LMFDB - Embedded newform 464.2.u.f.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(49,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("464.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			401.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	464.401
Dual form			464.2.u.f.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0990311 + 0.433884i) q^{3} +(0.222521 + 0.279032i) q^{5} +(-0.900969 - 3.94740i) q^{7} +(2.52446 - 1.21572i) q^{9} +(2.62349 + 1.26341i) q^{11} +(-4.67241 - 2.25011i) q^{13} +(-0.0990311 + 0.124181i) q^{15} +1.10992 q^{17} +(0.455927 - 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(2.57942 - 3.23449i) q^{23} +(1.08426 - 4.75046i) q^{25} +(1.60992 + 2.01877i) q^{27} +(4.38404 + 3.12733i) q^{29} +(3.96346 + 4.97002i) q^{31} +(-0.288364 + 1.26341i) q^{33} +(0.900969 - 1.12978i) q^{35} +(2.62349 - 1.26341i) q^{37} +(0.513574 - 2.25011i) q^{39} +0.396125 q^{41} +(-3.57942 + 4.48845i) q^{43} +(0.900969 + 0.433884i) q^{45} +(-7.02930 - 3.38513i) q^{47} +(-8.46346 + 4.07579i) q^{49} +(0.109916 + 0.481575i) q^{51} +(-2.71648 - 3.40636i) q^{53} +(0.231250 + 1.01317i) q^{55} +0.911854 q^{57} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(-7.07338 - 8.86973i) q^{63} +(-0.411854 - 1.80445i) q^{65} +(0.337282 - 0.162426i) q^{67} +(1.65883 + 0.798852i) q^{69} +(-10.2763 - 4.94880i) q^{71} +(-5.57942 + 6.99637i) q^{73} +2.16852 q^{75} +(2.62349 - 11.4943i) q^{77} +(-0.535344 + 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(-2.09903 + 9.19646i) q^{83} +(0.246980 + 0.309703i) q^{85} +(-0.922739 + 2.21187i) q^{87} +(0.887395 + 1.11276i) q^{89} +(-4.67241 + 20.4712i) q^{91} +(-1.76391 + 2.21187i) q^{93} +(0.658834 - 0.317278i) q^{95} +(-3.50484 + 15.3557i) q^{97} +8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{3} + q^{5} - q^{7} + 6 q^{9} + 11 q^{11} - 5 q^{13} - 5 q^{15} + 8 q^{17} - q^{19} + 5 q^{21} + 7 q^{23} - 24 q^{25} + 11 q^{27} + 6 q^{29} - 5 q^{31} + q^{33} + q^{35} + 11 q^{37} - 3 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) $ 6 * q + 5 * q^3 + q^5 - q^7 + 6 * q^9 + 11 * q^11 - 5 * q^13 - 5 * q^15 + 8 * q^17 - q^19 + 5 * q^21 + 7 * q^23 - 24 * q^25 + 11 * q^27 + 6 * q^29 - 5 * q^31 + q^33 + q^35 + 11 * q^37 - 3 * q^39 + 20 * q^41 - 13 * q^43 + q^45 - 11 * q^47 - 22 * q^49 + 2 * q^51 + 3 * q^53 + 17 * q^55 - 2 * q^57 + 56 * q^59 + 3 * q^61 - 15 * q^63 + 5 * q^65 - 19 * q^67 - 7 * q^69 - 21 * q^71 - 25 * q^73 - 48 * q^75 + 11 * q^77 + 9 * q^79 + 18 * q^81 - 17 * q^83 - 8 * q^85 + 5 * q^87 + 7 * q^89 - 5 * q^91 - 17 * q^93 - 13 * q^95 + q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{7}\right)$

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			0
$2$		0			0
$3$	0.0990311	+	0.433884i	0.0571757	+	0.250503i	0.995437	−	0.0954255i	$-0.0304212\pi$
$3$	0.0990311	+	0.433884i	0.0571757	+	0.250503i	−0.938261	+	0.345928i	$0.887564\pi$
$4$		0			0
$5$	0.222521	+	0.279032i	0.0995144	+	0.124787i	0.829095	−	0.559108i	$-0.188856\pi$
$5$	0.222521	+	0.279032i	0.0995144	+	0.124787i	−0.729581	+	0.683895i	$0.760285\pi$
$6$		0			0
$7$	−0.900969	−	3.94740i	−0.340534	−	1.49198i	−0.797949	−	0.602725i	$-0.794082\pi$
$7$	−0.900969	−	3.94740i	−0.340534	−	1.49198i	0.457415	−	0.889253i	$-0.348775\pi$
$8$		0			0
$9$	2.52446	−	1.21572i	0.841486	−	0.405238i
$10$		0			0
$11$	2.62349	+	1.26341i	0.791012	+	0.380931i	0.785349	−	0.619053i	$-0.212483\pi$
$11$	2.62349	+	1.26341i	0.791012	+	0.380931i	0.00566249	+	0.999984i	$0.498198\pi$
$12$		0			0
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.346467	−	0.938062i	$-0.612619\pi$
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.949425	+	0.313993i	$0.898333\pi$
$14$		0			0
$15$	−0.0990311	+	0.124181i	−0.0255697	+	0.0320634i
$16$		0			0
$17$	1.10992			0.269194			0.134597	−	0.990900i	$-0.457026\pi$
$17$	1.10992			0.269194			0.134597	+	0.990900i	$0.457026\pi$
$18$		0			0
$19$	0.455927	−	1.99755i	0.104597	−	0.458269i	−0.895321	−	0.445422i	$-0.853054\pi$
$19$	0.455927	−	1.99755i	0.104597	−	0.458269i	0.999917	−	0.0128465i	$-0.00408927\pi$
$20$		0			0
$21$	1.62349	−	0.781831i	0.354275	−	0.170610i
$22$		0			0
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	−0.436445	−	0.899731i	$-0.643763\pi$
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	0.974291	+	0.225294i	$0.0723342\pi$
$24$		0			0
$25$	1.08426	−	4.75046i	0.216852	−	0.950092i
$26$		0			0
$27$	1.60992	+	2.01877i	0.309829	+	0.388513i
$28$		0			0
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$30$		0			0
$31$	3.96346	+	4.97002i	0.711858	+	0.892642i	0.997847	−	0.0655910i	$-0.0208932\pi$
$31$	3.96346	+	4.97002i	0.711858	+	0.892642i	−0.285988	+	0.958233i	$0.592322\pi$
$32$		0			0
$33$	−0.288364	+	1.26341i	−0.0501978	+	0.219931i
$34$		0			0
$35$	0.900969	−	1.12978i	0.152292	−	0.190968i
$36$		0			0
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	−0.205622	−	0.978631i	$-0.565922\pi$
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	0.636921	+	0.770929i	$0.280208\pi$
$38$		0			0
$39$	0.513574	−	2.25011i	0.0822376	−	0.360306i
$40$		0			0
$41$	0.396125			0.0618643			0.0309321	−	0.999521i	$-0.490152\pi$
$41$	0.396125			0.0618643			0.0309321	+	0.999521i	$0.490152\pi$
$42$		0			0
$43$	−3.57942	+	4.48845i	−0.545856	+	0.684482i	−0.975873	−	0.218339i	$-0.929936\pi$
$43$	−3.57942	+	4.48845i	−0.545856	+	0.684482i	0.430017	+	0.902821i	$0.358508\pi$
$44$		0			0
$45$	0.900969	+	0.433884i	0.134309	+	0.0646796i
$46$		0			0
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.155870	−	0.987778i	$-0.549818\pi$
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.869459	+	0.494005i	$0.835532\pi$
$48$		0			0
$49$	−8.46346	+	4.07579i	−1.20907	+	0.582255i
$50$		0			0
$51$	0.109916	+	0.481575i	0.0153914	+	0.0674339i
$52$		0			0
$53$	−2.71648	−	3.40636i	−0.373137	−	0.467899i	0.559439	−	0.828871i	$-0.311016\pi$
$53$	−2.71648	−	3.40636i	−0.373137	−	0.467899i	−0.932577	+	0.360972i	$0.882445\pi$
$54$		0			0
$55$	0.231250	+	1.01317i	0.0311818	+	0.136616i
$56$		0			0
$57$	0.911854			0.120778
$58$		0			0
$59$	9.10992			1.18601			0.593005	−	0.805199i	$-0.297941\pi$
$59$	9.10992			1.18601			0.593005	+	0.805199i	$0.297941\pi$
$60$		0			0
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	0.985032	+	0.172374i	$0.0551437\pi$
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	−0.812693	+	0.582693i	$0.801999\pi$
$62$		0			0
$63$	−7.07338	−	8.86973i	−0.891162	−	1.11748i
$64$		0			0
$65$	−0.411854	−	1.80445i	−0.0510842	−	0.223815i
$66$		0			0
$67$	0.337282	−	0.162426i	0.0412055	−	0.0198435i	−0.413168	−	0.910655i	$-0.635578\pi$
$67$	0.337282	−	0.162426i	0.0412055	−	0.0198435i	0.454373	+	0.890812i	$0.349863\pi$
$68$		0			0
$69$	1.65883	+	0.798852i	0.199700	+	0.0961705i
$70$		0			0
$71$	−10.2763	−	4.94880i	−1.21957	−	0.587314i	−0.290379	−	0.956912i	$-0.593781\pi$
$71$	−10.2763	−	4.94880i	−1.21957	−	0.587314i	−0.929192	+	0.369598i	$0.879495\pi$
$72$		0			0
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	−0.992563	−	0.121728i	$-0.961156\pi$
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	0.339542	+	0.940591i	$0.389728\pi$
$74$		0			0
$75$	2.16852			0.250399
$76$		0			0
$77$	2.62349	−	11.4943i	0.298974	−	1.30989i
$78$		0			0
$79$	−0.535344	+	0.257808i	−0.0602309	+	0.0290057i	−0.463757	−	0.885963i	$-0.653499\pi$
$79$	−0.535344	+	0.257808i	−0.0602309	+	0.0290057i	0.403526	+	0.914968i	$0.367785\pi$
$80$		0			0
$81$	4.52446	−	5.67349i	0.502718	−	0.630388i
$82$		0			0
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	0.718912	+	0.695101i	$0.244641\pi$
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	−0.949310	+	0.314341i	$0.898217\pi$
$84$		0			0
$85$	0.246980	+	0.309703i	0.0267887	+	0.0335920i
$86$		0			0
$87$	−0.922739	+	2.21187i	−0.0989280	+	0.237137i
$88$		0			0
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	0.826636	−	0.562737i	$-0.190252\pi$
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	−0.732572	+	0.680689i	$0.761680\pi$
$90$		0			0
$91$	−4.67241	+	20.4712i	−0.489801	+	2.14596i
$92$		0			0
$93$	−1.76391	+	2.21187i	−0.182908	+	0.229360i
$94$		0			0
$95$	0.658834	−	0.317278i	0.0675949	−	0.0325520i
$96$		0			0
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	0.407523	+	0.913195i	$0.366393\pi$
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	−0.763386	+	0.645943i	$0.776464\pi$
$98$		0			0
$99$	8.15883			0.819994
$100$		0			0
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.152570	+	0.988293i	$0.548755\pi$
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.929564	+	0.368661i	$0.879816\pi$
$102$		0			0
$103$	−2.53534	−	1.22096i	−0.249815	−	0.120304i	0.304786	−	0.952421i	$-0.401415\pi$
$103$	−2.53534	−	1.22096i	−0.249815	−	0.120304i	−0.554601	+	0.832116i	$0.687129\pi$
$104$		0			0
$105$	0.579417	+	0.279032i	0.0565453	+	0.0272308i
$106$		0			0
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	−0.729580	−	0.683895i	$-0.760284\pi$
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	0.0798052	+	0.996810i	$0.474570\pi$
$108$		0			0
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	0.989482	−	0.144653i	$-0.0462066\pi$
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	−0.954255	+	0.298993i	$0.903349\pi$
$110$		0			0
$111$	0.807979	+	1.01317i	0.0766899	+	0.0961661i
$112$		0			0
$113$	−1.92274	−	8.42407i	−0.180876	−	0.792470i	−0.981214	−	0.192921i	$-0.938204\pi$
$113$	−1.92274	−	8.42407i	−0.180876	−	0.792470i	0.800338	−	0.599549i	$-0.204653\pi$
$114$		0			0
$115$	1.47650			0.137684
$116$		0			0
$117$	−14.5308			−1.34337
$118$		0			0
$119$	−1.00000	−	4.38129i	−0.0916698	−	0.401632i
$120$		0			0
$121$	−1.57188	−	1.97108i	−0.142899	−	0.179189i
$122$		0			0
$123$	0.0392287	+	0.171872i	0.00353713	+	0.0154972i
$124$		0			0
$125$	3.17456	−	1.52879i	0.283942	−	0.136739i
$126$		0			0
$127$	9.43512	+	4.54371i	0.837231	+	0.403189i	0.802822	−	0.596219i	$-0.203331\pi$
$127$	9.43512	+	4.54371i	0.837231	+	0.403189i	0.0344090	+	0.999408i	$0.489045\pi$
$128$		0			0
$129$	−2.30194	−	1.10855i	−0.202674	−	0.0976028i
$130$		0			0
$131$	0.283520	−	0.355523i	0.0247712	−	0.0310622i	−0.769292	−	0.638898i	$-0.779391\pi$
$131$	0.283520	−	0.355523i	0.0247712	−	0.0310622i	0.794063	+	0.607836i	$0.207962\pi$
$132$		0			0
$133$	−8.29590			−0.719345
$134$		0			0
$135$	−0.205063	+	0.898438i	−0.0176490	+	0.0773252i
$136$		0			0
$137$	11.9291	−	5.74474i	1.01917	−	0.490806i	0.151769	−	0.988416i	$-0.451503\pi$
$137$	11.9291	−	5.74474i	1.01917	−	0.490806i	0.867401	+	0.497610i	$0.165789\pi$
$138$		0			0
$139$	1.74363	−	2.18644i	0.147893	−	0.185451i	−0.702367	−	0.711815i	$-0.747873\pi$
$139$	1.74363	−	2.18644i	0.147893	−	0.185451i	0.850260	+	0.526364i	$0.176445\pi$
$140$		0			0
$141$	0.772635	−	3.38513i	0.0650676	−	0.285080i
$142$		0			0
$143$	−9.41521	−	11.8063i	−0.787339	−	0.987292i
$144$		0			0
$145$	0.102916	+	1.91919i	0.00854671	+	0.159380i
$146$		0			0
$147$	−2.60656	−	3.26853i	−0.214986	−	0.269584i
$148$		0			0
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	−0.993596	−	0.112988i	$-0.963958\pi$
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	0.944223	+	0.329307i	$0.106815\pi$
$150$		0			0
$151$	1.51842	−	1.90404i	0.123567	−	0.154948i	−0.716200	−	0.697895i	$-0.754120\pi$
$151$	1.51842	−	1.90404i	0.123567	−	0.154948i	0.839767	+	0.542947i	$0.182692\pi$
$152$		0			0
$153$	2.80194	−	1.34934i	0.226523	−	0.109088i
$154$		0			0
$155$	−0.504844	+	2.21187i	−0.0405501	+	0.177661i
$156$		0			0
$157$	17.6775			1.41082			0.705411	−	0.708799i	$-0.250762\pi$
$157$	17.6775			1.41082			0.705411	+	0.708799i	$0.250762\pi$
$158$		0			0
$159$	1.20895	−	1.51597i	0.0958758	−	0.120224i
$160$		0			0
$161$	−15.0918	−	7.26782i	−1.18940	−	0.572785i
$162$		0			0
$163$	−4.47434	−	2.15473i	−0.350458	−	0.168772i	0.250370	−	0.968150i	$-0.419448\pi$
$163$	−4.47434	−	2.15473i	−0.350458	−	0.168772i	−0.600827	+	0.799379i	$0.705162\pi$
$164$		0			0
$165$	−0.416698	+	0.200671i	−0.0324399	+	0.0156222i
$166$		0			0
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	0.932487	+	0.361203i	$0.117634\pi$
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	−0.683422	+	0.730024i	$0.739509\pi$
$168$		0			0
$169$	8.66301	+	10.8631i	0.666386	+	0.835621i
$170$		0			0
$171$	−1.27748	−	5.59700i	−0.0976913	−	0.428013i
$172$		0			0
$173$	10.5133			0.799314			0.399657	−	0.916665i	$-0.369129\pi$
$173$	10.5133			0.799314			0.399657	+	0.916665i	$0.369129\pi$
$174$		0			0
$175$	−19.7289			−1.49136
$176$		0			0
$177$	0.902165	+	3.95264i	0.0678109	+	0.297099i
$178$		0			0
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	0.897394	−	0.441230i	$-0.145458\pi$
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	−0.629856	+	0.776712i	$0.716886\pi$
$180$		0			0
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	0.999688	+	0.0249747i	$0.00795053\pi$
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	−0.889852	+	0.456250i	$0.849192\pi$
$182$		0			0
$183$	−2.42543	+	1.16802i	−0.179293	+	0.0863428i
$184$		0			0
$185$	0.936313	+	0.450904i	0.0688391	+	0.0331512i
$186$		0			0
$187$	2.91185	+	1.40227i	0.212936	+	0.102545i
$188$		0			0
$189$	6.51842	−	8.17384i	0.474145	−	0.594559i
$190$		0			0
$191$	18.8116			1.36116			0.680581	−	0.732673i	$-0.261728\pi$
$191$	18.8116			1.36116			0.680581	+	0.732673i	$0.261728\pi$
$192$		0			0
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	0.809832	+	0.586662i	$0.199558\pi$
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	−0.984176	+	0.177192i	$0.943299\pi$
$194$		0			0
$195$	0.742135	−	0.357394i	0.0531454	−	0.0255935i
$196$		0			0
$197$	−5.23759	+	6.56773i	−0.373163	+	0.467931i	−0.932584	−	0.360952i	$-0.882452\pi$
$197$	−5.23759	+	6.56773i	−0.373163	+	0.467931i	0.559422	+	0.828883i	$0.311023\pi$
$198$		0			0
$199$	−1.47339	+	6.45532i	−0.104446	+	0.457606i	0.895476	+	0.445109i	$0.146835\pi$
$199$	−1.47339	+	6.45532i	−0.104446	+	0.457606i	−0.999922	+	0.0124967i	$0.996022\pi$
$200$		0			0
$201$	0.103875	+	0.130256i	0.00732681	+	0.00918753i
$202$		0			0
$203$	8.39493	−	20.1232i	0.589208	−	1.41237i
$204$		0			0
$205$	0.0881460	+	0.110532i	0.00615638	+	0.00771986i
$206$		0			0
$207$	2.57942	−	11.3012i	0.179282	−	0.785485i
$208$		0			0
$209$	3.71983	−	4.66452i	0.257306	−	0.322652i
$210$		0			0
$211$	−7.29805	+	3.51456i	−0.502419	+	0.241952i	−0.667887	−	0.744263i	$-0.732801\pi$
$211$	−7.29805	+	3.51456i	−0.502419	+	0.241952i	0.165468	+	0.986215i	$0.447087\pi$
$212$		0			0
$213$	1.12953	−	4.94880i	0.0773942	−	0.339086i
$214$		0			0
$215$	−2.04892			−0.139735
$216$		0			0
$217$	16.0477	−	20.1232i	1.08939	−	1.36605i
$218$		0			0
$219$	−3.58815	−	1.72796i	−0.242464	−	0.116765i
$220$		0			0
$221$	−5.18598	−	2.49744i	−0.348847	−	0.167996i
$222$		0			0
$223$	19.7485	−	9.51036i	1.32246	−	0.636861i	0.366512	−	0.930413i	$-0.380552\pi$
$223$	19.7485	−	9.51036i	1.32246	−	0.636861i	0.955943	+	0.293552i	$0.0948374\pi$
$224$		0			0
$225$	−3.03803	−	13.3105i	−0.202535	−	0.887366i
$226$		0			0
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	0.999770	−	0.0214309i	$-0.00682218\pi$
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	−0.243363	+	0.969935i	$0.578251\pi$
$228$		0			0
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	−0.944876	−	0.327427i	$-0.893818\pi$
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	0.709239	−	0.704968i	$-0.249039\pi$
$230$		0			0
$231$	5.24698			0.345226
$232$		0			0
$233$	1.95646			0.128172			0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646			0.128172			0.0640860	+	0.997944i	$0.479587\pi$
$234$		0			0
$235$	−0.619605	−	2.71467i	−0.0404186	−	0.177085i
$236$		0			0
$237$	−0.164874	−	0.206746i	−0.0107097	−	0.0134296i
$238$		0			0
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	−0.997571	−	0.0696554i	$-0.977810\pi$
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	0.868558	−	0.495587i	$-0.165047\pi$
$240$		0			0
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.910506	−	0.413496i	$-0.864308\pi$
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.244407	+	0.969673i	$0.578593\pi$
$242$		0			0
$243$	9.88889	+	4.76224i	0.634372	+	0.305498i
$244$		0			0
$245$	−3.02057	−	1.45463i	−0.192977	−	0.0929330i
$246$		0			0
$247$	−6.62498	+	8.30746i	−0.421537	+	0.528591i
$248$		0			0
$249$	−4.19806			−0.266041
$250$		0			0
$251$	5.74214	−	25.1579i	0.362440	−	1.58795i	−0.384540	−	0.923108i	$-0.625640\pi$
$251$	5.74214	−	25.1579i	0.362440	−	1.58795i	0.746980	−	0.664847i	$-0.231503\pi$
$252$		0			0
$253$	10.8535	−	5.22679i	0.682356	−	0.328606i
$254$		0			0
$255$	−0.109916	+	0.137831i	−0.00688322	+	0.00863129i
$256$		0			0
$257$	−2.65937	+	11.6514i	−0.165887	+	0.726797i	0.821726	+	0.569883i	$0.193012\pi$
$257$	−2.65937	+	11.6514i	−0.165887	+	0.726797i	−0.987612	+	0.156914i	$0.949846\pi$
$258$		0			0
$259$	−7.35086	−	9.21768i	−0.456760	−	0.572759i
$260$		0			0
$261$	14.8693	+	2.56506i	0.920385	+	0.158773i
$262$		0			0
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	0.788186	−	0.615437i	$-0.211020\pi$
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	−0.775394	+	0.631477i	$0.782449\pi$
$264$		0			0
$265$	0.346011	−	1.51597i	0.0212553	−	0.0931254i
$266$		0			0
$267$	−0.394928	+	0.495224i	−0.0241692	+	0.0303072i
$268$		0			0
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	−0.404432	−	0.914568i	$-0.632531\pi$
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	0.462879	+	0.886421i	$0.346816\pi$
$270$		0			0
$271$	−3.66368	+	16.0516i	−0.222553	+	0.975067i	0.732996	+	0.680233i	$0.238121\pi$
$271$	−3.66368	+	16.0516i	−0.222553	+	0.975067i	−0.955549	+	0.294834i	$0.904736\pi$
$272$		0			0
$273$	−9.34481			−0.565574
$274$		0			0
$275$	8.84631	−	11.0929i	0.533452	−	0.668928i
$276$		0			0
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	0.246800	−	0.969066i	$-0.420621\pi$
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	−0.603769	+	0.797159i	$0.706335\pi$
$278$		0			0
$279$	16.0477	+	7.72818i	0.960752	+	0.462674i
$280$		0			0
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.641448	−	0.767166i	$-0.278334\pi$
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.999731	−	0.0231840i	$-0.00738037\pi$
$282$		0			0
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	0.945959	−	0.324286i	$-0.105124\pi$
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	−0.992982	+	0.118264i	$0.962267\pi$
$284$		0			0
$285$	0.202907	+	0.254437i	0.0120191	+	0.0150715i
$286$		0			0
$287$	−0.356896	−	1.56366i	−0.0210669	−	0.0923001i
$288$		0			0
$289$	−15.7681			−0.927534
$290$		0			0
$291$	−7.00969			−0.410915
$292$		0			0
$293$	−7.31647	−	32.0556i	−0.427433	−	1.87271i	−0.485246	−	0.874378i	$-0.661270\pi$
$293$	−7.31647	−	32.0556i	−0.427433	−	1.87271i	0.0578127	−	0.998327i	$-0.481587\pi$
$294$		0			0
$295$	2.02715	+	2.54196i	0.118025	+	0.147999i
$296$		0			0
$297$	1.67307	+	7.33020i	0.0970814	+	0.425342i
$298$		0			0
$299$	−19.3300	+	9.30886i	−1.11789	+	0.538345i
$300$		0			0
$301$	20.9426	+	10.0854i	1.20711	+	0.581316i
$302$		0			0
$303$	−6.99396	−	3.36811i	−0.401792	−	0.193493i
$304$		0			0
$305$	−1.34601	+	1.68784i	−0.0770724	+	0.0966457i
$306$		0			0
$307$	−14.6703			−0.837275			−0.418638	−	0.908153i	$-0.637492\pi$
$307$	−14.6703			−0.837275			−0.418638	+	0.908153i	$0.637492\pi$
$308$		0			0
$309$	0.278676	−	1.22096i	0.0158533	−	0.0694578i
$310$		0			0
$311$	16.6918	−	8.03834i	0.946504	−	0.455812i	0.104045	−	0.994573i	$-0.466821\pi$
$311$	16.6918	−	8.03834i	0.946504	−	0.455812i	0.842459	+	0.538760i	$0.181107\pi$
$312$		0			0
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	−0.189132	−	0.981952i	$-0.560567\pi$
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	0.999418	−	0.0341147i	$-0.0108612\pi$
$314$		0			0
$315$	0.900969	−	3.94740i	0.0507638	−	0.222411i
$316$		0			0
$317$	8.76540	+	10.9915i	0.492314	+	0.617342i	0.964476	−	0.264170i	$-0.0850979\pi$
$317$	8.76540	+	10.9915i	0.492314	+	0.617342i	−0.472162	+	0.881512i	$0.656526\pi$
$318$		0			0
$319$	7.55041	+	13.7433i	0.422742	+	0.769479i
$320$		0			0
$321$	−2.07002	−	2.59573i	−0.115537	−	0.144879i
$322$		0			0
$323$	0.506041	−	2.21711i	0.0281569	−	0.123363i
$324$		0			0
$325$	−15.7552	+	19.7564i	−0.873940	+	1.09589i
$326$		0			0
$327$	−0.662718	+	0.319148i	−0.0366484	+	0.0176489i
$328$		0			0
$329$	−7.02930	+	30.7974i	−0.387538	+	1.69792i
$330$		0			0
$331$	−13.9565			−0.767116			−0.383558	−	0.923517i	$-0.625301\pi$
$331$	−13.9565			−0.767116			−0.383558	+	0.923517i	$0.625301\pi$
$332$		0			0
$333$	5.08695	−	6.37883i	0.278763	−	0.349558i
$334$		0			0
$335$	0.120374	+	0.0579692i	0.00657676	+	0.00316720i
$336$		0			0
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	0.744607	−	0.667503i	$-0.232637\pi$
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	−0.0576199	+	0.998339i	$0.518351\pi$
$338$		0			0
$339$	3.46466	−	1.66849i	0.188174	−	0.0906200i
$340$		0			0
$341$	4.11894	+	18.0463i	0.223053	+	0.977260i
$342$		0			0
$343$	6.04288	+	7.57753i	0.326285	+	0.409148i
$344$		0			0
$345$	0.146220	+	0.640630i	0.00787220	+	0.0344903i
$346$		0			0
$347$	19.8538			1.06581			0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538			1.06581			0.532905	+	0.846175i	$0.321100\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$		0			0
$351$	−2.97972	−	13.0550i	−0.159046	−	0.696825i
$352$		0			0
$353$	−2.50335	−	3.13910i	−0.133240	−	0.167078i	0.710736	−	0.703459i	$-0.248362\pi$
$353$	−2.50335	−	3.13910i	−0.133240	−	0.167078i	−0.843976	+	0.536382i	$0.819791\pi$
$354$		0			0
$355$	−0.905813	−	3.96863i	−0.0480756	−	0.210633i
$356$		0			0
$357$	1.80194	−	0.867767i	0.0953687	−	0.0459271i
$358$		0			0
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	0.416055	−	0.909339i	$-0.363412\pi$
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	−0.451544	+	0.892249i	$0.649127\pi$
$360$		0			0
$361$	13.3361	+	6.42232i	0.701899	+	0.338017i
$362$		0			0
$363$	0.699554	−	0.877213i	0.0367171	−	0.0460418i
$364$		0			0
$365$	−3.19375			−0.167169
$366$		0			0
$367$	−7.57660	+	33.1952i	−0.395495	+	1.73278i	0.249304	+	0.968425i	$0.419798\pi$
$367$	−7.57660	+	33.1952i	−0.395495	+	1.73278i	−0.644799	+	0.764352i	$0.723059\pi$
$368$		0			0
$369$	1.00000	−	0.481575i	0.0520579	−	0.0250698i
$370$		0			0
$371$	−10.9988	+	13.7921i	−0.571029	+	0.716048i
$372$		0			0
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	0.510268	+	0.860015i	$0.329546\pi$
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	−0.832882	+	0.553450i	$0.813311\pi$
$374$		0			0
$375$	0.977697	+	1.22599i	0.0504881	+	0.0633100i
$376$		0			0
$377$	−13.4472	−	24.4767i	−0.692566	−	1.26062i
$378$		0			0
$379$	−14.2661	−	17.8891i	−0.732798	−	0.918900i	0.266188	−	0.963921i	$-0.414236\pi$
$379$	−14.2661	−	17.8891i	−0.732798	−	0.918900i	−0.998986	+	0.0450211i	$0.985664\pi$
$380$		0			0
$381$	−1.03707	+	4.54371i	−0.0531308	+	0.232781i
$382$		0			0
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	−0.933981	−	0.357323i	$-0.883690\pi$
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	0.556194	+	0.831052i	$0.312261\pi$
$384$		0			0
$385$	3.79105	−	1.82567i	0.193210	−	0.0930450i
$386$		0			0
$387$	−3.57942	+	15.6824i	−0.181952	+	0.797184i
$388$		0			0
$389$	−10.3913			−0.526862			−0.263431	−	0.964678i	$-0.584854\pi$
$389$	−10.3913			−0.526862			−0.263431	+	0.964678i	$0.584854\pi$
$390$		0			0
$391$	2.86294	−	3.59001i	0.144785	−	0.181555i
$392$		0			0
$393$	0.182333	+	0.0878068i	0.00919747	+	0.00442927i
$394$		0			0
$395$	−0.191062	−	0.0920106i	−0.00961337	−	0.00462956i
$396$		0			0
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	−0.610348	−	0.792133i	$-0.708970\pi$
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	0.238769	+	0.971076i	$0.423256\pi$
$398$		0			0
$399$	−0.821552	−	3.59945i	−0.0411290	−	0.180198i
$400$		0			0
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	0.999996	−	0.00286337i	$-0.000911439\pi$
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	−0.225312	+	0.974287i	$0.572340\pi$
$402$		0			0
$403$	−7.33579	−	32.1402i	−0.365422	−	1.60102i
$404$		0			0
$405$	2.58987			0.128692
$406$		0			0
$407$	8.47889			0.420283
$408$		0			0
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	−0.965958	−	0.258701i	$-0.916706\pi$
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	0.758052	−	0.652194i	$-0.226151\pi$
$410$		0			0
$411$	3.67390	+	4.60692i	0.181220	+	0.227243i
$412$		0			0
$413$	−8.20775	−	35.9605i	−0.403877	−	1.76950i
$414$		0			0
$415$	−3.03319	+	1.46071i	−0.148893	+	0.0717033i
$416$		0			0
$417$	1.12133	+	0.540006i	0.0549120	+	0.0264442i
$418$		0			0
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	0.178527	−	0.983935i	$-0.442867\pi$
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	−0.657962	+	0.753051i	$0.728581\pi$
$420$		0			0
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	−0.986383	−	0.164467i	$-0.947410\pi$
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	0.379834	+	0.925055i	$0.375981\pi$
$422$		0			0
$423$	−21.8605			−1.06290
$424$		0			0
$425$	1.20344	−	5.27261i	0.0583754	−	0.255759i
$426$		0			0
$427$	22.0661	−	10.6265i	1.06786	−	0.514252i
$428$		0			0
$429$	4.19016	−	5.25430i	0.202303	−	0.253680i
$430$		0			0
$431$	−6.71797	+	29.4334i	−0.323593	+	1.41776i	0.507514	+	0.861643i	$0.330564\pi$
$431$	−6.71797	+	29.4334i	−0.323593	+	1.41776i	−0.831108	+	0.556112i	$0.812293\pi$
$432$		0			0
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	0.381153	−	0.924512i	$-0.375527\pi$
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	−0.986147	+	0.165874i	$0.946956\pi$
$434$		0			0
$435$	−0.822512	+	0.234713i	−0.0394364	+	0.0112536i
$436$		0			0
$437$	−5.28501	−	6.62720i	−0.252816	−	0.317022i
$438$		0			0
$439$	−2.37316	+	10.3975i	−0.113265	+	0.496245i	0.886193	+	0.463316i	$0.153341\pi$
$439$	−2.37316	+	10.3975i	−0.113265	+	0.496245i	−0.999458	+	0.0329287i	$0.989517\pi$
$440$		0			0
$441$	−16.4107	+	20.5783i	−0.781460	+	0.979920i
$442$		0			0
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.815372	−	0.578937i	$-0.803468\pi$
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.0557448	+	0.998445i	$0.517753\pi$
$444$		0			0
$445$	−0.113032	+	0.495224i	−0.00535822	+	0.0234759i
$446$		0			0
$447$	−1.20536			−0.0570115
$448$		0			0
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	−0.409124	−	0.912479i	$-0.634166\pi$
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	0.980640	+	0.195820i	$0.0627369\pi$
$450$		0			0
$451$	1.03923	+	0.500466i	0.0489354	+	0.0235660i
$452$		0			0
$453$	0.976501	+	0.470258i	0.0458800	+	0.0220946i
$454$		0			0
$455$	−6.75182	+	3.25151i	−0.316530	+	0.152433i
$456$		0			0
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	0.997526	+	0.0703045i	$0.0223971\pi$
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	−0.868236	+	0.496152i	$0.834746\pi$
$458$		0			0
$459$	1.78687	+	2.24067i	0.0834041	+	0.104585i
$460$		0			0
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	0.951712	+	0.306991i	$0.0993223\pi$
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	−0.724265	+	0.689522i	$0.757821\pi$
$462$		0			0
$463$	33.0073			1.53398			0.766990	−	0.641660i	$-0.221754\pi$
$463$	33.0073			1.53398			0.766990	+	0.641660i	$0.221754\pi$
$464$		0			0
$465$	−1.00969			−0.0468232
$466$		0			0
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	−0.911427	−	0.411461i	$-0.865019\pi$
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	0.642642	−	0.766167i	$-0.277838\pi$
$468$		0			0
$469$	−0.945042	−	1.18505i	−0.0436380	−	0.0547203i
$470$		0			0
$471$	1.75063	+	7.67000i	0.0806647	+	0.353415i
$472$		0			0
$473$	−15.0613	+	7.25314i	−0.692519	+	0.333500i
$474$		0			0
$475$	−8.99492	−	4.33172i	−0.412715	−	0.198753i
$476$		0			0
$477$	−10.9988	−	5.29674i	−0.503601	−	0.242521i
$478$		0			0
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	0.0413068	+	0.999147i	$0.486848\pi$
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	−0.983287	+	0.182060i	$0.941724\pi$
$480$		0			0
$481$	−15.1008			−0.688538
$482$		0			0
$483$	1.65883	−	7.26782i	0.0754795	−	0.330697i
$484$		0			0
$485$	−5.06465	+	2.43901i	−0.229974	+	0.110750i
$486$		0			0
$487$	6.33244	−	7.94063i	0.286950	−	0.359824i	−0.617375	−	0.786669i	$-0.711804\pi$
$487$	6.33244	−	7.94063i	0.286950	−	0.359824i	0.904325	+	0.426845i	$0.140375\pi$
$488$		0			0
$489$	0.491803	−	2.15473i	0.0222401	−	0.0974403i
$490$		0			0
$491$	12.2714	+	15.3879i	0.553802	+	0.694446i	0.977399	−	0.211405i	$-0.0678039\pi$
$491$	12.2714	+	15.3879i	0.553802	+	0.694446i	−0.423596	+	0.905851i	$0.639232\pi$
$492$		0			0
$493$	4.86592	+	3.47107i	0.219150	+	0.156329i
$494$		0			0
$495$	1.81551	+	2.27658i	0.0816012	+	0.102325i
$496$		0			0
$497$	−10.2763	+	45.0233i	−0.460954	+	2.01957i
$498$		0			0
$499$	−17.3639	+	21.7736i	−0.777315	+	0.974722i	−1.00000		0.000168534i	$-0.999946\pi$
$499$	−17.3639	+	21.7736i	−0.777315	+	0.974722i	0.222685	+	0.974890i	$0.428518\pi$
$500$		0			0
$501$	−5.79978	+	2.79303i	−0.259115	+	0.124783i
$502$		0			0
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	−0.976033	−	0.217623i	$-0.930170\pi$
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	0.973798	+	0.227413i	$0.0730267\pi$
$504$		0			0
$505$	−6.22521			−0.277018
$506$		0			0
$507$	−3.85540	+	4.83452i	−0.171224	+	0.214709i
$508$		0			0
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.864481	−	0.502665i	$-0.167647\pi$
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.145995	+	0.989285i	$0.453362\pi$
$510$		0			0
$511$	32.6444	+	15.7207i	1.44410	+	0.695443i
$512$		0			0
$513$	4.76659	−	2.29547i	0.210450	−	0.101348i
$514$		0			0
$515$	−0.223480	−	0.979132i	−0.00984772	−	0.0431457i
$516$		0			0
$517$	−14.1645	−	17.7617i	−0.622954	−	0.781160i
$518$		0			0
$519$	1.04115	+	4.56157i	0.0457013	+	0.200231i
$520$		0			0
$521$	23.5797			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$522$		0			0
$523$	−3.96508			−0.173381			−0.0866905	−	0.996235i	$-0.527629\pi$
$523$	−3.96508			−0.173381			−0.0866905	+	0.996235i	$0.527629\pi$
$524$		0			0
$525$	−1.95377	−	8.56003i	−0.0852696	−	0.373590i
$526$		0			0
$527$	4.39911	+	5.51631i	0.191628	+	0.240294i
$528$		0			0
$529$	1.30947	+	5.73717i	0.0569335	+	0.249442i
$530$		0			0
$531$	22.9976	−	11.0751i	0.998011	−	0.480617i
$532$		0			0
$533$	−1.85086	−	0.891325i	−0.0801694	−	0.0386076i
$534$		0			0
$535$	−2.39881	−	1.15521i	−0.103710	−	0.0499440i
$536$		0			0
$537$	−1.59299	+	1.99755i	−0.0687426	+	0.0862005i
$538$		0			0
$539$	−27.3532			−1.17818
$540$		0			0
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	−0.708709	−	0.705501i	$-0.750722\pi$
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	0.944630	−	0.328137i	$-0.106421\pi$
$542$		0			0
$543$	−2.66272	+	1.28230i	−0.114268	+	0.0550287i
$544$		0			0
$545$	−0.367781	+	0.461183i	−0.0157540	+	0.0197549i
$546$		0			0
$547$	5.52768	−	24.2183i	0.236347	−	1.03550i	−0.707913	−	0.706300i	$-0.750363\pi$
$547$	5.52768	−	24.2183i	0.236347	−	1.03550i	0.944259	−	0.329202i	$-0.106780\pi$
$548$		0			0
$549$	10.5673	+	13.2510i	0.451003	+	0.565540i
$550$		0			0
$551$	8.24578	−	7.33150i	0.351282	−	0.312332i
$552$		0			0
$553$	1.50000	+	1.88094i	0.0637865	+	0.0799857i
$554$		0			0
$555$	−0.102916	+	0.450904i	−0.00436854	+	0.0191398i
$556$		0			0
$557$	4.84146	−	6.07100i	0.205139	−	0.257237i	−0.668610	−	0.743613i	$-0.733110\pi$
$557$	4.84146	−	6.07100i	0.205139	−	0.257237i	0.873749	+	0.486377i	$0.161682\pi$
$558$		0			0
$559$	26.8240	−	12.9178i	1.13453	−	0.546363i
$560$		0			0
$561$	−0.320060	+	1.40227i	−0.0135129	+	0.0592041i
$562$		0			0
$563$	−20.8009			−0.876652			−0.438326	−	0.898816i	$-0.644429\pi$
$563$	−20.8009			−0.876652			−0.438326	+	0.898816i	$0.644429\pi$
$564$		0			0
$565$	1.92274	−	2.41104i	0.0808902	−	0.101433i
$566$		0			0
$567$	−26.4720	−	12.7482i	−1.11172	−	0.535375i
$568$		0			0
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	0.380078	−	0.924955i	$-0.375897\pi$
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	−0.486184	+	0.873856i	$0.661612\pi$
$570$		0			0
$571$	2.60603	−	1.25500i	0.109059	−	0.0525201i	−0.378559	−	0.925577i	$-0.623580\pi$
$571$	2.60603	−	1.25500i	0.109059	−	0.0525201i	0.487618	+	0.873057i	$0.337866\pi$
$572$		0			0
$573$	1.86294	+	8.16206i	0.0778253	+	0.340975i
$574$		0			0
$575$	−12.5685	−	15.7604i	−0.524144	−	0.657256i
$576$		0			0
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	0.930653	−	0.365904i	$-0.119240\pi$
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	−0.997249	+	0.0741270i	$0.976383\pi$
$578$		0			0
$579$	−4.84415			−0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$		0			0
$583$	−2.82304	−	12.3686i	−0.116919	−	0.512254i
$584$		0			0
$585$	−3.23341	−	4.05456i	−0.133685	−	0.167636i
$586$		0			0
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	−0.891220	−	0.453570i	$-0.850150\pi$
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	0.606165	−	0.795339i	$-0.292707\pi$
$588$		0			0
$589$	11.7349	−	5.65123i	0.483528	−	0.232855i
$590$		0			0
$591$	−3.36831	−	1.62209i	−0.138554	−	0.0667240i
$592$		0			0
$593$	−32.8560	−	15.8226i	−1.34923	−	0.649757i	−0.387025	−	0.922069i	$-0.626497\pi$
$593$	−32.8560	−	15.8226i	−1.34923	−	0.649757i	−0.962209	+	0.272312i	$0.912212\pi$
$594$		0			0
$595$	1.00000	−	1.25396i	0.0409960	−	0.0514074i
$596$		0			0
$597$	−2.94677			−0.120603
$598$		0			0
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	−0.632615	−	0.774466i	$-0.718019\pi$
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	0.905995	−	0.423288i	$-0.139124\pi$
$600$		0			0
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.290420	−	0.956899i	$-0.406205\pi$
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.929208	+	0.369558i	$0.120491\pi$
$602$		0			0
$603$	0.653989	−	0.820077i	0.0266325	−	0.0333961i
$604$		0			0
$605$	0.200218	−	0.877213i	0.00814003	−	0.0356638i
$606$		0			0
$607$	9.42729	+	11.8214i	0.382642	+	0.479818i	0.935434	−	0.353502i	$-0.115009\pi$
$607$	9.42729	+	11.8214i	0.382642	+	0.479818i	−0.552792	+	0.833319i	$0.686438\pi$
$608$		0			0
$609$	9.56249	+	1.64960i	0.387492	+	0.0668451i
$610$		0			0
$611$	25.2268	+	31.6334i	1.02057	+	1.27975i
$612$		0			0
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	−0.988996	−	0.147942i	$-0.952735\pi$
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	0.955244	+	0.295818i	$0.0955923\pi$
$614$		0			0
$615$	−0.0392287	+	0.0491912i	−0.00158185	+	0.00198358i
$616$		0			0
$617$	−26.8995	+	12.9541i	−1.08293	+	0.521514i	−0.888254	−	0.459353i	$-0.848081\pi$
$617$	−26.8995	+	12.9541i	−1.08293	+	0.521514i	−0.194681	+	0.980867i	$0.562367\pi$
$618$		0			0
$619$	−10.2622	+	44.9615i	−0.412472	+	1.80716i	0.159866	+	0.987139i	$0.448894\pi$
$619$	−10.2622	+	44.9615i	−0.412472	+	1.80716i	−0.572338	+	0.820018i	$0.693963\pi$
$620$		0			0
$621$	10.6823			0.428667
$622$		0			0
$623$	3.59299	−	4.50547i	0.143950	−	0.180508i
$624$		0			0
$625$	−20.8174	−	10.0251i	−0.832697	−	0.401006i
$626$		0			0
$627$	2.39224	+	1.15204i	0.0955368	+	0.0460081i
$628$		0			0
$629$	2.91185	−	1.40227i	0.116103	−	0.0559124i
$630$		0			0
$631$	2.81043	+	12.3133i	0.111881	+	0.490185i	0.999558	+	0.0297178i	$0.00946085\pi$
$631$	2.81043	+	12.3133i	0.111881	+	0.490185i	−0.887677	+	0.460467i	$0.847682\pi$
$632$		0			0
$633$	−2.24764	−	2.81846i	−0.0893358	−	0.112024i
$634$		0			0
$635$	0.831668	+	3.64377i	0.0330037	+	0.144599i
$636$		0			0
$637$	48.7157			1.93019
$638$		0			0
$639$	−31.9584			−1.26425
$640$		0			0
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	−0.793157	−	0.609017i	$-0.791564\pi$
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	0.450368	−	0.892843i	$-0.351293\pi$
$642$		0			0
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.961523	−	0.274723i	$-0.911414\pi$
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.0538762	−	0.998548i	$-0.517158\pi$
$644$		0			0
$645$	−0.202907	−	0.888992i	−0.00798944	−	0.0350040i
$646$		0			0
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	−0.723306	−	0.690527i	$-0.757378\pi$
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	0.0889021	+	0.996040i	$0.471664\pi$
$648$		0			0
$649$	23.8998	+	11.5095i	0.938148	+	0.451788i
$650$		0			0
$651$	10.3204	+	4.97002i	0.404487	+	0.194790i
$652$		0			0
$653$	−8.30529	+	10.4145i	−0.325011	+	0.407551i	−0.917314	−	0.398164i	$-0.869647\pi$
$653$	−8.30529	+	10.4145i	−0.325011	+	0.407551i	0.592303	+	0.805715i	$0.298219\pi$
$654$		0			0
$655$	0.162291			0.00634125
$656$		0			0
$657$	−5.57942	+	24.4450i	−0.217674	+	0.953691i
$658$		0			0
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	−0.0745557	−	0.997217i	$-0.523754\pi$
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	0.733171	+	0.680045i	$0.238040\pi$
$660$		0			0
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	−0.985331	−	0.170655i	$-0.945412\pi$
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	0.385633	+	0.922652i	$0.373983\pi$
$662$		0			0
$663$	0.570024	−	2.49744i	0.0221379	−	0.0969924i
$664$		0			0
$665$	−1.84601	−	2.31482i	−0.0715852	−	0.0897650i
$666$		0			0
$667$	21.4236	−	6.11345i	0.829524	−	0.236714i
$668$		0			0
$669$	6.08211	+	7.62672i	0.235148	+	0.294866i
$670$		0			0
$671$	−3.91939	+	17.1720i	−0.151306	+	0.662916i
$672$		0			0
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	−0.375636	−	0.926767i	$-0.622576\pi$
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	0.987118	+	0.159992i	$0.0511470\pi$
$674$		0			0
$675$	11.3357	−	5.45897i	0.436310	−	0.210116i
$676$		0			0
$677$	−0.137195	+	0.601090i	−0.00527283	+	0.0231018i	−0.977496	−	0.210954i	$-0.932343\pi$
$677$	−0.137195	+	0.601090i	−0.00527283	+	0.0231018i	0.972223	+	0.234056i	$0.0752000\pi$
$678$		0			0
$679$	63.7730			2.44738
$680$		0			0
$681$	−5.07188	+	6.35994i	−0.194355	+	0.243713i
$682$		0			0
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	0.717924	−	0.696121i	$-0.245092\pi$
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	−0.0966308	+	0.995320i	$0.530807\pi$
$684$		0			0
$685$	4.25744	+	2.05027i	0.162668	+	0.0783369i
$686$		0			0
$687$	6.42543	−	3.09432i	0.245145	−	0.118056i
$688$		0			0
$689$	5.02781	+	22.0283i	0.191544	+	0.839211i
$690$		0			0
$691$	−7.69769	−	9.65260i	−0.292834	−	0.367202i	0.613551	−	0.789655i	$-0.289741\pi$
$691$	−7.69769	−	9.65260i	−0.292834	−	0.367202i	−0.906385	+	0.422453i	$0.861169\pi$
$692$		0			0
$693$	−7.35086	−	32.2062i	−0.279236	−	1.22341i
$694$		0			0
$695$	0.998081			0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$		0			0
$699$	0.193750	+	0.848876i	0.00732831	+	0.0321074i
$700$		0			0
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	−0.999651	−	0.0264091i	$-0.991593\pi$
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	0.196696	−	0.980464i	$-0.436979\pi$
$702$		0			0
$703$	−1.32759	−	5.81656i	−0.0500711	−	0.219376i
$704$		0			0
$705$	1.11649	−	0.537673i	0.0420494	−	0.0202499i
$706$		0			0
$707$	63.6299	+	30.6425i	2.39305	+	1.15243i
$708$		0			0
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.446426	−	0.894821i	$-0.647303\pi$
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.977941	+	0.208882i	$0.933018\pi$
$710$		0			0
$711$	−1.03803	+	1.30165i	−0.0389292	+	0.0488157i
$712$		0			0
$713$	26.2989			0.984901
$714$		0			0
$715$	1.19926	−	5.25430i	0.0448497	−	0.196500i
$716$		0			0
$717$	3.59395	−	1.73076i	0.134219	−	0.0646362i
$718$		0			0
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.431667	−	0.902033i	$-0.357926\pi$
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.783362	−	0.621566i	$-0.213503\pi$
$720$		0			0
$721$	−2.53534	+	11.1081i	−0.0944211	+	0.413686i
$722$		0			0
$723$	−5.52177	−	6.92408i	−0.205357	−	0.257509i
$724$		0			0
$725$	19.6097	−	17.4354i	0.728285	−	0.647534i
$726$		0			0
$727$	−18.6953	−	23.4432i	−0.693370	−	0.869459i	0.303138	−	0.952947i	$-0.401966\pi$
$727$	−18.6953	−	23.4432i	−0.693370	−	0.869459i	−0.996509	+	0.0834876i	$0.973394\pi$
$728$		0			0
$729$	3.75733	−	16.4619i	0.139160	−	0.609702i
$730$		0			0
$731$	−3.97285	+	4.98180i	−0.146941	+	0.184259i
$732$		0			0
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	−0.483369	−	0.875417i	$-0.660587\pi$
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	0.383053	+	0.923726i	$0.374873\pi$
$734$		0			0
$735$	0.332010	−	1.45463i	0.0122464	−	0.0536549i
$736$		0			0
$737$	1.09006			0.0401531
$738$		0			0
$739$	12.9919	−	16.2914i	0.477916	−	0.599288i	−0.483174	−	0.875525i	$-0.660516\pi$
$739$	12.9919	−	16.2914i	0.477916	−	0.599288i	0.961090	+	0.276237i	$0.0890874\pi$
$740$		0			0
$741$	−4.26055	−	2.05177i	−0.156515	−	0.0753738i
$742$		0			0
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.150266	−	0.988646i	$-0.548013\pi$
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.866643	+	0.498928i	$0.833727\pi$
$744$		0			0
$745$	−0.870896	+	0.419402i	−0.0319072	+	0.0153657i
$746$		0			0
$747$	5.88135	+	25.7679i	0.215188	+	0.942798i
$748$		0			0
$749$	18.8327	+	23.6155i	0.688133	+	0.862892i
$750$		0			0
$751$	−0.994492	−	4.35715i	−0.0362895	−	0.158995i	0.953537	−	0.301277i	$-0.0974130\pi$
$751$	−0.994492	−	4.35715i	−0.0362895	−	0.158995i	−0.989826	+	0.142283i	$0.954556\pi$
$752$		0			0
$753$	11.4843			0.418510
$754$		0			0
$755$	0.869167			0.0316322
$756$		0			0
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	0.997542	−	0.0700652i	$-0.0223207\pi$
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	−0.929155	+	0.369691i	$0.879464\pi$
$758$		0			0
$759$	3.34266	+	4.19156i	0.121331	+	0.152144i
$760$		0			0
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	−0.971415	−	0.237388i	$-0.923709\pi$
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	0.772216	−	0.635361i	$-0.219149\pi$
$762$		0			0
$763$	6.02930	−	2.90356i	0.218275	−	0.105116i
$764$		0			0
$765$	1.00000	+	0.481575i	0.0361551	+	0.0174114i
$766$		0			0
$767$	−42.5652	−	20.4983i	−1.53694	−	0.740152i
$768$		0			0
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	−0.317418	−	0.948286i	$-0.602816\pi$
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	0.995142	+	0.0984462i	$0.0313872\pi$
$770$		0			0
$771$	−5.31873			−0.191549
$772$		0			0
$773$	−1.26324	+	5.53462i	−0.0454356	+	0.199067i	−0.992552	−	0.121825i	$-0.961125\pi$
$773$	−1.26324	+	5.53462i	−0.0454356	+	0.199067i	0.947116	+	0.320892i	$0.103982\pi$
$774$		0			0
$775$	27.9073	−	13.4394i	1.00246	−	0.482759i
$776$		0			0
$777$	3.27144	−	4.10225i	0.117362	−	0.147168i
$778$		0			0
$779$	0.180604	−	0.791277i	0.00647081	−	0.0283504i
$780$		0			0
$781$	−20.7074	−	25.9662i	−0.740968	−	0.929145i
$782$		0			0
$783$	0.744587	+	13.8851i	0.0266094	+	0.496213i
$784$		0			0
$785$	3.93362	+	4.93261i	0.140397	+	0.176052i
$786$		0			0
$787$	−0.803134	+	3.51876i	−0.0286286	+	0.125430i	−0.987223	−	0.159345i	$-0.949062\pi$
$787$	−0.803134	+	3.51876i	−0.0286286	+	0.125430i	0.958594	+	0.284775i	$0.0919190\pi$
$788$		0			0
$789$	−0.0923264	+	0.115774i	−0.00328691	+	0.00412165i
$790$		0			0
$791$	−31.5209	+	15.1797i	−1.12075	+	0.539726i
$792$		0			0
$793$	6.98039	−	30.5831i	0.247881	−	1.08604i
$794$		0			0
$795$	0.692021			0.0245435
$796$		0			0
$797$	−19.1930	+	24.0672i	−0.679850	+	0.852505i	−0.995340	−	0.0964236i	$-0.969260\pi$
$797$	−19.1930	+	24.0672i	−0.679850	+	0.852505i	0.315490	+	0.948929i	$0.397831\pi$
$798$		0			0
$799$	−7.80194	−	3.75722i	−0.276013	−	0.132921i
$800$		0			0
$801$	3.59299	+	1.73029i	0.126952	+	0.0611369i
$802$		0			0
$803$	−23.4768	+	11.3058i	−0.828478	+	0.398974i
$804$		0			0
$805$	−1.33028	−	5.82834i	−0.0468863	−	0.205422i
$806$		0			0
$807$	0.295233	+	0.370210i	0.0103927	+	0.0130320i
$808$		0			0
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	0.950300	−	0.311334i	$-0.100776\pi$
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	−0.991274	+	0.131817i	$0.957919\pi$
$810$		0			0
$811$	−41.8646			−1.47006			−0.735032	−	0.678032i	$-0.762833\pi$
$811$	−41.8646			−1.47006			−0.735032	+	0.678032i	$0.762833\pi$
$812$		0			0
$813$	−7.32736			−0.256982
$814$		0			0
$815$	−0.394396	−	1.72796i	−0.0138151	−	0.0605278i
$816$		0			0
$817$	7.33393	+	9.19646i	0.256582	+	0.321743i
$818$		0			0
$819$	13.0918	+	57.3589i	0.457464	+	2.00428i
$820$		0			0
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	−0.660121	−	0.751159i	$-0.729495\pi$
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	0.175701	+	0.984444i	$0.443781\pi$
$822$		0			0
$823$	−32.1247	−	15.4705i	−1.11980	−	0.539266i	−0.219968	−	0.975507i	$-0.570595\pi$
$823$	−32.1247	−	15.4705i	−1.11980	−	0.539266i	−0.899830	+	0.436241i	$0.856310\pi$
$824$		0			0
$825$	5.68910	+	2.73972i	0.198069	+	0.0953850i
$826$		0			0
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.231760	−	0.972773i	$-0.425552\pi$
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.896812	−	0.442411i	$-0.145877\pi$
$828$		0			0
$829$	−13.4168			−0.465986			−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168			−0.465986			−0.232993	+	0.972478i	$0.574852\pi$
$830$		0			0
$831$	0.653030	−	2.86111i	0.0226534	−	0.0992508i
$832$		0			0
$833$	−9.39373	+	4.52378i	−0.325474	+	0.156740i
$834$		0			0
$835$	−3.21864	+	4.03604i	−0.111385	+	0.139673i
$836$		0			0
$837$	−3.65250	+	16.0026i	−0.126249	+	0.553132i
$838$		0			0
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	0.994227	−	0.107294i	$-0.0342185\pi$
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	−0.325840	+	0.945425i	$0.605647\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$		0			0
$843$	8.47285	+	10.6246i	0.291821	+	0.365931i
$844$		0			0
$845$	−1.10345	+	4.83452i	−0.0379598	+	0.166313i
$846$		0			0
$847$	−6.36443	+	7.98074i	−0.218684	+	0.274222i
$848$		0			0
$849$	1.42543	−	0.686450i	0.0489205	−	0.0235589i
$850$		0			0
$851$	2.68060	−	11.7445i	0.0918899	−	0.402596i
$852$		0			0
$853$	21.3357			0.730521			0.365261	−	0.930905i	$-0.380980\pi$
$853$	21.3357			0.730521			0.365261	+	0.930905i	$0.380980\pi$
$854$		0			0
$855$	1.27748	−	1.60191i	0.0436889	−	0.0547841i
$856$		0			0
$857$	8.85839	+	4.26597i	0.302597	+	0.145723i	0.579021	−	0.815313i	$-0.303435\pi$
$857$	8.85839	+	4.26597i	0.302597	+	0.145723i	−0.276424	+	0.961036i	$0.589149\pi$
$858$		0			0
$859$	−46.6555	−	22.4681i	−1.59187	−	0.766602i	−0.592623	−	0.805480i	$-0.701907\pi$
$859$	−46.6555	−	22.4681i	−1.59187	−	0.766602i	−0.999244	+	0.0388778i	$0.987622\pi$
$860$		0			0
$861$	0.643104	−	0.309703i	0.0219169	−	0.0105546i
$862$		0			0
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	−0.998417	−	0.0562402i	$-0.982089\pi$
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	0.875141	−	0.483868i	$-0.160768\pi$
$864$		0			0
$865$	2.33944	+	2.93356i	0.0795433	+	0.0997441i
$866$		0			0
$867$	−1.56153	−	6.84152i	−0.0530324	−	0.232350i
$868$		0			0
$869$	−1.73019			−0.0586925
$870$		0			0
$871$	−1.94139			−0.0657816
$872$		0			0
$873$	9.82036	+	43.0258i	0.332369	+	1.45620i
$874$		0			0
$875$	−8.89493	−	11.1539i	−0.300703	−	0.377070i
$876$		0			0
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	−0.999601	−	0.0282623i	$-0.991003\pi$
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	0.888346	−	0.459174i	$-0.151855\pi$
$878$		0			0
$879$	13.1838	−	6.34900i	0.444679	−	0.214146i
$880$		0			0
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	0.694813	−	0.719190i	$-0.255487\pi$
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	−0.129076	+	0.991635i	$0.541201\pi$
$882$		0			0
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.127325	−	0.991861i	$-0.540639\pi$
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.854854	+	0.518869i	$0.826353\pi$
$884$		0			0
$885$	−0.902165	+	1.13128i	−0.0303260	+	0.0380275i
$886$		0			0
$887$	6.16288			0.206929			0.103465	−	0.994633i	$-0.467007\pi$
$887$	6.16288			0.206929			0.103465	+	0.994633i	$0.467007\pi$
$888$		0			0
$889$	9.43512	−	41.3379i	0.316444	−	1.38643i
$890$		0			0
$891$	19.0378	−	9.16812i	0.637790	−	0.307144i
$892$		0			0
$893$	−9.96681	+	12.4980i	−0.333527	+	0.418229i
$894$		0			0
$895$	−0.455927	+	1.99755i	−0.0152400	+	0.0667706i
$896$		0			0
$897$	−5.95324	−	7.46513i	−0.198773	−	0.249253i
$898$		0			0
$899$	1.83310	+	34.1838i	0.0611373	+	1.14009i
$900$		0			0
$901$	−3.01507	−	3.78077i	−0.100446	−	0.125956i
$902$		0			0
$903$	−2.30194	+	10.0854i	−0.0766037	+	0.335623i
$904$		0			0
$905$	−1.47770	+	1.85297i	−0.0491203	+	0.0615949i
$906$		0			0
$907$	39.6284	−	19.0840i	1.31584	−	0.633675i	0.361492	−	0.932375i	$-0.382267\pi$
$907$	39.6284	−	19.0840i	1.31584	−	0.633675i	0.954347	+	0.298700i	$0.0965531\pi$
$908$		0			0
$909$	−10.8753	+	47.6479i	−0.360711	+	1.58038i
$910$		0			0
$911$	25.6233			0.848936			0.424468	−	0.905443i	$-0.360461\pi$
$911$	25.6233			0.848936			0.424468	+	0.905443i	$0.360461\pi$
$912$		0			0
$913$	−17.1256	+	21.4749i	−0.566776	+	0.710715i
$914$		0			0
$915$	−0.865625	−	0.416863i	−0.0286167	−	0.0137811i
$916$		0			0
$917$	−1.65883	−	0.798852i	−0.0547795	−	0.0263804i
$918$		0			0
$919$	−5.62349	+	2.70813i	−0.185502	+	0.0893330i	−0.524329	−	0.851516i	$-0.675684\pi$
$919$	−5.62349	+	2.70813i	−0.185502	+	0.0893330i	0.338828	+	0.940848i	$0.389970\pi$
$920$		0			0
$921$	−1.45281	−	6.36518i	−0.0478718	−	0.209740i
$922$		0			0
$923$	36.8796	+	46.2456i	1.21391	+	1.52219i
$924$		0			0
$925$	−3.15721	−	13.8326i	−0.103808	−	0.454814i
$926$		0			0
$927$	−7.88471			−0.258968
$928$		0			0
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$		0			0
$931$	4.28286	+	18.7644i	0.140365	+	0.614979i
$932$		0			0
$933$	5.14071	+	6.44625i	0.168299	+	0.211041i
$934$		0			0
$935$	0.256668	+	1.12454i	0.00839395	+	0.0367763i
$936$		0			0
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	−0.372731	−	0.927939i	$-0.621579\pi$
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	0.493098	+	0.869974i	$0.335864\pi$
$938$		0			0
$939$	9.21917	+	4.43972i	0.300856	+	0.144885i
$940$		0			0
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	0.341181	−	0.939998i	$-0.389173\pi$
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	−0.522197	+	0.852825i	$0.674887\pi$
$942$		0			0
$943$	1.02177	−	1.28126i	0.0332734	−	0.0417235i
$944$		0			0
$945$	3.73125			0.121378
$946$		0			0
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	0.395309	+	0.918548i	$0.370638\pi$
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	−0.754704	+	0.656065i	$0.772220\pi$
$948$		0			0
$949$	41.8119	−	20.1356i	1.35727	−	0.653628i
$950$		0			0
$951$	−3.90097	+	4.89166i	−0.126498	+	0.158623i
$952$		0			0
$953$	−3.93541	+	17.2422i	−0.127480	+	0.558529i	0.870335	+	0.492461i	$0.163902\pi$
$953$	−3.93541	+	17.2422i	−0.127480	+	0.558529i	−0.997815	+	0.0660678i	$0.978955\pi$
$954$		0			0
$955$	4.18598	+	5.24905i	0.135455	+	0.169855i
$956$		0			0
$957$	−5.21528	+	4.63702i	−0.168586	+	0.149893i
$958$		0			0
$959$	−33.4245	−	41.9130i	−1.07933	−	1.35344i
$960$		0			0
$961$	−2.09395	+	9.17419i	−0.0675468	+	0.295942i
$962$		0			0
$963$	−13.0327	+	16.3424i	−0.419971	+	0.526628i
$964$		0			0
$965$	−3.50000	+	1.68551i	−0.112669	+	0.0542585i
$966$		0			0
$967$	−2.86904	+	12.5701i	−0.0922620	+	0.404226i	−0.999879	−	0.0155736i	$-0.995043\pi$
$967$	−2.86904	+	12.5701i	−0.0922620	+	0.404226i	0.907617	+	0.419800i	$0.137900\pi$
$968$		0			0
$969$	1.01208			0.0325127
$970$		0			0
$971$	−3.01610	+	3.78207i	−0.0967912	+	0.121372i	−0.827868	−	0.560923i	$-0.810447\pi$
$971$	−3.01610	+	3.78207i	−0.0967912	+	0.121372i	0.731077	+	0.682295i	$0.239018\pi$
$972$		0			0
$973$	−10.2017	−	4.91288i	−0.327052	−	0.157500i
$974$		0			0
$975$	−10.1322	−	4.87942i	−0.324491	−	0.156266i
$976$		0			0
$977$	−14.8138	+	7.13394i	−0.473935	+	0.228235i	−0.655575	−	0.755130i	$-0.727574\pi$
$977$	−14.8138	+	7.13394i	−0.473935	+	0.228235i	0.181640	+	0.983365i	$0.441859\pi$
$978$		0			0
$979$	0.922207	+	4.04045i	0.0294739	+	0.129133i
$980$		0			0
$981$	2.88740	+	3.62068i	0.0921874	+	0.115599i
$982$		0			0
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	0.977631	+	0.210329i	$0.0674535\pi$
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	−0.789557	+	0.613678i	$0.789689\pi$
$984$		0			0
$985$	−2.99808			−0.0955268
$986$		0			0
$987$	−14.0586			−0.447490
$988$		0			0
$989$	5.28501	+	23.1551i	0.168054	+	0.736291i
$990$		0			0
$991$	−25.1930	−	31.5910i	−0.800281	−	1.00352i	−0.999721	−	0.0236111i	$-0.992484\pi$
$991$	−25.1930	−	31.5910i	−0.800281	−	1.00352i	0.199440	−	0.979910i	$-0.436088\pi$
$992$		0			0
$993$	−1.38212	−	6.05548i	−0.0438604	−	0.192165i
$994$		0			0
$995$	−2.12910	+	1.02532i	−0.0674971	+	0.0325049i
$996$		0			0
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	0.737483	−	0.675366i	$-0.236014\pi$
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	−0.0682093	+	0.997671i	$0.521729\pi$
$998$		0			0
$999$	6.77413	+	3.26225i	0.214324	+	0.103213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.f.401.1		6
4.3	odd	2		29.2.d.a.24.1	yes	6
12.11	even	2		261.2.k.a.82.1		6
20.3	even	4		725.2.r.b.24.1		12
20.7	even	4		725.2.r.b.24.2		12
20.19	odd	2		725.2.l.b.401.1		6
29.23	even	7	inner	464.2.u.f.81.1		6
116.3	even	28		841.2.e.b.651.2		12
116.7	odd	14		841.2.d.e.190.1		6
116.11	even	28		841.2.e.c.236.1		12
116.15	even	28		841.2.e.d.267.1		12
116.19	even	28		841.2.e.c.196.2		12
116.23	odd	14		29.2.d.a.23.1	✓	6
116.27	even	28		841.2.e.b.270.2		12
116.31	even	28		841.2.e.b.270.1		12
116.35	odd	14		841.2.d.d.574.1		6
116.39	even	28		841.2.e.c.196.1		12
116.43	even	28		841.2.e.d.267.2		12
116.47	even	28		841.2.e.c.236.2		12
116.51	odd	14		841.2.d.a.190.1		6
116.55	even	28		841.2.e.b.651.1		12
116.63	odd	14		841.2.d.a.571.1		6
116.67	odd	14		841.2.a.f.1.3		3
116.71	odd	14		841.2.d.c.605.1		6
116.75	even	4		841.2.e.d.63.1		12
116.79	even	28		841.2.b.c.840.6		6
116.83	odd	14		841.2.d.b.645.1		6
116.91	odd	14		841.2.d.c.645.1		6
116.95	even	28		841.2.b.c.840.1		6
116.99	even	4		841.2.e.d.63.2		12
116.103	odd	14		841.2.d.b.605.1		6
116.107	odd	14		841.2.a.e.1.1		3
116.111	odd	14		841.2.d.e.571.1		6
116.115	odd	2		841.2.d.d.778.1		6
348.23	even	14		261.2.k.a.226.1		6
348.107	even	14		7569.2.a.r.1.3		3
348.299	even	14		7569.2.a.p.1.1		3
580.23	even	28		725.2.r.b.574.2		12
580.139	odd	14		725.2.l.b.226.1		6
580.487	even	28		725.2.r.b.574.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	116.23	odd	14
29.2.d.a.24.1	yes	6	4.3	odd	2
261.2.k.a.82.1		6	12.11	even	2
261.2.k.a.226.1		6	348.23	even	14
464.2.u.f.81.1		6	29.23	even	7	inner
464.2.u.f.401.1		6	1.1	even	1	trivial
725.2.l.b.226.1		6	580.139	odd	14
725.2.l.b.401.1		6	20.19	odd	2
725.2.r.b.24.1		12	20.3	even	4
725.2.r.b.24.2		12	20.7	even	4
725.2.r.b.574.1		12	580.487	even	28
725.2.r.b.574.2		12	580.23	even	28
841.2.a.e.1.1		3	116.107	odd	14
841.2.a.f.1.3		3	116.67	odd	14
841.2.b.c.840.1		6	116.95	even	28
841.2.b.c.840.6		6	116.79	even	28
841.2.d.a.190.1		6	116.51	odd	14
841.2.d.a.571.1		6	116.63	odd	14
841.2.d.b.605.1		6	116.103	odd	14
841.2.d.b.645.1		6	116.83	odd	14
841.2.d.c.605.1		6	116.71	odd	14
841.2.d.c.645.1		6	116.91	odd	14
841.2.d.d.574.1		6	116.35	odd	14
841.2.d.d.778.1		6	116.115	odd	2
841.2.d.e.190.1		6	116.7	odd	14
841.2.d.e.571.1		6	116.111	odd	14
841.2.e.b.270.1		12	116.31	even	28
841.2.e.b.270.2		12	116.27	even	28
841.2.e.b.651.1		12	116.55	even	28
841.2.e.b.651.2		12	116.3	even	28
841.2.e.c.196.1		12	116.39	even	28
841.2.e.c.196.2		12	116.19	even	28
841.2.e.c.236.1		12	116.11	even	28
841.2.e.c.236.2		12	116.47	even	28
841.2.e.d.63.1		12	116.75	even	4
841.2.e.d.63.2		12	116.99	even	4
841.2.e.d.267.1		12	116.15	even	28
841.2.e.d.267.2		12	116.43	even	28
7569.2.a.p.1.1		3	348.299	even	14
7569.2.a.r.1.3		3	348.107	even	14

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0990311 + 0.433884i) q^{3} +(0.222521 + 0.279032i) q^{5} +(-0.900969 - 3.94740i) q^{7} +(2.52446 - 1.21572i) q^{9} +(2.62349 + 1.26341i) q^{11} +(-4.67241 - 2.25011i) q^{13} +(-0.0990311 + 0.124181i) q^{15} +1.10992 q^{17} +(0.455927 - 1.99755i) q^{19} +(1.62349 - 0.781831i) q^{21} +(2.57942 - 3.23449i) q^{23} +(1.08426 - 4.75046i) q^{25} +(1.60992 + 2.01877i) q^{27} +(4.38404 + 3.12733i) q^{29} +(3.96346 + 4.97002i) q^{31} +(-0.288364 + 1.26341i) q^{33} +(0.900969 - 1.12978i) q^{35} +(2.62349 - 1.26341i) q^{37} +(0.513574 - 2.25011i) q^{39} +0.396125 q^{41} +(-3.57942 + 4.48845i) q^{43} +(0.900969 + 0.433884i) q^{45} +(-7.02930 - 3.38513i) q^{47} +(-8.46346 + 4.07579i) q^{49} +(0.109916 + 0.481575i) q^{51} +(-2.71648 - 3.40636i) q^{53} +(0.231250 + 1.01317i) q^{55} +0.911854 q^{57} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(-7.07338 - 8.86973i) q^{63} +(-0.411854 - 1.80445i) q^{65} +(0.337282 - 0.162426i) q^{67} +(1.65883 + 0.798852i) q^{69} +(-10.2763 - 4.94880i) q^{71} +(-5.57942 + 6.99637i) q^{73} +2.16852 q^{75} +(2.62349 - 11.4943i) q^{77} +(-0.535344 + 0.257808i) q^{79} +(4.52446 - 5.67349i) q^{81} +(-2.09903 + 9.19646i) q^{83} +(0.246980 + 0.309703i) q^{85} +(-0.922739 + 2.21187i) q^{87} +(0.887395 + 1.11276i) q^{89} +(-4.67241 + 20.4712i) q^{91} +(-1.76391 + 2.21187i) q^{93} +(0.658834 - 0.317278i) q^{95} +(-3.50484 + 15.3557i) q^{97} +8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{3} + q^{5} - q^{7} + 6 q^{9} + 11 q^{11} - 5 q^{13} - 5 q^{15} + 8 q^{17} - q^{19} + 5 q^{21} + 7 q^{23} - 24 q^{25} + 11 q^{27} + 6 q^{29} - 5 q^{31} + q^{33} + q^{35} + 11 q^{37} - 3 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) \) 6 * q + 5 * q^3 + q^5 - q^7 + 6 * q^9 + 11 * q^11 - 5 * q^13 - 5 * q^15 + 8 * q^17 - q^19 + 5 * q^21 + 7 * q^23 - 24 * q^25 + 11 * q^27 + 6 * q^29 - 5 * q^31 + q^33 + q^35 + 11 * q^37 - 3 * q^39 + 20 * q^41 - 13 * q^43 + q^45 - 11 * q^47 - 22 * q^49 + 2 * q^51 + 3 * q^53 + 17 * q^55 - 2 * q^57 + 56 * q^59 + 3 * q^61 - 15 * q^63 + 5 * q^65 - 19 * q^67 - 7 * q^69 - 21 * q^71 - 25 * q^73 - 48 * q^75 + 11 * q^77 + 9 * q^79 + 18 * q^81 - 17 * q^83 - 8 * q^85 + 5 * q^87 + 7 * q^89 - 5 * q^91 - 17 * q^93 - 13 * q^95 + q^97 + 32 * q^99

Introduction

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