LMFDB - Embedded newform 945.2.bb.b.404.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(269,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("945.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bb (of order $6$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			404.8
Character	$\chi$	$=$	945.404
Dual form			945.2.bb.b.269.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.187042 + 0.323967i) q^{2} +(0.930030 + 1.61086i) q^{4} +(2.23199 + 0.135023i) q^{5} +(2.46237 + 0.967860i) q^{7} -1.44399 q^{8} +O(q^{10})$	\(q+(-0.187042 + 0.323967i) q^{2} +(0.930030 + 1.61086i) q^{4} +(2.23199 + 0.135023i) q^{5} +(2.46237 + 0.967860i) q^{7} -1.44399 q^{8} +(-0.461219 + 0.697834i) q^{10} +(0.947907 - 0.547275i) q^{11} +5.52806 q^{13} +(-0.774121 + 0.616694i) q^{14} +(-1.58997 + 2.75392i) q^{16} +(-0.343551 + 0.198349i) q^{17} +(-4.00979 - 2.31505i) q^{19} +(1.85831 + 3.72099i) q^{20} +0.409454i q^{22} +(1.81197 - 3.13842i) q^{23} +(4.96354 + 0.602738i) q^{25} +(-1.03398 + 1.79091i) q^{26} +(0.730988 + 4.86667i) q^{28} -7.19269i q^{29} +(-3.46215 + 1.99887i) q^{31} +(-2.03877 - 3.53126i) q^{32} -0.148399i q^{34} +(5.36529 + 2.49273i) q^{35} +(0.338363 + 0.195354i) q^{37} +(1.50000 - 0.866025i) q^{38} +(-3.22296 - 0.194971i) q^{40} -10.9717 q^{41} +3.44210i q^{43} +(1.76317 + 1.01796i) q^{44} +(0.677829 + 1.17403i) q^{46} +(-4.21599 - 2.43410i) q^{47} +(5.12649 + 4.76645i) q^{49} +(-1.12366 + 1.49528i) q^{50} +(5.14126 + 8.90493i) q^{52} +(2.58997 + 4.48597i) q^{53} +(2.18961 - 1.09352i) q^{55} +(-3.55563 - 1.39758i) q^{56} +(2.33019 + 1.34534i) q^{58} +(-4.11222 - 7.12257i) q^{59} +(-2.91120 - 1.68078i) q^{61} -1.49550i q^{62} -4.83455 q^{64} +(12.3386 + 0.746413i) q^{65} +(-4.20617 + 2.42844i) q^{67} +(-0.639026 - 0.368942i) q^{68} +(-1.81110 + 1.27193i) q^{70} +2.84053i q^{71} +(-0.357255 - 0.618785i) q^{73} +(-0.126576 + 0.0730788i) q^{74} -8.61228i q^{76} +(2.86378 - 0.430149i) q^{77} +(-2.40379 + 4.16348i) q^{79} +(-3.92064 + 5.93202i) q^{80} +(2.05218 - 3.55447i) q^{82} +12.9498i q^{83} +(-0.793583 + 0.396326i) q^{85} +(-1.11513 - 0.643818i) q^{86} +(-1.36877 + 0.790258i) q^{88} +(6.38611 - 11.0611i) q^{89} +(13.6121 + 5.35039i) q^{91} +6.74074 q^{92} +(1.57713 - 0.910559i) q^{94} +(-8.63722 - 5.70858i) q^{95} +4.84872 q^{97} +(-2.50304 + 0.769285i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 3 q^{5}+O(q^{10}) $ 32 * q - 16 * q^4 + 3 * q^5	$ 32 q - 16 q^{4} + 3 q^{5} - 3 q^{10} - 16 q^{16} + 6 q^{17} + 12 q^{19} - q^{25} - 6 q^{31} - 30 q^{32} + 12 q^{35} + 48 q^{38} + 24 q^{40} - 18 q^{46} + 6 q^{47} + 2 q^{49} + 72 q^{50} + 48 q^{53} + 12 q^{61} - 16 q^{64} - 30 q^{65} - 90 q^{68} - 24 q^{70} + 42 q^{77} + 10 q^{79} - 96 q^{80} + 10 q^{85} - 62 q^{91} - 84 q^{92} + 84 q^{94} - 36 q^{95} - 72 q^{98}+O(q^{100}) $ 32 * q - 16 * q^4 + 3 * q^5 - 3 * q^10 - 16 * q^16 + 6 * q^17 + 12 * q^19 - q^25 - 6 * q^31 - 30 * q^32 + 12 * q^35 + 48 * q^38 + 24 * q^40 - 18 * q^46 + 6 * q^47 + 2 * q^49 + 72 * q^50 + 48 * q^53 + 12 * q^61 - 16 * q^64 - 30 * q^65 - 90 * q^68 - 24 * q^70 + 42 * q^77 + 10 * q^79 - 96 * q^80 + 10 * q^85 - 62 * q^91 - 84 * q^92 + 84 * q^94 - 36 * q^95 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.187042	+	0.323967i	−0.132259	+	0.229079i	−0.924547	−	0.381068i	$-0.875556\pi$
$2$	−0.187042	+	0.323967i	−0.132259	+	0.229079i	0.792288	+	0.610147i	$0.208890\pi$
$3$		0			0
$3$		0			0
$4$	0.930030	+	1.61086i	0.465015	+	0.805430i
$5$	2.23199	+	0.135023i	0.998175	+	0.0603840i
$5$	2.23199	+	0.135023i	0.998175	+	0.0603840i
$6$		0			0
$7$	2.46237	+	0.967860i	0.930687	+	0.365817i
$7$	2.46237	+	0.967860i	0.930687	+	0.365817i
$8$	−1.44399			−0.510527
$9$		0			0
$10$	−0.461219	+	0.697834i	−0.145850	+	0.220675i
$11$	0.947907	−	0.547275i	0.285805	−	0.165009i	−0.350244	−	0.936659i	$-0.613901\pi$
$11$	0.947907	−	0.547275i	0.285805	−	0.165009i	0.636048	+	0.771649i	$0.280568\pi$
$12$		0			0
$13$	5.52806			1.53321			0.766604	−	0.642120i	$-0.221945\pi$
$13$	5.52806			1.53321			0.766604	+	0.642120i	$0.221945\pi$
$14$	−0.774121	+	0.616694i	−0.206892	+	0.164818i
$15$		0			0
$16$	−1.58997	+	2.75392i	−0.397494	+	0.688479i
$17$	−0.343551	+	0.198349i	−0.0833234	+	0.0481068i	−0.541083	−	0.840969i	$-0.681985\pi$
$17$	−0.343551	+	0.198349i	−0.0833234	+	0.0481068i	0.457759	+	0.889076i	$0.348652\pi$
$18$		0			0
$19$	−4.00979	−	2.31505i	−0.919909	−	0.531110i	−0.0363031	−	0.999341i	$-0.511558\pi$
$19$	−4.00979	−	2.31505i	−0.919909	−	0.531110i	−0.883606	+	0.468231i	$0.844892\pi$
$20$	1.85831	+	3.72099i	0.415532	+	0.832040i
$21$		0			0
$22$			0.409454i			0.0872958i
$23$	1.81197	−	3.13842i	0.377822	−	0.654406i	−0.612923	−	0.790142i	$-0.710007\pi$
$23$	1.81197	−	3.13842i	0.377822	−	0.654406i	0.990745	+	0.135736i	$0.0433400\pi$
$24$		0			0
$25$	4.96354	+	0.602738i	0.992708	+	0.120548i
$26$	−1.03398	+	1.79091i	−0.202780	+	0.351226i
$27$		0			0
$28$	0.730988	+	4.86667i	0.138144	+	0.919714i
$29$		−	7.19269i		−	1.33565i	−0.744319	−	0.667825i	$-0.767226\pi$
$29$		−	7.19269i		−	1.33565i	0.744319	−	0.667825i	$-0.232774\pi$
$30$		0			0
$31$	−3.46215	+	1.99887i	−0.621821	+	0.359008i	−0.777578	−	0.628787i	$-0.783552\pi$
$31$	−3.46215	+	1.99887i	−0.621821	+	0.359008i	0.155757	+	0.987795i	$0.450218\pi$
$32$	−2.03877	−	3.53126i	−0.360407	−	0.624244i
$33$		0			0
$34$		−	0.148399i		−	0.0254502i
$35$	5.36529	+	2.49273i	0.906899	+	0.421348i
$36$		0			0
$37$	0.338363	+	0.195354i	0.0556265	+	0.0321160i	0.527555	−	0.849521i	$-0.323109\pi$
$37$	0.338363	+	0.195354i	0.0556265	+	0.0321160i	−0.471929	+	0.881637i	$0.656442\pi$
$38$	1.50000	−	0.866025i	0.243332	−	0.140488i
$39$		0			0
$40$	−3.22296	−	0.194971i	−0.509595	−	0.0308276i
$41$	−10.9717			−1.71350			−0.856748	−	0.515735i	$-0.827519\pi$
$41$	−10.9717			−1.71350			−0.856748	+	0.515735i	$0.827519\pi$
$42$		0			0
$43$			3.44210i			0.524916i	0.964943	+	0.262458i	$0.0845331\pi$
$43$			3.44210i			0.524916i	−0.964943	+	0.262458i	$0.915467\pi$
$44$	1.76317	+	1.01796i	0.265807	+	0.153464i
$45$		0			0
$46$	0.677829	+	1.17403i	0.0999404	+	0.173102i
$47$	−4.21599	−	2.43410i	−0.614965	−	0.355050i	0.159941	−	0.987127i	$-0.448870\pi$
$47$	−4.21599	−	2.43410i	−0.614965	−	0.355050i	−0.774906	+	0.632076i	$0.782203\pi$
$48$		0			0
$49$	5.12649	+	4.76645i	0.732356	+	0.680922i
$50$	−1.12366	+	1.49528i	−0.158909	+	0.211465i
$51$		0			0
$52$	5.14126	+	8.90493i	0.712965	+	1.23489i
$53$	2.58997	+	4.48597i	0.355760	+	0.616195i	0.987248	−	0.159191i	$-0.0508886\pi$
$53$	2.58997	+	4.48597i	0.355760	+	0.616195i	−0.631487	+	0.775386i	$0.717555\pi$
$54$		0			0
$55$	2.18961	−	1.09352i	0.295247	−	0.147450i
$56$	−3.55563	−	1.39758i	−0.475141	−	0.186759i
$57$		0			0
$58$	2.33019	+	1.34534i	0.305969	+	0.176651i
$59$	−4.11222	−	7.12257i	−0.535365	−	0.927280i	−0.999146	−	0.0413294i	$-0.986841\pi$
$59$	−4.11222	−	7.12257i	−0.535365	−	0.927280i	0.463780	−	0.885950i	$-0.346493\pi$
$60$		0			0
$61$	−2.91120	−	1.68078i	−0.372741	−	0.215202i	0.301914	−	0.953335i	$-0.402374\pi$
$61$	−2.91120	−	1.68078i	−0.372741	−	0.215202i	−0.674655	+	0.738133i	$0.735708\pi$
$62$		−	1.49550i		−	0.189928i
$63$		0			0
$64$	−4.83455			−0.604319
$65$	12.3386	+	0.746413i	1.53041	+	0.0925811i
$66$		0			0
$67$	−4.20617	+	2.42844i	−0.513866	+	0.296681i	−0.734421	−	0.678694i	$-0.762546\pi$
$67$	−4.20617	+	2.42844i	−0.513866	+	0.296681i	0.220555	+	0.975374i	$0.429213\pi$
$68$	−0.639026	−	0.368942i	−0.0774933	−	0.0447408i
$69$		0			0
$70$	−1.81110	+	1.27193i	−0.216467	+	0.152025i
$71$			2.84053i			0.337109i	0.985692	+	0.168555i	$0.0539100\pi$
$71$			2.84053i			0.337109i	−0.985692	+	0.168555i	$0.946090\pi$
$72$		0			0
$73$	−0.357255	−	0.618785i	−0.0418136	−	0.0724233i	0.844361	−	0.535774i	$-0.179980\pi$
$73$	−0.357255	−	0.618785i	−0.0418136	−	0.0724233i	−0.886175	+	0.463351i	$0.846647\pi$
$74$	−0.126576	+	0.0730788i	−0.0147142	+	0.00849524i
$75$		0			0
$76$		−	8.61228i		−	0.987897i
$77$	2.86378	−	0.430149i	0.326358	−	0.0490200i
$78$		0			0
$79$	−2.40379	+	4.16348i	−0.270447	+	0.468428i	−0.968976	−	0.247153i	$-0.920505\pi$
$79$	−2.40379	+	4.16348i	−0.270447	+	0.468428i	0.698529	+	0.715582i	$0.253838\pi$
$80$	−3.92064	+	5.93202i	−0.438341	+	0.663220i
$81$		0			0
$82$	2.05218	−	3.55447i	0.226625	−	0.392526i
$83$			12.9498i			1.42143i	0.703481	+	0.710714i	$0.251628\pi$
$83$			12.9498i			1.42143i	−0.703481	+	0.710714i	$0.748372\pi$
$84$		0			0
$85$	−0.793583	+	0.396326i	−0.0860762	+	0.0429876i
$86$	−1.11513	−	0.643818i	−0.120247	−	0.0694247i
$87$		0			0
$88$	−1.36877	+	0.790258i	−0.145911	+	0.0842418i
$89$	6.38611	−	11.0611i	0.676926	−	1.17247i	−0.298975	−	0.954261i	$-0.596645\pi$
$89$	6.38611	−	11.0611i	0.676926	−	1.17247i	0.975902	−	0.218210i	$-0.0700218\pi$
$90$		0			0
$91$	13.6121	+	5.35039i	1.42694	+	0.560873i
$92$	6.74074			0.702771
$93$		0			0
$94$	1.57713	−	0.910559i	0.162669	−	0.0939170i
$95$	−8.63722	−	5.70858i	−0.886160	−	0.585688i
$96$		0			0
$97$	4.84872			0.492313			0.246156	−	0.969230i	$-0.420832\pi$
$97$	4.84872			0.492313			0.246156	+	0.969230i	$0.420832\pi$
$98$	−2.50304	+	0.769285i	−0.252845	+	0.0777095i
$99$		0			0
$100$	3.64532	+	8.55613i	0.364532	+	0.855613i
$101$	9.38987	+	16.2637i	0.934327	+	1.61830i	0.775829	+	0.630943i	$0.217332\pi$
$101$	9.38987	+	16.2637i	0.934327	+	1.61830i	0.158498	+	0.987359i	$0.449335\pi$
$102$		0			0
$103$	7.20360	−	12.4770i	0.709792	−	1.22940i	−0.255142	−	0.966904i	$-0.582122\pi$
$103$	7.20360	−	12.4770i	0.709792	−	1.22940i	0.964934	−	0.262492i	$-0.0845443\pi$
$104$	−7.98245			−0.782744
$105$		0			0
$106$	−1.93774			−0.188210
$107$	−6.79378	+	11.7672i	−0.656779	+	1.13758i	0.324665	+	0.945829i	$0.394748\pi$
$107$	−6.79378	+	11.7672i	−0.656779	+	1.13758i	−0.981445	+	0.191746i	$0.938585\pi$
$108$		0			0
$109$	3.09325	+	5.35766i	0.296279	+	0.513171i	0.975282	−	0.220965i	$-0.0709207\pi$
$109$	3.09325	+	5.35766i	0.296279	+	0.513171i	−0.679002	+	0.734136i	$0.737587\pi$
$110$	−0.0552855	+	0.913895i	−0.00527127	+	0.0871365i
$111$		0			0
$112$	−6.58050	+	5.24228i	−0.621799	+	0.495349i
$113$	−6.06737			−0.570770			−0.285385	−	0.958413i	$-0.592121\pi$
$113$	−6.06737			−0.570770			−0.285385	+	0.958413i	$0.592121\pi$
$114$		0			0
$115$	4.46805	−	6.76026i	0.416648	−	0.630398i
$116$	11.5864	−	6.68942i	1.07577	−	0.621097i
$117$		0			0
$118$	3.07663			0.283227
$119$	−1.03792	+	0.155899i	−0.0951462	+	0.0142913i
$120$		0			0
$121$	−4.90098	+	8.48875i	−0.445544	+	0.771704i
$122$	1.08903	−	0.628754i	0.0985965	−	0.0569247i
$123$		0			0
$124$	−6.43981	−	3.71803i	−0.578312	−	0.333889i
$125$	10.9972	+	2.01549i	0.983617	+	0.180271i
$126$		0			0
$127$		−	1.41561i		−	0.125615i	−0.998026	−	0.0628076i	$-0.979995\pi$
$127$		−	1.41561i		−	0.125615i	0.998026	−	0.0628076i	$-0.0200055\pi$
$128$	4.98181	−	8.62875i	0.440334	−	0.762681i
$129$		0			0
$130$	−2.54964	+	3.85767i	−0.223619	+	0.338340i
$131$	−6.05433	+	10.4864i	−0.528969	+	0.916201i	0.470460	+	0.882421i	$0.344088\pi$
$131$	−6.05433	+	10.4864i	−0.528969	+	0.916201i	−0.999429	+	0.0337801i	$0.989245\pi$
$132$		0			0
$133$	−7.63293	−	9.58143i	−0.661859	−	0.830815i
$134$		−	1.81688i		−	0.156955i
$135$		0			0
$136$	0.496084	−	0.286414i	0.0425388	−	0.0245598i
$137$	4.09062	+	7.08516i	0.349485	+	0.605326i	0.986158	−	0.165808i	$-0.0530231\pi$
$137$	4.09062	+	7.08516i	0.349485	+	0.605326i	−0.636673	+	0.771134i	$0.719690\pi$
$138$		0			0
$139$		−	10.6624i		−	0.904375i	−0.891923	−	0.452188i	$-0.850644\pi$
$139$		−	10.6624i		−	0.904375i	0.891923	−	0.452188i	$-0.149356\pi$
$140$	0.974447	+	10.9610i	0.0823558	+	0.926377i
$141$		0			0
$142$	−0.920237	−	0.531299i	−0.0772246	−	0.0445856i
$143$	5.24009	−	3.02537i	0.438198	−	0.252994i
$144$		0			0
$145$	0.971176	−	16.0540i	0.0806518	−	1.33321i
$146$	0.267287			0.0221209
$147$		0			0
$148$			0.726740i			0.0597377i
$149$	−20.4554	−	11.8100i	−1.67578	−	0.967509i	−0.964305	−	0.264793i	$-0.914696\pi$
$149$	−20.4554	−	11.8100i	−1.67578	−	0.967509i	−0.711470	−	0.702716i	$-0.751970\pi$
$150$		0			0
$151$	−6.70250	−	11.6091i	−0.545441	−	0.944732i	−0.998579	−	0.0532917i	$-0.983029\pi$
$151$	−6.70250	−	11.6091i	−0.545441	−	0.944732i	0.453138	−	0.891441i	$-0.350305\pi$
$152$	5.79009	+	3.34291i	0.469638	+	0.271146i
$153$		0			0
$154$	−0.396294	+	1.00822i	−0.0319343	+	0.0812451i
$155$	−7.99737	+	3.99399i	−0.642365	+	0.320805i
$156$		0			0
$157$	−7.11710	−	12.3272i	−0.568006	−	0.983816i	−0.996763	−	0.0803959i	$-0.974382\pi$
$157$	−7.11710	−	12.3272i	−0.568006	−	0.983816i	0.428757	−	0.903420i	$-0.358952\pi$
$158$	−0.899219	−	1.55749i	−0.0715381	−	0.123908i
$159$		0			0
$160$	−4.07372	−	8.15700i	−0.322055	−	0.644868i
$161$	7.49928	−	5.97421i	0.591026	−	0.470834i
$162$		0			0
$163$	−19.8150	−	11.4402i	−1.55203	−	0.896064i	−0.997977	−	0.0635808i	$-0.979748\pi$
$163$	−19.8150	−	11.4402i	−1.55203	−	0.896064i	−0.554051	−	0.832483i	$-0.686919\pi$
$164$	−10.2040	−	17.6739i	−0.796802	−	1.38010i
$165$		0			0
$166$	−4.19531	−	2.42216i	−0.325619	−	0.187996i
$167$		−	13.9243i		−	1.07750i	−0.842466	−	0.538749i	$-0.818897\pi$
$167$		−	13.9243i		−	1.07750i	0.842466	−	0.538749i	$-0.181103\pi$
$168$		0			0
$169$	17.5594			1.35073
$170$	0.0200372	−	0.331224i	0.00153678	−	0.0254037i
$171$		0			0
$172$	−5.54474	+	3.20126i	−0.422783	+	0.244094i
$173$	−17.3793	−	10.0339i	−1.32132	−	0.762865i	−0.337382	−	0.941368i	$-0.609541\pi$
$173$	−17.3793	−	10.0339i	−1.32132	−	0.762865i	−0.983939	+	0.178503i	$0.942875\pi$
$174$		0			0
$175$	11.6387	+	6.28817i	0.879802	+	0.475341i
$176$			3.48061i			0.262361i
$177$		0			0
$178$	2.38894	+	4.13777i	0.179059	+	0.310139i
$179$	−1.93844	+	1.11916i	−0.144886	+	0.0836501i	−0.570691	−	0.821165i	$-0.693324\pi$
$179$	−1.93844	+	1.11916i	−0.144886	+	0.0836501i	0.425805	+	0.904815i	$0.359991\pi$
$180$		0			0
$181$		−	4.19332i		−	0.311687i	−0.987782	−	0.155843i	$-0.950190\pi$
$181$		−	4.19332i		−	0.311687i	0.987782	−	0.155843i	$-0.0498095\pi$
$182$	−4.27938	+	3.40912i	−0.317209	+	0.252701i
$183$		0			0
$184$	−2.61646	+	4.53184i	−0.192888	+	0.334092i
$185$	0.728844	+	0.481714i	0.0535857	+	0.0354163i
$186$		0			0
$187$	−0.217103	+	0.376034i	−0.0158761	+	0.0274983i
$188$		−	9.05515i		−	0.660415i
$189$		0			0
$190$	3.46491	−	1.73042i	0.251371	−	0.125538i
$191$	5.82348	+	3.36219i	0.421372	+	0.243279i	0.695664	−	0.718367i	$-0.255110\pi$
$191$	5.82348	+	3.36219i	0.421372	+	0.243279i	−0.274292	+	0.961646i	$0.588444\pi$
$192$		0			0
$193$	2.64343	−	1.52618i	0.190278	−	0.109857i	−0.401835	−	0.915712i	$-0.631627\pi$
$193$	2.64343	−	1.52618i	0.190278	−	0.109857i	0.592113	+	0.805855i	$0.298294\pi$
$194$	−0.906915	+	1.57082i	−0.0651127	+	0.112779i
$195$		0			0
$196$	−2.91029	+	12.6910i	−0.207878	+	0.906501i
$197$	25.8426			1.84121			0.920606	−	0.390493i	$-0.127696\pi$
$197$	25.8426			1.84121			0.920606	+	0.390493i	$0.127696\pi$
$198$		0			0
$199$	14.9566	−	8.63522i	1.06025	−	0.612135i	0.134747	−	0.990880i	$-0.456978\pi$
$199$	14.9566	−	8.63522i	1.06025	−	0.612135i	0.925501	+	0.378745i	$0.123644\pi$
$200$	−7.16729	−	0.870346i	−0.506804	−	0.0615428i
$201$		0			0
$202$	−7.02521			−0.494292
$203$	6.96152	−	17.7110i	0.488603	−	1.24307i
$204$		0			0
$205$	−24.4888	−	1.48143i	−1.71037	−	0.103468i
$206$	2.69475	+	4.66745i	0.187752	+	0.325197i
$207$		0			0
$208$	−8.78947	+	15.2238i	−0.609440	+	1.05558i
$209$	−5.06788			−0.350553
$210$		0			0
$211$	23.0537			1.58708			0.793540	−	0.608518i	$-0.208236\pi$
$211$	23.0537			1.58708			0.793540	+	0.608518i	$0.208236\pi$
$212$	−4.81751	+	8.34417i	−0.330868	+	0.573080i
$213$		0			0
$214$	−2.54145	−	4.40191i	−0.173730	−	0.300909i
$215$	−0.464762	+	7.68273i	−0.0316965	+	0.523958i
$216$		0			0
$217$	−10.4597	+	1.57108i	−0.710052	+	0.106652i
$218$	−2.31427			−0.156742
$219$		0			0
$220$	3.79791	+	2.51015i	0.256055	+	0.169234i
$221$	−1.89917	+	1.09649i	−0.127752	+	0.0737577i
$222$		0			0
$223$	−18.2615			−1.22288			−0.611441	−	0.791290i	$-0.709410\pi$
$223$	−18.2615			−1.22288			−0.611441	+	0.791290i	$0.709410\pi$
$224$	−1.60244	−	10.6685i	−0.107068	−	0.712819i
$225$		0			0
$226$	1.13485	−	1.96562i	0.0754893	−	0.130751i
$227$	−8.75085	+	5.05231i	−0.580814	+	0.335333i	−0.761457	−	0.648216i	$-0.775516\pi$
$227$	−8.75085	+	5.05231i	−0.580814	+	0.335333i	0.180643	+	0.983549i	$0.442182\pi$
$228$		0			0
$229$	−19.3730	−	11.1850i	−1.28021	−	0.739128i	−0.303320	−	0.952889i	$-0.598095\pi$
$229$	−19.3730	−	11.1850i	−1.28021	−	0.739128i	−0.976886	+	0.213761i	$0.931429\pi$
$230$	1.35438	+	2.71195i	0.0893055	+	0.178821i
$231$		0			0
$232$			10.3862i			0.681885i
$233$	−11.3370	+	19.6362i	−0.742709	+	1.28641i	0.208549	+	0.978012i	$0.433126\pi$
$233$	−11.3370	+	19.6362i	−0.742709	+	1.28641i	−0.951258	+	0.308398i	$0.900207\pi$
$234$		0			0
$235$	−9.08137	−	6.00214i	−0.592403	−	0.391536i
$236$	7.64897	−	13.2484i	0.497906	−	0.862398i
$237$		0			0
$238$	0.143629	−	0.365412i	0.00931010	−	0.0236861i
$239$		−	16.5614i		−	1.07127i	−0.844451	−	0.535633i	$-0.820073\pi$
$239$		−	16.5614i		−	1.07127i	0.844451	−	0.535633i	$-0.179927\pi$
$240$		0			0
$241$	21.9504	−	12.6731i	1.41395	−	0.816344i	0.418192	−	0.908359i	$-0.362664\pi$
$241$	21.9504	−	12.6731i	1.41395	−	0.816344i	0.995758	+	0.0920147i	$0.0293307\pi$
$242$	−1.83338	−	3.17551i	−0.117854	−	0.204129i
$243$		0			0
$244$		−	6.25271i		−	0.400289i
$245$	10.7987	+	11.3309i	0.689903	+	0.723902i
$246$		0			0
$247$	−22.1664	−	12.7978i	−1.41041	−	0.814302i
$248$	4.99931	−	2.88635i	0.317456	−	0.183284i
$249$		0			0
$250$	−2.70989	+	3.18573i	−0.171388	+	0.201483i
$251$	16.2074			1.02300			0.511501	−	0.859283i	$-0.329090\pi$
$251$	16.2074			1.02300			0.511501	+	0.859283i	$0.329090\pi$
$252$		0			0
$253$		−	3.96658i		−	0.249377i
$254$	0.458611	+	0.264779i	0.0287758	+	0.0166137i
$255$		0			0
$256$	−2.97093	−	5.14581i	−0.185683	−	0.321613i
$257$	4.22870	+	2.44144i	0.263779	+	0.152293i	0.626057	−	0.779777i	$-0.284668\pi$
$257$	4.22870	+	2.44144i	0.263779	+	0.152293i	−0.362278	+	0.932070i	$0.618001\pi$
$258$		0			0
$259$	0.644098	+	0.808521i	0.0400223	+	0.0502390i
$260$	10.2729	+	20.5699i	0.637096	+	1.27569i
$261$		0			0
$262$	−2.26483	−	3.92280i	−0.139922	−	0.242351i
$263$	7.30925	+	12.6600i	0.450707	+	0.780648i	0.998430	−	0.0560119i	$-0.0178385\pi$
$263$	7.30925	+	12.6600i	0.450707	+	0.780648i	−0.547723	+	0.836660i	$0.684505\pi$
$264$		0			0
$265$	5.17508	+	10.3623i	0.317903	+	0.636553i
$266$	4.53174	−	0.680682i	0.277859	−	0.0417353i
$267$		0			0
$268$	−7.82374	−	4.51704i	−0.477911	−	0.275922i
$269$	−6.53241	−	11.3145i	−0.398288	−	0.689856i	0.595227	−	0.803558i	$-0.297062\pi$
$269$	−6.53241	−	11.3145i	−0.398288	−	0.689856i	−0.993515	+	0.113702i	$0.963729\pi$
$270$		0			0
$271$	−22.4053	−	12.9357i	−1.36102	−	0.785787i	−0.371264	−	0.928528i	$-0.621075\pi$
$271$	−22.4053	−	12.9357i	−1.36102	−	0.785787i	−0.989760	+	0.142740i	$0.954409\pi$
$272$		−	1.26148i		−	0.0764885i
$273$		0			0
$274$	−3.06047			−0.184890
$275$	5.03484	−	2.14508i	0.303612	−	0.129353i
$276$		0			0
$277$	28.3287	−	16.3556i	1.70210	−	0.982710i	0.758478	−	0.651699i	$-0.225943\pi$
$277$	28.3287	−	16.3556i	1.70210	−	0.982710i	0.943627	−	0.331011i	$-0.107390\pi$
$278$	3.45427	+	1.99432i	0.207173	+	0.119612i
$279$		0			0
$280$	−7.74741	−	3.59947i	−0.462996	−	0.215109i
$281$			21.1295i			1.26048i	0.776400	+	0.630241i	$0.217044\pi$
$281$			21.1295i			1.26048i	−0.776400	+	0.630241i	$0.782956\pi$
$282$		0			0
$283$	2.64369	+	4.57901i	0.157151	+	0.272194i	0.933840	−	0.357690i	$-0.116436\pi$
$283$	2.64369	+	4.57901i	0.157151	+	0.272194i	−0.776689	+	0.629884i	$0.783102\pi$
$284$	−4.57570	+	2.64178i	−0.271518	+	0.156761i
$285$		0			0
$286$			2.26348i			0.133843i
$287$	−27.0164	−	10.6191i	−1.59473	−	0.626826i
$288$		0			0
$289$	−8.42132	+	14.5861i	−0.495371	+	0.858009i
$290$	5.01931	+	3.31740i	0.294744	+	0.194805i
$291$		0			0
$292$	0.664517	−	1.15098i	0.0388879	−	0.0673558i
$293$			19.2536i			1.12481i	0.826862	+	0.562405i	$0.190124\pi$
$293$			19.2536i			1.12481i	−0.826862	+	0.562405i	$0.809876\pi$
$294$		0			0
$295$	−8.21671	−	16.4527i	−0.478395	−	0.957915i
$296$	−0.488592	−	0.282089i	−0.0283988	−	0.0163961i
$297$		0			0
$298$	7.65206	−	4.41792i	0.443272	−	0.255923i
$299$	10.0167	−	17.3494i	0.579279	−	1.00334i
$300$		0			0
$301$	−3.33147	+	8.47572i	−0.192023	+	0.488532i
$302$	5.01460			0.288558
$303$		0			0
$304$	12.7509	−	7.36175i	0.731316	−	0.422225i
$305$	−6.27082	−	4.14456i	−0.359066	−	0.237317i
$306$		0			0
$307$	−7.05816			−0.402831			−0.201415	−	0.979506i	$-0.564554\pi$
$307$	−7.05816			−0.402831			−0.201415	+	0.979506i	$0.564554\pi$
$308$	3.35631	+	4.21310i	0.191244	+	0.240063i
$309$		0			0
$310$	0.201926	−	3.33793i	0.0114686	−	0.189582i
$311$	0.923059	+	1.59878i	0.0523418	+	0.0906587i	0.891009	−	0.453985i	$-0.149998\pi$
$311$	0.923059	+	1.59878i	0.0523418	+	0.0906587i	−0.838667	+	0.544644i	$0.816665\pi$
$312$		0			0
$313$	8.91811	−	15.4466i	0.504081	−	0.873094i	−0.495908	−	0.868375i	$-0.665165\pi$
$313$	8.91811	−	15.4466i	0.504081	−	0.873094i	0.999989	−	0.00471916i	$-0.00150216\pi$
$314$	5.32479			0.300495
$315$		0			0
$316$	−8.94238			−0.503048
$317$	9.11366	−	15.7853i	0.511874	−	0.886592i	−0.488031	−	0.872826i	$-0.662285\pi$
$317$	9.11366	−	15.7853i	0.511874	−	0.886592i	0.999905	−	0.0137658i	$-0.00438193\pi$
$318$		0			0
$319$	−3.93638	−	6.81801i	−0.220395	−	0.381735i
$320$	−10.7907	−	0.652774i	−0.603216	−	0.0364912i
$321$		0			0
$322$	0.532762	+	3.54695i	0.0296897	+	0.197664i
$323$	1.83676			0.102200
$324$		0			0
$325$	27.4387	+	3.33197i	1.52203	+	0.184824i
$326$	7.41247	−	4.27959i	0.410539	−	0.237025i
$327$		0			0
$328$	15.8431			0.874786
$329$	−8.02543	−	10.0741i	−0.442457	−	0.555405i
$330$		0			0
$331$	−7.47999	+	12.9557i	−0.411138	+	0.712111i	−0.995014	−	0.0997311i	$-0.968202\pi$
$331$	−7.47999	+	12.9557i	−0.411138	+	0.712111i	0.583877	+	0.811842i	$0.301535\pi$
$332$	−20.8604	+	12.0437i	−1.14486	+	0.660986i
$333$		0			0
$334$	4.51102	+	2.60444i	0.246832	+	0.142509i
$335$	−9.71602	+	4.85231i	−0.530843	+	0.265110i
$336$		0			0
$337$		−	2.43956i		−	0.132891i	−0.997790	−	0.0664457i	$-0.978834\pi$
$337$		−	2.43956i		−	0.132891i	0.997790	−	0.0664457i	$-0.0211659\pi$
$338$	−3.28435	+	5.68867i	−0.178645	+	0.309423i
$339$		0			0
$340$	−1.37648	−	0.909757i	−0.0746502	−	0.0493385i
$341$	−2.18787	+	3.78950i	−0.118480	+	0.205213i
$342$		0			0
$343$	8.01005	+	16.6985i	0.432502	+	0.901633i
$344$		−	4.97036i		−	0.267984i
$345$		0			0
$346$	6.50131	−	3.75353i	0.349513	−	0.201791i
$347$	1.22403	+	2.12008i	0.0657093	+	0.113812i	0.897008	−	0.442013i	$-0.145736\pi$
$347$	1.22403	+	2.12008i	0.0657093	+	0.113812i	−0.831299	+	0.555825i	$0.812402\pi$
$348$		0			0
$349$			15.2047i			0.813889i	0.913453	+	0.406945i	$0.133406\pi$
$349$			15.2047i			0.813889i	−0.913453	+	0.406945i	$0.866594\pi$
$350$	−4.21408	+	2.59439i	−0.225252	+	0.138676i
$351$		0			0
$352$	−3.86513	−	2.23154i	−0.206012	−	0.118941i
$353$	22.4672	−	12.9714i	1.19581	−	0.690400i	0.236190	−	0.971707i	$-0.424101\pi$
$353$	22.4672	−	12.9714i	1.19581	−	0.690400i	0.959618	+	0.281307i	$0.0907678\pi$
$354$		0			0
$355$	−0.383536	+	6.34003i	−0.0203560	+	0.336494i
$356$	23.7571			1.25912
$357$		0			0
$358$		−	0.837322i		−	0.0442538i
$359$	−27.7489	−	16.0208i	−1.46453	−	0.845546i	−0.465313	−	0.885146i	$-0.654058\pi$
$359$	−27.7489	−	16.0208i	−1.46453	−	0.845546i	−0.999216	+	0.0396002i	$0.987392\pi$
$360$		0			0
$361$	1.21895	+	2.11128i	0.0641553	+	0.111120i
$362$	1.35849	+	0.784327i	0.0714009	+	0.0412233i
$363$		0			0
$364$	4.04095	+	26.9032i	0.211803	+	1.41011i
$365$	−0.713840	−	1.42936i	−0.0373641	−	0.0748160i
$366$		0			0
$367$	14.6515	+	25.3771i	0.764800	+	1.32467i	0.940352	+	0.340203i	$0.110496\pi$
$367$	14.6515	+	25.3771i	0.764800	+	1.32467i	−0.175552	+	0.984470i	$0.556171\pi$
$368$	5.76197	+	9.98002i	0.300363	+	0.520244i
$369$		0			0
$370$	−0.292384	+	0.146020i	−0.0152003	+	0.00759124i
$371$	2.03568	+	13.5528i	0.105687	+	0.703628i
$372$		0			0
$373$	14.6505	+	8.45847i	0.758574	+	0.437963i	0.828784	−	0.559569i	$-0.189033\pi$
$373$	14.6505	+	8.45847i	0.758574	+	0.437963i	−0.0702095	+	0.997532i	$0.522367\pi$
$374$	−0.0812148	−	0.140668i	−0.00419952	−	0.00727378i
$375$		0			0
$376$	6.08784	+	3.51481i	0.313956	+	0.181263i
$377$		−	39.7616i		−	2.04783i
$378$		0			0
$379$	11.5336			0.592443			0.296222	−	0.955119i	$-0.404273\pi$
$379$	11.5336			0.592443			0.296222	+	0.955119i	$0.404273\pi$
$380$	1.16285	−	19.2225i	0.0596531	−	0.986094i
$381$		0			0
$382$	−2.17847	+	1.25774i	−0.111460	+	0.0643516i
$383$	10.4841	+	6.05301i	0.535714	+	0.309294i	0.743340	−	0.668914i	$-0.233240\pi$
$383$	10.4841	+	6.05301i	0.535714	+	0.309294i	−0.207626	+	0.978208i	$0.566574\pi$
$384$		0			0
$385$	6.45000	−	0.573411i	0.328722	−	0.0292237i
$386$			1.14184i			0.0581182i
$387$		0			0
$388$	4.50946	+	7.81061i	0.228933	+	0.396524i
$389$	−5.80333	+	3.35055i	−0.294240	+	0.169880i	−0.639853	−	0.768498i	$-0.721005\pi$
$389$	−5.80333	+	3.35055i	−0.294240	+	0.169880i	0.345612	+	0.938377i	$0.387671\pi$
$390$		0			0
$391$			1.43761i			0.0727031i
$392$	−7.40260	−	6.88270i	−0.373888	−	0.347629i
$393$		0			0
$394$	−4.83366	+	8.37215i	−0.243516	+	0.421783i
$395$	−5.92739	+	8.96828i	−0.298239	+	0.451243i
$396$		0			0
$397$	12.4676	−	21.5945i	0.625732	−	1.08380i	−0.362667	−	0.931919i	$-0.618134\pi$
$397$	12.4676	−	21.5945i	0.625732	−	1.08380i	0.988399	−	0.151880i	$-0.0485328\pi$
$398$			6.46060i			0.323841i
$399$		0			0
$400$	−9.55179	+	12.7108i	−0.477589	+	0.635541i
$401$	14.6397	+	8.45226i	0.731074	+	0.422086i	0.818815	−	0.574058i	$-0.194631\pi$
$401$	14.6397	+	8.45226i	0.731074	+	0.422086i	−0.0877410	+	0.996143i	$0.527965\pi$
$402$		0			0
$403$	−19.1390	+	11.0499i	−0.953381	+	0.550435i
$404$	−17.4657	+	30.2515i	−0.868953	+	1.50507i
$405$		0			0
$406$	4.43569	+	5.56801i	0.220139	+	0.276336i
$407$	0.427649			0.0211978
$408$		0			0
$409$	18.4393	−	10.6459i	0.911765	−	0.526408i	0.0307664	−	0.999527i	$-0.490205\pi$
$409$	18.4393	−	10.6459i	0.911765	−	0.526408i	0.880999	+	0.473119i	$0.156872\pi$
$410$	5.06037	−	7.65645i	0.249914	−	0.378125i
$411$		0			0
$412$	26.7983			1.32026
$413$	−3.23213	−	21.5184i	−0.159043	−	1.05885i
$414$		0			0
$415$	−1.74852	+	28.9038i	−0.0858314	+	1.41883i
$416$	−11.2705	−	19.5210i	−0.552579	−	0.957096i
$417$		0			0
$418$	0.947907	−	1.64182i	0.0463637	−	0.0803042i
$419$	4.84467			0.236678			0.118339	−	0.992973i	$-0.462243\pi$
$419$	4.84467			0.236678			0.118339	+	0.992973i	$0.462243\pi$
$420$		0			0
$421$	10.3110			0.502527			0.251264	−	0.967919i	$-0.419154\pi$
$421$	10.3110			0.502527			0.251264	+	0.967919i	$0.419154\pi$
$422$	−4.31201	+	7.46862i	−0.209905	+	0.363567i
$423$		0			0
$424$	−3.73989	−	6.47768i	−0.181625	−	0.314584i
$425$	−1.82478	+	0.777443i	−0.0885149	+	0.0377115i
$426$		0			0
$427$	−5.54168	−	6.95633i	−0.268181	−	0.336641i
$428$	−25.2737			−1.22165
$429$		0			0
$430$	−2.40202	−	1.58756i	−0.115836	−	0.0765590i
$431$	−33.9307	+	19.5899i	−1.63439	+	0.943613i	−0.651667	+	0.758505i	$0.725930\pi$
$431$	−33.9307	+	19.5899i	−1.63439	+	0.943613i	−0.982718	+	0.185108i	$0.940736\pi$
$432$		0			0
$433$	15.1854			0.729763			0.364881	−	0.931054i	$-0.381110\pi$
$433$	15.1854			0.729763			0.364881	+	0.931054i	$0.381110\pi$
$434$	1.44743	−	3.68246i	0.0694789	−	0.176764i
$435$		0			0
$436$	−5.75363	+	9.96558i	−0.275549	+	0.477265i
$437$	−14.5312	+	8.38961i	−0.695123	+	0.401329i
$438$		0			0
$439$	−22.5340	−	13.0100i	−1.07549	−	0.620935i	−0.145814	−	0.989312i	$-0.546580\pi$
$439$	−22.5340	−	13.0100i	−1.07549	−	0.620935i	−0.929676	+	0.368377i	$0.879913\pi$
$440$	−3.16177	+	1.57903i	−0.150732	+	0.0752774i
$441$		0			0
$442$		−	0.820357i		−	0.0390204i
$443$	−1.42237	+	2.46361i	−0.0675787	+	0.117050i	−0.897835	−	0.440332i	$-0.854861\pi$
$443$	−1.42237	+	2.46361i	−0.0675787	+	0.117050i	0.830256	+	0.557382i	$0.188194\pi$
$444$		0			0
$445$	15.7472	−	23.8259i	0.746490	−	1.12946i
$446$	3.41567	−	5.91612i	0.161737	−	0.280137i
$447$		0			0
$448$	−11.9044	−	4.67917i	−0.562432	−	0.221070i
$449$			5.30598i			0.250405i	0.992131	+	0.125202i	$0.0399580\pi$
$449$			5.30598i			0.250405i	−0.992131	+	0.125202i	$0.960042\pi$
$450$		0			0
$451$	−10.4002	+	6.00455i	−0.489726	+	0.282743i
$452$	−5.64284	−	9.77368i	−0.265417	−	0.459715i
$453$		0			0
$454$		−	3.77998i		−	0.177403i
$455$	29.6596	+	13.7799i	1.39046	+	0.646014i
$456$		0			0
$457$	31.1234	+	17.9691i	1.45589	+	0.840560i	0.998806	−	0.0488621i	$-0.0155595\pi$
$457$	31.1234	+	17.9691i	1.45589	+	0.840560i	0.457087	+	0.889422i	$0.348893\pi$
$458$	7.24715	−	4.18414i	0.338637	−	0.195512i
$459$		0			0
$460$	15.0453	+	0.910153i	0.701489	+	0.0424361i
$461$	−14.1168			−0.657485			−0.328743	−	0.944420i	$-0.606625\pi$
$461$	−14.1168			−0.657485			−0.328743	+	0.944420i	$0.606625\pi$
$462$		0			0
$463$			17.9693i			0.835103i	0.908653	+	0.417552i	$0.137112\pi$
$463$			17.9693i			0.835103i	−0.908653	+	0.417552i	$0.862888\pi$
$464$	19.8081	+	11.4362i	0.919567	+	0.530912i
$465$		0			0
$466$	−4.24098	−	7.34559i	−0.196460	−	0.340278i
$467$	13.3901	+	7.73079i	0.619621	+	0.357738i	0.776721	−	0.629844i	$-0.216881\pi$
$467$	13.3901	+	7.73079i	0.619621	+	0.357738i	−0.157100	+	0.987583i	$0.550215\pi$
$468$		0			0
$469$	−12.7075	+	1.90871i	−0.586779	+	0.0881361i
$470$	3.64309	−	1.81941i	0.168043	−	0.0839230i
$471$		0			0
$472$	5.93799	+	10.2849i	0.273318	+	0.473401i
$473$	1.88377	+	3.26279i	0.0866161	+	0.150023i
$474$		0			0
$475$	−18.5074	−	13.9077i	−0.849177	−	0.638130i
$476$	−1.21643	−	1.52696i	−0.0557551	−	0.0699880i
$477$		0			0
$478$	5.36533	+	3.09767i	0.245404	+	0.141684i
$479$	11.6425	+	20.1654i	0.531959	+	0.921381i	0.999304	+	0.0373055i	$0.0118775\pi$
$479$	11.6425	+	20.1654i	0.531959	+	0.921381i	−0.467344	+	0.884075i	$0.654789\pi$
$480$		0			0
$481$	1.87049	+	1.07993i	0.0852870	+	0.0492405i
$482$			9.48159i			0.431875i
$483$		0			0
$484$	−18.2322			−0.828739
$485$	10.8223	+	0.654687i	0.491415	+	0.0297278i
$486$		0			0
$487$	−10.5395	+	6.08496i	−0.477588	+	0.275736i	−0.719411	−	0.694585i	$-0.755588\pi$
$487$	−10.5395	+	6.08496i	−0.477588	+	0.275736i	0.241823	+	0.970320i	$0.422255\pi$
$488$	4.20374	+	2.42703i	0.190294	+	0.109866i
$489$		0			0
$490$	−5.69063	+	1.37907i	−0.257076	+	0.0622999i
$491$		−	12.3672i		−	0.558126i	−0.960273	−	0.279063i	$-0.909976\pi$
$491$		−	12.3672i		−	0.558126i	0.960273	−	0.279063i	$-0.0900238\pi$
$492$		0			0
$493$	1.42667	+	2.47106i	0.0642538	+	0.111291i
$494$	8.29209	−	4.78744i	0.373079	−	0.215397i
$495$		0			0
$496$		−	12.7126i		−	0.570814i
$497$	−2.74924	+	6.99443i	−0.123320	+	0.313743i
$498$		0			0
$499$	−9.18807	+	15.9142i	−0.411314	+	0.712418i	−0.995034	−	0.0995380i	$-0.968264\pi$
$499$	−9.18807	+	15.9142i	−0.411314	+	0.712418i	0.583719	+	0.811956i	$0.301597\pi$
$500$	6.98103	+	19.5894i	0.312201	+	0.876063i
$501$		0			0
$502$	−3.03146	+	5.25065i	−0.135301	+	0.234348i
$503$		−	29.8980i		−	1.33308i	−0.745467	−	0.666542i	$-0.767774\pi$
$503$		−	29.8980i		−	1.33308i	0.745467	−	0.666542i	$-0.232226\pi$
$504$		0			0
$505$	18.7621	+	37.5683i	0.834903	+	1.67177i
$506$	1.28504	+	0.741917i	0.0571269	+	0.0329822i
$507$		0			0
$508$	2.28035	−	1.31656i	0.101174	−	0.0584130i
$509$	8.13717	−	14.0940i	0.360674	−	0.624705i	−0.627398	−	0.778699i	$-0.715880\pi$
$509$	8.13717	−	14.0940i	0.360674	−	0.624705i	0.988072	+	0.153993i	$0.0492134\pi$
$510$		0			0
$511$	−0.280797	−	1.86945i	−0.0124217	−	0.0826995i
$512$	22.1500			0.978901
$513$		0			0
$514$	−1.58189	+	0.913305i	−0.0697742	+	0.0402841i
$515$	17.7630	−	26.8759i	0.782732	−	1.18429i
$516$		0			0
$517$	−5.32849			−0.234347
$518$	−0.382407	+	0.0574387i	−0.0168020	+	0.00252371i
$519$		0			0
$520$	−17.8167	−	1.07781i	−0.781315	−	0.0472652i
$521$	−15.0293	−	26.0315i	−0.658446	−	1.14046i	−0.981018	−	0.193917i	$-0.937881\pi$
$521$	−15.0293	−	26.0315i	−0.658446	−	1.14046i	0.322572	−	0.946545i	$-0.395452\pi$
$522$		0			0
$523$	0.0349180	−	0.0604797i	0.00152686	−	0.00264459i	−0.865261	−	0.501322i	$-0.832847\pi$
$523$	0.0349180	−	0.0604797i	0.00152686	−	0.00264459i	0.866788	+	0.498677i	$0.166181\pi$
$524$	−22.5228			−0.983915
$525$		0			0
$526$	−5.46855			−0.238440
$527$	0.792951	−	1.37343i	0.0345415	−	0.0598276i
$528$		0			0
$529$	4.93354	+	8.54514i	0.214502	+	0.371528i
$530$	−4.32501	−	0.261638i	−0.187866	−	0.0113648i
$531$		0			0
$532$	8.33549	−	21.2066i	0.361389	−	0.919422i
$533$	−60.6524			−2.62715
$534$		0			0
$535$	−16.7525	+	25.3469i	−0.724272	+	1.09584i
$536$	6.07367	−	3.50663i	0.262342	−	0.151463i
$537$		0			0
$538$	4.88735			0.210708
$539$	7.46800	+	1.71255i	0.321669	+	0.0737650i
$540$		0			0
$541$	−16.4662	+	28.5203i	−0.707938	+	1.22618i	0.257683	+	0.966229i	$0.417041\pi$
$541$	−16.4662	+	28.5203i	−0.707938	+	1.22618i	−0.965621	+	0.259955i	$0.916292\pi$
$542$	8.38146	−	4.83904i	0.360015	−	0.207855i
$543$		0			0
$544$	1.40085	+	0.808778i	0.0600607	+	0.0346761i
$545$	6.18069	+	12.3759i	0.264752	+	0.530125i
$546$		0			0
$547$			18.8823i			0.807349i	0.914903	+	0.403674i	$0.132267\pi$
$547$			18.8823i			0.807349i	−0.914903	+	0.403674i	$0.867733\pi$
$548$	−7.60880	+	13.1788i	−0.325032	+	0.562972i
$549$		0			0
$550$	−0.246793	+	2.03234i	−0.0105233	+	0.0866592i
$551$	−16.6515	+	28.8412i	−0.709377	+	1.22868i
$552$		0			0
$553$	−9.94868	+	7.92549i	−0.423061	+	0.337026i
$554$			12.2367i			0.519888i
$555$		0			0
$556$	17.1757	−	9.91638i	0.728411	−	0.420548i
$557$	15.8907	+	27.5234i	0.673309	+	1.16620i	0.976960	+	0.213421i	$0.0684607\pi$
$557$	15.8907	+	27.5234i	0.673309	+	1.16620i	−0.303652	+	0.952783i	$0.598206\pi$
$558$		0			0
$559$			19.0281i			0.804805i
$560$	−15.3954	+	10.8122i	−0.650576	+	0.456898i
$561$		0			0
$562$	−6.84526	−	3.95211i	−0.288750	−	0.166710i
$563$	13.8669	−	8.00608i	0.584421	−	0.337416i	−0.178467	−	0.983946i	$-0.557114\pi$
$563$	13.8669	−	8.00608i	0.584421	−	0.337416i	0.762889	+	0.646530i	$0.223780\pi$
$564$		0			0
$565$	−13.5423	−	0.819232i	−0.569728	−	0.0344653i
$566$	−1.97793			−0.0831386
$567$		0			0
$568$		−	4.10170i		−	0.172103i
$569$	13.0585	+	7.53933i	0.547441	+	0.316065i	0.748089	−	0.663598i	$-0.230971\pi$
$569$	13.0585	+	7.53933i	0.547441	+	0.316065i	−0.200648	+	0.979663i	$0.564305\pi$
$570$		0			0
$571$	−8.49104	−	14.7069i	−0.355339	−	0.615465i	0.631837	−	0.775101i	$-0.282301\pi$
$571$	−8.49104	−	14.7069i	−0.355339	−	0.615465i	−0.987176	+	0.159636i	$0.948968\pi$
$572$	9.74688	+	5.62736i	0.407538	+	0.235292i
$573$		0			0
$574$	8.49344	−	6.76620i	0.354509	−	0.282416i
$575$	10.8854	−	14.4855i	0.453953	−	0.604088i
$576$		0			0
$577$	6.39492	+	11.0763i	0.266224	+	0.461114i	0.967884	−	0.251399i	$-0.0808906\pi$
$577$	6.39492	+	11.0763i	0.266224	+	0.461114i	−0.701660	+	0.712512i	$0.747557\pi$
$578$	−3.15028	−	5.45645i	−0.131034	−	0.226958i
$579$		0			0
$580$	26.7640	−	13.3663i	1.11131	−	0.555005i
$581$	−12.5336	+	31.8872i	−0.519982	+	1.32290i
$582$		0			0
$583$	4.91011	+	2.83485i	0.203356	+	0.117408i
$584$	0.515873	+	0.893518i	0.0213470	+	0.0369740i
$585$		0			0
$586$	−6.23753	−	3.60124i	−0.257670	−	0.148766i
$587$			31.0957i			1.28346i	0.766932	+	0.641728i	$0.221782\pi$
$587$			31.0957i			1.28346i	−0.766932	+	0.641728i	$0.778218\pi$
$588$		0			0
$589$	18.5100			0.762692
$590$	6.86700	+	0.415415i	0.282710	+	0.0171024i
$591$		0			0
$592$	−1.07598	+	0.621215i	−0.0442224	+	0.0255318i
$593$	−14.2922	−	8.25163i	−0.586912	−	0.338854i	0.176963	−	0.984217i	$-0.443373\pi$
$593$	−14.2922	−	8.25163i	−0.586912	−	0.338854i	−0.763876	+	0.645363i	$0.776706\pi$
$594$		0			0
$595$	−2.33768	+	0.207822i	−0.0958356	+	0.00851988i
$596$		−	43.9345i		−	1.79963i
$597$		0			0
$598$	3.74708	+	6.49013i	0.153229	+	0.265401i
$599$	37.2474	−	21.5048i	1.52189	−	0.878663i	0.522224	−	0.852808i	$-0.325103\pi$
$599$	37.2474	−	21.5048i	1.52189	−	0.878663i	0.999666	−	0.0258548i	$-0.00823076\pi$
$600$		0			0
$601$			22.2911i			0.909271i	0.890678	+	0.454636i	$0.150230\pi$
$601$			22.2911i			0.909271i	−0.890678	+	0.454636i	$0.849770\pi$
$602$	−2.12272	−	2.66460i	−0.0865157	−	0.108601i
$603$		0			0
$604$	12.4671	−	21.5936i	0.507277	−	0.878630i
$605$	−12.0851	+	18.2850i	−0.491329	+	0.743393i
$606$		0			0
$607$	2.75293	−	4.76821i	0.111738	−	0.193536i	−0.804733	−	0.593637i	$-0.797692\pi$
$607$	2.75293	−	4.76821i	0.111738	−	0.193536i	0.916471	+	0.400101i	$0.131025\pi$
$608$			18.8795i			0.765664i
$609$		0			0
$610$	2.51561	−	1.25633i	0.101854	−	0.0508672i
$611$	−23.3062	−	13.4559i	−0.942869	−	0.544366i
$612$		0			0
$613$	30.8640	−	17.8194i	1.24659	−	0.719717i	0.276159	−	0.961112i	$-0.410938\pi$
$613$	30.8640	−	17.8194i	1.24659	−	0.719717i	0.970427	+	0.241395i	$0.0776049\pi$
$614$	1.32017	−	2.28661i	0.0532779	−	0.0922800i
$615$		0			0
$616$	−4.13526	+	0.621130i	−0.166615	+	0.0250260i
$617$	12.9253			0.520352			0.260176	−	0.965561i	$-0.416219\pi$
$617$	12.9253			0.520352			0.260176	+	0.965561i	$0.416219\pi$
$618$		0			0
$619$	−27.2224	+	15.7168i	−1.09416	+	0.631713i	−0.934681	−	0.355489i	$-0.884314\pi$
$619$	−27.2224	+	15.7168i	−1.09416	+	0.631713i	−0.159478	+	0.987201i	$0.550981\pi$
$620$	−13.8716	−	9.16811i	−0.557096	−	0.368200i
$621$		0			0
$622$	−0.690603			−0.0276907
$623$	26.4305	−	21.0555i	1.05892	−	0.843572i
$624$		0			0
$625$	24.2734	+	5.98342i	0.970937	+	0.239337i
$626$	3.33612	+	5.77834i	0.133338	+	0.230949i
$627$		0			0
$628$	13.2382	−	22.9293i	0.528263	−	0.914979i
$629$	−0.154993			−0.00617998
$630$		0			0
$631$	−3.43480			−0.136737			−0.0683687	−	0.997660i	$-0.521779\pi$
$631$	−3.43480			−0.136737			−0.0683687	+	0.997660i	$0.521779\pi$
$632$	3.47104	−	6.01202i	0.138071	−	0.239145i
$633$		0			0
$634$	3.40928	+	5.90504i	0.135400	+	0.234519i
$635$	0.191140	−	3.15963i	0.00758515	−	0.125386i
$636$		0			0
$637$	28.3396	+	26.3492i	1.12285	+	1.04399i
$638$	2.94507			0.116597
$639$		0			0
$640$	12.2844	−	18.5866i	0.485584	−	0.734700i
$641$	−30.9544	+	17.8715i	−1.22262	+	0.705882i	−0.965476	−	0.260490i	$-0.916116\pi$
$641$	−30.9544	+	17.8715i	−1.22262	+	0.705882i	−0.257147	+	0.966372i	$0.582782\pi$
$642$		0			0
$643$	−32.9624			−1.29991			−0.649955	−	0.759973i	$-0.725212\pi$
$643$	−32.9624			−1.29991			−0.649955	+	0.759973i	$0.725212\pi$
$644$	16.5982	+	6.52410i	0.654060	+	0.257085i
$645$		0			0
$646$	−0.343551	+	0.595048i	−0.0135168	+	0.0234118i
$647$	−8.95584	+	5.17066i	−0.352090	+	0.203280i	−0.665606	−	0.746304i	$-0.731827\pi$
$647$	−8.95584	+	5.17066i	−0.352090	+	0.203280i	0.313515	+	0.949583i	$0.398493\pi$
$648$		0			0
$649$	−7.79600	−	4.50102i	−0.306020	−	0.176681i
$650$	−6.21164	+	8.26601i	−0.243641	+	0.324220i
$651$		0			0
$652$		−	42.5588i		−	1.66673i
$653$	10.5884	−	18.3396i	0.414356	−	0.717685i	−0.581005	−	0.813900i	$-0.697340\pi$
$653$	10.5884	−	18.3396i	0.414356	−	0.717685i	0.995361	+	0.0962151i	$0.0306737\pi$
$654$		0			0
$655$	−14.9291	+	22.5881i	−0.583328	+	0.882588i
$656$	17.4448	−	30.2152i	0.681104	−	1.17971i
$657$		0			0
$658$	4.76478	−	0.715684i	0.185750	−	0.0279003i
$659$		−	2.65393i		−	0.103382i	−0.998663	−	0.0516912i	$-0.983539\pi$
$659$		−	2.65393i		−	0.103382i	0.998663	−	0.0516912i	$-0.0164612\pi$
$660$		0			0
$661$	−0.456098	+	0.263328i	−0.0177402	+	0.0102423i	−0.508844	−	0.860859i	$-0.669927\pi$
$661$	−0.456098	+	0.263328i	−0.0177402	+	0.0102423i	0.491104	+	0.871101i	$0.336594\pi$
$662$	−2.79815	−	4.84653i	−0.108753	−	0.188366i
$663$		0			0
$664$		−	18.6994i		−	0.725677i
$665$	−15.7429	−	22.4162i	−0.610483	−	0.869265i
$666$		0			0
$667$	−22.5737	−	13.0329i	−0.874057	−	0.504637i
$668$	22.4302	−	12.9501i	0.867850	−	0.501053i
$669$		0			0
$670$	0.245320	−	4.05525i	0.00947753	−	0.156668i
$671$	−3.67940			−0.142042
$672$		0			0
$673$			0.728879i			0.0280962i	0.999901	+	0.0140481i	$0.00447180\pi$
$673$			0.728879i			0.0280962i	−0.999901	+	0.0140481i	$0.995528\pi$
$674$	0.790336	+	0.456301i	0.0304426	+	0.0175761i
$675$		0			0
$676$	16.3308	+	28.2858i	0.628108	+	1.08791i
$677$	−9.62828	−	5.55889i	−0.370045	−	0.213646i	0.303433	−	0.952853i	$-0.401867\pi$
$677$	−9.62828	−	5.55889i	−0.370045	−	0.213646i	−0.673478	+	0.739207i	$0.735200\pi$
$678$		0			0
$679$	11.9393	+	4.69288i	0.458189	+	0.180096i
$680$	1.14593	−	0.572290i	0.0439442	−	0.0219463i
$681$		0			0
$682$	−0.818446	−	1.41759i	−0.0313399	−	0.0542824i
$683$	17.7885	+	30.8105i	0.680656	+	1.17893i	0.974781	+	0.223164i	$0.0716387\pi$
$683$	17.7885	+	30.8105i	0.680656	+	1.17893i	−0.294124	+	0.955767i	$0.595028\pi$
$684$		0			0
$685$	8.17356	+	16.3663i	0.312296	+	0.625325i
$686$	−6.90796	−	0.528332i	−0.263747	−	0.0201718i
$687$		0			0
$688$	−9.47926	−	5.47285i	−0.361393	−	0.208651i
$689$	14.3175	+	24.7987i	0.545454	+	0.944755i
$690$		0			0
$691$	−8.11870	−	4.68733i	−0.308850	−	0.178315i	0.337562	−	0.941303i	$-0.390398\pi$
$691$	−8.11870	−	4.68733i	−0.308850	−	0.178315i	−0.646412	+	0.762989i	$0.723731\pi$
$692$		−	37.3274i		−	1.41898i
$693$		0			0
$694$	−0.915780			−0.0347625
$695$	1.43967	−	23.7984i	0.0546098	−	0.902725i
$696$		0			0
$697$	3.76935	−	2.17624i	0.142774	−	0.0824308i
$698$	−4.92582	−	2.84392i	−0.186445	−	0.107644i
$699$		0			0
$700$	0.694965	+	24.5965i	0.0262672	+	0.929659i
$701$			16.3197i			0.616388i	0.951324	+	0.308194i	$0.0997246\pi$
$701$			16.3197i			0.616388i	−0.951324	+	0.308194i	$0.900275\pi$
$702$		0			0
$703$	−0.904510	−	1.56666i	−0.0341142	−	0.0590876i
$704$	−4.58271	+	2.64583i	−0.172717	+	0.0997183i
$705$		0			0
$706$			9.70483i			0.365246i
$707$	7.38028	+	49.1354i	0.277564	+	1.84793i
$708$		0			0
$709$	18.4461	−	31.9496i	0.692758	−	1.19989i	−0.278173	−	0.960531i	$-0.589729\pi$
$709$	18.4461	−	31.9496i	0.692758	−	1.19989i	0.970931	−	0.239361i	$-0.0769379\pi$
$710$	−1.98222	−	1.31011i	−0.0743914	−	0.0491674i
$711$		0			0
$712$	−9.22147	+	15.9721i	−0.345589	+	0.598578i
$713$			14.4876i			0.542565i
$714$		0			0
$715$	12.1043	−	6.04505i	0.452675	−	0.226072i
$716$	−3.60563	−	2.08171i	−0.134749	−	0.0777971i
$717$		0			0
$718$	10.3804	−	5.99313i	0.387394	−	0.223662i
$719$	1.48159	−	2.56618i	0.0552538	−	0.0957024i	−0.837076	−	0.547087i	$-0.815737\pi$
$719$	1.48159	−	2.56618i	0.0552538	−	0.0957024i	0.892329	+	0.451385i	$0.149070\pi$
$720$		0			0
$721$	29.8139	−	23.7509i	1.11033	−	0.884529i
$722$	−0.911981			−0.0339404
$723$		0			0
$724$	6.75484	−	3.89991i	0.251042	−	0.144939i
$725$	4.33531	−	35.7012i	0.161009	−	1.32591i
$726$		0			0
$727$	31.9409			1.18462			0.592312	−	0.805709i	$-0.298215\pi$
$727$	31.9409			1.18462			0.592312	+	0.805709i	$0.298215\pi$
$728$	−19.6557	−	7.72590i	−0.728489	−	0.286341i
$729$		0			0
$730$	0.596582	+	0.0360898i	0.0220805	+	0.00133574i
$731$	−0.682739	−	1.18254i	−0.0252520	−	0.0437377i
$732$		0			0
$733$	−15.2819	+	26.4691i	−0.564450	+	0.977657i	0.432650	+	0.901562i	$0.357579\pi$
$733$	−15.2819	+	26.4691i	−0.564450	+	0.977657i	−0.997101	+	0.0760949i	$0.975755\pi$
$734$	−10.9618			−0.404606
$735$		0			0
$736$	−14.7768			−0.544679
$737$	−2.65804	+	4.60386i	−0.0979103	+	0.169586i
$738$		0			0
$739$	−1.58166	−	2.73951i	−0.0581822	−	0.100775i	0.835467	−	0.549540i	$-0.185197\pi$
$739$	−1.58166	−	2.73951i	−0.0581822	−	0.100775i	−0.893649	+	0.448766i	$0.851864\pi$
$740$	−0.0981264	+	1.62208i	−0.00360720	+	0.0596287i
$741$		0			0
$742$	−4.77142	−	1.87546i	−0.175164	−	0.0688503i
$743$	−38.4235			−1.40962			−0.704811	−	0.709395i	$-0.748968\pi$
$743$	−38.4235			−1.40962			−0.704811	+	0.709395i	$0.748968\pi$
$744$		0			0
$745$	−44.0617	−	29.1216i	−1.61430	−	1.06693i
$746$	−5.48052	+	3.16418i	−0.200656	+	0.115849i
$747$		0			0
$748$	−0.807650			−0.0295306
$749$	−28.1177	+	22.3997i	−1.02740	+	0.818465i
$750$		0			0
$751$	12.6749	−	21.9536i	0.462513	−	0.801097i	−0.536572	−	0.843854i	$-0.680281\pi$
$751$	12.6749	−	21.9536i	0.462513	−	0.801097i	0.999085	+	0.0427578i	$0.0136144\pi$
$752$	13.4066	−	7.74032i	0.488889	−	0.282260i
$753$		0			0
$754$	12.8814	+	7.43710i	0.469114	+	0.270843i
$755$	−13.3924	−	26.8163i	−0.487399	−	0.975944i
$756$		0			0
$757$			1.58908i			0.0577562i	0.999583	+	0.0288781i	$0.00919346\pi$
$757$			1.58908i			0.0577562i	−0.999583	+	0.0288781i	$0.990807\pi$
$758$	−2.15728	+	3.73651i	−0.0783558	+	0.135716i
$759$		0			0
$760$	12.4720	+	8.24313i	0.452409	+	0.299010i
$761$	15.7201	−	27.2279i	0.569852	−	0.987012i	−0.426728	−	0.904380i	$-0.640334\pi$
$761$	15.7201	−	27.2279i	0.569852	−	0.987012i	0.996580	−	0.0826325i	$-0.0263328\pi$
$762$		0			0
$763$	2.43124	+	16.1864i	0.0880169	+	0.585986i
$764$			12.5077i			0.452514i
$765$		0			0
$766$	−3.92195	+	2.26434i	−0.141706	+	0.0818138i
$767$	−22.7326	−	39.3740i	−0.820826	−	1.42171i
$768$		0			0
$769$			3.88576i			0.140124i	0.997543	+	0.0700620i	$0.0223197\pi$
$769$			3.88576i			0.140124i	−0.997543	+	0.0700620i	$0.977680\pi$
$770$	−1.02066	+	2.19684i	−0.0367819	+	0.0791685i
$771$		0			0
$772$	4.91693	+	2.83879i	0.176964	+	0.102170i
$773$	34.2935	−	19.7994i	1.23345	−	0.712133i	0.265703	−	0.964055i	$-0.414396\pi$
$773$	34.2935	−	19.7994i	1.23345	−	0.712133i	0.967748	+	0.251922i	$0.0810625\pi$
$774$		0			0
$775$	−18.3893	+	7.83472i	−0.660564	+	0.281431i
$776$	−7.00150			−0.251339
$777$		0			0
$778$		−	2.50678i		−	0.0898724i
$779$	43.9944	+	25.4002i	1.57626	+	0.910055i
$780$		0			0
$781$	1.55455	+	2.69256i	0.0556262	+	0.0963474i
$782$	−0.465738	−	0.268894i	−0.0166547	−	0.00961562i
$783$		0			0
$784$	−21.2774	+	6.53940i	−0.759907	+	0.233550i
$785$	−14.2208	−	28.4751i	−0.507563	−	1.01632i
$786$		0			0
$787$	−22.7573	−	39.4167i	−0.811209	−	1.40505i	−0.912019	−	0.410149i	$-0.865477\pi$
$787$	−22.7573	−	39.4167i	−0.811209	−	1.40505i	0.100810	−	0.994906i	$-0.467857\pi$
$788$	24.0344	+	41.6289i	0.856191	+	1.48297i
$789$		0			0
$790$	−1.79675	−	3.59772i	−0.0639255	−	0.128001i
$791$	−14.9401	−	5.87236i	−0.531208	−	0.208797i
$792$		0			0
$793$	−16.0933	−	9.29146i	−0.571489	−	0.329949i
$794$	4.66394	+	8.07818i	0.165517	+	0.286684i
$795$		0			0
$796$	27.8203	+	16.0620i	0.986063	+	0.569304i
$797$		−	8.62946i		−	0.305671i	−0.988252	−	0.152836i	$-0.951160\pi$
$797$		−	8.62946i		−	0.305671i	0.988252	−	0.152836i	$-0.0488405\pi$
$798$		0			0
$799$	1.93121			0.0683213
$800$	−7.99110	−	18.7564i	−0.282528	−	0.663138i
$801$		0			0
$802$	−5.47650	+	3.16186i	−0.193382	+	0.111649i
$803$	−0.677290	−	0.391034i	−0.0239010	−	0.0137993i
$804$		0			0
$805$	17.5450	−	12.3218i	0.618379	−	0.434286i
$806$		−	8.26719i		−	0.291199i
$807$		0			0
$808$	−13.5589	−	23.4846i	−0.476999	−	0.826187i
$809$	−15.8019	+	9.12322i	−0.555564	+	0.320755i	−0.751363	−	0.659889i	$-0.770603\pi$
$809$	−15.8019	+	9.12322i	−0.555564	+	0.320755i	0.195799	+	0.980644i	$0.437270\pi$
$810$		0			0
$811$		−	49.3072i		−	1.73141i	−0.500555	−	0.865704i	$-0.666871\pi$
$811$		−	49.3072i		−	1.73141i	0.500555	−	0.865704i	$-0.333129\pi$
$812$	35.0044	−	5.25777i	1.22841	−	0.184512i
$813$		0			0
$814$	−0.0799883	+	0.138544i	−0.00280359	+	0.00485596i
$815$	−42.6821	−	28.2098i	−1.49509	−	0.988146i
$816$		0			0
$817$	7.96865	−	13.8021i	0.278788	−	0.482875i
$818$			7.96496i			0.278488i
$819$		0			0
$820$	−20.3889	−	40.8258i	−0.712012	−	1.42570i
$821$	20.0547	+	11.5786i	0.699915	+	0.404096i	0.807316	−	0.590120i	$-0.200919\pi$
$821$	20.0547	+	11.5786i	0.699915	+	0.404096i	−0.107401	+	0.994216i	$0.534253\pi$
$822$		0			0
$823$	−12.5779	+	7.26186i	−0.438438	+	0.253132i	−0.702935	−	0.711254i	$-0.748128\pi$
$823$	−12.5779	+	7.26186i	−0.438438	+	0.253132i	0.264497	+	0.964387i	$0.414794\pi$
$824$	−10.4019	+	18.0166i	−0.362368	+	0.627640i
$825$		0			0
$826$	7.57579	+	2.97775i	0.263596	+	0.103609i
$827$	21.6632			0.753302			0.376651	−	0.926355i	$-0.377076\pi$
$827$	21.6632			0.753302			0.376651	+	0.926355i	$0.377076\pi$
$828$		0			0
$829$	−15.8166	+	9.13174i	−0.549334	+	0.317158i	−0.748853	−	0.662736i	$-0.769395\pi$
$829$	−15.8166	+	9.13174i	−0.549334	+	0.317158i	0.199519	+	0.979894i	$0.436062\pi$
$830$	−9.03683	−	5.97270i	−0.313673	−	0.207315i
$831$		0			0
$832$	−26.7257			−0.926546
$833$	−2.70663	−	0.620683i	−0.0937793	−	0.0215054i
$834$		0			0
$835$	1.88010	−	31.0790i	0.0650636	−	1.07553i
$836$	−4.71328	−	8.16365i	−0.163012	−	0.282346i
$837$		0			0
$838$	−0.906158	+	1.56951i	−0.0313027	+	0.0542179i
$839$	38.8296			1.34055			0.670273	−	0.742114i	$-0.266177\pi$
$839$	38.8296			1.34055			0.670273	+	0.742114i	$0.266177\pi$
$840$		0			0
$841$	−22.7348			−0.783959
$842$	−1.92859	+	3.34042i	−0.0664636	+	0.115118i
$843$		0			0
$844$	21.4406	+	37.1362i	0.738016	+	1.27828i
$845$	39.1924	+	2.37092i	1.34826	+	0.0815621i
$846$		0			0
$847$	−20.2839	+	16.1589i	−0.696964	+	0.555228i
$848$	−16.4720			−0.565650
$849$		0			0
$850$	0.0894455	−	0.736583i	0.00306796	−	0.0252646i
$851$	1.22621	−	0.707950i	0.0420338	−	0.0242682i
$852$		0			0
$853$	0.803330			0.0275055			0.0137527	−	0.999905i	$-0.495622\pi$
$853$	0.803330			0.0275055			0.0137527	+	0.999905i	$0.495622\pi$
$854$	3.29015	−	0.494190i	0.112586	−	0.0169108i
$855$		0			0
$856$	9.81014	−	16.9917i	0.335304	−	0.580763i
$857$	−9.24262	+	5.33623i	−0.315722	+	0.182282i	−0.649484	−	0.760375i	$-0.725015\pi$
$857$	−9.24262	+	5.33623i	−0.315722	+	0.182282i	0.333762	+	0.942657i	$0.391682\pi$
$858$		0			0
$859$	−43.8831	−	25.3359i	−1.49727	−	0.864450i	−0.497276	−	0.867593i	$-0.665666\pi$
$859$	−43.8831	−	25.3359i	−1.49727	−	0.864450i	−0.999995	+	0.00314281i	$0.999000\pi$
$860$	−12.8080	+	6.39651i	−0.436751	+	0.218119i
$861$		0			0
$862$		−	14.6566i		−	0.499204i
$863$	−18.2131	+	31.5460i	−0.619981	+	1.07384i	0.369508	+	0.929228i	$0.379526\pi$
$863$	−18.2131	+	31.5460i	−0.619981	+	1.07384i	−0.989489	+	0.144610i	$0.953807\pi$
$864$		0			0
$865$	−37.4355	−	24.7422i	−1.27285	−	0.841260i
$866$	−2.84031	+	4.91955i	−0.0965175	+	0.167173i
$867$		0			0
$868$	−12.2586	−	15.3880i	−0.416086	−	0.522302i
$869$			5.26213i			0.178505i
$870$		0			0
$871$	−23.2520	+	13.4245i	−0.787863	+	0.454873i
$872$	−4.46661	−	7.73640i	−0.151259	−	0.261988i
$873$		0			0
$874$		−	6.27684i		−	0.212317i
$875$	25.1283	+	15.6066i	0.849493	+	0.527600i
$876$		0			0
$877$	−20.6537	−	11.9244i	−0.697425	−	0.402659i	0.108963	−	0.994046i	$-0.465247\pi$
$877$	−20.6537	−	11.9244i	−0.697425	−	0.402659i	−0.806388	+	0.591387i	$0.798580\pi$
$878$	8.42962	−	4.86685i	0.284486	−	0.164248i
$879$		0			0
$880$	−0.469961	+	7.76868i	−0.0158424	+	0.261882i
$881$	−1.65600			−0.0557920			−0.0278960	−	0.999611i	$-0.508881\pi$
$881$	−1.65600			−0.0557920			−0.0278960	+	0.999611i	$0.508881\pi$
$882$		0			0
$883$		−	8.62010i		−	0.290089i	−0.989425	−	0.145045i	$-0.953667\pi$
$883$		−	8.62010i		−	0.290089i	0.989425	−	0.145045i	$-0.0463326\pi$
$884$	−3.53257	−	2.03953i	−0.118813	−	0.0685969i
$885$		0			0
$886$	−0.532085	−	0.921598i	−0.0178757	−	0.0309617i
$887$	−16.2378	−	9.37492i	−0.545213	−	0.314779i	0.201976	−	0.979390i	$-0.435264\pi$
$887$	−16.2378	−	9.37492i	−0.545213	−	0.314779i	−0.747189	+	0.664612i	$0.768597\pi$
$888$		0			0
$889$	1.37011	−	3.48576i	0.0459522	−	0.116909i
$890$	4.77340	+	9.55802i	0.160005	+	0.320386i
$891$		0			0
$892$	−16.9838	−	29.4168i	−0.568659	−	0.984946i
$893$	11.2702	+	19.5205i	0.377141	+	0.653228i
$894$		0			0
$895$	−4.47770	+	2.23622i	−0.149673	+	0.0747486i
$896$	20.6185	−	16.4254i	0.688814	−	0.548736i
$897$		0			0
$898$	−1.71896	−	0.992443i	−0.0573625	−	0.0331182i
$899$	14.3773	+	24.9022i	0.479509	+	0.830535i
$900$		0			0
$901$	−1.77958	−	1.02744i	−0.0592863	−	0.0342290i
$902$		−	4.49242i		−	0.149581i
$903$		0			0
$904$	8.76121			0.291393
$905$	0.566193	−	9.35943i	0.0188209	−	0.311118i
$906$		0			0
$907$	−32.7308	+	18.8971i	−1.08681	+	0.627469i	−0.932725	−	0.360588i	$-0.882576\pi$
$907$	−32.7308	+	18.8971i	−1.08681	+	0.627469i	−0.154084	+	0.988058i	$0.549243\pi$
$908$	−16.2771	−	9.39760i	−0.540175	−	0.311870i
$909$		0			0
$910$	−10.0118	+	7.03130i	−0.331889	+	0.233085i
$911$		−	27.9845i		−	0.927167i	−0.886053	−	0.463584i	$-0.846563\pi$
$911$		−	27.9845i		−	0.927167i	0.886053	−	0.463584i	$-0.153437\pi$
$912$		0			0
$913$	7.08711	+	12.2752i	0.234549	+	0.406251i
$914$	−11.6428	+	6.72197i	−0.385109	+	0.222343i
$915$		0			0
$916$		−	41.6097i		−	1.37482i
$917$	−25.0573	+	19.9616i	−0.827466	+	0.659191i
$918$		0			0
$919$	22.7199	−	39.3521i	0.749461	−	1.29810i	−0.198620	−	0.980077i	$-0.563646\pi$
$919$	22.7199	−	39.3521i	0.749461	−	1.29810i	0.948081	−	0.318028i	$-0.103021\pi$
$920$	−6.45181	+	9.76174i	−0.212710	+	0.321835i
$921$		0			0
$922$	2.64044	−	4.57337i	0.0869582	−	0.150616i
$923$			15.7026i			0.516858i
$924$		0			0
$925$	1.56173	+	1.17359i	0.0513493	+	0.0385874i
$926$	−5.82145	−	3.36101i	−0.191305	−	0.110450i
$927$		0			0
$928$	−25.3993	+	14.6643i	−0.833771	+	0.481378i
$929$	−23.6347	+	40.9366i	−0.775430	+	1.34308i	0.159122	+	0.987259i	$0.449134\pi$
$929$	−23.6347	+	40.9366i	−0.775430	+	1.34308i	−0.934552	+	0.355826i	$0.884200\pi$
$930$		0			0
$931$	−9.52158	−	30.9806i	−0.312057	−	1.01535i
$932$	−42.1749			−1.38148
$933$		0			0
$934$	−5.00904	+	2.89197i	−0.163901	+	0.0946281i
$935$	−0.535344	+	0.809988i	−0.0175076	+	0.0264895i
$936$		0			0
$937$	−39.3420			−1.28525			−0.642624	−	0.766182i	$-0.722154\pi$
$937$	−39.3420			−1.28525			−0.642624	+	0.766182i	$0.722154\pi$
$938$	1.75849	−	4.47382i	0.0574166	−	0.146076i
$939$		0			0
$940$	1.22265	−	20.2110i	0.0398785	−	0.659210i
$941$	−6.13749	−	10.6304i	−0.200076	−	0.346542i	0.748476	−	0.663161i	$-0.230786\pi$
$941$	−6.13749	−	10.6304i	−0.200076	−	0.346542i	−0.948553	+	0.316619i	$0.897452\pi$
$942$		0			0
$943$	−19.8804	+	34.4339i	−0.647396	+	1.12132i
$944$	26.1533			0.851217
$945$		0			0
$946$	−1.40938			−0.0458229
$947$	−10.1694	+	17.6139i	−0.330460	+	0.572374i	−0.982602	−	0.185723i	$-0.940537\pi$
$947$	−10.1694	+	17.6139i	−0.330460	+	0.572374i	0.652142	+	0.758097i	$0.273871\pi$
$948$		0			0
$949$	−1.97493	−	3.42068i	−0.0641089	−	0.111040i
$950$	7.96729	−	3.39444i	0.258493	−	0.110130i
$951$		0			0
$952$	1.49875	−	0.225117i	0.0485747	−	0.00729607i
$953$	30.6485			0.992804			0.496402	−	0.868093i	$-0.334654\pi$
$953$	30.6485			0.992804			0.496402	+	0.868093i	$0.334654\pi$
$954$		0			0
$955$	12.5440	+	8.29066i	0.405913	+	0.268279i
$956$	26.6780	−	15.4026i	0.862830	−	0.498155i
$957$		0			0
$958$	−8.71055			−0.281425
$959$	3.21516	+	21.4054i	0.103823	+	0.691217i
$960$		0			0
$961$	−7.50900	+	13.0060i	−0.242226	+	0.419547i
$962$	−0.699721	+	0.403984i	−0.0225599	+	0.0130250i
$963$		0			0
$964$	40.8291	+	23.5727i	1.31502	+	0.759225i
$965$	6.10616	−	3.04950i	0.196564	−	0.0981668i
$966$		0			0
$967$			52.7201i			1.69536i	0.530504	+	0.847682i	$0.322003\pi$
$967$			52.7201i			1.69536i	−0.530504	+	0.847682i	$0.677997\pi$
$968$	7.07696	−	12.2577i	0.227462	−	0.393976i
$969$		0			0
$970$	−2.23632	+	3.38360i	−0.0718039	+	0.108641i
$971$	−23.3979	+	40.5264i	−0.750876	+	1.30055i	0.196523	+	0.980499i	$0.437035\pi$
$971$	−23.3979	+	40.5264i	−0.750876	+	1.30055i	−0.947399	+	0.320056i	$0.896298\pi$
$972$		0			0
$973$	10.3197	−	26.2548i	0.330836	−	0.841690i
$974$		−	4.55257i		−	0.145874i
$975$		0			0
$976$	9.25746	−	5.34480i	0.296324	−	0.171083i
$977$	−7.77187	−	13.4613i	−0.248644	−	0.430664i	0.714506	−	0.699630i	$-0.246652\pi$
$977$	−7.77187	−	13.4613i	−0.248644	−	0.430664i	−0.963150	+	0.268965i	$0.913318\pi$
$978$		0			0
$979$		−	13.9798i		−	0.446797i
$980$	−8.20931	+	27.9332i	−0.262237	+	0.892294i
$981$		0			0
$982$	4.00657	+	2.31319i	0.127855	+	0.0738170i
$983$	27.3467	−	15.7886i	0.872225	−	0.503579i	0.00413812	−	0.999991i	$-0.498683\pi$
$983$	27.3467	−	15.7886i	0.872225	−	0.503579i	0.868087	+	0.496412i	$0.165349\pi$
$984$		0			0
$985$	57.6804	+	3.48934i	1.83785	+	0.111180i
$986$	−1.06739			−0.0339925
$987$		0			0
$988$		−	47.6092i		−	1.51465i
$989$	10.8028	+	6.23698i	0.343508	+	0.198324i
$990$		0			0
$991$	25.5907	+	44.3244i	0.812916	+	1.40801i	0.910815	+	0.412815i	$0.135454\pi$
$991$	25.5907	+	44.3244i	0.812916	+	1.40801i	−0.0978991	+	0.995196i	$0.531212\pi$
$992$	14.1171	+	8.15050i	0.448218	+	0.258779i
$993$		0			0
$994$	−1.75174	−	2.19891i	−0.0555618	−	0.0697453i
$995$	34.5490	−	17.2542i	1.09528	−	0.546996i
$996$		0			0
$997$	0.255934	+	0.443291i	0.00810551	+	0.0140392i	0.870050	−	0.492964i	$-0.164087\pi$
$997$	0.255934	+	0.443291i	0.00810551	+	0.0140392i	−0.861944	+	0.507003i	$0.830753\pi$
$998$	−3.43711	−	5.95325i	−0.108800	−	0.188447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bb.b.404.8	yes	32
3.2	odd	2		945.2.bb.a.404.9	yes	32
5.4	even	2		945.2.bb.a.404.10	yes	32
7.3	odd	6	inner	945.2.bb.b.269.7	yes	32
15.14	odd	2	inner	945.2.bb.b.404.7	yes	32
21.17	even	6		945.2.bb.a.269.10	yes	32
35.24	odd	6		945.2.bb.a.269.9	✓	32
105.59	even	6	inner	945.2.bb.b.269.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bb.a.269.9	✓	32	35.24	odd	6
945.2.bb.a.269.10	yes	32	21.17	even	6
945.2.bb.a.404.9	yes	32	3.2	odd	2
945.2.bb.a.404.10	yes	32	5.4	even	2
945.2.bb.b.269.7	yes	32	7.3	odd	6	inner
945.2.bb.b.269.8	yes	32	105.59	even	6	inner
945.2.bb.b.404.7	yes	32	15.14	odd	2	inner
945.2.bb.b.404.8	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.187042 + 0.323967i) q^{2} +(0.930030 + 1.61086i) q^{4} +(2.23199 + 0.135023i) q^{5} +(2.46237 + 0.967860i) q^{7} -1.44399 q^{8} +O(q^{10})\)	\(q+(-0.187042 + 0.323967i) q^{2} +(0.930030 + 1.61086i) q^{4} +(2.23199 + 0.135023i) q^{5} +(2.46237 + 0.967860i) q^{7} -1.44399 q^{8} +(-0.461219 + 0.697834i) q^{10} +(0.947907 - 0.547275i) q^{11} +5.52806 q^{13} +(-0.774121 + 0.616694i) q^{14} +(-1.58997 + 2.75392i) q^{16} +(-0.343551 + 0.198349i) q^{17} +(-4.00979 - 2.31505i) q^{19} +(1.85831 + 3.72099i) q^{20} +0.409454i q^{22} +(1.81197 - 3.13842i) q^{23} +(4.96354 + 0.602738i) q^{25} +(-1.03398 + 1.79091i) q^{26} +(0.730988 + 4.86667i) q^{28} -7.19269i q^{29} +(-3.46215 + 1.99887i) q^{31} +(-2.03877 - 3.53126i) q^{32} -0.148399i q^{34} +(5.36529 + 2.49273i) q^{35} +(0.338363 + 0.195354i) q^{37} +(1.50000 - 0.866025i) q^{38} +(-3.22296 - 0.194971i) q^{40} -10.9717 q^{41} +3.44210i q^{43} +(1.76317 + 1.01796i) q^{44} +(0.677829 + 1.17403i) q^{46} +(-4.21599 - 2.43410i) q^{47} +(5.12649 + 4.76645i) q^{49} +(-1.12366 + 1.49528i) q^{50} +(5.14126 + 8.90493i) q^{52} +(2.58997 + 4.48597i) q^{53} +(2.18961 - 1.09352i) q^{55} +(-3.55563 - 1.39758i) q^{56} +(2.33019 + 1.34534i) q^{58} +(-4.11222 - 7.12257i) q^{59} +(-2.91120 - 1.68078i) q^{61} -1.49550i q^{62} -4.83455 q^{64} +(12.3386 + 0.746413i) q^{65} +(-4.20617 + 2.42844i) q^{67} +(-0.639026 - 0.368942i) q^{68} +(-1.81110 + 1.27193i) q^{70} +2.84053i q^{71} +(-0.357255 - 0.618785i) q^{73} +(-0.126576 + 0.0730788i) q^{74} -8.61228i q^{76} +(2.86378 - 0.430149i) q^{77} +(-2.40379 + 4.16348i) q^{79} +(-3.92064 + 5.93202i) q^{80} +(2.05218 - 3.55447i) q^{82} +12.9498i q^{83} +(-0.793583 + 0.396326i) q^{85} +(-1.11513 - 0.643818i) q^{86} +(-1.36877 + 0.790258i) q^{88} +(6.38611 - 11.0611i) q^{89} +(13.6121 + 5.35039i) q^{91} +6.74074 q^{92} +(1.57713 - 0.910559i) q^{94} +(-8.63722 - 5.70858i) q^{95} +4.84872 q^{97} +(-2.50304 + 0.769285i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 3 q^{5}+O(q^{10}) \) 32 * q - 16 * q^4 + 3 * q^5	\( 32 q - 16 q^{4} + 3 q^{5} - 3 q^{10} - 16 q^{16} + 6 q^{17} + 12 q^{19} - q^{25} - 6 q^{31} - 30 q^{32} + 12 q^{35} + 48 q^{38} + 24 q^{40} - 18 q^{46} + 6 q^{47} + 2 q^{49} + 72 q^{50} + 48 q^{53} + 12 q^{61} - 16 q^{64} - 30 q^{65} - 90 q^{68} - 24 q^{70} + 42 q^{77} + 10 q^{79} - 96 q^{80} + 10 q^{85} - 62 q^{91} - 84 q^{92} + 84 q^{94} - 36 q^{95} - 72 q^{98}+O(q^{100}) \) 32 * q - 16 * q^4 + 3 * q^5 - 3 * q^10 - 16 * q^16 + 6 * q^17 + 12 * q^19 - q^25 - 6 * q^31 - 30 * q^32 + 12 * q^35 + 48 * q^38 + 24 * q^40 - 18 * q^46 + 6 * q^47 + 2 * q^49 + 72 * q^50 + 48 * q^53 + 12 * q^61 - 16 * q^64 - 30 * q^65 - 90 * q^68 - 24 * q^70 + 42 * q^77 + 10 * q^79 - 96 * q^80 + 10 * q^85 - 62 * q^91 - 84 * q^92 + 84 * q^94 - 36 * q^95 - 72 * q^98

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