LMFDB - Embedded newform 840.2.w.b.139.14

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)

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);

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")

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			139.14
Character	$\chi$	$=$	840.139
Dual form			840.2.w.b.139.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.911149 + 1.08158i) q^{2} +1.00000 q^{3} +(-0.339615 - 1.97095i) q^{4} +(-2.20852 + 0.349934i) q^{5} +(-0.911149 + 1.08158i) q^{6} +(0.795986 - 2.52317i) q^{7} +(2.44118 + 1.42851i) q^{8} +1.00000 q^{9} +(1.63381 - 2.70752i) q^{10} -1.30035 q^{11} +(-0.339615 - 1.97095i) q^{12} -1.98020i q^{13} +(2.00374 + 3.15991i) q^{14} +(-2.20852 + 0.349934i) q^{15} +(-3.76932 + 1.33873i) q^{16} -5.61979 q^{17} +(-0.911149 + 1.08158i) q^{18} +3.69919i q^{19} +(1.43975 + 4.23404i) q^{20} +(0.795986 - 2.52317i) q^{21} +(1.18481 - 1.40643i) q^{22} -7.46227 q^{23} +(2.44118 + 1.42851i) q^{24} +(4.75509 - 1.54567i) q^{25} +(2.14174 + 1.80426i) q^{26} +1.00000 q^{27} +(-5.24339 - 0.711945i) q^{28} +6.71456i q^{29} +(1.63381 - 2.70752i) q^{30} -10.3088 q^{31} +(1.98648 - 5.29659i) q^{32} -1.30035 q^{33} +(5.12046 - 6.07823i) q^{34} +(-0.875004 + 5.85101i) q^{35} +(-0.339615 - 1.97095i) q^{36} +1.94433 q^{37} +(-4.00095 - 3.37051i) q^{38} -1.98020i q^{39} +(-5.89127 - 2.30065i) q^{40} -2.70453i q^{41} +(2.00374 + 3.15991i) q^{42} -5.78886i q^{43} +(0.441619 + 2.56293i) q^{44} +(-2.20852 + 0.349934i) q^{45} +(6.79924 - 8.07102i) q^{46} -9.66070i q^{47} +(-3.76932 + 1.33873i) q^{48} +(-5.73281 - 4.01682i) q^{49} +(-2.66084 + 6.55133i) q^{50} -5.61979 q^{51} +(-3.90288 + 0.672505i) q^{52} -1.66702 q^{53} +(-0.911149 + 1.08158i) q^{54} +(2.87185 - 0.455037i) q^{55} +(5.54753 - 5.02244i) q^{56} +3.69919i q^{57} +(-7.26231 - 6.11796i) q^{58} -3.59059i q^{59} +(1.43975 + 4.23404i) q^{60} -5.08563 q^{61} +(9.39281 - 11.1497i) q^{62} +(0.795986 - 2.52317i) q^{63} +(3.91870 + 6.97451i) q^{64} +(0.692939 + 4.37330i) q^{65} +(1.18481 - 1.40643i) q^{66} +2.27909i q^{67} +(1.90856 + 11.0763i) q^{68} -7.46227 q^{69} +(-5.53106 - 6.27753i) q^{70} +7.30396i q^{71} +(2.44118 + 1.42851i) q^{72} -8.44901 q^{73} +(-1.77157 + 2.10294i) q^{74} +(4.75509 - 1.54567i) q^{75} +(7.29093 - 1.25630i) q^{76} +(-1.03506 + 3.28101i) q^{77} +(2.14174 + 1.80426i) q^{78} +7.73532i q^{79} +(7.85615 - 4.27562i) q^{80} +1.00000 q^{81} +(2.92516 + 2.46423i) q^{82} +6.73907 q^{83} +(-5.24339 - 0.711945i) q^{84} +(12.4114 - 1.96655i) q^{85} +(6.26109 + 5.27451i) q^{86} +6.71456i q^{87} +(-3.17439 - 1.85757i) q^{88} -2.02588i q^{89} +(1.63381 - 2.70752i) q^{90} +(-4.99639 - 1.57621i) q^{91} +(2.53430 + 14.7078i) q^{92} -10.3088 q^{93} +(10.4488 + 8.80233i) q^{94} +(-1.29447 - 8.16972i) q^{95} +(1.98648 - 5.29659i) q^{96} -1.76197 q^{97} +(9.56795 - 2.54055i) q^{98} -1.30035 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 $

$2$	−0.911149	+	1.08158i	−0.644280	+	0.764790i
$2$	−0.911149	+	1.08158i	−0.644280	+	0.764790i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.339615	−	1.97095i	−0.169807	−	0.985477i
$5$	−2.20852	+	0.349934i	−0.987679	+	0.156495i
$5$	−2.20852	+	0.349934i	−0.987679	+	0.156495i
$6$	−0.911149	+	1.08158i	−0.371975	+	0.441552i
$7$	0.795986	−	2.52317i	0.300854	−	0.953670i
$7$	0.795986	−	2.52317i	0.300854	−	0.953670i
$8$	2.44118	+	1.42851i	0.863087	+	0.505056i
$9$	1.00000			0.333333
$10$	1.63381	−	2.70752i	0.516655	−	0.856193i
$11$	−1.30035			−0.392071			−0.196035	−	0.980597i	$-0.562807\pi$
$11$	−1.30035			−0.392071			−0.196035	+	0.980597i	$0.562807\pi$
$12$	−0.339615	−	1.97095i	−0.0980384	−	0.568966i
$13$		−	1.98020i		−	0.549208i	−0.961557	−	0.274604i	$-0.911453\pi$
$13$		−	1.98020i		−	0.549208i	0.961557	−	0.274604i	$-0.0885468\pi$
$14$	2.00374	+	3.15991i	0.535523	+	0.844521i
$15$	−2.20852	+	0.349934i	−0.570237	+	0.0903526i
$16$	−3.76932	+	1.33873i	−0.942331	+	0.334683i
$17$	−5.61979			−1.36300			−0.681499	−	0.731819i	$-0.738672\pi$
$17$	−5.61979			−1.36300			−0.681499	+	0.731819i	$0.738672\pi$
$18$	−0.911149	+	1.08158i	−0.214760	+	0.254930i
$19$			3.69919i			0.848652i	0.905510	+	0.424326i	$0.139489\pi$
$19$			3.69919i			0.848652i	−0.905510	+	0.424326i	$0.860511\pi$
$20$	1.43975	+	4.23404i	0.321938	+	0.946761i
$21$	0.795986	−	2.52317i	0.173698	−	0.550602i
$22$	1.18481	−	1.40643i	0.252603	−	0.299852i
$23$	−7.46227			−1.55599			−0.777996	−	0.628270i	$-0.783763\pi$
$23$	−7.46227			−1.55599			−0.777996	+	0.628270i	$0.783763\pi$
$24$	2.44118	+	1.42851i	0.498303	+	0.291594i
$25$	4.75509	−	1.54567i	0.951018	−	0.309134i
$26$	2.14174	+	1.80426i	0.420029	+	0.353844i
$27$	1.00000			0.192450
$28$	−5.24339	−	0.711945i	−0.990907	−	0.134545i
$29$			6.71456i			1.24686i	0.781878	+	0.623431i	$0.214262\pi$
$29$			6.71456i			1.24686i	−0.781878	+	0.623431i	$0.785738\pi$
$30$	1.63381	−	2.70752i	0.298291	−	0.494324i
$31$	−10.3088			−1.85151			−0.925754	−	0.378128i	$-0.876568\pi$
$31$	−10.3088			−1.85151			−0.925754	+	0.378128i	$0.876568\pi$
$32$	1.98648	−	5.29659i	0.351163	−	0.936315i
$33$	−1.30035			−0.226362
$34$	5.12046	−	6.07823i	0.878152	−	1.04241i
$35$	−0.875004	+	5.85101i	−0.147903	+	0.989002i
$36$	−0.339615	−	1.97095i	−0.0566025	−	0.328492i
$37$	1.94433			0.319645			0.159823	−	0.987146i	$-0.448908\pi$
$37$	1.94433			0.319645			0.159823	+	0.987146i	$0.448908\pi$
$38$	−4.00095	−	3.37051i	−0.649040	−	0.546769i
$39$		−	1.98020i		−	0.317086i
$40$	−5.89127	−	2.30065i	−0.931491	−	0.363764i
$41$		−	2.70453i		−	0.422377i	−0.977445	−	0.211189i	$-0.932267\pi$
$41$		−	2.70453i		−	0.422377i	0.977445	−	0.211189i	$-0.0677335\pi$
$42$	2.00374	+	3.15991i	0.309184	+	0.487584i
$43$		−	5.78886i		−	0.882792i	−0.897312	−	0.441396i	$-0.854483\pi$
$43$		−	5.78886i		−	0.882792i	0.897312	−	0.441396i	$-0.145517\pi$
$44$	0.441619	+	2.56293i	0.0665765	+	0.386377i
$45$	−2.20852	+	0.349934i	−0.329226	+	0.0521651i
$46$	6.79924	−	8.07102i	1.00249	−	1.19001i
$47$		−	9.66070i		−	1.40916i	−0.709626	−	0.704579i	$-0.751136\pi$
$47$		−	9.66070i		−	1.40916i	0.709626	−	0.704579i	$-0.248864\pi$
$48$	−3.76932	+	1.33873i	−0.544055	+	0.193229i
$49$	−5.73281	−	4.01682i	−0.818973	−	0.573832i
$50$	−2.66084	+	6.55133i	−0.376299	+	0.926498i
$51$	−5.61979			−0.786927
$52$	−3.90288	+	0.672505i	−0.541232	+	0.0932597i
$53$	−1.66702			−0.228983			−0.114492	−	0.993424i	$-0.536524\pi$
$53$	−1.66702			−0.228983			−0.114492	+	0.993424i	$0.536524\pi$
$54$	−0.911149	+	1.08158i	−0.123992	+	0.147184i
$55$	2.87185	−	0.455037i	0.387240	−	0.0613572i
$56$	5.54753	−	5.02244i	0.741320	−	0.671152i
$57$			3.69919i			0.489969i
$58$	−7.26231	−	6.11796i	−0.953588	−	0.803328i
$59$		−	3.59059i		−	0.467455i	−0.972302	−	0.233727i	$-0.924908\pi$
$59$		−	3.59059i		−	0.467455i	0.972302	−	0.233727i	$-0.0750924\pi$
$60$	1.43975	+	4.23404i	0.185871	+	0.546613i
$61$	−5.08563			−0.651149			−0.325574	−	0.945516i	$-0.605558\pi$
$61$	−5.08563			−0.651149			−0.325574	+	0.945516i	$0.605558\pi$
$62$	9.39281	−	11.1497i	1.19289	−	1.41601i
$63$	0.795986	−	2.52317i	0.100285	−	0.317890i
$64$	3.91870	+	6.97451i	0.489837	+	0.871814i
$65$	0.692939	+	4.37330i	0.0859485	+	0.542441i
$66$	1.18481	−	1.40643i	0.145840	−	0.173119i
$67$			2.27909i			0.278435i	0.990262	+	0.139218i	$0.0444588\pi$
$67$			2.27909i			0.278435i	−0.990262	+	0.139218i	$0.955541\pi$
$68$	1.90856	+	11.0763i	0.231447	+	1.34320i
$69$	−7.46227			−0.898352
$70$	−5.53106	−	6.27753i	−0.661088	−	0.750308i
$71$			7.30396i			0.866821i	0.901197	+	0.433410i	$0.142690\pi$
$71$			7.30396i			0.866821i	−0.901197	+	0.433410i	$0.857310\pi$
$72$	2.44118	+	1.42851i	0.287696	+	0.168352i
$73$	−8.44901			−0.988882			−0.494441	−	0.869211i	$-0.664627\pi$
$73$	−8.44901			−0.988882			−0.494441	+	0.869211i	$0.664627\pi$
$74$	−1.77157	+	2.10294i	−0.205941	+	0.244461i
$75$	4.75509	−	1.54567i	0.549071	−	0.178479i
$76$	7.29093	−	1.25630i	0.836327	−	0.144107i
$77$	−1.03506	+	3.28101i	−0.117956	+	0.373906i
$78$	2.14174	+	1.80426i	0.242504	+	0.204292i
$79$			7.73532i			0.870292i	0.900360	+	0.435146i	$0.143303\pi$
$79$			7.73532i			0.870292i	−0.900360	+	0.435146i	$0.856697\pi$
$80$	7.85615	−	4.27562i	0.878344	−	0.478029i
$81$	1.00000			0.111111
$82$	2.92516	+	2.46423i	0.323030	+	0.272129i
$83$	6.73907			0.739709			0.369854	−	0.929090i	$-0.379408\pi$
$83$	6.73907			0.739709			0.369854	+	0.929090i	$0.379408\pi$
$84$	−5.24339	−	0.711945i	−0.572101	−	0.0776795i
$85$	12.4114	−	1.96655i	1.34620	−	0.213303i
$86$	6.26109	+	5.27451i	0.675151	+	0.568765i
$87$			6.71456i			0.719876i
$88$	−3.17439	−	1.85757i	−0.338391	−	0.198018i
$89$		−	2.02588i		−	0.214743i	−0.994219	−	0.107371i	$-0.965757\pi$
$89$		−	2.02588i		−	0.214743i	0.994219	−	0.107371i	$-0.0342434\pi$
$90$	1.63381	−	2.70752i	0.172218	−	0.285398i
$91$	−4.99639	−	1.57621i	−0.523763	−	0.165232i
$92$	2.53430	+	14.7078i	0.264219	+	1.53339i
$93$	−10.3088			−1.06897
$94$	10.4488	+	8.80233i	1.07771	+	0.907891i
$95$	−1.29447	−	8.16972i	−0.132810	−	0.838195i
$96$	1.98648	−	5.29659i	0.202744	−	0.540581i
$97$	−1.76197			−0.178901			−0.0894506	−	0.995991i	$-0.528511\pi$
$97$	−1.76197			−0.178901			−0.0894506	+	0.995991i	$0.528511\pi$
$98$	9.56795	−	2.54055i	0.966509	−	0.256634i
$99$	−1.30035			−0.130690
$100$	−4.66135	−	8.84714i	−0.466135	−	0.884714i
$101$	−2.52420			−0.251168			−0.125584	−	0.992083i	$-0.540080\pi$
$101$	−2.52420			−0.251168			−0.125584	+	0.992083i	$0.540080\pi$
$102$	5.12046	−	6.07823i	0.507001	−	0.601834i
$103$		−	13.8685i		−	1.36651i	−0.730181	−	0.683254i	$-0.760564\pi$
$103$		−	13.8685i		−	1.36651i	0.730181	−	0.683254i	$-0.239436\pi$
$104$	2.82874	−	4.83402i	0.277381	−	0.474014i
$105$	−0.875004	+	5.85101i	−0.0853917	+	0.571001i
$106$	1.51891	−	1.80301i	0.147529	−	0.175124i
$107$		−	8.20915i		−	0.793609i	−0.917903	−	0.396804i	$-0.870119\pi$
$107$		−	8.20915i		−	0.793609i	0.917903	−	0.396804i	$-0.129881\pi$
$108$	−0.339615	−	1.97095i	−0.0326795	−	0.189655i
$109$		−	9.34566i		−	0.895152i	−0.894246	−	0.447576i	$-0.852287\pi$
$109$		−	9.34566i		−	0.895152i	0.894246	−	0.447576i	$-0.147713\pi$
$110$	−2.12452	+	3.52073i	−0.202565	+	0.335688i
$111$	1.94433			0.184547
$112$	0.377523	+	10.5763i	0.0356726	+	0.999364i
$113$		−	12.5374i		−	1.17942i	−0.807614	−	0.589711i	$-0.799242\pi$
$113$		−	12.5374i		−	1.17942i	0.807614	−	0.589711i	$-0.200758\pi$
$114$	−4.00095	−	3.37051i	−0.374724	−	0.315677i
$115$	16.4806	−	2.61130i	1.53682	−	0.243505i
$116$	13.2341	−	2.28036i	1.22875	−	0.211727i
$117$		−	1.98020i		−	0.183069i
$118$	3.88350	+	3.27156i	0.357505	+	0.301172i
$119$	−4.47327	+	14.1797i	−0.410064	+	1.29985i
$120$	−5.89127	−	2.30065i	−0.537797	−	0.210019i
$121$	−9.30909			−0.846281
$122$	4.63377	−	5.50050i	0.419522	−	0.497992i
$123$		−	2.70453i		−	0.243860i
$124$	3.50101	+	20.3181i	0.314400	+	1.82462i
$125$	−9.96082	+	5.07761i	−0.890923	+	0.454155i
$126$	2.00374	+	3.15991i	0.178508	+	0.281507i
$127$	17.2027			1.52649			0.763247	−	0.646107i	$-0.223604\pi$
$127$	17.2027			1.52649			0.763247	+	0.646107i	$0.223604\pi$
$128$	−11.1140	−	2.11645i	−0.982347	−	0.187070i
$129$		−	5.78886i		−	0.509680i
$130$	−5.36143	−	3.23526i	−0.470229	−	0.283751i
$131$		−	14.1750i		−	1.23847i	−0.785205	−	0.619236i	$-0.787442\pi$
$131$		−	14.1750i		−	1.23847i	0.785205	−	0.619236i	$-0.212558\pi$
$132$	0.441619	+	2.56293i	0.0384380	+	0.223075i
$133$	9.33369	+	2.94450i	0.809334	+	0.255321i
$134$	−2.46501	−	2.07659i	−0.212945	−	0.179390i
$135$	−2.20852	+	0.349934i	−0.190079	+	0.0301175i
$136$	−13.7189	−	8.02794i	−1.17639	−	0.688390i
$137$			18.5295i			1.58308i	0.611116	+	0.791541i	$0.290721\pi$
$137$			18.5295i			1.58308i	−0.611116	+	0.791541i	$0.709279\pi$
$138$	6.79924	−	8.07102i	0.578790	−	0.687051i
$139$			14.7223i			1.24873i	0.781134	+	0.624363i	$0.214641\pi$
$139$			14.7223i			1.24873i	−0.781134	+	0.624363i	$0.785359\pi$
$140$	11.8292	−	0.262498i	0.999754	−	0.0221852i
$141$		−	9.66070i		−	0.813577i
$142$	−7.89979	−	6.65500i	−0.662936	−	0.558475i
$143$			2.57495i			0.215328i
$144$	−3.76932	+	1.33873i	−0.314110	+	0.111561i
$145$	−2.34965	−	14.8292i	−0.195128	−	1.23150i
$146$	7.69831	−	9.13825i	0.637117	−	0.756287i
$147$	−5.73281	−	4.01682i	−0.472834	−	0.331302i
$148$	−0.660322	−	3.83218i	−0.0542781	−	0.315003i
$149$			17.4926i			1.43305i	0.697560	+	0.716526i	$0.254269\pi$
$149$			17.4926i			1.43305i	−0.697560	+	0.716526i	$0.745731\pi$
$150$	−2.66084	+	6.55133i	−0.217256	+	0.534914i
$151$			1.12118i			0.0912400i	0.998959	+	0.0456200i	$0.0145263\pi$
$151$			1.12118i			0.0912400i	−0.998959	+	0.0456200i	$0.985474\pi$
$152$	−5.28434	+	9.03037i	−0.428616	+	0.732460i
$153$	−5.61979			−0.454333
$154$	−2.60557	−	4.10899i	−0.209963	−	0.331112i
$155$	22.7671	−	3.60738i	1.82869	−	0.289752i
$156$	−3.90288	+	0.672505i	−0.312481	+	0.0538435i
$157$			14.8336i			1.18385i	0.805994	+	0.591923i	$0.201631\pi$
$157$			14.8336i			1.18385i	−0.805994	+	0.591923i	$0.798369\pi$
$158$	−8.36634	−	7.04803i	−0.665590	−	0.560711i
$159$	−1.66702			−0.132203
$160$	−2.53371	+	12.3928i	−0.200307	+	0.979733i
$161$	−5.93986	+	18.8286i	−0.468127	+	1.48390i
$162$	−0.911149	+	1.08158i	−0.0715866	+	0.0849767i
$163$		−	12.8788i		−	1.00874i	−0.863486	−	0.504372i	$-0.831724\pi$
$163$		−	12.8788i		−	1.00874i	0.863486	−	0.504372i	$-0.168276\pi$
$164$	−5.33052	+	0.918500i	−0.416243	+	0.0717228i
$165$	2.87185	−	0.455037i	0.223573	−	0.0354246i
$166$	−6.14029	+	7.28881i	−0.476579	+	0.565722i
$167$		−	8.12780i		−	0.628948i	−0.949266	−	0.314474i	$-0.898172\pi$
$167$		−	8.12780i		−	0.628948i	0.949266	−	0.314474i	$-0.101828\pi$
$168$	5.54753	−	5.02244i	0.428001	−	0.387490i
$169$	9.07881			0.698370
$170$	−9.18165	+	15.2157i	−0.704200	+	1.16699i
$171$			3.69919i			0.282884i
$172$	−11.4096	+	1.96598i	−0.869972	+	0.149905i
$173$			23.5073i			1.78723i	0.448835	+	0.893615i	$0.351839\pi$
$173$			23.5073i			1.78723i	−0.448835	+	0.893615i	$0.648161\pi$
$174$	−7.26231	−	6.11796i	−0.550554	−	0.463802i
$175$	−0.115007	−	13.2283i	−0.00869372	−	0.999962i
$176$	4.90144	−	1.74082i	0.369460	−	0.131219i
$177$		−	3.59059i		−	0.269885i
$178$	2.19114	+	1.84588i	0.164233	+	0.138354i
$179$	21.4655			1.60441			0.802204	−	0.597050i	$-0.203661\pi$
$179$	21.4655			1.60441			0.802204	+	0.597050i	$0.203661\pi$
$180$	1.43975	+	4.23404i	0.107313	+	0.315587i
$181$	−1.03564			−0.0769787			−0.0384893	−	0.999259i	$-0.512255\pi$
$181$	−1.03564			−0.0769787			−0.0384893	+	0.999259i	$0.512255\pi$
$182$	6.25724	−	3.96781i	0.463818	−	0.294114i
$183$	−5.08563			−0.375941
$184$	−18.2167	−	10.6600i	−1.34296	−	0.785862i
$185$	−4.29408	+	0.680385i	−0.315707	+	0.0500229i
$186$	9.39281	−	11.1497i	0.688714	−	0.817536i
$187$	7.30769			0.534392
$188$	−19.0408	+	3.28092i	−1.38869	+	0.239285i
$189$	0.795986	−	2.52317i	0.0578995	−	0.183534i
$190$	10.0156	+	6.04376i	0.726610	+	0.438460i
$191$		−	25.2875i		−	1.82974i	−0.403748	−	0.914870i	$-0.632293\pi$
$191$		−	25.2875i		−	1.82974i	0.403748	−	0.914870i	$-0.367707\pi$
$192$	3.91870	+	6.97451i	0.282808	+	0.503342i
$193$			8.75697i			0.630341i	0.949035	+	0.315170i	$0.102062\pi$
$193$			8.75697i			0.630341i	−0.949035	+	0.315170i	$0.897938\pi$
$194$	1.60542	−	1.90571i	0.115262	−	0.136822i
$195$	0.692939	+	4.37330i	0.0496224	+	0.313179i
$196$	−5.97002	+	12.6633i	−0.426430	+	0.904520i
$197$	−12.2406			−0.872109			−0.436054	−	0.899920i	$-0.643624\pi$
$197$	−12.2406			−0.872109			−0.436054	+	0.899920i	$0.643624\pi$
$198$	1.18481	−	1.40643i	0.0842010	−	0.0999506i
$199$	−1.03389			−0.0732903			−0.0366452	−	0.999328i	$-0.511667\pi$
$199$	−1.03389			−0.0732903			−0.0366452	+	0.999328i	$0.511667\pi$
$200$	13.8160	+	3.01946i	0.976941	+	0.213508i
$201$			2.27909i			0.160755i
$202$	2.29993	−	2.73012i	0.161822	−	0.192091i
$203$	16.9420	+	5.34470i	1.18910	+	0.375124i
$204$	1.90856	+	11.0763i	0.133626	+	0.775499i
$205$	0.946409	+	5.97301i	0.0661000	+	0.417173i
$206$	14.9999	+	12.6363i	1.04509	+	0.880413i
$207$	−7.46227			−0.518664
$208$	2.65095	+	7.46401i	0.183811	+	0.517536i
$209$		−	4.81024i		−	0.332731i
$210$	−5.53106	−	6.27753i	−0.381679	−	0.433191i
$211$	−15.6365			−1.07646			−0.538231	−	0.842797i	$-0.680907\pi$
$211$	−15.6365			−1.07646			−0.538231	+	0.842797i	$0.680907\pi$
$212$	0.566146	+	3.28563i	0.0388830	+	0.225658i
$213$			7.30396i			0.500459i
$214$	8.87883	+	7.47976i	0.606944	+	0.511306i
$215$	2.02572	+	12.7848i	0.138153	+	0.871915i
$216$	2.44118	+	1.42851i	0.166101	+	0.0971981i
$217$	−8.20562	+	26.0108i	−0.557034	+	1.76573i
$218$	10.1080	+	8.51529i	0.684603	+	0.576728i
$219$	−8.44901			−0.570931
$220$	−1.87218	−	5.50574i	−0.126222	−	0.371197i
$221$			11.1283i			0.748570i
$222$	−1.77157	+	2.10294i	−0.118900	+	0.141140i
$223$			10.1557i			0.680077i	0.940412	+	0.340039i	$0.110440\pi$
$223$			10.1557i			0.680077i	−0.940412	+	0.340039i	$0.889560\pi$
$224$	−11.7830	−	9.22824i	−0.787286	−	0.616588i
$225$	4.75509	−	1.54567i	0.317006	−	0.103045i
$226$	13.5602	+	11.4235i	0.902011	+	0.759878i
$227$	12.4827			0.828509			0.414254	−	0.910161i	$-0.364042\pi$
$227$	12.4827			0.828509			0.414254	+	0.910161i	$0.364042\pi$
$228$	7.29093	−	1.25630i	0.482854	−	0.0832004i
$229$	9.62470			0.636018			0.318009	−	0.948088i	$-0.396986\pi$
$229$	9.62470			0.636018			0.318009	+	0.948088i	$0.396986\pi$
$230$	−12.1919	+	20.2043i	−0.803911	+	1.33223i
$231$	−1.03506	+	3.28101i	−0.0681020	+	0.215875i
$232$	−9.59184	+	16.3914i	−0.629735	+	1.07615i
$233$		−	21.1728i		−	1.38707i	−0.720421	−	0.693537i	$-0.756051\pi$
$233$		−	21.1728i		−	1.38707i	0.720421	−	0.693537i	$-0.243949\pi$
$234$	2.14174	+	1.80426i	0.140010	+	0.117948i
$235$	3.38061	+	21.3358i	0.220526	+	1.39179i
$236$	−7.07689	+	1.21942i	−0.460666	+	0.0793773i
$237$			7.73532i			0.502463i
$238$	−11.2606	−	17.7580i	−0.729917	−	1.15108i
$239$		−	11.4510i		−	0.740703i	−0.928892	−	0.370351i	$-0.879237\pi$
$239$		−	11.4510i		−	0.740703i	0.928892	−	0.370351i	$-0.120763\pi$
$240$	7.85615	−	4.27562i	0.507112	−	0.275990i
$241$			13.7870i			0.888101i	0.896002	+	0.444051i	$0.146459\pi$
$241$			13.7870i			0.888101i	−0.896002	+	0.444051i	$0.853541\pi$
$242$	8.48197	−	10.0685i	0.545241	−	0.647227i
$243$	1.00000			0.0641500
$244$	1.72716	+	10.0236i	0.110570	+	0.641692i
$245$	14.0666	+	6.86511i	0.898684	+	0.438596i
$246$	2.92516	+	2.46423i	0.186501	+	0.157114i
$247$	7.32512			0.466086
$248$	−25.1655	−	14.7262i	−1.59801	−	0.935115i
$249$	6.73907			0.427071
$250$	3.58397	−	15.3998i	0.226670	−	0.973972i
$251$			20.7067i			1.30700i	0.756927	+	0.653499i	$0.226700\pi$
$251$			20.7067i			1.30700i	−0.756927	+	0.653499i	$0.773300\pi$
$252$	−5.24339	−	0.711945i	−0.330302	−	0.0448483i
$253$	9.70357			0.610058
$254$	−15.6742	+	18.6060i	−0.983488	+	1.16745i
$255$	12.4114	−	1.96655i	0.777231	−	0.123150i
$256$	12.4156	−	10.0922i	0.775975	−	0.630764i
$257$	−6.02637			−0.375915			−0.187957	−	0.982177i	$-0.560187\pi$
$257$	−6.02637			−0.375915			−0.187957	+	0.982177i	$0.560187\pi$
$258$	6.26109	+	5.27451i	0.389798	+	0.328377i
$259$	1.54766	−	4.90587i	0.0961666	−	0.304836i
$260$	8.38425	−	2.85099i	0.519969	−	0.176811i
$261$			6.71456i			0.415621i
$262$	15.3313	+	12.9155i	0.947172	+	0.797923i
$263$	−3.54056			−0.218320			−0.109160	−	0.994024i	$-0.534816\pi$
$263$	−3.54056			−0.218320			−0.109160	+	0.994024i	$0.534816\pi$
$264$	−3.17439	−	1.85757i	−0.195370	−	0.114326i
$265$	3.68165	−	0.583348i	0.226162	−	0.0358348i
$266$	−11.6891	+	7.41222i	−0.716704	+	0.454472i
$267$		−	2.02588i		−	0.123982i
$268$	4.49199	−	0.774014i	0.274392	−	0.0472804i
$269$	21.7878			1.32842			0.664212	−	0.747544i	$-0.268767\pi$
$269$	21.7878			1.32842			0.664212	+	0.747544i	$0.268767\pi$
$270$	1.63381	−	2.70752i	0.0994304	−	0.164775i
$271$	13.3149			0.808824			0.404412	−	0.914577i	$-0.367476\pi$
$271$	13.3149			0.808824			0.404412	+	0.914577i	$0.367476\pi$
$272$	21.1828	−	7.52338i	1.28440	−	0.456172i
$273$	−4.99639	−	1.57621i	−0.302395	−	0.0953966i
$274$	−20.0411	−	16.8831i	−1.21073	−	1.01995i
$275$	−6.18329	+	2.00991i	−0.372866	+	0.121202i
$276$	2.53430	+	14.7078i	0.152547	+	0.885305i
$277$	−1.46216			−0.0878528			−0.0439264	−	0.999035i	$-0.513987\pi$
$277$	−1.46216			−0.0878528			−0.0439264	+	0.999035i	$0.513987\pi$
$278$	−15.9232	−	13.4142i	−0.955013	−	0.804529i
$279$	−10.3088			−0.617169
$280$	−10.4943	+	13.0334i	−0.627154	+	0.778895i
$281$	−27.3986			−1.63446			−0.817230	−	0.576311i	$-0.804492\pi$
$281$	−27.3986			−1.63446			−0.817230	+	0.576311i	$0.804492\pi$
$282$	10.4488	+	8.80233i	0.622216	+	0.524171i
$283$	−13.3187			−0.791717			−0.395858	−	0.918312i	$-0.629553\pi$
$283$	−13.3187			−0.791717			−0.395858	+	0.918312i	$0.629553\pi$
$284$	14.3958	−	2.48053i	0.854232	−	0.147193i
$285$	−1.29447	−	8.16972i	−0.0766778	−	0.483932i
$286$	−2.78501	−	2.34617i	−0.164681	−	0.138732i
$287$	−6.82401	−	2.15277i	−0.402809	−	0.127074i
$288$	1.98648	−	5.29659i	0.117054	−	0.312105i
$289$	14.5820			0.857764
$290$	18.1798	+	10.9703i	1.06756	+	0.644198i
$291$	−1.76197			−0.103289
$292$	2.86941	+	16.6526i	0.167920	+	0.974521i
$293$		−	8.59973i		−	0.502402i	−0.967935	−	0.251201i	$-0.919175\pi$
$293$		−	8.59973i		−	0.502402i	0.967935	−	0.251201i	$-0.0808255\pi$
$294$	9.56795	−	2.54055i	0.558014	−	0.148168i
$295$	1.25647	+	7.92988i	0.0731545	+	0.461695i
$296$	4.74644	+	2.77750i	0.275881	+	0.161439i
$297$	−1.30035			−0.0754540
$298$	−18.9196	−	15.9384i	−1.09598	−	0.923287i
$299$			14.7768i			0.854563i
$300$	−4.66135	−	8.84714i	−0.269123	−	0.510790i
$301$	−14.6063	−	4.60785i	−0.841893	−	0.265592i
$302$	−1.21264	−	1.02156i	−0.0697794	−	0.0587841i
$303$	−2.52420			−0.145012
$304$	−4.95222	−	13.9434i	−0.284029	−	0.799711i
$305$	11.2317	−	1.77964i	0.643126	−	0.101902i
$306$	5.12046	−	6.07823i	0.292717	−	0.347469i
$307$	0.730484			0.0416909			0.0208455	−	0.999783i	$-0.493364\pi$
$307$	0.730484			0.0416909			0.0208455	+	0.999783i	$0.493364\pi$
$308$	6.81825	+	0.925778i	0.388506	+	0.0527511i
$309$		−	13.8685i		−	0.788953i
$310$	−16.8425	+	27.9112i	−0.956591	+	1.58525i
$311$	3.97387			0.225337			0.112669	−	0.993633i	$-0.464060\pi$
$311$	3.97387			0.225337			0.112669	+	0.993633i	$0.464060\pi$
$312$	2.82874	−	4.83402i	0.160146	−	0.273672i
$313$	23.5606			1.33172			0.665861	−	0.746076i	$-0.268065\pi$
$313$	23.5606			1.33172			0.665861	+	0.746076i	$0.268065\pi$
$314$	−16.0436	−	13.5156i	−0.905394	−	0.762728i
$315$	−0.875004	+	5.85101i	−0.0493009	+	0.329667i
$316$	15.2460	−	2.62703i	0.857653	−	0.147782i
$317$	−19.6502			−1.10367			−0.551833	−	0.833955i	$-0.686071\pi$
$317$	−19.6502			−1.10367			−0.551833	+	0.833955i	$0.686071\pi$
$318$	1.51891	−	1.80301i	0.0851760	−	0.101108i
$319$		−	8.73129i		−	0.488858i
$320$	−11.0951	−	14.0320i	−0.620236	−	0.784415i
$321$		−	8.20915i		−	0.458190i
$322$	−14.9525	−	23.5801i	−0.833269	−	1.31407i
$323$		−	20.7886i		−	1.15671i
$324$	−0.339615	−	1.97095i	−0.0188675	−	0.109497i
$325$	−3.06073	−	9.41603i	−0.169779	−	0.522307i
$326$	13.9294	+	11.7345i	0.771477	+	0.649913i
$327$		−	9.34566i		−	0.516816i
$328$	3.86347	−	6.60225i	0.213324	−	0.364548i
$329$	−24.3756	−	7.68978i	−1.34387	−	0.423951i
$330$	−2.12452	+	3.52073i	−0.116951	+	0.193810i
$331$	−23.9573			−1.31681			−0.658406	−	0.752663i	$-0.728769\pi$
$331$	−23.9573			−1.31681			−0.658406	+	0.752663i	$0.728769\pi$
$332$	−2.28869	−	13.2824i	−0.125608	−	0.728966i
$333$	1.94433			0.106548
$334$	8.79084	+	7.40564i	0.481013	+	0.405218i
$335$	−0.797532	−	5.03341i	−0.0435738	−	0.275005i
$336$	0.377523	+	10.5763i	0.0205956	+	0.576983i
$337$		−	29.3836i		−	1.60063i	−0.599583	−	0.800313i	$-0.704667\pi$
$337$		−	29.3836i		−	1.60063i	0.599583	−	0.800313i	$-0.295333\pi$
$338$	−8.27215	+	9.81943i	−0.449946	+	0.534107i
$339$		−	12.5374i		−	0.680940i
$340$	−8.09108	−	23.7944i	−0.438800	−	1.29043i
$341$	13.4050			0.725922
$342$	−4.00095	−	3.37051i	−0.216347	−	0.182256i
$343$	−14.6984	+	11.2675i	−0.793638	+	0.608390i
$344$	8.26946	−	14.1316i	0.445859	−	0.761926i
$345$	16.4806	−	2.61130i	0.887283	−	0.140588i
$346$	−25.4250	−	21.4187i	−1.36686	−	1.15148i
$347$		−	8.16924i		−	0.438548i	−0.975663	−	0.219274i	$-0.929631\pi$
$347$		−	8.16924i		−	0.438548i	0.975663	−	0.219274i	$-0.0703688\pi$
$348$	13.2341	−	2.28036i	0.709422	−	0.122240i
$349$	16.5595			0.886408			0.443204	−	0.896421i	$-0.353842\pi$
$349$	16.5595			0.886408			0.443204	+	0.896421i	$0.353842\pi$
$350$	14.4122	+	11.9285i	0.770362	+	0.637606i
$351$		−	1.98020i		−	0.105695i
$352$	−2.58312	+	6.88743i	−0.137681	+	0.367101i
$353$	−16.7033			−0.889026			−0.444513	−	0.895772i	$-0.646623\pi$
$353$	−16.7033			−0.889026			−0.444513	+	0.895772i	$0.646623\pi$
$354$	3.88350	+	3.27156i	0.206406	+	0.173882i
$355$	−2.55590	−	16.1309i	−0.135653	−	0.856141i
$356$	−3.99292	+	0.688019i	−0.211624	+	0.0364649i
$357$	−4.47327	+	14.1797i	−0.236751	+	0.750469i
$358$	−19.5583	+	23.2166i	−1.03369	+	1.22704i
$359$		−	20.8523i		−	1.10054i	−0.834985	−	0.550272i	$-0.814524\pi$
$359$		−	20.8523i		−	1.10054i	0.834985	−	0.550272i	$-0.185476\pi$
$360$	−5.89127	−	2.30065i	−0.310497	−	0.121255i
$361$	5.31602			0.279791
$362$	0.943624	−	1.12013i	0.0495958	−	0.0588725i
$363$	−9.30909			−0.488600
$364$	−1.40979	+	10.3830i	−0.0738932	+	0.544215i
$365$	18.6598	−	2.95660i	0.976698	−	0.154755i
$366$	4.63377	−	5.50050i	0.242211	−	0.287516i
$367$		−	17.8487i		−	0.931693i	−0.884866	−	0.465847i	$-0.845750\pi$
$367$		−	17.8487i		−	0.931693i	0.884866	−	0.465847i	$-0.154250\pi$
$368$	28.1277	−	9.98997i	1.46626	−	0.520763i
$369$		−	2.70453i		−	0.140792i
$370$	3.17665	−	5.26430i	0.165146	−	0.273678i
$371$	−1.32693	+	4.20619i	−0.0688906	+	0.218374i
$372$	3.50101	+	20.3181i	0.181519	+	1.05344i
$373$	20.3709			1.05477			0.527384	−	0.849627i	$-0.323173\pi$
$373$	20.3709			1.05477			0.527384	+	0.849627i	$0.323173\pi$
$374$	−6.65840	+	7.90383i	−0.344298	+	0.408697i
$375$	−9.96082	+	5.07761i	−0.514374	+	0.262206i
$376$	13.8004	−	23.5835i	0.711703	−	1.21622i
$377$	13.2962			0.684787
$378$	2.00374	+	3.15991i	0.103061	+	0.162528i
$379$	33.2524			1.70806			0.854032	−	0.520221i	$-0.174150\pi$
$379$	33.2524			1.70806			0.854032	+	0.520221i	$0.174150\pi$
$380$	−15.6625	+	5.32590i	−0.803470	+	0.273213i
$381$	17.2027			0.881321
$382$	27.3504	+	23.0407i	1.39937	+	1.17886i
$383$			22.1178i			1.13017i	0.825034	+	0.565083i	$0.191156\pi$
$383$			22.1178i			1.13017i	−0.825034	+	0.565083i	$0.808844\pi$
$384$	−11.1140	−	2.11645i	−0.567158	−	0.108005i
$385$	1.13781	−	7.60837i	0.0579883	−	0.387759i
$386$	−9.47134	−	7.97891i	−0.482078	−	0.406116i
$387$		−	5.78886i		−	0.294264i
$388$	0.598392	+	3.47277i	0.0303788	+	0.176303i
$389$		−	16.9019i		−	0.856959i	−0.903551	−	0.428480i	$-0.859049\pi$
$389$		−	16.9019i		−	0.856959i	0.903551	−	0.428480i	$-0.140951\pi$
$390$	−5.36143	−	3.23526i	−0.271487	−	0.163824i
$391$	41.9364			2.12081
$392$	−8.25673	−	17.9952i	−0.417028	−	0.908894i
$393$		−	14.1750i		−	0.715033i
$394$	11.1530	−	13.2392i	0.561882	−	0.666980i
$395$	−2.70685	−	17.0836i	−0.136197	−	0.859569i
$396$	0.441619	+	2.56293i	0.0221922	+	0.128792i
$397$		−	13.6211i		−	0.683625i	−0.939768	−	0.341813i	$-0.888959\pi$
$397$		−	13.6211i		−	0.683625i	0.939768	−	0.341813i	$-0.111041\pi$
$398$	0.942025	−	1.11823i	0.0472195	−	0.0560517i
$399$	9.33369	+	2.94450i	0.467269	+	0.147409i
$400$	−15.8542	+	12.1919i	−0.792712	+	0.609596i
$401$	−17.0852			−0.853196			−0.426598	−	0.904441i	$-0.640288\pi$
$401$	−17.0852			−0.853196			−0.426598	+	0.904441i	$0.640288\pi$
$402$	−2.46501	−	2.07659i	−0.122944	−	0.103571i
$403$			20.4134i			1.01686i
$404$	0.857257	+	4.97509i	0.0426502	+	0.247520i
$405$	−2.20852	+	0.349934i	−0.109742	+	0.0173884i
$406$	−21.2174	+	13.4543i	−1.05300	+	0.667723i
$407$	−2.52831			−0.125323
$408$	−13.7189	−	8.02794i	−0.679186	−	0.397442i
$409$			19.1043i			0.944646i	0.881426	+	0.472323i	$0.156584\pi$
$409$			19.1043i			0.944646i	−0.881426	+	0.472323i	$0.843416\pi$
$410$	−7.32259	−	4.41869i	−0.361637	−	0.218224i
$411$			18.5295i			0.913993i
$412$	−27.3342	+	4.70996i	−1.34666	+	0.232043i
$413$	−9.05968	−	2.85806i	−0.445798	−	0.140636i
$414$	6.79924	−	8.07102i	0.334164	−	0.396669i
$415$	−14.8833	+	2.35823i	−0.730594	+	0.115761i
$416$	−10.4883	−	3.93362i	−0.514232	−	0.192861i
$417$			14.7223i			0.720952i
$418$	5.20264	+	4.38285i	0.254470	+	0.214372i
$419$		−	35.4795i		−	1.73329i	−0.498926	−	0.866645i	$-0.666272\pi$
$419$		−	35.4795i		−	1.73329i	0.498926	−	0.866645i	$-0.333728\pi$
$420$	11.8292	−	0.262498i	0.577208	−	0.0128086i
$421$		−	17.0251i		−	0.829751i	−0.909878	−	0.414875i	$-0.863825\pi$
$421$		−	17.0251i		−	0.829751i	0.909878	−	0.414875i	$-0.136175\pi$
$422$	14.2472	−	16.9121i	0.693542	−	0.823267i
$423$		−	9.66070i		−	0.469719i
$424$	−4.06950	−	2.38136i	−0.197632	−	0.115649i
$425$	−26.7226	+	8.68633i	−1.29624	+	0.421349i
$426$	−7.89979	−	6.65500i	−0.382746	−	0.322436i
$427$	−4.04809	+	12.8319i	−0.195901	+	0.620981i
$428$	−16.1799	+	2.78795i	−0.782083	+	0.134761i
$429$			2.57495i			0.124320i
$430$	−15.6735	−	9.45788i	−0.755841	−	0.456099i
$431$		−	21.6127i		−	1.04105i	−0.853847	−	0.520524i	$-0.825737\pi$
$431$		−	21.6127i		−	1.04105i	0.853847	−	0.520524i	$-0.174263\pi$
$432$	−3.76932	+	1.33873i	−0.181352	+	0.0644097i
$433$	−39.1417			−1.88103			−0.940515	−	0.339753i	$-0.889657\pi$
$433$	−39.1417			−1.88103			−0.940515	+	0.339753i	$0.889657\pi$
$434$	−20.6561	−	32.5747i	−0.991524	−	1.56364i
$435$	−2.34965	−	14.8292i	−0.112657	−	0.711007i
$436$	−18.4199	+	3.17393i	−0.882152	+	0.152004i
$437$		−	27.6043i		−	1.32049i
$438$	7.69831	−	9.13825i	0.367839	−	0.436643i
$439$	21.5089			1.02656			0.513282	−	0.858220i	$-0.328429\pi$
$439$	21.5089			1.02656			0.513282	+	0.858220i	$0.328429\pi$
$440$	7.66072	+	2.99165i	0.365210	+	0.142621i
$441$	−5.73281	−	4.01682i	−0.272991	−	0.191277i
$442$	−12.0361	−	10.1395i	−0.572499	−	0.482288i
$443$			19.5800i			0.930275i	0.885238	+	0.465138i	$0.153995\pi$
$443$			19.5800i			0.930275i	−0.885238	+	0.465138i	$0.846005\pi$
$444$	−0.660322	−	3.83218i	−0.0313375	−	0.181867i
$445$	0.708924	+	4.47419i	0.0336062	+	0.212097i
$446$	−10.9842	−	9.25337i	−0.520116	−	0.438160i
$447$			17.4926i			0.827373i
$448$	20.7171	−	4.33594i	0.978793	−	0.204854i
$449$	−13.9204			−0.656945			−0.328473	−	0.944513i	$-0.606534\pi$
$449$	−13.9204			−0.656945			−0.328473	+	0.944513i	$0.606534\pi$
$450$	−2.66084	+	6.55133i	−0.125433	+	0.308833i
$451$			3.51685i			0.165602i
$452$	−24.7107	+	4.25790i	−1.16229	+	0.200275i
$453$			1.12118i			0.0526774i
$454$	−11.3736	+	13.5010i	−0.533791	+	0.633635i
$455$	11.5862	+	1.73268i	0.543168	+	0.0812294i
$456$	−5.28434	+	9.03037i	−0.247462	+	0.422886i
$457$			24.9640i			1.16776i	0.811838	+	0.583882i	$0.198467\pi$
$457$			24.9640i			1.16776i	−0.811838	+	0.583882i	$0.801533\pi$
$458$	−8.76954	+	10.4099i	−0.409774	+	0.486420i
$459$	−5.61979			−0.262309
$460$	−10.7438	−	31.5956i	−0.500932	−	1.47315i
$461$	11.7567			0.547563			0.273781	−	0.961792i	$-0.411726\pi$
$461$	11.7567			0.547563			0.273781	+	0.961792i	$0.411726\pi$
$462$	−2.60557	−	4.10899i	−0.121222	−	0.191167i
$463$	−6.94099			−0.322575			−0.161288	−	0.986907i	$-0.551565\pi$
$463$	−6.94099			−0.322575			−0.161288	+	0.986907i	$0.551565\pi$
$464$	−8.98899	−	25.3093i	−0.417303	−	1.17496i
$465$	22.7671	−	3.60738i	1.05580	−	0.167288i
$466$	22.9000	+	19.2915i	1.06082	+	0.893663i
$467$	−33.2685			−1.53948			−0.769741	−	0.638356i	$-0.779615\pi$
$467$	−33.2685			−1.53948			−0.769741	+	0.638356i	$0.779615\pi$
$468$	−3.90288	+	0.672505i	−0.180411	+	0.0310866i
$469$	5.75055	+	1.81413i	0.265536	+	0.0837685i
$470$	−26.1565	−	15.7837i	−1.20651	−	0.728049i
$471$			14.8336i			0.683494i
$472$	5.12921	−	8.76527i	0.236091	−	0.403454i
$473$			7.52755i			0.346117i
$474$	−8.36634	−	7.04803i	−0.384279	−	0.323727i
$475$	5.71772	+	17.5900i	0.262347	+	0.807083i
$476$	29.4667	+	4.00098i	1.35061	+	0.183384i
$477$	−1.66702			−0.0763277
$478$	12.3851	+	10.4336i	0.566482	+	0.477220i
$479$	−10.8692			−0.496626			−0.248313	−	0.968680i	$-0.579876\pi$
$479$	−10.8692			−0.496626			−0.248313	+	0.968680i	$0.579876\pi$
$480$	−2.53371	+	12.3928i	−0.115647	+	0.565649i
$481$		−	3.85015i		−	0.175552i
$482$	−14.9117	−	12.5620i	−0.679211	−	0.572186i
$483$	−5.93986	+	18.8286i	−0.270273	+	0.856731i
$484$	3.16150	+	18.3478i	0.143705	+	0.833990i
$485$	3.89135	−	0.616574i	0.176697	−	0.0279972i
$486$	−0.911149	+	1.08158i	−0.0413306	+	0.0490613i
$487$	41.5766			1.88402			0.942008	−	0.335591i	$-0.108936\pi$
$487$	41.5766			1.88402			0.942008	+	0.335591i	$0.108936\pi$
$488$	−12.4149	−	7.26490i	−0.561998	−	0.328866i
$489$		−	12.8788i		−	0.582399i
$490$	−20.2419	+	8.95900i	−0.914438	+	0.404726i
$491$	24.8987			1.12366			0.561831	−	0.827252i	$-0.310097\pi$
$491$	24.8987			1.12366			0.561831	+	0.827252i	$0.310097\pi$
$492$	−5.33052	+	0.918500i	−0.240318	+	0.0414092i
$493$		−	37.7344i		−	1.69947i
$494$	−6.67428	+	7.92268i	−0.300290	+	0.356458i
$495$	2.87185	−	0.455037i	0.129080	−	0.0204524i
$496$	38.8570	−	13.8007i	1.74473	−	0.619668i
$497$	18.4292	+	5.81385i	0.826661	+	0.260787i
$498$	−6.14029	+	7.28881i	−0.275153	+	0.326620i
$499$	−21.7174			−0.972206			−0.486103	−	0.873902i	$-0.661582\pi$
$499$	−21.7174			−0.972206			−0.486103	+	0.873902i	$0.661582\pi$
$500$	13.3906	+	17.9079i	0.598845	+	0.800865i
$501$		−	8.12780i		−	0.363123i
$502$	−22.3959	−	18.8669i	−0.999579	−	0.842072i
$503$		−	21.1888i		−	0.944760i	−0.881395	−	0.472380i	$-0.843395\pi$
$503$		−	21.1888i		−	0.944760i	0.881395	−	0.472380i	$-0.156605\pi$
$504$	5.54753	−	5.02244i	0.247107	−	0.223717i
$505$	5.57475	−	0.883305i	0.248073	−	0.0393065i
$506$	−8.84140	+	10.4952i	−0.393048	+	0.466567i
$507$	9.07881			0.403204
$508$	−5.84229	−	33.9057i	−0.259210	−	1.50432i
$509$	−19.4366			−0.861512			−0.430756	−	0.902468i	$-0.641753\pi$
$509$	−19.4366			−0.861512			−0.430756	+	0.902468i	$0.641753\pi$
$510$	−9.18165	+	15.2157i	−0.406570	+	0.673762i
$511$	−6.72530	+	21.3183i	−0.297510	+	0.943067i
$512$	−0.396952	+	22.6239i	−0.0175430	+	0.999846i
$513$			3.69919i			0.163323i
$514$	5.49092	−	6.51798i	0.242194	−	0.287496i
$515$	4.85307	+	30.6289i	0.213852	+	1.34967i
$516$	−11.4096	+	1.96598i	−0.502278	+	0.0865475i
$517$			12.5623i			0.552489i
$518$	3.89593	+	6.14389i	0.171177	+	0.269947i
$519$			23.5073i			1.03186i
$520$	−4.55574	+	11.6659i	−0.199782	+	0.511583i
$521$		−	13.2081i		−	0.578659i	−0.957230	−	0.289329i	$-0.906568\pi$
$521$		−	13.2081i		−	0.578659i	0.957230	−	0.289329i	$-0.0934323\pi$
$522$	−7.26231	−	6.11796i	−0.317863	−	0.267776i
$523$	−1.05251			−0.0460232			−0.0230116	−	0.999735i	$-0.507325\pi$
$523$	−1.05251			−0.0460232			−0.0230116	+	0.999735i	$0.507325\pi$
$524$	−27.9382	+	4.81403i	−1.22049	+	0.210302i
$525$	−0.115007	−	13.2283i	−0.00501932	−	0.577328i
$526$	3.22598	−	3.82939i	0.140659	−	0.166969i
$527$	57.9330			2.52360
$528$	4.90144	−	1.74082i	0.213308	−	0.0757595i
$529$	32.6855			1.42111
$530$	−2.72359	+	4.51350i	−0.118305	+	0.196054i
$531$		−	3.59059i		−	0.155818i
$532$	2.63362	−	19.3963i	0.114182	−	0.840935i
$533$	−5.35552			−0.231973
$534$	2.19114	+	1.84588i	0.0948201	+	0.0798790i
$535$	2.87266	+	18.1301i	0.124196	+	0.783831i
$536$	−3.25572	+	5.56367i	−0.140625	+	0.240314i
$537$	21.4655			0.926306
$538$	−19.8519	+	23.5651i	−0.855877	+	1.01597i
$539$	7.45467	+	5.22328i	0.321095	+	0.224983i
$540$	1.43975	+	4.23404i	0.0619569	+	0.182204i
$541$			34.3179i			1.47544i	0.675107	+	0.737720i	$0.264098\pi$
$541$			34.3179i			1.47544i	−0.675107	+	0.737720i	$0.735902\pi$
$542$	−12.1319	+	14.4011i	−0.521109	+	0.618580i
$543$	−1.03564			−0.0444437
$544$	−11.1636	+	29.7657i	−0.478634	+	1.27619i
$545$	3.27036	+	20.6401i	0.140087	+	0.884123i
$546$	6.25724	−	3.96781i	0.267785	−	0.169807i
$547$		−	39.5446i		−	1.69080i	−0.534131	−	0.845402i	$-0.679361\pi$
$547$		−	39.5446i		−	1.69080i	0.534131	−	0.845402i	$-0.320639\pi$
$548$	36.5208	−	6.29289i	1.56009	−	0.268819i
$549$	−5.08563			−0.217050
$550$	3.46002	−	8.51903i	0.147536	−	0.363253i
$551$	−24.8384			−1.05815
$552$	−18.2167	−	10.6600i	−0.775356	−	0.453718i
$553$	19.5176	+	6.15721i	0.829971	+	0.261831i
$554$	1.33225	−	1.58144i	0.0566018	−	0.0671890i
$555$	−4.29408	+	0.680385i	−0.182273	+	0.0288808i
$556$	29.0169	−	4.99990i	1.23059	−	0.212043i
$557$	−12.2418			−0.518703			−0.259351	−	0.965783i	$-0.583509\pi$
$557$	−12.2418			−0.518703			−0.259351	+	0.965783i	$0.583509\pi$
$558$	9.39281	−	11.1497i	0.397629	−	0.472005i
$559$	−11.4631			−0.484837
$560$	−4.53476	−	23.2258i	−0.191629	−	0.981468i
$561$	7.30769			0.308531
$562$	24.9642	−	29.6336i	1.05305	−	1.25002i
$563$	9.18710			0.387190			0.193595	−	0.981082i	$-0.437985\pi$
$563$	9.18710			0.387190			0.193595	+	0.981082i	$0.437985\pi$
$564$	−19.0408	+	3.28092i	−0.801762	+	0.138152i
$565$	4.38727	+	27.6891i	0.184574	+	1.16489i
$566$	12.1354	−	14.4052i	0.510087	−	0.605497i
$567$	0.795986	−	2.52317i	0.0334283	−	0.105963i
$568$	−10.4338	+	17.8303i	−0.437793	+	0.748142i
$569$	25.2164			1.05713			0.528564	−	0.848893i	$-0.322731\pi$
$569$	25.2164			1.05713			0.528564	+	0.848893i	$0.322731\pi$
$570$	10.0156	+	6.04376i	0.419508	+	0.253145i
$571$	−16.5882			−0.694193			−0.347096	−	0.937829i	$-0.612832\pi$
$571$	−16.5882			−0.694193			−0.347096	+	0.937829i	$0.612832\pi$
$572$	5.07512	−	0.874493i	0.212201	−	0.0365644i
$573$		−	25.2875i		−	1.05640i
$574$	8.54608	−	5.41919i	0.356706	−	0.226193i
$575$	−35.4838	+	11.5342i	−1.47978	+	0.481010i
$576$	3.91870	+	6.97451i	0.163279	+	0.290605i
$577$	33.0170			1.37451			0.687257	−	0.726414i	$-0.258814\pi$
$577$	33.0170			1.37451			0.687257	+	0.726414i	$0.258814\pi$
$578$	−13.2864	+	15.7715i	−0.552640	+	0.656009i
$579$			8.75697i			0.363927i
$580$	−28.4297	+	9.66728i	−1.18048	+	0.401412i
$581$	5.36420	−	17.0038i	0.222545	−	0.705438i
$582$	1.60542	−	1.90571i	0.0665468	−	0.0789942i
$583$	2.16771			0.0897776
$584$	−20.6255	−	12.0695i	−0.853491	−	0.499441i
$585$	0.692939	+	4.37330i	0.0286495	+	0.180814i
$586$	9.30127	+	7.83564i	0.384232	+	0.323687i
$587$	−22.4990			−0.928633			−0.464316	−	0.885669i	$-0.653700\pi$
$587$	−22.4990			−0.928633			−0.464316	+	0.885669i	$0.653700\pi$
$588$	−5.97002	+	12.6633i	−0.246200	+	0.522225i
$589$		−	38.1340i		−	1.57128i
$590$	−9.72160	−	5.86633i	−0.400232	−	0.241513i
$591$	−12.2406			−0.503512
$592$	−7.32879	+	2.60293i	−0.301211	+	0.106980i
$593$	17.3914			0.714177			0.357089	−	0.934071i	$-0.383769\pi$
$593$	17.3914			0.714177			0.357089	+	0.934071i	$0.383769\pi$
$594$	1.18481	−	1.40643i	0.0486135	−	0.0577065i
$595$	4.91734	−	32.8814i	0.201591	−	1.34801i
$596$	34.4772	−	5.94076i	1.41224	−	0.243343i
$597$	−1.03389			−0.0423142
$598$	−15.9822	−	13.4638i	−0.653561	−	0.550578i
$599$		−	25.1318i		−	1.02686i	−0.858133	−	0.513428i	$-0.828375\pi$
$599$		−	25.1318i		−	1.02686i	0.858133	−	0.513428i	$-0.171625\pi$
$600$	13.8160	+	3.01946i	0.564037	+	0.123269i
$601$			3.67626i			0.149958i	0.997185	+	0.0749789i	$0.0238889\pi$
$601$			3.67626i			0.149958i	−0.997185	+	0.0749789i	$0.976111\pi$
$602$	18.2922	−	11.5994i	0.745536	−	0.472756i
$603$			2.27909i			0.0928118i
$604$	2.20979	−	0.380768i	0.0899149	−	0.0154932i
$605$	20.5593	−	3.25757i	0.835853	−	0.132439i
$606$	2.29993	−	2.73012i	0.0934281	−	0.110904i
$607$		−	8.13992i		−	0.330389i	−0.986261	−	0.165195i	$-0.947175\pi$
$607$		−	8.13992i		−	0.330389i	0.986261	−	0.165195i	$-0.0528252\pi$
$608$	19.5931	+	7.34834i	0.794605	+	0.298015i
$609$	16.9420	+	5.34470i	0.686525	+	0.216578i
$610$	−8.30895	+	13.7695i	−0.336419	+	0.557509i
$611$	−19.1301			−0.773921
$612$	1.90856	+	11.0763i	0.0771491	+	0.447735i
$613$	−20.2573			−0.818185			−0.409093	−	0.912493i	$-0.634155\pi$
$613$	−20.2573			−0.818185			−0.409093	+	0.912493i	$0.634155\pi$
$614$	−0.665580	+	0.790074i	−0.0268606	+	0.0318848i
$615$	0.946409	+	5.97301i	0.0381629	+	0.240855i
$616$	−7.21374	+	6.53093i	−0.290650	+	0.263139i
$617$		−	4.00904i		−	0.161398i	−0.996739	−	0.0806989i	$-0.974285\pi$
$617$		−	4.00904i		−	0.161398i	0.996739	−	0.0806989i	$-0.0257152\pi$
$618$	14.9999	+	12.6363i	0.603384	+	0.508307i
$619$			46.0413i			1.85056i	0.379289	+	0.925278i	$0.376169\pi$
$619$			46.0413i			1.85056i	−0.379289	+	0.925278i	$0.623831\pi$
$620$	−14.8420	−	43.6477i	−0.596070	−	1.75293i
$621$	−7.46227			−0.299451
$622$	−3.62079	+	4.29804i	−0.145180	+	0.172336i
$623$	−5.11165	−	1.61257i	−0.204794	−	0.0646063i
$624$	2.65095	+	7.46401i	0.106123	+	0.298799i
$625$	20.2218	−	14.6996i	0.808872	−	0.587984i
$626$	−21.4672	+	25.4825i	−0.858001	+	1.01849i
$627$		−	4.81024i		−	0.192103i
$628$	29.2363	−	5.03770i	1.16665	−	0.201026i
$629$	−10.9267			−0.435676
$630$	−5.53106	−	6.27753i	−0.220363	−	0.250103i
$631$			10.7739i			0.428900i	0.976735	+	0.214450i	$0.0687959\pi$
$631$			10.7739i			0.428900i	−0.976735	+	0.214450i	$0.931204\pi$
$632$	−11.0500	+	18.8833i	−0.439546	+	0.751137i
$633$	−15.6365			−0.621496
$634$	17.9043	−	21.2532i	0.711069	−	0.844072i
$635$	−37.9925	+	6.01981i	−1.50768	+	0.238889i
$636$	0.566146	+	3.28563i	0.0224491	+	0.130284i
$637$	−7.95410	+	11.3521i	−0.315153	+	0.449787i
$638$	9.44355	+	7.95550i	0.373874	+	0.314961i
$639$			7.30396i			0.288940i
$640$	25.2860	+	0.785055i	0.999518	+	0.0310320i
$641$	−32.5201			−1.28447			−0.642233	−	0.766509i	$-0.721992\pi$
$641$	−32.5201			−1.28447			−0.642233	+	0.766509i	$0.721992\pi$
$642$	8.87883	+	7.47976i	0.350419	+	0.295203i
$643$	−7.14506			−0.281774			−0.140887	−	0.990026i	$-0.544995\pi$
$643$	−7.14506			−0.281774			−0.140887	+	0.990026i	$0.544995\pi$
$644$	39.1276	+	5.31272i	1.54184	+	0.209351i
$645$	2.02572	+	12.7848i	0.0797625	+	0.503400i
$646$	22.4845	+	18.9415i	0.884641	+	0.745245i
$647$			23.1371i			0.909614i	0.890590	+	0.454807i	$0.150292\pi$
$647$			23.1371i			0.909614i	−0.890590	+	0.454807i	$0.849708\pi$
$648$	2.44118	+	1.42851i	0.0958985	+	0.0561173i
$649$			4.66903i			0.183275i
$650$	12.9729	+	5.26899i	0.508840	+	0.206667i
$651$	−8.20562	+	26.0108i	−0.321604	+	1.01944i
$652$	−25.3835	+	4.37383i	−0.994094	+	0.171292i
$653$	12.6552			0.495238			0.247619	−	0.968857i	$-0.420352\pi$
$653$	12.6552			0.495238			0.247619	+	0.968857i	$0.420352\pi$
$654$	10.1080	+	8.51529i	0.395256	+	0.332974i
$655$	4.96030	+	31.3057i	0.193815	+	1.22321i
$656$	3.62064	+	10.1943i	0.141362	+	0.398019i
$657$	−8.44901			−0.329627
$658$	30.5269	−	19.3576i	1.19006	−	0.754636i
$659$	6.16566			0.240180			0.120090	−	0.992763i	$-0.461682\pi$
$659$	6.16566			0.240180			0.120090	+	0.992763i	$0.461682\pi$
$660$	−1.87218	−	5.50574i	−0.0728745	−	0.214311i
$661$	−47.7018			−1.85538			−0.927692	−	0.373347i	$-0.878210\pi$
$661$	−47.7018			−1.85538			−0.927692	+	0.373347i	$0.878210\pi$
$662$	21.8287	−	25.9116i	0.848395	−	1.00708i
$663$			11.1283i			0.432187i
$664$	16.4513	+	9.62685i	0.638433	+	0.373594i
$665$	−21.6440	−	3.23680i	−0.839318	−	0.125518i
$666$	−1.77157	+	2.10294i	−0.0686469	+	0.0814871i
$667$		−	50.1059i		−	1.94011i
$668$	−16.0195	+	2.76032i	−0.619814	+	0.106800i
$669$			10.1557i			0.392643i
$670$	6.17069	+	3.72360i	0.238395	+	0.143855i
$671$	6.61311			0.255296
$672$	−11.7830	−	9.22824i	−0.454540	−	0.355987i
$673$		−	28.8374i		−	1.11160i	−0.831315	−	0.555801i	$-0.812412\pi$
$673$		−	28.8374i		−	1.11160i	0.831315	−	0.555801i	$-0.187588\pi$
$674$	31.7806	+	26.7728i	1.22414	+	1.03125i
$675$	4.75509	−	1.54567i	0.183024	−	0.0594929i
$676$	−3.08330	−	17.8939i	−0.118588	−	0.688228i
$677$		−	1.72096i		−	0.0661417i	−0.999453	−	0.0330708i	$-0.989471\pi$
$677$		−	1.72096i		−	0.0661417i	0.999453	−	0.0330708i	$-0.0105287\pi$
$678$	13.5602	+	11.4235i	0.520776	+	0.438716i
$679$	−1.40251	+	4.44576i	−0.0538232	+	0.170613i
$680$	33.1077	+	12.9291i	1.26962	+	0.495810i
$681$	12.4827			0.478340
$682$	−12.2140	+	14.4985i	−0.467696	+	0.555178i
$683$			7.04600i			0.269608i	0.990872	+	0.134804i	$0.0430405\pi$
$683$			7.04600i			0.269608i	−0.990872	+	0.134804i	$0.956960\pi$
$684$	7.29093	−	1.25630i	0.278776	−	0.0480358i
$685$	−6.48410	−	40.9227i	−0.247745	−	1.56358i
$686$	1.20570	−	26.1638i	0.0460338	−	0.998940i
$687$	9.62470			0.367205
$688$	7.74972	+	21.8201i	0.295455	+	0.831882i
$689$			3.30104i			0.125759i
$690$	−12.1919	+	20.2043i	−0.464138	+	0.769163i
$691$		−	37.9396i		−	1.44329i	−0.692264	−	0.721644i	$-0.743387\pi$
$691$		−	37.9396i		−	1.44329i	0.692264	−	0.721644i	$-0.256613\pi$
$692$	46.3319	−	7.98344i	1.76127	−	0.303485i
$693$	−1.03506	+	3.28101i	−0.0393187	+	0.124635i
$694$	8.83565	+	7.44339i	0.335397	+	0.282547i
$695$	−5.15182	−	32.5144i	−0.195420	−	1.23334i
$696$	−9.59184	+	16.3914i	−0.363578	+	0.621316i
$697$			15.1989i			0.575700i
$698$	−15.0881	+	17.9103i	−0.571095	+	0.677916i
$699$		−	21.1728i		−	0.800827i
$700$	−26.0332	+	4.71919i	−0.983964	+	0.178369i
$701$			4.82214i			0.182130i	0.995845	+	0.0910649i	$0.0290271\pi$
$701$			4.82214i			0.182130i	−0.995845	+	0.0910649i	$0.970973\pi$
$702$	2.14174	+	1.80426i	0.0808346	+	0.0680973i
$703$			7.19242i			0.271267i
$704$	−5.09568	−	9.06931i	−0.192051	−	0.341813i
$705$	3.38061	+	21.3358i	0.127321	+	0.803553i
$706$	15.2192	−	18.0659i	0.572781	−	0.679918i
$707$	−2.00923	+	6.36901i	−0.0755649	+	0.239531i
$708$	−7.07689	+	1.21942i	−0.265966	+	0.0458285i
$709$			29.7215i			1.11621i	0.829769	+	0.558107i	$0.188472\pi$
$709$			29.7215i			1.11621i	−0.829769	+	0.558107i	$0.811528\pi$
$710$	19.7756	+	11.9333i	0.742166	+	0.447848i
$711$			7.73532i			0.290097i
$712$	2.89400	−	4.94553i	0.108457	−	0.185342i
$713$	76.9267			2.88093
$714$	−11.2606	−	17.7580i	−0.421418	−	0.664576i
$715$	−0.901064	−	5.68683i	−0.0336979	−	0.212675i
$716$	−7.29001	−	42.3076i	−0.272441	−	1.58111i
$717$		−	11.4510i		−	0.427645i
$718$	22.5534	+	18.9996i	0.841686	+	0.709059i
$719$	−12.6120			−0.470348			−0.235174	−	0.971953i	$-0.575566\pi$
$719$	−12.6120			−0.470348			−0.235174	+	0.971953i	$0.575566\pi$
$720$	7.85615	−	4.27562i	0.292781	−	0.159343i
$721$	−34.9927	−	11.0392i	−1.30320	−	0.411120i
$722$	−4.84369	+	5.74968i	−0.180263	+	0.213981i
$723$			13.7870i			0.512746i
$724$	0.351719	+	2.04120i	0.0130716	+	0.0758607i
$725$	10.3785	+	31.9284i	0.385448	+	1.18579i
$726$	8.48197	−	10.0685i	0.314795	−	0.373677i
$727$			38.1524i			1.41500i	0.706716	+	0.707498i	$0.250176\pi$
$727$			38.1524i			1.41500i	−0.706716	+	0.707498i	$0.749824\pi$
$728$	−9.94543	−	10.9852i	−0.368602	−	0.407139i
$729$	1.00000			0.0370370
$730$	−13.8041	+	22.8759i	−0.510911	+	0.846675i
$731$			32.5321i			1.20324i
$732$	1.72716	+	10.0236i	0.0638376	+	0.370481i
$733$		−	8.51250i		−	0.314416i	−0.987565	−	0.157208i	$-0.949751\pi$
$733$		−	8.51250i		−	0.314416i	0.987565	−	0.157208i	$-0.0502493\pi$
$734$	19.3047	+	16.2628i	0.712550	+	0.600271i
$735$	14.0666	+	6.86511i	0.518856	+	0.253224i
$736$	−14.8236	+	39.5246i	−0.546406	+	1.45690i
$737$		−	2.96362i		−	0.109166i
$738$	2.92516	+	2.46423i	0.107677	+	0.0907097i
$739$	−29.1631			−1.07278			−0.536390	−	0.843970i	$-0.680213\pi$
$739$	−29.1631			−1.07278			−0.536390	+	0.843970i	$0.680213\pi$
$740$	2.79934	+	8.23236i	0.102906	+	0.302627i
$741$	7.32512			0.269095
$742$	−3.34029	−	5.26764i	−0.122626	−	0.193381i
$743$	39.8537			1.46209			0.731045	−	0.682329i	$-0.239033\pi$
$743$	39.8537			1.46209			0.731045	+	0.682329i	$0.239033\pi$
$744$	−25.1655	−	14.7262i	−0.922612	−	0.539889i
$745$	−6.12127	−	38.6328i	−0.224266	−	1.41540i
$746$	−18.5610	+	22.0327i	−0.679565	+	0.806676i
$747$	6.73907			0.246570
$748$	−2.48180	−	14.4031i	−0.0907437	−	0.526631i
$749$	−20.7131	−	6.53437i	−0.756841	−	0.238761i
$750$	3.58397	−	15.3998i	0.130868	−	0.562323i
$751$		−	52.3872i		−	1.91164i	−0.293959	−	0.955818i	$-0.594973\pi$
$751$		−	52.3872i		−	1.91164i	0.293959	−	0.955818i	$-0.405027\pi$
$752$	12.9331	+	36.4143i	0.471621	+	1.32789i
$753$			20.7067i			0.754596i
$754$	−12.1148	+	14.3808i	−0.441194	+	0.523718i
$755$	−0.392337	−	2.47613i	−0.0142786	−	0.0901158i
$756$	−5.24339	−	0.711945i	−0.190700	−	0.0258932i
$757$	−54.1507			−1.96814			−0.984071	−	0.177778i	$-0.943109\pi$
$757$	−54.1507			−1.96814			−0.984071	+	0.177778i	$0.943109\pi$
$758$	−30.2979	+	35.9651i	−1.10047	+	1.30631i
$759$	9.70357			0.352217
$760$	8.51052	−	21.7929i	0.308709	−	0.790511i
$761$			29.1269i			1.05585i	0.849291	+	0.527925i	$0.177030\pi$
$761$			29.1269i			1.05585i	−0.849291	+	0.527925i	$0.822970\pi$
$762$	−15.6742	+	18.6060i	−0.567817	+	0.674026i
$763$	−23.5807	−	7.43902i	−0.853680	−	0.269310i
$764$	−49.8405	+	8.58802i	−1.80317	+	0.310704i
$765$	12.4114	−	1.96655i	0.448735	−	0.0711009i
$766$	−23.9221	−	20.1526i	−0.864340	−	0.728143i
$767$	−7.11008			−0.256730
$768$	12.4156	−	10.0922i	0.448009	−	0.364172i
$769$			20.5536i			0.741183i	0.928796	+	0.370591i	$0.120845\pi$
$769$			20.5536i			0.741183i	−0.928796	+	0.370591i	$0.879155\pi$
$770$	7.19232	+	8.16299i	0.259193	+	0.294174i
$771$	−6.02637			−0.217034
$772$	17.2596	−	2.97400i	0.621187	−	0.107037i
$773$		−	2.88830i		−	0.103885i	−0.998650	−	0.0519425i	$-0.983459\pi$
$773$		−	2.88830i		−	0.103885i	0.998650	−	0.0519425i	$-0.0165413\pi$
$774$	6.26109	+	5.27451i	0.225050	+	0.189588i
$775$	−49.0191	+	15.9339i	−1.76082	+	0.572364i
$776$	−4.30129	−	2.51700i	−0.154407	−	0.0903551i
$777$	1.54766	−	4.90587i	0.0555218	−	0.175997i
$778$	18.2807	+	15.4001i	0.655394	+	0.552121i
$779$	10.0046			0.358451
$780$	8.38425	−	2.85099i	0.300204	−	0.102082i
$781$		−	9.49772i		−	0.339855i
$782$	−38.2103	+	45.3574i	−1.36640	+	1.62198i
$783$			6.71456i			0.239959i
$784$	26.9863	+	7.46601i	0.963795	+	0.266643i
$785$	−5.19077	−	32.7602i	−0.185266	−	1.16926i
$786$	15.3313	+	12.9155i	0.546850	+	0.460681i
$787$	−22.4624			−0.800700			−0.400350	−	0.916362i	$-0.631111\pi$
$787$	−22.4624			−0.800700			−0.400350	+	0.916362i	$0.631111\pi$
$788$	4.15710	+	24.1257i	0.148091	+	0.859443i
$789$	−3.54056			−0.126047
$790$	20.9436	+	12.6380i	0.745138	+	0.449641i
$791$	−31.6341	−	9.97962i	−1.12478	−	0.354835i
$792$	−3.17439	−	1.85757i	−0.112797	−	0.0660059i
$793$			10.0706i			0.357616i
$794$	14.7323	+	12.4109i	0.522830	+	0.440446i
$795$	3.68165	−	0.583348i	0.130575	−	0.0206892i
$796$	0.351124	+	2.03774i	0.0124452	+	0.0722260i
$797$			38.1473i			1.35125i	0.737247	+	0.675623i	$0.236125\pi$
$797$			38.1473i			1.35125i	−0.737247	+	0.675623i	$0.763875\pi$
$798$	−11.6891	+	7.41222i	−0.413789	+	0.262390i
$799$			54.2910i			1.92068i
$800$	1.25909	−	28.2562i	0.0445154	−	0.999009i
$801$		−	2.02588i		−	0.0715810i
$802$	15.5672	−	18.4790i	0.549697	−	0.652516i
$803$	10.9867			0.387712
$804$	4.49199	−	0.774014i	0.158420	−	0.0272974i
$805$	6.52952	−	43.6619i	0.230135	−	1.53888i
$806$	−22.0786	−	18.5996i	−0.777687	−	0.655144i
$807$	21.7878			0.766966
$808$	−6.16203	−	3.60586i	−0.216780	−	0.126854i
$809$	−14.1010			−0.495763			−0.247882	−	0.968790i	$-0.579734\pi$
$809$	−14.1010			−0.495763			−0.247882	+	0.968790i	$0.579734\pi$
$810$	1.63381	−	2.70752i	0.0574061	−	0.0951326i
$811$		−	28.4482i		−	0.998953i	−0.866327	−	0.499477i	$-0.833526\pi$
$811$		−	28.4482i		−	0.998953i	0.866327	−	0.499477i	$-0.166474\pi$
$812$	4.78040	−	35.2071i	0.167759	−	1.23553i
$813$	13.3149			0.466975
$814$	2.30366	−	2.73456i	0.0807434	−	0.0958461i
$815$	4.50672	+	28.4430i	0.157864	+	0.996315i
$816$	21.1828	−	7.52338i	0.741546	−	0.263371i
$817$	21.4141			0.749183
$818$	−20.6627	−	17.4068i	−0.722456	−	0.608616i
$819$	−4.99639	−	1.57621i	−0.174588	−	0.0550772i
$820$	11.4511	−	3.89385i	0.399890	−	0.135979i
$821$			25.3459i			0.884576i	0.896873	+	0.442288i	$0.145833\pi$
$821$			25.3459i			0.884576i	−0.896873	+	0.442288i	$0.854167\pi$
$822$	−20.0411	−	16.8831i	−0.699012	−	0.588867i
$823$	−21.7824			−0.759287			−0.379643	−	0.925133i	$-0.623953\pi$
$823$	−21.7824			−0.759287			−0.379643	+	0.925133i	$0.623953\pi$
$824$	19.8114	−	33.8556i	0.690163	−	1.17941i
$825$	−6.18329	+	2.00991i	−0.215275	+	0.0699762i
$826$	11.3459	−	7.19462i	0.394775	−	0.250333i
$827$		−	23.4875i		−	0.816741i	−0.912816	−	0.408371i	$-0.866097\pi$
$827$		−	23.4875i		−	0.816741i	0.912816	−	0.408371i	$-0.133903\pi$
$828$	2.53430	+	14.7078i	0.0880730	+	0.511131i
$829$	8.40558			0.291938			0.145969	−	0.989289i	$-0.453370\pi$
$829$	8.40558			0.291938			0.145969	+	0.989289i	$0.453370\pi$
$830$	11.0103	−	18.2462i	0.382174	−	0.633334i
$831$	−1.46216			−0.0507219
$832$	13.8109	−	7.75980i	0.478807	−	0.269023i
$833$	32.2172	+	22.5737i	1.11626	+	0.782132i
$834$	−15.9232	−	13.4142i	−0.551377	−	0.464495i
$835$	2.84419	+	17.9504i	0.0984274	+	0.621199i
$836$	−9.48077	+	1.63363i	−0.327899	+	0.0565003i
$837$	−10.3088			−0.356323
$838$	38.3738	+	32.3272i	1.32560	+	1.11672i
$839$	−35.0477			−1.20998			−0.604991	−	0.796232i	$-0.706823\pi$
$839$	−35.0477			−1.20998			−0.604991	+	0.796232i	$0.706823\pi$
$840$	−10.4943	+	13.0334i	−0.362088	+	0.449695i
$841$	−16.0853			−0.554666
$842$	18.4139	+	15.5124i	0.634585	+	0.534591i
$843$	−27.3986			−0.943656
$844$	5.31039	+	30.8189i	0.182791	+	1.06083i
$845$	−20.0507	+	3.17699i	−0.689765	+	0.109292i
$846$	10.4488	+	8.80233i	0.359236	+	0.302630i
$847$	−7.40990	+	23.4884i	−0.254607	+	0.807073i
$848$	6.28355	−	2.23169i	0.215778	−	0.0766367i
$849$	−13.3187			−0.457098
$850$	14.9533	−	36.8171i	0.512895	−	1.26282i
$851$	−14.5091			−0.497365
$852$	14.3958	−	2.48053i	0.493191	−	0.0849817i
$853$			0.728369i			0.0249389i	0.999922	+	0.0124694i	$0.00396925\pi$
$853$			0.728369i			0.0249389i	−0.999922	+	0.0124694i	$0.996031\pi$
$854$	−10.1903	−	16.0701i	−0.348705	−	0.549909i
$855$	−1.29447	−	8.16972i	−0.0442700	−	0.279398i
$856$	11.7269	−	20.0400i	0.400817	−	0.684953i
$857$	3.33966			0.114081			0.0570404	−	0.998372i	$-0.481834\pi$
$857$	3.33966			0.114081			0.0570404	+	0.998372i	$0.481834\pi$
$858$	−2.78501	−	2.34617i	−0.0950786	−	0.0800968i
$859$			9.72278i			0.331737i	0.986148	+	0.165869i	$0.0530427\pi$
$859$			9.72278i			0.331737i	−0.986148	+	0.165869i	$0.946957\pi$
$860$	24.5103	−	8.33450i	0.835793	−	0.284204i
$861$	−6.82401	−	2.15277i	−0.232562	−	0.0733663i
$862$	23.3758	+	19.6924i	0.796183	+	0.670726i
$863$	1.79337			0.0610472			0.0305236	−	0.999534i	$-0.490283\pi$
$863$	1.79337			0.0610472			0.0305236	+	0.999534i	$0.490283\pi$
$864$	1.98648	−	5.29659i	0.0675813	−	0.180194i
$865$	−8.22601	−	51.9163i	−0.279693	−	1.76521i
$866$	35.6639	−	42.3347i	1.21191	−	1.43859i
$867$	14.5820			0.495230
$868$	54.0528	+	7.33926i	1.83467	+	0.249111i
$869$		−	10.0586i		−	0.341216i
$870$	18.1798	+	10.9703i	0.616353	+	0.371928i
$871$	4.51306			0.152919
$872$	13.3504	−	22.8144i	0.452102	−	0.772594i
$873$	−1.76197			−0.0596337
$874$	29.8562	+	25.1517i	1.00990	+	0.850768i
$875$	4.88301	+	29.1746i	0.165076	+	0.986281i
$876$	2.86941	+	16.6526i	0.0969484	+	0.562640i
$877$	−15.2950			−0.516476			−0.258238	−	0.966081i	$-0.583142\pi$
$877$	−15.2950			−0.516476			−0.258238	+	0.966081i	$0.583142\pi$
$878$	−19.5978	+	23.2635i	−0.661395	+	0.785106i
$879$		−	8.59973i		−	0.290062i
$880$	−10.2157	+	5.55981i	−0.344373	+	0.187421i
$881$		−	29.5279i		−	0.994820i	−0.867516	−	0.497410i	$-0.834284\pi$
$881$		−	29.5279i		−	0.994820i	0.867516	−	0.497410i	$-0.165716\pi$
$882$	9.56795	−	2.54055i	0.322170	−	0.0855448i
$883$			49.8573i			1.67783i	0.544260	+	0.838917i	$0.316810\pi$
$883$			49.8573i			1.67783i	−0.544260	+	0.838917i	$0.683190\pi$
$884$	21.9334	−	3.77933i	0.737699	−	0.127113i
$885$	1.25647	+	7.92988i	0.0422358	+	0.266560i
$886$	−21.1773	−	17.8403i	−0.711465	−	0.599357i
$887$		−	40.5532i		−	1.36164i	−0.732449	−	0.680822i	$-0.761623\pi$
$887$		−	40.5532i		−	1.36164i	0.732449	−	0.680822i	$-0.238377\pi$
$888$	4.74644	+	2.77750i	0.159280	+	0.0932066i
$889$	13.6931	−	43.4054i	0.459252	−	1.45577i
$890$	−5.48511	−	3.30990i	−0.183861	−	0.110948i
$891$	−1.30035			−0.0435634
$892$	20.0165	−	3.44903i	0.670200	−	0.115482i
$893$	35.7367			1.19588
$894$	−18.9196	−	15.9384i	−0.632767	−	0.533060i
$895$	−47.4070	+	7.51151i	−1.58464	+	0.251082i
$896$	−14.1867	+	26.3578i	−0.473946	+	0.880554i
$897$			14.7768i			0.493382i
$898$	12.6836	−	15.0560i	0.423256	−	0.502425i
$899$		−	69.2188i		−	2.30857i
$900$	−4.66135	−	8.84714i	−0.155378	−	0.294905i
$901$	9.36831			0.312104
$902$	−3.80374	−	3.20437i	−0.126651	−	0.106694i
$903$	−14.6063	−	4.60785i	−0.486067	−	0.153340i
$904$	17.9099	−	30.6061i	0.595674	−	1.01794i
$905$	2.28723	−	0.362406i	0.0760302	−	0.0120468i
$906$	−1.21264	−	1.02156i	−0.0402872	−	0.0339390i
$907$			20.4289i			0.678330i	0.940727	+	0.339165i	$0.110144\pi$
$907$			20.4289i			0.678330i	−0.940727	+	0.339165i	$0.889856\pi$
$908$	−4.23933	−	24.6029i	−0.140687	−	0.816477i
$909$	−2.52420			−0.0837226
$910$	−12.4308	+	10.9526i	−0.412076	+	0.363075i
$911$			36.7825i			1.21866i	0.792917	+	0.609330i	$0.208561\pi$
$911$			36.7825i			1.21866i	−0.792917	+	0.609330i	$0.791439\pi$
$912$	−4.95222	−	13.9434i	−0.163984	−	0.461713i
$913$	−8.76315			−0.290018
$914$	−27.0004	−	22.7459i	−0.893095	−	0.752367i
$915$	11.2317	−	1.77964i	0.371309	−	0.0588329i
$916$	−3.26869	−	18.9699i	−0.108001	−	0.626782i
$917$	−35.7659	−	11.2831i	−1.18109	−	0.372600i
$918$	5.12046	−	6.07823i	0.169000	−	0.200611i
$919$		−	28.6461i		−	0.944947i	−0.881345	−	0.472474i	$-0.843361\pi$
$919$		−	28.6461i		−	0.944947i	0.881345	−	0.472474i	$-0.156639\pi$
$920$	43.9622	+	17.1680i	1.44939	+	0.566014i
$921$	0.730484			0.0240703
$922$	−10.7121	+	12.7157i	−0.352783	+	0.418770i
$923$	14.4633			0.476065
$924$	6.81825	+	0.925778i	0.224304	+	0.0304559i
$925$	9.24545	−	3.00529i	0.303988	−	0.0988132i
$926$	6.32428	−	7.50721i	0.207829	−	0.246702i
$927$		−	13.8685i		−	0.455502i
$928$	35.5643	+	13.3383i	1.16746	+	0.437851i
$929$		−	5.58128i		−	0.183116i	−0.995800	−	0.0915580i	$-0.970815\pi$
$929$		−	5.58128i		−	0.183116i	0.995800	−	0.0915580i	$-0.0291847\pi$
$930$	−16.8425	+	27.9112i	−0.552288	+	0.915243i
$931$	14.8590	−	21.2067i	0.486983	−	0.695023i
$932$	−41.7306	+	7.19059i	−1.36693	+	0.235535i
$933$	3.97387			0.130099
$934$	30.3125	−	35.9824i	0.991857	−	1.17738i
$935$	−16.1392	+	2.55721i	−0.527807	+	0.0836297i
$936$	2.82874	−	4.83402i	0.0924603	−	0.158005i
$937$	18.3328			0.598906			0.299453	−	0.954111i	$-0.403196\pi$
$937$	18.3328			0.598906			0.299453	+	0.954111i	$0.403196\pi$
$938$	−7.20172	+	4.56672i	−0.235145	+	0.149109i
$939$	23.5606			0.768870
$940$	40.9038	−	13.9090i	1.33414	−	0.453661i
$941$	−44.1662			−1.43978			−0.719889	−	0.694089i	$-0.755807\pi$
$941$	−44.1662			−1.43978			−0.719889	+	0.694089i	$0.755807\pi$
$942$	−16.0436	−	13.5156i	−0.522730	−	0.440361i
$943$			20.1820i			0.657215i
$944$	4.80683	+	13.5341i	0.156449	+	0.440497i
$945$	−0.875004	+	5.85101i	−0.0284639	+	0.190334i
$946$	−8.14162	−	6.85872i	−0.264707	−	0.222996i
$947$		−	4.76205i		−	0.154746i	−0.997002	−	0.0773729i	$-0.975347\pi$
$947$		−	4.76205i		−	0.154746i	0.997002	−	0.0773729i	$-0.0246532\pi$
$948$	15.2460	−	2.62703i	0.495166	−	0.0853220i
$949$			16.7307i			0.543102i
$950$	−24.2346	−	9.84293i	−0.786274	−	0.319347i
$951$	−19.6502			−0.637202
$952$	−31.1759	+	28.2250i	−1.01042	+	0.914778i
$953$		−	49.4494i		−	1.60182i	−0.598784	−	0.800911i	$-0.704349\pi$
$953$		−	49.4494i		−	1.60182i	0.598784	−	0.800911i	$-0.295651\pi$
$954$	1.51891	−	1.80301i	0.0491764	−	0.0583747i
$955$	8.84896	+	55.8479i	0.286346	+	1.80720i
$956$	−22.5694	+	3.88893i	−0.729946	+	0.125777i
$957$		−	8.73129i		−	0.282242i
$958$	9.90345	−	11.7559i	0.319966	−	0.379815i
$959$	46.7531	+	14.7492i	1.50974	+	0.476277i
$960$	−11.0951	−	14.0320i	−0.358094	−	0.452882i
$961$	75.2704			2.42808
$962$	4.16423	+	3.50806i	0.134260	+	0.113104i
$963$		−	8.20915i		−	0.264536i
$964$	27.1736	−	4.68228i	0.875204	−	0.150806i
$965$	−3.06436	−	19.3399i	−0.0986453	−	0.622574i
$966$	−14.9525	−	23.5801i	−0.481088	−	0.758677i
$967$	−28.1884			−0.906479			−0.453239	−	0.891389i	$-0.649732\pi$
$967$	−28.1884			−0.906479			−0.453239	+	0.891389i	$0.649732\pi$
$968$	−22.7251	−	13.2982i	−0.730413	−	0.427419i
$969$		−	20.7886i		−	0.667827i
$970$	−2.87872	+	4.77058i	−0.0924303	+	0.153174i
$971$			22.9249i			0.735694i	0.929886	+	0.367847i	$0.119905\pi$
$971$			22.9249i			0.735694i	−0.929886	+	0.367847i	$0.880095\pi$
$972$	−0.339615	−	1.97095i	−0.0108932	−	0.0632184i
$973$	37.1468	+	11.7187i	1.19087	+	0.375685i
$974$	−37.8825	+	44.9683i	−1.21383	+	1.44088i
$975$	−3.06073	−	9.41603i	−0.0980219	−	0.301554i
$976$	19.1694	−	6.80830i	0.613598	−	0.217928i
$977$			21.9679i			0.702814i	0.936223	+	0.351407i	$0.114297\pi$
$977$			21.9679i			0.702814i	−0.936223	+	0.351407i	$0.885703\pi$
$978$	13.9294	+	11.7345i	0.445413	+	0.375228i
$979$			2.63436i			0.0841944i
$980$	8.75359	−	30.0562i	0.279623	−	0.960110i
$981$		−	9.34566i		−	0.298384i
$982$	−22.6864	+	26.9298i	−0.723952	+	0.859365i
$983$			34.5387i			1.10161i	0.834632	+	0.550807i	$0.185680\pi$
$983$			34.5387i			1.10161i	−0.834632	+	0.550807i	$0.814320\pi$
$984$	3.86347	−	6.60225i	0.123163	−	0.210472i
$985$	27.0336	−	4.28341i	0.861363	−	0.136481i
$986$	40.8126	+	34.3816i	1.29974	+	1.09493i
$987$	−24.3756	−	7.68978i	−0.775884	−	0.244768i
$988$	−2.48772	−	14.4375i	−0.0791450	−	0.459318i
$989$			43.1980i			1.37362i
$990$	−2.12452	+	3.52073i	−0.0675218	+	0.111896i
$991$		−	6.79294i		−	0.215785i	−0.994163	−	0.107892i	$-0.965590\pi$
$991$		−	6.79294i		−	0.215785i	0.994163	−	0.107892i	$-0.0344102\pi$
$992$	−20.4781	+	54.6013i	−0.650180	+	1.73359i
$993$	−23.9573			−0.760262
$994$	−23.0798	+	14.6353i	−0.732048	+	0.464203i
$995$	2.28336	−	0.361792i	0.0723873	−	0.0114696i
$996$	−2.28869	−	13.2824i	−0.0725198	−	0.420869i
$997$		−	3.84060i		−	0.121633i	−0.998149	−	0.0608165i	$-0.980630\pi$
$997$		−	3.84060i		−	0.121633i	0.998149	−	0.0608165i	$-0.0193704\pi$
$998$	19.7878	−	23.4891i	0.626373	−	0.743533i
$999$	1.94433			0.0615157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.w.b.139.14	yes	48
4.3	odd	2		3360.2.w.a.559.4		48
5.4	even	2		840.2.w.a.139.35	yes	48
7.6	odd	2		840.2.w.a.139.14	yes	48
8.3	odd	2	inner	840.2.w.b.139.36	yes	48
8.5	even	2		3360.2.w.a.559.45		48
20.19	odd	2		3360.2.w.b.559.3		48
28.27	even	2		3360.2.w.b.559.45		48
35.34	odd	2	inner	840.2.w.b.139.35	yes	48
40.19	odd	2		840.2.w.a.139.13	✓	48
40.29	even	2		3360.2.w.b.559.46		48
56.13	odd	2		3360.2.w.b.559.4		48
56.27	even	2		840.2.w.a.139.36	yes	48
140.139	even	2		3360.2.w.a.559.46		48
280.69	odd	2		3360.2.w.a.559.3		48
280.139	even	2	inner	840.2.w.b.139.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.w.a.139.13	✓	48	40.19	odd	2
840.2.w.a.139.14	yes	48	7.6	odd	2
840.2.w.a.139.35	yes	48	5.4	even	2
840.2.w.a.139.36	yes	48	56.27	even	2
840.2.w.b.139.13	yes	48	280.139	even	2	inner
840.2.w.b.139.14	yes	48	1.1	even	1	trivial
840.2.w.b.139.35	yes	48	35.34	odd	2	inner
840.2.w.b.139.36	yes	48	8.3	odd	2	inner
3360.2.w.a.559.3		48	280.69	odd	2
3360.2.w.a.559.4		48	4.3	odd	2
3360.2.w.a.559.45		48	8.5	even	2
3360.2.w.a.559.46		48	140.139	even	2
3360.2.w.b.559.3		48	20.19	odd	2
3360.2.w.b.559.4		48	56.13	odd	2
3360.2.w.b.559.45		48	28.27	even	2
3360.2.w.b.559.46		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+(-0.911149 + 1.08158i) q^{2} +1.00000 q^{3} +(-0.339615 - 1.97095i) q^{4} +(-2.20852 + 0.349934i) q^{5} +(-0.911149 + 1.08158i) q^{6} +(0.795986 - 2.52317i) q^{7} +(2.44118 + 1.42851i) q^{8} +1.00000 q^{9} +(1.63381 - 2.70752i) q^{10} -1.30035 q^{11} +(-0.339615 - 1.97095i) q^{12} -1.98020i q^{13} +(2.00374 + 3.15991i) q^{14} +(-2.20852 + 0.349934i) q^{15} +(-3.76932 + 1.33873i) q^{16} -5.61979 q^{17} +(-0.911149 + 1.08158i) q^{18} +3.69919i q^{19} +(1.43975 + 4.23404i) q^{20} +(0.795986 - 2.52317i) q^{21} +(1.18481 - 1.40643i) q^{22} -7.46227 q^{23} +(2.44118 + 1.42851i) q^{24} +(4.75509 - 1.54567i) q^{25} +(2.14174 + 1.80426i) q^{26} +1.00000 q^{27} +(-5.24339 - 0.711945i) q^{28} +6.71456i q^{29} +(1.63381 - 2.70752i) q^{30} -10.3088 q^{31} +(1.98648 - 5.29659i) q^{32} -1.30035 q^{33} +(5.12046 - 6.07823i) q^{34} +(-0.875004 + 5.85101i) q^{35} +(-0.339615 - 1.97095i) q^{36} +1.94433 q^{37} +(-4.00095 - 3.37051i) q^{38} -1.98020i q^{39} +(-5.89127 - 2.30065i) q^{40} -2.70453i q^{41} +(2.00374 + 3.15991i) q^{42} -5.78886i q^{43} +(0.441619 + 2.56293i) q^{44} +(-2.20852 + 0.349934i) q^{45} +(6.79924 - 8.07102i) q^{46} -9.66070i q^{47} +(-3.76932 + 1.33873i) q^{48} +(-5.73281 - 4.01682i) q^{49} +(-2.66084 + 6.55133i) q^{50} -5.61979 q^{51} +(-3.90288 + 0.672505i) q^{52} -1.66702 q^{53} +(-0.911149 + 1.08158i) q^{54} +(2.87185 - 0.455037i) q^{55} +(5.54753 - 5.02244i) q^{56} +3.69919i q^{57} +(-7.26231 - 6.11796i) q^{58} -3.59059i q^{59} +(1.43975 + 4.23404i) q^{60} -5.08563 q^{61} +(9.39281 - 11.1497i) q^{62} +(0.795986 - 2.52317i) q^{63} +(3.91870 + 6.97451i) q^{64} +(0.692939 + 4.37330i) q^{65} +(1.18481 - 1.40643i) q^{66} +2.27909i q^{67} +(1.90856 + 11.0763i) q^{68} -7.46227 q^{69} +(-5.53106 - 6.27753i) q^{70} +7.30396i q^{71} +(2.44118 + 1.42851i) q^{72} -8.44901 q^{73} +(-1.77157 + 2.10294i) q^{74} +(4.75509 - 1.54567i) q^{75} +(7.29093 - 1.25630i) q^{76} +(-1.03506 + 3.28101i) q^{77} +(2.14174 + 1.80426i) q^{78} +7.73532i q^{79} +(7.85615 - 4.27562i) q^{80} +1.00000 q^{81} +(2.92516 + 2.46423i) q^{82} +6.73907 q^{83} +(-5.24339 - 0.711945i) q^{84} +(12.4114 - 1.96655i) q^{85} +(6.26109 + 5.27451i) q^{86} +6.71456i q^{87} +(-3.17439 - 1.85757i) q^{88} -2.02588i q^{89} +(1.63381 - 2.70752i) q^{90} +(-4.99639 - 1.57621i) q^{91} +(2.53430 + 14.7078i) q^{92} -10.3088 q^{93} +(10.4488 + 8.80233i) q^{94} +(-1.29447 - 8.16972i) q^{95} +(1.98648 - 5.29659i) q^{96} -1.76197 q^{97} +(9.56795 - 2.54055i) q^{98} -1.30035 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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