LMFDB - Embedded newform 460.2.m.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

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("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	460.81
Dual form			460.2.m.a.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.161849 + 1.12569i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(0.847514 + 0.978083i) q^{7} +(1.63751 + 0.480815i) q^{9} +O(q^{10})$	\(q+(-0.161849 + 1.12569i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(0.847514 + 0.978083i) q^{7} +(1.63751 + 0.480815i) q^{9} +(0.123375 + 0.0792885i) q^{11} +(-2.87486 + 3.31776i) q^{13} +(-0.161849 - 1.12569i) q^{15} +(0.0296401 + 0.0649028i) q^{17} +(-0.913223 + 1.99968i) q^{19} +(-1.23818 + 0.795732i) q^{21} +(-0.0966389 + 4.79486i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-2.22358 + 4.86896i) q^{27} +(-1.49193 - 3.26687i) q^{29} +(1.16431 + 8.09798i) q^{31} +(-0.109222 + 0.126049i) q^{33} +(-1.08874 - 0.699691i) q^{35} +(-4.22517 - 1.24062i) q^{37} +(-3.26946 - 3.77316i) q^{39} +(2.94012 - 0.863298i) q^{41} +(-0.290905 + 2.02329i) q^{43} -1.70664 q^{45} +7.11821 q^{47} +(0.757837 - 5.27087i) q^{49} +(-0.0778574 + 0.0228610i) q^{51} +(-2.31840 - 2.67558i) q^{53} +(-0.140716 - 0.0413179i) q^{55} +(-2.10321 - 1.35165i) q^{57} +(6.41962 - 7.40864i) q^{59} +(0.284809 + 1.98089i) q^{61} +(0.917532 + 2.00911i) q^{63} +(1.82368 - 3.99331i) q^{65} +(5.94685 - 3.82181i) q^{67} +(-5.38186 - 0.884828i) q^{69} +(3.06874 - 1.97216i) q^{71} +(-4.39721 + 9.62854i) q^{73} +(0.472435 + 1.03449i) q^{75} +(0.0270115 + 0.187869i) q^{77} +(1.28994 - 1.48867i) q^{79} +(-0.813891 - 0.523056i) q^{81} +(4.79463 + 1.40783i) q^{83} +(-0.0467247 - 0.0539232i) q^{85} +(3.91893 - 1.15070i) q^{87} +(2.53647 - 17.6415i) q^{89} -5.68152 q^{91} -9.30422 q^{93} +(0.312856 - 2.17596i) q^{95} +(3.38532 - 0.994019i) q^{97} +(0.163905 + 0.189156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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
$3$	−0.161849	+	1.12569i	−0.0934436	+	0.649915i	0.888238	+	0.459384i	$0.151930\pi$
$3$	−0.161849	+	1.12569i	−0.0934436	+	0.649915i	−0.981681	+	0.190530i	$0.938979\pi$
$4$		0			0
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$		0			0
$7$	0.847514	+	0.978083i	0.320330	+	0.369681i	0.892962	−	0.450132i	$-0.148623\pi$
$7$	0.847514	+	0.978083i	0.320330	+	0.369681i	−0.572632	+	0.819813i	$0.694078\pi$
$8$		0			0
$9$	1.63751	+	0.480815i	0.545836	+	0.160272i
$10$		0			0
$11$	0.123375	+	0.0792885i	0.0371991	+	0.0239064i	0.559108	−	0.829095i	$-0.311144\pi$
$11$	0.123375	+	0.0792885i	0.0371991	+	0.0239064i	−0.521909	+	0.853001i	$0.674780\pi$
$12$		0			0
$13$	−2.87486	+	3.31776i	−0.797342	+	0.920181i	−0.998232	−	0.0594325i	$-0.981071\pi$
$13$	−2.87486	+	3.31776i	−0.797342	+	0.920181i	0.200891	+	0.979614i	$0.435616\pi$
$14$		0			0
$15$	−0.161849	−	1.12569i	−0.0417893	−	0.290651i
$16$		0			0
$17$	0.0296401	+	0.0649028i	0.00718879	+	0.0157412i	0.913192	−	0.407529i	$-0.133609\pi$
$17$	0.0296401	+	0.0649028i	0.00718879	+	0.0157412i	−0.906004	+	0.423270i	$0.860882\pi$
$18$		0			0
$19$	−0.913223	+	1.99968i	−0.209508	+	0.458758i	−0.984990	−	0.172611i	$-0.944780\pi$
$19$	−0.913223	+	1.99968i	−0.209508	+	0.458758i	0.775482	+	0.631369i	$0.217507\pi$
$20$		0			0
$21$	−1.23818	+	0.795732i	−0.270194	+	0.173643i
$22$		0			0
$23$	−0.0966389	+	4.79486i	−0.0201506	+	0.999797i
$23$	−0.0966389	+	4.79486i	−0.0201506	+	0.999797i
$24$		0			0
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$		0			0
$27$	−2.22358	+	4.86896i	−0.427928	+	0.937033i
$28$		0			0
$29$	−1.49193	−	3.26687i	−0.277044	−	0.606642i	0.719048	−	0.694960i	$-0.244578\pi$
$29$	−1.49193	−	3.26687i	−0.277044	−	0.606642i	−0.996092	+	0.0883180i	$0.971851\pi$
$30$		0			0
$31$	1.16431	+	8.09798i	0.209117	+	1.45444i	0.776047	+	0.630675i	$0.217222\pi$
$31$	1.16431	+	8.09798i	0.209117	+	1.45444i	−0.566930	+	0.823766i	$0.691869\pi$
$32$		0			0
$33$	−0.109222	+	0.126049i	−0.0190131	+	0.0219423i
$34$		0			0
$35$	−1.08874	−	0.699691i	−0.184031	−	0.118269i
$36$		0			0
$37$	−4.22517	−	1.24062i	−0.694614	−	0.203957i	−0.0846786	−	0.996408i	$-0.526986\pi$
$37$	−4.22517	−	1.24062i	−0.694614	−	0.203957i	−0.609935	+	0.792451i	$0.708805\pi$
$38$		0			0
$39$	−3.26946	−	3.77316i	−0.523533	−	0.604189i
$40$		0			0
$41$	2.94012	−	0.863298i	0.459170	−	0.134824i	−0.0439636	−	0.999033i	$-0.513999\pi$
$41$	2.94012	−	0.863298i	0.459170	−	0.134824i	0.503134	+	0.864209i	$0.332180\pi$
$42$		0			0
$43$	−0.290905	+	2.02329i	−0.0443626	+	0.308548i	0.955544	+	0.294850i	$0.0952696\pi$
$43$	−0.290905	+	2.02329i	−0.0443626	+	0.308548i	−0.999906	+	0.0136986i	$0.995639\pi$
$44$		0			0
$45$	−1.70664			−0.254411
$46$		0			0
$47$	7.11821			1.03830			0.519149	−	0.854684i	$-0.326249\pi$
$47$	7.11821			1.03830			0.519149	+	0.854684i	$0.326249\pi$
$48$		0			0
$49$	0.757837	−	5.27087i	0.108262	−	0.752982i
$50$		0			0
$51$	−0.0778574	+	0.0228610i	−0.0109022	+	0.00320118i
$52$		0			0
$53$	−2.31840	−	2.67558i	−0.318457	−	0.367519i	0.573840	−	0.818967i	$-0.305453\pi$
$53$	−2.31840	−	2.67558i	−0.318457	−	0.367519i	−0.892297	+	0.451448i	$0.850908\pi$
$54$		0			0
$55$	−0.140716	−	0.0413179i	−0.0189741	−	0.00557131i
$56$		0			0
$57$	−2.10321	−	1.35165i	−0.278576	−	0.179030i
$58$		0			0
$59$	6.41962	−	7.40864i	0.835763	−	0.964522i	−0.163996	−	0.986461i	$-0.552438\pi$
$59$	6.41962	−	7.40864i	0.835763	−	0.964522i	0.999759	+	0.0219386i	$0.00698382\pi$
$60$		0			0
$61$	0.284809	+	1.98089i	0.0364660	+	0.253627i	0.999897	−	0.0143287i	$-0.00456113\pi$
$61$	0.284809	+	1.98089i	0.0364660	+	0.253627i	−0.963431	+	0.267955i	$0.913652\pi$
$62$		0			0
$63$	0.917532	+	2.00911i	0.115598	+	0.253125i
$64$		0			0
$65$	1.82368	−	3.99331i	0.226200	−	0.495309i
$66$		0			0
$67$	5.94685	−	3.82181i	0.726523	−	0.466908i	−0.124377	−	0.992235i	$-0.539693\pi$
$67$	5.94685	−	3.82181i	0.726523	−	0.466908i	0.850901	+	0.525327i	$0.176057\pi$
$68$		0			0
$69$	−5.38186	−	0.884828i	−0.647900	−	0.106521i
$70$		0			0
$71$	3.06874	−	1.97216i	0.364193	−	0.234053i	−0.345727	−	0.938335i	$-0.612368\pi$
$71$	3.06874	−	1.97216i	0.364193	−	0.234053i	0.709920	+	0.704283i	$0.248731\pi$
$72$		0			0
$73$	−4.39721	+	9.62854i	−0.514654	+	1.12694i	0.456770	+	0.889585i	$0.349006\pi$
$73$	−4.39721	+	9.62854i	−0.514654	+	1.12694i	−0.971424	+	0.237350i	$0.923721\pi$
$74$		0			0
$75$	0.472435	+	1.03449i	0.0545521	+	0.119452i
$76$		0			0
$77$	0.0270115	+	0.187869i	0.00307825	+	0.0214097i
$78$		0			0
$79$	1.28994	−	1.48867i	0.145129	−	0.167488i	−0.678531	−	0.734572i	$-0.737383\pi$
$79$	1.28994	−	1.48867i	0.145129	−	0.167488i	0.823660	+	0.567084i	$0.191928\pi$
$80$		0			0
$81$	−0.813891	−	0.523056i	−0.0904324	−	0.0581174i
$82$		0			0
$83$	4.79463	+	1.40783i	0.526279	+	0.154529i	0.534070	−	0.845440i	$-0.320662\pi$
$83$	4.79463	+	1.40783i	0.526279	+	0.154529i	−0.00779126	+	0.999970i	$0.502480\pi$
$84$		0			0
$85$	−0.0467247	−	0.0539232i	−0.00506801	−	0.00584879i
$86$		0			0
$87$	3.91893	−	1.15070i	0.420154	−	0.123368i
$88$		0			0
$89$	2.53647	−	17.6415i	0.268865	−	1.87000i	−0.190408	−	0.981705i	$-0.560981\pi$
$89$	2.53647	−	17.6415i	0.268865	−	1.87000i	0.459273	−	0.888295i	$-0.348110\pi$
$90$		0			0
$91$	−5.68152			−0.595586
$92$		0			0
$93$	−9.30422			−0.964803
$94$		0			0
$95$	0.312856	−	2.17596i	0.0320984	−	0.223249i
$96$		0			0
$97$	3.38532	−	0.994019i	0.343727	−	0.100927i	−0.105313	−	0.994439i	$-0.533584\pi$
$97$	3.38532	−	0.994019i	0.343727	−	0.100927i	0.449040	+	0.893512i	$0.351766\pi$
$98$		0			0
$99$	0.163905	+	0.189156i	0.0164730	+	0.0190109i
$100$		0			0
$101$	10.9470	+	3.21434i	1.08927	+	0.319839i	0.776582	−	0.630017i	$-0.216952\pi$
$101$	10.9470	+	3.21434i	1.08927	+	0.319839i	0.312689	+	0.949855i	$0.398770\pi$
$102$		0			0
$103$	11.9199	+	7.66047i	1.17451	+	0.754809i	0.974368	−	0.224959i	$-0.0722249\pi$
$103$	11.9199	+	7.66047i	1.17451	+	0.754809i	0.200137	+	0.979768i	$0.435861\pi$
$104$		0			0
$105$	0.963844	−	1.11234i	0.0940615	−	0.108553i
$106$		0			0
$107$	−0.0334566	−	0.232696i	−0.00323437	−	0.0224955i	0.988140	−	0.153553i	$-0.0490717\pi$
$107$	−0.0334566	−	0.232696i	−0.00323437	−	0.0224955i	−0.991375	+	0.131058i	$0.958163\pi$
$108$		0			0
$109$	−6.90497	−	15.1198i	−0.661376	−	1.44821i	−0.881234	−	0.472679i	$-0.843287\pi$
$109$	−6.90497	−	15.1198i	−0.661376	−	1.44821i	0.219859	−	0.975532i	$-0.429440\pi$
$110$		0			0
$111$	2.08039	−	4.55542i	0.197462	−	0.432381i
$112$		0			0
$113$	10.5444	−	6.77645i	0.991929	−	0.637474i	0.0592736	−	0.998242i	$-0.481122\pi$
$113$	10.5444	−	6.77645i	0.991929	−	0.637474i	0.932656	+	0.360767i	$0.117485\pi$
$114$		0			0
$115$	−1.25814	−	4.62786i	−0.117322	−	0.431550i
$116$		0			0
$117$	−6.30283	+	4.05058i	−0.582697	+	0.374476i
$118$		0			0
$119$	−0.0383599	+	0.0839965i	−0.00351645	+	0.00769995i
$120$		0			0
$121$	−4.56063	−	9.98639i	−0.414603	−	0.907853i
$122$		0			0
$123$	0.495946	+	3.44938i	0.0447179	+	0.311020i
$124$		0			0
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$		0			0
$127$	−2.73048	−	1.75477i	−0.242291	−	0.155711i	0.413860	−	0.910340i	$-0.364180\pi$
$127$	−2.73048	−	1.75477i	−0.242291	−	0.155711i	−0.656151	+	0.754630i	$0.727817\pi$
$128$		0			0
$129$	−2.23050	−	0.654934i	−0.196385	−	0.0576638i
$130$		0			0
$131$	−4.89170	−	5.64532i	−0.427390	−	0.493234i	0.500684	−	0.865630i	$-0.333082\pi$
$131$	−4.89170	−	5.64532i	−0.427390	−	0.493234i	−0.928074	+	0.372396i	$0.878536\pi$
$132$		0			0
$133$	−2.72982	+	0.801548i	−0.236706	+	0.0695030i
$134$		0			0
$135$	0.761765	−	5.29819i	0.0655623	−	0.455996i
$136$		0			0
$137$	−16.6394			−1.42160			−0.710801	−	0.703393i	$-0.751667\pi$
$137$	−16.6394			−1.42160			−0.710801	+	0.703393i	$0.751667\pi$
$138$		0			0
$139$	5.63655			0.478086			0.239043	−	0.971009i	$-0.423166\pi$
$139$	5.63655			0.478086			0.239043	+	0.971009i	$0.423166\pi$
$140$		0			0
$141$	−1.15208	+	8.01287i	−0.0970223	+	0.674805i
$142$		0			0
$143$	−0.617746	+	0.181387i	−0.0516585	+	0.0151683i
$144$		0			0
$145$	2.35188	+	2.71421i	0.195313	+	0.225403i
$146$		0			0
$147$	5.81069	+	1.70617i	0.479258	+	0.140723i
$148$		0			0
$149$	2.37434	+	1.52589i	0.194513	+	0.125006i	0.634272	−	0.773110i	$-0.281300\pi$
$149$	2.37434	+	1.52589i	0.194513	+	0.125006i	−0.439759	+	0.898116i	$0.644936\pi$
$150$		0			0
$151$	−8.85909	+	10.2239i	−0.720943	+	0.832012i	−0.991420	−	0.130714i	$-0.958273\pi$
$151$	−8.85909	+	10.2239i	−0.720943	+	0.832012i	0.270477	+	0.962726i	$0.412818\pi$
$152$		0			0
$153$	0.0173296	+	0.120530i	0.00140102	+	0.00974429i
$154$		0			0
$155$	−3.39862	−	7.44193i	−0.272983	−	0.597750i
$156$		0			0
$157$	2.51094	−	5.49819i	0.200395	−	0.438803i	−0.782578	−	0.622552i	$-0.786096\pi$
$157$	2.51094	−	5.49819i	0.200395	−	0.438803i	0.982973	+	0.183749i	$0.0588232\pi$
$158$		0			0
$159$	3.38709	−	2.17675i	0.268614	−	0.172627i
$160$		0			0
$161$	−4.77167	+	3.96919i	−0.376060	+	0.312816i
$162$		0			0
$163$	−1.21995	+	0.784011i	−0.0955535	+	0.0614085i	−0.587545	−	0.809192i	$-0.699905\pi$
$163$	−1.21995	+	0.784011i	−0.0955535	+	0.0614085i	0.491991	+	0.870600i	$0.336269\pi$
$164$		0			0
$165$	0.0692857	−	0.151715i	0.00539388	−	0.0118110i
$166$		0			0
$167$	−1.48242	−	3.24605i	−0.114713	−	0.251187i	0.843563	−	0.537030i	$-0.180454\pi$
$167$	−1.48242	−	3.24605i	−0.114713	−	0.251187i	−0.958277	+	0.285843i	$0.907726\pi$
$168$		0			0
$169$	−0.892646	−	6.20849i	−0.0686650	−	0.477576i
$170$		0			0
$171$	−2.45689	+	2.83540i	−0.187883	+	0.216828i
$172$		0			0
$173$	5.30307	+	3.40807i	0.403185	+	0.259111i	0.726481	−	0.687187i	$-0.241155\pi$
$173$	5.30307	+	3.40807i	0.403185	+	0.259111i	−0.323296	+	0.946298i	$0.604791\pi$
$174$		0			0
$175$	1.24177	+	0.364615i	0.0938686	+	0.0275623i
$176$		0			0
$177$	7.30078	+	8.42555i	0.548761	+	0.633303i
$178$		0			0
$179$	−0.491203	+	0.144230i	−0.0367143	+	0.0107803i	−0.300038	−	0.953927i	$-0.596999\pi$
$179$	−0.491203	+	0.144230i	−0.0367143	+	0.0107803i	0.263324	+	0.964707i	$0.415181\pi$
$180$		0			0
$181$	−1.13130	+	7.86835i	−0.0840887	+	0.584850i	0.903595	+	0.428387i	$0.140918\pi$
$181$	−1.13130	+	7.86835i	−0.0840887	+	0.584850i	−0.987684	+	0.156462i	$0.949991\pi$
$182$		0			0
$183$	−2.27595			−0.168243
$184$		0			0
$185$	4.40355			0.323755
$186$		0			0
$187$	−0.00148919	+	0.0103575i	−0.000108900	+	0.000757417i
$188$		0			0
$189$	−6.64677	+	1.95167i	−0.483481	+	0.141963i
$190$		0			0
$191$	−6.58494	−	7.59942i	−0.476469	−	0.549875i	0.465730	−	0.884927i	$-0.345792\pi$
$191$	−6.58494	−	7.59942i	−0.476469	−	0.549875i	−0.942200	+	0.335052i	$0.891246\pi$
$192$		0			0
$193$	19.1000	+	5.60827i	1.37485	+	0.403692i	0.883973	−	0.467537i	$-0.154859\pi$
$193$	19.1000	+	5.60827i	1.37485	+	0.403692i	0.490876	+	0.871230i	$0.336677\pi$
$194$		0			0
$195$	4.20005	+	2.69921i	0.300772	+	0.193294i
$196$		0			0
$197$	−7.70052	+	8.88688i	−0.548640	+	0.633164i	−0.960566	−	0.278054i	$-0.910311\pi$
$197$	−7.70052	+	8.88688i	−0.548640	+	0.633164i	0.411926	+	0.911217i	$0.364856\pi$
$198$		0			0
$199$	2.31515	+	16.1022i	0.164117	+	1.14146i	0.890770	+	0.454454i	$0.150165\pi$
$199$	2.31515	+	16.1022i	0.164117	+	1.14146i	−0.726654	+	0.687004i	$0.758925\pi$
$200$		0			0
$201$	3.33966	+	7.31284i	0.235561	+	0.515808i
$202$		0			0
$203$	1.93084	−	4.22795i	0.135518	−	0.296744i
$204$		0			0
$205$	−2.57781	+	1.65666i	−0.180042	+	0.115706i
$206$		0			0
$207$	−2.46369	+	7.80515i	−0.171238	+	0.542495i
$208$		0			0
$209$	−0.271221	+	0.174303i	−0.0187607	+	0.0120568i
$210$		0			0
$211$	−6.32195	+	13.8431i	−0.435221	+	0.953001i	0.557230	+	0.830358i	$0.311864\pi$
$211$	−6.32195	+	13.8431i	−0.435221	+	0.953001i	−0.992451	+	0.122643i	$0.960863\pi$
$212$		0			0
$213$	1.72336	+	3.77363i	0.118083	+	0.258565i
$214$		0			0
$215$	−0.290905	−	2.02329i	−0.0198395	−	0.137987i
$216$		0			0
$217$	−6.93373	+	8.00195i	−0.470692	+	0.543208i
$218$		0			0
$219$	−10.1270	−	6.50824i	−0.684321	−	0.439786i
$220$		0			0
$221$	−0.300543	−	0.0882474i	−0.0202167	−	0.00593616i
$222$		0			0
$223$	5.99921	+	6.92345i	0.401737	+	0.463629i	0.920187	−	0.391479i	$-0.128036\pi$
$223$	5.99921	+	6.92345i	0.401737	+	0.463629i	−0.518451	+	0.855108i	$0.673491\pi$
$224$		0			0
$225$	1.63751	−	0.480815i	0.109167	−	0.0320544i
$226$		0			0
$227$	2.32490	−	16.1701i	0.154309	−	1.07324i	−0.754580	−	0.656208i	$-0.772160\pi$
$227$	2.32490	−	16.1701i	0.154309	−	1.07324i	0.908890	−	0.417037i	$-0.136931\pi$
$228$		0			0
$229$	−10.2975			−0.680475			−0.340238	−	0.940339i	$-0.610508\pi$
$229$	−10.2975			−0.680475			−0.340238	+	0.940339i	$0.610508\pi$
$230$		0			0
$231$	−0.215854			−0.0142021
$232$		0			0
$233$	−0.620623	+	4.31653i	−0.0406584	+	0.282785i	0.959341	+	0.282248i	$0.0910801\pi$
$233$	−0.620623	+	4.31653i	−0.0406584	+	0.282785i	−1.00000		0.000537159i	$0.999829\pi$
$234$		0			0
$235$	−6.82987	+	2.00543i	−0.445532	+	0.130820i
$236$		0			0
$237$	1.46700	+	1.69300i	0.0952917	+	0.109972i
$238$		0			0
$239$	22.8596	+	6.71219i	1.47866	+	0.434175i	0.918905	−	0.394480i	$-0.129075\pi$
$239$	22.8596	+	6.71219i	1.47866	+	0.434175i	0.559760	+	0.828655i	$0.310893\pi$
$240$		0			0
$241$	15.2923	+	9.82776i	0.985063	+	0.633062i	0.930825	−	0.365466i	$-0.119090\pi$
$241$	15.2923	+	9.82776i	0.985063	+	0.633062i	0.0542385	+	0.998528i	$0.482727\pi$
$242$		0			0
$243$	−9.79525	+	11.3043i	−0.628365	+	0.725172i
$244$		0			0
$245$	0.757837	+	5.27087i	0.0484164	+	0.336744i
$246$		0			0
$247$	−4.00907	−	8.77865i	−0.255091	−	0.558572i
$248$		0			0
$249$	−2.36078	+	5.16939i	−0.149608	+	0.327596i
$250$		0			0
$251$	7.95141	−	5.11006i	0.501888	−	0.322544i	−0.265083	−	0.964226i	$-0.585399\pi$
$251$	7.95141	−	5.11006i	0.501888	−	0.322544i	0.766971	+	0.641682i	$0.221763\pi$
$252$		0			0
$253$	−0.392100	+	0.583905i	−0.0246511	+	0.0367098i
$254$		0			0
$255$	0.0682629	−	0.0438699i	0.00427479	−	0.00274724i
$256$		0			0
$257$	−0.798862	+	1.74926i	−0.0498316	+	0.109116i	−0.932910	−	0.360109i	$-0.882739\pi$
$257$	−0.798862	+	1.74926i	−0.0498316	+	0.109116i	0.883079	+	0.469225i	$0.155467\pi$
$258$		0			0
$259$	−2.36746	−	5.18401i	−0.147107	−	0.322119i
$260$		0			0
$261$	−0.872283	−	6.06686i	−0.0539930	−	0.375529i
$262$		0			0
$263$	−9.31681	+	10.7522i	−0.574499	+	0.663008i	−0.966413	−	0.256994i	$-0.917268\pi$
$263$	−9.31681	+	10.7522i	−0.574499	+	0.663008i	0.391913	+	0.920002i	$0.371813\pi$
$264$		0			0
$265$	2.97829	+	1.91403i	0.182955	+	0.117578i
$266$		0			0
$267$	19.4483	+	5.71054i	1.19022	+	0.349479i
$268$		0			0
$269$	7.75728	+	8.95237i	0.472970	+	0.545836i	0.941235	−	0.337752i	$-0.109666\pi$
$269$	7.75728	+	8.95237i	0.472970	+	0.545836i	−0.468266	+	0.883588i	$0.655121\pi$
$270$		0			0
$271$	−9.89565	+	2.90562i	−0.601118	+	0.176504i	−0.568112	−	0.822951i	$-0.692326\pi$
$271$	−9.89565	+	2.90562i	−0.601118	+	0.176504i	−0.0330054	+	0.999455i	$0.510508\pi$
$272$		0			0
$273$	0.919550	−	6.39561i	0.0556537	−	0.387080i
$274$		0			0
$275$	0.146656			0.00884372
$276$		0			0
$277$	−19.2636			−1.15743			−0.578717	−	0.815528i	$-0.696447\pi$
$277$	−19.2636			−1.15743			−0.578717	+	0.815528i	$0.696447\pi$
$278$		0			0
$279$	−1.98706	+	13.8203i	−0.118962	+	0.827401i
$280$		0			0
$281$	29.2929	−	8.60118i	1.74747	−	0.513103i	0.757311	−	0.653055i	$-0.226513\pi$
$281$	29.2929	−	8.60118i	1.74747	−	0.513103i	0.990158	+	0.139952i	$0.0446947\pi$
$282$		0			0
$283$	−15.1637	−	17.4999i	−0.901391	−	1.04026i	−0.998985	−	0.0450344i	$-0.985660\pi$
$283$	−15.1637	−	17.4999i	−0.901391	−	1.04026i	0.0975945	−	0.995226i	$-0.468885\pi$
$284$		0			0
$285$	2.39881	+	0.704356i	0.142094	+	0.0417224i
$286$		0			0
$287$	3.33617	+	2.14403i	0.196928	+	0.126558i
$288$		0			0
$289$	11.1293	−	12.8439i	0.654665	−	0.755523i
$290$		0			0
$291$	0.571042	+	3.97169i	0.0334751	+	0.232824i
$292$		0			0
$293$	−4.32120	−	9.46211i	−0.252447	−	0.552782i	0.740401	−	0.672165i	$-0.234636\pi$
$293$	−4.32120	−	9.46211i	−0.252447	−	0.552782i	−0.992848	+	0.119383i	$0.961908\pi$
$294$		0			0
$295$	−4.07233	+	8.91715i	−0.237100	+	0.519177i
$296$		0			0
$297$	−0.660388	+	0.424405i	−0.0383196	+	0.0246265i
$298$		0			0
$299$	−15.6304	−	14.1051i	−0.903927	−	0.815722i
$300$		0			0
$301$	−2.22549	+	1.43023i	−0.128275	+	0.0824373i
$302$		0			0
$303$	−5.39010	+	11.8027i	−0.309653	+	0.678046i
$304$		0			0
$305$	−0.831352	−	1.82041i	−0.0476031	−	0.104236i
$306$		0			0
$307$	4.38541	+	30.5012i	0.250288	+	1.74079i	0.596478	+	0.802630i	$0.296566\pi$
$307$	4.38541	+	30.5012i	0.250288	+	1.74079i	−0.346189	+	0.938165i	$0.612525\pi$
$308$		0			0
$309$	−10.5525	+	12.1782i	−0.600311	+	0.692796i
$310$		0			0
$311$	−24.1308	−	15.5079i	−1.36833	−	0.879372i	−0.369572	−	0.929202i	$-0.620496\pi$
$311$	−24.1308	−	15.5079i	−1.36833	−	0.879372i	−0.998758	+	0.0498301i	$0.984132\pi$
$312$		0			0
$313$	−18.6545	−	5.47746i	−1.05442	−	0.309604i	−0.291816	−	0.956475i	$-0.594259\pi$
$313$	−18.6545	−	5.47746i	−1.05442	−	0.309604i	−0.762600	+	0.646870i	$0.776078\pi$
$314$		0			0
$315$	−1.44640	−	1.66923i	−0.0814953	−	0.0940506i
$316$		0			0
$317$	13.0751	−	3.83918i	0.734369	−	0.215630i	0.106898	−	0.994270i	$-0.465908\pi$
$317$	13.0751	−	3.83918i	0.734369	−	0.215630i	0.627471	+	0.778640i	$0.284090\pi$
$318$		0			0
$319$	0.0749579	−	0.521344i	0.00419684	−	0.0291896i
$320$		0			0
$321$	0.267357			0.0149224
$322$		0			0
$323$	−0.156853			−0.00872753
$324$		0			0
$325$	−0.624766	+	4.34534i	−0.0346558	+	0.241036i
$326$		0			0
$327$	18.1377	−	5.32570i	1.00301	−	0.294512i
$328$		0			0
$329$	6.03278	+	6.96220i	0.332598	+	0.383839i
$330$		0			0
$331$	3.58665	+	1.05313i	0.197140	+	0.0578855i	0.378812	−	0.925474i	$-0.376333\pi$
$331$	3.58665	+	1.05313i	0.197140	+	0.0578855i	−0.181672	+	0.983359i	$0.558151\pi$
$332$		0			0
$333$	−6.32224	−	4.06305i	−0.346456	−	0.222654i
$334$		0			0
$335$	−4.62923	+	5.34242i	−0.252922	+	0.291888i
$336$		0			0
$337$	−4.44773	−	30.9346i	−0.242283	−	1.68512i	−0.640606	−	0.767870i	$-0.721317\pi$
$337$	−4.44773	−	30.9346i	−0.242283	−	1.68512i	0.398323	−	0.917245i	$-0.369592\pi$
$338$		0			0
$339$	5.92155	+	12.9664i	0.321614	+	0.704237i
$340$		0			0
$341$	−0.498429	+	1.09141i	−0.0269915	+	0.0591030i
$342$		0			0
$343$	13.4188	−	8.62375i	0.724548	−	0.465639i
$344$		0			0
$345$	5.41314	−	0.667258i	0.291434	−	0.0359240i
$346$		0			0
$347$	−3.71660	+	2.38851i	−0.199517	+	0.128222i	−0.636585	−	0.771207i	$-0.719653\pi$
$347$	−3.71660	+	2.38851i	−0.199517	+	0.128222i	0.437067	+	0.899429i	$0.356017\pi$
$348$		0			0
$349$	−11.2696	+	24.6771i	−0.603250	+	1.32093i	0.323846	+	0.946110i	$0.395024\pi$
$349$	−11.2696	+	24.6771i	−0.603250	+	1.32093i	−0.927096	+	0.374824i	$0.877703\pi$
$350$		0			0
$351$	−9.76158	−	21.3749i	−0.521035	−	1.14091i
$352$		0			0
$353$	−0.809559	−	5.63060i	−0.0430885	−	0.299687i	−0.999958	−	0.00916873i	$-0.997081\pi$
$353$	−0.809559	−	5.63060i	−0.0430885	−	0.299687i	0.956870	−	0.290518i	$-0.0938276\pi$
$354$		0			0
$355$	−2.38882	+	2.75684i	−0.126785	+	0.146318i
$356$		0			0
$357$	−0.0883451	−	0.0567760i	−0.00467572	−	0.00300490i
$358$		0			0
$359$	−21.5713	−	6.33392i	−1.13849	−	0.334291i	−0.342452	−	0.939535i	$-0.611257\pi$
$359$	−21.5713	−	6.33392i	−1.13849	−	0.334291i	−0.796040	+	0.605244i	$0.793076\pi$
$360$		0			0
$361$	9.27761	+	10.7069i	0.488295	+	0.563523i
$362$		0			0
$363$	11.9797	−	3.51755i	0.628769	−	0.184623i
$364$		0			0
$365$	1.50642	−	10.4774i	0.0788494	−	0.548410i
$366$		0			0
$367$	−13.5709			−0.708393			−0.354196	−	0.935171i	$-0.615246\pi$
$367$	−13.5709			−0.708393			−0.354196	+	0.935171i	$0.615246\pi$
$368$		0			0
$369$	5.22956			0.272240
$370$		0			0
$371$	0.652060	−	4.53518i	0.0338533	−	0.235455i
$372$		0			0
$373$	16.0298	−	4.70678i	0.829992	−	0.243708i	0.160979	−	0.986958i	$-0.448535\pi$
$373$	16.0298	−	4.70678i	0.829992	−	0.243708i	0.669014	+	0.743250i	$0.266717\pi$
$374$		0			0
$375$	−0.744747	−	0.859484i	−0.0384586	−	0.0443836i
$376$		0			0
$377$	15.1278	+	4.44191i	0.779120	+	0.228770i
$378$		0			0
$379$	16.6997	+	10.7323i	0.857807	+	0.551279i	0.894001	−	0.448066i	$-0.147887\pi$
$379$	16.6997	+	10.7323i	0.857807	+	0.551279i	−0.0361935	+	0.999345i	$0.511523\pi$
$380$		0			0
$381$	2.41724	−	2.78965i	0.123839	−	0.142918i
$382$		0			0
$383$	−4.26884	−	29.6904i	−0.218128	−	1.51711i	−0.744942	−	0.667130i	$-0.767523\pi$
$383$	−4.26884	−	29.6904i	−0.218128	−	1.51711i	0.526814	−	0.849981i	$-0.323386\pi$
$384$		0			0
$385$	−0.0788463	−	0.172649i	−0.00401838	−	0.00879902i
$386$		0			0
$387$	−1.44919	+	3.17328i	−0.0736663	+	0.161307i
$388$		0			0
$389$	−7.51283	+	4.82820i	−0.380915	+	0.244799i	−0.717061	−	0.697011i	$-0.754513\pi$
$389$	−7.51283	+	4.82820i	−0.380915	+	0.244799i	0.336145	+	0.941810i	$0.390877\pi$
$390$		0			0
$391$	−0.314064	+	0.135848i	−0.0158829	+	0.00687013i
$392$		0			0
$393$	7.14657	−	4.59282i	0.360497	−	0.231677i
$394$		0			0
$395$	−0.818280	+	1.79178i	−0.0411722	+	0.0901545i
$396$		0			0
$397$	−5.75471	−	12.6011i	−0.288821	−	0.632429i	0.708490	−	0.705721i	$-0.249377\pi$
$397$	−5.75471	−	12.6011i	−0.288821	−	0.632429i	−0.997311	+	0.0732919i	$0.976650\pi$
$398$		0			0
$399$	−0.460472	−	3.20265i	−0.0230524	−	0.160333i
$400$		0			0
$401$	−0.487003	+	0.562031i	−0.0243198	+	0.0280665i	−0.767779	−	0.640715i	$-0.778638\pi$
$401$	−0.487003	+	0.562031i	−0.0243198	+	0.0280665i	0.743459	+	0.668781i	$0.233184\pi$
$402$		0			0
$403$	−30.2144	−	19.4176i	−1.50509	−	0.967260i
$404$		0			0
$405$	0.928285	+	0.272569i	0.0461269	+	0.0135441i
$406$		0			0
$407$	−0.422915	−	0.488069i	−0.0209631	−	0.0241927i
$408$		0			0
$409$	18.5059	−	5.43383i	0.915059	−	0.268686i	0.209890	−	0.977725i	$-0.432689\pi$
$409$	18.5059	−	5.43383i	0.915059	−	0.268686i	0.705169	+	0.709039i	$0.250871\pi$
$410$		0			0
$411$	2.69308	−	18.7307i	0.132840	−	0.923920i
$412$		0			0
$413$	12.6870			0.624285
$414$		0			0
$415$	−4.99704			−0.245295
$416$		0			0
$417$	−0.912270	+	6.34498i	−0.0446741	+	0.310715i
$418$		0			0
$419$	−3.50879	+	1.03027i	−0.171415	+	0.0503321i	−0.366314	−	0.930491i	$-0.619380\pi$
$419$	−3.50879	+	1.03027i	−0.171415	+	0.0503321i	0.194899	+	0.980823i	$0.437562\pi$
$420$		0			0
$421$	6.52623	+	7.53167i	0.318069	+	0.367071i	0.892159	−	0.451721i	$-0.149190\pi$
$421$	6.52623	+	7.53167i	0.318069	+	0.367071i	−0.574090	+	0.818792i	$0.694644\pi$
$422$		0			0
$423$	11.6561	+	3.42255i	0.566740	+	0.166410i
$424$		0			0
$425$	0.0600240	+	0.0385751i	0.00291159	+	0.00187117i
$426$		0			0
$427$	−1.69609	+	1.95740i	−0.0820797	+	0.0947250i
$428$		0			0
$429$	−0.104203	−	0.724745i	−0.00503095	−	0.0349910i
$430$		0			0
$431$	−15.8418	−	34.6886i	−0.763071	−	1.67089i	−0.741342	−	0.671128i	$-0.765810\pi$
$431$	−15.8418	−	34.6886i	−0.763071	−	1.67089i	−0.0217290	−	0.999764i	$-0.506917\pi$
$432$		0			0
$433$	−4.46576	+	9.77865i	−0.214611	+	0.469932i	−0.986067	−	0.166351i	$-0.946802\pi$
$433$	−4.46576	+	9.77865i	−0.214611	+	0.469932i	0.771456	+	0.636283i	$0.219529\pi$
$434$		0			0
$435$	−3.43600	+	2.20818i	−0.164744	+	0.105874i
$436$		0			0
$437$	−9.49993	−	4.57202i	−0.454443	−	0.218710i
$438$		0			0
$439$	17.5570	−	11.2832i	0.837952	−	0.538519i	−0.0498435	−	0.998757i	$-0.515872\pi$
$439$	17.5570	−	11.2832i	0.837952	−	0.538519i	0.887796	+	0.460238i	$0.152236\pi$
$440$		0			0
$441$	3.77528	−	8.26671i	0.179775	−	0.393653i
$442$		0			0
$443$	−10.5849	−	23.1778i	−0.502905	−	1.10121i	−0.975514	−	0.219936i	$-0.929415\pi$
$443$	−10.5849	−	23.1778i	−0.502905	−	1.10121i	0.472609	−	0.881272i	$-0.343312\pi$
$444$		0			0
$445$	2.53647	+	17.6415i	0.120240	+	0.836290i
$446$		0			0
$447$	−2.10196	+	2.42579i	−0.0994194	+	0.114736i
$448$		0			0
$449$	19.9207	+	12.8023i	0.940116	+	0.604176i	0.918428	−	0.395589i	$-0.129459\pi$
$449$	19.9207	+	12.8023i	0.940116	+	0.604176i	0.0216886	+	0.999765i	$0.493096\pi$
$450$		0			0
$451$	0.431188	+	0.126608i	0.0203039	+	0.00596175i
$452$		0			0
$453$	−10.0751	−	11.6273i	−0.473369	−	0.546298i
$454$		0			0
$455$	5.45138	−	1.60067i	0.255565	−	0.0750406i
$456$		0			0
$457$	4.73409	−	32.9263i	0.221451	−	1.54023i	−0.511103	−	0.859519i	$-0.670763\pi$
$457$	4.73409	−	32.9263i	0.221451	−	1.54023i	0.732554	−	0.680708i	$-0.238328\pi$
$458$		0			0
$459$	−0.381917			−0.0178264
$460$		0			0
$461$	32.2765			1.50327			0.751633	−	0.659582i	$-0.229267\pi$
$461$	32.2765			1.50327			0.751633	+	0.659582i	$0.229267\pi$
$462$		0			0
$463$	2.12635	−	14.7891i	0.0988199	−	0.687307i	−0.878840	−	0.477116i	$-0.841682\pi$
$463$	2.12635	−	14.7891i	0.0988199	−	0.687307i	0.977660	−	0.210191i	$-0.0674087\pi$
$464$		0			0
$465$	8.92734	−	2.62130i	0.413995	−	0.121560i
$466$		0			0
$467$	11.4407	+	13.2032i	0.529411	+	0.610972i	0.955962	−	0.293491i	$-0.0948171\pi$
$467$	11.4407	+	13.2032i	0.529411	+	0.610972i	−0.426551	+	0.904463i	$0.640272\pi$
$468$		0			0
$469$	8.77808	+	2.57748i	0.405334	+	0.119017i
$470$		0			0
$471$	5.78284	+	3.71640i	0.266459	+	0.171243i
$472$		0			0
$473$	−0.196314	+	0.226558i	−0.00902652	+	0.0104172i
$474$		0			0
$475$	0.312856	+	2.17596i	0.0143548	+	0.0998401i
$476$		0			0
$477$	−2.50994	−	5.49600i	−0.114922	−	0.251644i
$478$		0			0
$479$	−5.46652	+	11.9700i	−0.249772	+	0.546924i	−0.992439	−	0.122736i	$-0.960833\pi$
$479$	−5.46652	+	11.9700i	−0.249772	+	0.546924i	0.742668	+	0.669660i	$0.233560\pi$
$480$		0			0
$481$	16.2628	−	10.4515i	0.741522	−	0.476547i
$482$		0			0
$483$	−3.69576	−	6.01381i	−0.168163	−	0.273638i
$484$		0			0
$485$	−2.96814	+	1.90751i	−0.134776	+	0.0866155i
$486$		0			0
$487$	14.1549	−	30.9949i	0.641421	−	1.40452i	−0.257446	−	0.966293i	$-0.582881\pi$
$487$	14.1549	−	30.9949i	0.641421	−	1.40452i	0.898867	−	0.438223i	$-0.144392\pi$
$488$		0			0
$489$	−0.685103	−	1.50017i	−0.0309814	−	0.0678399i
$490$		0			0
$491$	−0.901268	−	6.26845i	−0.0406736	−	0.282891i	−1.00000		0.000591419i	$-0.999812\pi$
$491$	−0.901268	−	6.26845i	−0.0406736	−	0.282891i	0.959326	−	0.282300i	$-0.0910973\pi$
$492$		0			0
$493$	0.167808	−	0.193661i	0.00755770	−	0.00872205i
$494$		0			0
$495$	−0.210557	−	0.135317i	−0.00946383	−	0.00608203i
$496$		0			0
$497$	4.52974	+	1.33005i	0.203187	+	0.0596610i
$498$		0			0
$499$	14.6008	+	16.8502i	0.653621	+	0.754319i	0.981721	−	0.190324i	$-0.0609538\pi$
$499$	14.6008	+	16.8502i	0.653621	+	0.754319i	−0.328100	+	0.944643i	$0.606408\pi$
$500$		0			0
$501$	3.89396	−	1.14337i	0.173969	−	0.0510820i
$502$		0			0
$503$	−0.934184	+	6.49739i	−0.0416532	+	0.289704i	0.958339	+	0.285635i	$0.0922044\pi$
$503$	−0.934184	+	6.49739i	−0.0416532	+	0.289704i	−0.999992	+	0.00406947i	$0.998705\pi$
$504$		0			0
$505$	−11.4092			−0.507702
$506$		0			0
$507$	7.13328			0.316800
$508$		0			0
$509$	−5.46645	+	38.0200i	−0.242296	+	1.68521i	0.398241	+	0.917281i	$0.369621\pi$
$509$	−5.46645	+	38.0200i	−0.242296	+	1.68521i	−0.640537	+	0.767927i	$0.721288\pi$
$510$		0			0
$511$	−13.1442	+	3.85949i	−0.581465	+	0.170734i
$512$		0			0
$513$	−7.70575	−	8.89290i	−0.340217	−	0.392631i
$514$		0			0
$515$	−13.5953	−	3.99194i	−0.599080	−	0.175906i
$516$		0			0
$517$	0.878211	+	0.564392i	0.0386237	+	0.0248219i
$518$		0			0
$519$	−4.69472	+	5.41799i	−0.206075	+	0.237823i
$520$		0			0
$521$	−0.668277	−	4.64797i	−0.0292778	−	0.203631i	0.969932	−	0.243376i	$-0.0782548\pi$
$521$	−0.668277	−	4.64797i	−0.0292778	−	0.203631i	−0.999210	+	0.0397443i	$0.987346\pi$
$522$		0			0
$523$	−2.76081	−	6.04533i	−0.120722	−	0.264344i	0.839617	−	0.543178i	$-0.182779\pi$
$523$	−2.76081	−	6.04533i	−0.120722	−	0.264344i	−0.960339	+	0.278834i	$0.910052\pi$
$524$		0			0
$525$	−0.611421	+	1.33882i	−0.0266846	+	0.0584311i
$526$		0			0
$527$	−0.491072	+	0.315593i	−0.0213914	+	0.0137474i
$528$		0			0
$529$	−22.9813	−	0.926739i	−0.999188	−	0.0402930i
$530$		0			0
$531$	14.0744	−	9.04504i	0.610775	−	0.392521i
$532$		0			0
$533$	−5.58821	+	12.2365i	−0.242052	+	0.530021i
$534$		0			0
$535$	0.0976593	+	0.213844i	0.00422218	+	0.00924528i
$536$		0			0
$537$	−0.0828571	−	0.576284i	−0.00357555	−	0.0248685i
$538$		0			0
$539$	0.511418	−	0.590208i	0.0220283	−	0.0254220i
$540$		0			0
$541$	−11.9439	−	7.67586i	−0.513507	−	0.330011i	0.258092	−	0.966120i	$-0.416906\pi$
$541$	−11.9439	−	7.67586i	−0.513507	−	0.330011i	−0.771599	+	0.636109i	$0.780543\pi$
$542$		0			0
$543$	−8.67419	−	2.54697i	−0.372245	−	0.109301i
$544$		0			0
$545$	10.8850	+	12.5620i	0.466262	+	0.538095i
$546$		0			0
$547$	−1.84741	+	0.542450i	−0.0789898	+	0.0231935i	−0.320989	−	0.947083i	$-0.604015\pi$
$547$	−1.84741	+	0.542450i	−0.0789898	+	0.0231935i	0.241999	+	0.970277i	$0.422197\pi$
$548$		0			0
$549$	−0.486065	+	3.38066i	−0.0207448	+	0.144283i
$550$		0			0
$551$	7.89516			0.336345
$552$		0			0
$553$	2.54928			0.108406
$554$		0			0
$555$	−0.712710	+	4.95701i	−0.0302528	+	0.210413i
$556$		0			0
$557$	−15.7314	+	4.61916i	−0.666561	+	0.195720i	−0.597471	−	0.801891i	$-0.703828\pi$
$557$	−15.7314	+	4.61916i	−0.666561	+	0.195720i	−0.0690898	+	0.997610i	$0.522009\pi$
$558$		0			0
$559$	−5.87647	−	6.78181i	−0.248548	−	0.286840i
$560$		0			0
$561$	−0.0114183	−	0.00335271i	−0.000482081	−	0.000141552i
$562$		0			0
$563$	14.5901	+	9.37651i	0.614901	+	0.395173i	0.810692	−	0.585473i	$-0.199091\pi$
$563$	14.5901	+	9.37651i	0.614901	+	0.395173i	−0.195791	+	0.980646i	$0.562728\pi$
$564$		0			0
$565$	−8.20809	+	9.47264i	−0.345317	+	0.398517i
$566$		0			0
$567$	−0.178192	−	1.23935i	−0.00748335	−	0.0520478i
$568$		0			0
$569$	7.25944	+	15.8960i	0.304332	+	0.666393i	0.998576	−	0.0533461i	$-0.0169886\pi$
$569$	7.25944	+	15.8960i	0.304332	+	0.666393i	−0.694245	+	0.719739i	$0.744261\pi$
$570$		0			0
$571$	−3.99142	+	8.73998i	−0.167036	+	0.365757i	−0.974577	−	0.224055i	$-0.928071\pi$
$571$	−3.99142	+	8.73998i	−0.167036	+	0.365757i	0.807541	+	0.589811i	$0.200798\pi$
$572$		0			0
$573$	9.62032	−	6.18261i	0.401895	−	0.258282i
$574$		0			0
$575$	2.51100	+	4.08594i	0.104716	+	0.170395i
$576$		0			0
$577$	0.123392	−	0.0792992i	0.00513688	−	0.00330127i	−0.538070	−	0.842900i	$-0.680846\pi$
$577$	0.123392	−	0.0792992i	0.00513688	−	0.00330127i	0.543207	+	0.839599i	$0.317210\pi$
$578$		0			0
$579$	−9.40447	+	20.5929i	−0.390836	+	0.855812i
$580$		0			0
$581$	2.68654	+	5.88270i	0.111456	+	0.244055i
$582$		0			0
$583$	−0.0738909	−	0.513923i	−0.00306025	−	0.0212845i
$584$		0			0
$585$	4.90634	−	5.66222i	0.202852	−	0.234104i
$586$		0			0
$587$	−19.1716	−	12.3208i	−0.791297	−	0.508536i	0.0814683	−	0.996676i	$-0.474039\pi$
$587$	−19.1716	−	12.3208i	−0.791297	−	0.508536i	−0.872765	+	0.488140i	$0.837675\pi$
$588$		0			0
$589$	−17.2567	−	5.06701i	−0.711048	−	0.208783i
$590$		0			0
$591$	−8.75750	−	10.1067i	−0.360236	−	0.415734i
$592$		0			0
$593$	−25.8292	+	7.58412i	−1.06068	+	0.311443i	−0.765123	−	0.643884i	$-0.777322\pi$
$593$	−25.8292	+	7.58412i	−1.06068	+	0.311443i	−0.295553	+	0.955326i	$0.595504\pi$
$594$		0			0
$595$	0.0131415	−	0.0914013i	0.000538750	−	0.00374709i
$596$		0			0
$597$	−18.5008			−0.757186
$598$		0			0
$599$	−21.7594			−0.889065			−0.444533	−	0.895763i	$-0.646630\pi$
$599$	−21.7594			−0.889065			−0.444533	+	0.895763i	$0.646630\pi$
$600$		0			0
$601$	−5.11741	+	35.5924i	−0.208744	+	1.45184i	0.568520	+	0.822669i	$0.307516\pi$
$601$	−5.11741	+	35.5924i	−0.208744	+	1.45184i	−0.777264	+	0.629175i	$0.783393\pi$
$602$		0			0
$603$	11.5756	−	3.39890i	0.471394	−	0.138414i
$604$		0			0
$605$	7.18938	+	8.29699i	0.292290	+	0.337321i
$606$		0			0
$607$	−3.57593	−	1.04999i	−0.145142	−	0.0426176i	0.208354	−	0.978053i	$-0.433189\pi$
$607$	−3.57593	−	1.04999i	−0.145142	−	0.0426176i	−0.353497	+	0.935436i	$0.615007\pi$
$608$		0			0
$609$	4.44683	+	2.85781i	0.180195	+	0.115804i
$610$		0			0
$611$	−20.4638	+	23.6165i	−0.827878	+	0.955422i
$612$		0			0
$613$	−4.17760	−	29.0558i	−0.168732	−	1.17355i	−0.881510	−	0.472165i	$-0.843473\pi$
$613$	−4.17760	−	29.0558i	−0.168732	−	1.17355i	0.712779	−	0.701389i	$-0.247436\pi$
$614$		0			0
$615$	−1.44766	−	3.16993i	−0.0583752	−	0.127824i
$616$		0			0
$617$	0.486818	−	1.06598i	0.0195986	−	0.0429149i	−0.899580	−	0.436757i	$-0.856127\pi$
$617$	0.486818	−	1.06598i	0.0195986	−	0.0429149i	0.919178	+	0.393842i	$0.128854\pi$
$618$		0			0
$619$	33.5034	−	21.5313i	1.34661	−	0.865416i	0.349183	−	0.937054i	$-0.386459\pi$
$619$	33.5034	−	21.5313i	1.34661	−	0.865416i	0.997431	+	0.0716380i	$0.0228226\pi$
$620$		0			0
$621$	−23.1311	−	11.1323i	−0.928219	−	0.446723i
$622$		0			0
$623$	19.4046	−	12.4706i	0.777428	−	0.499623i
$624$		0			0
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$		0			0
$627$	−0.152314	−	0.333520i	−0.00608282	−	0.0133195i
$628$		0			0
$629$	−0.0447147	−	0.310998i	−0.00178289	−	0.0124003i
$630$		0			0
$631$	−15.5777	+	17.9776i	−0.620137	+	0.715676i	−0.975733	−	0.218964i	$-0.929732\pi$
$631$	−15.5777	+	17.9776i	−0.620137	+	0.715676i	0.355596	+	0.934640i	$0.384278\pi$
$632$		0			0
$633$	−14.5598	−	9.35703i	−0.578701	−	0.371908i
$634$		0			0
$635$	3.11425	+	0.914426i	0.123585	+	0.0362879i
$636$		0			0
$637$	15.3088	+	17.6673i	0.606558	+	0.700005i
$638$		0			0
$639$	5.97333	−	1.75393i	0.236301	−	0.0693844i
$640$		0			0
$641$	2.51874	−	17.5182i	0.0994841	−	0.691927i	−0.877650	−	0.479302i	$-0.840890\pi$
$641$	2.51874	−	17.5182i	0.0994841	−	0.691927i	0.977134	−	0.212625i	$-0.0682012\pi$
$642$		0			0
$643$	27.7826			1.09564			0.547819	−	0.836597i	$-0.315458\pi$
$643$	27.7826			1.09564			0.547819	+	0.836597i	$0.315458\pi$
$644$		0			0
$645$	2.32467			0.0915337
$646$		0			0
$647$	−3.73708	+	25.9920i	−0.146920	+	1.02185i	0.774303	+	0.632815i	$0.218101\pi$
$647$	−3.73708	+	25.9920i	−0.146920	+	1.02185i	−0.921223	+	0.389035i	$0.872808\pi$
$648$		0			0
$649$	1.37944	−	0.405041i	0.0541478	−	0.0158992i
$650$		0			0
$651$	−7.88546	−	9.10030i	−0.309055	−	0.356669i
$652$		0			0
$653$	25.9558	+	7.62131i	1.01573	+	0.298245i	0.746895	−	0.664942i	$-0.231544\pi$
$653$	25.9558	+	7.62131i	1.01573	+	0.298245i	0.268834	+	0.963187i	$0.413362\pi$
$654$		0			0
$655$	6.28402	+	4.03850i	0.245537	+	0.157797i
$656$		0			0
$657$	−11.8300	+	13.6526i	−0.461533	+	0.532637i
$658$		0			0
$659$	7.20152	+	50.0877i	0.280531	+	1.95114i	0.307629	+	0.951507i	$0.400465\pi$
$659$	7.20152	+	50.0877i	0.280531	+	1.95114i	−0.0270971	+	0.999633i	$0.508626\pi$
$660$		0			0
$661$	3.27525	+	7.17179i	0.127392	+	0.278950i	0.962572	−	0.271028i	$-0.0873635\pi$
$661$	3.27525	+	7.17179i	0.127392	+	0.278950i	−0.835179	+	0.549978i	$0.814636\pi$
$662$		0			0
$663$	0.147981	−	0.324034i	0.00574712	−	0.0125844i
$664$		0			0
$665$	2.39342	−	1.53816i	0.0928130	−	0.0596473i
$666$		0			0
$667$	15.8083	−	6.83788i	0.612102	−	0.264764i
$668$		0			0
$669$	−8.76459	+	5.63266i	−0.338859	+	0.217771i
$670$		0			0
$671$	−0.121923	+	0.266975i	−0.00470679	+	0.0103064i
$672$		0			0
$673$	8.82588	+	19.3260i	0.340213	+	0.744962i	0.999979	−	0.00650935i	$-0.00207200\pi$
$673$	8.82588	+	19.3260i	0.340213	+	0.744962i	−0.659766	+	0.751471i	$0.729345\pi$
$674$		0			0
$675$	0.761765	+	5.29819i	0.0293204	+	0.203928i
$676$		0			0
$677$	−21.6947	+	25.0370i	−0.833795	+	0.962251i	−0.999715	−	0.0238881i	$-0.992395\pi$
$677$	−21.6947	+	25.0370i	−0.833795	+	0.962251i	0.165919	+	0.986139i	$0.446941\pi$
$678$		0			0
$679$	3.84134	+	2.46868i	0.147417	+	0.0947392i
$680$		0			0
$681$	17.8261	+	5.23422i	0.683098	+	0.200576i
$682$		0			0
$683$	−9.86271	−	11.3822i	−0.377386	−	0.435527i	0.535003	−	0.844850i	$-0.320310\pi$
$683$	−9.86271	−	11.3822i	−0.377386	−	0.435527i	−0.912390	+	0.409323i	$0.865765\pi$
$684$		0			0
$685$	15.9654	−	4.68787i	0.610007	−	0.179114i
$686$		0			0
$687$	1.66663	−	11.5917i	0.0635861	−	0.442251i
$688$		0			0
$689$	15.5420			0.592103
$690$		0			0
$691$	−28.1650			−1.07145			−0.535724	−	0.844393i	$-0.679961\pi$
$691$	−28.1650			−1.07145			−0.535724	+	0.844393i	$0.679961\pi$
$692$		0			0
$693$	−0.0460989	+	0.320625i	−0.00175115	+	0.0121795i
$694$		0			0
$695$	−5.40823	+	1.58800i	−0.205146	+	0.0602362i
$696$		0			0
$697$	0.143176	+	0.165234i	0.00542318	+	0.00625869i
$698$		0			0
$699$	−4.75860	−	1.39725i	−0.179987	−	0.0528489i
$700$		0			0
$701$	−7.42277	−	4.77033i	−0.280354	−	0.180173i	0.392905	−	0.919579i	$-0.371470\pi$
$701$	−7.42277	−	4.77033i	−0.280354	−	0.180173i	−0.673260	+	0.739406i	$0.735106\pi$
$702$		0			0
$703$	6.33937	−	7.31603i	0.239094	−	0.275929i
$704$		0			0
$705$	−1.15208	−	8.01287i	−0.0433897	−	0.301782i
$706$		0			0
$707$	6.13387	+	13.4313i	0.230688	+	0.505136i
$708$		0			0
$709$	−20.5822	+	45.0687i	−0.772981	+	1.69259i	−0.0530037	+	0.998594i	$0.516880\pi$
$709$	−20.5822	+	45.0687i	−0.772981	+	1.69259i	−0.719977	+	0.693998i	$0.755848\pi$
$710$		0			0
$711$	2.82806	−	1.81748i	0.106060	−	0.0681609i
$712$		0			0
$713$	−38.9412	+	4.80014i	−1.45836	+	0.179767i
$714$		0			0
$715$	0.541621	−	0.348079i	0.0202555	−	0.0130174i
$716$		0			0
$717$	−11.2556	+	24.6464i	−0.420349	+	0.920435i
$718$		0			0
$719$	−11.0701	−	24.2402i	−0.412846	−	0.904007i	−0.995805	−	0.0915052i	$-0.970832\pi$
$719$	−11.0701	−	24.2402i	−0.412846	−	0.904007i	0.582958	−	0.812502i	$-0.301895\pi$
$720$		0			0
$721$	2.60972	+	18.1510i	0.0971912	+	0.675980i
$722$		0			0
$723$	−13.5380	+	15.6237i	−0.503484	+	0.581051i
$724$		0			0
$725$	−3.02129	−	1.94167i	−0.112208	−	0.0721117i
$726$		0			0
$727$	10.9763	+	3.22292i	0.407087	+	0.119532i	0.478864	−	0.877889i	$-0.341049\pi$
$727$	10.9763	+	3.22292i	0.407087	+	0.119532i	−0.0717769	+	0.997421i	$0.522867\pi$
$728$		0			0
$729$	−13.0404	−	15.0495i	−0.482979	−	0.557387i
$730$		0			0
$731$	−0.139940	+	0.0410900i	−0.00517585	+	0.00151977i
$732$		0			0
$733$	3.86837	−	26.9051i	0.142882	−	0.993763i	−0.784629	−	0.619966i	$-0.787146\pi$
$733$	3.86837	−	26.9051i	0.142882	−	0.993763i	0.927510	−	0.373797i	$-0.121944\pi$
$734$		0			0
$735$	−6.05600			−0.223379
$736$		0			0
$737$	1.03672			0.0381881
$738$		0			0
$739$	−4.72428	+	32.8581i	−0.173785	+	1.20870i	0.697011	+	0.717061i	$0.254513\pi$
$739$	−4.72428	+	32.8581i	−0.173785	+	1.20870i	−0.870796	+	0.491644i	$0.836396\pi$
$740$		0			0
$741$	10.5309	−	3.09214i	0.386861	−	0.113593i
$742$		0			0
$743$	32.5407	+	37.5540i	1.19380	+	1.37772i	0.907751	+	0.419509i	$0.137798\pi$
$743$	32.5407	+	37.5540i	1.19380	+	1.37772i	0.286053	+	0.958214i	$0.407657\pi$
$744$		0			0
$745$	−2.70806	−	0.795157i	−0.0992155	−	0.0291323i
$746$		0			0
$747$	7.17433	+	4.61066i	0.262495	+	0.168695i
$748$		0			0
$749$	0.199241	−	0.229936i	0.00728009	−	0.00840168i
$750$		0			0
$751$	−0.395963	−	2.75398i	−0.0144489	−	0.100494i	0.981321	−	0.192378i	$-0.0616201\pi$
$751$	−0.395963	−	2.75398i	−0.0144489	−	0.100494i	−0.995770	+	0.0918843i	$0.970711\pi$
$752$		0			0
$753$	4.46539	+	9.77784i	0.162728	+	0.356324i
$754$		0			0
$755$	5.61982	−	12.3057i	0.204526	−	0.447850i
$756$		0			0
$757$	44.8193	−	28.8036i	1.62898	−	1.04688i	0.679212	−	0.733942i	$-0.262322\pi$
$757$	44.8193	−	28.8036i	1.62898	−	1.04688i	0.949772	−	0.312942i	$-0.101315\pi$
$758$		0			0
$759$	−0.593832	−	0.535885i	−0.0215547	−	0.0194514i
$760$		0			0
$761$	−30.8007	+	19.7944i	−1.11653	+	0.717547i	−0.962705	−	0.270552i	$-0.912794\pi$
$761$	−30.8007	+	19.7944i	−1.11653	+	0.717547i	−0.153820	+	0.988099i	$0.549158\pi$
$762$		0			0
$763$	8.93633	−	19.5678i	0.323517	−	0.708403i
$764$		0			0
$765$	−0.0505850	−	0.110766i	−0.00182890	−	0.00400474i
$766$		0			0
$767$	6.12460	+	42.5975i	0.221146	+	1.53811i
$768$		0			0
$769$	26.7788	−	30.9044i	0.965668	−	1.11444i	−0.0277173	−	0.999616i	$-0.508824\pi$
$769$	26.7788	−	30.9044i	0.965668	−	1.11444i	0.993386	−	0.114825i	$-0.0366307\pi$
$770$		0			0
$771$	−1.83983	−	1.18238i	−0.0662597	−	0.0425825i
$772$		0			0
$773$	29.9481	+	8.79354i	1.07716	+	0.316282i	0.771741	−	0.635937i	$-0.219386\pi$
$773$	29.9481	+	8.79354i	1.07716	+	0.316282i	0.305416	+	0.952219i	$0.401205\pi$
$774$		0			0
$775$	5.35758	+	6.18298i	0.192450	+	0.222099i
$776$		0			0
$777$	6.21874	−	1.82599i	0.223096	−	0.0655069i
$778$		0			0
$779$	−0.958669	+	6.66769i	−0.0343479	+	0.238895i
$780$		0			0
$781$	0.534977			0.0191430
$782$		0			0
$783$	19.2237			0.686999
$784$		0			0
$785$	−0.860210	+	5.98289i	−0.0307022	+	0.213538i
$786$		0			0
$787$	4.45260	−	1.30740i	0.158718	−	0.0466038i	−0.201408	−	0.979507i	$-0.564552\pi$
$787$	4.45260	−	1.30740i	0.158718	−	0.0466038i	0.360126	+	0.932904i	$0.382734\pi$
$788$		0			0
$789$	−10.5956	−	12.2280i	−0.377215	−	0.435329i
$790$		0			0
$791$	15.5644	+	4.57012i	0.553407	+	0.162495i
$792$		0			0
$793$	−7.39089	−	4.74984i	−0.262458	−	0.168672i
$794$		0			0
$795$	−2.63663	+	3.04283i	−0.0935115	+	0.107918i
$796$		0			0
$797$	−5.44166	−	37.8476i	−0.192753	−	1.34063i	−0.824679	−	0.565601i	$-0.808644\pi$
$797$	−5.44166	−	37.8476i	−0.192753	−	1.34063i	0.631926	−	0.775029i	$-0.282265\pi$
$798$		0			0
$799$	0.210985	+	0.461992i	0.00746410	+	0.0163441i
$800$		0			0
$801$	12.6358	−	27.6686i	0.446465	−	0.977621i
$802$		0			0
$803$	−1.30594	+	0.839276i	−0.0460856	+	0.0296174i
$804$		0			0
$805$	3.46014	−	5.15274i	0.121954	−	0.181610i
$806$		0			0
$807$	−11.3331	+	7.28332i	−0.398943	+	0.256385i
$808$		0			0
$809$	−2.62974	+	5.75834i	−0.0924569	+	0.202452i	−0.950211	−	0.311609i	$-0.899132\pi$
$809$	−2.62974	+	5.75834i	−0.0924569	+	0.202452i	0.857754	+	0.514061i	$0.171860\pi$
$810$		0			0
$811$	11.6202	+	25.4446i	0.408039	+	0.893480i	0.996392	+	0.0848759i	$0.0270494\pi$
$811$	11.6202	+	25.4446i	0.408039	+	0.893480i	−0.588353	+	0.808604i	$0.700223\pi$
$812$		0			0
$813$	−1.66922	−	11.6097i	−0.0585420	−	0.407168i
$814$		0			0
$815$	0.949648	−	1.09595i	0.0332647	−	0.0383895i
$816$		0			0
$817$	−3.78027	−	2.42943i	−0.132255	−	0.0849950i
$818$		0			0
$819$	−9.30353	−	2.73176i	−0.325092	−	0.0954556i
$820$		0			0
$821$	−8.51357	−	9.82518i	−0.297125	−	0.342901i	0.587482	−	0.809237i	$-0.300119\pi$
$821$	−8.51357	−	9.82518i	−0.297125	−	0.342901i	−0.884608	+	0.466336i	$0.845574\pi$
$822$		0			0
$823$	−30.7078	+	9.01663i	−1.07041	+	0.314300i	−0.769035	−	0.639207i	$-0.779263\pi$
$823$	−30.7078	+	9.01663i	−1.07041	+	0.314300i	−0.301372	+	0.953507i	$0.597445\pi$
$824$		0			0
$825$	−0.0237362	+	0.165089i	−0.000826389	+	0.00574766i
$826$		0			0
$827$	−39.6081			−1.37731			−0.688654	−	0.725091i	$-0.741798\pi$
$827$	−39.6081			−1.37731			−0.688654	+	0.725091i	$0.741798\pi$
$828$		0			0
$829$	−54.7701			−1.90224			−0.951122	−	0.308816i	$-0.900067\pi$
$829$	−54.7701			−1.90224			−0.951122	+	0.308816i	$0.900067\pi$
$830$		0			0
$831$	3.11779	−	21.6847i	0.108155	−	0.752234i
$832$		0			0
$833$	0.364557	−	0.107044i	0.0126312	−	0.00370884i
$834$		0			0
$835$	2.33689	+	2.69692i	0.0808715	+	0.0933307i
$836$		0			0
$837$	−42.0177	−	12.3375i	−1.45235	−	0.426447i
$838$		0			0
$839$	28.5577	+	18.3529i	0.985922	+	0.633614i	0.931055	−	0.364880i	$-0.118890\pi$
$839$	28.5577	+	18.3529i	0.985922	+	0.633614i	0.0548677	+	0.998494i	$0.482526\pi$
$840$		0			0
$841$	10.5444	−	12.1689i	0.363599	−	0.419616i
$842$		0			0
$843$	4.94119	+	34.3667i	0.170183	+	1.18365i
$844$		0			0
$845$	2.60562	+	5.70551i	0.0896360	+	0.196276i
$846$		0			0
$847$	5.90232	−	12.9243i	0.202806	−	0.444083i
$848$		0			0
$849$	22.1536	−	14.2373i	0.760310	−	0.488621i
$850$		0			0
$851$	6.35692	−	20.1392i	0.217912	−	0.690363i
$852$		0			0
$853$	−7.66843	+	4.92820i	−0.262562	+	0.168738i	−0.665298	−	0.746578i	$-0.731696\pi$
$853$	−7.66843	+	4.92820i	−0.262562	+	0.168738i	0.402736	+	0.915316i	$0.368059\pi$
$854$		0			0
$855$	1.55854	−	3.41273i	0.0533010	−	0.116713i
$856$		0			0
$857$	19.7296	+	43.2017i	0.673949	+	1.47574i	0.868929	+	0.494936i	$0.164809\pi$
$857$	19.7296	+	43.2017i	0.673949	+	1.47574i	−0.194980	+	0.980807i	$0.562464\pi$
$858$		0			0
$859$	−6.42179	−	44.6645i	−0.219109	−	1.52393i	−0.741340	−	0.671130i	$-0.765809\pi$
$859$	−6.42179	−	44.6645i	−0.219109	−	1.52393i	0.522231	−	0.852804i	$-0.325100\pi$
$860$		0			0
$861$	−2.95346	+	3.40847i	−0.100653	+	0.116160i
$862$		0			0
$863$	−23.0369	−	14.8049i	−0.784184	−	0.503964i	0.0862357	−	0.996275i	$-0.472516\pi$
$863$	−23.0369	−	14.8049i	−0.784184	−	0.503964i	−0.870420	+	0.492310i	$0.836153\pi$
$864$		0			0
$865$	−6.04842	−	1.77598i	−0.205652	−	0.0603850i
$866$		0			0
$867$	12.6569	+	14.6069i	0.429851	+	0.496075i
$868$		0			0
$869$	0.277181	−	0.0813876i	0.00940271	−	0.00276089i
$870$		0			0
$871$	−4.41649	+	30.7174i	−0.149647	+	1.04082i
$872$		0			0
$873$	6.02142			0.203794
$874$		0			0
$875$	−1.29419			−0.0437516
$876$		0			0
$877$	6.57369	−	45.7210i	0.221978	−	1.54389i	−0.508565	−	0.861023i	$-0.669824\pi$
$877$	6.57369	−	45.7210i	0.221978	−	1.54389i	0.730543	−	0.682867i	$-0.239267\pi$
$878$		0			0
$879$	11.3507	−	3.33288i	0.382851	−	0.112415i
$880$		0			0
$881$	9.14442	+	10.5532i	0.308083	+	0.355547i	0.888585	−	0.458712i	$-0.151689\pi$
$881$	9.14442	+	10.5532i	0.308083	+	0.355547i	−0.580502	+	0.814259i	$0.697144\pi$
$882$		0			0
$883$	11.1140	+	3.26336i	0.374016	+	0.109821i	0.463337	−	0.886182i	$-0.346652\pi$
$883$	11.1140	+	3.26336i	0.374016	+	0.109821i	−0.0893218	+	0.996003i	$0.528470\pi$
$884$		0			0
$885$	−9.37880	−	6.02739i	−0.315265	−	0.202609i
$886$		0			0
$887$	−37.4852	+	43.2603i	−1.25863	+	1.45254i	−0.420291	+	0.907390i	$0.638072\pi$
$887$	−37.4852	+	43.2603i	−1.25863	+	1.45254i	−0.838340	+	0.545148i	$0.816474\pi$
$888$		0			0
$889$	−0.597805	−	4.15782i	−0.0200497	−	0.139449i
$890$		0			0
$891$	−0.0589418	−	0.129064i	−0.00197462	−	0.00432382i
$892$		0			0
$893$	−6.50052	+	14.2341i	−0.217532	+	0.476328i
$894$		0			0
$895$	0.430672	−	0.276776i	0.0143958	−	0.00925160i
$896$		0			0
$897$	18.4077	−	15.3120i	0.614616	−	0.511252i
$898$		0			0
$899$	24.7180	−	15.8853i	0.824391	−	0.529804i
$900$		0			0
$901$	0.104935	−	0.229775i	0.00349589	−	0.00765492i
$902$		0			0
$903$	−1.24980	−	2.73668i	−0.0415908	−	0.0910711i
$904$		0			0
$905$	−1.13130	−	7.86835i	−0.0376056	−	0.261553i
$906$		0			0
$907$	11.5493	−	13.3286i	0.383489	−	0.442570i	−0.530883	−	0.847445i	$-0.678140\pi$
$907$	11.5493	−	13.3286i	0.383489	−	0.442570i	0.914372	+	0.404875i	$0.132685\pi$
$908$		0			0
$909$	16.3803	+	10.5270i	0.543302	+	0.349159i
$910$		0			0
$911$	−33.1735	−	9.74062i	−1.09909	−	0.322721i	−0.318598	−	0.947890i	$-0.603212\pi$
$911$	−33.1735	−	9.74062i	−1.09909	−	0.322721i	−0.780490	+	0.625169i	$0.785030\pi$
$912$		0			0
$913$	0.479914	+	0.553850i	0.0158828	+	0.0183298i
$914$		0			0
$915$	2.18376	−	0.641210i	0.0721929	−	0.0211977i
$916$		0			0
$917$	1.37581	−	9.56897i	0.0454333	−	0.315995i
$918$		0			0
$919$	19.6577			0.648446			0.324223	−	0.945981i	$-0.394897\pi$
$919$	19.6577			0.648446			0.324223	+	0.945981i	$0.394897\pi$
$920$		0			0
$921$	−35.0445			−1.15476
$922$		0			0
$923$	−2.27903	+	15.8510i	−0.0750153	+	0.521743i
$924$		0			0
$925$	−4.22517	+	1.24062i	−0.138923	+	0.0407914i
$926$		0			0
$927$	15.8357	+	18.2754i	0.520112	+	0.600242i
$928$		0			0
$929$	4.35919	+	1.27997i	0.143020	+	0.0419945i	0.352459	−	0.935827i	$-0.385346\pi$
$929$	4.35919	+	1.27997i	0.143020	+	0.0419945i	−0.209439	+	0.977822i	$0.567164\pi$
$930$		0			0
$931$	9.84799	+	6.32892i	0.322755	+	0.207422i
$932$		0			0
$933$	21.3625	−	24.6537i	0.699378	−	0.807126i
$934$		0			0
$935$	−0.00148919	−	0.0103575i	−4.87016e−5	−	0.000338727i
$936$		0			0
$937$	−22.2168	−	48.6479i	−0.725790	−	1.58926i	−0.805608	−	0.592448i	$-0.798161\pi$
$937$	−22.2168	−	48.6479i	−0.725790	−	1.58926i	0.0798186	−	0.996809i	$-0.474566\pi$
$938$		0			0
$939$	9.18511	−	20.1126i	0.299745	−	0.656350i
$940$		0			0
$941$	20.2129	−	12.9900i	0.658921	−	0.423463i	−0.167995	−	0.985788i	$-0.553729\pi$
$941$	20.2129	−	12.9900i	0.658921	−	0.423463i	0.826916	+	0.562325i	$0.190093\pi$
$942$		0			0
$943$	3.85526	+	14.1809i	0.125545	+	0.461794i
$944$		0			0
$945$	5.82768	−	3.74522i	0.189574	−	0.121832i
$946$		0			0
$947$	13.5431	−	29.6552i	0.440091	−	0.963665i	−0.551490	−	0.834181i	$-0.685941\pi$
$947$	13.5431	−	29.6552i	0.440091	−	0.963665i	0.991582	−	0.129484i	$-0.0413321\pi$
$948$		0			0
$949$	−19.3039	−	42.2695i	−0.626630	−	1.37213i
$950$		0			0
$951$	2.20553	+	15.3398i	0.0715191	+	0.497426i
$952$		0			0
$953$	−19.5449	+	22.5560i	−0.633120	+	0.730659i	−0.978143	−	0.207935i	$-0.933326\pi$
$953$	−19.5449	+	22.5560i	−0.633120	+	0.730659i	0.345023	+	0.938594i	$0.387871\pi$
$954$		0			0
$955$	8.45921	+	5.43640i	0.273733	+	0.175918i
$956$		0			0
$957$	0.574737	+	0.168758i	0.0185786	+	0.00545517i
$958$		0			0
$959$	−14.1021	−	16.2747i	−0.455382	−	0.525538i
$960$		0			0
$961$	−34.4774	+	10.1235i	−1.11217	+	0.326564i
$962$		0			0
$963$	0.0570982	−	0.397127i	0.00183997	−	0.0127972i
$964$		0			0
$965$	−19.9064			−0.640808
$966$		0			0
$967$	40.0316			1.28733			0.643665	−	0.765307i	$-0.277413\pi$
$967$	40.0316			1.28733			0.643665	+	0.765307i	$0.277413\pi$
$968$		0			0
$969$	0.0253865	−	0.176567i	0.000815532	−	0.00567215i
$970$		0			0
$971$	−0.698536	+	0.205109i	−0.0224171	+	0.00658225i	−0.292922	−	0.956136i	$-0.594628\pi$
$971$	−0.698536	+	0.205109i	−0.0224171	+	0.00658225i	0.270505	+	0.962719i	$0.412809\pi$
$972$		0			0
$973$	4.77705	+	5.51301i	0.153145	+	0.176739i
$974$		0			0
$975$	−4.79037	−	1.40658i	−0.153415	−	0.0450466i
$976$		0			0
$977$	−41.0268	−	26.3663i	−1.31256	−	0.843534i	−0.318044	−	0.948076i	$-0.603026\pi$
$977$	−41.0268	−	26.3663i	−1.31256	−	0.843534i	−0.994520	+	0.104542i	$0.966662\pi$
$978$		0			0
$979$	1.71171	−	1.97542i	0.0547065	−	0.0631346i
$980$		0			0
$981$	−4.03711	−	28.0787i	−0.128895	−	0.896485i
$982$		0			0
$983$	−8.36528	−	18.3174i	−0.266811	−	0.584234i	0.728046	−	0.685529i	$-0.240429\pi$
$983$	−8.36528	−	18.3174i	−0.266811	−	0.584234i	−0.994857	+	0.101294i	$0.967702\pi$
$984$		0			0
$985$	4.88487	−	10.6964i	0.155645	−	0.340815i
$986$		0			0
$987$	−8.81365	+	5.66419i	−0.280541	+	0.180293i
$988$		0			0
$989$	−9.67326	−	1.59038i	−0.307592	−	0.0505710i
$990$		0			0
$991$	48.8209	−	31.3753i	1.55085	−	0.996669i	0.565768	−	0.824564i	$-0.308580\pi$
$991$	48.8209	−	31.3753i	1.55085	−	0.996669i	0.985079	−	0.172105i	$-0.0550567\pi$
$992$		0			0
$993$	−1.76599	+	3.86699i	−0.0560421	+	0.122715i
$994$		0			0
$995$	−6.75790	−	14.7977i	−0.214240	−	0.469120i
$996$		0			0
$997$	1.32436	+	9.21114i	0.0419430	+	0.291720i	0.999987	+	0.00509875i	$0.00162299\pi$
$997$	1.32436	+	9.21114i	0.0419430	+	0.291720i	−0.958044	+	0.286621i	$0.907468\pi$
$998$		0			0
$999$	15.4356	−	17.8136i	0.488359	−	0.563597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.81.1	✓	30
23.2	even	11	inner	460.2.m.a.301.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.81.1	✓	30	1.1	even	1	trivial
460.2.m.a.301.1	yes	30	23.2	even	11	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.161849 + 1.12569i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(0.847514 + 0.978083i) q^{7} +(1.63751 + 0.480815i) q^{9} +O(q^{10})\)	\(q+(-0.161849 + 1.12569i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(0.847514 + 0.978083i) q^{7} +(1.63751 + 0.480815i) q^{9} +(0.123375 + 0.0792885i) q^{11} +(-2.87486 + 3.31776i) q^{13} +(-0.161849 - 1.12569i) q^{15} +(0.0296401 + 0.0649028i) q^{17} +(-0.913223 + 1.99968i) q^{19} +(-1.23818 + 0.795732i) q^{21} +(-0.0966389 + 4.79486i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-2.22358 + 4.86896i) q^{27} +(-1.49193 - 3.26687i) q^{29} +(1.16431 + 8.09798i) q^{31} +(-0.109222 + 0.126049i) q^{33} +(-1.08874 - 0.699691i) q^{35} +(-4.22517 - 1.24062i) q^{37} +(-3.26946 - 3.77316i) q^{39} +(2.94012 - 0.863298i) q^{41} +(-0.290905 + 2.02329i) q^{43} -1.70664 q^{45} +7.11821 q^{47} +(0.757837 - 5.27087i) q^{49} +(-0.0778574 + 0.0228610i) q^{51} +(-2.31840 - 2.67558i) q^{53} +(-0.140716 - 0.0413179i) q^{55} +(-2.10321 - 1.35165i) q^{57} +(6.41962 - 7.40864i) q^{59} +(0.284809 + 1.98089i) q^{61} +(0.917532 + 2.00911i) q^{63} +(1.82368 - 3.99331i) q^{65} +(5.94685 - 3.82181i) q^{67} +(-5.38186 - 0.884828i) q^{69} +(3.06874 - 1.97216i) q^{71} +(-4.39721 + 9.62854i) q^{73} +(0.472435 + 1.03449i) q^{75} +(0.0270115 + 0.187869i) q^{77} +(1.28994 - 1.48867i) q^{79} +(-0.813891 - 0.523056i) q^{81} +(4.79463 + 1.40783i) q^{83} +(-0.0467247 - 0.0539232i) q^{85} +(3.91893 - 1.15070i) q^{87} +(2.53647 - 17.6415i) q^{89} -5.68152 q^{91} -9.30422 q^{93} +(0.312856 - 2.17596i) q^{95} +(3.38532 - 0.994019i) q^{97} +(0.163905 + 0.189156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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