LMFDB - Embedded newform 588.3.g.h.295.10

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)

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);

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")

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			295.10
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.249300 - 1.98440i) q^{2} +1.73205i q^{3} +(-3.87570 + 0.989422i) q^{4} +4.12200 q^{5} +(3.43708 - 0.431800i) q^{6} +(2.92962 + 7.44428i) q^{8} -3.00000 q^{9} +(-1.02761 - 8.17970i) q^{10} +15.1066i q^{11} +(-1.71373 - 6.71291i) q^{12} -5.62702 q^{13} +7.13951i q^{15} +(14.0421 - 7.66940i) q^{16} -29.0822 q^{17} +(0.747900 + 5.95320i) q^{18} +7.26627i q^{19} +(-15.9756 + 4.07840i) q^{20} +(29.9775 - 3.76607i) q^{22} -25.3100i q^{23} +(-12.8939 + 5.07425i) q^{24} -8.00912 q^{25} +(1.40281 + 11.1663i) q^{26} -5.19615i q^{27} -8.59966 q^{29} +(14.1677 - 1.77988i) q^{30} -16.6913i q^{31} +(-18.7199 - 25.9532i) q^{32} -26.1653 q^{33} +(7.25018 + 57.7107i) q^{34} +(11.6271 - 2.96827i) q^{36} -22.4645 q^{37} +(14.4192 - 1.81148i) q^{38} -9.74628i q^{39} +(12.0759 + 30.6853i) q^{40} -49.2315 q^{41} +70.5845i q^{43} +(-14.9468 - 58.5485i) q^{44} -12.3660 q^{45} +(-50.2252 + 6.30978i) q^{46} +50.1714i q^{47} +(13.2838 + 24.3216i) q^{48} +(1.99667 + 15.8933i) q^{50} -50.3718i q^{51} +(21.8086 - 5.56750i) q^{52} +100.195 q^{53} +(-10.3113 + 1.29540i) q^{54} +62.2693i q^{55} -12.5855 q^{57} +(2.14389 + 17.0652i) q^{58} +76.7285i q^{59} +(-7.06399 - 27.6706i) q^{60} -111.159 q^{61} +(-33.1222 + 4.16113i) q^{62} +(-46.8346 + 43.6179i) q^{64} -23.1946 q^{65} +(6.52302 + 51.9226i) q^{66} +89.7844i q^{67} +(112.714 - 28.7745i) q^{68} +43.8382 q^{69} -52.9119i q^{71} +(-8.78887 - 22.3328i) q^{72} -32.8246 q^{73} +(5.60039 + 44.5785i) q^{74} -13.8722i q^{75} +(-7.18940 - 28.1619i) q^{76} +(-19.3405 + 2.42975i) q^{78} +16.2076i q^{79} +(57.8815 - 31.6133i) q^{80} +9.00000 q^{81} +(12.2734 + 97.6950i) q^{82} +25.6034i q^{83} -119.877 q^{85} +(140.068 - 17.5967i) q^{86} -14.8950i q^{87} +(-112.458 + 44.2565i) q^{88} -96.7198 q^{89} +(3.08284 + 24.5391i) q^{90} +(25.0423 + 98.0940i) q^{92} +28.9101 q^{93} +(99.5603 - 12.5077i) q^{94} +29.9515i q^{95} +(44.9522 - 32.4238i) q^{96} +54.1899 q^{97} -45.3197i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.364760\pi$
$5$	4.12200			0.824400			0.412200	+	0.911093i	$0.364760\pi$
$6$	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	$-0.569439\pi$
$13$	−5.62702			−0.432848			−0.216424	+	0.976300i	$0.569439\pi$
$14$		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	$-0.826663\pi$
$17$	−29.0822			−1.71072			−0.855358	+	0.518037i	$0.826663\pi$
$18$	0.747900	+	5.95320i	0.0415500	+	0.330734i
$19$			7.26627i			0.382435i	0.981548	+	0.191218i	$0.0612436\pi$
$19$			7.26627i			0.382435i	−0.981548	+	0.191218i	$0.938756\pi$
$20$	−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	$-0.913236\pi$
$31$		−	16.6913i		−	0.538428i	0.963080	−	0.269214i	$-0.0867639\pi$
$32$	−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	$-0.704986\pi$
$41$	−49.2315			−1.20077			−0.600384	+	0.799712i	$0.704986\pi$
$42$		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	$0.179213\pi$
$47$			50.1714i			1.06748i	−0.845649	+	0.533739i	$0.820787\pi$
$48$	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	$0.225332\pi$
$59$			76.7285i			1.30048i	−0.759728	+	0.650241i	$0.774668\pi$
$60$	−7.06399	−	27.6706i	−0.117733	−	0.461177i
$61$	−111.159			−1.82227			−0.911135	−	0.412107i	$-0.864793\pi$
$61$	−111.159			−1.82227			−0.911135	+	0.412107i	$0.864793\pi$
$62$	−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	$-0.572181\pi$
$73$	−32.8246			−0.449652			−0.224826	+	0.974399i	$0.572181\pi$
$74$	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	$0.0492921\pi$
$83$			25.6034i			0.308475i	−0.988034	+	0.154238i	$0.950708\pi$
$84$		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	$-0.682852\pi$
$89$	−96.7198			−1.08674			−0.543370	+	0.839493i	$0.682852\pi$
$90$	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	$-0.409888\pi$
$97$	54.1899			0.558659			0.279329	+	0.960195i	$0.409888\pi$
$98$		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	$-0.339850\pi$
$101$	97.3975			0.964331			0.482166	+	0.876080i	$0.339850\pi$
$102$	−99.9579	+	12.5577i	−0.979979	+	0.123115i
$103$		−	61.5579i		−	0.597650i	−0.954308	−	0.298825i	$-0.903405\pi$
$103$		−	61.5579i		−	0.597650i	0.954308	−	0.298825i	$-0.0965946\pi$
$104$	−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	$-0.887329\pi$
$131$		−	90.8145i		−	0.693240i	0.938006	−	0.346620i	$-0.112671\pi$
$132$	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	$0.173993\pi$
$139$			144.504i			1.03960i	−0.854289	+	0.519798i	$0.826007\pi$
$140$		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	$-0.773961\pi$
$157$	−238.100			−1.51656			−0.758281	+	0.651928i	$0.773961\pi$
$158$	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	$-0.716992\pi$
$167$		−	259.352i		−	1.55301i	0.630113	−	0.776503i	$-0.283008\pi$
$168$		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	$-0.457551\pi$
$173$	46.0046			0.265923			0.132961	+	0.991121i	$0.457551\pi$
$174$	−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	$-0.580674\pi$
$181$	−90.7676			−0.501478			−0.250739	+	0.968055i	$0.580674\pi$
$182$		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	$0.324813\pi$
$199$			339.228i			1.70466i	−0.523000	+	0.852332i	$0.675187\pi$
$200$	−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	$-0.863268\pi$
$223$		−	185.744i		−	0.832935i	0.909151	−	0.416467i	$-0.136732\pi$
$224$		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	$-0.799704\pi$
$227$		−	267.195i		−	1.17707i	0.808471	−	0.588536i	$-0.200296\pi$
$228$	48.7778	−	12.4524i	0.213938	−	0.0546158i
$229$	78.2349			0.341637			0.170819	−	0.985303i	$-0.445359\pi$
$229$	78.2349			0.341637			0.170819	+	0.985303i	$0.445359\pi$
$230$	−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	$-0.366229\pi$
$241$	196.652			0.815985			0.407993	+	0.912985i	$0.366229\pi$
$242$	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	$-0.780886\pi$
$251$		−	318.909i		−	1.27056i	0.772284	−	0.635278i	$-0.219114\pi$
$252$		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	$-0.409973\pi$
$257$	143.444			0.558147			0.279073	+	0.960270i	$0.409973\pi$
$258$	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	$-0.389735\pi$
$269$	182.663			0.679044			0.339522	+	0.940598i	$0.389735\pi$
$270$	−42.5030	+	5.33964i	−0.157418	+	0.0197764i
$271$		−	289.203i		−	1.06717i	−0.845747	−	0.533584i	$-0.820845\pi$
$271$		−	289.203i		−	1.06717i	0.845747	−	0.533584i	$-0.179155\pi$
$272$	−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	$0.173191\pi$
$283$			292.987i			1.03529i	−0.855595	+	0.517645i	$0.826809\pi$
$284$	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	$-0.474079\pi$
$293$	47.6676			0.162688			0.0813440	+	0.996686i	$0.474079\pi$
$294$		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	$0.154187\pi$
$307$			285.922i			0.931342i	−0.884958	+	0.465671i	$0.845813\pi$
$308$		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	$-0.964856\pi$
$311$		−	68.5345i		−	0.220368i	0.993911	−	0.110184i	$-0.0351440\pi$
$312$	72.5541	−	28.5529i	0.232545	−	0.0915158i
$313$	220.945			0.705894			0.352947	−	0.935643i	$-0.385180\pi$
$313$	220.945			0.705894			0.352947	+	0.935643i	$0.385180\pi$
$314$	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	$-0.612190\pi$
$349$	−240.951			−0.690405			−0.345203	+	0.938528i	$0.612190\pi$
$350$		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	$-0.325900\pi$
$353$	367.181			1.04017			0.520087	+	0.854113i	$0.325900\pi$
$354$	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	$0.343317\pi$
$367$			646.859i			1.76256i	−0.472597	+	0.881279i	$0.656683\pi$
$368$	−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	$0.342937\pi$
$383$			674.627i			1.76143i	−0.473647	+	0.880715i	$0.657063\pi$
$384$	−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	$-0.282056\pi$
$397$	502.153			1.26487			0.632435	+	0.774613i	$0.282056\pi$
$398$	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	$-0.505841\pi$
$409$	−15.0088			−0.0366962			−0.0183481	+	0.999832i	$0.505841\pi$
$410$	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	$-0.992093\pi$
$419$		−	20.8129i		−	0.0496729i	0.999692	−	0.0248364i	$-0.00790650\pi$
$420$		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	$-0.525942\pi$
$433$	−70.4995			−0.162816			−0.0814082	+	0.996681i	$0.525942\pi$
$434$		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	$-0.957163\pi$
$439$		−	117.803i		−	0.268343i	0.990958	−	0.134172i	$-0.0428373\pi$
$440$	−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	$-0.374662\pi$
$461$	353.738			0.767328			0.383664	+	0.923473i	$0.374662\pi$
$462$		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	$-0.862702\pi$
$467$		−	390.491i		−	0.836169i	0.908408	−	0.418085i	$-0.137298\pi$
$468$	−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	$0.0573936\pi$
$479$			171.800i			0.358664i	−0.983789	+	0.179332i	$0.942606\pi$
$480$	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	$0.222325\pi$
$503$			646.893i			1.28607i	−0.765837	+	0.643035i	$0.777675\pi$
$504$		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	$-0.752268\pi$
$509$	−724.945			−1.42425			−0.712126	+	0.702051i	$0.752268\pi$
$510$	−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	$-0.849435\pi$
$521$	−927.588			−1.78040			−0.890199	+	0.455571i	$0.849435\pi$
$522$	−6.43168	−	51.1955i	−0.0123212	−	0.0980757i
$523$		−	462.924i		−	0.885131i	−0.896736	−	0.442566i	$-0.854068\pi$
$523$		−	462.924i		−	0.885131i	0.896736	−	0.442566i	$-0.145932\pi$
$524$	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	$0.0235412\pi$
$563$			83.1996i			0.147779i	−0.997266	+	0.0738895i	$0.976459\pi$
$564$	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	$-0.367565\pi$
$577$	466.399			0.808316			0.404158	+	0.914689i	$0.367565\pi$
$578$	−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	$0.0754096\pi$
$587$			275.534i			0.469393i	−0.972069	+	0.234696i	$0.924590\pi$
$588$		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	$-0.516694\pi$
$593$	−62.1721			−0.104843			−0.0524217	+	0.998625i	$0.516694\pi$
$594$	−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	$-0.534489\pi$
$601$	−129.981			−0.216274			−0.108137	+	0.994136i	$0.534489\pi$
$602$		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	$0.336954\pi$
$607$			1058.19i			1.74331i	−0.490116	+	0.871657i	$0.663046\pi$
$608$	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	$0.0149456\pi$
$619$			58.1063i			0.0938712i	−0.998898	+	0.0469356i	$0.985054\pi$
$620$	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	$-0.912911\pi$
$643$		−	347.476i		−	0.540398i	0.962805	−	0.270199i	$-0.0870895\pi$
$644$		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	$0.200971\pi$
$647$			763.785i			1.18050i	−0.807220	+	0.590251i	$0.799029\pi$
$648$	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	$-0.515188\pi$
$661$	−63.0551			−0.0953935			−0.0476967	+	0.998862i	$0.515188\pi$
$662$	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	$-0.657720\pi$
$677$	−643.778			−0.950928			−0.475464	+	0.879735i	$0.657720\pi$
$678$	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	$-0.915743\pi$
$691$		−	361.559i		−	0.523240i	0.965171	−	0.261620i	$-0.0842567\pi$
$692$	−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	$-0.749642\pi$
$719$		−	1017.96i		−	1.41580i	0.706311	−	0.707902i	$-0.250358\pi$
$720$	−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	$0.0741730\pi$
$727$			335.755i			0.461836i	−0.972973	+	0.230918i	$0.925827\pi$
$728$		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	$-0.244720\pi$
$733$	1053.67			1.43747			0.718737	+	0.695282i	$0.244720\pi$
$734$	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	$-0.410107\pi$
$761$	424.134			0.557338			0.278669	+	0.960387i	$0.410107\pi$
$762$	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	$-0.765909\pi$
$769$	−1140.50			−1.48310			−0.741550	+	0.670898i	$0.765909\pi$
$770$		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	$-0.364247\pi$
$773$	639.533			0.827339			0.413669	+	0.910427i	$0.364247\pi$
$774$	−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	$0.0186153\pi$
$787$			91.9978i			0.116897i	−0.998290	+	0.0584484i	$0.981385\pi$
$788$	−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	$-0.408268\pi$
$797$	453.032			0.568422			0.284211	+	0.958762i	$0.408268\pi$
$798$		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	$-0.887385\pi$
$811$		−	561.951i		−	0.692912i	0.938066	−	0.346456i	$-0.112615\pi$
$812$		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	$-0.635514\pi$
$829$	−684.732			−0.825973			−0.412986	+	0.910737i	$0.635514\pi$
$830$	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	$0.285343\pi$
$839$			1310.69i			1.56221i	−0.624402	+	0.781103i	$0.714657\pi$
$840$		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	$-0.576224\pi$
$853$	−404.635			−0.474367			−0.237183	+	0.971465i	$0.576224\pi$
$854$		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	$-0.483738\pi$
$857$	87.5256			0.102130			0.0510651	+	0.998695i	$0.483738\pi$
$858$	−36.7051	−	292.169i	−0.0427799	−	0.340523i
$859$			246.795i			0.287305i	0.989628	+	0.143652i	$0.0458847\pi$
$859$			246.795i			0.287305i	−0.989628	+	0.143652i	$0.954115\pi$
$860$	−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	$-0.725183\pi$
$881$	−1145.10			−1.29977			−0.649885	+	0.760032i	$0.725183\pi$
$882$		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	$0.204522\pi$
$887$			1063.01i			1.19844i	−0.800585	+	0.599219i	$0.795478\pi$
$888$	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	$-0.493295\pi$
$929$	39.1354			0.0421264			0.0210632	+	0.999778i	$0.493295\pi$
$930$	−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	$-0.138448\pi$
$937$	1699.52			1.81378			0.906892	+	0.421363i	$0.138448\pi$
$938$		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	$-0.611807\pi$
$941$	−647.545			−0.688145			−0.344073	+	0.938943i	$0.611807\pi$
$942$	−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	$-0.919312\pi$
$971$		−	487.020i		−	0.501566i	0.968043	−	0.250783i	$-0.0806880\pi$
$972$	−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	$-0.724807\pi$
$983$		−	1495.73i		−	1.52160i	0.648987	−	0.760800i	$-0.275193\pi$
$984$	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	$-0.826546\pi$
$997$	−1705.20			−1.71034			−0.855168	+	0.518351i	$0.826546\pi$
$998$	−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.295.10	yes	24
4.3	odd	2	inner	588.3.g.h.295.11	yes	24
7.6	odd	2	inner	588.3.g.h.295.9	✓	24
28.27	even	2	inner	588.3.g.h.295.12	yes	24

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

Related objects

Downloads

Learn more