LMFDB - Embedded newform 448.2.j.d.335.2

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			335.2
Root			$0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	448.335
Dual form			448.2.j.d.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50619 + 1.50619i) q^{3} +(-2.54054 + 2.54054i) q^{5} +(-2.59286 - 0.526369i) q^{7} -1.53721i q^{9} +O(q^{10})$	\(q+(-1.50619 + 1.50619i) q^{3} +(-2.54054 + 2.54054i) q^{5} +(-2.59286 - 0.526369i) q^{7} -1.53721i q^{9} +(2.00000 - 2.00000i) q^{11} +(1.17573 + 1.17573i) q^{13} -7.65306i q^{15} -6.13381i q^{17} +(-0.979820 + 0.979820i) q^{19} +(4.69815 - 3.11253i) q^{21} -0.207188 q^{23} -7.90866i q^{25} +(-2.20324 - 2.20324i) q^{27} +(-3.46733 + 3.46733i) q^{29} +5.74198 q^{31} +6.02476i q^{33} +(7.92452 - 5.25000i) q^{35} +(-0.255601 - 0.255601i) q^{37} -3.54176 q^{39} -6.75794 q^{41} +(-0.207188 + 0.207188i) q^{43} +(3.90534 + 3.90534i) q^{45} -10.9321 q^{47} +(6.44587 + 2.72961i) q^{49} +(9.23868 + 9.23868i) q^{51} +(-7.19027 - 7.19027i) q^{53} +10.1621i q^{55} -2.95159i q^{57} +(-2.03256 - 2.03256i) q^{59} +(-7.51255 - 7.51255i) q^{61} +(-0.809141 + 3.98578i) q^{63} -5.97399 q^{65} +(-0.978537 - 0.978537i) q^{67} +(0.312065 - 0.312065i) q^{69} -2.09683 q^{71} +2.72961 q^{73} +(11.9119 + 11.9119i) q^{75} +(-6.23846 + 4.13299i) q^{77} +11.0315i q^{79} +11.2486 q^{81} +(-2.27616 + 2.27616i) q^{83} +(15.5832 + 15.5832i) q^{85} -10.4449i q^{87} +14.0814 q^{89} +(-2.42965 - 3.66739i) q^{91} +(-8.64851 + 8.64851i) q^{93} -4.97854i q^{95} +2.83866i q^{97} +(-3.07442 - 3.07442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

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

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
$3$	−1.50619	+	1.50619i	−0.869599	+	0.869599i	−0.992428	−	0.122829i	$-0.960803\pi$
$3$	−1.50619	+	1.50619i	−0.869599	+	0.869599i	0.122829	+	0.992428i	$0.460803\pi$
$4$		0			0
$5$	−2.54054	+	2.54054i	−1.13616	+	1.13616i	−0.147031	+	0.989132i	$0.546972\pi$
$5$	−2.54054	+	2.54054i	−1.13616	+	1.13616i	−0.989132	+	0.147031i	$0.953028\pi$
$6$		0			0
$7$	−2.59286	−	0.526369i	−0.980010	−	0.198949i
$7$	−2.59286	−	0.526369i	−0.980010	−	0.198949i
$8$		0			0
$9$		−	1.53721i		−	0.512404i
$10$		0			0
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	0.941113	+	0.338091i	$0.109781\pi$
$12$		0			0
$13$	1.17573	+	1.17573i	0.326090	+	0.326090i	0.851098	−	0.525008i	$-0.175938\pi$
$13$	1.17573	+	1.17573i	0.326090	+	0.326090i	−0.525008	+	0.851098i	$0.675938\pi$
$14$		0			0
$15$		−	7.65306i		−	1.97601i
$16$		0			0
$17$		−	6.13381i		−	1.48767i	−0.668364	−	0.743834i	$-0.733005\pi$
$17$		−	6.13381i		−	1.48767i	0.668364	−	0.743834i	$-0.266995\pi$
$18$		0			0
$19$	−0.979820	+	0.979820i	−0.224786	+	0.224786i	−0.810510	−	0.585724i	$-0.800810\pi$
$19$	−0.979820	+	0.979820i	−0.224786	+	0.224786i	0.585724	+	0.810510i	$0.300810\pi$
$20$		0			0
$21$	4.69815	−	3.11253i	1.02522	−	0.679210i
$22$		0			0
$23$	−0.207188			−0.0432017			−0.0216009	−	0.999767i	$-0.506876\pi$
$23$	−0.207188			−0.0432017			−0.0216009	+	0.999767i	$0.506876\pi$
$24$		0			0
$25$		−	7.90866i		−	1.58173i
$26$		0			0
$27$	−2.20324	−	2.20324i	−0.424013	−	0.424013i
$28$		0			0
$29$	−3.46733	+	3.46733i	−0.643868	+	0.643868i	−0.951504	−	0.307636i	$-0.900462\pi$
$29$	−3.46733	+	3.46733i	−0.643868	+	0.643868i	0.307636	+	0.951504i	$0.400462\pi$
$30$		0			0
$31$	5.74198			1.03129			0.515645	−	0.856802i	$-0.327552\pi$
$31$	5.74198			1.03129			0.515645	+	0.856802i	$0.327552\pi$
$32$		0			0
$33$			6.02476i			1.04878i
$34$		0			0
$35$	7.92452	−	5.25000i	1.33949	−	0.887412i
$36$		0			0
$37$	−0.255601	−	0.255601i	−0.0420206	−	0.0420206i	0.685784	−	0.727805i	$-0.259459\pi$
$37$	−0.255601	−	0.255601i	−0.0420206	−	0.0420206i	−0.727805	+	0.685784i	$0.759459\pi$
$38$		0			0
$39$	−3.54176			−0.567135
$40$		0			0
$41$	−6.75794			−1.05541			−0.527707	−	0.849427i	$-0.676948\pi$
$41$	−6.75794			−1.05541			−0.527707	+	0.849427i	$0.676948\pi$
$42$		0			0
$43$	−0.207188	+	0.207188i	−0.0315959	+	0.0315959i	−0.722728	−	0.691132i	$-0.757112\pi$
$43$	−0.207188	+	0.207188i	−0.0315959	+	0.0315959i	0.691132	+	0.722728i	$0.257112\pi$
$44$		0			0
$45$	3.90534	+	3.90534i	0.582174	+	0.582174i
$46$		0			0
$47$	−10.9321			−1.59461			−0.797307	−	0.603575i	$-0.793743\pi$
$47$	−10.9321			−1.59461			−0.797307	+	0.603575i	$0.793743\pi$
$48$		0			0
$49$	6.44587	+	2.72961i	0.920839	+	0.389944i
$50$		0			0
$51$	9.23868	+	9.23868i	1.29367	+	1.29367i
$52$		0			0
$53$	−7.19027	−	7.19027i	−0.987659	−	0.987659i	0.0122653	−	0.999925i	$-0.496096\pi$
$53$	−7.19027	−	7.19027i	−0.987659	−	0.987659i	−0.999925	+	0.0122653i	$0.996096\pi$
$54$		0			0
$55$			10.1621i			1.37026i
$56$		0			0
$57$		−	2.95159i		−	0.390947i
$58$		0			0
$59$	−2.03256	−	2.03256i	−0.264617	−	0.264617i	0.562310	−	0.826927i	$-0.309913\pi$
$59$	−2.03256	−	2.03256i	−0.264617	−	0.264617i	−0.826927	+	0.562310i	$0.809913\pi$
$60$		0			0
$61$	−7.51255	−	7.51255i	−0.961884	−	0.961884i	0.0374157	−	0.999300i	$-0.488087\pi$
$61$	−7.51255	−	7.51255i	−0.961884	−	0.961884i	−0.999300	+	0.0374157i	$0.988087\pi$
$62$		0			0
$63$	−0.809141	+	3.98578i	−0.101942	+	0.502160i
$64$		0			0
$65$	−5.97399			−0.740983
$66$		0			0
$67$	−0.978537	−	0.978537i	−0.119547	−	0.119547i	0.644802	−	0.764349i	$-0.276940\pi$
$67$	−0.978537	−	0.978537i	−0.119547	−	0.119547i	−0.764349	+	0.644802i	$0.776940\pi$
$68$		0			0
$69$	0.312065	−	0.312065i	0.0375682	−	0.0375682i
$70$		0			0
$71$	−2.09683			−0.248847			−0.124424	−	0.992229i	$-0.539708\pi$
$71$	−2.09683			−0.248847			−0.124424	+	0.992229i	$0.539708\pi$
$72$		0			0
$73$	2.72961			0.319476			0.159738	−	0.987159i	$-0.448935\pi$
$73$	2.72961			0.319476			0.159738	+	0.987159i	$0.448935\pi$
$74$		0			0
$75$	11.9119	+	11.9119i	1.37547	+	1.37547i
$76$		0			0
$77$	−6.23846	+	4.13299i	−0.710939	+	0.470997i
$78$		0			0
$79$			11.0315i			1.24114i	0.784151	+	0.620570i	$0.213099\pi$
$79$			11.0315i			1.24114i	−0.784151	+	0.620570i	$0.786901\pi$
$80$		0			0
$81$	11.2486			1.24985
$82$		0			0
$83$	−2.27616	+	2.27616i	−0.249841	+	0.249841i	−0.820905	−	0.571065i	$-0.806531\pi$
$83$	−2.27616	+	2.27616i	−0.249841	+	0.249841i	0.571065	+	0.820905i	$0.306531\pi$
$84$		0			0
$85$	15.5832	+	15.5832i	1.69023	+	1.69023i
$86$		0			0
$87$		−	10.4449i		−	1.11981i
$88$		0			0
$89$	14.0814			1.49263			0.746314	−	0.665594i	$-0.231822\pi$
$89$	14.0814			1.49263			0.746314	+	0.665594i	$0.231822\pi$
$90$		0			0
$91$	−2.42965	−	3.66739i	−0.254696	−	0.384447i
$92$		0			0
$93$	−8.64851	+	8.64851i	−0.896809	+	0.896809i
$94$		0			0
$95$		−	4.97854i		−	0.510787i
$96$		0			0
$97$			2.83866i			0.288223i	0.989561	+	0.144111i	$0.0460323\pi$
$97$			2.83866i			0.288223i	−0.989561	+	0.144111i	$0.953968\pi$
$98$		0			0
$99$	−3.07442	−	3.07442i	−0.308991	−	0.308991i
$100$		0			0
$101$	−4.95808	+	4.95808i	−0.493347	+	0.493347i	−0.909359	−	0.416012i	$-0.863427\pi$
$101$	−4.95808	+	4.95808i	−0.493347	+	0.493347i	0.416012	+	0.909359i	$0.363427\pi$
$102$		0			0
$103$		−	13.7987i		−	1.35962i	−0.733387	−	0.679811i	$-0.762062\pi$
$103$		−	13.7987i		−	1.35962i	0.733387	−	0.679811i	$-0.237938\pi$
$104$		0			0
$105$	−4.02834	+	19.8433i	−0.393125	+	1.93651i
$106$		0			0
$107$	−9.86025	+	9.86025i	−0.953226	+	0.953226i	−0.998954	−	0.0457279i	$-0.985439\pi$
$107$	−9.86025	+	9.86025i	−0.953226	+	0.953226i	0.0457279	+	0.998954i	$0.485439\pi$
$108$		0			0
$109$	4.66998	−	4.66998i	0.447303	−	0.447303i	−0.447154	−	0.894457i	$-0.647562\pi$
$109$	4.66998	−	4.66998i	0.447303	−	0.447303i	0.894457	+	0.447154i	$0.147562\pi$
$110$		0			0
$111$	0.769968			0.0730821
$112$		0			0
$113$	−14.2577			−1.34125			−0.670626	−	0.741796i	$-0.733974\pi$
$113$	−14.2577			−1.34125			−0.670626	+	0.741796i	$0.733974\pi$
$114$		0			0
$115$	0.526369	−	0.526369i	0.0490842	−	0.0490842i
$116$		0			0
$117$	1.80735	−	1.80735i	0.167090	−	0.167090i
$118$		0			0
$119$	−3.22865	+	15.9041i	−0.295970	+	1.45793i
$120$		0			0
$121$			3.00000i			0.272727i
$122$		0			0
$123$	10.1787	−	10.1787i	0.917786	−	0.917786i
$124$		0			0
$125$	7.38956	+	7.38956i	0.660942	+	0.660942i
$126$		0			0
$127$		−	6.16426i		−	0.546990i	−0.961873	−	0.273495i	$-0.911820\pi$
$127$		−	6.16426i		−	0.546990i	0.961873	−	0.273495i	$-0.0881797\pi$
$128$		0			0
$129$		−	0.624129i		−	0.0549515i
$130$		0			0
$131$	1.22342	−	1.22342i	0.106891	−	0.106891i	−0.651639	−	0.758529i	$-0.725918\pi$
$131$	1.22342	−	1.22342i	0.106891	−	0.106891i	0.758529	+	0.651639i	$0.225918\pi$
$132$		0			0
$133$	3.05628	−	2.02479i	0.265013	−	0.175572i
$134$		0			0
$135$	11.1948			0.963496
$136$		0			0
$137$			7.76342i			0.663274i	0.943407	+	0.331637i	$0.107601\pi$
$137$			7.76342i			0.663274i	−0.943407	+	0.331637i	$0.892399\pi$
$138$		0			0
$139$	−6.45272	−	6.45272i	−0.547313	−	0.547313i	0.378350	−	0.925663i	$-0.376492\pi$
$139$	−6.45272	−	6.45272i	−0.547313	−	0.547313i	−0.925663	+	0.378350i	$0.876492\pi$
$140$		0			0
$141$	16.4658	−	16.4658i	1.38667	−	1.38667i
$142$		0			0
$143$	4.70294			0.393279
$144$		0			0
$145$		−	17.6178i		−	1.46308i
$146$		0			0
$147$	−13.8200	+	5.59740i	−1.13985	+	0.461665i
$148$		0			0
$149$	5.83878	+	5.83878i	0.478332	+	0.478332i	0.904598	−	0.426266i	$-0.140171\pi$
$149$	5.83878	+	5.83878i	0.478332	+	0.478332i	−0.426266	+	0.904598i	$0.640171\pi$
$150$		0			0
$151$	−1.55623			−0.126644			−0.0633222	−	0.997993i	$-0.520170\pi$
$151$	−1.55623			−0.126644			−0.0633222	+	0.997993i	$0.520170\pi$
$152$		0			0
$153$	−9.42896			−0.762286
$154$		0			0
$155$	−14.5877	+	14.5877i	−1.17171	+	1.17171i
$156$		0			0
$157$	−2.85260	−	2.85260i	−0.227662	−	0.227662i	0.584053	−	0.811715i	$-0.301466\pi$
$157$	−2.85260	−	2.85260i	−0.227662	−	0.227662i	−0.811715	+	0.584053i	$0.801466\pi$
$158$		0			0
$159$	21.6598			1.71773
$160$		0			0
$161$	0.537211	+	0.109058i	0.0423381	+	0.00859494i
$162$		0			0
$163$	−0.814275	−	0.814275i	−0.0637790	−	0.0637790i	0.674498	−	0.738277i	$-0.264360\pi$
$163$	−0.814275	−	0.814275i	−0.0637790	−	0.0637790i	−0.738277	+	0.674498i	$0.764360\pi$
$164$		0			0
$165$	−15.3061	−	15.3061i	−1.19158	−	1.19158i
$166$		0			0
$167$		−	6.52564i		−	0.504969i	−0.967601	−	0.252485i	$-0.918752\pi$
$167$		−	6.52564i		−	0.504969i	0.967601	−	0.252485i	$-0.0812477\pi$
$168$		0			0
$169$		−	10.2353i		−	0.787331i
$170$		0			0
$171$	1.50619	+	1.50619i	0.115181	+	0.115181i
$172$		0			0
$173$	3.79628	+	3.79628i	0.288626	+	0.288626i	0.836537	−	0.547911i	$-0.184577\pi$
$173$	3.79628	+	3.79628i	0.288626	+	0.288626i	−0.547911	+	0.836537i	$0.684577\pi$
$174$		0			0
$175$	−4.16288	+	20.5061i	−0.314684	+	1.55011i
$176$		0			0
$177$	6.12283			0.460220
$178$		0			0
$179$	−16.1734	−	16.1734i	−1.20885	−	1.20885i	−0.971399	−	0.237454i	$-0.923687\pi$
$179$	−16.1734	−	16.1734i	−1.20885	−	1.20885i	−0.237454	−	0.971399i	$-0.576313\pi$
$180$		0			0
$181$	3.70233	−	3.70233i	0.275192	−	0.275192i	−0.555994	−	0.831186i	$-0.687662\pi$
$181$	3.70233	−	3.70233i	0.275192	−	0.275192i	0.831186	+	0.555994i	$0.187662\pi$
$182$		0			0
$183$	22.6307			1.67291
$184$		0			0
$185$	1.29873			0.0954845
$186$		0			0
$187$	−12.2676	−	12.2676i	−0.897098	−	0.897098i
$188$		0			0
$189$	4.55297	+	6.87241i	0.331180	+	0.499894i
$190$		0			0
$191$			1.60010i			0.115779i	0.998323	+	0.0578896i	$0.0184371\pi$
$191$			1.60010i			0.115779i	−0.998323	+	0.0578896i	$0.981563\pi$
$192$		0			0
$193$	−16.5034			−1.18794			−0.593969	−	0.804488i	$-0.702440\pi$
$193$	−16.5034			−1.18794			−0.593969	+	0.804488i	$0.702440\pi$
$194$		0			0
$195$	8.99796	−	8.99796i	0.644357	−	0.644357i
$196$		0			0
$197$	−12.2127	−	12.2127i	−0.870117	−	0.870117i	0.122368	−	0.992485i	$-0.460951\pi$
$197$	−12.2127	−	12.2127i	−0.870117	−	0.870117i	−0.992485	+	0.122368i	$0.960951\pi$
$198$		0			0
$199$			16.2006i			1.14843i	0.818705	+	0.574215i	$0.194693\pi$
$199$			16.2006i			1.14843i	−0.818705	+	0.574215i	$0.805307\pi$
$200$		0			0
$201$	2.94772			0.207916
$202$		0			0
$203$	10.8154	−	7.16522i	0.759094	−	0.502900i
$204$		0			0
$205$	17.1688	−	17.1688i	1.19912	−	1.19912i
$206$		0			0
$207$			0.318492i			0.0221367i
$208$		0			0
$209$			3.91928i			0.271102i
$210$		0			0
$211$	1.22959	+	1.22959i	0.0846487	+	0.0846487i	0.748163	−	0.663515i	$-0.230936\pi$
$211$	1.22959	+	1.22959i	0.0846487	+	0.0846487i	−0.663515	+	0.748163i	$0.730936\pi$
$212$		0			0
$213$	3.15822	−	3.15822i	0.216397	−	0.216397i
$214$		0			0
$215$		−	1.05274i		−	0.0717962i
$216$		0			0
$217$	−14.8882	−	3.02241i	−1.01068	−	0.205174i
$218$		0			0
$219$	−4.11130	+	4.11130i	−0.277816	+	0.277816i
$220$		0			0
$221$	7.21173	−	7.21173i	0.485114	−	0.485114i
$222$		0			0
$223$	3.08465			0.206564			0.103282	−	0.994652i	$-0.467066\pi$
$223$	3.08465			0.206564			0.103282	+	0.994652i	$0.467066\pi$
$224$		0			0
$225$	−12.1573			−0.810485
$226$		0			0
$227$	−6.16995	+	6.16995i	−0.409514	+	0.409514i	−0.881569	−	0.472055i	$-0.843512\pi$
$227$	−6.16995	+	6.16995i	−0.409514	+	0.409514i	0.472055	+	0.881569i	$0.343512\pi$
$228$		0			0
$229$	−11.9265	+	11.9265i	−0.788126	+	0.788126i	−0.981187	−	0.193060i	$-0.938159\pi$
$229$	−11.9265	+	11.9265i	−0.788126	+	0.788126i	0.193060	+	0.981187i	$0.438159\pi$
$230$		0			0
$231$	3.17125	−	15.6214i	0.208653	−	1.02781i
$232$		0			0
$233$			14.9886i			0.981934i	0.871178	+	0.490967i	$0.163356\pi$
$233$			14.9886i			0.981934i	−0.871178	+	0.490967i	$0.836644\pi$
$234$		0			0
$235$	27.7735	−	27.7735i	1.81174	−	1.81174i
$236$		0			0
$237$	−16.6155	−	16.6155i	−1.07929	−	1.07929i
$238$		0			0
$239$		−	18.9930i		−	1.22856i	−0.789090	−	0.614278i	$-0.789447\pi$
$239$		−	18.9930i		−	1.22856i	0.789090	−	0.614278i	$-0.210553\pi$
$240$		0			0
$241$			24.3526i			1.56869i	0.620324	+	0.784346i	$0.287001\pi$
$241$			24.3526i			1.56869i	−0.620324	+	0.784346i	$0.712999\pi$
$242$		0			0
$243$	−10.3328	+	10.3328i	−0.662851	+	0.662851i
$244$		0			0
$245$	−23.3106	+	9.44131i	−1.48926	+	0.603183i
$246$		0			0
$247$	−2.30401			−0.146601
$248$		0			0
$249$		−	6.85664i		−	0.434522i
$250$		0			0
$251$	13.3452	+	13.3452i	0.842342	+	0.842342i	0.989163	−	0.146821i	$-0.0469042\pi$
$251$	13.3452	+	13.3452i	0.842342	+	0.842342i	−0.146821	+	0.989163i	$0.546904\pi$
$252$		0			0
$253$	−0.414376	+	0.414376i	−0.0260516	+	0.0260516i
$254$		0			0
$255$	−46.9424			−2.93965
$256$		0			0
$257$			5.40063i			0.336882i	0.985712	+	0.168441i	$0.0538732\pi$
$257$			5.40063i			0.336882i	−0.985712	+	0.168441i	$0.946127\pi$
$258$		0			0
$259$	0.528198	+	0.797280i	0.0328206	+	0.0495405i
$260$		0			0
$261$	5.33002	+	5.33002i	0.329920	+	0.329920i
$262$		0			0
$263$	0.362360			0.0223441			0.0111721	−	0.999938i	$-0.496444\pi$
$263$	0.362360			0.0223441			0.0111721	+	0.999938i	$0.496444\pi$
$264$		0			0
$265$	36.5343			2.24428
$266$		0			0
$267$	−21.2093	+	21.2093i	−1.29799	+	1.29799i
$268$		0			0
$269$	−18.9026	−	18.9026i	−1.15251	−	1.15251i	−0.986048	−	0.166463i	$-0.946766\pi$
$269$	−18.9026	−	18.9026i	−1.15251	−	1.15251i	−0.166463	−	0.986048i	$-0.553234\pi$
$270$		0			0
$271$	−9.67495			−0.587712			−0.293856	−	0.955850i	$-0.594939\pi$
$271$	−9.67495			−0.587712			−0.293856	+	0.955850i	$0.594939\pi$
$272$		0			0
$273$	9.18328	+	1.86427i	0.555798	+	0.112831i
$274$		0			0
$275$	−15.8173	−	15.8173i	−0.953820	−	0.953820i
$276$		0			0
$277$	−2.95613	−	2.95613i	−0.177617	−	0.177617i	0.612699	−	0.790316i	$-0.290084\pi$
$277$	−2.95613	−	2.95613i	−0.177617	−	0.177617i	−0.790316	+	0.612699i	$0.790084\pi$
$278$		0			0
$279$		−	8.82664i		−	0.528437i
$280$		0			0
$281$		−	19.8602i		−	1.18476i	−0.805658	−	0.592382i	$-0.798188\pi$
$281$		−	19.8602i		−	1.18476i	0.805658	−	0.592382i	$-0.201812\pi$
$282$		0			0
$283$	19.5158	+	19.5158i	1.16009	+	1.16009i	0.984455	+	0.175639i	$0.0561993\pi$
$283$	19.5158	+	19.5158i	1.16009	+	1.16009i	0.175639	+	0.984455i	$0.443801\pi$
$284$		0			0
$285$	7.49862	+	7.49862i	0.444180	+	0.444180i
$286$		0			0
$287$	17.5224	+	3.55717i	1.03432	+	0.209973i
$288$		0			0
$289$	−20.6237			−1.21316
$290$		0			0
$291$	−4.27556	−	4.27556i	−0.250638	−	0.250638i
$292$		0			0
$293$	18.3063	−	18.3063i	1.06947	−	1.06947i	0.0720669	−	0.997400i	$-0.477041\pi$
$293$	18.3063	−	18.3063i	1.06947	−	1.06947i	0.997400	−	0.0720669i	$-0.0229595\pi$
$294$		0			0
$295$	10.3276			0.601295
$296$		0			0
$297$	−8.81295			−0.511379
$298$		0			0
$299$	−0.243598	−	0.243598i	−0.0140876	−	0.0140876i
$300$		0			0
$301$	0.646268	−	0.428153i	0.0372503	−	0.0246783i
$302$		0			0
$303$		−	14.9356i		−	0.858028i
$304$		0			0
$305$	38.1719			2.18571
$306$		0			0
$307$	10.7614	−	10.7614i	0.614188	−	0.614188i	−0.329847	−	0.944034i	$-0.606997\pi$
$307$	10.7614	−	10.7614i	0.614188	−	0.614188i	0.944034	+	0.329847i	$0.106997\pi$
$308$		0			0
$309$	20.7834	+	20.7834i	1.18233	+	1.18233i
$310$		0			0
$311$			1.88736i			0.107023i	0.998567	+	0.0535113i	$0.0170413\pi$
$311$			1.88736i			0.107023i	−0.998567	+	0.0535113i	$0.982959\pi$
$312$		0			0
$313$	−21.8411			−1.23453			−0.617267	−	0.786754i	$-0.711760\pi$
$313$	−21.8411			−1.23453			−0.617267	+	0.786754i	$0.711760\pi$
$314$		0			0
$315$	−8.07036	−	12.1817i	−0.454713	−	0.686359i
$316$		0			0
$317$	−14.2647	+	14.2647i	−0.801185	+	0.801185i	−0.983281	−	0.182096i	$-0.941712\pi$
$317$	−14.2647	+	14.2647i	−0.801185	+	0.801185i	0.182096	+	0.983281i	$0.441712\pi$
$318$		0			0
$319$			13.8693i			0.776534i
$320$		0			0
$321$		−	29.7028i		−	1.65785i
$322$		0			0
$323$	6.01003	+	6.01003i	0.334407	+	0.334407i
$324$		0			0
$325$	9.29848	−	9.29848i	0.515787	−	0.515787i
$326$		0			0
$327$			14.0677i			0.777948i
$328$		0			0
$329$	28.3455	+	5.75433i	1.56274	+	0.317247i
$330$		0			0
$331$	5.25316	−	5.25316i	0.288740	−	0.288740i	−0.547842	−	0.836582i	$-0.684551\pi$
$331$	5.25316	−	5.25316i	0.288740	−	0.288740i	0.836582	+	0.547842i	$0.184551\pi$
$332$		0			0
$333$	−0.392913	+	0.392913i	−0.0215315	+	0.0215315i
$334$		0			0
$335$	4.97202			0.271650
$336$		0			0
$337$	−12.0799			−0.658034			−0.329017	−	0.944324i	$-0.606717\pi$
$337$	−12.0799			−0.658034			−0.329017	+	0.944324i	$0.606717\pi$
$338$		0			0
$339$	21.4748	−	21.4748i	1.16635	−	1.16635i
$340$		0			0
$341$	11.4840	−	11.4840i	0.621892	−	0.621892i
$342$		0			0
$343$	−15.2765	−	10.4704i	−0.824852	−	0.565349i
$344$		0			0
$345$			1.58562i			0.0853671i
$346$		0			0
$347$	−19.3500	+	19.3500i	−1.03876	+	1.03876i	−0.0395438	+	0.999218i	$0.512590\pi$
$347$	−19.3500	+	19.3500i	−1.03876	+	1.03876i	−0.999218	+	0.0395438i	$0.987410\pi$
$348$		0			0
$349$	2.96915	+	2.96915i	0.158935	+	0.158935i	0.782095	−	0.623160i	$-0.214151\pi$
$349$	2.96915	+	2.96915i	0.158935	+	0.158935i	−0.623160	+	0.782095i	$0.714151\pi$
$350$		0			0
$351$		−	5.18084i		−	0.276533i
$352$		0			0
$353$			16.3191i			0.868576i	0.900774	+	0.434288i	$0.143000\pi$
$353$			16.3191i			0.868576i	−0.900774	+	0.434288i	$0.857000\pi$
$354$		0			0
$355$	5.32707	−	5.32707i	0.282731	−	0.282731i
$356$		0			0
$357$	−19.0917	−	28.8176i	−1.01044	−	1.52519i
$358$		0			0
$359$	−16.5357			−0.872721			−0.436361	−	0.899772i	$-0.643733\pi$
$359$	−16.5357			−0.872721			−0.436361	+	0.899772i	$0.643733\pi$
$360$		0			0
$361$			17.0799i			0.898942i
$362$		0			0
$363$	−4.51857	−	4.51857i	−0.237163	−	0.237163i
$364$		0			0
$365$	−6.93467	+	6.93467i	−0.362977	+	0.362977i
$366$		0			0
$367$	23.6780			1.23598			0.617992	−	0.786185i	$-0.287947\pi$
$367$	23.6780			1.23598			0.617992	+	0.786185i	$0.287947\pi$
$368$		0			0
$369$			10.3884i			0.540797i
$370$		0			0
$371$	14.8586	+	22.4281i	0.771422	+	1.16441i
$372$		0			0
$373$	21.9876	+	21.9876i	1.13848	+	1.13848i	0.988724	+	0.149753i	$0.0478477\pi$
$373$	21.9876	+	21.9876i	1.13848	+	1.13848i	0.149753	+	0.988724i	$0.452152\pi$
$374$		0			0
$375$	−22.2601			−1.14951
$376$		0			0
$377$	−8.15332			−0.419918
$378$		0			0
$379$	20.0100	−	20.0100i	1.02785	−	1.02785i	0.0282452	−	0.999601i	$-0.491008\pi$
$379$	20.0100	−	20.0100i	1.02785	−	1.02785i	0.999601	−	0.0282452i	$-0.00899192\pi$
$380$		0			0
$381$	9.28454	+	9.28454i	0.475662	+	0.475662i
$382$		0			0
$383$	5.17644			0.264504			0.132252	−	0.991216i	$-0.457779\pi$
$383$	5.17644			0.264504			0.132252	+	0.991216i	$0.457779\pi$
$384$		0			0
$385$	5.34904	−	26.3491i	0.272613	−	1.34287i
$386$		0			0
$387$	0.318492	+	0.318492i	0.0161899	+	0.0161899i
$388$		0			0
$389$	−4.15878	−	4.15878i	−0.210858	−	0.210858i	0.593774	−	0.804632i	$-0.297637\pi$
$389$	−4.15878	−	4.15878i	−0.210858	−	0.210858i	−0.804632	+	0.593774i	$0.797637\pi$
$390$		0			0
$391$			1.27085i			0.0642698i
$392$		0			0
$393$			3.68540i			0.185904i
$394$		0			0
$395$	−28.0259	−	28.0259i	−1.41014	−	1.41014i
$396$		0			0
$397$	14.8360	+	14.8360i	0.744599	+	0.744599i	0.973459	−	0.228860i	$-0.0734998\pi$
$397$	14.8360	+	14.8360i	0.744599	+	0.744599i	−0.228860	+	0.973459i	$0.573500\pi$
$398$		0			0
$399$	−1.55363	+	7.65306i	−0.0777785	+	0.383132i
$400$		0			0
$401$	22.1089			1.10406			0.552032	−	0.833823i	$-0.313853\pi$
$401$	22.1089			1.10406			0.552032	+	0.833823i	$0.313853\pi$
$402$		0			0
$403$	6.75105	+	6.75105i	0.336294	+	0.336294i
$404$		0			0
$405$	−28.5775	+	28.5775i	−1.42003	+	1.42003i
$406$		0			0
$407$	−1.02241			−0.0506787
$408$		0			0
$409$	−1.45826			−0.0721062			−0.0360531	−	0.999350i	$-0.511479\pi$
$409$	−1.45826			−0.0721062			−0.0360531	+	0.999350i	$0.511479\pi$
$410$		0			0
$411$	−11.6932	−	11.6932i	−0.576782	−	0.576782i
$412$		0			0
$413$	4.20027	+	6.34002i	0.206682	+	0.311972i
$414$		0			0
$415$		−	11.5653i		−	0.567719i
$416$		0			0
$417$	19.4380			0.951885
$418$		0			0
$419$	−24.2050	+	24.2050i	−1.18249	+	1.18249i	−0.203398	+	0.979096i	$0.565198\pi$
$419$	−24.2050	+	24.2050i	−1.18249	+	1.18249i	−0.979096	+	0.203398i	$0.934802\pi$
$420$		0			0
$421$	19.1878	+	19.1878i	0.935158	+	0.935158i	0.998022	−	0.0628646i	$-0.0200236\pi$
$421$	19.1878	+	19.1878i	0.935158	+	0.935158i	−0.0628646	+	0.998022i	$0.520024\pi$
$422$		0			0
$423$			16.8050i			0.817085i
$424$		0			0
$425$	−48.5102			−2.35309
$426$		0			0
$427$	15.5246	+	23.4334i	0.751290	+	1.13402i
$428$		0			0
$429$	−7.08351	+	7.08351i	−0.341995	+	0.341995i
$430$		0			0
$431$			20.4298i			0.984069i	0.870576	+	0.492034i	$0.163747\pi$
$431$			20.4298i			0.984069i	−0.870576	+	0.492034i	$0.836253\pi$
$432$		0			0
$433$			22.7267i			1.09218i	0.837727	+	0.546089i	$0.183884\pi$
$433$			22.7267i			1.09218i	−0.837727	+	0.546089i	$0.816116\pi$
$434$		0			0
$435$	26.5357	+	26.5357i	1.27229	+	1.27229i
$436$		0			0
$437$	0.203007	−	0.203007i	0.00971115	−	0.00971115i
$438$		0			0
$439$			35.6766i			1.70275i	0.524557	+	0.851375i	$0.324231\pi$
$439$			35.6766i			1.70275i	−0.524557	+	0.851375i	$0.675769\pi$
$440$		0			0
$441$	4.19598	−	9.90866i	0.199809	−	0.471841i
$442$		0			0
$443$	5.11829	−	5.11829i	0.243177	−	0.243177i	−0.574986	−	0.818163i	$-0.694993\pi$
$443$	5.11829	−	5.11829i	0.243177	−	0.243177i	0.818163	+	0.574986i	$0.194993\pi$
$444$		0			0
$445$	−35.7744	+	35.7744i	−1.69587	+	1.69587i
$446$		0			0
$447$	−17.5886			−0.831913
$448$		0			0
$449$	−35.6346			−1.68170			−0.840851	−	0.541266i	$-0.817945\pi$
$449$	−35.6346			−1.68170			−0.840851	+	0.541266i	$0.817945\pi$
$450$		0			0
$451$	−13.5159	+	13.5159i	−0.636438	+	0.636438i
$452$		0			0
$453$	2.34398	−	2.34398i	0.110130	−	0.110130i
$454$		0			0
$455$	15.4897	+	3.14453i	0.726170	+	0.147418i
$456$		0			0
$457$		−	4.78288i		−	0.223734i	−0.993723	−	0.111867i	$-0.964317\pi$
$457$		−	4.78288i		−	0.223734i	0.993723	−	0.111867i	$-0.0356830\pi$
$458$		0			0
$459$	−13.5142	+	13.5142i	−0.630791	+	0.630791i
$460$		0			0
$461$	6.54100	+	6.54100i	0.304645	+	0.304645i	0.842828	−	0.538183i	$-0.180889\pi$
$461$	6.54100	+	6.54100i	0.304645	+	0.304645i	−0.538183	+	0.842828i	$0.680889\pi$
$462$		0			0
$463$		−	0.771348i		−	0.0358476i	−0.999839	−	0.0179238i	$-0.994294\pi$
$463$		−	0.771348i		−	0.0358476i	0.999839	−	0.0179238i	$-0.00570563\pi$
$464$		0			0
$465$		−	43.9437i		−	2.03784i
$466$		0			0
$467$	2.51085	−	2.51085i	0.116188	−	0.116188i	−0.646622	−	0.762810i	$-0.723819\pi$
$467$	2.51085	−	2.51085i	0.116188	−	0.116188i	0.762810	+	0.646622i	$0.223819\pi$
$468$		0			0
$469$	2.02214	+	3.05228i	0.0933737	+	0.140941i
$470$		0			0
$471$	8.59312			0.395950
$472$		0			0
$473$			0.828753i			0.0381061i
$474$		0			0
$475$	7.74906	+	7.74906i	0.355551	+	0.355551i
$476$		0			0
$477$	−11.0530	+	11.0530i	−0.506080	+	0.506080i
$478$		0			0
$479$	9.93034			0.453729			0.226865	−	0.973926i	$-0.427153\pi$
$479$	9.93034			0.453729			0.226865	+	0.973926i	$0.427153\pi$
$480$		0			0
$481$		−	0.601038i		−	0.0274050i
$482$		0			0
$483$	−0.973402	+	0.644879i	−0.0442913	+	0.0293430i
$484$		0			0
$485$	−7.21173	−	7.21173i	−0.327468	−	0.327468i
$486$		0			0
$487$	−7.40739			−0.335661			−0.167830	−	0.985816i	$-0.553676\pi$
$487$	−7.40739			−0.335661			−0.167830	+	0.985816i	$0.553676\pi$
$488$		0			0
$489$	2.45290			0.110924
$490$		0			0
$491$	−21.4988	+	21.4988i	−0.970229	+	0.970229i	−0.999569	−	0.0293409i	$-0.990659\pi$
$491$	−21.4988	+	21.4988i	−0.970229	+	0.970229i	0.0293409	+	0.999569i	$0.490659\pi$
$492$		0			0
$493$	21.2680	+	21.2680i	0.957862	+	0.957862i
$494$		0			0
$495$	15.6214			0.702128
$496$		0			0
$497$	5.43678	+	1.10371i	0.243873	+	0.0495079i
$498$		0			0
$499$	23.3206	+	23.3206i	1.04397	+	1.04397i	0.998988	+	0.0449856i	$0.0143242\pi$
$499$	23.3206	+	23.3206i	1.04397	+	1.04397i	0.0449856	+	0.998988i	$0.485676\pi$
$500$		0			0
$501$	9.82885	+	9.82885i	0.439121	+	0.439121i
$502$		0			0
$503$		−	38.8858i		−	1.73383i	−0.498456	−	0.866915i	$-0.666099\pi$
$503$		−	38.8858i		−	1.73383i	0.498456	−	0.866915i	$-0.333901\pi$
$504$		0			0
$505$		−	25.1924i		−	1.12105i
$506$		0			0
$507$	15.4163	+	15.4163i	0.684662	+	0.684662i
$508$		0			0
$509$	−8.21025	−	8.21025i	−0.363913	−	0.363913i	0.501339	−	0.865251i	$-0.332841\pi$
$509$	−8.21025	−	8.21025i	−0.363913	−	0.363913i	−0.865251	+	0.501339i	$0.832841\pi$
$510$		0			0
$511$	−7.07749	−	1.43678i	−0.313090	−	0.0635595i
$512$		0			0
$513$	4.31755			0.190625
$514$		0			0
$515$	35.0560	+	35.0560i	1.54475	+	1.54475i
$516$		0			0
$517$	−21.8642	+	21.8642i	−0.961588	+	0.961588i
$518$		0			0
$519$	−11.4358			−0.501978
$520$		0			0
$521$	11.9433			0.523245			0.261623	−	0.965170i	$-0.415742\pi$
$521$	11.9433			0.523245			0.261623	+	0.965170i	$0.415742\pi$
$522$		0			0
$523$	−13.3060	−	13.3060i	−0.581832	−	0.581832i	0.353574	−	0.935406i	$-0.384966\pi$
$523$	−13.3060	−	13.3060i	−0.581832	−	0.581832i	−0.935406	+	0.353574i	$0.884966\pi$
$524$		0			0
$525$	−24.6159	−	37.1561i	−1.07433	−	1.62162i
$526$		0			0
$527$		−	35.2203i		−	1.53422i
$528$		0			0
$529$	−22.9571			−0.998134
$530$		0			0
$531$	−3.12447	+	3.12447i	−0.135590	+	0.135590i
$532$		0			0
$533$	−7.94554	−	7.94554i	−0.344160	−	0.344160i
$534$		0			0
$535$		−	50.1007i		−	2.16604i
$536$		0			0
$537$	48.7202			2.10243
$538$		0			0
$539$	18.3510	−	7.43253i	0.790432	−	0.320142i
$540$		0			0
$541$	12.1274	−	12.1274i	0.521397	−	0.521397i	−0.396596	−	0.917993i	$-0.629809\pi$
$541$	12.1274	−	12.1274i	0.521397	−	0.521397i	0.917993	+	0.396596i	$0.129809\pi$
$542$		0			0
$543$			11.1528i			0.478614i
$544$		0			0
$545$			23.7285i			1.01642i
$546$		0			0
$547$	−16.7858	−	16.7858i	−0.717710	−	0.717710i	0.250426	−	0.968136i	$-0.419429\pi$
$547$	−16.7858	−	16.7858i	−0.717710	−	0.717710i	−0.968136	+	0.250426i	$0.919429\pi$
$548$		0			0
$549$	−11.5484	+	11.5484i	−0.492873	+	0.492873i
$550$		0			0
$551$		−	6.79472i		−	0.289465i
$552$		0			0
$553$	5.80664	−	28.6031i	0.246923	−	1.21633i
$554$		0			0
$555$	−1.95613	+	1.95613i	−0.0830332	+	0.0830332i
$556$		0			0
$557$	10.2218	−	10.2218i	0.433110	−	0.433110i	−0.456575	−	0.889685i	$-0.650924\pi$
$557$	10.2218	−	10.2218i	0.433110	−	0.433110i	0.889685	+	0.456575i	$0.150924\pi$
$558$		0			0
$559$	−0.487196			−0.0206062
$560$		0			0
$561$	36.9547			1.56023
$562$		0			0
$563$	21.4500	−	21.4500i	0.904008	−	0.904008i	−0.0917721	−	0.995780i	$-0.529253\pi$
$563$	21.4500	−	21.4500i	0.904008	−	0.904008i	0.995780	+	0.0917721i	$0.0292531\pi$
$564$		0			0
$565$	36.2222	−	36.2222i	1.52388	−	1.52388i
$566$		0			0
$567$	−29.1661	−	5.92093i	−1.22486	−	0.248656i
$568$		0			0
$569$		−	39.9262i		−	1.67379i	−0.547361	−	0.836896i	$-0.684368\pi$
$569$		−	39.9262i		−	1.67379i	0.547361	−	0.836896i	$-0.315632\pi$
$570$		0			0
$571$	20.6416	−	20.6416i	0.863825	−	0.863825i	−0.127955	−	0.991780i	$-0.540841\pi$
$571$	20.6416	−	20.6416i	0.863825	−	0.863825i	0.991780	+	0.127955i	$0.0408413\pi$
$572$		0			0
$573$	−2.41005	−	2.41005i	−0.100681	−	0.100681i
$574$		0			0
$575$			1.63858i			0.0683336i
$576$		0			0
$577$		−	0.915806i		−	0.0381255i	−0.999818	−	0.0190628i	$-0.993932\pi$
$577$		−	0.915806i		−	0.0381255i	0.999818	−	0.0190628i	$-0.00606823\pi$
$578$		0			0
$579$	24.8572	−	24.8572i	1.03303	−	1.03303i
$580$		0			0
$581$	7.09986	−	4.70366i	0.294552	−	0.195141i
$582$		0			0
$583$	−28.7611			−1.19116
$584$		0			0
$585$			9.18328i			0.379682i
$586$		0			0
$587$	19.0031	+	19.0031i	0.784343	+	0.784343i	0.980560	−	0.196218i	$-0.0628659\pi$
$587$	19.0031	+	19.0031i	0.784343	+	0.784343i	−0.196218	+	0.980560i	$0.562866\pi$
$588$		0			0
$589$	−5.62611	+	5.62611i	−0.231820	+	0.231820i
$590$		0			0
$591$	36.7892			1.51331
$592$		0			0
$593$		−	36.4252i		−	1.49581i	−0.663808	−	0.747903i	$-0.731061\pi$
$593$		−	36.4252i		−	1.49581i	0.663808	−	0.747903i	$-0.268939\pi$
$594$		0			0
$595$	−32.2025	−	48.6076i	−1.32018	−	1.99272i
$596$		0			0
$597$	−24.4012	−	24.4012i	−0.998673	−	0.998673i
$598$		0			0
$599$	4.26923			0.174436			0.0872181	−	0.996189i	$-0.472202\pi$
$599$	4.26923			0.174436			0.0872181	+	0.996189i	$0.472202\pi$
$600$		0			0
$601$	−26.3491			−1.07480			−0.537400	−	0.843327i	$-0.680594\pi$
$601$	−26.3491			−1.07480			−0.537400	+	0.843327i	$0.680594\pi$
$602$		0			0
$603$	−1.50422	+	1.50422i	−0.0612564	+	0.0612564i
$604$		0			0
$605$	−7.62161	−	7.62161i	−0.309863	−	0.309863i
$606$		0			0
$607$	−30.8291			−1.25131			−0.625657	−	0.780098i	$-0.715169\pi$
$607$	−30.8291			−1.25131			−0.625657	+	0.780098i	$0.715169\pi$
$608$		0			0
$609$	−5.49789	+	27.0822i	−0.222786	+	1.09743i
$610$		0			0
$611$	−12.8533	−	12.8533i	−0.519987	−	0.519987i
$612$		0			0
$613$	2.17031	+	2.17031i	0.0876578	+	0.0876578i	0.749576	−	0.661918i	$-0.230257\pi$
$613$	2.17031	+	2.17031i	0.0876578	+	0.0876578i	−0.661918	+	0.749576i	$0.730257\pi$
$614$		0			0
$615$			51.7189i			2.08551i
$616$		0			0
$617$			36.8410i			1.48316i	0.670863	+	0.741581i	$0.265924\pi$
$617$			36.8410i			1.48316i	−0.670863	+	0.741581i	$0.734076\pi$
$618$		0			0
$619$	−31.0857	−	31.0857i	−1.24944	−	1.24944i	−0.955967	−	0.293474i	$-0.905188\pi$
$619$	−31.0857	−	31.0857i	−1.24944	−	1.24944i	−0.293474	−	0.955967i	$-0.594812\pi$
$620$		0			0
$621$	0.456485	+	0.456485i	0.0183181	+	0.0183181i
$622$		0			0
$623$	−36.5112	−	7.41203i	−1.46279	−	0.296957i
$624$		0			0
$625$	1.99640			0.0798559
$626$		0			0
$627$	−5.90317	−	5.90317i	−0.235750	−	0.235750i
$628$		0			0
$629$	−1.56781	+	1.56781i	−0.0625127	+	0.0625127i
$630$		0			0
$631$	29.6001			1.17836			0.589181	−	0.808001i	$-0.299451\pi$
$631$	29.6001			1.17836			0.589181	+	0.808001i	$0.299451\pi$
$632$		0			0
$633$	−3.70400			−0.147221
$634$		0			0
$635$	15.6605	+	15.6605i	0.621469	+	0.621469i
$636$		0			0
$637$	4.36934	+	10.7879i	0.173119	+	0.427433i
$638$		0			0
$639$			3.22326i			0.127510i
$640$		0			0
$641$	13.8524			0.547138			0.273569	−	0.961852i	$-0.411796\pi$
$641$	13.8524			0.547138			0.273569	+	0.961852i	$0.411796\pi$
$642$		0			0
$643$	−27.3875	+	27.3875i	−1.08006	+	1.08006i	−0.0835527	+	0.996503i	$0.526627\pi$
$643$	−27.3875	+	27.3875i	−1.08006	+	1.08006i	−0.996503	+	0.0835527i	$0.973373\pi$
$644$		0			0
$645$	1.58562	+	1.58562i	0.0624339	+	0.0624339i
$646$		0			0
$647$			22.7635i			0.894926i	0.894302	+	0.447463i	$0.147672\pi$
$647$			22.7635i			0.894926i	−0.894302	+	0.447463i	$0.852328\pi$
$648$		0			0
$649$	−8.13023			−0.319140
$650$		0			0
$651$	26.9767	−	17.8721i	1.05730	−	0.700463i
$652$		0			0
$653$	−1.97854	+	1.97854i	−0.0774261	+	0.0774261i	−0.744759	−	0.667333i	$-0.767436\pi$
$653$	−1.97854	+	1.97854i	−0.0774261	+	0.0774261i	0.667333	+	0.744759i	$0.267436\pi$
$654$		0			0
$655$			6.21628i			0.242890i
$656$		0			0
$657$		−	4.19598i		−	0.163701i
$658$		0			0
$659$	−2.71933	−	2.71933i	−0.105930	−	0.105930i	0.652155	−	0.758085i	$-0.273865\pi$
$659$	−2.71933	−	2.71933i	−0.105930	−	0.105930i	−0.758085	+	0.652155i	$0.773865\pi$
$660$		0			0
$661$	19.7141	−	19.7141i	0.766790	−	0.766790i	−0.210750	−	0.977540i	$-0.567591\pi$
$661$	19.7141	−	19.7141i	0.766790	−	0.766790i	0.977540	+	0.210750i	$0.0675906\pi$
$662$		0			0
$663$			21.7245i			0.843708i
$664$		0			0
$665$	−2.62055	+	12.9087i	−0.101621	+	0.500576i
$666$		0			0
$667$	0.718391	−	0.718391i	0.0278162	−	0.0278162i
$668$		0			0
$669$	−4.64607	+	4.64607i	−0.179628	+	0.179628i
$670$		0			0
$671$	−30.0502			−1.16008
$672$		0			0
$673$	3.95707			0.152534			0.0762670	−	0.997087i	$-0.475700\pi$
$673$	3.95707			0.152534			0.0762670	+	0.997087i	$0.475700\pi$
$674$		0			0
$675$	−17.4247	+	17.4247i	−0.670675	+	0.670675i
$676$		0			0
$677$	−8.07810	+	8.07810i	−0.310466	+	0.310466i	−0.845090	−	0.534624i	$-0.820453\pi$
$677$	−8.07810	+	8.07810i	−0.310466	+	0.310466i	0.534624	+	0.845090i	$0.320453\pi$
$678$		0			0
$679$	1.49419	−	7.36027i	0.0573416	−	0.282461i
$680$		0			0
$681$		−	18.5862i		−	0.712226i
$682$		0			0
$683$	17.1664	−	17.1664i	0.656853	−	0.656853i	−0.297781	−	0.954634i	$-0.596247\pi$
$683$	17.1664	−	17.1664i	0.656853	−	0.656853i	0.954634	+	0.297781i	$0.0962467\pi$
$684$		0			0
$685$	−19.7233	−	19.7233i	−0.753587	−	0.753587i
$686$		0			0
$687$		−	35.9272i		−	1.37071i
$688$		0			0
$689$		−	16.9077i		−	0.644132i
$690$		0			0
$691$	11.8005	−	11.8005i	0.448912	−	0.448912i	−0.446081	−	0.894993i	$-0.647181\pi$
$691$	11.8005	−	11.8005i	0.448912	−	0.448912i	0.894993	+	0.446081i	$0.147181\pi$
$692$		0			0
$693$	6.35327	+	9.58983i	0.241341	+	0.364288i
$694$		0			0
$695$	32.7868			1.24367
$696$		0			0
$697$			41.4520i			1.57010i
$698$		0			0
$699$	−22.5756	−	22.5756i	−0.853888	−	0.853888i
$700$		0			0
$701$	22.7735	−	22.7735i	0.860141	−	0.860141i	−0.131213	−	0.991354i	$-0.541887\pi$
$701$	22.7735	−	22.7735i	0.860141	−	0.860141i	0.991354	+	0.131213i	$0.0418871\pi$
$702$		0			0
$703$	0.500886			0.0188913
$704$		0			0
$705$			83.6641i			3.15097i
$706$		0			0
$707$	15.4654	−	10.2458i	0.581636	−	0.385334i
$708$		0			0
$709$	−18.6809	−	18.6809i	−0.701578	−	0.701578i	0.263171	−	0.964749i	$-0.415232\pi$
$709$	−18.6809	−	18.6809i	−0.701578	−	0.701578i	−0.964749	+	0.263171i	$0.915232\pi$
$710$		0			0
$711$	16.9577			0.635965
$712$		0			0
$713$	−1.18967			−0.0445536
$714$		0			0
$715$	−11.9480	+	11.9480i	−0.446829	+	0.446829i
$716$		0			0
$717$	28.6071	+	28.6071i	1.06835	+	1.06835i
$718$		0			0
$719$	−13.0150			−0.485378			−0.242689	−	0.970104i	$-0.578029\pi$
$719$	−13.0150			−0.485378			−0.242689	+	0.970104i	$0.578029\pi$
$720$		0			0
$721$	−7.26319	+	35.7780i	−0.270495	+	1.33244i
$722$		0			0
$723$	−36.6797	−	36.6797i	−1.36413	−	1.36413i
$724$		0			0
$725$	27.4220	+	27.4220i	1.01843	+	1.01843i
$726$		0			0
$727$			19.1133i			0.708874i	0.935080	+	0.354437i	$0.115327\pi$
$727$			19.1133i			0.708874i	−0.935080	+	0.354437i	$0.884673\pi$
$728$		0			0
$729$			2.61946i			0.0970171i
$730$		0			0
$731$	1.27085	+	1.27085i	0.0470042	+	0.0470042i
$732$		0			0
$733$	−33.5066	−	33.5066i	−1.23759	−	1.23759i	−0.960982	−	0.276611i	$-0.910789\pi$
$733$	−33.5066	−	33.5066i	−1.23759	−	1.23759i	−0.276611	−	0.960982i	$-0.589211\pi$
$734$		0			0
$735$	20.8898	−	49.3306i	0.770533	−	1.81959i
$736$		0			0
$737$	−3.91415			−0.144179
$738$		0			0
$739$	−8.01448	−	8.01448i	−0.294817	−	0.294817i	0.544163	−	0.838980i	$-0.316847\pi$
$739$	−8.01448	−	8.01448i	−0.294817	−	0.294817i	−0.838980	+	0.544163i	$0.816847\pi$
$740$		0			0
$741$	3.47028	−	3.47028i	0.127484	−	0.127484i
$742$		0			0
$743$	−38.9072			−1.42737			−0.713683	−	0.700469i	$-0.752974\pi$
$743$	−38.9072			−1.42737			−0.713683	+	0.700469i	$0.752974\pi$
$744$		0			0
$745$	−29.6673			−1.08693
$746$		0			0
$747$	3.49893	+	3.49893i	0.128019	+	0.128019i
$748$		0			0
$749$	30.7564	−	20.3761i	1.12381	−	0.744528i
$750$		0			0
$751$			17.6640i			0.644570i	0.946643	+	0.322285i	$0.104451\pi$
$751$			17.6640i			0.644570i	−0.946643	+	0.322285i	$0.895549\pi$
$752$		0			0
$753$	−40.2008			−1.46500
$754$		0			0
$755$	3.95367	−	3.95367i	0.143889	−	0.143889i
$756$		0			0
$757$	−21.2828	−	21.2828i	−0.773535	−	0.773535i	0.205187	−	0.978723i	$-0.434220\pi$
$757$	−21.2828	−	21.2828i	−0.773535	−	0.773535i	−0.978723	+	0.205187i	$0.934220\pi$
$758$		0			0
$759$		−	1.24826i		−	0.0453089i
$760$		0			0
$761$	−15.1923			−0.550719			−0.275359	−	0.961341i	$-0.588797\pi$
$761$	−15.1923			−0.550719			−0.275359	+	0.961341i	$0.588797\pi$
$762$		0			0
$763$	−14.5667	+	9.65048i	−0.527351	+	0.349371i
$764$		0			0
$765$	23.9546	−	23.9546i	0.866082	−	0.866082i
$766$		0			0
$767$		−	4.77950i		−	0.172578i
$768$		0			0
$769$		−	40.3950i		−	1.45668i	−0.685216	−	0.728340i	$-0.740292\pi$
$769$		−	40.3950i		−	1.45668i	0.685216	−	0.728340i	$-0.259708\pi$
$770$		0			0
$771$	−8.13436	−	8.13436i	−0.292952	−	0.292952i
$772$		0			0
$773$	−13.5959	+	13.5959i	−0.489010	+	0.489010i	−0.907994	−	0.418983i	$-0.862387\pi$
$773$	−13.5959	+	13.5959i	−0.489010	+	0.489010i	0.418983	+	0.907994i	$0.362387\pi$
$774$		0			0
$775$		−	45.4114i		−	1.63123i
$776$		0			0
$777$	−1.99642	−	0.405287i	−0.0716212	−	0.0145396i
$778$		0			0
$779$	6.62156	−	6.62156i	0.237242	−	0.237242i
$780$		0			0
$781$	−4.19365	+	4.19365i	−0.150061	+	0.150061i
$782$		0			0
$783$	15.2787			0.546017
$784$		0			0
$785$	14.4943			0.517323
$786$		0			0
$787$	−29.0146	+	29.0146i	−1.03426	+	1.03426i	−0.0348686	+	0.999392i	$0.511101\pi$
$787$	−29.0146	+	29.0146i	−1.03426	+	1.03426i	−0.999392	+	0.0348686i	$0.988899\pi$
$788$		0			0
$789$	−0.545783	+	0.545783i	−0.0194304	+	0.0194304i
$790$		0			0
$791$	36.9683	+	7.50482i	1.31444	+	0.266841i
$792$		0			0
$793$		−	17.6655i		−	0.627321i
$794$		0			0
$795$	−55.0276	+	55.0276i	−1.95163	+	1.95163i
$796$		0			0
$797$	21.9291	+	21.9291i	0.776770	+	0.776770i	0.979280	−	0.202510i	$-0.0649099\pi$
$797$	21.9291	+	21.9291i	0.776770	+	0.776770i	−0.202510	+	0.979280i	$0.564910\pi$
$798$		0			0
$799$			67.0556i			2.37226i
$800$		0			0
$801$		−	21.6461i		−	0.764828i
$802$		0			0
$803$	5.45921	−	5.45921i	0.192651	−	0.192651i
$804$		0			0
$805$	−1.64187	+	1.08774i	−0.0578682	+	0.0383378i
$806$		0			0
$807$	56.9417			2.00444
$808$		0			0
$809$		−	2.96068i		−	0.104092i	−0.998645	−	0.0520459i	$-0.983426\pi$
$809$		−	2.96068i		−	0.104092i	0.998645	−	0.0520459i	$-0.0165742\pi$
$810$		0			0
$811$	−10.4787	−	10.4787i	−0.367956	−	0.367956i	0.498775	−	0.866731i	$-0.333783\pi$
$811$	−10.4787	−	10.4787i	−0.367956	−	0.367956i	−0.866731	+	0.498775i	$0.833783\pi$
$812$		0			0
$813$	14.5723	−	14.5723i	0.511073	−	0.511073i
$814$		0			0
$815$	4.13739			0.144927
$816$		0			0
$817$		−	0.406014i		−	0.0142046i
$818$		0			0
$819$	−5.63755	+	3.73488i	−0.196992	+	0.130507i
$820$		0			0
$821$	−10.7214	−	10.7214i	−0.374181	−	0.374181i	0.494817	−	0.868997i	$-0.335235\pi$
$821$	−10.7214	−	10.7214i	−0.374181	−	0.374181i	−0.868997	+	0.494817i	$0.835235\pi$
$822$		0			0
$823$	−9.88500			−0.344569			−0.172285	−	0.985047i	$-0.555115\pi$
$823$	−9.88500			−0.344569			−0.172285	+	0.985047i	$0.555115\pi$
$824$		0			0
$825$	47.6477			1.65888
$826$		0			0
$827$	16.5166	−	16.5166i	0.574338	−	0.574338i	−0.359000	−	0.933338i	$-0.616882\pi$
$827$	16.5166	−	16.5166i	0.574338	−	0.574338i	0.933338	+	0.359000i	$0.116882\pi$
$828$		0			0
$829$	−23.8671	−	23.8671i	−0.828939	−	0.828939i	0.158431	−	0.987370i	$-0.449356\pi$
$829$	−23.8671	−	23.8671i	−0.828939	−	0.828939i	−0.987370	+	0.158431i	$0.949356\pi$
$830$		0			0
$831$	8.90499			0.308911
$832$		0			0
$833$	16.7429	−	39.5378i	0.580107	−	1.36990i
$834$		0			0
$835$	16.5786	+	16.5786i	0.573727	+	0.573727i
$836$		0			0
$837$	−12.6510	−	12.6510i	−0.437281	−	0.437281i
$838$		0			0
$839$		−	30.3282i		−	1.04705i	−0.852012	−	0.523523i	$-0.824617\pi$
$839$		−	30.3282i		−	1.04705i	0.852012	−	0.523523i	$-0.175383\pi$
$840$		0			0
$841$			4.95519i			0.170869i
$842$		0			0
$843$	29.9133	+	29.9133i	1.03027	+	1.03027i
$844$		0			0
$845$	26.0032	+	26.0032i	0.894536	+	0.894536i
$846$		0			0
$847$	1.57911	−	7.77859i	0.0542588	−	0.267275i
$848$		0			0
$849$	−58.7890			−2.01763
$850$		0			0
$851$	0.0529576	+	0.0529576i	0.00181536	+	0.00181536i
$852$		0			0
$853$	10.6402	−	10.6402i	0.364313	−	0.364313i	−0.501085	−	0.865398i	$-0.667066\pi$
$853$	10.6402	−	10.6402i	0.364313	−	0.364313i	0.865398	+	0.501085i	$0.167066\pi$
$854$		0			0
$855$	−7.65306			−0.261729
$856$		0			0
$857$	36.7524			1.25544			0.627719	−	0.778440i	$-0.283989\pi$
$857$	36.7524			1.25544			0.627719	+	0.778440i	$0.283989\pi$
$858$		0			0
$859$	19.5021	+	19.5021i	0.665403	+	0.665403i	0.956648	−	0.291245i	$-0.0940695\pi$
$859$	19.5021	+	19.5021i	0.665403	+	0.665403i	−0.291245	+	0.956648i	$0.594069\pi$
$860$		0			0
$861$	−31.7498	+	21.0343i	−1.08203	+	0.716847i
$862$		0			0
$863$			37.5305i			1.27755i	0.769392	+	0.638777i	$0.220559\pi$
$863$			37.5305i			1.27755i	−0.769392	+	0.638777i	$0.779441\pi$
$864$		0			0
$865$	−19.2892			−0.655852
$866$		0			0
$867$	31.0631	−	31.0631i	1.05496	−	1.05496i
$868$		0			0
$869$	22.0630	+	22.0630i	0.748436	+	0.748436i
$870$		0			0
$871$		−	2.30100i		−	0.0779663i
$872$		0			0
$873$	4.36362			0.147686
$874$		0			0
$875$	−15.2705	−	23.0497i	−0.516236	−	0.779224i
$876$		0			0
$877$	24.2169	−	24.2169i	0.817746	−	0.817746i	−0.168035	−	0.985781i	$-0.553742\pi$
$877$	24.2169	−	24.2169i	0.817746	−	0.817746i	0.985781	+	0.168035i	$0.0537422\pi$
$878$		0			0
$879$			55.1456i			1.86001i
$880$		0			0
$881$		−	11.3518i		−	0.382453i	−0.981546	−	0.191226i	$-0.938754\pi$
$881$		−	11.3518i		−	0.382453i	0.981546	−	0.191226i	$-0.0612464\pi$
$882$		0			0
$883$	3.21956	+	3.21956i	0.108347	+	0.108347i	0.759202	−	0.650855i	$-0.225589\pi$
$883$	3.21956	+	3.21956i	0.108347	+	0.108347i	−0.650855	+	0.759202i	$0.725589\pi$
$884$		0			0
$885$	−15.5553	+	15.5553i	−0.522885	+	0.522885i
$886$		0			0
$887$		−	27.1238i		−	0.910728i	−0.890305	−	0.455364i	$-0.849509\pi$
$887$		−	27.1238i		−	0.910728i	0.890305	−	0.455364i	$-0.150491\pi$
$888$		0			0
$889$	−3.24468	+	15.9831i	−0.108823	+	0.536055i
$890$		0			0
$891$	22.4972	−	22.4972i	0.753686	−	0.753686i
$892$		0			0
$893$	10.7115	−	10.7115i	0.358447	−	0.358447i
$894$		0			0
$895$	82.1780			2.74691
$896$		0			0
$897$	0.733810			0.0245012
$898$		0			0
$899$	−19.9094	+	19.9094i	−0.664015	+	0.664015i
$900$		0			0
$901$	−44.1038	+	44.1038i	−1.46931	+	1.46931i
$902$		0			0
$903$	−0.328523	+	1.61828i	−0.0109325	+	0.0538530i
$904$		0			0
$905$			18.8118i			0.625327i
$906$		0			0
$907$	−37.2429	+	37.2429i	−1.23663	+	1.23663i	−0.275260	+	0.961370i	$0.588764\pi$
$907$	−37.2429	+	37.2429i	−1.23663	+	1.23663i	−0.961370	+	0.275260i	$0.911236\pi$
$908$		0			0
$909$	7.62161	+	7.62161i	0.252793	+	0.252793i
$910$		0			0
$911$			18.3761i			0.608827i	0.952540	+	0.304414i	$0.0984605\pi$
$911$			18.3761i			0.608827i	−0.952540	+	0.304414i	$0.901540\pi$
$912$		0			0
$913$			9.10463i			0.301319i
$914$		0			0
$915$	−57.4940	+	57.4940i	−1.90069	+	1.90069i
$916$		0			0
$917$	−3.81612	+	2.52818i	−0.126020	+	0.0834880i
$918$		0			0
$919$	−44.0441			−1.45288			−0.726441	−	0.687229i	$-0.758827\pi$
$919$	−44.0441			−1.45288			−0.726441	+	0.687229i	$0.758827\pi$
$920$		0			0
$921$			32.4175i			1.06819i
$922$		0			0
$923$	−2.46531	−	2.46531i	−0.0811467	−	0.0811467i
$924$		0			0
$925$	−2.02146	+	2.02146i	−0.0664653	+	0.0664653i
$926$		0			0
$927$	−21.2114			−0.696675
$928$		0			0
$929$		−	21.2756i		−	0.698030i	−0.937117	−	0.349015i	$-0.886516\pi$
$929$		−	21.2756i		−	0.698030i	0.937117	−	0.349015i	$-0.113484\pi$
$930$		0			0
$931$	−8.99031	+	3.64127i	−0.294646	+	0.119338i
$932$		0			0
$933$	−2.84272	−	2.84272i	−0.0930666	−	0.0930666i
$934$		0			0
$935$	62.3327			2.03850
$936$		0			0
$937$	−1.53994			−0.0503075			−0.0251537	−	0.999684i	$-0.508008\pi$
$937$	−1.53994			−0.0503075			−0.0251537	+	0.999684i	$0.508008\pi$
$938$		0			0
$939$	32.8969	−	32.8969i	1.07355	−	1.07355i
$940$		0			0
$941$	−15.3157	−	15.3157i	−0.499279	−	0.499279i	0.411934	−	0.911214i	$-0.364853\pi$
$941$	−15.3157	−	15.3157i	−0.499279	−	0.499279i	−0.911214	+	0.411934i	$0.864853\pi$
$942$		0			0
$943$	1.40017			0.0455957
$944$		0			0
$945$	−29.0266	−	5.89261i	−0.944236	−	0.191687i
$946$		0			0
$947$	32.3969	+	32.3969i	1.05276	+	1.05276i	0.998529	+	0.0542293i	$0.0172702\pi$
$947$	32.3969	+	32.3969i	1.05276	+	1.05276i	0.0542293	+	0.998529i	$0.482730\pi$
$948$		0			0
$949$	3.20929	+	3.20929i	0.104178	+	0.104178i
$950$		0			0
$951$		−	42.9706i		−	1.39342i
$952$		0			0
$953$			41.8875i			1.35687i	0.734661	+	0.678435i	$0.237341\pi$
$953$			41.8875i			1.35687i	−0.734661	+	0.678435i	$0.762659\pi$
$954$		0			0
$955$	−4.06512	−	4.06512i	−0.131544	−	0.131544i
$956$		0			0
$957$	−20.8898	−	20.8898i	−0.675273	−	0.675273i
$958$		0			0
$959$	4.08643	−	20.1295i	0.131958	−	0.650015i
$960$		0			0
$961$	1.97039			0.0635609
$962$		0			0
$963$	15.1573	+	15.1573i	0.488436	+	0.488436i
$964$		0			0
$965$	41.9274	−	41.9274i	1.34969	−	1.34969i
$966$		0			0
$967$	1.99067			0.0640156			0.0320078	−	0.999488i	$-0.489810\pi$
$967$	1.99067			0.0640156			0.0320078	+	0.999488i	$0.489810\pi$
$968$		0			0
$969$	−18.1045			−0.581600
$970$		0			0
$971$	4.05078	+	4.05078i	0.129996	+	0.129996i	0.769111	−	0.639115i	$-0.220699\pi$
$971$	4.05078	+	4.05078i	0.129996	+	0.129996i	−0.639115	+	0.769111i	$0.720699\pi$
$972$		0			0
$973$	13.3345	+	20.1275i	0.427485	+	0.645259i
$974$		0			0
$975$			28.0105i			0.897055i
$976$		0			0
$977$	25.0406			0.801119			0.400560	−	0.916271i	$-0.368816\pi$
$977$	25.0406			0.801119			0.400560	+	0.916271i	$0.368816\pi$
$978$		0			0
$979$	28.1629	−	28.1629i	0.900089	−	0.900089i
$980$		0			0
$981$	−7.17874	−	7.17874i	−0.229199	−	0.229199i
$982$		0			0
$983$			31.4745i			1.00388i	0.864902	+	0.501941i	$0.167380\pi$
$983$			31.4745i			1.00388i	−0.864902	+	0.501941i	$0.832620\pi$
$984$		0			0
$985$	62.0535			1.97719
$986$		0			0
$987$	−51.3608	+	34.0265i	−1.63483	+	1.08308i
$988$		0			0
$989$	0.0429270	−	0.0429270i	0.00136500	−	0.00136500i
$990$		0			0
$991$		−	52.9886i		−	1.68324i	−0.540072	−	0.841619i	$-0.681603\pi$
$991$		−	52.9886i		−	1.68324i	0.540072	−	0.841619i	$-0.318397\pi$
$992$		0			0
$993$			15.8245i			0.502175i
$994$		0			0
$995$	−41.1582	−	41.1582i	−1.30480	−	1.30480i
$996$		0			0
$997$	−7.16513	+	7.16513i	−0.226922	+	0.226922i	−0.811405	−	0.584484i	$-0.801297\pi$
$997$	−7.16513	+	7.16513i	−0.226922	+	0.226922i	0.584484	+	0.811405i	$0.301297\pi$
$998$		0			0
$999$			1.12630i			0.0356346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.j.d.335.2		16
4.3	odd	2		112.2.j.d.27.8	yes	16
7.6	odd	2	inner	448.2.j.d.335.7		16
8.3	odd	2		896.2.j.h.671.2		16
8.5	even	2		896.2.j.g.671.7		16
16.3	odd	4	inner	448.2.j.d.111.7		16
16.5	even	4		896.2.j.h.223.7		16
16.11	odd	4		896.2.j.g.223.2		16
16.13	even	4		112.2.j.d.83.7	yes	16
28.3	even	6		784.2.w.e.411.4		32
28.11	odd	6		784.2.w.e.411.3		32
28.19	even	6		784.2.w.e.619.1		32
28.23	odd	6		784.2.w.e.619.2		32
28.27	even	2		112.2.j.d.27.7	✓	16
56.13	odd	2		896.2.j.g.671.2		16
56.27	even	2		896.2.j.h.671.7		16
112.13	odd	4		112.2.j.d.83.8	yes	16
112.27	even	4		896.2.j.g.223.7		16
112.45	odd	12		784.2.w.e.19.2		32
112.61	odd	12		784.2.w.e.227.3		32
112.69	odd	4		896.2.j.h.223.2		16
112.83	even	4	inner	448.2.j.d.111.2		16
112.93	even	12		784.2.w.e.227.4		32
112.109	even	12		784.2.w.e.19.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.d.27.7	✓	16	28.27	even	2
112.2.j.d.27.8	yes	16	4.3	odd	2
112.2.j.d.83.7	yes	16	16.13	even	4
112.2.j.d.83.8	yes	16	112.13	odd	4
448.2.j.d.111.2		16	112.83	even	4	inner
448.2.j.d.111.7		16	16.3	odd	4	inner
448.2.j.d.335.2		16	1.1	even	1	trivial
448.2.j.d.335.7		16	7.6	odd	2	inner
784.2.w.e.19.1		32	112.109	even	12
784.2.w.e.19.2		32	112.45	odd	12
784.2.w.e.227.3		32	112.61	odd	12
784.2.w.e.227.4		32	112.93	even	12
784.2.w.e.411.3		32	28.11	odd	6
784.2.w.e.411.4		32	28.3	even	6
784.2.w.e.619.1		32	28.19	even	6
784.2.w.e.619.2		32	28.23	odd	6
896.2.j.g.223.2		16	16.11	odd	4
896.2.j.g.223.7		16	112.27	even	4
896.2.j.g.671.2		16	56.13	odd	2
896.2.j.g.671.7		16	8.5	even	2
896.2.j.h.223.2		16	112.69	odd	4
896.2.j.h.223.7		16	16.5	even	4
896.2.j.h.671.2		16	8.3	odd	2
896.2.j.h.671.7		16	56.27	even	2

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)

\(f(q)\)	\(=\)	\(q+(-1.50619 + 1.50619i) q^{3} +(-2.54054 + 2.54054i) q^{5} +(-2.59286 - 0.526369i) q^{7} -1.53721i q^{9} +O(q^{10})\)	\(q+(-1.50619 + 1.50619i) q^{3} +(-2.54054 + 2.54054i) q^{5} +(-2.59286 - 0.526369i) q^{7} -1.53721i q^{9} +(2.00000 - 2.00000i) q^{11} +(1.17573 + 1.17573i) q^{13} -7.65306i q^{15} -6.13381i q^{17} +(-0.979820 + 0.979820i) q^{19} +(4.69815 - 3.11253i) q^{21} -0.207188 q^{23} -7.90866i q^{25} +(-2.20324 - 2.20324i) q^{27} +(-3.46733 + 3.46733i) q^{29} +5.74198 q^{31} +6.02476i q^{33} +(7.92452 - 5.25000i) q^{35} +(-0.255601 - 0.255601i) q^{37} -3.54176 q^{39} -6.75794 q^{41} +(-0.207188 + 0.207188i) q^{43} +(3.90534 + 3.90534i) q^{45} -10.9321 q^{47} +(6.44587 + 2.72961i) q^{49} +(9.23868 + 9.23868i) q^{51} +(-7.19027 - 7.19027i) q^{53} +10.1621i q^{55} -2.95159i q^{57} +(-2.03256 - 2.03256i) q^{59} +(-7.51255 - 7.51255i) q^{61} +(-0.809141 + 3.98578i) q^{63} -5.97399 q^{65} +(-0.978537 - 0.978537i) q^{67} +(0.312065 - 0.312065i) q^{69} -2.09683 q^{71} +2.72961 q^{73} +(11.9119 + 11.9119i) q^{75} +(-6.23846 + 4.13299i) q^{77} +11.0315i q^{79} +11.2486 q^{81} +(-2.27616 + 2.27616i) q^{83} +(15.5832 + 15.5832i) q^{85} -10.4449i q^{87} +14.0814 q^{89} +(-2.42965 - 3.66739i) q^{91} +(-8.64851 + 8.64851i) q^{93} -4.97854i q^{95} +2.83866i q^{97} +(-3.07442 - 3.07442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 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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