LMFDB - Embedded newform 216.3.b.a.163.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.b (of order $2$, degree $1$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 8x^{12} + 4x^{10} + 160x^{8} + 64x^{6} - 2048x^{4} + 4096x^{2} + 65536 $ x^16 + x^14 - 8x^12 + 4x^10 + 160x^8 + 64x^6 - 2048x^4 + 4096x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.9
Root			$0.316912 - 1.97473i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.a.163.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.316912 - 1.97473i) q^{2} +(-3.79913 - 1.25163i) q^{4} +4.41296i q^{5} +3.59985i q^{7} +(-3.67563 + 7.10561i) q^{8} +O(q^{10})$	\(q+(0.316912 - 1.97473i) q^{2} +(-3.79913 - 1.25163i) q^{4} +4.41296i q^{5} +3.59985i q^{7} +(-3.67563 + 7.10561i) q^{8} +(8.71442 + 1.39852i) q^{10} -18.7798 q^{11} +19.9181i q^{13} +(7.10873 + 1.14083i) q^{14} +(12.8668 + 9.51024i) q^{16} -8.00578 q^{17} +16.1354 q^{19} +(5.52341 - 16.7654i) q^{20} +(-5.95154 + 37.0851i) q^{22} +18.3926i q^{23} +5.52575 q^{25} +(39.3330 + 6.31230i) q^{26} +(4.50569 - 13.6763i) q^{28} -17.9287i q^{29} -29.7323i q^{31} +(22.8578 - 22.3946i) q^{32} +(-2.53713 + 15.8093i) q^{34} -15.8860 q^{35} +26.7200i q^{37} +(5.11350 - 31.8631i) q^{38} +(-31.3568 - 16.2204i) q^{40} -40.2437 q^{41} -71.8376 q^{43} +(71.3469 + 23.5054i) q^{44} +(36.3206 + 5.82885i) q^{46} -23.3952i q^{47} +36.0411 q^{49} +(1.75118 - 10.9119i) q^{50} +(24.9302 - 75.6717i) q^{52} +90.7227i q^{53} -82.8745i q^{55} +(-25.5791 - 13.2317i) q^{56} +(-35.4044 - 5.68183i) q^{58} -10.9410 q^{59} +90.9260i q^{61} +(-58.7133 - 9.42252i) q^{62} +(-36.9795 - 52.2352i) q^{64} -87.8980 q^{65} +74.0054 q^{67} +(30.4150 + 10.0203i) q^{68} +(-5.03446 + 31.3706i) q^{70} +13.9001i q^{71} -56.0158 q^{73} +(52.7648 + 8.46788i) q^{74} +(-61.3005 - 20.1956i) q^{76} -67.6044i q^{77} -118.415i q^{79} +(-41.9683 + 56.7809i) q^{80} +(-12.7537 + 79.4704i) q^{82} -8.08995 q^{83} -35.3292i q^{85} +(-22.7662 + 141.860i) q^{86} +(69.0276 - 133.442i) q^{88} +83.9483 q^{89} -71.7022 q^{91} +(23.0208 - 69.8761i) q^{92} +(-46.1992 - 7.41422i) q^{94} +71.2049i q^{95} -79.0054 q^{97} +(11.4219 - 71.1715i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.316912	−	1.97473i	0.158456	−	0.987366i
$2$	0.316912	−	1.97473i	0.158456	−	0.987366i
$3$		0			0
$3$		0			0
$4$	−3.79913	−	1.25163i	−0.949783	−	0.312908i
$5$			4.41296i			0.882593i	0.897361	+	0.441296i	$0.145481\pi$
$5$			4.41296i			0.882593i	−0.897361	+	0.441296i	$0.854519\pi$
$6$		0			0
$7$			3.59985i			0.514264i	0.966376	+	0.257132i	$0.0827775\pi$
$7$			3.59985i			0.514264i	−0.966376	+	0.257132i	$0.917223\pi$
$8$	−3.67563	+	7.10561i	−0.459454	+	0.888202i
$9$		0			0
$10$	8.71442	+	1.39852i	0.871442	+	0.139852i
$11$	−18.7798			−1.70725			−0.853627	−	0.520885i	$-0.825602\pi$
$11$	−18.7798			−1.70725			−0.853627	+	0.520885i	$0.825602\pi$
$12$		0			0
$13$			19.9181i			1.53216i	0.642743	+	0.766082i	$0.277796\pi$
$13$			19.9181i			1.53216i	−0.642743	+	0.766082i	$0.722204\pi$
$14$	7.10873	+	1.14083i	0.507767	+	0.0814882i
$15$		0			0
$16$	12.8668	+	9.51024i	0.804177	+	0.594390i
$17$	−8.00578			−0.470928			−0.235464	−	0.971883i	$-0.575661\pi$
$17$	−8.00578			−0.470928			−0.235464	+	0.971883i	$0.575661\pi$
$18$		0			0
$19$	16.1354			0.849231			0.424616	−	0.905374i	$-0.360409\pi$
$19$	16.1354			0.849231			0.424616	+	0.905374i	$0.360409\pi$
$20$	5.52341	−	16.7654i	0.276170	−	0.838272i
$21$		0			0
$22$	−5.95154	+	37.0851i	−0.270525	+	1.68568i
$23$			18.3926i			0.799680i	0.916585	+	0.399840i	$0.130934\pi$
$23$			18.3926i			0.799680i	−0.916585	+	0.399840i	$0.869066\pi$
$24$		0			0
$25$	5.52575			0.221030
$26$	39.3330	+	6.31230i	1.51281	+	0.242781i
$27$		0			0
$28$	4.50569	−	13.6763i	0.160917	−	0.488439i
$29$		−	17.9287i		−	0.618232i	−0.951024	−	0.309116i	$-0.899967\pi$
$29$		−	17.9287i		−	0.618232i	0.951024	−	0.309116i	$-0.100033\pi$
$30$		0			0
$31$		−	29.7323i		−	0.959106i	−0.877513	−	0.479553i	$-0.840799\pi$
$31$		−	29.7323i		−	0.959106i	0.877513	−	0.479553i	$-0.159201\pi$
$32$	22.8578	−	22.3946i	0.714307	−	0.699832i
$33$		0			0
$34$	−2.53713	+	15.8093i	−0.0746214	+	0.464978i
$35$	−15.8860			−0.453886
$36$		0			0
$37$			26.7200i			0.722162i	0.932535	+	0.361081i	$0.117592\pi$
$37$			26.7200i			0.722162i	−0.932535	+	0.361081i	$0.882408\pi$
$38$	5.11350	−	31.8631i	0.134566	−	0.838502i
$39$		0			0
$40$	−31.3568	−	16.2204i	−0.783920	−	0.405511i
$41$	−40.2437			−0.981553			−0.490776	−	0.871286i	$-0.663287\pi$
$41$	−40.2437			−0.981553			−0.490776	+	0.871286i	$0.663287\pi$
$42$		0			0
$43$	−71.8376			−1.67064			−0.835321	−	0.549762i	$-0.814718\pi$
$43$	−71.8376			−1.67064			−0.835321	+	0.549762i	$0.814718\pi$
$44$	71.3469	+	23.5054i	1.62152	+	0.534214i
$45$		0			0
$46$	36.3206	+	5.82885i	0.789577	+	0.126714i
$47$		−	23.3952i		−	0.497770i	−0.968533	−	0.248885i	$-0.919936\pi$
$47$		−	23.3952i		−	0.497770i	0.968533	−	0.248885i	$-0.0800641\pi$
$48$		0			0
$49$	36.0411			0.735533
$50$	1.75118	−	10.9119i	0.0350236	−	0.218238i
$51$		0			0
$52$	24.9302	−	75.6717i	0.479427	−	1.45522i
$53$			90.7227i			1.71175i	0.517183	+	0.855875i	$0.326981\pi$
$53$			90.7227i			1.71175i	−0.517183	+	0.855875i	$0.673019\pi$
$54$		0			0
$55$		−	82.8745i		−	1.50681i
$56$	−25.5791	−	13.2317i	−0.456770	−	0.236281i
$57$		0			0
$58$	−35.4044	−	5.68183i	−0.610421	−	0.0979626i
$59$	−10.9410			−0.185440			−0.0927200	−	0.995692i	$-0.529556\pi$
$59$	−10.9410			−0.185440			−0.0927200	+	0.995692i	$0.529556\pi$
$60$		0			0
$61$			90.9260i			1.49059i	0.666735	+	0.745295i	$0.267691\pi$
$61$			90.9260i			1.49059i	−0.666735	+	0.745295i	$0.732309\pi$
$62$	−58.7133	−	9.42252i	−0.946988	−	0.151976i
$63$		0			0
$64$	−36.9795	−	52.2352i	−0.577804	−	0.816175i
$65$	−87.8980			−1.35228
$66$		0			0
$67$	74.0054			1.10456			0.552279	−	0.833659i	$-0.313758\pi$
$67$	74.0054			1.10456			0.552279	+	0.833659i	$0.313758\pi$
$68$	30.4150	+	10.0203i	0.447280	+	0.147357i
$69$		0			0
$70$	−5.03446	+	31.3706i	−0.0719209	+	0.448151i
$71$			13.9001i			0.195776i	0.995197	+	0.0978882i	$0.0312088\pi$
$71$			13.9001i			0.195776i	−0.995197	+	0.0978882i	$0.968791\pi$
$72$		0			0
$73$	−56.0158			−0.767340			−0.383670	−	0.923470i	$-0.625340\pi$
$73$	−56.0158			−0.767340			−0.383670	+	0.923470i	$0.625340\pi$
$74$	52.7648	+	8.46788i	0.713038	+	0.114431i
$75$		0			0
$76$	−61.3005	−	20.1956i	−0.806586	−	0.265731i
$77$		−	67.6044i		−	0.877979i
$78$		0			0
$79$		−	118.415i		−	1.49893i	−0.662044	−	0.749465i	$-0.730311\pi$
$79$		−	118.415i		−	1.49893i	0.662044	−	0.749465i	$-0.269689\pi$
$80$	−41.9683	+	56.7809i	−0.524604	+	0.709761i
$81$		0			0
$82$	−12.7537	+	79.4704i	−0.155533	+	0.969152i
$83$	−8.08995			−0.0974693			−0.0487347	−	0.998812i	$-0.515519\pi$
$83$	−8.08995			−0.0974693			−0.0487347	+	0.998812i	$0.515519\pi$
$84$		0			0
$85$		−	35.3292i		−	0.415638i
$86$	−22.7662	+	141.860i	−0.264723	+	1.64954i
$87$		0			0
$88$	69.0276	−	133.442i	0.784404	−	1.51639i
$89$	83.9483			0.943239			0.471620	−	0.881802i	$-0.343670\pi$
$89$	83.9483			0.943239			0.471620	+	0.881802i	$0.343670\pi$
$90$		0			0
$91$	−71.7022			−0.787937
$92$	23.0208	−	69.8761i	0.250227	−	0.759523i
$93$		0			0
$94$	−46.1992	−	7.41422i	−0.491481	−	0.0788747i
$95$			71.2049i			0.749525i
$96$		0			0
$97$	−79.0054			−0.814489			−0.407244	−	0.913319i	$-0.633510\pi$
$97$	−79.0054			−0.814489			−0.407244	+	0.913319i	$0.633510\pi$
$98$	11.4219	−	71.1715i	0.116550	−	0.726240i
$99$		0			0
$100$	−20.9931	−	6.91621i	−0.209931	−	0.0691621i
$101$		−	87.0864i		−	0.862241i	−0.902294	−	0.431121i	$-0.858118\pi$
$101$		−	87.0864i		−	0.862241i	0.902294	−	0.431121i	$-0.141882\pi$
$102$		0			0
$103$		−	138.658i		−	1.34619i	−0.739556	−	0.673095i	$-0.764965\pi$
$103$		−	138.658i		−	1.34619i	0.739556	−	0.673095i	$-0.235035\pi$
$104$	−141.531	−	73.2117i	−1.36087	−	0.703959i
$105$		0			0
$106$	179.153	+	28.7511i	1.69012	+	0.271237i
$107$	54.4965			0.509313			0.254656	−	0.967032i	$-0.418038\pi$
$107$	54.4965			0.509313			0.254656	+	0.967032i	$0.418038\pi$
$108$		0			0
$109$			143.879i			1.31999i	0.751271	+	0.659994i	$0.229441\pi$
$109$			143.879i			1.31999i	−0.751271	+	0.659994i	$0.770559\pi$
$110$	−163.655	−	26.2639i	−1.48777	−	0.238763i
$111$		0			0
$112$	−34.2354	+	46.3186i	−0.305673	+	0.413559i
$113$	128.630			1.13832			0.569161	−	0.822226i	$-0.307268\pi$
$113$	128.630			1.13832			0.569161	+	0.822226i	$0.307268\pi$
$114$		0			0
$115$	−81.1661			−0.705792
$116$	−22.4402	+	68.1136i	−0.193450	+	0.587187i
$117$		0			0
$118$	−3.46732	+	21.6055i	−0.0293841	+	0.183097i
$119$		−	28.8196i		−	0.242181i
$120$		0			0
$121$	231.681			1.91472
$122$	179.555	+	28.8156i	1.47176	+	0.236193i
$123$		0			0
$124$	−37.2139	+	112.957i	−0.300112	+	0.910943i
$125$			134.709i			1.07767i
$126$		0			0
$127$			90.8699i			0.715511i	0.933815	+	0.357756i	$0.116458\pi$
$127$			90.8699i			0.715511i	−0.933815	+	0.357756i	$0.883542\pi$
$128$	−114.870	+	56.4706i	−0.897420	+	0.441176i
$129$		0			0
$130$	−27.8559	+	173.575i	−0.214276	+	1.33519i
$131$	78.5838			0.599876			0.299938	−	0.953959i	$-0.403034\pi$
$131$	78.5838			0.599876			0.299938	+	0.953959i	$0.403034\pi$
$132$		0			0
$133$			58.0850i			0.436729i
$134$	23.4532	−	146.141i	0.175024	−	1.09060i
$135$		0			0
$136$	29.4263	−	56.8860i	0.216370	−	0.418279i
$137$	271.485			1.98164			0.990821	−	0.135178i	$-0.0431606\pi$
$137$	271.485			1.98164			0.990821	+	0.135178i	$0.0431606\pi$
$138$		0			0
$139$	177.843			1.27945			0.639723	−	0.768605i	$-0.279049\pi$
$139$	177.843			1.27945			0.639723	+	0.768605i	$0.279049\pi$
$140$	60.3530	+	19.8834i	0.431093	+	0.142025i
$141$		0			0
$142$	27.4490	+	4.40512i	0.193303	+	0.0310220i
$143$		−	374.059i		−	2.61579i
$144$		0			0
$145$	79.1188			0.545647
$146$	−17.7521	+	110.616i	−0.121590	+	0.757645i
$147$		0			0
$148$	33.4436	−	101.513i	0.225970	−	0.685897i
$149$		−	206.173i		−	1.38371i	−0.722037	−	0.691854i	$-0.756794\pi$
$149$		−	206.173i		−	1.38371i	0.722037	−	0.691854i	$-0.243206\pi$
$150$		0			0
$151$			215.526i			1.42732i	0.700490	+	0.713662i	$0.252965\pi$
$151$			215.526i			1.42732i	−0.700490	+	0.713662i	$0.747035\pi$
$152$	−59.3078	+	114.652i	−0.390183	+	0.754289i
$153$		0			0
$154$	−133.501	−	21.4246i	−0.866887	−	0.139121i
$155$	131.207			0.846500
$156$		0			0
$157$			163.503i			1.04142i	0.853734	+	0.520709i	$0.174332\pi$
$157$			163.503i			1.04142i	−0.853734	+	0.520709i	$0.825668\pi$
$158$	−233.839	−	37.5273i	−1.47999	−	0.237514i
$159$		0			0
$160$	98.8267	+	100.871i	0.617667	+	0.630442i
$161$	−66.2107			−0.411247
$162$		0			0
$163$	−72.2438			−0.443214			−0.221607	−	0.975136i	$-0.571130\pi$
$163$	−72.2438			−0.443214			−0.221607	+	0.975136i	$0.571130\pi$
$164$	152.891	+	50.3703i	0.932262	+	0.307136i
$165$		0			0
$166$	−2.56380	+	15.9755i	−0.0154446	+	0.0962379i
$167$			211.488i			1.26639i	0.773990	+	0.633197i	$0.218258\pi$
$167$			211.488i			1.26639i	−0.773990	+	0.633197i	$0.781742\pi$
$168$		0			0
$169$	−227.732			−1.34753
$170$	−69.7657	−	11.1962i	−0.410386	−	0.0658603i
$171$		0			0
$172$	272.921	+	89.9144i	1.58675	+	0.522758i
$173$			113.539i			0.656292i	0.944627	+	0.328146i	$0.106424\pi$
$173$			113.539i			0.656292i	−0.944627	+	0.328146i	$0.893576\pi$
$174$		0			0
$175$			19.8919i			0.113668i
$176$	−241.636	−	178.600i	−1.37293	−	1.01477i
$177$		0			0
$178$	26.6042	−	165.775i	0.149462	−	0.931322i
$179$	−29.2370			−0.163335			−0.0816677	−	0.996660i	$-0.526025\pi$
$179$	−29.2370			−0.163335			−0.0816677	+	0.996660i	$0.526025\pi$
$180$		0			0
$181$		−	170.599i		−	0.942534i	−0.881991	−	0.471267i	$-0.843797\pi$
$181$		−	170.599i		−	0.942534i	0.881991	−	0.471267i	$-0.156203\pi$
$182$	−22.7233	+	141.593i	−0.124853	+	0.777982i
$183$		0			0
$184$	−130.691	−	67.6046i	−0.710277	−	0.367416i
$185$	−117.914			−0.637375
$186$		0			0
$187$	150.347			0.803994
$188$	−29.2822	+	88.8815i	−0.155756	+	0.472774i
$189$		0			0
$190$	140.611	+	22.5657i	0.740056	+	0.118767i
$191$			353.213i			1.84928i	0.380841	+	0.924641i	$0.375635\pi$
$191$			353.213i			1.84928i	−0.380841	+	0.924641i	$0.624365\pi$
$192$		0			0
$193$	−23.5773			−0.122162			−0.0610810	−	0.998133i	$-0.519455\pi$
$193$	−23.5773			−0.122162			−0.0610810	+	0.998133i	$0.519455\pi$
$194$	−25.0378	+	156.015i	−0.129061	+	0.804199i
$195$		0			0
$196$	−136.925	−	45.1102i	−0.698597	−	0.230154i
$197$			21.5269i			0.109273i	0.998506	+	0.0546367i	$0.0174001\pi$
$197$			21.5269i			0.109273i	−0.998506	+	0.0546367i	$0.982600\pi$
$198$		0			0
$199$		−	34.8638i		−	0.175195i	−0.996156	−	0.0875974i	$-0.972081\pi$
$199$		−	34.8638i		−	0.175195i	0.996156	−	0.0875974i	$-0.0279189\pi$
$200$	−20.3106	+	39.2639i	−0.101553	+	0.196319i
$201$		0			0
$202$	−171.972	−	27.5987i	−0.851348	−	0.136627i
$203$	64.5407			0.317934
$204$		0			0
$205$		−	177.594i		−	0.866311i
$206$	−273.811	−	43.9422i	−1.32918	−	0.213312i
$207$		0			0
$208$	−189.426	+	256.283i	−0.910703	+	1.23213i
$209$	−303.019			−1.44985
$210$		0			0
$211$	−179.116			−0.848889			−0.424444	−	0.905454i	$-0.639531\pi$
$211$	−179.116			−0.848889			−0.424444	+	0.905454i	$0.639531\pi$
$212$	113.552	−	344.668i	0.535620	−	1.62579i
$213$		0			0
$214$	17.2706	−	107.616i	0.0807037	−	0.502878i
$215$		−	317.017i		−	1.47450i
$216$		0			0
$217$	107.032			0.493233
$218$	284.122	+	45.5969i	1.30331	+	0.209160i
$219$		0			0
$220$	−103.729	+	314.851i	−0.471493	+	1.43114i
$221$		−	159.460i		−	0.721539i
$222$		0			0
$223$			1.38743i			0.00622167i	0.999995	+	0.00311084i	$0.000990211\pi$
$223$			1.38743i			0.00622167i	−0.999995	+	0.00311084i	$0.999010\pi$
$224$	80.6173	+	82.2847i	0.359898	+	0.367342i
$225$		0			0
$226$	40.7645	−	254.011i	0.180374	−	1.12394i
$227$	111.238			0.490033			0.245017	−	0.969519i	$-0.421207\pi$
$227$	111.238			0.490033			0.245017	+	0.969519i	$0.421207\pi$
$228$		0			0
$229$		−	385.872i		−	1.68503i	−0.538673	−	0.842515i	$-0.681074\pi$
$229$		−	385.872i		−	1.68503i	0.538673	−	0.842515i	$-0.318926\pi$
$230$	−25.7225	+	160.281i	−0.111837	+	0.696875i
$231$		0			0
$232$	127.395	+	65.8994i	0.549115	+	0.284049i
$233$	174.604			0.749372			0.374686	−	0.927152i	$-0.377750\pi$
$233$	174.604			0.749372			0.374686	+	0.927152i	$0.377750\pi$
$234$		0			0
$235$	103.242			0.439328
$236$	41.5662	+	13.6941i	0.176128	+	0.0580257i
$237$		0			0
$238$	−56.9109	−	9.13327i	−0.239122	−	0.0383751i
$239$			112.809i			0.472004i	0.971753	+	0.236002i	$0.0758373\pi$
$239$			112.809i			0.472004i	−0.971753	+	0.236002i	$0.924163\pi$
$240$		0			0
$241$	10.3355			0.0428861			0.0214430	−	0.999770i	$-0.493174\pi$
$241$	10.3355			0.0428861			0.0214430	+	0.999770i	$0.493174\pi$
$242$	73.4224	−	457.507i	0.303398	−	1.89053i
$243$		0			0
$244$	113.806	−	345.440i	0.466418	−	1.41574i
$245$			159.048i			0.649176i
$246$		0			0
$247$			321.387i			1.30116i
$248$	211.266	+	109.285i	0.851879	+	0.440665i
$249$		0			0
$250$	266.014	+	42.6909i	1.06406	+	0.170764i
$251$	−334.659			−1.33330			−0.666651	−	0.745370i	$-0.732273\pi$
$251$	−334.659			−1.33330			−0.666651	+	0.745370i	$0.732273\pi$
$252$		0			0
$253$		−	345.410i		−	1.36526i
$254$	179.444	+	28.7978i	0.706472	+	0.113377i
$255$		0			0
$256$	75.1107	+	244.733i	0.293401	+	0.955989i
$257$	−218.689			−0.850929			−0.425464	−	0.904975i	$-0.639889\pi$
$257$	−218.689			−0.850929			−0.425464	+	0.904975i	$0.639889\pi$
$258$		0			0
$259$	−96.1879			−0.371382
$260$	333.936	+	110.016i	1.28437	+	0.423139i
$261$		0			0
$262$	24.9041	−	155.182i	0.0950540	−	0.592297i
$263$		−	150.622i		−	0.572709i	−0.958124	−	0.286354i	$-0.907557\pi$
$263$		−	150.622i		−	0.572709i	0.958124	−	0.286354i	$-0.0924435\pi$
$264$		0			0
$265$	−400.356			−1.51078
$266$	114.702	+	18.4078i	0.431211	+	0.0692023i
$267$		0			0
$268$	−281.156	−	92.6276i	−1.04909	−	0.345625i
$269$			340.377i			1.26534i	0.774420	+	0.632672i	$0.218042\pi$
$269$			340.377i			1.26534i	−0.774420	+	0.632672i	$0.781958\pi$
$270$		0			0
$271$			137.486i			0.507328i	0.967292	+	0.253664i	$0.0816358\pi$
$271$			137.486i			0.507328i	−0.967292	+	0.253664i	$0.918364\pi$
$272$	−103.009	−	76.1369i	−0.378709	−	0.279915i
$273$		0			0
$274$	86.0369	−	536.110i	0.314003	−	1.95661i
$275$	−103.773			−0.377355
$276$		0			0
$277$		−	31.5211i		−	0.113795i	−0.998380	−	0.0568973i	$-0.981879\pi$
$277$		−	31.5211i		−	0.113795i	0.998380	−	0.0568973i	$-0.0181208\pi$
$278$	56.3606	−	351.192i	0.202736	−	1.26328i
$279$		0			0
$280$	58.3910	−	112.880i	0.208539	−	0.403142i
$281$	285.437			1.01579			0.507896	−	0.861419i	$-0.330424\pi$
$281$	285.437			1.01579			0.507896	+	0.861419i	$0.330424\pi$
$282$		0			0
$283$	−0.947759			−0.00334897			−0.00167449	−	0.999999i	$-0.500533\pi$
$283$	−0.947759			−0.00334897			−0.00167449	+	0.999999i	$0.500533\pi$
$284$	17.3979	−	52.8084i	0.0612600	−	0.185945i
$285$		0			0
$286$	−738.665	−	118.544i	−2.58275	−	0.414488i
$287$		−	144.871i		−	0.504777i
$288$		0			0
$289$	−224.908			−0.778227
$290$	25.0737	−	156.239i	0.0864611	−	0.538753i
$291$		0			0
$292$	212.812	+	70.1112i	0.728807	+	0.240107i
$293$		−	204.998i		−	0.699652i	−0.936815	−	0.349826i	$-0.886241\pi$
$293$		−	204.998i		−	0.699652i	0.936815	−	0.349826i	$-0.113759\pi$
$294$		0			0
$295$		−	48.2821i		−	0.163668i
$296$	−189.862	−	98.2128i	−0.641425	−	0.331800i
$297$		0			0
$298$	−407.136	−	65.3386i	−1.36623	−	0.219257i
$299$	−366.347			−1.22524
$300$		0			0
$301$		−	258.605i		−	0.859151i
$302$	425.606	+	68.3028i	1.40929	+	0.226168i
$303$		0			0
$304$	207.611	+	153.451i	0.682932	+	0.504775i
$305$	−401.253			−1.31558
$306$		0			0
$307$	229.805			0.748551			0.374276	−	0.927317i	$-0.377891\pi$
$307$	229.805			0.748551			0.374276	+	0.927317i	$0.377891\pi$
$308$	−84.6159	+	256.838i	−0.274727	+	0.833890i
$309$		0			0
$310$	41.5812	−	259.100i	0.134133	−	0.835805i
$311$			286.078i			0.919864i	0.887954	+	0.459932i	$0.152126\pi$
$311$			286.078i			0.919864i	−0.887954	+	0.459932i	$0.847874\pi$
$312$		0			0
$313$	447.913			1.43103			0.715517	−	0.698596i	$-0.246191\pi$
$313$	447.913			1.43103			0.715517	+	0.698596i	$0.246191\pi$
$314$	322.874	+	51.8160i	1.02826	+	0.165019i
$315$		0			0
$316$	−148.213	+	449.876i	−0.469027	+	1.42366i
$317$		−	387.037i		−	1.22094i	−0.792040	−	0.610469i	$-0.790981\pi$
$317$		−	387.037i		−	1.22094i	0.792040	−	0.610469i	$-0.209019\pi$
$318$		0			0
$319$			336.698i			1.05548i
$320$	230.512	−	163.189i	0.720350	−	0.509966i
$321$		0			0
$322$	−20.9830	+	130.748i	−0.0651645	+	0.406051i
$323$	−129.176			−0.399927
$324$		0			0
$325$			110.063i			0.338655i
$326$	−22.8949	+	142.662i	−0.0702299	+	0.437614i
$327$		0			0
$328$	147.921	−	285.956i	0.450978	−	0.871817i
$329$	84.2191			0.255985
$330$		0			0
$331$	−41.5163			−0.125427			−0.0627134	−	0.998032i	$-0.519975\pi$
$331$	−41.5163			−0.125427			−0.0627134	+	0.998032i	$0.519975\pi$
$332$	30.7348	+	10.1257i	0.0925747	+	0.0304990i
$333$		0			0
$334$	417.632	+	67.0231i	1.25039	+	0.200668i
$335$			326.583i			0.974875i
$336$		0			0
$337$	146.594			0.434997			0.217499	−	0.976061i	$-0.430210\pi$
$337$	146.594			0.434997			0.217499	+	0.976061i	$0.430210\pi$
$338$	−72.1711	+	449.710i	−0.213524	+	1.33050i
$339$		0			0
$340$	−44.2192	+	134.220i	−0.130056	+	0.394766i
$341$			558.366i			1.63744i
$342$		0			0
$343$			306.135i			0.892522i
$344$	264.049	−	510.451i	0.767583	−	1.48387i
$345$		0			0
$346$	224.208	+	35.9818i	0.648001	+	0.103994i
$347$	−109.781			−0.316373			−0.158186	−	0.987409i	$-0.550565\pi$
$347$	−109.781			−0.316373			−0.158186	+	0.987409i	$0.550565\pi$
$348$		0			0
$349$		−	430.104i		−	1.23239i	−0.787593	−	0.616195i	$-0.788673\pi$
$349$		−	430.104i		−	1.23239i	0.787593	−	0.616195i	$-0.211327\pi$
$350$	39.2811	+	6.30397i	0.112232	+	0.0180114i
$351$		0			0
$352$	−429.265	+	420.567i	−1.21950	+	1.19479i
$353$	−324.763			−0.920008			−0.460004	−	0.887917i	$-0.652152\pi$
$353$	−324.763			−0.920008			−0.460004	+	0.887917i	$0.652152\pi$
$354$		0			0
$355$	−61.3407			−0.172791
$356$	−318.931	−	105.072i	−0.895873	−	0.295147i
$357$		0			0
$358$	−9.26557	+	57.7353i	−0.0258815	+	0.161272i
$359$			160.539i			0.447185i	0.974683	+	0.223592i	$0.0717784\pi$
$359$			160.539i			0.447185i	−0.974683	+	0.223592i	$0.928222\pi$
$360$		0			0
$361$	−100.649			−0.278806
$362$	−336.886	−	54.0647i	−0.930626	−	0.149350i
$363$		0			0
$364$	272.406	+	89.7449i	0.748369	+	0.246552i
$365$		−	247.196i		−	0.677249i
$366$		0			0
$367$			373.416i			1.01748i	0.860919	+	0.508742i	$0.169889\pi$
$367$			373.416i			1.01748i	−0.860919	+	0.508742i	$0.830111\pi$
$368$	−174.919	+	236.655i	−0.475322	+	0.643085i
$369$		0			0
$370$	−37.3685	+	232.849i	−0.100996	+	0.629322i
$371$	−326.588			−0.880291
$372$		0			0
$373$			359.197i			0.962995i	0.876448	+	0.481497i	$0.159907\pi$
$373$			359.197i			0.962995i	−0.876448	+	0.481497i	$0.840093\pi$
$374$	47.6467	−	296.895i	0.127398	−	0.793836i
$375$		0			0
$376$	166.237	+	85.9921i	0.442120	+	0.228702i
$377$	357.107			0.947233
$378$		0			0
$379$	−258.439			−0.681896			−0.340948	−	0.940082i	$-0.610748\pi$
$379$	−258.439			−0.681896			−0.340948	+	0.940082i	$0.610748\pi$
$380$	89.1224	−	270.517i	0.234533	−	0.711887i
$381$		0			0
$382$	697.501	+	111.937i	1.82592	+	0.293030i
$383$			185.218i			0.483597i	0.970326	+	0.241799i	$0.0777373\pi$
$383$			185.218i			0.483597i	−0.970326	+	0.241799i	$0.922263\pi$
$384$		0			0
$385$	298.336			0.774898
$386$	−7.47192	+	46.5588i	−0.0193573	+	0.120619i
$387$		0			0
$388$	300.152	+	98.8858i	0.773588	+	0.254860i
$389$			107.100i			0.275321i	0.990479	+	0.137660i	$0.0439583\pi$
$389$			107.100i			0.275321i	−0.990479	+	0.137660i	$0.956042\pi$
$390$		0			0
$391$		−	147.247i		−	0.376592i
$392$	−132.474	+	256.094i	−0.337943	+	0.653301i
$393$		0			0
$394$	42.5098	+	6.82213i	0.107893	+	0.0173150i
$395$	522.563			1.32294
$396$		0			0
$397$			132.442i			0.333607i	0.985990	+	0.166803i	$0.0533446\pi$
$397$			132.442i			0.333607i	−0.985990	+	0.166803i	$0.946655\pi$
$398$	−68.8466	−	11.0488i	−0.172981	−	0.0277607i
$399$		0			0
$400$	71.0989	+	52.5512i	0.177747	+	0.131378i
$401$	−471.890			−1.17678			−0.588392	−	0.808576i	$-0.700239\pi$
$401$	−471.890			−1.17678			−0.588392	+	0.808576i	$0.700239\pi$
$402$		0			0
$403$	592.212			1.46951
$404$	−109.000	+	330.853i	−0.269802	+	0.818942i
$405$		0			0
$406$	20.4537	−	127.451i	0.0503786	−	0.313918i
$407$		−	501.796i		−	1.23291i
$408$		0			0
$409$	−386.361			−0.944649			−0.472324	−	0.881425i	$-0.656585\pi$
$409$	−386.361			−0.944649			−0.472324	+	0.881425i	$0.656585\pi$
$410$	−350.700	−	56.2816i	−0.855366	−	0.137272i
$411$		0			0
$412$	−173.548	+	526.778i	−0.421234	+	1.27859i
$413$		−	39.3858i		−	0.0953651i
$414$		0			0
$415$		−	35.7007i		−	0.0860257i
$416$	446.059	+	455.285i	1.07226	+	1.09444i
$417$		0			0
$418$	−96.0305	+	598.382i	−0.229738	+	1.43154i
$419$	41.3087			0.0985888			0.0492944	−	0.998784i	$-0.484303\pi$
$419$	41.3087			0.0985888			0.0492944	+	0.998784i	$0.484303\pi$
$420$		0			0
$421$		−	3.75696i		−	0.00892390i	−0.999990	−	0.00446195i	$-0.998580\pi$
$421$		−	3.75696i		−	0.00892390i	0.999990	−	0.00446195i	$-0.00142029\pi$
$422$	−56.7639	+	353.705i	−0.134512	+	0.838164i
$423$		0			0
$424$	−644.640	−	333.463i	−1.52038	−	0.786470i
$425$	−44.2379			−0.104089
$426$		0			0
$427$	−327.320			−0.766557
$428$	−207.039	−	68.2096i	−0.483737	−	0.159368i
$429$		0			0
$430$	−626.023	−	100.466i	−1.45587	−	0.233643i
$431$		−	451.946i		−	1.04860i	−0.851534	−	0.524299i	$-0.824327\pi$
$431$		−	451.946i		−	1.04860i	0.851534	−	0.524299i	$-0.175673\pi$
$432$		0			0
$433$	−127.903			−0.295389			−0.147694	−	0.989033i	$-0.547185\pi$
$433$	−127.903			−0.295389			−0.147694	+	0.989033i	$0.547185\pi$
$434$	33.9196	−	211.359i	0.0781558	−	0.487002i
$435$		0			0
$436$	180.083	−	546.614i	0.413035	−	1.25370i
$437$			296.773i			0.679114i
$438$		0			0
$439$		−	133.514i		−	0.304132i	−0.988370	−	0.152066i	$-0.951407\pi$
$439$		−	133.514i		−	0.304132i	0.988370	−	0.152066i	$-0.0485926\pi$
$440$	588.874	+	304.616i	1.33835	+	0.692310i
$441$		0			0
$442$	−314.891	−	50.5348i	−0.712423	−	0.114332i
$443$	631.208			1.42485			0.712424	−	0.701749i	$-0.247597\pi$
$443$	631.208			1.42485			0.712424	+	0.701749i	$0.247597\pi$
$444$		0			0
$445$			370.461i			0.832496i
$446$	2.73981	+	0.439694i	0.00614307	+	0.000985861i
$447$		0			0
$448$	188.039	−	133.120i	0.419729	−	0.297144i
$449$	−84.8691			−0.189018			−0.0945091	−	0.995524i	$-0.530128\pi$
$449$	−84.8691			−0.189018			−0.0945091	+	0.995524i	$0.530128\pi$
$450$		0			0
$451$	755.768			1.67576
$452$	−488.684	−	160.998i	−1.08116	−	0.356190i
$453$		0			0
$454$	35.2525	−	219.664i	0.0776487	−	0.483842i
$455$		−	316.419i		−	0.695427i
$456$		0			0
$457$	301.582			0.659917			0.329959	−	0.943995i	$-0.392965\pi$
$457$	301.582			0.659917			0.329959	+	0.943995i	$0.392965\pi$
$458$	−761.993	−	122.287i	−1.66374	−	0.267003i
$459$		0			0
$460$	308.361	+	101.590i	0.670350	+	0.220848i
$461$		−	185.028i		−	0.401362i	−0.979657	−	0.200681i	$-0.935685\pi$
$461$		−	185.028i		−	0.401362i	0.979657	−	0.200681i	$-0.0643154\pi$
$462$		0			0
$463$		−	515.131i		−	1.11259i	−0.830984	−	0.556297i	$-0.812222\pi$
$463$		−	515.131i		−	1.11259i	0.830984	−	0.556297i	$-0.187778\pi$
$464$	170.507	−	230.686i	0.367471	−	0.497168i
$465$		0			0
$466$	55.3340	−	344.796i	0.118743	−	0.739905i
$467$	301.784			0.646218			0.323109	−	0.946362i	$-0.395272\pi$
$467$	301.784			0.646218			0.323109	+	0.946362i	$0.395272\pi$
$468$		0			0
$469$			266.408i			0.568034i
$470$	32.7187	−	203.876i	0.0696142	−	0.433778i
$471$		0			0
$472$	40.2149	−	77.7422i	0.0852011	−	0.164708i
$473$	1349.10			2.85221
$474$		0			0
$475$	89.1602			0.187706
$476$	−36.0715	+	109.489i	−0.0757805	+	0.230020i
$477$		0			0
$478$	222.768	+	35.7506i	0.466041	+	0.0747919i
$479$		−	263.369i		−	0.549831i	−0.961468	−	0.274915i	$-0.911350\pi$
$479$		−	263.369i		−	0.549831i	0.961468	−	0.274915i	$-0.0886499\pi$
$480$		0			0
$481$	−532.212			−1.10647
$482$	3.27546	−	20.4099i	0.00679556	−	0.0423443i
$483$		0			0
$484$	−880.186	−	289.979i	−1.81857	−	0.599131i
$485$		−	348.648i		−	0.718862i
$486$		0			0
$487$		−	100.621i		−	0.206615i	−0.994649	−	0.103307i	$-0.967057\pi$
$487$		−	100.621i		−	0.206615i	0.994649	−	0.103307i	$-0.0329425\pi$
$488$	−646.085	−	334.210i	−1.32395	−	0.684858i
$489$		0			0
$490$	314.077	+	50.4042i	0.640974	+	0.102866i
$491$	506.967			1.03252			0.516260	−	0.856432i	$-0.327324\pi$
$491$	506.967			1.03252			0.516260	+	0.856432i	$0.327324\pi$
$492$		0			0
$493$			143.533i			0.291143i
$494$	634.653	+	101.851i	1.28472	+	0.206177i
$495$		0			0
$496$	282.761	−	382.560i	0.570083	−	0.771291i
$497$	−50.0383			−0.100681
$498$		0			0
$499$	−609.604			−1.22165			−0.610825	−	0.791765i	$-0.709162\pi$
$499$	−609.604			−1.22165			−0.610825	+	0.791765i	$0.709162\pi$
$500$	168.606	−	511.778i	0.337213	−	1.02356i
$501$		0			0
$502$	−106.057	+	660.861i	−0.211270	+	1.31646i
$503$			794.669i			1.57986i	0.613197	+	0.789930i	$0.289883\pi$
$503$			794.669i			1.57986i	−0.613197	+	0.789930i	$0.710117\pi$
$504$		0			0
$505$	384.309			0.761008
$506$	−682.093	−	109.465i	−1.34801	−	0.216333i
$507$		0			0
$508$	113.736	−	345.227i	0.223889	−	0.679581i
$509$			155.999i			0.306481i	0.988189	+	0.153241i	$0.0489709\pi$
$509$			155.999i			0.306481i	−0.988189	+	0.153241i	$0.951029\pi$
$510$		0			0
$511$		−	201.648i		−	0.394615i
$512$	507.086	−	70.7645i	0.990403	−	0.138212i
$513$		0			0
$514$	−69.3051	+	431.852i	−0.134835	+	0.840178i
$515$	611.891			1.18814
$516$		0			0
$517$			439.357i			0.849820i
$518$	−30.4831	+	189.945i	−0.0588477	+	0.366690i
$519$		0			0
$520$	323.081	−	624.569i	0.621309	−	1.20109i
$521$	719.474			1.38095			0.690474	−	0.723357i	$-0.257402\pi$
$521$	719.474			1.38095			0.690474	+	0.723357i	$0.257402\pi$
$522$		0			0
$523$	−963.965			−1.84314			−0.921572	−	0.388206i	$-0.873095\pi$
$523$	−963.965			−1.84314			−0.921572	+	0.388206i	$0.873095\pi$
$524$	−298.550	−	98.3580i	−0.569752	−	0.187706i
$525$		0			0
$526$	−297.439	−	47.7341i	−0.565473	−	0.0907492i
$527$			238.030i			0.451670i
$528$		0			0
$529$	190.710			0.360511
$530$	−126.878	+	790.596i	−0.239392	+	1.49169i
$531$		0			0
$532$	72.7010	−	220.672i	0.136656	−	0.414798i
$533$		−	801.579i		−	1.50390i
$534$		0			0
$535$			240.491i			0.449516i
$536$	−272.017	+	525.854i	−0.507494	+	0.981071i
$537$		0			0
$538$	672.154	+	107.870i	1.24936	+	0.200501i
$539$	−676.844			−1.25574
$540$		0			0
$541$		−	592.256i		−	1.09474i	−0.836890	−	0.547371i	$-0.815629\pi$
$541$		−	592.256i		−	1.09474i	0.836890	−	0.547371i	$-0.184371\pi$
$542$	271.498	+	43.5710i	0.500919	+	0.0803892i
$543$		0			0
$544$	−182.995	+	179.286i	−0.336387	+	0.329571i
$545$	−634.931			−1.16501
$546$		0			0
$547$	−285.828			−0.522538			−0.261269	−	0.965266i	$-0.584141\pi$
$547$	−285.828			−0.522538			−0.261269	+	0.965266i	$0.584141\pi$
$548$	−1031.41	−	339.800i	−1.88213	−	0.620072i
$549$		0			0
$550$	−32.8868	+	204.923i	−0.0597941	+	0.372587i
$551$		−	289.287i		−	0.525022i
$552$		0			0
$553$	426.277			0.770845
$554$	−62.2457	−	9.98942i	−0.112357	−	0.0180314i
$555$		0			0
$556$	−675.650	−	222.594i	−1.21520	−	0.400349i
$557$		−	148.974i		−	0.267459i	−0.991018	−	0.133729i	$-0.957305\pi$
$557$		−	148.974i		−	0.267459i	0.991018	−	0.133729i	$-0.0426953\pi$
$558$		0			0
$559$		−	1430.87i		−	2.55970i
$560$	−204.402	−	151.080i	−0.365004	−	0.269785i
$561$		0			0
$562$	90.4586	−	563.662i	0.160958	−	1.00296i
$563$	−107.185			−0.190382			−0.0951908	−	0.995459i	$-0.530346\pi$
$563$	−107.185			−0.190382			−0.0951908	+	0.995459i	$0.530346\pi$
$564$		0			0
$565$			567.641i			1.00467i
$566$	−0.300356	+	1.87157i	−0.000530665	+	0.00330666i
$567$		0			0
$568$	−98.7689	−	51.0917i	−0.173889	−	0.0899502i
$569$	119.321			0.209703			0.104851	−	0.994488i	$-0.466563\pi$
$569$	119.321			0.209703			0.104851	+	0.994488i	$0.466563\pi$
$570$		0			0
$571$	118.725			0.207926			0.103963	−	0.994581i	$-0.466848\pi$
$571$	118.725			0.207926			0.103963	+	0.994581i	$0.466848\pi$
$572$	−468.184	+	1421.10i	−0.818503	+	2.48444i
$573$		0			0
$574$	−286.081	−	45.9114i	−0.498400	−	0.0799850i
$575$			101.633i			0.176753i
$576$		0			0
$577$	490.151			0.849481			0.424741	−	0.905315i	$-0.360365\pi$
$577$	490.151			0.849481			0.424741	+	0.905315i	$0.360365\pi$
$578$	−71.2759	+	444.132i	−0.123315	+	0.768395i
$579$		0			0
$580$	−300.583	−	99.0277i	−0.518247	−	0.170737i
$581$		−	29.1226i		−	0.0501250i
$582$		0			0
$583$		−	1703.75i		−	2.92239i
$584$	205.893	−	398.027i	0.352557	−	0.681553i
$585$		0			0
$586$	−404.816	−	64.9664i	−0.690813	−	0.110864i
$587$	−686.259			−1.16909			−0.584547	−	0.811360i	$-0.698728\pi$
$587$	−686.259			−1.16909			−0.584547	+	0.811360i	$0.698728\pi$
$588$		0			0
$589$		−	479.742i		−	0.814503i
$590$	−95.3441	−	15.3012i	−0.161600	−	0.0259342i
$591$		0			0
$592$	−254.113	+	343.801i	−0.429246	+	0.580746i
$593$	−177.526			−0.299369			−0.149684	−	0.988734i	$-0.547826\pi$
$593$	−177.526			−0.299369			−0.149684	+	0.988734i	$0.547826\pi$
$594$		0			0
$595$	127.180			0.213747
$596$	−258.052	+	783.277i	−0.432974	+	1.31422i
$597$		0			0
$598$	−116.100	+	723.438i	−0.194147	+	1.20976i
$599$		−	192.768i		−	0.321817i	−0.986969	−	0.160908i	$-0.948558\pi$
$599$		−	192.768i		−	0.321817i	0.986969	−	0.160908i	$-0.0514423\pi$
$600$		0			0
$601$	−1097.74			−1.82652			−0.913261	−	0.407375i	$-0.866444\pi$
$601$	−1097.74			−1.82652			−0.913261	+	0.407375i	$0.866444\pi$
$602$	−510.675	−	81.9549i	−0.848297	−	0.136138i
$603$		0			0
$604$	269.759	−	818.812i	0.446621	−	1.35565i
$605$			1022.40i			1.68991i
$606$		0			0
$607$			4.30901i			0.00709886i	0.999994	+	0.00354943i	$0.00112982\pi$
$607$			4.30901i			0.00709886i	−0.999994	+	0.00354943i	$0.998870\pi$
$608$	368.820	−	361.346i	0.606612	−	0.594319i
$609$		0			0
$610$	−127.162	+	792.368i	−0.208462	+	1.29896i
$611$	465.989			0.762666
$612$		0			0
$613$			618.106i			1.00833i	0.863608	+	0.504165i	$0.168200\pi$
$613$			618.106i			1.00833i	−0.863608	+	0.504165i	$0.831800\pi$
$614$	72.8281	−	453.804i	0.118612	−	0.739094i
$615$		0			0
$616$	480.371	+	248.489i	0.779822	+	0.403391i
$617$	793.183			1.28555			0.642774	−	0.766056i	$-0.277783\pi$
$617$	793.183			1.28555			0.642774	+	0.766056i	$0.277783\pi$
$618$		0			0
$619$	635.387			1.02647			0.513237	−	0.858247i	$-0.328446\pi$
$619$	635.387			1.02647			0.513237	+	0.858247i	$0.328446\pi$
$620$	−498.475	−	164.224i	−0.803991	−	0.264877i
$621$		0			0
$622$	564.927	+	90.6615i	0.908243	+	0.145758i
$623$			302.201i			0.485074i
$624$		0			0
$625$	−456.322			−0.730116
$626$	141.949	−	884.509i	0.226756	−	1.41295i
$627$		0			0
$628$	204.645	−	621.169i	0.325868	−	0.989122i
$629$		−	213.914i		−	0.340086i
$630$		0			0
$631$			307.959i			0.488049i	0.969769	+	0.244024i	$0.0784677\pi$
$631$			307.959i			0.488049i	−0.969769	+	0.244024i	$0.921532\pi$
$632$	841.414	+	435.251i	1.33135	+	0.688689i
$633$		0			0
$634$	−764.295	−	122.657i	−1.20551	−	0.193465i
$635$	−401.006			−0.631505
$636$		0			0
$637$			717.872i			1.12696i
$638$	664.888	+	106.704i	1.04214	+	0.167247i
$639$		0			0
$640$	−249.203	−	506.916i	−0.389379	−	0.792057i
$641$	449.718			0.701588			0.350794	−	0.936453i	$-0.385912\pi$
$641$	449.718			0.701588			0.350794	+	0.936453i	$0.385912\pi$
$642$		0			0
$643$	−665.066			−1.03432			−0.517158	−	0.855890i	$-0.673010\pi$
$643$	−665.066			−1.03432			−0.517158	+	0.855890i	$0.673010\pi$
$644$	251.543	+	82.8715i	0.390595	+	0.128682i
$645$		0			0
$646$	−40.9375	+	255.089i	−0.0633708	+	0.394874i
$647$		−	9.25693i		−	0.0143075i	−0.999974	−	0.00715373i	$-0.997723\pi$
$647$		−	9.25693i		−	0.0143075i	0.999974	−	0.00715373i	$-0.00227712\pi$
$648$		0			0
$649$	205.469			0.316593
$650$	217.344	+	34.8802i	0.334376	+	0.0536619i
$651$		0			0
$652$	274.464	+	90.4227i	0.420957	+	0.138685i
$653$			692.725i			1.06083i	0.847737	+	0.530417i	$0.177965\pi$
$653$			692.725i			1.06083i	−0.847737	+	0.530417i	$0.822035\pi$
$654$		0			0
$655$			346.787i			0.529446i
$656$	−517.808	−	382.727i	−0.789342	−	0.583425i
$657$		0			0
$658$	26.6901	−	166.310i	0.0405624	−	0.252751i
$659$	−1008.98			−1.53108			−0.765538	−	0.643391i	$-0.777527\pi$
$659$	−1008.98			−1.53108			−0.765538	+	0.643391i	$0.777527\pi$
$660$		0			0
$661$			150.898i			0.228287i	0.993464	+	0.114144i	$0.0364124\pi$
$661$			150.898i			0.228287i	−0.993464	+	0.114144i	$0.963588\pi$
$662$	−13.1570	+	81.9836i	−0.0198746	+	0.123842i
$663$		0			0
$664$	29.7357	−	57.4841i	0.0447827	−	0.0865724i
$665$	−256.327			−0.385454
$666$		0			0
$667$	329.757			0.494388
$668$	264.705	−	803.471i	0.396265	−	1.20280i
$669$		0			0
$670$	644.914	+	103.498i	0.962559	+	0.154475i
$671$		−	1707.57i		−	2.54482i
$672$		0			0
$673$	−124.651			−0.185217			−0.0926084	−	0.995703i	$-0.529520\pi$
$673$	−124.651			−0.185217			−0.0926084	+	0.995703i	$0.529520\pi$
$674$	46.4574	−	289.484i	0.0689279	−	0.429501i
$675$		0			0
$676$	865.185	+	285.037i	1.27986	+	0.421653i
$677$			200.927i			0.296791i	0.988928	+	0.148395i	$0.0474108\pi$
$677$			200.927i			0.296791i	−0.988928	+	0.148395i	$0.952589\pi$
$678$		0			0
$679$		−	284.407i		−	0.418862i
$680$	251.036	+	129.857i	0.369170	+	0.190966i
$681$		0			0
$682$	1102.62	+	176.953i	1.61675	+	0.259462i
$683$	764.228			1.11893			0.559464	−	0.828855i	$-0.311007\pi$
$683$	764.228			1.11893			0.559464	+	0.828855i	$0.311007\pi$
$684$		0			0
$685$			1198.05i			1.74898i
$686$	604.535	+	97.0179i	0.881246	+	0.141425i
$687$		0			0
$688$	−924.323	−	683.193i	−1.34349	−	0.993013i
$689$	−1807.03			−2.62268
$690$		0			0
$691$	−130.928			−0.189476			−0.0947378	−	0.995502i	$-0.530201\pi$
$691$	−130.928			−0.189476			−0.0947378	+	0.995502i	$0.530201\pi$
$692$	142.109	−	431.348i	0.205359	−	0.623336i
$693$		0			0
$694$	−34.7910	+	216.789i	−0.0501312	+	0.312376i
$695$			784.815i			1.12923i
$696$		0			0
$697$	322.182			0.462241
$698$	−849.341	−	136.305i	−1.21682	−	0.195280i
$699$		0			0
$700$	24.8973	−	75.5719i	0.0355676	−	0.107960i
$701$		−	721.278i		−	1.02893i	−0.857512	−	0.514464i	$-0.827991\pi$
$701$		−	721.278i		−	1.02893i	0.857512	−	0.514464i	$-0.172009\pi$
$702$		0			0
$703$			431.137i			0.613282i
$704$	694.467	+	980.967i	0.986459	+	1.39342i
$705$		0			0
$706$	−102.921	+	641.319i	−0.145781	+	0.908384i
$707$	313.498			0.443420
$708$		0			0
$709$		−	4.66911i		−	0.00658548i	−0.999995	−	0.00329274i	$-0.998952\pi$
$709$		−	4.66911i		−	0.00658548i	0.999995	−	0.00329274i	$-0.00104811\pi$
$710$	−19.4396	+	121.132i	−0.0273798	+	0.170608i
$711$		0			0
$712$	−308.563	+	596.504i	−0.433375	+	0.837787i
$713$	546.855			0.766978
$714$		0			0
$715$	1650.71			2.30868
$716$	111.075	+	36.5940i	0.155133	+	0.0511090i
$717$		0			0
$718$	317.022	+	50.8769i	0.441535	+	0.0708591i
$719$			1307.39i			1.81835i	0.416417	+	0.909174i	$0.363286\pi$
$719$			1307.39i			1.81835i	−0.416417	+	0.909174i	$0.636714\pi$
$720$		0			0
$721$	499.146			0.692297
$722$	−31.8969	+	198.755i	−0.0441785	+	0.275284i
$723$		0			0
$724$	−213.527	+	648.127i	−0.294926	+	0.895203i
$725$		−	99.0698i		−	0.136648i
$726$		0			0
$727$			838.418i			1.15326i	0.817006	+	0.576629i	$0.195632\pi$
$727$			838.418i			1.15326i	−0.817006	+	0.576629i	$0.804368\pi$
$728$	263.551	−	509.488i	0.362021	−	0.699847i
$729$		0			0
$730$	−488.145	−	78.3393i	−0.668692	−	0.107314i
$731$	575.116			0.786753
$732$		0			0
$733$			1062.62i			1.44969i	0.688914	+	0.724843i	$0.258088\pi$
$733$			1062.62i			1.44969i	−0.688914	+	0.724843i	$0.741912\pi$
$734$	737.397	+	118.340i	1.00463	+	0.161226i
$735$		0			0
$736$	411.897	+	420.416i	0.559642	+	0.571217i
$737$	−1389.81			−1.88576
$738$		0			0
$739$	−518.771			−0.701991			−0.350996	−	0.936377i	$-0.614157\pi$
$739$	−518.771			−0.701991			−0.350996	+	0.936377i	$0.614157\pi$
$740$	447.972	+	147.585i	0.605368	+	0.199440i
$741$		0			0
$742$	−103.500	+	644.924i	−0.139487	+	0.869169i
$743$			130.095i			0.175094i	0.996160	+	0.0875471i	$0.0279028\pi$
$743$			130.095i			0.175094i	−0.996160	+	0.0875471i	$0.972097\pi$
$744$		0			0
$745$	909.832			1.22125
$746$	709.318	+	113.834i	0.950828	+	0.152592i
$747$		0			0
$748$	−571.188	−	188.179i	−0.763620	−	0.251576i
$749$			196.179i			0.261921i
$750$		0			0
$751$		−	144.284i		−	0.192122i	−0.995375	−	0.0960609i	$-0.969376\pi$
$751$		−	144.284i		−	0.192122i	0.995375	−	0.0960609i	$-0.0306244\pi$
$752$	222.494	−	301.022i	0.295870	−	0.400295i
$753$		0			0
$754$	113.171	−	705.191i	0.150095	−	0.935266i
$755$	−951.108			−1.25975
$756$		0			0
$757$		−	700.450i		−	0.925297i	−0.886542	−	0.462648i	$-0.846899\pi$
$757$		−	700.450i		−	0.925297i	0.886542	−	0.462648i	$-0.153101\pi$
$758$	−81.9023	+	510.347i	−0.108051	+	0.673281i
$759$		0			0
$760$	−505.955	−	261.723i	−0.665730	−	0.344372i
$761$	508.775			0.668561			0.334281	−	0.942474i	$-0.391507\pi$
$761$	508.775			0.668561			0.334281	+	0.942474i	$0.391507\pi$
$762$		0			0
$763$	−517.941			−0.678822
$764$	442.093	−	1341.90i	0.578655	−	1.75642i
$765$		0			0
$766$	365.755	+	58.6977i	0.477487	+	0.0766289i
$767$		−	217.924i		−	0.284125i
$768$		0			0
$769$	1485.01			1.93110			0.965548	−	0.260226i	$-0.0837971\pi$
$769$	1485.01			1.93110			0.965548	+	0.260226i	$0.0837971\pi$
$770$	94.5462	−	589.133i	0.122787	−	0.765108i
$771$		0			0
$772$	89.5732	+	29.5101i	0.116027	+	0.0382255i
$773$		−	1419.38i		−	1.83619i	−0.396359	−	0.918096i	$-0.629726\pi$
$773$		−	1419.38i		−	1.83619i	0.396359	−	0.918096i	$-0.370274\pi$
$774$		0			0
$775$		−	164.293i		−	0.211991i
$776$	290.395	−	561.382i	0.374220	−	0.723430i
$777$		0			0
$778$	211.493	+	33.9412i	0.271843	+	0.0436263i
$779$	−649.347			−0.833565
$780$		0			0
$781$		−	261.042i		−	0.334240i
$782$	−290.774	−	46.6645i	−0.371834	−	0.0596733i
$783$		0			0
$784$	463.735	+	342.760i	0.591498	+	0.437193i
$785$	−721.531			−0.919148
$786$		0			0
$787$	−277.527			−0.352639			−0.176319	−	0.984333i	$-0.556419\pi$
$787$	−277.527			−0.352639			−0.176319	+	0.984333i	$0.556419\pi$
$788$	26.9437	−	81.7835i	0.0341926	−	0.103786i
$789$		0			0
$790$	165.607	−	1031.92i	0.209628	−	1.30623i
$791$			463.050i			0.585398i
$792$		0			0
$793$	−1811.08			−2.28383
$794$	261.537	+	41.9725i	0.329392	+	0.0528620i
$795$		0			0
$796$	−43.6367	+	132.452i	−0.0548199	+	0.166397i
$797$			599.355i			0.752013i	0.926617	+	0.376007i	$0.122703\pi$
$797$			599.355i			0.752013i	−0.926617	+	0.376007i	$0.877297\pi$
$798$		0			0
$799$			187.297i			0.234414i
$800$	126.307	−	123.747i	0.157883	−	0.154684i
$801$		0			0
$802$	−149.548	+	931.857i	−0.186469	+	1.16192i
$803$	1051.97			1.31004
$804$		0			0
$805$		−	292.186i		−	0.362963i
$806$	187.679	−	1169.46i	0.232852	−	1.45094i
$807$		0			0
$808$	618.802	+	320.097i	0.765844	+	0.396160i
$809$	−297.174			−0.367336			−0.183668	−	0.982988i	$-0.558797\pi$
$809$	−297.174			−0.367336			−0.183668	+	0.982988i	$0.558797\pi$
$810$		0			0
$811$	−632.860			−0.780346			−0.390173	−	0.920742i	$-0.627585\pi$
$811$	−632.860			−0.780346			−0.390173	+	0.920742i	$0.627585\pi$
$812$	−245.199	−	80.7812i	−0.301969	−	0.0994843i
$813$		0			0
$814$	−990.912	−	159.025i	−1.21734	−	0.195363i
$815$		−	318.809i		−	0.391177i
$816$		0			0
$817$	−1159.13			−1.41876
$818$	−122.443	+	762.960i	−0.149685	+	0.932714i
$819$		0			0
$820$	−222.282	+	674.702i	−0.271076	+	0.822808i
$821$			1343.47i			1.63638i	0.574947	+	0.818190i	$0.305022\pi$
$821$			1343.47i			1.63638i	−0.574947	+	0.818190i	$0.694978\pi$
$822$		0			0
$823$		−	1078.41i		−	1.31034i	−0.755480	−	0.655172i	$-0.772596\pi$
$823$		−	1078.41i		−	1.31034i	0.755480	−	0.655172i	$-0.227404\pi$
$824$	985.247	+	509.654i	1.19569	+	0.618512i
$825$		0			0
$826$	−77.7764	−	12.4818i	−0.0941602	−	0.0151112i
$827$	−922.881			−1.11594			−0.557969	−	0.829862i	$-0.688419\pi$
$827$	−922.881			−1.11594			−0.557969	+	0.829862i	$0.688419\pi$
$828$		0			0
$829$		−	295.258i		−	0.356162i	−0.984016	−	0.178081i	$-0.943011\pi$
$829$		−	295.258i		−	0.356162i	0.984016	−	0.178081i	$-0.0569889\pi$
$830$	−70.4993	−	11.3140i	−0.0849389	−	0.0136313i
$831$		0			0
$832$	1040.43	−	736.562i	1.25051	−	0.885291i
$833$	−288.537			−0.346383
$834$		0			0
$835$	−933.288			−1.11771
$836$	1151.21	+	379.269i	1.37705	+	0.453671i
$837$		0			0
$838$	13.0912	−	81.5737i	0.0156220	−	0.0973433i
$839$			101.848i			0.121392i	0.998156	+	0.0606960i	$0.0193320\pi$
$839$			101.848i			0.121392i	−0.998156	+	0.0606960i	$0.980668\pi$
$840$		0			0
$841$	519.561			0.617789
$842$	−7.41899	−	1.19063i	−0.00881116	−	0.00141405i
$843$		0			0
$844$	680.484	+	224.187i	0.806260	+	0.265624i
$845$		−	1004.97i		−	1.18932i
$846$		0			0
$847$			834.015i			0.984670i
$848$	−862.795	+	1167.31i	−1.01745	+	1.37655i
$849$		0			0
$850$	−14.0195	+	87.3581i	−0.0164936	+	0.102774i
$851$	−491.451			−0.577499
$852$		0			0
$853$		−	740.329i		−	0.867912i	−0.900934	−	0.433956i	$-0.857117\pi$
$853$		−	740.329i		−	0.867912i	0.900934	−	0.433956i	$-0.142883\pi$
$854$	−103.732	+	646.369i	−0.121466	+	0.756872i
$855$		0			0
$856$	−200.309	+	387.231i	−0.234006	+	0.452373i
$857$	−553.996			−0.646436			−0.323218	−	0.946325i	$-0.604765\pi$
$857$	−553.996			−0.646436			−0.323218	+	0.946325i	$0.604765\pi$
$858$		0			0
$859$	1350.24			1.57187			0.785934	−	0.618310i	$-0.212182\pi$
$859$	1350.24			1.57187			0.785934	+	0.618310i	$0.212182\pi$
$860$	−396.789	+	1204.39i	−0.461382	+	1.40045i
$861$		0			0
$862$	−892.472	−	143.227i	−1.03535	−	0.166157i
$863$		−	656.568i		−	0.760798i	−0.924823	−	0.380399i	$-0.875787\pi$
$863$		−	656.568i		−	0.760798i	0.924823	−	0.380399i	$-0.124213\pi$
$864$		0			0
$865$	−501.042			−0.579239
$866$	−40.5341	+	252.575i	−0.0468061	+	0.291657i
$867$		0			0
$868$	−406.628	−	133.964i	−0.468465	−	0.154337i
$869$			2223.82i			2.55905i
$870$		0			0
$871$			1474.05i			1.69237i
$872$	−1022.35	−	528.845i	−1.17241	−	0.606473i
$873$		0			0
$874$	586.046	+	94.0508i	0.670534	+	0.107610i
$875$	−484.932			−0.554208
$876$		0			0
$877$		−	1238.69i		−	1.41242i	−0.708001	−	0.706211i	$-0.750403\pi$
$877$		−	1238.69i		−	1.41242i	0.708001	−	0.706211i	$-0.249597\pi$
$878$	−263.654	−	42.3122i	−0.300290	−	0.0481915i
$879$		0			0
$880$	788.157	−	1066.33i	0.895633	−	1.21174i
$881$	122.310			0.138831			0.0694154	−	0.997588i	$-0.477887\pi$
$881$	122.310			0.138831			0.0694154	+	0.997588i	$0.477887\pi$
$882$		0			0
$883$	1362.04			1.54251			0.771254	−	0.636527i	$-0.219630\pi$
$883$	1362.04			1.54251			0.771254	+	0.636527i	$0.219630\pi$
$884$	−199.586	+	605.810i	−0.225776	+	0.685306i
$885$		0			0
$886$	200.037	−	1246.47i	0.225776	−	1.40685i
$887$		−	519.056i		−	0.585182i	−0.956238	−	0.292591i	$-0.905483\pi$
$887$		−	519.056i		−	0.585182i	0.956238	−	0.292591i	$-0.0945174\pi$
$888$		0			0
$889$	−327.118			−0.367962
$890$	731.561	+	117.403i	0.821978	+	0.131914i
$891$		0			0
$892$	1.73656	−	5.27104i	0.00194681	−	0.00590924i
$893$		−	377.491i		−	0.422722i
$894$		0			0
$895$		−	129.022i		−	0.144159i
$896$	−203.285	−	413.514i	−0.226881	−	0.461511i
$897$		0			0
$898$	−26.8961	+	167.594i	−0.0299511	+	0.186630i
$899$	−533.062			−0.592950
$900$		0			0
$901$		−	726.306i		−	0.806111i
$902$	239.512	−	1492.44i	0.265534	−	1.65459i
$903$		0			0
$904$	−472.798	+	913.998i	−0.523007	+	1.01106i
$905$	752.845			0.831873
$906$		0			0
$907$	−169.347			−0.186711			−0.0933553	−	0.995633i	$-0.529759\pi$
$907$	−169.347			−0.186711			−0.0933553	+	0.995633i	$0.529759\pi$
$908$	−422.606	−	139.229i	−0.465425	−	0.153335i
$909$		0			0
$910$	−624.844	−	100.277i	−0.686641	−	0.110195i
$911$			266.499i			0.292535i	0.989245	+	0.146267i	$0.0467260\pi$
$911$			266.499i			0.292535i	−0.989245	+	0.146267i	$0.953274\pi$
$912$		0			0
$913$	151.928			0.166405
$914$	95.5750	−	595.544i	0.104568	−	0.651580i
$915$		0			0
$916$	−482.970	+	1465.98i	−0.527260	+	1.60041i
$917$			282.890i			0.308495i
$918$		0			0
$919$		−	10.0832i		−	0.0109720i	−0.999985	−	0.00548598i	$-0.998254\pi$
$919$		−	10.0832i		−	0.0109720i	0.999985	−	0.00548598i	$-0.00174625\pi$
$920$	298.337	−	576.735i	0.324279	−	0.626886i
$921$		0			0
$922$	−365.380	−	58.6375i	−0.396291	−	0.0635982i
$923$	−276.865			−0.299962
$924$		0			0
$925$			147.648i			0.159620i
$926$	−1017.25	−	163.251i	−1.09854	−	0.176297i
$927$		0			0
$928$	−401.507	−	409.812i	−0.432659	−	0.441608i
$929$	−832.048			−0.895639			−0.447819	−	0.894124i	$-0.647799\pi$
$929$	−832.048			−0.895639			−0.447819	+	0.894124i	$0.647799\pi$
$930$		0			0
$931$	581.537			0.624637
$932$	−663.343	−	218.540i	−0.711741	−	0.234485i
$933$		0			0
$934$	95.6390	−	595.943i	0.102397	−	0.638054i
$935$			663.475i			0.709599i
$936$		0			0
$937$	846.801			0.903736			0.451868	−	0.892085i	$-0.350758\pi$
$937$	846.801			0.903736			0.451868	+	0.892085i	$0.350758\pi$
$938$	526.085	+	84.4280i	0.560858	+	0.0900085i
$939$		0			0
$940$	−392.231	−	129.221i	−0.417267	−	0.137469i
$941$		−	239.064i		−	0.254053i	−0.991899	−	0.127027i	$-0.959457\pi$
$941$		−	239.064i		−	0.254053i	0.991899	−	0.127027i	$-0.0405433\pi$
$942$		0			0
$943$		−	740.187i		−	0.784928i
$944$	−140.775	−	104.051i	−0.149127	−	0.110224i
$945$		0			0
$946$	427.545	−	2664.10i	0.451950	−	2.81618i
$947$	−629.352			−0.664575			−0.332287	−	0.943178i	$-0.607820\pi$
$947$	−629.352			−0.664575			−0.332287	+	0.943178i	$0.607820\pi$
$948$		0			0
$949$		−	1115.73i		−	1.17569i
$950$	28.2559	−	176.068i	0.0297431	−	0.185334i
$951$		0			0
$952$	204.781	+	105.930i	0.215106	+	0.111271i
$953$	1221.93			1.28220			0.641098	−	0.767459i	$-0.278479\pi$
$953$	1221.93			1.28220			0.641098	+	0.767459i	$0.278479\pi$
$954$		0			0
$955$	−1558.71			−1.63216
$956$	141.196	−	428.577i	0.147694	−	0.448302i
$957$		0			0
$958$	−520.083	−	83.4648i	−0.542884	−	0.0871240i
$959$			977.305i			1.01909i
$960$		0			0
$961$	76.9918			0.0801163
$962$	−168.664	+	1050.98i	−0.175327	+	1.09249i
$963$		0			0
$964$	−39.2661	−	12.9363i	−0.0407325	−	0.0134194i
$965$		−	104.046i		−	0.107819i
$966$		0			0
$967$			1138.01i			1.17685i	0.808553	+	0.588423i	$0.200251\pi$
$967$			1138.01i			1.17685i	−0.808553	+	0.588423i	$0.799749\pi$
$968$	−851.573	+	1646.23i	−0.879724	+	1.70065i
$969$		0			0
$970$	−688.486	−	110.491i	−0.709780	−	0.113908i
$971$	1822.54			1.87697			0.938484	−	0.345322i	$-0.112230\pi$
$971$	1822.54			1.87697			0.938484	+	0.345322i	$0.112230\pi$
$972$		0			0
$973$			640.208i			0.657973i
$974$	−198.700	−	31.8881i	−0.204004	−	0.0327393i
$975$		0			0
$976$	−864.728	+	1169.93i	−0.885992	+	1.19870i
$977$	1695.80			1.73572			0.867862	−	0.496806i	$-0.165494\pi$
$977$	1695.80			1.73572			0.867862	+	0.496806i	$0.165494\pi$
$978$		0			0
$979$	−1576.53			−1.61035
$980$	199.070	−	604.245i	0.203132	−	0.616576i
$981$		0			0
$982$	160.664	−	1001.12i	0.163609	−	1.01948i
$983$		−	925.775i		−	0.941785i	−0.882191	−	0.470893i	$-0.843932\pi$
$983$		−	925.775i		−	0.941785i	0.882191	−	0.470893i	$-0.156068\pi$
$984$		0			0
$985$	−94.9973			−0.0964440
$986$	283.440	+	45.4875i	0.287465	+	0.0461333i
$987$		0			0
$988$	402.259	−	1220.99i	0.407144	−	1.23582i
$989$		−	1321.28i		−	1.33598i
$990$		0			0
$991$			820.777i			0.828231i	0.910224	+	0.414115i	$0.135909\pi$
$991$			820.777i			0.828231i	−0.910224	+	0.414115i	$0.864091\pi$
$992$	−665.843	−	679.615i	−0.671213	−	0.685096i
$993$		0			0
$994$	−15.8577	+	98.8123i	−0.0159535	+	0.0994087i
$995$	153.853			0.154626
$996$		0			0
$997$		−	990.056i		−	0.993035i	−0.868027	−	0.496517i	$-0.834612\pi$
$997$		−	990.056i		−	0.993035i	0.868027	−	0.496517i	$-0.165388\pi$
$998$	−193.191	+	1203.80i	−0.193578	+	1.20622i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.a.163.9	yes	16
3.2	odd	2	inner	216.3.b.a.163.8	yes	16
4.3	odd	2		864.3.b.a.271.11		16
8.3	odd	2	inner	216.3.b.a.163.10	yes	16
8.5	even	2		864.3.b.a.271.6		16
12.11	even	2		864.3.b.a.271.5		16
24.5	odd	2		864.3.b.a.271.12		16
24.11	even	2	inner	216.3.b.a.163.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.a.163.7	✓	16	24.11	even	2	inner
216.3.b.a.163.8	yes	16	3.2	odd	2	inner
216.3.b.a.163.9	yes	16	1.1	even	1	trivial
216.3.b.a.163.10	yes	16	8.3	odd	2	inner
864.3.b.a.271.5		16	12.11	even	2
864.3.b.a.271.6		16	8.5	even	2
864.3.b.a.271.11		16	4.3	odd	2
864.3.b.a.271.12		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.316912 - 1.97473i) q^{2} +(-3.79913 - 1.25163i) q^{4} +4.41296i q^{5} +3.59985i q^{7} +(-3.67563 + 7.10561i) q^{8} +O(q^{10})\)	\(q+(0.316912 - 1.97473i) q^{2} +(-3.79913 - 1.25163i) q^{4} +4.41296i q^{5} +3.59985i q^{7} +(-3.67563 + 7.10561i) q^{8} +(8.71442 + 1.39852i) q^{10} -18.7798 q^{11} +19.9181i q^{13} +(7.10873 + 1.14083i) q^{14} +(12.8668 + 9.51024i) q^{16} -8.00578 q^{17} +16.1354 q^{19} +(5.52341 - 16.7654i) q^{20} +(-5.95154 + 37.0851i) q^{22} +18.3926i q^{23} +5.52575 q^{25} +(39.3330 + 6.31230i) q^{26} +(4.50569 - 13.6763i) q^{28} -17.9287i q^{29} -29.7323i q^{31} +(22.8578 - 22.3946i) q^{32} +(-2.53713 + 15.8093i) q^{34} -15.8860 q^{35} +26.7200i q^{37} +(5.11350 - 31.8631i) q^{38} +(-31.3568 - 16.2204i) q^{40} -40.2437 q^{41} -71.8376 q^{43} +(71.3469 + 23.5054i) q^{44} +(36.3206 + 5.82885i) q^{46} -23.3952i q^{47} +36.0411 q^{49} +(1.75118 - 10.9119i) q^{50} +(24.9302 - 75.6717i) q^{52} +90.7227i q^{53} -82.8745i q^{55} +(-25.5791 - 13.2317i) q^{56} +(-35.4044 - 5.68183i) q^{58} -10.9410 q^{59} +90.9260i q^{61} +(-58.7133 - 9.42252i) q^{62} +(-36.9795 - 52.2352i) q^{64} -87.8980 q^{65} +74.0054 q^{67} +(30.4150 + 10.0203i) q^{68} +(-5.03446 + 31.3706i) q^{70} +13.9001i q^{71} -56.0158 q^{73} +(52.7648 + 8.46788i) q^{74} +(-61.3005 - 20.1956i) q^{76} -67.6044i q^{77} -118.415i q^{79} +(-41.9683 + 56.7809i) q^{80} +(-12.7537 + 79.4704i) q^{82} -8.08995 q^{83} -35.3292i q^{85} +(-22.7662 + 141.860i) q^{86} +(69.0276 - 133.442i) q^{88} +83.9483 q^{89} -71.7022 q^{91} +(23.0208 - 69.8761i) q^{92} +(-46.1992 - 7.41422i) q^{94} +71.2049i q^{95} -79.0054 q^{97} +(11.4219 - 71.1715i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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