LMFDB - Embedded newform 840.2.bt.a.97.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, 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("840.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-4] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.7
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.a.433.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(-2.19074 - 0.447937i) q^{5} +(1.88862 - 1.85286i) q^{7} +1.00000i q^{9} -4.29513 q^{11} +(1.47784 + 1.47784i) q^{13} +(-1.23235 - 1.86583i) q^{15} +(5.17651 - 5.17651i) q^{17} +7.34180 q^{19} +(2.64563 + 0.0252885i) q^{21} +(3.22191 - 3.22191i) q^{23} +(4.59871 + 1.96263i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.81726i q^{29} +1.72147i q^{31} +(-3.03711 - 3.03711i) q^{33} +(-4.96746 + 3.21316i) q^{35} +(-2.39795 - 2.39795i) q^{37} +2.08998i q^{39} +4.03046i q^{41} +(-1.67864 + 1.67864i) q^{43} +(0.447937 - 2.19074i) q^{45} +(7.92960 - 7.92960i) q^{47} +(0.133808 - 6.99872i) q^{49} +7.32070 q^{51} +(-7.69186 + 7.69186i) q^{53} +(9.40952 + 1.92395i) q^{55} +(5.19144 + 5.19144i) q^{57} +0.775921 q^{59} -9.86457i q^{61} +(1.85286 + 1.88862i) q^{63} +(-2.57558 - 3.89953i) q^{65} +(11.4771 + 11.4771i) q^{67} +4.55646 q^{69} +2.60505 q^{71} +(-8.77273 - 8.77273i) q^{73} +(1.86399 + 4.63956i) q^{75} +(-8.11189 + 7.95828i) q^{77} +0.421125i q^{79} -1.00000 q^{81} +(8.44531 + 8.44531i) q^{83} +(-13.6592 + 9.02166i) q^{85} +(4.11343 - 4.11343i) q^{87} +4.29336 q^{89} +(5.52930 + 0.0528524i) q^{91} +(-1.21726 + 1.21726i) q^{93} +(-16.0840 - 3.28866i) q^{95} +(-7.29681 + 7.29681i) q^{97} -4.29513i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 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} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 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 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	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
$7$	1.88862	−	1.85286i	0.713833	−	0.700316i
$7$	1.88862	−	1.85286i	0.713833	−	0.700316i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−4.29513			−1.29503			−0.647515	−	0.762053i	$-0.724192\pi$
$11$	−4.29513			−1.29503			−0.647515	+	0.762053i	$0.724192\pi$
$12$		0			0
$13$	1.47784	+	1.47784i	0.409878	+	0.409878i	0.881696	−	0.471818i	$-0.156402\pi$
$13$	1.47784	+	1.47784i	0.409878	+	0.409878i	−0.471818	+	0.881696i	$0.656402\pi$
$14$		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	$-0.402257\pi$
$17$	5.17651	−	5.17651i	1.25549	−	1.25549i	0.953224	−	0.302265i	$-0.0977429\pi$
$18$		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	−0.286320	−	0.958134i	$-0.592432\pi$
$23$	3.22191	−	3.22191i	0.671814	−	0.671814i	0.958134	+	0.286320i	$0.0924321\pi$
$24$		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
$35$	−4.96746	+	3.21316i	−0.839653	+	0.543123i
$36$		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	$0.101913\pi$
$41$			4.03046i			0.629452i	−0.949183	+	0.314726i	$0.898087\pi$
$42$		0			0
$43$	−1.67864	+	1.67864i	−0.255990	+	0.255990i	−0.823421	−	0.567431i	$-0.807937\pi$
$43$	−1.67864	+	1.67864i	−0.255990	+	0.255990i	0.567431	+	0.823421i	$0.307937\pi$
$44$		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	$-0.782434\pi$
$61$		−	9.86457i		−	1.26303i	0.775364	−	0.631514i	$-0.217566\pi$
$62$		0			0
$63$	1.85286	+	1.88862i	0.233439	+	0.237944i
$64$		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	$0.208393\pi$
$67$	11.4771	+	11.4771i	1.40215	+	1.40215i	0.608911	+	0.793239i	$0.291607\pi$
$68$		0			0
$69$	4.55646			0.548534
$70$		0			0
$71$	2.60505			0.309163			0.154581	−	0.987980i	$-0.450597\pi$
$71$	2.60505			0.309163			0.154581	+	0.987980i	$0.450597\pi$
$72$		0			0
$73$	−8.77273	−	8.77273i	−1.02677	−	1.02677i	−0.999632	−	0.0271389i	$-0.991360\pi$
$73$	−8.77273	−	8.77273i	−1.02677	−	1.02677i	−0.0271389	−	0.999632i	$-0.508640\pi$
$74$		0			0
$75$	1.86399	+	4.63956i	0.215235	+	0.535731i
$76$		0			0
$77$	−8.11189	+	7.95828i	−0.924435	+	0.906930i
$78$		0			0
$79$			0.421125i			0.0473802i	0.999719	+	0.0236901i	$0.00754150\pi$
$79$			0.421125i			0.0473802i	−0.999719	+	0.0236901i	$0.992458\pi$
$80$		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	$-0.426929\pi$
$89$	4.29336			0.455095			0.227548	+	0.973767i	$0.426929\pi$
$90$		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	−0.972747	−	0.231869i	$-0.925516\pi$
$97$	−7.29681	+	7.29681i	−0.740878	+	0.740878i	0.231869	+	0.972747i	$0.425516\pi$
$98$		0			0
$99$		−	4.29513i		−	0.431677i
$100$		0			0
$101$		−	0.162882i		−	0.0162074i	−0.999967	−	0.00810368i	$-0.997420\pi$
$101$		−	0.162882i		−	0.0162074i	0.999967	−	0.00810368i	$-0.00257951\pi$
$102$		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
$105$	−5.78457	−	1.24048i	−0.564516	−	0.121058i
$106$		0			0
$107$	−9.78150	−	9.78150i	−0.945614	−	0.945614i	0.0529817	−	0.998595i	$-0.483127\pi$
$107$	−9.78150	−	9.78150i	−0.945614	−	0.945614i	−0.998595	+	0.0529817i	$0.983127\pi$
$108$		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	$0.0485720\pi$
$127$	12.8515	+	12.8515i	1.14038	+	1.14038i	0.152002	+	0.988380i	$0.451428\pi$
$128$		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
$133$	13.8659	−	13.6033i	1.20233	−	1.17956i
$134$		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
$147$	5.04346	−	4.85423i	0.415978	−	0.400370i
$148$		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	$-0.535043\pi$
$151$	−2.70016			−0.219736			−0.109868	+	0.993946i	$0.535043\pi$
$152$		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	−0.789453	−	0.613811i	$-0.789636\pi$
$157$	−2.20080	+	2.20080i	−0.175643	+	0.175643i	0.613811	+	0.789453i	$0.289636\pi$
$158$		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	−0.524788	−	0.851233i	$-0.675856\pi$
$163$	4.16776	−	4.16776i	0.326444	−	0.326444i	0.851233	+	0.524788i	$0.175856\pi$
$164$		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	0.543179	−	0.839617i	$-0.317220\pi$
$173$	−3.89903	−	3.89903i	−0.296438	−	0.296438i	−0.839617	+	0.543179i	$0.817220\pi$
$174$		0			0
$175$	12.3217	−	4.81410i	0.931434	−	0.363912i
$176$		0			0
$177$	0.548659	+	0.548659i	0.0412397	+	0.0412397i
$178$		0			0
$179$			9.75005i			0.728753i	0.931252	+	0.364376i	$0.118718\pi$
$179$			9.75005i			0.728753i	−0.931252	+	0.364376i	$0.881282\pi$
$180$		0			0
$181$		−	3.48489i		−	0.259030i	−0.991577	−	0.129515i	$-0.958658\pi$
$181$		−	3.48489i		−	0.259030i	0.991577	−	0.129515i	$-0.0413420\pi$
$182$		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	$-0.478719\pi$
$191$	1.84660			0.133615			0.0668077	+	0.997766i	$0.478719\pi$
$192$		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
$203$	−10.7786	−	10.9866i	−0.756508	−	0.771110i
$204$		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	$-0.512577\pi$
$211$	−1.14759			−0.0790036			−0.0395018	+	0.999219i	$0.512577\pi$
$212$		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
$217$	3.18965	+	3.25121i	0.216527	+	0.220707i
$218$		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	$-0.555311\pi$
$229$	−5.23268			−0.345785			−0.172893	+	0.984941i	$0.555311\pi$
$230$		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	$0.0995895\pi$
$239$			9.51664i			0.615580i	−0.951454	+	0.307790i	$0.900411\pi$
$240$		0			0
$241$		−	0.132939i		−	0.00856333i	−0.999991	−	0.00428167i	$-0.998637\pi$
$241$		−	0.132939i		−	0.00856333i	0.999991	−	0.00428167i	$-0.00136290\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−3.42812	+	15.2725i	−0.219015	+	0.975722i
$246$		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	−0.232812	−	0.972522i	$-0.574793\pi$
$257$	11.8584	−	11.8584i	0.739709	−	0.739709i	0.972522	+	0.232812i	$0.0747928\pi$
$258$		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	$0.584840\pi$
$263$	−19.9161	+	19.9161i	−1.22808	+	1.22808i	−0.964690	+	0.263389i	$0.915160\pi$
$264$		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	$-0.478034\pi$
$269$	2.26182			0.137906			0.0689528	+	0.997620i	$0.478034\pi$
$270$		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
$273$	3.87244	+	3.94718i	0.234370	+	0.238894i
$274$		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
$287$	7.46789	+	7.61203i	0.440815	+	0.449324i
$288$		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	$0.104565\pi$
$293$	21.7244	+	21.7244i	1.26915	+	1.26915i	0.322625	+	0.946527i	$0.395435\pi$
$294$		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	0.992360	−	0.123374i	$-0.0393716\pi$
$313$	15.3739	+	15.3739i	0.868986	+	0.868986i	−0.123374	+	0.992360i	$0.539372\pi$
$314$		0			0
$315$	−3.21316	−	4.96746i	−0.181041	−	0.279884i
$316$		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	$-0.142586\pi$
$331$	32.7968			1.80268			0.901338	+	0.433116i	$0.142586\pi$
$332$		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
$343$	−12.7149	−	13.4659i	−0.686543	−	0.727090i
$344$		0			0
$345$	−9.98204	−	2.04101i	−0.537415	−	0.109884i
$346$		0			0
$347$	9.03562	+	9.03562i	0.485058	+	0.485058i	0.906742	−	0.421685i	$-0.138561\pi$
$347$	9.03562	+	9.03562i	0.485058	+	0.485058i	−0.421685	+	0.906742i	$0.638561\pi$
$348$		0			0
$349$	28.0691			1.50251			0.751253	−	0.660014i	$-0.229450\pi$
$349$	28.0691			1.50251			0.751253	+	0.660014i	$0.229450\pi$
$350$		0			0
$351$	−2.08998			−0.111555
$352$		0			0
$353$	9.07254	+	9.07254i	0.482883	+	0.482883i	0.906051	−	0.423168i	$-0.139082\pi$
$353$	9.07254	+	9.07254i	0.482883	+	0.482883i	−0.423168	+	0.906051i	$0.639082\pi$
$354$		0			0
$355$	−5.70700	−	1.16690i	−0.302896	−	0.0619325i
$356$		0			0
$357$	13.8261	−	13.5642i	0.731752	−	0.717896i
$358$		0			0
$359$		−	19.5255i		−	1.03052i	−0.857035	−	0.515258i	$-0.827696\pi$
$359$		−	19.5255i		−	1.03052i	0.857035	−	0.515258i	$-0.172304\pi$
$360$		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	$-0.949109\pi$
$379$		−	6.19850i		−	0.318396i	0.987247	−	0.159198i	$-0.0508908\pi$
$380$		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
$385$	21.3359	−	13.8009i	1.08738	−	0.703360i
$386$		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	−0.948107	−	0.317952i	$-0.897005\pi$
$397$	−12.5558	+	12.5558i	−0.630155	+	0.630155i	0.317952	+	0.948107i	$0.397005\pi$
$398$		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	$-0.442017\pi$
$409$	7.32725			0.362309			0.181154	+	0.983455i	$0.442017\pi$
$410$		0			0
$411$			7.82443i			0.385951i
$412$		0			0
$413$	1.46542	−	1.43767i	0.0721088	−	0.0707433i
$414$		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
$427$	−18.2777	−	18.6305i	−0.884519	−	0.901592i
$428$		0			0
$429$		−	8.97671i		−	0.433400i
$430$		0			0
$431$	−9.87897			−0.475853			−0.237927	−	0.971283i	$-0.576468\pi$
$431$	−9.87897			−0.475853			−0.237927	+	0.971283i	$0.576468\pi$
$432$		0			0
$433$	−11.3585	−	11.3585i	−0.545857	−	0.545857i	0.379383	−	0.925240i	$-0.376136\pi$
$433$	−11.3585	−	11.3585i	−0.545857	−	0.545857i	−0.925240	+	0.379383i	$0.876136\pi$
$434$		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	−0.580618	−	0.814176i	$-0.697189\pi$
$443$	4.91583	−	4.91583i	0.233558	−	0.233558i	0.814176	+	0.580618i	$0.197189\pi$
$444$		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
$455$	−12.0896	−	2.59256i	−0.566769	−	0.121541i
$456$		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	$-0.987008\pi$
$461$		−	1.75228i		−	0.0816116i	0.999167	−	0.0408058i	$-0.0129925\pi$
$462$		0			0
$463$	−0.630432	+	0.630432i	−0.0292986	+	0.0292986i	−0.721604	−	0.692306i	$-0.756595\pi$
$463$	−0.630432	+	0.630432i	−0.0292986	+	0.0292986i	0.692306	+	0.721604i	$0.256595\pi$
$464$		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
$483$	8.60545	−	8.44250i	0.391562	−	0.384147i
$484$		0			0
$485$	19.2539	−	12.7169i	0.874276	−	0.577445i
$486$		0			0
$487$	7.25362	+	7.25362i	0.328693	+	0.328693i	0.852089	−	0.523396i	$-0.175335\pi$
$487$	7.25362	+	7.25362i	0.328693	+	0.328693i	−0.523396	+	0.852089i	$0.675335\pi$
$488$		0			0
$489$	5.89410			0.266541
$490$		0			0
$491$	−0.696840			−0.0314480			−0.0157240	−	0.999876i	$-0.505005\pi$
$491$	−0.696840			−0.0314480			−0.0157240	+	0.999876i	$0.505005\pi$
$492$		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
$497$	4.91997	−	4.82680i	0.220691	−	0.216512i
$498$		0			0
$499$			31.9174i			1.42882i	0.699728	+	0.714409i	$0.253304\pi$
$499$			31.9174i			1.42882i	−0.699728	+	0.714409i	$0.746696\pi$
$500$		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	$-0.414648\pi$
$509$	11.9546			0.529880			0.264940	+	0.964265i	$0.414648\pi$
$510$		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	$0.281537\pi$
$521$			35.3147i			1.54716i	−0.633696	+	0.773582i	$0.718463\pi$
$522$		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
$525$	12.1168	+	5.30868i	0.528822	+	0.231690i
$526$		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	0.789407	−	0.613870i	$-0.210388\pi$
$547$	4.10546	+	4.10546i	0.175537	+	0.175537i	−0.613870	+	0.789407i	$0.710388\pi$
$548$		0			0
$549$	9.86457			0.421010
$550$		0			0
$551$		−	42.7092i		−	1.81947i
$552$		0			0
$553$	0.780286	+	0.795347i	0.0331811	+	0.0338216i
$554$		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
$567$	−1.88862	+	1.85286i	−0.0793148	+	0.0778129i
$568$		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	$-0.726228\pi$
$571$	−31.1779			−1.30475			−0.652376	+	0.757895i	$0.726228\pi$
$572$		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	−0.951814	−	0.306677i	$-0.900783\pi$
$577$	−15.4967	+	15.4967i	−0.645137	+	0.645137i	0.306677	+	0.951814i	$0.400783\pi$
$578$		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	0.860250	−	0.509872i	$-0.170307\pi$
$593$	8.53226	+	8.53226i	0.350378	+	0.350378i	−0.509872	+	0.860250i	$0.670307\pi$
$594$		0			0
$595$	−9.08114	+	42.3471i	−0.372291	+	1.73606i
$596$		0			0
$597$	9.61338	+	9.61338i	0.393449	+	0.393449i
$598$		0			0
$599$		−	0.751539i		−	0.0307070i	−0.999882	−	0.0153535i	$-0.995113\pi$
$599$		−	0.751539i		−	0.0307070i	0.999882	−	0.0153535i	$-0.00488737\pi$
$600$		0			0
$601$		−	26.6379i		−	1.08658i	−0.839544	−	0.543292i	$-0.817178\pi$
$601$		−	26.6379i		−	1.08658i	0.839544	−	0.543292i	$-0.182822\pi$
$602$		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
$623$	8.10855	−	7.95501i	0.324862	−	0.318711i
$624$		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	$-0.365285\pi$
$631$	20.6332			0.821396			0.410698	+	0.911772i	$0.365285\pi$
$632$		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
$637$	10.5407	−	10.1452i	0.417638	−	0.401968i
$638$		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	$0.0624454\pi$
$659$			10.0077i			0.389844i	−0.980819	+	0.194922i	$0.937555\pi$
$660$		0			0
$661$			9.82613i			0.382192i	0.981571	+	0.191096i	$0.0612042\pi$
$661$			9.82613i			0.382192i	−0.981571	+	0.191096i	$0.938796\pi$
$662$		0			0
$663$	10.8188	+	10.8188i	0.420167	+	0.420167i
$664$		0			0
$665$	−36.4701	+	23.5904i	−1.41425	+	0.914795i
$666$		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	−0.203224	−	0.979132i	$-0.565142\pi$
$677$	20.1885	−	20.1885i	0.775908	−	0.775908i	0.979132	+	0.203224i	$0.0651421\pi$
$678$		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	−0.637231	−	0.770673i	$-0.719920\pi$
$683$	3.48742	−	3.48742i	0.133442	−	0.133442i	0.770673	+	0.637231i	$0.219920\pi$
$684$		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
$693$	−7.95828	−	8.11189i	−0.302310	−	0.308145i
$694$		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
$707$	−0.301798	−	0.307623i	−0.0113503	−	0.0115693i
$708$		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	0.113861	−	0.993497i	$-0.463678\pi$
$733$	−23.8152	−	23.8152i	−0.879636	−	0.879636i	−0.993497	+	0.113861i	$0.963678\pi$
$734$		0			0
$735$	−13.2233	+	8.37521i	−0.487749	+	0.308924i
$736$		0			0
$737$	−49.2956	−	49.2956i	−1.81583	−	1.81583i
$738$		0			0
$739$		−	12.3116i		−	0.452889i	−0.974024	−	0.226444i	$-0.927290\pi$
$739$		−	12.3116i		−	0.452889i	0.974024	−	0.226444i	$-0.0727102\pi$
$740$		0			0
$741$			15.3442i			0.563683i
$742$		0			0
$743$	−4.86752	+	4.86752i	−0.178572	+	0.178572i	−0.790733	−	0.612161i	$-0.790300\pi$
$743$	−4.86752	+	4.86752i	−0.178572	+	0.178572i	0.612161	+	0.790733i	$0.290300\pi$
$744$		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	$-0.767459\pi$
$751$	−40.8220			−1.48962			−0.744808	+	0.667278i	$0.767459\pi$
$752$		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	$0.0141084\pi$
$761$			2.44460i			0.0886166i	−0.999018	+	0.0443083i	$0.985892\pi$
$762$		0			0
$763$	−13.5651	−	13.8269i	−0.491089	−	0.500568i
$764$		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	$-0.551684\pi$
$769$	−8.96572			−0.323312			−0.161656	+	0.986847i	$0.551684\pi$
$770$		0			0
$771$	16.7704			0.603970
$772$		0			0
$773$	3.20283	+	3.20283i	0.115198	+	0.115198i	0.762356	−	0.647158i	$-0.224043\pi$
$773$	3.20283	+	3.20283i	0.115198	+	0.115198i	−0.647158	+	0.762356i	$0.724043\pi$
$774$		0			0
$775$	−3.37860	+	7.91653i	−0.121363	+	0.284370i
$776$		0			0
$777$	−6.28344	−	6.40472i	−0.225417	−	0.229768i
$778$		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	−0.985046	−	0.172294i	$-0.944882\pi$
$797$	−22.9449	+	22.9449i	−0.812751	+	0.812751i	0.172294	+	0.985046i	$0.444882\pi$
$798$		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
$805$	−5.65218	+	26.3572i	−0.199213	+	0.928968i
$806$		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	$0.663267\pi$
$823$	−39.0741	+	39.0741i	−1.36204	+	1.36204i	−0.871316	+	0.490723i	$0.836733\pi$
$824$		0			0
$825$	−8.00607	−	19.9275i	−0.278736	−	0.693787i
$826$		0			0
$827$	14.9880	+	14.9880i	0.521184	+	0.521184i	0.917929	−	0.396745i	$-0.129860\pi$
$827$	14.9880	+	14.9880i	0.521184	+	0.521184i	−0.396745	+	0.917929i	$0.629860\pi$
$828$		0			0
$829$	−39.3244			−1.36579			−0.682896	−	0.730515i	$-0.739280\pi$
$829$	−39.3244			−1.36579			−0.682896	+	0.730515i	$0.739280\pi$
$830$		0			0
$831$		−	14.5349i		−	0.504209i
$832$		0			0
$833$	−35.5363	−	36.9216i	−1.23126	−	1.27926i
$834$		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
$847$	14.0667	−	13.8003i	0.483338	−	0.474186i
$848$		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	0.852995	−	0.521919i	$-0.174784\pi$
$853$	9.66947	+	9.66947i	0.331076	+	0.331076i	−0.521919	+	0.852995i	$0.674784\pi$
$854$		0			0
$855$	3.28866	−	16.0840i	0.112470	−	0.550061i
$856$		0			0
$857$	16.3114	−	16.3114i	0.557187	−	0.557187i	−0.371319	−	0.928506i	$-0.621094\pi$
$857$	16.3114	−	16.3114i	0.557187	−	0.557187i	0.928506	+	0.371319i	$0.121094\pi$
$858$		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	−0.885638	−	0.464376i	$-0.846279\pi$
$863$	−12.3753	+	12.3753i	−0.421262	+	0.421262i	0.464376	+	0.885638i	$0.346279\pi$
$864$		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
$875$	−29.1501	+	5.02710i	−0.985453	+	0.169947i
$876$		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	$-0.880203\pi$
$881$		−	21.8179i		−	0.735065i	0.930011	−	0.367532i	$-0.119797\pi$
$882$		0			0
$883$	28.3564	−	28.3564i	0.954268	−	0.954268i	−0.0447315	−	0.998999i	$-0.514243\pi$
$883$	28.3564	−	28.3564i	0.954268	−	0.954268i	0.998999	+	0.0447315i	$0.0142432\pi$
$884$		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
$903$	−4.48350	+	4.39860i	−0.149202	+	0.146376i
$904$		0			0
$905$	−1.56101	+	7.63449i	−0.0518897	+	0.253779i
$906$		0			0
$907$	−26.6993	−	26.6993i	−0.886535	−	0.886535i	0.107653	−	0.994189i	$-0.465666\pi$
$907$	−26.6993	−	26.6993i	−0.886535	−	0.886535i	−0.994189	+	0.107653i	$0.965666\pi$
$908$		0			0
$909$	0.162882			0.00540245
$910$		0			0
$911$	−17.7916			−0.589461			−0.294731	−	0.955580i	$-0.595230\pi$
$911$	−17.7916			−0.589461			−0.294731	+	0.955580i	$0.595230\pi$
$912$		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
$917$	25.6184	+	26.1128i	0.845993	+	0.862322i
$918$		0			0
$919$			42.0699i			1.38776i	0.720092	+	0.693879i	$0.244100\pi$
$919$			42.0699i			1.38776i	−0.720092	+	0.693879i	$0.755900\pi$
$920$		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	$-0.971581\pi$
$929$	−60.7162			−1.99203			−0.996017	+	0.0891609i	$0.971581\pi$
$930$		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	−0.649372	−	0.760471i	$-0.724968\pi$
$937$	3.40076	−	3.40076i	0.111098	−	0.111098i	0.760471	+	0.649372i	$0.224968\pi$
$938$		0			0
$939$			21.7420i			0.709524i
$940$		0			0
$941$		−	46.0560i		−	1.50138i	−0.660653	−	0.750691i	$-0.729721\pi$
$941$		−	46.0560i		−	1.50138i	0.660653	−	0.750691i	$-0.270279\pi$
$942$		0			0
$943$	12.9858	+	12.9858i	0.422875	+	0.422875i
$944$		0			0
$945$	1.24048	−	5.78457i	0.0403527	−	0.188172i
$946$		0			0
$947$	−8.22044	−	8.22044i	−0.267128	−	0.267128i	0.560814	−	0.827942i	$-0.310488\pi$
$947$	−8.22044	−	8.22044i	−0.267128	−	0.267128i	−0.827942	+	0.560814i	$0.810488\pi$
$948$		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	0.563737	−	0.825955i	$-0.309363\pi$
$967$	−8.15410	−	8.15410i	−0.262218	−	0.262218i	−0.825955	+	0.563737i	$0.809363\pi$
$968$		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
$973$	−18.3281	+	17.9811i	−0.587573	+	0.576447i
$974$		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
$987$	21.1793	−	20.7783i	0.674145	−	0.661379i
$988$		0			0
$989$			10.8168i			0.343955i
$990$		0			0
$991$	−13.9902			−0.444413			−0.222206	−	0.975000i	$-0.571326\pi$
$991$	−13.9902			−0.444413			−0.222206	+	0.975000i	$0.571326\pi$
$992$		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	−0.945741	−	0.324922i	$-0.894662\pi$
$997$	−19.6025	+	19.6025i	−0.620819	+	0.620819i	0.324922	+	0.945741i	$0.394662\pi$
$998$		0			0
$999$	3.39121			0.107293

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.7	✓	24	1.1	even	1	trivial
840.2.bt.a.433.7	yes	24	35.13	even	4	inner
840.2.bt.b.97.6	yes	24	7.6	odd	2
840.2.bt.b.433.6	yes	24	5.3	odd	4
1680.2.cz.e.97.12		24	28.27	even	2
1680.2.cz.e.433.12		24	20.3	even	4
1680.2.cz.f.97.1		24	4.3	odd	2
1680.2.cz.f.433.1		24	140.83	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.19074 - 0.447937i) q^{5} +(1.88862 - 1.85286i) q^{7} +1.00000i q^{9} -4.29513 q^{11} +(1.47784 + 1.47784i) q^{13} +(-1.23235 - 1.86583i) q^{15} +(5.17651 - 5.17651i) q^{17} +7.34180 q^{19} +(2.64563 + 0.0252885i) q^{21} +(3.22191 - 3.22191i) q^{23} +(4.59871 + 1.96263i) q^{25} +(-0.707107 + 0.707107i) q^{27} -5.81726i q^{29} +1.72147i q^{31} +(-3.03711 - 3.03711i) q^{33} +(-4.96746 + 3.21316i) q^{35} +(-2.39795 - 2.39795i) q^{37} +2.08998i q^{39} +4.03046i q^{41} +(-1.67864 + 1.67864i) q^{43} +(0.447937 - 2.19074i) q^{45} +(7.92960 - 7.92960i) q^{47} +(0.133808 - 6.99872i) q^{49} +7.32070 q^{51} +(-7.69186 + 7.69186i) q^{53} +(9.40952 + 1.92395i) q^{55} +(5.19144 + 5.19144i) q^{57} +0.775921 q^{59} -9.86457i q^{61} +(1.85286 + 1.88862i) q^{63} +(-2.57558 - 3.89953i) q^{65} +(11.4771 + 11.4771i) q^{67} +4.55646 q^{69} +2.60505 q^{71} +(-8.77273 - 8.77273i) q^{73} +(1.86399 + 4.63956i) q^{75} +(-8.11189 + 7.95828i) q^{77} +0.421125i q^{79} -1.00000 q^{81} +(8.44531 + 8.44531i) q^{83} +(-13.6592 + 9.02166i) q^{85} +(4.11343 - 4.11343i) q^{87} +4.29336 q^{89} +(5.52930 + 0.0528524i) q^{91} +(-1.21726 + 1.21726i) q^{93} +(-16.0840 - 3.28866i) q^{95} +(-7.29681 + 7.29681i) q^{97} -4.29513i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 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 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * 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

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