LMFDB - Embedded newform 560.2.x.b.463.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(127,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))

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

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

chi := DirichletCharacter("560.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.x (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.5
Character	$\chi$	$=$	560.463
Dual form			560.2.x.b.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.333196 + 0.333196i) q^{3} +(-2.17403 - 0.523047i) q^{5} +(0.707107 + 0.707107i) q^{7} +2.77796i q^{9} +O(q^{10})$	\(q+(-0.333196 + 0.333196i) q^{3} +(-2.17403 - 0.523047i) q^{5} +(0.707107 + 0.707107i) q^{7} +2.77796i q^{9} -3.81740i q^{11} +(2.82628 + 2.82628i) q^{13} +(0.898656 - 0.550102i) q^{15} +(-2.97020 + 2.97020i) q^{17} -5.82967 q^{19} -0.471210 q^{21} +(-6.07917 + 6.07917i) q^{23} +(4.45284 + 2.27424i) q^{25} +(-1.92519 - 1.92519i) q^{27} +9.62607i q^{29} +3.98706i q^{31} +(1.27194 + 1.27194i) q^{33} +(-1.16742 - 1.90712i) q^{35} +(1.50707 - 1.50707i) q^{37} -1.88341 q^{39} -9.04673 q^{41} +(7.59941 - 7.59941i) q^{43} +(1.45301 - 6.03938i) q^{45} +(4.02037 + 4.02037i) q^{47} +1.00000i q^{49} -1.97932i q^{51} +(2.08195 + 2.08195i) q^{53} +(-1.99668 + 8.29915i) q^{55} +(1.94242 - 1.94242i) q^{57} -1.30659 q^{59} -6.60862 q^{61} +(-1.96432 + 1.96432i) q^{63} +(-4.66615 - 7.62271i) q^{65} +(1.76751 + 1.76751i) q^{67} -4.05110i q^{69} -16.3833i q^{71} +(7.53966 + 7.53966i) q^{73} +(-2.24144 + 0.725900i) q^{75} +(2.69931 - 2.69931i) q^{77} +4.84221 q^{79} -7.05095 q^{81} +(-0.140128 + 0.140128i) q^{83} +(8.01087 - 4.90376i) q^{85} +(-3.20736 - 3.20736i) q^{87} -8.64739i q^{89} +3.99697i q^{91} +(-1.32847 - 1.32847i) q^{93} +(12.6739 + 3.04919i) q^{95} +(7.77699 - 7.77699i) q^{97} +10.6046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{13} + 8 q^{17} - 8 q^{21} + 32 q^{25} + 24 q^{33} - 16 q^{37} + 32 q^{41} - 24 q^{45} + 8 q^{53} + 40 q^{57} + 16 q^{61} - 16 q^{73} + 16 q^{77} - 104 q^{81} - 8 q^{85} - 8 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 8 * q^13 + 8 * q^17 - 8 * q^21 + 32 * q^25 + 24 * q^33 - 16 * q^37 + 32 * q^41 - 24 * q^45 + 8 * q^53 + 40 * q^57 + 16 * q^61 - 16 * q^73 + 16 * q^77 - 104 * q^81 - 8 * q^85 - 8 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−0.333196	+	0.333196i	−0.192371	+	0.192371i	−0.796720	−	0.604349i	$-0.793433\pi$
$3$	−0.333196	+	0.333196i	−0.192371	+	0.192371i	0.604349	+	0.796720i	$0.293433\pi$
$4$		0			0
$5$	−2.17403	−	0.523047i	−0.972257	−	0.233914i
$5$	−2.17403	−	0.523047i	−0.972257	−	0.233914i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$			2.77796i			0.925987i
$10$		0			0
$11$		−	3.81740i		−	1.15099i	−0.817806	−	0.575494i	$-0.804810\pi$
$11$		−	3.81740i		−	1.15099i	0.817806	−	0.575494i	$-0.195190\pi$
$12$		0			0
$13$	2.82628	+	2.82628i	0.783870	+	0.783870i	0.980481	−	0.196612i	$-0.0629938\pi$
$13$	2.82628	+	2.82628i	0.783870	+	0.783870i	−0.196612	+	0.980481i	$0.562994\pi$
$14$		0			0
$15$	0.898656	−	0.550102i	0.232032	−	0.142036i
$16$		0			0
$17$	−2.97020	+	2.97020i	−0.720379	+	0.720379i	−0.968682	−	0.248303i	$-0.920127\pi$
$17$	−2.97020	+	2.97020i	−0.720379	+	0.720379i	0.248303	+	0.968682i	$0.420127\pi$
$18$		0			0
$19$	−5.82967			−1.33742			−0.668709	−	0.743525i	$-0.733153\pi$
$19$	−5.82967			−1.33742			−0.668709	+	0.743525i	$0.733153\pi$
$20$		0			0
$21$	−0.471210			−0.102826
$22$		0			0
$23$	−6.07917	+	6.07917i	−1.26759	+	1.26759i	−0.320266	+	0.947328i	$0.603772\pi$
$23$	−6.07917	+	6.07917i	−1.26759	+	1.26759i	−0.947328	+	0.320266i	$0.896228\pi$
$24$		0			0
$25$	4.45284	+	2.27424i	0.890569	+	0.454849i
$26$		0			0
$27$	−1.92519	−	1.92519i	−0.370503	−	0.370503i
$28$		0			0
$29$			9.62607i			1.78752i	0.448550	+	0.893758i	$0.351941\pi$
$29$			9.62607i			1.78752i	−0.448550	+	0.893758i	$0.648059\pi$
$30$		0			0
$31$			3.98706i			0.716097i	0.933703	+	0.358049i	$0.116558\pi$
$31$			3.98706i			0.716097i	−0.933703	+	0.358049i	$0.883442\pi$
$32$		0			0
$33$	1.27194	+	1.27194i	0.221416	+	0.221416i
$34$		0			0
$35$	−1.16742	−	1.90712i	−0.197331	−	0.322363i
$36$		0			0
$37$	1.50707	−	1.50707i	0.247761	−	0.247761i	−0.572290	−	0.820051i	$-0.693945\pi$
$37$	1.50707	−	1.50707i	0.247761	−	0.247761i	0.820051	+	0.572290i	$0.193945\pi$
$38$		0			0
$39$	−1.88341			−0.301587
$40$		0			0
$41$	−9.04673			−1.41286			−0.706431	−	0.707782i	$-0.749696\pi$
$41$	−9.04673			−1.41286			−0.706431	+	0.707782i	$0.749696\pi$
$42$		0			0
$43$	7.59941	−	7.59941i	1.15890	−	1.15890i	0.174187	−	0.984713i	$-0.444270\pi$
$43$	7.59941	−	7.59941i	1.15890	−	1.15890i	0.984713	−	0.174187i	$-0.0557296\pi$
$44$		0			0
$45$	1.45301	−	6.03938i	0.216601	−	0.900298i
$46$		0			0
$47$	4.02037	+	4.02037i	0.586432	+	0.586432i	0.936663	−	0.350231i	$-0.113897\pi$
$47$	4.02037	+	4.02037i	0.586432	+	0.586432i	−0.350231	+	0.936663i	$0.613897\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	1.97932i		−	0.277160i
$52$		0			0
$53$	2.08195	+	2.08195i	0.285978	+	0.285978i	0.835488	−	0.549509i	$-0.185185\pi$
$53$	2.08195	+	2.08195i	0.285978	+	0.285978i	−0.549509	+	0.835488i	$0.685185\pi$
$54$		0			0
$55$	−1.99668	+	8.29915i	−0.269232	+	1.11906i
$56$		0			0
$57$	1.94242	−	1.94242i	0.257280	−	0.257280i
$58$		0			0
$59$	−1.30659			−0.170103			−0.0850517	−	0.996377i	$-0.527106\pi$
$59$	−1.30659			−0.170103			−0.0850517	+	0.996377i	$0.527106\pi$
$60$		0			0
$61$	−6.60862			−0.846147			−0.423074	−	0.906095i	$-0.639049\pi$
$61$	−6.60862			−0.846147			−0.423074	+	0.906095i	$0.639049\pi$
$62$		0			0
$63$	−1.96432	+	1.96432i	−0.247480	+	0.247480i
$64$		0			0
$65$	−4.66615	−	7.62271i	−0.578765	−	0.945481i
$66$		0			0
$67$	1.76751	+	1.76751i	0.215936	+	0.215936i	0.806783	−	0.590848i	$-0.201207\pi$
$67$	1.76751	+	1.76751i	0.215936	+	0.215936i	−0.590848	+	0.806783i	$0.701207\pi$
$68$		0			0
$69$		−	4.05110i		−	0.487696i
$70$		0			0
$71$		−	16.3833i		−	1.94434i	−0.234273	−	0.972171i	$-0.575271\pi$
$71$		−	16.3833i		−	1.94434i	0.234273	−	0.972171i	$-0.424729\pi$
$72$		0			0
$73$	7.53966	+	7.53966i	0.882450	+	0.882450i	0.993783	−	0.111333i	$-0.0355120\pi$
$73$	7.53966	+	7.53966i	0.882450	+	0.882450i	−0.111333	+	0.993783i	$0.535512\pi$
$74$		0			0
$75$	−2.24144	+	0.725900i	−0.258819	+	0.0838197i
$76$		0			0
$77$	2.69931	−	2.69931i	0.307615	−	0.307615i
$78$		0			0
$79$	4.84221			0.544792			0.272396	−	0.962185i	$-0.412184\pi$
$79$	4.84221			0.544792			0.272396	+	0.962185i	$0.412184\pi$
$80$		0			0
$81$	−7.05095			−0.783439
$82$		0			0
$83$	−0.140128	+	0.140128i	−0.0153810	+	0.0153810i	−0.714755	−	0.699374i	$-0.753462\pi$
$83$	−0.140128	+	0.140128i	−0.0153810	+	0.0153810i	0.699374	+	0.714755i	$0.253462\pi$
$84$		0			0
$85$	8.01087	−	4.90376i	0.868901	−	0.531887i
$86$		0			0
$87$	−3.20736	−	3.20736i	−0.343866	−	0.343866i
$88$		0			0
$89$		−	8.64739i		−	0.916621i	−0.888792	−	0.458310i	$-0.848455\pi$
$89$		−	8.64739i		−	0.916621i	0.888792	−	0.458310i	$-0.151545\pi$
$90$		0			0
$91$			3.99697i			0.418996i
$92$		0			0
$93$	−1.32847	−	1.32847i	−0.137756	−	0.137756i
$94$		0			0
$95$	12.6739	+	3.04919i	1.30031	+	0.312840i
$96$		0			0
$97$	7.77699	−	7.77699i	0.789634	−	0.789634i	−0.191800	−	0.981434i	$-0.561433\pi$
$97$	7.77699	−	7.77699i	0.789634	−	0.789634i	0.981434	+	0.191800i	$0.0614326\pi$
$98$		0			0
$99$	10.6046			1.06580
$100$		0			0
$101$	0.137557			0.0136875			0.00684374	−	0.999977i	$-0.497822\pi$
$101$	0.137557			0.0136875			0.00684374	+	0.999977i	$0.497822\pi$
$102$		0			0
$103$	−11.1193	+	11.1193i	−1.09562	+	1.09562i	−0.100701	+	0.994917i	$0.532108\pi$
$103$	−11.1193	+	11.1193i	−1.09562	+	1.09562i	−0.994917	+	0.100701i	$0.967892\pi$
$104$		0			0
$105$	1.02443	+	0.246465i	0.0999738	+	0.0240525i
$106$		0			0
$107$	−1.72055	−	1.72055i	−0.166332	−	0.166332i	0.619033	−	0.785365i	$-0.287525\pi$
$107$	−1.72055	−	1.72055i	−0.166332	−	0.166332i	−0.785365	+	0.619033i	$0.787525\pi$
$108$		0			0
$109$			2.60302i			0.249324i	0.992199	+	0.124662i	$0.0397846\pi$
$109$			2.60302i			0.249324i	−0.992199	+	0.124662i	$0.960215\pi$
$110$		0			0
$111$			1.00430i			0.0953238i
$112$		0			0
$113$	4.64057	+	4.64057i	0.436549	+	0.436549i	0.890849	−	0.454300i	$-0.150111\pi$
$113$	4.64057	+	4.64057i	0.436549	+	0.436549i	−0.454300	+	0.890849i	$0.650111\pi$
$114$		0			0
$115$	16.3960	−	10.0366i	1.52893	−	0.935919i
$116$		0			0
$117$	−7.85130	+	7.85130i	−0.725853	+	0.725853i
$118$		0			0
$119$	−4.20050			−0.385059
$120$		0			0
$121$	−3.57253			−0.324775
$122$		0			0
$123$	3.01433	−	3.01433i	0.271793	−	0.271793i
$124$		0			0
$125$	−8.49109	−	7.27333i	−0.759466	−	0.650547i
$126$		0			0
$127$	9.73689	+	9.73689i	0.864009	+	0.864009i	0.991801	−	0.127792i	$-0.0407890\pi$
$127$	9.73689	+	9.73689i	0.864009	+	0.864009i	−0.127792	+	0.991801i	$0.540789\pi$
$128$		0			0
$129$			5.06418i			0.445876i
$130$		0			0
$131$		−	5.27741i		−	0.461089i	−0.973062	−	0.230545i	$-0.925949\pi$
$131$		−	5.27741i		−	0.461089i	0.973062	−	0.230545i	$-0.0740508\pi$
$132$		0			0
$133$	−4.12220	−	4.12220i	−0.357440	−	0.357440i
$134$		0			0
$135$	3.17847	+	5.19240i	0.273559	+	0.446891i
$136$		0			0
$137$	10.4098	−	10.4098i	0.889370	−	0.889370i	−0.105093	−	0.994462i	$-0.533514\pi$
$137$	10.4098	−	10.4098i	0.889370	−	0.889370i	0.994462	+	0.105093i	$0.0335139\pi$
$138$		0			0
$139$	−21.5519			−1.82801			−0.914004	−	0.405705i	$-0.867026\pi$
$139$	−21.5519			−1.82801			−0.914004	+	0.405705i	$0.867026\pi$
$140$		0			0
$141$	−2.67914			−0.225625
$142$		0			0
$143$	10.7890	−	10.7890i	0.902226	−	0.902226i
$144$		0			0
$145$	5.03489	−	20.9274i	0.418125	−	1.73793i
$146$		0			0
$147$	−0.333196	−	0.333196i	−0.0274815	−	0.0274815i
$148$		0			0
$149$		−	2.55520i		−	0.209330i	−0.994508	−	0.104665i	$-0.966623\pi$
$149$		−	2.55520i		−	0.209330i	0.994508	−	0.104665i	$-0.0333770\pi$
$150$		0			0
$151$			5.09193i			0.414376i	0.978301	+	0.207188i	$0.0664311\pi$
$151$			5.09193i			0.414376i	−0.978301	+	0.207188i	$0.933569\pi$
$152$		0			0
$153$	−8.25110	−	8.25110i	−0.667062	−	0.667062i
$154$		0			0
$155$	2.08542	−	8.66800i	0.167505	−	0.696231i
$156$		0			0
$157$	11.4072	−	11.4072i	0.910396	−	0.910396i	−0.0859073	−	0.996303i	$-0.527379\pi$
$157$	11.4072	−	11.4072i	0.910396	−	0.910396i	0.996303	+	0.0859073i	$0.0273789\pi$
$158$		0			0
$159$	−1.38740			−0.110028
$160$		0			0
$161$	−8.59724			−0.677557
$162$		0			0
$163$	−8.35866	+	8.35866i	−0.654701	+	0.654701i	−0.954121	−	0.299420i	$-0.903207\pi$
$163$	−8.35866	+	8.35866i	−0.654701	+	0.654701i	0.299420	+	0.954121i	$0.403207\pi$
$164$		0			0
$165$	−2.09996	−	3.43053i	−0.163481	−	0.267066i
$166$		0			0
$167$	7.72096	+	7.72096i	0.597466	+	0.597466i	0.939637	−	0.342172i	$-0.111163\pi$
$167$	7.72096	+	7.72096i	0.597466	+	0.597466i	−0.342172	+	0.939637i	$0.611163\pi$
$168$		0			0
$169$			2.97575i			0.228904i
$170$		0			0
$171$		−	16.1946i		−	1.23843i
$172$		0			0
$173$	−4.11677	−	4.11677i	−0.312992	−	0.312992i	0.533075	−	0.846068i	$-0.321036\pi$
$173$	−4.11677	−	4.11677i	−0.312992	−	0.312992i	−0.846068	+	0.533075i	$0.821036\pi$
$174$		0			0
$175$	1.54050	+	4.75677i	0.116451	+	0.359578i
$176$		0			0
$177$	0.435350	−	0.435350i	0.0327229	−	0.0327229i
$178$		0			0
$179$	1.11797			0.0835612			0.0417806	−	0.999127i	$-0.486697\pi$
$179$	1.11797			0.0835612			0.0417806	+	0.999127i	$0.486697\pi$
$180$		0			0
$181$	3.22127			0.239435			0.119718	−	0.992808i	$-0.461801\pi$
$181$	3.22127			0.239435			0.119718	+	0.992808i	$0.461801\pi$
$182$		0			0
$183$	2.20196	−	2.20196i	0.162774	−	0.162774i
$184$		0			0
$185$	−4.06469	+	2.48815i	−0.298842	+	0.182933i
$186$		0			0
$187$	11.3384	+	11.3384i	0.829148	+	0.829148i
$188$		0			0
$189$		−	2.72263i		−	0.198042i
$190$		0			0
$191$			8.68124i			0.628152i	0.949398	+	0.314076i	$0.101695\pi$
$191$			8.68124i			0.628152i	−0.949398	+	0.314076i	$0.898305\pi$
$192$		0			0
$193$	4.69834	+	4.69834i	0.338194	+	0.338194i	0.855687	−	0.517493i	$-0.173135\pi$
$193$	4.69834	+	4.69834i	0.338194	+	0.338194i	−0.517493	+	0.855687i	$0.673135\pi$
$194$		0			0
$195$	4.09460	+	0.985113i	0.293220	+	0.0705454i
$196$		0			0
$197$	0.367432	−	0.367432i	0.0261784	−	0.0261784i	−0.693896	−	0.720075i	$-0.744107\pi$
$197$	0.367432	−	0.367432i	0.0261784	−	0.0261784i	0.720075	+	0.693896i	$0.244107\pi$
$198$		0			0
$199$	14.0339			0.994836			0.497418	−	0.867511i	$-0.334282\pi$
$199$	14.0339			0.994836			0.497418	+	0.867511i	$0.334282\pi$
$200$		0			0
$201$	−1.17785			−0.0830794
$202$		0			0
$203$	−6.80666	+	6.80666i	−0.477734	+	0.477734i
$204$		0			0
$205$	19.6679	+	4.73187i	1.37366	+	0.330488i
$206$		0			0
$207$	−16.8877	−	16.8877i	−1.17378	−	1.17378i
$208$		0			0
$209$			22.2542i			1.53935i
$210$		0			0
$211$		−	15.2984i		−	1.05319i	−0.850117	−	0.526594i	$-0.823469\pi$
$211$		−	15.2984i		−	1.05319i	0.850117	−	0.526594i	$-0.176531\pi$
$212$		0			0
$213$	5.45885	+	5.45885i	0.374034	+	0.374034i
$214$		0			0
$215$	−20.4962	+	12.5465i	−1.39783	+	0.855666i
$216$		0			0
$217$	−2.81928	+	2.81928i	−0.191385	+	0.191385i
$218$		0			0
$219$	−5.02436			−0.339515
$220$		0			0
$221$	−16.7892			−1.12937
$222$		0			0
$223$	−9.89248	+	9.89248i	−0.662449	+	0.662449i	−0.955957	−	0.293508i	$-0.905177\pi$
$223$	−9.89248	+	9.89248i	−0.662449	+	0.662449i	0.293508	+	0.955957i	$0.405177\pi$
$224$		0			0
$225$	−6.31776	+	12.3698i	−0.421184	+	0.824655i
$226$		0			0
$227$	0.567441	+	0.567441i	0.0376624	+	0.0376624i	0.725687	−	0.688025i	$-0.241522\pi$
$227$	0.567441	+	0.567441i	0.0376624	+	0.0376624i	−0.688025	+	0.725687i	$0.741522\pi$
$228$		0			0
$229$			11.7682i			0.777665i	0.921308	+	0.388833i	$0.127122\pi$
$229$			11.7682i			0.777665i	−0.921308	+	0.388833i	$0.872878\pi$
$230$		0			0
$231$			1.79880i			0.118352i
$232$		0			0
$233$	1.92993	+	1.92993i	0.126434	+	0.126434i	0.767492	−	0.641058i	$-0.221504\pi$
$233$	1.92993	+	1.92993i	0.126434	+	0.126434i	−0.641058	+	0.767492i	$0.721504\pi$
$234$		0			0
$235$	−6.63758	−	10.8433i	−0.432988	−	0.707337i
$236$		0			0
$237$	−1.61341	+	1.61341i	−0.104802	+	0.104802i
$238$		0			0
$239$	11.8823			0.768599			0.384300	−	0.923208i	$-0.374443\pi$
$239$	11.8823			0.768599			0.384300	+	0.923208i	$0.374443\pi$
$240$		0			0
$241$	−0.0826315			−0.00532276			−0.00266138	−	0.999996i	$-0.500847\pi$
$241$	−0.0826315			−0.00532276			−0.00266138	+	0.999996i	$0.500847\pi$
$242$		0			0
$243$	8.12492	−	8.12492i	0.521214	−	0.521214i
$244$		0			0
$245$	0.523047	−	2.17403i	0.0334163	−	0.138894i
$246$		0			0
$247$	−16.4763	−	16.4763i	−1.04836	−	1.04836i
$248$		0			0
$249$		−	0.0933799i		−	0.00591771i
$250$		0			0
$251$			21.5411i			1.35966i	0.733370	+	0.679830i	$0.237946\pi$
$251$			21.5411i			1.35966i	−0.733370	+	0.679830i	$0.762054\pi$
$252$		0			0
$253$	23.2066	+	23.2066i	1.45899	+	1.45899i
$254$		0			0
$255$	−1.03528	+	4.30310i	−0.0648315	+	0.269471i
$256$		0			0
$257$	2.29985	−	2.29985i	0.143461	−	0.143461i	−0.631729	−	0.775189i	$-0.717654\pi$
$257$	2.29985	−	2.29985i	0.143461	−	0.143461i	0.775189	+	0.631729i	$0.217654\pi$
$258$		0			0
$259$	2.13132			0.132434
$260$		0			0
$261$	−26.7408			−1.65522
$262$		0			0
$263$	−7.06625	+	7.06625i	−0.435724	+	0.435724i	−0.890570	−	0.454846i	$-0.849694\pi$
$263$	−7.06625	+	7.06625i	−0.435724	+	0.435724i	0.454846	+	0.890570i	$0.349694\pi$
$264$		0			0
$265$	−3.43728	−	5.61520i	−0.211150	−	0.344939i
$266$		0			0
$267$	2.88127	+	2.88127i	0.176331	+	0.176331i
$268$		0			0
$269$			18.9551i			1.15571i	0.816138	+	0.577857i	$0.196111\pi$
$269$			18.9551i			1.15571i	−0.816138	+	0.577857i	$0.803889\pi$
$270$		0			0
$271$		−	6.29238i		−	0.382235i	−0.981567	−	0.191117i	$-0.938789\pi$
$271$		−	6.29238i		−	0.382235i	0.981567	−	0.191117i	$-0.0612111\pi$
$272$		0			0
$273$	−1.33177	−	1.33177i	−0.0806026	−	0.0806026i
$274$		0			0
$275$	8.68170	−	16.9983i	0.523526	−	1.02503i
$276$		0			0
$277$	−9.90581	+	9.90581i	−0.595183	+	0.595183i	−0.939027	−	0.343844i	$-0.888271\pi$
$277$	−9.90581	+	9.90581i	−0.595183	+	0.595183i	0.343844	+	0.939027i	$0.388271\pi$
$278$		0			0
$279$	−11.0759			−0.663097
$280$		0			0
$281$	16.0267			0.956073			0.478037	−	0.878340i	$-0.341349\pi$
$281$	16.0267			0.956073			0.478037	+	0.878340i	$0.341349\pi$
$282$		0			0
$283$	−11.2462	+	11.2462i	−0.668519	+	0.668519i	−0.957373	−	0.288854i	$-0.906726\pi$
$283$	−11.2462	+	11.2462i	−0.668519	+	0.668519i	0.288854	+	0.957373i	$0.406726\pi$
$284$		0			0
$285$	−5.23886	+	3.20691i	−0.310323	+	0.189961i
$286$		0			0
$287$	−6.39700	−	6.39700i	−0.377603	−	0.377603i
$288$		0			0
$289$		−	0.644170i		−	0.0378924i
$290$		0			0
$291$			5.18252i			0.303805i
$292$		0			0
$293$	−0.0612109	−	0.0612109i	−0.00357598	−	0.00357598i	0.705317	−	0.708893i	$-0.250805\pi$
$293$	−0.0612109	−	0.0612109i	−0.00357598	−	0.00357598i	−0.708893	+	0.705317i	$0.750805\pi$
$294$		0			0
$295$	2.84057	+	0.683408i	0.165384	+	0.0397896i
$296$		0			0
$297$	−7.34923	+	7.34923i	−0.426445	+	0.426445i
$298$		0			0
$299$	−34.3629			−1.98726
$300$		0			0
$301$	10.7472			0.619458
$302$		0			0
$303$	−0.0458336	+	0.0458336i	−0.00263307	+	0.00263307i
$304$		0			0
$305$	14.3674	+	3.45662i	0.822673	+	0.197926i
$306$		0			0
$307$	2.06970	+	2.06970i	0.118124	+	0.118124i	0.763698	−	0.645574i	$-0.223382\pi$
$307$	2.06970	+	2.06970i	0.118124	+	0.118124i	−0.645574	+	0.763698i	$0.723382\pi$
$308$		0			0
$309$		−	7.40981i		−	0.421529i
$310$		0			0
$311$		−	5.71330i		−	0.323971i	−0.986793	−	0.161986i	$-0.948210\pi$
$311$		−	5.71330i		−	0.323971i	0.986793	−	0.161986i	$-0.0517899\pi$
$312$		0			0
$313$	12.9453	+	12.9453i	0.731710	+	0.731710i	0.970958	−	0.239248i	$-0.0769010\pi$
$313$	12.9453	+	12.9453i	0.731710	+	0.731710i	−0.239248	+	0.970958i	$0.576901\pi$
$314$		0			0
$315$	5.29792	−	3.24306i	0.298504	−	0.182726i
$316$		0			0
$317$	−2.42299	+	2.42299i	−0.136089	+	0.136089i	−0.771870	−	0.635781i	$-0.780678\pi$
$317$	−2.42299	+	2.42299i	−0.136089	+	0.136089i	0.635781	+	0.771870i	$0.280678\pi$
$318$		0			0
$319$	36.7465			2.05741
$320$		0			0
$321$	1.14656			0.0639947
$322$		0			0
$323$	17.3153	−	17.3153i	0.963447	−	0.963447i
$324$		0			0
$325$	6.15734	+	19.0127i	0.341548	+	1.05463i
$326$		0			0
$327$	−0.867315	−	0.867315i	−0.0479626	−	0.0479626i
$328$		0			0
$329$			5.68567i			0.313461i
$330$		0			0
$331$			19.4379i			1.06840i	0.845357	+	0.534201i	$0.179387\pi$
$331$			19.4379i			1.06840i	−0.845357	+	0.534201i	$0.820613\pi$
$332$		0			0
$333$	4.18658	+	4.18658i	0.229423	+	0.229423i
$334$		0			0
$335$	−2.91813	−	4.76712i	−0.159435	−	0.260455i
$336$		0			0
$337$	−9.92413	+	9.92413i	−0.540602	+	0.540602i	−0.923705	−	0.383103i	$-0.874855\pi$
$337$	−9.92413	+	9.92413i	−0.540602	+	0.540602i	0.383103	+	0.923705i	$0.374855\pi$
$338$		0			0
$339$	−3.09244			−0.167958
$340$		0			0
$341$	15.2202			0.824220
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	−2.11892	+	8.80724i	−0.114079	+	0.474166i
$346$		0			0
$347$	−3.03794	−	3.03794i	−0.163085	−	0.163085i	0.620847	−	0.783932i	$-0.286789\pi$
$347$	−3.03794	−	3.03794i	−0.163085	−	0.163085i	−0.783932	+	0.620847i	$0.786789\pi$
$348$		0			0
$349$		−	34.2112i		−	1.83128i	−0.401995	−	0.915642i	$-0.631683\pi$
$349$		−	34.2112i		−	1.83128i	0.401995	−	0.915642i	$-0.368317\pi$
$350$		0			0
$351$		−	10.8823i		−	0.580853i
$352$		0			0
$353$	−17.7240	−	17.7240i	−0.943353	−	0.943353i	0.0551265	−	0.998479i	$-0.482444\pi$
$353$	−17.7240	−	17.7240i	−0.943353	−	0.943353i	−0.998479	+	0.0551265i	$0.982444\pi$
$354$		0			0
$355$	−8.56925	+	35.6179i	−0.454808	+	1.89040i
$356$		0			0
$357$	1.39959	−	1.39959i	0.0740740	−	0.0740740i
$358$		0			0
$359$	−16.1630			−0.853053			−0.426527	−	0.904475i	$-0.640263\pi$
$359$	−16.1630			−0.853053			−0.426527	+	0.904475i	$0.640263\pi$
$360$		0			0
$361$	14.9850			0.788684
$362$		0			0
$363$	1.19035	−	1.19035i	0.0624773	−	0.0624773i
$364$		0			0
$365$	−12.4479	−	20.3351i	−0.651551	−	1.06439i
$366$		0			0
$367$	−4.88533	−	4.88533i	−0.255012	−	0.255012i	0.568010	−	0.823022i	$-0.307714\pi$
$367$	−4.88533	−	4.88533i	−0.255012	−	0.255012i	−0.823022	+	0.568010i	$0.807714\pi$
$368$		0			0
$369$		−	25.1315i		−	1.30829i
$370$		0			0
$371$			2.94433i			0.152862i
$372$		0			0
$373$	−20.1847	−	20.1847i	−1.04512	−	1.04512i	−0.998933	−	0.0461909i	$-0.985292\pi$
$373$	−20.1847	−	20.1847i	−1.04512	−	1.04512i	−0.0461909	−	0.998933i	$-0.514708\pi$
$374$		0			0
$375$	5.25264	−	0.405753i	0.271245	−	0.0209530i
$376$		0			0
$377$	−27.2060	+	27.2060i	−1.40118	+	1.40118i
$378$		0			0
$379$	−30.3515			−1.55905			−0.779525	−	0.626371i	$-0.784540\pi$
$379$	−30.3515			−1.55905			−0.779525	+	0.626371i	$0.784540\pi$
$380$		0			0
$381$	−6.48858			−0.332420
$382$		0			0
$383$	11.7350	−	11.7350i	0.599632	−	0.599632i	−0.340583	−	0.940215i	$-0.610624\pi$
$383$	11.7350	−	11.7350i	0.599632	−	0.599632i	0.940215	+	0.340583i	$0.110624\pi$
$384$		0			0
$385$	−7.28025	+	4.45652i	−0.371036	+	0.227125i
$386$		0			0
$387$	21.1109	+	21.1109i	1.07313	+	1.07313i
$388$		0			0
$389$			21.1406i			1.07187i	0.844260	+	0.535934i	$0.180041\pi$
$389$			21.1406i			1.07187i	−0.844260	+	0.535934i	$0.819959\pi$
$390$		0			0
$391$		−	36.1127i		−	1.82630i
$392$		0			0
$393$	1.75841	+	1.75841i	0.0887000	+	0.0887000i
$394$		0			0
$395$	−10.5271	−	2.53271i	−0.529678	−	0.127434i
$396$		0			0
$397$	−13.7106	+	13.7106i	−0.688116	+	0.688116i	−0.961815	−	0.273699i	$-0.911753\pi$
$397$	−13.7106	+	13.7106i	−0.688116	+	0.688116i	0.273699	+	0.961815i	$0.411753\pi$
$398$		0			0
$399$	2.74700			0.137522
$400$		0			0
$401$	0.204376			0.0102061			0.00510303	−	0.999987i	$-0.498376\pi$
$401$	0.204376			0.0102061			0.00510303	+	0.999987i	$0.498376\pi$
$402$		0			0
$403$	−11.2686	+	11.2686i	−0.561327	+	0.561327i
$404$		0			0
$405$	15.3290	+	3.68798i	0.761704	+	0.183257i
$406$		0			0
$407$	−5.75309	−	5.75309i	−0.285170	−	0.285170i
$408$		0			0
$409$		−	0.828467i		−	0.0409650i	−0.999790	−	0.0204825i	$-0.993480\pi$
$409$		−	0.828467i		−	0.0409650i	0.999790	−	0.0204825i	$-0.00652024\pi$
$410$		0			0
$411$			6.93701i			0.342177i
$412$		0			0
$413$	−0.923898	−	0.923898i	−0.0454621	−	0.0454621i
$414$		0			0
$415$	0.377936	−	0.231349i	0.0185521	−	0.0113565i
$416$		0			0
$417$	7.18100	−	7.18100i	0.351655	−	0.351655i
$418$		0			0
$419$	16.4341			0.802858			0.401429	−	0.915890i	$-0.368514\pi$
$419$	16.4341			0.802858			0.401429	+	0.915890i	$0.368514\pi$
$420$		0			0
$421$	25.3657			1.23625			0.618125	−	0.786080i	$-0.287893\pi$
$421$	25.3657			1.23625			0.618125	+	0.786080i	$0.287893\pi$
$422$		0			0
$423$	−11.1684	+	11.1684i	−0.543028	+	0.543028i
$424$		0			0
$425$	−19.9808	+	6.47087i	−0.969211	+	0.313883i
$426$		0			0
$427$	−4.67300	−	4.67300i	−0.226142	−	0.226142i
$428$		0			0
$429$			7.18973i			0.347123i
$430$		0			0
$431$		−	5.01988i		−	0.241799i	−0.992665	−	0.120899i	$-0.961422\pi$
$431$		−	5.01988i		−	0.241799i	0.992665	−	0.120899i	$-0.0385779\pi$
$432$		0			0
$433$	10.5692	+	10.5692i	0.507922	+	0.507922i	0.913888	−	0.405966i	$-0.133065\pi$
$433$	10.5692	+	10.5692i	0.507922	+	0.507922i	−0.405966	+	0.913888i	$0.633065\pi$
$434$		0			0
$435$	5.29532	+	8.65052i	0.253891	+	0.414761i
$436$		0			0
$437$	35.4395	−	35.4395i	1.69530	−	1.69530i
$438$		0			0
$439$	22.0536			1.05256			0.526281	−	0.850311i	$-0.323586\pi$
$439$	22.0536			1.05256			0.526281	+	0.850311i	$0.323586\pi$
$440$		0			0
$441$	−2.77796			−0.132284
$442$		0			0
$443$	3.29114	−	3.29114i	0.156367	−	0.156367i	−0.624588	−	0.780955i	$-0.714733\pi$
$443$	3.29114	−	3.29114i	0.156367	−	0.156367i	0.780955	+	0.624588i	$0.214733\pi$
$444$		0			0
$445$	−4.52299	+	18.7997i	−0.214410	+	0.891191i
$446$		0			0
$447$	0.851380	+	0.851380i	0.0402689	+	0.0402689i
$448$		0			0
$449$			4.98319i			0.235171i	0.993063	+	0.117586i	$0.0375154\pi$
$449$			4.98319i			0.235171i	−0.993063	+	0.117586i	$0.962485\pi$
$450$		0			0
$451$			34.5350i			1.62619i
$452$		0			0
$453$	−1.69661	−	1.69661i	−0.0797137	−	0.0797137i
$454$		0			0
$455$	2.09060	−	8.68954i	0.0980090	−	0.407372i
$456$		0			0
$457$	25.5710	−	25.5710i	1.19616	−	1.19616i	0.220852	−	0.975307i	$-0.429116\pi$
$457$	25.5710	−	25.5710i	1.19616	−	1.19616i	0.975307	−	0.220852i	$-0.0708839\pi$
$458$		0			0
$459$	11.4364			0.533806
$460$		0			0
$461$	23.0776			1.07483			0.537415	−	0.843318i	$-0.319401\pi$
$461$	23.0776			1.07483			0.537415	+	0.843318i	$0.319401\pi$
$462$		0			0
$463$	16.9238	−	16.9238i	0.786515	−	0.786515i	−0.194406	−	0.980921i	$-0.562278\pi$
$463$	16.9238	−	16.9238i	0.786515	−	0.786515i	0.980921	+	0.194406i	$0.0622780\pi$
$464$		0			0
$465$	2.19329	+	3.58299i	0.101711	+	0.166157i
$466$		0			0
$467$	22.7840	+	22.7840i	1.05432	+	1.05432i	0.998437	+	0.0558816i	$0.0177969\pi$
$467$	22.7840	+	22.7840i	1.05432	+	1.05432i	0.0558816	+	0.998437i	$0.482203\pi$
$468$		0			0
$469$			2.49964i			0.115423i
$470$		0			0
$471$			7.60168i			0.350267i
$472$		0			0
$473$	−29.0100	−	29.0100i	−1.33388	−	1.33388i
$474$		0			0
$475$	−25.9586	−	13.2581i	−1.19106	−	0.608323i
$476$		0			0
$477$	−5.78359	+	5.78359i	−0.264812	+	0.264812i
$478$		0			0
$479$	4.95663			0.226474			0.113237	−	0.993568i	$-0.463878\pi$
$479$	4.95663			0.226474			0.113237	+	0.993568i	$0.463878\pi$
$480$		0			0
$481$	8.51881			0.388424
$482$		0			0
$483$	2.86456	−	2.86456i	0.130342	−	0.130342i
$484$		0			0
$485$	−20.9752	+	12.8397i	−0.952433	+	0.583021i
$486$		0			0
$487$	−17.2990	−	17.2990i	−0.783890	−	0.783890i	0.196594	−	0.980485i	$-0.437012\pi$
$487$	−17.2990	−	17.2990i	−0.783890	−	0.783890i	−0.980485	+	0.196594i	$0.937012\pi$
$488$		0			0
$489$		−	5.57014i		−	0.251890i
$490$		0			0
$491$			33.3763i			1.50625i	0.657875	+	0.753127i	$0.271455\pi$
$491$			33.3763i			1.50625i	−0.657875	+	0.753127i	$0.728545\pi$
$492$		0			0
$493$	−28.5913	−	28.5913i	−1.28769	−	1.28769i
$494$		0			0
$495$	−23.0547	−	5.54670i	−1.03623	−	0.249306i
$496$		0			0
$497$	11.5848	−	11.5848i	0.519647	−	0.519647i
$498$		0			0
$499$	−1.33451			−0.0597409			−0.0298704	−	0.999554i	$-0.509509\pi$
$499$	−1.33451			−0.0597409			−0.0298704	+	0.999554i	$0.509509\pi$
$500$		0			0
$501$	−5.14518			−0.229870
$502$		0			0
$503$	6.91743	−	6.91743i	0.308433	−	0.308433i	−0.535868	−	0.844301i	$-0.680016\pi$
$503$	6.91743	−	6.91743i	0.308433	−	0.308433i	0.844301	+	0.535868i	$0.180016\pi$
$504$		0			0
$505$	−0.299054	−	0.0719490i	−0.0133077	−	0.00320169i
$506$		0			0
$507$	−0.991508	−	0.991508i	−0.0440344	−	0.0440344i
$508$		0			0
$509$		−	17.9574i		−	0.795948i	−0.917397	−	0.397974i	$-0.869713\pi$
$509$		−	17.9574i		−	0.795948i	0.917397	−	0.397974i	$-0.130287\pi$
$510$		0			0
$511$			10.6627i			0.471689i
$512$		0			0
$513$	11.2232	+	11.2232i	0.495518	+	0.495518i
$514$		0			0
$515$	29.9897	−	18.3578i	1.32150	−	0.808942i
$516$		0			0
$517$	15.3474	−	15.3474i	0.674977	−	0.674977i
$518$		0			0
$519$	2.74338			0.120421
$520$		0			0
$521$	−4.98311			−0.218314			−0.109157	−	0.994025i	$-0.534815\pi$
$521$	−4.98311			−0.218314			−0.109157	+	0.994025i	$0.534815\pi$
$522$		0			0
$523$	25.4478	−	25.4478i	1.11275	−	1.11275i	0.119978	−	0.992777i	$-0.461717\pi$
$523$	25.4478	−	25.4478i	1.11275	−	1.11275i	0.992777	−	0.119978i	$-0.0382825\pi$
$524$		0			0
$525$	−2.09822	−	1.07165i	−0.0915740	−	0.0467705i
$526$		0			0
$527$	−11.8424	−	11.8424i	−0.515861	−	0.515861i
$528$		0			0
$529$		−	50.9125i		−	2.21359i
$530$		0			0
$531$		−	3.62966i		−	0.157514i
$532$		0			0
$533$	−25.5686	−	25.5686i	−1.10750	−	1.10750i
$534$		0			0
$535$	2.84060	+	4.64046i	0.122810	+	0.200625i
$536$		0			0
$537$	−0.372504	+	0.372504i	−0.0160747	+	0.0160747i
$538$		0			0
$539$	3.81740			0.164427
$540$		0			0
$541$	25.6523			1.10288			0.551439	−	0.834215i	$-0.314079\pi$
$541$	25.6523			1.10288			0.551439	+	0.834215i	$0.314079\pi$
$542$		0			0
$543$	−1.07331	+	1.07331i	−0.0460603	+	0.0460603i
$544$		0			0
$545$	1.36150	−	5.65905i	0.0583203	−	0.242407i
$546$		0			0
$547$	16.0308	+	16.0308i	0.685427	+	0.685427i	0.961218	−	0.275791i	$-0.0889397\pi$
$547$	16.0308	+	16.0308i	0.685427	+	0.685427i	−0.275791	+	0.961218i	$0.588940\pi$
$548$		0			0
$549$		−	18.3585i		−	0.783521i
$550$		0			0
$551$		−	56.1168i		−	2.39065i
$552$		0			0
$553$	3.42396	+	3.42396i	0.145602	+	0.145602i
$554$		0			0
$555$	0.525296	−	2.18338i	0.0222976	−	0.0926793i
$556$		0			0
$557$	−21.1371	+	21.1371i	−0.895609	+	0.895609i	−0.995044	−	0.0994352i	$-0.968296\pi$
$557$	−21.1371	+	21.1371i	−0.895609	+	0.895609i	0.0994352	+	0.995044i	$0.468296\pi$
$558$		0			0
$559$	42.9562			1.81685
$560$		0			0
$561$	−7.55584			−0.319008
$562$		0			0
$563$	15.6782	−	15.6782i	0.660756	−	0.660756i	−0.294802	−	0.955558i	$-0.595254\pi$
$563$	15.6782	−	15.6782i	0.660756	−	0.660756i	0.955558	+	0.294802i	$0.0952537\pi$
$564$		0			0
$565$	−7.66152	−	12.5160i	−0.322323	−	0.526552i
$566$		0			0
$567$	−4.98578	−	4.98578i	−0.209383	−	0.209383i
$568$		0			0
$569$		−	18.9016i		−	0.792398i	−0.918165	−	0.396199i	$-0.870329\pi$
$569$		−	18.9016i		−	0.792398i	0.918165	−	0.396199i	$-0.129671\pi$
$570$		0			0
$571$			31.8188i			1.33158i	0.746141	+	0.665788i	$0.231904\pi$
$571$			31.8188i			1.33158i	−0.746141	+	0.665788i	$0.768096\pi$
$572$		0			0
$573$	−2.89255	−	2.89255i	−0.120838	−	0.120838i
$574$		0			0
$575$	−40.8951	+	13.2441i	−1.70544	+	0.552315i
$576$		0			0
$577$	−25.9993	+	25.9993i	−1.08236	+	1.08236i	−0.0860749	+	0.996289i	$0.527432\pi$
$577$	−25.9993	+	25.9993i	−1.08236	+	1.08236i	−0.996289	+	0.0860749i	$0.972568\pi$
$578$		0			0
$579$	−3.13093			−0.130117
$580$		0			0
$581$	−0.198171			−0.00822150
$582$		0			0
$583$	7.94765	−	7.94765i	0.329158	−	0.329158i
$584$		0			0
$585$	21.1756	−	12.9624i	0.875503	−	0.535929i
$586$		0			0
$587$	23.1808	+	23.1808i	0.956773	+	0.956773i	0.999104	−	0.0423309i	$-0.0134784\pi$
$587$	23.1808	+	23.1808i	0.956773	+	0.956773i	−0.0423309	+	0.999104i	$0.513478\pi$
$588$		0			0
$589$		−	23.2432i		−	0.957720i
$590$		0			0
$591$			0.244853i			0.0100719i
$592$		0			0
$593$	2.87270	+	2.87270i	0.117968	+	0.117968i	0.763626	−	0.645659i	$-0.223417\pi$
$593$	2.87270	+	2.87270i	0.117968	+	0.117968i	−0.645659	+	0.763626i	$0.723417\pi$
$594$		0			0
$595$	9.13202	+	2.19706i	0.374376	+	0.0900706i
$596$		0			0
$597$	−4.67603	+	4.67603i	−0.191377	+	0.191377i
$598$		0			0
$599$	−15.3151			−0.625757			−0.312878	−	0.949793i	$-0.601293\pi$
$599$	−15.3151			−0.625757			−0.312878	+	0.949793i	$0.601293\pi$
$600$		0			0
$601$	0.00274728			0.000112064			5.60320e−5	−	1.00000i	$-0.499982\pi$
$601$	0.00274728			0.000112064			5.60320e−5		1.00000i	$0.499982\pi$
$602$		0			0
$603$	−4.91007	+	4.91007i	−0.199954	+	0.199954i
$604$		0			0
$605$	7.76680	+	1.86860i	0.315765	+	0.0759695i
$606$		0			0
$607$	34.7364	+	34.7364i	1.40991	+	1.40991i	0.760091	+	0.649817i	$0.225155\pi$
$607$	34.7364	+	34.7364i	1.40991	+	1.40991i	0.649817	+	0.760091i	$0.274845\pi$
$608$		0			0
$609$		−	4.53590i		−	0.183804i
$610$		0			0
$611$			22.7254i			0.919373i
$612$		0			0
$613$	3.06336	+	3.06336i	0.123728	+	0.123728i	0.766259	−	0.642531i	$-0.222116\pi$
$613$	3.06336	+	3.06336i	0.123728	+	0.123728i	−0.642531	+	0.766259i	$0.722116\pi$
$614$		0			0
$615$	−8.12990	+	4.97662i	−0.327829	+	0.200677i
$616$		0			0
$617$	−9.24856	+	9.24856i	−0.372333	+	0.372333i	−0.868326	−	0.495993i	$-0.834804\pi$
$617$	−9.24856	+	9.24856i	−0.372333	+	0.372333i	0.495993	+	0.868326i	$0.334804\pi$
$618$		0			0
$619$	11.4110			0.458647			0.229323	−	0.973350i	$-0.426349\pi$
$619$	11.4110			0.458647			0.229323	+	0.973350i	$0.426349\pi$
$620$		0			0
$621$	23.4071			0.939296
$622$		0			0
$623$	6.11462	−	6.11462i	0.244977	−	0.244977i
$624$		0			0
$625$	14.6556	+	20.2537i	0.586225	+	0.810148i
$626$		0			0
$627$	−7.41499	−	7.41499i	−0.296126	−	0.296126i
$628$		0			0
$629$			8.95260i			0.356963i
$630$		0			0
$631$			11.5223i			0.458694i	0.973345	+	0.229347i	$0.0736591\pi$
$631$			11.5223i			0.458694i	−0.973345	+	0.229347i	$0.926341\pi$
$632$		0			0
$633$	5.09737	+	5.09737i	0.202602	+	0.202602i
$634$		0			0
$635$	−16.0755	−	26.2612i	−0.637935	−	1.04214i
$636$		0			0
$637$	−2.82628	+	2.82628i	−0.111981	+	0.111981i
$638$		0			0
$639$	45.5122			1.80044
$640$		0			0
$641$	41.4926			1.63886			0.819429	−	0.573180i	$-0.194291\pi$
$641$	41.4926			1.63886			0.819429	+	0.573180i	$0.194291\pi$
$642$		0			0
$643$	0.262424	−	0.262424i	0.0103490	−	0.0103490i	−0.701913	−	0.712262i	$-0.747671\pi$
$643$	0.262424	−	0.262424i	0.0103490	−	0.0103490i	0.712262	+	0.701913i	$0.247671\pi$
$644$		0			0
$645$	2.64881	−	11.0097i	0.104297	−	0.433507i
$646$		0			0
$647$	−16.3573	−	16.3573i	−0.643072	−	0.643072i	0.308237	−	0.951309i	$-0.400261\pi$
$647$	−16.3573	−	16.3573i	−0.643072	−	0.643072i	−0.951309	+	0.308237i	$0.900261\pi$
$648$		0			0
$649$			4.98777i			0.195787i
$650$		0			0
$651$		−	1.87874i		−	0.0736337i
$652$		0			0
$653$	5.04424	+	5.04424i	0.197397	+	0.197397i	0.798883	−	0.601486i	$-0.205425\pi$
$653$	5.04424	+	5.04424i	0.197397	+	0.197397i	−0.601486	+	0.798883i	$0.705425\pi$
$654$		0			0
$655$	−2.76033	+	11.4733i	−0.107855	+	0.448297i
$656$		0			0
$657$	−20.9449	+	20.9449i	−0.817137	+	0.817137i
$658$		0			0
$659$	−25.0645			−0.976374			−0.488187	−	0.872739i	$-0.662342\pi$
$659$	−25.0645			−0.976374			−0.488187	+	0.872739i	$0.662342\pi$
$660$		0			0
$661$	2.39811			0.0932757			0.0466378	−	0.998912i	$-0.485149\pi$
$661$	2.39811			0.0932757			0.0466378	+	0.998912i	$0.485149\pi$
$662$		0			0
$663$	5.59411	−	5.59411i	0.217257	−	0.217257i
$664$		0			0
$665$	6.80569	+	11.1179i	0.263913	+	0.431134i
$666$		0			0
$667$	−58.5185	−	58.5185i	−2.26584	−	2.26584i
$668$		0			0
$669$		−	6.59226i		−	0.254872i
$670$		0			0
$671$			25.2277i			0.973906i
$672$		0			0
$673$	−28.7100	−	28.7100i	−1.10669	−	1.10669i	−0.993583	−	0.113105i	$-0.963920\pi$
$673$	−28.7100	−	28.7100i	−1.10669	−	1.10669i	−0.113105	−	0.993583i	$-0.536080\pi$
$674$		0			0
$675$	−4.19422	−	12.9509i	−0.161436	−	0.498482i
$676$		0			0
$677$	−20.1474	+	20.1474i	−0.774328	+	0.774328i	−0.978860	−	0.204532i	$-0.934433\pi$
$677$	−20.1474	+	20.1474i	−0.774328	+	0.774328i	0.204532	+	0.978860i	$0.434433\pi$
$678$		0			0
$679$	10.9983			0.422077
$680$		0			0
$681$	−0.378138			−0.0144903
$682$		0			0
$683$	−28.9562	+	28.9562i	−1.10798	+	1.10798i	−0.114562	+	0.993416i	$0.536547\pi$
$683$	−28.9562	+	28.9562i	−1.10798	+	1.10798i	−0.993416	+	0.114562i	$0.963453\pi$
$684$		0			0
$685$	−28.0761	+	17.1864i	−1.07273	+	0.656660i
$686$		0			0
$687$	−3.92112	−	3.92112i	−0.149600	−	0.149600i
$688$		0			0
$689$			11.7684i			0.448340i
$690$		0			0
$691$		−	36.1260i		−	1.37430i	−0.726517	−	0.687149i	$-0.758862\pi$
$691$		−	36.1260i		−	1.37430i	0.726517	−	0.687149i	$-0.241138\pi$
$692$		0			0
$693$	7.49857	+	7.49857i	0.284847	+	0.284847i
$694$		0			0
$695$	46.8546	+	11.2727i	1.77729	+	0.427597i
$696$		0			0
$697$	26.8706	−	26.8706i	1.01780	−	1.01780i
$698$		0			0
$699$	−1.28609			−0.0486444
$700$		0			0
$701$	18.3685			0.693768			0.346884	−	0.937908i	$-0.387240\pi$
$701$	18.3685			0.693768			0.346884	+	0.937908i	$0.387240\pi$
$702$		0			0
$703$	−8.78571	+	8.78571i	−0.331359	+	0.331359i
$704$		0			0
$705$	5.82455	+	1.40132i	0.219365	+	0.0527767i
$706$		0			0
$707$	0.0972678	+	0.0972678i	0.00365813	+	0.00365813i
$708$		0			0
$709$			6.15273i			0.231071i	0.993303	+	0.115535i	$0.0368583\pi$
$709$			6.15273i			0.231071i	−0.993303	+	0.115535i	$0.963142\pi$
$710$		0			0
$711$			13.4515i			0.504470i
$712$		0			0
$713$	−24.2380	−	24.2380i	−0.907720	−	0.907720i
$714$		0			0
$715$	−29.0989	+	17.8126i	−1.08824	+	0.666152i
$716$		0			0
$717$	−3.95912	+	3.95912i	−0.147856	+	0.147856i
$718$		0			0
$719$	−20.8753			−0.778516			−0.389258	−	0.921129i	$-0.627269\pi$
$719$	−20.8753			−0.778516			−0.389258	+	0.921129i	$0.627269\pi$
$720$		0			0
$721$	−15.7251			−0.585632
$722$		0			0
$723$	0.0275325	−	0.0275325i	0.00102394	−	0.00102394i
$724$		0			0
$725$	−21.8920	+	42.8634i	−0.813050	+	1.59191i
$726$		0			0
$727$	−11.4058	−	11.4058i	−0.423018	−	0.423018i	0.463224	−	0.886241i	$-0.346693\pi$
$727$	−11.4058	−	11.4058i	−0.423018	−	0.423018i	−0.886241	+	0.463224i	$0.846693\pi$
$728$		0			0
$729$		−	15.7385i		−	0.582906i
$730$		0			0
$731$			45.1435i			1.66969i
$732$		0			0
$733$	15.7765	+	15.7765i	0.582720	+	0.582720i	0.935650	−	0.352930i	$-0.114815\pi$
$733$	15.7765	+	15.7765i	0.582720	+	0.582720i	−0.352930	+	0.935650i	$0.614815\pi$
$734$		0			0
$735$	0.550102	+	0.898656i	0.0202908	+	0.0331474i
$736$		0			0
$737$	6.74729	−	6.74729i	0.248540	−	0.248540i
$738$		0			0
$739$	−21.4438			−0.788821			−0.394411	−	0.918934i	$-0.629051\pi$
$739$	−21.4438			−0.788821			−0.394411	+	0.918934i	$0.629051\pi$
$740$		0			0
$741$	10.9797			0.403348
$742$		0			0
$743$	−36.7547	+	36.7547i	−1.34840	+	1.34840i	−0.460999	+	0.887401i	$0.652509\pi$
$743$	−36.7547	+	36.7547i	−1.34840	+	1.34840i	−0.887401	+	0.460999i	$0.847491\pi$
$744$		0			0
$745$	−1.33649	+	5.55508i	−0.0489651	+	0.203522i
$746$		0			0
$747$	−0.389269	−	0.389269i	−0.0142426	−	0.0142426i
$748$		0			0
$749$		−	2.43323i		−	0.0889081i
$750$		0			0
$751$		−	45.0404i		−	1.64355i	−0.569814	−	0.821773i	$-0.692985\pi$
$751$		−	45.0404i		−	1.64355i	0.569814	−	0.821773i	$-0.307015\pi$
$752$		0			0
$753$	−7.17739	−	7.17739i	−0.261559	−	0.261559i
$754$		0			0
$755$	2.66332	−	11.0700i	0.0969282	−	0.402880i
$756$		0			0
$757$	−15.5287	+	15.5287i	−0.564402	+	0.564402i	−0.930555	−	0.366153i	$-0.880675\pi$
$757$	−15.5287	+	15.5287i	−0.564402	+	0.564402i	0.366153	+	0.930555i	$0.380675\pi$
$758$		0			0
$759$	−15.4647			−0.561332
$760$		0			0
$761$	48.8503			1.77082			0.885410	−	0.464810i	$-0.153877\pi$
$761$	48.8503			1.77082			0.885410	+	0.464810i	$0.153877\pi$
$762$		0			0
$763$	−1.84061	+	1.84061i	−0.0666346	+	0.0666346i
$764$		0			0
$765$	13.6225	+	22.2539i	0.492521	+	0.804591i
$766$		0			0
$767$	−3.69279	−	3.69279i	−0.133339	−	0.133339i
$768$		0			0
$769$			42.0179i			1.51520i	0.652717	+	0.757602i	$0.273629\pi$
$769$			42.0179i			1.51520i	−0.652717	+	0.757602i	$0.726371\pi$
$770$		0			0
$771$			1.53260i			0.0551952i
$772$		0			0
$773$	22.2873	+	22.2873i	0.801617	+	0.801617i	0.983348	−	0.181731i	$-0.0581700\pi$
$773$	22.2873	+	22.2873i	0.801617	+	0.801617i	−0.181731	+	0.983348i	$0.558170\pi$
$774$		0			0
$775$	−9.06755	+	17.7538i	−0.325716	+	0.637734i
$776$		0			0
$777$	−0.710146	+	0.710146i	−0.0254764	+	0.0254764i
$778$		0			0
$779$	52.7394			1.88959
$780$		0			0
$781$	−62.5416			−2.23792
$782$		0			0
$783$	18.5320	−	18.5320i	0.662281	−	0.662281i
$784$		0			0
$785$	−30.7662	+	18.8332i	−1.09809	+	0.672185i
$786$		0			0
$787$	7.02249	+	7.02249i	0.250325	+	0.250325i	0.821104	−	0.570779i	$-0.193359\pi$
$787$	7.02249	+	7.02249i	0.250325	+	0.250325i	−0.570779	+	0.821104i	$0.693359\pi$
$788$		0			0
$789$		−	4.70889i		−	0.167641i
$790$		0			0
$791$			6.56276i			0.233345i
$792$		0			0
$793$	−18.6778	−	18.6778i	−0.663269	−	0.663269i
$794$		0			0
$795$	3.01625	+	0.725674i	0.106975	+	0.0257370i
$796$		0			0
$797$	32.5655	−	32.5655i	1.15353	−	1.15353i	0.167689	−	0.985840i	$-0.446370\pi$
$797$	32.5655	−	32.5655i	1.15353	−	1.15353i	0.985840	−	0.167689i	$-0.0536305\pi$
$798$		0			0
$799$	−23.8826			−0.844907
$800$		0			0
$801$	24.0221			0.848779
$802$		0			0
$803$	28.7819	−	28.7819i	1.01569	−	1.01569i
$804$		0			0
$805$	18.6907	+	4.49676i	0.658760	+	0.158490i
$806$		0			0
$807$	−6.31577	−	6.31577i	−0.222326	−	0.222326i
$808$		0			0
$809$			37.1322i			1.30550i	0.757574	+	0.652749i	$0.226385\pi$
$809$			37.1322i			1.30550i	−0.757574	+	0.652749i	$0.773615\pi$
$810$		0			0
$811$		−	38.6853i		−	1.35842i	−0.733942	−	0.679212i	$-0.762322\pi$
$811$		−	38.6853i		−	1.35842i	0.733942	−	0.679212i	$-0.237678\pi$
$812$		0			0
$813$	2.09660	+	2.09660i	0.0735308	+	0.0735308i
$814$		0			0
$815$	22.5440	−	13.8000i	0.789681	−	0.483394i
$816$		0			0
$817$	−44.3020	+	44.3020i	−1.54993	+	1.54993i
$818$		0			0
$819$	−11.1034			−0.387985
$820$		0			0
$821$	4.64526			0.162121			0.0810604	−	0.996709i	$-0.474169\pi$
$821$	4.64526			0.162121			0.0810604	+	0.996709i	$0.474169\pi$
$822$		0			0
$823$	1.06410	−	1.06410i	0.0370922	−	0.0370922i	−0.688317	−	0.725410i	$-0.741650\pi$
$823$	1.06410	−	1.06410i	0.0370922	−	0.0370922i	0.725410	+	0.688317i	$0.241650\pi$
$824$		0			0
$825$	2.77105	+	8.55646i	0.0964755	+	0.297898i
$826$		0			0
$827$	23.7207	+	23.7207i	0.824848	+	0.824848i	0.986799	−	0.161951i	$-0.0517786\pi$
$827$	23.7207	+	23.7207i	0.824848	+	0.824848i	−0.161951	+	0.986799i	$0.551779\pi$
$828$		0			0
$829$		−	26.1640i		−	0.908712i	−0.890820	−	0.454356i	$-0.849869\pi$
$829$		−	26.1640i		−	0.908712i	0.890820	−	0.454356i	$-0.150131\pi$
$830$		0			0
$831$		−	6.60115i		−	0.228991i
$832$		0			0
$833$	−2.97020	−	2.97020i	−0.102911	−	0.102911i
$834$		0			0
$835$	−12.7472	−	20.8240i	−0.441135	−	0.720646i
$836$		0			0
$837$	7.67586	−	7.67586i	0.265316	−	0.265316i
$838$		0			0
$839$	−13.6861			−0.472497			−0.236248	−	0.971693i	$-0.575918\pi$
$839$	−13.6861			−0.472497			−0.236248	+	0.971693i	$0.575918\pi$
$840$		0			0
$841$	−63.6612			−2.19521
$842$		0			0
$843$	−5.34003	+	5.34003i	−0.183920	+	0.183920i
$844$		0			0
$845$	1.55646	−	6.46939i	0.0535438	−	0.222554i
$846$		0			0
$847$	−2.52616	−	2.52616i	−0.0867999	−	0.0867999i
$848$		0			0
$849$		−	7.49439i		−	0.257207i
$850$		0			0
$851$			18.3235i			0.628120i
$852$		0			0
$853$	27.6605	+	27.6605i	0.947078	+	0.947078i	0.998668	−	0.0515899i	$-0.0164289\pi$
$853$	27.6605	+	27.6605i	0.947078	+	0.947078i	−0.0515899	+	0.998668i	$0.516429\pi$
$854$		0			0
$855$	−8.47053	+	35.2076i	−0.289686	+	1.20407i
$856$		0			0
$857$	13.1713	−	13.1713i	0.449924	−	0.449924i	−0.445405	−	0.895329i	$-0.646940\pi$
$857$	13.1713	−	13.1713i	0.449924	−	0.449924i	0.895329	+	0.445405i	$0.146940\pi$
$858$		0			0
$859$	10.4624			0.356972			0.178486	−	0.983942i	$-0.442880\pi$
$859$	10.4624			0.356972			0.178486	+	0.983942i	$0.442880\pi$
$860$		0			0
$861$	4.26291			0.145280
$862$		0			0
$863$	−21.3600	+	21.3600i	−0.727104	+	0.727104i	−0.970042	−	0.242938i	$-0.921889\pi$
$863$	−21.3600	+	21.3600i	−0.727104	+	0.727104i	0.242938	+	0.970042i	$0.421889\pi$
$864$		0			0
$865$	6.79673	+	11.1033i	0.231096	+	0.377522i
$866$		0			0
$867$	0.214635	+	0.214635i	0.00728938	+	0.00728938i
$868$		0			0
$869$		−	18.4847i		−	0.627049i
$870$		0			0
$871$			9.99097i			0.338531i
$872$		0			0
$873$	21.6042	+	21.6042i	0.731191	+	0.731191i
$874$		0			0
$875$	−0.861087	−	11.1471i	−0.0291100	−	0.376842i
$876$		0			0
$877$	−10.4351	+	10.4351i	−0.352367	+	0.352367i	−0.860990	−	0.508623i	$-0.830155\pi$
$877$	−10.4351	+	10.4351i	−0.352367	+	0.352367i	0.508623	+	0.860990i	$0.330155\pi$
$878$		0			0
$879$	0.0407904			0.00137583
$880$		0			0
$881$	39.8293			1.34188			0.670941	−	0.741511i	$-0.265890\pi$
$881$	39.8293			1.34188			0.670941	+	0.741511i	$0.265890\pi$
$882$		0			0
$883$	−29.3264	+	29.3264i	−0.986911	+	0.986911i	−0.999915	−	0.0130045i	$-0.995860\pi$
$883$	−29.3264	+	29.3264i	−0.986911	+	0.986911i	0.0130045	+	0.999915i	$0.495860\pi$
$884$		0			0
$885$	−1.17417	+	0.718757i	−0.0394694	+	0.0241608i
$886$		0			0
$887$	20.8366	+	20.8366i	0.699626	+	0.699626i	0.964330	−	0.264704i	$-0.0852743\pi$
$887$	20.8366	+	20.8366i	0.699626	+	0.699626i	−0.264704	+	0.964330i	$0.585274\pi$
$888$		0			0
$889$			13.7700i			0.461832i
$890$		0			0
$891$			26.9163i			0.901730i
$892$		0			0
$893$	−23.4374	−	23.4374i	−0.784304	−	0.784304i
$894$		0			0
$895$	−2.43051	−	0.584753i	−0.0812430	−	0.0195461i
$896$		0			0
$897$	11.4496	−	11.4496i	0.382290	−	0.382290i
$898$		0			0
$899$	−38.3797			−1.28003
$900$		0			0
$901$	−12.3676			−0.412026
$902$		0			0
$903$	−3.58092	+	3.58092i	−0.119165	+	0.119165i
$904$		0			0
$905$	−7.00315	−	1.68488i	−0.232792	−	0.0560072i
$906$		0			0
$907$	−7.86316	−	7.86316i	−0.261092	−	0.261092i	0.564406	−	0.825498i	$-0.309105\pi$
$907$	−7.86316	−	7.86316i	−0.261092	−	0.261092i	−0.825498	+	0.564406i	$0.809105\pi$
$908$		0			0
$909$			0.382129i			0.0126744i
$910$		0			0
$911$			6.94201i			0.229999i	0.993366	+	0.115000i	$0.0366867\pi$
$911$			6.94201i			0.229999i	−0.993366	+	0.115000i	$0.963313\pi$
$912$		0			0
$913$	0.534923	+	0.534923i	0.0177034	+	0.0177034i
$914$		0			0
$915$	−5.93888	+	3.63541i	−0.196333	+	0.120183i
$916$		0			0
$917$	3.73169	−	3.73169i	0.123231	−	0.123231i
$918$		0			0
$919$	−8.93888			−0.294867			−0.147433	−	0.989072i	$-0.547101\pi$
$919$	−8.93888			−0.294867			−0.147433	+	0.989072i	$0.547101\pi$
$920$		0			0
$921$	−1.37923			−0.0454471
$922$		0			0
$923$	46.3039	−	46.3039i	1.52411	−	1.52411i
$924$		0			0
$925$	10.1382	−	3.28330i	0.333342	−	0.107954i
$926$		0			0
$927$	−30.8890	−	30.8890i	−1.01453	−	1.01453i
$928$		0			0
$929$			9.13928i			0.299850i	0.988697	+	0.149925i	$0.0479032\pi$
$929$			9.13928i			0.299850i	−0.988697	+	0.149925i	$0.952097\pi$
$930$		0			0
$931$		−	5.82967i		−	0.191060i
$932$		0			0
$933$	1.90365	+	1.90365i	0.0623226	+	0.0623226i
$934$		0			0
$935$	−18.7196	−	30.5807i	−0.612196	−	1.00009i
$936$		0			0
$937$	−17.7955	+	17.7955i	−0.581354	+	0.581354i	−0.935275	−	0.353921i	$-0.884848\pi$
$937$	−17.7955	+	17.7955i	−0.581354	+	0.581354i	0.353921	+	0.935275i	$0.384848\pi$
$938$		0			0
$939$	−8.62662			−0.281519
$940$		0			0
$941$	0.510241			0.0166334			0.00831668	−	0.999965i	$-0.497353\pi$
$941$	0.510241			0.0166334			0.00831668	+	0.999965i	$0.497353\pi$
$942$		0			0
$943$	54.9966	−	54.9966i	1.79093	−	1.79093i
$944$		0			0
$945$	−1.42407	+	5.91910i	−0.0463249	+	0.192548i
$946$		0			0
$947$	8.77672	+	8.77672i	0.285205	+	0.285205i	0.835181	−	0.549976i	$-0.185363\pi$
$947$	8.77672	+	8.77672i	0.285205	+	0.285205i	−0.549976	+	0.835181i	$0.685363\pi$
$948$		0			0
$949$			42.6184i			1.38345i
$950$		0			0
$951$		−	1.61466i		−	0.0523590i
$952$		0			0
$953$	33.7810	+	33.7810i	1.09427	+	1.09427i	0.995067	+	0.0992066i	$0.0316305\pi$
$953$	33.7810	+	33.7810i	1.09427	+	1.09427i	0.0992066	+	0.995067i	$0.468370\pi$
$954$		0			0
$955$	4.54070	−	18.8733i	0.146934	−	0.610726i
$956$		0			0
$957$	−12.2438	+	12.2438i	−0.395785	+	0.395785i
$958$		0			0
$959$	14.7217			0.475388
$960$		0			0
$961$	15.1034			0.487205
$962$		0			0
$963$	4.77962	−	4.77962i	0.154021	−	0.154021i
$964$		0			0
$965$	−7.75689	−	12.6718i	−0.249703	−	0.407919i
$966$		0			0
$967$	−11.0215	−	11.0215i	−0.354428	−	0.354428i	0.507326	−	0.861754i	$-0.330634\pi$
$967$	−11.0215	−	11.0215i	−0.354428	−	0.354428i	−0.861754	+	0.507326i	$0.830634\pi$
$968$		0			0
$969$			11.5387i			0.370678i
$970$		0			0
$971$		−	3.58041i		−	0.114901i	−0.998348	−	0.0574504i	$-0.981703\pi$
$971$		−	3.58041i		−	0.114901i	0.998348	−	0.0574504i	$-0.0182971\pi$
$972$		0			0
$973$	−15.2395	−	15.2395i	−0.488556	−	0.488556i
$974$		0			0
$975$	−8.38653	−	4.28334i	−0.268584	−	0.137177i
$976$		0			0
$977$	42.4459	−	42.4459i	1.35796	−	1.35796i	0.481540	−	0.876424i	$-0.340078\pi$
$977$	42.4459	−	42.4459i	1.35796	−	1.35796i	0.876424	−	0.481540i	$-0.159922\pi$
$978$		0			0
$979$	−33.0105			−1.05502
$980$		0			0
$981$	−7.23108			−0.230871
$982$		0			0
$983$	−41.9216	+	41.9216i	−1.33709	+	1.33709i	−0.438228	+	0.898864i	$0.644394\pi$
$983$	−41.9216	+	41.9216i	−1.33709	+	1.33709i	−0.898864	+	0.438228i	$0.855606\pi$
$984$		0			0
$985$	−0.990993	+	0.606624i	−0.0315756	+	0.0193287i
$986$		0			0
$987$	−1.89444	−	1.89444i	−0.0603007	−	0.0603007i
$988$		0			0
$989$			92.3961i			2.93803i
$990$		0			0
$991$			61.0367i			1.93889i	0.245300	+	0.969447i	$0.421113\pi$
$991$			61.0367i			1.93889i	−0.245300	+	0.969447i	$0.578887\pi$
$992$		0			0
$993$	−6.47662	−	6.47662i	−0.205529	−	0.205529i
$994$		0			0
$995$	−30.5101	−	7.34039i	−0.967237	−	0.232706i
$996$		0			0
$997$	−30.2374	+	30.2374i	−0.957629	+	0.957629i	−0.999138	−	0.0415091i	$-0.986783\pi$
$997$	−30.2374	+	30.2374i	−0.957629	+	0.957629i	0.0415091	+	0.999138i	$0.486783\pi$
$998$		0			0
$999$	−5.80280			−0.183592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.b.463.5	yes	24
4.3	odd	2	inner	560.2.x.b.463.8	yes	24
5.2	odd	4	inner	560.2.x.b.127.8	yes	24
20.7	even	4	inner	560.2.x.b.127.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.b.127.5	✓	24	20.7	even	4	inner
560.2.x.b.127.8	yes	24	5.2	odd	4	inner
560.2.x.b.463.5	yes	24	1.1	even	1	trivial
560.2.x.b.463.8	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.333196 + 0.333196i) q^{3} +(-2.17403 - 0.523047i) q^{5} +(0.707107 + 0.707107i) q^{7} +2.77796i q^{9} +O(q^{10})\)	\(q+(-0.333196 + 0.333196i) q^{3} +(-2.17403 - 0.523047i) q^{5} +(0.707107 + 0.707107i) q^{7} +2.77796i q^{9} -3.81740i q^{11} +(2.82628 + 2.82628i) q^{13} +(0.898656 - 0.550102i) q^{15} +(-2.97020 + 2.97020i) q^{17} -5.82967 q^{19} -0.471210 q^{21} +(-6.07917 + 6.07917i) q^{23} +(4.45284 + 2.27424i) q^{25} +(-1.92519 - 1.92519i) q^{27} +9.62607i q^{29} +3.98706i q^{31} +(1.27194 + 1.27194i) q^{33} +(-1.16742 - 1.90712i) q^{35} +(1.50707 - 1.50707i) q^{37} -1.88341 q^{39} -9.04673 q^{41} +(7.59941 - 7.59941i) q^{43} +(1.45301 - 6.03938i) q^{45} +(4.02037 + 4.02037i) q^{47} +1.00000i q^{49} -1.97932i q^{51} +(2.08195 + 2.08195i) q^{53} +(-1.99668 + 8.29915i) q^{55} +(1.94242 - 1.94242i) q^{57} -1.30659 q^{59} -6.60862 q^{61} +(-1.96432 + 1.96432i) q^{63} +(-4.66615 - 7.62271i) q^{65} +(1.76751 + 1.76751i) q^{67} -4.05110i q^{69} -16.3833i q^{71} +(7.53966 + 7.53966i) q^{73} +(-2.24144 + 0.725900i) q^{75} +(2.69931 - 2.69931i) q^{77} +4.84221 q^{79} -7.05095 q^{81} +(-0.140128 + 0.140128i) q^{83} +(8.01087 - 4.90376i) q^{85} +(-3.20736 - 3.20736i) q^{87} -8.64739i q^{89} +3.99697i q^{91} +(-1.32847 - 1.32847i) q^{93} +(12.6739 + 3.04919i) q^{95} +(7.77699 - 7.77699i) q^{97} +10.6046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{13} + 8 q^{17} - 8 q^{21} + 32 q^{25} + 24 q^{33} - 16 q^{37} + 32 q^{41} - 24 q^{45} + 8 q^{53} + 40 q^{57} + 16 q^{61} - 16 q^{73} + 16 q^{77} - 104 q^{81} - 8 q^{85} - 8 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 8 * q^13 + 8 * q^17 - 8 * q^21 + 32 * q^25 + 24 * q^33 - 16 * q^37 + 32 * q^41 - 24 * q^45 + 8 * q^53 + 40 * q^57 + 16 * q^61 - 16 * q^73 + 16 * q^77 - 104 * q^81 - 8 * q^85 - 8 * q^93 - 24 * q^97

Introduction

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Modular forms

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Database

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