LMFDB - Embedded newform 1680.2.cz.e.97.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(97,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.12
Character	$\chi$	$=$	1680.97
Dual form			1680.2.cz.e.433.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(2.19074 + 0.447937i) q^{5} +(1.85286 - 1.88862i) q^{7} +1.00000i q^{9} +4.29513 q^{11} +(-1.47784 - 1.47784i) q^{13} +(1.23235 + 1.86583i) q^{15} +(-5.17651 + 5.17651i) q^{17} +7.34180 q^{19} +(2.64563 - 0.0252885i) q^{21} +(-3.22191 + 3.22191i) q^{23} +(4.59871 + 1.96263i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.81726i q^{29} +1.72147i q^{31} +(3.03711 + 3.03711i) q^{33} +(4.90513 - 3.30753i) q^{35} +(-2.39795 - 2.39795i) q^{37} -2.08998i q^{39} -4.03046i q^{41} +(1.67864 - 1.67864i) q^{43} +(-0.447937 + 2.19074i) q^{45} +(7.92960 - 7.92960i) q^{47} +(-0.133808 - 6.99872i) q^{49} -7.32070 q^{51} +(-7.69186 + 7.69186i) q^{53} +(9.40952 + 1.92395i) q^{55} +(5.19144 + 5.19144i) q^{57} +0.775921 q^{59} +9.86457i q^{61} +(1.88862 + 1.85286i) q^{63} +(-2.57558 - 3.89953i) q^{65} +(-11.4771 - 11.4771i) q^{67} -4.55646 q^{69} -2.60505 q^{71} +(8.77273 + 8.77273i) q^{73} +(1.86399 + 4.63956i) q^{75} +(7.95828 - 8.11189i) q^{77} -0.421125i q^{79} -1.00000 q^{81} +(8.44531 + 8.44531i) q^{83} +(-13.6592 + 9.02166i) q^{85} +(4.11343 - 4.11343i) q^{87} -4.29336 q^{89} +(-5.52930 + 0.0528524i) q^{91} +(-1.21726 + 1.21726i) q^{93} +(16.0840 + 3.28866i) q^{95} +(7.29681 - 7.29681i) q^{97} +4.29513i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{11} - 16 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} - 24 q^{23} - 4 q^{25} + 4 q^{37} + 16 q^{43} + 4 q^{45} - 24 q^{47} - 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} - 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 16 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 - 24 * q^23 - 4 * q^25 + 4 * q^37 + 16 * q^43 + 4 * q^45 - 24 * q^47 - 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 - 4 * q^63 + 24 * q^65 - 16 * q^67 + 8 * q^69 - 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 - 16 * q^89 - 24 * q^91 - 12 * q^93 - 24 * q^95 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	2.19074	+	0.447937i	0.979730	+	0.200323i
$5$	2.19074	+	0.447937i	0.979730	+	0.200323i
$6$		0			0
$7$	1.85286	−	1.88862i	0.700316	−	0.713833i
$7$	1.85286	−	1.88862i	0.700316	−	0.713833i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	4.29513			1.29503			0.647515	−	0.762053i	$-0.275808\pi$
$11$	4.29513			1.29503			0.647515	+	0.762053i	$0.275808\pi$
$12$		0			0
$13$	−1.47784	−	1.47784i	−0.409878	−	0.409878i	0.471818	−	0.881696i	$-0.343598\pi$
$13$	−1.47784	−	1.47784i	−0.409878	−	0.409878i	−0.881696	+	0.471818i	$0.843598\pi$
$14$		0			0
$15$	1.23235	+	1.86583i	0.318191	+	0.481755i
$16$		0			0
$17$	−5.17651	+	5.17651i	−1.25549	+	1.25549i	−0.302265	+	0.953224i	$0.597743\pi$
$17$	−5.17651	+	5.17651i	−1.25549	+	1.25549i	−0.953224	+	0.302265i	$0.902257\pi$
$18$		0			0
$19$	7.34180			1.68432			0.842162	−	0.539224i	$-0.181282\pi$
$19$	7.34180			1.68432			0.842162	+	0.539224i	$0.181282\pi$
$20$		0			0
$21$	2.64563	−	0.0252885i	0.577324	−	0.00551840i
$22$		0			0
$23$	−3.22191	+	3.22191i	−0.671814	+	0.671814i	−0.958134	−	0.286320i	$-0.907568\pi$
$23$	−3.22191	+	3.22191i	−0.671814	+	0.671814i	0.286320	+	0.958134i	$0.407568\pi$
$24$		0			0
$25$	4.59871	+	1.96263i	0.919741	+	0.392526i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	5.81726i		−	1.08024i	−0.841588	−	0.540119i	$-0.818379\pi$
$29$		−	5.81726i		−	1.08024i	0.841588	−	0.540119i	$-0.181621\pi$
$30$		0			0
$31$			1.72147i			0.309185i	0.987978	+	0.154593i	$0.0494065\pi$
$31$			1.72147i			0.309185i	−0.987978	+	0.154593i	$0.950594\pi$
$32$		0			0
$33$	3.03711	+	3.03711i	0.528694	+	0.528694i
$34$		0			0
$35$	4.90513	−	3.30753i	0.829118	−	0.559074i
$36$		0			0
$37$	−2.39795	−	2.39795i	−0.394220	−	0.394220i	0.481969	−	0.876188i	$-0.339922\pi$
$37$	−2.39795	−	2.39795i	−0.394220	−	0.394220i	−0.876188	+	0.481969i	$0.839922\pi$
$38$		0			0
$39$		−	2.08998i		−	0.334664i
$40$		0			0
$41$		−	4.03046i		−	0.629452i	−0.949183	−	0.314726i	$-0.898087\pi$
$41$		−	4.03046i		−	0.629452i	0.949183	−	0.314726i	$-0.101913\pi$
$42$		0			0
$43$	1.67864	−	1.67864i	0.255990	−	0.255990i	−0.567431	−	0.823421i	$-0.692063\pi$
$43$	1.67864	−	1.67864i	0.255990	−	0.255990i	0.823421	+	0.567431i	$0.192063\pi$
$44$		0			0
$45$	−0.447937	+	2.19074i	−0.0667745	+	0.326577i
$46$		0			0
$47$	7.92960	−	7.92960i	1.15665	−	1.15665i	0.171459	−	0.985191i	$-0.445152\pi$
$47$	7.92960	−	7.92960i	1.15665	−	1.15665i	0.985191	−	0.171459i	$-0.0548482\pi$
$48$		0			0
$49$	−0.133808	−	6.99872i	−0.0191154	−	0.999817i
$50$		0			0
$51$	−7.32070			−1.02510
$52$		0			0
$53$	−7.69186	+	7.69186i	−1.05656	+	1.05656i	−0.0582570	+	0.998302i	$0.518554\pi$
$53$	−7.69186	+	7.69186i	−1.05656	+	1.05656i	−0.998302	+	0.0582570i	$0.981446\pi$
$54$		0			0
$55$	9.40952	+	1.92395i	1.26878	+	0.259425i
$56$		0			0
$57$	5.19144	+	5.19144i	0.687623	+	0.687623i
$58$		0			0
$59$	0.775921			0.101016			0.0505081	−	0.998724i	$-0.483916\pi$
$59$	0.775921			0.101016			0.0505081	+	0.998724i	$0.483916\pi$
$60$		0			0
$61$			9.86457i			1.26303i	0.775364	+	0.631514i	$0.217566\pi$
$61$			9.86457i			1.26303i	−0.775364	+	0.631514i	$0.782434\pi$
$62$		0			0
$63$	1.88862	+	1.85286i	0.237944	+	0.233439i
$64$		0			0
$65$	−2.57558	−	3.89953i	−0.319461	−	0.483678i
$66$		0			0
$67$	−11.4771	−	11.4771i	−1.40215	−	1.40215i	−0.793239	−	0.608911i	$-0.791607\pi$
$67$	−11.4771	−	11.4771i	−1.40215	−	1.40215i	−0.608911	−	0.793239i	$-0.708393\pi$
$68$		0			0
$69$	−4.55646			−0.548534
$70$		0			0
$71$	−2.60505			−0.309163			−0.154581	−	0.987980i	$-0.549403\pi$
$71$	−2.60505			−0.309163			−0.154581	+	0.987980i	$0.549403\pi$
$72$		0			0
$73$	8.77273	+	8.77273i	1.02677	+	1.02677i	0.999632	+	0.0271389i	$0.00863965\pi$
$73$	8.77273	+	8.77273i	1.02677	+	1.02677i	0.0271389	+	0.999632i	$0.491360\pi$
$74$		0			0
$75$	1.86399	+	4.63956i	0.215235	+	0.535731i
$76$		0			0
$77$	7.95828	−	8.11189i	0.906930	−	0.924435i
$78$		0			0
$79$		−	0.421125i		−	0.0473802i	−0.999719	−	0.0236901i	$-0.992458\pi$
$79$		−	0.421125i		−	0.0473802i	0.999719	−	0.0236901i	$-0.00754150\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	8.44531	+	8.44531i	0.926993	+	0.926993i	0.997511	−	0.0705172i	$-0.0224650\pi$
$83$	8.44531	+	8.44531i	0.926993	+	0.926993i	−0.0705172	+	0.997511i	$0.522465\pi$
$84$		0			0
$85$	−13.6592	+	9.02166i	−1.48154	+	0.978536i
$86$		0			0
$87$	4.11343	−	4.11343i	0.441006	−	0.441006i
$88$		0			0
$89$	−4.29336			−0.455095			−0.227548	−	0.973767i	$-0.573071\pi$
$89$	−4.29336			−0.455095			−0.227548	+	0.973767i	$0.573071\pi$
$90$		0			0
$91$	−5.52930	+	0.0528524i	−0.579628	+	0.00554043i
$92$		0			0
$93$	−1.21726	+	1.21726i	−0.126224	+	0.126224i
$94$		0			0
$95$	16.0840	+	3.28866i	1.65018	+	0.337410i
$96$		0			0
$97$	7.29681	−	7.29681i	0.740878	−	0.740878i	−0.231869	−	0.972747i	$-0.574484\pi$
$97$	7.29681	−	7.29681i	0.740878	−	0.740878i	0.972747	+	0.231869i	$0.0744840\pi$
$98$		0			0
$99$			4.29513i			0.431677i
$100$		0			0
$101$			0.162882i			0.0162074i	0.999967	+	0.00810368i	$0.00257951\pi$
$101$			0.162882i			0.0162074i	−0.999967	+	0.00810368i	$0.997420\pi$
$102$		0			0
$103$	−4.46455	−	4.46455i	−0.439906	−	0.439906i	0.452075	−	0.891980i	$-0.350684\pi$
$103$	−4.46455	−	4.46455i	−0.439906	−	0.439906i	−0.891980	+	0.452075i	$0.850684\pi$
$104$		0			0
$105$	5.80722	+	1.12967i	0.566727	+	0.110245i
$106$		0			0
$107$	9.78150	+	9.78150i	0.945614	+	0.945614i	0.998595	−	0.0529817i	$-0.0168725\pi$
$107$	9.78150	+	9.78150i	0.945614	+	0.945614i	−0.0529817	+	0.998595i	$0.516873\pi$
$108$		0			0
$109$		−	7.32115i		−	0.701239i	−0.936518	−	0.350619i	$-0.885971\pi$
$109$		−	7.32115i		−	0.701239i	0.936518	−	0.350619i	$-0.114029\pi$
$110$		0			0
$111$		−	3.39121i		−	0.321879i
$112$		0			0
$113$	−13.2348	+	13.2348i	−1.24502	+	1.24502i	−0.287131	+	0.957891i	$0.592702\pi$
$113$	−13.2348	+	13.2348i	−1.24502	+	1.24502i	−0.957891	+	0.287131i	$0.907298\pi$
$114$		0			0
$115$	−8.50158	+	5.61516i	−0.792776	+	0.523616i
$116$		0			0
$117$	1.47784	−	1.47784i	0.136626	−	0.136626i
$118$		0			0
$119$	0.185129	+	19.3679i	0.0169708	+	1.77545i
$120$		0			0
$121$	7.44813			0.677102
$122$		0			0
$123$	2.84997	−	2.84997i	0.256973	−	0.256973i
$124$		0			0
$125$	9.19545	+	6.35954i	0.822466	+	0.568815i
$126$		0			0
$127$	−12.8515	−	12.8515i	−1.14038	−	1.14038i	−0.988380	−	0.152002i	$-0.951428\pi$
$127$	−12.8515	−	12.8515i	−1.14038	−	1.14038i	−0.152002	−	0.988380i	$-0.548572\pi$
$128$		0			0
$129$	2.37395			0.209015
$130$		0			0
$131$			13.8264i			1.20802i	0.796978	+	0.604008i	$0.206431\pi$
$131$			13.8264i			1.20802i	−0.796978	+	0.604008i	$0.793569\pi$
$132$		0			0
$133$	13.6033	−	13.8659i	1.17956	−	1.20233i
$134$		0			0
$135$	−1.86583	+	1.23235i	−0.160585	+	0.106064i
$136$		0			0
$137$	5.53271	+	5.53271i	0.472691	+	0.472691i	0.902784	−	0.430093i	$-0.141519\pi$
$137$	5.53271	+	5.53271i	0.472691	+	0.472691i	−0.430093	+	0.902784i	$0.641519\pi$
$138$		0			0
$139$	−9.70449			−0.823124			−0.411562	−	0.911382i	$-0.635017\pi$
$139$	−9.70449			−0.823124			−0.411562	+	0.911382i	$0.635017\pi$
$140$		0			0
$141$	11.2141			0.944401
$142$		0			0
$143$	−6.34749	−	6.34749i	−0.530804	−	0.530804i
$144$		0			0
$145$	2.60577	−	12.7441i	0.216397	−	1.05834i
$146$		0			0
$147$	4.85423	−	5.04346i	0.400370	−	0.415978i
$148$		0			0
$149$		−	9.48071i		−	0.776690i	−0.921514	−	0.388345i	$-0.873047\pi$
$149$		−	9.48071i		−	0.776690i	0.921514	−	0.388345i	$-0.126953\pi$
$150$		0			0
$151$	2.70016			0.219736			0.109868	−	0.993946i	$-0.464957\pi$
$151$	2.70016			0.219736			0.109868	+	0.993946i	$0.464957\pi$
$152$		0			0
$153$	−5.17651	−	5.17651i	−0.418496	−	0.418496i
$154$		0			0
$155$	−0.771109	+	3.77130i	−0.0619370	+	0.302918i
$156$		0			0
$157$	2.20080	−	2.20080i	0.175643	−	0.175643i	−0.613811	−	0.789453i	$-0.710364\pi$
$157$	2.20080	−	2.20080i	0.175643	−	0.175643i	0.789453	+	0.613811i	$0.210364\pi$
$158$		0			0
$159$	−10.8779			−0.862676
$160$		0			0
$161$	0.115226	+	12.0547i	0.00908109	+	0.950045i
$162$		0			0
$163$	−4.16776	+	4.16776i	−0.326444	+	0.326444i	−0.851233	−	0.524788i	$-0.824144\pi$
$163$	−4.16776	+	4.16776i	−0.326444	+	0.326444i	0.524788	+	0.851233i	$0.324144\pi$
$164$		0			0
$165$	5.29310	+	8.01397i	0.412067	+	0.623887i
$166$		0			0
$167$	−3.38827	+	3.38827i	−0.262192	+	0.262192i	−0.825944	−	0.563752i	$-0.809357\pi$
$167$	−3.38827	+	3.38827i	−0.262192	+	0.262192i	0.563752	+	0.825944i	$0.309357\pi$
$168$		0			0
$169$		−	8.63200i		−	0.664000i
$170$		0			0
$171$			7.34180i			0.561442i
$172$		0			0
$173$	3.89903	+	3.89903i	0.296438	+	0.296438i	0.839617	−	0.543179i	$-0.182780\pi$
$173$	3.89903	+	3.89903i	0.296438	+	0.296438i	−0.543179	+	0.839617i	$0.682780\pi$
$174$		0			0
$175$	12.2274	−	5.04875i	0.924307	−	0.381650i
$176$		0			0
$177$	0.548659	+	0.548659i	0.0412397	+	0.0412397i
$178$		0			0
$179$		−	9.75005i		−	0.728753i	−0.931252	−	0.364376i	$-0.881282\pi$
$179$		−	9.75005i		−	0.728753i	0.931252	−	0.364376i	$-0.118718\pi$
$180$		0			0
$181$			3.48489i			0.259030i	0.991577	+	0.129515i	$0.0413420\pi$
$181$			3.48489i			0.259030i	−0.991577	+	0.129515i	$0.958658\pi$
$182$		0			0
$183$	−6.97531	+	6.97531i	−0.515629	+	0.515629i
$184$		0			0
$185$	−4.17915	−	6.32741i	−0.307257	−	0.465200i
$186$		0			0
$187$	−22.2338	+	22.2338i	−1.62590	+	1.62590i
$188$		0			0
$189$	0.0252885	+	2.64563i	0.00183947	+	0.192441i
$190$		0			0
$191$	−1.84660			−0.133615			−0.0668077	−	0.997766i	$-0.521281\pi$
$191$	−1.84660			−0.133615			−0.0668077	+	0.997766i	$0.521281\pi$
$192$		0			0
$193$	−11.3415	+	11.3415i	−0.816378	+	0.816378i	−0.985581	−	0.169203i	$-0.945881\pi$
$193$	−11.3415	+	11.3415i	−0.816378	+	0.816378i	0.169203	+	0.985581i	$0.445881\pi$
$194$		0			0
$195$	0.936177	−	4.57860i	0.0670410	−	0.327880i
$196$		0			0
$197$	−9.51224	−	9.51224i	−0.677719	−	0.677719i	0.281765	−	0.959484i	$-0.409080\pi$
$197$	−9.51224	−	9.51224i	−0.677719	−	0.677719i	−0.959484	+	0.281765i	$0.909080\pi$
$198$		0			0
$199$	13.5954			0.963750			0.481875	−	0.876240i	$-0.339956\pi$
$199$	13.5954			0.963750			0.481875	+	0.876240i	$0.339956\pi$
$200$		0			0
$201$		−	16.2311i		−	1.14485i
$202$		0			0
$203$	−10.9866	−	10.7786i	−0.771110	−	0.756508i
$204$		0			0
$205$	1.80539	−	8.82970i	0.126094	−	0.616693i
$206$		0			0
$207$	−3.22191	−	3.22191i	−0.223938	−	0.223938i
$208$		0			0
$209$	31.5340			2.18125
$210$		0			0
$211$	1.14759			0.0790036			0.0395018	−	0.999219i	$-0.487423\pi$
$211$	1.14759			0.0790036			0.0395018	+	0.999219i	$0.487423\pi$
$212$		0			0
$213$	−1.84205	−	1.84205i	−0.126215	−	0.126215i
$214$		0			0
$215$	4.42938	−	2.92554i	0.302081	−	0.199520i
$216$		0			0
$217$	3.25121	+	3.18965i	0.220707	+	0.216527i
$218$		0			0
$219$			12.4065i			0.838355i
$220$		0			0
$221$	15.3001			1.02919
$222$		0			0
$223$	−4.38157	−	4.38157i	−0.293411	−	0.293411i	0.545015	−	0.838426i	$-0.316524\pi$
$223$	−4.38157	−	4.38157i	−0.293411	−	0.293411i	−0.838426	+	0.545015i	$0.816524\pi$
$224$		0			0
$225$	−1.96263	+	4.59871i	−0.130842	+	0.306580i
$226$		0			0
$227$	−13.5718	+	13.5718i	−0.900794	+	0.900794i	−0.995505	−	0.0947104i	$-0.969807\pi$
$227$	−13.5718	+	13.5718i	−0.900794	+	0.900794i	0.0947104	+	0.995505i	$0.469807\pi$
$228$		0			0
$229$	5.23268			0.345785			0.172893	−	0.984941i	$-0.444689\pi$
$229$	5.23268			0.345785			0.172893	+	0.984941i	$0.444689\pi$
$230$		0			0
$231$	11.3633	−	0.108617i	0.747652	−	0.00714650i
$232$		0			0
$233$	1.49743	−	1.49743i	0.0980999	−	0.0980999i	−0.656354	−	0.754453i	$-0.727902\pi$
$233$	1.49743	−	1.49743i	0.0980999	−	0.0980999i	0.754453	+	0.656354i	$0.227902\pi$
$234$		0			0
$235$	20.9237	−	13.8197i	1.36491	−	0.901501i
$236$		0			0
$237$	0.297780	−	0.297780i	0.0193429	−	0.0193429i
$238$		0			0
$239$		−	9.51664i		−	0.615580i	−0.951454	−	0.307790i	$-0.900411\pi$
$239$		−	9.51664i		−	0.615580i	0.951454	−	0.307790i	$-0.0995895\pi$
$240$		0			0
$241$			0.132939i			0.00856333i	0.999991	+	0.00428167i	$0.00136290\pi$
$241$			0.132939i			0.00856333i	−0.999991	+	0.00428167i	$0.998637\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	2.84184	−	15.3923i	0.181559	−	0.983380i
$246$		0			0
$247$	−10.8500	−	10.8500i	−0.690367	−	0.690367i
$248$		0			0
$249$			11.9435i			0.756887i
$250$		0			0
$251$			4.07694i			0.257334i	0.991688	+	0.128667i	$0.0410699\pi$
$251$			4.07694i			0.257334i	−0.991688	+	0.128667i	$0.958930\pi$
$252$		0			0
$253$	−13.8385	+	13.8385i	−0.870019	+	0.870019i
$254$		0			0
$255$	−16.0378	−	3.27921i	−1.00432	−	0.205352i
$256$		0			0
$257$	−11.8584	+	11.8584i	−0.739709	+	0.739709i	−0.972522	−	0.232812i	$-0.925207\pi$
$257$	−11.8584	+	11.8584i	−0.739709	+	0.739709i	0.232812	+	0.972522i	$0.425207\pi$
$258$		0			0
$259$	−8.97188	+	0.0857585i	−0.557485	+	0.00532878i
$260$		0			0
$261$	5.81726			0.360080
$262$		0			0
$263$	19.9161	−	19.9161i	1.22808	−	1.22808i	0.263389	−	0.964690i	$-0.415160\pi$
$263$	19.9161	−	19.9161i	1.22808	−	1.22808i	0.964690	−	0.263389i	$-0.0848402\pi$
$264$		0			0
$265$	−20.2964	+	13.4054i	−1.24680	+	0.823489i
$266$		0			0
$267$	−3.03587	−	3.03587i	−0.185792	−	0.185792i
$268$		0			0
$269$	−2.26182			−0.137906			−0.0689528	−	0.997620i	$-0.521966\pi$
$269$	−2.26182			−0.137906			−0.0689528	+	0.997620i	$0.521966\pi$
$270$		0			0
$271$		−	10.5437i		−	0.640484i	−0.947336	−	0.320242i	$-0.896236\pi$
$271$		−	10.5437i		−	0.640484i	0.947336	−	0.320242i	$-0.103764\pi$
$272$		0			0
$273$	−3.94718	−	3.87244i	−0.238894	−	0.234370i
$274$		0			0
$275$	19.7520	+	8.42974i	1.19109	+	0.508332i
$276$		0			0
$277$	−10.2777	−	10.2777i	−0.617528	−	0.617528i	0.327369	−	0.944897i	$-0.393838\pi$
$277$	−10.2777	−	10.2777i	−0.617528	−	0.617528i	−0.944897	+	0.327369i	$0.893838\pi$
$278$		0			0
$279$	−1.72147			−0.103062
$280$		0			0
$281$	−19.8867			−1.18634			−0.593170	−	0.805077i	$-0.702124\pi$
$281$	−19.8867			−1.18634			−0.593170	+	0.805077i	$0.702124\pi$
$282$		0			0
$283$	8.04861	+	8.04861i	0.478440	+	0.478440i	0.904632	−	0.426193i	$-0.140145\pi$
$283$	8.04861	+	8.04861i	0.478440	+	0.478440i	−0.426193	+	0.904632i	$0.640145\pi$
$284$		0			0
$285$	9.04767	+	13.6985i	0.535938	+	0.811431i
$286$		0			0
$287$	−7.61203	−	7.46789i	−0.449324	−	0.440815i
$288$		0			0
$289$		−	36.5926i		−	2.15251i
$290$		0			0
$291$	10.3192			0.604925
$292$		0			0
$293$	−21.7244	−	21.7244i	−1.26915	−	1.26915i	−0.946527	−	0.322625i	$-0.895435\pi$
$293$	−21.7244	−	21.7244i	−1.26915	−	1.26915i	−0.322625	−	0.946527i	$-0.604565\pi$
$294$		0			0
$295$	1.69984	+	0.347563i	0.0989686	+	0.0202359i
$296$		0			0
$297$	−3.03711	+	3.03711i	−0.176231	+	0.176231i
$298$		0			0
$299$	9.52290			0.550723
$300$		0			0
$301$	−0.0600337	−	6.28060i	−0.00346028	−	0.362008i
$302$		0			0
$303$	−0.115175	+	0.115175i	−0.00661662	+	0.00661662i
$304$		0			0
$305$	−4.41870	+	21.6107i	−0.253014	+	1.23743i
$306$		0			0
$307$	2.27695	−	2.27695i	0.129952	−	0.129952i	−0.639139	−	0.769091i	$-0.720709\pi$
$307$	2.27695	−	2.27695i	0.129952	−	0.129952i	0.769091	+	0.639139i	$0.220709\pi$
$308$		0			0
$309$		−	6.31383i		−	0.359181i
$310$		0			0
$311$		−	11.5995i		−	0.657745i	−0.944374	−	0.328872i	$-0.893331\pi$
$311$		−	11.5995i		−	0.657745i	0.944374	−	0.328872i	$-0.106669\pi$
$312$		0			0
$313$	−15.3739	−	15.3739i	−0.868986	−	0.868986i	0.123374	−	0.992360i	$-0.460628\pi$
$313$	−15.3739	−	15.3739i	−0.868986	−	0.868986i	−0.992360	+	0.123374i	$0.960628\pi$
$314$		0			0
$315$	3.30753	+	4.90513i	0.186358	+	0.276373i
$316$		0			0
$317$	21.7956	+	21.7956i	1.22416	+	1.22416i	0.966139	+	0.258023i	$0.0830710\pi$
$317$	21.7956	+	21.7956i	1.22416	+	1.22416i	0.258023	+	0.966139i	$0.416929\pi$
$318$		0			0
$319$		−	24.9859i		−	1.39894i
$320$		0			0
$321$			13.8331i			0.772090i
$322$		0			0
$323$	−38.0049	+	38.0049i	−2.11465	+	2.11465i
$324$		0			0
$325$	−3.89569	−	9.69657i	−0.216094	−	0.537869i
$326$		0			0
$327$	5.17683	−	5.17683i	0.286280	−	0.286280i
$328$		0			0
$329$	−0.283589	−	29.6685i	−0.0156348	−	1.63568i
$330$		0			0
$331$	−32.7968			−1.80268			−0.901338	−	0.433116i	$-0.857414\pi$
$331$	−32.7968			−1.80268			−0.901338	+	0.433116i	$0.857414\pi$
$332$		0			0
$333$	2.39795	−	2.39795i	0.131407	−	0.131407i
$334$		0			0
$335$	−20.0023	−	30.2844i	−1.09284	−	1.65461i
$336$		0			0
$337$	−3.05599	−	3.05599i	−0.166470	−	0.166470i	0.618956	−	0.785426i	$-0.287556\pi$
$337$	−3.05599	−	3.05599i	−0.166470	−	0.166470i	−0.785426	+	0.618956i	$0.787556\pi$
$338$		0			0
$339$	−18.7168			−1.01656
$340$		0			0
$341$			7.39393i			0.400404i
$342$		0			0
$343$	−13.4659	−	12.7149i	−0.727090	−	0.686543i
$344$		0			0
$345$	−9.98204	−	2.04101i	−0.537415	−	0.109884i
$346$		0			0
$347$	−9.03562	−	9.03562i	−0.485058	−	0.485058i	0.421685	−	0.906742i	$-0.361439\pi$
$347$	−9.03562	−	9.03562i	−0.485058	−	0.485058i	−0.906742	+	0.421685i	$0.861439\pi$
$348$		0			0
$349$	−28.0691			−1.50251			−0.751253	−	0.660014i	$-0.770550\pi$
$349$	−28.0691			−1.50251			−0.751253	+	0.660014i	$0.770550\pi$
$350$		0			0
$351$	2.08998			0.111555
$352$		0			0
$353$	−9.07254	−	9.07254i	−0.482883	−	0.482883i	0.423168	−	0.906051i	$-0.360918\pi$
$353$	−9.07254	−	9.07254i	−0.482883	−	0.482883i	−0.906051	+	0.423168i	$0.860918\pi$
$354$		0			0
$355$	−5.70700	−	1.16690i	−0.302896	−	0.0619325i
$356$		0			0
$357$	−13.5642	+	13.8261i	−0.717896	+	0.731752i
$358$		0			0
$359$			19.5255i			1.03052i	0.857035	+	0.515258i	$0.172304\pi$
$359$			19.5255i			1.03052i	−0.857035	+	0.515258i	$0.827696\pi$
$360$		0			0
$361$	34.9020			1.83695
$362$		0			0
$363$	5.26662	+	5.26662i	0.276426	+	0.276426i
$364$		0			0
$365$	15.2892	+	23.1484i	0.800272	+	1.21164i
$366$		0			0
$367$	8.27119	−	8.27119i	0.431753	−	0.431753i	−0.457472	−	0.889224i	$-0.651245\pi$
$367$	8.27119	−	8.27119i	0.431753	−	0.431753i	0.889224	+	0.457472i	$0.151245\pi$
$368$		0			0
$369$	4.03046			0.209817
$370$		0			0
$371$	0.275087	+	28.7790i	0.0142818	+	1.49413i
$372$		0			0
$373$	−25.5882	+	25.5882i	−1.32491	+	1.32491i	−0.415157	+	0.909750i	$0.636273\pi$
$373$	−25.5882	+	25.5882i	−1.32491	+	1.32491i	−0.909750	+	0.415157i	$0.863727\pi$
$374$		0			0
$375$	2.00529	+	10.9990i	0.103553	+	0.567988i
$376$		0			0
$377$	−8.59696	+	8.59696i	−0.442766	+	0.442766i
$378$		0			0
$379$			6.19850i			0.318396i	0.987247	+	0.159198i	$0.0508908\pi$
$379$			6.19850i			0.318396i	−0.987247	+	0.159198i	$0.949109\pi$
$380$		0			0
$381$		−	18.1747i		−	0.931118i
$382$		0			0
$383$	20.2892	+	20.2892i	1.03673	+	1.03673i	0.999299	+	0.0374314i	$0.0119176\pi$
$383$	20.2892	+	20.2892i	1.03673	+	1.03673i	0.0374314	+	0.999299i	$0.488082\pi$
$384$		0			0
$385$	21.0681	−	14.2062i	1.07373	−	0.724018i
$386$		0			0
$387$	1.67864	+	1.67864i	0.0853299	+	0.0853299i
$388$		0			0
$389$		−	5.15659i		−	0.261450i	−0.991419	−	0.130725i	$-0.958270\pi$
$389$		−	5.15659i		−	0.261450i	0.991419	−	0.130725i	$-0.0417304\pi$
$390$		0			0
$391$		−	33.3565i		−	1.68691i
$392$		0			0
$393$	−9.77673	+	9.77673i	−0.493171	+	0.493171i
$394$		0			0
$395$	0.188637	−	0.922576i	0.00949137	−	0.0464198i
$396$		0			0
$397$	12.5558	−	12.5558i	0.630155	−	0.630155i	−0.317952	−	0.948107i	$-0.602995\pi$
$397$	12.5558	−	12.5558i	0.630155	−	0.630155i	0.948107	+	0.317952i	$0.102995\pi$
$398$		0			0
$399$	19.4237	−	0.185663i	0.972401	−	0.00929478i
$400$		0			0
$401$	21.4175			1.06954			0.534768	−	0.844999i	$-0.320399\pi$
$401$	21.4175			1.06954			0.534768	+	0.844999i	$0.320399\pi$
$402$		0			0
$403$	2.54405	−	2.54405i	0.126728	−	0.126728i
$404$		0			0
$405$	−2.19074	−	0.447937i	−0.108859	−	0.0222582i
$406$		0			0
$407$	−10.2995	−	10.2995i	−0.510526	−	0.510526i
$408$		0			0
$409$	−7.32725			−0.362309			−0.181154	−	0.983455i	$-0.557983\pi$
$409$	−7.32725			−0.362309			−0.181154	+	0.983455i	$0.557983\pi$
$410$		0			0
$411$			7.82443i			0.385951i
$412$		0			0
$413$	1.43767	−	1.46542i	0.0707433	−	0.0721088i
$414$		0			0
$415$	14.7185	+	22.2845i	0.722505	+	1.09390i
$416$		0			0
$417$	−6.86211	−	6.86211i	−0.336039	−	0.336039i
$418$		0			0
$419$	−20.1356			−0.983687			−0.491843	−	0.870684i	$-0.663677\pi$
$419$	−20.1356			−0.983687			−0.491843	+	0.870684i	$0.663677\pi$
$420$		0			0
$421$	−15.1868			−0.740157			−0.370079	−	0.929000i	$-0.620669\pi$
$421$	−15.1868			−0.740157			−0.370079	+	0.929000i	$0.620669\pi$
$422$		0			0
$423$	7.92960	+	7.92960i	0.385550	+	0.385550i
$424$		0			0
$425$	−33.9648	+	13.6457i	−1.64754	+	0.661913i
$426$		0			0
$427$	18.6305	+	18.2777i	0.901592	+	0.884519i
$428$		0			0
$429$		−	8.97671i		−	0.433400i
$430$		0			0
$431$	9.87897			0.475853			0.237927	−	0.971283i	$-0.423532\pi$
$431$	9.87897			0.475853			0.237927	+	0.971283i	$0.423532\pi$
$432$		0			0
$433$	11.3585	+	11.3585i	0.545857	+	0.545857i	0.925240	−	0.379383i	$-0.123864\pi$
$433$	11.3585	+	11.3585i	0.545857	+	0.545857i	−0.379383	+	0.925240i	$0.623864\pi$
$434$		0			0
$435$	10.8540	−	7.16890i	0.520410	−	0.343723i
$436$		0			0
$437$	−23.6546	+	23.6546i	−1.13155	+	1.13155i
$438$		0			0
$439$	−26.3204			−1.25620			−0.628102	−	0.778131i	$-0.716168\pi$
$439$	−26.3204			−1.25620			−0.628102	+	0.778131i	$0.716168\pi$
$440$		0			0
$441$	6.99872	−	0.133808i	0.333272	−	0.00637181i
$442$		0			0
$443$	−4.91583	+	4.91583i	−0.233558	+	0.233558i	−0.814176	−	0.580618i	$-0.802811\pi$
$443$	−4.91583	+	4.91583i	−0.233558	+	0.233558i	0.580618	+	0.814176i	$0.302811\pi$
$444$		0			0
$445$	−9.40565	−	1.92315i	−0.445871	−	0.0911663i
$446$		0			0
$447$	6.70387	−	6.70387i	0.317082	−	0.317082i
$448$		0			0
$449$			23.4220i			1.10535i	0.833395	+	0.552677i	$0.186394\pi$
$449$			23.4220i			1.10535i	−0.833395	+	0.552677i	$0.813606\pi$
$450$		0			0
$451$		−	17.3113i		−	0.815159i
$452$		0			0
$453$	1.90930	+	1.90930i	0.0897068	+	0.0897068i
$454$		0			0
$455$	−12.1370	−	2.36099i	−0.568989	−	0.110685i
$456$		0			0
$457$	−26.7882	−	26.7882i	−1.25310	−	1.25310i	−0.954323	−	0.298777i	$-0.903421\pi$
$457$	−26.7882	−	26.7882i	−1.25310	−	1.25310i	−0.298777	−	0.954323i	$-0.596579\pi$
$458$		0			0
$459$		−	7.32070i		−	0.341701i
$460$		0			0
$461$			1.75228i			0.0816116i	0.999167	+	0.0408058i	$0.0129925\pi$
$461$			1.75228i			0.0816116i	−0.999167	+	0.0408058i	$0.987008\pi$
$462$		0			0
$463$	0.630432	−	0.630432i	0.0292986	−	0.0292986i	−0.692306	−	0.721604i	$-0.743405\pi$
$463$	0.630432	−	0.630432i	0.0292986	−	0.0292986i	0.721604	+	0.692306i	$0.243405\pi$
$464$		0			0
$465$	−3.21197	+	2.12145i	−0.148951	+	0.0983800i
$466$		0			0
$467$	16.6699	−	16.6699i	0.771390	−	0.771390i	−0.206959	−	0.978350i	$-0.566357\pi$
$467$	16.6699	−	16.6699i	0.771390	−	0.771390i	0.978350	+	0.206959i	$0.0663568\pi$
$468$		0			0
$469$	−42.9414	+	0.410459i	−1.98285	+	0.0189532i
$470$		0			0
$471$	3.11239			0.143412
$472$		0			0
$473$	7.20996	−	7.20996i	0.331514	−	0.331514i
$474$		0			0
$475$	33.7628	+	14.4092i	1.54914	+	0.661140i
$476$		0			0
$477$	−7.69186	−	7.69186i	−0.352186	−	0.352186i
$478$		0			0
$479$	36.3230			1.65964			0.829820	−	0.558031i	$-0.188443\pi$
$479$	36.3230			1.65964			0.829820	+	0.558031i	$0.188443\pi$
$480$		0			0
$481$			7.08754i			0.323164i
$482$		0			0
$483$	−8.44250	+	8.60545i	−0.384147	+	0.391562i
$484$		0			0
$485$	19.2539	−	12.7169i	0.874276	−	0.577445i
$486$		0			0
$487$	−7.25362	−	7.25362i	−0.328693	−	0.328693i	0.523396	−	0.852089i	$-0.324665\pi$
$487$	−7.25362	−	7.25362i	−0.328693	−	0.328693i	−0.852089	+	0.523396i	$0.824665\pi$
$488$		0			0
$489$	−5.89410			−0.266541
$490$		0			0
$491$	0.696840			0.0314480			0.0157240	−	0.999876i	$-0.494995\pi$
$491$	0.696840			0.0314480			0.0157240	+	0.999876i	$0.494995\pi$
$492$		0			0
$493$	30.1132	+	30.1132i	1.35623	+	1.35623i
$494$		0			0
$495$	−1.92395	+	9.40952i	−0.0864749	+	0.422926i
$496$		0			0
$497$	−4.82680	+	4.91997i	−0.216512	+	0.220691i
$498$		0			0
$499$		−	31.9174i		−	1.42882i	−0.699728	−	0.714409i	$-0.746696\pi$
$499$		−	31.9174i		−	1.42882i	0.699728	−	0.714409i	$-0.253304\pi$
$500$		0			0
$501$	−4.79174			−0.214079
$502$		0			0
$503$	−11.7973	−	11.7973i	−0.526018	−	0.526018i	0.393365	−	0.919382i	$-0.371311\pi$
$503$	−11.7973	−	11.7973i	−0.526018	−	0.526018i	−0.919382	+	0.393365i	$0.871311\pi$
$504$		0			0
$505$	−0.0729608	+	0.356832i	−0.00324671	+	0.0158788i
$506$		0			0
$507$	6.10375	−	6.10375i	0.271077	−	0.271077i
$508$		0			0
$509$	−11.9546			−0.529880			−0.264940	−	0.964265i	$-0.585352\pi$
$509$	−11.9546			−0.529880			−0.264940	+	0.964265i	$0.585352\pi$
$510$		0			0
$511$	32.8231	−	0.313742i	1.45201	−	0.0138791i
$512$		0			0
$513$	−5.19144	+	5.19144i	−0.229208	+	0.229208i
$514$		0			0
$515$	−7.78085	−	11.7805i	−0.342865	−	0.519112i
$516$		0			0
$517$	34.0586	−	34.0586i	1.49790	−	1.49790i
$518$		0			0
$519$			5.51406i			0.242040i
$520$		0			0
$521$		−	35.3147i		−	1.54716i	−0.633696	−	0.773582i	$-0.718463\pi$
$521$		−	35.3147i		−	1.54716i	0.633696	−	0.773582i	$-0.281537\pi$
$522$		0			0
$523$	−10.7252	−	10.7252i	−0.468981	−	0.468981i	0.432603	−	0.901584i	$-0.357595\pi$
$523$	−10.7252	−	10.7252i	−0.468981	−	0.468981i	−0.901584	+	0.432603i	$0.857595\pi$
$524$		0			0
$525$	12.2161	+	5.07609i	0.533155	+	0.221539i
$526$		0			0
$527$	−8.91121	−	8.91121i	−0.388179	−	0.388179i
$528$		0			0
$529$			2.23863i			0.0973319i
$530$		0			0
$531$			0.775921i			0.0336721i
$532$		0			0
$533$	−5.95636	+	5.95636i	−0.257999	+	0.257999i
$534$		0			0
$535$	17.0473	+	25.8103i	0.737017	+	1.11587i
$536$		0			0
$537$	6.89433	−	6.89433i	0.297512	−	0.297512i
$538$		0			0
$539$	−0.574723	−	30.0604i	−0.0247551	−	1.29479i
$540$		0			0
$541$	−28.3891			−1.22054			−0.610271	−	0.792193i	$-0.708939\pi$
$541$	−28.3891			−1.22054			−0.610271	+	0.792193i	$0.708939\pi$
$542$		0			0
$543$	−2.46419	+	2.46419i	−0.105748	+	0.105748i
$544$		0			0
$545$	3.27941	−	16.0388i	0.140475	−	0.687025i
$546$		0			0
$547$	−4.10546	−	4.10546i	−0.175537	−	0.175537i	0.613870	−	0.789407i	$-0.289612\pi$
$547$	−4.10546	−	4.10546i	−0.175537	−	0.175537i	−0.789407	+	0.613870i	$0.789612\pi$
$548$		0			0
$549$	−9.86457			−0.421010
$550$		0			0
$551$		−	42.7092i		−	1.81947i
$552$		0			0
$553$	−0.795347	−	0.780286i	−0.0338216	−	0.0331811i
$554$		0			0
$555$	1.51905	−	7.42926i	0.0644799	−	0.315355i
$556$		0			0
$557$	−0.765661	−	0.765661i	−0.0324421	−	0.0324421i	0.690700	−	0.723142i	$-0.257303\pi$
$557$	−0.765661	−	0.765661i	−0.0324421	−	0.0324421i	−0.723142	+	0.690700i	$0.757303\pi$
$558$		0			0
$559$	−4.96150			−0.209849
$560$		0			0
$561$	−31.4433			−1.32754
$562$		0			0
$563$	−18.0357	−	18.0357i	−0.760114	−	0.760114i	0.216229	−	0.976343i	$-0.430624\pi$
$563$	−18.0357	−	18.0357i	−0.760114	−	0.760114i	−0.976343	+	0.216229i	$0.930624\pi$
$564$		0			0
$565$	−34.9223	+	23.0656i	−1.46919	+	0.970379i
$566$		0			0
$567$	−1.85286	+	1.88862i	−0.0778129	+	0.0793148i
$568$		0			0
$569$			22.3471i			0.936838i	0.883506	+	0.468419i	$0.155176\pi$
$569$			22.3471i			0.936838i	−0.883506	+	0.468419i	$0.844824\pi$
$570$		0			0
$571$	31.1779			1.30475			0.652376	−	0.757895i	$-0.273772\pi$
$571$	31.1779			1.30475			0.652376	+	0.757895i	$0.273772\pi$
$572$		0			0
$573$	−1.30574	−	1.30574i	−0.0545482	−	0.0545482i
$574$		0			0
$575$	−21.1400	+	8.49320i	−0.881599	+	0.354191i
$576$		0			0
$577$	15.4967	−	15.4967i	0.645137	−	0.645137i	−0.306677	−	0.951814i	$-0.599217\pi$
$577$	15.4967	−	15.4967i	0.645137	−	0.645137i	0.951814	+	0.306677i	$0.0992171\pi$
$578$		0			0
$579$	−16.0393			−0.666570
$580$		0			0
$581$	31.5980	−	0.302033i	1.31091	−	0.0125304i
$582$		0			0
$583$	−33.0375	+	33.0375i	−1.36827	+	1.36827i
$584$		0			0
$585$	3.89953	−	2.57558i	0.161226	−	0.106487i
$586$		0			0
$587$	−19.3419	+	19.3419i	−0.798326	+	0.798326i	−0.982831	−	0.184506i	$-0.940932\pi$
$587$	−19.3419	+	19.3419i	−0.798326	+	0.798326i	0.184506	+	0.982831i	$0.440932\pi$
$588$		0			0
$589$			12.6387i			0.520768i
$590$		0			0
$591$		−	13.4523i		−	0.553355i
$592$		0			0
$593$	−8.53226	−	8.53226i	−0.350378	−	0.350378i	0.509872	−	0.860250i	$-0.329693\pi$
$593$	−8.53226	−	8.53226i	−0.350378	−	0.350378i	−0.860250	+	0.509872i	$0.829693\pi$
$594$		0			0
$595$	−8.27000	+	42.5129i	−0.339037	+	1.74286i
$596$		0			0
$597$	9.61338	+	9.61338i	0.393449	+	0.393449i
$598$		0			0
$599$			0.751539i			0.0307070i	0.999882	+	0.0153535i	$0.00488737\pi$
$599$			0.751539i			0.0307070i	−0.999882	+	0.0153535i	$0.995113\pi$
$600$		0			0
$601$			26.6379i			1.08658i	0.839544	+	0.543292i	$0.182822\pi$
$601$			26.6379i			1.08658i	−0.839544	+	0.543292i	$0.817178\pi$
$602$		0			0
$603$	11.4771	−	11.4771i	0.467383	−	0.467383i
$604$		0			0
$605$	16.3169	+	3.33629i	0.663377	+	0.135639i
$606$		0			0
$607$	−24.0798	+	24.0798i	−0.977367	+	0.977367i	−0.999749	−	0.0223823i	$-0.992875\pi$
$607$	−24.0798	+	24.0798i	−0.977367	+	0.977367i	0.0223823	+	0.999749i	$0.492875\pi$
$608$		0			0
$609$	−0.147110	−	15.3903i	−0.00596119	−	0.623648i
$610$		0			0
$611$	−23.4373			−0.948171
$612$		0			0
$613$	−5.56807	+	5.56807i	−0.224892	+	0.224892i	−0.810555	−	0.585663i	$-0.800834\pi$
$613$	−5.56807	+	5.56807i	−0.224892	+	0.224892i	0.585663	+	0.810555i	$0.300834\pi$
$614$		0			0
$615$	7.52015	−	4.96694i	0.303242	−	0.200286i
$616$		0			0
$617$	−1.34278	−	1.34278i	−0.0540582	−	0.0540582i	0.679561	−	0.733619i	$-0.262170\pi$
$617$	−1.34278	−	1.34278i	−0.0540582	−	0.0540582i	−0.733619	+	0.679561i	$0.762170\pi$
$618$		0			0
$619$	32.7537			1.31648			0.658241	−	0.752808i	$-0.271301\pi$
$619$	32.7537			1.31648			0.658241	+	0.752808i	$0.271301\pi$
$620$		0			0
$621$		−	4.55646i		−	0.182845i
$622$		0			0
$623$	−7.95501	+	8.10855i	−0.318711	+	0.324862i
$624$		0			0
$625$	17.2962	+	18.0511i	0.691847	+	0.722044i
$626$		0			0
$627$	22.2979	+	22.2979i	0.890492	+	0.890492i
$628$		0			0
$629$	24.8260			0.989877
$630$		0			0
$631$	−20.6332			−0.821396			−0.410698	−	0.911772i	$-0.634715\pi$
$631$	−20.6332			−0.821396			−0.410698	+	0.911772i	$0.634715\pi$
$632$		0			0
$633$	0.811471	+	0.811471i	0.0322531	+	0.0322531i
$634$		0			0
$635$	−22.3976	−	33.9109i	−0.888821	−	1.34571i
$636$		0			0
$637$	−10.1452	+	10.5407i	−0.401968	+	0.417638i
$638$		0			0
$639$		−	2.60505i		−	0.103054i
$640$		0			0
$641$	18.9477			0.748389			0.374194	−	0.927350i	$-0.377919\pi$
$641$	18.9477			0.748389			0.374194	+	0.927350i	$0.377919\pi$
$642$		0			0
$643$	28.6816	+	28.6816i	1.13109	+	1.13109i	0.989996	+	0.141096i	$0.0450626\pi$
$643$	28.6816	+	28.6816i	1.13109	+	1.13109i	0.141096	+	0.989996i	$0.454937\pi$
$644$		0			0
$645$	5.20071	+	1.06338i	0.204778	+	0.0418705i
$646$		0			0
$647$	12.1999	−	12.1999i	0.479627	−	0.479627i	−0.425385	−	0.905012i	$-0.639861\pi$
$647$	12.1999	−	12.1999i	0.479627	−	0.479627i	0.905012	+	0.425385i	$0.139861\pi$
$648$		0			0
$649$	3.33268			0.130819
$650$		0			0
$651$	0.0435334	+	4.55437i	0.00170621	+	0.178500i
$652$		0			0
$653$	−13.4392	+	13.4392i	−0.525918	+	0.525918i	−0.919353	−	0.393435i	$-0.871287\pi$
$653$	−13.4392	+	13.4392i	−0.525918	+	0.525918i	0.393435	+	0.919353i	$0.371287\pi$
$654$		0			0
$655$	−6.19334	+	30.2900i	−0.241994	+	1.18353i
$656$		0			0
$657$	−8.77273	+	8.77273i	−0.342257	+	0.342257i
$658$		0			0
$659$		−	10.0077i		−	0.389844i	−0.980819	−	0.194922i	$-0.937555\pi$
$659$		−	10.0077i		−	0.389844i	0.980819	−	0.194922i	$-0.0624454\pi$
$660$		0			0
$661$		−	9.82613i		−	0.382192i	−0.981571	−	0.191096i	$-0.938796\pi$
$661$		−	9.82613i		−	0.382192i	0.981571	−	0.191096i	$-0.0612042\pi$
$662$		0			0
$663$	10.8188	+	10.8188i	0.420167	+	0.420167i
$664$		0			0
$665$	36.0125	−	24.2832i	1.39650	−	0.941662i
$666$		0			0
$667$	18.7427	+	18.7427i	0.725720	+	0.725720i
$668$		0			0
$669$		−	6.19647i		−	0.239569i
$670$		0			0
$671$			42.3696i			1.63566i
$672$		0			0
$673$	26.8381	−	26.8381i	1.03453	−	1.03453i	0.0351501	−	0.999382i	$-0.488809\pi$
$673$	26.8381	−	26.8381i	1.03453	−	1.03453i	0.999382	−	0.0351501i	$-0.0111909\pi$
$674$		0			0
$675$	−4.63956	+	1.86399i	−0.178577	+	0.0717449i
$676$		0			0
$677$	−20.1885	+	20.1885i	−0.775908	+	0.775908i	−0.979132	−	0.203224i	$-0.934858\pi$
$677$	−20.1885	+	20.1885i	−0.775908	+	0.775908i	0.203224	+	0.979132i	$0.434858\pi$
$678$		0			0
$679$	−0.260958	−	27.3009i	−0.0100147	−	1.04771i
$680$		0			0
$681$	−19.1935			−0.735496
$682$		0			0
$683$	−3.48742	+	3.48742i	−0.133442	+	0.133442i	−0.770673	−	0.637231i	$-0.780080\pi$
$683$	−3.48742	+	3.48742i	−0.133442	+	0.133442i	0.637231	+	0.770673i	$0.280080\pi$
$684$		0			0
$685$	9.64243	+	14.5990i	0.368418	+	0.557801i
$686$		0			0
$687$	3.70006	+	3.70006i	0.141166	+	0.141166i
$688$		0			0
$689$	22.7346			0.866120
$690$		0			0
$691$		−	32.1247i		−	1.22208i	−0.791599	−	0.611041i	$-0.790751\pi$
$691$		−	32.1247i		−	1.22208i	0.791599	−	0.611041i	$-0.209249\pi$
$692$		0			0
$693$	8.11189	+	7.95828i	0.308145	+	0.302310i
$694$		0			0
$695$	−21.2600	−	4.34700i	−0.806439	−	0.164891i
$696$		0			0
$697$	20.8637	+	20.8637i	0.790270	+	0.790270i
$698$		0			0
$699$	2.11769			0.0800982
$700$		0			0
$701$	−19.6054			−0.740486			−0.370243	−	0.928935i	$-0.620726\pi$
$701$	−19.6054			−0.740486			−0.370243	+	0.928935i	$0.620726\pi$
$702$		0			0
$703$	−17.6052	−	17.6052i	−0.663994	−	0.663994i
$704$		0			0
$705$	24.5673	+	5.02323i	0.925258	+	0.189186i
$706$		0			0
$707$	0.307623	+	0.301798i	0.0115693	+	0.0113503i
$708$		0			0
$709$			32.5890i			1.22391i	0.790894	+	0.611953i	$0.209616\pi$
$709$			32.5890i			1.22391i	−0.790894	+	0.611953i	$0.790384\pi$
$710$		0			0
$711$	0.421125			0.0157934
$712$		0			0
$713$	−5.54642	−	5.54642i	−0.207715	−	0.207715i
$714$		0			0
$715$	−11.0625	−	16.7490i	−0.413712	−	0.626377i
$716$		0			0
$717$	6.72928	−	6.72928i	0.251310	−	0.251310i
$718$		0			0
$719$	28.2155			1.05226			0.526129	−	0.850404i	$-0.323643\pi$
$719$	28.2155			1.05226			0.526129	+	0.850404i	$0.323643\pi$
$720$		0			0
$721$	−16.7041	+	0.159667i	−0.622092	+	0.00594633i
$722$		0			0
$723$	−0.0940019	+	0.0940019i	−0.00349597	+	0.00349597i
$724$		0			0
$725$	11.4171	−	26.7519i	0.424021	−	0.993540i
$726$		0			0
$727$	−0.621604	+	0.621604i	−0.0230540	+	0.0230540i	−0.718540	−	0.695486i	$-0.755189\pi$
$727$	−0.621604	+	0.621604i	−0.0230540	+	0.0230540i	0.695486	+	0.718540i	$0.255189\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			17.3790i			0.642784i
$732$		0			0
$733$	23.8152	+	23.8152i	0.879636	+	0.879636i	0.993497	−	0.113861i	$-0.0363217\pi$
$733$	23.8152	+	23.8152i	0.879636	+	0.879636i	−0.113861	+	0.993497i	$0.536322\pi$
$734$		0			0
$735$	12.8935	−	8.87454i	0.475584	−	0.327342i
$736$		0			0
$737$	−49.2956	−	49.2956i	−1.81583	−	1.81583i
$738$		0			0
$739$			12.3116i			0.452889i	0.974024	+	0.226444i	$0.0727102\pi$
$739$			12.3116i			0.452889i	−0.974024	+	0.226444i	$0.927290\pi$
$740$		0			0
$741$		−	15.3442i		−	0.563683i
$742$		0			0
$743$	4.86752	−	4.86752i	0.178572	−	0.178572i	−0.612161	−	0.790733i	$-0.709700\pi$
$743$	4.86752	−	4.86752i	0.178572	−	0.178572i	0.790733	+	0.612161i	$0.209700\pi$
$744$		0			0
$745$	4.24676	−	20.7698i	0.155589	−	0.760946i
$746$		0			0
$747$	−8.44531	+	8.44531i	−0.308998	+	0.308998i
$748$		0			0
$749$	36.5974	−	0.349819i	1.33724	−	0.0127821i
$750$		0			0
$751$	40.8220			1.48962			0.744808	−	0.667278i	$-0.232541\pi$
$751$	40.8220			1.48962			0.744808	+	0.667278i	$0.232541\pi$
$752$		0			0
$753$	−2.88284	+	2.88284i	−0.105056	+	0.105056i
$754$		0			0
$755$	5.91535	+	1.20950i	0.215282	+	0.0440182i
$756$		0			0
$757$	−6.75219	−	6.75219i	−0.245412	−	0.245412i	0.573672	−	0.819085i	$-0.305518\pi$
$757$	−6.75219	−	6.75219i	−0.245412	−	0.245412i	−0.819085	+	0.573672i	$0.805518\pi$
$758$		0			0
$759$	−19.5706			−0.710368
$760$		0			0
$761$		−	2.44460i		−	0.0886166i	−0.999018	−	0.0443083i	$-0.985892\pi$
$761$		−	2.44460i		−	0.0886166i	0.999018	−	0.0443083i	$-0.0141084\pi$
$762$		0			0
$763$	−13.8269	−	13.5651i	−0.500568	−	0.491089i
$764$		0			0
$765$	−9.02166	−	13.6592i	−0.326179	−	0.493848i
$766$		0			0
$767$	−1.14668	−	1.14668i	−0.0414043	−	0.0414043i
$768$		0			0
$769$	8.96572			0.323312			0.161656	−	0.986847i	$-0.448316\pi$
$769$	8.96572			0.323312			0.161656	+	0.986847i	$0.448316\pi$
$770$		0			0
$771$	−16.7704			−0.603970
$772$		0			0
$773$	−3.20283	−	3.20283i	−0.115198	−	0.115198i	0.647158	−	0.762356i	$-0.275957\pi$
$773$	−3.20283	−	3.20283i	−0.115198	−	0.115198i	−0.762356	+	0.647158i	$0.775957\pi$
$774$		0			0
$775$	−3.37860	+	7.91653i	−0.121363	+	0.284370i
$776$		0			0
$777$	−6.40472	−	6.28344i	−0.229768	−	0.225417i
$778$		0			0
$779$		−	29.5908i		−	1.06020i
$780$		0			0
$781$	−11.1890			−0.400375
$782$		0			0
$783$	4.11343	+	4.11343i	0.147002	+	0.147002i
$784$		0			0
$785$	5.80719	−	3.83556i	0.207268	−	0.136897i
$786$		0			0
$787$	−13.8309	+	13.8309i	−0.493018	+	0.493018i	−0.909256	−	0.416238i	$-0.863348\pi$
$787$	−13.8309	+	13.8309i	−0.493018	+	0.493018i	0.416238	+	0.909256i	$0.363348\pi$
$788$		0			0
$789$	28.1656			1.00272
$790$		0			0
$791$	0.473320	+	49.5177i	0.0168293	+	1.76065i
$792$		0			0
$793$	14.5782	−	14.5782i	0.517688	−	0.517688i
$794$		0			0
$795$	−23.8308	−	4.87263i	−0.845190	−	0.172814i
$796$		0			0
$797$	22.9449	−	22.9449i	0.812751	−	0.812751i	−0.172294	−	0.985046i	$-0.555118\pi$
$797$	22.9449	−	22.9449i	0.812751	−	0.812751i	0.985046	+	0.172294i	$0.0551180\pi$
$798$		0			0
$799$			82.0953i			2.90432i
$800$		0			0
$801$		−	4.29336i		−	0.151698i
$802$		0			0
$803$	37.6800	+	37.6800i	1.32970	+	1.32970i
$804$		0			0
$805$	−5.14732	+	26.4604i	−0.181419	+	0.932607i
$806$		0			0
$807$	−1.59935	−	1.59935i	−0.0562997	−	0.0562997i
$808$		0			0
$809$			29.3160i			1.03070i	0.856981	+	0.515348i	$0.172337\pi$
$809$			29.3160i			1.03070i	−0.856981	+	0.515348i	$0.827663\pi$
$810$		0			0
$811$			18.7720i			0.659174i	0.944125	+	0.329587i	$0.106909\pi$
$811$			18.7720i			0.659174i	−0.944125	+	0.329587i	$0.893091\pi$
$812$		0			0
$813$	7.45552	−	7.45552i	0.261476	−	0.261476i
$814$		0			0
$815$	−10.9974	+	7.26360i	−0.385222	+	0.254433i
$816$		0			0
$817$	12.3242	−	12.3242i	0.431170	−	0.431170i
$818$		0			0
$819$	−0.0528524	−	5.52930i	−0.00184681	−	0.193209i
$820$		0			0
$821$	15.4560			0.539418			0.269709	−	0.962942i	$-0.413072\pi$
$821$	15.4560			0.539418			0.269709	+	0.962942i	$0.413072\pi$
$822$		0			0
$823$	39.0741	−	39.0741i	1.36204	−	1.36204i	0.490723	−	0.871316i	$-0.336733\pi$
$823$	39.0741	−	39.0741i	1.36204	−	1.36204i	0.871316	−	0.490723i	$-0.163267\pi$
$824$		0			0
$825$	8.00607	+	19.9275i	0.278736	+	0.693787i
$826$		0			0
$827$	−14.9880	−	14.9880i	−0.521184	−	0.521184i	0.396745	−	0.917929i	$-0.370140\pi$
$827$	−14.9880	−	14.9880i	−0.521184	−	0.521184i	−0.917929	+	0.396745i	$0.870140\pi$
$828$		0			0
$829$	39.3244			1.36579			0.682896	−	0.730515i	$-0.260720\pi$
$829$	39.3244			1.36579			0.682896	+	0.730515i	$0.260720\pi$
$830$		0			0
$831$		−	14.5349i		−	0.504209i
$832$		0			0
$833$	36.9216	+	35.5363i	1.27926	+	1.23126i
$834$		0			0
$835$	−8.94056	+	5.90510i	−0.309401	+	0.204354i
$836$		0			0
$837$	−1.21726	−	1.21726i	−0.0420748	−	0.0420748i
$838$		0			0
$839$	−20.2618			−0.699516			−0.349758	−	0.936840i	$-0.613736\pi$
$839$	−20.2618			−0.699516			−0.349758	+	0.936840i	$0.613736\pi$
$840$		0			0
$841$	−4.84056			−0.166916
$842$		0			0
$843$	−14.0620	−	14.0620i	−0.484321	−	0.484321i
$844$		0			0
$845$	3.86659	−	18.9105i	0.133015	−	0.650541i
$846$		0			0
$847$	13.8003	−	14.0667i	0.474186	−	0.483338i
$848$		0			0
$849$			11.3824i			0.390645i
$850$		0			0
$851$	15.4519			0.529685
$852$		0			0
$853$	−9.66947	−	9.66947i	−0.331076	−	0.331076i	0.521919	−	0.852995i	$-0.325216\pi$
$853$	−9.66947	−	9.66947i	−0.331076	−	0.331076i	−0.852995	+	0.521919i	$0.825216\pi$
$854$		0			0
$855$	−3.28866	+	16.0840i	−0.112470	+	0.550061i
$856$		0			0
$857$	−16.3114	+	16.3114i	−0.557187	+	0.557187i	−0.928506	−	0.371319i	$-0.878906\pi$
$857$	−16.3114	+	16.3114i	−0.557187	+	0.557187i	0.371319	+	0.928506i	$0.378906\pi$
$858$		0			0
$859$	12.9958			0.443411			0.221706	−	0.975114i	$-0.428838\pi$
$859$	12.9958			0.443411			0.221706	+	0.975114i	$0.428838\pi$
$860$		0			0
$861$	−0.101924	−	10.6631i	−0.00347357	−	0.363398i
$862$		0			0
$863$	12.3753	−	12.3753i	0.421262	−	0.421262i	−0.464376	−	0.885638i	$-0.653721\pi$
$863$	12.3753	−	12.3753i	0.421262	−	0.421262i	0.885638	+	0.464376i	$0.153721\pi$
$864$		0			0
$865$	6.79525	+	10.2883i	0.231046	+	0.349812i
$866$		0			0
$867$	25.8749	−	25.8749i	0.878757	−	0.878757i
$868$		0			0
$869$		−	1.80878i		−	0.0613588i
$870$		0			0
$871$			33.9225i			1.14942i
$872$		0			0
$873$	7.29681	+	7.29681i	0.246959	+	0.246959i
$874$		0			0
$875$	29.0487	−	5.58340i	0.982025	−	0.188753i
$876$		0			0
$877$	11.1110	+	11.1110i	0.375191	+	0.375191i	0.869364	−	0.494173i	$-0.164529\pi$
$877$	11.1110	+	11.1110i	0.375191	+	0.375191i	−0.494173	+	0.869364i	$0.664529\pi$
$878$		0			0
$879$		−	30.7229i		−	1.03626i
$880$		0			0
$881$			21.8179i			0.735065i	0.930011	+	0.367532i	$0.119797\pi$
$881$			21.8179i			0.735065i	−0.930011	+	0.367532i	$0.880203\pi$
$882$		0			0
$883$	−28.3564	+	28.3564i	−0.954268	+	0.954268i	−0.998999	−	0.0447315i	$-0.985757\pi$
$883$	−28.3564	+	28.3564i	−0.954268	+	0.954268i	0.0447315	+	0.998999i	$0.485757\pi$
$884$		0			0
$885$	0.956206	+	1.44773i	0.0321425	+	0.0486651i
$886$		0			0
$887$	8.04375	−	8.04375i	0.270083	−	0.270083i	−0.559051	−	0.829133i	$-0.688834\pi$
$887$	8.04375	−	8.04375i	0.270083	−	0.270083i	0.829133	+	0.559051i	$0.188834\pi$
$888$		0			0
$889$	−48.0835	+	0.459611i	−1.61267	+	0.0154149i
$890$		0			0
$891$	−4.29513			−0.143892
$892$		0			0
$893$	58.2175	−	58.2175i	1.94818	−	1.94818i
$894$		0			0
$895$	4.36740	−	21.3598i	0.145986	−	0.713981i
$896$		0			0
$897$	6.73371	+	6.73371i	0.224832	+	0.224832i
$898$		0			0
$899$	10.0142			0.333994
$900$		0			0
$901$		−	79.6341i		−	2.65300i
$902$		0			0
$903$	4.39860	−	4.48350i	0.146376	−	0.149202i
$904$		0			0
$905$	−1.56101	+	7.63449i	−0.0518897	+	0.253779i
$906$		0			0
$907$	26.6993	+	26.6993i	0.886535	+	0.886535i	0.994189	−	0.107653i	$-0.0343336\pi$
$907$	26.6993	+	26.6993i	0.886535	+	0.886535i	−0.107653	+	0.994189i	$0.534334\pi$
$908$		0			0
$909$	−0.162882			−0.00540245
$910$		0			0
$911$	17.7916			0.589461			0.294731	−	0.955580i	$-0.404770\pi$
$911$	17.7916			0.589461			0.294731	+	0.955580i	$0.404770\pi$
$912$		0			0
$913$	36.2737	+	36.2737i	1.20048	+	1.20048i
$914$		0			0
$915$	−18.4056	+	12.1566i	−0.608470	+	0.401885i
$916$		0			0
$917$	26.1128	+	25.6184i	0.862322	+	0.845993i
$918$		0			0
$919$		−	42.0699i		−	1.38776i	−0.720092	−	0.693879i	$-0.755900\pi$
$919$		−	42.0699i		−	1.38776i	0.720092	−	0.693879i	$-0.244100\pi$
$920$		0			0
$921$	3.22009			0.106106
$922$		0			0
$923$	3.84984	+	3.84984i	0.126719	+	0.126719i
$924$		0			0
$925$	−6.32117	−	15.7337i	−0.207839	−	0.517321i
$926$		0			0
$927$	4.46455	−	4.46455i	0.146635	−	0.146635i
$928$		0			0
$929$	60.7162			1.99203			0.996017	−	0.0891609i	$-0.0284185\pi$
$929$	60.7162			1.99203			0.996017	+	0.0891609i	$0.0284185\pi$
$930$		0			0
$931$	−0.982392	−	51.3832i	−0.0321966	−	1.68402i
$932$		0			0
$933$	8.20205	−	8.20205i	0.268523	−	0.268523i
$934$		0			0
$935$	−58.6678	+	38.7492i	−1.91864	+	1.26723i
$936$		0			0
$937$	−3.40076	+	3.40076i	−0.111098	+	0.111098i	−0.760471	−	0.649372i	$-0.775032\pi$
$937$	−3.40076	+	3.40076i	−0.111098	+	0.111098i	0.649372	+	0.760471i	$0.275032\pi$
$938$		0			0
$939$		−	21.7420i		−	0.709524i
$940$		0			0
$941$			46.0560i			1.50138i	0.660653	+	0.750691i	$0.270279\pi$
$941$			46.0560i			1.50138i	−0.660653	+	0.750691i	$0.729721\pi$
$942$		0			0
$943$	12.9858	+	12.9858i	0.422875	+	0.422875i
$944$		0			0
$945$	−1.12967	+	5.80722i	−0.0367483	+	0.188909i
$946$		0			0
$947$	8.22044	+	8.22044i	0.267128	+	0.267128i	0.827942	−	0.560814i	$-0.189512\pi$
$947$	8.22044	+	8.22044i	0.267128	+	0.267128i	−0.560814	+	0.827942i	$0.689512\pi$
$948$		0			0
$949$		−	25.9293i		−	0.841701i
$950$		0			0
$951$			30.8236i			0.999524i
$952$		0			0
$953$	−20.0312	+	20.0312i	−0.648874	+	0.648874i	−0.952721	−	0.303847i	$-0.901729\pi$
$953$	−20.0312	+	20.0312i	−0.648874	+	0.648874i	0.303847	+	0.952721i	$0.401729\pi$
$954$		0			0
$955$	−4.04543	−	0.827160i	−0.130907	−	0.0267663i
$956$		0			0
$957$	17.6677	−	17.6677i	0.571116	−	0.571116i
$958$		0			0
$959$	20.7005	−	0.197868i	0.668456	−	0.00638949i
$960$		0			0
$961$	28.0365			0.904405
$962$		0			0
$963$	−9.78150	+	9.78150i	−0.315205	+	0.315205i
$964$		0			0
$965$	−29.9265	+	19.7660i	−0.963369	+	0.636290i
$966$		0			0
$967$	8.15410	+	8.15410i	0.262218	+	0.262218i	0.825955	−	0.563737i	$-0.190637\pi$
$967$	8.15410	+	8.15410i	0.262218	+	0.262218i	−0.563737	+	0.825955i	$0.690637\pi$
$968$		0			0
$969$	−53.7471			−1.72661
$970$		0			0
$971$			4.11148i			0.131944i	0.997821	+	0.0659718i	$0.0210147\pi$
$971$			4.11148i			0.131944i	−0.997821	+	0.0659718i	$0.978985\pi$
$972$		0			0
$973$	−17.9811	+	18.3281i	−0.576447	+	0.587573i
$974$		0			0
$975$	4.10184	−	9.61118i	0.131364	−	0.307804i
$976$		0			0
$977$	−10.4853	−	10.4853i	−0.335454	−	0.335454i	0.519199	−	0.854653i	$-0.326230\pi$
$977$	−10.4853	−	10.4853i	−0.335454	−	0.335454i	−0.854653	+	0.519199i	$0.826230\pi$
$978$		0			0
$979$	−18.4405			−0.589362
$980$		0			0
$981$	7.32115			0.233746
$982$		0			0
$983$	−4.74100	−	4.74100i	−0.151214	−	0.151214i	0.627446	−	0.778660i	$-0.284100\pi$
$983$	−4.74100	−	4.74100i	−0.151214	−	0.151214i	−0.778660	+	0.627446i	$0.784100\pi$
$984$		0			0
$985$	−16.5780	−	25.0997i	−0.528219	−	0.799744i
$986$		0			0
$987$	20.7783	−	21.1793i	0.661379	−	0.674145i
$988$		0			0
$989$			10.8168i			0.343955i
$990$		0			0
$991$	13.9902			0.444413			0.222206	−	0.975000i	$-0.428674\pi$
$991$	13.9902			0.444413			0.222206	+	0.975000i	$0.428674\pi$
$992$		0			0
$993$	−23.1909	−	23.1909i	−0.735940	−	0.735940i
$994$		0			0
$995$	29.7840	+	6.08986i	0.944215	+	0.193062i
$996$		0			0
$997$	19.6025	−	19.6025i	0.620819	−	0.620819i	−0.324922	−	0.945741i	$-0.605338\pi$
$997$	19.6025	−	19.6025i	0.620819	−	0.620819i	0.945741	+	0.324922i	$0.105338\pi$
$998$		0			0
$999$	3.39121			0.107293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.e.97.12		24
4.3	odd	2		840.2.bt.b.97.6	yes	24
5.3	odd	4		1680.2.cz.f.433.1		24
7.6	odd	2		1680.2.cz.f.97.1		24
20.3	even	4		840.2.bt.a.433.7	yes	24
28.27	even	2		840.2.bt.a.97.7	✓	24
35.13	even	4	inner	1680.2.cz.e.433.12		24
140.83	odd	4		840.2.bt.b.433.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.7	✓	24	28.27	even	2
840.2.bt.a.433.7	yes	24	20.3	even	4
840.2.bt.b.97.6	yes	24	4.3	odd	2
840.2.bt.b.433.6	yes	24	140.83	odd	4
1680.2.cz.e.97.12		24	1.1	even	1	trivial
1680.2.cz.e.433.12		24	35.13	even	4	inner
1680.2.cz.f.97.1		24	7.6	odd	2
1680.2.cz.f.433.1		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(2.19074 + 0.447937i) q^{5} +(1.85286 - 1.88862i) q^{7} +1.00000i q^{9} +4.29513 q^{11} +(-1.47784 - 1.47784i) q^{13} +(1.23235 + 1.86583i) q^{15} +(-5.17651 + 5.17651i) q^{17} +7.34180 q^{19} +(2.64563 - 0.0252885i) q^{21} +(-3.22191 + 3.22191i) q^{23} +(4.59871 + 1.96263i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.81726i q^{29} +1.72147i q^{31} +(3.03711 + 3.03711i) q^{33} +(4.90513 - 3.30753i) q^{35} +(-2.39795 - 2.39795i) q^{37} -2.08998i q^{39} -4.03046i q^{41} +(1.67864 - 1.67864i) q^{43} +(-0.447937 + 2.19074i) q^{45} +(7.92960 - 7.92960i) q^{47} +(-0.133808 - 6.99872i) q^{49} -7.32070 q^{51} +(-7.69186 + 7.69186i) q^{53} +(9.40952 + 1.92395i) q^{55} +(5.19144 + 5.19144i) q^{57} +0.775921 q^{59} +9.86457i q^{61} +(1.88862 + 1.85286i) q^{63} +(-2.57558 - 3.89953i) q^{65} +(-11.4771 - 11.4771i) q^{67} -4.55646 q^{69} -2.60505 q^{71} +(8.77273 + 8.77273i) q^{73} +(1.86399 + 4.63956i) q^{75} +(7.95828 - 8.11189i) q^{77} -0.421125i q^{79} -1.00000 q^{81} +(8.44531 + 8.44531i) q^{83} +(-13.6592 + 9.02166i) q^{85} +(4.11343 - 4.11343i) q^{87} -4.29336 q^{89} +(-5.52930 + 0.0528524i) q^{91} +(-1.21726 + 1.21726i) q^{93} +(16.0840 + 3.28866i) q^{95} +(7.29681 - 7.29681i) q^{97} +4.29513i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{11} - 16 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} - 24 q^{23} - 4 q^{25} + 4 q^{37} + 16 q^{43} + 4 q^{45} - 24 q^{47} - 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} - 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 16 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 - 24 * q^23 - 4 * q^25 + 4 * q^37 + 16 * q^43 + 4 * q^45 - 24 * q^47 - 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 - 4 * q^63 + 24 * q^65 - 16 * q^67 + 8 * q^69 - 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 - 16 * q^89 - 24 * q^91 - 12 * q^93 - 24 * q^95 + 28 * q^97

Introduction

L-functions

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Database

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