LMFDB - Embedded newform 1148.2.n.d.365.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			365.4
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.d.953.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0323142 q^{3} +(-0.719662 + 2.21489i) q^{5} +(-0.809017 - 0.587785i) q^{7} -2.99896 q^{9} +O(q^{10})$	\(q-0.0323142 q^{3} +(-0.719662 + 2.21489i) q^{5} +(-0.809017 - 0.587785i) q^{7} -2.99896 q^{9} +(-0.332186 - 1.02236i) q^{11} +(2.86807 - 2.08377i) q^{13} +(0.0232553 - 0.0715725i) q^{15} +(-1.42577 - 4.38808i) q^{17} +(-1.24836 - 0.906987i) q^{19} +(0.0261428 + 0.0189938i) q^{21} +(-2.99955 + 2.17930i) q^{23} +(-0.342747 - 0.249020i) q^{25} +0.193852 q^{27} +(0.742663 - 2.28568i) q^{29} +(-1.15401 - 3.55167i) q^{31} +(0.0107343 + 0.0330369i) q^{33} +(1.88410 - 1.36888i) q^{35} +(2.86406 - 8.81466i) q^{37} +(-0.0926794 + 0.0673355i) q^{39} +(5.96303 - 2.33287i) q^{41} +(7.39938 - 5.37596i) q^{43} +(2.15823 - 6.64236i) q^{45} +(-0.695716 + 0.505468i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.0460728 + 0.141797i) q^{51} +(0.465753 - 1.43344i) q^{53} +2.50348 q^{55} +(0.0403398 + 0.0293086i) q^{57} +(-3.75650 + 2.72926i) q^{59} +(-8.51357 - 6.18547i) q^{61} +(2.42621 + 1.76274i) q^{63} +(2.55129 + 7.85207i) q^{65} +(-0.650634 + 2.00244i) q^{67} +(0.0969281 - 0.0704224i) q^{69} +(-2.49738 - 7.68616i) q^{71} +2.14822 q^{73} +(0.0110756 + 0.00804689i) q^{75} +(-0.332186 + 1.02236i) q^{77} -11.1652 q^{79} +8.99060 q^{81} -9.67861 q^{83} +10.7452 q^{85} +(-0.0239986 + 0.0738601i) q^{87} +(2.09856 + 1.52469i) q^{89} -3.54513 q^{91} +(0.0372908 + 0.114769i) q^{93} +(2.90728 - 2.11226i) q^{95} +(-1.67172 + 5.14502i) q^{97} +(0.996210 + 3.06602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.0323142			−0.0186566			−0.00932832	−	0.999956i	$-0.502969\pi$
$3$	−0.0323142			−0.0186566			−0.00932832	+	0.999956i	$0.502969\pi$
$4$		0			0
$5$	−0.719662	+	2.21489i	−0.321843	+	0.990530i	0.651003	+	0.759075i	$0.274348\pi$
$5$	−0.719662	+	2.21489i	−0.321843	+	0.990530i	−0.972846	+	0.231455i	$0.925652\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	−2.99896			−0.999652
$10$		0			0
$11$	−0.332186	−	1.02236i	−0.100158	−	0.308254i	0.888406	−	0.459059i	$-0.151813\pi$
$11$	−0.332186	−	1.02236i	−0.100158	−	0.308254i	−0.988564	+	0.150805i	$0.951813\pi$
$12$		0			0
$13$	2.86807	−	2.08377i	0.795459	−	0.577935i	−0.114120	−	0.993467i	$-0.536405\pi$
$13$	2.86807	−	2.08377i	0.795459	−	0.577935i	0.909578	+	0.415532i	$0.136405\pi$
$14$		0			0
$15$	0.0232553	−	0.0715725i	0.00600450	−	0.0184800i
$16$		0			0
$17$	−1.42577	−	4.38808i	−0.345801	−	1.06427i	−0.961154	−	0.276014i	$-0.910987\pi$
$17$	−1.42577	−	4.38808i	−0.345801	−	1.06427i	0.615353	−	0.788252i	$-0.289013\pi$
$18$		0			0
$19$	−1.24836	−	0.906987i	−0.286394	−	0.208077i	0.435308	−	0.900282i	$-0.356640\pi$
$19$	−1.24836	−	0.906987i	−0.286394	−	0.208077i	−0.721701	+	0.692205i	$0.756640\pi$
$20$		0			0
$21$	0.0261428	+	0.0189938i	0.00570482	+	0.00414479i
$22$		0			0
$23$	−2.99955	+	2.17930i	−0.625448	+	0.454415i	−0.854820	−	0.518924i	$-0.826333\pi$
$23$	−2.99955	+	2.17930i	−0.625448	+	0.454415i	0.229372	+	0.973339i	$0.426333\pi$
$24$		0			0
$25$	−0.342747	−	0.249020i	−0.0685493	−	0.0498040i
$26$		0			0
$27$	0.193852			0.0373068
$28$		0			0
$29$	0.742663	−	2.28568i	0.137909	−	0.424440i	−0.858122	−	0.513446i	$-0.828369\pi$
$29$	0.742663	−	2.28568i	0.137909	−	0.424440i	0.996031	+	0.0890053i	$0.0283688\pi$
$30$		0			0
$31$	−1.15401	−	3.55167i	−0.207266	−	0.637898i	−0.999613	−	0.0278274i	$-0.991141\pi$
$31$	−1.15401	−	3.55167i	−0.207266	−	0.637898i	0.792347	−	0.610070i	$-0.208859\pi$
$32$		0			0
$33$	0.0107343	+	0.0330369i	0.00186861	+	0.00575098i
$34$		0			0
$35$	1.88410	−	1.36888i	0.318471	−	0.231383i
$36$		0			0
$37$	2.86406	−	8.81466i	0.470848	−	1.44912i	−0.380629	−	0.924728i	$-0.624292\pi$
$37$	2.86406	−	8.81466i	0.470848	−	1.44912i	0.851477	−	0.524393i	$-0.175708\pi$
$38$		0			0
$39$	−0.0926794	+	0.0673355i	−0.0148406	+	0.0107823i
$40$		0			0
$41$	5.96303	−	2.33287i	0.931269	−	0.364332i
$41$	5.96303	−	2.33287i	0.931269	−	0.364332i
$42$		0			0
$43$	7.39938	−	5.37596i	1.12839	−	0.819827i	0.142935	−	0.989732i	$-0.454346\pi$
$43$	7.39938	−	5.37596i	1.12839	−	0.819827i	0.985460	+	0.169905i	$0.0543462\pi$
$44$		0			0
$45$	2.15823	−	6.64236i	0.321731	−	0.990185i
$46$		0			0
$47$	−0.695716	+	0.505468i	−0.101481	+	0.0737300i	−0.637368	−	0.770559i	$-0.719977\pi$
$47$	−0.695716	+	0.505468i	−0.101481	+	0.0737300i	0.535888	+	0.844289i	$0.319977\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	0.0460728	+	0.141797i	0.00645148	+	0.0198556i
$52$		0			0
$53$	0.465753	−	1.43344i	0.0639760	−	0.196898i	−0.913959	−	0.405806i	$-0.866991\pi$
$53$	0.465753	−	1.43344i	0.0639760	−	0.196898i	0.977935	+	0.208908i	$0.0669909\pi$
$54$		0			0
$55$	2.50348			0.337570
$56$		0			0
$57$	0.0403398	+	0.0293086i	0.00534314	+	0.00388202i
$58$		0			0
$59$	−3.75650	+	2.72926i	−0.489055	+	0.355319i	−0.804821	−	0.593518i	$-0.797739\pi$
$59$	−3.75650	+	2.72926i	−0.489055	+	0.355319i	0.315766	+	0.948837i	$0.397739\pi$
$60$		0			0
$61$	−8.51357	−	6.18547i	−1.09005	−	0.791968i	−0.110643	−	0.993860i	$-0.535291\pi$
$61$	−8.51357	−	6.18547i	−1.09005	−	0.791968i	−0.979408	+	0.201892i	$0.935291\pi$
$62$		0			0
$63$	2.42621	+	1.76274i	0.305673	+	0.222085i
$64$		0			0
$65$	2.55129	+	7.85207i	0.316449	+	0.973929i
$66$		0			0
$67$	−0.650634	+	2.00244i	−0.0794875	+	0.244638i	−0.982902	−	0.184132i	$-0.941053\pi$
$67$	−0.650634	+	2.00244i	−0.0794875	+	0.244638i	0.903414	+	0.428769i	$0.141053\pi$
$68$		0			0
$69$	0.0969281	−	0.0704224i	0.0116688	−	0.00847785i
$70$		0			0
$71$	−2.49738	−	7.68616i	−0.296385	−	0.912179i	−0.982753	−	0.184924i	$-0.940796\pi$
$71$	−2.49738	−	7.68616i	−0.296385	−	0.912179i	0.686368	−	0.727255i	$-0.259204\pi$
$72$		0			0
$73$	2.14822			0.251430			0.125715	−	0.992066i	$-0.459877\pi$
$73$	2.14822			0.251430			0.125715	+	0.992066i	$0.459877\pi$
$74$		0			0
$75$	0.0110756	+	0.00804689i	0.00127890	+	0.000929175i
$76$		0			0
$77$	−0.332186	+	1.02236i	−0.0378561	+	0.116509i
$78$		0			0
$79$	−11.1652			−1.25618			−0.628092	−	0.778139i	$-0.716164\pi$
$79$	−11.1652			−1.25618			−0.628092	+	0.778139i	$0.716164\pi$
$80$		0			0
$81$	8.99060			0.998956
$82$		0			0
$83$	−9.67861			−1.06237			−0.531183	−	0.847257i	$-0.678252\pi$
$83$	−9.67861			−1.06237			−0.531183	+	0.847257i	$0.678252\pi$
$84$		0			0
$85$	10.7452			1.16548
$86$		0			0
$87$	−0.0239986	+	0.0738601i	−0.00257292	+	0.00791863i
$88$		0			0
$89$	2.09856	+	1.52469i	0.222446	+	0.161617i	0.693427	−	0.720527i	$-0.256100\pi$
$89$	2.09856	+	1.52469i	0.222446	+	0.161617i	−0.470981	+	0.882143i	$0.656100\pi$
$90$		0			0
$91$	−3.54513			−0.371630
$92$		0			0
$93$	0.0372908	+	0.114769i	0.00386688	+	0.0119010i
$94$		0			0
$95$	2.90728	−	2.11226i	0.298280	−	0.216713i
$96$		0			0
$97$	−1.67172	+	5.14502i	−0.169737	+	0.522398i	−0.999354	−	0.0359355i	$-0.988559\pi$
$97$	−1.67172	+	5.14502i	−0.169737	+	0.522398i	0.829617	+	0.558333i	$0.188559\pi$
$98$		0			0
$99$	0.996210	+	3.06602i	0.100123	+	0.308147i
$100$		0			0
$101$	−11.1514	−	8.10195i	−1.10960	−	0.806174i	−0.127002	−	0.991902i	$-0.540536\pi$
$101$	−11.1514	−	8.10195i	−1.10960	−	0.806174i	−0.982601	+	0.185729i	$0.940536\pi$
$102$		0			0
$103$	2.12210	+	1.54180i	0.209097	+	0.151918i	0.687405	−	0.726274i	$-0.258750\pi$
$103$	2.12210	+	1.54180i	0.209097	+	0.151918i	−0.478308	+	0.878192i	$0.658750\pi$
$104$		0			0
$105$	−0.0608832	+	0.0442343i	−0.00594160	+	0.00431682i
$106$		0			0
$107$	−2.22358	−	1.61552i	−0.214961	−	0.156179i	0.475094	−	0.879935i	$-0.342414\pi$
$107$	−2.22358	−	1.61552i	−0.214961	−	0.156179i	−0.690056	+	0.723756i	$0.742414\pi$
$108$		0			0
$109$	10.5610			1.01156			0.505782	−	0.862661i	$-0.331204\pi$
$109$	10.5610			1.01156			0.505782	+	0.862661i	$0.331204\pi$
$110$		0			0
$111$	−0.0925498	+	0.284839i	−0.00878444	+	0.0270357i
$112$		0			0
$113$	−0.0760706	−	0.234121i	−0.00715612	−	0.0220243i	0.947415	−	0.320008i	$-0.103686\pi$
$113$	−0.0760706	−	0.234121i	−0.00715612	−	0.0220243i	−0.954571	+	0.297984i	$0.903686\pi$
$114$		0			0
$115$	−2.66825	−	8.21203i	−0.248815	−	0.765775i
$116$		0			0
$117$	−8.60121	+	6.24914i	−0.795182	+	0.577733i
$118$		0			0
$119$	−1.42577	+	4.38808i	−0.130700	+	0.402254i
$120$		0			0
$121$	7.96431	−	5.78641i	0.724028	−	0.526037i
$122$		0			0
$123$	−0.192691	+	0.0753848i	−0.0173743	+	0.00679722i
$124$		0			0
$125$	−8.62228	+	6.26446i	−0.771200	+	0.560310i
$126$		0			0
$127$	5.90322	−	18.1682i	0.523826	−	1.61217i	−0.242800	−	0.970076i	$-0.578066\pi$
$127$	5.90322	−	18.1682i	0.523826	−	1.61217i	0.766626	−	0.642094i	$-0.221934\pi$
$128$		0			0
$129$	−0.239105	+	0.173720i	−0.0210521	+	0.0152952i
$130$		0			0
$131$	−0.975564	−	3.00248i	−0.0852354	−	0.262328i	0.899351	−	0.437228i	$-0.144040\pi$
$131$	−0.975564	−	3.00248i	−0.0852354	−	0.262328i	−0.984586	+	0.174900i	$0.944040\pi$
$132$		0			0
$133$	0.476831	+	1.46754i	0.0413465	+	0.127251i
$134$		0			0
$135$	−0.139508	+	0.429361i	−0.0120069	+	0.0369535i
$136$		0			0
$137$	−6.02242			−0.514530			−0.257265	−	0.966341i	$-0.582821\pi$
$137$	−6.02242			−0.514530			−0.257265	+	0.966341i	$0.582821\pi$
$138$		0			0
$139$	−12.7678	−	9.27637i	−1.08295	−	0.786812i	−0.104758	−	0.994498i	$-0.533407\pi$
$139$	−12.7678	−	9.27637i	−1.08295	−	0.786812i	−0.978196	+	0.207686i	$0.933407\pi$
$140$		0			0
$141$	0.0224815	−	0.0163338i	0.00189329	−	0.00137555i
$142$		0			0
$143$	−3.08310	−	2.24000i	−0.257822	−	0.187319i
$144$		0			0
$145$	4.52807	+	3.28983i	0.376036	+	0.273206i
$146$		0			0
$147$	−0.00998565	−	0.0307327i	−0.000823603	−	0.00253479i
$148$		0			0
$149$	−1.84366	+	5.67421i	−0.151039	+	0.464849i	−0.997738	−	0.0672225i	$-0.978586\pi$
$149$	−1.84366	+	5.67421i	−0.151039	+	0.464849i	0.846699	+	0.532072i	$0.178586\pi$
$150$		0			0
$151$	−7.43455	+	5.40151i	−0.605015	+	0.439569i	−0.847655	−	0.530547i	$-0.821986\pi$
$151$	−7.43455	+	5.40151i	−0.605015	+	0.439569i	0.242640	+	0.970116i	$0.421986\pi$
$152$		0			0
$153$	4.27583	+	13.1597i	0.345680	+	1.06389i
$154$		0			0
$155$	8.69705			0.698564
$156$		0			0
$157$	10.1886	+	7.40246i	0.813140	+	0.590781i	0.914739	−	0.404045i	$-0.132396\pi$
$157$	10.1886	+	7.40246i	0.813140	+	0.590781i	−0.101599	+	0.994825i	$0.532396\pi$
$158$		0			0
$159$	−0.0150504	+	0.0463205i	−0.00119358	+	0.00367345i
$160$		0			0
$161$	3.70764			0.292203
$162$		0			0
$163$	−11.4755			−0.898831			−0.449416	−	0.893323i	$-0.648368\pi$
$163$	−11.4755			−0.898831			−0.449416	+	0.893323i	$0.648368\pi$
$164$		0			0
$165$	−0.0808982			−0.00629791
$166$		0			0
$167$	−11.0066			−0.851713			−0.425857	−	0.904791i	$-0.640027\pi$
$167$	−11.0066			−0.851713			−0.425857	+	0.904791i	$0.640027\pi$
$168$		0			0
$169$	−0.133521	+	0.410934i	−0.0102708	+	0.0316103i
$170$		0			0
$171$	3.74378	+	2.72001i	0.286294	+	0.208005i
$172$		0			0
$173$	−6.89947			−0.524557			−0.262278	−	0.964992i	$-0.584474\pi$
$173$	−6.89947			−0.524557			−0.262278	+	0.964992i	$0.584474\pi$
$174$		0			0
$175$	0.130918	+	0.402923i	0.00989644	+	0.0304581i
$176$		0			0
$177$	0.121389	−	0.0881939i	0.00912412	−	0.00662906i
$178$		0			0
$179$	−1.82770	+	5.62509i	−0.136609	+	0.420439i	−0.995837	−	0.0911540i	$-0.970944\pi$
$179$	−1.82770	+	5.62509i	−0.136609	+	0.420439i	0.859228	+	0.511593i	$0.170944\pi$
$180$		0			0
$181$	7.63671	+	23.5034i	0.567632	+	1.74699i	0.659998	+	0.751268i	$0.270557\pi$
$181$	7.63671	+	23.5034i	0.567632	+	1.74699i	−0.0923655	+	0.995725i	$0.529443\pi$
$182$		0			0
$183$	0.275109	+	0.199879i	0.0203367	+	0.0147755i
$184$		0			0
$185$	17.4624	+	12.6871i	1.28386	+	0.932778i
$186$		0			0
$187$	−4.01258	+	2.91531i	−0.293429	+	0.213189i
$188$		0			0
$189$	−0.156829	−	0.113943i	−0.0114077	−	0.00828815i
$190$		0			0
$191$	14.6054			1.05681			0.528406	−	0.848992i	$-0.322790\pi$
$191$	14.6054			1.05681			0.528406	+	0.848992i	$0.322790\pi$
$192$		0			0
$193$	6.48853	−	19.9696i	0.467055	−	1.43745i	−0.389326	−	0.921100i	$-0.627292\pi$
$193$	6.48853	−	19.9696i	0.467055	−	1.43745i	0.856380	−	0.516346i	$-0.172708\pi$
$194$		0			0
$195$	−0.0824431	−	0.253734i	−0.00590387	−	0.0181702i
$196$		0			0
$197$	3.41770	+	10.5186i	0.243501	+	0.749419i	0.995879	+	0.0906880i	$0.0289066\pi$
$197$	3.41770	+	10.5186i	0.243501	+	0.749419i	−0.752378	+	0.658731i	$0.771093\pi$
$198$		0			0
$199$	−14.7673	+	10.7290i	−1.04682	+	0.760562i	−0.971606	−	0.236605i	$-0.923965\pi$
$199$	−14.7673	+	10.7290i	−1.04682	+	0.760562i	−0.0752177	+	0.997167i	$0.523965\pi$
$200$		0			0
$201$	0.0210247	−	0.0647075i	0.00148297	−	0.00456411i
$202$		0			0
$203$	−1.94432	+	1.41263i	−0.136464	+	0.0991471i
$204$		0			0
$205$	0.875678	+	14.8863i	0.0611600	+	1.03971i
$206$		0			0
$207$	8.99550	−	6.53562i	0.625231	−	0.454257i
$208$		0			0
$209$	−0.512582	+	1.57757i	−0.0354560	+	0.109122i
$210$		0			0
$211$	12.5925	−	9.14896i	0.866901	−	0.629840i	−0.0628528	−	0.998023i	$-0.520020\pi$
$211$	12.5925	−	9.14896i	0.866901	−	0.629840i	0.929754	+	0.368183i	$0.120020\pi$
$212$		0			0
$213$	0.0807011	+	0.248372i	0.00552955	+	0.0170182i
$214$		0			0
$215$	6.58213	+	20.2577i	0.448897	+	1.38156i
$216$		0			0
$217$	−1.15401	+	3.55167i	−0.0783390	+	0.241103i
$218$		0			0
$219$	−0.0694181			−0.00469084
$220$		0			0
$221$	−13.2330	−	9.61432i	−0.890146	−	0.646729i
$222$		0			0
$223$	2.78085	−	2.02041i	0.186220	−	0.135296i	−0.490770	−	0.871289i	$-0.663284\pi$
$223$	2.78085	−	2.02041i	0.186220	−	0.135296i	0.676989	+	0.735993i	$0.263284\pi$
$224$		0			0
$225$	1.02788	+	0.746800i	0.0685254	+	0.0497867i
$226$		0			0
$227$	11.1547	+	8.10434i	0.740362	+	0.537904i	0.892824	−	0.450405i	$-0.148720\pi$
$227$	11.1547	+	8.10434i	0.740362	+	0.537904i	−0.152463	+	0.988309i	$0.548720\pi$
$228$		0			0
$229$	4.53706	+	13.9636i	0.299817	+	0.922743i	0.981561	+	0.191152i	$0.0612222\pi$
$229$	4.53706	+	13.9636i	0.299817	+	0.922743i	−0.681743	+	0.731592i	$0.738778\pi$
$230$		0			0
$231$	0.0107343	−	0.0330369i	0.000706267	−	0.00217367i
$232$		0			0
$233$	−4.54630	+	3.30308i	−0.297838	+	0.216392i	−0.726660	−	0.686997i	$-0.758929\pi$
$233$	−4.54630	+	3.30308i	−0.297838	+	0.216392i	0.428823	+	0.903389i	$0.358929\pi$
$234$		0			0
$235$	−0.618875	−	1.90470i	−0.0403710	−	0.124249i
$236$		0			0
$237$	0.360795			0.0234362
$238$		0			0
$239$	−17.0493	−	12.3870i	−1.10282	−	0.801249i	−0.121306	−	0.992615i	$-0.538708\pi$
$239$	−17.0493	−	12.3870i	−1.10282	−	0.801249i	−0.981519	+	0.191366i	$0.938708\pi$
$240$		0			0
$241$	5.48095	−	16.8686i	0.353059	−	1.08660i	−0.604067	−	0.796934i	$-0.706454\pi$
$241$	5.48095	−	16.8686i	0.353059	−	1.08660i	0.957126	−	0.289671i	$-0.0935460\pi$
$242$		0			0
$243$	−0.872080			−0.0559439
$244$		0			0
$245$	−2.32887			−0.148786
$246$		0			0
$247$	−5.47034			−0.348069
$248$		0			0
$249$	0.312757			0.0198202
$250$		0			0
$251$	−3.64428	+	11.2159i	−0.230025	+	0.707943i	0.767718	+	0.640788i	$0.221392\pi$
$251$	−3.64428	+	11.2159i	−0.230025	+	0.707943i	−0.997743	+	0.0671551i	$0.978608\pi$
$252$		0			0
$253$	3.22444	+	2.34269i	0.202719	+	0.147284i
$254$		0			0
$255$	−0.347223			−0.0217439
$256$		0			0
$257$	4.47367	+	13.7685i	0.279060	+	0.858858i	0.988117	+	0.153707i	$0.0491210\pi$
$257$	4.47367	+	13.7685i	0.279060	+	0.858858i	−0.709057	+	0.705152i	$0.750879\pi$
$258$		0			0
$259$	−7.49820	+	5.44776i	−0.465915	+	0.338507i
$260$		0			0
$261$	−2.22721	+	6.85466i	−0.137861	+	0.424293i
$262$		0			0
$263$	4.36117	+	13.4223i	0.268921	+	0.827654i	0.990764	+	0.135597i	$0.0432953\pi$
$263$	4.36117	+	13.4223i	0.268921	+	0.827654i	−0.721843	+	0.692057i	$0.756705\pi$
$264$		0			0
$265$	2.83973	+	2.06318i	0.174443	+	0.126740i
$266$		0			0
$267$	−0.0678132	−	0.0492692i	−0.00415010	−	0.00301523i
$268$		0			0
$269$	7.95350	−	5.77856i	0.484933	−	0.352325i	−0.318299	−	0.947990i	$-0.603112\pi$
$269$	7.95350	−	5.77856i	0.484933	−	0.352325i	0.803233	+	0.595666i	$0.203112\pi$
$270$		0			0
$271$	−8.61522	−	6.25932i	−0.523337	−	0.380227i	0.294522	−	0.955645i	$-0.404839\pi$
$271$	−8.61522	−	6.25932i	−0.523337	−	0.380227i	−0.817860	+	0.575418i	$0.804839\pi$
$272$		0			0
$273$	0.114558			0.00693337
$274$		0			0
$275$	−0.140733	+	0.433132i	−0.00848653	+	0.0261188i
$276$		0			0
$277$	−0.712915	−	2.19413i	−0.0428349	−	0.131832i	0.927352	−	0.374190i	$-0.122079\pi$
$277$	−0.712915	−	2.19413i	−0.0428349	−	0.131832i	−0.970187	+	0.242358i	$0.922079\pi$
$278$		0			0
$279$	3.46081	+	10.6513i	0.207193	+	0.637676i
$280$		0			0
$281$	22.5090	−	16.3537i	1.34277	−	0.975582i	0.343437	−	0.939176i	$-0.388409\pi$
$281$	22.5090	−	16.3537i	1.34277	−	0.975582i	0.999337	−	0.0364063i	$-0.0115910\pi$
$282$		0			0
$283$	7.73604	−	23.8091i	0.459860	−	1.41530i	−0.405474	−	0.914107i	$-0.632894\pi$
$283$	7.73604	−	23.8091i	0.459860	−	1.41530i	0.865334	−	0.501196i	$-0.167106\pi$
$284$		0			0
$285$	−0.0939464	+	0.0682561i	−0.00556490	+	0.00404314i
$286$		0			0
$287$	−6.19542	−	1.61765i	−0.365704	−	0.0954871i
$288$		0			0
$289$	−3.46911	+	2.52046i	−0.204065	+	0.148262i
$290$		0			0
$291$	0.0540203	−	0.166257i	0.00316673	−	0.00974618i
$292$		0			0
$293$	−12.5403	+	9.11103i	−0.732610	+	0.532272i	−0.890388	−	0.455202i	$-0.849567\pi$
$293$	−12.5403	+	9.11103i	−0.732610	+	0.532272i	0.157778	+	0.987475i	$0.449567\pi$
$294$		0			0
$295$	−3.34160	−	10.2844i	−0.194556	−	0.598780i
$296$		0			0
$297$	−0.0643948	−	0.198187i	−0.00373656	−	0.0115000i
$298$		0			0
$299$	−4.06174	+	12.5007i	−0.234896	+	0.722937i
$300$		0			0
$301$	−9.14614			−0.527175
$302$		0			0
$303$	0.360348	+	0.261808i	0.0207015	+	0.0150405i
$304$		0			0
$305$	19.8270	−	14.4052i	1.13529	−	0.824838i
$306$		0			0
$307$	−8.96210	−	6.51134i	−0.511494	−	0.371622i	0.301896	−	0.953341i	$-0.402380\pi$
$307$	−8.96210	−	6.51134i	−0.511494	−	0.371622i	−0.813390	+	0.581719i	$0.802380\pi$
$308$		0			0
$309$	−0.0685740	−	0.0498220i	−0.00390104	−	0.00283427i
$310$		0			0
$311$	8.60609	+	26.4868i	0.488007	+	1.50193i	0.827579	+	0.561350i	$0.189718\pi$
$311$	8.60609	+	26.4868i	0.488007	+	1.50193i	−0.339572	+	0.940580i	$0.610282\pi$
$312$		0			0
$313$	−2.47604	+	7.62046i	−0.139954	+	0.430734i	−0.996328	−	0.0856226i	$-0.972712\pi$
$313$	−2.47604	+	7.62046i	−0.139954	+	0.430734i	0.856374	+	0.516357i	$0.172712\pi$
$314$		0			0
$315$	−5.65033	+	4.10521i	−0.318360	+	0.231302i
$316$		0			0
$317$	3.93413	+	12.1080i	0.220963	+	0.680054i	0.998676	+	0.0514348i	$0.0163794\pi$
$317$	3.93413	+	12.1080i	0.220963	+	0.680054i	−0.777714	+	0.628619i	$0.783621\pi$
$318$		0			0
$319$	−2.58350			−0.144648
$320$		0			0
$321$	0.0718532	+	0.0522044i	0.00401046	+	0.00291377i
$322$		0			0
$323$	−2.20005	+	6.77106i	−0.122414	+	0.376752i
$324$		0			0
$325$	−1.50192			−0.0833116
$326$		0			0
$327$	−0.341272			−0.0188724
$328$		0			0
$329$	0.859953			0.0474107
$330$		0			0
$331$	−15.9713			−0.877864			−0.438932	−	0.898520i	$-0.644643\pi$
$331$	−15.9713			−0.877864			−0.438932	+	0.898520i	$0.644643\pi$
$332$		0			0
$333$	−8.58918	+	26.4348i	−0.470684	+	1.44862i
$334$		0			0
$335$	−3.96696	−	2.88217i	−0.216738	−	0.157470i
$336$		0			0
$337$	−13.9922			−0.762206			−0.381103	−	0.924533i	$-0.624456\pi$
$337$	−13.9922			−0.762206			−0.381103	+	0.924533i	$0.624456\pi$
$338$		0			0
$339$	0.00245816	+	0.00756545i	0.000133509	+	0.000410899i
$340$		0			0
$341$	−3.24774	+	2.35962i	−0.175875	+	0.127781i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	0.0862224	+	0.265365i	0.00464206	+	0.0142868i
$346$		0			0
$347$	12.6589	+	9.19722i	0.679565	+	0.493733i	0.873213	−	0.487338i	$-0.162032\pi$
$347$	12.6589	+	9.19722i	0.679565	+	0.493733i	−0.193649	+	0.981071i	$0.562032\pi$
$348$		0			0
$349$	−5.36724	−	3.89953i	−0.287302	−	0.208737i	0.434794	−	0.900530i	$-0.356821\pi$
$349$	−5.36724	−	3.89953i	−0.287302	−	0.208737i	−0.722096	+	0.691793i	$0.756821\pi$
$350$		0			0
$351$	0.555980	−	0.403943i	0.0296760	−	0.0215609i
$352$		0			0
$353$	4.32986	+	3.14583i	0.230455	+	0.167435i	0.697020	−	0.717051i	$-0.254509\pi$
$353$	4.32986	+	3.14583i	0.230455	+	0.167435i	−0.466565	+	0.884487i	$0.654509\pi$
$354$		0			0
$355$	18.8213			0.998930
$356$		0			0
$357$	0.0460728	−	0.141797i	0.00243843	−	0.00750472i
$358$		0			0
$359$	6.30569	+	19.4069i	0.332802	+	1.02426i	0.967795	+	0.251741i	$0.0810030\pi$
$359$	6.30569	+	19.4069i	0.332802	+	1.02426i	−0.634993	+	0.772518i	$0.718997\pi$
$360$		0			0
$361$	−5.13554	−	15.8056i	−0.270292	−	0.831873i
$362$		0			0
$363$	−0.257361	+	0.186983i	−0.0135079	+	0.00981409i
$364$		0			0
$365$	−1.54599	+	4.75807i	−0.0809209	+	0.249049i
$366$		0			0
$367$	−4.17222	+	3.03130i	−0.217788	+	0.158232i	−0.691330	−	0.722539i	$-0.742975\pi$
$367$	−4.17222	+	3.03130i	−0.217788	+	0.158232i	0.473542	+	0.880771i	$0.342975\pi$
$368$		0			0
$369$	−17.8829	+	6.99616i	−0.930945	+	0.364206i
$370$		0			0
$371$	−1.21936	+	0.885914i	−0.0633058	+	0.0459944i
$372$		0			0
$373$	0.975424	−	3.00205i	0.0505056	−	0.155440i	−0.922623	−	0.385704i	$-0.873959\pi$
$373$	0.975424	−	3.00205i	0.0505056	−	0.155440i	0.973128	+	0.230263i	$0.0739588\pi$
$374$		0			0
$375$	0.278623	−	0.202431i	0.0143880	−	0.0104535i
$376$		0			0
$377$	−2.63283	−	8.10303i	−0.135598	−	0.417327i
$378$		0			0
$379$	−5.50582	−	16.9452i	−0.282815	−	0.870416i	−0.987045	−	0.160444i	$-0.948708\pi$
$379$	−5.50582	−	16.9452i	−0.282815	−	0.870416i	0.704230	−	0.709972i	$-0.251292\pi$
$380$		0			0
$381$	−0.190758	+	0.587093i	−0.00977283	+	0.0300777i
$382$		0			0
$383$	−21.3034			−1.08855			−0.544276	−	0.838906i	$-0.683196\pi$
$383$	−21.3034			−1.08855			−0.544276	+	0.838906i	$0.683196\pi$
$384$		0			0
$385$	−2.02536	−	1.47151i	−0.103222	−	0.0749951i
$386$		0			0
$387$	−22.1904	+	16.1223i	−1.12800	+	0.819542i
$388$		0			0
$389$	−12.6170	−	9.16679i	−0.639708	−	0.464775i	0.220042	−	0.975490i	$-0.429381\pi$
$389$	−12.6170	−	9.16679i	−0.639708	−	0.464775i	−0.859750	+	0.510716i	$0.829381\pi$
$390$		0			0
$391$	13.8396	+	10.0551i	0.699899	+	0.508506i
$392$		0			0
$393$	0.0315246	+	0.0970227i	0.00159021	+	0.00489415i
$394$		0			0
$395$	8.03518	−	24.7297i	0.404294	−	1.24429i
$396$		0			0
$397$	−11.6600	+	8.47147i	−0.585197	+	0.425171i	−0.840594	−	0.541665i	$-0.817794\pi$
$397$	−11.6600	+	8.47147i	−0.585197	+	0.425171i	0.255397	+	0.966836i	$0.417794\pi$
$398$		0			0
$399$	−0.0154084	−	0.0474223i	−0.000771387	−	0.00237409i
$400$		0			0
$401$	23.8990			1.19346			0.596730	−	0.802442i	$-0.296466\pi$
$401$	23.8990			1.19346			0.596730	+	0.802442i	$0.296466\pi$
$402$		0			0
$403$	−10.7106	−	7.78173i	−0.533534	−	0.387635i
$404$		0			0
$405$	−6.47019	+	19.9132i	−0.321507	+	0.989495i
$406$		0			0
$407$	−9.96317			−0.493856
$408$		0			0
$409$	32.1824			1.59132			0.795659	−	0.605745i	$-0.207125\pi$
$409$	32.1824			1.59132			0.795659	+	0.605745i	$0.207125\pi$
$410$		0			0
$411$	0.194610			0.00959941
$412$		0			0
$413$	4.64329			0.228481
$414$		0			0
$415$	6.96533	−	21.4371i	0.341915	−	1.05230i
$416$		0			0
$417$	0.412583	+	0.299759i	0.0202043	+	0.0146793i
$418$		0			0
$419$	−19.1670			−0.936368			−0.468184	−	0.883631i	$-0.655092\pi$
$419$	−19.1670			−0.936368			−0.468184	+	0.883631i	$0.655092\pi$
$420$		0			0
$421$	−6.40853	−	19.7234i	−0.312333	−	0.961261i	−0.976838	−	0.213978i	$-0.931358\pi$
$421$	−6.40853	−	19.7234i	−0.312333	−	0.961261i	0.664506	−	0.747283i	$-0.268642\pi$
$422$		0			0
$423$	2.08642	−	1.51587i	0.101445	−	0.0737044i
$424$		0			0
$425$	−0.604040	+	1.85904i	−0.0293003	+	0.0901769i
$426$		0			0
$427$	3.25189	+	10.0083i	0.157370	+	0.484335i
$428$		0			0
$429$	0.0996281	+	0.0723841i	0.00481009	+	0.00349474i
$430$		0			0
$431$	1.67737	+	1.21868i	0.0807961	+	0.0587018i	0.627450	−	0.778657i	$-0.284099\pi$
$431$	1.67737	+	1.21868i	0.0807961	+	0.0587018i	−0.546654	+	0.837359i	$0.684099\pi$
$432$		0			0
$433$	15.3393	−	11.1446i	0.737158	−	0.535576i	−0.154662	−	0.987967i	$-0.549429\pi$
$433$	15.3393	−	11.1446i	0.737158	−	0.535576i	0.891820	+	0.452391i	$0.149429\pi$
$434$		0			0
$435$	−0.146321	−	0.106309i	−0.00701556	−	0.00509710i
$436$		0			0
$437$	5.72111			0.273678
$438$		0			0
$439$	4.39737	−	13.5337i	0.209875	−	0.645929i	−0.789603	−	0.613618i	$-0.789713\pi$
$439$	4.39737	−	13.5337i	0.209875	−	0.645929i	0.999478	−	0.0323107i	$-0.0102866\pi$
$440$		0			0
$441$	−0.926728	−	2.85218i	−0.0441299	−	0.135818i
$442$		0			0
$443$	9.77652	+	30.0890i	0.464496	+	1.42957i	0.859615	+	0.510943i	$0.170704\pi$
$443$	9.77652	+	30.0890i	0.464496	+	1.42957i	−0.395118	+	0.918630i	$0.629296\pi$
$444$		0			0
$445$	−4.88727	+	3.55081i	−0.231679	+	0.168325i
$446$		0			0
$447$	0.0595765	−	0.183358i	0.00281787	−	0.00867252i
$448$		0			0
$449$	29.3237	−	21.3049i	1.38387	−	1.00544i	0.387364	−	0.921927i	$-0.373386\pi$
$449$	29.3237	−	21.3049i	1.38387	−	1.00544i	0.996507	−	0.0835145i	$-0.0266145\pi$
$450$		0			0
$451$	−4.36587	−	5.32143i	−0.205581	−	0.250577i
$452$		0			0
$453$	0.240242	−	0.174546i	0.0112875	−	0.00820088i
$454$		0			0
$455$	2.55129	−	7.85207i	0.119606	−	0.368111i
$456$		0			0
$457$	14.4651	−	10.5095i	0.676647	−	0.491613i	−0.195597	−	0.980684i	$-0.562664\pi$
$457$	14.4651	−	10.5095i	0.676647	−	0.491613i	0.872244	+	0.489072i	$0.162664\pi$
$458$		0			0
$459$	−0.276389	−	0.850636i	−0.0129007	−	0.0397043i
$460$		0			0
$461$	−3.06593	−	9.43598i	−0.142795	−	0.439477i	0.853926	−	0.520394i	$-0.174215\pi$
$461$	−3.06593	−	9.43598i	−0.142795	−	0.439477i	−0.996721	+	0.0809172i	$0.974215\pi$
$462$		0			0
$463$	9.24213	−	28.4444i	0.429518	−	1.32192i	−0.469083	−	0.883154i	$-0.655415\pi$
$463$	9.24213	−	28.4444i	0.429518	−	1.32192i	0.898601	−	0.438767i	$-0.144585\pi$
$464$		0			0
$465$	−0.281039			−0.0130328
$466$		0			0
$467$	−1.81937	−	1.32185i	−0.0841906	−	0.0611680i	0.544894	−	0.838505i	$-0.316570\pi$
$467$	−1.81937	−	1.32185i	−0.0841906	−	0.0611680i	−0.629084	+	0.777337i	$0.716570\pi$
$468$		0			0
$469$	1.70338	−	1.23758i	0.0786548	−	0.0571461i
$470$		0			0
$471$	−0.329237	−	0.239205i	−0.0151705	−	0.0110220i
$472$		0			0
$473$	−7.95415	−	5.77903i	−0.365732	−	0.265720i
$474$		0			0
$475$	0.202013	+	0.621733i	0.00926901	+	0.0285271i
$476$		0			0
$477$	−1.39677	+	4.29882i	−0.0639538	+	0.196829i
$478$		0			0
$479$	31.0101	−	22.5301i	1.41689	−	1.02943i	0.424611	−	0.905376i	$-0.360411\pi$
$479$	31.0101	−	22.5301i	1.41689	−	1.02943i	0.992276	−	0.124053i	$-0.0395893\pi$
$480$		0			0
$481$	−10.1534	−	31.2491i	−0.462957	−	1.42483i
$482$		0			0
$483$	−0.119810			−0.00545153
$484$		0			0
$485$	−10.1926	−	7.40535i	−0.462822	−	0.336260i
$486$		0			0
$487$	−10.6472	+	32.7688i	−0.482472	+	1.48490i	0.353138	+	0.935571i	$0.385115\pi$
$487$	−10.6472	+	32.7688i	−0.482472	+	1.48490i	−0.835610	+	0.549324i	$0.814885\pi$
$488$		0			0
$489$	0.370822			0.0167692
$490$		0			0
$491$	37.6219			1.69785			0.848926	−	0.528512i	$-0.177250\pi$
$491$	37.6219			1.69785			0.848926	+	0.528512i	$0.177250\pi$
$492$		0			0
$493$	−11.0886			−0.499406
$494$		0			0
$495$	−7.50784			−0.337452
$496$		0			0
$497$	−2.49738	+	7.68616i	−0.112023	+	0.344771i
$498$		0			0
$499$	−2.46747	−	1.79272i	−0.110459	−	0.0802533i	0.531184	−	0.847256i	$-0.321747\pi$
$499$	−2.46747	−	1.79272i	−0.110459	−	0.0802533i	−0.641644	+	0.767003i	$0.721747\pi$
$500$		0			0
$501$	0.355669			0.0158901
$502$		0			0
$503$	−3.03979	−	9.35552i	−0.135538	−	0.417142i	0.860136	−	0.510065i	$-0.170379\pi$
$503$	−3.03979	−	9.35552i	−0.135538	−	0.417142i	−0.995673	+	0.0929235i	$0.970379\pi$
$504$		0			0
$505$	25.9702	−	18.8684i	1.15566	−	0.839634i
$506$		0			0
$507$	0.00431462	−	0.0132790i	0.000191619	−	0.000589742i
$508$		0			0
$509$	5.60588	+	17.2531i	0.248476	+	0.764732i	0.995045	+	0.0994234i	$0.0316998\pi$
$509$	5.60588	+	17.2531i	0.248476	+	0.764732i	−0.746569	+	0.665308i	$0.768300\pi$
$510$		0			0
$511$	−1.73795	−	1.26269i	−0.0768822	−	0.0558582i
$512$		0			0
$513$	−0.241997	−	0.175821i	−0.0106844	−	0.00776269i
$514$		0			0
$515$	−4.94210	+	3.59065i	−0.217775	+	0.158223i
$516$		0			0
$517$	0.747878	+	0.543365i	0.0328916	+	0.0238972i
$518$		0			0
$519$	0.222951			0.00978646
$520$		0			0
$521$	5.80187	−	17.8563i	0.254184	−	0.782299i	−0.739805	−	0.672821i	$-0.765082\pi$
$521$	5.80187	−	17.8563i	0.254184	−	0.782299i	0.993989	−	0.109478i	$-0.0349178\pi$
$522$		0			0
$523$	4.75703	+	14.6406i	0.208010	+	0.640190i	0.999576	+	0.0291063i	$0.00926612\pi$
$523$	4.75703	+	14.6406i	0.208010	+	0.640190i	−0.791566	+	0.611084i	$0.790734\pi$
$524$		0			0
$525$	−0.00423050	−	0.0130201i	−0.000184634	−	0.000568246i
$526$		0			0
$527$	−13.9396	+	10.1277i	−0.607220	+	0.441171i
$528$		0			0
$529$	−2.85945	+	8.80050i	−0.124324	+	0.382630i
$530$		0			0
$531$	11.2656	−	8.18493i	0.488885	−	0.355196i
$532$		0			0
$533$	12.2412	−	19.1164i	0.530226	−	0.828024i
$534$		0			0
$535$	5.17843	−	3.76235i	0.223883	−	0.162661i
$536$		0			0
$537$	0.0590608	−	0.181771i	0.00254866	−	0.00784398i
$538$		0			0
$539$	0.869673	−	0.631855i	0.0374595	−	0.0272159i
$540$		0			0
$541$	−3.68902	−	11.3536i	−0.158604	−	0.488132i	0.839905	−	0.542734i	$-0.182611\pi$
$541$	−3.68902	−	11.3536i	−0.158604	−	0.488132i	−0.998508	+	0.0546025i	$0.982611\pi$
$542$		0			0
$543$	−0.246775	−	0.759494i	−0.0105901	−	0.0325930i
$544$		0			0
$545$	−7.60038	+	23.3916i	−0.325565	+	1.00198i
$546$		0			0
$547$	−16.3824			−0.700463			−0.350231	−	0.936663i	$-0.613897\pi$
$547$	−16.3824			−0.700463			−0.350231	+	0.936663i	$0.613897\pi$
$548$		0			0
$549$	25.5318	+	18.5499i	1.08967	+	0.791692i
$550$		0			0
$551$	−3.00019	+	2.17977i	−0.127813	+	0.0928612i
$552$		0			0
$553$	9.03284	+	6.56275i	0.384116	+	0.279076i
$554$		0			0
$555$	−0.564283	−	0.409976i	−0.0239525	−	0.0174025i
$556$		0			0
$557$	−6.67671	−	20.5488i	−0.282901	−	0.870681i	−0.987020	−	0.160598i	$-0.948658\pi$
$557$	−6.67671	−	20.5488i	−0.282901	−	0.870681i	0.704119	−	0.710082i	$-0.251342\pi$
$558$		0			0
$559$	10.0196	−	30.8373i	0.423785	−	1.30428i
$560$		0			0
$561$	0.129664	−	0.0942062i	0.00547440	−	0.00397739i
$562$		0			0
$563$	−10.4540	−	32.1742i	−0.440585	−	1.35598i	−0.887254	−	0.461282i	$-0.847390\pi$
$563$	−10.4540	−	32.1742i	−0.440585	−	1.35598i	0.446669	−	0.894699i	$-0.352610\pi$
$564$		0			0
$565$	0.573298			0.0241188
$566$		0			0
$567$	−7.27355	−	5.28454i	−0.305460	−	0.221930i
$568$		0			0
$569$	3.35083	−	10.3128i	0.140474	−	0.432335i	−0.855927	−	0.517096i	$-0.827013\pi$
$569$	3.35083	−	10.3128i	0.140474	−	0.432335i	0.996401	+	0.0847616i	$0.0270129\pi$
$570$		0			0
$571$	4.28133			0.179168			0.0895840	−	0.995979i	$-0.471446\pi$
$571$	4.28133			0.179168			0.0895840	+	0.995979i	$0.471446\pi$
$572$		0			0
$573$	−0.471964			−0.0197166
$574$		0			0
$575$	1.57077			0.0655057
$576$		0			0
$577$	−31.9972			−1.33206			−0.666030	−	0.745925i	$-0.732008\pi$
$577$	−31.9972			−1.33206			−0.666030	+	0.745925i	$0.732008\pi$
$578$		0			0
$579$	−0.209672	+	0.645304i	−0.00871367	+	0.0268179i
$580$		0			0
$581$	7.83016	+	5.68895i	0.324850	+	0.236017i
$582$		0			0
$583$	−1.62021			−0.0671023
$584$		0			0
$585$	−7.65121	−	23.5480i	−0.316339	−	0.973590i
$586$		0			0
$587$	−5.68166	+	4.12796i	−0.234507	+	0.170379i	−0.698833	−	0.715285i	$-0.746297\pi$
$587$	−5.68166	+	4.12796i	−0.234507	+	0.170379i	0.464326	+	0.885665i	$0.346297\pi$
$588$		0			0
$589$	−1.78070	+	5.48043i	−0.0733724	+	0.225817i
$590$		0			0
$591$	−0.110440	−	0.339901i	−0.00454291	−	0.0139816i
$592$		0			0
$593$	−12.4685	−	9.05888i	−0.512019	−	0.372004i	0.301570	−	0.953444i	$-0.402489\pi$
$593$	−12.4685	−	9.05888i	−0.512019	−	0.372004i	−0.813589	+	0.581440i	$0.802489\pi$
$594$		0			0
$595$	−8.69304	−	6.31587i	−0.356380	−	0.258925i
$596$		0			0
$597$	0.477193	−	0.346701i	0.0195302	−	0.0141895i
$598$		0			0
$599$	3.08888	+	2.24420i	0.126208	+	0.0916955i	0.649098	−	0.760704i	$-0.275146\pi$
$599$	3.08888	+	2.24420i	0.126208	+	0.0916955i	−0.522890	+	0.852400i	$0.675146\pi$
$600$		0			0
$601$	−1.08133			−0.0441082			−0.0220541	−	0.999757i	$-0.507021\pi$
$601$	−1.08133			−0.0441082			−0.0220541	+	0.999757i	$0.507021\pi$
$602$		0			0
$603$	1.95122	−	6.00524i	0.0794599	−	0.244552i
$604$		0			0
$605$	7.08466	+	21.8043i	0.288032	+	0.886472i
$606$		0			0
$607$	−7.05178	−	21.7031i	−0.286223	−	0.880903i	−0.986029	−	0.166571i	$-0.946731\pi$
$607$	−7.05178	−	21.7031i	−0.286223	−	0.880903i	0.699807	−	0.714332i	$-0.253269\pi$
$608$		0			0
$609$	0.0628291	−	0.0456480i	0.00254596	−	0.00184975i
$610$		0			0
$611$	−0.942082	+	2.89943i	−0.0381125	+	0.117298i
$612$		0			0
$613$	22.2345	−	16.1543i	0.898041	−	0.652465i	−0.0399210	−	0.999203i	$-0.512711\pi$
$613$	22.2345	−	16.1543i	0.898041	−	0.652465i	0.937962	+	0.346738i	$0.112711\pi$
$614$		0			0
$615$	−0.0282969	−	0.481041i	−0.00114104	−	0.0193974i
$616$		0			0
$617$	−0.636981	+	0.462794i	−0.0256439	+	0.0186314i	−0.600533	−	0.799600i	$-0.705045\pi$
$617$	−0.636981	+	0.462794i	−0.0256439	+	0.0186314i	0.574889	+	0.818231i	$0.305045\pi$
$618$		0			0
$619$	5.61381	−	17.2775i	0.225638	−	0.694443i	−0.772588	−	0.634908i	$-0.781038\pi$
$619$	5.61381	−	17.2775i	0.225638	−	0.694443i	0.998226	−	0.0595354i	$-0.0189619\pi$
$620$		0			0
$621$	−0.581467	+	0.422461i	−0.0233335	+	0.0169528i
$622$		0			0
$623$	−0.801577	−	2.46700i	−0.0321145	−	0.0988383i
$624$		0			0
$625$	−8.32455	−	25.6203i	−0.332982	−	1.02481i
$626$		0			0
$627$	0.0165637	−	0.0509778i	0.000661490	−	0.00203586i
$628$		0			0
$629$	−42.7629			−1.70507
$630$		0			0
$631$	−16.8898	−	12.2711i	−0.672372	−	0.488507i	0.198447	−	0.980112i	$-0.436410\pi$
$631$	−16.8898	−	12.2711i	−0.672372	−	0.488507i	−0.870818	+	0.491605i	$0.836410\pi$
$632$		0			0
$633$	−0.406916	+	0.295642i	−0.0161735	+	0.0117507i
$634$		0			0
$635$	35.9923	+	26.1500i	1.42831	+	1.03773i
$636$		0			0
$637$	2.86807	+	2.08377i	0.113637	+	0.0825621i
$638$		0			0
$639$	7.48954	+	23.0504i	0.296282	+	0.911862i
$640$		0			0
$641$	0.453580	−	1.39598i	0.0179153	−	0.0551377i	−0.941699	−	0.336456i	$-0.890772\pi$
$641$	0.453580	−	1.39598i	0.0179153	−	0.0551377i	0.959615	+	0.281318i	$0.0907717\pi$
$642$		0			0
$643$	−10.7901	+	7.83945i	−0.425519	+	0.309158i	−0.779855	−	0.625961i	$-0.784707\pi$
$643$	−10.7901	+	7.83945i	−0.425519	+	0.309158i	0.354335	+	0.935118i	$0.384707\pi$
$644$		0			0
$645$	−0.212696	−	0.654612i	−0.00837491	−	0.0257753i
$646$		0			0
$647$	−38.1451			−1.49964			−0.749820	−	0.661642i	$-0.769860\pi$
$647$	−38.1451			−1.49964			−0.749820	+	0.661642i	$0.769860\pi$
$648$		0			0
$649$	4.03815	+	2.93389i	0.158511	+	0.115165i
$650$		0			0
$651$	0.0372908	−	0.114769i	0.00146154	−	0.00449817i
$652$		0			0
$653$	−36.5384			−1.42986			−0.714930	−	0.699196i	$-0.753541\pi$
$653$	−36.5384			−1.42986			−0.714930	+	0.699196i	$0.753541\pi$
$654$		0			0
$655$	7.35223			0.287276
$656$		0			0
$657$	−6.44242			−0.251343
$658$		0			0
$659$	18.6313			0.725771			0.362886	−	0.931834i	$-0.381792\pi$
$659$	18.6313			0.725771			0.362886	+	0.931834i	$0.381792\pi$
$660$		0			0
$661$	−3.12746	+	9.62535i	−0.121644	+	0.374383i	−0.993275	−	0.115781i	$-0.963063\pi$
$661$	−3.12746	+	9.62535i	−0.121644	+	0.374383i	0.871631	+	0.490164i	$0.163063\pi$
$662$		0			0
$663$	0.427613	+	0.310679i	0.0166071	+	0.0120658i
$664$		0			0
$665$	−3.59359			−0.139353
$666$		0			0
$667$	2.75353	+	8.47449i	0.106617	+	0.328133i
$668$		0			0
$669$	−0.0898611	+	0.0652879i	−0.00347423	+	0.00252418i
$670$		0			0
$671$	−3.49570	+	10.7587i	−0.134950	+	0.415334i
$672$		0			0
$673$	−1.02048	−	3.14073i	−0.0393368	−	0.121066i	0.929460	−	0.368924i	$-0.120274\pi$
$673$	−1.02048	−	3.14073i	−0.0393368	−	0.121066i	−0.968797	+	0.247857i	$0.920274\pi$
$674$		0			0
$675$	−0.0664420	−	0.0482729i	−0.00255735	−	0.00185803i
$676$		0			0
$677$	−8.36546	−	6.07786i	−0.321511	−	0.233591i	0.415309	−	0.909680i	$-0.363673\pi$
$677$	−8.36546	−	6.07786i	−0.321511	−	0.233591i	−0.736820	+	0.676089i	$0.763673\pi$
$678$		0			0
$679$	4.37662	−	3.17980i	0.167959	−	0.122029i
$680$		0			0
$681$	−0.360455	−	0.261886i	−0.0138127	−	0.0100355i
$682$		0			0
$683$	33.0740			1.26554			0.632770	−	0.774340i	$-0.281918\pi$
$683$	33.0740			1.26554			0.632770	+	0.774340i	$0.281918\pi$
$684$		0			0
$685$	4.33411	−	13.3390i	0.165598	−	0.509658i
$686$		0			0
$687$	−0.146612	−	0.451225i	−0.00559359	−	0.0172153i
$688$		0			0
$689$	−1.65115	−	5.08172i	−0.0629039	−	0.193598i
$690$		0			0
$691$	−17.2951	+	12.5656i	−0.657936	+	0.478019i	−0.865965	−	0.500104i	$-0.833295\pi$
$691$	−17.2951	+	12.5656i	−0.657936	+	0.478019i	0.208029	+	0.978123i	$0.433295\pi$
$692$		0			0
$693$	0.996210	−	3.06602i	0.0378429	−	0.116468i
$694$		0			0
$695$	29.7347	−	21.6035i	1.12790	−	0.819468i
$696$		0			0
$697$	−18.7387	−	22.8401i	−0.709780	−	0.865131i
$698$		0			0
$699$	0.146910	−	0.106736i	0.00555665	−	0.00403714i
$700$		0			0
$701$	9.06747	−	27.9068i	0.342473	−	1.05402i	−0.620449	−	0.784247i	$-0.713050\pi$
$701$	9.06747	−	27.9068i	0.342473	−	1.05402i	0.962922	−	0.269778i	$-0.0869504\pi$
$702$		0			0
$703$	−11.5702	+	8.40621i	−0.436377	+	0.317046i
$704$		0			0
$705$	0.0199985	+	0.0615490i	0.000753187	+	0.00231807i
$706$		0			0
$707$	4.25945	+	13.1092i	0.160193	+	0.493023i
$708$		0			0
$709$	6.94817	−	21.3843i	0.260944	−	0.803103i	−0.731656	−	0.681674i	$-0.761252\pi$
$709$	6.94817	−	21.3843i	0.260944	−	0.803103i	0.992600	−	0.121429i	$-0.0387478\pi$
$710$		0			0
$711$	33.4840			1.25575
$712$		0			0
$713$	11.2016	+	8.13846i	0.419504	+	0.304788i
$714$		0			0
$715$	7.18016	−	5.21669i	0.268523	−	0.195093i
$716$		0			0
$717$	0.550934	+	0.400277i	0.0205750	+	0.0149486i
$718$		0			0
$719$	−6.41498	−	4.66075i	−0.239238	−	0.173817i	0.461706	−	0.887033i	$-0.347238\pi$
$719$	−6.41498	−	4.66075i	−0.239238	−	0.173817i	−0.700944	+	0.713216i	$0.747238\pi$
$720$		0			0
$721$	−0.810570	−	2.49468i	−0.0301872	−	0.0929066i
$722$		0			0
$723$	−0.177113	+	0.545098i	−0.00658690	+	0.0202724i
$724$		0			0
$725$	−0.823725	+	0.598471i	−0.0305924	+	0.0222267i
$726$		0			0
$727$	7.57594	+	23.3163i	0.280976	+	0.864755i	0.987576	+	0.157142i	$0.0502280\pi$
$727$	7.57594	+	23.3163i	0.280976	+	0.864755i	−0.706600	+	0.707613i	$0.749772\pi$
$728$		0			0
$729$	−26.9436			−0.997912
$730$		0			0
$731$	−34.1400	−	24.8042i	−1.26271	−	0.917415i
$732$		0			0
$733$	−9.21929	+	28.3741i	−0.340522	+	1.04802i	0.623415	+	0.781891i	$0.285745\pi$
$733$	−9.21929	+	28.3741i	−0.340522	+	1.04802i	−0.963938	+	0.266129i	$0.914255\pi$
$734$		0			0
$735$	0.0752558			0.00277585
$736$		0			0
$737$	2.26336			0.0833718
$738$		0			0
$739$	−10.6846			−0.393039			−0.196519	−	0.980500i	$-0.562964\pi$
$739$	−10.6846			−0.393039			−0.196519	+	0.980500i	$0.562964\pi$
$740$		0			0
$741$	0.176770			0.00649380
$742$		0			0
$743$	−6.36836	+	19.5998i	−0.233633	+	0.719047i	0.763667	+	0.645610i	$0.223397\pi$
$743$	−6.36836	+	19.5998i	−0.233633	+	0.719047i	−0.997300	+	0.0734371i	$0.976603\pi$
$744$		0			0
$745$	−11.2409	−	8.16702i	−0.411836	−	0.299216i
$746$		0			0
$747$	29.0257			1.06200
$748$		0			0
$749$	0.849331	+	2.61397i	0.0310339	+	0.0955124i
$750$		0			0
$751$	28.3335	−	20.5855i	1.03391	−	0.751176i	0.0648190	−	0.997897i	$-0.479353\pi$
$751$	28.3335	−	20.5855i	1.03391	−	0.751176i	0.969087	+	0.246721i	$0.0793530\pi$
$752$		0			0
$753$	0.117762	−	0.362434i	0.00429149	−	0.0132078i
$754$		0			0
$755$	−6.61341	−	20.3540i	−0.240687	−	0.740757i
$756$		0			0
$757$	25.7192	+	18.6861i	0.934781	+	0.679158i	0.947159	−	0.320765i	$-0.103940\pi$
$757$	25.7192	+	18.6861i	0.934781	+	0.679158i	−0.0123776	+	0.999923i	$0.503940\pi$
$758$		0			0
$759$	−0.104195	−	0.0757023i	−0.00378205	−	0.00274782i
$760$		0			0
$761$	31.1628	−	22.6411i	1.12965	−	0.820740i	0.144008	−	0.989577i	$-0.454001\pi$
$761$	31.1628	−	22.6411i	1.12965	−	0.820740i	0.985644	+	0.168836i	$0.0540009\pi$
$762$		0			0
$763$	−8.54407	−	6.20763i	−0.309316	−	0.224731i
$764$		0			0
$765$	−32.2244			−1.16507
$766$		0			0
$767$	−5.08675	+	15.6554i	−0.183672	+	0.565284i
$768$		0			0
$769$	−0.493949	−	1.52022i	−0.0178122	−	0.0548204i	0.941755	−	0.336299i	$-0.109175\pi$
$769$	−0.493949	−	1.52022i	−0.0178122	−	0.0548204i	−0.959568	+	0.281478i	$0.909175\pi$
$770$		0			0
$771$	−0.144563	−	0.444920i	−0.00520632	−	0.0160234i
$772$		0			0
$773$	−29.6573	+	21.5473i	−1.06670	+	0.775002i	−0.975316	−	0.220814i	$-0.929129\pi$
$773$	−29.6573	+	21.5473i	−1.06670	+	0.775002i	−0.0913826	+	0.995816i	$0.529129\pi$
$774$		0			0
$775$	−0.488904	+	1.50469i	−0.0175619	+	0.0540501i
$776$		0			0
$777$	0.242299	−	0.176040i	0.00869241	−	0.00631541i
$778$		0			0
$779$	−9.55989	−	2.49613i	−0.342519	−	0.0894333i
$780$		0			0
$781$	−7.02844	+	5.10646i	−0.251498	+	0.182724i
$782$		0			0
$783$	0.143966	−	0.443083i	0.00514494	−	0.0158345i
$784$		0			0
$785$	−23.7280	+	17.2394i	−0.846889	+	0.615301i
$786$		0			0
$787$	−2.92958	−	9.01633i	−0.104428	−	0.321397i	0.885168	−	0.465272i	$-0.154044\pi$
$787$	−2.92958	−	9.01633i	−0.104428	−	0.321397i	−0.989596	+	0.143875i	$0.954044\pi$
$788$		0			0
$789$	−0.140928	−	0.433731i	−0.00501716	−	0.0154412i
$790$		0			0
$791$	−0.0760706	+	0.234121i	−0.00270476	+	0.00832439i
$792$		0			0
$793$	−37.3066			−1.32480
$794$		0			0
$795$	−0.0917637	−	0.0666702i	−0.00325452	−	0.00236455i
$796$		0			0
$797$	−3.15546	+	2.29258i	−0.111772	+	0.0812073i	−0.642267	−	0.766481i	$-0.722006\pi$
$797$	−3.15546	+	2.29258i	−0.111772	+	0.0812073i	0.530495	+	0.847688i	$0.322006\pi$
$798$		0			0
$799$	3.20996	+	2.33218i	0.113560	+	0.0825064i
$800$		0			0
$801$	−6.29347	−	4.57248i	−0.222369	−	0.161561i
$802$		0			0
$803$	−0.713608	−	2.19626i	−0.0251827	−	0.0775043i
$804$		0			0
$805$	−2.66825	+	8.21203i	−0.0940434	+	0.289436i
$806$		0			0
$807$	−0.257011	+	0.186730i	−0.00904723	+	0.00657319i
$808$		0			0
$809$	−12.0322	−	37.0313i	−0.423030	−	1.30195i	−0.904868	−	0.425692i	$-0.860031\pi$
$809$	−12.0322	−	37.0313i	−0.423030	−	1.30195i	0.481838	−	0.876260i	$-0.339969\pi$
$810$		0			0
$811$	20.5321			0.720980			0.360490	−	0.932763i	$-0.382609\pi$
$811$	20.5321			0.720980			0.360490	+	0.932763i	$0.382609\pi$
$812$		0			0
$813$	0.278394	+	0.202265i	0.00976371	+	0.00709375i
$814$		0			0
$815$	8.25849	−	25.4170i	0.289282	−	0.890319i
$816$		0			0
$817$	−14.1130			−0.493752
$818$		0			0
$819$	10.6317			0.371501
$820$		0			0
$821$	−16.8468			−0.587956			−0.293978	−	0.955812i	$-0.594979\pi$
$821$	−16.8468			−0.587956			−0.293978	+	0.955812i	$0.594979\pi$
$822$		0			0
$823$	39.0280			1.36043			0.680216	−	0.733012i	$-0.261886\pi$
$823$	39.0280			1.36043			0.680216	+	0.733012i	$0.261886\pi$
$824$		0			0
$825$	0.00454769	−	0.0139963i	0.000158330	−	0.000487290i
$826$		0			0
$827$	32.7090	+	23.7645i	1.13740	+	0.826372i	0.986755	−	0.162215i	$-0.0518639\pi$
$827$	32.7090	+	23.7645i	1.13740	+	0.826372i	0.150648	+	0.988587i	$0.451864\pi$
$828$		0			0
$829$	34.8632			1.21085			0.605424	−	0.795903i	$-0.293003\pi$
$829$	34.8632			1.21085			0.605424	+	0.795903i	$0.293003\pi$
$830$		0			0
$831$	0.0230373	+	0.0709015i	0.000799155	+	0.00245955i
$832$		0			0
$833$	3.73272	−	2.71198i	0.129331	−	0.0939646i
$834$		0			0
$835$	7.92100	−	24.3783i	0.274118	−	0.843647i
$836$		0			0
$837$	−0.223706	−	0.688496i	−0.00773241	−	0.0237979i
$838$		0			0
$839$	34.9994	+	25.4285i	1.20831	+	0.877890i	0.995076	−	0.0991106i	$-0.0315998\pi$
$839$	34.9994	+	25.4285i	1.20831	+	0.877890i	0.213236	+	0.977001i	$0.431600\pi$
$840$		0			0
$841$	18.7887	+	13.6508i	0.647886	+	0.470717i
$842$		0			0
$843$	−0.727361	+	0.528459i	−0.0250516	+	0.0182011i
$844$		0			0
$845$	−0.814085	−	0.591467i	−0.0280054	−	0.0203471i
$846$		0			0
$847$	−9.84443			−0.338259
$848$		0			0
$849$	−0.249984	+	0.769372i	−0.00857944	+	0.0264048i
$850$		0			0
$851$	10.6189	+	32.6816i	0.364011	+	1.12031i
$852$		0			0
$853$	9.30169	+	28.6277i	0.318484	+	0.980192i	0.974297	+	0.225269i	$0.0723260\pi$
$853$	9.30169	+	28.6277i	0.318484	+	0.980192i	−0.655813	+	0.754924i	$0.727674\pi$
$854$		0			0
$855$	−8.71879	+	6.33457i	−0.298176	+	0.216638i
$856$		0			0
$857$	−8.98102	+	27.6407i	−0.306786	+	0.944189i	0.672219	+	0.740352i	$0.265341\pi$
$857$	−8.98102	+	27.6407i	−0.306786	+	0.944189i	−0.979005	+	0.203837i	$0.934659\pi$
$858$		0			0
$859$	−3.66377	+	2.66188i	−0.125006	+	0.0908223i	−0.648531	−	0.761188i	$-0.724617\pi$
$859$	−3.66377	+	2.66188i	−0.125006	+	0.0908223i	0.523525	+	0.852010i	$0.324617\pi$
$860$		0			0
$861$	0.200200	+	0.0522733i	0.00682281	+	0.00178147i
$862$		0			0
$863$	6.83870	−	4.96861i	0.232792	−	0.169133i	−0.465274	−	0.885167i	$-0.654044\pi$
$863$	6.83870	−	4.96861i	0.232792	−	0.169133i	0.698066	+	0.716033i	$0.254044\pi$
$864$		0			0
$865$	4.96528	−	15.2816i	0.168825	−	0.519589i
$866$		0			0
$867$	0.112102	−	0.0814467i	0.00380717	−	0.00276607i
$868$		0			0
$869$	3.70892	+	11.4149i	0.125817	+	0.387224i
$870$		0			0
$871$	2.30658	+	7.09892i	0.0781554	+	0.240538i
$872$		0			0
$873$	5.01341	−	15.4297i	0.169678	−	0.522216i
$874$		0			0
$875$	10.6577			0.360297
$876$		0			0
$877$	33.9000	+	24.6298i	1.14472	+	0.831689i	0.987770	−	0.155917i	$-0.0498333\pi$
$877$	33.9000	+	24.6298i	1.14472	+	0.831689i	0.156952	+	0.987606i	$0.449833\pi$
$878$		0			0
$879$	0.405229	−	0.294416i	0.0136680	−	0.00993041i
$880$		0			0
$881$	−21.3829	−	15.5356i	−0.720407	−	0.523406i	0.166107	−	0.986108i	$-0.446880\pi$
$881$	−21.3829	−	15.5356i	−0.720407	−	0.523406i	−0.886514	+	0.462701i	$0.846880\pi$
$882$		0			0
$883$	18.1081	+	13.1563i	0.609387	+	0.442746i	0.849199	−	0.528074i	$-0.177086\pi$
$883$	18.1081	+	13.1563i	0.609387	+	0.442746i	−0.239811	+	0.970820i	$0.577086\pi$
$884$		0			0
$885$	0.107981	+	0.332332i	0.00362975	+	0.0111712i
$886$		0			0
$887$	10.0423	−	30.9071i	0.337188	−	1.03776i	−0.628446	−	0.777853i	$-0.716309\pi$
$887$	10.0423	−	30.9071i	0.337188	−	1.03776i	0.965634	−	0.259905i	$-0.0836913\pi$
$888$		0			0
$889$	−15.4548	+	11.2286i	−0.518338	+	0.376595i
$890$		0			0
$891$	−2.98655	−	9.19166i	−0.100053	−	0.307932i
$892$		0			0
$893$	1.32696			0.0444049
$894$		0			0
$895$	−11.1436	−	8.09633i	−0.372491	−	0.270630i
$896$		0			0
$897$	0.131252	−	0.403952i	0.00438238	−	0.0134876i
$898$		0			0
$899$	−8.97501			−0.299333
$900$		0			0
$901$	−6.95410			−0.231675
$902$		0			0
$903$	0.295551			0.00983531
$904$		0			0
$905$	−57.5533			−1.91314
$906$		0			0
$907$	11.1891	−	34.4365i	0.371528	−	1.14344i	−0.574264	−	0.818670i	$-0.694712\pi$
$907$	11.1891	−	34.4365i	0.371528	−	1.14344i	0.945792	−	0.324774i	$-0.105288\pi$
$908$		0			0
$909$	33.4425	+	24.2974i	1.10922	+	0.805893i
$910$		0			0
$911$	7.23216			0.239612			0.119806	−	0.992797i	$-0.461773\pi$
$911$	7.23216			0.239612			0.119806	+	0.992797i	$0.461773\pi$
$912$		0			0
$913$	3.21510	+	9.89505i	0.106404	+	0.327478i
$914$		0			0
$915$	−0.640695	+	0.465492i	−0.0211807	+	0.0153887i
$916$		0			0
$917$	−0.975564	+	3.00248i	−0.0322159	+	0.0991505i
$918$		0			0
$919$	3.34258	+	10.2874i	0.110262	+	0.339351i	0.990929	−	0.134384i	$-0.0429056\pi$
$919$	3.34258	+	10.2874i	0.110262	+	0.339351i	−0.880668	+	0.473735i	$0.842906\pi$
$920$		0			0
$921$	0.289603	+	0.210409i	0.00954276	+	0.00693322i
$922$		0			0
$923$	−23.1789	−	16.8404i	−0.762942	−	0.554310i
$924$		0			0
$925$	−3.17667	+	2.30799i	−0.104448	+	0.0758861i
$926$		0			0
$927$	−6.36408	−	4.62378i	−0.209024	−	0.151865i
$928$		0			0
$929$	−16.4471			−0.539613			−0.269806	−	0.962915i	$-0.586960\pi$
$929$	−16.4471			−0.539613			−0.269806	+	0.962915i	$0.586960\pi$
$930$		0			0
$931$	0.476831	−	1.46754i	0.0156275	−	0.0480965i
$932$		0			0
$933$	−0.278099	−	0.855902i	−0.00910456	−	0.0280210i
$934$		0			0
$935$	−3.56940	−	10.9855i	−0.116732	−	0.359264i
$936$		0			0
$937$	18.5977	−	13.5120i	0.607559	−	0.441417i	−0.240995	−	0.970526i	$-0.577474\pi$
$937$	18.5977	−	13.5120i	0.607559	−	0.441417i	0.848554	+	0.529109i	$0.177474\pi$
$938$		0			0
$939$	0.0800113	−	0.246249i	0.00261107	−	0.00803605i
$940$		0			0
$941$	11.8716	−	8.62521i	0.387002	−	0.281174i	−0.377224	−	0.926122i	$-0.623121\pi$
$941$	11.8716	−	8.62521i	0.387002	−	0.281174i	0.764226	+	0.644948i	$0.223121\pi$
$942$		0			0
$943$	−12.8024	+	19.9928i	−0.416903	+	0.651054i
$944$		0			0
$945$	0.365236	−	0.265359i	0.0118811	−	0.00863214i
$946$		0			0
$947$	−18.7331	+	57.6545i	−0.608744	+	1.87352i	−0.140088	+	0.990139i	$0.544739\pi$
$947$	−18.7331	+	57.6545i	−0.608744	+	1.87352i	−0.468656	+	0.883381i	$0.655261\pi$
$948$		0			0
$949$	6.16124	−	4.47640i	0.200002	−	0.145310i
$950$		0			0
$951$	−0.127128	−	0.391261i	−0.00412242	−	0.0126875i
$952$		0			0
$953$	7.57547	+	23.3149i	0.245393	+	0.755243i	0.995572	+	0.0940074i	$0.0299677\pi$
$953$	7.57547	+	23.3149i	0.245393	+	0.755243i	−0.750178	+	0.661236i	$0.770032\pi$
$954$		0			0
$955$	−10.5110	+	32.3495i	−0.340127	+	1.04680i
$956$		0			0
$957$	0.0834837			0.00269865
$958$		0			0
$959$	4.87224	+	3.53989i	0.157333	+	0.114309i
$960$		0			0
$961$	13.7969	−	10.0241i	0.445062	−	0.323357i
$962$		0			0
$963$	6.66841	+	4.84488i	0.214886	+	0.156124i
$964$		0			0
$965$	39.5610	+	28.7428i	1.27351	+	0.925263i
$966$		0			0
$967$	0.435654	+	1.34081i	0.0140097	+	0.0431174i	0.957817	−	0.287379i	$-0.0927839\pi$
$967$	0.435654	+	1.34081i	0.0140097	+	0.0431174i	−0.943807	+	0.330496i	$0.892784\pi$
$968$		0			0
$969$	0.0710930	−	0.218802i	0.00228384	−	0.00702892i
$970$		0			0
$971$	17.4611	−	12.6862i	0.560352	−	0.407120i	−0.271236	−	0.962513i	$-0.587432\pi$
$971$	17.4611	−	12.6862i	0.560352	−	0.407120i	0.831588	+	0.555393i	$0.187432\pi$
$972$		0			0
$973$	4.87688	+	15.0095i	0.156346	+	0.481182i
$974$		0			0
$975$	0.0485334			0.00155431
$976$		0			0
$977$	43.1192	+	31.3280i	1.37951	+	1.00227i	0.996926	+	0.0783481i	$0.0249646\pi$
$977$	43.1192	+	31.3280i	1.37951	+	1.00227i	0.382581	+	0.923922i	$0.375035\pi$
$978$		0			0
$979$	0.861675	−	2.65196i	0.0275393	−	0.0847572i
$980$		0			0
$981$	−31.6721			−1.01121
$982$		0			0
$983$	26.3135			0.839271			0.419636	−	0.907693i	$-0.362158\pi$
$983$	26.3135			0.839271			0.419636	+	0.907693i	$0.362158\pi$
$984$		0			0
$985$	−25.7571			−0.820691
$986$		0			0
$987$	−0.0277887			−0.000884525
$988$		0			0
$989$	−10.4790	+	32.2509i	−0.333211	+	1.02552i
$990$		0			0
$991$	24.4024	+	17.7294i	0.775169	+	0.563193i	0.903525	−	0.428535i	$-0.140970\pi$
$991$	24.4024	+	17.7294i	0.775169	+	0.563193i	−0.128356	+	0.991728i	$0.540970\pi$
$992$		0			0
$993$	0.516102			0.0163780
$994$		0			0
$995$	−13.1362	−	40.4292i	−0.416447	−	1.28169i
$996$		0			0
$997$	−31.5256	+	22.9047i	−0.998426	+	0.725399i	−0.961750	−	0.273928i	$-0.911677\pi$
$997$	−31.5256	+	22.9047i	−0.998426	+	0.725399i	−0.0366757	+	0.999327i	$0.511677\pi$
$998$		0			0
$999$	0.555202	−	1.70874i	0.0175658	−	0.0540620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.365.4	✓	24
41.10	even	5	inner	1148.2.n.d.953.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.365.4	✓	24	1.1	even	1	trivial
1148.2.n.d.953.4	yes	24	41.10	even	5	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.0323142 q^{3} +(-0.719662 + 2.21489i) q^{5} +(-0.809017 - 0.587785i) q^{7} -2.99896 q^{9} +O(q^{10})\)	\(q-0.0323142 q^{3} +(-0.719662 + 2.21489i) q^{5} +(-0.809017 - 0.587785i) q^{7} -2.99896 q^{9} +(-0.332186 - 1.02236i) q^{11} +(2.86807 - 2.08377i) q^{13} +(0.0232553 - 0.0715725i) q^{15} +(-1.42577 - 4.38808i) q^{17} +(-1.24836 - 0.906987i) q^{19} +(0.0261428 + 0.0189938i) q^{21} +(-2.99955 + 2.17930i) q^{23} +(-0.342747 - 0.249020i) q^{25} +0.193852 q^{27} +(0.742663 - 2.28568i) q^{29} +(-1.15401 - 3.55167i) q^{31} +(0.0107343 + 0.0330369i) q^{33} +(1.88410 - 1.36888i) q^{35} +(2.86406 - 8.81466i) q^{37} +(-0.0926794 + 0.0673355i) q^{39} +(5.96303 - 2.33287i) q^{41} +(7.39938 - 5.37596i) q^{43} +(2.15823 - 6.64236i) q^{45} +(-0.695716 + 0.505468i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.0460728 + 0.141797i) q^{51} +(0.465753 - 1.43344i) q^{53} +2.50348 q^{55} +(0.0403398 + 0.0293086i) q^{57} +(-3.75650 + 2.72926i) q^{59} +(-8.51357 - 6.18547i) q^{61} +(2.42621 + 1.76274i) q^{63} +(2.55129 + 7.85207i) q^{65} +(-0.650634 + 2.00244i) q^{67} +(0.0969281 - 0.0704224i) q^{69} +(-2.49738 - 7.68616i) q^{71} +2.14822 q^{73} +(0.0110756 + 0.00804689i) q^{75} +(-0.332186 + 1.02236i) q^{77} -11.1652 q^{79} +8.99060 q^{81} -9.67861 q^{83} +10.7452 q^{85} +(-0.0239986 + 0.0738601i) q^{87} +(2.09856 + 1.52469i) q^{89} -3.54513 q^{91} +(0.0372908 + 0.114769i) q^{93} +(2.90728 - 2.11226i) q^{95} +(-1.67172 + 5.14502i) q^{97} +(0.996210 + 3.06602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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