LMFDB - Embedded newform 960.2.bc.f.367.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(367,960)] 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, 3, 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("960.367"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,8,0,4,0,-20,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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:	$\Z[a_1, \ldots, a_{11}]$
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			367.4
Root			$0.0912451 + 1.41127i$ of defining polynomial
Character	$\chi$	$=$	960.367
Dual form			960.2.bc.f.463.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{3} +(-0.453294 + 2.18964i) q^{5} +(-1.25143 - 1.25143i) q^{7} -1.00000 q^{9} +(-2.47980 - 2.47980i) q^{11} -1.81790 q^{13} +(2.18964 + 0.453294i) q^{15} +(4.52932 + 4.52932i) q^{17} +(2.39150 + 2.39150i) q^{19} +(-1.25143 + 1.25143i) q^{21} +(-4.06513 + 4.06513i) q^{23} +(-4.58905 - 1.98510i) q^{25} +1.00000i q^{27} +(-6.27721 + 6.27721i) q^{29} +4.33993i q^{31} +(-2.47980 + 2.47980i) q^{33} +(3.30745 - 2.17292i) q^{35} -2.92026 q^{37} +1.81790i q^{39} -4.26875i q^{41} -10.4167 q^{43} +(0.453294 - 2.18964i) q^{45} +(-0.150104 + 0.150104i) q^{47} -3.86784i q^{49} +(4.52932 - 4.52932i) q^{51} +10.6378i q^{53} +(6.55396 - 4.30580i) q^{55} +(2.39150 - 2.39150i) q^{57} +(-3.17716 + 3.17716i) q^{59} +(-4.76865 - 4.76865i) q^{61} +(1.25143 + 1.25143i) q^{63} +(0.824041 - 3.98054i) q^{65} -10.8215 q^{67} +(4.06513 + 4.06513i) q^{69} +5.04598 q^{71} +(2.92958 + 2.92958i) q^{73} +(-1.98510 + 4.58905i) q^{75} +6.20661i q^{77} +4.75216 q^{79} +1.00000 q^{81} +15.3571i q^{83} +(-11.9707 + 7.86446i) q^{85} +(6.27721 + 6.27721i) q^{87} +3.95627 q^{89} +(2.27497 + 2.27497i) q^{91} +4.33993 q^{93} +(-6.32059 + 4.15248i) q^{95} +(2.46797 + 2.46797i) q^{97} +(2.47980 + 2.47980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{5} + 4 q^{7} - 20 q^{9} - 8 q^{11} + 8 q^{13} + 12 q^{17} + 16 q^{19} + 4 q^{21} + 16 q^{23} - 4 q^{25} - 8 q^{33} + 12 q^{35} + 24 q^{37} + 8 q^{43} - 8 q^{45} + 12 q^{51} + 4 q^{55} + 16 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 20 * q + 8 * q^5 + 4 * q^7 - 20 * q^9 - 8 * q^11 + 8 * q^13 + 12 * q^17 + 16 * q^19 + 4 * q^21 + 16 * q^23 - 4 * q^25 - 8 * q^33 + 12 * q^35 + 24 * q^37 + 8 * q^43 - 8 * q^45 + 12 * q^51 + 4 * q^55 + 16 * q^57 - 16 * q^59 - 12 * q^61 - 4 * q^63 + 4 * q^65 + 16 * q^67 - 16 * q^69 + 20 * q^73 + 8 * q^75 + 48 * q^79 + 20 * q^81 + 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$	−0.453294	+	2.18964i	−0.202719	+	0.979237i
$5$	−0.453294	+	2.18964i	−0.202719	+	0.979237i
$6$		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	0.226356	−	0.974045i	$-0.427319\pi$
$11$	−2.47980	−	2.47980i	−0.747689	−	0.747689i	−0.974045	+	0.226356i	$0.927319\pi$
$12$		0			0
$13$	−1.81790			−0.504194			−0.252097	−	0.967702i	$-0.581120\pi$
$13$	−1.81790			−0.504194			−0.252097	+	0.967702i	$0.581120\pi$
$14$		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	$-0.123182\pi$
$19$	2.39150	+	2.39150i	0.548649	+	0.548649i	−0.377401	+	0.926050i	$0.623182\pi$
$20$		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
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−6.27721	+	6.27721i	−1.16565	+	1.16565i	−0.182430	+	0.983219i	$0.558396\pi$
$29$	−6.27721	+	6.27721i	−1.16565	+	1.16565i	−0.983219	+	0.182430i	$0.941604\pi$
$30$		0			0
$31$			4.33993i			0.779474i	0.920926	+	0.389737i	$0.127434\pi$
$31$			4.33993i			0.779474i	−0.920926	+	0.389737i	$0.872566\pi$
$32$		0			0
$33$	−2.47980	+	2.47980i	−0.431679	+	0.431679i
$34$		0			0
$35$	3.30745	−	2.17292i	0.559061	−	0.367290i
$36$		0			0
$37$	−2.92026			−0.480087			−0.240044	−	0.970762i	$-0.577162\pi$
$37$	−2.92026			−0.480087			−0.240044	+	0.970762i	$0.577162\pi$
$38$		0			0
$39$			1.81790i			0.291096i
$40$		0			0
$41$		−	4.26875i		−	0.666667i	−0.942809	−	0.333334i	$-0.891826\pi$
$41$		−	4.26875i		−	0.666667i	0.942809	−	0.333334i	$-0.108174\pi$
$42$		0			0
$43$	−10.4167			−1.58853			−0.794264	−	0.607572i	$-0.792144\pi$
$43$	−10.4167			−1.58853			−0.794264	+	0.607572i	$0.792144\pi$
$44$		0			0
$45$	0.453294	−	2.18964i	0.0675731	−	0.326412i
$46$		0			0
$47$	−0.150104	+	0.150104i	−0.0218950	+	0.0218950i	−0.717970	−	0.696075i	$-0.754928\pi$
$47$	−0.150104	+	0.150104i	−0.0218950	+	0.0218950i	0.696075	+	0.717970i	$0.254928\pi$
$48$		0			0
$49$		−	3.86784i		−	0.552549i
$50$		0			0
$51$	4.52932	−	4.52932i	0.634231	−	0.634231i
$52$		0			0
$53$			10.6378i			1.46122i	0.682797	+	0.730608i	$0.260763\pi$
$53$			10.6378i			1.46122i	−0.682797	+	0.730608i	$0.739237\pi$
$54$		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	$-0.844481\pi$
$59$	−3.17716	+	3.17716i	−0.413632	+	0.413632i	0.469370	+	0.883002i	$0.344481\pi$
$60$		0			0
$61$	−4.76865	−	4.76865i	−0.610563	−	0.610563i	0.332530	−	0.943093i	$-0.392098\pi$
$61$	−4.76865	−	4.76865i	−0.610563	−	0.610563i	−0.943093	+	0.332530i	$0.892098\pi$
$62$		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
$67$	−10.8215			−1.32206			−0.661029	−	0.750361i	$-0.729880\pi$
$67$	−10.8215			−1.32206			−0.661029	+	0.750361i	$0.729880\pi$
$68$		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	0.857449	−	0.514568i	$-0.172048\pi$
$73$	2.92958	+	2.92958i	0.342881	+	0.342881i	−0.514568	+	0.857449i	$0.672048\pi$
$74$		0			0
$75$	−1.98510	+	4.58905i	−0.229220	+	0.529898i
$76$		0			0
$77$			6.20661i			0.707309i
$78$		0			0
$79$	4.75216			0.534660			0.267330	−	0.963605i	$-0.413859\pi$
$79$	4.75216			0.534660			0.267330	+	0.963605i	$0.413859\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$			15.3571i			1.68567i	0.538175	+	0.842833i	$0.319114\pi$
$83$			15.3571i			1.68567i	−0.538175	+	0.842833i	$0.680886\pi$
$84$		0			0
$85$	−11.9707	+	7.86446i	−1.29840	+	0.853020i
$86$		0			0
$87$	6.27721	+	6.27721i	0.672988	+	0.672988i
$88$		0			0
$89$	3.95627			0.419364			0.209682	−	0.977770i	$-0.432757\pi$
$89$	3.95627			0.419364			0.209682	+	0.977770i	$0.432757\pi$
$90$		0			0
$91$	2.27497	+	2.27497i	0.238482	+	0.238482i
$92$		0			0
$93$	4.33993			0.450030
$94$		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	−0.0626050	−	0.998038i	$-0.519941\pi$
$101$	9.40099	−	9.40099i	0.935433	−	0.935433i	0.998038	+	0.0626050i	$0.0199408\pi$
$102$		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
$107$		−	12.1814i		−	1.17762i	−0.808271	−	0.588810i	$-0.799597\pi$
$107$		−	12.1814i		−	1.17762i	0.808271	−	0.588810i	$-0.200403\pi$
$108$		0			0
$109$	4.04384	−	4.04384i	0.387329	−	0.387329i	−0.486404	−	0.873734i	$-0.661692\pi$
$109$	4.04384	−	4.04384i	0.387329	−	0.387329i	0.873734	+	0.486404i	$0.161692\pi$
$110$		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
$115$	−7.05848	−	10.7439i	−0.658207	−	1.00187i
$116$		0			0
$117$	1.81790			0.168065
$118$		0			0
$119$		−	11.3362i		−	1.03919i
$120$		0			0
$121$			1.29886i			0.118078i
$122$		0			0
$123$	−4.26875			−0.384900
$124$		0			0
$125$	6.42685	−	9.14853i	0.574835	−	0.818270i
$126$		0			0
$127$	−7.35799	+	7.35799i	−0.652916	+	0.652916i	−0.953694	−	0.300778i	$-0.902754\pi$
$127$	−7.35799	+	7.35799i	−0.652916	+	0.652916i	0.300778	+	0.953694i	$0.402754\pi$
$128$		0			0
$129$			10.4167i			0.917138i
$130$		0			0
$131$	4.51593	−	4.51593i	0.394559	−	0.394559i	−0.481750	−	0.876309i	$-0.659999\pi$
$131$	4.51593	−	4.51593i	0.394559	−	0.394559i	0.876309	+	0.481750i	$0.159999\pi$
$132$		0			0
$133$		−	5.98560i		−	0.519018i
$134$		0			0
$135$	−2.18964	−	0.453294i	−0.188454	−	0.0390133i
$136$		0			0
$137$	−2.55390	+	2.55390i	−0.218194	+	0.218194i	−0.807737	−	0.589543i	$-0.799308\pi$
$137$	−2.55390	+	2.55390i	−0.218194	+	0.218194i	0.589543	+	0.807737i	$0.299308\pi$
$138$		0			0
$139$	−2.95289	+	2.95289i	−0.250461	+	0.250461i	−0.821159	−	0.570699i	$-0.806672\pi$
$139$	−2.95289	+	2.95289i	−0.250461	+	0.250461i	0.570699	+	0.821159i	$0.306672\pi$
$140$		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
$147$	−3.86784			−0.319014
$148$		0			0
$149$	15.1940	+	15.1940i	1.24474	+	1.24474i	0.958012	+	0.286728i	$0.0925675\pi$
$149$	15.1940	+	15.1940i	1.24474	+	1.24474i	0.286728	+	0.958012i	$0.407432\pi$
$150$		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
$155$	−9.50288	−	1.96726i	−0.763290	−	0.158014i
$156$		0			0
$157$		−	3.79875i		−	0.303173i	−0.988444	−	0.151587i	$-0.951562\pi$
$157$		−	3.79875i		−	0.303173i	0.988444	−	0.151587i	$-0.0484383\pi$
$158$		0			0
$159$	10.6378			0.843633
$160$		0			0
$161$	10.1745			0.801860
$162$		0			0
$163$		−	20.0096i		−	1.56727i	−0.621219	−	0.783637i	$-0.713362\pi$
$163$		−	20.0096i		−	1.56727i	0.621219	−	0.783637i	$-0.286638\pi$
$164$		0			0
$165$	−4.30580	−	6.55396i	−0.335206	−	0.510225i
$166$		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
$173$	−15.3776			−1.16914			−0.584568	−	0.811345i	$-0.698736\pi$
$173$	−15.3776			−1.16914			−0.584568	+	0.811345i	$0.698736\pi$
$174$		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	$-0.153041\pi$
$179$	5.67467	+	5.67467i	0.424145	+	0.424145i	−0.462483	+	0.886628i	$0.653041\pi$
$180$		0			0
$181$	−0.760920	+	0.760920i	−0.0565587	+	0.0565587i	−0.734820	−	0.678262i	$-0.762734\pi$
$181$	−0.760920	+	0.760920i	−0.0565587	+	0.0565587i	0.678262	+	0.734820i	$0.262734\pi$
$182$		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
$187$		−	22.4636i		−	1.64270i
$188$		0			0
$189$	1.25143	−	1.25143i	0.0910282	−	0.0910282i
$190$		0			0
$191$		−	15.1246i		−	1.09437i	−0.837010	−	0.547187i	$-0.815699\pi$
$191$		−	15.1246i		−	1.09437i	0.837010	−	0.547187i	$-0.184301\pi$
$192$		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
$195$	−3.98054	−	0.824041i	−0.285052	−	0.0590108i
$196$		0			0
$197$	−25.5893			−1.82316			−0.911581	−	0.411120i	$-0.865138\pi$
$197$	−25.5893			−1.82316			−0.911581	+	0.411120i	$0.865138\pi$
$198$		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
$203$	15.7110			1.10270
$204$		0			0
$205$	9.34703	+	1.93500i	0.652825	+	0.135146i
$206$		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	−0.553940	−	0.832556i	$-0.686876\pi$
$211$	4.04713	−	4.04713i	0.278616	−	0.278616i	0.832556	+	0.553940i	$0.186876\pi$
$212$		0			0
$213$		−	5.04598i		−	0.345745i
$214$		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	0.900213	−	0.435450i	$-0.143411\pi$
$223$	6.94039	+	6.94039i	0.464763	+	0.464763i	−0.435450	+	0.900213i	$0.643411\pi$
$224$		0			0
$225$	4.58905	+	1.98510i	0.305937	+	0.132340i
$226$		0			0
$227$	3.34643			0.222110			0.111055	−	0.993814i	$-0.464577\pi$
$227$	3.34643			0.222110			0.111055	+	0.993814i	$0.464577\pi$
$228$		0			0
$229$	−11.9644	−	11.9644i	−0.790629	−	0.790629i	0.190968	−	0.981596i	$-0.438837\pi$
$229$	−11.9644	−	11.9644i	−0.790629	−	0.790629i	−0.981596	+	0.190968i	$0.938837\pi$
$230$		0			0
$231$	6.20661			0.408365
$232$		0			0
$233$	12.4324	+	12.4324i	0.814474	+	0.814474i	0.985301	−	0.170827i	$-0.0546439\pi$
$233$	12.4324	+	12.4324i	0.814474	+	0.814474i	−0.170827	+	0.985301i	$0.554644\pi$
$234$		0			0
$235$	−0.260633	−	0.396716i	−0.0170018	−	0.0258789i
$236$		0			0
$237$		−	4.75216i		−	0.308686i
$238$		0			0
$239$	−24.7355			−1.60000			−0.800002	−	0.599997i	$-0.795168\pi$
$239$	−24.7355			−1.60000			−0.800002	+	0.599997i	$0.795168\pi$
$240$		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
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	8.46918	+	1.75327i	0.541076	+	0.112012i
$246$		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	0.885692	+	0.464274i	$0.153685\pi$
$251$	21.3875	+	21.3875i	1.34997	+	1.34997i	0.464274	+	0.885692i	$0.346315\pi$
$252$		0			0
$253$	20.1615			1.26754
$254$		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
$267$		−	3.95627i		−	0.242120i
$268$		0			0
$269$	−14.1435	+	14.1435i	−0.862347	+	0.862347i	−0.991610	−	0.129263i	$-0.958739\pi$
$269$	−14.1435	+	14.1435i	−0.862347	+	0.862347i	0.129263	+	0.991610i	$0.458739\pi$
$270$		0			0
$271$		−	24.2463i		−	1.47286i	−0.676515	−	0.736429i	$-0.736510\pi$
$271$		−	24.2463i		−	1.47286i	0.676515	−	0.736429i	$-0.263490\pi$
$272$		0			0
$273$	2.27497	−	2.27497i	0.137687	−	0.137687i
$274$		0			0
$275$	6.45728	+	16.3026i	0.389389	+	0.983084i
$276$		0			0
$277$	0.247833			0.0148909			0.00744543	−	0.999972i	$-0.497630\pi$
$277$	0.247833			0.0148909			0.00744543	+	0.999972i	$0.497630\pi$
$278$		0			0
$279$		−	4.33993i		−	0.259825i
$280$		0			0
$281$			13.2279i			0.789109i	0.918872	+	0.394555i	$0.129101\pi$
$281$			13.2279i			0.789109i	−0.918872	+	0.394555i	$0.870899\pi$
$282$		0			0
$283$	22.2111			1.32031			0.660157	−	0.751128i	$-0.270490\pi$
$283$	22.2111			1.32031			0.660157	+	0.751128i	$0.270490\pi$
$284$		0			0
$285$	4.15248	+	6.32059i	0.245972	+	0.374399i
$286$		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
$293$		−	2.93570i		−	0.171505i	−0.996316	−	0.0857526i	$-0.972671\pi$
$293$		−	2.93570i		−	0.171505i	0.996316	−	0.0857526i	$-0.0273295\pi$
$294$		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
$307$	−20.2428			−1.15532			−0.577659	−	0.816278i	$-0.696034\pi$
$307$	−20.2428			−1.15532			−0.577659	+	0.816278i	$0.696034\pi$
$308$		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	0.936834	−	0.349775i	$-0.113742\pi$
$313$	10.3861	+	10.3861i	0.587058	+	0.587058i	−0.349775	+	0.936834i	$0.613742\pi$
$314$		0			0
$315$	−3.30745	+	2.17292i	−0.186354	+	0.122430i
$316$		0			0
$317$			11.6769i			0.655839i	0.944706	+	0.327920i	$0.106347\pi$
$317$			11.6769i			0.655839i	−0.944706	+	0.327920i	$0.893653\pi$
$318$		0			0
$319$	31.1325			1.74309
$320$		0			0
$321$	−12.1814			−0.679899
$322$		0			0
$323$			21.6637i			1.20540i
$324$		0			0
$325$	8.34241	+	3.60871i	0.462754	+	0.200175i
$326$		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	0.955814	−	0.293973i	$-0.0949775\pi$
$331$	12.0411	+	12.0411i	0.661841	+	0.661841i	−0.293973	+	0.955814i	$0.594978\pi$
$332$		0			0
$333$	2.92026			0.160029
$334$		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
$347$		−	0.0770157i		−	0.00413442i	−0.999998	−	0.00206721i	$-0.999342\pi$
$347$		−	0.0770157i		−	0.00413442i	0.999998	−	0.00206721i	$-0.000658013\pi$
$348$		0			0
$349$	15.0145	−	15.0145i	0.803708	−	0.803708i	−0.179965	−	0.983673i	$-0.557598\pi$
$349$	15.0145	−	15.0145i	0.803708	−	0.803708i	0.983673	+	0.179965i	$0.0575984\pi$
$350$		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
$355$	−2.28731	+	11.0489i	−0.121398	+	0.586413i
$356$		0			0
$357$	−11.3362			−0.599978
$358$		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
$363$	1.29886			0.0681725
$364$		0			0
$365$	−7.74268	+	5.08676i	−0.405270	+	0.266253i
$366$		0			0
$367$	−3.46414	+	3.46414i	−0.180827	+	0.180827i	−0.791716	−	0.610889i	$-0.790812\pi$
$367$	−3.46414	+	3.46414i	−0.180827	+	0.180827i	0.610889	+	0.791716i	$0.290812\pi$
$368$		0			0
$369$			4.26875i			0.222222i
$370$		0			0
$371$	13.3125	−	13.3125i	0.691150	−	0.691150i
$372$		0			0
$373$		−	19.1403i		−	0.991049i	−0.868594	−	0.495524i	$-0.834976\pi$
$373$		−	19.1403i		−	0.991049i	0.868594	−	0.495524i	$-0.165024\pi$
$374$		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	−0.0214054	+	0.999771i	$0.506814\pi$
$379$	−19.8802	+	19.8802i	−1.02118	+	1.02118i	−0.999771	+	0.0214054i	$0.993186\pi$
$380$		0			0
$381$	7.35799	+	7.35799i	0.376961	+	0.376961i
$382$		0			0
$383$	−8.84171	−	8.84171i	−0.451790	−	0.451790i	0.444158	−	0.895948i	$-0.353503\pi$
$383$	−8.84171	−	8.84171i	−0.451790	−	0.451790i	−0.895948	+	0.444158i	$0.853503\pi$
$384$		0			0
$385$	−13.5902	−	2.81342i	−0.692623	−	0.143385i
$386$		0			0
$387$	10.4167			0.529510
$388$		0			0
$389$	1.06003	+	1.06003i	0.0537454	+	0.0537454i	0.733469	−	0.679723i	$-0.237900\pi$
$389$	1.06003	+	1.06003i	0.0537454	+	0.0537454i	−0.679723	+	0.733469i	$0.737900\pi$
$390$		0			0
$391$	−36.8245			−1.86230
$392$		0			0
$393$	−4.51593	−	4.51593i	−0.227799	−	0.227799i
$394$		0			0
$395$	−2.15413	+	10.4055i	−0.108386	+	0.523559i
$396$		0			0
$397$			4.35137i			0.218389i	0.994020	+	0.109194i	$0.0348271\pi$
$397$			4.35137i			0.218389i	−0.994020	+	0.109194i	$0.965173\pi$
$398$		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
$403$		−	7.88954i		−	0.393006i
$404$		0			0
$405$	−0.453294	+	2.18964i	−0.0225244	+	0.108804i
$406$		0			0
$407$	7.24167	+	7.24167i	0.358956	+	0.358956i
$408$		0			0
$409$	−0.142915			−0.00706670			−0.00353335	−	0.999994i	$-0.501125\pi$
$409$	−0.142915			−0.00706670			−0.00353335	+	0.999994i	$0.501125\pi$
$410$		0			0
$411$	2.55390	+	2.55390i	0.125975	+	0.125975i
$412$		0			0
$413$	7.95200			0.391292
$414$		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	$-0.215386\pi$
$419$	3.14176	+	3.14176i	0.153485	+	0.153485i	−0.626187	+	0.779673i	$0.715386\pi$
$420$		0			0
$421$	25.8144	−	25.8144i	1.25812	−	1.25812i	0.306124	−	0.951992i	$-0.400968\pi$
$421$	25.8144	−	25.8144i	1.25812	−	1.25812i	0.951992	−	0.306124i	$-0.0990322\pi$
$422$		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
$427$			11.9353i			0.577588i
$428$		0			0
$429$	4.50803	−	4.50803i	0.217650	−	0.217650i
$430$		0			0
$431$		−	6.52096i		−	0.314104i	−0.987590	−	0.157052i	$-0.949801\pi$
$431$		−	6.52096i		−	0.314104i	0.987590	−	0.157052i	$-0.0501990\pi$
$432$		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
$435$	−16.5903	+	10.8994i	−0.795442	+	0.522587i
$436$		0			0
$437$	−19.4436			−0.930112
$438$		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
$443$	20.4880			0.973414			0.486707	−	0.873565i	$-0.338198\pi$
$443$	20.4880			0.973414			0.486707	+	0.873565i	$0.338198\pi$
$444$		0			0
$445$	−1.79335	+	8.66281i	−0.0850131	+	0.410656i
$446$		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
$453$		−	2.66712i		−	0.125312i
$454$		0			0
$455$	−6.01260	+	3.95014i	−0.281875	+	0.185185i
$456$		0			0
$457$	14.7916	−	14.7916i	0.691921	−	0.691921i	−0.270733	−	0.962654i	$-0.587266\pi$
$457$	14.7916	−	14.7916i	0.691921	−	0.691921i	0.962654	+	0.270733i	$0.0872661\pi$
$458$		0			0
$459$	−4.52932	+	4.52932i	−0.211410	+	0.211410i
$460$		0			0
$461$	−15.0255	−	15.0255i	−0.699809	−	0.699809i	0.264561	−	0.964369i	$-0.414773\pi$
$461$	−15.0255	−	15.0255i	−0.699809	−	0.699809i	−0.964369	+	0.264561i	$0.914773\pi$
$462$		0			0
$463$	−6.10691	−	6.10691i	−0.283812	−	0.283812i	0.550815	−	0.834627i	$-0.314317\pi$
$463$	−6.10691	−	6.10691i	−0.283812	−	0.283812i	−0.834627	+	0.550815i	$0.814317\pi$
$464$		0			0
$465$	−1.96726	+	9.50288i	−0.0912296	+	0.440686i
$466$		0			0
$467$	−23.9704			−1.10922			−0.554610	−	0.832111i	$-0.687132\pi$
$467$	−23.9704			−1.10922			−0.554610	+	0.832111i	$0.687132\pi$
$468$		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
$475$	−6.22735	−	15.7221i	−0.285730	−	0.721380i
$476$		0			0
$477$		−	10.6378i		−	0.487072i
$478$		0			0
$479$	−36.1197			−1.65035			−0.825176	−	0.564876i	$-0.808924\pi$
$479$	−36.1197			−1.65035			−0.825176	+	0.564876i	$0.808924\pi$
$480$		0			0
$481$	5.30872			0.242057
$482$		0			0
$483$		−	10.1745i		−	0.462954i
$484$		0			0
$485$	−6.52269	+	4.28526i	−0.296180	+	0.194583i
$486$		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	0.553623	−	0.832768i	$-0.313245\pi$
$491$	−6.18543	−	6.18543i	−0.279145	−	0.279145i	−0.832768	+	0.553623i	$0.813245\pi$
$492$		0			0
$493$	−56.8629			−2.56098
$494$		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	0.989678	+	0.143306i	$0.0457732\pi$
$499$	25.3089	+	25.3089i	1.13298	+	1.13298i	0.143306	+	0.989678i	$0.454227\pi$
$500$		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
$507$			9.69526i			0.430581i
$508$		0			0
$509$	17.9336	−	17.9336i	0.794891	−	0.794891i	−0.187394	−	0.982285i	$-0.560004\pi$
$509$	17.9336	−	17.9336i	0.794891	−	0.794891i	0.982285	+	0.187394i	$0.0600042\pi$
$510$		0			0
$511$		−	7.33232i		−	0.324363i
$512$		0			0
$513$	−2.39150	+	2.39150i	−0.105587	+	0.105587i
$514$		0			0
$515$	−6.58688	−	10.0261i	−0.290253	−	0.441801i
$516$		0			0
$517$	0.744459			0.0327413
$518$		0			0
$519$			15.3776i			0.675001i
$520$		0			0
$521$			11.3666i			0.497981i	0.968506	+	0.248990i	$0.0800988\pi$
$521$			11.3666i			0.497981i	−0.968506	+	0.248990i	$0.919901\pi$
$522$		0			0
$523$	−19.1692			−0.838209			−0.419104	−	0.907938i	$-0.637656\pi$
$523$	−19.1692			−0.838209			−0.419104	+	0.907938i	$0.637656\pi$
$524$		0			0
$525$	8.22709	−	3.25866i	0.359060	−	0.142220i
$526$		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
$533$			7.76015i			0.336129i
$534$		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	0.614305	−	0.789069i	$-0.289436\pi$
$541$	−4.06490	−	4.06490i	−0.174764	−	0.174764i	−0.789069	+	0.614305i	$0.789436\pi$
$542$		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
$547$	28.7783			1.23047			0.615235	−	0.788344i	$-0.289061\pi$
$547$	28.7783			1.23047			0.615235	+	0.788344i	$0.289061\pi$
$548$		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
$555$	−6.39431	−	1.32373i	−0.271423	−	0.0561894i
$556$		0			0
$557$			8.96058i			0.379672i	0.981816	+	0.189836i	$0.0607956\pi$
$557$			8.96058i			0.379672i	−0.981816	+	0.189836i	$0.939204\pi$
$558$		0			0
$559$	18.9364			0.800926
$560$		0			0
$561$	−22.4636			−0.948415
$562$		0			0
$563$			9.62086i			0.405471i	0.979234	+	0.202736i	$0.0649832\pi$
$563$			9.62086i			0.405471i	−0.979234	+	0.202736i	$0.935017\pi$
$564$		0			0
$565$	21.5690	+	32.8307i	0.907414	+	1.38120i
$566$		0			0
$567$	−1.25143	−	1.25143i	−0.0525552	−	0.0525552i
$568$		0			0
$569$	−26.7360			−1.12083			−0.560415	−	0.828212i	$-0.689358\pi$
$569$	−26.7360			−1.12083			−0.560415	+	0.828212i	$0.689358\pi$
$570$		0			0
$571$	28.0517	+	28.0517i	1.17393	+	1.17393i	0.981265	+	0.192661i	$0.0617117\pi$
$571$	28.0517	+	28.0517i	1.17393	+	1.17393i	0.192661	+	0.981265i	$0.438288\pi$
$572$		0			0
$573$	−15.1246			−0.631837
$574$		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
$587$			1.40264i			0.0578931i	0.999581	+	0.0289465i	$0.00921525\pi$
$587$			1.40264i			0.0578931i	−0.999581	+	0.0289465i	$0.990785\pi$
$588$		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
$595$	24.8223	+	5.13865i	1.01762	+	0.210664i
$596$		0			0
$597$	−13.0408			−0.533726
$598$		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	$0.202062\pi$
$601$			29.0758i			1.18603i	−0.805193	+	0.593013i	$0.797938\pi$
$602$		0			0
$603$	10.8215			0.440686
$604$		0			0
$605$	−2.84404	−	0.588766i	−0.115627	−	0.0239367i
$606$		0			0
$607$	8.32107	−	8.32107i	0.337742	−	0.337742i	−0.517775	−	0.855517i	$-0.673240\pi$
$607$	8.32107	−	8.32107i	0.337742	−	0.337742i	0.855517	+	0.517775i	$0.173240\pi$
$608$		0			0
$609$		−	15.7110i		−	0.636642i
$610$		0			0
$611$	0.272874	−	0.272874i	0.0110393	−	0.0110393i
$612$		0			0
$613$		−	17.2991i		−	0.698705i	−0.936991	−	0.349353i	$-0.886401\pi$
$613$		−	17.2991i		−	0.698705i	0.936991	−	0.349353i	$-0.113599\pi$
$614$		0			0
$615$	1.93500	−	9.34703i	0.0780267	−	0.376909i
$616$		0			0
$617$	−15.9755	+	15.9755i	−0.643149	+	0.643149i	−0.951328	−	0.308179i	$-0.900280\pi$
$617$	−15.9755	+	15.9755i	−0.643149	+	0.643149i	0.308179	+	0.951328i	$0.400280\pi$
$618$		0			0
$619$	−7.13212	+	7.13212i	−0.286664	+	0.286664i	−0.835760	−	0.549096i	$-0.814972\pi$
$619$	−7.13212	+	7.13212i	−0.286664	+	0.286664i	0.549096	+	0.835760i	$0.314972\pi$
$620$		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
$627$	−11.8609			−0.473680
$628$		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
$635$	−12.7760	−	19.4467i	−0.507001	−	0.771718i
$636$		0			0
$637$			7.03133i			0.278592i
$638$		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
$643$		−	5.29313i		−	0.208741i	−0.994539	−	0.104370i	$-0.966717\pi$
$643$		−	5.29313i		−	0.208741i	0.994539	−	0.104370i	$-0.0332827\pi$
$644$		0			0
$645$	−22.8088	−	4.72182i	−0.898095	−	0.185921i
$646$		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
$653$	7.81012			0.305634			0.152817	−	0.988255i	$-0.451166\pi$
$653$	7.81012			0.305634			0.152817	+	0.988255i	$0.451166\pi$
$654$		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	$-0.291646\pi$
$659$	−4.73630	−	4.73630i	−0.184500	−	0.184500i	−0.793313	+	0.608813i	$0.791646\pi$
$660$		0			0
$661$	−19.8678	+	19.8678i	−0.772766	+	0.772766i	−0.978589	−	0.205823i	$-0.934013\pi$
$661$	−19.8678	+	19.8678i	−0.772766	+	0.772766i	0.205823	+	0.978589i	$0.434013\pi$
$662$		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
$667$		−	51.0354i		−	1.97610i
$668$		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
$675$	1.98510	−	4.58905i	0.0764066	−	0.176633i
$676$		0			0
$677$	−4.91631			−0.188949			−0.0944745	−	0.995527i	$-0.530117\pi$
$677$	−4.91631			−0.188949			−0.0944745	+	0.995527i	$0.530117\pi$
$678$		0			0
$679$		−	6.17699i		−	0.237051i
$680$		0			0
$681$		−	3.34643i		−	0.128236i
$682$		0			0
$683$	38.8999			1.48846			0.744231	−	0.667922i	$-0.232816\pi$
$683$	38.8999			1.48846			0.744231	+	0.667922i	$0.232816\pi$
$684$		0			0
$685$	−4.43446	−	6.74979i	−0.169432	−	0.257896i
$686$		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	−0.879137	−	0.476570i	$-0.841880\pi$
$691$	−10.5822	+	10.5822i	−0.402567	+	0.402567i	0.476570	+	0.879137i	$0.341880\pi$
$692$		0			0
$693$		−	6.20661i		−	0.235770i
$694$		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	0.986341	+	0.164715i	$0.0526706\pi$
$701$	30.4758	+	30.4758i	1.15106	+	1.15106i	0.164715	+	0.986341i	$0.447329\pi$
$702$		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
$707$	−23.5294			−0.884913
$708$		0			0
$709$	−14.5515	−	14.5515i	−0.546493	−	0.546493i	0.378932	−	0.925425i	$-0.376291\pi$
$709$	−14.5515	−	14.5515i	−0.546493	−	0.546493i	−0.925425	+	0.378932i	$0.876291\pi$
$710$		0			0
$711$	−4.75216			−0.178220
$712$		0			0
$713$	−17.6424	−	17.6424i	−0.660713	−	0.660713i
$714$		0			0
$715$	−11.9144	+	7.82749i	−0.445574	+	0.292732i
$716$		0			0
$717$			24.7355i			0.923763i
$718$		0			0
$719$	31.9412			1.19120			0.595602	−	0.803279i	$-0.296913\pi$
$719$	31.9412			1.19120			0.595602	+	0.803279i	$0.296913\pi$
$720$		0			0
$721$	9.49468			0.353600
$722$		0			0
$723$		−	17.1334i		−	0.637197i
$724$		0			0
$725$	41.2673	−	16.3455i	1.53263	−	0.607058i
$726$		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
$733$	24.7535			0.914293			0.457146	−	0.889391i	$-0.348872\pi$
$733$	24.7535			0.914293			0.457146	+	0.889391i	$0.348872\pi$
$734$		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	$-0.401592\pi$
$739$	−17.6246	−	17.6246i	−0.648333	−	0.648333i	−0.952590	+	0.304257i	$0.901592\pi$
$740$		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
$747$		−	15.3571i		−	0.561889i
$748$		0			0
$749$	−15.2442	+	15.2442i	−0.557010	+	0.557010i
$750$		0			0
$751$		−	14.9291i		−	0.544770i	−0.962188	−	0.272385i	$-0.912188\pi$
$751$		−	14.9291i		−	0.544770i	0.962188	−	0.272385i	$-0.0878124\pi$
$752$		0			0
$753$	21.3875	−	21.3875i	0.779403	−	0.779403i
$754$		0			0
$755$	−1.20899	+	5.84002i	−0.0439995	+	0.212540i
$756$		0			0
$757$	43.9059			1.59579			0.797894	−	0.602798i	$-0.205947\pi$
$757$	43.9059			1.59579			0.797894	+	0.602798i	$0.205947\pi$
$758$		0			0
$759$		−	20.1615i		−	0.731815i
$760$		0			0
$761$			2.39481i			0.0868119i	0.999058	+	0.0434059i	$0.0138209\pi$
$761$			2.39481i			0.0868119i	−0.999058	+	0.0434059i	$0.986179\pi$
$762$		0			0
$763$	−10.1212			−0.366411
$764$		0			0
$765$	11.9707	−	7.86446i	0.432801	−	0.284340i
$766$		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
$773$			16.1575i			0.581143i	0.956853	+	0.290572i	$0.0938455\pi$
$773$			16.1575i			0.581143i	−0.956853	+	0.290572i	$0.906155\pi$
$774$		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
$787$	36.6090			1.30497			0.652485	−	0.757802i	$-0.273727\pi$
$787$	36.6090			1.30497			0.652485	+	0.757802i	$0.273727\pi$
$788$		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
$795$	−4.82206	+	23.2930i	−0.171021	+	0.826117i
$796$		0			0
$797$			3.96964i			0.140612i	0.997525	+	0.0703060i	$0.0223976\pi$
$797$			3.96964i			0.140612i	−0.997525	+	0.0703060i	$0.977602\pi$
$798$		0			0
$799$	−1.35974			−0.0481041
$800$		0			0
$801$	−3.95627			−0.139788
$802$		0			0
$803$		−	14.5295i		−	0.512737i
$804$		0			0
$805$	−4.61202	+	22.2784i	−0.162552	+	0.785211i
$806$		0			0
$807$	14.1435	+	14.1435i	0.497876	+	0.497876i
$808$		0			0
$809$	−54.3213			−1.90984			−0.954918	−	0.296868i	$-0.904058\pi$
$809$	−54.3213			−1.90984			−0.954918	+	0.296868i	$0.904058\pi$
$810$		0			0
$811$	15.8944	+	15.8944i	0.558127	+	0.558127i	0.928774	−	0.370647i	$-0.120864\pi$
$811$	15.8944	+	15.8944i	0.558127	+	0.558127i	−0.370647	+	0.928774i	$0.620864\pi$
$812$		0			0
$813$	−24.2463			−0.850355
$814$		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	−0.995344	−	0.0963881i	$-0.969271\pi$
$821$	−25.7579	+	25.7579i	−0.898956	+	0.898956i	0.0963881	+	0.995344i	$0.469271\pi$
$822$		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
$827$			40.4359i			1.40609i	0.711143	+	0.703047i	$0.248178\pi$
$827$			40.4359i			1.40609i	−0.711143	+	0.703047i	$0.751822\pi$
$828$		0			0
$829$	18.6969	−	18.6969i	0.649370	−	0.649370i	−0.303471	−	0.952841i	$-0.598145\pi$
$829$	18.6969	−	18.6969i	0.649370	−	0.649370i	0.952841	+	0.303471i	$0.0981454\pi$
$830$		0			0
$831$		−	0.247833i		−	0.00859724i
$832$		0			0
$833$	17.5187	−	17.5187i	0.606986	−	0.606986i
$834$		0			0
$835$	−19.8284	+	13.0268i	−0.686189	+	0.450810i
$836$		0			0
$837$	−4.33993			−0.150010
$838$		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
$843$	13.2279			0.455593
$844$		0			0
$845$	4.39480	−	21.2291i	0.151186	−	0.730304i
$846$		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
$853$		−	6.59967i		−	0.225968i	−0.993597	−	0.112984i	$-0.963959\pi$
$853$		−	6.59967i		−	0.225968i	0.993597	−	0.112984i	$-0.0360409\pi$
$854$		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	$-0.470964\pi$
$857$	31.8196	−	31.8196i	1.08694	−	1.08694i	0.995842	−	0.0910940i	$-0.0290364\pi$
$858$		0			0
$859$	12.6182	−	12.6182i	0.430527	−	0.430527i	−0.458280	−	0.888808i	$-0.651534\pi$
$859$	12.6182	−	12.6182i	0.430527	−	0.430527i	0.888808	+	0.458280i	$0.151534\pi$
$860$		0			0
$861$	5.34205	+	5.34205i	0.182056	+	0.182056i
$862$		0			0
$863$	6.97660	+	6.97660i	0.237486	+	0.237486i	0.815808	−	0.578322i	$-0.196292\pi$
$863$	6.97660	+	6.97660i	0.237486	+	0.237486i	−0.578322	+	0.815808i	$0.696292\pi$
$864$		0			0
$865$	6.97056	−	33.6714i	0.237006	−	1.14486i
$866$		0			0
$867$	24.0294			0.816081
$868$		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
$875$	−19.4915	+	3.40600i	−0.658933	+	0.115144i
$876$		0			0
$877$			22.3460i			0.754572i	0.926097	+	0.377286i	$0.123143\pi$
$877$			22.3460i			0.754572i	−0.926097	+	0.377286i	$0.876857\pi$
$878$		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
$883$		−	8.08610i		−	0.272119i	−0.990701	−	0.136060i	$-0.956556\pi$
$883$		−	8.08610i		−	0.272119i	0.990701	−	0.136060i	$-0.0434438\pi$
$884$		0			0
$885$	−8.39704	+	5.51666i	−0.282263	+	0.185440i
$886$		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
$893$	−0.717950			−0.0240253
$894$		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
$907$			8.71157i			0.289263i	0.989486	+	0.144631i	$0.0461997\pi$
$907$			8.71157i			0.289263i	−0.989486	+	0.144631i	$0.953800\pi$
$908$		0			0
$909$	−9.40099	+	9.40099i	−0.311811	+	0.311811i
$910$		0			0
$911$		−	2.71760i		−	0.0900381i	−0.998986	−	0.0450190i	$-0.985665\pi$
$911$		−	2.71760i		−	0.0900381i	0.998986	−	0.0450190i	$-0.0143348\pi$
$912$		0			0
$913$	38.0827	−	38.0827i	1.26035	−	1.26035i
$914$		0			0
$915$	−8.28003	−	12.6032i	−0.273729	−	0.416650i
$916$		0			0
$917$	−11.3027			−0.373250
$918$		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
$923$	−9.17306			−0.301935
$924$		0			0
$925$	13.4012	+	5.79701i	0.440629	+	0.190604i
$926$		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
$933$		−	14.0432i		−	0.459753i
$934$		0			0
$935$	49.1873	+	10.1826i	1.60860	+	0.333008i
$936$		0			0
$937$	−6.71407	+	6.71407i	−0.219339	+	0.219339i	−0.808220	−	0.588881i	$-0.799569\pi$
$937$	−6.71407	+	6.71407i	−0.219339	+	0.219339i	0.588881	+	0.808220i	$0.299569\pi$
$938$		0			0
$939$	10.3861	−	10.3861i	0.338938	−	0.338938i
$940$		0			0
$941$	10.9220	+	10.9220i	0.356048	+	0.356048i	0.862354	−	0.506306i	$-0.168989\pi$
$941$	10.9220	+	10.9220i	0.356048	+	0.356048i	−0.506306	+	0.862354i	$0.668989\pi$
$942$		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
$947$	−8.31220			−0.270110			−0.135055	−	0.990838i	$-0.543121\pi$
$947$	−8.31220			−0.270110			−0.135055	+	0.990838i	$0.543121\pi$
$948$		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	0.987402	−	0.158232i	$-0.0505794\pi$
$953$	25.5971	+	25.5971i	0.829170	+	0.829170i	−0.158232	+	0.987402i	$0.550579\pi$
$954$		0			0
$955$	33.1173	+	6.85587i	1.07165	+	0.221851i
$956$		0			0
$957$		−	31.1325i		−	1.00637i
$958$		0			0
$959$	6.39206			0.206410
$960$		0			0
$961$	12.1650			0.392420
$962$		0			0
$963$			12.1814i			0.392540i
$964$		0			0
$965$	−13.3136	−	20.2649i	−0.428580	−	0.652351i
$966$		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	0.610022	−	0.792384i	$-0.291161\pi$
$971$	−5.68257	−	5.68257i	−0.182362	−	0.182362i	−0.792384	+	0.610022i	$0.791161\pi$
$972$		0			0
$973$	7.39067			0.236934
$974$		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
$987$		−	0.375690i		−	0.0119584i
$988$		0			0
$989$	42.3452	−	42.3452i	1.34650	−	1.34650i
$990$		0			0
$991$			29.6786i			0.942771i	0.881927	+	0.471385i	$0.156246\pi$
$991$			29.6786i			0.942771i	−0.881927	+	0.471385i	$0.843754\pi$
$992$		0			0
$993$	12.0411	−	12.0411i	0.382114	−	0.382114i
$994$		0			0
$995$	28.5547	+	5.91133i	0.905246	+	0.187402i
$996$		0			0
$997$	−9.96003			−0.315437			−0.157719	−	0.987484i	$-0.550414\pi$
$997$	−9.96003			−0.315437			−0.157719	+	0.987484i	$0.550414\pi$
$998$		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.bc.f.367.4		20
4.3	odd	2		240.2.bc.f.67.5	yes	20
5.3	odd	4		960.2.y.f.943.1		20
8.3	odd	2		1920.2.bc.k.607.7		20
8.5	even	2		1920.2.bc.l.607.7		20
12.11	even	2		720.2.bd.h.307.6		20
16.3	odd	4		1920.2.y.k.1567.10		20
16.5	even	4		240.2.y.f.187.1	yes	20
16.11	odd	4		960.2.y.f.847.1		20
16.13	even	4		1920.2.y.l.1567.10		20
20.3	even	4		240.2.y.f.163.1	✓	20
40.3	even	4		1920.2.y.l.223.10		20
40.13	odd	4		1920.2.y.k.223.10		20
48.5	odd	4		720.2.z.h.667.10		20
60.23	odd	4		720.2.z.h.163.10		20
80.3	even	4		1920.2.bc.l.1183.7		20
80.13	odd	4		1920.2.bc.k.1183.7		20
80.43	even	4	inner	960.2.bc.f.463.4		20
80.53	odd	4		240.2.bc.f.43.5	yes	20
240.53	even	4		720.2.bd.h.523.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.1	✓	20	20.3	even	4
240.2.y.f.187.1	yes	20	16.5	even	4
240.2.bc.f.43.5	yes	20	80.53	odd	4
240.2.bc.f.67.5	yes	20	4.3	odd	2
720.2.z.h.163.10		20	60.23	odd	4
720.2.z.h.667.10		20	48.5	odd	4
720.2.bd.h.307.6		20	12.11	even	2
720.2.bd.h.523.6		20	240.53	even	4
960.2.y.f.847.1		20	16.11	odd	4
960.2.y.f.943.1		20	5.3	odd	4
960.2.bc.f.367.4		20	1.1	even	1	trivial
960.2.bc.f.463.4		20	80.43	even	4	inner
1920.2.y.k.223.10		20	40.13	odd	4
1920.2.y.k.1567.10		20	16.3	odd	4
1920.2.y.l.223.10		20	40.3	even	4
1920.2.y.l.1567.10		20	16.13	even	4
1920.2.bc.k.607.7		20	8.3	odd	2
1920.2.bc.k.1183.7		20	80.13	odd	4
1920.2.bc.l.607.7		20	8.5	even	2
1920.2.bc.l.1183.7		20	80.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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

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