LMFDB - Embedded newform 960.2.y.f.847.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(847,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.847"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [20,0,20,0,0] 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			847.1
Root			$0.0912451 + 1.41127i$ of defining polynomial
Character	$\chi$	$=$	960.847
Dual form			960.2.y.f.943.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-2.18964 - 0.453294i) q^{5} +(-1.25143 - 1.25143i) q^{7} +1.00000 q^{9} +(-2.47980 + 2.47980i) q^{11} +1.81790i q^{13} +(-2.18964 - 0.453294i) q^{15} +(4.52932 + 4.52932i) q^{17} +(-2.39150 + 2.39150i) q^{19} +(-1.25143 - 1.25143i) q^{21} +(-4.06513 + 4.06513i) q^{23} +(4.58905 + 1.98510i) q^{25} +1.00000 q^{27} +(6.27721 + 6.27721i) q^{29} -4.33993i q^{31} +(-2.47980 + 2.47980i) q^{33} +(2.17292 + 3.30745i) q^{35} -2.92026i q^{37} +1.81790i q^{39} +4.26875i q^{41} +10.4167i q^{43} +(-2.18964 - 0.453294i) q^{45} +(0.150104 - 0.150104i) q^{47} -3.86784i q^{49} +(4.52932 + 4.52932i) q^{51} -10.6378 q^{53} +(6.55396 - 4.30580i) q^{55} +(-2.39150 + 2.39150i) q^{57} +(3.17716 + 3.17716i) q^{59} +(-4.76865 + 4.76865i) q^{61} +(-1.25143 - 1.25143i) q^{63} +(0.824041 - 3.98054i) q^{65} -10.8215i q^{67} +(-4.06513 + 4.06513i) q^{69} +5.04598 q^{71} +(-2.92958 - 2.92958i) q^{73} +(4.58905 + 1.98510i) q^{75} +6.20661 q^{77} -4.75216 q^{79} +1.00000 q^{81} -15.3571 q^{83} +(-7.86446 - 11.9707i) q^{85} +(6.27721 + 6.27721i) q^{87} -3.95627 q^{89} +(2.27497 - 2.27497i) q^{91} -4.33993i q^{93} +(6.32059 - 4.15248i) q^{95} +(2.46797 + 2.46797i) q^{97} +(-2.47980 + 2.47980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Character values

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

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

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−2.18964	−	0.453294i	−0.979237	−	0.202719i
$5$	−2.18964	−	0.453294i	−0.979237	−	0.202719i
$6$		0			0
$7$	−1.25143	−	1.25143i	−0.472996	−	0.472996i	0.429887	−	0.902883i	$-0.358554\pi$
$7$	−1.25143	−	1.25143i	−0.472996	−	0.472996i	−0.902883	+	0.429887i	$0.858554\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.47980	+	2.47980i	−0.747689	+	0.747689i	−0.974045	−	0.226356i	$-0.927319\pi$
$11$	−2.47980	+	2.47980i	−0.747689	+	0.747689i	0.226356	+	0.974045i	$0.427319\pi$
$12$		0			0
$13$			1.81790i			0.504194i	0.967702	+	0.252097i	$0.0811201\pi$
$13$			1.81790i			0.504194i	−0.967702	+	0.252097i	$0.918880\pi$
$14$		0			0
$15$	−2.18964	−	0.453294i	−0.565363	−	0.117040i
$16$		0			0
$17$	4.52932	+	4.52932i	1.09852	+	1.09852i	0.994584	+	0.103936i	$0.0331438\pi$
$17$	4.52932	+	4.52932i	1.09852	+	1.09852i	0.103936	+	0.994584i	$0.466856\pi$
$18$		0			0
$19$	−2.39150	+	2.39150i	−0.548649	+	0.548649i	−0.926050	−	0.377401i	$-0.876818\pi$
$19$	−2.39150	+	2.39150i	−0.548649	+	0.548649i	0.377401	+	0.926050i	$0.376818\pi$
$20$		0			0
$21$	−1.25143	−	1.25143i	−0.273085	−	0.273085i
$22$		0			0
$23$	−4.06513	+	4.06513i	−0.847639	+	0.847639i	−0.989838	−	0.142199i	$-0.954583\pi$
$23$	−4.06513	+	4.06513i	−0.847639	+	0.847639i	0.142199	+	0.989838i	$0.454583\pi$
$24$		0			0
$25$	4.58905	+	1.98510i	0.917810	+	0.397020i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.27721	+	6.27721i	1.16565	+	1.16565i	0.983219	+	0.182430i	$0.0583963\pi$
$29$	6.27721	+	6.27721i	1.16565	+	1.16565i	0.182430	+	0.983219i	$0.441604\pi$
$30$		0			0
$31$		−	4.33993i		−	0.779474i	−0.920926	−	0.389737i	$-0.872566\pi$
$31$		−	4.33993i		−	0.779474i	0.920926	−	0.389737i	$-0.127434\pi$
$32$		0			0
$33$	−2.47980	+	2.47980i	−0.431679	+	0.431679i
$34$		0			0
$35$	2.17292	+	3.30745i	0.367290	+	0.559061i
$36$		0			0
$37$		−	2.92026i		−	0.480087i	−0.970762	−	0.240044i	$-0.922838\pi$
$37$		−	2.92026i		−	0.480087i	0.970762	−	0.240044i	$-0.0771617\pi$
$38$		0			0
$39$			1.81790i			0.291096i
$40$		0			0
$41$			4.26875i			0.666667i	0.942809	+	0.333334i	$0.108174\pi$
$41$			4.26875i			0.666667i	−0.942809	+	0.333334i	$0.891826\pi$
$42$		0			0
$43$			10.4167i			1.58853i	0.607572	+	0.794264i	$0.292144\pi$
$43$			10.4167i			1.58853i	−0.607572	+	0.794264i	$0.707856\pi$
$44$		0			0
$45$	−2.18964	−	0.453294i	−0.326412	−	0.0675731i
$46$		0			0
$47$	0.150104	−	0.150104i	0.0218950	−	0.0218950i	−0.696075	−	0.717970i	$-0.745072\pi$
$47$	0.150104	−	0.150104i	0.0218950	−	0.0218950i	0.717970	+	0.696075i	$0.245072\pi$
$48$		0			0
$49$		−	3.86784i		−	0.552549i
$50$		0			0
$51$	4.52932	+	4.52932i	0.634231	+	0.634231i
$52$		0			0
$53$	−10.6378			−1.46122			−0.730608	−	0.682797i	$-0.760763\pi$
$53$	−10.6378			−1.46122			−0.730608	+	0.682797i	$0.760763\pi$
$54$		0			0
$55$	6.55396	−	4.30580i	0.883736	−	0.580594i
$56$		0			0
$57$	−2.39150	+	2.39150i	−0.316762	+	0.316762i
$58$		0			0
$59$	3.17716	+	3.17716i	0.413632	+	0.413632i	0.883002	−	0.469370i	$-0.155519\pi$
$59$	3.17716	+	3.17716i	0.413632	+	0.413632i	−0.469370	+	0.883002i	$0.655519\pi$
$60$		0			0
$61$	−4.76865	+	4.76865i	−0.610563	+	0.610563i	−0.943093	−	0.332530i	$-0.892098\pi$
$61$	−4.76865	+	4.76865i	−0.610563	+	0.610563i	0.332530	+	0.943093i	$0.392098\pi$
$62$		0			0
$63$	−1.25143	−	1.25143i	−0.157665	−	0.157665i
$64$		0			0
$65$	0.824041	−	3.98054i	0.102210	−	0.493725i
$66$		0			0
$67$		−	10.8215i		−	1.32206i	−0.750361	−	0.661029i	$-0.770120\pi$
$67$		−	10.8215i		−	1.32206i	0.750361	−	0.661029i	$-0.229880\pi$
$68$		0			0
$69$	−4.06513	+	4.06513i	−0.489385	+	0.489385i
$70$		0			0
$71$	5.04598			0.598847			0.299424	−	0.954120i	$-0.403206\pi$
$71$	5.04598			0.598847			0.299424	+	0.954120i	$0.403206\pi$
$72$		0			0
$73$	−2.92958	−	2.92958i	−0.342881	−	0.342881i	0.514568	−	0.857449i	$-0.327952\pi$
$73$	−2.92958	−	2.92958i	−0.342881	−	0.342881i	−0.857449	+	0.514568i	$0.827952\pi$
$74$		0			0
$75$	4.58905	+	1.98510i	0.529898	+	0.229220i
$76$		0			0
$77$	6.20661			0.707309
$78$		0			0
$79$	−4.75216			−0.534660			−0.267330	−	0.963605i	$-0.586141\pi$
$79$	−4.75216			−0.534660			−0.267330	+	0.963605i	$0.586141\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−15.3571			−1.68567			−0.842833	−	0.538175i	$-0.819114\pi$
$83$	−15.3571			−1.68567			−0.842833	+	0.538175i	$0.819114\pi$
$84$		0			0
$85$	−7.86446	−	11.9707i	−0.853020	−	1.29840i
$86$		0			0
$87$	6.27721	+	6.27721i	0.672988	+	0.672988i
$88$		0			0
$89$	−3.95627			−0.419364			−0.209682	−	0.977770i	$-0.567243\pi$
$89$	−3.95627			−0.419364			−0.209682	+	0.977770i	$0.567243\pi$
$90$		0			0
$91$	2.27497	−	2.27497i	0.238482	−	0.238482i
$92$		0			0
$93$		−	4.33993i		−	0.450030i
$94$		0			0
$95$	6.32059	−	4.15248i	0.648478	−	0.426035i
$96$		0			0
$97$	2.46797	+	2.46797i	0.250585	+	0.250585i	0.821210	−	0.570626i	$-0.193299\pi$
$97$	2.46797	+	2.46797i	0.250585	+	0.250585i	−0.570626	+	0.821210i	$0.693299\pi$
$98$		0			0
$99$	−2.47980	+	2.47980i	−0.249230	+	0.249230i
$100$		0			0
$101$	9.40099	+	9.40099i	0.935433	+	0.935433i	0.998038	−	0.0626050i	$-0.0199408\pi$
$101$	9.40099	+	9.40099i	0.935433	+	0.935433i	−0.0626050	+	0.998038i	$0.519941\pi$
$102$		0			0
$103$	−3.79353	+	3.79353i	−0.373788	+	0.373788i	−0.868855	−	0.495067i	$-0.835143\pi$
$103$	−3.79353	+	3.79353i	−0.373788	+	0.373788i	0.495067	+	0.868855i	$0.335143\pi$
$104$		0			0
$105$	2.17292	+	3.30745i	0.212055	+	0.322774i
$106$		0			0
$107$	−12.1814			−1.17762			−0.588810	−	0.808271i	$-0.700403\pi$
$107$	−12.1814			−1.17762			−0.588810	+	0.808271i	$0.700403\pi$
$108$		0			0
$109$	−4.04384	−	4.04384i	−0.387329	−	0.387329i	0.486404	−	0.873734i	$-0.338308\pi$
$109$	−4.04384	−	4.04384i	−0.387329	−	0.387329i	−0.873734	+	0.486404i	$0.838308\pi$
$110$		0			0
$111$		−	2.92026i		−	0.277178i
$112$		0			0
$113$	12.4221	−	12.4221i	1.16857	−	1.16857i	0.186023	−	0.982545i	$-0.440440\pi$
$113$	12.4221	−	12.4221i	1.16857	−	1.16857i	0.982545	−	0.186023i	$-0.0595599\pi$
$114$		0			0
$115$	10.7439	−	7.05848i	1.00187	−	0.658207i
$116$		0			0
$117$			1.81790i			0.168065i
$118$		0			0
$119$		−	11.3362i		−	1.03919i
$120$		0			0
$121$		−	1.29886i		−	0.118078i
$122$		0			0
$123$			4.26875i			0.384900i
$124$		0			0
$125$	−9.14853	−	6.42685i	−0.818270	−	0.574835i
$126$		0			0
$127$	7.35799	−	7.35799i	0.652916	−	0.652916i	−0.300778	−	0.953694i	$-0.597246\pi$
$127$	7.35799	−	7.35799i	0.652916	−	0.652916i	0.953694	+	0.300778i	$0.0972463\pi$
$128$		0			0
$129$			10.4167i			0.917138i
$130$		0			0
$131$	4.51593	+	4.51593i	0.394559	+	0.394559i	0.876309	−	0.481750i	$-0.159999\pi$
$131$	4.51593	+	4.51593i	0.394559	+	0.394559i	−0.481750	+	0.876309i	$0.659999\pi$
$132$		0			0
$133$	5.98560			0.519018
$134$		0			0
$135$	−2.18964	−	0.453294i	−0.188454	−	0.0390133i
$136$		0			0
$137$	2.55390	−	2.55390i	0.218194	−	0.218194i	−0.589543	−	0.807737i	$-0.700692\pi$
$137$	2.55390	−	2.55390i	0.218194	−	0.218194i	0.807737	+	0.589543i	$0.200692\pi$
$138$		0			0
$139$	2.95289	+	2.95289i	0.250461	+	0.250461i	0.821159	−	0.570699i	$-0.193328\pi$
$139$	2.95289	+	2.95289i	0.250461	+	0.250461i	−0.570699	+	0.821159i	$0.693328\pi$
$140$		0			0
$141$	0.150104	−	0.150104i	0.0126411	−	0.0126411i
$142$		0			0
$143$	−4.50803	−	4.50803i	−0.376980	−	0.376980i
$144$		0			0
$145$	−10.8994	−	16.5903i	−0.905147	−	1.37775i
$146$		0			0
$147$		−	3.86784i		−	0.319014i
$148$		0			0
$149$	−15.1940	+	15.1940i	−1.24474	+	1.24474i	−0.286728	+	0.958012i	$0.592568\pi$
$149$	−15.1940	+	15.1940i	−1.24474	+	1.24474i	−0.958012	+	0.286728i	$0.907432\pi$
$150$		0			0
$151$	2.66712			0.217047			0.108523	−	0.994094i	$-0.465388\pi$
$151$	2.66712			0.217047			0.108523	+	0.994094i	$0.465388\pi$
$152$		0			0
$153$	4.52932	+	4.52932i	0.366173	+	0.366173i
$154$		0			0
$155$	−1.96726	+	9.50288i	−0.158014	+	0.763290i
$156$		0			0
$157$	−3.79875			−0.303173			−0.151587	−	0.988444i	$-0.548438\pi$
$157$	−3.79875			−0.303173			−0.151587	+	0.988444i	$0.548438\pi$
$158$		0			0
$159$	−10.6378			−0.843633
$160$		0			0
$161$	10.1745			0.801860
$162$		0			0
$163$	20.0096			1.56727			0.783637	−	0.621219i	$-0.213362\pi$
$163$	20.0096			1.56727			0.783637	+	0.621219i	$0.213362\pi$
$164$		0			0
$165$	6.55396	−	4.30580i	0.510225	−	0.335206i
$166$		0			0
$167$	7.50240	+	7.50240i	0.580553	+	0.580553i	0.935055	−	0.354502i	$-0.115350\pi$
$167$	7.50240	+	7.50240i	0.580553	+	0.580553i	−0.354502	+	0.935055i	$0.615350\pi$
$168$		0			0
$169$	9.69526			0.745789
$170$		0			0
$171$	−2.39150	+	2.39150i	−0.182883	+	0.182883i
$172$		0			0
$173$			15.3776i			1.16914i	0.811345	+	0.584568i	$0.198736\pi$
$173$			15.3776i			1.16914i	−0.811345	+	0.584568i	$0.801264\pi$
$174$		0			0
$175$	−3.25866	−	8.22709i	−0.246332	−	0.621910i
$176$		0			0
$177$	3.17716	+	3.17716i	0.238810	+	0.238810i
$178$		0			0
$179$	−5.67467	+	5.67467i	−0.424145	+	0.424145i	−0.886628	−	0.462483i	$-0.846959\pi$
$179$	−5.67467	+	5.67467i	−0.424145	+	0.424145i	0.462483	+	0.886628i	$0.346959\pi$
$180$		0			0
$181$	−0.760920	−	0.760920i	−0.0565587	−	0.0565587i	0.678262	−	0.734820i	$-0.262734\pi$
$181$	−0.760920	−	0.760920i	−0.0565587	−	0.0565587i	−0.734820	+	0.678262i	$0.762734\pi$
$182$		0			0
$183$	−4.76865	+	4.76865i	−0.352509	+	0.352509i
$184$		0			0
$185$	−1.32373	+	6.39431i	−0.0973229	+	0.470119i
$186$		0			0
$187$	−22.4636			−1.64270
$188$		0			0
$189$	−1.25143	−	1.25143i	−0.0910282	−	0.0910282i
$190$		0			0
$191$			15.1246i			1.09437i	0.837010	+	0.547187i	$0.184301\pi$
$191$			15.1246i			1.09437i	−0.837010	+	0.547187i	$0.815699\pi$
$192$		0			0
$193$	−7.66759	+	7.66759i	−0.551925	+	0.551925i	−0.926996	−	0.375071i	$-0.877618\pi$
$193$	−7.66759	+	7.66759i	−0.551925	+	0.551925i	0.375071	+	0.926996i	$0.377618\pi$
$194$		0			0
$195$	0.824041	−	3.98054i	0.0590108	−	0.285052i
$196$		0			0
$197$		−	25.5893i		−	1.82316i	−0.411120	−	0.911581i	$-0.634862\pi$
$197$		−	25.5893i		−	1.82316i	0.411120	−	0.911581i	$-0.365138\pi$
$198$		0			0
$199$		−	13.0408i		−	0.924440i	−0.886765	−	0.462220i	$-0.847053\pi$
$199$		−	13.0408i		−	0.924440i	0.886765	−	0.462220i	$-0.152947\pi$
$200$		0			0
$201$		−	10.8215i		−	0.763290i
$202$		0			0
$203$		−	15.7110i		−	1.10270i
$204$		0			0
$205$	1.93500	−	9.34703i	0.135146	−	0.652825i
$206$		0			0
$207$	−4.06513	+	4.06513i	−0.282546	+	0.282546i
$208$		0			0
$209$		−	11.8609i		−	0.820437i
$210$		0			0
$211$	4.04713	+	4.04713i	0.278616	+	0.278616i	0.832556	−	0.553940i	$-0.186876\pi$
$211$	4.04713	+	4.04713i	0.278616	+	0.278616i	−0.553940	+	0.832556i	$0.686876\pi$
$212$		0			0
$213$	5.04598			0.345745
$214$		0			0
$215$	4.72182	−	22.8088i	0.322025	−	1.55555i
$216$		0			0
$217$	−5.43112	+	5.43112i	−0.368688	+	0.368688i
$218$		0			0
$219$	−2.92958	−	2.92958i	−0.197962	−	0.197962i
$220$		0			0
$221$	−8.23382	+	8.23382i	−0.553867	+	0.553867i
$222$		0			0
$223$	−6.94039	−	6.94039i	−0.464763	−	0.464763i	0.435450	−	0.900213i	$-0.356589\pi$
$223$	−6.94039	−	6.94039i	−0.464763	−	0.464763i	−0.900213	+	0.435450i	$0.856589\pi$
$224$		0			0
$225$	4.58905	+	1.98510i	0.305937	+	0.132340i
$226$		0			0
$227$			3.34643i			0.222110i	0.993814	+	0.111055i	$0.0354230\pi$
$227$			3.34643i			0.222110i	−0.993814	+	0.111055i	$0.964577\pi$
$228$		0			0
$229$	11.9644	−	11.9644i	0.790629	−	0.790629i	−0.190968	−	0.981596i	$-0.561163\pi$
$229$	11.9644	−	11.9644i	0.790629	−	0.790629i	0.981596	+	0.190968i	$0.0611626\pi$
$230$		0			0
$231$	6.20661			0.408365
$232$		0			0
$233$	−12.4324	−	12.4324i	−0.814474	−	0.814474i	0.170827	−	0.985301i	$-0.445356\pi$
$233$	−12.4324	−	12.4324i	−0.814474	−	0.814474i	−0.985301	+	0.170827i	$0.945356\pi$
$234$		0			0
$235$	−0.396716	+	0.260633i	−0.0258789	+	0.0170018i
$236$		0			0
$237$	−4.75216			−0.308686
$238$		0			0
$239$	24.7355			1.60000			0.800002	−	0.599997i	$-0.204832\pi$
$239$	24.7355			1.60000			0.800002	+	0.599997i	$0.204832\pi$
$240$		0			0
$241$	17.1334			1.10366			0.551829	−	0.833957i	$-0.313930\pi$
$241$	17.1334			1.10366			0.551829	+	0.833957i	$0.313930\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.75327	+	8.46918i	−0.112012	+	0.541076i
$246$		0			0
$247$	−4.34750	−	4.34750i	−0.276625	−	0.276625i
$248$		0			0
$249$	−15.3571			−0.973219
$250$		0			0
$251$	21.3875	−	21.3875i	1.34997	−	1.34997i	0.464274	−	0.885692i	$-0.346315\pi$
$251$	21.3875	−	21.3875i	1.34997	−	1.34997i	0.885692	−	0.464274i	$-0.153685\pi$
$252$		0			0
$253$		−	20.1615i		−	1.26754i
$254$		0			0
$255$	−7.86446	−	11.9707i	−0.492492	−	0.749633i
$256$		0			0
$257$	−17.3996	−	17.3996i	−1.08536	−	1.08536i	−0.996000	−	0.0893560i	$-0.971519\pi$
$257$	−17.3996	−	17.3996i	−1.08536	−	1.08536i	−0.0893560	−	0.996000i	$-0.528481\pi$
$258$		0			0
$259$	−3.65450	+	3.65450i	−0.227080	+	0.227080i
$260$		0			0
$261$	6.27721	+	6.27721i	0.388550	+	0.388550i
$262$		0			0
$263$	−8.76818	+	8.76818i	−0.540669	+	0.540669i	−0.923725	−	0.383056i	$-0.874872\pi$
$263$	−8.76818	+	8.76818i	−0.540669	+	0.540669i	0.383056	+	0.923725i	$0.374872\pi$
$264$		0			0
$265$	23.2930	+	4.82206i	1.43088	+	0.296217i
$266$		0			0
$267$	−3.95627			−0.242120
$268$		0			0
$269$	14.1435	+	14.1435i	0.862347	+	0.862347i	0.991610	−	0.129263i	$-0.0412611\pi$
$269$	14.1435	+	14.1435i	0.862347	+	0.862347i	−0.129263	+	0.991610i	$0.541261\pi$
$270$		0			0
$271$			24.2463i			1.47286i	0.676515	+	0.736429i	$0.263490\pi$
$271$			24.2463i			1.47286i	−0.676515	+	0.736429i	$0.736510\pi$
$272$		0			0
$273$	2.27497	−	2.27497i	0.137687	−	0.137687i
$274$		0			0
$275$	−16.3026	+	6.45728i	−0.983084	+	0.389389i
$276$		0			0
$277$			0.247833i			0.0148909i	0.999972	+	0.00744543i	$0.00236998\pi$
$277$			0.247833i			0.0148909i	−0.999972	+	0.00744543i	$0.997630\pi$
$278$		0			0
$279$		−	4.33993i		−	0.259825i
$280$		0			0
$281$		−	13.2279i		−	0.789109i	−0.918872	−	0.394555i	$-0.870899\pi$
$281$		−	13.2279i		−	0.789109i	0.918872	−	0.394555i	$-0.129101\pi$
$282$		0			0
$283$		−	22.2111i		−	1.32031i	−0.751128	−	0.660157i	$-0.770490\pi$
$283$		−	22.2111i		−	1.32031i	0.751128	−	0.660157i	$-0.229510\pi$
$284$		0			0
$285$	6.32059	−	4.15248i	0.374399	−	0.245972i
$286$		0			0
$287$	5.34205	−	5.34205i	0.315331	−	0.315331i
$288$		0			0
$289$			24.0294i			1.41349i
$290$		0			0
$291$	2.46797	+	2.46797i	0.144675	+	0.144675i
$292$		0			0
$293$	2.93570			0.171505			0.0857526	−	0.996316i	$-0.472671\pi$
$293$	2.93570			0.171505			0.0857526	+	0.996316i	$0.472671\pi$
$294$		0			0
$295$	−5.51666	−	8.39704i	−0.321192	−	0.488894i
$296$		0			0
$297$	−2.47980	+	2.47980i	−0.143893	+	0.143893i
$298$		0			0
$299$	−7.38999	−	7.38999i	−0.427374	−	0.427374i
$300$		0			0
$301$	13.0358	−	13.0358i	0.751368	−	0.751368i
$302$		0			0
$303$	9.40099	+	9.40099i	0.540073	+	0.540073i
$304$		0			0
$305$	12.6032	−	8.28003i	0.721659	−	0.474113i
$306$		0			0
$307$		−	20.2428i		−	1.15532i	−0.816278	−	0.577659i	$-0.803966\pi$
$307$		−	20.2428i		−	1.15532i	0.816278	−	0.577659i	$-0.196034\pi$
$308$		0			0
$309$	−3.79353	+	3.79353i	−0.215806	+	0.215806i
$310$		0			0
$311$	14.0432			0.796315			0.398157	−	0.917317i	$-0.369650\pi$
$311$	14.0432			0.796315			0.398157	+	0.917317i	$0.369650\pi$
$312$		0			0
$313$	−10.3861	−	10.3861i	−0.587058	−	0.587058i	0.349775	−	0.936834i	$-0.386258\pi$
$313$	−10.3861	−	10.3861i	−0.587058	−	0.587058i	−0.936834	+	0.349775i	$0.886258\pi$
$314$		0			0
$315$	2.17292	+	3.30745i	0.122430	+	0.186354i
$316$		0			0
$317$	11.6769			0.655839			0.327920	−	0.944706i	$-0.393653\pi$
$317$	11.6769			0.655839			0.327920	+	0.944706i	$0.393653\pi$
$318$		0			0
$319$	−31.1325			−1.74309
$320$		0			0
$321$	−12.1814			−0.679899
$322$		0			0
$323$	−21.6637			−1.20540
$324$		0			0
$325$	−3.60871	+	8.34241i	−0.200175	+	0.462754i
$326$		0			0
$327$	−4.04384	−	4.04384i	−0.223625	−	0.223625i
$328$		0			0
$329$	−0.375690			−0.0207125
$330$		0			0
$331$	12.0411	−	12.0411i	0.661841	−	0.661841i	−0.293973	−	0.955814i	$-0.594978\pi$
$331$	12.0411	−	12.0411i	0.661841	−	0.661841i	0.955814	+	0.293973i	$0.0949775\pi$
$332$		0			0
$333$		−	2.92026i		−	0.160029i
$334$		0			0
$335$	−4.90532	+	23.6952i	−0.268006	+	1.29461i
$336$		0			0
$337$	−0.558895	−	0.558895i	−0.0304449	−	0.0304449i	0.691720	−	0.722165i	$-0.256853\pi$
$337$	−0.558895	−	0.558895i	−0.0304449	−	0.0304449i	−0.722165	+	0.691720i	$0.756853\pi$
$338$		0			0
$339$	12.4221	−	12.4221i	0.674673	−	0.674673i
$340$		0			0
$341$	10.7622	+	10.7622i	0.582804	+	0.582804i
$342$		0			0
$343$	−13.6004	+	13.6004i	−0.734350	+	0.734350i
$344$		0			0
$345$	10.7439	−	7.05848i	0.578431	−	0.380016i
$346$		0			0
$347$	−0.0770157			−0.00413442			−0.00206721	−	0.999998i	$-0.500658\pi$
$347$	−0.0770157			−0.00413442			−0.00206721	+	0.999998i	$0.500658\pi$
$348$		0			0
$349$	−15.0145	−	15.0145i	−0.803708	−	0.803708i	0.179965	−	0.983673i	$-0.442402\pi$
$349$	−15.0145	−	15.0145i	−0.803708	−	0.803708i	−0.983673	+	0.179965i	$0.942402\pi$
$350$		0			0
$351$			1.81790i			0.0970321i
$352$		0			0
$353$	−23.6193	+	23.6193i	−1.25713	+	1.25713i	−0.304668	+	0.952459i	$0.598546\pi$
$353$	−23.6193	+	23.6193i	−1.25713	+	1.25713i	−0.952459	+	0.304668i	$0.901454\pi$
$354$		0			0
$355$	−11.0489	−	2.28731i	−0.586413	−	0.121398i
$356$		0			0
$357$		−	11.3362i		−	0.599978i
$358$		0			0
$359$			9.21900i			0.486560i	0.969956	+	0.243280i	$0.0782234\pi$
$359$			9.21900i			0.486560i	−0.969956	+	0.243280i	$0.921777\pi$
$360$		0			0
$361$			7.56142i			0.397970i
$362$		0			0
$363$		−	1.29886i		−	0.0681725i
$364$		0			0
$365$	5.08676	+	7.74268i	0.266253	+	0.405270i
$366$		0			0
$367$	3.46414	−	3.46414i	0.180827	−	0.180827i	−0.610889	−	0.791716i	$-0.709188\pi$
$367$	3.46414	−	3.46414i	0.180827	−	0.180827i	0.791716	+	0.610889i	$0.209188\pi$
$368$		0			0
$369$			4.26875i			0.222222i
$370$		0			0
$371$	13.3125	+	13.3125i	0.691150	+	0.691150i
$372$		0			0
$373$	19.1403			0.991049			0.495524	−	0.868594i	$-0.334976\pi$
$373$	19.1403			0.991049			0.495524	+	0.868594i	$0.334976\pi$
$374$		0			0
$375$	−9.14853	−	6.42685i	−0.472428	−	0.331881i
$376$		0			0
$377$	−11.4113	+	11.4113i	−0.587713	+	0.587713i
$378$		0			0
$379$	19.8802	+	19.8802i	1.02118	+	1.02118i	0.999771	+	0.0214054i	$0.00681406\pi$
$379$	19.8802	+	19.8802i	1.02118	+	1.02118i	0.0214054	+	0.999771i	$0.493186\pi$
$380$		0			0
$381$	7.35799	−	7.35799i	0.376961	−	0.376961i
$382$		0			0
$383$	8.84171	+	8.84171i	0.451790	+	0.451790i	0.895948	−	0.444158i	$-0.146497\pi$
$383$	8.84171	+	8.84171i	0.451790	+	0.451790i	−0.444158	+	0.895948i	$0.646497\pi$
$384$		0			0
$385$	−13.5902	−	2.81342i	−0.692623	−	0.143385i
$386$		0			0
$387$			10.4167i			0.529510i
$388$		0			0
$389$	−1.06003	+	1.06003i	−0.0537454	+	0.0537454i	−0.733469	−	0.679723i	$-0.762100\pi$
$389$	−1.06003	+	1.06003i	−0.0537454	+	0.0537454i	0.679723	+	0.733469i	$0.262100\pi$
$390$		0			0
$391$	−36.8245			−1.86230
$392$		0			0
$393$	4.51593	+	4.51593i	0.227799	+	0.227799i
$394$		0			0
$395$	10.4055	+	2.15413i	0.523559	+	0.108386i
$396$		0			0
$397$	4.35137			0.218389			0.109194	−	0.994020i	$-0.465173\pi$
$397$	4.35137			0.218389			0.109194	+	0.994020i	$0.465173\pi$
$398$		0			0
$399$	5.98560			0.299655
$400$		0			0
$401$	−21.1334			−1.05535			−0.527676	−	0.849445i	$-0.676937\pi$
$401$	−21.1334			−1.05535			−0.527676	+	0.849445i	$0.676937\pi$
$402$		0			0
$403$	7.88954			0.393006
$404$		0			0
$405$	−2.18964	−	0.453294i	−0.108804	−	0.0225244i
$406$		0			0
$407$	7.24167	+	7.24167i	0.358956	+	0.358956i
$408$		0			0
$409$	0.142915			0.00706670			0.00353335	−	0.999994i	$-0.498875\pi$
$409$	0.142915			0.00706670			0.00353335	+	0.999994i	$0.498875\pi$
$410$		0			0
$411$	2.55390	−	2.55390i	0.125975	−	0.125975i
$412$		0			0
$413$		−	7.95200i		−	0.391292i
$414$		0			0
$415$	33.6266	+	6.96130i	1.65067	+	0.341717i
$416$		0			0
$417$	2.95289	+	2.95289i	0.144604	+	0.144604i
$418$		0			0
$419$	−3.14176	+	3.14176i	−0.153485	+	0.153485i	−0.779673	−	0.626187i	$-0.784614\pi$
$419$	−3.14176	+	3.14176i	−0.153485	+	0.153485i	0.626187	+	0.779673i	$0.284614\pi$
$420$		0			0
$421$	25.8144	+	25.8144i	1.25812	+	1.25812i	0.951992	+	0.306124i	$0.0990322\pi$
$421$	25.8144	+	25.8144i	1.25812	+	1.25812i	0.306124	+	0.951992i	$0.400968\pi$
$422$		0			0
$423$	0.150104	−	0.150104i	0.00729832	−	0.00729832i
$424$		0			0
$425$	11.7941	+	29.7764i	0.572098	+	1.44437i
$426$		0			0
$427$	11.9353			0.577588
$428$		0			0
$429$	−4.50803	−	4.50803i	−0.217650	−	0.217650i
$430$		0			0
$431$			6.52096i			0.314104i	0.987590	+	0.157052i	$0.0501990\pi$
$431$			6.52096i			0.314104i	−0.987590	+	0.157052i	$0.949801\pi$
$432$		0			0
$433$	−25.1367	+	25.1367i	−1.20799	+	1.20799i	−0.236314	+	0.971677i	$0.575939\pi$
$433$	−25.1367	+	25.1367i	−1.20799	+	1.20799i	−0.971677	+	0.236314i	$0.924061\pi$
$434$		0			0
$435$	−10.8994	−	16.5903i	−0.522587	−	0.795442i
$436$		0			0
$437$		−	19.4436i		−	0.930112i
$438$		0			0
$439$			39.1063i			1.86644i	0.359305	+	0.933220i	$0.383014\pi$
$439$			39.1063i			1.86644i	−0.359305	+	0.933220i	$0.616986\pi$
$440$		0			0
$441$		−	3.86784i		−	0.184183i
$442$		0			0
$443$		−	20.4880i		−	0.973414i	−0.873565	−	0.486707i	$-0.838198\pi$
$443$		−	20.4880i		−	0.973414i	0.873565	−	0.486707i	$-0.161802\pi$
$444$		0			0
$445$	8.66281	+	1.79335i	0.410656	+	0.0850131i
$446$		0			0
$447$	−15.1940	+	15.1940i	−0.718651	+	0.718651i
$448$		0			0
$449$		−	4.34217i		−	0.204920i	−0.994737	−	0.102460i	$-0.967329\pi$
$449$		−	4.34217i		−	0.204920i	0.994737	−	0.102460i	$-0.0326713\pi$
$450$		0			0
$451$	−10.5857	−	10.5857i	−0.498460	−	0.498460i
$452$		0			0
$453$	2.66712			0.125312
$454$		0			0
$455$	−6.01260	+	3.95014i	−0.281875	+	0.185185i
$456$		0			0
$457$	−14.7916	+	14.7916i	−0.691921	+	0.691921i	−0.962654	−	0.270733i	$-0.912734\pi$
$457$	−14.7916	+	14.7916i	−0.691921	+	0.691921i	0.270733	+	0.962654i	$0.412734\pi$
$458$		0			0
$459$	4.52932	+	4.52932i	0.211410	+	0.211410i
$460$		0			0
$461$	−15.0255	+	15.0255i	−0.699809	+	0.699809i	−0.964369	−	0.264561i	$-0.914773\pi$
$461$	−15.0255	+	15.0255i	−0.699809	+	0.699809i	0.264561	+	0.964369i	$0.414773\pi$
$462$		0			0
$463$	6.10691	+	6.10691i	0.283812	+	0.283812i	0.834627	−	0.550815i	$-0.185683\pi$
$463$	6.10691	+	6.10691i	0.283812	+	0.283812i	−0.550815	+	0.834627i	$0.685683\pi$
$464$		0			0
$465$	−1.96726	+	9.50288i	−0.0912296	+	0.440686i
$466$		0			0
$467$		−	23.9704i		−	1.10922i	−0.832111	−	0.554610i	$-0.812868\pi$
$467$		−	23.9704i		−	1.10922i	0.832111	−	0.554610i	$-0.187132\pi$
$468$		0			0
$469$	−13.5424	+	13.5424i	−0.625328	+	0.625328i
$470$		0			0
$471$	−3.79875			−0.175037
$472$		0			0
$473$	−25.8313	−	25.8313i	−1.18773	−	1.18773i
$474$		0			0
$475$	−15.7221	+	6.22735i	−0.721380	+	0.285730i
$476$		0			0
$477$	−10.6378			−0.487072
$478$		0			0
$479$	36.1197			1.65035			0.825176	−	0.564876i	$-0.191076\pi$
$479$	36.1197			1.65035			0.825176	+	0.564876i	$0.191076\pi$
$480$		0			0
$481$	5.30872			0.242057
$482$		0			0
$483$	10.1745			0.462954
$484$		0			0
$485$	−4.28526	−	6.52269i	−0.194583	−	0.296180i
$486$		0			0
$487$	25.3967	+	25.3967i	1.15083	+	1.15083i	0.986386	+	0.164447i	$0.0525839\pi$
$487$	25.3967	+	25.3967i	1.15083	+	1.15083i	0.164447	+	0.986386i	$0.447416\pi$
$488$		0			0
$489$	20.0096			0.904866
$490$		0			0
$491$	−6.18543	+	6.18543i	−0.279145	+	0.279145i	−0.832768	−	0.553623i	$-0.813245\pi$
$491$	−6.18543	+	6.18543i	−0.279145	+	0.279145i	0.553623	+	0.832768i	$0.313245\pi$
$492$		0			0
$493$			56.8629i			2.56098i
$494$		0			0
$495$	6.55396	−	4.30580i	0.294579	−	0.193531i
$496$		0			0
$497$	−6.31469	−	6.31469i	−0.283253	−	0.283253i
$498$		0			0
$499$	−25.3089	+	25.3089i	−1.13298	+	1.13298i	−0.143306	+	0.989678i	$0.545773\pi$
$499$	−25.3089	+	25.3089i	−1.13298	+	1.13298i	−0.989678	+	0.143306i	$0.954227\pi$
$500$		0			0
$501$	7.50240	+	7.50240i	0.335183	+	0.335183i
$502$		0			0
$503$	−1.94744	+	1.94744i	−0.0868322	+	0.0868322i	−0.749189	−	0.662357i	$-0.769556\pi$
$503$	−1.94744	+	1.94744i	−0.0868322	+	0.0868322i	0.662357	+	0.749189i	$0.269556\pi$
$504$		0			0
$505$	−16.3234	−	24.8462i	−0.726381	−	1.10564i
$506$		0			0
$507$	9.69526			0.430581
$508$		0			0
$509$	−17.9336	−	17.9336i	−0.794891	−	0.794891i	0.187394	−	0.982285i	$-0.439996\pi$
$509$	−17.9336	−	17.9336i	−0.794891	−	0.794891i	−0.982285	+	0.187394i	$0.939996\pi$
$510$		0			0
$511$			7.33232i			0.324363i
$512$		0			0
$513$	−2.39150	+	2.39150i	−0.105587	+	0.105587i
$514$		0			0
$515$	10.0261	−	6.58688i	0.441801	−	0.290253i
$516$		0			0
$517$			0.744459i			0.0327413i
$518$		0			0
$519$			15.3776i			0.675001i
$520$		0			0
$521$		−	11.3666i		−	0.497981i	−0.968506	−	0.248990i	$-0.919901\pi$
$521$		−	11.3666i		−	0.497981i	0.968506	−	0.248990i	$-0.0800988\pi$
$522$		0			0
$523$			19.1692i			0.838209i	0.907938	+	0.419104i	$0.137656\pi$
$523$			19.1692i			0.838209i	−0.907938	+	0.419104i	$0.862344\pi$
$524$		0			0
$525$	−3.25866	−	8.22709i	−0.142220	−	0.359060i
$526$		0			0
$527$	19.6569	−	19.6569i	0.856268	−	0.856268i
$528$		0			0
$529$		−	10.0506i		−	0.436983i
$530$		0			0
$531$	3.17716	+	3.17716i	0.137877	+	0.137877i
$532$		0			0
$533$	−7.76015			−0.336129
$534$		0			0
$535$	26.6729	+	5.52176i	1.15317	+	0.238726i
$536$		0			0
$537$	−5.67467	+	5.67467i	−0.244880	+	0.244880i
$538$		0			0
$539$	9.59149	+	9.59149i	0.413135	+	0.413135i
$540$		0			0
$541$	−4.06490	+	4.06490i	−0.174764	+	0.174764i	−0.789069	−	0.614305i	$-0.789436\pi$
$541$	−4.06490	+	4.06490i	−0.174764	+	0.174764i	0.614305	+	0.789069i	$0.289436\pi$
$542$		0			0
$543$	−0.760920	−	0.760920i	−0.0326542	−	0.0326542i
$544$		0			0
$545$	7.02150	+	10.6876i	0.300768	+	0.457806i
$546$		0			0
$547$			28.7783i			1.23047i	0.788344	+	0.615235i	$0.210939\pi$
$547$			28.7783i			1.23047i	−0.788344	+	0.615235i	$0.789061\pi$
$548$		0			0
$549$	−4.76865	+	4.76865i	−0.203521	+	0.203521i
$550$		0			0
$551$	−30.0239			−1.27906
$552$		0			0
$553$	5.94700	+	5.94700i	0.252892	+	0.252892i
$554$		0			0
$555$	−1.32373	+	6.39431i	−0.0561894	+	0.271423i
$556$		0			0
$557$	8.96058			0.379672			0.189836	−	0.981816i	$-0.439204\pi$
$557$	8.96058			0.379672			0.189836	+	0.981816i	$0.439204\pi$
$558$		0			0
$559$	−18.9364			−0.800926
$560$		0			0
$561$	−22.4636			−0.948415
$562$		0			0
$563$	−9.62086			−0.405471			−0.202736	−	0.979234i	$-0.564983\pi$
$563$	−9.62086			−0.405471			−0.202736	+	0.979234i	$0.564983\pi$
$564$		0			0
$565$	−32.8307	+	21.5690i	−1.38120	+	0.907414i
$566$		0			0
$567$	−1.25143	−	1.25143i	−0.0525552	−	0.0525552i
$568$		0			0
$569$	26.7360			1.12083			0.560415	−	0.828212i	$-0.310642\pi$
$569$	26.7360			1.12083			0.560415	+	0.828212i	$0.310642\pi$
$570$		0			0
$571$	28.0517	−	28.0517i	1.17393	−	1.17393i	0.192661	−	0.981265i	$-0.438288\pi$
$571$	28.0517	−	28.0517i	1.17393	−	1.17393i	0.981265	−	0.192661i	$-0.0617117\pi$
$572$		0			0
$573$			15.1246i			0.631837i
$574$		0			0
$575$	−26.7248	+	10.5854i	−1.11450	+	0.441441i
$576$		0			0
$577$	17.8580	+	17.8580i	0.743437	+	0.743437i	0.973238	−	0.229801i	$-0.0738075\pi$
$577$	17.8580	+	17.8580i	0.743437	+	0.743437i	−0.229801	+	0.973238i	$0.573808\pi$
$578$		0			0
$579$	−7.66759	+	7.66759i	−0.318654	+	0.318654i
$580$		0			0
$581$	19.2184	+	19.2184i	0.797314	+	0.797314i
$582$		0			0
$583$	26.3797	−	26.3797i	1.09254	−	1.09254i
$584$		0			0
$585$	0.824041	−	3.98054i	0.0340699	−	0.164575i
$586$		0			0
$587$	1.40264			0.0578931			0.0289465	−	0.999581i	$-0.490785\pi$
$587$	1.40264			0.0578931			0.0289465	+	0.999581i	$0.490785\pi$
$588$		0			0
$589$	10.3790	+	10.3790i	0.427657	+	0.427657i
$590$		0			0
$591$		−	25.5893i		−	1.05260i
$592$		0			0
$593$	5.81813	−	5.81813i	0.238922	−	0.238922i	−0.577482	−	0.816404i	$-0.695965\pi$
$593$	5.81813	−	5.81813i	0.238922	−	0.238922i	0.816404	+	0.577482i	$0.195965\pi$
$594$		0			0
$595$	−5.13865	+	24.8223i	−0.210664	+	1.01762i
$596$		0			0
$597$		−	13.0408i		−	0.533726i
$598$		0			0
$599$		−	13.1194i		−	0.536045i	−0.963413	−	0.268023i	$-0.913630\pi$
$599$		−	13.1194i		−	0.536045i	0.963413	−	0.268023i	$-0.0863702\pi$
$600$		0			0
$601$		−	29.0758i		−	1.18603i	−0.805193	−	0.593013i	$-0.797938\pi$
$601$		−	29.0758i		−	1.18603i	0.805193	−	0.593013i	$-0.202062\pi$
$602$		0			0
$603$		−	10.8215i		−	0.440686i
$604$		0			0
$605$	−0.588766	+	2.84404i	−0.0239367	+	0.115627i
$606$		0			0
$607$	−8.32107	+	8.32107i	−0.337742	+	0.337742i	−0.855517	−	0.517775i	$-0.826760\pi$
$607$	−8.32107	+	8.32107i	−0.337742	+	0.337742i	0.517775	+	0.855517i	$0.326760\pi$
$608$		0			0
$609$		−	15.7110i		−	0.636642i
$610$		0			0
$611$	0.272874	+	0.272874i	0.0110393	+	0.0110393i
$612$		0			0
$613$	17.2991			0.698705			0.349353	−	0.936991i	$-0.386401\pi$
$613$	17.2991			0.698705			0.349353	+	0.936991i	$0.386401\pi$
$614$		0			0
$615$	1.93500	−	9.34703i	0.0780267	−	0.376909i
$616$		0			0
$617$	15.9755	−	15.9755i	0.643149	−	0.643149i	−0.308179	−	0.951328i	$-0.599720\pi$
$617$	15.9755	−	15.9755i	0.643149	−	0.643149i	0.951328	+	0.308179i	$0.0997197\pi$
$618$		0			0
$619$	7.13212	+	7.13212i	0.286664	+	0.286664i	0.835760	−	0.549096i	$-0.185028\pi$
$619$	7.13212	+	7.13212i	0.286664	+	0.286664i	−0.549096	+	0.835760i	$0.685028\pi$
$620$		0			0
$621$	−4.06513	+	4.06513i	−0.163128	+	0.163128i
$622$		0			0
$623$	4.95100	+	4.95100i	0.198358	+	0.198358i
$624$		0			0
$625$	17.1187	+	18.2195i	0.684750	+	0.728778i
$626$		0			0
$627$		−	11.8609i		−	0.473680i
$628$		0			0
$629$	13.2268	−	13.2268i	0.527386	−	0.527386i
$630$		0			0
$631$	−20.4868			−0.815565			−0.407782	−	0.913079i	$-0.633698\pi$
$631$	−20.4868			−0.815565			−0.407782	+	0.913079i	$0.633698\pi$
$632$		0			0
$633$	4.04713	+	4.04713i	0.160859	+	0.160859i
$634$		0			0
$635$	−19.4467	+	12.7760i	−0.771718	+	0.507001i
$636$		0			0
$637$	7.03133			0.278592
$638$		0			0
$639$	5.04598			0.199616
$640$		0			0
$641$	0.884584			0.0349390			0.0174695	−	0.999847i	$-0.494439\pi$
$641$	0.884584			0.0349390			0.0174695	+	0.999847i	$0.494439\pi$
$642$		0			0
$643$	5.29313			0.208741			0.104370	−	0.994539i	$-0.466717\pi$
$643$	5.29313			0.208741			0.104370	+	0.994539i	$0.466717\pi$
$644$		0			0
$645$	4.72182	−	22.8088i	0.185921	−	0.898095i
$646$		0			0
$647$	−9.15703	−	9.15703i	−0.360000	−	0.360000i	0.503813	−	0.863813i	$-0.331930\pi$
$647$	−9.15703	−	9.15703i	−0.360000	−	0.360000i	−0.863813	+	0.503813i	$0.831930\pi$
$648$		0			0
$649$	−15.7575			−0.618536
$650$		0			0
$651$	−5.43112	+	5.43112i	−0.212862	+	0.212862i
$652$		0			0
$653$		−	7.81012i		−	0.305634i	−0.988255	−	0.152817i	$-0.951166\pi$
$653$		−	7.81012i		−	0.305634i	0.988255	−	0.152817i	$-0.0488345\pi$
$654$		0			0
$655$	−7.84122	−	11.9353i	−0.306382	−	0.466351i
$656$		0			0
$657$	−2.92958	−	2.92958i	−0.114294	−	0.114294i
$658$		0			0
$659$	4.73630	−	4.73630i	0.184500	−	0.184500i	−0.608813	−	0.793313i	$-0.708354\pi$
$659$	4.73630	−	4.73630i	0.184500	−	0.184500i	0.793313	+	0.608813i	$0.208354\pi$
$660$		0			0
$661$	−19.8678	−	19.8678i	−0.772766	−	0.772766i	0.205823	−	0.978589i	$-0.434013\pi$
$661$	−19.8678	−	19.8678i	−0.772766	−	0.772766i	−0.978589	+	0.205823i	$0.934013\pi$
$662$		0			0
$663$	−8.23382	+	8.23382i	−0.319775	+	0.319775i
$664$		0			0
$665$	−13.1063	−	2.71324i	−0.508241	−	0.105215i
$666$		0			0
$667$	−51.0354			−1.97610
$668$		0			0
$669$	−6.94039	−	6.94039i	−0.268331	−	0.268331i
$670$		0			0
$671$		−	23.6506i		−	0.913023i
$672$		0			0
$673$	−15.4993	+	15.4993i	−0.597455	+	0.597455i	−0.939635	−	0.342180i	$-0.888835\pi$
$673$	−15.4993	+	15.4993i	−0.597455	+	0.597455i	0.342180	+	0.939635i	$0.388835\pi$
$674$		0			0
$675$	4.58905	+	1.98510i	0.176633	+	0.0764066i
$676$		0			0
$677$		−	4.91631i		−	0.188949i	−0.995527	−	0.0944745i	$-0.969883\pi$
$677$		−	4.91631i		−	0.188949i	0.995527	−	0.0944745i	$-0.0301171\pi$
$678$		0			0
$679$		−	6.17699i		−	0.237051i
$680$		0			0
$681$			3.34643i			0.128236i
$682$		0			0
$683$		−	38.8999i		−	1.48846i	−0.667922	−	0.744231i	$-0.732816\pi$
$683$		−	38.8999i		−	1.48846i	0.667922	−	0.744231i	$-0.267184\pi$
$684$		0			0
$685$	−6.74979	+	4.43446i	−0.257896	+	0.169432i
$686$		0			0
$687$	11.9644	−	11.9644i	0.456470	−	0.456470i
$688$		0			0
$689$		−	19.3384i		−	0.736735i
$690$		0			0
$691$	−10.5822	−	10.5822i	−0.402567	−	0.402567i	0.476570	−	0.879137i	$-0.341880\pi$
$691$	−10.5822	−	10.5822i	−0.402567	−	0.402567i	−0.879137	+	0.476570i	$0.841880\pi$
$692$		0			0
$693$	6.20661			0.235770
$694$		0			0
$695$	−5.12724	−	7.80429i	−0.194487	−	0.296034i
$696$		0			0
$697$	−19.3345	+	19.3345i	−0.732347	+	0.732347i
$698$		0			0
$699$	−12.4324	−	12.4324i	−0.470237	−	0.470237i
$700$		0			0
$701$	30.4758	−	30.4758i	1.15106	−	1.15106i	0.164715	−	0.986341i	$-0.447329\pi$
$701$	30.4758	−	30.4758i	1.15106	−	1.15106i	0.986341	−	0.164715i	$-0.0526706\pi$
$702$		0			0
$703$	6.98380	+	6.98380i	0.263399	+	0.263399i
$704$		0			0
$705$	−0.396716	+	0.260633i	−0.0149412	+	0.00981601i
$706$		0			0
$707$		−	23.5294i		−	0.884913i
$708$		0			0
$709$	14.5515	−	14.5515i	0.546493	−	0.546493i	−0.378932	−	0.925425i	$-0.623709\pi$
$709$	14.5515	−	14.5515i	0.546493	−	0.546493i	0.925425	+	0.378932i	$0.123709\pi$
$710$		0			0
$711$	−4.75216			−0.178220
$712$		0			0
$713$	17.6424	+	17.6424i	0.660713	+	0.660713i
$714$		0			0
$715$	7.82749	+	11.9144i	0.292732	+	0.445574i
$716$		0			0
$717$	24.7355			0.923763
$718$		0			0
$719$	−31.9412			−1.19120			−0.595602	−	0.803279i	$-0.703087\pi$
$719$	−31.9412			−1.19120			−0.595602	+	0.803279i	$0.703087\pi$
$720$		0			0
$721$	9.49468			0.353600
$722$		0			0
$723$	17.1334			0.637197
$724$		0			0
$725$	16.3455	+	41.2673i	0.607058	+	1.53263i
$726$		0			0
$727$	32.0532	+	32.0532i	1.18879	+	1.18879i	0.977403	+	0.211384i	$0.0677970\pi$
$727$	32.0532	+	32.0532i	1.18879	+	1.18879i	0.211384	+	0.977403i	$0.432203\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−47.1804	+	47.1804i	−1.74503	+	1.74503i
$732$		0			0
$733$		−	24.7535i		−	0.914293i	−0.889391	−	0.457146i	$-0.848872\pi$
$733$		−	24.7535i		−	0.914293i	0.889391	−	0.457146i	$-0.151128\pi$
$734$		0			0
$735$	−1.75327	+	8.46918i	−0.0646703	+	0.312390i
$736$		0			0
$737$	26.8352	+	26.8352i	0.988488	+	0.988488i
$738$		0			0
$739$	17.6246	−	17.6246i	0.648333	−	0.648333i	−0.304257	−	0.952590i	$-0.598408\pi$
$739$	17.6246	−	17.6246i	0.648333	−	0.648333i	0.952590	+	0.304257i	$0.0984081\pi$
$740$		0			0
$741$	−4.34750	−	4.34750i	−0.159710	−	0.159710i
$742$		0			0
$743$	4.45488	−	4.45488i	0.163434	−	0.163434i	−0.620652	−	0.784086i	$-0.713132\pi$
$743$	4.45488	−	4.45488i	0.163434	−	0.163434i	0.784086	+	0.620652i	$0.213132\pi$
$744$		0			0
$745$	40.1567	−	26.3820i	1.47123	−	0.966563i
$746$		0			0
$747$	−15.3571			−0.561889
$748$		0			0
$749$	15.2442	+	15.2442i	0.557010	+	0.557010i
$750$		0			0
$751$			14.9291i			0.544770i	0.962188	+	0.272385i	$0.0878124\pi$
$751$			14.9291i			0.544770i	−0.962188	+	0.272385i	$0.912188\pi$
$752$		0			0
$753$	21.3875	−	21.3875i	0.779403	−	0.779403i
$754$		0			0
$755$	−5.84002	−	1.20899i	−0.212540	−	0.0439995i
$756$		0			0
$757$			43.9059i			1.59579i	0.602798	+	0.797894i	$0.294053\pi$
$757$			43.9059i			1.59579i	−0.602798	+	0.797894i	$0.705947\pi$
$758$		0			0
$759$		−	20.1615i		−	0.731815i
$760$		0			0
$761$		−	2.39481i		−	0.0868119i	−0.999058	−	0.0434059i	$-0.986179\pi$
$761$		−	2.39481i		−	0.0868119i	0.999058	−	0.0434059i	$-0.0138209\pi$
$762$		0			0
$763$			10.1212i			0.366411i
$764$		0			0
$765$	−7.86446	−	11.9707i	−0.284340	−	0.432801i
$766$		0			0
$767$	−5.77575	+	5.77575i	−0.208550	+	0.208550i
$768$		0			0
$769$			12.9527i			0.467085i	0.972347	+	0.233542i	$0.0750318\pi$
$769$			12.9527i			0.467085i	−0.972347	+	0.233542i	$0.924968\pi$
$770$		0			0
$771$	−17.3996	−	17.3996i	−0.626630	−	0.626630i
$772$		0			0
$773$	−16.1575			−0.581143			−0.290572	−	0.956853i	$-0.593845\pi$
$773$	−16.1575			−0.581143			−0.290572	+	0.956853i	$0.593845\pi$
$774$		0			0
$775$	8.61520	−	19.9161i	0.309467	−	0.715409i
$776$		0			0
$777$	−3.65450	+	3.65450i	−0.131104	+	0.131104i
$778$		0			0
$779$	−10.2087	−	10.2087i	−0.365766	−	0.365766i
$780$		0			0
$781$	−12.5130	+	12.5130i	−0.447752	+	0.447752i
$782$		0			0
$783$	6.27721	+	6.27721i	0.224329	+	0.224329i
$784$		0			0
$785$	8.31790	+	1.72195i	0.296878	+	0.0614590i
$786$		0			0
$787$			36.6090i			1.30497i	0.757802	+	0.652485i	$0.226273\pi$
$787$			36.6090i			1.30497i	−0.757802	+	0.652485i	$0.773727\pi$
$788$		0			0
$789$	−8.76818	+	8.76818i	−0.312155	+	0.312155i
$790$		0			0
$791$	−31.0907			−1.10546
$792$		0			0
$793$	−8.66891	−	8.66891i	−0.307842	−	0.307842i
$794$		0			0
$795$	23.2930	+	4.82206i	0.826117	+	0.171021i
$796$		0			0
$797$	3.96964			0.140612			0.0703060	−	0.997525i	$-0.477602\pi$
$797$	3.96964			0.140612			0.0703060	+	0.997525i	$0.477602\pi$
$798$		0			0
$799$	1.35974			0.0481041
$800$		0			0
$801$	−3.95627			−0.139788
$802$		0			0
$803$	14.5295			0.512737
$804$		0			0
$805$	−22.2784	−	4.61202i	−0.785211	−	0.162552i
$806$		0			0
$807$	14.1435	+	14.1435i	0.497876	+	0.497876i
$808$		0			0
$809$	54.3213			1.90984			0.954918	−	0.296868i	$-0.0959423\pi$
$809$	54.3213			1.90984			0.954918	+	0.296868i	$0.0959423\pi$
$810$		0			0
$811$	15.8944	−	15.8944i	0.558127	−	0.558127i	−0.370647	−	0.928774i	$-0.620864\pi$
$811$	15.8944	−	15.8944i	0.558127	−	0.558127i	0.928774	+	0.370647i	$0.120864\pi$
$812$		0			0
$813$			24.2463i			0.850355i
$814$		0			0
$815$	−43.8139	−	9.07024i	−1.53473	−	0.317717i
$816$		0			0
$817$	−24.9115	−	24.9115i	−0.871544	−	0.871544i
$818$		0			0
$819$	2.27497	−	2.27497i	0.0794939	−	0.0794939i
$820$		0			0
$821$	−25.7579	−	25.7579i	−0.898956	−	0.898956i	0.0963881	−	0.995344i	$-0.469271\pi$
$821$	−25.7579	−	25.7579i	−0.898956	−	0.898956i	−0.995344	+	0.0963881i	$0.969271\pi$
$822$		0			0
$823$	9.20810	−	9.20810i	0.320974	−	0.320974i	−0.528167	−	0.849141i	$-0.677120\pi$
$823$	9.20810	−	9.20810i	0.320974	−	0.320974i	0.849141	+	0.528167i	$0.177120\pi$
$824$		0			0
$825$	−16.3026	+	6.45728i	−0.567584	+	0.224814i
$826$		0			0
$827$	40.4359			1.40609			0.703047	−	0.711143i	$-0.251822\pi$
$827$	40.4359			1.40609			0.703047	+	0.711143i	$0.251822\pi$
$828$		0			0
$829$	−18.6969	−	18.6969i	−0.649370	−	0.649370i	0.303471	−	0.952841i	$-0.401855\pi$
$829$	−18.6969	−	18.6969i	−0.649370	−	0.649370i	−0.952841	+	0.303471i	$0.901855\pi$
$830$		0			0
$831$			0.247833i			0.00859724i
$832$		0			0
$833$	17.5187	−	17.5187i	0.606986	−	0.606986i
$834$		0			0
$835$	−13.0268	−	19.8284i	−0.450810	−	0.686189i
$836$		0			0
$837$		−	4.33993i		−	0.150010i
$838$		0			0
$839$		−	7.89003i		−	0.272394i	−0.990682	−	0.136197i	$-0.956512\pi$
$839$		−	7.89003i		−	0.272394i	0.990682	−	0.136197i	$-0.0434880\pi$
$840$		0			0
$841$			49.8068i			1.71748i
$842$		0			0
$843$		−	13.2279i		−	0.455593i
$844$		0			0
$845$	−21.2291	−	4.39480i	−0.730304	−	0.151186i
$846$		0			0
$847$	−1.62543	+	1.62543i	−0.0558506	+	0.0558506i
$848$		0			0
$849$		−	22.2111i		−	0.762283i
$850$		0			0
$851$	11.8712	+	11.8712i	0.406941	+	0.406941i
$852$		0			0
$853$	6.59967			0.225968			0.112984	−	0.993597i	$-0.463959\pi$
$853$	6.59967			0.225968			0.112984	+	0.993597i	$0.463959\pi$
$854$		0			0
$855$	6.32059	−	4.15248i	0.216159	−	0.142012i
$856$		0			0
$857$	−31.8196	+	31.8196i	−1.08694	+	1.08694i	−0.0910940	+	0.995842i	$0.529036\pi$
$857$	−31.8196	+	31.8196i	−1.08694	+	1.08694i	−0.995842	+	0.0910940i	$0.970964\pi$
$858$		0			0
$859$	−12.6182	−	12.6182i	−0.430527	−	0.430527i	0.458280	−	0.888808i	$-0.348466\pi$
$859$	−12.6182	−	12.6182i	−0.430527	−	0.430527i	−0.888808	+	0.458280i	$0.848466\pi$
$860$		0			0
$861$	5.34205	−	5.34205i	0.182056	−	0.182056i
$862$		0			0
$863$	−6.97660	−	6.97660i	−0.237486	−	0.237486i	0.578322	−	0.815808i	$-0.303708\pi$
$863$	−6.97660	−	6.97660i	−0.237486	−	0.237486i	−0.815808	+	0.578322i	$0.803708\pi$
$864$		0			0
$865$	6.97056	−	33.6714i	0.237006	−	1.14486i
$866$		0			0
$867$			24.0294i			0.816081i
$868$		0			0
$869$	11.7844	−	11.7844i	0.399760	−	0.399760i
$870$		0			0
$871$	19.6724			0.666573
$872$		0			0
$873$	2.46797	+	2.46797i	0.0835282	+	0.0835282i
$874$		0			0
$875$	3.40600	+	19.4915i	0.115144	+	0.658933i
$876$		0			0
$877$	22.3460			0.754572			0.377286	−	0.926097i	$-0.376857\pi$
$877$	22.3460			0.754572			0.377286	+	0.926097i	$0.376857\pi$
$878$		0			0
$879$	2.93570			0.0990185
$880$		0			0
$881$	−18.6246			−0.627478			−0.313739	−	0.949509i	$-0.601582\pi$
$881$	−18.6246			−0.627478			−0.313739	+	0.949509i	$0.601582\pi$
$882$		0			0
$883$	8.08610			0.272119			0.136060	−	0.990701i	$-0.456556\pi$
$883$	8.08610			0.272119			0.136060	+	0.990701i	$0.456556\pi$
$884$		0			0
$885$	−5.51666	−	8.39704i	−0.185440	−	0.282263i
$886$		0			0
$887$	−10.9628	−	10.9628i	−0.368095	−	0.368095i	0.498687	−	0.866782i	$-0.333816\pi$
$887$	−10.9628	−	10.9628i	−0.368095	−	0.368095i	−0.866782	+	0.498687i	$0.833816\pi$
$888$		0			0
$889$	−18.4160			−0.617654
$890$		0			0
$891$	−2.47980	+	2.47980i	−0.0830766	+	0.0830766i
$892$		0			0
$893$			0.717950i			0.0240253i
$894$		0			0
$895$	14.9978	−	9.85320i	0.501321	−	0.329356i
$896$		0			0
$897$	−7.38999	−	7.38999i	−0.246745	−	0.246745i
$898$		0			0
$899$	27.2426	−	27.2426i	0.908593	−	0.908593i
$900$		0			0
$901$	−48.1820	−	48.1820i	−1.60518	−	1.60518i
$902$		0			0
$903$	13.0358	−	13.0358i	0.433803	−	0.433803i
$904$		0			0
$905$	1.32122	+	2.01106i	0.0439189	+	0.0668499i
$906$		0			0
$907$	8.71157			0.289263			0.144631	−	0.989486i	$-0.453800\pi$
$907$	8.71157			0.289263			0.144631	+	0.989486i	$0.453800\pi$
$908$		0			0
$909$	9.40099	+	9.40099i	0.311811	+	0.311811i
$910$		0			0
$911$			2.71760i			0.0900381i	0.998986	+	0.0450190i	$0.0143348\pi$
$911$			2.71760i			0.0900381i	−0.998986	+	0.0450190i	$0.985665\pi$
$912$		0			0
$913$	38.0827	−	38.0827i	1.26035	−	1.26035i
$914$		0			0
$915$	12.6032	−	8.28003i	0.416650	−	0.273729i
$916$		0			0
$917$		−	11.3027i		−	0.373250i
$918$		0			0
$919$		−	26.3244i		−	0.868361i	−0.900826	−	0.434181i	$-0.857038\pi$
$919$		−	26.3244i		−	0.868361i	0.900826	−	0.434181i	$-0.142962\pi$
$920$		0			0
$921$		−	20.2428i		−	0.667023i
$922$		0			0
$923$			9.17306i			0.301935i
$924$		0			0
$925$	5.79701	−	13.4012i	0.190604	−	0.440629i
$926$		0			0
$927$	−3.79353	+	3.79353i	−0.124596	+	0.124596i
$928$		0			0
$929$			17.2416i			0.565677i	0.959168	+	0.282839i	$0.0912761\pi$
$929$			17.2416i			0.565677i	−0.959168	+	0.282839i	$0.908724\pi$
$930$		0			0
$931$	9.24996	+	9.24996i	0.303155	+	0.303155i
$932$		0			0
$933$	14.0432			0.459753
$934$		0			0
$935$	49.1873	+	10.1826i	1.60860	+	0.333008i
$936$		0			0
$937$	6.71407	−	6.71407i	0.219339	−	0.219339i	−0.588881	−	0.808220i	$-0.700431\pi$
$937$	6.71407	−	6.71407i	0.219339	−	0.219339i	0.808220	+	0.588881i	$0.200431\pi$
$938$		0			0
$939$	−10.3861	−	10.3861i	−0.338938	−	0.338938i
$940$		0			0
$941$	10.9220	−	10.9220i	0.356048	−	0.356048i	−0.506306	−	0.862354i	$-0.668989\pi$
$941$	10.9220	−	10.9220i	0.356048	−	0.356048i	0.862354	+	0.506306i	$0.168989\pi$
$942$		0			0
$943$	−17.3530	−	17.3530i	−0.565093	−	0.565093i
$944$		0			0
$945$	2.17292	+	3.30745i	0.0706850	+	0.107591i
$946$		0			0
$947$		−	8.31220i		−	0.270110i	−0.990838	−	0.135055i	$-0.956879\pi$
$947$		−	8.31220i		−	0.270110i	0.990838	−	0.135055i	$-0.0431212\pi$
$948$		0			0
$949$	5.32566	−	5.32566i	0.172878	−	0.172878i
$950$		0			0
$951$	11.6769			0.378649
$952$		0			0
$953$	−25.5971	−	25.5971i	−0.829170	−	0.829170i	0.158232	−	0.987402i	$-0.449421\pi$
$953$	−25.5971	−	25.5971i	−0.829170	−	0.829170i	−0.987402	+	0.158232i	$0.949421\pi$
$954$		0			0
$955$	6.85587	−	33.1173i	0.221851	−	1.07165i
$956$		0			0
$957$	−31.1325			−1.00637
$958$		0			0
$959$	−6.39206			−0.206410
$960$		0			0
$961$	12.1650			0.392420
$962$		0			0
$963$	−12.1814			−0.392540
$964$		0			0
$965$	20.2649	−	13.3136i	0.652351	−	0.428580i
$966$		0			0
$967$	−31.3819	−	31.3819i	−1.00918	−	1.00918i	−0.999958	−	0.00921754i	$-0.997066\pi$
$967$	−31.3819	−	31.3819i	−1.00918	−	1.00918i	−0.00921754	−	0.999958i	$-0.502934\pi$
$968$		0			0
$969$	−21.6637			−0.695940
$970$		0			0
$971$	−5.68257	+	5.68257i	−0.182362	+	0.182362i	−0.792384	−	0.610022i	$-0.791161\pi$
$971$	−5.68257	+	5.68257i	−0.182362	+	0.182362i	0.610022	+	0.792384i	$0.291161\pi$
$972$		0			0
$973$		−	7.39067i		−	0.236934i
$974$		0			0
$975$	−3.60871	+	8.34241i	−0.115571	+	0.267171i
$976$		0			0
$977$	15.4116	+	15.4116i	0.493062	+	0.493062i	0.909270	−	0.416208i	$-0.136641\pi$
$977$	15.4116	+	15.4116i	0.493062	+	0.493062i	−0.416208	+	0.909270i	$0.636641\pi$
$978$		0			0
$979$	9.81078	−	9.81078i	0.313554	−	0.313554i
$980$		0			0
$981$	−4.04384	−	4.04384i	−0.129110	−	0.129110i
$982$		0			0
$983$	−10.5760	+	10.5760i	−0.337323	+	0.337323i	−0.855359	−	0.518036i	$-0.826663\pi$
$983$	−10.5760	+	10.5760i	−0.337323	+	0.337323i	0.518036	+	0.855359i	$0.326663\pi$
$984$		0			0
$985$	−11.5995	+	56.0314i	−0.369590	+	1.78531i
$986$		0			0
$987$	−0.375690			−0.0119584
$988$		0			0
$989$	−42.3452	−	42.3452i	−1.34650	−	1.34650i
$990$		0			0
$991$		−	29.6786i		−	0.942771i	−0.881927	−	0.471385i	$-0.843754\pi$
$991$		−	29.6786i		−	0.942771i	0.881927	−	0.471385i	$-0.156246\pi$
$992$		0			0
$993$	12.0411	−	12.0411i	0.382114	−	0.382114i
$994$		0			0
$995$	−5.91133	+	28.5547i	−0.187402	+	0.905246i
$996$		0			0
$997$		−	9.96003i		−	0.315437i	−0.987484	−	0.157719i	$-0.949586\pi$
$997$		−	9.96003i		−	0.315437i	0.987484	−	0.157719i	$-0.0504139\pi$
$998$		0			0
$999$		−	2.92026i		−	0.0923928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.y.f.847.1		20
4.3	odd	2		240.2.y.f.187.1	yes	20
5.3	odd	4		960.2.bc.f.463.4		20
8.3	odd	2		1920.2.y.l.1567.10		20
8.5	even	2		1920.2.y.k.1567.10		20
12.11	even	2		720.2.z.h.667.10		20
16.3	odd	4		960.2.bc.f.367.4		20
16.5	even	4		1920.2.bc.k.607.7		20
16.11	odd	4		1920.2.bc.l.607.7		20
16.13	even	4		240.2.bc.f.67.5	yes	20
20.3	even	4		240.2.bc.f.43.5	yes	20
40.3	even	4		1920.2.bc.k.1183.7		20
40.13	odd	4		1920.2.bc.l.1183.7		20
48.29	odd	4		720.2.bd.h.307.6		20
60.23	odd	4		720.2.bd.h.523.6		20
80.3	even	4	inner	960.2.y.f.943.1		20
80.13	odd	4		240.2.y.f.163.1	✓	20
80.43	even	4		1920.2.y.k.223.10		20
80.53	odd	4		1920.2.y.l.223.10		20
240.173	even	4		720.2.z.h.163.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.1	✓	20	80.13	odd	4
240.2.y.f.187.1	yes	20	4.3	odd	2
240.2.bc.f.43.5	yes	20	20.3	even	4
240.2.bc.f.67.5	yes	20	16.13	even	4
720.2.z.h.163.10		20	240.173	even	4
720.2.z.h.667.10		20	12.11	even	2
720.2.bd.h.307.6		20	48.29	odd	4
720.2.bd.h.523.6		20	60.23	odd	4
960.2.y.f.847.1		20	1.1	even	1	trivial
960.2.y.f.943.1		20	80.3	even	4	inner
960.2.bc.f.367.4		20	16.3	odd	4
960.2.bc.f.463.4		20	5.3	odd	4
1920.2.y.k.223.10		20	80.43	even	4
1920.2.y.k.1567.10		20	8.5	even	2
1920.2.y.l.223.10		20	80.53	odd	4
1920.2.y.l.1567.10		20	8.3	odd	2
1920.2.bc.k.607.7		20	16.5	even	4
1920.2.bc.k.1183.7		20	40.3	even	4
1920.2.bc.l.607.7		20	16.11	odd	4
1920.2.bc.l.1183.7		20	40.13	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-2.18964 - 0.453294i) q^{5} +(-1.25143 - 1.25143i) q^{7} +1.00000 q^{9} +(-2.47980 + 2.47980i) q^{11} +1.81790i q^{13} +(-2.18964 - 0.453294i) q^{15} +(4.52932 + 4.52932i) q^{17} +(-2.39150 + 2.39150i) q^{19} +(-1.25143 - 1.25143i) q^{21} +(-4.06513 + 4.06513i) q^{23} +(4.58905 + 1.98510i) q^{25} +1.00000 q^{27} +(6.27721 + 6.27721i) q^{29} -4.33993i q^{31} +(-2.47980 + 2.47980i) q^{33} +(2.17292 + 3.30745i) q^{35} -2.92026i q^{37} +1.81790i q^{39} +4.26875i q^{41} +10.4167i q^{43} +(-2.18964 - 0.453294i) q^{45} +(0.150104 - 0.150104i) q^{47} -3.86784i q^{49} +(4.52932 + 4.52932i) q^{51} -10.6378 q^{53} +(6.55396 - 4.30580i) q^{55} +(-2.39150 + 2.39150i) q^{57} +(3.17716 + 3.17716i) q^{59} +(-4.76865 + 4.76865i) q^{61} +(-1.25143 - 1.25143i) q^{63} +(0.824041 - 3.98054i) q^{65} -10.8215i q^{67} +(-4.06513 + 4.06513i) q^{69} +5.04598 q^{71} +(-2.92958 - 2.92958i) q^{73} +(4.58905 + 1.98510i) q^{75} +6.20661 q^{77} -4.75216 q^{79} +1.00000 q^{81} -15.3571 q^{83} +(-7.86446 - 11.9707i) q^{85} +(6.27721 + 6.27721i) q^{87} -3.95627 q^{89} +(2.27497 - 2.27497i) q^{91} -4.33993i q^{93} +(6.32059 - 4.15248i) q^{95} +(2.46797 + 2.46797i) q^{97} +(-2.47980 + 2.47980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Introduction

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