LMFDB - Embedded newform 1764.2.x.b.1469.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

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, 3]))

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

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

chi := DirichletCharacter("1764.293");

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.x (of order $6$, degree $2$, 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			1469.4
Root			$1.08696 + 1.34852i$ of defining polynomial
Character	$\chi$	$=$	1764.1469
Dual form			1764.2.x.b.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.317569 - 1.70269i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(-2.79830 + 1.08144i) q^{9} +O(q^{10})$	\(q+(-0.317569 - 1.70269i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(-2.79830 + 1.08144i) q^{9} +(-4.66300 - 2.69219i) q^{11} +(-4.60313 + 2.65762i) q^{13} +(-0.100558 + 0.0860820i) q^{15} +3.78183 q^{17} +5.01070i q^{19} +(2.02463 - 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(2.73001 + 4.42120i) q^{27} +(8.84430 + 5.10626i) q^{29} +(-4.97636 + 2.87310i) q^{31} +(-3.10313 + 8.79460i) q^{33} -0.708972 q^{37} +(5.98691 + 6.99372i) q^{39} +(3.29910 + 5.71422i) q^{41} +(0.716520 - 1.24105i) q^{43} +(0.178505 + 0.143883i) q^{45} +(-1.46192 + 2.53213i) q^{47} +(-1.20099 - 6.43928i) q^{51} +12.1053i q^{53} +0.411498i q^{55} +(8.53166 - 1.59124i) q^{57} +(-0.289951 - 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(0.351792 + 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +(-2.63327 - 3.07610i) q^{69} -3.32103i q^{71} -7.12826i q^{73} +(-8.15724 - 2.87824i) q^{75} +(-0.469123 + 0.812544i) q^{79} +(6.66096 - 6.05240i) q^{81} +(-6.49790 + 11.2547i) q^{83} +(-0.144512 - 0.250303i) q^{85} +(5.88570 - 16.6807i) q^{87} +3.03588 q^{89} +(6.47234 + 7.56078i) q^{93} +(0.331636 - 0.191470i) q^{95} +(6.18183 + 3.56908i) q^{97} +(15.9599 + 2.49077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.317569	−	1.70269i	−0.183349	−	0.983048i
$3$	−0.317569	−	1.70269i	−0.183349	−	0.983048i
$4$		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
$9$	−2.79830	+	1.08144i	−0.932767	+	0.360481i
$10$		0			0
$11$	−4.66300	−	2.69219i	−1.40595	−	0.811725i	−0.410954	−	0.911656i	$-0.634804\pi$
$11$	−4.66300	−	2.69219i	−1.40595	−	0.811725i	−0.994994	+	0.0999316i	$0.968138\pi$
$12$		0			0
$13$	−4.60313	+	2.65762i	−1.27668	+	0.737091i	−0.976236	−	0.216709i	$-0.930468\pi$
$13$	−4.60313	+	2.65762i	−1.27668	+	0.737091i	−0.300442	+	0.953800i	$0.597134\pi$
$14$		0			0
$15$	−0.100558	+	0.0860820i	−0.0259641	+	0.0222263i
$16$		0			0
$17$	3.78183			0.917229			0.458615	−	0.888635i	$-0.348346\pi$
$17$	3.78183			0.917229			0.458615	+	0.888635i	$0.348346\pi$
$18$		0			0
$19$			5.01070i			1.14953i	0.818317	+	0.574767i	$0.194907\pi$
$19$			5.01070i			1.14953i	−0.818317	+	0.574767i	$0.805093\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.02463	−	1.16892i	0.422164	−	0.243737i	−0.273839	−	0.961776i	$-0.588293\pi$
$23$	2.02463	−	1.16892i	0.422164	−	0.243737i	0.696003	+	0.718039i	$0.254960\pi$
$24$		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	0.979997	+	0.199013i	$0.0637736\pi$
$29$	8.84430	+	5.10626i	1.64235	+	0.948209i	0.662349	+	0.749196i	$0.269560\pi$
$30$		0			0
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.875177	−	0.483803i	$-0.839255\pi$
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.0186031	+	0.999827i	$0.505922\pi$
$32$		0			0
$33$	−3.10313	+	8.79460i	−0.540185	+	1.53094i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.708972			−0.116554			−0.0582771	−	0.998300i	$-0.518561\pi$
$37$	−0.708972			−0.116554			−0.0582771	+	0.998300i	$0.518561\pi$
$38$		0			0
$39$	5.98691	+	6.99372i	0.958673	+	1.11989i
$40$		0			0
$41$	3.29910	+	5.71422i	0.515234	+	0.892411i	0.999844	+	0.0176805i	$0.00562816\pi$
$41$	3.29910	+	5.71422i	0.515234	+	0.892411i	−0.484610	+	0.874730i	$0.661039\pi$
$42$		0			0
$43$	0.716520	−	1.24105i	0.109268	−	0.189258i	−0.806206	−	0.591635i	$-0.798483\pi$
$43$	0.716520	−	1.24105i	0.109268	−	0.189258i	0.915474	+	0.402377i	$0.131816\pi$
$44$		0			0
$45$	0.178505	+	0.143883i	0.0266100	+	0.0214488i
$46$		0			0
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	−0.952728	−	0.303825i	$-0.901736\pi$
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	0.739484	+	0.673174i	$0.235069\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.20099	−	6.43928i	−0.168173	−	0.901680i
$52$		0			0
$53$			12.1053i			1.66279i	0.555683	+	0.831394i	$0.312457\pi$
$53$			12.1053i			1.66279i	−0.555683	+	0.831394i	$0.687543\pi$
$54$		0			0
$55$			0.411498i			0.0554863i
$56$		0			0
$57$	8.53166	−	1.59124i	1.13005	−	0.210765i
$58$		0			0
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	0.846534	−	0.532335i	$-0.178685\pi$
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	−0.884282	+	0.466953i	$0.845352\pi$
$60$		0			0
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	0.646080	−	0.763270i	$-0.276407\pi$
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	−0.337971	+	0.941156i	$0.609741\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.351792	+	0.203107i	0.0436344	+	0.0251923i
$66$		0			0
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	0.658877	−	0.752251i	$-0.271032\pi$
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	−0.980907	+	0.194479i	$0.937698\pi$
$68$		0			0
$69$	−2.63327	−	3.07610i	−0.317008	−	0.370319i
$70$		0			0
$71$		−	3.32103i		−	0.394134i	−0.980390	−	0.197067i	$-0.936858\pi$
$71$		−	3.32103i		−	0.394134i	0.980390	−	0.197067i	$-0.0631416\pi$
$72$		0			0
$73$		−	7.12826i		−	0.834300i	−0.908838	−	0.417150i	$-0.863029\pi$
$73$		−	7.12826i		−	0.834300i	0.908838	−	0.417150i	$-0.136971\pi$
$74$		0			0
$75$	−8.15724	−	2.87824i	−0.941917	−	0.332351i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	−0.891208	−	0.453594i	$-0.850142\pi$
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	0.838428	+	0.545012i	$0.183475\pi$
$80$		0			0
$81$	6.66096	−	6.05240i	0.740107	−	0.672489i
$82$		0			0
$83$	−6.49790	+	11.2547i	−0.713238	+	1.23536i	0.250398	+	0.968143i	$0.419439\pi$
$83$	−6.49790	+	11.2547i	−0.713238	+	1.23536i	−0.963635	+	0.267221i	$0.913895\pi$
$84$		0			0
$85$	−0.144512	−	0.250303i	−0.0156746	−	0.0271491i
$86$		0			0
$87$	5.88570	−	16.6807i	0.631013	−	1.78836i
$88$		0			0
$89$	3.03588			0.321802			0.160901	−	0.986971i	$-0.448560\pi$
$89$	3.03588			0.321802			0.160901	+	0.986971i	$0.448560\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.47234	+	7.56078i	0.671150	+	0.784016i
$94$		0			0
$95$	0.331636	−	0.191470i	0.0340251	−	0.0196444i
$96$		0			0
$97$	6.18183	+	3.56908i	0.627670	+	0.362385i	0.779849	−	0.625967i	$-0.215296\pi$
$97$	6.18183	+	3.56908i	0.627670	+	0.362385i	−0.152179	+	0.988353i	$0.548629\pi$
$98$		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	−0.783502	−	0.621390i	$-0.786568\pi$
$103$	−6.46599	+	3.73314i	−0.637113	+	0.367837i	0.146389	+	0.989227i	$0.453235\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.61870i		−	0.446507i	−0.974760	−	0.223253i	$-0.928332\pi$
$107$		−	4.61870i		−	0.446507i	0.974760	−	0.223253i	$-0.0716677\pi$
$108$		0			0
$109$	−10.4558			−1.00149			−0.500744	−	0.865595i	$-0.666940\pi$
$109$	−10.4558			−1.00149			−0.500744	+	0.865595i	$0.666940\pi$
$110$		0			0
$111$	0.225148	+	1.20716i	0.0213701	+	0.114578i
$112$		0			0
$113$	−16.6379	+	9.60591i	−1.56516	+	0.903648i	−0.568445	+	0.822721i	$0.692455\pi$
$113$	−16.6379	+	9.60591i	−1.56516	+	0.903648i	−0.996720	+	0.0809270i	$0.974212\pi$
$114$		0			0
$115$	−0.154731	−	0.0893340i	−0.0144287	−	0.00833044i
$116$		0			0
$117$	10.0069	−	12.4148i	0.925136	−	1.14775i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.99573	+	15.5811i	0.817793	+	1.41646i
$122$		0			0
$123$	8.68184	−	7.43201i	0.782815	−	0.670122i
$124$		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
$129$	−2.34067	−	0.825892i	−0.206084	−	0.0727157i
$130$		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
$135$	0.188300	−	0.349631i	0.0162062	−	0.0300915i
$136$		0			0
$137$	13.3414	+	7.70264i	1.13983	+	0.658081i	0.946389	−	0.323030i	$-0.104702\pi$
$137$	13.3414	+	7.70264i	1.13983	+	0.658081i	0.193442	+	0.981112i	$0.438035\pi$
$138$		0			0
$139$	−0.374701	+	0.216333i	−0.0317817	+	0.0183492i	−0.515807	−	0.856705i	$-0.672508\pi$
$139$	−0.374701	+	0.216333i	−0.0317817	+	0.0183492i	0.484025	+	0.875054i	$0.339174\pi$
$140$		0			0
$141$	4.77569	+	1.68508i	0.402185	+	0.141909i
$142$		0			0
$143$	28.6192			2.39326
$144$		0			0
$145$		−	0.780486i		−	0.0648159i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.04535	−	2.33558i	0.331408	−	0.191338i	−0.325058	−	0.945694i	$-0.605384\pi$
$149$	4.04535	−	2.33558i	0.331408	−	0.191338i	0.656466	+	0.754356i	$0.272051\pi$
$150$		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
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.964007	−	0.265875i	$-0.914339\pi$
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.251749	+	0.967793i	$0.581006\pi$
$158$		0			0
$159$	20.6115	−	3.84426i	1.63460	−	0.304870i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.5419			0.825709			0.412854	−	0.910797i	$-0.364532\pi$
$163$	10.5419			0.825709			0.412854	+	0.910797i	$0.364532\pi$
$164$		0			0
$165$	0.700653	−	0.130679i	0.0545457	−	0.0101733i
$166$		0			0
$167$	−4.59146	−	7.95265i	−0.355298	−	0.615395i	0.631871	−	0.775074i	$-0.282287\pi$
$167$	−4.59146	−	7.95265i	−0.355298	−	0.615395i	−0.987169	+	0.159679i	$0.948954\pi$
$168$		0			0
$169$	7.62587	−	13.2084i	0.586605	−	1.01603i
$170$		0			0
$171$	−5.41879	−	14.0214i	−0.414385	−	1.07225i
$172$		0			0
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	−0.908784	−	0.417268i	$-0.862988\pi$
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	0.815756	+	0.578396i	$0.196321\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.763028	+	0.653183i	−0.0573527	+	0.0490963i
$178$		0			0
$179$			5.83712i			0.436287i	0.975917	+	0.218143i	$0.0700001\pi$
$179$			5.83712i			0.436287i	−0.975917	+	0.218143i	$0.930000\pi$
$180$		0			0
$181$			16.0704i			1.19451i	0.802053	+	0.597253i	$0.203741\pi$
$181$			16.0704i			1.19451i	−0.802053	+	0.597253i	$0.796259\pi$
$182$		0			0
$183$	1.60141	−	4.53857i	0.118380	−	0.335501i
$184$		0			0
$185$	0.0270914	+	0.0469237i	0.00199180	+	0.00344990i
$186$		0			0
$187$	−17.6347	−	10.1814i	−1.28958	−	0.744537i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.90415	+	3.98611i	0.499567	+	0.288425i	0.728535	−	0.685009i	$-0.240202\pi$
$191$	6.90415	+	3.98611i	0.499567	+	0.288425i	−0.228968	+	0.973434i	$0.573535\pi$
$192$		0			0
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	0.852814	−	0.522214i	$-0.174894\pi$
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	−0.878658	+	0.477452i	$0.841560\pi$
$194$		0			0
$195$	0.234110	−	0.663492i	0.0167650	−	0.0475137i
$196$		0			0
$197$			13.5035i			0.962083i	0.876698	+	0.481042i	$0.159741\pi$
$197$			13.5035i			0.962083i	−0.876698	+	0.481042i	$0.840259\pi$
$198$		0			0
$199$			24.5452i			1.73997i	0.493082	+	0.869983i	$0.335870\pi$
$199$			24.5452i			1.73997i	−0.493082	+	0.869983i	$0.664130\pi$
$200$		0			0
$201$	−6.93663	+	5.93804i	−0.489272	+	0.418837i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.252132	−	0.436706i	0.0176097	−	0.0305009i
$206$		0			0
$207$	−4.40139	+	5.46051i	−0.305918	+	0.379531i
$208$		0			0
$209$	13.4897	−	23.3649i	0.933105	−	1.61618i
$210$		0			0
$211$	−11.7838	−	20.4101i	−0.811227	−	1.40509i	−0.912005	−	0.410178i	$-0.865467\pi$
$211$	−11.7838	−	20.4101i	−0.811227	−	1.40509i	0.100778	−	0.994909i	$-0.467867\pi$
$212$		0			0
$213$	−5.65468	+	1.05466i	−0.387453	+	0.0722639i
$214$		0			0
$215$	−0.109519			−0.00746916
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−12.1372	+	2.26372i	−0.820157	+	0.152968i
$220$		0			0
$221$	−17.4083	+	10.0507i	−1.17101	+	0.676081i
$222$		0			0
$223$	−6.47489	−	3.73828i	−0.433590	−	0.250334i	0.267285	−	0.963618i	$-0.413874\pi$
$223$	−6.47489	−	3.73828i	−0.433590	−	0.250334i	−0.700875	+	0.713284i	$0.747207\pi$
$224$		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	−0.551407	−	0.834236i	$-0.685909\pi$
$229$	−1.58351	+	0.914239i	−0.104641	+	0.0604146i	0.446766	+	0.894651i	$0.352576\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	20.1186i		−	1.31801i	−0.752136	−	0.659007i	$-0.770977\pi$
$233$		−	20.1186i		−	1.31801i	0.752136	−	0.659007i	$-0.229023\pi$
$234$		0			0
$235$	0.223454			0.0145765
$236$		0			0
$237$	1.53249	+	0.540731i	0.0995458	+	0.0351242i
$238$		0			0
$239$	−2.41455	+	1.39404i	−0.156184	+	0.0901730i	−0.576055	−	0.817411i	$-0.695409\pi$
$239$	−2.41455	+	1.39404i	−0.156184	+	0.0901730i	0.419871	+	0.907584i	$0.362075\pi$
$240$		0			0
$241$	−20.0304	−	11.5645i	−1.29027	−	0.744938i	−0.311568	−	0.950224i	$-0.600854\pi$
$241$	−20.0304	−	11.5645i	−1.29027	−	0.744938i	−0.978702	+	0.205286i	$0.934187\pi$
$242$		0			0
$243$	−12.4207	−	9.41949i	−0.796787	−	0.604261i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.3165	−	23.0649i	−0.847310	−	1.46758i
$248$		0			0
$249$	21.2268	+	7.48976i	1.34519	+	0.474645i
$250$		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
$255$	−0.380295	+	0.325548i	−0.0238150	+	0.0203866i
$256$		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
$261$	−30.2711	−	4.72424i	−1.87374	−	0.292423i
$262$		0			0
$263$	−16.4519	−	9.49852i	−1.01447	−	0.585704i	−0.101972	−	0.994787i	$-0.532515\pi$
$263$	−16.4519	−	9.49852i	−1.01447	−	0.585704i	−0.912497	+	0.409083i	$0.865849\pi$
$264$		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
$269$	8.59576			0.524093			0.262046	−	0.965055i	$-0.415603\pi$
$269$	8.59576			0.524093			0.262046	+	0.965055i	$0.415603\pi$
$270$		0			0
$271$		−	1.83258i		−	0.111322i	−0.998450	−	0.0556608i	$-0.982273\pi$
$271$		−	1.83258i		−	0.111322i	0.998450	−	0.0556608i	$-0.0177265\pi$
$272$		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	0.172609	−	0.984990i	$-0.444780\pi$
$281$	−9.95916	−	5.74992i	−0.594114	−	0.343012i	−0.766722	+	0.641979i	$0.778114\pi$
$282$		0			0
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	−0.222185	−	0.975005i	$-0.571319\pi$
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	0.733286	+	0.679920i	$0.237986\pi$
$284$		0			0
$285$	−0.431331	−	0.503868i	−0.0255499	−	0.0298466i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.69774			−0.158691
$290$		0			0
$291$	4.11388	−	11.6592i	0.241160	−	0.683473i
$292$		0			0
$293$	8.63598	+	14.9580i	0.504520	+	0.873854i	0.999986	+	0.00522664i	$0.00166370\pi$
$293$	8.63598	+	14.9580i	0.504520	+	0.873854i	−0.495467	+	0.868627i	$0.665003\pi$
$294$		0			0
$295$	−0.0221594	+	0.0383812i	−0.00129017	+	0.00223464i
$296$		0			0
$297$	−0.827372	−	27.9658i	−0.0480090	−	1.62274i
$298$		0			0
$299$	−6.21308	+	10.7614i	−0.359312	+	0.622346i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	13.3487	+	4.71003i	0.766863	+	0.270584i
$304$		0			0
$305$		−	0.212359i		−	0.0121596i
$306$		0			0
$307$		−	21.6425i		−	1.23520i	−0.786490	−	0.617602i	$-0.788104\pi$
$307$		−	21.6425i		−	1.23520i	0.786490	−	0.617602i	$-0.211896\pi$
$308$		0			0
$309$	8.40978	+	9.82404i	0.478416	+	0.558870i
$310$		0			0
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	0.996276	+	0.0862215i	$0.0274793\pi$
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	−0.423468	+	0.905911i	$0.639187\pi$
$312$		0			0
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.927939	−	0.372731i	$-0.121579\pi$
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.141175	+	0.989985i	$0.454912\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.5288	+	12.4297i	1.20918	+	0.698120i	0.962580	−	0.270997i	$-0.0873535\pi$
$317$	21.5288	+	12.4297i	1.20918	+	0.698120i	0.246599	+	0.969117i	$0.420687\pi$
$318$		0			0
$319$	−27.4940	−	47.6210i	−1.53937	−	2.66626i
$320$		0			0
$321$	−7.86421	+	1.46676i	−0.438938	+	0.0818664i
$322$		0			0
$323$			18.9496i			1.05439i
$324$		0			0
$325$			26.5451i			1.47246i
$326$		0			0
$327$	3.32045	+	17.8030i	0.183621	+	0.984511i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	−0.997960	−	0.0638459i	$-0.979663\pi$
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	0.554272	+	0.832336i	$0.312997\pi$
$332$		0			0
$333$	1.98392	−	0.766713i	0.108718	−	0.0420156i
$334$		0			0
$335$	−0.201449	+	0.348920i	−0.0110063	+	0.0190635i
$336$		0			0
$337$	−7.81522	−	13.5364i	−0.425722	−	0.737372i	0.570765	−	0.821113i	$-0.306647\pi$
$337$	−7.81522	−	13.5364i	−0.425722	−	0.737372i	−0.996488	+	0.0837408i	$0.973313\pi$
$338$		0			0
$339$	21.6396	+	25.2787i	1.17530	+	1.37295i
$340$		0			0
$341$	30.9397			1.67548
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.102970	+	0.291829i	−0.00554373	+	0.0157115i
$346$		0			0
$347$	−28.0445	+	16.1915i	−1.50551	+	0.869206i	−0.505529	+	0.862810i	$0.668703\pi$
$347$	−28.0445	+	16.1915i	−1.50551	+	0.869206i	−0.999980	+	0.00639573i	$0.997964\pi$
$348$		0			0
$349$	−26.0421	−	15.0354i	−1.39400	−	0.804827i	−0.400246	−	0.916408i	$-0.631075\pi$
$349$	−26.0421	−	15.0354i	−1.39400	−	0.804827i	−0.993755	+	0.111581i	$0.964409\pi$
$350$		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
$359$		−	29.1783i		−	1.53997i	−0.638060	−	0.769987i	$-0.720263\pi$
$359$		−	29.1783i		−	1.53997i	0.638060	−	0.769987i	$-0.279737\pi$
$360$		0			0
$361$	−6.10712			−0.321427
$362$		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	0.0307880	−	0.999526i	$-0.490198\pi$
$367$	−15.6981	−	9.06329i	−0.819433	−	0.473100i	−0.850221	+	0.526426i	$0.823532\pi$
$368$		0			0
$369$	−15.4115	−	12.4223i	−0.802290	−	0.646679i
$370$		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
$375$	0.242559	+	1.30051i	0.0125257	+	0.0671581i
$376$		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
$381$	−0.401686	−	2.15369i	−0.0205790	−	0.110337i
$382$		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
$387$	−0.662914	+	4.24770i	−0.0336978	+	0.215923i
$388$		0			0
$389$	13.6400	+	7.87504i	0.691574	+	0.399280i	0.804201	−	0.594357i	$-0.202593\pi$
$389$	13.6400	+	7.87504i	0.691574	+	0.399280i	−0.112628	+	0.993637i	$0.535927\pi$
$390$		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
$395$	0.0717049			0.00360786
$396$		0			0
$397$			3.41635i			0.171462i	0.996318	+	0.0857308i	$0.0273225\pi$
$397$			3.41635i			0.171462i	−0.996318	+	0.0857308i	$0.972678\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.851348	−	0.491526i	0.0425143	−	0.0245456i	−0.478592	−	0.878037i	$-0.658853\pi$
$401$	0.851348	−	0.491526i	0.0425143	−	0.0245456i	0.521106	+	0.853492i	$0.325519\pi$
$402$		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
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.968508	−	0.248984i	$-0.919903\pi$
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.268627	+	0.963244i	$0.586570\pi$
$410$		0			0
$411$	8.87840	−	25.1623i	0.437939	−	1.24117i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.993198			0.0487542
$416$		0			0
$417$	0.487342	+	0.569298i	0.0238652	+	0.0278786i
$418$		0			0
$419$	6.28926	+	10.8933i	0.307251	+	0.532174i	0.977760	−	0.209727i	$-0.0672577\pi$
$419$	6.28926	+	10.8933i	0.307251	+	0.532174i	−0.670509	+	0.741901i	$0.733924\pi$
$420$		0			0
$421$	−13.0232	+	22.5568i	−0.634710	+	1.09935i	0.351866	+	0.936050i	$0.385547\pi$
$421$	−13.0232	+	22.5568i	−0.634710	+	1.09935i	−0.986576	+	0.163300i	$0.947786\pi$
$422$		0			0
$423$	1.35255	−	8.66664i	0.0657633	−	0.421386i
$424$		0			0
$425$	9.44354	−	16.3567i	0.458079	−	0.793416i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−9.08858	−	48.7296i	−0.438801	−	2.35269i
$430$		0			0
$431$			7.25676i			0.349546i	0.984609	+	0.174773i	$0.0559192\pi$
$431$			7.25676i			0.349546i	−0.984609	+	0.174773i	$0.944081\pi$
$432$		0			0
$433$		−	8.29113i		−	0.398446i	−0.979954	−	0.199223i	$-0.936158\pi$
$433$		−	8.29113i		−	0.398446i	0.979954	−	0.199223i	$-0.0638419\pi$
$434$		0			0
$435$	−1.32893	+	0.247858i	−0.0637171	+	0.0118839i
$436$		0			0
$437$	5.85710	+	10.1448i	0.280183	+	0.485292i
$438$		0			0
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	0.566093	−	0.824341i	$-0.308454\pi$
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	−0.430854	+	0.902422i	$0.641788\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.46737	−	1.42454i	−0.117228	−	0.0676817i	0.440239	−	0.897880i	$-0.354894\pi$
$443$	−2.46737	−	1.42454i	−0.117228	−	0.0676817i	−0.557468	+	0.830199i	$0.688227\pi$
$444$		0			0
$445$	−0.116008	−	0.200931i	−0.00549929	−	0.00952505i
$446$		0			0
$447$	−5.26145	−	6.14626i	−0.248858	−	0.290708i
$448$		0			0
$449$		−	19.9802i		−	0.942925i	−0.881886	−	0.471463i	$-0.843726\pi$
$449$		−	19.9802i		−	0.942925i	0.881886	−	0.471463i	$-0.156274\pi$
$450$		0			0
$451$		−	35.5272i		−	1.67291i
$452$		0			0
$453$	−13.4679	−	4.75207i	−0.632776	−	0.223272i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	−0.996697	−	0.0812053i	$-0.974123\pi$
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	0.568675	+	0.822563i	$0.307456\pi$
$458$		0			0
$459$	10.3245	+	16.7202i	0.481904	+	0.780434i
$460$		0			0
$461$	4.52954	−	7.84539i	0.210962	−	0.365396i	−0.741054	−	0.671445i	$-0.765674\pi$
$461$	4.52954	−	7.84539i	0.210962	−	0.365396i	0.952016	+	0.306049i	$0.0990071\pi$
$462$		0			0
$463$	10.8227	+	18.7455i	0.502974	+	0.871176i	0.999994	+	0.00343694i	$0.00109401\pi$
$463$	10.8227	+	18.7455i	0.502974	+	0.871176i	−0.497021	+	0.867739i	$0.665573\pi$
$464$		0			0
$465$	0.253092	−	0.717289i	0.0117369	−	0.0332635i
$466$		0			0
$467$	27.5523			1.27497			0.637484	−	0.770464i	$-0.279975\pi$
$467$	27.5523			1.27497			0.637484	+	0.770464i	$0.279975\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	19.8128	+	23.1447i	0.912926	+	1.06645i
$472$		0			0
$473$	−6.68227	+	3.85801i	−0.307251	+	0.177392i
$474$		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
$485$		−	0.545530i		−	0.0247713i
$486$		0			0
$487$	9.57146			0.433724			0.216862	−	0.976202i	$-0.430418\pi$
$487$	9.57146			0.433724			0.216862	+	0.976202i	$0.430418\pi$
$488$		0			0
$489$	−3.34780	−	17.9496i	−0.151393	−	0.811711i
$490$		0			0
$491$	−33.0010	+	19.0531i	−1.48931	+	0.859855i	−0.999925	−	0.0122119i	$-0.996113\pi$
$491$	−33.0010	+	19.0531i	−1.48931	+	0.859855i	−0.489387	+	0.872067i	$0.662779\pi$
$492$		0			0
$493$	33.4477	+	19.3110i	1.50641	+	0.869725i
$494$		0			0
$495$	−0.445011	−	1.15149i	−0.0200018	−	0.0517558i
$496$		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
$501$	−12.0828	+	10.3434i	−0.539819	+	0.462107i
$502$		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
$507$	−24.9115	−	8.78990i	−1.10636	−	0.390373i
$508$		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
$513$	−22.1533	+	13.6793i	−0.978093	+	0.603955i
$514$		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
$521$	4.05257			0.177546			0.0887732	−	0.996052i	$-0.471705\pi$
$521$	4.05257			0.177546			0.0887732	+	0.996052i	$0.471705\pi$
$522$		0			0
$523$		−	30.3027i		−	1.32505i	−0.749042	−	0.662523i	$-0.769486\pi$
$523$		−	30.3027i		−	1.32505i	0.749042	−	0.662523i	$-0.230514\pi$
$524$		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
$535$	−0.305691	+	0.176491i	−0.0132162	+	0.00763037i
$536$		0			0
$537$	9.93880	−	1.85369i	0.428891	−	0.0799926i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−17.6536			−0.758988			−0.379494	−	0.925194i	$-0.623902\pi$
$541$	−17.6536			−0.758988			−0.379494	+	0.925194i	$0.623902\pi$
$542$		0			0
$543$	27.3630	−	5.10348i	1.17426	−	0.219011i
$544$		0			0
$545$	0.399541	+	0.692026i	0.0171145	+	0.0296431i
$546$		0			0
$547$	−2.18319	+	3.78140i	−0.0933466	+	0.161681i	−0.908917	−	0.416976i	$-0.863090\pi$
$547$	−2.18319	+	3.78140i	−0.0933466	+	0.161681i	0.815571	+	0.578657i	$0.196423\pi$
$548$		0			0
$549$	−8.23634	−	1.28540i	−0.351518	−	0.0548594i
$550$		0			0
$551$	−25.5859	+	44.3161i	−1.09000	+	1.88793i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.0712930	−	0.0610297i	0.00302622	−	0.00259057i
$556$		0			0
$557$		−	17.0350i		−	0.721796i	−0.932605	−	0.360898i	$-0.882470\pi$
$557$		−	17.0350i		−	0.721796i	0.932605	−	0.360898i	$-0.117530\pi$
$558$		0			0
$559$			7.61695i			0.322163i
$560$		0			0
$561$	−11.7355	+	33.2597i	−0.495474	+	1.40423i
$562$		0			0
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	0.697185	−	0.716891i	$-0.254436\pi$
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	−0.969438	+	0.245335i	$0.921102\pi$
$564$		0			0
$565$	1.27155	+	0.734127i	0.0534943	+	0.0308850i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.8280	+	10.8704i	0.789313	+	0.455710i	0.839720	−	0.543019i	$-0.182719\pi$
$569$	18.8280	+	10.8704i	0.789313	+	0.455710i	−0.0504079	+	0.998729i	$0.516052\pi$
$570$		0			0
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	0.967007	+	0.254748i	$0.0819925\pi$
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	−0.262885	+	0.964827i	$0.584674\pi$
$572$		0			0
$573$	4.59457	−	13.0215i	0.191941	−	0.543980i
$574$		0			0
$575$		−	11.6755i		−	0.486904i
$576$		0			0
$577$			14.5028i			0.603760i	0.953346	+	0.301880i	$0.0976142\pi$
$577$			14.5028i			0.603760i	−0.953346	+	0.301880i	$0.902386\pi$
$578$		0			0
$579$	−0.944806	+	0.808793i	−0.0392648	+	0.0336123i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	32.5897	−	56.4469i	1.34973	−	2.33779i
$584$		0			0
$585$	−1.20407	−	0.187912i	−0.0497821	−	0.00776919i
$586$		0			0
$587$	15.8417	−	27.4386i	0.653857	−	1.13251i	−0.328322	−	0.944566i	$-0.606483\pi$
$587$	15.8417	−	27.4386i	0.653857	−	1.13251i	0.982179	−	0.187948i	$-0.0601837\pi$
$588$		0			0
$589$	−14.3963	−	24.9350i	−0.593187	−	1.02743i
$590$		0			0
$591$	22.9922	−	4.28829i	0.945774	−	0.176397i
$592$		0			0
$593$	7.08201			0.290823			0.145412	−	0.989371i	$-0.453549\pi$
$593$	7.08201			0.290823			0.145412	+	0.989371i	$0.453549\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	41.7929	−	7.79481i	1.71047	−	0.319020i
$598$		0			0
$599$	5.20178	−	3.00325i	0.212539	−	0.122709i	−0.389952	−	0.920835i	$-0.627508\pi$
$599$	5.20178	−	3.00325i	0.212539	−	0.122709i	0.602491	+	0.798126i	$0.294175\pi$
$600$		0			0
$601$	−0.530083	−	0.306043i	−0.0216225	−	0.0124838i	0.489150	−	0.872200i	$-0.337307\pi$
$601$	−0.530083	−	0.306043i	−0.0216225	−	0.0124838i	−0.510772	+	0.859716i	$0.670640\pi$
$602$		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	−0.463545	−	0.886073i	$-0.653423\pi$
$607$	1.77500	−	1.02480i	0.0720450	−	0.0415952i	0.535590	+	0.844478i	$0.320089\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	15.5409i		−	0.628719i
$612$		0			0
$613$	9.86332			0.398376			0.199188	−	0.979961i	$-0.436170\pi$
$613$	9.86332			0.398376			0.199188	+	0.979961i	$0.436170\pi$
$614$		0			0
$615$	−0.823644	−	0.290619i	−0.0332125	−	0.0117189i
$616$		0			0
$617$	23.2143	−	13.4028i	0.934571	−	0.539575i	0.0463170	−	0.998927i	$-0.485252\pi$
$617$	23.2143	−	13.4028i	0.934571	−	0.539575i	0.888254	+	0.459352i	$0.151918\pi$
$618$		0			0
$619$	0.0603011	+	0.0348148i	0.00242370	+	0.00139933i	0.501211	−	0.865325i	$-0.332888\pi$
$619$	0.0603011	+	0.0348148i	0.00242370	+	0.00139933i	−0.498788	+	0.866724i	$0.666221\pi$
$620$		0			0
$621$	10.6953	+	5.76012i	0.429187	+	0.231146i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.4562	−	21.5748i	−0.498248	−	0.862992i
$626$		0			0
$627$	−44.0671	−	15.5489i	−1.75987	−	0.620961i
$628$		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
$633$	−31.0098	+	26.5457i	−1.23253	+	1.05510i
$634$		0			0
$635$	−0.0483338	−	0.0837165i	−0.00191807	−	0.00332219i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.59151	+	9.29324i	0.142078	+	0.367635i
$640$		0			0
$641$	17.7673	+	10.2580i	0.701766	+	0.405165i	0.808005	−	0.589176i	$-0.200547\pi$
$641$	17.7673	+	10.2580i	0.701766	+	0.405165i	−0.106239	+	0.994341i	$0.533881\pi$
$642$		0			0
$643$	−15.6081	+	9.01132i	−0.615522	+	0.355372i	−0.775123	−	0.631810i	$-0.782312\pi$
$643$	−15.6081	+	9.01132i	−0.615522	+	0.355372i	0.159602	+	0.987182i	$0.448979\pi$
$644$		0			0
$645$	0.0347800	+	0.186477i	0.00136946	+	0.00734254i
$646$		0			0
$647$	18.2365			0.716952			0.358476	−	0.933539i	$-0.383296\pi$
$647$	18.2365			0.716952			0.358476	+	0.933539i	$0.383296\pi$
$648$		0			0
$649$			3.12241i			0.122565i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.79559	−	4.50079i	0.305065	−	0.176129i	−0.339651	−	0.940552i	$-0.610309\pi$
$653$	7.79559	−	4.50079i	0.305065	−	0.176129i	0.644716	+	0.764422i	$0.276976\pi$
$654$		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	0.957704	−	0.287754i	$-0.0929086\pi$
$659$	30.4806	+	17.5980i	1.18735	+	0.685519i	0.229650	+	0.973273i	$0.426242\pi$
$660$		0			0
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	−0.273262	−	0.961940i	$-0.588102\pi$
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	0.696433	+	0.717621i	$0.254769\pi$
$662$		0			0
$663$	22.6415	+	26.4491i	0.879322	+	1.02720i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	23.8752			0.924452
$668$		0			0
$669$	−4.30890	+	12.2119i	−0.166592	+	0.472139i
$670$		0			0
$671$	−7.48072	−	12.9570i	−0.288790	−	0.500199i
$672$		0			0
$673$	23.8913	−	41.3810i	0.920942	−	1.59512i	0.122982	−	0.992409i	$-0.460754\pi$
$673$	23.8913	−	41.3810i	0.920942	−	1.59512i	0.797960	−	0.602710i	$-0.205913\pi$
$674$		0			0
$675$	25.9391	−	0.767411i	0.998395	−	0.0295377i
$676$		0			0
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	0.252219	+	0.967670i	$0.418840\pi$
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	−0.964136	+	0.265407i	$0.914494\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.04110	+	0.367348i	0.0398952	+	0.0140768i
$682$		0			0
$683$		−	25.0390i		−	0.958092i	−0.877790	−	0.479046i	$-0.840983\pi$
$683$		−	25.0390i		−	0.958092i	0.877790	−	0.479046i	$-0.159017\pi$
$684$		0			0
$685$		−	1.17734i		−	0.0449839i
$686$		0			0
$687$	2.05954	+	2.40589i	0.0785763	+	0.0917904i
$688$		0			0
$689$	−32.1712	−	55.7222i	−1.22563	−	2.12285i
$690$		0			0
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.999280	−	0.0379352i	$-0.987922\pi$
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.532493	−	0.846434i	$-0.678745\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.0286363	+	0.0165332i	0.00108624	+	0.000627139i
$696$		0			0
$697$	12.4767	+	21.6102i	0.472587	+	0.818545i
$698$		0			0
$699$	−34.2558	+	6.38905i	−1.29567	+	0.241656i
$700$		0			0
$701$			36.0041i			1.35986i	0.733279	+	0.679928i	$0.237989\pi$
$701$			36.0041i			1.35986i	−0.733279	+	0.679928i	$0.762011\pi$
$702$		0			0
$703$		−	3.55244i		−	0.133983i
$704$		0			0
$705$	−0.0709620	−	0.380472i	−0.00267258	−	0.0143294i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	0.395424	+	0.918499i	$0.370598\pi$
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	−0.993155	+	0.116802i	$0.962736\pi$
$710$		0			0
$711$	0.434025	−	2.78107i	0.0162772	−	0.104298i
$712$		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
$717$	3.14041	+	3.66852i	0.117281	+	0.137004i
$718$		0			0
$719$	40.0541			1.49377			0.746883	−	0.664955i	$-0.231550\pi$
$719$	40.0541			1.49377			0.746883	+	0.664955i	$0.231550\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−13.3298	+	37.7780i	−0.495740	+	1.40498i
$724$		0			0
$725$	44.1699	−	25.5015i	1.64043	−	0.947101i
$726$		0			0
$727$	−3.39242	−	1.95862i	−0.125818	−	0.0726411i	0.435770	−	0.900058i	$-0.356476\pi$
$727$	−3.39242	−	1.95862i	−0.125818	−	0.0726411i	−0.561588	+	0.827417i	$0.689809\pi$
$728$		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	−0.0728971	−	0.997339i	$-0.523224\pi$
$733$	20.4239	−	11.7918i	0.754376	−	0.435539i	0.827273	+	0.561800i	$0.189891\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			28.3856i			1.04560i
$738$		0			0
$739$	−33.7282			−1.24071			−0.620355	−	0.784321i	$-0.713011\pi$
$739$	−33.7282			−1.24071			−0.620355	+	0.784321i	$0.713011\pi$
$740$		0			0
$741$	−35.0434	+	29.9986i	−1.28735	+	1.10203i
$742$		0			0
$743$	29.4003	−	16.9743i	1.07859	−	0.622725i	0.148076	−	0.988976i	$-0.452692\pi$
$743$	29.4003	−	16.9743i	1.07859	−	0.622725i	0.930516	+	0.366251i	$0.119359\pi$
$744$		0			0
$745$	−0.309164	−	0.178496i	−0.0113269	−	0.00653958i
$746$		0			0
$747$	6.01177	−	38.5211i	0.219959	−	1.40941i
$748$		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
$753$	−5.92395	−	31.7621i	−0.215881	−	1.15747i
$754$		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
$759$	3.99749	+	21.4331i	0.145100	+	0.777972i
$760$		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
$765$	0.675077	+	0.544140i	0.0244074	+	0.0196734i
$766$		0			0
$767$	2.66937	+	1.54116i	0.0963852	+	0.0556480i
$768$		0			0
$769$	−24.0816	+	13.9035i	−0.868404	+	0.501373i	−0.866818	−	0.498625i	$-0.833838\pi$
$769$	−24.0816	+	13.9035i	−0.868404	+	0.501373i	−0.00158643	+	0.999999i	$0.500505\pi$
$770$		0			0
$771$	−14.3075	+	12.2478i	−0.515273	+	0.441095i
$772$		0			0
$773$	12.8448			0.461994			0.230997	−	0.972954i	$-0.425801\pi$
$773$	12.8448			0.461994			0.230997	+	0.972954i	$0.425801\pi$
$774$		0			0
$775$			28.6975i			1.03084i
$776$		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
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	−0.612217	−	0.790689i	$-0.709722\pi$
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	0.378648	+	0.925541i	$0.376389\pi$
$788$		0			0
$789$	−10.9484	+	31.0289i	−0.389774	+	1.10466i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.7693			−0.524474
$794$		0			0
$795$	−1.04205	−	1.21729i	−0.0369576	−	0.0431727i
$796$		0			0
$797$	−4.03362	−	6.98643i	−0.142878	−	0.247472i	0.785701	−	0.618606i	$-0.212302\pi$
$797$	−4.03362	−	6.98643i	−0.142878	−	0.247472i	−0.928579	+	0.371134i	$0.878969\pi$
$798$		0			0
$799$	−5.52875	+	9.57608i	−0.195593	+	0.338777i
$800$		0			0
$801$	−8.49529	+	3.28313i	−0.300166	+	0.116004i
$802$		0			0
$803$	−19.1906	+	33.2391i	−0.677222	+	1.17298i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.72975	−	14.6359i	−0.0960917	−	0.515208i
$808$		0			0
$809$		−	0.0980908i		−	0.00344869i	−0.999999	−	0.00172435i	$-0.999451\pi$
$809$		−	0.0980908i		−	0.00344869i	0.999999	−	0.00172435i	$-0.000548876\pi$
$810$		0			0
$811$			30.3085i			1.06428i	0.846658	+	0.532138i	$0.178611\pi$
$811$			30.3085i			1.06428i	−0.846658	+	0.532138i	$0.821389\pi$
$812$		0			0
$813$	−3.12032	+	0.581972i	−0.109434	+	0.0204107i
$814$		0			0
$815$	−0.402831	−	0.697724i	−0.0141106	−	0.0244402i
$816$		0			0
$817$	6.21853	+	3.59027i	0.217559	+	0.125608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.5499	+	11.2871i	0.682295	+	0.393923i	0.800719	−	0.599040i	$-0.204451\pi$
$821$	19.5499	+	11.2871i	0.682295	+	0.393923i	−0.118424	+	0.992963i	$0.537784\pi$
$822$		0			0
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	0.996655	−	0.0817282i	$-0.0260439\pi$
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	−0.569106	+	0.822264i	$0.692711\pi$
$824$		0			0
$825$	30.2885	+	35.3821i	1.05451	+	1.23185i
$826$		0			0
$827$		−	40.3057i		−	1.40157i	−0.713375	−	0.700783i	$-0.752834\pi$
$827$		−	40.3057i		−	1.40157i	0.713375	−	0.700783i	$-0.247166\pi$
$828$		0			0
$829$		−	54.0493i		−	1.87721i	−0.344993	−	0.938605i	$-0.612119\pi$
$829$		−	54.0493i		−	1.87721i	0.344993	−	0.938605i	$-0.387881\pi$
$830$		0			0
$831$	25.8374	+	9.11661i	0.896291	+	0.316252i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.350900	+	0.607777i	−0.0121434	+	0.0210330i
$836$		0			0
$837$	−26.2881	−	14.1579i	−0.908649	−	0.489368i
$838$		0			0
$839$	−11.8650	+	20.5507i	−0.409624	+	0.709489i	−0.994847	−	0.101383i	$-0.967673\pi$
$839$	−11.8650	+	20.5507i	−0.409624	+	0.709489i	0.585224	+	0.810872i	$0.301007\pi$
$840$		0			0
$841$	37.6478	+	65.2079i	1.29820	+	2.24855i
$842$		0			0
$843$	−6.62761	+	18.7833i	−0.228267	+	0.646933i
$844$		0			0
$845$	−1.16561			−0.0400980
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−11.1828	−	13.0634i	−0.383792	−	0.448334i
$850$		0			0
$851$	−1.43540	+	0.828731i	−0.0492050	+	0.0284085i
$852$		0			0
$853$	48.0748	+	27.7560i	1.64605	+	0.950347i	0.978621	+	0.205674i	$0.0659387\pi$
$853$	48.0748	+	27.7560i	1.64605	+	0.950347i	0.667429	+	0.744673i	$0.267395\pi$
$854$		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	−0.970143	−	0.242535i	$-0.922021\pi$
$859$	−36.4944	+	21.0700i	−1.24517	+	0.718900i	−0.275030	+	0.961436i	$0.588688\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	26.3020i		−	0.895330i	−0.894201	−	0.447665i	$-0.852256\pi$
$863$		−	26.3020i		−	0.895330i	0.894201	−	0.447665i	$-0.147744\pi$
$864$		0			0
$865$	0.187024			0.00635899
$866$		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
$873$	−21.1584	−	3.30206i	−0.716103	−	0.111758i
$874$		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
$879$	22.7262	−	19.4546i	0.766537	−	0.656187i
$880$		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
$885$	0.0723883	+	0.0255418i	0.00243331	+	0.000858580i
$886$		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
$891$	−47.3543	+	10.2898i	−1.58643	+	0.344722i
$892$		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
$899$	−58.6832			−1.95719
$900$		0			0
$901$			45.7801i			1.52516i
$902$		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	0.895136	−	0.445794i	$-0.147079\pi$
$911$	28.8739	+	16.6703i	0.956634	+	0.552313i	0.0614988	+	0.998107i	$0.480412\pi$
$912$		0			0
$913$	60.5995	−	34.9871i	2.00555	−	1.15791i
$914$		0			0
$915$	−0.361581	+	0.0674387i	−0.0119535	+	0.00222945i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.46967			0.114454			0.0572270	−	0.998361i	$-0.481774\pi$
$919$	3.46967			0.114454			0.0572270	+	0.998361i	$0.481774\pi$
$920$		0			0
$921$	−36.8505	+	6.87300i	−1.21427	+	0.226473i
$922$		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
$927$	14.0566	−	17.4390i	0.461679	−	0.572774i
$928$		0			0
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	−0.714547	−	0.699587i	$-0.753367\pi$
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	0.963134	+	0.269022i	$0.0867005\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	26.5831	−	22.7562i	0.870290	−	0.745004i
$934$		0			0
$935$			1.55622i			0.0508937i
$936$		0			0
$937$		−	33.6651i		−	1.09979i	−0.835233	−	0.549896i	$-0.814667\pi$
$937$		−	33.6651i		−	1.09979i	0.835233	−	0.549896i	$-0.185333\pi$
$938$		0			0
$939$	12.5872	−	35.6736i	0.410769	−	1.16416i
$940$		0			0
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	−0.990198	−	0.139671i	$-0.955395\pi$
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	0.374140	−	0.927372i	$-0.377938\pi$
$942$		0			0
$943$	13.3589	+	7.71277i	0.435026	+	0.251162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.47426	−	5.46997i	−0.307872	−	0.177750i	0.338102	−	0.941110i	$-0.390215\pi$
$947$	−9.47426	−	5.46997i	−0.307872	−	0.177750i	−0.645974	+	0.763360i	$0.723548\pi$
$948$		0			0
$949$	18.9442	+	32.8123i	0.614955	+	1.06513i
$950$		0			0
$951$	14.3270	−	40.6042i	0.464584	−	1.31668i
$952$		0			0
$953$		−	11.0914i		−	0.359284i	−0.983732	−	0.179642i	$-0.942506\pi$
$953$		−	11.0914i		−	0.359284i	0.983732	−	0.179642i	$-0.0574939\pi$
$954$		0			0
$955$		−	0.609273i		−	0.0197156i
$956$		0			0
$957$	−72.3525	+	61.9367i	−2.33882	+	2.00213i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.00942	−	1.74838i	0.0325621	−	0.0563992i
$962$		0			0
$963$	4.99486	+	12.9245i	0.160957	+	0.416487i
$964$		0			0
$965$	−0.0274384	+	0.0475248i	−0.000883275	+	0.00152988i
$966$		0			0
$967$	20.1446	+	34.8915i	0.647807	+	1.12203i	0.983646	+	0.180115i	$0.0576470\pi$
$967$	20.1446	+	34.8915i	0.647807	+	1.12203i	−0.335839	+	0.941920i	$0.609020\pi$
$968$		0			0
$969$	32.2653	−	6.01782i	1.03651	−	0.193320i
$970$		0			0
$971$	−47.6916			−1.53050			−0.765248	−	0.643736i	$-0.777384\pi$
$971$	−47.6916			−1.53050			−0.765248	+	0.643736i	$0.777384\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	45.1981	−	8.42992i	1.44750	−	0.269973i
$976$		0			0
$977$	14.4540	−	8.34504i	0.462426	−	0.266982i	−0.250638	−	0.968081i	$-0.580640\pi$
$977$	14.4540	−	8.34504i	0.462426	−	0.266982i	0.713064	+	0.701099i	$0.247307\pi$
$978$		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
$989$		−	3.35022i		−	0.106531i
$990$		0			0
$991$	8.19550			0.260339			0.130169	−	0.991492i	$-0.458448\pi$
$991$	8.19550			0.260339			0.130169	+	0.991492i	$0.458448\pi$
$992$		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	0.172997	−	0.984922i	$-0.444655\pi$
$997$	−18.7391	−	10.8190i	−0.593472	−	0.342641i	−0.766469	+	0.642281i	$0.777988\pi$
$998$		0			0
$999$	−1.93550	−	3.13451i	−0.0612366	−	0.0991714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.b.1469.4		16
3.2	odd	2		5292.2.x.b.4409.4		16
7.2	even	3		1764.2.w.b.1109.8		16
7.3	odd	6		1764.2.bm.a.1685.6		16
7.4	even	3		252.2.bm.a.173.3	yes	16
7.5	odd	6		252.2.w.a.101.1	yes	16
7.6	odd	2		1764.2.x.a.1469.5		16
9.4	even	3		5292.2.x.a.881.5		16
9.5	odd	6		1764.2.x.a.293.5		16
21.2	odd	6		5292.2.w.b.521.4		16
21.5	even	6		756.2.w.a.521.5		16
21.11	odd	6		756.2.bm.a.89.5		16
21.17	even	6		5292.2.bm.a.4625.4		16
21.20	even	2		5292.2.x.a.4409.5		16
28.11	odd	6		1008.2.df.d.929.6		16
28.19	even	6		1008.2.ca.d.353.8		16
63.4	even	3		756.2.w.a.341.5		16
63.5	even	6		252.2.bm.a.185.3	yes	16
63.11	odd	6		2268.2.t.b.2105.4		16
63.13	odd	6		5292.2.x.b.881.4		16
63.23	odd	6		1764.2.bm.a.1697.6		16
63.25	even	3		2268.2.t.a.2105.5		16
63.31	odd	6		5292.2.w.b.1097.4		16
63.32	odd	6		252.2.w.a.5.1	✓	16
63.40	odd	6		756.2.bm.a.17.5		16
63.41	even	6	inner	1764.2.x.b.293.4		16
63.47	even	6		2268.2.t.a.1781.5		16
63.58	even	3		5292.2.bm.a.2285.4		16
63.59	even	6		1764.2.w.b.509.8		16
63.61	odd	6		2268.2.t.b.1781.4		16
84.11	even	6		3024.2.df.d.1601.5		16
84.47	odd	6		3024.2.ca.d.2033.5		16
252.67	odd	6		3024.2.ca.d.2609.5		16
252.95	even	6		1008.2.ca.d.257.8		16
252.103	even	6		3024.2.df.d.17.5		16
252.131	odd	6		1008.2.df.d.689.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	63.32	odd	6
252.2.w.a.101.1	yes	16	7.5	odd	6
252.2.bm.a.173.3	yes	16	7.4	even	3
252.2.bm.a.185.3	yes	16	63.5	even	6
756.2.w.a.341.5		16	63.4	even	3
756.2.w.a.521.5		16	21.5	even	6
756.2.bm.a.17.5		16	63.40	odd	6
756.2.bm.a.89.5		16	21.11	odd	6
1008.2.ca.d.257.8		16	252.95	even	6
1008.2.ca.d.353.8		16	28.19	even	6
1008.2.df.d.689.6		16	252.131	odd	6
1008.2.df.d.929.6		16	28.11	odd	6
1764.2.w.b.509.8		16	63.59	even	6
1764.2.w.b.1109.8		16	7.2	even	3
1764.2.x.a.293.5		16	9.5	odd	6
1764.2.x.a.1469.5		16	7.6	odd	2
1764.2.x.b.293.4		16	63.41	even	6	inner
1764.2.x.b.1469.4		16	1.1	even	1	trivial
1764.2.bm.a.1685.6		16	7.3	odd	6
1764.2.bm.a.1697.6		16	63.23	odd	6
2268.2.t.a.1781.5		16	63.47	even	6
2268.2.t.a.2105.5		16	63.25	even	3
2268.2.t.b.1781.4		16	63.61	odd	6
2268.2.t.b.2105.4		16	63.11	odd	6
3024.2.ca.d.2033.5		16	84.47	odd	6
3024.2.ca.d.2609.5		16	252.67	odd	6
3024.2.df.d.17.5		16	252.103	even	6
3024.2.df.d.1601.5		16	84.11	even	6
5292.2.w.b.521.4		16	21.2	odd	6
5292.2.w.b.1097.4		16	63.31	odd	6
5292.2.x.a.881.5		16	9.4	even	3
5292.2.x.a.4409.5		16	21.20	even	2
5292.2.x.b.881.4		16	63.13	odd	6
5292.2.x.b.4409.4		16	3.2	odd	2
5292.2.bm.a.2285.4		16	63.58	even	3
5292.2.bm.a.4625.4		16	21.17	even	6

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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.317569 - 1.70269i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(-2.79830 + 1.08144i) q^{9} +O(q^{10})\)	\(q+(-0.317569 - 1.70269i) q^{3} +(-0.0382122 - 0.0661855i) q^{5} +(-2.79830 + 1.08144i) q^{9} +(-4.66300 - 2.69219i) q^{11} +(-4.60313 + 2.65762i) q^{13} +(-0.100558 + 0.0860820i) q^{15} +3.78183 q^{17} +5.01070i q^{19} +(2.02463 - 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(2.73001 + 4.42120i) q^{27} +(8.84430 + 5.10626i) q^{29} +(-4.97636 + 2.87310i) q^{31} +(-3.10313 + 8.79460i) q^{33} -0.708972 q^{37} +(5.98691 + 6.99372i) q^{39} +(3.29910 + 5.71422i) q^{41} +(0.716520 - 1.24105i) q^{43} +(0.178505 + 0.143883i) q^{45} +(-1.46192 + 2.53213i) q^{47} +(-1.20099 - 6.43928i) q^{51} +12.1053i q^{53} +0.411498i q^{55} +(8.53166 - 1.59124i) q^{57} +(-0.289951 - 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(0.351792 + 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +(-2.63327 - 3.07610i) q^{69} -3.32103i q^{71} -7.12826i q^{73} +(-8.15724 - 2.87824i) q^{75} +(-0.469123 + 0.812544i) q^{79} +(6.66096 - 6.05240i) q^{81} +(-6.49790 + 11.2547i) q^{83} +(-0.144512 - 0.250303i) q^{85} +(5.88570 - 16.6807i) q^{87} +3.03588 q^{89} +(6.47234 + 7.56078i) q^{93} +(0.331636 - 0.191470i) q^{95} +(6.18183 + 3.56908i) q^{97} +(15.9599 + 2.49077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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