LMFDB - Embedded newform 1764.2.w.b.509.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.8
Root			$1.08696 + 1.34852i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.b.1109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63336 - 0.576322i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(2.33571 - 1.88268i) q^{9} +O(q^{10})$	\(q+(1.63336 - 0.576322i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(2.33571 - 1.88268i) q^{9} +(4.66300 + 2.69219i) q^{11} +(-4.60313 - 2.65762i) q^{13} +(-0.100558 - 0.0860820i) q^{15} +(-1.89092 - 3.27516i) q^{17} +(4.33939 + 2.50535i) q^{19} +(-2.02463 + 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(2.73001 - 4.42120i) q^{27} +(8.84430 - 5.10626i) q^{29} +5.74620i q^{31} +(9.16791 + 1.70991i) q^{33} +(0.354486 - 0.613988i) q^{37} +(-9.05019 - 1.68795i) q^{39} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(-0.213859 - 0.0826487i) q^{45} +2.92385 q^{47} +(-4.97609 - 4.25973i) q^{51} +(-10.4835 + 6.05264i) q^{53} -0.411498i q^{55} +(8.53166 + 1.59124i) q^{57} +0.579903 q^{59} +2.77868i q^{61} +0.406214i q^{65} +5.27185 q^{67} +(-2.63327 + 3.07610i) q^{69} +3.32103i q^{71} +(6.17326 - 3.56413i) q^{73} +(1.58599 - 8.50350i) q^{75} +0.938245 q^{79} +(1.91105 - 8.79476i) q^{81} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(11.5031 - 13.4375i) q^{87} +(-1.51794 + 2.62915i) q^{89} +(3.31166 + 9.38560i) q^{93} -0.382940i q^{95} +(6.18183 - 3.56908i) q^{97} +(15.9599 - 2.49077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.63336	−	0.576322i	0.943019	−	0.332739i
$3$	1.63336	−	0.576322i	0.943019	−	0.332739i
$4$		0			0
$5$	−0.0382122	−	0.0661855i	−0.0170890	−	0.0295991i	0.857354	−	0.514727i	$-0.172107\pi$
$5$	−0.0382122	−	0.0661855i	−0.0170890	−	0.0295991i	−0.874443	+	0.485127i	$0.838773\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.33571	−	1.88268i	0.778569	−	0.627559i
$10$		0			0
$11$	4.66300	+	2.69219i	1.40595	+	0.811725i	0.994994	−	0.0999316i	$-0.0318624\pi$
$11$	4.66300	+	2.69219i	1.40595	+	0.811725i	0.410954	+	0.911656i	$0.365196\pi$
$12$		0			0
$13$	−4.60313	−	2.65762i	−1.27668	−	0.737091i	−0.300442	−	0.953800i	$-0.597134\pi$
$13$	−4.60313	−	2.65762i	−1.27668	−	0.737091i	−0.976236	+	0.216709i	$0.930468\pi$
$14$		0			0
$15$	−0.100558	−	0.0860820i	−0.0259641	−	0.0222263i
$16$		0			0
$17$	−1.89092	−	3.27516i	−0.458615	−	0.794344i	0.540273	−	0.841490i	$-0.318321\pi$
$17$	−1.89092	−	3.27516i	−0.458615	−	0.794344i	−0.998888	+	0.0471458i	$0.984987\pi$
$18$		0			0
$19$	4.33939	+	2.50535i	0.995525	+	0.574767i	0.906921	−	0.421300i	$-0.138426\pi$
$19$	4.33939	+	2.50535i	0.995525	+	0.574767i	0.0886040	+	0.996067i	$0.471759\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.02463	+	1.16892i	−0.422164	+	0.243737i	−0.696003	−	0.718039i	$-0.745040\pi$
$23$	−2.02463	+	1.16892i	−0.422164	+	0.243737i	0.273839	+	0.961776i	$0.411707\pi$
$24$		0			0
$25$	2.49708	−	4.32507i	0.499416	−	0.865014i
$26$		0			0
$27$	2.73001	−	4.42120i	0.525392	−	0.850861i
$28$		0			0
$29$	8.84430	−	5.10626i	1.64235	−	0.948209i	0.662349	−	0.749196i	$-0.269560\pi$
$29$	8.84430	−	5.10626i	1.64235	−	0.948209i	0.979997	−	0.199013i	$-0.0637736\pi$
$30$		0			0
$31$			5.74620i			1.03205i	0.856574	+	0.516024i	$0.172589\pi$
$31$			5.74620i			1.03205i	−0.856574	+	0.516024i	$0.827411\pi$
$32$		0			0
$33$	9.16791	+	1.70991i	1.59593	+	0.297657i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.354486	−	0.613988i	0.0582771	−	0.100939i	−0.835415	−	0.549620i	$-0.814773\pi$
$37$	0.354486	−	0.613988i	0.0582771	−	0.100939i	0.893692	+	0.448681i	$0.148106\pi$
$38$		0			0
$39$	−9.05019	−	1.68795i	−1.44919	−	0.270289i
$40$		0			0
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	−0.484610	−	0.874730i	$-0.661039\pi$
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	0.999844	−	0.0176805i	$-0.00562816\pi$
$42$		0			0
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	0.915474	−	0.402377i	$-0.131816\pi$
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	−0.806206	+	0.591635i	$0.798483\pi$
$44$		0			0
$45$	−0.213859	−	0.0826487i	−0.0318802	−	0.0123205i
$46$		0			0
$47$	2.92385			0.426487			0.213244	−	0.976999i	$-0.431597\pi$
$47$	2.92385			0.426487			0.213244	+	0.976999i	$0.431597\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.97609	−	4.25973i	−0.696792	−	0.596482i
$52$		0			0
$53$	−10.4835	+	6.05264i	−1.44002	+	0.831394i	−0.997850	−	0.0655390i	$-0.979123\pi$
$53$	−10.4835	+	6.05264i	−1.44002	+	0.831394i	−0.442167	+	0.896933i	$0.645790\pi$
$54$		0			0
$55$		−	0.411498i		−	0.0554863i
$56$		0			0
$57$	8.53166	+	1.59124i	1.13005	+	0.210765i
$58$		0			0
$59$	0.579903			0.0754969			0.0377484	−	0.999287i	$-0.487981\pi$
$59$	0.579903			0.0754969			0.0377484	+	0.999287i	$0.487981\pi$
$60$		0			0
$61$			2.77868i			0.355773i	0.984051	+	0.177887i	$0.0569261\pi$
$61$			2.77868i			0.355773i	−0.984051	+	0.177887i	$0.943074\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			0.406214i			0.0503847i
$66$		0			0
$67$	5.27185			0.644059			0.322030	−	0.946730i	$-0.395635\pi$
$67$	5.27185			0.644059			0.322030	+	0.946730i	$0.395635\pi$
$68$		0			0
$69$	−2.63327	+	3.07610i	−0.317008	+	0.370319i
$70$		0			0
$71$			3.32103i			0.394134i	0.980390	+	0.197067i	$0.0631416\pi$
$71$			3.32103i			0.394134i	−0.980390	+	0.197067i	$0.936858\pi$
$72$		0			0
$73$	6.17326	−	3.56413i	0.722525	−	0.417150i	−0.0931564	−	0.995651i	$-0.529696\pi$
$73$	6.17326	−	3.56413i	0.722525	−	0.417150i	0.815681	+	0.578502i	$0.196362\pi$
$74$		0			0
$75$	1.58599	−	8.50350i	0.183134	−	0.981900i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.938245			0.105561			0.0527804	−	0.998606i	$-0.483192\pi$
$79$	0.938245			0.105561			0.0527804	+	0.998606i	$0.483192\pi$
$80$		0			0
$81$	1.91105	−	8.79476i	0.212339	−	0.977196i
$82$		0			0
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	−0.963635	−	0.267221i	$-0.913895\pi$
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	0.250398	−	0.968143i	$-0.419439\pi$
$84$		0			0
$85$	−0.144512	+	0.250303i	−0.0156746	+	0.0271491i
$86$		0			0
$87$	11.5031	−	13.4375i	1.23326	−	1.44065i
$88$		0			0
$89$	−1.51794	+	2.62915i	−0.160901	+	0.278689i	−0.935192	−	0.354141i	$-0.884773\pi$
$89$	−1.51794	+	2.62915i	−0.160901	+	0.278689i	0.774291	+	0.632830i	$0.218107\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.31166	+	9.38560i	0.343403	+	0.973241i
$94$		0			0
$95$		−	0.382940i		−	0.0392888i
$96$		0			0
$97$	6.18183	−	3.56908i	0.627670	−	0.362385i	−0.152179	−	0.988353i	$-0.548629\pi$
$97$	6.18183	−	3.56908i	0.627670	−	0.362385i	0.779849	+	0.625967i	$0.215296\pi$
$98$		0			0
$99$	15.9599	−	2.49077i	1.60403	−	0.250332i
$100$		0			0
$101$	−4.08628	+	7.07765i	−0.406600	+	0.704252i	−0.994506	−	0.104677i	$-0.966619\pi$
$101$	−4.08628	+	7.07765i	−0.406600	+	0.704252i	0.587906	+	0.808929i	$0.299952\pi$
$102$		0			0
$103$	6.46599	−	3.73314i	0.637113	−	0.367837i	−0.146389	−	0.989227i	$-0.546765\pi$
$103$	6.46599	−	3.73314i	0.637113	−	0.367837i	0.783502	+	0.621390i	$0.213432\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.99991	−	2.30935i	−0.386686	−	0.223253i	0.294037	−	0.955794i	$-0.405001\pi$
$107$	−3.99991	−	2.30935i	−0.386686	−	0.223253i	−0.680723	+	0.732541i	$0.738334\pi$
$108$		0			0
$109$	5.22792	+	9.05503i	0.500744	+	0.867314i	1.00000		0.000859385i	$0.000273551\pi$
$109$	5.22792	+	9.05503i	0.500744	+	0.867314i	−0.499256	+	0.866455i	$0.666393\pi$
$110$		0			0
$111$	0.225148	−	1.20716i	0.0213701	−	0.114578i
$112$		0			0
$113$	−16.6379	−	9.60591i	−1.56516	−	0.903648i	−0.996720	−	0.0809270i	$-0.974212\pi$
$113$	−16.6379	−	9.60591i	−1.56516	−	0.903648i	−0.568445	−	0.822721i	$-0.692455\pi$
$114$		0			0
$115$	0.154731	+	0.0893340i	0.0144287	+	0.00833044i
$116$		0			0
$117$	−15.7550	+	2.45879i	−1.45655	+	0.227315i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.99573	+	15.5811i	0.817793	+	1.41646i
$122$		0			0
$123$	2.09539	−	11.2347i	0.188935	−	1.01300i
$124$		0			0
$125$	−0.763798			−0.0683162
$126$		0			0
$127$	1.26488			0.112240			0.0561198	−	0.998424i	$-0.482127\pi$
$127$	1.26488			0.112240			0.0561198	+	0.998424i	$0.482127\pi$
$128$		0			0
$129$	1.88558	+	1.61413i	0.166016	+	0.142116i
$130$		0			0
$131$	7.24394	+	12.5469i	0.632906	+	1.09623i	0.986955	+	0.160998i	$0.0514714\pi$
$131$	7.24394	+	12.5469i	0.632906	+	1.09623i	−0.354049	+	0.935227i	$0.615195\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.396940	−	0.0117435i	−0.0341631	−	0.00101072i
$136$		0			0
$137$	−13.3414	−	7.70264i	−1.13983	−	0.658081i	−0.193442	−	0.981112i	$-0.561965\pi$
$137$	−13.3414	−	7.70264i	−1.13983	−	0.658081i	−0.946389	+	0.323030i	$0.895298\pi$
$138$		0			0
$139$	−0.374701	−	0.216333i	−0.0317817	−	0.0183492i	0.484025	−	0.875054i	$-0.339174\pi$
$139$	−0.374701	−	0.216333i	−0.0317817	−	0.0183492i	−0.515807	+	0.856705i	$0.672508\pi$
$140$		0			0
$141$	4.77569	−	1.68508i	0.402185	−	0.141909i
$142$		0			0
$143$	−14.3096	−	24.7850i	−1.19663	−	2.07262i
$144$		0			0
$145$	−0.675921	−	0.390243i	−0.0561322	−	0.0324079i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.04535	+	2.33558i	−0.331408	+	0.191338i	−0.656466	−	0.754356i	$-0.727949\pi$
$149$	−4.04535	+	2.33558i	−0.331408	+	0.191338i	0.325058	+	0.945694i	$0.394616\pi$
$150$		0			0
$151$	4.12276	−	7.14083i	0.335506	−	0.581113i	−0.648076	−	0.761575i	$-0.724426\pi$
$151$	4.12276	−	7.14083i	0.335506	−	0.581113i	0.983582	+	0.180463i	$0.0577595\pi$
$152$		0			0
$153$	−10.5827	−	4.08984i	−0.855561	−	0.330644i
$154$		0			0
$155$	0.380316	−	0.219575i	0.0305477	−	0.0176367i
$156$		0			0
$157$			17.5900i			1.40383i	0.712258	+	0.701917i	$0.247672\pi$
$157$			17.5900i			1.40383i	−0.712258	+	0.701917i	$0.752328\pi$
$158$		0			0
$159$	−13.6350	+	15.9280i	−1.08133	+	1.26317i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.27097	+	9.12959i	−0.412854	+	0.715085i	−0.995201	−	0.0978563i	$-0.968801\pi$
$163$	−5.27097	+	9.12959i	−0.412854	+	0.715085i	0.582346	+	0.812941i	$0.302135\pi$
$164$		0			0
$165$	−0.237155	−	0.672123i	−0.0184625	−	0.0523247i
$166$		0			0
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	−0.987169	−	0.159679i	$-0.948954\pi$
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	0.631871	+	0.775074i	$0.282287\pi$
$168$		0			0
$169$	7.62587	+	13.2084i	0.586605	+	1.01603i
$170$		0			0
$171$	14.8523	−	2.31791i	1.13579	−	0.177255i
$172$		0			0
$173$	2.44717			0.186055			0.0930274	−	0.995664i	$-0.470346\pi$
$173$	2.44717			0.186055			0.0930274	+	0.995664i	$0.470346\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.947188	−	0.334210i	0.0711950	−	0.0251208i
$178$		0			0
$179$	−5.05509	+	2.91856i	−0.377835	+	0.218143i	−0.676876	−	0.736097i	$-0.736667\pi$
$179$	−5.05509	+	2.91856i	−0.377835	+	0.218143i	0.299041	+	0.954240i	$0.403333\pi$
$180$		0			0
$181$		−	16.0704i		−	1.19451i	−0.802053	−	0.597253i	$-0.796259\pi$
$181$		−	16.0704i		−	1.19451i	0.802053	−	0.597253i	$-0.203741\pi$
$182$		0			0
$183$	1.60141	+	4.53857i	0.118380	+	0.335501i
$184$		0			0
$185$	−0.0541828			−0.00398360
$186$		0			0
$187$		−	20.3628i		−	1.48907i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			7.97223i			0.576850i	0.957502	+	0.288425i	$0.0931316\pi$
$191$			7.97223i			0.576850i	−0.957502	+	0.288425i	$0.906868\pi$
$192$		0			0
$193$	0.718054			0.0516867			0.0258433	−	0.999666i	$-0.491773\pi$
$193$	0.718054			0.0516867			0.0258433	+	0.999666i	$0.491773\pi$
$194$		0			0
$195$	0.234110	+	0.663492i	0.0167650	+	0.0475137i
$196$		0			0
$197$		−	13.5035i		−	0.962083i	−0.876698	−	0.481042i	$-0.840259\pi$
$197$		−	13.5035i		−	0.962083i	0.876698	−	0.481042i	$-0.159741\pi$
$198$		0			0
$199$	−21.2568	+	12.2726i	−1.50685	+	0.869983i	−0.506886	+	0.862013i	$0.669203\pi$
$199$	−21.2568	+	12.2726i	−1.50685	+	0.869983i	−0.999968	+	0.00796947i	$0.997463\pi$
$200$		0			0
$201$	8.61081	−	3.03828i	0.607360	−	0.214304i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.504265			−0.0352194
$206$		0			0
$207$	−2.52824	+	6.54197i	−0.175725	+	0.454699i
$208$		0			0
$209$	13.4897	+	23.3649i	0.933105	+	1.61618i
$210$		0			0
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	0.100778	+	0.994909i	$0.467867\pi$
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	−0.912005	+	0.410178i	$0.865467\pi$
$212$		0			0
$213$	1.91398	+	5.42443i	0.131144	+	0.371676i
$214$		0			0
$215$	0.0547597	−	0.0948465i	0.00373458	−	0.00646848i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	8.02904	−	9.37928i	0.542552	−	0.633793i
$220$		0			0
$221$			20.1013i			1.35216i
$222$		0			0
$223$	−6.47489	+	3.73828i	−0.433590	+	0.250334i	−0.700875	−	0.713284i	$-0.747207\pi$
$223$	−6.47489	+	3.73828i	−0.433590	+	0.250334i	0.267285	+	0.963618i	$0.413874\pi$
$224$		0			0
$225$	−2.31026	−	14.8033i	−0.154017	−	0.986886i
$226$		0			0
$227$	−0.318701	+	0.552006i	−0.0211529	+	0.0366379i	−0.876408	−	0.481569i	$-0.840067\pi$
$227$	−0.318701	+	0.552006i	−0.0211529	+	0.0366379i	0.855255	+	0.518207i	$0.173400\pi$
$228$		0			0
$229$	1.58351	−	0.914239i	0.104641	−	0.0604146i	−0.446766	−	0.894651i	$-0.647424\pi$
$229$	1.58351	−	0.914239i	0.104641	−	0.0604146i	0.551407	+	0.834236i	$0.314091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.4232	−	10.0593i	−1.14143	−	0.659007i	−0.194649	−	0.980873i	$-0.562357\pi$
$233$	−17.4232	−	10.0593i	−1.14143	−	0.659007i	−0.946785	+	0.321866i	$0.895690\pi$
$234$		0			0
$235$	−0.111727	−	0.193516i	−0.00728825	−	0.0126236i
$236$		0			0
$237$	1.53249	−	0.540731i	0.0995458	−	0.0351242i
$238$		0			0
$239$	−2.41455	−	1.39404i	−0.156184	−	0.0901730i	0.419871	−	0.907584i	$-0.362075\pi$
$239$	−2.41455	−	1.39404i	−0.156184	−	0.0901730i	−0.576055	+	0.817411i	$0.695409\pi$
$240$		0			0
$241$	20.0304	+	11.5645i	1.29027	+	0.744938i	0.978702	−	0.205286i	$-0.0658126\pi$
$241$	20.0304	+	11.5645i	1.29027	+	0.744938i	0.311568	+	0.950224i	$0.399146\pi$
$242$		0			0
$243$	−1.94718	−	15.4664i	−0.124912	−	0.992168i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.3165	−	23.0649i	−0.847310	−	1.46758i
$248$		0			0
$249$	−17.0997	−	14.6381i	−1.08365	−	0.927649i
$250$		0			0
$251$	18.6541			1.17743			0.588717	−	0.808339i	$-0.299633\pi$
$251$	18.6541			1.17743			0.588717	+	0.808339i	$0.299633\pi$
$252$		0			0
$253$	−12.5878			−0.791388
$254$		0			0
$255$	−0.0917853	+	0.492119i	−0.00574782	+	0.0308177i
$256$		0			0
$257$	−5.43687	−	9.41694i	−0.339143	−	0.587413i	0.645129	−	0.764074i	$-0.276804\pi$
$257$	−5.43687	−	9.41694i	−0.339143	−	0.587413i	−0.984272	+	0.176661i	$0.943470\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	11.0443	−	28.5777i	0.683622	−	1.76891i
$262$		0			0
$263$	16.4519	+	9.49852i	1.01447	+	0.585704i	0.912497	−	0.409083i	$-0.134151\pi$
$263$	16.4519	+	9.49852i	1.01447	+	0.585704i	0.101972	+	0.994787i	$0.467485\pi$
$264$		0			0
$265$	0.801194	+	0.462570i	0.0492170	+	0.0284154i
$266$		0			0
$267$	−0.964101	+	5.16915i	−0.0590020	+	0.316347i
$268$		0			0
$269$	−4.29788	−	7.44415i	−0.262046	−	0.453878i	0.704739	−	0.709467i	$-0.251064\pi$
$269$	−4.29788	−	7.44415i	−0.262046	−	0.453878i	−0.966786	+	0.255589i	$0.917731\pi$
$270$		0			0
$271$	−1.58706	−	0.916292i	−0.0964073	−	0.0556608i	0.451021	−	0.892513i	$-0.351060\pi$
$271$	−1.58706	−	0.916292i	−0.0964073	−	0.0556608i	−0.547429	+	0.836852i	$0.684393\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	23.2878	−	13.4452i	1.40431	−	0.810776i
$276$		0			0
$277$	−7.90931	+	13.6993i	−0.475224	+	0.823113i	−0.999597	−	0.0283760i	$-0.990966\pi$
$277$	−7.90931	+	13.6993i	−0.475224	+	0.823113i	0.524373	+	0.851489i	$0.324300\pi$
$278$		0			0
$279$	10.8182	+	13.4214i	0.647671	+	0.803521i
$280$		0			0
$281$	−9.95916	+	5.74992i	−0.594114	+	0.343012i	−0.766722	−	0.641979i	$-0.778114\pi$
$281$	−9.95916	+	5.74992i	−0.594114	+	0.343012i	0.172609	+	0.984990i	$0.444780\pi$
$282$		0			0
$283$		−	9.92818i		−	0.590169i	−0.955471	−	0.295085i	$-0.904652\pi$
$283$		−	9.92818i		−	0.590169i	0.955471	−	0.295085i	$-0.0953478\pi$
$284$		0			0
$285$	−0.220697	−	0.625478i	−0.0130729	−	0.0370501i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.34887	−	2.33631i	0.0793454	−	0.137430i
$290$		0			0
$291$	8.04020	−	9.39231i	0.471325	−	0.550587i
$292$		0			0
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	−0.495467	−	0.868627i	$-0.665003\pi$
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	0.999986	−	0.00522664i	$-0.00166370\pi$
$294$		0			0
$295$	−0.0221594	−	0.0383812i	−0.00129017	−	0.00223464i
$296$		0			0
$297$	24.6328	−	13.2664i	1.42934	−	0.769793i
$298$		0			0
$299$	12.4262			0.718624
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.59535	+	13.9153i	−0.149099	+	0.799415i
$304$		0			0
$305$	0.183908	−	0.106180i	0.0105306	−	0.00607982i
$306$		0			0
$307$			21.6425i			1.23520i	0.786490	+	0.617602i	$0.211896\pi$
$307$			21.6425i			1.23520i	−0.786490	+	0.617602i	$0.788104\pi$
$308$		0			0
$309$	8.40978	−	9.82404i	0.478416	−	0.558870i
$310$		0			0
$311$	−20.2032			−1.14562			−0.572808	−	0.819690i	$-0.694146\pi$
$311$	−20.2032			−1.14562			−0.572808	+	0.819690i	$0.694146\pi$
$312$		0			0
$313$			21.8407i			1.23451i	0.786764	+	0.617254i	$0.211755\pi$
$313$			21.8407i			1.23451i	−0.786764	+	0.617254i	$0.788245\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			24.8594i			1.39624i	0.715981	+	0.698120i	$0.245980\pi$
$317$			24.8594i			1.39624i	−0.715981	+	0.698120i	$0.754020\pi$
$318$		0			0
$319$	54.9880			3.07874
$320$		0			0
$321$	−7.86421	−	1.46676i	−0.438938	−	0.0818664i
$322$		0			0
$323$		−	18.9496i		−	1.05439i
$324$		0			0
$325$	−22.9888	+	13.2726i	−1.27519	+	0.736230i
$326$		0			0
$327$	13.7577	+	11.7771i	0.760801	+	0.651276i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	16.1444			0.887375			0.443688	−	0.896181i	$-0.353670\pi$
$331$	16.1444			0.887375			0.443688	+	0.896181i	$0.353670\pi$
$332$		0			0
$333$	−0.327965	−	2.10148i	−0.0179724	−	0.115160i
$334$		0			0
$335$	−0.201449	−	0.348920i	−0.0110063	−	0.0190635i
$336$		0			0
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	−0.996488	−	0.0837408i	$-0.973313\pi$
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	0.570765	+	0.821113i	$0.306647\pi$
$338$		0			0
$339$	−32.7118	−	6.10108i	−1.77666	−	0.331365i
$340$		0			0
$341$	−15.4698	+	26.7946i	−0.837739	+	1.45101i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.304216	+	0.0567395i	0.0163784	+	0.00305475i
$346$		0			0
$347$			32.3830i			1.73841i	0.494451	+	0.869206i	$0.335369\pi$
$347$			32.3830i			1.73841i	−0.494451	+	0.869206i	$0.664631\pi$
$348$		0			0
$349$	−26.0421	+	15.0354i	−1.39400	+	0.804827i	−0.993755	−	0.111581i	$-0.964409\pi$
$349$	−26.0421	+	15.0354i	−1.39400	+	0.804827i	−0.400246	+	0.916408i	$0.631075\pi$
$350$		0			0
$351$	−24.3165	+	13.0960i	−1.29792	+	0.699014i
$352$		0			0
$353$	−8.50607	+	14.7329i	−0.452733	+	0.784156i	−0.998555	−	0.0537453i	$-0.982884\pi$
$353$	−8.50607	+	14.7329i	−0.452733	+	0.784156i	0.545822	+	0.837901i	$0.316217\pi$
$354$		0			0
$355$	0.219804	−	0.126904i	0.0116660	−	0.00673537i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−25.2692	−	14.5892i	−1.33366	−	0.769987i	−0.347798	−	0.937570i	$-0.613070\pi$
$359$	−25.2692	−	14.5892i	−1.33366	−	0.769987i	−0.985858	+	0.167583i	$0.946404\pi$
$360$		0			0
$361$	3.05356	+	5.28892i	0.160714	+	0.278364i
$362$		0			0
$363$	23.6729	+	20.2650i	1.24251	+	1.06364i
$364$		0			0
$365$	−0.471788	−	0.272387i	−0.0246945	−	0.0142574i
$366$		0			0
$367$	15.6981	+	9.06329i	0.819433	+	0.473100i	0.850221	−	0.526426i	$-0.176468\pi$
$367$	15.6981	+	9.06329i	0.819433	+	0.473100i	−0.0307880	+	0.999526i	$0.509802\pi$
$368$		0			0
$369$	−3.05228	−	19.5579i	−0.158896	−	1.01814i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.1823	+	17.6362i	0.527219	+	0.913170i	0.999497	+	0.0317200i	$0.0100985\pi$
$373$	10.1823	+	17.6362i	0.527219	+	0.913170i	−0.472278	+	0.881450i	$0.656568\pi$
$374$		0			0
$375$	−1.24755	+	0.440193i	−0.0644235	+	0.0227315i
$376$		0			0
$377$	−54.2820			−2.79566
$378$		0			0
$379$	−21.9961			−1.12986			−0.564931	−	0.825138i	$-0.691097\pi$
$379$	−21.9961			−1.12986			−0.564931	+	0.825138i	$0.691097\pi$
$380$		0			0
$381$	2.06599	−	0.728975i	0.105844	−	0.0373465i
$382$		0			0
$383$	−16.3127	−	28.2544i	−0.833538	−	1.44373i	−0.895215	−	0.445634i	$-0.852978\pi$
$383$	−16.3127	−	28.2544i	−0.833538	−	1.44373i	0.0616774	−	0.998096i	$-0.480355\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.01008	+	1.54975i	0.203844	+	0.0787783i
$388$		0			0
$389$	−13.6400	−	7.87504i	−0.691574	−	0.399280i	0.112628	−	0.993637i	$-0.464073\pi$
$389$	−13.6400	−	7.87504i	−0.691574	−	0.399280i	−0.804201	+	0.594357i	$0.797407\pi$
$390$		0			0
$391$	7.65680	+	4.42066i	0.387221	+	0.223562i
$392$		0			0
$393$	19.0630	+	16.3187i	0.961600	+	0.823168i
$394$		0			0
$395$	−0.0358524	−	0.0620983i	−0.00180393	−	0.00312450i
$396$		0			0
$397$	2.95864	+	1.70817i	0.148490	+	0.0857308i	0.572404	−	0.819972i	$-0.306011\pi$
$397$	2.95864	+	1.70817i	0.148490	+	0.0857308i	−0.423914	+	0.905702i	$0.639344\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.851348	+	0.491526i	−0.0425143	+	0.0245456i	−0.521106	−	0.853492i	$-0.674481\pi$
$401$	−0.851348	+	0.491526i	−0.0425143	+	0.0245456i	0.478592	+	0.878037i	$0.341147\pi$
$402$		0			0
$403$	15.2712	−	26.4505i	0.760713	−	1.31759i
$404$		0			0
$405$	−0.655112	+	0.209583i	−0.0325528	+	0.0104143i
$406$		0			0
$407$	3.30594	−	1.90868i	0.163869	−	0.0946099i
$408$		0			0
$409$			28.8900i			1.42852i	0.699880	+	0.714260i	$0.253237\pi$
$409$			28.8900i			1.42852i	−0.699880	+	0.714260i	$0.746763\pi$
$410$		0			0
$411$	−26.2304	−	4.89224i	−1.29385	−	0.241317i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.496599	+	0.860135i	−0.0243771	+	0.0422223i
$416$		0			0
$417$	−0.736697	−	0.137402i	−0.0360762	−	0.00672859i
$418$		0			0
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	−0.670509	−	0.741901i	$-0.733924\pi$
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	0.977760	+	0.209727i	$0.0672577\pi$
$420$		0			0
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	−0.986576	−	0.163300i	$-0.947786\pi$
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	0.351866	−	0.936050i	$-0.385547\pi$
$422$		0			0
$423$	6.82925	−	5.50466i	0.332050	−	0.267646i
$424$		0			0
$425$	−18.8871			−0.916158
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−37.6568	−	32.2357i	−1.81809	−	1.55636i
$430$		0			0
$431$	−6.28454	+	3.62838i	−0.302716	+	0.174773i	−0.643662	−	0.765310i	$-0.722586\pi$
$431$	−6.28454	+	3.62838i	−0.302716	+	0.174773i	0.340947	+	0.940083i	$0.389252\pi$
$432$		0			0
$433$			8.29113i			0.398446i	0.979954	+	0.199223i	$0.0638419\pi$
$433$			8.29113i			0.398446i	−0.979954	+	0.199223i	$0.936158\pi$
$434$		0			0
$435$	−1.32893	−	0.247858i	−0.0637171	−	0.0118839i
$436$		0			0
$437$	−11.7142			−0.560367
$438$		0			0
$439$			3.27192i			0.156160i	0.996947	+	0.0780802i	$0.0248790\pi$
$439$			3.27192i			0.156160i	−0.996947	+	0.0780802i	$0.975121\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	2.84907i		−	0.135363i	−0.997707	−	0.0676817i	$-0.978440\pi$
$443$		−	2.84907i		−	0.135363i	0.997707	−	0.0676817i	$-0.0215602\pi$
$444$		0			0
$445$	0.232015			0.0109986
$446$		0			0
$447$	−5.26145	+	6.14626i	−0.248858	+	0.290708i
$448$		0			0
$449$			19.9802i			0.942925i	0.881886	+	0.471463i	$0.156274\pi$
$449$			19.9802i			0.942925i	−0.881886	+	0.471463i	$0.843726\pi$
$450$		0			0
$451$	30.7675	−	17.7636i	1.44878	−	0.836455i
$452$		0			0
$453$	2.61852	−	14.0396i	0.123029	−	0.659636i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.3002			0.856046			0.428023	−	0.903768i	$-0.359210\pi$
$457$	18.3002			0.856046			0.428023	+	0.903768i	$0.359210\pi$
$458$		0			0
$459$	−19.6424	−	0.581123i	−0.916828	−	0.0271245i
$460$		0			0
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	0.952016	−	0.306049i	$-0.0990071\pi$
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	−0.741054	+	0.671445i	$0.765674\pi$
$462$		0			0
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	−0.497021	−	0.867739i	$-0.665573\pi$
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	0.999994	−	0.00343694i	$-0.00109401\pi$
$464$		0			0
$465$	0.494645	−	0.577829i	0.0229386	−	0.0267962i
$466$		0			0
$467$	−13.7761	+	23.8610i	−0.637484	+	1.10415i	0.348500	+	0.937309i	$0.386691\pi$
$467$	−13.7761	+	23.8610i	−0.637484	+	1.10415i	−0.985983	+	0.166845i	$0.946642\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	10.1375	+	28.7307i	0.467111	+	1.32384i
$472$		0			0
$473$			7.71602i			0.354783i
$474$		0			0
$475$	21.6716	−	12.5121i	0.994362	−	0.574095i
$476$		0			0
$477$	−13.0912	+	33.8742i	−0.599403	+	1.55099i
$478$		0			0
$479$	−2.47325	+	4.28380i	−0.113006	+	0.195732i	−0.916981	−	0.398931i	$-0.869381\pi$
$479$	−2.47325	+	4.28380i	−0.113006	+	0.195732i	0.803975	+	0.594663i	$0.202715\pi$
$480$		0			0
$481$	−3.26349	+	1.88418i	−0.148802	+	0.0859110i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.472443	−	0.272765i	−0.0214525	−	0.0123856i
$486$		0			0
$487$	−4.78573	−	8.28913i	−0.216862	−	0.375616i	0.736985	−	0.675909i	$-0.236249\pi$
$487$	−4.78573	−	8.28913i	−0.216862	−	0.375616i	−0.953847	+	0.300293i	$0.902916\pi$
$488$		0			0
$489$	−3.34780	+	17.9496i	−0.151393	+	0.811711i
$490$		0			0
$491$	−33.0010	−	19.0531i	−1.48931	−	0.859855i	−0.489387	−	0.872067i	$-0.662779\pi$
$491$	−33.0010	−	19.0531i	−1.48931	−	0.859855i	−0.999925	+	0.0122119i	$0.996113\pi$
$492$		0			0
$493$	−33.4477	−	19.3110i	−1.50641	−	0.869725i
$494$		0			0
$495$	−0.774717	−	0.961138i	−0.0348210	−	0.0431999i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.4192	+	21.5107i	0.555960	+	0.962951i	0.997828	+	0.0658709i	$0.0209825\pi$
$499$	12.4192	+	21.5107i	0.555960	+	0.962951i	−0.441868	+	0.897080i	$0.645684\pi$
$500$		0			0
$501$	−2.91622	+	15.6357i	−0.130287	+	0.698550i
$502$		0			0
$503$	27.2820			1.21645			0.608223	−	0.793766i	$-0.291883\pi$
$503$	27.2820			1.21645			0.608223	+	0.793766i	$0.291883\pi$
$504$		0			0
$505$	0.624584			0.0277936
$506$		0			0
$507$	20.0680	+	17.1791i	0.891253	+	0.762949i
$508$		0			0
$509$	−20.8860	−	36.1757i	−0.925758	−	1.60346i	−0.790338	−	0.612671i	$-0.790095\pi$
$509$	−20.8860	−	36.1757i	−0.925758	−	1.60346i	−0.135420	−	0.990788i	$-0.543238\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	22.9233	−	12.3457i	1.01209	−	0.545076i
$514$		0			0
$515$	−0.494160	−	0.285303i	−0.0217753	−	0.0125720i
$516$		0			0
$517$	13.6339	+	7.87154i	0.599619	+	0.346190i
$518$		0			0
$519$	3.99710	−	1.41036i	0.175453	−	0.0619078i
$520$		0			0
$521$	−2.02629	−	3.50963i	−0.0887732	−	0.153760i	0.818220	−	0.574906i	$-0.194961\pi$
$521$	−2.02629	−	3.50963i	−0.0887732	−	0.153760i	−0.906993	+	0.421146i	$0.861628\pi$
$522$		0			0
$523$	−26.2429	−	15.1514i	−1.14752	−	0.662523i	−0.199241	−	0.979951i	$-0.563848\pi$
$523$	−26.2429	−	15.1514i	−1.14752	−	0.662523i	−0.948282	+	0.317428i	$0.897181\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	18.8198	−	10.8656i	0.819801	−	0.473312i
$528$		0			0
$529$	−8.76726	+	15.1853i	−0.381185	+	0.660232i
$530$		0			0
$531$	1.35448	−	1.09177i	0.0587795	−	0.0473788i
$532$		0			0
$533$	−30.3724	+	17.5355i	−1.31558	+	0.759548i
$534$		0			0
$535$			0.352982i			0.0152607i
$536$		0			0
$537$	−6.57474	+	7.68041i	−0.283721	+	0.331434i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.82681	−	15.2885i	0.379494	−	0.657303i	−0.611495	−	0.791249i	$-0.709431\pi$
$541$	8.82681	−	15.2885i	0.379494	−	0.657303i	0.990989	+	0.133946i	$0.0427647\pi$
$542$		0			0
$543$	−9.26174	−	26.2488i	−0.397459	−	1.12644i
$544$		0			0
$545$	0.399541	−	0.692026i	0.0171145	−	0.0296431i
$546$		0			0
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	0.815571	−	0.578657i	$-0.196423\pi$
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	−0.908917	+	0.416976i	$0.863090\pi$
$548$		0			0
$549$	5.23135	+	6.49018i	0.223269	+	0.276994i
$550$		0			0
$551$	51.1719			2.18000
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0884998	+	0.0312267i	−0.00375661	+	0.00132550i
$556$		0			0
$557$	14.7527	−	8.51750i	0.625094	−	0.360898i	−0.153756	−	0.988109i	$-0.549137\pi$
$557$	14.7527	−	8.51750i	0.625094	−	0.360898i	0.778849	+	0.627211i	$0.215804\pi$
$558$		0			0
$559$		−	7.61695i		−	0.322163i
$560$		0			0
$561$	−11.7355	−	33.2597i	−0.495474	−	1.40423i
$562$		0			0
$563$	12.9198			0.544507			0.272253	−	0.962226i	$-0.412231\pi$
$563$	12.9198			0.544507			0.272253	+	0.962226i	$0.412231\pi$
$564$		0			0
$565$			1.46825i			0.0617699i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			21.7408i			0.911420i	0.890128	+	0.455710i	$0.150615\pi$
$569$			21.7408i			0.911420i	−0.890128	+	0.455710i	$0.849385\pi$
$570$		0			0
$571$	−33.6508			−1.40824			−0.704122	−	0.710079i	$-0.748659\pi$
$571$	−33.6508			−1.40824			−0.704122	+	0.710079i	$0.748659\pi$
$572$		0			0
$573$	4.59457	+	13.0215i	0.191941	+	0.543980i
$574$		0			0
$575$			11.6755i			0.486904i
$576$		0			0
$577$	−12.5598	+	7.25141i	−0.522871	+	0.301880i	−0.738109	−	0.674682i	$-0.764281\pi$
$577$	−12.5598	+	7.25141i	−0.522871	+	0.301880i	0.215237	+	0.976562i	$0.430948\pi$
$578$		0			0
$579$	1.17284	−	0.413830i	0.0487415	−	0.0171982i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−65.1793			−2.69945
$584$		0			0
$585$	0.764770	+	0.948797i	0.0316193	+	0.0392279i
$586$		0			0
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	0.982179	+	0.187948i	$0.0601837\pi$
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	−0.328322	+	0.944566i	$0.606483\pi$
$588$		0			0
$589$	−14.3963	+	24.9350i	−0.593187	+	1.02743i
$590$		0			0
$591$	−7.78235	−	22.0560i	−0.320123	−	0.907263i
$592$		0			0
$593$	−3.54101	+	6.13320i	−0.145412	+	0.251860i	−0.929526	−	0.368755i	$-0.879784\pi$
$593$	−3.54101	+	6.13320i	−0.145412	+	0.251860i	0.784115	+	0.620616i	$0.213117\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−27.6469	+	32.2963i	−1.13151	+	1.32180i
$598$		0			0
$599$		−	6.00650i		−	0.245419i	−0.992443	−	0.122709i	$-0.960842\pi$
$599$		−	6.00650i		−	0.245419i	0.992443	−	0.122709i	$-0.0391583\pi$
$600$		0			0
$601$	−0.530083	+	0.306043i	−0.0216225	+	0.0124838i	−0.510772	−	0.859716i	$-0.670640\pi$
$601$	−0.530083	+	0.306043i	−0.0216225	+	0.0124838i	0.489150	+	0.872200i	$0.337307\pi$
$602$		0			0
$603$	12.3135	−	9.92519i	0.501444	−	0.404185i
$604$		0			0
$605$	0.687494	−	1.19077i	0.0279506	−	0.0484119i
$606$		0			0
$607$	−1.77500	+	1.02480i	−0.0720450	+	0.0415952i	−0.535590	−	0.844478i	$-0.679911\pi$
$607$	−1.77500	+	1.02480i	−0.0720450	+	0.0415952i	0.463545	+	0.886073i	$0.346577\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.4588	−	7.77047i	−0.544487	−	0.314360i
$612$		0			0
$613$	−4.93166	−	8.54189i	−0.199188	−	0.345003i	0.749077	−	0.662482i	$-0.230497\pi$
$613$	−4.93166	−	8.54189i	−0.199188	−	0.345003i	−0.948265	+	0.317479i	$0.897164\pi$
$614$		0			0
$615$	−0.823644	+	0.290619i	−0.0332125	+	0.0117189i
$616$		0			0
$617$	23.2143	+	13.4028i	0.934571	+	0.539575i	0.888254	−	0.459352i	$-0.151918\pi$
$617$	23.2143	+	13.4028i	0.934571	+	0.539575i	0.0463170	+	0.998927i	$0.485252\pi$
$618$		0			0
$619$	−0.0603011	−	0.0348148i	−0.00242370	−	0.00139933i	0.498788	−	0.866724i	$-0.333779\pi$
$619$	−0.0603011	−	0.0348148i	−0.00242370	−	0.00139933i	−0.501211	+	0.865325i	$0.667112\pi$
$620$		0			0
$621$	−0.359236	+	12.1425i	−0.0144157	+	0.487260i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.4562	−	21.5748i	−0.498248	−	0.862992i
$626$		0			0
$627$	35.4992	+	30.3888i	1.41770	+	1.21361i
$628$		0			0
$629$	−2.68121			−0.106907
$630$		0			0
$631$	11.8214			0.470603			0.235301	−	0.971922i	$-0.424392\pi$
$631$	11.8214			0.470603			0.235301	+	0.971922i	$0.424392\pi$
$632$		0			0
$633$	−7.48432	+	40.1282i	−0.297475	+	1.59495i
$634$		0			0
$635$	−0.0483338	−	0.0837165i	−0.00191807	−	0.00332219i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.25243	+	7.75696i	0.247342	+	0.306860i
$640$		0			0
$641$	−17.7673	−	10.2580i	−0.701766	−	0.405165i	0.106239	−	0.994341i	$-0.466119\pi$
$641$	−17.7673	−	10.2580i	−0.701766	−	0.405165i	−0.808005	+	0.589176i	$0.799453\pi$
$642$		0			0
$643$	−15.6081	−	9.01132i	−0.615522	−	0.355372i	0.159602	−	0.987182i	$-0.448979\pi$
$643$	−15.6081	−	9.01132i	−0.615522	−	0.355372i	−0.775123	+	0.631810i	$0.782312\pi$
$644$		0			0
$645$	0.0347800	−	0.186477i	0.00136946	−	0.00734254i
$646$		0			0
$647$	−9.11827	−	15.7933i	−0.358476	−	0.620899i	0.629230	−	0.777219i	$-0.283370\pi$
$647$	−9.11827	−	15.7933i	−0.358476	−	0.620899i	−0.987706	+	0.156320i	$0.950037\pi$
$648$		0			0
$649$	2.70409	+	1.56121i	0.106145	+	0.0612827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.79559	+	4.50079i	−0.305065	+	0.176129i	−0.644716	−	0.764422i	$-0.723024\pi$
$653$	−7.79559	+	4.50079i	−0.305065	+	0.176129i	0.339651	+	0.940552i	$0.389691\pi$
$654$		0			0
$655$	0.553614	−	0.958888i	0.0216315	−	0.0374669i
$656$		0			0
$657$	7.70881	−	19.9470i	0.300749	−	0.778207i
$658$		0			0
$659$	30.4806	−	17.5980i	1.18735	−	0.685519i	0.229650	−	0.973273i	$-0.426242\pi$
$659$	30.4806	−	17.5980i	1.18735	−	0.685519i	0.957704	+	0.287754i	$0.0929086\pi$
$660$		0			0
$661$		−	12.5628i		−	0.488637i	−0.969695	−	0.244318i	$-0.921436\pi$
$661$		−	12.5628i		−	0.488637i	0.969695	−	0.244318i	$-0.0785642\pi$
$662$		0			0
$663$	11.5848	+	32.8326i	0.449918	+	1.27511i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−11.9376	+	20.6765i	−0.462226	+	0.800599i
$668$		0			0
$669$	−8.42135	+	9.83756i	−0.325588	+	0.380342i
$670$		0			0
$671$	−7.48072	+	12.9570i	−0.288790	+	0.500199i
$672$		0			0
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.797960	+	0.602710i	$0.205913\pi$
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.122982	+	0.992409i	$0.460754\pi$
$674$		0			0
$675$	−12.3049	−	22.8476i	−0.473617	−	0.879404i
$676$		0			0
$677$	37.0471			1.42384			0.711918	−	0.702263i	$-0.247827\pi$
$677$	37.0471			1.42384			0.711918	+	0.702263i	$0.247827\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.202419	+	1.08530i	−0.00775672	+	0.0415887i
$682$		0			0
$683$	21.6844	−	12.5195i	0.829732	−	0.479046i	−0.0240289	−	0.999711i	$-0.507649\pi$
$683$	21.6844	−	12.5195i	0.829732	−	0.479046i	0.853761	+	0.520665i	$0.174316\pi$
$684$		0			0
$685$			1.17734i			0.0449839i
$686$		0			0
$687$	2.05954	−	2.40589i	0.0785763	−	0.0917904i
$688$		0			0
$689$	64.3424			2.45125
$690$		0			0
$691$		−	46.4946i		−	1.76874i	−0.466787	−	0.884370i	$-0.654589\pi$
$691$		−	46.4946i		−	1.76874i	0.466787	−	0.884370i	$-0.345411\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			0.0330663i			0.00125428i
$696$		0			0
$697$	−24.9533			−0.945174
$698$		0			0
$699$	−34.2558	−	6.38905i	−1.29567	−	0.241656i
$700$		0			0
$701$		−	36.0041i		−	1.35986i	−0.733279	−	0.679928i	$-0.762011\pi$
$701$		−	36.0041i		−	1.35986i	0.733279	−	0.679928i	$-0.237989\pi$
$702$		0			0
$703$	3.07651	−	1.77622i	0.116033	−	0.0669915i
$704$		0			0
$705$	−0.294017	−	0.251691i	−0.0110733	−	0.00947922i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	31.8316			1.19546			0.597731	−	0.801697i	$-0.296069\pi$
$709$	31.8316			1.19546			0.597731	+	0.801697i	$0.296069\pi$
$710$		0			0
$711$	2.19147	−	1.76641i	0.0821864	−	0.0662456i
$712$		0			0
$713$	−6.71685	−	11.6339i	−0.251548	−	0.435694i
$714$		0			0
$715$	−1.09360	+	1.89418i	−0.0408985	+	0.0708382i
$716$		0			0
$717$	−4.74724	−	0.885409i	−0.177289	−	0.0330662i
$718$		0			0
$719$	−20.0271	+	34.6879i	−0.746883	+	1.29364i	0.202427	+	0.979297i	$0.435117\pi$
$719$	−20.0271	+	34.6879i	−0.746883	+	1.29364i	−0.949310	+	0.314342i	$0.898216\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	39.3816	+	7.34508i	1.46462	+	0.273167i
$724$		0			0
$725$		−	51.0030i		−	1.89420i
$726$		0			0
$727$	−3.39242	+	1.95862i	−0.125818	+	0.0726411i	−0.561588	−	0.827417i	$-0.689809\pi$
$727$	−3.39242	+	1.95862i	−0.125818	+	0.0726411i	0.435770	+	0.900058i	$0.356476\pi$
$728$		0			0
$729$	−12.0940	−	24.1399i	−0.447927	−	0.894070i
$730$		0			0
$731$	2.70976	−	4.69344i	0.100224	−	0.173593i
$732$		0			0
$733$	−20.4239	+	11.7918i	−0.754376	+	0.435539i	−0.827273	−	0.561800i	$-0.810109\pi$
$733$	−20.4239	+	11.7918i	−0.754376	+	0.435539i	0.0728971	+	0.997339i	$0.476776\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.5827	+	14.1928i	0.905514	+	0.522798i
$738$		0			0
$739$	16.8641	+	29.2094i	0.620355	+	1.07449i	0.989420	+	0.145083i	$0.0463448\pi$
$739$	16.8641	+	29.2094i	0.620355	+	1.07449i	−0.369065	+	0.929404i	$0.620322\pi$
$740$		0			0
$741$	−35.0434	−	29.9986i	−1.28735	−	1.10203i
$742$		0			0
$743$	29.4003	+	16.9743i	1.07859	+	0.622725i	0.930516	−	0.366251i	$-0.119359\pi$
$743$	29.4003	+	16.9743i	1.07859	+	0.622725i	0.148076	+	0.988976i	$0.452692\pi$
$744$		0			0
$745$	0.309164	+	0.178496i	0.0113269	+	0.00653958i
$746$		0			0
$747$	−36.3662	−	14.0542i	−1.33057	−	0.514217i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.69831	−	2.94157i	−0.0619724	−	0.107339i	0.833375	−	0.552709i	$-0.186406\pi$
$751$	−1.69831	−	2.94157i	−0.0619724	−	0.107339i	−0.895347	+	0.445369i	$0.853072\pi$
$752$		0			0
$753$	30.4687	−	10.7507i	1.11034	−	0.391779i
$754$		0			0
$755$	−0.630160			−0.0229339
$756$		0			0
$757$	29.1344			1.05891			0.529454	−	0.848339i	$-0.322397\pi$
$757$	29.1344			1.05891			0.529454	+	0.848339i	$0.322397\pi$
$758$		0			0
$759$	−20.5603	+	7.25461i	−0.746293	+	0.263326i
$760$		0			0
$761$	−8.36288	−	14.4849i	−0.303154	−	0.525079i	0.673694	−	0.739010i	$-0.264706\pi$
$761$	−8.36288	−	14.4849i	−0.303154	−	0.525079i	−0.976849	+	0.213931i	$0.931373\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.133701	+	0.856703i	0.00483396	+	0.0309742i
$766$		0			0
$767$	−2.66937	−	1.54116i	−0.0963852	−	0.0556480i
$768$		0			0
$769$	−24.0816	−	13.9035i	−0.868404	−	0.501373i	−0.00158643	−	0.999999i	$-0.500505\pi$
$769$	−24.0816	−	13.9035i	−0.868404	−	0.501373i	−0.866818	+	0.498625i	$0.833838\pi$
$770$		0			0
$771$	−14.3075	−	12.2478i	−0.515273	−	0.441095i
$772$		0			0
$773$	−6.42238	−	11.1239i	−0.230997	−	0.400098i	0.727105	−	0.686526i	$-0.240865\pi$
$773$	−6.42238	−	11.1239i	−0.230997	−	0.400098i	−0.958102	+	0.286428i	$0.907532\pi$
$774$		0			0
$775$	24.8527	+	14.3487i	0.892736	+	0.515421i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	28.6322	−	16.5308i	1.02586	−	0.592278i
$780$		0			0
$781$	−8.94083	+	15.4860i	−0.319928	+	0.554132i
$782$		0			0
$783$	1.56927	−	53.0426i	0.0560812	−	1.89559i
$784$		0			0
$785$	1.16420	−	0.672153i	0.0415522	−	0.0239902i
$786$		0			0
$787$			7.56610i			0.269702i	0.990866	+	0.134851i	$0.0430556\pi$
$787$			7.56610i			0.269702i	−0.990866	+	0.134851i	$0.956944\pi$
$788$		0			0
$789$	32.3461	+	6.03288i	1.15155	+	0.214776i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.38467	−	12.7906i	0.262237	−	0.454208i
$794$		0			0
$795$	1.57522	+	0.293796i	0.0558675	+	0.0104199i
$796$		0			0
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	−0.928579	−	0.371134i	$-0.878969\pi$
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	0.785701	+	0.618606i	$0.212302\pi$
$798$		0			0
$799$	−5.52875	−	9.57608i	−0.195593	−	0.338777i
$800$		0			0
$801$	1.40437	+	8.99870i	0.0496211	+	0.317953i
$802$		0			0
$803$	38.3812			1.35444
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.3102	−	9.68199i	−0.398138	−	0.340822i
$808$		0			0
$809$	0.0849492	−	0.0490454i	0.00298665	−	0.00172435i	−0.498506	−	0.866886i	$-0.666118\pi$
$809$	0.0849492	−	0.0490454i	0.00298665	−	0.00172435i	0.501493	+	0.865162i	$0.332784\pi$
$810$		0			0
$811$		−	30.3085i		−	1.06428i	−0.846658	−	0.532138i	$-0.821389\pi$
$811$		−	30.3085i		−	1.06428i	0.846658	−	0.532138i	$-0.178611\pi$
$812$		0			0
$813$	−3.12032	−	0.581972i	−0.109434	−	0.0204107i
$814$		0			0
$815$	0.805662			0.0282211
$816$		0			0
$817$			7.18054i			0.251215i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			22.5742i			0.787846i	0.919143	+	0.393923i	$0.128882\pi$
$821$			22.5742i			0.787846i	−0.919143	+	0.393923i	$0.871118\pi$
$822$		0			0
$823$	−24.5310			−0.855097			−0.427549	−	0.903992i	$-0.640623\pi$
$823$	−24.5310			−0.855097			−0.427549	+	0.903992i	$0.640623\pi$
$824$		0			0
$825$	30.2885	−	35.3821i	1.05451	−	1.23185i
$826$		0			0
$827$			40.3057i			1.40157i	0.713375	+	0.700783i	$0.247166\pi$
$827$			40.3057i			1.40157i	−0.713375	+	0.700783i	$0.752834\pi$
$828$		0			0
$829$	46.8081	−	27.0247i	1.62571	−	0.938605i	0.640359	−	0.768076i	$-0.278786\pi$
$829$	46.8081	−	27.0247i	1.62571	−	0.938605i	0.985353	−	0.170529i	$-0.0545478\pi$
$830$		0			0
$831$	−5.02351	+	26.9342i	−0.174263	+	0.934337i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.701801			0.0242868
$836$		0			0
$837$	25.4051	+	15.6872i	0.878129	+	0.542230i
$838$		0			0
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	0.585224	−	0.810872i	$-0.301007\pi$
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	−0.994847	+	0.101383i	$0.967673\pi$
$840$		0			0
$841$	37.6478	−	65.2079i	1.29820	−	2.24855i
$842$		0			0
$843$	−12.9531	+	15.1314i	−0.446127	+	0.521151i
$844$		0			0
$845$	0.582803	−	1.00944i	0.0200490	−	0.0347259i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−5.72182	−	16.2163i	−0.196373	−	0.556541i
$850$		0			0
$851$			1.65746i			0.0568170i
$852$		0			0
$853$	48.0748	−	27.7560i	1.64605	−	0.950347i	0.667429	−	0.744673i	$-0.267395\pi$
$853$	48.0748	−	27.7560i	1.64605	−	0.950347i	0.978621	−	0.205674i	$-0.0659387\pi$
$854$		0			0
$855$	−0.720953	−	0.894436i	−0.0246561	−	0.0305891i
$856$		0			0
$857$	−15.3048	+	26.5088i	−0.522803	+	0.905522i	0.476845	+	0.878988i	$0.341780\pi$
$857$	−15.3048	+	26.5088i	−0.522803	+	0.905522i	−0.999648	+	0.0265343i	$0.991553\pi$
$858$		0			0
$859$	36.4944	−	21.0700i	1.24517	−	0.718900i	0.275030	−	0.961436i	$-0.411312\pi$
$859$	36.4944	−	21.0700i	1.24517	−	0.718900i	0.970143	+	0.242535i	$0.0779790\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−22.7782	−	13.1510i	−0.775379	−	0.447665i	0.0594112	−	0.998234i	$-0.481078\pi$
$863$	−22.7782	−	13.1510i	−0.775379	−	0.447665i	−0.834790	+	0.550568i	$0.814411\pi$
$864$		0			0
$865$	−0.0935118	−	0.161967i	−0.00317950	−	0.00550705i
$866$		0			0
$867$	0.856720	−	4.59342i	0.0290957	−	0.156001i
$868$		0			0
$869$	4.37504	+	2.52593i	0.148413	+	0.0856863i
$870$		0			0
$871$	−24.2670	−	14.0106i	−0.822256	−	0.474730i
$872$		0			0
$873$	7.71952	−	19.9747i	0.261266	−	0.676042i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17.8533	−	30.9228i	−0.602863	−	1.04419i	−0.992385	−	0.123172i	$-0.960693\pi$
$877$	−17.8533	−	30.9228i	−0.602863	−	1.04419i	0.389522	−	0.921017i	$-0.372640\pi$
$878$		0			0
$879$	5.48504	−	29.4088i	0.185006	−	0.991934i
$880$		0			0
$881$	−12.4482			−0.419392			−0.209696	−	0.977767i	$-0.567247\pi$
$881$	−12.4482			−0.419392			−0.209696	+	0.977767i	$0.567247\pi$
$882$		0			0
$883$	2.35637			0.0792982			0.0396491	−	0.999214i	$-0.487376\pi$
$883$	2.35637			0.0792982			0.0396491	+	0.999214i	$0.487376\pi$
$884$		0			0
$885$	−0.0583140	−	0.0499192i	−0.00196021	−	0.00167802i
$886$		0			0
$887$	16.7299	+	28.9770i	0.561734	+	0.972952i	0.997345	+	0.0728170i	$0.0231989\pi$
$887$	16.7299	+	28.9770i	0.561734	+	0.972952i	−0.435611	+	0.900135i	$0.643468\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	32.5884	−	35.8651i	1.09175	−	1.20153i
$892$		0			0
$893$	12.6877	+	7.32526i	0.424579	+	0.245131i
$894$		0			0
$895$	0.386333	+	0.223049i	0.0129137	+	0.00745572i
$896$		0			0
$897$	20.2964	−	7.16147i	0.677676	−	0.239114i
$898$		0			0
$899$	29.3416	+	50.8212i	0.978597	+	1.69498i
$900$		0			0
$901$	39.6468	+	22.8901i	1.32083	+	0.762579i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.06363	+	0.614087i	−0.0353563	+	0.0204130i
$906$		0			0
$907$	0.467962	−	0.810535i	0.0155384	−	0.0269134i	−0.858152	−	0.513396i	$-0.828387\pi$
$907$	0.467962	−	0.810535i	0.0155384	−	0.0269134i	0.873690	+	0.486483i	$0.161720\pi$
$908$		0			0
$909$	3.78057	+	24.2245i	0.125394	+	0.803475i
$910$		0			0
$911$	28.8739	−	16.6703i	0.956634	−	0.552313i	0.0614988	−	0.998107i	$-0.480412\pi$
$911$	28.8739	−	16.6703i	0.956634	−	0.552313i	0.895136	+	0.445794i	$0.147079\pi$
$912$		0			0
$913$		−	69.9743i		−	2.31581i
$914$		0			0
$915$	0.239194	−	0.279419i	0.00790752	−	0.00923732i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.73484	+	3.00483i	−0.0572270	+	0.0991200i	−0.893220	−	0.449621i	$-0.851559\pi$
$919$	−1.73484	+	3.00483i	−0.0572270	+	0.0991200i	0.835993	+	0.548741i	$0.184893\pi$
$920$		0			0
$921$	12.4731	+	35.3500i	0.411001	+	1.16482i
$922$		0			0
$923$	8.82603	−	15.2871i	0.290512	−	0.503182i
$924$		0			0
$925$	−1.77036	−	3.06635i	−0.0582090	−	0.100821i
$926$		0			0
$927$	8.07436	−	20.8929i	0.265197	−	0.686213i
$928$		0			0
$929$	−15.1536			−0.497174			−0.248587	−	0.968610i	$-0.579966\pi$
$929$	−15.1536			−0.497174			−0.248587	+	0.968610i	$0.579966\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−32.9990	+	11.6435i	−1.08034	+	0.381192i
$934$		0			0
$935$	−1.34772	+	0.778108i	−0.0440752	+	0.0254468i
$936$		0			0
$937$			33.6651i			1.09979i	0.835233	+	0.549896i	$0.185333\pi$
$937$			33.6651i			1.09979i	−0.835233	+	0.549896i	$0.814667\pi$
$938$		0			0
$939$	12.5872	+	35.6736i	0.410769	+	1.16416i
$940$		0			0
$941$	37.7960			1.23212			0.616058	−	0.787701i	$-0.288729\pi$
$941$	37.7960			1.23212			0.616058	+	0.787701i	$0.288729\pi$
$942$		0			0
$943$			15.4255i			0.502325i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	10.9399i		−	0.355500i	−0.984076	−	0.177750i	$-0.943118\pi$
$947$		−	10.9399i		−	0.355500i	0.984076	−	0.177750i	$-0.0568818\pi$
$948$		0			0
$949$	−37.8884			−1.22991
$950$		0			0
$951$	14.3270	+	40.6042i	0.464584	+	1.31668i
$952$		0			0
$953$			11.0914i			0.359284i	0.983732	+	0.179642i	$0.0574939\pi$
$953$			11.0914i			0.359284i	−0.983732	+	0.179642i	$0.942506\pi$
$954$		0			0
$955$	0.527646	−	0.304637i	0.0170742	−	0.00985781i
$956$		0			0
$957$	89.8150	−	31.6908i	2.90331	−	1.02442i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.01885			−0.0651242
$962$		0			0
$963$	−13.6904	+	2.13658i	−0.441167	+	0.0688502i
$964$		0			0
$965$	−0.0274384	−	0.0475248i	−0.000883275	−	0.00152988i
$966$		0			0
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	−0.335839	−	0.941920i	$-0.609020\pi$
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	0.983646	−	0.180115i	$-0.0576470\pi$
$968$		0			0
$969$	−10.9211	−	30.9515i	−0.350836	−	0.994306i
$970$		0			0
$971$	23.8458	−	41.3021i	0.765248	−	1.32545i	−0.174867	−	0.984592i	$-0.555950\pi$
$971$	23.8458	−	41.3021i	0.765248	−	1.32545i	0.940115	−	0.340856i	$-0.110717\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−29.8996	+	34.9278i	−0.957553	+	1.11858i
$976$		0			0
$977$		−	16.6901i		−	0.533963i	−0.963702	−	0.266982i	$-0.913974\pi$
$977$		−	16.6901i		−	0.533963i	0.963702	−	0.266982i	$-0.0860263\pi$
$978$		0			0
$979$	−14.1563	+	8.17314i	−0.452437	+	0.261215i
$980$		0			0
$981$	29.2586	+	11.3074i	0.934155	+	0.361017i
$982$		0			0
$983$	−16.9255	+	29.3157i	−0.539838	+	0.935027i	0.459074	+	0.888398i	$0.348181\pi$
$983$	−16.9255	+	29.3157i	−0.539838	+	0.935027i	−0.998912	+	0.0466291i	$0.985152\pi$
$984$		0			0
$985$	−0.893735	+	0.515998i	−0.0284768	+	0.0164411i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.90137	−	1.67511i	−0.0922583	−	0.0532653i
$990$		0			0
$991$	−4.09775	−	7.09751i	−0.130169	−	0.225460i	0.793572	−	0.608476i	$-0.208219\pi$
$991$	−4.09775	−	7.09751i	−0.130169	−	0.225460i	−0.923742	+	0.383016i	$0.874885\pi$
$992$		0			0
$993$	26.3695	−	9.30435i	0.836812	−	0.295265i
$994$		0			0
$995$	1.62454	+	0.937928i	0.0515014	+	0.0297343i
$996$		0			0
$997$	18.7391	+	10.8190i	0.593472	+	0.342641i	0.766469	−	0.642281i	$-0.222012\pi$
$997$	18.7391	+	10.8190i	0.593472	+	0.342641i	−0.172997	+	0.984922i	$0.555345\pi$
$998$		0			0
$999$	−1.74681	−	3.24345i	−0.0552666	−	0.102618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.b.509.8		16
3.2	odd	2		5292.2.w.b.1097.4		16
7.2	even	3		1764.2.x.b.293.4		16
7.3	odd	6		1764.2.bm.a.1697.6		16
7.4	even	3		252.2.bm.a.185.3	yes	16
7.5	odd	6		1764.2.x.a.293.5		16
7.6	odd	2		252.2.w.a.5.1	✓	16
9.2	odd	6		1764.2.bm.a.1685.6		16
9.7	even	3		5292.2.bm.a.4625.4		16
21.2	odd	6		5292.2.x.b.881.4		16
21.5	even	6		5292.2.x.a.881.5		16
21.11	odd	6		756.2.bm.a.17.5		16
21.17	even	6		5292.2.bm.a.2285.4		16
21.20	even	2		756.2.w.a.341.5		16
28.11	odd	6		1008.2.df.d.689.6		16
28.27	even	2		1008.2.ca.d.257.8		16
63.2	odd	6		1764.2.x.a.1469.5		16
63.4	even	3		2268.2.t.a.1781.5		16
63.11	odd	6		252.2.w.a.101.1	yes	16
63.13	odd	6		2268.2.t.b.2105.4		16
63.16	even	3		5292.2.x.a.4409.5		16
63.20	even	6		252.2.bm.a.173.3	yes	16
63.25	even	3		756.2.w.a.521.5		16
63.32	odd	6		2268.2.t.b.1781.4		16
63.34	odd	6		756.2.bm.a.89.5		16
63.38	even	6	inner	1764.2.w.b.1109.8		16
63.41	even	6		2268.2.t.a.2105.5		16
63.47	even	6		1764.2.x.b.1469.4		16
63.52	odd	6		5292.2.w.b.521.4		16
63.61	odd	6		5292.2.x.b.4409.4		16
84.11	even	6		3024.2.df.d.17.5		16
84.83	odd	2		3024.2.ca.d.2609.5		16
252.11	even	6		1008.2.ca.d.353.8		16
252.83	odd	6		1008.2.df.d.929.6		16
252.151	odd	6		3024.2.ca.d.2033.5		16
252.223	even	6		3024.2.df.d.1601.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	7.6	odd	2
252.2.w.a.101.1	yes	16	63.11	odd	6
252.2.bm.a.173.3	yes	16	63.20	even	6
252.2.bm.a.185.3	yes	16	7.4	even	3
756.2.w.a.341.5		16	21.20	even	2
756.2.w.a.521.5		16	63.25	even	3
756.2.bm.a.17.5		16	21.11	odd	6
756.2.bm.a.89.5		16	63.34	odd	6
1008.2.ca.d.257.8		16	28.27	even	2
1008.2.ca.d.353.8		16	252.11	even	6
1008.2.df.d.689.6		16	28.11	odd	6
1008.2.df.d.929.6		16	252.83	odd	6
1764.2.w.b.509.8		16	1.1	even	1	trivial
1764.2.w.b.1109.8		16	63.38	even	6	inner
1764.2.x.a.293.5		16	7.5	odd	6
1764.2.x.a.1469.5		16	63.2	odd	6
1764.2.x.b.293.4		16	7.2	even	3
1764.2.x.b.1469.4		16	63.47	even	6
1764.2.bm.a.1685.6		16	9.2	odd	6
1764.2.bm.a.1697.6		16	7.3	odd	6
2268.2.t.a.1781.5		16	63.4	even	3
2268.2.t.a.2105.5		16	63.41	even	6
2268.2.t.b.1781.4		16	63.32	odd	6
2268.2.t.b.2105.4		16	63.13	odd	6
3024.2.ca.d.2033.5		16	252.151	odd	6
3024.2.ca.d.2609.5		16	84.83	odd	2
3024.2.df.d.17.5		16	84.11	even	6
3024.2.df.d.1601.5		16	252.223	even	6
5292.2.w.b.521.4		16	63.52	odd	6
5292.2.w.b.1097.4		16	3.2	odd	2
5292.2.x.a.881.5		16	21.5	even	6
5292.2.x.a.4409.5		16	63.16	even	3
5292.2.x.b.881.4		16	21.2	odd	6
5292.2.x.b.4409.4		16	63.61	odd	6
5292.2.bm.a.2285.4		16	21.17	even	6
5292.2.bm.a.4625.4		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63336 - 0.576322i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(2.33571 - 1.88268i) q^{9} +O(q^{10})\)	\(q+(1.63336 - 0.576322i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(2.33571 - 1.88268i) q^{9} +(4.66300 + 2.69219i) q^{11} +(-4.60313 - 2.65762i) q^{13} +(-0.100558 - 0.0860820i) q^{15} +(-1.89092 - 3.27516i) q^{17} +(4.33939 + 2.50535i) q^{19} +(-2.02463 + 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(2.73001 - 4.42120i) q^{27} +(8.84430 - 5.10626i) q^{29} +5.74620i q^{31} +(9.16791 + 1.70991i) q^{33} +(0.354486 - 0.613988i) q^{37} +(-9.05019 - 1.68795i) q^{39} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(-0.213859 - 0.0826487i) q^{45} +2.92385 q^{47} +(-4.97609 - 4.25973i) q^{51} +(-10.4835 + 6.05264i) q^{53} -0.411498i q^{55} +(8.53166 + 1.59124i) q^{57} +0.579903 q^{59} +2.77868i q^{61} +0.406214i q^{65} +5.27185 q^{67} +(-2.63327 + 3.07610i) q^{69} +3.32103i q^{71} +(6.17326 - 3.56413i) q^{73} +(1.58599 - 8.50350i) q^{75} +0.938245 q^{79} +(1.91105 - 8.79476i) q^{81} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(11.5031 - 13.4375i) q^{87} +(-1.51794 + 2.62915i) q^{89} +(3.31166 + 9.38560i) q^{93} -0.382940i q^{95} +(6.18183 - 3.56908i) q^{97} +(15.9599 - 2.49077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Introduction

L-functions

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