i	−0.0330469	+	0.999454i	$0.510521\pi$
$930$	−1.01213	+	3.07340i	−0.0331890	+	0.100781i
$931$	−43.1134	+	0.546272i	−1.41298	+	0.0179033i
$932$	45.1549	+	33.3585i	1.47910	+	1.09270i
$933$	3.57173	−	6.18641i	0.116933	−	0.202534i
$934$	−6.52394	−	31.3039i	−0.213470	−	1.02430i
$935$	−1.89187	+	1.09227i	−0.0618708	+	0.0357211i
$936$	−1.38753	−	14.9093i	−0.0453529	−	0.487326i
$937$		−	44.9045i		−	1.46697i	−0.679707	−	0.733484i	$-0.737893\pi$
$937$		−	44.9045i		−	1.46697i	0.679707	−	0.733484i	$-0.262107\pi$
$938$	27.3167	−	24.7131i	0.891921	−	0.806910i
$939$			13.0385i			0.425495i
$940$	9.24879	+	21.2256i	0.301662	+	0.692301i
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	−0.228048	−	0.973650i	$-0.573234\pi$
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	0.729182	+	0.684320i	$0.239901\pi$
$942$	−3.84632	+	0.801598i	−0.125320	+	0.0261175i
$943$	15.8484	−	27.4503i	0.516096	−	0.893905i
$944$	4.07957	+	13.2698i	0.132779	+	0.431894i
$945$	−6.25292	−	10.6737i	−0.203408	−	0.347214i
$946$	−29.1618	−	9.60352i	−0.948130	−	0.312237i
$947$	32.1100	+	18.5387i	1.04344	+	0.602428i	0.920804	−	0.390025i	$-0.127533\pi$
$947$	32.1100	+	18.5387i	1.04344	+	0.602428i	0.122631	+	0.992452i	$0.460867\pi$
$948$	−0.822218	−	0.0930316i	−0.0267044	−	0.00302153i
$949$	11.8562	+	20.5356i	0.384869	+	0.666613i
$950$	−6.49659	+	5.80297i	−0.210777	+	0.188273i
$951$	−3.18787			−0.103374
$952$	2.54775	+	3.54820i	0.0825730	+	0.114998i
$953$	−28.5420			−0.924567			−0.462283	−	0.886732i	$-0.652970\pi$
$953$	−28.5420			−0.924567			−0.462283	+	0.886732i	$0.652970\pi$
$954$	7.18736	−	6.41999i	0.232699	−	0.207855i
$955$	−10.0250	−	17.3638i	−0.324402	−	0.561881i
$956$	−27.0829	−	3.06435i	−0.875923	−	0.0991082i
$957$	1.27203	+	0.734408i	0.0411189	+	0.0237400i
$958$	29.5266	+	9.72368i	0.953962	+	0.314158i
$959$	0.131440	+	20.7481i	0.00424442	+	0.669991i
$960$	6.80226	+	2.39094i	0.219542	+	0.0771674i
$961$	12.2776	−	21.2655i	0.396052	−	0.685983i
$962$	37.8607	−	7.89042i	1.22068	−	0.254397i
$963$	−11.9966	+	6.92626i	−0.386586	+	0.223196i
$964$	3.36141	+	7.71428i	0.108264	+	0.248460i
$965$			19.3392i			0.622550i
$966$	−3.05694	−	14.2166i	−0.0983554	−	0.457413i
$967$		−	5.33936i		−	0.171702i	−0.996308	−	0.0858510i	$-0.972639\pi$
$967$		−	5.33936i		−	0.171702i	0.996308	−	0.0858510i	$-0.0273609\pi$
$968$	−8.46573	+	0.787860i	−0.272099	+	0.0253228i
$969$	2.80635	−	1.62025i	0.0901530	−	0.0520498i
$970$	−1.31006	−	6.28608i	−0.0420635	−	0.201834i
$971$	−5.49906	+	9.52465i	−0.176473	+	0.305660i	−0.940670	−	0.339323i	$-0.889802\pi$
$971$	−5.49906	+	9.52465i	−0.176473	+	0.305660i	0.764197	+	0.644983i	$0.223136\pi$
$972$	−25.9697	−	19.1853i	−0.832978	−	0.615368i
$973$	−40.0236	−	22.7708i	−1.28310	−	0.729999i
$974$	−11.2283	+	34.0955i	−0.359778	+	1.09249i
$975$	−1.88881	−	1.09050i	−0.0604902	−	0.0349241i
$976$	30.4323	+	28.2901i	0.974113	+	0.905544i
$977$	15.7434	+	27.2684i	0.503676	+	0.872392i	0.999991	+	0.00424979i	$0.00135275\pi$
$977$	15.7434	+	27.2684i	0.503676	+	0.872392i	−0.496315	+	0.868142i	$0.665314\pi$
$978$	3.83638	+	4.29493i	0.122674	+	0.137337i
$979$	36.9761			1.18176
$980$	−13.9301	−	1.39764i	−0.444979	−	0.0446460i
$981$	41.0424			1.31038
$982$	34.3526	+	38.4587i	1.09624	+	1.22727i
$983$	−17.2762	−	29.9232i	−0.551025	−	0.954402i	−0.998201	−	0.0599567i	$-0.980904\pi$
$983$	−17.2762	−	29.9232i	−0.551025	−	0.954402i	0.447176	−	0.894446i	$-0.352430\pi$
$984$	17.0263	+	7.82512i	0.542777	+	0.249456i
$985$	1.41801	+	0.818690i	0.0451817	+	0.0260856i
$986$	0.112442	−	0.341438i	0.00358088	−	0.0108736i
$987$	23.9935	+	13.6507i	0.763722	+	0.434507i
$988$	−17.7136	+	23.9776i	−0.563545	+	0.762829i
$989$	12.5072	−	21.6630i	0.397704	−	0.688844i
$990$	−2.36232	−	11.3352i	−0.0750794	−	0.360255i
$991$	47.8668	−	27.6359i	1.52054	−	0.877884i	0.520833	−	0.853659i	$-0.325622\pi$
$991$	47.8668	−	27.6359i	1.52054	−	0.877884i	0.999707	−	0.0242247i	$-0.00771173\pi$
$992$	12.2917	+	7.42608i	0.390261	+	0.235778i
$993$		−	21.2068i		−	0.672978i
$994$	−7.84033	−	36.4623i	−0.248680	−	1.15652i
$995$		−	0.783264i		−	0.0248311i
$996$	−4.29229	+	1.87032i	−0.136007	+	0.0592632i
$997$	13.2344	−	7.64087i	0.419137	−	0.241989i	−0.275571	−	0.961281i	$-0.588867\pi$
$997$	13.2344	−	7.64087i	0.419137	−	0.241989i	0.694708	+	0.719292i	$0.255534\pi$
$998$	−16.4459	+	3.42744i	−0.520587	+	0.108494i
$999$	26.4187	−	45.7586i	0.835851	−	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.131.13	yes	32
4.3	odd	2	inner	140.2.o.a.131.9	yes	32
5.2	odd	4		700.2.t.d.299.11		32
5.3	odd	4		700.2.t.c.299.6		32
5.4	even	2		700.2.p.c.551.4		32
7.2	even	3		980.2.g.a.391.5		32
7.3	odd	6	inner	140.2.o.a.31.9	✓	32
7.4	even	3		980.2.o.f.31.9		32
7.5	odd	6		980.2.g.a.391.6		32
7.6	odd	2		980.2.o.f.411.13		32
20.3	even	4		700.2.t.c.299.1		32
20.7	even	4		700.2.t.d.299.16		32
20.19	odd	2		700.2.p.c.551.8		32
28.3	even	6	inner	140.2.o.a.31.13	yes	32
28.11	odd	6		980.2.o.f.31.13		32
28.19	even	6		980.2.g.a.391.7		32
28.23	odd	6		980.2.g.a.391.8		32
28.27	even	2		980.2.o.f.411.9		32
35.3	even	12		700.2.t.d.199.16		32
35.17	even	12		700.2.t.c.199.1		32
35.24	odd	6		700.2.p.c.451.8		32
140.3	odd	12		700.2.t.d.199.11		32
140.59	even	6		700.2.p.c.451.4		32
140.87	odd	12		700.2.t.c.199.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	7.3	odd	6	inner
140.2.o.a.31.13	yes	32	28.3	even	6	inner
140.2.o.a.131.9	yes	32	4.3	odd	2	inner
140.2.o.a.131.13	yes	32	1.1	even	1	trivial
700.2.p.c.451.4		32	140.59	even	6
700.2.p.c.451.8		32	35.24	odd	6
700.2.p.c.551.4		32	5.4	even	2
700.2.p.c.551.8		32	20.19	odd	2
700.2.t.c.199.1		32	35.17	even	12
700.2.t.c.199.6		32	140.87	odd	12
700.2.t.c.299.1		32	20.3	even	4
700.2.t.c.299.6		32	5.3	odd	4
700.2.t.d.199.11		32	140.3	odd	12
700.2.t.d.199.16		32	35.3	even	12
700.2.t.d.299.11		32	5.2	odd	4
700.2.t.d.299.16		32	20.7	even	4
980.2.g.a.391.5		32	7.2	even	3
980.2.g.a.391.6		32	7.5	odd	6
980.2.g.a.391.7		32	28.19	even	6
980.2.g.a.391.8		32	28.23	odd	6
980.2.o.f.31.9		32	7.4	even	3
980.2.o.f.31.13		32	28.11	odd	6
980.2.o.f.411.9		32	28.27	even	2
980.2.o.f.411.13		32	7.6	odd	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05472 - 0.942109i) q^{2} +(0.450639 + 0.780530i) q^{3} +(0.224860 - 1.98732i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.21064 + 0.398687i) q^{6} +(2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 - 1.89460i) q^{9} +(-1.38447 + 0.288532i) q^{10} +(-3.24107 + 1.87123i) q^{11} +(1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +(3.65805 - 0.786573i) q^{14} -0.901278i q^{15} +(-3.89888 - 0.893735i) q^{16} +(-0.505515 + 0.291859i) q^{17} +(-0.631220 - 3.02880i) q^{18} +(-3.07977 + 5.33433i) q^{19} +(-1.18839 + 1.60864i) q^{20} +(0.0151060 + 2.38451i) q^{21} +(-1.65551 + 5.02706i) q^{22} +(-3.73439 - 2.15605i) q^{23} +(1.06454 - 2.31628i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.27981 + 2.55232i) q^{26} +4.67556 q^{27} +(3.11717 - 4.27589i) q^{28} -0.435463 q^{29} +(-0.849103 - 0.950594i) q^{30} +(-1.26933 - 2.19854i) q^{31} +(-4.95421 + 2.73053i) q^{32} +(-2.92110 - 1.68650i) q^{33} +(-0.258212 + 0.784080i) q^{34} +(-1.33736 - 2.28286i) q^{35} +(-3.51922 - 2.59985i) q^{36} +(5.65039 - 9.78676i) q^{37} +(1.77723 + 8.52769i) q^{38} +(-1.88881 + 1.09050i) q^{39} +(0.262094 + 2.81626i) q^{40} +7.35068i q^{41} +(2.26240 + 2.50075i) q^{42} +5.80096i q^{43} +(2.98995 + 6.86180i) q^{44} +(-1.89460 + 1.09385i) q^{45} +(-5.96996 + 1.24418i) q^{46} +(5.78826 - 10.0256i) q^{47} +(-1.05940 - 3.44594i) q^{48} +(3.57652 + 6.01735i) q^{49} +(1.34325 + 0.442358i) q^{50} +(-0.455610 - 0.263046i) q^{51} +(4.80912 + 0.544138i) q^{52} +(1.55746 + 2.69759i) q^{53} +(4.93139 - 4.40489i) q^{54} +3.74246 q^{55} +(-0.740624 - 7.44657i) q^{56} -5.55147 q^{57} +(-0.459290 + 0.410254i) q^{58} +(-1.73534 - 3.00569i) q^{59} +(-1.79113 - 0.202661i) q^{60} +(-8.99597 - 5.19383i) q^{61} +(-3.41004 - 1.12299i) q^{62} +(4.99421 - 2.92575i) q^{63} +(-2.65284 + 7.54735i) q^{64} +(1.20995 - 2.09570i) q^{65} +(-4.66981 + 0.973217i) q^{66} +(8.52602 - 4.92250i) q^{67} +(0.466348 + 1.07025i) q^{68} -3.88640i q^{69} +(-3.56125 - 1.14783i) q^{70} -9.96771i q^{71} +(-6.16112 + 0.573383i) q^{72} +(8.48612 - 4.89946i) q^{73} +(-3.26063 - 15.6456i) q^{74} +(-0.450639 + 0.780530i) q^{75} +(9.90849 + 7.31997i) q^{76} +(-9.90142 + 0.0627260i) q^{77} +(-0.964785 + 2.92964i) q^{78} +(-0.397549 - 0.229525i) q^{79} +(2.92966 + 2.72344i) q^{80} +(-1.17456 - 2.03439i) q^{81} +(6.92515 + 7.75290i) q^{82} -2.59747 q^{83} +(4.74218 + 0.506159i) q^{84} +0.583719 q^{85} +(5.46514 + 6.11837i) q^{86} +(-0.196236 - 0.339892i) q^{87} +(9.61812 + 4.42040i) q^{88} +(-8.55647 - 4.94008i) q^{89} +(-0.967745 + 2.93862i) q^{90} +(-3.16604 + 5.56486i) q^{91} +(-5.12447 + 6.93662i) q^{92} +(1.14402 - 1.98149i) q^{93} +(-3.34020 - 16.0273i) q^{94} +(5.33433 - 3.07977i) q^{95} +(-4.36382 - 2.63643i) q^{96} +4.54044i q^{97} +(9.44122 + 2.97713i) q^{98} +8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Introduction

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