LMFDB - Embedded newform 460.2.m.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	460.121
Dual form			460.2.m.a.441.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0447663 + 0.0131446i) q^{3} +(0.841254 - 0.540641i) q^{5} +(0.423834 - 2.94783i) q^{7} +(-2.52193 - 1.62075i) q^{9} +O(q^{10})$	\(q+(0.0447663 + 0.0131446i) q^{3} +(0.841254 - 0.540641i) q^{5} +(0.423834 - 2.94783i) q^{7} +(-2.52193 - 1.62075i) q^{9} +(0.116050 + 0.254114i) q^{11} +(-0.287174 - 1.99734i) q^{13} +(0.0447663 - 0.0131446i) q^{15} +(1.46880 - 1.69508i) q^{17} +(-2.64237 - 3.04946i) q^{19} +(0.0577214 - 0.126392i) q^{21} +(2.21614 + 4.25308i) q^{23} +(0.415415 - 0.909632i) q^{25} +(-0.183253 - 0.211486i) q^{27} +(4.42317 - 5.10461i) q^{29} +(-3.52347 + 1.03458i) q^{31} +(0.00185491 + 0.0129012i) q^{33} +(-1.23716 - 2.70901i) q^{35} +(5.26609 + 3.38431i) q^{37} +(0.0133984 - 0.0931882i) q^{39} +(7.90965 - 5.08323i) q^{41} +(1.04239 + 0.306072i) q^{43} -2.99782 q^{45} -4.44460 q^{47} +(-1.79360 - 0.526649i) q^{49} +(0.0880338 - 0.0565759i) q^{51} +(-0.0276399 + 0.192240i) q^{53} +(0.235012 + 0.151033i) q^{55} +(-0.0782053 - 0.171246i) q^{57} +(-1.27607 - 8.87523i) q^{59} +(-2.28267 + 0.670253i) q^{61} +(-5.84656 + 6.74729i) q^{63} +(-1.32143 - 1.52501i) q^{65} +(-4.17476 + 9.14146i) q^{67} +(0.0433035 + 0.219525i) q^{69} +(-5.39907 + 11.8223i) q^{71} +(8.19579 + 9.45844i) q^{73} +(0.0305533 - 0.0352604i) q^{75} +(0.798272 - 0.234394i) q^{77} +(-0.917054 - 6.37825i) q^{79} +(3.73060 + 8.16887i) q^{81} +(7.09216 + 4.55785i) q^{83} +(0.319200 - 2.22009i) q^{85} +(0.265107 - 0.170374i) q^{87} +(0.984393 + 0.289044i) q^{89} -6.00952 q^{91} -0.171332 q^{93} +(-3.87156 - 1.13679i) q^{95} +(-10.8010 + 6.94136i) q^{97} +(0.119185 - 0.828946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0447663	+	0.0131446i	0.0258458	+	0.00758902i	0.294630	−	0.955611i	$-0.404804\pi$
$3$	0.0447663	+	0.0131446i	0.0258458	+	0.00758902i	−0.268784	+	0.963200i	$0.586622\pi$
$4$		0			0
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$		0			0
$7$	0.423834	−	2.94783i	0.160194	−	1.11417i	−0.738072	−	0.674722i	$-0.764264\pi$
$7$	0.423834	−	2.94783i	0.160194	−	1.11417i	0.898266	−	0.439452i	$-0.144827\pi$
$8$		0			0
$9$	−2.52193	−	1.62075i	−0.840643	−	0.540249i
$10$		0			0
$11$	0.116050	+	0.254114i	0.0349904	+	0.0766184i	0.926320	−	0.376737i	$-0.122954\pi$
$11$	0.116050	+	0.254114i	0.0349904	+	0.0766184i	−0.891330	+	0.453356i	$0.850227\pi$
$12$		0			0
$13$	−0.287174	−	1.99734i	−0.0796477	−	0.553962i	−0.990102	−	0.140352i	$-0.955177\pi$
$13$	−0.287174	−	1.99734i	−0.0796477	−	0.553962i	0.910454	−	0.413610i	$-0.135732\pi$
$14$		0			0
$15$	0.0447663	−	0.0131446i	0.0115586	−	0.00339391i
$16$		0			0
$17$	1.46880	−	1.69508i	0.356236	−	0.411118i	−0.549139	−	0.835731i	$-0.685044\pi$
$17$	1.46880	−	1.69508i	0.356236	−	0.411118i	0.905375	+	0.424613i	$0.139590\pi$
$18$		0			0
$19$	−2.64237	−	3.04946i	−0.606201	−	0.699593i	0.366825	−	0.930290i	$-0.380445\pi$
$19$	−2.64237	−	3.04946i	−0.606201	−	0.699593i	−0.973026	+	0.230697i	$0.925899\pi$
$20$		0			0
$21$	0.0577214	−	0.126392i	0.0125958	−	0.0275811i
$22$		0			0
$23$	2.21614	+	4.25308i	0.462097	+	0.886829i
$23$	2.21614	+	4.25308i	0.462097	+	0.886829i
$24$		0			0
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$		0			0
$27$	−0.183253	−	0.211486i	−0.0352671	−	0.0407005i
$28$		0			0
$29$	4.42317	−	5.10461i	0.821362	−	0.947903i	−0.177985	−	0.984033i	$-0.556958\pi$
$29$	4.42317	−	5.10461i	0.821362	−	0.947903i	0.999347	+	0.0361307i	$0.0115032\pi$
$30$		0			0
$31$	−3.52347	+	1.03458i	−0.632833	+	0.185817i	−0.582389	−	0.812910i	$-0.697882\pi$
$31$	−3.52347	+	1.03458i	−0.632833	+	0.185817i	−0.0504442	+	0.998727i	$0.516064\pi$
$32$		0			0
$33$	0.00185491	+	0.0129012i	0.000322899	+	0.00224581i
$34$		0			0
$35$	−1.23716	−	2.70901i	−0.209119	−	0.457907i
$36$		0			0
$37$	5.26609	+	3.38431i	0.865739	+	0.556377i	0.896447	−	0.443151i	$-0.146140\pi$
$37$	5.26609	+	3.38431i	0.865739	+	0.556377i	−0.0307073	+	0.999528i	$0.509776\pi$
$38$		0			0
$39$	0.0133984	−	0.0931882i	0.00214547	−	0.0149221i
$40$		0			0
$41$	7.90965	−	5.08323i	1.23528	−	0.793866i	0.250575	−	0.968097i	$-0.419380\pi$
$41$	7.90965	−	5.08323i	1.23528	−	0.793866i	0.984705	+	0.174231i	$0.0557438\pi$
$42$		0			0
$43$	1.04239	+	0.306072i	0.158962	+	0.0466756i	0.360245	−	0.932858i	$-0.382693\pi$
$43$	1.04239	+	0.306072i	0.158962	+	0.0466756i	−0.201283	+	0.979533i	$0.564511\pi$
$44$		0			0
$45$	−2.99782			−0.446889
$46$		0			0
$47$	−4.44460			−0.648312			−0.324156	−	0.946004i	$-0.605080\pi$
$47$	−4.44460			−0.648312			−0.324156	+	0.946004i	$0.605080\pi$
$48$		0			0
$49$	−1.79360	−	0.526649i	−0.256229	−	0.0752356i
$50$		0			0
$51$	0.0880338	−	0.0565759i	0.0123272	−	0.00792221i
$52$		0			0
$53$	−0.0276399	+	0.192240i	−0.00379663	+	0.0264062i	−0.991632	−	0.129099i	$-0.958791\pi$
$53$	−0.0276399	+	0.192240i	−0.00379663	+	0.0264062i	0.987835	+	0.155505i	$0.0497006\pi$
$54$		0			0
$55$	0.235012	+	0.151033i	0.0316890	+	0.0203653i
$56$		0			0
$57$	−0.0782053	−	0.171246i	−0.0103585	−	0.0226821i
$58$		0			0
$59$	−1.27607	−	8.87523i	−0.166130	−	1.15546i	−0.886792	−	0.462170i	$-0.847071\pi$
$59$	−1.27607	−	8.87523i	−0.166130	−	1.15546i	0.720662	−	0.693287i	$-0.243838\pi$
$60$		0			0
$61$	−2.28267	+	0.670253i	−0.292266	+	0.0858171i	−0.424579	−	0.905391i	$-0.639578\pi$
$61$	−2.28267	+	0.670253i	−0.292266	+	0.0858171i	0.132313	+	0.991208i	$0.457760\pi$
$62$		0			0
$63$	−5.84656	+	6.74729i	−0.736597	+	0.850078i
$64$		0			0
$65$	−1.32143	−	1.52501i	−0.163903	−	0.189154i
$66$		0			0
$67$	−4.17476	+	9.14146i	−0.510029	+	1.11681i	0.463050	+	0.886332i	$0.346755\pi$
$67$	−4.17476	+	9.14146i	−0.510029	+	1.11681i	−0.973078	+	0.230474i	$0.925972\pi$
$68$		0			0
$69$	0.0433035	+	0.219525i	0.00521313	+	0.0264277i
$70$		0			0
$71$	−5.39907	+	11.8223i	−0.640752	+	1.40305i	0.258668	+	0.965966i	$0.416716\pi$
$71$	−5.39907	+	11.8223i	−0.640752	+	1.40305i	−0.899420	+	0.437085i	$0.856011\pi$
$72$		0			0
$73$	8.19579	+	9.45844i	0.959244	+	1.10703i	0.994190	+	0.107638i	$0.0343287\pi$
$73$	8.19579	+	9.45844i	0.959244	+	1.10703i	−0.0349459	+	0.999389i	$0.511126\pi$
$74$		0			0
$75$	0.0305533	−	0.0352604i	0.00352799	−	0.00407152i
$76$		0			0
$77$	0.798272	−	0.234394i	0.0909715	−	0.0267116i
$78$		0			0
$79$	−0.917054	−	6.37825i	−0.103177	−	0.717610i	−0.974088	−	0.226169i	$-0.927380\pi$
$79$	−0.917054	−	6.37825i	−0.103177	−	0.717610i	0.870911	−	0.491440i	$-0.163529\pi$
$80$		0			0
$81$	3.73060	+	8.16887i	0.414511	+	0.907652i
$82$		0			0
$83$	7.09216	+	4.55785i	0.778465	+	0.500289i	0.868524	−	0.495647i	$-0.165069\pi$
$83$	7.09216	+	4.55785i	0.778465	+	0.500289i	−0.0900587	+	0.995936i	$0.528705\pi$
$84$		0			0
$85$	0.319200	−	2.22009i	0.0346221	−	0.240802i
$86$		0			0
$87$	0.265107	−	0.170374i	0.0284225	−	0.0182660i
$88$		0			0
$89$	0.984393	+	0.289044i	0.104345	+	0.0306386i	0.333488	−	0.942754i	$-0.391774\pi$
$89$	0.984393	+	0.289044i	0.104345	+	0.0306386i	−0.229143	+	0.973393i	$0.573592\pi$
$90$		0			0
$91$	−6.00952			−0.629969
$92$		0			0
$93$	−0.171332			−0.0177663
$94$		0			0
$95$	−3.87156	−	1.13679i	−0.397214	−	0.116633i
$96$		0			0
$97$	−10.8010	+	6.94136i	−1.09667	+	0.704788i	−0.958349	−	0.285599i	$-0.907807\pi$
$97$	−10.8010	+	6.94136i	−1.09667	+	0.704788i	−0.138322	+	0.990387i	$0.544171\pi$
$98$		0			0
$99$	0.119185	−	0.828946i	0.0119785	−	0.0833123i
$100$		0			0
$101$	2.85238	+	1.83311i	0.283823	+	0.182402i	0.674804	−	0.737997i	$-0.264228\pi$
$101$	2.85238	+	1.83311i	0.283823	+	0.182402i	−0.390982	+	0.920398i	$0.627864\pi$
$102$		0			0
$103$	5.77460	+	12.6446i	0.568988	+	1.24591i	0.947335	+	0.320246i	$0.103765\pi$
$103$	5.77460	+	12.6446i	0.568988	+	1.24591i	−0.378347	+	0.925664i	$0.623507\pi$
$104$		0			0
$105$	−0.0197745	−	0.137534i	−0.00192979	−	0.0134220i
$106$		0			0
$107$	4.58015	−	1.34485i	0.442780	−	0.130012i	−0.0527406	−	0.998608i	$-0.516796\pi$
$107$	4.58015	−	1.34485i	0.442780	−	0.130012i	0.495520	+	0.868596i	$0.334977\pi$
$108$		0			0
$109$	−2.32042	+	2.67790i	−0.222256	+	0.256497i	−0.855916	−	0.517115i	$-0.827006\pi$
$109$	−2.32042	+	2.67790i	−0.222256	+	0.256497i	0.633661	+	0.773611i	$0.281552\pi$
$110$		0			0
$111$	0.191258	+	0.220724i	0.0181534	+	0.0209501i
$112$		0			0
$113$	1.30443	−	2.85631i	0.122711	−	0.268699i	−0.838301	−	0.545208i	$-0.816451\pi$
$113$	1.30443	−	2.85631i	0.122711	−	0.268699i	0.961011	+	0.276510i	$0.0891778\pi$
$114$		0			0
$115$	4.16373	+	2.37978i	0.388270	+	0.221916i
$116$		0			0
$117$	−2.51294	+	5.50258i	−0.232322	+	0.508714i
$118$		0			0
$119$	−4.37429	−	5.04819i	−0.400990	−	0.462767i
$120$		0			0
$121$	7.15236	−	8.25427i	0.650215	−	0.750388i
$122$		0			0
$123$	0.420903	−	0.123588i	0.0379515	−	0.0111436i
$124$		0			0
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$		0			0
$127$	−0.437510	−	0.958013i	−0.0388227	−	0.0850099i	0.889227	−	0.457466i	$-0.151243\pi$
$127$	−0.437510	−	0.958013i	−0.0388227	−	0.0850099i	−0.928050	+	0.372456i	$0.878516\pi$
$128$		0			0
$129$	0.0426406	+	0.0274034i	0.00375429	+	0.00241274i
$130$		0			0
$131$	−1.78544	+	12.4180i	−0.155995	+	1.08497i	0.749926	+	0.661522i	$0.230089\pi$
$131$	−1.78544	+	12.4180i	−0.155995	+	1.08497i	−0.905921	+	0.423447i	$0.860820\pi$
$132$		0			0
$133$	−10.1092	+	6.49679i	−0.876579	+	0.563343i
$134$		0			0
$135$	−0.268500	−	0.0788388i	−0.0231088	−	0.00678537i
$136$		0			0
$137$	8.45078			0.721999			0.360999	−	0.932566i	$-0.382436\pi$
$137$	8.45078			0.721999			0.360999	+	0.932566i	$0.382436\pi$
$138$		0			0
$139$	−13.6424			−1.15713			−0.578566	−	0.815636i	$-0.696387\pi$
$139$	−13.6424			−1.15713			−0.578566	+	0.815636i	$0.696387\pi$
$140$		0			0
$141$	−0.198968	−	0.0584224i	−0.0167562	−	0.00492005i
$142$		0			0
$143$	0.474226	−	0.304766i	0.0396568	−	0.0254858i
$144$		0			0
$145$	0.961247	−	6.68562i	0.0798272	−	0.555210i
$146$		0			0
$147$	−0.0733704	−	0.0471523i	−0.00605149	−	0.00388905i
$148$		0			0
$149$	−7.61559	−	16.6758i	−0.623893	−	1.36614i	−0.912654	−	0.408734i	$-0.865970\pi$
$149$	−7.61559	−	16.6758i	−0.623893	−	1.36614i	0.288761	−	0.957401i	$-0.406757\pi$
$150$		0			0
$151$	1.91145	+	13.2944i	0.155551	+	1.08188i	0.906708	+	0.421759i	$0.138587\pi$
$151$	1.91145	+	13.2944i	0.155551	+	1.08188i	−0.751157	+	0.660124i	$0.770504\pi$
$152$		0			0
$153$	−6.45150	+	1.89433i	−0.521573	+	0.153148i
$154$		0			0
$155$	−2.40479	+	2.77528i	−0.193157	+	0.222916i
$156$		0			0
$157$	−1.36233	−	1.57221i	−0.108726	−	0.125476i	0.698778	−	0.715338i	$-0.253727\pi$
$157$	−1.36233	−	1.57221i	−0.108726	−	0.125476i	−0.807504	+	0.589862i	$0.799182\pi$
$158$		0			0
$159$	−0.00376425	+	0.00824255i	−0.000298524	+	0.000653677i
$160$		0			0
$161$	13.4766	−	4.73020i	1.06211	−	0.372792i
$162$		0			0
$163$	−4.10288	+	8.98406i	−0.321363	+	0.703686i	−0.999512	−	0.0312380i	$-0.990055\pi$
$163$	−4.10288	+	8.98406i	−0.321363	+	0.703686i	0.678149	+	0.734924i	$0.262782\pi$
$164$		0			0
$165$	0.00853537	+	0.00985034i	0.000664477	+	0.000766848i
$166$		0			0
$167$	10.9281	−	12.6117i	0.845640	−	0.975921i	−0.154286	−	0.988026i	$-0.549308\pi$
$167$	10.9281	−	12.6117i	0.845640	−	0.975921i	0.999927	+	0.0121052i	$0.00385331\pi$
$168$		0			0
$169$	8.56652	−	2.51536i	0.658963	−	0.193489i
$170$		0			0
$171$	1.72147	+	11.9731i	0.131644	+	0.915607i
$172$		0			0
$173$	0.354550	+	0.776357i	0.0269560	+	0.0590253i	0.922631	−	0.385684i	$-0.126034\pi$
$173$	0.354550	+	0.776357i	0.0269560	+	0.0590253i	−0.895675	+	0.444709i	$0.853307\pi$
$174$		0			0
$175$	−2.50537	−	1.61010i	−0.189388	−	0.121712i
$176$		0			0
$177$	0.0595364	−	0.414085i	0.00447503	−	0.0311245i
$178$		0			0
$179$	1.61378	−	1.03711i	0.120619	−	0.0775174i	−0.478940	−	0.877848i	$-0.658979\pi$
$179$	1.61378	−	1.03711i	0.120619	−	0.0775174i	0.599559	+	0.800330i	$0.295342\pi$
$180$		0			0
$181$	−6.01911	−	1.76737i	−0.447397	−	0.131368i	0.0502701	−	0.998736i	$-0.483992\pi$
$181$	−6.01911	−	1.76737i	−0.447397	−	0.131368i	−0.497667	+	0.867368i	$0.665810\pi$
$182$		0			0
$183$	−0.110997			−0.00820514
$184$		0			0
$185$	6.25981			0.460230
$186$		0			0
$187$	0.601199	+	0.176528i	0.0439640	+	0.0129090i
$188$		0			0
$189$	−0.701093	+	0.450565i	−0.0509970	+	0.0327738i
$190$		0			0
$191$	2.52104	−	17.5342i	0.182416	−	1.26873i	−0.668611	−	0.743612i	$-0.733111\pi$
$191$	2.52104	−	17.5342i	0.182416	−	1.26873i	0.851028	−	0.525121i	$-0.175980\pi$
$192$		0			0
$193$	19.7149	+	12.6700i	1.41911	+	0.912005i	0.999992	+	0.00407167i	$0.00129606\pi$
$193$	19.7149	+	12.6700i	1.41911	+	0.912005i	0.419115	+	0.907933i	$0.362340\pi$
$194$		0			0
$195$	−0.0391099	−	0.0856387i	−0.00280072	−	0.00613271i
$196$		0			0
$197$	−1.88432	−	13.1057i	−0.134252	−	0.933744i	−0.939925	−	0.341382i	$-0.889105\pi$
$197$	−1.88432	−	13.1057i	−0.134252	−	0.933744i	0.805672	−	0.592361i	$-0.201804\pi$
$198$		0			0
$199$	−6.21074	+	1.82364i	−0.440268	+	0.129274i	−0.494351	−	0.869262i	$-0.664594\pi$
$199$	−6.21074	+	1.82364i	−0.440268	+	0.129274i	0.0540838	+	0.998536i	$0.482776\pi$
$200$		0			0
$201$	−0.307049	+	0.354354i	−0.0216576	+	0.0249942i
$202$		0			0
$203$	−13.1728	−	15.2023i	−0.924551	−	1.06699i
$204$		0			0
$205$	3.90582	−	8.55256i	0.272795	−	0.597337i
$206$		0			0
$207$	1.30421	−	14.3178i	0.0906491	−	0.995154i
$208$		0			0
$209$	0.468264	−	1.02535i	0.0323905	−	0.0709252i
$210$		0			0
$211$	−6.23790	−	7.19892i	−0.429435	−	0.495594i	0.499253	−	0.866456i	$-0.333608\pi$
$211$	−6.23790	−	7.19892i	−0.429435	−	0.495594i	−0.928688	+	0.370862i	$0.879062\pi$
$212$		0			0
$213$	−0.397096	+	0.458273i	−0.0272086	+	0.0314004i
$214$		0			0
$215$	1.04239	−	0.306072i	0.0710901	−	0.0208739i
$216$		0			0
$217$	1.55641	+	10.8251i	0.105656	+	0.734853i
$218$		0			0
$219$	0.242568	+	0.531150i	0.0163912	+	0.0358918i
$220$		0			0
$221$	−3.80745	−	2.44690i	−0.256117	−	0.164596i
$222$		0			0
$223$	3.66703	−	25.5048i	0.245562	−	1.70792i	−0.377713	−	0.925923i	$-0.623290\pi$
$223$	3.66703	−	25.5048i	0.245562	−	1.70792i	0.623276	−	0.782002i	$-0.285801\pi$
$224$		0			0
$225$	−2.52193	+	1.62075i	−0.168129	+	0.108050i
$226$		0			0
$227$	8.56609	+	2.51523i	0.568551	+	0.166942i	0.553359	−	0.832943i	$-0.313346\pi$
$227$	8.56609	+	2.51523i	0.568551	+	0.166942i	0.0151924	+	0.999885i	$0.495164\pi$
$228$		0			0
$229$	−16.1261			−1.06564			−0.532821	−	0.846228i	$-0.678868\pi$
$229$	−16.1261			−1.06564			−0.532821	+	0.846228i	$0.678868\pi$
$230$		0			0
$231$	0.0388167			0.00255395
$232$		0			0
$233$	10.6789	+	3.13561i	0.699599	+	0.205421i	0.612143	−	0.790747i	$-0.290308\pi$
$233$	10.6789	+	3.13561i	0.699599	+	0.205421i	0.0874569	+	0.996168i	$0.472126\pi$
$234$		0			0
$235$	−3.73904	+	2.40293i	−0.243908	+	0.156750i
$236$		0			0
$237$	0.0427863	−	0.297585i	0.00277927	−	0.0193302i
$238$		0			0
$239$	16.2462	+	10.4408i	1.05088	+	0.675359i	0.947654	−	0.319299i	$-0.103447\pi$
$239$	16.2462	+	10.4408i	1.05088	+	0.675359i	0.103225	+	0.994658i	$0.467084\pi$
$240$		0			0
$241$	−9.55704	−	20.9270i	−0.615623	−	1.34803i	−0.918661	−	0.395048i	$-0.870728\pi$
$241$	−9.55704	−	20.9270i	−0.615623	−	1.34803i	0.303038	−	0.952979i	$-0.401999\pi$
$242$		0			0
$243$	0.179103	+	1.24569i	0.0114895	+	0.0799110i
$244$		0			0
$245$	−1.79360	+	0.526649i	−0.114589	+	0.0336464i
$246$		0			0
$247$	−5.33198	+	6.15343i	−0.339265	+	0.391533i
$248$		0			0
$249$	0.257579	+	0.297262i	0.0163234	+	0.0188382i
$250$		0			0
$251$	3.15836	−	6.91583i	0.199354	−	0.436524i	−0.783382	−	0.621541i	$-0.786507\pi$
$251$	3.15836	−	6.91583i	0.199354	−	0.436524i	0.982735	+	0.185017i	$0.0592342\pi$
$252$		0			0
$253$	−0.823586	+	1.05672i	−0.0517784	+	0.0664357i
$254$		0			0
$255$	0.0434715	−	0.0951893i	0.00272229	−	0.00596099i
$256$		0			0
$257$	18.4932	+	21.3423i	1.15358	+	1.33130i	0.934656	+	0.355555i	$0.115708\pi$
$257$	18.4932	+	21.3423i	1.15358	+	1.33130i	0.218920	+	0.975743i	$0.429747\pi$
$258$		0			0
$259$	12.2083	−	14.0891i	0.758587	−	0.875456i
$260$		0			0
$261$	−19.4282	+	5.70463i	−1.20258	+	0.353108i
$262$		0			0
$263$	−0.220540	−	1.53389i	−0.0135991	−	0.0945835i	0.981892	−	0.189444i	$-0.0606686\pi$
$263$	−0.220540	−	1.53389i	−0.0135991	−	0.0945835i	−0.995491	+	0.0948605i	$0.969759\pi$
$264$		0			0
$265$	0.0806805	+	0.176666i	0.00495617	+	0.0108525i
$266$		0			0
$267$	0.0402683	+	0.0258789i	0.00246438	+	0.00158376i
$268$		0			0
$269$	3.16608	−	22.0206i	0.193039	−	1.34262i	−0.630867	−	0.775891i	$-0.717300\pi$
$269$	3.16608	−	22.0206i	0.193039	−	1.34262i	0.823906	−	0.566727i	$-0.191790\pi$
$270$		0			0
$271$	−4.20783	+	2.70421i	−0.255607	+	0.164269i	−0.662169	−	0.749354i	$-0.730364\pi$
$271$	−4.20783	+	2.70421i	−0.255607	+	0.164269i	0.406562	+	0.913623i	$0.366728\pi$
$272$		0			0
$273$	−0.269024	−	0.0789926i	−0.0162821	−	0.00478085i
$274$		0			0
$275$	0.279360			0.0168460
$276$		0			0
$277$	−24.2911			−1.45951			−0.729756	−	0.683708i	$-0.760366\pi$
$277$	−24.2911			−1.45951			−0.729756	+	0.683708i	$0.760366\pi$
$278$		0			0
$279$	10.5627	+	3.10150i	0.632374	+	0.185682i
$280$		0			0
$281$	16.4389	−	10.5647i	0.980665	−	0.630235i	0.0510225	−	0.998698i	$-0.483752\pi$
$281$	16.4389	−	10.5647i	0.980665	−	0.630235i	0.929643	+	0.368462i	$0.120116\pi$
$282$		0			0
$283$	1.50374	−	10.4587i	0.0893881	−	0.621708i	−0.895049	−	0.445969i	$-0.852859\pi$
$283$	1.50374	−	10.4587i	0.0893881	−	0.621708i	0.984437	−	0.175739i	$-0.0562316\pi$
$284$		0			0
$285$	−0.158373	−	0.101780i	−0.00938120	−	0.00602893i
$286$		0			0
$287$	−11.6321	−	25.4707i	−0.686621	−	1.50349i
$288$		0			0
$289$	1.70341	+	11.8475i	0.100201	+	0.696912i
$290$		0			0
$291$	−0.574760	+	0.168765i	−0.0336931	+	0.00989317i
$292$		0			0
$293$	3.04354	−	3.51243i	0.177805	−	0.205198i	−0.659850	−	0.751397i	$-0.729380\pi$
$293$	3.04354	−	3.51243i	0.177805	−	0.205198i	0.837656	+	0.546199i	$0.183926\pi$
$294$		0			0
$295$	−5.87180	−	6.77642i	−0.341870	−	0.394539i
$296$		0			0
$297$	0.0324750	−	0.0711103i	0.00188439	−	0.00412624i
$298$		0			0
$299$	7.85843	−	5.64776i	0.454464	−	0.326618i
$300$		0			0
$301$	1.34405	−	2.94305i	0.0774695	−	0.169635i
$302$		0			0
$303$	0.103595	+	0.119555i	0.00595138	+	0.00686826i
$304$		0			0
$305$	−1.55794	+	1.79796i	−0.0892074	+	0.102951i
$306$		0			0
$307$	24.9718	−	7.33238i	1.42521	−	0.418481i	0.523950	−	0.851749i	$-0.324458\pi$
$307$	24.9718	−	7.33238i	1.42521	−	0.418481i	0.901265	+	0.433268i	$0.142640\pi$
$308$		0			0
$309$	0.0922995	+	0.641957i	0.00525073	+	0.0365196i
$310$		0			0
$311$	5.31445	+	11.6370i	0.301355	+	0.659876i	0.998363	−	0.0571874i	$-0.0182133\pi$
$311$	5.31445	+	11.6370i	0.301355	+	0.659876i	−0.697008	+	0.717063i	$0.745486\pi$
$312$		0			0
$313$	−0.493249	−	0.316992i	−0.0278801	−	0.0179175i	0.526627	−	0.850097i	$-0.323457\pi$
$313$	−0.493249	−	0.316992i	−0.0278801	−	0.0179175i	−0.554507	+	0.832179i	$0.687093\pi$
$314$		0			0
$315$	−1.27058	+	8.83707i	−0.0715890	+	0.497912i
$316$		0			0
$317$	−12.8061	+	8.22995i	−0.719260	+	0.462240i	−0.848379	−	0.529389i	$-0.822421\pi$
$317$	−12.8061	+	8.22995i	−0.719260	+	0.462240i	0.129120	+	0.991629i	$0.458785\pi$
$318$		0			0
$319$	1.81047	+	0.531601i	0.101367	+	0.0297639i
$320$		0			0
$321$	0.222714			0.0124307
$322$		0			0
$323$	−9.05018			−0.503566
$324$		0			0
$325$	−1.93614	−	0.568502i	−0.107398	−	0.0315348i
$326$		0			0
$327$	−0.139076	+	0.0893789i	−0.00769094	+	0.00494267i
$328$		0			0
$329$	−1.88377	+	13.1019i	−0.103856	+	0.722332i
$330$		0			0
$331$	11.9894	+	7.70510i	0.658996	+	0.423511i	0.826943	−	0.562285i	$-0.190078\pi$
$331$	11.9894	+	7.70510i	0.658996	+	0.423511i	−0.167948	+	0.985796i	$0.553714\pi$
$332$		0			0
$333$	−7.79560	−	17.0700i	−0.427196	−	0.935429i
$334$		0			0
$335$	1.43021	+	9.94733i	0.0781407	+	0.543481i
$336$		0			0
$337$	−30.6673	+	9.00472i	−1.67055	+	0.490518i	−0.973916	−	0.226907i	$-0.927139\pi$
$337$	−30.6673	+	9.00472i	−1.67055	+	0.490518i	−0.696635	+	0.717425i	$0.745320\pi$
$338$		0			0
$339$	0.0959396	−	0.110720i	0.00521072	−	0.00601349i
$340$		0			0
$341$	−0.671801	−	0.775300i	−0.0363801	−	0.0419848i
$342$		0			0
$343$	6.34749	−	13.8991i	0.342732	−	0.750479i
$344$		0			0
$345$	0.155113	+	0.161265i	0.00835103	+	0.00868219i
$346$		0			0
$347$	−2.48941	+	5.45105i	−0.133639	+	0.292628i	−0.964607	−	0.263692i	$-0.915060\pi$
$347$	−2.48941	+	5.45105i	−0.133639	+	0.292628i	0.830968	+	0.556320i	$0.187787\pi$
$348$		0			0
$349$	19.1292	+	22.0763i	1.02396	+	1.18172i	0.983197	+	0.182549i	$0.0584347\pi$
$349$	19.1292	+	22.0763i	1.02396	+	1.18172i	0.0407670	+	0.999169i	$0.487020\pi$
$350$		0			0
$351$	−0.369783	+	0.426752i	−0.0197376	+	0.0227783i
$352$		0			0
$353$	20.6487	−	6.06300i	1.09902	−	0.322701i	0.318556	−	0.947904i	$-0.396802\pi$
$353$	20.6487	−	6.06300i	1.09902	−	0.322701i	0.780462	+	0.625203i	$0.214984\pi$
$354$		0			0
$355$	1.84964	+	12.8645i	0.0981687	+	0.682778i
$356$		0			0
$357$	−0.129464	−	0.283487i	−0.00685197	−	0.0150037i
$358$		0			0
$359$	7.81442	+	5.02203i	0.412430	+	0.265052i	0.730361	−	0.683061i	$-0.239352\pi$
$359$	7.81442	+	5.02203i	0.412430	+	0.265052i	−0.317932	+	0.948114i	$0.602988\pi$
$360$		0			0
$361$	0.386912	−	2.69103i	0.0203638	−	0.141633i
$362$		0			0
$363$	0.428684	−	0.275498i	0.0225001	−	0.0144599i
$364$		0			0
$365$	12.0084	+	3.52597i	0.628546	+	0.184558i
$366$		0			0
$367$	16.9124			0.882821			0.441411	−	0.897305i	$-0.354478\pi$
$367$	16.9124			0.882821			0.441411	+	0.897305i	$0.354478\pi$
$368$		0			0
$369$	−28.1862			−1.46732
$370$		0			0
$371$	0.554975	+	0.162955i	0.0288129	+	0.00846022i
$372$		0			0
$373$	−25.3642	+	16.3006i	−1.31331	+	0.844011i	−0.994594	−	0.103841i	$-0.966887\pi$
$373$	−25.3642	+	16.3006i	−1.31331	+	0.844011i	−0.318712	+	0.947852i	$0.603250\pi$
$374$		0			0
$375$	0.00663987	−	0.0461813i	0.000342882	−	0.00238479i
$376$		0			0
$377$	−11.4659	−	7.36866i	−0.590521	−	0.379505i
$378$		0			0
$379$	4.57823	+	10.0249i	0.235168	+	0.514946i	0.990016	−	0.140954i	$-0.0450168\pi$
$379$	4.57823	+	10.0249i	0.235168	+	0.514946i	−0.754848	+	0.655899i	$0.772290\pi$
$380$		0			0
$381$	−0.00699303	−	0.0486376i	−0.000358264	−	0.00249178i
$382$		0			0
$383$	−13.5374	+	3.97493i	−0.691727	+	0.203109i	−0.608656	−	0.793434i	$-0.708291\pi$
$383$	−13.5374	+	3.97493i	−0.691727	+	0.203109i	−0.0830709	+	0.996544i	$0.526473\pi$
$384$		0			0
$385$	0.544826	−	0.628763i	0.0277669	−	0.0320447i
$386$		0			0
$387$	−2.13276	−	2.46133i	−0.108414	−	0.125117i
$388$		0			0
$389$	−12.5461	+	27.4720i	−0.636111	+	1.39289i	0.267091	+	0.963671i	$0.413938\pi$
$389$	−12.5461	+	27.4720i	−0.636111	+	1.39289i	−0.903202	+	0.429217i	$0.858790\pi$
$390$		0			0
$391$	10.4644	+	2.49037i	0.529207	+	0.125944i
$392$		0			0
$393$	−0.243157	+	0.532440i	−0.0122657	+	0.0268581i
$394$		0			0
$395$	−4.21982	−	4.86993i	−0.212322	−	0.245033i
$396$		0			0
$397$	−14.1431	+	16.3220i	−0.709823	+	0.819179i	−0.990044	−	0.140756i	$-0.955047\pi$
$397$	−14.1431	+	16.3220i	−0.709823	+	0.819179i	0.280221	+	0.959935i	$0.409592\pi$
$398$		0			0
$399$	−0.537949	+	0.157956i	−0.0269311	+	0.00790769i
$400$		0			0
$401$	2.44544	+	17.0084i	0.122119	+	0.849358i	0.955148	+	0.296129i	$0.0956957\pi$
$401$	2.44544	+	17.0084i	0.122119	+	0.849358i	−0.833029	+	0.553230i	$0.813395\pi$
$402$		0			0
$403$	3.07826	+	6.74045i	0.153339	+	0.335766i
$404$		0			0
$405$	7.55480	+	4.85518i	0.375401	+	0.241256i
$406$		0			0
$407$	−0.248871	+	1.73094i	−0.0123361	+	0.0857994i
$408$		0			0
$409$	−14.6990	+	9.44646i	−0.726818	+	0.467097i	−0.851002	−	0.525162i	$-0.824005\pi$
$409$	−14.6990	+	9.44646i	−0.726818	+	0.467097i	0.124185	+	0.992259i	$0.460368\pi$
$410$		0			0
$411$	0.378310	+	0.111082i	0.0186607	+	0.00547927i
$412$		0			0
$413$	−26.7035			−1.31399
$414$		0			0
$415$	8.43046			0.413835
$416$		0			0
$417$	−0.610719	−	0.179323i	−0.0299070	−	0.00878150i
$418$		0			0
$419$	12.1199	−	7.78900i	0.592097	−	0.380518i	−0.210009	−	0.977699i	$-0.567349\pi$
$419$	12.1199	−	7.78900i	0.592097	−	0.380518i	0.802106	+	0.597182i	$0.203713\pi$
$420$		0			0
$421$	5.30471	−	36.8951i	0.258536	−	1.79816i	−0.284743	−	0.958604i	$-0.591908\pi$
$421$	5.30471	−	36.8951i	0.258536	−	1.79816i	0.543279	−	0.839552i	$-0.317183\pi$
$422$		0			0
$423$	11.2090	+	7.20357i	0.544999	+	0.350249i
$424$		0			0
$425$	−0.931741	−	2.04023i	−0.0451961	−	0.0989656i
$426$		0			0
$427$	1.00832	+	7.01300i	0.0487959	+	0.339383i
$428$		0			0
$429$	0.0252354	−	0.00740977i	0.00121837	−	0.000357747i
$430$		0			0
$431$	−24.7585	+	28.5728i	−1.19258	+	1.37631i	−0.283873	+	0.958862i	$0.591619\pi$
$431$	−24.7585	+	28.5728i	−1.19258	+	1.37631i	−0.908703	+	0.417444i	$0.862926\pi$
$432$		0			0
$433$	−13.0595	−	15.0714i	−0.627598	−	0.724287i	0.349533	−	0.936924i	$-0.386340\pi$
$433$	−13.0595	−	15.0714i	−0.627598	−	0.724287i	−0.977131	+	0.212637i	$0.931795\pi$
$434$		0			0
$435$	0.130911	−	0.286655i	0.00627671	−	0.0137441i
$436$		0			0
$437$	7.11373	−	17.9962i	0.340296	−	0.860877i
$438$		0			0
$439$	−8.76405	+	19.1906i	−0.418285	+	0.915917i	0.576799	+	0.816886i	$0.304302\pi$
$439$	−8.76405	+	19.1906i	−0.418285	+	0.915917i	−0.995084	+	0.0990311i	$0.968426\pi$
$440$		0			0
$441$	3.66977	+	4.23514i	0.174751	+	0.201674i
$442$		0			0
$443$	11.7673	−	13.5802i	0.559081	−	0.645214i	−0.403893	−	0.914806i	$-0.632343\pi$
$443$	11.7673	−	13.5802i	0.559081	−	0.645214i	0.962975	+	0.269592i	$0.0868888\pi$
$444$		0			0
$445$	0.984393	−	0.289044i	0.0466647	−	0.0137020i
$446$		0			0
$447$	−0.121725	−	0.846618i	−0.00575741	−	0.0400437i
$448$		0			0
$449$	11.9826	+	26.2382i	0.565493	+	1.23826i	0.949162	+	0.314787i	$0.101933\pi$
$449$	11.9826	+	26.2382i	0.565493	+	1.23826i	−0.383669	+	0.923471i	$0.625340\pi$
$450$		0			0
$451$	2.20964	+	1.42005i	0.104048	+	0.0668674i
$452$		0			0
$453$	−0.0891809	+	0.620267i	−0.00419008	+	0.0291427i
$454$		0			0
$455$	−5.05553	+	3.24899i	−0.237007	+	0.152315i
$456$		0			0
$457$	18.9640	+	5.56832i	0.887097	+	0.260475i	0.693371	−	0.720580i	$-0.256125\pi$
$457$	18.9640	+	5.56832i	0.887097	+	0.260475i	0.193726	+	0.981056i	$0.437943\pi$
$458$		0			0
$459$	−0.627648			−0.0292961
$460$		0			0
$461$	−28.7215			−1.33769			−0.668846	−	0.743401i	$-0.733212\pi$
$461$	−28.7215			−1.33769			−0.668846	+	0.743401i	$0.733212\pi$
$462$		0			0
$463$	−9.45598	−	2.77653i	−0.439457	−	0.129036i	0.0545173	−	0.998513i	$-0.482638\pi$
$463$	−9.45598	−	2.77653i	−0.439457	−	0.129036i	−0.493974	+	0.869477i	$0.664456\pi$
$464$		0			0
$465$	−0.144133	+	0.0926289i	−0.00668403	+	0.00429556i
$466$		0			0
$467$	4.94738	−	34.4098i	0.228938	−	1.59230i	−0.473659	−	0.880708i	$-0.657067\pi$
$467$	4.94738	−	34.4098i	0.228938	−	1.59230i	0.702597	−	0.711588i	$-0.252024\pi$
$468$		0			0
$469$	25.1780	+	16.1809i	1.16261	+	0.747166i
$470$		0			0
$471$	−0.0403204	−	0.0882893i	−0.00185786	−	0.00406816i
$472$		0			0
$473$	0.0431917	+	0.300405i	0.00198596	+	0.0138126i
$474$		0			0
$475$	−3.87156	+	1.13679i	−0.177639	+	0.0521597i
$476$		0			0
$477$	0.381278	−	0.440018i	0.0174575	−	0.0201470i
$478$		0			0
$479$	−3.07644	−	3.55040i	−0.140566	−	0.162222i	0.681101	−	0.732189i	$-0.261501\pi$
$479$	−3.07644	−	3.55040i	−0.140566	−	0.162222i	−0.821667	+	0.569967i	$0.806956\pi$
$480$		0			0
$481$	5.24733	−	11.4900i	0.239257	−	0.523901i
$482$		0			0
$483$	0.665476	−	0.0346092i	0.0302802	−	0.00157477i
$484$		0			0
$485$	−5.33357	+	11.6789i	−0.242185	+	0.530311i
$486$		0			0
$487$	10.5225	+	12.1436i	0.476820	+	0.550280i	0.942296	−	0.334781i	$-0.108662\pi$
$487$	10.5225	+	12.1436i	0.476820	+	0.550280i	−0.465476	+	0.885060i	$0.654117\pi$
$488$		0			0
$489$	−0.301763	+	0.348253i	−0.0136462	+	0.0157485i
$490$		0			0
$491$	−18.3137	+	5.37739i	−0.826486	+	0.242678i	−0.667507	−	0.744604i	$-0.732639\pi$
$491$	−18.3137	+	5.37739i	−0.826486	+	0.242678i	−0.158979	+	0.987282i	$0.550820\pi$
$492$		0			0
$493$	−2.15600	−	14.9953i	−0.0971012	−	0.675353i
$494$		0			0
$495$	−0.347898	−	0.761790i	−0.0156368	−	0.0342399i
$496$		0			0
$497$	32.5619	+	20.9262i	1.46060	+	0.938670i
$498$		0			0
$499$	−3.64675	+	25.3637i	−0.163251	+	1.13544i	0.729203	+	0.684298i	$0.239891\pi$
$499$	−3.64675	+	25.3637i	−0.163251	+	1.13544i	−0.892454	+	0.451139i	$0.851018\pi$
$500$		0			0
$501$	0.654985	−	0.420933i	0.0292626	−	0.0188059i
$502$		0			0
$503$	8.34924	+	2.45156i	0.372274	+	0.109310i	0.462517	−	0.886610i	$-0.346946\pi$
$503$	8.34924	+	2.45156i	0.372274	+	0.109310i	−0.0902432	+	0.995920i	$0.528764\pi$
$504$		0			0
$505$	3.39063			0.150881
$506$		0			0
$507$	0.416555			0.0184998
$508$		0			0
$509$	11.2681	+	3.30861i	0.499450	+	0.146652i	0.521748	−	0.853100i	$-0.325280\pi$
$509$	11.2681	+	3.30861i	0.499450	+	0.146652i	−0.0222980	+	0.999751i	$0.507098\pi$
$510$		0			0
$511$	31.3555	−	20.1510i	1.38709	−	0.891426i
$512$		0			0
$513$	−0.160693	+	1.11765i	−0.00709478	+	0.0493453i
$514$		0			0
$515$	11.6941	+	7.51533i	0.515303	+	0.331165i
$516$		0			0
$517$	−0.515797	−	1.12944i	−0.0226847	−	0.0496726i
$518$		0			0
$519$	0.00566703	+	0.0394150i	0.000248755	+	0.00173013i
$520$		0			0
$521$	1.42515	−	0.418463i	0.0624371	−	0.0183332i	−0.250365	−	0.968152i	$-0.580551\pi$
$521$	1.42515	−	0.418463i	0.0624371	−	0.0183332i	0.312802	+	0.949818i	$0.398732\pi$
$522$		0			0
$523$	0.404488	−	0.466804i	0.0176870	−	0.0204119i	−0.746837	−	0.665007i	$-0.768429\pi$
$523$	0.404488	−	0.466804i	0.0176870	−	0.0204119i	0.764524	+	0.644595i	$0.222974\pi$
$524$		0			0
$525$	−0.0909921	−	0.105010i	−0.00397122	−	0.00458303i
$526$		0			0
$527$	−3.42155	+	7.49216i	−0.149045	+	0.326363i
$528$		0			0
$529$	−13.1774	+	18.8509i	−0.572932	+	0.819603i
$530$		0			0
$531$	−11.1663	+	24.4509i	−0.484578	+	1.06108i
$532$		0			0
$533$	−12.4244	−	14.3385i	−0.538159	−	0.621069i
$534$		0			0
$535$	3.12598	−	3.60758i	0.135148	−	0.155969i
$536$		0			0
$537$	0.0858753	−	0.0252153i	0.00370579	−	0.00108812i
$538$		0			0
$539$	−0.0743187	−	0.516898i	−0.00320113	−	0.0222644i
$540$		0			0
$541$	−6.56383	−	14.3728i	−0.282201	−	0.617934i	0.714452	−	0.699685i	$-0.246676\pi$
$541$	−6.56383	−	14.3728i	−0.282201	−	0.617934i	−0.996653	+	0.0817507i	$0.973949\pi$
$542$		0			0
$543$	−0.246222	−	0.158237i	−0.0105664	−	0.00679062i
$544$		0			0
$545$	−0.504275	+	3.50731i	−0.0216007	+	0.150236i
$546$		0			0
$547$	−2.40938	+	1.54842i	−0.103018	+	0.0662055i	−0.591135	−	0.806572i	$-0.701320\pi$
$547$	−2.40938	+	1.54842i	−0.103018	+	0.0662055i	0.488118	+	0.872778i	$0.337684\pi$
$548$		0			0
$549$	6.84305	+	2.00930i	0.292054	+	0.0857548i
$550$		0			0
$551$	−27.2539			−1.16106
$552$		0			0
$553$	−19.1907			−0.816070
$554$		0			0
$555$	0.280229	+	0.0822825i	0.0118950	+	0.00349270i
$556$		0			0
$557$	−25.6497	+	16.4841i	−1.08681	+	0.698453i	−0.956122	−	0.292970i	$-0.905356\pi$
$557$	−25.6497	+	16.4841i	−1.08681	+	0.698453i	−0.130692	+	0.991423i	$0.541720\pi$
$558$		0			0
$559$	0.311983	−	2.16989i	0.0131955	−	0.0917767i
$560$		0			0
$561$	0.0245931	+	0.0158050i	0.00103832	+	0.000667288i
$562$		0			0
$563$	−7.17373	−	15.7083i	−0.302337	−	0.662025i	0.696099	−	0.717946i	$-0.254918\pi$
$563$	−7.17373	−	15.7083i	−0.302337	−	0.662025i	−0.998435	+	0.0559214i	$0.982190\pi$
$564$		0			0
$565$	−0.446878	−	3.10811i	−0.0188003	−	0.130759i
$566$		0			0
$567$	25.6616	−	7.53492i	1.07768	−	0.316437i
$568$		0			0
$569$	−20.5908	+	23.7630i	−0.863211	+	0.996199i	0.136773	+	0.990602i	$0.456327\pi$
$569$	−20.5908	+	23.7630i	−0.863211	+	0.996199i	−0.999984	+	0.00559615i	$0.998219\pi$
$570$		0			0
$571$	−26.3971	−	30.4638i	−1.10468	−	1.27487i	−0.958338	−	0.285638i	$-0.907794\pi$
$571$	−26.3971	−	30.4638i	−1.10468	−	1.27487i	−0.146345	−	0.989234i	$-0.546751\pi$
$572$		0			0
$573$	0.343338	−	0.751805i	0.0143431	−	0.0314071i
$574$		0			0
$575$	4.78936	−	0.249079i	0.199730	−	0.0103873i
$576$		0			0
$577$	−6.15706	+	13.4821i	−0.256322	+	0.561267i	−0.993421	−	0.114518i	$-0.963468\pi$
$577$	−6.15706	+	13.4821i	−0.256322	+	0.561267i	0.737099	+	0.675784i	$0.236195\pi$
$578$		0			0
$579$	0.716020	+	0.826332i	0.0297568	+	0.0343412i
$580$		0			0
$581$	16.4417	−	18.9747i	0.682115	−	0.787202i
$582$		0			0
$583$	−0.0520585	+	0.0152858i	−0.00215604	+	0.000633072i
$584$		0			0
$585$	0.860896	+	5.98767i	0.0355937	+	0.247560i
$586$		0			0
$587$	−15.8070	−	34.6125i	−0.652424	−	1.42861i	−0.889416	−	0.457098i	$-0.848889\pi$
$587$	−15.8070	−	34.6125i	−0.652424	−	1.42861i	0.236992	−	0.971512i	$-0.423838\pi$
$588$		0			0
$589$	12.4652	+	8.01091i	0.513620	+	0.330084i
$590$		0			0
$591$	0.0879151	−	0.611463i	0.00361635	−	0.0251522i
$592$		0			0
$593$	23.0636	−	14.8221i	0.947110	−	0.608670i	0.0267075	−	0.999643i	$-0.491498\pi$
$593$	23.0636	−	14.8221i	0.947110	−	0.608670i	0.920402	+	0.390973i	$0.127861\pi$
$594$		0			0
$595$	−6.40914	−	1.88189i	−0.262749	−	0.0771501i
$596$		0			0
$597$	−0.302003			−0.0123602
$598$		0			0
$599$	−14.9351			−0.610232			−0.305116	−	0.952315i	$-0.598695\pi$
$599$	−14.9351			−0.610232			−0.305116	+	0.952315i	$0.598695\pi$
$600$		0			0
$601$	10.0034	+	2.93726i	0.408047	+	0.119813i	0.479313	−	0.877644i	$-0.340886\pi$
$601$	10.0034	+	2.93726i	0.408047	+	0.119813i	−0.0712664	+	0.997457i	$0.522704\pi$
$602$		0			0
$603$	25.3444	−	16.2879i	1.03211	−	0.663294i
$604$		0			0
$605$	1.55436	−	10.8108i	0.0631936	−	0.439521i
$606$		0			0
$607$	−3.51535	−	2.25918i	−0.142684	−	0.0916971i	0.467351	−	0.884072i	$-0.345208\pi$
$607$	−3.51535	−	2.25918i	−0.142684	−	0.0916971i	−0.610035	+	0.792374i	$0.708845\pi$
$608$		0			0
$609$	−0.389872	−	0.853700i	−0.0157984	−	0.0345937i
$610$		0			0
$611$	1.27637	+	8.87737i	0.0516365	+	0.359140i
$612$		0			0
$613$	−22.3386	+	6.55921i	−0.902248	+	0.264924i	−0.699775	−	0.714364i	$-0.746716\pi$
$613$	−22.3386	+	6.55921i	−0.902248	+	0.264924i	−0.202474	+	0.979288i	$0.564898\pi$
$614$		0			0
$615$	0.287269	−	0.331526i	0.0115838	−	0.0133684i
$616$		0			0
$617$	1.56566	+	1.80687i	0.0630310	+	0.0727417i	0.786389	−	0.617731i	$-0.211948\pi$
$617$	1.56566	+	1.80687i	0.0630310	+	0.0727417i	−0.723358	+	0.690473i	$0.757403\pi$
$618$		0			0
$619$	16.0811	−	35.2128i	0.646356	−	1.41532i	−0.248352	−	0.968670i	$-0.579889\pi$
$619$	16.0811	−	35.2128i	0.646356	−	1.41532i	0.894708	−	0.446652i	$-0.147384\pi$
$620$		0			0
$621$	0.493351	−	1.24807i	0.0197975	−	0.0500835i
$622$		0			0
$623$	1.26927	−	2.77931i	0.0508522	−	0.111351i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$		0			0
$627$	0.0344403	−	0.0397462i	0.00137541	−	0.00158731i
$628$		0			0
$629$	13.4715	−	3.95559i	0.537144	−	0.157720i
$630$		0			0
$631$	−3.76199	−	26.1652i	−0.149763	−	1.04162i	−0.916607	−	0.399789i	$-0.869083\pi$
$631$	−3.76199	−	26.1652i	−0.149763	−	1.04162i	0.766844	−	0.641833i	$-0.221826\pi$
$632$		0			0
$633$	−0.184621	−	0.404263i	−0.00733802	−	0.0160680i
$634$		0			0
$635$	−0.885998	−	0.569396i	−0.0351597	−	0.0225958i
$636$		0			0
$637$	−0.536821	+	3.73367i	−0.0212696	+	0.147933i
$638$		0			0
$639$	32.7771	−	21.0645i	1.29664	−	0.833300i
$640$		0			0
$641$	6.23851	+	1.83179i	0.246406	+	0.0723514i	0.402603	−	0.915374i	$-0.368105\pi$
$641$	6.23851	+	1.83179i	0.246406	+	0.0723514i	−0.156197	+	0.987726i	$0.549924\pi$
$642$		0			0
$643$	−11.0497			−0.435757			−0.217879	−	0.975976i	$-0.569914\pi$
$643$	−11.0497			−0.435757			−0.217879	+	0.975976i	$0.569914\pi$
$644$		0			0
$645$	0.0506870			0.00199580
$646$		0			0
$647$	−39.4465	−	11.5825i	−1.55080	−	0.455356i	−0.609461	−	0.792816i	$-0.708614\pi$
$647$	−39.4465	−	11.5825i	−1.55080	−	0.455356i	−0.941340	+	0.337459i	$0.890432\pi$
$648$		0			0
$649$	2.10724	−	1.35424i	0.0827163	−	0.0531585i
$650$		0			0
$651$	−0.0726161	+	0.505056i	−0.00284605	+	0.0197947i
$652$		0			0
$653$	10.1759	+	6.53968i	0.398215	+	0.255918i	0.724388	−	0.689393i	$-0.242123\pi$
$653$	10.1759	+	6.53968i	0.398215	+	0.255918i	−0.326172	+	0.945310i	$0.605759\pi$
$654$		0			0
$655$	5.21168	+	11.4120i	0.203637	+	0.445903i
$656$		0			0
$657$	−5.33947	−	37.1368i	−0.208312	−	1.44884i
$658$		0			0
$659$	−20.0814	+	5.89644i	−0.782262	+	0.229693i	−0.648392	−	0.761306i	$-0.724558\pi$
$659$	−20.0814	+	5.89644i	−0.782262	+	0.229693i	−0.133869	+	0.990999i	$0.542740\pi$
$660$		0			0
$661$	14.1761	−	16.3601i	0.551387	−	0.636335i	−0.409818	−	0.912167i	$-0.634408\pi$
$661$	14.1761	−	16.3601i	0.551387	−	0.636335i	0.961206	+	0.275832i	$0.0889534\pi$
$662$		0			0
$663$	−0.138282	−	0.159586i	−0.00537043	−	0.00619781i
$664$		0			0
$665$	−4.99197	+	10.9309i	−0.193580	+	0.423882i
$666$		0			0
$667$	31.5127	+	7.49957i	1.22018	+	0.290385i
$668$		0			0
$669$	0.499409	−	1.09355i	0.0193083	−	0.0422792i
$670$		0			0
$671$	−0.435226	−	0.502277i	−0.0168017	−	0.0193902i
$672$		0			0
$673$	32.9869	−	38.0689i	1.27155	−	1.46745i	0.454653	−	0.890669i	$-0.349763\pi$
$673$	32.9869	−	38.0689i	1.27155	−	1.46745i	0.816899	−	0.576781i	$-0.195691\pi$
$674$		0			0
$675$	−0.268500	+	0.0788388i	−0.0103346	+	0.00303451i
$676$		0			0
$677$	1.11800	+	7.77585i	0.0429682	+	0.298850i	0.999962	+	0.00874126i	$0.00278246\pi$
$677$	1.11800	+	7.77585i	0.0429682	+	0.298850i	−0.956994	+	0.290109i	$0.906308\pi$
$678$		0			0
$679$	15.8841	+	34.7814i	0.609576	+	1.33479i
$680$		0			0
$681$	0.350411	+	0.225195i	0.0134278	+	0.00862950i
$682$		0			0
$683$	−2.42284	+	16.8513i	−0.0927076	+	0.644795i	0.889491	+	0.456952i	$0.151059\pi$
$683$	−2.42284	+	16.8513i	−0.0927076	+	0.644795i	−0.982199	+	0.187843i	$0.939850\pi$
$684$		0			0
$685$	7.10925	−	4.56884i	0.271630	−	0.174566i
$686$		0			0
$687$	−0.721905	−	0.211971i	−0.0275424	−	0.00808718i
$688$		0			0
$689$	0.391905			0.0149304
$690$		0			0
$691$	20.1063			0.764879			0.382439	−	0.923981i	$-0.375084\pi$
$691$	20.1063			0.764879			0.382439	+	0.923981i	$0.375084\pi$
$692$		0			0
$693$	−2.39308	−	0.702671i	−0.0909055	−	0.0266923i
$694$		0			0
$695$	−11.4767	+	7.37563i	−0.435336	+	0.279774i
$696$		0			0
$697$	3.00119	−	20.8737i	0.113678	−	0.790649i
$698$		0			0
$699$	0.436840	+	0.280740i	0.0165228	+	0.0106186i
$700$		0			0
$701$	1.77020	+	3.87619i	0.0668595	+	0.146402i	0.940112	−	0.340867i	$-0.110721\pi$
$701$	1.77020	+	3.87619i	0.0668595	+	0.146402i	−0.873252	+	0.487269i	$0.837993\pi$
$702$		0			0
$703$	−3.59464	−	25.0013i	−0.135575	−	0.942942i
$704$		0			0
$705$	−0.198968	+	0.0584224i	−0.00749358	+	0.00220031i
$706$		0			0
$707$	6.61264	−	7.63139i	0.248694	−	0.287008i
$708$		0			0
$709$	−2.18654	−	2.52340i	−0.0821172	−	0.0947683i	0.713204	−	0.700956i	$-0.247243\pi$
$709$	−2.18654	−	2.52340i	−0.0821172	−	0.0947683i	−0.795321	+	0.606188i	$0.792698\pi$
$710$		0			0
$711$	−8.02478	+	17.5718i	−0.300953	+	0.658995i
$712$		0			0
$713$	−12.2087	−	12.6928i	−0.457218	−	0.475349i
$714$		0			0
$715$	0.234175	−	0.512772i	0.00875765	−	0.0191766i
$716$		0			0
$717$	0.590042	+	0.680945i	0.0220355	+	0.0254304i
$718$		0			0
$719$	9.53735	−	11.0067i	0.355683	−	0.410480i	−0.549506	−	0.835490i	$-0.685184\pi$
$719$	9.53735	−	11.0067i	0.355683	−	0.410480i	0.905189	+	0.425010i	$0.139729\pi$
$720$		0			0
$721$	39.7216	−	11.6633i	1.47931	−	0.434364i
$722$		0			0
$723$	−0.152757	−	1.06245i	−0.00568109	−	0.0395129i
$724$		0			0
$725$	−2.80587	−	6.14399i	−0.104207	−	0.228182i
$726$		0			0
$727$	20.9525	+	13.4654i	0.777087	+	0.499403i	0.868066	−	0.496449i	$-0.165363\pi$
$727$	20.9525	+	13.4654i	0.777087	+	0.499403i	−0.0909789	+	0.995853i	$0.529000\pi$
$728$		0			0
$729$	3.82578	−	26.6089i	0.141696	−	0.985515i
$730$		0			0
$731$	2.04987	−	1.31737i	0.0758172	−	0.0487248i
$732$		0			0
$733$	−32.2166	−	9.45965i	−1.18995	−	0.349400i	−0.373947	−	0.927450i	$-0.621996\pi$
$733$	−32.2166	−	9.45965i	−1.18995	−	0.349400i	−0.816001	+	0.578050i	$0.803814\pi$
$734$		0			0
$735$	−0.0872155			−0.00321699
$736$		0			0
$737$	−2.80746			−0.103414
$738$		0			0
$739$	30.0785	+	8.83184i	1.10645	+	0.324884i	0.783414	−	0.621501i	$-0.213477\pi$
$739$	30.0785	+	8.83184i	1.10645	+	0.324884i	0.323041	+	0.946385i	$0.395295\pi$
$740$		0			0
$741$	−0.319577	+	0.205380i	−0.0117400	+	0.00754481i
$742$		0			0
$743$	1.06080	−	7.37806i	0.0389171	−	0.270675i	−0.961067	−	0.276316i	$-0.910886\pi$
$743$	1.06080	−	7.37806i	0.0389171	−	0.270675i	0.999984	+	0.00564092i	$0.00179557\pi$
$744$		0			0
$745$	−15.4223	−	9.91128i	−0.565028	−	0.363121i
$746$		0			0
$747$	−10.4988	−	22.9892i	−0.384131	−	0.841129i
$748$		0			0
$749$	−2.02317	−	14.0715i	−0.0739251	−	0.514161i
$750$		0			0
$751$	−24.1440	+	7.08932i	−0.881028	+	0.258693i	−0.690799	−	0.723047i	$-0.742741\pi$
$751$	−24.1440	+	7.08932i	−0.881028	+	0.258693i	−0.190229	+	0.981740i	$0.560923\pi$
$752$		0			0
$753$	0.232294	−	0.268081i	0.00846525	−	0.00976942i
$754$		0			0
$755$	8.79551	+	10.1506i	0.320101	+	0.369417i
$756$		0			0
$757$	−7.65858	+	16.7699i	−0.278356	+	0.609514i	−0.996239	−	0.0866495i	$-0.972384\pi$
$757$	−7.65858	+	16.7699i	−0.278356	+	0.609514i	0.717883	+	0.696164i	$0.245111\pi$
$758$		0			0
$759$	−0.0507591	+	0.0364800i	−0.00184244	+	0.00132414i
$760$		0			0
$761$	−1.42209	+	3.11394i	−0.0515507	+	0.112880i	−0.933655	−	0.358174i	$-0.883399\pi$
$761$	−1.42209	+	3.11394i	−0.0515507	+	0.112880i	0.882104	+	0.471055i	$0.156127\pi$
$762$		0			0
$763$	6.91052	+	7.97517i	0.250178	+	0.288721i
$764$		0			0
$765$	−4.40319	+	5.08156i	−0.159198	+	0.183724i
$766$		0			0
$767$	−17.3604	+	5.09747i	−0.626847	+	0.184059i
$768$		0			0
$769$	−6.13693	−	42.6833i	−0.221303	−	1.53920i	−0.733118	−	0.680102i	$-0.761936\pi$
$769$	−6.13693	−	42.6833i	−0.221303	−	1.53920i	0.511815	−	0.859096i	$-0.328973\pi$
$770$		0			0
$771$	0.547338	+	1.19850i	0.0197119	+	0.0431630i
$772$		0			0
$773$	23.3071	+	14.9786i	0.838297	+	0.538741i	0.887905	−	0.460028i	$-0.152161\pi$
$773$	23.3071	+	14.9786i	0.838297	+	0.538741i	−0.0496071	+	0.998769i	$0.515797\pi$
$774$		0			0
$775$	−0.522611	+	3.63484i	−0.0187727	+	0.130567i
$776$		0			0
$777$	0.731716	−	0.470246i	0.0262502	−	0.0168700i
$778$		0			0
$779$	−36.4013	−	10.6884i	−1.30421	−	0.382951i
$780$		0			0
$781$	−3.63079			−0.129920
$782$		0			0
$783$	−1.89011			−0.0675472
$784$		0			0
$785$	−1.99606	−	0.586097i	−0.0712426	−	0.0209187i
$786$		0			0
$787$	−40.1813	+	25.8229i	−1.43231	+	0.920489i	−0.432486	+	0.901641i	$0.642363\pi$
$787$	−40.1813	+	25.8229i	−1.43231	+	0.920489i	−0.999822	+	0.0188479i	$0.994000\pi$
$788$		0			0
$789$	0.0102895	−	0.0715654i	0.000366318	−	0.00254779i
$790$		0			0
$791$	−7.86704	−	5.05584i	−0.279720	−	0.179765i
$792$		0			0
$793$	1.99425	+	4.36679i	0.0708177	+	0.155069i
$794$		0			0
$795$	0.00128957	+	0.00896918i	4.57365e−5	+	0.000318104i
$796$		0			0
$797$	1.11687	−	0.327942i	0.0395615	−	0.0116163i	−0.261892	−	0.965097i	$-0.584346\pi$
$797$	1.11687	−	0.327942i	0.0395615	−	0.0116163i	0.301453	+	0.953481i	$0.402528\pi$
$798$		0			0
$799$	−6.52822	+	7.53396i	−0.230952	+	0.266533i
$800$		0			0
$801$	−2.01410	−	2.32440i	−0.0711648	−	0.0821286i
$802$		0			0
$803$	−1.45240	+	3.18032i	−0.0512542	+	0.112231i
$804$		0			0
$805$	8.77992	−	11.2653i	0.309452	−	0.397050i
$806$		0			0
$807$	0.431185	−	0.944163i	0.0151784	−	0.0332361i
$808$		0			0
$809$	13.8053	+	15.9322i	0.485370	+	0.560147i	0.944623	−	0.328159i	$-0.106428\pi$
$809$	13.8053	+	15.9322i	0.485370	+	0.560147i	−0.459252	+	0.888306i	$0.651883\pi$
$810$		0			0
$811$	12.7377	−	14.7001i	0.447282	−	0.516191i	−0.486672	−	0.873585i	$-0.661789\pi$
$811$	12.7377	−	14.7001i	0.447282	−	0.516191i	0.933954	+	0.357394i	$0.116335\pi$
$812$		0			0
$813$	−0.223914	+	0.0657472i	−0.00785302	+	0.00230586i
$814$		0			0
$815$	1.40559	+	9.77606i	0.0492355	+	0.342441i
$816$		0			0
$817$	−1.82101	−	3.98747i	−0.0637092	−	0.139504i
$818$		0			0
$819$	15.1556	+	9.73991i	0.529579	+	0.340340i
$820$		0			0
$821$	−0.389483	+	2.70892i	−0.0135931	+	0.0945418i	−0.995489	−	0.0948816i	$-0.969753\pi$
$821$	−0.389483	+	2.70892i	−0.0135931	+	0.0945418i	0.981896	+	0.189423i	$0.0606619\pi$
$822$		0			0
$823$	−18.7607	+	12.0568i	−0.653956	+	0.420272i	−0.825110	−	0.564972i	$-0.808887\pi$
$823$	−18.7607	+	12.0568i	−0.653956	+	0.420272i	0.171154	+	0.985244i	$0.445251\pi$
$824$		0			0
$825$	0.0125059	+	0.00367206i	0.000435400	+	0.000127845i
$826$		0			0
$827$	8.80241			0.306090			0.153045	−	0.988219i	$-0.451092\pi$
$827$	8.80241			0.306090			0.153045	+	0.988219i	$0.451092\pi$
$828$		0			0
$829$	−1.91551			−0.0665283			−0.0332642	−	0.999447i	$-0.510590\pi$
$829$	−1.91551			−0.0665283			−0.0332642	+	0.999447i	$0.510590\pi$
$830$		0			0
$831$	−1.08742	−	0.319296i	−0.0377223	−	0.0110763i
$832$		0			0
$833$	−3.52715	+	2.26676i	−0.122209	+	0.0785387i
$834$		0			0
$835$	2.37490	−	16.5178i	0.0821868	−	0.571622i
$836$		0			0
$837$	0.864487	+	0.555572i	0.0298810	+	0.0192034i
$838$		0			0
$839$	−8.33976	−	18.2615i	−0.287920	−	0.630458i	0.709305	−	0.704902i	$-0.249009\pi$
$839$	−8.33976	−	18.2615i	−0.287920	−	0.630458i	−0.997225	+	0.0744441i	$0.976282\pi$
$840$		0			0
$841$	−2.36549	−	16.4523i	−0.0815685	−	0.567321i
$842$		0			0
$843$	0.874779	−	0.256858i	0.0301290	−	0.00884667i
$844$		0			0
$845$	5.84671	−	6.74746i	0.201133	−	0.232120i
$846$		0			0
$847$	−21.3007	−	24.5824i	−0.731902	−	0.844660i
$848$		0			0
$849$	0.204793	−	0.448434i	0.00702847	−	0.0153902i
$850$		0			0
$851$	−2.72335	+	29.8972i	−0.0933553	+	1.02486i
$852$		0			0
$853$	−5.07462	+	11.1119i	−0.173752	+	0.380463i	−0.976394	−	0.215998i	$-0.930700\pi$
$853$	−5.07462	+	11.1119i	−0.173752	+	0.380463i	0.802642	+	0.596461i	$0.203427\pi$
$854$		0			0
$855$	7.92136	+	9.14173i	0.270905	+	0.312641i
$856$		0			0
$857$	6.38459	−	7.36821i	0.218094	−	0.251693i	−0.636151	−	0.771564i	$-0.719475\pi$
$857$	6.38459	−	7.36821i	0.218094	−	0.251693i	0.854245	+	0.519871i	$0.174020\pi$
$858$		0			0
$859$	−26.9782	+	7.92152i	−0.920485	+	0.270279i	−0.707448	−	0.706765i	$-0.750154\pi$
$859$	−26.9782	+	7.92152i	−0.920485	+	0.270279i	−0.213037	+	0.977044i	$0.568335\pi$
$860$		0			0
$861$	−0.185924	−	1.29313i	−0.00633627	−	0.0440698i
$862$		0			0
$863$	2.90772	+	6.36703i	0.0989801	+	0.216736i	0.952644	−	0.304088i	$-0.0983518\pi$
$863$	2.90772	+	6.36703i	0.0989801	+	0.216736i	−0.853664	+	0.520825i	$0.825625\pi$
$864$		0			0
$865$	0.717997	+	0.461429i	0.0244126	+	0.0156890i
$866$		0			0
$867$	−0.0794748	+	0.552760i	−0.00269911	+	0.0187727i
$868$		0			0
$869$	1.51438	−	0.973234i	0.0513719	−	0.0330147i
$870$		0			0
$871$	19.4575	+	5.71323i	0.659291	+	0.193585i
$872$		0			0
$873$	38.4894			1.30267
$874$		0			0
$875$	−2.97814			−0.100680
$876$		0			0
$877$	−18.3125	−	5.37704i	−0.618369	−	0.181570i	−0.0424800	−	0.999097i	$-0.513526\pi$
$877$	−18.3125	−	5.37704i	−0.618369	−	0.181570i	−0.575889	+	0.817528i	$0.695344\pi$
$878$		0			0
$879$	0.182417	−	0.117233i	0.00615279	−	0.00395416i
$880$		0			0
$881$	−4.37583	+	30.4346i	−0.147426	+	1.02537i	0.772988	+	0.634421i	$0.218761\pi$
$881$	−4.37583	+	30.4346i	−0.147426	+	1.02537i	−0.920413	+	0.390946i	$0.872148\pi$
$882$		0			0
$883$	−3.64108	−	2.33998i	−0.122532	−	0.0787466i	0.477939	−	0.878393i	$-0.341384\pi$
$883$	−3.64108	−	2.33998i	−0.122532	−	0.0787466i	−0.600471	+	0.799646i	$0.705020\pi$
$884$		0			0
$885$	−0.173786	−	0.380538i	−0.00584175	−	0.0127916i
$886$		0			0
$887$	6.04515	+	42.0449i	0.202976	+	1.41173i	0.795390	+	0.606097i	$0.207266\pi$
$887$	6.04515	+	42.0449i	0.202976	+	1.41173i	−0.592414	+	0.805634i	$0.701825\pi$
$888$		0			0
$889$	−3.00949	+	0.883666i	−0.100935	+	0.0296372i
$890$		0			0
$891$	−1.64289	+	1.89600i	−0.0550389	+	0.0635183i
$892$		0			0
$893$	11.7443	+	13.5536i	0.393007	+	0.453554i
$894$		0			0
$895$	0.796892	−	1.74495i	0.0266372	−	0.0583272i
$896$		0			0
$897$	0.426030	−	0.149534i	0.0142247	−	0.00499278i
$898$		0			0
$899$	−10.3037	+	22.5621i	−0.343649	+	0.752487i
$900$		0			0
$901$	0.285265	+	0.329213i	0.00950355	+	0.0109677i
$902$		0			0
$903$	0.0988531	−	0.114083i	0.00328963	−	0.00379643i
$904$		0			0
$905$	−6.01911	+	1.76737i	−0.200082	+	0.0587494i
$906$		0			0
$907$	6.50131	+	45.2176i	0.215872	+	1.50143i	0.753054	+	0.657959i	$0.228580\pi$
$907$	6.50131	+	45.2176i	0.215872	+	1.50143i	−0.537181	+	0.843467i	$0.680511\pi$
$908$		0			0
$909$	−4.22249	−	9.24597i	−0.140051	−	0.306669i
$910$		0			0
$911$	−1.02386	−	0.657993i	−0.0339219	−	0.0218003i	0.523570	−	0.851983i	$-0.324600\pi$
$911$	−1.02386	−	0.657993i	−0.0339219	−	0.0218003i	−0.557492	+	0.830182i	$0.688236\pi$
$912$		0			0
$913$	−0.335170	+	2.33116i	−0.0110925	+	0.0771501i
$914$		0			0
$915$	−0.0933766	+	0.0600095i	−0.00308694	+	0.00198385i
$916$		0			0
$917$	35.8495	+	10.5264i	1.18385	+	0.347611i
$918$		0			0
$919$	−44.0297			−1.45241			−0.726203	−	0.687480i	$-0.758717\pi$
$919$	−44.0297			−1.45241			−0.726203	+	0.687480i	$0.758717\pi$
$920$		0			0
$921$	1.21428			0.0400117
$922$		0			0
$923$	25.1636	+	7.38871i	0.828271	+	0.243202i
$924$		0			0
$925$	5.26609	−	3.38431i	0.173148	−	0.111275i
$926$		0			0
$927$	5.93056	−	41.2479i	0.194785	−	1.35476i
$928$		0			0
$929$	14.9269	+	9.59293i	0.489735	+	0.314734i	0.762099	−	0.647461i	$-0.224169\pi$
$929$	14.9269	+	9.59293i	0.489735	+	0.314734i	−0.272363	+	0.962194i	$0.587805\pi$
$930$		0			0
$931$	3.13337	+	6.86111i	0.102692	+	0.224864i
$932$		0			0
$933$	0.0849447	+	0.590803i	0.00278096	+	0.0193420i
$934$		0			0
$935$	0.601199	−	0.176528i	0.0196613	−	0.00577308i
$936$		0			0
$937$	−1.42968	+	1.64994i	−0.0467057	+	0.0539013i	−0.778622	−	0.627494i	$-0.784081\pi$
$937$	−1.42968	+	1.64994i	−0.0467057	+	0.0539013i	0.731916	+	0.681395i	$0.238626\pi$
$938$		0			0
$939$	−0.0179142	−	0.0206741i	−0.000584609	−	0.000674674i
$940$		0			0
$941$	−9.96049	+	21.8104i	−0.324703	+	0.711000i	−0.999639	−	0.0268765i	$-0.991444\pi$
$941$	−9.96049	+	21.8104i	−0.324703	+	0.711000i	0.674936	+	0.737876i	$0.264171\pi$
$942$		0			0
$943$	39.1483	+	22.3753i	1.27484	+	0.728639i
$944$		0			0
$945$	−0.346203	+	0.758078i	−0.0112620	+	0.0246603i
$946$		0			0
$947$	3.23129	+	3.72910i	0.105003	+	0.121180i	0.805818	−	0.592163i	$-0.201726\pi$
$947$	3.23129	+	3.72910i	0.105003	+	0.121180i	−0.700816	+	0.713343i	$0.747180\pi$
$948$		0			0
$949$	16.5381	−	19.0860i	0.536849	−	0.619557i
$950$		0			0
$951$	−0.681459	+	0.200094i	−0.0220978	+	0.00648851i
$952$		0			0
$953$	3.31975	+	23.0894i	0.107537	+	0.747938i	0.970226	+	0.242203i	$0.0778698\pi$
$953$	3.31975	+	23.0894i	0.107537	+	0.747938i	−0.862688	+	0.505736i	$0.831221\pi$
$954$		0			0
$955$	−7.35889	−	16.1137i	−0.238128	−	0.521428i
$956$		0			0
$957$	0.0740602	+	0.0475956i	0.00239403	+	0.00153855i
$958$		0			0
$959$	3.58172	−	24.9114i	0.115660	−	0.804432i
$960$		0			0
$961$	−14.7344	+	9.46923i	−0.475304	+	0.305459i
$962$		0			0
$963$	−13.7305	−	4.03163i	−0.442458	−	0.129917i
$964$		0			0
$965$	23.4351			0.754403
$966$		0			0
$967$	56.8799			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$967$	56.8799			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$968$		0			0
$969$	−0.405143	−	0.118961i	−0.0130151	−	0.00382157i
$970$		0			0
$971$	−46.9482	+	30.1717i	−1.50664	+	0.968257i	−0.512670	+	0.858586i	$0.671344\pi$
$971$	−46.9482	+	30.1717i	−1.50664	+	0.968257i	−0.993968	+	0.109672i	$0.965020\pi$
$972$		0			0
$973$	−5.78210	+	40.2154i	−0.185366	+	1.28925i
$974$		0			0
$975$	−0.0792011	−	0.0508994i	−0.00253646	−	0.00163009i
$976$		0			0
$977$	−1.36909	−	2.99790i	−0.0438012	−	0.0959112i	0.886466	−	0.462793i	$-0.153153\pi$
$977$	−1.36909	−	2.99790i	−0.0438012	−	0.0959112i	−0.930268	+	0.366882i	$0.880425\pi$
$978$		0			0
$979$	0.0407888	+	0.283692i	0.00130361	+	0.00906684i
$980$		0			0
$981$	10.1921	−	2.99268i	0.325409	−	0.0955488i
$982$		0			0
$983$	−38.5232	+	44.4582i	−1.22870	+	1.41800i	−0.352665	+	0.935750i	$0.614725\pi$
$983$	−38.5232	+	44.4582i	−1.22870	+	1.41800i	−0.876035	+	0.482247i	$0.839821\pi$
$984$		0			0
$985$	−8.67067	−	10.0065i	−0.276271	−	0.318833i
$986$		0			0
$987$	−0.256549	+	0.561763i	−0.00816603	+	0.0178811i
$988$		0			0
$989$	1.00832	+	5.11165i	0.0320629	+	0.162541i
$990$		0			0
$991$	−0.425967	+	0.932737i	−0.0135313	+	0.0296294i	−0.916277	−	0.400545i	$-0.868821\pi$
$991$	−0.425967	+	0.932737i	−0.0135313	+	0.0296294i	0.902746	+	0.430175i	$0.141548\pi$
$992$		0			0
$993$	0.435440	+	0.502524i	0.0138183	+	0.0159471i
$994$		0			0
$995$	−4.23887	+	4.89192i	−0.134381	+	0.155084i
$996$		0			0
$997$	38.2928	−	11.2438i	1.21275	−	0.356094i	0.388033	−	0.921645i	$-0.373155\pi$
$997$	38.2928	−	11.2438i	1.21275	−	0.356094i	0.824713	+	0.565551i	$0.191336\pi$
$998$		0			0
$999$	−0.249296	−	1.73389i	−0.00788736	−	0.0548578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.121.2	✓	30
23.4	even	11	inner	460.2.m.a.441.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.121.2	✓	30	1.1	even	1	trivial
460.2.m.a.441.2	yes	30	23.4	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0447663 + 0.0131446i) q^{3} +(0.841254 - 0.540641i) q^{5} +(0.423834 - 2.94783i) q^{7} +(-2.52193 - 1.62075i) q^{9} +O(q^{10})\)	\(q+(0.0447663 + 0.0131446i) q^{3} +(0.841254 - 0.540641i) q^{5} +(0.423834 - 2.94783i) q^{7} +(-2.52193 - 1.62075i) q^{9} +(0.116050 + 0.254114i) q^{11} +(-0.287174 - 1.99734i) q^{13} +(0.0447663 - 0.0131446i) q^{15} +(1.46880 - 1.69508i) q^{17} +(-2.64237 - 3.04946i) q^{19} +(0.0577214 - 0.126392i) q^{21} +(2.21614 + 4.25308i) q^{23} +(0.415415 - 0.909632i) q^{25} +(-0.183253 - 0.211486i) q^{27} +(4.42317 - 5.10461i) q^{29} +(-3.52347 + 1.03458i) q^{31} +(0.00185491 + 0.0129012i) q^{33} +(-1.23716 - 2.70901i) q^{35} +(5.26609 + 3.38431i) q^{37} +(0.0133984 - 0.0931882i) q^{39} +(7.90965 - 5.08323i) q^{41} +(1.04239 + 0.306072i) q^{43} -2.99782 q^{45} -4.44460 q^{47} +(-1.79360 - 0.526649i) q^{49} +(0.0880338 - 0.0565759i) q^{51} +(-0.0276399 + 0.192240i) q^{53} +(0.235012 + 0.151033i) q^{55} +(-0.0782053 - 0.171246i) q^{57} +(-1.27607 - 8.87523i) q^{59} +(-2.28267 + 0.670253i) q^{61} +(-5.84656 + 6.74729i) q^{63} +(-1.32143 - 1.52501i) q^{65} +(-4.17476 + 9.14146i) q^{67} +(0.0433035 + 0.219525i) q^{69} +(-5.39907 + 11.8223i) q^{71} +(8.19579 + 9.45844i) q^{73} +(0.0305533 - 0.0352604i) q^{75} +(0.798272 - 0.234394i) q^{77} +(-0.917054 - 6.37825i) q^{79} +(3.73060 + 8.16887i) q^{81} +(7.09216 + 4.55785i) q^{83} +(0.319200 - 2.22009i) q^{85} +(0.265107 - 0.170374i) q^{87} +(0.984393 + 0.289044i) q^{89} -6.00952 q^{91} -0.171332 q^{93} +(-3.87156 - 1.13679i) q^{95} +(-10.8010 + 6.94136i) q^{97} +(0.119185 - 0.828946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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