LMFDB - Embedded newform 680.2.cq.b.193.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(97,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 4, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cq (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			193.11
Character	$\chi$	$=$	680.193
Dual form			680.2.cq.b.377.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.79298 + 1.19803i) q^{3} +(0.347966 + 2.20883i) q^{5} +(3.50030 + 0.696254i) q^{7} +(0.631450 + 1.52445i) q^{9} +(-0.584025 + 2.93609i) q^{11} -3.18928 q^{13} +(-2.02235 + 4.37726i) q^{15} +(1.66751 - 3.77086i) q^{17} +(-0.568477 + 1.37243i) q^{19} +(5.44184 + 5.44184i) q^{21} +(-1.75474 - 2.62616i) q^{23} +(-4.75784 + 1.53720i) q^{25} +(0.567911 - 2.85508i) q^{27} +(4.59419 - 6.87569i) q^{29} +(-1.30893 - 6.58044i) q^{31} +(-4.56468 + 4.56468i) q^{33} +(-0.319916 + 7.97384i) q^{35} +(-4.50472 + 6.74179i) q^{37} +(-5.71832 - 3.82086i) q^{39} +(5.17262 + 7.74137i) q^{41} +(1.33716 + 0.553869i) q^{43} +(-3.14753 + 1.92522i) q^{45} -2.76193i q^{47} +(5.30020 + 2.19541i) q^{49} +(7.50743 - 4.76335i) q^{51} +(2.77567 + 6.70106i) q^{53} +(-6.68854 - 0.268349i) q^{55} +(-2.66348 + 1.77968i) q^{57} +(7.46530 - 3.09223i) q^{59} +(-6.94772 + 4.64232i) q^{61} +(1.14886 + 5.77570i) q^{63} +(-1.10976 - 7.04457i) q^{65} +(-3.73919 - 3.73919i) q^{67} -6.81089i q^{69} +(1.37331 - 0.273168i) q^{71} +(3.16256 - 0.629073i) q^{73} +(-10.3723 - 2.94388i) q^{75} +(-4.08853 + 9.87059i) q^{77} +(-15.8369 - 3.15015i) q^{79} +(7.93903 - 7.93903i) q^{81} +(7.54667 - 3.12593i) q^{83} +(8.90942 + 2.37111i) q^{85} +(16.4746 - 6.82400i) q^{87} +(11.6488 - 11.6488i) q^{89} +(-11.1635 - 2.22055i) q^{91} +(5.53669 - 13.3667i) q^{93} +(-3.22926 - 0.778110i) q^{95} +(11.0705 - 2.20206i) q^{97} +(-4.84472 + 0.963675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 24 q^{15} + 16 q^{25} - 24 q^{27} + 8 q^{29} + 16 q^{31} + 48 q^{33} - 32 q^{35} - 16 q^{41} - 16 q^{43} - 24 q^{45} + 80 q^{49} + 32 q^{51} - 24 q^{53} - 24 q^{55} + 48 q^{57} + 80 q^{59} - 24 q^{61}+ \cdots - 48 q^{99}+O(q^{100}) $ 112 * q - 24 * q^15 + 16 * q^25 - 24 * q^27 + 8 * q^29 + 16 * q^31 + 48 * q^33 - 32 * q^35 - 16 * q^41 - 16 * q^43 - 24 * q^45 + 80 * q^49 + 32 * q^51 - 24 * q^53 - 24 * q^55 + 48 * q^57 + 80 * q^59 - 24 * q^61 - 72 * q^63 + 32 * q^65 + 48 * q^67 - 40 * q^71 - 64 * q^73 + 32 * q^75 - 24 * q^77 - 40 * q^79 - 24 * q^83 - 32 * q^85 - 48 * q^87 + 16 * q^89 + 48 * q^93 + 168 * q^95 + 32 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.79298	+	1.19803i	1.03518	+	0.691684i	0.952390	−	0.304884i	$-0.0986175\pi$
$3$	1.79298	+	1.19803i	1.03518	+	0.691684i	0.0827881	+	0.996567i	$0.473618\pi$
$4$		0			0
$5$	0.347966	+	2.20883i	0.155615	+	0.987818i
$5$	0.347966	+	2.20883i	0.155615	+	0.987818i
$6$		0			0
$7$	3.50030	+	0.696254i	1.32299	+	0.263159i	0.805533	−	0.592550i	$-0.201879\pi$
$7$	3.50030	+	0.696254i	1.32299	+	0.263159i	0.517457	+	0.855709i	$0.326879\pi$
$8$		0			0
$9$	0.631450	+	1.52445i	0.210483	+	0.508151i
$10$		0			0
$11$	−0.584025	+	2.93609i	−0.176090	+	0.885265i	0.787178	+	0.616725i	$0.211541\pi$
$11$	−0.584025	+	2.93609i	−0.176090	+	0.885265i	−0.963269	+	0.268540i	$0.913459\pi$
$12$		0			0
$13$	−3.18928			−0.884548			−0.442274	−	0.896880i	$-0.645828\pi$
$13$	−3.18928			−0.884548			−0.442274	+	0.896880i	$0.645828\pi$
$14$		0			0
$15$	−2.02235	+	4.37726i	−0.522168	+	1.13020i
$16$		0			0
$17$	1.66751	−	3.77086i	0.404431	−	0.914568i
$17$	1.66751	−	3.77086i	0.404431	−	0.914568i
$18$		0			0
$19$	−0.568477	+	1.37243i	−0.130418	+	0.314856i	−0.975577	−	0.219659i	$-0.929506\pi$
$19$	−0.568477	+	1.37243i	−0.130418	+	0.314856i	0.845159	+	0.534515i	$0.179506\pi$
$20$		0			0
$21$	5.44184	+	5.44184i	1.18751	+	1.18751i
$22$		0			0
$23$	−1.75474	−	2.62616i	−0.365890	−	0.547593i	0.602152	−	0.798381i	$-0.294310\pi$
$23$	−1.75474	−	2.62616i	−0.365890	−	0.547593i	−0.968042	+	0.250789i	$0.919310\pi$
$24$		0			0
$25$	−4.75784	+	1.53720i	−0.951568	+	0.307439i
$26$		0			0
$27$	0.567911	−	2.85508i	0.109295	−	0.549461i
$28$		0			0
$29$	4.59419	−	6.87569i	0.853120	−	1.27678i	−0.106167	−	0.994348i	$-0.533858\pi$
$29$	4.59419	−	6.87569i	0.853120	−	1.27678i	0.959286	−	0.282435i	$-0.0911423\pi$
$30$		0			0
$31$	−1.30893	−	6.58044i	−0.235091	−	1.18188i	−0.900315	−	0.435239i	$-0.856664\pi$
$31$	−1.30893	−	6.58044i	−0.235091	−	1.18188i	0.665224	−	0.746644i	$-0.268336\pi$
$32$		0			0
$33$	−4.56468	+	4.56468i	−0.794608	+	0.794608i
$34$		0			0
$35$	−0.319916	+	7.97384i	−0.0540757	+	1.34782i
$36$		0			0
$37$	−4.50472	+	6.74179i	−0.740572	+	1.10834i	0.249581	+	0.968354i	$0.419707\pi$
$37$	−4.50472	+	6.74179i	−0.740572	+	1.10834i	−0.990153	+	0.139990i	$0.955293\pi$
$38$		0			0
$39$	−5.71832	−	3.82086i	−0.915664	−	0.611827i
$40$		0			0
$41$	5.17262	+	7.74137i	0.807827	+	1.20900i	0.974810	+	0.223038i	$0.0715975\pi$
$41$	5.17262	+	7.74137i	0.807827	+	1.20900i	−0.166983	+	0.985960i	$0.553402\pi$
$42$		0			0
$43$	1.33716	+	0.553869i	0.203915	+	0.0844642i	0.482303	−	0.876004i	$-0.339800\pi$
$43$	1.33716	+	0.553869i	0.203915	+	0.0844642i	−0.278389	+	0.960469i	$0.589800\pi$
$44$		0			0
$45$	−3.14753	+	1.92522i	−0.469207	+	0.286995i
$46$		0			0
$47$		−	2.76193i		−	0.402869i	−0.979502	−	0.201435i	$-0.935440\pi$
$47$		−	2.76193i		−	0.402869i	0.979502	−	0.201435i	$-0.0645603\pi$
$48$		0			0
$49$	5.30020	+	2.19541i	0.757171	+	0.313630i
$50$		0			0
$51$	7.50743	−	4.76335i	1.05125	−	0.667002i
$52$		0			0
$53$	2.77567	+	6.70106i	0.381267	+	0.920461i	0.991721	+	0.128409i	$0.0409871\pi$
$53$	2.77567	+	6.70106i	0.381267	+	0.920461i	−0.610454	+	0.792052i	$0.709013\pi$
$54$		0			0
$55$	−6.68854	−	0.268349i	−0.901883	−	0.0361842i
$56$		0			0
$57$	−2.66348	+	1.77968i	−0.352786	+	0.235724i
$58$		0			0
$59$	7.46530	−	3.09223i	0.971900	−	0.402574i	0.160481	−	0.987039i	$-0.448696\pi$
$59$	7.46530	−	3.09223i	0.971900	−	0.402574i	0.811419	+	0.584465i	$0.198696\pi$
$60$		0			0
$61$	−6.94772	+	4.64232i	−0.889564	+	0.594388i	−0.914180	−	0.405309i	$-0.867164\pi$
$61$	−6.94772	+	4.64232i	−0.889564	+	0.594388i	0.0246154	+	0.999697i	$0.492164\pi$
$62$		0			0
$63$	1.14886	+	5.77570i	0.144743	+	0.727670i
$64$		0			0
$65$	−1.10976	−	7.04457i	−0.137649	−	0.873772i
$66$		0			0
$67$	−3.73919	−	3.73919i	−0.456815	−	0.456815i	0.440794	−	0.897608i	$-0.354697\pi$
$67$	−3.73919	−	3.73919i	−0.456815	−	0.456815i	−0.897608	+	0.440794i	$0.854697\pi$
$68$		0			0
$69$		−	6.81089i		−	0.819935i
$70$		0			0
$71$	1.37331	−	0.273168i	0.162982	−	0.0324191i	−0.112925	−	0.993604i	$-0.536022\pi$
$71$	1.37331	−	0.273168i	0.162982	−	0.0324191i	0.275907	+	0.961184i	$0.411022\pi$
$72$		0			0
$73$	3.16256	−	0.629073i	0.370150	−	0.0736274i	−0.00651048	−	0.999979i	$-0.502072\pi$
$73$	3.16256	−	0.629073i	0.370150	−	0.0736274i	0.376660	+	0.926351i	$0.377072\pi$
$74$		0			0
$75$	−10.3723	−	2.94388i	−1.19769	−	0.339930i
$76$		0			0
$77$	−4.08853	+	9.87059i	−0.465931	+	1.12486i
$78$		0			0
$79$	−15.8369	−	3.15015i	−1.78179	−	0.354420i	−0.809305	−	0.587389i	$-0.800156\pi$
$79$	−15.8369	−	3.15015i	−1.78179	−	0.354420i	−0.972484	+	0.232970i	$0.925156\pi$
$80$		0			0
$81$	7.93903	−	7.93903i	0.882114	−	0.882114i
$82$		0			0
$83$	7.54667	−	3.12593i	0.828355	−	0.343116i	0.0721038	−	0.997397i	$-0.477029\pi$
$83$	7.54667	−	3.12593i	0.828355	−	0.343116i	0.756251	+	0.654281i	$0.227029\pi$
$84$		0			0
$85$	8.90942	+	2.37111i	0.966363	+	0.257184i
$86$		0			0
$87$	16.4746	−	6.82400i	1.76626	−	0.731609i
$88$		0			0
$89$	11.6488	−	11.6488i	1.23477	−	1.23477i	0.272663	−	0.962109i	$-0.412095\pi$
$89$	11.6488	−	11.6488i	1.23477	−	1.23477i	0.962109	−	0.272663i	$-0.0879045\pi$
$90$		0			0
$91$	−11.1635	−	2.22055i	−1.17025	−	0.232777i
$92$		0			0
$93$	5.53669	−	13.3667i	0.574128	−	1.38607i
$94$		0			0
$95$	−3.22926	−	0.778110i	−0.331315	−	0.0798324i
$96$		0			0
$97$	11.0705	−	2.20206i	1.12404	−	0.223585i	0.402137	−	0.915580i	$-0.368268\pi$
$97$	11.0705	−	2.20206i	1.12404	−	0.223585i	0.721903	+	0.691994i	$0.243268\pi$
$98$		0			0
$99$	−4.84472	+	0.963675i	−0.486913	+	0.0968530i
$100$		0			0
$101$			16.9816i			1.68973i	0.534978	+	0.844866i	$0.320320\pi$
$101$			16.9816i			1.68973i	−0.534978	+	0.844866i	$0.679680\pi$
$102$		0			0
$103$	3.64303	+	3.64303i	0.358959	+	0.358959i	0.863429	−	0.504470i	$-0.168312\pi$
$103$	3.64303	+	3.64303i	0.358959	+	0.358959i	−0.504470	+	0.863429i	$0.668312\pi$
$104$		0			0
$105$	−10.1265	+	13.9137i	−0.988246	+	1.35783i
$106$		0			0
$107$	0.187924	+	0.944757i	0.0181673	+	0.0913331i	0.988805	−	0.149212i	$-0.0476737\pi$
$107$	0.187924	+	0.944757i	0.0181673	+	0.0913331i	−0.970638	+	0.240545i	$0.922674\pi$
$108$		0			0
$109$	−2.42146	+	1.61797i	−0.231934	+	0.154973i	−0.666107	−	0.745856i	$-0.732041\pi$
$109$	−2.42146	+	1.61797i	−0.231934	+	0.154973i	0.434173	+	0.900829i	$0.357041\pi$
$110$		0			0
$111$	−16.1538	+	6.69110i	−1.53325	+	0.635091i
$112$		0			0
$113$	−0.265990	+	0.177729i	−0.0250222	+	0.0167193i	−0.568018	−	0.823016i	$-0.692290\pi$
$113$	−0.265990	+	0.177729i	−0.0250222	+	0.0167193i	0.542996	+	0.839735i	$0.317290\pi$
$114$		0			0
$115$	5.19015	−	4.78975i	0.483984	−	0.446646i
$116$		0			0
$117$	−2.01387	−	4.86191i	−0.186182	−	0.449484i
$118$		0			0
$119$	8.46228	−	12.0381i	0.775736	−	1.10354i
$120$		0			0
$121$	1.88312	+	0.780013i	0.171193	+	0.0709103i
$122$		0			0
$123$			20.0771i			1.81029i
$124$		0			0
$125$	−5.05097	−	9.97435i	−0.451772	−	0.892133i
$126$		0			0
$127$	−3.78336	−	1.56712i	−0.335719	−	0.139059i	0.208454	−	0.978032i	$-0.433157\pi$
$127$	−3.78336	−	1.56712i	−0.335719	−	0.139059i	−0.544174	+	0.838973i	$0.683157\pi$
$128$		0			0
$129$	1.73395	+	2.59503i	0.152665	+	0.228480i
$130$		0			0
$131$	−14.6869	−	9.81350i	−1.28320	−	0.857410i	−0.288232	−	0.957561i	$-0.593067\pi$
$131$	−14.6869	−	9.81350i	−1.28320	−	0.857410i	−0.994972	+	0.100151i	$0.968067\pi$
$132$		0			0
$133$	−2.94540	+	4.40810i	−0.255398	+	0.382231i
$134$		0			0
$135$	6.50400	+	0.260945i	0.559775	+	0.0224586i
$136$		0			0
$137$	−1.21496	+	1.21496i	−0.103801	+	0.103801i	−0.757100	−	0.653299i	$-0.773384\pi$
$137$	−1.21496	+	1.21496i	−0.103801	+	0.103801i	0.653299	+	0.757100i	$0.273384\pi$
$138$		0			0
$139$	−1.13885	−	5.72536i	−0.0965956	−	0.485619i	−0.998552	−	0.0537921i	$-0.982869\pi$
$139$	−1.13885	−	5.72536i	−0.0965956	−	0.485619i	0.901957	−	0.431827i	$-0.142131\pi$
$140$		0			0
$141$	3.30888	−	4.95209i	0.278658	−	0.417041i
$142$		0			0
$143$	1.86262	−	9.36403i	0.155760	−	0.783059i
$144$		0			0
$145$	16.7858	+	7.75526i	1.39399	+	0.644040i
$146$		0			0
$147$	6.87297	+	10.2861i	0.566873	+	0.848386i
$148$		0			0
$149$	−14.3725	−	14.3725i	−1.17744	−	1.17744i	−0.980394	−	0.197045i	$-0.936865\pi$
$149$	−14.3725	−	14.3725i	−1.17744	−	1.17744i	−0.197045	−	0.980394i	$-0.563135\pi$
$150$		0			0
$151$	4.24187	−	10.2408i	0.345199	−	0.833384i	−0.651974	−	0.758241i	$-0.726059\pi$
$151$	4.24187	−	10.2408i	0.345199	−	0.833384i	0.997173	−	0.0751424i	$-0.0239411\pi$
$152$		0			0
$153$	6.80146	+	0.160938i	0.549865	+	0.0130110i
$154$		0			0
$155$	14.0796	−	5.18098i	1.13090	−	0.416146i
$156$		0			0
$157$	−12.2792			−0.979984			−0.489992	−	0.871727i	$-0.663000\pi$
$157$	−12.2792			−0.979984			−0.489992	+	0.871727i	$0.663000\pi$
$158$		0			0
$159$	−3.05136	+	15.3402i	−0.241988	+	1.21656i
$160$		0			0
$161$	−4.31366	−	10.4141i	−0.339964	−	0.820747i
$162$		0			0
$163$	3.55285	+	0.706706i	0.278281	+	0.0553535i	0.332257	−	0.943189i	$-0.392190\pi$
$163$	3.55285	+	0.706706i	0.278281	+	0.0553535i	−0.0539768	+	0.998542i	$0.517190\pi$
$164$		0			0
$165$	−11.6709	−	8.49423i	−0.908581	−	0.661275i
$166$		0			0
$167$	−14.8737	−	9.93826i	−1.15096	−	0.769046i	−0.174480	−	0.984661i	$-0.555824\pi$
$167$	−14.8737	−	9.93826i	−1.15096	−	0.769046i	−0.976478	+	0.215615i	$0.930824\pi$
$168$		0			0
$169$	−2.82848			−0.217575
$170$		0			0
$171$	−2.45116			−0.187445
$172$		0			0
$173$	16.7951	+	11.2221i	1.27691	+	0.853202i	0.994361	−	0.106052i	$-0.0338209\pi$
$173$	16.7951	+	11.2221i	1.27691	+	0.853202i	0.282546	+	0.959254i	$0.408821\pi$
$174$		0			0
$175$	−17.7242	+	2.06799i	−1.33982	+	0.156325i
$176$		0			0
$177$	17.0897	+	3.39936i	1.28454	+	0.255511i
$178$		0			0
$179$	9.66314	+	23.3289i	0.722257	+	1.74368i	0.666819	+	0.745220i	$0.267656\pi$
$179$	9.66314	+	23.3289i	0.722257	+	1.74368i	0.0554380	+	0.998462i	$0.482344\pi$
$180$		0			0
$181$	2.77423	−	13.9470i	0.206207	−	1.03667i	−0.729523	−	0.683956i	$-0.760258\pi$
$181$	2.77423	−	13.9470i	0.206207	−	1.03667i	0.935730	−	0.352717i	$-0.114742\pi$
$182$		0			0
$183$	−18.0188			−1.33199
$184$		0			0
$185$	−16.4589	−	7.60423i	−1.21009	−	0.559074i
$186$		0			0
$187$	10.0977	+	7.09825i	0.738419	+	0.519076i
$188$		0			0
$189$	3.97572	−	9.59824i	0.289191	−	0.698169i
$190$		0			0
$191$	−16.6356	−	16.6356i	−1.20371	−	1.20371i	−0.973029	−	0.230682i	$-0.925904\pi$
$191$	−16.6356	−	16.6356i	−1.20371	−	1.20371i	−0.230682	−	0.973029i	$-0.574096\pi$
$192$		0			0
$193$	−0.952095	−	1.42491i	−0.0685333	−	0.102567i	0.795620	−	0.605796i	$-0.207145\pi$
$193$	−0.952095	−	1.42491i	−0.0685333	−	0.102567i	−0.864153	+	0.503229i	$0.832145\pi$
$194$		0			0
$195$	6.44984	−	13.9603i	0.461882	−	0.999719i
$196$		0			0
$197$	1.46726	−	7.37642i	0.104538	−	0.525548i	−0.892659	−	0.450732i	$-0.851163\pi$
$197$	1.46726	−	7.37642i	0.104538	−	0.525548i	0.997197	−	0.0748160i	$-0.0238370\pi$
$198$		0			0
$199$	5.36549	−	8.03003i	0.380350	−	0.569234i	−0.591064	−	0.806624i	$-0.701292\pi$
$199$	5.36549	−	8.03003i	0.380350	−	0.569234i	0.971414	+	0.237391i	$0.0762921\pi$
$200$		0			0
$201$	−2.22463	−	11.1840i	−0.156913	−	0.788856i
$202$		0			0
$203$	20.8683	−	20.8683i	1.46467	−	1.46467i
$204$		0			0
$205$	−15.2994	+	14.1192i	−1.06856	+	0.986124i
$206$		0			0
$207$	2.89543	−	4.33332i	0.201246	−	0.301186i
$208$		0			0
$209$	−3.69756	−	2.47063i	−0.255766	−	0.170897i
$210$		0			0
$211$	−3.82382	−	5.72275i	−0.263242	−	0.393970i	0.676177	−	0.736739i	$-0.263635\pi$
$211$	−3.82382	−	5.72275i	−0.263242	−	0.393970i	−0.939420	+	0.342769i	$0.888635\pi$
$212$		0			0
$213$	2.78958	+	1.15548i	0.191139	+	0.0791722i
$214$		0			0
$215$	−0.758115	+	3.14628i	−0.0517030	+	0.214574i
$216$		0			0
$217$		−	23.9449i		−	1.62549i
$218$		0			0
$219$	6.42406	+	2.66093i	0.434098	+	0.179809i
$220$		0			0
$221$	−5.31817	+	12.0263i	−0.357739	+	0.808979i
$222$		0			0
$223$	8.13956	+	19.6506i	0.545065	+	1.31590i	0.921110	+	0.389303i	$0.127284\pi$
$223$	8.13956	+	19.6506i	0.545065	+	1.31590i	−0.376044	+	0.926602i	$0.622716\pi$
$224$		0			0
$225$	−5.34772	−	6.28244i	−0.356515	−	0.418830i
$226$		0			0
$227$	13.8650	−	9.26430i	0.920252	−	0.614893i	−0.00262106	−	0.999997i	$-0.500834\pi$
$227$	13.8650	−	9.26430i	0.920252	−	0.614893i	0.922873	+	0.385104i	$0.125834\pi$
$228$		0			0
$229$	−1.26501	+	0.523985i	−0.0835944	+	0.0346259i	−0.424089	−	0.905621i	$-0.639406\pi$
$229$	−1.26501	+	0.523985i	−0.0835944	+	0.0346259i	0.340494	+	0.940247i	$0.389406\pi$
$230$		0			0
$231$	−19.1559	+	12.7996i	−1.26037	+	0.842150i
$232$		0			0
$233$	2.58715	+	13.0065i	0.169490	+	0.852082i	0.968164	+	0.250318i	$0.0805351\pi$
$233$	2.58715	+	13.0065i	0.169490	+	0.852082i	−0.798674	+	0.601764i	$0.794465\pi$
$234$		0			0
$235$	6.10063	−	0.961060i	0.397961	−	0.0626926i
$236$		0			0
$237$	−24.6212	−	24.6212i	−1.59932	−	1.59932i
$238$		0			0
$239$		−	2.74304i		−	0.177432i	−0.996057	−	0.0887162i	$-0.971724\pi$
$239$		−	2.74304i		−	0.177432i	0.996057	−	0.0887162i	$-0.0282764\pi$
$240$		0			0
$241$	−20.2804	+	4.03402i	−1.30638	+	0.259854i	−0.798719	−	0.601705i	$-0.794488\pi$
$241$	−20.2804	+	4.03402i	−1.30638	+	0.259854i	−0.507657	+	0.861559i	$0.669488\pi$
$242$		0			0
$243$	15.1805	−	3.01959i	0.973829	−	0.193707i
$244$		0			0
$245$	−3.00500	+	12.4711i	−0.191982	+	0.796752i
$246$		0			0
$247$	1.81303	−	4.37705i	0.115361	−	0.278505i
$248$		0			0
$249$	17.2760	+	3.43641i	1.09482	+	0.217774i
$250$		0			0
$251$	5.97237	−	5.97237i	0.376973	−	0.376973i	−0.493036	−	0.870009i	$-0.664113\pi$
$251$	5.97237	−	5.97237i	0.376973	−	0.376973i	0.870009	+	0.493036i	$0.164113\pi$
$252$		0			0
$253$	8.73547	−	3.61835i	0.549194	−	0.227484i
$254$		0			0
$255$	13.1338	+	14.9251i	0.822467	+	0.934648i
$256$		0			0
$257$	−13.6937	+	5.67211i	−0.854189	+	0.353817i	−0.766432	−	0.642325i	$-0.777970\pi$
$257$	−13.6937	+	5.67211i	−0.854189	+	0.353817i	−0.0877570	+	0.996142i	$0.527970\pi$
$258$		0			0
$259$	−20.4619	+	20.4619i	−1.27144	+	1.27144i
$260$		0			0
$261$	13.3827	+	2.66198i	0.828367	+	0.164772i
$262$		0			0
$263$	−9.08824	+	21.9410i	−0.560405	+	1.35294i	0.349038	+	0.937109i	$0.386508\pi$
$263$	−9.08824	+	21.9410i	−0.560405	+	1.35294i	−0.909443	+	0.415829i	$0.863492\pi$
$264$		0			0
$265$	−13.8356	+	8.46272i	−0.849917	+	0.519861i
$266$		0			0
$267$	34.8418	−	6.93046i	2.13228	−	0.424137i
$268$		0			0
$269$	−6.27724	+	1.24862i	−0.382730	+	0.0761297i	−0.382706	−	0.923870i	$-0.625008\pi$
$269$	−6.27724	+	1.24862i	−0.382730	+	0.0761297i	−2.42140e−5		1.00000i	$0.500008\pi$
$270$		0			0
$271$			1.45756i			0.0885406i	0.999020	+	0.0442703i	$0.0140963\pi$
$271$			1.45756i			0.0885406i	−0.999020	+	0.0442703i	$0.985904\pi$
$272$		0			0
$273$	−17.3556	−	17.3556i	−1.05041	−	1.05041i
$274$		0			0
$275$	−1.73465	−	14.8672i	−0.104603	−	0.896527i
$276$		0			0
$277$	−3.46646	−	17.4271i	−0.208280	−	1.04709i	−0.933501	−	0.358576i	$-0.883262\pi$
$277$	−3.46646	−	17.4271i	−0.208280	−	1.04709i	0.725221	−	0.688516i	$-0.241738\pi$
$278$		0			0
$279$	9.20506	−	6.15062i	0.551092	−	0.368228i
$280$		0			0
$281$	−10.2518	+	4.24643i	−0.611570	+	0.253321i	−0.666900	−	0.745148i	$-0.732379\pi$
$281$	−10.2518	+	4.24643i	−0.611570	+	0.253321i	0.0553296	+	0.998468i	$0.482379\pi$
$282$		0			0
$283$	−14.9426	+	9.98430i	−0.888243	+	0.593505i	−0.913798	−	0.406168i	$-0.866865\pi$
$283$	−14.9426	+	9.98430i	−0.888243	+	0.593505i	0.0255551	+	0.999673i	$0.491865\pi$
$284$		0			0
$285$	−4.85780	−	5.26389i	−0.287751	−	0.311806i
$286$		0			0
$287$	12.7158	+	30.6986i	0.750588	+	1.81208i
$288$		0			0
$289$	−11.4388	−	12.5759i	−0.672871	−	0.739760i
$290$		0			0
$291$	22.4873	+	9.31456i	1.31823	+	0.546029i
$292$		0			0
$293$			9.67627i			0.565294i	0.959224	+	0.282647i	$0.0912125\pi$
$293$			9.67627i			0.565294i	−0.959224	+	0.282647i	$0.908788\pi$
$294$		0			0
$295$	9.42788	+	15.4136i	0.548912	+	0.897413i
$296$		0			0
$297$	8.05111	+	3.33488i	0.467173	+	0.193509i
$298$		0			0
$299$	5.59638	+	8.37557i	0.323647	+	0.484372i
$300$		0			0
$301$	4.29482	+	2.86971i	0.247549	+	0.165407i
$302$		0			0
$303$	−20.3445	+	30.4477i	−1.16876	+	1.74917i
$304$		0			0
$305$	−12.6717	−	13.7309i	−0.725577	−	0.786231i
$306$		0			0
$307$	−11.0018	+	11.0018i	−0.627906	+	0.627906i	−0.947541	−	0.319635i	$-0.896440\pi$
$307$	−11.0018	+	11.0018i	−0.627906	+	0.627906i	0.319635	+	0.947541i	$0.396440\pi$
$308$		0			0
$309$	2.16742	+	10.8964i	0.123300	+	0.619872i
$310$		0			0
$311$	3.14541	−	4.70744i	0.178360	−	0.266934i	−0.731508	−	0.681833i	$-0.761183\pi$
$311$	3.14541	−	4.70744i	0.178360	−	0.266934i	0.909868	+	0.414899i	$0.136183\pi$
$312$		0			0
$313$	−6.25022	+	31.4220i	−0.353283	+	1.77607i	0.239687	+	0.970850i	$0.422955\pi$
$313$	−6.25022	+	31.4220i	−0.353283	+	1.77607i	−0.592971	+	0.805224i	$0.702045\pi$
$314$		0			0
$315$	−12.3578	+	4.54738i	−0.696281	+	0.256216i
$316$		0			0
$317$	8.39736	+	12.5675i	0.471643	+	0.705863i	0.988670	−	0.150106i	$-0.0479614\pi$
$317$	8.39736	+	12.5675i	0.471643	+	0.705863i	−0.517027	+	0.855969i	$0.672961\pi$
$318$		0			0
$319$	17.5045	+	17.5045i	0.980066	+	0.980066i
$320$		0			0
$321$	−0.794905	+	1.91907i	−0.0443673	+	0.107112i
$322$		0			0
$323$	4.22728	+	4.43219i	0.235212	+	0.246613i
$324$		0			0
$325$	15.1741	−	4.90255i	0.841707	−	0.271945i
$326$		0			0
$327$	−6.28000			−0.347285
$328$		0			0
$329$	1.92301	−	9.66760i	0.106019	−	0.532992i
$330$		0			0
$331$	−0.944647	−	2.28058i	−0.0519225	−	0.125352i	0.895790	−	0.444478i	$-0.146611\pi$
$331$	−0.944647	−	2.28058i	−0.0519225	−	0.125352i	−0.947712	+	0.319126i	$0.896611\pi$
$332$		0			0
$333$	−13.1221	−	2.61014i	−0.719084	−	0.143035i
$334$		0			0
$335$	6.95811	−	9.56034i	0.380162	−	0.522337i
$336$		0			0
$337$	14.8541	+	9.92520i	0.809155	+	0.540660i	0.889943	−	0.456071i	$-0.150744\pi$
$337$	14.8541	+	9.92520i	0.809155	+	0.540660i	−0.0807881	+	0.996731i	$0.525744\pi$
$338$		0			0
$339$	−0.689840			−0.0374670
$340$		0			0
$341$	20.0852			1.08768
$342$		0			0
$343$	−3.74817	−	2.50445i	−0.202382	−	0.135227i
$344$		0			0
$345$	15.0441	−	2.36996i	0.809947	−	0.127595i
$346$		0			0
$347$	34.0157	+	6.76613i	1.82606	+	0.363225i	0.984282	−	0.176605i	$-0.0565115\pi$
$347$	34.0157	+	6.76613i	1.82606	+	0.363225i	0.841774	+	0.539830i	$0.181511\pi$
$348$		0			0
$349$	6.94292	+	16.7617i	0.371646	+	0.897233i	0.993472	+	0.114078i	$0.0363912\pi$
$349$	6.94292	+	16.7617i	0.371646	+	0.897233i	−0.621826	+	0.783156i	$0.713609\pi$
$350$		0			0
$351$	−1.81123	+	9.10566i	−0.0966762	+	0.486024i
$352$		0			0
$353$	−2.72376			−0.144971			−0.0724855	−	0.997369i	$-0.523093\pi$
$353$	−2.72376			−0.144971			−0.0724855	+	0.997369i	$0.523093\pi$
$354$		0			0
$355$	1.08125	+	2.93835i	0.0573866	+	0.155951i
$356$		0			0
$357$	29.5948	−	11.4461i	1.56632	−	0.605791i
$358$		0			0
$359$	10.9942	−	26.5422i	0.580249	−	1.40085i	−0.312338	−	0.949971i	$-0.601112\pi$
$359$	10.9942	−	26.5422i	0.580249	−	1.40085i	0.892587	−	0.450875i	$-0.148888\pi$
$360$		0			0
$361$	11.8746	+	11.8746i	0.624981	+	0.624981i
$362$		0			0
$363$	2.44191	+	3.65458i	0.128167	+	0.191816i
$364$		0			0
$365$	2.48998	+	6.76666i	0.130331	+	0.354183i
$366$		0			0
$367$	−4.18549	+	21.0419i	−0.218481	+	1.09838i	0.703367	+	0.710827i	$0.251679\pi$
$367$	−4.18549	+	21.0419i	−0.218481	+	1.09838i	−0.921848	+	0.387551i	$0.873321\pi$
$368$		0			0
$369$	−8.53511	+	12.7737i	−0.444320	+	0.664972i
$370$		0			0
$371$	5.05005	+	25.3883i	0.262185	+	1.31809i
$372$		0			0
$373$	19.6466	−	19.6466i	1.01726	−	1.01726i	0.0174135	−	0.999848i	$-0.494457\pi$
$373$	19.6466	−	19.6466i	1.01726	−	1.01726i	0.999848	−	0.0174135i	$-0.00554318\pi$
$374$		0			0
$375$	2.89330	−	23.9350i	0.149409	−	1.23600i
$376$		0			0
$377$	−14.6522	+	21.9285i	−0.754625	+	1.12938i
$378$		0			0
$379$	−25.0333	−	16.7267i	−1.28587	−	0.859194i	−0.290653	−	0.956829i	$-0.593872\pi$
$379$	−25.0333	−	16.7267i	−1.28587	−	0.859194i	−0.995222	+	0.0976345i	$0.968872\pi$
$380$		0			0
$381$	−4.90603	−	7.34240i	−0.251344	−	0.376163i
$382$		0			0
$383$	−8.73512	−	3.61821i	−0.446344	−	0.184882i	0.148179	−	0.988961i	$-0.452659\pi$
$383$	−8.73512	−	3.61821i	−0.446344	−	0.184882i	−0.594523	+	0.804079i	$0.702659\pi$
$384$		0			0
$385$	−23.2251	−	5.59623i	−1.18366	−	0.285210i
$386$		0			0
$387$			2.38818i			0.121398i
$388$		0			0
$389$	1.74313	+	0.722027i	0.0883801	+	0.0366082i	0.426435	−	0.904518i	$-0.359769\pi$
$389$	1.74313	+	0.722027i	0.0883801	+	0.0366082i	−0.338055	+	0.941126i	$0.609769\pi$
$390$		0			0
$391$	−12.8290	+	2.23774i	−0.648788	+	0.113168i
$392$		0			0
$393$	−14.5765	−	35.1908i	−0.735288	−	1.77514i
$394$		0			0
$395$	1.44744	−	36.0771i	0.0728285	−	1.81524i
$396$		0			0
$397$	−22.2437	+	14.8627i	−1.11638	+	0.745940i	−0.969956	−	0.243282i	$-0.921776\pi$
$397$	−22.2437	+	14.8627i	−1.11638	+	0.745940i	−0.146422	+	0.989222i	$0.546776\pi$
$398$		0			0
$399$	−10.5621	+	4.37496i	−0.528766	+	0.219022i
$400$		0			0
$401$	−4.11241	+	2.74783i	−0.205364	+	0.137220i	−0.654000	−	0.756495i	$-0.726910\pi$
$401$	−4.11241	+	2.74783i	−0.205364	+	0.137220i	0.448635	+	0.893715i	$0.351910\pi$
$402$		0			0
$403$	4.17455	+	20.9869i	0.207949	+	1.04543i
$404$		0			0
$405$	20.2985	+	14.7734i	1.00864	+	0.734098i
$406$		0			0
$407$	−17.1637	−	17.1637i	−0.850771	−	0.850771i
$408$		0			0
$409$			9.36133i			0.462888i	0.972848	+	0.231444i	$0.0743450\pi$
$409$			9.36133i			0.462888i	−0.972848	+	0.231444i	$0.925655\pi$
$410$		0			0
$411$	−3.63396	+	0.722840i	−0.179250	+	0.0356551i
$412$		0			0
$413$	28.2838	−	5.62600i	1.39175	−	0.276837i
$414$		0			0
$415$	9.53064	+	15.5816i	0.467841	+	0.764870i
$416$		0			0
$417$	4.81723	−	11.6298i	0.235901	−	0.569515i
$418$		0			0
$419$	−6.29873	−	1.25289i	−0.307713	−	0.0612079i	0.0388184	−	0.999246i	$-0.487641\pi$
$419$	−6.29873	−	1.25289i	−0.307713	−	0.0612079i	−0.346531	+	0.938038i	$0.612641\pi$
$420$		0			0
$421$	−6.28214	+	6.28214i	−0.306173	+	0.306173i	−0.843423	−	0.537250i	$-0.819463\pi$
$421$	−6.28214	+	6.28214i	−0.306173	+	0.306173i	0.537250	+	0.843423i	$0.319463\pi$
$422$		0			0
$423$	4.21044	−	1.74402i	0.204719	−	0.0847972i
$424$		0			0
$425$	−2.13720	+	20.5044i	−0.103670	+	0.994612i
$426$		0			0
$427$	−27.5514	+	11.4121i	−1.33330	+	0.552272i
$428$		0			0
$429$	14.5580	−	14.5580i	0.702869	−	0.702869i
$430$		0			0
$431$	15.9001	+	3.16274i	0.765883	+	0.152344i	0.562547	−	0.826765i	$-0.309822\pi$
$431$	15.9001	+	3.16274i	0.765883	+	0.152344i	0.203336	+	0.979109i	$0.434822\pi$
$432$		0			0
$433$	−5.42127	+	13.0881i	−0.260530	+	0.628974i	−0.998971	−	0.0453430i	$-0.985562\pi$
$433$	−5.42127	+	13.0881i	−0.260530	+	0.628974i	0.738442	+	0.674317i	$0.235562\pi$
$434$		0			0
$435$	20.8056	+	34.0150i	0.997554	+	1.63089i
$436$		0			0
$437$	4.60174	−	0.915344i	0.220131	−	0.0437868i
$438$		0			0
$439$	−18.9806	+	3.77549i	−0.905897	+	0.180194i	−0.625988	−	0.779833i	$-0.715304\pi$
$439$	−18.9806	+	3.77549i	−0.905897	+	0.180194i	−0.279909	+	0.960027i	$0.590304\pi$
$440$		0			0
$441$			9.46620i			0.450771i
$442$		0			0
$443$	21.0038	+	21.0038i	0.997920	+	0.997920i	0.999998	−	0.00207769i	$-0.000661348\pi$
$443$	21.0038	+	21.0038i	0.997920	+	0.997920i	−0.00207769	+	0.999998i	$0.500661\pi$
$444$		0			0
$445$	29.7836	+	21.6768i	1.41188	+	1.02758i
$446$		0			0
$447$	−8.55090	−	42.9883i	−0.404444	−	2.03327i
$448$		0			0
$449$	6.79732	−	4.54183i	0.320786	−	0.214342i	−0.384743	−	0.923024i	$-0.625710\pi$
$449$	6.79732	−	4.54183i	0.320786	−	0.214342i	0.705528	+	0.708682i	$0.250710\pi$
$450$		0			0
$451$	−25.7503	+	10.6661i	−1.21253	+	0.502248i
$452$		0			0
$453$	19.8744	−	13.2796i	0.933780	−	0.623932i
$454$		0			0
$455$	1.02030	−	25.4308i	0.0478325	−	1.19222i
$456$		0			0
$457$	0.0253079	+	0.0610986i	0.00118385	+	0.00285807i	0.924470	−	0.381254i	$-0.124508\pi$
$457$	0.0253079	+	0.0610986i	0.00118385	+	0.00285807i	−0.923287	+	0.384112i	$0.874508\pi$
$458$		0			0
$459$	−9.81912	−	6.90240i	−0.458317	−	0.322176i
$460$		0			0
$461$	30.9050	+	12.8013i	1.43939	+	0.596215i	0.959650	−	0.281197i	$-0.0907313\pi$
$461$	30.9050	+	12.8013i	1.43939	+	0.596215i	0.479739	+	0.877411i	$0.340731\pi$
$462$		0			0
$463$			9.16247i			0.425816i	0.977072	+	0.212908i	$0.0682935\pi$
$463$			9.16247i			0.425816i	−0.977072	+	0.212908i	$0.931707\pi$
$464$		0			0
$465$	31.4514	+	7.57841i	1.45852	+	0.351440i
$466$		0			0
$467$	−31.6094	−	13.0930i	−1.46271	−	0.605874i	−0.497525	−	0.867450i	$-0.665758\pi$
$467$	−31.6094	−	13.0930i	−1.46271	−	0.605874i	−0.965183	+	0.261576i	$0.915758\pi$
$468$		0			0
$469$	−10.4849	−	15.6917i	−0.484146	−	0.724576i
$470$		0			0
$471$	−22.0163	−	14.7108i	−1.01446	−	0.677839i
$472$		0			0
$473$	−2.40714	+	3.60255i	−0.110681	+	0.165645i
$474$		0			0
$475$	0.595036	−	7.40364i	0.0273021	−	0.339702i
$476$		0			0
$477$	−8.46276	+	8.46276i	−0.387483	+	0.387483i
$478$		0			0
$479$	−5.82737	−	29.2962i	−0.266259	−	1.33858i	−0.850063	−	0.526681i	$-0.823436\pi$
$479$	−5.82737	−	29.2962i	−0.266259	−	1.33858i	0.583804	−	0.811895i	$-0.301564\pi$
$480$		0			0
$481$	14.3668	−	21.5015i	0.655071	−	0.980383i
$482$		0			0
$483$	4.74211	−	23.8402i	0.215773	−	1.08477i
$484$		0			0
$485$	8.71614	+	23.6866i	0.395779	+	1.07555i
$486$		0			0
$487$	10.6099	+	15.8788i	0.480779	+	0.719537i	0.989995	−	0.141102i	$-0.0450644\pi$
$487$	10.6099	+	15.8788i	0.480779	+	0.719537i	−0.509216	+	0.860639i	$0.670064\pi$
$488$		0			0
$489$	5.52353	+	5.52353i	0.249783	+	0.249783i
$490$		0			0
$491$	−3.23201	+	7.80276i	−0.145859	+	0.352134i	−0.979877	−	0.199603i	$-0.936035\pi$
$491$	−3.23201	+	7.80276i	−0.145859	+	0.352134i	0.834018	+	0.551737i	$0.186035\pi$
$492$		0			0
$493$	−18.2664	−	28.7894i	−0.822678	−	1.29661i
$494$		0			0
$495$	−3.81439	−	10.3658i	−0.171444	−	0.465909i
$496$		0			0
$497$	4.99719			0.224154
$498$		0			0
$499$	−1.09321	+	5.49594i	−0.0489388	+	0.246032i	−0.997509	−	0.0705337i	$-0.977530\pi$
$499$	−1.09321	+	5.49594i	−0.0489388	+	0.246032i	0.948571	+	0.316566i	$0.102530\pi$
$500$		0			0
$501$	−14.7618	−	35.6382i	−0.659510	−	1.59220i
$502$		0			0
$503$	−29.0180	−	5.77203i	−1.29385	−	0.257362i	−0.500290	−	0.865858i	$-0.666773\pi$
$503$	−29.0180	−	5.77203i	−1.29385	−	0.257362i	−0.793557	+	0.608496i	$0.791773\pi$
$504$		0			0
$505$	−37.5094	+	5.90902i	−1.66915	+	0.262948i
$506$		0			0
$507$	−5.07141	−	3.38861i	−0.225229	−	0.150493i
$508$		0			0
$509$	−31.9241			−1.41501			−0.707506	−	0.706708i	$-0.750180\pi$
$509$	−31.9241			−1.41501			−0.707506	+	0.706708i	$0.750180\pi$
$510$		0			0
$511$	11.5079			0.509080
$512$		0			0
$513$	3.59554	+	2.40246i	0.158747	+	0.106071i
$514$		0			0
$515$	−6.77918	+	9.31449i	−0.298726	+	0.410445i
$516$		0			0
$517$	8.10929	+	1.61304i	0.356646	+	0.0709413i
$518$		0			0
$519$	16.6688	+	40.2421i	0.731680	+	1.76643i
$520$		0			0
$521$	4.13347	−	20.7803i	0.181090	−	0.910403i	−0.778208	−	0.628007i	$-0.783871\pi$
$521$	4.13347	−	20.7803i	0.181090	−	0.910403i	0.959298	−	0.282396i	$-0.0911292\pi$
$522$		0			0
$523$	15.7160			0.687211			0.343605	−	0.939114i	$-0.388352\pi$
$523$	15.7160			0.687211			0.343605	+	0.939114i	$0.388352\pi$
$524$		0			0
$525$	−34.2566	−	17.5262i	−1.49508	−	0.764907i
$526$		0			0
$527$	−26.9966	−	6.03717i	−1.17599	−	0.262983i
$528$		0			0
$529$	4.98413	−	12.0327i	0.216701	−	0.523163i
$530$		0			0
$531$	9.42792	+	9.42792i	0.409137	+	0.409137i
$532$		0			0
$533$	−16.4969	−	24.6894i	−0.714561	−	1.06942i
$534$		0			0
$535$	−2.02141	+	0.743835i	−0.0873934	+	0.0321588i
$536$		0			0
$537$	−10.6229	+	53.4050i	−0.458412	+	2.30459i
$538$		0			0
$539$	−9.54138	+	14.2797i	−0.410976	+	0.615070i
$540$		0			0
$541$	4.63140	+	23.2836i	0.199119	+	1.00104i	0.943016	+	0.332746i	$0.107975\pi$
$541$	4.63140	+	23.2836i	0.199119	+	1.00104i	−0.743897	+	0.668294i	$0.767025\pi$
$542$		0			0
$543$	21.6831	−	21.6831i	0.930510	−	0.930510i
$544$		0			0
$545$	−4.41640	−	4.78559i	−0.189178	−	0.204992i
$546$		0			0
$547$	−2.38634	+	3.57141i	−0.102032	+	0.152702i	−0.878973	−	0.476872i	$-0.841771\pi$
$547$	−2.38634	+	3.57141i	−0.102032	+	0.152702i	0.776940	+	0.629574i	$0.216771\pi$
$548$		0			0
$549$	−11.4641	−	7.66009i	−0.489277	−	0.326925i
$550$		0			0
$551$	6.82468	+	10.2139i	0.290741	+	0.435125i
$552$		0			0
$553$	−53.2406	−	22.0530i	−2.26402	−	0.937788i
$554$		0			0
$555$	−20.4005	−	33.3526i	−0.865951	−	1.41574i
$556$		0			0
$557$			13.8976i			0.588861i	0.955673	+	0.294430i	$0.0951299\pi$
$557$			13.8976i			0.588861i	−0.955673	+	0.294430i	$0.904870\pi$
$558$		0			0
$559$	−4.26457	−	1.76644i	−0.180372	−	0.0747126i
$560$		0			0
$561$	9.60111	+	24.8244i	0.405359	+	1.04809i
$562$		0			0
$563$	−8.70372	−	21.0126i	−0.366818	−	0.885577i	−0.994268	−	0.106920i	$-0.965901\pi$
$563$	−8.70372	−	21.0126i	−0.366818	−	0.885577i	0.627450	−	0.778657i	$-0.284099\pi$
$564$		0			0
$565$	−0.485128	−	0.525683i	−0.0204095	−	0.0221156i
$566$		0			0
$567$	33.3166	−	22.2614i	1.39917	−	0.934892i
$568$		0			0
$569$	−26.9528	+	11.1642i	−1.12992	+	0.468029i	−0.867754	−	0.496994i	$-0.834437\pi$
$569$	−26.9528	+	11.1642i	−1.12992	+	0.468029i	−0.262167	+	0.965023i	$0.584437\pi$
$570$		0			0
$571$	27.8405	−	18.6024i	1.16509	−	0.778488i	0.186127	−	0.982526i	$-0.440406\pi$
$571$	27.8405	−	18.6024i	1.16509	−	0.778488i	0.978963	+	0.204037i	$0.0654064\pi$
$572$		0			0
$573$	−9.89735	−	49.7573i	−0.413468	−	2.07864i
$574$		0			0
$575$	12.3857	+	9.79747i	0.516520	+	0.408583i
$576$		0			0
$577$	−23.5100	−	23.5100i	−0.978732	−	0.978732i	0.0210461	−	0.999779i	$-0.493300\pi$
$577$	−23.5100	−	23.5100i	−0.978732	−	0.978732i	−0.999779	+	0.0210461i	$0.993300\pi$
$578$		0			0
$579$		−	3.69548i		−	0.153579i
$580$		0			0
$581$	28.5921	−	5.68732i	1.18620	−	0.235950i
$582$		0			0
$583$	−21.2960	+	4.23603i	−0.881990	+	0.175439i
$584$		0			0
$585$	10.0384	−	6.14008i	0.415036	−	0.253861i
$586$		0			0
$587$	−3.01800	+	7.28609i	−0.124566	+	0.300729i	−0.973844	−	0.227217i	$-0.927037\pi$
$587$	−3.01800	+	7.28609i	−0.124566	+	0.300729i	0.849278	+	0.527945i	$0.177037\pi$
$588$		0			0
$589$	9.77526	+	1.94442i	0.402783	+	0.0801185i
$590$		0			0
$591$	11.4679	−	11.4679i	0.471728	−	0.471728i
$592$		0			0
$593$	−11.9035	+	4.93059i	−0.488819	+	0.202475i	−0.613459	−	0.789727i	$-0.710222\pi$
$593$	−11.9035	+	4.93059i	−0.488819	+	0.202475i	0.124640	+	0.992202i	$0.460222\pi$
$594$		0			0
$595$	29.5348	+	14.5028i	1.21081	+	0.594558i
$596$		0			0
$597$	19.2405	−	7.96966i	0.787459	−	0.326176i
$598$		0			0
$599$	13.5320	−	13.5320i	0.552902	−	0.552902i	−0.374375	−	0.927277i	$-0.622143\pi$
$599$	13.5320	−	13.5320i	0.552902	−	0.552902i	0.927277	+	0.374375i	$0.122143\pi$
$600$		0			0
$601$	−37.8568	−	7.53019i	−1.54421	−	0.307163i	−0.651802	−	0.758389i	$-0.725987\pi$
$601$	−37.8568	−	7.53019i	−1.54421	−	0.307163i	−0.892409	+	0.451227i	$0.850987\pi$
$602$		0			0
$603$	3.33911	−	8.06133i	0.135979	−	0.328283i
$604$		0			0
$605$	−1.06765	+	4.43090i	−0.0434062	+	0.180142i
$606$		0			0
$607$	−46.7505	+	9.29925i	−1.89754	+	0.377445i	−0.998209	−	0.0598176i	$-0.980948\pi$
$607$	−46.7505	+	9.29925i	−1.89754	+	0.377445i	−0.899334	+	0.437262i	$0.855948\pi$
$608$		0			0
$609$	62.4173	−	12.4156i	2.52928	−	0.503104i
$610$		0			0
$611$			8.80858i			0.356357i
$612$		0			0
$613$	−14.3208	−	14.3208i	−0.578410	−	0.578410i	0.356055	−	0.934465i	$-0.384121\pi$
$613$	−14.3208	−	14.3208i	−0.578410	−	0.578410i	−0.934465	+	0.356055i	$0.884121\pi$
$614$		0			0
$615$	−44.3468	+	6.98615i	−1.78824	+	0.281709i
$616$		0			0
$617$	6.27158	+	31.5294i	0.252484	+	1.26932i	0.874001	+	0.485924i	$0.161517\pi$
$617$	6.27158	+	31.5294i	0.252484	+	1.26932i	−0.621517	+	0.783401i	$0.713483\pi$
$618$		0			0
$619$	25.3671	−	16.9498i	1.01959	−	0.681269i	0.0709038	−	0.997483i	$-0.477412\pi$
$619$	25.3671	−	16.9498i	1.01959	−	0.681269i	0.948688	+	0.316214i	$0.102412\pi$
$620$		0			0
$621$	−8.49444	+	3.51851i	−0.340870	+	0.141193i
$622$		0			0
$623$	48.8850	−	32.6639i	1.95853	−	1.30865i
$624$		0			0
$625$	20.2741	−	14.6275i	0.810962	−	0.585098i
$626$		0			0
$627$	−3.66976	−	8.85959i	−0.146556	−	0.353818i
$628$		0			0
$629$	17.9107	+	28.2287i	0.714146	+	1.12555i
$630$		0			0
$631$	32.5727	+	13.4921i	1.29670	+	0.537111i	0.920976	−	0.389620i	$-0.127394\pi$
$631$	32.5727	+	13.4921i	1.29670	+	0.537111i	0.375725	+	0.926731i	$0.377394\pi$
$632$		0			0
$633$		−	14.8418i		−	0.589909i
$634$		0			0
$635$	2.14501	−	8.90210i	0.0851223	−	0.353269i
$636$		0			0
$637$	−16.9038	−	7.00179i	−0.669754	−	0.277421i
$638$		0			0
$639$	1.28361	+	1.92105i	0.0507787	+	0.0759957i
$640$		0			0
$641$	17.4144	+	11.6359i	0.687827	+	0.459592i	0.849732	−	0.527215i	$-0.176764\pi$
$641$	17.4144	+	11.6359i	0.687827	+	0.459592i	−0.161905	+	0.986806i	$0.551764\pi$
$642$		0			0
$643$	17.2544	−	25.8230i	0.680445	−	1.01836i	−0.317104	−	0.948391i	$-0.602710\pi$
$643$	17.2544	−	25.8230i	0.680445	−	1.01836i	0.997549	−	0.0699674i	$-0.0222895\pi$
$644$		0			0
$645$	−5.12862	+	4.73297i	−0.201939	+	0.186361i
$646$		0			0
$647$	2.86127	−	2.86127i	0.112488	−	0.112488i	−0.648622	−	0.761111i	$-0.724654\pi$
$647$	2.86127	−	2.86127i	0.112488	−	0.112488i	0.761111	+	0.648622i	$0.224654\pi$
$648$		0			0
$649$	4.71915	+	23.7248i	0.185243	+	0.931278i
$650$		0			0
$651$	28.6867	−	42.9327i	1.12432	−	1.68267i
$652$		0			0
$653$	−3.30242	+	16.6024i	−0.129234	+	0.649702i	0.860808	+	0.508929i	$0.169959\pi$
$653$	−3.30242	+	16.6024i	−0.129234	+	0.649702i	−0.990042	+	0.140772i	$0.955041\pi$
$654$		0			0
$655$	16.5658	−	35.8557i	0.647278	−	1.40100i
$656$		0			0
$657$	2.95599	+	4.42395i	0.115324	+	0.172595i
$658$		0			0
$659$	−10.2584	−	10.2584i	−0.399609	−	0.399609i	0.478486	−	0.878095i	$-0.341186\pi$
$659$	−10.2584	−	10.2584i	−0.399609	−	0.399609i	−0.878095	+	0.478486i	$0.841186\pi$
$660$		0			0
$661$	−4.25104	+	10.2629i	−0.165346	+	0.399181i	−0.984736	−	0.174056i	$-0.944313\pi$
$661$	−4.25104	+	10.2629i	−0.165346	+	0.399181i	0.819389	+	0.573237i	$0.194313\pi$
$662$		0			0
$663$	−23.9433	+	15.1917i	−0.929881	+	0.589995i
$664$		0			0
$665$	−10.7616	−	4.97201i	−0.417318	−	0.192806i
$666$		0			0
$667$	−26.1183			−1.01130
$668$		0			0
$669$	−8.94801	+	44.9847i	−0.345950	+	1.73921i
$670$		0			0
$671$	−9.57263	−	23.1104i	−0.369547	−	0.892166i
$672$		0			0
$673$	21.2074	+	4.21841i	0.817484	+	0.162608i	0.586083	−	0.810251i	$-0.300669\pi$
$673$	21.2074	+	4.21841i	0.817484	+	0.162608i	0.231401	+	0.972858i	$0.425669\pi$
$674$		0			0
$675$	1.68679	+	14.4570i	0.0649246	+	0.556450i
$676$		0			0
$677$	−6.68370	−	4.46590i	−0.256875	−	0.171639i	0.420464	−	0.907309i	$-0.361867\pi$
$677$	−6.68370	−	4.46590i	−0.256875	−	0.171639i	−0.677340	+	0.735670i	$0.736867\pi$
$678$		0			0
$679$	40.2833			1.54593
$680$		0			0
$681$	35.9586			1.37794
$682$		0			0
$683$	−17.4176	−	11.6381i	−0.666467	−	0.445319i	0.175767	−	0.984432i	$-0.443760\pi$
$683$	−17.4176	−	11.6381i	−0.666467	−	0.445319i	−0.842233	+	0.539113i	$0.818760\pi$
$684$		0			0
$685$	−3.10640	−	2.26087i	−0.118690	−	0.0863835i
$686$		0			0
$687$	−2.89589	−	0.576029i	−0.110485	−	0.0219769i
$688$		0			0
$689$	−8.85239	−	21.3716i	−0.337249	−	0.814192i
$690$		0			0
$691$	−7.00516	+	35.2173i	−0.266489	+	1.33973i	0.583150	+	0.812364i	$0.301820\pi$
$691$	−7.00516	+	35.2173i	−0.266489	+	1.33973i	−0.849639	+	0.527365i	$0.823180\pi$
$692$		0			0
$693$	−17.6290			−0.669669
$694$		0			0
$695$	12.2501	−	4.50775i	0.464671	−	0.170989i
$696$		0			0
$697$	37.8170	−	6.59639i	1.43242	−	0.249856i
$698$		0			0
$699$	−10.9434	+	26.4198i	−0.413919	+	0.999289i
$700$		0			0
$701$	−28.5896	−	28.5896i	−1.07981	−	1.07981i	−0.996526	−	0.0832873i	$-0.973458\pi$
$701$	−28.5896	−	28.5896i	−1.07981	−	1.07981i	−0.0832873	−	0.996526i	$-0.526542\pi$
$702$		0			0
$703$	−6.69177	−	10.0149i	−0.252385	−	0.377721i
$704$		0			0
$705$	12.0897	+	5.58559i	0.455324	+	0.210365i
$706$		0			0
$707$	−11.8235	+	59.4407i	−0.444668	+	2.23550i
$708$		0			0
$709$	−2.69657	+	4.03571i	−0.101272	+	0.151564i	−0.878645	−	0.477476i	$-0.841552\pi$
$709$	−2.69657	+	4.03571i	−0.101272	+	0.151564i	0.777373	+	0.629040i	$0.216552\pi$
$710$		0			0
$711$	−5.19793	−	26.1318i	−0.194938	−	0.980018i
$712$		0			0
$713$	−14.9845	+	14.9845i	−0.561173	+	0.561173i
$714$		0			0
$715$	21.3317	+	0.855841i	0.797759	+	0.0320066i
$716$		0			0
$717$	3.28624	−	4.91821i	0.122727	−	0.183674i
$718$		0			0
$719$	33.2804	+	22.2373i	1.24115	+	0.829311i	0.990331	−	0.138723i	$-0.0442999\pi$
$719$	33.2804	+	22.2373i	1.24115	+	0.829311i	0.250820	+	0.968034i	$0.419300\pi$
$720$		0			0
$721$	10.2152	+	15.2882i	0.380436	+	0.569362i
$722$		0			0
$723$	−41.1953	−	17.0636i	−1.53207	−	0.634604i
$724$		0			0
$725$	−11.2891	+	39.7756i	−0.419268	+	1.47723i
$726$		0			0
$727$		−	21.2943i		−	0.789761i	−0.918732	−	0.394881i	$-0.870786\pi$
$727$		−	21.2943i		−	0.789761i	0.918732	−	0.394881i	$-0.129214\pi$
$728$		0			0
$729$	−0.282656	−	0.117080i	−0.0104687	−	0.00433629i
$730$		0			0
$731$	4.31829	−	4.11865i	0.159718	−	0.152334i
$732$		0			0
$733$	10.6854	+	25.7969i	0.394675	+	0.952829i	0.988907	+	0.148536i	$0.0474560\pi$
$733$	10.6854	+	25.7969i	0.394675	+	0.952829i	−0.594232	+	0.804293i	$0.702544\pi$
$734$		0			0
$735$	−20.3287	+	18.7604i	−0.749836	+	0.691989i
$736$		0			0
$737$	13.1624	−	8.79483i	0.484843	−	0.323962i
$738$		0			0
$739$	−19.2440	+	7.97111i	−0.707901	+	0.293222i	−0.707436	−	0.706778i	$-0.750148\pi$
$739$	−19.2440	+	7.97111i	−0.707901	+	0.293222i	−0.000465157		1.00000i	$0.500148\pi$
$740$		0			0
$741$	8.49458	−	5.67590i	0.312056	−	0.208509i
$742$		0			0
$743$	1.76528	+	8.87467i	0.0647619	+	0.325580i	0.999562	−	0.0295943i	$-0.00942152\pi$
$743$	1.76528	+	8.87467i	0.0647619	+	0.325580i	−0.934800	+	0.355174i	$0.884422\pi$
$744$		0			0
$745$	26.7452	−	36.7475i	0.979868	−	1.34632i
$746$		0			0
$747$	9.53069	+	9.53069i	0.348710	+	0.348710i
$748$		0			0
$749$			3.43778i			0.125614i
$750$		0			0
$751$	−3.50805	+	0.697795i	−0.128011	+	0.0254629i	−0.258680	−	0.965963i	$-0.583287\pi$
$751$	−3.50805	+	0.697795i	−0.128011	+	0.0254629i	0.130669	+	0.991426i	$0.458287\pi$
$752$		0			0
$753$	17.8634	−	3.55326i	0.650979	−	0.129488i
$754$		0			0
$755$	24.0962	+	5.80612i	0.876950	+	0.211306i
$756$		0			0
$757$	16.0287	−	38.6967i	0.582573	−	1.40645i	−0.307900	−	0.951419i	$-0.599626\pi$
$757$	16.0287	−	38.6967i	0.582573	−	1.40645i	0.890473	−	0.455036i	$-0.150374\pi$
$758$		0			0
$759$	19.9974	+	3.97773i	0.725860	+	0.144383i
$760$		0			0
$761$	13.8766	−	13.8766i	0.503028	−	0.503028i	−0.409350	−	0.912378i	$-0.634244\pi$
$761$	13.8766	−	13.8766i	0.503028	−	0.503028i	0.912378	+	0.409350i	$0.134244\pi$
$762$		0			0
$763$	−9.60235	+	3.97743i	−0.347629	+	0.143992i
$764$		0			0
$765$	2.01120	+	15.0792i	0.0727149	+	0.545191i
$766$		0			0
$767$	−23.8090	+	9.86199i	−0.859692	+	0.356096i
$768$		0			0
$769$	31.1138	−	31.1138i	1.12199	−	1.12199i	0.130551	−	0.991442i	$-0.458325\pi$
$769$	31.1138	−	31.1138i	1.12199	−	1.12199i	0.991442	−	0.130551i	$-0.0416747\pi$
$770$		0			0
$771$	−31.3479	−	6.23548i	−1.12897	−	0.224565i
$772$		0			0
$773$	−4.80306	+	11.5956i	−0.172754	+	0.417065i	−0.986415	−	0.164275i	$-0.947471\pi$
$773$	−4.80306	+	11.5956i	−0.172754	+	0.417065i	0.813661	+	0.581340i	$0.197471\pi$
$774$		0			0
$775$	16.3431	+	29.2966i	0.587062	+	1.05236i
$776$		0			0
$777$	−61.2017	+	12.1738i	−2.19560	+	0.436732i
$778$		0			0
$779$	−13.5650	+	2.69824i	−0.486015	+	0.0966744i
$780$		0			0
$781$			4.19170i			0.149991i
$782$		0			0
$783$	−17.0216	−	17.0216i	−0.608301	−	0.608301i
$784$		0			0
$785$	−4.27274	−	27.1226i	−0.152501	−	0.968046i
$786$		0			0
$787$	−8.82347	−	44.3586i	−0.314523	−	1.58121i	−0.737676	−	0.675155i	$-0.764077\pi$
$787$	−8.82347	−	44.3586i	−0.314523	−	1.58121i	0.423154	−	0.906058i	$-0.360923\pi$
$788$		0			0
$789$	−42.5810	+	28.4517i	−1.51592	+	1.01291i
$790$		0			0
$791$	−1.05479	+	0.436909i	−0.0375040	+	0.0155347i
$792$		0			0
$793$	22.1582	−	14.8057i	0.786862	−	0.525764i
$794$		0			0
$795$	−34.9456	−	1.40204i	−1.23939	−	0.0497253i
$796$		0			0
$797$	11.2894	+	27.2550i	0.399891	+	0.965423i	0.987691	+	0.156417i	$0.0499943\pi$
$797$	11.2894	+	27.2550i	0.399891	+	0.965423i	−0.587800	+	0.809006i	$0.700006\pi$
$798$		0			0
$799$	−10.4149	−	4.60556i	−0.368451	−	0.162933i
$800$		0			0
$801$	25.1137	+	10.4025i	0.887350	+	0.367553i
$802$		0			0
$803$			9.65297i			0.340646i
$804$		0			0
$805$	21.5020	−	13.1519i	0.757844	−	0.463544i
$806$		0			0
$807$	−12.7509	−	5.28158i	−0.448851	−	0.185920i
$808$		0			0
$809$	−5.88904	−	8.81358i	−0.207048	−	0.309869i	0.713383	−	0.700774i	$-0.247162\pi$
$809$	−5.88904	−	8.81358i	−0.207048	−	0.309869i	−0.920431	+	0.390905i	$0.872162\pi$
$810$		0			0
$811$	−43.8676	−	29.3114i	−1.54040	−	1.02926i	−0.979515	−	0.201369i	$-0.935461\pi$
$811$	−43.8676	−	29.3114i	−1.54040	−	1.02926i	−0.560885	−	0.827894i	$-0.689539\pi$
$812$		0			0
$813$	−1.74620	+	2.61338i	−0.0612421	+	0.0916552i
$814$		0			0
$815$	−0.324718	+	8.09354i	−0.0113744	+	0.283504i
$816$		0			0
$817$	−1.52029	+	1.52029i	−0.0531881	+	0.0531881i
$818$		0			0
$819$	−3.66403	−	18.4203i	−0.128032	−	0.643659i
$820$		0			0
$821$	−10.1260	+	15.1546i	−0.353399	+	0.528900i	−0.964994	−	0.262272i	$-0.915528\pi$
$821$	−10.1260	+	15.1546i	−0.353399	+	0.528900i	0.611595	+	0.791171i	$0.290528\pi$
$822$		0			0
$823$	5.47160	−	27.5076i	0.190728	−	0.958854i	−0.760258	−	0.649621i	$-0.774928\pi$
$823$	5.47160	−	27.5076i	0.190728	−	0.958854i	0.950986	−	0.309233i	$-0.100072\pi$
$824$		0			0
$825$	14.7012	−	28.7348i	0.511830	−	1.00042i
$826$		0			0
$827$	23.3548	+	34.9529i	0.812125	+	1.21543i	0.973534	+	0.228543i	$0.0733962\pi$
$827$	23.3548	+	34.9529i	0.812125	+	1.21543i	−0.161409	+	0.986888i	$0.551604\pi$
$828$		0			0
$829$	29.9305	+	29.9305i	1.03953	+	1.03953i	0.999186	+	0.0403449i	$0.0128457\pi$
$829$	29.9305	+	29.9305i	1.03953	+	1.03953i	0.0403449	+	0.999186i	$0.487154\pi$
$830$		0			0
$831$	14.6629	−	35.3993i	0.508650	−	1.22799i
$832$		0			0
$833$	17.1167	−	16.3254i	0.593060	−	0.565643i
$834$		0			0
$835$	16.7764	−	36.3115i	0.580570	−	1.25661i
$836$		0			0
$837$	−19.5311			−0.675092
$838$		0			0
$839$	−6.98750	+	35.1285i	−0.241235	+	1.21277i	0.650249	+	0.759721i	$0.274664\pi$
$839$	−6.98750	+	35.1285i	−0.241235	+	1.21277i	−0.891485	+	0.453051i	$0.850336\pi$
$840$		0			0
$841$	−15.0707	−	36.3840i	−0.519680	−	1.25462i
$842$		0			0
$843$	−23.4686	−	4.66819i	−0.808301	−	0.160781i
$844$		0			0
$845$	−0.984216	−	6.24762i	−0.0338580	−	0.214925i
$846$		0			0
$847$	6.04840	+	4.04141i	0.207825	+	0.138864i
$848$		0			0
$849$	−38.7532			−1.33001
$850$		0			0
$851$	25.6097			0.877888
$852$		0			0
$853$	−23.9402	−	15.9963i	−0.819697	−	0.547704i	0.0735388	−	0.997292i	$-0.476571\pi$
$853$	−23.9402	−	15.9963i	−0.819697	−	0.547704i	−0.893236	+	0.449588i	$0.851571\pi$
$854$		0			0
$855$	−0.852923	−	5.41420i	−0.0291694	−	0.185162i
$856$		0			0
$857$	−12.3923	−	2.46498i	−0.423313	−	0.0842022i	−0.0211631	−	0.999776i	$-0.506737\pi$
$857$	−12.3923	−	2.46498i	−0.423313	−	0.0842022i	−0.402150	+	0.915574i	$0.631737\pi$
$858$		0			0
$859$	−2.93187	−	7.07817i	−0.100034	−	0.241504i	0.865937	−	0.500153i	$-0.166723\pi$
$859$	−2.93187	−	7.07817i	−0.100034	−	0.241504i	−0.965971	+	0.258649i	$0.916723\pi$
$860$		0			0
$861$	−13.9787	+	70.2758i	−0.476394	+	2.39499i
$862$		0			0
$863$	24.1609			0.822445			0.411223	−	0.911535i	$-0.365102\pi$
$863$	24.1609			0.822445			0.411223	+	0.911535i	$0.365102\pi$
$864$		0			0
$865$	−18.9436	+	41.0024i	−0.644102	+	1.39412i
$866$		0			0
$867$	−5.44320	−	36.2524i	−0.184861	−	1.23120i
$868$		0			0
$869$	18.4983	−	44.6588i	0.627511	−	1.51495i
$870$		0			0
$871$	11.9253	+	11.9253i	0.404074	+	0.404074i
$872$		0			0
$873$	10.3474	+	15.4860i	0.350207	+	0.524121i
$874$		0			0
$875$	−10.7352	−	38.4300i	−0.362918	−	1.29917i
$876$		0			0
$877$	5.38016	−	27.0479i	0.181675	−	0.913342i	−0.777144	−	0.629323i	$-0.783332\pi$
$877$	5.38016	−	27.0479i	0.181675	−	0.913342i	0.958819	−	0.284019i	$-0.0916679\pi$
$878$		0			0
$879$	−11.5925	+	17.3494i	−0.391004	+	0.585180i
$880$		0			0
$881$	3.30989	+	16.6399i	0.111513	+	0.560614i	0.995633	+	0.0933539i	$0.0297588\pi$
$881$	3.30989	+	16.6399i	0.111513	+	0.560614i	−0.884120	+	0.467260i	$0.845241\pi$
$882$		0			0
$883$	−36.7432	+	36.7432i	−1.23651	+	1.23651i	−0.275089	+	0.961419i	$0.588707\pi$
$883$	−36.7432	+	36.7432i	−1.23651	+	1.23651i	−0.961419	+	0.275089i	$0.911293\pi$
$884$		0			0
$885$	−1.56194	+	38.9311i	−0.0525042	+	1.30866i
$886$		0			0
$887$	−11.6953	+	17.5033i	−0.392690	+	0.587702i	−0.974158	−	0.225867i	$-0.927479\pi$
$887$	−11.6953	+	17.5033i	−0.392690	+	0.587702i	0.581468	+	0.813569i	$0.302479\pi$
$888$		0			0
$889$	−12.1518	−	8.11957i	−0.407558	−	0.272322i
$890$		0			0
$891$	18.6731	+	27.9463i	0.625574	+	0.936237i
$892$		0			0
$893$	3.79055	+	1.57010i	0.126846	+	0.0525412i
$894$		0			0
$895$	−48.1670	+	29.4619i	−1.61005	+	0.984802i
$896$		0			0
$897$			21.7219i			0.725272i
$898$		0			0
$899$	−51.2586	−	21.2320i	−1.70957	−	0.708127i
$900$		0			0
$901$	29.8972	+	0.707435i	0.996021	+	0.0235681i
$902$		0			0
$903$	4.26253	+	10.2907i	0.141848	+	0.342452i
$904$		0			0
$905$	31.7719	+	1.27471i	1.05613	+	0.0423728i
$906$		0			0
$907$	7.28057	−	4.86472i	0.241747	−	0.161530i	−0.428795	−	0.903402i	$-0.641062\pi$
$907$	7.28057	−	4.86472i	0.241747	−	0.161530i	0.670542	+	0.741872i	$0.266062\pi$
$908$		0			0
$909$	−25.8877	+	10.7230i	−0.858639	+	0.355660i
$910$		0			0
$911$	40.6501	−	27.1615i	1.34680	−	0.899902i	0.347512	−	0.937675i	$-0.387026\pi$
$911$	40.6501	−	27.1615i	1.34680	−	0.899902i	0.999286	+	0.0377733i	$0.0120265\pi$
$912$		0			0
$913$	4.77059	+	23.9834i	0.157883	+	0.793733i
$914$		0			0
$915$	−6.26993	−	39.8003i	−0.207277	−	1.31576i
$916$		0			0
$917$	−44.5761	−	44.5761i	−1.47203	−	1.47203i
$918$		0			0
$919$		−	40.5315i		−	1.33701i	−0.743707	−	0.668506i	$-0.766934\pi$
$919$		−	40.5315i		−	1.33701i	0.743707	−	0.668506i	$-0.233066\pi$
$920$		0			0
$921$	−32.9065	+	6.54552i	−1.08431	+	0.215682i
$922$		0			0
$923$	−4.37987	+	0.871209i	−0.144165	+	0.0286762i
$924$		0			0
$925$	11.0693	−	39.0010i	0.363956	−	1.28234i
$926$		0			0
$927$	−3.25325	+	7.85403i	−0.106851	+	0.257960i
$928$		0			0
$929$	46.4806	+	9.24556i	1.52498	+	0.303337i	0.885195	−	0.465219i	$-0.154025\pi$
$929$	46.4806	+	9.24556i	1.52498	+	0.303337i	0.639782	+	0.768556i	$0.279025\pi$
$930$		0			0
$931$	−6.02608	+	6.02608i	−0.197497	+	0.197497i
$932$		0			0
$933$	11.2793	−	4.67205i	0.369268	−	0.152956i
$934$		0			0
$935$	−12.1651	+	24.7741i	−0.397843	+	0.810200i
$936$		0			0
$937$	5.96345	−	2.47014i	0.194818	−	0.0806961i	−0.283142	−	0.959078i	$-0.591377\pi$
$937$	5.96345	−	2.47014i	0.194818	−	0.0806961i	0.477959	+	0.878382i	$0.341377\pi$
$938$		0			0
$939$	−48.8510	+	48.8510i	−1.59419	+	1.59419i
$940$		0			0
$941$	−54.0330	−	10.7478i	−1.76143	−	0.350370i	−0.794862	−	0.606790i	$-0.792457\pi$
$941$	−54.0330	−	10.7478i	−1.76143	−	0.350370i	−0.966565	+	0.256421i	$0.917457\pi$
$942$		0			0
$943$	11.2535	−	27.1682i	0.366463	−	0.884720i
$944$		0			0
$945$	22.5843	+	5.44182i	0.734666	+	0.177022i
$946$		0			0
$947$	15.6118	−	3.10538i	0.507316	−	0.100911i	0.0652053	−	0.997872i	$-0.479230\pi$
$947$	15.6118	−	3.10538i	0.507316	−	0.100911i	0.442111	+	0.896960i	$0.354230\pi$
$948$		0			0
$949$	−10.0863	+	2.00629i	−0.327415	+	0.0651270i
$950$		0			0
$951$			32.5937i			1.05692i
$952$		0			0
$953$	4.56692	+	4.56692i	0.147937	+	0.147937i	0.777196	−	0.629259i	$-0.216641\pi$
$953$	4.56692	+	4.56692i	0.147937	+	0.147937i	−0.629259	+	0.777196i	$0.716641\pi$
$954$		0			0
$955$	30.9566	−	42.5338i	1.00173	−	1.37636i
$956$		0			0
$957$	10.4143	+	52.3563i	0.336647	+	1.69244i
$958$		0			0
$959$	−5.09865	+	3.40681i	−0.164644	+	0.110012i
$960$		0			0
$961$	−12.9487	+	5.36351i	−0.417699	+	0.173016i
$962$		0			0
$963$	−1.32157	+	0.883048i	−0.0425872	+	0.0284558i
$964$		0			0
$965$	2.81609	−	2.59884i	0.0906530	−	0.0836595i
$966$		0			0
$967$	−2.88260	−	6.95922i	−0.0926982	−	0.223793i	0.870729	−	0.491763i	$-0.163647\pi$
$967$	−2.88260	−	6.95922i	−0.0926982	−	0.223793i	−0.963427	+	0.267970i	$0.913647\pi$
$968$		0			0
$969$	2.26954	+	13.0112i	0.0729081	+	0.417981i
$970$		0			0
$971$	−0.743896	−	0.308132i	−0.0238728	−	0.00988843i	0.370715	−	0.928747i	$-0.379113\pi$
$971$	−0.743896	−	0.308132i	−0.0238728	−	0.00988843i	−0.394588	+	0.918858i	$0.629113\pi$
$972$		0			0
$973$		−	20.8334i		−	0.667889i
$974$		0			0
$975$	33.0803	+	9.38885i	1.05942	+	0.300684i
$976$		0			0
$977$	−10.8565	−	4.49689i	−0.347329	−	0.143868i	0.202197	−	0.979345i	$-0.435192\pi$
$977$	−10.8565	−	4.49689i	−0.347329	−	0.143868i	−0.549526	+	0.835476i	$0.685192\pi$
$978$		0			0
$979$	27.3988	+	41.0052i	0.875670	+	1.31053i
$980$		0			0
$981$	−3.99555	−	2.66974i	−0.127568	−	0.0852382i
$982$		0			0
$983$	−27.0070	+	40.4189i	−0.861390	+	1.28916i	0.0945262	+	0.995522i	$0.469866\pi$
$983$	−27.0070	+	40.4189i	−0.861390	+	1.28916i	−0.955916	+	0.293639i	$0.905134\pi$
$984$		0			0
$985$	16.8038	+	0.674180i	0.535413	+	0.0214812i
$986$		0			0
$987$	15.0300	−	15.0300i	0.478410	−	0.478410i
$988$		0			0
$989$	−0.891822	−	4.48349i	−0.0283583	−	0.142567i
$990$		0			0
$991$	−20.6524	+	30.9084i	−0.656044	+	0.981839i	0.343052	+	0.939316i	$0.388539\pi$
$991$	−20.6524	+	30.9084i	−0.656044	+	0.981839i	−0.999096	+	0.0425222i	$0.986461\pi$
$992$		0			0
$993$	1.03847	−	5.22075i	0.0329549	−	0.165675i
$994$		0			0
$995$	19.6040	+	9.05727i	0.621487	+	0.287135i
$996$		0			0
$997$	29.9899	+	44.8830i	0.949789	+	1.42146i	0.906409	+	0.422400i	$0.138812\pi$
$997$	29.9899	+	44.8830i	0.949789	+	1.42146i	0.0433793	+	0.999059i	$0.486188\pi$
$998$		0			0
$999$	16.6901	+	16.6901i	0.528051	+	0.528051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cq.b.193.11	yes	112
5.2	odd	4		680.2.cg.b.57.11	✓	112
17.3	odd	16		680.2.cg.b.513.11	yes	112
85.37	even	16	inner	680.2.cq.b.377.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cg.b.57.11	✓	112	5.2	odd	4
680.2.cg.b.513.11	yes	112	17.3	odd	16
680.2.cq.b.193.11	yes	112	1.1	even	1	trivial
680.2.cq.b.377.11	yes	112	85.37	even	16	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cq (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79298 + 1.19803i) q^{3} +(0.347966 + 2.20883i) q^{5} +(3.50030 + 0.696254i) q^{7} +(0.631450 + 1.52445i) q^{9} +(-0.584025 + 2.93609i) q^{11} -3.18928 q^{13} +(-2.02235 + 4.37726i) q^{15} +(1.66751 - 3.77086i) q^{17} +(-0.568477 + 1.37243i) q^{19} +(5.44184 + 5.44184i) q^{21} +(-1.75474 - 2.62616i) q^{23} +(-4.75784 + 1.53720i) q^{25} +(0.567911 - 2.85508i) q^{27} +(4.59419 - 6.87569i) q^{29} +(-1.30893 - 6.58044i) q^{31} +(-4.56468 + 4.56468i) q^{33} +(-0.319916 + 7.97384i) q^{35} +(-4.50472 + 6.74179i) q^{37} +(-5.71832 - 3.82086i) q^{39} +(5.17262 + 7.74137i) q^{41} +(1.33716 + 0.553869i) q^{43} +(-3.14753 + 1.92522i) q^{45} -2.76193i q^{47} +(5.30020 + 2.19541i) q^{49} +(7.50743 - 4.76335i) q^{51} +(2.77567 + 6.70106i) q^{53} +(-6.68854 - 0.268349i) q^{55} +(-2.66348 + 1.77968i) q^{57} +(7.46530 - 3.09223i) q^{59} +(-6.94772 + 4.64232i) q^{61} +(1.14886 + 5.77570i) q^{63} +(-1.10976 - 7.04457i) q^{65} +(-3.73919 - 3.73919i) q^{67} -6.81089i q^{69} +(1.37331 - 0.273168i) q^{71} +(3.16256 - 0.629073i) q^{73} +(-10.3723 - 2.94388i) q^{75} +(-4.08853 + 9.87059i) q^{77} +(-15.8369 - 3.15015i) q^{79} +(7.93903 - 7.93903i) q^{81} +(7.54667 - 3.12593i) q^{83} +(8.90942 + 2.37111i) q^{85} +(16.4746 - 6.82400i) q^{87} +(11.6488 - 11.6488i) q^{89} +(-11.1635 - 2.22055i) q^{91} +(5.53669 - 13.3667i) q^{93} +(-3.22926 - 0.778110i) q^{95} +(11.0705 - 2.20206i) q^{97} +(-4.84472 + 0.963675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 24 q^{15} + 16 q^{25} - 24 q^{27} + 8 q^{29} + 16 q^{31} + 48 q^{33} - 32 q^{35} - 16 q^{41} - 16 q^{43} - 24 q^{45} + 80 q^{49} + 32 q^{51} - 24 q^{53} - 24 q^{55} + 48 q^{57} + 80 q^{59} - 24 q^{61}+ \cdots - 48 q^{99}+O(q^{100}) \) 112 * q - 24 * q^15 + 16 * q^25 - 24 * q^27 + 8 * q^29 + 16 * q^31 + 48 * q^33 - 32 * q^35 - 16 * q^41 - 16 * q^43 - 24 * q^45 + 80 * q^49 + 32 * q^51 - 24 * q^53 - 24 * q^55 + 48 * q^57 + 80 * q^59 - 24 * q^61 - 72 * q^63 + 32 * q^65 + 48 * q^67 - 40 * q^71 - 64 * q^73 + 32 * q^75 - 24 * q^77 - 40 * q^79 - 24 * q^83 - 32 * q^85 - 48 * q^87 + 16 * q^89 + 48 * q^93 + 168 * q^95 + 32 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more