LMFDB - Embedded newform 252.2.l.b.205.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(193,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("252.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			205.4
Root			$-0.473632 - 1.66604i$ of defining polynomial
Character	$\chi$	$=$	252.205
Dual form			252.2.l.b.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.473632 - 1.66604i) q^{3} -1.90301 q^{5} +(-2.43415 - 1.03677i) q^{7} +(-2.55135 + 1.57817i) q^{9} +O(q^{10})$	\(q+(-0.473632 - 1.66604i) q^{3} -1.90301 q^{5} +(-2.43415 - 1.03677i) q^{7} +(-2.55135 + 1.57817i) q^{9} -3.06586 q^{11} +(1.13161 + 1.96000i) q^{13} +(0.901324 + 3.17048i) q^{15} +(-0.713726 - 1.23621i) q^{17} +(2.98444 - 5.16919i) q^{19} +(-0.574405 + 4.54643i) q^{21} -7.15543 q^{23} -1.37856 q^{25} +(3.83769 + 3.50316i) q^{27} +(0.468164 - 0.810884i) q^{29} +(4.11065 - 7.11985i) q^{31} +(1.45209 + 5.10784i) q^{33} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(2.72947 - 2.81362i) q^{39} +(-5.31672 - 9.20883i) q^{41} +(2.98444 - 5.16919i) q^{43} +(4.85523 - 3.00328i) q^{45} +(0.483340 + 0.837169i) q^{47} +(4.85021 + 5.04732i) q^{49} +(-1.72152 + 1.77460i) q^{51} +(5.45142 + 9.44213i) q^{53} +5.83436 q^{55} +(-10.0256 - 2.52388i) q^{57} +(5.68180 - 9.84117i) q^{59} +(-0.449718 - 0.778935i) q^{61} +(7.84657 - 1.19636i) q^{63} +(-2.15346 - 3.72990i) q^{65} +(-0.813810 + 1.40956i) q^{67} +(3.38904 + 11.9212i) q^{69} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(0.652931 + 2.29674i) q^{75} +(7.46279 + 3.17860i) q^{77} +(4.16945 + 7.22169i) q^{79} +(4.01873 - 8.05294i) q^{81} +(-7.98203 + 13.8253i) q^{83} +(1.35822 + 2.35251i) q^{85} +(-1.57270 - 0.395917i) q^{87} +(-2.58992 + 4.48587i) q^{89} +(-0.722433 - 5.94416i) q^{91} +(-13.8089 - 3.47630i) q^{93} +(-5.67940 + 9.83701i) q^{95} +(0.922890 - 1.59849i) q^{97} +(7.82208 - 4.83847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.473632	−	1.66604i	−0.273451	−	0.961886i
$3$	−0.473632	−	1.66604i	−0.273451	−	0.961886i
$4$		0			0
$5$	−1.90301			−0.851051			−0.425525	−	0.904947i	$-0.639911\pi$
$5$	−1.90301			−0.851051			−0.425525	+	0.904947i	$0.639911\pi$
$6$		0			0
$7$	−2.43415	−	1.03677i	−0.920024	−	0.391863i
$7$	−2.43415	−	1.03677i	−0.920024	−	0.391863i
$8$		0			0
$9$	−2.55135	+	1.57817i	−0.850449	+	0.526058i
$10$		0			0
$11$	−3.06586			−0.924393			−0.462196	−	0.886778i	$-0.652938\pi$
$11$	−3.06586			−0.924393			−0.462196	+	0.886778i	$0.652938\pi$
$12$		0			0
$13$	1.13161	+	1.96000i	0.313851	+	0.543607i	0.979193	−	0.202933i	$-0.0650473\pi$
$13$	1.13161	+	1.96000i	0.313851	+	0.543607i	−0.665341	+	0.746539i	$0.731714\pi$
$14$		0			0
$15$	0.901324	+	3.17048i	0.232721	+	0.818614i
$16$		0			0
$17$	−0.713726	−	1.23621i	−0.173104	−	0.299825i	0.766400	−	0.642364i	$-0.222046\pi$
$17$	−0.713726	−	1.23621i	−0.173104	−	0.299825i	−0.939503	+	0.342539i	$0.888713\pi$
$18$		0			0
$19$	2.98444	−	5.16919i	0.684677	−	1.18589i	−0.288862	−	0.957371i	$-0.593277\pi$
$19$	2.98444	−	5.16919i	0.684677	−	1.18589i	0.973538	−	0.228524i	$-0.0733898\pi$
$20$		0			0
$21$	−0.574405	+	4.54643i	−0.125346	+	0.992113i
$22$		0			0
$23$	−7.15543			−1.49201			−0.746005	−	0.665940i	$-0.768031\pi$
$23$	−7.15543			−1.49201			−0.746005	+	0.665940i	$0.768031\pi$
$24$		0			0
$25$	−1.37856			−0.275713
$26$		0			0
$27$	3.83769	+	3.50316i	0.738564	+	0.674183i
$28$		0			0
$29$	0.468164	−	0.810884i	0.0869359	−	0.150577i	−0.819279	−	0.573396i	$-0.805626\pi$
$29$	0.468164	−	0.810884i	0.0869359	−	0.150577i	0.906214	+	0.422818i	$0.138959\pi$
$30$		0			0
$31$	4.11065	−	7.11985i	0.738294	−	1.27876i	−0.214969	−	0.976621i	$-0.568965\pi$
$31$	4.11065	−	7.11985i	0.738294	−	1.27876i	0.953263	−	0.302142i	$-0.0977016\pi$
$32$		0			0
$33$	1.45209	+	5.10784i	0.252776	+	0.889160i
$34$		0			0
$35$	4.63221	+	1.97298i	0.782987	+	0.333495i
$36$		0			0
$37$	−1.41550	+	2.45171i	−0.232706	+	0.403059i	−0.958604	−	0.284744i	$-0.908091\pi$
$37$	−1.41550	+	2.45171i	−0.232706	+	0.403059i	0.725897	+	0.687803i	$0.241425\pi$
$38$		0			0
$39$	2.72947	−	2.81362i	0.437065	−	0.450539i
$40$		0			0
$41$	−5.31672	−	9.20883i	−0.830332	−	1.43818i	−0.897775	−	0.440454i	$-0.854817\pi$
$41$	−5.31672	−	9.20883i	−0.830332	−	1.43818i	0.0674429	−	0.997723i	$-0.478516\pi$
$42$		0			0
$43$	2.98444	−	5.16919i	0.455122	−	0.788295i	−0.543573	−	0.839362i	$-0.682929\pi$
$43$	2.98444	−	5.16919i	0.455122	−	0.788295i	0.998695	+	0.0510671i	$0.0162622\pi$
$44$		0			0
$45$	4.85523	−	3.00328i	0.723775	−	0.447702i
$46$		0			0
$47$	0.483340	+	0.837169i	0.0705023	+	0.122114i	0.899122	−	0.437699i	$-0.144206\pi$
$47$	0.483340	+	0.837169i	0.0705023	+	0.122114i	−0.828619	+	0.559813i	$0.810873\pi$
$48$		0			0
$49$	4.85021	+	5.04732i	0.692887	+	0.721046i
$50$		0			0
$51$	−1.72152	+	1.77460i	−0.241062	+	0.248494i
$52$		0			0
$53$	5.45142	+	9.44213i	0.748810	+	1.29698i	0.948393	+	0.317096i	$0.102708\pi$
$53$	5.45142	+	9.44213i	0.748810	+	1.29698i	−0.199583	+	0.979881i	$0.563959\pi$
$54$		0			0
$55$	5.83436			0.786705
$56$		0			0
$57$	−10.0256	−	2.52388i	−1.32792	−	0.334296i
$58$		0			0
$59$	5.68180	−	9.84117i	0.739708	−	1.28121i	−0.212919	−	0.977070i	$-0.568297\pi$
$59$	5.68180	−	9.84117i	0.739708	−	1.28121i	0.952627	−	0.304142i	$-0.0983697\pi$
$60$		0			0
$61$	−0.449718	−	0.778935i	−0.0575805	−	0.0997324i	0.835798	−	0.549037i	$-0.185005\pi$
$61$	−0.449718	−	0.778935i	−0.0575805	−	0.0997324i	−0.893379	+	0.449304i	$0.851672\pi$
$62$		0			0
$63$	7.84657	−	1.19636i	0.988575	−	0.150727i
$64$		0			0
$65$	−2.15346	−	3.72990i	−0.267104	−	0.462637i
$66$		0			0
$67$	−0.813810	+	1.40956i	−0.0994227	+	0.172205i	−0.911446	−	0.411420i	$-0.865033\pi$
$67$	−0.813810	+	1.40956i	−0.0994227	+	0.172205i	0.812023	+	0.583625i	$0.198366\pi$
$68$		0			0
$69$	3.38904	+	11.9212i	0.407992	+	1.43514i
$70$		0			0
$71$	−2.36378			−0.280529			−0.140264	−	0.990114i	$-0.544795\pi$
$71$	−2.36378			−0.280529			−0.140264	+	0.990114i	$0.544795\pi$
$72$		0			0
$73$	−0.996286	−	1.72562i	−0.116606	−	0.201968i	0.801814	−	0.597573i	$-0.203868\pi$
$73$	−0.996286	−	1.72562i	−0.116606	−	0.201968i	−0.918421	+	0.395605i	$0.870535\pi$
$74$		0			0
$75$	0.652931	+	2.29674i	0.0753940	+	0.265204i
$76$		0			0
$77$	7.46279	+	3.17860i	0.850463	+	0.362235i
$78$		0			0
$79$	4.16945	+	7.22169i	0.469099	+	0.812504i	0.999376	−	0.0353209i	$-0.0112453\pi$
$79$	4.16945	+	7.22169i	0.469099	+	0.812504i	−0.530277	+	0.847825i	$0.677912\pi$
$80$		0			0
$81$	4.01873	−	8.05294i	0.446526	−	0.894771i
$82$		0			0
$83$	−7.98203	+	13.8253i	−0.876141	+	1.51752i	−0.0205995	+	0.999788i	$0.506557\pi$
$83$	−7.98203	+	13.8253i	−0.876141	+	1.51752i	−0.855542	+	0.517734i	$0.826776\pi$
$84$		0			0
$85$	1.35822	+	2.35251i	0.147320	+	0.255166i
$86$		0			0
$87$	−1.57270	−	0.395917i	−0.168611	−	0.0424468i
$88$		0			0
$89$	−2.58992	+	4.48587i	−0.274531	+	0.475501i	−0.970017	−	0.243039i	$-0.921856\pi$
$89$	−2.58992	+	4.48587i	−0.274531	+	0.475501i	0.695486	+	0.718540i	$0.255189\pi$
$90$		0			0
$91$	−0.722433	−	5.94416i	−0.0757316	−	0.623118i
$92$		0			0
$93$	−13.8089	−	3.47630i	−1.43191	−	0.360475i
$94$		0			0
$95$	−5.67940	+	9.83701i	−0.582694	+	1.00926i
$96$		0			0
$97$	0.922890	−	1.59849i	0.0937053	−	0.162302i	−0.815362	−	0.578951i	$-0.803462\pi$
$97$	0.922890	−	1.59849i	0.0937053	−	0.162302i	0.909068	+	0.416649i	$0.136796\pi$
$98$		0			0
$99$	7.82208	−	4.83847i	0.786149	−	0.486284i
$100$		0			0
$101$	−8.06350			−0.802349			−0.401174	−	0.916002i	$-0.631398\pi$
$101$	−8.06350			−0.802349			−0.401174	+	0.916002i	$0.631398\pi$
$102$		0			0
$103$	−17.7986			−1.75375			−0.876875	−	0.480718i	$-0.840376\pi$
$103$	−17.7986			−1.75375			−0.876875	+	0.480718i	$0.840376\pi$
$104$		0			0
$105$	1.09310	−	8.65190i	0.106675	−	0.844339i
$106$		0			0
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	−0.0371245	−	0.999311i	$-0.511820\pi$
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	0.883991	−	0.467505i	$-0.154847\pi$
$108$		0			0
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	0.914448	−	0.404703i	$-0.132625\pi$
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	−0.807707	+	0.589584i	$0.799292\pi$
$110$		0			0
$111$	4.75507	+	1.19706i	0.451331	+	0.113620i
$112$		0			0
$113$	−7.59999	−	13.1636i	−0.714947	−	1.23832i	−0.962980	−	0.269573i	$-0.913118\pi$
$113$	−7.59999	−	13.1636i	−0.714947	−	1.23832i	0.248033	−	0.968751i	$-0.420216\pi$
$114$		0			0
$115$	13.6168			1.26978
$116$		0			0
$117$	−5.98035	−	3.21477i	−0.552883	−	0.297206i
$118$		0			0
$119$	0.455652	+	3.74909i	0.0417695	+	0.343679i
$120$		0			0
$121$	−1.60048			−0.145498
$122$		0			0
$123$	−12.8241	+	13.2194i	−1.15631	+	1.19196i
$124$		0			0
$125$	12.1385			1.08570
$126$		0			0
$127$	−16.9303			−1.50232			−0.751161	−	0.660119i	$-0.770506\pi$
$127$	−16.9303			−1.50232			−0.751161	+	0.660119i	$0.770506\pi$
$128$		0			0
$129$	−10.0256	−	2.52388i	−0.882703	−	0.222215i
$130$		0			0
$131$	2.38354			0.208251			0.104125	−	0.994564i	$-0.466796\pi$
$131$	2.38354			0.208251			0.104125	+	0.994564i	$0.466796\pi$
$132$		0			0
$133$	−12.6238	+	9.48844i	−1.09463	+	0.822752i
$134$		0			0
$135$	−7.30315	−	6.66654i	−0.628555	−	0.573764i
$136$		0			0
$137$	10.9820			0.938254			0.469127	−	0.883131i	$-0.344569\pi$
$137$	10.9820			0.938254			0.469127	+	0.883131i	$0.344569\pi$
$138$		0			0
$139$	−3.70422	−	6.41590i	−0.314188	−	0.544190i	0.665076	−	0.746775i	$-0.268399\pi$
$139$	−3.70422	−	6.41590i	−0.314188	−	0.544190i	−0.979265	+	0.202585i	$0.935066\pi$
$140$		0			0
$141$	1.16583	−	1.20177i	0.0981804	−	0.101207i
$142$		0			0
$143$	−3.46936	−	6.00910i	−0.290122	−	0.502506i
$144$		0			0
$145$	−0.890919	+	1.54312i	−0.0739868	+	0.128149i
$146$		0			0
$147$	6.11180	−	10.4712i	0.504093	−	0.863649i
$148$		0			0
$149$	17.6239			1.44381			0.721904	−	0.691993i	$-0.243267\pi$
$149$	17.6239			1.44381			0.721904	+	0.691993i	$0.243267\pi$
$150$		0			0
$151$	−20.3664			−1.65739			−0.828697	−	0.559697i	$-0.810917\pi$
$151$	−20.3664			−1.65739			−0.828697	+	0.559697i	$0.810917\pi$
$152$		0			0
$153$	3.77191	+	2.02761i	0.304941	+	0.163923i
$154$		0			0
$155$	−7.82259	+	13.5491i	−0.628326	+	1.08829i
$156$		0			0
$157$	−4.64118	+	8.03875i	−0.370406	+	0.641562i	−0.989628	−	0.143654i	$-0.954115\pi$
$157$	−4.64118	+	8.03875i	−0.370406	+	0.641562i	0.619222	+	0.785216i	$0.287448\pi$
$158$		0			0
$159$	13.1490	−	13.5543i	1.04278	−	1.07493i
$160$		0			0
$161$	17.4174	+	7.41854i	1.37268	+	0.584663i
$162$		0			0
$163$	−11.9069	+	20.6234i	−0.932623	+	1.61535i	−0.153803	+	0.988101i	$0.549152\pi$
$163$	−11.9069	+	20.6234i	−0.932623	+	1.61535i	−0.778819	+	0.627248i	$0.784181\pi$
$164$		0			0
$165$	−2.76334	−	9.72025i	−0.215126	−	0.756721i
$166$		0			0
$167$	−0.883505	−	1.53028i	−0.0683676	−	0.118416i	0.829815	−	0.558038i	$-0.188446\pi$
$167$	−0.883505	−	1.53028i	−0.0683676	−	0.118416i	−0.898183	+	0.439622i	$0.855112\pi$
$168$		0			0
$169$	3.93893	−	6.82242i	0.302994	−	0.524802i
$170$		0			0
$171$	0.543559	+	17.8984i	0.0415670	+	1.36872i
$172$		0			0
$173$	−0.180049	−	0.311855i	−0.0136889	−	0.0237099i	0.859100	−	0.511808i	$-0.171024\pi$
$173$	−0.180049	−	0.311855i	−0.0136889	−	0.0237099i	−0.872789	+	0.488098i	$0.837691\pi$
$174$		0			0
$175$	3.35564	+	1.42926i	0.253662	+	0.108042i
$176$		0			0
$177$	−19.0868	−	4.80499i	−1.43465	−	0.361166i
$178$		0			0
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	0.700821	−	0.713337i	$-0.252817\pi$
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	−0.968179	+	0.250260i	$0.919484\pi$
$180$		0			0
$181$	11.0542			0.821650			0.410825	−	0.911714i	$-0.365241\pi$
$181$	11.0542			0.821650			0.410825	+	0.911714i	$0.365241\pi$
$182$		0			0
$183$	−1.08473	+	1.11817i	−0.0801857	+	0.0826578i
$184$		0			0
$185$	2.69370	−	4.66563i	0.198045	−	0.343024i
$186$		0			0
$187$	2.18819	+	3.79005i	0.160016	+	0.277156i
$188$		0			0
$189$	−5.70956	−	12.5060i	−0.415309	−	0.909680i
$190$		0			0
$191$	4.35083	+	7.53586i	0.314815	+	0.545276i	0.979398	−	0.201939i	$-0.0647241\pi$
$191$	4.35083	+	7.53586i	0.314815	+	0.545276i	−0.664583	+	0.747214i	$0.731391\pi$
$192$		0			0
$193$	0.709644	−	1.22914i	0.0510813	−	0.0884754i	−0.839354	−	0.543585i	$-0.817067\pi$
$193$	0.709644	−	1.22914i	0.0510813	−	0.0884754i	0.890435	+	0.455110i	$0.150400\pi$
$194$		0			0
$195$	−5.19420	+	5.35433i	−0.371964	+	0.383432i
$196$		0			0
$197$	5.69424			0.405698			0.202849	−	0.979210i	$-0.434980\pi$
$197$	5.69424			0.405698			0.202849	+	0.979210i	$0.434980\pi$
$198$		0			0
$199$	2.61327	+	4.52631i	0.185250	+	0.320862i	0.943661	−	0.330915i	$-0.107357\pi$
$199$	2.61327	+	4.52631i	0.185250	+	0.320862i	−0.758411	+	0.651777i	$0.774024\pi$
$200$		0			0
$201$	2.73382	+	0.688224i	0.192829	+	0.0485435i
$202$		0			0
$203$	−1.98028	+	1.48844i	−0.138989	+	0.104468i
$204$		0			0
$205$	10.1178	+	17.5245i	0.706655	+	1.22396i
$206$		0			0
$207$	18.2560	−	11.2925i	1.26888	−	0.784884i
$208$		0			0
$209$	−9.14987	+	15.8480i	−0.632910	+	1.09623i
$210$		0			0
$211$	−5.93079	−	10.2724i	−0.408293	−	0.707183i	0.586406	−	0.810017i	$-0.300542\pi$
$211$	−5.93079	−	10.2724i	−0.408293	−	0.707183i	−0.994699	+	0.102834i	$0.967209\pi$
$212$		0			0
$213$	1.11956	+	3.93814i	0.0767110	+	0.269837i
$214$		0			0
$215$	−5.67940	+	9.83701i	−0.387332	+	0.670879i
$216$		0			0
$217$	−17.3876	+	13.0690i	−1.18035	+	0.887182i
$218$		0			0
$219$	−2.40307	+	2.47715i	−0.162384	+	0.167391i
$220$		0			0
$221$	1.61531	−	2.79781i	0.108658	−	0.188201i
$222$		0			0
$223$	12.2950	−	21.2955i	0.823333	−	1.42605i	−0.0798535	−	0.996807i	$-0.525445\pi$
$223$	12.2950	−	21.2955i	0.823333	−	1.42605i	0.903187	−	0.429248i	$-0.141221\pi$
$224$		0			0
$225$	3.51719	−	2.17561i	0.234479	−	0.145041i
$226$		0			0
$227$	15.3180			1.01669			0.508344	−	0.861154i	$-0.330258\pi$
$227$	15.3180			1.01669			0.508344	+	0.861154i	$0.330258\pi$
$228$		0			0
$229$	17.0459			1.12643			0.563214	−	0.826311i	$-0.309565\pi$
$229$	17.0459			1.12643			0.563214	+	0.826311i	$0.309565\pi$
$230$		0			0
$231$	1.76105	−	13.9387i	0.115868	−	0.917102i
$232$		0			0
$233$	9.88255	−	17.1171i	0.647427	−	1.12138i	−0.336308	−	0.941752i	$-0.609178\pi$
$233$	9.88255	−	17.1171i	0.647427	−	1.12138i	0.983735	−	0.179625i	$-0.0574884\pi$
$234$		0			0
$235$	−0.919799	−	1.59314i	−0.0600011	−	0.103925i
$236$		0			0
$237$	10.0568	−	10.3669i	0.653260	−	0.673400i
$238$		0			0
$239$	8.35041	+	14.4633i	0.540143	+	0.935555i	0.998895	+	0.0469909i	$0.0149632\pi$
$239$	8.35041	+	14.4633i	0.540143	+	0.935555i	−0.458752	+	0.888564i	$0.651703\pi$
$240$		0			0
$241$	6.39995			0.412257			0.206129	−	0.978525i	$-0.433914\pi$
$241$	6.39995			0.412257			0.206129	+	0.978525i	$0.433914\pi$
$242$		0			0
$243$	−15.3199	−	2.88123i	−0.982770	−	0.184831i
$244$		0			0
$245$	−9.22999	−	9.60509i	−0.589682	−	0.613647i
$246$		0			0
$247$	13.5088			0.859547
$248$		0			0
$249$	26.8139	+	6.75025i	1.69926	+	0.427780i
$250$		0			0
$251$	−26.8346			−1.69378			−0.846891	−	0.531766i	$-0.821529\pi$
$251$	−26.8346			−1.69378			−0.846891	+	0.531766i	$0.821529\pi$
$252$		0			0
$253$	21.9376			1.37920
$254$		0			0
$255$	3.27607	−	3.37708i	0.205156	−	0.211481i
$256$		0			0
$257$	7.17597			0.447625			0.223812	−	0.974632i	$-0.428150\pi$
$257$	7.17597			0.447625			0.223812	+	0.974632i	$0.428150\pi$
$258$		0			0
$259$	5.98741	−	4.50030i	0.372039	−	0.279635i
$260$		0			0
$261$	0.0852673	+	2.80769i	0.00527791	+	0.173792i
$262$		0			0
$263$	20.4137			1.25876			0.629382	−	0.777096i	$-0.283308\pi$
$263$	20.4137			1.25876			0.629382	+	0.777096i	$0.283308\pi$
$264$		0			0
$265$	−10.3741	−	17.9685i	−0.637275	−	1.10379i
$266$		0			0
$267$	8.70028	+	2.19024i	0.532448	+	0.134041i
$268$		0			0
$269$	−3.37251	−	5.84136i	−0.205626	−	0.356154i	0.744706	−	0.667392i	$-0.232590\pi$
$269$	−3.37251	−	5.84136i	−0.205626	−	0.356154i	−0.950332	+	0.311238i	$0.899256\pi$
$270$		0			0
$271$	−1.04632	+	1.81228i	−0.0635596	+	0.110088i	−0.896054	−	0.443945i	$-0.853579\pi$
$271$	−1.04632	+	1.81228i	−0.0635596	+	0.110088i	0.832495	+	0.554033i	$0.186912\pi$
$272$		0			0
$273$	−9.56102	+	4.01894i	−0.578659	+	0.243238i
$274$		0			0
$275$	4.22649			0.254867
$276$		0			0
$277$	−23.5410			−1.41444			−0.707221	−	0.706992i	$-0.750052\pi$
$277$	−23.5410			−1.41444			−0.707221	+	0.706992i	$0.750052\pi$
$278$		0			0
$279$	0.748677	+	24.6525i	0.0448221	+	1.47591i
$280$		0			0
$281$	9.66048	−	16.7324i	0.576296	−	0.998173i	−0.419604	−	0.907707i	$-0.637831\pi$
$281$	9.66048	−	16.7324i	0.576296	−	0.998173i	0.995900	−	0.0904661i	$-0.0288357\pi$
$282$		0			0
$283$	2.22658	−	3.85655i	0.132356	−	0.229248i	−0.792228	−	0.610225i	$-0.791079\pi$
$283$	2.22658	−	3.85655i	0.132356	−	0.229248i	0.924584	+	0.380977i	$0.124412\pi$
$284$		0			0
$285$	19.0788	+	4.80296i	1.13013	+	0.284503i
$286$		0			0
$287$	3.39426	+	27.9279i	0.200357	+	1.64853i
$288$		0			0
$289$	7.48119	−	12.9578i	0.440070	−	0.762224i
$290$		0			0
$291$	−3.10026	−	0.780471i	−0.181740	−	0.0457520i
$292$		0			0
$293$	−11.7314	−	20.3193i	−0.685354	−	1.18707i	−0.973325	−	0.229429i	$-0.926314\pi$
$293$	−11.7314	−	20.3193i	−0.685354	−	1.18707i	0.287972	−	0.957639i	$-0.407019\pi$
$294$		0			0
$295$	−10.8125	+	18.7278i	−0.629529	+	1.09038i
$296$		0			0
$297$	−11.7658	−	10.7402i	−0.682723	−	0.623210i
$298$		0			0
$299$	−8.09714	−	14.0247i	−0.468270	−	0.811067i
$300$		0			0
$301$	−12.6238	+	9.48844i	−0.727627	+	0.546904i
$302$		0			0
$303$	3.81913	+	13.4341i	0.219403	+	0.771768i
$304$		0			0
$305$	0.855817	+	1.48232i	0.0490039	+	0.0848773i
$306$		0			0
$307$	7.79955			0.445144			0.222572	−	0.974916i	$-0.428555\pi$
$307$	7.79955			0.445144			0.222572	+	0.974916i	$0.428555\pi$
$308$		0			0
$309$	8.42999	+	29.6531i	0.479565	+	1.68691i
$310$		0			0
$311$	−7.49449	+	12.9808i	−0.424974	+	0.736076i	−0.996418	−	0.0845650i	$-0.973050\pi$
$311$	−7.49449	+	12.9808i	−0.424974	+	0.736076i	0.571444	+	0.820641i	$0.306383\pi$
$312$		0			0
$313$	−3.46332	−	5.99864i	−0.195758	−	0.339063i	0.751391	−	0.659858i	$-0.229383\pi$
$313$	−3.46332	−	5.99864i	−0.195758	−	0.339063i	−0.947149	+	0.320794i	$0.896050\pi$
$314$		0			0
$315$	−14.9321	+	2.27667i	−0.841328	+	0.128276i
$316$		0			0
$317$	−5.42872	−	9.40282i	−0.304907	−	0.528115i	0.672333	−	0.740249i	$-0.265292\pi$
$317$	−5.42872	−	9.40282i	−0.304907	−	0.528115i	−0.977241	+	0.212133i	$0.931959\pi$
$318$		0			0
$319$	−1.43533	+	2.48606i	−0.0803629	+	0.139193i
$320$		0			0
$321$	−29.4275	−	7.40821i	−1.64249	−	0.413486i
$322$		0			0
$323$	−8.52027			−0.474081
$324$		0			0
$325$	−1.55999	−	2.70199i	−0.0865328	−	0.149879i
$326$		0			0
$327$	2.68798	−	2.77086i	0.148646	−	0.153229i
$328$		0			0
$329$	−0.308570	−	2.53891i	−0.0170120	−	0.139975i
$330$		0			0
$331$	4.02584	+	6.97297i	0.221280	+	0.383269i	0.955197	−	0.295971i	$-0.0956431\pi$
$331$	4.02584	+	6.97297i	0.221280	+	0.383269i	−0.733917	+	0.679240i	$0.762310\pi$
$332$		0			0
$333$	−0.257806	−	8.48907i	−0.0141277	−	0.465198i
$334$		0			0
$335$	1.54869	−	2.68240i	0.0846138	−	0.146555i
$336$		0			0
$337$	11.4293	+	19.7961i	0.622594	+	1.07836i	0.989001	+	0.147909i	$0.0472543\pi$
$337$	11.4293	+	19.7961i	0.622594	+	1.07836i	−0.366407	+	0.930455i	$0.619412\pi$
$338$		0			0
$339$	−18.3314	+	18.8965i	−0.995623	+	1.02632i
$340$		0			0
$341$	−12.6027	+	21.8285i	−0.682474	+	1.18208i
$342$		0			0
$343$	−6.57324	−	17.3145i	−0.354922	−	0.934896i
$344$		0			0
$345$	−6.44936	−	22.6861i	−0.347222	−	1.22138i
$346$		0			0
$347$	−12.8892	+	22.3247i	−0.691928	+	1.19845i	0.279278	+	0.960210i	$0.409905\pi$
$347$	−12.8892	+	22.3247i	−0.691928	+	1.19845i	−0.971205	+	0.238244i	$0.923428\pi$
$348$		0			0
$349$	6.90108	−	11.9530i	0.369406	−	0.639830i	−0.620067	−	0.784549i	$-0.712894\pi$
$349$	6.90108	−	11.9530i	0.369406	−	0.639830i	0.989473	+	0.144719i	$0.0462277\pi$
$350$		0			0
$351$	−2.52344	+	11.4861i	−0.134691	+	0.613082i
$352$		0			0
$353$	−24.9028			−1.32544			−0.662721	−	0.748866i	$-0.730598\pi$
$353$	−24.9028			−1.32544			−0.662721	+	0.748866i	$0.730598\pi$
$354$		0			0
$355$	4.49829			0.238744
$356$		0			0
$357$	6.03031	−	2.53482i	0.319158	−	0.134157i
$358$		0			0
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	−0.432465	−	0.901651i	$-0.642356\pi$
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	0.997085	−	0.0763002i	$-0.0243107\pi$
$360$		0			0
$361$	−8.31371	−	14.3998i	−0.437564	−	0.757883i
$362$		0			0
$363$	0.758036	+	2.66645i	0.0397866	+	0.139952i
$364$		0			0
$365$	1.89594	+	3.28386i	0.0992380	+	0.171885i
$366$		0			0
$367$	−11.5158			−0.601121			−0.300560	−	0.953763i	$-0.597174\pi$
$367$	−11.5158			−0.601121			−0.300560	+	0.953763i	$0.597174\pi$
$368$		0			0
$369$	28.0979	+	15.1042i	1.46272	+	0.786293i
$370$		0			0
$371$	−3.48026	−	28.6355i	−0.180686	−	1.48668i
$372$		0			0
$373$	−1.69398			−0.0877109			−0.0438555	−	0.999038i	$-0.513964\pi$
$373$	−1.69398			−0.0877109			−0.0438555	+	0.999038i	$0.513964\pi$
$374$		0			0
$375$	−5.74916	−	20.2231i	−0.296885	−	1.04432i
$376$		0			0
$377$	2.11911			0.109140
$378$		0			0
$379$	8.50319			0.436780			0.218390	−	0.975862i	$-0.429920\pi$
$379$	8.50319			0.436780			0.218390	+	0.975862i	$0.429920\pi$
$380$		0			0
$381$	8.01873	+	28.2065i	0.410812	+	1.44506i
$382$		0			0
$383$	−12.7819			−0.653124			−0.326562	−	0.945176i	$-0.605890\pi$
$383$	−12.7819			−0.653124			−0.326562	+	0.945176i	$0.605890\pi$
$384$		0			0
$385$	−14.2017	−	6.04890i	−0.723787	−	0.308280i
$386$		0			0
$387$	0.543559	+	17.8984i	0.0276307	+	0.909825i
$388$		0			0
$389$	3.55959			0.180479			0.0902393	−	0.995920i	$-0.471237\pi$
$389$	3.55959			0.180479			0.0902393	+	0.995920i	$0.471237\pi$
$390$		0			0
$391$	5.10701	+	8.84560i	0.258273	+	0.447341i
$392$		0			0
$393$	−1.12892	−	3.97106i	−0.0569464	−	0.200313i
$394$		0			0
$395$	−7.93448	−	13.7429i	−0.399227	−	0.691482i
$396$		0			0
$397$	11.0411	−	19.1238i	0.554138	−	0.959795i	−0.443832	−	0.896110i	$-0.646381\pi$
$397$	11.0411	−	19.1238i	0.554138	−	0.959795i	0.997970	−	0.0636848i	$-0.0202852\pi$
$398$		0			0
$399$	21.7871	+	16.5378i	1.09072	+	0.827923i
$400$		0			0
$401$	2.59853			0.129765			0.0648823	−	0.997893i	$-0.479333\pi$
$401$	2.59853			0.129765			0.0648823	+	0.997893i	$0.479333\pi$
$402$		0			0
$403$	18.6066			0.926859
$404$		0			0
$405$	−7.64768	+	15.3248i	−0.380016	+	0.761495i
$406$		0			0
$407$	4.33973	−	7.51662i	0.215112	−	0.372585i
$408$		0			0
$409$	−1.51604	+	2.62585i	−0.0749632	+	0.129840i	−0.901070	−	0.433673i	$-0.857217\pi$
$409$	−1.51604	+	2.62585i	−0.0749632	+	0.129840i	0.826107	+	0.563513i	$0.190551\pi$
$410$		0			0
$411$	−5.20142	−	18.2964i	−0.256567	−	0.902493i
$412$		0			0
$413$	−24.0334	+	18.0642i	−1.18261	+	0.888881i
$414$		0			0
$415$	15.1899	−	26.3096i	0.745641	−	1.29149i
$416$		0			0
$417$	−8.93468	+	9.21014i	−0.437533	+	0.451023i
$418$		0			0
$419$	−17.4979	−	30.3073i	−0.854829	−	1.48061i	−0.876804	−	0.480848i	$-0.840329\pi$
$419$	−17.4979	−	30.3073i	−0.854829	−	1.48061i	0.0219749	−	0.999759i	$-0.493005\pi$
$420$		0			0
$421$	13.3264	−	23.0820i	0.649488	−	1.12495i	−0.333757	−	0.942659i	$-0.608316\pi$
$421$	13.3264	−	23.0820i	0.649488	−	1.12495i	0.983245	−	0.182288i	$-0.0583502\pi$
$422$		0			0
$423$	−2.55436	−	1.37311i	−0.124197	−	0.0667631i
$424$		0			0
$425$	0.983916	+	1.70419i	0.0477269	+	0.0826655i
$426$		0			0
$427$	0.287106	+	2.36230i	0.0138940	+	0.114320i
$428$		0			0
$429$	−8.36818	+	8.62617i	−0.404019	+	0.416475i
$430$		0			0
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	0.573636	−	0.819110i	$-0.305532\pi$
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	−0.996188	+	0.0872286i	$0.972199\pi$
$432$		0			0
$433$	−18.0202			−0.865997			−0.432998	−	0.901395i	$-0.642544\pi$
$433$	−18.0202			−0.865997			−0.432998	+	0.901395i	$0.642544\pi$
$434$		0			0
$435$	2.99286	+	0.753434i	0.143496	+	0.0361244i
$436$		0			0
$437$	−21.3549	+	36.9878i	−1.02154	+	1.76937i
$438$		0			0
$439$	−18.7159	−	32.4169i	−0.893263	−	1.54718i	−0.835940	−	0.548820i	$-0.815077\pi$
$439$	−18.7159	−	32.4169i	−0.893263	−	1.54718i	−0.0573222	−	0.998356i	$-0.518256\pi$
$440$		0			0
$441$	−20.3401	−	5.22299i	−0.968577	−	0.248714i
$442$		0			0
$443$	−3.67162	−	6.35944i	−0.174444	−	0.302146i	0.765525	−	0.643407i	$-0.222479\pi$
$443$	−3.67162	−	6.35944i	−0.174444	−	0.302146i	−0.939969	+	0.341261i	$0.889146\pi$
$444$		0			0
$445$	4.92863	−	8.53664i	0.233639	−	0.404675i
$446$		0			0
$447$	−8.34725	−	29.3621i	−0.394812	−	1.38878i
$448$		0			0
$449$	−40.3618			−1.90479			−0.952395	−	0.304866i	$-0.901388\pi$
$449$	−40.3618			−1.90479			−0.952395	+	0.304866i	$0.901388\pi$
$450$		0			0
$451$	16.3003	+	28.2330i	0.767553	+	1.32944i
$452$		0			0
$453$	9.64617	+	33.9311i	0.453217	+	1.59422i
$454$		0			0
$455$	1.37480	+	11.3118i	0.0644514	+	0.530305i
$456$		0			0
$457$	13.7360	+	23.7914i	0.642543	+	1.11292i	0.984863	+	0.173333i	$0.0554538\pi$
$457$	13.7360	+	23.7914i	0.642543	+	1.11292i	−0.342321	+	0.939583i	$0.611213\pi$
$458$		0			0
$459$	1.59158	−	7.24448i	0.0742885	−	0.338143i
$460$		0			0
$461$	−3.36325	+	5.82532i	−0.156642	+	0.271312i	−0.933656	−	0.358172i	$-0.883400\pi$
$461$	−3.36325	+	5.82532i	−0.156642	+	0.271312i	0.777014	+	0.629484i	$0.216734\pi$
$462$		0			0
$463$	1.89569	+	3.28344i	0.0881004	+	0.152594i	0.906708	−	0.421759i	$-0.138587\pi$
$463$	1.89569	+	3.28344i	0.0881004	+	0.152594i	−0.818608	+	0.574353i	$0.805254\pi$
$464$		0			0
$465$	26.2783	+	6.61542i	1.21863	+	0.306783i
$466$		0			0
$467$	10.2166	−	17.6957i	0.472769	−	0.818860i	−0.526746	−	0.850023i	$-0.676588\pi$
$467$	10.2166	−	17.6957i	0.472769	−	0.818860i	0.999514	+	0.0311635i	$0.00992126\pi$
$468$		0			0
$469$	3.44233	−	2.58735i	0.158952	−	0.119473i
$470$		0			0
$471$	15.5911	+	3.92496i	0.718398	+	0.180852i
$472$		0			0
$473$	−9.14987	+	15.8480i	−0.420712	+	0.728694i
$474$		0			0
$475$	−4.11423	+	7.12606i	−0.188774	+	0.326966i
$476$		0			0
$477$	−28.8098	−	15.4869i	−1.31911	−	0.709095i
$478$		0			0
$479$	27.9079			1.27514			0.637572	−	0.770391i	$-0.279939\pi$
$479$	27.9079			1.27514			0.637572	+	0.770391i	$0.279939\pi$
$480$		0			0
$481$	−6.40715			−0.292141
$482$		0			0
$483$	4.11012	−	32.5317i	0.187017	−	1.48024i
$484$		0			0
$485$	−1.75627	+	3.04194i	−0.0797480	+	0.138128i
$486$		0			0
$487$	−5.89480	−	10.2101i	−0.267119	−	0.462663i	0.700998	−	0.713163i	$-0.252738\pi$
$487$	−5.89480	−	10.2101i	−0.267119	−	0.462663i	−0.968117	+	0.250500i	$0.919405\pi$
$488$		0			0
$489$	39.9988	+	10.0695i	1.80881	+	0.455357i
$490$		0			0
$491$	13.2596	+	22.9662i	0.598396	+	1.03645i	0.993058	+	0.117626i	$0.0375283\pi$
$491$	13.2596	+	22.9662i	0.598396	+	1.03645i	−0.394662	+	0.918826i	$0.629138\pi$
$492$		0			0
$493$	−1.33656			−0.0601957
$494$		0			0
$495$	−14.8855	+	9.20764i	−0.669052	+	0.413853i
$496$		0			0
$497$	5.75380	+	2.45070i	0.258093	+	0.109929i
$498$		0			0
$499$	42.3329			1.89508			0.947540	−	0.319637i	$-0.103561\pi$
$499$	42.3329			1.89508			0.947540	+	0.319637i	$0.103561\pi$
$500$		0			0
$501$	−2.13104	+	2.19674i	−0.0952077	+	0.0981430i
$502$		0			0
$503$	11.0768			0.493890			0.246945	−	0.969029i	$-0.420573\pi$
$503$	11.0768			0.493890			0.246945	+	0.969029i	$0.420573\pi$
$504$		0			0
$505$	15.3449			0.682839
$506$		0			0
$507$	−13.2320	−	3.33108i	−0.587654	−	0.147938i
$508$		0			0
$509$	24.7262			1.09597			0.547984	−	0.836489i	$-0.315395\pi$
$509$	24.7262			1.09597			0.547984	+	0.836489i	$0.315395\pi$
$510$		0			0
$511$	0.636042	+	5.23334i	0.0281368	+	0.231509i
$512$		0			0
$513$	29.5619	−	9.38282i	1.30519	−	0.414262i
$514$		0			0
$515$	33.8709			1.49253
$516$		0			0
$517$	−1.48185	−	2.56665i	−0.0651719	−	0.112881i
$518$		0			0
$519$	−0.434284	+	0.447673i	−0.0190629	+	0.0196507i
$520$		0			0
$521$	6.42298	+	11.1249i	0.281396	+	0.487392i	0.971729	−	0.236100i	$-0.0758693\pi$
$521$	6.42298	+	11.1249i	0.281396	+	0.487392i	−0.690333	+	0.723492i	$0.742536\pi$
$522$		0			0
$523$	−1.70453	+	2.95234i	−0.0745340	+	0.129097i	−0.900884	−	0.434061i	$-0.857080\pi$
$523$	−1.70453	+	2.95234i	−0.0745340	+	0.129097i	0.826350	+	0.563158i	$0.190414\pi$
$524$		0			0
$525$	0.791854	−	6.26755i	0.0345593	−	0.273538i
$526$		0			0
$527$	−11.7355			−0.511206
$528$		0			0
$529$	28.2002			1.22609
$530$		0			0
$531$	1.03483	+	34.0751i	0.0449080	+	1.47873i
$532$		0			0
$533$	12.0329	−	20.8416i	0.521202	−	0.902748i
$534$		0			0
$535$	−16.6704	+	28.8741i	−0.720726	+	1.24833i
$536$		0			0
$537$	−8.62783	+	8.89383i	−0.372318	+	0.383797i
$538$		0			0
$539$	−14.8701	−	15.4744i	−0.640500	−	0.666530i
$540$		0			0
$541$	−22.9553	+	39.7598i	−0.986926	+	1.70941i	−0.353884	+	0.935289i	$0.615139\pi$
$541$	−22.9553	+	39.7598i	−0.986926	+	1.70941i	−0.633043	+	0.774117i	$0.718194\pi$
$542$		0			0
$543$	−5.23560	−	18.4166i	−0.224681	−	0.790333i
$544$		0			0
$545$	−2.12073	−	3.67321i	−0.0908421	−	0.157343i
$546$		0			0
$547$	−12.5502	+	21.7376i	−0.536608	+	0.929432i	0.462476	+	0.886632i	$0.346961\pi$
$547$	−12.5502	+	21.7376i	−0.536608	+	0.929432i	−0.999084	+	0.0428004i	$0.986372\pi$
$548$		0			0
$549$	2.37668	+	1.27760i	0.101434	+	0.0545266i
$550$		0			0
$551$	−2.79441	−	4.84006i	−0.119046	−	0.206194i
$552$		0			0
$553$	−2.66183	−	21.9015i	−0.113192	−	0.931345i
$554$		0			0
$555$	−9.04893	−	2.27801i	−0.384106	−	0.0966963i
$556$		0			0
$557$	0.836144	+	1.44824i	0.0354285	+	0.0613640i	0.883196	−	0.469004i	$-0.155387\pi$
$557$	0.836144	+	1.44824i	0.0354285	+	0.0613640i	−0.847767	+	0.530368i	$0.822054\pi$
$558$		0			0
$559$	13.5088			0.571363
$560$		0			0
$561$	5.27796	−	5.44068i	0.222836	−	0.229706i
$562$		0			0
$563$	11.3764	−	19.7046i	0.479460	−	0.830449i	−0.520263	−	0.854006i	$-0.674166\pi$
$563$	11.3764	−	19.7046i	0.479460	−	0.830449i	0.999722	+	0.0235574i	$0.00749926\pi$
$564$		0			0
$565$	14.4628	+	25.0504i	0.608456	+	1.05388i
$566$		0			0
$567$	−18.1313	+	15.4356i	−0.761442	+	0.648233i
$568$		0			0
$569$	13.0292	+	22.5673i	0.546214	+	0.946071i	0.998529	+	0.0542125i	$0.0172649\pi$
$569$	13.0292	+	22.5673i	0.546214	+	0.946071i	−0.452315	+	0.891858i	$0.649402\pi$
$570$		0			0
$571$	−6.24174	+	10.8110i	−0.261209	+	0.452427i	−0.966563	−	0.256428i	$-0.917454\pi$
$571$	−6.24174	+	10.8110i	−0.261209	+	0.452427i	0.705355	+	0.708855i	$0.250788\pi$
$572$		0			0
$573$	10.4943	−	10.8179i	0.438407	−	0.451923i
$574$		0			0
$575$	9.86421			0.411366
$576$		0			0
$577$	−10.3756	−	17.9710i	−0.431941	−	0.748143i	0.565100	−	0.825023i	$-0.308838\pi$
$577$	−10.3756	−	17.9710i	−0.431941	−	0.748143i	−0.997040	+	0.0768793i	$0.975504\pi$
$578$		0			0
$579$	−2.38390	−	0.600133i	−0.0990715	−	0.0249407i
$580$		0			0
$581$	33.7631	−	25.3773i	1.40073	−	1.05283i
$582$		0			0
$583$	−16.7133	−	28.9483i	−0.692195	−	1.19892i
$584$		0			0
$585$	11.3806	+	6.11773i	0.470532	+	0.252937i
$586$		0			0
$587$	8.67294	−	15.0220i	0.357971	−	0.620023i	−0.629651	−	0.776878i	$-0.716802\pi$
$587$	8.67294	−	15.0220i	0.357971	−	0.620023i	0.987622	+	0.156855i	$0.0501355\pi$
$588$		0			0
$589$	−24.5359	−	42.4975i	−1.01099	−	1.75108i
$590$		0			0
$591$	−2.69697	−	9.48680i	−0.110939	−	0.390235i
$592$		0			0
$593$	−14.0203	+	24.2839i	−0.575745	+	0.997220i	0.420215	+	0.907425i	$0.361955\pi$
$593$	−14.0203	+	24.2839i	−0.575745	+	0.997220i	−0.995960	+	0.0897956i	$0.971379\pi$
$594$		0			0
$595$	−0.867109	−	7.13455i	−0.0355480	−	0.292488i
$596$		0			0
$597$	6.30327	−	6.49760i	0.257976	−	0.265929i
$598$		0			0
$599$	−11.6047	+	20.0999i	−0.474155	+	0.821260i	−0.999562	−	0.0295906i	$-0.990580\pi$
$599$	−11.6047	+	20.0999i	−0.474155	+	0.821260i	0.525407	+	0.850851i	$0.323913\pi$
$600$		0			0
$601$	−0.348014	+	0.602779i	−0.0141958	+	0.0245878i	−0.873036	−	0.487656i	$-0.837852\pi$
$601$	−0.348014	+	0.602779i	−0.0141958	+	0.0245878i	0.858840	+	0.512244i	$0.171185\pi$
$602$		0			0
$603$	−0.148220	−	4.88061i	−0.00603599	−	0.198754i
$604$		0			0
$605$	3.04572			0.123826
$606$		0			0
$607$	−1.71065			−0.0694333			−0.0347166	−	0.999397i	$-0.511053\pi$
$607$	−1.71065			−0.0694333			−0.0347166	+	0.999397i	$0.511053\pi$
$608$		0			0
$609$	3.41771	+	2.59425i	0.138493	+	0.105124i
$610$		0			0
$611$	−1.09390	+	1.89469i	−0.0442545	+	0.0766511i
$612$		0			0
$613$	1.77253	+	3.07010i	0.0715916	+	0.124000i	0.899599	−	0.436717i	$-0.143859\pi$
$613$	1.77253	+	3.07010i	0.0715916	+	0.124000i	−0.828007	+	0.560717i	$0.810525\pi$
$614$		0			0
$615$	24.4043	−	25.1567i	0.984076	−	1.01442i
$616$		0			0
$617$	5.58526	+	9.67395i	0.224854	+	0.389458i	0.956276	−	0.292467i	$-0.0944762\pi$
$617$	5.58526	+	9.67395i	0.224854	+	0.389458i	−0.731422	+	0.681925i	$0.761143\pi$
$618$		0			0
$619$	19.2172			0.772403			0.386201	−	0.922415i	$-0.373787\pi$
$619$	19.2172			0.772403			0.386201	+	0.922415i	$0.373787\pi$
$620$		0			0
$621$	−27.4603	−	25.0666i	−1.10195	−	1.00589i
$622$		0			0
$623$	10.9551	−	8.23414i	0.438906	−	0.329894i
$624$		0			0
$625$	−16.2067			−0.648270
$626$		0			0
$627$	30.7371	+	7.73788i	1.22752	+	0.309021i
$628$		0			0
$629$	4.04111			0.161130
$630$		0			0
$631$	−23.1101			−0.920000			−0.460000	−	0.887919i	$-0.652151\pi$
$631$	−23.1101			−0.920000			−0.460000	+	0.887919i	$0.652151\pi$
$632$		0			0
$633$	−14.3052	+	14.7463i	−0.568582	+	0.586111i
$634$		0			0
$635$	32.2185			1.27855
$636$		0			0
$637$	−4.40423	+	15.2180i	−0.174502	+	0.602960i
$638$		0			0
$639$	6.03082	−	3.73045i	0.238575	−	0.147574i
$640$		0			0
$641$	−20.3938			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$641$	−20.3938			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$642$		0			0
$643$	−1.31644	−	2.28015i	−0.0519154	−	0.0899202i	0.838900	−	0.544286i	$-0.183199\pi$
$643$	−1.31644	−	2.28015i	−0.0519154	−	0.0899202i	−0.890815	+	0.454366i	$0.849866\pi$
$644$		0			0
$645$	19.0788	+	4.80296i	0.751225	+	0.189117i
$646$		0			0
$647$	3.63856	+	6.30217i	0.143047	+	0.247764i	0.928642	−	0.370976i	$-0.120977\pi$
$647$	3.63856	+	6.30217i	0.143047	+	0.247764i	−0.785596	+	0.618740i	$0.787643\pi$
$648$		0			0
$649$	−17.4196	+	30.1717i	−0.683781	+	1.18434i
$650$		0			0
$651$	30.0087	+	22.7785i	1.17614	+	0.892758i
$652$		0			0
$653$	22.8671			0.894858			0.447429	−	0.894319i	$-0.352340\pi$
$653$	22.8671			0.894858			0.447429	+	0.894319i	$0.352340\pi$
$654$		0			0
$655$	−4.53589			−0.177232
$656$		0			0
$657$	5.26520	+	2.83034i	0.205415	+	0.110422i
$658$		0			0
$659$	−3.59545	+	6.22750i	−0.140059	+	0.242589i	−0.927519	−	0.373777i	$-0.878062\pi$
$659$	−3.59545	+	6.22750i	−0.140059	+	0.242589i	0.787460	+	0.616366i	$0.211396\pi$
$660$		0			0
$661$	17.2064	−	29.8023i	0.669250	−	1.15918i	−0.308864	−	0.951106i	$-0.599949\pi$
$661$	17.2064	−	29.8023i	0.669250	−	1.15918i	0.978114	−	0.208069i	$-0.0667179\pi$
$662$		0			0
$663$	−5.42631	−	1.36604i	−0.210740	−	0.0530526i
$664$		0			0
$665$	24.0233	−	18.0566i	0.931583	−	0.700204i
$666$		0			0
$667$	−3.34991	+	5.80222i	−0.129709	+	0.224663i
$668$		0			0
$669$	−41.3024	−	10.3976i	−1.59684	−	0.401996i
$670$		0			0
$671$	1.37877	+	2.38811i	0.0532270	+	0.0921919i
$672$		0			0
$673$	3.46705	−	6.00511i	0.133645	−	0.231480i	−0.791434	−	0.611255i	$-0.790665\pi$
$673$	3.46705	−	6.00511i	0.133645	−	0.231480i	0.925079	+	0.379775i	$0.123998\pi$
$674$		0			0
$675$	−5.29050	−	4.82933i	−0.203631	−	0.185881i
$676$		0			0
$677$	−17.3014	−	29.9668i	−0.664945	−	1.15172i	−0.979300	−	0.202413i	$-0.935122\pi$
$677$	−17.3014	−	29.9668i	−0.664945	−	1.15172i	0.314355	−	0.949306i	$-0.398212\pi$
$678$		0			0
$679$	−3.90373	+	2.93415i	−0.149811	+	0.112602i
$680$		0			0
$681$	−7.25507	−	25.5203i	−0.278015	−	0.977938i
$682$		0			0
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	−0.955506	−	0.294971i	$-0.904690\pi$
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	0.222300	−	0.974978i	$-0.428643\pi$
$684$		0			0
$685$	−20.8988			−0.798502
$686$		0			0
$687$	−8.07350	−	28.3991i	−0.308023	−	1.08349i
$688$		0			0
$689$	−12.3377	+	21.3696i	−0.470030	+	0.814116i
$690$		0			0
$691$	3.94953	+	6.84079i	0.150247	+	0.260236i	0.931318	−	0.364206i	$-0.118660\pi$
$691$	3.94953	+	6.84079i	0.150247	+	0.260236i	−0.781071	+	0.624442i	$0.785326\pi$
$692$		0			0
$693$	−24.0565	+	3.66786i	−0.913832	+	0.139331i
$694$		0			0
$695$	7.04916	+	12.2095i	0.267390	+	0.463133i
$696$		0			0
$697$	−7.58936	+	13.1452i	−0.287467	+	0.497908i
$698$		0			0
$699$	−33.1983	−	8.35748i	−1.25568	−	0.316109i
$700$		0			0
$701$	−25.9291			−0.979329			−0.489664	−	0.871911i	$-0.662881\pi$
$701$	−25.9291			−0.979329			−0.489664	+	0.871911i	$0.662881\pi$
$702$		0			0
$703$	8.44893	+	14.6340i	0.318657	+	0.551931i
$704$		0			0
$705$	−2.21858	+	2.28698i	−0.0835565	+	0.0861326i
$706$		0			0
$707$	19.6278	+	8.36001i	0.738180	+	0.314410i
$708$		0			0
$709$	−14.0523	−	24.3394i	−0.527746	−	0.914084i	−0.999477	−	0.0323408i	$-0.989704\pi$
$709$	−14.0523	−	24.3394i	−0.527746	−	0.914084i	0.471731	−	0.881743i	$-0.343630\pi$
$710$		0			0
$711$	−22.0348	−	11.8449i	−0.826369	−	0.444219i
$712$		0			0
$713$	−29.4134	+	50.9456i	−1.10154	+	1.90793i
$714$		0			0
$715$	6.60221	+	11.4354i	0.246909	+	0.427658i
$716$		0			0
$717$	20.1414	−	20.7624i	0.752194	−	0.775385i
$718$		0			0
$719$	−5.89461	+	10.2098i	−0.219832	+	0.380760i	−0.954756	−	0.297389i	$-0.903884\pi$
$719$	−5.89461	+	10.2098i	−0.219832	+	0.380760i	0.734924	+	0.678149i	$0.237218\pi$
$720$		0			0
$721$	43.3246	+	18.4531i	1.61349	+	0.687229i
$722$		0			0
$723$	−3.03122	−	10.6625i	−0.112732	−	0.396544i
$724$		0			0
$725$	−0.645394	+	1.11785i	−0.0239693	+	0.0415161i
$726$		0			0
$727$	−24.5207	+	42.4711i	−0.909423	+	1.57517i	−0.0945549	+	0.995520i	$0.530143\pi$
$727$	−24.5207	+	42.4711i	−0.909423	+	1.57517i	−0.814868	+	0.579647i	$0.803191\pi$
$728$		0			0
$729$	2.45575	+	26.8881i	0.0909537	+	0.995855i
$730$		0			0
$731$	−8.52027			−0.315134
$732$		0			0
$733$	15.0927			0.557461			0.278731	−	0.960369i	$-0.410086\pi$
$733$	15.0927			0.557461			0.278731	+	0.960369i	$0.410086\pi$
$734$		0			0
$735$	−11.6308	+	19.9268i	−0.429009	+	0.735009i
$736$		0			0
$737$	2.49503	−	4.32152i	0.0919056	−	0.159185i
$738$		0			0
$739$	15.9556	+	27.6359i	0.586937	+	1.01660i	0.994631	+	0.103486i	$0.0329996\pi$
$739$	15.9556	+	27.6359i	0.586937	+	1.01660i	−0.407694	+	0.913119i	$0.633667\pi$
$740$		0			0
$741$	−6.39821	−	22.5062i	−0.235044	−	0.826786i
$742$		0			0
$743$	12.1582	+	21.0586i	0.446041	+	0.772565i	0.998124	−	0.0612238i	$-0.0195003\pi$
$743$	12.1582	+	21.0586i	0.446041	+	0.772565i	−0.552083	+	0.833789i	$0.686167\pi$
$744$		0			0
$745$	−33.5385			−1.22875
$746$		0			0
$747$	−1.45378	−	47.8701i	−0.0531909	−	1.75148i
$748$		0			0
$749$	−37.0541	+	27.8509i	−1.35393	+	1.01765i
$750$		0			0
$751$	−33.4463			−1.22047			−0.610237	−	0.792219i	$-0.708926\pi$
$751$	−33.4463			−1.22047			−0.610237	+	0.792219i	$0.708926\pi$
$752$		0			0
$753$	12.7097	+	44.7073i	0.463167	+	1.62923i
$754$		0			0
$755$	38.7574			1.41053
$756$		0			0
$757$	−32.1248			−1.16759			−0.583797	−	0.811899i	$-0.698434\pi$
$757$	−32.1248			−1.16759			−0.583797	+	0.811899i	$0.698434\pi$
$758$		0			0
$759$	−10.3903	−	36.5488i	−0.377145	−	1.32664i
$760$		0			0
$761$	33.7957			1.22509			0.612547	−	0.790435i	$-0.290145\pi$
$761$	33.7957			1.22509			0.612547	+	0.790435i	$0.290145\pi$
$762$		0			0
$763$	−0.711454	−	5.85382i	−0.0257563	−	0.211923i
$764$		0			0
$765$	−7.17798	−	3.85856i	−0.259520	−	0.139507i
$766$		0			0
$767$	25.7183			0.928634
$768$		0			0
$769$	16.8957	+	29.2643i	0.609276	+	1.05530i	0.991360	+	0.131170i	$0.0418733\pi$
$769$	16.8957	+	29.2643i	0.609276	+	1.05530i	−0.382084	+	0.924128i	$0.624793\pi$
$770$		0			0
$771$	−3.39877	−	11.9554i	−0.122404	−	0.430564i
$772$		0			0
$773$	−12.0231	−	20.8247i	−0.432443	−	0.749012i	0.564640	−	0.825337i	$-0.309015\pi$
$773$	−12.0231	−	20.8247i	−0.432443	−	0.749012i	−0.997083	+	0.0763245i	$0.975682\pi$
$774$		0			0
$775$	−5.66679	+	9.81516i	−0.203557	+	0.352571i
$776$		0			0
$777$	−10.3335	−	7.84375i	−0.370712	−	0.281393i
$778$		0			0
$779$	−63.4696			−2.27404
$780$		0			0
$781$	7.24703			0.259319
$782$		0			0
$783$	4.63732	−	1.47187i	0.165724	−	0.0526003i
$784$		0			0
$785$	8.83219	−	15.2978i	0.315234	−	0.546002i
$786$		0			0
$787$	3.22897	−	5.59274i	0.115100	−	0.199360i	−0.802719	−	0.596357i	$-0.796614\pi$
$787$	3.22897	−	5.59274i	0.115100	−	0.199360i	0.917820	+	0.396997i	$0.129948\pi$
$788$		0			0
$789$	−9.66858	−	34.0100i	−0.344211	−	1.21079i
$790$		0			0
$791$	4.85193	+	39.9216i	0.172515	+	1.41945i
$792$		0			0
$793$	1.01781	−	1.76290i	0.0361435	−	0.0626023i
$794$		0			0
$795$	−25.0226	+	25.7940i	−0.887459	+	0.914820i
$796$		0			0
$797$	18.6987	+	32.3871i	0.662341	+	1.14721i	0.979999	+	0.199003i	$0.0637704\pi$
$797$	18.6987	+	32.3871i	0.662341	+	1.14721i	−0.317658	+	0.948205i	$0.602896\pi$
$798$		0			0
$799$	0.689944	−	1.19502i	0.0244085	−	0.0422767i
$800$		0			0
$801$	−0.471705	−	15.5323i	−0.0166669	−	0.548808i
$802$		0			0
$803$	3.05448	+	5.29051i	0.107790	+	0.186698i
$804$		0			0
$805$	−33.1455	−	14.1175i	−1.16822	−	0.497578i
$806$		0			0
$807$	−8.13459	+	8.38538i	−0.286351	+	0.295179i
$808$		0			0
$809$	−20.0048	−	34.6493i	−0.703331	−	1.21821i	−0.967290	−	0.253672i	$-0.918362\pi$
$809$	−20.0048	−	34.6493i	−0.703331	−	1.21821i	0.263959	−	0.964534i	$-0.414972\pi$
$810$		0			0
$811$	−27.6946			−0.972489			−0.486245	−	0.873823i	$-0.661634\pi$
$811$	−27.6946			−0.972489			−0.486245	+	0.873823i	$0.661634\pi$
$812$		0			0
$813$	3.51490	+	0.884855i	0.123273	+	0.0310332i
$814$		0			0
$815$	22.6590	−	39.2465i	0.793709	−	1.37474i
$816$		0			0
$817$	−17.8137	−	30.8543i	−0.623223	−	1.07945i
$818$		0			0
$819$	11.2241	+	14.0255i	0.392202	+	0.490091i
$820$		0			0
$821$	0.188732	+	0.326893i	0.00658679	+	0.0114087i	0.869300	−	0.494285i	$-0.164570\pi$
$821$	0.188732	+	0.326893i	0.00658679	+	0.0114087i	−0.862713	+	0.505693i	$0.831237\pi$
$822$		0			0
$823$	−5.50313	+	9.53170i	−0.191827	+	0.332254i	−0.945856	−	0.324587i	$-0.894775\pi$
$823$	−5.50313	+	9.53170i	−0.191827	+	0.332254i	0.754029	+	0.656841i	$0.228108\pi$
$824$		0			0
$825$	−2.00180	−	7.04148i	−0.0696937	−	0.245153i
$826$		0			0
$827$	28.2473			0.982254			0.491127	−	0.871088i	$-0.336585\pi$
$827$	28.2473			0.982254			0.491127	+	0.871088i	$0.336585\pi$
$828$		0			0
$829$	−14.7833	−	25.6054i	−0.513445	−	0.889313i	−0.999878	−	0.0155953i	$-0.995036\pi$
$829$	−14.7833	−	25.6054i	−0.513445	−	0.889313i	0.486433	−	0.873718i	$-0.338298\pi$
$830$		0			0
$831$	11.1498	+	39.2202i	0.386781	+	1.36053i
$832$		0			0
$833$	2.77783	−	9.59828i	0.0962460	−	0.332561i
$834$		0			0
$835$	1.68132	+	2.91212i	0.0581843	+	0.100778i
$836$		0			0
$837$	40.7174	−	12.9235i	1.40740	−	0.446703i
$838$		0			0
$839$	6.91508	−	11.9773i	0.238735	−	0.413501i	−0.721617	−	0.692293i	$-0.756601\pi$
$839$	6.91508	−	11.9773i	0.238735	−	0.413501i	0.960352	+	0.278792i	$0.0899339\pi$
$840$		0			0
$841$	14.0616	+	24.3555i	0.484884	+	0.839844i
$842$		0			0
$843$	−32.4523	−	8.16968i	−1.11772	−	0.281379i
$844$		0			0
$845$	−7.49581	+	12.9831i	−0.257864	+	0.446633i
$846$		0			0
$847$	3.89581	+	1.65933i	0.133861	+	0.0570152i
$848$		0			0
$849$	−7.47972	−	1.88297i	−0.256703	−	0.0646235i
$850$		0			0
$851$	10.1285	−	17.5431i	0.347200	−	0.601369i
$852$		0			0
$853$	4.59367	−	7.95647i	0.157284	−	0.272424i	−0.776604	−	0.629989i	$-0.783059\pi$
$853$	4.59367	−	7.95647i	0.157284	−	0.272424i	0.933888	+	0.357565i	$0.116393\pi$
$854$		0			0
$855$	−1.03440	−	34.0607i	−0.0353756	−	1.16485i
$856$		0			0
$857$	40.4460			1.38161			0.690805	−	0.723041i	$-0.257256\pi$
$857$	40.4460			1.38161			0.690805	+	0.723041i	$0.257256\pi$
$858$		0			0
$859$	−12.5128			−0.426933			−0.213466	−	0.976950i	$-0.568475\pi$
$859$	−12.5128			−0.426933			−0.213466	+	0.976950i	$0.568475\pi$
$860$		0			0
$861$	44.9213	−	18.8825i	1.53091	−	0.643514i
$862$		0			0
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	−0.993931	−	0.110010i	$-0.964912\pi$
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	0.592236	+	0.805764i	$0.298245\pi$
$864$		0			0
$865$	0.342635	+	0.593462i	0.0116499	+	0.0201783i
$866$		0			0
$867$	−25.1315	−	6.32670i	−0.853510	−	0.214866i
$868$		0			0
$869$	−12.7830	−	22.1407i	−0.433632	−	0.751073i
$870$		0			0
$871$	−3.68365			−0.124816
$872$		0			0
$873$	0.168087	+	5.53479i	0.00568889	+	0.187324i
$874$		0			0
$875$	−29.5469	−	12.5848i	−0.998866	−	0.425444i
$876$		0			0
$877$	−27.5467			−0.930185			−0.465092	−	0.885262i	$-0.653979\pi$
$877$	−27.5467			−0.930185			−0.465092	+	0.885262i	$0.653979\pi$
$878$		0			0
$879$	−28.2964	+	29.1687i	−0.954413	+	0.983837i
$880$		0			0
$881$	42.0894			1.41803			0.709014	−	0.705194i	$-0.249140\pi$
$881$	42.0894			1.41803			0.709014	+	0.705194i	$0.249140\pi$
$882$		0			0
$883$	8.58158			0.288793			0.144397	−	0.989520i	$-0.453876\pi$
$883$	8.58158			0.288793			0.144397	+	0.989520i	$0.453876\pi$
$884$		0			0
$885$	36.3224	+	9.14394i	1.22096	+	0.307370i
$886$		0			0
$887$	3.51907			0.118159			0.0590795	−	0.998253i	$-0.481183\pi$
$887$	3.51907			0.118159			0.0590795	+	0.998253i	$0.481183\pi$
$888$		0			0
$889$	41.2110	+	17.5529i	1.38217	+	0.588704i
$890$		0			0
$891$	−12.3209	+	24.6892i	−0.412765	+	0.827120i
$892$		0			0
$893$	5.76998			0.193085
$894$		0			0
$895$	6.80707	+	11.7902i	0.227535	+	0.394103i
$896$		0			0
$897$	−19.5305	+	20.1326i	−0.652105	+	0.672209i
$898$		0			0
$899$	−3.84891	−	6.66651i	−0.128368	−	0.222341i
$900$		0			0
$901$	7.78163	−	13.4782i	0.259244	−	0.449023i
$902$		0			0
$903$	21.7871	+	16.5378i	0.725030	+	0.550342i
$904$		0			0
$905$	−21.0362			−0.699266
$906$		0			0
$907$	37.2826			1.23795			0.618974	−	0.785412i	$-0.287549\pi$
$907$	37.2826			1.23795			0.618974	+	0.785412i	$0.287549\pi$
$908$		0			0
$909$	20.5728	−	12.7256i	0.682356	−	0.422082i
$910$		0			0
$911$	−10.6458	+	18.4391i	−0.352711	+	0.610914i	−0.986723	−	0.162409i	$-0.948074\pi$
$911$	−10.6458	+	18.4391i	−0.352711	+	0.610914i	0.634012	+	0.773323i	$0.281407\pi$
$912$		0			0
$913$	24.4718	−	42.3864i	0.809899	−	1.40279i
$914$		0			0
$915$	2.06425	−	2.12789i	0.0682421	−	0.0703460i
$916$		0			0
$917$	−5.80190	−	2.47118i	−0.191595	−	0.0816056i
$918$		0			0
$919$	6.00453	−	10.4001i	0.198071	−	0.343069i	−0.749832	−	0.661628i	$-0.769866\pi$
$919$	6.00453	−	10.4001i	0.198071	−	0.343069i	0.947903	+	0.318559i	$0.103199\pi$
$920$		0			0
$921$	−3.69412	−	12.9943i	−0.121725	−	0.428178i
$922$		0			0
$923$	−2.67487	−	4.63301i	−0.0880444	−	0.152497i
$924$		0			0
$925$	1.95135	−	3.37984i	0.0641601	−	0.111129i
$926$		0			0
$927$	45.4104	−	28.0893i	1.49147	−	0.922574i
$928$		0			0
$929$	−10.2602	−	17.7712i	−0.336626	−	0.583054i	0.647170	−	0.762346i	$-0.275953\pi$
$929$	−10.2602	−	17.7712i	−0.336626	−	0.583054i	−0.983796	+	0.179292i	$0.942619\pi$
$930$		0			0
$931$	40.5657	−	10.0083i	1.32949	−	0.328008i
$932$		0			0
$933$	25.1762	+	6.33795i	0.824230	+	0.207495i
$934$		0			0
$935$	−4.16413	−	7.21249i	−0.136182	−	0.235874i
$936$		0			0
$937$	−10.9040			−0.356217			−0.178109	−	0.984011i	$-0.556998\pi$
$937$	−10.9040			−0.356217			−0.178109	+	0.984011i	$0.556998\pi$
$938$		0			0
$939$	−8.35361	+	8.61115i	−0.272610	+	0.281014i
$940$		0			0
$941$	15.4807	−	26.8134i	0.504656	−	0.874090i	−0.495329	−	0.868705i	$-0.664953\pi$
$941$	15.4807	−	26.8134i	0.504656	−	0.874090i	0.999986	−	0.00538505i	$-0.00171412\pi$
$942$		0			0
$943$	38.0434	+	65.8931i	1.23886	+	2.14578i
$944$		0			0
$945$	10.8653	+	23.7991i	0.353449	+	0.774184i
$946$		0			0
$947$	16.0909	+	27.8702i	0.522884	+	0.905661i	0.999645	+	0.0266283i	$0.00847707\pi$
$947$	16.0909	+	27.8702i	0.522884	+	0.905661i	−0.476762	+	0.879032i	$0.658190\pi$
$948$		0			0
$949$	2.25481	−	3.90545i	0.0731942	−	0.126776i
$950$		0			0
$951$	−13.0942	+	13.4979i	−0.424609	+	0.437700i
$952$		0			0
$953$	39.0934			1.26636			0.633179	−	0.774005i	$-0.281750\pi$
$953$	39.0934			1.26636			0.633179	+	0.774005i	$0.281750\pi$
$954$		0			0
$955$	−8.27967	−	14.3408i	−0.267924	−	0.464057i
$956$		0			0
$957$	4.82168	+	1.21383i	0.155863	+	0.0392375i
$958$		0			0
$959$	−26.7318	−	11.3858i	−0.863216	−	0.367667i
$960$		0			0
$961$	−18.2948	−	31.6876i	−0.590156	−	1.02218i
$962$		0			0
$963$	1.59548	+	52.5361i	0.0514136	+	1.69295i
$964$		0			0
$965$	−1.35046	+	2.33906i	−0.0434728	+	0.0752971i
$966$		0			0
$967$	−12.7235	−	22.0377i	−0.409159	−	0.708684i	0.585637	−	0.810574i	$-0.300845\pi$
$967$	−12.7235	−	22.0377i	−0.409159	−	0.708684i	−0.994796	+	0.101889i	$0.967511\pi$
$968$		0			0
$969$	4.03547	+	14.1951i	0.129638	+	0.456011i
$970$		0			0
$971$	8.81455	−	15.2673i	0.282872	−	0.489949i	−0.689219	−	0.724553i	$-0.742046\pi$
$971$	8.81455	−	15.2673i	0.282872	−	0.489949i	0.972091	+	0.234604i	$0.0753794\pi$
$972$		0			0
$973$	2.36482	+	19.4577i	0.0758128	+	0.623786i
$974$		0			0
$975$	−3.76274	+	3.87875i	−0.120504	+	0.124219i
$976$		0			0
$977$	−13.6269	+	23.6025i	−0.435963	+	0.755109i	−0.997374	−	0.0724277i	$-0.976925\pi$
$977$	−13.6269	+	23.6025i	−0.435963	+	0.755109i	0.561411	+	0.827537i	$0.310259\pi$
$978$		0			0
$979$	7.94033	−	13.7531i	0.253774	−	0.439550i
$980$		0			0
$981$	−5.88946	−	3.16591i	−0.188036	−	0.101080i
$982$		0			0
$983$	−20.6741			−0.659402			−0.329701	−	0.944085i	$-0.606948\pi$
$983$	−20.6741			−0.659402			−0.329701	+	0.944085i	$0.606948\pi$
$984$		0			0
$985$	−10.8362			−0.345269
$986$		0			0
$987$	−4.08377	+	1.71660i	−0.129988	+	0.0546399i
$988$		0			0
$989$	−21.3549	+	36.9878i	−0.679047	+	1.17614i
$990$		0			0
$991$	−26.0081	−	45.0474i	−0.826175	−	1.43098i	−0.901018	−	0.433782i	$-0.857179\pi$
$991$	−26.0081	−	45.0474i	−0.826175	−	1.43098i	0.0748425	−	0.997195i	$-0.476155\pi$
$992$		0			0
$993$	9.71044	−	10.0098i	0.308151	−	0.317652i
$994$		0			0
$995$	−4.97307	−	8.61361i	−0.157657	−	0.273070i
$996$		0			0
$997$	−9.28538			−0.294071			−0.147035	−	0.989131i	$-0.546973\pi$
$997$	−9.28538			−0.294071			−0.147035	+	0.989131i	$0.546973\pi$
$998$		0			0
$999$	−14.0210	+	4.45021i	−0.443605	+	0.140798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.l.b.205.4	yes	14
3.2	odd	2		756.2.l.b.289.6		14
4.3	odd	2		1008.2.t.j.961.4		14
7.2	even	3		1764.2.j.g.1177.7		14
7.3	odd	6		1764.2.i.i.1537.6		14
7.4	even	3		252.2.i.b.25.2	✓	14
7.5	odd	6		1764.2.j.h.1177.1		14
7.6	odd	2		1764.2.l.i.961.4		14
9.2	odd	6		2268.2.k.f.1297.2		14
9.4	even	3		252.2.i.b.121.2	yes	14
9.5	odd	6		756.2.i.b.37.2		14
9.7	even	3		2268.2.k.e.1297.6		14
12.11	even	2		3024.2.t.j.289.6		14
21.2	odd	6		5292.2.j.h.3529.2		14
21.5	even	6		5292.2.j.g.3529.6		14
21.11	odd	6		756.2.i.b.613.2		14
21.17	even	6		5292.2.i.i.2125.6		14
21.20	even	2		5292.2.l.i.3313.2		14
28.11	odd	6		1008.2.q.j.529.6		14
36.23	even	6		3024.2.q.j.2305.2		14
36.31	odd	6		1008.2.q.j.625.6		14
63.4	even	3	inner	252.2.l.b.193.4	yes	14
63.5	even	6		5292.2.j.g.1765.6		14
63.11	odd	6		2268.2.k.f.1621.2		14
63.13	odd	6		1764.2.i.i.373.6		14
63.23	odd	6		5292.2.j.h.1765.2		14
63.25	even	3		2268.2.k.e.1621.6		14
63.31	odd	6		1764.2.l.i.949.4		14
63.32	odd	6		756.2.l.b.361.6		14
63.40	odd	6		1764.2.j.h.589.1		14
63.41	even	6		5292.2.i.i.1549.6		14
63.58	even	3		1764.2.j.g.589.7		14
63.59	even	6		5292.2.l.i.361.2		14
84.11	even	6		3024.2.q.j.2881.2		14
252.67	odd	6		1008.2.t.j.193.4		14
252.95	even	6		3024.2.t.j.1873.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.2	✓	14	7.4	even	3
252.2.i.b.121.2	yes	14	9.4	even	3
252.2.l.b.193.4	yes	14	63.4	even	3	inner
252.2.l.b.205.4	yes	14	1.1	even	1	trivial
756.2.i.b.37.2		14	9.5	odd	6
756.2.i.b.613.2		14	21.11	odd	6
756.2.l.b.289.6		14	3.2	odd	2
756.2.l.b.361.6		14	63.32	odd	6
1008.2.q.j.529.6		14	28.11	odd	6
1008.2.q.j.625.6		14	36.31	odd	6
1008.2.t.j.193.4		14	252.67	odd	6
1008.2.t.j.961.4		14	4.3	odd	2
1764.2.i.i.373.6		14	63.13	odd	6
1764.2.i.i.1537.6		14	7.3	odd	6
1764.2.j.g.589.7		14	63.58	even	3
1764.2.j.g.1177.7		14	7.2	even	3
1764.2.j.h.589.1		14	63.40	odd	6
1764.2.j.h.1177.1		14	7.5	odd	6
1764.2.l.i.949.4		14	63.31	odd	6
1764.2.l.i.961.4		14	7.6	odd	2
2268.2.k.e.1297.6		14	9.7	even	3
2268.2.k.e.1621.6		14	63.25	even	3
2268.2.k.f.1297.2		14	9.2	odd	6
2268.2.k.f.1621.2		14	63.11	odd	6
3024.2.q.j.2305.2		14	36.23	even	6
3024.2.q.j.2881.2		14	84.11	even	6
3024.2.t.j.289.6		14	12.11	even	2
3024.2.t.j.1873.6		14	252.95	even	6
5292.2.i.i.1549.6		14	63.41	even	6
5292.2.i.i.2125.6		14	21.17	even	6
5292.2.j.g.1765.6		14	63.5	even	6
5292.2.j.g.3529.6		14	21.5	even	6
5292.2.j.h.1765.2		14	63.23	odd	6
5292.2.j.h.3529.2		14	21.2	odd	6
5292.2.l.i.361.2		14	63.59	even	6
5292.2.l.i.3313.2		14	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.473632 - 1.66604i) q^{3} -1.90301 q^{5} +(-2.43415 - 1.03677i) q^{7} +(-2.55135 + 1.57817i) q^{9} +O(q^{10})\)	\(q+(-0.473632 - 1.66604i) q^{3} -1.90301 q^{5} +(-2.43415 - 1.03677i) q^{7} +(-2.55135 + 1.57817i) q^{9} -3.06586 q^{11} +(1.13161 + 1.96000i) q^{13} +(0.901324 + 3.17048i) q^{15} +(-0.713726 - 1.23621i) q^{17} +(2.98444 - 5.16919i) q^{19} +(-0.574405 + 4.54643i) q^{21} -7.15543 q^{23} -1.37856 q^{25} +(3.83769 + 3.50316i) q^{27} +(0.468164 - 0.810884i) q^{29} +(4.11065 - 7.11985i) q^{31} +(1.45209 + 5.10784i) q^{33} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(2.72947 - 2.81362i) q^{39} +(-5.31672 - 9.20883i) q^{41} +(2.98444 - 5.16919i) q^{43} +(4.85523 - 3.00328i) q^{45} +(0.483340 + 0.837169i) q^{47} +(4.85021 + 5.04732i) q^{49} +(-1.72152 + 1.77460i) q^{51} +(5.45142 + 9.44213i) q^{53} +5.83436 q^{55} +(-10.0256 - 2.52388i) q^{57} +(5.68180 - 9.84117i) q^{59} +(-0.449718 - 0.778935i) q^{61} +(7.84657 - 1.19636i) q^{63} +(-2.15346 - 3.72990i) q^{65} +(-0.813810 + 1.40956i) q^{67} +(3.38904 + 11.9212i) q^{69} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(0.652931 + 2.29674i) q^{75} +(7.46279 + 3.17860i) q^{77} +(4.16945 + 7.22169i) q^{79} +(4.01873 - 8.05294i) q^{81} +(-7.98203 + 13.8253i) q^{83} +(1.35822 + 2.35251i) q^{85} +(-1.57270 - 0.395917i) q^{87} +(-2.58992 + 4.48587i) q^{89} +(-0.722433 - 5.94416i) q^{91} +(-13.8089 - 3.47630i) q^{93} +(-5.67940 + 9.83701i) q^{95} +(0.922890 - 1.59849i) q^{97} +(7.82208 - 4.83847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

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