LMFDB - Embedded newform 1148.2.ba.a.113.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.16
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +O(q^{10})$	\(q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +(5.31657 + 1.72746i) q^{11} +(-2.00873 + 2.76478i) q^{13} +(-2.23990 + 0.727787i) q^{15} +(3.76112 + 1.22206i) q^{17} +(1.02272 + 1.40766i) q^{19} +(1.78384 - 1.29604i) q^{21} +(-3.68573 - 2.67784i) q^{23} +(3.12208 - 2.26832i) q^{25} +2.50966i q^{27} +(-7.36619 + 2.39342i) q^{29} +(-0.928450 + 2.85747i) q^{31} +(-3.80896 + 11.7228i) q^{33} +(0.627829 - 0.864133i) q^{35} +(1.05950 + 3.26080i) q^{37} +(-6.09621 - 4.42916i) q^{39} +(-5.26380 + 3.64587i) q^{41} +(4.90364 + 3.56270i) q^{43} +(-0.614526 - 1.89132i) q^{45} +(6.27597 - 8.63813i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.69458 + 8.29308i) q^{51} +(11.9239 - 3.87430i) q^{53} +5.97102i q^{55} +(-3.10382 + 2.25506i) q^{57} +(-7.16482 - 5.20554i) q^{59} +(-2.86047 + 2.07825i) q^{61} +(1.09434 + 1.50623i) q^{63} +(-3.47162 - 1.12800i) q^{65} +(-12.6075 + 4.09644i) q^{67} +(5.90450 - 8.12684i) q^{69} +(-13.7395 - 4.46425i) q^{71} -10.9081 q^{73} +(5.00155 + 6.88404i) q^{75} +(-1.72746 - 5.31657i) q^{77} -12.4283i q^{79} -11.1191 q^{81} -4.53262 q^{83} +4.22409i q^{85} +(-5.27738 - 16.2421i) q^{87} +(9.01885 + 12.4134i) q^{89} +3.41746 q^{91} +(-6.30059 - 2.04719i) q^{93} +(-1.09240 + 1.50356i) q^{95} +(15.9484 - 5.18194i) q^{97} +(-9.89844 - 3.21620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$			2.20495i			1.27303i	0.771265	+	0.636515i	$0.219624\pi$
$3$			2.20495i			1.27303i	−0.771265	+	0.636515i	$0.780376\pi$
$4$		0			0
$5$	0.330069	+	1.01585i	0.147612	+	0.454302i	0.997338	−	0.0729229i	$-0.0232327\pi$
$5$	0.330069	+	1.01585i	0.147612	+	0.454302i	−0.849726	+	0.527224i	$0.823233\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	−1.86181			−0.620603
$10$		0			0
$11$	5.31657	+	1.72746i	1.60301	+	0.520849i	0.967849	−	0.251533i	$-0.0809346\pi$
$11$	5.31657	+	1.72746i	1.60301	+	0.520849i	0.635159	+	0.772382i	$0.280935\pi$
$12$		0			0
$13$	−2.00873	+	2.76478i	−0.557122	+	0.766813i	−0.990957	−	0.134180i	$-0.957160\pi$
$13$	−2.00873	+	2.76478i	−0.557122	+	0.766813i	0.433835	+	0.900992i	$0.357160\pi$
$14$		0			0
$15$	−2.23990	+	0.727787i	−0.578339	+	0.187914i
$16$		0			0
$17$	3.76112	+	1.22206i	0.912205	+	0.296393i	0.727265	−	0.686357i	$-0.240791\pi$
$17$	3.76112	+	1.22206i	0.912205	+	0.296393i	0.184940	+	0.982750i	$0.440791\pi$
$18$		0			0
$19$	1.02272	+	1.40766i	0.234629	+	0.322939i	0.910054	−	0.414489i	$-0.136040\pi$
$19$	1.02272	+	1.40766i	0.234629	+	0.322939i	−0.675425	+	0.737429i	$0.736040\pi$
$20$		0			0
$21$	1.78384	−	1.29604i	0.389266	−	0.282819i
$22$		0			0
$23$	−3.68573	−	2.67784i	−0.768527	−	0.558368i	0.132987	−	0.991118i	$-0.457543\pi$
$23$	−3.68573	−	2.67784i	−0.768527	−	0.558368i	−0.901514	+	0.432750i	$0.857543\pi$
$24$		0			0
$25$	3.12208	−	2.26832i	0.624416	−	0.453665i
$26$		0			0
$27$			2.50966i			0.482984i
$28$		0			0
$29$	−7.36619	+	2.39342i	−1.36787	+	0.444447i	−0.898662	−	0.438642i	$-0.855460\pi$
$29$	−7.36619	+	2.39342i	−1.36787	+	0.444447i	−0.469206	+	0.883089i	$0.655460\pi$
$30$		0			0
$31$	−0.928450	+	2.85747i	−0.166754	+	0.513218i	−0.999161	−	0.0409475i	$-0.986962\pi$
$31$	−0.928450	+	2.85747i	−0.166754	+	0.513218i	0.832407	+	0.554165i	$0.186962\pi$
$32$		0			0
$33$	−3.80896	+	11.7228i	−0.663056	+	2.04068i
$34$		0			0
$35$	0.627829	−	0.864133i	0.106123	−	0.146065i
$36$		0			0
$37$	1.05950	+	3.26080i	0.174181	+	0.536073i	0.999595	−	0.0284545i	$-0.00905856\pi$
$37$	1.05950	+	3.26080i	0.174181	+	0.536073i	−0.825415	+	0.564527i	$0.809059\pi$
$38$		0			0
$39$	−6.09621	−	4.42916i	−0.976175	−	0.709233i
$40$		0			0
$41$	−5.26380	+	3.64587i	−0.822068	+	0.569390i
$41$	−5.26380	+	3.64587i	−0.822068	+	0.569390i
$42$		0			0
$43$	4.90364	+	3.56270i	0.747798	+	0.543307i	0.895143	−	0.445778i	$-0.147073\pi$
$43$	4.90364	+	3.56270i	0.747798	+	0.543307i	−0.147346	+	0.989085i	$0.547073\pi$
$44$		0			0
$45$	−0.614526	−	1.89132i	−0.0916081	−	0.281941i
$46$		0			0
$47$	6.27597	−	8.63813i	0.915444	−	1.26000i	−0.0498296	−	0.998758i	$-0.515868\pi$
$47$	6.27597	−	8.63813i	0.915444	−	1.26000i	0.965273	−	0.261242i	$-0.0841322\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−2.69458	+	8.29308i	−0.377317	+	1.16126i
$52$		0			0
$53$	11.9239	−	3.87430i	1.63787	−	0.532176i	0.661808	−	0.749673i	$-0.269789\pi$
$53$	11.9239	−	3.87430i	1.63787	−	0.532176i	0.976061	+	0.217497i	$0.0697893\pi$
$54$		0			0
$55$			5.97102i			0.805132i
$56$		0			0
$57$	−3.10382	+	2.25506i	−0.411111	+	0.298690i
$58$		0			0
$59$	−7.16482	−	5.20554i	−0.932779	−	0.677704i	0.0138923	−	0.999903i	$-0.495578\pi$
$59$	−7.16482	−	5.20554i	−0.932779	−	0.677704i	−0.946672	+	0.322200i	$0.895578\pi$
$60$		0			0
$61$	−2.86047	+	2.07825i	−0.366246	+	0.266093i	−0.755652	−	0.654973i	$-0.772680\pi$
$61$	−2.86047	+	2.07825i	−0.366246	+	0.266093i	0.389407	+	0.921066i	$0.372680\pi$
$62$		0			0
$63$	1.09434	+	1.50623i	0.137874	+	0.189768i
$64$		0			0
$65$	−3.47162	−	1.12800i	−0.430602	−	0.139911i
$66$		0			0
$67$	−12.6075	+	4.09644i	−1.54026	+	0.500460i	−0.951447	−	0.307812i	$-0.900403\pi$
$67$	−12.6075	+	4.09644i	−1.54026	+	0.500460i	−0.588809	+	0.808272i	$0.700403\pi$
$68$		0			0
$69$	5.90450	−	8.12684i	0.710818	−	0.978357i
$70$		0			0
$71$	−13.7395	−	4.46425i	−1.63058	−	0.529809i	−0.656178	−	0.754606i	$-0.727828\pi$
$71$	−13.7395	−	4.46425i	−1.63058	−	0.529809i	−0.974405	+	0.224798i	$0.927828\pi$
$72$		0			0
$73$	−10.9081			−1.27670			−0.638350	−	0.769746i	$-0.720383\pi$
$73$	−10.9081			−1.27670			−0.638350	+	0.769746i	$0.720383\pi$
$74$		0			0
$75$	5.00155	+	6.88404i	0.577529	+	0.794900i
$76$		0			0
$77$	−1.72746	−	5.31657i	−0.196862	−	0.605880i
$78$		0			0
$79$		−	12.4283i		−	1.39829i	−0.714979	−	0.699146i	$-0.753564\pi$
$79$		−	12.4283i		−	1.39829i	0.714979	−	0.699146i	$-0.246436\pi$
$80$		0			0
$81$	−11.1191			−1.23545
$82$		0			0
$83$	−4.53262			−0.497520			−0.248760	−	0.968565i	$-0.580023\pi$
$83$	−4.53262			−0.497520			−0.248760	+	0.968565i	$0.580023\pi$
$84$		0			0
$85$			4.22409i			0.458167i
$86$		0			0
$87$	−5.27738	−	16.2421i	−0.565794	−	1.74134i
$88$		0			0
$89$	9.01885	+	12.4134i	0.955997	+	1.31582i	0.948812	+	0.315842i	$0.102287\pi$
$89$	9.01885	+	12.4134i	0.955997	+	1.31582i	0.00718475	+	0.999974i	$0.497713\pi$
$90$		0			0
$91$	3.41746			0.358247
$92$		0			0
$93$	−6.30059	−	2.04719i	−0.653341	−	0.212283i
$94$		0			0
$95$	−1.09240	+	1.50356i	−0.112078	+	0.154262i
$96$		0			0
$97$	15.9484	−	5.18194i	1.61931	−	0.526147i	0.647533	−	0.762037i	$-0.275801\pi$
$97$	15.9484	−	5.18194i	1.61931	−	0.526147i	0.971780	+	0.235890i	$0.0758006\pi$
$98$		0			0
$99$	−9.89844	−	3.21620i	−0.994831	−	0.323240i
$100$		0			0
$101$	8.39981	+	11.5613i	0.835812	+	1.15040i	0.986813	+	0.161863i	$0.0517502\pi$
$101$	8.39981	+	11.5613i	0.835812	+	1.15040i	−0.151001	+	0.988534i	$0.548250\pi$
$102$		0			0
$103$	−8.14596	+	5.91839i	−0.802645	+	0.583156i	−0.911689	−	0.410881i	$-0.865221\pi$
$103$	−8.14596	+	5.91839i	−0.802645	+	0.583156i	0.109044	+	0.994037i	$0.465221\pi$
$104$		0			0
$105$	1.90537	+	1.38433i	0.185945	+	0.135097i
$106$		0			0
$107$	14.7104	−	10.6878i	1.42211	−	1.03322i	0.430692	−	0.902499i	$-0.358269\pi$
$107$	14.7104	−	10.6878i	1.42211	−	1.03322i	0.991419	−	0.130725i	$-0.0417306\pi$
$108$		0			0
$109$			5.37498i			0.514829i	0.966301	+	0.257415i	$0.0828706\pi$
$109$			5.37498i			0.514829i	−0.966301	+	0.257415i	$0.917129\pi$
$110$		0			0
$111$	−7.18991	+	2.33614i	−0.682436	+	0.221737i
$112$		0			0
$113$	−2.76907	+	8.52231i	−0.260492	+	0.801712i	0.732206	+	0.681083i	$0.238491\pi$
$113$	−2.76907	+	8.52231i	−0.260492	+	0.801712i	−0.992698	+	0.120628i	$0.961509\pi$
$114$		0			0
$115$	1.50373	−	4.62801i	0.140224	−	0.431564i
$116$		0			0
$117$	3.73988	−	5.14750i	0.345752	−	0.475886i
$118$		0			0
$119$	−1.22206	−	3.76112i	−0.112026	−	0.344781i
$120$		0			0
$121$	16.3827	+	11.9027i	1.48933	+	1.08206i
$122$		0			0
$123$	−8.03897	−	11.6064i	−0.724850	−	1.04652i
$124$		0			0
$125$	7.65544	+	5.56201i	0.684724	+	0.497481i
$126$		0			0
$127$	−4.21449	−	12.9709i	−0.373976	−	1.15098i	−0.944167	−	0.329467i	$-0.893131\pi$
$127$	−4.21449	−	12.9709i	−0.373976	−	1.15098i	0.570191	−	0.821512i	$-0.306869\pi$
$128$		0			0
$129$	−7.85558	+	10.8123i	−0.691645	+	0.951968i
$130$		0			0
$131$	−4.26107	+	13.1142i	−0.372291	+	1.14579i	0.572997	+	0.819558i	$0.305781\pi$
$131$	−4.26107	+	13.1142i	−0.372291	+	1.14579i	−0.945288	+	0.326237i	$0.894219\pi$
$132$		0			0
$133$	0.537678	−	1.65480i	0.0466226	−	0.143490i
$134$		0			0
$135$	−2.54943	+	0.828361i	−0.219420	+	0.0712939i
$136$		0			0
$137$		−	21.4026i		−	1.82855i	−0.405096	−	0.914274i	$-0.632762\pi$
$137$		−	21.4026i		−	1.82855i	0.405096	−	0.914274i	$-0.367238\pi$
$138$		0			0
$139$	14.8585	−	10.7953i	1.26028	−	0.915646i	0.261507	−	0.965201i	$-0.415780\pi$
$139$	14.8585	−	10.7953i	1.26028	−	0.915646i	0.998771	+	0.0495552i	$0.0157804\pi$
$140$		0			0
$141$	19.0466	+	13.8382i	1.60402	+	1.16539i
$142$		0			0
$143$	−15.4556	+	11.2292i	−1.29246	+	0.939030i
$144$		0			0
$145$	−4.86271	−	6.69295i	−0.403826	−	0.555819i
$146$		0			0
$147$	−2.09703	−	0.681367i	−0.172960	−	0.0561982i
$148$		0			0
$149$	−4.57343	+	1.48600i	−0.374670	+	0.121738i	−0.490298	−	0.871555i	$-0.663112\pi$
$149$	−4.57343	+	1.48600i	−0.374670	+	0.121738i	0.115628	+	0.993293i	$0.463112\pi$
$150$		0			0
$151$	6.53809	−	8.99891i	0.532062	−	0.732321i	−0.455381	−	0.890297i	$-0.650497\pi$
$151$	6.53809	−	8.99891i	0.532062	−	0.732321i	0.987443	+	0.157976i	$0.0504969\pi$
$152$		0			0
$153$	−7.00248	−	2.27524i	−0.566117	−	0.183943i
$154$		0			0
$155$	−3.20922			−0.257770
$156$		0			0
$157$	3.84359	+	5.29024i	0.306752	+	0.422207i	0.934365	−	0.356318i	$-0.115968\pi$
$157$	3.84359	+	5.29024i	0.306752	+	0.422207i	−0.627613	+	0.778525i	$0.715968\pi$
$158$		0			0
$159$	8.54264	+	26.2915i	0.677475	+	2.08505i
$160$		0			0
$161$			4.55581i			0.359048i
$162$		0			0
$163$	24.6077			1.92743			0.963713	−	0.266940i	$-0.0860124\pi$
$163$	24.6077			1.92743			0.963713	+	0.266940i	$0.0860124\pi$
$164$		0			0
$165$	−13.1658			−1.02496
$166$		0			0
$167$			8.59827i			0.665354i	0.943041	+	0.332677i	$0.107952\pi$
$167$			8.59827i			0.665354i	−0.943041	+	0.332677i	$0.892048\pi$
$168$		0			0
$169$	0.408202	+	1.25632i	0.0314001	+	0.0966396i
$170$		0			0
$171$	−1.90412	−	2.62079i	−0.145611	−	0.200417i
$172$		0			0
$173$	9.08318			0.690581			0.345291	−	0.938496i	$-0.387780\pi$
$173$	9.08318			0.690581			0.345291	+	0.938496i	$0.387780\pi$
$174$		0			0
$175$	−3.67023	−	1.19253i	−0.277443	−	0.0901467i
$176$		0			0
$177$	11.4780	−	15.7981i	0.862737	−	1.18746i
$178$		0			0
$179$	−13.4649	+	4.37502i	−1.00642	+	0.327004i	−0.765426	−	0.643523i	$-0.777472\pi$
$179$	−13.4649	+	4.37502i	−1.00642	+	0.327004i	−0.240989	+	0.970528i	$0.577472\pi$
$180$		0			0
$181$	1.33116	+	0.432519i	0.0989440	+	0.0321488i	0.358071	−	0.933695i	$-0.383435\pi$
$181$	1.33116	+	0.432519i	0.0989440	+	0.0321488i	−0.259127	+	0.965843i	$0.583435\pi$
$182$		0			0
$183$	−4.58244	−	6.30719i	−0.338744	−	0.466241i
$184$		0			0
$185$	−2.96278	+	2.15258i	−0.217828	+	0.158261i
$186$		0			0
$187$	17.8852	+	12.9944i	1.30789	+	0.950241i
$188$		0			0
$189$	2.03035	−	1.47514i	0.147687	−	0.107301i
$190$		0			0
$191$			9.92297i			0.718001i	0.933337	+	0.359000i	$0.116882\pi$
$191$			9.92297i			0.718001i	−0.933337	+	0.359000i	$0.883118\pi$
$192$		0			0
$193$	24.2100	−	7.86629i	1.74267	−	0.566228i	0.747489	−	0.664274i	$-0.231259\pi$
$193$	24.2100	−	7.86629i	1.74267	−	0.566228i	0.995182	+	0.0980465i	$0.0312594\pi$
$194$		0			0
$195$	2.48718	−	7.65476i	0.178111	−	0.548169i
$196$		0			0
$197$	−4.95627	+	15.2538i	−0.353119	+	1.08679i	0.603973	+	0.797005i	$0.293584\pi$
$197$	−4.95627	+	15.2538i	−0.353119	+	1.08679i	−0.957092	+	0.289784i	$0.906416\pi$
$198$		0			0
$199$	11.1025	−	15.2812i	0.787032	−	1.08326i	−0.207439	−	0.978248i	$-0.566513\pi$
$199$	11.1025	−	15.2812i	0.787032	−	1.08326i	0.994471	−	0.105009i	$-0.0334870\pi$
$200$		0			0
$201$	−9.03245	−	27.7990i	−0.637100	−	1.96079i
$202$		0			0
$203$	6.26606	+	4.55256i	0.439791	+	0.319527i
$204$		0			0
$205$	−5.44108	−	4.14384i	−0.380021	−	0.289418i
$206$		0			0
$207$	6.86212	+	4.98562i	0.476950	+	0.346524i
$208$		0			0
$209$	3.00572	+	9.25064i	0.207910	+	0.639880i
$210$		0			0
$211$	4.55354	−	6.26741i	0.313478	−	0.431466i	−0.622984	−	0.782235i	$-0.714080\pi$
$211$	4.55354	−	6.26741i	0.313478	−	0.431466i	0.936462	+	0.350769i	$0.114080\pi$
$212$		0			0
$213$	9.84345	−	30.2950i	0.674462	−	2.07578i
$214$		0			0
$215$	−2.00063	+	6.15729i	−0.136442	+	0.419924i
$216$		0			0
$217$	2.85747	−	0.928450i	0.193978	−	0.0630273i
$218$		0			0
$219$		−	24.0519i		−	1.62528i
$220$		0			0
$221$	−10.9338	+	7.94388i	−0.735488	+	0.534363i
$222$		0			0
$223$	−0.503414	−	0.365751i	−0.0337111	−	0.0244925i	0.570802	−	0.821088i	$-0.306632\pi$
$223$	−0.503414	−	0.365751i	−0.0337111	−	0.0244925i	−0.604513	+	0.796595i	$0.706632\pi$
$224$		0			0
$225$	−5.81272	+	4.22319i	−0.387515	+	0.281546i
$226$		0			0
$227$	0.914233	+	1.25833i	0.0606798	+	0.0835185i	0.838278	−	0.545242i	$-0.183562\pi$
$227$	0.914233	+	1.25833i	0.0606798	+	0.0835185i	−0.777599	+	0.628761i	$0.783562\pi$
$228$		0			0
$229$	−5.43963	−	1.76744i	−0.359461	−	0.116796i	0.123718	−	0.992317i	$-0.460518\pi$
$229$	−5.43963	−	1.76744i	−0.359461	−	0.116796i	−0.483179	+	0.875521i	$0.660518\pi$
$230$		0			0
$231$	11.7228	−	3.80896i	0.771303	−	0.250611i
$232$		0			0
$233$	1.87218	−	2.57683i	0.122650	−	0.168814i	−0.743277	−	0.668984i	$-0.766729\pi$
$233$	1.87218	−	2.57683i	0.122650	−	0.168814i	0.865927	+	0.500171i	$0.166729\pi$
$234$		0			0
$235$	10.8465	+	3.52425i	0.707550	+	0.229897i
$236$		0			0
$237$	27.4038			1.78007
$238$		0			0
$239$	−4.74546	−	6.53157i	−0.306959	−	0.422492i	0.627471	−	0.778640i	$-0.284090\pi$
$239$	−4.74546	−	6.53157i	−0.306959	−	0.422492i	−0.934430	+	0.356148i	$0.884090\pi$
$240$		0			0
$241$	−0.916839	−	2.82174i	−0.0590588	−	0.181764i	0.917175	−	0.398485i	$-0.130464\pi$
$241$	−0.916839	−	2.82174i	−0.0590588	−	0.181764i	−0.976234	+	0.216721i	$0.930464\pi$
$242$		0			0
$243$		−	16.9881i		−	1.08979i
$244$		0			0
$245$	−1.06813			−0.0682401
$246$		0			0
$247$	−5.94625			−0.378351
$248$		0			0
$249$		−	9.99420i		−	0.633357i
$250$		0			0
$251$	−0.791662	−	2.43649i	−0.0499693	−	0.153790i	0.922958	−	0.384900i	$-0.125764\pi$
$251$	−0.791662	−	2.43649i	−0.0499693	−	0.153790i	−0.972928	+	0.231111i	$0.925764\pi$
$252$		0			0
$253$	−14.9696	−	20.6039i	−0.941130	−	1.29535i
$254$		0			0
$255$	−9.31391			−0.583260
$256$		0			0
$257$	18.4365	+	5.99037i	1.15004	+	0.373669i	0.821156	−	0.570703i	$-0.193329\pi$
$257$	18.4365	+	5.99037i	1.15004	+	0.373669i	0.328879	+	0.944372i	$0.393329\pi$
$258$		0			0
$259$	2.01529	−	2.77380i	0.125224	−	0.172356i
$260$		0			0
$261$	13.7144	−	4.45609i	0.848903	−	0.275825i
$262$		0			0
$263$	6.91625	+	2.24722i	0.426474	+	0.138570i	0.514387	−	0.857558i	$-0.328020\pi$
$263$	6.91625	+	2.24722i	0.426474	+	0.138570i	−0.0879126	+	0.996128i	$0.528020\pi$
$264$		0			0
$265$	7.87141	+	10.8341i	0.483537	+	0.665531i
$266$		0			0
$267$	−27.3709	+	19.8861i	−1.67507	+	1.21701i
$268$		0			0
$269$	−6.56637	−	4.77074i	−0.400358	−	0.290877i	0.369329	−	0.929299i	$-0.379588\pi$
$269$	−6.56637	−	4.77074i	−0.400358	−	0.290877i	−0.769687	+	0.638421i	$0.779588\pi$
$270$		0			0
$271$	10.4038	−	7.55881i	0.631986	−	0.459165i	−0.225101	−	0.974335i	$-0.572271\pi$
$271$	10.4038	−	7.55881i	0.631986	−	0.459165i	0.857088	+	0.515170i	$0.172271\pi$
$272$		0			0
$273$			7.53533i			0.456059i
$274$		0			0
$275$	20.5172	−	6.66645i	1.23723	−	0.402002i
$276$		0			0
$277$	2.11028	−	6.49478i	0.126795	−	0.390234i	−0.867429	−	0.497561i	$-0.834229\pi$
$277$	2.11028	−	6.49478i	0.126795	−	0.390234i	0.994224	+	0.107327i	$0.0342292\pi$
$278$		0			0
$279$	1.72860	−	5.32007i	0.103488	−	0.318504i
$280$		0			0
$281$	−9.04328	+	12.4470i	−0.539477	+	0.742526i	−0.988538	−	0.150975i	$-0.951759\pi$
$281$	−9.04328	+	12.4470i	−0.539477	+	0.742526i	0.449061	+	0.893501i	$0.351759\pi$
$282$		0			0
$283$	−4.44165	−	13.6700i	−0.264029	−	0.812598i	−0.991916	−	0.126900i	$-0.959497\pi$
$283$	−4.44165	−	13.6700i	−0.264029	−	0.812598i	0.727887	−	0.685698i	$-0.240503\pi$
$284$		0			0
$285$	−3.31527	−	2.40869i	−0.196380	−	0.142678i
$286$		0			0
$287$	6.04356	+	2.11552i	0.356740	+	0.124875i
$288$		0			0
$289$	−1.10073	−	0.799726i	−0.0647487	−	0.0470427i
$290$		0			0
$291$	11.4259	+	35.1654i	0.669800	+	2.06143i
$292$		0			0
$293$	12.1292	−	16.6944i	0.708593	−	0.975295i	−0.291233	−	0.956652i	$-0.594065\pi$
$293$	12.1292	−	16.6944i	0.708593	−	0.975295i	0.999826	−	0.0186429i	$-0.00593457\pi$
$294$		0			0
$295$	2.92316	−	8.99656i	0.170193	−	0.523800i
$296$		0			0
$297$	−4.33533	+	13.3428i	−0.251561	+	0.774226i
$298$		0			0
$299$	14.8073	−	4.81117i	0.856327	−	0.278237i
$300$		0			0
$301$		−	6.06123i		−	0.349363i
$302$		0			0
$303$	−25.4922	+	18.5212i	−1.46449	+	1.06401i
$304$		0			0
$305$	−3.05534	−	2.21984i	−0.174948	−	0.127108i
$306$		0			0
$307$	3.82298	−	2.77756i	0.218189	−	0.158524i	−0.473322	−	0.880889i	$-0.656945\pi$
$307$	3.82298	−	2.77756i	0.218189	−	0.158524i	0.691511	+	0.722366i	$0.256945\pi$
$308$		0			0
$309$	−13.0498	−	17.9614i	−0.742374	−	1.02179i
$310$		0			0
$311$	1.54491	+	0.501971i	0.0876037	+	0.0284642i	0.352491	−	0.935815i	$-0.385335\pi$
$311$	1.54491	+	0.501971i	0.0876037	+	0.0284642i	−0.264887	+	0.964279i	$0.585335\pi$
$312$		0			0
$313$	−12.0227	+	3.90641i	−0.679562	+	0.220803i	−0.628404	−	0.777887i	$-0.716291\pi$
$313$	−12.0227	+	3.90641i	−0.679562	+	0.220803i	−0.0511584	+	0.998691i	$0.516291\pi$
$314$		0			0
$315$	−1.16890	+	1.60885i	−0.0658599	+	0.0906484i
$316$		0			0
$317$	2.83338	+	0.920620i	0.159138	+	0.0517072i	0.387503	−	0.921869i	$-0.373338\pi$
$317$	2.83338	+	0.920620i	0.159138	+	0.0517072i	−0.228364	+	0.973576i	$0.573338\pi$
$318$		0			0
$319$	−43.2975			−2.42419
$320$		0			0
$321$	23.5660	+	32.4358i	1.31532	+	1.81039i
$322$		0			0
$323$	2.12634	+	6.54420i	0.118313	+	0.364129i
$324$		0			0
$325$			13.1883i			0.731557i
$326$		0			0
$327$	−11.8516			−0.655393
$328$		0			0
$329$	−10.6773			−0.588659
$330$		0			0
$331$		−	8.86236i		−	0.487119i	−0.969886	−	0.243560i	$-0.921685\pi$
$331$		−	8.86236i		−	0.487119i	0.969886	−	0.243560i	$-0.0783152\pi$
$332$		0			0
$333$	−1.97258	−	6.07099i	−0.108097	−	0.332688i
$334$		0			0
$335$	−8.32273	−	11.4553i	−0.454719	−	0.625867i
$336$		0			0
$337$	8.39537			0.457325			0.228662	−	0.973506i	$-0.426565\pi$
$337$	8.39537			0.457325			0.228662	+	0.973506i	$0.426565\pi$
$338$		0			0
$339$	−18.7913	−	6.10566i	−1.02060	−	0.331614i
$340$		0			0
$341$	−9.87234	+	13.5881i	−0.534617	+	0.735838i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	10.2045	+	3.31566i	0.549394	+	0.178509i
$346$		0			0
$347$	−12.5449	−	17.2665i	−0.673443	−	0.926915i	0.326389	−	0.945236i	$-0.394168\pi$
$347$	−12.5449	−	17.2665i	−0.673443	−	0.926915i	−0.999832	+	0.0183206i	$0.994168\pi$
$348$		0			0
$349$	9.08784	−	6.60270i	0.486461	−	0.353434i	−0.317361	−	0.948305i	$-0.602797\pi$
$349$	9.08784	−	6.60270i	0.486461	−	0.353434i	0.803822	+	0.594870i	$0.202797\pi$
$350$		0			0
$351$	−6.93865	−	5.04123i	−0.370358	−	0.269081i
$352$		0			0
$353$	12.7785	−	9.28410i	0.680129	−	0.494143i	−0.193271	−	0.981145i	$-0.561910\pi$
$353$	12.7785	−	9.28410i	0.680129	−	0.494143i	0.873401	+	0.487003i	$0.161910\pi$
$354$		0			0
$355$		−	15.4308i		−	0.818982i
$356$		0			0
$357$	8.29308	−	2.69458i	0.438916	−	0.142612i
$358$		0			0
$359$	−6.15607	+	18.9464i	−0.324905	+	0.999954i	0.646579	+	0.762847i	$0.276199\pi$
$359$	−6.15607	+	18.9464i	−0.324905	+	0.999954i	−0.971484	+	0.237107i	$0.923801\pi$
$360$		0			0
$361$	4.93578	−	15.1908i	0.259778	−	0.799515i
$362$		0			0
$363$	−26.2449	+	36.1230i	−1.37750	+	1.89596i
$364$		0			0
$365$	−3.60044	−	11.0810i	−0.188456	−	0.580007i
$366$		0			0
$367$	15.0800	+	10.9562i	0.787167	+	0.571911i	0.907121	−	0.420869i	$-0.138275\pi$
$367$	15.0800	+	10.9562i	0.787167	+	0.571911i	−0.119954	+	0.992779i	$0.538275\pi$
$368$		0			0
$369$	9.80019	−	6.78792i	0.510178	−	0.353365i
$370$		0			0
$371$	−10.1430	−	7.36935i	−0.526601	−	0.382598i
$372$		0			0
$373$	5.79228	+	17.8268i	0.299913	+	0.923038i	0.981527	+	0.191325i	$0.0612786\pi$
$373$	5.79228	+	17.8268i	0.299913	+	0.923038i	−0.681614	+	0.731712i	$0.738721\pi$
$374$		0			0
$375$	−12.2639	+	16.8799i	−0.633308	+	0.871673i
$376$		0			0
$377$	8.17942	−	25.1737i	0.421262	−	1.29651i
$378$		0			0
$379$	2.80057	−	8.61927i	0.143856	−	0.442742i	−0.853006	−	0.521901i	$-0.825223\pi$
$379$	2.80057	−	8.61927i	0.143856	−	0.442742i	0.996862	+	0.0791582i	$0.0252232\pi$
$380$		0			0
$381$	28.6001	−	9.29275i	1.46523	−	0.476082i
$382$		0			0
$383$		−	9.82414i		−	0.501990i	−0.967988	−	0.250995i	$-0.919242\pi$
$383$		−	9.82414i		−	0.501990i	0.967988	−	0.250995i	$-0.0807578\pi$
$384$		0			0
$385$	4.83066	−	3.50968i	0.246193	−	0.178870i
$386$		0			0
$387$	−9.12964	−	6.63307i	−0.464085	−	0.337178i
$388$		0			0
$389$	24.1740	−	17.5634i	1.22567	−	0.890500i	0.229110	−	0.973401i	$-0.426418\pi$
$389$	24.1740	−	17.5634i	1.22567	−	0.890500i	0.996558	+	0.0829006i	$0.0264184\pi$
$390$		0			0
$391$	−10.5900	−	14.5758i	−0.535557	−	0.737132i
$392$		0			0
$393$	−28.9162	−	9.39545i	−1.45863	−	0.473938i
$394$		0			0
$395$	12.6253	−	4.10220i	0.635247	−	0.206404i
$396$		0			0
$397$	21.1494	−	29.1097i	1.06146	−	1.46097i	0.183026	−	0.983108i	$-0.441411\pi$
$397$	21.1494	−	29.1097i	1.06146	−	1.46097i	0.878433	−	0.477865i	$-0.158589\pi$
$398$		0			0
$399$	3.64876	+	1.18555i	0.182666	+	0.0593519i
$400$		0			0
$401$	−11.2722			−0.562906			−0.281453	−	0.959575i	$-0.590816\pi$
$401$	−11.2722			−0.562906			−0.281453	+	0.959575i	$0.590816\pi$
$402$		0			0
$403$	−6.03529	−	8.30686i	−0.300639	−	0.413794i
$404$		0			0
$405$	−3.67007	−	11.2953i	−0.182367	−	0.561269i
$406$		0			0
$407$			19.1665i			0.950050i
$408$		0			0
$409$	3.62406			0.179198			0.0895991	−	0.995978i	$-0.471441\pi$
$409$	3.62406			0.179198			0.0895991	+	0.995978i	$0.471441\pi$
$410$		0			0
$411$	47.1917			2.32779
$412$		0			0
$413$			8.85620i			0.435785i
$414$		0			0
$415$	−1.49608	−	4.60446i	−0.0734396	−	0.226024i
$416$		0			0
$417$	23.8031	+	32.7622i	1.16564	+	1.60437i
$418$		0			0
$419$	−37.7161			−1.84255			−0.921277	−	0.388907i	$-0.872853\pi$
$419$	−37.7161			−1.84255			−0.921277	+	0.388907i	$0.872853\pi$
$420$		0			0
$421$	−26.6788	−	8.66846i	−1.30024	−	0.422475i	−0.424577	−	0.905392i	$-0.639577\pi$
$421$	−26.6788	−	8.66846i	−1.30024	−	0.422475i	−0.875666	+	0.482917i	$0.839577\pi$
$422$		0			0
$423$	−11.6846	+	16.0825i	−0.568127	+	0.781960i
$424$		0			0
$425$	14.5145	−	4.71606i	0.704059	−	0.228763i
$426$		0			0
$427$	3.36268	+	1.09260i	0.162732	+	0.0528747i
$428$		0			0
$429$	−24.7598	−	34.0789i	−1.19541	−	1.64534i
$430$		0			0
$431$	1.39678	−	1.01482i	0.0672803	−	0.0488820i	−0.553637	−	0.832758i	$-0.686760\pi$
$431$	1.39678	−	1.01482i	0.0672803	−	0.0488820i	0.620917	+	0.783876i	$0.286760\pi$
$432$		0			0
$433$	−7.41555	−	5.38771i	−0.356368	−	0.258917i	0.395167	−	0.918609i	$-0.370687\pi$
$433$	−7.41555	−	5.38771i	−0.356368	−	0.258917i	−0.751536	+	0.659692i	$0.770687\pi$
$434$		0			0
$435$	14.7576	−	10.7220i	0.707574	−	0.514082i
$436$		0			0
$437$		−	7.92694i		−	0.379197i
$438$		0			0
$439$	7.29845	−	2.37141i	0.348336	−	0.113181i	−0.129623	−	0.991563i	$-0.541377\pi$
$439$	7.29845	−	2.37141i	0.348336	−	0.113181i	0.477959	+	0.878382i	$0.341377\pi$
$440$		0			0
$441$	0.575331	−	1.77069i	0.0273967	−	0.0843183i
$442$		0			0
$443$	−3.33269	+	10.2570i	−0.158341	+	0.487323i	−0.998484	−	0.0550417i	$-0.982471\pi$
$443$	−3.33269	+	10.2570i	−0.158341	+	0.487323i	0.840143	+	0.542365i	$0.182471\pi$
$444$		0			0
$445$	−9.63328	+	13.2591i	−0.456661	+	0.628540i
$446$		0			0
$447$	−3.27655	−	10.0842i	−0.154976	−	0.476966i
$448$		0			0
$449$	−7.16655	−	5.20680i	−0.338210	−	0.245724i	0.405696	−	0.914008i	$-0.367029\pi$
$449$	−7.16655	−	5.20680i	−0.338210	−	0.245724i	−0.743906	+	0.668284i	$0.767029\pi$
$450$		0			0
$451$	−34.2835	+	10.2905i	−1.61435	+	0.484563i
$452$		0			0
$453$	19.8421	+	14.4162i	0.932266	+	0.677331i
$454$		0			0
$455$	1.12800	+	3.47162i	0.0528814	+	0.162752i
$456$		0			0
$457$	−12.5036	+	17.2097i	−0.584894	+	0.805037i	−0.994221	−	0.107350i	$-0.965763\pi$
$457$	−12.5036	+	17.2097i	−0.584894	+	0.805037i	0.409328	+	0.912387i	$0.365763\pi$
$458$		0			0
$459$	−3.06695	+	9.43911i	−0.143153	+	0.440580i
$460$		0			0
$461$	−5.17138	+	15.9159i	−0.240855	+	0.741277i	0.755435	+	0.655223i	$0.227426\pi$
$461$	−5.17138	+	15.9159i	−0.240855	+	0.741277i	−0.996291	+	0.0860532i	$0.972574\pi$
$462$		0			0
$463$	2.22163	−	0.721852i	0.103248	−	0.0335473i	−0.256937	−	0.966428i	$-0.582713\pi$
$463$	2.22163	−	0.721852i	0.103248	−	0.0335473i	0.360185	+	0.932881i	$0.382713\pi$
$464$		0			0
$465$		−	7.07616i		−	0.328149i
$466$		0			0
$467$	12.4367	−	9.03582i	0.575504	−	0.418128i	−0.261596	−	0.965177i	$-0.584249\pi$
$467$	12.4367	−	9.03582i	0.575504	−	0.418128i	0.837100	+	0.547049i	$0.184249\pi$
$468$		0			0
$469$	10.7246	+	7.79189i	0.495217	+	0.359796i
$470$		0			0
$471$	−11.6647	+	8.47492i	−0.537482	+	0.390504i
$472$		0			0
$473$	19.9161	+	27.4122i	0.915745	+	1.26041i
$474$		0			0
$475$	6.38606	+	2.07496i	0.293012	+	0.0952055i
$476$		0			0
$477$	−22.2000	+	7.21320i	−1.01647	+	0.330270i
$478$		0			0
$479$	−4.79468	+	6.59932i	−0.219075	+	0.301530i	−0.904382	−	0.426723i	$-0.859668\pi$
$479$	−4.79468	+	6.59932i	−0.219075	+	0.301530i	0.685307	+	0.728254i	$0.259668\pi$
$480$		0			0
$481$	−11.1437	−	3.62080i	−0.508107	−	0.165094i
$482$		0			0
$483$	−10.0453			−0.457078
$484$		0			0
$485$	10.5281	+	14.4908i	0.478058	+	0.657991i
$486$		0			0
$487$	9.24971	+	28.4677i	0.419144	+	1.28999i	0.908491	+	0.417904i	$0.137235\pi$
$487$	9.24971	+	28.4677i	0.419144	+	1.28999i	−0.489347	+	0.872089i	$0.662765\pi$
$488$		0			0
$489$			54.2588i			2.45367i
$490$		0			0
$491$	−9.63713			−0.434918			−0.217459	−	0.976069i	$-0.569777\pi$
$491$	−9.63713			−0.434918			−0.217459	+	0.976069i	$0.569777\pi$
$492$		0			0
$493$	−30.6300			−1.37951
$494$		0			0
$495$		−	11.1169i		−	0.499667i
$496$		0			0
$497$	4.46425	+	13.7395i	0.200249	+	0.616303i
$498$		0			0
$499$	4.80684	+	6.61605i	0.215184	+	0.296175i	0.902940	−	0.429767i	$-0.141404\pi$
$499$	4.80684	+	6.61605i	0.215184	+	0.296175i	−0.687756	+	0.725942i	$0.741404\pi$
$500$		0			0
$501$	−18.9588			−0.847015
$502$		0			0
$503$	12.2337	+	3.97496i	0.545472	+	0.177235i	0.568774	−	0.822494i	$-0.307418\pi$
$503$	12.2337	+	3.97496i	0.545472	+	0.177235i	−0.0233018	+	0.999728i	$0.507418\pi$
$504$		0			0
$505$	−8.97206	+	12.3490i	−0.399251	+	0.549522i
$506$		0			0
$507$	−2.77011	+	0.900064i	−0.123025	+	0.0399733i
$508$		0			0
$509$	−10.9104	−	3.54501i	−0.483596	−	0.157130i	0.0570651	−	0.998370i	$-0.481826\pi$
$509$	−10.9104	−	3.54501i	−0.483596	−	0.157130i	−0.540661	+	0.841241i	$0.681826\pi$
$510$		0			0
$511$	6.41164	+	8.82486i	0.283634	+	0.390389i
$512$		0			0
$513$	−3.53274	+	2.56669i	−0.155974	+	0.113322i
$514$		0			0
$515$	−8.70092	−	6.32159i	−0.383408	−	0.278562i
$516$		0			0
$517$	48.2887	−	35.0838i	2.12373	−	1.54298i
$518$		0			0
$519$			20.0280i			0.879130i
$520$		0			0
$521$	−19.4065	+	6.30554i	−0.850213	+	0.276251i	−0.701535	−	0.712635i	$-0.747502\pi$
$521$	−19.4065	+	6.30554i	−0.850213	+	0.276251i	−0.148678	+	0.988886i	$0.547502\pi$
$522$		0			0
$523$	7.71513	−	23.7447i	0.337359	−	1.03828i	−0.628189	−	0.778061i	$-0.716204\pi$
$523$	7.71513	−	23.7447i	0.337359	−	1.03828i	0.965548	−	0.260224i	$-0.0837964\pi$
$524$		0			0
$525$	2.62947	−	8.09267i	0.114759	−	0.353193i
$526$		0			0
$527$	−6.98401	+	9.61267i	−0.304228	+	0.418734i
$528$		0			0
$529$	−0.693625	−	2.13476i	−0.0301576	−	0.0928156i
$530$		0			0
$531$	13.3395	+	9.69172i	0.578886	+	0.420585i
$532$		0			0
$533$	0.493523	−	21.8769i	0.0213768	−	0.947592i
$534$		0			0
$535$	15.7126	+	11.4159i	0.679315	+	0.493551i
$536$		0			0
$537$	−9.64670	−	29.6895i	−0.416286	−	1.28120i
$538$		0			0
$539$	−3.28582	+	4.52255i	−0.141530	+	0.194800i
$540$		0			0
$541$	5.41570	−	16.6678i	0.232839	−	0.716606i	−0.764561	−	0.644551i	$-0.777044\pi$
$541$	5.41570	−	16.6678i	0.232839	−	0.716606i	0.997401	−	0.0720548i	$-0.0229556\pi$
$542$		0			0
$543$	−0.953682	+	2.93513i	−0.0409264	+	0.125959i
$544$		0			0
$545$	−5.46017	+	1.77412i	−0.233888	+	0.0759947i
$546$		0			0
$547$			7.75156i			0.331433i	0.986173	+	0.165716i	$0.0529936\pi$
$547$			7.75156i			0.331433i	−0.986173	+	0.165716i	$0.947006\pi$
$548$		0			0
$549$	5.32565	−	3.86931i	0.227293	−	0.165138i
$550$		0			0
$551$	−10.9027	−	7.92128i	−0.464471	−	0.337458i
$552$		0			0
$553$	−10.0547	+	7.30517i	−0.427570	+	0.310647i
$554$		0			0
$555$	−4.74634	−	6.53277i	−0.201471	−	0.277301i
$556$		0			0
$557$	−0.305159	−	0.0991523i	−0.0129300	−	0.00420122i	0.302545	−	0.953135i	$-0.402164\pi$
$557$	−0.305159	−	0.0991523i	−0.0129300	−	0.00420122i	−0.315475	+	0.948934i	$0.602164\pi$
$558$		0			0
$559$	−19.7002	+	6.40098i	−0.833229	+	0.270733i
$560$		0			0
$561$	−28.6519	+	39.4360i	−1.20968	+	1.66499i
$562$		0			0
$563$	−32.5981	−	10.5918i	−1.37385	−	0.446389i	−0.473204	−	0.880953i	$-0.656903\pi$
$563$	−32.5981	−	10.5918i	−1.37385	−	0.446389i	−0.900641	+	0.434564i	$0.856903\pi$
$564$		0			0
$565$	−9.57137			−0.402671
$566$		0			0
$567$	6.53564	+	8.99554i	0.274471	+	0.377777i
$568$		0			0
$569$	7.39260	+	22.7521i	0.309914	+	0.953817i	0.977798	+	0.209551i	$0.0672004\pi$
$569$	7.39260	+	22.7521i	0.309914	+	0.953817i	−0.667884	+	0.744266i	$0.732800\pi$
$570$		0			0
$571$			27.2312i			1.13959i	0.821787	+	0.569795i	$0.192977\pi$
$571$			27.2312i			1.13959i	−0.821787	+	0.569795i	$0.807023\pi$
$572$		0			0
$573$	−21.8797			−0.914036
$574$		0			0
$575$	−17.5813			−0.733193
$576$		0			0
$577$		−	17.6446i		−	0.734556i	−0.930111	−	0.367278i	$-0.880290\pi$
$577$		−	17.6446i		−	0.734556i	0.930111	−	0.367278i	$-0.119710\pi$
$578$		0			0
$579$	17.3448	+	53.3818i	0.720825	+	2.21847i
$580$		0			0
$581$	2.66421	+	3.66697i	0.110530	+	0.152131i
$582$		0			0
$583$	70.0868			2.90270
$584$		0			0
$585$	6.46350	+	2.10012i	0.267233	+	0.0868292i
$586$		0			0
$587$	17.1829	−	23.6502i	0.709214	−	0.976150i	−0.290599	−	0.956845i	$-0.593855\pi$
$587$	17.1829	−	23.6502i	0.709214	−	0.976150i	0.999814	−	0.0193049i	$-0.00614531\pi$
$588$		0			0
$589$	−4.97190	+	1.61547i	−0.204864	+	0.0665642i
$590$		0			0
$591$	−33.6339	−	10.9283i	−1.38351	−	0.449531i
$592$		0			0
$593$	26.6676	+	36.7048i	1.09511	+	1.50728i	0.841716	+	0.539920i	$0.181546\pi$
$593$	26.6676	+	36.7048i	1.09511	+	1.50728i	0.253390	+	0.967364i	$0.418454\pi$
$594$		0			0
$595$	3.41736	−	2.48286i	0.140098	−	0.101787i
$596$		0			0
$597$	33.6943	+	24.4804i	1.37902	+	1.00191i
$598$		0			0
$599$	25.6826	−	18.6595i	1.04936	−	0.762408i	0.0772727	−	0.997010i	$-0.475379\pi$
$599$	25.6826	−	18.6595i	1.04936	−	0.762408i	0.972091	+	0.234602i	$0.0753788\pi$
$600$		0			0
$601$		−	1.02470i		−	0.0417982i	−0.999782	−	0.0208991i	$-0.993347\pi$
$601$		−	1.02470i		−	0.0417982i	0.999782	−	0.0208991i	$-0.00665288\pi$
$602$		0			0
$603$	23.4728	−	7.62679i	0.955888	−	0.310587i
$604$		0			0
$605$	−6.68393	+	20.5710i	−0.271741	+	0.836331i
$606$		0			0
$607$	−3.30145	+	10.1608i	−0.134002	+	0.412415i	−0.995433	−	0.0954583i	$-0.969568\pi$
$607$	−3.30145	+	10.1608i	−0.134002	+	0.412415i	0.861432	+	0.507874i	$0.169568\pi$
$608$		0			0
$609$	−10.0382	+	13.8164i	−0.406767	+	0.559867i
$610$		0			0
$611$	11.2758	+	34.7034i	0.456170	+	1.40395i
$612$		0			0
$613$	−33.4795	−	24.3243i	−1.35223	−	0.982450i	−0.998897	−	0.0469507i	$-0.985050\pi$
$613$	−33.4795	−	24.3243i	−1.35223	−	0.982450i	−0.353329	−	0.935499i	$-0.614950\pi$
$614$		0			0
$615$	9.13696	−	11.9973i	0.368438	−	0.483778i
$616$		0			0
$617$	−3.49118	−	2.53649i	−0.140550	−	0.102115i	0.515289	−	0.857017i	$-0.327685\pi$
$617$	−3.49118	−	2.53649i	−0.140550	−	0.102115i	−0.655838	+	0.754901i	$0.727685\pi$
$618$		0			0
$619$	11.5968	+	35.6912i	0.466114	+	1.43455i	0.857576	+	0.514357i	$0.171969\pi$
$619$	11.5968	+	35.6912i	0.466114	+	1.43455i	−0.391462	+	0.920194i	$0.628031\pi$
$620$		0			0
$621$	6.72045	−	9.24990i	0.269682	−	0.371186i
$622$		0			0
$623$	4.74149	−	14.5928i	0.189964	−	0.584649i
$624$		0			0
$625$	2.83931	−	8.73851i	0.113573	−	0.349540i
$626$		0			0
$627$	−20.3972	+	6.62746i	−0.814586	+	0.264675i
$628$		0			0
$629$			13.5590i			0.540634i
$630$		0			0
$631$	23.0099	−	16.7177i	0.916011	−	0.665521i	−0.0265172	−	0.999648i	$-0.508442\pi$
$631$	23.0099	−	16.7177i	0.916011	−	0.665521i	0.942528	+	0.334128i	$0.108442\pi$
$632$		0			0
$633$	13.8193	+	10.0403i	0.549269	+	0.399067i
$634$		0			0
$635$	11.7854	−	8.56258i	0.467688	−	0.339796i
$636$		0			0
$637$	−2.00873	−	2.76478i	−0.0795889	−	0.109545i
$638$		0			0
$639$	25.5804	+	8.31157i	1.01194	+	0.328801i
$640$		0			0
$641$	−2.20271	+	0.715703i	−0.0870017	+	0.0282686i	−0.352194	−	0.935927i	$-0.614564\pi$
$641$	−2.20271	+	0.715703i	−0.0870017	+	0.0282686i	0.265193	+	0.964195i	$0.414564\pi$
$642$		0			0
$643$	22.6102	−	31.1203i	0.891659	−	1.22726i	−0.0813941	−	0.996682i	$-0.525937\pi$
$643$	22.6102	−	31.1203i	0.891659	−	1.22726i	0.973053	−	0.230581i	$-0.0740628\pi$
$644$		0			0
$645$	−13.5765	−	4.41128i	−0.534575	−	0.173694i
$646$		0			0
$647$	−37.2154			−1.46309			−0.731545	−	0.681793i	$-0.761200\pi$
$647$	−37.2154			−1.46309			−0.731545	+	0.681793i	$0.761200\pi$
$648$		0			0
$649$	−29.0999	−	40.0526i	−1.14227	−	1.57220i
$650$		0			0
$651$	2.04719	+	6.30059i	0.0802355	+	0.246940i
$652$		0			0
$653$			3.29204i			0.128828i	0.997923	+	0.0644138i	$0.0205178\pi$
$653$			3.29204i			0.128828i	−0.997923	+	0.0644138i	$0.979482\pi$
$654$		0			0
$655$	−14.7285			−0.575491
$656$		0			0
$657$	20.3088			0.792324
$658$		0			0
$659$		−	35.7347i		−	1.39203i	−0.718029	−	0.696013i	$-0.754956\pi$
$659$		−	35.7347i		−	1.39203i	0.718029	−	0.696013i	$-0.245044\pi$
$660$		0			0
$661$	11.6180	+	35.7566i	0.451888	+	1.39077i	0.874750	+	0.484575i	$0.161026\pi$
$661$	11.6180	+	35.7566i	0.451888	+	1.39077i	−0.422862	+	0.906194i	$0.638974\pi$
$662$		0			0
$663$	−17.5159	−	24.1085i	−0.680260	−	0.936297i
$664$		0			0
$665$	1.85850			0.0720696
$666$		0			0
$667$	33.5590	+	10.9040i	1.29941	+	0.422203i
$668$		0			0
$669$	0.806464	−	1.11000i	0.0311797	−	0.0429152i
$670$		0			0
$671$	−18.7980	+	6.10784i	−0.725689	+	0.235790i
$672$		0			0
$673$	11.8961	+	3.86528i	0.458562	+	0.148996i	0.529183	−	0.848507i	$-0.322498\pi$
$673$	11.8961	+	3.86528i	0.458562	+	0.148996i	−0.0706218	+	0.997503i	$0.522498\pi$
$674$		0			0
$675$	5.69272	+	7.83535i	0.219113	+	0.301583i
$676$		0			0
$677$	−28.1060	+	20.4202i	−1.08020	+	0.784811i	−0.977718	−	0.209924i	$-0.932678\pi$
$677$	−28.1060	+	20.4202i	−1.08020	+	0.784811i	−0.102482	+	0.994735i	$0.532678\pi$
$678$		0			0
$679$	−13.5665	−	9.85664i	−0.520635	−	0.378263i
$680$		0			0
$681$	−2.77456	+	2.01584i	−0.106322	+	0.0772471i
$682$		0			0
$683$			22.9328i			0.877498i	0.898610	+	0.438749i	$0.144578\pi$
$683$			22.9328i			0.877498i	−0.898610	+	0.438749i	$0.855422\pi$
$684$		0			0
$685$	21.7418	−	7.06435i	0.830712	−	0.269915i
$686$		0			0
$687$	3.89712	−	11.9941i	0.148685	−	0.457604i
$688$		0			0
$689$	−13.2403	+	40.7493i	−0.504414	+	1.55243i
$690$		0			0
$691$	−5.68166	+	7.82013i	−0.216140	+	0.297492i	−0.903295	−	0.429019i	$-0.858859\pi$
$691$	−5.68166	+	7.82013i	−0.216140	+	0.297492i	0.687155	+	0.726511i	$0.258859\pi$
$692$		0			0
$693$	3.21620	+	9.89844i	0.122173	+	0.376011i
$694$		0			0
$695$	15.8707	+	11.5308i	0.602011	+	0.437387i
$696$		0			0
$697$	−24.2532	+	7.27986i	−0.918657	+	0.275745i
$698$		0			0
$699$	5.68178	+	4.12806i	0.214905	+	0.156137i
$700$		0			0
$701$	−14.2314	−	43.7998i	−0.537513	−	1.65429i	−0.738156	−	0.674630i	$-0.764303\pi$
$701$	−14.2314	−	43.7998i	−0.537513	−	1.65429i	0.200643	−	0.979664i	$-0.435697\pi$
$702$		0			0
$703$	−3.50652	+	4.82632i	−0.132251	+	0.182028i
$704$		0			0
$705$	−7.77081	+	23.9161i	−0.292665	+	0.900732i
$706$		0			0
$707$	4.41604	−	13.5912i	0.166082	−	0.511149i
$708$		0			0
$709$	−35.7980	+	11.6315i	−1.34442	+	0.436830i	−0.890813	−	0.454370i	$-0.849864\pi$
$709$	−35.7980	+	11.6315i	−1.34442	+	0.436830i	−0.453611	+	0.891200i	$0.649864\pi$
$710$		0			0
$711$			23.1391i			0.867785i
$712$		0			0
$713$	11.0739	−	8.04563i	0.414719	−	0.301311i
$714$		0			0
$715$	−16.5086	−	11.9942i	−0.617386	−	0.448557i
$716$		0			0
$717$	14.4018	−	10.4635i	0.537845	−	0.390767i
$718$		0			0
$719$	−21.4842	−	29.5704i	−0.801225	−	1.10279i	−0.992619	−	0.121278i	$-0.961301\pi$
$719$	−21.4842	−	29.5704i	−0.801225	−	1.10279i	0.191394	−	0.981513i	$-0.438699\pi$
$720$		0			0
$721$	9.57615	+	3.11148i	0.356634	+	0.115878i
$722$		0			0
$723$	6.22180	−	2.02159i	0.231391	−	0.0751836i
$724$		0			0
$725$	−17.5688	+	24.1814i	−0.652489	+	0.898074i
$726$		0			0
$727$	−20.8788	−	6.78394i	−0.774352	−	0.251602i	−0.104925	−	0.994480i	$-0.533460\pi$
$727$	−20.8788	−	6.78394i	−0.774352	−	0.251602i	−0.669427	+	0.742878i	$0.733460\pi$
$728$		0			0
$729$	4.10062			0.151875
$730$		0			0
$731$	14.0893	+	19.3923i	0.521112	+	0.717249i
$732$		0			0
$733$	−1.79225	−	5.51599i	−0.0661984	−	0.203738i	0.912486	−	0.409108i	$-0.134160\pi$
$733$	−1.79225	−	5.51599i	−0.0661984	−	0.203738i	−0.978684	+	0.205370i	$0.934160\pi$
$734$		0			0
$735$		−	2.35517i		−	0.0868717i
$736$		0			0
$737$	−74.1054			−2.72971
$738$		0			0
$739$	43.3353			1.59412			0.797058	−	0.603902i	$-0.206388\pi$
$739$	43.3353			1.59412			0.797058	+	0.603902i	$0.206388\pi$
$740$		0			0
$741$		−	13.1112i		−	0.481652i
$742$		0			0
$743$	15.3917	+	47.3708i	0.564667	+	1.73787i	0.668937	+	0.743319i	$0.266749\pi$
$743$	15.3917	+	47.3708i	0.564667	+	1.73787i	−0.104270	+	0.994549i	$0.533251\pi$
$744$		0			0
$745$	−3.01910	−	4.15543i	−0.110611	−	0.152243i
$746$		0			0
$747$	8.43887			0.308762
$748$		0			0
$749$	−17.2931	−	5.61888i	−0.631878	−	0.205310i
$750$		0			0
$751$	−1.55063	+	2.13427i	−0.0565835	+	0.0778804i	−0.836371	−	0.548164i	$-0.815327\pi$
$751$	−1.55063	+	2.13427i	−0.0565835	+	0.0778804i	0.779788	+	0.626044i	$0.215327\pi$
$752$		0			0
$753$	5.37233	−	1.74558i	0.195779	−	0.0636123i
$754$		0			0
$755$	11.2996	+	3.67145i	0.411233	+	0.133618i
$756$		0			0
$757$	−6.00879	−	8.27039i	−0.218393	−	0.300592i	0.685737	−	0.727849i	$-0.259480\pi$
$757$	−6.00879	−	8.27039i	−0.218393	−	0.300592i	−0.904130	+	0.427257i	$0.859480\pi$
$758$		0			0
$759$	45.4305	−	33.0072i	1.64902	−	1.19809i
$760$		0			0
$761$	3.18656	+	2.31517i	0.115513	+	0.0839250i	0.644042	−	0.764990i	$-0.277256\pi$
$761$	3.18656	+	2.31517i	0.115513	+	0.0839250i	−0.528529	+	0.848915i	$0.677256\pi$
$762$		0			0
$763$	4.34845	−	3.15933i	0.157424	−	0.114376i
$764$		0			0
$765$		−	7.86445i		−	0.284340i
$766$		0			0
$767$	28.7844	−	9.35262i	1.03934	−	0.337703i
$768$		0			0
$769$	−9.27027	+	28.5309i	−0.334294	+	1.02885i	0.632774	+	0.774336i	$0.281916\pi$
$769$	−9.27027	+	28.5309i	−0.334294	+	1.02885i	−0.967069	+	0.254516i	$0.918084\pi$
$770$		0			0
$771$	−13.2085	+	40.6515i	−0.475692	+	1.46403i
$772$		0			0
$773$	−19.2232	+	26.4584i	−0.691409	+	0.951643i	0.308591	+	0.951195i	$0.400143\pi$
$773$	−19.2232	+	26.4584i	−0.691409	+	0.951643i	−1.00000		0.000448177i	$0.999857\pi$
$774$		0			0
$775$	3.58298	+	11.0273i	0.128705	+	0.396112i
$776$		0			0
$777$	6.11610	+	4.44361i	0.219414	+	0.159414i
$778$		0			0
$779$	−10.5156	−	3.68092i	−0.376759	−	0.131883i
$780$		0			0
$781$	−65.3355	−	47.4690i	−2.33789	−	1.69857i
$782$		0			0
$783$	−6.00666	−	18.4866i	−0.214661	−	0.660658i
$784$		0			0
$785$	−4.10544	+	5.65065i	−0.146529	+	0.201680i
$786$		0			0
$787$	−4.66403	+	14.3544i	−0.166255	+	0.511679i	−0.999127	−	0.0417865i	$-0.986695\pi$
$787$	−4.66403	+	14.3544i	−0.166255	+	0.511679i	0.832872	+	0.553466i	$0.186695\pi$
$788$		0			0
$789$	−4.95502	+	15.2500i	−0.176403	+	0.542914i
$790$		0			0
$791$	8.52231	−	2.76907i	0.303019	−	0.0984567i
$792$		0			0
$793$		−	12.0832i		−	0.429088i
$794$		0			0
$795$	−23.8886	+	17.3561i	−0.847240	+	0.615556i
$796$		0			0
$797$	−37.6868	−	27.3811i	−1.33494	−	0.969888i	−0.999614	−	0.0277847i	$-0.991155\pi$
$797$	−37.6868	−	27.3811i	−1.33494	−	0.969888i	−0.335322	−	0.942103i	$-0.608845\pi$
$798$		0			0
$799$	34.1609	−	24.8194i	1.20853	−	0.878047i
$800$		0			0
$801$	−16.7914	−	23.1113i	−0.593294	−	0.816599i
$802$		0			0
$803$	−57.9939	−	18.8434i	−2.04656	−	0.664967i
$804$		0			0
$805$	−4.62801	+	1.50373i	−0.163116	+	0.0529996i
$806$		0			0
$807$	10.5193	−	14.4785i	0.370295	−	0.509668i
$808$		0			0
$809$	−7.99276	−	2.59701i	−0.281011	−	0.0913059i	0.165121	−	0.986273i	$-0.447199\pi$
$809$	−7.99276	−	2.59701i	−0.281011	−	0.0913059i	−0.446131	+	0.894967i	$0.647199\pi$
$810$		0			0
$811$	−10.8233			−0.380057			−0.190028	−	0.981779i	$-0.560858\pi$
$811$	−10.8233			−0.380057			−0.190028	+	0.981779i	$0.560858\pi$
$812$		0			0
$813$	16.6668	+	22.9399i	0.584530	+	0.804537i
$814$		0			0
$815$	8.12226	+	24.9977i	0.284510	+	0.875633i
$816$		0			0
$817$			10.5463i			0.368969i
$818$		0			0
$819$	−6.36266			−0.222329
$820$		0			0
$821$	−12.1495			−0.424020			−0.212010	−	0.977267i	$-0.568001\pi$
$821$	−12.1495			−0.424020			−0.212010	+	0.977267i	$0.568001\pi$
$822$		0			0
$823$		−	41.0413i		−	1.43061i	−0.698813	−	0.715305i	$-0.746288\pi$
$823$		−	41.0413i		−	1.43061i	0.698813	−	0.715305i	$-0.253712\pi$
$824$		0			0
$825$	14.6992	+	45.2395i	0.511760	+	1.57504i
$826$		0			0
$827$	2.33570	+	3.21482i	0.0812204	+	0.111790i	0.847694	−	0.530486i	$-0.177990\pi$
$827$	2.33570	+	3.21482i	0.0812204	+	0.111790i	−0.766474	+	0.642276i	$0.777990\pi$
$828$		0			0
$829$	22.2545			0.772929			0.386465	−	0.922304i	$-0.373696\pi$
$829$	22.2545			0.772929			0.386465	+	0.922304i	$0.373696\pi$
$830$		0			0
$831$	14.3207	+	4.65307i	0.496779	+	0.161413i
$832$		0			0
$833$	−2.32450	+	3.19940i	−0.0805391	+	0.110853i
$834$		0			0
$835$	−8.73454	+	2.83802i	−0.302271	+	0.0982139i
$836$		0			0
$837$	−7.17128	−	2.33009i	−0.247876	−	0.0805397i
$838$		0			0
$839$	−16.7056	−	22.9933i	−0.576742	−	0.793817i	0.416592	−	0.909094i	$-0.363225\pi$
$839$	−16.7056	−	22.9933i	−0.576742	−	0.793817i	−0.993333	+	0.115277i	$0.963225\pi$
$840$		0			0
$841$	25.0709	−	18.2150i	0.864512	−	0.628105i
$842$		0			0
$843$	−27.4450	−	19.9400i	−0.945257	−	0.686770i
$844$		0			0
$845$	−1.14149	+	0.829342i	−0.0392685	+	0.0285302i
$846$		0			0
$847$		−	20.2501i		−	0.695801i
$848$		0			0
$849$	30.1417	−	9.79363i	1.03446	−	0.336117i
$850$		0			0
$851$	4.82687	−	14.8556i	0.165463	−	0.509243i
$852$		0			0
$853$	−12.8474	+	39.5403i	−0.439888	+	1.35384i	0.448106	+	0.893980i	$0.352099\pi$
$853$	−12.8474	+	39.5403i	−0.439888	+	1.35384i	−0.887994	+	0.459855i	$0.847901\pi$
$854$		0			0
$855$	2.03384	−	2.79934i	0.0695558	−	0.0957354i
$856$		0			0
$857$	−11.7925	−	36.2936i	−0.402824	−	1.23977i	−0.922698	−	0.385522i	$-0.874021\pi$
$857$	−11.7925	−	36.2936i	−0.402824	−	1.23977i	0.519874	−	0.854243i	$-0.325979\pi$
$858$		0			0
$859$	−42.1355	−	30.6132i	−1.43764	−	1.04451i	−0.988528	−	0.151036i	$-0.951739\pi$
$859$	−42.1355	−	30.6132i	−1.43764	−	1.04451i	−0.449116	−	0.893473i	$-0.648261\pi$
$860$		0			0
$861$	−4.66461	+	13.3257i	−0.158969	+	0.454140i
$862$		0			0
$863$	−4.37606	−	3.17940i	−0.148963	−	0.108228i	0.510808	−	0.859695i	$-0.329346\pi$
$863$	−4.37606	−	3.17940i	−0.148963	−	0.108228i	−0.659770	+	0.751467i	$0.729346\pi$
$864$		0			0
$865$	2.99808	+	9.22714i	0.101938	+	0.313732i
$866$		0			0
$867$	1.76336	−	2.42705i	0.0598867	−	0.0824270i
$868$		0			0
$869$	21.4694	−	66.0760i	0.728299	−	2.24147i
$870$		0			0
$871$	13.9994	−	43.0858i	0.474352	−	1.45991i
$872$		0			0
$873$	−29.6928	+	9.64779i	−1.00495	+	0.326528i
$874$		0			0
$875$		−	9.46265i		−	0.319896i
$876$		0			0
$877$	15.4037	−	11.1914i	0.520145	−	0.377907i	−0.296514	−	0.955029i	$-0.595824\pi$
$877$	15.4037	−	11.1914i	0.520145	−	0.377907i	0.816658	+	0.577121i	$0.195824\pi$
$878$		0			0
$879$	36.8103	+	26.7442i	1.24158	+	0.902060i
$880$		0			0
$881$	4.02210	−	2.92223i	0.135508	−	0.0984523i	−0.517966	−	0.855401i	$-0.673311\pi$
$881$	4.02210	−	2.92223i	0.135508	−	0.0984523i	0.653474	+	0.756949i	$0.273311\pi$
$882$		0			0
$883$	−11.9656	−	16.4693i	−0.402676	−	0.554236i	0.558737	−	0.829345i	$-0.311286\pi$
$883$	−11.9656	−	16.4693i	−0.402676	−	0.554236i	−0.961413	+	0.275109i	$0.911286\pi$
$884$		0			0
$885$	19.8370	+	6.44542i	0.666813	+	0.216661i
$886$		0			0
$887$	11.7372	−	3.81364i	0.394096	−	0.128050i	−0.105264	−	0.994444i	$-0.533569\pi$
$887$	11.7372	−	3.81364i	0.394096	−	0.128050i	0.499360	+	0.866395i	$0.333569\pi$
$888$		0			0
$889$	−8.01644	+	11.0337i	−0.268863	+	0.370058i
$890$		0			0
$891$	−59.1155	−	19.2078i	−1.98044	−	0.643485i
$892$		0			0
$893$	18.5781			0.621693
$894$		0			0
$895$	−8.88872	−	12.2343i	−0.297117	−	0.408947i
$896$		0			0
$897$	10.6084	+	32.6493i	0.354204	+	1.09013i
$898$		0			0
$899$		−	23.2709i		−	0.776127i
$900$		0			0
$901$	49.5817			1.65181
$902$		0			0
$903$	13.3647			0.444750
$904$		0			0
$905$			1.49501i			0.0496959i
$906$		0			0
$907$	1.07583	+	3.31107i	0.0357224	+	0.109942i	0.967328	−	0.253529i	$-0.0815914\pi$
$907$	1.07583	+	3.31107i	0.0357224	+	0.109942i	−0.931605	+	0.363471i	$0.881591\pi$
$908$		0			0
$909$	−15.6388	−	21.5250i	−0.518707	−	0.713939i
$910$		0			0
$911$	23.7898			0.788190			0.394095	−	0.919070i	$-0.371058\pi$
$911$	23.7898			0.788190			0.394095	+	0.919070i	$0.371058\pi$
$912$		0			0
$913$	−24.0980	−	7.82992i	−0.797528	−	0.259132i
$914$		0			0
$915$	4.89463	−	6.73688i	0.161812	−	0.222714i
$916$		0			0
$917$	13.1142	−	4.26107i	0.433070	−	0.140713i
$918$		0			0
$919$	19.9393	+	6.47868i	0.657738	+	0.213712i	0.618823	−	0.785531i	$-0.287610\pi$
$919$	19.9393	+	6.47868i	0.657738	+	0.213712i	0.0389150	+	0.999243i	$0.487610\pi$
$920$		0			0
$921$	6.12438	+	8.42948i	0.201805	+	0.277761i
$922$		0			0
$923$	39.9417	−	29.0194i	1.31470	−	0.955184i
$924$		0			0
$925$	10.7044	+	7.77720i	0.351959	+	0.255713i
$926$		0			0
$927$	15.1662	−	11.0189i	0.498124	−	0.361908i
$928$		0			0
$929$		−	16.0637i		−	0.527032i	−0.964655	−	0.263516i	$-0.915118\pi$
$929$		−	16.0637i		−	0.527032i	0.964655	−	0.263516i	$-0.0848822\pi$
$930$		0			0
$931$	−1.65480	+	0.537678i	−0.0542340	+	0.0176217i
$932$		0			0
$933$	−1.10682	+	3.40644i	−0.0362357	+	0.111522i
$934$		0			0
$935$	−7.29695	+	22.4577i	−0.238636	+	0.734445i
$936$		0			0
$937$	24.6239	−	33.8919i	0.804428	−	1.10720i	−0.187731	−	0.982220i	$-0.560113\pi$
$937$	24.6239	−	33.8919i	0.804428	−	1.10720i	0.992159	−	0.124980i	$-0.0398866\pi$
$938$		0			0
$939$	−8.61343	−	26.5094i	−0.281089	−	0.865102i
$940$		0			0
$941$	26.1271	+	18.9825i	0.851720	+	0.618811i	0.925620	−	0.378455i	$-0.123544\pi$
$941$	26.1271	+	18.9825i	0.851720	+	0.618811i	−0.0738996	+	0.997266i	$0.523544\pi$
$942$		0			0
$943$	29.1640	+	0.657914i	0.949710	+	0.0214246i
$944$		0			0
$945$	2.16868	+	1.57564i	0.0705470	+	0.0512554i
$946$		0			0
$947$	−12.4552	−	38.3332i	−0.404740	−	1.24566i	−0.921112	−	0.389297i	$-0.872718\pi$
$947$	−12.4552	−	38.3332i	−0.404740	−	1.24566i	0.516373	−	0.856364i	$-0.327282\pi$
$948$		0			0
$949$	21.9115	−	30.1586i	0.711278	−	0.978990i
$950$		0			0
$951$	−2.02992	+	6.24746i	−0.0658247	+	0.202588i
$952$		0			0
$953$	−15.0337	+	46.2691i	−0.486991	+	1.49880i	0.342086	+	0.939669i	$0.388866\pi$
$953$	−15.0337	+	46.2691i	−0.486991	+	1.49880i	−0.829077	+	0.559135i	$0.811134\pi$
$954$		0			0
$955$	−10.0802	+	3.27527i	−0.326189	+	0.105985i
$956$		0			0
$957$		−	95.4688i		−	3.08607i
$958$		0			0
$959$	−17.3151	+	12.5801i	−0.559133	+	0.406234i
$960$		0			0
$961$	17.7764	+	12.9153i	0.573432	+	0.416623i
$962$		0			0
$963$	−27.3880	+	19.8986i	−0.882566	+	0.641222i
$964$		0			0
$965$	15.9819	+	21.9972i	0.514476	+	0.708116i
$966$		0			0
$967$	−27.5449	−	8.94988i	−0.885785	−	0.287809i	−0.169428	−	0.985543i	$-0.554192\pi$
$967$	−27.5449	−	8.94988i	−0.885785	−	0.287809i	−0.716357	+	0.697734i	$0.754192\pi$
$968$		0			0
$969$	−14.4296	+	4.68848i	−0.463547	+	0.150616i
$970$		0			0
$971$	0.663030	−	0.912583i	0.0212776	−	0.0292862i	−0.798246	−	0.602332i	$-0.794238\pi$
$971$	0.663030	−	0.912583i	0.0212776	−	0.0292862i	0.819523	+	0.573046i	$0.194238\pi$
$972$		0			0
$973$	−17.4672	−	5.67543i	−0.559972	−	0.181946i
$974$		0			0
$975$	−29.0796			−0.931294
$976$		0			0
$977$	−6.88505	−	9.47646i	−0.220272	−	0.303179i	0.684552	−	0.728964i	$-0.259998\pi$
$977$	−6.88505	−	9.47646i	−0.220272	−	0.303179i	−0.904824	+	0.425785i	$0.859998\pi$
$978$		0			0
$979$	26.5058	+	81.5764i	0.847128	+	2.60719i
$980$		0			0
$981$		−	10.0072i		−	0.319505i
$982$		0			0
$983$	18.3359			0.584826			0.292413	−	0.956292i	$-0.405542\pi$
$983$	18.3359			0.584826			0.292413	+	0.956292i	$0.405542\pi$
$984$		0			0
$985$	−17.1315			−0.545855
$986$		0			0
$987$		−	23.5429i		−	0.749380i
$988$		0			0
$989$	−8.53313	−	26.2623i	−0.271338	−	0.835092i
$990$		0			0
$991$	13.1554	+	18.1069i	0.417895	+	0.575184i	0.965122	−	0.261801i	$-0.0843164\pi$
$991$	13.1554	+	18.1069i	0.417895	+	0.575184i	−0.547227	+	0.836985i	$0.684316\pi$
$992$		0			0
$993$	19.5411			0.620117
$994$		0			0
$995$	19.1880	+	6.23455i	0.608300	+	0.197649i
$996$		0			0
$997$	−16.4486	+	22.6395i	−0.520932	+	0.717001i	−0.985715	−	0.168424i	$-0.946132\pi$
$997$	−16.4486	+	22.6395i	−0.520932	+	0.717001i	0.464783	+	0.885425i	$0.346132\pi$
$998$		0			0
$999$	−8.18349	+	2.65898i	−0.258914	+	0.0841263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.16	✓	80
41.4	even	10	inner	1148.2.ba.a.701.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.16	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.5	yes	80	41.4	even	10	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.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +O(q^{10})\)	\(q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +(5.31657 + 1.72746i) q^{11} +(-2.00873 + 2.76478i) q^{13} +(-2.23990 + 0.727787i) q^{15} +(3.76112 + 1.22206i) q^{17} +(1.02272 + 1.40766i) q^{19} +(1.78384 - 1.29604i) q^{21} +(-3.68573 - 2.67784i) q^{23} +(3.12208 - 2.26832i) q^{25} +2.50966i q^{27} +(-7.36619 + 2.39342i) q^{29} +(-0.928450 + 2.85747i) q^{31} +(-3.80896 + 11.7228i) q^{33} +(0.627829 - 0.864133i) q^{35} +(1.05950 + 3.26080i) q^{37} +(-6.09621 - 4.42916i) q^{39} +(-5.26380 + 3.64587i) q^{41} +(4.90364 + 3.56270i) q^{43} +(-0.614526 - 1.89132i) q^{45} +(6.27597 - 8.63813i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.69458 + 8.29308i) q^{51} +(11.9239 - 3.87430i) q^{53} +5.97102i q^{55} +(-3.10382 + 2.25506i) q^{57} +(-7.16482 - 5.20554i) q^{59} +(-2.86047 + 2.07825i) q^{61} +(1.09434 + 1.50623i) q^{63} +(-3.47162 - 1.12800i) q^{65} +(-12.6075 + 4.09644i) q^{67} +(5.90450 - 8.12684i) q^{69} +(-13.7395 - 4.46425i) q^{71} -10.9081 q^{73} +(5.00155 + 6.88404i) q^{75} +(-1.72746 - 5.31657i) q^{77} -12.4283i q^{79} -11.1191 q^{81} -4.53262 q^{83} +4.22409i q^{85} +(-5.27738 - 16.2421i) q^{87} +(9.01885 + 12.4134i) q^{89} +3.41746 q^{91} +(-6.30059 - 2.04719i) q^{93} +(-1.09240 + 1.50356i) q^{95} +(15.9484 - 5.18194i) q^{97} +(-9.89844 - 3.21620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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