LMFDB - Embedded newform 240.3.bg.e.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,3,Mod(97,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.97"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 269x^{4} - 1116x^{3} + 2312x^{2} + 680x + 100 $ x^8 - 4x^7 + 8x^6 + 269x^4 - 1116x^3 + 2312x^2 + 680x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.1
Root			$2.36263 + 2.36263i$ of defining polynomial
Character	$\chi$	$=$	240.193
Dual form			240.3.bg.e.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 1.22474i) q^{3} +(-3.36263 + 3.70037i) q^{5} +(8.78825 - 8.78825i) q^{7} +3.00000i q^{9} -13.7482 q^{11} +(-4.88927 - 4.88927i) q^{13} +(8.65037 - 0.413648i) q^{15} +(5.99029 - 5.99029i) q^{17} -25.5765i q^{19} -21.5267 q^{21} +(-18.4257 - 18.4257i) q^{23} +(-2.38547 - 24.8859i) q^{25} +(3.67423 - 3.67423i) q^{27} -37.2222i q^{29} -31.6955 q^{31} +(16.8380 + 16.8380i) q^{33} +(2.96816 + 62.0714i) q^{35} +(-32.5046 + 32.5046i) q^{37} +11.9762i q^{39} +36.7295 q^{41} +(24.5780 + 24.5780i) q^{43} +(-11.1011 - 10.0879i) q^{45} +(-20.4063 + 20.4063i) q^{47} -105.467i q^{49} -14.6732 q^{51} +(33.5559 + 33.5559i) q^{53} +(46.2300 - 50.8734i) q^{55} +(-31.3247 + 31.3247i) q^{57} -7.54615i q^{59} +43.6183 q^{61} +(26.3648 + 26.3648i) q^{63} +(34.5329 - 1.65131i) q^{65} +(60.1739 - 60.1739i) q^{67} +45.1336i q^{69} +18.1632 q^{71} +(68.8218 + 68.8218i) q^{73} +(-27.5573 + 33.4005i) q^{75} +(-120.823 + 120.823i) q^{77} +22.2628i q^{79} -9.00000 q^{81} +(0.00221809 + 0.00221809i) q^{83} +(2.02317 + 42.3094i) q^{85} +(-45.5877 + 45.5877i) q^{87} +77.1943i q^{89} -85.9363 q^{91} +(38.8189 + 38.8189i) q^{93} +(94.6425 + 86.0043i) q^{95} +(29.4309 - 29.4309i) q^{97} -41.2446i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} - 4 q^{7} - 32 q^{11} - 4 q^{13} + 52 q^{17} - 24 q^{21} + 40 q^{23} - 84 q^{25} - 96 q^{31} + 60 q^{33} - 24 q^{35} - 60 q^{37} - 152 q^{41} + 88 q^{43} + 16 q^{47} + 168 q^{51} + 108 q^{53}+ \cdots - 208 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 - 4 * q^7 - 32 * q^11 - 4 * q^13 + 52 * q^17 - 24 * q^21 + 40 * q^23 - 84 * q^25 - 96 * q^31 + 60 * q^33 - 24 * q^35 - 60 * q^37 - 152 * q^41 + 88 * q^43 + 16 * q^47 + 168 * q^51 + 108 * q^53 - 116 * q^55 - 24 * q^57 + 264 * q^61 - 12 * q^63 + 164 * q^65 + 216 * q^67 + 240 * q^71 - 208 * q^73 - 120 * q^75 + 168 * q^77 - 72 * q^81 - 336 * q^83 - 12 * q^85 - 252 * q^87 - 592 * q^91 + 264 * q^93 + 128 * q^95 - 208 * q^97

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
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		0			0
$5$	−3.36263	+	3.70037i	−0.672526	+	0.740074i
$5$	−3.36263	+	3.70037i	−0.672526	+	0.740074i
$6$		0			0
$7$	8.78825	−	8.78825i	1.25546	−	1.25546i	0.302229	−	0.953235i	$-0.402269\pi$
$7$	8.78825	−	8.78825i	1.25546	−	1.25546i	0.953235	−	0.302229i	$-0.0977309\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−13.7482			−1.24984			−0.624918	−	0.780691i	$-0.714867\pi$
$11$	−13.7482			−1.24984			−0.624918	+	0.780691i	$0.714867\pi$
$12$		0			0
$13$	−4.88927	−	4.88927i	−0.376098	−	0.376098i	0.493594	−	0.869692i	$-0.335683\pi$
$13$	−4.88927	−	4.88927i	−0.376098	−	0.376098i	−0.869692	+	0.493594i	$0.835683\pi$
$14$		0			0
$15$	8.65037	−	0.413648i	0.576691	−	0.0275765i
$16$		0			0
$17$	5.99029	−	5.99029i	0.352370	−	0.352370i	−0.508621	−	0.860991i	$-0.669844\pi$
$17$	5.99029	−	5.99029i	0.352370	−	0.352370i	0.860991	+	0.508621i	$0.169844\pi$
$18$		0			0
$19$		−	25.5765i		−	1.34613i	−0.739583	−	0.673066i	$-0.764977\pi$
$19$		−	25.5765i		−	1.34613i	0.739583	−	0.673066i	$-0.235023\pi$
$20$		0			0
$21$	−21.5267			−1.02508
$22$		0			0
$23$	−18.4257	−	18.4257i	−0.801118	−	0.801118i	0.182152	−	0.983270i	$-0.441694\pi$
$23$	−18.4257	−	18.4257i	−0.801118	−	0.801118i	−0.983270	+	0.182152i	$0.941694\pi$
$24$		0			0
$25$	−2.38547	−	24.8859i	−0.0954189	−	0.995437i
$26$		0			0
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$		0			0
$29$		−	37.2222i		−	1.28352i	−0.766904	−	0.641762i	$-0.778204\pi$
$29$		−	37.2222i		−	1.28352i	0.766904	−	0.641762i	$-0.221796\pi$
$30$		0			0
$31$	−31.6955			−1.02243			−0.511217	−	0.859452i	$-0.670805\pi$
$31$	−31.6955			−1.02243			−0.511217	+	0.859452i	$0.670805\pi$
$32$		0			0
$33$	16.8380	+	16.8380i	0.510243	+	0.510243i
$34$		0			0
$35$	2.96816	+	62.0714i	0.0848047	+	1.77347i
$36$		0			0
$37$	−32.5046	+	32.5046i	−0.878503	+	0.878503i	−0.993380	−	0.114877i	$-0.963353\pi$
$37$	−32.5046	+	32.5046i	−0.878503	+	0.878503i	0.114877	+	0.993380i	$0.463353\pi$
$38$		0			0
$39$			11.9762i			0.307083i
$40$		0			0
$41$	36.7295			0.895842			0.447921	−	0.894073i	$-0.352165\pi$
$41$	36.7295			0.895842			0.447921	+	0.894073i	$0.352165\pi$
$42$		0			0
$43$	24.5780	+	24.5780i	0.571581	+	0.571581i	0.932570	−	0.360989i	$-0.117561\pi$
$43$	24.5780	+	24.5780i	0.571581	+	0.571581i	−0.360989	+	0.932570i	$0.617561\pi$
$44$		0			0
$45$	−11.1011	−	10.0879i	−0.246691	−	0.224175i
$46$		0			0
$47$	−20.4063	+	20.4063i	−0.434177	+	0.434177i	−0.890046	−	0.455870i	$-0.849328\pi$
$47$	−20.4063	+	20.4063i	−0.434177	+	0.434177i	0.455870	+	0.890046i	$0.349328\pi$
$48$		0			0
$49$		−	105.467i		−	2.15238i
$50$		0			0
$51$	−14.6732			−0.287709
$52$		0			0
$53$	33.5559	+	33.5559i	0.633129	+	0.633129i	0.948852	−	0.315722i	$-0.102247\pi$
$53$	33.5559	+	33.5559i	0.633129	+	0.633129i	−0.315722	+	0.948852i	$0.602247\pi$
$54$		0			0
$55$	46.2300	−	50.8734i	0.840546	−	0.924971i
$56$		0			0
$57$	−31.3247	+	31.3247i	−0.549556	+	0.549556i
$58$		0			0
$59$		−	7.54615i		−	0.127901i	−0.997953	−	0.0639504i	$-0.979630\pi$
$59$		−	7.54615i		−	0.127901i	0.997953	−	0.0639504i	$-0.0203699\pi$
$60$		0			0
$61$	43.6183			0.715054			0.357527	−	0.933903i	$-0.383620\pi$
$61$	43.6183			0.715054			0.357527	+	0.933903i	$0.383620\pi$
$62$		0			0
$63$	26.3648	+	26.3648i	0.418488	+	0.418488i
$64$		0			0
$65$	34.5329	−	1.65131i	0.531276	−	0.0254048i
$66$		0			0
$67$	60.1739	−	60.1739i	0.898118	−	0.898118i	−0.0971517	−	0.995270i	$-0.530973\pi$
$67$	60.1739	−	60.1739i	0.898118	−	0.898118i	0.995270	+	0.0971517i	$0.0309732\pi$
$68$		0			0
$69$			45.1336i			0.654110i
$70$		0			0
$71$	18.1632			0.255820			0.127910	−	0.991786i	$-0.459173\pi$
$71$	18.1632			0.255820			0.127910	+	0.991786i	$0.459173\pi$
$72$		0			0
$73$	68.8218	+	68.8218i	0.942764	+	0.942764i	0.998448	−	0.0556839i	$-0.0177339\pi$
$73$	68.8218	+	68.8218i	0.942764	+	0.942764i	−0.0556839	+	0.998448i	$0.517734\pi$
$74$		0			0
$75$	−27.5573	+	33.4005i	−0.367431	+	0.445340i
$76$		0			0
$77$	−120.823	+	120.823i	−1.56912	+	1.56912i
$78$		0			0
$79$			22.2628i			0.281807i	0.990023	+	0.140904i	$0.0450007\pi$
$79$			22.2628i			0.281807i	−0.990023	+	0.140904i	$0.954999\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	0.00221809	+	0.00221809i	2.67240e−5	+	2.67240e-5i	0.707120	−	0.707093i	$-0.249994\pi$
$83$	0.00221809	+	0.00221809i	2.67240e−5	+	2.67240e-5i	−0.707093	+	0.707120i	$0.749994\pi$
$84$		0			0
$85$	2.02317	+	42.3094i	0.0238021	+	0.497758i
$86$		0			0
$87$	−45.5877	+	45.5877i	−0.523996	+	0.523996i
$88$		0			0
$89$			77.1943i			0.867352i	0.901069	+	0.433676i	$0.142784\pi$
$89$			77.1943i			0.867352i	−0.901069	+	0.433676i	$0.857216\pi$
$90$		0			0
$91$	−85.9363			−0.944355
$92$		0			0
$93$	38.8189	+	38.8189i	0.417407	+	0.417407i
$94$		0			0
$95$	94.6425	+	86.0043i	0.996237	+	0.905308i
$96$		0			0
$97$	29.4309	−	29.4309i	0.303411	−	0.303411i	−0.538936	−	0.842347i	$-0.681173\pi$
$97$	29.4309	−	29.4309i	0.303411	−	0.303411i	0.842347	+	0.538936i	$0.181173\pi$
$98$		0			0
$99$		−	41.2446i		−	0.416612i
$100$		0			0
$101$	−178.867			−1.77096			−0.885479	−	0.464679i	$-0.846170\pi$
$101$	−178.867			−1.77096			−0.885479	+	0.464679i	$0.846170\pi$
$102$		0			0
$103$	−41.0972	−	41.0972i	−0.399002	−	0.399002i	0.478879	−	0.877881i	$-0.341043\pi$
$103$	−41.0972	−	41.0972i	−0.399002	−	0.399002i	−0.877881	+	0.478879i	$0.841043\pi$
$104$		0			0
$105$	72.3864	−	79.6569i	0.689394	−	0.758637i
$106$		0			0
$107$	36.8104	−	36.8104i	0.344022	−	0.344022i	−0.513855	−	0.857877i	$-0.671783\pi$
$107$	36.8104	−	36.8104i	0.344022	−	0.344022i	0.857877	+	0.513855i	$0.171783\pi$
$108$		0			0
$109$		−	85.4905i		−	0.784316i	−0.919898	−	0.392158i	$-0.871729\pi$
$109$		−	85.4905i		−	0.784316i	0.919898	−	0.392158i	$-0.128271\pi$
$110$		0			0
$111$	79.6197			0.717295
$112$		0			0
$113$	−15.6917	−	15.6917i	−0.138864	−	0.138864i	0.634258	−	0.773122i	$-0.281306\pi$
$113$	−15.6917	−	15.6917i	−0.138864	−	0.138864i	−0.773122	+	0.634258i	$0.781306\pi$
$114$		0			0
$115$	130.141	−	6.22314i	1.13166	−	0.0541143i
$116$		0			0
$117$	14.6678	−	14.6678i	0.125366	−	0.125366i
$118$		0			0
$119$		−	105.288i		−	0.884777i
$120$		0			0
$121$	68.0127			0.562088
$122$		0			0
$123$	−44.9843	−	44.9843i	−0.365726	−	0.365726i
$124$		0			0
$125$	100.109	+	74.8550i	0.800869	+	0.598840i
$126$		0			0
$127$	−127.554	+	127.554i	−1.00436	+	1.00436i	−0.00436887	+	0.999990i	$0.501391\pi$
$127$	−127.554	+	127.554i	−1.00436	+	1.00436i	−0.999990	+	0.00436887i	$0.998609\pi$
$128$		0			0
$129$		−	60.2035i		−	0.466694i
$130$		0			0
$131$	−123.810			−0.945117			−0.472559	−	0.881299i	$-0.656670\pi$
$131$	−123.810			−0.945117			−0.472559	+	0.881299i	$0.656670\pi$
$132$		0			0
$133$	−224.773	−	224.773i	−1.69002	−	1.69002i
$134$		0			0
$135$	1.24094	+	25.9511i	0.00919218	+	0.192230i
$136$		0			0
$137$	173.145	−	173.145i	1.26383	−	1.26383i	0.314609	−	0.949221i	$-0.398127\pi$
$137$	173.145	−	173.145i	1.26383	−	1.26383i	0.949221	−	0.314609i	$-0.101873\pi$
$138$		0			0
$139$		−	1.06696i		−	0.00767601i	−0.999993	−	0.00383800i	$-0.998778\pi$
$139$		−	1.06696i		−	0.00767601i	0.999993	−	0.00383800i	$-0.00122168\pi$
$140$		0			0
$141$	49.9850			0.354504
$142$		0			0
$143$	67.2186	+	67.2186i	0.470060	+	0.470060i
$144$		0			0
$145$	137.736	+	125.164i	0.949903	+	0.863203i
$146$		0			0
$147$	−129.170	+	129.170i	−0.878707	+	0.878707i
$148$		0			0
$149$		−	65.2505i		−	0.437923i	−0.975734	−	0.218961i	$-0.929733\pi$
$149$		−	65.2505i		−	0.437923i	0.975734	−	0.218961i	$-0.0702669\pi$
$150$		0			0
$151$	−157.183			−1.04095			−0.520473	−	0.853878i	$-0.674244\pi$
$151$	−157.183			−1.04095			−0.520473	+	0.853878i	$0.674244\pi$
$152$		0			0
$153$	17.9709	+	17.9709i	0.117457	+	0.117457i
$154$		0			0
$155$	106.580	−	117.285i	0.687613	−	0.756677i
$156$		0			0
$157$	−121.763	+	121.763i	−0.775561	+	0.775561i	−0.979073	−	0.203512i	$-0.934765\pi$
$157$	−121.763	+	121.763i	−0.775561	+	0.775561i	0.203512	+	0.979073i	$0.434765\pi$
$158$		0			0
$159$		−	82.1947i		−	0.516948i
$160$		0			0
$161$	−323.860			−2.01155
$162$		0			0
$163$	196.095	+	196.095i	1.20304	+	1.20304i	0.973238	+	0.229801i	$0.0738074\pi$
$163$	196.095	+	196.095i	1.20304	+	1.20304i	0.229801	+	0.973238i	$0.426193\pi$
$164$		0			0
$165$	−118.927	+	5.68691i	−0.720769	+	0.0344661i
$166$		0			0
$167$	26.4088	−	26.4088i	0.158136	−	0.158136i	−0.623604	−	0.781740i	$-0.714332\pi$
$167$	26.4088	−	26.4088i	0.158136	−	0.158136i	0.781740	+	0.623604i	$0.214332\pi$
$168$		0			0
$169$		−	121.190i		−	0.717101i
$170$		0			0
$171$	76.7295			0.448711
$172$		0			0
$173$	−8.69052	−	8.69052i	−0.0502342	−	0.0502342i	0.681543	−	0.731778i	$-0.261309\pi$
$173$	−8.69052	−	8.69052i	−0.0502342	−	0.0502342i	−0.731778	+	0.681543i	$0.761309\pi$
$174$		0			0
$175$	−239.668	−	197.740i	−1.36953	−	1.12994i
$176$		0			0
$177$	−9.24211	+	9.24211i	−0.0522153	+	0.0522153i
$178$		0			0
$179$		−	9.67002i		−	0.0540225i	−0.999635	−	0.0270112i	$-0.991401\pi$
$179$		−	9.67002i		−	0.0540225i	0.999635	−	0.0270112i	$-0.00859899\pi$
$180$		0			0
$181$	249.048			1.37595			0.687977	−	0.725733i	$-0.258499\pi$
$181$	249.048			1.37595			0.687977	+	0.725733i	$0.258499\pi$
$182$		0			0
$183$	−53.4213	−	53.4213i	−0.291920	−	0.291920i
$184$		0			0
$185$	−10.9782	−	229.580i	−0.0593415	−	1.24097i
$186$		0			0
$187$	−82.3557	+	82.3557i	−0.440405	+	0.440405i
$188$		0			0
$189$		−	64.5802i		−	0.341694i
$190$		0			0
$191$	162.349			0.849996			0.424998	−	0.905194i	$-0.360275\pi$
$191$	162.349			0.849996			0.424998	+	0.905194i	$0.360275\pi$
$192$		0			0
$193$	−8.11418	−	8.11418i	−0.0420424	−	0.0420424i	0.685773	−	0.727815i	$-0.259464\pi$
$193$	−8.11418	−	8.11418i	−0.0420424	−	0.0420424i	−0.727815	+	0.685773i	$0.759464\pi$
$194$		0			0
$195$	−44.3165	−	40.2716i	−0.227264	−	0.206521i
$196$		0			0
$197$	229.057	−	229.057i	1.16272	−	1.16272i	0.178847	−	0.983877i	$-0.442763\pi$
$197$	229.057	−	229.057i	1.16272	−	1.16272i	0.983877	−	0.178847i	$-0.0572368\pi$
$198$		0			0
$199$		−	296.892i		−	1.49192i	−0.665992	−	0.745959i	$-0.731992\pi$
$199$		−	296.892i		−	1.49192i	0.665992	−	0.745959i	$-0.268008\pi$
$200$		0			0
$201$	−147.395			−0.733310
$202$		0			0
$203$	−327.118	−	327.118i	−1.61142	−	1.61142i
$204$		0			0
$205$	−123.508	+	135.913i	−0.602476	+	0.662989i
$206$		0			0
$207$	55.2771	−	55.2771i	0.267039	−	0.267039i
$208$		0			0
$209$			351.631i			1.68244i
$210$		0			0
$211$	273.424			1.29585			0.647923	−	0.761706i	$-0.275638\pi$
$211$	273.424			1.29585			0.647923	+	0.761706i	$0.275638\pi$
$212$		0			0
$213$	−22.2453	−	22.2453i	−0.104438	−	0.104438i
$214$		0			0
$215$	−173.594	+	8.30102i	−0.807415	+	0.0386094i
$216$		0			0
$217$	−278.548	+	278.548i	−1.28363	+	1.28363i
$218$		0			0
$219$		−	168.578i		−	0.769764i
$220$		0			0
$221$	−58.5764			−0.265051
$222$		0			0
$223$	232.809	+	232.809i	1.04399	+	1.04399i	0.998987	+	0.0450002i	$0.0143289\pi$
$223$	232.809	+	232.809i	1.04399	+	1.04399i	0.0450002	+	0.998987i	$0.485671\pi$
$224$		0			0
$225$	74.6578	−	7.15642i	0.331812	−	0.0318063i
$226$		0			0
$227$	−105.206	+	105.206i	−0.463465	+	0.463465i	−0.899789	−	0.436325i	$-0.856280\pi$
$227$	−105.206	+	105.206i	−0.463465	+	0.463465i	0.436325	+	0.899789i	$0.356280\pi$
$228$		0			0
$229$			154.353i			0.674032i	0.941499	+	0.337016i	$0.109418\pi$
$229$			154.353i			0.674032i	−0.941499	+	0.337016i	$0.890582\pi$
$230$		0			0
$231$	295.954			1.28118
$232$		0			0
$233$	16.6237	+	16.6237i	0.0713464	+	0.0713464i	0.741880	−	0.670533i	$-0.233935\pi$
$233$	16.6237	+	16.6237i	0.0713464	+	0.0713464i	−0.670533	+	0.741880i	$0.733935\pi$
$234$		0			0
$235$	−6.89207	−	144.130i	−0.0293280	−	0.613318i
$236$		0			0
$237$	27.2662	−	27.2662i	0.115047	−	0.115047i
$238$		0			0
$239$			97.2929i			0.407083i	0.979066	+	0.203542i	$0.0652452\pi$
$239$			97.2929i			0.407083i	−0.979066	+	0.203542i	$0.934755\pi$
$240$		0			0
$241$	−308.012			−1.27806			−0.639029	−	0.769183i	$-0.720663\pi$
$241$	−308.012			−1.27806			−0.639029	+	0.769183i	$0.720663\pi$
$242$		0			0
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		0			0
$245$	390.266	+	354.645i	1.59292	+	1.44753i
$246$		0			0
$247$	−125.051	+	125.051i	−0.506277	+	0.506277i
$248$		0			0
$249$		−	0.00543319i		−	2.18200e-5i
$250$		0			0
$251$	−155.213			−0.618379			−0.309190	−	0.951000i	$-0.600058\pi$
$251$	−155.213			−0.618379			−0.309190	+	0.951000i	$0.600058\pi$
$252$		0			0
$253$	253.320	+	253.320i	1.00127	+	1.00127i
$254$		0			0
$255$	49.3404	−	54.2961i	0.193492	−	0.212926i
$256$		0			0
$257$	206.538	−	206.538i	0.803648	−	0.803648i	−0.180015	−	0.983664i	$-0.557615\pi$
$257$	206.538	−	206.538i	0.803648	−	0.803648i	0.983664	+	0.180015i	$0.0576147\pi$
$258$		0			0
$259$			571.317i			2.20586i
$260$		0			0
$261$	111.667			0.427841
$262$		0			0
$263$	236.194	+	236.194i	0.898075	+	0.898075i	0.995266	−	0.0971908i	$-0.0309857\pi$
$263$	236.194	+	236.194i	0.898075	+	0.898075i	−0.0971908	+	0.995266i	$0.530986\pi$
$264$		0			0
$265$	−237.005	+	11.3332i	−0.894358	+	0.0427669i
$266$		0			0
$267$	94.5433	−	94.5433i	0.354095	−	0.354095i
$268$		0			0
$269$		−	376.885i		−	1.40106i	−0.713623	−	0.700530i	$-0.752947\pi$
$269$		−	376.885i		−	1.40106i	0.713623	−	0.700530i	$-0.247053\pi$
$270$		0			0
$271$	−196.495			−0.725074			−0.362537	−	0.931969i	$-0.618089\pi$
$271$	−196.495			−0.725074			−0.362537	+	0.931969i	$0.618089\pi$
$272$		0			0
$273$	105.250	+	105.250i	0.385531	+	0.385531i
$274$		0			0
$275$	32.7959	+	342.136i	0.119258	+	1.24413i
$276$		0			0
$277$	90.3781	−	90.3781i	0.326275	−	0.326275i	−0.524893	−	0.851168i	$-0.675895\pi$
$277$	90.3781	−	90.3781i	0.326275	−	0.326275i	0.851168	+	0.524893i	$0.175895\pi$
$278$		0			0
$279$		−	95.0864i		−	0.340811i
$280$		0			0
$281$	124.506			0.443083			0.221542	−	0.975151i	$-0.428891\pi$
$281$	124.506			0.443083			0.221542	+	0.975151i	$0.428891\pi$
$282$		0			0
$283$	91.3284	+	91.3284i	0.322715	+	0.322715i	0.849808	−	0.527093i	$-0.176718\pi$
$283$	91.3284	+	91.3284i	0.322715	+	0.322715i	−0.527093	+	0.849808i	$0.676718\pi$
$284$		0			0
$285$	−10.5797	−	221.246i	−0.0371216	−	0.776303i
$286$		0			0
$287$	322.788	−	322.788i	1.12470	−	1.12470i
$288$		0			0
$289$			217.233i			0.751670i
$290$		0			0
$291$	−72.0907			−0.247734
$292$		0			0
$293$	−311.623	−	311.623i	−1.06356	−	1.06356i	−0.997838	−	0.0657234i	$-0.979065\pi$
$293$	−311.623	−	311.623i	−1.06356	−	1.06356i	−0.0657234	−	0.997838i	$-0.520935\pi$
$294$		0			0
$295$	27.9235	+	25.3749i	0.0946560	+	0.0860166i
$296$		0			0
$297$	−50.5141	+	50.5141i	−0.170081	+	0.170081i
$298$		0			0
$299$			180.177i			0.602598i
$300$		0			0
$301$	431.995			1.43520
$302$		0			0
$303$	219.066	+	219.066i	0.722991	+	0.722991i
$304$		0			0
$305$	−146.672	+	161.404i	−0.480892	+	0.529193i
$306$		0			0
$307$	98.1938	−	98.1938i	0.319850	−	0.319850i	−0.528860	−	0.848709i	$-0.677380\pi$
$307$	98.1938	−	98.1938i	0.319850	−	0.319850i	0.848709	+	0.528860i	$0.177380\pi$
$308$		0			0
$309$			100.667i			0.325784i
$310$		0			0
$311$	−429.889			−1.38228			−0.691141	−	0.722720i	$-0.742891\pi$
$311$	−429.889			−1.38228			−0.691141	+	0.722720i	$0.742891\pi$
$312$		0			0
$313$	65.4997	+	65.4997i	0.209264	+	0.209264i	0.803955	−	0.594691i	$-0.202725\pi$
$313$	65.4997	+	65.4997i	0.209264	+	0.209264i	−0.594691	+	0.803955i	$0.702725\pi$
$314$		0			0
$315$	−186.214	+	8.90449i	−0.591156	+	0.0282682i
$316$		0			0
$317$	174.272	−	174.272i	0.549755	−	0.549755i	−0.376615	−	0.926370i	$-0.622912\pi$
$317$	174.272	−	174.272i	0.549755	−	0.549755i	0.926370	+	0.376615i	$0.122912\pi$
$318$		0			0
$319$			511.738i			1.60419i
$320$		0			0
$321$	−90.1667			−0.280893
$322$		0			0
$323$	−153.211	−	153.211i	−0.474337	−	0.474337i
$324$		0			0
$325$	−110.011	+	133.337i	−0.338495	+	0.410269i
$326$		0			0
$327$	−104.704	+	104.704i	−0.320196	+	0.320196i
$328$		0			0
$329$			358.671i			1.09019i
$330$		0			0
$331$	380.789			1.15042			0.575210	−	0.818006i	$-0.304920\pi$
$331$	380.789			1.15042			0.575210	+	0.818006i	$0.304920\pi$
$332$		0			0
$333$	−97.5138	−	97.5138i	−0.292834	−	0.292834i
$334$		0			0
$335$	20.3233	+	425.008i	0.0606665	+	1.26868i
$336$		0			0
$337$	245.960	−	245.960i	0.729851	−	0.729851i	−0.240739	−	0.970590i	$-0.577390\pi$
$337$	245.960	−	245.960i	0.729851	−	0.729851i	0.970590	+	0.240739i	$0.0773897\pi$
$338$		0			0
$339$			38.4366i			0.113382i
$340$		0			0
$341$	435.755			1.27787
$342$		0			0
$343$	−496.244	−	496.244i	−1.44678	−	1.44678i
$344$		0			0
$345$	−167.011	−	151.767i	−0.484090	−	0.439906i
$346$		0			0
$347$	172.320	−	172.320i	0.496600	−	0.496600i	−0.413778	−	0.910378i	$-0.635791\pi$
$347$	172.320	−	172.320i	0.496600	−	0.496600i	0.910378	+	0.413778i	$0.135791\pi$
$348$		0			0
$349$		−	221.895i		−	0.635803i	−0.948124	−	0.317902i	$-0.897022\pi$
$349$		−	221.895i		−	0.635803i	0.948124	−	0.317902i	$-0.102978\pi$
$350$		0			0
$351$	−35.9287			−0.102361
$352$		0			0
$353$	53.4623	+	53.4623i	0.151451	+	0.151451i	0.778766	−	0.627315i	$-0.215846\pi$
$353$	53.4623	+	53.4623i	0.151451	+	0.151451i	−0.627315	+	0.778766i	$0.715846\pi$
$354$		0			0
$355$	−61.0761	+	67.2106i	−0.172045	+	0.189326i
$356$		0			0
$357$	−128.951	+	128.951i	−0.361209	+	0.361209i
$358$		0			0
$359$		−	49.7577i		−	0.138601i	−0.997596	−	0.0693004i	$-0.977923\pi$
$359$		−	49.7577i		−	0.138601i	0.997596	−	0.0693004i	$-0.0220767\pi$
$360$		0			0
$361$	−293.158			−0.812071
$362$		0			0
$363$	−83.2982	−	83.2982i	−0.229472	−	0.229472i
$364$		0			0
$365$	−486.088	+	23.2440i	−1.33175	+	0.0636823i
$366$		0			0
$367$	56.5205	−	56.5205i	0.154007	−	0.154007i	−0.625898	−	0.779905i	$-0.715267\pi$
$367$	56.5205	−	56.5205i	0.154007	−	0.154007i	0.779905	+	0.625898i	$0.215267\pi$
$368$		0			0
$369$			110.189i			0.298614i
$370$		0			0
$371$	589.795			1.58974
$372$		0			0
$373$	−143.430	−	143.430i	−0.384531	−	0.384531i	0.488200	−	0.872732i	$-0.337654\pi$
$373$	−143.430	−	143.430i	−0.384531	−	0.384531i	−0.872732	+	0.488200i	$0.837654\pi$
$374$		0			0
$375$	−30.9292	−	214.286i	−0.0824779	−	0.571429i
$376$		0			0
$377$	−181.989	+	181.989i	−0.482731	+	0.482731i
$378$		0			0
$379$		−	659.728i		−	1.74071i	−0.492427	−	0.870354i	$-0.663890\pi$
$379$		−	659.728i		−	1.74071i	0.492427	−	0.870354i	$-0.336110\pi$
$380$		0			0
$381$	312.441			0.820056
$382$		0			0
$383$	−402.216	−	402.216i	−1.05017	−	1.05017i	−0.998673	−	0.0514981i	$-0.983600\pi$
$383$	−402.216	−	402.216i	−1.05017	−	1.05017i	−0.0514981	−	0.998673i	$-0.516400\pi$
$384$		0			0
$385$	−40.8069	−	853.369i	−0.105992	−	2.21654i
$386$		0			0
$387$	−73.7340	+	73.7340i	−0.190527	+	0.190527i
$388$		0			0
$389$			206.222i			0.530133i	0.964230	+	0.265067i	$0.0853940\pi$
$389$			206.222i			0.530133i	−0.964230	+	0.265067i	$0.914606\pi$
$390$		0			0
$391$	−220.751			−0.564580
$392$		0			0
$393$	151.636	+	151.636i	0.385843	+	0.385843i
$394$		0			0
$395$	−82.3804	−	74.8614i	−0.208558	−	0.189522i
$396$		0			0
$397$	−72.3916	+	72.3916i	−0.182347	+	0.182347i	−0.792378	−	0.610031i	$-0.791157\pi$
$397$	−72.3916	+	72.3916i	−0.182347	+	0.182347i	0.610031	+	0.792378i	$0.291157\pi$
$398$		0			0
$399$			550.579i			1.37990i
$400$		0			0
$401$	−489.191			−1.21993			−0.609964	−	0.792429i	$-0.708816\pi$
$401$	−489.191			−1.21993			−0.609964	+	0.792429i	$0.708816\pi$
$402$		0			0
$403$	154.968	+	154.968i	0.384535	+	0.384535i
$404$		0			0
$405$	30.2636	−	33.3033i	0.0747251	−	0.0822304i
$406$		0			0
$407$	446.879	−	446.879i	1.09798	−	1.09798i
$408$		0			0
$409$			724.079i			1.77037i	0.465244	+	0.885183i	$0.345967\pi$
$409$			724.079i			1.77037i	−0.465244	+	0.885183i	$0.654033\pi$
$410$		0			0
$411$	−424.116			−1.03191
$412$		0			0
$413$	−66.3174	−	66.3174i	−0.160575	−	0.160575i
$414$		0			0
$415$	−0.0156664		0.000749143i	−3.77503e−5		1.80516e-6i
$416$		0			0
$417$	−1.30676	+	1.30676i	−0.00313372	+	0.00313372i
$418$		0			0
$419$		−	20.3800i		−	0.0486395i	−0.999704	−	0.0243198i	$-0.992258\pi$
$419$		−	20.3800i		−	0.0486395i	0.999704	−	0.0243198i	$-0.00774199\pi$
$420$		0			0
$421$	471.915			1.12094			0.560469	−	0.828176i	$-0.310621\pi$
$421$	471.915			1.12094			0.560469	+	0.828176i	$0.310621\pi$
$422$		0			0
$423$	−61.2189	−	61.2189i	−0.144726	−	0.144726i
$424$		0			0
$425$	−163.364	−	134.784i	−0.384385	−	0.317140i
$426$		0			0
$427$	383.329	−	383.329i	0.897725	−	0.897725i
$428$		0			0
$429$		−	164.651i		−	0.383803i
$430$		0			0
$431$	433.846			1.00660			0.503302	−	0.864110i	$-0.332118\pi$
$431$	433.846			1.00660			0.503302	+	0.864110i	$0.332118\pi$
$432$		0			0
$433$	143.893	+	143.893i	0.332317	+	0.332317i	0.853466	−	0.521149i	$-0.174496\pi$
$433$	143.893	+	143.893i	0.332317	+	0.332317i	−0.521149	+	0.853466i	$0.674496\pi$
$434$		0			0
$435$	−15.3969	−	321.986i	−0.0353951	−	0.740197i
$436$		0			0
$437$	−471.265	+	471.265i	−1.07841	+	1.07841i
$438$		0			0
$439$			21.7905i			0.0496368i	0.999692	+	0.0248184i	$0.00790075\pi$
$439$			21.7905i			0.0496368i	−0.999692	+	0.0248184i	$0.992099\pi$
$440$		0			0
$441$	316.400			0.717461
$442$		0			0
$443$	−186.194	−	186.194i	−0.420302	−	0.420302i	0.465005	−	0.885308i	$-0.346052\pi$
$443$	−186.194	−	186.194i	−0.420302	−	0.420302i	−0.885308	+	0.465005i	$0.846052\pi$
$444$		0			0
$445$	−285.647	−	259.576i	−0.641904	−	0.583316i
$446$		0			0
$447$	−79.9152	+	79.9152i	−0.178781	+	0.178781i
$448$		0			0
$449$		−	173.546i		−	0.386517i	−0.981148	−	0.193258i	$-0.938094\pi$
$449$		−	173.546i		−	0.386517i	0.981148	−	0.193258i	$-0.0619056\pi$
$450$		0			0
$451$	−504.964			−1.11965
$452$		0			0
$453$	192.509	+	192.509i	0.424964	+	0.424964i
$454$		0			0
$455$	288.972	−	317.996i	0.635103	−	0.698893i
$456$		0			0
$457$	−195.883	+	195.883i	−0.428628	+	0.428628i	−0.888161	−	0.459533i	$-0.848017\pi$
$457$	−195.883	+	195.883i	−0.428628	+	0.428628i	0.459533	+	0.888161i	$0.348017\pi$
$458$		0			0
$459$		−	44.0195i		−	0.0959030i
$460$		0			0
$461$	710.784			1.54183			0.770916	−	0.636937i	$-0.219799\pi$
$461$	710.784			1.54183			0.770916	+	0.636937i	$0.219799\pi$
$462$		0			0
$463$	−407.194	−	407.194i	−0.879468	−	0.879468i	0.114011	−	0.993479i	$-0.463630\pi$
$463$	−407.194	−	407.194i	−0.879468	−	0.879468i	−0.993479	+	0.114011i	$0.963630\pi$
$464$		0			0
$465$	−274.177	+	13.1108i	−0.589629	+	0.0281952i
$466$		0			0
$467$	46.4766	−	46.4766i	0.0995215	−	0.0995215i	−0.655593	−	0.755114i	$-0.727581\pi$
$467$	46.4766	−	46.4766i	0.0995215	−	0.0995215i	0.755114	+	0.655593i	$0.227581\pi$
$468$		0			0
$469$		−	1057.65i		−	2.25511i
$470$		0			0
$471$	298.257			0.633243
$472$		0			0
$473$	−337.903	−	337.903i	−0.714382	−	0.714382i
$474$		0			0
$475$	−636.495	+	61.0120i	−1.33999	+	0.128446i
$476$		0			0
$477$	−100.668	+	100.668i	−0.211043	+	0.211043i
$478$		0			0
$479$			632.568i			1.32060i	0.751001	+	0.660301i	$0.229571\pi$
$479$			632.568i			1.32060i	−0.751001	+	0.660301i	$0.770429\pi$
$480$		0			0
$481$	317.848			0.660806
$482$		0			0
$483$	396.645	+	396.645i	0.821212	+	0.821212i
$484$		0			0
$485$	9.94005	+	207.870i	0.0204950	+	0.428599i
$486$		0			0
$487$	24.5000	−	24.5000i	0.0503080	−	0.0503080i	−0.681505	−	0.731813i	$-0.738674\pi$
$487$	24.5000	−	24.5000i	0.0503080	−	0.0503080i	0.731813	+	0.681505i	$0.238674\pi$
$488$		0			0
$489$		−	480.333i		−	0.982277i
$490$		0			0
$491$	−888.550			−1.80967			−0.904837	−	0.425759i	$-0.860007\pi$
$491$	−888.550			−1.80967			−0.904837	+	0.425759i	$0.860007\pi$
$492$		0			0
$493$	−222.972	−	222.972i	−0.452276	−	0.452276i
$494$		0			0
$495$	152.620	+	138.690i	0.308324	+	0.280182i
$496$		0			0
$497$	159.623	−	159.623i	0.321173	−	0.321173i
$498$		0			0
$499$		−	313.223i		−	0.627702i	−0.949472	−	0.313851i	$-0.898381\pi$
$499$		−	313.223i		−	0.627702i	0.949472	−	0.313851i	$-0.101619\pi$
$500$		0			0
$501$	−64.6880			−0.129118
$502$		0			0
$503$	22.1824	+	22.1824i	0.0441001	+	0.0441001i	0.728813	−	0.684713i	$-0.240072\pi$
$503$	22.1824	+	22.1824i	0.0441001	+	0.0441001i	−0.684713	+	0.728813i	$0.740072\pi$
$504$		0			0
$505$	601.462	−	661.873i	1.19101	−	1.31064i
$506$		0			0
$507$	−148.427	+	148.427i	−0.292755	+	0.292755i
$508$		0			0
$509$			510.456i			1.00286i	0.865198	+	0.501431i	$0.167193\pi$
$509$			510.456i			1.00286i	−0.865198	+	0.501431i	$0.832807\pi$
$510$		0			0
$511$	1209.65			2.36721
$512$		0			0
$513$	−93.9741	−	93.9741i	−0.183185	−	0.183185i
$514$		0			0
$515$	290.270	−	13.8803i	0.563630	−	0.0269520i
$516$		0			0
$517$	280.550	−	280.550i	0.542649	−	0.542649i
$518$		0			0
$519$			21.2874i			0.0410161i
$520$		0			0
$521$	−765.379			−1.46906			−0.734529	−	0.678578i	$-0.762597\pi$
$521$	−765.379			−1.46906			−0.734529	+	0.678578i	$0.762597\pi$
$522$		0			0
$523$	57.8350	+	57.8350i	0.110583	+	0.110583i	0.760233	−	0.649650i	$-0.225085\pi$
$523$	57.8350	+	57.8350i	0.110583	+	0.110583i	−0.649650	+	0.760233i	$0.725085\pi$
$524$		0			0
$525$	51.3514	+	535.713i	0.0978122	+	1.02041i
$526$		0			0
$527$	−189.865	+	189.865i	−0.360275	+	0.360275i
$528$		0			0
$529$			150.014i			0.283580i
$530$		0			0
$531$	22.6384			0.0426336
$532$		0			0
$533$	−179.581	−	179.581i	−0.336924	−	0.336924i
$534$		0			0
$535$	12.4324	+	259.992i	0.0232382	+	0.485966i
$536$		0			0
$537$	−11.8433	+	11.8433i	−0.0220546	+	0.0220546i
$538$		0			0
$539$			1449.98i			2.69012i
$540$		0			0
$541$	−650.947			−1.20323			−0.601615	−	0.798786i	$-0.705476\pi$
$541$	−650.947			−1.20323			−0.601615	+	0.798786i	$0.705476\pi$
$542$		0			0
$543$	−305.020	−	305.020i	−0.561731	−	0.561731i
$544$		0			0
$545$	316.346	+	287.473i	0.580452	+	0.527473i
$546$		0			0
$547$	−200.024	+	200.024i	−0.365674	+	0.365674i	−0.865897	−	0.500223i	$-0.833251\pi$
$547$	−200.024	+	200.024i	−0.365674	+	0.365674i	0.500223	+	0.865897i	$0.333251\pi$
$548$		0			0
$549$			130.855i			0.238351i
$550$		0			0
$551$	−952.014			−1.72779
$552$		0			0
$553$	195.651	+	195.651i	0.353799	+	0.353799i
$554$		0			0
$555$	−267.731	+	294.622i	−0.482399	+	0.530851i
$556$		0			0
$557$	169.939	−	169.939i	0.305097	−	0.305097i	−0.537907	−	0.843004i	$-0.680785\pi$
$557$	169.939	−	169.939i	0.305097	−	0.305097i	0.843004	+	0.537907i	$0.180785\pi$
$558$		0			0
$559$		−	240.337i		−	0.429941i
$560$		0			0
$561$	201.729			0.359589
$562$		0			0
$563$	288.641	+	288.641i	0.512684	+	0.512684i	0.915348	−	0.402664i	$-0.131916\pi$
$563$	288.641	+	288.641i	0.512684	+	0.512684i	−0.402664	+	0.915348i	$0.631916\pi$
$564$		0			0
$565$	110.830	−	5.29974i	0.196160	−	0.00938007i
$566$		0			0
$567$	−79.0943	+	79.0943i	−0.139496	+	0.139496i
$568$		0			0
$569$		−	119.228i		−	0.209540i	−0.994496	−	0.104770i	$-0.966589\pi$
$569$		−	119.228i		−	0.209540i	0.994496	−	0.104770i	$-0.0334107\pi$
$570$		0			0
$571$	1070.64			1.87503			0.937513	−	0.347951i	$-0.113122\pi$
$571$	1070.64			1.87503			0.937513	+	0.347951i	$0.113122\pi$
$572$		0			0
$573$	−198.836	−	198.836i	−0.347010	−	0.347010i
$574$		0			0
$575$	−414.587	+	502.495i	−0.721021	+	0.873904i
$576$		0			0
$577$	572.086	−	572.086i	0.991484	−	0.991484i	−0.00848018	−	0.999964i	$-0.502699\pi$
$577$	572.086	−	572.086i	0.991484	−	0.991484i	0.999964	+	0.00848018i	$0.00269936\pi$
$578$		0			0
$579$			19.8756i			0.0343275i
$580$		0			0
$581$	0.0389863			6.71020e−5
$582$		0			0
$583$	−461.332	−	461.332i	−0.791307	−	0.791307i
$584$		0			0
$585$	4.95394	+	103.599i	0.00846828	+	0.177092i
$586$		0			0
$587$	314.886	−	314.886i	0.536433	−	0.536433i	−0.386047	−	0.922479i	$-0.626160\pi$
$587$	314.886	−	314.886i	0.536433	−	0.536433i	0.922479	+	0.386047i	$0.126160\pi$
$588$		0			0
$589$			810.659i			1.37633i
$590$		0			0
$591$	−561.072			−0.949360
$592$		0			0
$593$	781.658	+	781.658i	1.31814	+	1.31814i	0.915246	+	0.402896i	$0.131996\pi$
$593$	781.658	+	781.658i	1.31814	+	1.31814i	0.402896	+	0.915246i	$0.368004\pi$
$594$		0			0
$595$	389.606	+	354.046i	0.654800	+	0.595035i
$596$		0			0
$597$	−363.616	+	363.616i	−0.609073	+	0.609073i
$598$		0			0
$599$		−	423.280i		−	0.706645i	−0.935502	−	0.353322i	$-0.885052\pi$
$599$		−	423.280i		−	0.706645i	0.935502	−	0.353322i	$-0.114948\pi$
$600$		0			0
$601$	−68.1617			−0.113414			−0.0567069	−	0.998391i	$-0.518060\pi$
$601$	−68.1617			−0.113414			−0.0567069	+	0.998391i	$0.518060\pi$
$602$		0			0
$603$	180.522	+	180.522i	0.299373	+	0.299373i
$604$		0			0
$605$	−228.701	+	251.672i	−0.378019	+	0.415987i
$606$		0			0
$607$	−186.390	+	186.390i	−0.307068	+	0.307068i	−0.843771	−	0.536703i	$-0.819669\pi$
$607$	−186.390	+	186.390i	−0.307068	+	0.307068i	0.536703	+	0.843771i	$0.319669\pi$
$608$		0			0
$609$			801.272i			1.31572i
$610$		0			0
$611$	199.544			0.326586
$612$		0			0
$613$	337.566	+	337.566i	0.550679	+	0.550679i	0.926637	−	0.375958i	$-0.122686\pi$
$613$	337.566	+	337.566i	0.550679	+	0.550679i	−0.375958	+	0.926637i	$0.622686\pi$
$614$		0			0
$615$	317.724	−	15.1931i	0.516624	−	0.0247042i
$616$		0			0
$617$	858.797	−	858.797i	1.39189	−	1.39189i	0.570808	−	0.821084i	$-0.306630\pi$
$617$	858.797	−	858.797i	1.39189	−	1.39189i	0.821084	−	0.570808i	$-0.193370\pi$
$618$		0			0
$619$		−	202.653i		−	0.327388i	−0.986511	−	0.163694i	$-0.947659\pi$
$619$		−	202.653i		−	0.327388i	0.986511	−	0.163694i	$-0.0523410\pi$
$620$		0			0
$621$	−135.401			−0.218037
$622$		0			0
$623$	678.403	+	678.403i	1.08893	+	1.08893i
$624$		0			0
$625$	−613.619	+	118.729i	−0.981790	+	0.189967i
$626$		0			0
$627$	430.658	−	430.658i	0.686855	−	0.686855i
$628$		0			0
$629$			389.424i			0.619116i
$630$		0			0
$631$	536.853			0.850797			0.425398	−	0.905006i	$-0.360134\pi$
$631$	536.853			0.850797			0.425398	+	0.905006i	$0.360134\pi$
$632$		0			0
$633$	−334.874	−	334.874i	−0.529027	−	0.529027i
$634$		0			0
$635$	−43.0802	−	900.911i	−0.0678429	−	1.41876i
$636$		0			0
$637$	−515.656	+	515.656i	−0.809507	+	0.809507i
$638$		0			0
$639$			54.4896i			0.0852733i
$640$		0			0
$641$	665.993			1.03899			0.519495	−	0.854473i	$-0.326120\pi$
$641$	665.993			1.03899			0.519495	+	0.854473i	$0.326120\pi$
$642$		0			0
$643$	7.83317	+	7.83317i	0.0121822	+	0.0121822i	0.713172	−	0.700989i	$-0.247258\pi$
$643$	7.83317	+	7.83317i	0.0121822	+	0.0121822i	−0.700989	+	0.713172i	$0.747258\pi$
$644$		0			0
$645$	222.775	+	202.442i	0.345388	+	0.313864i
$646$		0			0
$647$	287.426	−	287.426i	0.444244	−	0.444244i	−0.449191	−	0.893436i	$-0.648288\pi$
$647$	287.426	−	287.426i	0.444244	−	0.444244i	0.893436	+	0.449191i	$0.148288\pi$
$648$		0			0
$649$			103.746i			0.159855i
$650$		0			0
$651$	682.300			1.04808
$652$		0			0
$653$	−587.685	−	587.685i	−0.899976	−	0.899976i	0.0954571	−	0.995434i	$-0.469569\pi$
$653$	−587.685	−	587.685i	−0.899976	−	0.899976i	−0.995434	+	0.0954571i	$0.969569\pi$
$654$		0			0
$655$	416.328	−	458.144i	0.635616	−	0.699457i
$656$		0			0
$657$	−206.465	+	206.465i	−0.314255	+	0.314255i
$658$		0			0
$659$		−	754.028i		−	1.14420i	−0.820184	−	0.572101i	$-0.806129\pi$
$659$		−	754.028i		−	1.14420i	0.820184	−	0.572101i	$-0.193871\pi$
$660$		0			0
$661$	−818.290			−1.23796			−0.618978	−	0.785408i	$-0.712453\pi$
$661$	−818.290			−1.23796			−0.618978	+	0.785408i	$0.712453\pi$
$662$		0			0
$663$	71.7411	+	71.7411i	0.108207	+	0.108207i
$664$		0			0
$665$	1587.57	−	75.9152i	2.38732	−	0.114158i
$666$		0			0
$667$	−685.845	+	685.845i	−1.02825	+	1.02825i
$668$		0			0
$669$		−	570.264i		−	0.852412i
$670$		0			0
$671$	−599.672			−0.893700
$672$		0			0
$673$	202.080	+	202.080i	0.300268	+	0.300268i	0.841119	−	0.540851i	$-0.181898\pi$
$673$	202.080	+	202.080i	0.300268	+	0.300268i	−0.540851	+	0.841119i	$0.681898\pi$
$674$		0			0
$675$	−100.202	−	82.6720i	−0.148447	−	0.122477i
$676$		0			0
$677$	−47.2645	+	47.2645i	−0.0698147	+	0.0698147i	−0.741152	−	0.671337i	$-0.765720\pi$
$677$	−47.2645	+	47.2645i	−0.0698147	+	0.0698147i	0.671337	+	0.741152i	$0.265720\pi$
$678$		0			0
$679$		−	517.292i		−	0.761844i
$680$		0			0
$681$	257.702			0.378417
$682$		0			0
$683$	126.090	+	126.090i	0.184612	+	0.184612i	0.793362	−	0.608750i	$-0.208329\pi$
$683$	126.090	+	126.090i	0.184612	+	0.184612i	−0.608750	+	0.793362i	$0.708329\pi$
$684$		0			0
$685$	58.4783	+	1222.92i	0.0853698	+	1.78529i
$686$		0			0
$687$	189.043	−	189.043i	0.275172	−	0.275172i
$688$		0			0
$689$		−	328.127i		−	0.476237i
$690$		0			0
$691$	−485.927			−0.703223			−0.351612	−	0.936146i	$-0.614366\pi$
$691$	−485.927			−0.703223			−0.351612	+	0.936146i	$0.614366\pi$
$692$		0			0
$693$	−362.468	−	362.468i	−0.523041	−	0.523041i
$694$		0			0
$695$	3.94816	+	3.58781i	0.00568081	+	0.00516231i
$696$		0			0
$697$	220.021	−	220.021i	0.315668	−	0.315668i
$698$		0			0
$699$		−	40.7196i		−	0.0582541i
$700$		0			0
$701$	−94.5850			−0.134929			−0.0674643	−	0.997722i	$-0.521491\pi$
$701$	−94.5850			−0.134929			−0.0674643	+	0.997722i	$0.521491\pi$
$702$		0			0
$703$	831.354	+	831.354i	1.18258	+	1.18258i
$704$		0			0
$705$	−168.081	+	184.963i	−0.238413	+	0.262359i
$706$		0			0
$707$	−1571.93	+	1571.93i	−2.22338	+	2.22338i
$708$		0			0
$709$			24.3499i			0.0343440i	0.999853	+	0.0171720i	$0.00546629\pi$
$709$			24.3499i			0.0343440i	−0.999853	+	0.0171720i	$0.994534\pi$
$710$		0			0
$711$	−66.7883			−0.0939357
$712$		0			0
$713$	584.011	+	584.011i	0.819090	+	0.819090i
$714$		0			0
$715$	−474.765	+	22.7026i	−0.664007	+	0.0317518i
$716$		0			0
$717$	119.159	−	119.159i	0.166191	−	0.166191i
$718$		0			0
$719$		−	534.841i		−	0.743868i	−0.928259	−	0.371934i	$-0.878695\pi$
$719$		−	534.841i		−	0.743868i	0.928259	−	0.371934i	$-0.121305\pi$
$720$		0			0
$721$	−722.346			−1.00187
$722$		0			0
$723$	377.236	+	377.236i	0.521765	+	0.521765i
$724$		0			0
$725$	−926.309	+	88.7925i	−1.27767	+	0.122472i
$726$		0			0
$727$	−435.834	+	435.834i	−0.599497	+	0.599497i	−0.940179	−	0.340682i	$-0.889342\pi$
$727$	−435.834	+	435.834i	−0.599497	+	0.599497i	0.340682	+	0.940179i	$0.389342\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	294.459			0.402816
$732$		0			0
$733$	224.087	+	224.087i	0.305712	+	0.305712i	0.843244	−	0.537531i	$-0.180643\pi$
$733$	224.087	+	224.087i	0.305712	+	0.305712i	−0.537531	+	0.843244i	$0.680643\pi$
$734$		0			0
$735$	−43.6261	−	912.326i	−0.0593553	−	1.24126i
$736$		0			0
$737$	−827.282	+	827.282i	−1.12250	+	1.12250i
$738$		0			0
$739$		−	730.510i		−	0.988512i	−0.869317	−	0.494256i	$-0.835441\pi$
$739$		−	730.510i		−	0.988512i	0.869317	−	0.494256i	$-0.164559\pi$
$740$		0			0
$741$	306.310			0.413374
$742$		0			0
$743$	941.961	+	941.961i	1.26778	+	1.26778i	0.947232	+	0.320549i	$0.103867\pi$
$743$	941.961	+	941.961i	1.26778	+	1.26778i	0.320549	+	0.947232i	$0.396133\pi$
$744$		0			0
$745$	241.451	+	219.413i	0.324095	+	0.294514i
$746$		0			0
$747$	−0.00665427	+	0.00665427i	−8.90800e−6	+	8.90800e-6i
$748$		0			0
$749$		−	646.998i		−	0.863816i
$750$		0			0
$751$	−231.169			−0.307814			−0.153907	−	0.988085i	$-0.549186\pi$
$751$	−231.169			−0.307814			−0.153907	+	0.988085i	$0.549186\pi$
$752$		0			0
$753$	190.096	+	190.096i	0.252452	+	0.252452i
$754$		0			0
$755$	528.547	−	581.634i	0.700062	−	0.770377i
$756$		0			0
$757$	−382.911	+	382.911i	−0.505826	+	0.505826i	−0.913243	−	0.407416i	$-0.866430\pi$
$757$	−382.911	+	382.911i	−0.505826	+	0.505826i	0.407416	+	0.913243i	$0.366430\pi$
$758$		0			0
$759$		−	620.505i		−	0.817530i
$760$		0			0
$761$	−941.999			−1.23784			−0.618922	−	0.785453i	$-0.712430\pi$
$761$	−941.999			−1.23784			−0.618922	+	0.785453i	$0.712430\pi$
$762$		0			0
$763$	−751.312	−	751.312i	−0.984681	−	0.984681i
$764$		0			0
$765$	−126.928	+	6.06952i	−0.165919	+	0.00793402i
$766$		0			0
$767$	−36.8952	+	36.8952i	−0.0481032	+	0.0481032i
$768$		0			0
$769$		−	1388.76i		−	1.80593i	−0.429718	−	0.902963i	$-0.641387\pi$
$769$		−	1388.76i		−	1.80593i	0.429718	−	0.902963i	$-0.358613\pi$
$770$		0			0
$771$	−505.912			−0.656176
$772$		0			0
$773$	−185.158	−	185.158i	−0.239532	−	0.239532i	0.577124	−	0.816656i	$-0.304175\pi$
$773$	−185.158	−	185.158i	−0.239532	−	0.239532i	−0.816656	+	0.577124i	$0.804175\pi$
$774$		0			0
$775$	75.6086	+	788.771i	0.0975595	+	1.01777i
$776$		0			0
$777$	699.718	−	699.718i	0.900538	−	0.900538i
$778$		0			0
$779$		−	939.413i		−	1.20592i
$780$		0			0
$781$	−249.711			−0.319733
$782$		0			0
$783$	−136.763	−	136.763i	−0.174665	−	0.174665i
$784$		0			0
$785$	−41.1245	−	860.012i	−0.0523879	−	1.09556i
$786$		0			0
$787$	−194.815	+	194.815i	−0.247542	+	0.247542i	−0.819961	−	0.572419i	$-0.806005\pi$
$787$	−194.815	+	194.815i	−0.247542	+	0.247542i	0.572419	+	0.819961i	$0.306005\pi$
$788$		0			0
$789$		−	578.554i		−	0.733275i
$790$		0			0
$791$	−275.805			−0.348679
$792$		0			0
$793$	−213.262	−	213.262i	−0.268930	−	0.268930i
$794$		0			0
$795$	304.151	+	276.390i	0.382580	+	0.347661i
$796$		0			0
$797$	694.112	−	694.112i	0.870906	−	0.870906i	−0.121665	−	0.992571i	$-0.538823\pi$
$797$	694.112	−	694.112i	0.870906	−	0.870906i	0.992571	+	0.121665i	$0.0388233\pi$
$798$		0			0
$799$			244.479i			0.305982i
$800$		0			0
$801$	−231.583			−0.289117
$802$		0			0
$803$	−946.175	−	946.175i	−1.17830	−	1.17830i
$804$		0			0
$805$	1089.02	−	1198.40i	1.35282	−	1.48870i
$806$		0			0
$807$	−461.588	+	461.588i	−0.571980	+	0.571980i
$808$		0			0
$809$		−	1492.22i		−	1.84453i	−0.386563	−	0.922263i	$-0.626338\pi$
$809$		−	1492.22i		−	1.84453i	0.386563	−	0.922263i	$-0.373662\pi$
$810$		0			0
$811$	80.5721			0.0993490			0.0496745	−	0.998765i	$-0.484182\pi$
$811$	80.5721			0.0993490			0.0496745	+	0.998765i	$0.484182\pi$
$812$		0			0
$813$	240.656	+	240.656i	0.296010	+	0.296010i
$814$		0			0
$815$	−1385.02	+	66.2296i	−1.69941	+	0.0812634i
$816$		0			0
$817$	628.619	−	628.619i	0.769423	−	0.769423i
$818$		0			0
$819$		−	257.809i		−	0.314785i
$820$		0			0
$821$	−221.422			−0.269698			−0.134849	−	0.990866i	$-0.543055\pi$
$821$	−221.422			−0.269698			−0.134849	+	0.990866i	$0.543055\pi$
$822$		0			0
$823$	815.236	+	815.236i	0.990566	+	0.990566i	0.999956	−	0.00938979i	$-0.00298891\pi$
$823$	815.236	+	815.236i	0.990566	+	0.990566i	−0.00938979	+	0.999956i	$0.502989\pi$
$824$		0			0
$825$	378.863	−	459.197i	0.459228	−	0.556602i
$826$		0			0
$827$	29.5640	−	29.5640i	0.0357485	−	0.0357485i	−0.689007	−	0.724755i	$-0.741953\pi$
$827$	29.5640	−	29.5640i	0.0357485	−	0.0357485i	0.724755	+	0.689007i	$0.241953\pi$
$828$		0			0
$829$			558.092i			0.673211i	0.941646	+	0.336606i	$0.109279\pi$
$829$			558.092i			0.673211i	−0.941646	+	0.336606i	$0.890721\pi$
$830$		0			0
$831$	−221.380			−0.266402
$832$		0			0
$833$	−631.777	−	631.777i	−0.758436	−	0.758436i
$834$		0			0
$835$	8.91936	+	186.525i	0.0106819	+	0.223383i
$836$		0			0
$837$	−116.457	+	116.457i	−0.139136	+	0.139136i
$838$		0			0
$839$		−	623.755i		−	0.743451i	−0.928343	−	0.371725i	$-0.878766\pi$
$839$		−	623.755i		−	0.743451i	0.928343	−	0.371725i	$-0.121234\pi$
$840$		0			0
$841$	−544.492			−0.647434
$842$		0			0
$843$	−152.489	−	152.489i	−0.180888	−	0.180888i
$844$		0			0
$845$	448.448	+	407.517i	0.530708	+	0.482269i
$846$		0			0
$847$	597.713	−	597.713i	0.705682	−	0.705682i
$848$		0			0
$849$		−	223.708i		−	0.263496i
$850$		0			0
$851$	1197.84			1.40757
$852$		0			0
$853$	−454.178	−	454.178i	−0.532448	−	0.532448i	0.388852	−	0.921300i	$-0.372872\pi$
$853$	−454.178	−	454.178i	−0.532448	−	0.532448i	−0.921300	+	0.388852i	$0.872872\pi$
$854$		0			0
$855$	−258.013	+	283.928i	−0.301769	+	0.332079i
$856$		0			0
$857$	−769.104	+	769.104i	−0.897438	+	0.897438i	−0.995209	−	0.0977709i	$-0.968829\pi$
$857$	−769.104	+	769.104i	−0.897438	+	0.897438i	0.0977709	+	0.995209i	$0.468829\pi$
$858$		0			0
$859$			536.071i			0.624064i	0.950072	+	0.312032i	$0.101010\pi$
$859$			536.071i			0.624064i	−0.950072	+	0.312032i	$0.898990\pi$
$860$		0			0
$861$	−790.666			−0.918312
$862$		0			0
$863$	−500.177	−	500.177i	−0.579579	−	0.579579i	0.355208	−	0.934787i	$-0.384410\pi$
$863$	−500.177	−	500.177i	−0.579579	−	0.579579i	−0.934787	+	0.355208i	$0.884410\pi$
$864$		0			0
$865$	61.3812	−	2.93516i	0.0709609	−	0.00339324i
$866$		0			0
$867$	266.055	−	266.055i	0.306868	−	0.306868i
$868$		0			0
$869$		−	306.073i		−	0.352212i
$870$		0			0
$871$	−588.413			−0.675561
$872$		0			0
$873$	88.2927	+	88.2927i	0.101137	+	0.101137i
$874$		0			0
$875$	1537.62	−	221.935i	1.75728	−	0.253640i
$876$		0			0
$877$	−102.540	+	102.540i	−0.116922	+	0.116922i	−0.763147	−	0.646225i	$-0.776347\pi$
$877$	−102.540	+	102.540i	−0.116922	+	0.116922i	0.646225	+	0.763147i	$0.276347\pi$
$878$		0			0
$879$			763.318i			0.868394i
$880$		0			0
$881$	649.515			0.737247			0.368624	−	0.929579i	$-0.379829\pi$
$881$	649.515			0.737247			0.368624	+	0.929579i	$0.379829\pi$
$882$		0			0
$883$	341.476	+	341.476i	0.386723	+	0.386723i	0.873517	−	0.486794i	$-0.161834\pi$
$883$	341.476	+	341.476i	0.386723	+	0.386723i	−0.486794	+	0.873517i	$0.661834\pi$
$884$		0			0
$885$	−3.12145	−	65.2770i	−0.00352706	−	0.0737593i
$886$		0			0
$887$	−516.110	+	516.110i	−0.581860	+	0.581860i	−0.935414	−	0.353554i	$-0.884973\pi$
$887$	−516.110	+	516.110i	−0.581860	+	0.581860i	0.353554	+	0.935414i	$0.384973\pi$
$888$		0			0
$889$			2241.95i			2.52188i
$890$		0			0
$891$	123.734			0.138871
$892$		0			0
$893$	521.922	+	521.922i	0.584459	+	0.584459i
$894$		0			0
$895$	35.7827	+	32.5167i	0.0399806	+	0.0363315i
$896$		0			0
$897$	220.670	−	220.670i	0.246009	−	0.246009i
$898$		0			0
$899$			1179.77i			1.31232i
$900$		0			0
$901$	402.019			0.446192
$902$		0			0
$903$	−529.084	−	529.084i	−0.585918	−	0.585918i
$904$		0			0
$905$	−837.454	+	921.568i	−0.925364	+	1.01831i
$906$		0			0
$907$	62.4116	−	62.4116i	0.0688111	−	0.0688111i	−0.671864	−	0.740675i	$-0.734506\pi$
$907$	62.4116	−	62.4116i	0.0688111	−	0.0688111i	0.740675	+	0.671864i	$0.234506\pi$
$908$		0			0
$909$		−	536.600i		−	0.590319i
$910$		0			0
$911$	1140.91			1.25237			0.626183	−	0.779676i	$-0.284616\pi$
$911$	1140.91			1.25237			0.626183	+	0.779676i	$0.284616\pi$
$912$		0			0
$913$	−0.0304947	−	0.0304947i	−3.34006e−5	−	3.34006e-5i
$914$		0			0
$915$	377.314	−	18.0426i	0.412365	−	0.0197187i
$916$		0			0
$917$	−1088.08	+	1088.08i	−1.18656	+	1.18656i
$918$		0			0
$919$			1200.77i			1.30661i	0.757097	+	0.653303i	$0.226617\pi$
$919$			1200.77i			1.30661i	−0.757097	+	0.653303i	$0.773383\pi$
$920$		0			0
$921$	−240.525			−0.261156
$922$		0			0
$923$	−88.8049	−	88.8049i	−0.0962133	−	0.0962133i
$924$		0			0
$925$	886.446	+	731.368i	0.958320	+	0.790669i
$926$		0			0
$927$	123.292	−	123.292i	0.133001	−	0.133001i
$928$		0			0
$929$		−	87.8294i		−	0.0945419i	−0.998882	−	0.0472709i	$-0.984948\pi$
$929$		−	87.8294i		−	0.0945419i	0.998882	−	0.0472709i	$-0.0150524\pi$
$930$		0			0
$931$	−2697.47			−2.89739
$932$		0			0
$933$	526.505	+	526.505i	0.564314	+	0.564314i
$934$		0			0
$935$	−27.8150	−	581.678i	−0.0297486	−	0.622115i
$936$		0			0
$937$	−215.447	+	215.447i	−0.229933	+	0.229933i	−0.812665	−	0.582732i	$-0.801984\pi$
$937$	−215.447	+	215.447i	−0.229933	+	0.229933i	0.582732	+	0.812665i	$0.301984\pi$
$938$		0			0
$939$		−	160.441i		−	0.170863i
$940$		0			0
$941$	805.908			0.856438			0.428219	−	0.903675i	$-0.359141\pi$
$941$	805.908			0.856438			0.428219	+	0.903675i	$0.359141\pi$
$942$		0			0
$943$	−676.767	−	676.767i	−0.717675	−	0.717675i
$944$		0			0
$945$	238.971	+	217.159i	0.252879	+	0.229798i
$946$		0			0
$947$	739.218	−	739.218i	0.780589	−	0.780589i	−0.199341	−	0.979930i	$-0.563880\pi$
$947$	739.218	−	739.218i	0.780589	−	0.780589i	0.979930	+	0.199341i	$0.0638801\pi$
$948$		0			0
$949$		−	672.977i		−	0.709144i
$950$		0			0
$951$	−426.879			−0.448873
$952$		0			0
$953$	−790.131	−	790.131i	−0.829098	−	0.829098i	0.158294	−	0.987392i	$-0.449401\pi$
$953$	−790.131	−	790.131i	−0.829098	−	0.829098i	−0.987392	+	0.158294i	$0.949401\pi$
$954$		0			0
$955$	−545.920	+	600.752i	−0.571644	+	0.629060i
$956$		0			0
$957$	626.748	−	626.748i	0.654909	−	0.654909i
$958$		0			0
$959$		−	3043.28i		−	3.17339i
$960$		0			0
$961$	43.6021			0.0453716
$962$		0			0
$963$	110.431	+	110.431i	0.114674	+	0.114674i
$964$		0			0
$965$	57.3105	−	2.74050i	0.0593891	−	0.00283990i
$966$		0			0
$967$	213.927	−	213.927i	0.221227	−	0.221227i	−0.587788	−	0.809015i	$-0.700001\pi$
$967$	213.927	−	213.927i	0.221227	−	0.221227i	0.809015	+	0.587788i	$0.200001\pi$
$968$		0			0
$969$			375.288i			0.387294i
$970$		0			0
$971$	1356.34			1.39685			0.698423	−	0.715686i	$-0.253886\pi$
$971$	1356.34			1.39685			0.698423	+	0.715686i	$0.253886\pi$
$972$		0			0
$973$	−9.37676	−	9.37676i	−0.00963695	−	0.00963695i
$974$		0			0
$975$	298.039	−	28.5689i	0.305682	−	0.0293015i
$976$		0			0
$977$	−1047.93	+	1047.93i	−1.07260	+	1.07260i	−0.0754457	+	0.997150i	$0.524038\pi$
$977$	−1047.93	+	1047.93i	−1.07260	+	1.07260i	−0.997150	+	0.0754457i	$0.975962\pi$
$978$		0			0
$979$		−	1061.28i		−	1.08405i
$980$		0			0
$981$	256.471			0.261439
$982$		0			0
$983$	741.601	+	741.601i	0.754426	+	0.754426i	0.975302	−	0.220876i	$-0.0708915\pi$
$983$	741.601	+	741.601i	0.754426	+	0.754426i	−0.220876	+	0.975302i	$0.570891\pi$
$984$		0			0
$985$	77.3621	+	1617.83i	0.0785402	+	1.64246i
$986$		0			0
$987$	439.281	−	439.281i	0.445067	−	0.445067i
$988$		0			0
$989$		−	905.734i		−	0.915808i
$990$		0			0
$991$	−304.849			−0.307618			−0.153809	−	0.988101i	$-0.549154\pi$
$991$	−304.849			−0.307618			−0.153809	+	0.988101i	$0.549154\pi$
$992$		0			0
$993$	−466.369	−	466.369i	−0.469657	−	0.469657i
$994$		0			0
$995$	1098.61	+	998.336i	1.10413	+	1.00335i
$996$		0			0
$997$	−542.650	+	542.650i	−0.544283	+	0.544283i	−0.924782	−	0.380499i	$-0.875752\pi$
$997$	−542.650	+	542.650i	−0.544283	+	0.544283i	0.380499	+	0.924782i	$0.375752\pi$
$998$		0			0
$999$			238.859i			0.239098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bg.e.193.1		8
3.2	odd	2		720.3.bh.o.433.3		8
4.3	odd	2		120.3.u.b.73.3	✓	8
5.2	odd	4	inner	240.3.bg.e.97.1		8
5.3	odd	4		1200.3.bg.q.1057.3		8
5.4	even	2		1200.3.bg.q.193.3		8
8.3	odd	2		960.3.bg.l.193.2		8
8.5	even	2		960.3.bg.k.193.4		8
12.11	even	2		360.3.v.f.73.3		8
15.2	even	4		720.3.bh.o.577.3		8
20.3	even	4		600.3.u.h.457.2		8
20.7	even	4		120.3.u.b.97.3	yes	8
20.19	odd	2		600.3.u.h.193.2		8
40.27	even	4		960.3.bg.l.577.2		8
40.37	odd	4		960.3.bg.k.577.4		8
60.23	odd	4		1800.3.v.t.1657.4		8
60.47	odd	4		360.3.v.f.217.3		8
60.59	even	2		1800.3.v.t.793.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.b.73.3	✓	8	4.3	odd	2
120.3.u.b.97.3	yes	8	20.7	even	4
240.3.bg.e.97.1		8	5.2	odd	4	inner
240.3.bg.e.193.1		8	1.1	even	1	trivial
360.3.v.f.73.3		8	12.11	even	2
360.3.v.f.217.3		8	60.47	odd	4
600.3.u.h.193.2		8	20.19	odd	2
600.3.u.h.457.2		8	20.3	even	4
720.3.bh.o.433.3		8	3.2	odd	2
720.3.bh.o.577.3		8	15.2	even	4
960.3.bg.k.193.4		8	8.5	even	2
960.3.bg.k.577.4		8	40.37	odd	4
960.3.bg.l.193.2		8	8.3	odd	2
960.3.bg.l.577.2		8	40.27	even	4
1200.3.bg.q.193.3		8	5.4	even	2
1200.3.bg.q.1057.3		8	5.3	odd	4
1800.3.v.t.793.4		8	60.59	even	2
1800.3.v.t.1657.4		8	60.23	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 1.22474i) q^{3} +(-3.36263 + 3.70037i) q^{5} +(8.78825 - 8.78825i) q^{7} +3.00000i q^{9} -13.7482 q^{11} +(-4.88927 - 4.88927i) q^{13} +(8.65037 - 0.413648i) q^{15} +(5.99029 - 5.99029i) q^{17} -25.5765i q^{19} -21.5267 q^{21} +(-18.4257 - 18.4257i) q^{23} +(-2.38547 - 24.8859i) q^{25} +(3.67423 - 3.67423i) q^{27} -37.2222i q^{29} -31.6955 q^{31} +(16.8380 + 16.8380i) q^{33} +(2.96816 + 62.0714i) q^{35} +(-32.5046 + 32.5046i) q^{37} +11.9762i q^{39} +36.7295 q^{41} +(24.5780 + 24.5780i) q^{43} +(-11.1011 - 10.0879i) q^{45} +(-20.4063 + 20.4063i) q^{47} -105.467i q^{49} -14.6732 q^{51} +(33.5559 + 33.5559i) q^{53} +(46.2300 - 50.8734i) q^{55} +(-31.3247 + 31.3247i) q^{57} -7.54615i q^{59} +43.6183 q^{61} +(26.3648 + 26.3648i) q^{63} +(34.5329 - 1.65131i) q^{65} +(60.1739 - 60.1739i) q^{67} +45.1336i q^{69} +18.1632 q^{71} +(68.8218 + 68.8218i) q^{73} +(-27.5573 + 33.4005i) q^{75} +(-120.823 + 120.823i) q^{77} +22.2628i q^{79} -9.00000 q^{81} +(0.00221809 + 0.00221809i) q^{83} +(2.02317 + 42.3094i) q^{85} +(-45.5877 + 45.5877i) q^{87} +77.1943i q^{89} -85.9363 q^{91} +(38.8189 + 38.8189i) q^{93} +(94.6425 + 86.0043i) q^{95} +(29.4309 - 29.4309i) q^{97} -41.2446i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} - 4 q^{7} - 32 q^{11} - 4 q^{13} + 52 q^{17} - 24 q^{21} + 40 q^{23} - 84 q^{25} - 96 q^{31} + 60 q^{33} - 24 q^{35} - 60 q^{37} - 152 q^{41} + 88 q^{43} + 16 q^{47} + 168 q^{51} + 108 q^{53}+ \cdots - 208 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 - 4 * q^7 - 32 * q^11 - 4 * q^13 + 52 * q^17 - 24 * q^21 + 40 * q^23 - 84 * q^25 - 96 * q^31 + 60 * q^33 - 24 * q^35 - 60 * q^37 - 152 * q^41 + 88 * q^43 + 16 * q^47 + 168 * q^51 + 108 * q^53 - 116 * q^55 - 24 * q^57 + 264 * q^61 - 12 * q^63 + 164 * q^65 + 216 * q^67 + 240 * q^71 - 208 * q^73 - 120 * q^75 + 168 * q^77 - 72 * q^81 - 336 * q^83 - 12 * q^85 - 252 * q^87 - 592 * q^91 + 264 * q^93 + 128 * q^95 - 208 * q^97

Introduction

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