LMFDB - Embedded newform 1792.2.m.d.1345.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, 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:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.4
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.d.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89897 + 1.89897i) q^{3} +(0.372364 - 0.372364i) q^{5} -1.00000i q^{7} +4.21215i q^{9} +O(q^{10})$	\(q+(1.89897 + 1.89897i) q^{3} +(0.372364 - 0.372364i) q^{5} -1.00000i q^{7} +4.21215i q^{9} +(0.158942 - 0.158942i) q^{11} +(-1.48475 - 1.48475i) q^{13} +1.41421 q^{15} +3.79793 q^{17} +(2.94552 + 2.94552i) q^{19} +(1.89897 - 1.89897i) q^{21} +1.95687i q^{23} +4.72269i q^{25} +(-2.30182 + 2.30182i) q^{27} +(0.0304945 + 0.0304945i) q^{29} +9.16902 q^{31} +0.603650 q^{33} +(-0.372364 - 0.372364i) q^{35} +(-5.78530 + 5.78530i) q^{37} -5.63899i q^{39} +10.9442i q^{41} +(2.62636 - 2.62636i) q^{43} +(1.56845 + 1.56845i) q^{45} +7.79793 q^{47} -1.00000 q^{49} +(7.21215 + 7.21215i) q^{51} +(2.21215 - 2.21215i) q^{53} -0.118368i q^{55} +11.1869i q^{57} +(-9.17030 + 9.17030i) q^{59} +(4.97601 + 4.97601i) q^{61} +4.21215 q^{63} -1.10574 q^{65} +(-4.42429 - 4.42429i) q^{67} +(-3.71604 + 3.71604i) q^{69} -14.5174i q^{71} -12.0202i q^{73} +(-8.96823 + 8.96823i) q^{75} +(-0.158942 - 0.158942i) q^{77} -11.4165 q^{79} +3.89426 q^{81} +(0.123744 + 0.123744i) q^{83} +(1.41421 - 1.41421i) q^{85} +0.115816i q^{87} -6.79956i q^{89} +(-1.48475 + 1.48475i) q^{91} +(17.4117 + 17.4117i) q^{93} +2.19361 q^{95} +8.80572 q^{97} +(0.669485 + 0.669485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^5	$ 8 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} + 8 q^{17} + 4 q^{19} + 4 q^{21} - 8 q^{27} + 8 q^{31} - 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} - 12 q^{45} + 40 q^{47} - 8 q^{49} + 24 q^{51} - 16 q^{53} - 52 q^{59} + 20 q^{61} - 24 q^{65} + 32 q^{67} - 8 q^{69} - 28 q^{75} + 8 q^{77} + 16 q^{81} - 12 q^{83} - 12 q^{91} + 40 q^{93} + 80 q^{95} + 72 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 + 8 * q^17 + 4 * q^19 + 4 * q^21 - 8 * q^27 + 8 * q^31 - 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 - 12 * q^45 + 40 * q^47 - 8 * q^49 + 24 * q^51 - 16 * q^53 - 52 * q^59 + 20 * q^61 - 24 * q^65 + 32 * q^67 - 8 * q^69 - 28 * q^75 + 8 * q^77 + 16 * q^81 - 12 * q^83 - 12 * q^91 + 40 * q^93 + 80 * q^95 + 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.89897	+	1.89897i	1.09637	+	1.09637i	0.994832	+	0.101537i	$0.0323760\pi$
$3$	1.89897	+	1.89897i	1.09637	+	1.09637i	0.101537	+	0.994832i	$0.467624\pi$
$4$		0			0
$5$	0.372364	−	0.372364i	0.166526	−	0.166526i	−0.618924	−	0.785451i	$-0.712431\pi$
$5$	0.372364	−	0.372364i	0.166526	−	0.166526i	0.785451	+	0.618924i	$0.212431\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			4.21215i			1.40405i
$10$		0			0
$11$	0.158942	−	0.158942i	0.0479227	−	0.0479227i	−0.682739	−	0.730662i	$-0.739212\pi$
$11$	0.158942	−	0.158942i	0.0479227	−	0.0479227i	0.730662	+	0.682739i	$0.239212\pi$
$12$		0			0
$13$	−1.48475	−	1.48475i	−0.411796	−	0.411796i	0.470568	−	0.882364i	$-0.344049\pi$
$13$	−1.48475	−	1.48475i	−0.411796	−	0.411796i	−0.882364	+	0.470568i	$0.844049\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$		0			0
$17$	3.79793			0.921134			0.460567	−	0.887625i	$-0.347646\pi$
$17$	3.79793			0.921134			0.460567	+	0.887625i	$0.347646\pi$
$18$		0			0
$19$	2.94552	+	2.94552i	0.675748	+	0.675748i	0.959035	−	0.283287i	$-0.0914248\pi$
$19$	2.94552	+	2.94552i	0.675748	+	0.675748i	−0.283287	+	0.959035i	$0.591425\pi$
$20$		0			0
$21$	1.89897	−	1.89897i	0.414388	−	0.414388i
$22$		0			0
$23$			1.95687i			0.408036i	0.978967	+	0.204018i	$0.0654002\pi$
$23$			1.95687i			0.408036i	−0.978967	+	0.204018i	$0.934600\pi$
$24$		0			0
$25$			4.72269i			0.944538i
$26$		0			0
$27$	−2.30182	+	2.30182i	−0.442986	+	0.442986i
$28$		0			0
$29$	0.0304945	+	0.0304945i	0.00566268	+	0.00566268i	0.709932	−	0.704270i	$-0.248725\pi$
$29$	0.0304945	+	0.0304945i	0.00566268	+	0.00566268i	−0.704270	+	0.709932i	$0.748725\pi$
$30$		0			0
$31$	9.16902			1.64680			0.823402	−	0.567458i	$-0.192073\pi$
$31$	9.16902			1.64680			0.823402	+	0.567458i	$0.192073\pi$
$32$		0			0
$33$	0.603650			0.105082
$34$		0			0
$35$	−0.372364	−	0.372364i	−0.0629410	−	0.0629410i
$36$		0			0
$37$	−5.78530	+	5.78530i	−0.951098	+	0.951098i	−0.998859	−	0.0477611i	$-0.984791\pi$
$37$	−5.78530	+	5.78530i	−0.951098	+	0.951098i	0.0477611	+	0.998859i	$0.484791\pi$
$38$		0			0
$39$		−	5.63899i		−	0.902961i
$40$		0			0
$41$			10.9442i			1.70920i	0.519284	+	0.854602i	$0.326199\pi$
$41$			10.9442i			1.70920i	−0.519284	+	0.854602i	$0.673801\pi$
$42$		0			0
$43$	2.62636	−	2.62636i	0.400516	−	0.400516i	−0.477899	−	0.878415i	$-0.658601\pi$
$43$	2.62636	−	2.62636i	0.400516	−	0.400516i	0.878415	+	0.477899i	$0.158601\pi$
$44$		0			0
$45$	1.56845	+	1.56845i	0.233811	+	0.233811i
$46$		0			0
$47$	7.79793			1.13745			0.568723	−	0.822529i	$-0.307438\pi$
$47$	7.79793			1.13745			0.568723	+	0.822529i	$0.307438\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	7.21215	+	7.21215i	1.00990	+	1.00990i
$52$		0			0
$53$	2.21215	−	2.21215i	0.303862	−	0.303862i	−0.538661	−	0.842523i	$-0.681070\pi$
$53$	2.21215	−	2.21215i	0.303862	−	0.303862i	0.842523	+	0.538661i	$0.181070\pi$
$54$		0			0
$55$		−	0.118368i		−	0.0159608i
$56$		0			0
$57$			11.1869i			1.48174i
$58$		0			0
$59$	−9.17030	+	9.17030i	−1.19387	+	1.19387i	−0.217900	+	0.975971i	$0.569921\pi$
$59$	−9.17030	+	9.17030i	−1.19387	+	1.19387i	−0.975971	+	0.217900i	$0.930079\pi$
$60$		0			0
$61$	4.97601	+	4.97601i	0.637113	+	0.637113i	0.949842	−	0.312729i	$-0.101243\pi$
$61$	4.97601	+	4.97601i	0.637113	+	0.637113i	−0.312729	+	0.949842i	$0.601243\pi$
$62$		0			0
$63$	4.21215			0.530681
$64$		0			0
$65$	−1.10574			−0.137150
$66$		0			0
$67$	−4.42429	−	4.42429i	−0.540513	−	0.540513i	0.383166	−	0.923679i	$-0.374834\pi$
$67$	−4.42429	−	4.42429i	−0.540513	−	0.540513i	−0.923679	+	0.383166i	$0.874834\pi$
$68$		0			0
$69$	−3.71604	+	3.71604i	−0.447358	+	0.447358i
$70$		0			0
$71$		−	14.5174i		−	1.72290i	−0.507844	−	0.861449i	$-0.669557\pi$
$71$		−	14.5174i		−	1.72290i	0.507844	−	0.861449i	$-0.330443\pi$
$72$		0			0
$73$		−	12.0202i		−	1.40685i	−0.710768	−	0.703427i	$-0.751652\pi$
$73$		−	12.0202i		−	1.40685i	0.710768	−	0.703427i	$-0.248348\pi$
$74$		0			0
$75$	−8.96823	+	8.96823i	−1.03556	+	1.03556i
$76$		0			0
$77$	−0.158942	−	0.158942i	−0.0181131	−	0.0181131i
$78$		0			0
$79$	−11.4165			−1.28446			−0.642229	−	0.766513i	$-0.721990\pi$
$79$	−11.4165			−1.28446			−0.642229	+	0.766513i	$0.721990\pi$
$80$		0			0
$81$	3.89426			0.432696
$82$		0			0
$83$	0.123744	+	0.123744i	0.0135826	+	0.0135826i	0.713865	−	0.700283i	$-0.246943\pi$
$83$	0.123744	+	0.123744i	0.0135826	+	0.0135826i	−0.700283	+	0.713865i	$0.746943\pi$
$84$		0			0
$85$	1.41421	−	1.41421i	0.153393	−	0.153393i
$86$		0			0
$87$			0.115816i			0.0124168i
$88$		0			0
$89$		−	6.79956i		−	0.720751i	−0.932807	−	0.360376i	$-0.882648\pi$
$89$		−	6.79956i		−	0.720751i	0.932807	−	0.360376i	$-0.117352\pi$
$90$		0			0
$91$	−1.48475	+	1.48475i	−0.155644	+	0.155644i
$92$		0			0
$93$	17.4117	+	17.4117i	1.80551	+	1.80551i
$94$		0			0
$95$	2.19361			0.225060
$96$		0			0
$97$	8.80572			0.894085			0.447043	−	0.894513i	$-0.352477\pi$
$97$	8.80572			0.894085			0.447043	+	0.894513i	$0.352477\pi$
$98$		0			0
$99$	0.669485	+	0.669485i	0.0672858	+	0.0672858i
$100$		0			0
$101$	−4.82372	+	4.82372i	−0.479978	+	0.479978i	−0.905125	−	0.425146i	$-0.860223\pi$
$101$	−4.82372	+	4.82372i	−0.479978	+	0.479978i	0.425146	+	0.905125i	$0.360223\pi$
$102$		0			0
$103$		−	12.1158i		−	1.19381i	−0.802313	−	0.596903i	$-0.796398\pi$
$103$		−	12.1158i		−	1.19381i	0.802313	−	0.596903i	$-0.203602\pi$
$104$		0			0
$105$		−	1.41421i		−	0.138013i
$106$		0			0
$107$	13.4344	−	13.4344i	1.29875	−	1.29875i	0.369531	−	0.929218i	$-0.379518\pi$
$107$	13.4344	−	13.4344i	1.29875	−	1.29875i	0.929218	−	0.369531i	$-0.120482\pi$
$108$		0			0
$109$	−0.0963303	−	0.0963303i	−0.00922677	−	0.00922677i	0.702478	−	0.711705i	$-0.252077\pi$
$109$	−0.0963303	−	0.0963303i	−0.00922677	−	0.00922677i	−0.711705	+	0.702478i	$0.752077\pi$
$110$		0			0
$111$	−21.9722			−2.08551
$112$		0			0
$113$	−8.89426			−0.836702			−0.418351	−	0.908285i	$-0.637392\pi$
$113$	−8.89426			−0.836702			−0.418351	+	0.908285i	$0.637392\pi$
$114$		0			0
$115$	0.728670	+	0.728670i	0.0679488	+	0.0679488i
$116$		0			0
$117$	6.25400	−	6.25400i	0.578182	−	0.578182i
$118$		0			0
$119$		−	3.79793i		−	0.348156i
$120$		0			0
$121$			10.9495i			0.995407i
$122$		0			0
$123$	−20.7827	+	20.7827i	−1.87392	+	1.87392i
$124$		0			0
$125$	3.62038	+	3.62038i	0.323817	+	0.323817i
$126$		0			0
$127$	−4.61790			−0.409773			−0.204886	−	0.978786i	$-0.565682\pi$
$127$	−4.61790			−0.409773			−0.204886	+	0.978786i	$0.565682\pi$
$128$		0			0
$129$	9.97474			0.878227
$130$		0			0
$131$	−12.6411	−	12.6411i	−1.10446	−	1.10446i	−0.993865	−	0.110596i	$-0.964724\pi$
$131$	−12.6411	−	12.6411i	−1.10446	−	1.10446i	−0.110596	−	0.993865i	$-0.535276\pi$
$132$		0			0
$133$	2.94552	−	2.94552i	0.255409	−	0.255409i
$134$		0			0
$135$			1.71423i			0.147538i
$136$		0			0
$137$		−	14.6812i		−	1.25430i	−0.778899	−	0.627149i	$-0.784222\pi$
$137$		−	14.6812i		−	1.25430i	0.778899	−	0.627149i	$-0.215778\pi$
$138$		0			0
$139$	−0.688625	+	0.688625i	−0.0584084	+	0.0584084i	−0.735708	−	0.677299i	$-0.763150\pi$
$139$	−0.688625	+	0.688625i	−0.0584084	+	0.0584084i	0.677299	+	0.735708i	$0.263150\pi$
$140$		0			0
$141$	14.8080	+	14.8080i	1.24706	+	1.24706i
$142$		0			0
$143$	−0.471978			−0.0394688
$144$		0			0
$145$	0.0227101			0.00188597
$146$		0			0
$147$	−1.89897	−	1.89897i	−0.156624	−	0.156624i
$148$		0			0
$149$	−15.1133	+	15.1133i	−1.23813	+	1.23813i	−0.277361	+	0.960766i	$0.589460\pi$
$149$	−15.1133	+	15.1133i	−1.23813	+	1.23813i	−0.960766	+	0.277361i	$0.910540\pi$
$150$		0			0
$151$		−	9.55274i		−	0.777391i	−0.921366	−	0.388695i	$-0.872926\pi$
$151$		−	9.55274i		−	0.777391i	0.921366	−	0.388695i	$-0.127074\pi$
$152$		0			0
$153$			15.9974i			1.29332i
$154$		0			0
$155$	3.41421	−	3.41421i	0.274236	−	0.274236i
$156$		0			0
$157$	−4.77214	−	4.77214i	−0.380858	−	0.380858i	0.490553	−	0.871411i	$-0.336795\pi$
$157$	−4.77214	−	4.77214i	−0.380858	−	0.380858i	−0.871411	+	0.490553i	$0.836795\pi$
$158$		0			0
$159$	8.40158			0.666289
$160$		0			0
$161$	1.95687			0.154223
$162$		0			0
$163$	3.33051	+	3.33051i	0.260866	+	0.260866i	0.825406	−	0.564540i	$-0.190946\pi$
$163$	3.33051	+	3.33051i	0.260866	+	0.260866i	−0.564540	+	0.825406i	$0.690946\pi$
$164$		0			0
$165$	0.224777	−	0.224777i	0.0174989	−	0.0174989i
$166$		0			0
$167$			0.202067i			0.0156364i	0.999969	+	0.00781822i	$0.00248864\pi$
$167$			0.202067i			0.0156364i	−0.999969	+	0.00781822i	$0.997511\pi$
$168$		0			0
$169$		−	8.59102i		−	0.660848i
$170$		0			0
$171$	−12.4070	+	12.4070i	−0.948784	+	0.948784i
$172$		0			0
$173$	−4.48998	−	4.48998i	−0.341367	−	0.341367i	0.515514	−	0.856881i	$-0.327601\pi$
$173$	−4.48998	−	4.48998i	−0.341367	−	0.341367i	−0.856881	+	0.515514i	$0.827601\pi$
$174$		0			0
$175$	4.72269			0.357002
$176$		0			0
$177$	−34.8282			−2.61785
$178$		0			0
$179$	−8.10641	−	8.10641i	−0.605901	−	0.605901i	0.335971	−	0.941872i	$-0.390936\pi$
$179$	−8.10641	−	8.10641i	−0.605901	−	0.605901i	−0.941872	+	0.335971i	$0.890936\pi$
$180$		0			0
$181$	−15.7889	+	15.7889i	−1.17358	+	1.17358i	−0.192227	+	0.981350i	$0.561571\pi$
$181$	−15.7889	+	15.7889i	−1.17358	+	1.17358i	−0.981350	+	0.192227i	$0.938429\pi$
$182$		0			0
$183$			18.8986i			1.39702i
$184$		0			0
$185$			4.30848i			0.316765i
$186$		0			0
$187$	0.603650	−	0.603650i	0.0441432	−	0.0441432i
$188$		0			0
$189$	2.30182	+	2.30182i	0.167433	+	0.167433i
$190$		0			0
$191$	5.37470			0.388899			0.194450	−	0.980912i	$-0.437708\pi$
$191$	5.37470			0.388899			0.194450	+	0.980912i	$0.437708\pi$
$192$		0			0
$193$	16.4194			1.18190			0.590949	−	0.806709i	$-0.298754\pi$
$193$	16.4194			1.18190			0.590949	+	0.806709i	$0.298754\pi$
$194$		0			0
$195$	−2.09976	−	2.09976i	−0.150367	−	0.150367i
$196$		0			0
$197$	−12.0685	+	12.0685i	−0.859846	+	0.859846i	−0.991320	−	0.131474i	$-0.958029\pi$
$197$	−12.0685	+	12.0685i	−0.859846	+	0.859846i	0.131474	+	0.991320i	$0.458029\pi$
$198$		0			0
$199$		−	5.00162i		−	0.354556i	−0.984161	−	0.177278i	$-0.943271\pi$
$199$		−	5.00162i		−	0.354556i	0.984161	−	0.177278i	$-0.0567291\pi$
$200$		0			0
$201$		−	16.8032i		−	1.18520i
$202$		0			0
$203$	0.0304945	−	0.0304945i	0.00214029	−	0.00214029i
$204$		0			0
$205$	4.07524	+	4.07524i	0.284627	+	0.284627i
$206$		0			0
$207$	−8.24264			−0.572903
$208$		0			0
$209$	0.936331			0.0647674
$210$		0			0
$211$	7.59587	+	7.59587i	0.522921	+	0.522921i	0.918452	−	0.395531i	$-0.129440\pi$
$211$	7.59587	+	7.59587i	0.522921	+	0.522921i	−0.395531	+	0.918452i	$0.629440\pi$
$212$		0			0
$213$	27.5681	−	27.5681i	1.88893	−	1.88893i
$214$		0			0
$215$		−	1.95592i		−	0.133393i
$216$		0			0
$217$		−	9.16902i		−	0.622434i
$218$		0			0
$219$	22.8259	−	22.8259i	1.54243	−	1.54243i
$220$		0			0
$221$	−5.63899	−	5.63899i	−0.379320	−	0.379320i
$222$		0			0
$223$	−19.5995			−1.31248			−0.656239	−	0.754553i	$-0.727854\pi$
$223$	−19.5995			−1.31248			−0.656239	+	0.754553i	$0.727854\pi$
$224$		0			0
$225$	−19.8927			−1.32618
$226$		0			0
$227$	−12.2008	−	12.2008i	−0.809795	−	0.809795i	0.174808	−	0.984603i	$-0.444070\pi$
$227$	−12.2008	−	12.2008i	−0.809795	−	0.809795i	−0.984603	+	0.174808i	$0.944070\pi$
$228$		0			0
$229$	8.97166	−	8.97166i	0.592864	−	0.592864i	−0.345540	−	0.938404i	$-0.612304\pi$
$229$	8.97166	−	8.97166i	0.592864	−	0.592864i	0.938404	+	0.345540i	$0.112304\pi$
$230$		0			0
$231$		−	0.603650i		−	0.0397172i
$232$		0			0
$233$			20.7013i			1.35619i	0.734974	+	0.678095i	$0.237194\pi$
$233$			20.7013i			1.35619i	−0.734974	+	0.678095i	$0.762806\pi$
$234$		0			0
$235$	2.90367	−	2.90367i	0.189415	−	0.189415i
$236$		0			0
$237$	−21.6796	−	21.6796i	−1.40824	−	1.40824i
$238$		0			0
$239$	17.9926			1.16384			0.581922	−	0.813244i	$-0.302301\pi$
$239$	17.9926			1.16384			0.581922	+	0.813244i	$0.302301\pi$
$240$		0			0
$241$	6.45896			0.416058			0.208029	−	0.978123i	$-0.433295\pi$
$241$	6.45896			0.416058			0.208029	+	0.978123i	$0.433295\pi$
$242$		0			0
$243$	14.3005	+	14.3005i	0.917381	+	0.917381i
$244$		0			0
$245$	−0.372364	+	0.372364i	−0.0237895	+	0.0237895i
$246$		0			0
$247$		−	8.74674i		−	0.556541i
$248$		0			0
$249$			0.469970i			0.0297832i
$250$		0			0
$251$	−1.50099	+	1.50099i	−0.0947419	+	0.0947419i	−0.752889	−	0.658147i	$-0.771340\pi$
$251$	−1.50099	+	1.50099i	−0.0947419	+	0.0947419i	0.658147	+	0.752889i	$0.271340\pi$
$252$		0			0
$253$	0.311029	+	0.311029i	0.0195542	+	0.0195542i
$254$		0			0
$255$	5.37109			0.336351
$256$		0			0
$257$	11.0124			0.686933			0.343466	−	0.939165i	$-0.388399\pi$
$257$	11.0124			0.686933			0.343466	+	0.939165i	$0.388399\pi$
$258$		0			0
$259$	5.78530	+	5.78530i	0.359481	+	0.359481i
$260$		0			0
$261$	−0.128447	+	0.128447i	−0.00795068	+	0.00795068i
$262$		0			0
$263$			27.9018i			1.72050i	0.509874	+	0.860249i	$0.329692\pi$
$263$			27.9018i			1.72050i	−0.509874	+	0.860249i	$0.670308\pi$
$264$		0			0
$265$		−	1.64745i		−	0.101202i
$266$		0			0
$267$	12.9121	−	12.9121i	0.790209	−	0.790209i
$268$		0			0
$269$	−17.1069	−	17.1069i	−1.04303	−	1.04303i	−0.999032	−	0.0439967i	$-0.985991\pi$
$269$	−17.1069	−	17.1069i	−1.04303	−	1.04303i	−0.0439967	−	0.999032i	$-0.514009\pi$
$270$		0			0
$271$	21.3660			1.29789			0.648946	−	0.760835i	$-0.275210\pi$
$271$	21.3660			1.29789			0.648946	+	0.760835i	$0.275210\pi$
$272$		0			0
$273$	−5.63899			−0.341287
$274$		0			0
$275$	0.750632	+	0.750632i	0.0452648	+	0.0452648i
$276$		0			0
$277$	9.57839	−	9.57839i	0.575510	−	0.575510i	−0.358153	−	0.933663i	$-0.616593\pi$
$277$	9.57839	−	9.57839i	0.575510	−	0.575510i	0.933663	+	0.358153i	$0.116593\pi$
$278$		0			0
$279$			38.6213i			2.31219i
$280$		0			0
$281$			8.95365i			0.534130i	0.963679	+	0.267065i	$0.0860538\pi$
$281$			8.95365i			0.534130i	−0.963679	+	0.267065i	$0.913946\pi$
$282$		0			0
$283$	5.86685	−	5.86685i	0.348748	−	0.348748i	−0.510895	−	0.859643i	$-0.670686\pi$
$283$	5.86685	−	5.86685i	0.348748	−	0.348748i	0.859643	+	0.510895i	$0.170686\pi$
$284$		0			0
$285$	4.16559	+	4.16559i	0.246748	+	0.246748i
$286$		0			0
$287$	10.9442			0.646018
$288$		0			0
$289$	−2.57571			−0.151512
$290$		0			0
$291$	16.7218	+	16.7218i	0.980247	+	0.980247i
$292$		0			0
$293$	−7.63885	+	7.63885i	−0.446266	+	0.446266i	−0.894111	−	0.447845i	$-0.852192\pi$
$293$	−7.63885	+	7.63885i	−0.446266	+	0.446266i	0.447845	+	0.894111i	$0.352192\pi$
$294$		0			0
$295$			6.82938i			0.397622i
$296$		0			0
$297$			0.731712i			0.0424582i
$298$		0			0
$299$	2.90547	−	2.90547i	0.168028	−	0.168028i
$300$		0			0
$301$	−2.62636	−	2.62636i	−0.151381	−	0.151381i
$302$		0			0
$303$	−18.3202			−1.05247
$304$		0			0
$305$	3.70578			0.212192
$306$		0			0
$307$	6.58271	+	6.58271i	0.375695	+	0.375695i	0.869546	−	0.493851i	$-0.164411\pi$
$307$	6.58271	+	6.58271i	0.375695	+	0.375695i	−0.493851	+	0.869546i	$0.664411\pi$
$308$		0			0
$309$	23.0075	−	23.0075i	1.30885	−	1.30885i
$310$		0			0
$311$		−	23.6229i		−	1.33953i	−0.742573	−	0.669765i	$-0.766395\pi$
$311$		−	23.6229i		−	1.33953i	0.742573	−	0.669765i	$-0.233605\pi$
$312$		0			0
$313$		−	7.51578i		−	0.424817i	−0.977181	−	0.212408i	$-0.931869\pi$
$313$		−	7.51578i		−	0.424817i	0.977181	−	0.212408i	$-0.0681307\pi$
$314$		0			0
$315$	1.56845	−	1.56845i	0.0883722	−	0.0883722i
$316$		0			0
$317$	−0.661701	−	0.661701i	−0.0371648	−	0.0371648i	0.688280	−	0.725445i	$-0.258366\pi$
$317$	−0.661701	−	0.661701i	−0.0371648	−	0.0371648i	−0.725445	+	0.688280i	$0.758366\pi$
$318$		0			0
$319$	0.00969368			0.000542742
$320$		0			0
$321$	51.0228			2.84782
$322$		0			0
$323$	11.1869	+	11.1869i	0.622455	+	0.622455i
$324$		0			0
$325$	7.01203	−	7.01203i	0.388957	−	0.388957i
$326$		0			0
$327$		−	0.365856i		−	0.0202319i
$328$		0			0
$329$		−	7.79793i		−	0.429914i
$330$		0			0
$331$	23.5612	−	23.5612i	1.29504	−	1.29504i	0.363412	−	0.931629i	$-0.381612\pi$
$331$	23.5612	−	23.5612i	1.29504	−	1.29504i	0.931629	−	0.363412i	$-0.118388\pi$
$332$		0			0
$333$	−24.3685	−	24.3685i	−1.33539	−	1.33539i
$334$		0			0
$335$	−3.29489			−0.180019
$336$		0			0
$337$	17.8071			0.970014			0.485007	−	0.874510i	$-0.338817\pi$
$337$	17.8071			0.970014			0.485007	+	0.874510i	$0.338817\pi$
$338$		0			0
$339$	−16.8899	−	16.8899i	−0.917334	−	0.917334i
$340$		0			0
$341$	1.45734	−	1.45734i	0.0789193	−	0.0789193i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			2.76744i			0.148994i
$346$		0			0
$347$	1.31265	−	1.31265i	0.0704668	−	0.0704668i	−0.670995	−	0.741462i	$-0.734133\pi$
$347$	1.31265	−	1.31265i	0.0704668	−	0.0704668i	0.741462	+	0.670995i	$0.234133\pi$
$348$		0			0
$349$	−13.9134	−	13.9134i	−0.744767	−	0.744767i	0.228724	−	0.973491i	$-0.426545\pi$
$349$	−13.9134	−	13.9134i	−0.744767	−	0.744767i	−0.973491	+	0.228724i	$0.926545\pi$
$350$		0			0
$351$	6.83528			0.364840
$352$		0			0
$353$	−18.8807			−1.00492			−0.502459	−	0.864601i	$-0.667571\pi$
$353$	−18.8807			−1.00492			−0.502459	+	0.864601i	$0.667571\pi$
$354$		0			0
$355$	−5.40576	−	5.40576i	−0.286908	−	0.286908i
$356$		0			0
$357$	7.21215	−	7.21215i	0.381707	−	0.381707i
$358$		0			0
$359$			21.8252i			1.15189i	0.817488	+	0.575945i	$0.195366\pi$
$359$			21.8252i			1.15189i	−0.817488	+	0.575945i	$0.804634\pi$
$360$		0			0
$361$		−	1.64783i		−	0.0867280i
$362$		0			0
$363$	−20.7927	+	20.7927i	−1.09133	+	1.09133i
$364$		0			0
$365$	−4.47587	−	4.47587i	−0.234278	−	0.234278i
$366$		0			0
$367$	−7.61788			−0.397650			−0.198825	−	0.980035i	$-0.563713\pi$
$367$	−7.61788			−0.397650			−0.198825	+	0.980035i	$0.563713\pi$
$368$		0			0
$369$	−46.0988			−2.39981
$370$		0			0
$371$	−2.21215	−	2.21215i	−0.114849	−	0.114849i
$372$		0			0
$373$	15.7101	−	15.7101i	0.813436	−	0.813436i	−0.171711	−	0.985147i	$-0.554930\pi$
$373$	15.7101	−	15.7101i	0.813436	−	0.813436i	0.985147	+	0.171711i	$0.0549296\pi$
$374$		0			0
$375$			13.7500i			0.710045i
$376$		0			0
$377$		−	0.0905535i		−	0.00466374i
$378$		0			0
$379$	10.8259	−	10.8259i	0.556088	−	0.556088i	−0.372103	−	0.928191i	$-0.621363\pi$
$379$	10.8259	−	10.8259i	0.556088	−	0.556088i	0.928191	+	0.372103i	$0.121363\pi$
$380$		0			0
$381$	−8.76924	−	8.76924i	−0.449262	−	0.449262i
$382$		0			0
$383$	3.76582			0.192424			0.0962121	−	0.995361i	$-0.469327\pi$
$383$	3.76582			0.192424			0.0962121	+	0.995361i	$0.469327\pi$
$384$		0			0
$385$	−0.118368			−0.00603261
$386$		0			0
$387$	11.0626	+	11.0626i	0.562344	+	0.562344i
$388$		0			0
$389$	−25.0059	+	25.0059i	−1.26785	+	1.26785i	−0.320653	+	0.947197i	$0.603902\pi$
$389$	−25.0059	+	25.0059i	−1.26785	+	1.26785i	−0.947197	+	0.320653i	$0.896098\pi$
$390$		0			0
$391$			7.43208i			0.375856i
$392$		0			0
$393$		−	48.0102i		−	2.42179i
$394$		0			0
$395$	−4.25110	+	4.25110i	−0.213896	+	0.213896i
$396$		0			0
$397$	−11.8246	−	11.8246i	−0.593460	−	0.593460i	0.345105	−	0.938564i	$-0.387843\pi$
$397$	−11.8246	−	11.8246i	−0.593460	−	0.593460i	−0.938564	+	0.345105i	$0.887843\pi$
$398$		0			0
$399$	11.1869			0.560045
$400$		0			0
$401$	−5.39511			−0.269419			−0.134710	−	0.990885i	$-0.543010\pi$
$401$	−5.39511			−0.269419			−0.134710	+	0.990885i	$0.543010\pi$
$402$		0			0
$403$	−13.6137	−	13.6137i	−0.678148	−	0.678148i
$404$		0			0
$405$	1.45008	−	1.45008i	0.0720552	−	0.0720552i
$406$		0			0
$407$			1.83905i			0.0911584i
$408$		0			0
$409$			3.95203i			0.195415i	0.995215	+	0.0977076i	$0.0311510\pi$
$409$			3.95203i			0.195415i	−0.995215	+	0.0977076i	$0.968849\pi$
$410$		0			0
$411$	27.8791	−	27.8791i	1.37517	−	1.37517i
$412$		0			0
$413$	9.17030	+	9.17030i	0.451241	+	0.451241i
$414$		0			0
$415$	0.0921555			0.00452373
$416$		0			0
$417$	−2.61535			−0.128074
$418$		0			0
$419$	−14.2684	−	14.2684i	−0.697059	−	0.697059i	0.266717	−	0.963775i	$-0.414061\pi$
$419$	−14.2684	−	14.2684i	−0.697059	−	0.697059i	−0.963775	+	0.266717i	$0.914061\pi$
$420$		0			0
$421$	−23.3092	+	23.3092i	−1.13602	+	1.13602i	−0.146862	+	0.989157i	$0.546917\pi$
$421$	−23.3092	+	23.3092i	−1.13602	+	1.13602i	−0.989157	+	0.146862i	$0.953083\pi$
$422$		0			0
$423$			32.8460i			1.59703i
$424$		0			0
$425$			17.9365i			0.870046i
$426$		0			0
$427$	4.97601	−	4.97601i	0.240806	−	0.240806i
$428$		0			0
$429$	−0.896271	−	0.896271i	−0.0432723	−	0.0432723i
$430$		0			0
$431$	14.1697			0.682530			0.341265	−	0.939967i	$-0.389145\pi$
$431$	14.1697			0.682530			0.341265	+	0.939967i	$0.389145\pi$
$432$		0			0
$433$	−10.4860			−0.503924			−0.251962	−	0.967737i	$-0.581076\pi$
$433$	−10.4860			−0.503924			−0.251962	+	0.967737i	$0.581076\pi$
$434$		0			0
$435$	0.0431257	+	0.0431257i	0.00206772	+	0.00206772i
$436$		0			0
$437$	−5.76401	+	5.76401i	−0.275730	+	0.275730i
$438$		0			0
$439$			10.2381i			0.488637i	0.969695	+	0.244318i	$0.0785642\pi$
$439$			10.2381i			0.488637i	−0.969695	+	0.244318i	$0.921436\pi$
$440$		0			0
$441$		−	4.21215i		−	0.200578i
$442$		0			0
$443$	−1.33536	+	1.33536i	−0.0634449	+	0.0634449i	−0.738117	−	0.674672i	$-0.764285\pi$
$443$	−1.33536	+	1.33536i	−0.0634449	+	0.0634449i	0.674672	+	0.738117i	$0.264285\pi$
$444$		0			0
$445$	−2.53191	−	2.53191i	−0.120024	−	0.120024i
$446$		0			0
$447$	−57.3992			−2.71489
$448$		0			0
$449$	−35.7127			−1.68539			−0.842694	−	0.538393i	$-0.819032\pi$
$449$	−35.7127			−1.68539			−0.842694	+	0.538393i	$0.819032\pi$
$450$		0			0
$451$	1.73950	+	1.73950i	0.0819097	+	0.0819097i
$452$		0			0
$453$	18.1403	−	18.1403i	0.852307	−	0.852307i
$454$		0			0
$455$			1.10574i			0.0518378i
$456$		0			0
$457$		−	24.3144i		−	1.13738i	−0.822552	−	0.568689i	$-0.807451\pi$
$457$		−	24.3144i		−	1.13738i	0.822552	−	0.568689i	$-0.192549\pi$
$458$		0			0
$459$	−8.74218	+	8.74218i	−0.408050	+	0.408050i
$460$		0			0
$461$	−30.3124	−	30.3124i	−1.41179	−	1.41179i	−0.747269	−	0.664522i	$-0.768635\pi$
$461$	−30.3124	−	30.3124i	−1.41179	−	1.41179i	−0.664522	−	0.747269i	$-0.731365\pi$
$462$		0			0
$463$	4.33480			0.201455			0.100728	−	0.994914i	$-0.467883\pi$
$463$	4.33480			0.201455			0.100728	+	0.994914i	$0.467883\pi$
$464$		0			0
$465$	12.9670			0.601328
$466$		0			0
$467$	−19.0292	−	19.0292i	−0.880567	−	0.880567i	0.113025	−	0.993592i	$-0.463946\pi$
$467$	−19.0292	−	19.0292i	−0.880567	−	0.880567i	−0.993592	+	0.113025i	$0.963946\pi$
$468$		0			0
$469$	−4.42429	+	4.42429i	−0.204295	+	0.204295i
$470$		0			0
$471$		−	18.1243i		−	0.835122i
$472$		0			0
$473$		−	0.834876i		−	0.0383876i
$474$		0			0
$475$	−13.9108	+	13.9108i	−0.638270	+	0.638270i
$476$		0			0
$477$	9.31788	+	9.31788i	0.426637	+	0.426637i
$478$		0			0
$479$	4.69245			0.214404			0.107202	−	0.994237i	$-0.465811\pi$
$479$	4.69245			0.214404			0.107202	+	0.994237i	$0.465811\pi$
$480$		0			0
$481$	17.1795			0.783317
$482$		0			0
$483$	3.71604	+	3.71604i	0.169086	+	0.169086i
$484$		0			0
$485$	3.27893	−	3.27893i	0.148889	−	0.148889i
$486$		0			0
$487$			0.300020i			0.0135952i	0.999977	+	0.00679760i	$0.00216376\pi$
$487$			0.300020i			0.0135952i	−0.999977	+	0.00679760i	$0.997836\pi$
$488$		0			0
$489$			12.6491i			0.572011i
$490$		0			0
$491$	6.00361	−	6.00361i	0.270939	−	0.270939i	−0.558539	−	0.829478i	$-0.688638\pi$
$491$	6.00361	−	6.00361i	0.270939	−	0.270939i	0.829478	+	0.558539i	$0.188638\pi$
$492$		0			0
$493$	0.115816	+	0.115816i	0.00521609	+	0.00521609i
$494$		0			0
$495$	0.498585			0.0224097
$496$		0			0
$497$	−14.5174			−0.651194
$498$		0			0
$499$	−5.25367	−	5.25367i	−0.235187	−	0.235187i	0.579667	−	0.814854i	$-0.303183\pi$
$499$	−5.25367	−	5.25367i	−0.235187	−	0.235187i	−0.814854	+	0.579667i	$0.803183\pi$
$500$		0			0
$501$	−0.383719	+	0.383719i	−0.0171433	+	0.0171433i
$502$		0			0
$503$		−	0.645460i		−	0.0287797i	−0.999896	−	0.0143898i	$-0.995419\pi$
$503$		−	0.645460i		−	0.0287797i	0.999896	−	0.0143898i	$-0.00458058\pi$
$504$		0			0
$505$			3.59236i			0.159858i
$506$		0			0
$507$	16.3141	−	16.3141i	0.724533	−	0.724533i
$508$		0			0
$509$	22.9125	+	22.9125i	1.01558	+	1.01558i	0.999877	+	0.0157007i	$0.00499791\pi$
$509$	22.9125	+	22.9125i	1.01558	+	1.01558i	0.0157007	+	0.999877i	$0.495002\pi$
$510$		0			0
$511$	−12.0202			−0.531740
$512$		0			0
$513$	−13.5601			−0.598695
$514$		0			0
$515$	−4.51149	−	4.51149i	−0.198800	−	0.198800i
$516$		0			0
$517$	1.23942	−	1.23942i	0.0545095	−	0.0545095i
$518$		0			0
$519$		−	17.0527i		−	0.748529i
$520$		0			0
$521$		−	35.9433i		−	1.57471i	−0.616503	−	0.787353i	$-0.711451\pi$
$521$		−	35.9433i		−	1.57471i	0.616503	−	0.787353i	$-0.288549\pi$
$522$		0			0
$523$	−0.198239	+	0.198239i	−0.00866838	+	0.00866838i	−0.711428	−	0.702759i	$-0.751951\pi$
$523$	−0.198239	+	0.198239i	−0.00866838	+	0.00866838i	0.702759	+	0.711428i	$0.251951\pi$
$524$		0			0
$525$	8.96823	+	8.96823i	0.391406	+	0.391406i
$526$		0			0
$527$	34.8233			1.51693
$528$		0			0
$529$	19.1706			0.833506
$530$		0			0
$531$	−38.6266	−	38.6266i	−1.67625	−	1.67625i
$532$		0			0
$533$	16.2495	−	16.2495i	0.703844	−	0.703844i
$534$		0			0
$535$		−	10.0050i		−	0.432552i
$536$		0			0
$537$		−	30.7876i		−	1.32858i
$538$		0			0
$539$	−0.158942	+	0.158942i	−0.00684610	+	0.00684610i
$540$		0			0
$541$	19.4243	+	19.4243i	0.835116	+	0.835116i	0.988211	−	0.153096i	$-0.0489243\pi$
$541$	19.4243	+	19.4243i	0.835116	+	0.835116i	−0.153096	+	0.988211i	$0.548924\pi$
$542$		0			0
$543$	−59.9651			−2.57335
$544$		0			0
$545$	−0.0717399			−0.00307300
$546$		0			0
$547$	−6.42914	−	6.42914i	−0.274890	−	0.274890i	0.556175	−	0.831065i	$-0.312268\pi$
$547$	−6.42914	−	6.42914i	−0.274890	−	0.274890i	−0.831065	+	0.556175i	$0.812268\pi$
$548$		0			0
$549$	−20.9597	+	20.9597i	−0.894538	+	0.894538i
$550$		0			0
$551$			0.179644i			0.00765310i
$552$		0			0
$553$			11.4165i			0.485479i
$554$		0			0
$555$	−8.18165	+	8.18165i	−0.347292	+	0.347292i
$556$		0			0
$557$	14.3961	+	14.3961i	0.609982	+	0.609982i	0.942941	−	0.332959i	$-0.108047\pi$
$557$	14.3961	+	14.3961i	0.609982	+	0.609982i	−0.332959	+	0.942941i	$0.608047\pi$
$558$		0			0
$559$	−7.79899			−0.329862
$560$		0			0
$561$	2.29262			0.0967945
$562$		0			0
$563$	16.5187	+	16.5187i	0.696179	+	0.696179i	0.963584	−	0.267405i	$-0.0861662\pi$
$563$	16.5187	+	16.5187i	0.696179	+	0.696179i	−0.267405	+	0.963584i	$0.586166\pi$
$564$		0			0
$565$	−3.31190	+	3.31190i	−0.139333	+	0.139333i
$566$		0			0
$567$		−	3.89426i		−	0.163544i
$568$		0			0
$569$		−	34.1860i		−	1.43315i	−0.697510	−	0.716575i	$-0.745709\pi$
$569$		−	34.1860i		−	1.43315i	0.697510	−	0.716575i	$-0.254291\pi$
$570$		0			0
$571$	2.70390	−	2.70390i	0.113155	−	0.113155i	−0.648262	−	0.761417i	$-0.724504\pi$
$571$	2.70390	−	2.70390i	0.113155	−	0.113155i	0.761417	+	0.648262i	$0.224504\pi$
$572$		0			0
$573$	10.2064	+	10.2064i	0.426377	+	0.426377i
$574$		0			0
$575$	−9.24171			−0.385406
$576$		0			0
$577$	12.3564			0.514406			0.257203	−	0.966357i	$-0.417199\pi$
$577$	12.3564			0.514406			0.257203	+	0.966357i	$0.417199\pi$
$578$		0			0
$579$	31.1800	+	31.1800i	1.29580	+	1.29580i
$580$		0			0
$581$	0.123744	−	0.123744i	0.00513376	−	0.00513376i
$582$		0			0
$583$		−	0.703204i		−	0.0291237i
$584$		0			0
$585$		−	4.65753i		−	0.192565i
$586$		0			0
$587$	−9.74183	+	9.74183i	−0.402088	+	0.402088i	−0.878968	−	0.476880i	$-0.841768\pi$
$587$	−9.74183	+	9.74183i	−0.402088	+	0.402088i	0.476880	+	0.878968i	$0.341768\pi$
$588$		0			0
$589$	27.0075	+	27.0075i	1.11283	+	1.11283i
$590$		0			0
$591$	−45.8354			−1.88542
$592$		0			0
$593$	−32.0335			−1.31546			−0.657728	−	0.753255i	$-0.728482\pi$
$593$	−32.0335			−1.31546			−0.657728	+	0.753255i	$0.728482\pi$
$594$		0			0
$595$	−1.41421	−	1.41421i	−0.0579771	−	0.0579771i
$596$		0			0
$597$	9.49791	−	9.49791i	0.388724	−	0.388724i
$598$		0			0
$599$			4.42105i			0.180639i	0.995913	+	0.0903196i	$0.0287888\pi$
$599$			4.42105i			0.180639i	−0.995913	+	0.0903196i	$0.971211\pi$
$600$		0			0
$601$		−	17.7279i		−	0.723138i	−0.932345	−	0.361569i	$-0.882241\pi$
$601$		−	17.7279i		−	0.723138i	0.932345	−	0.361569i	$-0.117759\pi$
$602$		0			0
$603$	18.6358	−	18.6358i	0.758907	−	0.758907i
$604$		0			0
$605$	4.07719	+	4.07719i	0.165761	+	0.165761i
$606$		0			0
$607$	−32.3546			−1.31323			−0.656616	−	0.754225i	$-0.728013\pi$
$607$	−32.3546			−1.31323			−0.656616	+	0.754225i	$0.728013\pi$
$608$		0			0
$609$	0.115816			0.00469310
$610$		0			0
$611$	−11.5780	−	11.5780i	−0.468396	−	0.468396i
$612$		0			0
$613$	18.7860	−	18.7860i	0.758758	−	0.758758i	−0.217338	−	0.976096i	$-0.569737\pi$
$613$	18.7860	−	18.7860i	0.758758	−	0.758758i	0.976096	+	0.217338i	$0.0697374\pi$
$614$		0			0
$615$			15.4775i			0.624113i
$616$		0			0
$617$		−	7.06491i		−	0.284422i	−0.989836	−	0.142211i	$-0.954579\pi$
$617$		−	7.06491i		−	0.284422i	0.989836	−	0.142211i	$-0.0454212\pi$
$618$		0			0
$619$	−15.3058	+	15.3058i	−0.615191	+	0.615191i	−0.944294	−	0.329103i	$-0.893254\pi$
$619$	−15.3058	+	15.3058i	−0.615191	+	0.615191i	0.329103	+	0.944294i	$0.393254\pi$
$620$		0			0
$621$	−4.50438	−	4.50438i	−0.180755	−	0.180755i
$622$		0			0
$623$	−6.79956			−0.272418
$624$		0			0
$625$	−20.9173			−0.836690
$626$		0			0
$627$	1.77806	+	1.77806i	0.0710089	+	0.0710089i
$628$		0			0
$629$	−21.9722	+	21.9722i	−0.876088	+	0.876088i
$630$		0			0
$631$		−	43.3637i		−	1.72628i	−0.504963	−	0.863141i	$-0.668494\pi$
$631$		−	43.3637i		−	1.72628i	0.504963	−	0.863141i	$-0.331506\pi$
$632$		0			0
$633$			28.8486i			1.14663i
$634$		0			0
$635$	−1.71954	+	1.71954i	−0.0682379	+	0.0682379i
$636$		0			0
$637$	1.48475	+	1.48475i	0.0588280	+	0.0588280i
$638$		0			0
$639$	61.1494			2.41903
$640$		0			0
$641$	15.9439			0.629745			0.314872	−	0.949134i	$-0.398038\pi$
$641$	15.9439			0.629745			0.314872	+	0.949134i	$0.398038\pi$
$642$		0			0
$643$	15.1476	+	15.1476i	0.597363	+	0.597363i	0.939610	−	0.342247i	$-0.111188\pi$
$643$	15.1476	+	15.1476i	0.597363	+	0.597363i	−0.342247	+	0.939610i	$0.611188\pi$
$644$		0			0
$645$	3.71423	−	3.71423i	0.146248	−	0.146248i
$646$		0			0
$647$			41.6849i			1.63880i	0.573220	+	0.819402i	$0.305694\pi$
$647$			41.6849i			1.63880i	−0.573220	+	0.819402i	$0.694306\pi$
$648$		0			0
$649$			2.91508i			0.114427i
$650$		0			0
$651$	17.4117	−	17.4117i	0.682417	−	0.682417i
$652$		0			0
$653$	4.38694	+	4.38694i	0.171674	+	0.171674i	0.787715	−	0.616040i	$-0.211264\pi$
$653$	4.38694	+	4.38694i	0.171674	+	0.171674i	−0.616040	+	0.787715i	$0.711264\pi$
$654$		0			0
$655$	−9.41421			−0.367844
$656$		0			0
$657$	50.6307			1.97529
$658$		0			0
$659$	−33.6974	−	33.6974i	−1.31267	−	1.31267i	−0.919444	−	0.393222i	$-0.871360\pi$
$659$	−33.6974	−	33.6974i	−1.31267	−	1.31267i	−0.393222	−	0.919444i	$-0.628640\pi$
$660$		0			0
$661$	−21.0875	+	21.0875i	−0.820208	+	0.820208i	−0.986138	−	0.165930i	$-0.946937\pi$
$661$	−21.0875	+	21.0875i	−0.820208	+	0.820208i	0.165930	+	0.986138i	$0.446937\pi$
$662$		0			0
$663$		−	21.4165i		−	0.831748i
$664$		0			0
$665$		−	2.19361i		−	0.0850646i
$666$		0			0
$667$	−0.0596739	+	0.0596739i	−0.00231058	+	0.00231058i
$668$		0			0
$669$	−37.2187	−	37.2187i	−1.43896	−	1.43896i
$670$		0			0
$671$	1.58179			0.0610644
$672$		0			0
$673$	−24.6656			−0.950790			−0.475395	−	0.879773i	$-0.657695\pi$
$673$	−24.6656			−0.950790			−0.475395	+	0.879773i	$0.657695\pi$
$674$		0			0
$675$	−10.8708	−	10.8708i	−0.418417	−	0.418417i
$676$		0			0
$677$	−16.1104	+	16.1104i	−0.619172	+	0.619172i	−0.945319	−	0.326147i	$-0.894249\pi$
$677$	−16.1104	+	16.1104i	−0.619172	+	0.619172i	0.326147	+	0.945319i	$0.394249\pi$
$678$		0			0
$679$		−	8.80572i		−	0.337932i
$680$		0			0
$681$		−	46.3378i		−	1.77567i
$682$		0			0
$683$	−14.3105	+	14.3105i	−0.547575	+	0.547575i	−0.925739	−	0.378163i	$-0.876556\pi$
$683$	−14.3105	+	14.3105i	−0.547575	+	0.547575i	0.378163	+	0.925739i	$0.376556\pi$
$684$		0			0
$685$	−5.46675	−	5.46675i	−0.208874	−	0.208874i
$686$		0			0
$687$	34.0737			1.29999
$688$		0			0
$689$	−6.56898			−0.250258
$690$		0			0
$691$	14.0209	+	14.0209i	0.533382	+	0.533382i	0.921577	−	0.388195i	$-0.126901\pi$
$691$	14.0209	+	14.0209i	0.533382	+	0.533382i	−0.388195	+	0.921577i	$0.626901\pi$
$692$		0			0
$693$	0.669485	−	0.669485i	0.0254317	−	0.0254317i
$694$		0			0
$695$			0.512838i			0.0194531i
$696$		0			0
$697$			41.5655i			1.57441i
$698$		0			0
$699$	−39.3112	+	39.3112i	−1.48688	+	1.48688i
$700$		0			0
$701$	−26.3024	−	26.3024i	−0.993430	−	0.993430i	0.00654904	−	0.999979i	$-0.497915\pi$
$701$	−26.3024	−	26.3024i	−0.993430	−	0.993430i	−0.999979	+	0.00654904i	$0.997915\pi$
$702$		0			0
$703$	−34.0814			−1.28541
$704$		0			0
$705$	11.0279			0.415336
$706$		0			0
$707$	4.82372	+	4.82372i	0.181415	+	0.181415i
$708$		0			0
$709$	18.4665	−	18.4665i	0.693524	−	0.693524i	−0.269482	−	0.963005i	$-0.586852\pi$
$709$	18.4665	−	18.4665i	0.693524	−	0.693524i	0.963005	+	0.269482i	$0.0868524\pi$
$710$		0			0
$711$		−	48.0880i		−	1.80344i
$712$		0			0
$713$			17.9426i			0.671956i
$714$		0			0
$715$	−0.175748	+	0.175748i	−0.00657259	+	0.00657259i
$716$		0			0
$717$	34.1673	+	34.1673i	1.27600	+	1.27600i
$718$		0			0
$719$	12.0026			0.447620			0.223810	−	0.974633i	$-0.428151\pi$
$719$	12.0026			0.447620			0.223810	+	0.974633i	$0.428151\pi$
$720$		0			0
$721$	−12.1158			−0.451217
$722$		0			0
$723$	12.2654	+	12.2654i	0.456153	+	0.456153i
$724$		0			0
$725$	−0.144016	+	0.144016i	−0.00534862	+	0.00534862i
$726$		0			0
$727$		−	19.8622i		−	0.736647i	−0.929698	−	0.368323i	$-0.879932\pi$
$727$		−	19.8622i		−	0.736647i	0.929698	−	0.368323i	$-0.120068\pi$
$728$		0			0
$729$			42.6297i			1.57888i
$730$		0			0
$731$	9.97474	−	9.97474i	0.368929	−	0.368929i
$732$		0			0
$733$	29.1704	+	29.1704i	1.07743	+	1.07743i	0.996739	+	0.0806954i	$0.0257141\pi$
$733$	29.1704	+	29.1704i	1.07743	+	1.07743i	0.0806954	+	0.996739i	$0.474286\pi$
$734$		0			0
$735$	−1.41421			−0.0521641
$736$		0			0
$737$	−1.40641			−0.0518057
$738$		0			0
$739$	−16.4158	−	16.4158i	−0.603866	−	0.603866i	0.337470	−	0.941336i	$-0.390429\pi$
$739$	−16.4158	−	16.4158i	−0.603866	−	0.603866i	−0.941336	+	0.337470i	$0.890429\pi$
$740$		0			0
$741$	16.6098	−	16.6098i	0.610175	−	0.610175i
$742$		0			0
$743$			6.10225i			0.223870i	0.993716	+	0.111935i	$0.0357048\pi$
$743$			6.10225i			0.223870i	−0.993716	+	0.111935i	$0.964295\pi$
$744$		0			0
$745$			11.2553i			0.412361i
$746$		0			0
$747$	−0.521227	+	0.521227i	−0.0190707	+	0.0190707i
$748$		0			0
$749$	−13.4344	−	13.4344i	−0.490881	−	0.490881i
$750$		0			0
$751$	37.6119			1.37248			0.686238	−	0.727377i	$-0.259261\pi$
$751$	37.6119			1.37248			0.686238	+	0.727377i	$0.259261\pi$
$752$		0			0
$753$	−5.70067			−0.207744
$754$		0			0
$755$	−3.55710	−	3.55710i	−0.129456	−	0.129456i
$756$		0			0
$757$	33.5029	−	33.5029i	1.21768	−	1.21768i	0.249242	−	0.968441i	$-0.419819\pi$
$757$	33.5029	−	33.5029i	1.21768	−	1.21768i	0.968441	−	0.249242i	$-0.0801814\pi$
$758$		0			0
$759$			1.18127i			0.0428773i
$760$		0			0
$761$			31.2942i			1.13442i	0.823575	+	0.567208i	$0.191976\pi$
$761$			31.2942i			1.13442i	−0.823575	+	0.567208i	$0.808024\pi$
$762$		0			0
$763$	−0.0963303	+	0.0963303i	−0.00348739	+	0.00348739i
$764$		0			0
$765$	5.95687	+	5.95687i	0.215371	+	0.215371i
$766$		0			0
$767$	27.2312			0.983263
$768$		0			0
$769$	16.5011			0.595046			0.297523	−	0.954715i	$-0.403839\pi$
$769$	16.5011			0.595046			0.297523	+	0.954715i	$0.403839\pi$
$770$		0			0
$771$	20.9121	+	20.9121i	0.753132	+	0.753132i
$772$		0			0
$773$	−33.1931	+	33.1931i	−1.19387	+	1.19387i	−0.217904	+	0.975970i	$0.569922\pi$
$773$	−33.1931	+	33.1931i	−1.19387	+	1.19387i	−0.975970	+	0.217904i	$0.930078\pi$
$774$		0			0
$775$			43.3024i			1.55547i
$776$		0			0
$777$			21.9722i			0.788248i
$778$		0			0
$779$	−32.2365	+	32.2365i	−1.15499	+	1.15499i
$780$		0			0
$781$	−2.30742	−	2.30742i	−0.0825660	−	0.0825660i
$782$		0			0
$783$	−0.140386			−0.00501698
$784$		0			0
$785$	−3.55395			−0.126846
$786$		0			0
$787$	37.4484	+	37.4484i	1.33489	+	1.33489i	0.900933	+	0.433959i	$0.142884\pi$
$787$	37.4484	+	37.4484i	1.33489	+	1.33489i	0.433959	+	0.900933i	$0.357116\pi$
$788$		0			0
$789$	−52.9846	+	52.9846i	−1.88630	+	1.88630i
$790$		0			0
$791$			8.89426i			0.316244i
$792$		0			0
$793$		−	14.7763i		−	0.524722i
$794$		0			0
$795$	3.12845	−	3.12845i	0.110955	−	0.110955i
$796$		0			0
$797$	−36.2951	−	36.2951i	−1.28564	−	1.28564i	−0.937410	−	0.348227i	$-0.886784\pi$
$797$	−36.2951	−	36.2951i	−1.28564	−	1.28564i	−0.348227	−	0.937410i	$-0.613216\pi$
$798$		0			0
$799$	29.6160			1.04774
$800$		0			0
$801$	28.6407			1.01197
$802$		0			0
$803$	−1.91050	−	1.91050i	−0.0674202	−	0.0674202i
$804$		0			0
$805$	0.728670	−	0.728670i	0.0256822	−	0.0256822i
$806$		0			0
$807$		−	64.9710i		−	2.28709i
$808$		0			0
$809$			53.8799i			1.89432i	0.320768	+	0.947158i	$0.396059\pi$
$809$			53.8799i			1.89432i	−0.320768	+	0.947158i	$0.603941\pi$
$810$		0			0
$811$	−3.37216	+	3.37216i	−0.118413	+	0.118413i	−0.763830	−	0.645417i	$-0.776683\pi$
$811$	−3.37216	+	3.37216i	−0.118413	+	0.118413i	0.645417	+	0.763830i	$0.276683\pi$
$812$		0			0
$813$	40.5733	+	40.5733i	1.42297	+	1.42297i
$814$		0			0
$815$	2.48033			0.0868821
$816$		0			0
$817$	15.4720			0.541296
$818$		0			0
$819$	−6.25400	−	6.25400i	−0.218532	−	0.218532i
$820$		0			0
$821$	10.9339	−	10.9339i	0.381596	−	0.381596i	−0.490081	−	0.871677i	$-0.663033\pi$
$821$	10.9339	−	10.9339i	0.381596	−	0.381596i	0.871677	+	0.490081i	$0.163033\pi$
$822$		0			0
$823$			51.6379i			1.79999i	0.435905	+	0.899993i	$0.356428\pi$
$823$			51.6379i			1.79999i	−0.435905	+	0.899993i	$0.643572\pi$
$824$		0			0
$825$			2.85085i			0.0992539i
$826$		0			0
$827$	−31.2096	+	31.2096i	−1.08526	+	1.08526i	−0.0892551	+	0.996009i	$0.528449\pi$
$827$	−31.2096	+	31.2096i	−1.08526	+	1.08526i	−0.996009	+	0.0892551i	$0.971551\pi$
$828$		0			0
$829$	−15.3646	−	15.3646i	−0.533634	−	0.533634i	0.388018	−	0.921652i	$-0.373160\pi$
$829$	−15.3646	−	15.3646i	−0.533634	−	0.533634i	−0.921652	+	0.388018i	$0.873160\pi$
$830$		0			0
$831$	36.3781			1.26194
$832$		0			0
$833$	−3.79793			−0.131591
$834$		0			0
$835$	0.0752426	+	0.0752426i	0.00260388	+	0.00260388i
$836$		0			0
$837$	−21.1055	+	21.1055i	−0.729512	+	0.729512i
$838$		0			0
$839$		−	35.4882i		−	1.22519i	−0.790397	−	0.612595i	$-0.790126\pi$
$839$		−	35.4882i		−	1.22519i	0.790397	−	0.612595i	$-0.209874\pi$
$840$		0			0
$841$		−	28.9981i		−	0.999936i
$842$		0			0
$843$	−17.0027	+	17.0027i	−0.585603	+	0.585603i
$844$		0			0
$845$	−3.19899	−	3.19899i	−0.110048	−	0.110048i
$846$		0			0
$847$	10.9495			0.376228
$848$		0			0
$849$	22.2819			0.764713
$850$		0			0
$851$	−11.3211	−	11.3211i	−0.388083	−	0.388083i
$852$		0			0
$853$	35.3684	−	35.3684i	1.21099	−	1.21099i	0.240291	−	0.970701i	$-0.422757\pi$
$853$	35.3684	−	35.3684i	1.21099	−	1.21099i	0.970701	−	0.240291i	$-0.0772428\pi$
$854$		0			0
$855$			9.23981i			0.315995i
$856$		0			0
$857$			26.2359i			0.896202i	0.893983	+	0.448101i	$0.147900\pi$
$857$			26.2359i			0.896202i	−0.893983	+	0.448101i	$0.852100\pi$
$858$		0			0
$859$	14.4164	−	14.4164i	0.491880	−	0.491880i	−0.417018	−	0.908898i	$-0.636925\pi$
$859$	14.4164	−	14.4164i	0.491880	−	0.491880i	0.908898	+	0.417018i	$0.136925\pi$
$860$		0			0
$861$	20.7827	+	20.7827i	0.708274	+	0.708274i
$862$		0			0
$863$	42.9719			1.46278			0.731390	−	0.681959i	$-0.238872\pi$
$863$	42.9719			1.46278			0.731390	+	0.681959i	$0.238872\pi$
$864$		0			0
$865$	−3.34382			−0.113693
$866$		0			0
$867$	−4.89118	−	4.89118i	−0.166113	−	0.166113i
$868$		0			0
$869$	−1.81456	+	1.81456i	−0.0615547	+	0.0615547i
$870$		0			0
$871$			13.1380i			0.445163i
$872$		0			0
$873$			37.0910i			1.25534i
$874$		0			0
$875$	3.62038	−	3.62038i	0.122391	−	0.122391i
$876$		0			0
$877$	−2.33766	−	2.33766i	−0.0789370	−	0.0789370i	0.666536	−	0.745473i	$-0.267776\pi$
$877$	−2.33766	−	2.33766i	−0.0789370	−	0.0789370i	−0.745473	+	0.666536i	$0.767776\pi$
$878$		0			0
$879$	−29.0118			−0.978545
$880$		0			0
$881$	−0.183946			−0.00619731			−0.00309865	−	0.999995i	$-0.500986\pi$
$881$	−0.183946			−0.00619731			−0.00309865	+	0.999995i	$0.500986\pi$
$882$		0			0
$883$	32.7600	+	32.7600i	1.10246	+	1.10246i	0.994113	+	0.108350i	$0.0345568\pi$
$883$	32.7600	+	32.7600i	1.10246	+	1.10246i	0.108350	+	0.994113i	$0.465443\pi$
$884$		0			0
$885$	−12.9688	+	12.9688i	−0.435940	+	0.435940i
$886$		0			0
$887$		−	15.8506i		−	0.532210i	−0.963944	−	0.266105i	$-0.914263\pi$
$887$		−	15.8506i		−	0.532210i	0.963944	−	0.266105i	$-0.0857368\pi$
$888$		0			0
$889$			4.61790i			0.154880i
$890$		0			0
$891$	0.618961	−	0.618961i	0.0207360	−	0.0207360i
$892$		0			0
$893$	22.9690	+	22.9690i	0.768627	+	0.768627i
$894$		0			0
$895$	−6.03707			−0.201797
$896$		0			0
$897$	11.0348			0.368441
$898$		0			0
$899$	0.279604	+	0.279604i	0.00932533	+	0.00932533i
$900$		0			0
$901$	8.40158	−	8.40158i	0.279897	−	0.279897i
$902$		0			0
$903$		−	9.97474i		−	0.331938i
$904$		0			0
$905$			11.7584i			0.390863i
$906$		0			0
$907$	23.6027	−	23.6027i	0.783715	−	0.783715i	−0.196740	−	0.980456i	$-0.563036\pi$
$907$	23.6027	−	23.6027i	0.783715	−	0.783715i	0.980456	+	0.196740i	$0.0630356\pi$
$908$		0			0
$909$	−20.3182	−	20.3182i	−0.673913	−	0.673913i
$910$		0			0
$911$	14.3105			0.474127			0.237064	−	0.971494i	$-0.423815\pi$
$911$	14.3105			0.474127			0.237064	+	0.971494i	$0.423815\pi$
$912$		0			0
$913$	0.0393361			0.00130183
$914$		0			0
$915$	7.03715	+	7.03715i	0.232641	+	0.232641i
$916$		0			0
$917$	−12.6411	+	12.6411i	−0.417447	+	0.417447i
$918$		0			0
$919$		−	10.5848i		−	0.349162i	−0.984643	−	0.174581i	$-0.944143\pi$
$919$		−	10.5848i		−	0.349162i	0.984643	−	0.174581i	$-0.0558570\pi$
$920$		0			0
$921$			25.0007i			0.823800i
$922$		0			0
$923$	−21.5547	+	21.5547i	−0.709483	+	0.709483i
$924$		0			0
$925$	−27.3222	−	27.3222i	−0.898348	−	0.898348i
$926$		0			0
$927$	51.0336			1.67616
$928$		0			0
$929$	−37.3891			−1.22670			−0.613348	−	0.789813i	$-0.710178\pi$
$929$	−37.3891			−1.22670			−0.613348	+	0.789813i	$0.710178\pi$
$930$		0			0
$931$	−2.94552	−	2.94552i	−0.0965355	−	0.0965355i
$932$		0			0
$933$	44.8590	−	44.8590i	1.46862	−	1.46862i
$934$		0			0
$935$		−	0.449555i		−	0.0147020i
$936$		0			0
$937$			19.0986i			0.623925i	0.950094	+	0.311962i	$0.100986\pi$
$937$			19.0986i			0.623925i	−0.950094	+	0.311962i	$0.899014\pi$
$938$		0			0
$939$	14.2722	−	14.2722i	0.465756	−	0.465756i
$940$		0			0
$941$	8.07900	+	8.07900i	0.263368	+	0.263368i	0.826421	−	0.563053i	$-0.190373\pi$
$941$	8.07900	+	8.07900i	0.263368	+	0.263368i	−0.563053	+	0.826421i	$0.690373\pi$
$942$		0			0
$943$	−21.4165			−0.697417
$944$		0			0
$945$	1.71423			0.0557640
$946$		0			0
$947$	30.2015	+	30.2015i	0.981418	+	0.981418i	0.999830	−	0.0184129i	$-0.00586132\pi$
$947$	30.2015	+	30.2015i	0.981418	+	0.981418i	−0.0184129	+	0.999830i	$0.505861\pi$
$948$		0			0
$949$	−17.8470	+	17.8470i	−0.579337	+	0.579337i
$950$		0			0
$951$		−	2.51310i		−	0.0814927i
$952$		0			0
$953$			18.3192i			0.593418i	0.954968	+	0.296709i	$0.0958891\pi$
$953$			18.3192i			0.593418i	−0.954968	+	0.296709i	$0.904111\pi$
$954$		0			0
$955$	2.00134	−	2.00134i	0.0647620	−	0.0647620i
$956$		0			0
$957$	0.0184080	+	0.0184080i	0.000595045	+	0.000595045i
$958$		0			0
$959$	−14.6812			−0.474080
$960$		0			0
$961$	53.0709			1.71197
$962$		0			0
$963$	56.5875	+	56.5875i	1.82351	+	1.82351i
$964$		0			0
$965$	6.11401	−	6.11401i	0.196817	−	0.196817i
$966$		0			0
$967$		−	19.5495i		−	0.628669i	−0.949312	−	0.314335i	$-0.898219\pi$
$967$		−	19.5495i		−	0.628669i	0.949312	−	0.314335i	$-0.101781\pi$
$968$		0			0
$969$			42.4870i			1.36488i
$970$		0			0
$971$	37.1948	−	37.1948i	1.19364	−	1.19364i	0.217598	−	0.976038i	$-0.430178\pi$
$971$	37.1948	−	37.1948i	1.19364	−	1.19364i	0.976038	−	0.217598i	$-0.0698222\pi$
$972$		0			0
$973$	0.688625	+	0.688625i	0.0220763	+	0.0220763i
$974$		0			0
$975$	26.6312			0.852881
$976$		0			0
$977$	18.1324			0.580108			0.290054	−	0.957010i	$-0.406327\pi$
$977$	18.1324			0.580108			0.290054	+	0.957010i	$0.406327\pi$
$978$		0			0
$979$	−1.08073	−	1.08073i	−0.0345404	−	0.0345404i
$980$		0			0
$981$	0.405757	−	0.405757i	0.0129548	−	0.0129548i
$982$		0			0
$983$			1.72823i			0.0551220i	0.999620	+	0.0275610i	$0.00877404\pi$
$983$			1.72823i			0.0551220i	−0.999620	+	0.0275610i	$0.991226\pi$
$984$		0			0
$985$			8.98776i			0.286374i
$986$		0			0
$987$	14.8080	−	14.8080i	0.471344	−	0.471344i
$988$		0			0
$989$	5.13946	+	5.13946i	0.163425	+	0.163425i
$990$		0			0
$991$	−48.5830			−1.54329			−0.771645	−	0.636054i	$-0.780566\pi$
$991$	−48.5830			−1.54329			−0.771645	+	0.636054i	$0.780566\pi$
$992$		0			0
$993$	89.4838			2.83968
$994$		0			0
$995$	−1.86242	−	1.86242i	−0.0590428	−	0.0590428i
$996$		0			0
$997$	10.1609	−	10.1609i	0.321799	−	0.321799i	−0.527658	−	0.849457i	$-0.676930\pi$
$997$	10.1609	−	10.1609i	0.321799	−	0.321799i	0.849457	+	0.527658i	$0.176930\pi$
$998$		0			0
$999$		−	26.6335i		−	0.842647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.d.1345.4	yes	8
4.3	odd	2		1792.2.m.b.1345.1	yes	8
8.3	odd	2		1792.2.m.c.1345.4	yes	8
8.5	even	2		1792.2.m.a.1345.1	yes	8
16.3	odd	4		1792.2.m.c.449.4	yes	8
16.5	even	4	inner	1792.2.m.d.449.4	yes	8
16.11	odd	4		1792.2.m.b.449.1	yes	8
16.13	even	4		1792.2.m.a.449.1	✓	8
32.5	even	8		7168.2.a.t.1.1		4
32.11	odd	8		7168.2.a.w.1.1		4
32.21	even	8		7168.2.a.x.1.4		4
32.27	odd	8		7168.2.a.s.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.a.449.1	✓	8	16.13	even	4
1792.2.m.a.1345.1	yes	8	8.5	even	2
1792.2.m.b.449.1	yes	8	16.11	odd	4
1792.2.m.b.1345.1	yes	8	4.3	odd	2
1792.2.m.c.449.4	yes	8	16.3	odd	4
1792.2.m.c.1345.4	yes	8	8.3	odd	2
1792.2.m.d.449.4	yes	8	16.5	even	4	inner
1792.2.m.d.1345.4	yes	8	1.1	even	1	trivial
7168.2.a.s.1.4		4	32.27	odd	8
7168.2.a.t.1.1		4	32.5	even	8
7168.2.a.w.1.1		4	32.11	odd	8
7168.2.a.x.1.4		4	32.21	even	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89897 + 1.89897i) q^{3} +(0.372364 - 0.372364i) q^{5} -1.00000i q^{7} +4.21215i q^{9} +O(q^{10})\)	\(q+(1.89897 + 1.89897i) q^{3} +(0.372364 - 0.372364i) q^{5} -1.00000i q^{7} +4.21215i q^{9} +(0.158942 - 0.158942i) q^{11} +(-1.48475 - 1.48475i) q^{13} +1.41421 q^{15} +3.79793 q^{17} +(2.94552 + 2.94552i) q^{19} +(1.89897 - 1.89897i) q^{21} +1.95687i q^{23} +4.72269i q^{25} +(-2.30182 + 2.30182i) q^{27} +(0.0304945 + 0.0304945i) q^{29} +9.16902 q^{31} +0.603650 q^{33} +(-0.372364 - 0.372364i) q^{35} +(-5.78530 + 5.78530i) q^{37} -5.63899i q^{39} +10.9442i q^{41} +(2.62636 - 2.62636i) q^{43} +(1.56845 + 1.56845i) q^{45} +7.79793 q^{47} -1.00000 q^{49} +(7.21215 + 7.21215i) q^{51} +(2.21215 - 2.21215i) q^{53} -0.118368i q^{55} +11.1869i q^{57} +(-9.17030 + 9.17030i) q^{59} +(4.97601 + 4.97601i) q^{61} +4.21215 q^{63} -1.10574 q^{65} +(-4.42429 - 4.42429i) q^{67} +(-3.71604 + 3.71604i) q^{69} -14.5174i q^{71} -12.0202i q^{73} +(-8.96823 + 8.96823i) q^{75} +(-0.158942 - 0.158942i) q^{77} -11.4165 q^{79} +3.89426 q^{81} +(0.123744 + 0.123744i) q^{83} +(1.41421 - 1.41421i) q^{85} +0.115816i q^{87} -6.79956i q^{89} +(-1.48475 + 1.48475i) q^{91} +(17.4117 + 17.4117i) q^{93} +2.19361 q^{95} +8.80572 q^{97} +(0.669485 + 0.669485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^5	\( 8 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} + 8 q^{17} + 4 q^{19} + 4 q^{21} - 8 q^{27} + 8 q^{31} - 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} - 12 q^{45} + 40 q^{47} - 8 q^{49} + 24 q^{51} - 16 q^{53} - 52 q^{59} + 20 q^{61} - 24 q^{65} + 32 q^{67} - 8 q^{69} - 28 q^{75} + 8 q^{77} + 16 q^{81} - 12 q^{83} - 12 q^{91} + 40 q^{93} + 80 q^{95} + 72 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 + 8 * q^17 + 4 * q^19 + 4 * q^21 - 8 * q^27 + 8 * q^31 - 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 - 12 * q^45 + 40 * q^47 - 8 * q^49 + 24 * q^51 - 16 * q^53 - 52 * q^59 + 20 * q^61 - 24 * q^65 + 32 * q^67 - 8 * q^69 - 28 * q^75 + 8 * q^77 + 16 * q^81 - 12 * q^83 - 12 * q^91 + 40 * q^93 + 80 * q^95 + 72 * q^97 - 8 * q^99

Introduction

L-functions

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