LMFDB - Embedded newform 1148.2.i.e.165.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.15
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.e.821.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71186 - 2.96502i) q^{3} +(-1.17870 - 2.04157i) q^{5} +(1.97017 - 1.76591i) q^{7} +(-4.36091 - 7.55332i) q^{9} +O(q^{10})$	\(q+(1.71186 - 2.96502i) q^{3} +(-1.17870 - 2.04157i) q^{5} +(1.97017 - 1.76591i) q^{7} +(-4.36091 - 7.55332i) q^{9} +(0.0714606 - 0.123773i) q^{11} -2.89147 q^{13} -8.07106 q^{15} +(0.697221 - 1.20762i) q^{17} +(3.61698 + 6.26479i) q^{19} +(-1.86332 - 8.86458i) q^{21} +(2.35037 + 4.07095i) q^{23} +(-0.278666 + 0.482663i) q^{25} -19.5899 q^{27} +2.50126 q^{29} +(1.14934 - 1.99071i) q^{31} +(-0.244661 - 0.423765i) q^{33} +(-5.92746 - 1.94075i) q^{35} +(4.47884 + 7.75758i) q^{37} +(-4.94979 + 8.57328i) q^{39} -1.00000 q^{41} +10.0638 q^{43} +(-10.2804 + 17.8062i) q^{45} +(0.288758 + 0.500143i) q^{47} +(0.763121 - 6.95828i) q^{49} +(-2.38708 - 4.13455i) q^{51} +(1.33933 - 2.31978i) q^{53} -0.336922 q^{55} +24.7670 q^{57} +(2.50389 - 4.33687i) q^{59} +(-5.09097 - 8.81782i) q^{61} +(-21.9302 - 7.18033i) q^{63} +(3.40818 + 5.90313i) q^{65} +(-2.40794 + 4.17068i) q^{67} +16.0940 q^{69} -10.7912 q^{71} +(1.03436 - 1.79156i) q^{73} +(0.954072 + 1.65250i) q^{75} +(-0.0777834 - 0.370047i) q^{77} +(-1.37269 - 2.37757i) q^{79} +(-20.4524 + 35.4246i) q^{81} +8.58858 q^{83} -3.28725 q^{85} +(4.28181 - 7.41631i) q^{87} +(-5.67898 - 9.83628i) q^{89} +(-5.69668 + 5.10608i) q^{91} +(-3.93501 - 6.81563i) q^{93} +(8.52667 - 14.7686i) q^{95} -4.73305 q^{97} -1.24653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.71186	−	2.96502i	0.988341	−	1.71186i	0.362315	−	0.932056i	$-0.381986\pi$
$3$	1.71186	−	2.96502i	0.988341	−	1.71186i	0.626026	−	0.779802i	$-0.284680\pi$
$4$		0			0
$5$	−1.17870	−	2.04157i	−0.527130	−	0.913017i	−0.999500	−	0.0316162i	$-0.989935\pi$
$5$	−1.17870	−	2.04157i	−0.527130	−	0.913017i	0.472370	−	0.881401i	$-0.343399\pi$
$6$		0			0
$7$	1.97017	−	1.76591i	0.744653	−	0.667451i
$7$	1.97017	−	1.76591i	0.744653	−	0.667451i
$8$		0			0
$9$	−4.36091	−	7.55332i	−1.45364	−	2.51777i
$10$		0			0
$11$	0.0714606	−	0.123773i	0.0215462	−	0.0373191i	−0.855051	−	0.518543i	$-0.826474\pi$
$11$	0.0714606	−	0.123773i	0.0215462	−	0.0373191i	0.876597	+	0.481224i	$0.159808\pi$
$12$		0			0
$13$	−2.89147			−0.801950			−0.400975	−	0.916089i	$-0.631329\pi$
$13$	−2.89147			−0.801950			−0.400975	+	0.916089i	$0.631329\pi$
$14$		0			0
$15$	−8.07106			−2.08394
$16$		0			0
$17$	0.697221	−	1.20762i	0.169101	−	0.292891i	−0.769003	−	0.639245i	$-0.779247\pi$
$17$	0.697221	−	1.20762i	0.169101	−	0.292891i	0.938104	+	0.346354i	$0.112580\pi$
$18$		0			0
$19$	3.61698	+	6.26479i	0.829792	+	1.43724i	0.898201	+	0.439585i	$0.144874\pi$
$19$	3.61698	+	6.26479i	0.829792	+	1.43724i	−0.0684092	+	0.997657i	$0.521792\pi$
$20$		0			0
$21$	−1.86332	−	8.86458i	−0.406610	−	1.93441i
$22$		0			0
$23$	2.35037	+	4.07095i	0.490085	+	0.848853i	0.999935	−	0.0114110i	$-0.00363231\pi$
$23$	2.35037	+	4.07095i	0.490085	+	0.848853i	−0.509850	+	0.860264i	$0.670299\pi$
$24$		0			0
$25$	−0.278666	+	0.482663i	−0.0557331	+	0.0965326i
$26$		0			0
$27$	−19.5899			−3.77008
$28$		0			0
$29$	2.50126			0.464473			0.232236	−	0.972659i	$-0.425396\pi$
$29$	2.50126			0.464473			0.232236	+	0.972659i	$0.425396\pi$
$30$		0			0
$31$	1.14934	−	1.99071i	0.206427	−	0.357543i	−0.744159	−	0.668002i	$-0.767150\pi$
$31$	1.14934	−	1.99071i	0.206427	−	0.357543i	0.950587	+	0.310460i	$0.100483\pi$
$32$		0			0
$33$	−0.244661	−	0.423765i	−0.0425900	−	0.0737680i
$34$		0			0
$35$	−5.92746	−	1.94075i	−1.00192	−	0.328047i
$36$		0			0
$37$	4.47884	+	7.75758i	0.736317	+	1.27534i	0.954143	+	0.299351i	$0.0967703\pi$
$37$	4.47884	+	7.75758i	0.736317	+	1.27534i	−0.217826	+	0.975988i	$0.569896\pi$
$38$		0			0
$39$	−4.94979	+	8.57328i	−0.792600	+	1.37282i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	10.0638			1.53471			0.767355	−	0.641223i	$-0.221573\pi$
$43$	10.0638			1.53471			0.767355	+	0.641223i	$0.221573\pi$
$44$		0			0
$45$	−10.2804	+	17.8062i	−1.53251	+	2.65439i
$46$		0			0
$47$	0.288758	+	0.500143i	0.0421197	+	0.0729534i	0.886317	−	0.463080i	$-0.153256\pi$
$47$	0.288758	+	0.500143i	0.0421197	+	0.0729534i	−0.844197	+	0.536033i	$0.819922\pi$
$48$		0			0
$49$	0.763121	−	6.95828i	0.109017	−	0.994040i
$50$		0			0
$51$	−2.38708	−	4.13455i	−0.334259	−	0.578953i
$52$		0			0
$53$	1.33933	−	2.31978i	0.183971	−	0.318647i	−0.759258	−	0.650789i	$-0.774438\pi$
$53$	1.33933	−	2.31978i	0.183971	−	0.318647i	0.943229	+	0.332142i	$0.107771\pi$
$54$		0			0
$55$	−0.336922			−0.0454306
$56$		0			0
$57$	24.7670			3.28047
$58$		0			0
$59$	2.50389	−	4.33687i	0.325979	−	0.564613i	−0.655731	−	0.754995i	$-0.727639\pi$
$59$	2.50389	−	4.33687i	0.325979	−	0.564613i	0.981710	+	0.190382i	$0.0609727\pi$
$60$		0			0
$61$	−5.09097	−	8.81782i	−0.651832	−	1.12901i	−0.982678	−	0.185321i	$-0.940667\pi$
$61$	−5.09097	−	8.81782i	−0.651832	−	1.12901i	0.330846	−	0.943685i	$-0.392666\pi$
$62$		0			0
$63$	−21.9302	−	7.18033i	−2.76295	−	0.904637i
$64$		0			0
$65$	3.40818	+	5.90313i	0.422732	+	0.732194i
$66$		0			0
$67$	−2.40794	+	4.17068i	−0.294177	+	0.509530i	−0.974793	−	0.223111i	$-0.928379\pi$
$67$	−2.40794	+	4.17068i	−0.294177	+	0.509530i	0.680616	+	0.732640i	$0.261712\pi$
$68$		0			0
$69$	16.0940			1.93749
$70$		0			0
$71$	−10.7912			−1.28068			−0.640339	−	0.768092i	$-0.721206\pi$
$71$	−10.7912			−1.28068			−0.640339	+	0.768092i	$0.721206\pi$
$72$		0			0
$73$	1.03436	−	1.79156i	0.121063	−	0.209687i	−0.799124	−	0.601166i	$-0.794703\pi$
$73$	1.03436	−	1.79156i	0.121063	−	0.209687i	0.920187	+	0.391479i	$0.128036\pi$
$74$		0			0
$75$	0.954072	+	1.65250i	0.110167	+	0.190814i
$76$		0			0
$77$	−0.0777834	−	0.370047i	−0.00886424	−	0.0421708i
$78$		0			0
$79$	−1.37269	−	2.37757i	−0.154440	−	0.267498i	0.778415	−	0.627750i	$-0.216024\pi$
$79$	−1.37269	−	2.37757i	−0.154440	−	0.267498i	−0.932855	+	0.360252i	$0.882691\pi$
$80$		0			0
$81$	−20.4524	+	35.4246i	−2.27249	+	3.93606i
$82$		0			0
$83$	8.58858			0.942720			0.471360	−	0.881941i	$-0.343763\pi$
$83$	8.58858			0.942720			0.471360	+	0.881941i	$0.343763\pi$
$84$		0			0
$85$	−3.28725			−0.356553
$86$		0			0
$87$	4.28181	−	7.41631i	0.459058	−	0.795111i
$88$		0			0
$89$	−5.67898	−	9.83628i	−0.601970	−	1.04264i	−0.992522	−	0.122062i	$-0.961049\pi$
$89$	−5.67898	−	9.83628i	−0.601970	−	1.04264i	0.390552	−	0.920581i	$-0.372284\pi$
$90$		0			0
$91$	−5.69668	+	5.10608i	−0.597175	+	0.535263i
$92$		0			0
$93$	−3.93501	−	6.81563i	−0.408041	−	0.706748i
$94$		0			0
$95$	8.52667	−	14.7686i	0.874817	−	1.51523i
$96$		0			0
$97$	−4.73305			−0.480568			−0.240284	−	0.970703i	$-0.577241\pi$
$97$	−4.73305			−0.480568			−0.240284	+	0.970703i	$0.577241\pi$
$98$		0			0
$99$	−1.24653			−0.125281
$100$		0			0
$101$	−3.92591	+	6.79987i	−0.390643	+	0.676613i	−0.992534	−	0.121965i	$-0.961080\pi$
$101$	−3.92591	+	6.79987i	−0.390643	+	0.676613i	0.601892	+	0.798578i	$0.294414\pi$
$102$		0			0
$103$	7.68716	+	13.3145i	0.757438	+	1.31192i	0.944153	+	0.329507i	$0.106883\pi$
$103$	7.68716	+	13.3145i	0.757438	+	1.31192i	−0.186715	+	0.982414i	$0.559784\pi$
$104$		0			0
$105$	−15.9013	+	14.2528i	−1.55181	+	1.39093i
$106$		0			0
$107$	−8.94102	−	15.4863i	−0.864361	−	1.49712i	−0.867680	−	0.497123i	$-0.834390\pi$
$107$	−8.94102	−	15.4863i	−0.864361	−	1.49712i	0.00331842	−	0.999994i	$-0.498944\pi$
$108$		0			0
$109$	−6.35629	+	11.0094i	−0.608822	+	1.05451i	0.382613	+	0.923909i	$0.375024\pi$
$109$	−6.35629	+	11.0094i	−0.608822	+	1.05451i	−0.991435	+	0.130602i	$0.958309\pi$
$110$		0			0
$111$	30.6686			2.91093
$112$		0			0
$113$	8.71167			0.819525			0.409763	−	0.912192i	$-0.365612\pi$
$113$	8.71167			0.819525			0.409763	+	0.912192i	$0.365612\pi$
$114$		0			0
$115$	5.54075	−	9.59686i	0.516678	−	0.894912i
$116$		0			0
$117$	12.6095	+	21.8402i	1.16574	+	2.01913i
$118$		0			0
$119$	−0.758910	−	3.61045i	−0.0695691	−	0.330969i
$120$		0			0
$121$	5.48979	+	9.50859i	0.499072	+	0.864417i
$122$		0			0
$123$	−1.71186	+	2.96502i	−0.154353	+	0.267347i
$124$		0			0
$125$	−10.4731			−0.936746
$126$		0			0
$127$	−5.87321			−0.521163			−0.260581	−	0.965452i	$-0.583914\pi$
$127$	−5.87321			−0.521163			−0.260581	+	0.965452i	$0.583914\pi$
$128$		0			0
$129$	17.2277	−	29.8393i	1.51682	−	2.62720i
$130$		0			0
$131$	−5.55985	−	9.62994i	−0.485766	−	0.841372i	0.514100	−	0.857730i	$-0.328126\pi$
$131$	−5.55985	−	9.62994i	−0.485766	−	0.841372i	−0.999866	+	0.0163583i	$0.994793\pi$
$132$		0			0
$133$	18.1891	+	5.95543i	1.57720	+	0.516401i
$134$		0			0
$135$	23.0906	+	39.9941i	1.98732	+	3.44215i
$136$		0			0
$137$	−5.85584	+	10.1426i	−0.500298	+	0.866542i	0.499702	+	0.866198i	$0.333443\pi$
$137$	−5.85584	+	10.1426i	−0.500298	+	0.866542i	−1.00000		0.000344568i	$0.999890\pi$
$138$		0			0
$139$	6.11570			0.518727			0.259364	−	0.965780i	$-0.416487\pi$
$139$	6.11570			0.518727			0.259364	+	0.965780i	$0.416487\pi$
$140$		0			0
$141$	1.97725			0.166514
$142$		0			0
$143$	−0.206626	+	0.357887i	−0.0172790	+	0.0299280i
$144$		0			0
$145$	−2.94824	−	5.10650i	−0.244838	−	0.424072i
$146$		0			0
$147$	−19.3251	−	14.1743i	−1.59391	−	1.16907i
$148$		0			0
$149$	−7.54101	−	13.0614i	−0.617784	−	1.07003i	−0.989889	−	0.141842i	$-0.954697\pi$
$149$	−7.54101	−	13.0614i	−0.617784	−	1.07003i	0.372106	−	0.928190i	$-0.378636\pi$
$150$		0			0
$151$	−7.64755	+	13.2459i	−0.622349	+	1.07794i	0.366698	+	0.930340i	$0.380488\pi$
$151$	−7.64755	+	13.2459i	−0.622349	+	1.07794i	−0.989047	+	0.147600i	$0.952845\pi$
$152$		0			0
$153$	−12.1621			−0.983245
$154$		0			0
$155$	−5.41890			−0.435256
$156$		0			0
$157$	6.50156	−	11.2610i	0.518881	−	0.898728i	−0.480878	−	0.876787i	$-0.659682\pi$
$157$	6.50156	−	11.2610i	0.518881	−	0.898728i	0.999759	−	0.0219408i	$-0.00698454\pi$
$158$		0			0
$159$	−4.58548	−	7.94228i	−0.363652	−	0.629864i
$160$		0			0
$161$	11.8196	+	3.86993i	0.931511	+	0.304993i
$162$		0			0
$163$	0.126174	+	0.218541i	0.00988275	+	0.0171174i	0.870924	−	0.491417i	$-0.163521\pi$
$163$	0.126174	+	0.218541i	0.00988275	+	0.0171174i	−0.861042	+	0.508534i	$0.830188\pi$
$164$		0			0
$165$	−0.576763	+	0.998983i	−0.0449009	+	0.0777707i
$166$		0			0
$167$	−21.3675			−1.65347			−0.826733	−	0.562595i	$-0.809803\pi$
$167$	−21.3675			−1.65347			−0.826733	+	0.562595i	$0.809803\pi$
$168$		0			0
$169$	−4.63939			−0.356876
$170$		0			0
$171$	31.5467	−	54.6404i	2.41243	−	4.17846i
$172$		0			0
$173$	−0.792748	−	1.37308i	−0.0602715	−	0.104393i	0.834315	−	0.551288i	$-0.185863\pi$
$173$	−0.792748	−	1.37308i	−0.0602715	−	0.104393i	−0.894587	+	0.446894i	$0.852530\pi$
$174$		0			0
$175$	0.303322	+	1.44303i	0.0229290	+	0.109082i
$176$		0			0
$177$	−8.57262	−	14.8482i	−0.644358	−	1.11606i
$178$		0			0
$179$	8.47362	−	14.6767i	0.633348	−	1.09699i	−0.353515	−	0.935429i	$-0.615014\pi$
$179$	8.47362	−	14.6767i	0.633348	−	1.09699i	0.986863	−	0.161562i	$-0.0516531\pi$
$180$		0			0
$181$	18.3755			1.36584			0.682920	−	0.730493i	$-0.260710\pi$
$181$	18.3755			1.36584			0.682920	+	0.730493i	$0.260710\pi$
$182$		0			0
$183$	−34.8601			−2.57693
$184$		0			0
$185$	10.5584	−	18.2877i	0.776271	−	1.34454i
$186$		0			0
$187$	−0.0996476	−	0.172595i	−0.00728695	−	0.0126214i
$188$		0			0
$189$	−38.5954	+	34.5940i	−2.80740	+	2.51634i
$190$		0			0
$191$	12.7711	+	22.1202i	0.924083	+	1.60056i	0.793029	+	0.609184i	$0.208503\pi$
$191$	12.7711	+	22.1202i	0.924083	+	1.60056i	0.131054	+	0.991375i	$0.458164\pi$
$192$		0			0
$193$	2.00222	−	3.46794i	0.144123	−	0.249628i	−0.784923	−	0.619594i	$-0.787297\pi$
$193$	2.00222	−	3.46794i	0.144123	−	0.249628i	0.929045	+	0.369966i	$0.120631\pi$
$194$		0			0
$195$	23.3373			1.67122
$196$		0			0
$197$	12.0879			0.861228			0.430614	−	0.902536i	$-0.358297\pi$
$197$	12.0879			0.861228			0.430614	+	0.902536i	$0.358297\pi$
$198$		0			0
$199$	9.78922	−	16.9554i	0.693939	−	1.20194i	−0.276598	−	0.960986i	$-0.589207\pi$
$199$	9.78922	−	16.9554i	0.693939	−	1.20194i	0.970537	−	0.240952i	$-0.0774597\pi$
$200$		0			0
$201$	8.24411	+	14.2792i	0.581495	+	1.00718i
$202$		0			0
$203$	4.92791	−	4.41701i	0.345871	−	0.310013i
$204$		0			0
$205$	1.17870	+	2.04157i	0.0823240	+	0.142589i
$206$		0			0
$207$	20.4995	−	35.5062i	1.42481	−	2.46785i
$208$		0			0
$209$	1.03389			0.0715154
$210$		0			0
$211$	14.0250			0.965521			0.482761	−	0.875752i	$-0.339634\pi$
$211$	14.0250			0.965521			0.482761	+	0.875752i	$0.339634\pi$
$212$		0			0
$213$	−18.4730	+	31.9961i	−1.26575	+	2.19234i
$214$		0			0
$215$	−11.8622	−	20.5459i	−0.808992	−	1.40122i
$216$		0			0
$217$	−1.25103	−	5.95167i	−0.0849255	−	0.404025i
$218$		0			0
$219$	−3.54135	−	6.13380i	−0.239302	−	0.414484i
$220$		0			0
$221$	−2.01599	+	3.49180i	−0.135610	+	0.234884i
$222$		0			0
$223$	−14.7762			−0.989486			−0.494743	−	0.869039i	$-0.664738\pi$
$223$	−14.7762			−0.989486			−0.494743	+	0.869039i	$0.664738\pi$
$224$		0			0
$225$	4.86095			0.324063
$226$		0			0
$227$	9.12531	−	15.8055i	0.605668	−	1.04905i	−0.386278	−	0.922383i	$-0.626239\pi$
$227$	9.12531	−	15.8055i	0.605668	−	1.04905i	0.991946	−	0.126665i	$-0.0404273\pi$
$228$		0			0
$229$	2.96409	+	5.13395i	0.195872	+	0.339261i	0.947186	−	0.320684i	$-0.103913\pi$
$229$	2.96409	+	5.13395i	0.195872	+	0.339261i	−0.751314	+	0.659945i	$0.770579\pi$
$230$		0			0
$231$	−1.23035	−	0.402839i	−0.0809513	−	0.0265049i
$232$		0			0
$233$	−4.19912	−	7.27308i	−0.275093	−	0.476476i	0.695065	−	0.718947i	$-0.255375\pi$
$233$	−4.19912	−	7.27308i	−0.275093	−	0.476476i	−0.970159	+	0.242471i	$0.922042\pi$
$234$		0			0
$235$	0.680718	−	1.17904i	0.0444051	−	0.0769119i
$236$		0			0
$237$	−9.39941			−0.610557
$238$		0			0
$239$	27.2326			1.76153			0.880766	−	0.473552i	$-0.157028\pi$
$239$	27.2326			1.76153			0.880766	+	0.473552i	$0.157028\pi$
$240$		0			0
$241$	−0.0810646	+	0.140408i	−0.00522183	+	0.00904448i	−0.868625	−	0.495471i	$-0.834996\pi$
$241$	−0.0810646	+	0.140408i	−0.00522183	+	0.00904448i	0.863403	+	0.504515i	$0.168329\pi$
$242$		0			0
$243$	40.6383	+	70.3876i	2.60695	+	4.51537i
$244$		0			0
$245$	−15.1053	+	6.64376i	−0.965041	+	0.424454i
$246$		0			0
$247$	−10.4584	−	18.1145i	−0.665452	−	1.15260i
$248$		0			0
$249$	14.7024	−	25.4654i	0.931729	−	1.61380i
$250$		0			0
$251$	27.1939			1.71646			0.858232	−	0.513261i	$-0.171563\pi$
$251$	27.1939			1.71646			0.858232	+	0.513261i	$0.171563\pi$
$252$		0			0
$253$	0.671834			0.0422379
$254$		0			0
$255$	−5.62731	+	9.74679i	−0.352396	+	0.610368i
$256$		0			0
$257$	−11.0391	−	19.1202i	−0.688597	−	1.19269i	−0.972292	−	0.233771i	$-0.924894\pi$
$257$	−11.0391	−	19.1202i	−0.688597	−	1.19269i	0.283695	−	0.958915i	$-0.408440\pi$
$258$		0			0
$259$	22.5233	+	7.37451i	1.39953	+	0.458230i
$260$		0			0
$261$	−10.9078	−	18.8928i	−0.675175	−	1.16944i
$262$		0			0
$263$	−7.69249	+	13.3238i	−0.474339	+	0.821580i	−0.999568	−	0.0293811i	$-0.990646\pi$
$263$	−7.69249	+	13.3238i	−0.474339	+	0.821580i	0.525229	+	0.850961i	$0.323980\pi$
$264$		0			0
$265$	−6.31466			−0.387907
$266$		0			0
$267$	−38.8864			−2.37981
$268$		0			0
$269$	−10.3660	+	17.9545i	−0.632028	+	1.09470i	0.355109	+	0.934825i	$0.384444\pi$
$269$	−10.3660	+	17.9545i	−0.632028	+	1.09470i	−0.987137	+	0.159879i	$0.948890\pi$
$270$		0			0
$271$	−6.36161	−	11.0186i	−0.386440	−	0.669334i	0.605528	−	0.795824i	$-0.292962\pi$
$271$	−6.36161	−	11.0186i	−0.386440	−	0.669334i	−0.991968	+	0.126490i	$0.959629\pi$
$272$		0			0
$273$	5.38774	+	25.6317i	0.326081	+	1.55130i
$274$		0			0
$275$	0.0398272	+	0.0689828i	0.00240167	+	0.00415982i
$276$		0			0
$277$	−6.03738	+	10.4570i	−0.362751	+	0.628303i	−0.988413	−	0.151792i	$-0.951496\pi$
$277$	−6.03738	+	10.4570i	−0.362751	+	0.628303i	0.625662	+	0.780095i	$0.284829\pi$
$278$		0			0
$279$	−20.0487			−1.20028
$280$		0			0
$281$	0.165786			0.00988995			0.00494497	−	0.999988i	$-0.498426\pi$
$281$	0.165786			0.00988995			0.00494497	+	0.999988i	$0.498426\pi$
$282$		0			0
$283$	−4.47344	+	7.74822i	−0.265918	+	0.460584i	−0.967804	−	0.251706i	$-0.919008\pi$
$283$	−4.47344	+	7.74822i	−0.265918	+	0.460584i	0.701886	+	0.712290i	$0.252342\pi$
$284$		0			0
$285$	−29.1929	−	50.5635i	−1.72924	−	2.99513i
$286$		0			0
$287$	−1.97017	+	1.76591i	−0.116295	+	0.104238i
$288$		0			0
$289$	7.52777	+	13.0385i	0.442810	+	0.766969i
$290$		0			0
$291$	−8.10230	+	14.0336i	−0.474965	+	0.822664i
$292$		0			0
$293$	17.2016			1.00493			0.502465	−	0.864597i	$-0.332427\pi$
$293$	17.2016			1.00493			0.502465	+	0.864597i	$0.332427\pi$
$294$		0			0
$295$	−11.8054			−0.687334
$296$		0			0
$297$	−1.39991	+	2.42471i	−0.0812308	+	0.140696i
$298$		0			0
$299$	−6.79602	−	11.7710i	−0.393024	−	0.680737i
$300$		0			0
$301$	19.8273	−	17.7717i	1.14283	−	1.02434i
$302$		0			0
$303$	13.4412	+	23.2808i	0.772176	+	1.33745i
$304$		0			0
$305$	−12.0014	+	20.7871i	−0.687201	+	1.19027i
$306$		0			0
$307$	33.1945			1.89451			0.947256	−	0.320478i	$-0.103843\pi$
$307$	33.1945			1.89451			0.947256	+	0.320478i	$0.103843\pi$
$308$		0			0
$309$	52.6373			2.99443
$310$		0			0
$311$	−5.46469	+	9.46512i	−0.309874	+	0.536718i	−0.978335	−	0.207030i	$-0.933620\pi$
$311$	−5.46469	+	9.46512i	−0.309874	+	0.536718i	0.668460	+	0.743748i	$0.266954\pi$
$312$		0			0
$313$	5.29062	+	9.16362i	0.299043	+	0.517958i	0.975917	−	0.218141i	$-0.0699992\pi$
$313$	5.29062	+	9.16362i	0.299043	+	0.517958i	−0.676874	+	0.736099i	$0.736666\pi$
$314$		0			0
$315$	11.1900	+	53.2355i	0.630486	+	2.99948i
$316$		0			0
$317$	15.4774	+	26.8076i	0.869295	+	1.50566i	0.862719	+	0.505684i	$0.168760\pi$
$317$	15.4774	+	26.8076i	0.869295	+	1.50566i	0.00657627	+	0.999978i	$0.497907\pi$
$318$		0			0
$319$	0.178742	−	0.309590i	0.0100076	−	0.0173337i
$320$		0			0
$321$	−61.2230			−3.41714
$322$		0			0
$323$	10.0873			0.561274
$324$		0			0
$325$	0.805754	−	1.39561i	0.0446952	−	0.0774143i
$326$		0			0
$327$	21.7621	+	37.6931i	1.20345	+	2.08443i
$328$		0			0
$329$	1.45211	+	0.475446i	0.0800574	+	0.0262122i
$330$		0			0
$331$	12.6431	+	21.8984i	0.694925	+	1.20365i	0.970206	+	0.242282i	$0.0778959\pi$
$331$	12.6431	+	21.8984i	0.694925	+	1.20365i	−0.275281	+	0.961364i	$0.588771\pi$
$332$		0			0
$333$	39.0637	−	67.6603i	2.14068	−	3.70776i
$334$		0			0
$335$	11.3530			0.620279
$336$		0			0
$337$	5.87859			0.320227			0.160114	−	0.987099i	$-0.448814\pi$
$337$	5.87859			0.320227			0.160114	+	0.987099i	$0.448814\pi$
$338$		0			0
$339$	14.9131	−	25.8303i	0.809971	−	1.40291i
$340$		0			0
$341$	−0.164265	−	0.284515i	−0.00889544	−	0.0154074i
$342$		0			0
$343$	−10.7842	−	15.0566i	−0.582293	−	0.812979i
$344$		0			0
$345$	−18.9700	−	32.8569i	−1.02131	−	1.76896i
$346$		0			0
$347$	−3.67770	+	6.36996i	−0.197429	+	0.341957i	−0.947694	−	0.319180i	$-0.896593\pi$
$347$	−3.67770	+	6.36996i	−0.197429	+	0.341957i	0.750265	+	0.661137i	$0.229926\pi$
$348$		0			0
$349$	−4.99991			−0.267639			−0.133820	−	0.991006i	$-0.542724\pi$
$349$	−4.99991			−0.267639			−0.133820	+	0.991006i	$0.542724\pi$
$350$		0			0
$351$	56.6436			3.02341
$352$		0			0
$353$	−4.45744	+	7.72051i	−0.237245	+	0.410921i	−0.959923	−	0.280264i	$-0.909578\pi$
$353$	−4.45744	+	7.72051i	−0.237245	+	0.410921i	0.722677	+	0.691185i	$0.242911\pi$
$354$		0			0
$355$	12.7196	+	22.0309i	0.675085	+	1.16928i
$356$		0			0
$357$	−12.0042	−	3.93038i	−0.635330	−	0.208018i
$358$		0			0
$359$	−8.71061	−	15.0872i	−0.459728	−	0.796273i	0.539218	−	0.842166i	$-0.318720\pi$
$359$	−8.71061	−	15.0872i	−0.459728	−	0.796273i	−0.998946	+	0.0458932i	$0.985387\pi$
$360$		0			0
$361$	−16.6651	+	28.8648i	−0.877110	+	1.51920i
$362$		0			0
$363$	37.5909			1.97301
$364$		0			0
$365$	−4.87680			−0.255263
$366$		0			0
$367$	−0.331675	+	0.574478i	−0.0173133	+	0.0299875i	−0.874552	−	0.484931i	$-0.838845\pi$
$367$	−0.331675	+	0.574478i	−0.0173133	+	0.0299875i	0.857239	+	0.514919i	$0.172178\pi$
$368$		0			0
$369$	4.36091	+	7.55332i	0.227020	+	0.393210i
$370$		0			0
$371$	−1.45783	−	6.93550i	−0.0756868	−	0.360073i
$372$		0			0
$373$	8.68836	+	15.0487i	0.449866	+	0.779191i	0.998377	−	0.0569522i	$-0.0181383\pi$
$373$	8.68836	+	15.0487i	0.449866	+	0.779191i	−0.548511	+	0.836144i	$0.684805\pi$
$374$		0			0
$375$	−17.9285	+	31.0531i	−0.925825	+	1.60358i
$376$		0			0
$377$	−7.23233			−0.372484
$378$		0			0
$379$	18.2083			0.935297			0.467648	−	0.883915i	$-0.345101\pi$
$379$	18.2083			0.935297			0.467648	+	0.883915i	$0.345101\pi$
$380$		0			0
$381$	−10.0541	+	17.4142i	−0.515087	+	0.892156i
$382$		0			0
$383$	1.45452	+	2.51931i	0.0743227	+	0.128731i	0.900792	−	0.434252i	$-0.142987\pi$
$383$	1.45452	+	2.51931i	0.0743227	+	0.128731i	−0.826469	+	0.562982i	$0.809654\pi$
$384$		0			0
$385$	−0.663794	+	0.594975i	−0.0338301	+	0.0303227i
$386$		0			0
$387$	−43.8872	−	76.0149i	−2.23091	−	3.86405i
$388$		0			0
$389$	9.15199	−	15.8517i	0.464024	−	0.803714i	−0.535132	−	0.844768i	$-0.679738\pi$
$389$	9.15199	−	15.8517i	0.464024	−	0.803714i	0.999157	+	0.0410543i	$0.0130716\pi$
$390$		0			0
$391$	6.55489			0.331495
$392$		0			0
$393$	−38.0707			−1.92041
$394$		0			0
$395$	−3.23598	+	5.60488i	−0.162820	+	0.282012i
$396$		0			0
$397$	11.6819	+	20.2337i	0.586300	+	1.01550i	0.994712	+	0.102703i	$0.0327492\pi$
$397$	11.6819	+	20.2337i	0.586300	+	1.01550i	−0.408412	+	0.912798i	$0.633917\pi$
$398$		0			0
$399$	48.7952	−	43.7363i	2.44281	−	2.18956i
$400$		0			0
$401$	−1.51342	−	2.62131i	−0.0755764	−	0.130902i	0.825760	−	0.564021i	$-0.190746\pi$
$401$	−1.51342	−	2.62131i	−0.0755764	−	0.130902i	−0.901337	+	0.433119i	$0.857413\pi$
$402$		0			0
$403$	−3.32328	+	5.75609i	−0.165544	+	0.286731i
$404$		0			0
$405$	96.4289			4.79159
$406$		0			0
$407$	1.28024			0.0634593
$408$		0			0
$409$	3.76533	−	6.52175i	0.186184	−	0.322480i	−0.757791	−	0.652497i	$-0.773721\pi$
$409$	3.76533	−	6.52175i	0.186184	−	0.322480i	0.943975	+	0.330018i	$0.107055\pi$
$410$		0			0
$411$	20.0487	+	34.7254i	0.988931	+	1.71288i
$412$		0			0
$413$	−2.72544	−	12.9660i	−0.134110	−	0.638016i
$414$		0			0
$415$	−10.1234	−	17.5342i	−0.496936	−	0.860719i
$416$		0			0
$417$	10.4692	−	18.1332i	0.512679	−	0.887987i
$418$		0			0
$419$	40.5782			1.98238			0.991188	−	0.132463i	$-0.0422886\pi$
$419$	40.5782			1.98238			0.991188	+	0.132463i	$0.0422886\pi$
$420$		0			0
$421$	8.44073			0.411376			0.205688	−	0.978618i	$-0.434057\pi$
$421$	8.44073			0.411376			0.205688	+	0.978618i	$0.434057\pi$
$422$		0			0
$423$	2.51850	−	4.36216i	0.122453	−	0.212096i
$424$		0			0
$425$	0.388583	+	0.673045i	0.0188490	+	0.0326475i
$426$		0			0
$427$	−25.6015	−	8.38238i	−1.23895	−	0.405652i
$428$		0			0
$429$	0.707430	+	1.22530i	0.0341550	+	0.0591582i
$430$		0			0
$431$	−8.24033	+	14.2727i	−0.396923	+	0.687490i	−0.993345	−	0.115181i	$-0.963255\pi$
$431$	−8.24033	+	14.2727i	−0.396923	+	0.687490i	0.596422	+	0.802671i	$0.296589\pi$
$432$		0			0
$433$	−8.61281			−0.413905			−0.206953	−	0.978351i	$-0.566355\pi$
$433$	−8.61281			−0.413905			−0.206953	+	0.978351i	$0.566355\pi$
$434$		0			0
$435$	−20.1879			−0.967933
$436$		0			0
$437$	−17.0025	+	29.4491i	−0.813338	+	1.40874i
$438$		0			0
$439$	16.2270	+	28.1059i	0.774470	+	1.34142i	0.935092	+	0.354406i	$0.115317\pi$
$439$	16.2270	+	28.1059i	0.774470	+	1.34142i	−0.160621	+	0.987016i	$0.551350\pi$
$440$		0			0
$441$	−55.8860	+	24.5803i	−2.66124	+	1.17049i
$442$		0			0
$443$	−16.4022	−	28.4094i	−0.779290	−	1.34977i	−0.932352	−	0.361553i	$-0.882247\pi$
$443$	−16.4022	−	28.4094i	−0.779290	−	1.34977i	0.153062	−	0.988217i	$-0.451087\pi$
$444$		0			0
$445$	−13.3876	+	23.1880i	−0.634634	+	1.09922i
$446$		0			0
$447$	−51.6365			−2.44232
$448$		0			0
$449$	4.28694			0.202313			0.101157	−	0.994871i	$-0.467746\pi$
$449$	4.28694			0.202313			0.101157	+	0.994871i	$0.467746\pi$
$450$		0			0
$451$	−0.0714606	+	0.123773i	−0.00336495	+	0.00582826i
$452$		0			0
$453$	26.1830	+	45.3504i	1.23019	+	2.13075i
$454$		0			0
$455$	17.1391	+	5.61163i	0.803493	+	0.263077i
$456$		0			0
$457$	−5.08223	−	8.80269i	−0.237737	−	0.411772i	0.722328	−	0.691551i	$-0.243072\pi$
$457$	−5.08223	−	8.80269i	−0.237737	−	0.411772i	−0.960065	+	0.279779i	$0.909739\pi$
$458$		0			0
$459$	−13.6585	+	23.6572i	−0.637523	+	1.10422i
$460$		0			0
$461$	−26.9754			−1.25637			−0.628184	−	0.778065i	$-0.716201\pi$
$461$	−26.9754			−1.25637			−0.628184	+	0.778065i	$0.716201\pi$
$462$		0			0
$463$	−26.2945			−1.22201			−0.611005	−	0.791627i	$-0.709234\pi$
$463$	−26.2945			−1.22201			−0.611005	+	0.791627i	$0.709234\pi$
$464$		0			0
$465$	−9.27638	+	16.0672i	−0.430182	+	0.745097i
$466$		0			0
$467$	−13.1388	−	22.7570i	−0.607990	−	1.05307i	−0.991571	−	0.129563i	$-0.958643\pi$
$467$	−13.1388	−	22.7570i	−0.607990	−	1.05307i	0.383581	−	0.923507i	$-0.374691\pi$
$468$		0			0
$469$	2.62100	+	12.4692i	0.121026	+	0.575772i
$470$		0			0
$471$	−22.2595	−	38.5546i	−1.02566	−	1.77650i
$472$		0			0
$473$	0.719163	−	1.24563i	0.0330671	−	0.0572740i
$474$		0			0
$475$	−4.03171			−0.184988
$476$		0			0
$477$	−23.3628			−1.06971
$478$		0			0
$479$	−5.27278	+	9.13272i	−0.240919	+	0.417285i	−0.960976	−	0.276630i	$-0.910782\pi$
$479$	−5.27278	+	9.13272i	−0.240919	+	0.417285i	0.720057	+	0.693915i	$0.244116\pi$
$480$		0			0
$481$	−12.9504	−	22.4308i	−0.590490	−	1.02276i
$482$		0			0
$483$	31.7078	−	28.4205i	1.44276	−	1.29318i
$484$		0			0
$485$	5.57884	+	9.66283i	0.253322	+	0.438767i
$486$		0			0
$487$	−20.9420	+	36.2727i	−0.948974	+	1.64367i	−0.201383	+	0.979513i	$0.564544\pi$
$487$	−20.9420	+	36.2727i	−0.948974	+	1.64367i	−0.747591	+	0.664159i	$0.768790\pi$
$488$		0			0
$489$	0.863971			0.0390701
$490$		0			0
$491$	−9.42364			−0.425283			−0.212641	−	0.977130i	$-0.568207\pi$
$491$	−9.42364			−0.425283			−0.212641	+	0.977130i	$0.568207\pi$
$492$		0			0
$493$	1.74393	−	3.02058i	0.0785427	−	0.136040i
$494$		0			0
$495$	1.46929	+	2.54488i	0.0660396	+	0.114384i
$496$		0			0
$497$	−21.2604	+	19.0563i	−0.953661	+	0.854791i
$498$		0			0
$499$	−19.8460	−	34.3743i	−0.888430	−	1.53881i	−0.841731	−	0.539898i	$-0.818463\pi$
$499$	−19.8460	−	34.3743i	−0.888430	−	1.53881i	−0.0466999	−	0.998909i	$-0.514870\pi$
$500$		0			0
$501$	−36.5781	+	63.3551i	−1.63419	+	2.83050i
$502$		0			0
$503$	−14.7881			−0.659371			−0.329685	−	0.944091i	$-0.606943\pi$
$503$	−14.7881			−0.659371			−0.329685	+	0.944091i	$0.606943\pi$
$504$		0			0
$505$	18.5099			0.823678
$506$		0			0
$507$	−7.94198	+	13.7559i	−0.352716	+	0.610921i
$508$		0			0
$509$	1.68657	+	2.92123i	0.0747561	+	0.129481i	0.900980	−	0.433860i	$-0.142849\pi$
$509$	1.68657	+	2.92123i	0.0747561	+	0.129481i	−0.826224	+	0.563342i	$0.809516\pi$
$510$		0			0
$511$	−1.12588	−	5.35627i	−0.0498059	−	0.236947i
$512$		0			0
$513$	−70.8563	−	122.727i	−3.12838	−	5.41852i
$514$		0			0
$515$	18.1217	−	31.3877i	0.798538	−	1.38311i
$516$		0			0
$517$	0.0825392			0.00363007
$518$		0			0
$519$	−5.42829			−0.238275
$520$		0			0
$521$	−17.0055	+	29.4544i	−0.745025	+	1.29042i	0.205159	+	0.978729i	$0.434229\pi$
$521$	−17.0055	+	29.4544i	−0.745025	+	1.29042i	−0.950183	+	0.311692i	$0.899104\pi$
$522$		0			0
$523$	−16.4938	−	28.5681i	−0.721223	−	1.24919i	−0.960510	−	0.278246i	$-0.910247\pi$
$523$	−16.4938	−	28.5681i	−0.721223	−	1.24919i	0.239287	−	0.970949i	$-0.423086\pi$
$524$		0			0
$525$	4.79785	+	1.57090i	0.209395	+	0.0685596i
$526$		0			0
$527$	−1.60268	−	2.77593i	−0.0698140	−	0.120921i
$528$		0			0
$529$	0.451557	−	0.782120i	0.0196329	−	0.0340052i
$530$		0			0
$531$	−43.6771			−1.89542
$532$		0			0
$533$	2.89147			0.125244
$534$		0			0
$535$	−21.0776	+	36.5074i	−0.911263	+	1.57835i
$536$		0			0
$537$	−29.0112	−	50.2490i	−1.25193	−	2.16840i
$538$		0			0
$539$	−0.806717	−	0.591697i	−0.0347477	−	0.0254862i
$540$		0			0
$541$	5.51783	+	9.55716i	0.237230	+	0.410895i	0.959918	−	0.280279i	$-0.0904271\pi$
$541$	5.51783	+	9.55716i	0.237230	+	0.410895i	−0.722688	+	0.691174i	$0.757094\pi$
$542$		0			0
$543$	31.4562	−	54.4838i	1.34992	−	2.33812i
$544$		0			0
$545$	29.9686			1.28371
$546$		0			0
$547$	−1.82860			−0.0781851			−0.0390926	−	0.999236i	$-0.512447\pi$
$547$	−1.82860			−0.0781851			−0.0390926	+	0.999236i	$0.512447\pi$
$548$		0			0
$549$	−44.4025	+	76.9075i	−1.89505	+	3.28233i
$550$		0			0
$551$	9.04702	+	15.6699i	0.385416	+	0.667560i
$552$		0			0
$553$	−6.90301	−	2.26016i	−0.293546	−	0.0961119i
$554$		0			0
$555$	−36.1490	−	62.6120i	−1.53444	−	2.65773i
$556$		0			0
$557$	16.7053	−	28.9344i	0.707825	−	1.22599i	−0.257838	−	0.966188i	$-0.583010\pi$
$557$	16.7053	−	28.9344i	0.707825	−	1.22599i	0.965662	−	0.259800i	$-0.0836567\pi$
$558$		0			0
$559$	−29.0991			−1.23076
$560$		0			0
$561$	−0.682330			−0.0288080
$562$		0			0
$563$	7.53256	−	13.0468i	0.317459	−	0.549856i	−0.662498	−	0.749064i	$-0.730504\pi$
$563$	7.53256	−	13.0468i	0.317459	−	0.549856i	0.979957	+	0.199208i	$0.0638369\pi$
$564$		0			0
$565$	−10.2684	−	17.7855i	−0.431997	−	0.748240i
$566$		0			0
$567$	22.2620	+	105.909i	0.934916	+	4.44778i
$568$		0			0
$569$	19.5406	+	33.8454i	0.819186	+	1.41887i	0.906283	+	0.422671i	$0.138908\pi$
$569$	19.5406	+	33.8454i	0.819186	+	1.41887i	−0.0870973	+	0.996200i	$0.527759\pi$
$570$		0			0
$571$	−3.90793	+	6.76873i	−0.163542	+	0.283262i	−0.936136	−	0.351637i	$-0.885625\pi$
$571$	−3.90793	+	6.76873i	−0.163542	+	0.283262i	0.772595	+	0.634899i	$0.218958\pi$
$572$		0			0
$573$	87.4491			3.65324
$574$		0			0
$575$	−2.61987			−0.109256
$576$		0			0
$577$	−3.21140	+	5.56230i	−0.133692	+	0.231562i	−0.925097	−	0.379731i	$-0.876017\pi$
$577$	−3.21140	+	5.56230i	−0.133692	+	0.231562i	0.791405	+	0.611292i	$0.209350\pi$
$578$		0			0
$579$	−6.85502	−	11.8733i	−0.284885	−	0.493435i
$580$		0			0
$581$	16.9210	−	15.1667i	0.701999	−	0.629219i
$582$		0			0
$583$	−0.191418	−	0.331546i	−0.00792774	−	0.0137312i
$584$		0			0
$585$	29.7255	−	51.4861i	1.22900	−	2.12869i
$586$		0			0
$587$	−8.49043			−0.350438			−0.175219	−	0.984530i	$-0.556063\pi$
$587$	−8.49043			−0.350438			−0.175219	+	0.984530i	$0.556063\pi$
$588$		0			0
$589$	16.6285			0.685167
$590$		0			0
$591$	20.6928	−	35.8409i	0.851187	−	1.47430i
$592$		0			0
$593$	2.92916	+	5.07345i	0.120286	+	0.208342i	0.919880	−	0.392199i	$-0.128285\pi$
$593$	2.92916	+	5.07345i	0.120286	+	0.208342i	−0.799594	+	0.600540i	$0.794952\pi$
$594$		0			0
$595$	−6.47644	+	5.80500i	−0.265508	+	0.237982i
$596$		0			0
$597$	−33.5155	−	58.0505i	−1.37170	−	2.37585i
$598$		0			0
$599$	10.7131	−	18.5556i	0.437725	−	0.758162i	−0.559789	−	0.828636i	$-0.689118\pi$
$599$	10.7131	−	18.5556i	0.437725	−	0.758162i	0.997514	+	0.0704733i	$0.0224510\pi$
$600$		0			0
$601$	40.7091			1.66056			0.830279	−	0.557347i	$-0.188181\pi$
$601$	40.7091			1.66056			0.830279	+	0.557347i	$0.188181\pi$
$602$		0			0
$603$	42.0033			1.71051
$604$		0			0
$605$	12.9416	−	22.4155i	0.526152	−	0.911321i
$606$		0			0
$607$	−15.7650	−	27.3058i	−0.639882	−	1.10831i	−0.985458	−	0.169917i	$-0.945650\pi$
$607$	−15.7650	−	27.3058i	−0.639882	−	1.10831i	0.345577	−	0.938390i	$-0.387683\pi$
$608$		0			0
$609$	−4.66066	−	22.1727i	−0.188859	−	0.898481i
$610$		0			0
$611$	−0.834935	−	1.44615i	−0.0337779	−	0.0585050i
$612$		0			0
$613$	11.2595	−	19.5021i	0.454769	−	0.787683i	−0.543906	−	0.839146i	$-0.683055\pi$
$613$	11.2595	−	19.5021i	0.454769	−	0.787683i	0.998675	+	0.0514633i	$0.0163885\pi$
$614$		0			0
$615$	8.07106			0.325457
$616$		0			0
$617$	8.08398			0.325449			0.162724	−	0.986672i	$-0.447972\pi$
$617$	8.08398			0.325449			0.162724	+	0.986672i	$0.447972\pi$
$618$		0			0
$619$	−8.94078	+	15.4859i	−0.359360	+	0.622430i	−0.987854	−	0.155384i	$-0.950338\pi$
$619$	−8.94078	+	15.4859i	−0.359360	+	0.622430i	0.628494	+	0.777814i	$0.283672\pi$
$620$		0			0
$621$	−46.0434	−	79.7496i	−1.84766	−	3.20024i
$622$		0			0
$623$	−28.5585	−	9.35055i	−1.14417	−	0.374622i
$624$		0			0
$625$	13.7380	+	23.7949i	0.549521	+	0.951798i
$626$		0			0
$627$	1.76987	−	3.06550i	0.0706816	−	0.122424i
$628$		0			0
$629$	12.4910			0.498047
$630$		0			0
$631$	−2.38709			−0.0950284			−0.0475142	−	0.998871i	$-0.515130\pi$
$631$	−2.38709			−0.0950284			−0.0475142	+	0.998871i	$0.515130\pi$
$632$		0			0
$633$	24.0088	−	41.5845i	0.954265	−	1.65284i
$634$		0			0
$635$	6.92275	+	11.9905i	0.274721	+	0.475830i
$636$		0			0
$637$	−2.20654	+	20.1197i	−0.0874264	+	0.797170i
$638$		0			0
$639$	47.0594	+	81.5093i	1.86164	+	3.22446i
$640$		0			0
$641$	−3.55783	+	6.16235i	−0.140526	+	0.243398i	−0.927695	−	0.373339i	$-0.878213\pi$
$641$	−3.55783	+	6.16235i	−0.140526	+	0.243398i	0.787169	+	0.616738i	$0.211546\pi$
$642$		0			0
$643$	−3.43177			−0.135336			−0.0676679	−	0.997708i	$-0.521556\pi$
$643$	−3.43177			−0.135336			−0.0676679	+	0.997708i	$0.521556\pi$
$644$		0			0
$645$	−81.2253			−3.19824
$646$		0			0
$647$	4.28008	−	7.41332i	0.168267	−	0.291448i	−0.769543	−	0.638595i	$-0.779516\pi$
$647$	4.28008	−	7.41332i	0.168267	−	0.291448i	0.937811	+	0.347147i	$0.112849\pi$
$648$		0			0
$649$	−0.357860	−	0.619831i	−0.0140472	−	0.0243305i
$650$		0			0
$651$	−19.7884	−	6.47907i	−0.775569	−	0.253935i
$652$		0			0
$653$	6.17697	+	10.6988i	0.241724	+	0.418678i	0.961205	−	0.275834i	$-0.0889539\pi$
$653$	6.17697	+	10.6988i	0.241724	+	0.418678i	−0.719482	+	0.694511i	$0.755621\pi$
$654$		0			0
$655$	−13.1068	+	22.7016i	−0.512125	+	0.887026i
$656$		0			0
$657$	−18.0430			−0.703925
$658$		0			0
$659$	−48.6368			−1.89462			−0.947310	−	0.320320i	$-0.896210\pi$
$659$	−48.6368			−1.89462			−0.947310	+	0.320320i	$0.896210\pi$
$660$		0			0
$661$	−6.18333	+	10.7098i	−0.240504	+	0.416564i	−0.960858	−	0.277042i	$-0.910646\pi$
$661$	−6.18333	+	10.7098i	−0.240504	+	0.416564i	0.720354	+	0.693606i	$0.243979\pi$
$662$		0			0
$663$	6.90219	+	11.9549i	0.268059	+	0.464291i
$664$		0			0
$665$	−9.28109	−	44.1540i	−0.359905	−	1.71222i
$666$		0			0
$667$	5.87888	+	10.1825i	0.227631	+	0.394269i
$668$		0			0
$669$	−25.2947	+	43.8117i	−0.977950	+	1.69386i
$670$		0			0
$671$	−1.45521			−0.0561780
$672$		0			0
$673$	−44.1413			−1.70152			−0.850760	−	0.525554i	$-0.823858\pi$
$673$	−44.1413			−1.70152			−0.850760	+	0.525554i	$0.823858\pi$
$674$		0			0
$675$	5.45903	−	9.45532i	0.210118	−	0.363936i
$676$		0			0
$677$	5.17668	+	8.96627i	0.198956	+	0.344602i	0.948190	−	0.317703i	$-0.102912\pi$
$677$	5.17668	+	8.96627i	0.198956	+	0.344602i	−0.749234	+	0.662305i	$0.769578\pi$
$678$		0			0
$679$	−9.32490	+	8.35814i	−0.357857	+	0.320756i
$680$		0			0
$681$	−31.2425	−	54.1135i	−1.19721	−	2.07363i
$682$		0			0
$683$	11.5212	−	19.9553i	0.440846	−	0.763568i	−0.556906	−	0.830575i	$-0.688012\pi$
$683$	11.5212	−	19.9553i	0.440846	−	0.763568i	0.997752	+	0.0670071i	$0.0213450\pi$
$684$		0			0
$685$	27.6091			1.05489
$686$		0			0
$687$	20.2964			0.774355
$688$		0			0
$689$	−3.87263	+	6.70759i	−0.147535	+	0.255539i
$690$		0			0
$691$	−5.47880	−	9.48956i	−0.208423	−	0.361000i	0.742795	−	0.669519i	$-0.233500\pi$
$691$	−5.47880	−	9.48956i	−0.208423	−	0.361000i	−0.951218	+	0.308519i	$0.900167\pi$
$692$		0			0
$693$	−2.45588	+	2.20127i	−0.0932912	+	0.0836192i
$694$		0			0
$695$	−7.20858	−	12.4856i	−0.273437	−	0.473607i
$696$		0			0
$697$	−0.697221	+	1.20762i	−0.0264091	+	0.0457419i
$698$		0			0
$699$	−28.7532			−1.08754
$700$		0			0
$701$	3.05919			0.115544			0.0577721	−	0.998330i	$-0.481600\pi$
$701$	3.05919			0.115544			0.0577721	+	0.998330i	$0.481600\pi$
$702$		0			0
$703$	−32.3998	+	56.1181i	−1.22198	+	2.11653i
$704$		0			0
$705$	−2.33058	−	4.03669i	−0.0877748	−	0.152030i
$706$		0			0
$707$	4.27327	+	20.3297i	0.160713	+	0.764577i
$708$		0			0
$709$	12.1005	+	20.9586i	0.454442	+	0.787117i	0.998656	−	0.0518299i	$-0.0165054\pi$
$709$	12.1005	+	20.9586i	0.454442	+	0.787117i	−0.544214	+	0.838946i	$0.683172\pi$
$710$		0			0
$711$	−11.9724	+	20.7368i	−0.448999	+	0.777689i
$712$		0			0
$713$	10.8055			0.404668
$714$		0			0
$715$	0.974201			0.0364331
$716$		0			0
$717$	46.6184	−	80.7454i	1.74100	−	3.01549i
$718$		0			0
$719$	−0.437294	−	0.757416i	−0.0163083	−	0.0282469i	0.857756	−	0.514057i	$-0.171858\pi$
$719$	−0.437294	−	0.757416i	−0.0163083	−	0.0282469i	−0.874064	+	0.485810i	$0.838525\pi$
$720$		0			0
$721$	38.6573	+	12.6571i	1.43967	+	0.471374i
$722$		0			0
$723$	0.277542	+	0.480717i	0.0103219	+	0.0178781i
$724$		0			0
$725$	−0.697016	+	1.20727i	−0.0258865	+	0.0448368i
$726$		0			0
$727$	21.7602			0.807040			0.403520	−	0.914971i	$-0.367787\pi$
$727$	21.7602			0.807040			0.403520	+	0.914971i	$0.367787\pi$
$728$		0			0
$729$	155.554			5.76124
$730$		0			0
$731$	7.01666	−	12.1532i	0.259521	−	0.449503i
$732$		0			0
$733$	−4.66546	−	8.08081i	−0.172323	−	0.298471i	0.766909	−	0.641756i	$-0.221794\pi$
$733$	−4.66546	−	8.08081i	−0.172323	−	0.298471i	−0.939231	+	0.343285i	$0.888460\pi$
$734$		0			0
$735$	−6.15920	+	56.1607i	−0.227185	+	2.07152i
$736$		0			0
$737$	0.344146	+	0.596079i	0.0126768	+	0.0219568i
$738$		0			0
$739$	−17.5176	+	30.3413i	−0.644394	+	1.11612i	0.340047	+	0.940409i	$0.389557\pi$
$739$	−17.5176	+	30.3413i	−0.644394	+	1.11612i	−0.984441	+	0.175715i	$0.943776\pi$
$740$		0			0
$741$	−71.6131			−2.63077
$742$		0			0
$743$	−30.6618			−1.12487			−0.562436	−	0.826841i	$-0.690136\pi$
$743$	−30.6618			−1.12487			−0.562436	+	0.826841i	$0.690136\pi$
$744$		0			0
$745$	−17.7772	+	30.7910i	−0.651305	+	1.12809i
$746$		0			0
$747$	−37.4541	−	64.8723i	−1.37037	−	2.37356i
$748$		0			0
$749$	−44.9627	−	14.7216i	−1.64290	−	0.537915i
$750$		0			0
$751$	1.86035	+	3.22222i	0.0678851	+	0.117580i	0.897970	−	0.440056i	$-0.145042\pi$
$751$	1.86035	+	3.22222i	0.0678851	+	0.117580i	−0.830085	+	0.557637i	$0.811708\pi$
$752$		0			0
$753$	46.5521	−	80.6306i	1.69645	−	2.93834i
$754$		0			0
$755$	36.0567			1.31224
$756$		0			0
$757$	32.8896			1.19539			0.597697	−	0.801722i	$-0.296082\pi$
$757$	32.8896			1.19539			0.597697	+	0.801722i	$0.296082\pi$
$758$		0			0
$759$	1.15008	−	1.99201i	0.0417454	−	0.0723052i
$760$		0			0
$761$	−0.532364	−	0.922081i	−0.0192982	−	0.0334254i	0.856215	−	0.516620i	$-0.172810\pi$
$761$	−0.532364	−	0.922081i	−0.0192982	−	0.0334254i	−0.875513	+	0.483194i	$0.839477\pi$
$762$		0			0
$763$	6.91869	+	32.9150i	0.250473	+	1.19160i
$764$		0			0
$765$	14.3354	+	24.8297i	0.518299	+	0.897719i
$766$		0			0
$767$	−7.23994	+	12.5399i	−0.261419	+	0.452791i
$768$		0			0
$769$	51.5858			1.86023			0.930116	−	0.367267i	$-0.119706\pi$
$769$	51.5858			1.86023			0.930116	+	0.367267i	$0.119706\pi$
$770$		0			0
$771$	−75.5891			−2.72228
$772$		0			0
$773$	−18.1594	+	31.4529i	−0.653147	+	1.13128i	0.329208	+	0.944257i	$0.393218\pi$
$773$	−18.1594	+	31.4529i	−0.653147	+	1.13128i	−0.982355	+	0.187026i	$0.940115\pi$
$774$		0			0
$775$	0.640562	+	1.10949i	0.0230097	+	0.0398539i
$776$		0			0
$777$	60.4222	−	54.1579i	2.16764	−	1.94291i
$778$		0			0
$779$	−3.61698	−	6.26479i	−0.129592	−	0.224459i
$780$		0			0
$781$	−0.771145	+	1.33566i	−0.0275937	+	0.0477937i
$782$		0			0
$783$	−48.9995			−1.75110
$784$		0			0
$785$	−30.6535			−1.09407
$786$		0			0
$787$	4.95189	−	8.57693i	0.176516	−	0.305734i	−0.764169	−	0.645016i	$-0.776851\pi$
$787$	4.95189	−	8.57693i	0.176516	−	0.305734i	0.940685	+	0.339282i	$0.110184\pi$
$788$		0			0
$789$	26.3369	+	45.6169i	0.937619	+	1.62400i
$790$		0			0
$791$	17.1635	−	15.3840i	0.610262	−	0.546993i
$792$		0			0
$793$	14.7204	+	25.4965i	0.522736	+	0.905406i
$794$		0			0
$795$	−10.8098	+	18.7231i	−0.383384	+	0.664041i
$796$		0			0
$797$	7.09187			0.251207			0.125603	−	0.992081i	$-0.459913\pi$
$797$	7.09187			0.251207			0.125603	+	0.992081i	$0.459913\pi$
$798$		0			0
$799$	0.805312			0.0284899
$800$		0			0
$801$	−49.5310	+	85.7903i	−1.75009	+	3.03125i
$802$		0			0
$803$	−0.147832	−	0.256052i	−0.00521688	−	0.00903589i
$804$		0			0
$805$	−6.03099	−	28.6919i	−0.212564	−	1.01126i
$806$		0			0
$807$	35.4903	+	61.4710i	1.24932	+	2.16388i
$808$		0			0
$809$	−18.9346	+	32.7957i	−0.665706	+	1.15304i	0.313388	+	0.949625i	$0.398536\pi$
$809$	−18.9346	+	32.7957i	−0.665706	+	1.15304i	−0.979093	+	0.203411i	$0.934797\pi$
$810$		0			0
$811$	−27.2005			−0.955140			−0.477570	−	0.878594i	$-0.658482\pi$
$811$	−27.2005			−0.955140			−0.477570	+	0.878594i	$0.658482\pi$
$812$		0			0
$813$	−43.5607			−1.52774
$814$		0			0
$815$	0.297444	−	0.515187i	0.0104190	−	0.0180462i
$816$		0			0
$817$	36.4004	+	63.0474i	1.27349	+	2.20575i
$818$		0			0
$819$	63.4106	+	20.7617i	2.21575	+	0.725473i
$820$		0			0
$821$	−5.56651	−	9.64147i	−0.194272	−	0.336490i	0.752389	−	0.658719i	$-0.228901\pi$
$821$	−5.56651	−	9.64147i	−0.194272	−	0.336490i	−0.946662	+	0.322229i	$0.895568\pi$
$822$		0			0
$823$	23.2893	−	40.3383i	0.811815	−	1.40610i	−0.0997776	−	0.995010i	$-0.531813\pi$
$823$	23.2893	−	40.3383i	0.811815	−	1.40610i	0.911593	−	0.411095i	$-0.134854\pi$
$824$		0			0
$825$	0.272714			0.00949469
$826$		0			0
$827$	−22.1049			−0.768662			−0.384331	−	0.923195i	$-0.625568\pi$
$827$	−22.1049			−0.768662			−0.384331	+	0.923195i	$0.625568\pi$
$828$		0			0
$829$	0.0176775	−	0.0306183i	0.000613965	−	0.00106342i	−0.865718	−	0.500532i	$-0.833138\pi$
$829$	0.0176775	−	0.0306183i	0.000613965	−	0.00106342i	0.866332	+	0.499468i	$0.166471\pi$
$830$		0			0
$831$	20.6703	+	35.8019i	0.717043	+	1.24196i
$832$		0			0
$833$	−7.87090	−	5.77302i	−0.272711	−	0.200023i
$834$		0			0
$835$	25.1858	+	43.6231i	0.871592	+	1.50964i
$836$		0			0
$837$	−22.5154	+	38.9979i	−0.778247	+	1.34796i
$838$		0			0
$839$	19.0702			0.658375			0.329188	−	0.944265i	$-0.393225\pi$
$839$	19.0702			0.658375			0.329188	+	0.944265i	$0.393225\pi$
$840$		0			0
$841$	−22.7437			−0.784265
$842$		0			0
$843$	0.283802	−	0.491559i	0.00977464	−	0.0169302i
$844$		0			0
$845$	5.46845	+	9.47163i	0.188120	+	0.325834i
$846$		0			0
$847$	27.6071	+	9.03904i	0.948592	+	0.310585i
$848$		0			0
$849$	15.3158	+	26.5277i	0.525636	+	0.910428i
$850$		0			0
$851$	−21.0538	+	36.4663i	−0.721717	+	1.25005i
$852$		0			0
$853$	33.9594			1.16275			0.581373	−	0.813637i	$-0.302516\pi$
$853$	33.9594			1.16275			0.581373	+	0.813637i	$0.302516\pi$
$854$		0			0
$855$	−148.736			−5.08667
$856$		0			0
$857$	−4.15236	+	7.19210i	−0.141842	+	0.245678i	−0.928190	−	0.372106i	$-0.878636\pi$
$857$	−4.15236	+	7.19210i	−0.141842	+	0.245678i	0.786348	+	0.617783i	$0.211969\pi$
$858$		0			0
$859$	−23.6820	−	41.0185i	−0.808021	−	1.39953i	−0.914233	−	0.405190i	$-0.867206\pi$
$859$	−23.6820	−	41.0185i	−0.808021	−	1.39953i	0.106212	−	0.994344i	$-0.466128\pi$
$860$		0			0
$861$	1.86332	+	8.86458i	0.0635018	+	0.302104i
$862$		0			0
$863$	−3.41849	−	5.92099i	−0.116367	−	0.201553i	0.801959	−	0.597380i	$-0.203791\pi$
$863$	−3.41849	−	5.92099i	−0.116367	−	0.201553i	−0.918325	+	0.395827i	$0.870458\pi$
$864$		0			0
$865$	−1.86882	+	3.23690i	−0.0635419	+	0.110058i
$866$		0			0
$867$	51.5459			1.75059
$868$		0			0
$869$	−0.392373			−0.0133104
$870$		0			0
$871$	6.96250	−	12.0594i	0.235915	−	0.408617i
$872$		0			0
$873$	20.6404	+	35.7502i	0.698572	+	1.20996i
$874$		0			0
$875$	−20.6338	+	18.4946i	−0.697551	+	0.625233i
$876$		0			0
$877$	20.9968	+	36.3675i	0.709011	+	1.22804i	0.965225	+	0.261422i	$0.0841915\pi$
$877$	20.9968	+	36.3675i	0.709011	+	1.22804i	−0.256214	+	0.966620i	$0.582475\pi$
$878$		0			0
$879$	29.4468	−	51.0033i	0.993214	−	1.72030i
$880$		0			0
$881$	−26.1100			−0.879670			−0.439835	−	0.898079i	$-0.644963\pi$
$881$	−26.1100			−0.879670			−0.439835	+	0.898079i	$0.644963\pi$
$882$		0			0
$883$	−24.5630			−0.826611			−0.413305	−	0.910593i	$-0.635626\pi$
$883$	−24.5630			−0.826611			−0.413305	+	0.910593i	$0.635626\pi$
$884$		0			0
$885$	−20.2091	+	35.0032i	−0.679321	+	1.17662i
$886$		0			0
$887$	−24.0764	−	41.7015i	−0.808405	−	1.40020i	−0.913968	−	0.405786i	$-0.866998\pi$
$887$	−24.0764	−	41.7015i	−0.808405	−	1.40020i	0.105563	−	0.994413i	$-0.466336\pi$
$888$		0			0
$889$	−11.5712	+	10.3716i	−0.388086	+	0.347851i
$890$		0			0
$891$	2.92308	+	5.06292i	0.0979269	+	0.169614i
$892$		0			0
$893$	−2.08886	+	3.61802i	−0.0699011	+	0.121072i
$894$		0			0
$895$	−39.9514			−1.33543
$896$		0			0
$897$	−46.5353			−1.55377
$898$		0			0
$899$	2.87480	−	4.97930i	0.0958799	−	0.166069i
$900$		0			0
$901$	−1.86761	−	3.23480i	−0.0622193	−	0.107767i
$902$		0			0
$903$	−18.7520	−	89.2111i	−0.624028	−	2.96876i
$904$		0			0
$905$	−21.6592	−	37.5148i	−0.719976	−	1.24703i
$906$		0			0
$907$	−23.5037	+	40.7097i	−0.780429	+	1.35174i	0.151263	+	0.988494i	$0.451666\pi$
$907$	−23.5037	+	40.7097i	−0.780429	+	1.35174i	−0.931692	+	0.363249i	$0.881667\pi$
$908$		0			0
$909$	68.4822			2.27141
$910$		0			0
$911$	9.28031			0.307470			0.153735	−	0.988112i	$-0.450870\pi$
$911$	9.28031			0.307470			0.153735	+	0.988112i	$0.450870\pi$
$912$		0			0
$913$	0.613745	−	1.06304i	0.0203120	−	0.0351814i
$914$		0			0
$915$	41.0895	+	71.1692i	1.35838	+	2.35278i
$916$		0			0
$917$	−27.9595	−	9.15441i	−0.923303	−	0.302305i
$918$		0			0
$919$	−11.4610	−	19.8510i	−0.378063	−	0.654824i	0.612717	−	0.790302i	$-0.290076\pi$
$919$	−11.4610	−	19.8510i	−0.378063	−	0.654824i	−0.990780	+	0.135478i	$0.956743\pi$
$920$		0			0
$921$	56.8243	−	98.4226i	1.87242	−	3.24313i
$922$		0			0
$923$	31.2024			1.02704
$924$		0			0
$925$	−4.99240			−0.164149
$926$		0			0
$927$	67.0461	−	116.127i	2.20208	−	3.81412i
$928$		0			0
$929$	3.16962	+	5.48994i	0.103992	+	0.180119i	0.913326	−	0.407229i	$-0.133505\pi$
$929$	3.16962	+	5.48994i	0.103992	+	0.180119i	−0.809334	+	0.587349i	$0.800172\pi$
$930$		0			0
$931$	46.3524	−	20.3872i	1.51914	−	0.668162i
$932$		0			0
$933$	18.7095	+	32.4059i	0.612523	+	1.06092i
$934$		0			0
$935$	−0.234909	+	0.406875i	−0.00768235	+	0.0133062i
$936$		0			0
$937$	−37.6996			−1.23159			−0.615797	−	0.787905i	$-0.711166\pi$
$937$	−37.6996			−1.23159			−0.615797	+	0.787905i	$0.711166\pi$
$938$		0			0
$939$	36.2271			1.18223
$940$		0			0
$941$	−2.29145	+	3.96890i	−0.0746990	+	0.129382i	−0.900955	−	0.433912i	$-0.857133\pi$
$941$	−2.29145	+	3.96890i	−0.0746990	+	0.129382i	0.826256	+	0.563294i	$0.190466\pi$
$942$		0			0
$943$	−2.35037	−	4.07095i	−0.0765385	−	0.132568i
$944$		0			0
$945$	116.118	+	38.0192i	3.77733	+	1.23676i
$946$		0			0
$947$	14.9494	+	25.8931i	0.485791	+	0.841414i	0.999867	−	0.0163305i	$-0.00519840\pi$
$947$	14.9494	+	25.8931i	0.485791	+	0.841414i	−0.514076	+	0.857745i	$0.671865\pi$
$948$		0			0
$949$	−2.99082	+	5.18026i	−0.0970862	+	0.168158i
$950$		0			0
$951$	105.980			3.43664
$952$		0			0
$953$	14.5225			0.470429			0.235214	−	0.971944i	$-0.424421\pi$
$953$	14.5225			0.470429			0.235214	+	0.971944i	$0.424421\pi$
$954$		0			0
$955$	30.1065	−	52.1461i	0.974225	−	1.68741i
$956$		0			0
$957$	−0.611961	−	1.05995i	−0.0197819	−	0.0342632i
$958$		0			0
$959$	6.37396	+	30.3235i	0.205826	+	0.979198i
$960$		0			0
$961$	12.8580	+	22.2708i	0.414776	+	0.718412i
$962$		0			0
$963$	−77.9821	+	135.069i	−2.51294	+	4.35253i
$964$		0			0
$965$	−9.44006			−0.303886
$966$		0			0
$967$	−11.0380			−0.354957			−0.177479	−	0.984125i	$-0.556794\pi$
$967$	−11.0380			−0.354957			−0.177479	+	0.984125i	$0.556794\pi$
$968$		0			0
$969$	17.2681	−	29.9092i	0.554730	−	0.960821i
$970$		0			0
$971$	15.3878	+	26.6524i	0.493817	+	0.855315i	0.999975	−	0.00712542i	$-0.00226811\pi$
$971$	15.3878	+	26.6524i	0.493817	+	0.855315i	−0.506158	+	0.862441i	$0.668935\pi$
$972$		0			0
$973$	12.0490	−	10.7998i	0.386272	−	0.346225i
$974$		0			0
$975$	−2.75867	−	4.77816i	−0.0883482	−	0.153024i
$976$		0			0
$977$	15.6593	−	27.1227i	0.500985	−	0.867731i	−0.499015	−	0.866594i	$-0.666305\pi$
$977$	15.6593	−	27.1227i	0.500985	−	0.867731i	0.999999	−	0.00113757i	$-0.000362099\pi$
$978$		0			0
$979$	−1.62329			−0.0518807
$980$		0			0
$981$	110.877			3.54003
$982$		0			0
$983$	1.13666	−	1.96875i	0.0362538	−	0.0627934i	−0.847329	−	0.531068i	$-0.821791\pi$
$983$	1.13666	−	1.96875i	0.0362538	−	0.0627934i	0.883583	+	0.468275i	$0.155124\pi$
$984$		0			0
$985$	−14.2480	−	24.6783i	−0.453980	−	0.786316i
$986$		0			0
$987$	3.89551	−	3.49165i	0.123996	−	0.111140i
$988$		0			0
$989$	23.6535	+	40.9691i	0.752139	+	1.30274i
$990$		0			0
$991$	0.580270	−	1.00506i	0.0184329	−	0.0319267i	−0.856662	−	0.515878i	$-0.827466\pi$
$991$	0.580270	−	1.00506i	0.0184329	−	0.0319267i	0.875095	+	0.483952i	$0.160799\pi$
$992$		0			0
$993$	86.5724			2.74729
$994$		0			0
$995$	−46.1542			−1.46319
$996$		0			0
$997$	−0.765810	+	1.32642i	−0.0242534	+	0.0420082i	−0.877897	−	0.478849i	$-0.841054\pi$
$997$	−0.765810	+	1.32642i	−0.0242534	+	0.0420082i	0.853644	+	0.520857i	$0.174388\pi$
$998$		0			0
$999$	−87.7401	−	151.970i	−2.77597	−	4.80813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.165.15	✓	30
7.2	even	3	inner	1148.2.i.e.821.15	yes	30
7.3	odd	6		8036.2.a.r.1.15		15
7.4	even	3		8036.2.a.q.1.1		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.15	✓	30	1.1	even	1	trivial
1148.2.i.e.821.15	yes	30	7.2	even	3	inner
8036.2.a.q.1.1		15	7.4	even	3
8036.2.a.r.1.15		15	7.3	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71186 - 2.96502i) q^{3} +(-1.17870 - 2.04157i) q^{5} +(1.97017 - 1.76591i) q^{7} +(-4.36091 - 7.55332i) q^{9} +O(q^{10})\)	\(q+(1.71186 - 2.96502i) q^{3} +(-1.17870 - 2.04157i) q^{5} +(1.97017 - 1.76591i) q^{7} +(-4.36091 - 7.55332i) q^{9} +(0.0714606 - 0.123773i) q^{11} -2.89147 q^{13} -8.07106 q^{15} +(0.697221 - 1.20762i) q^{17} +(3.61698 + 6.26479i) q^{19} +(-1.86332 - 8.86458i) q^{21} +(2.35037 + 4.07095i) q^{23} +(-0.278666 + 0.482663i) q^{25} -19.5899 q^{27} +2.50126 q^{29} +(1.14934 - 1.99071i) q^{31} +(-0.244661 - 0.423765i) q^{33} +(-5.92746 - 1.94075i) q^{35} +(4.47884 + 7.75758i) q^{37} +(-4.94979 + 8.57328i) q^{39} -1.00000 q^{41} +10.0638 q^{43} +(-10.2804 + 17.8062i) q^{45} +(0.288758 + 0.500143i) q^{47} +(0.763121 - 6.95828i) q^{49} +(-2.38708 - 4.13455i) q^{51} +(1.33933 - 2.31978i) q^{53} -0.336922 q^{55} +24.7670 q^{57} +(2.50389 - 4.33687i) q^{59} +(-5.09097 - 8.81782i) q^{61} +(-21.9302 - 7.18033i) q^{63} +(3.40818 + 5.90313i) q^{65} +(-2.40794 + 4.17068i) q^{67} +16.0940 q^{69} -10.7912 q^{71} +(1.03436 - 1.79156i) q^{73} +(0.954072 + 1.65250i) q^{75} +(-0.0777834 - 0.370047i) q^{77} +(-1.37269 - 2.37757i) q^{79} +(-20.4524 + 35.4246i) q^{81} +8.58858 q^{83} -3.28725 q^{85} +(4.28181 - 7.41631i) q^{87} +(-5.67898 - 9.83628i) q^{89} +(-5.69668 + 5.10608i) q^{91} +(-3.93501 - 6.81563i) q^{93} +(8.52667 - 14.7686i) q^{95} -4.73305 q^{97} -1.24653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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