LMFDB - Embedded newform 560.2.x.b.463.4

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			463.4
Character	$\chi$	$=$	560.463
Dual form			560.2.x.b.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.636375 + 0.636375i) q^{3} +(1.68320 + 1.47202i) q^{5} +(-0.707107 - 0.707107i) q^{7} +2.19005i q^{9} +O(q^{10})$	\(q+(-0.636375 + 0.636375i) q^{3} +(1.68320 + 1.47202i) q^{5} +(-0.707107 - 0.707107i) q^{7} +2.19005i q^{9} -0.0126062i q^{11} +(1.39232 + 1.39232i) q^{13} +(-2.00790 + 0.134388i) q^{15} +(-1.83069 + 1.83069i) q^{17} +1.25703 q^{19} +0.899970 q^{21} +(-0.761068 + 0.761068i) q^{23} +(0.666311 + 4.95540i) q^{25} +(-3.30282 - 3.30282i) q^{27} -1.27726i q^{29} +8.86198i q^{31} +(0.00802225 + 0.00802225i) q^{33} +(-0.149325 - 2.23108i) q^{35} +(-0.649549 + 0.649549i) q^{37} -1.77207 q^{39} +5.52580 q^{41} +(-4.70260 + 4.70260i) q^{43} +(-3.22380 + 3.68629i) q^{45} +(2.07793 + 2.07793i) q^{47} +1.00000i q^{49} -2.33001i q^{51} +(-2.69362 - 2.69362i) q^{53} +(0.0185565 - 0.0212187i) q^{55} +(-0.799940 + 0.799940i) q^{57} +0.236325 q^{59} +12.3491 q^{61} +(1.54860 - 1.54860i) q^{63} +(0.294026 + 4.39307i) q^{65} +(-4.86571 - 4.86571i) q^{67} -0.968650i q^{69} +12.9813i q^{71} +(-4.87625 - 4.87625i) q^{73} +(-3.57752 - 2.72947i) q^{75} +(-0.00891390 + 0.00891390i) q^{77} +10.0991 q^{79} -2.36650 q^{81} +(12.2600 - 12.2600i) q^{83} +(-5.77622 + 0.386600i) q^{85} +(0.812819 + 0.812819i) q^{87} -8.25433i q^{89} -1.96903i q^{91} +(-5.63954 - 5.63954i) q^{93} +(2.11583 + 1.85037i) q^{95} +(4.81979 - 4.81979i) q^{97} +0.0276082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.636375	+	0.636375i	−0.367411	+	0.367411i	−0.866532	−	0.499121i	$-0.833656\pi$
$3$	−0.636375	+	0.636375i	−0.367411	+	0.367411i	0.499121	+	0.866532i	$0.333656\pi$
$4$		0			0
$5$	1.68320	+	1.47202i	0.752749	+	0.658308i
$5$	1.68320	+	1.47202i	0.752749	+	0.658308i
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$			2.19005i			0.730018i
$10$		0			0
$11$		−	0.0126062i		−	0.00380090i	−0.999998	−	0.00190045i	$-0.999395\pi$
$11$		−	0.0126062i		−	0.00380090i	0.999998	−	0.00190045i	$-0.000604932\pi$
$12$		0			0
$13$	1.39232	+	1.39232i	0.386159	+	0.386159i	0.873315	−	0.487156i	$-0.161966\pi$
$13$	1.39232	+	1.39232i	0.386159	+	0.386159i	−0.487156	+	0.873315i	$0.661966\pi$
$14$		0			0
$15$	−2.00790	+	0.134388i	−0.518438	+	0.0346989i
$16$		0			0
$17$	−1.83069	+	1.83069i	−0.444007	+	0.444007i	−0.893356	−	0.449349i	$-0.851656\pi$
$17$	−1.83069	+	1.83069i	−0.444007	+	0.444007i	0.449349	+	0.893356i	$0.351656\pi$
$18$		0			0
$19$	1.25703			0.288382			0.144191	−	0.989550i	$-0.453942\pi$
$19$	1.25703			0.288382			0.144191	+	0.989550i	$0.453942\pi$
$20$		0			0
$21$	0.899970			0.196390
$22$		0			0
$23$	−0.761068	+	0.761068i	−0.158694	+	0.158694i	−0.781988	−	0.623294i	$-0.785794\pi$
$23$	−0.761068	+	0.761068i	−0.158694	+	0.158694i	0.623294	+	0.781988i	$0.285794\pi$
$24$		0			0
$25$	0.666311	+	4.95540i	0.133262	+	0.991081i
$26$		0			0
$27$	−3.30282	−	3.30282i	−0.635628	−	0.635628i
$28$		0			0
$29$		−	1.27726i		−	0.237182i	−0.992943	−	0.118591i	$-0.962162\pi$
$29$		−	1.27726i		−	0.237182i	0.992943	−	0.118591i	$-0.0378377\pi$
$30$		0			0
$31$			8.86198i			1.59166i	0.605521	+	0.795829i	$0.292965\pi$
$31$			8.86198i			1.59166i	−0.605521	+	0.795829i	$0.707035\pi$
$32$		0			0
$33$	0.00802225	+	0.00802225i	0.00139649	+	0.00139649i
$34$		0			0
$35$	−0.149325	−	2.23108i	−0.0252406	−	0.377121i
$36$		0			0
$37$	−0.649549	+	0.649549i	−0.106785	+	0.106785i	−0.758481	−	0.651695i	$-0.774058\pi$
$37$	−0.649549	+	0.649549i	−0.106785	+	0.106785i	0.651695	+	0.758481i	$0.274058\pi$
$38$		0			0
$39$	−1.77207			−0.283759
$40$		0			0
$41$	5.52580			0.862985			0.431493	−	0.902116i	$-0.357987\pi$
$41$	5.52580			0.862985			0.431493	+	0.902116i	$0.357987\pi$
$42$		0			0
$43$	−4.70260	+	4.70260i	−0.717140	+	0.717140i	−0.968019	−	0.250879i	$-0.919280\pi$
$43$	−4.70260	+	4.70260i	−0.717140	+	0.717140i	0.250879	+	0.968019i	$0.419280\pi$
$44$		0			0
$45$	−3.22380	+	3.68629i	−0.480576	+	0.549520i
$46$		0			0
$47$	2.07793	+	2.07793i	0.303098	+	0.303098i	0.842225	−	0.539127i	$-0.181246\pi$
$47$	2.07793	+	2.07793i	0.303098	+	0.303098i	−0.539127	+	0.842225i	$0.681246\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	2.33001i		−	0.326267i
$52$		0			0
$53$	−2.69362	−	2.69362i	−0.369997	−	0.369997i	0.497479	−	0.867476i	$-0.334259\pi$
$53$	−2.69362	−	2.69362i	−0.369997	−	0.369997i	−0.867476	+	0.497479i	$0.834259\pi$
$54$		0			0
$55$	0.0185565	−	0.0212187i	0.00250216	−	0.00286112i
$56$		0			0
$57$	−0.799940	+	0.799940i	−0.105955	+	0.105955i
$58$		0			0
$59$	0.236325			0.0307669			0.0153834	−	0.999882i	$-0.495103\pi$
$59$	0.236325			0.0307669			0.0153834	+	0.999882i	$0.495103\pi$
$60$		0			0
$61$	12.3491			1.58114			0.790571	−	0.612371i	$-0.209784\pi$
$61$	12.3491			1.58114			0.790571	+	0.612371i	$0.209784\pi$
$62$		0			0
$63$	1.54860	−	1.54860i	0.195105	−	0.195105i
$64$		0			0
$65$	0.294026	+	4.39307i	0.0364695	+	0.544893i
$66$		0			0
$67$	−4.86571	−	4.86571i	−0.594441	−	0.594441i	0.344387	−	0.938828i	$-0.388087\pi$
$67$	−4.86571	−	4.86571i	−0.594441	−	0.594441i	−0.938828	+	0.344387i	$0.888087\pi$
$68$		0			0
$69$		−	0.968650i		−	0.116612i
$70$		0			0
$71$			12.9813i			1.54060i	0.637685	+	0.770298i	$0.279892\pi$
$71$			12.9813i			1.54060i	−0.637685	+	0.770298i	$0.720108\pi$
$72$		0			0
$73$	−4.87625	−	4.87625i	−0.570722	−	0.570722i	0.361608	−	0.932330i	$-0.382228\pi$
$73$	−4.87625	−	4.87625i	−0.570722	−	0.570722i	−0.932330	+	0.361608i	$0.882228\pi$
$74$		0			0
$75$	−3.57752	−	2.72947i	−0.413096	−	0.315172i
$76$		0			0
$77$	−0.00891390	+	0.00891390i	−0.00101583	+	0.00101583i
$78$		0			0
$79$	10.0991			1.13623			0.568117	−	0.822947i	$-0.307672\pi$
$79$	10.0991			1.13623			0.568117	+	0.822947i	$0.307672\pi$
$80$		0			0
$81$	−2.36650			−0.262944
$82$		0			0
$83$	12.2600	−	12.2600i	1.34571	−	1.34571i	0.455439	−	0.890267i	$-0.349482\pi$
$83$	12.2600	−	12.2600i	1.34571	−	1.34571i	0.890267	−	0.455439i	$-0.150518\pi$
$84$		0			0
$85$	−5.77622	+	0.386600i	−0.626519	+	0.0419327i
$86$		0			0
$87$	0.812819	+	0.812819i	0.0871433	+	0.0871433i
$88$		0			0
$89$		−	8.25433i		−	0.874957i	−0.899229	−	0.437479i	$-0.855872\pi$
$89$		−	8.25433i		−	0.874957i	0.899229	−	0.437479i	$-0.144128\pi$
$90$		0			0
$91$		−	1.96903i		−	0.206411i
$92$		0			0
$93$	−5.63954	−	5.63954i	−0.584793	−	0.584793i
$94$		0			0
$95$	2.11583	+	1.85037i	0.217079	+	0.189844i
$96$		0			0
$97$	4.81979	−	4.81979i	0.489376	−	0.489376i	−0.418734	−	0.908109i	$-0.637526\pi$
$97$	4.81979	−	4.81979i	0.489376	−	0.489376i	0.908109	+	0.418734i	$0.137526\pi$
$98$		0			0
$99$	0.0276082			0.00277473
$100$		0			0
$101$	−3.06982			−0.305458			−0.152729	−	0.988268i	$-0.548806\pi$
$101$	−3.06982			−0.305458			−0.152729	+	0.988268i	$0.548806\pi$
$102$		0			0
$103$	10.6653	−	10.6653i	1.05088	−	1.05088i	0.0522508	−	0.998634i	$-0.483360\pi$
$103$	10.6653	−	10.6653i	1.05088	−	1.05088i	0.998634	−	0.0522508i	$-0.0166395\pi$
$104$		0			0
$105$	1.51483	+	1.32477i	0.147832	+	0.129285i
$106$		0			0
$107$	−9.69150	−	9.69150i	−0.936913	−	0.936913i	0.0612121	−	0.998125i	$-0.480503\pi$
$107$	−9.69150	−	9.69150i	−0.936913	−	0.936913i	−0.998125	+	0.0612121i	$0.980503\pi$
$108$		0			0
$109$		−	16.5634i		−	1.58648i	−0.608906	−	0.793242i	$-0.708391\pi$
$109$		−	16.5634i		−	1.58648i	0.608906	−	0.793242i	$-0.291609\pi$
$110$		0			0
$111$		−	0.826714i		−	0.0784682i
$112$		0			0
$113$	−13.9941	−	13.9941i	−1.31645	−	1.31645i	−0.916566	−	0.399884i	$-0.869051\pi$
$113$	−13.9941	−	13.9941i	−1.31645	−	1.31645i	−0.399884	−	0.916566i	$-0.630949\pi$
$114$		0			0
$115$	−2.40134	+	0.160721i	−0.223926	+	0.0149873i
$116$		0			0
$117$	−3.04925	+	3.04925i	−0.281903	+	0.281903i
$118$		0			0
$119$	2.58899			0.237332
$120$		0			0
$121$	10.9998			0.999986
$122$		0			0
$123$	−3.51648	+	3.51648i	−0.317071	+	0.317071i
$124$		0			0
$125$	−6.17292	+	9.32175i	−0.552123	+	0.833763i
$126$		0			0
$127$	14.4362	+	14.4362i	1.28101	+	1.28101i	0.940094	+	0.340914i	$0.110737\pi$
$127$	14.4362	+	14.4362i	1.28101	+	1.28101i	0.340914	+	0.940094i	$0.389263\pi$
$128$		0			0
$129$		−	5.98523i		−	0.526970i
$130$		0			0
$131$		−	18.1631i		−	1.58692i	−0.608625	−	0.793458i	$-0.708279\pi$
$131$		−	18.1631i		−	1.58692i	0.608625	−	0.793458i	$-0.291721\pi$
$132$		0			0
$133$	−0.888852	−	0.888852i	−0.0770733	−	0.0770733i
$134$		0			0
$135$	−0.697482	−	10.4211i	−0.0600297	−	0.896907i
$136$		0			0
$137$	−10.5743	+	10.5743i	−0.903422	+	0.903422i	−0.995730	−	0.0923086i	$-0.970575\pi$
$137$	−10.5743	+	10.5743i	−0.903422	+	0.903422i	0.0923086	+	0.995730i	$0.470575\pi$
$138$		0			0
$139$	2.74672			0.232974			0.116487	−	0.993192i	$-0.462837\pi$
$139$	2.74672			0.232974			0.116487	+	0.993192i	$0.462837\pi$
$140$		0			0
$141$	−2.64469			−0.222723
$142$		0			0
$143$	0.0175518	−	0.0175518i	0.00146775	−	0.00146775i
$144$		0			0
$145$	1.88016	−	2.14989i	0.156139	−	0.178539i
$146$		0			0
$147$	−0.636375	−	0.636375i	−0.0524873	−	0.0524873i
$148$		0			0
$149$		−	10.1424i		−	0.830899i	−0.909616	−	0.415449i	$-0.863624\pi$
$149$		−	10.1424i		−	0.830899i	0.909616	−	0.415449i	$-0.136376\pi$
$150$		0			0
$151$			18.3408i			1.49255i	0.665636	+	0.746276i	$0.268160\pi$
$151$			18.3408i			1.49255i	−0.665636	+	0.746276i	$0.731840\pi$
$152$		0			0
$153$	−4.00931	−	4.00931i	−0.324133	−	0.324133i
$154$		0			0
$155$	−13.0450	+	14.9165i	−1.04780	+	1.19812i
$156$		0			0
$157$	5.42936	−	5.42936i	0.433310	−	0.433310i	−0.456443	−	0.889753i	$-0.650877\pi$
$157$	5.42936	−	5.42936i	0.433310	−	0.433310i	0.889753	+	0.456443i	$0.150877\pi$
$158$		0			0
$159$	3.42831			0.271882
$160$		0			0
$161$	1.07631			0.0848253
$162$		0			0
$163$	4.02344	−	4.02344i	0.315140	−	0.315140i	−0.531757	−	0.846897i	$-0.678468\pi$
$163$	4.02344	−	4.02344i	0.315140	−	0.315140i	0.846897	+	0.531757i	$0.178468\pi$
$164$		0			0
$165$	0.00169412	+	0.0253119i	0.000131887	+	0.00197053i
$166$		0			0
$167$	1.32244	+	1.32244i	0.102334	+	0.102334i	0.756420	−	0.654086i	$-0.226947\pi$
$167$	1.32244	+	1.32244i	0.102334	+	0.102334i	−0.654086	+	0.756420i	$0.726947\pi$
$168$		0			0
$169$		−	9.12291i		−	0.701762i
$170$		0			0
$171$			2.75296i			0.210524i
$172$		0			0
$173$	7.77402	+	7.77402i	0.591048	+	0.591048i	0.937914	−	0.346867i	$-0.112754\pi$
$173$	7.77402	+	7.77402i	0.591048	+	0.591048i	−0.346867	+	0.937914i	$0.612754\pi$
$174$		0			0
$175$	3.03285	−	3.97515i	0.229262	−	0.300493i
$176$		0			0
$177$	−0.150391	+	0.150391i	−0.0113041	+	0.0113041i
$178$		0			0
$179$	17.3485			1.29669			0.648345	−	0.761347i	$-0.275462\pi$
$179$	17.3485			1.29669			0.648345	+	0.761347i	$0.275462\pi$
$180$		0			0
$181$	14.2097			1.05620			0.528100	−	0.849182i	$-0.322905\pi$
$181$	14.2097			1.05620			0.528100	+	0.849182i	$0.322905\pi$
$182$		0			0
$183$	−7.85866	+	7.85866i	−0.580929	+	0.580929i
$184$		0			0
$185$	−2.04947	+	0.137170i	−0.150680	+	0.0100850i
$186$		0			0
$187$	0.0230780	+	0.0230780i	0.00168763	+	0.00168763i
$188$		0			0
$189$			4.67089i			0.339758i
$190$		0			0
$191$		−	2.45516i		−	0.177649i	−0.996047	−	0.0888245i	$-0.971689\pi$
$191$		−	2.45516i		−	0.177649i	0.996047	−	0.0888245i	$-0.0283110\pi$
$192$		0			0
$193$	−0.379176	−	0.379176i	−0.0272937	−	0.0272937i	0.693328	−	0.720622i	$-0.256144\pi$
$193$	−0.379176	−	0.379176i	−0.0272937	−	0.0272937i	−0.720622	+	0.693328i	$0.756144\pi$
$194$		0			0
$195$	−2.98275	−	2.60853i	−0.213599	−	0.186800i
$196$		0			0
$197$	−15.7726	+	15.7726i	−1.12375	+	1.12375i	−0.132583	+	0.991172i	$0.542327\pi$
$197$	−15.7726	+	15.7726i	−1.12375	+	1.12375i	−0.991172	+	0.132583i	$0.957673\pi$
$198$		0			0
$199$	−12.1965			−0.864588			−0.432294	−	0.901733i	$-0.642296\pi$
$199$	−12.1965			−0.864588			−0.432294	+	0.901733i	$0.642296\pi$
$200$		0			0
$201$	6.19283			0.436809
$202$		0			0
$203$	−0.903162	+	0.903162i	−0.0633895	+	0.0633895i
$204$		0			0
$205$	9.30102	+	8.13409i	0.649611	+	0.568110i
$206$		0			0
$207$	−1.66678	−	1.66678i	−0.115849	−	0.115849i
$208$		0			0
$209$		−	0.0158463i		−	0.00109611i
$210$		0			0
$211$			16.3803i			1.12766i	0.825890	+	0.563832i	$0.190673\pi$
$211$			16.3803i			1.12766i	−0.825890	+	0.563832i	$0.809327\pi$
$212$		0			0
$213$	−8.26097	−	8.26097i	−0.566032	−	0.566032i
$214$		0			0
$215$	−14.8377	+	0.993084i	−1.01192	+	0.0677277i
$216$		0			0
$217$	6.26637	−	6.26637i	0.425389	−	0.425389i
$218$		0			0
$219$	6.20625			0.419380
$220$		0			0
$221$	−5.09780			−0.342915
$222$		0			0
$223$	5.93470	−	5.93470i	0.397417	−	0.397417i	−0.479904	−	0.877321i	$-0.659329\pi$
$223$	5.93470	−	5.93470i	0.397417	−	0.397417i	0.877321	+	0.479904i	$0.159329\pi$
$224$		0			0
$225$	−10.8526	+	1.45926i	−0.723507	+	0.0972839i
$226$		0			0
$227$	−5.00335	−	5.00335i	−0.332084	−	0.332084i	0.521293	−	0.853378i	$-0.325450\pi$
$227$	−5.00335	−	5.00335i	−0.332084	−	0.332084i	−0.853378	+	0.521293i	$0.825450\pi$
$228$		0			0
$229$		−	4.11836i		−	0.272149i	−0.990699	−	0.136075i	$-0.956551\pi$
$229$		−	4.11836i		−	0.272149i	0.990699	−	0.136075i	$-0.0434487\pi$
$230$		0			0
$231$		−	0.0113452i		−	0.000746457i
$232$		0			0
$233$	6.45553	+	6.45553i	0.422916	+	0.422916i	0.886206	−	0.463291i	$-0.153331\pi$
$233$	6.45553	+	6.45553i	0.422916	+	0.422916i	−0.463291	+	0.886206i	$0.653331\pi$
$234$		0			0
$235$	0.438813	+	6.55633i	0.0286250	+	0.427688i
$236$		0			0
$237$	−6.42680	+	6.42680i	−0.417466	+	0.417466i
$238$		0			0
$239$	−17.1210			−1.10746			−0.553732	−	0.832695i	$-0.686797\pi$
$239$	−17.1210			−1.10746			−0.553732	+	0.832695i	$0.686797\pi$
$240$		0			0
$241$	16.9128			1.08945			0.544726	−	0.838614i	$-0.316634\pi$
$241$	16.9128			1.08945			0.544726	+	0.838614i	$0.316634\pi$
$242$		0			0
$243$	11.4144	−	11.4144i	0.732237	−	0.732237i
$244$		0			0
$245$	−1.47202	+	1.68320i	−0.0940439	+	0.107536i
$246$		0			0
$247$	1.75018	+	1.75018i	0.111361	+	0.111361i
$248$		0			0
$249$			15.6039i			0.988855i
$250$		0			0
$251$		−	17.0733i		−	1.07765i	−0.842416	−	0.538827i	$-0.818868\pi$
$251$		−	17.0733i		−	1.07765i	0.842416	−	0.538827i	$-0.181132\pi$
$252$		0			0
$253$	0.00959415	+	0.00959415i	0.000603179	+	0.000603179i
$254$		0			0
$255$	3.42982	−	3.92187i	0.214784	−	0.245597i
$256$		0			0
$257$	−16.9778	+	16.9778i	−1.05905	+	1.05905i	−0.0609033	+	0.998144i	$0.519398\pi$
$257$	−16.9778	+	16.9778i	−1.05905	+	1.05905i	−0.998144	+	0.0609033i	$0.980602\pi$
$258$		0			0
$259$	0.918601			0.0570791
$260$		0			0
$261$	2.79728			0.173147
$262$		0			0
$263$	−5.83249	+	5.83249i	−0.359646	+	0.359646i	−0.863683	−	0.504036i	$-0.831848\pi$
$263$	−5.83249	+	5.83249i	−0.359646	+	0.359646i	0.504036	+	0.863683i	$0.331848\pi$
$264$		0			0
$265$	−0.568832	−	8.49896i	−0.0349431	−	0.522087i
$266$		0			0
$267$	5.25285	+	5.25285i	0.321469	+	0.321469i
$268$		0			0
$269$			16.1951i			0.987435i	0.869622	+	0.493718i	$0.164362\pi$
$269$			16.1951i			0.987435i	−0.869622	+	0.493718i	$0.835638\pi$
$270$		0			0
$271$		−	23.2868i		−	1.41457i	−0.706927	−	0.707287i	$-0.749919\pi$
$271$		−	23.2868i		−	1.41457i	0.706927	−	0.707287i	$-0.250081\pi$
$272$		0			0
$273$	1.25304	+	1.25304i	0.0758377	+	0.0758377i
$274$		0			0
$275$	0.0624686	−	0.00839963i	0.00376700	−	0.000506517i
$276$		0			0
$277$	17.2838	−	17.2838i	1.03849	−	1.03849i	0.0392563	−	0.999229i	$-0.487501\pi$
$277$	17.2838	−	17.2838i	1.03849	−	1.03849i	0.999229	−	0.0392563i	$-0.0124989\pi$
$278$		0			0
$279$	−19.4082			−1.16194
$280$		0			0
$281$	−0.756410			−0.0451236			−0.0225618	−	0.999745i	$-0.507182\pi$
$281$	−0.756410			−0.0451236			−0.0225618	+	0.999745i	$0.507182\pi$
$282$		0			0
$283$	−15.0064	+	15.0064i	−0.892039	+	0.892039i	−0.994715	−	0.102676i	$-0.967260\pi$
$283$	−15.0064	+	15.0064i	−0.892039	+	0.892039i	0.102676	+	0.994715i	$0.467260\pi$
$284$		0			0
$285$	−2.52399	+	0.168930i	−0.149508	+	0.0100065i
$286$		0			0
$287$	−3.90733	−	3.90733i	−0.230643	−	0.230643i
$288$		0			0
$289$			10.2972i			0.605715i
$290$		0			0
$291$			6.13439i			0.359604i
$292$		0			0
$293$	15.0353	+	15.0353i	0.878370	+	0.878370i	0.993366	−	0.114996i	$-0.0366854\pi$
$293$	15.0353	+	15.0353i	0.878370	+	0.878370i	−0.114996	+	0.993366i	$0.536685\pi$
$294$		0			0
$295$	0.397782	+	0.347875i	0.0231597	+	0.0202541i
$296$		0			0
$297$	−0.0416359	+	0.0416359i	−0.00241596	+	0.00241596i
$298$		0			0
$299$	−2.11930			−0.122562
$300$		0			0
$301$	6.65048			0.383327
$302$		0			0
$303$	1.95356	−	1.95356i	0.112229	−	0.112229i
$304$		0			0
$305$	20.7860	+	18.1781i	1.19020	+	1.04088i
$306$		0			0
$307$	5.89239	+	5.89239i	0.336297	+	0.336297i	0.854972	−	0.518675i	$-0.173574\pi$
$307$	5.89239	+	5.89239i	0.336297	+	0.336297i	−0.518675	+	0.854972i	$0.673574\pi$
$308$		0			0
$309$			13.5743i			0.772214i
$310$		0			0
$311$			23.3700i			1.32519i	0.748977	+	0.662596i	$0.230545\pi$
$311$			23.3700i			1.32519i	−0.748977	+	0.662596i	$0.769455\pi$
$312$		0			0
$313$	11.9270	+	11.9270i	0.674154	+	0.674154i	0.958671	−	0.284517i	$-0.0918332\pi$
$313$	11.9270	+	11.9270i	0.674154	+	0.674154i	−0.284517	+	0.958671i	$0.591833\pi$
$314$		0			0
$315$	4.88618	−	0.327030i	0.275305	−	0.0184261i
$316$		0			0
$317$	10.5114	−	10.5114i	0.590378	−	0.590378i	−0.347355	−	0.937734i	$-0.612920\pi$
$317$	10.5114	−	10.5114i	0.590378	−	0.590378i	0.937734	+	0.347355i	$0.112920\pi$
$318$		0			0
$319$	−0.0161014			−0.000901505
$320$		0			0
$321$	12.3349			0.688465
$322$		0			0
$323$	−2.30122	+	2.30122i	−0.128044	+	0.128044i
$324$		0			0
$325$	−5.97178	+	7.82721i	−0.331255	+	0.434176i
$326$		0			0
$327$	10.5405	+	10.5405i	0.582892	+	0.582892i
$328$		0			0
$329$		−	2.93864i		−	0.162013i
$330$		0			0
$331$			18.5548i			1.01986i	0.860215	+	0.509932i	$0.170329\pi$
$331$			18.5548i			1.01986i	−0.860215	+	0.509932i	$0.829671\pi$
$332$		0			0
$333$	−1.42255	−	1.42255i	−0.0779551	−	0.0779551i
$334$		0			0
$335$	−1.02753	−	15.3524i	−0.0561399	−	0.838790i
$336$		0			0
$337$	3.59498	−	3.59498i	0.195831	−	0.195831i	−0.602379	−	0.798210i	$-0.705780\pi$
$337$	3.59498	−	3.59498i	0.195831	−	0.195831i	0.798210	+	0.602379i	$0.205780\pi$
$338$		0			0
$339$	17.8109			0.967357
$340$		0			0
$341$	0.111716			0.00604974
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	1.42587	−	1.63043i	0.0767664	−	0.0877793i
$346$		0			0
$347$	−13.5890	−	13.5890i	−0.729497	−	0.729497i	0.241022	−	0.970520i	$-0.422517\pi$
$347$	−13.5890	−	13.5890i	−0.729497	−	0.729497i	−0.970520	+	0.241022i	$0.922517\pi$
$348$		0			0
$349$			13.6178i			0.728942i	0.931215	+	0.364471i	$0.118750\pi$
$349$			13.6178i			0.728942i	−0.931215	+	0.364471i	$0.881250\pi$
$350$		0			0
$351$		−	9.19715i		−	0.490907i
$352$		0			0
$353$	1.30401	+	1.30401i	0.0694052	+	0.0694052i	0.740957	−	0.671552i	$-0.234372\pi$
$353$	1.30401	+	1.30401i	0.0694052	+	0.0694052i	−0.671552	+	0.740957i	$0.734372\pi$
$354$		0			0
$355$	−19.1087	+	21.8501i	−1.01419	+	1.15968i
$356$		0			0
$357$	−1.64757	+	1.64757i	−0.0871984	+	0.0871984i
$358$		0			0
$359$	−20.6449			−1.08960			−0.544798	−	0.838567i	$-0.683394\pi$
$359$	−20.6449			−1.08960			−0.544798	+	0.838567i	$0.683394\pi$
$360$		0			0
$361$	−17.4199			−0.916836
$362$		0			0
$363$	−7.00002	+	7.00002i	−0.367406	+	0.367406i
$364$		0			0
$365$	−1.02976	−	15.3856i	−0.0538999	−	0.805321i
$366$		0			0
$367$	1.91491	+	1.91491i	0.0999574	+	0.0999574i	0.755317	−	0.655360i	$-0.227483\pi$
$367$	1.91491	+	1.91491i	0.0999574	+	0.0999574i	−0.655360	+	0.755317i	$0.727483\pi$
$368$		0			0
$369$			12.1018i			0.629995i
$370$		0			0
$371$			3.80935i			0.197772i
$372$		0			0
$373$	4.57770	+	4.57770i	0.237024	+	0.237024i	0.815617	−	0.578593i	$-0.196398\pi$
$373$	4.57770	+	4.57770i	0.237024	+	0.237024i	−0.578593	+	0.815617i	$0.696398\pi$
$374$		0			0
$375$	−2.00384	−	9.86042i	−0.103478	−	0.509190i
$376$		0			0
$377$	1.77836	−	1.77836i	0.0915900	−	0.0915900i
$378$		0			0
$379$	−9.76336			−0.501510			−0.250755	−	0.968051i	$-0.580679\pi$
$379$	−9.76336			−0.501510			−0.250755	+	0.968051i	$0.580679\pi$
$380$		0			0
$381$	−18.3737			−0.941314
$382$		0			0
$383$	12.2995	−	12.2995i	0.628473	−	0.628473i	−0.319210	−	0.947684i	$-0.603418\pi$
$383$	12.2995	−	12.2995i	0.628473	−	0.628473i	0.947684	+	0.319210i	$0.103418\pi$
$384$		0			0
$385$	−0.0281253	+	0.00188242i	−0.00143340	+	9.59368e-5i
$386$		0			0
$387$	−10.2989	−	10.2989i	−0.523525	−	0.523525i
$388$		0			0
$389$		−	25.9951i		−	1.31800i	−0.752141	−	0.659002i	$-0.770979\pi$
$389$		−	25.9951i		−	1.31800i	0.752141	−	0.659002i	$-0.229021\pi$
$390$		0			0
$391$		−	2.78656i		−	0.140922i
$392$		0			0
$393$	11.5585	+	11.5585i	0.583051	+	0.583051i
$394$		0			0
$395$	16.9987	+	14.8660i	0.855300	+	0.747992i
$396$		0			0
$397$	2.24227	−	2.24227i	0.112536	−	0.112536i	−0.648596	−	0.761133i	$-0.724644\pi$
$397$	2.24227	−	2.24227i	0.112536	−	0.112536i	0.761133	+	0.648596i	$0.224644\pi$
$398$		0			0
$399$	1.13129			0.0566352
$400$		0			0
$401$	−34.7642			−1.73604			−0.868020	−	0.496529i	$-0.834608\pi$
$401$	−34.7642			−1.73604			−0.868020	+	0.496529i	$0.834608\pi$
$402$		0			0
$403$	−12.3387	+	12.3387i	−0.614634	+	0.614634i
$404$		0			0
$405$	−3.98328	−	3.48353i	−0.197931	−	0.173098i
$406$		0			0
$407$	0.00818832	+	0.00818832i	0.000405880	+	0.000405880i
$408$		0			0
$409$		−	4.17608i		−	0.206494i	−0.994656	−	0.103247i	$-0.967077\pi$
$409$		−	4.17608i		−	0.206494i	0.994656	−	0.103247i	$-0.0329232\pi$
$410$		0			0
$411$		−	13.4584i		−	0.663855i
$412$		0			0
$413$	−0.167107	−	0.167107i	−0.00822279	−	0.00822279i
$414$		0			0
$415$	38.6829	−	2.58903i	1.89887	−	0.127090i
$416$		0			0
$417$	−1.74795	+	1.74795i	−0.0855972	+	0.0855972i
$418$		0			0
$419$	21.4217			1.04652			0.523260	−	0.852173i	$-0.324716\pi$
$419$	21.4217			1.04652			0.523260	+	0.852173i	$0.324716\pi$
$420$		0			0
$421$	0.887140			0.0432366			0.0216183	−	0.999766i	$-0.493118\pi$
$421$	0.887140			0.0432366			0.0216183	+	0.999766i	$0.493118\pi$
$422$		0			0
$423$	−4.55079	+	4.55079i	−0.221267	+	0.221267i
$424$		0			0
$425$	−10.2916	−	7.85199i	−0.499217	−	0.380878i
$426$		0			0
$427$	−8.73214	−	8.73214i	−0.422578	−	0.422578i
$428$		0			0
$429$			0.0223390i			0.00107854i
$430$		0			0
$431$		−	11.7880i		−	0.567809i	−0.958853	−	0.283905i	$-0.908370\pi$
$431$		−	11.7880i		−	0.567809i	0.958853	−	0.283905i	$-0.0916299\pi$
$432$		0			0
$433$	−15.2964	−	15.2964i	−0.735099	−	0.735099i	0.236526	−	0.971625i	$-0.423991\pi$
$433$	−15.2964	−	15.2964i	−0.735099	−	0.735099i	−0.971625	+	0.236526i	$0.923991\pi$
$434$		0			0
$435$	0.171649	+	2.56462i	0.00822995	+	0.122964i
$436$		0			0
$437$	−0.956683	+	0.956683i	−0.0457644	+	0.0457644i
$438$		0			0
$439$	−26.5123			−1.26536			−0.632681	−	0.774413i	$-0.718045\pi$
$439$	−26.5123			−1.26536			−0.632681	+	0.774413i	$0.718045\pi$
$440$		0			0
$441$	−2.19005			−0.104288
$442$		0			0
$443$	−18.4849	+	18.4849i	−0.878245	+	0.878245i	−0.993353	−	0.115108i	$-0.963279\pi$
$443$	−18.4849	+	18.4849i	−0.878245	+	0.878245i	0.115108	+	0.993353i	$0.463279\pi$
$444$		0			0
$445$	12.1505	−	13.8937i	0.575991	−	0.658623i
$446$		0			0
$447$	6.45438	+	6.45438i	0.305282	+	0.305282i
$448$		0			0
$449$		−	13.6536i		−	0.644354i	−0.946680	−	0.322177i	$-0.895585\pi$
$449$		−	13.6536i		−	0.644354i	0.946680	−	0.322177i	$-0.104415\pi$
$450$		0			0
$451$		−	0.0696592i		−	0.00328012i
$452$		0			0
$453$	−11.6716	−	11.6716i	−0.548381	−	0.548381i
$454$		0			0
$455$	2.89846	−	3.31427i	0.135882	−	0.155376i
$456$		0			0
$457$	4.26210	−	4.26210i	0.199373	−	0.199373i	−0.600358	−	0.799731i	$-0.704975\pi$
$457$	4.26210	−	4.26210i	0.199373	−	0.199373i	0.799731	+	0.600358i	$0.204975\pi$
$458$		0			0
$459$	12.0929			0.564447
$460$		0			0
$461$	−24.2900			−1.13130			−0.565650	−	0.824645i	$-0.691375\pi$
$461$	−24.2900			−1.13130			−0.565650	+	0.824645i	$0.691375\pi$
$462$		0			0
$463$	25.3285	−	25.3285i	1.17712	−	1.17712i	0.196640	−	0.980476i	$-0.436997\pi$
$463$	25.3285	−	25.3285i	1.17712	−	1.17712i	0.980476	−	0.196640i	$-0.0630031\pi$
$464$		0			0
$465$	−1.19095	−	17.7940i	−0.0552288	−	0.825177i
$466$		0			0
$467$	19.0267	+	19.0267i	0.880453	+	0.880453i	0.993580	−	0.113128i	$-0.0360869\pi$
$467$	19.0267	+	19.0267i	0.880453	+	0.880453i	−0.113128	+	0.993580i	$0.536087\pi$
$468$		0			0
$469$			6.88115i			0.317742i
$470$		0			0
$471$			6.91021i			0.318406i
$472$		0			0
$473$	0.0592817	+	0.0592817i	0.00272578	+	0.00272578i
$474$		0			0
$475$	0.837571	+	6.22908i	0.0384304	+	0.285810i
$476$		0			0
$477$	5.89917	−	5.89917i	0.270105	−	0.270105i
$478$		0			0
$479$	12.7324			0.581758			0.290879	−	0.956760i	$-0.406052\pi$
$479$	12.7324			0.581758			0.290879	+	0.956760i	$0.406052\pi$
$480$		0			0
$481$	−1.80876			−0.0824722
$482$		0			0
$483$	−0.684939	+	0.684939i	−0.0311658	+	0.0311658i
$484$		0			0
$485$	15.2075	−	1.01783i	0.690537	−	0.0462174i
$486$		0			0
$487$	−18.5618	−	18.5618i	−0.841114	−	0.841114i	0.147889	−	0.989004i	$-0.452752\pi$
$487$	−18.5618	−	18.5618i	−0.841114	−	0.841114i	−0.989004	+	0.147889i	$0.952752\pi$
$488$		0			0
$489$			5.12083i			0.231572i
$490$		0			0
$491$		−	32.5946i		−	1.47097i	−0.677538	−	0.735487i	$-0.736953\pi$
$491$		−	32.5946i		−	1.47097i	0.677538	−	0.735487i	$-0.263047\pi$
$492$		0			0
$493$	2.33827	+	2.33827i	0.105311	+	0.105311i
$494$		0			0
$495$	0.0464700	+	0.0406398i	0.00208867	+	0.00182662i
$496$		0			0
$497$	9.17916	−	9.17916i	0.411741	−	0.411741i
$498$		0			0
$499$	34.6599			1.55159			0.775794	−	0.630986i	$-0.217350\pi$
$499$	34.6599			1.55159			0.775794	+	0.630986i	$0.217350\pi$
$500$		0			0
$501$	−1.68314			−0.0751970
$502$		0			0
$503$	−4.72427	+	4.72427i	−0.210645	+	0.210645i	−0.804541	−	0.593897i	$-0.797589\pi$
$503$	−4.72427	+	4.72427i	−0.210645	+	0.210645i	0.593897	+	0.804541i	$0.297589\pi$
$504$		0			0
$505$	−5.16711	−	4.51884i	−0.229934	−	0.201086i
$506$		0			0
$507$	5.80559	+	5.80559i	0.257835	+	0.257835i
$508$		0			0
$509$		−	32.3528i		−	1.43401i	−0.697068	−	0.717005i	$-0.745512\pi$
$509$		−	32.3528i		−	1.43401i	0.697068	−	0.717005i	$-0.254488\pi$
$510$		0			0
$511$			6.89606i			0.305064i
$512$		0			0
$513$	−4.15173	−	4.15173i	−0.183304	−	0.183304i
$514$		0			0
$515$	33.6514	−	2.25228i	1.48286	−	0.0992471i
$516$		0			0
$517$	0.0261948	−	0.0261948i	0.00115204	−	0.00115204i
$518$		0			0
$519$	−9.89438			−0.434315
$520$		0			0
$521$	−18.5227			−0.811495			−0.405748	−	0.913985i	$-0.632989\pi$
$521$	−18.5227			−0.811495			−0.405748	+	0.913985i	$0.632989\pi$
$522$		0			0
$523$	−5.45365	+	5.45365i	−0.238471	+	0.238471i	−0.816217	−	0.577745i	$-0.803933\pi$
$523$	−5.45365	+	5.45365i	−0.238471	+	0.238471i	0.577745	+	0.816217i	$0.303933\pi$
$524$		0			0
$525$	0.599661	+	4.45972i	0.0261713	+	0.194638i
$526$		0			0
$527$	−16.2235	−	16.2235i	−0.706708	−	0.706708i
$528$		0			0
$529$			21.8416i			0.949633i
$530$		0			0
$531$			0.517564i			0.0224604i
$532$		0			0
$533$	7.69367	+	7.69367i	0.333250	+	0.333250i
$534$		0			0
$535$	−2.04663	−	30.5788i	−0.0884834	−	1.32204i
$536$		0			0
$537$	−11.0402	+	11.0402i	−0.476418	+	0.476418i
$538$		0			0
$539$	0.0126062			0.000542986
$540$		0			0
$541$	−20.9517			−0.900785			−0.450393	−	0.892831i	$-0.648716\pi$
$541$	−20.9517			−0.900785			−0.450393	+	0.892831i	$0.648716\pi$
$542$		0			0
$543$	−9.04270	+	9.04270i	−0.388060	+	0.388060i
$544$		0			0
$545$	24.3816	−	27.8795i	1.04439	−	1.19422i
$546$		0			0
$547$	7.25167	+	7.25167i	0.310059	+	0.310059i	0.844932	−	0.534873i	$-0.179641\pi$
$547$	7.25167	+	7.25167i	0.310059	+	0.310059i	−0.534873	+	0.844932i	$0.679641\pi$
$548$		0			0
$549$			27.0452i			1.15426i
$550$		0			0
$551$		−	1.60556i		−	0.0683989i
$552$		0			0
$553$	−7.14113	−	7.14113i	−0.303672	−	0.303672i
$554$		0			0
$555$	1.21694	−	1.39152i	0.0516562	−	0.0590669i
$556$		0			0
$557$	4.55225	−	4.55225i	0.192885	−	0.192885i	−0.604056	−	0.796942i	$-0.706450\pi$
$557$	4.55225	−	4.55225i	0.192885	−	0.192885i	0.796942	+	0.604056i	$0.206450\pi$
$558$		0			0
$559$	−13.0950			−0.553860
$560$		0			0
$561$	−0.0293725			−0.00124011
$562$		0			0
$563$	8.04285	−	8.04285i	0.338966	−	0.338966i	−0.517012	−	0.855978i	$-0.672956\pi$
$563$	8.04285	−	8.04285i	0.338966	−	0.338966i	0.855978	+	0.517012i	$0.172956\pi$
$564$		0			0
$565$	−2.95523	−	44.1543i	−0.124327	−	1.85758i
$566$		0			0
$567$	1.67336	+	1.67336i	0.0702747	+	0.0702747i
$568$		0			0
$569$		−	12.2553i		−	0.513767i	−0.966442	−	0.256884i	$-0.917304\pi$
$569$		−	12.2553i		−	0.513767i	0.966442	−	0.256884i	$-0.0826957\pi$
$570$		0			0
$571$		−	8.79383i		−	0.368010i	−0.982925	−	0.184005i	$-0.941094\pi$
$571$		−	8.79383i		−	0.368010i	0.982925	−	0.184005i	$-0.0589063\pi$
$572$		0			0
$573$	1.56240	+	1.56240i	0.0652702	+	0.0652702i
$574$		0			0
$575$	−4.27851	−	3.26429i	−0.178426	−	0.136130i
$576$		0			0
$577$	25.2692	−	25.2692i	1.05197	−	1.05197i	0.0533988	−	0.998573i	$-0.482995\pi$
$577$	25.2692	−	25.2692i	1.05197	−	1.05197i	0.998573	−	0.0533988i	$-0.0170055\pi$
$578$		0			0
$579$	0.482597			0.0200560
$580$		0			0
$581$	−17.3382			−0.719310
$582$		0			0
$583$	−0.0339562	+	0.0339562i	−0.00140632	+	0.00140632i
$584$		0			0
$585$	−9.62105	+	0.643933i	−0.397781	+	0.0266234i
$586$		0			0
$587$	8.65200	+	8.65200i	0.357106	+	0.357106i	0.862745	−	0.505639i	$-0.168743\pi$
$587$	8.65200	+	8.65200i	0.357106	+	0.357106i	−0.505639	+	0.862745i	$0.668743\pi$
$588$		0			0
$589$			11.1397i			0.459005i
$590$		0			0
$591$		−	20.0746i		−	0.825760i
$592$		0			0
$593$	31.8049	+	31.8049i	1.30607	+	1.30607i	0.924226	+	0.381846i	$0.124712\pi$
$593$	31.8049	+	31.8049i	1.30607	+	1.30607i	0.381846	+	0.924226i	$0.375288\pi$
$594$		0			0
$595$	4.35777	+	3.81104i	0.178651	+	0.156237i
$596$		0			0
$597$	7.76156	−	7.76156i	0.317659	−	0.317659i
$598$		0			0
$599$	18.5112			0.756349			0.378174	−	0.925734i	$-0.376552\pi$
$599$	18.5112			0.756349			0.378174	+	0.925734i	$0.376552\pi$
$600$		0			0
$601$	−9.22362			−0.376239			−0.188120	−	0.982146i	$-0.560239\pi$
$601$	−9.22362			−0.376239			−0.188120	+	0.982146i	$0.560239\pi$
$602$		0			0
$603$	10.6562	−	10.6562i	0.433953	−	0.433953i
$604$		0			0
$605$	18.5149	+	16.1920i	0.752738	+	0.658298i
$606$		0			0
$607$	27.9989	+	27.9989i	1.13644	+	1.13644i	0.989084	+	0.147355i	$0.0470761\pi$
$607$	27.9989	+	27.9989i	1.13644	+	1.13644i	0.147355	+	0.989084i	$0.452924\pi$
$608$		0			0
$609$		−	1.14950i		−	0.0465801i
$610$		0			0
$611$			5.78629i			0.234088i
$612$		0			0
$613$	−3.68713	−	3.68713i	−0.148922	−	0.148922i	0.628714	−	0.777636i	$-0.283581\pi$
$613$	−3.68713	−	3.68713i	−0.148922	−	0.148922i	−0.777636	+	0.628714i	$0.783581\pi$
$614$		0			0
$615$	−11.0953	+	0.742602i	−0.447405	+	0.0299446i
$616$		0			0
$617$	17.7614	−	17.7614i	0.715047	−	0.715047i	−0.252540	−	0.967587i	$-0.581266\pi$
$617$	17.7614	−	17.7614i	0.715047	−	0.715047i	0.967587	+	0.252540i	$0.0812658\pi$
$618$		0			0
$619$	−19.2597			−0.774113			−0.387056	−	0.922056i	$-0.626508\pi$
$619$	−19.2597			−0.774113			−0.387056	+	0.922056i	$0.626508\pi$
$620$		0			0
$621$	5.02734			0.201740
$622$		0			0
$623$	−5.83669	+	5.83669i	−0.233842	+	0.233842i
$624$		0			0
$625$	−24.1121	+	6.60369i	−0.964482	+	0.264147i
$626$		0			0
$627$	0.0100842	+	0.0100842i	0.000402723	+	0.000402723i
$628$		0			0
$629$		−	2.37825i		−	0.0948268i
$630$		0			0
$631$		−	23.0818i		−	0.918871i	−0.888211	−	0.459435i	$-0.848052\pi$
$631$		−	23.0818i		−	0.918871i	0.888211	−	0.459435i	$-0.151948\pi$
$632$		0			0
$633$	−10.4240	−	10.4240i	−0.414316	−	0.414316i
$634$		0			0
$635$	3.04861	+	45.5495i	0.120980	+	1.80758i
$636$		0			0
$637$	−1.39232	+	1.39232i	−0.0551656	+	0.0551656i
$638$		0			0
$639$	−28.4297			−1.12466
$640$		0			0
$641$	−26.6893			−1.05416			−0.527081	−	0.849815i	$-0.676714\pi$
$641$	−26.6893			−1.05416			−0.527081	+	0.849815i	$0.676714\pi$
$642$		0			0
$643$	−8.81925	+	8.81925i	−0.347797	+	0.347797i	−0.859288	−	0.511491i	$-0.829093\pi$
$643$	−8.81925	+	8.81925i	−0.347797	+	0.347797i	0.511491	+	0.859288i	$0.329093\pi$
$644$		0			0
$645$	8.81039	−	10.0743i	0.346909	−	0.396677i
$646$		0			0
$647$	−24.9364	−	24.9364i	−0.980349	−	0.980349i	0.0194615	−	0.999811i	$-0.493805\pi$
$647$	−24.9364	−	24.9364i	−0.980349	−	0.980349i	−0.999811	+	0.0194615i	$0.993805\pi$
$648$		0			0
$649$		−	0.00297915i		−	0.000116942i
$650$		0			0
$651$			7.97552i			0.312585i
$652$		0			0
$653$	−19.7366	−	19.7366i	−0.772355	−	0.772355i	0.206163	−	0.978518i	$-0.433902\pi$
$653$	−19.7366	−	19.7366i	−0.772355	−	0.772355i	−0.978518	+	0.206163i	$0.933902\pi$
$654$		0			0
$655$	26.7364	−	30.5721i	1.04468	−	1.19455i
$656$		0			0
$657$	10.6793	−	10.6793i	0.416637	−	0.416637i
$658$		0			0
$659$	26.8854			1.04731			0.523654	−	0.851931i	$-0.324568\pi$
$659$	26.8854			1.04731			0.523654	+	0.851931i	$0.324568\pi$
$660$		0			0
$661$	−12.0525			−0.468789			−0.234395	−	0.972142i	$-0.575311\pi$
$661$	−12.0525			−0.468789			−0.234395	+	0.972142i	$0.575311\pi$
$662$		0			0
$663$	3.24411	−	3.24411i	0.125991	−	0.125991i
$664$		0			0
$665$	−0.187706	−	2.80452i	−0.00727891	−	0.108755i
$666$		0			0
$667$	0.972085	+	0.972085i	0.0376393	+	0.0376393i
$668$		0			0
$669$			7.55339i			0.292031i
$670$		0			0
$671$		−	0.155675i		−	0.00600976i
$672$		0			0
$673$	20.3536	+	20.3536i	0.784575	+	0.784575i	0.980599	−	0.196024i	$-0.0628032\pi$
$673$	20.3536	+	20.3536i	0.784575	+	0.784575i	−0.196024	+	0.980599i	$0.562803\pi$
$674$		0			0
$675$	14.1661	−	18.5675i	0.545254	−	0.714664i
$676$		0			0
$677$	−11.5836	+	11.5836i	−0.445192	+	0.445192i	−0.893753	−	0.448560i	$-0.851937\pi$
$677$	−11.5836	+	11.5836i	−0.445192	+	0.445192i	0.448560	+	0.893753i	$0.351937\pi$
$678$		0			0
$679$	−6.81621			−0.261582
$680$		0			0
$681$	6.36802			0.244023
$682$		0			0
$683$	−18.5355	+	18.5355i	−0.709241	+	0.709241i	−0.966376	−	0.257135i	$-0.917222\pi$
$683$	−18.5355	+	18.5355i	−0.709241	+	0.709241i	0.257135	+	0.966376i	$0.417222\pi$
$684$		0			0
$685$	−33.3642	+	2.23305i	−1.27478	+	0.0853205i
$686$		0			0
$687$	2.62082	+	2.62082i	0.0999906	+	0.0999906i
$688$		0			0
$689$		−	7.50075i		−	0.285756i
$690$		0			0
$691$		−	23.3166i		−	0.887007i	−0.896273	−	0.443503i	$-0.853735\pi$
$691$		−	23.3166i		−	0.887007i	0.896273	−	0.443503i	$-0.146265\pi$
$692$		0			0
$693$	−0.0195219	−	0.0195219i	−0.000741576	−	0.000741576i
$694$		0			0
$695$	4.62328	+	4.04323i	0.175371	+	0.153368i
$696$		0			0
$697$	−10.1160	+	10.1160i	−0.383172	+	0.383172i
$698$		0			0
$699$	−8.21627			−0.310768
$700$		0			0
$701$	12.2011			0.460829			0.230415	−	0.973093i	$-0.425992\pi$
$701$	12.2011			0.460829			0.230415	+	0.973093i	$0.425992\pi$
$702$		0			0
$703$	−0.816501	+	0.816501i	−0.0307949	+	0.0307949i
$704$		0			0
$705$	−4.45154	−	3.89304i	−0.167655	−	0.146620i
$706$		0			0
$707$	2.17069	+	2.17069i	0.0816372	+	0.0816372i
$708$		0			0
$709$			50.6963i			1.90394i	0.306194	+	0.951969i	$0.400945\pi$
$709$			50.6963i			1.90394i	−0.306194	+	0.951969i	$0.599055\pi$
$710$		0			0
$711$			22.1175i			0.829472i
$712$		0			0
$713$	−6.74457	−	6.74457i	−0.252586	−	0.252586i
$714$		0			0
$715$	0.0553797	−	0.00370654i	0.00207108	−	0.000138617i
$716$		0			0
$717$	10.8954	−	10.8954i	0.406895	−	0.406895i
$718$		0			0
$719$	−28.9636			−1.08016			−0.540079	−	0.841614i	$-0.681606\pi$
$719$	−28.9636			−1.08016			−0.540079	+	0.841614i	$0.681606\pi$
$720$		0			0
$721$	−15.0830			−0.561722
$722$		0			0
$723$	−10.7629	+	10.7629i	−0.400277	+	0.400277i
$724$		0			0
$725$	6.32936	−	0.851056i	0.235066	−	0.0316074i
$726$		0			0
$727$	28.6888	+	28.6888i	1.06401	+	1.06401i	0.997806	+	0.0662009i	$0.0210878\pi$
$727$	28.6888	+	28.6888i	1.06401	+	1.06401i	0.0662009	+	0.997806i	$0.478912\pi$
$728$		0			0
$729$			7.42824i			0.275120i
$730$		0			0
$731$		−	17.2180i		−	0.636831i
$732$		0			0
$733$	−1.92040	−	1.92040i	−0.0709315	−	0.0709315i	0.670751	−	0.741683i	$-0.265972\pi$
$733$	−1.92040	−	1.92040i	−0.0709315	−	0.0709315i	−0.741683	+	0.670751i	$0.765972\pi$
$734$		0			0
$735$	−0.134388	−	2.00790i	−0.00495698	−	0.0740626i
$736$		0			0
$737$	−0.0613379	+	0.0613379i	−0.00225941	+	0.00225941i
$738$		0			0
$739$	−11.7073			−0.430660			−0.215330	−	0.976541i	$-0.569083\pi$
$739$	−11.7073			−0.430660			−0.215330	+	0.976541i	$0.569083\pi$
$740$		0			0
$741$	−2.22754			−0.0818308
$742$		0			0
$743$	11.1456	−	11.1456i	0.408892	−	0.408892i	−0.472460	−	0.881352i	$-0.656634\pi$
$743$	11.1456	−	11.1456i	0.408892	−	0.408892i	0.881352	+	0.472460i	$0.156634\pi$
$744$		0			0
$745$	14.9298	−	17.0717i	0.546987	−	0.625458i
$746$		0			0
$747$	26.8500	+	26.8500i	0.982390	+	0.982390i
$748$		0			0
$749$			13.7059i			0.500801i
$750$		0			0
$751$			8.61901i			0.314512i	0.987558	+	0.157256i	$0.0502648\pi$
$751$			8.61901i			0.314512i	−0.987558	+	0.157256i	$0.949735\pi$
$752$		0			0
$753$	10.8650	+	10.8650i	0.395942	+	0.395942i
$754$		0			0
$755$	−26.9980	+	30.8712i	−0.982559	+	1.12352i
$756$		0			0
$757$	−18.5374	+	18.5374i	−0.673754	+	0.673754i	−0.958579	−	0.284825i	$-0.908064\pi$
$757$	−18.5374	+	18.5374i	−0.673754	+	0.673754i	0.284825	+	0.958579i	$0.408064\pi$
$758$		0			0
$759$	−0.0122110			−0.000443229
$760$		0			0
$761$	−8.11579			−0.294197			−0.147099	−	0.989122i	$-0.546993\pi$
$761$	−8.11579			−0.294197			−0.147099	+	0.989122i	$0.546993\pi$
$762$		0			0
$763$	−11.7121	+	11.7121i	−0.424006	+	0.424006i
$764$		0			0
$765$	−0.846676	−	12.6502i	−0.0306116	−	0.457370i
$766$		0			0
$767$	0.329039	+	0.329039i	0.0118809	+	0.0118809i
$768$		0			0
$769$			8.87668i			0.320101i	0.987109	+	0.160051i	$0.0511658\pi$
$769$			8.87668i			0.320101i	−0.987109	+	0.160051i	$0.948834\pi$
$770$		0			0
$771$		−	21.6085i		−	0.778212i
$772$		0			0
$773$	36.8841	+	36.8841i	1.32663	+	1.32663i	0.908291	+	0.418339i	$0.137388\pi$
$773$	36.8841	+	36.8841i	1.32663	+	1.32663i	0.418339	+	0.908291i	$0.362612\pi$
$774$		0			0
$775$	−43.9147	+	5.90484i	−1.57746	+	0.212108i
$776$		0			0
$777$	−0.584575	+	0.584575i	−0.0209715	+	0.0209715i
$778$		0			0
$779$	6.94608			0.248869
$780$		0			0
$781$	0.163644			0.00585565
$782$		0			0
$783$	−4.21857	+	4.21857i	−0.150760	+	0.150760i
$784$		0			0
$785$	17.1308	−	1.14656i	0.611425	−	0.0409224i
$786$		0			0
$787$	−36.7436	−	36.7436i	−1.30977	−	1.30977i	−0.921580	−	0.388189i	$-0.873101\pi$
$787$	−36.7436	−	36.7436i	−1.30977	−	1.30977i	−0.388189	−	0.921580i	$-0.626899\pi$
$788$		0			0
$789$		−	7.42330i		−	0.264276i
$790$		0			0
$791$			19.7906i			0.703672i
$792$		0			0
$793$	17.1939	+	17.1939i	0.610572	+	0.610572i
$794$		0			0
$795$	5.77052	+	5.04654i	0.204659	+	0.178982i
$796$		0			0
$797$	−19.1230	+	19.1230i	−0.677373	+	0.677373i	−0.959405	−	0.282032i	$-0.908991\pi$
$797$	−19.1230	+	19.1230i	−0.677373	+	0.677373i	0.282032	+	0.959405i	$0.408991\pi$
$798$		0			0
$799$	−7.60810			−0.269155
$800$		0			0
$801$	18.0774			0.638734
$802$		0			0
$803$	−0.0614708	+	0.0614708i	−0.00216926	+	0.00216926i
$804$		0			0
$805$	1.81165	+	1.58435i	0.0638522	+	0.0558412i
$806$		0			0
$807$	−10.3062	−	10.3062i	−0.362795	−	0.362795i
$808$		0			0
$809$			37.4021i			1.31499i	0.753460	+	0.657493i	$0.228383\pi$
$809$			37.4021i			1.31499i	−0.753460	+	0.657493i	$0.771617\pi$
$810$		0			0
$811$			17.7071i			0.621780i	0.950446	+	0.310890i	$0.100627\pi$
$811$			17.7071i			0.621780i	−0.950446	+	0.310890i	$0.899373\pi$
$812$		0			0
$813$	14.8192	+	14.8192i	0.519730	+	0.519730i
$814$		0			0
$815$	12.6948	−	0.849660i	0.444681	−	0.0297623i
$816$		0			0
$817$	−5.91129	+	5.91129i	−0.206810	+	0.206810i
$818$		0			0
$819$	4.31229			0.150684
$820$		0			0
$821$	6.57041			0.229309			0.114654	−	0.993405i	$-0.463424\pi$
$821$	6.57041			0.229309			0.114654	+	0.993405i	$0.463424\pi$
$822$		0			0
$823$	7.78041	−	7.78041i	0.271208	−	0.271208i	−0.558378	−	0.829586i	$-0.688576\pi$
$823$	7.78041	−	7.78041i	0.271208	−	0.271208i	0.829586	+	0.558378i	$0.188576\pi$
$824$		0			0
$825$	−0.0344082	+	0.0450988i	−0.00119794	+	0.00157014i
$826$		0			0
$827$	3.82070	+	3.82070i	0.132859	+	0.132859i	0.770409	−	0.637550i	$-0.220052\pi$
$827$	3.82070	+	3.82070i	0.132859	+	0.132859i	−0.637550	+	0.770409i	$0.720052\pi$
$828$		0			0
$829$			23.1480i			0.803962i	0.915648	+	0.401981i	$0.131678\pi$
$829$			23.1480i			0.803962i	−0.915648	+	0.401981i	$0.868322\pi$
$830$		0			0
$831$			21.9980i			0.763103i
$832$		0			0
$833$	−1.83069	−	1.83069i	−0.0634296	−	0.0634296i
$834$		0			0
$835$	0.279270	+	4.17259i	0.00966454	+	0.144399i
$836$		0			0
$837$	29.2695	−	29.2695i	1.01170	−	1.01170i
$838$		0			0
$839$	−10.9266			−0.377230			−0.188615	−	0.982051i	$-0.560400\pi$
$839$	−10.9266			−0.377230			−0.188615	+	0.982051i	$0.560400\pi$
$840$		0			0
$841$	27.3686			0.943745
$842$		0			0
$843$	0.481361	−	0.481361i	0.0165789	−	0.0165789i
$844$		0			0
$845$	13.4291	−	15.3557i	0.461975	−	0.528251i
$846$		0			0
$847$	−7.77806	−	7.77806i	−0.267257	−	0.267257i
$848$		0			0
$849$		−	19.0994i		−	0.655491i
$850$		0			0
$851$		−	0.988702i		−	0.0338923i
$852$		0			0
$853$	27.7923	+	27.7923i	0.951590	+	0.951590i	0.998881	−	0.0472916i	$-0.0150590\pi$
$853$	27.7923	+	27.7923i	0.951590	+	0.951590i	−0.0472916	+	0.998881i	$0.515059\pi$
$854$		0			0
$855$	−4.05241	+	4.63377i	−0.138589	+	0.158472i
$856$		0			0
$857$	−2.91794	+	2.91794i	−0.0996750	+	0.0996750i	−0.755186	−	0.655511i	$-0.772453\pi$
$857$	−2.91794	+	2.91794i	−0.0996750	+	0.0996750i	0.655511	+	0.755186i	$0.272453\pi$
$858$		0			0
$859$	−45.7629			−1.56141			−0.780705	−	0.624899i	$-0.785140\pi$
$859$	−45.7629			−1.56141			−0.780705	+	0.624899i	$0.785140\pi$
$860$		0			0
$861$	4.97306			0.169481
$862$		0			0
$863$	−31.2969	+	31.2969i	−1.06536	+	1.06536i	−0.0676512	+	0.997709i	$0.521551\pi$
$863$	−31.2969	+	31.2969i	−1.06536	+	1.06536i	−0.997709	+	0.0676512i	$0.978449\pi$
$864$		0			0
$865$	1.64170	+	24.5287i	0.0558194	+	0.834002i
$866$		0			0
$867$	−6.55285	−	6.55285i	−0.222547	−	0.222547i
$868$		0			0
$869$		−	0.127311i		−	0.00431872i
$870$		0			0
$871$		−	13.5492i		−	0.459098i
$872$		0			0
$873$	10.5556	+	10.5556i	0.357253	+	0.357253i
$874$		0			0
$875$	10.9564	−	2.22656i	0.370394	−	0.0752714i
$876$		0			0
$877$	−8.06545	+	8.06545i	−0.272351	+	0.272351i	−0.830046	−	0.557695i	$-0.811686\pi$
$877$	−8.06545	+	8.06545i	−0.272351	+	0.272351i	0.557695	+	0.830046i	$0.311686\pi$
$878$		0			0
$879$	−19.1362			−0.645446
$880$		0			0
$881$	1.67435			0.0564103			0.0282052	−	0.999602i	$-0.491021\pi$
$881$	1.67435			0.0564103			0.0282052	+	0.999602i	$0.491021\pi$
$882$		0			0
$883$	35.4215	−	35.4215i	1.19203	−	1.19203i	0.215532	−	0.976497i	$-0.430852\pi$
$883$	35.4215	−	35.4215i	1.19203	−	1.19203i	0.976497	−	0.215532i	$-0.0691484\pi$
$884$		0			0
$885$	−0.474517	+	0.0317593i	−0.0159507	+	0.00106758i
$886$		0			0
$887$	34.2864	+	34.2864i	1.15122	+	1.15122i	0.986308	+	0.164916i	$0.0527353\pi$
$887$	34.2864	+	34.2864i	1.15122	+	1.15122i	0.164916	+	0.986308i	$0.447265\pi$
$888$		0			0
$889$		−	20.4159i		−	0.684728i
$890$		0			0
$891$			0.0298324i			0.000999424i
$892$		0			0
$893$	2.61202	+	2.61202i	0.0874079	+	0.0874079i
$894$		0			0
$895$	29.2010	+	25.5374i	0.976082	+	0.853620i
$896$		0			0
$897$	1.34867	−	1.34867i	0.0450307	−	0.0450307i
$898$		0			0
$899$	11.3191			0.377513
$900$		0			0
$901$	9.86236			0.328563
$902$		0			0
$903$	−4.23220	+	4.23220i	−0.140839	+	0.140839i
$904$		0			0
$905$	23.9178	+	20.9170i	0.795053	+	0.695304i
$906$		0			0
$907$	−22.8523	−	22.8523i	−0.758797	−	0.758797i	0.217306	−	0.976103i	$-0.430273\pi$
$907$	−22.8523	−	22.8523i	−0.758797	−	0.758797i	−0.976103	+	0.217306i	$0.930273\pi$
$908$		0			0
$909$		−	6.72307i		−	0.222990i
$910$		0			0
$911$		−	51.1370i		−	1.69425i	−0.531398	−	0.847123i	$-0.678333\pi$
$911$		−	51.1370i		−	1.69425i	0.531398	−	0.847123i	$-0.321667\pi$
$912$		0			0
$913$	−0.154551	−	0.154551i	−0.00511489	−	0.00511489i
$914$		0			0
$915$	−24.7958	+	1.65957i	−0.819724	+	0.0548638i
$916$		0			0
$917$	−12.8432	+	12.8432i	−0.424121	+	0.424121i
$918$		0			0
$919$	28.9239			0.954112			0.477056	−	0.878873i	$-0.341704\pi$
$919$	28.9239			0.954112			0.477056	+	0.878873i	$0.341704\pi$
$920$		0			0
$921$	−7.49955			−0.247118
$922$		0			0
$923$	−18.0741	+	18.0741i	−0.594915	+	0.594915i
$924$		0			0
$925$	−3.65158	−	2.78598i	−0.120063	−	0.0916024i
$926$		0			0
$927$	23.3576	+	23.3576i	0.767165	+	0.767165i
$928$		0			0
$929$			8.21598i			0.269558i	0.990876	+	0.134779i	$0.0430324\pi$
$929$			8.21598i			0.269558i	−0.990876	+	0.134779i	$0.956968\pi$
$930$		0			0
$931$			1.25703i			0.0411974i
$932$		0			0
$933$	−14.8721	−	14.8721i	−0.486891	−	0.486891i
$934$		0			0
$935$	0.00487355	+	0.0728160i	0.000159382	+	0.00238134i
$936$		0			0
$937$	−22.0151	+	22.0151i	−0.719203	+	0.719203i	−0.968442	−	0.249239i	$-0.919820\pi$
$937$	−22.0151	+	22.0151i	−0.719203	+	0.719203i	0.249239	+	0.968442i	$0.419820\pi$
$938$		0			0
$939$	−15.1801			−0.495384
$940$		0			0
$941$	10.5394			0.343574			0.171787	−	0.985134i	$-0.445046\pi$
$941$	10.5394			0.343574			0.171787	+	0.985134i	$0.445046\pi$
$942$		0			0
$943$	−4.20551	+	4.20551i	−0.136950	+	0.136950i
$944$		0			0
$945$	−6.87565	+	7.86204i	−0.223665	+	0.255752i
$946$		0			0
$947$	−34.4225	−	34.4225i	−1.11858	−	1.11858i	−0.991950	−	0.126631i	$-0.959584\pi$
$947$	−34.4225	−	34.4225i	−1.11858	−	1.11858i	−0.126631	−	0.991950i	$-0.540416\pi$
$948$		0			0
$949$		−	13.5786i		−	0.440779i
$950$		0			0
$951$			13.3784i			0.433823i
$952$		0			0
$953$	30.9997	+	30.9997i	1.00418	+	1.00418i	0.999991	+	0.00418683i	$0.00133271\pi$
$953$	30.9997	+	30.9997i	1.00418	+	1.00418i	0.00418683	+	0.999991i	$0.498667\pi$
$954$		0			0
$955$	3.61404	−	4.13252i	0.116948	−	0.133725i
$956$		0			0
$957$	0.0102465	−	0.0102465i	0.000331223	−	0.000331223i
$958$		0			0
$959$	14.9543			0.482899
$960$		0			0
$961$	−47.5347			−1.53338
$962$		0			0
$963$	21.2249	−	21.2249i	0.683963	−	0.683963i
$964$		0			0
$965$	−0.0800735	−	1.19638i	−0.00257766	−	0.0385130i
$966$		0			0
$967$	8.59470	+	8.59470i	0.276387	+	0.276387i	0.831665	−	0.555278i	$-0.187388\pi$
$967$	8.59470	+	8.59470i	0.276387	+	0.276387i	−0.555278	+	0.831665i	$0.687388\pi$
$968$		0			0
$969$		−	2.92888i		−	0.0940893i
$970$		0			0
$971$		−	23.2614i		−	0.746493i	−0.927732	−	0.373247i	$-0.878245\pi$
$971$		−	23.2614i		−	0.746493i	0.927732	−	0.373247i	$-0.121755\pi$
$972$		0			0
$973$	−1.94223	−	1.94223i	−0.0622649	−	0.0622649i
$974$		0			0
$975$	−1.18075	−	8.78133i	−0.0378143	−	0.281228i
$976$		0			0
$977$	10.0551	−	10.0551i	0.321693	−	0.321693i	−0.527723	−	0.849416i	$-0.676954\pi$
$977$	10.0551	−	10.0551i	0.321693	−	0.321693i	0.849416	+	0.527723i	$0.176954\pi$
$978$		0			0
$979$	−0.104055			−0.00332562
$980$		0			0
$981$	36.2747			1.15816
$982$		0			0
$983$	22.4422	−	22.4422i	0.715795	−	0.715795i	−0.251946	−	0.967741i	$-0.581071\pi$
$983$	22.4422	−	22.4422i	0.715795	−	0.715795i	0.967741	+	0.251946i	$0.0810706\pi$
$984$		0			0
$985$	−49.7661	+	3.33083i	−1.58568	+	0.106129i
$986$		0			0
$987$	1.87008	+	1.87008i	0.0595253	+	0.0595253i
$988$		0			0
$989$		−	7.15800i		−	0.227611i
$990$		0			0
$991$			15.2779i			0.485319i	0.970112	+	0.242659i	$0.0780198\pi$
$991$			15.2779i			0.485319i	−0.970112	+	0.242659i	$0.921980\pi$
$992$		0			0
$993$	−11.8078	−	11.8078i	−0.374710	−	0.374710i
$994$		0			0
$995$	−20.5291	−	17.9535i	−0.650818	−	0.569165i
$996$		0			0
$997$	−26.7520	+	26.7520i	−0.847243	+	0.847243i	−0.989788	−	0.142545i	$-0.954471\pi$
$997$	−26.7520	+	26.7520i	−0.847243	+	0.847243i	0.142545	+	0.989788i	$0.454471\pi$
$998$		0			0
$999$	4.29069			0.135751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.b.463.4	yes	24
4.3	odd	2	inner	560.2.x.b.463.9	yes	24
5.2	odd	4	inner	560.2.x.b.127.9	yes	24
20.7	even	4	inner	560.2.x.b.127.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.b.127.4	✓	24	20.7	even	4	inner
560.2.x.b.127.9	yes	24	5.2	odd	4	inner
560.2.x.b.463.4	yes	24	1.1	even	1	trivial
560.2.x.b.463.9	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)

\(f(q)\)	\(=\)	\(q+(-0.636375 + 0.636375i) q^{3} +(1.68320 + 1.47202i) q^{5} +(-0.707107 - 0.707107i) q^{7} +2.19005i q^{9} +O(q^{10})\)	\(q+(-0.636375 + 0.636375i) q^{3} +(1.68320 + 1.47202i) q^{5} +(-0.707107 - 0.707107i) q^{7} +2.19005i q^{9} -0.0126062i q^{11} +(1.39232 + 1.39232i) q^{13} +(-2.00790 + 0.134388i) q^{15} +(-1.83069 + 1.83069i) q^{17} +1.25703 q^{19} +0.899970 q^{21} +(-0.761068 + 0.761068i) q^{23} +(0.666311 + 4.95540i) q^{25} +(-3.30282 - 3.30282i) q^{27} -1.27726i q^{29} +8.86198i q^{31} +(0.00802225 + 0.00802225i) q^{33} +(-0.149325 - 2.23108i) q^{35} +(-0.649549 + 0.649549i) q^{37} -1.77207 q^{39} +5.52580 q^{41} +(-4.70260 + 4.70260i) q^{43} +(-3.22380 + 3.68629i) q^{45} +(2.07793 + 2.07793i) q^{47} +1.00000i q^{49} -2.33001i q^{51} +(-2.69362 - 2.69362i) q^{53} +(0.0185565 - 0.0212187i) q^{55} +(-0.799940 + 0.799940i) q^{57} +0.236325 q^{59} +12.3491 q^{61} +(1.54860 - 1.54860i) q^{63} +(0.294026 + 4.39307i) q^{65} +(-4.86571 - 4.86571i) q^{67} -0.968650i q^{69} +12.9813i q^{71} +(-4.87625 - 4.87625i) q^{73} +(-3.57752 - 2.72947i) q^{75} +(-0.00891390 + 0.00891390i) q^{77} +10.0991 q^{79} -2.36650 q^{81} +(12.2600 - 12.2600i) q^{83} +(-5.77622 + 0.386600i) q^{85} +(0.812819 + 0.812819i) q^{87} -8.25433i q^{89} -1.96903i q^{91} +(-5.63954 - 5.63954i) q^{93} +(2.11583 + 1.85037i) q^{95} +(4.81979 - 4.81979i) q^{97} +0.0276082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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

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