LMFDB - Embedded newform 400.2.bi.c.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} - 64 x^{13} + 66 x^{12} - 28 x^{11} + 160 x^{10} - 392 x^{9} + 419 x^{8} + \cdots + 1 $ x^16 - 8x^15 + 32x^14 - 64x^13 + 66x^12 - 28x^11 + 160x^10 - 392x^9 + 419x^8 + 164x^7 + 200x^6 - 576x^5 + 726x^4 + 668x^3 + 288x^2 + 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.1
Root			$1.85565 + 1.85565i$ of defining polynomial
Character	$\chi$	$=$	400.223
Dual form			400.2.bi.c.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11764 - 2.19349i) q^{3} -2.23607 q^{5} +(-2.71130 - 2.71130i) q^{7} +(-1.79892 + 2.47599i) q^{9} +O(q^{10})$	\(q+(-1.11764 - 2.19349i) q^{3} -2.23607 q^{5} +(-2.71130 - 2.71130i) q^{7} +(-1.79892 + 2.47599i) q^{9} +(1.87346 + 2.57860i) q^{11} +(0.951057 + 6.00473i) q^{13} +(2.49911 + 4.90479i) q^{15} +(-2.48990 - 1.26867i) q^{17} +(0.812011 + 2.49911i) q^{19} +(-2.91695 + 8.97745i) q^{21} +(0.902924 - 5.70084i) q^{23} +5.00000 q^{25} +(0.147100 + 0.0232983i) q^{27} +(-3.50473 - 1.13876i) q^{29} +(-6.62706 + 2.15326i) q^{31} +(3.56227 - 6.99135i) q^{33} +(6.06265 + 6.06265i) q^{35} +(-8.82234 + 1.39732i) q^{37} +(12.1084 - 8.79725i) q^{39} +(1.43471 + 1.04238i) q^{41} +(-3.91095 + 3.91095i) q^{43} +(4.02250 - 5.53649i) q^{45} +(-7.95051 + 4.05099i) q^{47} +7.70228i q^{49} +6.87947i q^{51} +(5.97266 - 3.04322i) q^{53} +(-4.18919 - 5.76592i) q^{55} +(4.57424 - 4.57424i) q^{57} +(-2.77891 - 2.01900i) q^{59} +(2.82916 - 2.05551i) q^{61} +(11.5906 - 1.83576i) q^{63} +(-2.12663 - 13.4270i) q^{65} +(2.49911 - 4.90479i) q^{67} +(-13.5138 + 4.39092i) q^{69} +(-14.7144 - 4.78098i) q^{71} +(6.39237 + 1.01245i) q^{73} +(-5.58819 - 10.9674i) q^{75} +(1.91184 - 12.0709i) q^{77} +(-1.37161 + 4.22138i) q^{79} +(2.72394 + 8.38342i) q^{81} +(-8.26251 - 4.20996i) q^{83} +(5.56758 + 2.83682i) q^{85} +(1.41917 + 8.96031i) q^{87} +(-6.66016 - 9.16692i) q^{89} +(13.7020 - 18.8592i) q^{91} +(12.1298 + 12.1298i) q^{93} +(-1.81571 - 5.58819i) q^{95} +(-3.29528 - 6.46735i) q^{97} -9.75479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{9}+O(q^{10}) $ 16 * q + 20 * q^9	$ 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93} - 80 q^{97}+O(q^{100}) $ 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.11764	−	2.19349i	−0.645268	−	1.26641i	−0.949487	−	0.313808i	$-0.898395\pi$
$3$	−1.11764	−	2.19349i	−0.645268	−	1.26641i	0.304218	−	0.952602i	$-0.401605\pi$
$4$		0			0
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$		0			0
$7$	−2.71130	−	2.71130i	−1.02477	−	1.02477i	−0.999685	−	0.0250894i	$-0.992013\pi$
$7$	−2.71130	−	2.71130i	−1.02477	−	1.02477i	−0.0250894	−	0.999685i	$-0.507987\pi$
$8$		0			0
$9$	−1.79892	+	2.47599i	−0.599638	+	0.825331i
$10$		0			0
$11$	1.87346	+	2.57860i	0.564870	+	0.777477i	0.991935	−	0.126744i	$-0.0404527\pi$
$11$	1.87346	+	2.57860i	0.564870	+	0.777477i	−0.427066	+	0.904221i	$0.640453\pi$
$12$		0			0
$13$	0.951057	+	6.00473i	0.263776	+	1.66541i	0.663045	+	0.748580i	$0.269264\pi$
$13$	0.951057	+	6.00473i	0.263776	+	1.66541i	−0.399269	+	0.916834i	$0.630736\pi$
$14$		0			0
$15$	2.49911	+	4.90479i	0.645268	+	1.26641i
$16$		0			0
$17$	−2.48990	−	1.26867i	−0.603889	−	0.307697i	0.125183	−	0.992134i	$-0.460048\pi$
$17$	−2.48990	−	1.26867i	−0.603889	−	0.307697i	−0.729072	+	0.684437i	$0.760048\pi$
$18$		0			0
$19$	0.812011	+	2.49911i	0.186288	+	0.573336i	0.999968	−	0.00797709i	$-0.00253921\pi$
$19$	0.812011	+	2.49911i	0.186288	+	0.573336i	−0.813680	+	0.581313i	$0.802539\pi$
$20$		0			0
$21$	−2.91695	+	8.97745i	−0.636531	+	1.95904i
$22$		0			0
$23$	0.902924	−	5.70084i	0.188273	−	1.18871i	−0.694706	−	0.719294i	$-0.744466\pi$
$23$	0.902924	−	5.70084i	0.188273	−	1.18871i	0.882979	−	0.469413i	$-0.155534\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	0.147100	+	0.0232983i	0.0283093	+	0.00448376i
$28$		0			0
$29$	−3.50473	−	1.13876i	−0.650813	−	0.211462i	−0.0350403	−	0.999386i	$-0.511156\pi$
$29$	−3.50473	−	1.13876i	−0.650813	−	0.211462i	−0.615773	+	0.787924i	$0.711156\pi$
$30$		0			0
$31$	−6.62706	+	2.15326i	−1.19025	+	0.386737i	−0.836167	−	0.548475i	$-0.815209\pi$
$31$	−6.62706	+	2.15326i	−1.19025	+	0.386737i	−0.354088	+	0.935212i	$0.615209\pi$
$32$		0			0
$33$	3.56227	−	6.99135i	0.620112	−	1.21704i
$34$		0			0
$35$	6.06265	+	6.06265i	1.02477	+	1.02477i
$36$		0			0
$37$	−8.82234	+	1.39732i	−1.45038	+	0.229718i	−0.831395	−	0.555681i	$-0.812457\pi$
$37$	−8.82234	+	1.39732i	−1.45038	+	0.229718i	−0.618989	+	0.785400i	$0.712457\pi$
$38$		0			0
$39$	12.1084	−	8.79725i	1.93889	−	1.40869i
$40$		0			0
$41$	1.43471	+	1.04238i	0.224064	+	0.162792i	0.694154	−	0.719826i	$-0.255779\pi$
$41$	1.43471	+	1.04238i	0.224064	+	0.162792i	−0.470090	+	0.882618i	$0.655779\pi$
$42$		0			0
$43$	−3.91095	+	3.91095i	−0.596414	+	0.596414i	−0.939356	−	0.342942i	$-0.888576\pi$
$43$	−3.91095	+	3.91095i	−0.596414	+	0.596414i	0.342942	+	0.939356i	$0.388576\pi$
$44$		0			0
$45$	4.02250	−	5.53649i	0.599638	−	0.825331i
$46$		0			0
$47$	−7.95051	+	4.05099i	−1.15970	+	0.590897i	−0.924550	−	0.381062i	$-0.875559\pi$
$47$	−7.95051	+	4.05099i	−1.15970	+	0.590897i	−0.235151	+	0.971959i	$0.575559\pi$
$48$		0			0
$49$			7.70228i			1.10033i
$50$		0			0
$51$			6.87947i			0.963318i
$52$		0			0
$53$	5.97266	−	3.04322i	0.820407	−	0.418018i	0.00718691	−	0.999974i	$-0.497712\pi$
$53$	5.97266	−	3.04322i	0.820407	−	0.418018i	0.813220	+	0.581956i	$0.197712\pi$
$54$		0			0
$55$	−4.18919	−	5.76592i	−0.564870	−	0.777477i
$56$		0			0
$57$	4.57424	−	4.57424i	0.605873	−	0.605873i
$58$		0			0
$59$	−2.77891	−	2.01900i	−0.361784	−	0.262851i	0.392012	−	0.919960i	$-0.371779\pi$
$59$	−2.77891	−	2.01900i	−0.361784	−	0.262851i	−0.753796	+	0.657109i	$0.771779\pi$
$60$		0			0
$61$	2.82916	−	2.05551i	0.362237	−	0.263181i	−0.391747	−	0.920073i	$-0.628129\pi$
$61$	2.82916	−	2.05551i	0.362237	−	0.263181i	0.753985	+	0.656892i	$0.228129\pi$
$62$		0			0
$63$	11.5906	−	1.83576i	1.46027	−	0.231285i
$64$		0			0
$65$	−2.12663	−	13.4270i	−0.263776	−	1.66541i
$66$		0			0
$67$	2.49911	−	4.90479i	0.305315	−	0.599215i	−0.686466	−	0.727162i	$-0.740839\pi$
$67$	2.49911	−	4.90479i	0.305315	−	0.599215i	0.991781	+	0.127947i	$0.0408388\pi$
$68$		0			0
$69$	−13.5138	+	4.39092i	−1.62688	+	0.528604i
$70$		0			0
$71$	−14.7144	−	4.78098i	−1.74627	−	0.567398i	−0.750636	−	0.660716i	$-0.770253\pi$
$71$	−14.7144	−	4.78098i	−1.74627	−	0.567398i	−0.995636	+	0.0933171i	$0.970253\pi$
$72$		0			0
$73$	6.39237	+	1.01245i	0.748170	+	0.118498i	0.518865	−	0.854856i	$-0.326355\pi$
$73$	6.39237	+	1.01245i	0.748170	+	0.118498i	0.229305	+	0.973355i	$0.426355\pi$
$74$		0			0
$75$	−5.58819	−	10.9674i	−0.645268	−	1.26641i
$76$		0			0
$77$	1.91184	−	12.0709i	0.217874	−	1.37560i
$78$		0			0
$79$	−1.37161	+	4.22138i	−0.154318	+	0.474943i	−0.998091	−	0.0617575i	$-0.980329\pi$
$79$	−1.37161	+	4.22138i	−0.154318	+	0.474943i	0.843773	+	0.536700i	$0.180329\pi$
$80$		0			0
$81$	2.72394	+	8.38342i	0.302660	+	0.931491i
$82$		0			0
$83$	−8.26251	−	4.20996i	−0.906928	−	0.462103i	−0.0626665	−	0.998035i	$-0.519960\pi$
$83$	−8.26251	−	4.20996i	−0.906928	−	0.462103i	−0.844261	+	0.535932i	$0.819960\pi$
$84$		0			0
$85$	5.56758	+	2.83682i	0.603889	+	0.307697i
$86$		0			0
$87$	1.41917	+	8.96031i	0.152151	+	0.960646i
$88$		0			0
$89$	−6.66016	−	9.16692i	−0.705975	−	0.971692i	−0.999874	−	0.0158552i	$-0.994953\pi$
$89$	−6.66016	−	9.16692i	−0.705975	−	0.971692i	0.293899	−	0.955836i	$-0.405047\pi$
$90$		0			0
$91$	13.7020	−	18.8592i	1.43636	−	1.97698i
$92$		0			0
$93$	12.1298	+	12.1298i	1.25780	+	1.25780i
$94$		0			0
$95$	−1.81571	−	5.58819i	−0.186288	−	0.573336i
$96$		0			0
$97$	−3.29528	−	6.46735i	−0.334585	−	0.656659i	0.661015	−	0.750373i	$-0.270126\pi$
$97$	−3.29528	−	6.46735i	−0.334585	−	0.656659i	−0.995599	+	0.0937137i	$0.970126\pi$
$98$		0			0
$99$	−9.75479			−0.980394
$100$		0			0
$101$	1.10194			0.109648			0.0548238	−	0.998496i	$-0.482540\pi$
$101$	1.10194			0.109648			0.0548238	+	0.998496i	$0.482540\pi$
$102$		0			0
$103$	8.37488	+	16.4366i	0.825201	+	1.61955i	0.784297	+	0.620386i	$0.213024\pi$
$103$	8.37488	+	16.4366i	0.825201	+	1.61955i	0.0409049	+	0.999163i	$0.486976\pi$
$104$		0			0
$105$	6.52250	−	20.0742i	0.636531	−	1.95904i
$106$		0			0
$107$	−0.392448	−	0.392448i	−0.0379394	−	0.0379394i	0.687883	−	0.725822i	$-0.258540\pi$
$107$	−0.392448	−	0.392448i	−0.0379394	−	0.0379394i	−0.725822	+	0.687883i	$0.758540\pi$
$108$		0			0
$109$	3.58247	−	4.93085i	0.343139	−	0.472290i	−0.602216	−	0.798333i	$-0.705715\pi$
$109$	3.58247	−	4.93085i	0.343139	−	0.472290i	0.945355	+	0.326043i	$0.105715\pi$
$110$		0			0
$111$	12.9252	+	17.7900i	1.22680	+	1.68855i
$112$		0			0
$113$	−0.359790	−	2.27163i	−0.0338462	−	0.213697i	0.964969	−	0.262365i	$-0.0845024\pi$
$113$	−0.359790	−	2.27163i	−0.0338462	−	0.213697i	−0.998815	+	0.0486680i	$0.984502\pi$
$114$		0			0
$115$	−2.01900	+	12.7475i	−0.188273	+	1.18871i
$116$		0			0
$117$	−16.5786	−	8.44720i	−1.53269	−	0.780944i
$118$		0			0
$119$	3.31112	+	10.1906i	0.303530	+	0.934170i
$120$		0			0
$121$	0.259875	−	0.799813i	0.0236250	−	0.0727103i
$122$		0			0
$123$	0.682957	−	4.31202i	0.0615802	−	0.388802i
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	13.7180	+	2.17272i	1.21727	+	0.192797i	0.731841	−	0.681476i	$-0.238662\pi$
$127$	13.7180	+	2.17272i	1.21727	+	0.192797i	0.485434	+	0.874273i	$0.338662\pi$
$128$		0			0
$129$	12.9496	+	4.20759i	1.14015	+	0.370458i
$130$		0			0
$131$	9.90301	−	3.21768i	0.865230	−	0.281130i	0.157419	−	0.987532i	$-0.449683\pi$
$131$	9.90301	−	3.21768i	0.865230	−	0.281130i	0.707811	+	0.706402i	$0.249683\pi$
$132$		0			0
$133$	4.57424	−	8.97745i	0.396637	−	0.778443i
$134$		0			0
$135$	−0.328925	−	0.0520965i	−0.0283093	−	0.00448376i
$136$		0			0
$137$	2.61054	−	0.413468i	0.223033	−	0.0353250i	−0.0439175	−	0.999035i	$-0.513984\pi$
$137$	2.61054	−	0.413468i	0.223033	−	0.0353250i	0.266951	+	0.963710i	$0.413984\pi$
$138$		0			0
$139$	−16.8402	+	12.2351i	−1.42837	+	1.03777i	−0.438052	+	0.898950i	$0.644332\pi$
$139$	−16.8402	+	12.2351i	−1.42837	+	1.03777i	−0.990317	+	0.138822i	$0.955668\pi$
$140$		0			0
$141$	17.7716	+	12.9118i	1.49664	+	1.08737i
$142$		0			0
$143$	−13.7020	+	13.7020i	−1.14582	+	1.14582i
$144$		0			0
$145$	7.83682	+	2.54634i	0.650813	+	0.211462i
$146$		0			0
$147$	16.8949	−	8.60836i	1.39346	−	0.710005i
$148$		0			0
$149$			6.25512i			0.512439i	0.966619	+	0.256220i	$0.0824770\pi$
$149$			6.25512i			0.512439i	−0.966619	+	0.256220i	$0.917523\pi$
$150$		0			0
$151$		−	13.2445i		−	1.07782i	−0.842363	−	0.538911i	$-0.818836\pi$
$151$		−	13.2445i		−	1.07782i	0.842363	−	0.538911i	$-0.181164\pi$
$152$		0			0
$153$	7.62033	−	3.88275i	0.616067	−	0.313902i
$154$		0			0
$155$	14.8185	−	4.81484i	1.19025	−	0.386737i
$156$		0			0
$157$	−9.41570	+	9.41570i	−0.751454	+	0.751454i	−0.974751	−	0.223296i	$-0.928318\pi$
$157$	−9.41570	+	9.41570i	−0.751454	+	0.751454i	0.223296	+	0.974751i	$0.428318\pi$
$158$		0			0
$159$	−13.3505	−	9.69973i	−1.05877	−	0.769238i
$160$		0			0
$161$	−17.9048	+	13.0086i	−1.41109	+	1.02522i
$162$		0			0
$163$	−4.25427	+	0.673811i	−0.333220	+	0.0527769i	−0.320803	−	0.947146i	$-0.603953\pi$
$163$	−4.25427	+	0.673811i	−0.333220	+	0.0527769i	−0.0124175	+	0.999923i	$0.503953\pi$
$164$		0			0
$165$	−7.96548	+	15.6331i	−0.620112	+	1.21704i
$166$		0			0
$167$	1.98611	−	3.89796i	0.153690	−	0.301633i	−0.801305	−	0.598256i	$-0.795860\pi$
$167$	1.98611	−	3.89796i	0.153690	−	0.301633i	0.954995	+	0.296623i	$0.0958605\pi$
$168$		0			0
$169$	−22.7886	+	7.40446i	−1.75297	+	0.569574i
$170$		0			0
$171$	−7.64853	−	2.48516i	−0.584898	−	0.190045i
$172$		0			0
$173$	−25.0976	−	3.97506i	−1.90813	−	0.302218i	−0.913597	−	0.406622i	$-0.866707\pi$
$173$	−25.0976	−	3.97506i	−1.90813	−	0.302218i	−0.994535	+	0.104403i	$0.966707\pi$
$174$		0			0
$175$	−13.5565	−	13.5565i	−1.02477	−	1.02477i
$176$		0			0
$177$	−1.32283	+	8.35202i	−0.0994300	+	0.627776i
$178$		0			0
$179$	−0.154162	+	0.474462i	−0.0115226	+	0.0354629i	−0.956653	−	0.291232i	$-0.905935\pi$
$179$	−0.154162	+	0.474462i	−0.0115226	+	0.0354629i	0.945130	+	0.326695i	$0.105935\pi$
$180$		0			0
$181$	1.48163	+	4.55998i	0.110128	+	0.338940i	0.990900	−	0.134601i	$-0.0429753\pi$
$181$	1.48163	+	4.55998i	0.110128	+	0.338940i	−0.880771	+	0.473542i	$0.842975\pi$
$182$		0			0
$183$	−7.67071	−	3.90842i	−0.567035	−	0.288919i
$184$		0			0
$185$	19.7274	−	3.12451i	1.45038	−	0.229718i
$186$		0			0
$187$	−1.39335	−	8.79725i	−0.101892	−	0.643318i
$188$		0			0
$189$	−0.335662	−	0.461999i	−0.0244158	−	0.0336055i
$190$		0			0
$191$	14.6566	−	20.1731i	1.06051	−	1.45967i	0.181192	−	0.983448i	$-0.442005\pi$
$191$	14.6566	−	20.1731i	1.06051	−	1.45967i	0.879323	−	0.476226i	$-0.157995\pi$
$192$		0			0
$193$	6.83099	+	6.83099i	0.491706	+	0.491706i	0.908843	−	0.417138i	$-0.136967\pi$
$193$	6.83099	+	6.83099i	0.491706	+	0.491706i	−0.417138	+	0.908843i	$0.636967\pi$
$194$		0			0
$195$	−27.0751	+	19.6712i	−1.93889	+	1.40869i
$196$		0			0
$197$	−3.70171	−	7.26501i	−0.263736	−	0.517610i	0.720724	−	0.693222i	$-0.243810\pi$
$197$	−3.70171	−	7.26501i	−0.263736	−	0.517610i	−0.984459	+	0.175612i	$0.943810\pi$
$198$		0			0
$199$	5.25545			0.372549			0.186274	−	0.982498i	$-0.440359\pi$
$199$	5.25545			0.372549			0.186274	+	0.982498i	$0.440359\pi$
$200$		0			0
$201$	−13.5517			−0.955862
$202$		0			0
$203$	6.41487	+	12.5899i	0.450236	+	0.883637i
$204$		0			0
$205$	−3.20811	−	2.33083i	−0.224064	−	0.162792i
$206$		0			0
$207$	12.4910	+	12.4910i	0.868181	+	0.868181i
$208$		0			0
$209$	−4.92294	+	6.77584i	−0.340527	+	0.468695i
$210$		0			0
$211$	0.442264	+	0.608724i	0.0304467	+	0.0419063i	0.823969	−	0.566635i	$-0.191755\pi$
$211$	0.442264	+	0.608724i	0.0304467	+	0.0419063i	−0.793522	+	0.608541i	$0.791755\pi$
$212$		0			0
$213$	5.95829	+	37.6192i	0.408255	+	2.57762i
$214$		0			0
$215$	8.74515	−	8.74515i	0.596414	−	0.596414i
$216$		0			0
$217$	23.8061	+	12.1298i	1.61606	+	0.823424i
$218$		0			0
$219$	−4.92355	−	15.1531i	−0.332703	−	1.02395i
$220$		0			0
$221$	5.24997	−	16.1578i	0.353151	−	1.08689i
$222$		0			0
$223$	0.114902	−	0.725463i	0.00769441	−	0.0485806i	−0.983542	−	0.180677i	$-0.942171\pi$
$223$	0.114902	−	0.725463i	0.00769441	−	0.0485806i	0.991237	+	0.132097i	$0.0421710\pi$
$224$		0			0
$225$	−8.99458	+	12.3800i	−0.599638	+	0.825331i
$226$		0			0
$227$	−16.5097	−	2.61489i	−1.09579	−	0.173556i	−0.417736	−	0.908568i	$-0.637176\pi$
$227$	−16.5097	−	2.61489i	−1.09579	−	0.173556i	−0.678054	+	0.735012i	$0.737176\pi$
$228$		0			0
$229$	−9.11620	−	2.96203i	−0.602416	−	0.195737i	−0.00809818	−	0.999967i	$-0.502578\pi$
$229$	−9.11620	−	2.96203i	−0.602416	−	0.195737i	−0.594318	+	0.804230i	$0.702578\pi$
$230$		0			0
$231$	−28.6140	+	9.29726i	−1.88266	+	0.611715i
$232$		0			0
$233$	6.55915	−	12.8731i	0.429704	−	0.843342i	−0.570059	−	0.821604i	$-0.693080\pi$
$233$	6.55915	−	12.8731i	0.429704	−	0.843342i	0.999764	−	0.0217388i	$-0.00692021\pi$
$234$		0			0
$235$	17.7779	−	9.05828i	1.15970	−	0.590897i
$236$		0			0
$237$	10.7925	−	1.70937i	0.701049	−	0.111035i
$238$		0			0
$239$	−4.74879	+	3.45020i	−0.307173	+	0.223175i	−0.730683	−	0.682717i	$-0.760798\pi$
$239$	−4.74879	+	3.45020i	−0.307173	+	0.223175i	0.423509	+	0.905892i	$0.360798\pi$
$240$		0			0
$241$	−16.7888	−	12.1977i	−1.08146	−	0.785726i	−0.103522	−	0.994627i	$-0.533011\pi$
$241$	−16.7888	−	12.1977i	−1.08146	−	0.785726i	−0.977937	+	0.208901i	$0.933011\pi$
$242$		0			0
$243$	15.6605	−	15.6605i	1.00462	−	1.00462i
$244$		0			0
$245$		−	17.2228i		−	1.10033i
$246$		0			0
$247$	−14.2342	+	7.25271i	−0.905703	+	0.461479i
$248$		0			0
$249$			22.8289i			1.44672i
$250$		0			0
$251$			19.9371i			1.25842i	0.777236	+	0.629209i	$0.216621\pi$
$251$			19.9371i			1.25842i	−0.777236	+	0.629209i	$0.783379\pi$
$252$		0			0
$253$	16.3918	−	8.35202i	1.03054	−	0.525087i
$254$		0			0
$255$		−	15.3830i		−	0.963318i
$256$		0			0
$257$	−5.09132	+	5.09132i	−0.317588	+	0.317588i	−0.847840	−	0.530252i	$-0.822097\pi$
$257$	−5.09132	+	5.09132i	−0.317588	+	0.317588i	0.530252	+	0.847840i	$0.322097\pi$
$258$		0			0
$259$	27.7086	+	20.1315i	1.72173	+	1.25091i
$260$		0			0
$261$	9.12428	−	6.62918i	0.564779	−	0.410336i
$262$		0			0
$263$	14.8341	−	2.34949i	0.914708	−	0.144875i	0.318701	−	0.947855i	$-0.396753\pi$
$263$	14.8341	−	2.34949i	0.914708	−	0.144875i	0.596006	+	0.802980i	$0.296753\pi$
$264$		0			0
$265$	−13.3553	+	6.80485i	−0.820407	+	0.418018i
$266$		0			0
$267$	−12.6639	+	24.8543i	−0.775017	+	1.52106i
$268$		0			0
$269$	25.6091	−	8.32089i	1.56141	−	0.507334i	0.604228	−	0.796811i	$-0.293482\pi$
$269$	25.6091	−	8.32089i	1.56141	−	0.507334i	0.957185	+	0.289478i	$0.0934816\pi$
$270$		0			0
$271$	3.84036	+	1.24781i	0.233285	+	0.0757990i	0.423327	−	0.905977i	$-0.360862\pi$
$271$	3.84036	+	1.24781i	0.233285	+	0.0757990i	−0.190041	+	0.981776i	$0.560862\pi$
$272$		0			0
$273$	−56.6814	−	8.97745i	−3.43051	−	0.543340i
$274$		0			0
$275$	9.36731	+	12.8930i	0.564870	+	0.777477i
$276$		0			0
$277$	−3.19484	+	20.1714i	−0.191959	+	1.21198i	0.683957	+	0.729522i	$0.260257\pi$
$277$	−3.19484	+	20.1714i	−0.191959	+	1.21198i	−0.875917	+	0.482462i	$0.839743\pi$
$278$		0			0
$279$	6.59005	−	20.2821i	0.394536	−	1.21426i
$280$		0			0
$281$	2.08904	+	6.42940i	0.124622	+	0.383546i	0.993832	−	0.110897i	$-0.0353722\pi$
$281$	2.08904	+	6.42940i	0.124622	+	0.383546i	−0.869210	+	0.494443i	$0.835372\pi$
$282$		0			0
$283$	−3.56354	−	1.81571i	−0.211830	−	0.107933i	0.344856	−	0.938655i	$-0.387928\pi$
$283$	−3.56354	−	1.81571i	−0.211830	−	0.107933i	−0.556687	+	0.830723i	$0.687928\pi$
$284$		0			0
$285$	−10.2283	+	10.2283i	−0.605873	+	0.605873i
$286$		0			0
$287$	−1.06373	−	6.71613i	−0.0627901	−	0.396441i
$288$		0			0
$289$	−5.40227	−	7.43559i	−0.317781	−	0.437388i
$290$		0			0
$291$	−10.5031	+	14.4563i	−0.615703	+	0.847443i
$292$		0			0
$293$	0.165989	+	0.165989i	0.00969716	+	0.00969716i	0.711939	−	0.702242i	$-0.247817\pi$
$293$	0.165989	+	0.165989i	0.00969716	+	0.00969716i	−0.702242	+	0.711939i	$0.747817\pi$
$294$		0			0
$295$	6.21384	+	4.51462i	0.361784	+	0.262851i
$296$		0			0
$297$	0.215508	+	0.422959i	0.0125051	+	0.0245426i
$298$		0			0
$299$	35.0907			2.02935
$300$		0			0
$301$	21.2075			1.22238
$302$		0			0
$303$	−1.23157	−	2.41710i	−0.0707521	−	0.138859i
$304$		0			0
$305$	−6.32620	+	4.59626i	−0.362237	+	0.263181i
$306$		0			0
$307$	−6.44042	−	6.44042i	−0.367574	−	0.367574i	0.499018	−	0.866592i	$-0.333694\pi$
$307$	−6.44042	−	6.44042i	−0.367574	−	0.367574i	−0.866592	+	0.499018i	$0.833694\pi$
$308$		0			0
$309$	26.6934	−	36.7404i	1.51854	−	2.09009i
$310$		0			0
$311$	6.62041	+	9.11221i	0.375409	+	0.516706i	0.954361	−	0.298655i	$-0.0965381\pi$
$311$	6.62041	+	9.11221i	0.375409	+	0.516706i	−0.578952	+	0.815362i	$0.696538\pi$
$312$		0			0
$313$	0.925114	+	5.84094i	0.0522905	+	0.330149i	0.999941	+	0.0108405i	$0.00345072\pi$
$313$	0.925114	+	5.84094i	0.0522905	+	0.330149i	−0.947651	+	0.319309i	$0.896549\pi$
$314$		0			0
$315$	−25.9173	+	4.10489i	−1.46027	+	0.231285i
$316$		0			0
$317$	−11.2864	−	5.75071i	−0.633908	−	0.322992i	0.107341	−	0.994222i	$-0.465766\pi$
$317$	−11.2864	−	5.75071i	−0.633908	−	0.322992i	−0.741249	+	0.671230i	$0.765766\pi$
$318$		0			0
$319$	−3.62959	−	11.1707i	−0.203218	−	0.625440i
$320$		0			0
$321$	−0.422215	+	1.29945i	−0.0235658	+	0.0725279i
$322$		0			0
$323$	1.14872	−	7.25271i	0.0639163	−	0.403552i
$324$		0			0
$325$	4.75528	+	30.0237i	0.263776	+	1.66541i
$326$		0			0
$327$	−14.8197	−	2.34720i	−0.819530	−	0.129801i
$328$		0			0
$329$	32.5396	+	10.5728i	1.79397	+	0.582896i
$330$		0			0
$331$	−3.94456	+	1.28166i	−0.216812	+	0.0704466i	−0.415409	−	0.909635i	$-0.636362\pi$
$331$	−3.94456	+	1.28166i	−0.216812	+	0.0704466i	0.198597	+	0.980081i	$0.436362\pi$
$332$		0			0
$333$	12.4109	−	24.3577i	0.680113	−	1.33480i
$334$		0			0
$335$	−5.58819	+	10.9674i	−0.305315	+	0.599215i
$336$		0			0
$337$	3.50859	−	0.555707i	0.191125	−	0.0302713i	−0.0601379	−	0.998190i	$-0.519154\pi$
$337$	3.50859	−	0.555707i	0.191125	−	0.0302713i	0.251263	+	0.967919i	$0.419154\pi$
$338$		0			0
$339$	−4.58067	+	3.32805i	−0.248788	+	0.180755i
$340$		0			0
$341$	−17.9679	−	13.0545i	−0.973018	−	0.706939i
$342$		0			0
$343$	1.90410	−	1.90410i	0.102812	−	0.102812i
$344$		0			0
$345$	30.2179	−	9.81838i	1.62688	−	0.528604i
$346$		0			0
$347$	13.5549	−	6.90658i	0.727667	−	0.370765i	−0.0505827	−	0.998720i	$-0.516108\pi$
$347$	13.5549	−	6.90658i	0.727667	−	0.370765i	0.778250	+	0.627955i	$0.216108\pi$
$348$		0			0
$349$		−	22.4830i		−	1.20349i	−0.798690	−	0.601743i	$-0.794473\pi$
$349$		−	22.4830i		−	1.20349i	0.798690	−	0.601743i	$-0.205527\pi$
$350$		0			0
$351$			0.905452i			0.0483294i
$352$		0			0
$353$	−27.7757	+	14.1524i	−1.47835	+	0.753258i	−0.992668	−	0.120875i	$-0.961430\pi$
$353$	−27.7757	+	14.1524i	−1.47835	+	0.753258i	−0.485685	+	0.874134i	$0.661430\pi$
$354$		0			0
$355$	32.9023	+	10.6906i	1.74627	+	0.567398i
$356$		0			0
$357$	18.6523	−	18.6523i	0.987184	−	0.987184i
$358$		0			0
$359$	12.8457	+	9.33295i	0.677970	+	0.492574i	0.872684	−	0.488286i	$-0.162378\pi$
$359$	12.8457	+	9.33295i	0.677970	+	0.492574i	−0.194713	+	0.980860i	$0.562378\pi$
$360$		0			0
$361$	9.78512	−	7.10930i	0.515006	−	0.374174i
$362$		0			0
$363$	−2.04482	+	0.323868i	−0.107325	+	0.0169987i
$364$		0			0
$365$	−14.2938	−	2.26391i	−0.748170	−	0.118498i
$366$		0			0
$367$	−0.347414	+	0.681839i	−0.0181349	+	0.0355917i	−0.899896	−	0.436104i	$-0.856358\pi$
$367$	−0.347414	+	0.681839i	−0.0181349	+	0.0355917i	0.881761	+	0.471696i	$0.156358\pi$
$368$		0			0
$369$	−5.16185	+	1.67719i	−0.268715	+	0.0873108i
$370$		0			0
$371$	−24.4447	−	7.94258i	−1.26911	−	0.412358i
$372$		0			0
$373$	3.50859	+	0.555707i	0.181668	+	0.0287734i	0.246606	−	0.969116i	$-0.420685\pi$
$373$	3.50859	+	0.555707i	0.181668	+	0.0287734i	−0.0649375	+	0.997889i	$0.520685\pi$
$374$		0			0
$375$	12.4956	+	24.5239i	0.645268	+	1.26641i
$376$		0			0
$377$	3.50473	−	22.1280i	0.180503	−	1.13965i
$378$		0			0
$379$	−0.0934406	+	0.287581i	−0.00479972	+	0.0147720i	−0.953428	−	0.301622i	$-0.902472\pi$
$379$	−0.0934406	+	0.287581i	−0.00479972	+	0.0147720i	0.948628	+	0.316394i	$0.102472\pi$
$380$		0			0
$381$	−10.5659	−	32.5185i	−0.541308	−	1.66598i
$382$		0			0
$383$	−16.7245	−	8.52154i	−0.854580	−	0.435430i	−0.0289088	−	0.999582i	$-0.509203\pi$
$383$	−16.7245	−	8.52154i	−0.854580	−	0.435430i	−0.825671	+	0.564152i	$0.809203\pi$
$384$		0			0
$385$	−4.27500	+	26.9913i	−0.217874	+	1.37560i
$386$		0			0
$387$	−2.64802	−	16.7190i	−0.134607	−	0.849872i
$388$		0			0
$389$	−21.7258	−	29.9029i	−1.10154	−	1.51614i	−0.833328	−	0.552779i	$-0.813567\pi$
$389$	−21.7258	−	29.9029i	−1.10154	−	1.51614i	−0.268211	−	0.963360i	$-0.586433\pi$
$390$		0			0
$391$	−9.48065	+	13.0490i	−0.479457	+	0.659916i
$392$		0			0
$393$	−18.1259	−	18.1259i	−0.914332	−	0.914332i
$394$		0			0
$395$	3.06702	−	9.43930i	0.154318	−	0.474943i
$396$		0			0
$397$	5.60601	+	11.0024i	0.281358	+	0.552195i	0.987829	−	0.155547i	$-0.0497139\pi$
$397$	5.60601	+	11.0024i	0.281358	+	0.552195i	−0.706471	+	0.707742i	$0.749714\pi$
$398$		0			0
$399$	−24.8042			−1.24177
$400$		0			0
$401$	10.6083			0.529755			0.264878	−	0.964282i	$-0.414668\pi$
$401$	10.6083			0.529755			0.264878	+	0.964282i	$0.414668\pi$
$402$		0			0
$403$	−19.2325	−	37.7458i	−0.958037	−	1.88025i
$404$		0			0
$405$	−6.09091	−	18.7459i	−0.302660	−	0.931491i
$406$		0			0
$407$	−20.1315	−	20.1315i	−0.997879	−	0.997879i
$408$		0			0
$409$	15.4511	−	21.2667i	0.764010	−	1.05157i	−0.232860	−	0.972510i	$-0.574808\pi$
$409$	15.4511	−	21.2667i	0.764010	−	1.05157i	0.996870	−	0.0790591i	$-0.0251916\pi$
$410$		0			0
$411$	−3.82457	−	5.26407i	−0.188652	−	0.259657i
$412$		0			0
$413$	2.06036	+	13.0086i	0.101383	+	0.640110i
$414$		0			0
$415$	18.4755	+	9.41375i	0.906928	+	0.462103i
$416$		0			0
$417$	45.6589	+	23.2644i	2.23593	+	1.13926i
$418$		0			0
$419$	−10.8353	−	33.3477i	−0.529341	−	1.62914i	−0.755570	−	0.655068i	$-0.772640\pi$
$419$	−10.8353	−	33.3477i	−0.529341	−	1.62914i	0.226229	−	0.974074i	$-0.427360\pi$
$420$		0			0
$421$	2.22908	−	6.86042i	0.108639	−	0.334356i	−0.881928	−	0.471384i	$-0.843755\pi$
$421$	2.22908	−	6.86042i	0.108639	−	0.334356i	0.990567	+	0.137027i	$0.0437548\pi$
$422$		0			0
$423$	4.27207	−	26.9728i	0.207715	−	1.31146i
$424$		0			0
$425$	−12.4495	−	6.34333i	−0.603889	−	0.307697i
$426$		0			0
$427$	−13.2438	−	2.09761i	−0.640913	−	0.101511i
$428$		0			0
$429$	45.3691	+	14.7413i	2.19044	+	0.711718i
$430$		0			0
$431$	32.4130	−	10.5316i	1.56128	−	0.507291i	0.604132	−	0.796885i	$-0.293520\pi$
$431$	32.4130	−	10.5316i	1.56128	−	0.507291i	0.957150	+	0.289594i	$0.0935202\pi$
$432$		0			0
$433$	15.6916	−	30.7965i	0.754090	−	1.47998i	−0.119245	−	0.992865i	$-0.538047\pi$
$433$	15.6916	−	30.7965i	0.754090	−	1.47998i	0.873335	−	0.487120i	$-0.161953\pi$
$434$		0			0
$435$	−3.17337	−	20.0359i	−0.152151	−	0.960646i
$436$		0			0
$437$	14.9802	−	2.37263i	0.716601	−	0.113498i
$438$		0			0
$439$	10.4656	−	7.60369i	0.499495	−	0.362904i	−0.309329	−	0.950955i	$-0.600104\pi$
$439$	10.4656	−	7.60369i	0.499495	−	0.362904i	0.808824	+	0.588051i	$0.200104\pi$
$440$		0			0
$441$	−19.0708	−	13.8558i	−0.908134	−	0.659798i
$442$		0			0
$443$	−20.7302	+	20.7302i	−0.984920	+	0.984920i	−0.999888	−	0.0149683i	$-0.995235\pi$
$443$	−20.7302	+	20.7302i	−0.984920	+	0.984920i	0.0149683	+	0.999888i	$0.495235\pi$
$444$		0			0
$445$	14.8926	+	20.4979i	0.705975	+	0.971692i
$446$		0			0
$447$	13.7205	−	6.99095i	0.648958	−	0.330661i
$448$		0			0
$449$			30.7637i			1.45183i	0.687785	+	0.725915i	$0.258583\pi$
$449$			30.7637i			1.45183i	−0.687785	+	0.725915i	$0.741417\pi$
$450$		0			0
$451$			5.65240i			0.266161i
$452$		0			0
$453$	−29.0516	+	14.8025i	−1.36496	+	0.695484i
$454$		0			0
$455$	−30.6387	+	42.1705i	−1.43636	+	1.97698i
$456$		0			0
$457$	−20.8793	+	20.8793i	−0.976692	+	0.976692i	−0.999734	−	0.0230425i	$-0.992665\pi$
$457$	−20.8793	+	20.8793i	−0.976692	+	0.976692i	0.0230425	+	0.999734i	$0.492665\pi$
$458$		0			0
$459$	−0.336705	−	0.244631i	−0.0157160	−	0.0114184i
$460$		0			0
$461$	21.0420	−	15.2879i	0.980024	−	0.712029i	0.0223102	−	0.999751i	$-0.492898\pi$
$461$	21.0420	−	15.2879i	0.980024	−	0.712029i	0.957714	+	0.287722i	$0.0928979\pi$
$462$		0			0
$463$	−18.2173	+	2.88534i	−0.846632	+	0.134093i	−0.564654	−	0.825328i	$-0.690990\pi$
$463$	−18.2173	+	2.88534i	−0.846632	+	0.134093i	−0.281978	+	0.959421i	$0.590990\pi$
$464$		0			0
$465$	−27.1230	−	27.1230i	−1.25780	−	1.25780i
$466$		0			0
$467$	2.74166	−	5.38081i	0.126869	−	0.248994i	−0.818831	−	0.574034i	$-0.805378\pi$
$467$	2.74166	−	5.38081i	0.126869	−	0.248994i	0.945700	+	0.325040i	$0.105378\pi$
$468$		0			0
$469$	−20.0742	+	6.52250i	−0.926940	+	0.301181i
$470$		0			0
$471$	31.1765	+	10.1299i	1.43654	+	0.466760i
$472$		0			0
$473$	−17.4118	−	2.75776i	−0.800595	−	0.126802i
$474$		0			0
$475$	4.06006	+	12.4956i	0.186288	+	0.573336i
$476$		0			0
$477$	−3.20931	+	20.2628i	−0.146944	+	0.927768i
$478$		0			0
$479$	−9.84823	+	30.3097i	−0.449977	+	1.38489i	0.426955	+	0.904273i	$0.359586\pi$
$479$	−9.84823	+	30.3097i	−0.449977	+	1.38489i	−0.876932	+	0.480615i	$0.840414\pi$
$480$		0			0
$481$	−16.7811	−	51.6469i	−0.765152	−	2.35490i
$482$		0			0
$483$	48.5452	+	24.7350i	2.20888	+	1.12548i
$484$		0			0
$485$	7.36846	+	14.4614i	0.334585	+	0.656659i
$486$		0			0
$487$	−0.106721	−	0.673811i	−0.00483600	−	0.0305333i	0.985152	−	0.171682i	$-0.0549203\pi$
$487$	−0.106721	−	0.673811i	−0.00483600	−	0.0305333i	−0.989988	+	0.141149i	$0.954920\pi$
$488$		0			0
$489$	6.23273	+	8.57862i	0.281854	+	0.387938i
$490$		0			0
$491$	−5.31800	+	7.31960i	−0.239998	+	0.330329i	−0.911977	−	0.410241i	$-0.865445\pi$
$491$	−5.31800	+	7.31960i	−0.239998	+	0.330329i	0.671979	+	0.740570i	$0.265445\pi$
$492$		0			0
$493$	7.28173	+	7.28173i	0.327953	+	0.327953i
$494$		0			0
$495$	21.8124			0.980394
$496$		0			0
$497$	26.9323	+	52.8577i	1.20808	+	2.37099i
$498$		0			0
$499$	11.1157			0.497605			0.248802	−	0.968554i	$-0.419963\pi$
$499$	11.1157			0.497605			0.248802	+	0.968554i	$0.419963\pi$
$500$		0			0
$501$	−10.7699			−0.481162
$502$		0			0
$503$	−1.52476	−	2.99251i	−0.0679856	−	0.133429i	0.854513	−	0.519431i	$-0.173856\pi$
$503$	−1.52476	−	2.99251i	−0.0679856	−	0.133429i	−0.922498	+	0.386001i	$0.873856\pi$
$504$		0			0
$505$	−2.46402			−0.109648
$506$		0			0
$507$	41.7110	+	41.7110i	1.85245	+	1.85245i
$508$		0			0
$509$	8.30851	−	11.4357i	0.368268	−	0.506878i	−0.584161	−	0.811638i	$-0.698576\pi$
$509$	8.30851	−	11.4357i	0.368268	−	0.506878i	0.952429	+	0.304760i	$0.0985763\pi$
$510$		0			0
$511$	−14.5866	−	20.0767i	−0.645271	−	0.888140i
$512$		0			0
$513$	0.0612214	+	0.386537i	0.00270299	+	0.0170660i
$514$		0			0
$515$	−18.7268	−	36.7534i	−0.825201	−	1.61955i
$516$		0			0
$517$	−25.3408	−	12.9118i	−1.11449	−	0.567860i
$518$		0			0
$519$	19.3307	+	59.4938i	0.848524	+	2.61149i
$520$		0			0
$521$	−6.53962	+	20.1269i	−0.286506	+	0.881774i	0.699437	+	0.714694i	$0.253434\pi$
$521$	−6.53962	+	20.1269i	−0.286506	+	0.881774i	−0.985943	+	0.167080i	$0.946566\pi$
$522$		0			0
$523$	−5.95087	+	37.5723i	−0.260213	+	1.64292i	0.418281	+	0.908318i	$0.362633\pi$
$523$	−5.95087	+	37.5723i	−0.260213	+	1.64292i	−0.678495	+	0.734605i	$0.737367\pi$
$524$		0			0
$525$	−14.5847	+	44.8872i	−0.636531	+	1.95904i
$526$		0			0
$527$	19.2325	+	3.04612i	0.837779	+	0.132691i
$528$		0			0
$529$	−9.80995	−	3.18745i	−0.426520	−	0.138585i
$530$		0			0
$531$	9.99806	−	3.24857i	0.433879	−	0.140976i
$532$		0			0
$533$	−4.89472	+	9.60642i	−0.212014	+	0.416100i
$534$		0			0
$535$	0.877541	+	0.877541i	0.0379394	+	0.0379394i
$536$		0			0
$537$	1.21302	−	0.192124i	0.0523458	−	0.00829076i
$538$		0			0
$539$	−19.8611	+	14.4299i	−0.855478	+	0.621541i
$540$		0			0
$541$	12.3913	+	9.00280i	0.532743	+	0.387060i	0.821383	−	0.570377i	$-0.193203\pi$
$541$	12.3913	+	9.00280i	0.532743	+	0.387060i	−0.288640	+	0.957438i	$0.593203\pi$
$542$		0			0
$543$	8.34633	−	8.34633i	0.358175	−	0.358175i
$544$		0			0
$545$	−8.01066	+	11.0257i	−0.343139	+	0.472290i
$546$		0			0
$547$	−35.7840	+	18.2329i	−1.53001	+	0.779581i	−0.997753	−	0.0670000i	$-0.978657\pi$
$547$	−35.7840	+	18.2329i	−1.53001	+	0.779581i	−0.532260	+	0.846581i	$0.678657\pi$
$548$		0			0
$549$			10.7027i			0.456779i
$550$		0			0
$551$		−	9.68341i		−	0.412527i
$552$		0			0
$553$	15.1643	−	7.72659i	0.644851	−	0.328568i
$554$		0			0
$555$	−28.9016	−	39.7796i	−1.22680	−	1.68855i
$556$		0			0
$557$	29.6304	−	29.6304i	1.25548	−	1.25548i	0.302253	−	0.953228i	$-0.402261\pi$
$557$	29.6304	−	29.6304i	1.25548	−	1.25548i	0.953228	−	0.302253i	$-0.0977387\pi$
$558$		0			0
$559$	−27.2037	−	19.7647i	−1.15060	−	0.835957i
$560$		0			0
$561$	−17.7394	+	12.8884i	−0.748957	+	0.544149i
$562$		0			0
$563$	12.2351	−	1.93786i	0.515650	−	0.0816709i	0.106814	−	0.994279i	$-0.465935\pi$
$563$	12.2351	−	1.93786i	0.515650	−	0.0816709i	0.408836	+	0.912608i	$0.365935\pi$
$564$		0			0
$565$	0.804516	+	5.07951i	0.0338462	+	0.213697i
$566$		0			0
$567$	15.3445	−	30.1154i	0.644410	−	1.26473i
$568$		0			0
$569$	−3.01530	+	0.979730i	−0.126408	+	0.0410724i	−0.371538	−	0.928418i	$-0.621169\pi$
$569$	−3.01530	+	0.979730i	−0.126408	+	0.0410724i	0.245130	+	0.969490i	$0.421169\pi$
$570$		0			0
$571$	38.6626	+	12.5622i	1.61798	+	0.525713i	0.971464	−	0.237189i	$-0.0762259\pi$
$571$	38.6626	+	12.5622i	1.61798	+	0.525713i	0.646515	+	0.762902i	$0.276226\pi$
$572$		0			0
$573$	−60.6302	−	9.60288i	−2.53286	−	0.401166i
$574$		0			0
$575$	4.51462	−	28.5042i	0.188273	−	1.18871i
$576$		0			0
$577$	−0.832436	+	5.25580i	−0.0346548	+	0.218802i	−0.998938	−	0.0460710i	$-0.985330\pi$
$577$	−0.832436	+	5.25580i	−0.0346548	+	0.218802i	0.964283	+	0.264873i	$0.0853299\pi$
$578$		0			0
$579$	7.34912	−	22.6183i	0.305419	−	0.939983i
$580$		0			0
$581$	10.9877	+	33.8166i	0.455845	+	1.40295i
$582$		0			0
$583$	19.0368	+	9.69973i	0.788423	+	0.401722i
$584$		0			0
$585$	37.0708	+	18.8885i	1.53269	+	0.780944i
$586$		0			0
$587$	5.76592	+	36.4046i	0.237985	+	1.50258i	0.760158	+	0.649739i	$0.225122\pi$
$587$	5.76592	+	36.4046i	0.237985	+	1.50258i	−0.522173	+	0.852840i	$0.674878\pi$
$588$		0			0
$589$	−10.7625	−	14.8133i	−0.443461	−	0.610371i
$590$		0			0
$591$	−11.7985	+	16.2393i	−0.485327	+	0.667995i
$592$		0			0
$593$	4.04209	+	4.04209i	0.165989	+	0.165989i	0.785214	−	0.619225i	$-0.212553\pi$
$593$	4.04209	+	4.04209i	0.165989	+	0.165989i	−0.619225	+	0.785214i	$0.712553\pi$
$594$		0			0
$595$	−7.40390	−	22.7869i	−0.303530	−	0.934170i
$596$		0			0
$597$	−5.87368	−	11.5278i	−0.240394	−	0.471799i
$598$		0			0
$599$	−31.6767			−1.29428			−0.647138	−	0.762373i	$-0.724034\pi$
$599$	−31.6767			−1.29428			−0.647138	+	0.762373i	$0.724034\pi$
$600$		0			0
$601$	−32.1339			−1.31077			−0.655385	−	0.755295i	$-0.727493\pi$
$601$	−32.1339			−1.31077			−0.655385	+	0.755295i	$0.727493\pi$
$602$		0			0
$603$	7.64853	+	15.0111i	0.311472	+	0.611299i
$604$		0			0
$605$	−0.581098	+	1.78844i	−0.0236250	+	0.0727103i
$606$		0			0
$607$	−11.1651	−	11.1651i	−0.453176	−	0.453176i	0.443231	−	0.896407i	$-0.353832\pi$
$607$	−11.1651	−	11.1651i	−0.453176	−	0.453176i	−0.896407	+	0.443231i	$0.853832\pi$
$608$		0			0
$609$	20.4463	−	28.1419i	0.828524	−	1.14037i
$610$		0			0
$611$	−31.8865	−	43.8880i	−1.28999	−	1.77552i
$612$		0			0
$613$	3.85579	+	24.3445i	0.155734	+	0.983265i	0.934503	+	0.355955i	$0.115844\pi$
$613$	3.85579	+	24.3445i	0.155734	+	0.983265i	−0.778769	+	0.627310i	$0.784156\pi$
$614$		0			0
$615$	−1.52714	+	9.64198i	−0.0615802	+	0.388802i
$616$		0			0
$617$	−1.95651	−	0.996891i	−0.0787661	−	0.0401333i	0.414164	−	0.910202i	$-0.364074\pi$
$617$	−1.95651	−	0.996891i	−0.0787661	−	0.0401333i	−0.492930	+	0.870069i	$0.664074\pi$
$618$		0			0
$619$	−8.90525	−	27.4076i	−0.357932	−	1.10160i	−0.954290	−	0.298883i	$-0.903386\pi$
$619$	−8.90525	−	27.4076i	−0.357932	−	1.10160i	0.596357	−	0.802719i	$-0.296614\pi$
$620$		0			0
$621$	0.265639	−	0.817554i	0.0106597	−	0.0328073i
$622$		0			0
$623$	−6.79658	+	42.9119i	−0.272299	+	1.71923i
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	20.3648	+	3.22546i	0.813291	+	0.128813i
$628$		0			0
$629$	23.7395	+	7.71342i	0.946555	+	0.307554i
$630$		0			0
$631$	−8.95409	+	2.90936i	−0.356457	+	0.115820i	−0.481771	−	0.876297i	$-0.660006\pi$
$631$	−8.95409	+	2.90936i	−0.356457	+	0.115820i	0.125314	+	0.992117i	$0.460006\pi$
$632$		0			0
$633$	0.840938	−	1.65043i	0.0334243	−	0.0655989i
$634$		0			0
$635$	−30.6744	−	4.85834i	−1.21727	−	0.192797i
$636$		0			0
$637$	−46.2502	+	7.32531i	−1.83250	+	0.290239i
$638$		0			0
$639$	38.3076	−	27.8321i	1.51542	−	1.10102i
$640$		0			0
$641$	17.7266	+	12.8791i	0.700158	+	0.508694i	0.879984	−	0.475004i	$-0.157553\pi$
$641$	17.7266	+	12.8791i	0.700158	+	0.508694i	−0.179826	+	0.983698i	$0.557553\pi$
$642$		0			0
$643$	16.0055	−	16.0055i	0.631196	−	0.631196i	−0.317172	−	0.948368i	$-0.602733\pi$
$643$	16.0055	−	16.0055i	0.631196	−	0.631196i	0.948368	+	0.317172i	$0.102733\pi$
$644$		0			0
$645$	−28.9563	−	9.40846i	−1.14015	−	0.370458i
$646$		0			0
$647$	3.93031	−	2.00259i	0.154516	−	0.0787301i	−0.375022	−	0.927016i	$-0.622365\pi$
$647$	3.93031	−	2.00259i	0.154516	−	0.0787301i	0.529539	+	0.848286i	$0.322365\pi$
$648$		0			0
$649$		−	10.9482i		−	0.429755i
$650$		0			0
$651$		−	65.7750i		−	2.57793i
$652$		0			0
$653$	15.0083	−	7.64709i	0.587318	−	0.299254i	−0.134966	−	0.990850i	$-0.543092\pi$
$653$	15.0083	−	7.64709i	0.587318	−	0.299254i	0.722284	+	0.691597i	$0.243092\pi$
$654$		0			0
$655$	−22.1438	+	7.19496i	−0.865230	+	0.281130i
$656$		0			0
$657$	−14.0062	+	14.0062i	−0.546432	+	0.546432i
$658$		0			0
$659$	5.31800	+	3.86376i	0.207160	+	0.150511i	0.686528	−	0.727104i	$-0.259134\pi$
$659$	5.31800	+	3.86376i	0.207160	+	0.150511i	−0.479368	+	0.877614i	$0.659134\pi$
$660$		0			0
$661$	20.3552	−	14.7889i	0.791727	−	0.575223i	−0.116749	−	0.993161i	$-0.537247\pi$
$661$	20.3552	−	14.7889i	0.791727	−	0.575223i	0.908475	+	0.417938i	$0.137247\pi$
$662$		0			0
$663$	−41.3094	+	6.54276i	−1.60432	+	0.254100i
$664$		0			0
$665$	−10.2283	+	20.0742i	−0.396637	+	0.778443i
$666$		0			0
$667$	−9.65637	+	18.9517i	−0.373896	+	0.733813i
$668$		0			0
$669$	−1.71971	+	0.558769i	−0.0664880	+	0.0216032i
$670$		0			0
$671$	10.6007	+	3.44436i	0.409234	+	0.132968i
$672$		0			0
$673$	−41.0202	−	6.49696i	−1.58121	−	0.250439i	−0.696842	−	0.717225i	$-0.745412\pi$
$673$	−41.0202	−	6.49696i	−1.58121	−	0.250439i	−0.884371	+	0.466785i	$0.845412\pi$
$674$		0			0
$675$	0.735498	+	0.116491i	0.0283093	+	0.00448376i
$676$		0			0
$677$	−2.44236	+	15.4204i	−0.0938674	+	0.592655i	0.895254	+	0.445556i	$0.146994\pi$
$677$	−2.44236	+	15.4204i	−0.0938674	+	0.592655i	−0.989122	+	0.147100i	$0.953006\pi$
$678$		0			0
$679$	−8.60042	+	26.4694i	−0.330054	+	1.01580i
$680$		0			0
$681$	12.7162	+	39.1364i	0.487285	+	1.49971i
$682$		0			0
$683$	10.0684	+	5.13008i	0.385255	+	0.196297i	0.635882	−	0.771787i	$-0.280637\pi$
$683$	10.0684	+	5.13008i	0.385255	+	0.196297i	−0.250627	+	0.968084i	$0.580637\pi$
$684$		0			0
$685$	−5.83734	+	0.924544i	−0.223033	+	0.0353250i
$686$		0			0
$687$	3.69143	+	23.3068i	0.140837	+	0.889208i
$688$		0			0
$689$	23.9541	+	32.9699i	0.912577	+	1.25605i
$690$		0			0
$691$	−20.0614	+	27.6122i	−0.763172	+	1.05042i	0.233772	+	0.972292i	$0.424893\pi$
$691$	−20.0614	+	27.6122i	−0.763172	+	1.05042i	−0.996944	+	0.0781245i	$0.975107\pi$
$692$		0			0
$693$	26.4482	+	26.4482i	1.00468	+	1.00468i
$694$		0			0
$695$	37.6559	−	27.3586i	1.42837	−	1.03777i
$696$		0			0
$697$	−2.24985	−	4.41559i	−0.0852193	−	0.167252i
$698$		0			0
$699$	−35.5676			−1.34529
$700$		0			0
$701$	−27.4720			−1.03760			−0.518802	−	0.854894i	$-0.673622\pi$
$701$	−27.4720			−1.03760			−0.518802	+	0.854894i	$0.673622\pi$
$702$		0			0
$703$	−10.6559	−	20.9134i	−0.401895	−	0.788764i
$704$		0			0
$705$	−39.7384	−	28.8717i	−1.49664	−	1.08737i
$706$		0			0
$707$	−2.98770	−	2.98770i	−0.112364	−	0.112364i
$708$		0			0
$709$	−25.3077	+	34.8330i	−0.950450	+	1.30818i	0.000877309		1.00000i	$0.499721\pi$
$709$	−25.3077	+	34.8330i	−0.950450	+	1.30818i	−0.951327	+	0.308183i	$0.900279\pi$
$710$		0			0
$711$	−7.98471	−	10.9900i	−0.299450	−	0.412158i
$712$		0			0
$713$	6.29166	+	39.7240i	0.235625	+	1.48768i
$714$		0			0
$715$	30.6387	−	30.6387i	1.14582	−	1.14582i
$716$		0			0
$717$	12.8754	+	6.56033i	0.480840	+	0.245000i
$718$		0			0
$719$	4.03319	+	12.4129i	0.150413	+	0.462922i	0.997667	−	0.0682646i	$-0.0217462\pi$
$719$	4.03319	+	12.4129i	0.150413	+	0.462922i	−0.847255	+	0.531187i	$0.821746\pi$
$720$		0			0
$721$	21.8578	−	67.2714i	0.814027	−	2.50532i
$722$		0			0
$723$	−7.99185	+	50.4586i	−0.297220	+	1.87657i
$724$		0			0
$725$	−17.5237	−	5.69379i	−0.650813	−	0.211462i
$726$		0			0
$727$	47.8106	+	7.57246i	1.77320	+	0.280847i	0.955541	−	0.294858i	$-0.0952725\pi$
$727$	47.8106	+	7.57246i	1.77320	+	0.280847i	0.817657	+	0.575705i	$0.195273\pi$
$728$		0			0
$729$	−26.7035	−	8.67650i	−0.989020	−	0.321352i
$730$		0			0
$731$	14.6996	−	4.77618i	0.543683	−	0.176653i
$732$		0			0
$733$	7.89633	−	15.4974i	0.291657	−	0.572410i	−0.697960	−	0.716137i	$-0.745909\pi$
$733$	7.89633	−	15.4974i	0.291657	−	0.572410i	0.989617	+	0.143727i	$0.0459086\pi$
$734$		0			0
$735$	−37.7780	+	19.2489i	−1.39346	+	0.710005i
$736$		0			0
$737$	17.3295	−	2.74472i	0.638339	−	0.101103i
$738$		0			0
$739$	5.14942	−	3.74127i	0.189424	−	0.137625i	−0.489031	−	0.872266i	$-0.662650\pi$
$739$	5.14942	−	3.74127i	0.189424	−	0.137625i	0.678456	+	0.734641i	$0.262650\pi$
$740$		0			0
$741$	31.8174	+	23.1167i	1.16884	+	0.849214i
$742$		0			0
$743$	24.3150	−	24.3150i	0.892030	−	0.892030i	−0.102684	−	0.994714i	$-0.532743\pi$
$743$	24.3150	−	24.3150i	0.892030	−	0.892030i	0.994714	+	0.102684i	$0.0327429\pi$
$744$		0			0
$745$		−	13.9869i		−	0.512439i
$746$		0			0
$747$	25.2874	−	12.8846i	0.925217	−	0.471422i
$748$		0			0
$749$			2.12809i			0.0777587i
$750$		0			0
$751$		−	2.44679i		−	0.0892845i	−0.999003	−	0.0446422i	$-0.985785\pi$
$751$		−	2.44679i		−	0.0892845i	0.999003	−	0.0446422i	$-0.0142148\pi$
$752$		0			0
$753$	43.7317	−	22.2824i	1.59367	−	0.812017i
$754$		0			0
$755$			29.6156i			1.07782i
$756$		0			0
$757$	−3.26033	+	3.26033i	−0.118499	+	0.118499i	−0.763869	−	0.645371i	$-0.776703\pi$
$757$	−3.26033	+	3.26033i	−0.118499	+	0.118499i	0.645371	+	0.763869i	$0.276703\pi$
$758$		0			0
$759$	−36.6401	−	26.6206i	−1.32995	−	0.966266i
$760$		0			0
$761$	−28.4749	+	20.6882i	−1.03221	+	0.749947i	−0.968751	−	0.248037i	$-0.920215\pi$
$761$	−28.4749	+	20.6882i	−1.03221	+	0.749947i	−0.0634634	+	0.997984i	$0.520215\pi$
$762$		0			0
$763$	−23.0822	+	3.65586i	−0.835631	+	0.132351i
$764$		0			0
$765$	−17.0396	+	8.68209i	−0.616067	+	0.313902i
$766$		0			0
$767$	9.48065	−	18.6068i	0.342326	−	0.671853i
$768$		0			0
$769$	−3.32407	+	1.08005i	−0.119869	+	0.0389478i	−0.368337	−	0.929692i	$-0.620073\pi$
$769$	−3.32407	+	1.08005i	−0.119869	+	0.0389478i	0.248468	+	0.968640i	$0.420073\pi$
$770$		0			0
$771$	16.8580	+	5.47750i	0.607126	+	0.197267i
$772$		0			0
$773$	−4.37518	−	0.692961i	−0.157364	−	0.0249241i	0.0772551	−	0.997011i	$-0.475384\pi$
$773$	−4.37518	−	0.692961i	−0.157364	−	0.0249241i	−0.234619	+	0.972087i	$0.575384\pi$
$774$		0			0
$775$	−33.1353	+	10.7663i	−1.19025	+	0.386737i
$776$		0			0
$777$	13.1899	−	83.2780i	0.473187	−	2.98758i
$778$		0			0
$779$	−1.44002	+	4.43193i	−0.0515941	+	0.158790i
$780$		0			0
$781$	−15.2385	−	46.8994i	−0.545278	−	1.67819i
$782$		0			0
$783$	−0.489014	−	0.249165i	−0.0174759	−	0.00890443i
$784$		0			0
$785$	21.0541	−	21.0541i	0.751454	−	0.751454i
$786$		0			0
$787$	−3.34288	−	21.1061i	−0.119161	−	0.752351i	−0.972827	−	0.231531i	$-0.925626\pi$
$787$	−3.34288	−	21.1061i	−0.119161	−	0.752351i	0.853667	−	0.520820i	$-0.174374\pi$
$788$		0			0
$789$	−21.7327	−	29.9125i	−0.773704	−	1.06491i
$790$		0			0
$791$	−5.18356	+	7.13456i	−0.184306	+	0.253676i
$792$		0			0
$793$	15.0335	+	15.0335i	0.533854	+	0.533854i
$794$		0			0
$795$	29.8527	+	21.6892i	1.05877	+	0.769238i
$796$		0			0
$797$	11.2256	+	22.0314i	0.397631	+	0.780394i	0.999839	−	0.0179450i	$-0.00571239\pi$
$797$	11.2256	+	22.0314i	0.397631	+	0.780394i	−0.602208	+	0.798339i	$0.705712\pi$
$798$		0			0
$799$	24.9353			0.882148
$800$		0			0
$801$	34.6783			1.22530
$802$		0			0
$803$	9.36515	+	18.3801i	0.330489	+	0.648621i
$804$		0			0
$805$	40.0363	−	29.0881i	1.41109	−	1.02522i
$806$		0			0
$807$	−46.8734	−	46.8734i	−1.65002	−	1.65002i
$808$		0			0
$809$	−9.57329	+	13.1765i	−0.336579	+	0.463261i	−0.943438	−	0.331548i	$-0.892429\pi$
$809$	−9.57329	+	13.1765i	−0.336579	+	0.463261i	0.606859	+	0.794809i	$0.292429\pi$
$810$		0			0
$811$	9.11603	+	12.5471i	0.320107	+	0.440590i	0.938500	−	0.345280i	$-0.112216\pi$
$811$	9.11603	+	12.5471i	0.320107	+	0.440590i	−0.618393	+	0.785869i	$0.712216\pi$
$812$		0			0
$813$	−1.55508	−	9.81838i	−0.0545390	−	0.344346i
$814$		0			0
$815$	9.51284	−	1.50669i	0.333220	−	0.0527769i
$816$		0			0
$817$	−12.9496	−	6.59817i	−0.453051	−	0.230841i
$818$		0			0
$819$	22.0466	+	67.8523i	0.770369	+	2.37095i
$820$		0			0
$821$	−9.46921	+	29.1432i	−0.330478	+	1.01711i	0.638429	+	0.769680i	$0.279584\pi$
$821$	−9.46921	+	29.1432i	−0.330478	+	1.01711i	−0.968907	+	0.247425i	$0.920416\pi$
$822$		0			0
$823$	2.19889	−	13.8833i	0.0766486	−	0.483940i	−0.919266	−	0.393637i	$-0.871217\pi$
$823$	2.19889	−	13.8833i	0.0766486	−	0.483940i	0.995914	−	0.0903026i	$-0.0287834\pi$
$824$		0			0
$825$	17.8114	−	34.9568i	0.620112	−	1.21704i
$826$		0			0
$827$	−3.27030	−	0.517965i	−0.113720	−	0.0180114i	0.0993153	−	0.995056i	$-0.468335\pi$
$827$	−3.27030	−	0.517965i	−0.113720	−	0.0180114i	−0.213035	+	0.977045i	$0.568335\pi$
$828$		0			0
$829$	−6.30039	−	2.04712i	−0.218821	−	0.0710994i	0.197555	−	0.980292i	$-0.436700\pi$
$829$	−6.30039	−	2.04712i	−0.218821	−	0.0710994i	−0.416376	+	0.909192i	$0.636700\pi$
$830$		0			0
$831$	47.8165	−	15.5365i	1.65873	−	0.538955i
$832$		0			0
$833$	9.77163	−	19.1779i	0.338567	−	0.664475i
$834$		0			0
$835$	−4.44108	+	8.71610i	−0.153690	+	0.301633i
$836$		0			0
$837$	−1.02500	+	0.162345i	−0.0354293	+	0.00561145i
$838$		0			0
$839$	−1.17045	+	0.850383i	−0.0404085	+	0.0293585i	−0.607806	−	0.794085i	$-0.707950\pi$
$839$	−1.17045	+	0.850383i	−0.0404085	+	0.0293585i	0.567398	+	0.823444i	$0.307950\pi$
$840$		0			0
$841$	−12.4751	−	9.06369i	−0.430176	−	0.312541i
$842$		0			0
$843$	11.7680	−	11.7680i	0.405312	−	0.405312i
$844$		0			0
$845$	50.9568	−	16.5569i	1.75297	−	0.569574i
$846$		0			0
$847$	−2.87313	+	1.46393i	−0.0987219	+	0.0503013i
$848$		0			0
$849$			9.84587i			0.337910i
$850$		0			0
$851$			51.5564i			1.76733i
$852$		0			0
$853$	21.3575	−	10.8822i	0.731268	−	0.372600i	−0.0483707	−	0.998829i	$-0.515403\pi$
$853$	21.3575	−	10.8822i	0.731268	−	0.372600i	0.779638	+	0.626230i	$0.215403\pi$
$854$		0			0
$855$	17.1026	+	5.55698i	0.584898	+	0.190045i
$856$		0			0
$857$	24.2558	−	24.2558i	0.828563	−	0.828563i	−0.158755	−	0.987318i	$-0.550748\pi$
$857$	24.2558	−	24.2558i	0.828563	−	0.828563i	0.987318	+	0.158755i	$0.0507479\pi$
$858$		0			0
$859$	−12.0193	−	8.73251i	−0.410092	−	0.297949i	0.363547	−	0.931576i	$-0.381566\pi$
$859$	−12.0193	−	8.73251i	−0.410092	−	0.297949i	−0.773639	+	0.633627i	$0.781566\pi$
$860$		0			0
$861$	−13.5429	+	9.83948i	−0.461540	+	0.335329i
$862$		0			0
$863$	−11.4968	+	1.82092i	−0.391357	+	0.0619849i	−0.349012	−	0.937118i	$-0.613483\pi$
$863$	−11.4968	+	1.82092i	−0.391357	+	0.0619849i	−0.0423449	+	0.999103i	$0.513483\pi$
$864$		0			0
$865$	56.1198	+	8.88851i	1.90813	+	0.302218i
$866$		0			0
$867$	−10.2721	+	20.1601i	−0.348858	+	0.684673i
$868$		0			0
$869$	−13.4549	+	4.37177i	−0.456427	+	0.148302i
$870$		0			0
$871$	31.8287	+	10.3418i	1.07848	+	0.350418i
$872$		0			0
$873$	21.9410	+	3.47512i	0.742592	+	0.117615i
$874$		0			0
$875$	30.3132	+	30.3132i	1.02477	+	1.02477i
$876$		0			0
$877$	−5.14665	+	32.4947i	−0.173790	+	1.09727i	0.734403	+	0.678714i	$0.237462\pi$
$877$	−5.14665	+	32.4947i	−0.173790	+	1.09727i	−0.908193	+	0.418553i	$0.862538\pi$
$878$		0			0
$879$	0.178579	−	0.549609i	0.00602331	−	0.0185379i
$880$		0			0
$881$	12.0185	+	36.9892i	0.404914	+	1.24620i	0.920967	+	0.389641i	$0.127401\pi$
$881$	12.0185	+	36.9892i	0.404914	+	1.24620i	−0.516053	+	0.856557i	$0.672599\pi$
$882$		0			0
$883$	−28.4751	−	14.5088i	−0.958264	−	0.488260i	−0.0963681	−	0.995346i	$-0.530723\pi$
$883$	−28.4751	−	14.5088i	−0.958264	−	0.488260i	−0.861895	+	0.507086i	$0.830723\pi$
$884$		0			0
$885$	2.95794	−	18.6757i	0.0994300	−	0.627776i
$886$		0			0
$887$	4.48269	+	28.3026i	0.150514	+	0.950309i	0.941142	+	0.338012i	$0.109754\pi$
$887$	4.48269	+	28.3026i	0.150514	+	0.950309i	−0.790628	+	0.612297i	$0.790246\pi$
$888$		0			0
$889$	−31.3027	−	43.0845i	−1.04986	−	1.44501i
$890$		0			0
$891$	−16.5143	+	22.7300i	−0.553249	+	0.761482i
$892$		0			0
$893$	−16.5798	−	16.5798i	−0.554821	−	0.554821i
$894$		0			0
$895$	0.344717	−	1.06093i	0.0115226	−	0.0354629i
$896$		0			0
$897$	−39.2187	−	76.9711i	−1.30947	−	2.56999i
$898$		0			0
$899$	25.6781			0.856413
$900$		0			0
$901$	−18.7321			−0.624058
$902$		0			0
$903$	−23.7023	−	46.5184i	−0.788763	−	1.54803i
$904$		0			0
$905$	−3.31302	−	10.1964i	−0.110128	−	0.338940i
$906$		0			0
$907$	7.20247	+	7.20247i	0.239154	+	0.239154i	0.816500	−	0.577346i	$-0.195912\pi$
$907$	7.20247	+	7.20247i	0.239154	+	0.239154i	−0.577346	+	0.816500i	$0.695912\pi$
$908$		0			0
$909$	−1.98230	+	2.72841i	−0.0657489	+	0.0904956i
$910$		0			0
$911$	−28.1374	−	38.7278i	−0.932234	−	1.28311i	−0.958982	−	0.283467i	$-0.908515\pi$
$911$	−28.1374	−	38.7278i	−0.932234	−	1.28311i	0.0267482	−	0.999642i	$-0.491485\pi$
$912$		0			0
$913$	−4.62370	−	29.1929i	−0.153022	−	0.966143i
$914$		0			0
$915$	17.1522	+	8.73950i	0.567035	+	0.288919i
$916$		0			0
$917$	−35.5741	−	18.1259i	−1.17476	−	0.598571i
$918$		0			0
$919$	3.99933	+	12.3087i	0.131926	+	0.406026i	0.995099	−	0.0988817i	$-0.0315265\pi$
$919$	3.99933	+	12.3087i	0.131926	+	0.406026i	−0.863173	+	0.504908i	$0.831527\pi$
$920$		0			0
$921$	−6.92893	+	21.3250i	−0.228316	+	0.702684i
$922$		0			0
$923$	14.7144	−	92.9028i	0.484329	−	3.05793i
$924$		0			0
$925$	−44.1117	+	6.98661i	−1.45038	+	0.229718i
$926$		0			0
$927$	−55.7627	−	8.83194i	−1.83149	−	0.290079i
$928$		0			0
$929$	12.0350	+	3.91041i	0.394855	+	0.128296i	0.499713	−	0.866191i	$-0.333439\pi$
$929$	12.0350	+	3.91041i	0.394855	+	0.128296i	−0.104858	+	0.994487i	$0.533439\pi$
$930$		0			0
$931$	−19.2489	+	6.25434i	−0.630856	+	0.204978i
$932$		0			0
$933$	12.5883	−	24.7059i	0.412123	−	0.808836i
$934$		0			0
$935$	3.11562	+	19.6712i	0.101892	+	0.643318i
$936$		0			0
$937$	6.05841	−	0.959558i	0.197920	−	0.0313474i	−0.0566874	−	0.998392i	$-0.518054\pi$
$937$	6.05841	−	0.959558i	0.197920	−	0.0313474i	0.254607	+	0.967045i	$0.418054\pi$
$938$		0			0
$939$	11.7781	−	8.55728i	0.384363	−	0.279256i
$940$		0			0
$941$	12.5173	+	9.09433i	0.408052	+	0.296467i	0.772813	−	0.634634i	$-0.218849\pi$
$941$	12.5173	+	9.09433i	0.408052	+	0.296467i	−0.364761	+	0.931101i	$0.618849\pi$
$942$		0			0
$943$	7.23787	−	7.23787i	0.235697	−	0.235697i
$944$		0			0
$945$	0.750563	+	1.03306i	0.0244158	+	0.0336055i
$946$		0			0
$947$	−43.5817	+	22.2060i	−1.41621	+	0.721597i	−0.983664	−	0.180013i	$-0.942386\pi$
$947$	−43.5817	+	22.2060i	−1.41621	+	0.721597i	−0.432549	+	0.901610i	$0.642386\pi$
$948$		0			0
$949$			39.3474i			1.27727i
$950$		0			0
$951$			31.1838i			1.01120i
$952$		0			0
$953$	−5.53687	+	2.82118i	−0.179357	+	0.0913869i	−0.541364	−	0.840789i	$-0.682092\pi$
$953$	−5.53687	+	2.82118i	−0.179357	+	0.0913869i	0.362007	+	0.932175i	$0.382092\pi$
$954$		0			0
$955$	−32.7732	+	45.1084i	−1.06051	+	1.45967i
$956$		0			0
$957$	−20.4463	+	20.4463i	−0.660934	+	0.660934i
$958$		0			0
$959$	−8.19898	−	5.95691i	−0.264759	−	0.192359i
$960$		0			0
$961$	14.2018	−	10.3182i	0.458123	−	0.332846i
$962$		0			0
$963$	1.67768	−	0.265719i	0.0540625	−	0.00856266i
$964$		0			0
$965$	−15.2746	−	15.2746i	−0.491706	−	0.491706i
$966$		0			0
$967$	15.6468	−	30.7086i	0.503167	−	0.987521i	−0.490099	−	0.871667i	$-0.663039\pi$
$967$	15.6468	−	30.7086i	0.503167	−	0.987521i	0.993266	−	0.115854i	$-0.0369606\pi$
$968$		0			0
$969$	−17.1926	+	5.58620i	−0.552305	+	0.179455i
$970$		0			0
$971$	−7.69148	−	2.49911i	−0.246831	−	0.0802004i	0.182988	−	0.983115i	$-0.441423\pi$
$971$	−7.69148	−	2.49911i	−0.246831	−	0.0802004i	−0.429820	+	0.902915i	$0.641423\pi$
$972$		0			0
$973$	78.8320	+	12.4858i	2.52724	+	0.400275i
$974$		0			0
$975$	60.5418	−	43.9862i	1.93889	−	1.40869i
$976$		0			0
$977$	−6.60880	+	41.7264i	−0.211434	+	1.33494i	0.622300	+	0.782779i	$0.286198\pi$
$977$	−6.60880	+	41.7264i	−0.211434	+	1.33494i	−0.833735	+	0.552166i	$0.813802\pi$
$978$		0			0
$979$	11.1603	−	34.3477i	0.356683	−	1.09776i
$980$		0			0
$981$	5.76420	+	17.7404i	0.184037	+	0.566407i
$982$		0			0
$983$	5.28581	+	2.69325i	0.168591	+	0.0859014i	0.536250	−	0.844059i	$-0.319841\pi$
$983$	5.28581	+	2.69325i	0.168591	+	0.0859014i	−0.367659	+	0.929961i	$0.619841\pi$
$984$		0			0
$985$	8.27727	+	16.2450i	0.263736	+	0.517610i
$986$		0			0
$987$	−13.1763	−	83.1918i	−0.419406	−	2.64802i
$988$		0			0
$989$	18.7644	+	25.8270i	0.596673	+	0.821250i
$990$		0			0
$991$	−18.4035	+	25.3303i	−0.584607	+	0.804643i	−0.994191	−	0.107630i	$-0.965674\pi$
$991$	−18.4035	+	25.3303i	−0.584607	+	0.804643i	0.409584	+	0.912273i	$0.365674\pi$
$992$		0			0
$993$	7.21990	+	7.21990i	0.229116	+	0.229116i
$994$		0			0
$995$	−11.7515			−0.372549
$996$		0			0
$997$	−18.3846	−	36.0819i	−0.582247	−	1.14272i	−0.974818	−	0.223002i	$-0.928414\pi$
$997$	−18.3846	−	36.0819i	−0.582247	−	1.14272i	0.392571	−	0.919722i	$-0.371586\pi$
$998$		0			0
$999$	−1.33032			−0.0420894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.c.223.1	✓	16
4.3	odd	2	inner	400.2.bi.c.223.2	yes	16
25.12	odd	20	inner	400.2.bi.c.287.2	yes	16
100.87	even	20	inner	400.2.bi.c.287.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.c.223.1	✓	16	1.1	even	1	trivial
400.2.bi.c.223.2	yes	16	4.3	odd	2	inner
400.2.bi.c.287.1	yes	16	100.87	even	20	inner
400.2.bi.c.287.2	yes	16	25.12	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11764 - 2.19349i) q^{3} -2.23607 q^{5} +(-2.71130 - 2.71130i) q^{7} +(-1.79892 + 2.47599i) q^{9} +O(q^{10})\)	\(q+(-1.11764 - 2.19349i) q^{3} -2.23607 q^{5} +(-2.71130 - 2.71130i) q^{7} +(-1.79892 + 2.47599i) q^{9} +(1.87346 + 2.57860i) q^{11} +(0.951057 + 6.00473i) q^{13} +(2.49911 + 4.90479i) q^{15} +(-2.48990 - 1.26867i) q^{17} +(0.812011 + 2.49911i) q^{19} +(-2.91695 + 8.97745i) q^{21} +(0.902924 - 5.70084i) q^{23} +5.00000 q^{25} +(0.147100 + 0.0232983i) q^{27} +(-3.50473 - 1.13876i) q^{29} +(-6.62706 + 2.15326i) q^{31} +(3.56227 - 6.99135i) q^{33} +(6.06265 + 6.06265i) q^{35} +(-8.82234 + 1.39732i) q^{37} +(12.1084 - 8.79725i) q^{39} +(1.43471 + 1.04238i) q^{41} +(-3.91095 + 3.91095i) q^{43} +(4.02250 - 5.53649i) q^{45} +(-7.95051 + 4.05099i) q^{47} +7.70228i q^{49} +6.87947i q^{51} +(5.97266 - 3.04322i) q^{53} +(-4.18919 - 5.76592i) q^{55} +(4.57424 - 4.57424i) q^{57} +(-2.77891 - 2.01900i) q^{59} +(2.82916 - 2.05551i) q^{61} +(11.5906 - 1.83576i) q^{63} +(-2.12663 - 13.4270i) q^{65} +(2.49911 - 4.90479i) q^{67} +(-13.5138 + 4.39092i) q^{69} +(-14.7144 - 4.78098i) q^{71} +(6.39237 + 1.01245i) q^{73} +(-5.58819 - 10.9674i) q^{75} +(1.91184 - 12.0709i) q^{77} +(-1.37161 + 4.22138i) q^{79} +(2.72394 + 8.38342i) q^{81} +(-8.26251 - 4.20996i) q^{83} +(5.56758 + 2.83682i) q^{85} +(1.41917 + 8.96031i) q^{87} +(-6.66016 - 9.16692i) q^{89} +(13.7020 - 18.8592i) q^{91} +(12.1298 + 12.1298i) q^{93} +(-1.81571 - 5.58819i) q^{95} +(-3.29528 - 6.46735i) q^{97} -9.75479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{9}+O(q^{10}) \) 16 * q + 20 * q^9	\( 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93} - 80 q^{97}+O(q^{100}) \) 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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