LMFDB - Embedded newform 840.2.w.b.139.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(139,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.w (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.4
Character	$\chi$	$=$	840.139
Dual form			840.2.w.b.139.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38753 + 0.273429i) q^{2} +1.00000 q^{3} +(1.85047 - 0.758780i) q^{4} +(-0.840958 + 2.07190i) q^{5} +(-1.38753 + 0.273429i) q^{6} +(-2.31981 - 1.27219i) q^{7} +(-2.36011 + 1.55880i) q^{8} +1.00000 q^{9} +(0.600336 - 3.10477i) q^{10} -1.15873 q^{11} +(1.85047 - 0.758780i) q^{12} -0.698885i q^{13} +(3.56666 + 1.13089i) q^{14} +(-0.840958 + 2.07190i) q^{15} +(2.84850 - 2.80821i) q^{16} -6.87158 q^{17} +(-1.38753 + 0.273429i) q^{18} -4.94979i q^{19} +(0.0159494 + 4.47211i) q^{20} +(-2.31981 - 1.27219i) q^{21} +(1.60778 - 0.316831i) q^{22} +5.30311 q^{23} +(-2.36011 + 1.55880i) q^{24} +(-3.58558 - 3.48477i) q^{25} +(0.191095 + 0.969724i) q^{26} +1.00000 q^{27} +(-5.25807 - 0.593920i) q^{28} -10.0699i q^{29} +(0.600336 - 3.10477i) q^{30} +0.109215 q^{31} +(-3.18454 + 4.67533i) q^{32} -1.15873 q^{33} +(9.53452 - 1.87889i) q^{34} +(4.58672 - 3.73658i) q^{35} +(1.85047 - 0.758780i) q^{36} -4.30570 q^{37} +(1.35342 + 6.86798i) q^{38} -0.698885i q^{39} +(-1.24493 - 6.20082i) q^{40} -2.58861i q^{41} +(3.56666 + 1.13089i) q^{42} -7.55358i q^{43} +(-2.14421 + 0.879225i) q^{44} +(-0.840958 + 2.07190i) q^{45} +(-7.35822 + 1.45002i) q^{46} +3.53225i q^{47} +(2.84850 - 2.80821i) q^{48} +(3.76308 + 5.90248i) q^{49} +(5.92793 + 3.85482i) q^{50} -6.87158 q^{51} +(-0.530300 - 1.29327i) q^{52} +1.70909 q^{53} +(-1.38753 + 0.273429i) q^{54} +(0.974447 - 2.40079i) q^{55} +(7.45811 - 0.613625i) q^{56} -4.94979i q^{57} +(2.75339 + 13.9722i) q^{58} +12.3942i q^{59} +(0.0159494 + 4.47211i) q^{60} -4.88851 q^{61} +(-0.151539 + 0.0298626i) q^{62} +(-2.31981 - 1.27219i) q^{63} +(3.14027 - 7.35790i) q^{64} +(1.44802 + 0.587733i) q^{65} +(1.60778 - 0.316831i) q^{66} -8.12528i q^{67} +(-12.7157 + 5.21402i) q^{68} +5.30311 q^{69} +(-5.34252 + 6.43875i) q^{70} -5.80082i q^{71} +(-2.36011 + 1.55880i) q^{72} -3.86018 q^{73} +(5.97428 - 1.17730i) q^{74} +(-3.58558 - 3.48477i) q^{75} +(-3.75581 - 9.15946i) q^{76} +(2.68805 + 1.47413i) q^{77} +(0.191095 + 0.969724i) q^{78} +6.30589i q^{79} +(3.42286 + 8.26341i) q^{80} +1.00000 q^{81} +(0.707800 + 3.59177i) q^{82} -12.7204 q^{83} +(-5.25807 - 0.593920i) q^{84} +(5.77872 - 14.2373i) q^{85} +(2.06536 + 10.4808i) q^{86} -10.0699i q^{87} +(2.73474 - 1.80624i) q^{88} -0.841441i q^{89} +(0.600336 - 3.10477i) q^{90} +(-0.889113 + 1.62128i) q^{91} +(9.81326 - 4.02390i) q^{92} +0.109215 q^{93} +(-0.965818 - 4.90110i) q^{94} +(10.2555 + 4.16257i) q^{95} +(-3.18454 + 4.67533i) q^{96} -0.0488298 q^{97} +(-6.83529 - 7.16093i) q^{98} -1.15873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{9} + 8 q^{10} - 2 q^{14} + 8 q^{16} + 4 q^{20} + 48 q^{27} + 14 q^{28} + 8 q^{30} + 8 q^{35} - 12 q^{38} + 8 q^{40} - 2 q^{42} + 4 q^{44} - 8 q^{46} + 8 q^{48} - 12 q^{50} - 36 q^{52}+ \cdots + 40 q^{98}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^9 + 8 * q^10 - 2 * q^14 + 8 * q^16 + 4 * q^20 + 48 * q^27 + 14 * q^28 + 8 * q^30 + 8 * q^35 - 12 * q^38 + 8 * q^40 - 2 * q^42 + 4 * q^44 - 8 * q^46 + 8 * q^48 - 12 * q^50 - 36 * q^52 - 14 * q^56 + 4 * q^60 - 16 * q^62 + 24 * q^64 - 28 * q^68 + 6 * q^70 - 56 * q^74 - 20 * q^80 + 48 * q^81 + 36 * q^82 + 14 * q^84 - 20 * q^86 + 8 * q^90 - 16 * q^91 - 48 * q^97 + 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.38753	+	0.273429i	−0.981131	+	0.193343i
$2$	−1.38753	+	0.273429i	−0.981131	+	0.193343i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.85047	−	0.758780i	0.925237	−	0.379390i
$5$	−0.840958	+	2.07190i	−0.376088	+	0.926584i
$5$	−0.840958	+	2.07190i	−0.376088	+	0.926584i
$6$	−1.38753	+	0.273429i	−0.566456	+	0.111627i
$7$	−2.31981	−	1.27219i	−0.876807	−	0.480842i
$7$	−2.31981	−	1.27219i	−0.876807	−	0.480842i
$8$	−2.36011	+	1.55880i	−0.834426	+	0.551120i
$9$	1.00000			0.333333
$10$	0.600336	−	3.10477i	0.189843	−	0.981814i
$11$	−1.15873			−0.349372			−0.174686	−	0.984624i	$-0.555891\pi$
$11$	−1.15873			−0.349372			−0.174686	+	0.984624i	$0.555891\pi$
$12$	1.85047	−	0.758780i	0.534186	−	0.219041i
$13$		−	0.698885i		−	0.193836i	−0.995292	−	0.0969180i	$-0.969102\pi$
$13$		−	0.698885i		−	0.193836i	0.995292	−	0.0969180i	$-0.0308984\pi$
$14$	3.56666	+	1.13089i	0.953231	+	0.302244i
$15$	−0.840958	+	2.07190i	−0.217135	+	0.534963i
$16$	2.84850	−	2.80821i	0.712126	−	0.702052i
$17$	−6.87158			−1.66660			−0.833302	−	0.552818i	$-0.813552\pi$
$17$	−6.87158			−1.66660			−0.833302	+	0.552818i	$0.813552\pi$
$18$	−1.38753	+	0.273429i	−0.327044	+	0.0644478i
$19$		−	4.94979i		−	1.13556i	−0.823180	−	0.567780i	$-0.807802\pi$
$19$		−	4.94979i		−	1.13556i	0.823180	−	0.567780i	$-0.192198\pi$
$20$	0.0159494	+	4.47211i	0.00356639	+	0.999994i
$21$	−2.31981	−	1.27219i	−0.506225	−	0.277614i
$22$	1.60778	−	0.316831i	0.342779	−	0.0675486i
$23$	5.30311			1.10577			0.552887	−	0.833256i	$-0.313526\pi$
$23$	5.30311			1.10577			0.552887	+	0.833256i	$0.313526\pi$
$24$	−2.36011	+	1.55880i	−0.481756	+	0.318189i
$25$	−3.58558	−	3.48477i	−0.717116	−	0.696954i
$26$	0.191095	+	0.969724i	0.0374769	+	0.190178i
$27$	1.00000			0.192450
$28$	−5.25807	−	0.593920i	−0.993681	−	0.112240i
$29$		−	10.0699i		−	1.86993i	−0.354742	−	0.934964i	$-0.615431\pi$
$29$		−	10.0699i		−	1.86993i	0.354742	−	0.934964i	$-0.384569\pi$
$30$	0.600336	−	3.10477i	0.109606	−	0.566851i
$31$	0.109215			0.0196157			0.00980783	−	0.999952i	$-0.496878\pi$
$31$	0.109215			0.0196157			0.00980783	+	0.999952i	$0.496878\pi$
$32$	−3.18454	+	4.67533i	−0.562952	+	0.826489i
$33$	−1.15873			−0.201710
$34$	9.53452	−	1.87889i	1.63516	−	0.322227i
$35$	4.58672	−	3.73658i	0.775297	−	0.631597i
$36$	1.85047	−	0.758780i	0.308412	−	0.126463i
$37$	−4.30570			−0.707853			−0.353926	−	0.935273i	$-0.615154\pi$
$37$	−4.30570			−0.707853			−0.353926	+	0.935273i	$0.615154\pi$
$38$	1.35342	+	6.86798i	0.219553	+	1.11413i
$39$		−	0.698885i		−	0.111911i
$40$	−1.24493	−	6.20082i	−0.196841	−	0.980435i
$41$		−	2.58861i		−	0.404273i	−0.979357	−	0.202137i	$-0.935212\pi$
$41$		−	2.58861i		−	0.404273i	0.979357	−	0.202137i	$-0.0647885\pi$
$42$	3.56666	+	1.13089i	0.550348	+	0.174501i
$43$		−	7.55358i		−	1.15191i	−0.817481	−	0.575955i	$-0.804630\pi$
$43$		−	7.55358i		−	1.15191i	0.817481	−	0.575955i	$-0.195370\pi$
$44$	−2.14421	+	0.879225i	−0.323251	+	0.132548i
$45$	−0.840958	+	2.07190i	−0.125363	+	0.308861i
$46$	−7.35822	+	1.45002i	−1.08491	+	0.213794i
$47$			3.53225i			0.515231i	0.966247	+	0.257616i	$0.0829368\pi$
$47$			3.53225i			0.515231i	−0.966247	+	0.257616i	$0.917063\pi$
$48$	2.84850	−	2.80821i	0.411146	−	0.405330i
$49$	3.76308	+	5.90248i	0.537583	+	0.843211i
$50$	5.92793	+	3.85482i	0.838336	+	0.545154i
$51$	−6.87158			−0.962214
$52$	−0.530300	−	1.29327i	−0.0735394	−	0.179344i
$53$	1.70909			0.234762			0.117381	−	0.993087i	$-0.462550\pi$
$53$	1.70909			0.234762			0.117381	+	0.993087i	$0.462550\pi$
$54$	−1.38753	+	0.273429i	−0.188819	+	0.0372089i
$55$	0.974447	−	2.40079i	0.131394	−	0.323722i
$56$	7.45811	−	0.613625i	0.996632	−	0.0819991i
$57$		−	4.94979i		−	0.655616i
$58$	2.75339	+	13.9722i	0.361538	+	1.83464i
$59$			12.3942i			1.61359i	0.590834	+	0.806793i	$0.298799\pi$
$59$			12.3942i			1.61359i	−0.590834	+	0.806793i	$0.701201\pi$
$60$	0.0159494	+	4.47211i	0.00205906	+	0.577347i
$61$	−4.88851			−0.625909			−0.312955	−	0.949768i	$-0.601319\pi$
$61$	−4.88851			−0.625909			−0.312955	+	0.949768i	$0.601319\pi$
$62$	−0.151539	+	0.0298626i	−0.0192455	+	0.00379256i
$63$	−2.31981	−	1.27219i	−0.292269	−	0.160281i
$64$	3.14027	−	7.35790i	0.392534	−	0.919738i
$65$	1.44802	+	0.587733i	0.179605	+	0.0728994i
$66$	1.60778	−	0.316831i	0.197904	−	0.0389992i
$67$		−	8.12528i		−	0.992661i	−0.868134	−	0.496330i	$-0.834680\pi$
$67$		−	8.12528i		−	0.992661i	0.868134	−	0.496330i	$-0.165320\pi$
$68$	−12.7157	+	5.21402i	−1.54200	+	0.632293i
$69$	5.30311			0.638419
$70$	−5.34252	+	6.43875i	−0.638553	+	0.769578i
$71$		−	5.80082i		−	0.688431i	−0.938891	−	0.344215i	$-0.888145\pi$
$71$		−	5.80082i		−	0.688431i	0.938891	−	0.344215i	$-0.111855\pi$
$72$	−2.36011	+	1.55880i	−0.278142	+	0.183707i
$73$	−3.86018			−0.451799			−0.225900	−	0.974151i	$-0.572532\pi$
$73$	−3.86018			−0.451799			−0.225900	+	0.974151i	$0.572532\pi$
$74$	5.97428	−	1.17730i	0.694496	−	0.136859i
$75$	−3.58558	−	3.48477i	−0.414027	−	0.402387i
$76$	−3.75581	−	9.15946i	−0.430820	−	1.05066i
$77$	2.68805	+	1.47413i	0.306332	+	0.167992i
$78$	0.191095	+	0.969724i	0.0216373	+	0.109800i
$79$			6.30589i			0.709468i	0.934967	+	0.354734i	$0.115428\pi$
$79$			6.30589i			0.709468i	−0.934967	+	0.354734i	$0.884572\pi$
$80$	3.42286	+	8.26341i	0.382688	+	0.923878i
$81$	1.00000			0.111111
$82$	0.707800	+	3.59177i	0.0781635	+	0.396645i
$83$	−12.7204			−1.39624			−0.698121	−	0.715980i	$-0.745980\pi$
$83$	−12.7204			−1.39624			−0.698121	+	0.715980i	$0.745980\pi$
$84$	−5.25807	−	0.593920i	−0.573702	−	0.0648019i
$85$	5.77872	−	14.2373i	0.626790	−	1.54425i
$86$	2.06536	+	10.4808i	0.222714	+	1.13017i
$87$		−	10.0699i		−	1.07960i
$88$	2.73474	−	1.80624i	0.291525	−	0.192546i
$89$		−	0.841441i		−	0.0891926i	−0.999005	−	0.0445963i	$-0.985800\pi$
$89$		−	0.841441i		−	0.0891926i	0.999005	−	0.0445963i	$-0.0142002\pi$
$90$	0.600336	−	3.10477i	0.0632810	−	0.327271i
$91$	−0.889113	+	1.62128i	−0.0932044	+	0.169957i
$92$	9.81326	−	4.02390i	1.02310	−	0.419520i
$93$	0.109215			0.0113251
$94$	−0.965818	−	4.90110i	−0.0996165	−	0.505510i
$95$	10.2555	+	4.16257i	1.05219	+	0.427071i
$96$	−3.18454	+	4.67533i	−0.325021	+	0.477174i
$97$	−0.0488298			−0.00495792			−0.00247896	−	0.999997i	$-0.500789\pi$
$97$	−0.0488298			−0.00495792			−0.00247896	+	0.999997i	$0.500789\pi$
$98$	−6.83529	−	7.16093i	−0.690468	−	0.723363i
$99$	−1.15873			−0.116457
$100$	−9.27919	−	3.72781i	−0.927919	−	0.372781i
$101$	−15.0202			−1.49456			−0.747281	−	0.664508i	$-0.768641\pi$
$101$	−15.0202			−1.49456			−0.747281	+	0.664508i	$0.768641\pi$
$102$	9.53452	−	1.87889i	0.944058	−	0.186038i
$103$		−	16.0240i		−	1.57890i	−0.613817	−	0.789448i	$-0.710367\pi$
$103$		−	16.0240i		−	1.57890i	0.613817	−	0.789448i	$-0.289633\pi$
$104$	1.08942	+	1.64945i	0.106827	+	0.161742i
$105$	4.58672	−	3.73658i	0.447618	−	0.364653i
$106$	−2.37141	+	0.467314i	−0.230332	+	0.0453896i
$107$		−	9.62303i		−	0.930293i	−0.885234	−	0.465146i	$-0.846002\pi$
$107$		−	9.62303i		−	0.930293i	0.885234	−	0.465146i	$-0.153998\pi$
$108$	1.85047	−	0.758780i	0.178062	−	0.0730137i
$109$		−	4.74400i		−	0.454393i	−0.973849	−	0.227196i	$-0.927044\pi$
$109$		−	4.74400i		−	0.454393i	0.973849	−	0.227196i	$-0.0729559\pi$
$110$	−0.695630	+	3.59760i	−0.0663257	+	0.343018i
$111$	−4.30570			−0.408679
$112$	−10.1806	+	2.89068i	−0.961973	+	0.273144i
$113$		−	11.3962i		−	1.07206i	−0.844198	−	0.536031i	$-0.819923\pi$
$113$		−	11.3962i		−	1.07206i	0.844198	−	0.536031i	$-0.180077\pi$
$114$	1.35342	+	6.86798i	0.126759	+	0.643245i
$115$	−4.45969	+	10.9875i	−0.415869	+	1.02459i
$116$	−7.64082	−	18.6340i	−0.709432	−	1.73013i
$117$		−	0.698885i		−	0.0646120i
$118$	−3.38893	−	17.1973i	−0.311976	−	1.58314i
$119$	15.9408	+	8.74194i	1.46129	+	0.801373i
$120$	−1.24493	−	6.20082i	−0.113646	−	0.566055i
$121$	−9.65733			−0.877940
$122$	6.78295	−	1.33666i	0.614099	−	0.121015i
$123$		−	2.58861i		−	0.233407i
$124$	0.202100	−	0.0828705i	0.0181491	−	0.00744199i
$125$	10.2354	−	4.49843i	0.915485	−	0.402352i
$126$	3.56666	+	1.13089i	0.317744	+	0.100748i
$127$	11.4203			1.01339			0.506693	−	0.862126i	$-0.330868\pi$
$127$	11.4203			1.01339			0.506693	+	0.862126i	$0.330868\pi$
$128$	−2.34536	+	11.0679i	−0.207302	+	0.978277i
$129$		−	7.55358i		−	0.665055i
$130$	−2.16988	−	0.419566i	−0.190311	−	0.0367984i
$131$			1.20053i			0.104891i	0.998624	+	0.0524453i	$0.0167015\pi$
$131$			1.20053i			0.104891i	−0.998624	+	0.0524453i	$0.983298\pi$
$132$	−2.14421	+	0.879225i	−0.186629	+	0.0765267i
$133$	−6.29706	+	11.4826i	−0.546025	+	0.995668i
$134$	2.22168	+	11.2741i	0.191924	+	0.973931i
$135$	−0.840958	+	2.07190i	−0.0723782	+	0.178321i
$136$	16.2177	−	10.7114i	1.39066	−	0.918498i
$137$		−	4.29412i		−	0.366872i	−0.983032	−	0.183436i	$-0.941278\pi$
$137$		−	4.29412i		−	0.366872i	0.983032	−	0.183436i	$-0.0587219\pi$
$138$	−7.35822	+	1.45002i	−0.626373	+	0.123434i
$139$			12.0100i			1.01867i	0.860568	+	0.509336i	$0.170109\pi$
$139$			12.0100i			1.01867i	−0.860568	+	0.509336i	$0.829891\pi$
$140$	5.65236	−	10.3948i	0.477712	−	0.878517i
$141$			3.53225i			0.297469i
$142$	1.58611	+	8.04881i	0.133103	+	0.675441i
$143$			0.809822i			0.0677207i
$144$	2.84850	−	2.80821i	0.237375	−	0.234017i
$145$	20.8638	+	8.46834i	1.73265	+	0.703258i
$146$	5.35611	−	1.05548i	0.443274	−	0.0873524i
$147$	3.76308	+	5.90248i	0.310373	+	0.486828i
$148$	−7.96758	+	3.26708i	−0.654931	+	0.268552i
$149$		−	2.09953i		−	0.172000i	−0.996295	−	0.0860001i	$-0.972591\pi$
$149$		−	2.09953i		−	0.172000i	0.996295	−	0.0860001i	$-0.0274085\pi$
$150$	5.92793	+	3.85482i	0.484013	+	0.314745i
$151$			21.0358i			1.71187i	0.517083	+	0.855935i	$0.327018\pi$
$151$			21.0358i			1.71187i	−0.517083	+	0.855935i	$0.672982\pi$
$152$	7.71575	+	11.6821i	0.625830	+	0.947541i
$153$	−6.87158			−0.555535
$154$	−4.13281	−	1.31040i	−0.333032	−	0.105595i
$155$	−0.0918456	+	0.226284i	−0.00737721	+	0.0181756i
$156$	−0.530300	−	1.29327i	−0.0424580	−	0.103544i
$157$			5.76627i			0.460198i	0.973167	+	0.230099i	$0.0739051\pi$
$157$			5.76627i			0.460198i	−0.973167	+	0.230099i	$0.926095\pi$
$158$	−1.72421	−	8.74960i	−0.137171	−	0.696081i
$159$	1.70909			0.135540
$160$	−7.00877	−	10.5298i	−0.554092	−	0.832455i
$161$	−12.3022	−	6.74655i	−0.969552	−	0.531703i
$162$	−1.38753	+	0.273429i	−0.109015	+	0.0214826i
$163$			11.4647i			0.897984i	0.893536	+	0.448992i	$0.148217\pi$
$163$			11.4647i			0.897984i	−0.893536	+	0.448992i	$0.851783\pi$
$164$	−1.96419	−	4.79016i	−0.153377	−	0.374048i
$165$	0.974447	−	2.40079i	0.0758606	−	0.186901i
$166$	17.6499	−	3.47812i	1.36990	−	0.269954i
$167$			19.8534i			1.53630i	0.640271	+	0.768149i	$0.278822\pi$
$167$			19.8534i			1.53630i	−0.640271	+	0.768149i	$0.721178\pi$
$168$	7.45811	−	0.613625i	0.575406	−	0.0473422i
$169$	12.5116			0.962428
$170$	−4.12526	+	21.3347i	−0.316393	+	1.63630i
$171$		−	4.94979i		−	0.378520i
$172$	−5.73151	−	13.9777i	−0.437023	−	1.06579i
$173$		−	16.3132i		−	1.24027i	−0.784495	−	0.620135i	$-0.787078\pi$
$173$		−	16.3132i		−	1.24027i	0.784495	−	0.620135i	$-0.212922\pi$
$174$	2.75339	+	13.9722i	0.208734	+	1.05923i
$175$	3.88459	+	12.6456i	0.293648	+	0.955914i
$176$	−3.30066	+	3.25396i	−0.248797	+	0.245277i
$177$			12.3942i			0.931605i
$178$	0.230074	+	1.16752i	0.0172448	+	0.0875096i
$179$	−20.4707			−1.53005			−0.765025	−	0.644001i	$-0.777273\pi$
$179$	−20.4707			−1.53005			−0.765025	+	0.644001i	$0.777273\pi$
$180$	0.0159494	+	4.47211i	0.00118880	+	0.333331i
$181$	−14.5030			−1.07800			−0.538999	−	0.842306i	$-0.681197\pi$
$181$	−14.5030			−1.07800			−0.538999	+	0.842306i	$0.681197\pi$
$182$	0.790365	−	2.49269i	0.0585857	−	0.184770i
$183$	−4.88851			−0.361369
$184$	−12.5159	+	8.26650i	−0.922687	+	0.609414i
$185$	3.62091	−	8.92100i	0.266215	−	0.655885i
$186$	−0.151539	+	0.0298626i	−0.0111114	+	0.00218963i
$187$	7.96234			0.582264
$188$	2.68020	+	6.53633i	0.195474	+	0.476711i
$189$	−2.31981	−	1.27219i	−0.168742	−	0.0925380i
$190$	−15.3680	−	2.97154i	−1.11491	−	0.215578i
$191$			19.8316i			1.43496i	0.696578	+	0.717481i	$0.254705\pi$
$191$			19.8316i			1.43496i	−0.696578	+	0.717481i	$0.745295\pi$
$192$	3.14027	−	7.35790i	0.226630	−	0.531011i
$193$		−	0.938946i		−	0.0675868i	−0.999429	−	0.0337934i	$-0.989241\pi$
$193$		−	0.938946i		−	0.0675868i	0.999429	−	0.0337934i	$-0.0107588\pi$
$194$	0.0677528	−	0.0133515i	0.00486437	−	0.000958580i
$195$	1.44802	+	0.587733i	0.103695	+	0.0420885i
$196$	11.4422	+	8.06703i	0.817297	+	0.576216i
$197$	−22.2269			−1.58360			−0.791800	−	0.610780i	$-0.790856\pi$
$197$	−22.2269			−1.58360			−0.791800	+	0.610780i	$0.790856\pi$
$198$	1.60778	−	0.316831i	0.114260	−	0.0225162i
$199$	7.57854			0.537228			0.268614	−	0.963248i	$-0.413434\pi$
$199$	7.57854			0.537228			0.268614	+	0.963248i	$0.413434\pi$
$200$	13.8944	+	2.63525i	0.982485	+	0.186340i
$201$		−	8.12528i		−	0.573113i
$202$	20.8409	−	4.10694i	1.46636	−	0.288963i
$203$	−12.8108	+	23.3602i	−0.899139	+	1.63957i
$204$	−12.7157	+	5.21402i	−0.890276	+	0.365055i
$205$	5.36335	+	2.17691i	0.374593	+	0.152042i
$206$	4.38143	+	22.2338i	0.305269	+	1.54910i
$207$	5.30311			0.368592
$208$	−1.96261	−	1.99078i	−0.136083	−	0.138036i
$209$			5.73549i			0.396732i
$210$	−5.34252	+	6.43875i	−0.368669	+	0.444316i
$211$	20.4549			1.40817			0.704086	−	0.710115i	$-0.251357\pi$
$211$	20.4549			1.40817			0.704086	+	0.710115i	$0.251357\pi$
$212$	3.16263	−	1.29682i	0.217210	−	0.0890663i
$213$		−	5.80082i		−	0.397466i
$214$	2.63121	+	13.3522i	0.179866	+	0.912739i
$215$	15.6503	+	6.35224i	1.06734	+	0.433219i
$216$	−2.36011	+	1.55880i	−0.160585	+	0.106063i
$217$	−0.253359	−	0.138942i	−0.0171992	−	0.00943203i
$218$	1.29715	+	6.58244i	0.0878538	+	0.445819i
$219$	−3.86018			−0.260846
$220$	−0.0184811	−	5.18198i	−0.00124600	−	0.349369i
$221$			4.80245i			0.323048i
$222$	5.97428	−	1.17730i	0.400968	−	0.0790153i
$223$			4.53719i			0.303833i	0.988393	+	0.151916i	$0.0485445\pi$
$223$			4.53719i			0.303833i	−0.988393	+	0.151916i	$0.951456\pi$
$224$	13.3354	−	6.79457i	0.891011	−	0.453981i
$225$	−3.58558	−	3.48477i	−0.239039	−	0.232318i
$226$	3.11604	+	15.8125i	0.207276	+	1.05183i
$227$	12.4331			0.825215			0.412607	−	0.910909i	$-0.364618\pi$
$227$	12.4331			0.825215			0.412607	+	0.910909i	$0.364618\pi$
$228$	−3.75581	−	9.15946i	−0.248734	−	0.606600i
$229$	−3.24679			−0.214554			−0.107277	−	0.994229i	$-0.534213\pi$
$229$	−3.24679			−0.214554			−0.107277	+	0.994229i	$0.534213\pi$
$230$	3.18365	−	16.4649i	0.209924	−	1.08567i
$231$	2.68805	+	1.47413i	0.176861	+	0.0969905i
$232$	15.6969	+	23.7660i	1.03055	+	1.56032i
$233$			26.6500i			1.74590i	0.487812	+	0.872949i	$0.337795\pi$
$233$			26.6500i			1.74590i	−0.487812	+	0.872949i	$0.662205\pi$
$234$	0.191095	+	0.969724i	0.0124923	+	0.0633928i
$235$	−7.31848	−	2.97047i	−0.477405	−	0.193772i
$236$	9.40447	+	22.9351i	0.612179	+	1.49295i
$237$			6.30589i			0.409611i
$238$	−24.5086	−	7.77103i	−1.58866	−	0.503721i
$239$		−	10.8623i		−	0.702622i	−0.936259	−	0.351311i	$-0.885736\pi$
$239$		−	10.8623i		−	0.702622i	0.936259	−	0.351311i	$-0.114264\pi$
$240$	3.42286	+	8.26341i	0.220945	+	0.533401i
$241$			16.1547i			1.04061i	0.853979	+	0.520307i	$0.174182\pi$
$241$			16.1547i			1.04061i	−0.853979	+	0.520307i	$0.825818\pi$
$242$	13.3998	−	2.64059i	0.861374	−	0.169744i
$243$	1.00000			0.0641500
$244$	−9.04605	+	3.70930i	−0.579114	+	0.237464i
$245$	−15.3940	+	2.83300i	−0.983484	+	0.180994i
$246$	0.707800	+	3.59177i	0.0451277	+	0.229003i
$247$	−3.45934			−0.220112
$248$	−0.257761	+	0.170245i	−0.0163678	+	0.0108106i
$249$	−12.7204			−0.806121
$250$	−12.9720	+	9.04036i	−0.820419	+	0.571763i
$251$		−	22.5756i		−	1.42496i	−0.701694	−	0.712478i	$-0.747573\pi$
$251$		−	22.5756i		−	1.42496i	0.701694	−	0.712478i	$-0.252427\pi$
$252$	−5.25807	−	0.593920i	−0.331227	−	0.0374134i
$253$	−6.14490			−0.386326
$254$	−15.8460	+	3.12263i	−0.994265	+	0.195931i
$255$	5.77872	−	14.2373i	0.361877	−	0.891572i
$256$	0.227957	−	15.9984i	0.0142473	−	0.999899i
$257$	−12.0533			−0.751863			−0.375931	−	0.926648i	$-0.622677\pi$
$257$	−12.0533			−0.751863			−0.375931	+	0.926648i	$0.622677\pi$
$258$	2.06536	+	10.4808i	0.128584	+	0.652507i
$259$	9.98842	+	5.47766i	0.620650	+	0.340365i
$260$	3.12549	−	0.0111468i	0.193835	−	0.000691295i
$261$		−	10.0699i		−	0.623309i
$262$	−0.328259	−	1.66577i	−0.0202799	−	0.102911i
$263$	19.6608			1.21234			0.606169	−	0.795336i	$-0.292705\pi$
$263$	19.6608			1.21234			0.606169	+	0.795336i	$0.292705\pi$
$264$	2.73474	−	1.80624i	0.168312	−	0.111166i
$265$	−1.43727	+	3.54107i	−0.0882910	+	0.217526i
$266$	5.59769	−	17.6542i	0.343216	−	1.08245i
$267$		−	0.841441i		−	0.0514954i
$268$	−6.16530	−	15.0356i	−0.376606	−	0.918446i
$269$	−1.22906			−0.0749372			−0.0374686	−	0.999298i	$-0.511929\pi$
$269$	−1.22906			−0.0749372			−0.0374686	+	0.999298i	$0.511929\pi$
$270$	0.600336	−	3.10477i	0.0365353	−	0.188950i
$271$	−12.1597			−0.738648			−0.369324	−	0.929301i	$-0.620411\pi$
$271$	−12.1597			−0.738648			−0.369324	+	0.929301i	$0.620411\pi$
$272$	−19.5737	+	19.2968i	−1.18683	+	1.17004i
$273$	−0.889113	+	1.62128i	−0.0538116	+	0.0981246i
$274$	1.17414	+	5.95822i	0.0709322	+	0.359949i
$275$	4.15473	+	4.03792i	0.250540	+	0.243496i
$276$	9.81326	−	4.02390i	0.590689	−	0.242210i
$277$	24.1319			1.44995			0.724973	−	0.688778i	$-0.241852\pi$
$277$	24.1319			1.44995			0.724973	+	0.688778i	$0.241852\pi$
$278$	−3.28387	−	16.6642i	−0.196953	−	0.999451i
$279$	0.109215			0.00653855
$280$	−5.00059	+	15.9685i	−0.298842	+	0.954302i
$281$	2.45095			0.146211			0.0731056	−	0.997324i	$-0.476709\pi$
$281$	2.45095			0.146211			0.0731056	+	0.997324i	$0.476709\pi$
$282$	−0.965818	−	4.90110i	−0.0575136	−	0.291856i
$283$	−0.770452			−0.0457986			−0.0228993	−	0.999738i	$-0.507290\pi$
$283$	−0.770452			−0.0457986			−0.0228993	+	0.999738i	$0.507290\pi$
$284$	−4.40155	−	10.7343i	−0.261184	−	0.636962i
$285$	10.2555	+	4.16257i	0.607483	+	0.246569i
$286$	−0.221429	−	1.12365i	−0.0130933	−	0.0664429i
$287$	−3.29320	+	6.00510i	−0.194391	+	0.354470i
$288$	−3.18454	+	4.67533i	−0.187651	+	0.275496i
$289$	30.2187			1.77757
$290$	−31.2646	−	6.04531i	−1.83592	−	0.354993i
$291$	−0.0488298			−0.00286246
$292$	−7.14315	+	2.92903i	−0.418021	+	0.171408i
$293$		−	14.0583i		−	0.821295i	−0.911794	−	0.410648i	$-0.865303\pi$
$293$		−	14.0583i		−	0.821295i	0.911794	−	0.410648i	$-0.134697\pi$
$294$	−6.83529	−	7.16093i	−0.398642	−	0.417634i
$295$	−25.6796	−	10.4230i	−1.49512	−	0.606851i
$296$	10.1619	−	6.71173i	0.590651	−	0.390112i
$297$	−1.15873			−0.0672366
$298$	0.574071	+	2.91316i	0.0332551	+	0.168755i
$299$		−	3.70627i		−	0.214339i
$300$	−9.27919	−	3.72781i	−0.535734	−	0.215225i
$301$	−9.60957	+	17.5229i	−0.553886	+	1.01000i
$302$	−5.75179	−	29.1878i	−0.330979	−	1.67957i
$303$	−15.0202			−0.862886
$304$	−13.9000	−	14.0995i	−0.797222	−	0.808662i
$305$	4.11103	−	10.1285i	0.235397	−	0.579957i
$306$	9.53452	−	1.87889i	0.545052	−	0.107409i
$307$	33.8488			1.93185			0.965926	−	0.258819i	$-0.0833333\pi$
$307$	33.8488			1.93185			0.965926	+	0.258819i	$0.0833333\pi$
$308$	6.09270	+	0.688195i	0.347164	+	0.0392135i
$309$		−	16.0240i		−	0.911576i
$310$	0.0655659	−	0.339089i	0.00372389	−	0.0192589i
$311$	14.3608			0.814324			0.407162	−	0.913356i	$-0.366518\pi$
$311$	14.3608			0.814324			0.407162	+	0.913356i	$0.366518\pi$
$312$	1.08942	+	1.64945i	0.0616765	+	0.0933816i
$313$	−16.3655			−0.925033			−0.462516	−	0.886611i	$-0.653053\pi$
$313$	−16.3655			−0.925033			−0.462516	+	0.886611i	$0.653053\pi$
$314$	−1.57666	−	8.00086i	−0.0889762	−	0.451515i
$315$	4.58672	−	3.73658i	0.258432	−	0.210532i
$316$	4.78478	+	11.6689i	0.269165	+	0.656425i
$317$	−25.5784			−1.43662			−0.718312	−	0.695721i	$-0.755085\pi$
$317$	−25.5784			−1.43662			−0.718312	+	0.695721i	$0.755085\pi$
$318$	−2.37141	+	0.467314i	−0.132982	+	0.0262057i
$319$			11.6683i			0.653300i
$320$	12.6040	+	12.6940i	0.704587	+	0.709618i
$321$		−	9.62303i		−	0.537105i
$322$	18.9144	+	5.99725i	1.05406	+	0.334214i
$323$			34.0129i			1.89253i
$324$	1.85047	−	0.758780i	0.102804	−	0.0421545i
$325$	−2.43546	+	2.50591i	−0.135095	+	0.139003i
$326$	−3.13478	−	15.9076i	−0.173619	−	0.881041i
$327$		−	4.74400i		−	0.262344i
$328$	4.03513	+	6.10942i	0.222803	+	0.337336i
$329$	4.49368	−	8.19416i	0.247745	−	0.451759i
$330$	−0.695630	+	3.59760i	−0.0382932	+	0.198042i
$331$	−4.64867			−0.255514			−0.127757	−	0.991806i	$-0.540778\pi$
$331$	−4.64867			−0.255514			−0.127757	+	0.991806i	$0.540778\pi$
$332$	−23.5387	+	9.65197i	−1.29185	+	0.529721i
$333$	−4.30570			−0.235951
$334$	−5.42848	−	27.5471i	−0.297033	−	1.50731i
$335$	16.8348	+	6.83302i	0.919784	+	0.373328i
$336$	−10.1806	+	2.89068i	−0.555395	+	0.157700i
$337$			1.71956i			0.0936701i	0.998903	+	0.0468351i	$0.0149135\pi$
$337$			1.71956i			0.0936701i	−0.998903	+	0.0468351i	$0.985086\pi$
$338$	−17.3602	+	3.42102i	−0.944268	+	0.186079i
$339$		−	11.3962i		−	0.618955i
$340$	−0.109598	−	30.7305i	−0.00594376	−	1.66659i
$341$	−0.126552			−0.00685315
$342$	1.35342	+	6.86798i	0.0731843	+	0.371378i
$343$	−1.22058	−	18.4800i	−0.0659053	−	0.997826i
$344$	11.7745	+	17.8273i	0.634840	+	0.961184i
$345$	−4.45969	+	10.9875i	−0.240102	+	0.591549i
$346$	4.46050	+	22.6351i	0.239798	+	1.21687i
$347$		−	18.7988i		−	1.00917i	−0.863361	−	0.504587i	$-0.831645\pi$
$347$		−	18.7988i		−	1.00917i	0.863361	−	0.504587i	$-0.168355\pi$
$348$	−7.64082	−	18.6340i	−0.409591	−	0.998889i
$349$	27.6131			1.47809			0.739047	−	0.673654i	$-0.235276\pi$
$349$	27.6131			1.47809			0.739047	+	0.673654i	$0.235276\pi$
$350$	−8.84764	−	16.4839i	−0.472926	−	0.881102i
$351$		−	0.698885i		−	0.0373037i
$352$	3.69003	−	5.41747i	0.196679	−	0.288752i
$353$	20.2417			1.07736			0.538678	−	0.842512i	$-0.318924\pi$
$353$	20.2417			1.07736			0.538678	+	0.842512i	$0.318924\pi$
$354$	−3.38893	−	17.1973i	−0.180119	−	0.914026i
$355$	12.0187	+	4.87825i	0.637889	+	0.258911i
$356$	−0.638469	−	1.55706i	−0.0338388	−	0.0825243i
$357$	15.9408	+	8.74194i	0.843677	+	0.462673i
$358$	28.4037	−	5.59727i	1.50118	−	0.295825i
$359$		−	23.0400i		−	1.21601i	−0.793935	−	0.608003i	$-0.791971\pi$
$359$		−	23.0400i		−	1.21601i	0.793935	−	0.608003i	$-0.208029\pi$
$360$	−1.24493	−	6.20082i	−0.0656137	−	0.326812i
$361$	−5.50045			−0.289497
$362$	20.1233	−	3.96553i	1.05766	−	0.208424i
$363$	−9.65733			−0.506879
$364$	−0.415082	+	3.67479i	−0.0217562	+	0.192611i
$365$	3.24625	−	7.99792i	0.169916	−	0.418630i
$366$	6.78295	−	1.33666i	0.354550	−	0.0698682i
$367$			10.9328i			0.570689i	0.958425	+	0.285345i	$0.0921080\pi$
$367$			10.9328i			0.570689i	−0.958425	+	0.285345i	$0.907892\pi$
$368$	15.1059	−	14.8922i	0.787451	−	0.776311i
$369$		−	2.58861i		−	0.134758i
$370$	−2.58487	+	13.3682i	−0.134381	+	0.694980i
$371$	−3.96477	−	2.17428i	−0.205841	−	0.112883i
$372$	0.202100	−	0.0828705i	0.0104784	−	0.00429663i
$373$	−23.4976			−1.21666			−0.608330	−	0.793684i	$-0.708160\pi$
$373$	−23.4976			−1.21666			−0.608330	+	0.793684i	$0.708160\pi$
$374$	−11.0480	+	2.17713i	−0.571277	+	0.112577i
$375$	10.2354	−	4.49843i	0.528556	−	0.232298i
$376$	−5.50608	−	8.33651i	−0.283954	−	0.429922i
$377$	−7.03769			−0.362459
$378$	3.56666	+	1.13089i	0.183449	+	0.0581669i
$379$	−2.54308			−0.130629			−0.0653147	−	0.997865i	$-0.520805\pi$
$379$	−2.54308			−0.130629			−0.0653147	+	0.997865i	$0.520805\pi$
$380$	22.1360	−	0.0789462i	1.13555	−	0.00404985i
$381$	11.4203			0.585079
$382$	−5.42252	−	27.5169i	−0.277440	−	1.40789i
$383$			18.1612i			0.927992i	0.885837	+	0.463996i	$0.153585\pi$
$383$			18.1612i			0.927992i	−0.885837	+	0.463996i	$0.846415\pi$
$384$	−2.34536	+	11.0679i	−0.119686	+	0.564808i
$385$	−5.31479	+	4.32970i	−0.270867	+	0.220662i
$386$	0.256735	+	1.30281i	0.0130675	+	0.0663115i
$387$		−	7.55358i		−	0.383970i
$388$	−0.0903583	+	0.0370511i	−0.00458725	+	0.00188099i
$389$			16.7007i			0.846760i	0.905952	+	0.423380i	$0.139156\pi$
$389$			16.7007i			0.846760i	−0.905952	+	0.423380i	$0.860844\pi$
$390$	−2.16988	−	0.419566i	−0.109876	−	0.0212456i
$391$	−36.4408			−1.84289
$392$	−18.0821	−	8.06462i	−0.913283	−	0.407325i
$393$			1.20053i			0.0605586i
$394$	30.8405	−	6.07747i	1.55372	−	0.306178i
$395$	−13.0652	−	5.30299i	−0.657381	−	0.266822i
$396$	−2.14421	+	0.879225i	−0.107750	+	0.0441827i
$397$		−	11.8222i		−	0.593339i	−0.954980	−	0.296669i	$-0.904124\pi$
$397$		−	11.8222i		−	0.593339i	0.954980	−	0.296669i	$-0.0958759\pi$
$398$	−10.5154	+	2.07219i	−0.527092	+	0.103869i
$399$	−6.29706	+	11.4826i	−0.315248	+	0.574849i
$400$	−19.9995	+	0.142655i	−0.999975	+	0.00713274i
$401$	31.5542			1.57574			0.787871	−	0.615841i	$-0.211184\pi$
$401$	31.5542			1.57574			0.787871	+	0.615841i	$0.211184\pi$
$402$	2.22168	+	11.2741i	0.110808	+	0.562299i
$403$		−	0.0763290i		−	0.00380222i
$404$	−27.7944	+	11.3970i	−1.38282	+	0.567022i
$405$	−0.840958	+	2.07190i	−0.0417876	+	0.102954i
$406$	11.3880	−	35.9158i	0.565175	−	1.78247i
$407$	4.98916			0.247304
$408$	16.2177	−	10.7114i	0.802897	−	0.530295i
$409$		−	20.0561i		−	0.991709i	−0.868406	−	0.495855i	$-0.834855\pi$
$409$		−	20.0561i		−	0.991709i	0.868406	−	0.495855i	$-0.165145\pi$
$410$	−8.03704	−	1.55404i	−0.396921	−	0.0767484i
$411$		−	4.29412i		−	0.211813i
$412$	−12.1587	−	29.6521i	−0.599018	−	1.46085i
$413$	15.7677	−	28.7522i	0.775880	−	1.41480i
$414$	−7.35822	+	1.45002i	−0.361637	+	0.0712647i
$415$	10.6973	−	26.3554i	0.525110	−	1.29374i
$416$	3.26752	+	2.22563i	0.160203	+	0.109120i
$417$			12.0100i			0.588131i
$418$	−1.56825	−	7.95817i	−0.0767055	−	0.389247i
$419$		−	6.04413i		−	0.295275i	−0.989042	−	0.147638i	$-0.952833\pi$
$419$		−	6.04413i		−	0.295275i	0.989042	−	0.147638i	$-0.0471669\pi$
$420$	5.65236	−	10.3948i	0.275807	−	0.507212i
$421$		−	20.6123i		−	1.00458i	−0.864699	−	0.502290i	$-0.832491\pi$
$421$		−	20.6123i		−	1.00458i	0.864699	−	0.502290i	$-0.167509\pi$
$422$	−28.3817	+	5.59295i	−1.38160	+	0.272261i
$423$			3.53225i			0.171744i
$424$	−4.03365	+	2.66413i	−0.195891	+	0.129382i
$425$	24.6386	+	23.9459i	1.19515	+	1.16155i
$426$	1.58611	+	8.04881i	0.0768473	+	0.389966i
$427$	11.3404	+	6.21910i	0.548802	+	0.300963i
$428$	−7.30176	−	17.8072i	−0.352944	−	0.860741i
$429$			0.809822i			0.0390986i
$430$	−23.4521	−	4.53469i	−1.13096	−	0.218682i
$431$		−	4.31002i		−	0.207606i	−0.994598	−	0.103803i	$-0.966899\pi$
$431$		−	4.31002i		−	0.207606i	0.994598	−	0.103803i	$-0.0331012\pi$
$432$	2.84850	−	2.80821i	0.137049	−	0.135110i
$433$	24.8247			1.19300			0.596500	−	0.802613i	$-0.296558\pi$
$433$	24.8247			1.19300			0.596500	+	0.802613i	$0.296558\pi$
$434$	0.389534	+	0.123511i	0.0186982	+	0.00592871i
$435$	20.8638	+	8.46834i	1.00034	+	0.406026i
$436$	−3.59965	−	8.77864i	−0.172392	−	0.420421i
$437$		−	26.2493i		−	1.25567i
$438$	5.35611	−	1.05548i	0.255925	−	0.0504329i
$439$	1.81801			0.0867687			0.0433843	−	0.999058i	$-0.486186\pi$
$439$	1.81801			0.0867687			0.0433843	+	0.999058i	$0.486186\pi$
$440$	1.44255	+	7.18510i	0.0687707	+	0.342536i
$441$	3.76308	+	5.90248i	0.179194	+	0.281070i
$442$	−1.31313	−	6.66354i	−0.0624591	−	0.316952i
$443$		−	37.3237i		−	1.77330i	−0.462439	−	0.886651i	$-0.653025\pi$
$443$		−	37.3237i		−	1.77330i	0.462439	−	0.886651i	$-0.346975\pi$
$444$	−7.96758	+	3.26708i	−0.378125	+	0.155049i
$445$	1.74339	+	0.707617i	0.0826444	+	0.0335443i
$446$	−1.24060	−	6.29549i	−0.0587441	−	0.298100i
$447$		−	2.09953i		−	0.0993043i
$448$	−16.6455	+	13.0740i	−0.786425	+	0.617686i
$449$	−22.9898			−1.08496			−0.542478	−	0.840070i	$-0.682514\pi$
$449$	−22.9898			−1.08496			−0.542478	+	0.840070i	$0.682514\pi$
$450$	5.92793	+	3.85482i	0.279445	+	0.181718i
$451$			2.99951i			0.141242i
$452$	−8.64719	−	21.0883i	−0.406730	−	0.991911i
$453$			21.0358i			0.988349i
$454$	−17.2513	+	3.39957i	−0.809644	+	0.159550i
$455$	−2.61144	−	3.20559i	−0.122426	−	0.150280i
$456$	7.71575	+	11.6821i	0.361323	+	0.547063i
$457$			37.1559i			1.73808i	0.494741	+	0.869040i	$0.335263\pi$
$457$			37.1559i			1.73808i	−0.494741	+	0.869040i	$0.664737\pi$
$458$	4.50502	−	0.887766i	0.210506	−	0.0414826i
$459$	−6.87158			−0.320738
$460$	0.0845814	+	23.7161i	0.00394363	+	1.10577i
$461$	−33.7273			−1.57083			−0.785417	−	0.618966i	$-0.787552\pi$
$461$	−33.7273			−1.57083			−0.785417	+	0.618966i	$0.787552\pi$
$462$	−4.13281	−	1.31040i	−0.192276	−	0.0609656i
$463$	−17.3016			−0.804072			−0.402036	−	0.915624i	$-0.631697\pi$
$463$	−17.3016			−0.804072			−0.402036	+	0.915624i	$0.631697\pi$
$464$	−28.2783	−	28.6841i	−1.31279	−	1.33162i
$465$	−0.0918456	+	0.226284i	−0.00425924	+	0.0104937i
$466$	−7.28687	−	36.9776i	−0.337558	−	1.71295i
$467$	−6.46441			−0.299137			−0.149569	−	0.988751i	$-0.547789\pi$
$467$	−6.46441			−0.299137			−0.149569	+	0.988751i	$0.547789\pi$
$468$	−0.530300	−	1.29327i	−0.0245131	−	0.0597814i
$469$	−10.3369	+	18.8491i	−0.477313	+	0.870373i
$470$	10.9668	+	2.12054i	0.505862	+	0.0978130i
$471$			5.76627i			0.265696i
$472$	−19.3201	−	29.2517i	−0.889280	−	1.34642i
$473$			8.75259i			0.402444i
$474$	−1.72421	−	8.74960i	−0.0791956	−	0.401882i
$475$	−17.2489	+	17.7479i	−0.791434	+	0.814328i
$476$	36.1312	+	4.08117i	1.65607	+	0.187060i
$477$	1.70909			0.0782539
$478$	2.97006	+	15.0717i	0.135847	+	0.689365i
$479$	−29.1194			−1.33050			−0.665250	−	0.746621i	$-0.731675\pi$
$479$	−29.1194			−1.33050			−0.665250	+	0.746621i	$0.731675\pi$
$480$	−7.00877	−	10.5298i	−0.319905	−	0.480618i
$481$			3.00919i			0.137207i
$482$	−4.41715	−	22.4151i	−0.201196	−	1.02098i
$483$	−12.3022	−	6.74655i	−0.559771	−	0.306979i
$484$	−17.8706	+	7.32780i	−0.812302	+	0.333082i
$485$	0.0410639	−	0.101171i	0.00186461	−	0.00459393i
$486$	−1.38753	+	0.273429i	−0.0629396	+	0.0124030i
$487$	−9.61283			−0.435599			−0.217799	−	0.975994i	$-0.569888\pi$
$487$	−9.61283			−0.435599			−0.217799	+	0.975994i	$0.569888\pi$
$488$	11.5374	−	7.62022i	0.522275	−	0.344951i
$489$			11.4647i			0.518452i
$490$	20.5849	−	8.14002i	0.929933	−	0.367729i
$491$	−3.85331			−0.173897			−0.0869487	−	0.996213i	$-0.527712\pi$
$491$	−3.85331			−0.173897			−0.0869487	+	0.996213i	$0.527712\pi$
$492$	−1.96419	−	4.79016i	−0.0885524	−	0.215957i
$493$			69.1960i			3.11643i
$494$	4.79993	−	0.945882i	0.215959	−	0.0425572i
$495$	0.974447	−	2.40079i	0.0437981	−	0.107907i
$496$	0.311100	−	0.306699i	0.0139688	−	0.0137712i
$497$	−7.37973	+	13.4568i	−0.331026	+	0.603621i
$498$	17.6499	−	3.47812i	0.790910	−	0.155858i
$499$	11.4197			0.511218			0.255609	−	0.966780i	$-0.417724\pi$
$499$	11.4197			0.511218			0.255609	+	0.966780i	$0.417724\pi$
$500$	15.5271	−	16.0907i	0.694392	−	0.719597i
$501$			19.8534i			0.886982i
$502$	6.17281	+	31.3242i	0.275506	+	1.39807i
$503$		−	9.67677i		−	0.431466i	−0.976452	−	0.215733i	$-0.930786\pi$
$503$		−	9.67677i		−	0.431466i	0.976452	−	0.215733i	$-0.0692141\pi$
$504$	7.45811	−	0.613625i	0.332211	−	0.0273330i
$505$	12.6313	−	31.1203i	0.562087	−	1.38484i
$506$	8.52622	−	1.68019i	0.379037	−	0.0746936i
$507$	12.5116			0.555658
$508$	21.1329	−	8.66549i	0.937622	−	0.384469i
$509$	−29.4349			−1.30468			−0.652340	−	0.757927i	$-0.726212\pi$
$509$	−29.4349			−1.30468			−0.652340	+	0.757927i	$0.726212\pi$
$510$	−4.12526	+	21.3347i	−0.182670	+	0.944716i
$511$	8.95489	+	4.91087i	0.396141	+	0.217244i
$512$	4.05812	+	22.2605i	0.179345	+	0.983786i
$513$		−	4.94979i		−	0.218539i
$514$	16.7243	−	3.29571i	0.737676	−	0.145368i
$515$	33.2003	+	13.4756i	1.46298	+	0.593804i
$516$	−5.73151	−	13.9777i	−0.252316	−	0.615334i
$517$		−	4.09294i		−	0.180007i
$518$	−15.3570	−	4.86929i	−0.674747	−	0.213944i
$519$		−	16.3132i		−	0.716070i
$520$	−4.33366	+	0.870065i	−0.190044	+	0.0381549i
$521$		−	37.2925i		−	1.63381i	−0.576771	−	0.816906i	$-0.695687\pi$
$521$		−	37.2925i		−	1.63381i	0.576771	−	0.816906i	$-0.304313\pi$
$522$	2.75339	+	13.9722i	0.120513	+	0.611548i
$523$	−28.2787			−1.23654			−0.618271	−	0.785965i	$-0.712166\pi$
$523$	−28.2787			−1.23654			−0.618271	+	0.785965i	$0.712166\pi$
$524$	0.910937	+	2.22154i	0.0397945	+	0.0970486i
$525$	3.88459	+	12.6456i	0.169538	+	0.551897i
$526$	−27.2800	+	5.37583i	−1.18946	+	0.234397i
$527$	−0.750483			−0.0326915
$528$	−3.30066	+	3.25396i	−0.143643	+	0.141611i
$529$	5.12297			0.222738
$530$	1.02603	−	5.30633i	0.0445678	−	0.230492i
$531$			12.3942i			0.537862i
$532$	−2.93978	+	26.0263i	−0.127456	+	1.12838i
$533$	−1.80914			−0.0783626
$534$	0.230074	+	1.16752i	0.00995628	+	0.0505237i
$535$	19.9380	+	8.09256i	0.861995	+	0.349872i
$536$	12.6657	+	19.1766i	0.547075	+	0.828302i
$537$	−20.4707			−0.883375
$538$	1.70536	−	0.336061i	0.0735232	−	0.0144886i
$539$	−4.36041	−	6.83940i	−0.187816	−	0.294594i
$540$	0.0159494	+	4.47211i	0.000686352	+	0.192449i
$541$		−	11.0367i		−	0.474505i	−0.971448	−	0.237252i	$-0.923753\pi$
$541$		−	11.0367i		−	0.474505i	0.971448	−	0.237252i	$-0.0762468\pi$
$542$	16.8719	−	3.32481i	0.724711	−	0.142813i
$543$	−14.5030			−0.622382
$544$	21.8828	−	32.1269i	0.938218	−	1.37743i
$545$	9.82911	+	3.98951i	0.421033	+	0.170892i
$546$	0.790365	−	2.49269i	0.0338245	−	0.106677i
$547$			28.0990i			1.20143i	0.799464	+	0.600714i	$0.205117\pi$
$547$			28.0990i			1.20143i	−0.799464	+	0.600714i	$0.794883\pi$
$548$	−3.25830	−	7.94616i	−0.139187	−	0.339443i
$549$	−4.88851			−0.208636
$550$	−6.86890	−	4.46671i	−0.292891	−	0.190461i
$551$	−49.8438			−2.12342
$552$	−12.5159	+	8.26650i	−0.532714	+	0.351846i
$553$	8.02227	−	14.6285i	0.341142	−	0.622066i
$554$	−33.4837	+	6.59835i	−1.42259	+	0.280337i
$555$	3.62091	−	8.92100i	0.153699	−	0.378675i
$556$	9.11293	+	22.2241i	0.386474	+	0.942513i
$557$	−7.34006			−0.311008			−0.155504	−	0.987835i	$-0.549700\pi$
$557$	−7.34006			−0.311008			−0.155504	+	0.987835i	$0.549700\pi$
$558$	−0.151539	+	0.0298626i	−0.00641518	+	0.00126419i
$559$	−5.27908			−0.223281
$560$	2.57221	−	23.5241i	0.108696	−	0.994075i
$561$	7.96234			0.336170
$562$	−3.40076	+	0.670159i	−0.143452	+	0.0282690i
$563$	36.4524			1.53628			0.768142	−	0.640279i	$-0.221181\pi$
$563$	36.4524			1.53628			0.768142	+	0.640279i	$0.221181\pi$
$564$	2.68020	+	6.53633i	0.112857	+	0.275229i
$565$	23.6118	+	9.58371i	0.993355	+	0.403190i
$566$	1.06903	−	0.210664i	0.0449345	−	0.00885486i
$567$	−2.31981	−	1.27219i	−0.0974230	−	0.0534269i
$568$	9.04233	+	13.6906i	0.379408	+	0.574445i
$569$	1.02524			0.0429803			0.0214902	−	0.999769i	$-0.493159\pi$
$569$	1.02524			0.0429803			0.0214902	+	0.999769i	$0.493159\pi$
$570$	−15.3680	−	2.97154i	−0.643693	−	0.124464i
$571$	−10.7464			−0.449722			−0.224861	−	0.974391i	$-0.572193\pi$
$571$	−10.7464			−0.449722			−0.224861	+	0.974391i	$0.572193\pi$
$572$	0.614477	+	1.49855i	0.0256926	+	0.0626577i
$573$			19.8316i			0.828476i
$574$	2.92744	−	9.23270i	0.122189	−	0.385365i
$575$	−19.0147	−	18.4801i	−0.792968	−	0.770674i
$576$	3.14027	−	7.35790i	0.130845	−	0.306579i
$577$	−45.2022			−1.88179			−0.940897	−	0.338693i	$-0.890015\pi$
$577$	−45.2022			−1.88179			−0.940897	+	0.338693i	$0.890015\pi$
$578$	−41.9293	+	8.26265i	−1.74403	+	0.343681i
$579$		−	0.938946i		−	0.0390213i
$580$	45.0335	−	0.160608i	1.86992	−	0.00666890i
$581$	29.5089	+	16.1827i	1.22424	+	0.671372i
$582$	0.0677528	−	0.0133515i	0.00280844	−	0.000553437i
$583$	−1.98038			−0.0820190
$584$	9.11045	−	6.01725i	0.376993	−	0.248996i
$585$	1.44802	+	0.587733i	0.0598684	+	0.0242998i
$586$	3.84395	+	19.5063i	0.158792	+	0.805799i
$587$	9.41098			0.388433			0.194216	−	0.980959i	$-0.437784\pi$
$587$	9.41098			0.388433			0.194216	+	0.980959i	$0.437784\pi$
$588$	11.4422	+	8.06703i	0.471867	+	0.332679i
$589$		−	0.540593i		−	0.0222748i
$590$	38.4811	+	7.44068i	1.58424	+	0.306328i
$591$	−22.2269			−0.914292
$592$	−12.2648	+	12.0913i	−0.504080	+	0.496949i
$593$	28.1625			1.15650			0.578248	−	0.815861i	$-0.303736\pi$
$593$	28.1625			1.15650			0.578248	+	0.815861i	$0.303736\pi$
$594$	1.60778	−	0.316831i	0.0659679	−	0.0129997i
$595$	−31.5180	+	25.6762i	−1.29211	+	1.05262i
$596$	−1.59308	−	3.88512i	−0.0652552	−	0.159141i
$597$	7.57854			0.310169
$598$	1.01340	+	5.14255i	0.0414410	+	0.210295i
$599$		−	11.5112i		−	0.470336i	−0.971955	−	0.235168i	$-0.924436\pi$
$599$		−	11.5112i		−	0.470336i	0.971955	−	0.235168i	$-0.0755640\pi$
$600$	13.8944	+	2.63525i	0.567238	+	0.107584i
$601$		−	14.8292i		−	0.604894i	−0.953166	−	0.302447i	$-0.902196\pi$
$601$		−	14.8292i		−	0.604894i	0.953166	−	0.302447i	$-0.0978035\pi$
$602$	8.54229	−	26.9411i	0.348158	−	1.09804i
$603$		−	8.12528i		−	0.330887i
$604$	15.9616	+	38.9262i	0.649467	+	1.58389i
$605$	8.12142	−	20.0091i	0.330183	−	0.813485i
$606$	20.8409	−	4.10694i	0.846604	−	0.166833i
$607$		−	19.9890i		−	0.811327i	−0.914023	−	0.405663i	$-0.867041\pi$
$607$		−	19.9890i		−	0.811327i	0.914023	−	0.405663i	$-0.132959\pi$
$608$	23.1419	+	15.7628i	0.938529	+	0.639266i
$609$	−12.8108	+	23.3602i	−0.519118	+	0.946604i
$610$	−2.93475	+	15.1777i	−0.118824	+	0.614527i
$611$	2.46864			0.0998703
$612$	−12.7157	+	5.21402i	−0.514001	+	0.210764i
$613$	38.5925			1.55874			0.779368	−	0.626566i	$-0.215540\pi$
$613$	38.5925			1.55874			0.779368	+	0.626566i	$0.215540\pi$
$614$	−46.9662	+	9.25523i	−1.89540	+	0.373510i
$615$	5.36335	+	2.17691i	0.216271	+	0.0877816i
$616$	−8.64197	+	0.711029i	−0.348195	+	0.0286482i
$617$		−	16.2711i		−	0.655048i	−0.944843	−	0.327524i	$-0.893786\pi$
$617$		−	16.2711i		−	0.655048i	0.944843	−	0.327524i	$-0.106214\pi$
$618$	4.38143	+	22.2338i	0.176247	+	0.894376i
$619$		−	5.64262i		−	0.226796i	−0.993550	−	0.113398i	$-0.963826\pi$
$619$		−	5.64262i		−	0.226796i	0.993550	−	0.113398i	$-0.0361735\pi$
$620$	0.00174192	+	0.488423i	6.99571e−5	+	0.0196155i
$621$	5.30311			0.212806
$622$	−19.9260	+	3.92664i	−0.798958	+	0.157444i
$623$	−1.07047	+	1.95199i	−0.0428875	+	0.0782047i
$624$	−1.96261	−	1.99078i	−0.0785674	−	0.0796949i
$625$	0.712738	+	24.9898i	0.0285095	+	0.999594i
$626$	22.7076	−	4.47480i	0.907578	−	0.178849i
$627$			5.73549i			0.229054i
$628$	4.37533	+	10.6703i	0.174595	+	0.425792i
$629$	29.5870			1.17971
$630$	−5.34252	+	6.43875i	−0.212851	+	0.256526i
$631$		−	4.18154i		−	0.166465i	−0.996530	−	0.0832323i	$-0.973476\pi$
$631$		−	4.18154i		−	0.166465i	0.996530	−	0.0832323i	$-0.0265244\pi$
$632$	−9.82963	−	14.8826i	−0.391002	−	0.591998i
$633$	20.4549			0.813009
$634$	35.4907	−	6.99386i	1.40952	−	0.277762i
$635$	−9.60398	+	23.6617i	−0.381123	+	0.938988i
$636$	3.16263	−	1.29682i	0.125406	−	0.0514224i
$637$	4.12515	−	2.62996i	0.163445	−	0.104203i
$638$	−3.19045	−	16.1901i	−0.126311	−	0.640973i
$639$		−	5.80082i		−	0.229477i
$640$	−20.9594	−	14.1670i	−0.828492	−	0.560001i
$641$	−23.6502			−0.934127			−0.467064	−	0.884224i	$-0.654688\pi$
$641$	−23.6502			−0.934127			−0.467064	+	0.884224i	$0.654688\pi$
$642$	2.63121	+	13.3522i	0.103846	+	0.526970i
$643$	12.6788			0.500002			0.250001	−	0.968246i	$-0.419569\pi$
$643$	12.6788			0.500002			0.250001	+	0.968246i	$0.419569\pi$
$644$	−27.8841	−	3.14962i	−1.09879	−	0.124112i
$645$	15.6503	+	6.35224i	0.616230	+	0.250119i
$646$	−9.30011	−	47.1939i	−0.365908	−	1.85682i
$647$			4.87226i			0.191548i	0.995403	+	0.0957741i	$0.0305326\pi$
$647$			4.87226i			0.191548i	−0.995403	+	0.0957741i	$0.969467\pi$
$648$	−2.36011	+	1.55880i	−0.0927140	+	0.0612355i
$649$		−	14.3616i		−	0.563741i
$650$	2.69408	−	4.14294i	0.105670	−	0.162500i
$651$	−0.253359	−	0.138942i	−0.00992994	−	0.00544558i
$652$	8.69919	+	21.2151i	0.340687	+	0.830848i
$653$	18.1794			0.711414			0.355707	−	0.934597i	$-0.384240\pi$
$653$	18.1794			0.711414			0.355707	+	0.934597i	$0.384240\pi$
$654$	1.29715	+	6.58244i	0.0507224	+	0.257394i
$655$	−2.48738	−	1.00959i	−0.0971899	−	0.0394481i
$656$	−7.26935	−	7.37367i	−0.283821	−	0.287893i
$657$	−3.86018			−0.150600
$658$	−3.99460	+	12.5983i	−0.155726	+	0.491134i
$659$	38.8661			1.51401			0.757005	−	0.653409i	$-0.226662\pi$
$659$	38.8661			1.51401			0.757005	+	0.653409i	$0.226662\pi$
$660$	−0.0184811	−	5.18198i	−0.000719376	−	0.201708i
$661$	32.1806			1.25168			0.625841	−	0.779951i	$-0.284756\pi$
$661$	32.1806			1.25168			0.625841	+	0.779951i	$0.284756\pi$
$662$	6.45016	−	1.27108i	0.250693	−	0.0494019i
$663$			4.80245i			0.186512i
$664$	30.0215	−	19.8286i	1.16506	−	0.769497i
$665$	−18.4953	−	22.7033i	−0.717216	−	0.880397i
$666$	5.97428	−	1.17730i	0.231499	−	0.0456195i
$667$		−	53.4016i		−	2.06772i
$668$	15.0643	+	36.7381i	0.582857	+	1.42144i
$669$			4.53719i			0.175418i
$670$	−25.2271	−	4.87790i	−0.974609	−	0.188450i
$671$	5.66448			0.218675
$672$	13.3354	−	6.79457i	0.514426	−	0.262106i
$673$		−	40.4479i		−	1.55915i	−0.626308	−	0.779576i	$-0.715435\pi$
$673$		−	40.4479i		−	1.55915i	0.626308	−	0.779576i	$-0.284565\pi$
$674$	−0.470176	−	2.38593i	−0.0181105	−	0.0919027i
$675$	−3.58558	−	3.48477i	−0.138009	−	0.134129i
$676$	23.1523	−	9.49353i	0.890473	−	0.365136i
$677$			0.721800i			0.0277410i	0.999904	+	0.0138705i	$0.00441527\pi$
$677$			0.721800i			0.0277410i	−0.999904	+	0.0138705i	$0.995585\pi$
$678$	3.11604	+	15.8125i	0.119671	+	0.607276i
$679$	0.113276	+	0.0621207i	0.00434714	+	0.00238397i
$680$	8.55466	+	42.6094i	0.328056	+	1.63400i
$681$	12.4331			0.476438
$682$	0.175594	−	0.0346028i	0.00672384	−	0.00132501i
$683$		−	19.6600i		−	0.752270i	−0.926565	−	0.376135i	$-0.877253\pi$
$683$		−	19.6600i		−	0.752270i	0.926565	−	0.376135i	$-0.122747\pi$
$684$	−3.75581	−	9.15946i	−0.143607	−	0.350221i
$685$	8.89701	+	3.61118i	0.339937	+	0.137976i
$686$	6.74656	+	25.3078i	0.257585	+	0.966256i
$687$	−3.24679			−0.123873
$688$	−21.2120	−	21.5164i	−0.808700	−	0.820305i
$689$		−	1.19446i		−	0.0455052i
$690$	3.18365	−	16.4649i	0.121199	−	0.626809i
$691$		−	39.4005i		−	1.49886i	−0.662081	−	0.749432i	$-0.730327\pi$
$691$		−	39.4005i		−	1.49886i	0.662081	−	0.749432i	$-0.269673\pi$
$692$	−12.3781	−	30.1872i	−0.470546	−	1.14754i
$693$	2.68805	+	1.47413i	0.102111	+	0.0559975i
$694$	5.14014	+	26.0839i	0.195117	+	0.990133i
$695$	−24.8835	−	10.0999i	−0.943885	−	0.383110i
$696$	15.6969	+	23.7660i	0.594991	+	0.900849i
$697$			17.7879i			0.673763i
$698$	−38.3139	+	7.55020i	−1.45020	+	0.285779i
$699$			26.6500i			1.00799i
$700$	16.7835	+	20.4527i	0.634358	+	0.773040i
$701$			5.00623i			0.189083i	0.995521	+	0.0945413i	$0.0301384\pi$
$701$			5.00623i			0.189083i	−0.995521	+	0.0945413i	$0.969862\pi$
$702$	0.191095	+	0.969724i	0.00721243	+	0.0365999i
$703$			21.3123i			0.803809i
$704$	−3.63874	+	8.52585i	−0.137140	+	0.321330i
$705$	−7.31848	−	2.97047i	−0.275630	−	0.111875i
$706$	−28.0859	+	5.53465i	−1.05703	+	0.208299i
$707$	34.8440	+	19.1085i	1.31044	+	0.718648i
$708$	9.40447	+	22.9351i	0.353442	+	0.861955i
$709$			33.3192i			1.25133i	0.780093	+	0.625664i	$0.215172\pi$
$709$			33.3192i			1.25133i	−0.780093	+	0.625664i	$0.784828\pi$
$710$	−18.0102	−	3.48244i	−0.675911	−	0.130694i
$711$			6.30589i			0.236489i
$712$	1.31164	+	1.98590i	0.0491558	+	0.0744246i
$713$	0.579181			0.0216905
$714$	−24.5086	−	7.77103i	−0.917212	−	0.290823i
$715$	−1.67787	−	0.681027i	−0.0627490	−	0.0254690i
$716$	−37.8804	+	15.5327i	−1.41566	+	0.580486i
$717$		−	10.8623i		−	0.405659i
$718$	6.29980	+	31.9687i	0.235106	+	1.19306i
$719$	31.7733			1.18495			0.592473	−	0.805590i	$-0.298152\pi$
$719$	31.7733			1.18495			0.592473	+	0.805590i	$0.298152\pi$
$720$	3.42286	+	8.26341i	0.127563	+	0.307959i
$721$	−20.3856	+	37.1728i	−0.759199	+	1.38439i
$722$	7.63204	−	1.50398i	0.284035	−	0.0559724i
$723$			16.1547i			0.600798i
$724$	−26.8374	+	11.0046i	−0.997403	+	0.408982i
$725$	−35.0912	+	36.1063i	−1.30325	+	1.34095i
$726$	13.3998	−	2.64059i	0.497314	−	0.0980016i
$727$		−	19.6746i		−	0.729689i	−0.931068	−	0.364844i	$-0.881122\pi$
$727$		−	19.6746i		−	0.729689i	0.931068	−	0.364844i	$-0.118878\pi$
$728$	−0.428854	−	5.21237i	−0.0158944	−	0.193183i
$729$	1.00000			0.0370370
$730$	−2.31740	+	11.9850i	−0.0857709	+	0.443583i
$731$			51.9050i			1.91978i
$732$	−9.04605	+	3.70930i	−0.334352	+	0.137100i
$733$		−	29.8147i		−	1.10123i	−0.834758	−	0.550616i	$-0.814393\pi$
$733$		−	29.8147i		−	1.10123i	0.834758	−	0.550616i	$-0.185607\pi$
$734$	−2.98935	−	15.1696i	−0.110339	−	0.559921i
$735$	−15.3940	+	2.83300i	−0.567815	+	0.104497i
$736$	−16.8880	+	24.7938i	−0.622498	+	0.913911i
$737$			9.41504i			0.346807i
$738$	0.707800	+	3.59177i	0.0260545	+	0.132215i
$739$	−8.15114			−0.299845			−0.149922	−	0.988698i	$-0.547902\pi$
$739$	−8.15114			−0.299845			−0.149922	+	0.988698i	$0.547902\pi$
$740$	−0.0686733	−	19.2555i	−0.00252448	−	0.707848i
$741$	−3.45934			−0.127082
$742$	6.09575	+	1.93280i	0.223782	+	0.0709553i
$743$	22.4631			0.824092			0.412046	−	0.911163i	$-0.364814\pi$
$743$	22.4631			0.824092			0.412046	+	0.911163i	$0.364814\pi$
$744$	−0.257761	+	0.170245i	−0.00944996	+	0.00624149i
$745$	4.35002	+	1.76562i	0.159373	+	0.0646872i
$746$	32.6036	−	6.42492i	1.19370	−	0.235233i
$747$	−12.7204			−0.465414
$748$	14.7341	−	6.04167i	0.538732	−	0.220905i
$749$	−12.2423	+	22.3236i	−0.447324	+	0.815688i
$750$	−12.9720	+	9.04036i	−0.473669	+	0.330107i
$751$		−	36.0935i		−	1.31707i	−0.752551	−	0.658534i	$-0.771177\pi$
$751$		−	36.0935i		−	1.31707i	0.752551	−	0.658534i	$-0.228823\pi$
$752$	9.91928	+	10.0616i	0.361719	+	0.366910i
$753$		−	22.5756i		−	0.822699i
$754$	9.76499	−	1.92430i	0.355620	−	0.0700790i
$755$	−43.5842	−	17.6902i	−1.58619	−	0.643814i
$756$	−5.25807	−	0.593920i	−0.191234	−	0.0216006i
$757$	26.8241			0.974937			0.487469	−	0.873141i	$-0.337920\pi$
$757$	26.8241			0.974937			0.487469	+	0.873141i	$0.337920\pi$
$758$	3.52860	−	0.695352i	0.128165	−	0.0252563i
$759$	−6.14490			−0.223046
$760$	−30.6928	+	6.16216i	−1.11334	+	0.223525i
$761$			49.5586i			1.79650i	0.439488	+	0.898248i	$0.355160\pi$
$761$			49.5586i			1.79650i	−0.439488	+	0.898248i	$0.644840\pi$
$762$	−15.8460	+	3.12263i	−0.574039	+	0.113121i
$763$	−6.03526	+	11.0052i	−0.218491	+	0.398415i
$764$	15.0478	+	36.6978i	0.544410	+	1.32768i
$765$	5.77872	−	14.2373i	0.208930	−	0.514749i
$766$	−4.96578	−	25.1991i	−0.179421	−	0.910481i
$767$	8.66212			0.312771
$768$	0.227957	−	15.9984i	0.00822569	−	0.577292i
$769$		−	10.3517i		−	0.373292i	−0.982427	−	0.186646i	$-0.940238\pi$
$769$		−	10.3517i		−	0.373292i	0.982427	−	0.186646i	$-0.0597618\pi$
$770$	6.19056	−	7.46080i	0.223092	−	0.268869i
$771$	−12.0533			−0.434088
$772$	−0.712454	−	1.73749i	−0.0256418	−	0.0625338i
$773$		−	43.7636i		−	1.57407i	−0.616910	−	0.787033i	$-0.711616\pi$
$773$		−	43.7636i		−	1.57407i	0.616910	−	0.787033i	$-0.288384\pi$
$774$	2.06536	+	10.4808i	0.0742380	+	0.376725i
$775$	−0.391600	−	0.380591i	−0.0140667	−	0.0136712i
$776$	0.115244	−	0.0761161i	0.00413702	−	0.00273241i
$777$	9.98842	+	5.47766i	0.358333	+	0.196510i
$778$	−4.56645	−	23.1727i	−0.163715	−	0.830782i
$779$	−12.8131			−0.459077
$780$	3.12549	−	0.0111468i	0.111911	−	0.000399119i
$781$			6.72161i			0.240518i
$782$	50.5626	−	9.96395i	1.80812	−	0.356310i
$783$		−	10.0699i		−	0.359868i
$784$	27.2945	+	6.24574i	0.974804	+	0.223062i
$785$	−11.9472	−	4.84919i	−0.426412	−	0.173075i
$786$	−0.328259	−	1.66577i	−0.0117086	−	0.0594159i
$787$	−3.23802			−0.115423			−0.0577114	−	0.998333i	$-0.518380\pi$
$787$	−3.23802			−0.115423			−0.0577114	+	0.998333i	$0.518380\pi$
$788$	−41.1303	+	16.8653i	−1.46521	+	0.600803i
$789$	19.6608			0.699944
$790$	19.5783	+	3.78565i	0.696565	+	0.134687i
$791$	−14.4981	+	26.4370i	−0.515492	+	0.939992i
$792$	2.73474	−	1.80624i	0.0971749	−	0.0641819i
$793$			3.41651i			0.121324i
$794$	3.23253	+	16.4036i	0.114718	+	0.582143i
$795$	−1.43727	+	3.54107i	−0.0509749	+	0.125589i
$796$	14.0239	−	5.75045i	0.497063	−	0.203819i
$797$		−	24.9995i		−	0.885529i	−0.896638	−	0.442764i	$-0.853998\pi$
$797$		−	24.9995i		−	0.885529i	0.896638	−	0.442764i	$-0.146002\pi$
$798$	5.59769	−	17.6542i	0.198156	−	0.624953i
$799$		−	24.2721i		−	0.858687i
$800$	27.7109	−	5.66637i	0.979727	−	0.200336i
$801$		−	0.841441i		−	0.0297309i
$802$	−43.7824	+	8.62782i	−1.54601	+	0.304659i
$803$	4.47292			0.157846
$804$	−6.16530	−	15.0356i	−0.217433	−	0.530265i
$805$	24.3239	−	19.8155i	0.857304	−	0.698404i
$806$	0.0208705	+	0.105909i	0.000735133	+	0.00373048i
$807$	−1.22906			−0.0432650
$808$	35.4493	−	23.4135i	1.24710	−	0.823683i
$809$	−15.5950			−0.548290			−0.274145	−	0.961688i	$-0.588395\pi$
$809$	−15.5950			−0.548290			−0.274145	+	0.961688i	$0.588395\pi$
$810$	0.600336	−	3.10477i	0.0210937	−	0.109090i
$811$		−	12.4994i		−	0.438913i	−0.975622	−	0.219456i	$-0.929572\pi$
$811$		−	12.4994i		−	0.438913i	0.975622	−	0.219456i	$-0.0704283\pi$
$812$	−5.98069	+	52.9481i	−0.209881	+	1.85811i
$813$	−12.1597			−0.426459
$814$	−6.92261	+	1.36418i	−0.242637	+	0.0478145i
$815$	−23.7538	−	9.64133i	−0.832058	−	0.337721i
$816$	−19.5737	+	19.2968i	−0.685218	+	0.675524i
$817$	−37.3886			−1.30806
$818$	5.48391	+	27.8284i	0.191740	+	0.972997i
$819$	−0.889113	+	1.62128i	−0.0310681	+	0.0566523i
$820$	11.5765	−	0.0412868i	0.404271	−	0.00144180i
$821$			31.9570i			1.11531i	0.830074	+	0.557653i	$0.188298\pi$
$821$			31.9570i			1.11531i	−0.830074	+	0.557653i	$0.811702\pi$
$822$	1.17414	+	5.95822i	0.0409527	+	0.207817i
$823$	−16.0320			−0.558839			−0.279419	−	0.960169i	$-0.590142\pi$
$823$	−16.0320			−0.558839			−0.279419	+	0.960169i	$0.590142\pi$
$824$	24.9783	+	37.8186i	0.870161	+	1.31747i
$825$	4.15473	+	4.03792i	0.144649	+	0.140582i
$826$	−14.0165	+	44.2059i	−0.487697	+	1.53812i
$827$		−	21.7120i		−	0.755001i	−0.926009	−	0.377501i	$-0.876784\pi$
$827$		−	21.7120i		−	0.755001i	0.926009	−	0.377501i	$-0.123216\pi$
$828$	9.81326	−	4.02390i	0.341035	−	0.139840i
$829$	48.2421			1.67552			0.837759	−	0.546040i	$-0.183865\pi$
$829$	48.2421			1.67552			0.837759	+	0.546040i	$0.183865\pi$
$830$	−7.63650	+	39.4938i	−0.265067	+	1.37085i
$831$	24.1319			0.837126
$832$	−5.14233	−	2.19469i	−0.178278	−	0.0760872i
$833$	−25.8583	−	40.5594i	−0.895937	−	1.40530i
$834$	−3.28387	−	16.6642i	−0.113711	−	0.577033i
$835$	−41.1343	−	16.6958i	−1.42351	−	0.577783i
$836$	4.35198	+	10.6134i	0.150516	+	0.367071i
$837$	0.109215			0.00377504
$838$	1.65264	+	8.38641i	0.0570895	+	0.289704i
$839$	25.1122			0.866968			0.433484	−	0.901161i	$-0.357284\pi$
$839$	25.1122			0.866968			0.433484	+	0.901161i	$0.357284\pi$
$840$	−5.00059	+	15.9685i	−0.172537	+	0.550967i
$841$	−72.4023			−2.49663
$842$	5.63599	+	28.6001i	0.194229	+	0.985626i
$843$	2.45095			0.0844151
$844$	37.8512	−	15.5208i	1.30289	−	0.534247i
$845$	−10.5217	+	25.9228i	−0.361958	+	0.891770i
$846$	−0.965818	−	4.90110i	−0.0332055	−	0.168503i
$847$	22.4032	+	12.2859i	0.769784	+	0.422150i
$848$	4.86835	−	4.79948i	0.167180	−	0.164815i
$849$	−0.770452			−0.0264419
$850$	−40.7343	−	26.4887i	−1.39717	−	0.908556i
$851$	−22.8336			−0.782726
$852$	−4.40155	−	10.7343i	−0.150795	−	0.367750i
$853$			9.94325i			0.340450i	0.985405	+	0.170225i	$0.0544495\pi$
$853$			9.94325i			0.340450i	−0.985405	+	0.170225i	$0.945551\pi$
$854$	−17.4357	−	5.52838i	−0.596636	−	0.189177i
$855$	10.2555	+	4.16257i	0.350731	+	0.142357i
$856$	15.0004	+	22.7114i	0.512703	+	0.776261i
$857$	−22.3499			−0.763457			−0.381728	−	0.924275i	$-0.624671\pi$
$857$	−22.3499			−0.763457			−0.381728	+	0.924275i	$0.624671\pi$
$858$	−0.221429	−	1.12365i	−0.00755945	−	0.0383608i
$859$		−	11.5753i		−	0.394944i	−0.980309	−	0.197472i	$-0.936727\pi$
$859$		−	11.5753i		−	0.394944i	0.980309	−	0.197472i	$-0.0632731\pi$
$860$	33.7804	−	0.120475i	1.15190	−	0.00410816i
$861$	−3.29320	+	6.00510i	−0.112232	+	0.204653i
$862$	1.17848	+	5.98027i	0.0401393	+	0.203689i
$863$	42.1305			1.43414			0.717070	−	0.697001i	$-0.245483\pi$
$863$	42.1305			1.43414			0.717070	+	0.697001i	$0.245483\pi$
$864$	−3.18454	+	4.67533i	−0.108340	+	0.159058i
$865$	33.7994	+	13.7187i	1.14921	+	0.466451i
$866$	−34.4450	+	6.78779i	−1.17049	+	0.230658i
$867$	30.2187			1.02628
$868$	−0.574262	−	0.0648652i	−0.0194917	−	0.00220167i
$869$		−	7.30685i		−	0.247868i
$870$	−31.2646	−	6.04531i	−1.05997	−	0.204955i
$871$	−5.67864			−0.192413
$872$	7.39496	+	11.1964i	0.250425	+	0.379157i
$873$	−0.0488298			−0.00165264
$874$	7.17731	+	36.4217i	0.242776	+	1.23198i
$875$	−29.4672	−	2.58588i	−0.996172	−	0.0874185i
$876$	−7.14315	+	2.92903i	−0.241345	+	0.0989626i
$877$	−1.06166			−0.0358496			−0.0179248	−	0.999839i	$-0.505706\pi$
$877$	−1.06166			−0.0358496			−0.0179248	+	0.999839i	$0.505706\pi$
$878$	−2.52254	+	0.497095i	−0.0851315	+	0.0167761i
$879$		−	14.0583i		−	0.474175i
$880$	−3.96619	−	9.57510i	−0.133700	−	0.322777i
$881$		−	32.0206i		−	1.07880i	−0.842049	−	0.539401i	$-0.818651\pi$
$881$		−	32.0206i		−	1.07880i	0.842049	−	0.539401i	$-0.181349\pi$
$882$	−6.83529	−	7.16093i	−0.230156	−	0.241121i
$883$			28.8735i			0.971670i	0.874050	+	0.485835i	$0.161484\pi$
$883$			28.8735i			0.971670i	−0.874050	+	0.485835i	$0.838516\pi$
$884$	3.64400	+	8.88680i	0.122561	+	0.298896i
$885$	−25.6796	−	10.4230i	−0.863210	−	0.350365i
$886$	10.2054	+	51.7877i	0.342856	+	1.73984i
$887$			32.6544i			1.09643i	0.836339	+	0.548213i	$0.184692\pi$
$887$			32.6544i			1.09643i	−0.836339	+	0.548213i	$0.815308\pi$
$888$	10.1619	−	6.71173i	0.341012	−	0.225231i
$889$	−26.4929	−	14.5287i	−0.888545	−	0.487278i
$890$	−2.61248	−	0.505147i	−0.0875706	−	0.0169326i
$891$	−1.15873			−0.0388191
$892$	3.44273	+	8.39596i	0.115271	+	0.281117i
$893$	17.4839			0.585076
$894$	0.574071	+	2.91316i	0.0191998	+	0.0974306i
$895$	17.2150	−	42.4133i	0.575433	−	1.41772i
$896$	19.5213	−	22.6918i	0.652160	−	0.758081i
$897$		−	3.70627i		−	0.123749i
$898$	31.8990	−	6.28607i	1.06448	−	0.209769i
$899$		−	1.09978i		−	0.0366799i
$900$	−9.27919	−	3.72781i	−0.309306	−	0.124260i
$901$	−11.7442			−0.391255
$902$	−0.820153	−	4.16191i	−0.0273081	−	0.138576i
$903$	−9.60957	+	17.5229i	−0.319786	+	0.583126i
$904$	17.7644	+	26.8963i	0.590834	+	0.894556i
$905$	12.1964	−	30.0488i	0.405422	−	0.998856i
$906$	−5.75179	−	29.1878i	−0.191091	−	0.969700i
$907$		−	36.6780i		−	1.21787i	−0.793218	−	0.608937i	$-0.791596\pi$
$907$		−	36.6780i		−	1.21787i	0.793218	−	0.608937i	$-0.208404\pi$
$908$	23.0071	−	9.43400i	0.763519	−	0.313078i
$909$	−15.0202			−0.498187
$910$	4.49995	+	3.73381i	0.149172	+	0.123775i
$911$		−	38.1450i		−	1.26380i	−0.775049	−	0.631901i	$-0.782275\pi$
$911$		−	38.1450i		−	1.26380i	0.775049	−	0.631901i	$-0.217725\pi$
$912$	−13.9000	−	14.0995i	−0.460276	−	0.466881i
$913$	14.7395			0.487807
$914$	−10.1595	−	51.5549i	−0.336046	−	1.70529i
$915$	4.11103	−	10.1285i	0.135906	−	0.334839i
$916$	−6.00810	+	2.46360i	−0.198513	+	0.0813997i
$917$	1.52730	−	2.78500i	0.0504358	−	0.0919688i
$918$	9.53452	−	1.87889i	0.314686	−	0.0620125i
$919$		−	10.1269i		−	0.334056i	−0.985952	−	0.167028i	$-0.946583\pi$
$919$		−	10.1269i		−	0.334056i	0.985952	−	0.167028i	$-0.0534170\pi$
$920$	−6.60201	−	32.8836i	−0.217662	−	1.08414i
$921$	33.8488			1.11536
$922$	46.7975	−	9.22200i	1.54120	−	0.303710i
$923$	−4.05411			−0.133443
$924$	6.09270	+	0.688195i	0.200435	+	0.0226400i
$925$	15.4384	+	15.0044i	0.507612	+	0.493341i
$926$	24.0064	−	4.73074i	0.788900	−	0.155462i
$927$		−	16.0240i		−	0.526299i
$928$	47.0800	+	32.0679i	1.54548	+	1.05268i
$929$			28.8015i			0.944947i	0.881345	+	0.472474i	$0.156639\pi$
$929$			28.8015i			0.944947i	−0.881345	+	0.472474i	$0.843361\pi$
$930$	0.0655659	−	0.339089i	0.00214999	−	0.0111192i
$931$	29.2160	−	18.6265i	0.957517	−	0.610457i
$932$	20.2215	+	49.3151i	0.662377	+	1.61537i
$933$	14.3608			0.470150
$934$	8.96956	−	1.76756i	0.293493	−	0.0578362i
$935$	−6.69600	+	16.4972i	−0.218983	+	0.539516i
$936$	1.08942	+	1.64945i	0.0356089	+	0.0539139i
$937$	−31.8351			−1.04001			−0.520003	−	0.854164i	$-0.674069\pi$
$937$	−31.8351			−1.04001			−0.520003	+	0.854164i	$0.674069\pi$
$938$	9.18883	−	28.9801i	0.300026	−	0.946235i
$939$	−16.3655			−0.534068
$940$	−15.7966	+	0.0563372i	−0.515228	+	0.00183752i
$941$	−15.0378			−0.490217			−0.245109	−	0.969496i	$-0.578824\pi$
$941$	−15.0378			−0.490217			−0.245109	+	0.969496i	$0.578824\pi$
$942$	−1.57666	−	8.00086i	−0.0513705	−	0.260682i
$943$		−	13.7277i		−	0.447035i
$944$	34.8055	+	35.3049i	1.13282	+	1.14908i
$945$	4.58672	−	3.73658i	0.149206	−	0.121551i
$946$	−2.39321	−	12.1445i	−0.0778099	−	0.394851i
$947$		−	45.0438i		−	1.46373i	−0.681451	−	0.731864i	$-0.738651\pi$
$947$		−	45.0438i		−	1.46373i	0.681451	−	0.731864i	$-0.261349\pi$
$948$	4.78478	+	11.6689i	0.155402	+	0.378987i
$949$			2.69782i			0.0875749i
$950$	19.0806	−	29.3420i	0.619055	−	0.951981i
$951$	−25.5784			−0.829436
$952$	−51.2491	+	4.21658i	−1.66099	+	0.136660i
$953$		−	28.4561i		−	0.921782i	−0.887457	−	0.460891i	$-0.847530\pi$
$953$		−	28.4561i		−	0.921782i	0.887457	−	0.460891i	$-0.152470\pi$
$954$	−2.37141	+	0.467314i	−0.0767773	+	0.0151299i
$955$	−41.0891	−	16.6775i	−1.32961	−	0.539672i
$956$	−8.24208	−	20.1004i	−0.266568	−	0.650092i
$957$			11.6683i			0.377183i
$958$	40.4040	−	7.96208i	1.30540	−	0.257243i
$959$	−5.46293	+	9.96157i	−0.176407	+	0.321676i
$960$	12.6040	+	12.6940i	0.406793	+	0.409698i
$961$	−30.9881			−0.999615
$962$	−0.822799	−	4.17534i	−0.0265281	−	0.134618i
$963$		−	9.62303i		−	0.310098i
$964$	12.2578	+	29.8938i	0.394799	+	0.962814i
$965$	1.94541	+	0.789614i	0.0626248	+	0.0254186i
$966$	18.9144	+	5.99725i	0.608561	+	0.192958i
$967$	−16.7411			−0.538357			−0.269178	−	0.963090i	$-0.586752\pi$
$967$	−16.7411			−0.538357			−0.269178	+	0.963090i	$0.586752\pi$
$968$	22.7924	−	15.0539i	0.732576	−	0.483850i
$969$			34.0129i			1.09265i
$970$	−0.0293143	+	0.151605i	−0.000941226	+	0.00486776i
$971$			8.17899i			0.262476i	0.991351	+	0.131238i	$0.0418953\pi$
$971$			8.17899i			0.262476i	−0.991351	+	0.131238i	$0.958105\pi$
$972$	1.85047	−	0.758780i	0.0593540	−	0.0243379i
$973$	15.2789	−	27.8609i	0.489820	−	0.893179i
$974$	13.3381	−	2.62842i	0.427379	−	0.0842201i
$975$	−2.43546	+	2.50591i	−0.0779970	+	0.0802533i
$976$	−13.9249	+	13.7279i	−0.445726	+	0.439420i
$977$			44.9685i			1.43867i	0.694663	+	0.719335i	$0.255553\pi$
$977$			44.9685i			1.43867i	−0.694663	+	0.719335i	$0.744447\pi$
$978$	−3.13478	−	15.9076i	−0.100239	−	0.508669i
$979$			0.975007i			0.0311614i
$980$	−26.3365	+	16.9230i	−0.841289	+	0.540586i
$981$		−	4.74400i		−	0.151464i
$982$	5.34658	−	1.05360i	0.170616	−	0.0336219i
$983$			29.0890i			0.927794i	0.885889	+	0.463897i	$0.153549\pi$
$983$			29.0890i			0.927794i	−0.885889	+	0.463897i	$0.846451\pi$
$984$	4.03513	+	6.10942i	0.128635	+	0.194761i
$985$	18.6919	−	46.0520i	0.595573	−	1.46734i
$986$	−18.9202	−	96.0114i	−0.602541	−	3.05763i
$987$	4.49368	−	8.19416i	0.143035	−	0.260823i
$988$	−6.40141	+	2.62488i	−0.203656	+	0.0835085i
$989$		−	40.0575i		−	1.27375i
$990$	−0.695630	+	3.59760i	−0.0221086	+	0.114339i
$991$		−	0.727753i		−	0.0231178i	−0.999933	−	0.0115589i	$-0.996321\pi$
$991$		−	0.727753i		−	0.0231178i	0.999933	−	0.0115589i	$-0.00367940\pi$
$992$	−0.347801	+	0.510618i	−0.0110427	+	0.0162121i
$993$	−4.64867			−0.147521
$994$	6.56011	−	20.6896i	0.208074	−	0.656233i
$995$	−6.37324	+	15.7020i	−0.202045	+	0.497787i
$996$	−23.5387	+	9.65197i	−0.745853	+	0.305834i
$997$			15.1844i			0.480893i	0.970662	+	0.240447i	$0.0772939\pi$
$997$			15.1844i			0.480893i	−0.970662	+	0.240447i	$0.922706\pi$
$998$	−15.8452	+	3.12249i	−0.501572	+	0.0988406i
$999$	−4.30570			−0.136226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.w.b.139.4	yes	48
4.3	odd	2		3360.2.w.a.559.18		48
5.4	even	2		840.2.w.a.139.45	yes	48
7.6	odd	2		840.2.w.a.139.4	yes	48
8.3	odd	2	inner	840.2.w.b.139.46	yes	48
8.5	even	2		3360.2.w.a.559.31		48
20.19	odd	2		3360.2.w.b.559.17		48
28.27	even	2		3360.2.w.b.559.31		48
35.34	odd	2	inner	840.2.w.b.139.45	yes	48
40.19	odd	2		840.2.w.a.139.3	✓	48
40.29	even	2		3360.2.w.b.559.32		48
56.13	odd	2		3360.2.w.b.559.18		48
56.27	even	2		840.2.w.a.139.46	yes	48
140.139	even	2		3360.2.w.a.559.32		48
280.69	odd	2		3360.2.w.a.559.17		48
280.139	even	2	inner	840.2.w.b.139.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.w.a.139.3	✓	48	40.19	odd	2
840.2.w.a.139.4	yes	48	7.6	odd	2
840.2.w.a.139.45	yes	48	5.4	even	2
840.2.w.a.139.46	yes	48	56.27	even	2
840.2.w.b.139.3	yes	48	280.139	even	2	inner
840.2.w.b.139.4	yes	48	1.1	even	1	trivial
840.2.w.b.139.45	yes	48	35.34	odd	2	inner
840.2.w.b.139.46	yes	48	8.3	odd	2	inner
3360.2.w.a.559.17		48	280.69	odd	2
3360.2.w.a.559.18		48	4.3	odd	2
3360.2.w.a.559.31		48	8.5	even	2
3360.2.w.a.559.32		48	140.139	even	2
3360.2.w.b.559.17		48	20.19	odd	2
3360.2.w.b.559.18		48	56.13	odd	2
3360.2.w.b.559.31		48	28.27	even	2
3360.2.w.b.559.32		48	40.29	even	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.w (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38753 + 0.273429i) q^{2} +1.00000 q^{3} +(1.85047 - 0.758780i) q^{4} +(-0.840958 + 2.07190i) q^{5} +(-1.38753 + 0.273429i) q^{6} +(-2.31981 - 1.27219i) q^{7} +(-2.36011 + 1.55880i) q^{8} +1.00000 q^{9} +(0.600336 - 3.10477i) q^{10} -1.15873 q^{11} +(1.85047 - 0.758780i) q^{12} -0.698885i q^{13} +(3.56666 + 1.13089i) q^{14} +(-0.840958 + 2.07190i) q^{15} +(2.84850 - 2.80821i) q^{16} -6.87158 q^{17} +(-1.38753 + 0.273429i) q^{18} -4.94979i q^{19} +(0.0159494 + 4.47211i) q^{20} +(-2.31981 - 1.27219i) q^{21} +(1.60778 - 0.316831i) q^{22} +5.30311 q^{23} +(-2.36011 + 1.55880i) q^{24} +(-3.58558 - 3.48477i) q^{25} +(0.191095 + 0.969724i) q^{26} +1.00000 q^{27} +(-5.25807 - 0.593920i) q^{28} -10.0699i q^{29} +(0.600336 - 3.10477i) q^{30} +0.109215 q^{31} +(-3.18454 + 4.67533i) q^{32} -1.15873 q^{33} +(9.53452 - 1.87889i) q^{34} +(4.58672 - 3.73658i) q^{35} +(1.85047 - 0.758780i) q^{36} -4.30570 q^{37} +(1.35342 + 6.86798i) q^{38} -0.698885i q^{39} +(-1.24493 - 6.20082i) q^{40} -2.58861i q^{41} +(3.56666 + 1.13089i) q^{42} -7.55358i q^{43} +(-2.14421 + 0.879225i) q^{44} +(-0.840958 + 2.07190i) q^{45} +(-7.35822 + 1.45002i) q^{46} +3.53225i q^{47} +(2.84850 - 2.80821i) q^{48} +(3.76308 + 5.90248i) q^{49} +(5.92793 + 3.85482i) q^{50} -6.87158 q^{51} +(-0.530300 - 1.29327i) q^{52} +1.70909 q^{53} +(-1.38753 + 0.273429i) q^{54} +(0.974447 - 2.40079i) q^{55} +(7.45811 - 0.613625i) q^{56} -4.94979i q^{57} +(2.75339 + 13.9722i) q^{58} +12.3942i q^{59} +(0.0159494 + 4.47211i) q^{60} -4.88851 q^{61} +(-0.151539 + 0.0298626i) q^{62} +(-2.31981 - 1.27219i) q^{63} +(3.14027 - 7.35790i) q^{64} +(1.44802 + 0.587733i) q^{65} +(1.60778 - 0.316831i) q^{66} -8.12528i q^{67} +(-12.7157 + 5.21402i) q^{68} +5.30311 q^{69} +(-5.34252 + 6.43875i) q^{70} -5.80082i q^{71} +(-2.36011 + 1.55880i) q^{72} -3.86018 q^{73} +(5.97428 - 1.17730i) q^{74} +(-3.58558 - 3.48477i) q^{75} +(-3.75581 - 9.15946i) q^{76} +(2.68805 + 1.47413i) q^{77} +(0.191095 + 0.969724i) q^{78} +6.30589i q^{79} +(3.42286 + 8.26341i) q^{80} +1.00000 q^{81} +(0.707800 + 3.59177i) q^{82} -12.7204 q^{83} +(-5.25807 - 0.593920i) q^{84} +(5.77872 - 14.2373i) q^{85} +(2.06536 + 10.4808i) q^{86} -10.0699i q^{87} +(2.73474 - 1.80624i) q^{88} -0.841441i q^{89} +(0.600336 - 3.10477i) q^{90} +(-0.889113 + 1.62128i) q^{91} +(9.81326 - 4.02390i) q^{92} +0.109215 q^{93} +(-0.965818 - 4.90110i) q^{94} +(10.2555 + 4.16257i) q^{95} +(-3.18454 + 4.67533i) q^{96} -0.0488298 q^{97} +(-6.83529 - 7.16093i) q^{98} -1.15873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{9} + 8 q^{10} - 2 q^{14} + 8 q^{16} + 4 q^{20} + 48 q^{27} + 14 q^{28} + 8 q^{30} + 8 q^{35} - 12 q^{38} + 8 q^{40} - 2 q^{42} + 4 q^{44} - 8 q^{46} + 8 q^{48} - 12 q^{50} - 36 q^{52}+ \cdots + 40 q^{98}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^9 + 8 * q^10 - 2 * q^14 + 8 * q^16 + 4 * q^20 + 48 * q^27 + 14 * q^28 + 8 * q^30 + 8 * q^35 - 12 * q^38 + 8 * q^40 - 2 * q^42 + 4 * q^44 - 8 * q^46 + 8 * q^48 - 12 * q^50 - 36 * q^52 - 14 * q^56 + 4 * q^60 - 16 * q^62 + 24 * q^64 - 28 * q^68 + 6 * q^70 - 56 * q^74 - 20 * q^80 + 48 * q^81 + 36 * q^82 + 14 * q^84 - 20 * q^86 + 8 * q^90 - 16 * q^91 - 48 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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