LMFDB - Embedded newform 840.2.w.a.139.17

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			139.17
Character	$\chi$	$=$	840.139
Dual form			840.2.w.a.139.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.716255 - 1.21942i) q^{2} -1.00000 q^{3} +(-0.973958 + 1.74683i) q^{4} +(-0.151655 - 2.23092i) q^{5} +(0.716255 + 1.21942i) q^{6} +(-2.00273 + 1.72889i) q^{7} +(2.82771 - 0.0635119i) q^{8} +1.00000 q^{9} +(-2.61180 + 1.78284i) q^{10} +2.25539 q^{11} +(0.973958 - 1.74683i) q^{12} -6.09170i q^{13} +(3.54271 + 1.20383i) q^{14} +(0.151655 + 2.23092i) q^{15} +(-2.10281 - 3.40267i) q^{16} +2.64554 q^{17} +(-0.716255 - 1.21942i) q^{18} -1.31443i q^{19} +(4.04474 + 1.90791i) q^{20} +(2.00273 - 1.72889i) q^{21} +(-1.61544 - 2.75027i) q^{22} -6.62596 q^{23} +(-2.82771 + 0.0635119i) q^{24} +(-4.95400 + 0.676659i) q^{25} +(-7.42832 + 4.36321i) q^{26} -1.00000 q^{27} +(-1.06951 - 5.18229i) q^{28} +6.44459i q^{29} +(2.61180 - 1.78284i) q^{30} -6.67664 q^{31} +(-2.64313 + 5.00139i) q^{32} -2.25539 q^{33} +(-1.89488 - 3.22601i) q^{34} +(4.16075 + 4.20573i) q^{35} +(-0.973958 + 1.74683i) q^{36} +2.30302 q^{37} +(-1.60284 + 0.941468i) q^{38} +6.09170i q^{39} +(-0.570526 - 6.29877i) q^{40} -5.50180i q^{41} +(-3.54271 - 1.20383i) q^{42} +1.26915i q^{43} +(-2.19666 + 3.93978i) q^{44} +(-0.151655 - 2.23092i) q^{45} +(4.74588 + 8.07981i) q^{46} +0.599848i q^{47} +(2.10281 + 3.40267i) q^{48} +(1.02185 - 6.92501i) q^{49} +(4.37346 + 5.55634i) q^{50} -2.64554 q^{51} +(10.6411 + 5.93306i) q^{52} -10.4797 q^{53} +(0.716255 + 1.21942i) q^{54} +(-0.342041 - 5.03160i) q^{55} +(-5.55334 + 5.01602i) q^{56} +1.31443i q^{57} +(7.85864 - 4.61597i) q^{58} -0.847197i q^{59} +(-4.04474 - 1.90791i) q^{60} -11.7641 q^{61} +(4.78217 + 8.14161i) q^{62} +(-2.00273 + 1.72889i) q^{63} +(7.99193 - 0.359187i) q^{64} +(-13.5901 + 0.923835i) q^{65} +(1.61544 + 2.75027i) q^{66} +14.2814i q^{67} +(-2.57664 + 4.62129i) q^{68} +6.62596 q^{69} +(2.14839 - 8.08606i) q^{70} +3.94508i q^{71} +(2.82771 - 0.0635119i) q^{72} -8.34529 q^{73} +(-1.64955 - 2.80834i) q^{74} +(4.95400 - 0.676659i) q^{75} +(2.29609 + 1.28020i) q^{76} +(-4.51694 + 3.89934i) q^{77} +(7.42832 - 4.36321i) q^{78} -0.674858i q^{79} +(-7.27219 + 5.20723i) q^{80} +1.00000 q^{81} +(-6.70899 + 3.94069i) q^{82} -7.23405 q^{83} +(1.06951 + 5.18229i) q^{84} +(-0.401208 - 5.90198i) q^{85} +(1.54763 - 0.909036i) q^{86} -6.44459i q^{87} +(6.37761 - 0.143244i) q^{88} +5.66275i q^{89} +(-2.61180 + 1.78284i) q^{90} +(10.5319 + 12.2000i) q^{91} +(6.45341 - 11.5744i) q^{92} +6.67664 q^{93} +(0.731466 - 0.429644i) q^{94} +(-2.93239 + 0.199340i) q^{95} +(2.64313 - 5.00139i) q^{96} -11.6458 q^{97} +(-9.17639 + 3.71402i) q^{98} +2.25539 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} + 16 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 + 16 * 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 - 54 * 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 $

$2$	−0.716255	−	1.21942i	−0.506469	−	0.862258i
$2$	−0.716255	−	1.21942i	−0.506469	−	0.862258i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.973958	+	1.74683i	−0.486979	+	0.873414i
$5$	−0.151655	−	2.23092i	−0.0678221	−	0.997697i
$5$	−0.151655	−	2.23092i	−0.0678221	−	0.997697i
$6$	0.716255	+	1.21942i	0.292410	+	0.497825i
$7$	−2.00273	+	1.72889i	−0.756960	+	0.653461i
$7$	−2.00273	+	1.72889i	−0.756960	+	0.653461i
$8$	2.82771	−	0.0635119i	0.999748	−	0.0224549i
$9$	1.00000			0.333333
$10$	−2.61180	+	1.78284i	−0.825923	+	0.563783i
$11$	2.25539			0.680027			0.340013	−	0.940421i	$-0.389568\pi$
$11$	2.25539			0.680027			0.340013	+	0.940421i	$0.389568\pi$
$12$	0.973958	−	1.74683i	0.281157	−	0.504266i
$13$		−	6.09170i		−	1.68953i	−0.535135	−	0.844766i	$-0.679739\pi$
$13$		−	6.09170i		−	1.68953i	0.535135	−	0.844766i	$-0.320261\pi$
$14$	3.54271	+	1.20383i	0.946829	+	0.321738i
$15$	0.151655	+	2.23092i	0.0391571	+	0.576021i
$16$	−2.10281	−	3.40267i	−0.525703	−	0.850668i
$17$	2.64554			0.641637			0.320818	−	0.947141i	$-0.396042\pi$
$17$	2.64554			0.641637			0.320818	+	0.947141i	$0.396042\pi$
$18$	−0.716255	−	1.21942i	−0.168823	−	0.287419i
$19$		−	1.31443i		−	0.301551i	−0.988568	−	0.150776i	$-0.951823\pi$
$19$		−	1.31443i		−	0.301551i	0.988568	−	0.150776i	$-0.0481771\pi$
$20$	4.04474	+	1.90791i	0.904430	+	0.426621i
$21$	2.00273	−	1.72889i	0.437031	−	0.377276i
$22$	−1.61544	−	2.75027i	−0.344412	−	0.586359i
$23$	−6.62596			−1.38161			−0.690804	−	0.723042i	$-0.742743\pi$
$23$	−6.62596			−1.38161			−0.690804	+	0.723042i	$0.742743\pi$
$24$	−2.82771	+	0.0635119i	−0.577205	+	0.0129643i
$25$	−4.95400	+	0.676659i	−0.990800	+	0.135332i
$26$	−7.42832	+	4.36321i	−1.45681	+	0.855695i
$27$	−1.00000			−0.192450
$28$	−1.06951	−	5.18229i	−0.202118	−	0.979361i
$29$			6.44459i			1.19673i	0.801224	+	0.598365i	$0.204183\pi$
$29$			6.44459i			1.19673i	−0.801224	+	0.598365i	$0.795817\pi$
$30$	2.61180	−	1.78284i	0.476847	−	0.325500i
$31$	−6.67664			−1.19916			−0.599580	−	0.800315i	$-0.704666\pi$
$31$	−6.67664			−1.19916			−0.599580	+	0.800315i	$0.704666\pi$
$32$	−2.64313	+	5.00139i	−0.467244	+	0.884128i
$33$	−2.25539			−0.392614
$34$	−1.89488	−	3.22601i	−0.324969	−	0.553257i
$35$	4.16075	+	4.20573i	0.703295	+	0.710898i
$36$	−0.973958	+	1.74683i	−0.162326	+	0.291138i
$37$	2.30302			0.378614			0.189307	−	0.981918i	$-0.439376\pi$
$37$	2.30302			0.378614			0.189307	+	0.981918i	$0.439376\pi$
$38$	−1.60284	+	0.941468i	−0.260015	+	0.152726i
$39$			6.09170i			0.975452i
$40$	−0.570526	−	6.29877i	−0.0902081	−	0.995923i
$41$		−	5.50180i		−	0.859236i	−0.903011	−	0.429618i	$-0.858648\pi$
$41$		−	5.50180i		−	0.859236i	0.903011	−	0.429618i	$-0.141352\pi$
$42$	−3.54271	−	1.20383i	−0.546652	−	0.185756i
$43$			1.26915i			0.193544i	0.995307	+	0.0967719i	$0.0308517\pi$
$43$			1.26915i			0.193544i	−0.995307	+	0.0967719i	$0.969148\pi$
$44$	−2.19666	+	3.93978i	−0.331159	+	0.593945i
$45$	−0.151655	−	2.23092i	−0.0226074	−	0.332566i
$46$	4.74588	+	8.07981i	0.699741	+	1.19130i
$47$			0.599848i			0.0874969i	0.999043	+	0.0437484i	$0.0139300\pi$
$47$			0.599848i			0.0874969i	−0.999043	+	0.0437484i	$0.986070\pi$
$48$	2.10281	+	3.40267i	0.303515	+	0.491134i
$49$	1.02185	−	6.92501i	0.145978	−	0.989288i
$50$	4.37346	+	5.55634i	0.618500	+	0.785785i
$51$	−2.64554			−0.370449
$52$	10.6411	+	5.93306i	1.47566	+	0.822767i
$53$	−10.4797			−1.43950			−0.719750	−	0.694234i	$-0.755743\pi$
$53$	−10.4797			−1.43950			−0.719750	+	0.694234i	$0.755743\pi$
$54$	0.716255	+	1.21942i	0.0974699	+	0.165942i
$55$	−0.342041	−	5.03160i	−0.0461208	−	0.678461i
$56$	−5.55334	+	5.01602i	−0.742096	+	0.670293i
$57$			1.31443i			0.174101i
$58$	7.85864	−	4.61597i	1.03189	−	0.606106i
$59$		−	0.847197i		−	0.110296i	−0.998478	−	0.0551478i	$-0.982437\pi$
$59$		−	0.847197i		−	0.110296i	0.998478	−	0.0551478i	$-0.0175630\pi$
$60$	−4.04474	−	1.90791i	−0.522173	−	0.246310i
$61$	−11.7641			−1.50624			−0.753118	−	0.657886i	$-0.771451\pi$
$61$	−11.7641			−1.50624			−0.753118	+	0.657886i	$0.771451\pi$
$62$	4.78217	+	8.14161i	0.607337	+	1.03399i
$63$	−2.00273	+	1.72889i	−0.252320	+	0.217820i
$64$	7.99193	−	0.359187i	0.998992	−	0.0448984i
$65$	−13.5901	+	0.923835i	−1.68564	+	0.114588i
$66$	1.61544	+	2.75027i	0.198846	+	0.338534i
$67$			14.2814i			1.74475i	0.488840	+	0.872373i	$0.337420\pi$
$67$			14.2814i			1.74475i	−0.488840	+	0.872373i	$0.662580\pi$
$68$	−2.57664	+	4.62129i	−0.312464	+	0.560414i
$69$	6.62596			0.797672
$70$	2.14839	−	8.08606i	0.256781	−	0.966470i
$71$			3.94508i			0.468195i	0.972213	+	0.234097i	$0.0752134\pi$
$71$			3.94508i			0.468195i	−0.972213	+	0.234097i	$0.924787\pi$
$72$	2.82771	−	0.0635119i	0.333249	−	0.00748495i
$73$	−8.34529			−0.976742			−0.488371	−	0.872636i	$-0.662409\pi$
$73$	−8.34529			−0.976742			−0.488371	+	0.872636i	$0.662409\pi$
$74$	−1.64955	−	2.80834i	−0.191756	−	0.326463i
$75$	4.95400	−	0.676659i	0.572039	−	0.0781339i
$76$	2.29609	+	1.28020i	0.263379	+	0.146849i
$77$	−4.51694	+	3.89934i	−0.514753	+	0.444371i
$78$	7.42832	−	4.36321i	0.841092	−	0.494036i
$79$		−	0.674858i		−	0.0759274i	−0.999279	−	0.0379637i	$-0.987913\pi$
$79$		−	0.674858i		−	0.0759274i	0.999279	−	0.0379637i	$-0.0120871\pi$
$80$	−7.27219	+	5.20723i	−0.813055	+	0.582186i
$81$	1.00000			0.111111
$82$	−6.70899	+	3.94069i	−0.740884	+	0.435176i
$83$	−7.23405			−0.794040			−0.397020	−	0.917810i	$-0.629956\pi$
$83$	−7.23405			−0.794040			−0.397020	+	0.917810i	$0.629956\pi$
$84$	1.06951	+	5.18229i	0.116693	+	0.565434i
$85$	−0.401208	−	5.90198i	−0.0435171	−	0.640159i
$86$	1.54763	−	0.909036i	0.166885	−	0.0980239i
$87$		−	6.44459i		−	0.690932i
$88$	6.37761	−	0.143244i	0.679855	−	0.0152699i
$89$			5.66275i			0.600250i	0.953900	+	0.300125i	$0.0970284\pi$
$89$			5.66275i			0.600250i	−0.953900	+	0.300125i	$0.902972\pi$
$90$	−2.61180	+	1.78284i	−0.275308	+	0.187928i
$91$	10.5319	+	12.2000i	1.10404	+	1.27891i
$92$	6.45341	−	11.5744i	0.672814	−	1.20672i
$93$	6.67664			0.692335
$94$	0.731466	−	0.429644i	0.0754449	−	0.0443144i
$95$	−2.93239	+	0.199340i	−0.300857	+	0.0204518i
$96$	2.64313	−	5.00139i	0.269763	−	0.510452i
$97$	−11.6458			−1.18245			−0.591226	−	0.806506i	$-0.701356\pi$
$97$	−11.6458			−1.18245			−0.591226	+	0.806506i	$0.701356\pi$
$98$	−9.17639	+	3.71402i	−0.926955	+	0.375172i
$99$	2.25539			0.226676
$100$	3.64298	−	9.31282i	0.364298	−	0.931282i
$101$	16.9486			1.68645			0.843227	−	0.537558i	$-0.180653\pi$
$101$	16.9486			1.68645			0.843227	+	0.537558i	$0.180653\pi$
$102$	1.89488	+	3.22601i	0.187621	+	0.319423i
$103$		−	2.78168i		−	0.274088i	−0.990565	−	0.137044i	$-0.956240\pi$
$103$		−	2.78168i		−	0.274088i	0.990565	−	0.137044i	$-0.0437601\pi$
$104$	−0.386895	−	17.2256i	−0.0379382	−	1.68911i
$105$	−4.16075	−	4.20573i	−0.406047	−	0.410437i
$106$	7.50614	+	12.7791i	0.729061	+	1.24122i
$107$		−	10.4887i		−	1.01399i	−0.861950	−	0.506993i	$-0.830757\pi$
$107$		−	10.4887i		−	1.01399i	0.861950	−	0.506993i	$-0.169243\pi$
$108$	0.973958	−	1.74683i	0.0937192	−	0.168089i
$109$		−	12.0853i		−	1.15756i	−0.815482	−	0.578782i	$-0.803528\pi$
$109$		−	12.0853i		−	1.15756i	0.815482	−	0.578782i	$-0.196472\pi$
$110$	−5.89063	+	4.02100i	−0.561650	+	0.383387i
$111$	−2.30302			−0.218593
$112$	10.0942	+	3.17909i	0.953815	+	0.300396i
$113$		−	5.80202i		−	0.545808i	−0.962041	−	0.272904i	$-0.912016\pi$
$113$		−	5.80202i		−	0.545808i	0.962041	−	0.272904i	$-0.0879842\pi$
$114$	1.60284	−	0.941468i	0.150120	−	0.0881766i
$115$	1.00486	+	14.7820i	0.0937035	+	1.37843i
$116$	−11.2576	−	6.27676i	−1.04524	−	0.582782i
$117$		−	6.09170i		−	0.563178i
$118$	−1.03309	+	0.606809i	−0.0951033	+	0.0558613i
$119$	−5.29829	+	4.57385i	−0.485694	+	0.419284i
$120$	0.570526	+	6.29877i	0.0520817	+	0.574996i
$121$	−5.91320			−0.537564
$122$	8.42607	+	14.3453i	0.762861	+	1.29876i
$123$			5.50180i			0.496080i
$124$	6.50276	−	11.6629i	0.583965	−	1.04736i
$125$	2.26087	+	10.9494i	0.202218	+	0.979340i
$126$	3.54271	+	1.20383i	0.315610	+	0.107246i
$127$	−4.03740			−0.358261			−0.179131	−	0.983825i	$-0.557328\pi$
$127$	−4.03740			−0.358261			−0.179131	+	0.983825i	$0.557328\pi$
$128$	−6.16226	−	9.48823i	−0.544672	−	0.838649i
$129$		−	1.26915i		−	0.111743i
$130$	10.8605	+	15.9103i	0.952529	+	1.39542i
$131$		−	1.91397i		−	0.167225i	−0.996498	−	0.0836123i	$-0.973354\pi$
$131$		−	1.91397i		−	0.167225i	0.996498	−	0.0836123i	$-0.0266457\pi$
$132$	2.19666	−	3.93978i	0.191195	−	0.342914i
$133$	2.27251	+	2.63245i	0.197052	+	0.228262i
$134$	17.4150	−	10.2291i	1.50442	−	0.883660i
$135$	0.151655	+	2.23092i	0.0130524	+	0.192007i
$136$	7.48082	−	0.168023i	0.641475	−	0.0144079i
$137$			21.9496i			1.87528i	0.347608	+	0.937640i	$0.386994\pi$
$137$			21.9496i			1.87528i	−0.347608	+	0.937640i	$0.613006\pi$
$138$	−4.74588	−	8.07981i	−0.403996	−	0.687799i
$139$		−	0.792123i		−	0.0671870i	−0.999436	−	0.0335935i	$-0.989305\pi$
$139$		−	0.792123i		−	0.0671870i	0.999436	−	0.0335935i	$-0.0106951\pi$
$140$	−11.3991	+	3.17190i	−0.963398	+	0.268075i
$141$		−	0.599848i		−	0.0505163i
$142$	4.81070	−	2.82568i	0.403705	−	0.237126i
$143$		−	13.7392i		−	1.14893i
$144$	−2.10281	−	3.40267i	−0.175234	−	0.283556i
$145$	14.3774	−	0.977352i	1.19397	−	0.0811647i
$146$	5.97735	+	10.1764i	0.494689	+	0.842204i
$147$	−1.02185	+	6.92501i	−0.0842805	+	0.571166i
$148$	−2.24304	+	4.02297i	−0.184377	+	0.330686i
$149$		−	16.8637i		−	1.38153i	−0.723078	−	0.690766i	$-0.757274\pi$
$149$		−	16.8637i		−	1.38153i	0.723078	−	0.690766i	$-0.242726\pi$
$150$	−4.37346	−	5.55634i	−0.357091	−	0.453673i
$151$		−	18.8911i		−	1.53733i	−0.639649	−	0.768667i	$-0.720920\pi$
$151$		−	18.8911i		−	1.53733i	0.639649	−	0.768667i	$-0.279080\pi$
$152$	−0.0834821	−	3.71684i	−0.00677129	−	0.301475i
$153$	2.64554			0.213879
$154$	7.99020	+	2.71512i	0.643869	+	0.218791i
$155$	1.01254	+	14.8950i	0.0813295	+	1.19640i
$156$	−10.6411	−	5.93306i	−0.851973	−	0.475025i
$157$		−	14.0522i		−	1.12148i	−0.827991	−	0.560742i	$-0.810516\pi$
$157$		−	14.0522i		−	1.12148i	0.827991	−	0.560742i	$-0.189484\pi$
$158$	−0.822933	+	0.483370i	−0.0654691	+	0.0384549i
$159$	10.4797			0.831095
$160$	11.5585	+	5.13813i	0.913782	+	0.406205i
$161$	13.2700	−	11.4556i	1.04582	−	0.902827i
$162$	−0.716255	−	1.21942i	−0.0562743	−	0.0958065i
$163$		−	17.5803i		−	1.37699i	−0.725239	−	0.688497i	$-0.758271\pi$
$163$		−	17.5803i		−	1.37699i	0.725239	−	0.688497i	$-0.241729\pi$
$164$	9.61069	+	5.35852i	0.750469	+	0.418430i
$165$	0.342041	+	5.03160i	0.0266279	+	0.391710i
$166$	5.18142	+	8.82132i	0.402156	+	0.684667i
$167$			8.61637i			0.666754i	0.942794	+	0.333377i	$0.108188\pi$
$167$			8.61637i			0.666754i	−0.942794	+	0.333377i	$0.891812\pi$
$168$	5.55334	−	5.01602i	0.428449	−	0.386994i
$169$	−24.1088			−1.85452
$170$	−6.90961	+	4.71656i	−0.529943	+	0.361744i
$171$		−	1.31443i		−	0.100517i
$172$	−2.21699	−	1.23610i	−0.169044	−	0.0942518i
$173$			14.8810i			1.13138i	0.824618	+	0.565691i	$0.191390\pi$
$173$			14.8810i			1.13138i	−0.824618	+	0.565691i	$0.808610\pi$
$174$	−7.85864	+	4.61597i	−0.595762	+	0.349936i
$175$	8.75165	−	9.92011i	0.661563	−	0.749890i
$176$	−4.74267	−	7.67437i	−0.357492	−	0.578477i
$177$			0.847197i			0.0636792i
$178$	6.90526	−	4.05597i	0.517571	−	0.304008i
$179$	15.5132			1.15951			0.579756	−	0.814790i	$-0.303148\pi$
$179$	15.5132			1.15951			0.579756	+	0.814790i	$0.303148\pi$
$180$	4.04474	+	1.90791i	0.301477	+	0.142207i
$181$	−11.1760			−0.830707			−0.415354	−	0.909660i	$-0.636342\pi$
$181$	−11.1760			−0.830707			−0.415354	+	0.909660i	$0.636342\pi$
$182$	7.33339	−	21.5811i	0.543587	−	1.59970i
$183$	11.7641			0.869625
$184$	−18.7363	+	0.420828i	−1.38126	+	0.0310238i
$185$	−0.349263	−	5.13784i	−0.0256784	−	0.377742i
$186$	−4.78217	−	8.14161i	−0.350646	−	0.596972i
$187$	5.96672			0.436330
$188$	−1.04783	−	0.584227i	−0.0764210	−	0.0426091i
$189$	2.00273	−	1.72889i	0.145677	−	0.125759i
$190$	2.34342	+	3.43303i	0.170009	+	0.249058i
$191$		−	1.30024i		−	0.0940821i	−0.998893	−	0.0470410i	$-0.985021\pi$
$191$		−	1.30024i		−	0.0940821i	0.998893	−	0.0470410i	$-0.0149792\pi$
$192$	−7.99193	+	0.359187i	−0.576768	+	0.0259221i
$193$		−	10.2276i		−	0.736201i	−0.929786	−	0.368101i	$-0.880008\pi$
$193$		−	10.2276i		−	0.736201i	0.929786	−	0.368101i	$-0.119992\pi$
$194$	8.34136	+	14.2011i	0.598875	+	1.01958i
$195$	13.5901	−	0.923835i	0.973206	−	0.0661572i
$196$	11.1016	+	8.52966i	0.792969	+	0.609262i
$197$	−4.42625			−0.315357			−0.157678	−	0.987491i	$-0.550401\pi$
$197$	−4.42625			−0.315357			−0.157678	+	0.987491i	$0.550401\pi$
$198$	−1.61544	−	2.75027i	−0.114804	−	0.195453i
$199$	−9.94177			−0.704753			−0.352377	−	0.935858i	$-0.614626\pi$
$199$	−9.94177			−0.704753			−0.352377	+	0.935858i	$0.614626\pi$
$200$	−13.9655	+	2.22804i	−0.987512	+	0.157546i
$201$		−	14.2814i		−	1.00733i
$202$	−12.1395	−	20.6675i	−0.854136	−	1.45416i
$203$	−11.1420	−	12.9068i	−0.782016	−	0.905877i
$204$	2.57664	−	4.62129i	0.180401	−	0.323555i
$205$	−12.2741	+	0.834374i	−0.857258	+	0.0582752i
$206$	−3.39203	+	1.99239i	−0.236334	+	0.138817i
$207$	−6.62596			−0.460536
$208$	−20.7281	+	12.8097i	−1.43723	+	0.888192i
$209$		−	2.96456i		−	0.205063i
$210$	−2.14839	+	8.08606i	−0.148253	+	0.557991i
$211$	1.91888			0.132101			0.0660506	−	0.997816i	$-0.478960\pi$
$211$	1.91888			0.132101			0.0660506	+	0.997816i	$0.478960\pi$
$212$	10.2068	−	18.3062i	0.701006	−	1.25728i
$213$		−	3.94508i		−	0.270312i
$214$	−12.7902	+	7.51262i	−0.874318	+	0.513552i
$215$	2.83138	−	0.192473i	0.193098	−	0.0131265i
$216$	−2.82771	+	0.0635119i	−0.192402	+	0.00432144i
$217$	13.3715	−	11.5432i	0.907716	−	0.783603i
$218$	−14.7371	+	8.65617i	−0.998120	+	0.586270i
$219$	8.34529			0.563922
$220$	9.12247	+	4.30308i	0.615037	+	0.290114i
$221$		−	16.1158i		−	1.08407i
$222$	1.64955	+	2.80834i	0.110710	+	0.188483i
$223$			4.14126i			0.277319i	0.990340	+	0.138660i	$0.0442794\pi$
$223$			4.14126i			0.277319i	−0.990340	+	0.138660i	$0.955721\pi$
$224$	−3.35339	−	14.5861i	−0.224058	−	0.974576i
$225$	−4.95400	+	0.676659i	−0.330267	+	0.0451106i
$226$	−7.07509	+	4.15572i	−0.470628	+	0.276435i
$227$	−15.8502			−1.05202			−0.526008	−	0.850480i	$-0.676312\pi$
$227$	−15.8502			−1.05202			−0.526008	+	0.850480i	$0.676312\pi$
$228$	−2.29609	−	1.28020i	−0.152062	−	0.0847834i
$229$	23.7976			1.57259			0.786294	−	0.617852i	$-0.211997\pi$
$229$	23.7976			1.57259			0.786294	+	0.617852i	$0.211997\pi$
$230$	17.3057	−	11.8130i	1.14110	−	0.778927i
$231$	4.51694	−	3.89934i	0.297193	−	0.256558i
$232$	0.409308	+	18.2234i	0.0268724	+	1.19643i
$233$		−	3.56877i		−	0.233798i	−0.993144	−	0.116899i	$-0.962705\pi$
$233$		−	3.56877i		−	0.233798i	0.993144	−	0.116899i	$-0.0372954\pi$
$234$	−7.42832	+	4.36321i	−0.485605	+	0.285232i
$235$	1.33821	−	0.0909698i	0.0872954	−	0.00593422i
$236$	1.47991	+	0.825134i	0.0963337	+	0.0537117i
$237$			0.674858i			0.0438367i
$238$	9.37236	+	3.18479i	0.607520	+	0.206439i
$239$			25.3361i			1.63886i	0.573182	+	0.819428i	$0.305709\pi$
$239$			25.3361i			1.63886i	−0.573182	+	0.819428i	$0.694291\pi$
$240$	7.27219	−	5.20723i	0.469418	−	0.336125i
$241$		−	16.0641i		−	1.03478i	−0.855750	−	0.517390i	$-0.826904\pi$
$241$		−	16.0641i		−	1.03478i	0.855750	−	0.517390i	$-0.173096\pi$
$242$	4.23536	+	7.21066i	0.272259	+	0.463519i
$243$	−1.00000			−0.0641500
$244$	11.4577	−	20.5498i	0.733505	−	1.31557i
$245$	−15.6041	−	1.22945i	−0.996910	−	0.0785465i
$246$	6.70899	−	3.94069i	0.427749	−	0.251249i
$247$	−8.00712			−0.509481
$248$	−18.8796	+	0.424046i	−1.19886	+	0.0269269i
$249$	7.23405			0.458439
$250$	11.7325	−	10.5995i	0.742027	−	0.670370i
$251$		−	15.5779i		−	0.983268i	−0.870802	−	0.491634i	$-0.836400\pi$
$251$		−	15.5779i		−	0.983268i	0.870802	−	0.491634i	$-0.163600\pi$
$252$	−1.06951	−	5.18229i	−0.0673726	−	0.326454i
$253$	−14.9441			−0.939531
$254$	2.89180	+	4.92327i	0.181448	+	0.308914i
$255$	0.401208	+	5.90198i	0.0251246	+	0.369596i
$256$	−7.15637	+	14.3104i	−0.447273	+	0.894397i
$257$	18.8071			1.17316			0.586578	−	0.809893i	$-0.300475\pi$
$257$	18.8071			1.17316			0.586578	+	0.809893i	$0.300475\pi$
$258$	−1.54763	+	0.909036i	−0.0963510	+	0.0565941i
$259$	−4.61232	+	3.98167i	−0.286596	+	0.247409i
$260$	11.6224	−	24.6393i	0.720790	−	1.52806i
$261$			6.44459i			0.398910i
$262$	−2.33393	+	1.37089i	−0.144191	+	0.0846940i
$263$	20.2464			1.24844			0.624222	−	0.781247i	$-0.285416\pi$
$263$	20.2464			1.24844			0.624222	+	0.781247i	$0.285416\pi$
$264$	−6.37761	+	0.143244i	−0.392515	+	0.00881608i
$265$	1.58930	+	23.3794i	0.0976298	+	1.43618i
$266$	1.58236	−	4.65665i	0.0970206	−	0.285518i
$267$		−	5.66275i		−	0.346555i
$268$	−24.9471	−	13.9095i	−1.52389	−	0.849655i
$269$	9.68128			0.590278			0.295139	−	0.955454i	$-0.404634\pi$
$269$	9.68128			0.590278			0.295139	+	0.955454i	$0.404634\pi$
$270$	2.61180	−	1.78284i	0.158949	−	0.108500i
$271$	2.16142			0.131297			0.0656484	−	0.997843i	$-0.479088\pi$
$271$	2.16142			0.131297			0.0656484	+	0.997843i	$0.479088\pi$
$272$	−5.56306	−	9.00189i	−0.337310	−	0.545820i
$273$	−10.5319	−	12.2000i	−0.637420	−	0.738379i
$274$	26.7657	−	15.7215i	1.61698	−	0.949770i
$275$	−11.1732	+	1.52613i	−0.673771	+	0.0920292i
$276$	−6.45341	+	11.5744i	−0.388449	+	0.696698i
$277$	29.7723			1.78884			0.894422	−	0.447223i	$-0.147587\pi$
$277$	29.7723			1.78884			0.894422	+	0.447223i	$0.147587\pi$
$278$	−0.965928	+	0.567362i	−0.0579325	+	0.0340281i
$279$	−6.67664			−0.399720
$280$	12.0325	+	11.6283i	0.719080	+	0.694927i
$281$	−14.4325			−0.860973			−0.430486	−	0.902597i	$-0.641658\pi$
$281$	−14.4325			−0.860973			−0.430486	+	0.902597i	$0.641658\pi$
$282$	−0.731466	+	0.429644i	−0.0435581	+	0.0255849i
$283$	8.68571			0.516312			0.258156	−	0.966103i	$-0.416885\pi$
$283$	8.68571			0.516312			0.258156	+	0.966103i	$0.416885\pi$
$284$	−6.89137	−	3.84234i	−0.408927	−	0.228001i
$285$	2.93239	−	0.199340i	0.173700	−	0.0118079i
$286$	−16.7538	+	9.84075i	−0.990672	+	0.581896i
$287$	9.51203	+	11.0186i	0.561477	+	0.650408i
$288$	−2.64313	+	5.00139i	−0.155748	+	0.294709i
$289$	−10.0011			−0.588302
$290$	−11.4896	−	16.8320i	−0.674695	−	0.988407i
$291$	11.6458			0.682689
$292$	8.12796	−	14.5778i	0.475653	−	0.853100i
$293$			0.507697i			0.0296600i	0.999890	+	0.0148300i	$0.00472071\pi$
$293$			0.507697i			0.0296600i	−0.999890	+	0.0148300i	$0.995279\pi$
$294$	9.17639	−	3.71402i	0.535178	−	0.216606i
$295$	−1.89003	+	0.128481i	−0.110042	+	0.00748048i
$296$	6.51227	−	0.146269i	0.378518	−	0.00850171i
$297$	−2.25539			−0.130871
$298$	−20.5639	+	12.0787i	−1.19124	+	0.699702i
$299$			40.3633i			2.33427i
$300$	−3.64298	+	9.31282i	−0.210328	+	0.537676i
$301$	−2.19423	−	2.54177i	−0.126473	−	0.146505i
$302$	−23.0361	+	13.5308i	−1.32558	+	0.778612i
$303$	−16.9486			−0.973674
$304$	−4.47258	+	2.76400i	−0.256520	+	0.158526i
$305$	1.78408	+	26.2447i	0.102156	+	1.50277i
$306$	−1.89488	−	3.22601i	−0.108323	−	0.184419i
$307$	−18.2227			−1.04003			−0.520013	−	0.854158i	$-0.674073\pi$
$307$	−18.2227			−1.04003			−0.520013	+	0.854158i	$0.674073\pi$
$308$	−2.41216	−	11.6881i	−0.137445	−	0.665992i
$309$			2.78168i			0.158245i
$310$	17.4380	−	11.9034i	0.990413	−	0.676065i
$311$	−13.5269			−0.767040			−0.383520	−	0.923533i	$-0.625288\pi$
$311$	−13.5269			−0.767040			−0.383520	+	0.923533i	$0.625288\pi$
$312$	0.386895	+	17.2256i	0.0219036	+	0.975206i
$313$	−16.0061			−0.904717			−0.452359	−	0.891836i	$-0.649417\pi$
$313$	−16.0061			−0.904717			−0.452359	+	0.891836i	$0.649417\pi$
$314$	−17.1354	+	10.0649i	−0.967009	+	0.567996i
$315$	4.16075	+	4.20573i	0.234432	+	0.236966i
$316$	1.17886	+	0.657283i	0.0663160	+	0.0369751i
$317$	34.8304			1.95627			0.978135	−	0.207973i	$-0.0666867\pi$
$317$	34.8304			1.95627			0.978135	+	0.207973i	$0.0666867\pi$
$318$	−7.50614	−	12.7791i	−0.420924	−	0.716619i
$319$			14.5351i			0.813808i
$320$	−2.01333	−	17.7749i	−0.112549	−	0.993646i
$321$			10.4887i			0.585425i
$322$	−23.4738	−	7.97655i	−1.30815	−	0.444516i
$323$		−	3.47738i		−	0.193486i
$324$	−0.973958	+	1.74683i	−0.0541088	+	0.0970460i
$325$	4.12200	+	30.1783i	0.228648	+	1.67399i
$326$	−21.4377	+	12.5920i	−1.18733	+	0.697405i
$327$			12.0853i			0.668320i
$328$	−0.349430	−	15.5575i	−0.0192940	−	0.859020i
$329$	−1.03707	−	1.20133i	−0.0571758	−	0.0662317i
$330$	5.89063	−	4.02100i	0.324269	−	0.221349i
$331$	8.65367			0.475649			0.237824	−	0.971308i	$-0.423566\pi$
$331$	8.65367			0.475649			0.237824	+	0.971308i	$0.423566\pi$
$332$	7.04566	−	12.6366i	0.386681	−	0.693525i
$333$	2.30302			0.126205
$334$	10.5069	−	6.17151i	0.574915	−	0.337690i
$335$	31.8606	−	2.16584i	1.74073	−	0.118332i
$336$	−10.0942	−	3.17909i	−0.550685	−	0.173434i
$337$			13.8298i			0.753357i	0.926344	+	0.376679i	$0.122934\pi$
$337$			13.8298i			0.753357i	−0.926344	+	0.376679i	$0.877066\pi$
$338$	17.2680	+	29.3987i	0.939257	+	1.59908i
$339$			5.80202i			0.315122i
$340$	10.7005	+	5.04744i	0.580316	+	0.273736i
$341$	−15.0584			−0.815460
$342$	−1.60284	+	0.941468i	−0.0866717	+	0.0509088i
$343$	9.92614	+	15.6356i	0.535961	+	0.844243i
$344$	0.0806063	+	3.58880i	0.00434600	+	0.193495i
$345$	−1.00486	−	14.7820i	−0.0540998	−	0.795835i
$346$	18.1461	−	10.6586i	0.975543	−	0.573009i
$347$		−	30.3641i		−	1.63003i	−0.579439	−	0.815016i	$-0.696728\pi$
$347$		−	30.3641i		−	1.63003i	0.579439	−	0.815016i	$-0.303272\pi$
$348$	11.2576	+	6.27676i	0.603470	+	0.336470i
$349$	−3.85761			−0.206493			−0.103247	−	0.994656i	$-0.532923\pi$
$349$	−3.85761			−0.206493			−0.103247	+	0.994656i	$0.532923\pi$
$350$	−18.3652	−	3.56659i	−0.981660	−	0.190642i
$351$			6.09170i			0.325151i
$352$	−5.96130	+	11.2801i	−0.317738	+	0.601231i
$353$	28.7836			1.53200			0.765999	−	0.642841i	$-0.222244\pi$
$353$	28.7836			1.53200			0.765999	+	0.642841i	$0.222244\pi$
$354$	1.03309	−	0.606809i	0.0549079	−	0.0322515i
$355$	8.80115	−	0.598290i	0.467116	−	0.0317539i
$356$	−9.89185	−	5.51528i	−0.524267	−	0.292309i
$357$	5.29829	−	4.57385i	0.280415	−	0.242074i
$358$	−11.1114	−	18.9171i	−0.587257	−	0.999799i
$359$		−	11.4556i		−	0.604603i	−0.953212	−	0.302302i	$-0.902245\pi$
$359$		−	11.4556i		−	0.604603i	0.953212	−	0.302302i	$-0.0977550\pi$
$360$	−0.570526	−	6.29877i	−0.0300694	−	0.331974i
$361$	17.2723			0.909067
$362$	8.00488	+	13.6282i	0.420727	+	0.716284i
$363$	5.91320			0.310363
$364$	−31.5690	+	6.51511i	−1.65466	+	0.341484i
$365$	1.26560	+	18.6177i	0.0662447	+	0.974493i
$366$	−8.42607	−	14.3453i	−0.440438	−	0.749842i
$367$			32.8933i			1.71702i	0.512798	+	0.858509i	$0.328609\pi$
$367$			32.8933i			1.71702i	−0.512798	+	0.858509i	$0.671391\pi$
$368$	13.9331	+	22.5460i	0.726315	+	1.17529i
$369$		−	5.50180i		−	0.286412i
$370$	−6.01502	+	4.10590i	−0.312706	+	0.213456i
$371$	20.9880	−	18.1183i	1.08964	−	0.940656i
$372$	−6.50276	+	11.6629i	−0.337153	+	0.604695i
$373$	30.8246			1.59604			0.798019	−	0.602632i	$-0.205881\pi$
$373$	30.8246			1.59604			0.798019	+	0.602632i	$0.205881\pi$
$374$	−4.27370	−	7.27593i	−0.220988	−	0.376229i
$375$	−2.26087	−	10.9494i	−0.116751	−	0.565422i
$376$	0.0380975	+	1.69620i	0.00196473	+	0.0874748i
$377$	39.2585			2.02191
$378$	−3.54271	−	1.20383i	−0.182217	−	0.0619185i
$379$	−37.9641			−1.95009			−0.975043	−	0.222017i	$-0.928736\pi$
$379$	−37.9641			−1.95009			−0.975043	+	0.222017i	$0.928736\pi$
$380$	2.50781	−	5.31653i	0.128648	−	0.272732i
$381$	4.03740			0.206842
$382$	−1.58554	+	0.931303i	−0.0811230	+	0.0476496i
$383$		−	6.43538i		−	0.328833i	−0.986391	−	0.164416i	$-0.947426\pi$
$383$		−	6.43538i		−	0.328833i	0.986391	−	0.164416i	$-0.0525740\pi$
$384$	6.16226	+	9.48823i	0.314466	+	0.484194i
$385$	9.38412	+	9.48558i	0.478259	+	0.483430i
$386$	−12.4718	+	7.32559i	−0.634796	+	0.372863i
$387$			1.26915i			0.0645146i
$388$	11.3425	−	20.3432i	0.575830	−	1.03277i
$389$			19.9377i			1.01088i	0.862861	+	0.505441i	$0.168670\pi$
$389$			19.9377i			1.01088i	−0.862861	+	0.505441i	$0.831330\pi$
$390$	−10.8605	−	15.9103i	−0.549943	−	0.805649i
$391$	−17.5292			−0.886491
$392$	2.44967	−	19.6469i	0.123727	−	0.992316i
$393$			1.91397i			0.0965472i
$394$	3.17032	+	5.39744i	0.159718	+	0.271919i
$395$	−1.50555	+	0.102345i	−0.0757526	+	0.00514955i
$396$	−2.19666	+	3.93978i	−0.110386	+	0.197982i
$397$		−	26.3753i		−	1.32374i	−0.749618	−	0.661870i	$-0.769763\pi$
$397$		−	26.3753i		−	1.32374i	0.749618	−	0.661870i	$-0.230237\pi$
$398$	7.12084	+	12.1232i	0.356936	+	0.607680i
$399$	−2.27251	−	2.63245i	−0.113768	−	0.131787i
$400$	12.7198	+	15.4340i	0.635989	+	0.771698i
$401$	9.83846			0.491309			0.245655	−	0.969357i	$-0.420997\pi$
$401$	9.83846			0.491309			0.245655	+	0.969357i	$0.420997\pi$
$402$	−17.4150	+	10.2291i	−0.868579	+	0.510181i
$403$			40.6720i			2.02602i
$404$	−16.5073	+	29.6064i	−0.821267	+	1.47297i
$405$	−0.151655	−	2.23092i	−0.00753579	−	0.110855i
$406$	−7.75821	+	22.8313i	−0.385034	+	1.13310i
$407$	5.19421			0.257467
$408$	−7.48082	+	0.168023i	−0.370356	+	0.00831838i
$409$			22.6333i			1.11915i	0.828781	+	0.559573i	$0.189035\pi$
$409$			22.6333i			1.11915i	−0.828781	+	0.559573i	$0.810965\pi$
$410$	9.80881	+	14.3696i	0.484423	+	0.709663i
$411$		−	21.9496i		−	1.08269i
$412$	4.85912	+	2.70924i	0.239392	+	0.133475i
$413$	1.46471	+	1.69671i	0.0720739	+	0.0834894i
$414$	4.74588	+	8.07981i	0.233247	+	0.397101i
$415$	1.09708	+	16.1386i	0.0538534	+	0.792211i
$416$	30.4669	+	16.1012i	1.49376	+	0.789424i
$417$			0.792123i			0.0387904i
$418$	−3.61504	+	2.12338i	−0.176817	+	0.103858i
$419$		−	12.2039i		−	0.596202i	−0.954534	−	0.298101i	$-0.903647\pi$
$419$		−	12.2039i		−	0.596202i	0.954534	−	0.298101i	$-0.0963532\pi$
$420$	11.3991	−	3.17190i	0.556218	−	0.154773i
$421$			9.85973i			0.480534i	0.970707	+	0.240267i	$0.0772350\pi$
$421$			9.85973i			0.480534i	−0.970707	+	0.240267i	$0.922765\pi$
$422$	−1.37441	−	2.33992i	−0.0669051	−	0.113905i
$423$			0.599848i			0.0291656i
$424$	−29.6336	+	0.665587i	−1.43914	+	0.0323237i
$425$	−13.1060	+	1.79013i	−0.635734	+	0.0868339i
$426$	−4.81070	+	2.82568i	−0.233079	+	0.136905i
$427$	23.5602	−	20.3388i	1.14016	−	0.984265i
$428$	18.3220	+	10.2156i	0.885629	+	0.493790i
$429$			13.7392i			0.663334i
$430$	−2.26269	−	3.31477i	−0.109117	−	0.159852i
$431$			4.64900i			0.223934i	0.993712	+	0.111967i	$0.0357152\pi$
$431$			4.64900i			0.223934i	−0.993712	+	0.111967i	$0.964285\pi$
$432$	2.10281	+	3.40267i	0.101172	+	0.163711i
$433$	−34.1792			−1.64255			−0.821273	−	0.570535i	$-0.806736\pi$
$433$	−34.1792			−1.64255			−0.821273	+	0.570535i	$0.806736\pi$
$434$	−23.6534	−	8.03756i	−1.13540	−	0.385815i
$435$	−14.3774	+	0.977352i	−0.689341	+	0.0468605i
$436$	21.1110	+	11.7706i	1.01103	+	0.563710i
$437$			8.70938i			0.416626i
$438$	−5.97735	−	10.1764i	−0.285609	−	0.486247i
$439$	−28.0687			−1.33965			−0.669823	−	0.742521i	$-0.733630\pi$
$439$	−28.0687			−1.33965			−0.669823	+	0.742521i	$0.733630\pi$
$440$	−1.28676	−	14.2062i	−0.0613439	−	0.677254i
$441$	1.02185	−	6.92501i	0.0486594	−	0.329763i
$442$	−19.6519	+	11.5430i	−0.934745	+	0.549046i
$443$		−	28.5409i		−	1.35602i	−0.735052	−	0.678011i	$-0.762842\pi$
$443$		−	28.5409i		−	1.35602i	0.735052	−	0.678011i	$-0.237158\pi$
$444$	2.24304	−	4.02297i	0.106450	−	0.190922i
$445$	12.6331	−	0.858783i	0.598868	−	0.0407102i
$446$	5.04993	−	2.96620i	0.239121	−	0.140454i
$447$			16.8637i			0.797628i
$448$	−15.3847	+	14.5366i	−0.726858	+	0.686788i
$449$	0.0355608			0.00167822			0.000839109	−	1.00000i	$-0.499733\pi$
$449$	0.0355608			0.00167822			0.000839109		1.00000i	$0.499733\pi$
$450$	4.37346	+	5.55634i	0.206167	+	0.261928i
$451$		−	12.4087i		−	0.584304i
$452$	10.1351	+	5.65092i	0.476716	+	0.265797i
$453$			18.8911i			0.887581i
$454$	11.3528	+	19.3280i	0.532813	+	0.907110i
$455$	25.6200	−	25.3460i	1.20109	−	1.18824i
$456$	0.0834821	+	3.71684i	0.00390941	+	0.174057i
$457$			7.06267i			0.330378i	0.986262	+	0.165189i	$0.0528234\pi$
$457$			7.06267i			0.330378i	−0.986262	+	0.165189i	$0.947177\pi$
$458$	−17.0451	−	29.0192i	−0.796467	−	1.35598i
$459$	−2.64554			−0.123483
$460$	−26.8003	−	12.6417i	−1.24957	−	0.589423i
$461$	−28.2442			−1.31546			−0.657732	−	0.753252i	$-0.728484\pi$
$461$	−28.2442			−1.31546			−0.657732	+	0.753252i	$0.728484\pi$
$462$	−7.99020	−	2.71512i	−0.371738	−	0.126319i
$463$	30.3492			1.41045			0.705223	−	0.708986i	$-0.250847\pi$
$463$	30.3492			1.41045			0.705223	+	0.708986i	$0.250847\pi$
$464$	21.9288	−	13.5518i	1.01802	−	0.629124i
$465$	−1.01254	−	14.8950i	−0.0469556	−	0.690741i
$466$	−4.35183	+	2.55615i	−0.201594	+	0.118411i
$467$	−34.6180			−1.60193			−0.800965	−	0.598712i	$-0.795680\pi$
$467$	−34.6180			−1.60193			−0.800965	+	0.598712i	$0.795680\pi$
$468$	10.6411	+	5.93306i	0.491887	+	0.274256i
$469$	−24.6910	−	28.6017i	−1.14012	−	1.32070i
$470$	−1.06943	−	1.56668i	−0.0493292	−	0.0722657i
$471$			14.0522i			0.647489i
$472$	−0.0538071	−	2.39563i	−0.00247667	−	0.110268i
$473$			2.86244i			0.131615i
$474$	0.822933	−	0.483370i	0.0377986	−	0.0222019i
$475$	0.889422	+	6.51170i	0.0408095	+	0.298777i
$476$	−2.82942	−	13.7099i	−0.129686	−	0.628394i
$477$	−10.4797			−0.479833
$478$	30.8953	−	18.1471i	1.41312	−	0.830029i
$479$	4.10045			0.187354			0.0936772	−	0.995603i	$-0.470138\pi$
$479$	4.10045			0.187354			0.0936772	+	0.995603i	$0.470138\pi$
$480$	−11.5585	−	5.13813i	−0.527572	−	0.234522i
$481$		−	14.0293i		−	0.639680i
$482$	−19.5888	+	11.5060i	−0.892247	+	0.524083i
$483$	−13.2700	+	11.4556i	−0.603806	+	0.521247i
$484$	5.75921	−	10.3293i	0.261782	−	0.469515i
$485$	1.76614	+	25.9809i	0.0801964	+	1.17973i
$486$	0.716255	+	1.21942i	0.0324900	+	0.0553139i
$487$	−40.3511			−1.82848			−0.914241	−	0.405171i	$-0.867212\pi$
$487$	−40.3511			−1.82848			−0.914241	+	0.405171i	$0.867212\pi$
$488$	−33.2654	+	0.747159i	−1.50586	+	0.0338223i
$489$			17.5803i			0.795008i
$490$	9.67731	+	19.9085i	0.437176	+	0.899376i
$491$	−13.3376			−0.601917			−0.300958	−	0.953637i	$-0.597307\pi$
$491$	−13.3376			−0.601917			−0.300958	+	0.953637i	$0.597307\pi$
$492$	−9.61069	−	5.35852i	−0.433283	−	0.241581i
$493$			17.0494i			0.767866i
$494$	5.73514	+	9.76403i	0.258036	+	0.439304i
$495$	−0.342041	−	5.03160i	−0.0153736	−	0.226154i
$496$	14.0397	+	22.7184i	0.630401	+	1.02009i
$497$	−6.82062	−	7.90092i	−0.305947	−	0.354405i
$498$	−5.18142	−	8.82132i	−0.232185	−	0.395293i
$499$	−21.3838			−0.957270			−0.478635	−	0.878014i	$-0.658868\pi$
$499$	−21.3838			−0.957270			−0.478635	+	0.878014i	$0.658868\pi$
$500$	−21.3286	−	6.71487i	−0.953845	−	0.300298i
$501$		−	8.61637i		−	0.384951i
$502$	−18.9960	+	11.1577i	−0.847831	+	0.497995i
$503$		−	26.6346i		−	1.18758i	−0.804621	−	0.593788i	$-0.797632\pi$
$503$		−	26.6346i		−	1.18758i	0.804621	−	0.593788i	$-0.202368\pi$
$504$	−5.55334	+	5.01602i	−0.247365	+	0.223431i
$505$	−2.57034	−	37.8111i	−0.114379	−	1.68257i
$506$	10.7038	+	18.2232i	0.475843	+	0.810118i
$507$	24.1088			1.07071
$508$	3.93226	−	7.05263i	0.174466	−	0.312910i
$509$	−14.1420			−0.626835			−0.313417	−	0.949615i	$-0.601474\pi$
$509$	−14.1420			−0.626835			−0.313417	+	0.949615i	$0.601474\pi$
$510$	6.90961	−	4.71656i	0.305963	−	0.208853i
$511$	16.7133	−	14.4281i	0.739355	−	0.638263i
$512$	22.5761	−	1.52326i	0.997731	−	0.0673193i
$513$			1.31443i			0.0580336i
$514$	−13.4707	−	22.9337i	−0.594167	−	1.01156i
$515$	−6.20571	+	0.421856i	−0.273456	+	0.0185892i
$516$	2.21699	+	1.23610i	0.0975975	+	0.0544163i
$517$			1.35289i			0.0595002i
$518$	8.15892	+	2.77245i	0.358482	+	0.121814i
$519$		−	14.8810i		−	0.653203i
$520$	−38.3702	+	3.47547i	−1.68264	+	0.152410i
$521$		−	4.69309i		−	0.205608i	−0.994702	−	0.102804i	$-0.967219\pi$
$521$		−	4.69309i		−	0.205608i	0.994702	−	0.102804i	$-0.0327815\pi$
$522$	7.85864	−	4.61597i	0.343963	−	0.202035i
$523$	16.2038			0.708541			0.354270	−	0.935143i	$-0.384729\pi$
$523$	16.2038			0.708541			0.354270	+	0.935143i	$0.384729\pi$
$524$	3.34338	+	1.86413i	0.146056	+	0.0814349i
$525$	−8.75165	+	9.92011i	−0.381953	+	0.432949i
$526$	−14.5016	−	24.6888i	−0.632298	−	1.07648i
$527$	−17.6633			−0.769425
$528$	4.74267	+	7.67437i	0.206398	+	0.333984i
$529$	20.9033			0.908841
$530$	27.3709	−	18.6836i	1.18892	−	0.811565i
$531$		−	0.847197i		−	0.0367652i
$532$	−6.81177	+	1.40579i	−0.295328	+	0.0609489i
$533$	−33.5153			−1.45171
$534$	−6.90526	+	4.05597i	−0.298820	+	0.175519i
$535$	−23.3996	+	1.59067i	−1.01165	+	0.0687706i
$536$	0.907037	+	40.3836i	0.0391780	+	1.74431i
$537$	−15.5132			−0.669445
$538$	−6.93426	−	11.8055i	−0.298957	−	0.508972i
$539$	2.30467	−	15.6186i	0.0992691	−	0.672742i
$540$	−4.04474	−	1.90791i	−0.174058	−	0.0821033i
$541$		−	2.77873i		−	0.119467i	−0.998214	−	0.0597335i	$-0.980975\pi$
$541$		−	2.77873i		−	0.119467i	0.998214	−	0.0597335i	$-0.0190251\pi$
$542$	−1.54813	−	2.63567i	−0.0664978	−	0.113212i
$543$	11.1760			0.479609
$544$	−6.99250	+	13.2313i	−0.299801	+	0.567289i
$545$	−26.9614	+	1.83280i	−1.15490	+	0.0785084i
$546$	−7.33339	+	21.5811i	−0.313840	+	0.923586i
$547$			21.8861i			0.935783i	0.883786	+	0.467891i	$0.154986\pi$
$547$			21.8861i			0.935783i	−0.883786	+	0.467891i	$0.845014\pi$
$548$	−38.3421	−	21.3780i	−1.63789	−	0.913222i
$549$	−11.7641			−0.502078
$550$	9.86387	+	12.5317i	0.420597	+	0.534355i
$551$	8.47097			0.360876
$552$	18.7363	−	0.420828i	0.797471	−	0.0179116i
$553$	1.16676	+	1.35156i	0.0496156	+	0.0574741i
$554$	−21.3246	−	36.3049i	−0.905994	−	1.54245i
$555$	0.349263	+	5.13784i	0.0148254	+	0.218089i
$556$	1.38370	+	0.771494i	0.0586820	+	0.0327186i
$557$	12.8730			0.545447			0.272723	−	0.962093i	$-0.412076\pi$
$557$	12.8730			0.545447			0.272723	+	0.962093i	$0.412076\pi$
$558$	4.78217	+	8.14161i	0.202446	+	0.344662i
$559$	7.73129			0.326999
$560$	5.56146	−	23.0015i	0.235015	−	0.971992i
$561$	−5.96672			−0.251915
$562$	10.3374	+	17.5993i	0.436056	+	0.742381i
$563$	22.8118			0.961402			0.480701	−	0.876885i	$-0.340382\pi$
$563$	22.8118			0.961402			0.480701	+	0.876885i	$0.340382\pi$
$564$	1.04783	+	0.584227i	0.0441217	+	0.0246004i
$565$	−12.9438	+	0.879904i	−0.544551	+	0.0370178i
$566$	−6.22118	−	10.5915i	−0.261496	−	0.445194i
$567$	−2.00273	+	1.72889i	−0.0841067	+	0.0726067i
$568$	0.250559	+	11.1555i	0.0105132	+	0.468076i
$569$	6.15721			0.258124			0.129062	−	0.991637i	$-0.458803\pi$
$569$	6.15721			0.258124			0.129062	+	0.991637i	$0.458803\pi$
$570$	−2.34342	−	3.43303i	−0.0981550	−	0.143794i
$571$	35.8831			1.50166			0.750831	−	0.660495i	$-0.229653\pi$
$571$	35.8831			1.50166			0.750831	+	0.660495i	$0.229653\pi$
$572$	24.0000	+	13.3814i	1.00349	+	0.559504i
$573$			1.30024i			0.0543183i
$574$	6.62325	−	19.4913i	0.276449	−	0.813550i
$575$	32.8250	−	4.48352i	1.36890	−	0.186976i
$576$	7.99193	−	0.359187i	0.332997	−	0.0149661i
$577$	10.5632			0.439751			0.219875	−	0.975528i	$-0.429435\pi$
$577$	10.5632			0.439751			0.219875	+	0.975528i	$0.429435\pi$
$578$	7.16336	+	12.1956i	0.297957	+	0.507269i
$579$			10.2276i			0.425046i
$580$	−12.2957	+	26.0667i	−0.510550	+	1.08236i
$581$	14.4878	−	12.5069i	0.601057	−	0.518874i
$582$	−8.34136	−	14.2011i	−0.345761	−	0.588655i
$583$	−23.6359			−0.978898
$584$	−23.5981	+	0.530025i	−0.976496	+	0.0219326i
$585$	−13.5901	+	0.923835i	−0.561881	+	0.0381959i
$586$	0.619095	−	0.363641i	0.0255746	−	0.0150219i
$587$	33.0773			1.36525			0.682624	−	0.730770i	$-0.260839\pi$
$587$	33.0773			1.36525			0.682624	+	0.730770i	$0.260839\pi$
$588$	−11.1016	−	8.52966i	−0.457821	−	0.351757i
$589$			8.77598i			0.361608i
$590$	1.51041	+	2.21271i	0.0621828	+	0.0910957i
$591$	4.42625			0.182071
$592$	−4.84281	−	7.83641i	−0.199038	−	0.322075i
$593$	5.05822			0.207716			0.103858	−	0.994592i	$-0.466881\pi$
$593$	5.05822			0.207716			0.103858	+	0.994592i	$0.466881\pi$
$594$	1.61544	+	2.75027i	0.0662822	+	0.112845i
$595$	11.0074	+	11.1264i	0.451260	+	0.456139i
$596$	29.4580	+	16.4246i	1.20665	+	0.672777i
$597$	9.94177			0.406890
$598$	49.2198	−	28.9104i	2.01275	−	1.18224i
$599$		−	32.6303i		−	1.33324i	−0.745398	−	0.666620i	$-0.767741\pi$
$599$		−	32.6303i		−	1.33324i	0.745398	−	0.666620i	$-0.232259\pi$
$600$	13.9655	−	2.22804i	0.570140	−	0.0909592i
$601$			9.09684i			0.371068i	0.982638	+	0.185534i	$0.0594015\pi$
$601$			9.09684i			0.371068i	−0.982638	+	0.185534i	$0.940599\pi$
$602$	−1.52785	+	4.49624i	−0.0622704	+	0.183253i
$603$			14.2814i			0.581582i
$604$	32.9995	+	18.3991i	1.34273	+	0.748650i
$605$	0.896765	+	13.1919i	0.0364587	+	0.536326i
$606$	12.1395	+	20.6675i	0.493135	+	0.839559i
$607$		−	22.9677i		−	0.932229i	−0.884724	−	0.466115i	$-0.845653\pi$
$607$		−	22.9677i		−	0.932229i	0.884724	−	0.466115i	$-0.154347\pi$
$608$	6.57398	+	3.47422i	0.266610	+	0.140898i
$609$	11.1420	+	12.9068i	0.451497	+	0.523008i
$610$	30.7254	−	20.9734i	1.24403	−	0.849189i
$611$	3.65409			0.147829
$612$	−2.57664	+	4.62129i	−0.104155	+	0.186805i
$613$	−19.0237			−0.768361			−0.384181	−	0.923258i	$-0.625516\pi$
$613$	−19.0237			−0.768361			−0.384181	+	0.923258i	$0.625516\pi$
$614$	13.0521	+	22.2211i	0.526740	+	0.896771i
$615$	12.2741	−	0.834374i	0.494938	−	0.0336452i
$616$	−12.5250	+	11.3131i	−0.504645	+	0.455817i
$617$		−	5.41496i		−	0.217998i	−0.994042	−	0.108999i	$-0.965235\pi$
$617$		−	5.41496i		−	0.217998i	0.994042	−	0.108999i	$-0.0347645\pi$
$618$	3.39203	−	1.99239i	0.136448	−	0.0801459i
$619$		−	34.2500i		−	1.37663i	−0.725414	−	0.688313i	$-0.758352\pi$
$619$		−	34.2500i		−	1.37663i	0.725414	−	0.688313i	$-0.241648\pi$
$620$	−27.0052	−	12.7384i	−1.08456	−	0.511587i
$621$	6.62596			0.265891
$622$	9.68871	+	16.4949i	0.388482	+	0.661387i
$623$	−9.79030	−	11.3410i	−0.392240	−	0.454366i
$624$	20.7281	−	12.8097i	0.829786	−	0.512798i
$625$	24.0843	−	6.70434i	0.963371	−	0.268174i
$626$	11.4644	+	19.5181i	0.458211	+	0.780100i
$627$			2.96456i			0.118393i
$628$	24.5467	+	13.6862i	0.979519	+	0.546139i
$629$	6.09271			0.242932
$630$	2.14839	−	8.08606i	0.0855938	−	0.322157i
$631$			10.6858i			0.425396i	0.977118	+	0.212698i	$0.0682251\pi$
$631$			10.6858i			0.425396i	−0.977118	+	0.212698i	$0.931775\pi$
$632$	−0.0428615	−	1.90830i	−0.00170494	−	0.0759083i
$633$	−1.91888			−0.0762687
$634$	−24.9474	−	42.4728i	−0.990789	−	1.68681i
$635$	0.612290	+	9.00711i	0.0242980	+	0.357436i
$636$	−10.2068	+	18.3062i	−0.404726	+	0.725890i
$637$	−42.1851	−	6.22478i	−1.67143	−	0.246635i
$638$	17.7243	−	10.4108i	0.701713	−	0.412168i
$639$			3.94508i			0.156065i
$640$	−20.2329	+	15.1864i	−0.799777	+	0.600297i
$641$	14.9830			0.591793			0.295896	−	0.955220i	$-0.404382\pi$
$641$	14.9830			0.591793			0.295896	+	0.955220i	$0.404382\pi$
$642$	12.7902	−	7.51262i	0.504787	−	0.296499i
$643$	1.83462			0.0723504			0.0361752	−	0.999345i	$-0.488483\pi$
$643$	1.83462			0.0723504			0.0361752	+	0.999345i	$0.488483\pi$
$644$	7.08650	+	34.3377i	0.279247	+	1.35309i
$645$	−2.83138	+	0.192473i	−0.111485	+	0.00757861i
$646$	−4.24038	+	2.49069i	−0.166835	+	0.0979948i
$647$		−	0.627991i		−	0.0246889i	−0.999924	−	0.0123444i	$-0.996071\pi$
$647$		−	0.627991i		−	0.0246889i	0.999924	−	0.0123444i	$-0.00392946\pi$
$648$	2.82771	−	0.0635119i	0.111083	−	0.00249498i
$649$		−	1.91076i		−	0.0750040i
$650$	33.8475	−	26.6418i	1.32761	−	1.04498i
$651$	−13.3715	+	11.5432i	−0.524070	+	0.452414i
$652$	30.7097	+	17.1225i	1.20269	+	0.670567i
$653$	−8.04969			−0.315009			−0.157504	−	0.987518i	$-0.550345\pi$
$653$	−8.04969			−0.315009			−0.157504	+	0.987518i	$0.550345\pi$
$654$	14.7371	−	8.65617i	0.576265	−	0.338483i
$655$	−4.26992	+	0.290263i	−0.166840	+	0.0113415i
$656$	−18.7208	+	11.5692i	−0.730925	+	0.451703i
$657$	−8.34529			−0.325581
$658$	−0.722118	+	2.12509i	−0.0281511	+	0.0828445i
$659$	−36.0309			−1.40357			−0.701783	−	0.712391i	$-0.747612\pi$
$659$	−36.0309			−1.40357			−0.701783	+	0.712391i	$0.747612\pi$
$660$	−9.12247	−	4.30308i	−0.355092	−	0.167497i
$661$	−6.25833			−0.243421			−0.121710	−	0.992566i	$-0.538838\pi$
$661$	−6.25833			−0.243421			−0.121710	+	0.992566i	$0.538838\pi$
$662$	−6.19823	−	10.5524i	−0.240901	−	0.410132i
$663$			16.1158i			0.625886i
$664$	−20.4558	+	0.459448i	−0.793839	+	0.0178300i
$665$	5.52815	−	5.46902i	0.214372	−	0.212080i
$666$	−1.64955	−	2.80834i	−0.0639186	−	0.108821i
$667$		−	42.7016i		−	1.65341i
$668$	−15.0513	−	8.39198i	−0.582352	−	0.324695i
$669$		−	4.14126i		−	0.160110i
$670$	−25.4614	−	37.3001i	−0.983658	−	1.44103i
$671$	−26.5326			−1.02428
$672$	3.35339	+	14.5861i	0.129360	+	0.562672i
$673$		−	22.7479i		−	0.876866i	−0.898764	−	0.438433i	$-0.855534\pi$
$673$		−	22.7479i		−	0.876866i	0.898764	−	0.438433i	$-0.144466\pi$
$674$	16.8643	−	9.90566i	0.649589	−	0.381552i
$675$	4.95400	−	0.676659i	0.190680	−	0.0260446i
$676$	23.4809	−	42.1139i	0.903113	−	1.61976i
$677$		−	41.9971i		−	1.61408i	−0.590497	−	0.807040i	$-0.701068\pi$
$677$		−	41.9971i		−	1.61408i	0.590497	−	0.807040i	$-0.298932\pi$
$678$	7.07509	−	4.15572i	0.271717	−	0.159600i
$679$	23.3234	−	20.1344i	0.895070	−	0.772686i
$680$	−1.50935	−	16.6636i	−0.0578808	−	0.639021i
$681$	15.8502			0.607382
$682$	10.7857	+	18.3625i	0.413005	+	0.703137i
$683$		−	7.05862i		−	0.270091i	−0.990839	−	0.135045i	$-0.956882\pi$
$683$		−	7.05862i		−	0.270091i	0.990839	−	0.135045i	$-0.0431180\pi$
$684$	2.29609	+	1.28020i	0.0877930	+	0.0489497i
$685$	48.9678	−	3.32876i	1.87096	−	0.127185i
$686$	11.9567	−	23.3032i	0.456508	−	0.889719i
$687$	−23.7976			−0.907935
$688$	4.31851	−	2.66879i	0.164642	−	0.101747i
$689$			63.8392i			2.43208i
$690$	−17.3057	+	11.8130i	−0.658816	+	0.449714i
$691$		−	12.3825i		−	0.471054i	−0.971868	−	0.235527i	$-0.924318\pi$
$691$		−	12.3825i		−	0.471054i	0.971868	−	0.235527i	$-0.0756816\pi$
$692$	−25.9945	−	14.4935i	−0.988164	−	0.550959i
$693$	−4.51694	+	3.89934i	−0.171584	+	0.148124i
$694$	−37.0266	+	21.7485i	−1.40551	+	0.825560i
$695$	−1.76716	+	0.120129i	−0.0670323	+	0.00455676i
$696$	−0.409308	−	18.2234i	−0.0155148	−	0.690758i
$697$		−	14.5552i		−	0.551318i
$698$	2.76303	+	4.70404i	0.104582	+	0.178050i
$699$			3.56877i			0.134983i
$700$	8.80498	+	24.9494i	0.332797	+	0.942999i
$701$		−	2.78452i		−	0.105170i	−0.998616	−	0.0525850i	$-0.983254\pi$
$701$		−	2.78452i		−	0.105170i	0.998616	−	0.0525850i	$-0.0167461\pi$
$702$	7.42832	−	4.36321i	0.280364	−	0.164679i
$703$		−	3.02716i		−	0.114171i
$704$	18.0250	−	0.810108i	0.679341	−	0.0305321i
$705$	−1.33821	+	0.0909698i	−0.0504000	+	0.00342612i
$706$	−20.6164	−	35.0993i	−0.775909	−	1.32098i
$707$	−33.9435	+	29.3024i	−1.27658	+	1.10203i
$708$	−1.47991	−	0.825134i	−0.0556183	−	0.0310104i
$709$			16.1923i			0.608115i	0.952654	+	0.304058i	$0.0983416\pi$
$709$			16.1923i			0.608115i	−0.952654	+	0.304058i	$0.901658\pi$
$710$	−7.03343	−	10.3037i	−0.263960	−	0.386693i
$711$		−	0.674858i		−	0.0253091i
$712$	0.359652	+	16.0126i	0.0134785	+	0.600099i
$713$	44.2391			1.65677
$714$	−9.37236	−	3.18479i	−0.350752	−	0.119188i
$715$	−30.6510	+	2.08361i	−1.14628	+	0.0779226i
$716$	−15.1092	+	27.0989i	−0.564658	+	1.01273i
$717$		−	25.3361i		−	0.946194i
$718$	−13.9692	+	8.20513i	−0.521324	+	0.306213i
$719$	38.4252			1.43302			0.716509	−	0.697577i	$-0.245739\pi$
$719$	38.4252			1.43302			0.716509	+	0.697577i	$0.245739\pi$
$720$	−7.27219	+	5.20723i	−0.271018	+	0.194062i
$721$	4.80924	+	5.57096i	0.179105	+	0.207473i
$722$	−12.3713	−	21.0621i	−0.460414	−	0.783850i
$723$			16.0641i			0.597430i
$724$	10.8850	−	19.5226i	0.404537	−	0.725551i
$725$	−4.36079	−	31.9265i	−0.161956	−	1.18572i
$726$	−4.23536	−	7.21066i	−0.157189	−	0.267613i
$727$			36.2701i			1.34518i	0.740013	+	0.672592i	$0.234819\pi$
$727$			36.2701i			1.34518i	−0.740013	+	0.672592i	$0.765181\pi$
$728$	30.5561	+	33.8293i	1.13248	+	1.25380i
$729$	1.00000			0.0370370
$730$	21.7962	−	14.8783i	0.806714	−	0.550670i
$731$			3.35759i			0.124185i
$732$	−11.4577	+	20.5498i	−0.423489	+	0.759543i
$733$		−	0.292182i		−	0.0107920i	−0.999985	−	0.00539599i	$-0.998282\pi$
$733$		−	0.292182i		−	0.0107920i	0.999985	−	0.00539599i	$-0.00171761\pi$
$734$	40.1107	−	23.5600i	1.48051	−	0.869616i
$735$	15.6041	+	1.22945i	0.575567	+	0.0453488i
$736$	17.5133	−	33.1390i	0.645548	−	1.22152i
$737$			32.2101i			1.18647i
$738$	−6.70899	+	3.94069i	−0.246961	+	0.145059i
$739$	−17.1153			−0.629598			−0.314799	−	0.949158i	$-0.601937\pi$
$739$	−17.1153			−0.629598			−0.314799	+	0.949158i	$0.601937\pi$
$740$	9.31509	+	4.39394i	0.342430	+	0.161525i
$741$	8.00712			0.294149
$742$	−37.1266	−	12.6158i	−1.36296	−	0.463142i
$743$	20.6194			0.756453			0.378227	−	0.925713i	$-0.376534\pi$
$743$	20.6194			0.756453			0.378227	+	0.925713i	$0.376534\pi$
$744$	18.8796	−	0.424046i	0.692160	−	0.0155463i
$745$	−37.6217	+	2.55747i	−1.37835	+	0.0936983i
$746$	−22.0783	−	37.5881i	−0.808343	−	1.37620i
$747$	−7.23405			−0.264680
$748$	−5.81134	+	10.4228i	−0.212484	+	0.381097i
$749$	18.1339	+	21.0061i	0.662600	+	0.767547i
$750$	−11.7325	+	10.5995i	−0.428410	+	0.387038i
$751$		−	36.0405i		−	1.31514i	−0.753395	−	0.657568i	$-0.771585\pi$
$751$		−	36.0405i		−	1.31514i	0.753395	−	0.657568i	$-0.228415\pi$
$752$	2.04109	−	1.26137i	0.0744308	−	0.0459973i
$753$			15.5779i			0.567690i
$754$	−28.1191	−	47.8725i	−1.02404	−	1.74341i
$755$	−42.1445	+	2.86492i	−1.53379	+	0.104265i
$756$	1.06951	+	5.18229i	0.0388976	+	0.188478i
$757$	9.02856			0.328149			0.164074	−	0.986448i	$-0.447536\pi$
$757$	9.02856			0.328149			0.164074	+	0.986448i	$0.447536\pi$
$758$	27.1920	+	46.2941i	0.987657	+	1.68148i
$759$	14.9441			0.542438
$760$	−8.27931	+	0.749918i	−0.300322	+	0.0272024i
$761$			49.6369i			1.79934i	0.436575	+	0.899668i	$0.356191\pi$
$761$			49.6369i			1.79934i	−0.436575	+	0.899668i	$0.643809\pi$
$762$	−2.89180	−	4.92327i	−0.104759	−	0.178351i
$763$	20.8943	+	24.2036i	0.756423	+	0.876230i
$764$	2.27129	+	1.26638i	0.0821726	+	0.0458160i
$765$	−0.401208	−	5.90198i	−0.0145057	−	0.213386i
$766$	−7.84742	+	4.60937i	−0.283539	+	0.166543i
$767$	−5.16087			−0.186348
$768$	7.15637	−	14.3104i	0.258233	−	0.516381i
$769$		−	25.0729i		−	0.904151i	−0.891980	−	0.452075i	$-0.850684\pi$
$769$		−	25.0729i		−	0.904151i	0.891980	−	0.452075i	$-0.149316\pi$
$770$	4.84546	−	18.2373i	0.174618	−	0.657225i
$771$	−18.8071			−0.677322
$772$	17.8659	+	9.96129i	0.643008	+	0.358515i
$773$		−	38.7317i		−	1.39308i	−0.717516	−	0.696542i	$-0.754721\pi$
$773$		−	38.7317i		−	1.39308i	0.717516	−	0.696542i	$-0.245279\pi$
$774$	1.54763	−	0.909036i	0.0556283	−	0.0326746i
$775$	33.0761	−	4.51781i	1.18813	−	0.162284i
$776$	−32.9310	+	0.739648i	−1.18215	+	0.0265518i
$777$	4.61232	−	3.98167i	0.165466	−	0.142842i
$778$	24.3124	−	14.2805i	0.871641	−	0.511980i
$779$	−7.23174			−0.259104
$780$	−11.6224	+	24.6393i	−0.416148	+	0.882229i
$781$			8.89770i			0.318385i
$782$	12.5554	+	21.3754i	0.448980	+	0.764384i
$783$		−	6.44459i		−	0.230311i
$784$	−25.7123	+	11.0850i	−0.918297	+	0.395892i
$785$	−31.3492	+	2.13108i	−1.11890	+	0.0760614i
$786$	2.33393	−	1.37089i	0.0832486	−	0.0488981i
$787$	−53.0239			−1.89010			−0.945049	−	0.326928i	$-0.893987\pi$
$787$	−53.0239			−1.89010			−0.945049	+	0.326928i	$0.893987\pi$
$788$	4.31098	−	7.73189i	0.153572	−	0.275437i
$789$	−20.2464			−0.720790
$790$	1.20316	+	1.76259i	0.0428066	+	0.0627102i
$791$	10.0311	+	11.6199i	0.356664	+	0.413155i
$792$	6.37761	−	0.143244i	0.226618	−	0.00508997i
$793$			71.6632i			2.54483i
$794$	−32.1626	+	18.8915i	−1.14141	+	0.670433i
$795$	−1.58930	−	23.3794i	−0.0563666	−	0.829182i
$796$	9.68287	−	17.3666i	0.343200	−	0.615541i
$797$		−	13.5559i		−	0.480175i	−0.970751	−	0.240088i	$-0.922824\pi$
$797$		−	13.5559i		−	0.480175i	0.970751	−	0.240088i	$-0.0771761\pi$
$798$	−1.58236	+	4.65665i	−0.0560149	+	0.164844i
$799$			1.58692i			0.0561412i
$800$	9.70984	−	26.5654i	0.343295	−	0.939228i
$801$			5.66275i			0.200083i
$802$	−7.04685	−	11.9972i	−0.248833	−	0.423636i
$803$	−18.8219			−0.664211
$804$	24.9471	+	13.9095i	0.879816	+	0.490549i
$805$	−27.5689	−	27.8670i	−0.971678	−	0.982183i
$806$	49.5962	−	29.1315i	1.74695	−	1.02611i
$807$	−9.68128			−0.340797
$808$	47.9259	−	1.07644i	1.68603	−	0.0378691i
$809$	23.6664			0.832066			0.416033	−	0.909350i	$-0.363420\pi$
$809$	23.6664			0.832066			0.416033	+	0.909350i	$0.363420\pi$
$810$	−2.61180	+	1.78284i	−0.0917692	+	0.0626425i
$811$			0.303856i			0.0106698i	0.999986	+	0.00533491i	$0.00169816\pi$
$811$			0.303856i			0.0106698i	−0.999986	+	0.00533491i	$0.998302\pi$
$812$	33.3977	−	6.89253i	1.17203	−	0.241880i
$813$	−2.16142			−0.0758043
$814$	−3.72038	−	6.33391i	−0.130399	−	0.222003i
$815$	−39.2202	+	2.66613i	−1.37382	+	0.0933906i
$816$	5.56306	+	9.00189i	0.194746	+	0.315129i
$817$	1.66821			0.0583634
$818$	27.5995	−	16.2112i	0.964993	−	0.566813i
$819$	10.5319	+	12.2000i	0.368014	+	0.426303i
$820$	10.4969	−	22.2533i	0.366568	−	0.777120i
$821$			17.5436i			0.612275i	0.951987	+	0.306138i	$0.0990368\pi$
$821$			17.5436i			0.612275i	−0.951987	+	0.306138i	$0.900963\pi$
$822$	−26.7657	+	15.7215i	−0.933561	+	0.548350i
$823$	−23.7171			−0.826726			−0.413363	−	0.910566i	$-0.635646\pi$
$823$	−23.7171			−0.826726			−0.413363	+	0.910566i	$0.635646\pi$
$824$	−0.176670	−	7.86581i	−0.00615460	−	0.274018i
$825$	11.1732	−	1.52613i	0.389002	−	0.0531331i
$826$	1.01988	−	3.00137i	0.0354863	−	0.104431i
$827$		−	23.2251i		−	0.807614i	−0.914844	−	0.403807i	$-0.867687\pi$
$827$		−	23.2251i		−	0.807614i	0.914844	−	0.403807i	$-0.132313\pi$
$828$	6.45341	−	11.5744i	0.224271	−	0.402238i
$829$	−10.5085			−0.364975			−0.182488	−	0.983208i	$-0.558415\pi$
$829$	−10.5085			−0.364975			−0.182488	+	0.983208i	$0.558415\pi$
$830$	18.8939	−	12.8971i	0.655816	−	0.447666i
$831$	−29.7723			−1.03279
$832$	−2.18806	−	48.6844i	−0.0758573	−	1.68783i
$833$	2.70333	−	18.3204i	0.0936650	−	0.634763i
$834$	0.965928	−	0.567362i	0.0334474	−	0.0196461i
$835$	19.2224	−	1.30671i	0.665219	−	0.0452207i
$836$	5.17858	+	2.88736i	0.179105	+	0.0998614i
$837$	6.67664			0.230778
$838$	−14.8817	+	8.74113i	−0.514080	+	0.301957i
$839$	30.2907			1.04575			0.522875	−	0.852409i	$-0.324860\pi$
$839$	30.2907			1.04575			0.522875	+	0.852409i	$0.324860\pi$
$840$	−12.0325	−	11.6283i	−0.415161	−	0.401216i
$841$	−12.5327			−0.432162
$842$	12.0231	−	7.06208i	0.414344	−	0.243375i
$843$	14.4325			0.497083
$844$	−1.86891	+	3.35195i	−0.0643305	+	0.115379i
$845$	3.65621	+	53.7847i	0.125777	+	1.85025i
$846$	0.731466	−	0.429644i	0.0251483	−	0.0147715i
$847$	11.8425	−	10.2233i	0.406914	−	0.351277i
$848$	22.0369	+	35.6590i	0.756749	+	1.22454i
$849$	−8.68571			−0.298093
$850$	11.5701	+	14.6995i	0.396852	+	0.504188i
$851$	−15.2597			−0.523096
$852$	6.89137	+	3.84234i	0.236094	+	0.131636i
$853$		−	1.54149i		−	0.0527798i	−0.999652	−	0.0263899i	$-0.991599\pi$
$853$		−	1.54149i		−	0.0527798i	0.999652	−	0.0263899i	$-0.00840114\pi$
$854$	−41.6767	−	14.1620i	−1.42615	−	0.484613i
$855$	−2.93239	+	0.199340i	−0.100286	+	0.00681728i
$856$	−0.666161	−	29.6592i	−0.0227689	−	1.01373i
$857$	−27.6511			−0.944544			−0.472272	−	0.881453i	$-0.656566\pi$
$857$	−27.6511			−0.944544			−0.472272	+	0.881453i	$0.656566\pi$
$858$	16.7538	−	9.84075i	0.571965	−	0.335958i
$859$		−	41.1094i		−	1.40264i	−0.712848	−	0.701318i	$-0.752595\pi$
$859$		−	41.1094i		−	1.40264i	0.712848	−	0.701318i	$-0.247405\pi$
$860$	−2.42142	+	5.13339i	−0.0825699	+	0.175047i
$861$	−9.51203	−	11.0186i	−0.324169	−	0.375513i
$862$	5.66907	−	3.32987i	0.193089	−	0.113416i
$863$	−32.7261			−1.11401			−0.557005	−	0.830509i	$-0.688049\pi$
$863$	−32.7261			−1.11401			−0.557005	+	0.830509i	$0.688049\pi$
$864$	2.64313	−	5.00139i	0.0899211	−	0.170151i
$865$	33.1983	−	2.25677i	1.12878	−	0.0767326i
$866$	24.4810	+	41.6787i	0.831898	+	1.41630i
$867$	10.0011			0.339656
$868$	7.14070	+	34.6003i	0.242371	+	1.17441i
$869$		−	1.52207i		−	0.0516327i
$870$	11.4896	+	16.8320i	0.389536	+	0.570657i
$871$	86.9978			2.94781
$872$	−0.767562	−	34.1738i	−0.0259929	−	1.15727i
$873$	−11.6458			−0.394151
$874$	10.6204	−	6.23813i	0.359239	−	0.211008i
$875$	−23.4582	−	18.0198i	−0.793032	−	0.609180i
$876$	−8.12796	+	14.5778i	−0.274618	+	0.492537i
$877$	41.3462			1.39616			0.698081	−	0.716019i	$-0.254038\pi$
$877$	41.3462			1.39616			0.698081	+	0.716019i	$0.254038\pi$
$878$	20.1043	+	34.2274i	0.678488	+	1.15512i
$879$		−	0.507697i		−	0.0171242i
$880$	−16.4016	+	11.7444i	−0.552899	+	0.395902i
$881$		−	48.5383i		−	1.63530i	−0.575717	−	0.817649i	$-0.695277\pi$
$881$		−	48.5383i		−	1.63530i	0.575717	−	0.817649i	$-0.304723\pi$
$882$	−9.17639	+	3.71402i	−0.308985	+	0.125057i
$883$			34.7724i			1.17018i	0.810967	+	0.585092i	$0.198941\pi$
$883$			34.7724i			1.17018i	−0.810967	+	0.585092i	$0.801059\pi$
$884$	28.1515	+	15.6961i	0.946838	+	0.527918i
$885$	1.89003	−	0.128481i	0.0635326	−	0.00431886i
$886$	−34.8033	+	20.4426i	−1.16924	+	0.686782i
$887$		−	10.4851i		−	0.352055i	−0.984385	−	0.176027i	$-0.943675\pi$
$887$		−	10.4851i		−	0.352055i	0.984385	−	0.176027i	$-0.0563247\pi$
$888$	−6.51227	+	0.146269i	−0.218538	+	0.00490847i
$889$	8.08581	−	6.98023i	0.271189	−	0.234110i
$890$	−10.0958	−	14.7900i	−0.338411	−	0.495761i
$891$	2.25539			0.0755585
$892$	−7.23407	−	4.03342i	−0.242215	−	0.135049i
$893$	0.788460			0.0263848
$894$	20.5639	−	12.0787i	0.687761	−	0.403973i
$895$	−2.35265	−	34.6087i	−0.0786405	−	1.15684i
$896$	28.7455	+	8.34846i	0.960319	+	0.278903i
$897$		−	40.3633i		−	1.34769i
$898$	−0.0254706	−	0.0433634i	−0.000849964	−	0.00144706i
$899$		−	43.0282i		−	1.43507i
$900$	3.64298	−	9.31282i	0.121433	−	0.310427i
$901$	−27.7245			−0.923635
$902$	−15.1314	+	8.88780i	−0.503821	+	0.295932i
$903$	2.19423	+	2.54177i	0.0730194	+	0.0845847i
$904$	−0.368497	−	16.4065i	−0.0122560	−	0.545671i
$905$	1.69490	+	24.9328i	0.0563403	+	0.828795i
$906$	23.0361	−	13.5308i	0.765324	−	0.449532i
$907$		−	29.5291i		−	0.980497i	−0.871583	−	0.490248i	$-0.836906\pi$
$907$		−	29.5291i		−	0.980497i	0.871583	−	0.490248i	$-0.163094\pi$
$908$	15.4374	−	27.6876i	0.512310	−	0.918845i
$909$	16.9486			0.562151
$910$	−49.2579	−	13.0873i	−1.63288	−	0.433841i
$911$		−	40.5949i		−	1.34497i	−0.740111	−	0.672484i	$-0.765227\pi$
$911$		−	40.5949i		−	1.34497i	0.740111	−	0.672484i	$-0.234773\pi$
$912$	4.47258	−	2.76400i	0.148102	−	0.0915253i
$913$	−16.3156			−0.539968
$914$	8.61234	−	5.05867i	0.284871	−	0.167326i
$915$	−1.78408	−	26.2447i	−0.0589798	−	0.867623i
$916$	−23.1779	+	41.5703i	−0.765818	+	1.37352i
$917$	3.30906	+	3.83317i	0.109275	+	0.126582i
$918$	1.89488	+	3.22601i	0.0625403	+	0.106474i
$919$			28.8509i			0.951704i	0.879525	+	0.475852i	$0.157860\pi$
$919$			28.8509i			0.951704i	−0.879525	+	0.475852i	$0.842140\pi$
$920$	3.78028	+	41.7354i	0.124632	+	1.37598i
$921$	18.2227			0.600459
$922$	20.2300	+	34.4415i	0.666241	+	1.13427i
$923$	24.0322			0.791030
$924$	2.41216	+	11.6881i	0.0793541	+	0.384511i
$925$	−11.4091	+	1.55836i	−0.375130	+	0.0512385i
$926$	−21.7377	−	37.0083i	−0.714346	−	1.21617i
$927$		−	2.78168i		−	0.0913625i
$928$	−32.2319	−	17.0339i	−1.05806	−	0.559165i
$929$		−	9.41194i		−	0.308796i	−0.988009	−	0.154398i	$-0.950656\pi$
$929$		−	9.41194i		−	0.308796i	0.988009	−	0.154398i	$-0.0493438\pi$
$930$	−17.4380	+	11.9034i	−0.571815	+	0.390326i
$931$	−9.10246	−	1.34315i	−0.298321	−	0.0440199i
$932$	6.23403	+	3.47584i	0.204203	+	0.113855i
$933$	13.5269			0.442851
$934$	24.7953	+	42.2138i	0.811327	+	1.38128i
$935$	−0.904882	−	13.3113i	−0.0295928	−	0.435325i
$936$	−0.386895	−	17.2256i	−0.0126461	−	0.563036i
$937$	33.2172			1.08516			0.542580	−	0.840004i	$-0.317448\pi$
$937$	33.2172			1.08516			0.542580	+	0.840004i	$0.317448\pi$
$938$	−17.1924	+	50.5947i	−0.561352	+	1.65198i
$939$	16.0061			0.522339
$940$	−1.14445	+	2.42623i	−0.0373280	+	0.0791348i
$941$	21.5599			0.702832			0.351416	−	0.936219i	$-0.385700\pi$
$941$	21.5599			0.702832			0.351416	+	0.936219i	$0.385700\pi$
$942$	17.1354	−	10.0649i	0.558303	−	0.327933i
$943$			36.4547i			1.18713i
$944$	−2.88273	+	1.78150i	−0.0938250	+	0.0579827i
$945$	−4.16075	−	4.20573i	−0.135349	−	0.136812i
$946$	3.49051	−	2.05023i	0.113486	−	0.0666589i
$947$			1.89362i			0.0615345i	0.999527	+	0.0307673i	$0.00979507\pi$
$947$			1.89362i			0.0615345i	−0.999527	+	0.0307673i	$0.990205\pi$
$948$	−1.17886	−	0.657283i	−0.0382876	−	0.0213476i
$949$			50.8370i			1.65024i
$950$	7.30343	−	5.74861i	0.236954	−	0.186510i
$951$	−34.8304			−1.12945
$952$	−14.6916	+	13.2701i	−0.476156	+	0.430085i
$953$			25.7345i			0.833624i	0.908993	+	0.416812i	$0.136853\pi$
$953$			25.7345i			0.833624i	−0.908993	+	0.416812i	$0.863147\pi$
$954$	7.50614	+	12.7791i	0.243020	+	0.413740i
$955$	−2.90073	+	0.197188i	−0.0938654	+	0.00638084i
$956$	−44.2578	−	24.6763i	−1.43140	−	0.798089i
$957$		−	14.5351i		−	0.469852i
$958$	−2.93697	−	5.00016i	−0.0948891	−	0.161548i
$959$	−37.9485	−	43.9591i	−1.22542	−	1.41951i
$960$	2.01333	+	17.7749i	0.0649800	+	0.573682i
$961$	13.5775			0.437983
$962$	−17.1075	+	10.0485i	−0.551570	+	0.323978i
$963$		−	10.4887i		−	0.337995i
$964$	28.0612	+	15.6458i	0.903790	+	0.503916i
$965$	−22.8170	+	1.55107i	−0.734506	+	0.0499307i
$966$	23.4738	+	7.97655i	0.755259	+	0.256641i
$967$	28.1142			0.904091			0.452046	−	0.891995i	$-0.350694\pi$
$967$	28.1142			0.904091			0.452046	+	0.891995i	$0.350694\pi$
$968$	−16.7208	+	0.375559i	−0.537428	+	0.0120709i
$969$			3.47738i			0.111709i
$970$	30.4165	−	20.7626i	0.976615	−	0.666646i
$971$		−	19.6014i		−	0.629039i	−0.949251	−	0.314520i	$-0.898157\pi$
$971$		−	19.6014i		−	0.629039i	0.949251	−	0.314520i	$-0.101843\pi$
$972$	0.973958	−	1.74683i	0.0312397	−	0.0560295i
$973$	1.36950	+	1.58641i	0.0439040	+	0.0508579i
$974$	28.9017	+	49.2048i	0.926069	+	1.57662i
$975$	−4.12200	−	30.1783i	−0.132010	−	0.966478i
$976$	24.7376	+	40.0293i	0.791832	+	1.28131i
$977$			45.0903i			1.44257i	0.692641	+	0.721283i	$0.256447\pi$
$977$			45.0903i			1.44257i	−0.692641	+	0.721283i	$0.743553\pi$
$978$	21.4377	−	12.5920i	0.685502	−	0.402647i
$979$			12.7717i			0.408186i
$980$	17.3454	−	26.0603i	0.554078	−	0.832465i
$981$		−	12.0853i		−	0.385855i
$982$	9.55311	+	16.2641i	0.304852	+	0.519008i
$983$		−	44.6188i		−	1.42312i	−0.702625	−	0.711560i	$-0.747989\pi$
$983$		−	44.6188i		−	1.42312i	0.702625	−	0.711560i	$-0.252011\pi$
$984$	0.349430	+	15.5575i	0.0111394	+	0.495955i
$985$	0.671261	+	9.87460i	0.0213882	+	0.314631i
$986$	20.7903	−	12.2117i	0.662099	−	0.388900i
$987$	1.03707	+	1.20133i	0.0330104	+	0.0382389i
$988$	7.79860	−	13.9871i	0.248107	−	0.444988i
$989$		−	8.40935i		−	0.267402i
$990$	−5.89063	+	4.02100i	−0.187217	+	0.127796i
$991$		−	30.3906i		−	0.965390i	−0.875788	−	0.482695i	$-0.839658\pi$
$991$		−	30.3906i		−	0.965390i	0.875788	−	0.482695i	$-0.160342\pi$
$992$	17.6472	−	33.3924i	0.560300	−	1.06021i
$993$	−8.65367			−0.274616
$994$	−4.74922	+	13.9763i	−0.150636	+	0.443300i
$995$	1.50772	+	22.1793i	0.0477978	+	0.703131i
$996$	−7.04566	+	12.6366i	−0.223250	+	0.400407i
$997$			5.15017i			0.163107i	0.996669	+	0.0815537i	$0.0259882\pi$
$997$			5.15017i			0.163107i	−0.996669	+	0.0815537i	$0.974012\pi$
$998$	15.3162	+	26.0758i	0.484827	+	0.825414i
$999$	−2.30302			−0.0728642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.w.a.139.17	✓	48
4.3	odd	2		3360.2.w.b.559.23		48
5.4	even	2		840.2.w.b.139.32	yes	48
7.6	odd	2		840.2.w.b.139.17	yes	48
8.3	odd	2	inner	840.2.w.a.139.31	yes	48
8.5	even	2		3360.2.w.b.559.26		48
20.19	odd	2		3360.2.w.a.559.24		48
28.27	even	2		3360.2.w.a.559.26		48
35.34	odd	2	inner	840.2.w.a.139.32	yes	48
40.19	odd	2		840.2.w.b.139.18	yes	48
40.29	even	2		3360.2.w.a.559.25		48
56.13	odd	2		3360.2.w.a.559.23		48
56.27	even	2		840.2.w.b.139.31	yes	48
140.139	even	2		3360.2.w.b.559.25		48
280.69	odd	2		3360.2.w.b.559.24		48
280.139	even	2	inner	840.2.w.a.139.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.w.a.139.17	✓	48	1.1	even	1	trivial
840.2.w.a.139.18	yes	48	280.139	even	2	inner
840.2.w.a.139.31	yes	48	8.3	odd	2	inner
840.2.w.a.139.32	yes	48	35.34	odd	2	inner
840.2.w.b.139.17	yes	48	7.6	odd	2
840.2.w.b.139.18	yes	48	40.19	odd	2
840.2.w.b.139.31	yes	48	56.27	even	2
840.2.w.b.139.32	yes	48	5.4	even	2
3360.2.w.a.559.23		48	56.13	odd	2
3360.2.w.a.559.24		48	20.19	odd	2
3360.2.w.a.559.25		48	40.29	even	2
3360.2.w.a.559.26		48	28.27	even	2
3360.2.w.b.559.23		48	4.3	odd	2
3360.2.w.b.559.24		48	280.69	odd	2
3360.2.w.b.559.25		48	140.139	even	2
3360.2.w.b.559.26		48	8.5	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+(-0.716255 - 1.21942i) q^{2} -1.00000 q^{3} +(-0.973958 + 1.74683i) q^{4} +(-0.151655 - 2.23092i) q^{5} +(0.716255 + 1.21942i) q^{6} +(-2.00273 + 1.72889i) q^{7} +(2.82771 - 0.0635119i) q^{8} +1.00000 q^{9} +(-2.61180 + 1.78284i) q^{10} +2.25539 q^{11} +(0.973958 - 1.74683i) q^{12} -6.09170i q^{13} +(3.54271 + 1.20383i) q^{14} +(0.151655 + 2.23092i) q^{15} +(-2.10281 - 3.40267i) q^{16} +2.64554 q^{17} +(-0.716255 - 1.21942i) q^{18} -1.31443i q^{19} +(4.04474 + 1.90791i) q^{20} +(2.00273 - 1.72889i) q^{21} +(-1.61544 - 2.75027i) q^{22} -6.62596 q^{23} +(-2.82771 + 0.0635119i) q^{24} +(-4.95400 + 0.676659i) q^{25} +(-7.42832 + 4.36321i) q^{26} -1.00000 q^{27} +(-1.06951 - 5.18229i) q^{28} +6.44459i q^{29} +(2.61180 - 1.78284i) q^{30} -6.67664 q^{31} +(-2.64313 + 5.00139i) q^{32} -2.25539 q^{33} +(-1.89488 - 3.22601i) q^{34} +(4.16075 + 4.20573i) q^{35} +(-0.973958 + 1.74683i) q^{36} +2.30302 q^{37} +(-1.60284 + 0.941468i) q^{38} +6.09170i q^{39} +(-0.570526 - 6.29877i) q^{40} -5.50180i q^{41} +(-3.54271 - 1.20383i) q^{42} +1.26915i q^{43} +(-2.19666 + 3.93978i) q^{44} +(-0.151655 - 2.23092i) q^{45} +(4.74588 + 8.07981i) q^{46} +0.599848i q^{47} +(2.10281 + 3.40267i) q^{48} +(1.02185 - 6.92501i) q^{49} +(4.37346 + 5.55634i) q^{50} -2.64554 q^{51} +(10.6411 + 5.93306i) q^{52} -10.4797 q^{53} +(0.716255 + 1.21942i) q^{54} +(-0.342041 - 5.03160i) q^{55} +(-5.55334 + 5.01602i) q^{56} +1.31443i q^{57} +(7.85864 - 4.61597i) q^{58} -0.847197i q^{59} +(-4.04474 - 1.90791i) q^{60} -11.7641 q^{61} +(4.78217 + 8.14161i) q^{62} +(-2.00273 + 1.72889i) q^{63} +(7.99193 - 0.359187i) q^{64} +(-13.5901 + 0.923835i) q^{65} +(1.61544 + 2.75027i) q^{66} +14.2814i q^{67} +(-2.57664 + 4.62129i) q^{68} +6.62596 q^{69} +(2.14839 - 8.08606i) q^{70} +3.94508i q^{71} +(2.82771 - 0.0635119i) q^{72} -8.34529 q^{73} +(-1.64955 - 2.80834i) q^{74} +(4.95400 - 0.676659i) q^{75} +(2.29609 + 1.28020i) q^{76} +(-4.51694 + 3.89934i) q^{77} +(7.42832 - 4.36321i) q^{78} -0.674858i q^{79} +(-7.27219 + 5.20723i) q^{80} +1.00000 q^{81} +(-6.70899 + 3.94069i) q^{82} -7.23405 q^{83} +(1.06951 + 5.18229i) q^{84} +(-0.401208 - 5.90198i) q^{85} +(1.54763 - 0.909036i) q^{86} -6.44459i q^{87} +(6.37761 - 0.143244i) q^{88} +5.66275i q^{89} +(-2.61180 + 1.78284i) q^{90} +(10.5319 + 12.2000i) q^{91} +(6.45341 - 11.5744i) q^{92} +6.67664 q^{93} +(0.731466 - 0.429644i) q^{94} +(-2.93239 + 0.199340i) q^{95} +(2.64313 - 5.00139i) q^{96} -11.6458 q^{97} +(-9.17639 + 3.71402i) q^{98} +2.25539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{3} + 48 q^{9} - 8 q^{10} - 2 q^{14} + 8 q^{16} - 4 q^{20} - 48 q^{27} - 14 q^{28} + 8 q^{30} + 16 q^{35} + 12 q^{38} - 8 q^{40} + 2 q^{42} + 4 q^{44} - 8 q^{46} - 8 q^{48} - 12 q^{50} + 36 q^{52}+ \cdots - 40 q^{98}+O(q^{100}) \) 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 + 16 * 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 - 54 * 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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