LMFDB - Embedded newform 680.2.z.d.89.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(89,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.89"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.z (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [26,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.11
Character	$\chi$	$=$	680.89
Dual form			680.2.z.d.489.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68588 + 1.68588i) q^{3} +(2.22887 + 0.179214i) q^{5} +(-0.196476 + 0.196476i) q^{7} +2.68435i q^{9} +(-0.480221 - 0.480221i) q^{11} +5.44160i q^{13} +(3.45547 + 4.05974i) q^{15} +(-3.39647 + 2.33752i) q^{17} -2.29906i q^{19} -0.662468 q^{21} +(5.23411 - 5.23411i) q^{23} +(4.93576 + 0.798889i) q^{25} +(0.532143 - 0.532143i) q^{27} +(-1.54376 + 1.54376i) q^{29} +(-0.282886 + 0.282886i) q^{31} -1.61918i q^{33} +(-0.473131 + 0.402709i) q^{35} +(-5.09347 - 5.09347i) q^{37} +(-9.17386 + 9.17386i) q^{39} +(0.0550219 + 0.0550219i) q^{41} +6.98789 q^{43} +(-0.481072 + 5.98308i) q^{45} -3.42893i q^{47} +6.92279i q^{49} +(-9.66679 - 1.78524i) q^{51} -4.63380 q^{53} +(-0.984289 - 1.15641i) q^{55} +(3.87593 - 3.87593i) q^{57} -2.84666i q^{59} +(-10.3603 - 10.3603i) q^{61} +(-0.527410 - 0.527410i) q^{63} +(-0.975209 + 12.1286i) q^{65} +0.574878i q^{67} +17.6481 q^{69} +(2.98158 - 2.98158i) q^{71} +(10.8744 + 10.8744i) q^{73} +(6.97426 + 9.66791i) q^{75} +0.188703 q^{77} +(-9.61845 - 9.61845i) q^{79} +9.84731 q^{81} -15.1433 q^{83} +(-7.98921 + 4.60136i) q^{85} -5.20516 q^{87} +13.2264 q^{89} +(-1.06914 - 1.06914i) q^{91} -0.953820 q^{93} +(0.412023 - 5.12432i) q^{95} +(-3.25088 - 3.25088i) q^{97} +(1.28908 - 1.28908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{15} + 2 q^{17} - 12 q^{21} - 2 q^{23} + 10 q^{25} + 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} - 6 q^{37} + 8 q^{39} - 10 q^{41} + 32 q^{43} + 28 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 26 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^15 + 2 * q^17 - 12 * q^21 - 2 * q^23 + 10 * q^25 + 20 * q^27 + 10 * q^29 - 10 * q^31 + 22 * q^35 - 6 * q^37 + 8 * q^39 - 10 * q^41 + 32 * q^43 + 28 * q^45 - 6 * q^51 - 32 * q^53 - 26 * q^55 + 20 * q^57 + 6 * q^61 - 54 * q^63 + 24 * q^65 - 20 * q^69 - 30 * q^71 + 42 * q^73 - 78 * q^75 - 4 * q^77 + 14 * q^79 - 54 * q^81 - 16 * q^83 - 26 * q^85 + 8 * q^87 + 40 * q^89 + 24 * q^91 + 88 * q^93 + 44 * q^95 + 66 * q^97 - 22 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.68588	+	1.68588i	0.973341	+	0.973341i	0.999654	−	0.0263131i	$-0.00837669\pi$
$3$	1.68588	+	1.68588i	0.973341	+	0.973341i	−0.0263131	+	0.999654i	$0.508377\pi$
$4$		0			0
$5$	2.22887	+	0.179214i	0.996783	+	0.0801468i
$5$	2.22887	+	0.179214i	0.996783	+	0.0801468i
$6$		0			0
$7$	−0.196476	+	0.196476i	−0.0742609	+	0.0742609i	−0.743262	−	0.669001i	$-0.766722\pi$
$7$	−0.196476	+	0.196476i	−0.0742609	+	0.0742609i	0.669001	+	0.743262i	$0.266722\pi$
$8$		0			0
$9$			2.68435i			0.894784i
$10$		0			0
$11$	−0.480221	−	0.480221i	−0.144792	−	0.144792i	0.630995	−	0.775787i	$-0.282647\pi$
$11$	−0.480221	−	0.480221i	−0.144792	−	0.144792i	−0.775787	+	0.630995i	$0.782647\pi$
$12$		0			0
$13$			5.44160i			1.50923i	0.656169	+	0.754614i	$0.272176\pi$
$13$			5.44160i			1.50923i	−0.656169	+	0.754614i	$0.727824\pi$
$14$		0			0
$15$	3.45547	+	4.05974i	0.892199	+	1.04822i
$16$		0			0
$17$	−3.39647	+	2.33752i	−0.823764	+	0.566933i
$17$	−3.39647	+	2.33752i	−0.823764	+	0.566933i
$18$		0			0
$19$		−	2.29906i		−	0.527441i	−0.964599	−	0.263720i	$-0.915050\pi$
$19$		−	2.29906i		−	0.527441i	0.964599	−	0.263720i	$-0.0849496\pi$
$20$		0			0
$21$	−0.662468			−0.144562
$22$		0			0
$23$	5.23411	−	5.23411i	1.09139	−	1.09139i	0.0960064	−	0.995381i	$-0.469393\pi$
$23$	5.23411	−	5.23411i	1.09139	−	1.09139i	0.995381	−	0.0960064i	$-0.0306069\pi$
$24$		0			0
$25$	4.93576	+	0.798889i	0.987153	+	0.159778i
$26$		0			0
$27$	0.532143	−	0.532143i	0.102411	−	0.102411i
$28$		0			0
$29$	−1.54376	+	1.54376i	−0.286669	+	0.286669i	−0.835761	−	0.549093i	$-0.814973\pi$
$29$	−1.54376	+	1.54376i	−0.286669	+	0.286669i	0.549093	+	0.835761i	$0.314973\pi$
$30$		0			0
$31$	−0.282886	+	0.282886i	−0.0508077	+	0.0508077i	−0.732054	−	0.681246i	$-0.761438\pi$
$31$	−0.282886	+	0.282886i	−0.0508077	+	0.0508077i	0.681246	+	0.732054i	$0.261438\pi$
$32$		0			0
$33$		−	1.61918i		−	0.281864i
$34$		0			0
$35$	−0.473131	+	0.402709i	−0.0799738	+	0.0680702i
$36$		0			0
$37$	−5.09347	−	5.09347i	−0.837361	−	0.837361i	0.151150	−	0.988511i	$-0.451702\pi$
$37$	−5.09347	−	5.09347i	−0.837361	−	0.837361i	−0.988511	+	0.151150i	$0.951702\pi$
$38$		0			0
$39$	−9.17386	+	9.17386i	−1.46899	+	1.46899i
$40$		0			0
$41$	0.0550219	+	0.0550219i	0.00859298	+	0.00859298i	0.711390	−	0.702797i	$-0.248066\pi$
$41$	0.0550219	+	0.0550219i	0.00859298	+	0.00859298i	−0.702797	+	0.711390i	$0.748066\pi$
$42$		0			0
$43$	6.98789			1.06564			0.532821	−	0.846228i	$-0.321132\pi$
$43$	6.98789			1.06564			0.532821	+	0.846228i	$0.321132\pi$
$44$		0			0
$45$	−0.481072	+	5.98308i	−0.0717140	+	0.891906i
$46$		0			0
$47$		−	3.42893i		−	0.500160i	−0.968225	−	0.250080i	$-0.919543\pi$
$47$		−	3.42893i		−	0.500160i	0.968225	−	0.250080i	$-0.0804570\pi$
$48$		0			0
$49$			6.92279i			0.988971i
$50$		0			0
$51$	−9.66679	−	1.78524i	−1.35362	−	0.249984i
$52$		0			0
$53$	−4.63380			−0.636502			−0.318251	−	0.948007i	$-0.603095\pi$
$53$	−4.63380			−0.636502			−0.318251	+	0.948007i	$0.603095\pi$
$54$		0			0
$55$	−0.984289	−	1.15641i	−0.132722	−	0.155931i
$56$		0			0
$57$	3.87593	−	3.87593i	0.513379	−	0.513379i
$58$		0			0
$59$		−	2.84666i		−	0.370604i	−0.982682	−	0.185302i	$-0.940674\pi$
$59$		−	2.84666i		−	0.370604i	0.982682	−	0.185302i	$-0.0593263\pi$
$60$		0			0
$61$	−10.3603	−	10.3603i	−1.32650	−	1.32650i	−0.908405	−	0.418091i	$-0.862699\pi$
$61$	−10.3603	−	10.3603i	−1.32650	−	1.32650i	−0.418091	−	0.908405i	$-0.637301\pi$
$62$		0			0
$63$	−0.527410	−	0.527410i	−0.0664475	−	0.0664475i
$64$		0			0
$65$	−0.975209	+	12.1286i	−0.120960	+	1.50437i
$66$		0			0
$67$			0.574878i			0.0702326i	0.999383	+	0.0351163i	$0.0111802\pi$
$67$			0.574878i			0.0702326i	−0.999383	+	0.0351163i	$0.988820\pi$
$68$		0			0
$69$	17.6481			2.12458
$70$		0			0
$71$	2.98158	−	2.98158i	0.353848	−	0.353848i	−0.507691	−	0.861539i	$-0.669501\pi$
$71$	2.98158	−	2.98158i	0.353848	−	0.353848i	0.861539	+	0.507691i	$0.169501\pi$
$72$		0			0
$73$	10.8744	+	10.8744i	1.27275	+	1.27275i	0.944640	+	0.328107i	$0.106411\pi$
$73$	10.8744	+	10.8744i	1.27275	+	1.27275i	0.328107	+	0.944640i	$0.393589\pi$
$74$		0			0
$75$	6.97426	+	9.66791i	0.805318	+	1.11635i
$76$		0			0
$77$	0.188703			0.0215048
$78$		0			0
$79$	−9.61845	−	9.61845i	−1.08216	−	1.08216i	−0.996308	−	0.0858524i	$-0.972639\pi$
$79$	−9.61845	−	9.61845i	−1.08216	−	1.08216i	−0.0858524	−	0.996308i	$-0.527361\pi$
$80$		0			0
$81$	9.84731			1.09415
$82$		0			0
$83$	−15.1433			−1.66219			−0.831095	−	0.556130i	$-0.812286\pi$
$83$	−15.1433			−1.66219			−0.831095	+	0.556130i	$0.812286\pi$
$84$		0			0
$85$	−7.98921	+	4.60136i	−0.866552	+	0.499087i
$86$		0			0
$87$	−5.20516			−0.558052
$88$		0			0
$89$	13.2264			1.40199			0.700997	−	0.713164i	$-0.252739\pi$
$89$	13.2264			1.40199			0.700997	+	0.713164i	$0.252739\pi$
$90$		0			0
$91$	−1.06914	−	1.06914i	−0.112077	−	0.112077i
$92$		0			0
$93$	−0.953820			−0.0989065
$94$		0			0
$95$	0.412023	−	5.12432i	0.0422727	−	0.525744i
$96$		0			0
$97$	−3.25088	−	3.25088i	−0.330077	−	0.330077i	0.522539	−	0.852616i	$-0.324985\pi$
$97$	−3.25088	−	3.25088i	−0.330077	−	0.330077i	−0.852616	+	0.522539i	$0.824985\pi$
$98$		0			0
$99$	1.28908	−	1.28908i	0.129558	−	0.129558i
$100$		0			0
$101$	−5.20731			−0.518146			−0.259073	−	0.965858i	$-0.583417\pi$
$101$	−5.20731			−0.518146			−0.259073	+	0.965858i	$0.583417\pi$
$102$		0			0
$103$		−	0.662913i		−	0.0653187i	−0.999467	−	0.0326594i	$-0.989602\pi$
$103$		−	0.662913i		−	0.0653187i	0.999467	−	0.0326594i	$-0.0103976\pi$
$104$		0			0
$105$	−1.47656	−	0.118723i	−0.144097	−	0.0115862i
$106$		0			0
$107$	3.64288	+	3.64288i	0.352171	+	0.352171i	0.860917	−	0.508746i	$-0.169891\pi$
$107$	3.64288	+	3.64288i	0.352171	+	0.352171i	−0.508746	+	0.860917i	$0.669891\pi$
$108$		0			0
$109$	2.15718	+	2.15718i	0.206620	+	0.206620i	0.802829	−	0.596209i	$-0.203327\pi$
$109$	2.15718	+	2.15718i	0.206620	+	0.206620i	−0.596209	+	0.802829i	$0.703327\pi$
$110$		0			0
$111$		−	17.1739i		−	1.63007i
$112$		0			0
$113$	3.50766	−	3.50766i	0.329973	−	0.329973i	−0.522603	−	0.852576i	$-0.675039\pi$
$113$	3.50766	−	3.50766i	0.329973	−	0.329973i	0.852576	+	0.522603i	$0.175039\pi$
$114$		0			0
$115$	12.6042	−	10.7281i	1.17535	−	1.00041i
$116$		0			0
$117$	−14.6072			−1.35043
$118$		0			0
$119$	0.208057	−	1.12659i	0.0190725	−	0.103274i
$120$		0			0
$121$		−	10.5388i		−	0.958071i
$122$		0			0
$123$			0.185520i			0.0167278i
$124$		0			0
$125$	10.8580	+	2.66518i	0.971172	+	0.238381i
$126$		0			0
$127$	−8.34577			−0.740567			−0.370284	−	0.928919i	$-0.620739\pi$
$127$	−8.34577			−0.740567			−0.370284	+	0.928919i	$0.620739\pi$
$128$		0			0
$129$	11.7807	+	11.7807i	1.03723	+	1.03723i
$130$		0			0
$131$	6.17119	−	6.17119i	0.539179	−	0.539179i	−0.384109	−	0.923288i	$-0.625491\pi$
$131$	6.17119	−	6.17119i	0.539179	−	0.539179i	0.923288	+	0.384109i	$0.125491\pi$
$132$		0			0
$133$	0.451710	+	0.451710i	0.0391682	+	0.0391682i
$134$		0			0
$135$	1.28145	−	1.09071i	0.110289	−	0.0938736i
$136$		0			0
$137$		−	12.9981i		−	1.11050i	−0.831683	−	0.555251i	$-0.812622\pi$
$137$		−	12.9981i		−	1.11050i	0.831683	−	0.555251i	$-0.187378\pi$
$138$		0			0
$139$	0.352402	−	0.352402i	0.0298903	−	0.0298903i	−0.692004	−	0.721894i	$-0.743272\pi$
$139$	0.352402	−	0.352402i	0.0298903	−	0.0298903i	0.721894	+	0.692004i	$0.243272\pi$
$140$		0			0
$141$	5.78074	−	5.78074i	0.486827	−	0.486827i
$142$		0			0
$143$	2.61317	−	2.61317i	0.218524	−	0.218524i
$144$		0			0
$145$	−3.71750	+	3.16418i	−0.308722	+	0.262771i
$146$		0			0
$147$	−11.6710	+	11.6710i	−0.962605	+	0.962605i
$148$		0			0
$149$	2.46372			0.201836			0.100918	−	0.994895i	$-0.467822\pi$
$149$	2.46372			0.201836			0.100918	+	0.994895i	$0.467822\pi$
$150$		0			0
$151$		−	14.4751i		−	1.17797i	−0.808145	−	0.588983i	$-0.799528\pi$
$151$		−	14.4751i		−	1.17797i	0.808145	−	0.588983i	$-0.200472\pi$
$152$		0			0
$153$	−6.27474	−	9.11731i	−0.507282	−	0.737091i
$154$		0			0
$155$	−0.681213	+	0.579820i	−0.0547164	+	0.0465722i
$156$		0			0
$157$			11.0195i			0.879455i	0.898131	+	0.439727i	$0.144925\pi$
$157$			11.0195i			0.879455i	−0.898131	+	0.439727i	$0.855075\pi$
$158$		0			0
$159$	−7.81201	−	7.81201i	−0.619533	−	0.619533i
$160$		0			0
$161$			2.05675i			0.162095i
$162$		0			0
$163$	−9.83513	+	9.83513i	−0.770347	+	0.770347i	−0.978167	−	0.207820i	$-0.933363\pi$
$163$	−9.83513	+	9.83513i	−0.770347	+	0.770347i	0.207820	+	0.978167i	$0.433363\pi$
$164$		0			0
$165$	0.290180	−	3.60896i	0.0225905	−	0.280957i
$166$		0			0
$167$	11.6232	+	11.6232i	0.899431	+	0.899431i	0.995386	−	0.0959547i	$-0.0305904\pi$
$167$	11.6232	+	11.6232i	0.899431	+	0.899431i	−0.0959547	+	0.995386i	$0.530590\pi$
$168$		0			0
$169$	−16.6110			−1.27777
$170$		0			0
$171$	6.17149			0.471945
$172$		0			0
$173$	−1.77335	−	1.77335i	−0.134825	−	0.134825i	0.636473	−	0.771299i	$-0.280392\pi$
$173$	−1.77335	−	1.77335i	−0.134825	−	0.134825i	−0.771299	+	0.636473i	$0.780392\pi$
$174$		0			0
$175$	−1.12672	+	0.812796i	−0.0851721	+	0.0614416i
$176$		0			0
$177$	4.79912	−	4.79912i	0.360724	−	0.360724i
$178$		0			0
$179$		−	11.5262i		−	0.861508i	−0.902469	−	0.430754i	$-0.858248\pi$
$179$		−	11.5262i		−	0.861508i	0.902469	−	0.430754i	$-0.141752\pi$
$180$		0			0
$181$	−13.8451	−	13.8451i	−1.02910	−	1.02910i	−0.999564	−	0.0295352i	$-0.990597\pi$
$181$	−13.8451	−	13.8451i	−1.02910	−	1.02910i	−0.0295352	−	0.999564i	$-0.509403\pi$
$182$		0			0
$183$		−	34.9322i		−	2.58227i
$184$		0			0
$185$	−10.4399	−	12.2655i	−0.767555	−	0.901779i
$186$		0			0
$187$	2.75358	+	0.508526i	0.201362	+	0.0371871i
$188$		0			0
$189$			0.209107i			0.0152103i
$190$		0			0
$191$	−9.95000			−0.719957			−0.359978	−	0.932961i	$-0.617216\pi$
$191$	−9.95000			−0.719957			−0.359978	+	0.932961i	$0.617216\pi$
$192$		0			0
$193$	−10.2596	+	10.2596i	−0.738504	+	0.738504i	−0.972289	−	0.233784i	$-0.924889\pi$
$193$	−10.2596	+	10.2596i	−0.738504	+	0.738504i	0.233784	+	0.972289i	$0.424889\pi$
$194$		0			0
$195$	−22.0915	+	18.8033i	−1.58200	+	1.34653i
$196$		0			0
$197$	6.54514	−	6.54514i	0.466322	−	0.466322i	−0.434399	−	0.900721i	$-0.643039\pi$
$197$	6.54514	−	6.54514i	0.466322	−	0.466322i	0.900721	+	0.434399i	$0.143039\pi$
$198$		0			0
$199$	−8.10781	+	8.10781i	−0.574747	+	0.574747i	−0.933451	−	0.358704i	$-0.883219\pi$
$199$	−8.10781	+	8.10781i	−0.574747	+	0.574747i	0.358704	+	0.933451i	$0.383219\pi$
$200$		0			0
$201$	−0.969173	+	0.969173i	−0.0683602	+	0.0683602i
$202$		0			0
$203$		−	0.606622i		−	0.0425765i
$204$		0			0
$205$	0.112776	+	0.132498i	0.00787663	+	0.00925403i
$206$		0			0
$207$	14.0502	+	14.0502i	0.976556	+	0.976556i
$208$		0			0
$209$	−1.10406	+	1.10406i	−0.0763691	+	0.0763691i
$210$		0			0
$211$	12.2709	+	12.2709i	0.844762	+	0.844762i	0.989474	−	0.144711i	$-0.0462254\pi$
$211$	12.2709	+	12.2709i	0.844762	+	0.844762i	−0.144711	+	0.989474i	$0.546225\pi$
$212$		0			0
$213$	10.0531			0.688829
$214$		0			0
$215$	15.5751	+	1.25232i	1.06221	+	0.0854078i
$216$		0			0
$217$		−	0.111160i		−	0.00754606i
$218$		0			0
$219$			36.6656i			2.47763i
$220$		0			0
$221$	−12.7199	−	18.4822i	−0.855631	−	1.24325i
$222$		0			0
$223$	−29.5852			−1.98117			−0.990585	−	0.136902i	$-0.956285\pi$
$223$	−29.5852			−1.98117			−0.990585	+	0.136902i	$0.956285\pi$
$224$		0			0
$225$	−2.14450	+	13.2493i	−0.142967	+	0.883289i
$226$		0			0
$227$	14.8160	−	14.8160i	0.983373	−	0.983373i	−0.0164907	−	0.999864i	$-0.505249\pi$
$227$	14.8160	−	14.8160i	0.983373	−	0.983373i	0.999864	+	0.0164907i	$0.00524939\pi$
$228$		0			0
$229$		−	1.19218i		−	0.0787816i	−0.999224	−	0.0393908i	$-0.987458\pi$
$229$		−	1.19218i		−	0.0787816i	0.999224	−	0.0393908i	$-0.0125417\pi$
$230$		0			0
$231$	0.318131	+	0.318131i	0.0209315	+	0.0209315i
$232$		0			0
$233$	−7.58463	−	7.58463i	−0.496886	−	0.496886i	0.413581	−	0.910467i	$-0.364278\pi$
$233$	−7.58463	−	7.58463i	−0.496886	−	0.496886i	−0.910467	+	0.413581i	$0.864278\pi$
$234$		0			0
$235$	0.614510	−	7.64265i	0.0400862	−	0.498552i
$236$		0			0
$237$		−	32.4310i		−	2.10662i
$238$		0			0
$239$	24.1886			1.56463			0.782314	−	0.622884i	$-0.214039\pi$
$239$	24.1886			1.56463			0.782314	+	0.622884i	$0.214039\pi$
$240$		0			0
$241$	1.03944	−	1.03944i	0.0669560	−	0.0669560i	−0.672836	−	0.739792i	$-0.734924\pi$
$241$	1.03944	−	1.03944i	0.0669560	−	0.0669560i	0.739792	+	0.672836i	$0.234924\pi$
$242$		0			0
$243$	15.0049	+	15.0049i	0.962565	+	0.962565i
$244$		0			0
$245$	−1.24066	+	15.4300i	−0.0792628	+	0.985789i
$246$		0			0
$247$	12.5106			0.796028
$248$		0			0
$249$	−25.5297	−	25.5297i	−1.61788	−	1.61788i
$250$		0			0
$251$	5.23091			0.330172			0.165086	−	0.986279i	$-0.447210\pi$
$251$	5.23091			0.330172			0.165086	+	0.986279i	$0.447210\pi$
$252$		0			0
$253$	−5.02705			−0.316048
$254$		0			0
$255$	−21.2261	−	5.71151i	−1.32923	−	0.357668i
$256$		0			0
$257$	3.10191			0.193492			0.0967460	−	0.995309i	$-0.469157\pi$
$257$	3.10191			0.193492			0.0967460	+	0.995309i	$0.469157\pi$
$258$		0			0
$259$	2.00149			0.124366
$260$		0			0
$261$	−4.14399	−	4.14399i	−0.256506	−	0.256506i
$262$		0			0
$263$	24.3804			1.50336			0.751681	−	0.659527i	$-0.229244\pi$
$263$	24.3804			1.50336			0.751681	+	0.659527i	$0.229244\pi$
$264$		0			0
$265$	−10.3282	−	0.830441i	−0.634454	−	0.0510136i
$266$		0			0
$267$	22.2980	+	22.2980i	1.36462	+	1.36462i
$268$		0			0
$269$	−14.5159	+	14.5159i	−0.885050	+	0.885050i	−0.994043	−	0.108993i	$-0.965237\pi$
$269$	−14.5159	+	14.5159i	−0.885050	+	0.885050i	0.108993	+	0.994043i	$0.465237\pi$
$270$		0			0
$271$	−17.8267			−1.08289			−0.541446	−	0.840736i	$-0.682123\pi$
$271$	−17.8267			−1.08289			−0.541446	+	0.840736i	$0.682123\pi$
$272$		0			0
$273$		−	3.60488i		−	0.218178i
$274$		0			0
$275$	−1.98661	−	2.75390i	−0.119797	−	0.166066i
$276$		0			0
$277$	14.9446	+	14.9446i	0.897931	+	0.897931i	0.995253	−	0.0973216i	$-0.0310275\pi$
$277$	14.9446	+	14.9446i	0.897931	+	0.897931i	−0.0973216	+	0.995253i	$0.531028\pi$
$278$		0			0
$279$	−0.759364	−	0.759364i	−0.0454620	−	0.0454620i
$280$		0			0
$281$			4.17777i			0.249225i	0.992205	+	0.124613i	$0.0397688\pi$
$281$			4.17777i			0.249225i	−0.992205	+	0.124613i	$0.960231\pi$
$282$		0			0
$283$	−20.9070	+	20.9070i	−1.24279	+	1.24279i	−0.283953	+	0.958838i	$0.591646\pi$
$283$	−20.9070	+	20.9070i	−1.24279	+	1.24279i	−0.958838	+	0.283953i	$0.908354\pi$
$284$		0			0
$285$	9.33358	−	7.94434i	0.552873	−	0.470582i
$286$		0			0
$287$	−0.0216210			−0.00127624
$288$		0			0
$289$	6.07196	−	15.8786i	0.357174	−	0.934038i
$290$		0			0
$291$		−	10.9612i		−	0.642555i
$292$		0			0
$293$			6.71528i			0.392311i	0.980573	+	0.196155i	$0.0628457\pi$
$293$			6.71528i			0.392311i	−0.980573	+	0.196155i	$0.937154\pi$
$294$		0			0
$295$	0.510161	−	6.34486i	0.0297027	−	0.369412i
$296$		0			0
$297$	−0.511092			−0.0296566
$298$		0			0
$299$	28.4819	+	28.4819i	1.64715	+	1.64715i
$300$		0			0
$301$	−1.37295	+	1.37295i	−0.0791356	+	0.0791356i
$302$		0			0
$303$	−8.77887	−	8.77887i	−0.504333	−	0.504333i
$304$		0			0
$305$	−21.2350	−	24.9484i	−1.21591	−	1.42854i
$306$		0			0
$307$			28.5823i			1.63128i	0.578562	+	0.815638i	$0.303614\pi$
$307$			28.5823i			1.63128i	−0.578562	+	0.815638i	$0.696386\pi$
$308$		0			0
$309$	1.11759	−	1.11759i	0.0635774	−	0.0635774i
$310$		0			0
$311$	1.24431	−	1.24431i	0.0705582	−	0.0705582i	−0.670947	−	0.741505i	$-0.734112\pi$
$311$	1.24431	−	1.24431i	0.0705582	−	0.0705582i	0.741505	+	0.670947i	$0.234112\pi$
$312$		0			0
$313$	7.33210	−	7.33210i	0.414435	−	0.414435i	−0.468845	−	0.883280i	$-0.655330\pi$
$313$	7.33210	−	7.33210i	0.414435	−	0.414435i	0.883280	+	0.468845i	$0.155330\pi$
$314$		0			0
$315$	−1.08101	−	1.27005i	−0.0609082	−	0.0715593i
$316$		0			0
$317$	5.11957	−	5.11957i	0.287544	−	0.287544i	−0.548564	−	0.836108i	$-0.684825\pi$
$317$	5.11957	−	5.11957i	0.287544	−	0.287544i	0.836108	+	0.548564i	$0.184825\pi$
$318$		0			0
$319$	1.48269			0.0830146
$320$		0			0
$321$			12.2829i			0.685564i
$322$		0			0
$323$	5.37411	+	7.80868i	0.299023	+	0.434487i
$324$		0			0
$325$	−4.34724	+	26.8585i	−0.241141	+	1.48984i
$326$		0			0
$327$			7.27348i			0.402224i
$328$		0			0
$329$	0.673702	+	0.673702i	0.0371424	+	0.0371424i
$330$		0			0
$331$			18.5705i			1.02073i	0.859958	+	0.510364i	$0.170489\pi$
$331$			18.5705i			1.02073i	−0.859958	+	0.510364i	$0.829511\pi$
$332$		0			0
$333$	13.6727	−	13.6727i	0.749257	−	0.749257i
$334$		0			0
$335$	−0.103026	+	1.28133i	−0.00562891	+	0.0700066i
$336$		0			0
$337$	6.82548	+	6.82548i	0.371808	+	0.371808i	0.868135	−	0.496328i	$-0.165319\pi$
$337$	6.82548	+	6.82548i	0.371808	+	0.371808i	−0.496328	+	0.868135i	$0.665319\pi$
$338$		0			0
$339$	11.8270			0.642352
$340$		0			0
$341$	0.271695			0.0147131
$342$		0			0
$343$	−2.73549	−	2.73549i	−0.147703	−	0.147703i
$344$		0			0
$345$	39.3354	+	3.16278i	2.11775	+	0.170278i
$346$		0			0
$347$	−3.67442	+	3.67442i	−0.197253	+	0.197253i	−0.798821	−	0.601568i	$-0.794543\pi$
$347$	−3.67442	+	3.67442i	−0.197253	+	0.197253i	0.601568	+	0.798821i	$0.294543\pi$
$348$		0			0
$349$			18.5401i			0.992427i	0.868200	+	0.496214i	$0.165277\pi$
$349$			18.5401i			0.992427i	−0.868200	+	0.496214i	$0.834723\pi$
$350$		0			0
$351$	2.89571	+	2.89571i	0.154562	+	0.154562i
$352$		0			0
$353$			29.5665i			1.57367i	0.617166	+	0.786833i	$0.288281\pi$
$353$			29.5665i			1.57367i	−0.617166	+	0.786833i	$0.711719\pi$
$354$		0			0
$355$	7.17990	−	6.11122i	0.381069	−	0.324350i
$356$		0			0
$357$	2.25005	−	1.54853i	0.119085	−	0.0819571i
$358$		0			0
$359$		−	28.4722i		−	1.50271i	−0.659900	−	0.751353i	$-0.729401\pi$
$359$		−	28.4722i		−	1.50271i	0.659900	−	0.751353i	$-0.270599\pi$
$360$		0			0
$361$	13.7143			0.721806
$362$		0			0
$363$	17.7671	−	17.7671i	0.932529	−	0.932529i
$364$		0			0
$365$	22.2888	+	26.1864i	1.16665	+	1.37066i
$366$		0			0
$367$	−18.1404	+	18.1404i	−0.946923	+	0.946923i	−0.998661	−	0.0517378i	$-0.983524\pi$
$367$	−18.1404	+	18.1404i	−0.946923	+	0.946923i	0.0517378	+	0.998661i	$0.483524\pi$
$368$		0			0
$369$	−0.147698	+	0.147698i	−0.00768886	+	0.00768886i
$370$		0			0
$371$	0.910431	−	0.910431i	0.0472672	−	0.0472672i
$372$		0			0
$373$			27.1362i			1.40506i	0.711655	+	0.702529i	$0.247946\pi$
$373$			27.1362i			1.40506i	−0.711655	+	0.702529i	$0.752054\pi$
$374$		0			0
$375$	13.8121	+	22.7984i	0.713255	+	1.17731i
$376$		0			0
$377$	−8.40051	−	8.40051i	−0.432648	−	0.432648i
$378$		0			0
$379$	7.42612	−	7.42612i	0.381454	−	0.381454i	−0.490172	−	0.871626i	$-0.663066\pi$
$379$	7.42612	−	7.42612i	0.381454	−	0.381454i	0.871626	+	0.490172i	$0.163066\pi$
$380$		0			0
$381$	−14.0699	−	14.0699i	−0.720824	−	0.720824i
$382$		0			0
$383$	10.3836			0.530576			0.265288	−	0.964169i	$-0.414533\pi$
$383$	10.3836			0.530576			0.265288	+	0.964169i	$0.414533\pi$
$384$		0			0
$385$	0.420596	+	0.0338182i	0.0214356	+	0.00172354i
$386$		0			0
$387$			18.7580i			0.953520i
$388$		0			0
$389$		−	0.386877i		−	0.0196155i	−0.999952	−	0.00980773i	$-0.996878\pi$
$389$		−	0.386877i		−	0.0196155i	0.999952	−	0.00980773i	$-0.00312195\pi$
$390$		0			0
$391$	−5.54262	+	30.0123i	−0.280302	+	1.51779i
$392$		0			0
$393$	20.8077			1.04961
$394$		0			0
$395$	−19.7146	−	23.1621i	−0.991947	−	1.16541i
$396$		0			0
$397$	21.6141	−	21.6141i	1.08478	−	1.08478i	0.0887256	−	0.996056i	$-0.471721\pi$
$397$	21.6141	−	21.6141i	1.08478	−	1.08478i	0.996056	−	0.0887256i	$-0.0282794\pi$
$398$		0			0
$399$			1.52305i			0.0762480i
$400$		0			0
$401$	22.5963	+	22.5963i	1.12840	+	1.12840i	0.990437	+	0.137968i	$0.0440571\pi$
$401$	22.5963	+	22.5963i	1.12840	+	1.12840i	0.137968	+	0.990437i	$0.455943\pi$
$402$		0			0
$403$	−1.53935	−	1.53935i	−0.0766805	−	0.0766805i
$404$		0			0
$405$	21.9484	+	1.76477i	1.09063	+	0.0876922i
$406$		0			0
$407$			4.89198i			0.242486i
$408$		0			0
$409$	−32.8759			−1.62561			−0.812803	−	0.582538i	$-0.802060\pi$
$409$	−32.8759			−1.62561			−0.812803	+	0.582538i	$0.802060\pi$
$410$		0			0
$411$	21.9132	−	21.9132i	1.08090	−	1.08090i
$412$		0			0
$413$	0.559301	+	0.559301i	0.0275214	+	0.0275214i
$414$		0			0
$415$	−33.7525	−	2.71388i	−1.65684	−	0.133219i
$416$		0			0
$417$	1.18821			0.0581870
$418$		0			0
$419$	7.47234	+	7.47234i	0.365048	+	0.365048i	0.865667	−	0.500620i	$-0.166894\pi$
$419$	7.47234	+	7.47234i	0.365048	+	0.365048i	−0.500620	+	0.865667i	$0.666894\pi$
$420$		0			0
$421$	−9.78077			−0.476685			−0.238343	−	0.971181i	$-0.576604\pi$
$421$	−9.78077			−0.476685			−0.238343	+	0.971181i	$0.576604\pi$
$422$		0			0
$423$	9.20445			0.447536
$424$		0			0
$425$	−18.6316	+	8.82407i	−0.903764	+	0.428030i
$426$		0			0
$427$	4.07108			0.197014
$428$		0			0
$429$	8.81095			0.425397
$430$		0			0
$431$	−19.1797	−	19.1797i	−0.923854	−	0.923854i	0.0734451	−	0.997299i	$-0.476601\pi$
$431$	−19.1797	−	19.1797i	−0.923854	−	0.923854i	−0.997299	+	0.0734451i	$0.976601\pi$
$432$		0			0
$433$	−20.7341			−0.996418			−0.498209	−	0.867057i	$-0.666009\pi$
$433$	−20.7341			−0.996418			−0.498209	+	0.867057i	$0.666009\pi$
$434$		0			0
$435$	−11.6017	−	0.932836i	−0.556257	−	0.0447261i
$436$		0			0
$437$	−12.0335	−	12.0335i	−0.575642	−	0.575642i
$438$		0			0
$439$	−24.8014	+	24.8014i	−1.18371	+	1.18371i	−0.204932	+	0.978776i	$0.565697\pi$
$439$	−24.8014	+	24.8014i	−1.18371	+	1.18371i	−0.978776	+	0.204932i	$0.934303\pi$
$440$		0			0
$441$	−18.5832			−0.884915
$442$		0			0
$443$			12.2299i			0.581059i	0.956866	+	0.290530i	$0.0938315\pi$
$443$			12.2299i			0.581059i	−0.956866	+	0.290530i	$0.906168\pi$
$444$		0			0
$445$	29.4800	+	2.37035i	1.39748	+	0.112365i
$446$		0			0
$447$	4.15352	+	4.15352i	0.196455	+	0.196455i
$448$		0			0
$449$	16.6487	+	16.6487i	0.785703	+	0.785703i	0.980787	−	0.195084i	$-0.0624979\pi$
$449$	16.6487	+	16.6487i	0.785703	+	0.785703i	−0.195084	+	0.980787i	$0.562498\pi$
$450$		0			0
$451$		−	0.0528453i		−	0.00248839i
$452$		0			0
$453$	24.4032	−	24.4032i	1.14656	−	1.14656i
$454$		0			0
$455$	−2.19138	−	2.57459i	−0.102734	−	0.120699i
$456$		0			0
$457$	−34.7063			−1.62349			−0.811747	−	0.584010i	$-0.801483\pi$
$457$	−34.7063			−1.62349			−0.811747	+	0.584010i	$0.801483\pi$
$458$		0			0
$459$	−0.563508	+	3.05130i	−0.0263023	+	0.142423i
$460$		0			0
$461$			41.9948i			1.95589i	0.208852	+	0.977947i	$0.433027\pi$
$461$			41.9948i			1.95589i	−0.208852	+	0.977947i	$0.566973\pi$
$462$		0			0
$463$		−	24.8042i		−	1.15275i	−0.817186	−	0.576373i	$-0.804467\pi$
$463$		−	24.8042i		−	1.15275i	0.817186	−	0.576373i	$-0.195533\pi$
$464$		0			0
$465$	−2.12594	−	0.170937i	−0.0985883	−	0.00792704i
$466$		0			0
$467$	−38.3301			−1.77371			−0.886853	−	0.462051i	$-0.847114\pi$
$467$	−38.3301			−1.77371			−0.886853	+	0.462051i	$0.847114\pi$
$468$		0			0
$469$	−0.112950	−	0.112950i	−0.00521553	−	0.00521553i
$470$		0			0
$471$	−18.5776	+	18.5776i	−0.856009	+	0.856009i
$472$		0			0
$473$	−3.35573	−	3.35573i	−0.154297	−	0.154297i
$474$		0			0
$475$	1.83669	−	11.3476i	0.0842733	−	0.520664i
$476$		0			0
$477$		−	12.4388i		−	0.569532i
$478$		0			0
$479$	21.4212	−	21.4212i	0.978761	−	0.978761i	−0.0210181	−	0.999779i	$-0.506691\pi$
$479$	21.4212	−	21.4212i	0.978761	−	0.978761i	0.999779	+	0.0210181i	$0.00669077\pi$
$480$		0			0
$481$	27.7166	−	27.7166i	1.26377	−	1.26377i
$482$		0			0
$483$	−3.46743	+	3.46743i	−0.157773	+	0.157773i
$484$		0			0
$485$	−6.66320	−	7.82841i	−0.302560	−	0.355470i
$486$		0			0
$487$	26.2816	−	26.2816i	1.19093	−	1.19093i	0.214126	−	0.976806i	$-0.431310\pi$
$487$	26.2816	−	26.2816i	1.19093	−	1.19093i	0.976806	−	0.214126i	$-0.0686902\pi$
$488$		0			0
$489$	−33.1616			−1.49962
$490$		0			0
$491$			18.6045i			0.839610i	0.907614	+	0.419805i	$0.137902\pi$
$491$			18.6045i			0.839610i	−0.907614	+	0.419805i	$0.862098\pi$
$492$		0			0
$493$	1.63475	−	8.85189i	0.0736254	−	0.398669i
$494$		0			0
$495$	3.10422	−	2.64218i	0.139524	−	0.118757i
$496$		0			0
$497$			1.17162i			0.0525541i
$498$		0			0
$499$	−26.5738	−	26.5738i	−1.18961	−	1.18961i	−0.977176	−	0.212432i	$-0.931862\pi$
$499$	−26.5738	−	26.5738i	−1.18961	−	1.18961i	−0.212432	−	0.977176i	$-0.568138\pi$
$500$		0			0
$501$			39.1906i			1.75091i
$502$		0			0
$503$	−25.6622	+	25.6622i	−1.14422	+	1.14422i	−0.156549	+	0.987670i	$0.550037\pi$
$503$	−25.6622	+	25.6622i	−1.14422	+	1.14422i	−0.987670	+	0.156549i	$0.949963\pi$
$504$		0			0
$505$	−11.6064	−	0.933220i	−0.516480	−	0.0415278i
$506$		0			0
$507$	−28.0041	−	28.0041i	−1.24371	−	1.24371i
$508$		0			0
$509$	−23.7125			−1.05104			−0.525519	−	0.850782i	$-0.676129\pi$
$509$	−23.7125			−1.05104			−0.525519	+	0.850782i	$0.676129\pi$
$510$		0			0
$511$	−4.27310			−0.189031
$512$		0			0
$513$	−1.22343	−	1.22343i	−0.0540157	−	0.0540157i
$514$		0			0
$515$	0.118803	−	1.47755i	0.00523508	−	0.0651086i
$516$		0			0
$517$	−1.64664	+	1.64664i	−0.0724192	+	0.0724192i
$518$		0			0
$519$		−	5.97928i		−	0.262461i
$520$		0			0
$521$	1.85454	+	1.85454i	0.0812489	+	0.0812489i	0.746563	−	0.665314i	$-0.231703\pi$
$521$	1.85454	+	1.85454i	0.0812489	+	0.0812489i	−0.665314	+	0.746563i	$0.731703\pi$
$522$		0			0
$523$			15.1083i			0.660641i	0.943869	+	0.330320i	$0.107157\pi$
$523$			15.1083i			0.660641i	−0.943869	+	0.330320i	$0.892843\pi$
$524$		0			0
$525$	−3.26978	−	0.529238i	−0.142705	−	0.0230979i
$526$		0			0
$527$	0.299559	−	1.62206i	0.0130490	−	0.0706582i
$528$		0			0
$529$		−	31.7918i		−	1.38225i
$530$		0			0
$531$	7.64145			0.331611
$532$		0			0
$533$	−0.299407	+	0.299407i	−0.0129688	+	0.0129688i
$534$		0			0
$535$	7.46668	+	8.77239i	0.322813	+	0.379263i
$536$		0			0
$537$	19.4317	−	19.4317i	0.838541	−	0.838541i
$538$		0			0
$539$	3.32447	−	3.32447i	0.143195	−	0.143195i
$540$		0			0
$541$	9.13391	−	9.13391i	0.392697	−	0.392697i	−0.482950	−	0.875648i	$-0.660435\pi$
$541$	9.13391	−	9.13391i	0.392697	−	0.392697i	0.875648	+	0.482950i	$0.160435\pi$
$542$		0			0
$543$		−	46.6823i		−	2.00333i
$544$		0			0
$545$	4.42149	+	5.19468i	0.189396	+	0.222516i
$546$		0			0
$547$	−28.0616	−	28.0616i	−1.19983	−	1.19983i	−0.974218	−	0.225609i	$-0.927563\pi$
$547$	−28.0616	−	28.0616i	−1.19983	−	1.19983i	−0.225609	−	0.974218i	$-0.572437\pi$
$548$		0			0
$549$	27.8106	−	27.8106i	1.18693	−	1.18693i
$550$		0			0
$551$	3.54919	+	3.54919i	0.151201	+	0.151201i
$552$		0			0
$553$	3.77959			0.160724
$554$		0			0
$555$	3.07780	−	38.2785i	0.130645	−	1.62483i
$556$		0			0
$557$			20.0351i			0.848913i	0.905448	+	0.424456i	$0.139535\pi$
$557$			20.0351i			0.848913i	−0.905448	+	0.424456i	$0.860465\pi$
$558$		0			0
$559$			38.0253i			1.60830i
$560$		0			0
$561$	3.78488	+	5.49950i	0.159798	+	0.232189i
$562$		0			0
$563$	5.38746			0.227054			0.113527	−	0.993535i	$-0.463785\pi$
$563$	5.38746			0.227054			0.113527	+	0.993535i	$0.463785\pi$
$564$		0			0
$565$	8.44675	−	7.18951i	0.355358	−	0.302465i
$566$		0			0
$567$	−1.93476	+	1.93476i	−0.0812522	+	0.0812522i
$568$		0			0
$569$		−	14.4615i		−	0.606256i	−0.952950	−	0.303128i	$-0.901969\pi$
$569$		−	14.4615i		−	0.606256i	0.952950	−	0.303128i	$-0.0980309\pi$
$570$		0			0
$571$	−22.1103	−	22.1103i	−0.925287	−	0.925287i	0.0721101	−	0.997397i	$-0.477027\pi$
$571$	−22.1103	−	22.1103i	−0.925287	−	0.925287i	−0.997397	+	0.0721101i	$0.977027\pi$
$572$		0			0
$573$	−16.7745	−	16.7745i	−0.700763	−	0.700763i
$574$		0			0
$575$	30.0158	−	21.6529i	1.25175	−	0.902987i
$576$		0			0
$577$		−	5.84065i		−	0.243150i	−0.992582	−	0.121575i	$-0.961206\pi$
$577$		−	5.84065i		−	0.243150i	0.992582	−	0.121575i	$-0.0387944\pi$
$578$		0			0
$579$	−34.5929			−1.43763
$580$		0			0
$581$	2.97529	−	2.97529i	0.123436	−	0.123436i
$582$		0			0
$583$	2.22525	+	2.22525i	0.0921603	+	0.0921603i
$584$		0			0
$585$	−32.5576	−	2.61780i	−1.34609	−	0.108233i
$586$		0			0
$587$	16.3276			0.673913			0.336956	−	0.941520i	$-0.390603\pi$
$587$	16.3276			0.673913			0.336956	+	0.941520i	$0.390603\pi$
$588$		0			0
$589$	0.650371	+	0.650371i	0.0267981	+	0.0267981i
$590$		0			0
$591$	22.0686			0.907780
$592$		0			0
$593$	−18.8517			−0.774146			−0.387073	−	0.922049i	$-0.626514\pi$
$593$	−18.8517			−0.774146			−0.387073	+	0.922049i	$0.626514\pi$
$594$		0			0
$595$	0.665632	−	2.47374i	0.0272883	−	0.101414i
$596$		0			0
$597$	−27.3375			−1.11885
$598$		0			0
$599$	27.7899			1.13546			0.567732	−	0.823214i	$-0.307821\pi$
$599$	27.7899			1.13546			0.567732	+	0.823214i	$0.307821\pi$
$600$		0			0
$601$	20.7225	+	20.7225i	0.845290	+	0.845290i	0.989541	−	0.144251i	$-0.0460772\pi$
$601$	20.7225	+	20.7225i	0.845290	+	0.845290i	−0.144251	+	0.989541i	$0.546077\pi$
$602$		0			0
$603$	−1.54318			−0.0628430
$604$		0			0
$605$	1.88869	−	23.4896i	0.0767863	−	0.954989i
$606$		0			0
$607$	13.0560	+	13.0560i	0.529927	+	0.529927i	0.920550	−	0.390624i	$-0.127741\pi$
$607$	13.0560	+	13.0560i	0.529927	+	0.529927i	−0.390624	+	0.920550i	$0.627741\pi$
$608$		0			0
$609$	1.02269	−	1.02269i	0.0414415	−	0.0414415i
$610$		0			0
$611$	18.6589			0.754856
$612$		0			0
$613$			31.2958i			1.26402i	0.774958	+	0.632012i	$0.217771\pi$
$613$			31.2958i			1.26402i	−0.774958	+	0.632012i	$0.782229\pi$
$614$		0			0
$615$	−0.0332477	+	0.413501i	−0.00134068	+	0.0166740i
$616$		0			0
$617$	−34.0753	−	34.0753i	−1.37182	−	1.37182i	−0.857744	−	0.514078i	$-0.828134\pi$
$617$	−34.0753	−	34.0753i	−1.37182	−	1.37182i	−0.514078	−	0.857744i	$-0.671866\pi$
$618$		0			0
$619$	20.4433	+	20.4433i	0.821684	+	0.821684i	0.986349	−	0.164666i	$-0.0526545\pi$
$619$	20.4433	+	20.4433i	0.821684	+	0.821684i	−0.164666	+	0.986349i	$0.552654\pi$
$620$		0			0
$621$		−	5.57059i		−	0.223540i
$622$		0			0
$623$	−2.59867	+	2.59867i	−0.104113	+	0.104113i
$624$		0			0
$625$	23.7236	+	7.88626i	0.948942	+	0.315450i
$626$		0			0
$627$	−3.72260			−0.148666
$628$		0			0
$629$	29.2059	+	5.39369i	1.16452	+	0.215060i
$630$		0			0
$631$			13.0499i			0.519507i	0.965675	+	0.259754i	$0.0836414\pi$
$631$			13.0499i			0.519507i	−0.965675	+	0.259754i	$0.916359\pi$
$632$		0			0
$633$			41.3744i			1.64448i
$634$		0			0
$635$	−18.6017	−	1.49568i	−0.738185	−	0.0593541i
$636$		0			0
$637$	−37.6711			−1.49258
$638$		0			0
$639$	8.00360	+	8.00360i	0.316618	+	0.316618i
$640$		0			0
$641$	0.449205	−	0.449205i	0.0177425	−	0.0177425i	−0.698180	−	0.715922i	$-0.746006\pi$
$641$	0.449205	−	0.449205i	0.0177425	−	0.0177425i	0.715922	+	0.698180i	$0.246006\pi$
$642$		0			0
$643$	13.7523	+	13.7523i	0.542337	+	0.542337i	0.924213	−	0.381876i	$-0.124722\pi$
$643$	13.7523	+	13.7523i	0.542337	+	0.542337i	−0.381876	+	0.924213i	$0.624722\pi$
$644$		0			0
$645$	24.1465	+	28.3690i	0.950766	+	1.11703i
$646$		0			0
$647$		−	9.92104i		−	0.390036i	−0.980800	−	0.195018i	$-0.937523\pi$
$647$		−	9.92104i		−	0.390036i	0.980800	−	0.195018i	$-0.0624766\pi$
$648$		0			0
$649$	−1.36703	+	1.36703i	−0.0536605	+	0.0536605i
$650$		0			0
$651$	0.187403	−	0.187403i	0.00734489	−	0.00734489i
$652$		0			0
$653$	−26.0617	+	26.0617i	−1.01987	+	1.01987i	−0.0200765	+	0.999798i	$0.506391\pi$
$653$	−26.0617	+	26.0617i	−1.01987	+	1.01987i	−0.999798	+	0.0200765i	$0.993609\pi$
$654$		0			0
$655$	14.8608	−	12.6488i	0.580658	−	0.494231i
$656$		0			0
$657$	−29.1906	+	29.1906i	−1.13883	+	1.13883i
$658$		0			0
$659$	−16.5253			−0.643732			−0.321866	−	0.946785i	$-0.604310\pi$
$659$	−16.5253			−0.643732			−0.321866	+	0.946785i	$0.604310\pi$
$660$		0			0
$661$			0.916882i			0.0356626i	0.999841	+	0.0178313i	$0.00567618\pi$
$661$			0.916882i			0.0356626i	−0.999841	+	0.0178313i	$0.994324\pi$
$662$		0			0
$663$	9.71458	−	52.6028i	0.377283	−	2.04292i
$664$		0			0
$665$	0.925852	+	1.08776i	0.0359030	+	0.0421814i
$666$		0			0
$667$			16.1604i			0.625733i
$668$		0			0
$669$	−49.8769	−	49.8769i	−1.92835	−	1.92835i
$670$		0			0
$671$			9.95042i			0.384132i
$672$		0			0
$673$	0.894136	−	0.894136i	0.0344664	−	0.0344664i	−0.689664	−	0.724130i	$-0.742242\pi$
$673$	0.894136	−	0.894136i	0.0344664	−	0.0344664i	0.724130	+	0.689664i	$0.242242\pi$
$674$		0			0
$675$	3.05166	−	2.20141i	0.117458	−	0.0847323i
$676$		0			0
$677$	−8.83072	−	8.83072i	−0.339392	−	0.339392i	0.516746	−	0.856138i	$-0.327143\pi$
$677$	−8.83072	−	8.83072i	−0.339392	−	0.339392i	−0.856138	+	0.516746i	$0.827143\pi$
$678$		0			0
$679$	1.27744			0.0490236
$680$		0			0
$681$	49.9559			1.91431
$682$		0			0
$683$	28.8758	+	28.8758i	1.10490	+	1.10490i	0.993810	+	0.111090i	$0.0354342\pi$
$683$	28.8758	+	28.8758i	1.10490	+	1.10490i	0.111090	+	0.993810i	$0.464566\pi$
$684$		0			0
$685$	2.32943	−	28.9711i	0.0890031	−	1.10693i
$686$		0			0
$687$	2.00987	−	2.00987i	0.0766814	−	0.0766814i
$688$		0			0
$689$		−	25.2153i		−	0.960626i
$690$		0			0
$691$	11.4578	+	11.4578i	0.435875	+	0.435875i	0.890621	−	0.454746i	$-0.150270\pi$
$691$	11.4578	+	11.4578i	0.435875	+	0.435875i	−0.454746	+	0.890621i	$0.650270\pi$
$692$		0			0
$693$			0.506547i			0.0192421i
$694$		0			0
$695$	0.848615	−	0.722304i	0.0321898	−	0.0273986i
$696$		0			0
$697$	−0.315495	−	0.0582650i	−0.0119502	−	0.00220694i
$698$		0			0
$699$		−	25.5735i		−	0.967278i
$700$		0			0
$701$	−29.9171			−1.12995			−0.564977	−	0.825107i	$-0.691115\pi$
$701$	−29.9171			−1.12995			−0.564977	+	0.825107i	$0.691115\pi$
$702$		0			0
$703$	−11.7102	+	11.7102i	−0.441658	+	0.441658i
$704$		0			0
$705$	13.9205	−	11.8486i	0.524278	−	0.446243i
$706$		0			0
$707$	1.02311	−	1.02311i	0.0384780	−	0.0384780i
$708$		0			0
$709$	8.04944	−	8.04944i	0.302303	−	0.302303i	−0.539611	−	0.841914i	$-0.681429\pi$
$709$	8.04944	−	8.04944i	0.302303	−	0.302303i	0.841914	+	0.539611i	$0.181429\pi$
$710$		0			0
$711$	25.8193	−	25.8193i	0.968300	−	0.968300i
$712$		0			0
$713$			2.96131i			0.110902i
$714$		0			0
$715$	6.29274	−	5.35611i	0.235335	−	0.200307i
$716$		0			0
$717$	40.7789	+	40.7789i	1.52292	+	1.52292i
$718$		0			0
$719$	20.9713	−	20.9713i	0.782096	−	0.782096i	−0.198088	−	0.980184i	$-0.563473\pi$
$719$	20.9713	−	20.9713i	0.782096	−	0.782096i	0.980184	+	0.198088i	$0.0634732\pi$
$720$		0			0
$721$	0.130246	+	0.130246i	0.00485063	+	0.00485063i
$722$		0			0
$723$	3.50472			0.130342
$724$		0			0
$725$	−8.85291	+	6.38633i	−0.328789	+	0.237182i
$726$		0			0
$727$			1.70243i			0.0631397i	0.999502	+	0.0315699i	$0.0100507\pi$
$727$			1.70243i			0.0631397i	−0.999502	+	0.0315699i	$0.989949\pi$
$728$		0			0
$729$			21.0509i			0.779662i
$730$		0			0
$731$	−23.7341	+	16.3344i	−0.877838	+	0.604148i
$732$		0			0
$733$	29.1568			1.07693			0.538465	−	0.842648i	$-0.319004\pi$
$733$	29.1568			1.07693			0.538465	+	0.842648i	$0.319004\pi$
$734$		0			0
$735$	−28.1047	+	23.9215i	−1.03666	+	0.882359i
$736$		0			0
$737$	0.276068	−	0.276068i	0.0101691	−	0.0101691i
$738$		0			0
$739$		−	33.3164i		−	1.22556i	−0.790252	−	0.612782i	$-0.790050\pi$
$739$		−	33.3164i		−	1.22556i	0.790252	−	0.612782i	$-0.209950\pi$
$740$		0			0
$741$	21.0913	+	21.0913i	0.774807	+	0.774807i
$742$		0			0
$743$	−25.3185	−	25.3185i	−0.928844	−	0.928844i	0.0687874	−	0.997631i	$-0.478087\pi$
$743$	−25.3185	−	25.3185i	−0.928844	−	0.928844i	−0.997631	+	0.0687874i	$0.978087\pi$
$744$		0			0
$745$	5.49132	+	0.441532i	0.201187	+	0.0161765i
$746$		0			0
$747$		−	40.6499i		−	1.48730i
$748$		0			0
$749$	−1.43148			−0.0523051
$750$		0			0
$751$	−9.19571	+	9.19571i	−0.335556	+	0.335556i	−0.854692	−	0.519136i	$-0.826254\pi$
$751$	−9.19571	+	9.19571i	−0.335556	+	0.335556i	0.519136	+	0.854692i	$0.326254\pi$
$752$		0			0
$753$	8.81867	+	8.81867i	0.321370	+	0.321370i
$754$		0			0
$755$	2.59413	−	32.2632i	0.0944102	−	1.17418i
$756$		0			0
$757$	−14.6086			−0.530960			−0.265480	−	0.964116i	$-0.585530\pi$
$757$	−14.6086			−0.530960			−0.265480	+	0.964116i	$0.585530\pi$
$758$		0			0
$759$	−8.47499	−	8.47499i	−0.307622	−	0.307622i
$760$		0			0
$761$	6.96389			0.252441			0.126220	−	0.992002i	$-0.459715\pi$
$761$	6.96389			0.252441			0.126220	+	0.992002i	$0.459715\pi$
$762$		0			0
$763$	−0.847668			−0.0306876
$764$		0			0
$765$	−12.3517	−	21.4459i	−0.446575	−	0.775377i
$766$		0			0
$767$	15.4904			0.559326
$768$		0			0
$769$	41.0392			1.47991			0.739955	−	0.672656i	$-0.234847\pi$
$769$	41.0392			1.47991			0.739955	+	0.672656i	$0.234847\pi$
$770$		0			0
$771$	5.22944	+	5.22944i	0.188334	+	0.188334i
$772$		0			0
$773$	−24.1208			−0.867565			−0.433783	−	0.901018i	$-0.642821\pi$
$773$	−24.1208			−0.867565			−0.433783	+	0.901018i	$0.642821\pi$
$774$		0			0
$775$	−1.62225	+	1.17026i	−0.0582730	+	0.0420371i
$776$		0			0
$777$	3.37426	+	3.37426i	0.121051	+	0.121051i
$778$		0			0
$779$	0.126499	−	0.126499i	0.00453228	−	0.00453228i
$780$		0			0
$781$	−2.86363			−0.102469
$782$		0			0
$783$			1.64300i			0.0587160i
$784$		0			0
$785$	−1.97485	+	24.5612i	−0.0704855	+	0.876626i
$786$		0			0
$787$	−25.1417	−	25.1417i	−0.896205	−	0.896205i	0.0988933	−	0.995098i	$-0.468470\pi$
$787$	−25.1417	−	25.1417i	−0.896205	−	0.896205i	−0.995098	+	0.0988933i	$0.968470\pi$
$788$		0			0
$789$	41.1024	+	41.1024i	1.46328	+	1.46328i
$790$		0			0
$791$			1.37834i			0.0490081i
$792$		0			0
$793$	56.3764	−	56.3764i	2.00199	−	2.00199i
$794$		0			0
$795$	−16.0120	−	18.8120i	−0.567887	−	0.667194i
$796$		0			0
$797$	−25.0727			−0.888120			−0.444060	−	0.895997i	$-0.646462\pi$
$797$	−25.0727			−0.888120			−0.444060	+	0.895997i	$0.646462\pi$
$798$		0			0
$799$	8.01520	+	11.6462i	0.283557	+	0.412014i
$800$		0			0
$801$			35.5043i			1.25448i
$802$		0			0
$803$		−	10.4442i		−	0.368567i
$804$		0			0
$805$	−0.368598	+	4.58424i	−0.0129914	+	0.161573i
$806$		0			0
$807$	−48.9440			−1.72291
$808$		0			0
$809$	17.0926	+	17.0926i	0.600942	+	0.600942i	0.940563	−	0.339620i	$-0.110299\pi$
$809$	17.0926	+	17.0926i	0.600942	+	0.600942i	−0.339620	+	0.940563i	$0.610299\pi$
$810$		0			0
$811$	−16.0708	+	16.0708i	−0.564323	+	0.564323i	−0.930533	−	0.366209i	$-0.880655\pi$
$811$	−16.0708	+	16.0708i	−0.564323	+	0.564323i	0.366209	+	0.930533i	$0.380655\pi$
$812$		0			0
$813$	−30.0535	−	30.0535i	−1.05402	−	1.05402i
$814$		0			0
$815$	−23.6839	+	20.1587i	−0.829610	+	0.706128i
$816$		0			0
$817$		−	16.0656i		−	0.562063i
$818$		0			0
$819$	2.86996	−	2.86996i	0.100284	−	0.100284i
$820$		0			0
$821$	7.46573	−	7.46573i	0.260556	−	0.260556i	−0.564724	−	0.825280i	$-0.691017\pi$
$821$	7.46573	−	7.46573i	0.260556	−	0.260556i	0.825280	+	0.564724i	$0.191017\pi$
$822$		0			0
$823$	−22.1139	+	22.1139i	−0.770844	+	0.770844i	−0.978254	−	0.207410i	$-0.933496\pi$
$823$	−22.1139	+	22.1139i	−0.770844	+	0.770844i	0.207410	+	0.978254i	$0.433496\pi$
$824$		0			0
$825$	1.29355	−	7.99191i	0.0450356	−	0.278243i
$826$		0			0
$827$	0.917838	−	0.917838i	0.0319164	−	0.0319164i	−0.690969	−	0.722885i	$-0.742816\pi$
$827$	0.917838	−	0.917838i	0.0319164	−	0.0319164i	0.722885	+	0.690969i	$0.242816\pi$
$828$		0			0
$829$	−19.9006			−0.691177			−0.345588	−	0.938386i	$-0.612321\pi$
$829$	−19.9006			−0.691177			−0.345588	+	0.938386i	$0.612321\pi$
$830$		0			0
$831$			50.3893i			1.74799i
$832$		0			0
$833$	−16.1822	−	23.5130i	−0.560680	−	0.814678i
$834$		0			0
$835$	23.8236	+	27.9897i	0.824451	+	0.968624i
$836$		0			0
$837$			0.301071i			0.0104065i
$838$		0			0
$839$	−14.0278	−	14.0278i	−0.484292	−	0.484292i	0.422207	−	0.906499i	$-0.361255\pi$
$839$	−14.0278	−	14.0278i	−0.484292	−	0.484292i	−0.906499	+	0.422207i	$0.861255\pi$
$840$		0			0
$841$			24.2336i			0.835642i
$842$		0			0
$843$	−7.04320	+	7.04320i	−0.242581	+	0.242581i
$844$		0			0
$845$	−37.0239	−	2.97692i	−1.27366	−	0.102409i
$846$		0			0
$847$	2.07062	+	2.07062i	0.0711472	+	0.0711472i
$848$		0			0
$849$	−70.4931			−2.41932
$850$		0			0
$851$	−53.3195			−1.82777
$852$		0			0
$853$	17.0219	+	17.0219i	0.582818	+	0.582818i	0.935677	−	0.352859i	$-0.114790\pi$
$853$	17.0219	+	17.0219i	0.582818	+	0.582818i	−0.352859	+	0.935677i	$0.614790\pi$
$854$		0			0
$855$	13.7555	+	1.10601i	0.470427	+	0.0378249i
$856$		0			0
$857$	21.8120	−	21.8120i	0.745085	−	0.745085i	−0.228467	−	0.973552i	$-0.573371\pi$
$857$	21.8120	−	21.8120i	0.745085	−	0.745085i	0.973552	+	0.228467i	$0.0733712\pi$
$858$		0			0
$859$		−	50.8322i		−	1.73437i	−0.497984	−	0.867186i	$-0.665926\pi$
$859$		−	50.8322i		−	1.73437i	0.497984	−	0.867186i	$-0.334074\pi$
$860$		0			0
$861$	−0.0364502	−	0.0364502i	−0.00124222	−	0.00124222i
$862$		0			0
$863$		−	13.3621i		−	0.454852i	−0.973795	−	0.227426i	$-0.926969\pi$
$863$		−	13.3621i		−	0.454852i	0.973795	−	0.227426i	$-0.0730309\pi$
$864$		0			0
$865$	−3.63476	−	4.27038i	−0.123586	−	0.145197i
$866$		0			0
$867$	37.0060	−	16.5328i	1.25679	−	0.561485i
$868$		0			0
$869$			9.23795i			0.313376i
$870$		0			0
$871$	−3.12826			−0.105997
$872$		0			0
$873$	8.72651	−	8.72651i	0.295348	−	0.295348i
$874$		0			0
$875$	−2.65698	+	1.60970i	−0.0898225	+	0.0544177i
$876$		0			0
$877$	−1.68022	+	1.68022i	−0.0567370	+	0.0567370i	−0.734906	−	0.678169i	$-0.762774\pi$
$877$	−1.68022	+	1.68022i	−0.0567370	+	0.0567370i	0.678169	+	0.734906i	$0.262774\pi$
$878$		0			0
$879$	−11.3211	+	11.3211i	−0.381852	+	0.381852i
$880$		0			0
$881$	14.0859	−	14.0859i	0.474567	−	0.474567i	−0.428822	−	0.903389i	$-0.641071\pi$
$881$	14.0859	−	14.0859i	0.474567	−	0.474567i	0.903389	+	0.428822i	$0.141071\pi$
$882$		0			0
$883$		−	26.6658i		−	0.897377i	−0.893688	−	0.448689i	$-0.851891\pi$
$883$		−	26.6658i		−	0.897377i	0.893688	−	0.448689i	$-0.148109\pi$
$884$		0			0
$885$	11.5567	−	9.83657i	0.388474	−	0.330653i
$886$		0			0
$887$	17.0234	+	17.0234i	0.571590	+	0.571590i	0.932573	−	0.360982i	$-0.117559\pi$
$887$	17.0234	+	17.0234i	0.571590	+	0.571590i	−0.360982	+	0.932573i	$0.617559\pi$
$888$		0			0
$889$	1.63974	−	1.63974i	0.0549952	−	0.0549952i
$890$		0			0
$891$	−4.72888	−	4.72888i	−0.158423	−	0.158423i
$892$		0			0
$893$	−7.88331			−0.263805
$894$		0			0
$895$	2.06565	−	25.6904i	0.0690471	−	0.858736i
$896$		0			0
$897$			96.0340i			3.20648i
$898$		0			0
$899$		−	0.873413i		−	0.0291300i
$900$		0			0
$901$	15.7386	−	10.8316i	0.524327	−	0.360854i
$902$		0			0
$903$	−4.62925			−0.154052
$904$		0			0
$905$	−28.3778	−	33.3402i	−0.943309	−	1.10827i
$906$		0			0
$907$	−2.43322	+	2.43322i	−0.0807936	+	0.0807936i	−0.746349	−	0.665555i	$-0.768195\pi$
$907$	−2.43322	+	2.43322i	−0.0807936	+	0.0807936i	0.665555	+	0.746349i	$0.268195\pi$
$908$		0			0
$909$		−	13.9782i		−	0.463629i
$910$		0			0
$911$	−12.0319	−	12.0319i	−0.398633	−	0.398633i	0.479118	−	0.877751i	$-0.340957\pi$
$911$	−12.0319	−	12.0319i	−0.398633	−	0.398633i	−0.877751	+	0.479118i	$0.840957\pi$
$912$		0			0
$913$	7.27211	+	7.27211i	0.240672	+	0.240672i
$914$		0			0
$915$	6.26033	−	77.8596i	0.206960	−	2.57396i
$916$		0			0
$917$			2.42498i			0.0800798i
$918$		0			0
$919$	−38.9441			−1.28465			−0.642324	−	0.766433i	$-0.722030\pi$
$919$	−38.9441			−1.28465			−0.642324	+	0.766433i	$0.722030\pi$
$920$		0			0
$921$	−48.1862	+	48.1862i	−1.58779	+	1.58779i
$922$		0			0
$923$	16.2245	+	16.2245i	0.534037	+	0.534037i
$924$		0			0
$925$	−21.0710	−	29.2093i	−0.692812	−	0.960395i
$926$		0			0
$927$	1.77949			0.0584461
$928$		0			0
$929$	30.2215	+	30.2215i	0.991536	+	0.991536i	0.999964	−	0.00842808i	$-0.00268277\pi$
$929$	30.2215	+	30.2215i	0.991536	+	0.991536i	−0.00842808	+	0.999964i	$0.502683\pi$
$930$		0			0
$931$	15.9159			0.521623
$932$		0			0
$933$	4.19549			0.137354
$934$		0			0
$935$	6.04625	+	1.62692i	0.197734	+	0.0532059i
$936$		0			0
$937$	59.8100			1.95391			0.976953	−	0.213454i	$-0.0684714\pi$
$937$	59.8100			1.95391			0.976953	+	0.213454i	$0.0684714\pi$
$938$		0			0
$939$	24.7220			0.806773
$940$		0			0
$941$	−17.2584	−	17.2584i	−0.562607	−	0.562607i	0.367440	−	0.930047i	$-0.380234\pi$
$941$	−17.2584	−	17.2584i	−0.562607	−	0.562607i	−0.930047	+	0.367440i	$0.880234\pi$
$942$		0			0
$943$	0.575981			0.0187565
$944$		0			0
$945$	−0.0374747	+	0.466072i	−0.00121905	+	0.0151613i
$946$		0			0
$947$	33.8129	+	33.8129i	1.09877	+	1.09877i	0.994554	+	0.104219i	$0.0332342\pi$
$947$	33.8129	+	33.8129i	1.09877	+	1.09877i	0.104219	+	0.994554i	$0.466766\pi$
$948$		0			0
$949$	−59.1739	+	59.1739i	−1.92087	+	1.92087i
$950$		0			0
$951$	17.2619			0.559756
$952$		0			0
$953$			23.7253i			0.768539i	0.923221	+	0.384269i	$0.125547\pi$
$953$			23.7253i			0.768539i	−0.923221	+	0.384269i	$0.874453\pi$
$954$		0			0
$955$	−22.1773	−	1.78318i	−0.717641	−	0.0577022i
$956$		0			0
$957$	2.49963	+	2.49963i	0.0808015	+	0.0808015i
$958$		0			0
$959$	2.55381	+	2.55381i	0.0824668	+	0.0824668i
$960$		0			0
$961$			30.8400i			0.994837i
$962$		0			0
$963$	−9.77878	+	9.77878i	−0.315117	+	0.315117i
$964$		0			0
$965$	−24.7061	+	21.0288i	−0.795317	+	0.676940i
$966$		0			0
$967$	14.9120			0.479537			0.239769	−	0.970830i	$-0.422928\pi$
$967$	14.9120			0.479537			0.239769	+	0.970830i	$0.422928\pi$
$968$		0			0
$969$	−4.10438	+	22.2245i	−0.131852	+	0.713955i
$970$		0			0
$971$			39.3858i			1.26395i	0.774988	+	0.631976i	$0.217756\pi$
$971$			39.3858i			1.26395i	−0.774988	+	0.631976i	$0.782244\pi$
$972$		0			0
$973$			0.138477i			0.00443937i
$974$		0			0
$975$	−52.6089	+	37.9511i	−1.68483	+	1.21541i
$976$		0			0
$977$	31.2054			0.998349			0.499175	−	0.866501i	$-0.333637\pi$
$977$	31.2054			0.998349			0.499175	+	0.866501i	$0.333637\pi$
$978$		0			0
$979$	−6.35158	−	6.35158i	−0.202997	−	0.202997i
$980$		0			0
$981$	−5.79063	+	5.79063i	−0.184881	+	0.184881i
$982$		0			0
$983$	32.8444	+	32.8444i	1.04757	+	1.04757i	0.998810	+	0.0487626i	$0.0155278\pi$
$983$	32.8444	+	32.8444i	1.04757	+	1.04757i	0.0487626	+	0.998810i	$0.484472\pi$
$984$		0			0
$985$	15.7613	−	13.4153i	0.502196	−	0.427448i
$986$		0			0
$987$			2.27155i			0.0723044i
$988$		0			0
$989$	36.5754	−	36.5754i	1.16303	−	1.16303i
$990$		0			0
$991$	26.1464	−	26.1464i	0.830568	−	0.830568i	−0.157026	−	0.987594i	$-0.550191\pi$
$991$	26.1464	−	26.1464i	0.830568	−	0.830568i	0.987594	+	0.157026i	$0.0501907\pi$
$992$		0			0
$993$	−31.3076	+	31.3076i	−0.993516	+	0.993516i
$994$		0			0
$995$	−19.5243	+	16.6183i	−0.618962	+	0.526834i
$996$		0			0
$997$	3.43513	−	3.43513i	0.108792	−	0.108792i	−0.650616	−	0.759407i	$-0.725489\pi$
$997$	3.43513	−	3.43513i	0.108792	−	0.108792i	0.759407	+	0.650616i	$0.225489\pi$
$998$		0			0
$999$	−5.42091			−0.171510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.z.d.89.11	yes	26
5.4	even	2		680.2.z.c.89.3	✓	26
17.13	even	4		680.2.z.c.489.3	yes	26
85.64	even	4	inner	680.2.z.d.489.11	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.z.c.89.3	✓	26	5.4	even	2
680.2.z.c.489.3	yes	26	17.13	even	4
680.2.z.d.89.11	yes	26	1.1	even	1	trivial
680.2.z.d.489.11	yes	26	85.64	even	4	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.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68588 + 1.68588i) q^{3} +(2.22887 + 0.179214i) q^{5} +(-0.196476 + 0.196476i) q^{7} +2.68435i q^{9} +(-0.480221 - 0.480221i) q^{11} +5.44160i q^{13} +(3.45547 + 4.05974i) q^{15} +(-3.39647 + 2.33752i) q^{17} -2.29906i q^{19} -0.662468 q^{21} +(5.23411 - 5.23411i) q^{23} +(4.93576 + 0.798889i) q^{25} +(0.532143 - 0.532143i) q^{27} +(-1.54376 + 1.54376i) q^{29} +(-0.282886 + 0.282886i) q^{31} -1.61918i q^{33} +(-0.473131 + 0.402709i) q^{35} +(-5.09347 - 5.09347i) q^{37} +(-9.17386 + 9.17386i) q^{39} +(0.0550219 + 0.0550219i) q^{41} +6.98789 q^{43} +(-0.481072 + 5.98308i) q^{45} -3.42893i q^{47} +6.92279i q^{49} +(-9.66679 - 1.78524i) q^{51} -4.63380 q^{53} +(-0.984289 - 1.15641i) q^{55} +(3.87593 - 3.87593i) q^{57} -2.84666i q^{59} +(-10.3603 - 10.3603i) q^{61} +(-0.527410 - 0.527410i) q^{63} +(-0.975209 + 12.1286i) q^{65} +0.574878i q^{67} +17.6481 q^{69} +(2.98158 - 2.98158i) q^{71} +(10.8744 + 10.8744i) q^{73} +(6.97426 + 9.66791i) q^{75} +0.188703 q^{77} +(-9.61845 - 9.61845i) q^{79} +9.84731 q^{81} -15.1433 q^{83} +(-7.98921 + 4.60136i) q^{85} -5.20516 q^{87} +13.2264 q^{89} +(-1.06914 - 1.06914i) q^{91} -0.953820 q^{93} +(0.412023 - 5.12432i) q^{95} +(-3.25088 - 3.25088i) q^{97} +(1.28908 - 1.28908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{15} + 2 q^{17} - 12 q^{21} - 2 q^{23} + 10 q^{25} + 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} - 6 q^{37} + 8 q^{39} - 10 q^{41} + 32 q^{43} + 28 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 26 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^15 + 2 * q^17 - 12 * q^21 - 2 * q^23 + 10 * q^25 + 20 * q^27 + 10 * q^29 - 10 * q^31 + 22 * q^35 - 6 * q^37 + 8 * q^39 - 10 * q^41 + 32 * q^43 + 28 * q^45 - 6 * q^51 - 32 * q^53 - 26 * q^55 + 20 * q^57 + 6 * q^61 - 54 * q^63 + 24 * q^65 - 20 * q^69 - 30 * q^71 + 42 * q^73 - 78 * q^75 - 4 * q^77 + 14 * q^79 - 54 * q^81 - 16 * q^83 - 26 * q^85 + 8 * q^87 + 40 * q^89 + 24 * q^91 + 88 * q^93 + 44 * q^95 + 66 * q^97 - 22 * q^99

Introduction

L-functions

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