LMFDB - Embedded newform 448.2.j.d.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(111,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("448.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.3
Root			$-0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	448.111
Dual form			448.2.j.d.335.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28999 - 1.28999i) q^{3} +(0.599312 + 0.599312i) q^{5} +(0.152445 - 2.64136i) q^{7} +0.328129i q^{9} +O(q^{10})$	\(q+(-1.28999 - 1.28999i) q^{3} +(0.599312 + 0.599312i) q^{5} +(0.152445 - 2.64136i) q^{7} +0.328129i q^{9} +(2.00000 + 2.00000i) q^{11} +(-1.00197 + 1.00197i) q^{13} -1.54621i q^{15} -6.48134i q^{17} +(-3.93134 - 3.93134i) q^{19} +(-3.60396 + 3.21066i) q^{21} -4.40731 q^{23} -4.28165i q^{25} +(-3.44668 + 3.44668i) q^{27} +(0.241319 + 0.241319i) q^{29} +3.38529 q^{31} -5.15994i q^{33} +(1.67436 - 1.49163i) q^{35} +(2.73544 - 2.73544i) q^{37} +2.58506 q^{39} -4.88941 q^{41} +(-4.40731 - 4.40731i) q^{43} +(-0.196652 + 0.196652i) q^{45} +9.45461 q^{47} +(-6.95352 - 0.805321i) q^{49} +(-8.36083 + 8.36083i) q^{51} +(3.21808 - 3.21808i) q^{53} +2.39725i q^{55} +10.1428i q^{57} +(1.35137 - 1.35137i) q^{59} +(-9.84334 + 9.84334i) q^{61} +(0.866705 + 0.0500215i) q^{63} -1.20099 q^{65} +(8.71220 - 8.71220i) q^{67} +(5.68537 + 5.68537i) q^{69} +12.2855 q^{71} +0.805321 q^{73} +(-5.52327 + 5.52327i) q^{75} +(5.58760 - 4.97782i) q^{77} +10.7681i q^{79} +9.87672 q^{81} +(5.76738 + 5.76738i) q^{83} +(3.88434 - 3.88434i) q^{85} -0.622597i q^{87} +13.3281 q^{89} +(2.49382 + 2.79931i) q^{91} +(-4.36698 - 4.36698i) q^{93} -4.71220i q^{95} +10.8360i q^{97} +(-0.656257 + 0.656257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) $ 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.28999	−	1.28999i	−0.744774	−	0.744774i	0.228719	−	0.973493i	$-0.426546\pi$
$3$	−1.28999	−	1.28999i	−0.744774	−	0.744774i	−0.973493	+	0.228719i	$0.926546\pi$
$4$		0			0
$5$	0.599312	+	0.599312i	0.268021	+	0.268021i	0.828302	−	0.560282i	$-0.189307\pi$
$5$	0.599312	+	0.599312i	0.268021	+	0.268021i	−0.560282	+	0.828302i	$0.689307\pi$
$6$		0			0
$7$	0.152445	−	2.64136i	0.0576187	−	0.998339i
$7$	0.152445	−	2.64136i	0.0576187	−	0.998339i
$8$		0			0
$9$			0.328129i			0.109376i
$10$		0			0
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	0.941113	−	0.338091i	$-0.109781\pi$
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	−0.338091	+	0.941113i	$0.609781\pi$
$12$		0			0
$13$	−1.00197	+	1.00197i	−0.277897	+	0.277897i	−0.832269	−	0.554372i	$-0.812959\pi$
$13$	−1.00197	+	1.00197i	−0.277897	+	0.277897i	0.554372	+	0.832269i	$0.312959\pi$
$14$		0			0
$15$		−	1.54621i		−	0.399229i
$16$		0			0
$17$		−	6.48134i		−	1.57195i	−0.618255	−	0.785977i	$-0.712160\pi$
$17$		−	6.48134i		−	1.57195i	0.618255	−	0.785977i	$-0.287840\pi$
$18$		0			0
$19$	−3.93134	−	3.93134i	−0.901912	−	0.901912i	0.0936897	−	0.995601i	$-0.470134\pi$
$19$	−3.93134	−	3.93134i	−0.901912	−	0.901912i	−0.995601	+	0.0936897i	$0.970134\pi$
$20$		0			0
$21$	−3.60396	+	3.21066i	−0.786449	+	0.700624i
$22$		0			0
$23$	−4.40731			−0.918988			−0.459494	−	0.888181i	$-0.651969\pi$
$23$	−4.40731			−0.918988			−0.459494	+	0.888181i	$0.651969\pi$
$24$		0			0
$25$		−	4.28165i		−	0.856330i
$26$		0			0
$27$	−3.44668	+	3.44668i	−0.663313	+	0.663313i
$28$		0			0
$29$	0.241319	+	0.241319i	0.0448119	+	0.0448119i	0.729158	−	0.684346i	$-0.239912\pi$
$29$	0.241319	+	0.241319i	0.0448119	+	0.0448119i	−0.684346	+	0.729158i	$0.739912\pi$
$30$		0			0
$31$	3.38529			0.608017			0.304008	−	0.952669i	$-0.401675\pi$
$31$	3.38529			0.608017			0.304008	+	0.952669i	$0.401675\pi$
$32$		0			0
$33$		−	5.15994i		−	0.898231i
$34$		0			0
$35$	1.67436	−	1.49163i	0.283018	−	0.252132i
$36$		0			0
$37$	2.73544	−	2.73544i	0.449704	−	0.449704i	−0.445552	−	0.895256i	$-0.646993\pi$
$37$	2.73544	−	2.73544i	0.449704	−	0.449704i	0.895256	+	0.445552i	$0.146993\pi$
$38$		0			0
$39$	2.58506			0.413941
$40$		0			0
$41$	−4.88941			−0.763597			−0.381799	−	0.924246i	$-0.624695\pi$
$41$	−4.88941			−0.763597			−0.381799	+	0.924246i	$0.624695\pi$
$42$		0			0
$43$	−4.40731	−	4.40731i	−0.672109	−	0.672109i	0.286093	−	0.958202i	$-0.407643\pi$
$43$	−4.40731	−	4.40731i	−0.672109	−	0.672109i	−0.958202	+	0.286093i	$0.907643\pi$
$44$		0			0
$45$	−0.196652	+	0.196652i	−0.0293151	+	0.0293151i
$46$		0			0
$47$	9.45461			1.37910			0.689548	−	0.724240i	$-0.257809\pi$
$47$	9.45461			1.37910			0.689548	+	0.724240i	$0.257809\pi$
$48$		0			0
$49$	−6.95352	−	0.805321i	−0.993360	−	0.115046i
$50$		0			0
$51$	−8.36083	+	8.36083i	−1.17075	+	1.17075i
$52$		0			0
$53$	3.21808	−	3.21808i	0.442037	−	0.442037i	−0.450659	−	0.892696i	$-0.648811\pi$
$53$	3.21808	−	3.21808i	0.442037	−	0.442037i	0.892696	+	0.450659i	$0.148811\pi$
$54$		0			0
$55$			2.39725i			0.323245i
$56$		0			0
$57$			10.1428i			1.34344i
$58$		0			0
$59$	1.35137	−	1.35137i	0.175933	−	0.175933i	−0.613647	−	0.789580i	$-0.710298\pi$
$59$	1.35137	−	1.35137i	0.175933	−	0.175933i	0.789580	+	0.613647i	$0.210298\pi$
$60$		0			0
$61$	−9.84334	+	9.84334i	−1.26031	+	1.26031i	−0.309369	+	0.950942i	$0.600118\pi$
$61$	−9.84334	+	9.84334i	−1.26031	+	1.26031i	−0.950942	+	0.309369i	$0.899882\pi$
$62$		0			0
$63$	0.866705	+	0.0500215i	0.109195	+	0.00630211i
$64$		0			0
$65$	−1.20099			−0.148964
$66$		0			0
$67$	8.71220	−	8.71220i	1.06436	−	1.06436i	0.0665840	−	0.997781i	$-0.478790\pi$
$67$	8.71220	−	8.71220i	1.06436	−	1.06436i	0.997781	−	0.0665840i	$-0.0212101\pi$
$68$		0			0
$69$	5.68537	+	5.68537i	0.684438	+	0.684438i
$70$		0			0
$71$	12.2855			1.45802			0.729011	−	0.684502i	$-0.239980\pi$
$71$	12.2855			1.45802			0.729011	+	0.684502i	$0.239980\pi$
$72$		0			0
$73$	0.805321			0.0942557			0.0471279	−	0.998889i	$-0.484993\pi$
$73$	0.805321			0.0942557			0.0471279	+	0.998889i	$0.484993\pi$
$74$		0			0
$75$	−5.52327	+	5.52327i	−0.637772	+	0.637772i
$76$		0			0
$77$	5.58760	−	4.97782i	0.636766	−	0.567276i
$78$		0			0
$79$			10.7681i			1.21151i	0.795651	+	0.605756i	$0.207129\pi$
$79$			10.7681i			1.21151i	−0.795651	+	0.605756i	$0.792871\pi$
$80$		0			0
$81$	9.87672			1.09741
$82$		0			0
$83$	5.76738	+	5.76738i	0.633052	+	0.633052i	0.948832	−	0.315780i	$-0.102266\pi$
$83$	5.76738	+	5.76738i	0.633052	+	0.633052i	−0.315780	+	0.948832i	$0.602266\pi$
$84$		0			0
$85$	3.88434	−	3.88434i	0.421316	−	0.421316i
$86$		0			0
$87$		−	0.622597i		−	0.0667494i
$88$		0			0
$89$	13.3281			1.41278			0.706389	−	0.707824i	$-0.250323\pi$
$89$	13.3281			1.41278			0.706389	+	0.707824i	$0.250323\pi$
$90$		0			0
$91$	2.49382	+	2.79931i	0.261423	+	0.293448i
$92$		0			0
$93$	−4.36698	−	4.36698i	−0.452835	−	0.452835i
$94$		0			0
$95$		−	4.71220i		−	0.483462i
$96$		0			0
$97$			10.8360i			1.10022i	0.835091	+	0.550112i	$0.185415\pi$
$97$			10.8360i			1.10022i	−0.835091	+	0.550112i	$0.814585\pi$
$98$		0			0
$99$	−0.656257	+	0.656257i	−0.0659564	+	0.0659564i
$100$		0			0
$101$	5.47936	+	5.47936i	0.545217	+	0.545217i	0.925054	−	0.379837i	$-0.124020\pi$
$101$	5.47936	+	5.47936i	0.545217	+	0.545217i	−0.379837	+	0.925054i	$0.624020\pi$
$102$		0			0
$103$			11.5535i			1.13840i	0.822200	+	0.569199i	$0.192746\pi$
$103$			11.5535i			1.13840i	−0.822200	+	0.569199i	$0.807254\pi$
$104$		0			0
$105$	−4.08409	−	0.235711i	−0.398566	−	0.0230031i
$106$		0			0
$107$	−4.86110	−	4.86110i	−0.469941	−	0.469941i	0.431955	−	0.901895i	$-0.357824\pi$
$107$	−4.86110	−	4.86110i	−0.469941	−	0.469941i	−0.901895	+	0.431955i	$0.857824\pi$
$108$		0			0
$109$	10.0792	+	10.0792i	0.965411	+	0.965411i	0.999421	−	0.0340107i	$-0.0108280\pi$
$109$	10.0792	+	10.0792i	0.965411	+	0.965411i	−0.0340107	+	0.999421i	$0.510828\pi$
$110$		0			0
$111$	−7.05736			−0.669855
$112$		0			0
$113$	−3.05034			−0.286952			−0.143476	−	0.989654i	$-0.545828\pi$
$113$	−3.05034			−0.286952			−0.143476	+	0.989654i	$0.545828\pi$
$114$		0			0
$115$	−2.64136	−	2.64136i	−0.246308	−	0.246308i
$116$		0			0
$117$	−0.328776	−	0.328776i	−0.0303954	−	0.0303954i
$118$		0			0
$119$	−17.1195	−	0.988045i	−1.56934	−	0.0905739i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	6.30727	+	6.30727i	0.568707	+	0.568707i
$124$		0			0
$125$	5.56261	−	5.56261i	0.497535	−	0.497535i
$126$		0			0
$127$		−	9.01709i		−	0.800137i	−0.916485	−	0.400069i	$-0.868986\pi$
$127$		−	9.01709i		−	0.800137i	0.916485	−	0.400069i	$-0.131014\pi$
$128$		0			0
$129$			11.3707i			1.00114i
$130$		0			0
$131$	−0.484665	−	0.484665i	−0.0423454	−	0.0423454i	0.685617	−	0.727962i	$-0.259532\pi$
$131$	−0.484665	−	0.484665i	−0.0423454	−	0.0423454i	−0.727962	+	0.685617i	$0.759532\pi$
$132$		0			0
$133$	−10.9834	+	9.78476i	−0.952380	+	0.848446i
$134$		0			0
$135$	−4.13127			−0.355563
$136$		0			0
$137$		−	17.1466i		−	1.46493i	−0.680803	−	0.732467i	$-0.738369\pi$
$137$		−	17.1466i		−	1.46493i	0.680803	−	0.732467i	$-0.261631\pi$
$138$		0			0
$139$	7.13391	−	7.13391i	0.605090	−	0.605090i	−0.336568	−	0.941659i	$-0.609266\pi$
$139$	7.13391	−	7.13391i	0.605090	−	0.605090i	0.941659	+	0.336568i	$0.109266\pi$
$140$		0			0
$141$	−12.1963	−	12.1963i	−1.02712	−	1.02712i
$142$		0			0
$143$	−4.00789			−0.335157
$144$		0			0
$145$			0.289251i			0.0240210i
$146$		0			0
$147$	7.93109	+	10.0088i	0.654146	+	0.825512i
$148$		0			0
$149$	−8.85110	+	8.85110i	−0.725110	+	0.725110i	−0.969641	−	0.244531i	$-0.921366\pi$
$149$	−8.85110	+	8.85110i	−0.725110	+	0.725110i	0.244531	+	0.969641i	$0.421366\pi$
$150$		0			0
$151$	−6.73930			−0.548436			−0.274218	−	0.961668i	$-0.588419\pi$
$151$	−6.73930			−0.548436			−0.274218	+	0.961668i	$0.588419\pi$
$152$		0			0
$153$	2.12671			0.171935
$154$		0			0
$155$	2.02885	+	2.02885i	0.162961	+	0.162961i
$156$		0			0
$157$	−5.08606	+	5.08606i	−0.405912	+	0.405912i	−0.880310	−	0.474398i	$-0.842666\pi$
$157$	−5.08606	+	5.08606i	−0.405912	+	0.405912i	0.474398	+	0.880310i	$0.342666\pi$
$158$		0			0
$159$	−8.30256			−0.658436
$160$		0			0
$161$	−0.671871	+	11.6413i	−0.0529509	+	0.917461i
$162$		0			0
$163$	−6.30489	+	6.30489i	−0.493837	+	0.493837i	−0.909513	−	0.415676i	$-0.863545\pi$
$163$	−6.30489	+	6.30489i	−0.493837	+	0.493837i	0.415676	+	0.909513i	$0.363545\pi$
$164$		0			0
$165$	3.09242	−	3.09242i	0.240744	−	0.240744i
$166$		0			0
$167$		−	16.3480i		−	1.26504i	−0.774543	−	0.632522i	$-0.782020\pi$
$167$		−	16.3480i		−	1.26504i	0.774543	−	0.632522i	$-0.217980\pi$
$168$		0			0
$169$			10.9921i			0.845546i
$170$		0			0
$171$	1.28999	−	1.28999i	0.0986477	−	0.0986477i
$172$		0			0
$173$	11.4446	−	11.4446i	0.870119	−	0.870119i	−0.122366	−	0.992485i	$-0.539048\pi$
$173$	11.4446	−	11.4446i	0.870119	−	0.870119i	0.992485	+	0.122366i	$0.0390482\pi$
$174$		0			0
$175$	−11.3094	−	0.652715i	−0.854907	−	0.0493406i
$176$		0			0
$177$	−3.48650			−0.262061
$178$		0			0
$179$	8.84347	−	8.84347i	0.660992	−	0.660992i	−0.294622	−	0.955614i	$-0.595194\pi$
$179$	8.84347	−	8.84347i	0.660992	−	0.660992i	0.955614	+	0.294622i	$0.0951937\pi$
$180$		0			0
$181$	−17.5233	−	17.5233i	−1.30250	−	1.30250i	−0.926703	−	0.375794i	$-0.877370\pi$
$181$	−17.5233	−	17.5233i	−1.30250	−	1.30250i	−0.375794	−	0.926703i	$-0.622630\pi$
$182$		0			0
$183$	25.3956			1.87729
$184$		0			0
$185$	3.27877			0.241060
$186$		0			0
$187$	12.9627	−	12.9627i	0.947924	−	0.947924i
$188$		0			0
$189$	8.57847	+	9.62933i	0.623992	+	0.700431i
$190$		0			0
$191$		−	4.50974i		−	0.326313i	−0.986600	−	0.163157i	$-0.947832\pi$
$191$		−	4.50974i		−	0.326313i	0.986600	−	0.163157i	$-0.0521676\pi$
$192$		0			0
$193$	13.9227			1.00217			0.501087	−	0.865397i	$-0.332934\pi$
$193$	13.9227			1.00217			0.501087	+	0.865397i	$0.332934\pi$
$194$		0			0
$195$	1.54926	+	1.54926i	0.110945	+	0.110945i
$196$		0			0
$197$	10.1598	−	10.1598i	0.723859	−	0.723859i	−0.245530	−	0.969389i	$-0.578962\pi$
$197$	10.1598	−	10.1598i	0.723859	−	0.723859i	0.969389	+	0.245530i	$0.0789620\pi$
$198$		0			0
$199$			9.91320i			0.702728i	0.936239	+	0.351364i	$0.114282\pi$
$199$			9.91320i			0.702728i	−0.936239	+	0.351364i	$0.885718\pi$
$200$		0			0
$201$	−22.4772			−1.58542
$202$		0			0
$203$	0.674198	−	0.600623i	0.0473194	−	0.0421554i
$204$		0			0
$205$	−2.93028	−	2.93028i	−0.204660	−	0.204660i
$206$		0			0
$207$		−	1.44617i		−	0.100515i
$208$		0			0
$209$		−	15.7254i		−	1.08775i
$210$		0			0
$211$	−6.53445	+	6.53445i	−0.449850	+	0.449850i	−0.895305	−	0.445454i	$-0.853042\pi$
$211$	−6.53445	+	6.53445i	−0.449850	+	0.449850i	0.445454	+	0.895305i	$0.353042\pi$
$212$		0			0
$213$	−15.8481	−	15.8481i	−1.08590	−	1.08590i
$214$		0			0
$215$		−	5.28271i		−	0.360278i
$216$		0			0
$217$	0.516070	−	8.94176i	0.0350331	−	0.607007i
$218$		0			0
$219$	−1.03885	−	1.03885i	−0.0701992	−	0.0701992i
$220$		0			0
$221$	6.49412	+	6.49412i	0.436842	+	0.436842i
$222$		0			0
$223$	−2.27448			−0.152311			−0.0761553	−	0.997096i	$-0.524264\pi$
$223$	−2.27448			−0.152311			−0.0761553	+	0.997096i	$0.524264\pi$
$224$		0			0
$225$	1.40493			0.0936622
$226$		0			0
$227$	8.90856	+	8.90856i	0.591282	+	0.591282i	0.937978	−	0.346696i	$-0.112696\pi$
$227$	8.90856	+	8.90856i	0.591282	+	0.591282i	−0.346696	+	0.937978i	$0.612696\pi$
$228$		0			0
$229$	−6.03915	−	6.03915i	−0.399078	−	0.399078i	0.478830	−	0.877908i	$-0.341061\pi$
$229$	−6.03915	−	6.03915i	−0.399078	−	0.399078i	−0.877908	+	0.478830i	$0.841061\pi$
$230$		0			0
$231$	−13.6293	−	0.786606i	−0.896739	−	0.0517549i
$232$		0			0
$233$			26.1926i			1.71593i	0.513707	+	0.857966i	$0.328272\pi$
$233$			26.1926i			1.71593i	−0.513707	+	0.857966i	$0.671728\pi$
$234$		0			0
$235$	5.66626	+	5.66626i	0.369626	+	0.369626i
$236$		0			0
$237$	13.8908	−	13.8908i	0.902302	−	0.902302i
$238$		0			0
$239$			20.6122i			1.33329i	0.745375	+	0.666645i	$0.232270\pi$
$239$			20.6122i			1.33329i	−0.745375	+	0.666645i	$0.767730\pi$
$240$		0			0
$241$			0.710410i			0.0457615i	0.999738	+	0.0228808i	$0.00728381\pi$
$241$			0.710410i			0.0457615i	−0.999738	+	0.0228808i	$0.992716\pi$
$242$		0			0
$243$	−2.40080	−	2.40080i	−0.154011	−	0.154011i
$244$		0			0
$245$	−3.68469	−	4.64997i	−0.235406	−	0.297076i
$246$		0			0
$247$	7.87820			0.501278
$248$		0			0
$249$		−	14.8797i		−	0.942961i
$250$		0			0
$251$	4.98077	−	4.98077i	0.314383	−	0.314383i	−0.532222	−	0.846605i	$-0.678643\pi$
$251$	4.98077	−	4.98077i	0.314383	−	0.314383i	0.846605	+	0.532222i	$0.178643\pi$
$252$		0			0
$253$	−8.81463	−	8.81463i	−0.554171	−	0.554171i
$254$		0			0
$255$	−10.0215			−0.627571
$256$		0			0
$257$			6.21080i			0.387419i	0.981059	+	0.193710i	$0.0620519\pi$
$257$			6.21080i			0.387419i	−0.981059	+	0.193710i	$0.937948\pi$
$258$		0			0
$259$	−6.80827	−	7.64228i	−0.423045	−	0.474868i
$260$		0			0
$261$	−0.0791838	+	0.0791838i	−0.00490136	+	0.00490136i
$262$		0			0
$263$	−0.783397			−0.0483063			−0.0241532	−	0.999708i	$-0.507689\pi$
$263$	−0.783397			−0.0483063			−0.0241532	+	0.999708i	$0.507689\pi$
$264$		0			0
$265$	3.85727			0.236950
$266$		0			0
$267$	−17.1931	−	17.1931i	−1.05220	−	1.05220i
$268$		0			0
$269$	12.3540	−	12.3540i	0.753237	−	0.753237i	−0.221845	−	0.975082i	$-0.571208\pi$
$269$	12.3540	−	12.3540i	0.753237	−	0.753237i	0.975082	+	0.221845i	$0.0712079\pi$
$270$		0			0
$271$	−6.43477			−0.390884			−0.195442	−	0.980715i	$-0.562614\pi$
$271$	−6.43477			−0.390884			−0.195442	+	0.980715i	$0.562614\pi$
$272$		0			0
$273$	0.394079	−	6.82807i	0.0238507	−	0.413254i
$274$		0			0
$275$	8.56330	−	8.56330i	0.516386	−	0.516386i
$276$		0			0
$277$	−5.22956	+	5.22956i	−0.314214	+	0.314214i	−0.846540	−	0.532326i	$-0.821318\pi$
$277$	−5.22956	+	5.22956i	−0.314214	+	0.314214i	0.532326	+	0.846540i	$0.321318\pi$
$278$		0			0
$279$			1.11081i			0.0665026i
$280$		0			0
$281$			14.8611i			0.886539i	0.896388	+	0.443270i	$0.146182\pi$
$281$			14.8611i			0.886539i	−0.896388	+	0.443270i	$0.853818\pi$
$282$		0			0
$283$	−8.28739	+	8.28739i	−0.492634	+	0.492634i	−0.909135	−	0.416501i	$-0.863256\pi$
$283$	−8.28739	+	8.28739i	−0.492634	+	0.492634i	0.416501	+	0.909135i	$0.363256\pi$
$284$		0			0
$285$	−6.07868	+	6.07868i	−0.360070	+	0.360070i
$286$		0			0
$287$	−0.745364	+	12.9147i	−0.0439975	+	0.762329i
$288$		0			0
$289$	−25.0077			−1.47104
$290$		0			0
$291$	13.9782	−	13.9782i	0.819419	−	0.819419i
$292$		0			0
$293$	8.11929	+	8.11929i	0.474334	+	0.474334i	0.903314	−	0.428980i	$-0.141127\pi$
$293$	8.11929	+	8.11929i	0.474334	+	0.474334i	−0.428980	+	0.903314i	$0.641127\pi$
$294$		0			0
$295$	1.61978			0.0943075
$296$		0			0
$297$	−13.7867			−0.799986
$298$		0			0
$299$	4.41601	−	4.41601i	0.255384	−	0.255384i
$300$		0			0
$301$	−12.3132	+	10.9694i	−0.709718	+	0.632266i
$302$		0			0
$303$		−	14.1366i		−	0.812127i
$304$		0			0
$305$	−11.7985			−0.675578
$306$		0			0
$307$	−14.2527	−	14.2527i	−0.813442	−	0.813442i	0.171706	−	0.985148i	$-0.445072\pi$
$307$	−14.2527	−	14.2527i	−0.813442	−	0.813442i	−0.985148	+	0.171706i	$0.945072\pi$
$308$		0			0
$309$	14.9038	−	14.9038i	0.847848	−	0.847848i
$310$		0			0
$311$		−	12.7171i		−	0.721123i	−0.932735	−	0.360561i	$-0.882585\pi$
$311$		−	12.7171i		−	0.721123i	0.932735	−	0.360561i	$-0.117415\pi$
$312$		0			0
$313$	24.7983			1.40168			0.700841	−	0.713317i	$-0.252808\pi$
$313$	24.7983			1.40168			0.700841	+	0.713317i	$0.252808\pi$
$314$		0			0
$315$	0.489448	+	0.549405i	0.0275773	+	0.0309555i
$316$		0			0
$317$	−1.43818	−	1.43818i	−0.0807761	−	0.0807761i	0.665564	−	0.746340i	$-0.268191\pi$
$317$	−1.43818	−	1.43818i	−0.0807761	−	0.0807761i	−0.746340	+	0.665564i	$0.768191\pi$
$318$		0			0
$319$			0.965278i			0.0540452i
$320$		0			0
$321$			12.5415i			0.699999i
$322$		0			0
$323$	−25.4803	+	25.4803i	−1.41776	+	1.41776i
$324$		0			0
$325$	4.29010	+	4.29010i	0.237972	+	0.237972i
$326$		0			0
$327$		−	26.0040i		−	1.43803i
$328$		0			0
$329$	1.44131	−	24.9730i	0.0794617	−	1.37681i
$330$		0			0
$331$	−1.03647	−	1.03647i	−0.0569697	−	0.0569697i	0.678048	−	0.735018i	$-0.262826\pi$
$331$	−1.03647	−	1.03647i	−0.0569697	−	0.0569697i	−0.735018	+	0.678048i	$0.762826\pi$
$332$		0			0
$333$	0.897577	+	0.897577i	0.0491869	+	0.0491869i
$334$		0			0
$335$	10.4427			0.570543
$336$		0			0
$337$	16.9109			0.921195			0.460598	−	0.887609i	$-0.347635\pi$
$337$	16.9109			0.921195			0.460598	+	0.887609i	$0.347635\pi$
$338$		0			0
$339$	3.93489	+	3.93489i	0.213714	+	0.213714i
$340$		0			0
$341$	6.77059	+	6.77059i	0.366648	+	0.366648i
$342$		0			0
$343$	−3.18717	+	18.2440i	−0.172091	+	0.985081i
$344$		0			0
$345$			6.81463i			0.366887i
$346$		0			0
$347$	1.32198	+	1.32198i	0.0709676	+	0.0709676i	0.741700	−	0.670732i	$-0.234020\pi$
$347$	1.32198	+	1.32198i	0.0709676	+	0.0709676i	−0.670732	+	0.741700i	$0.734020\pi$
$348$		0			0
$349$	−17.2528	+	17.2528i	−0.923520	+	0.923520i	−0.997276	−	0.0737567i	$-0.976501\pi$
$349$	−17.2528	+	17.2528i	−0.923520	+	0.923520i	0.0737567	+	0.997276i	$0.476501\pi$
$350$		0			0
$351$		−	6.90695i		−	0.368666i
$352$		0			0
$353$			2.98951i			0.159116i	0.996830	+	0.0795579i	$0.0253509\pi$
$353$			2.98951i			0.159116i	−0.996830	+	0.0795579i	$0.974649\pi$
$354$		0			0
$355$	7.36285	+	7.36285i	0.390780	+	0.390780i
$356$		0			0
$357$	20.8094	+	23.3585i	1.10135	+	1.23626i
$358$		0			0
$359$	9.62687			0.508087			0.254043	−	0.967193i	$-0.418239\pi$
$359$	9.62687			0.508087			0.254043	+	0.967193i	$0.418239\pi$
$360$		0			0
$361$			11.9109i			0.626889i
$362$		0			0
$363$	−3.86996	+	3.86996i	−0.203120	+	0.203120i
$364$		0			0
$365$	0.482639	+	0.482639i	0.0252625	+	0.0252625i
$366$		0			0
$367$	7.38157			0.385315			0.192657	−	0.981266i	$-0.438289\pi$
$367$	7.38157			0.385315			0.192657	+	0.981266i	$0.438289\pi$
$368$		0			0
$369$		−	1.60436i		−	0.0835194i
$370$		0			0
$371$	−8.00952	−	8.99067i	−0.415833	−	0.466773i
$372$		0			0
$373$	2.46142	−	2.46142i	0.127447	−	0.127447i	−0.640506	−	0.767953i	$-0.721275\pi$
$373$	2.46142	−	2.46142i	0.127447	−	0.127447i	0.767953	+	0.640506i	$0.221275\pi$
$374$		0			0
$375$	−14.3514			−0.741101
$376$		0			0
$377$	−0.483591			−0.0249062
$378$		0			0
$379$	−11.4803	−	11.4803i	−0.589706	−	0.589706i	0.347846	−	0.937552i	$-0.386913\pi$
$379$	−11.4803	−	11.4803i	−0.589706	−	0.589706i	−0.937552	+	0.347846i	$0.886913\pi$
$380$		0			0
$381$	−11.6319	+	11.6319i	−0.595921	+	0.595921i
$382$		0			0
$383$	−0.164009			−0.00838045			−0.00419023	−	0.999991i	$-0.501334\pi$
$383$	−0.164009			−0.00838045			−0.00419023	+	0.999991i	$0.501334\pi$
$384$		0			0
$385$	6.33199	+	0.365448i	0.322708	+	0.0186249i
$386$		0			0
$387$	1.44617	−	1.44617i	0.0735127	−	0.0735127i
$388$		0			0
$389$	−15.5501	+	15.5501i	−0.788420	+	0.788420i	−0.981235	−	0.192815i	$-0.938238\pi$
$389$	−15.5501	+	15.5501i	−0.788420	+	0.788420i	0.192815	+	0.981235i	$0.438238\pi$
$390$		0			0
$391$			28.5653i			1.44461i
$392$		0			0
$393$			1.25042i			0.0630755i
$394$		0			0
$395$	−6.45348	+	6.45348i	−0.324710	+	0.324710i
$396$		0			0
$397$	18.2821	−	18.2821i	0.917550	−	0.917550i	−0.0793007	−	0.996851i	$-0.525269\pi$
$397$	18.2821	−	18.2821i	0.917550	−	0.917550i	0.996851	+	0.0793007i	$0.0252687\pi$
$398$		0			0
$399$	26.7906	+	1.54621i	1.34121	+	0.0774073i
$400$		0			0
$401$	15.7378			0.785909			0.392955	−	0.919558i	$-0.371453\pi$
$401$	15.7378			0.785909			0.392955	+	0.919558i	$0.371453\pi$
$402$		0			0
$403$	−3.39197	+	3.39197i	−0.168966	+	0.168966i
$404$		0			0
$405$	5.91924	+	5.91924i	0.294129	+	0.294129i
$406$		0			0
$407$	10.9418			0.542363
$408$		0			0
$409$	27.8252			1.37587			0.687935	−	0.725773i	$-0.258518\pi$
$409$	27.8252			1.37587			0.687935	+	0.725773i	$0.258518\pi$
$410$		0			0
$411$	−22.1189	+	22.1189i	−1.09104	+	1.09104i
$412$		0			0
$413$	−3.36344	−	3.77546i	−0.165504	−	0.185778i
$414$		0			0
$415$			6.91292i			0.339342i
$416$		0			0
$417$	−18.4053			−0.901311
$418$		0			0
$419$	−0.380613	−	0.380613i	−0.0185942	−	0.0185942i	0.697749	−	0.716343i	$-0.254185\pi$
$419$	−0.380613	−	0.380613i	−0.0185942	−	0.0185942i	−0.716343	+	0.697749i	$0.754185\pi$
$420$		0			0
$421$	5.48089	−	5.48089i	0.267122	−	0.267122i	−0.560817	−	0.827940i	$-0.689513\pi$
$421$	5.48089	−	5.48089i	0.267122	−	0.267122i	0.827940	+	0.560817i	$0.189513\pi$
$422$		0			0
$423$			3.10233i			0.150840i
$424$		0			0
$425$	−27.7508			−1.34611
$426$		0			0
$427$	24.4992	+	27.5003i	1.18560	+	1.33083i
$428$		0			0
$429$	5.17012	+	5.17012i	0.249616	+	0.249616i
$430$		0			0
$431$		−	18.4850i		−	0.890392i	−0.895433	−	0.445196i	$-0.853134\pi$
$431$		−	18.4850i		−	0.890392i	0.895433	−	0.445196i	$-0.146866\pi$
$432$		0			0
$433$		−	30.9347i		−	1.48663i	−0.668944	−	0.743313i	$-0.733254\pi$
$433$		−	30.9347i		−	1.48663i	0.668944	−	0.743313i	$-0.266746\pi$
$434$		0			0
$435$	0.373130	−	0.373130i	0.0178902	−	0.0178902i
$436$		0			0
$437$	17.3267	+	17.3267i	0.828846	+	0.828846i
$438$		0			0
$439$			20.0317i			0.956059i	0.878344	+	0.478029i	$0.158649\pi$
$439$			20.0317i			0.956059i	−0.878344	+	0.478029i	$0.841351\pi$
$440$		0			0
$441$	0.264249	−	2.28165i	0.0125833	−	0.108650i
$442$		0			0
$443$	0.426694	+	0.426694i	0.0202729	+	0.0202729i	0.717171	−	0.696898i	$-0.245437\pi$
$443$	0.426694	+	0.426694i	0.0202729	+	0.0202729i	−0.696898	+	0.717171i	$0.745437\pi$
$444$		0			0
$445$	7.98770	+	7.98770i	0.378653	+	0.378653i
$446$		0			0
$447$	22.8356			1.08009
$448$		0			0
$449$	13.1266			0.619483			0.309741	−	0.950821i	$-0.399758\pi$
$449$	13.1266			0.619483			0.309741	+	0.950821i	$0.399758\pi$
$450$		0			0
$451$	−9.77882	−	9.77882i	−0.460467	−	0.460467i
$452$		0			0
$453$	8.69360	+	8.69360i	0.408461	+	0.408461i
$454$		0			0
$455$	−0.183084	+	3.17224i	−0.00858313	+	0.148717i
$456$		0			0
$457$		−	15.6449i		−	0.731836i	−0.930647	−	0.365918i	$-0.880755\pi$
$457$		−	15.6449i		−	0.731836i	0.930647	−	0.365918i	$-0.119245\pi$
$458$		0			0
$459$	22.3391	+	22.3391i	1.04270	+	1.04270i
$460$		0			0
$461$	−28.3593	+	28.3593i	−1.32082	+	1.32082i	−0.407712	+	0.913111i	$0.633673\pi$
$461$	−28.3593	+	28.3593i	−1.32082	+	1.32082i	−0.913111	+	0.407712i	$0.866327\pi$
$462$		0			0
$463$		−	13.1195i		−	0.609716i	−0.952398	−	0.304858i	$-0.901391\pi$
$463$		−	13.1195i		−	0.609716i	0.952398	−	0.304858i	$-0.0986089\pi$
$464$		0			0
$465$		−	5.23437i		−	0.242738i
$466$		0			0
$467$	28.4475	+	28.4475i	1.31639	+	1.31639i	0.916610	+	0.399782i	$0.130914\pi$
$467$	28.4475	+	28.4475i	1.31639	+	1.31639i	0.399782	+	0.916610i	$0.369086\pi$
$468$		0			0
$469$	−21.6839	−	24.3402i	−1.00127	−	1.12392i
$470$		0			0
$471$	13.1219			0.604625
$472$		0			0
$473$		−	17.6293i		−	0.810594i
$474$		0			0
$475$	−16.8326	+	16.8326i	−0.772334	+	0.772334i
$476$		0			0
$477$	1.05594	+	1.05594i	0.0483484	+	0.0483484i
$478$		0			0
$479$	33.5612			1.53345			0.766725	−	0.641975i	$-0.221885\pi$
$479$	33.5612			1.53345			0.766725	+	0.641975i	$0.221885\pi$
$480$		0			0
$481$			5.48168i			0.249943i
$482$		0			0
$483$	15.8838	−	14.1504i	0.722738	−	0.643865i
$484$		0			0
$485$	−6.49412	+	6.49412i	−0.294883	+	0.294883i
$486$		0			0
$487$	−17.4268			−0.789683			−0.394841	−	0.918749i	$-0.629200\pi$
$487$	−17.4268			−0.789683			−0.394841	+	0.918749i	$0.629200\pi$
$488$		0			0
$489$	16.2664			0.735594
$490$		0			0
$491$	4.00947	+	4.00947i	0.180945	+	0.180945i	0.791767	−	0.610823i	$-0.209161\pi$
$491$	4.00947	+	4.00947i	0.180945	+	0.180945i	−0.610823	+	0.791767i	$0.709161\pi$
$492$		0			0
$493$	1.56407	−	1.56407i	0.0704423	−	0.0704423i
$494$		0			0
$495$	−0.786606			−0.0353553
$496$		0			0
$497$	1.87286	−	32.4504i	0.0840093	−	1.45560i
$498$		0			0
$499$	16.2319	−	16.2319i	0.726642	−	0.726642i	−0.243308	−	0.969949i	$-0.578232\pi$
$499$	16.2319	−	16.2319i	0.726642	−	0.726642i	0.969949	+	0.243308i	$0.0782324\pi$
$500$		0			0
$501$	−21.0886	+	21.0886i	−0.942171	+	0.942171i
$502$		0			0
$503$			1.85332i			0.0826356i	0.999146	+	0.0413178i	$0.0131556\pi$
$503$			1.85332i			0.0826356i	−0.999146	+	0.0413178i	$0.986844\pi$
$504$		0			0
$505$			6.56770i			0.292259i
$506$		0			0
$507$	14.1797	−	14.1797i	0.629741	−	0.629741i
$508$		0			0
$509$	−7.64044	+	7.64044i	−0.338656	+	0.338656i	−0.855861	−	0.517205i	$-0.826972\pi$
$509$	−7.64044	+	7.64044i	−0.338656	+	0.338656i	0.517205	+	0.855861i	$0.326972\pi$
$510$		0			0
$511$	0.122767	−	2.12714i	0.00543089	−	0.0940991i
$512$		0			0
$513$	27.1001			1.19650
$514$		0			0
$515$	−6.92413	+	6.92413i	−0.305114	+	0.305114i
$516$		0			0
$517$	18.9092	+	18.9092i	0.831627	+	0.831627i
$518$		0			0
$519$	−29.5268			−1.29608
$520$		0			0
$521$	−33.9055			−1.48543			−0.742713	−	0.669610i	$-0.766461\pi$
$521$	−33.9055			−1.48543			−0.742713	+	0.669610i	$0.766461\pi$
$522$		0			0
$523$	1.20989	−	1.20989i	0.0529047	−	0.0529047i	−0.680159	−	0.733064i	$-0.738089\pi$
$523$	1.20989	−	1.20989i	0.0529047	−	0.0529047i	0.733064	+	0.680159i	$0.238089\pi$
$524$		0			0
$525$	13.7469	+	15.4309i	0.599965	+	0.673460i
$526$		0			0
$527$		−	21.9412i		−	0.955775i
$528$		0			0
$529$	−3.57560			−0.155461
$530$		0			0
$531$	0.443423	+	0.443423i	0.0192429	+	0.0192429i
$532$		0			0
$533$	4.89905	−	4.89905i	0.212202	−	0.212202i
$534$		0			0
$535$		−	5.82664i		−	0.251907i
$536$		0			0
$537$	−22.8159			−0.984579
$538$		0			0
$539$	−12.2964	−	15.5177i	−0.529643	−	0.668394i
$540$		0			0
$541$	−2.39969	−	2.39969i	−0.103171	−	0.103171i	0.653637	−	0.756808i	$-0.273242\pi$
$541$	−2.39969	−	2.39969i	−0.103171	−	0.103171i	−0.756808	+	0.653637i	$0.773242\pi$
$542$		0			0
$543$			45.2096i			1.94013i
$544$		0			0
$545$			12.0812i			0.517500i
$546$		0			0
$547$	−14.2048	+	14.2048i	−0.607355	+	0.607355i	−0.942254	−	0.334899i	$-0.891298\pi$
$547$	−14.2048	+	14.2048i	−0.607355	+	0.607355i	0.334899	+	0.942254i	$0.391298\pi$
$548$		0			0
$549$	−3.22988	−	3.22988i	−0.137848	−	0.137848i
$550$		0			0
$551$		−	1.89742i		−	0.0808327i
$552$		0			0
$553$	28.4425	+	1.64155i	1.20950	+	0.0698057i
$554$		0			0
$555$	−4.22956	−	4.22956i	−0.179535	−	0.179535i
$556$		0			0
$557$	−21.9862	−	21.9862i	−0.931586	−	0.931586i	0.0662188	−	0.997805i	$-0.478906\pi$
$557$	−21.9862	−	21.9862i	−0.931586	−	0.931586i	−0.997805	+	0.0662188i	$0.978906\pi$
$558$		0			0
$559$	8.83201			0.373554
$560$		0			0
$561$	−33.4433			−1.41198
$562$		0			0
$563$	−19.2913	−	19.2913i	−0.813030	−	0.813030i	0.172057	−	0.985087i	$-0.444959\pi$
$563$	−19.2913	−	19.2913i	−0.813030	−	0.813030i	−0.985087	+	0.172057i	$0.944959\pi$
$564$		0			0
$565$	−1.82810	−	1.82810i	−0.0769089	−	0.0769089i
$566$		0			0
$567$	1.50565	−	26.0879i	0.0632315	−	1.09559i
$568$		0			0
$569$			9.17452i			0.384616i	0.981335	+	0.192308i	$0.0615973\pi$
$569$			9.17452i			0.384616i	−0.981335	+	0.192308i	$0.938403\pi$
$570$		0			0
$571$	−29.7388	−	29.7388i	−1.24453	−	1.24453i	−0.958102	−	0.286426i	$-0.907533\pi$
$571$	−29.7388	−	29.7388i	−1.24453	−	1.24453i	−0.286426	−	0.958102i	$-0.592467\pi$
$572$		0			0
$573$	−5.81750	+	5.81750i	−0.243029	+	0.243029i
$574$		0			0
$575$			18.8706i			0.786957i
$576$		0			0
$577$		−	25.4855i		−	1.06097i	−0.847693	−	0.530487i	$-0.822009\pi$
$577$		−	25.4855i		−	1.06097i	0.847693	−	0.530487i	$-0.177991\pi$
$578$		0			0
$579$	−17.9600	−	17.9600i	−0.746394	−	0.746394i
$580$		0			0
$581$	16.1129	−	14.3545i	0.668476	−	0.595525i
$582$		0			0
$583$	12.8723			0.533117
$584$		0			0
$585$		−	0.394079i		−	0.0162932i
$586$		0			0
$587$	−18.3219	+	18.3219i	−0.756227	+	0.756227i	−0.975634	−	0.219406i	$-0.929588\pi$
$587$	−18.3219	+	18.3219i	−0.756227	+	0.756227i	0.219406	+	0.975634i	$0.429588\pi$
$588$		0			0
$589$	−13.3087	−	13.3087i	−0.548377	−	0.548377i
$590$		0			0
$591$	−26.2121			−1.07822
$592$		0			0
$593$			15.4985i			0.636449i	0.948015	+	0.318225i	$0.103087\pi$
$593$			15.4985i			0.636449i	−0.948015	+	0.318225i	$0.896913\pi$
$594$		0			0
$595$	−9.66779	−	10.8521i	−0.396341	−	0.444892i
$596$		0			0
$597$	12.7879	−	12.7879i	0.523374	−	0.523374i
$598$		0			0
$599$	−13.4750			−0.550574			−0.275287	−	0.961362i	$-0.588773\pi$
$599$	−13.4750			−0.550574			−0.275287	+	0.961362i	$0.588773\pi$
$600$		0			0
$601$	−0.365448			−0.0149069			−0.00745346	−	0.999972i	$-0.502373\pi$
$601$	−0.365448			−0.0149069			−0.00745346	+	0.999972i	$0.502373\pi$
$602$		0			0
$603$	2.85872	+	2.85872i	0.116416	+	0.116416i
$604$		0			0
$605$	1.79794	−	1.79794i	0.0730965	−	0.0730965i
$606$		0			0
$607$	6.31485			0.256312			0.128156	−	0.991754i	$-0.459094\pi$
$607$	6.31485			0.256312			0.128156	+	0.991754i	$0.459094\pi$
$608$		0			0
$609$	−1.64450	−	0.0949116i	−0.0666385	−	0.00384601i
$610$		0			0
$611$	−9.47326	+	9.47326i	−0.383247	+	0.383247i
$612$		0			0
$613$	7.02472	−	7.02472i	0.283726	−	0.283726i	−0.550867	−	0.834593i	$-0.685703\pi$
$613$	7.02472	−	7.02472i	0.283726	−	0.283726i	0.834593	+	0.550867i	$0.185703\pi$
$614$		0			0
$615$			7.56005i			0.304850i
$616$		0			0
$617$			33.7832i			1.36006i	0.733184	+	0.680031i	$0.238034\pi$
$617$			33.7832i			1.36006i	−0.733184	+	0.680031i	$0.761966\pi$
$618$		0			0
$619$	19.0472	−	19.0472i	0.765570	−	0.765570i	−0.211753	−	0.977323i	$-0.567917\pi$
$619$	19.0472	−	19.0472i	0.765570	−	0.765570i	0.977323	+	0.211753i	$0.0679173\pi$
$620$		0			0
$621$	15.1906	−	15.1906i	0.609577	−	0.609577i
$622$		0			0
$623$	2.03180	−	35.2043i	0.0814024	−	1.41043i
$624$		0			0
$625$	−14.7408			−0.589631
$626$		0			0
$627$	−20.2855	+	20.2855i	−0.810125	+	0.810125i
$628$		0			0
$629$	−17.7293	−	17.7293i	−0.706914	−	0.706914i
$630$		0			0
$631$	32.5097			1.29419			0.647096	−	0.762408i	$-0.275983\pi$
$631$	32.5097			1.29419			0.647096	+	0.762408i	$0.275983\pi$
$632$		0			0
$633$	16.8587			0.670073
$634$		0			0
$635$	5.40405	−	5.40405i	0.214453	−	0.214453i
$636$		0			0
$637$	7.77415	−	6.16033i	0.308023	−	0.244081i
$638$		0			0
$639$			4.03123i			0.159473i
$640$		0			0
$641$	−15.5907			−0.615794			−0.307897	−	0.951420i	$-0.599625\pi$
$641$	−15.5907			−0.615794			−0.307897	+	0.951420i	$0.599625\pi$
$642$		0			0
$643$	−12.1182	−	12.1182i	−0.477896	−	0.477896i	0.426562	−	0.904458i	$-0.359725\pi$
$643$	−12.1182	−	12.1182i	−0.477896	−	0.477896i	−0.904458	+	0.426562i	$0.859725\pi$
$644$		0			0
$645$	−6.81463	+	6.81463i	−0.268326	+	0.268326i
$646$		0			0
$647$		−	24.1478i		−	0.949350i	−0.880161	−	0.474675i	$-0.842566\pi$
$647$		−	24.1478i		−	0.949350i	0.880161	−	0.474675i	$-0.157434\pi$
$648$		0			0
$649$	5.40548			0.212184
$650$		0			0
$651$	−12.2005	+	10.8690i	−0.478174	+	0.425991i
$652$		0			0
$653$	7.71220	+	7.71220i	0.301802	+	0.301802i	0.841718	−	0.539917i	$-0.181544\pi$
$653$	7.71220	+	7.71220i	0.301802	+	0.301802i	−0.539917	+	0.841718i	$0.681544\pi$
$654$		0			0
$655$		−	0.580931i		−	0.0226989i
$656$		0			0
$657$			0.264249i			0.0103093i
$658$		0			0
$659$	20.7175	−	20.7175i	0.807041	−	0.807041i	−0.177144	−	0.984185i	$-0.556686\pi$
$659$	20.7175	−	20.7175i	0.807041	−	0.807041i	0.984185	+	0.177144i	$0.0566859\pi$
$660$		0			0
$661$	−0.243222	−	0.243222i	−0.00946024	−	0.00946024i	0.702361	−	0.711821i	$-0.252129\pi$
$661$	−0.243222	−	0.243222i	−0.00946024	−	0.00946024i	−0.711821	+	0.702361i	$0.752129\pi$
$662$		0			0
$663$		−	16.7547i		−	0.650697i
$664$		0			0
$665$	−12.4466	−	0.718350i	−0.482659	−	0.0278564i
$666$		0			0
$667$	−1.06357	−	1.06357i	−0.0411816	−	0.0411816i
$668$		0			0
$669$	2.93405	+	2.93405i	0.113437	+	0.113437i
$670$		0			0
$671$	−39.3734			−1.51999
$672$		0			0
$673$	−15.4244			−0.594567			−0.297284	−	0.954789i	$-0.596081\pi$
$673$	−15.4244			−0.594567			−0.297284	+	0.954789i	$0.596081\pi$
$674$		0			0
$675$	14.7575	+	14.7575i	0.568015	+	0.568015i
$676$		0			0
$677$	−13.3926	−	13.3926i	−0.514721	−	0.514721i	0.401248	−	0.915969i	$-0.368576\pi$
$677$	−13.3926	−	13.3926i	−0.514721	−	0.514721i	−0.915969	+	0.401248i	$0.868576\pi$
$678$		0			0
$679$	28.6216	+	1.65188i	1.09840	+	0.0633935i
$680$		0			0
$681$		−	22.9838i		−	0.880743i
$682$		0			0
$683$	−6.23131	−	6.23131i	−0.238435	−	0.238435i	0.577767	−	0.816202i	$-0.303924\pi$
$683$	−6.23131	−	6.23131i	−0.238435	−	0.238435i	−0.816202	+	0.577767i	$0.803924\pi$
$684$		0			0
$685$	10.2762	−	10.2762i	0.392632	−	0.392632i
$686$		0			0
$687$			15.5808i			0.594446i
$688$		0			0
$689$			6.44886i			0.245682i
$690$		0			0
$691$	−6.85947	−	6.85947i	−0.260947	−	0.260947i	0.564492	−	0.825439i	$-0.309072\pi$
$691$	−6.85947	−	6.85947i	−0.260947	−	0.260947i	−0.825439	+	0.564492i	$0.809072\pi$
$692$		0			0
$693$	1.63337	+	1.83345i	0.0620465	+	0.0696471i
$694$		0			0
$695$	8.55088			0.324353
$696$		0			0
$697$			31.6899i			1.20034i
$698$		0			0
$699$	33.7880	−	33.7880i	1.27798	−	1.27798i
$700$		0			0
$701$	0.666263	+	0.666263i	0.0251644	+	0.0251644i	0.719577	−	0.694413i	$-0.244336\pi$
$701$	0.666263	+	0.666263i	0.0251644	+	0.0251644i	−0.694413	+	0.719577i	$0.744336\pi$
$702$		0			0
$703$	−21.5079			−0.811186
$704$		0			0
$705$		−	14.6188i		−	0.550576i
$706$		0			0
$707$	15.3082	−	13.6376i	0.575726	−	0.512897i
$708$		0			0
$709$	29.0551	−	29.0551i	1.09119	−	1.09119i	0.0957864	−	0.995402i	$-0.469463\pi$
$709$	29.0551	−	29.0551i	1.09119	−	1.09119i	0.995402	−	0.0957864i	$-0.0305366\pi$
$710$		0			0
$711$	−3.53334			−0.132511
$712$		0			0
$713$	−14.9200			−0.558760
$714$		0			0
$715$	−2.40198	−	2.40198i	−0.0898289	−	0.0898289i
$716$		0			0
$717$	26.5894	−	26.5894i	0.992999	−	0.992999i
$718$		0			0
$719$	−31.2867			−1.16680			−0.583399	−	0.812186i	$-0.698278\pi$
$719$	−31.2867			−1.16680			−0.583399	+	0.812186i	$0.698278\pi$
$720$		0			0
$721$	30.5168	+	1.76126i	1.13651	+	0.0655929i
$722$		0			0
$723$	0.916419	−	0.916419i	0.0340820	−	0.0340820i
$724$		0			0
$725$	1.03325	−	1.03325i	0.0383738	−	0.0383738i
$726$		0			0
$727$		−	22.8730i		−	0.848313i	−0.905589	−	0.424157i	$-0.860571\pi$
$727$		−	22.8730i		−	0.848313i	0.905589	−	0.424157i	$-0.139429\pi$
$728$		0			0
$729$		−	23.4362i		−	0.868006i
$730$		0			0
$731$	−28.5653	+	28.5653i	−1.05652	+	1.05652i
$732$		0			0
$733$	−13.2886	+	13.2886i	−0.490825	+	0.490825i	−0.908566	−	0.417741i	$-0.862822\pi$
$733$	−13.2886	+	13.2886i	−0.490825	+	0.490825i	0.417741	+	0.908566i	$0.362822\pi$
$734$		0			0
$735$	−1.24519	+	10.7516i	−0.0459297	+	0.396579i
$736$		0			0
$737$	34.8488			1.28367
$738$		0			0
$739$	−19.3244	+	19.3244i	−0.710858	+	0.710858i	−0.966715	−	0.255857i	$-0.917642\pi$
$739$	−19.3244	+	19.3244i	−0.710858	+	0.710858i	0.255857	+	0.966715i	$0.417642\pi$
$740$		0			0
$741$	−10.1628	−	10.1628i	−0.373338	−	0.373338i
$742$		0			0
$743$	−1.76335			−0.0646911			−0.0323455	−	0.999477i	$-0.510298\pi$
$743$	−1.76335			−0.0646911			−0.0323455	+	0.999477i	$0.510298\pi$
$744$		0			0
$745$	−10.6091			−0.388689
$746$		0			0
$747$	−1.89244	+	1.89244i	−0.0692408	+	0.0692408i
$748$		0			0
$749$	−13.5810	+	12.0989i	−0.496237	+	0.442083i
$750$		0			0
$751$			44.6805i			1.63042i	0.579169	+	0.815208i	$0.303377\pi$
$751$			44.6805i			1.63042i	−0.579169	+	0.815208i	$0.696623\pi$
$752$		0			0
$753$	−12.8503			−0.468289
$754$		0			0
$755$	−4.03894	−	4.03894i	−0.146992	−	0.146992i
$756$		0			0
$757$	−36.5033	+	36.5033i	−1.32674	+	1.32674i	−0.418535	+	0.908201i	$0.637456\pi$
$757$	−36.5033	+	36.5033i	−1.32674	+	1.32674i	−0.908201	+	0.418535i	$0.862544\pi$
$758$		0			0
$759$			22.7415i			0.825464i
$760$		0			0
$761$	41.3290			1.49817			0.749087	−	0.662471i	$-0.230492\pi$
$761$	41.3290			1.49817			0.749087	+	0.662471i	$0.230492\pi$
$762$		0			0
$763$	28.1592	−	25.0862i	1.01943	−	0.908181i
$764$		0			0
$765$	1.27456	+	1.27456i	0.0460820	+	0.0460820i
$766$		0			0
$767$			2.70807i			0.0977828i
$768$		0			0
$769$			11.7612i			0.424120i	0.977257	+	0.212060i	$0.0680171\pi$
$769$			11.7612i			0.424120i	−0.977257	+	0.212060i	$0.931983\pi$
$770$		0			0
$771$	8.01185	−	8.01185i	0.288540	−	0.288540i
$772$		0			0
$773$	−22.8247	−	22.8247i	−0.820949	−	0.820949i	0.165296	−	0.986244i	$-0.447142\pi$
$773$	−22.8247	−	22.8247i	−0.820949	−	0.820949i	−0.986244	+	0.165296i	$0.947142\pi$
$774$		0			0
$775$		−	14.4946i		−	0.520663i
$776$		0			0
$777$	−1.07586	+	18.6410i	−0.0385962	+	0.668742i
$778$		0			0
$779$	19.2219	+	19.2219i	0.688697	+	0.688697i
$780$		0			0
$781$	24.5710	+	24.5710i	0.879220	+	0.879220i
$782$		0			0
$783$	−1.66350			−0.0594486
$784$		0			0
$785$	−6.09628			−0.217585
$786$		0			0
$787$	28.2460	+	28.2460i	1.00686	+	1.00686i	0.999976	+	0.00688641i	$0.00219203\pi$
$787$	28.2460	+	28.2460i	1.00686	+	1.00686i	0.00688641	+	0.999976i	$0.497808\pi$
$788$		0			0
$789$	1.01057	+	1.01057i	0.0359773	+	0.0359773i
$790$		0			0
$791$	−0.465008	+	8.05702i	−0.0165338	+	0.286475i
$792$		0			0
$793$		−	19.7255i		−	0.700474i
$794$		0			0
$795$	−4.97582	−	4.97582i	−0.176474	−	0.176474i
$796$		0			0
$797$	34.7459	−	34.7459i	1.23076	−	1.23076i	0.267092	−	0.963671i	$-0.413937\pi$
$797$	34.7459	−	34.7459i	1.23076	−	1.23076i	0.963671	−	0.267092i	$-0.0860628\pi$
$798$		0			0
$799$		−	61.2785i		−	2.16788i
$800$		0			0
$801$			4.37334i			0.154524i
$802$		0			0
$803$	1.61064	+	1.61064i	0.0568383	+	0.0568383i
$804$		0			0
$805$	−7.37942	+	6.57410i	−0.260090	+	0.231707i
$806$		0			0
$807$	−31.8730			−1.12198
$808$		0			0
$809$			0.316372i			0.0111231i	0.999985	+	0.00556153i	$0.00177030\pi$
$809$			0.316372i			0.0111231i	−0.999985	+	0.00556153i	$0.998230\pi$
$810$		0			0
$811$	16.0273	−	16.0273i	0.562795	−	0.562795i	−0.367305	−	0.930100i	$-0.619720\pi$
$811$	16.0273	−	16.0273i	0.562795	−	0.562795i	0.930100	+	0.367305i	$0.119720\pi$
$812$		0			0
$813$	8.30076	+	8.30076i	0.291120	+	0.291120i
$814$		0			0
$815$	−7.55719			−0.264717
$816$		0			0
$817$			34.6533i			1.21237i
$818$		0			0
$819$	−0.918535	+	0.818294i	−0.0320962	+	0.0285935i
$820$		0			0
$821$	20.9318	−	20.9318i	0.730523	−	0.730523i	−0.240200	−	0.970723i	$-0.577213\pi$
$821$	20.9318	−	20.9318i	0.730523	−	0.730523i	0.970723	+	0.240200i	$0.0772130\pi$
$822$		0			0
$823$	−43.9383			−1.53159			−0.765796	−	0.643084i	$-0.777655\pi$
$823$	−43.9383			−1.53159			−0.765796	+	0.643084i	$0.777655\pi$
$824$		0			0
$825$	−22.0931			−0.769182
$826$		0			0
$827$	31.6799	+	31.6799i	1.10162	+	1.10162i	0.994216	+	0.107401i	$0.0342528\pi$
$827$	31.6799	+	31.6799i	1.10162	+	1.10162i	0.107401	+	0.994216i	$0.465747\pi$
$828$		0			0
$829$	−8.78620	+	8.78620i	−0.305157	+	0.305157i	−0.843028	−	0.537870i	$-0.819229\pi$
$829$	−8.78620	+	8.78620i	−0.305157	+	0.305157i	0.537870	+	0.843028i	$0.319229\pi$
$830$		0			0
$831$	13.4921			0.468037
$832$		0			0
$833$	−5.21956	+	45.0681i	−0.180847	+	1.56152i
$834$		0			0
$835$	9.79753	−	9.79753i	0.339058	−	0.339058i
$836$		0			0
$837$	−11.6680	+	11.6680i	−0.403306	+	0.403306i
$838$		0			0
$839$			15.1931i			0.524523i	0.964997	+	0.262261i	$0.0844682\pi$
$839$			15.1931i			0.524523i	−0.964997	+	0.262261i	$0.915532\pi$
$840$		0			0
$841$		−	28.8835i		−	0.995984i
$842$		0			0
$843$	19.1706	−	19.1706i	0.660271	−	0.660271i
$844$		0			0
$845$	−6.58770	+	6.58770i	−0.226624	+	0.226624i
$846$		0			0
$847$	−7.92407	−	0.457334i	−0.272274	−	0.0157142i
$848$		0			0
$849$	21.3812			0.733802
$850$		0			0
$851$	−12.0559	+	12.0559i	−0.413272	+	0.413272i
$852$		0			0
$853$	−1.19631	−	1.19631i	−0.0409610	−	0.0409610i	0.686330	−	0.727291i	$-0.259221\pi$
$853$	−1.19631	−	1.19631i	−0.0409610	−	0.0409610i	−0.727291	+	0.686330i	$0.759221\pi$
$854$		0			0
$855$	1.54621			0.0528792
$856$		0			0
$857$	−19.4253			−0.663555			−0.331778	−	0.943358i	$-0.607648\pi$
$857$	−19.4253			−0.663555			−0.331778	+	0.943358i	$0.607648\pi$
$858$		0			0
$859$	4.38850	−	4.38850i	0.149734	−	0.149734i	−0.628265	−	0.777999i	$-0.716235\pi$
$859$	4.38850	−	4.38850i	0.149734	−	0.149734i	0.777999	+	0.628265i	$0.216235\pi$
$860$		0			0
$861$	17.6213	−	15.6982i	0.600531	−	0.534994i
$862$		0			0
$863$		−	25.3161i		−	0.861770i	−0.902407	−	0.430885i	$-0.858201\pi$
$863$		−	25.3161i		−	0.861770i	0.902407	−	0.430885i	$-0.141799\pi$
$864$		0			0
$865$	13.7178			0.466420
$866$		0			0
$867$	32.2596	+	32.2596i	1.09559	+	1.09559i
$868$		0			0
$869$	−21.5363	+	21.5363i	−0.730569	+	0.730569i
$870$		0			0
$871$			17.4588i			0.591568i
$872$		0			0
$873$	−3.55559			−0.120338
$874$		0			0
$875$	−13.8448	−	15.5408i	−0.468041	−	0.525375i
$876$		0			0
$877$	−14.5883	−	14.5883i	−0.492612	−	0.492612i	0.416517	−	0.909128i	$-0.363251\pi$
$877$	−14.5883	−	14.5883i	−0.492612	−	0.492612i	−0.909128	+	0.416517i	$0.863251\pi$
$878$		0			0
$879$		−	20.9476i		−	0.706543i
$880$		0			0
$881$			12.5228i			0.421904i	0.977496	+	0.210952i	$0.0676563\pi$
$881$			12.5228i			0.421904i	−0.977496	+	0.210952i	$0.932344\pi$
$882$		0			0
$883$	26.9459	−	26.9459i	0.906802	−	0.906802i	−0.0892111	−	0.996013i	$-0.528435\pi$
$883$	26.9459	−	26.9459i	0.906802	−	0.906802i	0.996013	+	0.0892111i	$0.0284346\pi$
$884$		0			0
$885$	−2.08950	−	2.08950i	−0.0702378	−	0.0702378i
$886$		0			0
$887$			19.2631i			0.646790i	0.946264	+	0.323395i	$0.104824\pi$
$887$			19.2631i			0.646790i	−0.946264	+	0.323395i	$0.895176\pi$
$888$		0			0
$889$	−23.8173	−	1.37461i	−0.798808	−	0.0461029i
$890$		0			0
$891$	19.7534	+	19.7534i	0.661765	+	0.661765i
$892$		0			0
$893$	−37.1693	−	37.1693i	−1.24382	−	1.24382i
$894$		0			0
$895$	10.6000			0.354319
$896$		0			0
$897$	−11.3932			−0.380407
$898$		0			0
$899$	0.816937	+	0.816937i	0.0272464	+	0.0272464i
$900$		0			0
$901$	−20.8575	−	20.8575i	−0.694863	−	0.694863i
$902$		0			0
$903$	30.0342	+	1.73341i	0.999475	+	0.0576843i
$904$		0			0
$905$		−	21.0039i		−	0.698192i
$906$		0			0
$907$	−3.21072	−	3.21072i	−0.106610	−	0.106610i	0.651790	−	0.758400i	$-0.274019\pi$
$907$	−3.21072	−	3.21072i	−0.106610	−	0.106610i	−0.758400	+	0.651790i	$0.774019\pi$
$908$		0			0
$909$	−1.79794	+	1.79794i	−0.0596338	+	0.0596338i
$910$		0			0
$911$			45.2409i			1.49890i	0.662063	+	0.749448i	$0.269681\pi$
$911$			45.2409i			1.49890i	−0.662063	+	0.749448i	$0.730319\pi$
$912$		0			0
$913$			23.0695i			0.763489i
$914$		0			0
$915$	15.2199	+	15.2199i	0.503153	+	0.503153i
$916$		0			0
$917$	−1.35406	+	1.20629i	−0.0447149	+	0.0398351i
$918$		0			0
$919$	2.91404			0.0961253			0.0480626	−	0.998844i	$-0.484695\pi$
$919$	2.91404			0.0961253			0.0480626	+	0.998844i	$0.484695\pi$
$920$		0			0
$921$			36.7715i			1.21166i
$922$		0			0
$923$	−12.3097	+	12.3097i	−0.405180	+	0.405180i
$924$		0			0
$925$	−11.7122	−	11.7122i	−0.385095	−	0.385095i
$926$		0			0
$927$	−3.79102			−0.124514
$928$		0			0
$929$		−	28.3476i		−	0.930054i	−0.885296	−	0.465027i	$-0.846045\pi$
$929$		−	28.3476i		−	0.930054i	0.885296	−	0.465027i	$-0.153955\pi$
$930$		0			0
$931$	24.1707	+	30.5027i	0.792162	+	0.999684i
$932$		0			0
$933$	−16.4049	+	16.4049i	−0.537073	+	0.537073i
$934$		0			0
$935$	15.5374			0.508126
$936$		0			0
$937$	14.1147			0.461108			0.230554	−	0.973060i	$-0.425946\pi$
$937$	14.1147			0.461108			0.230554	+	0.973060i	$0.425946\pi$
$938$		0			0
$939$	−31.9895	−	31.9895i	−1.04394	−	1.04394i
$940$		0			0
$941$	−20.1476	+	20.1476i	−0.656793	+	0.656793i	−0.954620	−	0.297827i	$-0.903738\pi$
$941$	−20.1476	+	20.1476i	−0.656793	+	0.656793i	0.297827	+	0.954620i	$0.403738\pi$
$942$		0			0
$943$	21.5492			0.701737
$944$		0			0
$945$	−0.629790	+	10.9122i	−0.0204871	+	0.354972i
$946$		0			0
$947$	−20.4197	+	20.4197i	−0.663552	+	0.663552i	−0.956216	−	0.292663i	$-0.905458\pi$
$947$	−20.4197	+	20.4197i	−0.663552	+	0.663552i	0.292663	+	0.956216i	$0.405458\pi$
$948$		0			0
$949$	−0.806910	+	0.806910i	−0.0261934	+	0.0261934i
$950$		0			0
$951$			3.71046i			0.120320i
$952$		0			0
$953$		−	7.38196i		−	0.239125i	−0.992827	−	0.119563i	$-0.961851\pi$
$953$		−	7.38196i		−	0.239125i	0.992827	−	0.119563i	$-0.0381492\pi$
$954$		0			0
$955$	2.70274	−	2.70274i	0.0874586	−	0.0874586i
$956$		0			0
$957$	1.24519	−	1.24519i	0.0402514	−	0.0402514i
$958$		0			0
$959$	−45.2903	−	2.61391i	−1.46250	−	0.0844075i
$960$		0			0
$961$	−19.5398			−0.630316
$962$		0			0
$963$	1.59507	−	1.59507i	0.0514003	−	0.0514003i
$964$		0			0
$965$	8.34402	+	8.34402i	0.268603	+	0.268603i
$966$		0			0
$967$	−47.4068			−1.52450			−0.762250	−	0.647283i	$-0.775905\pi$
$967$	−47.4068			−1.52450			−0.762250	+	0.647283i	$0.775905\pi$
$968$		0			0
$969$	65.7386			2.11183
$970$		0			0
$971$	14.3328	−	14.3328i	0.459960	−	0.459960i	−0.438682	−	0.898642i	$-0.644555\pi$
$971$	14.3328	−	14.3328i	0.459960	−	0.459960i	0.898642	+	0.438682i	$0.144555\pi$
$972$		0			0
$973$	−17.7557	−	19.9307i	−0.569221	−	0.638950i
$974$		0			0
$975$		−	11.0683i		−	0.354470i
$976$		0			0
$977$	−6.59453			−0.210978			−0.105489	−	0.994420i	$-0.533641\pi$
$977$	−6.59453			−0.210978			−0.105489	+	0.994420i	$0.533641\pi$
$978$		0			0
$979$	26.6562	+	26.6562i	0.851937	+	0.851937i
$980$		0			0
$981$	−3.30727	+	3.30727i	−0.105593	+	0.105593i
$982$		0			0
$983$			37.5317i			1.19707i	0.801095	+	0.598537i	$0.204251\pi$
$983$			37.5317i			1.19707i	−0.801095	+	0.598537i	$0.795749\pi$
$984$		0			0
$985$	12.1778			0.388018
$986$		0			0
$987$	−34.0741	+	30.3556i	−1.08459	+	0.966228i
$988$		0			0
$989$	19.4244	+	19.4244i	0.617660	+	0.617660i
$990$		0			0
$991$			11.8074i			0.375076i	0.982257	+	0.187538i	$0.0600508\pi$
$991$			11.8074i			0.375076i	−0.982257	+	0.187538i	$0.939949\pi$
$992$		0			0
$993$			2.67407i			0.0848591i
$994$		0			0
$995$	−5.94110	+	5.94110i	−0.188346	+	0.188346i
$996$		0			0
$997$	16.9885	+	16.9885i	0.538032	+	0.538032i	0.922950	−	0.384919i	$-0.125771\pi$
$997$	16.9885	+	16.9885i	0.538032	+	0.538032i	−0.384919	+	0.922950i	$0.625771\pi$
$998$		0			0
$999$			18.8564i			0.596589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.j.d.111.3		16
4.3	odd	2		112.2.j.d.83.4	yes	16
7.6	odd	2	inner	448.2.j.d.111.6		16
8.3	odd	2		896.2.j.h.223.3		16
8.5	even	2		896.2.j.g.223.6		16
16.3	odd	4		896.2.j.g.671.3		16
16.5	even	4		112.2.j.d.27.3	✓	16
16.11	odd	4	inner	448.2.j.d.335.6		16
16.13	even	4		896.2.j.h.671.6		16
28.3	even	6		784.2.w.e.19.3		32
28.11	odd	6		784.2.w.e.19.4		32
28.19	even	6		784.2.w.e.227.8		32
28.23	odd	6		784.2.w.e.227.7		32
28.27	even	2		112.2.j.d.83.3	yes	16
56.13	odd	2		896.2.j.g.223.3		16
56.27	even	2		896.2.j.h.223.6		16
112.5	odd	12		784.2.w.e.619.4		32
112.13	odd	4		896.2.j.h.671.3		16
112.27	even	4	inner	448.2.j.d.335.3		16
112.37	even	12		784.2.w.e.619.3		32
112.53	even	12		784.2.w.e.411.8		32
112.69	odd	4		112.2.j.d.27.4	yes	16
112.83	even	4		896.2.j.g.671.6		16
112.101	odd	12		784.2.w.e.411.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.d.27.3	✓	16	16.5	even	4
112.2.j.d.27.4	yes	16	112.69	odd	4
112.2.j.d.83.3	yes	16	28.27	even	2
112.2.j.d.83.4	yes	16	4.3	odd	2
448.2.j.d.111.3		16	1.1	even	1	trivial
448.2.j.d.111.6		16	7.6	odd	2	inner
448.2.j.d.335.3		16	112.27	even	4	inner
448.2.j.d.335.6		16	16.11	odd	4	inner
784.2.w.e.19.3		32	28.3	even	6
784.2.w.e.19.4		32	28.11	odd	6
784.2.w.e.227.7		32	28.23	odd	6
784.2.w.e.227.8		32	28.19	even	6
784.2.w.e.411.7		32	112.101	odd	12
784.2.w.e.411.8		32	112.53	even	12
784.2.w.e.619.3		32	112.37	even	12
784.2.w.e.619.4		32	112.5	odd	12
896.2.j.g.223.3		16	56.13	odd	2
896.2.j.g.223.6		16	8.5	even	2
896.2.j.g.671.3		16	16.3	odd	4
896.2.j.g.671.6		16	112.83	even	4
896.2.j.h.223.3		16	8.3	odd	2
896.2.j.h.223.6		16	56.27	even	2
896.2.j.h.671.3		16	112.13	odd	4
896.2.j.h.671.6		16	16.13	even	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28999 - 1.28999i) q^{3} +(0.599312 + 0.599312i) q^{5} +(0.152445 - 2.64136i) q^{7} +0.328129i q^{9} +O(q^{10})\)	\(q+(-1.28999 - 1.28999i) q^{3} +(0.599312 + 0.599312i) q^{5} +(0.152445 - 2.64136i) q^{7} +0.328129i q^{9} +(2.00000 + 2.00000i) q^{11} +(-1.00197 + 1.00197i) q^{13} -1.54621i q^{15} -6.48134i q^{17} +(-3.93134 - 3.93134i) q^{19} +(-3.60396 + 3.21066i) q^{21} -4.40731 q^{23} -4.28165i q^{25} +(-3.44668 + 3.44668i) q^{27} +(0.241319 + 0.241319i) q^{29} +3.38529 q^{31} -5.15994i q^{33} +(1.67436 - 1.49163i) q^{35} +(2.73544 - 2.73544i) q^{37} +2.58506 q^{39} -4.88941 q^{41} +(-4.40731 - 4.40731i) q^{43} +(-0.196652 + 0.196652i) q^{45} +9.45461 q^{47} +(-6.95352 - 0.805321i) q^{49} +(-8.36083 + 8.36083i) q^{51} +(3.21808 - 3.21808i) q^{53} +2.39725i q^{55} +10.1428i q^{57} +(1.35137 - 1.35137i) q^{59} +(-9.84334 + 9.84334i) q^{61} +(0.866705 + 0.0500215i) q^{63} -1.20099 q^{65} +(8.71220 - 8.71220i) q^{67} +(5.68537 + 5.68537i) q^{69} +12.2855 q^{71} +0.805321 q^{73} +(-5.52327 + 5.52327i) q^{75} +(5.58760 - 4.97782i) q^{77} +10.7681i q^{79} +9.87672 q^{81} +(5.76738 + 5.76738i) q^{83} +(3.88434 - 3.88434i) q^{85} -0.622597i q^{87} +13.3281 q^{89} +(2.49382 + 2.79931i) q^{91} +(-4.36698 - 4.36698i) q^{93} -4.71220i q^{95} +10.8360i q^{97} +(-0.656257 + 0.656257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) \) 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Introduction

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