LMFDB - Embedded newform 1792.2.m.b.1345.2

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			1345.2
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.b.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23681 - 1.23681i) q^{3} +(-0.571717 + 0.571717i) q^{5} +1.00000i q^{7} +0.0594122i q^{9} +O(q^{10})$	\(q+(-1.23681 - 1.23681i) q^{3} +(-0.571717 + 0.571717i) q^{5} +1.00000i q^{7} +0.0594122i q^{9} +(4.55765 - 4.55765i) q^{11} +(-3.65103 - 3.65103i) q^{13} +1.41421 q^{15} +2.47363 q^{17} +(5.54358 + 5.54358i) q^{19} +(1.23681 - 1.23681i) q^{21} +4.08402i q^{23} +4.34628i q^{25} +(-3.63696 + 3.63696i) q^{27} +(-4.30205 - 4.30205i) q^{29} +1.02461 q^{31} -11.2739 q^{33} +(-0.571717 - 0.571717i) q^{35} +(5.91245 - 5.91245i) q^{37} +9.03127i q^{39} -5.47010i q^{41} +(4.35480 - 4.35480i) q^{43} +(-0.0339670 - 0.0339670i) q^{45} -6.47363 q^{47} -1.00000 q^{49} +(-3.05941 - 3.05941i) q^{51} +(-1.94059 + 1.94059i) q^{53} +5.21137i q^{55} -13.7127i q^{57} +(6.90191 - 6.90191i) q^{59} +(-7.84563 - 7.84563i) q^{61} -0.0594122 q^{63} +4.17471 q^{65} +(-3.88118 - 3.88118i) q^{67} +(5.05117 - 5.05117i) q^{69} -9.44196i q^{71} -1.06608i q^{73} +(5.37553 - 5.37553i) q^{75} +(4.55765 + 4.55765i) q^{77} +12.3400 q^{79} +9.17471 q^{81} +(-5.68230 - 5.68230i) q^{83} +(-1.41421 + 1.41421i) q^{85} +10.6417i q^{87} -2.81900i q^{89} +(3.65103 - 3.65103i) q^{91} +(-1.26725 - 1.26725i) q^{93} -6.33871 q^{95} -1.74754 q^{97} +(0.270780 + 0.270780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.23681	−	1.23681i	−0.714074	−	0.714074i	0.253311	−	0.967385i	$-0.418480\pi$
$3$	−1.23681	−	1.23681i	−0.714074	−	0.714074i	−0.967385	+	0.253311i	$0.918480\pi$
$4$		0			0
$5$	−0.571717	+	0.571717i	−0.255680	+	0.255680i	−0.823294	−	0.567615i	$-0.807866\pi$
$5$	−0.571717	+	0.571717i	−0.255680	+	0.255680i	0.567615	+	0.823294i	$0.307866\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			0.0594122i			0.0198041i
$10$		0			0
$11$	4.55765	−	4.55765i	1.37418	−	1.37418i	0.520041	−	0.854141i	$-0.325917\pi$
$11$	4.55765	−	4.55765i	1.37418	−	1.37418i	0.854141	−	0.520041i	$-0.174083\pi$
$12$		0			0
$13$	−3.65103	−	3.65103i	−1.01261	−	1.01261i	−0.999919	−	0.0126931i	$-0.995960\pi$
$13$	−3.65103	−	3.65103i	−1.01261	−	1.01261i	−0.0126931	−	0.999919i	$-0.504040\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$		0			0
$17$	2.47363			0.599942			0.299971	−	0.953948i	$-0.403023\pi$
$17$	2.47363			0.599942			0.299971	+	0.953948i	$0.403023\pi$
$18$		0			0
$19$	5.54358	+	5.54358i	1.27178	+	1.27178i	0.945151	+	0.326633i	$0.105914\pi$
$19$	5.54358	+	5.54358i	1.27178	+	1.27178i	0.326633	+	0.945151i	$0.394086\pi$
$20$		0			0
$21$	1.23681	−	1.23681i	0.269895	−	0.269895i
$22$		0			0
$23$			4.08402i			0.851577i	0.904823	+	0.425789i	$0.140003\pi$
$23$			4.08402i			0.851577i	−0.904823	+	0.425789i	$0.859997\pi$
$24$		0			0
$25$			4.34628i			0.869256i
$26$		0			0
$27$	−3.63696	+	3.63696i	−0.699933	+	0.699933i
$28$		0			0
$29$	−4.30205	−	4.30205i	−0.798871	−	0.798871i	0.184046	−	0.982918i	$-0.441080\pi$
$29$	−4.30205	−	4.30205i	−0.798871	−	0.798871i	−0.982918	+	0.184046i	$0.941080\pi$
$30$		0			0
$31$	1.02461			0.184025			0.0920126	−	0.995758i	$-0.470670\pi$
$31$	1.02461			0.184025			0.0920126	+	0.995758i	$0.470670\pi$
$32$		0			0
$33$	−11.2739			−1.96254
$34$		0			0
$35$	−0.571717	−	0.571717i	−0.0966378	−	0.0966378i
$36$		0			0
$37$	5.91245	−	5.91245i	0.972001	−	0.972001i	−0.0276180	−	0.999619i	$-0.508792\pi$
$37$	5.91245	−	5.91245i	0.972001	−	0.972001i	0.999619	+	0.0276180i	$0.00879219\pi$
$38$		0			0
$39$			9.03127i			1.44616i
$40$		0			0
$41$		−	5.47010i		−	0.854285i	−0.904184	−	0.427143i	$-0.859520\pi$
$41$		−	5.47010i		−	0.854285i	0.904184	−	0.427143i	$-0.140480\pi$
$42$		0			0
$43$	4.35480	−	4.35480i	0.664101	−	0.664101i	−0.292243	−	0.956344i	$-0.594402\pi$
$43$	4.35480	−	4.35480i	0.664101	−	0.664101i	0.956344	+	0.292243i	$0.0944016\pi$
$44$		0			0
$45$	−0.0339670	−	0.0339670i	−0.00506349	−	0.00506349i
$46$		0			0
$47$	−6.47363			−0.944275			−0.472138	−	0.881525i	$-0.656517\pi$
$47$	−6.47363			−0.944275			−0.472138	+	0.881525i	$0.656517\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−3.05941	−	3.05941i	−0.428403	−	0.428403i
$52$		0			0
$53$	−1.94059	+	1.94059i	−0.266560	+	0.266560i	−0.827713	−	0.561152i	$-0.810358\pi$
$53$	−1.94059	+	1.94059i	−0.266560	+	0.266560i	0.561152	+	0.827713i	$0.310358\pi$
$54$		0			0
$55$			5.21137i			0.702701i
$56$		0			0
$57$		−	13.7127i		−	1.81630i
$58$		0			0
$59$	6.90191	−	6.90191i	0.898552	−	0.898552i	−0.0967561	−	0.995308i	$-0.530847\pi$
$59$	6.90191	−	6.90191i	0.898552	−	0.898552i	0.995308	+	0.0967561i	$0.0308467\pi$
$60$		0			0
$61$	−7.84563	−	7.84563i	−1.00453	−	1.00453i	−0.999990	−	0.00454037i	$-0.998555\pi$
$61$	−7.84563	−	7.84563i	−1.00453	−	1.00453i	−0.00454037	−	0.999990i	$-0.501445\pi$
$62$		0			0
$63$	−0.0594122			−0.00748523
$64$		0			0
$65$	4.17471			0.517809
$66$		0			0
$67$	−3.88118	−	3.88118i	−0.474161	−	0.474161i	0.429097	−	0.903258i	$-0.358832\pi$
$67$	−3.88118	−	3.88118i	−0.474161	−	0.474161i	−0.903258	+	0.429097i	$0.858832\pi$
$68$		0			0
$69$	5.05117	−	5.05117i	0.608089	−	0.608089i
$70$		0			0
$71$		−	9.44196i		−	1.12055i	−0.828305	−	0.560277i	$-0.810695\pi$
$71$		−	9.44196i		−	1.12055i	0.828305	−	0.560277i	$-0.189305\pi$
$72$		0			0
$73$		−	1.06608i		−	0.124775i	−0.998052	−	0.0623874i	$-0.980129\pi$
$73$		−	1.06608i		−	0.124775i	0.998052	−	0.0623874i	$-0.0198714\pi$
$74$		0			0
$75$	5.37553	−	5.37553i	0.620713	−	0.620713i
$76$		0			0
$77$	4.55765	+	4.55765i	0.519392	+	0.519392i
$78$		0			0
$79$	12.3400			1.38836			0.694179	−	0.719803i	$-0.255768\pi$
$79$	12.3400			1.38836			0.694179	+	0.719803i	$0.255768\pi$
$80$		0			0
$81$	9.17471			1.01941
$82$		0			0
$83$	−5.68230	−	5.68230i	−0.623713	−	0.623713i	0.322766	−	0.946479i	$-0.395387\pi$
$83$	−5.68230	−	5.68230i	−0.623713	−	0.623713i	−0.946479	+	0.322766i	$0.895387\pi$
$84$		0			0
$85$	−1.41421	+	1.41421i	−0.153393	+	0.153393i
$86$		0			0
$87$			10.6417i			1.14091i
$88$		0			0
$89$		−	2.81900i		−	0.298814i	−0.988776	−	0.149407i	$-0.952264\pi$
$89$		−	2.81900i		−	0.298814i	0.988776	−	0.149407i	$-0.0477364\pi$
$90$		0			0
$91$	3.65103	−	3.65103i	0.382732	−	0.382732i
$92$		0			0
$93$	−1.26725	−	1.26725i	−0.131408	−	0.131408i
$94$		0			0
$95$	−6.33871			−0.650338
$96$		0			0
$97$	−1.74754			−0.177436			−0.0887179	−	0.996057i	$-0.528277\pi$
$97$	−1.74754			−0.177436			−0.0887179	+	0.996057i	$0.528277\pi$
$98$		0			0
$99$	0.270780	+	0.270780i	0.0272144	+	0.0272144i
$100$		0			0
$101$	−5.10947	+	5.10947i	−0.508411	+	0.508411i	−0.914038	−	0.405628i	$-0.867053\pi$
$101$	−5.10947	+	5.10947i	−0.508411	+	0.508411i	0.405628	+	0.914038i	$0.367053\pi$
$102$		0			0
$103$			1.35833i			0.133840i	0.997758	+	0.0669202i	$0.0213173\pi$
$103$			1.35833i			0.133840i	−0.997758	+	0.0669202i	$0.978683\pi$
$104$		0			0
$105$			1.41421i			0.138013i
$106$		0			0
$107$	0.348138	−	0.348138i	0.0336557	−	0.0336557i	−0.690079	−	0.723734i	$-0.742424\pi$
$107$	0.348138	−	0.348138i	0.0336557	−	0.0336557i	0.723734	+	0.690079i	$0.242424\pi$
$108$		0			0
$109$	−6.70108	−	6.70108i	−0.641847	−	0.641847i	0.309162	−	0.951009i	$-0.399951\pi$
$109$	−6.70108	−	6.70108i	−0.641847	−	0.641847i	−0.951009	+	0.309162i	$0.899951\pi$
$110$		0			0
$111$	−14.6252			−1.38816
$112$		0			0
$113$	−14.1747			−1.33344			−0.666722	−	0.745306i	$-0.732303\pi$
$113$	−14.1747			−1.33344			−0.666722	+	0.745306i	$0.732303\pi$
$114$		0			0
$115$	−2.33490	−	2.33490i	−0.217731	−	0.217731i
$116$		0			0
$117$	0.216915	−	0.216915i	0.0200538	−	0.0200538i
$118$		0			0
$119$			2.47363i			0.226757i
$120$		0			0
$121$		−	30.5443i		−	2.77675i
$122$		0			0
$123$	−6.76549	+	6.76549i	−0.610023	+	0.610023i
$124$		0			0
$125$	−5.34343	−	5.34343i	−0.477931	−	0.477931i
$126$		0			0
$127$	0.457538			0.0405999			0.0203000	−	0.999794i	$-0.493538\pi$
$127$	0.457538			0.0405999			0.0203000	+	0.999794i	$0.493538\pi$
$128$		0			0
$129$	−10.7721			−0.948435
$130$		0			0
$131$	−5.75966	−	5.75966i	−0.503224	−	0.503224i	0.409215	−	0.912438i	$-0.365803\pi$
$131$	−5.75966	−	5.75966i	−0.503224	−	0.503224i	−0.912438	+	0.409215i	$0.865803\pi$
$132$		0			0
$133$	−5.54358	+	5.54358i	−0.480689	+	0.480689i
$134$		0			0
$135$		−	4.15862i		−	0.357917i
$136$		0			0
$137$		−	5.60764i		−	0.479093i	−0.970885	−	0.239546i	$-0.923001\pi$
$137$		−	5.60764i		−	0.479093i	0.970885	−	0.239546i	$-0.0769987\pi$
$138$		0			0
$139$	−7.03239	+	7.03239i	−0.596479	+	0.596479i	−0.939374	−	0.342894i	$-0.888593\pi$
$139$	−7.03239	+	7.03239i	−0.596479	+	0.596479i	0.342894	+	0.939374i	$0.388593\pi$
$140$		0			0
$141$	8.00666	+	8.00666i	0.674283	+	0.674283i
$142$		0			0
$143$	−33.2802			−2.78303
$144$		0			0
$145$	4.91911			0.408510
$146$		0			0
$147$	1.23681	+	1.23681i	0.102011	+	0.102011i
$148$		0			0
$149$	11.4947	−	11.4947i	0.941683	−	0.941683i	−0.0567079	−	0.998391i	$-0.518060\pi$
$149$	11.4947	−	11.4947i	0.941683	−	0.941683i	0.998391	+	0.0567079i	$0.0180604\pi$
$150$		0			0
$151$			0.863230i			0.0702487i	0.999383	+	0.0351243i	$0.0111827\pi$
$151$			0.863230i			0.0702487i	−0.999383	+	0.0351243i	$0.988817\pi$
$152$		0			0
$153$			0.146964i			0.0118813i
$154$		0			0
$155$	−0.585786	+	0.585786i	−0.0470515	+	0.0470515i
$156$		0			0
$157$	−1.83778	−	1.83778i	−0.146671	−	0.146671i	0.629958	−	0.776629i	$-0.283072\pi$
$157$	−1.83778	−	1.83778i	−0.146671	−	0.146671i	−0.776629	+	0.629958i	$0.783072\pi$
$158$		0			0
$159$	4.80029			0.380688
$160$		0			0
$161$	−4.08402			−0.321866
$162$		0			0
$163$	−4.27078	−	4.27078i	−0.334513	−	0.334513i	0.519784	−	0.854298i	$-0.326012\pi$
$163$	−4.27078	−	4.27078i	−0.334513	−	0.334513i	−0.854298	+	0.519784i	$0.826012\pi$
$164$		0			0
$165$	6.44549	−	6.44549i	0.501780	−	0.501780i
$166$		0			0
$167$		−	1.52637i		−	0.118114i	−0.998255	−	0.0590572i	$-0.981191\pi$
$167$		−	1.52637i		−	0.118114i	0.998255	−	0.0590572i	$-0.0188094\pi$
$168$		0			0
$169$			13.6600i			1.05077i
$170$		0			0
$171$	−0.329356	+	0.329356i	−0.0251865	+	0.0251865i
$172$		0			0
$173$	18.4232	+	18.4232i	1.40069	+	1.40069i	0.797905	+	0.602783i	$0.205941\pi$
$173$	18.4232	+	18.4232i	1.40069	+	1.40069i	0.602783	+	0.797905i	$0.294059\pi$
$174$		0			0
$175$	−4.34628			−0.328548
$176$		0			0
$177$	−17.0727			−1.28327
$178$		0			0
$179$	9.23412	+	9.23412i	0.690190	+	0.690190i	0.962274	−	0.272083i	$-0.0877126\pi$
$179$	9.23412	+	9.23412i	0.690190	+	0.690190i	−0.272083	+	0.962274i	$0.587713\pi$
$180$		0			0
$181$	−15.7683	+	15.7683i	−1.17205	+	1.17205i	−0.190325	+	0.981721i	$0.560954\pi$
$181$	−15.7683	+	15.7683i	−1.17205	+	1.17205i	−0.981721	+	0.190325i	$0.939046\pi$
$182$		0			0
$183$			19.4072i			1.43462i
$184$		0			0
$185$			6.76049i			0.497041i
$186$		0			0
$187$	11.2739	−	11.2739i	0.824430	−	0.824430i
$188$		0			0
$189$	−3.63696	−	3.63696i	−0.264550	−	0.264550i
$190$		0			0
$191$	25.9178			1.87535			0.937674	−	0.347517i	$-0.112975\pi$
$191$	25.9178			1.87535			0.937674	+	0.347517i	$0.112975\pi$
$192$		0			0
$193$	−11.4884			−0.826954			−0.413477	−	0.910515i	$-0.635686\pi$
$193$	−11.4884			−0.826954			−0.413477	+	0.910515i	$0.635686\pi$
$194$		0			0
$195$	−5.16333	−	5.16333i	−0.369754	−	0.369754i
$196$		0			0
$197$	17.9241	−	17.9241i	1.27704	−	1.27704i	0.334723	−	0.942317i	$-0.391357\pi$
$197$	17.9241	−	17.9241i	1.27704	−	1.27704i	0.942317	−	0.334723i	$-0.108643\pi$
$198$		0			0
$199$			2.34538i			0.166259i	0.996539	+	0.0831297i	$0.0264916\pi$
$199$			2.34538i			0.166259i	−0.996539	+	0.0831297i	$0.973508\pi$
$200$		0			0
$201$			9.60058i			0.677172i
$202$		0			0
$203$	4.30205	−	4.30205i	0.301945	−	0.301945i
$204$		0			0
$205$	3.12735	+	3.12735i	0.218423	+	0.218423i
$206$		0			0
$207$	−0.242641			−0.0168647
$208$		0			0
$209$	50.5313			3.49533
$210$		0			0
$211$	−4.94725	−	4.94725i	−0.340583	−	0.340583i	0.516004	−	0.856586i	$-0.327419\pi$
$211$	−4.94725	−	4.94725i	−0.340583	−	0.340583i	−0.856586	+	0.516004i	$0.827419\pi$
$212$		0			0
$213$	−11.6779	+	11.6779i	−0.800159	+	0.800159i
$214$		0			0
$215$			4.97943i			0.339594i
$216$		0			0
$217$			1.02461i			0.0695550i
$218$		0			0
$219$	−1.31854	+	1.31854i	−0.0890984	+	0.0890984i
$220$		0			0
$221$	−9.03127	−	9.03127i	−0.607509	−	0.607509i
$222$		0			0
$223$	−5.47233			−0.366454			−0.183227	−	0.983071i	$-0.558654\pi$
$223$	−5.47233			−0.366454			−0.183227	+	0.983071i	$0.558654\pi$
$224$		0			0
$225$	−0.258222			−0.0172148
$226$		0			0
$227$	5.59986	+	5.59986i	0.371675	+	0.371675i	0.868087	−	0.496412i	$-0.165349\pi$
$227$	5.59986	+	5.59986i	0.371675	+	0.371675i	−0.496412	+	0.868087i	$0.665349\pi$
$228$		0			0
$229$	−8.48888	+	8.48888i	−0.560961	+	0.560961i	−0.929580	−	0.368620i	$-0.879831\pi$
$229$	−8.48888	+	8.48888i	−0.560961	+	0.560961i	0.368620	+	0.929580i	$0.379831\pi$
$230$		0			0
$231$		−	11.2739i		−	0.741769i
$232$		0			0
$233$			0.673711i			0.0441363i	0.999756	+	0.0220682i	$0.00702508\pi$
$233$			0.673711i			0.0441363i	−0.999756	+	0.0220682i	$0.992975\pi$
$234$		0			0
$235$	3.70108	−	3.70108i	0.241432	−	0.241432i
$236$		0			0
$237$	−15.2623	−	15.2623i	−0.991390	−	0.991390i
$238$		0			0
$239$	17.4603			1.12941			0.564706	−	0.825292i	$-0.308990\pi$
$239$	17.4603			1.12941			0.564706	+	0.825292i	$0.308990\pi$
$240$		0			0
$241$	7.01519			0.451888			0.225944	−	0.974140i	$-0.427453\pi$
$241$	7.01519			0.451888			0.225944	+	0.974140i	$0.427453\pi$
$242$		0			0
$243$	−0.436525	−	0.436525i	−0.0280031	−	0.0280031i
$244$		0			0
$245$	0.571717	−	0.571717i	0.0365257	−	0.0365257i
$246$		0			0
$247$		−	40.4795i		−	2.57565i
$248$		0			0
$249$			14.0559i			0.890755i
$250$		0			0
$251$	−8.38248	+	8.38248i	−0.529097	+	0.529097i	−0.920303	−	0.391206i	$-0.872058\pi$
$251$	−8.38248	+	8.38248i	−0.529097	+	0.529097i	0.391206	+	0.920303i	$0.372058\pi$
$252$		0			0
$253$	18.6135	+	18.6135i	1.17022	+	1.17022i
$254$		0			0
$255$	3.49824			0.219068
$256$		0			0
$257$	9.28724			0.579322			0.289661	−	0.957129i	$-0.406457\pi$
$257$	9.28724			0.579322			0.289661	+	0.957129i	$0.406457\pi$
$258$		0			0
$259$	5.91245	+	5.91245i	0.367382	+	0.367382i
$260$		0			0
$261$	0.255594	−	0.255594i	0.0158209	−	0.0158209i
$262$		0			0
$263$		−	11.8547i		−	0.730993i	−0.930813	−	0.365496i	$-0.880899\pi$
$263$		−	11.8547i		−	0.730993i	0.930813	−	0.365496i	$-0.119101\pi$
$264$		0			0
$265$		−	2.21893i		−	0.136308i
$266$		0			0
$267$	−3.48658	+	3.48658i	−0.213375	+	0.213375i
$268$		0			0
$269$	0.902189	+	0.902189i	0.0550074	+	0.0550074i	0.734075	−	0.679068i	$-0.237616\pi$
$269$	0.902189	+	0.902189i	0.0550074	+	0.0550074i	−0.679068	+	0.734075i	$0.737616\pi$
$270$		0			0
$271$	19.2043			1.16658			0.583289	−	0.812264i	$-0.301765\pi$
$271$	19.2043			1.16658			0.583289	+	0.812264i	$0.301765\pi$
$272$		0			0
$273$	−9.03127			−0.546598
$274$		0			0
$275$	19.8088	+	19.8088i	1.19452	+	1.19452i
$276$		0			0
$277$	−23.0461	+	23.0461i	−1.38470	+	1.38470i	−0.548655	+	0.836049i	$0.684860\pi$
$277$	−23.0461	+	23.0461i	−1.38470	+	1.38470i	−0.836049	+	0.548655i	$0.815140\pi$
$278$		0			0
$279$			0.0608743i			0.00364445i
$280$		0			0
$281$		−	19.3459i		−	1.15408i	−0.816716	−	0.577039i	$-0.804208\pi$
$281$		−	19.3459i		−	1.15408i	0.816716	−	0.577039i	$-0.195792\pi$
$282$		0			0
$283$	−12.1935	+	12.1935i	−0.724828	+	0.724828i	−0.969584	−	0.244757i	$-0.921292\pi$
$283$	−12.1935	+	12.1935i	−0.724828	+	0.724828i	0.244757	+	0.969584i	$0.421292\pi$
$284$		0			0
$285$	7.83980	+	7.83980i	0.464390	+	0.464390i
$286$		0			0
$287$	5.47010			0.322890
$288$		0			0
$289$	−10.8812			−0.640069
$290$		0			0
$291$	2.16138	+	2.16138i	0.126702	+	0.126702i
$292$		0			0
$293$	14.5139	−	14.5139i	0.847909	−	0.847909i	−0.141963	−	0.989872i	$-0.545341\pi$
$293$	14.5139	−	14.5139i	0.847909	−	0.847909i	0.989872	+	0.141963i	$0.0453415\pi$
$294$		0			0
$295$			7.89188i			0.459483i
$296$		0			0
$297$			33.1519i			1.92367i
$298$		0			0
$299$	14.9109	−	14.9109i	0.862318	−	0.862318i
$300$		0			0
$301$	4.35480	+	4.35480i	0.251007	+	0.251007i
$302$		0			0
$303$	12.6389			0.726086
$304$		0			0
$305$	8.97096			0.513676
$306$		0			0
$307$	−12.6975	−	12.6975i	−0.724684	−	0.724684i	0.244872	−	0.969555i	$-0.421254\pi$
$307$	−12.6975	−	12.6975i	−0.724684	−	0.724684i	−0.969555	+	0.244872i	$0.921254\pi$
$308$		0			0
$309$	1.68000	−	1.68000i	0.0955719	−	0.0955719i
$310$		0			0
$311$		−	17.7155i		−	1.00455i	−0.864707	−	0.502277i	$-0.832496\pi$
$311$		−	17.7155i		−	1.00455i	0.864707	−	0.502277i	$-0.167504\pi$
$312$		0			0
$313$			13.7873i			0.779306i	0.920962	+	0.389653i	$0.127405\pi$
$313$			13.7873i			0.779306i	−0.920962	+	0.389653i	$0.872595\pi$
$314$		0			0
$315$	0.0339670	−	0.0339670i	0.00191382	−	0.00191382i
$316$		0			0
$317$	−8.95039	−	8.95039i	−0.502704	−	0.502704i	0.409573	−	0.912277i	$-0.365678\pi$
$317$	−8.95039	−	8.95039i	−0.502704	−	0.502704i	−0.912277	+	0.409573i	$0.865678\pi$
$318$		0			0
$319$	−39.2145			−2.19559
$320$		0			0
$321$	−0.861162			−0.0480654
$322$		0			0
$323$	13.7127	+	13.7127i	0.762997	+	0.762997i
$324$		0			0
$325$	15.8684	−	15.8684i	0.880219	−	0.880219i
$326$		0			0
$327$			16.5760i			0.916653i
$328$		0			0
$329$		−	6.47363i		−	0.356903i
$330$		0			0
$331$	−12.0509	+	12.0509i	−0.662377	+	0.662377i	−0.955940	−	0.293563i	$-0.905159\pi$
$331$	−12.0509	+	12.0509i	−0.662377	+	0.662377i	0.293563	+	0.955940i	$0.405159\pi$
$332$		0			0
$333$	0.351272	+	0.351272i	0.0192496	+	0.0192496i
$334$		0			0
$335$	4.43787			0.242467
$336$		0			0
$337$	−7.50100			−0.408605			−0.204303	−	0.978908i	$-0.565493\pi$
$337$	−7.50100			−0.408605			−0.204303	+	0.978908i	$0.565493\pi$
$338$		0			0
$339$	17.5315	+	17.5315i	0.952178	+	0.952178i
$340$		0			0
$341$	4.66981	−	4.66981i	0.252884	−	0.252884i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			5.77568i			0.310952i
$346$		0			0
$347$	−16.9589	+	16.9589i	−0.910402	+	0.910402i	−0.996304	−	0.0859018i	$-0.972623\pi$
$347$	−16.9589	+	16.9589i	−0.910402	+	0.910402i	0.0859018	+	0.996304i	$0.472623\pi$
$348$		0			0
$349$	−12.4131	−	12.4131i	−0.664458	−	0.664458i	0.291970	−	0.956428i	$-0.405689\pi$
$349$	−12.4131	−	12.4131i	−0.664458	−	0.664458i	−0.956428	+	0.291970i	$0.905689\pi$
$350$		0			0
$351$	26.5573			1.41752
$352$		0			0
$353$	4.71903			0.251168			0.125584	−	0.992083i	$-0.459919\pi$
$353$	4.71903			0.251168			0.125584	+	0.992083i	$0.459919\pi$
$354$		0			0
$355$	5.39813	+	5.39813i	0.286503	+	0.286503i
$356$		0			0
$357$	3.05941	−	3.05941i	0.161921	−	0.161921i
$358$		0			0
$359$			6.09029i			0.321433i	0.987001	+	0.160717i	$0.0513805\pi$
$359$			6.09029i			0.321433i	−0.987001	+	0.160717i	$0.948619\pi$
$360$		0			0
$361$			42.4625i			2.23487i
$362$		0			0
$363$	−37.7776	+	37.7776i	−1.98281	+	1.98281i
$364$		0			0
$365$	0.609494	+	0.609494i	0.0319024	+	0.0319024i
$366$		0			0
$367$	31.0286			1.61968			0.809841	−	0.586649i	$-0.199553\pi$
$367$	31.0286			1.61968			0.809841	+	0.586649i	$0.199553\pi$
$368$		0			0
$369$	0.324990			0.0169183
$370$		0			0
$371$	−1.94059	−	1.94059i	−0.100750	−	0.100750i
$372$		0			0
$373$	4.96021	−	4.96021i	0.256830	−	0.256830i	−0.566934	−	0.823763i	$-0.691870\pi$
$373$	4.96021	−	4.96021i	0.256830	−	0.256830i	0.823763	+	0.566934i	$0.191870\pi$
$374$		0			0
$375$			13.2176i			0.682556i
$376$		0			0
$377$			31.4138i			1.61789i
$378$		0			0
$379$	10.6815	−	10.6815i	0.548670	−	0.548670i	−0.377386	−	0.926056i	$-0.623177\pi$
$379$	10.6815	−	10.6815i	0.548670	−	0.548670i	0.926056	+	0.377386i	$0.123177\pi$
$380$		0			0
$381$	−0.565889	−	0.565889i	−0.0289914	−	0.0289914i
$382$		0			0
$383$	−9.43030			−0.481866			−0.240933	−	0.970542i	$-0.577453\pi$
$383$	−9.43030			−0.481866			−0.240933	+	0.970542i	$0.577453\pi$
$384$		0			0
$385$	−5.21137			−0.265596
$386$		0			0
$387$	0.258728	+	0.258728i	0.0131519	+	0.0131519i
$388$		0			0
$389$	−6.33462	+	6.33462i	−0.321178	+	0.321178i	−0.849219	−	0.528041i	$-0.822927\pi$
$389$	−6.33462	+	6.33462i	−0.321178	+	0.321178i	0.528041	+	0.849219i	$0.322927\pi$
$390$		0			0
$391$			10.1023i			0.510897i
$392$		0			0
$393$			14.2472i			0.718678i
$394$		0			0
$395$	−7.05498	+	7.05498i	−0.354975	+	0.354975i
$396$		0			0
$397$	17.6080	+	17.6080i	0.883719	+	0.883719i	0.993910	−	0.110191i	$-0.0351463\pi$
$397$	17.6080	+	17.6080i	0.883719	+	0.883719i	−0.110191	+	0.993910i	$0.535146\pi$
$398$		0			0
$399$	13.7127			0.686495
$400$		0			0
$401$	24.7529			1.23610			0.618051	−	0.786138i	$-0.287923\pi$
$401$	24.7529			1.23610			0.618051	+	0.786138i	$0.287923\pi$
$402$		0			0
$403$	−3.74088	−	3.74088i	−0.186346	−	0.186346i
$404$		0			0
$405$	−5.24533	+	5.24533i	−0.260643	+	0.260643i
$406$		0			0
$407$		−	53.8937i		−	2.67141i
$408$		0			0
$409$		−	21.6913i		−	1.07256i	−0.844039	−	0.536282i	$-0.819828\pi$
$409$		−	21.6913i		−	1.07256i	0.844039	−	0.536282i	$-0.180172\pi$
$410$		0			0
$411$	−6.93560	+	6.93560i	−0.342108	+	0.342108i
$412$		0			0
$413$	6.90191	+	6.90191i	0.339621	+	0.339621i
$414$		0			0
$415$	6.49733			0.318942
$416$		0			0
$417$	17.3955			0.851861
$418$		0			0
$419$	7.39320	+	7.39320i	0.361181	+	0.361181i	0.864248	−	0.503066i	$-0.167795\pi$
$419$	7.39320	+	7.39320i	0.361181	+	0.361181i	−0.503066	+	0.864248i	$0.667795\pi$
$420$		0			0
$421$	−4.59821	+	4.59821i	−0.224103	+	0.224103i	−0.810224	−	0.586121i	$-0.800654\pi$
$421$	−4.59821	+	4.59821i	−0.224103	+	0.224103i	0.586121	+	0.810224i	$0.300654\pi$
$422$		0			0
$423$		−	0.384612i		−	0.0187005i
$424$		0			0
$425$			10.7511i			0.521503i
$426$		0			0
$427$	7.84563	−	7.84563i	0.379677	−	0.379677i
$428$		0			0
$429$	41.1614	+	41.1614i	1.98729	+	1.98729i
$430$		0			0
$431$	−10.3842			−0.500190			−0.250095	−	0.968221i	$-0.580462\pi$
$431$	−10.3842			−0.500190			−0.250095	+	0.968221i	$0.580462\pi$
$432$		0			0
$433$	27.6476			1.32866			0.664329	−	0.747441i	$-0.268718\pi$
$433$	27.6476			1.32866			0.664329	+	0.747441i	$0.268718\pi$
$434$		0			0
$435$	−6.08402	−	6.08402i	−0.291707	−	0.291707i
$436$		0			0
$437$	−22.6401	+	22.6401i	−1.08302	+	1.08302i
$438$		0			0
$439$		−	33.2404i		−	1.58648i	−0.608911	−	0.793239i	$-0.708393\pi$
$439$		−	33.2404i		−	1.58648i	0.608911	−	0.793239i	$-0.291607\pi$
$440$		0			0
$441$		−	0.0594122i		−	0.00282915i
$442$		0			0
$443$	21.8780	−	21.8780i	1.03946	−	1.03946i	0.0402671	−	0.999189i	$-0.487179\pi$
$443$	21.8780	−	21.8780i	1.03946	−	1.03946i	0.999189	−	0.0402671i	$-0.0128209\pi$
$444$		0			0
$445$	1.61167	+	1.61167i	0.0764006	+	0.0764006i
$446$		0			0
$447$	−28.4336			−1.34486
$448$		0			0
$449$	15.9670			0.753531			0.376765	−	0.926309i	$-0.377036\pi$
$449$	15.9670			0.753531			0.376765	+	0.926309i	$0.377036\pi$
$450$		0			0
$451$	−24.9308	−	24.9308i	−1.17394	−	1.17394i
$452$		0			0
$453$	1.06765	−	1.06765i	0.0501628	−	0.0501628i
$454$		0			0
$455$			4.17471i			0.195713i
$456$		0			0
$457$		−	8.09512i		−	0.378674i	−0.981912	−	0.189337i	$-0.939366\pi$
$457$		−	8.09512i		−	0.378674i	0.981912	−	0.189337i	$-0.0606338\pi$
$458$		0			0
$459$	−8.99647	+	8.99647i	−0.419919	+	0.419919i
$460$		0			0
$461$	0.240227	+	0.240227i	0.0111885	+	0.0111885i	0.712679	−	0.701490i	$-0.247482\pi$
$461$	0.240227	+	0.240227i	0.0111885	+	0.0111885i	−0.701490	+	0.712679i	$0.747482\pi$
$462$		0			0
$463$	10.7400			0.499129			0.249564	−	0.968358i	$-0.419713\pi$
$463$	10.7400			0.499129			0.249564	+	0.968358i	$0.419713\pi$
$464$		0			0
$465$	1.44902			0.0671965
$466$		0			0
$467$	6.77143	+	6.77143i	0.313344	+	0.313344i	0.846204	−	0.532859i	$-0.178883\pi$
$467$	6.77143	+	6.77143i	0.313344	+	0.313344i	−0.532859	+	0.846204i	$0.678883\pi$
$468$		0			0
$469$	3.88118	−	3.88118i	0.179216	−	0.179216i
$470$		0			0
$471$			4.54599i			0.209468i
$472$		0			0
$473$		−	39.6953i		−	1.82519i
$474$		0			0
$475$	−24.0939	+	24.0939i	−1.10551	+	1.10551i
$476$		0			0
$477$	−0.115295	−	0.115295i	−0.00527898	−	0.00527898i
$478$		0			0
$479$	−20.7472			−0.947962			−0.473981	−	0.880535i	$-0.657184\pi$
$479$	−20.7472			−0.947962			−0.473981	+	0.880535i	$0.657184\pi$
$480$		0			0
$481$	−43.1730			−1.96852
$482$		0			0
$483$	5.05117	+	5.05117i	0.229836	+	0.229836i
$484$		0			0
$485$	0.999098	−	0.999098i	0.0453667	−	0.0453667i
$486$		0			0
$487$		−	5.57283i		−	0.252529i	−0.991997	−	0.126265i	$-0.959701\pi$
$487$		−	5.57283i		−	0.252529i	0.991997	−	0.126265i	$-0.0402988\pi$
$488$		0			0
$489$			10.5643i			0.477735i
$490$		0			0
$491$	16.4196	−	16.4196i	0.741005	−	0.741005i	−0.231766	−	0.972772i	$-0.574450\pi$
$491$	16.4196	−	16.4196i	0.741005	−	0.741005i	0.972772	+	0.231766i	$0.0744505\pi$
$492$		0			0
$493$	−10.6417	−	10.6417i	−0.479277	−	0.479277i
$494$		0			0
$495$	−0.309619			−0.0139163
$496$		0			0
$497$	9.44196			0.423530
$498$		0			0
$499$	−17.7731	−	17.7731i	−0.795631	−	0.795631i	0.186772	−	0.982403i	$-0.440197\pi$
$499$	−17.7731	−	17.7731i	−0.795631	−	0.795631i	−0.982403	+	0.186772i	$0.940197\pi$
$500$		0			0
$501$	−1.88784	+	1.88784i	−0.0843424	+	0.0843424i
$502$		0			0
$503$			20.9839i			0.935625i	0.883828	+	0.467813i	$0.154958\pi$
$503$			20.9839i			0.935625i	−0.883828	+	0.467813i	$0.845042\pi$
$504$		0			0
$505$		−	5.84234i		−	0.259981i
$506$		0			0
$507$	16.8948	−	16.8948i	0.750327	−	0.750327i
$508$		0			0
$509$	2.90544	+	2.90544i	0.128781	+	0.128781i	0.768560	−	0.639778i	$-0.220974\pi$
$509$	2.90544	+	2.90544i	0.128781	+	0.128781i	−0.639778	+	0.768560i	$0.720974\pi$
$510$		0			0
$511$	1.06608			0.0471604
$512$		0			0
$513$	−40.3235			−1.78033
$514$		0			0
$515$	−0.776581	−	0.776581i	−0.0342202	−	0.0342202i
$516$		0			0
$517$	−29.5045	+	29.5045i	−1.29761	+	1.29761i
$518$		0			0
$519$		−	45.5720i		−	2.00039i
$520$		0			0
$521$		−	1.02225i		−	0.0447854i	−0.999749	−	0.0223927i	$-0.992872\pi$
$521$		−	1.02225i		−	0.0447854i	0.999749	−	0.0223927i	$-0.00712841\pi$
$522$		0			0
$523$	−22.2532	+	22.2532i	−0.973064	+	0.973064i	−0.999647	−	0.0265830i	$-0.991537\pi$
$523$	−22.2532	+	22.2532i	−0.973064	+	0.973064i	0.0265830	+	0.999647i	$0.491537\pi$
$524$		0			0
$525$	5.37553	+	5.37553i	0.234608	+	0.234608i
$526$		0			0
$527$	2.53450			0.110405
$528$		0			0
$529$	6.32077			0.274816
$530$		0			0
$531$	0.410058	+	0.410058i	0.0177950	+	0.0177950i
$532$		0			0
$533$	−19.9715	+	19.9715i	−0.865060	+	0.865060i
$534$		0			0
$535$			0.398072i			0.0172102i
$536$		0			0
$537$		−	22.8418i		−	0.985694i
$538$		0			0
$539$	−4.55765	+	4.55765i	−0.196312	+	0.196312i
$540$		0			0
$541$	11.1188	+	11.1188i	0.478036	+	0.478036i	0.904503	−	0.426467i	$-0.140242\pi$
$541$	11.1188	+	11.1188i	0.478036	+	0.478036i	−0.426467	+	0.904503i	$0.640242\pi$
$542$		0			0
$543$	39.0048			1.67386
$544$		0			0
$545$	7.66224			0.328214
$546$		0			0
$547$	17.7261	+	17.7261i	0.757912	+	0.757912i	0.975942	−	0.218030i	$-0.0699631\pi$
$547$	17.7261	+	17.7261i	0.757912	+	0.757912i	−0.218030	+	0.975942i	$0.569963\pi$
$548$		0			0
$549$	0.466126	−	0.466126i	0.0198938	−	0.0198938i
$550$		0			0
$551$		−	47.6975i		−	2.03198i
$552$		0			0
$553$			12.3400i			0.524750i
$554$		0			0
$555$	8.36147	−	8.36147i	0.354924	−	0.354924i
$556$		0			0
$557$	14.1751	+	14.1751i	0.600617	+	0.600617i	0.940476	−	0.339859i	$-0.110379\pi$
$557$	14.1751	+	14.1751i	0.600617	+	0.600617i	−0.339859	+	0.940476i	$0.610379\pi$
$558$		0			0
$559$	−31.7990			−1.34495
$560$		0			0
$561$	−27.8874			−1.17741
$562$		0			0
$563$	−0.484561	−	0.484561i	−0.0204218	−	0.0204218i	0.696822	−	0.717244i	$-0.254597\pi$
$563$	−0.484561	−	0.484561i	−0.0204218	−	0.0204218i	−0.717244	+	0.696822i	$0.754597\pi$
$564$		0			0
$565$	8.10392	−	8.10392i	0.340934	−	0.340934i
$566$		0			0
$567$			9.17471i			0.385301i
$568$		0			0
$569$			9.22040i			0.386539i	0.981146	+	0.193270i	$0.0619092\pi$
$569$			9.22040i			0.386539i	−0.981146	+	0.193270i	$0.938091\pi$
$570$		0			0
$571$	1.47325	−	1.47325i	0.0616537	−	0.0616537i	−0.675608	−	0.737261i	$-0.736119\pi$
$571$	1.47325	−	1.47325i	0.0616537	−	0.0616537i	0.737261	+	0.675608i	$0.236119\pi$
$572$		0			0
$573$	−32.0555	−	32.0555i	−1.33914	−	1.33914i
$574$		0			0
$575$	−17.7503			−0.740239
$576$		0			0
$577$	40.4518			1.68403			0.842014	−	0.539455i	$-0.181370\pi$
$577$	40.4518			1.68403			0.842014	+	0.539455i	$0.181370\pi$
$578$		0			0
$579$	14.2090	+	14.2090i	0.590507	+	0.590507i
$580$		0			0
$581$	5.68230	−	5.68230i	0.235742	−	0.235742i
$582$		0			0
$583$			17.6890i			0.732605i
$584$		0			0
$585$			0.248028i			0.0102547i
$586$		0			0
$587$	2.58467	−	2.58467i	0.106681	−	0.106681i	−0.651752	−	0.758432i	$-0.725966\pi$
$587$	2.58467	−	2.58467i	0.106681	−	0.106681i	0.758432	+	0.651752i	$0.225966\pi$
$588$		0			0
$589$	5.68000	+	5.68000i	0.234040	+	0.234040i
$590$		0			0
$591$	−44.3375			−1.82380
$592$		0			0
$593$	−37.8610			−1.55476			−0.777382	−	0.629029i	$-0.783453\pi$
$593$	−37.8610			−1.55476			−0.777382	+	0.629029i	$0.783453\pi$
$594$		0			0
$595$	−1.41421	−	1.41421i	−0.0579771	−	0.0579771i
$596$		0			0
$597$	2.90079	−	2.90079i	0.118722	−	0.118722i
$598$		0			0
$599$		−	1.42807i		−	0.0583493i	−0.999574	−	0.0291747i	$-0.990712\pi$
$599$		−	1.42807i		−	0.0583493i	0.999574	−	0.0291747i	$-0.00928790\pi$
$600$		0			0
$601$			35.2990i			1.43988i	0.694038	+	0.719939i	$0.255830\pi$
$601$			35.2990i			1.43988i	−0.694038	+	0.719939i	$0.744170\pi$
$602$		0			0
$603$	0.230589	−	0.230589i	0.00939032	−	0.00939032i
$604$		0			0
$605$	17.4627	+	17.4627i	0.709959	+	0.709959i
$606$		0			0
$607$	23.4364			0.951256			0.475628	−	0.879647i	$-0.342221\pi$
$607$	23.4364			0.951256			0.475628	+	0.879647i	$0.342221\pi$
$608$		0			0
$609$	−10.6417			−0.431222
$610$		0			0
$611$	23.6354	+	23.6354i	0.956185	+	0.956185i
$612$		0			0
$613$	13.4964	−	13.4964i	0.545114	−	0.545114i	−0.379910	−	0.925023i	$-0.624045\pi$
$613$	13.4964	−	13.4964i	0.545114	−	0.545114i	0.925023	+	0.379910i	$0.124045\pi$
$614$		0			0
$615$		−	7.73588i		−	0.311941i
$616$		0			0
$617$			0.504525i			0.0203114i	0.999948	+	0.0101557i	$0.00323272\pi$
$617$			0.504525i			0.0203114i	−0.999948	+	0.0101557i	$0.996767\pi$
$618$		0			0
$619$	−23.6377	+	23.6377i	−0.950078	+	0.950078i	−0.998812	−	0.0487334i	$-0.984482\pi$
$619$	−23.6377	+	23.6377i	−0.950078	+	0.950078i	0.0487334	+	0.998812i	$0.484482\pi$
$620$		0			0
$621$	−14.8534	−	14.8534i	−0.596047	−	0.596047i
$622$		0			0
$623$	2.81900			0.112941
$624$		0			0
$625$	−15.6215			−0.624862
$626$		0			0
$627$	−62.4978	−	62.4978i	−2.49592	−	2.49592i
$628$		0			0
$629$	14.6252	−	14.6252i	0.583144	−	0.583144i
$630$		0			0
$631$			38.0329i			1.51407i	0.653376	+	0.757033i	$0.273352\pi$
$631$			38.0329i			1.51407i	−0.653376	+	0.757033i	$0.726648\pi$
$632$		0			0
$633$			12.2376i			0.486403i
$634$		0			0
$635$	−0.261582	+	0.261582i	−0.0103806	+	0.0103806i
$636$		0			0
$637$	3.65103	+	3.65103i	0.144659	+	0.144659i
$638$		0			0
$639$	0.560967			0.0221915
$640$		0			0
$641$	44.2113			1.74624			0.873122	−	0.487503i	$-0.162092\pi$
$641$	44.2113			1.74624			0.873122	+	0.487503i	$0.162092\pi$
$642$		0			0
$643$	−7.98280	−	7.98280i	−0.314811	−	0.314811i	0.531959	−	0.846770i	$-0.321456\pi$
$643$	−7.98280	−	7.98280i	−0.314811	−	0.314811i	−0.846770	+	0.531959i	$0.821456\pi$
$644$		0			0
$645$	6.15862	−	6.15862i	0.242495	−	0.242495i
$646$		0			0
$647$			46.5922i			1.83173i	0.401487	+	0.915865i	$0.368493\pi$
$647$			46.5922i			1.83173i	−0.401487	+	0.915865i	$0.631507\pi$
$648$		0			0
$649$		−	62.9129i		−	2.46955i
$650$		0			0
$651$	1.26725	−	1.26725i	0.0496674	−	0.0496674i
$652$		0			0
$653$	28.1497	+	28.1497i	1.10158	+	1.10158i	0.994220	+	0.107363i	$0.0342407\pi$
$653$	28.1497	+	28.1497i	1.10158	+	1.10158i	0.107363	+	0.994220i	$0.465759\pi$
$654$		0			0
$655$	6.58579			0.257328
$656$		0			0
$657$	0.0633379			0.00247105
$658$		0			0
$659$	12.5741	+	12.5741i	0.489819	+	0.489819i	0.908249	−	0.418430i	$-0.137420\pi$
$659$	12.5741	+	12.5741i	0.489819	+	0.489819i	−0.418430	+	0.908249i	$0.637420\pi$
$660$		0			0
$661$	7.13055	−	7.13055i	0.277346	−	0.277346i	−0.554703	−	0.832049i	$-0.687168\pi$
$661$	7.13055	−	7.13055i	0.277346	−	0.277346i	0.832049	+	0.554703i	$0.187168\pi$
$662$		0			0
$663$			22.3400i			0.867613i
$664$		0			0
$665$		−	6.33871i		−	0.245805i
$666$		0			0
$667$	17.5697	−	17.5697i	0.680301	−	0.680301i
$668$		0			0
$669$	6.76825	+	6.76825i	0.261675	+	0.261675i
$670$		0			0
$671$	−71.5152			−2.76081
$672$		0			0
$673$	−34.0500			−1.31253			−0.656265	−	0.754531i	$-0.727865\pi$
$673$	−34.0500			−1.31253			−0.656265	+	0.754531i	$0.727865\pi$
$674$		0			0
$675$	−15.8072	−	15.8072i	−0.608421	−	0.608421i
$676$		0			0
$677$	15.7666	−	15.7666i	0.605960	−	0.605960i	−0.335928	−	0.941888i	$-0.609050\pi$
$677$	15.7666	−	15.7666i	0.605960	−	0.605960i	0.941888	+	0.335928i	$0.109050\pi$
$678$		0			0
$679$		−	1.74754i		−	0.0670644i
$680$		0			0
$681$		−	13.8519i		−	0.530808i
$682$		0			0
$683$	−30.5756	+	30.5756i	−1.16994	+	1.16994i	−0.187719	+	0.982223i	$0.560109\pi$
$683$	−30.5756	+	30.5756i	−1.16994	+	1.16994i	−0.982223	+	0.187719i	$0.939891\pi$
$684$		0			0
$685$	3.20598	+	3.20598i	0.122494	+	0.122494i
$686$		0			0
$687$	20.9983			0.801135
$688$		0			0
$689$	14.1703			0.539844
$690$		0			0
$691$	3.97140	+	3.97140i	0.151079	+	0.151079i	0.778600	−	0.627521i	$-0.215930\pi$
$691$	3.97140	+	3.97140i	0.151079	+	0.151079i	−0.627521	+	0.778600i	$0.715930\pi$
$692$		0			0
$693$	−0.270780	+	0.270780i	−0.0102861	+	0.0102861i
$694$		0			0
$695$		−	8.04107i		−	0.305015i
$696$		0			0
$697$		−	13.5310i		−	0.512522i
$698$		0			0
$699$	0.833255	−	0.833255i	0.0315166	−	0.0315166i
$700$		0			0
$701$	21.4532	+	21.4532i	0.810278	+	0.810278i	0.984675	−	0.174398i	$-0.0557978\pi$
$701$	21.4532	+	21.4532i	0.810278	+	0.810278i	−0.174398	+	0.984675i	$0.555798\pi$
$702$		0			0
$703$	65.5522			2.47235
$704$		0			0
$705$	−9.15509			−0.344801
$706$		0			0
$707$	−5.10947	−	5.10947i	−0.192161	−	0.192161i
$708$		0			0
$709$	−2.30481	+	2.30481i	−0.0865591	+	0.0865591i	−0.749061	−	0.662502i	$-0.769495\pi$
$709$	−2.30481	+	2.30481i	−0.0865591	+	0.0865591i	0.662502	+	0.749061i	$0.269495\pi$
$710$		0			0
$711$			0.733146i			0.0274951i
$712$		0			0
$713$			4.18453i			0.156712i
$714$		0			0
$715$	19.0268	−	19.0268i	0.711564	−	0.711564i
$716$		0			0
$717$	−21.5951	−	21.5951i	−0.806484	−	0.806484i
$718$		0			0
$719$	−27.8530			−1.03874			−0.519371	−	0.854549i	$-0.673834\pi$
$719$	−27.8530			−1.03874			−0.519371	+	0.854549i	$0.673834\pi$
$720$		0			0
$721$	−1.35833			−0.0505869
$722$		0			0
$723$	−8.67647	−	8.67647i	−0.322681	−	0.322681i
$724$		0			0
$725$	18.6979	−	18.6979i	0.694423	−	0.694423i
$726$		0			0
$727$			4.56027i			0.169131i	0.996418	+	0.0845656i	$0.0269503\pi$
$727$			4.56027i			0.169131i	−0.996418	+	0.0845656i	$0.973050\pi$
$728$		0			0
$729$		−	26.4443i		−	0.979419i
$730$		0			0
$731$	10.7721	−	10.7721i	0.398422	−	0.398422i
$732$		0			0
$733$	−29.8784	−	29.8784i	−1.10358	−	1.10358i	−0.993975	−	0.109608i	$-0.965041\pi$
$733$	−29.8784	−	29.8784i	−1.10358	−	1.10358i	−0.109608	−	0.993975i	$-0.534959\pi$
$734$		0			0
$735$	−1.41421			−0.0521641
$736$		0			0
$737$	−35.3781			−1.30317
$738$		0			0
$739$	10.9312	+	10.9312i	0.402109	+	0.402109i	0.878976	−	0.476866i	$-0.158227\pi$
$739$	10.9312	+	10.9312i	0.402109	+	0.402109i	−0.476866	+	0.878976i	$0.658227\pi$
$740$		0			0
$741$	−50.0656	+	50.0656i	−1.83920	+	1.83920i
$742$		0			0
$743$			33.5354i			1.23029i	0.788412	+	0.615147i	$0.210903\pi$
$743$			33.5354i			1.23029i	−0.788412	+	0.615147i	$0.789097\pi$
$744$		0			0
$745$			13.1434i			0.481538i
$746$		0			0
$747$	0.337598	−	0.337598i	0.0123521	−	0.0123521i
$748$		0			0
$749$	0.348138	+	0.348138i	0.0127207	+	0.0127207i
$750$		0			0
$751$	16.7562			0.611442			0.305721	−	0.952121i	$-0.401102\pi$
$751$	16.7562			0.611442			0.305721	+	0.952121i	$0.401102\pi$
$752$		0			0
$753$	20.7351			0.755630
$754$		0			0
$755$	−0.493523	−	0.493523i	−0.0179611	−	0.0179611i
$756$		0			0
$757$	−10.2722	+	10.2722i	−0.373351	+	0.373351i	−0.868696	−	0.495345i	$-0.835042\pi$
$757$	−10.2722	+	10.2722i	−0.373351	+	0.373351i	0.495345	+	0.868696i	$0.335042\pi$
$758$		0			0
$759$		−	46.0429i		−	1.67125i
$760$		0			0
$761$		−	1.54207i		−	0.0558998i	−0.999609	−	0.0279499i	$-0.991102\pi$
$761$		−	1.54207i		−	0.0558998i	0.999609	−	0.0279499i	$-0.00889790\pi$
$762$		0			0
$763$	6.70108	−	6.70108i	0.242595	−	0.242595i
$764$		0			0
$765$	−0.0840215	−	0.0840215i	−0.00303780	−	0.00303780i
$766$		0			0
$767$	−50.3981			−1.81977
$768$		0			0
$769$	32.1627			1.15982			0.579908	−	0.814682i	$-0.303089\pi$
$769$	32.1627			1.15982			0.579908	+	0.814682i	$0.303089\pi$
$770$		0			0
$771$	−11.4866	−	11.4866i	−0.413679	−	0.413679i
$772$		0			0
$773$	20.9593	−	20.9593i	0.753852	−	0.753852i	−0.221344	−	0.975196i	$-0.571044\pi$
$773$	20.9593	−	20.9593i	0.753852	−	0.753852i	0.975196	+	0.221344i	$0.0710443\pi$
$774$		0			0
$775$			4.45324i			0.159965i
$776$		0			0
$777$		−	14.6252i		−	0.524676i
$778$		0			0
$779$	30.3239	−	30.3239i	1.08647	−	1.08647i
$780$		0			0
$781$	−43.0331	−	43.0331i	−1.53985	−	1.53985i
$782$		0			0
$783$	31.2928			1.11831
$784$		0			0
$785$	2.10139			0.0750016
$786$		0			0
$787$	14.8158	+	14.8158i	0.528127	+	0.528127i	0.920014	−	0.391887i	$-0.128177\pi$
$787$	14.8158	+	14.8158i	0.528127	+	0.528127i	−0.391887	+	0.920014i	$0.628177\pi$
$788$		0			0
$789$	−14.6621	+	14.6621i	−0.521983	+	0.521983i
$790$		0			0
$791$		−	14.1747i		−	0.503995i
$792$		0			0
$793$			57.2892i			2.03440i
$794$		0			0
$795$	−2.74441	+	2.74441i	−0.0973340	+	0.0973340i
$796$		0			0
$797$	−35.4119	−	35.4119i	−1.25435	−	1.25435i	−0.953749	−	0.300605i	$-0.902811\pi$
$797$	−35.4119	−	35.4119i	−1.25435	−	1.25435i	−0.300605	−	0.953749i	$-0.597189\pi$
$798$		0			0
$799$	−16.0133			−0.566511
$800$		0			0
$801$	0.167483			0.00591773
$802$		0			0
$803$	−4.85880	−	4.85880i	−0.171463	−	0.171463i
$804$		0			0
$805$	2.33490	−	2.33490i	0.0822946	−	0.0822946i
$806$		0			0
$807$		−	2.23168i		−	0.0785588i
$808$		0			0
$809$		−	17.4359i		−	0.613012i	−0.951869	−	0.306506i	$-0.900840\pi$
$809$		−	17.4359i		−	0.613012i	0.951869	−	0.306506i	$-0.0991599\pi$
$810$		0			0
$811$	38.5546	−	38.5546i	1.35383	−	1.35383i	0.472506	−	0.881327i	$-0.343349\pi$
$811$	38.5546	−	38.5546i	1.35383	−	1.35383i	0.881327	−	0.472506i	$-0.156651\pi$
$812$		0			0
$813$	−23.7521	−	23.7521i	−0.833024	−	0.833024i
$814$		0			0
$815$	4.88335			0.171056
$816$		0			0
$817$	48.2824			1.68919
$818$		0			0
$819$	0.216915	+	0.216915i	0.00757964	+	0.00757964i
$820$		0			0
$821$	−12.1020	+	12.1020i	−0.422362	+	0.422362i	−0.886016	−	0.463655i	$-0.846538\pi$
$821$	−12.1020	+	12.1020i	−0.422362	+	0.422362i	0.463655	+	0.886016i	$0.346538\pi$
$822$		0			0
$823$			32.3555i			1.12784i	0.825829	+	0.563921i	$0.190708\pi$
$823$			32.3555i			1.12784i	−0.825829	+	0.563921i	$0.809292\pi$
$824$		0			0
$825$		−	48.9996i		−	1.70595i
$826$		0			0
$827$	11.2064	−	11.2064i	0.389684	−	0.389684i	−0.484891	−	0.874575i	$-0.661141\pi$
$827$	11.2064	−	11.2064i	0.389684	−	0.389684i	0.874575	+	0.484891i	$0.161141\pi$
$828$		0			0
$829$	−23.6494	−	23.6494i	−0.821379	−	0.821379i	0.164927	−	0.986306i	$-0.447261\pi$
$829$	−23.6494	−	23.6494i	−0.821379	−	0.821379i	−0.986306	+	0.164927i	$0.947261\pi$
$830$		0			0
$831$	57.0073			1.97756
$832$		0			0
$833$	−2.47363			−0.0857061
$834$		0			0
$835$	0.872654	+	0.872654i	0.0301994	+	0.0301994i
$836$		0			0
$837$	−3.72646	+	3.72646i	−0.128805	+	0.128805i
$838$		0			0
$839$			28.6777i			0.990066i	0.868874	+	0.495033i	$0.164844\pi$
$839$			28.6777i			0.990066i	−0.868874	+	0.495033i	$0.835156\pi$
$840$		0			0
$841$			8.01532i			0.276390i
$842$		0			0
$843$	−23.9272	+	23.9272i	−0.824098	+	0.824098i
$844$		0			0
$845$	−7.80965	−	7.80965i	−0.268660	−	0.268660i
$846$		0			0
$847$	30.5443			1.04951
$848$		0			0
$849$	30.1621			1.03516
$850$		0			0
$851$	24.1466	+	24.1466i	0.827734	+	0.827734i
$852$		0			0
$853$	24.0950	−	24.0950i	0.824998	−	0.824998i	−0.161822	−	0.986820i	$-0.551737\pi$
$853$	24.0950	−	24.0950i	0.824998	−	0.824998i	0.986820	+	0.161822i	$0.0517370\pi$
$854$		0			0
$855$		−	0.376597i		−	0.0128793i
$856$		0			0
$857$		−	38.8652i		−	1.32761i	−0.747906	−	0.663805i	$-0.768941\pi$
$857$		−	38.8652i		−	1.32761i	0.747906	−	0.663805i	$-0.231059\pi$
$858$		0			0
$859$	10.2051	−	10.2051i	0.348195	−	0.348195i	−0.511242	−	0.859437i	$-0.670814\pi$
$859$	10.2051	−	10.2051i	0.348195	−	0.348195i	0.859437	+	0.511242i	$0.170814\pi$
$860$		0			0
$861$	−6.76549	−	6.76549i	−0.230567	−	0.230567i
$862$		0			0
$863$	−21.8471			−0.743684			−0.371842	−	0.928296i	$-0.621274\pi$
$863$	−21.8471			−0.743684			−0.371842	+	0.928296i	$0.621274\pi$
$864$		0			0
$865$	−21.0657			−0.716255
$866$		0			0
$867$	13.4580	+	13.4580i	0.457057	+	0.457057i
$868$		0			0
$869$	56.2413	−	56.2413i	1.90786	−	1.90786i
$870$		0			0
$871$			28.3405i			0.960283i
$872$		0			0
$873$		−	0.103825i		−	0.00351395i
$874$		0			0
$875$	5.34343	−	5.34343i	0.180641	−	0.180641i
$876$		0			0
$877$	−26.6322	−	26.6322i	−0.899306	−	0.899306i	0.0960685	−	0.995375i	$-0.469373\pi$
$877$	−26.6322	−	26.6322i	−0.899306	−	0.899306i	−0.995375	+	0.0960685i	$0.969373\pi$
$878$		0			0
$879$	−35.9019			−1.21094
$880$		0			0
$881$	−4.11567			−0.138660			−0.0693302	−	0.997594i	$-0.522086\pi$
$881$	−4.11567			−0.138660			−0.0693302	+	0.997594i	$0.522086\pi$
$882$		0			0
$883$	−0.315403	−	0.315403i	−0.0106141	−	0.0106141i	0.701780	−	0.712394i	$-0.252389\pi$
$883$	−0.315403	−	0.315403i	−0.0106141	−	0.0106141i	−0.712394	+	0.701780i	$0.752389\pi$
$884$		0			0
$885$	9.76077	−	9.76077i	0.328105	−	0.328105i
$886$		0			0
$887$		−	20.5273i		−	0.689240i	−0.938742	−	0.344620i	$-0.888008\pi$
$887$		−	20.5273i		−	0.689240i	0.938742	−	0.344620i	$-0.111992\pi$
$888$		0			0
$889$			0.457538i			0.0153453i
$890$		0			0
$891$	41.8151	−	41.8151i	1.40086	−	1.40086i
$892$		0			0
$893$	−35.8870	−	35.8870i	−1.20091	−	1.20091i
$894$		0			0
$895$	−10.5586			−0.352935
$896$		0			0
$897$	−36.8839			−1.23152
$898$		0			0
$899$	−4.40792	−	4.40792i	−0.147012	−	0.147012i
$900$		0			0
$901$	−4.80029	+	4.80029i	−0.159921	+	0.159921i
$902$		0			0
$903$		−	10.7721i		−	0.358475i
$904$		0			0
$905$		−	18.0300i		−	0.599337i
$906$		0			0
$907$	6.78157	−	6.78157i	0.225178	−	0.225178i	−0.585497	−	0.810675i	$-0.699100\pi$
$907$	6.78157	−	6.78157i	0.225178	−	0.225178i	0.810675	+	0.585497i	$0.199100\pi$
$908$		0			0
$909$	−0.303565	−	0.303565i	−0.0100686	−	0.0100686i
$910$		0			0
$911$	30.5756			1.01301			0.506507	−	0.862236i	$-0.330936\pi$
$911$	30.5756			1.01301			0.506507	+	0.862236i	$0.330936\pi$
$912$		0			0
$913$	−51.7958			−1.71419
$914$		0			0
$915$	−11.0954	−	11.0954i	−0.366803	−	0.366803i
$916$		0			0
$917$	5.75966	−	5.75966i	0.190201	−	0.190201i
$918$		0			0
$919$			22.4777i			0.741470i	0.928739	+	0.370735i	$0.120894\pi$
$919$			22.4777i			0.741470i	−0.928739	+	0.370735i	$0.879106\pi$
$920$		0			0
$921$			31.4088i			1.03496i
$922$		0			0
$923$	−34.4728	+	34.4728i	−1.13469	+	1.13469i
$924$		0			0
$925$	25.6972	+	25.6972i	0.844917	+	0.844917i
$926$		0			0
$927$	−0.0807014			−0.00265058
$928$		0			0
$929$	15.3955			0.505111			0.252555	−	0.967582i	$-0.418729\pi$
$929$	15.3955			0.505111			0.252555	+	0.967582i	$0.418729\pi$
$930$		0			0
$931$	−5.54358	−	5.54358i	−0.181683	−	0.181683i
$932$		0			0
$933$	−21.9108	+	21.9108i	−0.717326	+	0.717326i
$934$		0			0
$935$			12.8910i			0.421580i
$936$		0			0
$937$			29.4553i			0.962262i	0.876649	+	0.481131i	$0.159774\pi$
$937$			29.4553i			0.962262i	−0.876649	+	0.481131i	$0.840226\pi$
$938$		0			0
$939$	17.0524	−	17.0524i	0.556482	−	0.556482i
$940$		0			0
$941$	10.2529	+	10.2529i	0.334235	+	0.334235i	0.854192	−	0.519957i	$-0.174052\pi$
$941$	10.2529	+	10.2529i	0.334235	+	0.334235i	−0.519957	+	0.854192i	$0.674052\pi$
$942$		0			0
$943$	22.3400			0.727490
$944$		0			0
$945$	4.15862			0.135280
$946$		0			0
$947$	31.6627	+	31.6627i	1.02890	+	1.02890i	0.999570	+	0.0293306i	$0.00933755\pi$
$947$	31.6627	+	31.6627i	1.02890	+	1.02890i	0.0293306	+	0.999570i	$0.490662\pi$
$948$		0			0
$949$	−3.89227	+	3.89227i	−0.126348	+	0.126348i
$950$		0			0
$951$			22.1399i			0.717936i
$952$		0			0
$953$			21.7024i			0.703008i	0.936186	+	0.351504i	$0.114330\pi$
$953$			21.7024i			0.703008i	−0.936186	+	0.351504i	$0.885670\pi$
$954$		0			0
$955$	−14.8177	+	14.8177i	−0.479488	+	0.479488i
$956$		0			0
$957$	48.5010	+	48.5010i	1.56781	+	1.56781i
$958$		0			0
$959$	5.60764			0.181080
$960$		0			0
$961$	−29.9502			−0.966135
$962$		0			0
$963$	0.0206836	+	0.0206836i	0.000666520	+	0.000666520i
$964$		0			0
$965$	6.56812	−	6.56812i	0.211435	−	0.211435i
$966$		0			0
$967$			16.1725i			0.520072i	0.965599	+	0.260036i	$0.0837344\pi$
$967$			16.1725i			0.520072i	−0.965599	+	0.260036i	$0.916266\pi$
$968$		0			0
$969$		−	33.9202i		−	1.08967i
$970$		0			0
$971$	19.6139	−	19.6139i	0.629439	−	0.629439i	−0.318488	−	0.947927i	$-0.603175\pi$
$971$	19.6139	−	19.6139i	0.629439	−	0.629439i	0.947927	+	0.318488i	$0.103175\pi$
$972$		0			0
$973$	−7.03239	−	7.03239i	−0.225448	−	0.225448i
$974$		0			0
$975$	−39.2524			−1.25708
$976$		0			0
$977$	−49.3566			−1.57906			−0.789529	−	0.613713i	$-0.789675\pi$
$977$	−49.3566			−1.57906			−0.789529	+	0.613713i	$0.789675\pi$
$978$		0			0
$979$	−12.8480	−	12.8480i	−0.410625	−	0.410625i
$980$		0			0
$981$	0.398126	−	0.398126i	0.0127112	−	0.0127112i
$982$		0			0
$983$			0.208762i			0.00665848i	0.999994	+	0.00332924i	$0.00105973\pi$
$983$			0.208762i			0.00665848i	−0.999994	+	0.00332924i	$0.998940\pi$
$984$		0			0
$985$			20.4950i			0.653026i
$986$		0			0
$987$	−8.00666	+	8.00666i	−0.254855	+	0.254855i
$988$		0			0
$989$	17.7851	+	17.7851i	0.565533	+	0.565533i
$990$		0			0
$991$	23.4623			0.745306			0.372653	−	0.927971i	$-0.378448\pi$
$991$	23.4623			0.745306			0.372653	+	0.927971i	$0.378448\pi$
$992$		0			0
$993$	29.8094			0.945972
$994$		0			0
$995$	−1.34089	−	1.34089i	−0.0425091	−	0.0425091i
$996$		0			0
$997$	19.7777	−	19.7777i	0.626366	−	0.626366i	−0.320786	−	0.947152i	$-0.603947\pi$
$997$	19.7777	−	19.7777i	0.626366	−	0.626366i	0.947152	+	0.320786i	$0.103947\pi$
$998$		0			0
$999$			43.0066i			1.36067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.b.1345.2	yes	8
4.3	odd	2		1792.2.m.d.1345.3	yes	8
8.3	odd	2		1792.2.m.a.1345.2	yes	8
8.5	even	2		1792.2.m.c.1345.3	yes	8
16.3	odd	4		1792.2.m.a.449.2	✓	8
16.5	even	4	inner	1792.2.m.b.449.2	yes	8
16.11	odd	4		1792.2.m.d.449.3	yes	8
16.13	even	4		1792.2.m.c.449.3	yes	8
32.5	even	8		7168.2.a.w.1.4		4
32.11	odd	8		7168.2.a.t.1.4		4
32.21	even	8		7168.2.a.s.1.1		4
32.27	odd	8		7168.2.a.x.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.a.449.2	✓	8	16.3	odd	4
1792.2.m.a.1345.2	yes	8	8.3	odd	2
1792.2.m.b.449.2	yes	8	16.5	even	4	inner
1792.2.m.b.1345.2	yes	8	1.1	even	1	trivial
1792.2.m.c.449.3	yes	8	16.13	even	4
1792.2.m.c.1345.3	yes	8	8.5	even	2
1792.2.m.d.449.3	yes	8	16.11	odd	4
1792.2.m.d.1345.3	yes	8	4.3	odd	2
7168.2.a.s.1.1		4	32.21	even	8
7168.2.a.t.1.4		4	32.11	odd	8
7168.2.a.w.1.4		4	32.5	even	8
7168.2.a.x.1.1		4	32.27	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.23681 - 1.23681i) q^{3} +(-0.571717 + 0.571717i) q^{5} +1.00000i q^{7} +0.0594122i q^{9} +O(q^{10})\)	\(q+(-1.23681 - 1.23681i) q^{3} +(-0.571717 + 0.571717i) q^{5} +1.00000i q^{7} +0.0594122i q^{9} +(4.55765 - 4.55765i) q^{11} +(-3.65103 - 3.65103i) q^{13} +1.41421 q^{15} +2.47363 q^{17} +(5.54358 + 5.54358i) q^{19} +(1.23681 - 1.23681i) q^{21} +4.08402i q^{23} +4.34628i q^{25} +(-3.63696 + 3.63696i) q^{27} +(-4.30205 - 4.30205i) q^{29} +1.02461 q^{31} -11.2739 q^{33} +(-0.571717 - 0.571717i) q^{35} +(5.91245 - 5.91245i) q^{37} +9.03127i q^{39} -5.47010i q^{41} +(4.35480 - 4.35480i) q^{43} +(-0.0339670 - 0.0339670i) q^{45} -6.47363 q^{47} -1.00000 q^{49} +(-3.05941 - 3.05941i) q^{51} +(-1.94059 + 1.94059i) q^{53} +5.21137i q^{55} -13.7127i q^{57} +(6.90191 - 6.90191i) q^{59} +(-7.84563 - 7.84563i) q^{61} -0.0594122 q^{63} +4.17471 q^{65} +(-3.88118 - 3.88118i) q^{67} +(5.05117 - 5.05117i) q^{69} -9.44196i q^{71} -1.06608i q^{73} +(5.37553 - 5.37553i) q^{75} +(4.55765 + 4.55765i) q^{77} +12.3400 q^{79} +9.17471 q^{81} +(-5.68230 - 5.68230i) q^{83} +(-1.41421 + 1.41421i) q^{85} +10.6417i q^{87} -2.81900i q^{89} +(3.65103 - 3.65103i) q^{91} +(-1.26725 - 1.26725i) q^{93} -6.33871 q^{95} -1.74754 q^{97} +(0.270780 + 0.270780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5}+O(q^{10}) \) 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

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