LMFDB - Embedded newform 4020.2.q.m.3781.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.8
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.m.841.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(0.440752 + 0.763405i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.440752 + 0.763405i) q^{7} +1.00000 q^{9} +(1.63603 + 2.83369i) q^{11} +(0.784613 - 1.35899i) q^{13} +1.00000 q^{15} +(-3.66818 + 6.35347i) q^{17} +(4.31259 - 7.46962i) q^{19} +(0.440752 + 0.763405i) q^{21} +(-1.92198 + 3.32897i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-0.0681421 - 0.118026i) q^{29} +(-0.841907 - 1.45823i) q^{31} +(1.63603 + 2.83369i) q^{33} +(0.440752 + 0.763405i) q^{35} +(-1.66657 + 2.88658i) q^{37} +(0.784613 - 1.35899i) q^{39} +(2.87693 + 4.98299i) q^{41} +11.1706 q^{43} +1.00000 q^{45} +(5.00257 + 8.66471i) q^{47} +(3.11148 - 5.38923i) q^{49} +(-3.66818 + 6.35347i) q^{51} +1.34067 q^{53} +(1.63603 + 2.83369i) q^{55} +(4.31259 - 7.46962i) q^{57} +2.31882 q^{59} +(-2.41476 + 4.18248i) q^{61} +(0.440752 + 0.763405i) q^{63} +(0.784613 - 1.35899i) q^{65} +(-7.65965 + 2.88612i) q^{67} +(-1.92198 + 3.32897i) q^{69} +(-4.49875 - 7.79207i) q^{71} +(-3.99144 + 6.91338i) q^{73} +1.00000 q^{75} +(-1.44217 + 2.49791i) q^{77} +(-0.710582 - 1.23076i) q^{79} +1.00000 q^{81} +(-0.575104 + 0.996110i) q^{83} +(-3.66818 + 6.35347i) q^{85} +(-0.0681421 - 0.118026i) q^{87} +7.60241 q^{89} +1.38328 q^{91} +(-0.841907 - 1.45823i) q^{93} +(4.31259 - 7.46962i) q^{95} +(1.95069 - 3.37870i) q^{97} +(1.63603 + 2.83369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.440752	+	0.763405i	0.166589	+	0.288540i	0.937218	−	0.348743i	$-0.113392\pi$
$7$	0.440752	+	0.763405i	0.166589	+	0.288540i	−0.770630	+	0.637283i	$0.780058\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.63603	+	2.83369i	0.493282	+	0.854389i	0.999970	−	0.00773998i	$-0.00246374\pi$
$11$	1.63603	+	2.83369i	0.493282	+	0.854389i	−0.506688	+	0.862129i	$0.669130\pi$
$12$		0			0
$13$	0.784613	−	1.35899i	0.217613	−	0.376916i	−0.736465	−	0.676476i	$-0.763506\pi$
$13$	0.784613	−	1.35899i	0.217613	−	0.376916i	0.954078	+	0.299560i	$0.0968398\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.66818	+	6.35347i	−0.889663	+	1.54094i	−0.0493892	+	0.998780i	$0.515727\pi$
$17$	−3.66818	+	6.35347i	−0.889663	+	1.54094i	−0.840274	+	0.542162i	$0.817606\pi$
$18$		0			0
$19$	4.31259	−	7.46962i	0.989375	−	1.71365i	0.368780	−	0.929517i	$-0.379776\pi$
$19$	4.31259	−	7.46962i	0.989375	−	1.71365i	0.620595	−	0.784131i	$-0.286891\pi$
$20$		0			0
$21$	0.440752	+	0.763405i	0.0961799	+	0.166589i
$22$		0			0
$23$	−1.92198	+	3.32897i	−0.400761	+	0.694139i	−0.993818	−	0.111022i	$-0.964588\pi$
$23$	−1.92198	+	3.32897i	−0.400761	+	0.694139i	0.593057	+	0.805161i	$0.297921\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.0681421	−	0.118026i	−0.0126537	−	0.0219168i	0.859629	−	0.510918i	$-0.170695\pi$
$29$	−0.0681421	−	0.118026i	−0.0126537	−	0.0219168i	−0.872283	+	0.489002i	$0.837361\pi$
$30$		0			0
$31$	−0.841907	−	1.45823i	−0.151211	−	0.261905i	0.780462	−	0.625203i	$-0.214984\pi$
$31$	−0.841907	−	1.45823i	−0.151211	−	0.261905i	−0.931673	+	0.363298i	$0.881651\pi$
$32$		0			0
$33$	1.63603	+	2.83369i	0.284796	+	0.493282i
$34$		0			0
$35$	0.440752	+	0.763405i	0.0745007	+	0.129039i
$36$		0			0
$37$	−1.66657	+	2.88658i	−0.273982	+	0.474552i	−0.969878	−	0.243592i	$-0.921674\pi$
$37$	−1.66657	+	2.88658i	−0.273982	+	0.474552i	0.695895	+	0.718143i	$0.255008\pi$
$38$		0			0
$39$	0.784613	−	1.35899i	0.125639	−	0.217613i
$40$		0			0
$41$	2.87693	+	4.98299i	0.449301	+	0.778212i	0.998341	−	0.0575844i	$-0.0183398\pi$
$41$	2.87693	+	4.98299i	0.449301	+	0.778212i	−0.549040	+	0.835796i	$0.685006\pi$
$42$		0			0
$43$	11.1706			1.70350			0.851752	−	0.523945i	$-0.175540\pi$
$43$	11.1706			1.70350			0.851752	+	0.523945i	$0.175540\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	5.00257	+	8.66471i	0.729700	+	1.26388i	0.957010	+	0.290055i	$0.0936736\pi$
$47$	5.00257	+	8.66471i	0.729700	+	1.26388i	−0.227310	+	0.973822i	$0.572993\pi$
$48$		0			0
$49$	3.11148	−	5.38923i	0.444497	−	0.769891i
$50$		0			0
$51$	−3.66818	+	6.35347i	−0.513647	+	0.889663i
$52$		0			0
$53$	1.34067			0.184155			0.0920773	−	0.995752i	$-0.470649\pi$
$53$	1.34067			0.184155			0.0920773	+	0.995752i	$0.470649\pi$
$54$		0			0
$55$	1.63603	+	2.83369i	0.220602	+	0.382095i
$56$		0			0
$57$	4.31259	−	7.46962i	0.571216	−	0.989375i
$58$		0			0
$59$	2.31882			0.301884			0.150942	−	0.988543i	$-0.451769\pi$
$59$	2.31882			0.301884			0.150942	+	0.988543i	$0.451769\pi$
$60$		0			0
$61$	−2.41476	+	4.18248i	−0.309178	+	0.535512i	−0.978183	−	0.207746i	$-0.933387\pi$
$61$	−2.41476	+	4.18248i	−0.309178	+	0.535512i	0.669005	+	0.743258i	$0.266720\pi$
$62$		0			0
$63$	0.440752	+	0.763405i	0.0555295	+	0.0961799i
$64$		0			0
$65$	0.784613	−	1.35899i	0.0973193	−	0.168562i
$66$		0			0
$67$	−7.65965	+	2.88612i	−0.935776	+	0.352596i
$67$	−7.65965	+	2.88612i	−0.935776	+	0.352596i
$68$		0			0
$69$	−1.92198	+	3.32897i	−0.231380	+	0.400761i
$70$		0			0
$71$	−4.49875	−	7.79207i	−0.533904	−	0.924748i	−0.999216	−	0.0396013i	$-0.987391\pi$
$71$	−4.49875	−	7.79207i	−0.533904	−	0.924748i	0.465312	−	0.885147i	$-0.345942\pi$
$72$		0			0
$73$	−3.99144	+	6.91338i	−0.467163	+	0.809150i	−0.999296	−	0.0375108i	$-0.988057\pi$
$73$	−3.99144	+	6.91338i	−0.467163	+	0.809150i	0.532133	+	0.846661i	$0.321390\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−1.44217	+	2.49791i	−0.164350	+	0.284663i
$78$		0			0
$79$	−0.710582	−	1.23076i	−0.0799468	−	0.138472i	0.823280	−	0.567635i	$-0.192142\pi$
$79$	−0.710582	−	1.23076i	−0.0799468	−	0.138472i	−0.903227	+	0.429164i	$0.858808\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−0.575104	+	0.996110i	−0.0631259	+	0.109337i	−0.895861	−	0.444334i	$-0.853440\pi$
$83$	−0.575104	+	0.996110i	−0.0631259	+	0.109337i	0.832735	+	0.553671i	$0.186774\pi$
$84$		0			0
$85$	−3.66818	+	6.35347i	−0.397869	+	0.689130i
$86$		0			0
$87$	−0.0681421	−	0.118026i	−0.00730560	−	0.0126537i
$88$		0			0
$89$	7.60241			0.805854			0.402927	−	0.915232i	$-0.367993\pi$
$89$	7.60241			0.805854			0.402927	+	0.915232i	$0.367993\pi$
$90$		0			0
$91$	1.38328			0.145007
$92$		0			0
$93$	−0.841907	−	1.45823i	−0.0873017	−	0.151211i
$94$		0			0
$95$	4.31259	−	7.46962i	0.442462	−	0.766367i
$96$		0			0
$97$	1.95069	−	3.37870i	0.198063	−	0.343055i	−0.749837	−	0.661622i	$-0.769868\pi$
$97$	1.95069	−	3.37870i	0.198063	−	0.343055i	0.947900	+	0.318567i	$0.103202\pi$
$98$		0			0
$99$	1.63603	+	2.83369i	0.164427	+	0.284796i
$100$		0			0
$101$	−2.71660	−	4.70530i	−0.270312	−	0.468195i	0.698629	−	0.715484i	$-0.253794\pi$
$101$	−2.71660	−	4.70530i	−0.270312	−	0.468195i	−0.968942	+	0.247289i	$0.920460\pi$
$102$		0			0
$103$	5.38301	+	9.32365i	0.530404	+	0.918686i	0.999371	+	0.0354706i	$0.0112930\pi$
$103$	5.38301	+	9.32365i	0.530404	+	0.918686i	−0.468967	+	0.883216i	$0.655374\pi$
$104$		0			0
$105$	0.440752	+	0.763405i	0.0430130	+	0.0745007i
$106$		0			0
$107$	−11.2495			−1.08753			−0.543767	−	0.839236i	$-0.683003\pi$
$107$	−11.2495			−1.08753			−0.543767	+	0.839236i	$0.683003\pi$
$108$		0			0
$109$	−5.99050			−0.573786			−0.286893	−	0.957963i	$-0.592622\pi$
$109$	−5.99050			−0.573786			−0.286893	+	0.957963i	$0.592622\pi$
$110$		0			0
$111$	−1.66657	+	2.88658i	−0.158184	+	0.273982i
$112$		0			0
$113$	3.59371	+	6.22449i	0.338068	+	0.585550i	0.984069	−	0.177786i	$-0.0568934\pi$
$113$	3.59371	+	6.22449i	0.338068	+	0.585550i	−0.646002	+	0.763336i	$0.723560\pi$
$114$		0			0
$115$	−1.92198	+	3.32897i	−0.179226	+	0.310428i
$116$		0			0
$117$	0.784613	−	1.35899i	0.0725375	−	0.125639i
$118$		0			0
$119$	−6.46702			−0.592831
$120$		0			0
$121$	0.146803	−	0.254270i	0.0133457	−	0.0231155i
$122$		0			0
$123$	2.87693	+	4.98299i	0.259404	+	0.449301i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	7.80687	+	13.5219i	0.692748	+	1.19987i	0.970934	+	0.239347i	$0.0769334\pi$
$127$	7.80687	+	13.5219i	0.692748	+	1.19987i	−0.278186	+	0.960527i	$0.589733\pi$
$128$		0			0
$129$	11.1706			0.983518
$130$		0			0
$131$	8.44101			0.737495			0.368747	−	0.929530i	$-0.379787\pi$
$131$	8.44101			0.737495			0.368747	+	0.929530i	$0.379787\pi$
$132$		0			0
$133$	7.60312			0.659274
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	21.4284			1.83075			0.915374	−	0.402604i	$-0.131895\pi$
$137$	21.4284			1.83075			0.915374	+	0.402604i	$0.131895\pi$
$138$		0			0
$139$	−15.5895			−1.32228			−0.661140	−	0.750262i	$-0.729927\pi$
$139$	−15.5895			−1.32228			−0.661140	+	0.750262i	$0.729927\pi$
$140$		0			0
$141$	5.00257	+	8.66471i	0.421292	+	0.729700i
$142$		0			0
$143$	5.13461			0.429377
$144$		0			0
$145$	−0.0681421	−	0.118026i	−0.00565889	−	0.00980149i
$146$		0			0
$147$	3.11148	−	5.38923i	0.256630	−	0.444497i
$148$		0			0
$149$	−6.73543			−0.551788			−0.275894	−	0.961188i	$-0.588974\pi$
$149$	−6.73543			−0.551788			−0.275894	+	0.961188i	$0.588974\pi$
$150$		0			0
$151$	−5.19852	+	9.00410i	−0.423049	+	0.732743i	−0.996236	−	0.0866818i	$-0.972374\pi$
$151$	−5.19852	+	9.00410i	−0.423049	+	0.732743i	0.573187	+	0.819425i	$0.305707\pi$
$152$		0			0
$153$	−3.66818	+	6.35347i	−0.296554	+	0.513647i
$154$		0			0
$155$	−0.841907	−	1.45823i	−0.0676236	−	0.117128i
$156$		0			0
$157$	9.91396	−	17.1715i	0.791220	−	1.37043i	−0.133992	−	0.990982i	$-0.542780\pi$
$157$	9.91396	−	17.1715i	0.791220	−	1.37043i	0.925212	−	0.379451i	$-0.123887\pi$
$158$		0			0
$159$	1.34067			0.106322
$160$		0			0
$161$	−3.38847			−0.267049
$162$		0			0
$163$	−6.33987	−	10.9810i	−0.496577	−	0.860096i	0.503416	−	0.864044i	$-0.332076\pi$
$163$	−6.33987	−	10.9810i	−0.496577	−	0.860096i	−0.999992	+	0.00394851i	$0.998743\pi$
$164$		0			0
$165$	1.63603	+	2.83369i	0.127365	+	0.220602i
$166$		0			0
$167$	−0.887831	−	1.53777i	−0.0687025	−	0.118996i	0.829628	−	0.558317i	$-0.188553\pi$
$167$	−0.887831	−	1.53777i	−0.0687025	−	0.118996i	−0.898330	+	0.439321i	$0.855219\pi$
$168$		0			0
$169$	5.26876	+	9.12577i	0.405290	+	0.701982i
$170$		0			0
$171$	4.31259	−	7.46962i	0.329792	−	0.571216i
$172$		0			0
$173$	7.93185	−	13.7384i	0.603047	−	1.04451i	−0.389310	−	0.921107i	$-0.627286\pi$
$173$	7.93185	−	13.7384i	0.603047	−	1.04451i	0.992357	−	0.123401i	$-0.0393802\pi$
$174$		0			0
$175$	0.440752	+	0.763405i	0.0333177	+	0.0577080i
$176$		0			0
$177$	2.31882			0.174293
$178$		0			0
$179$	4.62390			0.345607			0.172803	−	0.984956i	$-0.444718\pi$
$179$	4.62390			0.345607			0.172803	+	0.984956i	$0.444718\pi$
$180$		0			0
$181$	−2.11768	−	3.66794i	−0.157406	−	0.272636i	0.776526	−	0.630085i	$-0.216980\pi$
$181$	−2.11768	−	3.66794i	−0.157406	−	0.272636i	−0.933933	+	0.357449i	$0.883647\pi$
$182$		0			0
$183$	−2.41476	+	4.18248i	−0.178504	+	0.309178i
$184$		0			0
$185$	−1.66657	+	2.88658i	−0.122529	+	0.212226i
$186$		0			0
$187$	−24.0050			−1.75542
$188$		0			0
$189$	0.440752	+	0.763405i	0.0320600	+	0.0555295i
$190$		0			0
$191$	−6.02525	+	10.4360i	−0.435972	+	0.755125i	−0.997374	−	0.0724176i	$-0.976929\pi$
$191$	−6.02525	+	10.4360i	−0.435972	+	0.755125i	0.561403	+	0.827543i	$0.310262\pi$
$192$		0			0
$193$	2.67601			0.192623			0.0963117	−	0.995351i	$-0.469295\pi$
$193$	2.67601			0.192623			0.0963117	+	0.995351i	$0.469295\pi$
$194$		0			0
$195$	0.784613	−	1.35899i	0.0561873	−	0.0973193i
$196$		0			0
$197$	−4.85598	−	8.41081i	−0.345974	−	0.599245i	0.639556	−	0.768745i	$-0.279118\pi$
$197$	−4.85598	−	8.41081i	−0.345974	−	0.599245i	−0.985530	+	0.169499i	$0.945785\pi$
$198$		0			0
$199$	−6.40674	+	11.0968i	−0.454162	+	0.786631i	−0.998640	−	0.0521440i	$-0.983395\pi$
$199$	−6.40674	+	11.0968i	−0.454162	+	0.786631i	0.544478	+	0.838775i	$0.316728\pi$
$200$		0			0
$201$	−7.65965	+	2.88612i	−0.540270	+	0.203571i
$202$		0			0
$203$	0.0600675	−	0.104040i	0.00421591	−	0.00730218i
$204$		0			0
$205$	2.87693	+	4.98299i	0.200933	+	0.348027i
$206$		0			0
$207$	−1.92198	+	3.32897i	−0.133587	+	0.231380i
$208$		0			0
$209$	28.2221			1.95216
$210$		0			0
$211$	1.16533	−	2.01841i	0.0802247	−	0.138953i	−0.823122	−	0.567865i	$-0.807770\pi$
$211$	1.16533	−	2.01841i	0.0802247	−	0.138953i	0.903346	+	0.428912i	$0.141103\pi$
$212$		0			0
$213$	−4.49875	−	7.79207i	−0.308249	−	0.533904i
$214$		0			0
$215$	11.1706			0.761830
$216$		0			0
$217$	0.742145	−	1.28543i	0.0503801	−	0.0872608i
$218$		0			0
$219$	−3.99144	+	6.91338i	−0.269717	+	0.467163i
$220$		0			0
$221$	5.75620	+	9.97002i	0.387204	+	0.670656i
$222$		0			0
$223$	15.2802			1.02324			0.511620	−	0.859212i	$-0.329045\pi$
$223$	15.2802			1.02324			0.511620	+	0.859212i	$0.329045\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−10.7460	−	18.6127i	−0.713240	−	1.23537i	−0.963634	−	0.267224i	$-0.913893\pi$
$227$	−10.7460	−	18.6127i	−0.713240	−	1.23537i	0.250394	−	0.968144i	$-0.419440\pi$
$228$		0			0
$229$	−0.0377926	+	0.0654588i	−0.00249741	+	0.00432564i	−0.867271	−	0.497836i	$-0.834128\pi$
$229$	−0.0377926	+	0.0654588i	−0.00249741	+	0.00432564i	0.864774	+	0.502161i	$0.167462\pi$
$230$		0			0
$231$	−1.44217	+	2.49791i	−0.0948877	+	0.164350i
$232$		0			0
$233$	8.59682	+	14.8901i	0.563196	+	0.975484i	0.997215	+	0.0745805i	$0.0237618\pi$
$233$	8.59682	+	14.8901i	0.563196	+	0.975484i	−0.434019	+	0.900904i	$0.642905\pi$
$234$		0			0
$235$	5.00257	+	8.66471i	0.326332	+	0.565223i
$236$		0			0
$237$	−0.710582	−	1.23076i	−0.0461573	−	0.0799468i
$238$		0			0
$239$	13.4948	+	23.3737i	0.872908	+	1.51192i	0.858974	+	0.512019i	$0.171102\pi$
$239$	13.4948	+	23.3737i	0.872908	+	1.51192i	0.0139340	+	0.999903i	$0.495565\pi$
$240$		0			0
$241$	7.84451			0.505309			0.252655	−	0.967557i	$-0.418696\pi$
$241$	7.84451			0.505309			0.252655	+	0.967557i	$0.418696\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	3.11148	−	5.38923i	0.198785	−	0.344306i
$246$		0			0
$247$	−6.76742	−	11.7215i	−0.430601	−	0.745822i
$248$		0			0
$249$	−0.575104	+	0.996110i	−0.0364458	+	0.0631259i
$250$		0			0
$251$	1.89190	−	3.27687i	0.119416	−	0.206834i	−0.800121	−	0.599839i	$-0.795231\pi$
$251$	1.89190	−	3.27687i	0.119416	−	0.206834i	0.919536	+	0.393005i	$0.128565\pi$
$252$		0			0
$253$	−12.5777			−0.790753
$254$		0			0
$255$	−3.66818	+	6.35347i	−0.229710	+	0.397869i
$256$		0			0
$257$	−4.23582	−	7.33665i	−0.264223	−	0.457648i	0.703137	−	0.711055i	$-0.251782\pi$
$257$	−4.23582	−	7.33665i	−0.264223	−	0.457648i	−0.967360	+	0.253407i	$0.918449\pi$
$258$		0			0
$259$	−2.93818			−0.182569
$260$		0			0
$261$	−0.0681421	−	0.118026i	−0.00421789	−	0.00730560i
$262$		0			0
$263$	13.4466			0.829150			0.414575	−	0.910015i	$-0.363930\pi$
$263$	13.4466			0.829150			0.414575	+	0.910015i	$0.363930\pi$
$264$		0			0
$265$	1.34067			0.0823564
$266$		0			0
$267$	7.60241			0.465260
$268$		0			0
$269$	−24.6192			−1.50106			−0.750530	−	0.660836i	$-0.770202\pi$
$269$	−24.6192			−1.50106			−0.750530	+	0.660836i	$0.770202\pi$
$270$		0			0
$271$	12.3115			0.747867			0.373934	−	0.927455i	$-0.378009\pi$
$271$	12.3115			0.747867			0.373934	+	0.927455i	$0.378009\pi$
$272$		0			0
$273$	1.38328			0.0837198
$274$		0			0
$275$	1.63603	+	2.83369i	0.0986564	+	0.170878i
$276$		0			0
$277$	4.21969			0.253536			0.126768	−	0.991932i	$-0.459540\pi$
$277$	4.21969			0.253536			0.126768	+	0.991932i	$0.459540\pi$
$278$		0			0
$279$	−0.841907	−	1.45823i	−0.0504037	−	0.0873017i
$280$		0			0
$281$	4.32751	−	7.49546i	0.258157	−	0.447142i	−0.707591	−	0.706622i	$-0.750218\pi$
$281$	4.32751	−	7.49546i	0.258157	−	0.447142i	0.965748	+	0.259480i	$0.0835513\pi$
$282$		0			0
$283$	−4.72243			−0.280719			−0.140360	−	0.990101i	$-0.544826\pi$
$283$	−4.72243			−0.280719			−0.140360	+	0.990101i	$0.544826\pi$
$284$		0			0
$285$	4.31259	−	7.46962i	0.255456	−	0.442462i
$286$		0			0
$287$	−2.53602	+	4.39252i	−0.149697	+	0.259282i
$288$		0			0
$289$	−18.4110	−	31.8888i	−1.08300	−	1.87581i
$290$		0			0
$291$	1.95069	−	3.37870i	0.114352	−	0.198063i
$292$		0			0
$293$	−6.78024			−0.396106			−0.198053	−	0.980191i	$-0.563462\pi$
$293$	−6.78024			−0.396106			−0.198053	+	0.980191i	$0.563462\pi$
$294$		0			0
$295$	2.31882			0.135007
$296$		0			0
$297$	1.63603	+	2.83369i	0.0949322	+	0.164427i
$298$		0			0
$299$	3.01603	+	5.22391i	0.174421	+	0.302107i
$300$		0			0
$301$	4.92347	+	8.52770i	0.283784	+	0.491529i
$302$		0			0
$303$	−2.71660	−	4.70530i	−0.156065	−	0.270312i
$304$		0			0
$305$	−2.41476	+	4.18248i	−0.138269	+	0.239488i
$306$		0			0
$307$	−0.390812	+	0.676906i	−0.0223048	+	0.0386331i	−0.876962	−	0.480559i	$-0.840434\pi$
$307$	−0.390812	+	0.676906i	−0.0223048	+	0.0386331i	0.854658	+	0.519192i	$0.173767\pi$
$308$		0			0
$309$	5.38301	+	9.32365i	0.306229	+	0.530404i
$310$		0			0
$311$	20.9630			1.18870			0.594351	−	0.804206i	$-0.297409\pi$
$311$	20.9630			1.18870			0.594351	+	0.804206i	$0.297409\pi$
$312$		0			0
$313$	−20.3178			−1.14843			−0.574216	−	0.818704i	$-0.694693\pi$
$313$	−20.3178			−1.14843			−0.574216	+	0.818704i	$0.694693\pi$
$314$		0			0
$315$	0.440752	+	0.763405i	0.0248336	+	0.0430130i
$316$		0			0
$317$	−6.42026	+	11.1202i	−0.360598	+	0.624574i	−0.988059	−	0.154074i	$-0.950761\pi$
$317$	−6.42026	+	11.1202i	−0.360598	+	0.624574i	0.627462	+	0.778648i	$0.284094\pi$
$318$		0			0
$319$	0.222965	−	0.386187i	0.0124837	−	0.0216223i
$320$		0			0
$321$	−11.2495			−0.627889
$322$		0			0
$323$	31.6386	+	54.7997i	1.76042	+	3.04914i
$324$		0			0
$325$	0.784613	−	1.35899i	0.0435225	−	0.0753832i
$326$		0			0
$327$	−5.99050			−0.331275
$328$		0			0
$329$	−4.40978	+	7.63797i	−0.243119	+	0.421095i
$330$		0			0
$331$	−3.34522	−	5.79409i	−0.183870	−	0.318472i	0.759325	−	0.650711i	$-0.225529\pi$
$331$	−3.34522	−	5.79409i	−0.183870	−	0.318472i	−0.943195	+	0.332239i	$0.892196\pi$
$332$		0			0
$333$	−1.66657	+	2.88658i	−0.0913275	+	0.158184i
$334$		0			0
$335$	−7.65965	+	2.88612i	−0.418492	+	0.157686i
$336$		0			0
$337$	12.6979	−	21.9935i	0.691701	−	1.19806i	−0.279579	−	0.960123i	$-0.590195\pi$
$337$	12.6979	−	21.9935i	0.691701	−	1.19806i	0.971280	−	0.237939i	$-0.0764718\pi$
$338$		0			0
$339$	3.59371	+	6.22449i	0.195183	+	0.338068i
$340$		0			0
$341$	2.75477	−	4.77141i	0.149179	−	0.258386i
$342$		0			0
$343$	11.6561			0.629369
$344$		0			0
$345$	−1.92198	+	3.32897i	−0.103476	+	0.179226i
$346$		0			0
$347$	−2.32542	−	4.02774i	−0.124835	−	0.216221i	0.796833	−	0.604199i	$-0.206507\pi$
$347$	−2.32542	−	4.02774i	−0.124835	−	0.216221i	−0.921668	+	0.387978i	$0.873173\pi$
$348$		0			0
$349$	6.78145			0.363003			0.181501	−	0.983391i	$-0.441904\pi$
$349$	6.78145			0.363003			0.181501	+	0.983391i	$0.441904\pi$
$350$		0			0
$351$	0.784613	−	1.35899i	0.0418795	−	0.0725375i
$352$		0			0
$353$	0.828702	−	1.43535i	0.0441074	−	0.0763962i	−0.843129	−	0.537712i	$-0.819289\pi$
$353$	0.828702	−	1.43535i	0.0441074	−	0.0763962i	0.887236	+	0.461315i	$0.152622\pi$
$354$		0			0
$355$	−4.49875	−	7.79207i	−0.238769	−	0.413560i
$356$		0			0
$357$	−6.46702			−0.342271
$358$		0			0
$359$	−25.2938			−1.33496			−0.667479	−	0.744629i	$-0.732627\pi$
$359$	−25.2938			−1.33496			−0.667479	+	0.744629i	$0.732627\pi$
$360$		0			0
$361$	−27.6968	−	47.9723i	−1.45773	−	2.52486i
$362$		0			0
$363$	0.146803	−	0.254270i	0.00770516	−	0.0133457i
$364$		0			0
$365$	−3.99144	+	6.91338i	−0.208922	+	0.361863i
$366$		0			0
$367$	−1.23981	−	2.14742i	−0.0647178	−	0.112094i	0.831851	−	0.554999i	$-0.187281\pi$
$367$	−1.23981	−	2.14742i	−0.0647178	−	0.112094i	−0.896569	+	0.442905i	$0.853948\pi$
$368$		0			0
$369$	2.87693	+	4.98299i	0.149767	+	0.259404i
$370$		0			0
$371$	0.590901	+	1.02347i	0.0306780	+	0.0531359i
$372$		0			0
$373$	−15.7497	−	27.2793i	−0.815488	−	1.41247i	−0.908977	−	0.416846i	$-0.863135\pi$
$373$	−15.7497	−	27.2793i	−0.815488	−	1.41247i	0.0934894	−	0.995620i	$-0.470198\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−0.213861			−0.0110144
$378$		0			0
$379$	3.15055	−	5.45692i	0.161833	−	0.280303i	−0.773693	−	0.633561i	$-0.781593\pi$
$379$	3.15055	−	5.45692i	0.161833	−	0.280303i	0.935526	+	0.353257i	$0.114926\pi$
$380$		0			0
$381$	7.80687	+	13.5219i	0.399958	+	0.692748i
$382$		0			0
$383$	−13.1312	+	22.7439i	−0.670973	+	1.16216i	0.306656	+	0.951820i	$0.400790\pi$
$383$	−13.1312	+	22.7439i	−0.670973	+	1.16216i	−0.977629	+	0.210338i	$0.932543\pi$
$384$		0			0
$385$	−1.44217	+	2.49791i	−0.0734997	+	0.127305i
$386$		0			0
$387$	11.1706			0.567835
$388$		0			0
$389$	1.87018	−	3.23925i	0.0948219	−	0.164236i	−0.814712	−	0.579865i	$-0.803105\pi$
$389$	1.87018	−	3.23925i	0.0948219	−	0.164236i	0.909534	+	0.415629i	$0.136439\pi$
$390$		0			0
$391$	−14.1003	−	24.4225i	−0.713085	−	1.23510i
$392$		0			0
$393$	8.44101			0.425793
$394$		0			0
$395$	−0.710582	−	1.23076i	−0.0357533	−	0.0619265i
$396$		0			0
$397$	11.6295			0.583670			0.291835	−	0.956469i	$-0.405734\pi$
$397$	11.6295			0.583670			0.291835	+	0.956469i	$0.405734\pi$
$398$		0			0
$399$	7.60312			0.380632
$400$		0			0
$401$	−4.88406			−0.243899			−0.121949	−	0.992536i	$-0.538915\pi$
$401$	−4.88406			−0.243899			−0.121949	+	0.992536i	$0.538915\pi$
$402$		0			0
$403$	−2.64229			−0.131622
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−10.9062			−0.540603
$408$		0			0
$409$	6.23061	+	10.7917i	0.308084	+	0.533617i	0.977943	−	0.208871i	$-0.0669790\pi$
$409$	6.23061	+	10.7917i	0.308084	+	0.533617i	−0.669859	+	0.742488i	$0.733646\pi$
$410$		0			0
$411$	21.4284			1.05698
$412$		0			0
$413$	1.02202	+	1.77020i	0.0502904	+	0.0871056i
$414$		0			0
$415$	−0.575104	+	0.996110i	−0.0282308	+	0.0488971i
$416$		0			0
$417$	−15.5895			−0.763419
$418$		0			0
$419$	−1.01069	+	1.75056i	−0.0493753	+	0.0855205i	−0.889657	−	0.456630i	$-0.849056\pi$
$419$	−1.01069	+	1.75056i	−0.0493753	+	0.0855205i	0.840281	+	0.542150i	$0.182390\pi$
$420$		0			0
$421$	15.8653	−	27.4795i	0.773228	−	1.33927i	−0.162557	−	0.986699i	$-0.551974\pi$
$421$	15.8653	−	27.4795i	0.773228	−	1.33927i	0.935785	−	0.352571i	$-0.114693\pi$
$422$		0			0
$423$	5.00257	+	8.66471i	0.243233	+	0.421292i
$424$		0			0
$425$	−3.66818	+	6.35347i	−0.177933	+	0.308188i
$426$		0			0
$427$	−4.25723			−0.206022
$428$		0			0
$429$	5.13461			0.247901
$430$		0			0
$431$	2.16007	+	3.74135i	0.104047	+	0.180215i	0.913348	−	0.407179i	$-0.133487\pi$
$431$	2.16007	+	3.74135i	0.104047	+	0.180215i	−0.809301	+	0.587393i	$0.800154\pi$
$432$		0			0
$433$	12.7929	+	22.1580i	0.614790	+	1.06485i	0.990421	+	0.138078i	$0.0440925\pi$
$433$	12.7929	+	22.1580i	0.614790	+	1.06485i	−0.375632	+	0.926769i	$0.622574\pi$
$434$		0			0
$435$	−0.0681421	−	0.118026i	−0.00326716	−	0.00565889i
$436$		0			0
$437$	16.5774	+	28.7130i	0.793006	+	1.37353i
$438$		0			0
$439$	−15.4989	+	26.8449i	−0.739722	+	1.28124i	0.212898	+	0.977074i	$0.431710\pi$
$439$	−15.4989	+	26.8449i	−0.739722	+	1.28124i	−0.952620	+	0.304162i	$0.901623\pi$
$440$		0			0
$441$	3.11148	−	5.38923i	0.148166	−	0.256630i
$442$		0			0
$443$	−12.0753	−	20.9150i	−0.573714	−	0.993702i	−0.996180	−	0.0873235i	$-0.972169\pi$
$443$	−12.0753	−	20.9150i	−0.573714	−	0.993702i	0.422466	−	0.906379i	$-0.361165\pi$
$444$		0			0
$445$	7.60241			0.360389
$446$		0			0
$447$	−6.73543			−0.318575
$448$		0			0
$449$	−1.57251	−	2.72367i	−0.0742114	−	0.128538i	0.826532	−	0.562890i	$-0.190311\pi$
$449$	−1.57251	−	2.72367i	−0.0742114	−	0.128538i	−0.900743	+	0.434352i	$0.856977\pi$
$450$		0			0
$451$	−9.41349	+	16.3046i	−0.443264	+	0.767756i
$452$		0			0
$453$	−5.19852	+	9.00410i	−0.244248	+	0.423049i
$454$		0			0
$455$	1.38328			0.0648491
$456$		0			0
$457$	−12.1386	−	21.0246i	−0.567819	−	0.983492i	−0.996781	−	0.0801691i	$-0.974454\pi$
$457$	−12.1386	−	21.0246i	−0.567819	−	0.983492i	0.428962	−	0.903322i	$-0.358879\pi$
$458$		0			0
$459$	−3.66818	+	6.35347i	−0.171216	+	0.296554i
$460$		0			0
$461$	−7.79739			−0.363161			−0.181580	−	0.983376i	$-0.558121\pi$
$461$	−7.79739			−0.363161			−0.181580	+	0.983376i	$0.558121\pi$
$462$		0			0
$463$	16.2333	−	28.1169i	0.754426	−	1.30670i	−0.191233	−	0.981545i	$-0.561249\pi$
$463$	16.2333	−	28.1169i	0.754426	−	1.30670i	0.945659	−	0.325159i	$-0.105418\pi$
$464$		0			0
$465$	−0.841907	−	1.45823i	−0.0390425	−	0.0676236i
$466$		0			0
$467$	5.11465	−	8.85883i	0.236678	−	0.409938i	−0.723081	−	0.690763i	$-0.757275\pi$
$467$	5.11465	−	8.85883i	0.236678	−	0.409938i	0.959759	+	0.280825i	$0.0906081\pi$
$468$		0			0
$469$	−5.57929	−	4.57535i	−0.257628	−	0.211270i
$470$		0			0
$471$	9.91396	−	17.1715i	0.456811	−	0.791220i
$472$		0			0
$473$	18.2755	+	31.6541i	0.840308	+	1.45546i
$474$		0			0
$475$	4.31259	−	7.46962i	0.197875	−	0.342730i
$476$		0			0
$477$	1.34067			0.0613848
$478$		0			0
$479$	19.5827	−	33.9182i	0.894755	−	1.54976i	0.0606471	−	0.998159i	$-0.480684\pi$
$479$	19.5827	−	33.9182i	0.894755	−	1.54976i	0.834108	−	0.551602i	$-0.185983\pi$
$480$		0			0
$481$	2.61523	+	4.52970i	0.119244	+	0.206537i
$482$		0			0
$483$	−3.38847			−0.154181
$484$		0			0
$485$	1.95069	−	3.37870i	0.0885764	−	0.153419i
$486$		0			0
$487$	−18.1351	+	31.4109i	−0.821780	+	1.42336i	0.0825754	+	0.996585i	$0.473685\pi$
$487$	−18.1351	+	31.4109i	−0.821780	+	1.42336i	−0.904355	+	0.426780i	$0.859648\pi$
$488$		0			0
$489$	−6.33987	−	10.9810i	−0.286699	−	0.496577i
$490$		0			0
$491$	−10.2595			−0.463004			−0.231502	−	0.972834i	$-0.574364\pi$
$491$	−10.2595			−0.463004			−0.231502	+	0.972834i	$0.574364\pi$
$492$		0			0
$493$	0.999829			0.0450300
$494$		0			0
$495$	1.63603	+	2.83369i	0.0735341	+	0.127365i
$496$		0			0
$497$	3.96567	−	6.86874i	0.177884	−	0.308105i
$498$		0			0
$499$	14.4225	−	24.9805i	0.645639	−	1.11828i	−0.338515	−	0.940961i	$-0.609925\pi$
$499$	14.4225	−	24.9805i	0.645639	−	1.11828i	0.984154	−	0.177318i	$-0.0567420\pi$
$500$		0			0
$501$	−0.887831	−	1.53777i	−0.0396654	−	0.0687025i
$502$		0			0
$503$	7.00448	+	12.1321i	0.312314	+	0.540944i	0.978863	−	0.204517i	$-0.0655624\pi$
$503$	7.00448	+	12.1321i	0.312314	+	0.540944i	−0.666549	+	0.745462i	$0.732229\pi$
$504$		0			0
$505$	−2.71660	−	4.70530i	−0.120887	−	0.209383i
$506$		0			0
$507$	5.26876	+	9.12577i	0.233994	+	0.405290i
$508$		0			0
$509$	−21.8224			−0.967261			−0.483631	−	0.875272i	$-0.660682\pi$
$509$	−21.8224			−0.967261			−0.483631	+	0.875272i	$0.660682\pi$
$510$		0			0
$511$	−7.03694			−0.311296
$512$		0			0
$513$	4.31259	−	7.46962i	0.190405	−	0.329792i
$514$		0			0
$515$	5.38301	+	9.32365i	0.237204	+	0.410849i
$516$		0			0
$517$	−16.3687	+	28.3515i	−0.719896	+	1.24690i
$518$		0			0
$519$	7.93185	−	13.7384i	0.348169	−	0.603047i
$520$		0			0
$521$	−1.24896			−0.0547178			−0.0273589	−	0.999626i	$-0.508710\pi$
$521$	−1.24896			−0.0547178			−0.0273589	+	0.999626i	$0.508710\pi$
$522$		0			0
$523$	−16.2479	+	28.1422i	−0.710472	+	1.23057i	0.254209	+	0.967149i	$0.418185\pi$
$523$	−16.2479	+	28.1422i	−0.710472	+	1.23057i	−0.964680	+	0.263424i	$0.915148\pi$
$524$		0			0
$525$	0.440752	+	0.763405i	0.0192360	+	0.0333177i
$526$		0			0
$527$	12.3531			0.538108
$528$		0			0
$529$	4.11196	+	7.12213i	0.178781	+	0.309658i
$530$		0			0
$531$	2.31882			0.100628
$532$		0			0
$533$	9.02910			0.391094
$534$		0			0
$535$	−11.2495			−0.486360
$536$		0			0
$537$	4.62390			0.199536
$538$		0			0
$539$	20.3619			0.877049
$540$		0			0
$541$	7.32526			0.314938			0.157469	−	0.987524i	$-0.449667\pi$
$541$	7.32526			0.314938			0.157469	+	0.987524i	$0.449667\pi$
$542$		0			0
$543$	−2.11768	−	3.66794i	−0.0908786	−	0.157406i
$544$		0			0
$545$	−5.99050			−0.256605
$546$		0			0
$547$	−4.70224	−	8.14451i	−0.201053	−	0.348234i	0.747815	−	0.663907i	$-0.231103\pi$
$547$	−4.70224	−	8.14451i	−0.201053	−	0.348234i	−0.948868	+	0.315673i	$0.897770\pi$
$548$		0			0
$549$	−2.41476	+	4.18248i	−0.103059	+	0.178504i
$550$		0			0
$551$	−1.17547			−0.0500769
$552$		0			0
$553$	0.626381	−	1.08492i	0.0266364	−	0.0461357i
$554$		0			0
$555$	−1.66657	+	2.88658i	−0.0707420	+	0.122529i
$556$		0			0
$557$	−6.24286	−	10.8130i	−0.264519	−	0.458160i	0.702919	−	0.711270i	$-0.251880\pi$
$557$	−6.24286	−	10.8130i	−0.264519	−	0.458160i	−0.967437	+	0.253110i	$0.918546\pi$
$558$		0			0
$559$	8.76461	−	15.1808i	0.370704	−	0.642078i
$560$		0			0
$561$	−24.0050			−1.01349
$562$		0			0
$563$	14.7224			0.620475			0.310238	−	0.950659i	$-0.399591\pi$
$563$	14.7224			0.620475			0.310238	+	0.950659i	$0.399591\pi$
$564$		0			0
$565$	3.59371	+	6.22449i	0.151188	+	0.261866i
$566$		0			0
$567$	0.440752	+	0.763405i	0.0185098	+	0.0320600i
$568$		0			0
$569$	−8.39643	−	14.5430i	−0.351997	−	0.609676i	0.634602	−	0.772839i	$-0.281164\pi$
$569$	−8.39643	−	14.5430i	−0.351997	−	0.609676i	−0.986599	+	0.163162i	$0.947831\pi$
$570$		0			0
$571$	1.71848	+	2.97650i	0.0719163	+	0.124563i	0.899741	−	0.436424i	$-0.143755\pi$
$571$	1.71848	+	2.97650i	0.0719163	+	0.124563i	−0.827825	+	0.560987i	$0.810422\pi$
$572$		0			0
$573$	−6.02525	+	10.4360i	−0.251708	+	0.435972i
$574$		0			0
$575$	−1.92198	+	3.32897i	−0.0801522	+	0.138828i
$576$		0			0
$577$	−8.51633	−	14.7507i	−0.354540	−	0.614080i	0.632500	−	0.774561i	$-0.282029\pi$
$577$	−8.51633	−	14.7507i	−0.354540	−	0.614080i	−0.987039	+	0.160480i	$0.948696\pi$
$578$		0			0
$579$	2.67601			0.111211
$580$		0			0
$581$	−1.01391			−0.0420642
$582$		0			0
$583$	2.19337	+	3.79903i	0.0908401	+	0.157340i
$584$		0			0
$585$	0.784613	−	1.35899i	0.0324398	−	0.0561873i
$586$		0			0
$587$	−12.2720	+	21.2558i	−0.506521	+	0.877320i	0.493450	+	0.869774i	$0.335735\pi$
$587$	−12.2720	+	21.2558i	−0.506521	+	0.877320i	−0.999972	+	0.00754647i	$0.997598\pi$
$588$		0			0
$589$	−14.5232			−0.598418
$590$		0			0
$591$	−4.85598	−	8.41081i	−0.199748	−	0.345974i
$592$		0			0
$593$	22.3077	−	38.6381i	0.916069	−	1.58668i	0.110739	−	0.993849i	$-0.464678\pi$
$593$	22.3077	−	38.6381i	0.916069	−	1.58668i	0.805329	−	0.592828i	$-0.201989\pi$
$594$		0			0
$595$	−6.46702			−0.265122
$596$		0			0
$597$	−6.40674	+	11.0968i	−0.262210	+	0.454162i
$598$		0			0
$599$	−14.4768	−	25.0746i	−0.591506	−	1.02452i	−0.994030	−	0.109109i	$-0.965200\pi$
$599$	−14.4768	−	25.0746i	−0.591506	−	1.02452i	0.402524	−	0.915410i	$-0.368133\pi$
$600$		0			0
$601$	−13.8663	+	24.0172i	−0.565620	+	0.979683i	0.431372	+	0.902174i	$0.358030\pi$
$601$	−13.8663	+	24.0172i	−0.565620	+	0.979683i	−0.996992	+	0.0775085i	$0.975304\pi$
$602$		0			0
$603$	−7.65965	+	2.88612i	−0.311925	+	0.117532i
$604$		0			0
$605$	0.146803	−	0.254270i	0.00596839	−	0.0103376i
$606$		0			0
$607$	−14.7935	−	25.6231i	−0.600449	−	1.04001i	−0.992753	−	0.120173i	$-0.961655\pi$
$607$	−14.7935	−	25.6231i	−0.600449	−	1.04001i	0.392304	−	0.919836i	$-0.371678\pi$
$608$		0			0
$609$	0.0600675	−	0.104040i	0.00243406	−	0.00421591i
$610$		0			0
$611$	15.7003			0.635167
$612$		0			0
$613$	−0.224234	+	0.388384i	−0.00905672	+	0.0156867i	−0.870518	−	0.492136i	$-0.836216\pi$
$613$	−0.224234	+	0.388384i	−0.00905672	+	0.0156867i	0.861462	+	0.507823i	$0.169550\pi$
$614$		0			0
$615$	2.87693	+	4.98299i	0.116009	+	0.200933i
$616$		0			0
$617$	−2.38516			−0.0960229			−0.0480114	−	0.998847i	$-0.515288\pi$
$617$	−2.38516			−0.0960229			−0.0480114	+	0.998847i	$0.515288\pi$
$618$		0			0
$619$	−12.1591	+	21.0602i	−0.488716	+	0.846481i	−0.999916	−	0.0129812i	$-0.995868\pi$
$619$	−12.1591	+	21.0602i	−0.488716	+	0.846481i	0.511200	+	0.859462i	$0.329201\pi$
$620$		0			0
$621$	−1.92198	+	3.32897i	−0.0771265	+	0.133587i
$622$		0			0
$623$	3.35078	+	5.80371i	0.134246	+	0.232521i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	28.2221			1.12708
$628$		0			0
$629$	−12.2265	−	21.1770i	−0.487504	−	0.844382i
$630$		0			0
$631$	−12.7575	+	22.0966i	−0.507868	+	0.879653i	0.492091	+	0.870544i	$0.336233\pi$
$631$	−12.7575	+	22.0966i	−0.507868	+	0.879653i	−0.999959	+	0.00910892i	$0.997101\pi$
$632$		0			0
$633$	1.16533	−	2.01841i	0.0463177	−	0.0802247i
$634$		0			0
$635$	7.80687	+	13.5219i	0.309806	+	0.536600i
$636$		0			0
$637$	−4.88261	−	8.45693i	−0.193456	−	0.335076i
$638$		0			0
$639$	−4.49875	−	7.79207i	−0.177968	−	0.308249i
$640$		0			0
$641$	−7.77495	−	13.4666i	−0.307092	−	0.531899i	0.670633	−	0.741789i	$-0.266023\pi$
$641$	−7.77495	−	13.4666i	−0.307092	−	0.531899i	−0.977725	+	0.209890i	$0.932689\pi$
$642$		0			0
$643$	17.5109			0.690561			0.345280	−	0.938500i	$-0.387784\pi$
$643$	17.5109			0.690561			0.345280	+	0.938500i	$0.387784\pi$
$644$		0			0
$645$	11.1706			0.439843
$646$		0			0
$647$	−1.10864	+	1.92021i	−0.0435850	+	0.0754914i	−0.886995	−	0.461779i	$-0.847211\pi$
$647$	−1.10864	+	1.92021i	−0.0435850	+	0.0754914i	0.843410	+	0.537271i	$0.180545\pi$
$648$		0			0
$649$	3.79366	+	6.57080i	0.148914	+	0.257927i
$650$		0			0
$651$	0.742145	−	1.28543i	0.0290869	−	0.0503801i
$652$		0			0
$653$	4.77060	−	8.26292i	0.186688	−	0.323353i	−0.757456	−	0.652886i	$-0.773558\pi$
$653$	4.77060	−	8.26292i	0.186688	−	0.323353i	0.944144	+	0.329533i	$0.106891\pi$
$654$		0			0
$655$	8.44101			0.329818
$656$		0			0
$657$	−3.99144	+	6.91338i	−0.155721	+	0.269717i
$658$		0			0
$659$	−5.90138	−	10.2215i	−0.229885	−	0.398172i	0.727889	−	0.685695i	$-0.240502\pi$
$659$	−5.90138	−	10.2215i	−0.229885	−	0.398172i	−0.957774	+	0.287523i	$0.907168\pi$
$660$		0			0
$661$	−1.98432			−0.0771812			−0.0385906	−	0.999255i	$-0.512287\pi$
$661$	−1.98432			−0.0771812			−0.0385906	+	0.999255i	$0.512287\pi$
$662$		0			0
$663$	5.75620	+	9.97002i	0.223552	+	0.387204i
$664$		0			0
$665$	7.60312			0.294836
$666$		0			0
$667$	0.523872			0.0202844
$668$		0			0
$669$	15.2802			0.590768
$670$		0			0
$671$	−15.8025			−0.610047
$672$		0			0
$673$	6.28438			0.242245			0.121123	−	0.992638i	$-0.461351\pi$
$673$	6.28438			0.242245			0.121123	+	0.992638i	$0.461351\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−4.77394	−	8.26871i	−0.183477	−	0.317792i	0.759585	−	0.650408i	$-0.225402\pi$
$677$	−4.77394	−	8.26871i	−0.183477	−	0.317792i	−0.943062	+	0.332616i	$0.892069\pi$
$678$		0			0
$679$	3.43908			0.131980
$680$		0			0
$681$	−10.7460	−	18.6127i	−0.411789	−	0.713240i
$682$		0			0
$683$	−5.68411	+	9.84517i	−0.217496	+	0.376715i	−0.954042	−	0.299673i	$-0.903122\pi$
$683$	−5.68411	+	9.84517i	−0.217496	+	0.376715i	0.736546	+	0.676388i	$0.236456\pi$
$684$		0			0
$685$	21.4284			0.818736
$686$		0			0
$687$	−0.0377926	+	0.0654588i	−0.00144188	+	0.00249741i
$688$		0			0
$689$	1.05190	−	1.82195i	0.0400743	−	0.0694108i
$690$		0			0
$691$	−20.0593	−	34.7437i	−0.763091	−	1.32171i	−0.941250	−	0.337710i	$-0.890348\pi$
$691$	−20.0593	−	34.7437i	−0.763091	−	1.32171i	0.178160	−	0.984002i	$-0.442986\pi$
$692$		0			0
$693$	−1.44217	+	2.49791i	−0.0547834	+	0.0948877i
$694$		0			0
$695$	−15.5895			−0.591342
$696$		0			0
$697$	−42.2123			−1.59891
$698$		0			0
$699$	8.59682	+	14.8901i	0.325161	+	0.563196i
$700$		0			0
$701$	3.67205	+	6.36017i	0.138691	+	0.240220i	0.927001	−	0.375058i	$-0.122377\pi$
$701$	3.67205	+	6.36017i	0.138691	+	0.240220i	−0.788310	+	0.615278i	$0.789044\pi$
$702$		0			0
$703$	14.3745	+	24.8973i	0.542143	+	0.939019i
$704$		0			0
$705$	5.00257	+	8.66471i	0.188408	+	0.326332i
$706$		0			0
$707$	2.39470	−	4.14774i	0.0900619	−	0.155992i
$708$		0			0
$709$	9.69767	−	16.7969i	0.364204	−	0.630819i	−0.624444	−	0.781069i	$-0.714675\pi$
$709$	9.69767	−	16.7969i	0.364204	−	0.630819i	0.988648	+	0.150250i	$0.0480079\pi$
$710$		0			0
$711$	−0.710582	−	1.23076i	−0.0266489	−	0.0461573i
$712$		0			0
$713$	6.47253			0.242398
$714$		0			0
$715$	5.13461			0.192023
$716$		0			0
$717$	13.4948	+	23.3737i	0.503974	+	0.872908i
$718$		0			0
$719$	19.1547	−	33.1769i	0.714350	−	1.23729i	−0.248859	−	0.968540i	$-0.580056\pi$
$719$	19.1547	−	33.1769i	0.714350	−	1.23729i	0.963210	−	0.268751i	$-0.0866110\pi$
$720$		0			0
$721$	−4.74514	+	8.21883i	−0.176718	+	0.306085i
$722$		0			0
$723$	7.84451			0.291740
$724$		0			0
$725$	−0.0681421	−	0.118026i	−0.00253073	−	0.00438336i
$726$		0			0
$727$	−3.63712	+	6.29968i	−0.134893	+	0.233642i	−0.925557	−	0.378609i	$-0.876403\pi$
$727$	−3.63712	+	6.29968i	−0.134893	+	0.233642i	0.790663	+	0.612251i	$0.209736\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−40.9758	+	70.9722i	−1.51554	+	2.62500i
$732$		0			0
$733$	−10.2322	−	17.7227i	−0.377935	−	0.654603i	0.612826	−	0.790218i	$-0.290032\pi$
$733$	−10.2322	−	17.7227i	−0.377935	−	0.654603i	−0.990762	+	0.135615i	$0.956699\pi$
$734$		0			0
$735$	3.11148	−	5.38923i	0.114769	−	0.198785i
$736$		0			0
$737$	−20.7098	−	16.9833i	−0.762856	−	0.625588i
$738$		0			0
$739$	23.6808	−	41.0164i	0.871114	−	1.50881i	0.0102682	−	0.999947i	$-0.496731\pi$
$739$	23.6808	−	41.0164i	0.871114	−	1.50881i	0.860846	−	0.508866i	$-0.169935\pi$
$740$		0			0
$741$	−6.76742	−	11.7215i	−0.248607	−	0.430601i
$742$		0			0
$743$	−5.69321	+	9.86093i	−0.208864	+	0.361763i	−0.951357	−	0.308091i	$-0.900310\pi$
$743$	−5.69321	+	9.86093i	−0.208864	+	0.361763i	0.742493	+	0.669854i	$0.233643\pi$
$744$		0			0
$745$	−6.73543			−0.246767
$746$		0			0
$747$	−0.575104	+	0.996110i	−0.0210420	+	0.0364458i
$748$		0			0
$749$	−4.95826	−	8.58796i	−0.181171	−	0.313797i
$750$		0			0
$751$	−51.8224			−1.89103			−0.945513	−	0.325583i	$-0.894439\pi$
$751$	−51.8224			−1.89103			−0.945513	+	0.325583i	$0.894439\pi$
$752$		0			0
$753$	1.89190	−	3.27687i	0.0689447	−	0.119416i
$754$		0			0
$755$	−5.19852	+	9.00410i	−0.189193	+	0.327693i
$756$		0			0
$757$	−21.0364	−	36.4362i	−0.764582	−	1.32429i	−0.940467	−	0.339884i	$-0.889612\pi$
$757$	−21.0364	−	36.4362i	−0.764582	−	1.32429i	0.175886	−	0.984411i	$-0.443721\pi$
$758$		0			0
$759$	−12.5777			−0.456542
$760$		0			0
$761$	32.0795			1.16288			0.581440	−	0.813589i	$-0.302489\pi$
$761$	32.0795			1.16288			0.581440	+	0.813589i	$0.302489\pi$
$762$		0			0
$763$	−2.64032	−	4.57318i	−0.0955862	−	0.165560i
$764$		0			0
$765$	−3.66818	+	6.35347i	−0.132623	+	0.229710i
$766$		0			0
$767$	1.81937	−	3.15125i	0.0656938	−	0.113785i
$768$		0			0
$769$	−0.103555	−	0.179363i	−0.00373430	−	0.00646801i	0.864152	−	0.503231i	$-0.167855\pi$
$769$	−0.103555	−	0.179363i	−0.00373430	−	0.00646801i	−0.867887	+	0.496763i	$0.834522\pi$
$770$		0			0
$771$	−4.23582	−	7.33665i	−0.152549	−	0.264223i
$772$		0			0
$773$	16.8144	+	29.1234i	0.604772	+	1.04750i	0.992087	+	0.125549i	$0.0400693\pi$
$773$	16.8144	+	29.1234i	0.604772	+	1.04750i	−0.387315	+	0.921947i	$0.626597\pi$
$774$		0			0
$775$	−0.841907	−	1.45823i	−0.0302422	−	0.0523810i
$776$		0			0
$777$	−2.93818			−0.105406
$778$		0			0
$779$	49.6280			1.77811
$780$		0			0
$781$	14.7202	−	25.4961i	0.526730	−	0.912323i
$782$		0			0
$783$	−0.0681421	−	0.118026i	−0.00243520	−	0.00421789i
$784$		0			0
$785$	9.91396	−	17.1715i	0.353844	−	0.612876i
$786$		0			0
$787$	3.41364	−	5.91259i	0.121683	−	0.210761i	−0.798748	−	0.601665i	$-0.794504\pi$
$787$	3.41364	−	5.91259i	0.121683	−	0.210761i	0.920431	+	0.390904i	$0.127838\pi$
$788$		0			0
$789$	13.4466			0.478710
$790$		0			0
$791$	−3.16787	+	5.48691i	−0.112636	+	0.195092i
$792$		0			0
$793$	3.78930	+	6.56326i	0.134562	+	0.233068i
$794$		0			0
$795$	1.34067			0.0475485
$796$		0			0
$797$	−18.5169	−	32.0722i	−0.655902	−	1.13606i	−0.981667	−	0.190605i	$-0.938955\pi$
$797$	−18.5169	−	32.0722i	−0.655902	−	1.13606i	0.325765	−	0.945451i	$-0.394378\pi$
$798$		0			0
$799$	−73.4012			−2.59675
$800$		0			0
$801$	7.60241			0.268618
$802$		0			0
$803$	−26.1205			−0.921772
$804$		0			0
$805$	−3.38847			−0.119428
$806$		0			0
$807$	−24.6192			−0.866637
$808$		0			0
$809$	−16.7381			−0.588480			−0.294240	−	0.955732i	$-0.595066\pi$
$809$	−16.7381			−0.588480			−0.294240	+	0.955732i	$0.595066\pi$
$810$		0			0
$811$	−24.1534	−	41.8349i	−0.848140	−	1.46902i	−0.882866	−	0.469624i	$-0.844389\pi$
$811$	−24.1534	−	41.8349i	−0.848140	−	1.46902i	0.0347265	−	0.999397i	$-0.488944\pi$
$812$		0			0
$813$	12.3115			0.431781
$814$		0			0
$815$	−6.33987	−	10.9810i	−0.222076	−	0.384647i
$816$		0			0
$817$	48.1743	−	83.4403i	1.68540	−	2.91921i
$818$		0			0
$819$	1.38328			0.0483357
$820$		0			0
$821$	6.03327	−	10.4499i	0.210562	−	0.364705i	−0.741328	−	0.671143i	$-0.765804\pi$
$821$	6.03327	−	10.4499i	0.210562	−	0.364705i	0.951891	+	0.306438i	$0.0991371\pi$
$822$		0			0
$823$	−21.4076	+	37.0791i	−0.746223	+	1.29250i	0.203398	+	0.979096i	$0.434802\pi$
$823$	−21.4076	+	37.0791i	−0.746223	+	1.29250i	−0.949621	+	0.313401i	$0.898532\pi$
$824$		0			0
$825$	1.63603	+	2.83369i	0.0569593	+	0.0986564i
$826$		0			0
$827$	−11.8692	+	20.5580i	−0.412731	+	0.714871i	−0.995187	−	0.0979907i	$-0.968758\pi$
$827$	−11.8692	+	20.5580i	−0.412731	+	0.714871i	0.582456	+	0.812862i	$0.302092\pi$
$828$		0			0
$829$	−51.2000			−1.77825			−0.889125	−	0.457665i	$-0.848686\pi$
$829$	−51.2000			−1.77825			−0.889125	+	0.457665i	$0.848686\pi$
$830$		0			0
$831$	4.21969			0.146379
$832$		0			0
$833$	22.8269	+	39.5373i	0.790904	+	1.36989i
$834$		0			0
$835$	−0.887831	−	1.53777i	−0.0307247	−	0.0532167i
$836$		0			0
$837$	−0.841907	−	1.45823i	−0.0291006	−	0.0504037i
$838$		0			0
$839$	−26.1568	−	45.3049i	−0.903033	−	1.56410i	−0.823536	−	0.567263i	$-0.808002\pi$
$839$	−26.1568	−	45.3049i	−0.903033	−	1.56410i	−0.0794962	−	0.996835i	$-0.525331\pi$
$840$		0			0
$841$	14.4907	−	25.0987i	0.499680	−	0.865471i
$842$		0			0
$843$	4.32751	−	7.49546i	0.149047	−	0.258157i
$844$		0			0
$845$	5.26876	+	9.12577i	0.181251	+	0.313936i
$846$		0			0
$847$	0.258815			0.00889298
$848$		0			0
$849$	−4.72243			−0.162073
$850$		0			0
$851$	−6.40624	−	11.0959i	−0.219603	−	0.380364i
$852$		0			0
$853$	17.2473	−	29.8731i	0.590535	−	1.02284i	−0.403625	−	0.914924i	$-0.632250\pi$
$853$	17.2473	−	29.8731i	0.590535	−	1.02284i	0.994160	−	0.107913i	$-0.0344166\pi$
$854$		0			0
$855$	4.31259	−	7.46962i	0.147487	−	0.255456i
$856$		0			0
$857$	22.3017			0.761813			0.380907	−	0.924614i	$-0.375612\pi$
$857$	22.3017			0.761813			0.380907	+	0.924614i	$0.375612\pi$
$858$		0			0
$859$	18.0945	+	31.3406i	0.617376	+	1.06933i	0.989963	+	0.141329i	$0.0451376\pi$
$859$	18.0945	+	31.3406i	0.617376	+	1.06933i	−0.372587	+	0.927997i	$0.621529\pi$
$860$		0			0
$861$	−2.53602	+	4.39252i	−0.0864274	+	0.149697i
$862$		0			0
$863$	−53.6982			−1.82791			−0.913955	−	0.405816i	$-0.866987\pi$
$863$	−53.6982			−1.82791			−0.913955	+	0.405816i	$0.866987\pi$
$864$		0			0
$865$	7.93185	−	13.7384i	0.269691	−	0.467118i
$866$		0			0
$867$	−18.4110	−	31.8888i	−0.625271	−	1.08300i
$868$		0			0
$869$	2.32507	−	4.02714i	0.0788726	−	0.136611i
$870$		0			0
$871$	−2.08765	+	12.6739i	−0.0707374	+	0.429438i
$872$		0			0
$873$	1.95069	−	3.37870i	0.0660209	−	0.114352i
$874$		0			0
$875$	0.440752	+	0.763405i	0.0149001	+	0.0258078i
$876$		0			0
$877$	6.23826	−	10.8050i	0.210651	−	0.364858i	−0.741267	−	0.671210i	$-0.765775\pi$
$877$	6.23826	−	10.8050i	0.210651	−	0.364858i	0.951918	+	0.306352i	$0.0991083\pi$
$878$		0			0
$879$	−6.78024			−0.228692
$880$		0			0
$881$	9.21734	−	15.9649i	0.310540	−	0.537871i	−0.667939	−	0.744216i	$-0.732823\pi$
$881$	9.21734	−	15.9649i	0.310540	−	0.537871i	0.978479	+	0.206344i	$0.0661567\pi$
$882$		0			0
$883$	10.9878	+	19.0314i	0.369767	+	0.640456i	0.989529	−	0.144334i	$-0.0461040\pi$
$883$	10.9878	+	19.0314i	0.369767	+	0.640456i	−0.619762	+	0.784790i	$0.712771\pi$
$884$		0			0
$885$	2.31882			0.0779462
$886$		0			0
$887$	−0.288240	+	0.499246i	−0.00967814	+	0.0167630i	−0.870824	−	0.491595i	$-0.836414\pi$
$887$	−0.288240	+	0.499246i	−0.00967814	+	0.0167630i	0.861146	+	0.508358i	$0.169747\pi$
$888$		0			0
$889$	−6.88179	+	11.9196i	−0.230808	+	0.399771i
$890$		0			0
$891$	1.63603	+	2.83369i	0.0548091	+	0.0949322i
$892$		0			0
$893$	86.2961			2.88779
$894$		0			0
$895$	4.62390			0.154560
$896$		0			0
$897$	3.01603	+	5.22391i	0.100702	+	0.174421i
$898$		0			0
$899$	−0.114739	+	0.198733i	−0.00382675	+	0.00662813i
$900$		0			0
$901$	−4.91779	+	8.51787i	−0.163836	+	0.283771i
$902$		0			0
$903$	4.92347	+	8.52770i	0.163843	+	0.283784i
$904$		0			0
$905$	−2.11768	−	3.66794i	−0.0703942	−	0.121926i
$906$		0			0
$907$	12.4717	+	21.6016i	0.414115	+	0.717268i	0.995335	−	0.0964782i	$-0.0307578\pi$
$907$	12.4717	+	21.6016i	0.414115	+	0.717268i	−0.581220	+	0.813746i	$0.697424\pi$
$908$		0			0
$909$	−2.71660	−	4.70530i	−0.0901041	−	0.156065i
$910$		0			0
$911$	−10.3144			−0.341730			−0.170865	−	0.985294i	$-0.554656\pi$
$911$	−10.3144			−0.341730			−0.170865	+	0.985294i	$0.554656\pi$
$912$		0			0
$913$	−3.76355			−0.124555
$914$		0			0
$915$	−2.41476	+	4.18248i	−0.0798294	+	0.138269i
$916$		0			0
$917$	3.72039	+	6.44391i	0.122858	+	0.212797i
$918$		0			0
$919$	−15.1643	+	26.2654i	−0.500225	+	0.866415i	0.499775	+	0.866155i	$0.333416\pi$
$919$	−15.1643	+	26.2654i	−0.500225	+	0.866415i	−1.00000		0.000260000i	$0.999917\pi$
$920$		0			0
$921$	−0.390812	+	0.676906i	−0.0128777	+	0.0223048i
$922$		0			0
$923$	−14.1191			−0.464736
$924$		0			0
$925$	−1.66657	+	2.88658i	−0.0547965	+	0.0949103i
$926$		0			0
$927$	5.38301	+	9.32365i	0.176801	+	0.306229i
$928$		0			0
$929$	−45.8504			−1.50430			−0.752151	−	0.658991i	$-0.770983\pi$
$929$	−45.8504			−1.50430			−0.752151	+	0.658991i	$0.770983\pi$
$930$		0			0
$931$	−26.8370	−	46.4831i	−0.879548	−	1.52342i
$932$		0			0
$933$	20.9630			0.686298
$934$		0			0
$935$	−24.0050			−0.785047
$936$		0			0
$937$	−38.7268			−1.26515			−0.632574	−	0.774500i	$-0.718002\pi$
$937$	−38.7268			−1.26515			−0.632574	+	0.774500i	$0.718002\pi$
$938$		0			0
$939$	−20.3178			−0.663047
$940$		0			0
$941$	−30.9924			−1.01032			−0.505161	−	0.863025i	$-0.668567\pi$
$941$	−30.9924			−1.01032			−0.505161	+	0.863025i	$0.668567\pi$
$942$		0			0
$943$	−22.1176			−0.720249
$944$		0			0
$945$	0.440752	+	0.763405i	0.0143377	+	0.0248336i
$946$		0			0
$947$	14.7720			0.480027			0.240013	−	0.970770i	$-0.422848\pi$
$947$	14.7720			0.480027			0.240013	+	0.970770i	$0.422848\pi$
$948$		0			0
$949$	6.26347	+	10.8487i	0.203321	+	0.352162i
$950$		0			0
$951$	−6.42026	+	11.1202i	−0.208191	+	0.360598i
$952$		0			0
$953$	20.3891			0.660468			0.330234	−	0.943899i	$-0.392872\pi$
$953$	20.3891			0.660468			0.330234	+	0.943899i	$0.392872\pi$
$954$		0			0
$955$	−6.02525	+	10.4360i	−0.194972	+	0.337702i
$956$		0			0
$957$	0.222965	−	0.386187i	0.00720744	−	0.0124837i
$958$		0			0
$959$	9.44459	+	16.3585i	0.304982	+	0.528244i
$960$		0			0
$961$	14.0824	−	24.3914i	0.454270	−	0.786819i
$962$		0			0
$963$	−11.2495			−0.362512
$964$		0			0
$965$	2.67601			0.0861438
$966$		0			0
$967$	1.69179	+	2.93027i	0.0544043	+	0.0942311i	0.891945	−	0.452144i	$-0.149341\pi$
$967$	1.69179	+	2.93027i	0.0544043	+	0.0942311i	−0.837541	+	0.546375i	$0.816007\pi$
$968$		0			0
$969$	31.6386	+	54.7997i	1.01638	+	1.76042i
$970$		0			0
$971$	25.7883	+	44.6667i	0.827587	+	1.43342i	0.899926	+	0.436042i	$0.143620\pi$
$971$	25.7883	+	44.6667i	0.827587	+	1.43342i	−0.0723395	+	0.997380i	$0.523047\pi$
$972$		0			0
$973$	−6.87108	−	11.9011i	−0.220277	−	0.381531i
$974$		0			0
$975$	0.784613	−	1.35899i	0.0251277	−	0.0435225i
$976$		0			0
$977$	24.2176	−	41.9461i	0.774789	−	1.34197i	−0.160125	−	0.987097i	$-0.551190\pi$
$977$	24.2176	−	41.9461i	0.774789	−	1.34197i	0.934913	−	0.354876i	$-0.115477\pi$
$978$		0			0
$979$	12.4378	+	21.5429i	0.397513	+	0.688513i
$980$		0			0
$981$	−5.99050			−0.191262
$982$		0			0
$983$	19.4703			0.621007			0.310503	−	0.950572i	$-0.399502\pi$
$983$	19.4703			0.621007			0.310503	+	0.950572i	$0.399502\pi$
$984$		0			0
$985$	−4.85598	−	8.41081i	−0.154724	−	0.267991i
$986$		0			0
$987$	−4.40978	+	7.63797i	−0.140365	+	0.243119i
$988$		0			0
$989$	−21.4697	+	37.1867i	−0.682698	+	1.18247i
$990$		0			0
$991$	−38.4226			−1.22053			−0.610267	−	0.792196i	$-0.708938\pi$
$991$	−38.4226			−1.22053			−0.610267	+	0.792196i	$0.708938\pi$
$992$		0			0
$993$	−3.34522	−	5.79409i	−0.106157	−	0.183870i
$994$		0			0
$995$	−6.40674	+	11.0968i	−0.203107	+	0.351792i
$996$		0			0
$997$	10.0214			0.317380			0.158690	−	0.987328i	$-0.449273\pi$
$997$	10.0214			0.317380			0.158690	+	0.987328i	$0.449273\pi$
$998$		0			0
$999$	−1.66657	+	2.88658i	−0.0527280	+	0.0913275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.3781.8	yes	24
67.37	even	3	inner	4020.2.q.m.841.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.8	✓	24	67.37	even	3	inner
4020.2.q.m.3781.8	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.440752 + 0.763405i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.440752 + 0.763405i) q^{7} +1.00000 q^{9} +(1.63603 + 2.83369i) q^{11} +(0.784613 - 1.35899i) q^{13} +1.00000 q^{15} +(-3.66818 + 6.35347i) q^{17} +(4.31259 - 7.46962i) q^{19} +(0.440752 + 0.763405i) q^{21} +(-1.92198 + 3.32897i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-0.0681421 - 0.118026i) q^{29} +(-0.841907 - 1.45823i) q^{31} +(1.63603 + 2.83369i) q^{33} +(0.440752 + 0.763405i) q^{35} +(-1.66657 + 2.88658i) q^{37} +(0.784613 - 1.35899i) q^{39} +(2.87693 + 4.98299i) q^{41} +11.1706 q^{43} +1.00000 q^{45} +(5.00257 + 8.66471i) q^{47} +(3.11148 - 5.38923i) q^{49} +(-3.66818 + 6.35347i) q^{51} +1.34067 q^{53} +(1.63603 + 2.83369i) q^{55} +(4.31259 - 7.46962i) q^{57} +2.31882 q^{59} +(-2.41476 + 4.18248i) q^{61} +(0.440752 + 0.763405i) q^{63} +(0.784613 - 1.35899i) q^{65} +(-7.65965 + 2.88612i) q^{67} +(-1.92198 + 3.32897i) q^{69} +(-4.49875 - 7.79207i) q^{71} +(-3.99144 + 6.91338i) q^{73} +1.00000 q^{75} +(-1.44217 + 2.49791i) q^{77} +(-0.710582 - 1.23076i) q^{79} +1.00000 q^{81} +(-0.575104 + 0.996110i) q^{83} +(-3.66818 + 6.35347i) q^{85} +(-0.0681421 - 0.118026i) q^{87} +7.60241 q^{89} +1.38328 q^{91} +(-0.841907 - 1.45823i) q^{93} +(4.31259 - 7.46962i) q^{95} +(1.95069 - 3.37870i) q^{97} +(1.63603 + 2.83369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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