LMFDB - Embedded newform 228.3.r.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(13,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("228.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.r (of order $18$, 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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	228.193
Dual form			228.3.r.b.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.592396 - 1.62760i) q^{3} +(-0.523375 + 2.96821i) q^{5} +(2.50080 + 4.33150i) q^{7} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+(-0.592396 - 1.62760i) q^{3} +(-0.523375 + 2.96821i) q^{5} +(2.50080 + 4.33150i) q^{7} +(-2.29813 + 1.92836i) q^{9} +(-5.38633 + 9.32941i) q^{11} +(-0.0113445 + 0.0311687i) q^{13} +(5.14109 - 0.906513i) q^{15} +(6.37968 + 5.35319i) q^{17} +(12.9520 + 13.9013i) q^{19} +(5.56847 - 6.63625i) q^{21} +(5.08449 + 28.8356i) q^{23} +(14.9560 + 5.44353i) q^{25} +(4.50000 + 2.59808i) q^{27} +(-0.651064 - 0.775908i) q^{29} +(3.25746 - 1.88070i) q^{31} +(18.3753 + 3.24007i) q^{33} +(-14.1657 + 5.15588i) q^{35} -22.2026i q^{37} +0.0574504 q^{39} +(-5.63007 - 15.4685i) q^{41} +(-0.144778 + 0.821079i) q^{43} +(-4.52100 - 7.83060i) q^{45} +(-65.3576 + 54.8415i) q^{47} +(11.9920 - 20.7708i) q^{49} +(4.93353 - 13.5547i) q^{51} +(-18.0739 + 3.18692i) q^{53} +(-24.8725 - 20.8705i) q^{55} +(14.9529 - 29.3157i) q^{57} +(-22.1278 + 26.3709i) q^{59} +(0.704266 + 3.99409i) q^{61} +(-14.0999 - 5.13193i) q^{63} +(-0.0865777 - 0.0499857i) q^{65} +(-77.8620 - 92.7924i) q^{67} +(43.9207 - 25.3576i) q^{69} +(13.3516 + 2.35424i) q^{71} +(93.5748 - 34.0584i) q^{73} -27.5670i q^{75} -53.8805 q^{77} +(-17.7305 - 48.7140i) q^{79} +(1.56283 - 8.86327i) q^{81} +(-16.6791 - 28.8890i) q^{83} +(-19.2283 + 16.1345i) q^{85} +(-0.877176 + 1.51931i) q^{87} +(13.4798 - 37.0354i) q^{89} +(-0.163377 + 0.0288078i) q^{91} +(-4.99073 - 4.18772i) q^{93} +(-48.0407 + 31.1687i) q^{95} +(26.3770 - 31.4348i) q^{97} +(-5.61196 - 31.8270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{7}+O(q^{10}) $ 24 * q - 9 * q^7	$ 24 q - 9 q^{7} + 15 q^{11} - 9 q^{13} - 18 q^{15} + 18 q^{17} + 33 q^{19} + 18 q^{21} - 21 q^{23} - 18 q^{25} + 108 q^{27} + 30 q^{29} + 216 q^{31} - 63 q^{33} + 30 q^{35} + 18 q^{39} - 54 q^{41} - 189 q^{43} - 9 q^{45} - 321 q^{47} - 225 q^{49} + 63 q^{51} + 138 q^{53} + 309 q^{55} - 45 q^{57} - 30 q^{59} - 105 q^{61} - 27 q^{63} + 99 q^{65} + 207 q^{67} + 108 q^{69} + 144 q^{71} - 72 q^{73} - 36 q^{77} - 282 q^{79} - 531 q^{83} - 909 q^{85} - 135 q^{87} - 411 q^{89} + 444 q^{91} + 126 q^{93} - 24 q^{95} + 405 q^{97} - 117 q^{99}+O(q^{100}) $ 24 * q - 9 * q^7 + 15 * q^11 - 9 * q^13 - 18 * q^15 + 18 * q^17 + 33 * q^19 + 18 * q^21 - 21 * q^23 - 18 * q^25 + 108 * q^27 + 30 * q^29 + 216 * q^31 - 63 * q^33 + 30 * q^35 + 18 * q^39 - 54 * q^41 - 189 * q^43 - 9 * q^45 - 321 * q^47 - 225 * q^49 + 63 * q^51 + 138 * q^53 + 309 * q^55 - 45 * q^57 - 30 * q^59 - 105 * q^61 - 27 * q^63 + 99 * q^65 + 207 * q^67 + 108 * q^69 + 144 * q^71 - 72 * q^73 - 36 * q^77 - 282 * q^79 - 531 * q^83 - 909 * q^85 - 135 * q^87 - 411 * q^89 + 444 * q^91 + 126 * q^93 - 24 * q^95 + 405 * q^97 - 117 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$1$

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
$3$	−0.592396	−	1.62760i	−0.197465	−	0.542532i
$3$	−0.592396	−	1.62760i	−0.197465	−	0.542532i
$4$		0			0
$5$	−0.523375	+	2.96821i	−0.104675	+	0.593642i	0.886675	+	0.462394i	$0.153009\pi$
$5$	−0.523375	+	2.96821i	−0.104675	+	0.593642i	−0.991350	+	0.131248i	$0.958102\pi$
$6$		0			0
$7$	2.50080	+	4.33150i	0.357256	+	0.618786i	0.987501	−	0.157610i	$-0.0503789\pi$
$7$	2.50080	+	4.33150i	0.357256	+	0.618786i	−0.630245	+	0.776396i	$0.717046\pi$
$8$		0			0
$9$	−2.29813	+	1.92836i	−0.255348	+	0.214263i
$10$		0			0
$11$	−5.38633	+	9.32941i	−0.489667	+	0.848128i	−0.999929	−	0.0118910i	$-0.996215\pi$
$11$	−5.38633	+	9.32941i	−0.489667	+	0.848128i	0.510263	+	0.860019i	$0.329548\pi$
$12$		0			0
$13$	−0.0113445	+	0.0311687i	−0.000872651	+	0.00239759i	−0.940128	−	0.340821i	$-0.889295\pi$
$13$	−0.0113445	+	0.0311687i	−0.000872651	+	0.00239759i	0.939256	+	0.343219i	$0.111517\pi$
$14$		0			0
$15$	5.14109	−	0.906513i	0.342739	−	0.0604342i
$16$		0			0
$17$	6.37968	+	5.35319i	0.375275	+	0.314893i	0.810844	−	0.585262i	$-0.199008\pi$
$17$	6.37968	+	5.35319i	0.375275	+	0.314893i	−0.435569	+	0.900155i	$0.643453\pi$
$18$		0			0
$19$	12.9520	+	13.9013i	0.681685	+	0.731646i
$19$	12.9520	+	13.9013i	0.681685	+	0.731646i
$20$		0			0
$21$	5.56847	−	6.63625i	0.265165	−	0.316012i
$22$		0			0
$23$	5.08449	+	28.8356i	0.221065	+	1.25372i	0.870066	+	0.492935i	$0.164076\pi$
$23$	5.08449	+	28.8356i	0.221065	+	1.25372i	−0.649001	+	0.760787i	$0.724813\pi$
$24$		0			0
$25$	14.9560	+	5.44353i	0.598239	+	0.217741i
$26$		0			0
$27$	4.50000	+	2.59808i	0.166667	+	0.0962250i
$28$		0			0
$29$	−0.651064	−	0.775908i	−0.0224505	−	0.0267554i	0.754702	−	0.656067i	$-0.227781\pi$
$29$	−0.651064	−	0.775908i	−0.0224505	−	0.0267554i	−0.777153	+	0.629312i	$0.783337\pi$
$30$		0			0
$31$	3.25746	−	1.88070i	0.105080	−	0.0606677i	−0.446539	−	0.894764i	$-0.647344\pi$
$31$	3.25746	−	1.88070i	0.105080	−	0.0606677i	0.551619	+	0.834096i	$0.314010\pi$
$32$		0			0
$33$	18.3753	+	3.24007i	0.556829	+	0.0981839i
$34$		0			0
$35$	−14.1657	+	5.15588i	−0.404733	+	0.147311i
$36$		0			0
$37$		−	22.2026i		−	0.600069i	−0.953928	−	0.300035i	$-0.903002\pi$
$37$		−	22.2026i		−	0.600069i	0.953928	−	0.300035i	$-0.0969983\pi$
$38$		0			0
$39$	0.0574504			0.00147309
$40$		0			0
$41$	−5.63007	−	15.4685i	−0.137319	−	0.377280i	0.851904	−	0.523698i	$-0.175448\pi$
$41$	−5.63007	−	15.4685i	−0.137319	−	0.377280i	−0.989223	+	0.146418i	$0.953226\pi$
$42$		0			0
$43$	−0.144778	+	0.821079i	−0.00336694	+	0.0190949i	−0.986445	−	0.164093i	$-0.947530\pi$
$43$	−0.144778	+	0.821079i	−0.00336694	+	0.0190949i	0.983078	+	0.183187i	$0.0586415\pi$
$44$		0			0
$45$	−4.52100	−	7.83060i	−0.100467	−	0.174013i
$46$		0			0
$47$	−65.3576	+	54.8415i	−1.39059	+	1.16684i	−0.425485	+	0.904966i	$0.639896\pi$
$47$	−65.3576	+	54.8415i	−1.39059	+	1.16684i	−0.965102	+	0.261875i	$0.915659\pi$
$48$		0			0
$49$	11.9920	−	20.7708i	0.244736	−	0.423895i
$50$		0			0
$51$	4.93353	−	13.5547i	0.0967358	−	0.265779i
$52$		0			0
$53$	−18.0739	+	3.18692i	−0.341018	+	0.0601306i	−0.341534	−	0.939869i	$-0.610947\pi$
$53$	−18.0739	+	3.18692i	−0.341018	+	0.0601306i	0.000516780		1.00000i	$0.499836\pi$
$54$		0			0
$55$	−24.8725	−	20.8705i	−0.452228	−	0.379464i
$56$		0			0
$57$	14.9529	−	29.3157i	0.262332	−	0.514310i
$58$		0			0
$59$	−22.1278	+	26.3709i	−0.375047	+	0.446964i	−0.920245	−	0.391344i	$-0.872010\pi$
$59$	−22.1278	+	26.3709i	−0.375047	+	0.446964i	0.545197	+	0.838308i	$0.316455\pi$
$60$		0			0
$61$	0.704266	+	3.99409i	0.0115453	+	0.0654769i	0.990036	−	0.140814i	$-0.0449719\pi$
$61$	0.704266	+	3.99409i	0.0115453	+	0.0654769i	−0.978491	+	0.206291i	$0.933861\pi$
$62$		0			0
$63$	−14.0999	−	5.13193i	−0.223807	−	0.0814593i
$64$		0			0
$65$	−0.0865777	−	0.0499857i	−0.00133196	−	0.000769010i
$66$		0			0
$67$	−77.8620	−	92.7924i	−1.16212	−	1.38496i	−0.908619	−	0.417625i	$-0.862863\pi$
$67$	−77.8620	−	92.7924i	−1.16212	−	1.38496i	−0.253500	−	0.967335i	$-0.581582\pi$
$68$		0			0
$69$	43.9207	−	25.3576i	0.636531	−	0.367501i
$70$		0			0
$71$	13.3516	+	2.35424i	0.188050	+	0.0331583i	0.266880	−	0.963730i	$-0.414007\pi$
$71$	13.3516	+	2.35424i	0.188050	+	0.0331583i	−0.0788298	+	0.996888i	$0.525118\pi$
$72$		0			0
$73$	93.5748	−	34.0584i	1.28185	−	0.466554i	0.390804	−	0.920474i	$-0.372197\pi$
$73$	93.5748	−	34.0584i	1.28185	−	0.466554i	0.891042	+	0.453920i	$0.149975\pi$
$74$		0			0
$75$		−	27.5670i		−	0.367560i
$76$		0			0
$77$	−53.8805			−0.699746
$78$		0			0
$79$	−17.7305	−	48.7140i	−0.224436	−	0.616633i	0.775455	−	0.631403i	$-0.217521\pi$
$79$	−17.7305	−	48.7140i	−0.224436	−	0.616633i	−0.999891	+	0.0147699i	$0.995298\pi$
$80$		0			0
$81$	1.56283	−	8.86327i	0.0192942	−	0.109423i
$82$		0			0
$83$	−16.6791	−	28.8890i	−0.200952	−	0.348060i	0.747883	−	0.663830i	$-0.231070\pi$
$83$	−16.6791	−	28.8890i	−0.200952	−	0.348060i	−0.948836	+	0.315771i	$0.897737\pi$
$84$		0			0
$85$	−19.2283	+	16.1345i	−0.226216	+	0.189818i
$86$		0			0
$87$	−0.877176	+	1.51931i	−0.0100825	+	0.0174634i
$88$		0			0
$89$	13.4798	−	37.0354i	0.151458	−	0.416128i	−0.840640	−	0.541595i	$-0.817821\pi$
$89$	13.4798	−	37.0354i	0.151458	−	0.416128i	0.992098	+	0.125467i	$0.0400430\pi$
$90$		0			0
$91$	−0.163377	+	0.0288078i	−0.00179536	+	0.000316570i
$92$		0			0
$93$	−4.99073	−	4.18772i	−0.0536637	−	0.0450292i
$94$		0			0
$95$	−48.0407	+	31.1687i	−0.505691	+	0.328091i
$96$		0			0
$97$	26.3770	−	31.4348i	0.271927	−	0.324071i	−0.612748	−	0.790279i	$-0.709936\pi$
$97$	26.3770	−	31.4348i	0.271927	−	0.324071i	0.884675	+	0.466208i	$0.154380\pi$
$98$		0			0
$99$	−5.61196	−	31.8270i	−0.0566865	−	0.321485i
$100$		0			0
$101$	−37.0616	−	13.4893i	−0.366947	−	0.133558i	0.151964	−	0.988386i	$-0.451440\pi$
$101$	−37.0616	−	13.4893i	−0.366947	−	0.133558i	−0.518911	+	0.854828i	$0.673662\pi$
$102$		0			0
$103$	144.146	+	83.2226i	1.39947	+	0.807987i	0.994337	−	0.106270i	$-0.0338906\pi$
$103$	144.146	+	83.2226i	1.39947	+	0.807987i	0.405137	+	0.914256i	$0.367224\pi$
$104$		0			0
$105$	16.7834	+	20.0016i	0.159842	+	0.190492i
$106$		0			0
$107$	0.773114	−	0.446357i	0.00722536	−	0.00417156i	−0.496383	−	0.868104i	$-0.665339\pi$
$107$	0.773114	−	0.446357i	0.00722536	−	0.00417156i	0.503608	+	0.863932i	$0.332005\pi$
$108$		0			0
$109$	78.4792	+	13.8380i	0.719993	+	0.126954i	0.521627	−	0.853174i	$-0.325325\pi$
$109$	78.4792	+	13.8380i	0.719993	+	0.126954i	0.198366	+	0.980128i	$0.436436\pi$
$110$		0			0
$111$	−36.1368	+	13.1527i	−0.325557	+	0.118493i
$112$		0			0
$113$		−	83.1572i		−	0.735905i	−0.929845	−	0.367952i	$-0.880059\pi$
$113$		−	83.1572i		−	0.735905i	0.929845	−	0.367952i	$-0.119941\pi$
$114$		0			0
$115$	−88.2512			−0.767402
$116$		0			0
$117$	−0.0340334	−	0.0935060i	−0.000290884	−	0.000799197i
$118$		0			0
$119$	−7.23308	+	41.0208i	−0.0607822	+	0.344713i
$120$		0			0
$121$	2.47480	+	4.28648i	0.0204529	+	0.0354254i
$122$		0			0
$123$	−21.8412	+	18.3269i	−0.177571	+	0.149000i
$124$		0			0
$125$	−61.6601	+	106.798i	−0.493281	+	0.854387i
$126$		0			0
$127$	−12.8868	+	35.4063i	−0.101471	+	0.278790i	−0.980032	−	0.198841i	$-0.936282\pi$
$127$	−12.8868	+	35.4063i	−0.101471	+	0.278790i	0.878561	+	0.477631i	$0.158504\pi$
$128$		0			0
$129$	1.42215	−	0.250763i	0.0110244	−	0.00194390i
$130$		0			0
$131$	107.836	+	90.4848i	0.823172	+	0.690724i	0.953713	−	0.300719i	$-0.0972268\pi$
$131$	107.836	+	90.4848i	0.823172	+	0.690724i	−0.130540	+	0.991443i	$0.541671\pi$
$132$		0			0
$133$	−27.8231	+	90.8659i	−0.209196	+	0.683202i
$134$		0			0
$135$	−10.0668	+	11.9972i	−0.0745690	+	0.0888679i
$136$		0			0
$137$	−7.14394	−	40.5153i	−0.0521456	−	0.295732i	0.947571	−	0.319546i	$-0.103530\pi$
$137$	−7.14394	−	40.5153i	−0.0521456	−	0.295732i	−0.999716	+	0.0238135i	$0.992419\pi$
$138$		0			0
$139$	−162.290	−	59.0686i	−1.16755	−	0.424954i	−0.315762	−	0.948838i	$-0.602260\pi$
$139$	−162.290	−	59.0686i	−1.16755	−	0.424954i	−0.851789	+	0.523885i	$0.824482\pi$
$140$		0			0
$141$	127.977	+	73.8878i	0.907641	+	0.524027i
$142$		0			0
$143$	−0.229680	−	0.273722i	−0.00160615	−	0.00191414i
$144$		0			0
$145$	2.64381	−	1.52640i	0.0182331	−	0.0105269i
$146$		0			0
$147$	−40.9106	−	7.21364i	−0.278303	−	0.0490724i
$148$		0			0
$149$	161.246	−	58.6886i	1.08219	−	0.393883i	0.261465	−	0.965213i	$-0.415794\pi$
$149$	161.246	−	58.6886i	1.08219	−	0.393883i	0.820721	+	0.571330i	$0.193572\pi$
$150$		0			0
$151$			216.060i			1.43086i	0.698683	+	0.715432i	$0.253770\pi$
$151$			216.060i			1.43086i	−0.698683	+	0.715432i	$0.746230\pi$
$152$		0			0
$153$	−24.9842			−0.163296
$154$		0			0
$155$	3.87743	+	10.6531i	0.0250157	+	0.0687300i
$156$		0			0
$157$	16.5922	−	94.0989i	0.105683	−	0.599356i	−0.885263	−	0.465091i	$-0.846022\pi$
$157$	16.5922	−	94.0989i	0.105683	−	0.599356i	0.990945	−	0.134265i	$-0.0428673\pi$
$158$		0			0
$159$	15.8940	+	27.5291i	0.0999620	+	0.173139i
$160$		0			0
$161$	−112.186	+	94.1354i	−0.696809	+	0.584692i
$162$		0			0
$163$	8.68289	−	15.0392i	0.0532693	−	0.0922651i	−0.838161	−	0.545423i	$-0.816369\pi$
$163$	8.68289	−	15.0392i	0.0532693	−	0.0922651i	0.891430	+	0.453158i	$0.149703\pi$
$164$		0			0
$165$	−19.2344	+	52.8461i	−0.116572	+	0.320279i
$166$		0			0
$167$	304.203	−	53.6392i	1.82157	−	0.321193i	0.844737	−	0.535181i	$-0.179757\pi$
$167$	304.203	−	53.6392i	1.82157	−	0.321193i	0.976836	+	0.213989i	$0.0686455\pi$
$168$		0			0
$169$	129.461	+	108.630i	0.766039	+	0.642783i
$170$		0			0
$171$	−56.5721	−	6.97082i	−0.330831	−	0.0407650i
$172$		0			0
$173$	−6.31205	+	7.52241i	−0.0364858	+	0.0434821i	−0.783979	−	0.620788i	$-0.786813\pi$
$173$	−6.31205	+	7.52241i	−0.0364858	+	0.0434821i	0.747493	+	0.664270i	$0.231257\pi$
$174$		0			0
$175$	13.8232	+	78.3950i	0.0789895	+	0.447972i
$176$		0			0
$177$	56.0295	+	20.3931i	0.316551	+	0.115215i
$178$		0			0
$179$	186.378	+	107.605i	1.04122	+	0.601148i	0.920178	−	0.391500i	$-0.128044\pi$
$179$	186.378	+	107.605i	1.04122	+	0.601148i	0.121040	+	0.992648i	$0.461377\pi$
$180$		0			0
$181$	−103.305	−	123.114i	−0.570744	−	0.680187i	0.401039	−	0.916061i	$-0.368649\pi$
$181$	−103.305	−	123.114i	−0.570744	−	0.680187i	−0.971784	+	0.235874i	$0.924205\pi$
$182$		0			0
$183$	6.08356	−	3.51234i	0.0332435	−	0.0191931i
$184$		0			0
$185$	65.9018	+	11.6203i	0.356226	+	0.0628123i
$186$		0			0
$187$	−84.3052	+	30.6846i	−0.450830	+	0.164089i
$188$		0			0
$189$			25.9890i			0.137508i
$190$		0			0
$191$	195.779			1.02502			0.512511	−	0.858681i	$-0.328715\pi$
$191$	195.779			1.02502			0.512511	+	0.858681i	$0.328715\pi$
$192$		0			0
$193$	17.6984	+	48.6259i	0.0917015	+	0.251948i	0.977061	−	0.212959i	$-0.0683100\pi$
$193$	17.6984	+	48.6259i	0.0917015	+	0.251948i	−0.885360	+	0.464907i	$0.846088\pi$
$194$		0			0
$195$	−0.0300681	+	0.170525i	−0.000154195	+	0.000874486i
$196$		0			0
$197$	−103.486	−	179.244i	−0.525312	−	0.909867i	−0.999565	−	0.0294784i	$-0.990615\pi$
$197$	−103.486	−	179.244i	−0.525312	−	0.909867i	0.474254	−	0.880388i	$-0.342718\pi$
$198$		0			0
$199$	−36.2768	+	30.4398i	−0.182295	+	0.152964i	−0.729369	−	0.684121i	$-0.760186\pi$
$199$	−36.2768	+	30.4398i	−0.182295	+	0.152964i	0.547074	+	0.837084i	$0.315742\pi$
$200$		0			0
$201$	−104.903	+	181.698i	−0.521907	+	0.903969i
$202$		0			0
$203$	1.73267	−	4.76047i	0.00853532	−	0.0234506i
$204$		0			0
$205$	48.8603	−	8.61540i	0.238343	−	0.0420263i
$206$		0			0
$207$	−67.2903	−	56.4633i	−0.325074	−	0.272770i
$208$		0			0
$209$	−199.454	+	45.9576i	−0.954328	+	0.219893i
$210$		0			0
$211$	−65.4118	+	77.9547i	−0.310008	+	0.369454i	−0.898442	−	0.439092i	$-0.855300\pi$
$211$	−65.4118	+	77.9547i	−0.310008	+	0.369454i	0.588434	+	0.808545i	$0.299745\pi$
$212$		0			0
$213$	−4.07767	−	23.1256i	−0.0191440	−	0.108571i
$214$		0			0
$215$	−2.36136	−	0.859465i	−0.0109831	−	0.00399751i
$216$		0			0
$217$	16.2925	+	9.40648i	0.0750807	+	0.0433478i
$218$		0			0
$219$	−110.867	−	132.126i	−0.506241	−	0.603314i
$220$		0			0
$221$	−0.239226	+	0.138117i	−0.00108247	+	0.000624964i
$222$		0			0
$223$	125.639	+	22.1536i	0.563405	+	0.0993435i	0.448095	−	0.893986i	$-0.352103\pi$
$223$	125.639	+	22.1536i	0.563405	+	0.0993435i	0.115310	+	0.993330i	$0.463214\pi$
$224$		0			0
$225$	−44.8679	+	16.3306i	−0.199413	+	0.0725804i
$226$		0			0
$227$		−	347.205i		−	1.52954i	−0.644305	−	0.764769i	$-0.722853\pi$
$227$		−	347.205i		−	1.52954i	0.644305	−	0.764769i	$-0.277147\pi$
$228$		0			0
$229$	142.564			0.622552			0.311276	−	0.950320i	$-0.399244\pi$
$229$	142.564			0.622552			0.311276	+	0.950320i	$0.399244\pi$
$230$		0			0
$231$	31.9186	+	87.6956i	0.138176	+	0.379635i
$232$		0			0
$233$	71.6549	−	406.375i	0.307532	−	1.74410i	−0.303811	−	0.952732i	$-0.598259\pi$
$233$	71.6549	−	406.375i	0.307532	−	1.74410i	0.611343	−	0.791366i	$-0.290630\pi$
$234$		0			0
$235$	−128.575	−	222.698i	−0.547126	−	0.947649i
$236$		0			0
$237$	−68.7833	+	57.7160i	−0.290225	+	0.243527i
$238$		0			0
$239$	102.244	−	177.092i	0.427799	−	0.740969i	−0.568879	−	0.822422i	$-0.692623\pi$
$239$	102.244	−	177.092i	0.427799	−	0.740969i	0.996677	+	0.0814525i	$0.0259559\pi$
$240$		0			0
$241$	−156.332	+	429.518i	−0.648680	+	1.78223i	−0.0261241	+	0.999659i	$0.508317\pi$
$241$	−156.332	+	429.518i	−0.648680	+	1.78223i	−0.622556	+	0.782575i	$0.713906\pi$
$242$		0			0
$243$	−15.3516	+	2.70691i	−0.0631754	+	0.0111395i
$244$		0			0
$245$	55.3758	+	46.4658i	0.226024	+	0.189657i
$246$		0			0
$247$	−0.580218	+	0.245994i	−0.00234906	+	0.000995928i
$248$		0			0
$249$	−37.1389	+	44.2605i	−0.149152	+	0.177753i
$250$		0			0
$251$	−18.9878	−	107.685i	−0.0756486	−	0.429025i	−0.998985	−	0.0450337i	$-0.985660\pi$
$251$	−18.9878	−	107.685i	−0.0756486	−	0.429025i	0.923337	−	0.383991i	$-0.125451\pi$
$252$		0			0
$253$	−296.406	−	107.883i	−1.17156	−	0.426415i
$254$		0			0
$255$	37.6512	+	21.7380i	0.147652	+	0.0852469i
$256$		0			0
$257$	−243.915	−	290.687i	−0.949086	−	1.13108i	−0.991254	−	0.131966i	$-0.957871\pi$
$257$	−243.915	−	290.687i	−0.949086	−	1.13108i	0.0421679	−	0.999111i	$-0.486574\pi$
$258$		0			0
$259$	96.1705	−	55.5241i	0.371315	−	0.214379i
$260$		0			0
$261$	2.99246	+	0.527652i	0.0114654	+	0.00202165i
$262$		0			0
$263$	31.3283	−	11.4026i	0.119119	−	0.0433558i	−0.281773	−	0.959481i	$-0.590922\pi$
$263$	31.3283	−	11.4026i	0.119119	−	0.0433558i	0.400892	+	0.916125i	$0.368700\pi$
$264$		0			0
$265$		−	55.3152i		−	0.208737i
$266$		0			0
$267$	−68.2639			−0.255670
$268$		0			0
$269$	16.6214	+	45.6670i	0.0617896	+	0.169766i	0.966746	−	0.255739i	$-0.0823188\pi$
$269$	16.6214	+	45.6670i	0.0617896	+	0.169766i	−0.904956	+	0.425505i	$0.860097\pi$
$270$		0			0
$271$	64.2786	−	364.542i	0.237190	−	1.34517i	−0.600761	−	0.799428i	$-0.705136\pi$
$271$	64.2786	−	364.542i	0.237190	−	1.34517i	0.837952	−	0.545744i	$-0.183753\pi$
$272$		0			0
$273$	0.143672	+	0.248847i	0.000526270	+	0.000911526i
$274$		0			0
$275$	−131.343	+	110.210i	−0.477610	+	0.400762i
$276$		0			0
$277$	−176.869	+	306.346i	−0.638517	+	1.10594i	0.347242	+	0.937776i	$0.387118\pi$
$277$	−176.869	+	306.346i	−0.638517	+	1.10594i	−0.985758	+	0.168168i	$0.946215\pi$
$278$		0			0
$279$	−3.85942	+	10.6037i	−0.0138330	+	0.0380060i
$280$		0			0
$281$	423.030	−	74.5916i	1.50545	−	0.265451i	0.640751	−	0.767749i	$-0.278623\pi$
$281$	423.030	−	74.5916i	1.50545	−	0.265451i	0.864694	+	0.502298i	$0.167512\pi$
$282$		0			0
$283$	−88.0552	−	73.8871i	−0.311149	−	0.261085i	0.473818	−	0.880623i	$-0.342876\pi$
$283$	−88.0552	−	73.8871i	−0.311149	−	0.261085i	−0.784967	+	0.619538i	$0.787320\pi$
$284$		0			0
$285$	79.1891	+	59.7265i	0.277856	+	0.209567i
$286$		0			0
$287$	52.9222	−	63.0702i	0.184398	−	0.219757i
$288$		0			0
$289$	−38.1406	−	216.306i	−0.131974	−	0.748464i
$290$		0			0
$291$	−66.7888	−	24.3091i	−0.229515	−	0.0835366i
$292$		0			0
$293$	−327.735	−	189.218i	−1.11855	−	0.645794i	−0.177519	−	0.984117i	$-0.556807\pi$
$293$	−327.735	−	189.218i	−1.11855	−	0.645794i	−0.941030	+	0.338323i	$0.890140\pi$
$294$		0			0
$295$	−66.6931	−	79.4818i	−0.226078	−	0.269430i
$296$		0			0
$297$	−48.4770	+	27.9882i	−0.163222	+	0.0942364i
$298$		0			0
$299$	−0.956448	−	0.168648i	−0.00319882	−	0.000564039i
$300$		0			0
$301$	−3.91857	+	1.42624i	−0.0130185	+	0.00473834i
$302$		0			0
$303$			68.3123i			0.225453i
$304$		0			0
$305$	−12.2239			−0.0400783
$306$		0			0
$307$	−121.494	−	333.803i	−0.395747	−	1.08731i	−0.964335	−	0.264684i	$-0.914732\pi$
$307$	−121.494	−	333.803i	−0.395747	−	1.08731i	0.568588	−	0.822622i	$-0.307490\pi$
$308$		0			0
$309$	50.0613	−	283.912i	0.162011	−	0.918808i
$310$		0			0
$311$	216.828	+	375.557i	0.697195	+	1.20758i	0.969435	+	0.245348i	$0.0789023\pi$
$311$	216.828	+	375.557i	0.697195	+	1.20758i	−0.272240	+	0.962229i	$0.587764\pi$
$312$		0			0
$313$	−267.627	+	224.565i	−0.855037	+	0.717461i	−0.960893	−	0.276920i	$-0.910686\pi$
$313$	−267.627	+	224.565i	−0.855037	+	0.717461i	0.105856	+	0.994381i	$0.466242\pi$
$314$		0			0
$315$	22.6122	−	39.1654i	0.0717847	−	0.124335i
$316$		0			0
$317$	−50.6524	+	139.166i	−0.159787	+	0.439010i	−0.993589	−	0.113053i	$-0.963937\pi$
$317$	−50.6524	+	139.166i	−0.159787	+	0.439010i	0.833802	+	0.552063i	$0.186159\pi$
$318$		0			0
$319$	10.7456	−	1.89474i	0.0336853	−	0.00593962i
$320$		0			0
$321$	−1.18448	−	0.993896i	−0.00368996	−	0.00309625i
$322$		0			0
$323$	8.21352	+	158.020i	0.0254289	+	0.489227i
$324$		0			0
$325$	−0.339335	+	0.404404i	−0.00104411	+	0.00124432i
$326$		0			0
$327$	−23.9681	−	135.930i	−0.0732970	−	0.415688i
$328$		0			0
$329$	−400.992	−	145.949i	−1.21882	−	0.443615i
$330$		0			0
$331$	447.835	+	258.557i	1.35297	+	0.781140i	0.988665	−	0.150137i	$-0.0479716\pi$
$331$	447.835	+	258.557i	1.35297	+	0.781140i	0.364310	+	0.931278i	$0.381305\pi$
$332$		0			0
$333$	42.8146	+	51.0245i	0.128572	+	0.153227i
$334$		0			0
$335$	316.178	−	182.546i	0.943815	−	0.544912i
$336$		0			0
$337$	142.447	+	25.1172i	0.422691	+	0.0745318i	0.380948	−	0.924597i	$-0.375598\pi$
$337$	142.447	+	25.1172i	0.422691	+	0.0745318i	0.0417431	+	0.999128i	$0.486709\pi$
$338$		0			0
$339$	−135.346	+	49.2620i	−0.399252	+	0.145316i
$340$		0			0
$341$			40.5203i			0.118828i
$342$		0			0
$343$	365.037			1.06425
$344$		0			0
$345$	52.2797	+	143.637i	0.151535	+	0.416340i
$346$		0			0
$347$	53.3086	−	302.328i	0.153627	−	0.871263i	−0.806403	−	0.591366i	$-0.798589\pi$
$347$	53.3086	−	302.328i	0.153627	−	0.871263i	0.960030	−	0.279896i	$-0.0903002\pi$
$348$		0			0
$349$	12.9451	+	22.4216i	0.0370920	+	0.0642452i	0.883975	−	0.467533i	$-0.154857\pi$
$349$	12.9451	+	22.4216i	0.0370920	+	0.0642452i	−0.846883	+	0.531779i	$0.821524\pi$
$350$		0			0
$351$	−0.132029	+	0.110785i	−0.000376150	+	0.000315627i
$352$		0			0
$353$	−134.451	+	232.876i	−0.380881	+	0.659705i	−0.991188	−	0.132459i	$-0.957713\pi$
$353$	−134.451	+	232.876i	−0.380881	+	0.659705i	0.610307	+	0.792165i	$0.291046\pi$
$354$		0			0
$355$	−13.9758	+	38.3981i	−0.0393683	+	0.108164i
$356$		0			0
$357$	71.0502	−	12.5281i	0.199020	−	0.0350926i
$358$		0			0
$359$	321.031	+	269.377i	0.894236	+	0.750353i	0.969055	−	0.246844i	$-0.0793935\pi$
$359$	321.031	+	269.377i	0.894236	+	0.750353i	−0.0748191	+	0.997197i	$0.523838\pi$
$360$		0			0
$361$	−25.4910	+	360.099i	−0.0706123	+	0.997504i
$362$		0			0
$363$	5.51059	−	6.56726i	0.0151807	−	0.0180916i
$364$		0			0
$365$	52.1178	+	295.575i	0.142789	+	0.809794i
$366$		0			0
$367$	−303.973	−	110.637i	−0.828265	−	0.301464i	−0.107118	−	0.994246i	$-0.534162\pi$
$367$	−303.973	−	110.637i	−0.828265	−	0.301464i	−0.721147	+	0.692782i	$0.756385\pi$
$368$		0			0
$369$	42.7675	+	24.6918i	0.115901	+	0.0669155i
$370$		0			0
$371$	−59.0034	−	70.3175i	−0.159039	−	0.189535i
$372$		0			0
$373$	367.516	−	212.185i	0.985297	−	0.568861i	0.0814318	−	0.996679i	$-0.474051\pi$
$373$	367.516	−	212.185i	0.985297	−	0.568861i	0.903865	+	0.427817i	$0.140717\pi$
$374$		0			0
$375$	210.352	+	37.0907i	0.560938	+	0.0989085i
$376$		0			0
$377$	0.0315700	−	0.0114905i	8.37400e−5	−	3.04789e-5i
$378$		0			0
$379$		−	434.110i		−	1.14541i	−0.819762	−	0.572705i	$-0.805894\pi$
$379$		−	434.110i		−	1.14541i	0.819762	−	0.572705i	$-0.194106\pi$
$380$		0			0
$381$	65.2612			0.171289
$382$		0			0
$383$	193.915	+	532.777i	0.506306	+	1.39106i	0.885021	+	0.465551i	$0.154144\pi$
$383$	193.915	+	532.777i	0.506306	+	1.39106i	−0.378715	+	0.925513i	$0.623634\pi$
$384$		0			0
$385$	28.1997	−	159.929i	0.0732460	−	0.415399i
$386$		0			0
$387$	−1.25062	−	2.16613i	−0.00323157	−	0.00559724i
$388$		0			0
$389$	−260.363	+	218.470i	−0.669313	+	0.561620i	−0.912862	−	0.408268i	$-0.866133\pi$
$389$	−260.363	+	218.470i	−0.669313	+	0.561620i	0.243549	+	0.969889i	$0.421688\pi$
$390$		0			0
$391$	−121.925	+	211.180i	−0.311829	+	0.540103i
$392$		0			0
$393$	83.3912	−	229.116i	0.212191	−	0.582991i
$394$		0			0
$395$	153.873	−	27.1320i	0.389552	−	0.0686885i
$396$		0			0
$397$	16.7677	+	14.0698i	0.0422360	+	0.0354402i	0.663661	−	0.748033i	$-0.269002\pi$
$397$	16.7677	+	14.0698i	0.0422360	+	0.0354402i	−0.621425	+	0.783473i	$0.713446\pi$
$398$		0			0
$399$	164.375	−	8.54384i	0.411968	−	0.0214131i
$400$		0			0
$401$	−150.290	+	179.109i	−0.374789	+	0.446656i	−0.920162	−	0.391537i	$-0.871943\pi$
$401$	−150.290	+	179.109i	−0.374789	+	0.446656i	0.545373	+	0.838193i	$0.316388\pi$
$402$		0			0
$403$	0.0216647	+	0.122866i	5.37585e−5	+	0.000304879i
$404$		0			0
$405$	25.4901	+	9.27763i	0.0629385	+	0.0229077i
$406$		0			0
$407$	207.137	+	119.590i	0.508935	+	0.293834i
$408$		0			0
$409$	−11.4200	−	13.6099i	−0.0279219	−	0.0332760i	0.751903	−	0.659274i	$-0.229136\pi$
$409$	−11.4200	−	13.6099i	−0.0279219	−	0.0332760i	−0.779825	+	0.625998i	$0.784692\pi$
$410$		0			0
$411$	−61.7105	+	35.6286i	−0.150147	+	0.0866875i
$412$		0			0
$413$	−169.563	−	29.8985i	−0.410563	−	0.0723934i
$414$		0			0
$415$	94.4779	−	34.3871i	0.227658	−	0.0828606i
$416$		0			0
$417$			299.134i			0.717347i
$418$		0			0
$419$	−683.131			−1.63038			−0.815192	−	0.579190i	$-0.803369\pi$
$419$	−683.131			−1.63038			−0.815192	+	0.579190i	$0.803369\pi$
$420$		0			0
$421$	237.659	+	652.963i	0.564511	+	1.55098i	0.812949	+	0.582334i	$0.197861\pi$
$421$	237.659	+	652.963i	0.564511	+	1.55098i	−0.248438	+	0.968648i	$0.579917\pi$
$422$		0			0
$423$	44.4461	−	252.066i	0.105073	−	0.595901i
$424$		0			0
$425$	66.2741	+	114.790i	0.155939	+	0.270094i
$426$		0			0
$427$	−15.5392	+	13.0389i	−0.0363916	+	0.0305361i
$428$		0			0
$429$	−0.309447	+	0.535978i	−0.000721322	+	0.00124937i
$430$		0			0
$431$	−169.291	+	465.123i	−0.392786	+	1.07917i	0.572937	+	0.819599i	$0.305804\pi$
$431$	−169.291	+	465.123i	−0.392786	+	1.07917i	−0.965724	+	0.259573i	$0.916418\pi$
$432$		0			0
$433$	−192.879	+	34.0097i	−0.445447	+	0.0785443i	−0.391873	−	0.920020i	$-0.628173\pi$
$433$	−192.879	+	34.0097i	−0.445447	+	0.0785443i	−0.0535745	+	0.998564i	$0.517061\pi$
$434$		0			0
$435$	−4.05055	−	3.39881i	−0.00931160	−	0.00781336i
$436$		0			0
$437$	−334.997	+	444.160i	−0.766584	+	1.01638i
$438$		0			0
$439$	−508.652	+	606.188i	−1.15866	+	1.38084i	−0.247449	+	0.968901i	$0.579592\pi$
$439$	−508.652	+	606.188i	−1.15866	+	1.38084i	−0.911212	+	0.411938i	$0.864852\pi$
$440$		0			0
$441$	12.4944	+	70.8592i	0.0283319	+	0.160678i
$442$		0			0
$443$	−529.580	−	192.751i	−1.19544	−	0.435105i	−0.333810	−	0.942641i	$-0.608334\pi$
$443$	−529.580	−	192.751i	−1.19544	−	0.435105i	−0.861631	+	0.507536i	$0.830556\pi$
$444$		0			0
$445$	102.874	+	59.3941i	0.231177	+	0.133470i
$446$		0			0
$447$	−191.043	−	227.676i	−0.427388	−	0.509342i
$448$		0			0
$449$	317.401	−	183.251i	0.706906	−	0.408132i	−0.103009	−	0.994680i	$-0.532847\pi$
$449$	317.401	−	183.251i	0.706906	−	0.408132i	0.809914	+	0.586548i	$0.199514\pi$
$450$		0			0
$451$	174.637	+	30.7933i	0.387222	+	0.0682777i
$452$		0			0
$453$	351.659	−	127.993i	0.776289	−	0.282546i
$454$		0			0
$455$		−	0.500016i		−	0.00109894i
$456$		0			0
$457$	623.292			1.36388			0.681939	−	0.731409i	$-0.261137\pi$
$457$	623.292			1.36388			0.681939	+	0.731409i	$0.261137\pi$
$458$		0			0
$459$	14.8006	+	40.6642i	0.0322453	+	0.0885931i
$460$		0			0
$461$	−47.4251	+	268.961i	−0.102874	+	0.583429i	0.889174	+	0.457570i	$0.151280\pi$
$461$	−47.4251	+	268.961i	−0.102874	+	0.583429i	−0.992048	+	0.125860i	$0.959831\pi$
$462$		0			0
$463$	1.23966	+	2.14715i	0.00267745	+	0.00463748i	0.867361	−	0.497679i	$-0.165814\pi$
$463$	1.23966	+	2.14715i	0.00267745	+	0.00463748i	−0.864684	+	0.502317i	$0.832481\pi$
$464$		0			0
$465$	15.0420	−	12.6218i	0.0323485	−	0.0271436i
$466$		0			0
$467$	317.490	−	549.909i	0.679851	−	1.17754i	−0.295175	−	0.955443i	$-0.595378\pi$
$467$	317.490	−	549.909i	0.679851	−	1.17754i	0.975026	−	0.222093i	$-0.0712888\pi$
$468$		0			0
$469$	207.213	−	569.314i	0.441820	−	1.21389i
$470$		0			0
$471$	−162.984	+	28.7385i	−0.346038	+	0.0610159i
$472$		0			0
$473$	−6.88035	−	5.77330i	−0.0145462	−	0.0122057i
$474$		0			0
$475$	118.038	+	278.412i	0.248501	+	0.586130i
$476$		0			0
$477$	35.3908	−	42.1771i	0.0741945	−	0.0884216i
$478$		0			0
$479$	−18.5438	−	105.167i	−0.0387136	−	0.219556i	0.959313	−	0.282344i	$-0.0911119\pi$
$479$	−18.5438	−	105.167i	−0.0387136	−	0.219556i	−0.998027	+	0.0627882i	$0.980001\pi$
$480$		0			0
$481$	0.692024	+	0.251876i	0.00143872	+	0.000523651i
$482$		0			0
$483$	219.673	+	126.828i	0.454810	+	0.262585i
$484$		0			0
$485$	79.5001	+	94.7446i	0.163918	+	0.195350i
$486$		0			0
$487$	640.406	−	369.739i	1.31500	−	0.759217i	0.332083	−	0.943250i	$-0.392249\pi$
$487$	640.406	−	369.739i	1.31500	−	0.759217i	0.982920	+	0.184033i	$0.0589154\pi$
$488$		0			0
$489$	−29.6215	−	5.22306i	−0.0605756	−	0.0106811i
$490$		0			0
$491$	−107.820	+	39.2431i	−0.219592	+	0.0799249i	−0.449473	−	0.893294i	$-0.648388\pi$
$491$	−107.820	+	39.2431i	−0.219592	+	0.0799249i	0.229882	+	0.973219i	$0.426166\pi$
$492$		0			0
$493$		−	8.43531i		−	0.0171102i
$494$		0			0
$495$	97.4064			0.196781
$496$		0			0
$497$	23.1921	+	63.7199i	0.0466642	+	0.128209i
$498$		0			0
$499$	86.9829	−	493.304i	0.174314	−	0.988586i	−0.764618	−	0.644484i	$-0.777072\pi$
$499$	86.9829	−	493.304i	0.174314	−	0.988586i	0.938932	−	0.344102i	$-0.111817\pi$
$500$		0			0
$501$	−267.511	−	463.343i	−0.533955	−	0.924837i
$502$		0			0
$503$	−653.090	+	548.008i	−1.29839	+	1.08948i	−0.307969	+	0.951396i	$0.599649\pi$
$503$	−653.090	+	548.008i	−1.29839	+	1.08948i	−0.990421	+	0.138082i	$0.955906\pi$
$504$		0			0
$505$	59.4362	−	102.947i	0.117696	−	0.203855i
$506$		0			0
$507$	100.114	−	275.062i	0.197464	−	0.542528i
$508$		0			0
$509$	507.720	−	89.5247i	0.997485	−	0.175884i	0.349010	−	0.937119i	$-0.386518\pi$
$509$	507.720	−	89.5247i	0.997485	−	0.175884i	0.648475	+	0.761236i	$0.275407\pi$
$510$		0			0
$511$	381.536	+	320.146i	0.746645	+	0.626510i
$512$		0			0
$513$	22.1675	+	96.2060i	0.0432114	+	0.187536i
$514$		0			0
$515$	−322.464	+	384.298i	−0.626145	+	0.746210i
$516$		0			0
$517$	−159.601	−	905.142i	−0.308706	−	1.75076i
$518$		0			0
$519$	15.9827	+	5.81721i	0.0307951	+	0.0112085i
$520$		0			0
$521$	−216.675	−	125.098i	−0.415884	−	0.240110i	0.277431	−	0.960746i	$-0.410517\pi$
$521$	−216.675	−	125.098i	−0.415884	−	0.240110i	−0.693315	+	0.720635i	$0.743850\pi$
$522$		0			0
$523$	−224.502	−	267.551i	−0.429257	−	0.511569i	0.507451	−	0.861681i	$-0.330588\pi$
$523$	−224.502	−	267.551i	−0.429257	−	0.511569i	−0.936708	+	0.350112i	$0.886144\pi$
$524$		0			0
$525$	119.407	−	68.9394i	0.227441	−	0.131313i
$526$		0			0
$527$	30.8493	+	5.43957i	0.0585376	+	0.0103218i
$528$		0			0
$529$	−308.542	+	112.300i	−0.583256	+	0.212288i
$530$		0			0
$531$		−	103.274i		−	0.194490i
$532$		0			0
$533$	0.546002			0.00102439
$534$		0			0
$535$	0.920253	+	2.52837i	0.00172010	+	0.00472593i
$536$		0			0
$537$	64.7284	−	367.093i	0.120537	−	0.683600i
$538$		0			0
$539$	129.186	+	223.757i	0.239678	+	0.415134i
$540$		0			0
$541$	19.5992	−	16.4456i	0.0362277	−	0.0303986i	−0.624494	−	0.781030i	$-0.714695\pi$
$541$	19.5992	−	16.4456i	0.0362277	−	0.0303986i	0.660722	+	0.750631i	$0.270250\pi$
$542$		0			0
$543$	−139.182	+	241.070i	−0.256321	+	0.443960i
$544$		0			0
$545$	−82.1482	+	225.700i	−0.150731	+	0.414129i
$546$		0			0
$547$	−255.979	+	45.1359i	−0.467968	+	0.0825154i	−0.402660	−	0.915350i	$-0.631914\pi$
$547$	−255.979	+	45.1359i	−0.467968	+	0.0825154i	−0.0653085	+	0.997865i	$0.520803\pi$
$548$		0			0
$549$	−9.32055	−	7.82087i	−0.0169773	−	0.0142457i
$550$		0			0
$551$	2.35352	−	19.1002i	0.00427137	−	0.0346646i
$552$		0			0
$553$	166.665	−	198.623i	0.301383	−	0.359174i
$554$		0			0
$555$	−20.1269	−	114.145i	−0.0362647	−	0.205667i
$556$		0			0
$557$	−741.393	−	269.845i	−1.33105	−	0.484462i	−0.424066	−	0.905631i	$-0.639397\pi$
$557$	−741.393	−	269.845i	−1.33105	−	0.484462i	−0.906982	+	0.421170i	$0.861620\pi$
$558$		0			0
$559$	−0.0239495	−	0.0138272i	−4.28435e−5	−	2.47357e-5i
$560$		0			0
$561$	99.8841	+	119.037i	0.178047	+	0.212188i
$562$		0			0
$563$	87.7193	−	50.6447i	0.155807	−	0.0899551i	−0.420069	−	0.907492i	$-0.637994\pi$
$563$	87.7193	−	50.6447i	0.155807	−	0.0899551i	0.575876	+	0.817537i	$0.304661\pi$
$564$		0			0
$565$	246.828	+	43.5224i	0.436864	+	0.0770309i
$566$		0			0
$567$	42.2996	−	15.3958i	0.0746025	−	0.0271531i
$568$		0			0
$569$		−	904.073i		−	1.58888i	−0.607342	−	0.794440i	$-0.707764\pi$
$569$		−	904.073i		−	1.58888i	0.607342	−	0.794440i	$-0.292236\pi$
$570$		0			0
$571$	−887.039			−1.55348			−0.776742	−	0.629819i	$-0.783129\pi$
$571$	−887.039			−1.55348			−0.776742	+	0.629819i	$0.783129\pi$
$572$		0			0
$573$	−115.979	−	318.649i	−0.202406	−	0.556107i
$574$		0			0
$575$	−80.9239	+	458.942i	−0.140737	+	0.798160i
$576$		0			0
$577$	−424.695	−	735.593i	−0.736039	−	1.27486i	−0.954266	−	0.298959i	$-0.903361\pi$
$577$	−424.695	−	735.593i	−0.736039	−	1.27486i	0.218227	−	0.975898i	$-0.429973\pi$
$578$		0			0
$579$	68.6589	−	57.6117i	0.118582	−	0.0995020i
$580$		0			0
$581$	83.4218	−	144.491i	0.143583	−	0.248693i
$582$		0			0
$583$	67.6202	−	185.785i	0.115987	−	0.318671i
$584$		0			0
$585$	0.295358	−	0.0520795i	0.000504885	−	8.90248e-5i
$586$		0			0
$587$	234.907	+	197.110i	0.400182	+	0.335793i	0.820564	−	0.571555i	$-0.193659\pi$
$587$	234.907	+	197.110i	0.400182	+	0.335793i	−0.420382	+	0.907347i	$0.638104\pi$
$588$		0			0
$589$	68.3348	+	20.9241i	0.116018	+	0.0355248i
$590$		0			0
$591$	−230.431	+	274.617i	−0.389901	+	0.464666i
$592$		0			0
$593$	22.7774	+	129.177i	0.0384105	+	0.217837i	0.997971	−	0.0636645i	$-0.0202788\pi$
$593$	22.7774	+	129.177i	0.0384105	+	0.217837i	−0.959561	+	0.281501i	$0.909168\pi$
$594$		0			0
$595$	−117.973	−	42.9386i	−0.198274	−	0.0721657i
$596$		0			0
$597$	71.0339	+	41.0114i	0.118985	+	0.0686959i
$598$		0			0
$599$	−685.298	−	816.706i	−1.14407	−	1.36345i	−0.921428	−	0.388549i	$-0.872976\pi$
$599$	−685.298	−	816.706i	−1.14407	−	1.36345i	−0.222642	−	0.974900i	$-0.571468\pi$
$600$		0			0
$601$	−849.528	+	490.475i	−1.41352	+	0.816098i	−0.995718	−	0.0924384i	$-0.970534\pi$
$601$	−849.528	+	490.475i	−1.41352	+	0.816098i	−0.417805	+	0.908537i	$0.637201\pi$
$602$		0			0
$603$	357.875	+	63.1030i	0.593490	+	0.104648i
$604$		0			0
$605$	−14.0184	+	5.10228i	−0.0231709	+	0.00843353i
$606$		0			0
$607$			130.395i			0.214819i	0.994215	+	0.107409i	$0.0342556\pi$
$607$			130.395i			0.214819i	−0.994215	+	0.107409i	$0.965744\pi$
$608$		0			0
$609$	−8.77455			−0.0144081
$610$		0			0
$611$	−0.967890	−	2.65926i	−0.00158411	−	0.00435230i
$612$		0			0
$613$	181.228	−	1027.79i	0.295641	−	1.67666i	−0.368947	−	0.929451i	$-0.620282\pi$
$613$	181.228	−	1027.79i	0.295641	−	1.67666i	0.664587	−	0.747211i	$-0.268607\pi$
$614$		0			0
$615$	−42.9671	−	74.4211i	−0.0698651	−	0.121010i
$616$		0			0
$617$	689.389	−	578.466i	1.11732	−	0.937546i	0.118858	−	0.992911i	$-0.462077\pi$
$617$	689.389	−	578.466i	1.11732	−	0.937546i	0.998466	+	0.0553649i	$0.0176322\pi$
$618$		0			0
$619$	−169.604	+	293.763i	−0.273997	+	0.474577i	−0.969882	−	0.243577i	$-0.921679\pi$
$619$	−169.604	+	293.763i	−0.273997	+	0.474577i	0.695884	+	0.718154i	$0.255013\pi$
$620$		0			0
$621$	−52.0369	+	142.970i	−0.0837953	+	0.230226i
$622$		0			0
$623$	194.129	−	34.2302i	0.311603	−	0.0549441i
$624$		0			0
$625$	20.0769	+	16.8465i	0.0321230	+	0.0269544i
$626$		0			0
$627$	192.956	+	297.406i	0.307746	+	0.474332i
$628$		0			0
$629$	118.855	−	141.645i	0.188958	−	0.225191i
$630$		0			0
$631$	44.6700	+	253.336i	0.0707925	+	0.401484i	0.999527	+	0.0307397i	$0.00978628\pi$
$631$	44.6700	+	253.336i	0.0707925	+	0.401484i	−0.928735	+	0.370744i	$0.879103\pi$
$632$		0			0
$633$	165.628	+	60.2838i	0.261656	+	0.0952351i
$634$		0			0
$635$	−98.3486	−	56.7816i	−0.154880	−	0.0894198i
$636$		0			0
$637$	0.511356	+	0.609410i	0.000802757	+	0.000956688i
$638$		0			0
$639$	−35.2235	+	20.3363i	−0.0551229	+	0.0318252i
$640$		0			0
$641$	125.671	+	22.1592i	0.196055	+	0.0345698i	0.270813	−	0.962632i	$-0.412707\pi$
$641$	125.671	+	22.1592i	0.196055	+	0.0345698i	−0.0747584	+	0.997202i	$0.523819\pi$
$642$		0			0
$643$	−431.862	+	157.185i	−0.671636	+	0.244455i	−0.655252	−	0.755410i	$-0.727438\pi$
$643$	−431.862	+	157.185i	−0.671636	+	0.244455i	−0.0163837	+	0.999866i	$0.505215\pi$
$644$		0			0
$645$			4.35248i			0.00674803i
$646$		0			0
$647$	−717.205			−1.10851			−0.554254	−	0.832347i	$-0.686997\pi$
$647$	−717.205			−1.10851			−0.554254	+	0.832347i	$0.686997\pi$
$648$		0			0
$649$	−126.837	−	348.481i	−0.195434	−	0.536951i
$650$		0			0
$651$	5.65833	−	32.0900i	0.00869175	−	0.0492933i
$652$		0			0
$653$	324.310	+	561.721i	0.496646	+	0.860216i	0.999993	−	0.00386880i	$-0.00123148\pi$
$653$	324.310	+	561.721i	0.496646	+	0.860216i	−0.503347	+	0.864085i	$0.667898\pi$
$654$		0			0
$655$	−325.016	+	272.721i	−0.496208	+	0.416368i
$656$		0			0
$657$	−149.370	+	258.717i	−0.227352	+	0.393785i
$658$		0			0
$659$	−207.813	+	570.960i	−0.315345	+	0.866404i	0.676209	+	0.736710i	$0.263622\pi$
$659$	−207.813	+	570.960i	−0.315345	+	0.866404i	−0.991554	+	0.129694i	$0.958600\pi$
$660$		0			0
$661$	457.460	−	80.6626i	0.692073	−	0.122031i	0.183461	−	0.983027i	$-0.441270\pi$
$661$	457.460	−	80.6626i	0.692073	−	0.122031i	0.508612	+	0.860996i	$0.330159\pi$
$662$		0			0
$663$	0.366515	+	0.307543i	0.000552813	+	0.000463866i
$664$		0			0
$665$	−255.147	−	130.142i	−0.383680	−	0.195702i
$666$		0			0
$667$	19.0634	−	22.7189i	0.0285809	−	0.0340613i
$668$		0			0
$669$	−38.3712	−	217.614i	−0.0573560	−	0.325282i
$670$		0			0
$671$	−41.0559	−	14.9431i	−0.0611861	−	0.0222699i
$672$		0			0
$673$	427.744	+	246.958i	0.635577	+	0.366951i	0.782909	−	0.622136i	$-0.213735\pi$
$673$	427.744	+	246.958i	0.635577	+	0.366951i	−0.147332	+	0.989087i	$0.547068\pi$
$674$		0			0
$675$	53.1592	+	63.3526i	0.0787543	+	0.0938558i
$676$		0			0
$677$	487.283	−	281.333i	0.719767	−	0.415558i	−0.0948996	−	0.995487i	$-0.530253\pi$
$677$	487.283	−	281.333i	0.719767	−	0.415558i	0.814667	+	0.579929i	$0.196920\pi$
$678$		0			0
$679$	202.124	+	35.6398i	0.297678	+	0.0524887i
$680$		0			0
$681$	−565.109	+	205.683i	−0.829823	+	0.302031i
$682$		0			0
$683$		−	1145.88i		−	1.67771i	−0.544354	−	0.838856i	$-0.683225\pi$
$683$		−	1145.88i		−	1.67771i	0.544354	−	0.838856i	$-0.316775\pi$
$684$		0			0
$685$	123.997			0.181017
$686$		0			0
$687$	−84.4546	−	232.037i	−0.122932	−	0.337754i
$688$		0			0
$689$	0.105707	−	0.599495i	0.000153421	−	0.000870094i
$690$		0			0
$691$	278.603	+	482.554i	0.403188	+	0.698341i	0.994109	−	0.108388i	$-0.0345689\pi$
$691$	278.603	+	482.554i	0.403188	+	0.698341i	−0.590921	+	0.806729i	$0.701236\pi$
$692$		0			0
$693$	123.825	−	103.901i	0.178679	−	0.149929i
$694$		0			0
$695$	260.266	−	450.794i	0.374484	−	0.648625i
$696$		0			0
$697$	46.8877	−	128.823i	0.0672707	−	0.184825i
$698$		0			0
$699$	−703.862	+	124.110i	−1.00696	+	0.177553i
$700$		0			0
$701$	648.949	+	544.532i	0.925747	+	0.776794i	0.975049	−	0.221990i	$-0.0712553\pi$
$701$	648.949	+	544.532i	0.925747	+	0.776794i	−0.0493021	+	0.998784i	$0.515700\pi$
$702$		0			0
$703$	308.644	−	287.568i	0.439038	−	0.409058i
$704$		0			0
$705$	−286.294	+	341.192i	−0.406091	+	0.483961i
$706$		0			0
$707$	−34.2544	−	194.266i	−0.0484504	−	0.274776i
$708$		0			0
$709$	695.133	+	253.008i	0.980442	+	0.356852i	0.782012	−	0.623264i	$-0.214194\pi$
$709$	695.133	+	253.008i	0.980442	+	0.356852i	0.198430	+	0.980115i	$0.436416\pi$
$710$		0			0
$711$	134.685	+	77.7606i	0.189431	+	0.109368i
$712$		0			0
$713$	70.7936	+	84.3686i	0.0992898	+	0.118329i
$714$		0			0
$715$	0.932673	−	0.538479i	0.00130444	−	0.000753117i
$716$		0			0
$717$	−348.802	−	61.5033i	−0.486475	−	0.0857786i
$718$		0			0
$719$	152.441	−	55.4841i	0.212018	−	0.0771684i	−0.233828	−	0.972278i	$-0.575125\pi$
$719$	152.441	−	55.4841i	0.212018	−	0.0771684i	0.445846	+	0.895110i	$0.352903\pi$
$720$		0			0
$721$			832.491i			1.15463i
$722$		0			0
$723$	791.693			1.09501
$724$		0			0
$725$	−5.51362	−	15.1485i	−0.00760499	−	0.0208945i
$726$		0			0
$727$	−87.2516	+	494.828i	−0.120016	+	0.680644i	0.864128	+	0.503272i	$0.167871\pi$
$727$	−87.2516	+	494.828i	−0.120016	+	0.680644i	−0.984144	+	0.177372i	$0.943240\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.0185185	+	0.0320750i
$730$		0			0
$731$	−5.31903	+	4.46320i	−0.00727637	+	0.00610560i
$732$		0			0
$733$	−328.882	+	569.640i	−0.448679	+	0.777135i	−0.998300	−	0.0582790i	$-0.981439\pi$
$733$	−328.882	+	569.640i	−0.448679	+	0.777135i	0.549621	+	0.835414i	$0.314772\pi$
$734$		0			0
$735$	42.8232	−	117.656i	0.0582628	−	0.160076i
$736$		0			0
$737$	1285.09	−	226.596i	1.74367	−	0.307457i
$738$		0			0
$739$	382.707	+	321.129i	0.517871	+	0.434545i	0.863889	−	0.503683i	$-0.168022\pi$
$739$	382.707	+	321.129i	0.517871	+	0.434545i	−0.346018	+	0.938228i	$0.612466\pi$
$740$		0			0
$741$	0.744098	+	0.798634i	0.00100418	+	0.00107778i
$742$		0			0
$743$	−69.0142	+	82.2479i	−0.0928858	+	0.110697i	−0.810485	−	0.585759i	$-0.800796\pi$
$743$	−69.0142	+	82.2479i	−0.0928858	+	0.110697i	0.717599	+	0.696456i	$0.245241\pi$
$744$		0			0
$745$	89.8081	+	509.327i	0.120548	+	0.683660i
$746$		0			0
$747$	94.0391	+	34.2274i	0.125889	+	0.0458199i
$748$		0			0
$749$	3.86680	+	2.23250i	0.00516261	+	0.00298064i
$750$		0			0
$751$	−404.415	−	481.963i	−0.538502	−	0.641761i	0.426349	−	0.904559i	$-0.359799\pi$
$751$	−404.415	−	481.963i	−0.538502	−	0.641761i	−0.964851	+	0.262797i	$0.915355\pi$
$752$		0			0
$753$	−164.020	+	94.6968i	−0.217822	+	0.125759i
$754$		0			0
$755$	−641.312	−	113.081i	−0.849420	−	0.149776i
$756$		0			0
$757$	241.689	−	87.9676i	0.319272	−	0.116206i	−0.177413	−	0.984137i	$-0.556773\pi$
$757$	241.689	−	87.9676i	0.319272	−	0.116206i	0.496685	+	0.867931i	$0.334551\pi$
$758$		0			0
$759$			546.338i			0.719813i
$760$		0			0
$761$	1328.77			1.74609			0.873045	−	0.487640i	$-0.162142\pi$
$761$	1328.77			1.74609			0.873045	+	0.487640i	$0.162142\pi$
$762$		0			0
$763$	136.321	+	374.539i	0.178665	+	0.490877i
$764$		0			0
$765$	13.0761	−	74.1585i	0.0170930	−	0.0969392i
$766$		0			0
$767$	−0.570917	−	0.988857i	−0.000744351	−	0.00128925i
$768$		0			0
$769$	−564.170	+	473.395i	−0.733641	+	0.615598i	−0.931122	−	0.364709i	$-0.881169\pi$
$769$	−564.170	+	473.395i	−0.733641	+	0.615598i	0.197480	+	0.980307i	$0.436724\pi$
$770$		0			0
$771$	−328.626	+	569.197i	−0.426233	+	0.738258i
$772$		0			0
$773$	−426.640	+	1172.18i	−0.551928	+	1.51641i	0.279146	+	0.960249i	$0.409949\pi$
$773$	−426.640	+	1172.18i	−0.551928	+	1.51641i	−0.831074	+	0.556161i	$0.812274\pi$
$774$		0			0
$775$	58.9562	−	10.3956i	0.0760725	−	0.0134136i
$776$		0			0
$777$	−147.342	−	123.634i	−0.189629	−	0.159118i
$778$		0			0
$779$	142.111	−	278.613i	0.182428	−	0.357655i
$780$		0			0
$781$	−93.8797	+	111.881i	−0.120204	+	0.143254i
$782$		0			0
$783$	−0.913920	−	5.18310i	−0.00116720	−	0.00661954i
$784$		0			0
$785$	270.621	+	98.4980i	0.344740	+	0.125475i
$786$		0			0
$787$	419.663	+	242.292i	0.533244	+	0.307868i	0.742336	−	0.670028i	$-0.233718\pi$
$787$	419.663	+	242.292i	0.533244	+	0.307868i	−0.209093	+	0.977896i	$0.567051\pi$
$788$		0			0
$789$	−37.1176	−	44.2350i	−0.0470438	−	0.0560646i
$790$		0			0
$791$	360.196	−	207.959i	0.455368	−	0.262907i
$792$		0			0
$793$	−0.132480	−	0.0233598i	−0.000167062	−	2.94575e-5i
$794$		0			0
$795$	−90.0307	+	32.7685i	−0.113246	+	0.0412182i
$796$		0			0
$797$			325.526i			0.408439i	0.978925	+	0.204220i	$0.0654657\pi$
$797$			325.526i			0.408439i	−0.978925	+	0.204220i	$0.934534\pi$
$798$		0			0
$799$	−710.537			−0.889283
$800$		0			0
$801$	40.4393	+	111.106i	0.0504860	+	0.138709i
$802$		0			0
$803$	−186.280	+	1056.45i	−0.231980	+	1.31563i
$804$		0			0
$805$	−220.698	−	382.260i	−0.274159	−	0.474858i
$806$		0			0
$807$	64.4809	−	54.1059i	0.0799019	−	0.0670457i
$808$		0			0
$809$	758.520	−	1313.79i	0.937601	−	1.62397i	0.167673	−	0.985843i	$-0.446375\pi$
$809$	758.520	−	1313.79i	0.937601	−	1.62397i	0.769928	−	0.638131i	$-0.220292\pi$
$810$		0			0
$811$	−14.1363	+	38.8392i	−0.0174307	+	0.0478906i	−0.948103	−	0.317964i	$-0.897001\pi$
$811$	−14.1363	+	38.8392i	−0.0174307	+	0.0478906i	0.930672	+	0.365854i	$0.119223\pi$
$812$		0			0
$813$	−631.405	+	111.334i	−0.776636	+	0.136942i
$814$		0			0
$815$	40.0951	+	33.6438i	0.0491964	+	0.0412807i
$816$		0			0
$817$	−13.2892	+	8.62201i	−0.0162659	+	0.0105533i
$818$		0			0
$819$	0.319911	−	0.381255i	0.000390612	−	0.000465513i
$820$		0			0
$821$	109.966	+	623.649i	0.133942	+	0.759621i	0.975591	+	0.219596i	$0.0704740\pi$
$821$	109.966	+	623.649i	0.133942	+	0.759621i	−0.841649	+	0.540025i	$0.818415\pi$
$822$		0			0
$823$	740.404	+	269.485i	0.899641	+	0.327442i	0.750109	−	0.661314i	$-0.230001\pi$
$823$	740.404	+	269.485i	0.899641	+	0.327442i	0.149532	+	0.988757i	$0.452223\pi$
$824$		0			0
$825$	257.184	+	148.485i	0.311738	+	0.179982i
$826$		0			0
$827$	390.646	+	465.554i	0.472366	+	0.562943i	0.948642	−	0.316352i	$-0.102458\pi$
$827$	390.646	+	465.554i	0.472366	+	0.562943i	−0.476276	+	0.879296i	$0.658014\pi$
$828$		0			0
$829$	−1132.74	+	653.989i	−1.36639	+	0.788888i	−0.990466	−	0.137760i	$-0.956010\pi$
$829$	−1132.74	+	653.989i	−1.36639	+	0.788888i	−0.375929	+	0.926648i	$0.622676\pi$
$830$		0			0
$831$	603.384	+	106.393i	0.726094	+	0.128030i
$832$		0			0
$833$	187.696	−	68.3156i	0.225325	−	0.0820116i
$834$		0			0
$835$			931.011i			1.11498i
$836$		0			0
$837$	19.5448			0.0233510
$838$		0			0
$839$	−389.356	−	1069.75i	−0.464072	−	1.27503i	−0.922397	−	0.386243i	$-0.873773\pi$
$839$	−389.356	−	1069.75i	−0.464072	−	1.27503i	0.458325	−	0.888785i	$-0.348449\pi$
$840$		0			0
$841$	145.860	−	827.213i	0.173436	−	0.983606i
$842$		0			0
$843$	−372.006	−	644.334i	−0.441289	−	0.764334i
$844$		0			0
$845$	−390.194	+	327.412i	−0.461768	+	0.387470i
$846$		0			0
$847$	−12.3779	+	21.4392i	−0.0146138	+	0.0253119i
$848$		0			0
$849$	−68.0947	+	187.089i	−0.0802057	+	0.220363i
$850$		0			0
$851$	640.224	−	112.889i	0.752320	−	0.132654i
$852$		0			0
$853$	−1115.12	−	935.700i	−1.30730	−	1.09695i	−0.988835	−	0.149016i	$-0.952389\pi$
$853$	−1115.12	−	935.700i	−1.30730	−	1.09695i	−0.318462	−	0.947936i	$-0.603166\pi$
$854$		0			0
$855$	50.2993	−	164.270i	0.0588296	−	0.192128i
$856$		0			0
$857$	770.515	−	918.264i	0.899084	−	1.07149i	−0.0980004	−	0.995186i	$-0.531245\pi$
$857$	770.515	−	918.264i	0.899084	−	1.07149i	0.997085	−	0.0763008i	$-0.0243109\pi$
$858$		0			0
$859$	−5.89180	−	33.4141i	−0.00685891	−	0.0388988i	0.981186	−	0.193064i	$-0.0618424\pi$
$859$	−5.89180	−	33.4141i	−0.00685891	−	0.0388988i	−0.988045	+	0.154165i	$0.950731\pi$
$860$		0			0
$861$	−134.004	−	48.7733i	−0.155637	−	0.0566473i
$862$		0			0
$863$	−634.958	−	366.593i	−0.735756	−	0.424789i	0.0847680	−	0.996401i	$-0.472985\pi$
$863$	−634.958	−	366.593i	−0.735756	−	0.424789i	−0.820524	+	0.571612i	$0.806318\pi$
$864$		0			0
$865$	−19.0245	−	22.6725i	−0.0219936	−	0.0262110i
$866$		0			0
$867$	−329.465	+	190.216i	−0.380005	+	0.219396i
$868$		0			0
$869$	549.975	+	96.9754i	0.632883	+	0.111594i
$870$		0			0
$871$	3.77552	−	1.37418i	0.00433469	−	0.00157770i
$872$		0			0
$873$			123.106i			0.141015i
$874$		0			0
$875$	−616.797			−0.704911
$876$		0			0
$877$	352.371	+	968.131i	0.401791	+	1.10391i	0.961400	+	0.275155i	$0.0887291\pi$
$877$	352.371	+	968.131i	0.401791	+	1.10391i	−0.559609	+	0.828757i	$0.689049\pi$
$878$		0			0
$879$	−113.821	+	645.511i	−0.129489	+	0.734370i
$880$		0			0
$881$	222.214	+	384.886i	0.252230	+	0.436874i	0.964139	−	0.265396i	$-0.0855028\pi$
$881$	222.214	+	384.886i	0.252230	+	0.436874i	−0.711910	+	0.702271i	$0.752170\pi$
$882$		0			0
$883$	950.570	−	797.623i	1.07652	−	0.903310i	0.0808958	−	0.996723i	$-0.474222\pi$
$883$	950.570	−	797.623i	1.07652	−	0.903310i	0.995628	+	0.0934123i	$0.0297775\pi$
$884$		0			0
$885$	−89.8554	+	155.634i	−0.101532	+	0.175858i
$886$		0			0
$887$	350.568	−	963.178i	0.395229	−	1.08588i	−0.569351	−	0.822094i	$-0.692806\pi$
$887$	350.568	−	963.178i	0.395229	−	1.08588i	0.964580	−	0.263789i	$-0.0849722\pi$
$888$		0			0
$889$	−185.590	+	32.7245i	−0.208762	+	0.0368104i
$890$		0			0
$891$	74.2711	+	62.3208i	0.0833570	+	0.0699448i
$892$		0			0
$893$	−1608.88	−	198.246i	−1.80166	−	0.222000i
$894$		0			0
$895$	−416.941	+	496.891i	−0.465856	+	0.555186i
$896$		0			0
$897$	0.292106	+	1.65662i	0.000325648	+	0.00184684i
$898$		0			0
$899$	−3.58007	−	1.30304i	−0.00398228	−	0.00144943i
$900$		0			0
$901$	−132.366	−	76.4216i	−0.146910	−	0.0848187i
$902$		0			0
$903$	4.64269	+	5.53294i	0.00514140	+	0.00612729i
$904$		0			0
$905$	419.494	−	242.195i	0.463530	−	0.267619i
$906$		0			0
$907$	−552.758	−	97.4662i	−0.609436	−	0.107460i	−0.139591	−	0.990209i	$-0.544579\pi$
$907$	−552.758	−	97.4662i	−0.609436	−	0.107460i	−0.469844	+	0.882749i	$0.655690\pi$
$908$		0			0
$909$	111.185	−	40.4680i	0.122316	−	0.0445192i
$910$		0			0
$911$		−	723.369i		−	0.794039i	−0.917810	−	0.397019i	$-0.870045\pi$
$911$		−	723.369i		−	0.794039i	0.917810	−	0.397019i	$-0.129955\pi$
$912$		0			0
$913$	359.356			0.393599
$914$		0			0
$915$	7.24139	+	19.8955i	0.00791408	+	0.0217438i
$916$		0			0
$917$	−122.261	+	693.374i	−0.133327	+	0.756133i
$918$		0			0
$919$	−171.132	−	296.410i	−0.186216	−	0.322535i	0.757770	−	0.652522i	$-0.226289\pi$
$919$	−171.132	−	296.410i	−0.186216	−	0.322535i	−0.943986	+	0.329987i	$0.892956\pi$
$920$		0			0
$921$	−471.324	+	395.487i	−0.511752	+	0.429411i
$922$		0			0
$923$	−0.224845	+	0.389443i	−0.000243602	+	0.000421932i
$924$		0			0
$925$	120.860	−	332.061i	0.130660	−	0.358985i
$926$		0			0
$927$	−491.750	+	86.7087i	−0.530474	+	0.0935369i
$928$		0			0
$929$	−149.899	−	125.780i	−0.161355	−	0.135393i	0.558535	−	0.829481i	$-0.311364\pi$
$929$	−149.899	−	125.780i	−0.161355	−	0.135393i	−0.719890	+	0.694088i	$0.755808\pi$
$930$		0			0
$931$	444.062	−	102.319i	0.476973	−	0.109903i
$932$		0			0
$933$	482.806	−	575.386i	0.517477	−	0.616705i
$934$		0			0
$935$	−46.9550	−	266.295i	−0.0502192	−	0.284807i
$936$		0			0
$937$	−587.183	−	213.717i	−0.626663	−	0.228087i	0.00911542	−	0.999958i	$-0.497098\pi$
$937$	−587.183	−	213.717i	−0.626663	−	0.228087i	−0.635778	+	0.771872i	$0.719321\pi$
$938$		0			0
$939$	524.043	+	302.556i	0.558086	+	0.322211i
$940$		0			0
$941$	505.662	+	602.624i	0.537366	+	0.640408i	0.964595	−	0.263735i	$-0.0849546\pi$
$941$	505.662	+	602.624i	0.537366	+	0.640408i	−0.427229	+	0.904144i	$0.640510\pi$
$942$		0			0
$943$	417.417	−	240.996i	0.442648	−	0.255563i
$944$		0			0
$945$	−77.1409	−	13.6020i	−0.0816305	−	0.0143937i
$946$		0			0
$947$	909.986	−	331.208i	0.960914	−	0.349744i	0.186523	−	0.982451i	$-0.440278\pi$
$947$	909.986	−	331.208i	0.960914	−	0.349744i	0.774392	+	0.632707i	$0.218056\pi$
$948$		0			0
$949$			3.30298i			0.00348048i
$950$		0			0
$951$	256.513			0.269729
$952$		0			0
$953$	−118.803	−	326.408i	−0.124662	−	0.342506i	0.861625	−	0.507545i	$-0.169447\pi$
$953$	−118.803	−	326.408i	−0.124662	−	0.342506i	−0.986287	+	0.165039i	$0.947225\pi$
$954$		0			0
$955$	−102.466	+	581.113i	−0.107294	+	0.608496i
$956$		0			0
$957$	−9.44953	−	16.3671i	−0.00987411	−	0.0171025i
$958$		0			0
$959$	157.627	−	132.265i	0.164366	−	0.137919i
$960$		0			0
$961$	−473.426	+	819.998i	−0.492639	+	0.853276i
$962$		0			0
$963$	−0.915979	+	2.51663i	−0.000951173	+	0.00261333i
$964$		0			0
$965$	−153.595	+	27.0829i	−0.159166	+	0.0280652i
$966$		0			0
$967$	−625.621	−	524.958i	−0.646971	−	0.542873i	0.259179	−	0.965829i	$-0.416548\pi$
$967$	−625.621	−	524.958i	−0.646971	−	0.542873i	−0.906150	+	0.422956i	$0.860992\pi$
$968$		0			0
$969$	252.327	−	106.979i	0.260400	−	0.110401i
$970$		0			0
$971$	1124.55	−	1340.18i	1.15813	−	1.38021i	0.246528	−	0.969136i	$-0.420710\pi$
$971$	1124.55	−	1340.18i	1.15813	−	1.38021i	0.911603	−	0.411072i	$-0.134845\pi$
$972$		0			0
$973$	−149.997	−	850.676i	−0.154160	−	0.874282i
$974$		0			0
$975$	0.859227	+	0.312733i	0.000881258	+	0.000320752i
$976$		0			0
$977$	−1329.25	−	767.440i	−1.36054	−	0.785507i	−0.370842	−	0.928696i	$-0.620931\pi$
$977$	−1329.25	−	767.440i	−1.36054	−	0.785507i	−0.989695	+	0.143189i	$0.954264\pi$
$978$		0			0
$979$	272.911	+	325.243i	0.278765	+	0.332220i
$980$		0			0
$981$	−207.040	+	119.535i	−0.211050	+	0.121850i
$982$		0			0
$983$	−659.318	−	116.256i	−0.670721	−	0.118266i	−0.172091	−	0.985081i	$-0.555052\pi$
$983$	−659.318	−	116.256i	−0.670721	−	0.118266i	−0.498630	+	0.866815i	$0.666163\pi$
$984$		0			0
$985$	586.195	−	213.358i	0.595122	−	0.216607i
$986$		0			0
$987$			739.113i			0.748848i
$988$		0			0
$989$	−24.4124			−0.0246839
$990$		0			0
$991$	−354.092	−	972.859i	−0.357308	−	0.981695i	−0.979960	−	0.199196i	$-0.936167\pi$
$991$	−354.092	−	972.859i	−0.357308	−	0.981695i	0.622652	−	0.782499i	$-0.286055\pi$
$992$		0			0
$993$	155.531	−	882.062i	0.156628	−	0.888280i
$994$		0			0
$995$	−71.3654	−	123.608i	−0.0717240	−	0.124230i
$996$		0			0
$997$	295.307	−	247.792i	0.296196	−	0.248538i	−0.482563	−	0.875861i	$-0.660294\pi$
$997$	295.307	−	247.792i	0.296196	−	0.248538i	0.778759	+	0.627324i	$0.215850\pi$
$998$		0			0
$999$	57.6840	−	99.9115i	0.0577417	−	0.100012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.r.b.193.2	yes	24
19.13	odd	18	inner	228.3.r.b.13.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.r.b.13.2	✓	24	19.13	odd	18	inner
228.3.r.b.193.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.r (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.592396 - 1.62760i) q^{3} +(-0.523375 + 2.96821i) q^{5} +(2.50080 + 4.33150i) q^{7} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+(-0.592396 - 1.62760i) q^{3} +(-0.523375 + 2.96821i) q^{5} +(2.50080 + 4.33150i) q^{7} +(-2.29813 + 1.92836i) q^{9} +(-5.38633 + 9.32941i) q^{11} +(-0.0113445 + 0.0311687i) q^{13} +(5.14109 - 0.906513i) q^{15} +(6.37968 + 5.35319i) q^{17} +(12.9520 + 13.9013i) q^{19} +(5.56847 - 6.63625i) q^{21} +(5.08449 + 28.8356i) q^{23} +(14.9560 + 5.44353i) q^{25} +(4.50000 + 2.59808i) q^{27} +(-0.651064 - 0.775908i) q^{29} +(3.25746 - 1.88070i) q^{31} +(18.3753 + 3.24007i) q^{33} +(-14.1657 + 5.15588i) q^{35} -22.2026i q^{37} +0.0574504 q^{39} +(-5.63007 - 15.4685i) q^{41} +(-0.144778 + 0.821079i) q^{43} +(-4.52100 - 7.83060i) q^{45} +(-65.3576 + 54.8415i) q^{47} +(11.9920 - 20.7708i) q^{49} +(4.93353 - 13.5547i) q^{51} +(-18.0739 + 3.18692i) q^{53} +(-24.8725 - 20.8705i) q^{55} +(14.9529 - 29.3157i) q^{57} +(-22.1278 + 26.3709i) q^{59} +(0.704266 + 3.99409i) q^{61} +(-14.0999 - 5.13193i) q^{63} +(-0.0865777 - 0.0499857i) q^{65} +(-77.8620 - 92.7924i) q^{67} +(43.9207 - 25.3576i) q^{69} +(13.3516 + 2.35424i) q^{71} +(93.5748 - 34.0584i) q^{73} -27.5670i q^{75} -53.8805 q^{77} +(-17.7305 - 48.7140i) q^{79} +(1.56283 - 8.86327i) q^{81} +(-16.6791 - 28.8890i) q^{83} +(-19.2283 + 16.1345i) q^{85} +(-0.877176 + 1.51931i) q^{87} +(13.4798 - 37.0354i) q^{89} +(-0.163377 + 0.0288078i) q^{91} +(-4.99073 - 4.18772i) q^{93} +(-48.0407 + 31.1687i) q^{95} +(26.3770 - 31.4348i) q^{97} +(-5.61196 - 31.8270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7}+O(q^{10}) \) 24 * q - 9 * q^7	\( 24 q - 9 q^{7} + 15 q^{11} - 9 q^{13} - 18 q^{15} + 18 q^{17} + 33 q^{19} + 18 q^{21} - 21 q^{23} - 18 q^{25} + 108 q^{27} + 30 q^{29} + 216 q^{31} - 63 q^{33} + 30 q^{35} + 18 q^{39} - 54 q^{41} - 189 q^{43} - 9 q^{45} - 321 q^{47} - 225 q^{49} + 63 q^{51} + 138 q^{53} + 309 q^{55} - 45 q^{57} - 30 q^{59} - 105 q^{61} - 27 q^{63} + 99 q^{65} + 207 q^{67} + 108 q^{69} + 144 q^{71} - 72 q^{73} - 36 q^{77} - 282 q^{79} - 531 q^{83} - 909 q^{85} - 135 q^{87} - 411 q^{89} + 444 q^{91} + 126 q^{93} - 24 q^{95} + 405 q^{97} - 117 q^{99}+O(q^{100}) \) 24 * q - 9 * q^7 + 15 * q^11 - 9 * q^13 - 18 * q^15 + 18 * q^17 + 33 * q^19 + 18 * q^21 - 21 * q^23 - 18 * q^25 + 108 * q^27 + 30 * q^29 + 216 * q^31 - 63 * q^33 + 30 * q^35 + 18 * q^39 - 54 * q^41 - 189 * q^43 - 9 * q^45 - 321 * q^47 - 225 * q^49 + 63 * q^51 + 138 * q^53 + 309 * q^55 - 45 * q^57 - 30 * q^59 - 105 * q^61 - 27 * q^63 + 99 * q^65 + 207 * q^67 + 108 * q^69 + 144 * q^71 - 72 * q^73 - 36 * q^77 - 282 * q^79 - 531 * q^83 - 909 * q^85 - 135 * q^87 - 411 * q^89 + 444 * q^91 + 126 * q^93 - 24 * q^95 + 405 * q^97 - 117 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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