LMFDB - Embedded newform 672.2.bk.a.529.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(529,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("672.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bk (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.8
Character	$\chi$	$=$	672.529
Dual form			672.2.bk.a.625.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(3.08781 - 1.78275i) q^{5} +(2.38336 + 1.14873i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(3.08781 - 1.78275i) q^{5} +(2.38336 + 1.14873i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.52552 + 2.03546i) q^{11} -1.44065i q^{13} -3.56550 q^{15} +(-3.49555 + 6.05447i) q^{17} +(0.261102 - 0.150747i) q^{19} +(-1.48968 - 2.18651i) q^{21} +(-1.21250 - 2.10010i) q^{23} +(3.85640 - 6.67947i) q^{25} -1.00000i q^{27} +0.151350i q^{29} +(-2.37719 + 4.11741i) q^{31} +(-2.03546 - 3.52552i) q^{33} +(9.40728 - 0.701863i) q^{35} +(9.82338 - 5.67153i) q^{37} +(-0.720323 + 1.24764i) q^{39} -0.239424 q^{41} -1.32831i q^{43} +(3.08781 + 1.78275i) q^{45} +(-3.17936 - 5.50681i) q^{47} +(4.36082 + 5.47569i) q^{49} +(6.05447 - 3.49555i) q^{51} +(-5.18376 - 2.99285i) q^{53} +14.5149 q^{55} -0.301495 q^{57} +(-9.73654 - 5.62140i) q^{59} +(-3.64539 + 2.10467i) q^{61} +(0.196849 + 2.63842i) q^{63} +(-2.56831 - 4.44845i) q^{65} +(3.79384 + 2.19037i) q^{67} +2.42499i q^{69} +8.46387 q^{71} +(-0.284724 + 0.493156i) q^{73} +(-6.67947 + 3.85640i) q^{75} +(6.06439 + 8.90112i) q^{77} +(-0.746916 - 1.29370i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.0352i q^{83} +24.9268i q^{85} +(0.0756749 - 0.131073i) q^{87} +(1.83434 + 3.17718i) q^{89} +(1.65492 - 3.43358i) q^{91} +(4.11741 - 2.37719i) q^{93} +(0.537490 - 0.930960i) q^{95} +10.4657 q^{97} +4.07092i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	3.08781	−	1.78275i	1.38091	−	0.797270i	0.388645	−	0.921388i	$-0.372943\pi$
$5$	3.08781	−	1.78275i	1.38091	−	0.797270i	0.992268	+	0.124118i	$0.0396100\pi$
$6$		0			0
$7$	2.38336	+	1.14873i	0.900826	+	0.434180i
$7$	2.38336	+	1.14873i	0.900826	+	0.434180i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.52552	+	2.03546i	1.06298	+	0.613714i	0.926256	−	0.376894i	$-0.123008\pi$
$11$	3.52552	+	2.03546i	1.06298	+	0.613714i	0.136728	+	0.990609i	$0.456341\pi$
$12$		0			0
$13$		−	1.44065i		−	0.399564i	−0.979840	−	0.199782i	$-0.935977\pi$
$13$		−	1.44065i		−	0.399564i	0.979840	−	0.199782i	$-0.0640233\pi$
$14$		0			0
$15$	−3.56550			−0.920608
$16$		0			0
$17$	−3.49555	+	6.05447i	−0.847796	+	1.46843i	0.0353755	+	0.999374i	$0.488737\pi$
$17$	−3.49555	+	6.05447i	−0.847796	+	1.46843i	−0.883171	+	0.469051i	$0.844596\pi$
$18$		0			0
$19$	0.261102	−	0.150747i	0.0599010	−	0.0345838i	−0.469750	−	0.882799i	$-0.655656\pi$
$19$	0.261102	−	0.150747i	0.0599010	−	0.0345838i	0.529651	+	0.848215i	$0.322323\pi$
$20$		0			0
$21$	−1.48968	−	2.18651i	−0.325076	−	0.477136i
$22$		0			0
$23$	−1.21250	−	2.10010i	−0.252823	−	0.437902i	0.711479	−	0.702707i	$-0.248026\pi$
$23$	−1.21250	−	2.10010i	−0.252823	−	0.437902i	−0.964302	+	0.264805i	$0.914692\pi$
$24$		0			0
$25$	3.85640	−	6.67947i	0.771279	−	1.33589i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			0.151350i			0.0281050i	0.999901	+	0.0140525i	$0.00447319\pi$
$29$			0.151350i			0.0281050i	−0.999901	+	0.0140525i	$0.995527\pi$
$30$		0			0
$31$	−2.37719	+	4.11741i	−0.426956	+	0.739509i	−0.996601	−	0.0823815i	$-0.973747\pi$
$31$	−2.37719	+	4.11741i	−0.426956	+	0.739509i	0.569645	+	0.821891i	$0.307081\pi$
$32$		0			0
$33$	−2.03546	−	3.52552i	−0.354328	−	0.613714i
$34$		0			0
$35$	9.40728	−	0.701863i	1.59012	−	0.118637i
$36$		0			0
$37$	9.82338	−	5.67153i	1.61495	−	0.932394i	0.626755	−	0.779216i	$-0.284383\pi$
$37$	9.82338	−	5.67153i	1.61495	−	0.932394i	0.988199	−	0.153178i	$-0.0489508\pi$
$38$		0			0
$39$	−0.720323	+	1.24764i	−0.115344	+	0.199782i
$40$		0			0
$41$	−0.239424			−0.0373917			−0.0186959	−	0.999825i	$-0.505951\pi$
$41$	−0.239424			−0.0373917			−0.0186959	+	0.999825i	$0.505951\pi$
$42$		0			0
$43$		−	1.32831i		−	0.202566i	−0.994858	−	0.101283i	$-0.967705\pi$
$43$		−	1.32831i		−	0.202566i	0.994858	−	0.101283i	$-0.0322947\pi$
$44$		0			0
$45$	3.08781	+	1.78275i	0.460304	+	0.265757i
$46$		0			0
$47$	−3.17936	−	5.50681i	−0.463757	−	0.803251i	0.535387	−	0.844607i	$-0.320166\pi$
$47$	−3.17936	−	5.50681i	−0.463757	−	0.803251i	−0.999144	+	0.0413556i	$0.986832\pi$
$48$		0			0
$49$	4.36082	+	5.47569i	0.622975	+	0.782242i
$50$		0			0
$51$	6.05447	−	3.49555i	0.847796	−	0.489475i
$52$		0			0
$53$	−5.18376	−	2.99285i	−0.712045	−	0.411099i	0.0997730	−	0.995010i	$-0.468188\pi$
$53$	−5.18376	−	2.99285i	−0.712045	−	0.411099i	−0.811818	+	0.583911i	$0.801522\pi$
$54$		0			0
$55$	14.5149			1.95718
$56$		0			0
$57$	−0.301495			−0.0399340
$58$		0			0
$59$	−9.73654	−	5.62140i	−1.26759	−	0.731843i	−0.293059	−	0.956094i	$-0.594673\pi$
$59$	−9.73654	−	5.62140i	−1.26759	−	0.731843i	−0.974531	+	0.224251i	$0.928006\pi$
$60$		0			0
$61$	−3.64539	+	2.10467i	−0.466744	+	0.269475i	−0.714876	−	0.699251i	$-0.753517\pi$
$61$	−3.64539	+	2.10467i	−0.466744	+	0.269475i	0.248132	+	0.968726i	$0.420183\pi$
$62$		0			0
$63$	0.196849	+	2.63842i	0.0248006	+	0.332409i
$64$		0			0
$65$	−2.56831	−	4.44845i	−0.318560	−	0.551762i
$66$		0			0
$67$	3.79384	+	2.19037i	0.463491	+	0.267597i	0.713511	−	0.700644i	$-0.247104\pi$
$67$	3.79384	+	2.19037i	0.463491	+	0.267597i	−0.250020	+	0.968241i	$0.580437\pi$
$68$		0			0
$69$			2.42499i			0.291935i
$70$		0			0
$71$	8.46387			1.00448			0.502238	−	0.864729i	$-0.332510\pi$
$71$	8.46387			1.00448			0.502238	+	0.864729i	$0.332510\pi$
$72$		0			0
$73$	−0.284724	+	0.493156i	−0.0333244	+	0.0577196i	−0.882207	−	0.470863i	$-0.843943\pi$
$73$	−0.284724	+	0.493156i	−0.0333244	+	0.0577196i	0.848882	+	0.528582i	$0.177276\pi$
$74$		0			0
$75$	−6.67947	+	3.85640i	−0.771279	+	0.445298i
$76$		0			0
$77$	6.06439	+	8.90112i	0.691101	+	1.01438i
$78$		0			0
$79$	−0.746916	−	1.29370i	−0.0840347	−	0.145552i	0.820945	−	0.571008i	$-0.193447\pi$
$79$	−0.746916	−	1.29370i	−0.0840347	−	0.145552i	−0.904979	+	0.425455i	$0.860114\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	10.0352i		−	1.10151i	−0.834668	−	0.550753i	$-0.814340\pi$
$83$		−	10.0352i		−	1.10151i	0.834668	−	0.550753i	$-0.185660\pi$
$84$		0			0
$85$			24.9268i			2.70369i
$86$		0			0
$87$	0.0756749	−	0.131073i	0.00811320	−	0.0140525i
$88$		0			0
$89$	1.83434	+	3.17718i	0.194440	+	0.336780i	0.946717	−	0.322067i	$-0.104378\pi$
$89$	1.83434	+	3.17718i	0.194440	+	0.336780i	−0.752277	+	0.658847i	$0.771044\pi$
$90$		0			0
$91$	1.65492	−	3.43358i	0.173483	−	0.359937i
$92$		0			0
$93$	4.11741	−	2.37719i	0.426956	−	0.246503i
$94$		0			0
$95$	0.537490	−	0.930960i	0.0551453	−	0.0955145i
$96$		0			0
$97$	10.4657			1.06264			0.531318	−	0.847173i	$-0.321697\pi$
$97$	10.4657			1.06264			0.531318	+	0.847173i	$0.321697\pi$
$98$		0			0
$99$			4.07092i			0.409143i
$100$		0			0
$101$	−11.0277	−	6.36685i	−1.09730	−	0.633526i	−0.161789	−	0.986825i	$-0.551726\pi$
$101$	−11.0277	−	6.36685i	−1.09730	−	0.633526i	−0.935510	+	0.353300i	$0.885060\pi$
$102$		0			0
$103$	−3.00437	−	5.20373i	−0.296030	−	0.512739i	0.679194	−	0.733959i	$-0.262329\pi$
$103$	−3.00437	−	5.20373i	−0.296030	−	0.512739i	−0.975224	+	0.221220i	$0.928996\pi$
$104$		0			0
$105$	−8.49788	−	4.09581i	−0.829308	−	0.399710i
$106$		0			0
$107$	−13.8269	+	7.98297i	−1.33670	+	0.771743i	−0.986316	−	0.164864i	$-0.947281\pi$
$107$	−13.8269	+	7.98297i	−1.33670	+	0.771743i	−0.350382	+	0.936607i	$0.613948\pi$
$108$		0			0
$109$	−12.0127	−	6.93554i	−1.15061	−	0.664304i	−0.201573	−	0.979474i	$-0.564605\pi$
$109$	−12.0127	−	6.93554i	−1.15061	−	0.664304i	−0.949035	+	0.315170i	$0.897939\pi$
$110$		0			0
$111$	−11.3431			−1.07664
$112$		0			0
$113$	−16.4495			−1.54744			−0.773719	−	0.633529i	$-0.781606\pi$
$113$	−16.4495			−1.54744			−0.773719	+	0.633529i	$0.781606\pi$
$114$		0			0
$115$	−7.48792	−	4.32315i	−0.698252	−	0.403136i
$116$		0			0
$117$	1.24764	−	0.720323i	0.115344	−	0.0665939i
$118$		0			0
$119$	−15.2861	+	10.4145i	−1.40128	+	0.954699i
$120$		0			0
$121$	2.78620	+	4.82583i	0.253291	+	0.438712i
$122$		0			0
$123$	0.207347	+	0.119712i	0.0186959	+	0.0107941i
$124$		0			0
$125$		−	9.67245i		−	0.865131i
$126$		0			0
$127$	3.33297			0.295754			0.147877	−	0.989006i	$-0.452756\pi$
$127$	3.33297			0.295754			0.147877	+	0.989006i	$0.452756\pi$
$128$		0			0
$129$	−0.664156	+	1.15035i	−0.0584757	+	0.101283i
$130$		0			0
$131$	−3.54089	+	2.04433i	−0.309369	+	0.178614i	−0.646644	−	0.762792i	$-0.723828\pi$
$131$	−3.54089	+	2.04433i	−0.309369	+	0.178614i	0.337275	+	0.941406i	$0.390495\pi$
$132$		0			0
$133$	0.795470	−	0.0593488i	0.0689760	−	0.00514620i
$134$		0			0
$135$	−1.78275	−	3.08781i	−0.153435	−	0.265757i
$136$		0			0
$137$	−4.14368	+	7.17707i	−0.354019	+	0.613178i	−0.986950	−	0.161030i	$-0.948518\pi$
$137$	−4.14368	+	7.17707i	−0.354019	+	0.613178i	0.632931	+	0.774208i	$0.281852\pi$
$138$		0			0
$139$			18.4180i			1.56219i	0.624411	+	0.781096i	$0.285339\pi$
$139$			18.4180i			1.56219i	−0.624411	+	0.781096i	$0.714661\pi$
$140$		0			0
$141$			6.35872i			0.535501i
$142$		0			0
$143$	2.93238	−	5.07903i	0.245218	−	0.424730i
$144$		0			0
$145$	0.269819	+	0.467340i	0.0224072	+	0.0388105i
$146$		0			0
$147$	−1.03874	−	6.92250i	−0.0856736	−	0.570958i
$148$		0			0
$149$	−4.42715	+	2.55602i	−0.362686	+	0.209397i	−0.670258	−	0.742128i	$-0.733817\pi$
$149$	−4.42715	+	2.55602i	−0.362686	+	0.209397i	0.307572	+	0.951525i	$0.400483\pi$
$150$		0			0
$151$	−2.08563	+	3.61242i	−0.169726	+	0.293974i	−0.938324	−	0.345758i	$-0.887622\pi$
$151$	−2.08563	+	3.61242i	−0.169726	+	0.293974i	0.768597	+	0.639733i	$0.220955\pi$
$152$		0			0
$153$	−6.99110			−0.565197
$154$		0			0
$155$			16.9517i			1.36160i
$156$		0			0
$157$	−7.83645	−	4.52438i	−0.625417	−	0.361084i	0.153558	−	0.988140i	$-0.450927\pi$
$157$	−7.83645	−	4.52438i	−0.625417	−	0.361084i	−0.778975	+	0.627055i	$0.784260\pi$
$158$		0			0
$159$	2.99285	+	5.18376i	0.237348	+	0.411099i
$160$		0			0
$161$	−0.477356	−	6.39814i	−0.0376209	−	0.504244i
$162$		0			0
$163$	11.6491	−	6.72560i	0.912426	−	0.526790i	0.0312153	−	0.999513i	$-0.490062\pi$
$163$	11.6491	−	6.72560i	0.912426	−	0.526790i	0.881211	+	0.472723i	$0.156729\pi$
$164$		0			0
$165$	−12.5702	−	7.25743i	−0.978592	−	0.564990i
$166$		0			0
$167$	−17.2099			−1.33174			−0.665872	−	0.746066i	$-0.731940\pi$
$167$	−17.2099			−1.33174			−0.665872	+	0.746066i	$0.731940\pi$
$168$		0			0
$169$	10.9245			0.840349
$170$		0			0
$171$	0.261102	+	0.150747i	0.0199670	+	0.0115279i
$172$		0			0
$173$	−2.98726	+	1.72470i	−0.227117	+	0.131126i	−0.609242	−	0.792985i	$-0.708526\pi$
$173$	−2.98726	+	1.72470i	−0.227117	+	0.131126i	0.382124	+	0.924111i	$0.375193\pi$
$174$		0			0
$175$	16.8641	−	11.4896i	1.27481	−	0.868534i
$176$		0			0
$177$	5.62140	+	9.73654i	0.422530	+	0.731843i
$178$		0			0
$179$	9.78752	+	5.65083i	0.731554	+	0.422363i	0.818990	−	0.573807i	$-0.194534\pi$
$179$	9.78752	+	5.65083i	0.731554	+	0.422363i	−0.0874365	+	0.996170i	$0.527867\pi$
$180$		0			0
$181$		−	10.0566i		−	0.747502i	−0.927529	−	0.373751i	$-0.878071\pi$
$181$		−	10.0566i		−	0.747502i	0.927529	−	0.373751i	$-0.121929\pi$
$182$		0			0
$183$	4.20933			0.311163
$184$		0			0
$185$	20.2218	−	35.0253i	1.48674	−	2.57511i
$186$		0			0
$187$	−24.6473	+	14.2301i	−1.80239	+	1.04061i
$188$		0			0
$189$	1.14873	−	2.38336i	0.0835581	−	0.173364i
$190$		0			0
$191$	10.7430	+	18.6075i	0.777338	+	1.34639i	0.933471	+	0.358652i	$0.116764\pi$
$191$	10.7430	+	18.6075i	0.777338	+	1.34639i	−0.156134	+	0.987736i	$0.549903\pi$
$192$		0			0
$193$	8.20798	−	14.2166i	0.590823	−	1.02334i	−0.403299	−	0.915068i	$-0.632136\pi$
$193$	8.20798	−	14.2166i	0.590823	−	1.02334i	0.994122	−	0.108267i	$-0.0345302\pi$
$194$		0			0
$195$			5.13663i			0.367841i
$196$		0			0
$197$			15.7045i			1.11890i	0.828864	+	0.559450i	$0.188988\pi$
$197$			15.7045i			1.11890i	−0.828864	+	0.559450i	$0.811012\pi$
$198$		0			0
$199$	3.13717	−	5.43374i	0.222388	−	0.385188i	−0.733144	−	0.680073i	$-0.761948\pi$
$199$	3.13717	−	5.43374i	0.222388	−	0.385188i	0.955533	+	0.294885i	$0.0952814\pi$
$200$		0			0
$201$	−2.19037	−	3.79384i	−0.154497	−	0.267597i
$202$		0			0
$203$	−0.173861	+	0.360721i	−0.0122026	+	0.0253177i
$204$		0			0
$205$	−0.739296	+	0.426833i	−0.0516347	+	0.0298113i
$206$		0			0
$207$	1.21250	−	2.10010i	0.0842743	−	0.145967i
$208$		0			0
$209$	1.22736			0.0848984
$210$		0			0
$211$			9.40458i			0.647438i	0.946153	+	0.323719i	$0.104933\pi$
$211$			9.40458i			0.647438i	−0.946153	+	0.323719i	$0.895067\pi$
$212$		0			0
$213$	−7.32993	−	4.23194i	−0.502238	−	0.289967i
$214$		0			0
$215$	−2.36805	−	4.10158i	−0.161500	−	0.279726i
$216$		0			0
$217$	−10.3955	+	7.08253i	−0.705693	+	0.480793i
$218$		0			0
$219$	0.493156	−	0.284724i	0.0333244	−	0.0192399i
$220$		0			0
$221$	8.72235	+	5.03585i	0.586729	+	0.338748i
$222$		0			0
$223$	−4.34741			−0.291124			−0.145562	−	0.989349i	$-0.546499\pi$
$223$	−4.34741			−0.291124			−0.145562	+	0.989349i	$0.546499\pi$
$224$		0			0
$225$	7.71279			0.514186
$226$		0			0
$227$	−6.30643	−	3.64102i	−0.418572	−	0.241663i	0.275894	−	0.961188i	$-0.411026\pi$
$227$	−6.30643	−	3.64102i	−0.418572	−	0.241663i	−0.694466	+	0.719525i	$0.744359\pi$
$228$		0			0
$229$	−0.885272	+	0.511112i	−0.0585004	+	0.0337752i	−0.528965	−	0.848644i	$-0.677420\pi$
$229$	−0.885272	+	0.511112i	−0.0585004	+	0.0337752i	0.470465	+	0.882419i	$0.344086\pi$
$230$		0			0
$231$	−0.801355	−	10.7408i	−0.0527253	−	0.706692i
$232$		0			0
$233$	11.0331	+	19.1098i	0.722800	+	1.25193i	0.959873	+	0.280434i	$0.0904783\pi$
$233$	11.0331	+	19.1098i	0.722800	+	1.25193i	−0.237074	+	0.971492i	$0.576188\pi$
$234$		0			0
$235$	−19.6345	−	11.3360i	−1.28082	−	0.739480i
$236$		0			0
$237$			1.49383i			0.0970349i
$238$		0			0
$239$	−4.80475			−0.310794			−0.155397	−	0.987852i	$-0.549666\pi$
$239$	−4.80475			−0.310794			−0.155397	+	0.987852i	$0.549666\pi$
$240$		0			0
$241$	−11.8844	+	20.5844i	−0.765542	+	1.32596i	0.174418	+	0.984672i	$0.444196\pi$
$241$	−11.8844	+	20.5844i	−0.765542	+	1.32596i	−0.939960	+	0.341286i	$0.889138\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	23.2272	+	9.13366i	1.48393	+	0.583528i
$246$		0			0
$247$	−0.217174	−	0.376156i	−0.0138184	−	0.0239342i
$248$		0			0
$249$	−5.01760	+	8.69074i	−0.317978	+	0.550753i
$250$		0			0
$251$		−	14.0888i		−	0.889280i	−0.895709	−	0.444640i	$-0.853332\pi$
$251$		−	14.0888i		−	0.889280i	0.895709	−	0.444640i	$-0.146668\pi$
$252$		0			0
$253$		−	9.87195i		−	0.620644i
$254$		0			0
$255$	12.4634	−	21.5872i	0.780488	−	1.35184i
$256$		0			0
$257$	2.89962	+	5.02229i	0.180873	+	0.313282i	0.942178	−	0.335112i	$-0.108774\pi$
$257$	2.89962	+	5.02229i	0.180873	+	0.313282i	−0.761305	+	0.648394i	$0.775441\pi$
$258$		0			0
$259$	29.9277	−	2.23287i	1.85962	−	0.138743i
$260$		0			0
$261$	−0.131073	+	0.0756749i	−0.00811320	+	0.00468416i
$262$		0			0
$263$	1.21627	−	2.10664i	0.0749983	−	0.129901i	−0.826087	−	0.563542i	$-0.809438\pi$
$263$	1.21627	−	2.10664i	0.0749983	−	0.129901i	0.901086	+	0.433641i	$0.142772\pi$
$264$		0			0
$265$	−21.3420			−1.31103
$266$		0			0
$267$		−	3.66869i		−	0.224520i
$268$		0			0
$269$	4.98470	+	2.87792i	0.303923	+	0.175470i	0.644204	−	0.764854i	$-0.277189\pi$
$269$	4.98470	+	2.87792i	0.303923	+	0.175470i	−0.340281	+	0.940324i	$0.610522\pi$
$270$		0			0
$271$	8.50926	+	14.7385i	0.516901	+	0.895299i	0.999807	+	0.0196268i	$0.00624782\pi$
$271$	8.50926	+	14.7385i	0.516901	+	0.895299i	−0.482906	+	0.875672i	$0.660419\pi$
$272$		0			0
$273$	−3.14999	+	2.14611i	−0.190646	+	0.129888i
$274$		0			0
$275$	27.1916	−	15.6991i	1.63972	−	0.946690i
$276$		0			0
$277$	19.4599	+	11.2352i	1.16923	+	0.675057i	0.953499	−	0.301395i	$-0.0974523\pi$
$277$	19.4599	+	11.2352i	1.16923	+	0.675057i	0.215734	+	0.976452i	$0.430786\pi$
$278$		0			0
$279$	−4.75438			−0.284637
$280$		0			0
$281$	7.29261			0.435041			0.217520	−	0.976056i	$-0.430203\pi$
$281$	7.29261			0.435041			0.217520	+	0.976056i	$0.430203\pi$
$282$		0			0
$283$	−9.21249	−	5.31883i	−0.547626	−	0.316172i	0.200538	−	0.979686i	$-0.435731\pi$
$283$	−9.21249	−	5.31883i	−0.547626	−	0.316172i	−0.748164	+	0.663514i	$0.769064\pi$
$284$		0			0
$285$	−0.930960	+	0.537490i	−0.0551453	+	0.0318382i
$286$		0			0
$287$	−0.570633	−	0.275034i	−0.0336834	−	0.0162348i
$288$		0			0
$289$	−15.9378	−	27.6050i	−0.937515	−	1.62382i
$290$		0			0
$291$	−9.06360	−	5.23287i	−0.531318	−	0.306757i
$292$		0			0
$293$		−	26.4432i		−	1.54483i	−0.635120	−	0.772414i	$-0.719049\pi$
$293$		−	26.4432i		−	1.54483i	0.635120	−	0.772414i	$-0.280951\pi$
$294$		0			0
$295$	−40.0862			−2.33391
$296$		0			0
$297$	2.03546	−	3.52552i	0.118109	−	0.204571i
$298$		0			0
$299$	−3.02551	+	1.74678i	−0.174970	+	0.101019i
$300$		0			0
$301$	1.52588	−	3.16585i	0.0879501	−	0.182477i
$302$		0			0
$303$	6.36685	+	11.0277i	0.365766	+	0.633526i
$304$		0			0
$305$	−7.50419	+	12.9976i	−0.429689	+	0.744243i
$306$		0			0
$307$		−	23.6553i		−	1.35008i	−0.737780	−	0.675041i	$-0.764126\pi$
$307$		−	23.6553i		−	1.35008i	0.737780	−	0.675041i	$-0.235874\pi$
$308$		0			0
$309$			6.00875i			0.341826i
$310$		0			0
$311$	−1.62606	+	2.81643i	−0.0922056	+	0.159705i	−0.908439	−	0.418018i	$-0.862725\pi$
$311$	−1.62606	+	2.81643i	−0.0922056	+	0.159705i	0.816233	+	0.577722i	$0.196058\pi$
$312$		0			0
$313$	−3.47621	−	6.02097i	−0.196487	−	0.340325i	0.750900	−	0.660416i	$-0.229620\pi$
$313$	−3.47621	−	6.02097i	−0.196487	−	0.340325i	−0.947387	+	0.320091i	$0.896287\pi$
$314$		0			0
$315$	5.31147	+	7.79601i	0.299268	+	0.439256i
$316$		0			0
$317$	5.44303	−	3.14254i	0.305711	−	0.176502i	−0.339295	−	0.940680i	$-0.610188\pi$
$317$	5.44303	−	3.14254i	0.305711	−	0.176502i	0.645006	+	0.764178i	$0.276855\pi$
$318$		0			0
$319$	−0.308067	+	0.533587i	−0.0172484	+	0.0298751i
$320$		0			0
$321$	15.9659			0.891132
$322$		0			0
$323$			2.10778i			0.117280i
$324$		0			0
$325$	−9.62276	−	5.55570i	−0.533775	−	0.308175i
$326$		0			0
$327$	6.93554	+	12.0127i	0.383536	+	0.664304i
$328$		0			0
$329$	−1.25170	−	16.7770i	−0.0690087	−	0.924944i
$330$		0			0
$331$	21.9584	−	12.6777i	1.20694	−	0.696827i	0.244851	−	0.969561i	$-0.421261\pi$
$331$	21.9584	−	12.6777i	1.20694	−	0.696827i	0.962090	+	0.272733i	$0.0879277\pi$
$332$		0			0
$333$	9.82338	+	5.67153i	0.538318	+	0.310798i
$334$		0			0
$335$	15.6196			0.853388
$336$		0			0
$337$	−18.0761			−0.984668			−0.492334	−	0.870406i	$-0.663856\pi$
$337$	−18.0761			−0.984668			−0.492334	+	0.870406i	$0.663856\pi$
$338$		0			0
$339$	14.2457	+	8.22474i	0.773719	+	0.446707i
$340$		0			0
$341$	−16.7617	+	9.67735i	−0.907695	+	0.524058i
$342$		0			0
$343$	4.10331	+	18.0600i	0.221558	+	0.975147i
$344$		0			0
$345$	4.32315	+	7.48792i	0.232751	+	0.403136i
$346$		0			0
$347$	−6.46167	−	3.73065i	−0.346881	−	0.200272i	0.316430	−	0.948616i	$-0.397516\pi$
$347$	−6.46167	−	3.73065i	−0.346881	−	0.200272i	−0.663311	+	0.748344i	$0.730849\pi$
$348$		0			0
$349$			23.2053i			1.24215i	0.783750	+	0.621077i	$0.213305\pi$
$349$			23.2053i			1.24215i	−0.783750	+	0.621077i	$0.786695\pi$
$350$		0			0
$351$	−1.44065			−0.0768960
$352$		0			0
$353$	2.14531	−	3.71578i	0.114183	−	0.197771i	−0.803270	−	0.595615i	$-0.796908\pi$
$353$	2.14531	−	3.71578i	0.114183	−	0.197771i	0.917453	+	0.397844i	$0.130242\pi$
$354$		0			0
$355$	26.1349	−	15.0890i	1.38709	−	0.800839i
$356$		0			0
$357$	18.4454	−	1.37619i	0.976237	−	0.0728356i
$358$		0			0
$359$	3.00706	+	5.20837i	0.158706	+	0.274888i	0.934402	−	0.356219i	$-0.115934\pi$
$359$	3.00706	+	5.20837i	0.158706	+	0.274888i	−0.775696	+	0.631107i	$0.782601\pi$
$360$		0			0
$361$	−9.45455	+	16.3758i	−0.497608	+	0.861882i
$362$		0			0
$363$		−	5.57239i		−	0.292475i
$364$		0			0
$365$			2.03037i			0.106274i
$366$		0			0
$367$	−7.78693	+	13.4874i	−0.406475	+	0.704035i	−0.994492	−	0.104814i	$-0.966575\pi$
$367$	−7.78693	+	13.4874i	−0.406475	+	0.704035i	0.588017	+	0.808848i	$0.299909\pi$
$368$		0			0
$369$	−0.119712	−	0.207347i	−0.00623195	−	0.0107941i
$370$		0			0
$371$	−8.91680	−	13.0878i	−0.462937	−	0.679485i
$372$		0			0
$373$	9.84545	−	5.68427i	0.509778	−	0.294320i	−0.222964	−	0.974827i	$-0.571573\pi$
$373$	9.84545	−	5.68427i	0.509778	−	0.294320i	0.732742	+	0.680506i	$0.238240\pi$
$374$		0			0
$375$	−4.83623	+	8.37659i	−0.249742	+	0.432565i
$376$		0			0
$377$	0.218042			0.0112297
$378$		0			0
$379$			31.9644i			1.64190i	0.571000	+	0.820950i	$0.306556\pi$
$379$			31.9644i			1.64190i	−0.571000	+	0.820950i	$0.693444\pi$
$380$		0			0
$381$	−2.88644	−	1.66649i	−0.147877	−	0.0853767i
$382$		0			0
$383$	−4.75224	−	8.23112i	−0.242828	−	0.420590i	0.718691	−	0.695330i	$-0.244742\pi$
$383$	−4.75224	−	8.23112i	−0.242828	−	0.420590i	−0.961519	+	0.274739i	$0.911408\pi$
$384$		0			0
$385$	34.5942	+	16.6737i	1.76308	+	0.849771i
$386$		0			0
$387$	1.15035	−	0.664156i	0.0584757	−	0.0337610i
$388$		0			0
$389$	−9.83845	−	5.68023i	−0.498829	−	0.287999i	0.229401	−	0.973332i	$-0.426323\pi$
$389$	−9.83845	−	5.68023i	−0.498829	−	0.287999i	−0.728230	+	0.685333i	$0.759657\pi$
$390$		0			0
$391$	16.9534			0.857368
$392$		0			0
$393$	4.08867			0.206246
$394$		0			0
$395$	−4.61268	−	2.66313i	−0.232089	−	0.133997i
$396$		0			0
$397$	18.7003	−	10.7967i	0.938544	−	0.541868i	0.0490401	−	0.998797i	$-0.484384\pi$
$397$	18.7003	−	10.7967i	0.938544	−	0.541868i	0.889503	+	0.456928i	$0.151050\pi$
$398$		0			0
$399$	−0.718571	−	0.346337i	−0.0359736	−	0.0173385i
$400$		0			0
$401$	−14.1230	−	24.4617i	−0.705267	−	1.22156i	−0.966595	−	0.256308i	$-0.917494\pi$
$401$	−14.1230	−	24.4617i	−0.705267	−	1.22156i	0.261329	−	0.965250i	$-0.415839\pi$
$402$		0			0
$403$	5.93174	+	3.42469i	0.295481	+	0.170596i
$404$		0			0
$405$			3.56550i			0.177171i
$406$		0			0
$407$	46.1767			2.28889
$408$		0			0
$409$	−6.74458	+	11.6820i	−0.333498	+	0.577635i	−0.983195	−	0.182558i	$-0.941562\pi$
$409$	−6.74458	+	11.6820i	−0.333498	+	0.577635i	0.649697	+	0.760193i	$0.274896\pi$
$410$		0			0
$411$	7.17707	−	4.14368i	0.354019	−	0.204393i
$412$		0			0
$413$	−16.7482	−	24.5825i	−0.824126	−	1.20963i
$414$		0			0
$415$	−17.8903	−	30.9868i	−0.878198	−	1.52108i
$416$		0			0
$417$	9.20899	−	15.9504i	0.450966	−	0.781096i
$418$		0			0
$419$			25.0575i			1.22414i	0.790804	+	0.612069i	$0.209663\pi$
$419$			25.0575i			1.22414i	−0.790804	+	0.612069i	$0.790337\pi$
$420$		0			0
$421$		−	23.0346i		−	1.12264i	−0.827600	−	0.561318i	$-0.810294\pi$
$421$		−	23.0346i		−	1.12264i	0.827600	−	0.561318i	$-0.189706\pi$
$422$		0			0
$423$	3.17936	−	5.50681i	0.154586	−	0.267750i
$424$		0			0
$425$	26.9604	+	46.6969i	1.30777	+	2.26513i
$426$		0			0
$427$	−11.1060	+	0.828601i	−0.537456	+	0.0400988i
$428$		0			0
$429$	−5.07903	+	2.93238i	−0.245218	+	0.141577i
$430$		0			0
$431$	0.0929281	−	0.160956i	0.00447619	−	0.00775299i	−0.863779	−	0.503871i	$-0.831909\pi$
$431$	0.0929281	−	0.160956i	0.00447619	−	0.00775299i	0.868255	+	0.496118i	$0.165242\pi$
$432$		0			0
$433$	34.7454			1.66976			0.834878	−	0.550435i	$-0.185538\pi$
$433$	34.7454			1.66976			0.834878	+	0.550435i	$0.185538\pi$
$434$		0			0
$435$		−	0.539638i		−	0.0258737i
$436$		0			0
$437$	−0.633171	−	0.365561i	−0.0302887	−	0.0174872i
$438$		0			0
$439$	−13.5890	−	23.5369i	−0.648570	−	1.12336i	−0.983465	−	0.181100i	$-0.942034\pi$
$439$	−13.5890	−	23.5369i	−0.648570	−	1.12336i	0.334895	−	0.942255i	$-0.391299\pi$
$440$		0			0
$441$	−2.56168	+	6.51443i	−0.121985	+	0.310211i
$442$		0			0
$443$	3.43698	−	1.98434i	0.163296	−	0.0942789i	−0.416125	−	0.909307i	$-0.636612\pi$
$443$	3.43698	−	1.98434i	0.163296	−	0.0942789i	0.579421	+	0.815029i	$0.303279\pi$
$444$		0			0
$445$	11.3282	+	6.54035i	0.537009	+	0.310042i
$446$		0			0
$447$	5.11203			0.241791
$448$		0			0
$449$	−12.1637			−0.574040			−0.287020	−	0.957925i	$-0.592665\pi$
$449$	−12.1637			−0.574040			−0.287020	+	0.957925i	$0.592665\pi$
$450$		0			0
$451$	−0.844094	−	0.487338i	−0.0397468	−	0.0229478i
$452$		0			0
$453$	3.61242	−	2.08563i	0.169726	−	0.0979915i
$454$		0			0
$455$	−1.01114	−	13.5526i	−0.0474028	−	0.635354i
$456$		0			0
$457$	−12.8791	−	22.3072i	−0.602459	−	1.04349i	−0.992448	−	0.122670i	$-0.960854\pi$
$457$	−12.8791	−	22.3072i	−0.602459	−	1.04349i	0.389989	−	0.920820i	$-0.372479\pi$
$458$		0			0
$459$	6.05447	+	3.49555i	0.282599	+	0.163158i
$460$		0			0
$461$			17.0423i			0.793737i	0.917875	+	0.396868i	$0.129903\pi$
$461$			17.0423i			0.793737i	−0.917875	+	0.396868i	$0.870097\pi$
$462$		0			0
$463$	−34.1343			−1.58635			−0.793177	−	0.608991i	$-0.791574\pi$
$463$	−34.1343			−1.58635			−0.793177	+	0.608991i	$0.791574\pi$
$464$		0			0
$465$	8.47587	−	14.6806i	0.393059	−	0.680798i
$466$		0			0
$467$	14.0940	−	8.13715i	0.652191	−	0.376543i	−0.137104	−	0.990557i	$-0.543780\pi$
$467$	14.0940	−	8.13715i	0.652191	−	0.376543i	0.789295	+	0.614014i	$0.210446\pi$
$468$		0			0
$469$	6.52593	+	9.57856i	0.301340	+	0.442297i
$470$		0			0
$471$	4.52438	+	7.83645i	0.208472	+	0.361084i
$472$		0			0
$473$	2.70373	−	4.68299i	0.124318	−	0.215324i
$474$		0			0
$475$		−	2.32537i		−	0.106695i
$476$		0			0
$477$		−	5.98569i		−	0.274066i
$478$		0			0
$479$	−10.0045	+	17.3284i	−0.457119	+	0.791754i	−0.998807	−	0.0488257i	$-0.984452\pi$
$479$	−10.0045	+	17.3284i	−0.457119	+	0.791754i	0.541688	+	0.840580i	$0.317785\pi$
$480$		0			0
$481$	−8.17067	−	14.1520i	−0.372551	−	0.645277i
$482$		0			0
$483$	−2.78567	+	5.77963i	−0.126752	+	0.262982i
$484$		0			0
$485$	32.3163	−	18.6578i	1.46741	−	0.847208i
$486$		0			0
$487$	8.27889	−	14.3394i	0.375152	−	0.649782i	−0.615198	−	0.788373i	$-0.710924\pi$
$487$	8.27889	−	14.3394i	0.375152	−	0.649782i	0.990350	+	0.138590i	$0.0442571\pi$
$488$		0			0
$489$	−13.4512			−0.608284
$490$		0			0
$491$			9.49257i			0.428394i	0.976791	+	0.214197i	$0.0687134\pi$
$491$			9.49257i			0.428394i	−0.976791	+	0.214197i	$0.931287\pi$
$492$		0			0
$493$	−0.916343	−	0.529051i	−0.0412700	−	0.0238273i
$494$		0			0
$495$	7.25743	+	12.5702i	0.326197	+	0.564990i
$496$		0			0
$497$	20.1725	+	9.72273i	0.904859	+	0.436124i
$498$		0			0
$499$	−29.6441	+	17.1150i	−1.32705	+	0.766174i	−0.984843	−	0.173449i	$-0.944509\pi$
$499$	−29.6441	+	17.1150i	−1.32705	+	0.766174i	−0.342210	+	0.939624i	$0.611175\pi$
$500$		0			0
$501$	14.9042	+	8.60496i	0.665872	+	0.384441i
$502$		0			0
$503$	21.0469			0.938436			0.469218	−	0.883082i	$-0.344536\pi$
$503$	21.0469			0.938436			0.469218	+	0.883082i	$0.344536\pi$
$504$		0			0
$505$	−45.4020			−2.02036
$506$		0			0
$507$	−9.46093	−	5.46227i	−0.420174	−	0.242588i
$508$		0			0
$509$	−13.0298	+	7.52276i	−0.577536	+	0.333440i	−0.760153	−	0.649744i	$-0.774876\pi$
$509$	−13.0298	+	7.52276i	−0.577536	+	0.333440i	0.182618	+	0.983184i	$0.441543\pi$
$510$		0			0
$511$	−1.24510	+	0.848298i	−0.0550802	+	0.0375265i
$512$		0			0
$513$	−0.150747	−	0.261102i	−0.00665566	−	0.0115279i
$514$		0			0
$515$	−18.5539	−	10.7121i	−0.817582	−	0.472031i
$516$		0			0
$517$		−	25.8858i		−	1.13846i
$518$		0			0
$519$	3.44940			0.151412
$520$		0			0
$521$	4.48956	−	7.77615i	0.196691	−	0.340679i	−0.750762	−	0.660572i	$-0.770314\pi$
$521$	4.48956	−	7.77615i	0.196691	−	0.340679i	0.947454	+	0.319893i	$0.103647\pi$
$522$		0			0
$523$	8.55073	−	4.93677i	0.373897	−	0.215870i	−0.301262	−	0.953541i	$-0.597408\pi$
$523$	8.55073	−	4.93677i	0.373897	−	0.215870i	0.675160	+	0.737672i	$0.264075\pi$
$524$		0			0
$525$	−20.3496	+	1.51825i	−0.888128	+	0.0662619i
$526$		0			0
$527$	−16.6192	−	28.7853i	−0.723943	−	1.25391i
$528$		0			0
$529$	8.55971	−	14.8259i	0.372161	−	0.644602i
$530$		0			0
$531$		−	11.2428i		−	0.487896i
$532$		0			0
$533$			0.344925i			0.0149404i
$534$		0			0
$535$	−28.4633	+	49.2998i	−1.23057	+	2.13142i
$536$		0			0
$537$	−5.65083	−	9.78752i	−0.243851	−	0.422363i
$538$		0			0
$539$	4.22862	+	28.1810i	0.182139	+	1.21384i
$540$		0			0
$541$	−17.1313	+	9.89077i	−0.736533	+	0.425237i	−0.820807	−	0.571205i	$-0.806476\pi$
$541$	−17.1313	+	9.89077i	−0.736533	+	0.425237i	0.0842746	+	0.996443i	$0.473143\pi$
$542$		0			0
$543$	−5.02831	+	8.70928i	−0.215785	+	0.373751i
$544$		0			0
$545$	−49.4573			−2.11852
$546$		0			0
$547$		−	39.3961i		−	1.68446i	−0.539122	−	0.842228i	$-0.681244\pi$
$547$		−	39.3961i		−	1.68446i	0.539122	−	0.842228i	$-0.318756\pi$
$548$		0			0
$549$	−3.64539	−	2.10467i	−0.155581	−	0.0898250i
$550$		0			0
$551$	0.0228156	+	0.0395178i	0.000971977	+	0.00168351i
$552$		0			0
$553$	−0.294059	−	3.94136i	−0.0125047	−	0.167604i
$554$		0			0
$555$	−35.0253	+	20.2218i	−1.48674	+	0.858370i
$556$		0			0
$557$	−5.84611	−	3.37525i	−0.247708	−	0.143014i	0.371006	−	0.928630i	$-0.379013\pi$
$557$	−5.84611	−	3.37525i	−0.247708	−	0.143014i	−0.618714	+	0.785616i	$0.712346\pi$
$558$		0			0
$559$	−1.91363			−0.0809379
$560$		0			0
$561$	28.4602			1.20159
$562$		0			0
$563$	25.1027	+	14.4930i	1.05795	+	0.610809i	0.924865	−	0.380296i	$-0.124178\pi$
$563$	25.1027	+	14.4930i	1.05795	+	0.610809i	0.133087	+	0.991104i	$0.457511\pi$
$564$		0			0
$565$	−50.7929	+	29.3253i	−2.13688	+	1.23373i
$566$		0			0
$567$	−2.18651	+	1.48968i	−0.0918249	+	0.0625609i
$568$		0			0
$569$	19.9834	+	34.6123i	0.837748	+	1.45102i	0.891773	+	0.452483i	$0.149462\pi$
$569$	19.9834	+	34.6123i	0.837748	+	1.45102i	−0.0540248	+	0.998540i	$0.517205\pi$
$570$		0			0
$571$	−7.01347	−	4.04923i	−0.293505	−	0.169455i	0.346017	−	0.938228i	$-0.387534\pi$
$571$	−7.01347	−	4.04923i	−0.293505	−	0.169455i	−0.639521	+	0.768773i	$0.720867\pi$
$572$		0			0
$573$		−	21.4860i		−	0.897592i
$574$		0			0
$575$	−18.7034			−0.779988
$576$		0			0
$577$	−23.7611	+	41.1555i	−0.989188	+	1.71332i	−0.367589	+	0.929988i	$0.619817\pi$
$577$	−23.7611	+	41.1555i	−0.989188	+	1.71332i	−0.621599	+	0.783336i	$0.713517\pi$
$578$		0			0
$579$	−14.2166	+	8.20798i	−0.590823	+	0.341112i
$580$		0			0
$581$	11.5278	−	23.9175i	0.478253	−	0.992266i
$582$		0			0
$583$	−12.1836	−	21.1027i	−0.504595	−	0.873984i
$584$		0			0
$585$	2.56831	−	4.44845i	0.106187	−	0.183921i
$586$		0			0
$587$			11.8785i			0.490279i	0.969488	+	0.245140i	$0.0788338\pi$
$587$			11.8785i			0.490279i	−0.969488	+	0.245140i	$0.921166\pi$
$588$		0			0
$589$			1.43342i			0.0590631i
$590$		0			0
$591$	7.85225	−	13.6005i	0.322999	−	0.559450i
$592$		0			0
$593$	−16.1160	−	27.9138i	−0.661806	−	1.14628i	−0.980141	−	0.198303i	$-0.936457\pi$
$593$	−16.1160	−	27.9138i	−0.661806	−	1.14628i	0.318335	−	0.947978i	$-0.396876\pi$
$594$		0			0
$595$	−28.6342	+	59.4095i	−1.17389	+	2.43555i
$596$		0			0
$597$	−5.43374	+	3.13717i	−0.222388	+	0.128396i
$598$		0			0
$599$	19.8427	−	34.3686i	0.810752	−	1.40426i	−0.101586	−	0.994827i	$-0.532392\pi$
$599$	19.8427	−	34.3686i	0.810752	−	1.40426i	0.912338	−	0.409437i	$-0.134275\pi$
$600$		0			0
$601$	22.3599			0.912081			0.456040	−	0.889959i	$-0.349267\pi$
$601$	22.3599			0.912081			0.456040	+	0.889959i	$0.349267\pi$
$602$		0			0
$603$			4.38075i			0.178398i
$604$		0			0
$605$	17.2065	+	9.93418i	0.699544	+	0.403882i
$606$		0			0
$607$	7.38757	+	12.7956i	0.299852	+	0.519359i	0.976102	−	0.217313i	$-0.0697294\pi$
$607$	7.38757	+	12.7956i	0.299852	+	0.519359i	−0.676250	+	0.736672i	$0.736396\pi$
$608$		0			0
$609$	0.330928	−	0.225464i	0.0134099	−	0.00913625i
$610$		0			0
$611$	−7.93337	+	4.58033i	−0.320950	+	0.185300i
$612$		0			0
$613$	−22.7453	−	13.1320i	−0.918676	−	0.530398i	−0.0354633	−	0.999371i	$-0.511291\pi$
$613$	−22.7453	−	13.1320i	−0.918676	−	0.530398i	−0.883212	+	0.468973i	$0.844624\pi$
$614$		0			0
$615$	0.853666			0.0344231
$616$		0			0
$617$	33.8882			1.36429			0.682144	−	0.731218i	$-0.261048\pi$
$617$	33.8882			1.36429			0.682144	+	0.731218i	$0.261048\pi$
$618$		0			0
$619$	5.24132	+	3.02608i	0.210667	+	0.121628i	0.601621	−	0.798782i	$-0.294522\pi$
$619$	5.24132	+	3.02608i	0.210667	+	0.121628i	−0.390955	+	0.920410i	$0.627855\pi$
$620$		0			0
$621$	−2.10010	+	1.21250i	−0.0842743	+	0.0486558i
$622$		0			0
$623$	0.722176	+	9.67953i	0.0289334	+	0.387802i
$624$		0			0
$625$	2.03841	+	3.53063i	0.0815364	+	0.141225i
$626$		0			0
$627$	−1.06293	−	0.613681i	−0.0424492	−	0.0245081i
$628$		0			0
$629$			79.3005i			3.16192i
$630$		0			0
$631$	14.6555			0.583426			0.291713	−	0.956506i	$-0.405775\pi$
$631$	14.6555			0.583426			0.291713	+	0.956506i	$0.405775\pi$
$632$		0			0
$633$	4.70229	−	8.14460i	0.186899	−	0.323719i
$634$		0			0
$635$	10.2916	−	5.94186i	0.408410	−	0.235796i
$636$		0			0
$637$	7.88854	−	6.28241i	0.312555	−	0.248918i
$638$		0			0
$639$	4.23194	+	7.32993i	0.167413	+	0.289967i
$640$		0			0
$641$	−7.77488	+	13.4665i	−0.307089	+	0.531894i	−0.977724	−	0.209893i	$-0.932688\pi$
$641$	−7.77488	+	13.4665i	−0.307089	+	0.531894i	0.670635	+	0.741787i	$0.266022\pi$
$642$		0			0
$643$		−	28.3180i		−	1.11675i	−0.829587	−	0.558377i	$-0.811424\pi$
$643$		−	28.3180i		−	1.11675i	0.829587	−	0.558377i	$-0.188576\pi$
$644$		0			0
$645$			4.73610i			0.186484i
$646$		0			0
$647$	12.9342	−	22.4026i	0.508495	−	0.880739i	−0.491457	−	0.870902i	$-0.663535\pi$
$647$	12.9342	−	22.4026i	0.508495	−	0.880739i	0.999952	−	0.00983684i	$-0.00313121\pi$
$648$		0			0
$649$	−22.8843	−	39.6367i	−0.898286	−	1.55588i
$650$		0			0
$651$	12.5440	−	0.935893i	0.491640	−	0.0366805i
$652$		0			0
$653$	−24.4781	+	14.1324i	−0.957902	+	0.553045i	−0.895527	−	0.445008i	$-0.853201\pi$
$653$	−24.4781	+	14.1324i	−0.957902	+	0.553045i	−0.0623752	+	0.998053i	$0.519868\pi$
$654$		0			0
$655$	−7.28907	+	12.6250i	−0.284808	+	0.493301i
$656$		0			0
$657$	−0.569448			−0.0222163
$658$		0			0
$659$			21.7217i			0.846159i	0.906093	+	0.423079i	$0.139051\pi$
$659$			21.7217i			0.846159i	−0.906093	+	0.423079i	$0.860949\pi$
$660$		0			0
$661$	−27.5252	−	15.8917i	−1.07061	−	0.618115i	−0.142260	−	0.989829i	$-0.545437\pi$
$661$	−27.5252	−	15.8917i	−1.07061	−	0.618115i	−0.928347	+	0.371714i	$0.878770\pi$
$662$		0			0
$663$	−5.03585	−	8.72235i	−0.195576	−	0.338748i
$664$		0			0
$665$	2.35046	−	1.60138i	0.0911469	−	0.0620989i
$666$		0			0
$667$	0.317850	−	0.183511i	0.0123072	−	0.00710557i
$668$		0			0
$669$	3.76497	+	2.17370i	0.145562	+	0.0840403i
$670$		0			0
$671$	−17.1359			−0.661523
$672$		0			0
$673$	16.1882			0.624009			0.312004	−	0.950081i	$-0.399000\pi$
$673$	16.1882			0.624009			0.312004	+	0.950081i	$0.399000\pi$
$674$		0			0
$675$	−6.67947	−	3.85640i	−0.257093	−	0.148433i
$676$		0			0
$677$	−20.6873	+	11.9438i	−0.795078	+	0.459038i	−0.841747	−	0.539872i	$-0.818473\pi$
$677$	−20.6873	+	11.9438i	−0.795078	+	0.459038i	0.0466693	+	0.998910i	$0.485139\pi$
$678$		0			0
$679$	24.9437	+	12.0224i	0.957250	+	0.461376i
$680$		0			0
$681$	3.64102	+	6.30643i	0.139524	+	0.241663i
$682$		0			0
$683$	−21.8511	−	12.6157i	−0.836110	−	0.482728i	0.0198304	−	0.999803i	$-0.493687\pi$
$683$	−21.8511	−	12.6157i	−0.836110	−	0.482728i	−0.855940	+	0.517075i	$0.827021\pi$
$684$		0			0
$685$			29.5486i			1.12899i
$686$		0			0
$687$	1.02222			0.0390003
$688$		0			0
$689$	−4.31164	+	7.46797i	−0.164260	+	0.284507i
$690$		0			0
$691$	−13.8089	+	7.97260i	−0.525317	+	0.303292i	−0.739107	−	0.673588i	$-0.764752\pi$
$691$	−13.8089	+	7.97260i	−0.525317	+	0.303292i	0.213790	+	0.976880i	$0.431419\pi$
$692$		0			0
$693$	−4.67640	+	9.70247i	−0.177642	+	0.368567i
$694$		0			0
$695$	32.8346	+	56.8713i	1.24549	+	2.15725i
$696$		0			0
$697$	0.836918	−	1.44958i	0.0317005	−	0.0549069i
$698$		0			0
$699$		−	22.0661i		−	0.834617i
$700$		0			0
$701$		−	46.5568i		−	1.75842i	−0.476430	−	0.879212i	$-0.658069\pi$
$701$		−	46.5568i		−	1.75842i	0.476430	−	0.879212i	$-0.341931\pi$
$702$		0			0
$703$	1.70994	−	2.96170i	0.0644915	−	0.111703i
$704$		0			0
$705$	11.3360	+	19.6345i	0.426939	+	0.739480i
$706$		0			0
$707$	−18.9692	−	27.8424i	−0.713411	−	1.04712i
$708$		0			0
$709$	4.68128	−	2.70274i	0.175809	−	0.101503i	−0.409513	−	0.912304i	$-0.634301\pi$
$709$	4.68128	−	2.70274i	0.175809	−	0.101503i	0.585322	+	0.810801i	$0.300968\pi$
$710$		0			0
$711$	0.746916	−	1.29370i	0.0280116	−	0.0485174i
$712$		0			0
$713$	11.5293			0.431777
$714$		0			0
$715$		−	20.9108i		−	0.782019i
$716$		0			0
$717$	4.16104	+	2.40238i	0.155397	+	0.0897184i
$718$		0			0
$719$	9.74035	+	16.8708i	0.363254	+	0.629174i	0.988494	−	0.151258i	$-0.0483324\pi$
$719$	9.74035	+	16.8708i	0.363254	+	0.629174i	−0.625240	+	0.780432i	$0.714999\pi$
$720$		0			0
$721$	−1.18281	−	15.8536i	−0.0440503	−	0.590419i
$722$		0			0
$723$	20.5844	−	11.8844i	0.765542	−	0.441986i
$724$		0			0
$725$	1.01094	+	0.583665i	0.0375453	+	0.0216768i
$726$		0			0
$727$	−22.4025			−0.830864			−0.415432	−	0.909624i	$-0.636370\pi$
$727$	−22.4025			−0.830864			−0.415432	+	0.909624i	$0.636370\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.04223	+	4.64318i	0.297453	+	0.171734i
$732$		0			0
$733$	40.3059	−	23.2706i	1.48873	−	0.859520i	0.488815	−	0.872388i	$-0.337429\pi$
$733$	40.3059	−	23.2706i	1.48873	−	0.859520i	0.999917	+	0.0128680i	$0.00409614\pi$
$734$		0			0
$735$	−15.5485	−	19.5236i	−0.573516	−	0.720138i
$736$		0			0
$737$	8.91684	+	15.4444i	0.328456	+	0.568902i
$738$		0			0
$739$	27.6623	+	15.9708i	1.01757	+	0.587497i	0.913400	−	0.407062i	$-0.133447\pi$
$739$	27.6623	+	15.9708i	1.01757	+	0.587497i	0.104174	+	0.994559i	$0.466780\pi$
$740$		0			0
$741$			0.434348i			0.0159562i
$742$		0			0
$743$	−14.3888			−0.527874			−0.263937	−	0.964540i	$-0.585021\pi$
$743$	−14.3888			−0.527874			−0.263937	+	0.964540i	$0.585021\pi$
$744$		0			0
$745$	−9.11347	+	15.7850i	−0.333892	+	0.578318i
$746$		0			0
$747$	8.69074	−	5.01760i	0.317978	−	0.183584i
$748$		0			0
$749$	−42.1248	+	3.14287i	−1.53921	+	0.114838i
$750$		0			0
$751$	−15.1568	−	26.2524i	−0.553080	−	0.957963i	−0.998050	−	0.0624177i	$-0.980119\pi$
$751$	−15.1568	−	26.2524i	−0.553080	−	0.957963i	0.444970	−	0.895546i	$-0.353214\pi$
$752$		0			0
$753$	−7.04442	+	12.2013i	−0.256713	+	0.444640i
$754$		0			0
$755$			14.8726i			0.541270i
$756$		0			0
$757$			51.0353i			1.85491i	0.373937	+	0.927454i	$0.378007\pi$
$757$			51.0353i			1.85491i	−0.373937	+	0.927454i	$0.621993\pi$
$758$		0			0
$759$	−4.93597	+	8.54936i	−0.179164	+	0.310322i
$760$		0			0
$761$	−15.1055	−	26.1636i	−0.547576	−	0.948429i	−0.998440	−	0.0558364i	$-0.982217\pi$
$761$	−15.1055	−	26.1636i	−0.547576	−	0.948429i	0.450864	−	0.892593i	$-0.351116\pi$
$762$		0			0
$763$	−20.6635	−	30.3293i	−0.748070	−	1.09799i
$764$		0			0
$765$	−21.5872	+	12.4634i	−0.780488	+	0.450615i
$766$		0			0
$767$	−8.09845	+	14.0269i	−0.292418	+	0.506483i
$768$		0			0
$769$	4.26448			0.153781			0.0768906	−	0.997040i	$-0.475501\pi$
$769$	4.26448			0.153781			0.0768906	+	0.997040i	$0.475501\pi$
$770$		0			0
$771$		−	5.79924i		−	0.208854i
$772$		0			0
$773$	4.66804	+	2.69509i	0.167898	+	0.0969357i	0.581594	−	0.813479i	$-0.302429\pi$
$773$	4.66804	+	2.69509i	0.167898	+	0.0969357i	−0.413697	+	0.910415i	$0.635763\pi$
$774$		0			0
$775$	18.3348	+	31.7568i	0.658604	+	1.14074i
$776$		0			0
$777$	−27.0346	−	13.0302i	−0.969862	−	0.467454i
$778$		0			0
$779$	−0.0625141	+	0.0360925i	−0.00223980	+	0.00129315i
$780$		0			0
$781$	29.8396	+	17.2279i	1.06774	+	0.616462i
$782$		0			0
$783$	0.151350			0.00540880
$784$		0			0
$785$	−32.2633			−1.15153
$786$		0			0
$787$	−5.36826	−	3.09937i	−0.191358	−	0.110480i	0.401260	−	0.915964i	$-0.368572\pi$
$787$	−5.36826	−	3.09937i	−0.191358	−	0.110480i	−0.592618	+	0.805484i	$0.701906\pi$
$788$		0			0
$789$	−2.10664	+	1.21627i	−0.0749983	+	0.0433003i
$790$		0			0
$791$	−39.2051	−	18.8961i	−1.39397	−	0.671867i
$792$		0			0
$793$	3.03208	+	5.25172i	0.107672	+	0.186494i
$794$		0			0
$795$	18.4827	+	10.6710i	0.655514	+	0.378461i
$796$		0			0
$797$			2.24353i			0.0794699i	0.999210	+	0.0397349i	$0.0126514\pi$
$797$			2.24353i			0.0794699i	−0.999210	+	0.0397349i	$0.987349\pi$
$798$		0			0
$799$	44.4545			1.57269
$800$		0			0
$801$	−1.83434	+	3.17718i	−0.0648134	+	0.112260i
$802$		0			0
$803$	−2.00760	+	1.15909i	−0.0708466	+	0.0409033i
$804$		0			0
$805$	−12.8803	−	18.9053i	−0.453970	−	0.666323i
$806$		0			0
$807$	−2.87792	−	4.98470i	−0.101308	−	0.175470i
$808$		0			0
$809$	7.66844	−	13.2821i	0.269608	−	0.466974i	−0.699153	−	0.714972i	$-0.746439\pi$
$809$	7.66844	−	13.2821i	0.269608	−	0.466974i	0.968761	+	0.247998i	$0.0797726\pi$
$810$		0			0
$811$			15.1509i			0.532019i	0.963970	+	0.266010i	$0.0857053\pi$
$811$			15.1509i			0.532019i	−0.963970	+	0.266010i	$0.914295\pi$
$812$		0			0
$813$		−	17.0185i		−	0.596866i
$814$		0			0
$815$	23.9801	−	41.5348i	0.839987	−	1.45490i
$816$		0			0
$817$	−0.200240	−	0.346825i	−0.00700550	−	0.0121339i
$818$		0			0
$819$	3.80103	−	0.283589i	0.132819	−	0.00990941i
$820$		0			0
$821$	−1.41618	+	0.817631i	−0.0494249	+	0.0285355i	−0.524509	−	0.851405i	$-0.675751\pi$
$821$	−1.41618	+	0.817631i	−0.0494249	+	0.0285355i	0.475084	+	0.879940i	$0.342418\pi$
$822$		0			0
$823$	22.5067	−	38.9828i	0.784535	−	1.35886i	−0.144741	−	0.989470i	$-0.546235\pi$
$823$	22.5067	−	38.9828i	0.784535	−	1.35886i	0.929276	−	0.369385i	$-0.120432\pi$
$824$		0			0
$825$	−31.3982			−1.09314
$826$		0			0
$827$		−	42.4945i		−	1.47768i	−0.673882	−	0.738839i	$-0.735374\pi$
$827$		−	42.4945i		−	1.47768i	0.673882	−	0.738839i	$-0.264626\pi$
$828$		0			0
$829$	39.6168	+	22.8728i	1.37595	+	0.794405i	0.991669	−	0.128811i	$-0.0411161\pi$
$829$	39.6168	+	22.8728i	1.37595	+	0.794405i	0.384281	+	0.923216i	$0.374449\pi$
$830$		0			0
$831$	−11.2352	−	19.4599i	−0.389744	−	0.675057i
$832$		0			0
$833$	−48.3959	+	7.26192i	−1.67682	+	0.251611i
$834$		0			0
$835$	−53.1410	+	30.6810i	−1.83902	+	1.06176i
$836$		0			0
$837$	4.11741	+	2.37719i	0.142319	+	0.0821677i
$838$		0			0
$839$	−30.4207			−1.05024			−0.525120	−	0.851028i	$-0.675980\pi$
$839$	−30.4207			−1.05024			−0.525120	+	0.851028i	$0.675980\pi$
$840$		0			0
$841$	28.9771			0.999210
$842$		0			0
$843$	−6.31559	−	3.64631i	−0.217520	−	0.125585i
$844$		0			0
$845$	33.7329	−	19.4757i	1.16045	−	0.669985i
$846$		0			0
$847$	1.09692	+	14.7023i	0.0376905	+	0.505177i
$848$		0			0
$849$	5.31883	+	9.21249i	0.182542	+	0.316172i
$850$		0			0
$851$	−23.8216	−	13.7534i	−0.816594	−	0.471461i
$852$		0			0
$853$		−	0.386158i		−	0.0132218i	−0.999978	−	0.00661090i	$-0.997896\pi$
$853$		−	0.386158i		−	0.0132218i	0.999978	−	0.00661090i	$-0.00210433\pi$
$854$		0			0
$855$	1.07498			0.0367635
$856$		0			0
$857$	13.1617	−	22.7967i	0.449595	−	0.778721i	−0.548765	−	0.835977i	$-0.684902\pi$
$857$	13.1617	−	22.7967i	0.449595	−	0.778721i	0.998360	+	0.0572556i	$0.0182350\pi$
$858$		0			0
$859$	20.1570	−	11.6377i	0.687749	−	0.397072i	−0.115019	−	0.993363i	$-0.536693\pi$
$859$	20.1570	−	11.6377i	0.687749	−	0.397072i	0.802768	+	0.596291i	$0.203360\pi$
$860$		0			0
$861$	0.356666	+	0.523503i	0.0121551	+	0.0178409i
$862$		0			0
$863$	8.25613	+	14.3000i	0.281042	+	0.486779i	0.971642	−	0.236458i	$-0.0759866\pi$
$863$	8.25613	+	14.3000i	0.281042	+	0.486779i	−0.690600	+	0.723237i	$0.742653\pi$
$864$		0			0
$865$	−6.14941	+	10.6511i	−0.209086	+	0.362148i
$866$		0			0
$867$			31.8755i			1.08255i
$868$		0			0
$869$		−	6.08128i		−	0.206293i
$870$		0			0
$871$	3.15555	−	5.46558i	0.106922	−	0.185194i
$872$		0			0
$873$	5.23287	+	9.06360i	0.177106	+	0.306757i
$874$		0			0
$875$	11.1111	−	23.0530i	0.375623	−	0.779332i
$876$		0			0
$877$	−24.8320	+	14.3368i	−0.838518	+	0.484119i	−0.856760	−	0.515715i	$-0.827526\pi$
$877$	−24.8320	+	14.3368i	−0.838518	+	0.484119i	0.0182421	+	0.999834i	$0.494193\pi$
$878$		0			0
$879$	−13.2216	+	22.9005i	−0.445953	+	0.772414i
$880$		0			0
$881$	5.88181			0.198163			0.0990816	−	0.995079i	$-0.468410\pi$
$881$	5.88181			0.198163			0.0990816	+	0.995079i	$0.468410\pi$
$882$		0			0
$883$			1.69703i			0.0571095i	0.999592	+	0.0285548i	$0.00909050\pi$
$883$			1.69703i			0.0571095i	−0.999592	+	0.0285548i	$0.990910\pi$
$884$		0			0
$885$	34.7156	+	20.0431i	1.16695	+	0.673741i
$886$		0			0
$887$	−28.8622	−	49.9909i	−0.969099	−	1.67853i	−0.698173	−	0.715929i	$-0.746004\pi$
$887$	−28.8622	−	49.9909i	−0.969099	−	1.67853i	−0.270926	−	0.962600i	$-0.587330\pi$
$888$		0			0
$889$	7.94368	+	3.82870i	0.266423	+	0.128410i
$890$		0			0
$891$	−3.52552	+	2.03546i	−0.118109	+	0.0681905i
$892$		0			0
$893$	−1.66028	−	0.958561i	−0.0555590	−	0.0320770i
$894$		0			0
$895$	40.2961			1.34695
$896$		0			0
$897$	3.49356			0.116646
$898$		0			0
$899$	−0.623170	−	0.359787i	−0.0207839	−	0.0119996i
$900$		0			0
$901$	36.2402	−	20.9233i	1.20734	−	0.697056i
$902$		0			0
$903$	−2.90437	+	1.97877i	−0.0966515	+	0.0658493i
$904$		0			0
$905$	−17.9284	−	31.0529i	−0.595961	−	1.03223i
$906$		0			0
$907$	39.2549	+	22.6638i	1.30344	+	0.752540i	0.980992	−	0.194047i	$-0.0621615\pi$
$907$	39.2549	+	22.6638i	1.30344	+	0.752540i	0.322446	+	0.946588i	$0.395495\pi$
$908$		0			0
$909$		−	12.7337i		−	0.422350i
$910$		0			0
$911$	26.4254			0.875511			0.437755	−	0.899094i	$-0.355774\pi$
$911$	26.4254			0.875511			0.437755	+	0.899094i	$0.355774\pi$
$912$		0			0
$913$	20.4263	−	35.3793i	0.676011	−	1.17088i
$914$		0			0
$915$	12.9976	−	7.50419i	0.429689	−	0.248081i
$916$		0			0
$917$	−10.7876	+	0.804848i	−0.356238	+	0.0265784i
$918$		0			0
$919$	−0.150333	−	0.260384i	−0.00495901	−	0.00858926i	0.863535	−	0.504288i	$-0.168245\pi$
$919$	−0.150333	−	0.260384i	−0.00495901	−	0.00858926i	−0.868494	+	0.495699i	$0.834912\pi$
$920$		0			0
$921$	−11.8277	+	20.4861i	−0.389735	+	0.675041i
$922$		0			0
$923$		−	12.1934i		−	0.401352i
$924$		0			0
$925$		−	87.4867i		−	2.87654i
$926$		0			0
$927$	3.00437	−	5.20373i	0.0986766	−	0.170913i
$928$		0			0
$929$	19.3333	+	33.4862i	0.634304	+	1.09865i	0.986662	+	0.162782i	$0.0520467\pi$
$929$	19.3333	+	33.4862i	0.634304	+	1.09865i	−0.352358	+	0.935865i	$0.614620\pi$
$930$		0			0
$931$	1.96407	+	0.772333i	0.0643697	+	0.0253122i
$932$		0			0
$933$	2.81643	−	1.62606i	0.0922056	−	0.0532349i
$934$		0			0
$935$	−50.7375	+	87.8798i	−1.65929	+	2.87398i
$936$		0			0
$937$	23.9292			0.781734			0.390867	−	0.920447i	$-0.372175\pi$
$937$	23.9292			0.781734			0.390867	+	0.920447i	$0.372175\pi$
$938$		0			0
$939$			6.95242i			0.226884i
$940$		0			0
$941$	36.7253	+	21.2034i	1.19721	+	0.691210i	0.959932	−	0.280232i	$-0.0904113\pi$
$941$	36.7253	+	21.2034i	1.19721	+	0.691210i	0.237279	+	0.971442i	$0.423745\pi$
$942$		0			0
$943$	0.290300	+	0.502815i	0.00945348	+	0.0163739i
$944$		0			0
$945$	−0.701863	−	9.40728i	−0.0228316	−	0.306019i
$946$		0			0
$947$	−11.9347	+	6.89051i	−0.387826	+	0.223911i	−0.681218	−	0.732081i	$-0.738549\pi$
$947$	−11.9347	+	6.89051i	−0.387826	+	0.223911i	0.293392	+	0.955992i	$0.405216\pi$
$948$		0			0
$949$	0.710464	+	0.410186i	0.0230626	+	0.0133152i
$950$		0			0
$951$	−6.28507			−0.203807
$952$		0			0
$953$	57.0092			1.84671			0.923354	−	0.383950i	$-0.125436\pi$
$953$	57.0092			1.84671			0.923354	+	0.383950i	$0.125436\pi$
$954$		0			0
$955$	66.3449	+	38.3042i	2.14687	+	1.23950i
$956$		0			0
$957$	0.533587	−	0.308067i	0.0172484	−	0.00995838i
$958$		0			0
$959$	−18.1204	+	12.3456i	−0.585139	+	0.398659i
$960$		0			0
$961$	4.19793	+	7.27103i	0.135417	+	0.234549i
$962$		0			0
$963$	−13.8269	−	7.98297i	−0.445566	−	0.257248i
$964$		0			0
$965$		−	58.5311i		−	1.88418i
$966$		0			0
$967$	20.0555			0.644941			0.322470	−	0.946580i	$-0.395487\pi$
$967$	20.0555			0.644941			0.322470	+	0.946580i	$0.395487\pi$
$968$		0			0
$969$	1.05389	−	1.82539i	0.0338559	−	0.0586401i
$970$		0			0
$971$	−0.979533	+	0.565534i	−0.0314347	+	0.0181488i	−0.515635	−	0.856808i	$-0.672444\pi$
$971$	−0.979533	+	0.565534i	−0.0314347	+	0.0181488i	0.484200	+	0.874957i	$0.339111\pi$
$972$		0			0
$973$	−21.1573	+	43.8967i	−0.678273	+	1.40726i
$974$		0			0
$975$	5.55570	+	9.62276i	0.177925	+	0.308175i
$976$		0			0
$977$	15.5033	−	26.8526i	0.495996	−	0.859089i	−0.503994	−	0.863707i	$-0.668137\pi$
$977$	15.5033	−	26.8526i	0.495996	−	0.859089i	0.999989	+	0.00461783i	$0.00146990\pi$
$978$		0			0
$979$			14.9349i			0.477323i
$980$		0			0
$981$		−	13.8711i		−	0.442869i
$982$		0			0
$983$	−4.59402	+	7.95708i	−0.146527	+	0.253791i	−0.929941	−	0.367708i	$-0.880143\pi$
$983$	−4.59402	+	7.95708i	−0.146527	+	0.253791i	0.783415	+	0.621499i	$0.213476\pi$
$984$		0			0
$985$	27.9972	+	48.4926i	0.892065	+	1.54510i
$986$		0			0
$987$	−7.30447	+	15.1551i	−0.232504	+	0.482393i
$988$		0			0
$989$	−2.78959	+	1.61057i	−0.0887040	+	0.0512133i
$990$		0			0
$991$	20.0275	−	34.6886i	0.636194	−	1.10192i	−0.350067	−	0.936725i	$-0.613841\pi$
$991$	20.0275	−	34.6886i	0.636194	−	1.10192i	0.986261	−	0.165195i	$-0.0528255\pi$
$992$		0			0
$993$	−25.3553			−0.804627
$994$		0			0
$995$		−	22.3712i		−	0.709214i
$996$		0			0
$997$	−22.5912	−	13.0430i	−0.715470	−	0.413077i	0.0976129	−	0.995224i	$-0.468879\pi$
$997$	−22.5912	−	13.0430i	−0.715470	−	0.413077i	−0.813083	+	0.582147i	$0.802213\pi$
$998$		0			0
$999$	−5.67153	−	9.82338i	−0.179439	−	0.310798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bk.a.529.8		32
3.2	odd	2		2016.2.cr.e.1873.2		32
4.3	odd	2		168.2.bc.a.109.12	yes	32
7.2	even	3	inner	672.2.bk.a.625.9		32
7.3	odd	6		4704.2.c.f.2353.1		16
7.4	even	3		4704.2.c.e.2353.16		16
8.3	odd	2		168.2.bc.a.109.10	yes	32
8.5	even	2	inner	672.2.bk.a.529.9		32
12.11	even	2		504.2.cj.e.109.5		32
21.2	odd	6		2016.2.cr.e.1297.15		32
24.5	odd	2		2016.2.cr.e.1873.15		32
24.11	even	2		504.2.cj.e.109.7		32
28.3	even	6		1176.2.c.f.589.2		16
28.11	odd	6		1176.2.c.e.589.2		16
28.23	odd	6		168.2.bc.a.37.10	✓	32
56.3	even	6		1176.2.c.f.589.1		16
56.11	odd	6		1176.2.c.e.589.1		16
56.37	even	6	inner	672.2.bk.a.625.8		32
56.45	odd	6		4704.2.c.f.2353.16		16
56.51	odd	6		168.2.bc.a.37.12	yes	32
56.53	even	6		4704.2.c.e.2353.1		16
84.23	even	6		504.2.cj.e.37.7		32
168.107	even	6		504.2.cj.e.37.5		32
168.149	odd	6		2016.2.cr.e.1297.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.10	✓	32	28.23	odd	6
168.2.bc.a.37.12	yes	32	56.51	odd	6
168.2.bc.a.109.10	yes	32	8.3	odd	2
168.2.bc.a.109.12	yes	32	4.3	odd	2
504.2.cj.e.37.5		32	168.107	even	6
504.2.cj.e.37.7		32	84.23	even	6
504.2.cj.e.109.5		32	12.11	even	2
504.2.cj.e.109.7		32	24.11	even	2
672.2.bk.a.529.8		32	1.1	even	1	trivial
672.2.bk.a.529.9		32	8.5	even	2	inner
672.2.bk.a.625.8		32	56.37	even	6	inner
672.2.bk.a.625.9		32	7.2	even	3	inner
1176.2.c.e.589.1		16	56.11	odd	6
1176.2.c.e.589.2		16	28.11	odd	6
1176.2.c.f.589.1		16	56.3	even	6
1176.2.c.f.589.2		16	28.3	even	6
2016.2.cr.e.1297.2		32	168.149	odd	6
2016.2.cr.e.1297.15		32	21.2	odd	6
2016.2.cr.e.1873.2		32	3.2	odd	2
2016.2.cr.e.1873.15		32	24.5	odd	2
4704.2.c.e.2353.1		16	56.53	even	6
4704.2.c.e.2353.16		16	7.4	even	3
4704.2.c.f.2353.1		16	7.3	odd	6
4704.2.c.f.2353.16		16	56.45	odd	6

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(3.08781 - 1.78275i) q^{5} +(2.38336 + 1.14873i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(3.08781 - 1.78275i) q^{5} +(2.38336 + 1.14873i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.52552 + 2.03546i) q^{11} -1.44065i q^{13} -3.56550 q^{15} +(-3.49555 + 6.05447i) q^{17} +(0.261102 - 0.150747i) q^{19} +(-1.48968 - 2.18651i) q^{21} +(-1.21250 - 2.10010i) q^{23} +(3.85640 - 6.67947i) q^{25} -1.00000i q^{27} +0.151350i q^{29} +(-2.37719 + 4.11741i) q^{31} +(-2.03546 - 3.52552i) q^{33} +(9.40728 - 0.701863i) q^{35} +(9.82338 - 5.67153i) q^{37} +(-0.720323 + 1.24764i) q^{39} -0.239424 q^{41} -1.32831i q^{43} +(3.08781 + 1.78275i) q^{45} +(-3.17936 - 5.50681i) q^{47} +(4.36082 + 5.47569i) q^{49} +(6.05447 - 3.49555i) q^{51} +(-5.18376 - 2.99285i) q^{53} +14.5149 q^{55} -0.301495 q^{57} +(-9.73654 - 5.62140i) q^{59} +(-3.64539 + 2.10467i) q^{61} +(0.196849 + 2.63842i) q^{63} +(-2.56831 - 4.44845i) q^{65} +(3.79384 + 2.19037i) q^{67} +2.42499i q^{69} +8.46387 q^{71} +(-0.284724 + 0.493156i) q^{73} +(-6.67947 + 3.85640i) q^{75} +(6.06439 + 8.90112i) q^{77} +(-0.746916 - 1.29370i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.0352i q^{83} +24.9268i q^{85} +(0.0756749 - 0.131073i) q^{87} +(1.83434 + 3.17718i) q^{89} +(1.65492 - 3.43358i) q^{91} +(4.11741 - 2.37719i) q^{93} +(0.537490 - 0.930960i) q^{95} +10.4657 q^{97} +4.07092i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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