LMFDB - Embedded newform 588.3.g.h.295.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,4,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.9
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.249300 - 1.98440i) q^{2} -1.73205i q^{3} +(-3.87570 + 0.989422i) q^{4} -4.12200 q^{5} +(-3.43708 + 0.431800i) q^{6} +(2.92962 + 7.44428i) q^{8} -3.00000 q^{9} +(1.02761 + 8.17970i) q^{10} +15.1066i q^{11} +(1.71373 + 6.71291i) q^{12} +5.62702 q^{13} +7.13951i q^{15} +(14.0421 - 7.66940i) q^{16} +29.0822 q^{17} +(0.747900 + 5.95320i) q^{18} -7.26627i q^{19} +(15.9756 - 4.07840i) q^{20} +(29.9775 - 3.76607i) q^{22} -25.3100i q^{23} +(12.8939 - 5.07425i) q^{24} -8.00912 q^{25} +(-1.40281 - 11.1663i) q^{26} +5.19615i q^{27} -8.59966 q^{29} +(14.1677 - 1.77988i) q^{30} +16.6913i q^{31} +(-18.7199 - 25.9532i) q^{32} +26.1653 q^{33} +(-7.25018 - 57.7107i) q^{34} +(11.6271 - 2.96827i) q^{36} -22.4645 q^{37} +(-14.4192 + 1.81148i) q^{38} -9.74628i q^{39} +(-12.0759 - 30.6853i) q^{40} +49.2315 q^{41} +70.5845i q^{43} +(-14.9468 - 58.5485i) q^{44} +12.3660 q^{45} +(-50.2252 + 6.30978i) q^{46} -50.1714i q^{47} +(-13.2838 - 24.3216i) q^{48} +(1.99667 + 15.8933i) q^{50} -50.3718i q^{51} +(-21.8086 + 5.56750i) q^{52} +100.195 q^{53} +(10.3113 - 1.29540i) q^{54} -62.2693i q^{55} -12.5855 q^{57} +(2.14389 + 17.0652i) q^{58} -76.7285i q^{59} +(-7.06399 - 27.6706i) q^{60} +111.159 q^{61} +(33.1222 - 4.16113i) q^{62} +(-46.8346 + 43.6179i) q^{64} -23.1946 q^{65} +(-6.52302 - 51.9226i) q^{66} +89.7844i q^{67} +(-112.714 + 28.7745i) q^{68} -43.8382 q^{69} -52.9119i q^{71} +(-8.78887 - 22.3328i) q^{72} +32.8246 q^{73} +(5.60039 + 44.5785i) q^{74} +13.8722i q^{75} +(7.18940 + 28.1619i) q^{76} +(-19.3405 + 2.42975i) q^{78} +16.2076i q^{79} +(-57.8815 + 31.6133i) q^{80} +9.00000 q^{81} +(-12.2734 - 97.6950i) q^{82} -25.6034i q^{83} -119.877 q^{85} +(140.068 - 17.5967i) q^{86} +14.8950i q^{87} +(-112.458 + 44.2565i) q^{88} +96.7198 q^{89} +(-3.08284 - 24.5391i) q^{90} +(25.0423 + 98.0940i) q^{92} +28.9101 q^{93} +(-99.5603 + 12.5077i) q^{94} +29.9515i q^{95} +(-44.9522 + 32.4238i) q^{96} -54.1899 q^{97} -45.3197i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) $ 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.249300	−	1.98440i	−0.124650	−	0.992201i
$2$	−0.249300	−	1.98440i	−0.124650	−	0.992201i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.87570	+	0.989422i	−0.968925	+	0.247356i
$5$	−4.12200			−0.824400			−0.412200	−	0.911093i	$-0.635240\pi$
$5$	−4.12200			−0.824400			−0.412200	+	0.911093i	$0.635240\pi$
$6$	−3.43708	+	0.431800i	−0.572847	+	0.0719667i
$7$		0			0
$7$		0			0
$8$	2.92962	+	7.44428i	0.366203	+	0.930535i
$9$	−3.00000			−0.333333
$10$	1.02761	+	8.17970i	0.102761	+	0.817970i
$11$			15.1066i			1.37332i	0.726977	+	0.686662i	$0.240925\pi$
$11$			15.1066i			1.37332i	−0.726977	+	0.686662i	$0.759075\pi$
$12$	1.71373	+	6.71291i	0.142811	+	0.559409i
$13$	5.62702			0.432848			0.216424	−	0.976300i	$-0.430561\pi$
$13$	5.62702			0.432848			0.216424	+	0.976300i	$0.430561\pi$
$14$		0			0
$15$			7.13951i			0.475968i
$16$	14.0421	−	7.66940i	0.877630	−	0.479338i
$17$	29.0822			1.71072			0.855358	−	0.518037i	$-0.173337\pi$
$17$	29.0822			1.71072			0.855358	+	0.518037i	$0.173337\pi$
$18$	0.747900	+	5.95320i	0.0415500	+	0.330734i
$19$		−	7.26627i		−	0.382435i	−0.981548	−	0.191218i	$-0.938756\pi$
$19$		−	7.26627i		−	0.382435i	0.981548	−	0.191218i	$-0.0612436\pi$
$20$	15.9756	−	4.07840i	0.798782	−	0.203920i
$21$		0			0
$22$	29.9775	−	3.76607i	1.36261	−	0.171185i
$23$		−	25.3100i		−	1.10043i	−0.835021	−	0.550217i	$-0.814545\pi$
$23$		−	25.3100i		−	1.10043i	0.835021	−	0.550217i	$-0.185455\pi$
$24$	12.8939	−	5.07425i	0.537245	−	0.211427i
$25$	−8.00912			−0.320365
$26$	−1.40281	−	11.1663i	−0.0539544	−	0.429472i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−8.59966			−0.296540			−0.148270	−	0.988947i	$-0.547370\pi$
$29$	−8.59966			−0.296540			−0.148270	+	0.988947i	$0.547370\pi$
$30$	14.1677	−	1.77988i	0.472255	−	0.0593293i
$31$			16.6913i			0.538428i	0.963080	+	0.269214i	$0.0867639\pi$
$31$			16.6913i			0.538428i	−0.963080	+	0.269214i	$0.913236\pi$
$32$	−18.7199	−	25.9532i	−0.584996	−	0.811036i
$33$	26.1653			0.792889
$34$	−7.25018	−	57.7107i	−0.213241	−	1.69737i
$35$		0			0
$36$	11.6271	−	2.96827i	0.322975	−	0.0824518i
$37$	−22.4645			−0.607147			−0.303574	−	0.952808i	$-0.598180\pi$
$37$	−22.4645			−0.607147			−0.303574	+	0.952808i	$0.598180\pi$
$38$	−14.4192	+	1.81148i	−0.379452	+	0.0476705i
$39$		−	9.74628i		−	0.249905i
$40$	−12.0759	−	30.6853i	−0.301898	−	0.767133i
$41$	49.2315			1.20077			0.600384	−	0.799712i	$-0.295014\pi$
$41$	49.2315			1.20077			0.600384	+	0.799712i	$0.295014\pi$
$42$		0			0
$43$			70.5845i			1.64150i	0.571287	+	0.820750i	$0.306444\pi$
$43$			70.5845i			1.64150i	−0.571287	+	0.820750i	$0.693556\pi$
$44$	−14.9468	−	58.5485i	−0.339699	−	1.33065i
$45$	12.3660			0.274800
$46$	−50.2252	+	6.30978i	−1.09185	+	0.137169i
$47$		−	50.1714i		−	1.06748i	−0.845649	−	0.533739i	$-0.820787\pi$
$47$		−	50.1714i		−	1.06748i	0.845649	−	0.533739i	$-0.179213\pi$
$48$	−13.2838	−	24.3216i	−0.276746	−	0.506700i
$49$		0			0
$50$	1.99667	+	15.8933i	0.0399334	+	0.317866i
$51$		−	50.3718i		−	0.987683i
$52$	−21.8086	+	5.56750i	−0.419397	+	0.107067i
$53$	100.195			1.89046			0.945232	−	0.326399i	$-0.105835\pi$
$53$	100.195			1.89046			0.945232	+	0.326399i	$0.105835\pi$
$54$	10.3113	−	1.29540i	0.190949	−	0.0239889i
$55$		−	62.2693i		−	1.13217i
$56$		0			0
$57$	−12.5855			−0.220799
$58$	2.14389	+	17.0652i	0.0369637	+	0.294227i
$59$		−	76.7285i		−	1.30048i	−0.759728	−	0.650241i	$-0.774668\pi$
$59$		−	76.7285i		−	1.30048i	0.759728	−	0.650241i	$-0.225332\pi$
$60$	−7.06399	−	27.6706i	−0.117733	−	0.461177i
$61$	111.159			1.82227			0.911135	−	0.412107i	$-0.135207\pi$
$61$	111.159			1.82227			0.911135	+	0.412107i	$0.135207\pi$
$62$	33.1222	−	4.16113i	0.534229	−	0.0671150i
$63$		0			0
$64$	−46.8346	+	43.6179i	−0.731791	+	0.681529i
$65$	−23.1946			−0.356840
$66$	−6.52302	−	51.9226i	−0.0988336	−	0.786705i
$67$			89.7844i			1.34007i	0.742331	+	0.670033i	$0.233720\pi$
$67$			89.7844i			1.34007i	−0.742331	+	0.670033i	$0.766280\pi$
$68$	−112.714	+	28.7745i	−1.65756	+	0.423155i
$69$	−43.8382			−0.635336
$70$		0			0
$71$		−	52.9119i		−	0.745238i	−0.927984	−	0.372619i	$-0.878460\pi$
$71$		−	52.9119i		−	0.745238i	0.927984	−	0.372619i	$-0.121540\pi$
$72$	−8.78887	−	22.3328i	−0.122068	−	0.310178i
$73$	32.8246			0.449652			0.224826	−	0.974399i	$-0.427819\pi$
$73$	32.8246			0.449652			0.224826	+	0.974399i	$0.427819\pi$
$74$	5.60039	+	44.5785i	0.0756809	+	0.602412i
$75$			13.8722i			0.184963i
$76$	7.18940	+	28.1619i	0.0945974	+	0.370551i
$77$		0			0
$78$	−19.3405	+	2.42975i	−0.247956	+	0.0311506i
$79$			16.2076i			0.205160i	0.994725	+	0.102580i	$0.0327097\pi$
$79$			16.2076i			0.205160i	−0.994725	+	0.102580i	$0.967290\pi$
$80$	−57.8815	+	31.6133i	−0.723519	+	0.395166i
$81$	9.00000			0.111111
$82$	−12.2734	−	97.6950i	−0.149676	−	1.19140i
$83$		−	25.6034i		−	0.308475i	−0.988034	−	0.154238i	$-0.950708\pi$
$83$		−	25.6034i		−	0.308475i	0.988034	−	0.154238i	$-0.0492921\pi$
$84$		0			0
$85$	−119.877			−1.41031
$86$	140.068	−	17.5967i	1.62870	−	0.204613i
$87$			14.8950i			0.171207i
$88$	−112.458	+	44.2565i	−1.27793	+	0.502915i
$89$	96.7198			1.08674			0.543370	−	0.839493i	$-0.317148\pi$
$89$	96.7198			1.08674			0.543370	+	0.839493i	$0.317148\pi$
$90$	−3.08284	−	24.5391i	−0.0342538	−	0.272657i
$91$		0			0
$92$	25.0423	+	98.0940i	0.272199	+	1.06624i
$93$	28.9101			0.310862
$94$	−99.5603	+	12.5077i	−1.05915	+	0.133061i
$95$			29.9515i			0.315279i
$96$	−44.9522	+	32.4238i	−0.468252	+	0.337748i
$97$	−54.1899			−0.558659			−0.279329	−	0.960195i	$-0.590112\pi$
$97$	−54.1899			−0.558659			−0.279329	+	0.960195i	$0.590112\pi$
$98$		0			0
$99$		−	45.3197i		−	0.457775i
$100$	31.0409	−	7.92440i	0.310409	−	0.0792440i
$101$	−97.3975			−0.964331			−0.482166	−	0.876080i	$-0.660150\pi$
$101$	−97.3975			−0.964331			−0.482166	+	0.876080i	$0.660150\pi$
$102$	−99.9579	+	12.5577i	−0.979979	+	0.123115i
$103$			61.5579i			0.597650i	0.954308	+	0.298825i	$0.0965946\pi$
$103$			61.5579i			0.597650i	−0.954308	+	0.298825i	$0.903405\pi$
$104$	16.4850	+	41.8891i	0.158510	+	0.402780i
$105$		0			0
$106$	−24.9785	−	198.826i	−0.235646	−	1.87572i
$107$		−	67.2613i		−	0.628610i	−0.949322	−	0.314305i	$-0.898229\pi$
$107$		−	67.2613i		−	0.628610i	0.949322	−	0.314305i	$-0.101771\pi$
$108$	−5.14119	−	20.1387i	−0.0476036	−	0.186470i
$109$	170.761			1.56661			0.783305	−	0.621637i	$-0.213532\pi$
$109$	170.761			1.56661			0.783305	+	0.621637i	$0.213532\pi$
$110$	−123.567	+	15.5237i	−1.12334	+	0.141125i
$111$			38.9096i			0.350537i
$112$		0			0
$113$	23.9776			0.212191			0.106095	−	0.994356i	$-0.466165\pi$
$113$	23.9776			0.212191			0.106095	+	0.994356i	$0.466165\pi$
$114$	3.13757	+	24.9748i	0.0275226	+	0.219077i
$115$			104.328i			0.907199i
$116$	33.3297	−	8.50869i	0.287325	−	0.0733508i
$117$	−16.8811			−0.144283
$118$	−152.260	+	19.1284i	−1.29034	+	0.162105i
$119$		0			0
$120$	−53.1485	+	20.9161i	−0.442905	+	0.174301i
$121$	−107.208			−0.886020
$122$	−27.7118	−	220.583i	−0.227146	−	1.80806i
$123$		−	85.2714i		−	0.693264i
$124$	−16.5147	−	64.6903i	−0.133183	−	0.521696i
$125$	136.064			1.08851
$126$		0			0
$127$			6.99328i			0.0550652i	0.999621	+	0.0275326i	$0.00876501\pi$
$127$			6.99328i			0.0550652i	−0.999621	+	0.0275326i	$0.991235\pi$
$128$	98.2312	+	82.0648i	0.767431	+	0.641131i
$129$	122.256			0.947721
$130$	5.78240	+	46.0273i	0.0444800	+	0.354056i
$131$			90.8145i			0.693240i	0.938006	+	0.346620i	$0.112671\pi$
$131$			90.8145i			0.693240i	−0.938006	+	0.346620i	$0.887329\pi$
$132$	−101.409	+	25.8886i	−0.768250	+	0.196126i
$133$		0			0
$134$	178.168	−	22.3832i	1.32961	−	0.167039i
$135$		−	21.4185i		−	0.158656i
$136$	85.1998	+	216.496i	0.626469	+	1.59188i
$137$	257.139			1.87693			0.938465	−	0.345375i	$-0.112248\pi$
$137$	257.139			1.87693			0.938465	+	0.345375i	$0.112248\pi$
$138$	10.9289	+	86.9926i	0.0791946	+	0.630381i
$139$		−	144.504i		−	1.03960i	−0.854289	−	0.519798i	$-0.826007\pi$
$139$		−	144.504i		−	1.03960i	0.854289	−	0.519798i	$-0.173993\pi$
$140$		0			0
$141$	−86.8995			−0.616308
$142$	−104.998	+	13.1909i	−0.739425	+	0.0928938i
$143$			85.0049i			0.594440i
$144$	−42.1263	+	23.0082i	−0.292543	+	0.159779i
$145$	35.4478			0.244468
$146$	−8.18316	−	65.1371i	−0.0560490	−	0.446145i
$147$		0			0
$148$	87.0655	−	22.2268i	0.588280	−	0.150181i
$149$	−7.22195			−0.0484695			−0.0242347	−	0.999706i	$-0.507715\pi$
$149$	−7.22195			−0.0484695			−0.0242347	+	0.999706i	$0.507715\pi$
$150$	27.5280	−	3.45834i	0.183520	−	0.0230556i
$151$		−	173.071i		−	1.14616i	−0.819499	−	0.573081i	$-0.805748\pi$
$151$		−	173.071i		−	1.14616i	0.819499	−	0.573081i	$-0.194252\pi$
$152$	54.0921	−	21.2874i	0.355869	−	0.140049i
$153$	−87.2465			−0.570239
$154$		0			0
$155$		−	68.8014i		−	0.443880i
$156$	9.64319	+	37.7737i	0.0618153	+	0.242139i
$157$	238.100			1.51656			0.758281	−	0.651928i	$-0.226039\pi$
$157$	238.100			1.51656			0.758281	+	0.651928i	$0.226039\pi$
$158$	32.1624	−	4.04056i	0.203560	−	0.0255731i
$159$		−	173.542i		−	1.09146i
$160$	77.1633	+	106.979i	0.482271	+	0.668618i
$161$		0			0
$162$	−2.24370	−	17.8596i	−0.0138500	−	0.110245i
$163$			306.628i			1.88115i	0.339581	+	0.940577i	$0.389715\pi$
$163$			306.628i			1.88115i	−0.339581	+	0.940577i	$0.610285\pi$
$164$	−190.806	+	48.7107i	−1.16345	+	0.297017i
$165$	−107.854			−0.653658
$166$	−50.8075	+	6.38294i	−0.306069	+	0.0384514i
$167$			259.352i			1.55301i	0.630113	+	0.776503i	$0.283008\pi$
$167$			259.352i			1.55301i	−0.630113	+	0.776503i	$0.716992\pi$
$168$		0			0
$169$	−137.337			−0.812643
$170$	29.8853	+	237.884i	0.175796	+	1.39932i
$171$			21.7988i			0.127478i
$172$	−69.8379	−	273.564i	−0.406034	−	1.59049i
$173$	−46.0046			−0.265923			−0.132961	−	0.991121i	$-0.542449\pi$
$173$	−46.0046			−0.265923			−0.132961	+	0.991121i	$0.542449\pi$
$174$	29.5577	−	3.71333i	0.169872	−	0.0213410i
$175$		0			0
$176$	115.858	+	212.128i	0.658286	+	1.20527i
$177$	−132.898			−0.750834
$178$	−24.1122	−	191.931i	−0.135462	−	1.07826i
$179$		−	56.0284i		−	0.313008i	−0.987677	−	0.156504i	$-0.949978\pi$
$179$		−	56.0284i		−	0.313008i	0.987677	−	0.156504i	$-0.0500224\pi$
$180$	−47.9269	+	12.2352i	−0.266261	+	0.0679733i
$181$	90.7676			0.501478			0.250739	−	0.968055i	$-0.419326\pi$
$181$	90.7676			0.501478			0.250739	+	0.968055i	$0.419326\pi$
$182$		0			0
$183$		−	192.532i		−	1.05209i
$184$	188.415	−	74.1487i	1.02399	−	0.402982i
$185$	92.5985			0.500532
$186$	−7.20729	−	57.3693i	−0.0387489	−	0.308437i
$187$			439.332i			2.34937i
$188$	49.6407	+	194.449i	0.264046	+	1.03431i
$189$		0			0
$190$	59.4359	−	7.46692i	0.312821	−	0.0392996i
$191$			147.135i			0.770342i	0.922845	+	0.385171i	$0.125858\pi$
$191$			147.135i			0.770342i	−0.922845	+	0.385171i	$0.874142\pi$
$192$	75.5483	+	81.1200i	0.393481	+	0.422500i
$193$	−231.648			−1.20025			−0.600124	−	0.799907i	$-0.704882\pi$
$193$	−231.648			−1.20025			−0.600124	+	0.799907i	$0.704882\pi$
$194$	13.5095	+	107.534i	0.0696368	+	0.554301i
$195$			40.1742i			0.206021i
$196$		0			0
$197$	270.736			1.37429			0.687147	−	0.726519i	$-0.258863\pi$
$197$	270.736			1.37429			0.687147	+	0.726519i	$0.258863\pi$
$198$	−89.9325	+	11.2982i	−0.454205	+	0.0570616i
$199$		−	339.228i		−	1.70466i	−0.523000	−	0.852332i	$-0.675187\pi$
$199$		−	339.228i		−	1.70466i	0.523000	−	0.852332i	$-0.324813\pi$
$200$	−23.4637	−	59.6221i	−0.117318	−	0.298110i
$201$	155.511			0.773687
$202$	24.2812	+	193.276i	0.120204	+	0.956810i
$203$		0			0
$204$	49.8390	+	195.226i	0.244309	+	0.956990i
$205$	−202.932			−0.989913
$206$	122.156	−	15.3464i	0.592989	−	0.0744970i
$207$			75.9300i			0.366812i
$208$	79.0151	−	43.1559i	0.379880	−	0.207480i
$209$	109.768			0.525207
$210$		0			0
$211$			160.362i			0.760008i	0.924985	+	0.380004i	$0.124077\pi$
$211$			160.362i			0.760008i	−0.924985	+	0.380004i	$0.875923\pi$
$212$	−388.324	+	99.1348i	−1.83172	+	0.467617i
$213$	−91.6461			−0.430263
$214$	−133.473	+	16.7682i	−0.623708	+	0.0783562i
$215$		−	290.949i		−	1.35325i
$216$	−38.6816	+	15.2228i	−0.179082	+	0.0704758i
$217$		0			0
$218$	−42.5706	−	338.858i	−0.195278	−	1.55439i
$219$		−	56.8538i		−	0.259606i
$220$	61.6106	+	241.337i	0.280048	+	1.09699i
$221$	163.646			0.740479
$222$	77.2122	−	9.70015i	0.347803	−	0.0436944i
$223$			185.744i			0.832935i	0.909151	+	0.416467i	$0.136732\pi$
$223$			185.744i			0.832935i	−0.909151	+	0.416467i	$0.863268\pi$
$224$		0			0
$225$	24.0273			0.106788
$226$	−5.97761	−	47.5811i	−0.0264496	−	0.210536i
$227$			267.195i			1.17707i	0.808471	+	0.588536i	$0.200296\pi$
$227$			267.195i			1.17707i	−0.808471	+	0.588536i	$0.799704\pi$
$228$	48.7778	−	12.4524i	0.213938	−	0.0546158i
$229$	−78.2349			−0.341637			−0.170819	−	0.985303i	$-0.554641\pi$
$229$	−78.2349			−0.341637			−0.170819	+	0.985303i	$0.554641\pi$
$230$	207.028	−	26.0089i	0.900123	−	0.113082i
$231$		0			0
$232$	−25.1937	−	64.0183i	−0.108594	−	0.275941i
$233$	10.1047			0.0433676			0.0216838	−	0.999765i	$-0.493097\pi$
$233$	10.1047			0.0433676			0.0216838	+	0.999765i	$0.493097\pi$
$234$	4.20844	+	33.4988i	0.0179848	+	0.143157i
$235$			206.807i			0.880029i
$236$	75.9169	+	297.377i	0.321682	+	1.26007i
$237$	28.0724			0.118449
$238$		0			0
$239$			105.518i			0.441497i	0.975331	+	0.220749i	$0.0708500\pi$
$239$			105.518i			0.441497i	−0.975331	+	0.220749i	$0.929150\pi$
$240$	54.7558	+	100.254i	0.228149	+	0.417724i
$241$	−196.652			−0.815985			−0.407993	−	0.912985i	$-0.633771\pi$
$241$	−196.652			−0.815985			−0.407993	+	0.912985i	$0.633771\pi$
$242$	26.7270	+	212.745i	0.110442	+	0.879110i
$243$		−	15.5885i		−	0.0641500i
$244$	−430.817	+	109.983i	−1.76564	+	0.450749i
$245$		0			0
$246$	−169.213	+	21.2582i	−0.687857	+	0.0864153i
$247$		−	40.8874i		−	0.165536i
$248$	−124.255	+	48.8991i	−0.501026	+	0.197174i
$249$	−44.3465			−0.178098
$250$	−33.9206	−	270.005i	−0.135683	−	1.08002i
$251$			318.909i			1.27056i	0.772284	+	0.635278i	$0.219114\pi$
$251$			318.909i			1.27056i	−0.772284	+	0.635278i	$0.780886\pi$
$252$		0			0
$253$	382.347			1.51125
$254$	13.8775	−	1.74342i	0.0546358	−	0.00686388i
$255$			207.633i			0.814245i
$256$	138.360	−	215.389i	0.540471	−	0.841363i
$257$	−143.444			−0.558147			−0.279073	−	0.960270i	$-0.590027\pi$
$257$	−143.444			−0.558147			−0.279073	+	0.960270i	$0.590027\pi$
$258$	−30.4784	−	242.605i	−0.118133	−	0.940329i
$259$		0			0
$260$	89.8952	−	22.9492i	0.345751	−	0.0882662i
$261$	25.7990			0.0988466
$262$	180.212	−	22.6400i	0.687833	−	0.0864123i
$263$		−	203.715i		−	0.774582i	−0.921957	−	0.387291i	$-0.873411\pi$
$263$		−	203.715i		−	0.774582i	0.921957	−	0.387291i	$-0.126589\pi$
$264$	76.6546	+	194.782i	0.290358	+	0.737811i
$265$	−413.002			−1.55850
$266$		0			0
$267$		−	167.524i		−	0.627430i
$268$	−88.8347	−	347.977i	−0.331473	−	1.29842i
$269$	−182.663			−0.679044			−0.339522	−	0.940598i	$-0.610265\pi$
$269$	−182.663			−0.679044			−0.339522	+	0.940598i	$0.610265\pi$
$270$	−42.5030	+	5.33964i	−0.157418	+	0.0197764i
$271$			289.203i			1.06717i	0.845747	+	0.533584i	$0.179155\pi$
$271$			289.203i			1.06717i	−0.845747	+	0.533584i	$0.820845\pi$
$272$	408.374	−	223.043i	1.50138	−	0.820011i
$273$		0			0
$274$	−64.1048	−	510.268i	−0.233959	−	1.86229i
$275$		−	120.990i		−	0.439965i
$276$	169.904	−	43.3745i	0.615593	−	0.157154i
$277$	−289.032			−1.04344			−0.521719	−	0.853117i	$-0.674709\pi$
$277$	−289.032			−1.04344			−0.521719	+	0.853117i	$0.674709\pi$
$278$	−286.754	+	36.0248i	−1.03149	+	0.129586i
$279$		−	50.0738i		−	0.179476i
$280$		0			0
$281$	−145.700			−0.518504			−0.259252	−	0.965810i	$-0.583476\pi$
$281$	−145.700			−0.518504			−0.259252	+	0.965810i	$0.583476\pi$
$282$	21.6640	+	172.443i	0.0768228	+	0.611502i
$283$		−	292.987i		−	1.03529i	−0.855595	−	0.517645i	$-0.826809\pi$
$283$		−	292.987i		−	1.03529i	0.855595	−	0.517645i	$-0.173191\pi$
$284$	52.3522	+	205.071i	0.184339	+	0.722079i
$285$	51.8776			0.182027
$286$	168.684	−	21.1917i	0.589804	−	0.0740969i
$287$		0			0
$288$	56.1596	+	77.8595i	0.194999	+	0.270345i
$289$	556.773			1.92655
$290$	−8.83713	−	70.3426i	−0.0304729	−	0.242561i
$291$			93.8596i			0.322542i
$292$	−127.218	+	32.4773i	−0.435678	+	0.111224i
$293$	−47.6676			−0.162688			−0.0813440	−	0.996686i	$-0.525921\pi$
$293$	−47.6676			−0.162688			−0.0813440	+	0.996686i	$0.525921\pi$
$294$		0			0
$295$			316.275i			1.07212i
$296$	−65.8124	−	167.232i	−0.222339	−	0.564972i
$297$	−78.4960			−0.264296
$298$	1.80043	+	14.3312i	0.00604172	+	0.0480914i
$299$		−	142.420i		−	0.476321i
$300$	−13.7255	−	53.7645i	−0.0457515	−	0.179215i
$301$		0			0
$302$	−343.441	+	43.1465i	−1.13722	+	0.142869i
$303$			168.697i			0.556757i
$304$	−55.7279	−	102.034i	−0.183316	−	0.335637i
$305$	−458.195			−1.50228
$306$	21.7505	+	173.132i	0.0710802	+	0.565791i
$307$		−	285.922i		−	0.931342i	−0.884958	−	0.465671i	$-0.845813\pi$
$307$		−	285.922i		−	0.931342i	0.884958	−	0.465671i	$-0.154187\pi$
$308$		0			0
$309$	106.621			0.345053
$310$	−136.530	+	17.1522i	−0.440418	+	0.0553296i
$311$			68.5345i			0.220368i	0.993911	+	0.110184i	$0.0351440\pi$
$311$			68.5345i			0.220368i	−0.993911	+	0.110184i	$0.964856\pi$
$312$	72.5541	−	28.5529i	0.232545	−	0.0915158i
$313$	−220.945			−0.705894			−0.352947	−	0.935643i	$-0.614820\pi$
$313$	−220.945			−0.705894			−0.352947	+	0.935643i	$0.614820\pi$
$314$	−59.3584	−	472.487i	−0.189039	−	1.50473i
$315$		0			0
$316$	−16.0362	−	62.8158i	−0.0507474	−	0.198784i
$317$	209.864			0.662031			0.331015	−	0.943625i	$-0.392609\pi$
$317$	209.864			0.662031			0.331015	+	0.943625i	$0.392609\pi$
$318$	−344.377	+	43.2640i	−1.08295	+	0.136050i
$319$		−	129.911i		−	0.407246i
$320$	193.052	−	179.793i	0.603289	−	0.561853i
$321$	−116.500			−0.362928
$322$		0			0
$323$		−	211.319i		−	0.654238i
$324$	−34.8813	+	8.90480i	−0.107658	+	0.0274839i
$325$	−45.0674			−0.138669
$326$	608.473	−	76.4423i	1.86648	−	0.234486i
$327$		−	295.766i		−	0.904483i
$328$	144.230	+	366.493i	0.439725	+	1.11736i
$329$		0			0
$330$	26.8879	+	214.025i	0.0814784	+	0.648560i
$331$			37.7245i			0.113971i	0.998375	+	0.0569856i	$0.0181489\pi$
$331$			37.7245i			0.113971i	−0.998375	+	0.0569856i	$0.981851\pi$
$332$	25.3326	+	99.2313i	0.0763031	+	0.298889i
$333$	67.3934			0.202382
$334$	514.659	−	64.6564i	1.54089	−	0.193582i
$335$		−	370.091i		−	1.10475i
$336$		0			0
$337$	−323.798			−0.960826			−0.480413	−	0.877042i	$-0.659513\pi$
$337$	−323.798			−0.960826			−0.480413	+	0.877042i	$0.659513\pi$
$338$	34.2380	+	272.531i	0.101296	+	0.806305i
$339$		−	41.5304i		−	0.122509i
$340$	464.606	−	118.609i	1.36649	−	0.348849i
$341$	−252.148			−0.739436
$342$	43.2576	−	5.43444i	0.126484	−	0.0158902i
$343$		0			0
$344$	−525.451	+	206.786i	−1.52747	+	0.601122i
$345$	180.701			0.523771
$346$	11.4690	+	91.2917i	0.0331473	+	0.263849i
$347$			580.940i			1.67418i	0.547065	+	0.837090i	$0.315745\pi$
$347$			580.940i			1.67418i	−0.547065	+	0.837090i	$0.684255\pi$
$348$	−14.7375	−	57.7287i	−0.0423491	−	0.165887i
$349$	240.951			0.690405			0.345203	−	0.938528i	$-0.387810\pi$
$349$	240.951			0.690405			0.345203	+	0.938528i	$0.387810\pi$
$350$		0			0
$351$			29.2388i			0.0833015i
$352$	392.063	−	282.793i	1.11382	−	0.803389i
$353$	−367.181			−1.04017			−0.520087	−	0.854113i	$-0.674100\pi$
$353$	−367.181			−1.04017			−0.520087	+	0.854113i	$0.674100\pi$
$354$	33.1314	+	263.722i	0.0935914	+	0.744978i
$355$			218.103i			0.614374i
$356$	−374.857	+	95.6967i	−1.05297	+	0.268811i
$357$		0			0
$358$	−111.183	+	13.9679i	−0.310567	+	0.0390164i
$359$		−	243.016i		−	0.676925i	−0.940980	−	0.338463i	$-0.890093\pi$
$359$		−	243.016i		−	0.676925i	0.940980	−	0.338463i	$-0.109907\pi$
$360$	36.2277	+	92.0560i	0.100633	+	0.255711i
$361$	308.201			0.853743
$362$	−22.6283	−	180.119i	−0.0625092	−	0.497567i
$363$			185.690i			0.511544i
$364$		0			0
$365$	−135.303			−0.370693
$366$	−382.061	+	47.9983i	−1.04388	+	0.131143i
$367$		−	646.859i		−	1.76256i	−0.472597	−	0.881279i	$-0.656683\pi$
$367$		−	646.859i		−	1.76256i	0.472597	−	0.881279i	$-0.343317\pi$
$368$	−194.113	−	355.405i	−0.527480	−	0.965775i
$369$	−147.694			−0.400256
$370$	−23.0848	−	183.753i	−0.0623913	−	0.496629i
$371$		0			0
$372$	−112.047	+	28.6043i	−0.301202	+	0.0768933i
$373$	250.103			0.670518			0.335259	−	0.942126i	$-0.391176\pi$
$373$	250.103			0.670518			0.335259	+	0.942126i	$0.391176\pi$
$374$	871.811	−	109.525i	2.33105	−	0.292849i
$375$		−	235.669i		−	0.628451i
$376$	373.490	−	146.983i	0.993325	−	0.390913i
$377$	−48.3904			−0.128357
$378$		0			0
$379$			410.032i			1.08188i	0.841062	+	0.540939i	$0.181931\pi$
$379$			410.032i			1.08188i	−0.841062	+	0.540939i	$0.818069\pi$
$380$	−29.6347	−	116.083i	−0.0779861	−	0.305482i
$381$	12.1127			0.0317919
$382$	291.976	−	36.6808i	0.764334	−	0.0960231i
$383$		−	674.627i		−	1.76143i	−0.473647	−	0.880715i	$-0.657063\pi$
$383$		−	674.627i		−	1.76143i	0.473647	−	0.880715i	$-0.342937\pi$
$384$	142.140	−	170.141i	0.370157	−	0.443077i
$385$		0			0
$386$	57.7497	+	459.682i	0.149611	+	1.19089i
$387$		−	211.754i		−	0.547167i
$388$	210.024	−	53.6167i	0.541298	−	0.138187i
$389$	−386.485			−0.993534			−0.496767	−	0.867884i	$-0.665480\pi$
$389$	−386.485			−0.993534			−0.496767	+	0.867884i	$0.665480\pi$
$390$	79.7217	−	10.0154i	0.204415	−	0.0256806i
$391$		−	736.070i		−	1.88253i
$392$		0			0
$393$	157.295			0.400242
$394$	−67.4944	−	537.249i	−0.171306	−	1.36358i
$395$		−	66.8078i		−	0.169134i
$396$	44.8403	+	175.646i	0.113233	+	0.443549i
$397$	−502.153			−1.26487			−0.632435	−	0.774613i	$-0.717944\pi$
$397$	−502.153			−1.26487			−0.632435	+	0.774613i	$0.717944\pi$
$398$	−673.165	+	84.5696i	−1.69137	+	0.212486i
$399$		0			0
$400$	−112.465	+	61.4251i	−0.281162	+	0.153563i
$401$	−70.7612			−0.176462			−0.0882309	−	0.996100i	$-0.528121\pi$
$401$	−70.7612			−0.176462			−0.0882309	+	0.996100i	$0.528121\pi$
$402$	−38.7689	−	308.597i	−0.0964401	−	0.767653i
$403$			93.9221i			0.233057i
$404$	377.483	−	96.3672i	0.934364	−	0.238533i
$405$	−37.0980			−0.0916000
$406$		0			0
$407$		−	339.361i		−	0.833810i
$408$	374.982	−	147.570i	0.919073	−	0.361692i
$409$	15.0088			0.0366962			0.0183481	−	0.999832i	$-0.494159\pi$
$409$	15.0088			0.0366962			0.0183481	+	0.999832i	$0.494159\pi$
$410$	50.5910	+	402.699i	0.123393	+	0.982192i
$411$		−	445.378i		−	1.08365i
$412$	−60.9068	−	238.580i	−0.147832	−	0.579078i
$413$		0			0
$414$	150.676	−	18.9293i	0.363951	−	0.0457230i
$415$			105.537i			0.254307i
$416$	−105.337	−	146.039i	−0.253214	−	0.351055i
$417$	−250.288			−0.600212
$418$	−27.3652	−	217.824i	−0.0654671	−	0.521111i
$419$			20.8129i			0.0496729i	0.999692	+	0.0248364i	$0.00790650\pi$
$419$			20.8129i			0.0496729i	−0.999692	+	0.0248364i	$0.992093\pi$
$420$		0			0
$421$	101.765			0.241723			0.120862	−	0.992669i	$-0.461434\pi$
$421$	101.765			0.241723			0.120862	+	0.992669i	$0.461434\pi$
$422$	318.222	−	39.9782i	0.754081	−	0.0947350i
$423$			150.514i			0.355826i
$424$	293.532	+	745.877i	0.692293	+	1.75914i
$425$	−232.922			−0.548053
$426$	22.8473	+	181.863i	0.0536323	+	0.426907i
$427$		0			0
$428$	66.5498	+	260.685i	0.155490	+	0.609076i
$429$	147.233			0.343200
$430$	−577.361	+	72.5337i	−1.34270	+	0.168683i
$431$		−	446.365i		−	1.03565i	−0.855486	−	0.517825i	$-0.826742\pi$
$431$		−	446.365i		−	1.03565i	0.855486	−	0.517825i	$-0.173258\pi$
$432$	39.8514	+	72.9648i	0.0922486	+	0.168900i
$433$	70.4995			0.162816			0.0814082	−	0.996681i	$-0.474058\pi$
$433$	70.4995			0.162816			0.0814082	+	0.996681i	$0.474058\pi$
$434$		0			0
$435$		−	61.3974i		−	0.141143i
$436$	−661.817	+	168.954i	−1.51793	+	0.387510i
$437$	−183.909			−0.420845
$438$	−112.821	+	14.1736i	−0.257582	+	0.0323599i
$439$			117.803i			0.268343i	0.990958	+	0.134172i	$0.0428373\pi$
$439$			117.803i			0.268343i	−0.990958	+	0.134172i	$0.957163\pi$
$440$	463.550	−	182.425i	1.05352	−	0.414603i
$441$		0			0
$442$	−40.7969	−	324.739i	−0.0923007	−	0.734704i
$443$		−	398.375i		−	0.899266i	−0.893213	−	0.449633i	$-0.851555\pi$
$443$		−	398.375i		−	0.899266i	0.893213	−	0.449633i	$-0.148445\pi$
$444$	−38.4980	−	150.802i	−0.0867072	−	0.339644i
$445$	−398.679			−0.895908
$446$	368.592	−	46.3061i	0.826438	−	0.103825i
$447$			12.5088i			0.0279839i
$448$		0			0
$449$	171.356			0.381640			0.190820	−	0.981625i	$-0.438885\pi$
$449$	171.356			0.381640			0.190820	+	0.981625i	$0.438885\pi$
$450$	−5.99001	−	47.6799i	−0.0133111	−	0.105955i
$451$			743.719i			1.64904i
$452$	−92.9299	+	23.7239i	−0.205597	+	0.0524866i
$453$	−299.767			−0.661737
$454$	530.223	−	66.6118i	1.16789	−	0.146722i
$455$		0			0
$456$	−36.8709	−	93.6903i	−0.0808572	−	0.205461i
$457$	−375.430			−0.821511			−0.410755	−	0.911746i	$-0.634735\pi$
$457$	−375.430			−0.821511			−0.410755	+	0.911746i	$0.634735\pi$
$458$	19.5039	+	155.249i	0.0425850	+	0.338973i
$459$			151.115i			0.329228i
$460$	−103.224	−	404.343i	−0.224401	−	0.879007i
$461$	−353.738			−0.767328			−0.383664	−	0.923473i	$-0.625338\pi$
$461$	−353.738			−0.767328			−0.383664	+	0.923473i	$0.625338\pi$
$462$		0			0
$463$			741.091i			1.60063i	0.599581	+	0.800314i	$0.295334\pi$
$463$			741.091i			1.60063i	−0.599581	+	0.800314i	$0.704666\pi$
$464$	−120.757	+	65.9543i	−0.260252	+	0.142143i
$465$	−119.168			−0.256274
$466$	−2.51909	−	20.0517i	−0.00540577	−	0.0430294i
$467$			390.491i			0.836169i	0.908408	+	0.418085i	$0.137298\pi$
$467$			390.491i			0.836169i	−0.908408	+	0.418085i	$0.862702\pi$
$468$	65.4259	−	16.7025i	0.139799	−	0.0356891i
$469$		0			0
$470$	410.388	−	51.5569i	0.873165	−	0.109695i
$471$		−	412.402i		−	0.875588i
$472$	571.188	−	224.785i	1.21014	−	0.476240i
$473$	−1066.29			−2.25431
$474$	−6.99845	−	55.7069i	−0.0147647	−	0.117525i
$475$			58.1964i			0.122519i
$476$		0			0
$477$	−300.584			−0.630155
$478$	209.390	−	26.3056i	0.438054	−	0.0550326i
$479$		−	171.800i		−	0.358664i	−0.983789	−	0.179332i	$-0.942606\pi$
$479$		−	171.800i		−	0.358664i	0.983789	−	0.179332i	$-0.0573936\pi$
$480$	185.293	−	133.651i	0.386027	−	0.278439i
$481$	−126.408			−0.262802
$482$	49.0254	+	390.237i	0.101713	+	0.809621i
$483$		0			0
$484$	415.508	−	106.074i	0.858487	−	0.219162i
$485$	223.371			0.460558
$486$	−30.9338	+	3.88620i	−0.0636497	+	0.00799630i
$487$		−	104.317i		−	0.214204i	−0.994248	−	0.107102i	$-0.965843\pi$
$487$		−	104.317i		−	0.214204i	0.994248	−	0.107102i	$-0.0341571\pi$
$488$	325.652	+	827.495i	0.667321	+	1.69569i
$489$	531.095			1.08608
$490$		0			0
$491$		−	142.568i		−	0.290362i	−0.989405	−	0.145181i	$-0.953624\pi$
$491$		−	142.568i		−	0.290362i	0.989405	−	0.145181i	$-0.0463764\pi$
$492$	84.3694	+	330.486i	0.171483	+	0.671720i
$493$	−250.097			−0.507296
$494$	−81.1370	+	10.1932i	−0.164245	+	0.0206341i
$495$			186.808i			0.377390i
$496$	128.012	+	234.380i	0.258089	+	0.472541i
$497$		0			0
$498$	11.0556	+	88.0012i	0.0221999	+	0.176709i
$499$		−	560.161i		−	1.12257i	−0.827624	−	0.561283i	$-0.810308\pi$
$499$		−	560.161i		−	1.12257i	0.827624	−	0.561283i	$-0.189692\pi$
$500$	−527.341	+	134.624i	−1.05468	+	0.269249i
$501$	449.211			0.896629
$502$	632.844	−	79.5041i	1.26065	−	0.158375i
$503$		−	646.893i		−	1.28607i	−0.765837	−	0.643035i	$-0.777675\pi$
$503$		−	646.893i		−	1.28607i	0.765837	−	0.643035i	$-0.222325\pi$
$504$		0			0
$505$	401.472			0.794995
$506$	−95.3191	−	758.731i	−0.188378	−	1.49947i
$507$			237.874i			0.469180i
$508$	−6.91931	−	27.1039i	−0.0136207	−	0.0533541i
$509$	724.945			1.42425			0.712126	−	0.702051i	$-0.247732\pi$
$509$	724.945			1.42425			0.712126	+	0.702051i	$0.247732\pi$
$510$	412.026	−	51.7628i	0.807895	−	0.101496i
$511$		0			0
$512$	−461.911	−	220.866i	−0.902171	−	0.431379i
$513$	37.7566			0.0735997
$514$	35.7605	+	284.650i	0.0695730	+	0.553794i
$515$		−	253.742i		−	0.492702i
$516$	−473.827	+	120.963i	−0.918270	+	0.234424i
$517$	757.918			1.46599
$518$		0			0
$519$			79.6824i			0.153531i
$520$	−67.9513	−	172.667i	−0.130676	−	0.332052i
$521$	927.588			1.78040			0.890199	−	0.455571i	$-0.150565\pi$
$521$	927.588			1.78040			0.890199	+	0.455571i	$0.150565\pi$
$522$	−6.43168	−	51.1955i	−0.0123212	−	0.0980757i
$523$			462.924i			0.885131i	0.896736	+	0.442566i	$0.145932\pi$
$523$			462.924i			0.885131i	−0.896736	+	0.442566i	$0.854068\pi$
$524$	−89.8538	−	351.970i	−0.171477	−	0.671698i
$525$		0			0
$526$	−404.253	+	50.7862i	−0.768541	+	0.0965516i
$527$			485.419i			0.921098i
$528$	367.416	−	200.673i	0.695864	−	0.380062i
$529$	−111.596			−0.210957
$530$	102.961	+	819.562i	0.194267	+	1.54634i
$531$			230.185i			0.433494i
$532$		0			0
$533$	277.026			0.519749
$534$	−332.434	+	41.7636i	−0.622536	+	0.0782090i
$535$			277.251i			0.518226i
$536$	−668.380	+	263.034i	−1.24698	+	0.490736i
$537$	−97.0441			−0.180715
$538$	45.5378	+	362.476i	0.0846428	+	0.673748i
$539$		0			0
$540$	21.1920	+	83.0118i	0.0392444	+	0.153726i
$541$	77.5318			0.143312			0.0716560	−	0.997429i	$-0.477172\pi$
$541$	77.5318			0.143312			0.0716560	+	0.997429i	$0.477172\pi$
$542$	573.894	−	72.0982i	1.05885	−	0.133022i
$543$		−	157.214i		−	0.289529i
$544$	−544.415	−	754.774i	−1.00076	−	1.38745i
$545$	−703.875			−1.29151
$546$		0			0
$547$		−	791.000i		−	1.44607i	−0.690812	−	0.723035i	$-0.742747\pi$
$547$		−	791.000i		−	1.44607i	0.690812	−	0.723035i	$-0.257253\pi$
$548$	−996.595	+	254.419i	−1.81860	+	0.464269i
$549$	−333.476			−0.607424
$550$	−240.093	+	30.1629i	−0.436533	+	0.0548416i
$551$			62.4874i			0.113407i
$552$	−128.429	−	326.344i	−0.232662	−	0.591203i
$553$		0			0
$554$	72.0557	+	573.556i	0.130064	+	1.03530i
$555$		−	160.385i		−	0.288983i
$556$	142.975	+	560.054i	0.257150	+	1.00729i
$557$	422.621			0.758745			0.379373	−	0.925244i	$-0.376140\pi$
$557$	422.621			0.758745			0.379373	+	0.925244i	$0.376140\pi$
$558$	−99.3666	+	12.4834i	−0.178076	+	0.0223717i
$559$			397.180i			0.710520i
$560$		0			0
$561$	760.945			1.35641
$562$	36.3229	+	289.127i	0.0646315	+	0.514461i
$563$		−	83.1996i		−	0.147779i	−0.997266	−	0.0738895i	$-0.976459\pi$
$563$		−	83.1996i		−	0.147779i	0.997266	−	0.0738895i	$-0.0235412\pi$
$564$	336.796	−	85.9803i	0.597157	−	0.152447i
$565$	−98.8356			−0.174930
$566$	−581.404	+	73.0417i	−1.02722	+	0.129049i
$567$		0			0
$568$	393.891	−	155.012i	0.693470	−	0.272908i
$569$	183.560			0.322601			0.161300	−	0.986905i	$-0.448431\pi$
$569$	183.560			0.322601			0.161300	+	0.986905i	$0.448431\pi$
$570$	−12.9331	−	102.946i	−0.0226896	−	0.180607i
$571$			670.736i			1.17467i	0.809344	+	0.587334i	$0.199823\pi$
$571$			670.736i			1.17467i	−0.809344	+	0.587334i	$0.800177\pi$
$572$	−84.1058	−	329.454i	−0.147038	−	0.575968i
$573$	254.846			0.444757
$574$		0			0
$575$			202.711i			0.352540i
$576$	140.504	−	130.854i	0.243930	−	0.227176i
$577$	−466.399			−0.808316			−0.404158	−	0.914689i	$-0.632435\pi$
$577$	−466.399			−0.808316			−0.404158	+	0.914689i	$0.632435\pi$
$578$	−138.803	−	1104.86i	−0.240144	−	1.91152i
$579$			401.226i			0.692963i
$580$	−137.385	+	35.0728i	−0.236871	+	0.0604704i
$581$		0			0
$582$	186.255	−	23.3992i	0.320026	−	0.0402048i
$583$			1513.60i			2.59622i
$584$	96.1636	+	244.355i	0.164664	+	0.418417i
$585$	69.5837			0.118947
$586$	11.8835	+	94.5916i	0.0202790	+	0.161419i
$587$		−	275.534i		−	0.469393i	−0.972069	−	0.234696i	$-0.924590\pi$
$587$		−	275.534i		−	0.469393i	0.972069	−	0.234696i	$-0.0754096\pi$
$588$		0			0
$589$	121.283			0.205914
$590$	627.616	−	78.8473i	1.06376	−	0.133639i
$591$		−	468.928i		−	0.793449i
$592$	−315.448	+	172.289i	−0.532851	+	0.291029i
$593$	62.1721			0.104843			0.0524217	−	0.998625i	$-0.483306\pi$
$593$	62.1721			0.104843			0.0524217	+	0.998625i	$0.483306\pi$
$594$	19.5691	+	155.768i	0.0329445	+	0.262235i
$595$		0			0
$596$	27.9901	−	7.14556i	0.0469633	−	0.0119892i
$597$	−587.561			−0.984189
$598$	−282.618	+	35.5052i	−0.472606	+	0.0593733i
$599$		−	201.686i		−	0.336705i	−0.985727	−	0.168353i	$-0.946155\pi$
$599$		−	201.686i		−	0.336705i	0.985727	−	0.168353i	$-0.0538447\pi$
$600$	−103.269	+	40.6403i	−0.172114	+	0.0677338i
$601$	129.981			0.216274			0.108137	−	0.994136i	$-0.465511\pi$
$601$	129.981			0.216274			0.108137	+	0.994136i	$0.465511\pi$
$602$		0			0
$603$		−	269.353i		−	0.446689i
$604$	171.240	+	670.769i	0.283510	+	1.11055i
$605$	441.913			0.730435
$606$	334.763	−	42.0562i	0.552415	−	0.0693997i
$607$		−	1058.19i		−	1.74331i	−0.490116	−	0.871657i	$-0.663046\pi$
$607$		−	1058.19i		−	1.74331i	0.490116	−	0.871657i	$-0.336954\pi$
$608$	−188.583	+	136.024i	−0.310169	+	0.223723i
$609$		0			0
$610$	114.228	+	909.244i	0.187259	+	1.49056i
$611$		−	282.316i		−	0.462055i
$612$	338.141	−	86.3236i	0.552518	−	0.141052i
$613$	−121.671			−0.198485			−0.0992425	−	0.995063i	$-0.531642\pi$
$613$	−121.671			−0.198485			−0.0992425	+	0.995063i	$0.531642\pi$
$614$	−567.384	+	71.2803i	−0.924078	+	0.116092i
$615$			351.489i			0.571527i
$616$		0			0
$617$	18.6957			0.0303010			0.0151505	−	0.999885i	$-0.495177\pi$
$617$	18.6957			0.0303010			0.0151505	+	0.999885i	$0.495177\pi$
$618$	−26.5807	−	211.580i	−0.0430109	−	0.342362i
$619$		−	58.1063i		−	0.0938712i	−0.998898	−	0.0469356i	$-0.985054\pi$
$619$		−	58.1063i		−	0.0938712i	0.998898	−	0.0469356i	$-0.0149456\pi$
$620$	68.0737	+	266.654i	0.109796	+	0.430086i
$621$	131.515			0.211779
$622$	136.000	−	17.0856i	0.218649	−	0.0274689i
$623$		0			0
$624$	−74.7482	−	136.858i	−0.119789	−	0.219324i
$625$	−360.626			−0.577002
$626$	55.0815	+	438.443i	0.0879896	+	0.700388i
$627$		−	190.124i		−	0.303229i
$628$	−922.805	+	235.582i	−1.46943	+	0.375130i
$629$	−653.315			−1.03866
$630$		0			0
$631$			837.654i			1.32750i	0.747954	+	0.663751i	$0.231036\pi$
$631$			837.654i			1.32750i	−0.747954	+	0.663751i	$0.768964\pi$
$632$	−120.654	+	47.4822i	−0.190908	+	0.0751300i
$633$	277.755			0.438791
$634$	−52.3190	−	416.454i	−0.0825221	−	0.656867i
$635$		−	28.8263i		−	0.0453958i
$636$	171.706	+	672.597i	0.269979	+	1.05754i
$637$		0			0
$638$	−257.796	+	32.3869i	−0.404069	+	0.0507631i
$639$			158.736i			0.248413i
$640$	−404.909	−	338.271i	−0.632670	−	0.528549i
$641$	549.160			0.856724			0.428362	−	0.903607i	$-0.359091\pi$
$641$	549.160			0.856724			0.428362	+	0.903607i	$0.359091\pi$
$642$	29.0434	+	231.183i	0.0452390	+	0.360098i
$643$			347.476i			0.540398i	0.962805	+	0.270199i	$0.0870895\pi$
$643$			347.476i			0.540398i	−0.962805	+	0.270199i	$0.912911\pi$
$644$		0			0
$645$	−503.939			−0.781301
$646$	−419.341	+	52.6818i	−0.649135	+	0.0815507i
$647$		−	763.785i		−	1.18050i	−0.807220	−	0.590251i	$-0.799029\pi$
$647$		−	763.785i		−	1.18050i	0.807220	−	0.590251i	$-0.200971\pi$
$648$	26.3666	+	66.9985i	0.0406892	+	0.103393i
$649$	1159.10			1.78598
$650$	11.2353	+	89.4319i	0.0172851	+	0.137588i
$651$		0			0
$652$	−303.385	−	1188.40i	−0.465314	−	1.82270i
$653$	146.645			0.224571			0.112286	−	0.993676i	$-0.464183\pi$
$653$	146.645			0.224571			0.112286	+	0.993676i	$0.464183\pi$
$654$	−586.919	+	73.7344i	−0.897429	+	0.112744i
$655$		−	374.337i		−	0.571507i
$656$	691.313	−	377.576i	1.05383	−	0.575573i
$657$	−98.4737			−0.149884
$658$		0			0
$659$		−	850.491i		−	1.29058i	−0.763938	−	0.645289i	$-0.776737\pi$
$659$		−	850.491i		−	1.29058i	0.763938	−	0.645289i	$-0.223263\pi$
$660$	418.008	−	106.713i	0.633345	−	0.161686i
$661$	63.0551			0.0953935			0.0476967	−	0.998862i	$-0.484812\pi$
$661$	63.0551			0.0953935			0.0476967	+	0.998862i	$0.484812\pi$
$662$	74.8605	−	9.40470i	0.113082	−	0.0142065i
$663$		−	283.443i		−	0.427516i
$664$	190.599	−	75.0084i	0.287047	−	0.112965i
$665$		0			0
$666$	−16.8012	−	133.736i	−0.0252270	−	0.200804i
$667$			217.657i			0.326323i
$668$	−256.609	−	1005.17i	−0.384145	−	1.50475i
$669$	321.719			0.480895
$670$	−734.410	+	92.2637i	−1.09613	+	0.137707i
$671$			1679.22i			2.50257i
$672$		0			0
$673$	−371.202			−0.551563			−0.275781	−	0.961220i	$-0.588937\pi$
$673$	−371.202			−0.551563			−0.275781	+	0.961220i	$0.588937\pi$
$674$	80.7229	+	642.546i	0.119767	+	0.953332i
$675$		−	41.6166i		−	0.0616542i
$676$	532.276	−	135.884i	0.787390	−	0.201012i
$677$	643.778			0.950928			0.475464	−	0.879735i	$-0.342280\pi$
$677$	643.778			0.950928			0.475464	+	0.879735i	$0.342280\pi$
$678$	−82.4130	+	10.3535i	−0.121553	+	0.0152707i
$679$		0			0
$680$	−351.194	−	892.396i	−0.516461	−	1.31235i
$681$	462.796			0.679583
$682$	62.8604	+	500.363i	0.0921707	+	0.733669i
$683$			446.466i			0.653684i	0.945079	+	0.326842i	$0.105984\pi$
$683$			446.466i			0.653684i	−0.945079	+	0.326842i	$0.894016\pi$
$684$	−21.5682	−	84.4856i	−0.0315325	−	0.123517i
$685$	−1059.93			−1.54734
$686$		0			0
$687$			135.507i			0.197244i
$688$	541.341	+	991.154i	0.786833	+	1.44063i
$689$	563.797			0.818283
$690$	−45.0488	−	358.584i	−0.0652881	−	0.519686i
$691$			361.559i			0.523240i	0.965171	+	0.261620i	$0.0842567\pi$
$691$			361.559i			0.523240i	−0.965171	+	0.261620i	$0.915743\pi$
$692$	178.300	−	45.5180i	0.257659	−	0.0657775i
$693$		0			0
$694$	1152.82	−	144.828i	1.66112	−	0.208686i
$695$			595.645i			0.857044i
$696$	−110.883	+	43.6368i	−0.159314	+	0.0626966i
$697$	1431.76			2.05417
$698$	−60.0692	−	478.144i	−0.0860590	−	0.685021i
$699$		−	17.5018i		−	0.0250383i
$700$		0			0
$701$	−1266.88			−1.80724			−0.903621	−	0.428333i	$-0.859101\pi$
$701$	−1266.88			−1.80724			−0.903621	+	0.428333i	$0.859101\pi$
$702$	58.0216	−	7.28924i	0.0826519	−	0.0103835i
$703$			163.233i			0.232194i
$704$	−658.916	−	707.511i	−0.935960	−	1.00499i
$705$	358.200			0.508085
$706$	91.5382	+	728.635i	0.129658	+	1.03206i
$707$		0			0
$708$	515.071	−	131.492i	0.727502	−	0.185723i
$709$	−294.589			−0.415499			−0.207750	−	0.978182i	$-0.566614\pi$
$709$	−294.589			−0.415499			−0.207750	+	0.978182i	$0.566614\pi$
$710$	432.803	−	54.3730i	0.609582	−	0.0765817i
$711$		−	48.6228i		−	0.0683866i
$712$	283.353	+	720.010i	0.397967	+	1.01125i
$713$	422.456			0.592505
$714$		0			0
$715$		−	350.390i		−	0.490056i
$716$	55.4357	+	217.149i	0.0774242	+	0.303281i
$717$	182.762			0.254898
$718$	−482.242	+	60.5839i	−0.671646	+	0.0843787i
$719$			1017.96i			1.41580i	0.706311	+	0.707902i	$0.250358\pi$
$719$			1017.96i			1.41580i	−0.706311	+	0.707902i	$0.749642\pi$
$720$	173.644	−	94.8399i	0.241173	−	0.131722i
$721$		0			0
$722$	−76.8346	−	611.595i	−0.106419	−	0.847085i
$723$			340.612i			0.471109i
$724$	−351.788	+	89.8074i	−0.485895	+	0.124043i
$725$	68.8756			0.0950009
$726$	368.484	−	46.2926i	0.507554	−	0.0637639i
$727$		−	335.755i		−	0.461836i	−0.972973	−	0.230918i	$-0.925827\pi$
$727$		−	335.755i		−	0.461836i	0.972973	−	0.230918i	$-0.0741730\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	33.7310	+	268.495i	0.0462068	+	0.367802i
$731$			2052.75i			2.80814i
$732$	190.496	+	746.197i	0.260240	+	1.01939i
$733$	−1053.67			−1.43747			−0.718737	−	0.695282i	$-0.755280\pi$
$733$	−1053.67			−1.43747			−0.718737	+	0.695282i	$0.755280\pi$
$734$	−1283.63	+	161.262i	−1.74881	+	0.219703i
$735$		0			0
$736$	−656.875	+	473.800i	−0.892493	+	0.643750i
$737$	−1356.33			−1.84034
$738$	36.8202	+	293.085i	0.0498919	+	0.397134i
$739$			255.139i			0.345249i	0.984988	+	0.172624i	$0.0552247\pi$
$739$			255.139i			0.345249i	−0.984988	+	0.172624i	$0.944775\pi$
$740$	−358.884	+	91.6190i	−0.484978	+	0.123809i
$741$	−70.8191			−0.0955723
$742$		0			0
$743$			534.992i			0.720044i	0.932944	+	0.360022i	$0.117231\pi$
$743$			534.992i			0.720044i	−0.932944	+	0.360022i	$0.882769\pi$
$744$	84.6958	+	215.215i	0.113838	+	0.289268i
$745$	29.7689			0.0399582
$746$	−62.3507	−	496.305i	−0.0835801	−	0.665289i
$747$			76.8103i			0.102825i
$748$	−434.685	−	1702.72i	−0.581129	−	2.27636i
$749$		0			0
$750$	−467.662	+	58.7523i	−0.623549	+	0.0783363i
$751$			287.539i			0.382874i	0.981505	+	0.191437i	$0.0613148\pi$
$751$			287.539i			0.382874i	−0.981505	+	0.191437i	$0.938685\pi$
$752$	−384.785	−	704.512i	−0.511682	−	0.936851i
$753$	552.367			0.733556
$754$	12.0637	+	96.0260i	0.0159996	+	0.127355i
$755$			713.397i			0.944896i
$756$		0			0
$757$	80.9110			0.106884			0.0534418	−	0.998571i	$-0.482981\pi$
$757$	80.9110			0.106884			0.0534418	+	0.998571i	$0.482981\pi$
$758$	813.668	−	102.221i	1.07344	−	0.134856i
$759$		−	662.245i		−	0.872523i
$760$	−222.968	+	87.7467i	−0.293379	+	0.115456i
$761$	−424.134			−0.557338			−0.278669	−	0.960387i	$-0.589893\pi$
$761$	−424.134			−0.557338			−0.278669	+	0.960387i	$0.589893\pi$
$762$	−3.01970	−	24.0365i	−0.00396286	−	0.0315440i
$763$		0			0
$764$	−145.579	−	570.252i	−0.190548	−	0.746403i
$765$	359.630			0.470105
$766$	−1338.73	+	168.185i	−1.74769	+	0.219562i
$767$		−	431.753i		−	0.562911i
$768$	−373.065	−	239.647i	−0.485761	−	0.312041i
$769$	1140.50			1.48310			0.741550	−	0.670898i	$-0.234091\pi$
$769$	1140.50			1.48310			0.741550	+	0.670898i	$0.234091\pi$
$770$		0			0
$771$			248.452i			0.322246i
$772$	897.797	−	229.197i	1.16295	−	0.296888i
$773$	−639.533			−0.827339			−0.413669	−	0.910427i	$-0.635753\pi$
$773$	−639.533			−0.827339			−0.413669	+	0.910427i	$0.635753\pi$
$774$	−420.204	+	52.7901i	−0.542899	+	0.0682043i
$775$		−	133.682i		−	0.172493i
$776$	−158.756	−	403.405i	−0.204582	−	0.519851i
$777$		0			0
$778$	96.3506	+	766.941i	0.123844	+	0.985786i
$779$		−	357.729i		−	0.459216i
$780$	−39.7492	−	155.703i	−0.0509605	−	0.199619i
$781$	799.317			1.02345
$782$	−1460.66	+	183.502i	−1.86785	+	0.234657i
$783$		−	44.6851i		−	0.0570691i
$784$		0			0
$785$	−981.449			−1.25025
$786$	−39.2137	−	312.137i	−0.0498902	−	0.397121i
$787$		−	91.9978i		−	0.116897i	−0.998290	−	0.0584484i	$-0.981385\pi$
$787$		−	91.9978i		−	0.116897i	0.998290	−	0.0584484i	$-0.0186153\pi$
$788$	−1049.29	+	267.872i	−1.33159	+	0.339939i
$789$	−352.845			−0.447205
$790$	−132.573	+	16.6552i	−0.167815	+	0.0210825i
$791$		0			0
$792$	337.373	−	132.770i	0.425976	−	0.167638i
$793$	625.491			0.788765
$794$	125.187	+	996.474i	0.157666	+	1.25501i
$795$			715.341i			0.899800i
$796$	335.640	+	1314.75i	0.421658	+	1.65169i
$797$	−453.032			−0.568422			−0.284211	−	0.958762i	$-0.591732\pi$
$797$	−453.032			−0.568422			−0.284211	+	0.958762i	$0.591732\pi$
$798$		0			0
$799$		−	1459.09i		−	1.82615i
$800$	149.930	+	207.862i	0.187412	+	0.259827i
$801$	−290.160			−0.362247
$802$	17.6408	+	140.419i	0.0219959	+	0.175086i
$803$			495.866i			0.617517i
$804$	−602.714	+	153.866i	−0.749645	+	0.191376i
$805$		0			0
$806$	186.379	−	23.4148i	0.231240	−	0.0290506i
$807$			316.381i			0.392046i
$808$	−285.338	−	725.054i	−0.353141	−	0.897344i
$809$	189.784			0.234590			0.117295	−	0.993097i	$-0.462578\pi$
$809$	189.784			0.234590			0.117295	+	0.993097i	$0.462578\pi$
$810$	9.24853	+	73.6173i	0.0114179	+	0.0908856i
$811$			561.951i			0.692912i	0.938066	+	0.346456i	$0.112615\pi$
$811$			561.951i			0.692912i	−0.938066	+	0.346456i	$0.887385\pi$
$812$		0			0
$813$	500.914			0.616130
$814$	−673.428	+	84.6026i	−0.827307	+	0.103934i
$815$		−	1263.92i		−	1.55082i
$816$	−386.322	−	707.325i	−0.473434	−	0.866820i
$817$	512.886			0.627767
$818$	−3.74168	−	29.7834i	−0.00457418	−	0.0364100i
$819$		0			0
$820$	786.504	−	200.786i	0.959151	−	0.244860i
$821$	−935.573			−1.13955			−0.569776	−	0.821800i	$-0.692970\pi$
$821$	−935.573			−1.13955			−0.569776	+	0.821800i	$0.692970\pi$
$822$	−883.809	+	111.033i	−1.07519	+	0.135076i
$823$		−	140.769i		−	0.171044i	−0.996336	−	0.0855219i	$-0.972744\pi$
$823$		−	140.769i		−	0.171044i	0.996336	−	0.0855219i	$-0.0272558\pi$
$824$	−458.254	+	180.341i	−0.556134	+	0.218861i
$825$	−209.561			−0.254014
$826$		0			0
$827$		−	134.169i		−	0.162236i	−0.996705	−	0.0811179i	$-0.974151\pi$
$827$		−	134.169i		−	0.162236i	0.996705	−	0.0811179i	$-0.0258490\pi$
$828$	−75.1268	−	294.282i	−0.0907329	−	0.355413i
$829$	684.732			0.825973			0.412986	−	0.910737i	$-0.364486\pi$
$829$	684.732			0.825973			0.412986	+	0.910737i	$0.364486\pi$
$830$	209.429	−	26.3105i	0.252324	−	0.0316994i
$831$			500.619i			0.602429i
$832$	−263.539	+	245.438i	−0.316754	+	0.294998i
$833$		0			0
$834$	62.3968	+	496.672i	0.0748163	+	0.595530i
$835$		−	1069.05i		−	1.28030i
$836$	−425.429	+	108.607i	−0.508886	+	0.129913i
$837$	−86.7304			−0.103621
$838$	41.3012	−	5.18866i	0.0492855	−	0.00619172i
$839$		−	1310.69i		−	1.56221i	−0.624402	−	0.781103i	$-0.714657\pi$
$839$		−	1310.69i		−	1.56221i	0.624402	−	0.781103i	$-0.285343\pi$
$840$		0			0
$841$	−767.046			−0.912064
$842$	−25.3701	−	201.944i	−0.0301308	−	0.239838i
$843$			252.359i			0.299359i
$844$	−158.665	−	621.514i	−0.187992	−	0.736391i
$845$	566.102			0.669943
$846$	298.681	−	37.5232i	0.353051	−	0.0443537i
$847$		0			0
$848$	1406.94	−	768.433i	1.65913	−	0.906171i
$849$	−507.469			−0.597725
$850$	58.0675	+	462.212i	0.0683148	+	0.543779i
$851$			568.575i			0.668126i
$852$	355.193	−	90.6766i	0.416893	−	0.106428i
$853$	404.635			0.474367			0.237183	−	0.971465i	$-0.423776\pi$
$853$	404.635			0.474367			0.237183	+	0.971465i	$0.423776\pi$
$854$		0			0
$855$		−	89.8546i		−	0.105093i
$856$	500.712	−	197.050i	0.584944	−	0.230199i
$857$	−87.5256			−0.102130			−0.0510651	−	0.998695i	$-0.516262\pi$
$857$	−87.5256			−0.102130			−0.0510651	+	0.998695i	$0.516262\pi$
$858$	−36.7051	−	292.169i	−0.0427799	−	0.340523i
$859$		−	246.795i		−	0.287305i	−0.989628	−	0.143652i	$-0.954115\pi$
$859$		−	246.795i		−	0.287305i	0.989628	−	0.143652i	$-0.0458847\pi$
$860$	287.872	+	1127.63i	0.334735	+	1.31120i
$861$		0			0
$862$	−885.768	+	111.279i	−1.02757	+	0.129094i
$863$		−	96.6734i		−	0.112020i	−0.998430	−	0.0560101i	$-0.982162\pi$
$863$		−	96.6734i		−	0.112020i	0.998430	−	0.0560101i	$-0.0178379\pi$
$864$	134.857	−	97.2713i	0.156084	−	0.112583i
$865$	189.631			0.219227
$866$	−17.5755	−	139.899i	−0.0202951	−	0.161547i
$867$		−	964.359i		−	1.11229i
$868$		0			0
$869$	−244.841			−0.281751
$870$	−121.837	+	15.3064i	−0.140043	+	0.0175935i
$871$			505.218i			0.580044i
$872$	500.264	+	1271.19i	0.573697	+	1.45779i
$873$	162.570			0.186220
$874$	45.8485	+	364.950i	0.0524583	+	0.417563i
$875$		0			0
$876$	56.2524	+	220.348i	0.0642151	+	0.251539i
$877$	−1301.53			−1.48408			−0.742038	−	0.670358i	$-0.766141\pi$
$877$	−1301.53			−1.48408			−0.742038	+	0.670358i	$0.766141\pi$
$878$	233.768	−	29.3682i	0.266250	−	0.0334490i
$879$			82.5627i			0.0939279i
$880$	−477.568	−	874.391i	−0.542691	−	0.993626i
$881$	1145.10			1.29977			0.649885	−	0.760032i	$-0.274817\pi$
$881$	1145.10			1.29977			0.649885	+	0.760032i	$0.274817\pi$
$882$		0			0
$883$		−	1139.35i		−	1.29032i	−0.764049	−	0.645158i	$-0.776792\pi$
$883$		−	1139.35i		−	1.29032i	0.764049	−	0.645158i	$-0.223208\pi$
$884$	−634.242	+	161.915i	−0.717469	+	0.183162i
$885$	547.804			0.618988
$886$	−790.535	+	99.3148i	−0.892252	+	0.112093i
$887$		−	1063.01i		−	1.19844i	−0.800585	−	0.599219i	$-0.795478\pi$
$887$		−	1063.01i		−	1.19844i	0.800585	−	0.599219i	$-0.204522\pi$
$888$	−289.654	+	113.990i	−0.326187	+	0.128368i
$889$		0			0
$890$	99.3907	+	791.140i	0.111675	+	0.888921i
$891$			135.959i			0.152592i
$892$	−183.780	−	719.889i	−0.206031	−	0.807051i
$893$	−364.559			−0.408241
$894$	24.8225	−	3.11844i	0.0277656	−	0.00348819i
$895$			230.949i			0.258044i
$896$		0			0
$897$	−246.678			−0.275004
$898$	−42.7191	−	340.040i	−0.0475714	−	0.378664i
$899$		−	143.539i		−	0.159665i
$900$	−93.1228	+	23.7732i	−0.103470	+	0.0264147i
$901$	2913.88			3.23405
$902$	1475.84	−	185.409i	1.63618	−	0.205553i
$903$		0			0
$904$	70.2452	+	178.496i	0.0777049	+	0.197451i
$905$	−374.144			−0.413419
$906$	74.7319	+	594.858i	0.0824855	+	0.656576i
$907$			737.550i			0.813175i	0.913612	+	0.406587i	$0.133281\pi$
$907$			737.550i			0.813175i	−0.913612	+	0.406587i	$0.866719\pi$
$908$	−264.369	−	1035.57i	−0.291155	−	1.14049i
$909$	292.192			0.321444
$910$		0			0
$911$			1529.04i			1.67842i	0.543807	+	0.839210i	$0.316982\pi$
$911$			1529.04i			1.67842i	−0.543807	+	0.839210i	$0.683018\pi$
$912$	−176.727	+	96.5236i	−0.193780	+	0.105837i
$913$	386.780			0.423637
$914$	93.5947	+	745.005i	0.102401	+	0.815103i
$915$			793.618i			0.867342i
$916$	303.215	−	77.4073i	0.331021	−	0.0845058i
$917$		0			0
$918$	299.874	−	37.6731i	0.326660	−	0.0410382i
$919$		−	637.406i		−	0.693586i	−0.937942	−	0.346793i	$-0.887271\pi$
$919$		−	637.406i		−	0.693586i	0.937942	−	0.346793i	$-0.112729\pi$
$920$	−776.646	+	305.641i	−0.844180	+	0.332219i
$921$	−495.231			−0.537710
$922$	88.1869	+	701.959i	0.0956474	+	0.761343i
$923$		−	297.736i		−	0.322574i
$924$		0			0
$925$	179.920			0.194509
$926$	1470.62	−	184.754i	1.58814	−	0.199518i
$927$		−	184.674i		−	0.199217i
$928$	160.984	+	223.188i	0.173475	+	0.240505i
$929$	−39.1354			−0.0421264			−0.0210632	−	0.999778i	$-0.506705\pi$
$929$	−39.1354			−0.0421264			−0.0210632	+	0.999778i	$0.506705\pi$
$930$	29.7085	+	236.476i	0.0319446	+	0.254276i
$931$		0			0
$932$	−39.1626	+	9.99777i	−0.0420200	+	0.0107272i
$933$	118.705			0.127230
$934$	774.891	−	97.3493i	0.829648	−	0.104228i
$935$		−	1810.93i		−	1.93682i
$936$	−49.4551	−	125.667i	−0.0528367	−	0.134260i
$937$	−1699.52			−1.81378			−0.906892	−	0.421363i	$-0.861552\pi$
$937$	−1699.52			−1.81378			−0.906892	+	0.421363i	$0.861552\pi$
$938$		0			0
$939$			382.687i			0.407548i
$940$	−204.619	−	801.521i	−0.217680	−	0.852681i
$941$	647.545			0.688145			0.344073	−	0.938943i	$-0.388193\pi$
$941$	647.545			0.688145			0.344073	+	0.938943i	$0.388193\pi$
$942$	−818.371	+	102.812i	−0.868759	+	0.109142i
$943$		−	1246.05i		−	1.32137i
$944$	−588.462	−	1077.43i	−0.623371	−	1.14134i
$945$		0			0
$946$	265.826	+	2115.95i	0.281000	+	2.23673i
$947$			887.073i			0.936719i	0.883538	+	0.468360i	$0.155155\pi$
$947$			887.073i			0.936719i	−0.883538	+	0.468360i	$0.844845\pi$
$948$	−108.800	+	27.7755i	−0.114768	+	0.0292990i
$949$	184.704			0.194631
$950$	115.485	−	14.5083i	0.121563	−	0.0152719i
$951$		−	363.495i		−	0.382224i
$952$		0			0
$953$	160.697			0.168622			0.0843109	−	0.996439i	$-0.473131\pi$
$953$	160.697			0.168622			0.0843109	+	0.996439i	$0.473131\pi$
$954$	74.9355	+	596.479i	0.0785487	+	0.625240i
$955$		−	606.492i		−	0.635070i
$956$	−104.402	−	408.955i	−0.109207	−	0.427778i
$957$	−225.013			−0.235123
$958$	−340.920	+	42.8297i	−0.355867	+	0.0447074i
$959$		0			0
$960$	−311.410	−	334.376i	−0.324386	−	0.348309i
$961$	682.401			0.710095
$962$	31.5135	+	250.844i	0.0327583	+	0.260753i
$963$			201.784i			0.209537i
$964$	762.166	−	194.572i	0.790628	−	0.201838i
$965$	954.852			0.989484
$966$		0			0
$967$		−	333.092i		−	0.344459i	−0.985057	−	0.172230i	$-0.944903\pi$
$967$		−	333.092i		−	0.344459i	0.985057	−	0.172230i	$-0.0550971\pi$
$968$	−314.080	−	798.090i	−0.324463	−	0.824473i
$969$	−366.015			−0.377724
$970$	−55.6863	−	443.257i	−0.0574085	−	0.456966i
$971$			487.020i			0.501566i	0.968043	+	0.250783i	$0.0806880\pi$
$971$			487.020i			0.501566i	−0.968043	+	0.250783i	$0.919312\pi$
$972$	15.4236	+	60.4162i	0.0158679	+	0.0621566i
$973$		0			0
$974$	−207.008	+	26.0063i	−0.212533	+	0.0267005i
$975$			78.0591i			0.0800606i
$976$	1560.90	−	852.520i	1.59928	−	0.873483i
$977$	1664.91			1.70410			0.852050	−	0.523460i	$-0.175359\pi$
$977$	1664.91			1.70410			0.852050	+	0.523460i	$0.175359\pi$
$978$	−132.402	−	1053.91i	−0.135380	−	1.07761i
$979$			1461.10i			1.49245i
$980$		0			0
$981$	−512.282			−0.522204
$982$	−282.911	+	35.5421i	−0.288097	+	0.0361935i
$983$			1495.73i			1.52160i	0.648987	+	0.760800i	$0.275193\pi$
$983$			1495.73i			1.52160i	−0.648987	+	0.760800i	$0.724807\pi$
$984$	634.784	−	249.813i	0.645106	−	0.253875i
$985$	−1115.97			−1.13297
$986$	62.3491	+	496.292i	0.0632344	+	0.503339i
$987$		0			0
$988$	40.4549	+	158.467i	0.0409463	+	0.160392i
$989$	1786.49			1.80636
$990$	370.702	−	46.5712i	0.374446	−	0.0470416i
$991$		−	1417.01i		−	1.42988i	−0.699188	−	0.714938i	$-0.746455\pi$
$991$		−	1417.01i		−	1.42988i	0.699188	−	0.714938i	$-0.253545\pi$
$992$	433.191	−	312.458i	0.436685	−	0.314978i
$993$	65.3407			0.0658013
$994$		0			0
$995$			1398.30i			1.40533i
$996$	171.874	−	43.8774i	0.172564	−	0.0440536i
$997$	1705.20			1.71034			0.855168	−	0.518351i	$-0.173454\pi$
$997$	1705.20			1.71034			0.855168	+	0.518351i	$0.173454\pi$
$998$	−1111.58	+	139.648i	−1.11381	+	0.139928i
$999$		−	116.729i		−	0.116846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.h.295.9	✓	24
4.3	odd	2	inner	588.3.g.h.295.12	yes	24
7.6	odd	2	inner	588.3.g.h.295.10	yes	24
28.27	even	2	inner	588.3.g.h.295.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.g.h.295.9	✓	24	1.1	even	1	trivial
588.3.g.h.295.10	yes	24	7.6	odd	2	inner
588.3.g.h.295.11	yes	24	28.27	even	2	inner
588.3.g.h.295.12	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.249300 - 1.98440i) q^{2} -1.73205i q^{3} +(-3.87570 + 0.989422i) q^{4} -4.12200 q^{5} +(-3.43708 + 0.431800i) q^{6} +(2.92962 + 7.44428i) q^{8} -3.00000 q^{9} +(1.02761 + 8.17970i) q^{10} +15.1066i q^{11} +(1.71373 + 6.71291i) q^{12} +5.62702 q^{13} +7.13951i q^{15} +(14.0421 - 7.66940i) q^{16} +29.0822 q^{17} +(0.747900 + 5.95320i) q^{18} -7.26627i q^{19} +(15.9756 - 4.07840i) q^{20} +(29.9775 - 3.76607i) q^{22} -25.3100i q^{23} +(12.8939 - 5.07425i) q^{24} -8.00912 q^{25} +(-1.40281 - 11.1663i) q^{26} +5.19615i q^{27} -8.59966 q^{29} +(14.1677 - 1.77988i) q^{30} +16.6913i q^{31} +(-18.7199 - 25.9532i) q^{32} +26.1653 q^{33} +(-7.25018 - 57.7107i) q^{34} +(11.6271 - 2.96827i) q^{36} -22.4645 q^{37} +(-14.4192 + 1.81148i) q^{38} -9.74628i q^{39} +(-12.0759 - 30.6853i) q^{40} +49.2315 q^{41} +70.5845i q^{43} +(-14.9468 - 58.5485i) q^{44} +12.3660 q^{45} +(-50.2252 + 6.30978i) q^{46} -50.1714i q^{47} +(-13.2838 - 24.3216i) q^{48} +(1.99667 + 15.8933i) q^{50} -50.3718i q^{51} +(-21.8086 + 5.56750i) q^{52} +100.195 q^{53} +(10.3113 - 1.29540i) q^{54} -62.2693i q^{55} -12.5855 q^{57} +(2.14389 + 17.0652i) q^{58} -76.7285i q^{59} +(-7.06399 - 27.6706i) q^{60} +111.159 q^{61} +(33.1222 - 4.16113i) q^{62} +(-46.8346 + 43.6179i) q^{64} -23.1946 q^{65} +(-6.52302 - 51.9226i) q^{66} +89.7844i q^{67} +(-112.714 + 28.7745i) q^{68} -43.8382 q^{69} -52.9119i q^{71} +(-8.78887 - 22.3328i) q^{72} +32.8246 q^{73} +(5.60039 + 44.5785i) q^{74} +13.8722i q^{75} +(7.18940 + 28.1619i) q^{76} +(-19.3405 + 2.42975i) q^{78} +16.2076i q^{79} +(-57.8815 + 31.6133i) q^{80} +9.00000 q^{81} +(-12.2734 - 97.6950i) q^{82} -25.6034i q^{83} -119.877 q^{85} +(140.068 - 17.5967i) q^{86} +14.8950i q^{87} +(-112.458 + 44.2565i) q^{88} +96.7198 q^{89} +(-3.08284 - 24.5391i) q^{90} +(25.0423 + 98.0940i) q^{92} +28.9101 q^{93} +(-99.5603 + 12.5077i) q^{94} +29.9515i q^{95} +(-44.9522 + 32.4238i) q^{96} -54.1899 q^{97} -45.3197i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) \) 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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