LMFDB - Embedded newform 240.2.w.b.223.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(127,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.w (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.3
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	240.223
Dual form			240.2.w.b.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.224745 - 2.22474i) q^{5} +(3.14626 + 3.14626i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.224745 - 2.22474i) q^{5} +(3.14626 + 3.14626i) q^{7} -1.00000i q^{9} -1.41421i q^{11} +(-2.44949 - 2.44949i) q^{13} +(-1.73205 - 1.41421i) q^{15} +(4.44949 - 4.44949i) q^{17} +0.635674 q^{19} +4.44949 q^{21} +(-2.04989 + 2.04989i) q^{23} +(-4.89898 + 1.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} +9.34847i q^{29} +8.48528i q^{31} +(-1.00000 - 1.00000i) q^{33} +(6.29253 - 7.70674i) q^{35} +(-1.55051 + 1.55051i) q^{37} -3.46410 q^{39} -1.10102 q^{41} +(0.635674 - 0.635674i) q^{43} +(-2.22474 + 0.224745i) q^{45} +(-5.51399 - 5.51399i) q^{47} +12.7980i q^{49} -6.29253i q^{51} +(-2.00000 - 2.00000i) q^{53} +(-3.14626 + 0.317837i) q^{55} +(0.449490 - 0.449490i) q^{57} -9.89949 q^{59} +2.89898 q^{61} +(3.14626 - 3.14626i) q^{63} +(-4.89898 + 6.00000i) q^{65} +(6.29253 + 6.29253i) q^{67} +2.89898i q^{69} +12.5851i q^{71} +(3.00000 + 3.00000i) q^{73} +(-2.75699 + 4.17121i) q^{75} +(4.44949 - 4.44949i) q^{77} -9.75663 q^{79} -1.00000 q^{81} +(1.41421 - 1.41421i) q^{83} +(-10.8990 - 8.89898i) q^{85} +(6.61037 + 6.61037i) q^{87} -2.00000i q^{89} -15.4135i q^{91} +(6.00000 + 6.00000i) q^{93} +(-0.142865 - 1.41421i) q^{95} +(3.00000 - 3.00000i) q^{97} -1.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5}+O(q^{10}) $ 8 * q + 8 * q^5	$ 8 q + 8 q^{5} + 16 q^{17} + 16 q^{21} - 8 q^{33} - 32 q^{37} - 48 q^{41} - 8 q^{45} - 16 q^{53} - 16 q^{57} - 16 q^{61} + 24 q^{73} + 16 q^{77} - 8 q^{81} - 48 q^{85} + 48 q^{93} + 24 q^{97}+O(q^{100}) $ 8 * q + 8 * q^5 + 16 * q^17 + 16 * q^21 - 8 * q^33 - 32 * q^37 - 48 * q^41 - 8 * q^45 - 16 * q^53 - 16 * q^57 - 16 * q^61 + 24 * q^73 + 16 * q^77 - 8 * q^81 - 48 * q^85 + 48 * q^93 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−0.224745	−	2.22474i	−0.100509	−	0.994936i
$5$	−0.224745	−	2.22474i	−0.100509	−	0.994936i
$6$		0			0
$7$	3.14626	+	3.14626i	1.18918	+	1.18918i	0.977296	+	0.211881i	$0.0679588\pi$
$7$	3.14626	+	3.14626i	1.18918	+	1.18918i	0.211881	+	0.977296i	$0.432041\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$		0			0
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	0.280491	−	0.959857i	$-0.409503\pi$
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	−0.959857	+	0.280491i	$0.909503\pi$
$14$		0			0
$15$	−1.73205	−	1.41421i	−0.447214	−	0.365148i
$16$		0			0
$17$	4.44949	−	4.44949i	1.07916	−	1.07916i	0.0825749	−	0.996585i	$-0.473686\pi$
$17$	4.44949	−	4.44949i	1.07916	−	1.07916i	0.996585	−	0.0825749i	$-0.0263144\pi$
$18$		0			0
$19$	0.635674			0.145834			0.0729169	−	0.997338i	$-0.476769\pi$
$19$	0.635674			0.145834			0.0729169	+	0.997338i	$0.476769\pi$
$20$		0			0
$21$	4.44949			0.970958
$22$		0			0
$23$	−2.04989	+	2.04989i	−0.427431	+	0.427431i	−0.887752	−	0.460321i	$-0.847734\pi$
$23$	−2.04989	+	2.04989i	−0.427431	+	0.427431i	0.460321	+	0.887752i	$0.347734\pi$
$24$		0			0
$25$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			9.34847i			1.73597i	0.496593	+	0.867984i	$0.334584\pi$
$29$			9.34847i			1.73597i	−0.496593	+	0.867984i	$0.665416\pi$
$30$		0			0
$31$			8.48528i			1.52400i	0.647576	+	0.762001i	$0.275783\pi$
$31$			8.48528i			1.52400i	−0.647576	+	0.762001i	$0.724217\pi$
$32$		0			0
$33$	−1.00000	−	1.00000i	−0.174078	−	0.174078i
$34$		0			0
$35$	6.29253	−	7.70674i	1.06363	−	1.30268i
$36$		0			0
$37$	−1.55051	+	1.55051i	−0.254902	+	0.254902i	−0.822977	−	0.568075i	$-0.807688\pi$
$37$	−1.55051	+	1.55051i	−0.254902	+	0.254902i	0.568075	+	0.822977i	$0.307688\pi$
$38$		0			0
$39$	−3.46410			−0.554700
$40$		0			0
$41$	−1.10102			−0.171951			−0.0859753	−	0.996297i	$-0.527401\pi$
$41$	−1.10102			−0.171951			−0.0859753	+	0.996297i	$0.527401\pi$
$42$		0			0
$43$	0.635674	−	0.635674i	0.0969395	−	0.0969395i	−0.656974	−	0.753913i	$-0.728164\pi$
$43$	0.635674	−	0.635674i	0.0969395	−	0.0969395i	0.753913	+	0.656974i	$0.228164\pi$
$44$		0			0
$45$	−2.22474	+	0.224745i	−0.331645	+	0.0335030i
$46$		0			0
$47$	−5.51399	−	5.51399i	−0.804298	−	0.804298i	0.179466	−	0.983764i	$-0.442563\pi$
$47$	−5.51399	−	5.51399i	−0.804298	−	0.804298i	−0.983764	+	0.179466i	$0.942563\pi$
$48$		0			0
$49$			12.7980i			1.82828i
$50$		0			0
$51$		−	6.29253i		−	0.881130i
$52$		0			0
$53$	−2.00000	−	2.00000i	−0.274721	−	0.274721i	0.556276	−	0.830997i	$-0.312230\pi$
$53$	−2.00000	−	2.00000i	−0.274721	−	0.274721i	−0.830997	+	0.556276i	$0.812230\pi$
$54$		0			0
$55$	−3.14626	+	0.317837i	−0.424242	+	0.0428572i
$56$		0			0
$57$	0.449490	−	0.449490i	0.0595364	−	0.0595364i
$58$		0			0
$59$	−9.89949			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$60$		0			0
$61$	2.89898			0.371176			0.185588	−	0.982628i	$-0.440581\pi$
$61$	2.89898			0.371176			0.185588	+	0.982628i	$0.440581\pi$
$62$		0			0
$63$	3.14626	−	3.14626i	0.396392	−	0.396392i
$64$		0			0
$65$	−4.89898	+	6.00000i	−0.607644	+	0.744208i
$66$		0			0
$67$	6.29253	+	6.29253i	0.768755	+	0.768755i	0.977887	−	0.209133i	$-0.0670640\pi$
$67$	6.29253	+	6.29253i	0.768755	+	0.768755i	−0.209133	+	0.977887i	$0.567064\pi$
$68$		0			0
$69$			2.89898i			0.348996i
$70$		0			0
$71$			12.5851i			1.49357i	0.665065	+	0.746786i	$0.268404\pi$
$71$			12.5851i			1.49357i	−0.665065	+	0.746786i	$0.731596\pi$
$72$		0			0
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	0.860527	−	0.509404i	$-0.170134\pi$
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	−0.509404	+	0.860527i	$0.670134\pi$
$74$		0			0
$75$	−2.75699	+	4.17121i	−0.318350	+	0.481650i
$76$		0			0
$77$	4.44949	−	4.44949i	0.507066	−	0.507066i
$78$		0			0
$79$	−9.75663			−1.09771			−0.548853	−	0.835919i	$-0.684935\pi$
$79$	−9.75663			−1.09771			−0.548853	+	0.835919i	$0.684935\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.41421	−	1.41421i	0.155230	−	0.155230i	−0.625219	−	0.780449i	$-0.714990\pi$
$83$	1.41421	−	1.41421i	0.155230	−	0.155230i	0.780449	+	0.625219i	$0.214990\pi$
$84$		0			0
$85$	−10.8990	−	8.89898i	−1.18216	−	0.965230i
$86$		0			0
$87$	6.61037	+	6.61037i	0.708706	+	0.708706i
$88$		0			0
$89$		−	2.00000i		−	0.212000i	−0.994366	−	0.106000i	$-0.966196\pi$
$89$		−	2.00000i		−	0.212000i	0.994366	−	0.106000i	$-0.0338043\pi$
$90$		0			0
$91$		−	15.4135i		−	1.61577i
$92$		0			0
$93$	6.00000	+	6.00000i	0.622171	+	0.622171i
$94$		0			0
$95$	−0.142865	−	1.41421i	−0.0146576	−	0.145095i
$96$		0			0
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$		0			0
$99$	−1.41421			−0.142134
$100$		0			0
$101$	8.44949			0.840756			0.420378	−	0.907349i	$-0.361898\pi$
$101$	8.44949			0.840756			0.420378	+	0.907349i	$0.361898\pi$
$102$		0			0
$103$	8.80312	−	8.80312i	0.867397	−	0.867397i	−0.124787	−	0.992184i	$-0.539825\pi$
$103$	8.80312	−	8.80312i	0.867397	−	0.867397i	0.992184	+	0.124787i	$0.0398246\pi$
$104$		0			0
$105$	−1.00000	−	9.89898i	−0.0975900	−	0.966041i
$106$		0			0
$107$	−2.68556	−	2.68556i	−0.259623	−	0.259623i	0.565278	−	0.824901i	$-0.308769\pi$
$107$	−2.68556	−	2.68556i	−0.259623	−	0.259623i	−0.824901	+	0.565278i	$0.808769\pi$
$108$		0			0
$109$		−	14.8990i		−	1.42706i	−0.700623	−	0.713532i	$-0.747094\pi$
$109$		−	14.8990i		−	1.42706i	0.700623	−	0.713532i	$-0.252906\pi$
$110$		0			0
$111$			2.19275i			0.208127i
$112$		0			0
$113$	−11.3485	−	11.3485i	−1.06757	−	1.06757i	−0.997545	−	0.0700292i	$-0.977691\pi$
$113$	−11.3485	−	11.3485i	−1.06757	−	1.06757i	−0.0700292	−	0.997545i	$-0.522309\pi$
$114$		0			0
$115$	5.02118	+	4.09978i	0.468227	+	0.382306i
$116$		0			0
$117$	−2.44949	+	2.44949i	−0.226455	+	0.226455i
$118$		0			0
$119$	27.9985			2.56662
$120$		0			0
$121$	9.00000			0.818182
$122$		0			0
$123$	−0.778539	+	0.778539i	−0.0701985	+	0.0701985i
$124$		0			0
$125$	3.32577	+	10.6742i	0.297465	+	0.954733i
$126$		0			0
$127$	−2.51059	−	2.51059i	−0.222779	−	0.222779i	0.586889	−	0.809668i	$-0.300353\pi$
$127$	−2.51059	−	2.51059i	−0.222779	−	0.222779i	−0.809668	+	0.586889i	$0.800353\pi$
$128$		0			0
$129$		−	0.898979i		−	0.0791507i
$130$		0			0
$131$			19.3704i			1.69240i	0.532866	+	0.846200i	$0.321115\pi$
$131$			19.3704i			1.69240i	−0.532866	+	0.846200i	$0.678885\pi$
$132$		0			0
$133$	2.00000	+	2.00000i	0.173422	+	0.173422i
$134$		0			0
$135$	−1.41421	+	1.73205i	−0.121716	+	0.149071i
$136$		0			0
$137$	5.55051	−	5.55051i	0.474212	−	0.474212i	−0.429063	−	0.903275i	$-0.641156\pi$
$137$	5.55051	−	5.55051i	0.474212	−	0.474212i	0.903275	+	0.429063i	$0.141156\pi$
$138$		0			0
$139$	−10.3923			−0.881464			−0.440732	−	0.897639i	$-0.645281\pi$
$139$	−10.3923			−0.881464			−0.440732	+	0.897639i	$0.645281\pi$
$140$		0			0
$141$	−7.79796			−0.656707
$142$		0			0
$143$	−3.46410	+	3.46410i	−0.289683	+	0.289683i
$144$		0			0
$145$	20.7980	−	2.10102i	1.72718	−	0.174480i
$146$		0			0
$147$	9.04952	+	9.04952i	0.746392	+	0.746392i
$148$		0			0
$149$		−	1.34847i		−	0.110471i	−0.998473	−	0.0552355i	$-0.982409\pi$
$149$		−	1.34847i		−	0.110471i	0.998473	−	0.0552355i	$-0.0175909\pi$
$150$		0			0
$151$		−	9.12096i		−	0.742253i	−0.928582	−	0.371126i	$-0.878972\pi$
$151$		−	9.12096i		−	0.742253i	0.928582	−	0.371126i	$-0.121028\pi$
$152$		0			0
$153$	−4.44949	−	4.44949i	−0.359720	−	0.359720i
$154$		0			0
$155$	18.8776	−	1.90702i	1.51628	−	0.153176i
$156$		0			0
$157$	9.34847	−	9.34847i	0.746089	−	0.746089i	−0.227653	−	0.973742i	$-0.573105\pi$
$157$	9.34847	−	9.34847i	0.746089	−	0.746089i	0.973742	+	0.227653i	$0.0731053\pi$
$158$		0			0
$159$	−2.82843			−0.224309
$160$		0			0
$161$	−12.8990			−1.01658
$162$		0			0
$163$	−6.92820	+	6.92820i	−0.542659	+	0.542659i	−0.924307	−	0.381649i	$-0.875356\pi$
$163$	−6.92820	+	6.92820i	−0.542659	+	0.542659i	0.381649	+	0.924307i	$0.375356\pi$
$164$		0			0
$165$	−2.00000	+	2.44949i	−0.155700	+	0.190693i
$166$		0			0
$167$	−16.1920	−	16.1920i	−1.25298	−	1.25298i	−0.954379	−	0.298597i	$-0.903481\pi$
$167$	−16.1920	−	16.1920i	−1.25298	−	1.25298i	−0.298597	−	0.954379i	$-0.596519\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$		−	0.635674i		−	0.0486112i
$172$		0			0
$173$	−1.55051	−	1.55051i	−0.117883	−	0.117883i	0.645704	−	0.763587i	$-0.276564\pi$
$173$	−1.55051	−	1.55051i	−0.117883	−	0.117883i	−0.763587	+	0.645704i	$0.776564\pi$
$174$		0			0
$175$	−18.5597	−	12.2672i	−1.40299	−	0.927315i
$176$		0			0
$177$	−7.00000	+	7.00000i	−0.526152	+	0.526152i
$178$		0			0
$179$	5.51399			0.412135			0.206067	−	0.978538i	$-0.433933\pi$
$179$	5.51399			0.412135			0.206067	+	0.978538i	$0.433933\pi$
$180$		0			0
$181$	−10.8990			−0.810115			−0.405057	−	0.914291i	$-0.632748\pi$
$181$	−10.8990			−0.810115			−0.405057	+	0.914291i	$0.632748\pi$
$182$		0			0
$183$	2.04989	−	2.04989i	0.151532	−	0.151532i
$184$		0			0
$185$	3.79796	+	3.10102i	0.279231	+	0.227992i
$186$		0			0
$187$	−6.29253	−	6.29253i	−0.460155	−	0.460155i
$188$		0			0
$189$		−	4.44949i		−	0.323653i
$190$		0			0
$191$			1.55708i			0.112666i	0.998412	+	0.0563331i	$0.0179409\pi$
$191$			1.55708i			0.112666i	−0.998412	+	0.0563331i	$0.982059\pi$
$192$		0			0
$193$	4.79796	+	4.79796i	0.345365	+	0.345365i	0.858380	−	0.513015i	$-0.171471\pi$
$193$	4.79796	+	4.79796i	0.345365	+	0.345365i	−0.513015	+	0.858380i	$0.671471\pi$
$194$		0			0
$195$	0.778539	+	7.70674i	0.0557523	+	0.551891i
$196$		0			0
$197$	−11.7980	+	11.7980i	−0.840570	+	0.840570i	−0.988933	−	0.148363i	$-0.952600\pi$
$197$	−11.7980	+	11.7980i	−0.840570	+	0.840570i	0.148363	+	0.988933i	$0.452600\pi$
$198$		0			0
$199$	20.4347			1.44857			0.724287	−	0.689498i	$-0.242169\pi$
$199$	20.4347			1.44857			0.724287	+	0.689498i	$0.242169\pi$
$200$		0			0
$201$	8.89898			0.627686
$202$		0			0
$203$	−29.4128	+	29.4128i	−2.06437	+	2.06437i
$204$		0			0
$205$	0.247449	+	2.44949i	0.0172826	+	0.171080i
$206$		0			0
$207$	2.04989	+	2.04989i	0.142477	+	0.142477i
$208$		0			0
$209$		−	0.898979i		−	0.0621837i
$210$		0			0
$211$		−	14.7778i		−	1.01735i	−0.860960	−	0.508673i	$-0.830136\pi$
$211$		−	14.7778i		−	1.01735i	0.860960	−	0.508673i	$-0.169864\pi$
$212$		0			0
$213$	8.89898	+	8.89898i	0.609748	+	0.609748i
$214$		0			0
$215$	−1.55708	−	1.27135i	−0.106192	−	0.0867053i
$216$		0			0
$217$	−26.6969	+	26.6969i	−1.81231	+	1.81231i
$218$		0			0
$219$	4.24264			0.286691
$220$		0			0
$221$	−21.7980			−1.46629
$222$		0			0
$223$	12.9029	−	12.9029i	0.864042	−	0.864042i	−0.127763	−	0.991805i	$-0.540780\pi$
$223$	12.9029	−	12.9029i	0.864042	−	0.864042i	0.991805	+	0.127763i	$0.0407797\pi$
$224$		0			0
$225$	1.00000	+	4.89898i	0.0666667	+	0.326599i
$226$		0			0
$227$	4.38551	+	4.38551i	0.291076	+	0.291076i	0.837505	−	0.546429i	$-0.184013\pi$
$227$	4.38551	+	4.38551i	0.291076	+	0.291076i	−0.546429	+	0.837505i	$0.684013\pi$
$228$		0			0
$229$		−	3.79796i		−	0.250976i	−0.992095	−	0.125488i	$-0.959950\pi$
$229$		−	3.79796i		−	0.250976i	0.992095	−	0.125488i	$-0.0400497\pi$
$230$		0			0
$231$		−	6.29253i		−	0.414018i
$232$		0			0
$233$	18.2474	+	18.2474i	1.19543	+	1.19543i	0.975520	+	0.219910i	$0.0705763\pi$
$233$	18.2474	+	18.2474i	1.19543	+	1.19543i	0.219910	+	0.975520i	$0.429424\pi$
$234$		0			0
$235$	−11.0280	+	13.5065i	−0.719386	+	0.881064i
$236$		0			0
$237$	−6.89898	+	6.89898i	−0.448137	+	0.448137i
$238$		0			0
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$		0			0
$241$	8.00000			0.515325			0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000			0.515325			0.257663	+	0.966235i	$0.417048\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	28.4722	−	2.87628i	1.81902	−	0.183759i
$246$		0			0
$247$	−1.55708	−	1.55708i	−0.0990745	−	0.0990745i
$248$		0			0
$249$		−	2.00000i		−	0.126745i
$250$		0			0
$251$		−	25.3130i		−	1.59774i	−0.601503	−	0.798871i	$-0.705431\pi$
$251$		−	25.3130i		−	1.59774i	0.601503	−	0.798871i	$-0.294569\pi$
$252$		0			0
$253$	2.89898	+	2.89898i	0.182257	+	0.182257i
$254$		0			0
$255$	−13.9993	+	1.41421i	−0.876668	+	0.0885615i
$256$		0			0
$257$	2.44949	−	2.44949i	0.152795	−	0.152795i	−0.626570	−	0.779365i	$-0.715542\pi$
$257$	2.44949	−	2.44949i	0.152795	−	0.152795i	0.779365	+	0.626570i	$0.215542\pi$
$258$		0			0
$259$	−9.75663			−0.606248
$260$		0			0
$261$	9.34847			0.578656
$262$		0			0
$263$	13.3636	−	13.3636i	0.824035	−	0.824035i	−0.162649	−	0.986684i	$-0.552004\pi$
$263$	13.3636	−	13.3636i	0.824035	−	0.824035i	0.986684	+	0.162649i	$0.0520039\pi$
$264$		0			0
$265$	−4.00000	+	4.89898i	−0.245718	+	0.300942i
$266$		0			0
$267$	−1.41421	−	1.41421i	−0.0865485	−	0.0865485i
$268$		0			0
$269$			10.6515i			0.649435i	0.945811	+	0.324718i	$0.105269\pi$
$269$			10.6515i			0.649435i	−0.945811	+	0.324718i	$0.894731\pi$
$270$		0			0
$271$			0.921404i			0.0559713i	0.999608	+	0.0279856i	$0.00890927\pi$
$271$			0.921404i			0.0559713i	−0.999608	+	0.0279856i	$0.991091\pi$
$272$		0			0
$273$	−10.8990	−	10.8990i	−0.659636	−	0.659636i
$274$		0			0
$275$	1.41421	+	6.92820i	0.0852803	+	0.417786i
$276$		0			0
$277$	−7.34847	+	7.34847i	−0.441527	+	0.441527i	−0.892525	−	0.450998i	$-0.851068\pi$
$277$	−7.34847	+	7.34847i	−0.441527	+	0.441527i	0.450998	+	0.892525i	$0.351068\pi$
$278$		0			0
$279$	8.48528			0.508001
$280$		0			0
$281$	−24.6969			−1.47330			−0.736648	−	0.676276i	$-0.763592\pi$
$281$	−24.6969			−1.47330			−0.736648	+	0.676276i	$0.763592\pi$
$282$		0			0
$283$	−7.84961	+	7.84961i	−0.466611	+	0.466611i	−0.900815	−	0.434204i	$-0.857030\pi$
$283$	−7.84961	+	7.84961i	−0.466611	+	0.466611i	0.434204	+	0.900815i	$0.357030\pi$
$284$		0			0
$285$	−1.10102	−	0.898979i	−0.0652188	−	0.0532509i
$286$		0			0
$287$	−3.46410	−	3.46410i	−0.204479	−	0.204479i
$288$		0			0
$289$		−	22.5959i		−	1.32917i
$290$		0			0
$291$		−	4.24264i		−	0.248708i
$292$		0			0
$293$	−9.10102	−	9.10102i	−0.531687	−	0.531687i	0.389387	−	0.921074i	$-0.372687\pi$
$293$	−9.10102	−	9.10102i	−0.531687	−	0.531687i	−0.921074	+	0.389387i	$0.872687\pi$
$294$		0			0
$295$	2.22486	+	22.0239i	0.129536	+	1.28228i
$296$		0			0
$297$	−1.00000	+	1.00000i	−0.0580259	+	0.0580259i
$298$		0			0
$299$	10.0424			0.580765
$300$		0			0
$301$	4.00000			0.230556
$302$		0			0
$303$	5.97469	−	5.97469i	0.343237	−	0.343237i
$304$		0			0
$305$	−0.651531	−	6.44949i	−0.0373065	−	0.369297i
$306$		0			0
$307$	16.0492	+	16.0492i	0.915974	+	0.915974i	0.996734	−	0.0807597i	$-0.0257346\pi$
$307$	16.0492	+	16.0492i	0.915974	+	0.915974i	−0.0807597	+	0.996734i	$0.525735\pi$
$308$		0			0
$309$		−	12.4495i		−	0.708227i
$310$		0			0
$311$			15.1278i			0.857816i	0.903348	+	0.428908i	$0.141102\pi$
$311$			15.1278i			0.857816i	−0.903348	+	0.428908i	$0.858898\pi$
$312$		0			0
$313$	−0.797959	−	0.797959i	−0.0451033	−	0.0451033i	0.684195	−	0.729299i	$-0.260154\pi$
$313$	−0.797959	−	0.797959i	−0.0451033	−	0.0451033i	−0.729299	+	0.684195i	$0.760154\pi$
$314$		0			0
$315$	−7.70674	−	6.29253i	−0.434226	−	0.354544i
$316$		0			0
$317$	0.651531	−	0.651531i	0.0365936	−	0.0365936i	−0.688573	−	0.725167i	$-0.741763\pi$
$317$	0.651531	−	0.651531i	0.0365936	−	0.0365936i	0.725167	+	0.688573i	$0.241763\pi$
$318$		0			0
$319$	13.2207			0.740219
$320$		0			0
$321$	−3.79796			−0.211981
$322$		0			0
$323$	2.82843	−	2.82843i	0.157378	−	0.157378i
$324$		0			0
$325$	14.4495	+	9.55051i	0.801513	+	0.529767i
$326$		0			0
$327$	−10.5352	−	10.5352i	−0.582596	−	0.582596i
$328$		0			0
$329$		−	34.6969i		−	1.91290i
$330$		0			0
$331$			20.1489i			1.10749i	0.832688	+	0.553743i	$0.186801\pi$
$331$			20.1489i			1.10749i	−0.832688	+	0.553743i	$0.813199\pi$
$332$		0			0
$333$	1.55051	+	1.55051i	0.0849674	+	0.0849674i
$334$		0			0
$335$	12.5851	−	15.4135i	0.687595	−	0.842129i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	−16.0492			−0.871671
$340$		0			0
$341$	12.0000			0.649836
$342$		0			0
$343$	−18.2419	+	18.2419i	−0.984971	+	0.984971i
$344$		0			0
$345$	6.44949	−	0.651531i	0.347229	−	0.0350772i
$346$		0			0
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.997887	−	0.0649788i	$-0.979302\pi$
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.0649788	−	0.997887i	$-0.520698\pi$
$348$		0			0
$349$		−	18.8990i		−	1.01164i	−0.862639	−	0.505820i	$-0.831190\pi$
$349$		−	18.8990i		−	1.01164i	0.862639	−	0.505820i	$-0.168810\pi$
$350$		0			0
$351$			3.46410i			0.184900i
$352$		0			0
$353$	24.4495	+	24.4495i	1.30132	+	1.30132i	0.927505	+	0.373810i	$0.121949\pi$
$353$	24.4495	+	24.4495i	1.30132	+	1.30132i	0.373810	+	0.927505i	$0.378051\pi$
$354$		0			0
$355$	27.9985	−	2.82843i	1.48601	−	0.150117i
$356$		0			0
$357$	19.7980	−	19.7980i	1.04782	−	1.04782i
$358$		0			0
$359$	12.8708			0.679294			0.339647	−	0.940553i	$-0.389692\pi$
$359$	12.8708			0.679294			0.339647	+	0.940553i	$0.389692\pi$
$360$		0			0
$361$	−18.5959			−0.978733
$362$		0			0
$363$	6.36396	−	6.36396i	0.334021	−	0.334021i
$364$		0			0
$365$	6.00000	−	7.34847i	0.314054	−	0.384636i
$366$		0			0
$367$	−0.953512	−	0.953512i	−0.0497729	−	0.0497729i	0.681782	−	0.731555i	$-0.261205\pi$
$367$	−0.953512	−	0.953512i	−0.0497729	−	0.0497729i	−0.731555	+	0.681782i	$0.761205\pi$
$368$		0			0
$369$			1.10102i			0.0573168i
$370$		0			0
$371$		−	12.5851i		−	0.653384i
$372$		0			0
$373$	−6.24745	−	6.24745i	−0.323481	−	0.323481i	0.526620	−	0.850101i	$-0.323459\pi$
$373$	−6.24745	−	6.24745i	−0.323481	−	0.323481i	−0.850101	+	0.526620i	$0.823459\pi$
$374$		0			0
$375$	9.89949	+	5.19615i	0.511208	+	0.268328i
$376$		0			0
$377$	22.8990	−	22.8990i	1.17936	−	1.17936i
$378$		0			0
$379$	24.2487			1.24557			0.622786	−	0.782392i	$-0.286001\pi$
$379$	24.2487			1.24557			0.622786	+	0.782392i	$0.286001\pi$
$380$		0			0
$381$	−3.55051			−0.181898
$382$		0			0
$383$	−5.51399	+	5.51399i	−0.281752	+	0.281752i	−0.833807	−	0.552056i	$-0.813844\pi$
$383$	−5.51399	+	5.51399i	−0.281752	+	0.281752i	0.552056	+	0.833807i	$0.313844\pi$
$384$		0			0
$385$	−10.8990	−	8.89898i	−0.555463	−	0.453534i
$386$		0			0
$387$	−0.635674	−	0.635674i	−0.0323132	−	0.0323132i
$388$		0			0
$389$			5.34847i			0.271178i	0.990765	+	0.135589i	$0.0432927\pi$
$389$			5.34847i			0.271178i	−0.990765	+	0.135589i	$0.956707\pi$
$390$		0			0
$391$			18.2419i			0.922533i
$392$		0			0
$393$	13.6969	+	13.6969i	0.690919	+	0.690919i
$394$		0			0
$395$	2.19275	+	21.7060i	0.110329	+	1.09215i
$396$		0			0
$397$	−1.34847	+	1.34847i	−0.0676777	+	0.0676777i	−0.740135	−	0.672458i	$-0.765239\pi$
$397$	−1.34847	+	1.34847i	−0.0676777	+	0.0676777i	0.672458	+	0.740135i	$0.265239\pi$
$398$		0			0
$399$	2.82843			0.141598
$400$		0			0
$401$	15.7980			0.788912			0.394456	−	0.918915i	$-0.370933\pi$
$401$	15.7980			0.788912			0.394456	+	0.918915i	$0.370933\pi$
$402$		0			0
$403$	20.7846	−	20.7846i	1.03536	−	1.03536i
$404$		0			0
$405$	0.224745	+	2.22474i	0.0111677	+	0.110548i
$406$		0			0
$407$	2.19275	+	2.19275i	0.108691	+	0.108691i
$408$		0			0
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$		0			0
$411$		−	7.84961i		−	0.387193i
$412$		0			0
$413$	−31.1464	−	31.1464i	−1.53262	−	1.53262i
$414$		0			0
$415$	−3.46410	−	2.82843i	−0.170046	−	0.138842i
$416$		0			0
$417$	−7.34847	+	7.34847i	−0.359856	+	0.359856i
$418$		0			0
$419$	−8.62815			−0.421513			−0.210756	−	0.977539i	$-0.567593\pi$
$419$	−8.62815			−0.421513			−0.210756	+	0.977539i	$0.567593\pi$
$420$		0			0
$421$	−29.5959			−1.44242			−0.721208	−	0.692718i	$-0.756413\pi$
$421$	−29.5959			−1.44242			−0.721208	+	0.692718i	$0.756413\pi$
$422$		0			0
$423$	−5.51399	+	5.51399i	−0.268099	+	0.268099i
$424$		0			0
$425$	−17.3485	+	26.2474i	−0.841524	+	1.27319i
$426$		0			0
$427$	9.12096	+	9.12096i	0.441394	+	0.441394i
$428$		0			0
$429$			4.89898i			0.236525i
$430$		0			0
$431$			8.48528i			0.408722i	0.978896	+	0.204361i	$0.0655116\pi$
$431$			8.48528i			0.408722i	−0.978896	+	0.204361i	$0.934488\pi$
$432$		0			0
$433$	−10.1010	−	10.1010i	−0.485424	−	0.485424i	0.421435	−	0.906859i	$-0.361527\pi$
$433$	−10.1010	−	10.1010i	−0.485424	−	0.485424i	−0.906859	+	0.421435i	$0.861527\pi$
$434$		0			0
$435$	13.2207	−	16.1920i	0.633886	−	0.776348i
$436$		0			0
$437$	−1.30306	+	1.30306i	−0.0623339	+	0.0623339i
$438$		0			0
$439$	−11.6637			−0.556676			−0.278338	−	0.960483i	$-0.589784\pi$
$439$	−11.6637			−0.556676			−0.278338	+	0.960483i	$0.589784\pi$
$440$		0			0
$441$	12.7980			0.609427
$442$		0			0
$443$	13.8564	−	13.8564i	0.658338	−	0.658338i	−0.296649	−	0.954987i	$-0.595869\pi$
$443$	13.8564	−	13.8564i	0.658338	−	0.658338i	0.954987	+	0.296649i	$0.0958691\pi$
$444$		0			0
$445$	−4.44949	+	0.449490i	−0.210926	+	0.0213079i
$446$		0			0
$447$	−0.953512	−	0.953512i	−0.0450996	−	0.0450996i
$448$		0			0
$449$		−	7.30306i		−	0.344653i	−0.985040	−	0.172326i	$-0.944872\pi$
$449$		−	7.30306i		−	0.344653i	0.985040	−	0.172326i	$-0.0551284\pi$
$450$		0			0
$451$			1.55708i			0.0733199i
$452$		0			0
$453$	−6.44949	−	6.44949i	−0.303023	−	0.303023i
$454$		0			0
$455$	−34.2911	+	3.46410i	−1.60759	+	0.162400i
$456$		0			0
$457$	14.5959	−	14.5959i	0.682768	−	0.682768i	−0.277855	−	0.960623i	$-0.589623\pi$
$457$	14.5959	−	14.5959i	0.682768	−	0.682768i	0.960623	+	0.277855i	$0.0896234\pi$
$458$		0			0
$459$	−6.29253			−0.293710
$460$		0			0
$461$	27.1464			1.26434			0.632168	−	0.774832i	$-0.282165\pi$
$461$	27.1464			1.26434			0.632168	+	0.774832i	$0.282165\pi$
$462$		0			0
$463$	−0.953512	+	0.953512i	−0.0443134	+	0.0443134i	−0.728916	−	0.684603i	$-0.759976\pi$
$463$	−0.953512	+	0.953512i	−0.0443134	+	0.0443134i	0.684603	+	0.728916i	$0.259976\pi$
$464$		0			0
$465$	12.0000	−	14.6969i	0.556487	−	0.681554i
$466$		0			0
$467$	−4.24264	−	4.24264i	−0.196326	−	0.196326i	0.602097	−	0.798423i	$-0.294332\pi$
$467$	−4.24264	−	4.24264i	−0.196326	−	0.196326i	−0.798423	+	0.602097i	$0.794332\pi$
$468$		0			0
$469$			39.5959i			1.82837i
$470$		0			0
$471$		−	13.2207i		−	0.609179i
$472$		0			0
$473$	−0.898979	−	0.898979i	−0.0413351	−	0.0413351i
$474$		0			0
$475$	−3.11416	+	0.635674i	−0.142887	+	0.0291667i
$476$		0			0
$477$	−2.00000	+	2.00000i	−0.0915737	+	0.0915737i
$478$		0			0
$479$	−32.0983			−1.46661			−0.733305	−	0.679900i	$-0.762023\pi$
$479$	−32.0983			−1.46661			−0.733305	+	0.679900i	$0.762023\pi$
$480$		0			0
$481$	7.59592			0.346344
$482$		0			0
$483$	−9.12096	+	9.12096i	−0.415018	+	0.415018i
$484$		0			0
$485$	−7.34847	−	6.00000i	−0.333677	−	0.272446i
$486$		0			0
$487$	3.14626	+	3.14626i	0.142571	+	0.142571i	0.774790	−	0.632219i	$-0.217856\pi$
$487$	3.14626	+	3.14626i	0.142571	+	0.142571i	−0.632219	+	0.774790i	$0.717856\pi$
$488$		0			0
$489$			9.79796i			0.443079i
$490$		0			0
$491$		−	23.7559i		−	1.07209i	−0.844190	−	0.536044i	$-0.819918\pi$
$491$		−	23.7559i		−	1.07209i	0.844190	−	0.536044i	$-0.180082\pi$
$492$		0			0
$493$	41.5959	+	41.5959i	1.87339	+	1.87339i
$494$		0			0
$495$	0.317837	+	3.14626i	0.0142857	+	0.141414i
$496$		0			0
$497$	−39.5959	+	39.5959i	−1.77612	+	1.77612i
$498$		0			0
$499$	−34.5768			−1.54787			−0.773935	−	0.633265i	$-0.781714\pi$
$499$	−34.5768			−1.54787			−0.773935	+	0.633265i	$0.781714\pi$
$500$		0			0
$501$	−22.8990			−1.02305
$502$		0			0
$503$	5.51399	−	5.51399i	0.245857	−	0.245857i	−0.573411	−	0.819268i	$-0.694380\pi$
$503$	5.51399	−	5.51399i	0.245857	−	0.245857i	0.819268	+	0.573411i	$0.194380\pi$
$504$		0			0
$505$	−1.89898	−	18.7980i	−0.0845035	−	0.836498i
$506$		0			0
$507$	−0.707107	−	0.707107i	−0.0314037	−	0.0314037i
$508$		0			0
$509$			11.5505i			0.511967i	0.966681	+	0.255984i	$0.0823993\pi$
$509$			11.5505i			0.511967i	−0.966681	+	0.255984i	$0.917601\pi$
$510$		0			0
$511$			18.8776i			0.835095i
$512$		0			0
$513$	−0.449490	−	0.449490i	−0.0198455	−	0.0198455i
$514$		0			0
$515$	−21.5631	−	17.6062i	−0.950186	−	0.775824i
$516$		0			0
$517$	−7.79796	+	7.79796i	−0.342954	+	0.342954i
$518$		0			0
$519$	−2.19275			−0.0962512
$520$		0			0
$521$	26.4949			1.16076			0.580381	−	0.814345i	$-0.302904\pi$
$521$	26.4949			1.16076			0.580381	+	0.814345i	$0.302904\pi$
$522$		0			0
$523$	−8.83523	+	8.83523i	−0.386337	+	0.386337i	−0.873379	−	0.487041i	$-0.838076\pi$
$523$	−8.83523	+	8.83523i	−0.386337	+	0.386337i	0.487041	+	0.873379i	$0.338076\pi$
$524$		0			0
$525$	−21.7980	+	4.44949i	−0.951341	+	0.194192i
$526$		0			0
$527$	37.7552	+	37.7552i	1.64464	+	1.64464i
$528$		0			0
$529$			14.5959i			0.634605i
$530$		0			0
$531$			9.89949i			0.429601i
$532$		0			0
$533$	2.69694	+	2.69694i	0.116817	+	0.116817i
$534$		0			0
$535$	−5.37113	+	6.57826i	−0.232214	+	0.284403i
$536$		0			0
$537$	3.89898	−	3.89898i	0.168253	−	0.168253i
$538$		0			0
$539$	18.0990			0.779581
$540$		0			0
$541$	26.4949			1.13910			0.569552	−	0.821955i	$-0.307117\pi$
$541$	26.4949			1.13910			0.569552	+	0.821955i	$0.307117\pi$
$542$		0			0
$543$	−7.70674	+	7.70674i	−0.330728	+	0.330728i
$544$		0			0
$545$	−33.1464	+	3.34847i	−1.41984	+	0.143433i
$546$		0			0
$547$	−17.3205	−	17.3205i	−0.740571	−	0.740571i	0.232117	−	0.972688i	$-0.425435\pi$
$547$	−17.3205	−	17.3205i	−0.740571	−	0.740571i	−0.972688	+	0.232117i	$0.925435\pi$
$548$		0			0
$549$		−	2.89898i		−	0.123725i
$550$		0			0
$551$			5.94258i			0.253163i
$552$		0			0
$553$	−30.6969	−	30.6969i	−1.30537	−	1.30537i
$554$		0			0
$555$	4.87832	−	0.492810i	0.207073	−	0.0209186i
$556$		0			0
$557$	−12.2020	+	12.2020i	−0.517017	+	0.517017i	−0.916668	−	0.399651i	$-0.869131\pi$
$557$	−12.2020	+	12.2020i	−0.517017	+	0.517017i	0.399651	+	0.916668i	$0.369131\pi$
$558$		0			0
$559$	−3.11416			−0.131715
$560$		0			0
$561$	−8.89898			−0.375715
$562$		0			0
$563$	15.4135	−	15.4135i	0.649601	−	0.649601i	−0.303296	−	0.952897i	$-0.598087\pi$
$563$	15.4135	−	15.4135i	0.649601	−	0.649601i	0.952897	+	0.303296i	$0.0980870\pi$
$564$		0			0
$565$	−22.6969	+	27.7980i	−0.954867	+	1.16947i
$566$		0			0
$567$	−3.14626	−	3.14626i	−0.132131	−	0.132131i
$568$		0			0
$569$			21.5959i			0.905348i	0.891676	+	0.452674i	$0.149530\pi$
$569$			21.5959i			0.905348i	−0.891676	+	0.452674i	$0.850470\pi$
$570$		0			0
$571$		−	37.1195i		−	1.55340i	−0.629869	−	0.776701i	$-0.716891\pi$
$571$		−	37.1195i		−	1.55340i	0.629869	−	0.776701i	$-0.283109\pi$
$572$		0			0
$573$	1.10102	+	1.10102i	0.0459958	+	0.0459958i
$574$		0			0
$575$	7.99247	−	12.0922i	0.333309	−	0.504282i
$576$		0			0
$577$	17.4949	−	17.4949i	0.728322	−	0.728322i	−0.241963	−	0.970285i	$-0.577791\pi$
$577$	17.4949	−	17.4949i	0.728322	−	0.728322i	0.970285	+	0.241963i	$0.0777914\pi$
$578$		0			0
$579$	6.78534			0.281989
$580$		0			0
$581$	8.89898			0.369192
$582$		0			0
$583$	−2.82843	+	2.82843i	−0.117141	+	0.117141i
$584$		0			0
$585$	6.00000	+	4.89898i	0.248069	+	0.202548i
$586$		0			0
$587$	20.9275	+	20.9275i	0.863769	+	0.863769i	0.991774	−	0.128004i	$-0.0408571\pi$
$587$	20.9275	+	20.9275i	0.863769	+	0.863769i	−0.128004	+	0.991774i	$0.540857\pi$
$588$		0			0
$589$			5.39388i			0.222251i
$590$		0			0
$591$			16.6848i			0.686322i
$592$		0			0
$593$	9.55051	+	9.55051i	0.392192	+	0.392192i	0.875468	−	0.483276i	$-0.160553\pi$
$593$	9.55051	+	9.55051i	0.392192	+	0.392192i	−0.483276	+	0.875468i	$0.660553\pi$
$594$		0			0
$595$	−6.29253	−	62.2896i	−0.257969	−	2.55363i
$596$		0			0
$597$	14.4495	−	14.4495i	0.591378	−	0.591378i
$598$		0			0
$599$	−27.9985			−1.14399			−0.571995	−	0.820257i	$-0.693830\pi$
$599$	−27.9985			−1.14399			−0.571995	+	0.820257i	$0.693830\pi$
$600$		0			0
$601$	−8.20204			−0.334568			−0.167284	−	0.985909i	$-0.553500\pi$
$601$	−8.20204			−0.334568			−0.167284	+	0.985909i	$0.553500\pi$
$602$		0			0
$603$	6.29253	−	6.29253i	0.256252	−	0.256252i
$604$		0			0
$605$	−2.02270	−	20.0227i	−0.0822346	−	0.814039i
$606$		0			0
$607$	0.603566	+	0.603566i	0.0244980	+	0.0244980i	0.719250	−	0.694752i	$-0.244486\pi$
$607$	0.603566	+	0.603566i	0.0244980	+	0.0244980i	−0.694752	+	0.719250i	$0.744486\pi$
$608$		0			0
$609$			41.5959i			1.68555i
$610$		0			0
$611$			27.0129i			1.09283i
$612$		0			0
$613$	−18.2474	−	18.2474i	−0.737008	−	0.737008i	0.234990	−	0.971998i	$-0.424494\pi$
$613$	−18.2474	−	18.2474i	−0.737008	−	0.737008i	−0.971998	+	0.234990i	$0.924494\pi$
$614$		0			0
$615$	1.90702	+	1.55708i	0.0768986	+	0.0627875i
$616$		0			0
$617$	16.4495	−	16.4495i	0.662232	−	0.662232i	−0.293674	−	0.955906i	$-0.594878\pi$
$617$	16.4495	−	16.4495i	0.662232	−	0.662232i	0.955906	+	0.293674i	$0.0948780\pi$
$618$		0			0
$619$	5.30691			0.213303			0.106651	−	0.994296i	$-0.465987\pi$
$619$	5.30691			0.213303			0.106651	+	0.994296i	$0.465987\pi$
$620$		0			0
$621$	2.89898			0.116332
$622$		0			0
$623$	6.29253	−	6.29253i	0.252105	−	0.252105i
$624$		0			0
$625$	23.0000	−	9.79796i	0.920000	−	0.391918i
$626$		0			0
$627$	−0.635674	−	0.635674i	−0.0253864	−	0.0253864i
$628$		0			0
$629$			13.7980i			0.550161i
$630$		0			0
$631$		−	38.0409i		−	1.51438i	−0.653192	−	0.757192i	$-0.726571\pi$
$631$		−	38.0409i		−	1.51438i	0.653192	−	0.757192i	$-0.273429\pi$
$632$		0			0
$633$	−10.4495	−	10.4495i	−0.415330	−	0.415330i
$634$		0			0
$635$	−5.02118	+	6.14966i	−0.199259	+	0.244042i
$636$		0			0
$637$	31.3485	−	31.3485i	1.24207	−	1.24207i
$638$		0			0
$639$	12.5851			0.497857
$640$		0			0
$641$	−1.59592			−0.0630350			−0.0315175	−	0.999503i	$-0.510034\pi$
$641$	−1.59592			−0.0630350			−0.0315175	+	0.999503i	$0.510034\pi$
$642$		0			0
$643$	−17.9562	+	17.9562i	−0.708123	+	0.708123i	−0.966140	−	0.258018i	$-0.916931\pi$
$643$	−17.9562	+	17.9562i	−0.708123	+	0.708123i	0.258018	+	0.966140i	$0.416931\pi$
$644$		0			0
$645$	−2.00000	+	0.202041i	−0.0787499	+	0.00795536i
$646$		0			0
$647$	9.61377	+	9.61377i	0.377956	+	0.377956i	0.870364	−	0.492408i	$-0.163883\pi$
$647$	9.61377	+	9.61377i	0.377956	+	0.377956i	−0.492408	+	0.870364i	$0.663883\pi$
$648$		0			0
$649$			14.0000i			0.549548i
$650$		0			0
$651$			37.7552i			1.47974i
$652$		0			0
$653$	−3.34847	−	3.34847i	−0.131036	−	0.131036i	0.638547	−	0.769583i	$-0.279536\pi$
$653$	−3.34847	−	3.34847i	−0.131036	−	0.131036i	−0.769583	+	0.638547i	$0.779536\pi$
$654$		0			0
$655$	43.0942	−	4.35340i	1.68383	−	0.170101i
$656$		0			0
$657$	3.00000	−	3.00000i	0.117041	−	0.117041i
$658$		0			0
$659$	−1.69994			−0.0662204			−0.0331102	−	0.999452i	$-0.510541\pi$
$659$	−1.69994			−0.0662204			−0.0331102	+	0.999452i	$0.510541\pi$
$660$		0			0
$661$	18.8990			0.735085			0.367543	−	0.930007i	$-0.380199\pi$
$661$	18.8990			0.735085			0.367543	+	0.930007i	$0.380199\pi$
$662$		0			0
$663$	−15.4135	+	15.4135i	−0.598610	+	0.598610i
$664$		0			0
$665$	4.00000	−	4.89898i	0.155113	−	0.189974i
$666$		0			0
$667$	−19.1633	−	19.1633i	−0.742007	−	0.742007i
$668$		0			0
$669$		−	18.2474i		−	0.705487i
$670$		0			0
$671$		−	4.09978i		−	0.158270i
$672$		0			0
$673$	−21.8990	−	21.8990i	−0.844144	−	0.844144i	0.145251	−	0.989395i	$-0.453601\pi$
$673$	−21.8990	−	21.8990i	−0.844144	−	0.844144i	−0.989395	+	0.145251i	$0.953601\pi$
$674$		0			0
$675$	4.17121	+	2.75699i	0.160550	+	0.106117i
$676$		0			0
$677$	22.9444	−	22.9444i	0.881824	−	0.881824i	−0.111896	−	0.993720i	$-0.535692\pi$
$677$	22.9444	−	22.9444i	0.881824	−	0.881824i	0.993720	+	0.111896i	$0.0356922\pi$
$678$		0			0
$679$	18.8776			0.724455
$680$		0			0
$681$	6.20204			0.237663
$682$		0			0
$683$	−4.24264	+	4.24264i	−0.162340	+	0.162340i	−0.783603	−	0.621262i	$-0.786620\pi$
$683$	−4.24264	+	4.24264i	−0.162340	+	0.162340i	0.621262	+	0.783603i	$0.286620\pi$
$684$		0			0
$685$	−13.5959	−	11.1010i	−0.519473	−	0.424148i
$686$		0			0
$687$	−2.68556	−	2.68556i	−0.102461	−	0.102461i
$688$		0			0
$689$			9.79796i			0.373273i
$690$		0			0
$691$			44.0477i			1.67565i	0.545936	+	0.837827i	$0.316174\pi$
$691$			44.0477i			1.67565i	−0.545936	+	0.837827i	$0.683826\pi$
$692$		0			0
$693$	−4.44949	−	4.44949i	−0.169022	−	0.169022i
$694$		0			0
$695$	2.33562	+	23.1202i	0.0885950	+	0.877000i
$696$		0			0
$697$	−4.89898	+	4.89898i	−0.185562	+	0.185562i
$698$		0			0
$699$	25.8058			0.976065
$700$		0			0
$701$	−24.9444			−0.942137			−0.471068	−	0.882097i	$-0.656131\pi$
$701$	−24.9444			−0.942137			−0.471068	+	0.882097i	$0.656131\pi$
$702$		0			0
$703$	−0.985620	+	0.985620i	−0.0371734	+	0.0371734i
$704$		0			0
$705$	1.75255	+	17.3485i	0.0660049	+	0.653381i
$706$		0			0
$707$	26.5843	+	26.5843i	0.999807	+	0.999807i
$708$		0			0
$709$		−	14.0000i		−	0.525781i	−0.964826	−	0.262891i	$-0.915324\pi$
$709$		−	14.0000i		−	0.525781i	0.964826	−	0.262891i	$-0.0846758\pi$
$710$		0			0
$711$			9.75663i			0.365902i
$712$		0			0
$713$	−17.3939	−	17.3939i	−0.651406	−	0.651406i
$714$		0			0
$715$	8.48528	+	6.92820i	0.317332	+	0.259100i
$716$		0			0
$717$	−8.00000	+	8.00000i	−0.298765	+	0.298765i
$718$		0			0
$719$	−21.3561			−0.796447			−0.398223	−	0.917288i	$-0.630373\pi$
$719$	−21.3561			−0.796447			−0.398223	+	0.917288i	$0.630373\pi$
$720$		0			0
$721$	55.3939			2.06298
$722$		0			0
$723$	5.65685	−	5.65685i	0.210381	−	0.210381i
$724$		0			0
$725$	−9.34847	−	45.7980i	−0.347193	−	1.70089i
$726$		0			0
$727$	−35.8803	−	35.8803i	−1.33073	−	1.33073i	−0.904721	−	0.426004i	$-0.859921\pi$
$727$	−35.8803	−	35.8803i	−1.33073	−	1.33073i	−0.426004	−	0.904721i	$-0.640079\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	5.65685i		−	0.209226i
$732$		0			0
$733$	25.1464	+	25.1464i	0.928805	+	0.928805i	0.997629	−	0.0688243i	$-0.0219248\pi$
$733$	25.1464	+	25.1464i	0.928805	+	0.928805i	−0.0688243	+	0.997629i	$0.521925\pi$
$734$		0			0
$735$	18.0990	−	22.1667i	0.667593	−	0.817632i
$736$		0			0
$737$	8.89898	−	8.89898i	0.327798	−	0.327798i
$738$		0			0
$739$	−6.29253			−0.231474			−0.115737	−	0.993280i	$-0.536923\pi$
$739$	−6.29253			−0.231474			−0.115737	+	0.993280i	$0.536923\pi$
$740$		0			0
$741$	−2.20204			−0.0808940
$742$		0			0
$743$	−7.35680	+	7.35680i	−0.269895	+	0.269895i	−0.829058	−	0.559163i	$-0.811123\pi$
$743$	−7.35680	+	7.35680i	−0.269895	+	0.269895i	0.559163	+	0.829058i	$0.311123\pi$
$744$		0			0
$745$	−3.00000	+	0.303062i	−0.109911	+	0.0111033i
$746$		0			0
$747$	−1.41421	−	1.41421i	−0.0517434	−	0.0517434i
$748$		0			0
$749$		−	16.8990i		−	0.617475i
$750$		0			0
$751$			19.2275i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$751$			19.2275i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$752$		0			0
$753$	−17.8990	−	17.8990i	−0.652275	−	0.652275i
$754$		0			0
$755$	−20.2918	+	2.04989i	−0.738494	+	0.0746031i
$756$		0			0
$757$	33.1464	−	33.1464i	1.20473	−	1.20473i	0.232015	−	0.972712i	$-0.425468\pi$
$757$	33.1464	−	33.1464i	1.20473	−	1.20473i	0.972712	−	0.232015i	$-0.0745319\pi$
$758$		0			0
$759$	4.09978			0.148812
$760$		0			0
$761$	−13.1010			−0.474912			−0.237456	−	0.971398i	$-0.576313\pi$
$761$	−13.1010			−0.474912			−0.237456	+	0.971398i	$0.576313\pi$
$762$		0			0
$763$	46.8761	−	46.8761i	1.69703	−	1.69703i
$764$		0			0
$765$	−8.89898	+	10.8990i	−0.321743	+	0.394053i
$766$		0			0
$767$	24.2487	+	24.2487i	0.875570	+	0.875570i
$768$		0			0
$769$		−	43.3939i		−	1.56482i	−0.622762	−	0.782412i	$-0.713989\pi$
$769$		−	43.3939i		−	1.56482i	0.622762	−	0.782412i	$-0.286011\pi$
$770$		0			0
$771$		−	3.46410i		−	0.124757i
$772$		0			0
$773$	3.75255	+	3.75255i	0.134970	+	0.134970i	0.771364	−	0.636394i	$-0.219575\pi$
$773$	3.75255	+	3.75255i	0.134970	+	0.134970i	−0.636394	+	0.771364i	$0.719575\pi$
$774$		0			0
$775$	−8.48528	−	41.5692i	−0.304800	−	1.49321i
$776$		0			0
$777$	−6.89898	+	6.89898i	−0.247500	+	0.247500i
$778$		0			0
$779$	−0.699891			−0.0250762
$780$		0			0
$781$	17.7980			0.636861
$782$		0			0
$783$	6.61037	−	6.61037i	0.236235	−	0.236235i
$784$		0			0
$785$	−22.8990	−	18.6969i	−0.817300	−	0.667322i
$786$		0			0
$787$	0.921404	+	0.921404i	0.0328445	+	0.0328445i	0.723338	−	0.690494i	$-0.242607\pi$
$787$	0.921404	+	0.921404i	0.0328445	+	0.0328445i	−0.690494	+	0.723338i	$0.742607\pi$
$788$		0			0
$789$		−	18.8990i		−	0.672821i
$790$		0			0
$791$		−	71.4106i		−	2.53907i
$792$		0			0
$793$	−7.10102	−	7.10102i	−0.252165	−	0.252165i
$794$		0			0
$795$	0.635674	+	6.29253i	0.0225451	+	0.223173i
$796$		0			0
$797$	−34.0454	+	34.0454i	−1.20595	+	1.20595i	−0.233623	+	0.972327i	$0.575058\pi$
$797$	−34.0454	+	34.0454i	−1.20595	+	1.20595i	−0.972327	+	0.233623i	$0.924942\pi$
$798$		0			0
$799$	−49.0689			−1.73593
$800$		0			0
$801$	−2.00000			−0.0706665
$802$		0			0
$803$	4.24264	−	4.24264i	0.149720	−	0.149720i
$804$		0			0
$805$	2.89898	+	28.6969i	0.102176	+	1.01143i
$806$		0			0
$807$	7.53177	+	7.53177i	0.265131	+	0.265131i
$808$		0			0
$809$			9.59592i			0.337375i	0.985670	+	0.168687i	$0.0539528\pi$
$809$			9.59592i			0.337375i	−0.985670	+	0.168687i	$0.946047\pi$
$810$		0			0
$811$			34.2911i			1.20412i	0.798450	+	0.602061i	$0.205654\pi$
$811$			34.2911i			1.20412i	−0.798450	+	0.602061i	$0.794346\pi$
$812$		0			0
$813$	0.651531	+	0.651531i	0.0228502	+	0.0228502i
$814$		0			0
$815$	16.9706	+	13.8564i	0.594453	+	0.485369i
$816$		0			0
$817$	0.404082	−	0.404082i	0.0141370	−	0.0141370i
$818$		0			0
$819$	−15.4135			−0.538591
$820$		0			0
$821$	27.1464			0.947417			0.473708	−	0.880682i	$-0.342915\pi$
$821$	27.1464			0.947417			0.473708	+	0.880682i	$0.342915\pi$
$822$		0			0
$823$	1.58919	−	1.58919i	0.0553955	−	0.0553955i	−0.678866	−	0.734262i	$-0.737528\pi$
$823$	1.58919	−	1.58919i	0.0553955	−	0.0553955i	0.734262	+	0.678866i	$0.237528\pi$
$824$		0			0
$825$	5.89898	+	3.89898i	0.205376	+	0.135745i
$826$		0			0
$827$	23.6130	+	23.6130i	0.821106	+	0.821106i	0.986267	−	0.165161i	$-0.0528143\pi$
$827$	23.6130	+	23.6130i	0.821106	+	0.821106i	−0.165161	+	0.986267i	$0.552814\pi$
$828$		0			0
$829$			46.4949i			1.61483i	0.589981	+	0.807417i	$0.299135\pi$
$829$			46.4949i			1.61483i	−0.589981	+	0.807417i	$0.700865\pi$
$830$		0			0
$831$			10.3923i			0.360505i
$832$		0			0
$833$	56.9444	+	56.9444i	1.97301	+	1.97301i
$834$		0			0
$835$	−32.3840	+	39.6622i	−1.12070	+	1.37257i
$836$		0			0
$837$	6.00000	−	6.00000i	0.207390	−	0.207390i
$838$		0			0
$839$	21.0703			0.727429			0.363714	−	0.931510i	$-0.381508\pi$
$839$	21.0703			0.727429			0.363714	+	0.931510i	$0.381508\pi$
$840$		0			0
$841$	−58.3939			−2.01358
$842$		0			0
$843$	−17.4634	+	17.4634i	−0.601471	+	0.601471i
$844$		0			0
$845$	−2.22474	+	0.224745i	−0.0765336	+	0.00773146i
$846$		0			0
$847$	28.3164	+	28.3164i	0.972962	+	0.972962i
$848$		0			0
$849$			11.1010i			0.380986i
$850$		0			0
$851$		−	6.35674i		−	0.217906i
$852$		0			0
$853$	10.6515	+	10.6515i	0.364701	+	0.364701i	0.865540	−	0.500839i	$-0.166975\pi$
$853$	10.6515	+	10.6515i	0.364701	+	0.364701i	−0.500839	+	0.865540i	$0.666975\pi$
$854$		0			0
$855$	−1.41421	+	0.142865i	−0.0483651	+	0.00488587i
$856$		0			0
$857$	19.1464	−	19.1464i	0.654030	−	0.654030i	−0.299931	−	0.953961i	$-0.596964\pi$
$857$	19.1464	−	19.1464i	0.654030	−	0.654030i	0.953961	+	0.299931i	$0.0969638\pi$
$858$		0			0
$859$	56.9185			1.94203			0.971017	−	0.239011i	$-0.0768232\pi$
$859$	56.9185			1.94203			0.971017	+	0.239011i	$0.0768232\pi$
$860$		0			0
$861$	−4.89898			−0.166957
$862$		0			0
$863$	27.2200	−	27.2200i	0.926580	−	0.926580i	−0.0709035	−	0.997483i	$-0.522588\pi$
$863$	27.2200	−	27.2200i	0.926580	−	0.926580i	0.997483	+	0.0709035i	$0.0225882\pi$
$864$		0			0
$865$	−3.10102	+	3.79796i	−0.105438	+	0.129134i
$866$		0			0
$867$	−15.9777	−	15.9777i	−0.542632	−	0.542632i
$868$		0			0
$869$			13.7980i			0.468064i
$870$		0			0
$871$		−	30.8270i		−	1.04453i
$872$		0			0
$873$	−3.00000	−	3.00000i	−0.101535	−	0.101535i
$874$		0			0
$875$	−23.1202	+	44.0477i	−0.781606	+	1.48908i
$876$		0			0
$877$	−28.4495	+	28.4495i	−0.960671	+	0.960671i	−0.999255	−	0.0385843i	$-0.987715\pi$
$877$	−28.4495	+	28.4495i	−0.960671	+	0.960671i	0.0385843	+	0.999255i	$0.487715\pi$
$878$		0			0
$879$	−12.8708			−0.434121
$880$		0			0
$881$	3.79796			0.127956			0.0639782	−	0.997951i	$-0.479621\pi$
$881$	3.79796			0.127956			0.0639782	+	0.997951i	$0.479621\pi$
$882$		0			0
$883$	−19.5133	+	19.5133i	−0.656674	+	0.656674i	−0.954591	−	0.297918i	$-0.903708\pi$
$883$	−19.5133	+	19.5133i	−0.656674	+	0.656674i	0.297918	+	0.954591i	$0.403708\pi$
$884$		0			0
$885$	17.1464	+	14.0000i	0.576371	+	0.470605i
$886$		0			0
$887$	−14.6349	−	14.6349i	−0.491393	−	0.491393i	0.417352	−	0.908745i	$-0.362958\pi$
$887$	−14.6349	−	14.6349i	−0.491393	−	0.491393i	−0.908745	+	0.417352i	$0.862958\pi$
$888$		0			0
$889$		−	15.7980i		−	0.529847i
$890$		0			0
$891$			1.41421i			0.0473779i
$892$		0			0
$893$	−3.50510	−	3.50510i	−0.117294	−	0.117294i
$894$		0			0
$895$	−1.23924	−	12.2672i	−0.0414233	−	0.410048i
$896$		0			0
$897$	7.10102	−	7.10102i	0.237096	−	0.237096i
$898$		0			0
$899$	−79.3244			−2.64562
$900$		0			0
$901$	−17.7980			−0.592936
$902$		0			0
$903$	2.82843	−	2.82843i	0.0941242	−	0.0941242i
$904$		0			0
$905$	2.44949	+	24.2474i	0.0814238	+	0.806012i
$906$		0			0
$907$	−17.9562	−	17.9562i	−0.596225	−	0.596225i	0.343081	−	0.939306i	$-0.388530\pi$
$907$	−17.9562	−	17.9562i	−0.596225	−	0.596225i	−0.939306	+	0.343081i	$0.888530\pi$
$908$		0			0
$909$		−	8.44949i		−	0.280252i
$910$		0			0
$911$		−	36.7696i		−	1.21823i	−0.793082	−	0.609115i	$-0.791525\pi$
$911$		−	36.7696i		−	1.21823i	0.793082	−	0.609115i	$-0.208475\pi$
$912$		0			0
$913$	−2.00000	−	2.00000i	−0.0661903	−	0.0661903i
$914$		0			0
$915$	−5.02118	−	4.09978i	−0.165995	−	0.135534i
$916$		0			0
$917$	−60.9444	+	60.9444i	−2.01256	+	2.01256i
$918$		0			0
$919$	−11.5994			−0.382630			−0.191315	−	0.981529i	$-0.561275\pi$
$919$	−11.5994			−0.382630			−0.191315	+	0.981529i	$0.561275\pi$
$920$		0			0
$921$	22.6969			0.747890
$922$		0			0
$923$	30.8270	−	30.8270i	1.01468	−	1.01468i
$924$		0			0
$925$	6.04541	−	9.14643i	0.198772	−	0.300733i
$926$		0			0
$927$	−8.80312	−	8.80312i	−0.289132	−	0.289132i
$928$		0			0
$929$		−	30.4949i		−	1.00051i	−0.865880	−	0.500253i	$-0.833240\pi$
$929$		−	30.4949i		−	1.00051i	0.865880	−	0.500253i	$-0.166760\pi$
$930$		0			0
$931$			8.13534i			0.266625i
$932$		0			0
$933$	10.6969	+	10.6969i	0.350202	+	0.350202i
$934$		0			0
$935$	−12.5851	+	15.4135i	−0.411575	+	0.504075i
$936$		0			0
$937$	−23.0000	+	23.0000i	−0.751377	+	0.751377i	−0.974736	−	0.223359i	$-0.928298\pi$
$937$	−23.0000	+	23.0000i	−0.751377	+	0.751377i	0.223359	+	0.974736i	$0.428298\pi$
$938$		0			0
$939$	−1.12848			−0.0368267
$940$		0			0
$941$	10.6515			0.347230			0.173615	−	0.984814i	$-0.444455\pi$
$941$	10.6515			0.347230			0.173615	+	0.984814i	$0.444455\pi$
$942$		0			0
$943$	2.25697	−	2.25697i	0.0734970	−	0.0734970i
$944$		0			0
$945$	−9.89898	+	1.00000i	−0.322014	+	0.0325300i
$946$		0			0
$947$	−29.5556	−	29.5556i	−0.960429	−	0.960429i	0.0388177	−	0.999246i	$-0.487641\pi$
$947$	−29.5556	−	29.5556i	−0.960429	−	0.960429i	−0.999246	+	0.0388177i	$0.987641\pi$
$948$		0			0
$949$		−	14.6969i		−	0.477083i
$950$		0			0
$951$		−	0.921404i		−	0.0298786i
$952$		0			0
$953$	23.8434	+	23.8434i	0.772362	+	0.772362i	0.978519	−	0.206157i	$-0.0660956\pi$
$953$	23.8434	+	23.8434i	0.772362	+	0.772362i	−0.206157	+	0.978519i	$0.566096\pi$
$954$		0			0
$955$	3.46410	−	0.349945i	0.112096	−	0.0113240i
$956$		0			0
$957$	9.34847	−	9.34847i	0.302193	−	0.302193i
$958$		0			0
$959$	34.9267			1.12784
$960$		0			0
$961$	−41.0000			−1.32258
$962$		0			0
$963$	−2.68556	+	2.68556i	−0.0865410	+	0.0865410i
$964$		0			0
$965$	9.59592	−	11.7526i	0.308904	−	0.378328i
$966$		0			0
$967$	−29.2378	−	29.2378i	−0.940224	−	0.940224i	0.0580878	−	0.998311i	$-0.481500\pi$
$967$	−29.2378	−	29.2378i	−0.940224	−	0.940224i	−0.998311	+	0.0580878i	$0.981500\pi$
$968$		0			0
$969$		−	4.00000i		−	0.128499i
$970$		0			0
$971$			47.3689i			1.52014i	0.649840	+	0.760071i	$0.274836\pi$
$971$			47.3689i			1.52014i	−0.649840	+	0.760071i	$0.725164\pi$
$972$		0			0
$973$	−32.6969	−	32.6969i	−1.04822	−	1.04822i
$974$		0			0
$975$	16.9706	−	3.46410i	0.543493	−	0.110940i
$976$		0			0
$977$	0.449490	−	0.449490i	0.0143805	−	0.0143805i	−0.699880	−	0.714260i	$-0.746763\pi$
$977$	0.449490	−	0.449490i	0.0143805	−	0.0143805i	0.714260	+	0.699880i	$0.246763\pi$
$978$		0			0
$979$	−2.82843			−0.0903969
$980$		0			0
$981$	−14.8990			−0.475688
$982$		0			0
$983$	−38.1838	+	38.1838i	−1.21787	+	1.21787i	−0.249498	+	0.968375i	$0.580265\pi$
$983$	−38.1838	+	38.1838i	−1.21787	+	1.21787i	−0.968375	+	0.249498i	$0.919735\pi$
$984$		0			0
$985$	28.8990	+	23.5959i	0.920798	+	0.751828i
$986$		0			0
$987$	−24.5344	−	24.5344i	−0.780940	−	0.780940i
$988$		0			0
$989$			2.60612i			0.0828699i
$990$		0			0
$991$		−	3.46410i		−	0.110041i	−0.998485	−	0.0550204i	$-0.982478\pi$
$991$		−	3.46410i		−	0.110041i	0.998485	−	0.0550204i	$-0.0175224\pi$
$992$		0			0
$993$	14.2474	+	14.2474i	0.452129	+	0.452129i
$994$		0			0
$995$	−4.59259	−	45.4619i	−0.145595	−	1.44124i
$996$		0			0
$997$	−22.9444	+	22.9444i	−0.726656	+	0.726656i	−0.969952	−	0.243296i	$-0.921771\pi$
$997$	−22.9444	+	22.9444i	−0.726656	+	0.726656i	0.243296	+	0.969952i	$0.421771\pi$
$998$		0			0
$999$	2.19275			0.0693756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.w.b.223.3	yes	8
3.2	odd	2		720.2.x.f.703.4		8
4.3	odd	2	inner	240.2.w.b.223.1	yes	8
5.2	odd	4	inner	240.2.w.b.127.1	✓	8
5.3	odd	4		1200.2.w.b.607.4		8
5.4	even	2		1200.2.w.b.943.1		8
8.3	odd	2		960.2.w.d.703.4		8
8.5	even	2		960.2.w.d.703.2		8
12.11	even	2		720.2.x.f.703.3		8
15.2	even	4		720.2.x.f.127.3		8
15.8	even	4		3600.2.x.n.3007.4		8
15.14	odd	2		3600.2.x.n.2143.1		8
20.3	even	4		1200.2.w.b.607.1		8
20.7	even	4	inner	240.2.w.b.127.3	yes	8
20.19	odd	2		1200.2.w.b.943.4		8
40.27	even	4		960.2.w.d.127.2		8
40.37	odd	4		960.2.w.d.127.4		8
60.23	odd	4		3600.2.x.n.3007.1		8
60.47	odd	4		720.2.x.f.127.4		8
60.59	even	2		3600.2.x.n.2143.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.w.b.127.1	✓	8	5.2	odd	4	inner
240.2.w.b.127.3	yes	8	20.7	even	4	inner
240.2.w.b.223.1	yes	8	4.3	odd	2	inner
240.2.w.b.223.3	yes	8	1.1	even	1	trivial
720.2.x.f.127.3		8	15.2	even	4
720.2.x.f.127.4		8	60.47	odd	4
720.2.x.f.703.3		8	12.11	even	2
720.2.x.f.703.4		8	3.2	odd	2
960.2.w.d.127.2		8	40.27	even	4
960.2.w.d.127.4		8	40.37	odd	4
960.2.w.d.703.2		8	8.5	even	2
960.2.w.d.703.4		8	8.3	odd	2
1200.2.w.b.607.1		8	20.3	even	4
1200.2.w.b.607.4		8	5.3	odd	4
1200.2.w.b.943.1		8	5.4	even	2
1200.2.w.b.943.4		8	20.19	odd	2
3600.2.x.n.2143.1		8	15.14	odd	2
3600.2.x.n.2143.4		8	60.59	even	2
3600.2.x.n.3007.1		8	60.23	odd	4
3600.2.x.n.3007.4		8	15.8	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.224745 - 2.22474i) q^{5} +(3.14626 + 3.14626i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.224745 - 2.22474i) q^{5} +(3.14626 + 3.14626i) q^{7} -1.00000i q^{9} -1.41421i q^{11} +(-2.44949 - 2.44949i) q^{13} +(-1.73205 - 1.41421i) q^{15} +(4.44949 - 4.44949i) q^{17} +0.635674 q^{19} +4.44949 q^{21} +(-2.04989 + 2.04989i) q^{23} +(-4.89898 + 1.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} +9.34847i q^{29} +8.48528i q^{31} +(-1.00000 - 1.00000i) q^{33} +(6.29253 - 7.70674i) q^{35} +(-1.55051 + 1.55051i) q^{37} -3.46410 q^{39} -1.10102 q^{41} +(0.635674 - 0.635674i) q^{43} +(-2.22474 + 0.224745i) q^{45} +(-5.51399 - 5.51399i) q^{47} +12.7980i q^{49} -6.29253i q^{51} +(-2.00000 - 2.00000i) q^{53} +(-3.14626 + 0.317837i) q^{55} +(0.449490 - 0.449490i) q^{57} -9.89949 q^{59} +2.89898 q^{61} +(3.14626 - 3.14626i) q^{63} +(-4.89898 + 6.00000i) q^{65} +(6.29253 + 6.29253i) q^{67} +2.89898i q^{69} +12.5851i q^{71} +(3.00000 + 3.00000i) q^{73} +(-2.75699 + 4.17121i) q^{75} +(4.44949 - 4.44949i) q^{77} -9.75663 q^{79} -1.00000 q^{81} +(1.41421 - 1.41421i) q^{83} +(-10.8990 - 8.89898i) q^{85} +(6.61037 + 6.61037i) q^{87} -2.00000i q^{89} -15.4135i q^{91} +(6.00000 + 6.00000i) q^{93} +(-0.142865 - 1.41421i) q^{95} +(3.00000 - 3.00000i) q^{97} -1.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5}+O(q^{10}) \) 8 * q + 8 * q^5	\( 8 q + 8 q^{5} + 16 q^{17} + 16 q^{21} - 8 q^{33} - 32 q^{37} - 48 q^{41} - 8 q^{45} - 16 q^{53} - 16 q^{57} - 16 q^{61} + 24 q^{73} + 16 q^{77} - 8 q^{81} - 48 q^{85} + 48 q^{93} + 24 q^{97}+O(q^{100}) \) 8 * q + 8 * q^5 + 16 * q^17 + 16 * q^21 - 8 * q^33 - 32 * q^37 - 48 * q^41 - 8 * q^45 - 16 * q^53 - 16 * q^57 - 16 * q^61 + 24 * q^73 + 16 * q^77 - 8 * q^81 - 48 * q^85 + 48 * q^93 + 24 * q^97

Introduction

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