LMFDB - Embedded newform 76.4.i.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	76.9
Dual form			76.4.i.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.23895 - 5.23510i) q^{3} +(12.3313 + 4.48821i) q^{5} +(-4.34015 + 7.51736i) q^{7} +(6.82973 - 38.7333i) q^{9} +O(q^{10})$	\(q+(6.23895 - 5.23510i) q^{3} +(12.3313 + 4.48821i) q^{5} +(-4.34015 + 7.51736i) q^{7} +(6.82973 - 38.7333i) q^{9} +(7.27759 + 12.6052i) q^{11} +(-60.6757 - 50.9129i) q^{13} +(100.430 - 36.5537i) q^{15} +(6.75806 + 38.3269i) q^{17} +(82.6796 - 4.80376i) q^{19} +(12.2762 + 69.6216i) q^{21} +(-114.599 + 41.7107i) q^{23} +(36.1605 + 30.3423i) q^{25} +(-50.2134 - 86.9722i) q^{27} +(25.0284 - 141.943i) q^{29} +(-150.191 + 260.138i) q^{31} +(111.394 + 40.5440i) q^{33} +(-87.2590 + 73.2190i) q^{35} -279.946 q^{37} -645.087 q^{39} +(-21.4220 + 17.9752i) q^{41} +(196.878 + 71.6577i) q^{43} +(258.063 - 446.977i) q^{45} +(-74.0727 + 420.087i) q^{47} +(133.826 + 231.794i) q^{49} +(242.808 + 203.740i) q^{51} +(432.873 - 157.553i) q^{53} +(33.1673 + 188.101i) q^{55} +(490.686 - 462.807i) q^{57} +(-151.695 - 860.302i) q^{59} +(634.926 - 231.094i) q^{61} +(261.530 + 219.450i) q^{63} +(-519.700 - 900.147i) q^{65} +(-92.2995 + 523.456i) q^{67} +(-496.619 + 860.169i) q^{69} +(-433.790 - 157.886i) q^{71} +(-110.587 + 92.7938i) q^{73} +384.449 q^{75} -126.343 q^{77} +(579.784 - 486.496i) q^{79} +(229.303 + 83.4593i) q^{81} +(34.1249 - 59.1060i) q^{83} +(-88.6838 + 502.951i) q^{85} +(-586.935 - 1016.60i) q^{87} +(-1084.15 - 909.711i) q^{89} +(646.072 - 235.151i) q^{91} +(424.816 + 2409.25i) q^{93} +(1041.11 + 311.848i) q^{95} +(-93.7766 - 531.834i) q^{97} +(537.943 - 195.795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	6.23895	−	5.23510i	1.20069	−	1.00750i	0.201077	−	0.979575i	$-0.435556\pi$
$3$	6.23895	−	5.23510i	1.20069	−	1.00750i	0.999610	−	0.0279205i	$-0.00888851\pi$
$4$		0			0
$5$	12.3313	+	4.48821i	1.10294	+	0.401438i	0.828400	−	0.560137i	$-0.189252\pi$
$5$	12.3313	+	4.48821i	1.10294	+	0.401438i	0.274542	+	0.961575i	$0.411474\pi$
$6$		0			0
$7$	−4.34015	+	7.51736i	−0.234346	+	0.405899i	−0.959082	−	0.283127i	$-0.908628\pi$
$7$	−4.34015	+	7.51736i	−0.234346	+	0.405899i	0.724736	+	0.689026i	$0.241962\pi$
$8$		0			0
$9$	6.82973	−	38.7333i	0.252953	−	1.43457i
$10$		0			0
$11$	7.27759	+	12.6052i	0.199480	+	0.345509i	0.948360	−	0.317197i	$-0.102741\pi$
$11$	7.27759	+	12.6052i	0.199480	+	0.345509i	−0.748880	+	0.662705i	$0.769408\pi$
$12$		0			0
$13$	−60.6757	−	50.9129i	−1.29449	−	1.08621i	−0.991069	−	0.133353i	$-0.957426\pi$
$13$	−60.6757	−	50.9129i	−1.29449	−	1.08621i	−0.303424	−	0.952856i	$-0.598130\pi$
$14$		0			0
$15$	100.430	−	36.5537i	1.72874	−	0.629208i
$16$		0			0
$17$	6.75806	+	38.3269i	0.0964160	+	0.546802i	0.994304	+	0.106579i	$0.0339896\pi$
$17$	6.75806	+	38.3269i	0.0964160	+	0.546802i	−0.897888	+	0.440223i	$0.854899\pi$
$18$		0			0
$19$	82.6796	−	4.80376i	0.998316	−	0.0580030i
$19$	82.6796	−	4.80376i	0.998316	−	0.0580030i
$20$		0			0
$21$	12.2762	+	69.6216i	0.127566	+	0.723460i
$22$		0			0
$23$	−114.599	+	41.7107i	−1.03894	+	0.378142i	−0.804477	−	0.593983i	$-0.797554\pi$
$23$	−114.599	+	41.7107i	−1.03894	+	0.378142i	−0.234460	+	0.972126i	$0.575332\pi$
$24$		0			0
$25$	36.1605	+	30.3423i	0.289284	+	0.242738i
$26$		0			0
$27$	−50.2134	−	86.9722i	−0.357910	−	0.619919i
$28$		0			0
$29$	25.0284	−	141.943i	0.160264	−	0.908901i	−0.793550	−	0.608504i	$-0.791770\pi$
$29$	25.0284	−	141.943i	0.160264	−	0.908901i	0.953814	−	0.300397i	$-0.0971191\pi$
$30$		0			0
$31$	−150.191	+	260.138i	−0.870162	+	1.50716i	−0.00833294	+	0.999965i	$0.502652\pi$
$31$	−150.191	+	260.138i	−0.870162	+	1.50716i	−0.861829	+	0.507199i	$0.830681\pi$
$32$		0			0
$33$	111.394	+	40.5440i	0.587611	+	0.213873i
$34$		0			0
$35$	−87.2590	+	73.2190i	−0.421413	+	0.353608i
$36$		0			0
$37$	−279.946			−1.24386			−0.621930	−	0.783073i	$-0.713651\pi$
$37$	−279.946			−1.24386			−0.621930	+	0.783073i	$0.713651\pi$
$38$		0			0
$39$	−645.087			−2.64863
$40$		0			0
$41$	−21.4220	+	17.9752i	−0.0815990	+	0.0684697i	−0.682675	−	0.730722i	$-0.739183\pi$
$41$	−21.4220	+	17.9752i	−0.0815990	+	0.0684697i	0.601076	+	0.799192i	$0.294739\pi$
$42$		0			0
$43$	196.878	+	71.6577i	0.698223	+	0.254133i	0.666652	−	0.745369i	$-0.267727\pi$
$43$	196.878	+	71.6577i	0.698223	+	0.254133i	0.0315712	+	0.999502i	$0.489949\pi$
$44$		0			0
$45$	258.063	−	446.977i	0.854882	−	1.48070i
$46$		0			0
$47$	−74.0727	+	420.087i	−0.229886	+	1.30375i	0.623236	+	0.782034i	$0.285818\pi$
$47$	−74.0727	+	420.087i	−0.229886	+	1.30375i	−0.853122	+	0.521712i	$0.825294\pi$
$48$		0			0
$49$	133.826	+	231.794i	0.390164	+	0.675784i
$50$		0			0
$51$	242.808	+	203.740i	0.666666	+	0.559399i
$52$		0			0
$53$	432.873	−	157.553i	1.12188	−	0.408331i	0.286542	−	0.958068i	$-0.407494\pi$
$53$	432.873	−	157.553i	1.12188	−	0.408331i	0.835338	+	0.549736i	$0.185272\pi$
$54$		0			0
$55$	33.1673	+	188.101i	0.0813141	+	0.461155i
$56$		0			0
$57$	490.686	−	462.807i	1.14023	−	1.07544i
$58$		0			0
$59$	−151.695	−	860.302i	−0.334728	−	1.89834i	−0.429902	−	0.902875i	$-0.641452\pi$
$59$	−151.695	−	860.302i	−0.334728	−	1.89834i	0.0951743	−	0.995461i	$-0.469659\pi$
$60$		0			0
$61$	634.926	−	231.094i	1.33269	−	0.485058i	0.425185	−	0.905106i	$-0.360209\pi$
$61$	634.926	−	231.094i	1.33269	−	0.485058i	0.907502	+	0.420048i	$0.137987\pi$
$62$		0			0
$63$	261.530	+	219.450i	0.523011	+	0.438858i
$64$		0			0
$65$	−519.700	−	900.147i	−0.991705	−	1.71768i
$66$		0			0
$67$	−92.2995	+	523.456i	−0.168301	+	0.954483i	0.777294	+	0.629137i	$0.216592\pi$
$67$	−92.2995	+	523.456i	−0.168301	+	0.954483i	−0.945595	+	0.325346i	$0.894519\pi$
$68$		0			0
$69$	−496.619	+	860.169i	−0.866462	+	1.50076i
$70$		0			0
$71$	−433.790	−	157.886i	−0.725089	−	0.263911i	−0.0470046	−	0.998895i	$-0.514968\pi$
$71$	−433.790	−	157.886i	−0.725089	−	0.263911i	−0.678085	+	0.734984i	$0.737190\pi$
$72$		0			0
$73$	−110.587	+	92.7938i	−0.177305	+	0.148777i	−0.727121	−	0.686509i	$-0.759142\pi$
$73$	−110.587	+	92.7938i	−0.177305	+	0.148777i	0.549816	+	0.835286i	$0.314698\pi$
$74$		0			0
$75$	384.449			0.591898
$76$		0			0
$77$	−126.343			−0.186989
$78$		0			0
$79$	579.784	−	486.496i	0.825706	−	0.692849i	−0.128595	−	0.991697i	$-0.541047\pi$
$79$	579.784	−	486.496i	0.825706	−	0.692849i	0.954301	+	0.298848i	$0.0966023\pi$
$80$		0			0
$81$	229.303	+	83.4593i	0.314544	+	0.114485i
$82$		0			0
$83$	34.1249	−	59.1060i	0.0451288	−	0.0781654i	−0.842579	−	0.538573i	$-0.818964\pi$
$83$	34.1249	−	59.1060i	0.0451288	−	0.0781654i	0.887707	+	0.460408i	$0.152297\pi$
$84$		0			0
$85$	−88.6838	+	502.951i	−0.113166	+	0.641796i
$86$		0			0
$87$	−586.935	−	1016.60i	−0.723288	−	1.25277i
$88$		0			0
$89$	−1084.15	−	909.711i	−1.29123	−	1.08347i	−0.991590	−	0.129422i	$-0.958688\pi$
$89$	−1084.15	−	909.711i	−1.29123	−	1.08347i	−0.299644	−	0.954051i	$-0.596868\pi$
$90$		0			0
$91$	646.072	−	235.151i	0.744250	−	0.270885i
$92$		0			0
$93$	424.816	+	2409.25i	0.473670	+	2.68632i
$94$		0			0
$95$	1041.11	+	311.848i	1.12437	+	0.336788i
$96$		0			0
$97$	−93.7766	−	531.834i	−0.0981606	−	0.556696i	−0.993733	−	0.111780i	$-0.964345\pi$
$97$	−93.7766	−	531.834i	−0.0981606	−	0.556696i	0.895572	−	0.444916i	$-0.146766\pi$
$98$		0			0
$99$	537.943	−	195.795i	0.546115	−	0.198769i
$100$		0			0
$101$	−298.068	−	250.109i	−0.293652	−	0.246404i	0.484044	−	0.875044i	$-0.339167\pi$
$101$	−298.068	−	250.109i	−0.293652	−	0.246404i	−0.777696	+	0.628640i	$0.783612\pi$
$102$		0			0
$103$	463.047	+	802.022i	0.442965	+	0.767238i	0.997908	−	0.0646502i	$-0.0205932\pi$
$103$	463.047	+	802.022i	0.442965	+	0.767238i	−0.554943	+	0.831889i	$0.687260\pi$
$104$		0			0
$105$	−161.096	+	913.620i	−0.149727	+	0.849145i
$106$		0			0
$107$	288.439	−	499.591i	0.260602	−	0.451376i	−0.705800	−	0.708411i	$-0.749412\pi$
$107$	288.439	−	499.591i	0.260602	−	0.451376i	0.966402	+	0.257035i	$0.0827456\pi$
$108$		0			0
$109$	−1528.41	−	556.296i	−1.34308	−	0.488839i	−0.432295	−	0.901732i	$-0.642296\pi$
$109$	−1528.41	−	556.296i	−1.34308	−	0.488839i	−0.910780	+	0.412893i	$0.864518\pi$
$110$		0			0
$111$	−1746.57	+	1465.55i	−1.49349	+	1.25318i
$112$		0			0
$113$	835.015			0.695147			0.347573	−	0.937653i	$-0.387006\pi$
$113$	835.015			0.695147			0.347573	+	0.937653i	$0.387006\pi$
$114$		0			0
$115$	−1600.36			−1.29769
$116$		0			0
$117$	−2386.42	+	2002.45i	−1.88568	+	1.58228i
$118$		0			0
$119$	−317.448	−	115.542i	−0.244541	−	0.0890057i
$120$		0			0
$121$	559.573	−	969.209i	0.420416	−	0.728181i
$122$		0			0
$123$	−39.5489	+	224.293i	−0.0289919	+	0.164421i
$124$		0			0
$125$	−510.444	−	884.114i	−0.365244	−	0.632621i
$126$		0			0
$127$	428.609	+	359.646i	0.299472	+	0.251287i	0.780124	−	0.625624i	$-0.215156\pi$
$127$	428.609	+	359.646i	0.299472	+	0.251287i	−0.480653	+	0.876911i	$0.659600\pi$
$128$		0			0
$129$	1603.45	−	583.607i	1.09439	−	0.398324i
$130$		0			0
$131$	−309.481	−	1755.15i	−0.206408	−	1.17060i	−0.895208	−	0.445648i	$-0.852973\pi$
$131$	−309.481	−	1755.15i	−0.206408	−	1.17060i	0.688800	−	0.724951i	$-0.258138\pi$
$132$		0			0
$133$	−322.730	+	642.381i	−0.210408	+	0.418809i
$134$		0			0
$135$	−228.845	−	1297.85i	−0.145895	−	0.827413i
$136$		0			0
$137$	−909.185	+	330.916i	−0.566985	+	0.206366i	−0.609577	−	0.792727i	$-0.708661\pi$
$137$	−909.185	+	330.916i	−0.566985	+	0.206366i	0.0425922	+	0.999093i	$0.486438\pi$
$138$		0			0
$139$	7.89204	+	6.62221i	0.00481578	+	0.00404092i	0.645192	−	0.764020i	$-0.276777\pi$
$139$	7.89204	+	6.62221i	0.00481578	+	0.00404092i	−0.640377	+	0.768061i	$0.721222\pi$
$140$		0			0
$141$	1737.06	+	3008.68i	1.03750	+	1.79700i
$142$		0			0
$143$	200.193	−	1135.35i	0.117070	−	0.663935i
$144$		0			0
$145$	945.702	−	1638.00i	0.541629	−	0.938130i
$146$		0			0
$147$	2048.40	+	745.557i	1.14931	+	0.418316i
$148$		0			0
$149$	2226.95	−	1868.63i	1.22442	−	1.02741i	0.225842	−	0.974164i	$-0.427487\pi$
$149$	2226.95	−	1868.63i	1.22442	−	1.02741i	0.998581	−	0.0532489i	$-0.0169577\pi$
$150$		0			0
$151$	1079.93			0.582008			0.291004	−	0.956722i	$-0.406011\pi$
$151$	1079.93			0.582008			0.291004	+	0.956722i	$0.406011\pi$
$152$		0			0
$153$	1530.68			0.808813
$154$		0			0
$155$	−3019.59	+	2533.74i	−1.56477	+	1.31300i
$156$		0			0
$157$	−363.679	−	132.368i	−0.184871	−	0.0672875i	0.247926	−	0.968779i	$-0.420251\pi$
$157$	−363.679	−	132.368i	−0.184871	−	0.0672875i	−0.432797	+	0.901492i	$0.642473\pi$
$158$		0			0
$159$	1875.87	−	3249.10i	0.935635	−	1.62057i
$160$		0			0
$161$	183.823	−	1042.51i	0.0899832	−	0.510320i
$162$		0			0
$163$	528.534	+	915.447i	0.253975	+	0.439898i	0.964617	−	0.263656i	$-0.0849285\pi$
$163$	528.534	+	915.447i	0.253975	+	0.439898i	−0.710642	+	0.703554i	$0.751595\pi$
$164$		0			0
$165$	1191.66	+	999.919i	0.562245	+	0.471779i
$166$		0			0
$167$	1050.58	−	382.379i	0.486804	−	0.177182i	−0.0869456	−	0.996213i	$-0.527711\pi$
$167$	1050.58	−	382.379i	0.486804	−	0.177182i	0.573749	+	0.819031i	$0.305488\pi$
$168$		0			0
$169$	707.906	+	4014.73i	0.322215	+	1.82737i
$170$		0			0
$171$	378.614	−	3235.26i	0.169318	−	1.44682i
$172$		0			0
$173$	−134.982	−	765.521i	−0.0593208	−	0.336425i	0.940675	−	0.339309i	$-0.110193\pi$
$173$	−134.982	−	765.521i	−0.0593208	−	0.336425i	−0.999996	+	0.00288396i	$0.999082\pi$
$174$		0			0
$175$	−385.036	+	140.142i	−0.166320	+	0.0605355i
$176$		0			0
$177$	−5450.19	−	4573.25i	−2.31447	−	1.94207i
$178$		0			0
$179$	2155.39	+	3733.25i	0.900010	+	1.55886i	0.827479	+	0.561496i	$0.189774\pi$
$179$	2155.39	+	3733.25i	0.900010	+	1.55886i	0.0725302	+	0.997366i	$0.476893\pi$
$180$		0			0
$181$	−518.063	+	2938.08i	−0.212748	+	1.20655i	0.672024	+	0.740529i	$0.265425\pi$
$181$	−518.063	+	2938.08i	−0.212748	+	1.20655i	−0.884772	+	0.466024i	$0.845686\pi$
$182$		0			0
$183$	2751.47	−	4765.69i	1.11145	−	1.92508i
$184$		0			0
$185$	−3452.09	−	1256.46i	−1.37191	−	0.499333i
$186$		0			0
$187$	−433.934	+	364.114i	−0.169692	+	0.142388i
$188$		0			0
$189$	871.735			0.335499
$190$		0			0
$191$	−675.989			−0.256088			−0.128044	−	0.991768i	$-0.540870\pi$
$191$	−675.989			−0.256088			−0.128044	+	0.991768i	$0.540870\pi$
$192$		0			0
$193$	2479.27	−	2080.36i	0.924673	−	0.775893i	−0.0501800	−	0.998740i	$-0.515980\pi$
$193$	2479.27	−	2080.36i	0.924673	−	0.775893i	0.974853	+	0.222847i	$0.0715351\pi$
$194$		0			0
$195$	−7954.74	−	2895.29i	−2.92129	−	1.06326i
$196$		0			0
$197$	−2452.84	+	4248.44i	−0.887094	+	1.53649i	−0.0437999	+	0.999040i	$0.513946\pi$
$197$	−2452.84	+	4248.44i	−0.887094	+	1.53649i	−0.843294	+	0.537452i	$0.819387\pi$
$198$		0			0
$199$	61.8508	−	350.774i	0.0220326	−	0.124953i	−0.971808	−	0.235775i	$-0.924237\pi$
$199$	61.8508	−	350.774i	0.0220326	−	0.124953i	0.993840	+	0.110822i	$0.0353483\pi$
$200$		0			0
$201$	2164.50	+	3749.02i	0.759561	+	1.31560i
$202$		0			0
$203$	958.409	+	804.201i	0.331365	+	0.278048i
$204$		0			0
$205$	−344.837	+	125.511i	−0.117485	+	0.0427612i
$206$		0			0
$207$	832.911	+	4723.67i	0.279668	+	1.58608i
$208$		0			0
$209$	662.261	+	1007.23i	0.219184	+	0.333357i
$210$		0			0
$211$	179.768	+	1019.51i	0.0586526	+	0.332636i	0.999988	−	0.00483605i	$-0.00153937\pi$
$211$	179.768	+	1019.51i	0.0586526	+	0.332636i	−0.941336	+	0.337472i	$0.890428\pi$
$212$		0			0
$213$	−3532.94	+	1285.89i	−1.13649	+	0.413650i
$214$		0			0
$215$	2106.14	+	1767.26i	0.668082	+	0.560587i
$216$		0			0
$217$	−1303.70	−	2258.07i	−0.407838	−	0.706396i
$218$		0			0
$219$	−204.164	+	1157.87i	−0.0629961	+	0.357268i
$220$		0			0
$221$	1541.28	−	2669.58i	0.469131	−	0.812559i
$222$		0			0
$223$	−446.782	−	162.615i	−0.134165	−	0.0488320i	0.274065	−	0.961711i	$-0.411632\pi$
$223$	−446.782	−	162.615i	−0.134165	−	0.0488320i	−0.408230	+	0.912879i	$0.633854\pi$
$224$		0			0
$225$	1422.22	−	1193.39i	0.421400	−	0.353596i
$226$		0			0
$227$	1860.03			0.543852			0.271926	−	0.962318i	$-0.412339\pi$
$227$	1860.03			0.543852			0.271926	+	0.962318i	$0.412339\pi$
$228$		0			0
$229$	439.880			0.126935			0.0634674	−	0.997984i	$-0.479784\pi$
$229$	439.880			0.126935			0.0634674	+	0.997984i	$0.479784\pi$
$230$		0			0
$231$	−788.250	+	661.420i	−0.224515	+	0.188391i
$232$		0			0
$233$	−5997.77	−	2183.01i	−1.68638	−	0.613793i	−0.692220	−	0.721687i	$-0.743367\pi$
$233$	−5997.77	−	2183.01i	−1.68638	−	0.613793i	−0.994162	+	0.107894i	$0.965589\pi$
$234$		0			0
$235$	−2798.85	+	4847.76i	−0.776924	+	1.34567i
$236$		0			0
$237$	1070.38	−	6070.45i	0.293371	−	1.66379i
$238$		0			0
$239$	1902.95	+	3296.01i	0.515028	+	0.892055i	0.999848	+	0.0174408i	$0.00555185\pi$
$239$	1902.95	+	3296.01i	0.515028	+	0.892055i	−0.484820	+	0.874614i	$0.661115\pi$
$240$		0			0
$241$	2716.52	+	2279.43i	0.726085	+	0.609258i	0.929061	−	0.369926i	$-0.120617\pi$
$241$	2716.52	+	2279.43i	0.726085	+	0.609258i	−0.202976	+	0.979184i	$0.565061\pi$
$242$		0			0
$243$	4415.52	−	1607.12i	1.16566	−	0.424267i
$244$		0			0
$245$	609.907	+	3458.95i	0.159043	+	0.901977i
$246$		0			0
$247$	−5261.22	−	3917.99i	−1.35532	−	1.00930i
$248$		0			0
$249$	−96.5226	−	547.407i	−0.0245657	−	0.139319i
$250$		0			0
$251$	1241.31	−	451.798i	0.312154	−	0.113615i	−0.181193	−	0.983448i	$-0.557996\pi$
$251$	1241.31	−	451.798i	0.312154	−	0.113615i	0.493346	+	0.869833i	$0.335774\pi$
$252$		0			0
$253$	−1359.77	−	1140.99i	−0.337898	−	0.283530i
$254$		0			0
$255$	2079.70	+	3602.15i	0.510730	+	0.884610i
$256$		0			0
$257$	−157.199	+	891.519i	−0.0381549	+	0.216387i	−0.997924	−	0.0644036i	$-0.979486\pi$
$257$	−157.199	+	891.519i	−0.0381549	+	0.216387i	0.959769	+	0.280791i	$0.0905966\pi$
$258$		0			0
$259$	1215.01	−	2104.45i	0.291494	−	0.504882i
$260$		0			0
$261$	−5326.98	−	1938.86i	−1.26334	−	0.459818i
$262$		0			0
$263$	−3630.43	+	3046.29i	−0.851187	+	0.714230i	−0.960051	−	0.279826i	$-0.909723\pi$
$263$	−3630.43	+	3046.29i	−0.851187	+	0.714230i	0.108864	+	0.994057i	$0.465279\pi$
$264$		0			0
$265$	6045.00			1.40129
$266$		0			0
$267$	−11526.4			−2.64196
$268$		0			0
$269$	546.376	−	458.464i	0.123841	−	0.103915i	−0.578764	−	0.815495i	$-0.696465\pi$
$269$	546.376	−	458.464i	0.123841	−	0.103915i	0.702605	+	0.711581i	$0.252020\pi$
$270$		0			0
$271$	−7962.07	−	2897.96i	−1.78473	−	0.649588i	−0.999540	−	0.0303293i	$-0.990344\pi$
$271$	−7962.07	−	2897.96i	−1.78473	−	0.649588i	−0.785187	−	0.619258i	$-0.787433\pi$
$272$		0			0
$273$	2799.77	−	4849.35i	0.620696	−	1.07508i
$274$		0			0
$275$	−119.308	+	676.628i	−0.0261619	+	0.148372i
$276$		0			0
$277$	−563.695	−	976.348i	−0.122271	−	0.211780i	0.798392	−	0.602138i	$-0.205684\pi$
$277$	−563.695	−	976.348i	−0.122271	−	0.211780i	−0.920663	+	0.390358i	$0.872351\pi$
$278$		0			0
$279$	9050.23	+	7594.04i	1.94202	+	1.62955i
$280$		0			0
$281$	3616.02	−	1316.12i	0.767665	−	0.279407i	0.0716454	−	0.997430i	$-0.477175\pi$
$281$	3616.02	−	1316.12i	0.767665	−	0.279407i	0.696019	+	0.718023i	$0.254953\pi$
$282$		0			0
$283$	−69.2789	−	392.900i	−0.0145520	−	0.0825282i	0.976667	−	0.214760i	$-0.0688969\pi$
$283$	−69.2789	−	392.900i	−0.0145520	−	0.0825282i	−0.991219	+	0.132232i	$0.957786\pi$
$284$		0			0
$285$	8127.96	−	3504.69i	1.68933	−	0.728421i
$286$		0			0
$287$	−42.1514	−	239.052i	−0.00866939	−	0.0491666i
$288$		0			0
$289$	3193.43	−	1162.31i	0.649996	−	0.236579i
$290$		0			0
$291$	−3369.27	−	2827.16i	−0.678729	−	0.569522i
$292$		0			0
$293$	3409.41	+	5905.27i	0.679795	+	1.17744i	0.975043	+	0.222018i	$0.0712644\pi$
$293$	3409.41	+	5905.27i	0.679795	+	1.17744i	−0.295248	+	0.955421i	$0.595402\pi$
$294$		0			0
$295$	1990.64	−	11289.5i	0.392879	−	2.22813i
$296$		0			0
$297$	730.865	−	1265.90i	0.142792	−	0.247322i
$298$		0			0
$299$	9076.99	+	3303.75i	1.75564	+	0.639000i
$300$		0			0
$301$	−1393.16	+	1169.00i	−0.266778	+	0.223853i
$302$		0			0
$303$	−3168.98			−0.600835
$304$		0			0
$305$	8866.64			1.66460
$306$		0			0
$307$	249.693	−	209.517i	0.0464193	−	0.0389504i	−0.619283	−	0.785168i	$-0.712577\pi$
$307$	249.693	−	209.517i	0.0464193	−	0.0389504i	0.665702	+	0.746218i	$0.268132\pi$
$308$		0			0
$309$	7087.60	+	2579.67i	1.30485	+	0.474927i
$310$		0			0
$311$	3308.70	−	5730.84i	0.603277	−	1.04491i	−0.389044	−	0.921219i	$-0.627195\pi$
$311$	3308.70	−	5730.84i	0.603277	−	1.04491i	0.992321	−	0.123687i	$-0.0394720\pi$
$312$		0			0
$313$	−5.41238	+	30.6951i	−0.000977398	+	0.00554310i	−0.985293	−	0.170876i	$-0.945340\pi$
$313$	−5.41238	+	30.6951i	−0.000977398	+	0.00554310i	0.984315	+	0.176419i	$0.0564514\pi$
$314$		0			0
$315$	2240.06	+	3879.90i	0.400676	+	0.693992i
$316$		0			0
$317$	−4777.12	−	4008.48i	−0.846404	−	0.710217i	0.112591	−	0.993641i	$-0.464085\pi$
$317$	−4777.12	−	4008.48i	−0.846404	−	0.710217i	−0.958995	+	0.283424i	$0.908530\pi$
$318$		0			0
$319$	1971.36	−	717.516i	0.346003	−	0.125935i
$320$		0			0
$321$	−815.852	−	4626.93i	−0.141858	−	0.804517i
$322$		0			0
$323$	742.867	+	3136.39i	0.127970	+	0.540289i
$324$		0			0
$325$	−649.250	−	3682.08i	−0.110812	−	0.628446i
$326$		0			0
$327$	−12447.9	+	4530.68i	−2.10512	+	0.766200i
$328$		0			0
$329$	−2836.46	−	2380.07i	−0.475317	−	0.398838i
$330$		0			0
$331$	−1476.15	−	2556.76i	−0.245125	−	0.424569i	0.717042	−	0.697030i	$-0.245496\pi$
$331$	−1476.15	−	2556.76i	−0.245125	−	0.424569i	−0.962167	+	0.272461i	$0.912162\pi$
$332$		0			0
$333$	−1911.95	+	10843.2i	−0.314638	+	1.78440i
$334$		0			0
$335$	−3487.55	+	6040.62i	−0.568792	+	0.985177i
$336$		0			0
$337$	−5326.46	−	1938.67i	−0.860981	−	0.313372i	−0.126472	−	0.991970i	$-0.540365\pi$
$337$	−5326.46	−	1938.67i	−0.860981	−	0.313372i	−0.734509	+	0.678599i	$0.762588\pi$
$338$		0			0
$339$	5209.62	−	4371.39i	0.834654	−	0.700358i
$340$		0			0
$341$	−4372.10			−0.694318
$342$		0			0
$343$	−5300.64			−0.834425
$344$		0			0
$345$	−9984.56	+	8378.04i	−1.55812	+	1.30742i
$346$		0			0
$347$	7743.17	+	2818.28i	1.19791	+	0.436004i	0.862495	−	0.506066i	$-0.168901\pi$
$347$	7743.17	+	2818.28i	1.19791	+	0.436004i	0.335417	+	0.942070i	$0.391123\pi$
$348$		0			0
$349$	−78.6789	+	136.276i	−0.0120676	+	0.0209017i	−0.871996	−	0.489513i	$-0.837175\pi$
$349$	−78.6789	+	136.276i	−0.0120676	+	0.0209017i	0.859929	+	0.510414i	$0.170508\pi$
$350$		0			0
$351$	−1381.28	+	7833.61i	−0.210049	+	1.19125i
$352$		0			0
$353$	−4689.58	−	8122.59i	−0.707085	−	1.22471i	−0.965934	−	0.258790i	$-0.916676\pi$
$353$	−4689.58	−	8122.59i	−0.707085	−	1.22471i	0.258848	−	0.965918i	$-0.416657\pi$
$354$		0			0
$355$	−4640.55	−	3893.88i	−0.693788	−	0.582157i
$356$		0			0
$357$	−2585.41	+	941.014i	−0.383290	+	0.139506i
$358$		0			0
$359$	1088.13	+	6171.10i	0.159970	+	0.907238i	0.954100	+	0.299489i	$0.0968161\pi$
$359$	1088.13	+	6171.10i	0.159970	+	0.907238i	−0.794129	+	0.607749i	$0.792073\pi$
$360$		0			0
$361$	6812.85	−	794.346i	0.993271	−	0.115811i
$362$		0			0
$363$	−1582.76	−	8976.28i	−0.228852	−	1.29788i
$364$		0			0
$365$	−1780.16	+	647.926i	−0.255282	+	0.0929150i
$366$		0			0
$367$	5004.42	+	4199.21i	0.711794	+	0.597266i	0.925102	−	0.379719i	$-0.123979\pi$
$367$	5004.42	+	4199.21i	0.711794	+	0.597266i	−0.213308	+	0.976985i	$0.568424\pi$
$368$		0			0
$369$	549.933	+	952.512i	0.0775837	+	0.134379i
$370$		0			0
$371$	−694.352	+	3937.86i	−0.0971670	+	0.551061i
$372$		0			0
$373$	−1727.94	+	2992.88i	−0.239864	+	0.415456i	−0.960675	−	0.277675i	$-0.910436\pi$
$373$	−1727.94	+	2992.88i	−0.239864	+	0.415456i	0.720811	+	0.693131i	$0.243769\pi$
$374$		0			0
$375$	−7813.06	−	2843.72i	−1.07591	−	0.391598i
$376$		0			0
$377$	−8745.35	+	7338.22i	−1.19472	+	1.00249i
$378$		0			0
$379$	55.6354			0.00754037			0.00377018	−	0.999993i	$-0.498800\pi$
$379$	55.6354			0.00754037			0.00377018	+	0.999993i	$0.498800\pi$
$380$		0			0
$381$	4556.85			0.612742
$382$		0			0
$383$	355.838	−	298.583i	0.0474738	−	0.0398353i	−0.618742	−	0.785594i	$-0.712357\pi$
$383$	355.838	−	298.583i	0.0474738	−	0.0398353i	0.666216	+	0.745759i	$0.267913\pi$
$384$		0			0
$385$	−1557.97	−	567.056i	−0.206238	−	0.0750645i
$386$		0			0
$387$	4120.16	−	7136.33i	0.541188	−	0.937364i
$388$		0			0
$389$	1051.05	−	5960.83i	0.136994	−	0.776930i	−0.836457	−	0.548033i	$-0.815377\pi$
$389$	1051.05	−	5960.83i	0.136994	−	0.776930i	0.973451	−	0.228897i	$-0.0735120\pi$
$390$		0			0
$391$	−2373.11	−	4110.34i	−0.306939	−	0.531634i
$392$		0			0
$393$	−11119.2	−	9330.15i	−1.42721	−	1.19757i
$394$		0			0
$395$	9332.97	−	3396.92i	1.18884	−	0.432703i
$396$		0			0
$397$	2455.33	+	13924.9i	0.310402	+	1.76037i	0.596921	+	0.802300i	$0.296391\pi$
$397$	2455.33	+	13924.9i	0.310402	+	1.76037i	−0.286519	+	0.958075i	$0.592498\pi$
$398$		0			0
$399$	1349.43	+	5697.31i	0.169314	+	0.714843i
$400$		0			0
$401$	1164.17	+	6602.33i	0.144977	+	0.822206i	0.967386	+	0.253308i	$0.0815188\pi$
$401$	1164.17	+	6602.33i	0.144977	+	0.822206i	−0.822408	+	0.568897i	$0.807370\pi$
$402$		0			0
$403$	22357.3	−	8137.39i	2.76351	−	1.00584i
$404$		0			0
$405$	2453.01	+	2058.32i	0.300965	+	0.252540i
$406$		0			0
$407$	−2037.33	−	3528.76i	−0.248125	−	0.429765i
$408$		0			0
$409$	−2708.90	+	15362.9i	−0.327497	+	1.85733i	0.164017	+	0.986458i	$0.447555\pi$
$409$	−2708.90	+	15362.9i	−0.327497	+	1.85733i	−0.491514	+	0.870870i	$0.663556\pi$
$410$		0			0
$411$	−3939.98	+	6824.24i	−0.472859	+	0.819015i
$412$		0			0
$413$	7125.58	+	2593.50i	0.848975	+	0.309002i
$414$		0			0
$415$	686.083	−	575.692i	0.0811530	−	0.0680955i
$416$		0			0
$417$	83.9060			0.00985346
$418$		0			0
$419$	−11230.4			−1.30940			−0.654702	−	0.755887i	$-0.727206\pi$
$419$	−11230.4			−1.30940			−0.654702	+	0.755887i	$0.727206\pi$
$420$		0			0
$421$	2296.25	−	1926.78i	0.265825	−	0.223054i	−0.500126	−	0.865953i	$-0.666713\pi$
$421$	2296.25	−	1926.78i	0.265825	−	0.223054i	0.765951	+	0.642899i	$0.222268\pi$
$422$		0			0
$423$	15765.5	+	5738.16i	1.81216	+	0.659572i
$424$		0			0
$425$	−918.551	+	1590.98i	−0.104838	+	0.181585i
$426$		0			0
$427$	−1018.46	+	5775.95i	−0.115425	+	0.654608i
$428$		0			0
$429$	−4694.68	−	8131.43i	−0.528348	−	0.915126i
$430$		0			0
$431$	−7803.00	−	6547.50i	−0.872059	−	0.731745i	0.0924715	−	0.995715i	$-0.470523\pi$
$431$	−7803.00	−	6547.50i	−0.872059	−	0.731745i	−0.964531	+	0.263971i	$0.914968\pi$
$432$		0			0
$433$	−6991.69	+	2544.77i	−0.775980	+	0.282434i	−0.699495	−	0.714637i	$-0.746592\pi$
$433$	−6991.69	+	2544.77i	−0.775980	+	0.282434i	−0.0764846	+	0.997071i	$0.524370\pi$
$434$		0			0
$435$	−2674.93	−	15170.3i	−0.294834	−	1.67209i
$436$		0			0
$437$	−9274.64	+	3999.13i	−1.01525	+	0.437767i
$438$		0			0
$439$	−46.6298	−	264.451i	−0.00506952	−	0.0287507i	0.982168	−	0.188005i	$-0.0602021\pi$
$439$	−46.6298	−	264.451i	−0.00506952	−	0.0287507i	−0.987238	+	0.159254i	$0.949091\pi$
$440$		0			0
$441$	9892.14	−	3600.44i	1.06815	−	0.388775i
$442$		0			0
$443$	2702.44	+	2267.61i	0.289835	+	0.243200i	0.776098	−	0.630612i	$-0.217196\pi$
$443$	2702.44	+	2267.61i	0.289835	+	0.243200i	−0.486264	+	0.873812i	$0.661641\pi$
$444$		0			0
$445$	−9285.98	−	16083.8i	−0.989208	−	1.71336i
$446$		0			0
$447$	4111.35	−	23316.6i	0.435034	−	2.46720i
$448$		0			0
$449$	1514.45	−	2623.11i	0.159179	−	0.275706i	−0.775394	−	0.631478i	$-0.782449\pi$
$449$	1514.45	−	2623.11i	0.159179	−	0.275706i	0.934573	+	0.355772i	$0.115782\pi$
$450$		0			0
$451$	−382.481	−	139.212i	−0.0399342	−	0.0145349i
$452$		0			0
$453$	6737.61	−	5653.53i	0.698809	−	0.586371i
$454$		0			0
$455$	9022.30			0.929609
$456$		0			0
$457$	−1299.23			−0.132988			−0.0664939	−	0.997787i	$-0.521181\pi$
$457$	−1299.23			−0.132988			−0.0664939	+	0.997787i	$0.521181\pi$
$458$		0			0
$459$	2994.03	−	2512.29i	0.304465	−	0.255476i
$460$		0			0
$461$	9023.00	+	3284.10i	0.911590	+	0.331792i	0.754888	−	0.655854i	$-0.227691\pi$
$461$	9023.00	+	3284.10i	0.911590	+	0.331792i	0.156703	+	0.987646i	$0.449914\pi$
$462$		0			0
$463$	−2455.54	+	4253.11i	−0.246476	+	0.426909i	−0.962546	−	0.271120i	$-0.912606\pi$
$463$	−2455.54	+	4253.11i	−0.246476	+	0.426909i	0.716070	+	0.698029i	$0.245939\pi$
$464$		0			0
$465$	−5574.71	+	31615.8i	−0.555959	+	3.15300i
$466$		0			0
$467$	−3453.27	−	5981.24i	−0.342181	−	0.592674i	0.642657	−	0.766154i	$-0.277832\pi$
$467$	−3453.27	−	5981.24i	−0.342181	−	0.592674i	−0.984837	+	0.173480i	$0.944499\pi$
$468$		0			0
$469$	−3534.41	−	2965.73i	−0.347983	−	0.291993i
$470$		0			0
$471$	−2961.93	+	1078.06i	−0.289764	+	0.105465i
$472$		0			0
$473$	529.540	+	3003.17i	0.0514763	+	0.291937i
$474$		0			0
$475$	3135.50	+	2334.98i	0.302877	+	0.225550i
$476$		0			0
$477$	−3146.14	−	17842.6i	−0.301995	−	1.71270i
$478$		0			0
$479$	10564.4	−	3845.14i	1.00773	−	0.366783i	0.215167	−	0.976577i	$-0.430970\pi$
$479$	10564.4	−	3845.14i	1.00773	−	0.366783i	0.792560	+	0.609795i	$0.208748\pi$
$480$		0			0
$481$	16985.9	+	14252.9i	1.61017	+	1.35109i
$482$		0			0
$483$	−4310.80	−	7466.52i	−0.406104	−	0.703392i
$484$		0			0
$485$	1230.60	−	6979.07i	0.115214	−	0.653409i
$486$		0			0
$487$	−3679.67	+	6373.37i	−0.342385	+	0.593029i	−0.984875	−	0.173265i	$-0.944568\pi$
$487$	−3679.67	+	6373.37i	−0.342385	+	0.593029i	0.642490	+	0.766294i	$0.277901\pi$
$488$		0			0
$489$	8089.95	+	2944.50i	0.748140	+	0.272301i
$490$		0			0
$491$	−6610.28	+	5546.68i	−0.607572	+	0.509813i	−0.893869	−	0.448327i	$-0.852020\pi$
$491$	−6610.28	+	5546.68i	−0.607572	+	0.509813i	0.286298	+	0.958141i	$0.407575\pi$
$492$		0			0
$493$	5609.37			0.512441
$494$		0			0
$495$	7512.29			0.682126
$496$		0			0
$497$	3069.60	−	2575.70i	0.277043	−	0.232467i
$498$		0			0
$499$	−15680.1	−	5707.08i	−1.40669	−	0.511992i	−0.476531	−	0.879158i	$-0.658106\pi$
$499$	−15680.1	−	5707.08i	−1.40669	−	0.511992i	−0.930156	+	0.367166i	$0.880328\pi$
$500$		0			0
$501$	4552.71	−	7885.53i	0.405989	−	0.703193i
$502$		0			0
$503$	1233.11	−	6993.31i	0.109307	−	0.619913i	−0.880105	−	0.474780i	$-0.842528\pi$
$503$	1233.11	−	6993.31i	0.109307	−	0.619913i	0.989412	−	0.145133i	$-0.0463611\pi$
$504$		0			0
$505$	−2553.02	−	4421.95i	−0.224966	−	0.389652i
$506$		0			0
$507$	25434.1	+	21341.8i	2.22795	+	1.86947i
$508$		0			0
$509$	−1546.57	+	562.904i	−0.134677	+	0.0490182i	−0.408479	−	0.912768i	$-0.633941\pi$
$509$	−1546.57	+	562.904i	−0.134677	+	0.0490182i	0.273803	+	0.961786i	$0.411719\pi$
$510$		0			0
$511$	−217.599	−	1234.06i	−0.0188376	−	0.106833i
$512$		0			0
$513$	−4569.42	−	6949.62i	−0.393265	−	0.598115i
$514$		0			0
$515$	2110.32	+	11968.2i	0.180566	+	1.02404i
$516$		0			0
$517$	−5834.34	+	2123.53i	−0.496313	+	0.180643i
$518$		0			0
$519$	−4849.73	−	4069.40i	−0.410172	−	0.344175i
$520$		0			0
$521$	3869.41	+	6702.02i	0.325378	+	0.563572i	0.981589	−	0.191006i	$-0.0611750\pi$
$521$	3869.41	+	6702.02i	0.325378	+	0.563572i	−0.656211	+	0.754578i	$0.727842\pi$
$522$		0			0
$523$	−1899.96	+	10775.2i	−0.158852	+	0.900893i	0.796328	+	0.604865i	$0.206773\pi$
$523$	−1899.96	+	10775.2i	−0.158852	+	0.900893i	−0.955179	+	0.296027i	$0.904338\pi$
$524$		0			0
$525$	−1668.57	+	2890.04i	−0.138709	+	0.240251i
$526$		0			0
$527$	−10985.3	−	3998.31i	−0.908018	−	0.330492i
$528$		0			0
$529$	2072.71	−	1739.21i	0.170355	−	0.142945i
$530$		0			0
$531$	−34358.4			−2.80796
$532$		0			0
$533$	2214.97			0.180002
$534$		0			0
$535$	5799.09	−	4866.01i	0.468629	−	0.393226i
$536$		0			0
$537$	32991.4	+	12007.9i	2.65118	+	0.964950i
$538$		0			0
$539$	−1947.87	+	3373.80i	−0.155660	+	0.269610i
$540$		0			0
$541$	509.975	−	2892.21i	0.0405278	−	0.229844i	−0.957815	−	0.287384i	$-0.907214\pi$
$541$	509.975	−	2892.21i	0.0405278	−	0.229844i	0.998343	+	0.0575395i	$0.0183255\pi$
$542$		0			0
$543$	12149.0	+	21042.7i	0.960153	+	1.66303i
$544$		0			0
$545$	−16350.5	−	13719.7i	−1.28510	−	1.07832i
$546$		0			0
$547$	−8186.64	+	2979.69i	−0.639918	+	0.232911i	−0.641543	−	0.767087i	$-0.721705\pi$
$547$	−8186.64	+	2979.69i	−0.639918	+	0.232911i	0.00162425	+	0.999999i	$0.499483\pi$
$548$		0			0
$549$	−4614.67	−	26171.1i	−0.358742	−	2.03453i
$550$		0			0
$551$	1387.48	−	11856.0i	0.107275	−	0.916667i
$552$		0			0
$553$	1140.82	+	6469.91i	0.0877261	+	0.497520i
$554$		0			0
$555$	−28115.1	+	10233.1i	−2.15030	+	0.782647i
$556$		0			0
$557$	−8272.31	−	6941.30i	−0.629280	−	0.528029i	0.271425	−	0.962460i	$-0.412505\pi$
$557$	−8272.31	−	6941.30i	−0.629280	−	0.528029i	−0.900705	+	0.434431i	$0.856950\pi$
$558$		0			0
$559$	−8297.40	−	14371.5i	−0.627804	−	1.08739i
$560$		0			0
$561$	−801.120	+	4543.38i	−0.0602911	+	0.341928i
$562$		0			0
$563$	−11584.8	+	20065.5i	−0.867213	+	1.50206i	−0.00238033	+	0.999997i	$0.500758\pi$
$563$	−11584.8	+	20065.5i	−0.867213	+	1.50206i	−0.864833	+	0.502060i	$0.832576\pi$
$564$		0			0
$565$	10296.8	+	3747.73i	0.766707	+	0.279058i
$566$		0			0
$567$	−1622.60	+	1361.52i	−0.120181	+	0.100844i
$568$		0			0
$569$	−15773.5			−1.16214			−0.581072	−	0.813852i	$-0.697367\pi$
$569$	−15773.5			−1.16214			−0.581072	+	0.813852i	$0.697367\pi$
$570$		0			0
$571$	11812.3			0.865722			0.432861	−	0.901461i	$-0.357504\pi$
$571$	11812.3			0.865722			0.432861	+	0.901461i	$0.357504\pi$
$572$		0			0
$573$	−4217.47	+	3538.87i	−0.307482	+	0.258008i
$574$		0			0
$575$	−5409.56	−	1968.92i	−0.392338	−	0.142799i
$576$		0			0
$577$	−10312.3	+	17861.4i	−0.744033	+	1.28870i	0.206612	+	0.978423i	$0.433756\pi$
$577$	−10312.3	+	17861.4i	−0.744033	+	1.28870i	−0.950645	+	0.310280i	$0.899577\pi$
$578$		0			0
$579$	4577.18	−	25958.5i	0.328534	−	1.86321i
$580$		0			0
$581$	296.214	+	513.058i	0.0211515	+	0.0366355i
$582$		0			0
$583$	5136.25	+	4309.83i	0.364874	+	0.306166i
$584$		0			0
$585$	−38415.1	+	13981.9i	−2.71499	+	0.988174i
$586$		0			0
$587$	−1460.38	−	8282.22i	−0.102685	−	0.582358i	−0.992120	−	0.125294i	$-0.960012\pi$
$587$	−1460.38	−	8282.22i	−0.102685	−	0.582358i	0.889434	−	0.457063i	$-0.151099\pi$
$588$		0			0
$589$	−11168.1	+	22229.6i	−0.781277	+	1.55510i
$590$		0			0
$591$	6937.88	+	39346.7i	0.482887	+	2.73859i
$592$		0			0
$593$	−8819.83	+	3210.16i	−0.610771	+	0.222302i	−0.628840	−	0.777534i	$-0.716470\pi$
$593$	−8819.83	+	3210.16i	−0.610771	+	0.222302i	0.0180697	+	0.999837i	$0.494248\pi$
$594$		0			0
$595$	−3395.96	−	2849.55i	−0.233985	−	0.196336i
$596$		0			0
$597$	−1450.45	−	2512.25i	−0.0994355	−	0.172227i
$598$		0			0
$599$	1907.81	−	10819.8i	0.130136	−	0.738035i	−0.847989	−	0.530014i	$-0.822187\pi$
$599$	1907.81	−	10819.8i	0.130136	−	0.738035i	0.978124	−	0.208021i	$-0.0667023\pi$
$600$		0			0
$601$	8114.85	−	14055.3i	0.550768	−	0.953958i	−0.447451	−	0.894308i	$-0.647668\pi$
$601$	8114.85	−	14055.3i	0.550768	−	0.953958i	0.998219	−	0.0596498i	$-0.0189984\pi$
$602$		0			0
$603$	19644.8	+	7150.13i	1.32670	+	0.482878i
$604$		0			0
$605$	11250.3	−	9440.10i	0.756014	−	0.634371i
$606$		0			0
$607$	10177.5			0.680545			0.340273	−	0.940327i	$-0.389481\pi$
$607$	10177.5			0.680545			0.340273	+	0.940327i	$0.389481\pi$
$608$		0			0
$609$	10189.5			0.677998
$610$		0			0
$611$	25882.3	−	21717.8i	1.71372	−	1.43799i
$612$		0			0
$613$	280.228	+	101.995i	0.0184638	+	0.00672027i	0.351236	−	0.936287i	$-0.385762\pi$
$613$	280.228	+	101.995i	0.0184638	+	0.00672027i	−0.332772	+	0.943007i	$0.607984\pi$
$614$		0			0
$615$	−1494.36	+	2588.31i	−0.0979814	+	0.169709i
$616$		0			0
$617$	2917.09	−	16543.6i	0.190336	−	1.07945i	−0.728569	−	0.684972i	$-0.759814\pi$
$617$	2917.09	−	16543.6i	0.190336	−	1.07945i	0.918905	−	0.394478i	$-0.129075\pi$
$618$		0			0
$619$	7970.50	+	13805.3i	0.517547	+	0.896418i	0.999792	+	0.0203815i	$0.00648807\pi$
$619$	7970.50	+	13805.3i	0.517547	+	0.896418i	−0.482245	+	0.876036i	$0.660179\pi$
$620$		0			0
$621$	9382.08	+	7872.50i	0.606264	+	0.508716i
$622$		0			0
$623$	11544.0	−	4201.67i	0.742376	−	0.270203i
$624$		0			0
$625$	−3350.94	−	19004.1i	−0.214460	−	1.21626i
$626$		0			0
$627$	9404.77	+	2817.06i	0.599027	+	0.179430i
$628$		0			0
$629$	−1891.89	−	10729.5i	−0.119928	−	0.680145i
$630$		0			0
$631$	−9558.08	+	3478.86i	−0.603013	+	0.219479i	−0.625443	−	0.780270i	$-0.715082\pi$
$631$	−9558.08	+	3478.86i	−0.603013	+	0.219479i	0.0224305	+	0.999748i	$0.492860\pi$
$632$		0			0
$633$	6458.81	+	5419.59i	0.405553	+	0.340299i
$634$		0			0
$635$	3671.13	+	6358.58i	0.229424	+	0.397374i
$636$		0			0
$637$	3681.31	−	20877.7i	0.228978	−	1.29860i
$638$		0			0
$639$	−9078.13	+	15723.8i	−0.562011	+	0.973432i
$640$		0			0
$641$	−5734.78	−	2087.29i	−0.353370	−	0.128616i	0.159235	−	0.987241i	$-0.449097\pi$
$641$	−5734.78	−	2087.29i	−0.353370	−	0.128616i	−0.512605	+	0.858625i	$0.671319\pi$
$642$		0			0
$643$	3531.42	−	2963.22i	0.216588	−	0.181739i	−0.528038	−	0.849220i	$-0.677072\pi$
$643$	3531.42	−	2963.22i	0.216588	−	0.181739i	0.744626	+	0.667482i	$0.232628\pi$
$644$		0			0
$645$	22391.9			1.36695
$646$		0			0
$647$	12735.1			0.773829			0.386915	−	0.922116i	$-0.373541\pi$
$647$	12735.1			0.773829			0.386915	+	0.922116i	$0.373541\pi$
$648$		0			0
$649$	9740.28	−	8173.06i	0.589121	−	0.494331i
$650$		0			0
$651$	−19954.9	−	7263.01i	−1.20138	−	0.437265i
$652$		0			0
$653$	−9020.50	+	15624.0i	−0.540581	+	0.936314i	0.458289	+	0.888803i	$0.348462\pi$
$653$	−9020.50	+	15624.0i	−0.540581	+	0.936314i	−0.998871	+	0.0475113i	$0.984871\pi$
$654$		0			0
$655$	4061.21	−	23032.3i	0.242267	−	1.37396i
$656$		0			0
$657$	2838.93	+	4917.17i	0.168580	+	0.291989i
$658$		0			0
$659$	−9344.80	−	7841.22i	−0.552385	−	0.463506i	0.323363	−	0.946275i	$-0.395187\pi$
$659$	−9344.80	−	7841.22i	−0.552385	−	0.463506i	−0.875748	+	0.482769i	$0.839631\pi$
$660$		0			0
$661$	26475.9	−	9636.44i	1.55793	−	0.567041i	0.587670	−	0.809101i	$-0.300045\pi$
$661$	26475.9	−	9636.44i	1.55793	−	0.567041i	0.970261	+	0.242060i	$0.0778230\pi$
$662$		0			0
$663$	−4359.54	−	24724.2i	−0.255370	−	1.44828i
$664$		0			0
$665$	−6862.82	+	6472.89i	−0.400194	+	0.377456i
$666$		0			0
$667$	3052.30	+	17310.5i	0.177190	+	1.00489i
$668$		0			0
$669$	−3638.76	+	1324.40i	−0.210288	+	0.0765386i
$670$		0			0
$671$	7533.71	+	6321.53i	0.433436	+	0.363696i
$672$		0			0
$673$	17122.1	+	29656.3i	0.980695	+	1.69861i	0.659693	+	0.751535i	$0.270686\pi$
$673$	17122.1	+	29656.3i	0.980695	+	1.69861i	0.321002	+	0.947078i	$0.395980\pi$
$674$		0			0
$675$	823.192	−	4668.55i	0.0469402	−	0.266211i
$676$		0			0
$677$	15867.8	−	27483.8i	0.900811	−	1.56025i	0.0743666	−	0.997231i	$-0.476307\pi$
$677$	15867.8	−	27483.8i	0.900811	−	1.56025i	0.826444	−	0.563019i	$-0.190360\pi$
$678$		0			0
$679$	4404.99	+	1603.28i	0.248966	+	0.0906162i
$680$		0			0
$681$	11604.6	−	9737.44i	0.652996	−	0.547929i
$682$		0			0
$683$	−19486.1			−1.09168			−0.545839	−	0.837890i	$-0.683789\pi$
$683$	−19486.1			−1.09168			−0.545839	+	0.837890i	$0.683789\pi$
$684$		0			0
$685$	−12696.6			−0.708194
$686$		0			0
$687$	2744.39	−	2302.82i	0.152409	−	0.127886i
$688$		0			0
$689$	−34286.3	−	12479.2i	−1.89580	−	0.690014i
$690$		0			0
$691$	−12806.8	+	22182.0i	−0.705056	+	1.22119i	0.261616	+	0.965172i	$0.415745\pi$
$691$	−12806.8	+	22182.0i	−0.705056	+	1.22119i	−0.966671	+	0.256020i	$0.917589\pi$
$692$		0			0
$693$	−862.890	+	4893.69i	−0.0472994	+	0.268248i
$694$		0			0
$695$	67.5969	+	117.081i	0.00368935	+	0.00639014i
$696$		0			0
$697$	−833.706	−	699.562i	−0.0453068	−	0.0380169i
$698$		0			0
$699$	−48848.1	+	17779.3i	−2.64321	+	0.962050i
$700$		0			0
$701$	−3107.64	−	17624.3i	−0.167438	−	0.949586i	−0.946515	−	0.322659i	$-0.895423\pi$
$701$	−3107.64	−	17624.3i	−0.167438	−	0.949586i	0.779078	−	0.626927i	$-0.215688\pi$
$702$		0			0
$703$	−23145.8	+	1344.79i	−1.24177	+	0.0721476i
$704$		0			0
$705$	7916.59	+	44897.2i	0.422916	+	2.39848i
$706$		0			0
$707$	3173.82	−	1155.18i	0.168831	−	0.0614496i
$708$		0			0
$709$	9738.33	+	8171.43i	0.515840	+	0.432841i	0.863179	−	0.504899i	$-0.168470\pi$
$709$	9738.33	+	8171.43i	0.515840	+	0.432841i	−0.347339	+	0.937740i	$0.612915\pi$
$710$		0			0
$711$	−14883.8	−	25779.6i	−0.785074	−	1.35979i
$712$		0			0
$713$	6361.19	−	36076.1i	0.334121	−	1.89489i
$714$		0			0
$715$	7564.33	−	13101.8i	0.395650	−	0.685286i
$716$		0			0
$717$	29127.4	+	10601.5i	1.51713	+	0.552190i
$718$		0			0
$719$	−3976.20	+	3336.43i	−0.206241	+	0.173057i	−0.740057	−	0.672544i	$-0.765202\pi$
$719$	−3976.20	+	3336.43i	−0.206241	+	0.173057i	0.533817	+	0.845600i	$0.320757\pi$
$720$		0			0
$721$	−8038.78			−0.415229
$722$		0			0
$723$	28881.3			1.48563
$724$		0			0
$725$	5211.91	−	4373.32i	0.266987	−	0.224029i
$726$		0			0
$727$	24334.1	+	8856.90i	1.24141	+	0.451835i	0.877490	−	0.479596i	$-0.159217\pi$
$727$	24334.1	+	8856.90i	1.24141	+	0.451835i	0.363918	+	0.931431i	$0.381439\pi$
$728$		0			0
$729$	15840.6	−	27436.7i	0.804784	−	1.39393i
$730$		0			0
$731$	−1415.90	+	8029.99i	−0.0716403	+	0.406292i
$732$		0			0
$733$	−10770.9	−	18655.8i	−0.542746	−	0.940064i	−0.998745	−	0.0500836i	$-0.984051\pi$
$733$	−10770.9	−	18655.8i	−0.542746	−	0.940064i	0.455999	−	0.889980i	$-0.349282\pi$
$734$		0			0
$735$	21913.1	+	18387.3i	1.09970	+	0.922757i
$736$		0			0
$737$	−7269.97	+	2646.05i	−0.363355	+	0.132250i
$738$		0			0
$739$	2771.47	+	15717.8i	0.137957	+	0.782392i	0.972755	+	0.231836i	$0.0744733\pi$
$739$	2771.47	+	15717.8i	0.137957	+	0.782392i	−0.834798	+	0.550556i	$0.814416\pi$
$740$		0			0
$741$	−53335.6	+	3098.84i	−2.64417	+	0.153629i
$742$		0			0
$743$	−3272.37	−	18558.5i	−0.161577	−	0.916347i	−0.952524	−	0.304463i	$-0.901523\pi$
$743$	−3272.37	−	18558.5i	−0.161577	−	0.916347i	0.790947	−	0.611884i	$-0.209588\pi$
$744$		0			0
$745$	35848.0	−	13047.6i	1.76291	−	0.641647i
$746$		0			0
$747$	−2056.31	−	1725.45i	−0.100718	−	0.0845124i
$748$		0			0
$749$	2503.73	+	4336.60i	0.122142	+	0.211556i
$750$		0			0
$751$	−2473.06	+	14025.4i	−0.120164	+	0.681485i	0.863899	+	0.503665i	$0.168016\pi$
$751$	−2473.06	+	14025.4i	−0.120164	+	0.681485i	−0.984063	+	0.177820i	$0.943096\pi$
$752$		0			0
$753$	5379.24	−	9317.11i	0.260332	−	0.450909i
$754$		0			0
$755$	13316.9	+	4846.94i	0.641921	+	0.233640i
$756$		0			0
$757$	−18878.9	+	15841.3i	−0.906429	+	0.760584i	−0.971436	−	0.237300i	$-0.923737\pi$
$757$	−18878.9	+	15841.3i	−0.906429	+	0.760584i	0.0650071	+	0.997885i	$0.479293\pi$
$758$		0			0
$759$	−14456.8			−0.691366
$760$		0			0
$761$	29437.7			1.40226			0.701128	−	0.713035i	$-0.252680\pi$
$761$	29437.7			1.40226			0.701128	+	0.713035i	$0.252680\pi$
$762$		0			0
$763$	10815.4	−	9075.20i	0.513164	−	0.430596i
$764$		0			0
$765$	18875.3	+	6870.03i	0.892074	+	0.324688i
$766$		0			0
$767$	−34596.4	+	59922.7i	−1.62869	+	2.82097i
$768$		0			0
$769$	−2653.23	+	15047.2i	−0.124419	+	0.705614i	0.857233	+	0.514929i	$0.172182\pi$
$769$	−2653.23	+	15047.2i	−0.124419	+	0.705614i	−0.981651	+	0.190684i	$0.938929\pi$
$770$		0			0
$771$	3686.44	+	6385.10i	0.172197	+	0.298254i
$772$		0			0
$773$	8577.45	+	7197.33i	0.399107	+	0.334890i	0.820148	−	0.572151i	$-0.193891\pi$
$773$	8577.45	+	7197.33i	0.399107	+	0.334890i	−0.421042	+	0.907041i	$0.638335\pi$
$774$		0			0
$775$	−13324.1	+	4849.59i	−0.617571	+	0.224777i
$776$		0			0
$777$	−3436.66	−	19490.3i	−0.158674	−	0.899884i
$778$		0			0
$779$	−1684.82	+	1589.09i	−0.0774902	+	0.0730874i
$780$		0			0
$781$	−1166.76	−	6617.02i	−0.0534570	−	0.303170i
$782$		0			0
$783$	−13601.8	+	4950.67i	−0.620805	+	0.225955i
$784$		0			0
$785$	−3890.52	−	3264.54i	−0.176890	−	0.148428i
$786$		0			0
$787$	−9094.26	−	15751.7i	−0.411913	−	0.713454i	0.583186	−	0.812339i	$-0.301806\pi$
$787$	−9094.26	−	15751.7i	−0.411913	−	0.713454i	−0.995099	+	0.0988846i	$0.968473\pi$
$788$		0			0
$789$	−6702.43	+	38011.4i	−0.302424	+	1.71513i
$790$		0			0
$791$	−3624.09	+	6277.10i	−0.162905	+	0.282159i
$792$		0			0
$793$	−50290.2	−	18304.2i	−2.25203	−	0.819671i
$794$		0			0
$795$	37714.5	−	31646.2i	1.68251	−	1.41179i
$796$		0			0
$797$	23668.4			1.05192			0.525958	−	0.850510i	$-0.323707\pi$
$797$	23668.4			1.05192			0.525958	+	0.850510i	$0.323707\pi$
$798$		0			0
$799$	−16601.2			−0.735056
$800$		0			0
$801$	−42640.6	+	35779.7i	−1.88094	+	1.57829i
$802$		0			0
$803$	−1974.49	−	718.656i	−0.0867724	−	0.0315826i
$804$		0			0
$805$	6945.79	−	12030.5i	0.304108	−	0.526731i
$806$		0			0
$807$	1008.71	−	5720.66i	0.0440002	−	0.249538i
$808$		0			0
$809$	9008.33	+	15602.9i	0.391491	+	0.678082i	0.992646	−	0.121050i	$-0.0386261\pi$
$809$	9008.33	+	15602.9i	0.391491	+	0.678082i	−0.601156	+	0.799132i	$0.705293\pi$
$810$		0			0
$811$	−21246.7	−	17828.1i	−0.919940	−	0.771921i	0.0540442	−	0.998539i	$-0.482789\pi$
$811$	−21246.7	−	17828.1i	−0.919940	−	0.771921i	−0.973984	+	0.226618i	$0.927233\pi$
$812$		0			0
$813$	−64846.0	+	23602.0i	−2.79736	+	1.01815i
$814$		0			0
$815$	2408.77	+	13660.8i	0.103528	+	0.587137i
$816$		0			0
$817$	16622.0	+	4978.88i	0.711788	+	0.213206i
$818$		0			0
$819$	−4695.68	−	26630.5i	−0.200342	−	1.13620i
$820$		0			0
$821$	−2396.35	+	872.198i	−0.101867	+	0.0370766i	−0.392451	−	0.919773i	$-0.628373\pi$
$821$	−2396.35	+	872.198i	−0.101867	+	0.0370766i	0.290584	+	0.956850i	$0.406151\pi$
$822$		0			0
$823$	−24032.8	−	20165.9i	−1.01790	−	0.854119i	−0.0285368	−	0.999593i	$-0.509085\pi$
$823$	−24032.8	−	20165.9i	−1.01790	−	0.854119i	−0.989362	+	0.145474i	$0.953529\pi$
$824$		0			0
$825$	2797.86	+	4846.04i	0.118072	+	0.204506i
$826$		0			0
$827$	−2132.39	+	12093.4i	−0.0896621	+	0.508499i	0.906591	+	0.422011i	$0.138676\pi$
$827$	−2132.39	+	12093.4i	−0.0896621	+	0.508499i	−0.996253	+	0.0864882i	$0.972436\pi$
$828$		0			0
$829$	−1929.67	+	3342.28i	−0.0808445	+	0.140027i	−0.903613	−	0.428350i	$-0.859095\pi$
$829$	−1929.67	+	3342.28i	−0.0808445	+	0.140027i	0.822768	+	0.568377i	$0.192428\pi$
$830$		0			0
$831$	−8628.15	−	3140.39i	−0.360177	−	0.131094i
$832$		0			0
$833$	−7979.53	+	6695.62i	−0.331902	+	0.278499i
$834$		0			0
$835$	14671.2			0.608044
$836$		0			0
$837$	30166.3			1.24576
$838$		0			0
$839$	3115.24	−	2614.00i	0.128188	−	0.107563i	−0.576440	−	0.817140i	$-0.695558\pi$
$839$	3115.24	−	2614.00i	0.128188	−	0.107563i	0.704628	+	0.709577i	$0.251114\pi$
$840$		0			0
$841$	3396.79	+	1236.33i	0.139275	+	0.0506921i
$842$		0			0
$843$	15670.1	−	27141.5i	0.640223	−	1.10890i
$844$		0			0
$845$	−9289.61	+	52684.0i	−0.378192	+	2.14483i
$846$		0			0
$847$	4857.26	+	8413.03i	0.197045	+	0.341293i
$848$		0			0
$849$	−2489.10	−	2088.60i	−0.100619	−	0.0844295i
$850$		0			0
$851$	32081.5	−	11676.7i	1.29229	−	0.470356i
$852$		0			0
$853$	348.409	+	1975.93i	0.0139851	+	0.0793136i	0.991002	−	0.133851i	$-0.0427342\pi$
$853$	348.409	+	1975.93i	0.0139851	+	0.0793136i	−0.977016	+	0.213164i	$0.931623\pi$
$854$		0			0
$855$	19189.3	−	38195.6i	0.767558	−	1.52779i
$856$		0			0
$857$	1128.93	+	6402.47i	0.0449982	+	0.255197i	0.999006	−	0.0445857i	$-0.0141968\pi$
$857$	1128.93	+	6402.47i	0.0449982	+	0.255197i	−0.954007	+	0.299783i	$0.903086\pi$
$858$		0			0
$859$	−32925.2	+	11983.8i	−1.30779	+	0.475998i	−0.899527	−	0.436865i	$-0.856089\pi$
$859$	−32925.2	+	11983.8i	−1.30779	+	0.475998i	−0.408266	+	0.912863i	$0.633866\pi$
$860$		0			0
$861$	−1514.44	−	1270.77i	−0.0599443	−	0.0502993i
$862$		0			0
$863$	−12438.3	−	21543.8i	−0.490620	−	0.849779i	0.509321	−	0.860576i	$-0.329896\pi$
$863$	−12438.3	−	21543.8i	−0.490620	−	0.849779i	−0.999942	+	0.0107971i	$0.996563\pi$
$864$		0			0
$865$	1771.32	−	10045.7i	0.0696263	−	0.394871i
$866$		0			0
$867$	13838.8	−	23969.6i	0.542089	−	0.938926i
$868$		0			0
$869$	10351.8	+	3767.74i	0.404097	+	0.147079i
$870$		0			0
$871$	32251.0	−	27061.8i	1.25463	−	1.05276i
$872$		0			0
$873$	−21240.1			−0.823448
$874$		0			0
$875$	8861.61			0.342374
$876$		0			0
$877$	−16061.5	+	13477.2i	−0.618424	+	0.518920i	−0.897308	−	0.441405i	$-0.854480\pi$
$877$	−16061.5	+	13477.2i	−0.618424	+	0.518920i	0.278884	+	0.960325i	$0.410036\pi$
$878$		0			0
$879$	52185.8	+	18994.1i	2.00249	+	0.728845i
$880$		0			0
$881$	2146.65	−	3718.10i	0.0820912	−	0.142186i	−0.822057	−	0.569405i	$-0.807173\pi$
$881$	2146.65	−	3718.10i	0.0820912	−	0.142186i	0.904148	+	0.427219i	$0.140507\pi$
$882$		0			0
$883$	3786.44	−	21474.0i	0.144308	−	0.818411i	−0.823612	−	0.567153i	$-0.808045\pi$
$883$	3786.44	−	21474.0i	0.144308	−	0.818411i	0.967920	−	0.251258i	$-0.0808442\pi$
$884$		0			0
$885$	−46682.0	−	80855.6i	−1.77310	−	3.07111i
$886$		0			0
$887$	−23592.0	−	19796.1i	−0.893058	−	0.749365i	0.0757628	−	0.997126i	$-0.475861\pi$
$887$	−23592.0	−	19796.1i	−0.893058	−	0.749365i	−0.968821	+	0.247761i	$0.920305\pi$
$888$		0			0
$889$	−4563.81	+	1661.09i	−0.172177	+	0.0626673i
$890$		0			0
$891$	616.752	+	3497.78i	0.0231897	+	0.131515i
$892$		0			0
$893$	−4106.31	+	35088.5i	−0.153877	+	1.31488i
$894$		0			0
$895$	9823.11	+	55709.6i	0.366872	+	2.08063i
$896$		0			0
$897$	73926.4	−	26907.0i	2.75176	−	1.00156i
$898$		0			0
$899$	33165.7	+	27829.3i	1.23041	+	1.03244i
$900$		0			0
$901$	8963.90	+	15525.9i	0.331444	+	0.574077i
$902$		0			0
$903$	−2572.02	+	14586.6i	−0.0947855	+	0.537556i
$904$		0			0
$905$	−19575.1	+	33905.1i	−0.719005	+	1.24535i
$906$		0			0
$907$	13019.5	+	4738.72i	0.476634	+	0.173480i	0.569155	−	0.822230i	$-0.307270\pi$
$907$	13019.5	+	4738.72i	0.476634	+	0.173480i	−0.0925214	+	0.995711i	$0.529493\pi$
$908$		0			0
$909$	−11723.3	+	9836.99i	−0.427763	+	0.358936i
$910$		0			0
$911$	8039.96			0.292399			0.146200	−	0.989255i	$-0.453296\pi$
$911$	8039.96			0.292399			0.146200	+	0.989255i	$0.453296\pi$
$912$		0			0
$913$	993.387			0.0360091
$914$		0			0
$915$	55318.5	−	46417.8i	1.99866	−	1.67708i
$916$		0			0
$917$	14537.3	+	5291.15i	0.523516	+	0.190544i
$918$		0			0
$919$	12958.0	−	22443.9i	0.465120	−	0.805612i	−0.534087	−	0.845430i	$-0.679344\pi$
$919$	12958.0	−	22443.9i	0.465120	−	0.805612i	0.999207	+	0.0398177i	$0.0126777\pi$
$920$		0			0
$921$	460.978	−	2614.33i	0.0164926	−	0.0935345i
$922$		0			0
$923$	18282.0	+	31665.4i	0.651961	+	1.12923i
$924$		0			0
$925$	−10123.0	−	8494.20i	−0.359829	−	0.301933i
$926$		0			0
$927$	34227.4	−	12457.8i	1.21270	−	0.441388i
$928$		0			0
$929$	−3683.71	−	20891.3i	−0.130095	−	0.737807i	−0.978150	−	0.207899i	$-0.933338\pi$
$929$	−3683.71	−	20891.3i	−0.130095	−	0.737807i	0.848055	−	0.529908i	$-0.177774\pi$
$930$		0			0
$931$	12178.2	+	18521.8i	0.428705	+	0.652015i
$932$		0			0
$933$	−9358.69	−	53075.8i	−0.328392	−	1.86240i
$934$		0			0
$935$	−6985.18	+	2542.40i	−0.244321	+	0.0889254i
$936$		0			0
$937$	18765.3	+	15746.0i	0.654255	+	0.548985i	0.908359	−	0.418192i	$-0.137336\pi$
$937$	18765.3	+	15746.0i	0.654255	+	0.548985i	−0.254104	+	0.967177i	$0.581781\pi$
$938$		0			0
$939$	126.925	+	219.840i	0.00441110	+	0.00764025i
$940$		0			0
$941$	1377.52	−	7812.29i	0.0477214	−	0.270641i	−0.951606	−	0.307322i	$-0.900567\pi$
$941$	1377.52	−	7812.29i	0.0477214	−	0.270641i	0.999327	+	0.0366804i	$0.0116784\pi$
$942$		0			0
$943$	1705.19	−	2953.47i	0.0588850	−	0.101992i
$944$		0			0
$945$	10749.6	+	3912.53i	0.370036	+	0.134682i
$946$		0			0
$947$	−31465.1	+	26402.3i	−1.07970	+	0.905977i	−0.995896	−	0.0905046i	$-0.971152\pi$
$947$	−31465.1	+	26402.3i	−1.07970	+	0.905977i	−0.0838059	+	0.996482i	$0.526708\pi$
$948$		0			0
$949$	11434.4			0.391123
$950$		0			0
$951$	−50789.1			−1.73181
$952$		0			0
$953$	−24304.8	+	20394.1i	−0.826137	+	0.693211i	−0.954401	−	0.298529i	$-0.903504\pi$
$953$	−24304.8	+	20394.1i	−0.826137	+	0.693211i	0.128264	+	0.991740i	$0.459060\pi$
$954$		0			0
$955$	−8335.81	−	3033.99i	−0.282451	−	0.102804i
$956$		0			0
$957$	8542.95	−	14796.8i	0.288562	−	0.499805i
$958$		0			0
$959$	1458.38	−	8270.89i	0.0491070	−	0.278499i
$960$		0			0
$961$	−30218.9	−	52340.7i	−1.01436	−	1.75693i
$962$		0			0
$963$	−17380.8	−	14584.3i	−0.581609	−	0.488028i
$964$		0			0
$965$	39909.7	−	14525.9i	1.33133	−	0.484566i
$966$		0			0
$967$	177.593	+	1007.18i	0.00590589	+	0.0334940i	0.987618	−	0.156876i	$-0.0501423\pi$
$967$	177.593	+	1007.18i	0.00590589	+	0.0334940i	−0.981712	+	0.190370i	$0.939031\pi$
$968$		0			0
$969$	21054.0	+	15678.8i	0.697991	+	0.519789i
$970$		0			0
$971$	−8199.28	−	46500.4i	−0.270986	−	1.53684i	−0.751430	−	0.659813i	$-0.770636\pi$
$971$	−8199.28	−	46500.4i	−0.270986	−	1.53684i	0.480444	−	0.877025i	$-0.340475\pi$
$972$		0			0
$973$	−84.0341	+	30.5859i	−0.00276877	+	0.00100775i
$974$		0			0
$975$	−23326.7	−	19573.4i	−0.766208	−	0.642924i
$976$		0			0
$977$	3600.46	+	6236.18i	0.117901	+	0.204210i	0.918936	−	0.394408i	$-0.129050\pi$
$977$	3600.46	+	6236.18i	0.117901	+	0.204210i	−0.801035	+	0.598618i	$0.795717\pi$
$978$		0			0
$979$	3577.04	−	20286.4i	0.116775	−	0.662264i
$980$		0			0
$981$	−31985.8	+	55401.0i	−1.04101	+	1.80308i
$982$		0			0
$983$	3835.68	+	1396.07i	0.124455	+	0.0452979i	0.403497	−	0.914981i	$-0.367795\pi$
$983$	3835.68	+	1396.07i	0.124455	+	0.0452979i	−0.279042	+	0.960279i	$0.590017\pi$
$984$		0			0
$985$	−49314.5	+	41379.8i	−1.59522	+	1.33855i
$986$		0			0
$987$	−30156.5			−0.972534
$988$		0			0
$989$	−25550.9			−0.821509
$990$		0			0
$991$	−13926.3	+	11685.5i	−0.446400	+	0.374574i	−0.838098	−	0.545520i	$-0.816332\pi$
$991$	−13926.3	+	11685.5i	−0.446400	+	0.374574i	0.391698	+	0.920094i	$0.371888\pi$
$992$		0			0
$993$	−22594.5	−	8223.73i	−0.722070	−	0.262812i
$994$		0			0
$995$	2337.05	−	4047.88i	0.0744617	−	0.128971i
$996$		0			0
$997$	7196.14	−	40811.4i	0.228590	−	1.29640i	−0.627112	−	0.778929i	$-0.715763\pi$
$997$	7196.14	−	40811.4i	0.228590	−	1.29640i	0.855702	−	0.517469i	$-0.173126\pi$
$998$		0			0
$999$	14057.0	+	24347.5i	0.445190	+	0.771092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.9.5	✓	30
19.6	even	9		1444.4.a.j.1.13		15
19.13	odd	18		1444.4.a.k.1.3		15
19.17	even	9	inner	76.4.i.a.17.5	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.9.5	✓	30	1.1	even	1	trivial
76.4.i.a.17.5	yes	30	19.17	even	9	inner
1444.4.a.j.1.13		15	19.6	even	9
1444.4.a.k.1.3		15	19.13	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(6.23895 - 5.23510i) q^{3} +(12.3313 + 4.48821i) q^{5} +(-4.34015 + 7.51736i) q^{7} +(6.82973 - 38.7333i) q^{9} +O(q^{10})\)	\(q+(6.23895 - 5.23510i) q^{3} +(12.3313 + 4.48821i) q^{5} +(-4.34015 + 7.51736i) q^{7} +(6.82973 - 38.7333i) q^{9} +(7.27759 + 12.6052i) q^{11} +(-60.6757 - 50.9129i) q^{13} +(100.430 - 36.5537i) q^{15} +(6.75806 + 38.3269i) q^{17} +(82.6796 - 4.80376i) q^{19} +(12.2762 + 69.6216i) q^{21} +(-114.599 + 41.7107i) q^{23} +(36.1605 + 30.3423i) q^{25} +(-50.2134 - 86.9722i) q^{27} +(25.0284 - 141.943i) q^{29} +(-150.191 + 260.138i) q^{31} +(111.394 + 40.5440i) q^{33} +(-87.2590 + 73.2190i) q^{35} -279.946 q^{37} -645.087 q^{39} +(-21.4220 + 17.9752i) q^{41} +(196.878 + 71.6577i) q^{43} +(258.063 - 446.977i) q^{45} +(-74.0727 + 420.087i) q^{47} +(133.826 + 231.794i) q^{49} +(242.808 + 203.740i) q^{51} +(432.873 - 157.553i) q^{53} +(33.1673 + 188.101i) q^{55} +(490.686 - 462.807i) q^{57} +(-151.695 - 860.302i) q^{59} +(634.926 - 231.094i) q^{61} +(261.530 + 219.450i) q^{63} +(-519.700 - 900.147i) q^{65} +(-92.2995 + 523.456i) q^{67} +(-496.619 + 860.169i) q^{69} +(-433.790 - 157.886i) q^{71} +(-110.587 + 92.7938i) q^{73} +384.449 q^{75} -126.343 q^{77} +(579.784 - 486.496i) q^{79} +(229.303 + 83.4593i) q^{81} +(34.1249 - 59.1060i) q^{83} +(-88.6838 + 502.951i) q^{85} +(-586.935 - 1016.60i) q^{87} +(-1084.15 - 909.711i) q^{89} +(646.072 - 235.151i) q^{91} +(424.816 + 2409.25i) q^{93} +(1041.11 + 311.848i) q^{95} +(-93.7766 - 531.834i) q^{97} +(537.943 - 195.795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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