LMFDB - Embedded newform 460.2.m.a.301.1

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			301.1
Character	$\chi$	$=$	460.301
Dual form			460.2.m.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.161849 - 1.12569i) q^{3} +(-0.959493 - 0.281733i) q^{5} +(0.847514 - 0.978083i) q^{7} +(1.63751 - 0.480815i) q^{9} +O(q^{10})$	\(q+(-0.161849 - 1.12569i) q^{3} +(-0.959493 - 0.281733i) q^{5} +(0.847514 - 0.978083i) q^{7} +(1.63751 - 0.480815i) q^{9} +(0.123375 - 0.0792885i) q^{11} +(-2.87486 - 3.31776i) q^{13} +(-0.161849 + 1.12569i) q^{15} +(0.0296401 - 0.0649028i) q^{17} +(-0.913223 - 1.99968i) q^{19} +(-1.23818 - 0.795732i) q^{21} +(-0.0966389 - 4.79486i) q^{23} +(0.841254 + 0.540641i) q^{25} +(-2.22358 - 4.86896i) q^{27} +(-1.49193 + 3.26687i) q^{29} +(1.16431 - 8.09798i) q^{31} +(-0.109222 - 0.126049i) q^{33} +(-1.08874 + 0.699691i) q^{35} +(-4.22517 + 1.24062i) q^{37} +(-3.26946 + 3.77316i) q^{39} +(2.94012 + 0.863298i) q^{41} +(-0.290905 - 2.02329i) q^{43} -1.70664 q^{45} +7.11821 q^{47} +(0.757837 + 5.27087i) q^{49} +(-0.0778574 - 0.0228610i) q^{51} +(-2.31840 + 2.67558i) q^{53} +(-0.140716 + 0.0413179i) q^{55} +(-2.10321 + 1.35165i) q^{57} +(6.41962 + 7.40864i) q^{59} +(0.284809 - 1.98089i) q^{61} +(0.917532 - 2.00911i) q^{63} +(1.82368 + 3.99331i) q^{65} +(5.94685 + 3.82181i) q^{67} +(-5.38186 + 0.884828i) q^{69} +(3.06874 + 1.97216i) q^{71} +(-4.39721 - 9.62854i) q^{73} +(0.472435 - 1.03449i) q^{75} +(0.0270115 - 0.187869i) q^{77} +(1.28994 + 1.48867i) q^{79} +(-0.813891 + 0.523056i) q^{81} +(4.79463 - 1.40783i) q^{83} +(-0.0467247 + 0.0539232i) q^{85} +(3.91893 + 1.15070i) q^{87} +(2.53647 + 17.6415i) q^{89} -5.68152 q^{91} -9.30422 q^{93} +(0.312856 + 2.17596i) q^{95} +(3.38532 + 0.994019i) q^{97} +(0.163905 - 0.189156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

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	−0.981681	−	0.190530i	$-0.938979\pi$
$3$	−0.161849	−	1.12569i	−0.0934436	−	0.649915i	0.888238	−	0.459384i	$-0.151930\pi$
$4$		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	−0.572632	−	0.819813i	$-0.694078\pi$
$7$	0.847514	−	0.978083i	0.320330	−	0.369681i	0.892962	+	0.450132i	$0.148623\pi$
$8$		0			0
$9$	1.63751	−	0.480815i	0.545836	−	0.160272i
$10$		0			0
$11$	0.123375	−	0.0792885i	0.0371991	−	0.0239064i	−0.521909	−	0.853001i	$-0.674780\pi$
$11$	0.123375	−	0.0792885i	0.0371991	−	0.0239064i	0.559108	+	0.829095i	$0.311144\pi$
$12$		0			0
$13$	−2.87486	−	3.31776i	−0.797342	−	0.920181i	0.200891	−	0.979614i	$-0.435616\pi$
$13$	−2.87486	−	3.31776i	−0.797342	−	0.920181i	−0.998232	+	0.0594325i	$0.981071\pi$
$14$		0			0
$15$	−0.161849	+	1.12569i	−0.0417893	+	0.290651i
$16$		0			0
$17$	0.0296401	−	0.0649028i	0.00718879	−	0.0157412i	−0.906004	−	0.423270i	$-0.860882\pi$
$17$	0.0296401	−	0.0649028i	0.00718879	−	0.0157412i	0.913192	+	0.407529i	$0.133609\pi$
$18$		0			0
$19$	−0.913223	−	1.99968i	−0.209508	−	0.458758i	0.775482	−	0.631369i	$-0.217507\pi$
$19$	−0.913223	−	1.99968i	−0.209508	−	0.458758i	−0.984990	+	0.172611i	$0.944780\pi$
$20$		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	−0.996092	−	0.0883180i	$-0.971851\pi$
$29$	−1.49193	+	3.26687i	−0.277044	+	0.606642i	0.719048	+	0.694960i	$0.244578\pi$
$30$		0			0
$31$	1.16431	−	8.09798i	0.209117	−	1.45444i	−0.566930	−	0.823766i	$-0.691869\pi$
$31$	1.16431	−	8.09798i	0.209117	−	1.45444i	0.776047	−	0.630675i	$-0.217222\pi$
$32$		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	−0.609935	−	0.792451i	$-0.708805\pi$
$37$	−4.22517	+	1.24062i	−0.694614	+	0.203957i	−0.0846786	+	0.996408i	$0.526986\pi$
$38$		0			0
$39$	−3.26946	+	3.77316i	−0.523533	+	0.604189i
$40$		0			0
$41$	2.94012	+	0.863298i	0.459170	+	0.134824i	0.503134	−	0.864209i	$-0.332180\pi$
$41$	2.94012	+	0.863298i	0.459170	+	0.134824i	−0.0439636	+	0.999033i	$0.513999\pi$
$42$		0			0
$43$	−0.290905	−	2.02329i	−0.0443626	−	0.308548i	−0.999906	−	0.0136986i	$-0.995639\pi$
$43$	−0.290905	−	2.02329i	−0.0443626	−	0.308548i	0.955544	−	0.294850i	$-0.0952696\pi$
$44$		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	−0.892297	−	0.451448i	$-0.850908\pi$
$53$	−2.31840	+	2.67558i	−0.318457	+	0.367519i	0.573840	+	0.818967i	$0.305453\pi$
$54$		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	0.999759	−	0.0219386i	$-0.00698382\pi$
$59$	6.41962	+	7.40864i	0.835763	+	0.964522i	−0.163996	+	0.986461i	$0.552438\pi$
$60$		0			0
$61$	0.284809	−	1.98089i	0.0364660	−	0.253627i	−0.963431	−	0.267955i	$-0.913652\pi$
$61$	0.284809	−	1.98089i	0.0364660	−	0.253627i	0.999897	+	0.0143287i	$0.00456113\pi$
$62$		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	0.850901	−	0.525327i	$-0.176057\pi$
$67$	5.94685	+	3.82181i	0.726523	+	0.466908i	−0.124377	+	0.992235i	$0.539693\pi$
$68$		0			0
$69$	−5.38186	+	0.884828i	−0.647900	+	0.106521i
$70$		0			0
$71$	3.06874	+	1.97216i	0.364193	+	0.234053i	0.709920	−	0.704283i	$-0.248731\pi$
$71$	3.06874	+	1.97216i	0.364193	+	0.234053i	−0.345727	+	0.938335i	$0.612368\pi$
$72$		0			0
$73$	−4.39721	−	9.62854i	−0.514654	−	1.12694i	−0.971424	−	0.237350i	$-0.923721\pi$
$73$	−4.39721	−	9.62854i	−0.514654	−	1.12694i	0.456770	−	0.889585i	$-0.349006\pi$
$74$		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	0.823660	−	0.567084i	$-0.191928\pi$
$79$	1.28994	+	1.48867i	0.145129	+	0.167488i	−0.678531	+	0.734572i	$0.737383\pi$
$80$		0			0
$81$	−0.813891	+	0.523056i	−0.0904324	+	0.0581174i
$82$		0			0
$83$	4.79463	−	1.40783i	0.526279	−	0.154529i	−0.00779126	−	0.999970i	$-0.502480\pi$
$83$	4.79463	−	1.40783i	0.526279	−	0.154529i	0.534070	+	0.845440i	$0.320662\pi$
$84$		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	0.459273	+	0.888295i	$0.348110\pi$
$89$	2.53647	+	17.6415i	0.268865	+	1.87000i	−0.190408	+	0.981705i	$0.560981\pi$
$90$		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	0.449040	−	0.893512i	$-0.351766\pi$
$97$	3.38532	+	0.994019i	0.343727	+	0.100927i	−0.105313	+	0.994439i	$0.533584\pi$
$98$		0			0
$99$	0.163905	−	0.189156i	0.0164730	−	0.0190109i
$100$		0			0
$101$	10.9470	−	3.21434i	1.08927	−	0.319839i	0.312689	−	0.949855i	$-0.398770\pi$
$101$	10.9470	−	3.21434i	1.08927	−	0.319839i	0.776582	+	0.630017i	$0.216952\pi$
$102$		0			0
$103$	11.9199	−	7.66047i	1.17451	−	0.754809i	0.200137	−	0.979768i	$-0.435861\pi$
$103$	11.9199	−	7.66047i	1.17451	−	0.754809i	0.974368	+	0.224959i	$0.0722249\pi$
$104$		0			0
$105$	0.963844	+	1.11234i	0.0940615	+	0.108553i
$106$		0			0
$107$	−0.0334566	+	0.232696i	−0.00323437	+	0.0224955i	−0.991375	−	0.131058i	$-0.958163\pi$
$107$	−0.0334566	+	0.232696i	−0.00323437	+	0.0224955i	0.988140	+	0.153553i	$0.0490717\pi$
$108$		0			0
$109$	−6.90497	+	15.1198i	−0.661376	+	1.44821i	0.219859	+	0.975532i	$0.429440\pi$
$109$	−6.90497	+	15.1198i	−0.661376	+	1.44821i	−0.881234	+	0.472679i	$0.843287\pi$
$110$		0			0
$111$	2.08039	+	4.55542i	0.197462	+	0.432381i
$112$		0			0
$113$	10.5444	+	6.77645i	0.991929	+	0.637474i	0.932656	−	0.360767i	$-0.117485\pi$
$113$	10.5444	+	6.77645i	0.991929	+	0.637474i	0.0592736	+	0.998242i	$0.481122\pi$
$114$		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	−0.656151	−	0.754630i	$-0.727817\pi$
$127$	−2.73048	+	1.75477i	−0.242291	+	0.155711i	0.413860	+	0.910340i	$0.364180\pi$
$128$		0			0
$129$	−2.23050	+	0.654934i	−0.196385	+	0.0576638i
$130$		0			0
$131$	−4.89170	+	5.64532i	−0.427390	+	0.493234i	−0.928074	−	0.372396i	$-0.878536\pi$
$131$	−4.89170	+	5.64532i	−0.427390	+	0.493234i	0.500684	+	0.865630i	$0.333082\pi$
$132$		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	−0.439759	−	0.898116i	$-0.644936\pi$
$149$	2.37434	−	1.52589i	0.194513	−	0.125006i	0.634272	+	0.773110i	$0.281300\pi$
$150$		0			0
$151$	−8.85909	−	10.2239i	−0.720943	−	0.832012i	0.270477	−	0.962726i	$-0.412818\pi$
$151$	−8.85909	−	10.2239i	−0.720943	−	0.832012i	−0.991420	+	0.130714i	$0.958273\pi$
$152$		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	0.982973	−	0.183749i	$-0.0588232\pi$
$157$	2.51094	+	5.49819i	0.200395	+	0.438803i	−0.782578	+	0.622552i	$0.786096\pi$
$158$		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	0.491991	−	0.870600i	$-0.336269\pi$
$163$	−1.21995	−	0.784011i	−0.0955535	−	0.0614085i	−0.587545	+	0.809192i	$0.699905\pi$
$164$		0			0
$165$	0.0692857	+	0.151715i	0.00539388	+	0.0118110i
$166$		0			0
$167$	−1.48242	+	3.24605i	−0.114713	+	0.251187i	−0.958277	−	0.285843i	$-0.907726\pi$
$167$	−1.48242	+	3.24605i	−0.114713	+	0.251187i	0.843563	+	0.537030i	$0.180454\pi$
$168$		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	−0.323296	−	0.946298i	$-0.604791\pi$
$173$	5.30307	−	3.40807i	0.403185	−	0.259111i	0.726481	+	0.687187i	$0.241155\pi$
$174$		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	0.263324	−	0.964707i	$-0.415181\pi$
$179$	−0.491203	−	0.144230i	−0.0367143	−	0.0107803i	−0.300038	+	0.953927i	$0.596999\pi$
$180$		0			0
$181$	−1.13130	−	7.86835i	−0.0840887	−	0.584850i	−0.987684	−	0.156462i	$-0.949991\pi$
$181$	−1.13130	−	7.86835i	−0.0840887	−	0.584850i	0.903595	−	0.428387i	$-0.140918\pi$
$182$		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	−0.942200	−	0.335052i	$-0.891246\pi$
$191$	−6.58494	+	7.59942i	−0.476469	+	0.549875i	0.465730	+	0.884927i	$0.345792\pi$
$192$		0			0
$193$	19.1000	−	5.60827i	1.37485	−	0.403692i	0.490876	−	0.871230i	$-0.336677\pi$
$193$	19.1000	−	5.60827i	1.37485	−	0.403692i	0.883973	+	0.467537i	$0.154859\pi$
$194$		0			0
$195$	4.20005	−	2.69921i	0.300772	−	0.193294i
$196$		0			0
$197$	−7.70052	−	8.88688i	−0.548640	−	0.633164i	0.411926	−	0.911217i	$-0.364856\pi$
$197$	−7.70052	−	8.88688i	−0.548640	−	0.633164i	−0.960566	+	0.278054i	$0.910311\pi$
$198$		0			0
$199$	2.31515	−	16.1022i	0.164117	−	1.14146i	−0.726654	−	0.687004i	$-0.758925\pi$
$199$	2.31515	−	16.1022i	0.164117	−	1.14146i	0.890770	−	0.454454i	$-0.150165\pi$
$200$		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	−0.992451	−	0.122643i	$-0.960863\pi$
$211$	−6.32195	−	13.8431i	−0.435221	−	0.953001i	0.557230	−	0.830358i	$-0.311864\pi$
$212$		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	−0.518451	−	0.855108i	$-0.673491\pi$
$223$	5.99921	−	6.92345i	0.401737	−	0.463629i	0.920187	+	0.391479i	$0.128036\pi$
$224$		0			0
$225$	1.63751	+	0.480815i	0.109167	+	0.0320544i
$226$		0			0
$227$	2.32490	+	16.1701i	0.154309	+	1.07324i	0.908890	+	0.417037i	$0.136931\pi$
$227$	2.32490	+	16.1701i	0.154309	+	1.07324i	−0.754580	+	0.656208i	$0.772160\pi$
$228$		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	−1.00000		0.000537159i	$-0.999829\pi$
$233$	−0.620623	−	4.31653i	−0.0406584	−	0.282785i	0.959341	−	0.282248i	$-0.0910801\pi$
$234$		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	0.559760	−	0.828655i	$-0.310893\pi$
$239$	22.8596	−	6.71219i	1.47866	−	0.434175i	0.918905	+	0.394480i	$0.129075\pi$
$240$		0			0
$241$	15.2923	−	9.82776i	0.985063	−	0.633062i	0.0542385	−	0.998528i	$-0.482727\pi$
$241$	15.2923	−	9.82776i	0.985063	−	0.633062i	0.930825	+	0.365466i	$0.119090\pi$
$242$		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	0.766971	−	0.641682i	$-0.221763\pi$
$251$	7.95141	+	5.11006i	0.501888	+	0.322544i	−0.265083	+	0.964226i	$0.585399\pi$
$252$		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	0.883079	−	0.469225i	$-0.155467\pi$
$257$	−0.798862	−	1.74926i	−0.0498316	−	0.109116i	−0.932910	+	0.360109i	$0.882739\pi$
$258$		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	0.391913	−	0.920002i	$-0.371813\pi$
$263$	−9.31681	−	10.7522i	−0.574499	−	0.663008i	−0.966413	+	0.256994i	$0.917268\pi$
$264$		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	−0.468266	−	0.883588i	$-0.655121\pi$
$269$	7.75728	−	8.95237i	0.472970	−	0.545836i	0.941235	+	0.337752i	$0.109666\pi$
$270$		0			0
$271$	−9.89565	−	2.90562i	−0.601118	−	0.176504i	−0.0330054	−	0.999455i	$-0.510508\pi$
$271$	−9.89565	−	2.90562i	−0.601118	−	0.176504i	−0.568112	+	0.822951i	$0.692326\pi$
$272$		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	0.990158	−	0.139952i	$-0.0446947\pi$
$281$	29.2929	+	8.60118i	1.74747	+	0.513103i	0.757311	+	0.653055i	$0.226513\pi$
$282$		0			0
$283$	−15.1637	+	17.4999i	−0.901391	+	1.04026i	0.0975945	+	0.995226i	$0.468885\pi$
$283$	−15.1637	+	17.4999i	−0.901391	+	1.04026i	−0.998985	+	0.0450344i	$0.985660\pi$
$284$		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	−0.992848	−	0.119383i	$-0.961908\pi$
$293$	−4.32120	+	9.46211i	−0.252447	+	0.552782i	0.740401	+	0.672165i	$0.234636\pi$
$294$		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	−0.346189	−	0.938165i	$-0.612525\pi$
$307$	4.38541	−	30.5012i	0.250288	−	1.74079i	0.596478	−	0.802630i	$-0.296566\pi$
$308$		0			0
$309$	−10.5525	−	12.1782i	−0.600311	−	0.692796i
$310$		0			0
$311$	−24.1308	+	15.5079i	−1.36833	+	0.879372i	−0.998758	−	0.0498301i	$-0.984132\pi$
$311$	−24.1308	+	15.5079i	−1.36833	+	0.879372i	−0.369572	+	0.929202i	$0.620496\pi$
$312$		0			0
$313$	−18.6545	+	5.47746i	−1.05442	+	0.309604i	−0.762600	−	0.646870i	$-0.776078\pi$
$313$	−18.6545	+	5.47746i	−1.05442	+	0.309604i	−0.291816	+	0.956475i	$0.594259\pi$
$314$		0			0
$315$	−1.44640	+	1.66923i	−0.0814953	+	0.0940506i
$316$		0			0
$317$	13.0751	+	3.83918i	0.734369	+	0.215630i	0.627471	−	0.778640i	$-0.284090\pi$
$317$	13.0751	+	3.83918i	0.734369	+	0.215630i	0.106898	+	0.994270i	$0.465908\pi$
$318$		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	−0.181672	−	0.983359i	$-0.558151\pi$
$331$	3.58665	−	1.05313i	0.197140	−	0.0578855i	0.378812	+	0.925474i	$0.376333\pi$
$332$		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	0.398323	+	0.917245i	$0.369592\pi$
$337$	−4.44773	+	30.9346i	−0.242283	+	1.68512i	−0.640606	+	0.767870i	$0.721317\pi$
$338$		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	0.437067	−	0.899429i	$-0.356017\pi$
$347$	−3.71660	−	2.38851i	−0.199517	−	0.128222i	−0.636585	+	0.771207i	$0.719653\pi$
$348$		0			0
$349$	−11.2696	−	24.6771i	−0.603250	−	1.32093i	−0.927096	−	0.374824i	$-0.877703\pi$
$349$	−11.2696	−	24.6771i	−0.603250	−	1.32093i	0.323846	−	0.946110i	$-0.395024\pi$
$350$		0			0
$351$	−9.76158	+	21.3749i	−0.521035	+	1.14091i
$352$		0			0
$353$	−0.809559	+	5.63060i	−0.0430885	+	0.299687i	0.956870	+	0.290518i	$0.0938276\pi$
$353$	−0.809559	+	5.63060i	−0.0430885	+	0.299687i	−0.999958	+	0.00916873i	$0.997081\pi$
$354$		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	−0.796040	−	0.605244i	$-0.793076\pi$
$359$	−21.5713	+	6.33392i	−1.13849	+	0.334291i	−0.342452	+	0.939535i	$0.611257\pi$
$360$		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	0.669014	−	0.743250i	$-0.266717\pi$
$373$	16.0298	+	4.70678i	0.829992	+	0.243708i	0.160979	+	0.986958i	$0.448535\pi$
$374$		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	−0.0361935	−	0.999345i	$-0.511523\pi$
$379$	16.6997	−	10.7323i	0.857807	−	0.551279i	0.894001	+	0.448066i	$0.147887\pi$
$380$		0			0
$381$	2.41724	+	2.78965i	0.123839	+	0.142918i
$382$		0			0
$383$	−4.26884	+	29.6904i	−0.218128	+	1.51711i	0.526814	+	0.849981i	$0.323386\pi$
$383$	−4.26884	+	29.6904i	−0.218128	+	1.51711i	−0.744942	+	0.667130i	$0.767523\pi$
$384$		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	0.336145	−	0.941810i	$-0.390877\pi$
$389$	−7.51283	−	4.82820i	−0.380915	−	0.244799i	−0.717061	+	0.697011i	$0.754513\pi$
$390$		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	−0.997311	−	0.0732919i	$-0.976650\pi$
$397$	−5.75471	+	12.6011i	−0.288821	+	0.632429i	0.708490	+	0.705721i	$0.249377\pi$
$398$		0			0
$399$	−0.460472	+	3.20265i	−0.0230524	+	0.160333i
$400$		0			0
$401$	−0.487003	−	0.562031i	−0.0243198	−	0.0280665i	0.743459	−	0.668781i	$-0.233184\pi$
$401$	−0.487003	−	0.562031i	−0.0243198	−	0.0280665i	−0.767779	+	0.640715i	$0.778638\pi$
$402$		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	0.705169	−	0.709039i	$-0.250871\pi$
$409$	18.5059	+	5.43383i	0.915059	+	0.268686i	0.209890	+	0.977725i	$0.432689\pi$
$410$		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	0.194899	−	0.980823i	$-0.437562\pi$
$419$	−3.50879	−	1.03027i	−0.171415	−	0.0503321i	−0.366314	+	0.930491i	$0.619380\pi$
$420$		0			0
$421$	6.52623	−	7.53167i	0.318069	−	0.367071i	−0.574090	−	0.818792i	$-0.694644\pi$
$421$	6.52623	−	7.53167i	0.318069	−	0.367071i	0.892159	+	0.451721i	$0.149190\pi$
$422$		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	−0.0217290	+	0.999764i	$0.506917\pi$
$431$	−15.8418	+	34.6886i	−0.763071	+	1.67089i	−0.741342	+	0.671128i	$0.765810\pi$
$432$		0			0
$433$	−4.46576	−	9.77865i	−0.214611	−	0.469932i	0.771456	−	0.636283i	$-0.219529\pi$
$433$	−4.46576	−	9.77865i	−0.214611	−	0.469932i	−0.986067	+	0.166351i	$0.946802\pi$
$434$		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	0.887796	−	0.460238i	$-0.152236\pi$
$439$	17.5570	+	11.2832i	0.837952	+	0.538519i	−0.0498435	+	0.998757i	$0.515872\pi$
$440$		0			0
$441$	3.77528	+	8.26671i	0.179775	+	0.393653i
$442$		0			0
$443$	−10.5849	+	23.1778i	−0.502905	+	1.10121i	0.472609	+	0.881272i	$0.343312\pi$
$443$	−10.5849	+	23.1778i	−0.502905	+	1.10121i	−0.975514	+	0.219936i	$0.929415\pi$
$444$		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	0.0216886	−	0.999765i	$-0.493096\pi$
$449$	19.9207	−	12.8023i	0.940116	−	0.604176i	0.918428	+	0.395589i	$0.129459\pi$
$450$		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	0.732554	+	0.680708i	$0.238328\pi$
$457$	4.73409	+	32.9263i	0.221451	+	1.54023i	−0.511103	+	0.859519i	$0.670763\pi$
$458$		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	0.977660	+	0.210191i	$0.0674087\pi$
$463$	2.12635	+	14.7891i	0.0988199	+	0.687307i	−0.878840	+	0.477116i	$0.841682\pi$
$464$		0			0
$465$	8.92734	+	2.62130i	0.413995	+	0.121560i
$466$		0			0
$467$	11.4407	−	13.2032i	0.529411	−	0.610972i	−0.426551	−	0.904463i	$-0.640272\pi$
$467$	11.4407	−	13.2032i	0.529411	−	0.610972i	0.955962	+	0.293491i	$0.0948171\pi$
$468$		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	0.742668	−	0.669660i	$-0.233560\pi$
$479$	−5.46652	−	11.9700i	−0.249772	−	0.546924i	−0.992439	+	0.122736i	$0.960833\pi$
$480$		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	0.898867	+	0.438223i	$0.144392\pi$
$487$	14.1549	+	30.9949i	0.641421	+	1.40452i	−0.257446	+	0.966293i	$0.582881\pi$
$488$		0			0
$489$	−0.685103	+	1.50017i	−0.0309814	+	0.0678399i
$490$		0			0
$491$	−0.901268	+	6.26845i	−0.0406736	+	0.282891i	0.959326	+	0.282300i	$0.0910973\pi$
$491$	−0.901268	+	6.26845i	−0.0406736	+	0.282891i	−1.00000		0.000591419i	$0.999812\pi$
$492$		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	−0.328100	−	0.944643i	$-0.606408\pi$
$499$	14.6008	−	16.8502i	0.653621	−	0.754319i	0.981721	+	0.190324i	$0.0609538\pi$
$500$		0			0
$501$	3.89396	+	1.14337i	0.173969	+	0.0510820i
$502$		0			0
$503$	−0.934184	−	6.49739i	−0.0416532	−	0.289704i	−0.999992	−	0.00406947i	$-0.998705\pi$
$503$	−0.934184	−	6.49739i	−0.0416532	−	0.289704i	0.958339	−	0.285635i	$-0.0922044\pi$
$504$		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	−0.640537	−	0.767927i	$-0.721288\pi$
$509$	−5.46645	−	38.0200i	−0.242296	−	1.68521i	0.398241	−	0.917281i	$-0.369621\pi$
$510$		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	−0.999210	−	0.0397443i	$-0.987346\pi$
$521$	−0.668277	+	4.64797i	−0.0292778	+	0.203631i	0.969932	+	0.243376i	$0.0782548\pi$
$522$		0			0
$523$	−2.76081	+	6.04533i	−0.120722	+	0.264344i	−0.960339	−	0.278834i	$-0.910052\pi$
$523$	−2.76081	+	6.04533i	−0.120722	+	0.264344i	0.839617	+	0.543178i	$0.182779\pi$
$524$		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	−0.771599	−	0.636109i	$-0.780543\pi$
$541$	−11.9439	+	7.67586i	−0.513507	+	0.330011i	0.258092	+	0.966120i	$0.416906\pi$
$542$		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	0.241999	−	0.970277i	$-0.422197\pi$
$547$	−1.84741	−	0.542450i	−0.0789898	−	0.0231935i	−0.320989	+	0.947083i	$0.604015\pi$
$548$		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	−0.0690898	−	0.997610i	$-0.522009\pi$
$557$	−15.7314	−	4.61916i	−0.666561	−	0.195720i	−0.597471	+	0.801891i	$0.703828\pi$
$558$		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	−0.195791	−	0.980646i	$-0.562728\pi$
$563$	14.5901	−	9.37651i	0.614901	−	0.395173i	0.810692	+	0.585473i	$0.199091\pi$
$564$		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	−0.694245	−	0.719739i	$-0.744261\pi$
$569$	7.25944	−	15.8960i	0.304332	−	0.666393i	0.998576	+	0.0533461i	$0.0169886\pi$
$570$		0			0
$571$	−3.99142	−	8.73998i	−0.167036	−	0.365757i	0.807541	−	0.589811i	$-0.200798\pi$
$571$	−3.99142	−	8.73998i	−0.167036	−	0.365757i	−0.974577	+	0.224055i	$0.928071\pi$
$572$		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	0.543207	−	0.839599i	$-0.317210\pi$
$577$	0.123392	+	0.0792992i	0.00513688	+	0.00330127i	−0.538070	+	0.842900i	$0.680846\pi$
$578$		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	−0.872765	−	0.488140i	$-0.837675\pi$
$587$	−19.1716	+	12.3208i	−0.791297	+	0.508536i	0.0814683	+	0.996676i	$0.474039\pi$
$588$		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	−0.295553	−	0.955326i	$-0.595504\pi$
$593$	−25.8292	−	7.58412i	−1.06068	−	0.311443i	−0.765123	+	0.643884i	$0.777322\pi$
$594$		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	−0.777264	−	0.629175i	$-0.783393\pi$
$601$	−5.11741	−	35.5924i	−0.208744	−	1.45184i	0.568520	−	0.822669i	$-0.307516\pi$
$602$		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	−0.353497	−	0.935436i	$-0.615007\pi$
$607$	−3.57593	+	1.04999i	−0.145142	+	0.0426176i	0.208354	+	0.978053i	$0.433189\pi$
$608$		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	0.712779	+	0.701389i	$0.247436\pi$
$613$	−4.17760	+	29.0558i	−0.168732	+	1.17355i	−0.881510	+	0.472165i	$0.843473\pi$
$614$		0			0
$615$	−1.44766	+	3.16993i	−0.0583752	+	0.127824i
$616$		0			0
$617$	0.486818	+	1.06598i	0.0195986	+	0.0429149i	0.919178	−	0.393842i	$-0.128854\pi$
$617$	0.486818	+	1.06598i	0.0195986	+	0.0429149i	−0.899580	+	0.436757i	$0.856127\pi$
$618$		0			0
$619$	33.5034	+	21.5313i	1.34661	+	0.865416i	0.997431	−	0.0716380i	$-0.0228226\pi$
$619$	33.5034	+	21.5313i	1.34661	+	0.865416i	0.349183	+	0.937054i	$0.386459\pi$
$620$		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	0.355596	−	0.934640i	$-0.384278\pi$
$631$	−15.5777	−	17.9776i	−0.620137	−	0.715676i	−0.975733	+	0.218964i	$0.929732\pi$
$632$		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	0.977134	+	0.212625i	$0.0682012\pi$
$641$	2.51874	+	17.5182i	0.0994841	+	0.691927i	−0.877650	+	0.479302i	$0.840890\pi$
$642$		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	−0.921223	−	0.389035i	$-0.872808\pi$
$647$	−3.73708	−	25.9920i	−0.146920	−	1.02185i	0.774303	−	0.632815i	$-0.218101\pi$
$648$		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	0.268834	−	0.963187i	$-0.413362\pi$
$653$	25.9558	−	7.62131i	1.01573	−	0.298245i	0.746895	+	0.664942i	$0.231544\pi$
$654$		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	−0.0270971	−	0.999633i	$-0.508626\pi$
$659$	7.20152	−	50.0877i	0.280531	−	1.95114i	0.307629	−	0.951507i	$-0.400465\pi$
$660$		0			0
$661$	3.27525	−	7.17179i	0.127392	−	0.278950i	−0.835179	−	0.549978i	$-0.814636\pi$
$661$	3.27525	−	7.17179i	0.127392	−	0.278950i	0.962572	+	0.271028i	$0.0873635\pi$
$662$		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	−0.659766	−	0.751471i	$-0.729345\pi$
$673$	8.82588	−	19.3260i	0.340213	−	0.744962i	0.999979	+	0.00650935i	$0.00207200\pi$
$674$		0			0
$675$	0.761765	−	5.29819i	0.0293204	−	0.203928i
$676$		0			0
$677$	−21.6947	−	25.0370i	−0.833795	−	0.962251i	0.165919	−	0.986139i	$-0.446941\pi$
$677$	−21.6947	−	25.0370i	−0.833795	−	0.962251i	−0.999715	+	0.0238881i	$0.992395\pi$
$678$		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	−0.912390	−	0.409323i	$-0.865765\pi$
$683$	−9.86271	+	11.3822i	−0.377386	+	0.435527i	0.535003	+	0.844850i	$0.320310\pi$
$684$		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	−0.673260	−	0.739406i	$-0.735106\pi$
$701$	−7.42277	+	4.77033i	−0.280354	+	0.180173i	0.392905	+	0.919579i	$0.371470\pi$
$702$		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	−0.719977	−	0.693998i	$-0.755848\pi$
$709$	−20.5822	−	45.0687i	−0.772981	−	1.69259i	−0.0530037	−	0.998594i	$-0.516880\pi$
$710$		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	0.582958	+	0.812502i	$0.301895\pi$
$719$	−11.0701	+	24.2402i	−0.412846	+	0.904007i	−0.995805	+	0.0915052i	$0.970832\pi$
$720$		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	−0.0717769	−	0.997421i	$-0.522867\pi$
$727$	10.9763	−	3.22292i	0.407087	−	0.119532i	0.478864	+	0.877889i	$0.341049\pi$
$728$		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	0.927510	+	0.373797i	$0.121944\pi$
$733$	3.86837	+	26.9051i	0.142882	+	0.993763i	−0.784629	+	0.619966i	$0.787146\pi$
$734$		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	−0.870796	−	0.491644i	$-0.836396\pi$
$739$	−4.72428	−	32.8581i	−0.173785	−	1.20870i	0.697011	−	0.717061i	$-0.254513\pi$
$740$		0			0
$741$	10.5309	+	3.09214i	0.386861	+	0.113593i
$742$		0			0
$743$	32.5407	−	37.5540i	1.19380	−	1.37772i	0.286053	−	0.958214i	$-0.407657\pi$
$743$	32.5407	−	37.5540i	1.19380	−	1.37772i	0.907751	−	0.419509i	$-0.137798\pi$
$744$		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	−0.995770	−	0.0918843i	$-0.970711\pi$
$751$	−0.395963	+	2.75398i	−0.0144489	+	0.100494i	0.981321	+	0.192378i	$0.0616201\pi$
$752$		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	0.949772	+	0.312942i	$0.101315\pi$
$757$	44.8193	+	28.8036i	1.62898	+	1.04688i	0.679212	+	0.733942i	$0.262322\pi$
$758$		0			0
$759$	−0.593832	+	0.535885i	−0.0215547	+	0.0194514i
$760$		0			0
$761$	−30.8007	−	19.7944i	−1.11653	−	0.717547i	−0.153820	−	0.988099i	$-0.549158\pi$
$761$	−30.8007	−	19.7944i	−1.11653	−	0.717547i	−0.962705	+	0.270552i	$0.912794\pi$
$762$		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	0.993386	+	0.114825i	$0.0366307\pi$
$769$	26.7788	+	30.9044i	0.965668	+	1.11444i	−0.0277173	+	0.999616i	$0.508824\pi$
$770$		0			0
$771$	−1.83983	+	1.18238i	−0.0662597	+	0.0425825i
$772$		0			0
$773$	29.9481	−	8.79354i	1.07716	−	0.316282i	0.305416	−	0.952219i	$-0.401205\pi$
$773$	29.9481	−	8.79354i	1.07716	−	0.316282i	0.771741	+	0.635937i	$0.219386\pi$
$774$		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	0.360126	−	0.932904i	$-0.382734\pi$
$787$	4.45260	+	1.30740i	0.158718	+	0.0466038i	−0.201408	+	0.979507i	$0.564552\pi$
$788$		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	0.631926	+	0.775029i	$0.282265\pi$
$797$	−5.44166	+	37.8476i	−0.192753	+	1.34063i	−0.824679	+	0.565601i	$0.808644\pi$
$798$		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	0.857754	−	0.514061i	$-0.171860\pi$
$809$	−2.62974	−	5.75834i	−0.0924569	−	0.202452i	−0.950211	+	0.311609i	$0.899132\pi$
$810$		0			0
$811$	11.6202	−	25.4446i	0.408039	−	0.893480i	−0.588353	−	0.808604i	$-0.700223\pi$
$811$	11.6202	−	25.4446i	0.408039	−	0.893480i	0.996392	−	0.0848759i	$-0.0270494\pi$
$812$		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	−0.884608	−	0.466336i	$-0.845574\pi$
$821$	−8.51357	+	9.82518i	−0.297125	+	0.342901i	0.587482	+	0.809237i	$0.300119\pi$
$822$		0			0
$823$	−30.7078	−	9.01663i	−1.07041	−	0.314300i	−0.301372	−	0.953507i	$-0.597445\pi$
$823$	−30.7078	−	9.01663i	−1.07041	−	0.314300i	−0.769035	+	0.639207i	$0.779263\pi$
$824$		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	0.0548677	−	0.998494i	$-0.482526\pi$
$839$	28.5577	−	18.3529i	0.985922	−	0.633614i	0.931055	+	0.364880i	$0.118890\pi$
$840$		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	0.402736	−	0.915316i	$-0.368059\pi$
$853$	−7.66843	−	4.92820i	−0.262562	−	0.168738i	−0.665298	+	0.746578i	$0.731696\pi$
$854$		0			0
$855$	1.55854	+	3.41273i	0.0533010	+	0.116713i
$856$		0			0
$857$	19.7296	−	43.2017i	0.673949	−	1.47574i	−0.194980	−	0.980807i	$-0.562464\pi$
$857$	19.7296	−	43.2017i	0.673949	−	1.47574i	0.868929	−	0.494936i	$-0.164809\pi$
$858$		0			0
$859$	−6.42179	+	44.6645i	−0.219109	+	1.52393i	0.522231	+	0.852804i	$0.325100\pi$
$859$	−6.42179	+	44.6645i	−0.219109	+	1.52393i	−0.741340	+	0.671130i	$0.765809\pi$
$860$		0			0
$861$	−2.95346	−	3.40847i	−0.100653	−	0.116160i
$862$		0			0
$863$	−23.0369	+	14.8049i	−0.784184	+	0.503964i	−0.870420	−	0.492310i	$-0.836153\pi$
$863$	−23.0369	+	14.8049i	−0.784184	+	0.503964i	0.0862357	+	0.996275i	$0.472516\pi$
$864$		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	0.730543	+	0.682867i	$0.239267\pi$
$877$	6.57369	+	45.7210i	0.221978	+	1.54389i	−0.508565	+	0.861023i	$0.669824\pi$
$878$		0			0
$879$	11.3507	+	3.33288i	0.382851	+	0.112415i
$880$		0			0
$881$	9.14442	−	10.5532i	0.308083	−	0.355547i	−0.580502	−	0.814259i	$-0.697144\pi$
$881$	9.14442	−	10.5532i	0.308083	−	0.355547i	0.888585	+	0.458712i	$0.151689\pi$
$882$		0			0
$883$	11.1140	−	3.26336i	0.374016	−	0.109821i	−0.0893218	−	0.996003i	$-0.528470\pi$
$883$	11.1140	−	3.26336i	0.374016	−	0.109821i	0.463337	+	0.886182i	$0.346652\pi$
$884$		0			0
$885$	−9.37880	+	6.02739i	−0.315265	+	0.202609i
$886$		0			0
$887$	−37.4852	−	43.2603i	−1.25863	−	1.45254i	−0.838340	−	0.545148i	$-0.816474\pi$
$887$	−37.4852	−	43.2603i	−1.25863	−	1.45254i	−0.420291	−	0.907390i	$-0.638072\pi$
$888$		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	0.914372	−	0.404875i	$-0.132685\pi$
$907$	11.5493	+	13.3286i	0.383489	+	0.442570i	−0.530883	+	0.847445i	$0.678140\pi$
$908$		0			0
$909$	16.3803	−	10.5270i	0.543302	−	0.349159i
$910$		0			0
$911$	−33.1735	+	9.74062i	−1.09909	+	0.322721i	−0.780490	−	0.625169i	$-0.785030\pi$
$911$	−33.1735	+	9.74062i	−1.09909	+	0.322721i	−0.318598	+	0.947890i	$0.603212\pi$
$912$		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	−0.209439	−	0.977822i	$-0.567164\pi$
$929$	4.35919	−	1.27997i	0.143020	−	0.0419945i	0.352459	+	0.935827i	$0.385346\pi$
$930$		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	0.0798186	+	0.996809i	$0.474566\pi$
$937$	−22.2168	+	48.6479i	−0.725790	+	1.58926i	−0.805608	+	0.592448i	$0.798161\pi$
$938$		0			0
$939$	9.18511	+	20.1126i	0.299745	+	0.656350i
$940$		0			0
$941$	20.2129	+	12.9900i	0.658921	+	0.423463i	0.826916	−	0.562325i	$-0.190093\pi$
$941$	20.2129	+	12.9900i	0.658921	+	0.423463i	−0.167995	+	0.985788i	$0.553729\pi$
$942$		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	0.991582	+	0.129484i	$0.0413321\pi$
$947$	13.5431	+	29.6552i	0.440091	+	0.963665i	−0.551490	+	0.834181i	$0.685941\pi$
$948$		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	0.345023	−	0.938594i	$-0.387871\pi$
$953$	−19.5449	−	22.5560i	−0.633120	−	0.730659i	−0.978143	+	0.207935i	$0.933326\pi$
$954$		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	0.270505	−	0.962719i	$-0.412809\pi$
$971$	−0.698536	−	0.205109i	−0.0224171	−	0.00658225i	−0.292922	+	0.956136i	$0.594628\pi$
$972$		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	−0.994520	−	0.104542i	$-0.966662\pi$
$977$	−41.0268	+	26.3663i	−1.31256	+	0.843534i	−0.318044	+	0.948076i	$0.603026\pi$
$978$		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	−0.994857	−	0.101294i	$-0.967702\pi$
$983$	−8.36528	+	18.3174i	−0.266811	+	0.584234i	0.728046	+	0.685529i	$0.240429\pi$
$984$		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	0.985079	+	0.172105i	$0.0550567\pi$
$991$	48.8209	+	31.3753i	1.55085	+	0.996669i	0.565768	+	0.824564i	$0.308580\pi$
$992$		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	−0.958044	−	0.286621i	$-0.907468\pi$
$997$	1.32436	−	9.21114i	0.0419430	−	0.291720i	0.999987	−	0.00509875i	$-0.00162299\pi$
$998$		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.301.1	yes	30
23.12	even	11	inner	460.2.m.a.81.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.81.1	✓	30	23.12	even	11	inner
460.2.m.a.301.1	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
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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