LMFDB - Embedded newform 144.4.i.e.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("144.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, not 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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5206055409.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + 9x^{5} - 23x^{4} + 27x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + 9x^5 - 23x^4 + 27x^3 + 9x^2 - 81x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.3
Root			$0.172469 - 1.72344i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.4.i.e.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.78092 - 4.38936i) q^{3} +(-8.65944 - 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +(-11.5330 - 24.4129i) q^{9} +(-26.1082 + 45.2208i) q^{11} +(-6.84965 - 11.8639i) q^{13} +(-89.9154 - 3.70048i) q^{15} -82.9217 q^{17} +126.803 q^{19} +(5.72218 + 10.9254i) q^{21} +(-27.1831 - 47.0825i) q^{23} +(-87.4718 + 151.506i) q^{25} +(-139.229 - 17.2680i) q^{27} +(106.425 - 184.334i) q^{29} +(-112.061 - 194.095i) q^{31} +(125.885 + 240.354i) q^{33} +41.1068 q^{35} -32.2229 q^{37} +(-71.1234 - 2.92709i) q^{39} +(-250.331 - 433.586i) q^{41} +(-6.41270 + 11.1071i) q^{43} +(-266.290 + 384.380i) q^{45} +(104.770 - 181.467i) q^{47} +(168.683 + 292.168i) q^{49} +(-230.599 + 363.973i) q^{51} +371.213 q^{53} +904.331 q^{55} +(352.629 - 556.584i) q^{57} +(2.90924 + 5.03895i) q^{59} +(302.016 - 523.107i) q^{61} +(63.8685 + 5.26595i) q^{63} +(-118.628 + 205.470i) q^{65} +(377.033 + 653.040i) q^{67} +(-282.256 - 11.6163i) q^{69} -43.4780 q^{71} +671.029 q^{73} +(421.761 + 805.270i) q^{75} +(-61.9686 - 107.333i) q^{77} +(-324.601 + 562.226i) q^{79} +(-462.981 + 563.107i) q^{81} +(67.2629 - 116.503i) q^{83} +(718.056 + 1243.71i) q^{85} +(-513.148 - 979.757i) q^{87} -206.076 q^{89} +32.5156 q^{91} +(-1163.59 - 47.8876i) q^{93} +(-1098.04 - 1901.87i) q^{95} +(726.420 - 1258.20i) q^{97} +(1405.08 + 115.848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 5 q^{5} - 3 q^{7} - 15 q^{9} - 16 q^{11} + 29 q^{13} - 141 q^{15} - 34 q^{17} + 218 q^{19} + 27 q^{21} - 37 q^{23} + 97 q^{25} + 216 q^{27} - 3 q^{29} - 331 q^{31} + 468 q^{33} + 342 q^{35}+ \cdots + 5133 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 5 * q^5 - 3 * q^7 - 15 * q^9 - 16 * q^11 + 29 * q^13 - 141 * q^15 - 34 * q^17 + 218 * q^19 + 27 * q^21 - 37 * q^23 + 97 * q^25 + 216 * q^27 - 3 * q^29 - 331 * q^31 + 468 * q^33 + 342 * q^35 - 732 * q^37 + 375 * q^39 - 378 * q^41 - 506 * q^43 - 993 * q^45 - 171 * q^47 + 829 * q^49 - 2193 * q^51 + 820 * q^53 + 2326 * q^55 + 507 * q^57 - 616 * q^59 + 1331 * q^61 + 1899 * q^63 - 815 * q^65 - 1162 * q^67 + 1113 * q^69 + 688 * q^71 - 2614 * q^73 + 1755 * q^75 - 741 * q^77 - 1853 * q^79 - 2547 * q^81 - 1421 * q^83 + 2074 * q^85 - 5877 * q^87 + 1632 * q^89 + 3990 * q^91 + 537 * q^93 - 1292 * q^95 + 2506 * q^97 + 5133 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	2.78092	−	4.38936i	0.535188	−	0.844733i
$3$	2.78092	−	4.38936i	0.535188	−	0.844733i
$4$		0			0
$5$	−8.65944	−	14.9986i	−0.774524	−	1.34151i	−0.935062	−	0.354485i	$-0.884656\pi$
$5$	−8.65944	−	14.9986i	−0.774524	−	1.34151i	0.160538	−	0.987030i	$-0.448677\pi$
$6$		0			0
$7$	−1.18676	+	2.05553i	−0.0640792	+	0.110988i	−0.896285	−	0.443478i	$-0.853744\pi$
$7$	−1.18676	+	2.05553i	−0.0640792	+	0.110988i	0.832206	+	0.554467i	$0.187078\pi$
$8$		0			0
$9$	−11.5330	−	24.4129i	−0.427147	−	0.904182i
$10$		0			0
$11$	−26.1082	+	45.2208i	−0.715630	+	1.23951i	0.247086	+	0.968994i	$0.420527\pi$
$11$	−26.1082	+	45.2208i	−0.715630	+	1.23951i	−0.962716	+	0.270514i	$0.912806\pi$
$12$		0			0
$13$	−6.84965	−	11.8639i	−0.146135	−	0.253113i	0.783661	−	0.621189i	$-0.213350\pi$
$13$	−6.84965	−	11.8639i	−0.146135	−	0.253113i	−0.929796	+	0.368076i	$0.880017\pi$
$14$		0			0
$15$	−89.9154	−	3.70048i	−1.54774	−	0.0636973i
$16$		0			0
$17$	−82.9217			−1.18303			−0.591514	−	0.806295i	$-0.701469\pi$
$17$	−82.9217			−1.18303			−0.591514	+	0.806295i	$0.701469\pi$
$18$		0			0
$19$	126.803			1.53108			0.765542	−	0.643386i	$-0.222471\pi$
$19$	126.803			1.53108			0.765542	+	0.643386i	$0.222471\pi$
$20$		0			0
$21$	5.72218	+	10.9254i	0.0594611	+	0.113529i
$22$		0			0
$23$	−27.1831	−	47.0825i	−0.246437	−	0.426842i	0.716097	−	0.698000i	$-0.245927\pi$
$23$	−27.1831	−	47.0825i	−0.246437	−	0.426842i	−0.962535	+	0.271158i	$0.912593\pi$
$24$		0			0
$25$	−87.4718	+	151.506i	−0.699775	+	1.21205i
$26$		0			0
$27$	−139.229	−	17.2680i	−0.992396	−	0.123083i
$28$		0			0
$29$	106.425	−	184.334i	0.681471	−	1.18034i	−0.293060	−	0.956094i	$-0.594674\pi$
$29$	106.425	−	184.334i	0.681471	−	1.18034i	0.974532	−	0.224249i	$-0.0719929\pi$
$30$		0			0
$31$	−112.061	−	194.095i	−0.649250	−	1.12453i	−0.983302	−	0.181980i	$-0.941749\pi$
$31$	−112.061	−	194.095i	−0.649250	−	1.12453i	0.334052	−	0.942555i	$-0.391584\pi$
$32$		0			0
$33$	125.885	+	240.354i	0.664056	+	1.26789i
$34$		0			0
$35$	41.1068			0.198523
$36$		0			0
$37$	−32.2229			−0.143173			−0.0715866	−	0.997434i	$-0.522806\pi$
$37$	−32.2229			−0.143173			−0.0715866	+	0.997434i	$0.522806\pi$
$38$		0			0
$39$	−71.1234	−	2.92709i	−0.292022	−	0.0120182i
$40$		0			0
$41$	−250.331	−	433.586i	−0.953540	−	1.65158i	−0.737673	−	0.675158i	$-0.764076\pi$
$41$	−250.331	−	433.586i	−0.953540	−	1.65158i	−0.215867	−	0.976423i	$-0.569258\pi$
$42$		0			0
$43$	−6.41270	+	11.1071i	−0.0227425	+	0.0393912i	−0.877173	−	0.480175i	$-0.840573\pi$
$43$	−6.41270	+	11.1071i	−0.0227425	+	0.0393912i	0.854430	+	0.519566i	$0.173906\pi$
$44$		0			0
$45$	−266.290	+	384.380i	−0.882138	+	1.27333i
$46$		0			0
$47$	104.770	−	181.467i	0.325156	−	0.563186i	−0.656388	−	0.754423i	$-0.727917\pi$
$47$	104.770	−	181.467i	0.325156	−	0.563186i	0.981544	+	0.191237i	$0.0612500\pi$
$48$		0			0
$49$	168.683	+	292.168i	0.491788	+	0.851801i
$50$		0			0
$51$	−230.599	+	363.973i	−0.633143	+	0.999342i
$52$		0			0
$53$	371.213			0.962075			0.481038	−	0.876700i	$-0.340260\pi$
$53$	371.213			0.962075			0.481038	+	0.876700i	$0.340260\pi$
$54$		0			0
$55$	904.331			2.21709
$56$		0			0
$57$	352.629	−	556.584i	0.819418	−	1.29336i
$58$		0			0
$59$	2.90924	+	5.03895i	0.00641950	+	0.0111189i	0.869217	−	0.494430i	$-0.164623\pi$
$59$	2.90924	+	5.03895i	0.00641950	+	0.0111189i	−0.862798	+	0.505549i	$0.831290\pi$
$60$		0			0
$61$	302.016	−	523.107i	0.633921	−	1.09798i	−0.352822	−	0.935691i	$-0.614778\pi$
$61$	302.016	−	523.107i	0.633921	−	1.09798i	0.986743	−	0.162293i	$-0.0518889\pi$
$62$		0			0
$63$	63.8685	+	5.26595i	0.127725	+	0.0105309i
$64$		0			0
$65$	−118.628	+	205.470i	−0.226370	+	0.392083i
$66$		0			0
$67$	377.033	+	653.040i	0.687491	+	1.19077i	0.972647	+	0.232288i	$0.0746213\pi$
$67$	377.033	+	653.040i	0.687491	+	1.19077i	−0.285156	+	0.958481i	$0.592045\pi$
$68$		0			0
$69$	−282.256	−	11.6163i	−0.492458	−	0.0202672i
$70$		0			0
$71$	−43.4780			−0.0726744			−0.0363372	−	0.999340i	$-0.511569\pi$
$71$	−43.4780			−0.0726744			−0.0363372	+	0.999340i	$0.511569\pi$
$72$		0			0
$73$	671.029			1.07586			0.537931	−	0.842989i	$-0.319206\pi$
$73$	671.029			1.07586			0.537931	+	0.842989i	$0.319206\pi$
$74$		0			0
$75$	421.761	+	805.270i	0.649343	+	1.23979i
$76$		0			0
$77$	−61.9686	−	107.333i	−0.0917139	−	0.158853i
$78$		0			0
$79$	−324.601	+	562.226i	−0.462284	+	0.800700i	−0.999074	−	0.0430157i	$-0.986303\pi$
$79$	−324.601	+	562.226i	−0.462284	+	0.800700i	0.536790	+	0.843716i	$0.319637\pi$
$80$		0			0
$81$	−462.981	+	563.107i	−0.635091	+	0.772437i
$82$		0			0
$83$	67.2629	−	116.503i	0.0889526	−	0.154070i	−0.818116	−	0.575053i	$-0.804981\pi$
$83$	67.2629	−	116.503i	0.0889526	−	0.154070i	0.907069	+	0.420983i	$0.138315\pi$
$84$		0			0
$85$	718.056	+	1243.71i	0.916283	+	1.58705i
$86$		0			0
$87$	−513.148	−	979.757i	−0.632359	−	1.20737i
$88$		0			0
$89$	−206.076			−0.245439			−0.122719	−	0.992441i	$-0.539162\pi$
$89$	−206.076			−0.245439			−0.122719	+	0.992441i	$0.539162\pi$
$90$		0			0
$91$	32.5156			0.0374567
$92$		0			0
$93$	−1163.59	−	47.8876i	−1.29740	−	0.0533947i
$94$		0			0
$95$	−1098.04	−	1901.87i	−1.18586	−	2.05397i
$96$		0			0
$97$	726.420	−	1258.20i	0.760379	−	1.31702i	−0.182276	−	0.983247i	$-0.558347\pi$
$97$	726.420	−	1258.20i	0.760379	−	1.31702i	0.942655	−	0.333768i	$-0.108320\pi$
$98$		0			0
$99$	1405.08	+	115.848i	1.42642	+	0.117608i
$100$		0			0
$101$	−101.980	+	176.634i	−0.100469	+	0.174017i	−0.911878	−	0.410461i	$-0.865368\pi$
$101$	−101.980	+	176.634i	−0.100469	+	0.174017i	0.811409	+	0.584479i	$0.198701\pi$
$102$		0			0
$103$	−777.773	−	1347.14i	−0.744042	−	1.28872i	−0.950641	−	0.310292i	$-0.899573\pi$
$103$	−777.773	−	1347.14i	−0.744042	−	1.28872i	0.206600	−	0.978426i	$-0.433760\pi$
$104$		0			0
$105$	114.315	−	180.433i	0.106247	−	0.167699i
$106$		0			0
$107$	584.436			0.528033			0.264016	−	0.964518i	$-0.414953\pi$
$107$	584.436			0.528033			0.264016	+	0.964518i	$0.414953\pi$
$108$		0			0
$109$	−782.671			−0.687764			−0.343882	−	0.939013i	$-0.611742\pi$
$109$	−782.671			−0.687764			−0.343882	+	0.939013i	$0.611742\pi$
$110$		0			0
$111$	−89.6093	+	141.438i	−0.0766247	+	0.120943i
$112$		0			0
$113$	435.124	+	753.658i	0.362239	+	0.627417i	0.988329	−	0.152334i	$-0.0486789\pi$
$113$	435.124	+	753.658i	0.362239	+	0.627417i	−0.626090	+	0.779751i	$0.715346\pi$
$114$		0			0
$115$	−470.780	+	815.415i	−0.381743	+	0.661199i
$116$		0			0
$117$	−210.637	+	304.046i	−0.166439	+	0.240249i
$118$		0			0
$119$	98.4084	−	170.448i	0.0758074	−	0.131302i
$120$		0			0
$121$	−697.780	−	1208.59i	−0.524253	−	0.908032i
$122$		0			0
$123$	−2599.32	−	106.975i	−1.90547	−	0.0784198i
$124$		0			0
$125$	864.968			0.618921
$126$		0			0
$127$	−994.050			−0.694548			−0.347274	−	0.937764i	$-0.612893\pi$
$127$	−994.050			−0.694548			−0.347274	+	0.937764i	$0.612893\pi$
$128$		0			0
$129$	30.9200	+	59.0357i	0.0211035	+	0.0402930i
$130$		0			0
$131$	−401.039	−	694.620i	−0.267473	−	0.463277i	0.700736	−	0.713421i	$-0.252855\pi$
$131$	−401.039	−	694.620i	−0.267473	−	0.463277i	−0.968209	+	0.250144i	$0.919522\pi$
$132$		0			0
$133$	−150.485	+	260.648i	−0.0981106	+	0.169933i
$134$		0			0
$135$	946.652	+	2237.78i	0.603517	+	1.42664i
$136$		0			0
$137$	−659.936	+	1143.04i	−0.411548	+	0.712822i	−0.995059	−	0.0992828i	$-0.968345\pi$
$137$	−659.936	+	1143.04i	−0.411548	+	0.712822i	0.583511	+	0.812105i	$0.301678\pi$
$138$		0			0
$139$	263.397	+	456.216i	0.160727	+	0.278387i	0.935130	−	0.354306i	$-0.115283\pi$
$139$	263.397	+	456.216i	0.160727	+	0.278387i	−0.774403	+	0.632693i	$0.781950\pi$
$140$		0			0
$141$	−505.168	−	964.521i	−0.301722	−	0.576080i
$142$		0			0
$143$	715.329			0.418313
$144$		0			0
$145$	−3686.33			−2.11126
$146$		0			0
$147$	1751.52	+	72.0842i	0.982744	+	0.0404449i
$148$		0			0
$149$	−1538.88	−	2665.41i	−0.846105	−	1.46550i	−0.884659	−	0.466239i	$-0.845609\pi$
$149$	−1538.88	−	2665.41i	−0.846105	−	1.46550i	0.0385540	−	0.999257i	$-0.487725\pi$
$150$		0			0
$151$	41.0954	−	71.1794i	0.0221477	−	0.0383609i	−0.854739	−	0.519058i	$-0.826283\pi$
$151$	41.0954	−	71.1794i	0.0221477	−	0.0383609i	0.876887	+	0.480697i	$0.159616\pi$
$152$		0			0
$153$	956.333	+	2024.36i	0.505327	+	1.06967i
$154$		0			0
$155$	−1940.77	+	3361.52i	−1.00572	+	1.74196i
$156$		0			0
$157$	1192.09	+	2064.76i	0.605981	+	1.04959i	0.991896	+	0.127055i	$0.0405526\pi$
$157$	1192.09	+	2064.76i	0.605981	+	1.04959i	−0.385915	+	0.922534i	$0.626114\pi$
$158$		0			0
$159$	1032.31	−	1629.39i	0.514891	−	0.812696i
$160$		0			0
$161$	129.039			0.0631660
$162$		0			0
$163$	−1226.77			−0.589496			−0.294748	−	0.955575i	$-0.595236\pi$
$163$	−1226.77			−0.589496			−0.294748	+	0.955575i	$0.595236\pi$
$164$		0			0
$165$	2514.87	−	3969.43i	1.18656	−	1.87285i
$166$		0			0
$167$	1948.20	+	3374.38i	0.902733	+	1.56358i	0.823932	+	0.566689i	$0.191776\pi$
$167$	1948.20	+	3374.38i	0.902733	+	1.56358i	0.0788009	+	0.996890i	$0.474891\pi$
$168$		0			0
$169$	1004.66	−	1740.13i	0.457289	−	0.792048i
$170$		0			0
$171$	−1462.41	−	3095.63i	−0.653998	−	1.38438i
$172$		0			0
$173$	−73.2019	+	126.789i	−0.0321701	+	0.0557203i	−0.881662	−	0.471881i	$-0.843575\pi$
$173$	−73.2019	+	126.789i	−0.0321701	+	0.0557203i	0.849492	+	0.527601i	$0.176909\pi$
$174$		0			0
$175$	−207.617	−	359.602i	−0.0896819	−	0.155334i
$176$		0			0
$177$	30.2081	+	1.24322i	0.0128282	+	0.000527944i
$178$		0			0
$179$	1540.84			0.643396			0.321698	−	0.946842i	$-0.395746\pi$
$179$	1540.84			0.643396			0.321698	+	0.946842i	$0.395746\pi$
$180$		0			0
$181$	1173.94			0.482090			0.241045	−	0.970514i	$-0.422510\pi$
$181$	1173.94			0.482090			0.241045	+	0.970514i	$0.422510\pi$
$182$		0			0
$183$	−1456.22	−	2780.38i	−0.588235	−	1.12312i
$184$		0			0
$185$	279.032	+	483.298i	0.110891	+	0.192069i
$186$		0			0
$187$	2164.94	−	3749.79i	0.846610	−	1.46637i
$188$		0			0
$189$	200.727	−	265.698i	0.0772527	−	0.102257i
$190$		0			0
$191$	−1096.82	+	1899.74i	−0.415513	+	0.719689i	−0.995482	−	0.0949489i	$-0.969731\pi$
$191$	−1096.82	+	1899.74i	−0.415513	+	0.719689i	0.579969	+	0.814638i	$0.303065\pi$
$192$		0			0
$193$	−1231.66	−	2133.29i	−0.459360	−	0.795635i	0.539567	−	0.841943i	$-0.318588\pi$
$193$	−1231.66	−	2133.29i	−0.459360	−	0.795635i	−0.998927	+	0.0463073i	$0.985255\pi$
$194$		0			0
$195$	571.987	+	1092.10i	0.210055	+	0.401060i
$196$		0			0
$197$	3593.52			1.29963			0.649816	−	0.760091i	$-0.274846\pi$
$197$	3593.52			1.29963			0.649816	+	0.760091i	$0.274846\pi$
$198$		0			0
$199$	4599.36			1.63839			0.819197	−	0.573513i	$-0.194420\pi$
$199$	4599.36			1.63839			0.819197	+	0.573513i	$0.194420\pi$
$200$		0			0
$201$	3914.93	+	161.119i	1.37382	+	0.0565397i
$202$		0			0
$203$	252.603	+	437.521i	0.0873362	+	0.151271i
$204$		0			0
$205$	−4335.46	+	7509.23i	−1.47708	+	2.55838i
$206$		0			0
$207$	−835.919	+	1206.62i	−0.280678	+	0.405149i
$208$		0			0
$209$	−3310.60	+	5734.13i	−1.09569	+	1.89779i
$210$		0			0
$211$	−1166.12	−	2019.78i	−0.380469	−	0.658992i	0.610660	−	0.791893i	$-0.290904\pi$
$211$	−1166.12	−	2019.78i	−0.380469	−	0.658992i	−0.991129	+	0.132901i	$0.957571\pi$
$212$		0			0
$213$	−120.909	+	190.840i	−0.0388945	+	0.0613905i
$214$		0			0
$215$	222.122			0.0704584
$216$		0			0
$217$	531.959			0.166414
$218$		0			0
$219$	1866.08	−	2945.39i	0.575789	−	0.908816i
$220$		0			0
$221$	567.984	+	983.778i	0.172881	+	0.299439i
$222$		0			0
$223$	−2028.55	+	3513.55i	−0.609156	+	1.05509i	0.382224	+	0.924070i	$0.375158\pi$
$223$	−2028.55	+	3513.55i	−0.609156	+	1.05509i	−0.991380	+	0.131019i	$0.958175\pi$
$224$		0			0
$225$	4707.50	+	388.133i	1.39482	+	0.115002i
$226$		0			0
$227$	648.626	−	1123.45i	0.189651	−	0.328486i	−0.755483	−	0.655169i	$-0.772598\pi$
$227$	648.626	−	1123.45i	0.189651	−	0.328486i	0.945134	+	0.326683i	$0.105931\pi$
$228$		0			0
$229$	−1555.98	−	2695.04i	−0.449005	−	0.777699i	0.549317	−	0.835614i	$-0.314888\pi$
$229$	−1555.98	−	2695.04i	−0.449005	−	0.777699i	−0.998322	+	0.0579149i	$0.981555\pi$
$230$		0			0
$231$	−643.452	−	26.4813i	−0.183273	−	0.00754261i
$232$		0			0
$233$	2034.74			0.572103			0.286052	−	0.958214i	$-0.407657\pi$
$233$	2034.74			0.572103			0.286052	+	0.958214i	$0.407657\pi$
$234$		0			0
$235$	−3629.01			−1.00736
$236$		0			0
$237$	1565.12	+	2988.30i	0.428968	+	0.819032i
$238$		0			0
$239$	734.229	+	1271.72i	0.198717	+	0.344188i	0.948113	−	0.317935i	$-0.102989\pi$
$239$	734.229	+	1271.72i	0.198717	+	0.344188i	−0.749396	+	0.662122i	$0.769656\pi$
$240$		0			0
$241$	−329.582	+	570.852i	−0.0880922	+	0.152580i	−0.906705	−	0.421766i	$-0.861410\pi$
$241$	−329.582	+	570.852i	−0.0880922	+	0.152580i	0.818612	+	0.574346i	$0.194744\pi$
$242$		0			0
$243$	1184.16	+	3598.15i	0.312610	+	0.949882i
$244$		0			0
$245$	2921.40	−	5060.02i	0.761803	−	1.31948i
$246$		0			0
$247$	−868.555	−	1504.38i	−0.223744	−	0.387537i
$248$		0			0
$249$	−324.320	−	619.226i	−0.0825419	−	0.157598i
$250$		0			0
$251$	5509.13			1.38539			0.692696	−	0.721230i	$-0.256423\pi$
$251$	5509.13			1.38539			0.692696	+	0.721230i	$0.256423\pi$
$252$		0			0
$253$	2838.81			0.705432
$254$		0			0
$255$	7455.94	+	306.850i	1.83102	+	0.0753557i
$256$		0			0
$257$	−1833.82	−	3176.26i	−0.445098	−	0.770933i	0.552961	−	0.833207i	$-0.313498\pi$
$257$	−1833.82	−	3176.26i	−0.445098	−	0.770933i	−0.998059	+	0.0622742i	$0.980165\pi$
$258$		0			0
$259$	38.2409	−	66.2352i	0.00917443	−	0.0158906i
$260$		0			0
$261$	−5727.53	−	472.234i	−1.35833	−	0.111994i
$262$		0			0
$263$	−2496.38	+	4323.86i	−0.585299	+	1.01377i	0.409539	+	0.912292i	$0.365689\pi$
$263$	−2496.38	+	4323.86i	−0.585299	+	1.01377i	−0.994838	+	0.101475i	$0.967644\pi$
$264$		0			0
$265$	−3214.49	−	5567.67i	−0.745150	−	1.29064i
$266$		0			0
$267$	−573.082	+	904.544i	−0.131356	+	0.207330i
$268$		0			0
$269$	88.5142			0.0200625			0.0100312	−	0.999950i	$-0.496807\pi$
$269$	88.5142			0.0200625			0.0100312	+	0.999950i	$0.496807\pi$
$270$		0			0
$271$	−5226.56			−1.17155			−0.585777	−	0.810472i	$-0.699211\pi$
$271$	−5226.56			−1.17155			−0.585777	+	0.810472i	$0.699211\pi$
$272$		0			0
$273$	90.4233	−	142.723i	0.0200464	−	0.0316409i
$274$		0			0
$275$	−4567.47	−	7911.09i	−1.00156	−	1.73475i
$276$		0			0
$277$	1056.13	−	1829.26i	0.229085	−	0.396787i	−0.728452	−	0.685097i	$-0.759760\pi$
$277$	1056.13	−	1829.26i	0.229085	−	0.396787i	0.957537	+	0.288310i	$0.0930933\pi$
$278$		0			0
$279$	−3446.04	+	4974.23i	−0.739459	+	1.06738i
$280$		0			0
$281$	−862.569	+	1494.01i	−0.183120	+	0.317172i	−0.942941	−	0.332959i	$-0.891953\pi$
$281$	−862.569	+	1494.01i	−0.183120	+	0.317172i	0.759822	+	0.650131i	$0.225286\pi$
$282$		0			0
$283$	1670.90	+	2894.08i	0.350970	+	0.607898i	0.986420	−	0.164244i	$-0.0525186\pi$
$283$	1670.90	+	2894.08i	0.350970	+	0.607898i	−0.635450	+	0.772142i	$0.719185\pi$
$284$		0			0
$285$	−11401.5	−	469.232i	−2.36972	−	0.0975260i
$286$		0			0
$287$	1188.33			0.244408
$288$		0			0
$289$	1963.01			0.399554
$290$		0			0
$291$	−3502.56	−	6687.46i	−0.705580	−	1.34717i
$292$		0			0
$293$	2629.21	+	4553.92i	0.524232	+	0.907997i	0.999602	+	0.0282107i	$0.00898093\pi$
$293$	2629.21	+	4553.92i	0.524232	+	0.907997i	−0.475370	+	0.879786i	$0.657686\pi$
$294$		0			0
$295$	50.3848	−	87.2690i	0.00994412	−	0.0172237i
$296$		0			0
$297$	4415.91	−	5845.22i	0.862751	−	1.14200i
$298$		0			0
$299$	−372.389	+	644.996i	−0.0720261	+	0.124753i
$300$		0			0
$301$	−15.2207	−	26.3630i	−0.00291464	−	0.00504831i
$302$		0			0
$303$	491.714	+	938.832i	0.0932284	+	0.178002i
$304$		0			0
$305$	−10461.2			−1.96395
$306$		0			0
$307$	−2582.56			−0.480112			−0.240056	−	0.970759i	$-0.577166\pi$
$307$	−2582.56			−0.480112			−0.240056	+	0.970759i	$0.577166\pi$
$308$		0			0
$309$	−8076.02	−	332.370i	−1.48682	−	0.0611905i
$310$		0			0
$311$	−2544.26	−	4406.79i	−0.463897	−	0.803493i	0.535254	−	0.844691i	$-0.320216\pi$
$311$	−2544.26	−	4406.79i	−0.463897	−	0.803493i	−0.999151	+	0.0411980i	$0.986883\pi$
$312$		0			0
$313$	1465.53	−	2538.38i	0.264654	−	0.458395i	−0.702819	−	0.711369i	$-0.748076\pi$
$313$	1465.53	−	2538.38i	0.264654	−	0.458395i	0.967473	+	0.252974i	$0.0814088\pi$
$314$		0			0
$315$	−474.083	−	1003.54i	−0.0847986	−	0.179501i
$316$		0			0
$317$	−1799.78	+	3117.32i	−0.318883	+	0.552322i	−0.980255	−	0.197736i	$-0.936641\pi$
$317$	−1799.78	+	3117.32i	−0.318883	+	0.552322i	0.661372	+	0.750058i	$0.269974\pi$
$318$		0			0
$319$	5557.15	+	9625.27i	0.975363	+	1.68938i
$320$		0			0
$321$	1625.27	−	2565.30i	0.282597	−	0.446047i
$322$		0			0
$323$	−10514.7			−1.81131
$324$		0			0
$325$	2396.60			0.409045
$326$		0			0
$327$	−2176.55	+	3435.42i	−0.368083	+	0.580977i
$328$		0			0
$329$	248.675	+	430.718i	0.0416714	+	0.0721770i
$330$		0			0
$331$	1838.91	−	3185.08i	0.305364	−	0.528905i	−0.671979	−	0.740571i	$-0.734555\pi$
$331$	1838.91	−	3185.08i	0.305364	−	0.528905i	0.977342	+	0.211665i	$0.0678886\pi$
$332$		0			0
$333$	371.626	+	786.655i	0.0611560	+	0.129455i
$334$		0			0
$335$	6529.79	−	11309.9i	1.06496	−	1.84456i
$336$		0			0
$337$	2778.02	+	4811.67i	0.449046	+	0.777770i	0.998324	−	0.0578696i	$-0.0184308\pi$
$337$	2778.02	+	4811.67i	0.449046	+	0.777770i	−0.549279	+	0.835639i	$0.685097\pi$
$338$		0			0
$339$	4518.12	+	185.944i	0.723866	+	0.0297908i
$340$		0			0
$341$	11702.9			1.85849
$342$		0			0
$343$	−1614.87			−0.254212
$344$		0			0
$345$	2269.95	+	4334.03i	0.354232	+	0.676337i
$346$		0			0
$347$	−1534.56	−	2657.94i	−0.237405	−	0.411198i	0.722564	−	0.691304i	$-0.242964\pi$
$347$	−1534.56	−	2657.94i	−0.237405	−	0.411198i	−0.959969	+	0.280106i	$0.909630\pi$
$348$		0			0
$349$	595.716	−	1031.81i	0.0913694	−	0.158256i	−0.816718	−	0.577037i	$-0.804209\pi$
$349$	595.716	−	1031.81i	0.0913694	−	0.158256i	0.908088	+	0.418780i	$0.137542\pi$
$350$		0			0
$351$	748.805	+	1770.09i	0.113870	+	0.269175i
$352$		0			0
$353$	−3215.50	+	5569.41i	−0.484827	+	0.839745i	−0.999848	−	0.0174329i	$-0.994451\pi$
$353$	−3215.50	+	5569.41i	−0.484827	+	0.839745i	0.515021	+	0.857177i	$0.327784\pi$
$354$		0			0
$355$	376.495	+	652.108i	0.0562881	+	0.0974938i
$356$		0			0
$357$	−474.493	−	905.953i	−0.0703441	−	0.134308i
$358$		0			0
$359$	−4236.73			−0.622858			−0.311429	−	0.950270i	$-0.600808\pi$
$359$	−4236.73			−0.622858			−0.311429	+	0.950270i	$0.600808\pi$
$360$		0			0
$361$	9219.99			1.34422
$362$		0			0
$363$	−7245.41	−	298.186i	−1.04762	−	0.0431149i
$364$		0			0
$365$	−5810.73	−	10064.5i	−0.833281	−	1.44329i
$366$		0			0
$367$	3686.39	−	6385.02i	0.524327	−	0.908161i	−0.475272	−	0.879839i	$-0.657650\pi$
$367$	3686.39	−	6385.02i	0.524327	−	0.908161i	0.999599	−	0.0283220i	$-0.00901638\pi$
$368$		0			0
$369$	−7698.05	+	11111.9i	−1.08603	+	1.56764i
$370$		0			0
$371$	−440.541	+	763.040i	−0.0616490	+	0.106779i
$372$		0			0
$373$	5992.51	+	10379.3i	0.831852	+	1.44081i	0.896568	+	0.442905i	$0.146052\pi$
$373$	5992.51	+	10379.3i	0.831852	+	1.44081i	−0.0647168	+	0.997904i	$0.520614\pi$
$374$		0			0
$375$	2405.41	−	3796.66i	0.331239	−	0.522823i
$376$		0			0
$377$	−2915.90			−0.398346
$378$		0			0
$379$	3872.02			0.524782			0.262391	−	0.964962i	$-0.415489\pi$
$379$	3872.02			0.524782			0.262391	+	0.964962i	$0.415489\pi$
$380$		0			0
$381$	−2764.37	+	4363.24i	−0.371714	+	0.586708i
$382$		0			0
$383$	3621.33	+	6272.33i	0.483137	+	0.836818i	0.999813	−	0.0193636i	$-0.00616401\pi$
$383$	3621.33	+	6272.33i	0.483137	+	0.836818i	−0.516676	+	0.856181i	$0.672831\pi$
$384$		0			0
$385$	−1073.23	+	1858.88i	−0.142069	+	0.246071i
$386$		0			0
$387$	345.115	+	28.4547i	0.0453312	+	0.00373755i
$388$		0			0
$389$	4866.16	−	8428.44i	0.634253	−	1.09856i	−0.352420	−	0.935842i	$-0.614641\pi$
$389$	4866.16	−	8428.44i	0.634253	−	1.09856i	0.986673	−	0.162716i	$-0.0520254\pi$
$390$		0			0
$391$	2254.07	+	3904.16i	0.291542	+	0.504966i
$392$		0			0
$393$	−4164.20	−	171.378i	−0.534494	−	0.0219971i
$394$		0			0
$395$	11243.5			1.43220
$396$		0			0
$397$	−1393.66			−0.176186			−0.0880930	−	0.996112i	$-0.528077\pi$
$397$	−1393.66			−0.176186			−0.0880930	+	0.996112i	$0.528077\pi$
$398$		0			0
$399$	725.590	+	1385.37i	0.0910399	+	0.173823i
$400$		0			0
$401$	612.828	+	1061.45i	0.0763171	+	0.132185i	0.901658	−	0.432449i	$-0.142351\pi$
$401$	612.828	+	1061.45i	0.0763171	+	0.132185i	−0.825341	+	0.564634i	$0.809017\pi$
$402$		0			0
$403$	−1535.16	+	2658.97i	−0.189756	+	0.328667i
$404$		0			0
$405$	12455.0	+	2067.88i	1.52813	+	0.253713i
$406$		0			0
$407$	841.283	−	1457.15i	0.102459	−	0.177464i
$408$		0			0
$409$	−4081.41	−	7069.22i	−0.493430	−	0.854646i	0.506541	−	0.862216i	$-0.330924\pi$
$409$	−4081.41	−	7069.22i	−0.493430	−	0.854646i	−0.999971	+	0.00756956i	$0.997591\pi$
$410$		0			0
$411$	3181.99	+	6075.40i	0.381889	+	0.729142i
$412$		0			0
$413$	−13.8103			−0.00164543
$414$		0			0
$415$	−2329.84			−0.275584
$416$		0			0
$417$	2734.98	+	112.559i	0.321181	+	0.0132183i
$418$		0			0
$419$	1410.80	+	2443.58i	0.164492	+	0.284908i	0.936475	−	0.350735i	$-0.114068\pi$
$419$	1410.80	+	2443.58i	0.164492	+	0.284908i	−0.771983	+	0.635643i	$0.780735\pi$
$420$		0			0
$421$	2319.95	−	4018.27i	0.268569	−	0.465175i	−0.699924	−	0.714218i	$-0.746783\pi$
$421$	2319.95	−	4018.27i	0.268569	−	0.465175i	0.968492	+	0.249043i	$0.0801160\pi$
$422$		0			0
$423$	−5638.46	−	464.891i	−0.648112	−	0.0534368i
$424$		0			0
$425$	7253.31	−	12563.1i	0.827853	−	1.43388i
$426$		0			0
$427$	716.843	+	1241.61i	0.0812423	+	0.140716i
$428$		0			0
$429$	1989.27	−	3139.84i	0.223876	−	0.353363i
$430$		0			0
$431$	−5998.72			−0.670413			−0.335207	−	0.942145i	$-0.608806\pi$
$431$	−5998.72			−0.670413			−0.335207	+	0.942145i	$0.608806\pi$
$432$		0			0
$433$	−10187.5			−1.13067			−0.565334	−	0.824862i	$-0.691253\pi$
$433$	−10187.5			−1.13067			−0.565334	+	0.824862i	$0.691253\pi$
$434$		0			0
$435$	−10251.4	+	16180.6i	−1.12992	+	1.78345i
$436$		0			0
$437$	−3446.89	−	5970.19i	−0.377316	−	0.653531i
$438$		0			0
$439$	7872.72	−	13636.0i	0.855910	−	1.48248i	−0.0198884	−	0.999802i	$-0.506331\pi$
$439$	7872.72	−	13636.0i	0.855910	−	1.48248i	0.875798	−	0.482677i	$-0.160336\pi$
$440$		0			0
$441$	5187.25	−	7487.61i	0.560118	−	0.808510i
$442$		0			0
$443$	1216.83	−	2107.61i	0.130504	−	0.226040i	−0.793367	−	0.608744i	$-0.791674\pi$
$443$	1216.83	−	2107.61i	0.130504	−	0.226040i	0.923871	+	0.382704i	$0.125007\pi$
$444$		0			0
$445$	1784.51	+	3090.86i	0.190098	+	0.329260i
$446$		0			0
$447$	−15978.9	−	657.615i	−1.69078	−	0.0695842i
$448$		0			0
$449$	7394.75			0.777238			0.388619	−	0.921399i	$-0.372952\pi$
$449$	7394.75			0.777238			0.388619	+	0.921399i	$0.372952\pi$
$450$		0			0
$451$	26142.8			2.72953
$452$		0			0
$453$	−198.149	−	378.327i	−0.0205515	−	0.0392392i
$454$		0			0
$455$	−281.567	−	487.688i	−0.0290111	−	0.0502488i
$456$		0			0
$457$	−1064.96	+	1844.56i	−0.109008	+	0.188807i	−0.915369	−	0.402617i	$-0.868101\pi$
$457$	−1064.96	+	1844.56i	−0.109008	+	0.188807i	0.806361	+	0.591424i	$0.201434\pi$
$458$		0			0
$459$	11545.1	+	1431.90i	1.17403	+	0.145610i
$460$		0			0
$461$	4156.89	−	7199.95i	0.419969	−	0.727408i	−0.575967	−	0.817473i	$-0.695374\pi$
$461$	4156.89	−	7199.95i	0.419969	−	0.727408i	0.995936	+	0.0900653i	$0.0287076\pi$
$462$		0			0
$463$	−922.797	−	1598.33i	−0.0926263	−	0.160434i	0.815989	−	0.578067i	$-0.196193\pi$
$463$	−922.797	−	1598.33i	−0.0926263	−	0.160434i	−0.908615	+	0.417634i	$0.862860\pi$
$464$		0			0
$465$	9357.77	+	17866.9i	0.933239	+	1.78184i
$466$		0			0
$467$	15653.2			1.55106			0.775529	−	0.631312i	$-0.217483\pi$
$467$	15653.2			1.55106			0.775529	+	0.631312i	$0.217483\pi$
$468$		0			0
$469$	−1789.79			−0.176215
$470$		0			0
$471$	12378.1	+	509.421i	1.21094	+	0.0498363i
$472$		0			0
$473$	−334.849	−	579.975i	−0.0325504	−	0.0563790i
$474$		0			0
$475$	−11091.7	+	19211.4i	−1.07141	+	1.85574i
$476$		0			0
$477$	−4281.18	−	9062.38i	−0.410947	−	0.869891i
$478$		0			0
$479$	986.975	−	1709.49i	0.0941462	−	0.163066i	−0.815106	−	0.579312i	$-0.803321\pi$
$479$	986.975	−	1709.49i	0.0941462	−	0.163066i	0.909252	+	0.416246i	$0.136655\pi$
$480$		0			0
$481$	220.715	+	382.290i	0.0209226	+	0.0362390i
$482$		0			0
$483$	358.848	−	566.400i	0.0338057	−	0.0533584i
$484$		0			0
$485$	−25161.6			−2.35573
$486$		0			0
$487$	1753.49			0.163158			0.0815792	−	0.996667i	$-0.474004\pi$
$487$	1753.49			0.163158			0.0815792	+	0.996667i	$0.474004\pi$
$488$		0			0
$489$	−3411.54	+	5384.72i	−0.315491	+	0.497966i
$490$		0			0
$491$	3111.09	+	5388.56i	0.285950	+	0.495280i	0.972839	−	0.231482i	$-0.0743576\pi$
$491$	3111.09	+	5388.56i	0.285950	+	0.495280i	−0.686889	+	0.726762i	$0.741024\pi$
$492$		0			0
$493$	−8824.96	+	15285.3i	−0.806199	+	1.39638i
$494$		0			0
$495$	−10429.6	−	22077.4i	−0.947023	−	2.00465i
$496$		0			0
$497$	51.5980	−	89.3704i	0.00465692	−	0.00806602i
$498$		0			0
$499$	−8646.88	−	14976.8i	−0.775727	−	1.34360i	−0.934385	−	0.356264i	$-0.884050\pi$
$499$	−8646.88	−	14976.8i	−0.775727	−	1.34360i	0.158659	−	0.987333i	$-0.449283\pi$
$500$		0			0
$501$	20229.2	+	832.535i	1.80394	+	0.0742413i
$502$		0			0
$503$	−20578.6			−1.82416			−0.912082	−	0.410007i	$-0.865526\pi$
$503$	−20578.6			−1.82416			−0.912082	+	0.410007i	$0.865526\pi$
$504$		0			0
$505$	3532.35			0.311263
$506$		0			0
$507$	−4844.17	−	9249.00i	−0.424333	−	0.810182i
$508$		0			0
$509$	9277.57	+	16069.2i	0.807900	+	1.39932i	0.914316	+	0.405003i	$0.132729\pi$
$509$	9277.57	+	16069.2i	0.807900	+	1.39932i	−0.106415	+	0.994322i	$0.533937\pi$
$510$		0			0
$511$	−796.352	+	1379.32i	−0.0689404	+	0.119408i
$512$		0			0
$513$	−17654.7	−	2189.64i	−1.51944	−	0.188450i
$514$		0			0
$515$	−13470.2	+	23331.0i	−1.15256	+	1.99629i
$516$		0			0
$517$	5470.73	+	9475.59i	0.465382	+	0.806066i
$518$		0			0
$519$	352.956	+	673.900i	0.0298517	+	0.0569960i
$520$		0			0
$521$	−5321.51			−0.447485			−0.223742	−	0.974648i	$-0.571827\pi$
$521$	−5321.51			−0.447485			−0.223742	+	0.974648i	$0.571827\pi$
$522$		0			0
$523$	−7766.94			−0.649378			−0.324689	−	0.945821i	$-0.605260\pi$
$523$	−7766.94			−0.649378			−0.324689	+	0.945821i	$0.605260\pi$
$524$		0			0
$525$	−2155.79	−	88.7218i	−0.179212	−	0.00737550i
$526$		0			0
$527$	9292.29	+	16094.7i	0.768081	+	1.33036i
$528$		0			0
$529$	4605.66	−	7977.24i	0.378537	−	0.655646i
$530$		0			0
$531$	89.4634	−	129.137i	0.00731145	−	0.0105538i
$532$		0			0
$533$	−3429.36	+	5939.83i	−0.278691	+	0.482706i
$534$		0			0
$535$	−5060.88	−	8765.71i	−0.408974	−	0.708364i
$536$		0			0
$537$	4284.96	−	6763.31i	0.344338	−	0.543498i
$538$		0			0
$539$	−17616.1			−1.40775
$540$		0			0
$541$	−1292.25			−0.102695			−0.0513476	−	0.998681i	$-0.516352\pi$
$541$	−1292.25			−0.102695			−0.0513476	+	0.998681i	$0.516352\pi$
$542$		0			0
$543$	3264.63	−	5152.85i	0.258009	−	0.407237i
$544$		0			0
$545$	6777.49	+	11739.0i	0.532690	+	0.922646i
$546$		0			0
$547$	3766.48	−	6523.73i	0.294411	−	0.509935i	−0.680437	−	0.732807i	$-0.738210\pi$
$547$	3766.48	−	6523.73i	0.294411	−	0.509935i	0.974848	+	0.222872i	$0.0715432\pi$
$548$		0			0
$549$	−16253.7	−	1340.12i	−1.26355	−	0.104180i
$550$		0			0
$551$	13495.0	−	23374.1i	1.04339	−	1.80720i
$552$		0			0
$553$	−770.449	−	1334.46i	−0.0592456	−	0.102616i
$554$		0			0
$555$	2897.34	+	119.240i	0.221595	+	0.00911976i
$556$		0			0
$557$	−9856.22			−0.749769			−0.374884	−	0.927072i	$-0.622318\pi$
$557$	−9856.22			−0.749769			−0.374884	+	0.927072i	$0.622318\pi$
$558$		0			0
$559$	175.699			0.0132939
$560$		0			0
$561$	−10438.6	−	19930.6i	−0.785596	−	1.49994i
$562$		0			0
$563$	−5141.10	−	8904.65i	−0.384852	−	0.666583i	0.606897	−	0.794781i	$-0.292414\pi$
$563$	−5141.10	−	8904.65i	−0.384852	−	0.666583i	−0.991749	+	0.128198i	$0.959081\pi$
$564$		0			0
$565$	7535.87	−	13052.5i	0.561126	−	0.971899i
$566$		0			0
$567$	−608.036	−	1619.95i	−0.0450354	−	0.119985i
$568$		0			0
$569$	661.321	−	1145.44i	0.0487241	−	0.0843927i	−0.840635	−	0.541602i	$-0.817818\pi$
$569$	661.321	−	1145.44i	0.0487241	−	0.0843927i	0.889359	+	0.457210i	$0.151151\pi$
$570$		0			0
$571$	−2127.29	−	3684.57i	−0.155909	−	0.270043i	0.777480	−	0.628907i	$-0.216497\pi$
$571$	−2127.29	−	3684.57i	−0.155909	−	0.270043i	−0.933390	+	0.358864i	$0.883164\pi$
$572$		0			0
$573$	5288.50	+	10097.4i	0.385568	+	0.736167i
$574$		0			0
$575$	9511.01			0.689803
$576$		0			0
$577$	−13268.4			−0.957312			−0.478656	−	0.878003i	$-0.658876\pi$
$577$	−13268.4			−0.957312			−0.478656	+	0.878003i	$0.658876\pi$
$578$		0			0
$579$	−12788.9	−	526.329i	−0.917944	−	0.0377781i
$580$		0			0
$581$	159.650	+	276.522i	0.0114000	+	0.0197454i
$582$		0			0
$583$	−9691.71	+	16786.5i	−0.688490	+	1.19250i
$584$		0			0
$585$	6384.26	+	526.382i	0.451208	+	0.0372020i
$586$		0			0
$587$	2355.25	−	4079.42i	0.165608	−	0.286841i	−0.771263	−	0.636516i	$-0.780375\pi$
$587$	2355.25	−	4079.42i	0.165608	−	0.286841i	0.936871	+	0.349676i	$0.113708\pi$
$588$		0			0
$589$	−14209.7	−	24611.9i	−0.994057	−	1.72176i
$590$		0			0
$591$	9993.29	−	15773.3i	0.695548	−	1.09784i
$592$		0			0
$593$	16303.6			1.12902			0.564510	−	0.825426i	$-0.309065\pi$
$593$	16303.6			1.12902			0.564510	+	0.825426i	$0.309065\pi$
$594$		0			0
$595$	−3408.65			−0.234859
$596$		0			0
$597$	12790.5	−	20188.3i	0.876849	−	1.38400i
$598$		0			0
$599$	−5279.43	−	9144.25i	−0.360120	−	0.623746i	0.627860	−	0.778326i	$-0.283931\pi$
$599$	−5279.43	−	9144.25i	−0.360120	−	0.623746i	−0.987980	+	0.154580i	$0.950598\pi$
$600$		0			0
$601$	936.177	−	1621.51i	0.0635399	−	0.110054i	−0.832505	−	0.554017i	$-0.813094\pi$
$601$	936.177	−	1621.51i	0.0635399	−	0.110054i	0.896045	+	0.443962i	$0.146428\pi$
$602$		0			0
$603$	11594.3	−	16736.0i	0.783013	−	1.13025i
$604$		0			0
$605$	−12084.8	+	20931.4i	−0.812092	+	1.40659i
$606$		0			0
$607$	−11535.9	−	19980.7i	−0.771378	−	1.33607i	−0.936808	−	0.349844i	$-0.886235\pi$
$607$	−11535.9	−	19980.7i	−0.771378	−	1.33607i	0.165430	−	0.986222i	$-0.447099\pi$
$608$		0			0
$609$	2622.91	+	107.946i	0.174525	+	0.00718259i
$610$		0			0
$611$	−2870.56			−0.190066
$612$		0			0
$613$	−24292.0			−1.60056			−0.800281	−	0.599625i	$-0.795317\pi$
$613$	−24292.0			−1.60056			−0.800281	+	0.599625i	$0.795317\pi$
$614$		0			0
$615$	20904.2	+	39912.4i	1.37063	+	2.61695i
$616$		0			0
$617$	3886.97	+	6732.43i	0.253620	+	0.439283i	0.964520	−	0.264010i	$-0.0850453\pi$
$617$	3886.97	+	6732.43i	0.253620	+	0.439283i	−0.710900	+	0.703293i	$0.751712\pi$
$618$		0			0
$619$	−15287.6	+	26478.8i	−0.992664	+	1.71934i	−0.391626	+	0.920125i	$0.628087\pi$
$619$	−15287.6	+	26478.8i	−0.992664	+	1.71934i	−0.601038	+	0.799220i	$0.705246\pi$
$620$		0			0
$621$	2971.66	+	7024.66i	0.192027	+	0.453929i
$622$		0			0
$623$	244.564	−	423.597i	0.0157275	−	0.0272409i
$624$		0			0
$625$	3443.84	+	5964.90i	0.220406	+	0.381754i
$626$		0			0
$627$	15962.6	+	30477.6i	1.01673	+	1.94124i
$628$		0			0
$629$	2671.98			0.169378
$630$		0			0
$631$	−14474.9			−0.913209			−0.456605	−	0.889670i	$-0.650935\pi$
$631$	−14474.9			−0.913209			−0.456605	+	0.889670i	$0.650935\pi$
$632$		0			0
$633$	−12108.4	−	498.323i	−0.760294	−	0.0312900i
$634$		0			0
$635$	8607.91	+	14909.3i	0.537944	+	0.931747i
$636$		0			0
$637$	2310.84	−	4002.49i	0.143734	−	0.248955i
$638$		0			0
$639$	501.430	+	1061.42i	0.0310427	+	0.0657109i
$640$		0			0
$641$	6841.90	−	11850.5i	0.421589	−	0.730214i	−0.574506	−	0.818501i	$-0.694806\pi$
$641$	6841.90	−	11850.5i	0.421589	−	0.730214i	0.996095	+	0.0882864i	$0.0281391\pi$
$642$		0			0
$643$	8007.76	+	13869.8i	0.491128	+	0.850658i	0.999948	−	0.0102148i	$-0.00325153\pi$
$643$	8007.76	+	13869.8i	0.491128	+	0.850658i	−0.508820	+	0.860873i	$0.669918\pi$
$644$		0			0
$645$	617.702	−	974.972i	0.0377085	−	0.0595186i
$646$		0			0
$647$	−12224.1			−0.742783			−0.371392	−	0.928476i	$-0.621119\pi$
$647$	−12224.1			−0.742783			−0.371392	+	0.928476i	$0.621119\pi$
$648$		0			0
$649$	−303.821			−0.0183760
$650$		0			0
$651$	1479.34	−	2334.96i	0.0890626	−	0.140575i
$652$		0			0
$653$	8064.97	+	13968.9i	0.483318	+	0.837131i	0.999816	−	0.0191568i	$-0.00609816\pi$
$653$	8064.97	+	13968.9i	0.483318	+	0.837131i	−0.516498	+	0.856288i	$0.672765\pi$
$654$		0			0
$655$	−6945.55	+	12030.0i	−0.414328	+	0.717638i
$656$		0			0
$657$	−7738.95	−	16381.8i	−0.459551	−	0.972776i
$658$		0			0
$659$	3579.31	−	6199.55i	0.211579	−	0.366465i	−0.740630	−	0.671913i	$-0.765473\pi$
$659$	3579.31	−	6199.55i	0.211579	−	0.366465i	0.952209	+	0.305448i	$0.0988062\pi$
$660$		0			0
$661$	−4760.03	−	8244.61i	−0.280096	−	0.485141i	0.691312	−	0.722556i	$-0.257033\pi$
$661$	−4760.03	−	8244.61i	−0.280096	−	0.485141i	−0.971408	+	0.237415i	$0.923700\pi$
$662$		0			0
$663$	5897.67	+	242.719i	0.345470	+	0.0142179i
$664$		0			0
$665$	5212.46			0.303956
$666$		0			0
$667$	−11571.9			−0.671760
$668$		0			0
$669$	9781.01	+	18674.9i	0.565255	+	1.07925i
$670$		0			0
$671$	15770.2	+	27314.8i	0.907306	+	1.57150i
$672$		0			0
$673$	3801.82	−	6584.95i	0.217755	−	0.377163i	−0.736366	−	0.676583i	$-0.763460\pi$
$673$	3801.82	−	6584.95i	0.217755	−	0.377163i	0.954121	+	0.299420i	$0.0967932\pi$
$674$		0			0
$675$	14794.9	−	19583.6i	0.843636	−	1.11670i
$676$		0			0
$677$	2475.98	−	4288.53i	0.140561	−	0.243459i	−0.787147	−	0.616765i	$-0.788443\pi$
$677$	2475.98	−	4288.53i	0.140561	−	0.243459i	0.927708	+	0.373307i	$0.121776\pi$
$678$		0			0
$679$	1724.18	+	2986.36i	0.0974489	+	0.168786i
$680$		0			0
$681$	−3127.46	−	5971.29i	−0.175983	−	0.336006i
$682$		0			0
$683$	28231.4			1.58162			0.790809	−	0.612063i	$-0.209660\pi$
$683$	28231.4			1.58162			0.790809	+	0.612063i	$0.209660\pi$
$684$		0			0
$685$	22858.7			1.27502
$686$		0			0
$687$	−16156.6	−	664.925i	−0.897250	−	0.0369265i
$688$		0			0
$689$	−2542.68	−	4404.04i	−0.140592	−	0.243513i
$690$		0			0
$691$	12755.1	−	22092.5i	0.702212	−	1.21627i	−0.265477	−	0.964117i	$-0.585529\pi$
$691$	12755.1	−	22092.5i	0.702212	−	1.21627i	0.967688	−	0.252149i	$-0.0811373\pi$
$692$		0			0
$693$	−1905.62	+	2750.70i	−0.104457	+	0.150780i
$694$		0			0
$695$	4561.73	−	7901.16i	0.248973	−	0.431234i
$696$		0			0
$697$	20757.9	+	35953.7i	1.12806	+	1.95387i
$698$		0			0
$699$	5658.44	−	8931.20i	0.306183	−	0.483274i
$700$		0			0
$701$	17524.1			0.944191			0.472095	−	0.881547i	$-0.343498\pi$
$701$	17524.1			0.944191			0.472095	+	0.881547i	$0.343498\pi$
$702$		0			0
$703$	−4085.96			−0.219210
$704$		0			0
$705$	−10092.0	+	15929.0i	−0.539129	+	0.850953i
$706$		0			0
$707$	−242.052	−	419.246i	−0.0128759	−	0.0223018i
$708$		0			0
$709$	17490.8	−	30295.0i	0.926490	−	1.60473i	0.137343	−	0.990524i	$-0.456144\pi$
$709$	17490.8	−	30295.0i	0.926490	−	1.60473i	0.789147	−	0.614205i	$-0.210523\pi$
$710$		0			0
$711$	17469.2	+	1440.33i	0.921442	+	0.0759728i
$712$		0			0
$713$	−6092.32	+	10552.2i	−0.319999	+	0.554255i
$714$		0			0
$715$	−6194.35	−	10728.9i	−0.323994	−	0.561173i
$716$		0			0
$717$	7623.88	+	313.762i	0.397098	+	0.0163426i
$718$		0			0
$719$	−30485.5			−1.58125			−0.790623	−	0.612303i	$-0.790243\pi$
$719$	−30485.5			−1.58125			−0.790623	+	0.612303i	$0.790243\pi$
$720$		0			0
$721$	3692.13			0.190710
$722$		0			0
$723$	1589.14	+	3034.15i	0.0817435	+	0.156073i
$724$		0			0
$725$	18618.4	+	32248.0i	0.953753	+	1.65195i
$726$		0			0
$727$	13348.9	−	23121.0i	0.680994	−	1.17952i	−0.293683	−	0.955903i	$-0.594881\pi$
$727$	13348.9	−	23121.0i	0.680994	−	1.17952i	0.974678	−	0.223614i	$-0.0717856\pi$
$728$		0			0
$729$	19086.6	+	4808.44i	0.969701	+	0.244294i
$730$		0			0
$731$	531.752	−	921.022i	0.0269050	−	0.0466008i
$732$		0			0
$733$	−15258.5	−	26428.4i	−0.768874	−	1.33173i	−0.938174	−	0.346164i	$-0.887484\pi$
$733$	−15258.5	−	26428.4i	−0.768874	−	1.33173i	0.169301	−	0.985564i	$-0.445849\pi$
$734$		0			0
$735$	−14086.1	−	26894.6i	−0.706901	−	1.34969i
$736$		0			0
$737$	−39374.7			−1.96796
$738$		0			0
$739$	20020.0			0.996544			0.498272	−	0.867021i	$-0.333968\pi$
$739$	20020.0			0.996544			0.498272	+	0.867021i	$0.333968\pi$
$740$		0			0
$741$	−9018.66	−	371.164i	−0.447110	−	0.0184009i
$742$		0			0
$743$	8017.35	+	13886.5i	0.395866	+	0.685659i	0.993211	−	0.116325i	$-0.0371113\pi$
$743$	8017.35	+	13886.5i	0.395866	+	0.685659i	−0.597346	+	0.801984i	$0.703778\pi$
$744$		0			0
$745$	−26651.6	+	46161.9i	−1.31066	+	2.27012i
$746$		0			0
$747$	−3619.92	−	298.462i	−0.177304	−	0.0146187i
$748$		0			0
$749$	−693.586	+	1201.33i	−0.0338359	+	0.0586055i
$750$		0			0
$751$	12362.5	+	21412.5i	0.600686	+	1.04042i	0.992717	+	0.120467i	$0.0384392\pi$
$751$	12362.5	+	21412.5i	0.600686	+	1.04042i	−0.392031	+	0.919952i	$0.628227\pi$
$752$		0			0
$753$	15320.5	−	24181.6i	0.741446	−	1.17029i
$754$		0			0
$755$	−1423.45			−0.0686156
$756$		0			0
$757$	−13567.6			−0.651419			−0.325709	−	0.945470i	$-0.605603\pi$
$757$	−13567.6			−0.651419			−0.325709	+	0.945470i	$0.605603\pi$
$758$		0			0
$759$	7894.50	−	12460.6i	0.377539	−	0.595902i
$760$		0			0
$761$	1108.70	+	1920.32i	0.0528124	+	0.0914737i	0.891223	−	0.453565i	$-0.149848\pi$
$761$	1108.70	+	1920.32i	0.0528124	+	0.0914737i	−0.838411	+	0.545039i	$0.816515\pi$
$762$		0			0
$763$	928.845	−	1608.81i	0.0440713	−	0.0763338i
$764$		0			0
$765$	22081.3	−	31873.5i	1.04359	−	1.50639i
$766$		0			0
$767$	39.8545	−	69.0301i	0.00187622	−	0.00324971i
$768$		0			0
$769$	17449.5	+	30223.4i	0.818263	+	1.41727i	0.906961	+	0.421215i	$0.138396\pi$
$769$	17449.5	+	30223.4i	0.818263	+	1.41727i	−0.0886978	+	0.996059i	$0.528271\pi$
$770$		0			0
$771$	−19041.5	−	783.654i	−0.889444	−	0.0366052i
$772$		0			0
$773$	−10244.1			−0.476656			−0.238328	−	0.971185i	$-0.576599\pi$
$773$	−10244.1			−0.476656			−0.238328	+	0.971185i	$0.576599\pi$
$774$		0			0
$775$	39208.7			1.81732
$776$		0			0
$777$	−184.385	−	352.048i	−0.00851324	−	0.0162544i
$778$		0			0
$779$	−31742.7	−	54980.0i	−1.45995	−	2.52871i
$780$		0			0
$781$	1135.13	−	1966.11i	0.0520080	−	0.0900805i
$782$		0			0
$783$	−18000.6	+	23826.9i	−0.821570	+	1.08749i
$784$		0			0
$785$	20645.6	−	35759.3i	0.938693	−	1.62586i
$786$		0			0
$787$	−5430.76	−	9406.36i	−0.245979	−	0.426049i	0.716427	−	0.697662i	$-0.245776\pi$
$787$	−5430.76	−	9406.36i	−0.245979	−	0.426049i	−0.962407	+	0.271613i	$0.912443\pi$
$788$		0			0
$789$	12036.7	+	22981.8i	0.543117	+	1.03698i
$790$		0			0
$791$	−2065.56			−0.0928480
$792$		0			0
$793$	−8274.81			−0.370551
$794$		0			0
$795$	−33377.7	−	1373.67i	−1.48904	−	0.0612816i
$796$		0			0
$797$	−17802.4	−	30834.7i	−0.791209	−	1.37041i	−0.925219	−	0.379434i	$-0.876119\pi$
$797$	−17802.4	−	30834.7i	−0.791209	−	1.37041i	0.134010	−	0.990980i	$-0.457214\pi$
$798$		0			0
$799$	−8687.73	+	15047.6i	−0.384668	+	0.666265i
$800$		0			0
$801$	2376.67	+	5030.93i	0.104838	+	0.221922i
$802$		0			0
$803$	−17519.4	+	30344.4i	−0.769919	+	1.33354i
$804$		0			0
$805$	−1117.41	−	1935.41i	−0.0489236	−	0.0847381i
$806$		0			0
$807$	246.151	−	388.521i	0.0107372	−	0.0169474i
$808$		0			0
$809$	13929.4			0.605355			0.302678	−	0.953093i	$-0.402119\pi$
$809$	13929.4			0.605355			0.302678	+	0.953093i	$0.402119\pi$
$810$		0			0
$811$	−41996.6			−1.81837			−0.909187	−	0.416388i	$-0.863296\pi$
$811$	−41996.6			−1.81837			−0.909187	+	0.416388i	$0.863296\pi$
$812$		0			0
$813$	−14534.7	+	22941.3i	−0.627002	+	0.989650i
$814$		0			0
$815$	10623.1	+	18399.8i	0.456579	+	0.790817i
$816$		0			0
$817$	−813.149	+	1408.42i	−0.0348207	+	0.0603112i
$818$		0			0
$819$	−375.002	−	793.801i	−0.0159995	−	0.0338677i
$820$		0			0
$821$	−10540.1	+	18255.9i	−0.448052	+	0.776049i	−0.998259	−	0.0589791i	$-0.981215\pi$
$821$	−10540.1	+	18255.9i	−0.448052	+	0.776049i	0.550207	+	0.835028i	$0.314549\pi$
$822$		0			0
$823$	17182.6	+	29761.1i	0.727760	+	1.26052i	0.957828	+	0.287343i	$0.0927719\pi$
$823$	17182.6	+	29761.1i	0.727760	+	1.26052i	−0.230068	+	0.973175i	$0.573895\pi$
$824$		0			0
$825$	−47426.4	−	1951.84i	−2.00142	−	0.0823689i
$826$		0			0
$827$	32925.7			1.38445			0.692225	−	0.721682i	$-0.256631\pi$
$827$	32925.7			1.38445			0.692225	+	0.721682i	$0.256631\pi$
$828$		0			0
$829$	21195.7			0.888008			0.444004	−	0.896025i	$-0.353558\pi$
$829$	21195.7			0.888008			0.444004	+	0.896025i	$0.353558\pi$
$830$		0			0
$831$	−5092.30	−	9722.76i	−0.212575	−	0.405871i
$832$		0			0
$833$	−13987.5	−	24227.1i	−0.581798	−	1.00770i
$834$		0			0
$835$	33740.7	−	58440.6i	1.39838	−	2.42206i
$836$		0			0
$837$	12250.5	+	28958.9i	0.505903	+	1.19590i
$838$		0			0
$839$	−11868.4	+	20556.7i	−0.488370	+	0.845882i	−0.999911	−	0.0133775i	$-0.995742\pi$
$839$	−11868.4	+	20556.7i	−0.488370	+	0.845882i	0.511541	+	0.859259i	$0.329075\pi$
$840$		0			0
$841$	−10458.2	−	18114.1i	−0.428806	−	0.742715i
$842$		0			0
$843$	4159.03	+	7940.86i	0.169922	+	0.324434i
$844$		0			0
$845$	−34799.3			−1.41673
$846$		0			0
$847$	3312.40			0.134375
$848$		0			0
$849$	17349.8	+	714.032i	0.701346	+	0.0288640i
$850$		0			0
$851$	875.917	+	1517.13i	0.0352833	+	0.0611124i
$852$		0			0
$853$	−10964.2	+	18990.6i	−0.440104	+	0.762282i	−0.997697	−	0.0678324i	$-0.978392\pi$
$853$	−10964.2	+	18990.6i	−0.440104	+	0.762282i	0.557593	+	0.830114i	$0.311725\pi$
$854$		0			0
$855$	−33766.4	+	48740.6i	−1.35063	+	1.94958i
$856$		0			0
$857$	20166.3	−	34929.1i	0.803814	−	1.39225i	−0.113275	−	0.993564i	$-0.536134\pi$
$857$	20166.3	−	34929.1i	0.803814	−	1.39225i	0.917089	−	0.398683i	$-0.130533\pi$
$858$		0			0
$859$	11472.6	+	19871.1i	0.455691	+	0.789280i	0.998728	−	0.0504289i	$-0.0160588\pi$
$859$	11472.6	+	19871.1i	0.455691	+	0.789280i	−0.543037	+	0.839709i	$0.682725\pi$
$860$		0			0
$861$	3304.66	−	5216.03i	0.130804	−	0.206460i
$862$		0			0
$863$	40453.2			1.59565			0.797824	−	0.602890i	$-0.205984\pi$
$863$	40453.2			1.59565			0.797824	+	0.602890i	$0.205984\pi$
$864$		0			0
$865$	2535.55			0.0996662
$866$		0			0
$867$	5458.97	−	8616.36i	0.213837	−	0.337516i
$868$		0			0
$869$	−16949.5	−	29357.4i	−0.661649	−	1.14601i
$870$		0			0
$871$	5165.08	−	8946.19i	0.200932	−	0.348025i
$872$		0			0
$873$	−39094.0	−	3223.30i	−1.51562	−	0.124962i
$874$		0			0
$875$	−1026.51	+	1777.97i	−0.0396599	+	0.0686930i
$876$		0			0
$877$	−2280.71	−	3950.30i	−0.0878153	−	0.152101i	0.818772	−	0.574119i	$-0.194655\pi$
$877$	−2280.71	−	3950.30i	−0.0878153	−	0.152101i	−0.906587	+	0.422018i	$0.861322\pi$
$878$		0			0
$879$	27300.4	+	1123.55i	1.04758	+	0.0431132i
$880$		0			0
$881$	31553.9			1.20667			0.603336	−	0.797487i	$-0.293838\pi$
$881$	31553.9			1.20667			0.603336	+	0.797487i	$0.293838\pi$
$882$		0			0
$883$	−22726.0			−0.866128			−0.433064	−	0.901363i	$-0.642568\pi$
$883$	−22726.0			−0.866128			−0.433064	+	0.901363i	$0.642568\pi$
$884$		0			0
$885$	−242.939	−	463.845i	−0.00922746	−	0.0176181i
$886$		0			0
$887$	817.180	+	1415.40i	0.0309337	+	0.0535788i	0.881078	−	0.472971i	$-0.156819\pi$
$887$	817.180	+	1415.40i	0.0309337	+	0.0535788i	−0.850144	+	0.526550i	$0.823485\pi$
$888$		0			0
$889$	1179.70	−	2043.30i	0.0445061	−	0.0770868i
$890$		0			0
$891$	−13376.5	−	35638.1i	−0.502952	−	1.33998i
$892$		0			0
$893$	13285.2	−	23010.6i	0.497841	−	0.862285i
$894$		0			0
$895$	−13342.8	−	23110.4i	−0.498325	−	0.863125i
$896$		0			0
$897$	1795.54	+	3428.23i	0.0668353	+	0.127609i
$898$		0			0
$899$	−47704.5			−1.76978
$900$		0			0
$901$	−30781.6			−1.13816
$902$		0			0
$903$	−158.044	−	6.50434i	−0.00582435	−	0.000239702i
$904$		0			0
$905$	−10165.7	−	17607.5i	−0.373390	−	0.646731i
$906$		0			0
$907$	−3267.67	+	5659.76i	−0.119626	+	0.207199i	−0.919620	−	0.392810i	$-0.871503\pi$
$907$	−3267.67	+	5659.76i	−0.119626	+	0.207199i	0.799993	+	0.600009i	$0.204836\pi$
$908$		0			0
$909$	5488.29	+	452.509i	0.200259	+	0.0165113i
$910$		0			0
$911$	23043.3	−	39912.2i	0.838046	−	1.45154i	−0.0534801	−	0.998569i	$-0.517031\pi$
$911$	23043.3	−	39912.2i	0.838046	−	1.45154i	0.891526	−	0.452969i	$-0.149635\pi$
$912$		0			0
$913$	3512.23	+	6083.37i	0.127314	+	0.220515i
$914$		0			0
$915$	−29091.6	+	45917.8i	−1.05108	+	1.65901i
$916$		0			0
$917$	1903.75			0.0685578
$918$		0			0
$919$	−1857.94			−0.0666898			−0.0333449	−	0.999444i	$-0.510616\pi$
$919$	−1857.94			−0.0666898			−0.0333449	+	0.999444i	$0.510616\pi$
$920$		0			0
$921$	−7181.89	+	11335.8i	−0.256950	+	0.405566i
$922$		0			0
$923$	297.809	+	515.820i	0.0106202	+	0.0183948i
$924$		0			0
$925$	2818.60	−	4881.95i	0.100189	−	0.173532i
$926$		0			0
$927$	−23917.7	+	34524.3i	−0.847421	+	1.22322i
$928$		0			0
$929$	−12150.8	+	21045.8i	−0.429123	+	0.743263i	−0.996796	−	0.0799916i	$-0.974511\pi$
$929$	−12150.8	+	21045.8i	−0.429123	+	0.743263i	0.567672	+	0.823254i	$0.307844\pi$
$930$		0			0
$931$	21389.5	+	37047.8i	0.752968	+	1.30418i
$932$		0			0
$933$	−26418.4	−	1087.25i	−0.927009	−	0.0381512i
$934$		0			0
$935$	−74988.7			−2.62288
$936$		0			0
$937$	52069.9			1.81542			0.907710	−	0.419597i	$-0.137829\pi$
$937$	52069.9			1.81542			0.907710	+	0.419597i	$0.137829\pi$
$938$		0			0
$939$	−7066.32	−	13491.8i	−0.245581	−	0.468890i
$940$		0			0
$941$	−7854.48	−	13604.4i	−0.272103	−	0.471296i	0.697297	−	0.716782i	$-0.254386\pi$
$941$	−7854.48	−	13604.4i	−0.272103	−	0.471296i	−0.969400	+	0.245486i	$0.921052\pi$
$942$		0			0
$943$	−13609.5	+	23572.4i	−0.469976	+	0.814023i
$944$		0			0
$945$	−5723.27	−	709.834i	−0.197014	−	0.0244348i
$946$		0			0
$947$	26244.3	−	45456.5i	0.900556	−	1.55981i	0.0737816	−	0.997274i	$-0.476493\pi$
$947$	26244.3	−	45456.5i	0.900556	−	1.55981i	0.826774	−	0.562534i	$-0.190173\pi$
$948$		0			0
$949$	−4596.31	−	7961.04i	−0.157221	−	0.272314i
$950$		0			0
$951$	8677.97	+	16568.9i	0.295902	+	0.564967i
$952$		0			0
$953$	2447.37			0.0831880			0.0415940	−	0.999135i	$-0.486756\pi$
$953$	2447.37			0.0831880			0.0415940	+	0.999135i	$0.486756\pi$
$954$		0			0
$955$	37991.3			1.28730
$956$		0			0
$957$	57702.8	+	2374.76i	1.94908	+	0.0802144i
$958$		0			0
$959$	−1566.37	−	2713.04i	−0.0527433	−	0.0913541i
$960$		0			0
$961$	−10219.9	+	17701.3i	−0.343052	+	0.594183i
$962$		0			0
$963$	−6740.27	−	14267.8i	−0.225548	−	0.477438i
$964$		0			0
$965$	−21330.9	+	36946.2i	−0.711571	+	1.23248i
$966$		0			0
$967$	−14696.1	−	25454.4i	−0.488723	−	0.846494i	0.511193	−	0.859466i	$-0.329204\pi$
$967$	−14696.1	−	25454.4i	−0.488723	−	0.846494i	−0.999916	+	0.0129726i	$0.995871\pi$
$968$		0			0
$969$	−29240.6	+	46152.9i	−0.969394	+	1.53008i
$970$		0			0
$971$	32763.9			1.08285			0.541423	−	0.840751i	$-0.317886\pi$
$971$	32763.9			1.08285			0.541423	+	0.840751i	$0.317886\pi$
$972$		0			0
$973$	−1250.36			−0.0411969
$974$		0			0
$975$	6664.76	−	10519.6i	0.218916	−	0.345534i
$976$		0			0
$977$	−334.690	−	579.701i	−0.0109598	−	0.0189829i	0.860494	−	0.509461i	$-0.170155\pi$
$977$	−334.690	−	579.701i	−0.0109598	−	0.0189829i	−0.871453	+	0.490479i	$0.836822\pi$
$978$		0			0
$979$	5380.29	−	9318.94i	0.175643	−	0.304223i
$980$		0			0
$981$	9026.52	+	19107.3i	0.293776	+	0.621864i
$982$		0			0
$983$	11895.5	−	20603.6i	0.385969	−	0.668518i	−0.605934	−	0.795515i	$-0.707200\pi$
$983$	11895.5	−	20603.6i	0.385969	−	0.668518i	0.991903	+	0.126997i	$0.0405338\pi$
$984$		0			0
$985$	−31117.9	−	53897.7i	−1.00660	−	1.74348i
$986$		0			0
$987$	2582.12	+	106.267i	0.0832723	+	0.00342708i
$988$		0			0
$989$	697.267			0.0224184
$990$		0			0
$991$	−7069.41			−0.226607			−0.113303	−	0.993560i	$-0.536143\pi$
$991$	−7069.41			−0.226607			−0.113303	+	0.993560i	$0.536143\pi$
$992$		0			0
$993$	−8866.60	−	16929.1i	−0.283357	−	0.541015i
$994$		0			0
$995$	−39827.9	−	68984.0i	−1.26897	−	2.19793i
$996$		0			0
$997$	−17162.3	+	29726.0i	−0.545172	+	0.944266i	0.453424	+	0.891295i	$0.350202\pi$
$997$	−17162.3	+	29726.0i	−0.545172	+	0.944266i	−0.998596	+	0.0529711i	$0.983131\pi$
$998$		0			0
$999$	4486.37	+	556.426i	0.142085	+	0.0176222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.i.e.97.3		8
3.2	odd	2		432.4.i.e.289.4		8
4.3	odd	2		72.4.i.a.25.2	✓	8
9.2	odd	6		1296.4.a.y.1.1		4
9.4	even	3	inner	144.4.i.e.49.3		8
9.5	odd	6		432.4.i.e.145.4		8
9.7	even	3		1296.4.a.ba.1.4		4
12.11	even	2		216.4.i.a.73.4		8
36.7	odd	6		648.4.a.i.1.4		4
36.11	even	6		648.4.a.h.1.1		4
36.23	even	6		216.4.i.a.145.4		8
36.31	odd	6		72.4.i.a.49.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.i.a.25.2	✓	8	4.3	odd	2
72.4.i.a.49.2	yes	8	36.31	odd	6
144.4.i.e.49.3		8	9.4	even	3	inner
144.4.i.e.97.3		8	1.1	even	1	trivial
216.4.i.a.73.4		8	12.11	even	2
216.4.i.a.145.4		8	36.23	even	6
432.4.i.e.145.4		8	9.5	odd	6
432.4.i.e.289.4		8	3.2	odd	2
648.4.a.h.1.1		4	36.11	even	6
648.4.a.i.1.4		4	36.7	odd	6
1296.4.a.y.1.1		4	9.2	odd	6
1296.4.a.ba.1.4		4	9.7	even	3

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.78092 - 4.38936i) q^{3} +(-8.65944 - 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +(-11.5330 - 24.4129i) q^{9} +(-26.1082 + 45.2208i) q^{11} +(-6.84965 - 11.8639i) q^{13} +(-89.9154 - 3.70048i) q^{15} -82.9217 q^{17} +126.803 q^{19} +(5.72218 + 10.9254i) q^{21} +(-27.1831 - 47.0825i) q^{23} +(-87.4718 + 151.506i) q^{25} +(-139.229 - 17.2680i) q^{27} +(106.425 - 184.334i) q^{29} +(-112.061 - 194.095i) q^{31} +(125.885 + 240.354i) q^{33} +41.1068 q^{35} -32.2229 q^{37} +(-71.1234 - 2.92709i) q^{39} +(-250.331 - 433.586i) q^{41} +(-6.41270 + 11.1071i) q^{43} +(-266.290 + 384.380i) q^{45} +(104.770 - 181.467i) q^{47} +(168.683 + 292.168i) q^{49} +(-230.599 + 363.973i) q^{51} +371.213 q^{53} +904.331 q^{55} +(352.629 - 556.584i) q^{57} +(2.90924 + 5.03895i) q^{59} +(302.016 - 523.107i) q^{61} +(63.8685 + 5.26595i) q^{63} +(-118.628 + 205.470i) q^{65} +(377.033 + 653.040i) q^{67} +(-282.256 - 11.6163i) q^{69} -43.4780 q^{71} +671.029 q^{73} +(421.761 + 805.270i) q^{75} +(-61.9686 - 107.333i) q^{77} +(-324.601 + 562.226i) q^{79} +(-462.981 + 563.107i) q^{81} +(67.2629 - 116.503i) q^{83} +(718.056 + 1243.71i) q^{85} +(-513.148 - 979.757i) q^{87} -206.076 q^{89} +32.5156 q^{91} +(-1163.59 - 47.8876i) q^{93} +(-1098.04 - 1901.87i) q^{95} +(726.420 - 1258.20i) q^{97} +(1405.08 + 115.848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 5 q^{5} - 3 q^{7} - 15 q^{9} - 16 q^{11} + 29 q^{13} - 141 q^{15} - 34 q^{17} + 218 q^{19} + 27 q^{21} - 37 q^{23} + 97 q^{25} + 216 q^{27} - 3 q^{29} - 331 q^{31} + 468 q^{33} + 342 q^{35}+ \cdots + 5133 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 5 * q^5 - 3 * q^7 - 15 * q^9 - 16 * q^11 + 29 * q^13 - 141 * q^15 - 34 * q^17 + 218 * q^19 + 27 * q^21 - 37 * q^23 + 97 * q^25 + 216 * q^27 - 3 * q^29 - 331 * q^31 + 468 * q^33 + 342 * q^35 - 732 * q^37 + 375 * q^39 - 378 * q^41 - 506 * q^43 - 993 * q^45 - 171 * q^47 + 829 * q^49 - 2193 * q^51 + 820 * q^53 + 2326 * q^55 + 507 * q^57 - 616 * q^59 + 1331 * q^61 + 1899 * q^63 - 815 * q^65 - 1162 * q^67 + 1113 * q^69 + 688 * q^71 - 2614 * q^73 + 1755 * q^75 - 741 * q^77 - 1853 * q^79 - 2547 * q^81 - 1421 * q^83 + 2074 * q^85 - 5877 * q^87 + 1632 * q^89 + 3990 * q^91 + 537 * q^93 - 1292 * q^95 + 2506 * q^97 + 5133 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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