LMFDB - Embedded newform 1148.2.n.d.365.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			365.5
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.d.953.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.51551 q^{3} +(0.929786 - 2.86159i) q^{5} +(-0.809017 - 0.587785i) q^{7} -0.703221 q^{9} +O(q^{10})$	\(q+1.51551 q^{3} +(0.929786 - 2.86159i) q^{5} +(-0.809017 - 0.587785i) q^{7} -0.703221 q^{9} +(-0.853343 - 2.62632i) q^{11} +(-5.09880 + 3.70449i) q^{13} +(1.40910 - 4.33677i) q^{15} +(-1.66557 - 5.12610i) q^{17} +(0.116046 + 0.0843126i) q^{19} +(-1.22608 - 0.890796i) q^{21} +(5.98609 - 4.34915i) q^{23} +(-3.27909 - 2.38240i) q^{25} -5.61228 q^{27} +(2.17056 - 6.68031i) q^{29} +(-0.0687112 - 0.211471i) q^{31} +(-1.29325 - 3.98022i) q^{33} +(-2.43421 + 1.76856i) q^{35} +(-0.744317 + 2.29077i) q^{37} +(-7.72729 + 5.61420i) q^{39} +(6.33807 + 0.910393i) q^{41} +(-3.24257 + 2.35586i) q^{43} +(-0.653845 + 2.01233i) q^{45} +(0.527699 - 0.383396i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-2.52419 - 7.76867i) q^{51} +(-1.68630 + 5.18990i) q^{53} -8.30886 q^{55} +(0.175870 + 0.127777i) q^{57} +(1.54818 - 1.12482i) q^{59} +(-0.168309 - 0.122284i) q^{61} +(0.568918 + 0.413343i) q^{63} +(5.85994 + 18.0350i) q^{65} +(-0.547611 + 1.68537i) q^{67} +(9.07200 - 6.59119i) q^{69} +(-4.31812 - 13.2898i) q^{71} +10.5732 q^{73} +(-4.96950 - 3.61056i) q^{75} +(-0.853343 + 2.62632i) q^{77} -2.49453 q^{79} -6.39582 q^{81} -4.79122 q^{83} -16.2174 q^{85} +(3.28952 - 10.1241i) q^{87} +(0.0253670 + 0.0184302i) q^{89} +6.30246 q^{91} +(-0.104133 - 0.320487i) q^{93} +(0.349166 - 0.253684i) q^{95} +(3.12354 - 9.61328i) q^{97} +(0.600089 + 1.84688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.51551			0.874982			0.437491	−	0.899223i	$-0.355867\pi$
$3$	1.51551			0.874982			0.437491	+	0.899223i	$0.355867\pi$
$4$		0			0
$5$	0.929786	−	2.86159i	0.415813	−	1.27974i	−0.495709	−	0.868489i	$-0.665092\pi$
$5$	0.929786	−	2.86159i	0.415813	−	1.27974i	0.911522	−	0.411252i	$-0.134908\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	−0.703221			−0.234407
$10$		0			0
$11$	−0.853343	−	2.62632i	−0.257293	−	0.791865i	−0.993369	−	0.114967i	$-0.963324\pi$
$11$	−0.853343	−	2.62632i	−0.257293	−	0.791865i	0.736077	−	0.676898i	$-0.236676\pi$
$12$		0			0
$13$	−5.09880	+	3.70449i	−1.41415	+	1.02744i	−0.421449	+	0.906852i	$0.638478\pi$
$13$	−5.09880	+	3.70449i	−1.41415	+	1.02744i	−0.992703	+	0.120589i	$0.961522\pi$
$14$		0			0
$15$	1.40910	−	4.33677i	0.363829	−	1.11975i
$16$		0			0
$17$	−1.66557	−	5.12610i	−0.403960	−	1.24326i	−0.921760	−	0.387760i	$-0.873249\pi$
$17$	−1.66557	−	5.12610i	−0.403960	−	1.24326i	0.517800	−	0.855502i	$-0.326751\pi$
$18$		0			0
$19$	0.116046	+	0.0843126i	0.0266228	+	0.0193426i	0.601017	−	0.799236i	$-0.294762\pi$
$19$	0.116046	+	0.0843126i	0.0266228	+	0.0193426i	−0.574394	+	0.818579i	$0.694762\pi$
$20$		0			0
$21$	−1.22608	−	0.890796i	−0.267552	−	0.194388i
$22$		0			0
$23$	5.98609	−	4.34915i	1.24819	−	0.906861i	0.250071	−	0.968227i	$-0.419546\pi$
$23$	5.98609	−	4.34915i	1.24819	−	0.906861i	0.998115	+	0.0613669i	$0.0195460\pi$
$24$		0			0
$25$	−3.27909	−	2.38240i	−0.655818	−	0.476480i
$26$		0			0
$27$	−5.61228			−1.08008
$28$		0			0
$29$	2.17056	−	6.68031i	0.403063	−	1.24050i	−0.519438	−	0.854508i	$-0.673859\pi$
$29$	2.17056	−	6.68031i	0.403063	−	1.24050i	0.922501	−	0.385994i	$-0.126141\pi$
$30$		0			0
$31$	−0.0687112	−	0.211471i	−0.0123409	−	0.0379814i	0.944696	−	0.327946i	$-0.106356\pi$
$31$	−0.0687112	−	0.211471i	−0.0123409	−	0.0379814i	−0.957037	+	0.289965i	$0.906356\pi$
$32$		0			0
$33$	−1.29325	−	3.98022i	−0.225126	−	0.692867i
$34$		0			0
$35$	−2.43421	+	1.76856i	−0.411457	+	0.298941i
$36$		0			0
$37$	−0.744317	+	2.29077i	−0.122365	+	0.376601i	−0.993412	−	0.114599i	$-0.963442\pi$
$37$	−0.744317	+	2.29077i	−0.122365	+	0.376601i	0.871047	+	0.491200i	$0.163442\pi$
$38$		0			0
$39$	−7.72729	+	5.61420i	−1.23736	+	0.898992i
$40$		0			0
$41$	6.33807	+	0.910393i	0.989841	+	0.142180i
$41$	6.33807	+	0.910393i	0.989841	+	0.142180i
$42$		0			0
$43$	−3.24257	+	2.35586i	−0.494487	+	0.359266i	−0.806907	−	0.590678i	$-0.798860\pi$
$43$	−3.24257	+	2.35586i	−0.494487	+	0.359266i	0.312421	+	0.949944i	$0.398860\pi$
$44$		0			0
$45$	−0.653845	+	2.01233i	−0.0974695	+	0.299980i
$46$		0			0
$47$	0.527699	−	0.383396i	0.0769728	−	0.0559240i	−0.548633	−	0.836063i	$-0.684852\pi$
$47$	0.527699	−	0.383396i	0.0769728	−	0.0559240i	0.625606	+	0.780139i	$0.284852\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	−2.52419	−	7.76867i	−0.353458	−	1.08783i
$52$		0			0
$53$	−1.68630	+	5.18990i	−0.231631	+	0.712888i	0.765919	+	0.642937i	$0.222284\pi$
$53$	−1.68630	+	5.18990i	−0.231631	+	0.712888i	−0.997550	+	0.0699509i	$0.977716\pi$
$54$		0			0
$55$	−8.30886			−1.12037
$56$		0			0
$57$	0.175870	+	0.127777i	0.0232945	+	0.0169244i
$58$		0			0
$59$	1.54818	−	1.12482i	0.201556	−	0.146439i	−0.482429	−	0.875935i	$-0.660245\pi$
$59$	1.54818	−	1.12482i	0.201556	−	0.146439i	0.683985	+	0.729496i	$0.260245\pi$
$60$		0			0
$61$	−0.168309	−	0.122284i	−0.0215498	−	0.0156569i	0.576958	−	0.816774i	$-0.304240\pi$
$61$	−0.168309	−	0.122284i	−0.0215498	−	0.0156569i	−0.598508	+	0.801117i	$0.704240\pi$
$62$		0			0
$63$	0.568918	+	0.413343i	0.0716769	+	0.0520763i
$64$		0			0
$65$	5.85994	+	18.0350i	0.726836	+	2.23697i
$66$		0			0
$67$	−0.547611	+	1.68537i	−0.0669013	+	0.205901i	−0.978919	−	0.204251i	$-0.934524\pi$
$67$	−0.547611	+	1.68537i	−0.0669013	+	0.205901i	0.912017	+	0.410152i	$0.134524\pi$
$68$		0			0
$69$	9.07200	−	6.59119i	1.09214	−	0.793486i
$70$		0			0
$71$	−4.31812	−	13.2898i	−0.512466	−	1.57721i	−0.787845	−	0.615873i	$-0.788803\pi$
$71$	−4.31812	−	13.2898i	−0.512466	−	1.57721i	0.275379	−	0.961336i	$-0.411197\pi$
$72$		0			0
$73$	10.5732			1.23750			0.618751	−	0.785587i	$-0.287639\pi$
$73$	10.5732			1.23750			0.618751	+	0.785587i	$0.287639\pi$
$74$		0			0
$75$	−4.96950	−	3.61056i	−0.573829	−	0.416911i
$76$		0			0
$77$	−0.853343	+	2.62632i	−0.0972474	+	0.299297i
$78$		0			0
$79$	−2.49453			−0.280656			−0.140328	−	0.990105i	$-0.544816\pi$
$79$	−2.49453			−0.280656			−0.140328	+	0.990105i	$0.544816\pi$
$80$		0			0
$81$	−6.39582			−0.710646
$82$		0			0
$83$	−4.79122			−0.525905			−0.262952	−	0.964809i	$-0.584696\pi$
$83$	−4.79122			−0.525905			−0.262952	+	0.964809i	$0.584696\pi$
$84$		0			0
$85$	−16.2174			−1.75902
$86$		0			0
$87$	3.28952	−	10.1241i	0.352673	−	1.08542i
$88$		0			0
$89$	0.0253670	+	0.0184302i	0.00268889	+	0.00195360i	0.589129	−	0.808039i	$-0.299471\pi$
$89$	0.0253670	+	0.0184302i	0.00268889	+	0.00195360i	−0.586440	+	0.809993i	$0.699471\pi$
$90$		0			0
$91$	6.30246			0.660677
$92$		0			0
$93$	−0.104133	−	0.320487i	−0.0107981	−	0.0332330i
$94$		0			0
$95$	0.349166	−	0.253684i	0.0358237	−	0.0260274i
$96$		0			0
$97$	3.12354	−	9.61328i	0.317148	−	0.976080i	−0.657714	−	0.753268i	$-0.728476\pi$
$97$	3.12354	−	9.61328i	0.317148	−	0.976080i	0.974861	−	0.222812i	$-0.0715237\pi$
$98$		0			0
$99$	0.600089	+	1.84688i	0.0603112	+	0.185619i
$100$		0			0
$101$	14.6367	+	10.6342i	1.45641	+	1.05814i	0.984280	+	0.176615i	$0.0565148\pi$
$101$	14.6367	+	10.6342i	1.45641	+	1.05814i	0.472130	+	0.881529i	$0.343485\pi$
$102$		0			0
$103$	13.0026	+	9.44692i	1.28118	+	0.930833i	0.999588	−	0.0287011i	$-0.00913709\pi$
$103$	13.0026	+	9.44692i	1.28118	+	0.930833i	0.281593	+	0.959534i	$0.409137\pi$
$104$		0			0
$105$	−3.68908	+	2.68027i	−0.360017	+	0.261568i
$106$		0			0
$107$	3.54649	+	2.57667i	0.342852	+	0.249096i	0.745864	−	0.666098i	$-0.232037\pi$
$107$	3.54649	+	2.57667i	0.342852	+	0.249096i	−0.403012	+	0.915195i	$0.632037\pi$
$108$		0			0
$109$	11.7224			1.12280			0.561402	−	0.827543i	$-0.310262\pi$
$109$	11.7224			1.12280			0.561402	+	0.827543i	$0.310262\pi$
$110$		0			0
$111$	−1.12802	+	3.47170i	−0.107067	+	0.329519i
$112$		0			0
$113$	−4.66060	−	14.3438i	−0.438432	−	1.34936i	−0.889528	−	0.456880i	$-0.848967\pi$
$113$	−4.66060	−	14.3438i	−0.438432	−	1.34936i	0.451096	−	0.892475i	$-0.351033\pi$
$114$		0			0
$115$	−6.87969	−	21.1735i	−0.641534	−	1.97444i
$116$		0			0
$117$	3.58558	−	2.60508i	0.331487	−	0.240839i
$118$		0			0
$119$	−1.66557	+	5.12610i	−0.152683	+	0.469909i
$120$		0			0
$121$	2.72983	−	1.98334i	0.248166	−	0.180303i
$122$		0			0
$123$	9.60543	+	1.37971i	0.866093	+	0.124405i
$124$		0			0
$125$	2.30476	−	1.67451i	0.206144	−	0.149773i
$126$		0			0
$127$	−1.52421	+	4.69102i	−0.135251	+	0.416261i	−0.995629	−	0.0933962i	$-0.970228\pi$
$127$	−1.52421	+	4.69102i	−0.135251	+	0.416261i	0.860378	+	0.509657i	$0.170228\pi$
$128$		0			0
$129$	−4.91415	+	3.57034i	−0.432667	+	0.314351i
$130$		0			0
$131$	−2.85131	−	8.77543i	−0.249120	−	0.766713i	−0.994931	−	0.100556i	$-0.967938\pi$
$131$	−2.85131	−	8.77543i	−0.249120	−	0.766713i	0.745811	−	0.666157i	$-0.232062\pi$
$132$		0			0
$133$	−0.0443257	−	0.136421i	−0.00384353	−	0.0118292i
$134$		0			0
$135$	−5.21822	+	16.0600i	−0.449113	+	1.38223i
$136$		0			0
$137$	−6.09557			−0.520779			−0.260390	−	0.965504i	$-0.583851\pi$
$137$	−6.09557			−0.520779			−0.260390	+	0.965504i	$0.583851\pi$
$138$		0			0
$139$	4.98760	+	3.62370i	0.423042	+	0.307358i	0.778861	−	0.627197i	$-0.215798\pi$
$139$	4.98760	+	3.62370i	0.423042	+	0.307358i	−0.355818	+	0.934555i	$0.615798\pi$
$140$		0			0
$141$	0.799735	−	0.581041i	0.0673498	−	0.0489325i
$142$		0			0
$143$	14.0802	+	10.2299i	1.17745	+	0.855464i
$144$		0			0
$145$	−17.0981	−	12.4225i	−1.41992	−	1.03163i
$146$		0			0
$147$	0.468319	+	1.44134i	0.0386263	+	0.118880i
$148$		0			0
$149$	−3.40642	+	10.4839i	−0.279064	+	0.858872i	0.709051	+	0.705157i	$0.249124\pi$
$149$	−3.40642	+	10.4839i	−0.279064	+	0.858872i	−0.988115	+	0.153715i	$0.950876\pi$
$150$		0			0
$151$	3.18028	−	2.31061i	0.258808	−	0.188035i	−0.450813	−	0.892618i	$-0.648866\pi$
$151$	3.18028	−	2.31061i	0.258808	−	0.188035i	0.709621	+	0.704583i	$0.248866\pi$
$152$		0			0
$153$	1.17126	+	3.60478i	0.0946912	+	0.291429i
$154$		0			0
$155$	−0.669030			−0.0537378
$156$		0			0
$157$	3.86434	+	2.80761i	0.308408	+	0.224072i	0.731213	−	0.682149i	$-0.238954\pi$
$157$	3.86434	+	2.80761i	0.308408	+	0.224072i	−0.422805	+	0.906221i	$0.638954\pi$
$158$		0			0
$159$	−2.55561	+	7.86536i	−0.202673	+	0.623764i
$160$		0			0
$161$	−7.39922			−0.583140
$162$		0			0
$163$	−2.63168			−0.206129			−0.103065	−	0.994675i	$-0.532865\pi$
$163$	−2.63168			−0.206129			−0.103065	+	0.994675i	$0.532865\pi$
$164$		0			0
$165$	−12.5922			−0.980301
$166$		0			0
$167$	−6.60494			−0.511105			−0.255553	−	0.966795i	$-0.582257\pi$
$167$	−6.60494			−0.511105			−0.255553	+	0.966795i	$0.582257\pi$
$168$		0			0
$169$	8.25723	−	25.4132i	0.635172	−	1.95486i
$170$		0			0
$171$	−0.0816062	−	0.0592904i	−0.00624058	−	0.00453405i
$172$		0			0
$173$	22.3252			1.69735			0.848677	−	0.528912i	$-0.177400\pi$
$173$	22.3252			1.69735			0.848677	+	0.528912i	$0.177400\pi$
$174$		0			0
$175$	1.25250	+	3.85480i	0.0946802	+	0.291396i
$176$		0			0
$177$	2.34629	−	1.70468i	0.176358	−	0.128131i
$178$		0			0
$179$	6.70550	−	20.6374i	0.501192	−	1.54251i	−0.305887	−	0.952068i	$-0.598953\pi$
$179$	6.70550	−	20.6374i	0.501192	−	1.54251i	0.807079	−	0.590444i	$-0.201047\pi$
$180$		0			0
$181$	−0.123948	−	0.381472i	−0.00921297	−	0.0283546i	0.946344	−	0.323160i	$-0.104745\pi$
$181$	−0.123948	−	0.381472i	−0.00921297	−	0.0283546i	−0.955557	+	0.294805i	$0.904745\pi$
$182$		0			0
$183$	−0.255075	−	0.185323i	−0.0188557	−	0.0136995i
$184$		0			0
$185$	5.86319	+	4.25986i	0.431070	+	0.313191i
$186$		0			0
$187$	−12.0415	+	8.74864i	−0.880560	+	0.639764i
$188$		0			0
$189$	4.54043	+	3.29881i	0.330268	+	0.239953i
$190$		0			0
$191$	−23.6473			−1.71106			−0.855529	−	0.517756i	$-0.826768\pi$
$191$	−23.6473			−1.71106			−0.855529	+	0.517756i	$0.826768\pi$
$192$		0			0
$193$	1.07665	−	3.31359i	0.0774991	−	0.238518i	−0.904800	−	0.425837i	$-0.859980\pi$
$193$	1.07665	−	3.31359i	0.0774991	−	0.238518i	0.982299	+	0.187319i	$0.0599798\pi$
$194$		0			0
$195$	8.88081	+	27.3323i	0.635968	+	1.95731i
$196$		0			0
$197$	1.32870	+	4.08933i	0.0946662	+	0.291352i	0.987167	−	0.159694i	$-0.0510508\pi$
$197$	1.32870	+	4.08933i	0.0946662	+	0.291352i	−0.892500	+	0.451047i	$0.851051\pi$
$198$		0			0
$199$	−20.0994	+	14.6031i	−1.42481	+	1.03518i	−0.433853	+	0.900984i	$0.642846\pi$
$199$	−20.0994	+	14.6031i	−1.42481	+	1.03518i	−0.990954	+	0.134199i	$0.957154\pi$
$200$		0			0
$201$	−0.829911	+	2.55420i	−0.0585374	+	0.180160i
$202$		0			0
$203$	−5.68261	+	4.12866i	−0.398841	+	0.289775i
$204$		0			0
$205$	8.49822	−	17.2905i	0.593541	−	1.20762i
$206$		0			0
$207$	−4.20955	+	3.05841i	−0.292584	+	0.212575i
$208$		0			0
$209$	0.122404	−	0.376722i	0.00846689	−	0.0260584i
$210$		0			0
$211$	18.5073	−	13.4463i	1.27409	−	0.925684i	0.274737	−	0.961520i	$-0.411409\pi$
$211$	18.5073	−	13.4463i	1.27409	−	0.925684i	0.999358	+	0.0358359i	$0.0114094\pi$
$212$		0			0
$213$	−6.54416	−	20.1409i	−0.448399	−	1.38003i
$214$		0			0
$215$	3.72661	+	11.4693i	0.254153	+	0.782202i
$216$		0			0
$217$	−0.0687112	+	0.211471i	−0.00466442	+	0.0143556i
$218$		0			0
$219$	16.0239			1.08279
$220$		0			0
$221$	27.4820	+	19.9668i	1.84864	+	1.34312i
$222$		0			0
$223$	−13.0205	+	9.45997i	−0.871919	+	0.633486i	−0.931101	−	0.364761i	$-0.881151\pi$
$223$	−13.0205	+	9.45997i	−0.871919	+	0.633486i	0.0591820	+	0.998247i	$0.481151\pi$
$224$		0			0
$225$	2.30593	+	1.67535i	0.153728	+	0.111690i
$226$		0			0
$227$	−10.0699	−	7.31622i	−0.668363	−	0.485594i	0.201114	−	0.979568i	$-0.435544\pi$
$227$	−10.0699	−	7.31622i	−0.668363	−	0.485594i	−0.869477	+	0.493974i	$0.835544\pi$
$228$		0			0
$229$	4.30567	+	13.2515i	0.284526	+	0.875682i	0.986540	+	0.163519i	$0.0522845\pi$
$229$	4.30567	+	13.2515i	0.284526	+	0.875682i	−0.702014	+	0.712163i	$0.747716\pi$
$230$		0			0
$231$	−1.29325	+	3.98022i	−0.0850897	+	0.261879i
$232$		0			0
$233$	−19.4534	+	14.1337i	−1.27444	+	0.925932i	−0.999370	−	0.0354934i	$-0.988700\pi$
$233$	−19.4534	+	14.1337i	−1.27444	+	0.925932i	−0.275066	+	0.961425i	$0.588700\pi$
$234$		0			0
$235$	−0.606473	−	1.86653i	−0.0395620	−	0.121759i
$236$		0			0
$237$	−3.78049			−0.245569
$238$		0			0
$239$	8.47700	+	6.15890i	0.548332	+	0.398386i	0.827170	−	0.561952i	$-0.189949\pi$
$239$	8.47700	+	6.15890i	0.548332	+	0.398386i	−0.278838	+	0.960338i	$0.589949\pi$
$240$		0			0
$241$	−1.56288	+	4.81005i	−0.100674	+	0.309842i	−0.988691	−	0.149968i	$-0.952083\pi$
$241$	−1.56288	+	4.81005i	−0.100674	+	0.309842i	0.888017	+	0.459811i	$0.152083\pi$
$242$		0			0
$243$	7.14390			0.458281
$244$		0			0
$245$	3.00885			0.192228
$246$		0			0
$247$	−0.904032			−0.0575222
$248$		0			0
$249$	−7.26115			−0.460157
$250$		0			0
$251$	−4.62450	+	14.2328i	−0.291896	+	0.898363i	0.692351	+	0.721561i	$0.256575\pi$
$251$	−4.62450	+	14.2328i	−0.291896	+	0.898363i	−0.984246	+	0.176802i	$0.943425\pi$
$252$		0			0
$253$	−16.5304	−	12.0101i	−1.03926	−	0.755067i
$254$		0			0
$255$	−24.5777			−1.53911
$256$		0			0
$257$	−2.39970	−	7.38551i	−0.149689	−	0.460696i	0.847895	−	0.530164i	$-0.177870\pi$
$257$	−2.39970	−	7.38551i	−0.149689	−	0.460696i	−0.997584	+	0.0694684i	$0.977870\pi$
$258$		0			0
$259$	1.94865	−	1.41578i	0.121083	−	0.0879720i
$260$		0			0
$261$	−1.52639	+	4.69773i	−0.0944809	+	0.290782i
$262$		0			0
$263$	3.67372	+	11.3066i	0.226532	+	0.697192i	0.998133	+	0.0610856i	$0.0194563\pi$
$263$	3.67372	+	11.3066i	0.226532	+	0.697192i	−0.771601	+	0.636107i	$0.780544\pi$
$264$		0			0
$265$	13.2835	+	9.65099i	0.815996	+	0.592856i
$266$		0			0
$267$	0.0384440	+	0.0279312i	0.00235273	+	0.00170936i
$268$		0			0
$269$	4.64429	−	3.37427i	0.283167	−	0.205733i	−0.437130	−	0.899398i	$-0.644005\pi$
$269$	4.64429	−	3.37427i	0.283167	−	0.205733i	0.720298	+	0.693665i	$0.244005\pi$
$270$		0			0
$271$	14.6453	+	10.6404i	0.889637	+	0.646359i	0.935783	−	0.352576i	$-0.114694\pi$
$271$	14.6453	+	10.6404i	0.889637	+	0.646359i	−0.0461464	+	0.998935i	$0.514694\pi$
$272$		0			0
$273$	9.55145			0.578080
$274$		0			0
$275$	−3.45875	+	10.6449i	−0.208570	+	0.641914i
$276$		0			0
$277$	0.684362	+	2.10625i	0.0411194	+	0.126552i	0.969509	−	0.245056i	$-0.0788064\pi$
$277$	0.684362	+	2.10625i	0.0411194	+	0.126552i	−0.928390	+	0.371608i	$0.878806\pi$
$278$		0			0
$279$	0.0483192	+	0.148711i	0.00289279	+	0.00890310i
$280$		0			0
$281$	20.2360	−	14.7023i	1.20718	−	0.877067i	0.212207	−	0.977225i	$-0.431935\pi$
$281$	20.2360	−	14.7023i	1.20718	−	0.877067i	0.994972	+	0.100158i	$0.0319349\pi$
$282$		0			0
$283$	−0.516000	+	1.58809i	−0.0306730	+	0.0944019i	−0.965221	−	0.261435i	$-0.915804\pi$
$283$	−0.516000	+	1.58809i	−0.0306730	+	0.0944019i	0.934548	+	0.355837i	$0.115804\pi$
$284$		0			0
$285$	0.529165	−	0.384461i	0.0313451	−	0.0227735i
$286$		0			0
$287$	−4.59249	−	4.46195i	−0.271086	−	0.263381i
$288$		0			0
$289$	−9.74949	+	7.08342i	−0.573500	+	0.416672i
$290$		0			0
$291$	4.73377	−	14.5690i	0.277498	−	0.854052i
$292$		0			0
$293$	9.52788	−	6.92241i	0.556625	−	0.404412i	−0.273597	−	0.961844i	$-0.588214\pi$
$293$	9.52788	−	6.92241i	0.556625	−	0.404412i	0.830222	+	0.557433i	$0.188214\pi$
$294$		0			0
$295$	−1.77929	−	5.47609i	−0.103594	−	0.318830i
$296$		0			0
$297$	4.78920	+	14.7396i	0.277897	+	0.855280i
$298$		0			0
$299$	−14.4105	+	44.3509i	−0.833379	+	2.56488i
$300$		0			0
$301$	4.00803			0.231019
$302$		0			0
$303$	22.1822	+	16.1163i	1.27433	+	0.925857i
$304$		0			0
$305$	−0.506418	+	0.367934i	−0.0289974	+	0.0210678i
$306$		0			0
$307$	−25.5520	−	18.5646i	−1.45833	−	1.05954i	−0.983795	−	0.179299i	$-0.942617\pi$
$307$	−25.5520	−	18.5646i	−1.45833	−	1.05954i	−0.474533	−	0.880238i	$-0.657383\pi$
$308$		0			0
$309$	19.7056	+	14.3169i	1.12101	+	0.814462i
$310$		0			0
$311$	−3.28869	−	10.1215i	−0.186485	−	0.573940i	0.813486	−	0.581584i	$-0.197567\pi$
$311$	−3.28869	−	10.1215i	−0.186485	−	0.573940i	−0.999971	+	0.00764373i	$0.997567\pi$
$312$		0			0
$313$	1.34254	−	4.13192i	0.0758850	−	0.233550i	−0.905918	−	0.423454i	$-0.860818\pi$
$313$	1.34254	−	4.13192i	0.0758850	−	0.233550i	0.981803	+	0.189904i	$0.0608176\pi$
$314$		0			0
$315$	1.71179	−	1.24369i	0.0964484	−	0.0700738i
$316$		0			0
$317$	6.29871	+	19.3854i	0.353771	+	1.08879i	0.956719	+	0.291014i	$0.0939925\pi$
$317$	6.29871	+	19.3854i	0.353771	+	1.08879i	−0.602948	+	0.797780i	$0.706007\pi$
$318$		0			0
$319$	−19.3968			−1.08601
$320$		0			0
$321$	5.37474	+	3.90498i	0.299989	+	0.217955i
$322$		0			0
$323$	0.238911	−	0.735294i	0.0132934	−	0.0409128i
$324$		0			0
$325$	25.5450			1.41698
$326$		0			0
$327$	17.7655			0.982433
$328$		0			0
$329$	−0.652272			−0.0359609
$330$		0			0
$331$	−0.121834			−0.00669660			−0.00334830	−	0.999994i	$-0.501066\pi$
$331$	−0.121834			−0.00669660			−0.00334830	+	0.999994i	$0.501066\pi$
$332$		0			0
$333$	0.523420	−	1.61092i	0.0286832	−	0.0882779i
$334$		0			0
$335$	4.31368	+	3.13407i	0.235681	+	0.171233i
$336$		0			0
$337$	34.9572			1.90424			0.952119	−	0.305728i	$-0.0989000\pi$
$337$	34.9572			1.90424			0.952119	+	0.305728i	$0.0989000\pi$
$338$		0			0
$339$	−7.06319	−	21.7383i	−0.383620	−	1.18066i
$340$		0			0
$341$	−0.496757	+	0.360915i	−0.0269009	+	0.0195446i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	−10.4263	−	32.0887i	−0.561331	−	1.72760i
$346$		0			0
$347$	8.58988	+	6.24091i	0.461129	+	0.335030i	0.793974	−	0.607952i	$-0.208009\pi$
$347$	8.58988	+	6.24091i	0.461129	+	0.335030i	−0.332845	+	0.942981i	$0.608009\pi$
$348$		0			0
$349$	27.5319	+	20.0031i	1.47375	+	1.07074i	0.979505	+	0.201419i	$0.0645554\pi$
$349$	27.5319	+	20.0031i	1.47375	+	1.07074i	0.494245	+	0.869323i	$0.335445\pi$
$350$		0			0
$351$	28.6159	−	20.7906i	1.52740	−	1.10972i
$352$		0			0
$353$	−2.86165	−	2.07911i	−0.152310	−	0.110660i	0.509020	−	0.860755i	$-0.330008\pi$
$353$	−2.86165	−	2.07911i	−0.152310	−	0.110660i	−0.661330	+	0.750095i	$0.730008\pi$
$354$		0			0
$355$	−42.0448			−2.23151
$356$		0			0
$357$	−2.52419	+	7.76867i	−0.133595	+	0.411162i
$358$		0			0
$359$	−2.65459	−	8.16998i	−0.140104	−	0.431195i	0.856245	−	0.516570i	$-0.172791\pi$
$359$	−2.65459	−	8.16998i	−0.140104	−	0.431195i	−0.996349	+	0.0853745i	$0.972791\pi$
$360$		0			0
$361$	−5.86496	−	18.0505i	−0.308682	−	0.950027i
$362$		0			0
$363$	4.13709	−	3.00577i	0.217141	−	0.157762i
$364$		0			0
$365$	9.83084	−	30.2562i	0.514569	−	1.58368i
$366$		0			0
$367$	13.7842	−	10.0148i	0.719532	−	0.522770i	−0.166703	−	0.986007i	$-0.553312\pi$
$367$	13.7842	−	10.0148i	0.719532	−	0.522770i	0.886235	+	0.463237i	$0.153312\pi$
$368$		0			0
$369$	−4.45707	−	0.640208i	−0.232026	−	0.0333279i
$370$		0			0
$371$	4.41479	−	3.20754i	0.229205	−	0.166527i
$372$		0			0
$373$	−0.949175	+	2.92126i	−0.0491464	+	0.151257i	−0.972618	−	0.232410i	$-0.925339\pi$
$373$	−0.949175	+	2.92126i	−0.0491464	+	0.151257i	0.923472	+	0.383667i	$0.125339\pi$
$374$		0			0
$375$	3.49290	−	2.53774i	0.180373	−	0.131048i
$376$		0			0
$377$	13.6799	+	42.1023i	0.704550	+	2.16838i
$378$		0			0
$379$	−1.56174	−	4.80655i	−0.0802213	−	0.246896i	0.902900	−	0.429851i	$-0.141434\pi$
$379$	−1.56174	−	4.80655i	−0.0802213	−	0.246896i	−0.983121	+	0.182955i	$0.941434\pi$
$380$		0			0
$381$	−2.30995	+	7.10930i	−0.118342	+	0.364221i
$382$		0			0
$383$	−8.06620			−0.412164			−0.206082	−	0.978535i	$-0.566071\pi$
$383$	−8.06620			−0.412164			−0.206082	+	0.978535i	$0.566071\pi$
$384$		0			0
$385$	6.72201	+	4.88383i	0.342585	+	0.248903i
$386$		0			0
$387$	2.28024	−	1.65669i	0.115911	−	0.0842144i
$388$		0			0
$389$	5.60230	+	4.07031i	0.284048	+	0.206373i	0.720681	−	0.693267i	$-0.243829\pi$
$389$	5.60230	+	4.07031i	0.284048	+	0.206373i	−0.436633	+	0.899640i	$0.643829\pi$
$390$		0			0
$391$	−32.2644	−	23.4415i	−1.63168	−	1.18549i
$392$		0			0
$393$	−4.32120	−	13.2993i	−0.217976	−	0.670860i
$394$		0			0
$395$	−2.31937	+	7.13830i	−0.116700	+	0.359167i
$396$		0			0
$397$	−4.41734	+	3.20939i	−0.221700	+	0.161074i	−0.693092	−	0.720850i	$-0.743752\pi$
$397$	−4.41734	+	3.20939i	−0.221700	+	0.161074i	0.471392	+	0.881924i	$0.343752\pi$
$398$		0			0
$399$	−0.0671762	−	0.206747i	−0.00336302	−	0.0103503i
$400$		0			0
$401$	2.25332			0.112525			0.0562627	−	0.998416i	$-0.482082\pi$
$401$	2.25332			0.112525			0.0562627	+	0.998416i	$0.482082\pi$
$402$		0			0
$403$	1.13374	+	0.823709i	0.0564755	+	0.0410319i
$404$		0			0
$405$	−5.94674	+	18.3022i	−0.295496	+	0.909443i
$406$		0			0
$407$	6.65146			0.329701
$408$		0			0
$409$	−37.9717			−1.87758			−0.938790	−	0.344489i	$-0.888052\pi$
$409$	−37.9717			−1.87758			−0.938790	+	0.344489i	$0.888052\pi$
$410$		0			0
$411$	−9.23791			−0.455672
$412$		0			0
$413$	−1.91366			−0.0941648
$414$		0			0
$415$	−4.45481	+	13.7105i	−0.218678	+	0.673021i
$416$		0			0
$417$	7.55877	+	5.49176i	0.370154	+	0.268933i
$418$		0			0
$419$	14.2657			0.696926			0.348463	−	0.937323i	$-0.386704\pi$
$419$	14.2657			0.696926			0.348463	+	0.937323i	$0.386704\pi$
$420$		0			0
$421$	−5.45696	−	16.7948i	−0.265956	−	0.818529i	−0.991472	−	0.130323i	$-0.958399\pi$
$421$	−5.45696	−	16.7948i	−0.265956	−	0.818529i	0.725515	−	0.688206i	$-0.241601\pi$
$422$		0			0
$423$	−0.371089	+	0.269612i	−0.0180430	+	0.0131090i
$424$		0			0
$425$	−6.75086	+	20.7770i	−0.327465	+	1.00783i
$426$		0			0
$427$	0.0642885	+	0.197860i	0.00311114	+	0.00957509i
$428$		0			0
$429$	21.3387	+	15.5035i	1.03024	+	0.748515i
$430$		0			0
$431$	−5.19955	−	3.77769i	−0.250454	−	0.181965i	0.455474	−	0.890249i	$-0.349470\pi$
$431$	−5.19955	−	3.77769i	−0.250454	−	0.181965i	−0.705928	+	0.708284i	$0.749470\pi$
$432$		0			0
$433$	−14.0684	+	10.2213i	−0.676084	+	0.491204i	−0.872056	−	0.489406i	$-0.837214\pi$
$433$	−14.0684	+	10.2213i	−0.676084	+	0.491204i	0.195972	+	0.980609i	$0.437214\pi$
$434$		0			0
$435$	−25.9124	−	18.8265i	−1.24240	−	0.902660i
$436$		0			0
$437$	1.06135			0.0507714
$438$		0			0
$439$	−7.46912	+	22.9876i	−0.356482	+	1.09714i	0.598663	+	0.801001i	$0.295699\pi$
$439$	−7.46912	+	22.9876i	−0.356482	+	1.09714i	−0.955145	+	0.296138i	$0.904301\pi$
$440$		0			0
$441$	−0.217307	−	0.668803i	−0.0103480	−	0.0318478i
$442$		0			0
$443$	3.32341	+	10.2284i	0.157900	+	0.485967i	0.998443	−	0.0557781i	$-0.0177639\pi$
$443$	3.32341	+	10.2284i	0.157900	+	0.485967i	−0.840543	+	0.541745i	$0.817764\pi$
$444$		0			0
$445$	0.0763254	−	0.0554537i	0.00361817	−	0.00262876i
$446$		0			0
$447$	−5.16247	+	15.8884i	−0.244176	+	0.751497i
$448$		0			0
$449$	−24.6721	+	17.9253i	−1.16435	+	0.845949i	−0.990322	−	0.138792i	$-0.955678\pi$
$449$	−24.6721	+	17.9253i	−1.16435	+	0.845949i	−0.174027	+	0.984741i	$0.555678\pi$
$450$		0			0
$451$	−3.01757	−	17.4227i	−0.142092	−	0.820402i
$452$		0			0
$453$	4.81976	−	3.50176i	0.226452	−	0.164527i
$454$		0			0
$455$	5.85994	−	18.0350i	0.274718	−	0.845495i
$456$		0			0
$457$	29.1764	−	21.1979i	1.36482	−	0.991597i	0.366695	−	0.930341i	$-0.380489\pi$
$457$	29.1764	−	21.1979i	1.36482	−	0.991597i	0.998122	−	0.0612560i	$-0.0195106\pi$
$458$		0			0
$459$	9.34765	+	28.7691i	0.436311	+	1.34283i
$460$		0			0
$461$	10.8874	+	33.5079i	0.507076	+	1.56062i	0.797253	+	0.603646i	$0.206286\pi$
$461$	10.8874	+	33.5079i	0.507076	+	1.56062i	−0.290177	+	0.956973i	$0.593714\pi$
$462$		0			0
$463$	−5.82861	+	17.9386i	−0.270878	+	0.833678i	0.719402	+	0.694594i	$0.244416\pi$
$463$	−5.82861	+	17.9386i	−0.270878	+	0.833678i	−0.990281	+	0.139084i	$0.955584\pi$
$464$		0			0
$465$	−1.01392			−0.0470196
$466$		0			0
$467$	3.76124	+	2.73270i	0.174049	+	0.126454i	0.671399	−	0.741096i	$-0.265694\pi$
$467$	3.76124	+	2.73270i	0.174049	+	0.126454i	−0.497350	+	0.867550i	$0.665694\pi$
$468$		0			0
$469$	1.43366	−	1.04162i	0.0662004	−	0.0480974i
$470$		0			0
$471$	5.85646	+	4.25497i	0.269852	+	0.196059i
$472$		0			0
$473$	8.95426	+	6.50565i	0.411717	+	0.299130i
$474$		0			0
$475$	−0.179660	−	0.552937i	−0.00824337	−	0.0253705i
$476$		0			0
$477$	1.18584	−	3.64965i	0.0542960	−	0.167106i
$478$		0			0
$479$	−34.5781	+	25.1224i	−1.57991	+	1.14787i	−0.663116	+	0.748517i	$0.730766\pi$
$479$	−34.5781	+	25.1224i	−1.57991	+	1.14787i	−0.916796	+	0.399356i	$0.869234\pi$
$480$		0			0
$481$	−4.69103	−	14.4375i	−0.213892	−	0.658293i
$482$		0			0
$483$	−11.2136			−0.510237
$484$		0			0
$485$	−24.6050	−	17.8766i	−1.11726	−	0.811734i
$486$		0			0
$487$	11.3911	−	35.0582i	0.516180	−	1.58864i	−0.264945	−	0.964264i	$-0.585354\pi$
$487$	11.3911	−	35.0582i	0.516180	−	1.58864i	0.781125	−	0.624375i	$-0.214646\pi$
$488$		0			0
$489$	−3.98835			−0.180359
$490$		0			0
$491$	−37.3376			−1.68502			−0.842512	−	0.538678i	$-0.818924\pi$
$491$	−37.3376			−1.68502			−0.842512	+	0.538678i	$0.818924\pi$
$492$		0			0
$493$	−37.8591			−1.70509
$494$		0			0
$495$	5.84297			0.262622
$496$		0			0
$497$	−4.31812	+	13.2898i	−0.193694	+	0.596129i
$498$		0			0
$499$	−14.2618	−	10.3618i	−0.638444	−	0.463857i	0.220871	−	0.975303i	$-0.429110\pi$
$499$	−14.2618	−	10.3618i	−0.638444	−	0.463857i	−0.859315	+	0.511446i	$0.829110\pi$
$500$		0			0
$501$	−10.0099			−0.447208
$502$		0			0
$503$	−10.8064	−	33.2587i	−0.481834	−	1.48293i	−0.836514	−	0.547946i	$-0.815410\pi$
$503$	−10.8064	−	33.2587i	−0.481834	−	1.48293i	0.354679	−	0.934988i	$-0.384590\pi$
$504$		0			0
$505$	44.0398	−	31.9968i	1.95974	−	1.42384i
$506$		0			0
$507$	12.5139	−	38.5140i	0.555764	−	1.71046i
$508$		0			0
$509$	3.23270	+	9.94924i	0.143287	+	0.440992i	0.996787	−	0.0801011i	$-0.0255243\pi$
$509$	3.23270	+	9.94924i	0.143287	+	0.440992i	−0.853500	+	0.521093i	$0.825524\pi$
$510$		0			0
$511$	−8.55392	−	6.21479i	−0.378403	−	0.274926i
$512$		0			0
$513$	−0.651284	−	0.473186i	−0.0287549	−	0.0208917i
$514$		0			0
$515$	39.1228	−	28.4244i	1.72396	−	1.25253i
$516$		0			0
$517$	−1.45723	−	1.05874i	−0.0640888	−	0.0465633i
$518$		0			0
$519$	33.8341			1.48515
$520$		0			0
$521$	10.5896	−	32.5915i	0.463940	−	1.42786i	−0.396371	−	0.918090i	$-0.629731\pi$
$521$	10.5896	−	32.5915i	0.463940	−	1.42786i	0.860311	−	0.509770i	$-0.170269\pi$
$522$		0			0
$523$	11.1001	+	34.1626i	0.485373	+	1.49383i	0.831440	+	0.555615i	$0.187517\pi$
$523$	11.1001	+	34.1626i	0.485373	+	1.49383i	−0.346066	+	0.938210i	$0.612483\pi$
$524$		0			0
$525$	1.89818	+	5.84200i	0.0828434	+	0.254966i
$526$		0			0
$527$	−0.969580	+	0.704441i	−0.0422356	+	0.0306859i
$528$		0			0
$529$	9.81080	−	30.1945i	0.426556	−	1.31281i
$530$		0			0
$531$	−1.08871	+	0.790996i	−0.0472461	+	0.0343263i
$532$		0			0
$533$	−35.6891	+	18.8374i	−1.54587	+	0.815940i
$534$		0			0
$535$	10.6708	−	7.75282i	0.461341	−	0.335184i
$536$		0			0
$537$	10.1623	−	31.2762i	0.438534	−	1.34967i
$538$		0			0
$539$	2.23408	−	1.62315i	0.0962287	−	0.0699142i
$540$		0			0
$541$	−9.14087	−	28.1327i	−0.392997	−	1.20952i	−0.930511	−	0.366265i	$-0.880637\pi$
$541$	−9.14087	−	28.1327i	−0.392997	−	1.20952i	0.537514	−	0.843255i	$-0.319363\pi$
$542$		0			0
$543$	−0.187844	−	0.578126i	−0.00806118	−	0.0248097i
$544$		0			0
$545$	10.8993	−	33.5447i	0.466876	−	1.43690i
$546$		0			0
$547$	−29.4863			−1.26075			−0.630373	−	0.776293i	$-0.717098\pi$
$547$	−29.4863			−1.26075			−0.630373	+	0.776293i	$0.717098\pi$
$548$		0			0
$549$	0.118359	+	0.0859927i	0.00505143	+	0.00367008i
$550$		0			0
$551$	0.815120	−	0.592219i	0.0347253	−	0.0252294i
$552$		0			0
$553$	2.01811	+	1.46625i	0.0858189	+	0.0623511i
$554$		0			0
$555$	8.88574	+	6.45587i	0.377179	+	0.274036i
$556$		0			0
$557$	−11.1460	−	34.3039i	−0.472272	−	1.45350i	−0.849601	−	0.527425i	$-0.823157\pi$
$557$	−11.1460	−	34.3039i	−0.472272	−	1.45350i	0.377329	−	0.926079i	$-0.376843\pi$
$558$		0			0
$559$	7.80591	−	24.0241i	0.330155	−	1.01611i
$560$		0			0
$561$	−18.2490	+	13.2587i	−0.770474	+	0.559782i
$562$		0			0
$563$	0.304702	+	0.937776i	0.0128417	+	0.0395225i	0.957272	−	0.289189i	$-0.0933856\pi$
$563$	0.304702	+	0.937776i	0.0128417	+	0.0395225i	−0.944430	+	0.328712i	$0.893386\pi$
$564$		0			0
$565$	−45.3795			−1.90913
$566$		0			0
$567$	5.17432	+	3.75937i	0.217301	+	0.157879i
$568$		0			0
$569$	−13.0605	+	40.1960i	−0.547523	+	1.68510i	0.167390	+	0.985891i	$0.446466\pi$
$569$	−13.0605	+	40.1960i	−0.547523	+	1.68510i	−0.714913	+	0.699213i	$0.753534\pi$
$570$		0			0
$571$	−12.4557			−0.521257			−0.260628	−	0.965439i	$-0.583930\pi$
$571$	−12.4557			−0.521257			−0.260628	+	0.965439i	$0.583930\pi$
$572$		0			0
$573$	−35.8378			−1.49714
$574$		0			0
$575$	−29.9903			−1.25068
$576$		0			0
$577$	8.07534			0.336181			0.168090	−	0.985772i	$-0.446240\pi$
$577$	8.07534			0.336181			0.168090	+	0.985772i	$0.446240\pi$
$578$		0			0
$579$	1.63168	−	5.02179i	0.0678103	−	0.208699i
$580$		0			0
$581$	3.87618	+	2.81621i	0.160811	+	0.116836i
$582$		0			0
$583$	15.0693			0.624108
$584$		0			0
$585$	−4.12083	−	12.6826i	−0.170375	−	0.524362i
$586$		0			0
$587$	28.9873	−	21.0605i	1.19644	−	0.869261i	0.202506	−	0.979281i	$-0.435091\pi$
$587$	28.9873	−	21.0605i	1.19644	−	0.869261i	0.993929	+	0.110020i	$0.0350915\pi$
$588$		0			0
$589$	0.00985601	−	0.0303337i	0.000406110	−	0.00124988i
$590$		0			0
$591$	2.01367	+	6.19743i	0.0828311	+	0.254928i
$592$		0			0
$593$	−8.52382	−	6.19291i	−0.350031	−	0.254313i	0.398851	−	0.917016i	$-0.369409\pi$
$593$	−8.52382	−	6.19291i	−0.350031	−	0.254313i	−0.748882	+	0.662703i	$0.769409\pi$
$594$		0			0
$595$	13.1202	+	9.53235i	0.537874	+	0.390788i
$596$		0			0
$597$	−30.4609	+	22.1311i	−1.24668	+	0.905766i
$598$		0			0
$599$	−22.3437	−	16.2336i	−0.912937	−	0.663288i	0.0288187	−	0.999585i	$-0.490825\pi$
$599$	−22.3437	−	16.2336i	−0.912937	−	0.663288i	−0.941756	+	0.336297i	$0.890825\pi$
$600$		0			0
$601$	48.3159			1.97085			0.985423	−	0.170121i	$-0.0544157\pi$
$601$	48.3159			1.97085			0.985423	+	0.170121i	$0.0544157\pi$
$602$		0			0
$603$	0.385092	−	1.18519i	0.0156821	−	0.0482647i
$604$		0			0
$605$	−3.13733	−	9.65572i	−0.127551	−	0.392561i
$606$		0			0
$607$	5.21125	+	16.0386i	0.211518	+	0.650986i	0.999382	+	0.0351373i	$0.0111869\pi$
$607$	5.21125	+	16.0386i	0.211518	+	0.650986i	−0.787864	+	0.615849i	$0.788813\pi$
$608$		0			0
$609$	−8.61206	+	6.25703i	−0.348978	+	0.253548i
$610$		0			0
$611$	−1.27034	+	3.90971i	−0.0513926	+	0.158170i
$612$		0			0
$613$	−10.3878	+	7.54720i	−0.419561	+	0.304829i	−0.777461	−	0.628931i	$-0.783493\pi$
$613$	−10.3878	+	7.54720i	−0.419561	+	0.304829i	0.357900	+	0.933760i	$0.383493\pi$
$614$		0			0
$615$	12.8792	−	26.2039i	0.519338	−	1.05664i
$616$		0			0
$617$	4.45814	−	3.23903i	0.179478	−	0.130398i	−0.494419	−	0.869224i	$-0.664619\pi$
$617$	4.45814	−	3.23903i	0.179478	−	0.130398i	0.673897	+	0.738825i	$0.264619\pi$
$618$		0			0
$619$	5.84128	−	17.9776i	0.234781	−	0.722581i	−0.762370	−	0.647142i	$-0.775964\pi$
$619$	5.84128	−	17.9776i	0.234781	−	0.722581i	0.997150	−	0.0754392i	$-0.0240359\pi$
$620$		0			0
$621$	−33.5956	+	24.4086i	−1.34815	+	0.979485i
$622$		0			0
$623$	−0.00968932	−	0.0298207i	−0.000388195	−	0.00119474i
$624$		0			0
$625$	−8.91132	−	27.4262i	−0.356453	−	1.09705i
$626$		0			0
$627$	0.185505	−	0.570927i	0.00740838	−	0.0228006i
$628$		0			0
$629$	12.9824			0.517644
$630$		0			0
$631$	−13.3838	−	9.72388i	−0.532800	−	0.387102i	0.288604	−	0.957448i	$-0.406809\pi$
$631$	−13.3838	−	9.72388i	−0.532800	−	0.387102i	−0.821404	+	0.570347i	$0.806809\pi$
$632$		0			0
$633$	28.0480	−	20.3781i	1.11481	−	0.809956i
$634$		0			0
$635$	12.0066	+	8.72329i	0.476467	+	0.346173i
$636$		0			0
$637$	−5.09880	−	3.70449i	−0.202022	−	0.146777i
$638$		0			0
$639$	3.03659	+	9.34567i	0.120126	+	0.369709i
$640$		0			0
$641$	11.4742	−	35.3139i	0.453203	−	1.39482i	−0.420029	−	0.907511i	$-0.637980\pi$
$641$	11.4742	−	35.3139i	0.453203	−	1.39482i	0.873232	−	0.487305i	$-0.162020\pi$
$642$		0			0
$643$	−25.5501	+	18.5632i	−1.00760	+	0.732063i	−0.963704	−	0.266973i	$-0.913976\pi$
$643$	−25.5501	+	18.5632i	−1.00760	+	0.732063i	−0.0438941	+	0.999036i	$0.513976\pi$
$644$		0			0
$645$	5.64773	+	17.3819i	0.222379	+	0.684412i
$646$		0			0
$647$	11.4908			0.451749			0.225875	−	0.974156i	$-0.427476\pi$
$647$	11.4908			0.451749			0.225875	+	0.974156i	$0.427476\pi$
$648$		0			0
$649$	−4.27526	−	3.10616i	−0.167819	−	0.121927i
$650$		0			0
$651$	−0.104133	+	0.320487i	−0.00408128	+	0.0125609i
$652$		0			0
$653$	−37.5228			−1.46838			−0.734190	−	0.678944i	$-0.762438\pi$
$653$	−37.5228			−1.46838			−0.734190	+	0.678944i	$0.762438\pi$
$654$		0			0
$655$	−27.7628			−1.08478
$656$		0			0
$657$	−7.43532			−0.290079
$658$		0			0
$659$	−33.6096			−1.30924			−0.654622	−	0.755956i	$-0.727172\pi$
$659$	−33.6096			−1.30924			−0.654622	+	0.755956i	$0.727172\pi$
$660$		0			0
$661$	4.71256	−	14.5038i	0.183297	−	0.564131i	−0.816617	−	0.577179i	$-0.804153\pi$
$661$	4.71256	−	14.5038i	0.183297	−	0.564131i	0.999915	+	0.0130479i	$0.00415338\pi$
$662$		0			0
$663$	41.6493	+	30.2600i	1.61753	+	1.17520i
$664$		0			0
$665$	−0.431593			−0.0167365
$666$		0			0
$667$	−16.0605	−	49.4290i	−0.621864	−	1.91390i
$668$		0			0
$669$	−19.7328	+	14.3367i	−0.762913	+	0.554289i
$670$		0			0
$671$	−0.177531	+	0.546384i	−0.00685351	+	0.0210929i
$672$		0			0
$673$	−3.20123	−	9.85236i	−0.123398	−	0.379781i	0.870208	−	0.492685i	$-0.163985\pi$
$673$	−3.20123	−	9.85236i	−0.123398	−	0.379781i	−0.993606	+	0.112905i	$0.963985\pi$
$674$		0			0
$675$	18.4032	+	13.3707i	0.708338	+	0.514638i
$676$		0			0
$677$	28.9891	+	21.0618i	1.11414	+	0.809472i	0.983311	−	0.181932i	$-0.0582352\pi$
$677$	28.9891	+	21.0618i	1.11414	+	0.809472i	0.130832	+	0.991405i	$0.458235\pi$
$678$		0			0
$679$	−8.17754	+	5.94133i	−0.313825	+	0.228007i
$680$		0			0
$681$	−15.2611	−	11.0878i	−0.584806	−	0.424886i
$682$		0			0
$683$	1.89475			0.0725006			0.0362503	−	0.999343i	$-0.488459\pi$
$683$	1.89475			0.0725006			0.0362503	+	0.999343i	$0.488459\pi$
$684$		0			0
$685$	−5.66757	+	17.4430i	−0.216547	+	0.666462i
$686$		0			0
$687$	6.52529	+	20.0828i	0.248955	+	0.766206i
$688$		0			0
$689$	−10.6278	−	32.7091i	−0.404889	−	1.24612i
$690$		0			0
$691$	39.4710	−	28.6774i	1.50155	−	1.09094i	0.531790	−	0.846877i	$-0.321520\pi$
$691$	39.4710	−	28.6774i	1.50155	−	1.09094i	0.969759	−	0.244063i	$-0.0784803\pi$
$692$		0			0
$693$	0.600089	−	1.84688i	0.0227955	−	0.0701573i
$694$		0			0
$695$	15.0069	−	10.9032i	0.569245	−	0.413581i
$696$		0			0
$697$	−5.88974	−	34.0059i	−0.223090	−	1.28807i
$698$		0			0
$699$	−29.4819	+	21.4199i	−1.11511	+	0.810173i
$700$		0			0
$701$	−5.79683	+	17.8408i	−0.218943	+	0.673838i	0.779907	+	0.625896i	$0.215266\pi$
$701$	−5.79683	+	17.8408i	−0.218943	+	0.673838i	−0.998850	+	0.0479423i	$0.984734\pi$
$702$		0			0
$703$	−0.279516	+	0.203080i	−0.0105422	+	0.00765932i
$704$		0			0
$705$	−0.919118	−	2.82875i	−0.0346160	−	0.106537i
$706$		0			0
$707$	−5.59074	−	17.2065i	−0.210261	−	0.647118i
$708$		0			0
$709$	3.54060	−	10.8968i	0.132970	−	0.409239i	−0.862299	−	0.506400i	$-0.830976\pi$
$709$	3.54060	−	10.8968i	0.132970	−	0.409239i	0.995269	+	0.0971605i	$0.0309760\pi$
$710$		0			0
$711$	1.75420			0.0657878
$712$		0			0
$713$	−1.33103	−	0.967051i	−0.0498475	−	0.0362164i
$714$		0			0
$715$	42.3652	−	30.7801i	1.58437	−	1.15111i
$716$		0			0
$717$	12.8470	+	9.33390i	0.479780	+	0.348581i
$718$		0			0
$719$	15.2285	+	11.0641i	0.567927	+	0.412623i	0.834352	−	0.551233i	$-0.185842\pi$
$719$	15.2285	+	11.0641i	0.567927	+	0.412623i	−0.266425	+	0.963856i	$0.585842\pi$
$720$		0			0
$721$	−4.96654	−	15.2854i	−0.184964	−	0.569259i
$722$		0			0
$723$	−2.36856	+	7.28969i	−0.0880878	+	0.271106i
$724$		0			0
$725$	−23.0326	+	16.7342i	−0.855410	+	0.621492i
$726$		0			0
$727$	−10.5558	−	32.4874i	−0.391493	−	1.20489i	−0.931660	−	0.363332i	$-0.881639\pi$
$727$	−10.5558	−	32.4874i	−0.391493	−	1.20489i	0.540167	−	0.841558i	$-0.318361\pi$
$728$		0			0
$729$	30.0141			1.11163
$730$		0			0
$731$	17.4771	+	12.6979i	0.646414	+	0.469647i
$732$		0			0
$733$	−11.9653	+	36.8254i	−0.441949	+	1.36018i	0.443847	+	0.896103i	$0.353614\pi$
$733$	−11.9653	+	36.8254i	−0.441949	+	1.36018i	−0.885795	+	0.464076i	$0.846386\pi$
$734$		0			0
$735$	4.55995			0.168196
$736$		0			0
$737$	4.89363			0.180259
$738$		0			0
$739$	49.3940			1.81699			0.908494	−	0.417899i	$-0.137233\pi$
$739$	49.3940			1.81699			0.908494	+	0.417899i	$0.137233\pi$
$740$		0			0
$741$	−1.37007			−0.0503308
$742$		0			0
$743$	13.9681	−	42.9894i	0.512440	−	1.57713i	−0.275453	−	0.961315i	$-0.588828\pi$
$743$	13.9681	−	42.9894i	0.512440	−	1.57713i	0.787893	−	0.615813i	$-0.211172\pi$
$744$		0			0
$745$	26.8333	+	19.4955i	0.983095	+	0.714260i
$746$		0			0
$747$	3.36929			0.123276
$748$		0			0
$749$	−1.35464	−	4.16914i	−0.0494974	−	0.152337i
$750$		0			0
$751$	38.2664	−	27.8021i	1.39636	−	1.01451i	0.401226	−	0.915979i	$-0.368584\pi$
$751$	38.2664	−	27.8021i	1.39636	−	1.01451i	0.995134	−	0.0985359i	$-0.0314159\pi$
$752$		0			0
$753$	−7.00849	+	21.5699i	−0.255404	+	0.786051i
$754$		0			0
$755$	−3.65503	−	11.2490i	−0.133020	−	0.409394i
$756$		0			0
$757$	−19.9709	−	14.5097i	−0.725855	−	0.527365i	0.162394	−	0.986726i	$-0.448078\pi$
$757$	−19.9709	−	14.5097i	−0.725855	−	0.527365i	−0.888249	+	0.459361i	$0.848078\pi$
$758$		0			0
$759$	−25.0521	−	18.2014i	−0.909334	−	0.660669i
$760$		0			0
$761$	−4.12165	+	2.99455i	−0.149410	+	0.108552i	−0.659979	−	0.751284i	$-0.729435\pi$
$761$	−4.12165	+	2.99455i	−0.149410	+	0.108552i	0.510569	+	0.859837i	$0.329435\pi$
$762$		0			0
$763$	−9.48363	−	6.89026i	−0.343331	−	0.249444i
$764$		0			0
$765$	11.4044			0.412328
$766$		0			0
$767$	−3.72697	+	11.4704i	−0.134573	+	0.414173i
$768$		0			0
$769$	−6.80740	−	20.9510i	−0.245481	−	0.755513i	−0.995557	−	0.0941614i	$-0.969983\pi$
$769$	−6.80740	−	20.9510i	−0.245481	−	0.755513i	0.750076	−	0.661352i	$-0.230017\pi$
$770$		0			0
$771$	−3.63677	−	11.1928i	−0.130975	−	0.403100i
$772$		0			0
$773$	37.5441	−	27.2774i	1.35037	−	0.981100i	0.351375	−	0.936235i	$-0.385714\pi$
$773$	37.5441	−	27.2774i	1.35037	−	0.981100i	0.998993	−	0.0448653i	$-0.0142859\pi$
$774$		0			0
$775$	−0.278499	+	0.857131i	−0.0100040	+	0.0307891i
$776$		0			0
$777$	2.95320	−	2.14563i	0.105945	−	0.0769739i
$778$		0			0
$779$	0.658753	+	0.640027i	0.0236023	+	0.0229314i
$780$		0			0
$781$	−31.2184	+	22.6815i	−1.11708	+	0.811608i
$782$		0			0
$783$	−12.1818	+	37.4917i	−0.435342	+	1.33985i
$784$		0			0
$785$	11.6272	−	8.44768i	0.414994	−	0.301511i
$786$		0			0
$787$	10.9054	+	33.5635i	0.388737	+	1.19641i	0.933733	+	0.357970i	$0.116531\pi$
$787$	10.9054	+	33.5635i	0.388737	+	1.19641i	−0.544996	+	0.838439i	$0.683469\pi$
$788$		0			0
$789$	5.56758	+	17.1352i	0.198211	+	0.610031i
$790$		0			0
$791$	−4.66060	+	14.3438i	−0.165712	+	0.510008i
$792$		0			0
$793$	1.31117			0.0465612
$794$		0			0
$795$	20.1312	+	14.6262i	0.713982	+	0.518738i
$796$		0			0
$797$	−19.3935	+	14.0902i	−0.686953	+	0.499101i	−0.875657	−	0.482933i	$-0.839571\pi$
$797$	−19.3935	+	14.0902i	−0.686953	+	0.499101i	0.188704	+	0.982034i	$0.439571\pi$
$798$		0			0
$799$	−2.84425	−	2.06647i	−0.100622	−	0.0731063i
$800$		0			0
$801$	−0.0178386	−	0.0129605i	−0.000630296	−	0.000457937i
$802$		0			0
$803$	−9.02259	−	27.7687i	−0.318400	−	0.979935i
$804$		0			0
$805$	−6.87969	+	21.1735i	−0.242477	+	0.746268i
$806$		0			0
$807$	7.03848	−	5.11376i	0.247766	−	0.180013i
$808$		0			0
$809$	13.8670	+	42.6782i	0.487538	+	1.50049i	0.828271	+	0.560327i	$0.189325\pi$
$809$	13.8670	+	42.6782i	0.487538	+	1.50049i	−0.340733	+	0.940160i	$0.610675\pi$
$810$		0			0
$811$	−26.2735			−0.922587			−0.461293	−	0.887248i	$-0.652614\pi$
$811$	−26.2735			−0.922587			−0.461293	+	0.887248i	$0.652614\pi$
$812$		0			0
$813$	22.1951	+	16.1257i	0.778416	+	0.565552i
$814$		0			0
$815$	−2.44690	+	7.53078i	−0.0857112	+	0.263792i
$816$		0			0
$817$	−0.574917			−0.0201138
$818$		0			0
$819$	−4.43202			−0.154867
$820$		0			0
$821$	−22.7145			−0.792741			−0.396371	−	0.918091i	$-0.629730\pi$
$821$	−22.7145			−0.792741			−0.396371	+	0.918091i	$0.629730\pi$
$822$		0			0
$823$	−30.7934			−1.07339			−0.536695	−	0.843776i	$-0.680327\pi$
$823$	−30.7934			−1.07339			−0.536695	+	0.843776i	$0.680327\pi$
$824$		0			0
$825$	−5.24178	+	16.1325i	−0.182495	+	0.561663i
$826$		0			0
$827$	27.2276	+	19.7820i	0.946797	+	0.687889i	0.950047	−	0.312106i	$-0.101034\pi$
$827$	27.2276	+	19.7820i	0.946797	+	0.687889i	−0.00324978	+	0.999995i	$0.501034\pi$
$828$		0			0
$829$	43.0804			1.49624			0.748122	−	0.663561i	$-0.230956\pi$
$829$	43.0804			1.49624			0.748122	+	0.663561i	$0.230956\pi$
$830$		0			0
$831$	1.03716	+	3.19205i	0.0359787	+	0.110731i
$832$		0			0
$833$	4.36052	−	3.16810i	0.151083	−	0.109768i
$834$		0			0
$835$	−6.14118	+	18.9006i	−0.212524	+	0.654082i
$836$		0			0
$837$	0.385626	+	1.18684i	0.0133292	+	0.0410231i
$838$		0			0
$839$	21.9307	+	15.9336i	0.757131	+	0.550088i	0.898029	−	0.439936i	$-0.144999\pi$
$839$	21.9307	+	15.9336i	0.757131	+	0.550088i	−0.140898	+	0.990024i	$0.544999\pi$
$840$		0			0
$841$	−16.4536	−	11.9543i	−0.567367	−	0.412216i
$842$		0			0
$843$	30.6679	−	22.2815i	1.05626	−	0.767417i
$844$		0			0
$845$	−65.0445	−	47.2576i	−2.23760	−	1.62571i
$846$		0			0
$847$	−3.37426			−0.115941
$848$		0			0
$849$	−0.782005	+	2.40676i	−0.0268383	+	0.0825999i
$850$		0			0
$851$	5.50736	+	16.9499i	0.188790	+	0.581036i
$852$		0			0
$853$	14.2620	+	43.8939i	0.488321	+	1.50290i	0.827113	+	0.562036i	$0.189982\pi$
$853$	14.2620	+	43.8939i	0.488321	+	1.50290i	−0.338792	+	0.940861i	$0.610018\pi$
$854$		0			0
$855$	−0.245541	+	0.178396i	−0.00839732	+	0.00610101i
$856$		0			0
$857$	−15.1665	+	46.6776i	−0.518077	+	1.59448i	0.259536	+	0.965733i	$0.416430\pi$
$857$	−15.1665	+	46.6776i	−0.518077	+	1.59448i	−0.777613	+	0.628743i	$0.783570\pi$
$858$		0			0
$859$	−13.2202	+	9.60500i	−0.451066	+	0.327719i	−0.790016	−	0.613086i	$-0.789928\pi$
$859$	−13.2202	+	9.60500i	−0.451066	+	0.327719i	0.338951	+	0.940804i	$0.389928\pi$
$860$		0			0
$861$	−6.95998	−	6.76214i	−0.237196	−	0.230453i
$862$		0			0
$863$	31.7859	−	23.0938i	1.08200	−	0.786122i	0.103973	−	0.994580i	$-0.466845\pi$
$863$	31.7859	−	23.0938i	1.08200	−	0.786122i	0.978031	+	0.208458i	$0.0668445\pi$
$864$		0			0
$865$	20.7577	−	63.8855i	0.705781	−	2.17217i
$866$		0			0
$867$	−14.7755	+	10.7350i	−0.501802	+	0.364580i
$868$		0			0
$869$	2.12869	+	6.55142i	0.0722107	+	0.222242i
$870$		0			0
$871$	−3.45129	−	10.6220i	−0.116943	−	0.359912i
$872$		0			0
$873$	−2.19654	+	6.76026i	−0.0743417	+	0.228800i
$874$		0			0
$875$	−2.84884			−0.0963085
$876$		0			0
$877$	10.2023	+	7.41244i	0.344509	+	0.250300i	0.746562	−	0.665316i	$-0.231703\pi$
$877$	10.2023	+	7.41244i	0.344509	+	0.250300i	−0.402053	+	0.915616i	$0.631703\pi$
$878$		0			0
$879$	14.4396	−	10.4910i	0.487036	−	0.353853i
$880$		0			0
$881$	−7.35653	−	5.34484i	−0.247848	−	0.180072i	0.456925	−	0.889505i	$-0.348951\pi$
$881$	−7.35653	−	5.34484i	−0.247848	−	0.180072i	−0.704773	+	0.709433i	$0.748951\pi$
$882$		0			0
$883$	1.19463	+	0.867949i	0.0402025	+	0.0292088i	0.607705	−	0.794163i	$-0.292090\pi$
$883$	1.19463	+	0.867949i	0.0402025	+	0.0292088i	−0.567503	+	0.823372i	$0.692090\pi$
$884$		0			0
$885$	−2.69654	−	8.29908i	−0.0906431	−	0.278971i
$886$		0			0
$887$	−14.1104	+	43.4275i	−0.473783	+	1.45815i	0.373810	+	0.927505i	$0.378051\pi$
$887$	−14.1104	+	43.4275i	−0.473783	+	1.45815i	−0.847593	+	0.530647i	$0.821949\pi$
$888$		0			0
$889$	3.99042	−	2.89921i	0.133834	−	0.0972364i
$890$		0			0
$891$	5.45782	+	16.7975i	0.182844	+	0.562736i
$892$		0			0
$893$	0.0935627			0.00313095
$894$		0			0
$895$	−52.8210	−	38.3767i	−1.76561	−	1.28279i
$896$		0			0
$897$	−21.8392	+	67.2143i	−0.729191	+	2.24422i
$898$		0			0
$899$	−1.56184			−0.0520901
$900$		0			0
$901$	29.4126			0.979876
$902$		0			0
$903$	6.07422			0.202137
$904$		0			0
$905$	−1.20686			−0.0401174
$906$		0			0
$907$	−12.7243	+	39.1613i	−0.422502	+	1.30033i	0.482864	+	0.875696i	$0.339597\pi$
$907$	−12.7243	+	39.1613i	−0.422502	+	1.30033i	−0.905366	+	0.424633i	$0.860403\pi$
$908$		0			0
$909$	−10.2929	−	7.47821i	−0.341393	−	0.248036i
$910$		0			0
$911$	−17.5074			−0.580046			−0.290023	−	0.957020i	$-0.593663\pi$
$911$	−17.5074			−0.580046			−0.290023	+	0.957020i	$0.593663\pi$
$912$		0			0
$913$	4.08855	+	12.5833i	0.135311	+	0.416446i
$914$		0			0
$915$	−0.767482	+	0.557609i	−0.0253722	+	0.0184340i
$916$		0			0
$917$	−2.85131	+	8.77543i	−0.0941586	+	0.289790i
$918$		0			0
$919$	14.7273	+	45.3259i	0.485808	+	1.49516i	0.830808	+	0.556560i	$0.187879\pi$
$919$	14.7273	+	45.3259i	0.485808	+	1.49516i	−0.345000	+	0.938603i	$0.612121\pi$
$920$		0			0
$921$	−38.7243	−	28.1349i	−1.27601	−	0.927075i
$922$		0			0
$923$	71.2491	+	51.7655i	2.34519	+	1.70388i
$924$		0			0
$925$	7.89822	−	5.73839i	0.259692	−	0.188677i
$926$		0			0
$927$	−9.14368	−	6.64328i	−0.300318	−	0.218194i
$928$		0			0
$929$	−20.4846			−0.672076			−0.336038	−	0.941848i	$-0.609087\pi$
$929$	−20.4846			−0.672076			−0.336038	+	0.941848i	$0.609087\pi$
$930$		0			0
$931$	−0.0443257	+	0.136421i	−0.00145272	+	0.00447101i
$932$		0			0
$933$	−4.98405	−	15.3393i	−0.163171	−	0.502187i
$934$		0			0
$935$	13.8390	+	42.5921i	0.452584	+	1.39291i
$936$		0			0
$937$	−23.7061	+	17.2235i	−0.774444	+	0.562666i	−0.903306	−	0.428996i	$-0.858867\pi$
$937$	−23.7061	+	17.2235i	−0.774444	+	0.562666i	0.128863	+	0.991662i	$0.458867\pi$
$938$		0			0
$939$	2.03464	−	6.26198i	0.0663980	−	0.204352i
$940$		0			0
$941$	−12.8269	+	9.31932i	−0.418146	+	0.303801i	−0.776892	−	0.629634i	$-0.783205\pi$
$941$	−12.8269	+	9.31932i	−0.418146	+	0.303801i	0.358745	+	0.933436i	$0.383205\pi$
$942$		0			0
$943$	41.8997	−	22.1155i	1.36444	−	0.720181i
$944$		0			0
$945$	13.6615	−	9.92564i	0.444408	−	0.322881i
$946$		0			0
$947$	−2.04888	+	6.30581i	−0.0665797	+	0.204911i	−0.978812	−	0.204763i	$-0.934358\pi$
$947$	−2.04888	+	6.30581i	−0.0665797	+	0.204911i	0.912232	+	0.409674i	$0.134358\pi$
$948$		0			0
$949$	−53.9107	+	39.1684i	−1.75002	+	1.27146i
$950$		0			0
$951$	9.54577	+	29.3789i	0.309543	+	0.952675i
$952$		0			0
$953$	3.62629	+	11.1606i	0.117467	+	0.361526i	0.992454	−	0.122621i	$-0.0391299\pi$
$953$	3.62629	+	11.1606i	0.117467	+	0.361526i	−0.874987	+	0.484147i	$0.839130\pi$
$954$		0			0
$955$	−21.9869	+	67.6687i	−0.711480	+	2.18971i
$956$		0			0
$957$	−29.3962			−0.950243
$958$		0			0
$959$	4.93142	+	3.58288i	0.159244	+	0.115697i
$960$		0			0
$961$	25.0395	−	18.1923i	0.807727	−	0.586848i
$962$		0			0
$963$	−2.49396	−	1.81197i	−0.0803669	−	0.0583899i
$964$		0			0
$965$	−8.48108	−	6.16186i	−0.273016	−	0.198357i
$966$		0			0
$967$	12.1460	+	37.3814i	0.390588	+	1.20210i	0.932345	+	0.361570i	$0.117759\pi$
$967$	12.1460	+	37.3814i	0.390588	+	1.20210i	−0.541757	+	0.840535i	$0.682241\pi$
$968$		0			0
$969$	0.362073	−	1.11435i	0.0116315	−	0.0357980i
$970$		0			0
$971$	34.5959	−	25.1354i	1.11023	−	0.806632i	0.127534	−	0.991834i	$-0.459294\pi$
$971$	34.5959	−	25.1354i	1.11023	−	0.806632i	0.982701	+	0.185202i	$0.0592939\pi$
$972$		0			0
$973$	−1.90509	−	5.86327i	−0.0610745	−	0.187968i
$974$		0			0
$975$	38.7137			1.23983
$976$		0			0
$977$	−32.3064	−	23.4720i	−1.03357	−	0.750936i	−0.0645533	−	0.997914i	$-0.520562\pi$
$977$	−32.3064	−	23.4720i	−1.03357	−	0.750936i	−0.969021	+	0.246979i	$0.920562\pi$
$978$		0			0
$979$	0.0267568	−	0.0823491i	0.000855152	−	0.00263189i
$980$		0			0
$981$	−8.24345			−0.263193
$982$		0			0
$983$	36.4743			1.16335			0.581675	−	0.813421i	$-0.302398\pi$
$983$	36.4743			1.16335			0.581675	+	0.813421i	$0.302398\pi$
$984$		0			0
$985$	12.9374			0.412219
$986$		0			0
$987$	−0.988527			−0.0314652
$988$		0			0
$989$	−9.16430	+	28.2048i	−0.291408	+	0.896861i
$990$		0			0
$991$	−5.49178	−	3.99001i	−0.174452	−	0.126747i	0.497133	−	0.867674i	$-0.334386\pi$
$991$	−5.49178	−	3.99001i	−0.174452	−	0.126747i	−0.671585	+	0.740928i	$0.734386\pi$
$992$		0			0
$993$	−0.184641			−0.00585940
$994$		0			0
$995$	23.0998	+	71.0938i	0.732312	+	2.25383i
$996$		0			0
$997$	−43.3940	+	31.5276i	−1.37430	+	0.998488i	−0.376913	+	0.926249i	$0.623015\pi$
$997$	−43.3940	+	31.5276i	−1.37430	+	0.998488i	−0.997387	+	0.0722394i	$0.976985\pi$
$998$		0			0
$999$	4.17732	−	12.8565i	0.132164	−	0.406760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.365.5	✓	24
41.10	even	5	inner	1148.2.n.d.953.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.365.5	✓	24	1.1	even	1	trivial
1148.2.n.d.953.5	yes	24	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.51551 q^{3} +(0.929786 - 2.86159i) q^{5} +(-0.809017 - 0.587785i) q^{7} -0.703221 q^{9} +O(q^{10})\)	\(q+1.51551 q^{3} +(0.929786 - 2.86159i) q^{5} +(-0.809017 - 0.587785i) q^{7} -0.703221 q^{9} +(-0.853343 - 2.62632i) q^{11} +(-5.09880 + 3.70449i) q^{13} +(1.40910 - 4.33677i) q^{15} +(-1.66557 - 5.12610i) q^{17} +(0.116046 + 0.0843126i) q^{19} +(-1.22608 - 0.890796i) q^{21} +(5.98609 - 4.34915i) q^{23} +(-3.27909 - 2.38240i) q^{25} -5.61228 q^{27} +(2.17056 - 6.68031i) q^{29} +(-0.0687112 - 0.211471i) q^{31} +(-1.29325 - 3.98022i) q^{33} +(-2.43421 + 1.76856i) q^{35} +(-0.744317 + 2.29077i) q^{37} +(-7.72729 + 5.61420i) q^{39} +(6.33807 + 0.910393i) q^{41} +(-3.24257 + 2.35586i) q^{43} +(-0.653845 + 2.01233i) q^{45} +(0.527699 - 0.383396i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-2.52419 - 7.76867i) q^{51} +(-1.68630 + 5.18990i) q^{53} -8.30886 q^{55} +(0.175870 + 0.127777i) q^{57} +(1.54818 - 1.12482i) q^{59} +(-0.168309 - 0.122284i) q^{61} +(0.568918 + 0.413343i) q^{63} +(5.85994 + 18.0350i) q^{65} +(-0.547611 + 1.68537i) q^{67} +(9.07200 - 6.59119i) q^{69} +(-4.31812 - 13.2898i) q^{71} +10.5732 q^{73} +(-4.96950 - 3.61056i) q^{75} +(-0.853343 + 2.62632i) q^{77} -2.49453 q^{79} -6.39582 q^{81} -4.79122 q^{83} -16.2174 q^{85} +(3.28952 - 10.1241i) q^{87} +(0.0253670 + 0.0184302i) q^{89} +6.30246 q^{91} +(-0.104133 - 0.320487i) q^{93} +(0.349166 - 0.253684i) q^{95} +(3.12354 - 9.61328i) q^{97} +(0.600089 + 1.84688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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