LMFDB - Embedded newform 280.2.n.b.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(139,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("280.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.n (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.9
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918230 - 1.07557i) q^{2} -1.19038 q^{3} +(-0.313707 + 1.97524i) q^{4} +(2.22369 - 0.234978i) q^{5} +(1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 - 1.47631i) q^{8} -1.58299 q^{9} +O(q^{10})$	\(q+(-0.918230 - 1.07557i) q^{2} -1.19038 q^{3} +(-0.313707 + 1.97524i) q^{4} +(2.22369 - 0.234978i) q^{5} +(1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 - 1.47631i) q^{8} -1.58299 q^{9} +(-2.29459 - 2.17597i) q^{10} -3.65078 q^{11} +(0.373431 - 2.35130i) q^{12} +5.56044i q^{13} +(3.65023 + 0.822064i) q^{14} +(-2.64704 + 0.279713i) q^{15} +(-3.80318 - 1.23930i) q^{16} +0.808468 q^{17} +(1.45355 + 1.70262i) q^{18} +4.54845i q^{19} +(-0.233448 + 4.46604i) q^{20} +(2.52120 - 1.88750i) q^{21} +(3.35225 + 3.92667i) q^{22} +1.75488 q^{23} +(-2.87188 + 1.75738i) q^{24} +(4.88957 - 1.04503i) q^{25} +(5.98065 - 5.10576i) q^{26} +5.45551 q^{27} +(-2.46757 - 4.68093i) q^{28} +8.36272i q^{29} +(2.73144 + 2.59024i) q^{30} -4.73282 q^{31} +(2.15924 + 5.22855i) q^{32} +4.34582 q^{33} +(-0.742360 - 0.869565i) q^{34} +(-4.33712 + 4.02360i) q^{35} +(0.496595 - 3.12679i) q^{36} -6.15399 q^{37} +(4.89218 - 4.17652i) q^{38} -6.61905i q^{39} +(5.01790 - 3.84976i) q^{40} -7.65085i q^{41} +(-4.34517 - 0.978571i) q^{42} +2.66483i q^{43} +(1.14527 - 7.21117i) q^{44} +(-3.52008 + 0.371968i) q^{45} +(-1.61138 - 1.88750i) q^{46} +4.79391i q^{47} +(4.52723 + 1.47524i) q^{48} +(1.97161 - 6.71660i) q^{49} +(-5.61376 - 4.29950i) q^{50} -0.962386 q^{51} +(-10.9832 - 1.74435i) q^{52} -2.98963 q^{53} +(-5.00941 - 5.86779i) q^{54} +(-8.11818 + 0.857851i) q^{55} +(-2.76888 + 6.95222i) q^{56} -5.41439i q^{57} +(8.99470 - 7.67890i) q^{58} +8.92626i q^{59} +(0.277892 - 5.31629i) q^{60} +4.08673 q^{61} +(4.34582 + 5.09049i) q^{62} +(3.35273 - 2.51002i) q^{63} +(3.64099 - 7.12342i) q^{64} +(1.30658 + 12.3647i) q^{65} +(-3.99046 - 4.67424i) q^{66} -11.7723i q^{67} +(-0.253622 + 1.59692i) q^{68} -2.08897 q^{69} +(8.31015 + 0.970289i) q^{70} -8.17275i q^{71} +(-3.81908 + 2.33699i) q^{72} -15.1783 q^{73} +(5.65078 + 6.61905i) q^{74} +(-5.82046 + 1.24399i) q^{75} +(-8.98430 - 1.42688i) q^{76} +(7.73224 - 5.78875i) q^{77} +(-7.11926 + 6.07781i) q^{78} -2.49307i q^{79} +(-8.74828 - 1.86214i) q^{80} -1.74517 q^{81} +(-8.22903 + 7.02524i) q^{82} +5.75885 q^{83} +(2.93735 + 5.57210i) q^{84} +(1.79778 - 0.189972i) q^{85} +(2.86621 - 2.44692i) q^{86} -9.95483i q^{87} +(-8.80775 + 5.38969i) q^{88} +4.95764i q^{89} +(3.63232 + 3.44454i) q^{90} +(-8.81676 - 11.7769i) q^{91} +(-0.550517 + 3.46631i) q^{92} +5.63387 q^{93} +(5.15619 - 4.40191i) q^{94} +(1.06878 + 10.1143i) q^{95} +(-2.57032 - 6.22397i) q^{96} +11.7195 q^{97} +(-9.03458 + 4.04678i) q^{98} +5.77914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 12 * q^4 + 40 * q^9	$ 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) $ 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.918230	−	1.07557i	−0.649287	−	0.760544i
$2$	−0.918230	−	1.07557i	−0.649287	−	0.760544i
$3$	−1.19038			−0.687268			−0.343634	−	0.939104i	$-0.611658\pi$
$3$	−1.19038			−0.687268			−0.343634	+	0.939104i	$0.611658\pi$
$4$	−0.313707	+	1.97524i	−0.156854	+	0.987622i
$5$	2.22369	−	0.234978i	0.994463	−	0.105085i
$5$	2.22369	−	0.234978i	0.994463	−	0.105085i
$6$	1.09304	+	1.28034i	0.446234	+	0.522697i
$7$	−2.11797	+	1.58562i	−0.800518	+	0.599309i
$7$	−2.11797	+	1.58562i	−0.800518	+	0.599309i
$8$	2.41257	−	1.47631i	0.852973	−	0.521956i
$9$	−1.58299			−0.527663
$10$	−2.29459	−	2.17597i	−0.725614	−	0.688102i
$11$	−3.65078			−1.10075			−0.550375	−	0.834917i	$-0.685515\pi$
$11$	−3.65078			−1.10075			−0.550375	+	0.834917i	$0.685515\pi$
$12$	0.373431	−	2.35130i	0.107800	−	0.678760i
$13$			5.56044i			1.54219i	0.636721	+	0.771095i	$0.280290\pi$
$13$			5.56044i			1.54219i	−0.636721	+	0.771095i	$0.719710\pi$
$14$	3.65023	+	0.822064i	0.975566	+	0.219706i
$15$	−2.64704	+	0.279713i	−0.683462	+	0.0722217i
$16$	−3.80318	−	1.23930i	−0.950794	−	0.309824i
$17$	0.808468			0.196082			0.0980411	−	0.995182i	$-0.468742\pi$
$17$	0.808468			0.196082			0.0980411	+	0.995182i	$0.468742\pi$
$18$	1.45355	+	1.70262i	0.342605	+	0.401311i
$19$			4.54845i			1.04349i	0.853103	+	0.521743i	$0.174718\pi$
$19$			4.54845i			1.04349i	−0.853103	+	0.521743i	$0.825282\pi$
$20$	−0.233448	+	4.46604i	−0.0522005	+	0.998637i
$21$	2.52120	−	1.88750i	0.550170	−	0.411885i
$22$	3.35225	+	3.92667i	0.714703	+	0.837169i
$23$	1.75488			0.365917			0.182959	−	0.983121i	$-0.441433\pi$
$23$	1.75488			0.365917			0.182959	+	0.983121i	$0.441433\pi$
$24$	−2.87188	+	1.75738i	−0.586220	+	0.358723i
$25$	4.88957	−	1.04503i	0.977914	−	0.209007i
$26$	5.98065	−	5.10576i	1.17290	−	1.00132i
$27$	5.45551			1.04991
$28$	−2.46757	−	4.68093i	−0.466326	−	0.884613i
$29$			8.36272i			1.55292i	0.630168	+	0.776459i	$0.282986\pi$
$29$			8.36272i			1.55292i	−0.630168	+	0.776459i	$0.717014\pi$
$30$	2.73144	+	2.59024i	0.498691	+	0.472910i
$31$	−4.73282			−0.850040			−0.425020	−	0.905184i	$-0.639733\pi$
$31$	−4.73282			−0.850040			−0.425020	+	0.905184i	$0.639733\pi$
$32$	2.15924	+	5.22855i	0.381703	+	0.924285i
$33$	4.34582			0.756510
$34$	−0.742360	−	0.869565i	−0.127314	−	0.149129i
$35$	−4.33712	+	4.02360i	−0.733107	+	0.680113i
$36$	0.496595	−	3.12679i	0.0827659	−	0.521132i
$37$	−6.15399			−1.01171			−0.505855	−	0.862619i	$-0.668823\pi$
$37$	−6.15399			−1.01171			−0.505855	+	0.862619i	$0.668823\pi$
$38$	4.89218	−	4.17652i	0.793617	−	0.677521i
$39$		−	6.61905i		−	1.05990i
$40$	5.01790	−	3.84976i	0.793400	−	0.608701i
$41$		−	7.65085i		−	1.19486i	−0.801920	−	0.597431i	$-0.796188\pi$
$41$		−	7.65085i		−	1.19486i	0.801920	−	0.597431i	$-0.203812\pi$
$42$	−4.34517	−	0.978571i	−0.670475	−	0.150997i
$43$			2.66483i			0.406382i	0.979139	+	0.203191i	$0.0651312\pi$
$43$			2.66483i			0.406382i	−0.979139	+	0.203191i	$0.934869\pi$
$44$	1.14527	−	7.21117i	0.172657	−	1.08713i
$45$	−3.52008	+	0.371968i	−0.524742	+	0.0554497i
$46$	−1.61138	−	1.88750i	−0.237585	−	0.278296i
$47$			4.79391i			0.699263i	0.936887	+	0.349632i	$0.113693\pi$
$47$			4.79391i			0.699263i	−0.936887	+	0.349632i	$0.886307\pi$
$48$	4.52723	+	1.47524i	0.653450	+	0.212932i
$49$	1.97161	−	6.71660i	0.281658	−	0.959515i
$50$	−5.61376	−	4.29950i	−0.793906	−	0.608041i
$51$	−0.962386			−0.134761
$52$	−10.9832	−	1.74435i	−1.52310	−	0.241898i
$53$	−2.98963			−0.410658			−0.205329	−	0.978693i	$-0.565826\pi$
$53$	−2.98963			−0.410658			−0.205329	+	0.978693i	$0.565826\pi$
$54$	−5.00941	−	5.86779i	−0.681695	−	0.798505i
$55$	−8.11818	+	0.857851i	−1.09466	+	0.115673i
$56$	−2.76888	+	6.95222i	−0.370007	+	0.929029i
$57$		−	5.41439i		−	0.717154i
$58$	8.99470	−	7.67890i	1.18106	−	1.00829i
$59$			8.92626i			1.16210i	0.813868	+	0.581050i	$0.197358\pi$
$59$			8.92626i			1.16210i	−0.813868	+	0.581050i	$0.802642\pi$
$60$	0.277892	−	5.31629i	0.0358757	−	0.686331i
$61$	4.08673			0.523253			0.261626	−	0.965169i	$-0.415741\pi$
$61$	4.08673			0.523253			0.261626	+	0.965169i	$0.415741\pi$
$62$	4.34582	+	5.09049i	0.551919	+	0.646492i
$63$	3.35273	−	2.51002i	0.422404	−	0.316233i
$64$	3.64099	−	7.12342i	0.455124	−	0.890428i
$65$	1.30658	+	12.3647i	0.162061	+	1.53365i
$66$	−3.99046	−	4.67424i	−0.491192	−	0.575359i
$67$		−	11.7723i		−	1.43821i	−0.694901	−	0.719105i	$-0.744552\pi$
$67$		−	11.7723i		−	1.43821i	0.694901	−	0.719105i	$-0.255448\pi$
$68$	−0.253622	+	1.59692i	−0.0307562	+	0.193655i
$69$	−2.08897			−0.251483
$70$	8.31015	+	0.970289i	0.993253	+	0.115972i
$71$		−	8.17275i		−	0.969927i	−0.874534	−	0.484963i	$-0.838833\pi$
$71$		−	8.17275i		−	0.969927i	0.874534	−	0.484963i	$-0.161167\pi$
$72$	−3.81908	+	2.33699i	−0.450082	+	0.275417i
$73$	−15.1783			−1.77648			−0.888241	−	0.459378i	$-0.848072\pi$
$73$	−15.1783			−1.77648			−0.888241	+	0.459378i	$0.848072\pi$
$74$	5.65078	+	6.61905i	0.656889	+	0.769449i
$75$	−5.82046	+	1.24399i	−0.672089	+	0.143644i
$76$	−8.98430	−	1.42688i	−1.03057	−	0.163674i
$77$	7.73224	−	5.78875i	0.881170	−	0.659689i
$78$	−7.11926	+	6.07781i	−0.806098	+	0.688177i
$79$		−	2.49307i		−	0.280492i	−0.990117	−	0.140246i	$-0.955211\pi$
$79$		−	2.49307i		−	0.280492i	0.990117	−	0.140246i	$-0.0447893\pi$
$80$	−8.74828	−	1.86214i	−0.978088	−	0.208194i
$81$	−1.74517			−0.193908
$82$	−8.22903	+	7.02524i	−0.908745	+	0.775808i
$83$	5.75885			0.632116			0.316058	−	0.948740i	$-0.397641\pi$
$83$	5.75885			0.632116			0.316058	+	0.948740i	$0.397641\pi$
$84$	2.93735	+	5.57210i	0.320491	+	0.607966i
$85$	1.79778	−	0.189972i	0.194997	−	0.0206054i
$86$	2.86621	−	2.44692i	0.309071	−	0.263858i
$87$		−	9.95483i		−	1.06727i
$88$	−8.80775	+	5.38969i	−0.938910	+	0.574543i
$89$			4.95764i			0.525509i	0.964863	+	0.262755i	$0.0846310\pi$
$89$			4.95764i			0.525509i	−0.964863	+	0.262755i	$0.915369\pi$
$90$	3.63232	+	3.44454i	0.382880	+	0.363086i
$91$	−8.81676	−	11.7769i	−0.924247	−	1.23455i
$92$	−0.550517	+	3.46631i	−0.0573954	+	0.361388i
$93$	5.63387			0.584205
$94$	5.15619	−	4.40191i	0.531820	−	0.454022i
$95$	1.06878	+	10.1143i	0.109655	+	1.03771i
$96$	−2.57032	−	6.22397i	−0.262332	−	0.635231i
$97$	11.7195			1.18993			0.594967	−	0.803750i	$-0.297165\pi$
$97$	11.7195			1.18993			0.594967	+	0.803750i	$0.297165\pi$
$98$	−9.03458	+	4.04678i	−0.912630	+	0.408787i
$99$	5.77914			0.580826
$100$	0.530305	+	9.98593i	0.0530305	+	0.998593i
$101$	7.10724			0.707197			0.353598	−	0.935397i	$-0.384958\pi$
$101$	7.10724			0.707197			0.353598	+	0.935397i	$0.384958\pi$
$102$	0.883692	+	1.03511i	0.0874985	+	0.102492i
$103$			5.06789i			0.499354i	0.968329	+	0.249677i	$0.0803244\pi$
$103$			5.06789i			0.499354i	−0.968329	+	0.249677i	$0.919676\pi$
$104$	8.20896	+	13.4150i	0.804955	+	1.31544i
$105$	5.16283	−	4.78963i	0.503841	−	0.467420i
$106$	2.74517	+	3.21556i	0.266635	+	0.312323i
$107$		−	10.8670i		−	1.05056i	−0.850931	−	0.525278i	$-0.823961\pi$
$107$		−	10.8670i		−	1.05056i	0.850931	−	0.525278i	$-0.176039\pi$
$108$	−1.71143	+	10.7760i	−0.164683	+	1.03692i
$109$		−	7.15158i		−	0.684997i	−0.939518	−	0.342498i	$-0.888727\pi$
$109$		−	7.15158i		−	0.684997i	0.939518	−	0.342498i	$-0.111273\pi$
$110$	8.37704	+	7.94398i	0.798719	+	0.757429i
$111$	7.32560			0.695315
$112$	10.0201	−	3.40560i	0.946808	−	0.321799i
$113$			0.0847428i			0.00797193i	0.999992	+	0.00398597i	$0.00126878\pi$
$113$			0.0847428i			0.00797193i	−0.999992	+	0.00398597i	$0.998731\pi$
$114$	−5.82357	+	4.97166i	−0.545427	+	0.465638i
$115$	3.90230	−	0.412357i	0.363891	−	0.0384525i
$116$	−16.5184	−	2.62344i	−1.53370	−	0.243581i
$117$		−	8.80212i		−	0.813757i
$118$	9.60083	−	8.19636i	0.883828	−	0.754536i
$119$	−1.71231	+	1.28192i	−0.156967	+	0.117514i
$120$	−5.97322	+	4.58269i	−0.545278	+	0.418340i
$121$	2.32816			0.211651
$122$	−3.75256	−	4.39557i	−0.339741	−	0.397956i
$123$			9.10743i			0.821190i
$124$	1.48472	−	9.34847i	0.133332	−	0.839518i
$125$	10.6273	−	3.47277i	0.950536	−	0.310614i
$126$	−5.77828	−	1.30132i	−0.514771	−	0.115931i
$127$	5.93446			0.526598			0.263299	−	0.964714i	$-0.415189\pi$
$127$	5.93446			0.526598			0.263299	+	0.964714i	$0.415189\pi$
$128$	−11.0050	+	2.62479i	−0.972716	+	0.232001i
$129$		−	3.17216i		−	0.279293i
$130$	12.0994	−	12.7589i	1.06118	−	1.11903i
$131$			17.2792i			1.50969i	0.655905	+	0.754844i	$0.272287\pi$
$131$			17.2792i			1.50969i	−0.655905	+	0.754844i	$0.727713\pi$
$132$	−1.36331	+	8.58405i	−0.118661	+	0.747146i
$133$	−7.21212	−	9.63349i	−0.625370	−	0.835329i
$134$	−12.6619	+	10.8096i	−1.09382	+	0.933811i
$135$	12.1313	−	1.28192i	1.04410	−	0.110330i
$136$	1.95049	−	1.19355i	0.167253	−	0.102346i
$137$		−	6.59924i		−	0.563811i	−0.959442	−	0.281906i	$-0.909033\pi$
$137$		−	6.59924i		−	0.563811i	0.959442	−	0.281906i	$-0.0909665\pi$
$138$	1.91816	+	2.24684i	0.163285	+	0.191264i
$139$		−	6.37544i		−	0.540757i	−0.962754	−	0.270379i	$-0.912851\pi$
$139$		−	6.37544i		−	0.540757i	0.962754	−	0.270379i	$-0.0871489\pi$
$140$	−6.58701	−	9.82910i	−0.556704	−	0.830711i
$141$		−	5.70658i		−	0.480581i
$142$	−8.79037	+	7.50446i	−0.737672	+	0.629760i
$143$		−	20.2999i		−	1.69756i
$144$	6.02039	+	1.96179i	0.501699	+	0.163483i
$145$	1.96505	+	18.5961i	0.163189	+	1.54432i
$146$	13.9371	+	16.3253i	1.15345	+	1.35109i
$147$	−2.34697	+	7.99533i	−0.193575	+	0.659443i
$148$	1.93055	−	12.1556i	0.158690	−	0.999186i
$149$			17.0131i			1.39377i	0.717184	+	0.696883i	$0.245431\pi$
$149$			17.0131i			1.39377i	−0.717184	+	0.696883i	$0.754569\pi$
$150$	6.68252	+	5.11805i	0.545626	+	0.417887i
$151$			14.7918i			1.20374i	0.798594	+	0.601870i	$0.205577\pi$
$151$			14.7918i			1.20374i	−0.798594	+	0.601870i	$0.794423\pi$
$152$	6.71494	+	10.9735i	0.544653	+	0.890065i
$153$	−1.27980			−0.103465
$154$	−13.3262	−	3.00117i	−1.07385	−	0.241841i
$155$	−10.5243	+	1.11211i	−0.845333	+	0.0893267i
$156$	13.0742	+	2.07644i	1.04678	+	0.166248i
$157$			16.6742i			1.33075i	0.746510	+	0.665374i	$0.231728\pi$
$157$			16.6742i			1.33075i	−0.746510	+	0.665374i	$0.768272\pi$
$158$	−2.68147	+	2.28921i	−0.213326	+	0.182120i
$159$	3.55881			0.282232
$160$	6.03007	+	11.1193i	0.476719	+	0.879056i
$161$	−3.71678	+	2.78257i	−0.292923	+	0.219297i
$162$	1.60247	+	1.87706i	0.125902	+	0.147476i
$163$			10.8670i			0.851172i	0.904918	+	0.425586i	$0.139932\pi$
$163$			10.8670i			0.851172i	−0.904918	+	0.425586i	$0.860068\pi$
$164$	15.1123	+	2.40012i	1.18007	+	0.187418i
$165$	9.66374	−	1.02117i	0.752321	−	0.0794981i
$166$	−5.28795	−	6.19406i	−0.410425	−	0.480752i
$167$		−	5.06789i		−	0.392165i	−0.980587	−	0.196082i	$-0.937178\pi$
$167$		−	5.06789i		−	0.392165i	0.980587	−	0.196082i	$-0.0628220\pi$
$168$	3.29603	−	8.27579i	0.254294	−	0.638491i
$169$	−17.9185			−1.37835
$170$	−1.85510	−	1.75920i	−0.142280	−	0.134925i
$171$		−	7.20015i		−	0.550609i
$172$	−5.26368	−	0.835974i	−0.401352	−	0.0637424i
$173$		−	3.71164i		−	0.282191i	−0.989996	−	0.141095i	$-0.954938\pi$
$173$		−	3.71164i		−	0.282191i	0.989996	−	0.141095i	$-0.0450624\pi$
$174$	−10.7071	+	9.14083i	−0.811706	+	0.692964i
$175$	−8.69894	+	9.96636i	−0.657578	+	0.753386i
$176$	13.8845	+	4.52439i	1.04659	+	0.341039i
$177$		−	10.6257i		−	0.798674i
$178$	5.33230	−	4.55226i	0.399673	−	0.341206i
$179$	7.26949			0.543347			0.271673	−	0.962390i	$-0.412423\pi$
$179$	7.26949			0.543347			0.271673	+	0.962390i	$0.412423\pi$
$180$	0.369546	−	7.06970i	0.0275443	−	0.526944i
$181$	−18.2341			−1.35533			−0.677666	−	0.735370i	$-0.737008\pi$
$181$	−18.2341			−1.35533			−0.677666	+	0.735370i	$0.737008\pi$
$182$	−4.57104	+	20.2969i	−0.338828	+	1.50451i
$183$	−4.86477			−0.359614
$184$	4.23377	−	2.59075i	0.312117	−	0.190993i
$185$	−13.6845	+	1.44605i	−1.00611	+	0.106316i
$186$	−5.17318	−	6.05962i	−0.379316	−	0.444313i
$187$	−2.95153			−0.215838
$188$	−9.46913	−	1.50388i	−0.690608	−	0.109682i
$189$	−11.5546	+	8.65037i	−0.840475	+	0.629222i
$190$	9.89729	−	10.4368i	0.718025	−	0.757168i
$191$			2.49307i			0.180392i	0.995924	+	0.0901960i	$0.0287494\pi$
$191$			2.49307i			0.180392i	−0.995924	+	0.0901960i	$0.971251\pi$
$192$	−4.33417	+	8.47960i	−0.312792	+	0.611962i
$193$			14.0190i			1.00911i	0.863380	+	0.504554i	$0.168343\pi$
$193$			14.0190i			1.00911i	−0.863380	+	0.504554i	$0.831657\pi$
$194$	−10.7612	−	12.6051i	−0.772608	−	0.904997i
$195$	−1.55533	−	14.7187i	−0.111380	−	1.05403i
$196$	12.6484	+	6.00145i	0.903459	+	0.428675i
$197$	8.27025			0.589231			0.294615	−	0.955616i	$-0.404808\pi$
$197$	8.27025			0.589231			0.294615	+	0.955616i	$0.404808\pi$
$198$	−5.30658	−	6.21588i	−0.377122	−	0.441743i
$199$	27.1530			1.92483			0.962413	−	0.271592i	$-0.0875500\pi$
$199$	27.1530			1.92483			0.962413	+	0.271592i	$0.0875500\pi$
$200$	10.2536	−	9.73976i	0.725042	−	0.688705i
$201$			14.0135i			0.988435i
$202$	−6.52608	−	7.64434i	−0.459174	−	0.537854i
$203$	−13.2601	−	17.7120i	−0.930677	−	1.24314i
$204$	0.301907	−	1.90095i	0.0211377	−	0.133093i
$205$	−1.79778	−	17.0131i	−0.125562	−	1.18825i
$206$	5.45087	−	4.65349i	0.379780	−	0.324224i
$207$	−2.77795			−0.193081
$208$	6.89103	−	21.1473i	0.477807	−	1.46630i
$209$		−	16.6054i		−	1.14862i
$210$	−9.89225	−	1.15502i	−0.682630	−	0.0797036i
$211$	20.1183			1.38500			0.692501	−	0.721417i	$-0.256509\pi$
$211$	20.1183			1.38500			0.692501	+	0.721417i	$0.256509\pi$
$212$	0.937869	−	5.90526i	0.0644131	−	0.405575i
$213$			9.72869i			0.666599i
$214$	−11.6883	+	9.97844i	−0.798994	+	0.682112i
$215$	0.626175	+	5.92574i	0.0427048	+	0.404132i
$216$	13.1618	−	8.05405i	0.895547	−	0.548008i
$217$	10.0240	−	7.50446i	0.680472	−	0.509436i
$218$	−7.69203	+	6.56679i	−0.520970	+	0.444759i
$219$	18.0679			1.22092
$220$	0.852265	−	16.3045i	0.0574597	−	1.09925i
$221$			4.49544i			0.302396i
$222$	−6.72658	−	7.87920i	−0.451459	−	0.528817i
$223$			15.7322i			1.05350i	0.850019	+	0.526752i	$0.176590\pi$
$223$			15.7322i			1.05350i	−0.850019	+	0.526752i	$0.823410\pi$
$224$	−12.8637	−	7.65017i	−0.859492	−	0.511149i
$225$	−7.74014	+	1.65428i	−0.516009	+	0.110285i
$226$	0.0911469	−	0.0778134i	0.00606300	−	0.00517607i
$227$	17.5252			1.16319			0.581595	−	0.813478i	$-0.302429\pi$
$227$	17.5252			1.16319			0.581595	+	0.813478i	$0.302429\pi$
$228$	10.6947	+	1.69853i	0.708277	+	0.112488i
$229$	−16.5729			−1.09517			−0.547583	−	0.836751i	$-0.684452\pi$
$229$	−16.5729			−1.09517			−0.547583	+	0.836751i	$0.684452\pi$
$230$	−4.02673	−	3.81856i	−0.265515	−	0.251788i
$231$	−9.20432	+	6.89082i	−0.605600	+	0.453383i
$232$	12.3460	+	20.1757i	0.810555	+	1.32460i
$233$		−	14.1037i		−	0.923964i	−0.886889	−	0.461982i	$-0.847138\pi$
$233$		−	14.1037i		−	0.923964i	0.886889	−	0.461982i	$-0.152862\pi$
$234$	−9.46731	+	8.08238i	−0.618898	+	0.528361i
$235$	1.12646	+	10.6602i	0.0734823	+	0.695392i
$236$	−17.6315	−	2.80023i	−1.14772	−	0.182279i
$237$			2.96770i			0.192773i
$238$	2.95110	+	0.664613i	0.191291	+	0.0430804i
$239$		−	22.7217i		−	1.46975i	−0.678205	−	0.734873i	$-0.737242\pi$
$239$		−	22.7217i		−	1.46975i	0.678205	−	0.734873i	$-0.262758\pi$
$240$	10.4138	+	2.21666i	0.672208	+	0.143085i
$241$			15.0216i			0.967629i	0.875171	+	0.483814i	$0.160749\pi$
$241$			15.0216i			0.967629i	−0.875171	+	0.483814i	$0.839251\pi$
$242$	−2.13779	−	2.50410i	−0.137422	−	0.160970i
$243$	−14.2891			−0.916647
$244$	−1.28204	+	8.07229i	−0.0820740	+	0.516776i
$245$	2.80599	−	15.3989i	0.179268	−	0.983800i
$246$	9.79569	−	8.36272i	0.624551	−	0.533188i
$247$	−25.2914			−1.60925
$248$	−11.4183	+	6.98713i	−0.725061	+	0.443683i
$249$	−6.85524			−0.434433
$250$	−13.4935	−	8.24163i	−0.853406	−	0.521247i
$251$		−	15.4522i		−	0.975332i	−0.873030	−	0.487666i	$-0.837848\pi$
$251$		−	15.4522i		−	0.975332i	0.873030	−	0.487666i	$-0.162152\pi$
$252$	3.90613	+	7.40987i	0.246063	+	0.466778i
$253$	−6.40666			−0.402783
$254$	−5.44920	−	6.38293i	−0.341913	−	0.400501i
$255$	−2.14005	+	0.226139i	−0.134015	+	0.0141614i
$256$	12.9283	+	9.42652i	0.808018	+	0.589157i
$257$	19.9954			1.24728			0.623640	−	0.781712i	$-0.285653\pi$
$257$	19.9954			1.24728			0.623640	+	0.781712i	$0.285653\pi$
$258$	−3.41188	+	2.91277i	−0.212415	+	0.181341i
$259$	13.0340	−	9.75789i	0.809891	−	0.606326i
$260$	−24.8331	−	1.29807i	−1.54009	−	0.0805031i
$261$		−	13.2381i		−	0.819418i
$262$	18.5850	−	15.8662i	1.14818	−	0.980220i
$263$	3.10990			0.191764			0.0958822	−	0.995393i	$-0.469433\pi$
$263$	3.10990			0.191764			0.0958822	+	0.995393i	$0.469433\pi$
$264$	10.4846	−	6.41579i	0.645282	−	0.394865i
$265$	−6.64801	+	0.702498i	−0.408384	+	0.0431541i
$266$	−3.73912	+	16.6029i	−0.229260	+	1.01799i
$267$		−	5.90149i		−	0.361165i
$268$	23.2531	+	3.69304i	1.42041	+	0.225588i
$269$	−11.2181			−0.683980			−0.341990	−	0.939704i	$-0.611101\pi$
$269$	−11.2181			−0.683980			−0.341990	+	0.939704i	$0.611101\pi$
$270$	−12.5182	−	11.8710i	−0.761832	−	0.722448i
$271$	−6.60431			−0.401183			−0.200592	−	0.979675i	$-0.564286\pi$
$271$	−6.60431			−0.401183			−0.200592	+	0.979675i	$0.564286\pi$
$272$	−3.07475	−	1.00193i	−0.186434	−	0.0607510i
$273$	10.4953	+	14.0190i	0.635205	+	0.848466i
$274$	−7.09796	+	6.05962i	−0.428803	+	0.366075i
$275$	−17.8507	+	3.81519i	−1.07644	+	0.230064i
$276$	0.655326	−	4.12623i	0.0394460	−	0.248370i
$277$	−16.0704			−0.965577			−0.482789	−	0.875737i	$-0.660376\pi$
$277$	−16.0704			−0.965577			−0.482789	+	0.875737i	$0.660376\pi$
$278$	−6.85724	+	5.85412i	−0.411270	+	0.351107i
$279$	7.49201			0.448535
$280$	−4.52351	+	16.1102i	−0.270331	+	0.962767i
$281$	21.1540			1.26194			0.630972	−	0.775806i	$-0.282656\pi$
$281$	21.1540			1.26194			0.630972	+	0.775806i	$0.282656\pi$
$282$	−6.13784	+	5.23996i	−0.365503	+	0.312035i
$283$	24.7231			1.46964			0.734819	−	0.678263i	$-0.237267\pi$
$283$	24.7231			1.46964			0.734819	+	0.678263i	$0.237267\pi$
$284$	16.1432	+	2.56385i	0.957921	+	0.152136i
$285$	−1.27226	−	12.0399i	−0.0753623	−	0.713183i
$286$	−21.8340	+	18.6400i	−1.29107	+	1.10221i
$287$	12.1313	+	16.2043i	0.716091	+	0.956508i
$288$	−3.41806	−	8.27674i	−0.201411	−	0.487711i
$289$	−16.3464			−0.961552
$290$	18.1970	−	19.1890i	1.06857	−	1.12682i
$291$	−13.9507			−0.817803
$292$	4.76153	−	29.9808i	0.278647	−	1.75449i
$293$			11.4011i			0.666060i	0.942916	+	0.333030i	$0.108071\pi$
$293$			11.4011i			0.666060i	−0.942916	+	0.333030i	$0.891929\pi$
$294$	10.7546	−	4.81722i	0.627221	−	0.280946i
$295$	2.09747	+	19.8492i	0.122120	+	1.15567i
$296$	−14.8469	+	9.08522i	−0.862960	+	0.528067i
$297$	−19.9168			−1.15569
$298$	18.2988	−	15.6219i	1.06002	−	0.904954i
$299$			9.75789i			0.564314i
$300$	−0.631266	−	11.8871i	−0.0364462	−	0.686300i
$301$	−4.22540	−	5.64402i	−0.243548	−	0.325316i
$302$	15.9096	−	13.5823i	0.915496	−	0.781572i
$303$	−8.46033			−0.486034
$304$	5.63687	−	17.2986i	0.323297	−	0.992140i
$305$	9.08762	−	0.960292i	0.520355	−	0.0549861i
$306$	1.17515	+	1.37651i	0.0671787	+	0.0786900i
$307$	0.426554			0.0243447			0.0121723	−	0.999926i	$-0.496125\pi$
$307$	0.426554			0.0243447			0.0121723	+	0.999926i	$0.496125\pi$
$308$	9.00853	+	17.0890i	0.513309	+	0.973738i
$309$		−	6.03272i		−	0.343190i
$310$	10.8599	+	10.2985i	0.616800	+	0.584914i
$311$	−0.586913			−0.0332808			−0.0166404	−	0.999862i	$-0.505297\pi$
$311$	−0.586913			−0.0332808			−0.0166404	+	0.999862i	$0.505297\pi$
$312$	−9.77180	−	15.9689i	−0.553219	−	0.904063i
$313$	−6.45704			−0.364973			−0.182487	−	0.983208i	$-0.558415\pi$
$313$	−6.45704			−0.364973			−0.182487	+	0.983208i	$0.558415\pi$
$314$	17.9343	−	15.3108i	1.01209	−	0.864038i
$315$	6.86562	−	6.36932i	0.386834	−	0.358871i
$316$	4.92442	+	0.782093i	0.277020	+	0.0439962i
$317$	−10.3086			−0.578986			−0.289493	−	0.957180i	$-0.593487\pi$
$317$	−10.3086			−0.578986			−0.289493	+	0.957180i	$0.593487\pi$
$318$	−3.26780	−	3.82775i	−0.183249	−	0.214650i
$319$		−	30.5304i		−	1.70937i
$320$	6.42259	−	16.6958i	0.359033	−	0.933325i
$321$			12.9359i			0.722013i
$322$	6.40571	+	1.44262i	0.356976	+	0.0803942i
$323$			3.67728i			0.204609i
$324$	0.547473	−	3.44714i	0.0304151	−	0.191508i
$325$	5.81085	+	27.1882i	0.322328	+	1.50813i
$326$	11.6883	−	9.97844i	0.647354	−	0.552655i
$327$			8.51311i			0.470776i
$328$	−11.2951	−	18.4582i	−0.623665	−	1.01918i
$329$	−7.60132	−	10.1534i	−0.419074	−	0.559773i
$330$	−9.97188	−	9.45637i	−0.548934	−	0.520556i
$331$	8.02828			0.441274			0.220637	−	0.975356i	$-0.429186\pi$
$331$	8.02828			0.441274			0.220637	+	0.975356i	$0.429186\pi$
$332$	−1.80659	+	11.3751i	−0.0991497	+	0.624292i
$333$	9.74170			0.533842
$334$	−5.45087	+	4.65349i	−0.298259	+	0.254627i
$335$	−2.76622	−	26.1778i	−0.151135	−	1.43025i
$336$	−11.9277	+	4.05397i	−0.650710	+	0.221162i
$337$			33.3339i			1.81582i	0.419170	+	0.907908i	$0.362321\pi$
$337$			33.3339i			1.81582i	−0.419170	+	0.907908i	$0.637679\pi$
$338$	16.4533	+	19.2726i	0.894942	+	1.04829i
$339$		−	0.100876i		−	0.00547885i
$340$	−0.188735	+	3.61065i	−0.0102356	+	0.195815i
$341$	17.2785			0.935681
$342$	−7.74427	+	6.61139i	−0.418762	+	0.357503i
$343$	6.47418	+	17.3518i	0.349573	+	0.936909i
$344$	3.93412	+	6.42908i	0.212113	+	0.346633i
$345$	−4.64523	+	0.490863i	−0.250091	+	0.0264272i
$346$	−3.99213	+	3.40814i	−0.214618	+	0.183223i
$347$			16.7685i			0.900182i	0.892983	+	0.450091i	$0.148608\pi$
$347$			16.7685i			0.900182i	−0.892983	+	0.450091i	$0.851392\pi$
$348$	19.6632	+	3.12290i	1.05406	+	0.167405i
$349$	0.234376			0.0125458			0.00627292	−	0.999980i	$-0.498003\pi$
$349$	0.234376			0.0125458			0.00627292	+	0.999980i	$0.498003\pi$
$350$	18.7072	+	0.204920i	0.999940	+	0.0109534i
$351$			30.3350i			1.61916i
$352$	−7.88290	−	19.0882i	−0.420160	−	1.01741i
$353$	14.2235			0.757039			0.378519	−	0.925593i	$-0.376433\pi$
$353$	14.2235			0.757039			0.378519	+	0.925593i	$0.376433\pi$
$354$	−11.4287	+	9.75680i	−0.607426	+	0.518568i
$355$	−1.92041	−	18.1736i	−0.101925	−	0.964556i
$356$	−9.79256	−	1.55525i	−0.519004	−	0.0824280i
$357$	2.03831	−	1.52598i	0.107879	−	0.0807634i
$358$	−6.67506	−	7.81885i	−0.352788	−	0.413239i
$359$			14.2398i			0.751549i	0.926711	+	0.375774i	$0.122623\pi$
$359$			14.2398i			0.751549i	−0.926711	+	0.375774i	$0.877377\pi$
$360$	−7.94329	+	6.09413i	−0.418648	+	0.321189i
$361$	−1.68839			−0.0888626
$362$	16.7431	+	19.6121i	0.879999	+	1.03079i
$363$	−2.77140			−0.145461
$364$	26.0280	−	13.7208i	1.36424	−	0.719163i
$365$	−33.7517	+	3.56656i	−1.76665	+	0.186682i
$366$	4.46698	+	5.23241i	0.233493	+	0.273503i
$367$		−	5.09891i		−	0.266161i	−0.991105	−	0.133080i	$-0.957513\pi$
$367$		−	5.09891i		−	0.266161i	0.991105	−	0.133080i	$-0.0424868\pi$
$368$	−6.67411	−	2.17481i	−0.347912	−	0.113370i
$369$			12.1112i			0.630485i
$370$	14.1209	+	13.3909i	0.734110	+	0.696159i
$371$	6.33196	−	4.74043i	0.328739	−	0.246111i
$372$	−1.76738	+	11.1283i	−0.0916346	+	0.576973i
$373$	25.1282			1.30109			0.650545	−	0.759468i	$-0.274541\pi$
$373$	25.1282			1.30109			0.650545	+	0.759468i	$0.274541\pi$
$374$	2.71019	+	3.17459i	0.140140	+	0.164154i
$375$	−12.6506	+	4.13393i	−0.653273	+	0.213475i
$376$	7.07731	+	11.5656i	0.364984	+	0.596452i
$377$	−46.5004			−2.39489
$378$	19.9139	+	4.48478i	1.02426	+	0.230672i
$379$	−5.77914			−0.296855			−0.148427	−	0.988923i	$-0.547421\pi$
$379$	−5.77914			−0.296855			−0.148427	+	0.988923i	$0.547421\pi$
$380$	−20.3136	−	1.06183i	−1.04206	−	0.0544705i
$381$	−7.06428			−0.361914
$382$	2.68147	−	2.28921i	0.137196	−	0.117126i
$383$			24.8199i			1.26824i	0.773237	+	0.634118i	$0.218636\pi$
$383$			24.8199i			1.26824i	−0.773237	+	0.634118i	$0.781364\pi$
$384$	13.1002	−	3.12451i	0.668516	−	0.159447i
$385$	15.8339	−	14.6893i	0.806968	−	0.748635i
$386$	15.0784	−	12.8726i	0.767470	−	0.655200i
$387$		−	4.21839i		−	0.214433i
$388$	−3.67649	+	23.1488i	−0.186645	+	1.17520i
$389$		−	7.34694i		−	0.372505i	−0.982502	−	0.186252i	$-0.940366\pi$
$389$		−	7.34694i		−	0.372505i	0.982502	−	0.186252i	$-0.0596342\pi$
$390$	−14.4029	+	15.1880i	−0.729317	+	0.769075i
$391$	1.41876			0.0717499
$392$	−5.15917	−	19.1150i	−0.260577	−	0.965453i
$393$		−	20.5688i		−	1.03756i
$394$	−7.59399	−	8.89524i	−0.382580	−	0.448136i
$395$	−0.585816	−	5.54380i	−0.0294756	−	0.278939i
$396$	−1.81296	+	11.4152i	−0.0911045	+	0.573636i
$397$		−	10.0197i		−	0.502872i	−0.967874	−	0.251436i	$-0.919097\pi$
$397$		−	10.0197i		−	0.502872i	0.967874	−	0.251436i	$-0.0809029\pi$
$398$	−24.9327	−	29.2050i	−1.24976	−	1.46391i
$399$	8.58518	+	11.4675i	0.429796	+	0.574095i
$400$	−19.8910	−	2.08517i	−0.994550	−	0.104259i
$401$	11.7525			0.586893			0.293447	−	0.955975i	$-0.405198\pi$
$401$	11.7525			0.586893			0.293447	+	0.955975i	$0.405198\pi$
$402$	15.0725	−	12.8676i	0.751748	−	0.641778i
$403$		−	26.3166i		−	1.31092i
$404$	−2.22959	+	14.0385i	−0.110926	+	0.698443i
$405$	−3.88072	+	0.410077i	−0.192834	+	0.0203769i
$406$	−6.87469	+	30.5259i	−0.341185	+	1.51497i
$407$	22.4668			1.11364
$408$	−2.32182	+	1.42078i	−0.114947	+	0.0703393i
$409$			4.67758i			0.231292i	0.993291	+	0.115646i	$0.0368938\pi$
$409$			4.67758i			0.231292i	−0.993291	+	0.115646i	$0.963106\pi$
$410$	−16.6480	+	17.5556i	−0.822187	+	0.867008i
$411$			7.85562i			0.387489i
$412$	−10.0103	−	1.58983i	−0.493173	−	0.0783254i
$413$	−14.1537	−	18.9056i	−0.696457	−	0.930282i
$414$	2.55080	+	2.98789i	0.125365	+	0.146847i
$415$	12.8059	−	1.35320i	0.628616	−	0.0664261i
$416$	−29.0730	+	12.0063i	−1.42542	+	0.588659i
$417$			7.58921i			0.371645i
$418$	−17.8603	+	15.2475i	−0.873574	+	0.745782i
$419$			21.7400i			1.06207i	0.847351	+	0.531034i	$0.178196\pi$
$419$			21.7400i			1.06207i	−0.847351	+	0.531034i	$0.821804\pi$
$420$	7.84106	+	11.7004i	0.382605	+	0.570921i
$421$			9.76923i			0.476123i	0.971250	+	0.238062i	$0.0765120\pi$
$421$			9.76923i			0.476123i	−0.971250	+	0.238062i	$0.923488\pi$
$422$	−18.4732	−	21.6387i	−0.899263	−	1.05335i
$423$		−	7.58871i		−	0.368976i
$424$	−7.21270	+	4.41364i	−0.350280	+	0.214345i
$425$	3.95306	−	0.844877i	0.191752	−	0.0409826i
$426$	10.4639	−	8.93318i	0.506978	−	0.432814i
$427$	−8.65559	+	6.48001i	−0.418873	+	0.313590i
$428$	21.4651	+	3.40907i	1.03755	+	0.164783i
$429$			24.1647i			1.16668i
$430$	5.79858	−	6.11469i	0.279632	−	0.294876i
$431$			2.12901i			0.102551i	0.998685	+	0.0512753i	$0.0163286\pi$
$431$			2.12901i			0.102551i	−0.998685	+	0.0512753i	$0.983671\pi$
$432$	−20.7483	−	6.76099i	−0.998251	−	0.325288i
$433$	1.12265			0.0539513			0.0269756	−	0.999636i	$-0.491412\pi$
$433$	1.12265			0.0539513			0.0269756	+	0.999636i	$0.491412\pi$
$434$	−17.2759	−	3.89068i	−0.829270	−	0.186759i
$435$	−2.33917	−	22.1364i	−0.112154	−	1.06136i
$436$	14.1261	+	2.24350i	0.676518	+	0.107444i
$437$			7.98197i			0.381829i
$438$	−16.5905	−	19.4334i	−0.792726	−	0.928562i
$439$	17.9973			0.858964			0.429482	−	0.903075i	$-0.358696\pi$
$439$	17.9973			0.858964			0.429482	+	0.903075i	$0.358696\pi$
$440$	−18.3192	+	14.0546i	−0.873335	+	0.670027i
$441$	−3.12104	+	10.6323i	−0.148621	+	0.506301i
$442$	4.83516	−	4.12785i	0.229985	−	0.196342i
$443$			10.1199i			0.480810i	0.970673	+	0.240405i	$0.0772803\pi$
$443$			10.1199i			0.480810i	−0.970673	+	0.240405i	$0.922720\pi$
$444$	−2.29809	+	14.4698i	−0.109063	+	0.686708i
$445$	1.16494	+	11.0243i	0.0552233	+	0.522600i
$446$	16.9211	−	14.4457i	0.801235	−	0.684026i
$447$		−	20.2521i		−	0.957891i
$448$	3.58353	+	20.8604i	0.169306	+	0.985564i
$449$	0.750627			0.0354243			0.0177121	−	0.999843i	$-0.494362\pi$
$449$	0.750627			0.0354243			0.0177121	+	0.999843i	$0.494362\pi$
$450$	8.88653	+	6.80607i	0.418915	+	0.320841i
$451$			27.9315i			1.31524i
$452$	−0.167388	−	0.0265844i	−0.00787325	−	0.00125043i
$453$		−	17.6079i		−	0.827291i
$454$	−16.0922	−	18.8496i	−0.755244	−	0.884657i
$455$	−22.3730	−	24.1163i	−1.04886	−	1.13059i
$456$	−7.99334	−	13.0626i	−0.374323	−	0.611713i
$457$		−	20.4998i		−	0.958941i	−0.877558	−	0.479471i	$-0.840829\pi$
$457$		−	20.4998i		−	0.958941i	0.877558	−	0.479471i	$-0.159171\pi$
$458$	15.2177	+	17.8253i	0.711077	+	0.832922i
$459$	4.41060			0.205869
$460$	−0.409672	+	7.83735i	−0.0191011	+	0.365418i
$461$	14.9599			0.696752			0.348376	−	0.937355i	$-0.386733\pi$
$461$	14.9599			0.696752			0.348376	+	0.937355i	$0.386733\pi$
$462$	15.8633	+	3.57254i	0.738025	+	0.166210i
$463$	−23.1072			−1.07388			−0.536941	−	0.843619i	$-0.680420\pi$
$463$	−23.1072			−1.07388			−0.536941	+	0.843619i	$0.680420\pi$
$464$	10.3639	−	31.8049i	0.481131	−	1.47651i
$465$	12.5280	−	1.32383i	0.580970	−	0.0613913i
$466$	−15.1695	+	12.9504i	−0.702715	+	0.599918i
$467$	−22.3760			−1.03544			−0.517720	−	0.855550i	$-0.673219\pi$
$467$	−22.3760			−1.03544			−0.517720	+	0.855550i	$0.673219\pi$
$468$	17.3863	+	2.76129i	0.803684	+	0.127641i
$469$	18.6663	+	24.9333i	0.861932	+	1.15131i
$470$	10.4314	−	11.0001i	0.481165	−	0.507395i
$471$		−	19.8487i		−	0.914580i
$472$	13.1780	+	21.5352i	0.606565	+	0.991239i
$473$		−	9.72868i		−	0.447325i
$474$	3.19198	−	2.72503i	0.146612	−	0.125165i
$475$	4.75329	+	22.2400i	0.218096	+	1.02044i
$476$	−1.99495	−	3.78438i	−0.0914383	−	0.173457i
$477$	4.73256			0.216689
$478$	−24.4388	+	20.8638i	−1.11781	+	0.954287i
$479$	−32.6071			−1.48986			−0.744928	−	0.667145i	$-0.767516\pi$
$479$	−32.6071			−1.48986			−0.744928	+	0.667145i	$0.767516\pi$
$480$	−7.17808	−	13.2362i	−0.327633	−	0.604147i
$481$		−	34.2189i		−	1.56025i
$482$	16.1568	−	13.7933i	0.735924	−	0.628268i
$483$	4.42439	−	3.31232i	0.201317	−	0.150716i
$484$	−0.730361	+	4.59869i	−0.0331982	+	0.209031i
$485$	26.0605	−	2.75382i	1.18335	−	0.125045i
$486$	13.1207	+	15.3690i	0.595167	+	0.697150i
$487$	3.90400			0.176907			0.0884536	−	0.996080i	$-0.471808\pi$
$487$	3.90400			0.176907			0.0884536	+	0.996080i	$0.471808\pi$
$488$	9.85953	−	6.03330i	0.446320	−	0.273115i
$489$		−	12.9359i		−	0.584983i
$490$	−19.1392	+	11.1217i	−0.864619	+	0.502427i
$491$	−20.5527			−0.927532			−0.463766	−	0.885958i	$-0.653502\pi$
$491$	−20.5527			−0.927532			−0.463766	+	0.885958i	$0.653502\pi$
$492$	−17.9894	−	2.85707i	−0.811025	−	0.128806i
$493$			6.76099i			0.304500i
$494$	23.2233	+	27.2027i	1.04487	+	1.22391i
$495$	12.8510	−	1.35797i	0.577610	−	0.0610362i
$496$	17.9997	+	5.86536i	0.808213	+	0.263363i
$497$	12.9589	+	17.3096i	0.581285	+	0.776444i
$498$	6.29468	+	7.37329i	0.282072	+	0.330405i
$499$	−25.8654			−1.15789			−0.578947	−	0.815365i	$-0.696536\pi$
$499$	−25.8654			−1.15789			−0.578947	+	0.815365i	$0.696536\pi$
$500$	3.52571	+	22.0810i	0.157674	+	0.987491i
$501$			6.03272i			0.269522i
$502$	−16.6199	+	14.1886i	−0.741783	+	0.633270i
$503$		−	31.0150i		−	1.38289i	−0.722428	−	0.691446i	$-0.756974\pi$
$503$		−	31.0150i		−	1.38289i	0.722428	−	0.691446i	$-0.243026\pi$
$504$	4.38311	−	11.0053i	0.195239	−	0.490214i
$505$	15.8043	−	1.67004i	0.703281	−	0.0743160i
$506$	5.88279	+	6.89082i	0.261522	+	0.306334i
$507$	21.3299			0.947293
$508$	−1.86168	+	11.7220i	−0.0825988	+	0.520080i
$509$	14.2066			0.629695			0.314847	−	0.949142i	$-0.398047\pi$
$509$	14.2066			0.629695			0.314847	+	0.949142i	$0.398047\pi$
$510$	2.20828	+	2.09412i	0.0977844	+	0.0927293i
$511$	32.1471	−	24.0670i	1.42211	−	1.06466i
$512$	−1.73225	−	22.5610i	−0.0765556	−	0.997065i
$513$			24.8141i			1.09557i
$514$	−18.3604	−	21.5065i	−0.809842	−	0.948611i
$515$	1.19084	+	11.2694i	0.0524747	+	0.496589i
$516$	6.26579	+	0.995129i	0.275836	+	0.0438081i
$517$		−	17.5015i		−	0.769714i
$518$	−22.4635	−	5.05897i	−0.986989	−	0.222278i
$519$			4.41827i			0.193940i
$520$	21.4064	+	27.9017i	0.938732	+	1.22357i
$521$		−	37.9559i		−	1.66288i	−0.555617	−	0.831438i	$-0.687518\pi$
$521$		−	37.9559i		−	1.66288i	0.555617	−	0.831438i	$-0.312482\pi$
$522$	−14.2385	+	12.1556i	−0.623203	+	0.532037i
$523$	−20.8846			−0.913219			−0.456609	−	0.889667i	$-0.650936\pi$
$523$	−20.8846			−0.913219			−0.456609	+	0.889667i	$0.650936\pi$
$524$	−34.1305	−	5.42059i	−1.49100	−	0.236800i
$525$	10.3551	−	11.8638i	0.451932	−	0.517778i
$526$	−2.85560	−	3.34492i	−0.124510	−	0.145845i
$527$	−3.82633			−0.166678
$528$	−16.5279	−	5.38575i	−0.719285	−	0.234385i
$529$	−19.9204			−0.866105
$530$	6.85999	+	6.50536i	0.297979	+	0.282575i
$531$		−	14.1302i		−	0.613198i
$532$	21.2910	−	11.2236i	0.923081	−	0.486605i
$533$	42.5421			1.84270
$534$	−6.34747	+	5.41893i	−0.274682	+	0.234500i
$535$	−2.55351	−	24.1649i	−0.110398	−	1.04474i
$536$	−17.3795	−	28.4014i	−0.750682	−	1.22675i
$537$	−8.65347			−0.373425
$538$	10.3008	+	12.0659i	0.444099	+	0.520196i
$539$	−7.19790	+	24.5208i	−0.310036	+	1.05619i
$540$	−1.27358	+	24.3645i	−0.0548060	+	1.04848i
$541$			1.19268i			0.0512773i	0.999671	+	0.0256387i	$0.00816194\pi$
$541$			1.19268i			0.0512773i	−0.999671	+	0.0256387i	$0.991838\pi$
$542$	6.06428	+	7.10341i	0.260483	+	0.305118i
$543$	21.7056			0.931476
$544$	1.74568	+	4.22711i	0.0748452	+	0.181236i
$545$	−1.68046	−	15.9029i	−0.0719831	−	0.681204i
$546$	5.44128	−	24.1611i	0.232865	−	1.03400i
$547$			15.5500i			0.664872i	0.943126	+	0.332436i	$0.107871\pi$
$547$			15.5500i			0.664872i	−0.943126	+	0.332436i	$0.892129\pi$
$548$	13.0351	+	2.07023i	0.556833	+	0.0884358i
$549$	−6.46926			−0.276101
$550$	20.4946	+	15.6965i	0.873892	+	0.669301i
$551$	−38.0374			−1.62045
$552$	−5.03980	+	3.08398i	−0.214508	+	0.131263i
$553$	3.95306	+	5.28025i	0.168101	+	0.224539i
$554$	14.7563	+	17.2849i	0.626936	+	0.734364i
$555$	16.2898	−	1.72135i	0.691465	−	0.0730674i
$556$	12.5930	+	2.00002i	0.534064	+	0.0848197i
$557$	31.9739			1.35478			0.677390	−	0.735624i	$-0.263111\pi$
$557$	31.9739			1.35478			0.677390	+	0.735624i	$0.263111\pi$
$558$	−6.87939	−	8.05819i	−0.291228	−	0.341130i
$559$	−14.8176			−0.626718
$560$	21.4813	−	9.92749i	0.907749	−	0.419513i
$561$	3.51345			0.148338
$562$	−19.4243	−	22.7527i	−0.819363	−	0.959763i
$563$	6.48451			0.273290			0.136645	−	0.990620i	$-0.456368\pi$
$563$	6.48451			0.273290			0.136645	+	0.990620i	$0.456368\pi$
$564$	11.2719	+	1.79019i	0.474632	+	0.0753808i
$565$	0.0199127	+	0.188441i	0.000837733	+	0.00792779i
$566$	−22.7015	−	26.5915i	−0.954217	−	1.11772i
$567$	3.69622	−	2.76718i	0.155227	−	0.116211i
$568$	−12.0655	−	19.7173i	−0.506259	−	0.827321i
$569$	36.4610			1.52853			0.764263	−	0.644905i	$-0.223103\pi$
$569$	36.4610			1.52853			0.764263	+	0.644905i	$0.223103\pi$
$570$	−11.7816	+	12.4238i	−0.493475	+	0.520377i
$571$	24.9527			1.04424			0.522119	−	0.852872i	$-0.325142\pi$
$571$	24.9527			1.04424			0.522119	+	0.852872i	$0.325142\pi$
$572$	40.0973	+	6.36823i	1.67655	+	0.266269i
$573$		−	2.96770i		−	0.123978i
$574$	6.28949	−	27.9274i	0.262518	−	1.16567i
$575$	8.58060	−	1.83391i	0.357836	−	0.0764792i
$576$	−5.76366	+	11.2763i	−0.240152	+	0.469846i
$577$	−21.7435			−0.905192			−0.452596	−	0.891716i	$-0.649502\pi$
$577$	−21.7435			−0.905192			−0.452596	+	0.891716i	$0.649502\pi$
$578$	15.0097	+	17.5817i	0.624323	+	0.731302i
$579$		−	16.6879i		−	0.693526i
$580$	−37.3482	−	1.95226i	−1.55080	−	0.0810631i
$581$	−12.1971	+	9.13136i	−0.506020	+	0.378833i
$582$	12.8099	+	15.0049i	0.530988	+	0.621975i
$583$	10.9145			0.452032
$584$	−36.6186	+	22.4079i	−1.51529	+	0.927245i
$585$	−2.06830	−	19.5732i	−0.0855139	−	0.809251i
$586$	12.2627	−	10.4688i	0.506568	−	0.432464i
$587$	−24.7885			−1.02313			−0.511565	−	0.859245i	$-0.670934\pi$
$587$	−24.7885			−1.02313			−0.511565	+	0.859245i	$0.670934\pi$
$588$	−15.0565	−	7.14402i	−0.620918	−	0.294615i
$589$		−	21.5270i		−	0.887004i
$590$	19.4233	−	20.4821i	0.799644	−	0.843236i
$591$	−9.84476			−0.404959
$592$	23.4047	+	7.62661i	0.961927	+	0.313452i
$593$	41.5751			1.70728			0.853642	−	0.520860i	$-0.174389\pi$
$593$	41.5751			1.70728			0.853642	+	0.520860i	$0.174389\pi$
$594$	18.2882	+	21.4220i	0.750376	+	0.878955i
$595$	−3.50642	+	3.25295i	−0.143749	+	0.133358i
$596$	−33.6050	−	5.33713i	−1.37651	−	0.218617i
$597$	−32.3224			−1.32287
$598$	10.4953	−	8.95999i	0.429185	−	0.366401i
$599$		−	38.2863i		−	1.56434i	−0.623068	−	0.782168i	$-0.714114\pi$
$599$		−	38.2863i		−	1.56434i	0.623068	−	0.782168i	$-0.285886\pi$
$600$	−12.2057	+	11.5940i	−0.498297	+	0.473325i
$601$			22.8512i			0.932121i	0.884753	+	0.466060i	$0.154327\pi$
$601$			22.8512i			0.932121i	−0.884753	+	0.466060i	$0.845673\pi$
$602$	−2.19066	+	9.72724i	−0.0892845	+	0.396453i
$603$			18.6354i			0.758891i
$604$	−29.2174	−	4.64029i	−1.18884	−	0.188811i
$605$	5.17710	−	0.547067i	0.210479	−	0.0222414i
$606$	7.76853	+	9.09969i	0.315575	+	0.369650i
$607$		−	3.04718i		−	0.123681i	−0.998086	−	0.0618407i	$-0.980303\pi$
$607$		−	3.04718i		−	0.123681i	0.998086	−	0.0618407i	$-0.0196971\pi$
$608$	−23.7818	+	9.82119i	−0.964478	+	0.398302i
$609$	15.7846	+	21.0841i	0.639624	+	0.854369i
$610$	−9.37739	−	8.89261i	−0.379679	−	0.360051i
$611$	−26.6562			−1.07840
$612$	0.401481	−	2.52791i	0.0162289	−	0.102185i
$613$	−36.3023			−1.46624			−0.733118	−	0.680101i	$-0.761936\pi$
$613$	−36.3023			−1.46624			−0.733118	+	0.680101i	$0.761936\pi$
$614$	−0.391674	−	0.458789i	−0.0158067	−	0.0185152i
$615$	2.14005	+	20.2521i	0.0862950	+	0.816643i
$616$	10.1086	−	25.3810i	0.407286	−	1.02263i
$617$			15.0501i			0.605894i	0.953007	+	0.302947i	$0.0979705\pi$
$617$			15.0501i			0.605894i	−0.953007	+	0.302947i	$0.902029\pi$
$618$	−6.48862	+	5.53943i	−0.261011	+	0.222828i
$619$			1.73303i			0.0696563i	0.999393	+	0.0348281i	$0.0110884\pi$
$619$			1.73303i			0.0696563i	−0.999393	+	0.0348281i	$0.988912\pi$
$620$	1.10487	−	21.1370i	0.0443725	−	0.848881i
$621$	9.57375			0.384181
$622$	0.538921	+	0.631267i	0.0216088	+	0.0253115i
$623$	−7.86095	−	10.5002i	−0.314942	−	0.420680i
$624$	−8.20296	+	25.1734i	−0.328381	+	1.00774i
$625$	22.8158	−	10.2195i	0.912632	−	0.408782i
$626$	5.92904	+	6.94500i	0.236972	+	0.277578i
$627$			19.7667i			0.789407i
$628$	−32.9357	−	5.23082i	−1.31428	−	0.208733i
$629$	−4.97530			−0.198378
$630$	−13.1549	−	1.53596i	−0.524103	−	0.0611941i
$631$		−	19.5984i		−	0.780202i	−0.920772	−	0.390101i	$-0.872440\pi$
$631$		−	19.5984i		−	0.780202i	0.920772	−	0.390101i	$-0.127560\pi$
$632$	−3.68055	−	6.01470i	−0.146404	−	0.239252i
$633$	−23.9485			−0.951866
$634$	9.46563	+	11.0876i	0.375928	+	0.440344i
$635$	13.1964	−	1.39447i	0.523682	−	0.0553377i
$636$	−1.11642	+	7.02951i	−0.0442690	+	0.278738i
$637$	37.3473	+	10.9630i	1.47975	+	0.434371i
$638$	−32.8376	+	28.0339i	−1.30005	+	1.10987i
$639$			12.9374i			0.511795i
$640$	−23.8550	+	8.42266i	−0.942950	+	0.332935i
$641$	5.76448			0.227683			0.113842	−	0.993499i	$-0.463684\pi$
$641$	5.76448			0.227683			0.113842	+	0.993499i	$0.463684\pi$
$642$	13.9135	−	11.8782i	0.549123	−	0.468794i
$643$	−12.8313			−0.506017			−0.253009	−	0.967464i	$-0.581420\pi$
$643$	−12.8313			−0.506017			−0.253009	+	0.967464i	$0.581420\pi$
$644$	−4.33028	−	8.21446i	−0.170637	−	0.323695i
$645$	−0.745388	−	7.05389i	−0.0293496	−	0.277747i
$646$	3.95517	−	3.37658i	0.155614	−	0.132850i
$647$		−	1.42452i		−	0.0560037i	−0.999608	−	0.0280018i	$-0.991086\pi$
$647$		−	1.42452i		−	0.0560037i	0.999608	−	0.0280018i	$-0.00891443\pi$
$648$	−4.21035	+	2.57642i	−0.165398	+	0.101211i
$649$		−	32.5878i		−	1.27918i
$650$	23.9071	−	31.2150i	0.937714	−	1.22435i
$651$	−11.9324	+	8.93318i	−0.467666	+	0.350119i
$652$	−21.4651	−	3.40907i	−0.840636	−	0.133509i
$653$	−29.1628			−1.14123			−0.570615	−	0.821218i	$-0.693295\pi$
$653$	−29.1628			−1.14123			−0.570615	+	0.821218i	$0.693295\pi$
$654$	9.15646	−	7.81699i	0.358046	−	0.305669i
$655$	4.06022	+	38.4234i	0.158646	+	1.50133i
$656$	−9.48166	+	29.0975i	−0.370197	+	1.13607i
$657$	24.0270			0.937384
$658$	−3.94090	+	17.4989i	−0.153632	+	0.682178i
$659$	−7.06968			−0.275396			−0.137698	−	0.990474i	$-0.543970\pi$
$659$	−7.06968			−0.275396			−0.137698	+	0.990474i	$0.543970\pi$
$660$	−1.01452	+	19.4086i	−0.0394902	+	0.755478i
$661$	−3.04463			−0.118423			−0.0592113	−	0.998245i	$-0.518859\pi$
$661$	−3.04463			−0.118423			−0.0592113	+	0.998245i	$0.518859\pi$
$662$	−7.37181	−	8.63498i	−0.286513	−	0.335608i
$663$		−	5.35129i		−	0.207827i
$664$	13.8936	−	8.50188i	0.539178	−	0.329937i
$665$	−18.3012	−	19.7272i	−0.709688	−	0.764987i
$666$	−8.94512	−	10.4779i	−0.346616	−	0.406010i
$667$			14.6755i			0.568239i
$668$	10.0103	+	1.58983i	0.387311	+	0.0615124i
$669$		−	18.7273i		−	0.724038i
$670$	−25.6161	+	27.0125i	−0.989636	+	1.04359i
$671$	−14.9197			−0.575970
$672$	15.3127	+	9.10663i	0.590701	+	0.351296i
$673$		−	45.1287i		−	1.73958i	−0.493420	−	0.869791i	$-0.664253\pi$
$673$		−	45.1287i		−	1.73958i	0.493420	−	0.869791i	$-0.335747\pi$
$674$	35.8530	−	30.6082i	1.38101	−	1.17898i
$675$	26.6751	−	5.70120i	1.02673	−	0.219439i
$676$	5.62116	−	35.3934i	0.216199	−	1.36129i
$677$		−	3.41915i		−	0.131408i	−0.997839	−	0.0657042i	$-0.979071\pi$
$677$		−	3.41915i		−	0.131408i	0.997839	−	0.0657042i	$-0.0209294\pi$
$678$	−0.108500	+	0.0926277i	−0.00416690	+	0.00355734i
$679$	−24.8215	+	18.5827i	−0.952563	+	0.713138i
$680$	4.05681	−	3.11241i	0.155572	−	0.119355i
$681$	−20.8617			−0.799423
$682$	−15.8656	−	18.5842i	−0.607526	−	0.711627i
$683$		−	52.1925i		−	1.99709i	−0.0539068	−	0.998546i	$-0.517167\pi$
$683$		−	52.1925i		−	1.99709i	0.0539068	−	0.998546i	$-0.482833\pi$
$684$	14.2221	+	2.25874i	0.543794	+	0.0863650i
$685$	−1.55068	−	14.6747i	−0.0592483	−	0.560690i
$686$	12.7183	−	22.8964i	0.485587	−	0.874188i
$687$	19.7281			0.752673
$688$	3.30251	−	10.1348i	0.125907	−	0.386386i
$689$		−	16.6237i		−	0.633312i
$690$	4.79335	+	4.54555i	0.182480	+	0.173046i
$691$		−	22.1744i		−	0.843554i	−0.906700	−	0.421777i	$-0.861406\pi$
$691$		−	22.1744i		−	0.843554i	0.906700	−	0.421777i	$-0.138594\pi$
$692$	7.33139	+	1.16437i	0.278698	+	0.0442626i
$693$	−12.2401	+	9.16353i	−0.464961	+	0.348094i
$694$	18.0357	−	15.3974i	0.684628	−	0.584476i
$695$	−1.49809	−	14.1770i	−0.0568256	−	0.537763i
$696$	−14.6965	−	24.0167i	−0.557068	−	0.910352i
$697$		−	6.18546i		−	0.234291i
$698$	−0.215211	−	0.252088i	−0.00814585	−	0.00954166i
$699$			16.7888i			0.635011i
$700$	−16.9571	−	20.3091i	−0.640917	−	0.767610i
$701$		−	17.3192i		−	0.654138i	−0.945001	−	0.327069i	$-0.893939\pi$
$701$		−	17.3192i		−	0.654138i	0.945001	−	0.327069i	$-0.106061\pi$
$702$	32.6275	−	27.8546i	1.23145	−	1.05130i
$703$		−	27.9911i		−	1.05570i
$704$	−13.2925	+	26.0060i	−0.500978	+	0.980139i
$705$	−1.34092	−	12.6897i	−0.0505020	−	0.477920i
$706$	−13.0604	−	15.2983i	−0.491535	−	0.575761i
$707$	−15.0529	+	11.2694i	−0.566124	+	0.423829i
$708$	20.9883	+	3.33334i	0.788788	+	0.125275i
$709$			3.57195i			0.134147i	0.997748	+	0.0670737i	$0.0213663\pi$
$709$			3.57195i			0.134147i	−0.997748	+	0.0670737i	$0.978634\pi$
$710$	−17.7837	+	18.7531i	−0.667409	+	0.703792i
$711$			3.94650i			0.148005i
$712$	7.31904	+	11.9607i	0.274293	+	0.448245i
$713$	−8.30552			−0.311044
$714$	−3.51293	−	0.791143i	−0.131468	−	0.0296078i
$715$	−4.77003	−	45.1407i	−0.178389	−	1.68817i
$716$	−2.28049	+	14.3590i	−0.0852259	+	0.536621i
$717$			27.0475i			1.01011i
$718$	15.3159	−	13.0754i	0.571586	−	0.487971i
$719$	−1.20606			−0.0449783			−0.0224891	−	0.999747i	$-0.507159\pi$
$719$	−1.20606			−0.0449783			−0.0224891	+	0.999747i	$0.507159\pi$
$720$	13.8484	+	2.94776i	0.516101	+	0.109856i
$721$	−8.03575	−	10.7336i	−0.299267	−	0.399742i
$722$	1.55033	+	1.81598i	0.0576973	+	0.0675839i
$723$		−	17.8815i		−	0.665020i
$724$	5.72017	−	36.0168i	0.212589	−	1.33856i
$725$	8.73933	+	40.8901i	0.324571	+	1.51862i
$726$	2.54479	+	2.98084i	0.0944458	+	0.110629i
$727$			28.9323i			1.07304i	0.843888	+	0.536520i	$0.180261\pi$
$727$			28.9323i			1.07304i	−0.843888	+	0.536520i	$0.819739\pi$
$728$	−38.6574	−	15.3962i	−1.43274	−	0.570621i
$729$	22.2450			0.823890
$730$	34.8279	+	33.0275i	1.28904	+	1.22240i
$731$			2.15443i			0.0796843i
$732$	1.52611	−	9.60912i	0.0564068	−	0.355163i
$733$		−	11.5527i		−	0.426710i	−0.976975	−	0.213355i	$-0.931561\pi$
$733$		−	11.5527i		−	0.426710i	0.976975	−	0.213355i	$-0.0684391\pi$
$734$	−5.48424	+	4.68197i	−0.202427	+	0.172815i
$735$	−3.34020	+	18.3306i	−0.123205	+	0.676134i
$736$	3.78920	+	9.17546i	0.139672	+	0.338212i
$737$			42.9779i			1.58311i
$738$	13.0265	−	11.1209i	0.479511	−	0.409365i
$739$	−11.3868			−0.418869			−0.209434	−	0.977823i	$-0.567162\pi$
$739$	−11.3868			−0.418869			−0.209434	+	0.977823i	$0.567162\pi$
$740$	1.43663	−	27.4839i	0.0528117	−	1.01033i
$741$	30.1064			1.10599
$742$	−10.9129	−	2.45767i	−0.400624	−	0.0902239i
$743$	−48.8376			−1.79168			−0.895840	−	0.444377i	$-0.853425\pi$
$743$	−48.8376			−1.79168			−0.895840	+	0.444377i	$0.853425\pi$
$744$	13.5921	−	8.31735i	0.498311	−	0.304929i
$745$	3.99770	+	37.8318i	0.146464	+	1.38605i
$746$	−23.0735	−	27.0272i	−0.844780	−	0.989536i
$747$	−9.11621			−0.333545
$748$	0.925917	−	5.83000i	0.0338549	−	0.213166i
$749$	17.2310	+	23.0161i	0.629607	+	0.840989i
$750$	16.0625	+	9.81069i	0.586518	+	0.358236i
$751$			0.434842i			0.0158676i	0.999969	+	0.00793381i	$0.00252544\pi$
$751$			0.434842i			0.0158676i	−0.999969	+	0.00793381i	$0.997475\pi$
$752$	5.94107	−	18.2321i	0.216648	−	0.664855i
$753$			18.3940i			0.670314i
$754$	42.6981	+	50.0145i	1.55497	+	1.82142i
$755$	3.47575	+	32.8923i	0.126495	+	1.19707i
$756$	−13.4618	−	25.5369i	−0.489602	−	0.928767i
$757$	−13.5346			−0.491923			−0.245962	−	0.969280i	$-0.579104\pi$
$757$	−13.5346			−0.491923			−0.245962	+	0.969280i	$0.579104\pi$
$758$	5.30658	+	6.21588i	0.192744	+	0.225771i
$759$	7.62638			0.276820
$760$	17.5104	+	22.8237i	0.635171	+	0.827902i
$761$		−	28.4347i		−	1.03076i	−0.856963	−	0.515378i	$-0.827651\pi$
$761$		−	28.4347i		−	1.03076i	0.856963	−	0.515378i	$-0.172349\pi$
$762$	6.48663	+	7.59813i	0.234986	+	0.275251i
$763$	11.3397	+	15.1468i	0.410524	+	0.548352i
$764$	−4.92442	−	0.782093i	−0.178159	−	0.0282951i
$765$	−2.84587	+	0.300724i	−0.102893	+	0.0108727i
$766$	26.6955	−	22.7903i	0.964548	−	0.823448i
$767$	−49.6339			−1.79218
$768$	−15.3896	−	11.2212i	−0.555325	−	0.404909i
$769$			37.6894i			1.35912i	0.733622	+	0.679558i	$0.237828\pi$
$769$			37.6894i			1.35912i	−0.733622	+	0.679558i	$0.762172\pi$
$770$	−30.3385	−	3.54231i	−1.09332	−	0.127656i
$771$	−23.8022			−0.857215
$772$	−27.6909	−	4.39785i	−0.996616	−	0.158282i
$773$			8.24274i			0.296471i	0.988952	+	0.148235i	$0.0473593\pi$
$773$			8.24274i			0.296471i	−0.988952	+	0.148235i	$0.952641\pi$
$774$	−4.53718	+	3.87345i	−0.163086	+	0.139228i
$775$	−23.1415	+	4.94596i	−0.831266	+	0.177664i
$776$	28.2741	−	17.3016i	1.01498	−	0.621093i
$777$	−15.5154	+	11.6156i	−0.556612	+	0.416708i
$778$	−7.90216	+	6.74618i	−0.283306	+	0.241862i
$779$	34.7995			1.24682
$780$	29.5609	+	1.54520i	1.05845	+	0.0553271i
$781$			29.8369i			1.06765i
$782$	−1.30275	−	1.52598i	−0.0465862	−	0.0545689i
$783$			45.6229i			1.63043i
$784$	−15.8222	+	23.1010i	−0.565080	+	0.825036i
$785$	3.91808	+	37.0783i	0.139842	+	1.32338i
$786$	−22.1232	+	18.8869i	−0.789109	+	0.673673i
$787$	−22.9785			−0.819095			−0.409547	−	0.912289i	$-0.634313\pi$
$787$	−22.9785			−0.819095			−0.409547	+	0.912289i	$0.634313\pi$
$788$	−2.59444	+	16.3358i	−0.0924230	+	0.581937i
$789$	−3.70197			−0.131793
$790$	−5.42484	+	5.72057i	−0.193007	+	0.203529i
$791$	−0.134370	−	0.179483i	−0.00477765	−	0.00638167i
$792$	13.9426	−	8.53183i	0.495428	−	0.303165i
$793$			22.7240i			0.806954i
$794$	−10.7769	+	9.20035i	−0.382456	+	0.326508i
$795$	7.91367	−	0.836241i	0.280669	−	0.0296584i
$796$	−8.51809	+	53.6338i	−0.301916	+	1.90100i
$797$			33.7838i			1.19668i	0.801241	+	0.598341i	$0.204173\pi$
$797$			33.7838i			1.19668i	−0.801241	+	0.598341i	$0.795827\pi$
$798$	4.45098	−	19.7638i	0.157563	−	0.699631i
$799$			3.87572i			0.137113i
$800$	16.0218	+	23.3089i	0.566455	+	0.824093i
$801$		−	7.84790i		−	0.277292i
$802$	−10.7915	−	12.6407i	−0.381062	−	0.446358i
$803$	55.4124			1.95546
$804$	−27.6801	−	4.39613i	−0.976200	−	0.155040i
$805$	−7.61112	+	7.06093i	−0.268257	+	0.248865i
$806$	−28.3053	+	24.1647i	−0.997013	+	0.851164i
$807$	13.3538			0.470077
$808$	17.1467	−	10.4925i	0.603220	−	0.369126i
$809$	20.4803			0.720049			0.360024	−	0.932943i	$-0.382768\pi$
$809$	20.4803			0.720049			0.360024	+	0.932943i	$0.382768\pi$
$810$	4.00446	+	3.79744i	0.140702	+	0.133429i
$811$			12.3156i			0.432460i	0.976342	+	0.216230i	$0.0693762\pi$
$811$			12.3156i			0.432460i	−0.976342	+	0.216230i	$0.930624\pi$
$812$	39.1453	−	20.6356i	1.37373	−	0.724166i
$813$	7.86166			0.275720
$814$	−20.6297	−	24.1647i	−0.723071	−	0.846971i
$815$	2.55351	+	24.1649i	0.0894457	+	0.846459i
$816$	3.66012	+	1.19268i	0.128130	+	0.0417522i
$817$	−12.1208			−0.424054
$818$	5.03108	−	4.29510i	0.175907	−	0.150175i
$819$	13.9568	+	18.6427i	0.487691	+	0.651427i
$820$	34.1690	+	1.78607i	1.19323	+	0.0623724i
$821$		−	26.8208i		−	0.936053i	−0.883715	−	0.468026i	$-0.844965\pi$
$821$		−	26.8208i		−	0.936053i	0.883715	−	0.468026i	$-0.155035\pi$
$822$	8.44928	−	7.21327i	0.294703	−	0.251592i
$823$	26.3764			0.919425			0.459712	−	0.888068i	$-0.347953\pi$
$823$	26.3764			0.919425			0.459712	+	0.888068i	$0.347953\pi$
$824$	7.48179	+	12.2266i	0.260641	+	0.425935i
$825$	21.2492	−	4.54153i	0.739802	−	0.158116i
$826$	−7.33796	+	32.5829i	−0.255320	+	1.13371i
$827$			13.0913i			0.455228i	0.973751	+	0.227614i	$0.0730924\pi$
$827$			13.0913i			0.455228i	−0.973751	+	0.227614i	$0.926908\pi$
$828$	0.871464	−	5.48714i	0.0302855	−	0.190691i
$829$	13.7348			0.477030			0.238515	−	0.971139i	$-0.423339\pi$
$829$	13.7348			0.477030			0.238515	+	0.971139i	$0.423339\pi$
$830$	−13.2142	−	12.5311i	−0.458672	−	0.434961i
$831$	19.1299			0.663610
$832$	39.6094	+	20.2455i	1.37321	+	0.701888i
$833$	1.59398	−	5.43016i	0.0552282	−	0.188144i
$834$	8.16273	−	6.96864i	0.282652	−	0.241304i
$835$	−1.19084	−	11.2694i	−0.0412108	−	0.389994i
$836$	32.7996	+	5.20922i	1.13440	+	0.180165i
$837$	−25.8200			−0.892468
$838$	23.3829	−	19.9623i	0.807749	−	0.689586i
$839$	25.7342			0.888445			0.444222	−	0.895917i	$-0.353480\pi$
$839$	25.7342			0.888445			0.444222	+	0.895917i	$0.353480\pi$
$840$	5.38471	−	19.1773i	0.185790	−	0.661679i
$841$	−40.9351			−1.41155
$842$	10.5075	−	8.97040i	0.362112	−	0.309140i
$843$	−25.1814			−0.867293
$844$	−6.31125	+	39.7386i	−0.217242	+	1.36786i
$845$	−39.8452	+	4.21045i	−1.37072	+	0.144844i
$846$	−8.16220	+	6.96818i	−0.280622	+	0.239571i
$847$	−4.93098	+	3.69158i	−0.169431	+	0.126844i
$848$	11.3701	+	3.70504i	0.390451	+	0.127232i
$849$	−29.4300			−1.01003
$850$	−4.53854	−	3.47601i	−0.155671	−	0.119226i
$851$	−10.7995			−0.370202
$852$	−19.2165	−	3.05196i	−0.658348	−	0.104558i
$853$			8.40578i			0.287808i	0.989592	+	0.143904i	$0.0459657\pi$
$853$			8.40578i			0.287808i	−0.989592	+	0.143904i	$0.954034\pi$
$854$	14.9175	+	3.35956i	0.510467	+	0.114962i
$855$	−1.69188	−	16.0109i	−0.0578609	−	0.547561i
$856$	−16.0432	−	26.2175i	−0.548344	−	0.896096i
$857$	25.2022			0.860892			0.430446	−	0.902616i	$-0.358356\pi$
$857$	25.2022			0.860892			0.430446	+	0.902616i	$0.358356\pi$
$858$	25.9908	−	22.1887i	0.887312	−	0.757511i
$859$		−	44.9663i		−	1.53423i	−0.641510	−	0.767114i	$-0.721692\pi$
$859$		−	44.9663i		−	1.53423i	0.641510	−	0.767114i	$-0.278308\pi$
$860$	−11.9012	−	0.622098i	−0.405828	−	0.0212133i
$861$	−14.4409	−	19.2893i	−0.492146	−	0.657377i
$862$	2.28990	−	1.95492i	0.0779942	−	0.0665847i
$863$	21.2327			0.722768			0.361384	−	0.932417i	$-0.382304\pi$
$863$	21.2327			0.722768			0.361384	+	0.932417i	$0.382304\pi$
$864$	11.7798	+	28.5244i	0.400755	+	0.970419i
$865$	−0.872153	−	8.25352i	−0.0296541	−	0.280628i
$866$	−1.03085	−	1.20749i	−0.0350299	−	0.0410323i
$867$	19.4584			0.660843
$868$	11.6785	+	22.1540i	0.396396	+	0.751956i
$869$			9.10163i			0.308752i
$870$	−21.6614	+	22.8423i	−0.734391	+	0.774426i
$871$	65.4590			2.21799
$872$	−10.5580	−	17.2537i	−0.357538	−	0.584283i
$873$	−18.5518			−0.627884
$874$	8.58518	−	7.32929i	0.290398	−	0.247917i
$875$	−17.0019	+	24.2061i	−0.574768	+	0.818317i
$876$	−5.66804	+	35.6886i	−0.191505	+	1.20581i
$877$	23.4510			0.791884			0.395942	−	0.918275i	$-0.370418\pi$
$877$	23.4510			0.791884			0.395942	+	0.918275i	$0.370418\pi$
$878$	−16.5257	−	19.3574i	−0.557714	−	0.653280i
$879$		−	13.5717i		−	0.457762i
$880$	31.9380	+	6.79827i	1.07663	+	0.229170i
$881$			30.2220i			1.01821i	0.860706	+	0.509103i	$0.170023\pi$
$881$			30.2220i			1.01821i	−0.860706	+	0.509103i	$0.829977\pi$
$882$	14.3016	−	6.40601i	0.481561	−	0.215702i
$883$			55.2980i			1.86092i	0.366387	+	0.930462i	$0.380595\pi$
$883$			55.2980i			1.86092i	−0.366387	+	0.930462i	$0.619405\pi$
$884$	−8.87959	−	1.41025i	−0.298653	−	0.0474319i
$885$	−2.49680	−	23.6281i	−0.0839289	−	0.794252i
$886$	10.8847	−	9.29238i	0.365677	−	0.312184i
$887$			8.28733i			0.278261i	0.990274	+	0.139131i	$0.0444308\pi$
$887$			8.28733i			0.278261i	−0.990274	+	0.139131i	$0.955569\pi$
$888$	17.6735	−	10.8149i	0.593084	−	0.362924i
$889$	−12.5690	+	9.40981i	−0.421551	+	0.315595i
$890$	10.7877	−	11.3758i	0.361604	−	0.381317i
$891$	6.37123			0.213444
$892$	−31.0748	−	4.93529i	−1.04046	−	0.165246i
$893$	−21.8048			−0.729671
$894$	−21.7826	+	18.5961i	−0.728518	+	0.621946i
$895$	16.1651	−	1.70817i	0.540338	−	0.0570978i
$896$	19.1464	−	23.0090i	0.639636	−	0.768678i
$897$		−	11.6156i		−	0.387834i
$898$	−0.689248	−	0.807352i	−0.0230005	−	0.0269417i
$899$		−	39.5793i		−	1.32004i
$900$	−0.839468	−	15.8076i	−0.0279823	−	0.526921i
$901$	−2.41702			−0.0805227
$902$	30.0423	−	25.6476i	1.00030	−	0.853971i
$903$	5.02985	+	6.71855i	0.167383	+	0.223579i
$904$	0.125107	+	0.204448i	0.00416100	+	0.00679984i
$905$	−40.5470	+	4.28462i	−1.34783	+	0.142425i
$906$	−18.9385	+	16.1681i	−0.629191	+	0.537149i
$907$		−	18.0875i		−	0.600587i	−0.953847	−	0.300293i	$-0.902915\pi$
$907$		−	18.0875i		−	0.600587i	0.953847	−	0.300293i	$-0.0970845\pi$
$908$	−5.49779	+	34.6166i	−0.182451	+	1.14879i
$909$	−11.2507			−0.373162
$910$	−5.39524	+	46.2081i	−0.178850	+	1.53178i
$911$			6.16833i			0.204366i	0.994766	+	0.102183i	$0.0325827\pi$
$911$			6.16833i			0.204366i	−0.994766	+	0.102183i	$0.967417\pi$
$912$	−6.71003	+	20.5919i	−0.222191	+	0.681866i
$913$	−21.0243			−0.695802
$914$	−22.0490	+	18.8236i	−0.729317	+	0.622628i
$915$	−10.8177	+	1.14311i	−0.357623	+	0.0377902i
$916$	5.19903	−	32.7355i	0.171781	−	1.08161i
$917$	−27.3982	−	36.5968i	−0.904768	−	1.20853i
$918$	−4.04995	−	4.74392i	−0.133668	−	0.156573i
$919$			55.8085i			1.84095i	0.390797	+	0.920477i	$0.372199\pi$
$919$			55.8085i			1.84095i	−0.390797	+	0.920477i	$0.627801\pi$
$920$	8.80580	−	6.75586i	0.290319	−	0.222734i
$921$	−0.507762			−0.0167313
$922$	−13.7366	−	16.0904i	−0.452392	−	0.529910i
$923$	45.4441			1.49581
$924$	−10.7236	−	20.3425i	−0.352780	−	0.669218i
$925$	−30.0904	+	6.43113i	−0.989365	+	0.211454i
$926$	21.2177	+	24.8534i	0.697258	+	0.816735i
$927$		−	8.02241i		−	0.263491i
$928$	−43.7249	+	18.0571i	−1.43534	+	0.592754i
$929$			14.2579i			0.467787i	0.972262	+	0.233894i	$0.0751467\pi$
$929$			14.2579i			0.467787i	−0.972262	+	0.233894i	$0.924853\pi$
$930$	−12.9274	−	12.2591i	−0.423907	−	0.401993i
$931$	30.5501	+	8.96776i	1.00124	+	0.293907i
$932$	27.8583	+	4.42443i	0.912528	+	0.144927i
$933$	0.698651			0.0228728
$934$	20.5464	+	24.0670i	0.672297	+	0.787497i
$935$	−6.56329	+	0.693545i	−0.214643	+	0.0226814i
$936$	−12.9947	−	21.2357i	−0.424745	−	0.694112i
$937$	22.5672			0.737237			0.368618	−	0.929581i	$-0.379831\pi$
$937$	22.5672			0.737237			0.368618	+	0.929581i	$0.379831\pi$
$938$	9.67755	−	42.9715i	0.315983	−	1.40307i
$939$	7.68634			0.250834
$940$	−21.4098	−	1.11913i	−0.698310	−	0.0365019i
$941$	12.3410			0.402307			0.201153	−	0.979560i	$-0.435531\pi$
$941$	12.3410			0.402307			0.201153	+	0.979560i	$0.435531\pi$
$942$	−21.3487	+	18.2257i	−0.695578	+	0.593825i
$943$		−	13.4263i		−	0.437220i
$944$	11.0623	−	33.9481i	0.360046	−	1.10492i
$945$	−23.6612	+	21.9508i	−0.769699	+	0.714060i
$946$	−10.4639	+	8.93317i	−0.340210	+	0.290442i
$947$		−	38.9941i		−	1.26714i	−0.773687	−	0.633568i	$-0.781590\pi$
$947$		−	38.9941i		−	1.26714i	0.773687	−	0.633568i	$-0.218410\pi$
$948$	−5.86194	−	0.930989i	−0.190387	−	0.0302371i
$949$		−	84.3979i		−	2.73967i
$950$	19.5561	−	25.5339i	0.634482	−	0.828429i
$951$	12.2711			0.397918
$952$	−2.23855	+	5.62064i	−0.0725519	+	0.182166i
$953$		−	57.1070i		−	1.84988i	−0.380117	−	0.924938i	$-0.624116\pi$
$953$		−	57.1070i		−	1.84988i	0.380117	−	0.924938i	$-0.375884\pi$
$954$	−4.34558	−	5.09021i	−0.140693	−	0.164802i
$955$	0.585816	+	5.54380i	0.0189565	+	0.179393i
$956$	44.8809	+	7.12796i	1.45155	+	0.230535i
$957$			36.3429i			1.17480i
$958$	29.9408	+	35.0713i	0.967344	+	1.13310i
$959$	10.4639	+	13.9770i	0.337897	+	0.451341i
$960$	−7.64533	+	19.8744i	−0.246752	+	0.641444i
$961$	−8.60041			−0.277433
$962$	−36.8048	+	31.4208i	−1.18664	+	1.01305i
$963$			17.2024i			0.554340i
$964$	−29.6714	−	4.71239i	−0.955651	−	0.151776i
$965$	3.29415	+	31.1738i	0.106042	+	1.00352i
$966$	−7.62525	−	1.71727i	−0.245338	−	0.0552523i
$967$	11.1371			0.358146			0.179073	−	0.983836i	$-0.442690\pi$
$967$	11.1371			0.358146			0.179073	+	0.983836i	$0.442690\pi$
$968$	5.61686	−	3.43710i	0.180533	−	0.110473i
$969$		−	4.37736i		−	0.140621i
$970$	−26.8914	−	25.5013i	−0.863432	−	0.818796i
$971$		−	7.38403i		−	0.236965i	−0.992956	−	0.118482i	$-0.962197\pi$
$971$		−	7.38403i		−	0.236965i	0.992956	−	0.118482i	$-0.0378029\pi$
$972$	4.48259	−	28.2245i	0.143779	−	0.905300i
$973$	10.1090	+	13.5030i	0.324081	+	0.432886i
$974$	−3.58477	−	4.19903i	−0.114863	−	0.134546i
$975$	−6.91714	−	32.3643i	−0.221526	−	1.03649i
$976$	−15.5426	−	5.06467i	−0.497505	−	0.162116i
$977$		−	23.4951i		−	0.751675i	−0.926686	−	0.375838i	$-0.877355\pi$
$977$		−	23.4951i		−	0.751675i	0.926686	−	0.375838i	$-0.122645\pi$
$978$	−13.9135	+	11.8782i	−0.444905	+	0.379822i
$979$		−	18.0992i		−	0.578454i
$980$	29.5363	+	10.3733i	0.943504	+	0.331362i
$981$			11.3209i			0.361448i
$982$	18.8721	+	22.1059i	0.602234	+	0.705429i
$983$			60.7158i			1.93653i	0.249918	+	0.968267i	$0.419596\pi$
$983$			60.7158i			1.93653i	−0.249918	+	0.968267i	$0.580404\pi$
$984$	13.4454	+	21.9723i	0.428625	+	0.700452i
$985$	18.3905	−	1.94333i	0.585969	−	0.0619195i
$986$	7.27193	−	6.20814i	0.231585	−	0.197708i
$987$	9.04848	+	12.0864i	0.288016	+	0.384714i
$988$	7.93409	−	49.9567i	0.252417	−	1.58933i
$989$			4.67644i			0.148702i
$990$	−13.2608	−	12.5752i	−0.421455	−	0.399667i
$991$		−	8.22655i		−	0.261325i	−0.991427	−	0.130663i	$-0.958290\pi$
$991$		−	8.22655i		−	0.261325i	0.991427	−	0.130663i	$-0.0417104\pi$
$992$	−10.2193	−	24.7458i	−0.324463	−	0.785679i
$993$	−9.55672			−0.303273
$994$	6.71852	−	29.8324i	0.213099	−	0.946228i
$995$	60.3798	−	6.38035i	1.91417	−	0.202271i
$996$	2.15054	−	13.5408i	0.0681423	−	0.429055i
$997$		−	49.5766i		−	1.57011i	−0.619428	−	0.785054i	$-0.712635\pi$
$997$		−	49.5766i		−	1.57011i	0.619428	−	0.785054i	$-0.287365\pi$
$998$	23.7504	+	27.8201i	0.751805	+	0.880629i
$999$	−33.5731			−1.06221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.n.b.139.9	✓	40
4.3	odd	2		1120.2.n.b.559.26		40
5.4	even	2	inner	280.2.n.b.139.32	yes	40
7.6	odd	2	inner	280.2.n.b.139.10	yes	40
8.3	odd	2	inner	280.2.n.b.139.29	yes	40
8.5	even	2		1120.2.n.b.559.28		40
20.19	odd	2		1120.2.n.b.559.13		40
28.27	even	2		1120.2.n.b.559.15		40
35.34	odd	2	inner	280.2.n.b.139.31	yes	40
40.19	odd	2	inner	280.2.n.b.139.12	yes	40
40.29	even	2		1120.2.n.b.559.14		40
56.13	odd	2		1120.2.n.b.559.16		40
56.27	even	2	inner	280.2.n.b.139.30	yes	40
140.139	even	2		1120.2.n.b.559.25		40
280.69	odd	2		1120.2.n.b.559.27		40
280.139	even	2	inner	280.2.n.b.139.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.n.b.139.9	✓	40	1.1	even	1	trivial
280.2.n.b.139.10	yes	40	7.6	odd	2	inner
280.2.n.b.139.11	yes	40	280.139	even	2	inner
280.2.n.b.139.12	yes	40	40.19	odd	2	inner
280.2.n.b.139.29	yes	40	8.3	odd	2	inner
280.2.n.b.139.30	yes	40	56.27	even	2	inner
280.2.n.b.139.31	yes	40	35.34	odd	2	inner
280.2.n.b.139.32	yes	40	5.4	even	2	inner
1120.2.n.b.559.13		40	20.19	odd	2
1120.2.n.b.559.14		40	40.29	even	2
1120.2.n.b.559.15		40	28.27	even	2
1120.2.n.b.559.16		40	56.13	odd	2
1120.2.n.b.559.25		40	140.139	even	2
1120.2.n.b.559.26		40	4.3	odd	2
1120.2.n.b.559.27		40	280.69	odd	2
1120.2.n.b.559.28		40	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.918230 - 1.07557i) q^{2} -1.19038 q^{3} +(-0.313707 + 1.97524i) q^{4} +(2.22369 - 0.234978i) q^{5} +(1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 - 1.47631i) q^{8} -1.58299 q^{9} +O(q^{10})\)	\(q+(-0.918230 - 1.07557i) q^{2} -1.19038 q^{3} +(-0.313707 + 1.97524i) q^{4} +(2.22369 - 0.234978i) q^{5} +(1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 - 1.47631i) q^{8} -1.58299 q^{9} +(-2.29459 - 2.17597i) q^{10} -3.65078 q^{11} +(0.373431 - 2.35130i) q^{12} +5.56044i q^{13} +(3.65023 + 0.822064i) q^{14} +(-2.64704 + 0.279713i) q^{15} +(-3.80318 - 1.23930i) q^{16} +0.808468 q^{17} +(1.45355 + 1.70262i) q^{18} +4.54845i q^{19} +(-0.233448 + 4.46604i) q^{20} +(2.52120 - 1.88750i) q^{21} +(3.35225 + 3.92667i) q^{22} +1.75488 q^{23} +(-2.87188 + 1.75738i) q^{24} +(4.88957 - 1.04503i) q^{25} +(5.98065 - 5.10576i) q^{26} +5.45551 q^{27} +(-2.46757 - 4.68093i) q^{28} +8.36272i q^{29} +(2.73144 + 2.59024i) q^{30} -4.73282 q^{31} +(2.15924 + 5.22855i) q^{32} +4.34582 q^{33} +(-0.742360 - 0.869565i) q^{34} +(-4.33712 + 4.02360i) q^{35} +(0.496595 - 3.12679i) q^{36} -6.15399 q^{37} +(4.89218 - 4.17652i) q^{38} -6.61905i q^{39} +(5.01790 - 3.84976i) q^{40} -7.65085i q^{41} +(-4.34517 - 0.978571i) q^{42} +2.66483i q^{43} +(1.14527 - 7.21117i) q^{44} +(-3.52008 + 0.371968i) q^{45} +(-1.61138 - 1.88750i) q^{46} +4.79391i q^{47} +(4.52723 + 1.47524i) q^{48} +(1.97161 - 6.71660i) q^{49} +(-5.61376 - 4.29950i) q^{50} -0.962386 q^{51} +(-10.9832 - 1.74435i) q^{52} -2.98963 q^{53} +(-5.00941 - 5.86779i) q^{54} +(-8.11818 + 0.857851i) q^{55} +(-2.76888 + 6.95222i) q^{56} -5.41439i q^{57} +(8.99470 - 7.67890i) q^{58} +8.92626i q^{59} +(0.277892 - 5.31629i) q^{60} +4.08673 q^{61} +(4.34582 + 5.09049i) q^{62} +(3.35273 - 2.51002i) q^{63} +(3.64099 - 7.12342i) q^{64} +(1.30658 + 12.3647i) q^{65} +(-3.99046 - 4.67424i) q^{66} -11.7723i q^{67} +(-0.253622 + 1.59692i) q^{68} -2.08897 q^{69} +(8.31015 + 0.970289i) q^{70} -8.17275i q^{71} +(-3.81908 + 2.33699i) q^{72} -15.1783 q^{73} +(5.65078 + 6.61905i) q^{74} +(-5.82046 + 1.24399i) q^{75} +(-8.98430 - 1.42688i) q^{76} +(7.73224 - 5.78875i) q^{77} +(-7.11926 + 6.07781i) q^{78} -2.49307i q^{79} +(-8.74828 - 1.86214i) q^{80} -1.74517 q^{81} +(-8.22903 + 7.02524i) q^{82} +5.75885 q^{83} +(2.93735 + 5.57210i) q^{84} +(1.79778 - 0.189972i) q^{85} +(2.86621 - 2.44692i) q^{86} -9.95483i q^{87} +(-8.80775 + 5.38969i) q^{88} +4.95764i q^{89} +(3.63232 + 3.44454i) q^{90} +(-8.81676 - 11.7769i) q^{91} +(-0.550517 + 3.46631i) q^{92} +5.63387 q^{93} +(5.15619 - 4.40191i) q^{94} +(1.06878 + 10.1143i) q^{95} +(-2.57032 - 6.22397i) q^{96} +11.7195 q^{97} +(-9.03458 + 4.04678i) q^{98} +5.77914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 12 * q^4 + 40 * q^9	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) \) 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Introduction

L-functions

Modular forms

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