LMFDB - Embedded newform 960.3.bg.b.577.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,3,Mod(193,960)] 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("960.193"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-12,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	960.577
Dual form			960.3.bg.b.193.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 1.22474i) q^{3} +(-4.22474 - 2.67423i) q^{5} +(7.44949 + 7.44949i) q^{7} -3.00000i q^{9} +16.2474 q^{11} +(-12.2474 + 12.2474i) q^{13} +(-8.44949 + 1.89898i) q^{15} +(-7.55051 - 7.55051i) q^{17} +14.4949i q^{19} +18.2474 q^{21} +(-2.65153 + 2.65153i) q^{23} +(10.6969 + 22.5959i) q^{25} +(-3.67423 - 3.67423i) q^{27} +34.2474i q^{29} -20.4949 q^{31} +(19.8990 - 19.8990i) q^{33} +(-11.5505 - 51.3939i) q^{35} +(-7.34847 - 7.34847i) q^{37} +30.0000i q^{39} +25.5051 q^{41} +(-25.1010 + 25.1010i) q^{43} +(-8.02270 + 12.6742i) q^{45} +(22.0454 + 22.0454i) q^{47} +61.9898i q^{49} -18.4949 q^{51} +(35.3031 - 35.3031i) q^{53} +(-68.6413 - 43.4495i) q^{55} +(17.7526 + 17.7526i) q^{57} +88.7423i q^{59} +102.495 q^{61} +(22.3485 - 22.3485i) q^{63} +(84.4949 - 18.9898i) q^{65} +(24.6969 + 24.6969i) q^{67} +6.49490i q^{69} +77.9796 q^{71} +(-44.1918 + 44.1918i) q^{73} +(40.7753 + 14.5732i) q^{75} +(121.035 + 121.035i) q^{77} -48.4949i q^{79} -9.00000 q^{81} +(101.641 - 101.641i) q^{83} +(11.7071 + 52.0908i) q^{85} +(41.9444 + 41.9444i) q^{87} +156.969i q^{89} -182.474 q^{91} +(-25.1010 + 25.1010i) q^{93} +(38.7628 - 61.2372i) q^{95} +(55.4041 + 55.4041i) q^{97} -48.7423i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{5} + 20 q^{7} + 16 q^{11} - 24 q^{15} - 40 q^{17} + 24 q^{21} - 40 q^{23} - 16 q^{25} + 16 q^{31} + 60 q^{33} - 56 q^{35} + 200 q^{41} - 120 q^{43} + 12 q^{45} + 24 q^{51} + 200 q^{53} - 108 q^{55}+ \cdots + 300 q^{97}+O(q^{100}) $ 4 * q - 12 * q^5 + 20 * q^7 + 16 * q^11 - 24 * q^15 - 40 * q^17 + 24 * q^21 - 40 * q^23 - 16 * q^25 + 16 * q^31 + 60 * q^33 - 56 * q^35 + 200 * q^41 - 120 * q^43 + 12 * q^45 + 24 * q^51 + 200 * q^53 - 108 * q^55 + 120 * q^57 + 312 * q^61 + 60 * q^63 + 240 * q^65 + 40 * q^67 - 80 * q^71 - 20 * q^73 + 168 * q^75 + 200 * q^77 - 36 * q^81 + 240 * q^83 + 184 * q^85 + 60 * q^87 - 240 * q^91 - 120 * q^93 + 400 * q^95 + 300 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$5$	−4.22474	−	2.67423i	−0.844949	−	0.534847i
$5$	−4.22474	−	2.67423i	−0.844949	−	0.534847i
$6$		0			0
$7$	7.44949	+	7.44949i	1.06421	+	1.06421i	0.997792	+	0.0664211i	$0.0211581\pi$
$7$	7.44949	+	7.44949i	1.06421	+	1.06421i	0.0664211	+	0.997792i	$0.478842\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	16.2474			1.47704			0.738520	−	0.674231i	$-0.235525\pi$
$11$	16.2474			1.47704			0.738520	+	0.674231i	$0.235525\pi$
$12$		0			0
$13$	−12.2474	+	12.2474i	−0.942111	+	0.942111i	−0.998414	−	0.0563023i	$-0.982069\pi$
$13$	−12.2474	+	12.2474i	−0.942111	+	0.942111i	0.0563023	+	0.998414i	$0.482069\pi$
$14$		0			0
$15$	−8.44949	+	1.89898i	−0.563299	+	0.126599i
$16$		0			0
$17$	−7.55051	−	7.55051i	−0.444148	−	0.444148i	0.449256	−	0.893403i	$-0.351689\pi$
$17$	−7.55051	−	7.55051i	−0.444148	−	0.444148i	−0.893403	+	0.449256i	$0.851689\pi$
$18$		0			0
$19$			14.4949i			0.762889i	0.924392	+	0.381445i	$0.124573\pi$
$19$			14.4949i			0.762889i	−0.924392	+	0.381445i	$0.875427\pi$
$20$		0			0
$21$	18.2474			0.868926
$22$		0			0
$23$	−2.65153	+	2.65153i	−0.115284	+	0.115284i	−0.762395	−	0.647111i	$-0.775977\pi$
$23$	−2.65153	+	2.65153i	−0.115284	+	0.115284i	0.647111	+	0.762395i	$0.275977\pi$
$24$		0			0
$25$	10.6969	+	22.5959i	0.427878	+	0.903837i
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$		0			0
$29$			34.2474i			1.18095i	0.807057	+	0.590473i	$0.201059\pi$
$29$			34.2474i			1.18095i	−0.807057	+	0.590473i	$0.798941\pi$
$30$		0			0
$31$	−20.4949			−0.661126			−0.330563	−	0.943784i	$-0.607239\pi$
$31$	−20.4949			−0.661126			−0.330563	+	0.943784i	$0.607239\pi$
$32$		0			0
$33$	19.8990	−	19.8990i	0.602999	−	0.602999i
$34$		0			0
$35$	−11.5505	−	51.3939i	−0.330015	−	1.46840i
$36$		0			0
$37$	−7.34847	−	7.34847i	−0.198607	−	0.198607i	0.600795	−	0.799403i	$-0.294851\pi$
$37$	−7.34847	−	7.34847i	−0.198607	−	0.198607i	−0.799403	+	0.600795i	$0.794851\pi$
$38$		0			0
$39$			30.0000i			0.769231i
$40$		0			0
$41$	25.5051			0.622076			0.311038	−	0.950398i	$-0.399323\pi$
$41$	25.5051			0.622076			0.311038	+	0.950398i	$0.399323\pi$
$42$		0			0
$43$	−25.1010	+	25.1010i	−0.583745	+	0.583745i	−0.935930	−	0.352186i	$-0.885439\pi$
$43$	−25.1010	+	25.1010i	−0.583745	+	0.583745i	0.352186	+	0.935930i	$0.385439\pi$
$44$		0			0
$45$	−8.02270	+	12.6742i	−0.178282	+	0.281650i
$46$		0			0
$47$	22.0454	+	22.0454i	0.469051	+	0.469051i	0.901607	−	0.432556i	$-0.142388\pi$
$47$	22.0454	+	22.0454i	0.469051	+	0.469051i	−0.432556	+	0.901607i	$0.642388\pi$
$48$		0			0
$49$			61.9898i			1.26510i
$50$		0			0
$51$	−18.4949			−0.362645
$52$		0			0
$53$	35.3031	−	35.3031i	0.666096	−	0.666096i	−0.290714	−	0.956810i	$-0.593893\pi$
$53$	35.3031	−	35.3031i	0.666096	−	0.666096i	0.956810	+	0.290714i	$0.0938929\pi$
$54$		0			0
$55$	−68.6413	−	43.4495i	−1.24802	−	0.789991i
$56$		0			0
$57$	17.7526	+	17.7526i	0.311448	+	0.311448i
$58$		0			0
$59$			88.7423i			1.50411i	0.659102	+	0.752054i	$0.270937\pi$
$59$			88.7423i			1.50411i	−0.659102	+	0.752054i	$0.729063\pi$
$60$		0			0
$61$	102.495			1.68024			0.840122	−	0.542397i	$-0.182483\pi$
$61$	102.495			1.68024			0.840122	+	0.542397i	$0.182483\pi$
$62$		0			0
$63$	22.3485	−	22.3485i	0.354738	−	0.354738i
$64$		0			0
$65$	84.4949	−	18.9898i	1.29992	−	0.292151i
$66$		0			0
$67$	24.6969	+	24.6969i	0.368611	+	0.368611i	0.866970	−	0.498359i	$-0.166064\pi$
$67$	24.6969	+	24.6969i	0.368611	+	0.368611i	−0.498359	+	0.866970i	$0.666064\pi$
$68$		0			0
$69$			6.49490i			0.0941289i
$70$		0			0
$71$	77.9796			1.09830			0.549152	−	0.835722i	$-0.314951\pi$
$71$	77.9796			1.09830			0.549152	+	0.835722i	$0.314951\pi$
$72$		0			0
$73$	−44.1918	+	44.1918i	−0.605368	+	0.605368i	−0.941732	−	0.336364i	$-0.890803\pi$
$73$	−44.1918	+	44.1918i	−0.605368	+	0.605368i	0.336364	+	0.941732i	$0.390803\pi$
$74$		0			0
$75$	40.7753	+	14.5732i	0.543670	+	0.194310i
$76$		0			0
$77$	121.035	+	121.035i	1.57189	+	1.57189i
$78$		0			0
$79$		−	48.4949i		−	0.613859i	−0.951732	−	0.306930i	$-0.900698\pi$
$79$		−	48.4949i		−	0.613859i	0.951732	−	0.306930i	$-0.0993017\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	101.641	−	101.641i	1.22459	−	1.22459i	0.258613	−	0.965981i	$-0.416734\pi$
$83$	101.641	−	101.641i	1.22459	−	1.22459i	0.965981	−	0.258613i	$-0.0832656\pi$
$84$		0			0
$85$	11.7071	+	52.0908i	0.137731	+	0.612833i
$86$		0			0
$87$	41.9444	+	41.9444i	0.482119	+	0.482119i
$88$		0			0
$89$			156.969i			1.76370i	0.471529	+	0.881850i	$0.343702\pi$
$89$			156.969i			1.76370i	−0.471529	+	0.881850i	$0.656298\pi$
$90$		0			0
$91$	−182.474			−2.00521
$92$		0			0
$93$	−25.1010	+	25.1010i	−0.269903	+	0.269903i
$94$		0			0
$95$	38.7628	−	61.2372i	0.408029	−	0.644603i
$96$		0			0
$97$	55.4041	+	55.4041i	0.571176	+	0.571176i	0.932457	−	0.361281i	$-0.117660\pi$
$97$	55.4041	+	55.4041i	0.571176	+	0.571176i	−0.361281	+	0.932457i	$0.617660\pi$
$98$		0			0
$99$		−	48.7423i		−	0.492347i
$100$		0			0
$101$	−45.7526			−0.452996			−0.226498	−	0.974012i	$-0.572728\pi$
$101$	−45.7526			−0.452996			−0.226498	+	0.974012i	$0.572728\pi$
$102$		0			0
$103$	23.1566	−	23.1566i	0.224822	−	0.224822i	−0.585704	−	0.810525i	$-0.699182\pi$
$103$	23.1566	−	23.1566i	0.224822	−	0.224822i	0.810525	+	0.585704i	$0.199182\pi$
$104$		0			0
$105$	−77.0908	−	48.7980i	−0.734198	−	0.464742i
$106$		0			0
$107$	−16.3383	−	16.3383i	−0.152694	−	0.152694i	0.626626	−	0.779320i	$-0.284435\pi$
$107$	−16.3383	−	16.3383i	−0.152694	−	0.152694i	−0.779320	+	0.626626i	$0.784435\pi$
$108$		0			0
$109$		−	159.485i		−	1.46316i	−0.681754	−	0.731581i	$-0.738783\pi$
$109$		−	159.485i		−	1.46316i	0.681754	−	0.731581i	$-0.261217\pi$
$110$		0			0
$111$	−18.0000			−0.162162
$112$		0			0
$113$	13.0556	−	13.0556i	0.115536	−	0.115536i	−0.646975	−	0.762511i	$-0.723966\pi$
$113$	13.0556	−	13.0556i	0.115536	−	0.115536i	0.762511	+	0.646975i	$0.223966\pi$
$114$		0			0
$115$	18.2929	−	4.11123i	0.159068	−	0.0357498i
$116$		0			0
$117$	36.7423	+	36.7423i	0.314037	+	0.314037i
$118$		0			0
$119$		−	112.495i		−	0.945335i
$120$		0			0
$121$	142.980			1.18165
$122$		0			0
$123$	31.2372	−	31.2372i	0.253961	−	0.253961i
$124$		0			0
$125$	15.2350	−	124.068i	0.121880	−	0.992545i
$126$		0			0
$127$	7.44949	+	7.44949i	0.0586574	+	0.0586574i	0.735827	−	0.677170i	$-0.236794\pi$
$127$	7.44949	+	7.44949i	0.0586574	+	0.0586574i	−0.677170	+	0.735827i	$0.736794\pi$
$128$		0			0
$129$			61.4847i			0.476626i
$130$		0			0
$131$	−19.7526			−0.150783			−0.0753914	−	0.997154i	$-0.524021\pi$
$131$	−19.7526			−0.150783			−0.0753914	+	0.997154i	$0.524021\pi$
$132$		0			0
$133$	−107.980	+	107.980i	−0.811877	+	0.811877i
$134$		0			0
$135$	5.69694	+	25.3485i	0.0421995	+	0.187766i
$136$		0			0
$137$	−101.641	−	101.641i	−0.741907	−	0.741907i	0.231037	−	0.972945i	$-0.425788\pi$
$137$	−101.641	−	101.641i	−0.741907	−	0.741907i	−0.972945	+	0.231037i	$0.925788\pi$
$138$		0			0
$139$		−	24.0204i		−	0.172809i	−0.996260	−	0.0864044i	$-0.972462\pi$
$139$		−	24.0204i		−	0.172809i	0.996260	−	0.0864044i	$-0.0275377\pi$
$140$		0			0
$141$	54.0000			0.382979
$142$		0			0
$143$	−198.990	+	198.990i	−1.39154	+	1.39154i
$144$		0			0
$145$	91.5857	−	144.687i	0.631626	−	0.997840i
$146$		0			0
$147$	75.9217	+	75.9217i	0.516474	+	0.516474i
$148$		0			0
$149$			199.732i			1.34048i	0.742143	+	0.670242i	$0.233810\pi$
$149$			199.732i			1.34048i	−0.742143	+	0.670242i	$0.766190\pi$
$150$		0			0
$151$	−158.990			−1.05291			−0.526456	−	0.850202i	$-0.676480\pi$
$151$	−158.990			−1.05291			−0.526456	+	0.850202i	$0.676480\pi$
$152$		0			0
$153$	−22.6515	+	22.6515i	−0.148049	+	0.148049i
$154$		0			0
$155$	86.5857	+	54.8082i	0.558618	+	0.353601i
$156$		0			0
$157$	37.3485	+	37.3485i	0.237888	+	0.237888i	0.815975	−	0.578087i	$-0.196201\pi$
$157$	37.3485	+	37.3485i	0.237888	+	0.237888i	−0.578087	+	0.815975i	$0.696201\pi$
$158$		0			0
$159$		−	86.4745i		−	0.543865i
$160$		0			0
$161$	−39.5051			−0.245373
$162$		0			0
$163$	−8.98979	+	8.98979i	−0.0551521	+	0.0551521i	−0.734145	−	0.678993i	$-0.762417\pi$
$163$	−8.98979	+	8.98979i	−0.0551521	+	0.0551521i	0.678993	+	0.734145i	$0.262417\pi$
$164$		0			0
$165$	−137.283	+	30.8536i	−0.832016	+	0.186991i
$166$		0			0
$167$	88.3587	+	88.3587i	0.529094	+	0.529094i	0.920302	−	0.391208i	$-0.127943\pi$
$167$	88.3587	+	88.3587i	0.529094	+	0.529094i	−0.391208	+	0.920302i	$0.627943\pi$
$168$		0			0
$169$		−	131.000i		−	0.775148i
$170$		0			0
$171$	43.4847			0.254296
$172$		0			0
$173$	−170.631	+	170.631i	−0.986307	+	0.986307i	−0.999908	−	0.0136005i	$-0.995671\pi$
$173$	−170.631	+	170.631i	−0.986307	+	0.986307i	0.0136005	+	0.999908i	$0.495671\pi$
$174$		0			0
$175$	−88.6413	+	248.015i	−0.506522	+	1.41723i
$176$		0			0
$177$	108.687	+	108.687i	0.614049	+	0.614049i
$178$		0			0
$179$		−	75.7526i		−	0.423199i	−0.977357	−	0.211599i	$-0.932133\pi$
$179$		−	75.7526i		−	0.423199i	0.977357	−	0.211599i	$-0.0678672\pi$
$180$		0			0
$181$	279.444			1.54389			0.771944	−	0.635690i	$-0.219284\pi$
$181$	279.444			1.54389			0.771944	+	0.635690i	$0.219284\pi$
$182$		0			0
$183$	125.530	−	125.530i	0.685957	−	0.685957i
$184$		0			0
$185$	11.3939	+	50.6969i	0.0615885	+	0.274038i
$186$		0			0
$187$	−122.677	−	122.677i	−0.656024	−	0.656024i
$188$		0			0
$189$		−	54.7423i		−	0.289642i
$190$		0			0
$191$	−69.4847			−0.363794			−0.181897	−	0.983318i	$-0.558224\pi$
$191$	−69.4847			−0.363794			−0.181897	+	0.983318i	$0.558224\pi$
$192$		0			0
$193$	−53.5857	+	53.5857i	−0.277646	+	0.277646i	−0.832169	−	0.554523i	$-0.812901\pi$
$193$	−53.5857	+	53.5857i	−0.277646	+	0.277646i	0.554523	+	0.832169i	$0.312901\pi$
$194$		0			0
$195$	80.2270	−	126.742i	0.411421	−	0.649961i
$196$		0			0
$197$	−260.252	−	260.252i	−1.32108	−	1.32108i	−0.912906	−	0.408171i	$-0.866167\pi$
$197$	−260.252	−	260.252i	−1.32108	−	1.32108i	−0.408171	−	0.912906i	$-0.633833\pi$
$198$		0			0
$199$		−	65.0102i		−	0.326684i	−0.986569	−	0.163342i	$-0.947773\pi$
$199$		−	65.0102i		−	0.326684i	0.986569	−	0.163342i	$-0.0522275\pi$
$200$		0			0
$201$	60.4949			0.300970
$202$		0			0
$203$	−255.126	+	255.126i	−1.25678	+	1.25678i
$204$		0			0
$205$	−107.753	−	68.2066i	−0.525622	−	0.332715i
$206$		0			0
$207$	7.95459	+	7.95459i	0.0384280	+	0.0384280i
$208$		0			0
$209$			235.505i			1.12682i
$210$		0			0
$211$	−12.0204			−0.0569688			−0.0284844	−	0.999594i	$-0.509068\pi$
$211$	−12.0204			−0.0569688			−0.0284844	+	0.999594i	$0.509068\pi$
$212$		0			0
$213$	95.5051	−	95.5051i	0.448381	−	0.448381i
$214$		0			0
$215$	173.171	−	38.9194i	0.805448	−	0.181020i
$216$		0			0
$217$	−152.677	−	152.677i	−0.703578	−	0.703578i
$218$		0			0
$219$			108.247i			0.494281i
$220$		0			0
$221$	184.949			0.836873
$222$		0			0
$223$	−239.722	+	239.722i	−1.07499	+	1.07499i	−0.0780357	+	0.996951i	$0.524865\pi$
$223$	−239.722	+	239.722i	−1.07499	+	1.07499i	−0.996951	+	0.0780357i	$0.975135\pi$
$224$		0			0
$225$	67.7878	−	32.0908i	0.301279	−	0.142626i
$226$		0			0
$227$	−2.02041	−	2.02041i	−0.00890049	−	0.00890049i	0.702643	−	0.711543i	$-0.252003\pi$
$227$	−2.02041	−	2.02041i	−0.00890049	−	0.00890049i	−0.711543	+	0.702643i	$0.752003\pi$
$228$		0			0
$229$			284.969i			1.24441i	0.782855	+	0.622204i	$0.213763\pi$
$229$			284.969i			1.24441i	−0.782855	+	0.622204i	$0.786237\pi$
$230$		0			0
$231$	296.474			1.28344
$232$		0			0
$233$	151.237	−	151.237i	0.649087	−	0.649087i	−0.303685	−	0.952772i	$-0.598217\pi$
$233$	151.237	−	151.237i	0.649087	−	0.649087i	0.952772	+	0.303685i	$0.0982172\pi$
$234$		0			0
$235$	−34.1816	−	152.091i	−0.145454	−	0.647195i
$236$		0			0
$237$	−59.3939	−	59.3939i	−0.250607	−	0.250607i
$238$		0			0
$239$		−	50.9694i		−	0.213261i	−0.994299	−	0.106631i	$-0.965994\pi$
$239$		−	50.9694i		−	0.213261i	0.994299	−	0.106631i	$-0.0340062\pi$
$240$		0			0
$241$	−32.0000			−0.132780			−0.0663900	−	0.997794i	$-0.521148\pi$
$241$	−32.0000			−0.132780			−0.0663900	+	0.997794i	$0.521148\pi$
$242$		0			0
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	165.775	−	261.891i	0.676634	−	1.06894i
$246$		0			0
$247$	−177.526	−	177.526i	−0.718727	−	0.718727i
$248$		0			0
$249$		−	248.969i		−	0.999877i
$250$		0			0
$251$	373.237			1.48700			0.743500	−	0.668735i	$-0.233164\pi$
$251$	373.237			1.48700			0.743500	+	0.668735i	$0.233164\pi$
$252$		0			0
$253$	−43.0806	+	43.0806i	−0.170279	+	0.170279i
$254$		0			0
$255$	78.1362	+	49.4597i	0.306417	+	0.193960i
$256$		0			0
$257$	−206.136	−	206.136i	−0.802086	−	0.802086i	0.181335	−	0.983421i	$-0.441958\pi$
$257$	−206.136	−	206.136i	−0.802086	−	0.802086i	−0.983421	+	0.181335i	$0.941958\pi$
$258$		0			0
$259$		−	109.485i		−	0.422721i
$260$		0			0
$261$	102.742			0.393649
$262$		0			0
$263$	210.833	−	210.833i	0.801647	−	0.801647i	−0.181706	−	0.983353i	$-0.558162\pi$
$263$	210.833	−	210.833i	0.801647	−	0.801647i	0.983353	+	0.181706i	$0.0581619\pi$
$264$		0			0
$265$	−243.555	+	54.7378i	−0.919076	+	0.206558i
$266$		0			0
$267$	192.247	+	192.247i	0.720028	+	0.720028i
$268$		0			0
$269$		−	205.258i		−	0.763040i	−0.924361	−	0.381520i	$-0.875401\pi$
$269$		−	205.258i		−	0.763040i	0.924361	−	0.381520i	$-0.124599\pi$
$270$		0			0
$271$	−66.0000			−0.243542			−0.121771	−	0.992558i	$-0.538857\pi$
$271$	−66.0000			−0.243542			−0.121771	+	0.992558i	$0.538857\pi$
$272$		0			0
$273$	−223.485	+	223.485i	−0.818625	+	0.818625i
$274$		0			0
$275$	173.798	+	367.126i	0.631993	+	1.33500i
$276$		0			0
$277$	−148.157	−	148.157i	−0.534861	−	0.534861i	0.387154	−	0.922015i	$-0.373458\pi$
$277$	−148.157	−	148.157i	−0.534861	−	0.534861i	−0.922015	+	0.387154i	$0.873458\pi$
$278$		0			0
$279$			61.4847i			0.220375i
$280$		0			0
$281$	324.434			1.15457			0.577284	−	0.816543i	$-0.304113\pi$
$281$	324.434			1.15457			0.577284	+	0.816543i	$0.304113\pi$
$282$		0			0
$283$	−304.747	+	304.747i	−1.07684	+	1.07684i	−0.0800537	+	0.996791i	$0.525509\pi$
$283$	−304.747	+	304.747i	−1.07684	+	1.07684i	−0.996791	+	0.0800537i	$0.974491\pi$
$284$		0			0
$285$	−27.5255	−	122.474i	−0.0965807	−	0.429735i
$286$		0			0
$287$	190.000	+	190.000i	0.662021	+	0.662021i
$288$		0			0
$289$		−	174.980i		−	0.605466i
$290$		0			0
$291$	135.712			0.466363
$292$		0			0
$293$	145.151	−	145.151i	0.495396	−	0.495396i	−0.414605	−	0.910001i	$-0.636080\pi$
$293$	145.151	−	145.151i	0.495396	−	0.495396i	0.910001	+	0.414605i	$0.136080\pi$
$294$		0			0
$295$	237.318	−	374.914i	0.804467	−	1.27089i
$296$		0			0
$297$	−59.6969	−	59.6969i	−0.201000	−	0.201000i
$298$		0			0
$299$		−	64.9490i		−	0.217221i
$300$		0			0
$301$	−373.980			−1.24246
$302$		0			0
$303$	−56.0352	+	56.0352i	−0.184935	+	0.184935i
$304$		0			0
$305$	−433.015	−	274.095i	−1.41972	−	0.898673i
$306$		0			0
$307$	−120.606	−	120.606i	−0.392854	−	0.392854i	0.482850	−	0.875703i	$-0.339602\pi$
$307$	−120.606	−	120.606i	−0.392854	−	0.392854i	−0.875703	+	0.482850i	$0.839602\pi$
$308$		0			0
$309$		−	56.7219i		−	0.183566i
$310$		0			0
$311$	−18.0204			−0.0579434			−0.0289717	−	0.999580i	$-0.509223\pi$
$311$	−18.0204			−0.0579434			−0.0289717	+	0.999580i	$0.509223\pi$
$312$		0			0
$313$	−323.586	+	323.586i	−1.03382	+	1.03382i	−0.0344125	+	0.999408i	$0.510956\pi$
$313$	−323.586	+	323.586i	−1.03382	+	1.03382i	−0.999408	+	0.0344125i	$0.989044\pi$
$314$		0			0
$315$	−154.182	+	34.6515i	−0.489465	+	0.110005i
$316$		0			0
$317$	−62.4495	−	62.4495i	−0.197002	−	0.197002i	0.601712	−	0.798713i	$-0.294486\pi$
$317$	−62.4495	−	62.4495i	−0.197002	−	0.197002i	−0.798713	+	0.601712i	$0.794486\pi$
$318$		0			0
$319$			556.434i			1.74431i
$320$		0			0
$321$	−40.0204			−0.124674
$322$		0			0
$323$	109.444	−	109.444i	0.338836	−	0.338836i
$324$		0			0
$325$	−407.753	−	145.732i	−1.25462	−	0.448407i
$326$		0			0
$327$	−195.328	−	195.328i	−0.597334	−	0.597334i
$328$		0			0
$329$			328.454i			0.998341i
$330$		0			0
$331$	−618.413			−1.86832			−0.934159	−	0.356857i	$-0.883848\pi$
$331$	−618.413			−1.86832			−0.934159	+	0.356857i	$0.883848\pi$
$332$		0			0
$333$	−22.0454	+	22.0454i	−0.0662024	+	0.0662024i
$334$		0			0
$335$	−38.2929	−	170.384i	−0.114307	−	0.508608i
$336$		0			0
$337$	−55.4041	−	55.4041i	−0.164404	−	0.164404i	0.620111	−	0.784514i	$-0.287088\pi$
$337$	−55.4041	−	55.4041i	−0.164404	−	0.164404i	−0.784514	+	0.620111i	$0.787088\pi$
$338$		0			0
$339$		−	31.9796i		−	0.0943351i
$340$		0			0
$341$	−332.990			−0.976510
$342$		0			0
$343$	−96.7673	+	96.7673i	−0.282121	+	0.282121i
$344$		0			0
$345$	17.3689	−	27.4393i	0.0503446	−	0.0795342i
$346$		0			0
$347$	−413.081	−	413.081i	−1.19043	−	1.19043i	−0.976946	−	0.213488i	$-0.931517\pi$
$347$	−413.081	−	413.081i	−1.19043	−	1.19043i	−0.213488	−	0.976946i	$-0.568483\pi$
$348$		0			0
$349$			258.454i			0.740556i	0.928921	+	0.370278i	$0.120738\pi$
$349$			258.454i			0.740556i	−0.928921	+	0.370278i	$0.879262\pi$
$350$		0			0
$351$	90.0000			0.256410
$352$		0			0
$353$	−83.9138	+	83.9138i	−0.237716	+	0.237716i	−0.815904	−	0.578188i	$-0.803760\pi$
$353$	−83.9138	+	83.9138i	−0.237716	+	0.237716i	0.578188	+	0.815904i	$0.303760\pi$
$354$		0			0
$355$	−329.444	−	208.536i	−0.928011	−	0.587425i
$356$		0			0
$357$	−137.778	−	137.778i	−0.385932	−	0.385932i
$358$		0			0
$359$		−	138.515i		−	0.385837i	−0.981215	−	0.192918i	$-0.938205\pi$
$359$		−	138.515i		−	0.385837i	0.981215	−	0.192918i	$-0.0617952\pi$
$360$		0			0
$361$	150.898			0.418000
$362$		0			0
$363$	175.114	−	175.114i	0.482406	−	0.482406i
$364$		0			0
$365$	304.879	−	68.5199i	0.835284	−	0.187726i
$366$		0			0
$367$	−408.964	−	408.964i	−1.11434	−	1.11434i	−0.992556	−	0.121786i	$-0.961138\pi$
$367$	−408.964	−	408.964i	−1.11434	−	1.11434i	−0.121786	−	0.992556i	$-0.538862\pi$
$368$		0			0
$369$		−	76.5153i		−	0.207359i
$370$		0			0
$371$	525.980			1.41773
$372$		0			0
$373$	143.106	−	143.106i	0.383661	−	0.383661i	−0.488758	−	0.872419i	$-0.662550\pi$
$373$	143.106	−	143.106i	0.383661	−	0.383661i	0.872419	+	0.488758i	$0.162550\pi$
$374$		0			0
$375$	−133.293	−	170.611i	−0.355448	−	0.454962i
$376$		0			0
$377$	−419.444	−	419.444i	−1.11258	−	1.11258i
$378$		0			0
$379$			194.000i			0.511873i	0.966694	+	0.255937i	$0.0823839\pi$
$379$			194.000i			0.511873i	−0.966694	+	0.255937i	$0.917616\pi$
$380$		0			0
$381$	18.2474			0.0478936
$382$		0			0
$383$	51.4893	−	51.4893i	0.134437	−	0.134437i	−0.636686	−	0.771123i	$-0.719695\pi$
$383$	51.4893	−	51.4893i	0.134437	−	0.134437i	0.771123	+	0.636686i	$0.219695\pi$
$384$		0			0
$385$	−187.666	−	835.019i	−0.487445	−	2.16888i
$386$		0			0
$387$	75.3031	+	75.3031i	0.194582	+	0.194582i
$388$		0			0
$389$			35.1964i			0.0904792i	0.998976	+	0.0452396i	$0.0144051\pi$
$389$			35.1964i			0.0904792i	−0.998976	+	0.0452396i	$0.985595\pi$
$390$		0			0
$391$	40.0408			0.102406
$392$		0			0
$393$	−24.1918	+	24.1918i	−0.0615568	+	0.0615568i
$394$		0			0
$395$	−129.687	+	204.879i	−0.328321	+	0.518680i
$396$		0			0
$397$	−409.267	−	409.267i	−1.03090	−	1.03090i	−0.999507	−	0.0313917i	$-0.990006\pi$
$397$	−409.267	−	409.267i	−1.03090	−	1.03090i	−0.0313917	−	0.999507i	$-0.509994\pi$
$398$		0			0
$399$			264.495i			0.662894i
$400$		0			0
$401$	375.898			0.937401			0.468701	−	0.883357i	$-0.344722\pi$
$401$	375.898			0.937401			0.468701	+	0.883357i	$0.344722\pi$
$402$		0			0
$403$	251.010	−	251.010i	0.622854	−	0.622854i
$404$		0			0
$405$	38.0227	+	24.0681i	0.0938832	+	0.0594274i
$406$		0			0
$407$	−119.394	−	119.394i	−0.293351	−	0.293351i
$408$		0			0
$409$			207.959i			0.508458i	0.967144	+	0.254229i	$0.0818216\pi$
$409$			207.959i			0.508458i	−0.967144	+	0.254229i	$0.918178\pi$
$410$		0			0
$411$	−248.969			−0.605765
$412$		0			0
$413$	−661.085	+	661.085i	−1.60069	+	1.60069i
$414$		0			0
$415$	−701.221	+	157.596i	−1.68969	+	0.379749i
$416$		0			0
$417$	−29.4189	−	29.4189i	−0.0705489	−	0.0705489i
$418$		0			0
$419$		−	810.186i		−	1.93362i	−0.255499	−	0.966809i	$-0.582240\pi$
$419$		−	810.186i		−	1.93362i	0.255499	−	0.966809i	$-0.417760\pi$
$420$		0			0
$421$	505.959			1.20180			0.600902	−	0.799323i	$-0.294808\pi$
$421$	505.959			1.20180			0.600902	+	0.799323i	$0.294808\pi$
$422$		0			0
$423$	66.1362	−	66.1362i	0.156350	−	0.156350i
$424$		0			0
$425$	89.8434	−	251.378i	0.211396	−	0.591478i
$426$		0			0
$427$	763.535	+	763.535i	1.78814	+	1.78814i
$428$		0			0
$429$			487.423i			1.13619i
$430$		0			0
$431$	−92.4541			−0.214511			−0.107255	−	0.994232i	$-0.534206\pi$
$431$	−92.4541			−0.214511			−0.107255	+	0.994232i	$0.534206\pi$
$432$		0			0
$433$	69.8990	−	69.8990i	0.161430	−	0.161430i	−0.621770	−	0.783200i	$-0.713586\pi$
$433$	69.8990	−	69.8990i	0.161430	−	0.161430i	0.783200	+	0.621770i	$0.213586\pi$
$434$		0			0
$435$	−65.0352	−	289.373i	−0.149506	−	0.665226i
$436$		0			0
$437$	−38.4337	−	38.4337i	−0.0879489	−	0.0879489i
$438$		0			0
$439$			128.929i			0.293687i	0.989160	+	0.146843i	$0.0469114\pi$
$439$			128.929i			0.293687i	−0.989160	+	0.146843i	$0.953089\pi$
$440$		0			0
$441$	185.969			0.421699
$442$		0			0
$443$	335.555	−	335.555i	0.757461	−	0.757461i	−0.218399	−	0.975860i	$-0.570083\pi$
$443$	335.555	−	335.555i	0.757461	−	0.757461i	0.975860	+	0.218399i	$0.0700834\pi$
$444$		0			0
$445$	419.773	−	663.156i	0.943310	−	1.49024i
$446$		0			0
$447$	244.621	+	244.621i	0.547250	+	0.547250i
$448$		0			0
$449$		−	521.423i		−	1.16130i	−0.814153	−	0.580650i	$-0.802799\pi$
$449$		−	521.423i		−	1.16130i	0.814153	−	0.580650i	$-0.197201\pi$
$450$		0			0
$451$	414.393			0.918831
$452$		0			0
$453$	−194.722	+	194.722i	−0.429850	+	0.429850i
$454$		0			0
$455$	770.908	+	487.980i	1.69430	+	1.07248i
$456$		0			0
$457$	548.939	+	548.939i	1.20118	+	1.20118i	0.973808	+	0.227371i	$0.0730129\pi$
$457$	548.939	+	548.939i	1.20118	+	1.20118i	0.227371	+	0.973808i	$0.426987\pi$
$458$		0			0
$459$			55.4847i			0.120882i
$460$		0			0
$461$	−142.288			−0.308651			−0.154326	−	0.988020i	$-0.549320\pi$
$461$	−142.288			−0.308651			−0.154326	+	0.988020i	$0.549320\pi$
$462$		0			0
$463$	537.045	−	537.045i	1.15993	−	1.15993i	0.175434	−	0.984491i	$-0.443867\pi$
$463$	537.045	−	537.045i	1.15993	−	1.15993i	0.984491	−	0.175434i	$-0.0561329\pi$
$464$		0			0
$465$	173.171	−	38.9194i	0.372412	−	0.0836976i
$466$		0			0
$467$	367.044	+	367.044i	0.785962	+	0.785962i	0.980830	−	0.194867i	$-0.0624276\pi$
$467$	367.044	+	367.044i	0.785962	+	0.785962i	−0.194867	+	0.980830i	$0.562428\pi$
$468$		0			0
$469$			367.959i			0.784561i
$470$		0			0
$471$	91.4847			0.194235
$472$		0			0
$473$	−407.828	+	407.828i	−0.862215	+	0.862215i
$474$		0			0
$475$	−327.526	+	155.051i	−0.689527	+	0.326423i
$476$		0			0
$477$	−105.909	−	105.909i	−0.222032	−	0.222032i
$478$		0			0
$479$			94.9694i			0.198266i	0.995074	+	0.0991330i	$0.0316069\pi$
$479$			94.9694i			0.198266i	−0.995074	+	0.0991330i	$0.968393\pi$
$480$		0			0
$481$	180.000			0.374220
$482$		0			0
$483$	−48.3837	+	48.3837i	−0.100173	+	0.100173i
$484$		0			0
$485$	−85.9046	−	382.232i	−0.177123	−	0.788106i
$486$		0			0
$487$	244.621	+	244.621i	0.502302	+	0.502302i	0.912153	−	0.409851i	$-0.134419\pi$
$487$	244.621	+	244.621i	0.502302	+	0.502302i	−0.409851	+	0.912153i	$0.634419\pi$
$488$		0			0
$489$			22.0204i			0.0450315i
$490$		0			0
$491$	−163.217			−0.332417			−0.166209	−	0.986091i	$-0.553153\pi$
$491$	−163.217			−0.332417			−0.166209	+	0.986091i	$0.553153\pi$
$492$		0			0
$493$	258.586	−	258.586i	0.524515	−	0.524515i
$494$		0			0
$495$	−130.348	+	205.924i	−0.263330	+	0.416008i
$496$		0			0
$497$	580.908	+	580.908i	1.16883	+	1.16883i
$498$		0			0
$499$		−	8.55613i		−	0.0171465i	−0.999963	−	0.00857327i	$-0.997271\pi$
$499$		−	8.55613i		−	0.0171465i	0.999963	−	0.00857327i	$-0.00272899\pi$
$500$		0			0
$501$	216.434			0.432003
$502$		0			0
$503$	46.5903	−	46.5903i	0.0926249	−	0.0926249i	−0.659276	−	0.751901i	$-0.729137\pi$
$503$	46.5903	−	46.5903i	0.0926249	−	0.0926249i	0.751901	+	0.659276i	$0.229137\pi$
$504$		0			0
$505$	193.293	+	122.353i	0.382758	+	0.242283i
$506$		0			0
$507$	−160.442	−	160.442i	−0.316453	−	0.316453i
$508$		0			0
$509$			336.227i			0.660564i	0.943882	+	0.330282i	$0.107144\pi$
$509$			336.227i			0.660564i	−0.943882	+	0.330282i	$0.892856\pi$
$510$		0			0
$511$	−658.413			−1.28848
$512$		0			0
$513$	53.2577	−	53.2577i	0.103816	−	0.103816i
$514$		0			0
$515$	−159.757	+	35.9046i	−0.310208	+	0.0697177i
$516$		0			0
$517$	358.182	+	358.182i	0.692808	+	0.692808i
$518$		0			0
$519$			417.959i			0.805316i
$520$		0			0
$521$	252.556			0.484753			0.242376	−	0.970182i	$-0.422073\pi$
$521$	252.556			0.484753			0.242376	+	0.970182i	$0.422073\pi$
$522$		0			0
$523$	33.6867	−	33.6867i	0.0644106	−	0.0644106i	−0.674168	−	0.738578i	$-0.735498\pi$
$523$	33.6867	−	33.6867i	0.0644106	−	0.0644106i	0.738578	+	0.674168i	$0.235498\pi$
$524$		0			0
$525$	195.192	+	412.318i	0.371794	+	0.785367i
$526$		0			0
$527$	154.747	+	154.747i	0.293637	+	0.293637i
$528$		0			0
$529$			514.939i			0.973419i
$530$		0			0
$531$	266.227			0.501369
$532$		0			0
$533$	−312.372	+	312.372i	−0.586065	+	0.586065i
$534$		0			0
$535$	25.3326	+	112.717i	0.0473507	+	0.210687i
$536$		0			0
$537$	−92.7775	−	92.7775i	−0.172770	−	0.172770i
$538$		0			0
$539$			1007.18i			1.86860i
$540$		0			0
$541$	604.474			1.11733			0.558664	−	0.829394i	$-0.311314\pi$
$541$	604.474			1.11733			0.558664	+	0.829394i	$0.311314\pi$
$542$		0			0
$543$	342.247	−	342.247i	0.630290	−	0.630290i
$544$		0			0
$545$	−426.499	+	673.782i	−0.782568	+	1.23630i
$546$		0			0
$547$	−615.353	−	615.353i	−1.12496	−	1.12496i	−0.990985	−	0.133975i	$-0.957226\pi$
$547$	−615.353	−	615.353i	−1.12496	−	1.12496i	−0.133975	−	0.990985i	$-0.542774\pi$
$548$		0			0
$549$		−	307.485i		−	0.560081i
$550$		0			0
$551$	−496.413			−0.900931
$552$		0			0
$553$	361.262	−	361.262i	0.653277	−	0.653277i
$554$		0			0
$555$	76.0454	+	48.1362i	0.137019	+	0.0867319i
$556$		0			0
$557$	439.040	+	439.040i	0.788222	+	0.788222i	0.981203	−	0.192980i	$-0.0618154\pi$
$557$	439.040	+	439.040i	0.788222	+	0.788222i	−0.192980	+	0.981203i	$0.561815\pi$
$558$		0			0
$559$		−	614.847i		−	1.09991i
$560$		0			0
$561$	−300.495			−0.535642
$562$		0			0
$563$	52.5765	−	52.5765i	0.0933864	−	0.0933864i	−0.658870	−	0.752257i	$-0.728965\pi$
$563$	52.5765	−	52.5765i	0.0933864	−	0.0933864i	0.752257	+	0.658870i	$0.228965\pi$
$564$		0			0
$565$	−90.0704	+	20.2429i	−0.159417	+	0.0358281i
$566$		0			0
$567$	−67.0454	−	67.0454i	−0.118246	−	0.118246i
$568$		0			0
$569$		−	680.929i		−	1.19671i	−0.801231	−	0.598356i	$-0.795821\pi$
$569$		−	680.929i		−	1.19671i	0.801231	−	0.598356i	$-0.204179\pi$
$570$		0			0
$571$	−254.495			−0.445700			−0.222850	−	0.974853i	$-0.571536\pi$
$571$	−254.495			−0.445700			−0.222850	+	0.974853i	$0.571536\pi$
$572$		0			0
$573$	−85.1010	+	85.1010i	−0.148518	+	0.148518i
$574$		0			0
$575$	−88.2770	−	31.5505i	−0.153525	−	0.0548705i
$576$		0			0
$577$	−279.999	−	279.999i	−0.485267	−	0.485267i	0.421542	−	0.906809i	$-0.361489\pi$
$577$	−279.999	−	279.999i	−0.485267	−	0.485267i	−0.906809	+	0.421542i	$0.861489\pi$
$578$		0			0
$579$			131.258i			0.226697i
$580$		0			0
$581$	1514.35			2.60646
$582$		0			0
$583$	573.585	−	573.585i	0.983850	−	0.983850i
$584$		0			0
$585$	−56.9694	−	253.485i	−0.0973836	−	0.433307i
$586$		0			0
$587$	−312.347	−	312.347i	−0.532108	−	0.532108i	0.389091	−	0.921199i	$-0.372789\pi$
$587$	−312.347	−	312.347i	−0.532108	−	0.532108i	−0.921199	+	0.389091i	$0.872789\pi$
$588$		0			0
$589$		−	297.071i		−	0.504366i
$590$		0			0
$591$	−637.485			−1.07865
$592$		0			0
$593$	−424.570	+	424.570i	−0.715969	+	0.715969i	−0.967777	−	0.251808i	$-0.918975\pi$
$593$	−424.570	+	424.570i	−0.715969	+	0.715969i	0.251808	+	0.967777i	$0.418975\pi$
$594$		0			0
$595$	−300.838	+	475.262i	−0.505610	+	0.798760i
$596$		0			0
$597$	−79.6209	−	79.6209i	−0.133368	−	0.133368i
$598$		0			0
$599$		−	396.536i		−	0.661996i	−0.943631	−	0.330998i	$-0.892615\pi$
$599$		−	396.536i		−	0.661996i	0.943631	−	0.330998i	$-0.107385\pi$
$600$		0			0
$601$	238.908			0.397518			0.198759	−	0.980048i	$-0.436309\pi$
$601$	238.908			0.397518			0.198759	+	0.980048i	$0.436309\pi$
$602$		0			0
$603$	74.0908	−	74.0908i	0.122870	−	0.122870i
$604$		0			0
$605$	−604.052	−	382.361i	−0.998434	−	0.632002i
$606$		0			0
$607$	92.8025	+	92.8025i	0.152887	+	0.152887i	0.779406	−	0.626519i	$-0.215521\pi$
$607$	92.8025	+	92.8025i	0.152887	+	0.152887i	−0.626519	+	0.779406i	$0.715521\pi$
$608$		0			0
$609$			624.929i			1.02616i
$610$		0			0
$611$	−540.000			−0.883797
$612$		0			0
$613$	−301.943	+	301.943i	−0.492567	+	0.492567i	−0.909114	−	0.416547i	$-0.863240\pi$
$613$	−301.943	+	301.943i	−0.492567	+	0.492567i	0.416547	+	0.909114i	$0.363240\pi$
$614$		0			0
$615$	−215.505	+	48.4337i	−0.350415	+	0.0787539i
$616$		0			0
$617$	−372.904	−	372.904i	−0.604382	−	0.604382i	0.337090	−	0.941472i	$-0.390557\pi$
$617$	−372.904	−	372.904i	−0.604382	−	0.604382i	−0.941472	+	0.337090i	$0.890557\pi$
$618$		0			0
$619$			815.939i			1.31816i	0.752074	+	0.659078i	$0.229053\pi$
$619$			815.939i			1.31816i	−0.752074	+	0.659078i	$0.770947\pi$
$620$		0			0
$621$	19.4847			0.0313763
$622$		0			0
$623$	−1169.34	+	1169.34i	−1.87695	+	1.87695i
$624$		0			0
$625$	−396.151	+	483.414i	−0.633842	+	0.773463i
$626$		0			0
$627$	288.434	+	288.434i	0.460022	+	0.460022i
$628$		0			0
$629$			110.969i			0.176422i
$630$		0			0
$631$	550.434			0.872320			0.436160	−	0.899869i	$-0.356338\pi$
$631$	550.434			0.872320			0.436160	+	0.899869i	$0.356338\pi$
$632$		0			0
$633$	−14.7219	+	14.7219i	−0.0232574	+	0.0232574i
$634$		0			0
$635$	−11.5505	−	51.3939i	−0.0181898	−	0.0809352i
$636$		0			0
$637$	−759.217	−	759.217i	−1.19186	−	1.19186i
$638$		0			0
$639$		−	233.939i		−	0.366101i
$640$		0			0
$641$	927.939			1.44764			0.723821	−	0.689988i	$-0.242384\pi$
$641$	927.939			1.44764			0.723821	+	0.689988i	$0.242384\pi$
$642$		0			0
$643$	−190.960	+	190.960i	−0.296983	+	0.296983i	−0.839831	−	0.542848i	$-0.817346\pi$
$643$	−190.960	+	190.960i	−0.296983	+	0.296983i	0.542848	+	0.839831i	$0.317346\pi$
$644$		0			0
$645$	164.424	−	259.757i	0.254922	−	0.402724i
$646$		0			0
$647$	−637.146	−	637.146i	−0.984770	−	0.984770i	0.0151154	−	0.999886i	$-0.495188\pi$
$647$	−637.146	−	637.146i	−0.984770	−	0.984770i	−0.999886	+	0.0151154i	$0.995188\pi$
$648$		0			0
$649$			1441.84i			2.22163i
$650$		0			0
$651$	−373.980			−0.574469
$652$		0			0
$653$	404.116	−	404.116i	0.618860	−	0.618860i	−0.326379	−	0.945239i	$-0.605828\pi$
$653$	404.116	−	404.116i	0.618860	−	0.618860i	0.945239	+	0.326379i	$0.105828\pi$
$654$		0			0
$655$	83.4495	+	52.8230i	0.127404	+	0.0806457i
$656$		0			0
$657$	132.576	+	132.576i	0.201789	+	0.201789i
$658$		0			0
$659$		−	453.196i		−	0.687703i	−0.939024	−	0.343852i	$-0.888268\pi$
$659$		−	453.196i		−	0.687703i	0.939024	−	0.343852i	$-0.111732\pi$
$660$		0			0
$661$	−717.546			−1.08555			−0.542773	−	0.839879i	$-0.682626\pi$
$661$	−717.546			−1.08555			−0.542773	+	0.839879i	$0.682626\pi$
$662$		0			0
$663$	226.515	−	226.515i	0.341652	−	0.341652i
$664$		0			0
$665$	744.949	−	167.423i	1.12022	−	0.251765i
$666$		0			0
$667$	−90.8082	−	90.8082i	−0.136144	−	0.136144i
$668$		0			0
$669$			587.196i			0.877723i
$670$		0			0
$671$	1665.28			2.48179
$672$		0			0
$673$	−121.413	+	121.413i	−0.180406	+	0.180406i	−0.791533	−	0.611127i	$-0.790717\pi$
$673$	−121.413	+	121.413i	−0.180406	+	0.180406i	0.611127	+	0.791533i	$0.290717\pi$
$674$		0			0
$675$	43.7196	−	122.326i	0.0647698	−	0.181223i
$676$		0			0
$677$	671.943	+	671.943i	0.992531	+	0.992531i	0.999972	−	0.00744150i	$-0.00236873\pi$
$677$	671.943	+	671.943i	0.992531	+	0.992531i	−0.00744150	+	0.999972i	$0.502369\pi$
$678$		0			0
$679$			825.464i			1.21571i
$680$		0			0
$681$	−4.94897			−0.00726722
$682$		0			0
$683$	−802.095	+	802.095i	−1.17437	+	1.17437i	−0.193214	+	0.981157i	$0.561891\pi$
$683$	−802.095	+	802.095i	−1.17437	+	1.17437i	−0.981157	+	0.193214i	$0.938109\pi$
$684$		0			0
$685$	157.596	+	701.221i	0.230067	+	1.02368i
$686$		0			0
$687$	349.015	+	349.015i	0.508027	+	0.508027i
$688$		0			0
$689$			864.745i			1.25507i
$690$		0			0
$691$	1146.49			1.65918			0.829591	−	0.558371i	$-0.188574\pi$
$691$	1146.49			1.65918			0.829591	+	0.558371i	$0.188574\pi$
$692$		0			0
$693$	363.106	−	363.106i	0.523962	−	0.523962i
$694$		0			0
$695$	−64.2362	+	101.480i	−0.0924262	+	0.146015i
$696$		0			0
$697$	−192.577	−	192.577i	−0.276293	−	0.276293i
$698$		0			0
$699$		−	370.454i		−	0.529977i
$700$		0			0
$701$	673.217			0.960366			0.480183	−	0.877168i	$-0.340570\pi$
$701$	673.217			0.960366			0.480183	+	0.877168i	$0.340570\pi$
$702$		0			0
$703$	106.515	−	106.515i	0.151515	−	0.151515i
$704$		0			0
$705$	−228.136	−	144.409i	−0.323597	−	0.204835i
$706$		0			0
$707$	−340.833	−	340.833i	−0.482084	−	0.482084i
$708$		0			0
$709$			955.939i			1.34829i	0.738598	+	0.674146i	$0.235488\pi$
$709$			955.939i			1.34829i	−0.738598	+	0.674146i	$0.764512\pi$
$710$		0			0
$711$	−145.485			−0.204620
$712$		0			0
$713$	54.3429	−	54.3429i	0.0762172	−	0.0762172i
$714$		0			0
$715$	1372.83	−	308.536i	1.92004	−	0.431518i
$716$		0			0
$717$	−62.4245	−	62.4245i	−0.0870634	−	0.0870634i
$718$		0			0
$719$			89.0306i			0.123826i	0.998082	+	0.0619128i	$0.0197201\pi$
$719$			89.0306i			0.123826i	−0.998082	+	0.0619128i	$0.980280\pi$
$720$		0			0
$721$	345.010			0.478516
$722$		0			0
$723$	−39.1918	+	39.1918i	−0.0542072	+	0.0542072i
$724$		0			0
$725$	−773.853	+	366.343i	−1.06738	+	0.505300i
$726$		0			0
$727$	332.703	+	332.703i	0.457638	+	0.457638i	0.897879	−	0.440242i	$-0.145107\pi$
$727$	332.703	+	332.703i	0.457638	+	0.457638i	−0.440242	+	0.897879i	$0.645107\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	379.051			0.518538
$732$		0			0
$733$	−229.823	+	229.823i	−0.313537	+	0.313537i	−0.846278	−	0.532741i	$-0.821162\pi$
$733$	−229.823	+	229.823i	−0.313537	+	0.313537i	0.532741	+	0.846278i	$0.321162\pi$
$734$		0			0
$735$	−117.717	−	523.782i	−0.160160	−	0.712629i
$736$		0			0
$737$	401.262	+	401.262i	0.544454	+	0.544454i
$738$		0			0
$739$		−	923.281i		−	1.24936i	−0.780879	−	0.624682i	$-0.785228\pi$
$739$		−	923.281i		−	1.24936i	0.780879	−	0.624682i	$-0.214772\pi$
$740$		0			0
$741$	−434.847			−0.586838
$742$		0			0
$743$	−585.782	+	585.782i	−0.788401	+	0.788401i	−0.981232	−	0.192831i	$-0.938233\pi$
$743$	−585.782	+	585.782i	−0.788401	+	0.788401i	0.192831	+	0.981232i	$0.438233\pi$
$744$		0			0
$745$	534.131	−	843.817i	0.716954	−	1.13264i
$746$		0			0
$747$	−304.924	−	304.924i	−0.408198	−	0.408198i
$748$		0			0
$749$		−	243.423i		−	0.324998i
$750$		0			0
$751$	1354.27			1.80329			0.901645	−	0.432477i	$-0.142361\pi$
$751$	1354.27			1.80329			0.901645	+	0.432477i	$0.142361\pi$
$752$		0			0
$753$	457.120	−	457.120i	0.607066	−	0.607066i
$754$		0			0
$755$	671.691	+	425.176i	0.889657	+	0.563147i
$756$		0			0
$757$	985.832	+	985.832i	1.30229	+	1.30229i	0.926846	+	0.375442i	$0.122509\pi$
$757$	985.832	+	985.832i	1.30229	+	1.30229i	0.375442	+	0.926846i	$0.377491\pi$
$758$		0			0
$759$			105.526i			0.139032i
$760$		0			0
$761$	206.495			0.271347			0.135673	−	0.990754i	$-0.456680\pi$
$761$	206.495			0.271347			0.135673	+	0.990754i	$0.456680\pi$
$762$		0			0
$763$	1188.08	−	1188.08i	1.55712	−	1.55712i
$764$		0			0
$765$	156.272	−	35.1214i	0.204278	−	0.0459104i
$766$		0			0
$767$	−1086.87	−	1086.87i	−1.41704	−	1.41704i
$768$		0			0
$769$		−	852.969i		−	1.10919i	−0.832119	−	0.554596i	$-0.812873\pi$
$769$		−	852.969i		−	1.10919i	0.832119	−	0.554596i	$-0.187127\pi$
$770$		0			0
$771$	−504.929			−0.654901
$772$		0			0
$773$	491.035	−	491.035i	0.635233	−	0.635233i	−0.314143	−	0.949376i	$-0.601717\pi$
$773$	491.035	−	491.035i	0.635233	−	0.635233i	0.949376	+	0.314143i	$0.101717\pi$
$774$		0			0
$775$	−219.233	−	463.101i	−0.282881	−	0.597550i
$776$		0			0
$777$	−134.091	−	134.091i	−0.172575	−	0.172575i
$778$		0			0
$779$			369.694i			0.474575i
$780$		0			0
$781$	1266.97			1.62224
$782$		0			0
$783$	125.833	−	125.833i	0.160706	−	0.160706i
$784$		0			0
$785$	−57.9092	−	257.666i	−0.0737697	−	0.328237i
$786$		0			0
$787$	958.586	+	958.586i	1.21803	+	1.21803i	0.968323	+	0.249702i	$0.0803328\pi$
$787$	958.586	+	958.586i	1.21803	+	1.21803i	0.249702	+	0.968323i	$0.419667\pi$
$788$		0			0
$789$		−	516.434i		−	0.654542i
$790$		0			0
$791$	194.515			0.245911
$792$		0			0
$793$	−1255.30	+	1255.30i	−1.58298	+	1.58298i
$794$		0			0
$795$	−231.253	+	365.333i	−0.290884	+	0.459538i
$796$		0			0
$797$	−169.065	−	169.065i	−0.212126	−	0.212126i	0.593044	−	0.805170i	$-0.297926\pi$
$797$	−169.065	−	169.065i	−0.212126	−	0.212126i	−0.805170	+	0.593044i	$0.797926\pi$
$798$		0			0
$799$		−	332.908i		−	0.416656i
$800$		0			0
$801$	470.908			0.587900
$802$		0			0
$803$	−718.005	+	718.005i	−0.894153	+	0.894153i
$804$		0			0
$805$	166.899	+	105.646i	0.207328	+	0.131237i
$806$		0			0
$807$	−251.388	−	251.388i	−0.311510	−	0.311510i
$808$		0			0
$809$		−	126.082i		−	0.155849i	−0.996959	−	0.0779244i	$-0.975171\pi$
$809$		−	126.082i		−	0.155849i	0.996959	−	0.0779244i	$-0.0248293\pi$
$810$		0			0
$811$	−32.9286			−0.0406024			−0.0203012	−	0.999794i	$-0.506463\pi$
$811$	−32.9286			−0.0406024			−0.0203012	+	0.999794i	$0.506463\pi$
$812$		0			0
$813$	−80.8332	+	80.8332i	−0.0994258	+	0.0994258i
$814$		0			0
$815$	62.0204	−	13.9388i	0.0760987	−	0.0171028i
$816$		0			0
$817$	−363.837	−	363.837i	−0.445333	−	0.445333i
$818$		0			0
$819$			547.423i			0.668405i
$820$		0			0
$821$	−980.064			−1.19374			−0.596872	−	0.802337i	$-0.703590\pi$
$821$	−980.064			−1.19374			−0.596872	+	0.802337i	$0.703590\pi$
$822$		0			0
$823$	−503.863	+	503.863i	−0.612227	+	0.612227i	−0.943526	−	0.331299i	$-0.892513\pi$
$823$	−503.863	+	503.863i	−0.612227	+	0.612227i	0.331299	+	0.943526i	$0.392513\pi$
$824$		0			0
$825$	662.494	+	236.778i	0.803023	+	0.287003i
$826$		0			0
$827$	−1078.84	−	1078.84i	−1.30452	−	1.30452i	−0.925311	−	0.379208i	$-0.876196\pi$
$827$	−1078.84	−	1078.84i	−1.30452	−	1.30452i	−0.379208	−	0.925311i	$-0.623804\pi$
$828$		0			0
$829$		−	124.352i		−	0.150002i	−0.997183	−	0.0750012i	$-0.976104\pi$
$829$		−	124.352i		−	0.150002i	0.997183	−	0.0750012i	$-0.0238961\pi$
$830$		0			0
$831$	−362.908			−0.436713
$832$		0			0
$833$	468.055	−	468.055i	0.561890	−	0.561890i
$834$		0			0
$835$	−137.001	−	609.585i	−0.164073	−	0.730042i
$836$		0			0
$837$	75.3031	+	75.3031i	0.0899678	+	0.0899678i
$838$		0			0
$839$		−	1125.48i		−	1.34146i	−0.741702	−	0.670730i	$-0.765981\pi$
$839$		−	1125.48i		−	1.34146i	0.741702	−	0.670730i	$-0.234019\pi$
$840$		0			0
$841$	−331.888			−0.394635
$842$		0			0
$843$	397.348	−	397.348i	0.471350	−	0.471350i
$844$		0			0
$845$	−350.325	+	553.442i	−0.414585	+	0.654960i
$846$		0			0
$847$	1065.12	+	1065.12i	1.25753	+	1.25753i
$848$		0			0
$849$			746.474i			0.879240i
$850$		0			0
$851$	38.9694			0.0457925
$852$		0			0
$853$	−1039.87	+	1039.87i	−1.21908	+	1.21908i	−0.251122	+	0.967955i	$0.580799\pi$
$853$	−1039.87	+	1039.87i	−1.21908	+	1.21908i	−0.967955	+	0.251122i	$0.919201\pi$
$854$		0			0
$855$	−183.712	−	116.288i	−0.214868	−	0.136010i
$856$		0			0
$857$	620.177	+	620.177i	0.723660	+	0.723660i	0.969349	−	0.245688i	$-0.0790140\pi$
$857$	620.177	+	620.177i	0.723660	+	0.723660i	−0.245688	+	0.969349i	$0.579014\pi$
$858$		0			0
$859$		−	948.888i		−	1.10464i	−0.833631	−	0.552321i	$-0.813742\pi$
$859$		−	948.888i		−	1.10464i	0.833631	−	0.552321i	$-0.186258\pi$
$860$		0			0
$861$	465.403			0.540538
$862$		0			0
$863$	−1064.42	+	1064.42i	−1.23339	+	1.23339i	−0.270740	+	0.962652i	$0.587268\pi$
$863$	−1064.42	+	1064.42i	−1.23339	+	1.23339i	−0.962652	+	0.270740i	$0.912732\pi$
$864$		0			0
$865$	1177.18	−	264.565i	1.36090	−	0.305856i
$866$		0			0
$867$	−214.305	−	214.305i	−0.247180	−	0.247180i
$868$		0			0
$869$		−	787.918i		−	0.906695i
$870$		0			0
$871$	−604.949			−0.694545
$872$		0			0
$873$	166.212	−	166.212i	0.190392	−	0.190392i
$874$		0			0
$875$	1037.74	−	810.752i	1.18598	−	0.926573i
$876$		0			0
$877$	329.975	+	329.975i	0.376254	+	0.376254i	0.869749	−	0.493495i	$-0.164281\pi$
$877$	329.975	+	329.975i	0.376254	+	0.376254i	−0.493495	+	0.869749i	$0.664281\pi$
$878$		0			0
$879$		−	355.546i		−	0.404489i
$880$		0			0
$881$	135.857			0.154208			0.0771039	−	0.997023i	$-0.475433\pi$
$881$	135.857			0.154208			0.0771039	+	0.997023i	$0.475433\pi$
$882$		0			0
$883$	46.8694	−	46.8694i	0.0530797	−	0.0530797i	−0.680069	−	0.733148i	$-0.738050\pi$
$883$	46.8694	−	46.8694i	0.0530797	−	0.0530797i	0.733148	+	0.680069i	$0.238050\pi$
$884$		0			0
$885$	−168.520	−	749.828i	−0.190418	−	0.847263i
$886$		0			0
$887$	−43.5097	−	43.5097i	−0.0490526	−	0.0490526i	0.682155	−	0.731208i	$-0.261043\pi$
$887$	−43.5097	−	43.5097i	−0.0490526	−	0.0490526i	−0.731208	+	0.682155i	$0.761043\pi$
$888$		0			0
$889$			110.990i			0.124848i
$890$		0			0
$891$	−146.227			−0.164116
$892$		0			0
$893$	−319.546	+	319.546i	−0.357834	+	0.357834i
$894$		0			0
$895$	−202.580	+	320.035i	−0.226346	+	0.357581i
$896$		0			0
$897$	−79.5459	−	79.5459i	−0.0886800	−	0.0886800i
$898$		0			0
$899$		−	701.898i		−	0.780754i
$900$		0			0
$901$	−533.112			−0.591690
$902$		0			0
$903$	−458.030	+	458.030i	−0.507231	+	0.507231i
$904$		0			0
$905$	−1180.58	−	747.298i	−1.30451	−	0.825744i
$906$		0			0
$907$	−638.938	−	638.938i	−0.704452	−	0.704452i	0.260911	−	0.965363i	$-0.415977\pi$
$907$	−638.938	−	638.938i	−0.704452	−	0.704452i	−0.965363	+	0.260911i	$0.915977\pi$
$908$		0			0
$909$			137.258i			0.150999i
$910$		0			0
$911$	347.546			0.381499			0.190750	−	0.981639i	$-0.438908\pi$
$911$	347.546			0.381499			0.190750	+	0.981639i	$0.438908\pi$
$912$		0			0
$913$	1651.41	−	1651.41i	1.80878	−	1.80878i
$914$		0			0
$915$	−866.030	+	194.636i	−0.946480	+	0.212717i
$916$		0			0
$917$	−147.146	−	147.146i	−0.160465	−	0.160465i
$918$		0			0
$919$			27.6684i			0.0301071i	0.999887	+	0.0150535i	$0.00479187\pi$
$919$			27.6684i			0.0301071i	−0.999887	+	0.0150535i	$0.995208\pi$
$920$		0			0
$921$	−295.423			−0.320764
$922$		0			0
$923$	−955.051	+	955.051i	−1.03472	+	1.03472i
$924$		0			0
$925$	87.4393	−	244.652i	0.0945290	−	0.264488i
$926$		0			0
$927$	−69.4699	−	69.4699i	−0.0749406	−	0.0749406i
$928$		0			0
$929$			1070.49i			1.15231i	0.817341	+	0.576154i	$0.195447\pi$
$929$			1070.49i			1.15231i	−0.817341	+	0.576154i	$0.804553\pi$
$930$		0			0
$931$	−898.536			−0.965130
$932$		0			0
$933$	−22.0704	+	22.0704i	−0.0236553	+	0.0236553i
$934$		0			0
$935$	190.211	+	846.343i	0.203434	+	0.905180i
$936$		0			0
$937$	60.5551	+	60.5551i	0.0646266	+	0.0646266i	0.738681	−	0.674055i	$-0.235449\pi$
$937$	60.5551	+	60.5551i	0.0646266	+	0.0646266i	−0.674055	+	0.738681i	$0.735449\pi$
$938$		0			0
$939$			792.620i			0.844111i
$940$		0			0
$941$	264.064			0.280620			0.140310	−	0.990108i	$-0.455190\pi$
$941$	264.064			0.280620			0.140310	+	0.990108i	$0.455190\pi$
$942$		0			0
$943$	−67.6276	+	67.6276i	−0.0717153	+	0.0717153i
$944$		0			0
$945$	−146.394	+	231.272i	−0.154914	+	0.244733i
$946$		0			0
$947$	115.455	+	115.455i	0.121917	+	0.121917i	0.765433	−	0.643516i	$-0.222525\pi$
$947$	115.455	+	115.455i	0.121917	+	0.121917i	−0.643516	+	0.765433i	$0.722525\pi$
$948$		0			0
$949$		−	1082.47i		−	1.14065i
$950$		0			0
$951$	−152.969			−0.160851
$952$		0			0
$953$	−378.359	+	378.359i	−0.397019	+	0.397019i	−0.877180	−	0.480162i	$-0.840578\pi$
$953$	−378.359	+	378.359i	−0.397019	+	0.397019i	0.480162	+	0.877180i	$0.340578\pi$
$954$		0			0
$955$	293.555	+	185.818i	0.307388	+	0.194574i
$956$		0			0
$957$	681.489	+	681.489i	0.712110	+	0.712110i
$958$		0			0
$959$		−	1514.35i		−	1.57909i
$960$		0			0
$961$	−540.959			−0.562913
$962$		0			0
$963$	−49.0148	+	49.0148i	−0.0508980	+	0.0508980i
$964$		0			0
$965$	369.687	−	83.0852i	0.383095	−	0.0860987i
$966$		0			0
$967$	−52.1964	−	52.1964i	−0.0539777	−	0.0539777i	0.679603	−	0.733580i	$-0.262152\pi$
$967$	−52.1964	−	52.1964i	−0.0539777	−	0.0539777i	−0.733580	+	0.679603i	$0.762152\pi$
$968$		0			0
$969$		−	268.082i		−	0.276658i
$970$		0			0
$971$	1545.61			1.59177			0.795886	−	0.605447i	$-0.207006\pi$
$971$	1545.61			1.59177			0.795886	+	0.605447i	$0.207006\pi$
$972$		0			0
$973$	178.940	−	178.940i	0.183905	−	0.183905i
$974$		0			0
$975$	−677.878	+	320.908i	−0.695259	+	0.329137i
$976$		0			0
$977$	−843.206	−	843.206i	−0.863056	−	0.863056i	0.128636	−	0.991692i	$-0.458940\pi$
$977$	−843.206	−	843.206i	−0.863056	−	0.863056i	−0.991692	+	0.128636i	$0.958940\pi$
$978$		0			0
$979$			2550.35i			2.60506i
$980$		0			0
$981$	−478.454			−0.487721
$982$		0			0
$983$	1241.39	−	1241.39i	1.26286	−	1.26286i	0.313153	−	0.949703i	$-0.398615\pi$
$983$	1241.39	−	1241.39i	1.26286	−	1.26286i	0.949703	−	0.313153i	$-0.101385\pi$
$984$		0			0
$985$	403.523	+	1795.47i	0.409668	+	1.82282i
$986$		0			0
$987$	402.272	+	402.272i	0.407571	+	0.407571i
$988$		0			0
$989$		−	133.112i		−	0.134593i
$990$		0			0
$991$	219.816			0.221813			0.110906	−	0.993831i	$-0.464625\pi$
$991$	219.816			0.221813			0.110906	+	0.993831i	$0.464625\pi$
$992$		0			0
$993$	−757.398	+	757.398i	−0.762738	+	0.762738i
$994$		0			0
$995$	−173.853	+	274.652i	−0.174726	+	0.276032i
$996$		0			0
$997$	−599.571	−	599.571i	−0.601375	−	0.601375i	0.339302	−	0.940677i	$-0.389809\pi$
$997$	−599.571	−	599.571i	−0.601375	−	0.601375i	−0.940677	+	0.339302i	$0.889809\pi$
$998$		0			0
$999$			54.0000i			0.0540541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.bg.b.577.2		4
4.3	odd	2		960.3.bg.a.577.1		4
5.3	odd	4	inner	960.3.bg.b.193.2		4
8.3	odd	2		240.3.bg.d.97.2		4
8.5	even	2		60.3.k.a.37.1	yes	4
20.3	even	4		960.3.bg.a.193.1		4
24.5	odd	2		180.3.l.b.37.1		4
24.11	even	2		720.3.bh.f.577.1		4
40.3	even	4		240.3.bg.d.193.2		4
40.13	odd	4		60.3.k.a.13.1	✓	4
40.19	odd	2		1200.3.bg.o.1057.1		4
40.27	even	4		1200.3.bg.o.193.1		4
40.29	even	2		300.3.k.a.157.2		4
40.37	odd	4		300.3.k.a.193.2		4
120.29	odd	2		900.3.l.b.757.1		4
120.53	even	4		180.3.l.b.73.1		4
120.77	even	4		900.3.l.b.793.1		4
120.83	odd	4		720.3.bh.f.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.k.a.13.1	✓	4	40.13	odd	4
60.3.k.a.37.1	yes	4	8.5	even	2
180.3.l.b.37.1		4	24.5	odd	2
180.3.l.b.73.1		4	120.53	even	4
240.3.bg.d.97.2		4	8.3	odd	2
240.3.bg.d.193.2		4	40.3	even	4
300.3.k.a.157.2		4	40.29	even	2
300.3.k.a.193.2		4	40.37	odd	4
720.3.bh.f.433.1		4	120.83	odd	4
720.3.bh.f.577.1		4	24.11	even	2
900.3.l.b.757.1		4	120.29	odd	2
900.3.l.b.793.1		4	120.77	even	4
960.3.bg.a.193.1		4	20.3	even	4
960.3.bg.a.577.1		4	4.3	odd	2
960.3.bg.b.193.2		4	5.3	odd	4	inner
960.3.bg.b.577.2		4	1.1	even	1	trivial
1200.3.bg.o.193.1		4	40.27	even	4
1200.3.bg.o.1057.1		4	40.19	odd	2

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{3} +(-4.22474 - 2.67423i) q^{5} +(7.44949 + 7.44949i) q^{7} -3.00000i q^{9} +16.2474 q^{11} +(-12.2474 + 12.2474i) q^{13} +(-8.44949 + 1.89898i) q^{15} +(-7.55051 - 7.55051i) q^{17} +14.4949i q^{19} +18.2474 q^{21} +(-2.65153 + 2.65153i) q^{23} +(10.6969 + 22.5959i) q^{25} +(-3.67423 - 3.67423i) q^{27} +34.2474i q^{29} -20.4949 q^{31} +(19.8990 - 19.8990i) q^{33} +(-11.5505 - 51.3939i) q^{35} +(-7.34847 - 7.34847i) q^{37} +30.0000i q^{39} +25.5051 q^{41} +(-25.1010 + 25.1010i) q^{43} +(-8.02270 + 12.6742i) q^{45} +(22.0454 + 22.0454i) q^{47} +61.9898i q^{49} -18.4949 q^{51} +(35.3031 - 35.3031i) q^{53} +(-68.6413 - 43.4495i) q^{55} +(17.7526 + 17.7526i) q^{57} +88.7423i q^{59} +102.495 q^{61} +(22.3485 - 22.3485i) q^{63} +(84.4949 - 18.9898i) q^{65} +(24.6969 + 24.6969i) q^{67} +6.49490i q^{69} +77.9796 q^{71} +(-44.1918 + 44.1918i) q^{73} +(40.7753 + 14.5732i) q^{75} +(121.035 + 121.035i) q^{77} -48.4949i q^{79} -9.00000 q^{81} +(101.641 - 101.641i) q^{83} +(11.7071 + 52.0908i) q^{85} +(41.9444 + 41.9444i) q^{87} +156.969i q^{89} -182.474 q^{91} +(-25.1010 + 25.1010i) q^{93} +(38.7628 - 61.2372i) q^{95} +(55.4041 + 55.4041i) q^{97} -48.7423i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{5} + 20 q^{7} + 16 q^{11} - 24 q^{15} - 40 q^{17} + 24 q^{21} - 40 q^{23} - 16 q^{25} + 16 q^{31} + 60 q^{33} - 56 q^{35} + 200 q^{41} - 120 q^{43} + 12 q^{45} + 24 q^{51} + 200 q^{53} - 108 q^{55}+ \cdots + 300 q^{97}+O(q^{100}) \) 4 * q - 12 * q^5 + 20 * q^7 + 16 * q^11 - 24 * q^15 - 40 * q^17 + 24 * q^21 - 40 * q^23 - 16 * q^25 + 16 * q^31 + 60 * q^33 - 56 * q^35 + 200 * q^41 - 120 * q^43 + 12 * q^45 + 24 * q^51 + 200 * q^53 - 108 * q^55 + 120 * q^57 + 312 * q^61 + 60 * q^63 + 240 * q^65 + 40 * q^67 - 80 * q^71 - 20 * q^73 + 168 * q^75 + 200 * q^77 - 36 * q^81 + 240 * q^83 + 184 * q^85 + 60 * q^87 - 240 * q^91 - 120 * q^93 + 400 * q^95 + 300 * q^97

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